1,1,95,0,0.396978," ","integrate(x^2*(e*x+d)*(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","-\frac{30 \, d^{5} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) - {\left(24 \, e^{4} x^{4} + 30 \, d e^{3} x^{3} - 8 \, d^{2} e^{2} x^{2} - 15 \, d^{3} e x - 16 \, d^{4}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{120 \, e^{3}}"," ",0,"-1/120*(30*d^5*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) - (24*e^4*x^4 + 30*d*e^3*x^3 - 8*d^2*e^2*x^2 - 15*d^3*e*x - 16*d^4)*sqrt(-e^2*x^2 + d^2))/e^3","A",0
2,1,138,0,0.398832," ","integrate(x^4*(e*x+d)*(-e^2*x^2+d^2)^(3/2),x, algorithm=""fricas"")","-\frac{1890 \, d^{9} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(4480 \, e^{8} x^{8} + 5040 \, d e^{7} x^{7} - 6400 \, d^{2} e^{6} x^{6} - 7560 \, d^{3} e^{5} x^{5} + 384 \, d^{4} e^{4} x^{4} + 630 \, d^{5} e^{3} x^{3} + 512 \, d^{6} e^{2} x^{2} + 945 \, d^{7} e x + 1024 \, d^{8}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{40320 \, e^{5}}"," ",0,"-1/40320*(1890*d^9*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (4480*e^8*x^8 + 5040*d*e^7*x^7 - 6400*d^2*e^6*x^6 - 7560*d^3*e^5*x^5 + 384*d^4*e^4*x^4 + 630*d^5*e^3*x^3 + 512*d^6*e^2*x^2 + 945*d^7*e*x + 1024*d^8)*sqrt(-e^2*x^2 + d^2))/e^5","A",0
3,1,127,0,0.413102," ","integrate(x^3*(e*x+d)*(-e^2*x^2+d^2)^(3/2),x, algorithm=""fricas"")","-\frac{210 \, d^{8} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(560 \, e^{7} x^{7} + 640 \, d e^{6} x^{6} - 840 \, d^{2} e^{5} x^{5} - 1024 \, d^{3} e^{4} x^{4} + 70 \, d^{4} e^{3} x^{3} + 128 \, d^{5} e^{2} x^{2} + 105 \, d^{6} e x + 256 \, d^{7}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{4480 \, e^{4}}"," ",0,"-1/4480*(210*d^8*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (560*e^7*x^7 + 640*d*e^6*x^6 - 840*d^2*e^5*x^5 - 1024*d^3*e^4*x^4 + 70*d^4*e^3*x^3 + 128*d^5*e^2*x^2 + 105*d^6*e*x + 256*d^7)*sqrt(-e^2*x^2 + d^2))/e^4","A",0
4,1,116,0,0.396648," ","integrate(x^2*(e*x+d)*(-e^2*x^2+d^2)^(3/2),x, algorithm=""fricas"")","-\frac{210 \, d^{7} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(240 \, e^{6} x^{6} + 280 \, d e^{5} x^{5} - 384 \, d^{2} e^{4} x^{4} - 490 \, d^{3} e^{3} x^{3} + 48 \, d^{4} e^{2} x^{2} + 105 \, d^{5} e x + 96 \, d^{6}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{1680 \, e^{3}}"," ",0,"-1/1680*(210*d^7*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (240*e^6*x^6 + 280*d*e^5*x^5 - 384*d^2*e^4*x^4 - 490*d^3*e^3*x^3 + 48*d^4*e^2*x^2 + 105*d^5*e*x + 96*d^6)*sqrt(-e^2*x^2 + d^2))/e^3","A",0
5,1,105,0,0.403375," ","integrate(x*(e*x+d)*(-e^2*x^2+d^2)^(3/2),x, algorithm=""fricas"")","-\frac{30 \, d^{6} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(40 \, e^{5} x^{5} + 48 \, d e^{4} x^{4} - 70 \, d^{2} e^{3} x^{3} - 96 \, d^{3} e^{2} x^{2} + 15 \, d^{4} e x + 48 \, d^{5}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{240 \, e^{2}}"," ",0,"-1/240*(30*d^6*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (40*e^5*x^5 + 48*d*e^4*x^4 - 70*d^2*e^3*x^3 - 96*d^3*e^2*x^2 + 15*d^4*e*x + 48*d^5)*sqrt(-e^2*x^2 + d^2))/e^2","A",0
6,1,105,0,0.414540," ","integrate(x*(e*x+d)*(-e^2*x^2+d^2)^(3/2),x, algorithm=""fricas"")","-\frac{30 \, d^{6} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(40 \, e^{5} x^{5} + 48 \, d e^{4} x^{4} - 70 \, d^{2} e^{3} x^{3} - 96 \, d^{3} e^{2} x^{2} + 15 \, d^{4} e x + 48 \, d^{5}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{240 \, e^{2}}"," ",0,"-1/240*(30*d^6*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (40*e^5*x^5 + 48*d*e^4*x^4 - 70*d^2*e^3*x^3 - 96*d^3*e^2*x^2 + 15*d^4*e*x + 48*d^5)*sqrt(-e^2*x^2 + d^2))/e^2","A",0
7,1,107,0,0.414490," ","integrate((e*x+d)*(-e^2*x^2+d^2)^(3/2)/x,x, algorithm=""fricas"")","-\frac{3}{4} \, d^{4} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + d^{4} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) - \frac{1}{24} \, {\left(6 \, e^{3} x^{3} + 8 \, d e^{2} x^{2} - 15 \, d^{2} e x - 32 \, d^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}}"," ",0,"-3/4*d^4*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + d^4*log(-(d - sqrt(-e^2*x^2 + d^2))/x) - 1/24*(6*e^3*x^3 + 8*d*e^2*x^2 - 15*d^2*e*x - 32*d^3)*sqrt(-e^2*x^2 + d^2)","A",0
8,1,124,0,0.407819," ","integrate((e*x+d)*(-e^2*x^2+d^2)^(3/2)/x^2,x, algorithm=""fricas"")","\frac{18 \, d^{3} e x \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + 6 \, d^{3} e x \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) + 8 \, d^{3} e x - {\left(2 \, e^{3} x^{3} + 3 \, d e^{2} x^{2} - 8 \, d^{2} e x + 6 \, d^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{6 \, x}"," ",0,"1/6*(18*d^3*e*x*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + 6*d^3*e*x*log(-(d - sqrt(-e^2*x^2 + d^2))/x) + 8*d^3*e*x - (2*e^3*x^3 + 3*d*e^2*x^2 - 8*d^2*e*x + 6*d^3)*sqrt(-e^2*x^2 + d^2))/x","A",0
9,1,133,0,0.414543," ","integrate((e*x+d)*(-e^2*x^2+d^2)^(3/2)/x^3,x, algorithm=""fricas"")","\frac{6 \, d^{2} e^{2} x^{2} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) - 3 \, d^{2} e^{2} x^{2} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) - 2 \, d^{2} e^{2} x^{2} - {\left(e^{3} x^{3} + 2 \, d e^{2} x^{2} + 2 \, d^{2} e x + d^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{2 \, x^{2}}"," ",0,"1/2*(6*d^2*e^2*x^2*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) - 3*d^2*e^2*x^2*log(-(d - sqrt(-e^2*x^2 + d^2))/x) - 2*d^2*e^2*x^2 - (e^3*x^3 + 2*d*e^2*x^2 + 2*d^2*e*x + d^3)*sqrt(-e^2*x^2 + d^2))/x^2","A",0
10,1,129,0,0.416800," ","integrate((e*x+d)*(-e^2*x^2+d^2)^(3/2)/x^4,x, algorithm=""fricas"")","-\frac{12 \, d e^{3} x^{3} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + 9 \, d e^{3} x^{3} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) + 6 \, d e^{3} x^{3} + {\left(6 \, e^{3} x^{3} - 8 \, d e^{2} x^{2} + 3 \, d^{2} e x + 2 \, d^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{6 \, x^{3}}"," ",0,"-1/6*(12*d*e^3*x^3*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + 9*d*e^3*x^3*log(-(d - sqrt(-e^2*x^2 + d^2))/x) + 6*d*e^3*x^3 + (6*e^3*x^3 - 8*d*e^2*x^2 + 3*d^2*e*x + 2*d^3)*sqrt(-e^2*x^2 + d^2))/x^3","A",0
11,1,119,0,0.407732," ","integrate((e*x+d)*(-e^2*x^2+d^2)^(3/2)/x^5,x, algorithm=""fricas"")","-\frac{48 \, e^{4} x^{4} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) - 9 \, e^{4} x^{4} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) - {\left(32 \, e^{3} x^{3} + 15 \, d e^{2} x^{2} - 8 \, d^{2} e x - 6 \, d^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{24 \, x^{4}}"," ",0,"-1/24*(48*e^4*x^4*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) - 9*e^4*x^4*log(-(d - sqrt(-e^2*x^2 + d^2))/x) - (32*e^3*x^3 + 15*d*e^2*x^2 - 8*d^2*e*x - 6*d^3)*sqrt(-e^2*x^2 + d^2))/x^4","A",0
12,1,98,0,0.394624," ","integrate((e*x+d)*(-e^2*x^2+d^2)^(3/2)/x^6,x, algorithm=""fricas"")","\frac{15 \, e^{5} x^{5} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) - {\left(8 \, e^{4} x^{4} - 25 \, d e^{3} x^{3} - 16 \, d^{2} e^{2} x^{2} + 10 \, d^{3} e x + 8 \, d^{4}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{40 \, d x^{5}}"," ",0,"1/40*(15*e^5*x^5*log(-(d - sqrt(-e^2*x^2 + d^2))/x) - (8*e^4*x^4 - 25*d*e^3*x^3 - 16*d^2*e^2*x^2 + 10*d^3*e*x + 8*d^4)*sqrt(-e^2*x^2 + d^2))/(d*x^5)","A",0
13,1,109,0,0.427040," ","integrate((e*x+d)*(-e^2*x^2+d^2)^(3/2)/x^7,x, algorithm=""fricas"")","\frac{15 \, e^{6} x^{6} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) - {\left(48 \, e^{5} x^{5} + 15 \, d e^{4} x^{4} - 96 \, d^{2} e^{3} x^{3} - 70 \, d^{3} e^{2} x^{2} + 48 \, d^{4} e x + 40 \, d^{5}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{240 \, d^{2} x^{6}}"," ",0,"1/240*(15*e^6*x^6*log(-(d - sqrt(-e^2*x^2 + d^2))/x) - (48*e^5*x^5 + 15*d*e^4*x^4 - 96*d^2*e^3*x^3 - 70*d^3*e^2*x^2 + 48*d^4*e*x + 40*d^5)*sqrt(-e^2*x^2 + d^2))/(d^2*x^6)","A",0
14,1,120,0,0.421122," ","integrate((e*x+d)*(-e^2*x^2+d^2)^(3/2)/x^8,x, algorithm=""fricas"")","\frac{105 \, e^{7} x^{7} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) - {\left(96 \, e^{6} x^{6} + 105 \, d e^{5} x^{5} + 48 \, d^{2} e^{4} x^{4} - 490 \, d^{3} e^{3} x^{3} - 384 \, d^{4} e^{2} x^{2} + 280 \, d^{5} e x + 240 \, d^{6}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{1680 \, d^{3} x^{7}}"," ",0,"1/1680*(105*e^7*x^7*log(-(d - sqrt(-e^2*x^2 + d^2))/x) - (96*e^6*x^6 + 105*d*e^5*x^5 + 48*d^2*e^4*x^4 - 490*d^3*e^3*x^3 - 384*d^4*e^2*x^2 + 280*d^5*e*x + 240*d^6)*sqrt(-e^2*x^2 + d^2))/(d^3*x^7)","A",0
15,1,131,0,0.446397," ","integrate((e*x+d)*(-e^2*x^2+d^2)^(3/2)/x^9,x, algorithm=""fricas"")","\frac{105 \, e^{8} x^{8} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) - {\left(256 \, e^{7} x^{7} + 105 \, d e^{6} x^{6} + 128 \, d^{2} e^{5} x^{5} + 70 \, d^{3} e^{4} x^{4} - 1024 \, d^{4} e^{3} x^{3} - 840 \, d^{5} e^{2} x^{2} + 640 \, d^{6} e x + 560 \, d^{7}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{4480 \, d^{4} x^{8}}"," ",0,"1/4480*(105*e^8*x^8*log(-(d - sqrt(-e^2*x^2 + d^2))/x) - (256*e^7*x^7 + 105*d*e^6*x^6 + 128*d^2*e^5*x^5 + 70*d^3*e^4*x^4 - 1024*d^4*e^3*x^3 - 840*d^5*e^2*x^2 + 640*d^6*e*x + 560*d^7)*sqrt(-e^2*x^2 + d^2))/(d^4*x^8)","A",0
16,1,72,0,0.404649," ","integrate(x^2*(e*x+d)/(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","-\frac{6 \, d^{3} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(2 \, e^{2} x^{2} + 3 \, d e x + 4 \, d^{2}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{6 \, e^{3}}"," ",0,"-1/6*(6*d^3*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (2*e^2*x^2 + 3*d*e*x + 4*d^2)*sqrt(-e^2*x^2 + d^2))/e^3","A",0
17,1,87,0,0.402798," ","integrate(x^2*(e*x+d)/(-e^2*x^2+d^2)^(3/2),x, algorithm=""fricas"")","\frac{2 \, d e x - 2 \, d^{2} + 2 \, {\left(d e x - d^{2}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + \sqrt{-e^{2} x^{2} + d^{2}} {\left(e x - 2 \, d\right)}}{e^{4} x - d e^{3}}"," ",0,"(2*d*e*x - 2*d^2 + 2*(d*e*x - d^2)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + sqrt(-e^2*x^2 + d^2)*(e*x - 2*d))/(e^4*x - d*e^3)","A",0
18,1,104,0,0.390879," ","integrate(x^2*(e*x+d)/(-e^2*x^2+d^2)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, e^{3} x^{3} - 2 \, d e^{2} x^{2} - 2 \, d^{2} e x + 2 \, d^{3} - {\left(e^{2} x^{2} + 2 \, d e x - 2 \, d^{2}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{3 \, {\left(d e^{6} x^{3} - d^{2} e^{5} x^{2} - d^{3} e^{4} x + d^{4} e^{3}\right)}}"," ",0,"-1/3*(2*e^3*x^3 - 2*d*e^2*x^2 - 2*d^2*e*x + 2*d^3 - (e^2*x^2 + 2*d*e*x - 2*d^2)*sqrt(-e^2*x^2 + d^2))/(d*e^6*x^3 - d^2*e^5*x^2 - d^3*e^4*x + d^4*e^3)","B",0
19,1,278,0,0.466965," ","integrate(x^7*(e*x+d)/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","\frac{96 \, d^{2} e^{5} x^{5} - 96 \, d^{3} e^{4} x^{4} - 192 \, d^{4} e^{3} x^{3} + 192 \, d^{5} e^{2} x^{2} + 96 \, d^{6} e x - 96 \, d^{7} + 210 \, {\left(d^{2} e^{5} x^{5} - d^{3} e^{4} x^{4} - 2 \, d^{4} e^{3} x^{3} + 2 \, d^{5} e^{2} x^{2} + d^{6} e x - d^{7}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(15 \, e^{6} x^{6} + 15 \, d e^{5} x^{5} - 176 \, d^{2} e^{4} x^{4} - 4 \, d^{3} e^{3} x^{3} + 249 \, d^{4} e^{2} x^{2} - 9 \, d^{5} e x - 96 \, d^{6}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{30 \, {\left(e^{13} x^{5} - d e^{12} x^{4} - 2 \, d^{2} e^{11} x^{3} + 2 \, d^{3} e^{10} x^{2} + d^{4} e^{9} x - d^{5} e^{8}\right)}}"," ",0,"1/30*(96*d^2*e^5*x^5 - 96*d^3*e^4*x^4 - 192*d^4*e^3*x^3 + 192*d^5*e^2*x^2 + 96*d^6*e*x - 96*d^7 + 210*(d^2*e^5*x^5 - d^3*e^4*x^4 - 2*d^4*e^3*x^3 + 2*d^5*e^2*x^2 + d^6*e*x - d^7)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (15*e^6*x^6 + 15*d*e^5*x^5 - 176*d^2*e^4*x^4 - 4*d^3*e^3*x^3 + 249*d^4*e^2*x^2 - 9*d^5*e*x - 96*d^6)*sqrt(-e^2*x^2 + d^2))/(e^13*x^5 - d*e^12*x^4 - 2*d^2*e^11*x^3 + 2*d^3*e^10*x^2 + d^4*e^9*x - d^5*e^8)","A",0
20,1,263,0,0.419796," ","integrate(x^6*(e*x+d)/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","\frac{48 \, d e^{5} x^{5} - 48 \, d^{2} e^{4} x^{4} - 96 \, d^{3} e^{3} x^{3} + 96 \, d^{4} e^{2} x^{2} + 48 \, d^{5} e x - 48 \, d^{6} + 30 \, {\left(d e^{5} x^{5} - d^{2} e^{4} x^{4} - 2 \, d^{3} e^{3} x^{3} + 2 \, d^{4} e^{2} x^{2} + d^{5} e x - d^{6}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(15 \, e^{5} x^{5} - 38 \, d e^{4} x^{4} - 52 \, d^{2} e^{3} x^{3} + 87 \, d^{3} e^{2} x^{2} + 33 \, d^{4} e x - 48 \, d^{5}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(e^{12} x^{5} - d e^{11} x^{4} - 2 \, d^{2} e^{10} x^{3} + 2 \, d^{3} e^{9} x^{2} + d^{4} e^{8} x - d^{5} e^{7}\right)}}"," ",0,"1/15*(48*d*e^5*x^5 - 48*d^2*e^4*x^4 - 96*d^3*e^3*x^3 + 96*d^4*e^2*x^2 + 48*d^5*e*x - 48*d^6 + 30*(d*e^5*x^5 - d^2*e^4*x^4 - 2*d^3*e^3*x^3 + 2*d^4*e^2*x^2 + d^5*e*x - d^6)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (15*e^5*x^5 - 38*d*e^4*x^4 - 52*d^2*e^3*x^3 + 87*d^3*e^2*x^2 + 33*d^4*e*x - 48*d^5)*sqrt(-e^2*x^2 + d^2))/(e^12*x^5 - d*e^11*x^4 - 2*d^2*e^10*x^3 + 2*d^3*e^9*x^2 + d^4*e^8*x - d^5*e^7)","B",0
21,1,247,0,0.407500," ","integrate(x^5*(e*x+d)/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","\frac{8 \, e^{5} x^{5} - 8 \, d e^{4} x^{4} - 16 \, d^{2} e^{3} x^{3} + 16 \, d^{3} e^{2} x^{2} + 8 \, d^{4} e x - 8 \, d^{5} + 30 \, {\left(e^{5} x^{5} - d e^{4} x^{4} - 2 \, d^{2} e^{3} x^{3} + 2 \, d^{3} e^{2} x^{2} + d^{4} e x - d^{5}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) - {\left(23 \, e^{4} x^{4} - 8 \, d e^{3} x^{3} - 27 \, d^{2} e^{2} x^{2} + 7 \, d^{3} e x + 8 \, d^{4}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(e^{11} x^{5} - d e^{10} x^{4} - 2 \, d^{2} e^{9} x^{3} + 2 \, d^{3} e^{8} x^{2} + d^{4} e^{7} x - d^{5} e^{6}\right)}}"," ",0,"1/15*(8*e^5*x^5 - 8*d*e^4*x^4 - 16*d^2*e^3*x^3 + 16*d^3*e^2*x^2 + 8*d^4*e*x - 8*d^5 + 30*(e^5*x^5 - d*e^4*x^4 - 2*d^2*e^3*x^3 + 2*d^3*e^2*x^2 + d^4*e*x - d^5)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) - (23*e^4*x^4 - 8*d*e^3*x^3 - 27*d^2*e^2*x^2 + 7*d^3*e*x + 8*d^4)*sqrt(-e^2*x^2 + d^2))/(e^11*x^5 - d*e^10*x^4 - 2*d^2*e^9*x^3 + 2*d^3*e^8*x^2 + d^4*e^7*x - d^5*e^6)","B",0
22,1,171,0,0.390611," ","integrate(x^4*(e*x+d)/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","\frac{8 \, e^{5} x^{5} - 8 \, d e^{4} x^{4} - 16 \, d^{2} e^{3} x^{3} + 16 \, d^{3} e^{2} x^{2} + 8 \, d^{4} e x - 8 \, d^{5} - {\left(3 \, e^{4} x^{4} + 12 \, d e^{3} x^{3} - 12 \, d^{2} e^{2} x^{2} - 8 \, d^{3} e x + 8 \, d^{4}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(d e^{10} x^{5} - d^{2} e^{9} x^{4} - 2 \, d^{3} e^{8} x^{3} + 2 \, d^{4} e^{7} x^{2} + d^{5} e^{6} x - d^{6} e^{5}\right)}}"," ",0,"1/15*(8*e^5*x^5 - 8*d*e^4*x^4 - 16*d^2*e^3*x^3 + 16*d^3*e^2*x^2 + 8*d^4*e*x - 8*d^5 - (3*e^4*x^4 + 12*d*e^3*x^3 - 12*d^2*e^2*x^2 - 8*d^3*e*x + 8*d^4)*sqrt(-e^2*x^2 + d^2))/(d*e^10*x^5 - d^2*e^9*x^4 - 2*d^3*e^8*x^3 + 2*d^4*e^7*x^2 + d^5*e^6*x - d^6*e^5)","B",0
23,1,172,0,0.406587," ","integrate(x^3*(e*x+d)/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","-\frac{2 \, e^{5} x^{5} - 2 \, d e^{4} x^{4} - 4 \, d^{2} e^{3} x^{3} + 4 \, d^{3} e^{2} x^{2} + 2 \, d^{4} e x - 2 \, d^{5} + {\left(3 \, e^{4} x^{4} - 3 \, d e^{3} x^{3} + 3 \, d^{2} e^{2} x^{2} + 2 \, d^{3} e x - 2 \, d^{4}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(d^{2} e^{9} x^{5} - d^{3} e^{8} x^{4} - 2 \, d^{4} e^{7} x^{3} + 2 \, d^{5} e^{6} x^{2} + d^{6} e^{5} x - d^{7} e^{4}\right)}}"," ",0,"-1/15*(2*e^5*x^5 - 2*d*e^4*x^4 - 4*d^2*e^3*x^3 + 4*d^3*e^2*x^2 + 2*d^4*e*x - 2*d^5 + (3*e^4*x^4 - 3*d*e^3*x^3 + 3*d^2*e^2*x^2 + 2*d^3*e*x - 2*d^4)*sqrt(-e^2*x^2 + d^2))/(d^2*e^9*x^5 - d^3*e^8*x^4 - 2*d^4*e^7*x^3 + 2*d^5*e^6*x^2 + d^6*e^5*x - d^7*e^4)","B",0
24,1,173,0,0.415785," ","integrate(x^2*(e*x+d)/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","-\frac{2 \, e^{5} x^{5} - 2 \, d e^{4} x^{4} - 4 \, d^{2} e^{3} x^{3} + 4 \, d^{3} e^{2} x^{2} + 2 \, d^{4} e x - 2 \, d^{5} - {\left(2 \, e^{4} x^{4} - 2 \, d e^{3} x^{3} - 3 \, d^{2} e^{2} x^{2} - 2 \, d^{3} e x + 2 \, d^{4}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(d^{3} e^{8} x^{5} - d^{4} e^{7} x^{4} - 2 \, d^{5} e^{6} x^{3} + 2 \, d^{6} e^{5} x^{2} + d^{7} e^{4} x - d^{8} e^{3}\right)}}"," ",0,"-1/15*(2*e^5*x^5 - 2*d*e^4*x^4 - 4*d^2*e^3*x^3 + 4*d^3*e^2*x^2 + 2*d^4*e*x - 2*d^5 - (2*e^4*x^4 - 2*d*e^3*x^3 - 3*d^2*e^2*x^2 - 2*d^3*e*x + 2*d^4)*sqrt(-e^2*x^2 + d^2))/(d^3*e^8*x^5 - d^4*e^7*x^4 - 2*d^5*e^6*x^3 + 2*d^6*e^5*x^2 + d^7*e^4*x - d^8*e^3)","B",0
25,1,172,0,0.415087," ","integrate(x*(e*x+d)/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","\frac{3 \, e^{5} x^{5} - 3 \, d e^{4} x^{4} - 6 \, d^{2} e^{3} x^{3} + 6 \, d^{3} e^{2} x^{2} + 3 \, d^{4} e x - 3 \, d^{5} + {\left(2 \, e^{4} x^{4} - 2 \, d e^{3} x^{3} - 3 \, d^{2} e^{2} x^{2} + 3 \, d^{3} e x - 3 \, d^{4}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(d^{4} e^{7} x^{5} - d^{5} e^{6} x^{4} - 2 \, d^{6} e^{5} x^{3} + 2 \, d^{7} e^{4} x^{2} + d^{8} e^{3} x - d^{9} e^{2}\right)}}"," ",0,"1/15*(3*e^5*x^5 - 3*d*e^4*x^4 - 6*d^2*e^3*x^3 + 6*d^3*e^2*x^2 + 3*d^4*e*x - 3*d^5 + (2*e^4*x^4 - 2*d*e^3*x^3 - 3*d^2*e^2*x^2 + 3*d^3*e*x - 3*d^4)*sqrt(-e^2*x^2 + d^2))/(d^4*e^7*x^5 - d^5*e^6*x^4 - 2*d^6*e^5*x^3 + 2*d^7*e^4*x^2 + d^8*e^3*x - d^9*e^2)","B",0
26,1,171,0,0.420463," ","integrate((e*x+d)/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","\frac{3 \, e^{5} x^{5} - 3 \, d e^{4} x^{4} - 6 \, d^{2} e^{3} x^{3} + 6 \, d^{3} e^{2} x^{2} + 3 \, d^{4} e x - 3 \, d^{5} - {\left(8 \, e^{4} x^{4} - 8 \, d e^{3} x^{3} - 12 \, d^{2} e^{2} x^{2} + 12 \, d^{3} e x + 3 \, d^{4}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(d^{5} e^{6} x^{5} - d^{6} e^{5} x^{4} - 2 \, d^{7} e^{4} x^{3} + 2 \, d^{8} e^{3} x^{2} + d^{9} e^{2} x - d^{10} e\right)}}"," ",0,"1/15*(3*e^5*x^5 - 3*d*e^4*x^4 - 6*d^2*e^3*x^3 + 6*d^3*e^2*x^2 + 3*d^4*e*x - 3*d^5 - (8*e^4*x^4 - 8*d*e^3*x^3 - 12*d^2*e^2*x^2 + 12*d^3*e*x + 3*d^4)*sqrt(-e^2*x^2 + d^2))/(d^5*e^6*x^5 - d^6*e^5*x^4 - 2*d^7*e^4*x^3 + 2*d^8*e^3*x^2 + d^9*e^2*x - d^10*e)","B",0
27,1,244,0,0.423051," ","integrate((e*x+d)/x/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","\frac{23 \, e^{5} x^{5} - 23 \, d e^{4} x^{4} - 46 \, d^{2} e^{3} x^{3} + 46 \, d^{3} e^{2} x^{2} + 23 \, d^{4} e x - 23 \, d^{5} + 15 \, {\left(e^{5} x^{5} - d e^{4} x^{4} - 2 \, d^{2} e^{3} x^{3} + 2 \, d^{3} e^{2} x^{2} + d^{4} e x - d^{5}\right)} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) - {\left(8 \, e^{4} x^{4} + 7 \, d e^{3} x^{3} - 27 \, d^{2} e^{2} x^{2} - 8 \, d^{3} e x + 23 \, d^{4}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(d^{6} e^{5} x^{5} - d^{7} e^{4} x^{4} - 2 \, d^{8} e^{3} x^{3} + 2 \, d^{9} e^{2} x^{2} + d^{10} e x - d^{11}\right)}}"," ",0,"1/15*(23*e^5*x^5 - 23*d*e^4*x^4 - 46*d^2*e^3*x^3 + 46*d^3*e^2*x^2 + 23*d^4*e*x - 23*d^5 + 15*(e^5*x^5 - d*e^4*x^4 - 2*d^2*e^3*x^3 + 2*d^3*e^2*x^2 + d^4*e*x - d^5)*log(-(d - sqrt(-e^2*x^2 + d^2))/x) - (8*e^4*x^4 + 7*d*e^3*x^3 - 27*d^2*e^2*x^2 - 8*d^3*e*x + 23*d^4)*sqrt(-e^2*x^2 + d^2))/(d^6*e^5*x^5 - d^7*e^4*x^4 - 2*d^8*e^3*x^3 + 2*d^9*e^2*x^2 + d^10*e*x - d^11)","B",0
28,1,270,0,0.442284," ","integrate((e*x+d)/x^2/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","\frac{23 \, e^{6} x^{6} - 23 \, d e^{5} x^{5} - 46 \, d^{2} e^{4} x^{4} + 46 \, d^{3} e^{3} x^{3} + 23 \, d^{4} e^{2} x^{2} - 23 \, d^{5} e x + 15 \, {\left(e^{6} x^{6} - d e^{5} x^{5} - 2 \, d^{2} e^{4} x^{4} + 2 \, d^{3} e^{3} x^{3} + d^{4} e^{2} x^{2} - d^{5} e x\right)} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) - {\left(48 \, e^{5} x^{5} - 33 \, d e^{4} x^{4} - 87 \, d^{2} e^{3} x^{3} + 52 \, d^{3} e^{2} x^{2} + 38 \, d^{4} e x - 15 \, d^{5}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(d^{7} e^{5} x^{6} - d^{8} e^{4} x^{5} - 2 \, d^{9} e^{3} x^{4} + 2 \, d^{10} e^{2} x^{3} + d^{11} e x^{2} - d^{12} x\right)}}"," ",0,"1/15*(23*e^6*x^6 - 23*d*e^5*x^5 - 46*d^2*e^4*x^4 + 46*d^3*e^3*x^3 + 23*d^4*e^2*x^2 - 23*d^5*e*x + 15*(e^6*x^6 - d*e^5*x^5 - 2*d^2*e^4*x^4 + 2*d^3*e^3*x^3 + d^4*e^2*x^2 - d^5*e*x)*log(-(d - sqrt(-e^2*x^2 + d^2))/x) - (48*e^5*x^5 - 33*d*e^4*x^4 - 87*d^2*e^3*x^3 + 52*d^3*e^2*x^2 + 38*d^4*e*x - 15*d^5)*sqrt(-e^2*x^2 + d^2))/(d^7*e^5*x^6 - d^8*e^4*x^5 - 2*d^9*e^3*x^4 + 2*d^10*e^2*x^3 + d^11*e*x^2 - d^12*x)","A",0
29,1,291,0,0.511229," ","integrate((e*x+d)/x^3/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","\frac{116 \, e^{7} x^{7} - 116 \, d e^{6} x^{6} - 232 \, d^{2} e^{5} x^{5} + 232 \, d^{3} e^{4} x^{4} + 116 \, d^{4} e^{3} x^{3} - 116 \, d^{5} e^{2} x^{2} + 105 \, {\left(e^{7} x^{7} - d e^{6} x^{6} - 2 \, d^{2} e^{5} x^{5} + 2 \, d^{3} e^{4} x^{4} + d^{4} e^{3} x^{3} - d^{5} e^{2} x^{2}\right)} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) - {\left(96 \, e^{6} x^{6} + 9 \, d e^{5} x^{5} - 249 \, d^{2} e^{4} x^{4} + 4 \, d^{3} e^{3} x^{3} + 176 \, d^{4} e^{2} x^{2} - 15 \, d^{5} e x - 15 \, d^{6}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{30 \, {\left(d^{8} e^{5} x^{7} - d^{9} e^{4} x^{6} - 2 \, d^{10} e^{3} x^{5} + 2 \, d^{11} e^{2} x^{4} + d^{12} e x^{3} - d^{13} x^{2}\right)}}"," ",0,"1/30*(116*e^7*x^7 - 116*d*e^6*x^6 - 232*d^2*e^5*x^5 + 232*d^3*e^4*x^4 + 116*d^4*e^3*x^3 - 116*d^5*e^2*x^2 + 105*(e^7*x^7 - d*e^6*x^6 - 2*d^2*e^5*x^5 + 2*d^3*e^4*x^4 + d^4*e^3*x^3 - d^5*e^2*x^2)*log(-(d - sqrt(-e^2*x^2 + d^2))/x) - (96*e^6*x^6 + 9*d*e^5*x^5 - 249*d^2*e^4*x^4 + 4*d^3*e^3*x^3 + 176*d^4*e^2*x^2 - 15*d^5*e*x - 15*d^6)*sqrt(-e^2*x^2 + d^2))/(d^8*e^5*x^7 - d^9*e^4*x^6 - 2*d^10*e^3*x^5 + 2*d^11*e^2*x^4 + d^12*e*x^3 - d^13*x^2)","A",0
30,1,239,0,0.469218," ","integrate(x^2*(e*x+d)/(-e^2*x^2+d^2)^(9/2),x, algorithm=""fricas"")","-\frac{6 \, e^{7} x^{7} - 6 \, d e^{6} x^{6} - 18 \, d^{2} e^{5} x^{5} + 18 \, d^{3} e^{4} x^{4} + 18 \, d^{4} e^{3} x^{3} - 18 \, d^{5} e^{2} x^{2} - 6 \, d^{6} e x + 6 \, d^{7} - {\left(8 \, e^{6} x^{6} - 8 \, d e^{5} x^{5} - 20 \, d^{2} e^{4} x^{4} + 20 \, d^{3} e^{3} x^{3} + 15 \, d^{4} e^{2} x^{2} + 6 \, d^{5} e x - 6 \, d^{6}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{105 \, {\left(d^{5} e^{10} x^{7} - d^{6} e^{9} x^{6} - 3 \, d^{7} e^{8} x^{5} + 3 \, d^{8} e^{7} x^{4} + 3 \, d^{9} e^{6} x^{3} - 3 \, d^{10} e^{5} x^{2} - d^{11} e^{4} x + d^{12} e^{3}\right)}}"," ",0,"-1/105*(6*e^7*x^7 - 6*d*e^6*x^6 - 18*d^2*e^5*x^5 + 18*d^3*e^4*x^4 + 18*d^4*e^3*x^3 - 18*d^5*e^2*x^2 - 6*d^6*e*x + 6*d^7 - (8*e^6*x^6 - 8*d*e^5*x^5 - 20*d^2*e^4*x^4 + 20*d^3*e^3*x^3 + 15*d^4*e^2*x^2 + 6*d^5*e*x - 6*d^6)*sqrt(-e^2*x^2 + d^2))/(d^5*e^10*x^7 - d^6*e^9*x^6 - 3*d^7*e^8*x^5 + 3*d^8*e^7*x^4 + 3*d^9*e^6*x^3 - 3*d^10*e^5*x^2 - d^11*e^4*x + d^12*e^3)","B",0
31,1,305,0,0.762097," ","integrate(x^2*(e*x+d)/(-e^2*x^2+d^2)^(11/2),x, algorithm=""fricas"")","-\frac{10 \, e^{9} x^{9} - 10 \, d e^{8} x^{8} - 40 \, d^{2} e^{7} x^{7} + 40 \, d^{3} e^{6} x^{6} + 60 \, d^{4} e^{5} x^{5} - 60 \, d^{5} e^{4} x^{4} - 40 \, d^{6} e^{3} x^{3} + 40 \, d^{7} e^{2} x^{2} + 10 \, d^{8} e x - 10 \, d^{9} - {\left(16 \, e^{8} x^{8} - 16 \, d e^{7} x^{7} - 56 \, d^{2} e^{6} x^{6} + 56 \, d^{3} e^{5} x^{5} + 70 \, d^{4} e^{4} x^{4} - 70 \, d^{5} e^{3} x^{3} - 35 \, d^{6} e^{2} x^{2} - 10 \, d^{7} e x + 10 \, d^{8}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{315 \, {\left(d^{7} e^{12} x^{9} - d^{8} e^{11} x^{8} - 4 \, d^{9} e^{10} x^{7} + 4 \, d^{10} e^{9} x^{6} + 6 \, d^{11} e^{8} x^{5} - 6 \, d^{12} e^{7} x^{4} - 4 \, d^{13} e^{6} x^{3} + 4 \, d^{14} e^{5} x^{2} + d^{15} e^{4} x - d^{16} e^{3}\right)}}"," ",0,"-1/315*(10*e^9*x^9 - 10*d*e^8*x^8 - 40*d^2*e^7*x^7 + 40*d^3*e^6*x^6 + 60*d^4*e^5*x^5 - 60*d^5*e^4*x^4 - 40*d^6*e^3*x^3 + 40*d^7*e^2*x^2 + 10*d^8*e*x - 10*d^9 - (16*e^8*x^8 - 16*d*e^7*x^7 - 56*d^2*e^6*x^6 + 56*d^3*e^5*x^5 + 70*d^4*e^4*x^4 - 70*d^5*e^3*x^3 - 35*d^6*e^2*x^2 - 10*d^7*e*x + 10*d^8)*sqrt(-e^2*x^2 + d^2))/(d^7*e^12*x^9 - d^8*e^11*x^8 - 4*d^9*e^10*x^7 + 4*d^10*e^9*x^6 + 6*d^11*e^8*x^5 - 6*d^12*e^7*x^4 - 4*d^13*e^6*x^3 + 4*d^14*e^5*x^2 + d^15*e^4*x - d^16*e^3)","B",0
32,1,66,0,0.400823," ","integrate(x^2*(-a*x+1)/(-a^2*x^2+1)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, a x - 2 \, {\left(a x + 1\right)} \arctan\left(\frac{\sqrt{-a^{2} x^{2} + 1} - 1}{a x}\right) + \sqrt{-a^{2} x^{2} + 1} {\left(a x + 2\right)} + 2}{a^{4} x + a^{3}}"," ",0,"-(2*a*x - 2*(a*x + 1)*arctan((sqrt(-a^2*x^2 + 1) - 1)/(a*x)) + sqrt(-a^2*x^2 + 1)*(a*x + 2) + 2)/(a^4*x + a^3)","A",0
33,1,105,0,0.409727," ","integrate(x^4*(e*x+d)^2/(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","-\frac{330 \, d^{6} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(40 \, e^{5} x^{5} + 96 \, d e^{4} x^{4} + 110 \, d^{2} e^{3} x^{3} + 128 \, d^{3} e^{2} x^{2} + 165 \, d^{4} e x + 256 \, d^{5}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{240 \, e^{5}}"," ",0,"-1/240*(330*d^6*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (40*e^5*x^5 + 96*d*e^4*x^4 + 110*d^2*e^3*x^3 + 128*d^3*e^2*x^2 + 165*d^4*e*x + 256*d^5)*sqrt(-e^2*x^2 + d^2))/e^5","A",0
34,1,94,0,0.413259," ","integrate(x^3*(e*x+d)^2/(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","-\frac{30 \, d^{5} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(4 \, e^{4} x^{4} + 10 \, d e^{3} x^{3} + 12 \, d^{2} e^{2} x^{2} + 15 \, d^{3} e x + 24 \, d^{4}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{20 \, e^{4}}"," ",0,"-1/20*(30*d^5*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (4*e^4*x^4 + 10*d*e^3*x^3 + 12*d^2*e^2*x^2 + 15*d^3*e*x + 24*d^4)*sqrt(-e^2*x^2 + d^2))/e^4","A",0
35,1,83,0,0.397639," ","integrate(x^2*(e*x+d)^2/(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","-\frac{42 \, d^{4} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(6 \, e^{3} x^{3} + 16 \, d e^{2} x^{2} + 21 \, d^{2} e x + 32 \, d^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{24 \, e^{3}}"," ",0,"-1/24*(42*d^4*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (6*e^3*x^3 + 16*d*e^2*x^2 + 21*d^2*e*x + 32*d^3)*sqrt(-e^2*x^2 + d^2))/e^3","A",0
36,1,71,0,0.400714," ","integrate(x*(e*x+d)^2/(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","-\frac{6 \, d^{3} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(e^{2} x^{2} + 3 \, d e x + 5 \, d^{2}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{3 \, e^{2}}"," ",0,"-1/3*(6*d^3*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (e^2*x^2 + 3*d*e*x + 5*d^2)*sqrt(-e^2*x^2 + d^2))/e^2","A",0
37,1,60,0,0.414391," ","integrate((e*x+d)^2/(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","-\frac{6 \, d^{2} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + \sqrt{-e^{2} x^{2} + d^{2}} {\left(e x + 4 \, d\right)}}{2 \, e}"," ",0,"-1/2*(6*d^2*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + sqrt(-e^2*x^2 + d^2)*(e*x + 4*d))/e","A",0
38,1,73,0,0.396557," ","integrate((e*x+d)^2/x/(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","-4 \, d \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + d \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) - \sqrt{-e^{2} x^{2} + d^{2}}"," ",0,"-4*d*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + d*log(-(d - sqrt(-e^2*x^2 + d^2))/x) - sqrt(-e^2*x^2 + d^2)","A",0
39,1,79,0,0.402837," ","integrate((e*x+d)^2/x^2/(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, e x \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) - 2 \, e x \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) + \sqrt{-e^{2} x^{2} + d^{2}}}{x}"," ",0,"-(2*e*x*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) - 2*e*x*log(-(d - sqrt(-e^2*x^2 + d^2))/x) + sqrt(-e^2*x^2 + d^2))/x","A",0
40,1,63,0,0.392347," ","integrate((e*x+d)^2/x^3/(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","\frac{3 \, e^{2} x^{2} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) - \sqrt{-e^{2} x^{2} + d^{2}} {\left(4 \, e x + d\right)}}{2 \, d x^{2}}"," ",0,"1/2*(3*e^2*x^2*log(-(d - sqrt(-e^2*x^2 + d^2))/x) - sqrt(-e^2*x^2 + d^2)*(4*e*x + d))/(d*x^2)","A",0
41,1,74,0,0.401954," ","integrate((e*x+d)^2/x^4/(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","\frac{3 \, e^{3} x^{3} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) - {\left(5 \, e^{2} x^{2} + 3 \, d e x + d^{2}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{3 \, d^{2} x^{3}}"," ",0,"1/3*(3*e^3*x^3*log(-(d - sqrt(-e^2*x^2 + d^2))/x) - (5*e^2*x^2 + 3*d*e*x + d^2)*sqrt(-e^2*x^2 + d^2))/(d^2*x^3)","A",0
42,1,87,0,0.401609," ","integrate((e*x+d)^2/x^5/(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","\frac{21 \, e^{4} x^{4} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) - {\left(32 \, e^{3} x^{3} + 21 \, d e^{2} x^{2} + 16 \, d^{2} e x + 6 \, d^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{24 \, d^{3} x^{4}}"," ",0,"1/24*(21*e^4*x^4*log(-(d - sqrt(-e^2*x^2 + d^2))/x) - (32*e^3*x^3 + 21*d*e^2*x^2 + 16*d^2*e*x + 6*d^3)*sqrt(-e^2*x^2 + d^2))/(d^3*x^4)","A",0
43,1,98,0,0.396043," ","integrate((e*x+d)^2/x^6/(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","\frac{15 \, e^{5} x^{5} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) - {\left(24 \, e^{4} x^{4} + 15 \, d e^{3} x^{3} + 12 \, d^{2} e^{2} x^{2} + 10 \, d^{3} e x + 4 \, d^{4}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{20 \, d^{4} x^{5}}"," ",0,"1/20*(15*e^5*x^5*log(-(d - sqrt(-e^2*x^2 + d^2))/x) - (24*e^4*x^4 + 15*d*e^3*x^3 + 12*d^2*e^2*x^2 + 10*d^3*e*x + 4*d^4)*sqrt(-e^2*x^2 + d^2))/(d^4*x^5)","A",0
44,1,188,0,0.402241," ","integrate(x^5*(e*x+d)^2/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","\frac{56 \, d e^{4} x^{4} - 112 \, d^{2} e^{3} x^{3} + 112 \, d^{4} e x - 56 \, d^{5} + 60 \, {\left(d e^{4} x^{4} - 2 \, d^{2} e^{3} x^{3} + 2 \, d^{4} e x - d^{5}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(15 \, e^{4} x^{4} - 76 \, d e^{3} x^{3} + 32 \, d^{2} e^{2} x^{2} + 82 \, d^{3} e x - 56 \, d^{4}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(e^{10} x^{4} - 2 \, d e^{9} x^{3} + 2 \, d^{3} e^{7} x - d^{4} e^{6}\right)}}"," ",0,"1/15*(56*d*e^4*x^4 - 112*d^2*e^3*x^3 + 112*d^4*e*x - 56*d^5 + 60*(d*e^4*x^4 - 2*d^2*e^3*x^3 + 2*d^4*e*x - d^5)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (15*e^4*x^4 - 76*d*e^3*x^3 + 32*d^2*e^2*x^2 + 82*d^3*e*x - 56*d^4)*sqrt(-e^2*x^2 + d^2))/(e^10*x^4 - 2*d*e^9*x^3 + 2*d^3*e^7*x - d^4*e^6)","A",0
45,1,172,0,0.420457," ","integrate(x^4*(e*x+d)^2/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","\frac{16 \, e^{4} x^{4} - 32 \, d e^{3} x^{3} + 32 \, d^{3} e x - 16 \, d^{4} + 30 \, {\left(e^{4} x^{4} - 2 \, d e^{3} x^{3} + 2 \, d^{3} e x - d^{4}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) - {\left(26 \, e^{3} x^{3} - 22 \, d e^{2} x^{2} - 17 \, d^{2} e x + 16 \, d^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(e^{9} x^{4} - 2 \, d e^{8} x^{3} + 2 \, d^{3} e^{6} x - d^{4} e^{5}\right)}}"," ",0,"1/15*(16*e^4*x^4 - 32*d*e^3*x^3 + 32*d^3*e*x - 16*d^4 + 30*(e^4*x^4 - 2*d*e^3*x^3 + 2*d^3*e*x - d^4)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) - (26*e^3*x^3 - 22*d*e^2*x^2 - 17*d^2*e*x + 16*d^3)*sqrt(-e^2*x^2 + d^2))/(e^9*x^4 - 2*d*e^8*x^3 + 2*d^3*e^6*x - d^4*e^5)","A",0
46,1,116,0,0.400226," ","integrate(x^3*(e*x+d)^2/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","\frac{2 \, e^{4} x^{4} - 4 \, d e^{3} x^{3} + 4 \, d^{3} e x - 2 \, d^{4} - {\left(2 \, e^{3} x^{3} + d e^{2} x^{2} - 4 \, d^{2} e x + 2 \, d^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{5 \, {\left(d e^{8} x^{4} - 2 \, d^{2} e^{7} x^{3} + 2 \, d^{4} e^{5} x - d^{5} e^{4}\right)}}"," ",0,"1/5*(2*e^4*x^4 - 4*d*e^3*x^3 + 4*d^3*e*x - 2*d^4 - (2*e^3*x^3 + d*e^2*x^2 - 4*d^2*e*x + 2*d^3)*sqrt(-e^2*x^2 + d^2))/(d*e^8*x^4 - 2*d^2*e^7*x^3 + 2*d^4*e^5*x - d^5*e^4)","A",0
47,1,117,0,0.400090," ","integrate(x^2*(e*x+d)^2/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","-\frac{4 \, e^{4} x^{4} - 8 \, d e^{3} x^{3} + 8 \, d^{3} e x - 4 \, d^{4} + {\left(e^{3} x^{3} - 2 \, d e^{2} x^{2} + 8 \, d^{2} e x - 4 \, d^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(d^{2} e^{7} x^{4} - 2 \, d^{3} e^{6} x^{3} + 2 \, d^{5} e^{4} x - d^{6} e^{3}\right)}}"," ",0,"-1/15*(4*e^4*x^4 - 8*d*e^3*x^3 + 8*d^3*e*x - 4*d^4 + (e^3*x^3 - 2*d*e^2*x^2 + 8*d^2*e*x - 4*d^3)*sqrt(-e^2*x^2 + d^2))/(d^2*e^7*x^4 - 2*d^3*e^6*x^3 + 2*d^5*e^4*x - d^6*e^3)","A",0
48,1,117,0,0.411049," ","integrate(x*(e*x+d)^2/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","\frac{e^{4} x^{4} - 2 \, d e^{3} x^{3} + 2 \, d^{3} e x - d^{4} + {\left(4 \, e^{3} x^{3} - 8 \, d e^{2} x^{2} + 2 \, d^{2} e x - d^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(d^{3} e^{6} x^{4} - 2 \, d^{4} e^{5} x^{3} + 2 \, d^{6} e^{3} x - d^{7} e^{2}\right)}}"," ",0,"1/15*(e^4*x^4 - 2*d*e^3*x^3 + 2*d^3*e*x - d^4 + (4*e^3*x^3 - 8*d*e^2*x^2 + 2*d^2*e*x - d^3)*sqrt(-e^2*x^2 + d^2))/(d^3*e^6*x^4 - 2*d^4*e^5*x^3 + 2*d^6*e^3*x - d^7*e^2)","A",0
49,1,116,0,0.403795," ","integrate((e*x+d)^2/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","\frac{2 \, e^{4} x^{4} - 4 \, d e^{3} x^{3} + 4 \, d^{3} e x - 2 \, d^{4} - {\left(2 \, e^{3} x^{3} - 4 \, d e^{2} x^{2} + d^{2} e x + 2 \, d^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{5 \, {\left(d^{4} e^{5} x^{4} - 2 \, d^{5} e^{4} x^{3} + 2 \, d^{7} e^{2} x - d^{8} e\right)}}"," ",0,"1/5*(2*e^4*x^4 - 4*d*e^3*x^3 + 4*d^3*e*x - 2*d^4 - (2*e^3*x^3 - 4*d*e^2*x^2 + d^2*e*x + 2*d^3)*sqrt(-e^2*x^2 + d^2))/(d^4*e^5*x^4 - 2*d^5*e^4*x^3 + 2*d^7*e^2*x - d^8*e)","A",0
50,1,169,0,0.392596," ","integrate((e*x+d)^2/x/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","\frac{26 \, e^{4} x^{4} - 52 \, d e^{3} x^{3} + 52 \, d^{3} e x - 26 \, d^{4} + 15 \, {\left(e^{4} x^{4} - 2 \, d e^{3} x^{3} + 2 \, d^{3} e x - d^{4}\right)} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) - {\left(16 \, e^{3} x^{3} - 17 \, d e^{2} x^{2} - 22 \, d^{2} e x + 26 \, d^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(d^{5} e^{4} x^{4} - 2 \, d^{6} e^{3} x^{3} + 2 \, d^{8} e x - d^{9}\right)}}"," ",0,"1/15*(26*e^4*x^4 - 52*d*e^3*x^3 + 52*d^3*e*x - 26*d^4 + 15*(e^4*x^4 - 2*d*e^3*x^3 + 2*d^3*e*x - d^4)*log(-(d - sqrt(-e^2*x^2 + d^2))/x) - (16*e^3*x^3 - 17*d*e^2*x^2 - 22*d^2*e*x + 26*d^3)*sqrt(-e^2*x^2 + d^2))/(d^5*e^4*x^4 - 2*d^6*e^3*x^3 + 2*d^8*e*x - d^9)","A",0
51,1,195,0,0.416846," ","integrate((e*x+d)^2/x^2/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","\frac{46 \, e^{5} x^{5} - 92 \, d e^{4} x^{4} + 92 \, d^{3} e^{2} x^{2} - 46 \, d^{4} e x + 30 \, {\left(e^{5} x^{5} - 2 \, d e^{4} x^{4} + 2 \, d^{3} e^{2} x^{2} - d^{4} e x\right)} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) - {\left(56 \, e^{4} x^{4} - 82 \, d e^{3} x^{3} - 32 \, d^{2} e^{2} x^{2} + 76 \, d^{3} e x - 15 \, d^{4}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(d^{6} e^{4} x^{5} - 2 \, d^{7} e^{3} x^{4} + 2 \, d^{9} e x^{2} - d^{10} x\right)}}"," ",0,"1/15*(46*e^5*x^5 - 92*d*e^4*x^4 + 92*d^3*e^2*x^2 - 46*d^4*e*x + 30*(e^5*x^5 - 2*d*e^4*x^4 + 2*d^3*e^2*x^2 - d^4*e*x)*log(-(d - sqrt(-e^2*x^2 + d^2))/x) - (56*e^4*x^4 - 82*d*e^3*x^3 - 32*d^2*e^2*x^2 + 76*d^3*e*x - 15*d^4)*sqrt(-e^2*x^2 + d^2))/(d^6*e^4*x^5 - 2*d^7*e^3*x^4 + 2*d^9*e*x^2 - d^10*x)","A",0
52,1,216,0,0.428234," ","integrate((e*x+d)^2/x^3/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","\frac{54 \, e^{6} x^{6} - 108 \, d e^{5} x^{5} + 108 \, d^{3} e^{3} x^{3} - 54 \, d^{4} e^{2} x^{2} + 45 \, {\left(e^{6} x^{6} - 2 \, d e^{5} x^{5} + 2 \, d^{3} e^{3} x^{3} - d^{4} e^{2} x^{2}\right)} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) - {\left(64 \, e^{5} x^{5} - 83 \, d e^{4} x^{4} - 58 \, d^{2} e^{3} x^{3} + 94 \, d^{3} e^{2} x^{2} - 10 \, d^{4} e x - 5 \, d^{5}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{10 \, {\left(d^{7} e^{4} x^{6} - 2 \, d^{8} e^{3} x^{5} + 2 \, d^{10} e x^{3} - d^{11} x^{2}\right)}}"," ",0,"1/10*(54*e^6*x^6 - 108*d*e^5*x^5 + 108*d^3*e^3*x^3 - 54*d^4*e^2*x^2 + 45*(e^6*x^6 - 2*d*e^5*x^5 + 2*d^3*e^3*x^3 - d^4*e^2*x^2)*log(-(d - sqrt(-e^2*x^2 + d^2))/x) - (64*e^5*x^5 - 83*d*e^4*x^4 - 58*d^2*e^3*x^3 + 94*d^3*e^2*x^2 - 10*d^4*e*x - 5*d^5)*sqrt(-e^2*x^2 + d^2))/(d^7*e^4*x^6 - 2*d^8*e^3*x^5 + 2*d^10*e*x^3 - d^11*x^2)","A",0
53,1,227,0,0.472756," ","integrate((e*x+d)^2/x^4/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","\frac{116 \, e^{7} x^{7} - 232 \, d e^{6} x^{6} + 232 \, d^{3} e^{4} x^{4} - 116 \, d^{4} e^{3} x^{3} + 105 \, {\left(e^{7} x^{7} - 2 \, d e^{6} x^{6} + 2 \, d^{3} e^{4} x^{4} - d^{4} e^{3} x^{3}\right)} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) - {\left(176 \, e^{6} x^{6} - 247 \, d e^{5} x^{5} - 122 \, d^{2} e^{4} x^{4} + 246 \, d^{3} e^{3} x^{3} - 40 \, d^{4} e^{2} x^{2} - 5 \, d^{5} e x - 5 \, d^{6}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(d^{8} e^{4} x^{7} - 2 \, d^{9} e^{3} x^{6} + 2 \, d^{11} e x^{4} - d^{12} x^{3}\right)}}"," ",0,"1/15*(116*e^7*x^7 - 232*d*e^6*x^6 + 232*d^3*e^4*x^4 - 116*d^4*e^3*x^3 + 105*(e^7*x^7 - 2*d*e^6*x^6 + 2*d^3*e^4*x^4 - d^4*e^3*x^3)*log(-(d - sqrt(-e^2*x^2 + d^2))/x) - (176*e^6*x^6 - 247*d*e^5*x^5 - 122*d^2*e^4*x^4 + 246*d^3*e^3*x^3 - 40*d^4*e^2*x^2 - 5*d^5*e*x - 5*d^6)*sqrt(-e^2*x^2 + d^2))/(d^8*e^4*x^7 - 2*d^9*e^3*x^6 + 2*d^11*e*x^4 - d^12*x^3)","A",0
54,1,50,0,0.399719," ","integrate(x^3*(1+x)^2/(-x^2+1)^(1/2),x, algorithm=""fricas"")","-\frac{1}{20} \, {\left(4 \, x^{4} + 10 \, x^{3} + 12 \, x^{2} + 15 \, x + 24\right)} \sqrt{-x^{2} + 1} - \frac{3}{2} \, \arctan\left(\frac{\sqrt{-x^{2} + 1} - 1}{x}\right)"," ",0,"-1/20*(4*x^4 + 10*x^3 + 12*x^2 + 15*x + 24)*sqrt(-x^2 + 1) - 3/2*arctan((sqrt(-x^2 + 1) - 1)/x)","A",0
55,1,45,0,0.384161," ","integrate(x^2*(1+x)^2/(-x^2+1)^(1/2),x, algorithm=""fricas"")","-\frac{1}{24} \, {\left(6 \, x^{3} + 16 \, x^{2} + 21 \, x + 32\right)} \sqrt{-x^{2} + 1} - \frac{7}{4} \, \arctan\left(\frac{\sqrt{-x^{2} + 1} - 1}{x}\right)"," ",0,"-1/24*(6*x^3 + 16*x^2 + 21*x + 32)*sqrt(-x^2 + 1) - 7/4*arctan((sqrt(-x^2 + 1) - 1)/x)","A",0
56,1,38,0,0.396024," ","integrate(x*(1+x)^2/(-x^2+1)^(1/2),x, algorithm=""fricas"")","-\frac{1}{3} \, {\left(x^{2} + 3 \, x + 5\right)} \sqrt{-x^{2} + 1} - 2 \, \arctan\left(\frac{\sqrt{-x^{2} + 1} - 1}{x}\right)"," ",0,"-1/3*(x^2 + 3*x + 5)*sqrt(-x^2 + 1) - 2*arctan((sqrt(-x^2 + 1) - 1)/x)","A",0
57,1,33,0,0.396262," ","integrate((1+x)^2/(-x^2+1)^(1/2),x, algorithm=""fricas"")","-\frac{1}{2} \, \sqrt{-x^{2} + 1} {\left(x + 4\right)} - 3 \, \arctan\left(\frac{\sqrt{-x^{2} + 1} - 1}{x}\right)"," ",0,"-1/2*sqrt(-x^2 + 1)*(x + 4) - 3*arctan((sqrt(-x^2 + 1) - 1)/x)","A",0
58,1,46,0,0.389879," ","integrate((1+x)^2/x/(-x^2+1)^(1/2),x, algorithm=""fricas"")","-\sqrt{-x^{2} + 1} - 4 \, \arctan\left(\frac{\sqrt{-x^{2} + 1} - 1}{x}\right) + \log\left(\frac{\sqrt{-x^{2} + 1} - 1}{x}\right)"," ",0,"-sqrt(-x^2 + 1) - 4*arctan((sqrt(-x^2 + 1) - 1)/x) + log((sqrt(-x^2 + 1) - 1)/x)","A",0
59,1,53,0,0.404119," ","integrate((1+x)^2/x^2/(-x^2+1)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, x \arctan\left(\frac{\sqrt{-x^{2} + 1} - 1}{x}\right) - 2 \, x \log\left(\frac{\sqrt{-x^{2} + 1} - 1}{x}\right) + \sqrt{-x^{2} + 1}}{x}"," ",0,"-(2*x*arctan((sqrt(-x^2 + 1) - 1)/x) - 2*x*log((sqrt(-x^2 + 1) - 1)/x) + sqrt(-x^2 + 1))/x","A",0
60,1,43,0,0.402731," ","integrate((1+x)^2/x^3/(-x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{3 \, x^{2} \log\left(\frac{\sqrt{-x^{2} + 1} - 1}{x}\right) - \sqrt{-x^{2} + 1} {\left(4 \, x + 1\right)}}{2 \, x^{2}}"," ",0,"1/2*(3*x^2*log((sqrt(-x^2 + 1) - 1)/x) - sqrt(-x^2 + 1)*(4*x + 1))/x^2","A",0
61,1,48,0,0.396025," ","integrate((1+x)^2/x^4/(-x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{3 \, x^{3} \log\left(\frac{\sqrt{-x^{2} + 1} - 1}{x}\right) - {\left(5 \, x^{2} + 3 \, x + 1\right)} \sqrt{-x^{2} + 1}}{3 \, x^{3}}"," ",0,"1/3*(3*x^3*log((sqrt(-x^2 + 1) - 1)/x) - (5*x^2 + 3*x + 1)*sqrt(-x^2 + 1))/x^3","A",0
62,1,53,0,0.402664," ","integrate((1+x)^2/x^5/(-x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{21 \, x^{4} \log\left(\frac{\sqrt{-x^{2} + 1} - 1}{x}\right) - {\left(32 \, x^{3} + 21 \, x^{2} + 16 \, x + 6\right)} \sqrt{-x^{2} + 1}}{24 \, x^{4}}"," ",0,"1/24*(21*x^4*log((sqrt(-x^2 + 1) - 1)/x) - (32*x^3 + 21*x^2 + 16*x + 6)*sqrt(-x^2 + 1))/x^4","A",0
63,1,58,0,0.402786," ","integrate((1+x)^2/x^6/(-x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{15 \, x^{5} \log\left(\frac{\sqrt{-x^{2} + 1} - 1}{x}\right) - {\left(24 \, x^{4} + 15 \, x^{3} + 12 \, x^{2} + 10 \, x + 4\right)} \sqrt{-x^{2} + 1}}{20 \, x^{5}}"," ",0,"1/20*(15*x^5*log((sqrt(-x^2 + 1) - 1)/x) - (24*x^4 + 15*x^3 + 12*x^2 + 10*x + 4)*sqrt(-x^2 + 1))/x^5","A",0
64,1,111,0,0.420135," ","integrate((e*x+d)^3*(-e^2*x^2+d^2)^(1/2)/x^5,x, algorithm=""fricas"")","\frac{16 \, e^{4} x^{4} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) - 13 \, e^{4} x^{4} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) - {\left(11 \, d e^{2} x^{2} + 8 \, d^{2} e x + 2 \, d^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{8 \, x^{4}}"," ",0,"1/8*(16*e^4*x^4*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) - 13*e^4*x^4*log(-(d - sqrt(-e^2*x^2 + d^2))/x) - (11*d*e^2*x^2 + 8*d^2*e*x + 2*d^3)*sqrt(-e^2*x^2 + d^2))/x^4","A",0
65,1,194,0,0.432780," ","integrate(x^5*(e*x+d)^3*(-e^2*x^2+d^2)^(5/2),x, algorithm=""fricas"")","-\frac{630630 \, d^{14} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) - {\left(1317888 \, e^{13} x^{13} + 4257792 \, d e^{12} x^{12} + 1427712 \, d^{2} e^{11} x^{11} - 8773632 \, d^{3} e^{10} x^{10} - 9499776 \, d^{4} e^{9} x^{9} + 2551808 \, d^{5} e^{8} x^{8} + 7763184 \, d^{6} e^{7} x^{7} + 2916352 \, d^{7} e^{6} x^{6} - 168168 \, d^{8} e^{5} x^{5} - 190464 \, d^{9} e^{4} x^{4} - 210210 \, d^{10} e^{3} x^{3} - 253952 \, d^{11} e^{2} x^{2} - 315315 \, d^{12} e x - 507904 \, d^{13}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{18450432 \, e^{6}}"," ",0,"-1/18450432*(630630*d^14*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) - (1317888*e^13*x^13 + 4257792*d*e^12*x^12 + 1427712*d^2*e^11*x^11 - 8773632*d^3*e^10*x^10 - 9499776*d^4*e^9*x^9 + 2551808*d^5*e^8*x^8 + 7763184*d^6*e^7*x^7 + 2916352*d^7*e^6*x^6 - 168168*d^8*e^5*x^5 - 190464*d^9*e^4*x^4 - 210210*d^10*e^3*x^3 - 253952*d^11*e^2*x^2 - 315315*d^12*e*x - 507904*d^13)*sqrt(-e^2*x^2 + d^2))/e^6","A",0
66,1,183,0,0.414951," ","integrate(x^4*(e*x+d)^3*(-e^2*x^2+d^2)^(5/2),x, algorithm=""fricas"")","-\frac{270270 \, d^{13} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) - {\left(394240 \, e^{12} x^{12} + 1281280 \, d e^{11} x^{11} + 430080 \, d^{2} e^{10} x^{10} - 2690688 \, d^{3} e^{9} x^{9} - 2938880 \, d^{4} e^{8} x^{8} + 816816 \, d^{5} e^{7} x^{7} + 2498560 \, d^{6} e^{6} x^{6} + 952952 \, d^{7} e^{5} x^{5} - 76800 \, d^{8} e^{4} x^{4} - 90090 \, d^{9} e^{3} x^{3} - 102400 \, d^{10} e^{2} x^{2} - 135135 \, d^{11} e x - 204800 \, d^{12}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{5125120 \, e^{5}}"," ",0,"-1/5125120*(270270*d^13*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) - (394240*e^12*x^12 + 1281280*d*e^11*x^11 + 430080*d^2*e^10*x^10 - 2690688*d^3*e^9*x^9 - 2938880*d^4*e^8*x^8 + 816816*d^5*e^7*x^7 + 2498560*d^6*e^6*x^6 + 952952*d^7*e^5*x^5 - 76800*d^8*e^4*x^4 - 90090*d^9*e^3*x^3 - 102400*d^10*e^2*x^2 - 135135*d^11*e*x - 204800*d^12)*sqrt(-e^2*x^2 + d^2))/e^5","A",0
67,1,172,0,0.414414," ","integrate(x^3*(e*x+d)^3*(-e^2*x^2+d^2)^(5/2),x, algorithm=""fricas"")","-\frac{284130 \, d^{12} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) - {\left(295680 \, e^{11} x^{11} + 967680 \, d e^{10} x^{10} + 325248 \, d^{2} e^{9} x^{9} - 2078720 \, d^{3} e^{8} x^{8} - 2295216 \, d^{4} e^{7} x^{7} + 665600 \, d^{5} e^{6} x^{6} + 2053128 \, d^{6} e^{5} x^{5} + 798720 \, d^{7} e^{4} x^{4} - 94710 \, d^{8} e^{3} x^{3} - 117760 \, d^{9} e^{2} x^{2} - 142065 \, d^{10} e x - 235520 \, d^{11}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{3548160 \, e^{4}}"," ",0,"-1/3548160*(284130*d^12*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) - (295680*e^11*x^11 + 967680*d*e^10*x^10 + 325248*d^2*e^9*x^9 - 2078720*d^3*e^8*x^8 - 2295216*d^4*e^7*x^7 + 665600*d^5*e^6*x^6 + 2053128*d^6*e^5*x^5 + 798720*d^7*e^4*x^4 - 94710*d^8*e^3*x^3 - 117760*d^9*e^2*x^2 - 142065*d^10*e*x - 235520*d^11)*sqrt(-e^2*x^2 + d^2))/e^4","A",0
68,1,161,0,0.418975," ","integrate(x^2*(e*x+d)^3*(-e^2*x^2+d^2)^(5/2),x, algorithm=""fricas"")","-\frac{131670 \, d^{11} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) - {\left(80640 \, e^{10} x^{10} + 266112 \, d e^{9} x^{9} + 89600 \, d^{2} e^{8} x^{8} - 587664 \, d^{3} e^{7} x^{7} - 657920 \, d^{4} e^{6} x^{6} + 201432 \, d^{5} e^{5} x^{5} + 629760 \, d^{6} e^{4} x^{4} + 251790 \, d^{7} e^{3} x^{3} - 47360 \, d^{8} e^{2} x^{2} - 65835 \, d^{9} e x - 94720 \, d^{10}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{887040 \, e^{3}}"," ",0,"-1/887040*(131670*d^11*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) - (80640*e^10*x^10 + 266112*d*e^9*x^9 + 89600*d^2*e^8*x^8 - 587664*d^3*e^7*x^7 - 657920*d^4*e^6*x^6 + 201432*d^5*e^5*x^5 + 629760*d^6*e^4*x^4 + 251790*d^7*e^3*x^3 - 47360*d^8*e^2*x^2 - 65835*d^9*e*x - 94720*d^10)*sqrt(-e^2*x^2 + d^2))/e^3","A",0
69,1,150,0,0.403951," ","integrate(x*(e*x+d)^3*(-e^2*x^2+d^2)^(5/2),x, algorithm=""fricas"")","-\frac{6930 \, d^{10} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) - {\left(2688 \, e^{9} x^{9} + 8960 \, d e^{8} x^{8} + 3024 \, d^{2} e^{7} x^{7} - 20480 \, d^{3} e^{6} x^{6} - 23352 \, d^{4} e^{5} x^{5} + 7680 \, d^{5} e^{4} x^{4} + 24570 \, d^{6} e^{3} x^{3} + 10240 \, d^{7} e^{2} x^{2} - 3465 \, d^{8} e x - 6400 \, d^{9}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{26880 \, e^{2}}"," ",0,"-1/26880*(6930*d^10*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) - (2688*e^9*x^9 + 8960*d*e^8*x^8 + 3024*d^2*e^7*x^7 - 20480*d^3*e^6*x^6 - 23352*d^4*e^5*x^5 + 7680*d^5*e^4*x^4 + 24570*d^6*e^3*x^3 + 10240*d^7*e^2*x^2 - 3465*d^8*e*x - 6400*d^9)*sqrt(-e^2*x^2 + d^2))/e^2","A",0
70,1,139,0,0.406360," ","integrate((e*x+d)^3*(-e^2*x^2+d^2)^(5/2),x, algorithm=""fricas"")","-\frac{6930 \, d^{9} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) - {\left(896 \, e^{8} x^{8} + 3024 \, d e^{7} x^{7} + 1024 \, d^{2} e^{6} x^{6} - 7224 \, d^{3} e^{5} x^{5} - 8448 \, d^{4} e^{4} x^{4} + 3066 \, d^{5} e^{3} x^{3} + 10240 \, d^{6} e^{2} x^{2} + 4599 \, d^{7} e x - 3712 \, d^{8}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{8064 \, e}"," ",0,"-1/8064*(6930*d^9*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) - (896*e^8*x^8 + 3024*d*e^7*x^7 + 1024*d^2*e^6*x^6 - 7224*d^3*e^5*x^5 - 8448*d^4*e^4*x^4 + 3066*d^5*e^3*x^3 + 10240*d^6*e^2*x^2 + 4599*d^7*e*x - 3712*d^8)*sqrt(-e^2*x^2 + d^2))/e","A",0
71,1,151,0,0.426215," ","integrate((e*x+d)^3*(-e^2*x^2+d^2)^(5/2)/x,x, algorithm=""fricas"")","-\frac{125}{64} \, d^{8} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + d^{8} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) + \frac{1}{13440} \, {\left(1680 \, e^{7} x^{7} + 5760 \, d e^{6} x^{6} + 1960 \, d^{2} e^{5} x^{5} - 14592 \, d^{3} e^{4} x^{4} - 17710 \, d^{4} e^{3} x^{3} + 7424 \, d^{5} e^{2} x^{2} + 27195 \, d^{6} e x + 14848 \, d^{7}\right)} \sqrt{-e^{2} x^{2} + d^{2}}"," ",0,"-125/64*d^8*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + d^8*log(-(d - sqrt(-e^2*x^2 + d^2))/x) + 1/13440*(1680*e^7*x^7 + 5760*d*e^6*x^6 + 1960*d^2*e^5*x^5 - 14592*d^3*e^4*x^4 - 17710*d^4*e^3*x^3 + 7424*d^5*e^2*x^2 + 27195*d^6*e*x + 14848*d^7)*sqrt(-e^2*x^2 + d^2)","A",0
72,1,167,0,0.427343," ","integrate((e*x+d)^3*(-e^2*x^2+d^2)^(5/2)/x^2,x, algorithm=""fricas"")","\frac{1050 \, d^{7} e x \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + 1680 \, d^{7} e x \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) + 2496 \, d^{7} e x + {\left(80 \, e^{7} x^{7} + 280 \, d e^{6} x^{6} + 96 \, d^{2} e^{5} x^{5} - 770 \, d^{3} e^{4} x^{4} - 992 \, d^{4} e^{3} x^{3} + 525 \, d^{5} e^{2} x^{2} + 2496 \, d^{6} e x - 560 \, d^{7}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{560 \, x}"," ",0,"1/560*(1050*d^7*e*x*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + 1680*d^7*e*x*log(-(d - sqrt(-e^2*x^2 + d^2))/x) + 2496*d^7*e*x + (80*e^7*x^7 + 280*d*e^6*x^6 + 96*d^2*e^5*x^5 - 770*d^3*e^4*x^4 - 992*d^4*e^3*x^3 + 525*d^5*e^2*x^2 + 2496*d^6*e*x - 560*d^7)*sqrt(-e^2*x^2 + d^2))/x","A",0
73,1,179,0,0.426593," ","integrate((e*x+d)^3*(-e^2*x^2+d^2)^(5/2)/x^3,x, algorithm=""fricas"")","\frac{2550 \, d^{6} e^{2} x^{2} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + 120 \, d^{6} e^{2} x^{2} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) + 544 \, d^{6} e^{2} x^{2} + {\left(40 \, e^{7} x^{7} + 144 \, d e^{6} x^{6} + 50 \, d^{2} e^{5} x^{5} - 448 \, d^{3} e^{4} x^{4} - 645 \, d^{4} e^{3} x^{3} + 544 \, d^{5} e^{2} x^{2} - 720 \, d^{6} e x - 120 \, d^{7}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{240 \, x^{2}}"," ",0,"1/240*(2550*d^6*e^2*x^2*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + 120*d^6*e^2*x^2*log(-(d - sqrt(-e^2*x^2 + d^2))/x) + 544*d^6*e^2*x^2 + (40*e^7*x^7 + 144*d*e^6*x^6 + 50*d^2*e^5*x^5 - 448*d^3*e^4*x^4 - 645*d^4*e^3*x^3 + 544*d^5*e^2*x^2 - 720*d^6*e*x - 120*d^7)*sqrt(-e^2*x^2 + d^2))/x^2","A",0
74,1,179,0,0.422082," ","integrate((e*x+d)^3*(-e^2*x^2+d^2)^(5/2)/x^4,x, algorithm=""fricas"")","\frac{750 \, d^{5} e^{3} x^{3} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) - 780 \, d^{5} e^{3} x^{3} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) - 656 \, d^{5} e^{3} x^{3} + {\left(24 \, e^{7} x^{7} + 90 \, d e^{6} x^{6} + 32 \, d^{2} e^{5} x^{5} - 345 \, d^{3} e^{4} x^{4} - 656 \, d^{4} e^{3} x^{3} - 80 \, d^{5} e^{2} x^{2} - 180 \, d^{6} e x - 40 \, d^{7}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{120 \, x^{3}}"," ",0,"1/120*(750*d^5*e^3*x^3*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) - 780*d^5*e^3*x^3*log(-(d - sqrt(-e^2*x^2 + d^2))/x) - 656*d^5*e^3*x^3 + (24*e^7*x^7 + 90*d*e^6*x^6 + 32*d^2*e^5*x^5 - 345*d^3*e^4*x^4 - 656*d^4*e^3*x^3 - 80*d^5*e^2*x^2 - 180*d^6*e*x - 40*d^7)*sqrt(-e^2*x^2 + d^2))/x^3","A",0
75,1,180,0,0.424187," ","integrate((e*x+d)^3*(-e^2*x^2+d^2)^(5/2)/x^5,x, algorithm=""fricas"")","-\frac{90 \, d^{4} e^{4} x^{4} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + 45 \, d^{4} e^{4} x^{4} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) + 48 \, d^{4} e^{4} x^{4} - {\left(2 \, e^{7} x^{7} + 8 \, d e^{6} x^{6} + 3 \, d^{2} e^{5} x^{5} - 48 \, d^{3} e^{4} x^{4} + 48 \, d^{4} e^{3} x^{3} - 3 \, d^{5} e^{2} x^{2} - 8 \, d^{6} e x - 2 \, d^{7}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{8 \, x^{4}}"," ",0,"-1/8*(90*d^4*e^4*x^4*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + 45*d^4*e^4*x^4*log(-(d - sqrt(-e^2*x^2 + d^2))/x) + 48*d^4*e^4*x^4 - (2*e^7*x^7 + 8*d*e^6*x^6 + 3*d^2*e^5*x^5 - 48*d^3*e^4*x^4 + 48*d^4*e^3*x^3 - 3*d^5*e^2*x^2 - 8*d^6*e*x - 2*d^7)*sqrt(-e^2*x^2 + d^2))/x^4","A",0
76,1,180,0,0.434105," ","integrate((e*x+d)^3*(-e^2*x^2+d^2)^(5/2)/x^6,x, algorithm=""fricas"")","-\frac{1560 \, d^{3} e^{5} x^{5} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) - 375 \, d^{3} e^{5} x^{5} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) - 80 \, d^{3} e^{5} x^{5} - {\left(40 \, e^{7} x^{7} + 180 \, d e^{6} x^{6} + 80 \, d^{2} e^{5} x^{5} + 656 \, d^{3} e^{4} x^{4} + 345 \, d^{4} e^{3} x^{3} - 32 \, d^{5} e^{2} x^{2} - 90 \, d^{6} e x - 24 \, d^{7}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{120 \, x^{5}}"," ",0,"-1/120*(1560*d^3*e^5*x^5*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) - 375*d^3*e^5*x^5*log(-(d - sqrt(-e^2*x^2 + d^2))/x) - 80*d^3*e^5*x^5 - (40*e^7*x^7 + 180*d*e^6*x^6 + 80*d^2*e^5*x^5 + 656*d^3*e^4*x^4 + 345*d^4*e^3*x^3 - 32*d^5*e^2*x^2 - 90*d^6*e*x - 24*d^7)*sqrt(-e^2*x^2 + d^2))/x^5","A",0
77,1,179,0,0.440228," ","integrate((e*x+d)^3*(-e^2*x^2+d^2)^(5/2)/x^7,x, algorithm=""fricas"")","\frac{240 \, d^{2} e^{6} x^{6} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + 1275 \, d^{2} e^{6} x^{6} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) + 720 \, d^{2} e^{6} x^{6} + {\left(120 \, e^{7} x^{7} + 720 \, d e^{6} x^{6} - 544 \, d^{2} e^{5} x^{5} + 645 \, d^{3} e^{4} x^{4} + 448 \, d^{4} e^{3} x^{3} - 50 \, d^{5} e^{2} x^{2} - 144 \, d^{6} e x - 40 \, d^{7}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{240 \, x^{6}}"," ",0,"1/240*(240*d^2*e^6*x^6*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + 1275*d^2*e^6*x^6*log(-(d - sqrt(-e^2*x^2 + d^2))/x) + 720*d^2*e^6*x^6 + (120*e^7*x^7 + 720*d*e^6*x^6 - 544*d^2*e^5*x^5 + 645*d^3*e^4*x^4 + 448*d^4*e^3*x^3 - 50*d^5*e^2*x^2 - 144*d^6*e*x - 40*d^7)*sqrt(-e^2*x^2 + d^2))/x^6","A",0
78,1,173,0,0.412418," ","integrate((e*x+d)^3*(-e^2*x^2+d^2)^(5/2)/x^8,x, algorithm=""fricas"")","\frac{3360 \, d e^{7} x^{7} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + 525 \, d e^{7} x^{7} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) + 560 \, d e^{7} x^{7} + {\left(560 \, e^{7} x^{7} - 2496 \, d e^{6} x^{6} - 525 \, d^{2} e^{5} x^{5} + 992 \, d^{3} e^{4} x^{4} + 770 \, d^{4} e^{3} x^{3} - 96 \, d^{5} e^{2} x^{2} - 280 \, d^{6} e x - 80 \, d^{7}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{560 \, x^{7}}"," ",0,"1/560*(3360*d*e^7*x^7*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + 525*d*e^7*x^7*log(-(d - sqrt(-e^2*x^2 + d^2))/x) + 560*d*e^7*x^7 + (560*e^7*x^7 - 2496*d*e^6*x^6 - 525*d^2*e^5*x^5 + 992*d^3*e^4*x^4 + 770*d^4*e^3*x^3 - 96*d^5*e^2*x^2 - 280*d^6*e*x - 80*d^7)*sqrt(-e^2*x^2 + d^2))/x^7","A",0
79,1,163,0,0.483174," ","integrate((e*x+d)^3*(-e^2*x^2+d^2)^(5/2)/x^9,x, algorithm=""fricas"")","\frac{26880 \, e^{8} x^{8} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) - 13125 \, e^{8} x^{8} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) - {\left(14848 \, e^{7} x^{7} + 27195 \, d e^{6} x^{6} + 7424 \, d^{2} e^{5} x^{5} - 17710 \, d^{3} e^{4} x^{4} - 14592 \, d^{4} e^{3} x^{3} + 1960 \, d^{5} e^{2} x^{2} + 5760 \, d^{6} e x + 1680 \, d^{7}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{13440 \, x^{8}}"," ",0,"1/13440*(26880*e^8*x^8*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) - 13125*e^8*x^8*log(-(d - sqrt(-e^2*x^2 + d^2))/x) - (14848*e^7*x^7 + 27195*d*e^6*x^6 + 7424*d^2*e^5*x^5 - 17710*d^3*e^4*x^4 - 14592*d^4*e^3*x^3 + 1960*d^5*e^2*x^2 + 5760*d^6*e*x + 1680*d^7)*sqrt(-e^2*x^2 + d^2))/x^8","A",0
80,1,142,0,0.462614," ","integrate((e*x+d)^3*(-e^2*x^2+d^2)^(5/2)/x^10,x, algorithm=""fricas"")","-\frac{3465 \, e^{9} x^{9} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) - {\left(3712 \, e^{8} x^{8} - 4599 \, d e^{7} x^{7} - 10240 \, d^{2} e^{6} x^{6} - 3066 \, d^{3} e^{5} x^{5} + 8448 \, d^{4} e^{4} x^{4} + 7224 \, d^{5} e^{3} x^{3} - 1024 \, d^{6} e^{2} x^{2} - 3024 \, d^{7} e x - 896 \, d^{8}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{8064 \, d x^{9}}"," ",0,"-1/8064*(3465*e^9*x^9*log(-(d - sqrt(-e^2*x^2 + d^2))/x) - (3712*e^8*x^8 - 4599*d*e^7*x^7 - 10240*d^2*e^6*x^6 - 3066*d^3*e^5*x^5 + 8448*d^4*e^4*x^4 + 7224*d^5*e^3*x^3 - 1024*d^6*e^2*x^2 - 3024*d^7*e*x - 896*d^8)*sqrt(-e^2*x^2 + d^2))/(d*x^9)","A",0
81,1,153,0,0.517863," ","integrate((e*x+d)^3*(-e^2*x^2+d^2)^(5/2)/x^11,x, algorithm=""fricas"")","-\frac{3465 \, e^{10} x^{10} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) - {\left(6400 \, e^{9} x^{9} + 3465 \, d e^{8} x^{8} - 10240 \, d^{2} e^{7} x^{7} - 24570 \, d^{3} e^{6} x^{6} - 7680 \, d^{4} e^{5} x^{5} + 23352 \, d^{5} e^{4} x^{4} + 20480 \, d^{6} e^{3} x^{3} - 3024 \, d^{7} e^{2} x^{2} - 8960 \, d^{8} e x - 2688 \, d^{9}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{26880 \, d^{2} x^{10}}"," ",0,"-1/26880*(3465*e^10*x^10*log(-(d - sqrt(-e^2*x^2 + d^2))/x) - (6400*e^9*x^9 + 3465*d*e^8*x^8 - 10240*d^2*e^7*x^7 - 24570*d^3*e^6*x^6 - 7680*d^4*e^5*x^5 + 23352*d^5*e^4*x^4 + 20480*d^6*e^3*x^3 - 3024*d^7*e^2*x^2 - 8960*d^8*e*x - 2688*d^9)*sqrt(-e^2*x^2 + d^2))/(d^2*x^10)","A",0
82,1,164,0,0.575555," ","integrate((e*x+d)^3*(-e^2*x^2+d^2)^(5/2)/x^12,x, algorithm=""fricas"")","-\frac{65835 \, e^{11} x^{11} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) - {\left(94720 \, e^{10} x^{10} + 65835 \, d e^{9} x^{9} + 47360 \, d^{2} e^{8} x^{8} - 251790 \, d^{3} e^{7} x^{7} - 629760 \, d^{4} e^{6} x^{6} - 201432 \, d^{5} e^{5} x^{5} + 657920 \, d^{6} e^{4} x^{4} + 587664 \, d^{7} e^{3} x^{3} - 89600 \, d^{8} e^{2} x^{2} - 266112 \, d^{9} e x - 80640 \, d^{10}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{887040 \, d^{3} x^{11}}"," ",0,"-1/887040*(65835*e^11*x^11*log(-(d - sqrt(-e^2*x^2 + d^2))/x) - (94720*e^10*x^10 + 65835*d*e^9*x^9 + 47360*d^2*e^8*x^8 - 251790*d^3*e^7*x^7 - 629760*d^4*e^6*x^6 - 201432*d^5*e^5*x^5 + 657920*d^6*e^4*x^4 + 587664*d^7*e^3*x^3 - 89600*d^8*e^2*x^2 - 266112*d^9*e*x - 80640*d^10)*sqrt(-e^2*x^2 + d^2))/(d^3*x^11)","A",0
83,1,192,0,0.433872," ","integrate(x^5*(e*x+d)^3/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","\frac{304 \, d^{2} e^{3} x^{3} - 912 \, d^{3} e^{2} x^{2} + 912 \, d^{4} e x - 304 \, d^{5} + 390 \, {\left(d^{2} e^{3} x^{3} - 3 \, d^{3} e^{2} x^{2} + 3 \, d^{4} e x - d^{5}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(15 \, e^{4} x^{4} + 45 \, d e^{3} x^{3} - 479 \, d^{2} e^{2} x^{2} + 717 \, d^{3} e x - 304 \, d^{4}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{30 \, {\left(e^{9} x^{3} - 3 \, d e^{8} x^{2} + 3 \, d^{2} e^{7} x - d^{3} e^{6}\right)}}"," ",0,"1/30*(304*d^2*e^3*x^3 - 912*d^3*e^2*x^2 + 912*d^4*e*x - 304*d^5 + 390*(d^2*e^3*x^3 - 3*d^3*e^2*x^2 + 3*d^4*e*x - d^5)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (15*e^4*x^4 + 45*d*e^3*x^3 - 479*d^2*e^2*x^2 + 717*d^3*e*x - 304*d^4)*sqrt(-e^2*x^2 + d^2))/(e^9*x^3 - 3*d*e^8*x^2 + 3*d^2*e^7*x - d^3*e^6)","A",0
84,1,177,0,0.416643," ","integrate(x^4*(e*x+d)^3/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","\frac{24 \, d e^{3} x^{3} - 72 \, d^{2} e^{2} x^{2} + 72 \, d^{3} e x - 24 \, d^{4} + 30 \, {\left(d e^{3} x^{3} - 3 \, d^{2} e^{2} x^{2} + 3 \, d^{3} e x - d^{4}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(5 \, e^{3} x^{3} - 39 \, d e^{2} x^{2} + 57 \, d^{2} e x - 24 \, d^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{5 \, {\left(e^{8} x^{3} - 3 \, d e^{7} x^{2} + 3 \, d^{2} e^{6} x - d^{3} e^{5}\right)}}"," ",0,"1/5*(24*d*e^3*x^3 - 72*d^2*e^2*x^2 + 72*d^3*e*x - 24*d^4 + 30*(d*e^3*x^3 - 3*d^2*e^2*x^2 + 3*d^3*e*x - d^4)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (5*e^3*x^3 - 39*d*e^2*x^2 + 57*d^2*e*x - 24*d^3)*sqrt(-e^2*x^2 + d^2))/(e^8*x^3 - 3*d*e^7*x^2 + 3*d^2*e^6*x - d^3*e^5)","A",0
85,1,161,0,0.403574," ","integrate(x^3*(e*x+d)^3/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","\frac{22 \, e^{3} x^{3} - 66 \, d e^{2} x^{2} + 66 \, d^{2} e x - 22 \, d^{3} + 30 \, {\left(e^{3} x^{3} - 3 \, d e^{2} x^{2} + 3 \, d^{2} e x - d^{3}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) - {\left(32 \, e^{2} x^{2} - 51 \, d e x + 22 \, d^{2}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(e^{7} x^{3} - 3 \, d e^{6} x^{2} + 3 \, d^{2} e^{5} x - d^{3} e^{4}\right)}}"," ",0,"1/15*(22*e^3*x^3 - 66*d*e^2*x^2 + 66*d^2*e*x - 22*d^3 + 30*(e^3*x^3 - 3*d*e^2*x^2 + 3*d^2*e*x - d^3)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) - (32*e^2*x^2 - 51*d*e*x + 22*d^2)*sqrt(-e^2*x^2 + d^2))/(e^7*x^3 - 3*d*e^6*x^2 + 3*d^2*e^5*x - d^3*e^4)","A",0
86,1,106,0,0.398140," ","integrate(x^2*(e*x+d)^3/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","\frac{2 \, e^{3} x^{3} - 6 \, d e^{2} x^{2} + 6 \, d^{2} e x - 2 \, d^{3} - {\left(7 \, e^{2} x^{2} - 6 \, d e x + 2 \, d^{2}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(d e^{6} x^{3} - 3 \, d^{2} e^{5} x^{2} + 3 \, d^{3} e^{4} x - d^{4} e^{3}\right)}}"," ",0,"1/15*(2*e^3*x^3 - 6*d*e^2*x^2 + 6*d^2*e*x - 2*d^3 - (7*e^2*x^2 - 6*d*e*x + 2*d^2)*sqrt(-e^2*x^2 + d^2))/(d*e^6*x^3 - 3*d^2*e^5*x^2 + 3*d^3*e^4*x - d^4*e^3)","A",0
87,1,104,0,0.390417," ","integrate(x*(e*x+d)^3/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","-\frac{e^{3} x^{3} - 3 \, d e^{2} x^{2} + 3 \, d^{2} e x - d^{3} - {\left(e^{2} x^{2} - 3 \, d e x + d^{2}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{5 \, {\left(d^{2} e^{5} x^{3} - 3 \, d^{3} e^{4} x^{2} + 3 \, d^{4} e^{3} x - d^{5} e^{2}\right)}}"," ",0,"-1/5*(e^3*x^3 - 3*d*e^2*x^2 + 3*d^2*e*x - d^3 - (e^2*x^2 - 3*d*e*x + d^2)*sqrt(-e^2*x^2 + d^2))/(d^2*e^5*x^3 - 3*d^3*e^4*x^2 + 3*d^4*e^3*x - d^5*e^2)","A",0
88,1,106,0,0.401550," ","integrate((e*x+d)^3/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","\frac{7 \, e^{3} x^{3} - 21 \, d e^{2} x^{2} + 21 \, d^{2} e x - 7 \, d^{3} - {\left(2 \, e^{2} x^{2} - 6 \, d e x + 7 \, d^{2}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(d^{3} e^{4} x^{3} - 3 \, d^{4} e^{3} x^{2} + 3 \, d^{5} e^{2} x - d^{6} e\right)}}"," ",0,"1/15*(7*e^3*x^3 - 21*d*e^2*x^2 + 21*d^2*e*x - 7*d^3 - (2*e^2*x^2 - 6*d*e*x + 7*d^2)*sqrt(-e^2*x^2 + d^2))/(d^3*e^4*x^3 - 3*d^4*e^3*x^2 + 3*d^5*e^2*x - d^6*e)","A",0
89,1,158,0,0.405974," ","integrate((e*x+d)^3/x/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","\frac{32 \, e^{3} x^{3} - 96 \, d e^{2} x^{2} + 96 \, d^{2} e x - 32 \, d^{3} + 15 \, {\left(e^{3} x^{3} - 3 \, d e^{2} x^{2} + 3 \, d^{2} e x - d^{3}\right)} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) - {\left(22 \, e^{2} x^{2} - 51 \, d e x + 32 \, d^{2}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(d^{4} e^{3} x^{3} - 3 \, d^{5} e^{2} x^{2} + 3 \, d^{6} e x - d^{7}\right)}}"," ",0,"1/15*(32*e^3*x^3 - 96*d*e^2*x^2 + 96*d^2*e*x - 32*d^3 + 15*(e^3*x^3 - 3*d*e^2*x^2 + 3*d^2*e*x - d^3)*log(-(d - sqrt(-e^2*x^2 + d^2))/x) - (22*e^2*x^2 - 51*d*e*x + 32*d^2)*sqrt(-e^2*x^2 + d^2))/(d^4*e^3*x^3 - 3*d^5*e^2*x^2 + 3*d^6*e*x - d^7)","A",0
90,1,184,0,0.423087," ","integrate((e*x+d)^3/x^2/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","\frac{24 \, e^{4} x^{4} - 72 \, d e^{3} x^{3} + 72 \, d^{2} e^{2} x^{2} - 24 \, d^{3} e x + 15 \, {\left(e^{4} x^{4} - 3 \, d e^{3} x^{3} + 3 \, d^{2} e^{2} x^{2} - d^{3} e x\right)} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) - {\left(24 \, e^{3} x^{3} - 57 \, d e^{2} x^{2} + 39 \, d^{2} e x - 5 \, d^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{5 \, {\left(d^{5} e^{3} x^{4} - 3 \, d^{6} e^{2} x^{3} + 3 \, d^{7} e x^{2} - d^{8} x\right)}}"," ",0,"1/5*(24*e^4*x^4 - 72*d*e^3*x^3 + 72*d^2*e^2*x^2 - 24*d^3*e*x + 15*(e^4*x^4 - 3*d*e^3*x^3 + 3*d^2*e^2*x^2 - d^3*e*x)*log(-(d - sqrt(-e^2*x^2 + d^2))/x) - (24*e^3*x^3 - 57*d*e^2*x^2 + 39*d^2*e*x - 5*d^3)*sqrt(-e^2*x^2 + d^2))/(d^5*e^3*x^4 - 3*d^6*e^2*x^3 + 3*d^7*e*x^2 - d^8*x)","A",0
91,1,205,0,0.417573," ","integrate((e*x+d)^3/x^3/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","\frac{254 \, e^{5} x^{5} - 762 \, d e^{4} x^{4} + 762 \, d^{2} e^{3} x^{3} - 254 \, d^{3} e^{2} x^{2} + 195 \, {\left(e^{5} x^{5} - 3 \, d e^{4} x^{4} + 3 \, d^{2} e^{3} x^{3} - d^{3} e^{2} x^{2}\right)} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) - {\left(304 \, e^{4} x^{4} - 717 \, d e^{3} x^{3} + 479 \, d^{2} e^{2} x^{2} - 45 \, d^{3} e x - 15 \, d^{4}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{30 \, {\left(d^{6} e^{3} x^{5} - 3 \, d^{7} e^{2} x^{4} + 3 \, d^{8} e x^{3} - d^{9} x^{2}\right)}}"," ",0,"1/30*(254*e^5*x^5 - 762*d*e^4*x^4 + 762*d^2*e^3*x^3 - 254*d^3*e^2*x^2 + 195*(e^5*x^5 - 3*d*e^4*x^4 + 3*d^2*e^3*x^3 - d^3*e^2*x^2)*log(-(d - sqrt(-e^2*x^2 + d^2))/x) - (304*e^4*x^4 - 717*d*e^3*x^3 + 479*d^2*e^2*x^2 - 45*d^3*e*x - 15*d^4)*sqrt(-e^2*x^2 + d^2))/(d^6*e^3*x^5 - 3*d^7*e^2*x^4 + 3*d^8*e*x^3 - d^9*x^2)","A",0
92,1,95,0,0.405007," ","integrate(x^4*(-e^2*x^2+d^2)^(1/2)/(e*x+d),x, algorithm=""fricas"")","-\frac{90 \, d^{5} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) - {\left(24 \, e^{4} x^{4} - 30 \, d e^{3} x^{3} + 32 \, d^{2} e^{2} x^{2} - 45 \, d^{3} e x + 64 \, d^{4}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{120 \, e^{5}}"," ",0,"-1/120*(90*d^5*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) - (24*e^4*x^4 - 30*d*e^3*x^3 + 32*d^2*e^2*x^2 - 45*d^3*e*x + 64*d^4)*sqrt(-e^2*x^2 + d^2))/e^5","A",0
93,1,83,0,0.403617," ","integrate(x^3*(-e^2*x^2+d^2)^(1/2)/(e*x+d),x, algorithm=""fricas"")","\frac{18 \, d^{4} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(6 \, e^{3} x^{3} - 8 \, d e^{2} x^{2} + 9 \, d^{2} e x - 16 \, d^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{24 \, e^{4}}"," ",0,"1/24*(18*d^4*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (6*e^3*x^3 - 8*d*e^2*x^2 + 9*d^2*e*x - 16*d^3)*sqrt(-e^2*x^2 + d^2))/e^4","A",0
94,1,73,0,0.403746," ","integrate(x^2*(-e^2*x^2+d^2)^(1/2)/(e*x+d),x, algorithm=""fricas"")","-\frac{6 \, d^{3} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) - {\left(2 \, e^{2} x^{2} - 3 \, d e x + 4 \, d^{2}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{6 \, e^{3}}"," ",0,"-1/6*(6*d^3*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) - (2*e^2*x^2 - 3*d*e*x + 4*d^2)*sqrt(-e^2*x^2 + d^2))/e^3","A",0
95,1,60,0,0.400746," ","integrate(x*(-e^2*x^2+d^2)^(1/2)/(e*x+d),x, algorithm=""fricas"")","\frac{2 \, d^{2} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + \sqrt{-e^{2} x^{2} + d^{2}} {\left(e x - 2 \, d\right)}}{2 \, e^{2}}"," ",0,"1/2*(2*d^2*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + sqrt(-e^2*x^2 + d^2)*(e*x - 2*d))/e^2","A",0
96,1,52,0,0.389620," ","integrate((-e^2*x^2+d^2)^(1/2)/(e*x+d),x, algorithm=""fricas"")","-\frac{2 \, d \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) - \sqrt{-e^{2} x^{2} + d^{2}}}{e}"," ",0,"-(2*d*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) - sqrt(-e^2*x^2 + d^2))/e","A",0
97,1,54,0,0.425009," ","integrate((-e^2*x^2+d^2)^(1/2)/x/(e*x+d),x, algorithm=""fricas"")","2 \, \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right)"," ",0,"2*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + log(-(d - sqrt(-e^2*x^2 + d^2))/x)","A",0
98,1,50,0,0.395107," ","integrate((-e^2*x^2+d^2)^(1/2)/x^2/(e*x+d),x, algorithm=""fricas"")","-\frac{e x \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) + \sqrt{-e^{2} x^{2} + d^{2}}}{d x}"," ",0,"-(e*x*log(-(d - sqrt(-e^2*x^2 + d^2))/x) + sqrt(-e^2*x^2 + d^2))/(d*x)","A",0
99,1,63,0,0.385317," ","integrate((-e^2*x^2+d^2)^(1/2)/x^3/(e*x+d),x, algorithm=""fricas"")","\frac{e^{2} x^{2} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) + \sqrt{-e^{2} x^{2} + d^{2}} {\left(2 \, e x - d\right)}}{2 \, d^{2} x^{2}}"," ",0,"1/2*(e^2*x^2*log(-(d - sqrt(-e^2*x^2 + d^2))/x) + sqrt(-e^2*x^2 + d^2)*(2*e*x - d))/(d^2*x^2)","A",0
100,1,75,0,0.396038," ","integrate((-e^2*x^2+d^2)^(1/2)/x^4/(e*x+d),x, algorithm=""fricas"")","-\frac{3 \, e^{3} x^{3} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) + {\left(4 \, e^{2} x^{2} - 3 \, d e x + 2 \, d^{2}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{6 \, d^{3} x^{3}}"," ",0,"-1/6*(3*e^3*x^3*log(-(d - sqrt(-e^2*x^2 + d^2))/x) + (4*e^2*x^2 - 3*d*e*x + 2*d^2)*sqrt(-e^2*x^2 + d^2))/(d^3*x^3)","A",0
101,1,86,0,0.391652," ","integrate((-e^2*x^2+d^2)^(1/2)/x^5/(e*x+d),x, algorithm=""fricas"")","\frac{9 \, e^{4} x^{4} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) + {\left(16 \, e^{3} x^{3} - 9 \, d e^{2} x^{2} + 8 \, d^{2} e x - 6 \, d^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{24 \, d^{4} x^{4}}"," ",0,"1/24*(9*e^4*x^4*log(-(d - sqrt(-e^2*x^2 + d^2))/x) + (16*e^3*x^3 - 9*d*e^2*x^2 + 8*d^2*e*x - 6*d^3)*sqrt(-e^2*x^2 + d^2))/(d^4*x^4)","A",0
102,1,94,0,0.393789," ","integrate(x^2*(-e^2*x^2+d^2)^(3/2)/(e*x+d),x, algorithm=""fricas"")","-\frac{30 \, d^{5} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(24 \, e^{4} x^{4} - 30 \, d e^{3} x^{3} - 8 \, d^{2} e^{2} x^{2} + 15 \, d^{3} e x - 16 \, d^{4}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{120 \, e^{3}}"," ",0,"-1/120*(30*d^5*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (24*e^4*x^4 - 30*d*e^3*x^3 - 8*d^2*e^2*x^2 + 15*d^3*e*x - 16*d^4)*sqrt(-e^2*x^2 + d^2))/e^3","A",0
103,1,139,0,0.409682," ","integrate(x^4*(-e^2*x^2+d^2)^(5/2)/(e*x+d),x, algorithm=""fricas"")","-\frac{1890 \, d^{9} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) - {\left(4480 \, e^{8} x^{8} - 5040 \, d e^{7} x^{7} - 6400 \, d^{2} e^{6} x^{6} + 7560 \, d^{3} e^{5} x^{5} + 384 \, d^{4} e^{4} x^{4} - 630 \, d^{5} e^{3} x^{3} + 512 \, d^{6} e^{2} x^{2} - 945 \, d^{7} e x + 1024 \, d^{8}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{40320 \, e^{5}}"," ",0,"-1/40320*(1890*d^9*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) - (4480*e^8*x^8 - 5040*d*e^7*x^7 - 6400*d^2*e^6*x^6 + 7560*d^3*e^5*x^5 + 384*d^4*e^4*x^4 - 630*d^5*e^3*x^3 + 512*d^6*e^2*x^2 - 945*d^7*e*x + 1024*d^8)*sqrt(-e^2*x^2 + d^2))/e^5","A",0
104,1,127,0,0.402309," ","integrate(x^3*(-e^2*x^2+d^2)^(5/2)/(e*x+d),x, algorithm=""fricas"")","\frac{210 \, d^{8} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(560 \, e^{7} x^{7} - 640 \, d e^{6} x^{6} - 840 \, d^{2} e^{5} x^{5} + 1024 \, d^{3} e^{4} x^{4} + 70 \, d^{4} e^{3} x^{3} - 128 \, d^{5} e^{2} x^{2} + 105 \, d^{6} e x - 256 \, d^{7}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{4480 \, e^{4}}"," ",0,"1/4480*(210*d^8*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (560*e^7*x^7 - 640*d*e^6*x^6 - 840*d^2*e^5*x^5 + 1024*d^3*e^4*x^4 + 70*d^4*e^3*x^3 - 128*d^5*e^2*x^2 + 105*d^6*e*x - 256*d^7)*sqrt(-e^2*x^2 + d^2))/e^4","A",0
105,1,117,0,0.406239," ","integrate(x^2*(-e^2*x^2+d^2)^(5/2)/(e*x+d),x, algorithm=""fricas"")","-\frac{210 \, d^{7} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) - {\left(240 \, e^{6} x^{6} - 280 \, d e^{5} x^{5} - 384 \, d^{2} e^{4} x^{4} + 490 \, d^{3} e^{3} x^{3} + 48 \, d^{4} e^{2} x^{2} - 105 \, d^{5} e x + 96 \, d^{6}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{1680 \, e^{3}}"," ",0,"-1/1680*(210*d^7*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) - (240*e^6*x^6 - 280*d*e^5*x^5 - 384*d^2*e^4*x^4 + 490*d^3*e^3*x^3 + 48*d^4*e^2*x^2 - 105*d^5*e*x + 96*d^6)*sqrt(-e^2*x^2 + d^2))/e^3","A",0
106,1,105,0,0.402833," ","integrate(x*(-e^2*x^2+d^2)^(5/2)/(e*x+d),x, algorithm=""fricas"")","\frac{30 \, d^{6} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(40 \, e^{5} x^{5} - 48 \, d e^{4} x^{4} - 70 \, d^{2} e^{3} x^{3} + 96 \, d^{3} e^{2} x^{2} + 15 \, d^{4} e x - 48 \, d^{5}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{240 \, e^{2}}"," ",0,"1/240*(30*d^6*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (40*e^5*x^5 - 48*d*e^4*x^4 - 70*d^2*e^3*x^3 + 96*d^3*e^2*x^2 + 15*d^4*e*x - 48*d^5)*sqrt(-e^2*x^2 + d^2))/e^2","A",0
107,1,95,0,0.396831," ","integrate((-e^2*x^2+d^2)^(5/2)/(e*x+d),x, algorithm=""fricas"")","-\frac{30 \, d^{5} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) - {\left(8 \, e^{4} x^{4} - 10 \, d e^{3} x^{3} - 16 \, d^{2} e^{2} x^{2} + 25 \, d^{3} e x + 8 \, d^{4}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{40 \, e}"," ",0,"-1/40*(30*d^5*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) - (8*e^4*x^4 - 10*d*e^3*x^3 - 16*d^2*e^2*x^2 + 25*d^3*e*x + 8*d^4)*sqrt(-e^2*x^2 + d^2))/e","A",0
108,1,107,0,0.414730," ","integrate((-e^2*x^2+d^2)^(5/2)/x/(e*x+d),x, algorithm=""fricas"")","\frac{3}{4} \, d^{4} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + d^{4} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) + \frac{1}{24} \, {\left(6 \, e^{3} x^{3} - 8 \, d e^{2} x^{2} - 15 \, d^{2} e x + 32 \, d^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}}"," ",0,"3/4*d^4*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + d^4*log(-(d - sqrt(-e^2*x^2 + d^2))/x) + 1/24*(6*e^3*x^3 - 8*d*e^2*x^2 - 15*d^2*e*x + 32*d^3)*sqrt(-e^2*x^2 + d^2)","A",0
109,1,123,0,0.394339," ","integrate((-e^2*x^2+d^2)^(5/2)/x^2/(e*x+d),x, algorithm=""fricas"")","\frac{18 \, d^{3} e x \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) - 6 \, d^{3} e x \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) - 8 \, d^{3} e x + {\left(2 \, e^{3} x^{3} - 3 \, d e^{2} x^{2} - 8 \, d^{2} e x - 6 \, d^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{6 \, x}"," ",0,"1/6*(18*d^3*e*x*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) - 6*d^3*e*x*log(-(d - sqrt(-e^2*x^2 + d^2))/x) - 8*d^3*e*x + (2*e^3*x^3 - 3*d*e^2*x^2 - 8*d^2*e*x - 6*d^3)*sqrt(-e^2*x^2 + d^2))/x","A",0
110,1,135,0,0.422974," ","integrate((-e^2*x^2+d^2)^(5/2)/x^3/(e*x+d),x, algorithm=""fricas"")","-\frac{6 \, d^{2} e^{2} x^{2} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + 3 \, d^{2} e^{2} x^{2} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) + 2 \, d^{2} e^{2} x^{2} - {\left(e^{3} x^{3} - 2 \, d e^{2} x^{2} + 2 \, d^{2} e x - d^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{2 \, x^{2}}"," ",0,"-1/2*(6*d^2*e^2*x^2*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + 3*d^2*e^2*x^2*log(-(d - sqrt(-e^2*x^2 + d^2))/x) + 2*d^2*e^2*x^2 - (e^3*x^3 - 2*d*e^2*x^2 + 2*d^2*e*x - d^3)*sqrt(-e^2*x^2 + d^2))/x^2","A",0
111,1,130,0,0.411608," ","integrate((-e^2*x^2+d^2)^(5/2)/x^4/(e*x+d),x, algorithm=""fricas"")","-\frac{12 \, d e^{3} x^{3} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) - 9 \, d e^{3} x^{3} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) - 6 \, d e^{3} x^{3} - {\left(6 \, e^{3} x^{3} + 8 \, d e^{2} x^{2} + 3 \, d^{2} e x - 2 \, d^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{6 \, x^{3}}"," ",0,"-1/6*(12*d*e^3*x^3*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) - 9*d*e^3*x^3*log(-(d - sqrt(-e^2*x^2 + d^2))/x) - 6*d*e^3*x^3 - (6*e^3*x^3 + 8*d*e^2*x^2 + 3*d^2*e*x - 2*d^3)*sqrt(-e^2*x^2 + d^2))/x^3","A",0
112,1,119,0,0.414254," ","integrate((-e^2*x^2+d^2)^(5/2)/x^5/(e*x+d),x, algorithm=""fricas"")","\frac{48 \, e^{4} x^{4} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + 9 \, e^{4} x^{4} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) - {\left(32 \, e^{3} x^{3} - 15 \, d e^{2} x^{2} - 8 \, d^{2} e x + 6 \, d^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{24 \, x^{4}}"," ",0,"1/24*(48*e^4*x^4*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + 9*e^4*x^4*log(-(d - sqrt(-e^2*x^2 + d^2))/x) - (32*e^3*x^3 - 15*d*e^2*x^2 - 8*d^2*e*x + 6*d^3)*sqrt(-e^2*x^2 + d^2))/x^4","A",0
113,1,97,0,0.404597," ","integrate((-e^2*x^2+d^2)^(5/2)/x^6/(e*x+d),x, algorithm=""fricas"")","-\frac{15 \, e^{5} x^{5} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) + {\left(8 \, e^{4} x^{4} + 25 \, d e^{3} x^{3} - 16 \, d^{2} e^{2} x^{2} - 10 \, d^{3} e x + 8 \, d^{4}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{40 \, d x^{5}}"," ",0,"-1/40*(15*e^5*x^5*log(-(d - sqrt(-e^2*x^2 + d^2))/x) + (8*e^4*x^4 + 25*d*e^3*x^3 - 16*d^2*e^2*x^2 - 10*d^3*e*x + 8*d^4)*sqrt(-e^2*x^2 + d^2))/(d*x^5)","A",0
114,1,108,0,0.418999," ","integrate((-e^2*x^2+d^2)^(5/2)/x^7/(e*x+d),x, algorithm=""fricas"")","\frac{15 \, e^{6} x^{6} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) + {\left(48 \, e^{5} x^{5} - 15 \, d e^{4} x^{4} - 96 \, d^{2} e^{3} x^{3} + 70 \, d^{3} e^{2} x^{2} + 48 \, d^{4} e x - 40 \, d^{5}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{240 \, d^{2} x^{6}}"," ",0,"1/240*(15*e^6*x^6*log(-(d - sqrt(-e^2*x^2 + d^2))/x) + (48*e^5*x^5 - 15*d*e^4*x^4 - 96*d^2*e^3*x^3 + 70*d^3*e^2*x^2 + 48*d^4*e*x - 40*d^5)*sqrt(-e^2*x^2 + d^2))/(d^2*x^6)","A",0
115,1,119,0,0.425031," ","integrate((-e^2*x^2+d^2)^(5/2)/x^8/(e*x+d),x, algorithm=""fricas"")","-\frac{105 \, e^{7} x^{7} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) + {\left(96 \, e^{6} x^{6} - 105 \, d e^{5} x^{5} + 48 \, d^{2} e^{4} x^{4} + 490 \, d^{3} e^{3} x^{3} - 384 \, d^{4} e^{2} x^{2} - 280 \, d^{5} e x + 240 \, d^{6}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{1680 \, d^{3} x^{7}}"," ",0,"-1/1680*(105*e^7*x^7*log(-(d - sqrt(-e^2*x^2 + d^2))/x) + (96*e^6*x^6 - 105*d*e^5*x^5 + 48*d^2*e^4*x^4 + 490*d^3*e^3*x^3 - 384*d^4*e^2*x^2 - 280*d^5*e*x + 240*d^6)*sqrt(-e^2*x^2 + d^2))/(d^3*x^7)","A",0
116,1,130,0,0.460001," ","integrate((-e^2*x^2+d^2)^(5/2)/x^9/(e*x+d),x, algorithm=""fricas"")","\frac{105 \, e^{8} x^{8} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) + {\left(256 \, e^{7} x^{7} - 105 \, d e^{6} x^{6} + 128 \, d^{2} e^{5} x^{5} - 70 \, d^{3} e^{4} x^{4} - 1024 \, d^{4} e^{3} x^{3} + 840 \, d^{5} e^{2} x^{2} + 640 \, d^{6} e x - 560 \, d^{7}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{4480 \, d^{4} x^{8}}"," ",0,"1/4480*(105*e^8*x^8*log(-(d - sqrt(-e^2*x^2 + d^2))/x) + (256*e^7*x^7 - 105*d*e^6*x^6 + 128*d^2*e^5*x^5 - 70*d^3*e^4*x^4 - 1024*d^4*e^3*x^3 + 840*d^5*e^2*x^2 + 640*d^6*e*x - 560*d^7)*sqrt(-e^2*x^2 + d^2))/(d^4*x^8)","A",0
117,1,31,0,0.410353," ","integrate(x*(-x^2+1)^(1/2)/(1+x),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{-x^{2} + 1} {\left(x - 2\right)} + \arctan\left(\frac{\sqrt{-x^{2} + 1} - 1}{x}\right)"," ",0,"1/2*sqrt(-x^2 + 1)*(x - 2) + arctan((sqrt(-x^2 + 1) - 1)/x)","A",0
118,1,74,0,0.410213," ","integrate((-a^2*x^2+1)^(3/2)/x^2/(-a*x+1),x, algorithm=""fricas"")","\frac{2 \, a x \arctan\left(\frac{\sqrt{-a^{2} x^{2} + 1} - 1}{a x}\right) + a x \log\left(\frac{\sqrt{-a^{2} x^{2} + 1} - 1}{x}\right) + a x + \sqrt{-a^{2} x^{2} + 1} {\left(a x - 1\right)}}{x}"," ",0,"(2*a*x*arctan((sqrt(-a^2*x^2 + 1) - 1)/(a*x)) + a*x*log((sqrt(-a^2*x^2 + 1) - 1)/x) + a*x + sqrt(-a^2*x^2 + 1)*(a*x - 1))/x","A",0
119,1,112,0,0.406603," ","integrate(x^4/(e*x+d)/(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","-\frac{16 \, d^{3} e x + 16 \, d^{4} - 18 \, {\left(d^{3} e x + d^{4}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(2 \, e^{3} x^{3} - d e^{2} x^{2} + 7 \, d^{2} e x + 16 \, d^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{6 \, {\left(e^{6} x + d e^{5}\right)}}"," ",0,"-1/6*(16*d^3*e*x + 16*d^4 - 18*(d^3*e*x + d^4)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (2*e^3*x^3 - d*e^2*x^2 + 7*d^2*e*x + 16*d^3)*sqrt(-e^2*x^2 + d^2))/(e^6*x + d*e^5)","A",0
120,1,101,0,0.404708," ","integrate(x^3/(e*x+d)/(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","\frac{4 \, d^{2} e x + 4 \, d^{3} - 6 \, {\left(d^{2} e x + d^{3}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) - {\left(e^{2} x^{2} - d e x - 4 \, d^{2}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{2 \, {\left(e^{5} x + d e^{4}\right)}}"," ",0,"1/2*(4*d^2*e*x + 4*d^3 - 6*(d^2*e*x + d^3)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) - (e^2*x^2 - d*e*x - 4*d^2)*sqrt(-e^2*x^2 + d^2))/(e^5*x + d*e^4)","A",0
121,1,85,0,0.408735," ","integrate(x^2/(e*x+d)/(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, d e x + 2 \, d^{2} - 2 \, {\left(d e x + d^{2}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + \sqrt{-e^{2} x^{2} + d^{2}} {\left(e x + 2 \, d\right)}}{e^{4} x + d e^{3}}"," ",0,"-(2*d*e*x + 2*d^2 - 2*(d*e*x + d^2)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + sqrt(-e^2*x^2 + d^2)*(e*x + 2*d))/(e^4*x + d*e^3)","A",0
122,1,67,0,0.397455," ","integrate(x/(e*x+d)/(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","\frac{e x - 2 \, {\left(e x + d\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + d + \sqrt{-e^{2} x^{2} + d^{2}}}{e^{3} x + d e^{2}}"," ",0,"(e*x - 2*(e*x + d)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + d + sqrt(-e^2*x^2 + d^2))/(e^3*x + d*e^2)","A",0
123,1,35,0,0.383503," ","integrate(1/(e*x+d)/(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","-\frac{e x + d + \sqrt{-e^{2} x^{2} + d^{2}}}{d e^{2} x + d^{2} e}"," ",0,"-(e*x + d + sqrt(-e^2*x^2 + d^2))/(d*e^2*x + d^2*e)","A",0
124,1,62,0,0.384948," ","integrate(1/x/(e*x+d)/(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","\frac{e x + {\left(e x + d\right)} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) + d + \sqrt{-e^{2} x^{2} + d^{2}}}{d^{2} e x + d^{3}}"," ",0,"(e*x + (e*x + d)*log(-(d - sqrt(-e^2*x^2 + d^2))/x) + d + sqrt(-e^2*x^2 + d^2))/(d^2*e*x + d^3)","A",0
125,1,88,0,0.408104," ","integrate(1/x^2/(e*x+d)/(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","-\frac{e^{2} x^{2} + d e x + {\left(e^{2} x^{2} + d e x\right)} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) + \sqrt{-e^{2} x^{2} + d^{2}} {\left(2 \, e x + d\right)}}{d^{3} e x^{2} + d^{4} x}"," ",0,"-(e^2*x^2 + d*e*x + (e^2*x^2 + d*e*x)*log(-(d - sqrt(-e^2*x^2 + d^2))/x) + sqrt(-e^2*x^2 + d^2)*(2*e*x + d))/(d^3*e*x^2 + d^4*x)","A",0
126,1,113,0,0.406849," ","integrate(1/x^3/(e*x+d)/(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, e^{3} x^{3} + 2 \, d e^{2} x^{2} + 3 \, {\left(e^{3} x^{3} + d e^{2} x^{2}\right)} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) + {\left(4 \, e^{2} x^{2} + d e x - d^{2}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{2 \, {\left(d^{4} e x^{3} + d^{5} x^{2}\right)}}"," ",0,"1/2*(2*e^3*x^3 + 2*d*e^2*x^2 + 3*(e^3*x^3 + d*e^2*x^2)*log(-(d - sqrt(-e^2*x^2 + d^2))/x) + (4*e^2*x^2 + d*e*x - d^2)*sqrt(-e^2*x^2 + d^2))/(d^4*e*x^3 + d^5*x^2)","A",0
127,1,190,0,0.403193," ","integrate(x^5/(e*x+d)/(-e^2*x^2+d^2)^(3/2),x, algorithm=""fricas"")","-\frac{16 \, d^{2} e^{3} x^{3} + 16 \, d^{3} e^{2} x^{2} - 16 \, d^{4} e x - 16 \, d^{5} - 30 \, {\left(d^{2} e^{3} x^{3} + d^{3} e^{2} x^{2} - d^{4} e x - d^{5}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) - {\left(3 \, e^{4} x^{4} - 3 \, d e^{3} x^{3} - 23 \, d^{2} e^{2} x^{2} + d^{3} e x + 16 \, d^{4}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{6 \, {\left(e^{9} x^{3} + d e^{8} x^{2} - d^{2} e^{7} x - d^{3} e^{6}\right)}}"," ",0,"-1/6*(16*d^2*e^3*x^3 + 16*d^3*e^2*x^2 - 16*d^4*e*x - 16*d^5 - 30*(d^2*e^3*x^3 + d^3*e^2*x^2 - d^4*e*x - d^5)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) - (3*e^4*x^4 - 3*d*e^3*x^3 - 23*d^2*e^2*x^2 + d^3*e*x + 16*d^4)*sqrt(-e^2*x^2 + d^2))/(e^9*x^3 + d*e^8*x^2 - d^2*e^7*x - d^3*e^6)","A",0
128,1,175,0,0.423445," ","integrate(x^4/(e*x+d)/(-e^2*x^2+d^2)^(3/2),x, algorithm=""fricas"")","\frac{8 \, d e^{3} x^{3} + 8 \, d^{2} e^{2} x^{2} - 8 \, d^{3} e x - 8 \, d^{4} - 6 \, {\left(d e^{3} x^{3} + d^{2} e^{2} x^{2} - d^{3} e x - d^{4}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(3 \, e^{3} x^{3} + 7 \, d e^{2} x^{2} - 5 \, d^{2} e x - 8 \, d^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{3 \, {\left(e^{8} x^{3} + d e^{7} x^{2} - d^{2} e^{6} x - d^{3} e^{5}\right)}}"," ",0,"1/3*(8*d*e^3*x^3 + 8*d^2*e^2*x^2 - 8*d^3*e*x - 8*d^4 - 6*(d*e^3*x^3 + d^2*e^2*x^2 - d^3*e*x - d^4)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (3*e^3*x^3 + 7*d*e^2*x^2 - 5*d^2*e*x - 8*d^3)*sqrt(-e^2*x^2 + d^2))/(e^8*x^3 + d*e^7*x^2 - d^2*e^6*x - d^3*e^5)","A",0
129,1,157,0,0.419297," ","integrate(x^3/(e*x+d)/(-e^2*x^2+d^2)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, e^{3} x^{3} + 2 \, d e^{2} x^{2} - 2 \, d^{2} e x - 2 \, d^{3} - 6 \, {\left(e^{3} x^{3} + d e^{2} x^{2} - d^{2} e x - d^{3}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(4 \, e^{2} x^{2} + d e x - 2 \, d^{2}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{3 \, {\left(e^{7} x^{3} + d e^{6} x^{2} - d^{2} e^{5} x - d^{3} e^{4}\right)}}"," ",0,"-1/3*(2*e^3*x^3 + 2*d*e^2*x^2 - 2*d^2*e*x - 2*d^3 - 6*(e^3*x^3 + d*e^2*x^2 - d^2*e*x - d^3)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (4*e^2*x^2 + d*e*x - 2*d^2)*sqrt(-e^2*x^2 + d^2))/(e^7*x^3 + d*e^6*x^2 - d^2*e^5*x - d^3*e^4)","A",0
130,1,103,0,0.402979," ","integrate(x^2/(e*x+d)/(-e^2*x^2+d^2)^(3/2),x, algorithm=""fricas"")","\frac{2 \, e^{3} x^{3} + 2 \, d e^{2} x^{2} - 2 \, d^{2} e x - 2 \, d^{3} + {\left(e^{2} x^{2} - 2 \, d e x - 2 \, d^{2}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{3 \, {\left(d e^{6} x^{3} + d^{2} e^{5} x^{2} - d^{3} e^{4} x - d^{4} e^{3}\right)}}"," ",0,"1/3*(2*e^3*x^3 + 2*d*e^2*x^2 - 2*d^2*e*x - 2*d^3 + (e^2*x^2 - 2*d*e*x - 2*d^2)*sqrt(-e^2*x^2 + d^2))/(d*e^6*x^3 + d^2*e^5*x^2 - d^3*e^4*x - d^4*e^3)","A",0
131,1,101,0,0.410604," ","integrate(x/(e*x+d)/(-e^2*x^2+d^2)^(3/2),x, algorithm=""fricas"")","\frac{e^{3} x^{3} + d e^{2} x^{2} - d^{2} e x - d^{3} - {\left(e^{2} x^{2} + d e x + d^{2}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{3 \, {\left(d^{2} e^{5} x^{3} + d^{3} e^{4} x^{2} - d^{4} e^{3} x - d^{5} e^{2}\right)}}"," ",0,"1/3*(e^3*x^3 + d*e^2*x^2 - d^2*e*x - d^3 - (e^2*x^2 + d*e*x + d^2)*sqrt(-e^2*x^2 + d^2))/(d^2*e^5*x^3 + d^3*e^4*x^2 - d^4*e^3*x - d^5*e^2)","B",0
132,1,102,0,0.395324," ","integrate(1/(e*x+d)/(-e^2*x^2+d^2)^(3/2),x, algorithm=""fricas"")","-\frac{e^{3} x^{3} + d e^{2} x^{2} - d^{2} e x - d^{3} + {\left(2 \, e^{2} x^{2} + 2 \, d e x - d^{2}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{3 \, {\left(d^{3} e^{4} x^{3} + d^{4} e^{3} x^{2} - d^{5} e^{2} x - d^{6} e\right)}}"," ",0,"-1/3*(e^3*x^3 + d*e^2*x^2 - d^2*e*x - d^3 + (2*e^2*x^2 + 2*d*e*x - d^2)*sqrt(-e^2*x^2 + d^2))/(d^3*e^4*x^3 + d^4*e^3*x^2 - d^5*e^2*x - d^6*e)","B",0
133,1,155,0,0.400816," ","integrate(1/x/(e*x+d)/(-e^2*x^2+d^2)^(3/2),x, algorithm=""fricas"")","\frac{4 \, e^{3} x^{3} + 4 \, d e^{2} x^{2} - 4 \, d^{2} e x - 4 \, d^{3} + 3 \, {\left(e^{3} x^{3} + d e^{2} x^{2} - d^{2} e x - d^{3}\right)} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) + {\left(2 \, e^{2} x^{2} - d e x - 4 \, d^{2}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{3 \, {\left(d^{4} e^{3} x^{3} + d^{5} e^{2} x^{2} - d^{6} e x - d^{7}\right)}}"," ",0,"1/3*(4*e^3*x^3 + 4*d*e^2*x^2 - 4*d^2*e*x - 4*d^3 + 3*(e^3*x^3 + d*e^2*x^2 - d^2*e*x - d^3)*log(-(d - sqrt(-e^2*x^2 + d^2))/x) + (2*e^2*x^2 - d*e*x - 4*d^2)*sqrt(-e^2*x^2 + d^2))/(d^4*e^3*x^3 + d^5*e^2*x^2 - d^6*e*x - d^7)","A",0
134,1,181,0,0.391099," ","integrate(1/x^2/(e*x+d)/(-e^2*x^2+d^2)^(3/2),x, algorithm=""fricas"")","-\frac{4 \, e^{4} x^{4} + 4 \, d e^{3} x^{3} - 4 \, d^{2} e^{2} x^{2} - 4 \, d^{3} e x + 3 \, {\left(e^{4} x^{4} + d e^{3} x^{3} - d^{2} e^{2} x^{2} - d^{3} e x\right)} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) + {\left(8 \, e^{3} x^{3} + 5 \, d e^{2} x^{2} - 7 \, d^{2} e x - 3 \, d^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{3 \, {\left(d^{5} e^{3} x^{4} + d^{6} e^{2} x^{3} - d^{7} e x^{2} - d^{8} x\right)}}"," ",0,"-1/3*(4*e^4*x^4 + 4*d*e^3*x^3 - 4*d^2*e^2*x^2 - 4*d^3*e*x + 3*(e^4*x^4 + d*e^3*x^3 - d^2*e^2*x^2 - d^3*e*x)*log(-(d - sqrt(-e^2*x^2 + d^2))/x) + (8*e^3*x^3 + 5*d*e^2*x^2 - 7*d^2*e*x - 3*d^3)*sqrt(-e^2*x^2 + d^2))/(d^5*e^3*x^4 + d^6*e^2*x^3 - d^7*e*x^2 - d^8*x)","A",0
135,1,201,0,0.418416," ","integrate(1/x^3/(e*x+d)/(-e^2*x^2+d^2)^(3/2),x, algorithm=""fricas"")","\frac{14 \, e^{5} x^{5} + 14 \, d e^{4} x^{4} - 14 \, d^{2} e^{3} x^{3} - 14 \, d^{3} e^{2} x^{2} + 15 \, {\left(e^{5} x^{5} + d e^{4} x^{4} - d^{2} e^{3} x^{3} - d^{3} e^{2} x^{2}\right)} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) + {\left(16 \, e^{4} x^{4} + d e^{3} x^{3} - 23 \, d^{2} e^{2} x^{2} - 3 \, d^{3} e x + 3 \, d^{4}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{6 \, {\left(d^{6} e^{3} x^{5} + d^{7} e^{2} x^{4} - d^{8} e x^{3} - d^{9} x^{2}\right)}}"," ",0,"1/6*(14*e^5*x^5 + 14*d*e^4*x^4 - 14*d^2*e^3*x^3 - 14*d^3*e^2*x^2 + 15*(e^5*x^5 + d*e^4*x^4 - d^2*e^3*x^3 - d^3*e^2*x^2)*log(-(d - sqrt(-e^2*x^2 + d^2))/x) + (16*e^4*x^4 + d*e^3*x^3 - 23*d^2*e^2*x^2 - 3*d^3*e*x + 3*d^4)*sqrt(-e^2*x^2 + d^2))/(d^6*e^3*x^5 + d^7*e^2*x^4 - d^8*e*x^3 - d^9*x^2)","A",0
136,1,274,0,0.462865," ","integrate(x^7/(e*x+d)/(-e^2*x^2+d^2)^(5/2),x, algorithm=""fricas"")","\frac{96 \, d^{2} e^{5} x^{5} + 96 \, d^{3} e^{4} x^{4} - 192 \, d^{4} e^{3} x^{3} - 192 \, d^{5} e^{2} x^{2} + 96 \, d^{6} e x + 96 \, d^{7} - 210 \, {\left(d^{2} e^{5} x^{5} + d^{3} e^{4} x^{4} - 2 \, d^{4} e^{3} x^{3} - 2 \, d^{5} e^{2} x^{2} + d^{6} e x + d^{7}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) - {\left(15 \, e^{6} x^{6} - 15 \, d e^{5} x^{5} - 176 \, d^{2} e^{4} x^{4} + 4 \, d^{3} e^{3} x^{3} + 249 \, d^{4} e^{2} x^{2} + 9 \, d^{5} e x - 96 \, d^{6}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{30 \, {\left(e^{13} x^{5} + d e^{12} x^{4} - 2 \, d^{2} e^{11} x^{3} - 2 \, d^{3} e^{10} x^{2} + d^{4} e^{9} x + d^{5} e^{8}\right)}}"," ",0,"1/30*(96*d^2*e^5*x^5 + 96*d^3*e^4*x^4 - 192*d^4*e^3*x^3 - 192*d^5*e^2*x^2 + 96*d^6*e*x + 96*d^7 - 210*(d^2*e^5*x^5 + d^3*e^4*x^4 - 2*d^4*e^3*x^3 - 2*d^5*e^2*x^2 + d^6*e*x + d^7)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) - (15*e^6*x^6 - 15*d*e^5*x^5 - 176*d^2*e^4*x^4 + 4*d^3*e^3*x^3 + 249*d^4*e^2*x^2 + 9*d^5*e*x - 96*d^6)*sqrt(-e^2*x^2 + d^2))/(e^13*x^5 + d*e^12*x^4 - 2*d^2*e^11*x^3 - 2*d^3*e^10*x^2 + d^4*e^9*x + d^5*e^8)","A",0
137,1,258,0,0.437070," ","integrate(x^6/(e*x+d)/(-e^2*x^2+d^2)^(5/2),x, algorithm=""fricas"")","-\frac{48 \, d e^{5} x^{5} + 48 \, d^{2} e^{4} x^{4} - 96 \, d^{3} e^{3} x^{3} - 96 \, d^{4} e^{2} x^{2} + 48 \, d^{5} e x + 48 \, d^{6} - 30 \, {\left(d e^{5} x^{5} + d^{2} e^{4} x^{4} - 2 \, d^{3} e^{3} x^{3} - 2 \, d^{4} e^{2} x^{2} + d^{5} e x + d^{6}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(15 \, e^{5} x^{5} + 38 \, d e^{4} x^{4} - 52 \, d^{2} e^{3} x^{3} - 87 \, d^{3} e^{2} x^{2} + 33 \, d^{4} e x + 48 \, d^{5}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(e^{12} x^{5} + d e^{11} x^{4} - 2 \, d^{2} e^{10} x^{3} - 2 \, d^{3} e^{9} x^{2} + d^{4} e^{8} x + d^{5} e^{7}\right)}}"," ",0,"-1/15*(48*d*e^5*x^5 + 48*d^2*e^4*x^4 - 96*d^3*e^3*x^3 - 96*d^4*e^2*x^2 + 48*d^5*e*x + 48*d^6 - 30*(d*e^5*x^5 + d^2*e^4*x^4 - 2*d^3*e^3*x^3 - 2*d^4*e^2*x^2 + d^5*e*x + d^6)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (15*e^5*x^5 + 38*d*e^4*x^4 - 52*d^2*e^3*x^3 - 87*d^3*e^2*x^2 + 33*d^4*e*x + 48*d^5)*sqrt(-e^2*x^2 + d^2))/(e^12*x^5 + d*e^11*x^4 - 2*d^2*e^10*x^3 - 2*d^3*e^9*x^2 + d^4*e^8*x + d^5*e^7)","A",0
138,1,241,0,0.426885," ","integrate(x^5/(e*x+d)/(-e^2*x^2+d^2)^(5/2),x, algorithm=""fricas"")","\frac{8 \, e^{5} x^{5} + 8 \, d e^{4} x^{4} - 16 \, d^{2} e^{3} x^{3} - 16 \, d^{3} e^{2} x^{2} + 8 \, d^{4} e x + 8 \, d^{5} - 30 \, {\left(e^{5} x^{5} + d e^{4} x^{4} - 2 \, d^{2} e^{3} x^{3} - 2 \, d^{3} e^{2} x^{2} + d^{4} e x + d^{5}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(23 \, e^{4} x^{4} + 8 \, d e^{3} x^{3} - 27 \, d^{2} e^{2} x^{2} - 7 \, d^{3} e x + 8 \, d^{4}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(e^{11} x^{5} + d e^{10} x^{4} - 2 \, d^{2} e^{9} x^{3} - 2 \, d^{3} e^{8} x^{2} + d^{4} e^{7} x + d^{5} e^{6}\right)}}"," ",0,"1/15*(8*e^5*x^5 + 8*d*e^4*x^4 - 16*d^2*e^3*x^3 - 16*d^3*e^2*x^2 + 8*d^4*e*x + 8*d^5 - 30*(e^5*x^5 + d*e^4*x^4 - 2*d^2*e^3*x^3 - 2*d^3*e^2*x^2 + d^4*e*x + d^5)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (23*e^4*x^4 + 8*d*e^3*x^3 - 27*d^2*e^2*x^2 - 7*d^3*e*x + 8*d^4)*sqrt(-e^2*x^2 + d^2))/(e^11*x^5 + d*e^10*x^4 - 2*d^2*e^9*x^3 - 2*d^3*e^8*x^2 + d^4*e^7*x + d^5*e^6)","B",0
139,1,168,0,0.406019," ","integrate(x^4/(e*x+d)/(-e^2*x^2+d^2)^(5/2),x, algorithm=""fricas"")","-\frac{8 \, e^{5} x^{5} + 8 \, d e^{4} x^{4} - 16 \, d^{2} e^{3} x^{3} - 16 \, d^{3} e^{2} x^{2} + 8 \, d^{4} e x + 8 \, d^{5} + {\left(3 \, e^{4} x^{4} - 12 \, d e^{3} x^{3} - 12 \, d^{2} e^{2} x^{2} + 8 \, d^{3} e x + 8 \, d^{4}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(d e^{10} x^{5} + d^{2} e^{9} x^{4} - 2 \, d^{3} e^{8} x^{3} - 2 \, d^{4} e^{7} x^{2} + d^{5} e^{6} x + d^{6} e^{5}\right)}}"," ",0,"-1/15*(8*e^5*x^5 + 8*d*e^4*x^4 - 16*d^2*e^3*x^3 - 16*d^3*e^2*x^2 + 8*d^4*e*x + 8*d^5 + (3*e^4*x^4 - 12*d*e^3*x^3 - 12*d^2*e^2*x^2 + 8*d^3*e*x + 8*d^4)*sqrt(-e^2*x^2 + d^2))/(d*e^10*x^5 + d^2*e^9*x^4 - 2*d^3*e^8*x^3 - 2*d^4*e^7*x^2 + d^5*e^6*x + d^6*e^5)","B",0
140,1,171,0,0.405642," ","integrate(x^3/(e*x+d)/(-e^2*x^2+d^2)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, e^{5} x^{5} + 2 \, d e^{4} x^{4} - 4 \, d^{2} e^{3} x^{3} - 4 \, d^{3} e^{2} x^{2} + 2 \, d^{4} e x + 2 \, d^{5} - {\left(3 \, e^{4} x^{4} + 3 \, d e^{3} x^{3} + 3 \, d^{2} e^{2} x^{2} - 2 \, d^{3} e x - 2 \, d^{4}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(d^{2} e^{9} x^{5} + d^{3} e^{8} x^{4} - 2 \, d^{4} e^{7} x^{3} - 2 \, d^{5} e^{6} x^{2} + d^{6} e^{5} x + d^{7} e^{4}\right)}}"," ",0,"-1/15*(2*e^5*x^5 + 2*d*e^4*x^4 - 4*d^2*e^3*x^3 - 4*d^3*e^2*x^2 + 2*d^4*e*x + 2*d^5 - (3*e^4*x^4 + 3*d*e^3*x^3 + 3*d^2*e^2*x^2 - 2*d^3*e*x - 2*d^4)*sqrt(-e^2*x^2 + d^2))/(d^2*e^9*x^5 + d^3*e^8*x^4 - 2*d^4*e^7*x^3 - 2*d^5*e^6*x^2 + d^6*e^5*x + d^7*e^4)","B",0
141,1,170,0,0.409999," ","integrate(x^2/(e*x+d)/(-e^2*x^2+d^2)^(5/2),x, algorithm=""fricas"")","\frac{2 \, e^{5} x^{5} + 2 \, d e^{4} x^{4} - 4 \, d^{2} e^{3} x^{3} - 4 \, d^{3} e^{2} x^{2} + 2 \, d^{4} e x + 2 \, d^{5} + {\left(2 \, e^{4} x^{4} + 2 \, d e^{3} x^{3} - 3 \, d^{2} e^{2} x^{2} + 2 \, d^{3} e x + 2 \, d^{4}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(d^{3} e^{8} x^{5} + d^{4} e^{7} x^{4} - 2 \, d^{5} e^{6} x^{3} - 2 \, d^{6} e^{5} x^{2} + d^{7} e^{4} x + d^{8} e^{3}\right)}}"," ",0,"1/15*(2*e^5*x^5 + 2*d*e^4*x^4 - 4*d^2*e^3*x^3 - 4*d^3*e^2*x^2 + 2*d^4*e*x + 2*d^5 + (2*e^4*x^4 + 2*d*e^3*x^3 - 3*d^2*e^2*x^2 + 2*d^3*e*x + 2*d^4)*sqrt(-e^2*x^2 + d^2))/(d^3*e^8*x^5 + d^4*e^7*x^4 - 2*d^5*e^6*x^3 - 2*d^6*e^5*x^2 + d^7*e^4*x + d^8*e^3)","B",0
142,1,171,0,0.417647," ","integrate(x/(e*x+d)/(-e^2*x^2+d^2)^(5/2),x, algorithm=""fricas"")","\frac{3 \, e^{5} x^{5} + 3 \, d e^{4} x^{4} - 6 \, d^{2} e^{3} x^{3} - 6 \, d^{3} e^{2} x^{2} + 3 \, d^{4} e x + 3 \, d^{5} - {\left(2 \, e^{4} x^{4} + 2 \, d e^{3} x^{3} - 3 \, d^{2} e^{2} x^{2} - 3 \, d^{3} e x - 3 \, d^{4}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(d^{4} e^{7} x^{5} + d^{5} e^{6} x^{4} - 2 \, d^{6} e^{5} x^{3} - 2 \, d^{7} e^{4} x^{2} + d^{8} e^{3} x + d^{9} e^{2}\right)}}"," ",0,"1/15*(3*e^5*x^5 + 3*d*e^4*x^4 - 6*d^2*e^3*x^3 - 6*d^3*e^2*x^2 + 3*d^4*e*x + 3*d^5 - (2*e^4*x^4 + 2*d*e^3*x^3 - 3*d^2*e^2*x^2 - 3*d^3*e*x - 3*d^4)*sqrt(-e^2*x^2 + d^2))/(d^4*e^7*x^5 + d^5*e^6*x^4 - 2*d^6*e^5*x^3 - 2*d^7*e^4*x^2 + d^8*e^3*x + d^9*e^2)","B",0
143,1,168,0,0.414075," ","integrate(1/(e*x+d)/(-e^2*x^2+d^2)^(5/2),x, algorithm=""fricas"")","-\frac{3 \, e^{5} x^{5} + 3 \, d e^{4} x^{4} - 6 \, d^{2} e^{3} x^{3} - 6 \, d^{3} e^{2} x^{2} + 3 \, d^{4} e x + 3 \, d^{5} + {\left(8 \, e^{4} x^{4} + 8 \, d e^{3} x^{3} - 12 \, d^{2} e^{2} x^{2} - 12 \, d^{3} e x + 3 \, d^{4}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(d^{5} e^{6} x^{5} + d^{6} e^{5} x^{4} - 2 \, d^{7} e^{4} x^{3} - 2 \, d^{8} e^{3} x^{2} + d^{9} e^{2} x + d^{10} e\right)}}"," ",0,"-1/15*(3*e^5*x^5 + 3*d*e^4*x^4 - 6*d^2*e^3*x^3 - 6*d^3*e^2*x^2 + 3*d^4*e*x + 3*d^5 + (8*e^4*x^4 + 8*d*e^3*x^3 - 12*d^2*e^2*x^2 - 12*d^3*e*x + 3*d^4)*sqrt(-e^2*x^2 + d^2))/(d^5*e^6*x^5 + d^6*e^5*x^4 - 2*d^7*e^4*x^3 - 2*d^8*e^3*x^2 + d^9*e^2*x + d^10*e)","B",0
144,1,237,0,0.422142," ","integrate(1/x/(e*x+d)/(-e^2*x^2+d^2)^(5/2),x, algorithm=""fricas"")","\frac{23 \, e^{5} x^{5} + 23 \, d e^{4} x^{4} - 46 \, d^{2} e^{3} x^{3} - 46 \, d^{3} e^{2} x^{2} + 23 \, d^{4} e x + 23 \, d^{5} + 15 \, {\left(e^{5} x^{5} + d e^{4} x^{4} - 2 \, d^{2} e^{3} x^{3} - 2 \, d^{3} e^{2} x^{2} + d^{4} e x + d^{5}\right)} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) + {\left(8 \, e^{4} x^{4} - 7 \, d e^{3} x^{3} - 27 \, d^{2} e^{2} x^{2} + 8 \, d^{3} e x + 23 \, d^{4}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(d^{6} e^{5} x^{5} + d^{7} e^{4} x^{4} - 2 \, d^{8} e^{3} x^{3} - 2 \, d^{9} e^{2} x^{2} + d^{10} e x + d^{11}\right)}}"," ",0,"1/15*(23*e^5*x^5 + 23*d*e^4*x^4 - 46*d^2*e^3*x^3 - 46*d^3*e^2*x^2 + 23*d^4*e*x + 23*d^5 + 15*(e^5*x^5 + d*e^4*x^4 - 2*d^2*e^3*x^3 - 2*d^3*e^2*x^2 + d^4*e*x + d^5)*log(-(d - sqrt(-e^2*x^2 + d^2))/x) + (8*e^4*x^4 - 7*d*e^3*x^3 - 27*d^2*e^2*x^2 + 8*d^3*e*x + 23*d^4)*sqrt(-e^2*x^2 + d^2))/(d^6*e^5*x^5 + d^7*e^4*x^4 - 2*d^8*e^3*x^3 - 2*d^9*e^2*x^2 + d^10*e*x + d^11)","B",0
145,1,265,0,0.448428," ","integrate(1/x^2/(e*x+d)/(-e^2*x^2+d^2)^(5/2),x, algorithm=""fricas"")","-\frac{23 \, e^{6} x^{6} + 23 \, d e^{5} x^{5} - 46 \, d^{2} e^{4} x^{4} - 46 \, d^{3} e^{3} x^{3} + 23 \, d^{4} e^{2} x^{2} + 23 \, d^{5} e x + 15 \, {\left(e^{6} x^{6} + d e^{5} x^{5} - 2 \, d^{2} e^{4} x^{4} - 2 \, d^{3} e^{3} x^{3} + d^{4} e^{2} x^{2} + d^{5} e x\right)} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) + {\left(48 \, e^{5} x^{5} + 33 \, d e^{4} x^{4} - 87 \, d^{2} e^{3} x^{3} - 52 \, d^{3} e^{2} x^{2} + 38 \, d^{4} e x + 15 \, d^{5}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(d^{7} e^{5} x^{6} + d^{8} e^{4} x^{5} - 2 \, d^{9} e^{3} x^{4} - 2 \, d^{10} e^{2} x^{3} + d^{11} e x^{2} + d^{12} x\right)}}"," ",0,"-1/15*(23*e^6*x^6 + 23*d*e^5*x^5 - 46*d^2*e^4*x^4 - 46*d^3*e^3*x^3 + 23*d^4*e^2*x^2 + 23*d^5*e*x + 15*(e^6*x^6 + d*e^5*x^5 - 2*d^2*e^4*x^4 - 2*d^3*e^3*x^3 + d^4*e^2*x^2 + d^5*e*x)*log(-(d - sqrt(-e^2*x^2 + d^2))/x) + (48*e^5*x^5 + 33*d*e^4*x^4 - 87*d^2*e^3*x^3 - 52*d^3*e^2*x^2 + 38*d^4*e*x + 15*d^5)*sqrt(-e^2*x^2 + d^2))/(d^7*e^5*x^6 + d^8*e^4*x^5 - 2*d^9*e^3*x^4 - 2*d^10*e^2*x^3 + d^11*e*x^2 + d^12*x)","A",0
146,1,286,0,0.507935," ","integrate(1/x^3/(e*x+d)/(-e^2*x^2+d^2)^(5/2),x, algorithm=""fricas"")","\frac{116 \, e^{7} x^{7} + 116 \, d e^{6} x^{6} - 232 \, d^{2} e^{5} x^{5} - 232 \, d^{3} e^{4} x^{4} + 116 \, d^{4} e^{3} x^{3} + 116 \, d^{5} e^{2} x^{2} + 105 \, {\left(e^{7} x^{7} + d e^{6} x^{6} - 2 \, d^{2} e^{5} x^{5} - 2 \, d^{3} e^{4} x^{4} + d^{4} e^{3} x^{3} + d^{5} e^{2} x^{2}\right)} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) + {\left(96 \, e^{6} x^{6} - 9 \, d e^{5} x^{5} - 249 \, d^{2} e^{4} x^{4} - 4 \, d^{3} e^{3} x^{3} + 176 \, d^{4} e^{2} x^{2} + 15 \, d^{5} e x - 15 \, d^{6}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{30 \, {\left(d^{8} e^{5} x^{7} + d^{9} e^{4} x^{6} - 2 \, d^{10} e^{3} x^{5} - 2 \, d^{11} e^{2} x^{4} + d^{12} e x^{3} + d^{13} x^{2}\right)}}"," ",0,"1/30*(116*e^7*x^7 + 116*d*e^6*x^6 - 232*d^2*e^5*x^5 - 232*d^3*e^4*x^4 + 116*d^4*e^3*x^3 + 116*d^5*e^2*x^2 + 105*(e^7*x^7 + d*e^6*x^6 - 2*d^2*e^5*x^5 - 2*d^3*e^4*x^4 + d^4*e^3*x^3 + d^5*e^2*x^2)*log(-(d - sqrt(-e^2*x^2 + d^2))/x) + (96*e^6*x^6 - 9*d*e^5*x^5 - 249*d^2*e^4*x^4 - 4*d^3*e^3*x^3 + 176*d^4*e^2*x^2 + 15*d^5*e*x - 15*d^6)*sqrt(-e^2*x^2 + d^2))/(d^8*e^5*x^7 + d^9*e^4*x^6 - 2*d^10*e^3*x^5 - 2*d^11*e^2*x^4 + d^12*e*x^3 + d^13*x^2)","A",0
147,1,297,0,0.519652," ","integrate(1/x^4/(e*x+d)/(-e^2*x^2+d^2)^(5/2),x, algorithm=""fricas"")","-\frac{116 \, e^{8} x^{8} + 116 \, d e^{7} x^{7} - 232 \, d^{2} e^{6} x^{6} - 232 \, d^{3} e^{5} x^{5} + 116 \, d^{4} e^{4} x^{4} + 116 \, d^{5} e^{3} x^{3} + 105 \, {\left(e^{8} x^{8} + d e^{7} x^{7} - 2 \, d^{2} e^{6} x^{6} - 2 \, d^{3} e^{5} x^{5} + d^{4} e^{4} x^{4} + d^{5} e^{3} x^{3}\right)} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) + {\left(256 \, e^{7} x^{7} + 151 \, d e^{6} x^{6} - 489 \, d^{2} e^{5} x^{5} - 244 \, d^{3} e^{4} x^{4} + 236 \, d^{4} e^{3} x^{3} + 75 \, d^{5} e^{2} x^{2} - 5 \, d^{6} e x + 10 \, d^{7}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{30 \, {\left(d^{9} e^{5} x^{8} + d^{10} e^{4} x^{7} - 2 \, d^{11} e^{3} x^{6} - 2 \, d^{12} e^{2} x^{5} + d^{13} e x^{4} + d^{14} x^{3}\right)}}"," ",0,"-1/30*(116*e^8*x^8 + 116*d*e^7*x^7 - 232*d^2*e^6*x^6 - 232*d^3*e^5*x^5 + 116*d^4*e^4*x^4 + 116*d^5*e^3*x^3 + 105*(e^8*x^8 + d*e^7*x^7 - 2*d^2*e^6*x^6 - 2*d^3*e^5*x^5 + d^4*e^4*x^4 + d^5*e^3*x^3)*log(-(d - sqrt(-e^2*x^2 + d^2))/x) + (256*e^7*x^7 + 151*d*e^6*x^6 - 489*d^2*e^5*x^5 - 244*d^3*e^4*x^4 + 236*d^4*e^3*x^3 + 75*d^5*e^2*x^2 - 5*d^6*e*x + 10*d^7)*sqrt(-e^2*x^2 + d^2))/(d^9*e^5*x^8 + d^10*e^4*x^7 - 2*d^11*e^3*x^6 - 2*d^12*e^2*x^5 + d^13*e*x^4 + d^14*x^3)","A",0
148,1,239,0,0.487613," ","integrate(x^3/(e*x+d)/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","-\frac{2 \, e^{7} x^{7} + 2 \, d e^{6} x^{6} - 6 \, d^{2} e^{5} x^{5} - 6 \, d^{3} e^{4} x^{4} + 6 \, d^{4} e^{3} x^{3} + 6 \, d^{5} e^{2} x^{2} - 2 \, d^{6} e x - 2 \, d^{7} - {\left(2 \, e^{6} x^{6} + 2 \, d e^{5} x^{5} - 5 \, d^{2} e^{4} x^{4} - 5 \, d^{3} e^{3} x^{3} - 5 \, d^{4} e^{2} x^{2} + 2 \, d^{5} e x + 2 \, d^{6}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{35 \, {\left(d^{4} e^{11} x^{7} + d^{5} e^{10} x^{6} - 3 \, d^{6} e^{9} x^{5} - 3 \, d^{7} e^{8} x^{4} + 3 \, d^{8} e^{7} x^{3} + 3 \, d^{9} e^{6} x^{2} - d^{10} e^{5} x - d^{11} e^{4}\right)}}"," ",0,"-1/35*(2*e^7*x^7 + 2*d*e^6*x^6 - 6*d^2*e^5*x^5 - 6*d^3*e^4*x^4 + 6*d^4*e^3*x^3 + 6*d^5*e^2*x^2 - 2*d^6*e*x - 2*d^7 - (2*e^6*x^6 + 2*d*e^5*x^5 - 5*d^2*e^4*x^4 - 5*d^3*e^3*x^3 - 5*d^4*e^2*x^2 + 2*d^5*e*x + 2*d^6)*sqrt(-e^2*x^2 + d^2))/(d^4*e^11*x^7 + d^5*e^10*x^6 - 3*d^6*e^9*x^5 - 3*d^7*e^8*x^4 + 3*d^8*e^7*x^3 + 3*d^9*e^6*x^2 - d^10*e^5*x - d^11*e^4)","B",0
149,1,238,0,0.490738," ","integrate(x^2/(e*x+d)/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","\frac{6 \, e^{7} x^{7} + 6 \, d e^{6} x^{6} - 18 \, d^{2} e^{5} x^{5} - 18 \, d^{3} e^{4} x^{4} + 18 \, d^{4} e^{3} x^{3} + 18 \, d^{5} e^{2} x^{2} - 6 \, d^{6} e x - 6 \, d^{7} + {\left(8 \, e^{6} x^{6} + 8 \, d e^{5} x^{5} - 20 \, d^{2} e^{4} x^{4} - 20 \, d^{3} e^{3} x^{3} + 15 \, d^{4} e^{2} x^{2} - 6 \, d^{5} e x - 6 \, d^{6}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{105 \, {\left(d^{5} e^{10} x^{7} + d^{6} e^{9} x^{6} - 3 \, d^{7} e^{8} x^{5} - 3 \, d^{8} e^{7} x^{4} + 3 \, d^{9} e^{6} x^{3} + 3 \, d^{10} e^{5} x^{2} - d^{11} e^{4} x - d^{12} e^{3}\right)}}"," ",0,"1/105*(6*e^7*x^7 + 6*d*e^6*x^6 - 18*d^2*e^5*x^5 - 18*d^3*e^4*x^4 + 18*d^4*e^3*x^3 + 18*d^5*e^2*x^2 - 6*d^6*e*x - 6*d^7 + (8*e^6*x^6 + 8*d*e^5*x^5 - 20*d^2*e^4*x^4 - 20*d^3*e^3*x^3 + 15*d^4*e^2*x^2 - 6*d^5*e*x - 6*d^6)*sqrt(-e^2*x^2 + d^2))/(d^5*e^10*x^7 + d^6*e^9*x^6 - 3*d^7*e^8*x^5 - 3*d^8*e^7*x^4 + 3*d^9*e^6*x^3 + 3*d^10*e^5*x^2 - d^11*e^4*x - d^12*e^3)","B",0
150,1,75,0,0.415303," ","integrate(x^3/(a*x+1)/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{4 \, a x - 6 \, {\left(a x + 1\right)} \arctan\left(\frac{\sqrt{-a^{2} x^{2} + 1} - 1}{a x}\right) - {\left(a^{2} x^{2} - a x - 4\right)} \sqrt{-a^{2} x^{2} + 1} + 4}{2 \, {\left(a^{5} x + a^{4}\right)}}"," ",0,"1/2*(4*a*x - 6*(a*x + 1)*arctan((sqrt(-a^2*x^2 + 1) - 1)/(a*x)) - (a^2*x^2 - a*x - 4)*sqrt(-a^2*x^2 + 1) + 4)/(a^5*x + a^4)","A",0
151,1,66,0,0.399936," ","integrate(x^2/(a*x+1)/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, a x - 2 \, {\left(a x + 1\right)} \arctan\left(\frac{\sqrt{-a^{2} x^{2} + 1} - 1}{a x}\right) + \sqrt{-a^{2} x^{2} + 1} {\left(a x + 2\right)} + 2}{a^{4} x + a^{3}}"," ",0,"-(2*a*x - 2*(a*x + 1)*arctan((sqrt(-a^2*x^2 + 1) - 1)/(a*x)) + sqrt(-a^2*x^2 + 1)*(a*x + 2) + 2)/(a^4*x + a^3)","A",0
152,1,58,0,0.405063," ","integrate(x/(a*x+1)/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{a x - 2 \, {\left(a x + 1\right)} \arctan\left(\frac{\sqrt{-a^{2} x^{2} + 1} - 1}{a x}\right) + \sqrt{-a^{2} x^{2} + 1} + 1}{a^{3} x + a^{2}}"," ",0,"(a*x - 2*(a*x + 1)*arctan((sqrt(-a^2*x^2 + 1) - 1)/(a*x)) + sqrt(-a^2*x^2 + 1) + 1)/(a^3*x + a^2)","A",0
153,1,28,0,0.387092," ","integrate(1/(a*x+1)/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","-\frac{a x + \sqrt{-a^{2} x^{2} + 1} + 1}{a^{2} x + a}"," ",0,"-(a*x + sqrt(-a^2*x^2 + 1) + 1)/(a^2*x + a)","A",0
154,1,52,0,0.399650," ","integrate(1/x/(-a*x+1)/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{a x + {\left(a x - 1\right)} \log\left(\frac{\sqrt{-a^{2} x^{2} + 1} - 1}{x}\right) - \sqrt{-a^{2} x^{2} + 1} - 1}{a x - 1}"," ",0,"(a*x + (a*x - 1)*log((sqrt(-a^2*x^2 + 1) - 1)/x) - sqrt(-a^2*x^2 + 1) - 1)/(a*x - 1)","A",0
155,1,76,0,0.398417," ","integrate(1/x^2/(-a*x+1)/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{a^{2} x^{2} - a x + {\left(a^{2} x^{2} - a x\right)} \log\left(\frac{\sqrt{-a^{2} x^{2} + 1} - 1}{x}\right) - \sqrt{-a^{2} x^{2} + 1} {\left(2 \, a x - 1\right)}}{a x^{2} - x}"," ",0,"(a^2*x^2 - a*x + (a^2*x^2 - a*x)*log((sqrt(-a^2*x^2 + 1) - 1)/x) - sqrt(-a^2*x^2 + 1)*(2*a*x - 1))/(a*x^2 - x)","A",0
156,1,97,0,0.402185," ","integrate(1/x^3/(-a*x+1)/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{2 \, a^{3} x^{3} - 2 \, a^{2} x^{2} + 3 \, {\left(a^{3} x^{3} - a^{2} x^{2}\right)} \log\left(\frac{\sqrt{-a^{2} x^{2} + 1} - 1}{x}\right) - {\left(4 \, a^{2} x^{2} - a x - 1\right)} \sqrt{-a^{2} x^{2} + 1}}{2 \, {\left(a x^{3} - x^{2}\right)}}"," ",0,"1/2*(2*a^3*x^3 - 2*a^2*x^2 + 3*(a^3*x^3 - a^2*x^2)*log((sqrt(-a^2*x^2 + 1) - 1)/x) - (4*a^2*x^2 - a*x - 1)*sqrt(-a^2*x^2 + 1))/(a*x^3 - x^2)","A",0
157,1,138,0,0.402029," ","integrate(x^5*(-e^2*x^2+d^2)^(5/2)/(e*x+d)^2,x, algorithm=""fricas"")","\frac{630 \, d^{9} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(448 \, e^{8} x^{8} - 1008 \, d e^{7} x^{7} + 512 \, d^{2} e^{6} x^{6} + 168 \, d^{3} e^{5} x^{5} - 192 \, d^{4} e^{4} x^{4} + 210 \, d^{5} e^{3} x^{3} - 256 \, d^{6} e^{2} x^{2} + 315 \, d^{7} e x - 512 \, d^{8}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{4032 \, e^{6}}"," ",0,"1/4032*(630*d^9*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (448*e^8*x^8 - 1008*d*e^7*x^7 + 512*d^2*e^6*x^6 + 168*d^3*e^5*x^5 - 192*d^4*e^4*x^4 + 210*d^5*e^3*x^3 - 256*d^6*e^2*x^2 + 315*d^7*e*x - 512*d^8)*sqrt(-e^2*x^2 + d^2))/e^6","A",0
158,1,128,0,0.403702," ","integrate(x^4*(-e^2*x^2+d^2)^(5/2)/(e*x+d)^2,x, algorithm=""fricas"")","-\frac{2730 \, d^{8} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) - {\left(1680 \, e^{7} x^{7} - 3840 \, d e^{6} x^{6} + 1960 \, d^{2} e^{5} x^{5} + 768 \, d^{3} e^{4} x^{4} - 910 \, d^{4} e^{3} x^{3} + 1024 \, d^{5} e^{2} x^{2} - 1365 \, d^{6} e x + 2048 \, d^{7}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{13440 \, e^{5}}"," ",0,"-1/13440*(2730*d^8*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) - (1680*e^7*x^7 - 3840*d*e^6*x^6 + 1960*d^2*e^5*x^5 + 768*d^3*e^4*x^4 - 910*d^4*e^3*x^3 + 1024*d^5*e^2*x^2 - 1365*d^6*e*x + 2048*d^7)*sqrt(-e^2*x^2 + d^2))/e^5","A",0
159,1,116,0,0.410650," ","integrate(x^3*(-e^2*x^2+d^2)^(5/2)/(e*x+d)^2,x, algorithm=""fricas"")","\frac{210 \, d^{7} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(120 \, e^{6} x^{6} - 280 \, d e^{5} x^{5} + 144 \, d^{2} e^{4} x^{4} + 70 \, d^{3} e^{3} x^{3} - 88 \, d^{4} e^{2} x^{2} + 105 \, d^{5} e x - 176 \, d^{6}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{840 \, e^{4}}"," ",0,"1/840*(210*d^7*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (120*e^6*x^6 - 280*d*e^5*x^5 + 144*d^2*e^4*x^4 + 70*d^3*e^3*x^3 - 88*d^4*e^2*x^2 + 105*d^5*e*x - 176*d^6)*sqrt(-e^2*x^2 + d^2))/e^4","A",0
160,1,106,0,0.405627," ","integrate(x^2*(-e^2*x^2+d^2)^(5/2)/(e*x+d)^2,x, algorithm=""fricas"")","-\frac{90 \, d^{6} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) - {\left(40 \, e^{5} x^{5} - 96 \, d e^{4} x^{4} + 50 \, d^{2} e^{3} x^{3} + 32 \, d^{3} e^{2} x^{2} - 45 \, d^{4} e x + 64 \, d^{5}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{240 \, e^{3}}"," ",0,"-1/240*(90*d^6*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) - (40*e^5*x^5 - 96*d*e^4*x^4 + 50*d^2*e^3*x^3 + 32*d^3*e^2*x^2 - 45*d^4*e*x + 64*d^5)*sqrt(-e^2*x^2 + d^2))/e^3","A",0
161,1,94,0,0.393100," ","integrate(x*(-e^2*x^2+d^2)^(5/2)/(e*x+d)^2,x, algorithm=""fricas"")","\frac{30 \, d^{5} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(12 \, e^{4} x^{4} - 30 \, d e^{3} x^{3} + 16 \, d^{2} e^{2} x^{2} + 15 \, d^{3} e x - 28 \, d^{4}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{60 \, e^{2}}"," ",0,"1/60*(30*d^5*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (12*e^4*x^4 - 30*d*e^3*x^3 + 16*d^2*e^2*x^2 + 15*d^3*e*x - 28*d^4)*sqrt(-e^2*x^2 + d^2))/e^2","A",0
162,1,84,0,0.397799," ","integrate((-e^2*x^2+d^2)^(5/2)/(e*x+d)^2,x, algorithm=""fricas"")","-\frac{30 \, d^{4} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) - {\left(6 \, e^{3} x^{3} - 16 \, d e^{2} x^{2} + 9 \, d^{2} e x + 16 \, d^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{24 \, e}"," ",0,"-1/24*(30*d^4*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) - (6*e^3*x^3 - 16*d*e^2*x^2 + 9*d^2*e*x + 16*d^3)*sqrt(-e^2*x^2 + d^2))/e","A",0
163,1,95,0,0.413502," ","integrate((-e^2*x^2+d^2)^(5/2)/x/(e*x+d)^2,x, algorithm=""fricas"")","2 \, d^{3} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + d^{3} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) + \frac{1}{3} \, {\left(e^{2} x^{2} - 3 \, d e x + 2 \, d^{2}\right)} \sqrt{-e^{2} x^{2} + d^{2}}"," ",0,"2*d^3*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + d^3*log(-(d - sqrt(-e^2*x^2 + d^2))/x) + 1/3*(e^2*x^2 - 3*d*e*x + 2*d^2)*sqrt(-e^2*x^2 + d^2)","A",0
164,1,111,0,0.403805," ","integrate((-e^2*x^2+d^2)^(5/2)/x^2/(e*x+d)^2,x, algorithm=""fricas"")","\frac{2 \, d^{2} e x \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) - 4 \, d^{2} e x \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) - 4 \, d^{2} e x + {\left(e^{2} x^{2} - 4 \, d e x - 2 \, d^{2}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{2 \, x}"," ",0,"1/2*(2*d^2*e*x*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) - 4*d^2*e*x*log(-(d - sqrt(-e^2*x^2 + d^2))/x) - 4*d^2*e*x + (e^2*x^2 - 4*d*e*x - 2*d^2)*sqrt(-e^2*x^2 + d^2))/x","A",0
165,1,119,0,0.405640," ","integrate((-e^2*x^2+d^2)^(5/2)/x^3/(e*x+d)^2,x, algorithm=""fricas"")","-\frac{8 \, d e^{2} x^{2} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) - d e^{2} x^{2} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) - 2 \, d e^{2} x^{2} - {\left(2 \, e^{2} x^{2} + 4 \, d e x - d^{2}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{2 \, x^{2}}"," ",0,"-1/2*(8*d*e^2*x^2*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) - d*e^2*x^2*log(-(d - sqrt(-e^2*x^2 + d^2))/x) - 2*d*e^2*x^2 - (2*e^2*x^2 + 4*d*e*x - d^2)*sqrt(-e^2*x^2 + d^2))/x^2","A",0
166,1,106,0,0.417088," ","integrate((-e^2*x^2+d^2)^(5/2)/x^4/(e*x+d)^2,x, algorithm=""fricas"")","\frac{6 \, e^{3} x^{3} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + 3 \, e^{3} x^{3} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) - {\left(2 \, e^{2} x^{2} - 3 \, d e x + d^{2}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{3 \, x^{3}}"," ",0,"1/3*(6*e^3*x^3*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + 3*e^3*x^3*log(-(d - sqrt(-e^2*x^2 + d^2))/x) - (2*e^2*x^2 - 3*d*e*x + d^2)*sqrt(-e^2*x^2 + d^2))/x^3","A",0
167,1,86,0,0.392368," ","integrate((-e^2*x^2+d^2)^(5/2)/x^5/(e*x+d)^2,x, algorithm=""fricas"")","-\frac{15 \, e^{4} x^{4} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) + {\left(16 \, e^{3} x^{3} + 9 \, d e^{2} x^{2} - 16 \, d^{2} e x + 6 \, d^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{24 \, d x^{4}}"," ",0,"-1/24*(15*e^4*x^4*log(-(d - sqrt(-e^2*x^2 + d^2))/x) + (16*e^3*x^3 + 9*d*e^2*x^2 - 16*d^2*e*x + 6*d^3)*sqrt(-e^2*x^2 + d^2))/(d*x^4)","A",0
168,1,97,0,0.408417," ","integrate((-e^2*x^2+d^2)^(5/2)/x^6/(e*x+d)^2,x, algorithm=""fricas"")","\frac{15 \, e^{5} x^{5} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) + {\left(28 \, e^{4} x^{4} - 15 \, d e^{3} x^{3} - 16 \, d^{2} e^{2} x^{2} + 30 \, d^{3} e x - 12 \, d^{4}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{60 \, d^{2} x^{5}}"," ",0,"1/60*(15*e^5*x^5*log(-(d - sqrt(-e^2*x^2 + d^2))/x) + (28*e^4*x^4 - 15*d*e^3*x^3 - 16*d^2*e^2*x^2 + 30*d^3*e*x - 12*d^4)*sqrt(-e^2*x^2 + d^2))/(d^2*x^5)","A",0
169,1,108,0,0.416136," ","integrate((-e^2*x^2+d^2)^(5/2)/x^7/(e*x+d)^2,x, algorithm=""fricas"")","-\frac{45 \, e^{6} x^{6} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) + {\left(64 \, e^{5} x^{5} - 45 \, d e^{4} x^{4} + 32 \, d^{2} e^{3} x^{3} + 50 \, d^{3} e^{2} x^{2} - 96 \, d^{4} e x + 40 \, d^{5}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{240 \, d^{3} x^{6}}"," ",0,"-1/240*(45*e^6*x^6*log(-(d - sqrt(-e^2*x^2 + d^2))/x) + (64*e^5*x^5 - 45*d*e^4*x^4 + 32*d^2*e^3*x^3 + 50*d^3*e^2*x^2 - 96*d^4*e*x + 40*d^5)*sqrt(-e^2*x^2 + d^2))/(d^3*x^6)","A",0
170,1,119,0,0.404296," ","integrate((-e^2*x^2+d^2)^(5/2)/x^8/(e*x+d)^2,x, algorithm=""fricas"")","\frac{105 \, e^{7} x^{7} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) + {\left(176 \, e^{6} x^{6} - 105 \, d e^{5} x^{5} + 88 \, d^{2} e^{4} x^{4} - 70 \, d^{3} e^{3} x^{3} - 144 \, d^{4} e^{2} x^{2} + 280 \, d^{5} e x - 120 \, d^{6}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{840 \, d^{4} x^{7}}"," ",0,"1/840*(105*e^7*x^7*log(-(d - sqrt(-e^2*x^2 + d^2))/x) + (176*e^6*x^6 - 105*d*e^5*x^5 + 88*d^2*e^4*x^4 - 70*d^3*e^3*x^3 - 144*d^4*e^2*x^2 + 280*d^5*e*x - 120*d^6)*sqrt(-e^2*x^2 + d^2))/(d^4*x^7)","A",0
171,1,171,0,0.409855," ","integrate(x^4/(e*x+d)^2/(-e^2*x^2+d^2)^(3/2),x, algorithm=""fricas"")","-\frac{16 \, e^{4} x^{4} + 32 \, d e^{3} x^{3} - 32 \, d^{3} e x - 16 \, d^{4} - 30 \, {\left(e^{4} x^{4} + 2 \, d e^{3} x^{3} - 2 \, d^{3} e x - d^{4}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(26 \, e^{3} x^{3} + 22 \, d e^{2} x^{2} - 17 \, d^{2} e x - 16 \, d^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(e^{9} x^{4} + 2 \, d e^{8} x^{3} - 2 \, d^{3} e^{6} x - d^{4} e^{5}\right)}}"," ",0,"-1/15*(16*e^4*x^4 + 32*d*e^3*x^3 - 32*d^3*e*x - 16*d^4 - 30*(e^4*x^4 + 2*d*e^3*x^3 - 2*d^3*e*x - d^4)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (26*e^3*x^3 + 22*d*e^2*x^2 - 17*d^2*e*x - 16*d^3)*sqrt(-e^2*x^2 + d^2))/(e^9*x^4 + 2*d*e^8*x^3 - 2*d^3*e^6*x - d^4*e^5)","A",0
172,1,116,0,0.398453," ","integrate(x^3/(e*x+d)^2/(-e^2*x^2+d^2)^(3/2),x, algorithm=""fricas"")","\frac{2 \, e^{4} x^{4} + 4 \, d e^{3} x^{3} - 4 \, d^{3} e x - 2 \, d^{4} + {\left(2 \, e^{3} x^{3} - d e^{2} x^{2} - 4 \, d^{2} e x - 2 \, d^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{5 \, {\left(d e^{8} x^{4} + 2 \, d^{2} e^{7} x^{3} - 2 \, d^{4} e^{5} x - d^{5} e^{4}\right)}}"," ",0,"1/5*(2*e^4*x^4 + 4*d*e^3*x^3 - 4*d^3*e*x - 2*d^4 + (2*e^3*x^3 - d*e^2*x^2 - 4*d^2*e*x - 2*d^3)*sqrt(-e^2*x^2 + d^2))/(d*e^8*x^4 + 2*d^2*e^7*x^3 - 2*d^4*e^5*x - d^5*e^4)","A",0
173,1,118,0,0.390411," ","integrate(x^2/(e*x+d)^2/(-e^2*x^2+d^2)^(3/2),x, algorithm=""fricas"")","\frac{4 \, e^{4} x^{4} + 8 \, d e^{3} x^{3} - 8 \, d^{3} e x - 4 \, d^{4} - {\left(e^{3} x^{3} + 2 \, d e^{2} x^{2} + 8 \, d^{2} e x + 4 \, d^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(d^{2} e^{7} x^{4} + 2 \, d^{3} e^{6} x^{3} - 2 \, d^{5} e^{4} x - d^{6} e^{3}\right)}}"," ",0,"1/15*(4*e^4*x^4 + 8*d*e^3*x^3 - 8*d^3*e*x - 4*d^4 - (e^3*x^3 + 2*d*e^2*x^2 + 8*d^2*e*x + 4*d^3)*sqrt(-e^2*x^2 + d^2))/(d^2*e^7*x^4 + 2*d^3*e^6*x^3 - 2*d^5*e^4*x - d^6*e^3)","A",0
174,1,116,0,0.397653," ","integrate(x/(e*x+d)^2/(-e^2*x^2+d^2)^(3/2),x, algorithm=""fricas"")","\frac{e^{4} x^{4} + 2 \, d e^{3} x^{3} - 2 \, d^{3} e x - d^{4} - {\left(4 \, e^{3} x^{3} + 8 \, d e^{2} x^{2} + 2 \, d^{2} e x + d^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(d^{3} e^{6} x^{4} + 2 \, d^{4} e^{5} x^{3} - 2 \, d^{6} e^{3} x - d^{7} e^{2}\right)}}"," ",0,"1/15*(e^4*x^4 + 2*d*e^3*x^3 - 2*d^3*e*x - d^4 - (4*e^3*x^3 + 8*d*e^2*x^2 + 2*d^2*e*x + d^3)*sqrt(-e^2*x^2 + d^2))/(d^3*e^6*x^4 + 2*d^4*e^5*x^3 - 2*d^6*e^3*x - d^7*e^2)","A",0
175,1,115,0,0.385444," ","integrate(1/(e*x+d)^2/(-e^2*x^2+d^2)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, e^{4} x^{4} + 4 \, d e^{3} x^{3} - 4 \, d^{3} e x - 2 \, d^{4} + {\left(2 \, e^{3} x^{3} + 4 \, d e^{2} x^{2} + d^{2} e x - 2 \, d^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{5 \, {\left(d^{4} e^{5} x^{4} + 2 \, d^{5} e^{4} x^{3} - 2 \, d^{7} e^{2} x - d^{8} e\right)}}"," ",0,"-1/5*(2*e^4*x^4 + 4*d*e^3*x^3 - 4*d^3*e*x - 2*d^4 + (2*e^3*x^3 + 4*d*e^2*x^2 + d^2*e*x - 2*d^3)*sqrt(-e^2*x^2 + d^2))/(d^4*e^5*x^4 + 2*d^5*e^4*x^3 - 2*d^7*e^2*x - d^8*e)","A",0
176,1,168,0,0.403533," ","integrate(1/x/(e*x+d)^2/(-e^2*x^2+d^2)^(3/2),x, algorithm=""fricas"")","\frac{26 \, e^{4} x^{4} + 52 \, d e^{3} x^{3} - 52 \, d^{3} e x - 26 \, d^{4} + 15 \, {\left(e^{4} x^{4} + 2 \, d e^{3} x^{3} - 2 \, d^{3} e x - d^{4}\right)} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) + {\left(16 \, e^{3} x^{3} + 17 \, d e^{2} x^{2} - 22 \, d^{2} e x - 26 \, d^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(d^{5} e^{4} x^{4} + 2 \, d^{6} e^{3} x^{3} - 2 \, d^{8} e x - d^{9}\right)}}"," ",0,"1/15*(26*e^4*x^4 + 52*d*e^3*x^3 - 52*d^3*e*x - 26*d^4 + 15*(e^4*x^4 + 2*d*e^3*x^3 - 2*d^3*e*x - d^4)*log(-(d - sqrt(-e^2*x^2 + d^2))/x) + (16*e^3*x^3 + 17*d*e^2*x^2 - 22*d^2*e*x - 26*d^3)*sqrt(-e^2*x^2 + d^2))/(d^5*e^4*x^4 + 2*d^6*e^3*x^3 - 2*d^8*e*x - d^9)","A",0
177,1,194,0,0.420133," ","integrate(1/x^2/(e*x+d)^2/(-e^2*x^2+d^2)^(3/2),x, algorithm=""fricas"")","-\frac{46 \, e^{5} x^{5} + 92 \, d e^{4} x^{4} - 92 \, d^{3} e^{2} x^{2} - 46 \, d^{4} e x + 30 \, {\left(e^{5} x^{5} + 2 \, d e^{4} x^{4} - 2 \, d^{3} e^{2} x^{2} - d^{4} e x\right)} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) + {\left(56 \, e^{4} x^{4} + 82 \, d e^{3} x^{3} - 32 \, d^{2} e^{2} x^{2} - 76 \, d^{3} e x - 15 \, d^{4}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(d^{6} e^{4} x^{5} + 2 \, d^{7} e^{3} x^{4} - 2 \, d^{9} e x^{2} - d^{10} x\right)}}"," ",0,"-1/15*(46*e^5*x^5 + 92*d*e^4*x^4 - 92*d^3*e^2*x^2 - 46*d^4*e*x + 30*(e^5*x^5 + 2*d*e^4*x^4 - 2*d^3*e^2*x^2 - d^4*e*x)*log(-(d - sqrt(-e^2*x^2 + d^2))/x) + (56*e^4*x^4 + 82*d*e^3*x^3 - 32*d^2*e^2*x^2 - 76*d^3*e*x - 15*d^4)*sqrt(-e^2*x^2 + d^2))/(d^6*e^4*x^5 + 2*d^7*e^3*x^4 - 2*d^9*e*x^2 - d^10*x)","A",0
178,1,215,0,0.432205," ","integrate(1/x^3/(e*x+d)^2/(-e^2*x^2+d^2)^(3/2),x, algorithm=""fricas"")","\frac{54 \, e^{6} x^{6} + 108 \, d e^{5} x^{5} - 108 \, d^{3} e^{3} x^{3} - 54 \, d^{4} e^{2} x^{2} + 45 \, {\left(e^{6} x^{6} + 2 \, d e^{5} x^{5} - 2 \, d^{3} e^{3} x^{3} - d^{4} e^{2} x^{2}\right)} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) + {\left(64 \, e^{5} x^{5} + 83 \, d e^{4} x^{4} - 58 \, d^{2} e^{3} x^{3} - 94 \, d^{3} e^{2} x^{2} - 10 \, d^{4} e x + 5 \, d^{5}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{10 \, {\left(d^{7} e^{4} x^{6} + 2 \, d^{8} e^{3} x^{5} - 2 \, d^{10} e x^{3} - d^{11} x^{2}\right)}}"," ",0,"1/10*(54*e^6*x^6 + 108*d*e^5*x^5 - 108*d^3*e^3*x^3 - 54*d^4*e^2*x^2 + 45*(e^6*x^6 + 2*d*e^5*x^5 - 2*d^3*e^3*x^3 - d^4*e^2*x^2)*log(-(d - sqrt(-e^2*x^2 + d^2))/x) + (64*e^5*x^5 + 83*d*e^4*x^4 - 58*d^2*e^3*x^3 - 94*d^3*e^2*x^2 - 10*d^4*e*x + 5*d^5)*sqrt(-e^2*x^2 + d^2))/(d^7*e^4*x^6 + 2*d^8*e^3*x^5 - 2*d^10*e*x^3 - d^11*x^2)","A",0
179,1,190,0,0.433517," ","integrate(x^5/(e*x+d)^3/(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","\frac{304 \, d^{2} e^{3} x^{3} + 912 \, d^{3} e^{2} x^{2} + 912 \, d^{4} e x + 304 \, d^{5} - 390 \, {\left(d^{2} e^{3} x^{3} + 3 \, d^{3} e^{2} x^{2} + 3 \, d^{4} e x + d^{5}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) - {\left(15 \, e^{4} x^{4} - 45 \, d e^{3} x^{3} - 479 \, d^{2} e^{2} x^{2} - 717 \, d^{3} e x - 304 \, d^{4}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{30 \, {\left(e^{9} x^{3} + 3 \, d e^{8} x^{2} + 3 \, d^{2} e^{7} x + d^{3} e^{6}\right)}}"," ",0,"1/30*(304*d^2*e^3*x^3 + 912*d^3*e^2*x^2 + 912*d^4*e*x + 304*d^5 - 390*(d^2*e^3*x^3 + 3*d^3*e^2*x^2 + 3*d^4*e*x + d^5)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) - (15*e^4*x^4 - 45*d*e^3*x^3 - 479*d^2*e^2*x^2 - 717*d^3*e*x - 304*d^4)*sqrt(-e^2*x^2 + d^2))/(e^9*x^3 + 3*d*e^8*x^2 + 3*d^2*e^7*x + d^3*e^6)","A",0
180,1,174,0,0.412582," ","integrate(x^4/(e*x+d)^3/(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","-\frac{24 \, d e^{3} x^{3} + 72 \, d^{2} e^{2} x^{2} + 72 \, d^{3} e x + 24 \, d^{4} - 30 \, {\left(d e^{3} x^{3} + 3 \, d^{2} e^{2} x^{2} + 3 \, d^{3} e x + d^{4}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(5 \, e^{3} x^{3} + 39 \, d e^{2} x^{2} + 57 \, d^{2} e x + 24 \, d^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{5 \, {\left(e^{8} x^{3} + 3 \, d e^{7} x^{2} + 3 \, d^{2} e^{6} x + d^{3} e^{5}\right)}}"," ",0,"-1/5*(24*d*e^3*x^3 + 72*d^2*e^2*x^2 + 72*d^3*e*x + 24*d^4 - 30*(d*e^3*x^3 + 3*d^2*e^2*x^2 + 3*d^3*e*x + d^4)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (5*e^3*x^3 + 39*d*e^2*x^2 + 57*d^2*e*x + 24*d^3)*sqrt(-e^2*x^2 + d^2))/(e^8*x^3 + 3*d*e^7*x^2 + 3*d^2*e^6*x + d^3*e^5)","A",0
181,1,157,0,0.407484," ","integrate(x^3/(e*x+d)^3/(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","\frac{22 \, e^{3} x^{3} + 66 \, d e^{2} x^{2} + 66 \, d^{2} e x + 22 \, d^{3} - 30 \, {\left(e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(32 \, e^{2} x^{2} + 51 \, d e x + 22 \, d^{2}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(e^{7} x^{3} + 3 \, d e^{6} x^{2} + 3 \, d^{2} e^{5} x + d^{3} e^{4}\right)}}"," ",0,"1/15*(22*e^3*x^3 + 66*d*e^2*x^2 + 66*d^2*e*x + 22*d^3 - 30*(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (32*e^2*x^2 + 51*d*e*x + 22*d^2)*sqrt(-e^2*x^2 + d^2))/(e^7*x^3 + 3*d*e^6*x^2 + 3*d^2*e^5*x + d^3*e^4)","A",0
182,1,104,0,0.397459," ","integrate(x^2/(e*x+d)^3/(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, e^{3} x^{3} + 6 \, d e^{2} x^{2} + 6 \, d^{2} e x + 2 \, d^{3} + {\left(7 \, e^{2} x^{2} + 6 \, d e x + 2 \, d^{2}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(d e^{6} x^{3} + 3 \, d^{2} e^{5} x^{2} + 3 \, d^{3} e^{4} x + d^{4} e^{3}\right)}}"," ",0,"-1/15*(2*e^3*x^3 + 6*d*e^2*x^2 + 6*d^2*e*x + 2*d^3 + (7*e^2*x^2 + 6*d*e*x + 2*d^2)*sqrt(-e^2*x^2 + d^2))/(d*e^6*x^3 + 3*d^2*e^5*x^2 + 3*d^3*e^4*x + d^4*e^3)","A",0
183,1,100,0,0.396876," ","integrate(x/(e*x+d)^3/(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","-\frac{e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3} + {\left(e^{2} x^{2} + 3 \, d e x + d^{2}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{5 \, {\left(d^{2} e^{5} x^{3} + 3 \, d^{3} e^{4} x^{2} + 3 \, d^{4} e^{3} x + d^{5} e^{2}\right)}}"," ",0,"-1/5*(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3 + (e^2*x^2 + 3*d*e*x + d^2)*sqrt(-e^2*x^2 + d^2))/(d^2*e^5*x^3 + 3*d^3*e^4*x^2 + 3*d^4*e^3*x + d^5*e^2)","A",0
184,1,104,0,0.405531," ","integrate(1/(e*x+d)^3/(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","-\frac{7 \, e^{3} x^{3} + 21 \, d e^{2} x^{2} + 21 \, d^{2} e x + 7 \, d^{3} + {\left(2 \, e^{2} x^{2} + 6 \, d e x + 7 \, d^{2}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(d^{3} e^{4} x^{3} + 3 \, d^{4} e^{3} x^{2} + 3 \, d^{5} e^{2} x + d^{6} e\right)}}"," ",0,"-1/15*(7*e^3*x^3 + 21*d*e^2*x^2 + 21*d^2*e*x + 7*d^3 + (2*e^2*x^2 + 6*d*e*x + 7*d^2)*sqrt(-e^2*x^2 + d^2))/(d^3*e^4*x^3 + 3*d^4*e^3*x^2 + 3*d^5*e^2*x + d^6*e)","A",0
185,1,153,0,0.400890," ","integrate(1/x/(e*x+d)^3/(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","\frac{32 \, e^{3} x^{3} + 96 \, d e^{2} x^{2} + 96 \, d^{2} e x + 32 \, d^{3} + 15 \, {\left(e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}\right)} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) + {\left(22 \, e^{2} x^{2} + 51 \, d e x + 32 \, d^{2}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(d^{4} e^{3} x^{3} + 3 \, d^{5} e^{2} x^{2} + 3 \, d^{6} e x + d^{7}\right)}}"," ",0,"1/15*(32*e^3*x^3 + 96*d*e^2*x^2 + 96*d^2*e*x + 32*d^3 + 15*(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)*log(-(d - sqrt(-e^2*x^2 + d^2))/x) + (22*e^2*x^2 + 51*d*e*x + 32*d^2)*sqrt(-e^2*x^2 + d^2))/(d^4*e^3*x^3 + 3*d^5*e^2*x^2 + 3*d^6*e*x + d^7)","A",0
186,1,181,0,0.407224," ","integrate(1/x^2/(e*x+d)^3/(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","-\frac{24 \, e^{4} x^{4} + 72 \, d e^{3} x^{3} + 72 \, d^{2} e^{2} x^{2} + 24 \, d^{3} e x + 15 \, {\left(e^{4} x^{4} + 3 \, d e^{3} x^{3} + 3 \, d^{2} e^{2} x^{2} + d^{3} e x\right)} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) + {\left(24 \, e^{3} x^{3} + 57 \, d e^{2} x^{2} + 39 \, d^{2} e x + 5 \, d^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{5 \, {\left(d^{5} e^{3} x^{4} + 3 \, d^{6} e^{2} x^{3} + 3 \, d^{7} e x^{2} + d^{8} x\right)}}"," ",0,"-1/5*(24*e^4*x^4 + 72*d*e^3*x^3 + 72*d^2*e^2*x^2 + 24*d^3*e*x + 15*(e^4*x^4 + 3*d*e^3*x^3 + 3*d^2*e^2*x^2 + d^3*e*x)*log(-(d - sqrt(-e^2*x^2 + d^2))/x) + (24*e^3*x^3 + 57*d*e^2*x^2 + 39*d^2*e*x + 5*d^3)*sqrt(-e^2*x^2 + d^2))/(d^5*e^3*x^4 + 3*d^6*e^2*x^3 + 3*d^7*e*x^2 + d^8*x)","A",0
187,1,202,0,0.421320," ","integrate(1/x^3/(e*x+d)^3/(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","\frac{254 \, e^{5} x^{5} + 762 \, d e^{4} x^{4} + 762 \, d^{2} e^{3} x^{3} + 254 \, d^{3} e^{2} x^{2} + 195 \, {\left(e^{5} x^{5} + 3 \, d e^{4} x^{4} + 3 \, d^{2} e^{3} x^{3} + d^{3} e^{2} x^{2}\right)} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) + {\left(304 \, e^{4} x^{4} + 717 \, d e^{3} x^{3} + 479 \, d^{2} e^{2} x^{2} + 45 \, d^{3} e x - 15 \, d^{4}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{30 \, {\left(d^{6} e^{3} x^{5} + 3 \, d^{7} e^{2} x^{4} + 3 \, d^{8} e x^{3} + d^{9} x^{2}\right)}}"," ",0,"1/30*(254*e^5*x^5 + 762*d*e^4*x^4 + 762*d^2*e^3*x^3 + 254*d^3*e^2*x^2 + 195*(e^5*x^5 + 3*d*e^4*x^4 + 3*d^2*e^3*x^3 + d^3*e^2*x^2)*log(-(d - sqrt(-e^2*x^2 + d^2))/x) + (304*e^4*x^4 + 717*d*e^3*x^3 + 479*d^2*e^2*x^2 + 45*d^3*e*x - 15*d^4)*sqrt(-e^2*x^2 + d^2))/(d^6*e^3*x^5 + 3*d^7*e^2*x^4 + 3*d^8*e*x^3 + d^9*x^2)","A",0
188,1,200,0,0.440164," ","integrate(x^5*(-e^2*x^2+d^2)^(1/2)/(e*x+d)^4,x, algorithm=""fricas"")","\frac{424 \, d^{3} e^{3} x^{3} + 1272 \, d^{4} e^{2} x^{2} + 1272 \, d^{5} e x + 424 \, d^{6} - 540 \, {\left(d^{3} e^{3} x^{3} + 3 \, d^{4} e^{2} x^{2} + 3 \, d^{5} e x + d^{6}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(5 \, e^{5} x^{5} - 15 \, d e^{4} x^{4} + 70 \, d^{2} e^{3} x^{3} + 674 \, d^{3} e^{2} x^{2} + 1002 \, d^{4} e x + 424 \, d^{5}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(e^{9} x^{3} + 3 \, d e^{8} x^{2} + 3 \, d^{2} e^{7} x + d^{3} e^{6}\right)}}"," ",0,"1/15*(424*d^3*e^3*x^3 + 1272*d^4*e^2*x^2 + 1272*d^5*e*x + 424*d^6 - 540*(d^3*e^3*x^3 + 3*d^4*e^2*x^2 + 3*d^5*e*x + d^6)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (5*e^5*x^5 - 15*d*e^4*x^4 + 70*d^2*e^3*x^3 + 674*d^3*e^2*x^2 + 1002*d^4*e*x + 424*d^5)*sqrt(-e^2*x^2 + d^2))/(e^9*x^3 + 3*d*e^8*x^2 + 3*d^2*e^7*x + d^3*e^6)","A",0
189,1,190,0,0.427887," ","integrate(x^4*(-e^2*x^2+d^2)^(1/2)/(e*x+d)^4,x, algorithm=""fricas"")","-\frac{448 \, d^{2} e^{3} x^{3} + 1344 \, d^{3} e^{2} x^{2} + 1344 \, d^{4} e x + 448 \, d^{5} - 570 \, {\left(d^{2} e^{3} x^{3} + 3 \, d^{3} e^{2} x^{2} + 3 \, d^{4} e x + d^{5}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) - {\left(15 \, e^{4} x^{4} - 75 \, d e^{3} x^{3} - 713 \, d^{2} e^{2} x^{2} - 1059 \, d^{3} e x - 448 \, d^{4}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{30 \, {\left(e^{8} x^{3} + 3 \, d e^{7} x^{2} + 3 \, d^{2} e^{6} x + d^{3} e^{5}\right)}}"," ",0,"-1/30*(448*d^2*e^3*x^3 + 1344*d^3*e^2*x^2 + 1344*d^4*e*x + 448*d^5 - 570*(d^2*e^3*x^3 + 3*d^3*e^2*x^2 + 3*d^4*e*x + d^5)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) - (15*e^4*x^4 - 75*d*e^3*x^3 - 713*d^2*e^2*x^2 - 1059*d^3*e*x - 448*d^4)*sqrt(-e^2*x^2 + d^2))/(e^8*x^3 + 3*d*e^7*x^2 + 3*d^2*e^6*x + d^3*e^5)","A",0
190,1,174,0,0.418081," ","integrate(x^3*(-e^2*x^2+d^2)^(1/2)/(e*x+d)^4,x, algorithm=""fricas"")","\frac{94 \, d e^{3} x^{3} + 282 \, d^{2} e^{2} x^{2} + 282 \, d^{3} e x + 94 \, d^{4} - 120 \, {\left(d e^{3} x^{3} + 3 \, d^{2} e^{2} x^{2} + 3 \, d^{3} e x + d^{4}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(15 \, e^{3} x^{3} + 149 \, d e^{2} x^{2} + 222 \, d^{2} e x + 94 \, d^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(e^{7} x^{3} + 3 \, d e^{6} x^{2} + 3 \, d^{2} e^{5} x + d^{3} e^{4}\right)}}"," ",0,"1/15*(94*d*e^3*x^3 + 282*d^2*e^2*x^2 + 282*d^3*e*x + 94*d^4 - 120*(d*e^3*x^3 + 3*d^2*e^2*x^2 + 3*d^3*e*x + d^4)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (15*e^3*x^3 + 149*d*e^2*x^2 + 222*d^2*e*x + 94*d^3)*sqrt(-e^2*x^2 + d^2))/(e^7*x^3 + 3*d*e^6*x^2 + 3*d^2*e^5*x + d^3*e^4)","A",0
191,1,157,0,0.412818," ","integrate(x^2*(-e^2*x^2+d^2)^(1/2)/(e*x+d)^4,x, algorithm=""fricas"")","-\frac{8 \, e^{3} x^{3} + 24 \, d e^{2} x^{2} + 24 \, d^{2} e x + 8 \, d^{3} - 10 \, {\left(e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(13 \, e^{2} x^{2} + 19 \, d e x + 8 \, d^{2}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{5 \, {\left(e^{6} x^{3} + 3 \, d e^{5} x^{2} + 3 \, d^{2} e^{4} x + d^{3} e^{3}\right)}}"," ",0,"-1/5*(8*e^3*x^3 + 24*d*e^2*x^2 + 24*d^2*e*x + 8*d^3 - 10*(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (13*e^2*x^2 + 19*d*e*x + 8*d^2)*sqrt(-e^2*x^2 + d^2))/(e^6*x^3 + 3*d*e^5*x^2 + 3*d^2*e^4*x + d^3*e^3)","A",0
192,1,102,0,0.395384," ","integrate(x*(-e^2*x^2+d^2)^(1/2)/(e*x+d)^4,x, algorithm=""fricas"")","-\frac{e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3} - {\left(4 \, e^{2} x^{2} - 3 \, d e x - d^{2}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(d e^{5} x^{3} + 3 \, d^{2} e^{4} x^{2} + 3 \, d^{3} e^{3} x + d^{4} e^{2}\right)}}"," ",0,"-1/15*(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3 - (4*e^2*x^2 - 3*d*e*x - d^2)*sqrt(-e^2*x^2 + d^2))/(d*e^5*x^3 + 3*d^2*e^4*x^2 + 3*d^3*e^3*x + d^4*e^2)","A",0
193,1,104,0,0.408439," ","integrate((-e^2*x^2+d^2)^(1/2)/(e*x+d)^4,x, algorithm=""fricas"")","-\frac{4 \, e^{3} x^{3} + 12 \, d e^{2} x^{2} + 12 \, d^{2} e x + 4 \, d^{3} - {\left(e^{2} x^{2} + 3 \, d e x - 4 \, d^{2}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(d^{2} e^{4} x^{3} + 3 \, d^{3} e^{3} x^{2} + 3 \, d^{4} e^{2} x + d^{5} e\right)}}"," ",0,"-1/15*(4*e^3*x^3 + 12*d*e^2*x^2 + 12*d^2*e*x + 4*d^3 - (e^2*x^2 + 3*d*e*x - 4*d^2)*sqrt(-e^2*x^2 + d^2))/(d^2*e^4*x^3 + 3*d^3*e^3*x^2 + 3*d^4*e^2*x + d^5*e)","A",0
194,1,153,0,0.408266," ","integrate((-e^2*x^2+d^2)^(1/2)/x/(e*x+d)^4,x, algorithm=""fricas"")","\frac{13 \, e^{3} x^{3} + 39 \, d e^{2} x^{2} + 39 \, d^{2} e x + 13 \, d^{3} + 5 \, {\left(e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}\right)} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) + {\left(8 \, e^{2} x^{2} + 19 \, d e x + 13 \, d^{2}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{5 \, {\left(d^{3} e^{3} x^{3} + 3 \, d^{4} e^{2} x^{2} + 3 \, d^{5} e x + d^{6}\right)}}"," ",0,"1/5*(13*e^3*x^3 + 39*d*e^2*x^2 + 39*d^2*e*x + 13*d^3 + 5*(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)*log(-(d - sqrt(-e^2*x^2 + d^2))/x) + (8*e^2*x^2 + 19*d*e*x + 13*d^2)*sqrt(-e^2*x^2 + d^2))/(d^3*e^3*x^3 + 3*d^4*e^2*x^2 + 3*d^5*e*x + d^6)","A",0
195,1,181,0,0.415197," ","integrate((-e^2*x^2+d^2)^(1/2)/x^2/(e*x+d)^4,x, algorithm=""fricas"")","-\frac{104 \, e^{4} x^{4} + 312 \, d e^{3} x^{3} + 312 \, d^{2} e^{2} x^{2} + 104 \, d^{3} e x + 60 \, {\left(e^{4} x^{4} + 3 \, d e^{3} x^{3} + 3 \, d^{2} e^{2} x^{2} + d^{3} e x\right)} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) + {\left(94 \, e^{3} x^{3} + 222 \, d e^{2} x^{2} + 149 \, d^{2} e x + 15 \, d^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(d^{4} e^{3} x^{4} + 3 \, d^{5} e^{2} x^{3} + 3 \, d^{6} e x^{2} + d^{7} x\right)}}"," ",0,"-1/15*(104*e^4*x^4 + 312*d*e^3*x^3 + 312*d^2*e^2*x^2 + 104*d^3*e*x + 60*(e^4*x^4 + 3*d*e^3*x^3 + 3*d^2*e^2*x^2 + d^3*e*x)*log(-(d - sqrt(-e^2*x^2 + d^2))/x) + (94*e^3*x^3 + 222*d*e^2*x^2 + 149*d^2*e*x + 15*d^3)*sqrt(-e^2*x^2 + d^2))/(d^4*e^3*x^4 + 3*d^5*e^2*x^3 + 3*d^6*e*x^2 + d^7*x)","A",0
196,1,202,0,0.423050," ","integrate((-e^2*x^2+d^2)^(1/2)/x^3/(e*x+d)^4,x, algorithm=""fricas"")","\frac{398 \, e^{5} x^{5} + 1194 \, d e^{4} x^{4} + 1194 \, d^{2} e^{3} x^{3} + 398 \, d^{3} e^{2} x^{2} + 285 \, {\left(e^{5} x^{5} + 3 \, d e^{4} x^{4} + 3 \, d^{2} e^{3} x^{3} + d^{3} e^{2} x^{2}\right)} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) + {\left(448 \, e^{4} x^{4} + 1059 \, d e^{3} x^{3} + 713 \, d^{2} e^{2} x^{2} + 75 \, d^{3} e x - 15 \, d^{4}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{30 \, {\left(d^{5} e^{3} x^{5} + 3 \, d^{6} e^{2} x^{4} + 3 \, d^{7} e x^{3} + d^{8} x^{2}\right)}}"," ",0,"1/30*(398*e^5*x^5 + 1194*d*e^4*x^4 + 1194*d^2*e^3*x^3 + 398*d^3*e^2*x^2 + 285*(e^5*x^5 + 3*d*e^4*x^4 + 3*d^2*e^3*x^3 + d^3*e^2*x^2)*log(-(d - sqrt(-e^2*x^2 + d^2))/x) + (448*e^4*x^4 + 1059*d*e^3*x^3 + 713*d^2*e^2*x^2 + 75*d^3*e*x - 15*d^4)*sqrt(-e^2*x^2 + d^2))/(d^5*e^3*x^5 + 3*d^6*e^2*x^4 + 3*d^7*e*x^3 + d^8*x^2)","A",0
197,1,213,0,0.455694," ","integrate((-e^2*x^2+d^2)^(1/2)/x^4/(e*x+d)^4,x, algorithm=""fricas"")","-\frac{324 \, e^{6} x^{6} + 972 \, d e^{5} x^{5} + 972 \, d^{2} e^{4} x^{4} + 324 \, d^{3} e^{3} x^{3} + 270 \, {\left(e^{6} x^{6} + 3 \, d e^{5} x^{5} + 3 \, d^{2} e^{4} x^{4} + d^{3} e^{3} x^{3}\right)} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) + {\left(424 \, e^{5} x^{5} + 1002 \, d e^{4} x^{4} + 674 \, d^{2} e^{3} x^{3} + 70 \, d^{3} e^{2} x^{2} - 15 \, d^{4} e x + 5 \, d^{5}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(d^{6} e^{3} x^{6} + 3 \, d^{7} e^{2} x^{5} + 3 \, d^{8} e x^{4} + d^{9} x^{3}\right)}}"," ",0,"-1/15*(324*e^6*x^6 + 972*d*e^5*x^5 + 972*d^2*e^4*x^4 + 324*d^3*e^3*x^3 + 270*(e^6*x^6 + 3*d*e^5*x^5 + 3*d^2*e^4*x^4 + d^3*e^3*x^3)*log(-(d - sqrt(-e^2*x^2 + d^2))/x) + (424*e^5*x^5 + 1002*d*e^4*x^4 + 674*d^2*e^3*x^3 + 70*d^3*e^2*x^2 - 15*d^4*e*x + 5*d^5)*sqrt(-e^2*x^2 + d^2))/(d^6*e^3*x^6 + 3*d^7*e^2*x^5 + 3*d^8*e*x^4 + d^9*x^3)","A",0
198,1,156,0,0.425548," ","integrate(x^5*(-e^2*x^2+d^2)^(5/2)/(e*x+d)^4,x, algorithm=""fricas"")","\frac{2144 \, d^{7} e x + 2144 \, d^{8} - 2730 \, {\left(d^{7} e x + d^{8}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(12 \, e^{7} x^{7} - 44 \, d e^{6} x^{6} + 76 \, d^{2} e^{5} x^{5} - 106 \, d^{3} e^{4} x^{4} + 162 \, d^{4} e^{3} x^{3} - 293 \, d^{5} e^{2} x^{2} + 779 \, d^{6} e x + 2144 \, d^{7}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{84 \, {\left(e^{7} x + d e^{6}\right)}}"," ",0,"1/84*(2144*d^7*e*x + 2144*d^8 - 2730*(d^7*e*x + d^8)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (12*e^7*x^7 - 44*d*e^6*x^6 + 76*d^2*e^5*x^5 - 106*d^3*e^4*x^4 + 162*d^4*e^3*x^3 - 293*d^5*e^2*x^2 + 779*d^6*e*x + 2144*d^7)*sqrt(-e^2*x^2 + d^2))/(e^7*x + d*e^6)","A",0
199,1,146,0,0.413041," ","integrate(x^4*(-e^2*x^2+d^2)^(5/2)/(e*x+d)^4,x, algorithm=""fricas"")","-\frac{5632 \, d^{6} e x + 5632 \, d^{7} - 7170 \, {\left(d^{6} e x + d^{7}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) - {\left(40 \, e^{6} x^{6} - 152 \, d e^{5} x^{5} + 278 \, d^{2} e^{4} x^{4} - 426 \, d^{3} e^{3} x^{3} + 769 \, d^{4} e^{2} x^{2} - 2047 \, d^{5} e x - 5632 \, d^{6}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{240 \, {\left(e^{6} x + d e^{5}\right)}}"," ",0,"-1/240*(5632*d^6*e*x + 5632*d^7 - 7170*(d^6*e*x + d^7)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) - (40*e^6*x^6 - 152*d*e^5*x^5 + 278*d^2*e^4*x^4 - 426*d^3*e^3*x^3 + 769*d^4*e^2*x^2 - 2047*d^5*e*x - 5632*d^6)*sqrt(-e^2*x^2 + d^2))/(e^6*x + d*e^5)","A",0
200,1,134,0,0.402422," ","integrate(x^3*(-e^2*x^2+d^2)^(5/2)/(e*x+d)^4,x, algorithm=""fricas"")","\frac{212 \, d^{5} e x + 212 \, d^{6} - 270 \, {\left(d^{5} e x + d^{6}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(2 \, e^{5} x^{5} - 8 \, d e^{4} x^{4} + 16 \, d^{2} e^{3} x^{3} - 29 \, d^{3} e^{2} x^{2} + 77 \, d^{4} e x + 212 \, d^{5}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{10 \, {\left(e^{5} x + d e^{4}\right)}}"," ",0,"1/10*(212*d^5*e*x + 212*d^6 - 270*(d^5*e*x + d^6)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (2*e^5*x^5 - 8*d*e^4*x^4 + 16*d^2*e^3*x^3 - 29*d^3*e^2*x^2 + 77*d^4*e*x + 212*d^5)*sqrt(-e^2*x^2 + d^2))/(e^5*x + d*e^4)","A",0
201,1,124,0,0.407277," ","integrate(x^2*(-e^2*x^2+d^2)^(5/2)/(e*x+d)^4,x, algorithm=""fricas"")","-\frac{448 \, d^{4} e x + 448 \, d^{5} - 570 \, {\left(d^{4} e x + d^{5}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) - {\left(6 \, e^{4} x^{4} - 26 \, d e^{3} x^{3} + 61 \, d^{2} e^{2} x^{2} - 163 \, d^{3} e x - 448 \, d^{4}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{24 \, {\left(e^{4} x + d e^{3}\right)}}"," ",0,"-1/24*(448*d^4*e*x + 448*d^5 - 570*(d^4*e*x + d^5)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) - (6*e^4*x^4 - 26*d*e^3*x^3 + 61*d^2*e^2*x^2 - 163*d^3*e*x - 448*d^4)*sqrt(-e^2*x^2 + d^2))/(e^4*x + d*e^3)","A",0
202,1,111,0,0.401151," ","integrate(x*(-e^2*x^2+d^2)^(5/2)/(e*x+d)^4,x, algorithm=""fricas"")","\frac{47 \, d^{3} e x + 47 \, d^{4} - 60 \, {\left(d^{3} e x + d^{4}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(e^{3} x^{3} - 5 \, d e^{2} x^{2} + 17 \, d^{2} e x + 47 \, d^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{3 \, {\left(e^{3} x + d e^{2}\right)}}"," ",0,"1/3*(47*d^3*e*x + 47*d^4 - 60*(d^3*e*x + d^4)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (e^3*x^3 - 5*d*e^2*x^2 + 17*d^2*e*x + 47*d^3)*sqrt(-e^2*x^2 + d^2))/(e^3*x + d*e^2)","A",0
203,1,99,0,0.403822," ","integrate((-e^2*x^2+d^2)^(5/2)/(e*x+d)^4,x, algorithm=""fricas"")","-\frac{24 \, d^{2} e x + 24 \, d^{3} - 30 \, {\left(d^{2} e x + d^{3}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) - {\left(e^{2} x^{2} - 7 \, d e x - 24 \, d^{2}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{2 \, {\left(e^{2} x + d e\right)}}"," ",0,"-1/2*(24*d^2*e*x + 24*d^3 - 30*(d^2*e*x + d^3)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) - (e^2*x^2 - 7*d*e*x - 24*d^2)*sqrt(-e^2*x^2 + d^2))/(e^2*x + d*e)","A",0
204,1,111,0,0.414330," ","integrate((-e^2*x^2+d^2)^(5/2)/x/(e*x+d)^4,x, algorithm=""fricas"")","\frac{9 \, d e x + 9 \, d^{2} - 8 \, {\left(d e x + d^{2}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(d e x + d^{2}\right)} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) + \sqrt{-e^{2} x^{2} + d^{2}} {\left(e x + 9 \, d\right)}}{e x + d}"," ",0,"(9*d*e*x + 9*d^2 - 8*(d*e*x + d^2)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (d*e*x + d^2)*log(-(d - sqrt(-e^2*x^2 + d^2))/x) + sqrt(-e^2*x^2 + d^2)*(e*x + 9*d))/(e*x + d)","A",0
205,1,127,0,0.421293," ","integrate((-e^2*x^2+d^2)^(5/2)/x^2/(e*x+d)^4,x, algorithm=""fricas"")","-\frac{8 \, e^{2} x^{2} + 8 \, d e x - 2 \, {\left(e^{2} x^{2} + d e x\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + 4 \, {\left(e^{2} x^{2} + d e x\right)} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) + \sqrt{-e^{2} x^{2} + d^{2}} {\left(9 \, e x + d\right)}}{e x^{2} + d x}"," ",0,"-(8*e^2*x^2 + 8*d*e*x - 2*(e^2*x^2 + d*e*x)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + 4*(e^2*x^2 + d*e*x)*log(-(d - sqrt(-e^2*x^2 + d^2))/x) + sqrt(-e^2*x^2 + d^2)*(9*e*x + d))/(e*x^2 + d*x)","A",0
206,1,112,0,0.410703," ","integrate((-e^2*x^2+d^2)^(5/2)/x^3/(e*x+d)^4,x, algorithm=""fricas"")","\frac{16 \, e^{3} x^{3} + 16 \, d e^{2} x^{2} + 15 \, {\left(e^{3} x^{3} + d e^{2} x^{2}\right)} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) + {\left(24 \, e^{2} x^{2} + 7 \, d e x - d^{2}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{2 \, {\left(d e x^{3} + d^{2} x^{2}\right)}}"," ",0,"1/2*(16*e^3*x^3 + 16*d*e^2*x^2 + 15*(e^3*x^3 + d*e^2*x^2)*log(-(d - sqrt(-e^2*x^2 + d^2))/x) + (24*e^2*x^2 + 7*d*e*x - d^2)*sqrt(-e^2*x^2 + d^2))/(d*e*x^3 + d^2*x^2)","A",0
207,1,123,0,0.397134," ","integrate((-e^2*x^2+d^2)^(5/2)/x^4/(e*x+d)^4,x, algorithm=""fricas"")","-\frac{24 \, e^{4} x^{4} + 24 \, d e^{3} x^{3} + 30 \, {\left(e^{4} x^{4} + d e^{3} x^{3}\right)} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) + {\left(47 \, e^{3} x^{3} + 17 \, d e^{2} x^{2} - 5 \, d^{2} e x + d^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{3 \, {\left(d^{2} e x^{4} + d^{3} x^{3}\right)}}"," ",0,"-1/3*(24*e^4*x^4 + 24*d*e^3*x^3 + 30*(e^4*x^4 + d*e^3*x^3)*log(-(d - sqrt(-e^2*x^2 + d^2))/x) + (47*e^3*x^3 + 17*d*e^2*x^2 - 5*d^2*e*x + d^3)*sqrt(-e^2*x^2 + d^2))/(d^2*e*x^4 + d^3*x^3)","A",0
208,1,136,0,0.397636," ","integrate((-e^2*x^2+d^2)^(5/2)/x^5/(e*x+d)^4,x, algorithm=""fricas"")","\frac{192 \, e^{5} x^{5} + 192 \, d e^{4} x^{4} + 285 \, {\left(e^{5} x^{5} + d e^{4} x^{4}\right)} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) + {\left(448 \, e^{4} x^{4} + 163 \, d e^{3} x^{3} - 61 \, d^{2} e^{2} x^{2} + 26 \, d^{3} e x - 6 \, d^{4}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{24 \, {\left(d^{3} e x^{5} + d^{4} x^{4}\right)}}"," ",0,"1/24*(192*e^5*x^5 + 192*d*e^4*x^4 + 285*(e^5*x^5 + d*e^4*x^4)*log(-(d - sqrt(-e^2*x^2 + d^2))/x) + (448*e^4*x^4 + 163*d*e^3*x^3 - 61*d^2*e^2*x^2 + 26*d^3*e*x - 6*d^4)*sqrt(-e^2*x^2 + d^2))/(d^3*e*x^5 + d^4*x^4)","A",0
209,1,147,0,0.406197," ","integrate((-e^2*x^2+d^2)^(5/2)/x^6/(e*x+d)^4,x, algorithm=""fricas"")","-\frac{80 \, e^{6} x^{6} + 80 \, d e^{5} x^{5} + 135 \, {\left(e^{6} x^{6} + d e^{5} x^{5}\right)} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) + {\left(212 \, e^{5} x^{5} + 77 \, d e^{4} x^{4} - 29 \, d^{2} e^{3} x^{3} + 16 \, d^{3} e^{2} x^{2} - 8 \, d^{4} e x + 2 \, d^{5}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{10 \, {\left(d^{4} e x^{6} + d^{5} x^{5}\right)}}"," ",0,"-1/10*(80*e^6*x^6 + 80*d*e^5*x^5 + 135*(e^6*x^6 + d*e^5*x^5)*log(-(d - sqrt(-e^2*x^2 + d^2))/x) + (212*e^5*x^5 + 77*d*e^4*x^4 - 29*d^2*e^3*x^3 + 16*d^3*e^2*x^2 - 8*d^4*e*x + 2*d^5)*sqrt(-e^2*x^2 + d^2))/(d^4*e*x^6 + d^5*x^5)","A",0
210,1,126,0,0.403578," ","integrate(x^2*(-a^2*x^2+1)^(1/2)/(-a*x+1)^4,x, algorithm=""fricas"")","\frac{8 \, a^{3} x^{3} - 24 \, a^{2} x^{2} + 24 \, a x + 10 \, {\left(a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1\right)} \arctan\left(\frac{\sqrt{-a^{2} x^{2} + 1} - 1}{a x}\right) - {\left(13 \, a^{2} x^{2} - 19 \, a x + 8\right)} \sqrt{-a^{2} x^{2} + 1} - 8}{5 \, {\left(a^{6} x^{3} - 3 \, a^{5} x^{2} + 3 \, a^{4} x - a^{3}\right)}}"," ",0,"1/5*(8*a^3*x^3 - 24*a^2*x^2 + 24*a*x + 10*(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)*arctan((sqrt(-a^2*x^2 + 1) - 1)/(a*x)) - (13*a^2*x^2 - 19*a*x + 8)*sqrt(-a^2*x^2 + 1) - 8)/(a^6*x^3 - 3*a^5*x^2 + 3*a^4*x - a^3)","A",0
211,1,102,0,0.402244," ","integrate(x^2*(-a^2*x^2+1)^(1/2)/(-a*x+1)^5,x, algorithm=""fricas"")","\frac{2 \, a^{4} x^{4} - 8 \, a^{3} x^{3} + 12 \, a^{2} x^{2} - 8 \, a x + {\left(23 \, a^{3} x^{3} + 13 \, a^{2} x^{2} - 8 \, a x + 2\right)} \sqrt{-a^{2} x^{2} + 1} + 2}{105 \, {\left(a^{7} x^{4} - 4 \, a^{6} x^{3} + 6 \, a^{5} x^{2} - 4 \, a^{4} x + a^{3}\right)}}"," ",0,"1/105*(2*a^4*x^4 - 8*a^3*x^3 + 12*a^2*x^2 - 8*a*x + (23*a^3*x^3 + 13*a^2*x^2 - 8*a*x + 2)*sqrt(-a^2*x^2 + 1) + 2)/(a^7*x^4 - 4*a^6*x^3 + 6*a^5*x^2 - 4*a^4*x + a^3)","A",0
212,1,316,0,0.922385," ","integrate(x^3/(e*x+d)^4/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","\frac{90 \, e^{10} x^{10} + 360 \, d e^{9} x^{9} + 270 \, d^{2} e^{8} x^{8} - 720 \, d^{3} e^{7} x^{7} - 1260 \, d^{4} e^{6} x^{6} + 1260 \, d^{6} e^{4} x^{4} + 720 \, d^{7} e^{3} x^{3} - 270 \, d^{8} e^{2} x^{2} - 360 \, d^{9} e x - 90 \, d^{10} + {\left(64 \, e^{9} x^{9} + 256 \, d e^{8} x^{8} + 224 \, d^{2} e^{7} x^{7} - 384 \, d^{3} e^{6} x^{6} - 776 \, d^{4} e^{5} x^{5} - 160 \, d^{5} e^{4} x^{4} + 540 \, d^{6} e^{3} x^{3} - 315 \, d^{7} e^{2} x^{2} - 360 \, d^{8} e x - 90 \, d^{9}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{5005 \, {\left(d^{7} e^{14} x^{10} + 4 \, d^{8} e^{13} x^{9} + 3 \, d^{9} e^{12} x^{8} - 8 \, d^{10} e^{11} x^{7} - 14 \, d^{11} e^{10} x^{6} + 14 \, d^{13} e^{8} x^{4} + 8 \, d^{14} e^{7} x^{3} - 3 \, d^{15} e^{6} x^{2} - 4 \, d^{16} e^{5} x - d^{17} e^{4}\right)}}"," ",0,"1/5005*(90*e^10*x^10 + 360*d*e^9*x^9 + 270*d^2*e^8*x^8 - 720*d^3*e^7*x^7 - 1260*d^4*e^6*x^6 + 1260*d^6*e^4*x^4 + 720*d^7*e^3*x^3 - 270*d^8*e^2*x^2 - 360*d^9*e*x - 90*d^10 + (64*e^9*x^9 + 256*d*e^8*x^8 + 224*d^2*e^7*x^7 - 384*d^3*e^6*x^6 - 776*d^4*e^5*x^5 - 160*d^5*e^4*x^4 + 540*d^6*e^3*x^3 - 315*d^7*e^2*x^2 - 360*d^8*e*x - 90*d^9)*sqrt(-e^2*x^2 + d^2))/(d^7*e^14*x^10 + 4*d^8*e^13*x^9 + 3*d^9*e^12*x^8 - 8*d^10*e^11*x^7 - 14*d^11*e^10*x^6 + 14*d^13*e^8*x^4 + 8*d^14*e^7*x^3 - 3*d^15*e^6*x^2 - 4*d^16*e^5*x - d^17*e^4)","A",0
213,1,317,0,0.964865," ","integrate(x^2/(e*x+d)^4/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","\frac{200 \, e^{10} x^{10} + 800 \, d e^{9} x^{9} + 600 \, d^{2} e^{8} x^{8} - 1600 \, d^{3} e^{7} x^{7} - 2800 \, d^{4} e^{6} x^{6} + 2800 \, d^{6} e^{4} x^{4} + 1600 \, d^{7} e^{3} x^{3} - 600 \, d^{8} e^{2} x^{2} - 800 \, d^{9} e x - 200 \, d^{10} - {\left(112 \, e^{9} x^{9} + 448 \, d e^{8} x^{8} + 392 \, d^{2} e^{7} x^{7} - 672 \, d^{3} e^{6} x^{6} - 1358 \, d^{4} e^{5} x^{5} - 280 \, d^{5} e^{4} x^{4} + 945 \, d^{6} e^{3} x^{3} + 700 \, d^{7} e^{2} x^{2} + 800 \, d^{8} e x + 200 \, d^{9}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{6435 \, {\left(d^{8} e^{13} x^{10} + 4 \, d^{9} e^{12} x^{9} + 3 \, d^{10} e^{11} x^{8} - 8 \, d^{11} e^{10} x^{7} - 14 \, d^{12} e^{9} x^{6} + 14 \, d^{14} e^{7} x^{4} + 8 \, d^{15} e^{6} x^{3} - 3 \, d^{16} e^{5} x^{2} - 4 \, d^{17} e^{4} x - d^{18} e^{3}\right)}}"," ",0,"1/6435*(200*e^10*x^10 + 800*d*e^9*x^9 + 600*d^2*e^8*x^8 - 1600*d^3*e^7*x^7 - 2800*d^4*e^6*x^6 + 2800*d^6*e^4*x^4 + 1600*d^7*e^3*x^3 - 600*d^8*e^2*x^2 - 800*d^9*e*x - 200*d^10 - (112*e^9*x^9 + 448*d*e^8*x^8 + 392*d^2*e^7*x^7 - 672*d^3*e^6*x^6 - 1358*d^4*e^5*x^5 - 280*d^5*e^4*x^4 + 945*d^6*e^3*x^3 + 700*d^7*e^2*x^2 + 800*d^8*e*x + 200*d^9)*sqrt(-e^2*x^2 + d^2))/(d^8*e^13*x^10 + 4*d^9*e^12*x^9 + 3*d^10*e^11*x^8 - 8*d^11*e^10*x^7 - 14*d^12*e^9*x^6 + 14*d^14*e^7*x^4 + 8*d^15*e^6*x^3 - 3*d^16*e^5*x^2 - 4*d^17*e^4*x - d^18*e^3)","A",0
214,1,316,0,1.042078," ","integrate(x/(e*x+d)^4/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","-\frac{5 \, e^{10} x^{10} + 20 \, d e^{9} x^{9} + 15 \, d^{2} e^{8} x^{8} - 40 \, d^{3} e^{7} x^{7} - 70 \, d^{4} e^{6} x^{6} + 70 \, d^{6} e^{4} x^{4} + 40 \, d^{7} e^{3} x^{3} - 15 \, d^{8} e^{2} x^{2} - 20 \, d^{9} e x - 5 \, d^{10} + {\left(512 \, e^{9} x^{9} + 2048 \, d e^{8} x^{8} + 1792 \, d^{2} e^{7} x^{7} - 3072 \, d^{3} e^{6} x^{6} - 6208 \, d^{4} e^{5} x^{5} - 1280 \, d^{5} e^{4} x^{4} + 4320 \, d^{6} e^{3} x^{3} + 3200 \, d^{7} e^{2} x^{2} - 20 \, d^{8} e x - 5 \, d^{9}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{6435 \, {\left(d^{9} e^{12} x^{10} + 4 \, d^{10} e^{11} x^{9} + 3 \, d^{11} e^{10} x^{8} - 8 \, d^{12} e^{9} x^{7} - 14 \, d^{13} e^{8} x^{6} + 14 \, d^{15} e^{6} x^{4} + 8 \, d^{16} e^{5} x^{3} - 3 \, d^{17} e^{4} x^{2} - 4 \, d^{18} e^{3} x - d^{19} e^{2}\right)}}"," ",0,"-1/6435*(5*e^10*x^10 + 20*d*e^9*x^9 + 15*d^2*e^8*x^8 - 40*d^3*e^7*x^7 - 70*d^4*e^6*x^6 + 70*d^6*e^4*x^4 + 40*d^7*e^3*x^3 - 15*d^8*e^2*x^2 - 20*d^9*e*x - 5*d^10 + (512*e^9*x^9 + 2048*d*e^8*x^8 + 1792*d^2*e^7*x^7 - 3072*d^3*e^6*x^6 - 6208*d^4*e^5*x^5 - 1280*d^5*e^4*x^4 + 4320*d^6*e^3*x^3 + 3200*d^7*e^2*x^2 - 20*d^8*e*x - 5*d^9)*sqrt(-e^2*x^2 + d^2))/(d^9*e^12*x^10 + 4*d^10*e^11*x^9 + 3*d^11*e^10*x^8 - 8*d^12*e^9*x^7 - 14*d^13*e^8*x^6 + 14*d^15*e^6*x^4 + 8*d^16*e^5*x^3 - 3*d^17*e^4*x^2 - 4*d^18*e^3*x - d^19*e^2)","A",0
215,1,314,0,1.139364," ","integrate(1/(e*x+d)^4/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","-\frac{180 \, e^{10} x^{10} + 720 \, d e^{9} x^{9} + 540 \, d^{2} e^{8} x^{8} - 1440 \, d^{3} e^{7} x^{7} - 2520 \, d^{4} e^{6} x^{6} + 2520 \, d^{6} e^{4} x^{4} + 1440 \, d^{7} e^{3} x^{3} - 540 \, d^{8} e^{2} x^{2} - 720 \, d^{9} e x - 180 \, d^{10} + {\left(128 \, e^{9} x^{9} + 512 \, d e^{8} x^{8} + 448 \, d^{2} e^{7} x^{7} - 768 \, d^{3} e^{6} x^{6} - 1552 \, d^{4} e^{5} x^{5} - 320 \, d^{5} e^{4} x^{4} + 1080 \, d^{6} e^{3} x^{3} + 800 \, d^{7} e^{2} x^{2} - 5 \, d^{8} e x - 180 \, d^{9}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{715 \, {\left(d^{10} e^{11} x^{10} + 4 \, d^{11} e^{10} x^{9} + 3 \, d^{12} e^{9} x^{8} - 8 \, d^{13} e^{8} x^{7} - 14 \, d^{14} e^{7} x^{6} + 14 \, d^{16} e^{5} x^{4} + 8 \, d^{17} e^{4} x^{3} - 3 \, d^{18} e^{3} x^{2} - 4 \, d^{19} e^{2} x - d^{20} e\right)}}"," ",0,"-1/715*(180*e^10*x^10 + 720*d*e^9*x^9 + 540*d^2*e^8*x^8 - 1440*d^3*e^7*x^7 - 2520*d^4*e^6*x^6 + 2520*d^6*e^4*x^4 + 1440*d^7*e^3*x^3 - 540*d^8*e^2*x^2 - 720*d^9*e*x - 180*d^10 + (128*e^9*x^9 + 512*d*e^8*x^8 + 448*d^2*e^7*x^7 - 768*d^3*e^6*x^6 - 1552*d^4*e^5*x^5 - 320*d^5*e^4*x^4 + 1080*d^6*e^3*x^3 + 800*d^7*e^2*x^2 - 5*d^8*e*x - 180*d^9)*sqrt(-e^2*x^2 + d^2))/(d^10*e^11*x^10 + 4*d^11*e^10*x^9 + 3*d^12*e^9*x^8 - 8*d^13*e^8*x^7 - 14*d^14*e^7*x^6 + 14*d^16*e^5*x^4 + 8*d^17*e^4*x^3 - 3*d^18*e^3*x^2 - 4*d^19*e^2*x - d^20*e)","A",0
216,1,432,0,1.180649," ","integrate(1/x/(e*x+d)^4/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","\frac{9839 \, e^{10} x^{10} + 39356 \, d e^{9} x^{9} + 29517 \, d^{2} e^{8} x^{8} - 78712 \, d^{3} e^{7} x^{7} - 137746 \, d^{4} e^{6} x^{6} + 137746 \, d^{6} e^{4} x^{4} + 78712 \, d^{7} e^{3} x^{3} - 29517 \, d^{8} e^{2} x^{2} - 39356 \, d^{9} e x - 9839 \, d^{10} + 4095 \, {\left(e^{10} x^{10} + 4 \, d e^{9} x^{9} + 3 \, d^{2} e^{8} x^{8} - 8 \, d^{3} e^{7} x^{7} - 14 \, d^{4} e^{6} x^{6} + 14 \, d^{6} e^{4} x^{4} + 8 \, d^{7} e^{3} x^{3} - 3 \, d^{8} e^{2} x^{2} - 4 \, d^{9} e x - d^{10}\right)} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) + {\left(5120 \, e^{9} x^{9} + 16385 \, d e^{8} x^{8} + 1540 \, d^{2} e^{7} x^{7} - 45735 \, d^{3} e^{6} x^{6} - 40240 \, d^{4} e^{5} x^{5} + 34156 \, d^{5} e^{4} x^{4} + 56304 \, d^{6} e^{3} x^{3} + 4466 \, d^{7} e^{2} x^{2} - 22976 \, d^{8} e x - 9839 \, d^{9}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{4095 \, {\left(d^{11} e^{10} x^{10} + 4 \, d^{12} e^{9} x^{9} + 3 \, d^{13} e^{8} x^{8} - 8 \, d^{14} e^{7} x^{7} - 14 \, d^{15} e^{6} x^{6} + 14 \, d^{17} e^{4} x^{4} + 8 \, d^{18} e^{3} x^{3} - 3 \, d^{19} e^{2} x^{2} - 4 \, d^{20} e x - d^{21}\right)}}"," ",0,"1/4095*(9839*e^10*x^10 + 39356*d*e^9*x^9 + 29517*d^2*e^8*x^8 - 78712*d^3*e^7*x^7 - 137746*d^4*e^6*x^6 + 137746*d^6*e^4*x^4 + 78712*d^7*e^3*x^3 - 29517*d^8*e^2*x^2 - 39356*d^9*e*x - 9839*d^10 + 4095*(e^10*x^10 + 4*d*e^9*x^9 + 3*d^2*e^8*x^8 - 8*d^3*e^7*x^7 - 14*d^4*e^6*x^6 + 14*d^6*e^4*x^4 + 8*d^7*e^3*x^3 - 3*d^8*e^2*x^2 - 4*d^9*e*x - d^10)*log(-(d - sqrt(-e^2*x^2 + d^2))/x) + (5120*e^9*x^9 + 16385*d*e^8*x^8 + 1540*d^2*e^7*x^7 - 45735*d^3*e^6*x^6 - 40240*d^4*e^5*x^5 + 34156*d^5*e^4*x^4 + 56304*d^6*e^3*x^3 + 4466*d^7*e^2*x^2 - 22976*d^8*e*x - 9839*d^9)*sqrt(-e^2*x^2 + d^2))/(d^11*e^10*x^10 + 4*d^12*e^9*x^9 + 3*d^13*e^8*x^8 - 8*d^14*e^7*x^7 - 14*d^15*e^6*x^6 + 14*d^17*e^4*x^4 + 8*d^18*e^3*x^3 - 3*d^19*e^2*x^2 - 4*d^20*e*x - d^21)","B",0
217,1,458,0,1.778947," ","integrate(1/x^2/(e*x+d)^4/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","-\frac{366136 \, e^{11} x^{11} + 1464544 \, d e^{10} x^{10} + 1098408 \, d^{2} e^{9} x^{9} - 2929088 \, d^{3} e^{8} x^{8} - 5125904 \, d^{4} e^{7} x^{7} + 5125904 \, d^{6} e^{5} x^{5} + 2929088 \, d^{7} e^{4} x^{4} - 1098408 \, d^{8} e^{3} x^{3} - 1464544 \, d^{9} e^{2} x^{2} - 366136 \, d^{10} e x + 180180 \, {\left(e^{11} x^{11} + 4 \, d e^{10} x^{10} + 3 \, d^{2} e^{9} x^{9} - 8 \, d^{3} e^{8} x^{8} - 14 \, d^{4} e^{7} x^{7} + 14 \, d^{6} e^{5} x^{5} + 8 \, d^{7} e^{4} x^{4} - 3 \, d^{8} e^{3} x^{3} - 4 \, d^{9} e^{2} x^{2} - d^{10} e x\right)} \log\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{x}\right) + {\left(305920 \, e^{10} x^{10} + 1043500 \, d e^{9} x^{9} + 350000 \, d^{2} e^{8} x^{8} - 2496180 \, d^{3} e^{7} x^{7} - 2748320 \, d^{4} e^{6} x^{6} + 1301264 \, d^{5} e^{5} x^{5} + 3157776 \, d^{6} e^{4} x^{4} + 700504 \, d^{7} e^{3} x^{3} - 1014094 \, d^{8} e^{2} x^{2} - 546316 \, d^{9} e x - 45045 \, d^{10}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{45045 \, {\left(d^{12} e^{10} x^{11} + 4 \, d^{13} e^{9} x^{10} + 3 \, d^{14} e^{8} x^{9} - 8 \, d^{15} e^{7} x^{8} - 14 \, d^{16} e^{6} x^{7} + 14 \, d^{18} e^{4} x^{5} + 8 \, d^{19} e^{3} x^{4} - 3 \, d^{20} e^{2} x^{3} - 4 \, d^{21} e x^{2} - d^{22} x\right)}}"," ",0,"-1/45045*(366136*e^11*x^11 + 1464544*d*e^10*x^10 + 1098408*d^2*e^9*x^9 - 2929088*d^3*e^8*x^8 - 5125904*d^4*e^7*x^7 + 5125904*d^6*e^5*x^5 + 2929088*d^7*e^4*x^4 - 1098408*d^8*e^3*x^3 - 1464544*d^9*e^2*x^2 - 366136*d^10*e*x + 180180*(e^11*x^11 + 4*d*e^10*x^10 + 3*d^2*e^9*x^9 - 8*d^3*e^8*x^8 - 14*d^4*e^7*x^7 + 14*d^6*e^5*x^5 + 8*d^7*e^4*x^4 - 3*d^8*e^3*x^3 - 4*d^9*e^2*x^2 - d^10*e*x)*log(-(d - sqrt(-e^2*x^2 + d^2))/x) + (305920*e^10*x^10 + 1043500*d*e^9*x^9 + 350000*d^2*e^8*x^8 - 2496180*d^3*e^7*x^7 - 2748320*d^4*e^6*x^6 + 1301264*d^5*e^5*x^5 + 3157776*d^6*e^4*x^4 + 700504*d^7*e^3*x^3 - 1014094*d^8*e^2*x^2 - 546316*d^9*e*x - 45045*d^10)*sqrt(-e^2*x^2 + d^2))/(d^12*e^10*x^11 + 4*d^13*e^9*x^10 + 3*d^14*e^8*x^9 - 8*d^15*e^7*x^8 - 14*d^16*e^6*x^7 + 14*d^18*e^4*x^5 + 8*d^19*e^3*x^4 - 3*d^20*e^2*x^3 - 4*d^21*e*x^2 - d^22*x)","A",0
218,1,217,0,0.418554," ","integrate((-a*c*x+c)^(1/2)*(-a^2*x^2+1)^(1/2)/x^2,x, algorithm=""fricas"")","\left[\frac{{\left(a^{2} x^{2} - a x\right)} \sqrt{c} \log\left(-\frac{a^{2} c x^{2} + a c x - 2 \, \sqrt{-a^{2} x^{2} + 1} \sqrt{-a c x + c} \sqrt{c} - 2 \, c}{a x^{2} - x}\right) + 2 \, \sqrt{-a^{2} x^{2} + 1} \sqrt{-a c x + c} {\left(2 \, a x + 1\right)}}{2 \, {\left(a x^{2} - x\right)}}, \frac{{\left(a^{2} x^{2} - a x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-a^{2} x^{2} + 1} \sqrt{-a c x + c} \sqrt{-c}}{a^{2} c x^{2} - c}\right) + \sqrt{-a^{2} x^{2} + 1} \sqrt{-a c x + c} {\left(2 \, a x + 1\right)}}{a x^{2} - x}\right]"," ",0,"[1/2*((a^2*x^2 - a*x)*sqrt(c)*log(-(a^2*c*x^2 + a*c*x - 2*sqrt(-a^2*x^2 + 1)*sqrt(-a*c*x + c)*sqrt(c) - 2*c)/(a*x^2 - x)) + 2*sqrt(-a^2*x^2 + 1)*sqrt(-a*c*x + c)*(2*a*x + 1))/(a*x^2 - x), ((a^2*x^2 - a*x)*sqrt(-c)*arctan(sqrt(-a^2*x^2 + 1)*sqrt(-a*c*x + c)*sqrt(-c)/(a^2*c*x^2 - c)) + sqrt(-a^2*x^2 + 1)*sqrt(-a*c*x + c)*(2*a*x + 1))/(a*x^2 - x)]","A",0
219,1,110,0,0.405557," ","integrate((-a*c*x+c)^(1/2)/x/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","\left[\sqrt{c} \log\left(-\frac{a^{2} c x^{2} + a c x + 2 \, \sqrt{-a^{2} x^{2} + 1} \sqrt{-a c x + c} \sqrt{c} - 2 \, c}{a x^{2} - x}\right), -2 \, \sqrt{-c} \arctan\left(\frac{\sqrt{-a^{2} x^{2} + 1} \sqrt{-a c x + c} \sqrt{-c}}{a^{2} c x^{2} - c}\right)\right]"," ",0,"[sqrt(c)*log(-(a^2*c*x^2 + a*c*x + 2*sqrt(-a^2*x^2 + 1)*sqrt(-a*c*x + c)*sqrt(c) - 2*c)/(a*x^2 - x)), -2*sqrt(-c)*arctan(sqrt(-a^2*x^2 + 1)*sqrt(-a*c*x + c)*sqrt(-c)/(a^2*c*x^2 - c))]","A",0
220,1,92,0,0.400417," ","integrate((-a*x+1)^(1/2)/x^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{-a x + 1} a \sqrt{x} - \sqrt{-a} \log\left(-2 \, a x + 2 \, \sqrt{-a x + 1} \sqrt{-a} \sqrt{x} + 1\right)}{2 \, a}, \frac{\sqrt{-a x + 1} a \sqrt{x} - \sqrt{a} \arctan\left(\frac{\sqrt{-a x + 1}}{\sqrt{a} \sqrt{x}}\right)}{a}\right]"," ",0,"[1/2*(2*sqrt(-a*x + 1)*a*sqrt(x) - sqrt(-a)*log(-2*a*x + 2*sqrt(-a*x + 1)*sqrt(-a)*sqrt(x) + 1))/a, (sqrt(-a*x + 1)*a*sqrt(x) - sqrt(a)*arctan(sqrt(-a*x + 1)/(sqrt(a)*sqrt(x))))/a]","A",0
221,1,199,0,0.440357," ","integrate((-a^2*x^2+1)^(1/2)/x^(1/2)/(a*x+1)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{-a^{2} x^{2} + 1} \sqrt{a x + 1} a \sqrt{x} - {\left(a x + 1\right)} \sqrt{-a} \log\left(-\frac{8 \, a^{3} x^{3} - 4 \, \sqrt{-a^{2} x^{2} + 1} {\left(2 \, a x - 1\right)} \sqrt{a x + 1} \sqrt{-a} \sqrt{x} - 7 \, a x + 1}{a x + 1}\right)}{4 \, {\left(a^{2} x + a\right)}}, \frac{2 \, \sqrt{-a^{2} x^{2} + 1} \sqrt{a x + 1} a \sqrt{x} - {\left(a x + 1\right)} \sqrt{a} \arctan\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1} \sqrt{a x + 1} \sqrt{a} \sqrt{x}}{2 \, a^{2} x^{2} + a x - 1}\right)}{2 \, {\left(a^{2} x + a\right)}}\right]"," ",0,"[1/4*(4*sqrt(-a^2*x^2 + 1)*sqrt(a*x + 1)*a*sqrt(x) - (a*x + 1)*sqrt(-a)*log(-(8*a^3*x^3 - 4*sqrt(-a^2*x^2 + 1)*(2*a*x - 1)*sqrt(a*x + 1)*sqrt(-a)*sqrt(x) - 7*a*x + 1)/(a*x + 1)))/(a^2*x + a), 1/2*(2*sqrt(-a^2*x^2 + 1)*sqrt(a*x + 1)*a*sqrt(x) - (a*x + 1)*sqrt(a)*arctan(2*sqrt(-a^2*x^2 + 1)*sqrt(a*x + 1)*sqrt(a)*sqrt(x)/(2*a^2*x^2 + a*x - 1)))/(a^2*x + a)]","B",0
222,1,90,0,0.418247," ","integrate((a*x+1)^(1/2)/x^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{a x + 1} a \sqrt{x} + \sqrt{a} \log\left(2 \, a x + 2 \, \sqrt{a x + 1} \sqrt{a} \sqrt{x} + 1\right)}{2 \, a}, \frac{\sqrt{a x + 1} a \sqrt{x} - \sqrt{-a} \arctan\left(\frac{\sqrt{a x + 1} \sqrt{-a}}{a \sqrt{x}}\right)}{a}\right]"," ",0,"[1/2*(2*sqrt(a*x + 1)*a*sqrt(x) + sqrt(a)*log(2*a*x + 2*sqrt(a*x + 1)*sqrt(a)*sqrt(x) + 1))/a, (sqrt(a*x + 1)*a*sqrt(x) - sqrt(-a)*arctan(sqrt(a*x + 1)*sqrt(-a)/(a*sqrt(x))))/a]","A",0
223,1,208,0,0.451115," ","integrate((-a^2*x^2+1)^(1/2)/x^(1/2)/(-a*x+1)^(1/2),x, algorithm=""fricas"")","\left[-\frac{4 \, \sqrt{-a^{2} x^{2} + 1} \sqrt{-a x + 1} a \sqrt{x} - {\left(a x - 1\right)} \sqrt{a} \log\left(-\frac{8 \, a^{3} x^{3} - 4 \, \sqrt{-a^{2} x^{2} + 1} {\left(2 \, a x + 1\right)} \sqrt{-a x + 1} \sqrt{a} \sqrt{x} - 7 \, a x - 1}{a x - 1}\right)}{4 \, {\left(a^{2} x - a\right)}}, -\frac{2 \, \sqrt{-a^{2} x^{2} + 1} \sqrt{-a x + 1} a \sqrt{x} - {\left(a x - 1\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1} \sqrt{-a x + 1} \sqrt{-a} \sqrt{x}}{2 \, a^{2} x^{2} - a x - 1}\right)}{2 \, {\left(a^{2} x - a\right)}}\right]"," ",0,"[-1/4*(4*sqrt(-a^2*x^2 + 1)*sqrt(-a*x + 1)*a*sqrt(x) - (a*x - 1)*sqrt(a)*log(-(8*a^3*x^3 - 4*sqrt(-a^2*x^2 + 1)*(2*a*x + 1)*sqrt(-a*x + 1)*sqrt(a)*sqrt(x) - 7*a*x - 1)/(a*x - 1)))/(a^2*x - a), -1/2*(2*sqrt(-a^2*x^2 + 1)*sqrt(-a*x + 1)*a*sqrt(x) - (a*x - 1)*sqrt(-a)*arctan(2*sqrt(-a^2*x^2 + 1)*sqrt(-a*x + 1)*sqrt(-a)*sqrt(x)/(2*a^2*x^2 - a*x - 1)))/(a^2*x - a)]","B",0
224,1,111,0,0.414335," ","integrate(x^(1/2)*(-a*x+1)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(2 \, a^{2} x - a\right)} \sqrt{-a x + 1} \sqrt{x} - \sqrt{-a} \log\left(-2 \, a x + 2 \, \sqrt{-a x + 1} \sqrt{-a} \sqrt{x} + 1\right)}{8 \, a^{2}}, \frac{{\left(2 \, a^{2} x - a\right)} \sqrt{-a x + 1} \sqrt{x} - \sqrt{a} \arctan\left(\frac{\sqrt{-a x + 1}}{\sqrt{a} \sqrt{x}}\right)}{4 \, a^{2}}\right]"," ",0,"[1/8*(2*(2*a^2*x - a)*sqrt(-a*x + 1)*sqrt(x) - sqrt(-a)*log(-2*a*x + 2*sqrt(-a*x + 1)*sqrt(-a)*sqrt(x) + 1))/a^2, 1/4*((2*a^2*x - a)*sqrt(-a*x + 1)*sqrt(x) - sqrt(a)*arctan(sqrt(-a*x + 1)/(sqrt(a)*sqrt(x))))/a^2]","A",0
225,1,221,0,0.445479," ","integrate(x^(1/2)*(-a^2*x^2+1)^(1/2)/(a*x+1)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{-a^{2} x^{2} + 1} {\left(2 \, a^{2} x - a\right)} \sqrt{a x + 1} \sqrt{x} - {\left(a x + 1\right)} \sqrt{-a} \log\left(-\frac{8 \, a^{3} x^{3} - 4 \, \sqrt{-a^{2} x^{2} + 1} {\left(2 \, a x - 1\right)} \sqrt{a x + 1} \sqrt{-a} \sqrt{x} - 7 \, a x + 1}{a x + 1}\right)}{16 \, {\left(a^{3} x + a^{2}\right)}}, \frac{2 \, \sqrt{-a^{2} x^{2} + 1} {\left(2 \, a^{2} x - a\right)} \sqrt{a x + 1} \sqrt{x} - {\left(a x + 1\right)} \sqrt{a} \arctan\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1} \sqrt{a x + 1} \sqrt{a} \sqrt{x}}{2 \, a^{2} x^{2} + a x - 1}\right)}{8 \, {\left(a^{3} x + a^{2}\right)}}\right]"," ",0,"[1/16*(4*sqrt(-a^2*x^2 + 1)*(2*a^2*x - a)*sqrt(a*x + 1)*sqrt(x) - (a*x + 1)*sqrt(-a)*log(-(8*a^3*x^3 - 4*sqrt(-a^2*x^2 + 1)*(2*a*x - 1)*sqrt(a*x + 1)*sqrt(-a)*sqrt(x) - 7*a*x + 1)/(a*x + 1)))/(a^3*x + a^2), 1/8*(2*sqrt(-a^2*x^2 + 1)*(2*a^2*x - a)*sqrt(a*x + 1)*sqrt(x) - (a*x + 1)*sqrt(a)*arctan(2*sqrt(-a^2*x^2 + 1)*sqrt(a*x + 1)*sqrt(a)*sqrt(x)/(2*a^2*x^2 + a*x - 1)))/(a^3*x + a^2)]","B",0
226,0,0,0,0.409138," ","integrate((g*x)^m*(e*x+d)^3*(-e^2*x^2+d^2)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{7} x^{7} + 3 \, d e^{6} x^{6} + d^{2} e^{5} x^{5} - 5 \, d^{3} e^{4} x^{4} - 5 \, d^{4} e^{3} x^{3} + d^{5} e^{2} x^{2} + 3 \, d^{6} e x + d^{7}\right)} \sqrt{-e^{2} x^{2} + d^{2}} \left(g x\right)^{m}, x\right)"," ",0,"integral((e^7*x^7 + 3*d*e^6*x^6 + d^2*e^5*x^5 - 5*d^3*e^4*x^4 - 5*d^4*e^3*x^3 + d^5*e^2*x^2 + 3*d^6*e*x + d^7)*sqrt(-e^2*x^2 + d^2)*(g*x)^m, x)","F",0
227,0,0,0,0.417117," ","integrate((g*x)^m*(e*x+d)^2*(-e^2*x^2+d^2)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{6} x^{6} + 2 \, d e^{5} x^{5} - d^{2} e^{4} x^{4} - 4 \, d^{3} e^{3} x^{3} - d^{4} e^{2} x^{2} + 2 \, d^{5} e x + d^{6}\right)} \sqrt{-e^{2} x^{2} + d^{2}} \left(g x\right)^{m}, x\right)"," ",0,"integral((e^6*x^6 + 2*d*e^5*x^5 - d^2*e^4*x^4 - 4*d^3*e^3*x^3 - d^4*e^2*x^2 + 2*d^5*e*x + d^6)*sqrt(-e^2*x^2 + d^2)*(g*x)^m, x)","F",0
228,0,0,0,0.418741," ","integrate((g*x)^m*(e*x+d)*(-e^2*x^2+d^2)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{5} x^{5} + d e^{4} x^{4} - 2 \, d^{2} e^{3} x^{3} - 2 \, d^{3} e^{2} x^{2} + d^{4} e x + d^{5}\right)} \sqrt{-e^{2} x^{2} + d^{2}} \left(g x\right)^{m}, x\right)"," ",0,"integral((e^5*x^5 + d*e^4*x^4 - 2*d^2*e^3*x^3 - 2*d^3*e^2*x^2 + d^4*e*x + d^5)*sqrt(-e^2*x^2 + d^2)*(g*x)^m, x)","F",0
229,0,0,0,0.409371," ","integrate((g*x)^m*(-e^2*x^2+d^2)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{4} x^{4} - 2 \, d^{2} e^{2} x^{2} + d^{4}\right)} \sqrt{-e^{2} x^{2} + d^{2}} \left(g x\right)^{m}, x\right)"," ",0,"integral((e^4*x^4 - 2*d^2*e^2*x^2 + d^4)*sqrt(-e^2*x^2 + d^2)*(g*x)^m, x)","F",0
230,0,0,0,0.415663," ","integrate((g*x)^m*(-e^2*x^2+d^2)^(5/2)/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{3} x^{3} - d e^{2} x^{2} - d^{2} e x + d^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}} \left(g x\right)^{m}, x\right)"," ",0,"integral((e^3*x^3 - d*e^2*x^2 - d^2*e*x + d^3)*sqrt(-e^2*x^2 + d^2)*(g*x)^m, x)","F",0
231,0,0,0,0.411924," ","integrate((g*x)^m*(-e^2*x^2+d^2)^(5/2)/(e*x+d)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{2} x^{2} - 2 \, d e x + d^{2}\right)} \sqrt{-e^{2} x^{2} + d^{2}} \left(g x\right)^{m}, x\right)"," ",0,"integral((e^2*x^2 - 2*d*e*x + d^2)*sqrt(-e^2*x^2 + d^2)*(g*x)^m, x)","F",0
232,0,0,0,0.418514," ","integrate((g*x)^m*(-e^2*x^2+d^2)^(5/2)/(e*x+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{2} x^{2} - 2 \, d e x + d^{2}\right)} \sqrt{-e^{2} x^{2} + d^{2}} \left(g x\right)^{m}}{e x + d}, x\right)"," ",0,"integral((e^2*x^2 - 2*d*e*x + d^2)*sqrt(-e^2*x^2 + d^2)*(g*x)^m/(e*x + d), x)","F",0
233,0,0,0,0.423673," ","integrate((g*x)^m*(e*x+d)^3/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-e^{2} x^{2} + d^{2}} \left(g x\right)^{m}}{e^{5} x^{5} - 3 \, d e^{4} x^{4} + 2 \, d^{2} e^{3} x^{3} + 2 \, d^{3} e^{2} x^{2} - 3 \, d^{4} e x + d^{5}}, x\right)"," ",0,"integral(sqrt(-e^2*x^2 + d^2)*(g*x)^m/(e^5*x^5 - 3*d*e^4*x^4 + 2*d^2*e^3*x^3 + 2*d^3*e^2*x^2 - 3*d^4*e*x + d^5), x)","F",0
234,0,0,0,0.418017," ","integrate((g*x)^m*(e*x+d)^2/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-e^{2} x^{2} + d^{2}} \left(g x\right)^{m}}{e^{6} x^{6} - 2 \, d e^{5} x^{5} - d^{2} e^{4} x^{4} + 4 \, d^{3} e^{3} x^{3} - d^{4} e^{2} x^{2} - 2 \, d^{5} e x + d^{6}}, x\right)"," ",0,"integral(sqrt(-e^2*x^2 + d^2)*(g*x)^m/(e^6*x^6 - 2*d*e^5*x^5 - d^2*e^4*x^4 + 4*d^3*e^3*x^3 - d^4*e^2*x^2 - 2*d^5*e*x + d^6), x)","F",0
235,0,0,0,0.427320," ","integrate((g*x)^m*(e*x+d)/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-e^{2} x^{2} + d^{2}} \left(g x\right)^{m}}{e^{7} x^{7} - d e^{6} x^{6} - 3 \, d^{2} e^{5} x^{5} + 3 \, d^{3} e^{4} x^{4} + 3 \, d^{4} e^{3} x^{3} - 3 \, d^{5} e^{2} x^{2} - d^{6} e x + d^{7}}, x\right)"," ",0,"integral(sqrt(-e^2*x^2 + d^2)*(g*x)^m/(e^7*x^7 - d*e^6*x^6 - 3*d^2*e^5*x^5 + 3*d^3*e^4*x^4 + 3*d^4*e^3*x^3 - 3*d^5*e^2*x^2 - d^6*e*x + d^7), x)","F",0
236,0,0,0,0.424627," ","integrate((g*x)^m/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-e^{2} x^{2} + d^{2}} \left(g x\right)^{m}}{e^{8} x^{8} - 4 \, d^{2} e^{6} x^{6} + 6 \, d^{4} e^{4} x^{4} - 4 \, d^{6} e^{2} x^{2} + d^{8}}, x\right)"," ",0,"integral(sqrt(-e^2*x^2 + d^2)*(g*x)^m/(e^8*x^8 - 4*d^2*e^6*x^6 + 6*d^4*e^4*x^4 - 4*d^6*e^2*x^2 + d^8), x)","F",0
237,0,0,0,0.422889," ","integrate((g*x)^m/(e*x+d)/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-e^{2} x^{2} + d^{2}} \left(g x\right)^{m}}{e^{9} x^{9} + d e^{8} x^{8} - 4 \, d^{2} e^{7} x^{7} - 4 \, d^{3} e^{6} x^{6} + 6 \, d^{4} e^{5} x^{5} + 6 \, d^{5} e^{4} x^{4} - 4 \, d^{6} e^{3} x^{3} - 4 \, d^{7} e^{2} x^{2} + d^{8} e x + d^{9}}, x\right)"," ",0,"integral(sqrt(-e^2*x^2 + d^2)*(g*x)^m/(e^9*x^9 + d*e^8*x^8 - 4*d^2*e^7*x^7 - 4*d^3*e^6*x^6 + 6*d^4*e^5*x^5 + 6*d^5*e^4*x^4 - 4*d^6*e^3*x^3 - 4*d^7*e^2*x^2 + d^8*e*x + d^9), x)","F",0
238,0,0,0,0.434965," ","integrate((g*x)^m/(e*x+d)^2/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-e^{2} x^{2} + d^{2}} \left(g x\right)^{m}}{e^{10} x^{10} + 2 \, d e^{9} x^{9} - 3 \, d^{2} e^{8} x^{8} - 8 \, d^{3} e^{7} x^{7} + 2 \, d^{4} e^{6} x^{6} + 12 \, d^{5} e^{5} x^{5} + 2 \, d^{6} e^{4} x^{4} - 8 \, d^{7} e^{3} x^{3} - 3 \, d^{8} e^{2} x^{2} + 2 \, d^{9} e x + d^{10}}, x\right)"," ",0,"integral(sqrt(-e^2*x^2 + d^2)*(g*x)^m/(e^10*x^10 + 2*d*e^9*x^9 - 3*d^2*e^8*x^8 - 8*d^3*e^7*x^7 + 2*d^4*e^6*x^6 + 12*d^5*e^5*x^5 + 2*d^6*e^4*x^4 - 8*d^7*e^3*x^3 - 3*d^8*e^2*x^2 + 2*d^9*e*x + d^10), x)","F",0
239,0,0,0,0.445146," ","integrate((g*x)^m/(e*x+d)^3/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-e^{2} x^{2} + d^{2}} \left(g x\right)^{m}}{e^{11} x^{11} + 3 \, d e^{10} x^{10} - d^{2} e^{9} x^{9} - 11 \, d^{3} e^{8} x^{8} - 6 \, d^{4} e^{7} x^{7} + 14 \, d^{5} e^{6} x^{6} + 14 \, d^{6} e^{5} x^{5} - 6 \, d^{7} e^{4} x^{4} - 11 \, d^{8} e^{3} x^{3} - d^{9} e^{2} x^{2} + 3 \, d^{10} e x + d^{11}}, x\right)"," ",0,"integral(sqrt(-e^2*x^2 + d^2)*(g*x)^m/(e^11*x^11 + 3*d*e^10*x^10 - d^2*e^9*x^9 - 11*d^3*e^8*x^8 - 6*d^4*e^7*x^7 + 14*d^5*e^6*x^6 + 14*d^6*e^5*x^5 - 6*d^7*e^4*x^4 - 11*d^8*e^3*x^3 - d^9*e^2*x^2 + 3*d^10*e*x + d^11), x)","F",0
240,0,0,0,0.418037," ","integrate(x^5*(e*x+d)*(-e^2*x^2+d^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e x^{6} + d x^{5}\right)} {\left(-e^{2} x^{2} + d^{2}\right)}^{p}, x\right)"," ",0,"integral((e*x^6 + d*x^5)*(-e^2*x^2 + d^2)^p, x)","F",0
241,0,0,0,0.416126," ","integrate(x^4*(e*x+d)*(-e^2*x^2+d^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e x^{5} + d x^{4}\right)} {\left(-e^{2} x^{2} + d^{2}\right)}^{p}, x\right)"," ",0,"integral((e*x^5 + d*x^4)*(-e^2*x^2 + d^2)^p, x)","F",0
242,0,0,0,0.412802," ","integrate(x^3*(e*x+d)*(-e^2*x^2+d^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e x^{4} + d x^{3}\right)} {\left(-e^{2} x^{2} + d^{2}\right)}^{p}, x\right)"," ",0,"integral((e*x^4 + d*x^3)*(-e^2*x^2 + d^2)^p, x)","F",0
243,0,0,0,0.412153," ","integrate(x^2*(e*x+d)*(-e^2*x^2+d^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e x^{3} + d x^{2}\right)} {\left(-e^{2} x^{2} + d^{2}\right)}^{p}, x\right)"," ",0,"integral((e*x^3 + d*x^2)*(-e^2*x^2 + d^2)^p, x)","F",0
244,0,0,0,0.401320," ","integrate(x*(e*x+d)*(-e^2*x^2+d^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e x^{2} + d x\right)} {\left(-e^{2} x^{2} + d^{2}\right)}^{p}, x\right)"," ",0,"integral((e*x^2 + d*x)*(-e^2*x^2 + d^2)^p, x)","F",0
245,0,0,0,0.414369," ","integrate((e*x+d)*(-e^2*x^2+d^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e x + d\right)} {\left(-e^{2} x^{2} + d^{2}\right)}^{p}, x\right)"," ",0,"integral((e*x + d)*(-e^2*x^2 + d^2)^p, x)","F",0
246,0,0,0,0.418555," ","integrate((e*x+d)*(-e^2*x^2+d^2)^p/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)} {\left(-e^{2} x^{2} + d^{2}\right)}^{p}}{x}, x\right)"," ",0,"integral((e*x + d)*(-e^2*x^2 + d^2)^p/x, x)","F",0
247,0,0,0,0.398883," ","integrate((e*x+d)*(-e^2*x^2+d^2)^p/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)} {\left(-e^{2} x^{2} + d^{2}\right)}^{p}}{x^{2}}, x\right)"," ",0,"integral((e*x + d)*(-e^2*x^2 + d^2)^p/x^2, x)","F",0
248,0,0,0,0.407576," ","integrate((e*x+d)*(-e^2*x^2+d^2)^p/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)} {\left(-e^{2} x^{2} + d^{2}\right)}^{p}}{x^{3}}, x\right)"," ",0,"integral((e*x + d)*(-e^2*x^2 + d^2)^p/x^3, x)","F",0
249,0,0,0,0.405386," ","integrate(x^5*(e*x+d)^2*(-e^2*x^2+d^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{2} x^{7} + 2 \, d e x^{6} + d^{2} x^{5}\right)} {\left(-e^{2} x^{2} + d^{2}\right)}^{p}, x\right)"," ",0,"integral((e^2*x^7 + 2*d*e*x^6 + d^2*x^5)*(-e^2*x^2 + d^2)^p, x)","F",0
250,0,0,0,0.404586," ","integrate(x^4*(e*x+d)^2*(-e^2*x^2+d^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{2} x^{6} + 2 \, d e x^{5} + d^{2} x^{4}\right)} {\left(-e^{2} x^{2} + d^{2}\right)}^{p}, x\right)"," ",0,"integral((e^2*x^6 + 2*d*e*x^5 + d^2*x^4)*(-e^2*x^2 + d^2)^p, x)","F",0
251,0,0,0,0.407999," ","integrate(x^3*(e*x+d)^2*(-e^2*x^2+d^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{2} x^{5} + 2 \, d e x^{4} + d^{2} x^{3}\right)} {\left(-e^{2} x^{2} + d^{2}\right)}^{p}, x\right)"," ",0,"integral((e^2*x^5 + 2*d*e*x^4 + d^2*x^3)*(-e^2*x^2 + d^2)^p, x)","F",0
252,0,0,0,0.401311," ","integrate(x^2*(e*x+d)^2*(-e^2*x^2+d^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{2} x^{4} + 2 \, d e x^{3} + d^{2} x^{2}\right)} {\left(-e^{2} x^{2} + d^{2}\right)}^{p}, x\right)"," ",0,"integral((e^2*x^4 + 2*d*e*x^3 + d^2*x^2)*(-e^2*x^2 + d^2)^p, x)","F",0
253,0,0,0,0.412488," ","integrate(x*(e*x+d)^2*(-e^2*x^2+d^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{2} x^{3} + 2 \, d e x^{2} + d^{2} x\right)} {\left(-e^{2} x^{2} + d^{2}\right)}^{p}, x\right)"," ",0,"integral((e^2*x^3 + 2*d*e*x^2 + d^2*x)*(-e^2*x^2 + d^2)^p, x)","F",0
254,0,0,0,0.410546," ","integrate((e*x+d)^2*(-e^2*x^2+d^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{2} x^{2} + 2 \, d e x + d^{2}\right)} {\left(-e^{2} x^{2} + d^{2}\right)}^{p}, x\right)"," ",0,"integral((e^2*x^2 + 2*d*e*x + d^2)*(-e^2*x^2 + d^2)^p, x)","F",0
255,0,0,0,0.412231," ","integrate((e*x+d)^2*(-e^2*x^2+d^2)^p/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{2} x^{2} + 2 \, d e x + d^{2}\right)} {\left(-e^{2} x^{2} + d^{2}\right)}^{p}}{x}, x\right)"," ",0,"integral((e^2*x^2 + 2*d*e*x + d^2)*(-e^2*x^2 + d^2)^p/x, x)","F",0
256,0,0,0,0.404948," ","integrate((e*x+d)^2*(-e^2*x^2+d^2)^p/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{2} x^{2} + 2 \, d e x + d^{2}\right)} {\left(-e^{2} x^{2} + d^{2}\right)}^{p}}{x^{2}}, x\right)"," ",0,"integral((e^2*x^2 + 2*d*e*x + d^2)*(-e^2*x^2 + d^2)^p/x^2, x)","F",0
257,0,0,0,0.415169," ","integrate((e*x+d)^2*(-e^2*x^2+d^2)^p/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{2} x^{2} + 2 \, d e x + d^{2}\right)} {\left(-e^{2} x^{2} + d^{2}\right)}^{p}}{x^{3}}, x\right)"," ",0,"integral((e^2*x^2 + 2*d*e*x + d^2)*(-e^2*x^2 + d^2)^p/x^3, x)","F",0
258,0,0,0,0.412826," ","integrate(x^5*(e*x+d)^3*(-e^2*x^2+d^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{3} x^{8} + 3 \, d e^{2} x^{7} + 3 \, d^{2} e x^{6} + d^{3} x^{5}\right)} {\left(-e^{2} x^{2} + d^{2}\right)}^{p}, x\right)"," ",0,"integral((e^3*x^8 + 3*d*e^2*x^7 + 3*d^2*e*x^6 + d^3*x^5)*(-e^2*x^2 + d^2)^p, x)","F",0
259,0,0,0,0.395326," ","integrate(x^4*(e*x+d)^3*(-e^2*x^2+d^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{3} x^{7} + 3 \, d e^{2} x^{6} + 3 \, d^{2} e x^{5} + d^{3} x^{4}\right)} {\left(-e^{2} x^{2} + d^{2}\right)}^{p}, x\right)"," ",0,"integral((e^3*x^7 + 3*d*e^2*x^6 + 3*d^2*e*x^5 + d^3*x^4)*(-e^2*x^2 + d^2)^p, x)","F",0
260,0,0,0,0.407271," ","integrate(x^3*(e*x+d)^3*(-e^2*x^2+d^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{3} x^{6} + 3 \, d e^{2} x^{5} + 3 \, d^{2} e x^{4} + d^{3} x^{3}\right)} {\left(-e^{2} x^{2} + d^{2}\right)}^{p}, x\right)"," ",0,"integral((e^3*x^6 + 3*d*e^2*x^5 + 3*d^2*e*x^4 + d^3*x^3)*(-e^2*x^2 + d^2)^p, x)","F",0
261,0,0,0,0.409090," ","integrate(x^2*(e*x+d)^3*(-e^2*x^2+d^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{3} x^{5} + 3 \, d e^{2} x^{4} + 3 \, d^{2} e x^{3} + d^{3} x^{2}\right)} {\left(-e^{2} x^{2} + d^{2}\right)}^{p}, x\right)"," ",0,"integral((e^3*x^5 + 3*d*e^2*x^4 + 3*d^2*e*x^3 + d^3*x^2)*(-e^2*x^2 + d^2)^p, x)","F",0
262,0,0,0,0.402446," ","integrate(x*(e*x+d)^3*(-e^2*x^2+d^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{3} x^{4} + 3 \, d e^{2} x^{3} + 3 \, d^{2} e x^{2} + d^{3} x\right)} {\left(-e^{2} x^{2} + d^{2}\right)}^{p}, x\right)"," ",0,"integral((e^3*x^4 + 3*d*e^2*x^3 + 3*d^2*e*x^2 + d^3*x)*(-e^2*x^2 + d^2)^p, x)","F",0
263,0,0,0,0.408911," ","integrate((e*x+d)^3*(-e^2*x^2+d^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}\right)} {\left(-e^{2} x^{2} + d^{2}\right)}^{p}, x\right)"," ",0,"integral((e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)*(-e^2*x^2 + d^2)^p, x)","F",0
264,0,0,0,0.411470," ","integrate((e*x+d)^3*(-e^2*x^2+d^2)^p/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}\right)} {\left(-e^{2} x^{2} + d^{2}\right)}^{p}}{x}, x\right)"," ",0,"integral((e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)*(-e^2*x^2 + d^2)^p/x, x)","F",0
265,0,0,0,0.406433," ","integrate((e*x+d)^3*(-e^2*x^2+d^2)^p/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}\right)} {\left(-e^{2} x^{2} + d^{2}\right)}^{p}}{x^{2}}, x\right)"," ",0,"integral((e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)*(-e^2*x^2 + d^2)^p/x^2, x)","F",0
266,0,0,0,0.413358," ","integrate((e*x+d)^3*(-e^2*x^2+d^2)^p/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}\right)} {\left(-e^{2} x^{2} + d^{2}\right)}^{p}}{x^{3}}, x\right)"," ",0,"integral((e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)*(-e^2*x^2 + d^2)^p/x^3, x)","F",0
267,0,0,0,0.414658," ","integrate(x^4*(-e^2*x^2+d^2)^p/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{p} x^{4}}{e x + d}, x\right)"," ",0,"integral((-e^2*x^2 + d^2)^p*x^4/(e*x + d), x)","F",0
268,0,0,0,0.405677," ","integrate(x^3*(-e^2*x^2+d^2)^p/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{p} x^{3}}{e x + d}, x\right)"," ",0,"integral((-e^2*x^2 + d^2)^p*x^3/(e*x + d), x)","F",0
269,0,0,0,0.403246," ","integrate(x^2*(-e^2*x^2+d^2)^p/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{p} x^{2}}{e x + d}, x\right)"," ",0,"integral((-e^2*x^2 + d^2)^p*x^2/(e*x + d), x)","F",0
270,0,0,0,0.411927," ","integrate(x*(-e^2*x^2+d^2)^p/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{p} x}{e x + d}, x\right)"," ",0,"integral((-e^2*x^2 + d^2)^p*x/(e*x + d), x)","F",0
271,0,0,0,0.415626," ","integrate((-e^2*x^2+d^2)^p/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{p}}{e x + d}, x\right)"," ",0,"integral((-e^2*x^2 + d^2)^p/(e*x + d), x)","F",0
272,0,0,0,0.414875," ","integrate((-e^2*x^2+d^2)^p/x/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{p}}{e x^{2} + d x}, x\right)"," ",0,"integral((-e^2*x^2 + d^2)^p/(e*x^2 + d*x), x)","F",0
273,0,0,0,0.414610," ","integrate((-e^2*x^2+d^2)^p/x^2/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{p}}{e x^{3} + d x^{2}}, x\right)"," ",0,"integral((-e^2*x^2 + d^2)^p/(e*x^3 + d*x^2), x)","F",0
274,0,0,0,0.420544," ","integrate((-e^2*x^2+d^2)^p/x^3/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{p}}{e x^{4} + d x^{3}}, x\right)"," ",0,"integral((-e^2*x^2 + d^2)^p/(e*x^4 + d*x^3), x)","F",0
275,0,0,0,0.422481," ","integrate(x^5*(-e^2*x^2+d^2)^p/(e*x+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{p} x^{5}}{e^{2} x^{2} + 2 \, d e x + d^{2}}, x\right)"," ",0,"integral((-e^2*x^2 + d^2)^p*x^5/(e^2*x^2 + 2*d*e*x + d^2), x)","F",0
276,0,0,0,0.416901," ","integrate(x^4*(-e^2*x^2+d^2)^p/(e*x+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{p} x^{4}}{e^{2} x^{2} + 2 \, d e x + d^{2}}, x\right)"," ",0,"integral((-e^2*x^2 + d^2)^p*x^4/(e^2*x^2 + 2*d*e*x + d^2), x)","F",0
277,0,0,0,0.415973," ","integrate(x^3*(-e^2*x^2+d^2)^p/(e*x+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{p} x^{3}}{e^{2} x^{2} + 2 \, d e x + d^{2}}, x\right)"," ",0,"integral((-e^2*x^2 + d^2)^p*x^3/(e^2*x^2 + 2*d*e*x + d^2), x)","F",0
278,0,0,0,0.418322," ","integrate(x^2*(-e^2*x^2+d^2)^p/(e*x+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{p} x^{2}}{e^{2} x^{2} + 2 \, d e x + d^{2}}, x\right)"," ",0,"integral((-e^2*x^2 + d^2)^p*x^2/(e^2*x^2 + 2*d*e*x + d^2), x)","F",0
279,0,0,0,0.418903," ","integrate(x*(-e^2*x^2+d^2)^p/(e*x+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{p} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}, x\right)"," ",0,"integral((-e^2*x^2 + d^2)^p*x/(e^2*x^2 + 2*d*e*x + d^2), x)","F",0
280,0,0,0,0.417311," ","integrate((-e^2*x^2+d^2)^p/(e*x+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{p}}{e^{2} x^{2} + 2 \, d e x + d^{2}}, x\right)"," ",0,"integral((-e^2*x^2 + d^2)^p/(e^2*x^2 + 2*d*e*x + d^2), x)","F",0
281,0,0,0,0.423326," ","integrate((-e^2*x^2+d^2)^p/x/(e*x+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{p}}{e^{2} x^{3} + 2 \, d e x^{2} + d^{2} x}, x\right)"," ",0,"integral((-e^2*x^2 + d^2)^p/(e^2*x^3 + 2*d*e*x^2 + d^2*x), x)","F",0
282,0,0,0,0.424814," ","integrate((-e^2*x^2+d^2)^p/x^2/(e*x+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{p}}{e^{2} x^{4} + 2 \, d e x^{3} + d^{2} x^{2}}, x\right)"," ",0,"integral((-e^2*x^2 + d^2)^p/(e^2*x^4 + 2*d*e*x^3 + d^2*x^2), x)","F",0
283,0,0,0,0.409383," ","integrate((-e^2*x^2+d^2)^p/x^3/(e*x+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{p}}{e^{2} x^{5} + 2 \, d e x^{4} + d^{2} x^{3}}, x\right)"," ",0,"integral((-e^2*x^2 + d^2)^p/(e^2*x^5 + 2*d*e*x^4 + d^2*x^3), x)","F",0
284,0,0,0,0.407700," ","integrate((-e^2*x^2+d^2)^p/x^4/(e*x+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{p}}{e^{2} x^{6} + 2 \, d e x^{5} + d^{2} x^{4}}, x\right)"," ",0,"integral((-e^2*x^2 + d^2)^p/(e^2*x^6 + 2*d*e*x^5 + d^2*x^4), x)","F",0
285,0,0,0,0.420820," ","integrate((-e^2*x^2+d^2)^p/x^5/(e*x+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{p}}{e^{2} x^{7} + 2 \, d e x^{6} + d^{2} x^{5}}, x\right)"," ",0,"integral((-e^2*x^2 + d^2)^p/(e^2*x^7 + 2*d*e*x^6 + d^2*x^5), x)","F",0
286,0,0,0,0.420163," ","integrate(x^4*(-e^2*x^2+d^2)^p/(e*x+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{p} x^{4}}{e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}}, x\right)"," ",0,"integral((-e^2*x^2 + d^2)^p*x^4/(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3), x)","F",0
287,0,0,0,0.419025," ","integrate(x^3*(-e^2*x^2+d^2)^p/(e*x+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{p} x^{3}}{e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}}, x\right)"," ",0,"integral((-e^2*x^2 + d^2)^p*x^3/(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3), x)","F",0
288,0,0,0,0.417873," ","integrate(x^2*(-e^2*x^2+d^2)^p/(e*x+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{p} x^{2}}{e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}}, x\right)"," ",0,"integral((-e^2*x^2 + d^2)^p*x^2/(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3), x)","F",0
289,0,0,0,0.419490," ","integrate(x*(-e^2*x^2+d^2)^p/(e*x+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{p} x}{e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}}, x\right)"," ",0,"integral((-e^2*x^2 + d^2)^p*x/(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3), x)","F",0
290,0,0,0,0.424213," ","integrate((-e^2*x^2+d^2)^p/(e*x+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{p}}{e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}}, x\right)"," ",0,"integral((-e^2*x^2 + d^2)^p/(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3), x)","F",0
291,0,0,0,0.421583," ","integrate((-e^2*x^2+d^2)^p/x/(e*x+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{p}}{e^{3} x^{4} + 3 \, d e^{2} x^{3} + 3 \, d^{2} e x^{2} + d^{3} x}, x\right)"," ",0,"integral((-e^2*x^2 + d^2)^p/(e^3*x^4 + 3*d*e^2*x^3 + 3*d^2*e*x^2 + d^3*x), x)","F",0
292,0,0,0,0.421735," ","integrate((-e^2*x^2+d^2)^p/x^2/(e*x+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{p}}{e^{3} x^{5} + 3 \, d e^{2} x^{4} + 3 \, d^{2} e x^{3} + d^{3} x^{2}}, x\right)"," ",0,"integral((-e^2*x^2 + d^2)^p/(e^3*x^5 + 3*d*e^2*x^4 + 3*d^2*e*x^3 + d^3*x^2), x)","F",0
293,0,0,0,0.422554," ","integrate((-e^2*x^2+d^2)^p/x^3/(e*x+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{p}}{e^{3} x^{6} + 3 \, d e^{2} x^{5} + 3 \, d^{2} e x^{4} + d^{3} x^{3}}, x\right)"," ",0,"integral((-e^2*x^2 + d^2)^p/(e^3*x^6 + 3*d*e^2*x^5 + 3*d^2*e*x^4 + d^3*x^3), x)","F",0
294,0,0,0,0.420364," ","integrate((-e^2*x^2+d^2)^p/x^4/(e*x+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{p}}{e^{3} x^{7} + 3 \, d e^{2} x^{6} + 3 \, d^{2} e x^{5} + d^{3} x^{4}}, x\right)"," ",0,"integral((-e^2*x^2 + d^2)^p/(e^3*x^7 + 3*d*e^2*x^6 + 3*d^2*e*x^5 + d^3*x^4), x)","F",0
295,0,0,0,0.422645," ","integrate((-e^2*x^2+d^2)^p/x^5/(e*x+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{p}}{e^{3} x^{8} + 3 \, d e^{2} x^{7} + 3 \, d^{2} e x^{6} + d^{3} x^{5}}, x\right)"," ",0,"integral((-e^2*x^2 + d^2)^p/(e^3*x^8 + 3*d*e^2*x^7 + 3*d^2*e*x^6 + d^3*x^5), x)","F",0
296,0,0,0,0.414361," ","integrate(x^4*(-e^2*x^2+d^2)^p/(e*x+d)^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{p} x^{4}}{e^{4} x^{4} + 4 \, d e^{3} x^{3} + 6 \, d^{2} e^{2} x^{2} + 4 \, d^{3} e x + d^{4}}, x\right)"," ",0,"integral((-e^2*x^2 + d^2)^p*x^4/(e^4*x^4 + 4*d*e^3*x^3 + 6*d^2*e^2*x^2 + 4*d^3*e*x + d^4), x)","F",0
297,0,0,0,0.413844," ","integrate(x^3*(-e^2*x^2+d^2)^p/(e*x+d)^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{p} x^{3}}{e^{4} x^{4} + 4 \, d e^{3} x^{3} + 6 \, d^{2} e^{2} x^{2} + 4 \, d^{3} e x + d^{4}}, x\right)"," ",0,"integral((-e^2*x^2 + d^2)^p*x^3/(e^4*x^4 + 4*d*e^3*x^3 + 6*d^2*e^2*x^2 + 4*d^3*e*x + d^4), x)","F",0
298,0,0,0,0.411955," ","integrate(x^2*(-e^2*x^2+d^2)^p/(e*x+d)^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{p} x^{2}}{e^{4} x^{4} + 4 \, d e^{3} x^{3} + 6 \, d^{2} e^{2} x^{2} + 4 \, d^{3} e x + d^{4}}, x\right)"," ",0,"integral((-e^2*x^2 + d^2)^p*x^2/(e^4*x^4 + 4*d*e^3*x^3 + 6*d^2*e^2*x^2 + 4*d^3*e*x + d^4), x)","F",0
299,0,0,0,0.418224," ","integrate(x*(-e^2*x^2+d^2)^p/(e*x+d)^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{p} x}{e^{4} x^{4} + 4 \, d e^{3} x^{3} + 6 \, d^{2} e^{2} x^{2} + 4 \, d^{3} e x + d^{4}}, x\right)"," ",0,"integral((-e^2*x^2 + d^2)^p*x/(e^4*x^4 + 4*d*e^3*x^3 + 6*d^2*e^2*x^2 + 4*d^3*e*x + d^4), x)","F",0
300,0,0,0,0.416477," ","integrate((-e^2*x^2+d^2)^p/(e*x+d)^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{p}}{e^{4} x^{4} + 4 \, d e^{3} x^{3} + 6 \, d^{2} e^{2} x^{2} + 4 \, d^{3} e x + d^{4}}, x\right)"," ",0,"integral((-e^2*x^2 + d^2)^p/(e^4*x^4 + 4*d*e^3*x^3 + 6*d^2*e^2*x^2 + 4*d^3*e*x + d^4), x)","F",0
301,0,0,0,0.411759," ","integrate((-e^2*x^2+d^2)^p/x/(e*x+d)^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{p}}{e^{4} x^{5} + 4 \, d e^{3} x^{4} + 6 \, d^{2} e^{2} x^{3} + 4 \, d^{3} e x^{2} + d^{4} x}, x\right)"," ",0,"integral((-e^2*x^2 + d^2)^p/(e^4*x^5 + 4*d*e^3*x^4 + 6*d^2*e^2*x^3 + 4*d^3*e*x^2 + d^4*x), x)","F",0
302,0,0,0,0.421714," ","integrate((-e^2*x^2+d^2)^p/x^2/(e*x+d)^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{p}}{e^{4} x^{6} + 4 \, d e^{3} x^{5} + 6 \, d^{2} e^{2} x^{4} + 4 \, d^{3} e x^{3} + d^{4} x^{2}}, x\right)"," ",0,"integral((-e^2*x^2 + d^2)^p/(e^4*x^6 + 4*d*e^3*x^5 + 6*d^2*e^2*x^4 + 4*d^3*e*x^3 + d^4*x^2), x)","F",0
303,0,0,0,0.419952," ","integrate((-e^2*x^2+d^2)^p/x^3/(e*x+d)^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{p}}{e^{4} x^{7} + 4 \, d e^{3} x^{6} + 6 \, d^{2} e^{2} x^{5} + 4 \, d^{3} e x^{4} + d^{4} x^{3}}, x\right)"," ",0,"integral((-e^2*x^2 + d^2)^p/(e^4*x^7 + 4*d*e^3*x^6 + 6*d^2*e^2*x^5 + 4*d^3*e*x^4 + d^4*x^3), x)","F",0
304,0,0,0,0.424546," ","integrate((-e^2*x^2+d^2)^p/x^4/(e*x+d)^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{p}}{e^{4} x^{8} + 4 \, d e^{3} x^{7} + 6 \, d^{2} e^{2} x^{6} + 4 \, d^{3} e x^{5} + d^{4} x^{4}}, x\right)"," ",0,"integral((-e^2*x^2 + d^2)^p/(e^4*x^8 + 4*d*e^3*x^7 + 6*d^2*e^2*x^6 + 4*d^3*e*x^5 + d^4*x^4), x)","F",0
305,0,0,0,0.412893," ","integrate((-e^2*x^2+d^2)^p/x^5/(e*x+d)^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{p}}{e^{4} x^{9} + 4 \, d e^{3} x^{8} + 6 \, d^{2} e^{2} x^{7} + 4 \, d^{3} e x^{6} + d^{4} x^{5}}, x\right)"," ",0,"integral((-e^2*x^2 + d^2)^p/(e^4*x^9 + 4*d*e^3*x^8 + 6*d^2*e^2*x^7 + 4*d^3*e*x^6 + d^4*x^5), x)","F",0
306,0,0,0,0.422034," ","integrate((g*x)^m*(e*x+d)^3*(-e^2*x^2+d^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}\right)} {\left(-e^{2} x^{2} + d^{2}\right)}^{p} \left(g x\right)^{m}, x\right)"," ",0,"integral((e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)*(-e^2*x^2 + d^2)^p*(g*x)^m, x)","F",0
307,0,0,0,0.430375," ","integrate((g*x)^m*(e*x+d)^2*(-e^2*x^2+d^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{2} x^{2} + 2 \, d e x + d^{2}\right)} {\left(-e^{2} x^{2} + d^{2}\right)}^{p} \left(g x\right)^{m}, x\right)"," ",0,"integral((e^2*x^2 + 2*d*e*x + d^2)*(-e^2*x^2 + d^2)^p*(g*x)^m, x)","F",0
308,0,0,0,0.421387," ","integrate((g*x)^m*(e*x+d)*(-e^2*x^2+d^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e x + d\right)} {\left(-e^{2} x^{2} + d^{2}\right)}^{p} \left(g x\right)^{m}, x\right)"," ",0,"integral((e*x + d)*(-e^2*x^2 + d^2)^p*(g*x)^m, x)","F",0
309,0,0,0,0.423908," ","integrate((g*x)^m*(-e^2*x^2+d^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(-e^{2} x^{2} + d^{2}\right)}^{p} \left(g x\right)^{m}, x\right)"," ",0,"integral((-e^2*x^2 + d^2)^p*(g*x)^m, x)","F",0
310,0,0,0,0.423650," ","integrate((g*x)^m*(-e^2*x^2+d^2)^p/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{p} \left(g x\right)^{m}}{e x + d}, x\right)"," ",0,"integral((-e^2*x^2 + d^2)^p*(g*x)^m/(e*x + d), x)","F",0
311,0,0,0,0.428826," ","integrate((g*x)^m*(-e^2*x^2+d^2)^p/(e*x+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{p} \left(g x\right)^{m}}{e^{2} x^{2} + 2 \, d e x + d^{2}}, x\right)"," ",0,"integral((-e^2*x^2 + d^2)^p*(g*x)^m/(e^2*x^2 + 2*d*e*x + d^2), x)","F",0
312,0,0,0,0.432979," ","integrate((g*x)^m*(-e^2*x^2+d^2)^p/(e*x+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{p} \left(g x\right)^{m}}{e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}}, x\right)"," ",0,"integral((-e^2*x^2 + d^2)^p*(g*x)^m/(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3), x)","F",0
313,0,0,0,0.418945," ","integrate((g*x)^m*(-a^2*x^2+1)^p/(a*x+1),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-a^{2} x^{2} + 1\right)}^{p} \left(g x\right)^{m}}{a x + 1}, x\right)"," ",0,"integral((-a^2*x^2 + 1)^p*(g*x)^m/(a*x + 1), x)","F",0
314,0,0,0,0.429555," ","integrate((g*x)^m*(e*x+d)^n*(-e^2*x^2+d^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(-e^{2} x^{2} + d^{2}\right)}^{p} {\left(e x + d\right)}^{n} \left(g x\right)^{m}, x\right)"," ",0,"integral((-e^2*x^2 + d^2)^p*(e*x + d)^n*(g*x)^m, x)","F",0
315,1,307,0,0.420416," ","integrate(x*(1+x)^(1/2)/(x^2+1),x, algorithm=""fricas"")","-\frac{1}{8} \cdot 2^{\frac{1}{4}} {\left(\sqrt{2} + 2\right)} \sqrt{-2 \, \sqrt{2} + 4} \log\left(\frac{1}{2} \cdot 2^{\frac{1}{4}} \sqrt{x + 1} {\left(\sqrt{2} + 2\right)} \sqrt{-2 \, \sqrt{2} + 4} + x + \sqrt{2} + 1\right) + \frac{1}{8} \cdot 2^{\frac{1}{4}} {\left(\sqrt{2} + 2\right)} \sqrt{-2 \, \sqrt{2} + 4} \log\left(-\frac{1}{2} \cdot 2^{\frac{1}{4}} \sqrt{x + 1} {\left(\sqrt{2} + 2\right)} \sqrt{-2 \, \sqrt{2} + 4} + x + \sqrt{2} + 1\right) + \frac{1}{2} \cdot 2^{\frac{3}{4}} \sqrt{-2 \, \sqrt{2} + 4} \arctan\left(\frac{1}{4} \cdot 2^{\frac{3}{4}} \sqrt{2^{\frac{1}{4}} \sqrt{x + 1} {\left(\sqrt{2} + 2\right)} \sqrt{-2 \, \sqrt{2} + 4} + 2 \, x + 2 \, \sqrt{2} + 2} {\left(\sqrt{2} + 2\right)} \sqrt{-2 \, \sqrt{2} + 4} - \frac{1}{2} \cdot 2^{\frac{3}{4}} \sqrt{x + 1} {\left(\sqrt{2} + 1\right)} \sqrt{-2 \, \sqrt{2} + 4} - \sqrt{2} - 1\right) + \frac{1}{2} \cdot 2^{\frac{3}{4}} \sqrt{-2 \, \sqrt{2} + 4} \arctan\left(\frac{1}{4} \cdot 2^{\frac{3}{4}} \sqrt{-2^{\frac{1}{4}} \sqrt{x + 1} {\left(\sqrt{2} + 2\right)} \sqrt{-2 \, \sqrt{2} + 4} + 2 \, x + 2 \, \sqrt{2} + 2} {\left(\sqrt{2} + 2\right)} \sqrt{-2 \, \sqrt{2} + 4} - \frac{1}{2} \cdot 2^{\frac{3}{4}} \sqrt{x + 1} {\left(\sqrt{2} + 1\right)} \sqrt{-2 \, \sqrt{2} + 4} + \sqrt{2} + 1\right) + 2 \, \sqrt{x + 1}"," ",0,"-1/8*2^(1/4)*(sqrt(2) + 2)*sqrt(-2*sqrt(2) + 4)*log(1/2*2^(1/4)*sqrt(x + 1)*(sqrt(2) + 2)*sqrt(-2*sqrt(2) + 4) + x + sqrt(2) + 1) + 1/8*2^(1/4)*(sqrt(2) + 2)*sqrt(-2*sqrt(2) + 4)*log(-1/2*2^(1/4)*sqrt(x + 1)*(sqrt(2) + 2)*sqrt(-2*sqrt(2) + 4) + x + sqrt(2) + 1) + 1/2*2^(3/4)*sqrt(-2*sqrt(2) + 4)*arctan(1/4*2^(3/4)*sqrt(2^(1/4)*sqrt(x + 1)*(sqrt(2) + 2)*sqrt(-2*sqrt(2) + 4) + 2*x + 2*sqrt(2) + 2)*(sqrt(2) + 2)*sqrt(-2*sqrt(2) + 4) - 1/2*2^(3/4)*sqrt(x + 1)*(sqrt(2) + 1)*sqrt(-2*sqrt(2) + 4) - sqrt(2) - 1) + 1/2*2^(3/4)*sqrt(-2*sqrt(2) + 4)*arctan(1/4*2^(3/4)*sqrt(-2^(1/4)*sqrt(x + 1)*(sqrt(2) + 2)*sqrt(-2*sqrt(2) + 4) + 2*x + 2*sqrt(2) + 2)*(sqrt(2) + 2)*sqrt(-2*sqrt(2) + 4) - 1/2*2^(3/4)*sqrt(x + 1)*(sqrt(2) + 1)*sqrt(-2*sqrt(2) + 4) + sqrt(2) + 1) + 2*sqrt(x + 1)","A",0
316,1,1104,0,6.899928," ","integrate(x^4*(c*x^2+a)^(1/2)/(e*x+d),x, algorithm=""fricas"")","\left[\frac{120 \, \sqrt{c d^{2} + a e^{2}} c^{2} d^{4} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 15 \, {\left(8 \, c^{2} d^{5} + 4 \, a c d^{3} e^{2} - a^{2} d e^{4}\right)} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(24 \, c^{2} e^{5} x^{4} - 30 \, c^{2} d e^{4} x^{3} + 120 \, c^{2} d^{4} e + 40 \, a c d^{2} e^{3} - 16 \, a^{2} e^{5} + 8 \, {\left(5 \, c^{2} d^{2} e^{3} + a c e^{5}\right)} x^{2} - 15 \, {\left(4 \, c^{2} d^{3} e^{2} + a c d e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{240 \, c^{2} e^{6}}, -\frac{240 \, \sqrt{-c d^{2} - a e^{2}} c^{2} d^{4} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) + 15 \, {\left(8 \, c^{2} d^{5} + 4 \, a c d^{3} e^{2} - a^{2} d e^{4}\right)} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) - 2 \, {\left(24 \, c^{2} e^{5} x^{4} - 30 \, c^{2} d e^{4} x^{3} + 120 \, c^{2} d^{4} e + 40 \, a c d^{2} e^{3} - 16 \, a^{2} e^{5} + 8 \, {\left(5 \, c^{2} d^{2} e^{3} + a c e^{5}\right)} x^{2} - 15 \, {\left(4 \, c^{2} d^{3} e^{2} + a c d e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{240 \, c^{2} e^{6}}, \frac{60 \, \sqrt{c d^{2} + a e^{2}} c^{2} d^{4} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 15 \, {\left(8 \, c^{2} d^{5} + 4 \, a c d^{3} e^{2} - a^{2} d e^{4}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) + {\left(24 \, c^{2} e^{5} x^{4} - 30 \, c^{2} d e^{4} x^{3} + 120 \, c^{2} d^{4} e + 40 \, a c d^{2} e^{3} - 16 \, a^{2} e^{5} + 8 \, {\left(5 \, c^{2} d^{2} e^{3} + a c e^{5}\right)} x^{2} - 15 \, {\left(4 \, c^{2} d^{3} e^{2} + a c d e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{120 \, c^{2} e^{6}}, -\frac{120 \, \sqrt{-c d^{2} - a e^{2}} c^{2} d^{4} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - 15 \, {\left(8 \, c^{2} d^{5} + 4 \, a c d^{3} e^{2} - a^{2} d e^{4}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(24 \, c^{2} e^{5} x^{4} - 30 \, c^{2} d e^{4} x^{3} + 120 \, c^{2} d^{4} e + 40 \, a c d^{2} e^{3} - 16 \, a^{2} e^{5} + 8 \, {\left(5 \, c^{2} d^{2} e^{3} + a c e^{5}\right)} x^{2} - 15 \, {\left(4 \, c^{2} d^{3} e^{2} + a c d e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{120 \, c^{2} e^{6}}\right]"," ",0,"[1/240*(120*sqrt(c*d^2 + a*e^2)*c^2*d^4*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) - 15*(8*c^2*d^5 + 4*a*c*d^3*e^2 - a^2*d*e^4)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(24*c^2*e^5*x^4 - 30*c^2*d*e^4*x^3 + 120*c^2*d^4*e + 40*a*c*d^2*e^3 - 16*a^2*e^5 + 8*(5*c^2*d^2*e^3 + a*c*e^5)*x^2 - 15*(4*c^2*d^3*e^2 + a*c*d*e^4)*x)*sqrt(c*x^2 + a))/(c^2*e^6), -1/240*(240*sqrt(-c*d^2 - a*e^2)*c^2*d^4*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) + 15*(8*c^2*d^5 + 4*a*c*d^3*e^2 - a^2*d*e^4)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) - 2*(24*c^2*e^5*x^4 - 30*c^2*d*e^4*x^3 + 120*c^2*d^4*e + 40*a*c*d^2*e^3 - 16*a^2*e^5 + 8*(5*c^2*d^2*e^3 + a*c*e^5)*x^2 - 15*(4*c^2*d^3*e^2 + a*c*d*e^4)*x)*sqrt(c*x^2 + a))/(c^2*e^6), 1/120*(60*sqrt(c*d^2 + a*e^2)*c^2*d^4*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + 15*(8*c^2*d^5 + 4*a*c*d^3*e^2 - a^2*d*e^4)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) + (24*c^2*e^5*x^4 - 30*c^2*d*e^4*x^3 + 120*c^2*d^4*e + 40*a*c*d^2*e^3 - 16*a^2*e^5 + 8*(5*c^2*d^2*e^3 + a*c*e^5)*x^2 - 15*(4*c^2*d^3*e^2 + a*c*d*e^4)*x)*sqrt(c*x^2 + a))/(c^2*e^6), -1/120*(120*sqrt(-c*d^2 - a*e^2)*c^2*d^4*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - 15*(8*c^2*d^5 + 4*a*c*d^3*e^2 - a^2*d*e^4)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (24*c^2*e^5*x^4 - 30*c^2*d*e^4*x^3 + 120*c^2*d^4*e + 40*a*c*d^2*e^3 - 16*a^2*e^5 + 8*(5*c^2*d^2*e^3 + a*c*e^5)*x^2 - 15*(4*c^2*d^3*e^2 + a*c*d*e^4)*x)*sqrt(c*x^2 + a))/(c^2*e^6)]","A",0
317,1,963,0,7.039239," ","integrate(x^3*(c*x^2+a)^(1/2)/(e*x+d),x, algorithm=""fricas"")","\left[\frac{24 \, \sqrt{c d^{2} + a e^{2}} c^{2} d^{3} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 3 \, {\left(8 \, c^{2} d^{4} + 4 \, a c d^{2} e^{2} - a^{2} e^{4}\right)} \sqrt{c} \log\left(-2 \, c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(6 \, c^{2} e^{4} x^{3} - 8 \, c^{2} d e^{3} x^{2} - 24 \, c^{2} d^{3} e - 8 \, a c d e^{3} + 3 \, {\left(4 \, c^{2} d^{2} e^{2} + a c e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{48 \, c^{2} e^{5}}, \frac{48 \, \sqrt{-c d^{2} - a e^{2}} c^{2} d^{3} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - 3 \, {\left(8 \, c^{2} d^{4} + 4 \, a c d^{2} e^{2} - a^{2} e^{4}\right)} \sqrt{c} \log\left(-2 \, c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(6 \, c^{2} e^{4} x^{3} - 8 \, c^{2} d e^{3} x^{2} - 24 \, c^{2} d^{3} e - 8 \, a c d e^{3} + 3 \, {\left(4 \, c^{2} d^{2} e^{2} + a c e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{48 \, c^{2} e^{5}}, \frac{12 \, \sqrt{c d^{2} + a e^{2}} c^{2} d^{3} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 3 \, {\left(8 \, c^{2} d^{4} + 4 \, a c d^{2} e^{2} - a^{2} e^{4}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) + {\left(6 \, c^{2} e^{4} x^{3} - 8 \, c^{2} d e^{3} x^{2} - 24 \, c^{2} d^{3} e - 8 \, a c d e^{3} + 3 \, {\left(4 \, c^{2} d^{2} e^{2} + a c e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{24 \, c^{2} e^{5}}, \frac{24 \, \sqrt{-c d^{2} - a e^{2}} c^{2} d^{3} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - 3 \, {\left(8 \, c^{2} d^{4} + 4 \, a c d^{2} e^{2} - a^{2} e^{4}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) + {\left(6 \, c^{2} e^{4} x^{3} - 8 \, c^{2} d e^{3} x^{2} - 24 \, c^{2} d^{3} e - 8 \, a c d e^{3} + 3 \, {\left(4 \, c^{2} d^{2} e^{2} + a c e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{24 \, c^{2} e^{5}}\right]"," ",0,"[1/48*(24*sqrt(c*d^2 + a*e^2)*c^2*d^3*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 + 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) - 3*(8*c^2*d^4 + 4*a*c*d^2*e^2 - a^2*e^4)*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(6*c^2*e^4*x^3 - 8*c^2*d*e^3*x^2 - 24*c^2*d^3*e - 8*a*c*d*e^3 + 3*(4*c^2*d^2*e^2 + a*c*e^4)*x)*sqrt(c*x^2 + a))/(c^2*e^5), 1/48*(48*sqrt(-c*d^2 - a*e^2)*c^2*d^3*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - 3*(8*c^2*d^4 + 4*a*c*d^2*e^2 - a^2*e^4)*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(6*c^2*e^4*x^3 - 8*c^2*d*e^3*x^2 - 24*c^2*d^3*e - 8*a*c*d*e^3 + 3*(4*c^2*d^2*e^2 + a*c*e^4)*x)*sqrt(c*x^2 + a))/(c^2*e^5), 1/24*(12*sqrt(c*d^2 + a*e^2)*c^2*d^3*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 + 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) - 3*(8*c^2*d^4 + 4*a*c*d^2*e^2 - a^2*e^4)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) + (6*c^2*e^4*x^3 - 8*c^2*d*e^3*x^2 - 24*c^2*d^3*e - 8*a*c*d*e^3 + 3*(4*c^2*d^2*e^2 + a*c*e^4)*x)*sqrt(c*x^2 + a))/(c^2*e^5), 1/24*(24*sqrt(-c*d^2 - a*e^2)*c^2*d^3*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - 3*(8*c^2*d^4 + 4*a*c*d^2*e^2 - a^2*e^4)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) + (6*c^2*e^4*x^3 - 8*c^2*d*e^3*x^2 - 24*c^2*d^3*e - 8*a*c*d*e^3 + 3*(4*c^2*d^2*e^2 + a*c*e^4)*x)*sqrt(c*x^2 + a))/(c^2*e^5)]","A",0
318,1,776,0,0.689019," ","integrate(x^2*(c*x^2+a)^(1/2)/(e*x+d),x, algorithm=""fricas"")","\left[\frac{6 \, \sqrt{c d^{2} + a e^{2}} c d^{2} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 3 \, {\left(2 \, c d^{3} + a d e^{2}\right)} \sqrt{c} \log\left(-2 \, c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(2 \, c e^{3} x^{2} - 3 \, c d e^{2} x + 6 \, c d^{2} e + 2 \, a e^{3}\right)} \sqrt{c x^{2} + a}}{12 \, c e^{4}}, -\frac{12 \, \sqrt{-c d^{2} - a e^{2}} c d^{2} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - 3 \, {\left(2 \, c d^{3} + a d e^{2}\right)} \sqrt{c} \log\left(-2 \, c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) - 2 \, {\left(2 \, c e^{3} x^{2} - 3 \, c d e^{2} x + 6 \, c d^{2} e + 2 \, a e^{3}\right)} \sqrt{c x^{2} + a}}{12 \, c e^{4}}, \frac{3 \, \sqrt{c d^{2} + a e^{2}} c d^{2} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 3 \, {\left(2 \, c d^{3} + a d e^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) + {\left(2 \, c e^{3} x^{2} - 3 \, c d e^{2} x + 6 \, c d^{2} e + 2 \, a e^{3}\right)} \sqrt{c x^{2} + a}}{6 \, c e^{4}}, -\frac{6 \, \sqrt{-c d^{2} - a e^{2}} c d^{2} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - 3 \, {\left(2 \, c d^{3} + a d e^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(2 \, c e^{3} x^{2} - 3 \, c d e^{2} x + 6 \, c d^{2} e + 2 \, a e^{3}\right)} \sqrt{c x^{2} + a}}{6 \, c e^{4}}\right]"," ",0,"[1/12*(6*sqrt(c*d^2 + a*e^2)*c*d^2*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + 3*(2*c*d^3 + a*d*e^2)*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(2*c*e^3*x^2 - 3*c*d*e^2*x + 6*c*d^2*e + 2*a*e^3)*sqrt(c*x^2 + a))/(c*e^4), -1/12*(12*sqrt(-c*d^2 - a*e^2)*c*d^2*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - 3*(2*c*d^3 + a*d*e^2)*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) - 2*(2*c*e^3*x^2 - 3*c*d*e^2*x + 6*c*d^2*e + 2*a*e^3)*sqrt(c*x^2 + a))/(c*e^4), 1/6*(3*sqrt(c*d^2 + a*e^2)*c*d^2*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + 3*(2*c*d^3 + a*d*e^2)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) + (2*c*e^3*x^2 - 3*c*d*e^2*x + 6*c*d^2*e + 2*a*e^3)*sqrt(c*x^2 + a))/(c*e^4), -1/6*(6*sqrt(-c*d^2 - a*e^2)*c*d^2*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - 3*(2*c*d^3 + a*d*e^2)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (2*c*e^3*x^2 - 3*c*d*e^2*x + 6*c*d^2*e + 2*a*e^3)*sqrt(c*x^2 + a))/(c*e^4)]","A",0
319,1,684,0,0.675653," ","integrate(x*(c*x^2+a)^(1/2)/(e*x+d),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{c d^{2} + a e^{2}} c d \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + {\left(2 \, c d^{2} + a e^{2}\right)} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(c e^{2} x - 2 \, c d e\right)} \sqrt{c x^{2} + a}}{4 \, c e^{3}}, \frac{4 \, \sqrt{-c d^{2} - a e^{2}} c d \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) + {\left(2 \, c d^{2} + a e^{2}\right)} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(c e^{2} x - 2 \, c d e\right)} \sqrt{c x^{2} + a}}{4 \, c e^{3}}, \frac{\sqrt{c d^{2} + a e^{2}} c d \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - {\left(2 \, c d^{2} + a e^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) + {\left(c e^{2} x - 2 \, c d e\right)} \sqrt{c x^{2} + a}}{2 \, c e^{3}}, \frac{2 \, \sqrt{-c d^{2} - a e^{2}} c d \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - {\left(2 \, c d^{2} + a e^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) + {\left(c e^{2} x - 2 \, c d e\right)} \sqrt{c x^{2} + a}}{2 \, c e^{3}}\right]"," ",0,"[1/4*(2*sqrt(c*d^2 + a*e^2)*c*d*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 + 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + (2*c*d^2 + a*e^2)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(c*e^2*x - 2*c*d*e)*sqrt(c*x^2 + a))/(c*e^3), 1/4*(4*sqrt(-c*d^2 - a*e^2)*c*d*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) + (2*c*d^2 + a*e^2)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(c*e^2*x - 2*c*d*e)*sqrt(c*x^2 + a))/(c*e^3), 1/2*(sqrt(c*d^2 + a*e^2)*c*d*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 + 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) - (2*c*d^2 + a*e^2)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) + (c*e^2*x - 2*c*d*e)*sqrt(c*x^2 + a))/(c*e^3), 1/2*(2*sqrt(-c*d^2 - a*e^2)*c*d*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - (2*c*d^2 + a*e^2)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) + (c*e^2*x - 2*c*d*e)*sqrt(c*x^2 + a))/(c*e^3)]","A",0
320,1,574,0,0.510167," ","integrate((c*x^2+a)^(1/2)/(e*x+d),x, algorithm=""fricas"")","\left[\frac{\sqrt{c} d \log\left(-2 \, c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, \sqrt{c x^{2} + a} e + \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right)}{2 \, e^{2}}, \frac{2 \, \sqrt{-c} d \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) + 2 \, \sqrt{c x^{2} + a} e + \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right)}{2 \, e^{2}}, \frac{\sqrt{c} d \log\left(-2 \, c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, \sqrt{c x^{2} + a} e - 2 \, \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right)}{2 \, e^{2}}, \frac{\sqrt{-c} d \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) + \sqrt{c x^{2} + a} e - \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right)}{e^{2}}\right]"," ",0,"[1/2*(sqrt(c)*d*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*sqrt(c*x^2 + a)*e + sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)))/e^2, 1/2*(2*sqrt(-c)*d*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) + 2*sqrt(c*x^2 + a)*e + sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)))/e^2, 1/2*(sqrt(c)*d*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*sqrt(c*x^2 + a)*e - 2*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)))/e^2, (sqrt(-c)*d*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) + sqrt(c*x^2 + a)*e - sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)))/e^2]","A",0
321,1,1316,0,1.150295," ","integrate((c*x^2+a)^(1/2)/x/(e*x+d),x, algorithm=""fricas"")","\left[\frac{\sqrt{c} d \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + \sqrt{a} e \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right)}{2 \, d e}, -\frac{2 \, \sqrt{-c} d \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - \sqrt{a} e \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right)}{2 \, d e}, \frac{\sqrt{c} d \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + \sqrt{a} e \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right)}{2 \, d e}, -\frac{2 \, \sqrt{-c} d \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - \sqrt{a} e \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - 2 \, \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right)}{2 \, d e}, \frac{2 \, \sqrt{-a} e \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) + \sqrt{c} d \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right)}{2 \, d e}, -\frac{2 \, \sqrt{-c} d \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - 2 \, \sqrt{-a} e \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) - \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right)}{2 \, d e}, \frac{2 \, \sqrt{-a} e \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) + \sqrt{c} d \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right)}{2 \, d e}, -\frac{\sqrt{-c} d \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - \sqrt{-a} e \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) - \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right)}{d e}\right]"," ",0,"[1/2*(sqrt(c)*d*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + sqrt(a)*e*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) + sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 + 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)))/(d*e), -1/2*(2*sqrt(-c)*d*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - sqrt(a)*e*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) - sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 + 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)))/(d*e), 1/2*(sqrt(c)*d*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + sqrt(a)*e*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)))/(d*e), -1/2*(2*sqrt(-c)*d*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - sqrt(a)*e*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) - 2*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)))/(d*e), 1/2*(2*sqrt(-a)*e*arctan(sqrt(-a)/sqrt(c*x^2 + a)) + sqrt(c)*d*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 + 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)))/(d*e), -1/2*(2*sqrt(-c)*d*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - 2*sqrt(-a)*e*arctan(sqrt(-a)/sqrt(c*x^2 + a)) - sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 + 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)))/(d*e), 1/2*(2*sqrt(-a)*e*arctan(sqrt(-a)/sqrt(c*x^2 + a)) + sqrt(c)*d*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)))/(d*e), -(sqrt(-c)*d*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - sqrt(-a)*e*arctan(sqrt(-a)/sqrt(c*x^2 + a)) - sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)))/(d*e)]","A",0
322,1,599,0,0.481084," ","integrate((c*x^2+a)^(1/2)/x^2/(e*x+d),x, algorithm=""fricas"")","\left[\frac{\sqrt{a} e x \log\left(-\frac{c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + \sqrt{c d^{2} + a e^{2}} x \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 2 \, \sqrt{c x^{2} + a} d}{2 \, d^{2} x}, \frac{\sqrt{a} e x \log\left(-\frac{c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - 2 \, \sqrt{-c d^{2} - a e^{2}} x \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - 2 \, \sqrt{c x^{2} + a} d}{2 \, d^{2} x}, -\frac{2 \, \sqrt{-a} e x \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) - \sqrt{c d^{2} + a e^{2}} x \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, \sqrt{c x^{2} + a} d}{2 \, d^{2} x}, -\frac{\sqrt{-a} e x \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) + \sqrt{-c d^{2} - a e^{2}} x \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) + \sqrt{c x^{2} + a} d}{d^{2} x}\right]"," ",0,"[1/2*(sqrt(a)*e*x*log(-(c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) + sqrt(c*d^2 + a*e^2)*x*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) - 2*sqrt(c*x^2 + a)*d)/(d^2*x), 1/2*(sqrt(a)*e*x*log(-(c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) - 2*sqrt(-c*d^2 - a*e^2)*x*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - 2*sqrt(c*x^2 + a)*d)/(d^2*x), -1/2*(2*sqrt(-a)*e*x*arctan(sqrt(-a)/sqrt(c*x^2 + a)) - sqrt(c*d^2 + a*e^2)*x*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*sqrt(c*x^2 + a)*d)/(d^2*x), -(sqrt(-a)*e*x*arctan(sqrt(-a)/sqrt(c*x^2 + a)) + sqrt(-c*d^2 - a*e^2)*x*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) + sqrt(c*x^2 + a)*d)/(d^2*x)]","A",0
323,1,726,0,0.488930," ","integrate((c*x^2+a)^(1/2)/x^3/(e*x+d),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{c d^{2} + a e^{2}} a e x^{2} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + {\left(c d^{2} + 2 \, a e^{2}\right)} \sqrt{a} x^{2} \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(2 \, a d e x - a d^{2}\right)} \sqrt{c x^{2} + a}}{4 \, a d^{3} x^{2}}, \frac{4 \, \sqrt{-c d^{2} - a e^{2}} a e x^{2} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) + {\left(c d^{2} + 2 \, a e^{2}\right)} \sqrt{a} x^{2} \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(2 \, a d e x - a d^{2}\right)} \sqrt{c x^{2} + a}}{4 \, a d^{3} x^{2}}, \frac{\sqrt{c d^{2} + a e^{2}} a e x^{2} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + {\left(c d^{2} + 2 \, a e^{2}\right)} \sqrt{-a} x^{2} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) + {\left(2 \, a d e x - a d^{2}\right)} \sqrt{c x^{2} + a}}{2 \, a d^{3} x^{2}}, \frac{2 \, \sqrt{-c d^{2} - a e^{2}} a e x^{2} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) + {\left(c d^{2} + 2 \, a e^{2}\right)} \sqrt{-a} x^{2} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) + {\left(2 \, a d e x - a d^{2}\right)} \sqrt{c x^{2} + a}}{2 \, a d^{3} x^{2}}\right]"," ",0,"[1/4*(2*sqrt(c*d^2 + a*e^2)*a*e*x^2*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 + 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + (c*d^2 + 2*a*e^2)*sqrt(a)*x^2*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(2*a*d*e*x - a*d^2)*sqrt(c*x^2 + a))/(a*d^3*x^2), 1/4*(4*sqrt(-c*d^2 - a*e^2)*a*e*x^2*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) + (c*d^2 + 2*a*e^2)*sqrt(a)*x^2*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(2*a*d*e*x - a*d^2)*sqrt(c*x^2 + a))/(a*d^3*x^2), 1/2*(sqrt(c*d^2 + a*e^2)*a*e*x^2*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 + 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + (c*d^2 + 2*a*e^2)*sqrt(-a)*x^2*arctan(sqrt(-a)/sqrt(c*x^2 + a)) + (2*a*d*e*x - a*d^2)*sqrt(c*x^2 + a))/(a*d^3*x^2), 1/2*(2*sqrt(-c*d^2 - a*e^2)*a*e*x^2*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) + (c*d^2 + 2*a*e^2)*sqrt(-a)*x^2*arctan(sqrt(-a)/sqrt(c*x^2 + a)) + (2*a*d*e*x - a*d^2)*sqrt(c*x^2 + a))/(a*d^3*x^2)]","A",0
324,1,824,0,0.505667," ","integrate((c*x^2+a)^(1/2)/x^4/(e*x+d),x, algorithm=""fricas"")","\left[\frac{6 \, \sqrt{c d^{2} + a e^{2}} a e^{2} x^{3} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 3 \, {\left(c d^{2} e + 2 \, a e^{3}\right)} \sqrt{a} x^{3} \log\left(-\frac{c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(3 \, a d^{2} e x - 2 \, a d^{3} - 2 \, {\left(c d^{3} + 3 \, a d e^{2}\right)} x^{2}\right)} \sqrt{c x^{2} + a}}{12 \, a d^{4} x^{3}}, -\frac{12 \, \sqrt{-c d^{2} - a e^{2}} a e^{2} x^{3} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - 3 \, {\left(c d^{2} e + 2 \, a e^{3}\right)} \sqrt{a} x^{3} \log\left(-\frac{c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - 2 \, {\left(3 \, a d^{2} e x - 2 \, a d^{3} - 2 \, {\left(c d^{3} + 3 \, a d e^{2}\right)} x^{2}\right)} \sqrt{c x^{2} + a}}{12 \, a d^{4} x^{3}}, \frac{3 \, \sqrt{c d^{2} + a e^{2}} a e^{2} x^{3} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 3 \, {\left(c d^{2} e + 2 \, a e^{3}\right)} \sqrt{-a} x^{3} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) + {\left(3 \, a d^{2} e x - 2 \, a d^{3} - 2 \, {\left(c d^{3} + 3 \, a d e^{2}\right)} x^{2}\right)} \sqrt{c x^{2} + a}}{6 \, a d^{4} x^{3}}, -\frac{6 \, \sqrt{-c d^{2} - a e^{2}} a e^{2} x^{3} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) + 3 \, {\left(c d^{2} e + 2 \, a e^{3}\right)} \sqrt{-a} x^{3} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) - {\left(3 \, a d^{2} e x - 2 \, a d^{3} - 2 \, {\left(c d^{3} + 3 \, a d e^{2}\right)} x^{2}\right)} \sqrt{c x^{2} + a}}{6 \, a d^{4} x^{3}}\right]"," ",0,"[1/12*(6*sqrt(c*d^2 + a*e^2)*a*e^2*x^3*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + 3*(c*d^2*e + 2*a*e^3)*sqrt(a)*x^3*log(-(c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(3*a*d^2*e*x - 2*a*d^3 - 2*(c*d^3 + 3*a*d*e^2)*x^2)*sqrt(c*x^2 + a))/(a*d^4*x^3), -1/12*(12*sqrt(-c*d^2 - a*e^2)*a*e^2*x^3*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - 3*(c*d^2*e + 2*a*e^3)*sqrt(a)*x^3*log(-(c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) - 2*(3*a*d^2*e*x - 2*a*d^3 - 2*(c*d^3 + 3*a*d*e^2)*x^2)*sqrt(c*x^2 + a))/(a*d^4*x^3), 1/6*(3*sqrt(c*d^2 + a*e^2)*a*e^2*x^3*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) - 3*(c*d^2*e + 2*a*e^3)*sqrt(-a)*x^3*arctan(sqrt(-a)/sqrt(c*x^2 + a)) + (3*a*d^2*e*x - 2*a*d^3 - 2*(c*d^3 + 3*a*d*e^2)*x^2)*sqrt(c*x^2 + a))/(a*d^4*x^3), -1/6*(6*sqrt(-c*d^2 - a*e^2)*a*e^2*x^3*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) + 3*(c*d^2*e + 2*a*e^3)*sqrt(-a)*x^3*arctan(sqrt(-a)/sqrt(c*x^2 + a)) - (3*a*d^2*e*x - 2*a*d^3 - 2*(c*d^3 + 3*a*d*e^2)*x^2)*sqrt(c*x^2 + a))/(a*d^4*x^3)]","A",0
325,1,1007,0,0.575391," ","integrate((c*x^2+a)^(1/2)/x^5/(e*x+d),x, algorithm=""fricas"")","\left[\frac{24 \, \sqrt{c d^{2} + a e^{2}} a^{2} e^{3} x^{4} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 3 \, {\left(c^{2} d^{4} - 4 \, a c d^{2} e^{2} - 8 \, a^{2} e^{4}\right)} \sqrt{a} x^{4} \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(8 \, a^{2} d^{3} e x - 6 \, a^{2} d^{4} + 8 \, {\left(a c d^{3} e + 3 \, a^{2} d e^{3}\right)} x^{3} - 3 \, {\left(a c d^{4} + 4 \, a^{2} d^{2} e^{2}\right)} x^{2}\right)} \sqrt{c x^{2} + a}}{48 \, a^{2} d^{5} x^{4}}, \frac{48 \, \sqrt{-c d^{2} - a e^{2}} a^{2} e^{3} x^{4} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - 3 \, {\left(c^{2} d^{4} - 4 \, a c d^{2} e^{2} - 8 \, a^{2} e^{4}\right)} \sqrt{a} x^{4} \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(8 \, a^{2} d^{3} e x - 6 \, a^{2} d^{4} + 8 \, {\left(a c d^{3} e + 3 \, a^{2} d e^{3}\right)} x^{3} - 3 \, {\left(a c d^{4} + 4 \, a^{2} d^{2} e^{2}\right)} x^{2}\right)} \sqrt{c x^{2} + a}}{48 \, a^{2} d^{5} x^{4}}, \frac{12 \, \sqrt{c d^{2} + a e^{2}} a^{2} e^{3} x^{4} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 3 \, {\left(c^{2} d^{4} - 4 \, a c d^{2} e^{2} - 8 \, a^{2} e^{4}\right)} \sqrt{-a} x^{4} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) + {\left(8 \, a^{2} d^{3} e x - 6 \, a^{2} d^{4} + 8 \, {\left(a c d^{3} e + 3 \, a^{2} d e^{3}\right)} x^{3} - 3 \, {\left(a c d^{4} + 4 \, a^{2} d^{2} e^{2}\right)} x^{2}\right)} \sqrt{c x^{2} + a}}{24 \, a^{2} d^{5} x^{4}}, \frac{24 \, \sqrt{-c d^{2} - a e^{2}} a^{2} e^{3} x^{4} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - 3 \, {\left(c^{2} d^{4} - 4 \, a c d^{2} e^{2} - 8 \, a^{2} e^{4}\right)} \sqrt{-a} x^{4} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) + {\left(8 \, a^{2} d^{3} e x - 6 \, a^{2} d^{4} + 8 \, {\left(a c d^{3} e + 3 \, a^{2} d e^{3}\right)} x^{3} - 3 \, {\left(a c d^{4} + 4 \, a^{2} d^{2} e^{2}\right)} x^{2}\right)} \sqrt{c x^{2} + a}}{24 \, a^{2} d^{5} x^{4}}\right]"," ",0,"[1/48*(24*sqrt(c*d^2 + a*e^2)*a^2*e^3*x^4*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 + 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) - 3*(c^2*d^4 - 4*a*c*d^2*e^2 - 8*a^2*e^4)*sqrt(a)*x^4*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(8*a^2*d^3*e*x - 6*a^2*d^4 + 8*(a*c*d^3*e + 3*a^2*d*e^3)*x^3 - 3*(a*c*d^4 + 4*a^2*d^2*e^2)*x^2)*sqrt(c*x^2 + a))/(a^2*d^5*x^4), 1/48*(48*sqrt(-c*d^2 - a*e^2)*a^2*e^3*x^4*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - 3*(c^2*d^4 - 4*a*c*d^2*e^2 - 8*a^2*e^4)*sqrt(a)*x^4*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(8*a^2*d^3*e*x - 6*a^2*d^4 + 8*(a*c*d^3*e + 3*a^2*d*e^3)*x^3 - 3*(a*c*d^4 + 4*a^2*d^2*e^2)*x^2)*sqrt(c*x^2 + a))/(a^2*d^5*x^4), 1/24*(12*sqrt(c*d^2 + a*e^2)*a^2*e^3*x^4*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 + 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) - 3*(c^2*d^4 - 4*a*c*d^2*e^2 - 8*a^2*e^4)*sqrt(-a)*x^4*arctan(sqrt(-a)/sqrt(c*x^2 + a)) + (8*a^2*d^3*e*x - 6*a^2*d^4 + 8*(a*c*d^3*e + 3*a^2*d*e^3)*x^3 - 3*(a*c*d^4 + 4*a^2*d^2*e^2)*x^2)*sqrt(c*x^2 + a))/(a^2*d^5*x^4), 1/24*(24*sqrt(-c*d^2 - a*e^2)*a^2*e^3*x^4*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - 3*(c^2*d^4 - 4*a*c*d^2*e^2 - 8*a^2*e^4)*sqrt(-a)*x^4*arctan(sqrt(-a)/sqrt(c*x^2 + a)) + (8*a^2*d^3*e*x - 6*a^2*d^4 + 8*(a*c*d^3*e + 3*a^2*d*e^3)*x^3 - 3*(a*c*d^4 + 4*a^2*d^2*e^2)*x^2)*sqrt(c*x^2 + a))/(a^2*d^5*x^4)]","A",0
326,1,1060,0,2.879185," ","integrate(x^4/(e*x+d)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{6 \, \sqrt{c d^{2} + a e^{2}} c^{2} d^{4} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 3 \, {\left(2 \, c^{2} d^{5} + a c d^{3} e^{2} - a^{2} d e^{4}\right)} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(6 \, c^{2} d^{4} e + 2 \, a c d^{2} e^{3} - 4 \, a^{2} e^{5} + 2 \, {\left(c^{2} d^{2} e^{3} + a c e^{5}\right)} x^{2} - 3 \, {\left(c^{2} d^{3} e^{2} + a c d e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{12 \, {\left(c^{3} d^{2} e^{4} + a c^{2} e^{6}\right)}}, -\frac{12 \, \sqrt{-c d^{2} - a e^{2}} c^{2} d^{4} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) + 3 \, {\left(2 \, c^{2} d^{5} + a c d^{3} e^{2} - a^{2} d e^{4}\right)} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) - 2 \, {\left(6 \, c^{2} d^{4} e + 2 \, a c d^{2} e^{3} - 4 \, a^{2} e^{5} + 2 \, {\left(c^{2} d^{2} e^{3} + a c e^{5}\right)} x^{2} - 3 \, {\left(c^{2} d^{3} e^{2} + a c d e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{12 \, {\left(c^{3} d^{2} e^{4} + a c^{2} e^{6}\right)}}, \frac{3 \, \sqrt{c d^{2} + a e^{2}} c^{2} d^{4} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 3 \, {\left(2 \, c^{2} d^{5} + a c d^{3} e^{2} - a^{2} d e^{4}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) + {\left(6 \, c^{2} d^{4} e + 2 \, a c d^{2} e^{3} - 4 \, a^{2} e^{5} + 2 \, {\left(c^{2} d^{2} e^{3} + a c e^{5}\right)} x^{2} - 3 \, {\left(c^{2} d^{3} e^{2} + a c d e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{6 \, {\left(c^{3} d^{2} e^{4} + a c^{2} e^{6}\right)}}, -\frac{6 \, \sqrt{-c d^{2} - a e^{2}} c^{2} d^{4} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - 3 \, {\left(2 \, c^{2} d^{5} + a c d^{3} e^{2} - a^{2} d e^{4}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(6 \, c^{2} d^{4} e + 2 \, a c d^{2} e^{3} - 4 \, a^{2} e^{5} + 2 \, {\left(c^{2} d^{2} e^{3} + a c e^{5}\right)} x^{2} - 3 \, {\left(c^{2} d^{3} e^{2} + a c d e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{6 \, {\left(c^{3} d^{2} e^{4} + a c^{2} e^{6}\right)}}\right]"," ",0,"[1/12*(6*sqrt(c*d^2 + a*e^2)*c^2*d^4*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) - 3*(2*c^2*d^5 + a*c*d^3*e^2 - a^2*d*e^4)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(6*c^2*d^4*e + 2*a*c*d^2*e^3 - 4*a^2*e^5 + 2*(c^2*d^2*e^3 + a*c*e^5)*x^2 - 3*(c^2*d^3*e^2 + a*c*d*e^4)*x)*sqrt(c*x^2 + a))/(c^3*d^2*e^4 + a*c^2*e^6), -1/12*(12*sqrt(-c*d^2 - a*e^2)*c^2*d^4*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) + 3*(2*c^2*d^5 + a*c*d^3*e^2 - a^2*d*e^4)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) - 2*(6*c^2*d^4*e + 2*a*c*d^2*e^3 - 4*a^2*e^5 + 2*(c^2*d^2*e^3 + a*c*e^5)*x^2 - 3*(c^2*d^3*e^2 + a*c*d*e^4)*x)*sqrt(c*x^2 + a))/(c^3*d^2*e^4 + a*c^2*e^6), 1/6*(3*sqrt(c*d^2 + a*e^2)*c^2*d^4*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + 3*(2*c^2*d^5 + a*c*d^3*e^2 - a^2*d*e^4)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) + (6*c^2*d^4*e + 2*a*c*d^2*e^3 - 4*a^2*e^5 + 2*(c^2*d^2*e^3 + a*c*e^5)*x^2 - 3*(c^2*d^3*e^2 + a*c*d*e^4)*x)*sqrt(c*x^2 + a))/(c^3*d^2*e^4 + a*c^2*e^6), -1/6*(6*sqrt(-c*d^2 - a*e^2)*c^2*d^4*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - 3*(2*c^2*d^5 + a*c*d^3*e^2 - a^2*d*e^4)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (6*c^2*d^4*e + 2*a*c*d^2*e^3 - 4*a^2*e^5 + 2*(c^2*d^2*e^3 + a*c*e^5)*x^2 - 3*(c^2*d^3*e^2 + a*c*d*e^4)*x)*sqrt(c*x^2 + a))/(c^3*d^2*e^4 + a*c^2*e^6)]","A",0
327,1,924,0,2.802076," ","integrate(x^3/(e*x+d)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{c d^{2} + a e^{2}} c^{2} d^{3} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - {\left(2 \, c^{2} d^{4} + a c d^{2} e^{2} - a^{2} e^{4}\right)} \sqrt{c} \log\left(-2 \, c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) - 2 \, {\left(2 \, c^{2} d^{3} e + 2 \, a c d e^{3} - {\left(c^{2} d^{2} e^{2} + a c e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{4 \, {\left(c^{3} d^{2} e^{3} + a c^{2} e^{5}\right)}}, \frac{4 \, \sqrt{-c d^{2} - a e^{2}} c^{2} d^{3} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - {\left(2 \, c^{2} d^{4} + a c d^{2} e^{2} - a^{2} e^{4}\right)} \sqrt{c} \log\left(-2 \, c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) - 2 \, {\left(2 \, c^{2} d^{3} e + 2 \, a c d e^{3} - {\left(c^{2} d^{2} e^{2} + a c e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{4 \, {\left(c^{3} d^{2} e^{3} + a c^{2} e^{5}\right)}}, \frac{\sqrt{c d^{2} + a e^{2}} c^{2} d^{3} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - {\left(2 \, c^{2} d^{4} + a c d^{2} e^{2} - a^{2} e^{4}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(2 \, c^{2} d^{3} e + 2 \, a c d e^{3} - {\left(c^{2} d^{2} e^{2} + a c e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{2 \, {\left(c^{3} d^{2} e^{3} + a c^{2} e^{5}\right)}}, \frac{2 \, \sqrt{-c d^{2} - a e^{2}} c^{2} d^{3} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - {\left(2 \, c^{2} d^{4} + a c d^{2} e^{2} - a^{2} e^{4}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(2 \, c^{2} d^{3} e + 2 \, a c d e^{3} - {\left(c^{2} d^{2} e^{2} + a c e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{2 \, {\left(c^{3} d^{2} e^{3} + a c^{2} e^{5}\right)}}\right]"," ",0,"[1/4*(2*sqrt(c*d^2 + a*e^2)*c^2*d^3*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 + 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) - (2*c^2*d^4 + a*c*d^2*e^2 - a^2*e^4)*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) - 2*(2*c^2*d^3*e + 2*a*c*d*e^3 - (c^2*d^2*e^2 + a*c*e^4)*x)*sqrt(c*x^2 + a))/(c^3*d^2*e^3 + a*c^2*e^5), 1/4*(4*sqrt(-c*d^2 - a*e^2)*c^2*d^3*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - (2*c^2*d^4 + a*c*d^2*e^2 - a^2*e^4)*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) - 2*(2*c^2*d^3*e + 2*a*c*d*e^3 - (c^2*d^2*e^2 + a*c*e^4)*x)*sqrt(c*x^2 + a))/(c^3*d^2*e^3 + a*c^2*e^5), 1/2*(sqrt(c*d^2 + a*e^2)*c^2*d^3*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 + 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) - (2*c^2*d^4 + a*c*d^2*e^2 - a^2*e^4)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (2*c^2*d^3*e + 2*a*c*d*e^3 - (c^2*d^2*e^2 + a*c*e^4)*x)*sqrt(c*x^2 + a))/(c^3*d^2*e^3 + a*c^2*e^5), 1/2*(2*sqrt(-c*d^2 - a*e^2)*c^2*d^3*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - (2*c^2*d^4 + a*c*d^2*e^2 - a^2*e^4)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (2*c^2*d^3*e + 2*a*c*d*e^3 - (c^2*d^2*e^2 + a*c*e^4)*x)*sqrt(c*x^2 + a))/(c^3*d^2*e^3 + a*c^2*e^5)]","A",0
328,1,745,0,0.528921," ","integrate(x^2/(e*x+d)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{c d^{2} + a e^{2}} c d^{2} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + {\left(c d^{3} + a d e^{2}\right)} \sqrt{c} \log\left(-2 \, c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(c d^{2} e + a e^{3}\right)} \sqrt{c x^{2} + a}}{2 \, {\left(c^{2} d^{2} e^{2} + a c e^{4}\right)}}, -\frac{2 \, \sqrt{-c d^{2} - a e^{2}} c d^{2} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - {\left(c d^{3} + a d e^{2}\right)} \sqrt{c} \log\left(-2 \, c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) - 2 \, {\left(c d^{2} e + a e^{3}\right)} \sqrt{c x^{2} + a}}{2 \, {\left(c^{2} d^{2} e^{2} + a c e^{4}\right)}}, \frac{\sqrt{c d^{2} + a e^{2}} c d^{2} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(c d^{3} + a d e^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) + 2 \, {\left(c d^{2} e + a e^{3}\right)} \sqrt{c x^{2} + a}}{2 \, {\left(c^{2} d^{2} e^{2} + a c e^{4}\right)}}, -\frac{\sqrt{-c d^{2} - a e^{2}} c d^{2} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - {\left(c d^{3} + a d e^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(c d^{2} e + a e^{3}\right)} \sqrt{c x^{2} + a}}{c^{2} d^{2} e^{2} + a c e^{4}}\right]"," ",0,"[1/2*(sqrt(c*d^2 + a*e^2)*c*d^2*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + (c*d^3 + a*d*e^2)*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(c*d^2*e + a*e^3)*sqrt(c*x^2 + a))/(c^2*d^2*e^2 + a*c*e^4), -1/2*(2*sqrt(-c*d^2 - a*e^2)*c*d^2*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - (c*d^3 + a*d*e^2)*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) - 2*(c*d^2*e + a*e^3)*sqrt(c*x^2 + a))/(c^2*d^2*e^2 + a*c*e^4), 1/2*(sqrt(c*d^2 + a*e^2)*c*d^2*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(c*d^3 + a*d*e^2)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) + 2*(c*d^2*e + a*e^3)*sqrt(c*x^2 + a))/(c^2*d^2*e^2 + a*c*e^4), -(sqrt(-c*d^2 - a*e^2)*c*d^2*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - (c*d^3 + a*d*e^2)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (c*d^2*e + a*e^3)*sqrt(c*x^2 + a))/(c^2*d^2*e^2 + a*c*e^4)]","A",0
329,1,631,0,0.532187," ","integrate(x/(e*x+d)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{c d^{2} + a e^{2}} c d \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + {\left(c d^{2} + a e^{2}\right)} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right)}{2 \, {\left(c^{2} d^{2} e + a c e^{3}\right)}}, \frac{2 \, \sqrt{-c d^{2} - a e^{2}} c d \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) + {\left(c d^{2} + a e^{2}\right)} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right)}{2 \, {\left(c^{2} d^{2} e + a c e^{3}\right)}}, \frac{\sqrt{c d^{2} + a e^{2}} c d \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 2 \, {\left(c d^{2} + a e^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right)}{2 \, {\left(c^{2} d^{2} e + a c e^{3}\right)}}, \frac{\sqrt{-c d^{2} - a e^{2}} c d \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - {\left(c d^{2} + a e^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right)}{c^{2} d^{2} e + a c e^{3}}\right]"," ",0,"[1/2*(sqrt(c*d^2 + a*e^2)*c*d*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 + 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + (c*d^2 + a*e^2)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a))/(c^2*d^2*e + a*c*e^3), 1/2*(2*sqrt(-c*d^2 - a*e^2)*c*d*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) + (c*d^2 + a*e^2)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a))/(c^2*d^2*e + a*c*e^3), 1/2*(sqrt(c*d^2 + a*e^2)*c*d*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 + 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) - 2*(c*d^2 + a*e^2)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)))/(c^2*d^2*e + a*c*e^3), (sqrt(-c*d^2 - a*e^2)*c*d*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - (c*d^2 + a*e^2)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)))/(c^2*d^2*e + a*c*e^3)]","A",0
330,1,211,0,0.424922," ","integrate(1/(e*x+d)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right)}{2 \, \sqrt{c d^{2} + a e^{2}}}, -\frac{\sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right)}{c d^{2} + a e^{2}}\right]"," ",0,"[1/2*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2))/sqrt(c*d^2 + a*e^2), -sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2))/(c*d^2 + a*e^2)]","B",0
331,1,634,0,0.460890," ","integrate(1/x/(e*x+d)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{c d^{2} + a e^{2}} a e \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + {\left(c d^{2} + a e^{2}\right)} \sqrt{a} \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right)}{2 \, {\left(a c d^{3} + a^{2} d e^{2}\right)}}, \frac{2 \, \sqrt{-c d^{2} - a e^{2}} a e \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) + {\left(c d^{2} + a e^{2}\right)} \sqrt{a} \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right)}{2 \, {\left(a c d^{3} + a^{2} d e^{2}\right)}}, \frac{\sqrt{c d^{2} + a e^{2}} a e \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(c d^{2} + a e^{2}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right)}{2 \, {\left(a c d^{3} + a^{2} d e^{2}\right)}}, \frac{\sqrt{-c d^{2} - a e^{2}} a e \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) + {\left(c d^{2} + a e^{2}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right)}{a c d^{3} + a^{2} d e^{2}}\right]"," ",0,"[1/2*(sqrt(c*d^2 + a*e^2)*a*e*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 + 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + (c*d^2 + a*e^2)*sqrt(a)*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2))/(a*c*d^3 + a^2*d*e^2), 1/2*(2*sqrt(-c*d^2 - a*e^2)*a*e*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) + (c*d^2 + a*e^2)*sqrt(a)*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2))/(a*c*d^3 + a^2*d*e^2), 1/2*(sqrt(c*d^2 + a*e^2)*a*e*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 + 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(c*d^2 + a*e^2)*sqrt(-a)*arctan(sqrt(-a)/sqrt(c*x^2 + a)))/(a*c*d^3 + a^2*d*e^2), (sqrt(-c*d^2 - a*e^2)*a*e*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) + (c*d^2 + a*e^2)*sqrt(-a)*arctan(sqrt(-a)/sqrt(c*x^2 + a)))/(a*c*d^3 + a^2*d*e^2)]","A",0
332,1,767,0,0.483501," ","integrate(1/x^2/(e*x+d)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{c d^{2} + a e^{2}} a e^{2} x \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + {\left(c d^{2} e + a e^{3}\right)} \sqrt{a} x \log\left(-\frac{c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - 2 \, {\left(c d^{3} + a d e^{2}\right)} \sqrt{c x^{2} + a}}{2 \, {\left(a c d^{4} + a^{2} d^{2} e^{2}\right)} x}, -\frac{2 \, \sqrt{-c d^{2} - a e^{2}} a e^{2} x \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - {\left(c d^{2} e + a e^{3}\right)} \sqrt{a} x \log\left(-\frac{c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(c d^{3} + a d e^{2}\right)} \sqrt{c x^{2} + a}}{2 \, {\left(a c d^{4} + a^{2} d^{2} e^{2}\right)} x}, \frac{\sqrt{c d^{2} + a e^{2}} a e^{2} x \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 2 \, {\left(c d^{2} e + a e^{3}\right)} \sqrt{-a} x \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) - 2 \, {\left(c d^{3} + a d e^{2}\right)} \sqrt{c x^{2} + a}}{2 \, {\left(a c d^{4} + a^{2} d^{2} e^{2}\right)} x}, -\frac{\sqrt{-c d^{2} - a e^{2}} a e^{2} x \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) + {\left(c d^{2} e + a e^{3}\right)} \sqrt{-a} x \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) + {\left(c d^{3} + a d e^{2}\right)} \sqrt{c x^{2} + a}}{{\left(a c d^{4} + a^{2} d^{2} e^{2}\right)} x}\right]"," ",0,"[1/2*(sqrt(c*d^2 + a*e^2)*a*e^2*x*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + (c*d^2*e + a*e^3)*sqrt(a)*x*log(-(c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) - 2*(c*d^3 + a*d*e^2)*sqrt(c*x^2 + a))/((a*c*d^4 + a^2*d^2*e^2)*x), -1/2*(2*sqrt(-c*d^2 - a*e^2)*a*e^2*x*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - (c*d^2*e + a*e^3)*sqrt(a)*x*log(-(c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(c*d^3 + a*d*e^2)*sqrt(c*x^2 + a))/((a*c*d^4 + a^2*d^2*e^2)*x), 1/2*(sqrt(c*d^2 + a*e^2)*a*e^2*x*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) - 2*(c*d^2*e + a*e^3)*sqrt(-a)*x*arctan(sqrt(-a)/sqrt(c*x^2 + a)) - 2*(c*d^3 + a*d*e^2)*sqrt(c*x^2 + a))/((a*c*d^4 + a^2*d^2*e^2)*x), -(sqrt(-c*d^2 - a*e^2)*a*e^2*x*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) + (c*d^2*e + a*e^3)*sqrt(-a)*x*arctan(sqrt(-a)/sqrt(c*x^2 + a)) + (c*d^3 + a*d*e^2)*sqrt(c*x^2 + a))/((a*c*d^4 + a^2*d^2*e^2)*x)]","A",0
333,1,956,0,0.503517," ","integrate(1/x^3/(e*x+d)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{c d^{2} + a e^{2}} a^{2} e^{3} x^{2} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - {\left(c^{2} d^{4} - a c d^{2} e^{2} - 2 \, a^{2} e^{4}\right)} \sqrt{a} x^{2} \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - 2 \, {\left(a c d^{4} + a^{2} d^{2} e^{2} - 2 \, {\left(a c d^{3} e + a^{2} d e^{3}\right)} x\right)} \sqrt{c x^{2} + a}}{4 \, {\left(a^{2} c d^{5} + a^{3} d^{3} e^{2}\right)} x^{2}}, \frac{4 \, \sqrt{-c d^{2} - a e^{2}} a^{2} e^{3} x^{2} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - {\left(c^{2} d^{4} - a c d^{2} e^{2} - 2 \, a^{2} e^{4}\right)} \sqrt{a} x^{2} \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - 2 \, {\left(a c d^{4} + a^{2} d^{2} e^{2} - 2 \, {\left(a c d^{3} e + a^{2} d e^{3}\right)} x\right)} \sqrt{c x^{2} + a}}{4 \, {\left(a^{2} c d^{5} + a^{3} d^{3} e^{2}\right)} x^{2}}, \frac{\sqrt{c d^{2} + a e^{2}} a^{2} e^{3} x^{2} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - {\left(c^{2} d^{4} - a c d^{2} e^{2} - 2 \, a^{2} e^{4}\right)} \sqrt{-a} x^{2} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) - {\left(a c d^{4} + a^{2} d^{2} e^{2} - 2 \, {\left(a c d^{3} e + a^{2} d e^{3}\right)} x\right)} \sqrt{c x^{2} + a}}{2 \, {\left(a^{2} c d^{5} + a^{3} d^{3} e^{2}\right)} x^{2}}, \frac{2 \, \sqrt{-c d^{2} - a e^{2}} a^{2} e^{3} x^{2} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - {\left(c^{2} d^{4} - a c d^{2} e^{2} - 2 \, a^{2} e^{4}\right)} \sqrt{-a} x^{2} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) - {\left(a c d^{4} + a^{2} d^{2} e^{2} - 2 \, {\left(a c d^{3} e + a^{2} d e^{3}\right)} x\right)} \sqrt{c x^{2} + a}}{2 \, {\left(a^{2} c d^{5} + a^{3} d^{3} e^{2}\right)} x^{2}}\right]"," ",0,"[1/4*(2*sqrt(c*d^2 + a*e^2)*a^2*e^3*x^2*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 + 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) - (c^2*d^4 - a*c*d^2*e^2 - 2*a^2*e^4)*sqrt(a)*x^2*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) - 2*(a*c*d^4 + a^2*d^2*e^2 - 2*(a*c*d^3*e + a^2*d*e^3)*x)*sqrt(c*x^2 + a))/((a^2*c*d^5 + a^3*d^3*e^2)*x^2), 1/4*(4*sqrt(-c*d^2 - a*e^2)*a^2*e^3*x^2*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - (c^2*d^4 - a*c*d^2*e^2 - 2*a^2*e^4)*sqrt(a)*x^2*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) - 2*(a*c*d^4 + a^2*d^2*e^2 - 2*(a*c*d^3*e + a^2*d*e^3)*x)*sqrt(c*x^2 + a))/((a^2*c*d^5 + a^3*d^3*e^2)*x^2), 1/2*(sqrt(c*d^2 + a*e^2)*a^2*e^3*x^2*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 + 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) - (c^2*d^4 - a*c*d^2*e^2 - 2*a^2*e^4)*sqrt(-a)*x^2*arctan(sqrt(-a)/sqrt(c*x^2 + a)) - (a*c*d^4 + a^2*d^2*e^2 - 2*(a*c*d^3*e + a^2*d*e^3)*x)*sqrt(c*x^2 + a))/((a^2*c*d^5 + a^3*d^3*e^2)*x^2), 1/2*(2*sqrt(-c*d^2 - a*e^2)*a^2*e^3*x^2*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - (c^2*d^4 - a*c*d^2*e^2 - 2*a^2*e^4)*sqrt(-a)*x^2*arctan(sqrt(-a)/sqrt(c*x^2 + a)) - (a*c*d^4 + a^2*d^2*e^2 - 2*(a*c*d^3*e + a^2*d*e^3)*x)*sqrt(c*x^2 + a))/((a^2*c*d^5 + a^3*d^3*e^2)*x^2)]","A",0
334,1,1525,0,4.653102," ","integrate(x^4/(e*x+d)/(c*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(a c^{2} d^{5} + 2 \, a^{2} c d^{3} e^{2} + a^{3} d e^{4} + {\left(c^{3} d^{5} + 2 \, a c^{2} d^{3} e^{2} + a^{2} c d e^{4}\right)} x^{2}\right)} \sqrt{c} \log\left(-2 \, c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + {\left(c^{3} d^{4} x^{2} + a c^{2} d^{4}\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(a c^{2} d^{4} e + 3 \, a^{2} c d^{2} e^{3} + 2 \, a^{3} e^{5} + {\left(c^{3} d^{4} e + 2 \, a c^{2} d^{2} e^{3} + a^{2} c e^{5}\right)} x^{2} + {\left(a c^{2} d^{3} e^{2} + a^{2} c d e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{2 \, {\left(a c^{4} d^{4} e^{2} + 2 \, a^{2} c^{3} d^{2} e^{4} + a^{3} c^{2} e^{6} + {\left(c^{5} d^{4} e^{2} + 2 \, a c^{4} d^{2} e^{4} + a^{2} c^{3} e^{6}\right)} x^{2}\right)}}, -\frac{2 \, {\left(c^{3} d^{4} x^{2} + a c^{2} d^{4}\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - {\left(a c^{2} d^{5} + 2 \, a^{2} c d^{3} e^{2} + a^{3} d e^{4} + {\left(c^{3} d^{5} + 2 \, a c^{2} d^{3} e^{2} + a^{2} c d e^{4}\right)} x^{2}\right)} \sqrt{c} \log\left(-2 \, c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) - 2 \, {\left(a c^{2} d^{4} e + 3 \, a^{2} c d^{2} e^{3} + 2 \, a^{3} e^{5} + {\left(c^{3} d^{4} e + 2 \, a c^{2} d^{2} e^{3} + a^{2} c e^{5}\right)} x^{2} + {\left(a c^{2} d^{3} e^{2} + a^{2} c d e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{2 \, {\left(a c^{4} d^{4} e^{2} + 2 \, a^{2} c^{3} d^{2} e^{4} + a^{3} c^{2} e^{6} + {\left(c^{5} d^{4} e^{2} + 2 \, a c^{4} d^{2} e^{4} + a^{2} c^{3} e^{6}\right)} x^{2}\right)}}, \frac{2 \, {\left(a c^{2} d^{5} + 2 \, a^{2} c d^{3} e^{2} + a^{3} d e^{4} + {\left(c^{3} d^{5} + 2 \, a c^{2} d^{3} e^{2} + a^{2} c d e^{4}\right)} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) + {\left(c^{3} d^{4} x^{2} + a c^{2} d^{4}\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(a c^{2} d^{4} e + 3 \, a^{2} c d^{2} e^{3} + 2 \, a^{3} e^{5} + {\left(c^{3} d^{4} e + 2 \, a c^{2} d^{2} e^{3} + a^{2} c e^{5}\right)} x^{2} + {\left(a c^{2} d^{3} e^{2} + a^{2} c d e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{2 \, {\left(a c^{4} d^{4} e^{2} + 2 \, a^{2} c^{3} d^{2} e^{4} + a^{3} c^{2} e^{6} + {\left(c^{5} d^{4} e^{2} + 2 \, a c^{4} d^{2} e^{4} + a^{2} c^{3} e^{6}\right)} x^{2}\right)}}, -\frac{{\left(c^{3} d^{4} x^{2} + a c^{2} d^{4}\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - {\left(a c^{2} d^{5} + 2 \, a^{2} c d^{3} e^{2} + a^{3} d e^{4} + {\left(c^{3} d^{5} + 2 \, a c^{2} d^{3} e^{2} + a^{2} c d e^{4}\right)} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(a c^{2} d^{4} e + 3 \, a^{2} c d^{2} e^{3} + 2 \, a^{3} e^{5} + {\left(c^{3} d^{4} e + 2 \, a c^{2} d^{2} e^{3} + a^{2} c e^{5}\right)} x^{2} + {\left(a c^{2} d^{3} e^{2} + a^{2} c d e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{a c^{4} d^{4} e^{2} + 2 \, a^{2} c^{3} d^{2} e^{4} + a^{3} c^{2} e^{6} + {\left(c^{5} d^{4} e^{2} + 2 \, a c^{4} d^{2} e^{4} + a^{2} c^{3} e^{6}\right)} x^{2}}\right]"," ",0,"[1/2*((a*c^2*d^5 + 2*a^2*c*d^3*e^2 + a^3*d*e^4 + (c^3*d^5 + 2*a*c^2*d^3*e^2 + a^2*c*d*e^4)*x^2)*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + (c^3*d^4*x^2 + a*c^2*d^4)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(a*c^2*d^4*e + 3*a^2*c*d^2*e^3 + 2*a^3*e^5 + (c^3*d^4*e + 2*a*c^2*d^2*e^3 + a^2*c*e^5)*x^2 + (a*c^2*d^3*e^2 + a^2*c*d*e^4)*x)*sqrt(c*x^2 + a))/(a*c^4*d^4*e^2 + 2*a^2*c^3*d^2*e^4 + a^3*c^2*e^6 + (c^5*d^4*e^2 + 2*a*c^4*d^2*e^4 + a^2*c^3*e^6)*x^2), -1/2*(2*(c^3*d^4*x^2 + a*c^2*d^4)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - (a*c^2*d^5 + 2*a^2*c*d^3*e^2 + a^3*d*e^4 + (c^3*d^5 + 2*a*c^2*d^3*e^2 + a^2*c*d*e^4)*x^2)*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) - 2*(a*c^2*d^4*e + 3*a^2*c*d^2*e^3 + 2*a^3*e^5 + (c^3*d^4*e + 2*a*c^2*d^2*e^3 + a^2*c*e^5)*x^2 + (a*c^2*d^3*e^2 + a^2*c*d*e^4)*x)*sqrt(c*x^2 + a))/(a*c^4*d^4*e^2 + 2*a^2*c^3*d^2*e^4 + a^3*c^2*e^6 + (c^5*d^4*e^2 + 2*a*c^4*d^2*e^4 + a^2*c^3*e^6)*x^2), 1/2*(2*(a*c^2*d^5 + 2*a^2*c*d^3*e^2 + a^3*d*e^4 + (c^3*d^5 + 2*a*c^2*d^3*e^2 + a^2*c*d*e^4)*x^2)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) + (c^3*d^4*x^2 + a*c^2*d^4)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(a*c^2*d^4*e + 3*a^2*c*d^2*e^3 + 2*a^3*e^5 + (c^3*d^4*e + 2*a*c^2*d^2*e^3 + a^2*c*e^5)*x^2 + (a*c^2*d^3*e^2 + a^2*c*d*e^4)*x)*sqrt(c*x^2 + a))/(a*c^4*d^4*e^2 + 2*a^2*c^3*d^2*e^4 + a^3*c^2*e^6 + (c^5*d^4*e^2 + 2*a*c^4*d^2*e^4 + a^2*c^3*e^6)*x^2), -((c^3*d^4*x^2 + a*c^2*d^4)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - (a*c^2*d^5 + 2*a^2*c*d^3*e^2 + a^3*d*e^4 + (c^3*d^5 + 2*a*c^2*d^3*e^2 + a^2*c*d*e^4)*x^2)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (a*c^2*d^4*e + 3*a^2*c*d^2*e^3 + 2*a^3*e^5 + (c^3*d^4*e + 2*a*c^2*d^2*e^3 + a^2*c*e^5)*x^2 + (a*c^2*d^3*e^2 + a^2*c*d*e^4)*x)*sqrt(c*x^2 + a))/(a*c^4*d^4*e^2 + 2*a^2*c^3*d^2*e^4 + a^3*c^2*e^6 + (c^5*d^4*e^2 + 2*a*c^4*d^2*e^4 + a^2*c^3*e^6)*x^2)]","B",0
335,1,1323,0,4.689756," ","integrate(x^3/(e*x+d)/(c*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4} + {\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} x^{2}\right)} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + {\left(c^{3} d^{3} x^{2} + a c^{2} d^{3}\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(a c^{2} d^{3} e + a^{2} c d e^{3} - {\left(a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{2 \, {\left(a c^{4} d^{4} e + 2 \, a^{2} c^{3} d^{2} e^{3} + a^{3} c^{2} e^{5} + {\left(c^{5} d^{4} e + 2 \, a c^{4} d^{2} e^{3} + a^{2} c^{3} e^{5}\right)} x^{2}\right)}}, \frac{2 \, {\left(c^{3} d^{3} x^{2} + a c^{2} d^{3}\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) + {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4} + {\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} x^{2}\right)} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(a c^{2} d^{3} e + a^{2} c d e^{3} - {\left(a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{2 \, {\left(a c^{4} d^{4} e + 2 \, a^{2} c^{3} d^{2} e^{3} + a^{3} c^{2} e^{5} + {\left(c^{5} d^{4} e + 2 \, a c^{4} d^{2} e^{3} + a^{2} c^{3} e^{5}\right)} x^{2}\right)}}, -\frac{2 \, {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4} + {\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(c^{3} d^{3} x^{2} + a c^{2} d^{3}\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 2 \, {\left(a c^{2} d^{3} e + a^{2} c d e^{3} - {\left(a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{2 \, {\left(a c^{4} d^{4} e + 2 \, a^{2} c^{3} d^{2} e^{3} + a^{3} c^{2} e^{5} + {\left(c^{5} d^{4} e + 2 \, a c^{4} d^{2} e^{3} + a^{2} c^{3} e^{5}\right)} x^{2}\right)}}, \frac{{\left(c^{3} d^{3} x^{2} + a c^{2} d^{3}\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4} + {\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) + {\left(a c^{2} d^{3} e + a^{2} c d e^{3} - {\left(a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{a c^{4} d^{4} e + 2 \, a^{2} c^{3} d^{2} e^{3} + a^{3} c^{2} e^{5} + {\left(c^{5} d^{4} e + 2 \, a c^{4} d^{2} e^{3} + a^{2} c^{3} e^{5}\right)} x^{2}}\right]"," ",0,"[1/2*((a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4 + (c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4)*x^2)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + (c^3*d^3*x^2 + a*c^2*d^3)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 + 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(a*c^2*d^3*e + a^2*c*d*e^3 - (a*c^2*d^2*e^2 + a^2*c*e^4)*x)*sqrt(c*x^2 + a))/(a*c^4*d^4*e + 2*a^2*c^3*d^2*e^3 + a^3*c^2*e^5 + (c^5*d^4*e + 2*a*c^4*d^2*e^3 + a^2*c^3*e^5)*x^2), 1/2*(2*(c^3*d^3*x^2 + a*c^2*d^3)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) + (a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4 + (c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4)*x^2)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(a*c^2*d^3*e + a^2*c*d*e^3 - (a*c^2*d^2*e^2 + a^2*c*e^4)*x)*sqrt(c*x^2 + a))/(a*c^4*d^4*e + 2*a^2*c^3*d^2*e^3 + a^3*c^2*e^5 + (c^5*d^4*e + 2*a*c^4*d^2*e^3 + a^2*c^3*e^5)*x^2), -1/2*(2*(a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4 + (c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4)*x^2)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (c^3*d^3*x^2 + a*c^2*d^3)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 + 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) - 2*(a*c^2*d^3*e + a^2*c*d*e^3 - (a*c^2*d^2*e^2 + a^2*c*e^4)*x)*sqrt(c*x^2 + a))/(a*c^4*d^4*e + 2*a^2*c^3*d^2*e^3 + a^3*c^2*e^5 + (c^5*d^4*e + 2*a*c^4*d^2*e^3 + a^2*c^3*e^5)*x^2), ((c^3*d^3*x^2 + a*c^2*d^3)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - (a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4 + (c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4)*x^2)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) + (a*c^2*d^3*e + a^2*c*d*e^3 - (a*c^2*d^2*e^2 + a^2*c*e^4)*x)*sqrt(c*x^2 + a))/(a*c^4*d^4*e + 2*a^2*c^3*d^2*e^3 + a^3*c^2*e^5 + (c^5*d^4*e + 2*a*c^4*d^2*e^3 + a^2*c^3*e^5)*x^2)]","B",0
336,1,455,0,0.473577," ","integrate(x^2/(e*x+d)/(c*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(c^{2} d^{2} x^{2} + a c d^{2}\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 2 \, {\left(a c d^{2} e + a^{2} e^{3} + {\left(c^{2} d^{3} + a c d e^{2}\right)} x\right)} \sqrt{c x^{2} + a}}{2 \, {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4} + {\left(c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)} x^{2}\right)}}, -\frac{{\left(c^{2} d^{2} x^{2} + a c d^{2}\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) + {\left(a c d^{2} e + a^{2} e^{3} + {\left(c^{2} d^{3} + a c d e^{2}\right)} x\right)} \sqrt{c x^{2} + a}}{a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4} + {\left(c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)} x^{2}}\right]"," ",0,"[1/2*((c^2*d^2*x^2 + a*c*d^2)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) - 2*(a*c*d^2*e + a^2*e^3 + (c^2*d^3 + a*c*d*e^2)*x)*sqrt(c*x^2 + a))/(a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4 + (c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4)*x^2), -((c^2*d^2*x^2 + a*c*d^2)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) + (a*c*d^2*e + a^2*e^3 + (c^2*d^3 + a*c*d*e^2)*x)*sqrt(c*x^2 + a))/(a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4 + (c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4)*x^2)]","B",0
337,1,425,0,0.478754," ","integrate(x/(e*x+d)/(c*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(c d e x^{2} + a d e\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 2 \, {\left(c d^{3} + a d e^{2} - {\left(c d^{2} e + a e^{3}\right)} x\right)} \sqrt{c x^{2} + a}}{2 \, {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4} + {\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} x^{2}\right)}}, \frac{{\left(c d e x^{2} + a d e\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - {\left(c d^{3} + a d e^{2} - {\left(c d^{2} e + a e^{3}\right)} x\right)} \sqrt{c x^{2} + a}}{a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4} + {\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} x^{2}}\right]"," ",0,"[1/2*((c*d*e*x^2 + a*d*e)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 + 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) - 2*(c*d^3 + a*d*e^2 - (c*d^2*e + a*e^3)*x)*sqrt(c*x^2 + a))/(a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4 + (c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4)*x^2), ((c*d*e*x^2 + a*d*e)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - (c*d^3 + a*d*e^2 - (c*d^2*e + a*e^3)*x)*sqrt(c*x^2 + a))/(a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4 + (c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4)*x^2)]","B",0
338,1,456,0,0.485907," ","integrate(1/(e*x+d)/(c*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(a c e^{2} x^{2} + a^{2} e^{2}\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(a c d^{2} e + a^{2} e^{3} + {\left(c^{2} d^{3} + a c d e^{2}\right)} x\right)} \sqrt{c x^{2} + a}}{2 \, {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4} + {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} x^{2}\right)}}, -\frac{{\left(a c e^{2} x^{2} + a^{2} e^{2}\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - {\left(a c d^{2} e + a^{2} e^{3} + {\left(c^{2} d^{3} + a c d e^{2}\right)} x\right)} \sqrt{c x^{2} + a}}{a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4} + {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} x^{2}}\right]"," ",0,"[1/2*((a*c*e^2*x^2 + a^2*e^2)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(a*c*d^2*e + a^2*e^3 + (c^2*d^3 + a*c*d*e^2)*x)*sqrt(c*x^2 + a))/(a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4 + (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)*x^2), -((a*c*e^2*x^2 + a^2*e^2)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - (a*c*d^2*e + a^2*e^3 + (c^2*d^3 + a*c*d*e^2)*x)*sqrt(c*x^2 + a))/(a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4 + (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)*x^2)]","B",0
339,1,1325,0,0.692090," ","integrate(1/x/(e*x+d)/(c*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(a^{2} c e^{3} x^{2} + a^{3} e^{3}\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4} + {\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} x^{2}\right)} \sqrt{a} \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(a c^{2} d^{4} + a^{2} c d^{2} e^{2} - {\left(a c^{2} d^{3} e + a^{2} c d e^{3}\right)} x\right)} \sqrt{c x^{2} + a}}{2 \, {\left(a^{3} c^{2} d^{5} + 2 \, a^{4} c d^{3} e^{2} + a^{5} d e^{4} + {\left(a^{2} c^{3} d^{5} + 2 \, a^{3} c^{2} d^{3} e^{2} + a^{4} c d e^{4}\right)} x^{2}\right)}}, \frac{2 \, {\left(a^{2} c e^{3} x^{2} + a^{3} e^{3}\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) + {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4} + {\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} x^{2}\right)} \sqrt{a} \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(a c^{2} d^{4} + a^{2} c d^{2} e^{2} - {\left(a c^{2} d^{3} e + a^{2} c d e^{3}\right)} x\right)} \sqrt{c x^{2} + a}}{2 \, {\left(a^{3} c^{2} d^{5} + 2 \, a^{4} c d^{3} e^{2} + a^{5} d e^{4} + {\left(a^{2} c^{3} d^{5} + 2 \, a^{3} c^{2} d^{3} e^{2} + a^{4} c d e^{4}\right)} x^{2}\right)}}, \frac{2 \, {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4} + {\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} x^{2}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) + {\left(a^{2} c e^{3} x^{2} + a^{3} e^{3}\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(a c^{2} d^{4} + a^{2} c d^{2} e^{2} - {\left(a c^{2} d^{3} e + a^{2} c d e^{3}\right)} x\right)} \sqrt{c x^{2} + a}}{2 \, {\left(a^{3} c^{2} d^{5} + 2 \, a^{4} c d^{3} e^{2} + a^{5} d e^{4} + {\left(a^{2} c^{3} d^{5} + 2 \, a^{3} c^{2} d^{3} e^{2} + a^{4} c d e^{4}\right)} x^{2}\right)}}, \frac{{\left(a^{2} c e^{3} x^{2} + a^{3} e^{3}\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) + {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4} + {\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} x^{2}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) + {\left(a c^{2} d^{4} + a^{2} c d^{2} e^{2} - {\left(a c^{2} d^{3} e + a^{2} c d e^{3}\right)} x\right)} \sqrt{c x^{2} + a}}{a^{3} c^{2} d^{5} + 2 \, a^{4} c d^{3} e^{2} + a^{5} d e^{4} + {\left(a^{2} c^{3} d^{5} + 2 \, a^{3} c^{2} d^{3} e^{2} + a^{4} c d e^{4}\right)} x^{2}}\right]"," ",0,"[1/2*((a^2*c*e^3*x^2 + a^3*e^3)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 + 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + (a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4 + (c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4)*x^2)*sqrt(a)*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(a*c^2*d^4 + a^2*c*d^2*e^2 - (a*c^2*d^3*e + a^2*c*d*e^3)*x)*sqrt(c*x^2 + a))/(a^3*c^2*d^5 + 2*a^4*c*d^3*e^2 + a^5*d*e^4 + (a^2*c^3*d^5 + 2*a^3*c^2*d^3*e^2 + a^4*c*d*e^4)*x^2), 1/2*(2*(a^2*c*e^3*x^2 + a^3*e^3)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) + (a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4 + (c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4)*x^2)*sqrt(a)*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(a*c^2*d^4 + a^2*c*d^2*e^2 - (a*c^2*d^3*e + a^2*c*d*e^3)*x)*sqrt(c*x^2 + a))/(a^3*c^2*d^5 + 2*a^4*c*d^3*e^2 + a^5*d*e^4 + (a^2*c^3*d^5 + 2*a^3*c^2*d^3*e^2 + a^4*c*d*e^4)*x^2), 1/2*(2*(a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4 + (c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4)*x^2)*sqrt(-a)*arctan(sqrt(-a)/sqrt(c*x^2 + a)) + (a^2*c*e^3*x^2 + a^3*e^3)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 + 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(a*c^2*d^4 + a^2*c*d^2*e^2 - (a*c^2*d^3*e + a^2*c*d*e^3)*x)*sqrt(c*x^2 + a))/(a^3*c^2*d^5 + 2*a^4*c*d^3*e^2 + a^5*d*e^4 + (a^2*c^3*d^5 + 2*a^3*c^2*d^3*e^2 + a^4*c*d*e^4)*x^2), ((a^2*c*e^3*x^2 + a^3*e^3)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) + (a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4 + (c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4)*x^2)*sqrt(-a)*arctan(sqrt(-a)/sqrt(c*x^2 + a)) + (a*c^2*d^4 + a^2*c*d^2*e^2 - (a*c^2*d^3*e + a^2*c*d*e^3)*x)*sqrt(c*x^2 + a))/(a^3*c^2*d^5 + 2*a^4*c*d^3*e^2 + a^5*d*e^4 + (a^2*c^3*d^5 + 2*a^3*c^2*d^3*e^2 + a^4*c*d*e^4)*x^2)]","B",0
340,1,1556,0,0.717265," ","integrate(1/x^2/(e*x+d)/(c*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(a^{2} c e^{4} x^{3} + a^{3} e^{4} x\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + {\left({\left(c^{3} d^{4} e + 2 \, a c^{2} d^{2} e^{3} + a^{2} c e^{5}\right)} x^{3} + {\left(a c^{2} d^{4} e + 2 \, a^{2} c d^{2} e^{3} + a^{3} e^{5}\right)} x\right)} \sqrt{a} \log\left(-\frac{c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - 2 \, {\left(a c^{2} d^{5} + 2 \, a^{2} c d^{3} e^{2} + a^{3} d e^{4} + {\left(2 \, c^{3} d^{5} + 3 \, a c^{2} d^{3} e^{2} + a^{2} c d e^{4}\right)} x^{2} + {\left(a c^{2} d^{4} e + a^{2} c d^{2} e^{3}\right)} x\right)} \sqrt{c x^{2} + a}}{2 \, {\left({\left(a^{2} c^{3} d^{6} + 2 \, a^{3} c^{2} d^{4} e^{2} + a^{4} c d^{2} e^{4}\right)} x^{3} + {\left(a^{3} c^{2} d^{6} + 2 \, a^{4} c d^{4} e^{2} + a^{5} d^{2} e^{4}\right)} x\right)}}, -\frac{2 \, {\left(a^{2} c e^{4} x^{3} + a^{3} e^{4} x\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - {\left({\left(c^{3} d^{4} e + 2 \, a c^{2} d^{2} e^{3} + a^{2} c e^{5}\right)} x^{3} + {\left(a c^{2} d^{4} e + 2 \, a^{2} c d^{2} e^{3} + a^{3} e^{5}\right)} x\right)} \sqrt{a} \log\left(-\frac{c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(a c^{2} d^{5} + 2 \, a^{2} c d^{3} e^{2} + a^{3} d e^{4} + {\left(2 \, c^{3} d^{5} + 3 \, a c^{2} d^{3} e^{2} + a^{2} c d e^{4}\right)} x^{2} + {\left(a c^{2} d^{4} e + a^{2} c d^{2} e^{3}\right)} x\right)} \sqrt{c x^{2} + a}}{2 \, {\left({\left(a^{2} c^{3} d^{6} + 2 \, a^{3} c^{2} d^{4} e^{2} + a^{4} c d^{2} e^{4}\right)} x^{3} + {\left(a^{3} c^{2} d^{6} + 2 \, a^{4} c d^{4} e^{2} + a^{5} d^{2} e^{4}\right)} x\right)}}, -\frac{2 \, {\left({\left(c^{3} d^{4} e + 2 \, a c^{2} d^{2} e^{3} + a^{2} c e^{5}\right)} x^{3} + {\left(a c^{2} d^{4} e + 2 \, a^{2} c d^{2} e^{3} + a^{3} e^{5}\right)} x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) - {\left(a^{2} c e^{4} x^{3} + a^{3} e^{4} x\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(a c^{2} d^{5} + 2 \, a^{2} c d^{3} e^{2} + a^{3} d e^{4} + {\left(2 \, c^{3} d^{5} + 3 \, a c^{2} d^{3} e^{2} + a^{2} c d e^{4}\right)} x^{2} + {\left(a c^{2} d^{4} e + a^{2} c d^{2} e^{3}\right)} x\right)} \sqrt{c x^{2} + a}}{2 \, {\left({\left(a^{2} c^{3} d^{6} + 2 \, a^{3} c^{2} d^{4} e^{2} + a^{4} c d^{2} e^{4}\right)} x^{3} + {\left(a^{3} c^{2} d^{6} + 2 \, a^{4} c d^{4} e^{2} + a^{5} d^{2} e^{4}\right)} x\right)}}, -\frac{{\left(a^{2} c e^{4} x^{3} + a^{3} e^{4} x\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) + {\left({\left(c^{3} d^{4} e + 2 \, a c^{2} d^{2} e^{3} + a^{2} c e^{5}\right)} x^{3} + {\left(a c^{2} d^{4} e + 2 \, a^{2} c d^{2} e^{3} + a^{3} e^{5}\right)} x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) + {\left(a c^{2} d^{5} + 2 \, a^{2} c d^{3} e^{2} + a^{3} d e^{4} + {\left(2 \, c^{3} d^{5} + 3 \, a c^{2} d^{3} e^{2} + a^{2} c d e^{4}\right)} x^{2} + {\left(a c^{2} d^{4} e + a^{2} c d^{2} e^{3}\right)} x\right)} \sqrt{c x^{2} + a}}{{\left(a^{2} c^{3} d^{6} + 2 \, a^{3} c^{2} d^{4} e^{2} + a^{4} c d^{2} e^{4}\right)} x^{3} + {\left(a^{3} c^{2} d^{6} + 2 \, a^{4} c d^{4} e^{2} + a^{5} d^{2} e^{4}\right)} x}\right]"," ",0,"[1/2*((a^2*c*e^4*x^3 + a^3*e^4*x)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + ((c^3*d^4*e + 2*a*c^2*d^2*e^3 + a^2*c*e^5)*x^3 + (a*c^2*d^4*e + 2*a^2*c*d^2*e^3 + a^3*e^5)*x)*sqrt(a)*log(-(c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) - 2*(a*c^2*d^5 + 2*a^2*c*d^3*e^2 + a^3*d*e^4 + (2*c^3*d^5 + 3*a*c^2*d^3*e^2 + a^2*c*d*e^4)*x^2 + (a*c^2*d^4*e + a^2*c*d^2*e^3)*x)*sqrt(c*x^2 + a))/((a^2*c^3*d^6 + 2*a^3*c^2*d^4*e^2 + a^4*c*d^2*e^4)*x^3 + (a^3*c^2*d^6 + 2*a^4*c*d^4*e^2 + a^5*d^2*e^4)*x), -1/2*(2*(a^2*c*e^4*x^3 + a^3*e^4*x)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - ((c^3*d^4*e + 2*a*c^2*d^2*e^3 + a^2*c*e^5)*x^3 + (a*c^2*d^4*e + 2*a^2*c*d^2*e^3 + a^3*e^5)*x)*sqrt(a)*log(-(c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(a*c^2*d^5 + 2*a^2*c*d^3*e^2 + a^3*d*e^4 + (2*c^3*d^5 + 3*a*c^2*d^3*e^2 + a^2*c*d*e^4)*x^2 + (a*c^2*d^4*e + a^2*c*d^2*e^3)*x)*sqrt(c*x^2 + a))/((a^2*c^3*d^6 + 2*a^3*c^2*d^4*e^2 + a^4*c*d^2*e^4)*x^3 + (a^3*c^2*d^6 + 2*a^4*c*d^4*e^2 + a^5*d^2*e^4)*x), -1/2*(2*((c^3*d^4*e + 2*a*c^2*d^2*e^3 + a^2*c*e^5)*x^3 + (a*c^2*d^4*e + 2*a^2*c*d^2*e^3 + a^3*e^5)*x)*sqrt(-a)*arctan(sqrt(-a)/sqrt(c*x^2 + a)) - (a^2*c*e^4*x^3 + a^3*e^4*x)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(a*c^2*d^5 + 2*a^2*c*d^3*e^2 + a^3*d*e^4 + (2*c^3*d^5 + 3*a*c^2*d^3*e^2 + a^2*c*d*e^4)*x^2 + (a*c^2*d^4*e + a^2*c*d^2*e^3)*x)*sqrt(c*x^2 + a))/((a^2*c^3*d^6 + 2*a^3*c^2*d^4*e^2 + a^4*c*d^2*e^4)*x^3 + (a^3*c^2*d^6 + 2*a^4*c*d^4*e^2 + a^5*d^2*e^4)*x), -((a^2*c*e^4*x^3 + a^3*e^4*x)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) + ((c^3*d^4*e + 2*a*c^2*d^2*e^3 + a^2*c*e^5)*x^3 + (a*c^2*d^4*e + 2*a^2*c*d^2*e^3 + a^3*e^5)*x)*sqrt(-a)*arctan(sqrt(-a)/sqrt(c*x^2 + a)) + (a*c^2*d^5 + 2*a^2*c*d^3*e^2 + a^3*d*e^4 + (2*c^3*d^5 + 3*a*c^2*d^3*e^2 + a^2*c*d*e^4)*x^2 + (a*c^2*d^4*e + a^2*c*d^2*e^3)*x)*sqrt(c*x^2 + a))/((a^2*c^3*d^6 + 2*a^3*c^2*d^4*e^2 + a^4*c*d^2*e^4)*x^3 + (a^3*c^2*d^6 + 2*a^4*c*d^4*e^2 + a^5*d^2*e^4)*x)]","B",0
341,1,1943,0,1.044491," ","integrate(1/x^3/(e*x+d)/(c*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(a^{3} c e^{5} x^{4} + a^{4} e^{5} x^{2}\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - {\left({\left(3 \, c^{4} d^{6} + 4 \, a c^{3} d^{4} e^{2} - a^{2} c^{2} d^{2} e^{4} - 2 \, a^{3} c e^{6}\right)} x^{4} + {\left(3 \, a c^{3} d^{6} + 4 \, a^{2} c^{2} d^{4} e^{2} - a^{3} c d^{2} e^{4} - 2 \, a^{4} e^{6}\right)} x^{2}\right)} \sqrt{a} \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - 2 \, {\left(a^{2} c^{2} d^{6} + 2 \, a^{3} c d^{4} e^{2} + a^{4} d^{2} e^{4} - 2 \, {\left(2 \, a c^{3} d^{5} e + 3 \, a^{2} c^{2} d^{3} e^{3} + a^{3} c d e^{5}\right)} x^{3} + {\left(3 \, a c^{3} d^{6} + 4 \, a^{2} c^{2} d^{4} e^{2} + a^{3} c d^{2} e^{4}\right)} x^{2} - 2 \, {\left(a^{2} c^{2} d^{5} e + 2 \, a^{3} c d^{3} e^{3} + a^{4} d e^{5}\right)} x\right)} \sqrt{c x^{2} + a}}{4 \, {\left({\left(a^{3} c^{3} d^{7} + 2 \, a^{4} c^{2} d^{5} e^{2} + a^{5} c d^{3} e^{4}\right)} x^{4} + {\left(a^{4} c^{2} d^{7} + 2 \, a^{5} c d^{5} e^{2} + a^{6} d^{3} e^{4}\right)} x^{2}\right)}}, \frac{4 \, {\left(a^{3} c e^{5} x^{4} + a^{4} e^{5} x^{2}\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - {\left({\left(3 \, c^{4} d^{6} + 4 \, a c^{3} d^{4} e^{2} - a^{2} c^{2} d^{2} e^{4} - 2 \, a^{3} c e^{6}\right)} x^{4} + {\left(3 \, a c^{3} d^{6} + 4 \, a^{2} c^{2} d^{4} e^{2} - a^{3} c d^{2} e^{4} - 2 \, a^{4} e^{6}\right)} x^{2}\right)} \sqrt{a} \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - 2 \, {\left(a^{2} c^{2} d^{6} + 2 \, a^{3} c d^{4} e^{2} + a^{4} d^{2} e^{4} - 2 \, {\left(2 \, a c^{3} d^{5} e + 3 \, a^{2} c^{2} d^{3} e^{3} + a^{3} c d e^{5}\right)} x^{3} + {\left(3 \, a c^{3} d^{6} + 4 \, a^{2} c^{2} d^{4} e^{2} + a^{3} c d^{2} e^{4}\right)} x^{2} - 2 \, {\left(a^{2} c^{2} d^{5} e + 2 \, a^{3} c d^{3} e^{3} + a^{4} d e^{5}\right)} x\right)} \sqrt{c x^{2} + a}}{4 \, {\left({\left(a^{3} c^{3} d^{7} + 2 \, a^{4} c^{2} d^{5} e^{2} + a^{5} c d^{3} e^{4}\right)} x^{4} + {\left(a^{4} c^{2} d^{7} + 2 \, a^{5} c d^{5} e^{2} + a^{6} d^{3} e^{4}\right)} x^{2}\right)}}, -\frac{{\left({\left(3 \, c^{4} d^{6} + 4 \, a c^{3} d^{4} e^{2} - a^{2} c^{2} d^{2} e^{4} - 2 \, a^{3} c e^{6}\right)} x^{4} + {\left(3 \, a c^{3} d^{6} + 4 \, a^{2} c^{2} d^{4} e^{2} - a^{3} c d^{2} e^{4} - 2 \, a^{4} e^{6}\right)} x^{2}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) - {\left(a^{3} c e^{5} x^{4} + a^{4} e^{5} x^{2}\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + {\left(a^{2} c^{2} d^{6} + 2 \, a^{3} c d^{4} e^{2} + a^{4} d^{2} e^{4} - 2 \, {\left(2 \, a c^{3} d^{5} e + 3 \, a^{2} c^{2} d^{3} e^{3} + a^{3} c d e^{5}\right)} x^{3} + {\left(3 \, a c^{3} d^{6} + 4 \, a^{2} c^{2} d^{4} e^{2} + a^{3} c d^{2} e^{4}\right)} x^{2} - 2 \, {\left(a^{2} c^{2} d^{5} e + 2 \, a^{3} c d^{3} e^{3} + a^{4} d e^{5}\right)} x\right)} \sqrt{c x^{2} + a}}{2 \, {\left({\left(a^{3} c^{3} d^{7} + 2 \, a^{4} c^{2} d^{5} e^{2} + a^{5} c d^{3} e^{4}\right)} x^{4} + {\left(a^{4} c^{2} d^{7} + 2 \, a^{5} c d^{5} e^{2} + a^{6} d^{3} e^{4}\right)} x^{2}\right)}}, \frac{2 \, {\left(a^{3} c e^{5} x^{4} + a^{4} e^{5} x^{2}\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - {\left({\left(3 \, c^{4} d^{6} + 4 \, a c^{3} d^{4} e^{2} - a^{2} c^{2} d^{2} e^{4} - 2 \, a^{3} c e^{6}\right)} x^{4} + {\left(3 \, a c^{3} d^{6} + 4 \, a^{2} c^{2} d^{4} e^{2} - a^{3} c d^{2} e^{4} - 2 \, a^{4} e^{6}\right)} x^{2}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) - {\left(a^{2} c^{2} d^{6} + 2 \, a^{3} c d^{4} e^{2} + a^{4} d^{2} e^{4} - 2 \, {\left(2 \, a c^{3} d^{5} e + 3 \, a^{2} c^{2} d^{3} e^{3} + a^{3} c d e^{5}\right)} x^{3} + {\left(3 \, a c^{3} d^{6} + 4 \, a^{2} c^{2} d^{4} e^{2} + a^{3} c d^{2} e^{4}\right)} x^{2} - 2 \, {\left(a^{2} c^{2} d^{5} e + 2 \, a^{3} c d^{3} e^{3} + a^{4} d e^{5}\right)} x\right)} \sqrt{c x^{2} + a}}{2 \, {\left({\left(a^{3} c^{3} d^{7} + 2 \, a^{4} c^{2} d^{5} e^{2} + a^{5} c d^{3} e^{4}\right)} x^{4} + {\left(a^{4} c^{2} d^{7} + 2 \, a^{5} c d^{5} e^{2} + a^{6} d^{3} e^{4}\right)} x^{2}\right)}}\right]"," ",0,"[1/4*(2*(a^3*c*e^5*x^4 + a^4*e^5*x^2)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 + 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) - ((3*c^4*d^6 + 4*a*c^3*d^4*e^2 - a^2*c^2*d^2*e^4 - 2*a^3*c*e^6)*x^4 + (3*a*c^3*d^6 + 4*a^2*c^2*d^4*e^2 - a^3*c*d^2*e^4 - 2*a^4*e^6)*x^2)*sqrt(a)*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) - 2*(a^2*c^2*d^6 + 2*a^3*c*d^4*e^2 + a^4*d^2*e^4 - 2*(2*a*c^3*d^5*e + 3*a^2*c^2*d^3*e^3 + a^3*c*d*e^5)*x^3 + (3*a*c^3*d^6 + 4*a^2*c^2*d^4*e^2 + a^3*c*d^2*e^4)*x^2 - 2*(a^2*c^2*d^5*e + 2*a^3*c*d^3*e^3 + a^4*d*e^5)*x)*sqrt(c*x^2 + a))/((a^3*c^3*d^7 + 2*a^4*c^2*d^5*e^2 + a^5*c*d^3*e^4)*x^4 + (a^4*c^2*d^7 + 2*a^5*c*d^5*e^2 + a^6*d^3*e^4)*x^2), 1/4*(4*(a^3*c*e^5*x^4 + a^4*e^5*x^2)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - ((3*c^4*d^6 + 4*a*c^3*d^4*e^2 - a^2*c^2*d^2*e^4 - 2*a^3*c*e^6)*x^4 + (3*a*c^3*d^6 + 4*a^2*c^2*d^4*e^2 - a^3*c*d^2*e^4 - 2*a^4*e^6)*x^2)*sqrt(a)*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) - 2*(a^2*c^2*d^6 + 2*a^3*c*d^4*e^2 + a^4*d^2*e^4 - 2*(2*a*c^3*d^5*e + 3*a^2*c^2*d^3*e^3 + a^3*c*d*e^5)*x^3 + (3*a*c^3*d^6 + 4*a^2*c^2*d^4*e^2 + a^3*c*d^2*e^4)*x^2 - 2*(a^2*c^2*d^5*e + 2*a^3*c*d^3*e^3 + a^4*d*e^5)*x)*sqrt(c*x^2 + a))/((a^3*c^3*d^7 + 2*a^4*c^2*d^5*e^2 + a^5*c*d^3*e^4)*x^4 + (a^4*c^2*d^7 + 2*a^5*c*d^5*e^2 + a^6*d^3*e^4)*x^2), -1/2*(((3*c^4*d^6 + 4*a*c^3*d^4*e^2 - a^2*c^2*d^2*e^4 - 2*a^3*c*e^6)*x^4 + (3*a*c^3*d^6 + 4*a^2*c^2*d^4*e^2 - a^3*c*d^2*e^4 - 2*a^4*e^6)*x^2)*sqrt(-a)*arctan(sqrt(-a)/sqrt(c*x^2 + a)) - (a^3*c*e^5*x^4 + a^4*e^5*x^2)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 + 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + (a^2*c^2*d^6 + 2*a^3*c*d^4*e^2 + a^4*d^2*e^4 - 2*(2*a*c^3*d^5*e + 3*a^2*c^2*d^3*e^3 + a^3*c*d*e^5)*x^3 + (3*a*c^3*d^6 + 4*a^2*c^2*d^4*e^2 + a^3*c*d^2*e^4)*x^2 - 2*(a^2*c^2*d^5*e + 2*a^3*c*d^3*e^3 + a^4*d*e^5)*x)*sqrt(c*x^2 + a))/((a^3*c^3*d^7 + 2*a^4*c^2*d^5*e^2 + a^5*c*d^3*e^4)*x^4 + (a^4*c^2*d^7 + 2*a^5*c*d^5*e^2 + a^6*d^3*e^4)*x^2), 1/2*(2*(a^3*c*e^5*x^4 + a^4*e^5*x^2)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - ((3*c^4*d^6 + 4*a*c^3*d^4*e^2 - a^2*c^2*d^2*e^4 - 2*a^3*c*e^6)*x^4 + (3*a*c^3*d^6 + 4*a^2*c^2*d^4*e^2 - a^3*c*d^2*e^4 - 2*a^4*e^6)*x^2)*sqrt(-a)*arctan(sqrt(-a)/sqrt(c*x^2 + a)) - (a^2*c^2*d^6 + 2*a^3*c*d^4*e^2 + a^4*d^2*e^4 - 2*(2*a*c^3*d^5*e + 3*a^2*c^2*d^3*e^3 + a^3*c*d*e^5)*x^3 + (3*a*c^3*d^6 + 4*a^2*c^2*d^4*e^2 + a^3*c*d^2*e^4)*x^2 - 2*(a^2*c^2*d^5*e + 2*a^3*c*d^3*e^3 + a^4*d*e^5)*x)*sqrt(c*x^2 + a))/((a^3*c^3*d^7 + 2*a^4*c^2*d^5*e^2 + a^5*c*d^3*e^4)*x^4 + (a^4*c^2*d^7 + 2*a^5*c*d^5*e^2 + a^6*d^3*e^4)*x^2)]","A",0
342,1,2025,0,41.858238," ","integrate(x^5/(e*x+d)^2/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(4 \, c^{3} d^{8} + 7 \, a c^{2} d^{6} e^{2} + 2 \, a^{2} c d^{4} e^{4} - a^{3} d^{2} e^{6} + {\left(4 \, c^{3} d^{7} e + 7 \, a c^{2} d^{5} e^{3} + 2 \, a^{2} c d^{3} e^{5} - a^{3} d e^{7}\right)} x\right)} \sqrt{c} \log\left(-2 \, c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 3 \, {\left(4 \, c^{3} d^{7} + 5 \, a c^{2} d^{5} e^{2} + {\left(4 \, c^{3} d^{6} e + 5 \, a c^{2} d^{4} e^{3}\right)} x\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(12 \, c^{3} d^{7} e + 19 \, a c^{2} d^{5} e^{3} + 5 \, a^{2} c d^{3} e^{5} - 2 \, a^{3} d e^{7} + {\left(c^{3} d^{4} e^{4} + 2 \, a c^{2} d^{2} e^{6} + a^{2} c e^{8}\right)} x^{3} - 2 \, {\left(c^{3} d^{5} e^{3} + 2 \, a c^{2} d^{3} e^{5} + a^{2} c d e^{7}\right)} x^{2} + 2 \, {\left(3 \, c^{3} d^{6} e^{2} + 5 \, a c^{2} d^{4} e^{4} + a^{2} c d^{2} e^{6} - a^{3} e^{8}\right)} x\right)} \sqrt{c x^{2} + a}}{6 \, {\left(c^{4} d^{5} e^{5} + 2 \, a c^{3} d^{3} e^{7} + a^{2} c^{2} d e^{9} + {\left(c^{4} d^{4} e^{6} + 2 \, a c^{3} d^{2} e^{8} + a^{2} c^{2} e^{10}\right)} x\right)}}, -\frac{6 \, {\left(4 \, c^{3} d^{7} + 5 \, a c^{2} d^{5} e^{2} + {\left(4 \, c^{3} d^{6} e + 5 \, a c^{2} d^{4} e^{3}\right)} x\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - 3 \, {\left(4 \, c^{3} d^{8} + 7 \, a c^{2} d^{6} e^{2} + 2 \, a^{2} c d^{4} e^{4} - a^{3} d^{2} e^{6} + {\left(4 \, c^{3} d^{7} e + 7 \, a c^{2} d^{5} e^{3} + 2 \, a^{2} c d^{3} e^{5} - a^{3} d e^{7}\right)} x\right)} \sqrt{c} \log\left(-2 \, c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) - 2 \, {\left(12 \, c^{3} d^{7} e + 19 \, a c^{2} d^{5} e^{3} + 5 \, a^{2} c d^{3} e^{5} - 2 \, a^{3} d e^{7} + {\left(c^{3} d^{4} e^{4} + 2 \, a c^{2} d^{2} e^{6} + a^{2} c e^{8}\right)} x^{3} - 2 \, {\left(c^{3} d^{5} e^{3} + 2 \, a c^{2} d^{3} e^{5} + a^{2} c d e^{7}\right)} x^{2} + 2 \, {\left(3 \, c^{3} d^{6} e^{2} + 5 \, a c^{2} d^{4} e^{4} + a^{2} c d^{2} e^{6} - a^{3} e^{8}\right)} x\right)} \sqrt{c x^{2} + a}}{6 \, {\left(c^{4} d^{5} e^{5} + 2 \, a c^{3} d^{3} e^{7} + a^{2} c^{2} d e^{9} + {\left(c^{4} d^{4} e^{6} + 2 \, a c^{3} d^{2} e^{8} + a^{2} c^{2} e^{10}\right)} x\right)}}, \frac{6 \, {\left(4 \, c^{3} d^{8} + 7 \, a c^{2} d^{6} e^{2} + 2 \, a^{2} c d^{4} e^{4} - a^{3} d^{2} e^{6} + {\left(4 \, c^{3} d^{7} e + 7 \, a c^{2} d^{5} e^{3} + 2 \, a^{2} c d^{3} e^{5} - a^{3} d e^{7}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) + 3 \, {\left(4 \, c^{3} d^{7} + 5 \, a c^{2} d^{5} e^{2} + {\left(4 \, c^{3} d^{6} e + 5 \, a c^{2} d^{4} e^{3}\right)} x\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(12 \, c^{3} d^{7} e + 19 \, a c^{2} d^{5} e^{3} + 5 \, a^{2} c d^{3} e^{5} - 2 \, a^{3} d e^{7} + {\left(c^{3} d^{4} e^{4} + 2 \, a c^{2} d^{2} e^{6} + a^{2} c e^{8}\right)} x^{3} - 2 \, {\left(c^{3} d^{5} e^{3} + 2 \, a c^{2} d^{3} e^{5} + a^{2} c d e^{7}\right)} x^{2} + 2 \, {\left(3 \, c^{3} d^{6} e^{2} + 5 \, a c^{2} d^{4} e^{4} + a^{2} c d^{2} e^{6} - a^{3} e^{8}\right)} x\right)} \sqrt{c x^{2} + a}}{6 \, {\left(c^{4} d^{5} e^{5} + 2 \, a c^{3} d^{3} e^{7} + a^{2} c^{2} d e^{9} + {\left(c^{4} d^{4} e^{6} + 2 \, a c^{3} d^{2} e^{8} + a^{2} c^{2} e^{10}\right)} x\right)}}, -\frac{3 \, {\left(4 \, c^{3} d^{7} + 5 \, a c^{2} d^{5} e^{2} + {\left(4 \, c^{3} d^{6} e + 5 \, a c^{2} d^{4} e^{3}\right)} x\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - 3 \, {\left(4 \, c^{3} d^{8} + 7 \, a c^{2} d^{6} e^{2} + 2 \, a^{2} c d^{4} e^{4} - a^{3} d^{2} e^{6} + {\left(4 \, c^{3} d^{7} e + 7 \, a c^{2} d^{5} e^{3} + 2 \, a^{2} c d^{3} e^{5} - a^{3} d e^{7}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(12 \, c^{3} d^{7} e + 19 \, a c^{2} d^{5} e^{3} + 5 \, a^{2} c d^{3} e^{5} - 2 \, a^{3} d e^{7} + {\left(c^{3} d^{4} e^{4} + 2 \, a c^{2} d^{2} e^{6} + a^{2} c e^{8}\right)} x^{3} - 2 \, {\left(c^{3} d^{5} e^{3} + 2 \, a c^{2} d^{3} e^{5} + a^{2} c d e^{7}\right)} x^{2} + 2 \, {\left(3 \, c^{3} d^{6} e^{2} + 5 \, a c^{2} d^{4} e^{4} + a^{2} c d^{2} e^{6} - a^{3} e^{8}\right)} x\right)} \sqrt{c x^{2} + a}}{3 \, {\left(c^{4} d^{5} e^{5} + 2 \, a c^{3} d^{3} e^{7} + a^{2} c^{2} d e^{9} + {\left(c^{4} d^{4} e^{6} + 2 \, a c^{3} d^{2} e^{8} + a^{2} c^{2} e^{10}\right)} x\right)}}\right]"," ",0,"[1/6*(3*(4*c^3*d^8 + 7*a*c^2*d^6*e^2 + 2*a^2*c*d^4*e^4 - a^3*d^2*e^6 + (4*c^3*d^7*e + 7*a*c^2*d^5*e^3 + 2*a^2*c*d^3*e^5 - a^3*d*e^7)*x)*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 3*(4*c^3*d^7 + 5*a*c^2*d^5*e^2 + (4*c^3*d^6*e + 5*a*c^2*d^4*e^3)*x)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(12*c^3*d^7*e + 19*a*c^2*d^5*e^3 + 5*a^2*c*d^3*e^5 - 2*a^3*d*e^7 + (c^3*d^4*e^4 + 2*a*c^2*d^2*e^6 + a^2*c*e^8)*x^3 - 2*(c^3*d^5*e^3 + 2*a*c^2*d^3*e^5 + a^2*c*d*e^7)*x^2 + 2*(3*c^3*d^6*e^2 + 5*a*c^2*d^4*e^4 + a^2*c*d^2*e^6 - a^3*e^8)*x)*sqrt(c*x^2 + a))/(c^4*d^5*e^5 + 2*a*c^3*d^3*e^7 + a^2*c^2*d*e^9 + (c^4*d^4*e^6 + 2*a*c^3*d^2*e^8 + a^2*c^2*e^10)*x), -1/6*(6*(4*c^3*d^7 + 5*a*c^2*d^5*e^2 + (4*c^3*d^6*e + 5*a*c^2*d^4*e^3)*x)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - 3*(4*c^3*d^8 + 7*a*c^2*d^6*e^2 + 2*a^2*c*d^4*e^4 - a^3*d^2*e^6 + (4*c^3*d^7*e + 7*a*c^2*d^5*e^3 + 2*a^2*c*d^3*e^5 - a^3*d*e^7)*x)*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) - 2*(12*c^3*d^7*e + 19*a*c^2*d^5*e^3 + 5*a^2*c*d^3*e^5 - 2*a^3*d*e^7 + (c^3*d^4*e^4 + 2*a*c^2*d^2*e^6 + a^2*c*e^8)*x^3 - 2*(c^3*d^5*e^3 + 2*a*c^2*d^3*e^5 + a^2*c*d*e^7)*x^2 + 2*(3*c^3*d^6*e^2 + 5*a*c^2*d^4*e^4 + a^2*c*d^2*e^6 - a^3*e^8)*x)*sqrt(c*x^2 + a))/(c^4*d^5*e^5 + 2*a*c^3*d^3*e^7 + a^2*c^2*d*e^9 + (c^4*d^4*e^6 + 2*a*c^3*d^2*e^8 + a^2*c^2*e^10)*x), 1/6*(6*(4*c^3*d^8 + 7*a*c^2*d^6*e^2 + 2*a^2*c*d^4*e^4 - a^3*d^2*e^6 + (4*c^3*d^7*e + 7*a*c^2*d^5*e^3 + 2*a^2*c*d^3*e^5 - a^3*d*e^7)*x)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) + 3*(4*c^3*d^7 + 5*a*c^2*d^5*e^2 + (4*c^3*d^6*e + 5*a*c^2*d^4*e^3)*x)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(12*c^3*d^7*e + 19*a*c^2*d^5*e^3 + 5*a^2*c*d^3*e^5 - 2*a^3*d*e^7 + (c^3*d^4*e^4 + 2*a*c^2*d^2*e^6 + a^2*c*e^8)*x^3 - 2*(c^3*d^5*e^3 + 2*a*c^2*d^3*e^5 + a^2*c*d*e^7)*x^2 + 2*(3*c^3*d^6*e^2 + 5*a*c^2*d^4*e^4 + a^2*c*d^2*e^6 - a^3*e^8)*x)*sqrt(c*x^2 + a))/(c^4*d^5*e^5 + 2*a*c^3*d^3*e^7 + a^2*c^2*d*e^9 + (c^4*d^4*e^6 + 2*a*c^3*d^2*e^8 + a^2*c^2*e^10)*x), -1/3*(3*(4*c^3*d^7 + 5*a*c^2*d^5*e^2 + (4*c^3*d^6*e + 5*a*c^2*d^4*e^3)*x)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - 3*(4*c^3*d^8 + 7*a*c^2*d^6*e^2 + 2*a^2*c*d^4*e^4 - a^3*d^2*e^6 + (4*c^3*d^7*e + 7*a*c^2*d^5*e^3 + 2*a^2*c*d^3*e^5 - a^3*d*e^7)*x)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (12*c^3*d^7*e + 19*a*c^2*d^5*e^3 + 5*a^2*c*d^3*e^5 - 2*a^3*d*e^7 + (c^3*d^4*e^4 + 2*a*c^2*d^2*e^6 + a^2*c*e^8)*x^3 - 2*(c^3*d^5*e^3 + 2*a*c^2*d^3*e^5 + a^2*c*d*e^7)*x^2 + 2*(3*c^3*d^6*e^2 + 5*a*c^2*d^4*e^4 + a^2*c*d^2*e^6 - a^3*e^8)*x)*sqrt(c*x^2 + a))/(c^4*d^5*e^5 + 2*a*c^3*d^3*e^7 + a^2*c^2*d*e^9 + (c^4*d^4*e^6 + 2*a*c^3*d^2*e^8 + a^2*c^2*e^10)*x)]","B",0
343,1,1786,0,66.283157," ","integrate(x^4/(e*x+d)^2/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(6 \, c^{3} d^{7} + 11 \, a c^{2} d^{5} e^{2} + 4 \, a^{2} c d^{3} e^{4} - a^{3} d e^{6} + {\left(6 \, c^{3} d^{6} e + 11 \, a c^{2} d^{4} e^{3} + 4 \, a^{2} c d^{2} e^{5} - a^{3} e^{7}\right)} x\right)} \sqrt{c} \log\left(-2 \, c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) - 2 \, {\left(3 \, c^{3} d^{6} + 4 \, a c^{2} d^{4} e^{2} + {\left(3 \, c^{3} d^{5} e + 4 \, a c^{2} d^{3} e^{3}\right)} x\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(6 \, c^{3} d^{6} e + 10 \, a c^{2} d^{4} e^{3} + 4 \, a^{2} c d^{2} e^{5} - {\left(c^{3} d^{4} e^{3} + 2 \, a c^{2} d^{2} e^{5} + a^{2} c e^{7}\right)} x^{2} + 3 \, {\left(c^{3} d^{5} e^{2} + 2 \, a c^{2} d^{3} e^{4} + a^{2} c d e^{6}\right)} x\right)} \sqrt{c x^{2} + a}}{4 \, {\left(c^{4} d^{5} e^{4} + 2 \, a c^{3} d^{3} e^{6} + a^{2} c^{2} d e^{8} + {\left(c^{4} d^{4} e^{5} + 2 \, a c^{3} d^{2} e^{7} + a^{2} c^{2} e^{9}\right)} x\right)}}, \frac{4 \, {\left(3 \, c^{3} d^{6} + 4 \, a c^{2} d^{4} e^{2} + {\left(3 \, c^{3} d^{5} e + 4 \, a c^{2} d^{3} e^{3}\right)} x\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - {\left(6 \, c^{3} d^{7} + 11 \, a c^{2} d^{5} e^{2} + 4 \, a^{2} c d^{3} e^{4} - a^{3} d e^{6} + {\left(6 \, c^{3} d^{6} e + 11 \, a c^{2} d^{4} e^{3} + 4 \, a^{2} c d^{2} e^{5} - a^{3} e^{7}\right)} x\right)} \sqrt{c} \log\left(-2 \, c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) - 2 \, {\left(6 \, c^{3} d^{6} e + 10 \, a c^{2} d^{4} e^{3} + 4 \, a^{2} c d^{2} e^{5} - {\left(c^{3} d^{4} e^{3} + 2 \, a c^{2} d^{2} e^{5} + a^{2} c e^{7}\right)} x^{2} + 3 \, {\left(c^{3} d^{5} e^{2} + 2 \, a c^{2} d^{3} e^{4} + a^{2} c d e^{6}\right)} x\right)} \sqrt{c x^{2} + a}}{4 \, {\left(c^{4} d^{5} e^{4} + 2 \, a c^{3} d^{3} e^{6} + a^{2} c^{2} d e^{8} + {\left(c^{4} d^{4} e^{5} + 2 \, a c^{3} d^{2} e^{7} + a^{2} c^{2} e^{9}\right)} x\right)}}, -\frac{{\left(6 \, c^{3} d^{7} + 11 \, a c^{2} d^{5} e^{2} + 4 \, a^{2} c d^{3} e^{4} - a^{3} d e^{6} + {\left(6 \, c^{3} d^{6} e + 11 \, a c^{2} d^{4} e^{3} + 4 \, a^{2} c d^{2} e^{5} - a^{3} e^{7}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(3 \, c^{3} d^{6} + 4 \, a c^{2} d^{4} e^{2} + {\left(3 \, c^{3} d^{5} e + 4 \, a c^{2} d^{3} e^{3}\right)} x\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + {\left(6 \, c^{3} d^{6} e + 10 \, a c^{2} d^{4} e^{3} + 4 \, a^{2} c d^{2} e^{5} - {\left(c^{3} d^{4} e^{3} + 2 \, a c^{2} d^{2} e^{5} + a^{2} c e^{7}\right)} x^{2} + 3 \, {\left(c^{3} d^{5} e^{2} + 2 \, a c^{2} d^{3} e^{4} + a^{2} c d e^{6}\right)} x\right)} \sqrt{c x^{2} + a}}{2 \, {\left(c^{4} d^{5} e^{4} + 2 \, a c^{3} d^{3} e^{6} + a^{2} c^{2} d e^{8} + {\left(c^{4} d^{4} e^{5} + 2 \, a c^{3} d^{2} e^{7} + a^{2} c^{2} e^{9}\right)} x\right)}}, \frac{2 \, {\left(3 \, c^{3} d^{6} + 4 \, a c^{2} d^{4} e^{2} + {\left(3 \, c^{3} d^{5} e + 4 \, a c^{2} d^{3} e^{3}\right)} x\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - {\left(6 \, c^{3} d^{7} + 11 \, a c^{2} d^{5} e^{2} + 4 \, a^{2} c d^{3} e^{4} - a^{3} d e^{6} + {\left(6 \, c^{3} d^{6} e + 11 \, a c^{2} d^{4} e^{3} + 4 \, a^{2} c d^{2} e^{5} - a^{3} e^{7}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(6 \, c^{3} d^{6} e + 10 \, a c^{2} d^{4} e^{3} + 4 \, a^{2} c d^{2} e^{5} - {\left(c^{3} d^{4} e^{3} + 2 \, a c^{2} d^{2} e^{5} + a^{2} c e^{7}\right)} x^{2} + 3 \, {\left(c^{3} d^{5} e^{2} + 2 \, a c^{2} d^{3} e^{4} + a^{2} c d e^{6}\right)} x\right)} \sqrt{c x^{2} + a}}{2 \, {\left(c^{4} d^{5} e^{4} + 2 \, a c^{3} d^{3} e^{6} + a^{2} c^{2} d e^{8} + {\left(c^{4} d^{4} e^{5} + 2 \, a c^{3} d^{2} e^{7} + a^{2} c^{2} e^{9}\right)} x\right)}}\right]"," ",0,"[-1/4*((6*c^3*d^7 + 11*a*c^2*d^5*e^2 + 4*a^2*c*d^3*e^4 - a^3*d*e^6 + (6*c^3*d^6*e + 11*a*c^2*d^4*e^3 + 4*a^2*c*d^2*e^5 - a^3*e^7)*x)*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) - 2*(3*c^3*d^6 + 4*a*c^2*d^4*e^2 + (3*c^3*d^5*e + 4*a*c^2*d^3*e^3)*x)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 + 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(6*c^3*d^6*e + 10*a*c^2*d^4*e^3 + 4*a^2*c*d^2*e^5 - (c^3*d^4*e^3 + 2*a*c^2*d^2*e^5 + a^2*c*e^7)*x^2 + 3*(c^3*d^5*e^2 + 2*a*c^2*d^3*e^4 + a^2*c*d*e^6)*x)*sqrt(c*x^2 + a))/(c^4*d^5*e^4 + 2*a*c^3*d^3*e^6 + a^2*c^2*d*e^8 + (c^4*d^4*e^5 + 2*a*c^3*d^2*e^7 + a^2*c^2*e^9)*x), 1/4*(4*(3*c^3*d^6 + 4*a*c^2*d^4*e^2 + (3*c^3*d^5*e + 4*a*c^2*d^3*e^3)*x)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - (6*c^3*d^7 + 11*a*c^2*d^5*e^2 + 4*a^2*c*d^3*e^4 - a^3*d*e^6 + (6*c^3*d^6*e + 11*a*c^2*d^4*e^3 + 4*a^2*c*d^2*e^5 - a^3*e^7)*x)*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) - 2*(6*c^3*d^6*e + 10*a*c^2*d^4*e^3 + 4*a^2*c*d^2*e^5 - (c^3*d^4*e^3 + 2*a*c^2*d^2*e^5 + a^2*c*e^7)*x^2 + 3*(c^3*d^5*e^2 + 2*a*c^2*d^3*e^4 + a^2*c*d*e^6)*x)*sqrt(c*x^2 + a))/(c^4*d^5*e^4 + 2*a*c^3*d^3*e^6 + a^2*c^2*d*e^8 + (c^4*d^4*e^5 + 2*a*c^3*d^2*e^7 + a^2*c^2*e^9)*x), -1/2*((6*c^3*d^7 + 11*a*c^2*d^5*e^2 + 4*a^2*c*d^3*e^4 - a^3*d*e^6 + (6*c^3*d^6*e + 11*a*c^2*d^4*e^3 + 4*a^2*c*d^2*e^5 - a^3*e^7)*x)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (3*c^3*d^6 + 4*a*c^2*d^4*e^2 + (3*c^3*d^5*e + 4*a*c^2*d^3*e^3)*x)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 + 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + (6*c^3*d^6*e + 10*a*c^2*d^4*e^3 + 4*a^2*c*d^2*e^5 - (c^3*d^4*e^3 + 2*a*c^2*d^2*e^5 + a^2*c*e^7)*x^2 + 3*(c^3*d^5*e^2 + 2*a*c^2*d^3*e^4 + a^2*c*d*e^6)*x)*sqrt(c*x^2 + a))/(c^4*d^5*e^4 + 2*a*c^3*d^3*e^6 + a^2*c^2*d*e^8 + (c^4*d^4*e^5 + 2*a*c^3*d^2*e^7 + a^2*c^2*e^9)*x), 1/2*(2*(3*c^3*d^6 + 4*a*c^2*d^4*e^2 + (3*c^3*d^5*e + 4*a*c^2*d^3*e^3)*x)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - (6*c^3*d^7 + 11*a*c^2*d^5*e^2 + 4*a^2*c*d^3*e^4 - a^3*d*e^6 + (6*c^3*d^6*e + 11*a*c^2*d^4*e^3 + 4*a^2*c*d^2*e^5 - a^3*e^7)*x)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (6*c^3*d^6*e + 10*a*c^2*d^4*e^3 + 4*a^2*c*d^2*e^5 - (c^3*d^4*e^3 + 2*a*c^2*d^2*e^5 + a^2*c*e^7)*x^2 + 3*(c^3*d^5*e^2 + 2*a*c^2*d^3*e^4 + a^2*c*d*e^6)*x)*sqrt(c*x^2 + a))/(c^4*d^5*e^4 + 2*a*c^3*d^3*e^6 + a^2*c^2*d*e^8 + (c^4*d^4*e^5 + 2*a*c^3*d^2*e^7 + a^2*c^2*e^9)*x)]","B",0
344,1,1449,0,6.774366," ","integrate(x^3/(e*x+d)^2/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(c^{2} d^{6} + 2 \, a c d^{4} e^{2} + a^{2} d^{2} e^{4} + {\left(c^{2} d^{5} e + 2 \, a c d^{3} e^{3} + a^{2} d e^{5}\right)} x\right)} \sqrt{c} \log\left(-2 \, c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + {\left(2 \, c^{2} d^{5} + 3 \, a c d^{3} e^{2} + {\left(2 \, c^{2} d^{4} e + 3 \, a c d^{2} e^{3}\right)} x\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(2 \, c^{2} d^{5} e + 3 \, a c d^{3} e^{3} + a^{2} d e^{5} + {\left(c^{2} d^{4} e^{2} + 2 \, a c d^{2} e^{4} + a^{2} e^{6}\right)} x\right)} \sqrt{c x^{2} + a}}{2 \, {\left(c^{3} d^{5} e^{3} + 2 \, a c^{2} d^{3} e^{5} + a^{2} c d e^{7} + {\left(c^{3} d^{4} e^{4} + 2 \, a c^{2} d^{2} e^{6} + a^{2} c e^{8}\right)} x\right)}}, -\frac{{\left(2 \, c^{2} d^{5} + 3 \, a c d^{3} e^{2} + {\left(2 \, c^{2} d^{4} e + 3 \, a c d^{2} e^{3}\right)} x\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - {\left(c^{2} d^{6} + 2 \, a c d^{4} e^{2} + a^{2} d^{2} e^{4} + {\left(c^{2} d^{5} e + 2 \, a c d^{3} e^{3} + a^{2} d e^{5}\right)} x\right)} \sqrt{c} \log\left(-2 \, c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) - {\left(2 \, c^{2} d^{5} e + 3 \, a c d^{3} e^{3} + a^{2} d e^{5} + {\left(c^{2} d^{4} e^{2} + 2 \, a c d^{2} e^{4} + a^{2} e^{6}\right)} x\right)} \sqrt{c x^{2} + a}}{c^{3} d^{5} e^{3} + 2 \, a c^{2} d^{3} e^{5} + a^{2} c d e^{7} + {\left(c^{3} d^{4} e^{4} + 2 \, a c^{2} d^{2} e^{6} + a^{2} c e^{8}\right)} x}, \frac{4 \, {\left(c^{2} d^{6} + 2 \, a c d^{4} e^{2} + a^{2} d^{2} e^{4} + {\left(c^{2} d^{5} e + 2 \, a c d^{3} e^{3} + a^{2} d e^{5}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) + {\left(2 \, c^{2} d^{5} + 3 \, a c d^{3} e^{2} + {\left(2 \, c^{2} d^{4} e + 3 \, a c d^{2} e^{3}\right)} x\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(2 \, c^{2} d^{5} e + 3 \, a c d^{3} e^{3} + a^{2} d e^{5} + {\left(c^{2} d^{4} e^{2} + 2 \, a c d^{2} e^{4} + a^{2} e^{6}\right)} x\right)} \sqrt{c x^{2} + a}}{2 \, {\left(c^{3} d^{5} e^{3} + 2 \, a c^{2} d^{3} e^{5} + a^{2} c d e^{7} + {\left(c^{3} d^{4} e^{4} + 2 \, a c^{2} d^{2} e^{6} + a^{2} c e^{8}\right)} x\right)}}, -\frac{{\left(2 \, c^{2} d^{5} + 3 \, a c d^{3} e^{2} + {\left(2 \, c^{2} d^{4} e + 3 \, a c d^{2} e^{3}\right)} x\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - 2 \, {\left(c^{2} d^{6} + 2 \, a c d^{4} e^{2} + a^{2} d^{2} e^{4} + {\left(c^{2} d^{5} e + 2 \, a c d^{3} e^{3} + a^{2} d e^{5}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(2 \, c^{2} d^{5} e + 3 \, a c d^{3} e^{3} + a^{2} d e^{5} + {\left(c^{2} d^{4} e^{2} + 2 \, a c d^{2} e^{4} + a^{2} e^{6}\right)} x\right)} \sqrt{c x^{2} + a}}{c^{3} d^{5} e^{3} + 2 \, a c^{2} d^{3} e^{5} + a^{2} c d e^{7} + {\left(c^{3} d^{4} e^{4} + 2 \, a c^{2} d^{2} e^{6} + a^{2} c e^{8}\right)} x}\right]"," ",0,"[1/2*(2*(c^2*d^6 + 2*a*c*d^4*e^2 + a^2*d^2*e^4 + (c^2*d^5*e + 2*a*c*d^3*e^3 + a^2*d*e^5)*x)*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + (2*c^2*d^5 + 3*a*c*d^3*e^2 + (2*c^2*d^4*e + 3*a*c*d^2*e^3)*x)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(2*c^2*d^5*e + 3*a*c*d^3*e^3 + a^2*d*e^5 + (c^2*d^4*e^2 + 2*a*c*d^2*e^4 + a^2*e^6)*x)*sqrt(c*x^2 + a))/(c^3*d^5*e^3 + 2*a*c^2*d^3*e^5 + a^2*c*d*e^7 + (c^3*d^4*e^4 + 2*a*c^2*d^2*e^6 + a^2*c*e^8)*x), -((2*c^2*d^5 + 3*a*c*d^3*e^2 + (2*c^2*d^4*e + 3*a*c*d^2*e^3)*x)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - (c^2*d^6 + 2*a*c*d^4*e^2 + a^2*d^2*e^4 + (c^2*d^5*e + 2*a*c*d^3*e^3 + a^2*d*e^5)*x)*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) - (2*c^2*d^5*e + 3*a*c*d^3*e^3 + a^2*d*e^5 + (c^2*d^4*e^2 + 2*a*c*d^2*e^4 + a^2*e^6)*x)*sqrt(c*x^2 + a))/(c^3*d^5*e^3 + 2*a*c^2*d^3*e^5 + a^2*c*d*e^7 + (c^3*d^4*e^4 + 2*a*c^2*d^2*e^6 + a^2*c*e^8)*x), 1/2*(4*(c^2*d^6 + 2*a*c*d^4*e^2 + a^2*d^2*e^4 + (c^2*d^5*e + 2*a*c*d^3*e^3 + a^2*d*e^5)*x)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) + (2*c^2*d^5 + 3*a*c*d^3*e^2 + (2*c^2*d^4*e + 3*a*c*d^2*e^3)*x)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(2*c^2*d^5*e + 3*a*c*d^3*e^3 + a^2*d*e^5 + (c^2*d^4*e^2 + 2*a*c*d^2*e^4 + a^2*e^6)*x)*sqrt(c*x^2 + a))/(c^3*d^5*e^3 + 2*a*c^2*d^3*e^5 + a^2*c*d*e^7 + (c^3*d^4*e^4 + 2*a*c^2*d^2*e^6 + a^2*c*e^8)*x), -((2*c^2*d^5 + 3*a*c*d^3*e^2 + (2*c^2*d^4*e + 3*a*c*d^2*e^3)*x)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - 2*(c^2*d^6 + 2*a*c*d^4*e^2 + a^2*d^2*e^4 + (c^2*d^5*e + 2*a*c*d^3*e^3 + a^2*d*e^5)*x)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (2*c^2*d^5*e + 3*a*c*d^3*e^3 + a^2*d*e^5 + (c^2*d^4*e^2 + 2*a*c*d^2*e^4 + a^2*e^6)*x)*sqrt(c*x^2 + a))/(c^3*d^5*e^3 + 2*a*c^2*d^3*e^5 + a^2*c*d*e^7 + (c^3*d^4*e^4 + 2*a*c^2*d^2*e^6 + a^2*c*e^8)*x)]","B",0
345,1,1260,0,6.366733," ","integrate(x^2/(e*x+d)^2/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(c^{2} d^{5} + 2 \, a c d^{3} e^{2} + a^{2} d e^{4} + {\left(c^{2} d^{4} e + 2 \, a c d^{2} e^{3} + a^{2} e^{5}\right)} x\right)} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + {\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + {\left(c^{2} d^{3} e + 2 \, a c d e^{3}\right)} x\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 2 \, {\left(c^{2} d^{4} e + a c d^{2} e^{3}\right)} \sqrt{c x^{2} + a}}{2 \, {\left(c^{3} d^{5} e^{2} + 2 \, a c^{2} d^{3} e^{4} + a^{2} c d e^{6} + {\left(c^{3} d^{4} e^{3} + 2 \, a c^{2} d^{2} e^{5} + a^{2} c e^{7}\right)} x\right)}}, \frac{2 \, {\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + {\left(c^{2} d^{3} e + 2 \, a c d e^{3}\right)} x\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) + {\left(c^{2} d^{5} + 2 \, a c d^{3} e^{2} + a^{2} d e^{4} + {\left(c^{2} d^{4} e + 2 \, a c d^{2} e^{3} + a^{2} e^{5}\right)} x\right)} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) - 2 \, {\left(c^{2} d^{4} e + a c d^{2} e^{3}\right)} \sqrt{c x^{2} + a}}{2 \, {\left(c^{3} d^{5} e^{2} + 2 \, a c^{2} d^{3} e^{4} + a^{2} c d e^{6} + {\left(c^{3} d^{4} e^{3} + 2 \, a c^{2} d^{2} e^{5} + a^{2} c e^{7}\right)} x\right)}}, -\frac{2 \, {\left(c^{2} d^{5} + 2 \, a c d^{3} e^{2} + a^{2} d e^{4} + {\left(c^{2} d^{4} e + 2 \, a c d^{2} e^{3} + a^{2} e^{5}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + {\left(c^{2} d^{3} e + 2 \, a c d e^{3}\right)} x\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(c^{2} d^{4} e + a c d^{2} e^{3}\right)} \sqrt{c x^{2} + a}}{2 \, {\left(c^{3} d^{5} e^{2} + 2 \, a c^{2} d^{3} e^{4} + a^{2} c d e^{6} + {\left(c^{3} d^{4} e^{3} + 2 \, a c^{2} d^{2} e^{5} + a^{2} c e^{7}\right)} x\right)}}, \frac{{\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + {\left(c^{2} d^{3} e + 2 \, a c d e^{3}\right)} x\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - {\left(c^{2} d^{5} + 2 \, a c d^{3} e^{2} + a^{2} d e^{4} + {\left(c^{2} d^{4} e + 2 \, a c d^{2} e^{3} + a^{2} e^{5}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(c^{2} d^{4} e + a c d^{2} e^{3}\right)} \sqrt{c x^{2} + a}}{c^{3} d^{5} e^{2} + 2 \, a c^{2} d^{3} e^{4} + a^{2} c d e^{6} + {\left(c^{3} d^{4} e^{3} + 2 \, a c^{2} d^{2} e^{5} + a^{2} c e^{7}\right)} x}\right]"," ",0,"[1/2*((c^2*d^5 + 2*a*c*d^3*e^2 + a^2*d*e^4 + (c^2*d^4*e + 2*a*c*d^2*e^3 + a^2*e^5)*x)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + (c^2*d^4 + 2*a*c*d^2*e^2 + (c^2*d^3*e + 2*a*c*d*e^3)*x)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 + 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) - 2*(c^2*d^4*e + a*c*d^2*e^3)*sqrt(c*x^2 + a))/(c^3*d^5*e^2 + 2*a*c^2*d^3*e^4 + a^2*c*d*e^6 + (c^3*d^4*e^3 + 2*a*c^2*d^2*e^5 + a^2*c*e^7)*x), 1/2*(2*(c^2*d^4 + 2*a*c*d^2*e^2 + (c^2*d^3*e + 2*a*c*d*e^3)*x)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) + (c^2*d^5 + 2*a*c*d^3*e^2 + a^2*d*e^4 + (c^2*d^4*e + 2*a*c*d^2*e^3 + a^2*e^5)*x)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) - 2*(c^2*d^4*e + a*c*d^2*e^3)*sqrt(c*x^2 + a))/(c^3*d^5*e^2 + 2*a*c^2*d^3*e^4 + a^2*c*d*e^6 + (c^3*d^4*e^3 + 2*a*c^2*d^2*e^5 + a^2*c*e^7)*x), -1/2*(2*(c^2*d^5 + 2*a*c*d^3*e^2 + a^2*d*e^4 + (c^2*d^4*e + 2*a*c*d^2*e^3 + a^2*e^5)*x)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (c^2*d^4 + 2*a*c*d^2*e^2 + (c^2*d^3*e + 2*a*c*d*e^3)*x)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 + 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(c^2*d^4*e + a*c*d^2*e^3)*sqrt(c*x^2 + a))/(c^3*d^5*e^2 + 2*a*c^2*d^3*e^4 + a^2*c*d*e^6 + (c^3*d^4*e^3 + 2*a*c^2*d^2*e^5 + a^2*c*e^7)*x), ((c^2*d^4 + 2*a*c*d^2*e^2 + (c^2*d^3*e + 2*a*c*d*e^3)*x)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - (c^2*d^5 + 2*a*c*d^3*e^2 + a^2*d*e^4 + (c^2*d^4*e + 2*a*c*d^2*e^3 + a^2*e^5)*x)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (c^2*d^4*e + a*c*d^2*e^3)*sqrt(c*x^2 + a))/(c^3*d^5*e^2 + 2*a*c^2*d^3*e^4 + a^2*c*d*e^6 + (c^3*d^4*e^3 + 2*a*c^2*d^2*e^5 + a^2*c*e^7)*x)]","B",0
346,1,382,0,0.457845," ","integrate(x/(e*x+d)^2/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(a e^{2} x + a d e\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(c d^{3} + a d e^{2}\right)} \sqrt{c x^{2} + a}}{2 \, {\left(c^{2} d^{5} + 2 \, a c d^{3} e^{2} + a^{2} d e^{4} + {\left(c^{2} d^{4} e + 2 \, a c d^{2} e^{3} + a^{2} e^{5}\right)} x\right)}}, -\frac{{\left(a e^{2} x + a d e\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - {\left(c d^{3} + a d e^{2}\right)} \sqrt{c x^{2} + a}}{c^{2} d^{5} + 2 \, a c d^{3} e^{2} + a^{2} d e^{4} + {\left(c^{2} d^{4} e + 2 \, a c d^{2} e^{3} + a^{2} e^{5}\right)} x}\right]"," ",0,"[1/2*((a*e^2*x + a*d*e)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(c*d^3 + a*d*e^2)*sqrt(c*x^2 + a))/(c^2*d^5 + 2*a*c*d^3*e^2 + a^2*d*e^4 + (c^2*d^4*e + 2*a*c*d^2*e^3 + a^2*e^5)*x), -((a*e^2*x + a*d*e)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - (c*d^3 + a*d*e^2)*sqrt(c*x^2 + a))/(c^2*d^5 + 2*a*c*d^3*e^2 + a^2*d*e^4 + (c^2*d^4*e + 2*a*c*d^2*e^3 + a^2*e^5)*x)]","B",0
347,1,381,0,0.457765," ","integrate(1/(e*x+d)^2/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(c d e x + c d^{2}\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 2 \, {\left(c d^{2} e + a e^{3}\right)} \sqrt{c x^{2} + a}}{2 \, {\left(c^{2} d^{5} + 2 \, a c d^{3} e^{2} + a^{2} d e^{4} + {\left(c^{2} d^{4} e + 2 \, a c d^{2} e^{3} + a^{2} e^{5}\right)} x\right)}}, -\frac{{\left(c d e x + c d^{2}\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) + {\left(c d^{2} e + a e^{3}\right)} \sqrt{c x^{2} + a}}{c^{2} d^{5} + 2 \, a c d^{3} e^{2} + a^{2} d e^{4} + {\left(c^{2} d^{4} e + 2 \, a c d^{2} e^{3} + a^{2} e^{5}\right)} x}\right]"," ",0,"[1/2*((c*d*e*x + c*d^2)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) - 2*(c*d^2*e + a*e^3)*sqrt(c*x^2 + a))/(c^2*d^5 + 2*a*c*d^3*e^2 + a^2*d*e^4 + (c^2*d^4*e + 2*a*c*d^2*e^3 + a^2*e^5)*x), -((c*d*e*x + c*d^2)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) + (c*d^2*e + a*e^3)*sqrt(c*x^2 + a))/(c^2*d^5 + 2*a*c*d^3*e^2 + a^2*d*e^4 + (c^2*d^4*e + 2*a*c*d^2*e^3 + a^2*e^5)*x)]","B",0
348,1,1261,0,0.808317," ","integrate(1/x/(e*x+d)^2/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(2 \, a c d^{3} e + a^{2} d e^{3} + {\left(2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} x\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + {\left(c^{2} d^{5} + 2 \, a c d^{3} e^{2} + a^{2} d e^{4} + {\left(c^{2} d^{4} e + 2 \, a c d^{2} e^{3} + a^{2} e^{5}\right)} x\right)} \sqrt{a} \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(a c d^{3} e^{2} + a^{2} d e^{4}\right)} \sqrt{c x^{2} + a}}{2 \, {\left(a c^{2} d^{7} + 2 \, a^{2} c d^{5} e^{2} + a^{3} d^{3} e^{4} + {\left(a c^{2} d^{6} e + 2 \, a^{2} c d^{4} e^{3} + a^{3} d^{2} e^{5}\right)} x\right)}}, \frac{2 \, {\left(2 \, a c d^{3} e + a^{2} d e^{3} + {\left(2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} x\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) + {\left(c^{2} d^{5} + 2 \, a c d^{3} e^{2} + a^{2} d e^{4} + {\left(c^{2} d^{4} e + 2 \, a c d^{2} e^{3} + a^{2} e^{5}\right)} x\right)} \sqrt{a} \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(a c d^{3} e^{2} + a^{2} d e^{4}\right)} \sqrt{c x^{2} + a}}{2 \, {\left(a c^{2} d^{7} + 2 \, a^{2} c d^{5} e^{2} + a^{3} d^{3} e^{4} + {\left(a c^{2} d^{6} e + 2 \, a^{2} c d^{4} e^{3} + a^{3} d^{2} e^{5}\right)} x\right)}}, \frac{2 \, {\left(c^{2} d^{5} + 2 \, a c d^{3} e^{2} + a^{2} d e^{4} + {\left(c^{2} d^{4} e + 2 \, a c d^{2} e^{3} + a^{2} e^{5}\right)} x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) + {\left(2 \, a c d^{3} e + a^{2} d e^{3} + {\left(2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} x\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(a c d^{3} e^{2} + a^{2} d e^{4}\right)} \sqrt{c x^{2} + a}}{2 \, {\left(a c^{2} d^{7} + 2 \, a^{2} c d^{5} e^{2} + a^{3} d^{3} e^{4} + {\left(a c^{2} d^{6} e + 2 \, a^{2} c d^{4} e^{3} + a^{3} d^{2} e^{5}\right)} x\right)}}, \frac{{\left(2 \, a c d^{3} e + a^{2} d e^{3} + {\left(2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} x\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) + {\left(c^{2} d^{5} + 2 \, a c d^{3} e^{2} + a^{2} d e^{4} + {\left(c^{2} d^{4} e + 2 \, a c d^{2} e^{3} + a^{2} e^{5}\right)} x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) + {\left(a c d^{3} e^{2} + a^{2} d e^{4}\right)} \sqrt{c x^{2} + a}}{a c^{2} d^{7} + 2 \, a^{2} c d^{5} e^{2} + a^{3} d^{3} e^{4} + {\left(a c^{2} d^{6} e + 2 \, a^{2} c d^{4} e^{3} + a^{3} d^{2} e^{5}\right)} x}\right]"," ",0,"[1/2*((2*a*c*d^3*e + a^2*d*e^3 + (2*a*c*d^2*e^2 + a^2*e^4)*x)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 + 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + (c^2*d^5 + 2*a*c*d^3*e^2 + a^2*d*e^4 + (c^2*d^4*e + 2*a*c*d^2*e^3 + a^2*e^5)*x)*sqrt(a)*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(a*c*d^3*e^2 + a^2*d*e^4)*sqrt(c*x^2 + a))/(a*c^2*d^7 + 2*a^2*c*d^5*e^2 + a^3*d^3*e^4 + (a*c^2*d^6*e + 2*a^2*c*d^4*e^3 + a^3*d^2*e^5)*x), 1/2*(2*(2*a*c*d^3*e + a^2*d*e^3 + (2*a*c*d^2*e^2 + a^2*e^4)*x)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) + (c^2*d^5 + 2*a*c*d^3*e^2 + a^2*d*e^4 + (c^2*d^4*e + 2*a*c*d^2*e^3 + a^2*e^5)*x)*sqrt(a)*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(a*c*d^3*e^2 + a^2*d*e^4)*sqrt(c*x^2 + a))/(a*c^2*d^7 + 2*a^2*c*d^5*e^2 + a^3*d^3*e^4 + (a*c^2*d^6*e + 2*a^2*c*d^4*e^3 + a^3*d^2*e^5)*x), 1/2*(2*(c^2*d^5 + 2*a*c*d^3*e^2 + a^2*d*e^4 + (c^2*d^4*e + 2*a*c*d^2*e^3 + a^2*e^5)*x)*sqrt(-a)*arctan(sqrt(-a)/sqrt(c*x^2 + a)) + (2*a*c*d^3*e + a^2*d*e^3 + (2*a*c*d^2*e^2 + a^2*e^4)*x)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 + 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(a*c*d^3*e^2 + a^2*d*e^4)*sqrt(c*x^2 + a))/(a*c^2*d^7 + 2*a^2*c*d^5*e^2 + a^3*d^3*e^4 + (a*c^2*d^6*e + 2*a^2*c*d^4*e^3 + a^3*d^2*e^5)*x), ((2*a*c*d^3*e + a^2*d*e^3 + (2*a*c*d^2*e^2 + a^2*e^4)*x)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) + (c^2*d^5 + 2*a*c*d^3*e^2 + a^2*d*e^4 + (c^2*d^4*e + 2*a*c*d^2*e^3 + a^2*e^5)*x)*sqrt(-a)*arctan(sqrt(-a)/sqrt(c*x^2 + a)) + (a*c*d^3*e^2 + a^2*d*e^4)*sqrt(c*x^2 + a))/(a*c^2*d^7 + 2*a^2*c*d^5*e^2 + a^3*d^3*e^4 + (a*c^2*d^6*e + 2*a^2*c*d^4*e^3 + a^3*d^2*e^5)*x)]","A",0
349,1,1512,0,0.760679," ","integrate(1/x^2/(e*x+d)^2/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{c d^{2} + a e^{2}} {\left({\left(3 \, a c d^{2} e^{3} + 2 \, a^{2} e^{5}\right)} x^{2} + {\left(3 \, a c d^{3} e^{2} + 2 \, a^{2} d e^{4}\right)} x\right)} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left({\left(c^{2} d^{4} e^{2} + 2 \, a c d^{2} e^{4} + a^{2} e^{6}\right)} x^{2} + {\left(c^{2} d^{5} e + 2 \, a c d^{3} e^{3} + a^{2} d e^{5}\right)} x\right)} \sqrt{a} \log\left(-\frac{c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - 2 \, {\left(c^{2} d^{6} + 2 \, a c d^{4} e^{2} + a^{2} d^{2} e^{4} + {\left(c^{2} d^{5} e + 3 \, a c d^{3} e^{3} + 2 \, a^{2} d e^{5}\right)} x\right)} \sqrt{c x^{2} + a}}{2 \, {\left({\left(a c^{2} d^{7} e + 2 \, a^{2} c d^{5} e^{3} + a^{3} d^{3} e^{5}\right)} x^{2} + {\left(a c^{2} d^{8} + 2 \, a^{2} c d^{6} e^{2} + a^{3} d^{4} e^{4}\right)} x\right)}}, -\frac{\sqrt{-c d^{2} - a e^{2}} {\left({\left(3 \, a c d^{2} e^{3} + 2 \, a^{2} e^{5}\right)} x^{2} + {\left(3 \, a c d^{3} e^{2} + 2 \, a^{2} d e^{4}\right)} x\right)} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - {\left({\left(c^{2} d^{4} e^{2} + 2 \, a c d^{2} e^{4} + a^{2} e^{6}\right)} x^{2} + {\left(c^{2} d^{5} e + 2 \, a c d^{3} e^{3} + a^{2} d e^{5}\right)} x\right)} \sqrt{a} \log\left(-\frac{c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + {\left(c^{2} d^{6} + 2 \, a c d^{4} e^{2} + a^{2} d^{2} e^{4} + {\left(c^{2} d^{5} e + 3 \, a c d^{3} e^{3} + 2 \, a^{2} d e^{5}\right)} x\right)} \sqrt{c x^{2} + a}}{{\left(a c^{2} d^{7} e + 2 \, a^{2} c d^{5} e^{3} + a^{3} d^{3} e^{5}\right)} x^{2} + {\left(a c^{2} d^{8} + 2 \, a^{2} c d^{6} e^{2} + a^{3} d^{4} e^{4}\right)} x}, -\frac{4 \, {\left({\left(c^{2} d^{4} e^{2} + 2 \, a c d^{2} e^{4} + a^{2} e^{6}\right)} x^{2} + {\left(c^{2} d^{5} e + 2 \, a c d^{3} e^{3} + a^{2} d e^{5}\right)} x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) - \sqrt{c d^{2} + a e^{2}} {\left({\left(3 \, a c d^{2} e^{3} + 2 \, a^{2} e^{5}\right)} x^{2} + {\left(3 \, a c d^{3} e^{2} + 2 \, a^{2} d e^{4}\right)} x\right)} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(c^{2} d^{6} + 2 \, a c d^{4} e^{2} + a^{2} d^{2} e^{4} + {\left(c^{2} d^{5} e + 3 \, a c d^{3} e^{3} + 2 \, a^{2} d e^{5}\right)} x\right)} \sqrt{c x^{2} + a}}{2 \, {\left({\left(a c^{2} d^{7} e + 2 \, a^{2} c d^{5} e^{3} + a^{3} d^{3} e^{5}\right)} x^{2} + {\left(a c^{2} d^{8} + 2 \, a^{2} c d^{6} e^{2} + a^{3} d^{4} e^{4}\right)} x\right)}}, -\frac{\sqrt{-c d^{2} - a e^{2}} {\left({\left(3 \, a c d^{2} e^{3} + 2 \, a^{2} e^{5}\right)} x^{2} + {\left(3 \, a c d^{3} e^{2} + 2 \, a^{2} d e^{4}\right)} x\right)} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) + 2 \, {\left({\left(c^{2} d^{4} e^{2} + 2 \, a c d^{2} e^{4} + a^{2} e^{6}\right)} x^{2} + {\left(c^{2} d^{5} e + 2 \, a c d^{3} e^{3} + a^{2} d e^{5}\right)} x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) + {\left(c^{2} d^{6} + 2 \, a c d^{4} e^{2} + a^{2} d^{2} e^{4} + {\left(c^{2} d^{5} e + 3 \, a c d^{3} e^{3} + 2 \, a^{2} d e^{5}\right)} x\right)} \sqrt{c x^{2} + a}}{{\left(a c^{2} d^{7} e + 2 \, a^{2} c d^{5} e^{3} + a^{3} d^{3} e^{5}\right)} x^{2} + {\left(a c^{2} d^{8} + 2 \, a^{2} c d^{6} e^{2} + a^{3} d^{4} e^{4}\right)} x}\right]"," ",0,"[1/2*(sqrt(c*d^2 + a*e^2)*((3*a*c*d^2*e^3 + 2*a^2*e^5)*x^2 + (3*a*c*d^3*e^2 + 2*a^2*d*e^4)*x)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*((c^2*d^4*e^2 + 2*a*c*d^2*e^4 + a^2*e^6)*x^2 + (c^2*d^5*e + 2*a*c*d^3*e^3 + a^2*d*e^5)*x)*sqrt(a)*log(-(c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) - 2*(c^2*d^6 + 2*a*c*d^4*e^2 + a^2*d^2*e^4 + (c^2*d^5*e + 3*a*c*d^3*e^3 + 2*a^2*d*e^5)*x)*sqrt(c*x^2 + a))/((a*c^2*d^7*e + 2*a^2*c*d^5*e^3 + a^3*d^3*e^5)*x^2 + (a*c^2*d^8 + 2*a^2*c*d^6*e^2 + a^3*d^4*e^4)*x), -(sqrt(-c*d^2 - a*e^2)*((3*a*c*d^2*e^3 + 2*a^2*e^5)*x^2 + (3*a*c*d^3*e^2 + 2*a^2*d*e^4)*x)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - ((c^2*d^4*e^2 + 2*a*c*d^2*e^4 + a^2*e^6)*x^2 + (c^2*d^5*e + 2*a*c*d^3*e^3 + a^2*d*e^5)*x)*sqrt(a)*log(-(c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) + (c^2*d^6 + 2*a*c*d^4*e^2 + a^2*d^2*e^4 + (c^2*d^5*e + 3*a*c*d^3*e^3 + 2*a^2*d*e^5)*x)*sqrt(c*x^2 + a))/((a*c^2*d^7*e + 2*a^2*c*d^5*e^3 + a^3*d^3*e^5)*x^2 + (a*c^2*d^8 + 2*a^2*c*d^6*e^2 + a^3*d^4*e^4)*x), -1/2*(4*((c^2*d^4*e^2 + 2*a*c*d^2*e^4 + a^2*e^6)*x^2 + (c^2*d^5*e + 2*a*c*d^3*e^3 + a^2*d*e^5)*x)*sqrt(-a)*arctan(sqrt(-a)/sqrt(c*x^2 + a)) - sqrt(c*d^2 + a*e^2)*((3*a*c*d^2*e^3 + 2*a^2*e^5)*x^2 + (3*a*c*d^3*e^2 + 2*a^2*d*e^4)*x)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(c^2*d^6 + 2*a*c*d^4*e^2 + a^2*d^2*e^4 + (c^2*d^5*e + 3*a*c*d^3*e^3 + 2*a^2*d*e^5)*x)*sqrt(c*x^2 + a))/((a*c^2*d^7*e + 2*a^2*c*d^5*e^3 + a^3*d^3*e^5)*x^2 + (a*c^2*d^8 + 2*a^2*c*d^6*e^2 + a^3*d^4*e^4)*x), -(sqrt(-c*d^2 - a*e^2)*((3*a*c*d^2*e^3 + 2*a^2*e^5)*x^2 + (3*a*c*d^3*e^2 + 2*a^2*d*e^4)*x)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) + 2*((c^2*d^4*e^2 + 2*a*c*d^2*e^4 + a^2*e^6)*x^2 + (c^2*d^5*e + 2*a*c*d^3*e^3 + a^2*d*e^5)*x)*sqrt(-a)*arctan(sqrt(-a)/sqrt(c*x^2 + a)) + (c^2*d^6 + 2*a*c*d^4*e^2 + a^2*d^2*e^4 + (c^2*d^5*e + 3*a*c*d^3*e^3 + 2*a^2*d*e^5)*x)*sqrt(c*x^2 + a))/((a*c^2*d^7*e + 2*a^2*c*d^5*e^3 + a^3*d^3*e^5)*x^2 + (a*c^2*d^8 + 2*a^2*c*d^6*e^2 + a^3*d^4*e^4)*x)]","A",0
350,1,1867,0,1.290699," ","integrate(1/x^3/(e*x+d)^2/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left({\left(4 \, a^{2} c d^{2} e^{4} + 3 \, a^{3} e^{6}\right)} x^{3} + {\left(4 \, a^{2} c d^{3} e^{3} + 3 \, a^{3} d e^{5}\right)} x^{2}\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - {\left({\left(c^{3} d^{6} e - 4 \, a c^{2} d^{4} e^{3} - 11 \, a^{2} c d^{2} e^{5} - 6 \, a^{3} e^{7}\right)} x^{3} + {\left(c^{3} d^{7} - 4 \, a c^{2} d^{5} e^{2} - 11 \, a^{2} c d^{3} e^{4} - 6 \, a^{3} d e^{6}\right)} x^{2}\right)} \sqrt{a} \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - 2 \, {\left(a c^{2} d^{7} + 2 \, a^{2} c d^{5} e^{2} + a^{3} d^{3} e^{4} - 2 \, {\left(2 \, a c^{2} d^{5} e^{2} + 5 \, a^{2} c d^{3} e^{4} + 3 \, a^{3} d e^{6}\right)} x^{2} - 3 \, {\left(a c^{2} d^{6} e + 2 \, a^{2} c d^{4} e^{3} + a^{3} d^{2} e^{5}\right)} x\right)} \sqrt{c x^{2} + a}}{4 \, {\left({\left(a^{2} c^{2} d^{8} e + 2 \, a^{3} c d^{6} e^{3} + a^{4} d^{4} e^{5}\right)} x^{3} + {\left(a^{2} c^{2} d^{9} + 2 \, a^{3} c d^{7} e^{2} + a^{4} d^{5} e^{4}\right)} x^{2}\right)}}, \frac{4 \, {\left({\left(4 \, a^{2} c d^{2} e^{4} + 3 \, a^{3} e^{6}\right)} x^{3} + {\left(4 \, a^{2} c d^{3} e^{3} + 3 \, a^{3} d e^{5}\right)} x^{2}\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - {\left({\left(c^{3} d^{6} e - 4 \, a c^{2} d^{4} e^{3} - 11 \, a^{2} c d^{2} e^{5} - 6 \, a^{3} e^{7}\right)} x^{3} + {\left(c^{3} d^{7} - 4 \, a c^{2} d^{5} e^{2} - 11 \, a^{2} c d^{3} e^{4} - 6 \, a^{3} d e^{6}\right)} x^{2}\right)} \sqrt{a} \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - 2 \, {\left(a c^{2} d^{7} + 2 \, a^{2} c d^{5} e^{2} + a^{3} d^{3} e^{4} - 2 \, {\left(2 \, a c^{2} d^{5} e^{2} + 5 \, a^{2} c d^{3} e^{4} + 3 \, a^{3} d e^{6}\right)} x^{2} - 3 \, {\left(a c^{2} d^{6} e + 2 \, a^{2} c d^{4} e^{3} + a^{3} d^{2} e^{5}\right)} x\right)} \sqrt{c x^{2} + a}}{4 \, {\left({\left(a^{2} c^{2} d^{8} e + 2 \, a^{3} c d^{6} e^{3} + a^{4} d^{4} e^{5}\right)} x^{3} + {\left(a^{2} c^{2} d^{9} + 2 \, a^{3} c d^{7} e^{2} + a^{4} d^{5} e^{4}\right)} x^{2}\right)}}, -\frac{{\left({\left(c^{3} d^{6} e - 4 \, a c^{2} d^{4} e^{3} - 11 \, a^{2} c d^{2} e^{5} - 6 \, a^{3} e^{7}\right)} x^{3} + {\left(c^{3} d^{7} - 4 \, a c^{2} d^{5} e^{2} - 11 \, a^{2} c d^{3} e^{4} - 6 \, a^{3} d e^{6}\right)} x^{2}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) - {\left({\left(4 \, a^{2} c d^{2} e^{4} + 3 \, a^{3} e^{6}\right)} x^{3} + {\left(4 \, a^{2} c d^{3} e^{3} + 3 \, a^{3} d e^{5}\right)} x^{2}\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + {\left(a c^{2} d^{7} + 2 \, a^{2} c d^{5} e^{2} + a^{3} d^{3} e^{4} - 2 \, {\left(2 \, a c^{2} d^{5} e^{2} + 5 \, a^{2} c d^{3} e^{4} + 3 \, a^{3} d e^{6}\right)} x^{2} - 3 \, {\left(a c^{2} d^{6} e + 2 \, a^{2} c d^{4} e^{3} + a^{3} d^{2} e^{5}\right)} x\right)} \sqrt{c x^{2} + a}}{2 \, {\left({\left(a^{2} c^{2} d^{8} e + 2 \, a^{3} c d^{6} e^{3} + a^{4} d^{4} e^{5}\right)} x^{3} + {\left(a^{2} c^{2} d^{9} + 2 \, a^{3} c d^{7} e^{2} + a^{4} d^{5} e^{4}\right)} x^{2}\right)}}, \frac{2 \, {\left({\left(4 \, a^{2} c d^{2} e^{4} + 3 \, a^{3} e^{6}\right)} x^{3} + {\left(4 \, a^{2} c d^{3} e^{3} + 3 \, a^{3} d e^{5}\right)} x^{2}\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - {\left({\left(c^{3} d^{6} e - 4 \, a c^{2} d^{4} e^{3} - 11 \, a^{2} c d^{2} e^{5} - 6 \, a^{3} e^{7}\right)} x^{3} + {\left(c^{3} d^{7} - 4 \, a c^{2} d^{5} e^{2} - 11 \, a^{2} c d^{3} e^{4} - 6 \, a^{3} d e^{6}\right)} x^{2}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right) - {\left(a c^{2} d^{7} + 2 \, a^{2} c d^{5} e^{2} + a^{3} d^{3} e^{4} - 2 \, {\left(2 \, a c^{2} d^{5} e^{2} + 5 \, a^{2} c d^{3} e^{4} + 3 \, a^{3} d e^{6}\right)} x^{2} - 3 \, {\left(a c^{2} d^{6} e + 2 \, a^{2} c d^{4} e^{3} + a^{3} d^{2} e^{5}\right)} x\right)} \sqrt{c x^{2} + a}}{2 \, {\left({\left(a^{2} c^{2} d^{8} e + 2 \, a^{3} c d^{6} e^{3} + a^{4} d^{4} e^{5}\right)} x^{3} + {\left(a^{2} c^{2} d^{9} + 2 \, a^{3} c d^{7} e^{2} + a^{4} d^{5} e^{4}\right)} x^{2}\right)}}\right]"," ",0,"[1/4*(2*((4*a^2*c*d^2*e^4 + 3*a^3*e^6)*x^3 + (4*a^2*c*d^3*e^3 + 3*a^3*d*e^5)*x^2)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 + 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) - ((c^3*d^6*e - 4*a*c^2*d^4*e^3 - 11*a^2*c*d^2*e^5 - 6*a^3*e^7)*x^3 + (c^3*d^7 - 4*a*c^2*d^5*e^2 - 11*a^2*c*d^3*e^4 - 6*a^3*d*e^6)*x^2)*sqrt(a)*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) - 2*(a*c^2*d^7 + 2*a^2*c*d^5*e^2 + a^3*d^3*e^4 - 2*(2*a*c^2*d^5*e^2 + 5*a^2*c*d^3*e^4 + 3*a^3*d*e^6)*x^2 - 3*(a*c^2*d^6*e + 2*a^2*c*d^4*e^3 + a^3*d^2*e^5)*x)*sqrt(c*x^2 + a))/((a^2*c^2*d^8*e + 2*a^3*c*d^6*e^3 + a^4*d^4*e^5)*x^3 + (a^2*c^2*d^9 + 2*a^3*c*d^7*e^2 + a^4*d^5*e^4)*x^2), 1/4*(4*((4*a^2*c*d^2*e^4 + 3*a^3*e^6)*x^3 + (4*a^2*c*d^3*e^3 + 3*a^3*d*e^5)*x^2)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - ((c^3*d^6*e - 4*a*c^2*d^4*e^3 - 11*a^2*c*d^2*e^5 - 6*a^3*e^7)*x^3 + (c^3*d^7 - 4*a*c^2*d^5*e^2 - 11*a^2*c*d^3*e^4 - 6*a^3*d*e^6)*x^2)*sqrt(a)*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2) - 2*(a*c^2*d^7 + 2*a^2*c*d^5*e^2 + a^3*d^3*e^4 - 2*(2*a*c^2*d^5*e^2 + 5*a^2*c*d^3*e^4 + 3*a^3*d*e^6)*x^2 - 3*(a*c^2*d^6*e + 2*a^2*c*d^4*e^3 + a^3*d^2*e^5)*x)*sqrt(c*x^2 + a))/((a^2*c^2*d^8*e + 2*a^3*c*d^6*e^3 + a^4*d^4*e^5)*x^3 + (a^2*c^2*d^9 + 2*a^3*c*d^7*e^2 + a^4*d^5*e^4)*x^2), -1/2*(((c^3*d^6*e - 4*a*c^2*d^4*e^3 - 11*a^2*c*d^2*e^5 - 6*a^3*e^7)*x^3 + (c^3*d^7 - 4*a*c^2*d^5*e^2 - 11*a^2*c*d^3*e^4 - 6*a^3*d*e^6)*x^2)*sqrt(-a)*arctan(sqrt(-a)/sqrt(c*x^2 + a)) - ((4*a^2*c*d^2*e^4 + 3*a^3*e^6)*x^3 + (4*a^2*c*d^3*e^3 + 3*a^3*d*e^5)*x^2)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 + 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + (a*c^2*d^7 + 2*a^2*c*d^5*e^2 + a^3*d^3*e^4 - 2*(2*a*c^2*d^5*e^2 + 5*a^2*c*d^3*e^4 + 3*a^3*d*e^6)*x^2 - 3*(a*c^2*d^6*e + 2*a^2*c*d^4*e^3 + a^3*d^2*e^5)*x)*sqrt(c*x^2 + a))/((a^2*c^2*d^8*e + 2*a^3*c*d^6*e^3 + a^4*d^4*e^5)*x^3 + (a^2*c^2*d^9 + 2*a^3*c*d^7*e^2 + a^4*d^5*e^4)*x^2), 1/2*(2*((4*a^2*c*d^2*e^4 + 3*a^3*e^6)*x^3 + (4*a^2*c*d^3*e^3 + 3*a^3*d*e^5)*x^2)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - ((c^3*d^6*e - 4*a*c^2*d^4*e^3 - 11*a^2*c*d^2*e^5 - 6*a^3*e^7)*x^3 + (c^3*d^7 - 4*a*c^2*d^5*e^2 - 11*a^2*c*d^3*e^4 - 6*a^3*d*e^6)*x^2)*sqrt(-a)*arctan(sqrt(-a)/sqrt(c*x^2 + a)) - (a*c^2*d^7 + 2*a^2*c*d^5*e^2 + a^3*d^3*e^4 - 2*(2*a*c^2*d^5*e^2 + 5*a^2*c*d^3*e^4 + 3*a^3*d*e^6)*x^2 - 3*(a*c^2*d^6*e + 2*a^2*c*d^4*e^3 + a^3*d^2*e^5)*x)*sqrt(c*x^2 + a))/((a^2*c^2*d^8*e + 2*a^3*c*d^6*e^3 + a^4*d^4*e^5)*x^3 + (a^2*c^2*d^9 + 2*a^3*c*d^7*e^2 + a^4*d^5*e^4)*x^2)]","A",0
351,1,368,0,0.415078," ","integrate(x^2*(b*x+a)^n*(d*x^2+c),x, algorithm=""fricas"")","\frac{{\left(2 \, a^{3} b^{2} c n^{2} + 18 \, a^{3} b^{2} c n + 40 \, a^{3} b^{2} c + 24 \, a^{5} d + {\left(b^{5} d n^{4} + 10 \, b^{5} d n^{3} + 35 \, b^{5} d n^{2} + 50 \, b^{5} d n + 24 \, b^{5} d\right)} x^{5} + {\left(a b^{4} d n^{4} + 6 \, a b^{4} d n^{3} + 11 \, a b^{4} d n^{2} + 6 \, a b^{4} d n\right)} x^{4} + {\left(b^{5} c n^{4} + 40 \, b^{5} c + 4 \, {\left(3 \, b^{5} c - a^{2} b^{3} d\right)} n^{3} + {\left(49 \, b^{5} c - 12 \, a^{2} b^{3} d\right)} n^{2} + 2 \, {\left(39 \, b^{5} c - 4 \, a^{2} b^{3} d\right)} n\right)} x^{3} + {\left(a b^{4} c n^{4} + 10 \, a b^{4} c n^{3} + {\left(29 \, a b^{4} c + 12 \, a^{3} b^{2} d\right)} n^{2} + 4 \, {\left(5 \, a b^{4} c + 3 \, a^{3} b^{2} d\right)} n\right)} x^{2} - 2 \, {\left(a^{2} b^{3} c n^{3} + 9 \, a^{2} b^{3} c n^{2} + 4 \, {\left(5 \, a^{2} b^{3} c + 3 \, a^{4} b d\right)} n\right)} x\right)} {\left(b x + a\right)}^{n}}{b^{5} n^{5} + 15 \, b^{5} n^{4} + 85 \, b^{5} n^{3} + 225 \, b^{5} n^{2} + 274 \, b^{5} n + 120 \, b^{5}}"," ",0,"(2*a^3*b^2*c*n^2 + 18*a^3*b^2*c*n + 40*a^3*b^2*c + 24*a^5*d + (b^5*d*n^4 + 10*b^5*d*n^3 + 35*b^5*d*n^2 + 50*b^5*d*n + 24*b^5*d)*x^5 + (a*b^4*d*n^4 + 6*a*b^4*d*n^3 + 11*a*b^4*d*n^2 + 6*a*b^4*d*n)*x^4 + (b^5*c*n^4 + 40*b^5*c + 4*(3*b^5*c - a^2*b^3*d)*n^3 + (49*b^5*c - 12*a^2*b^3*d)*n^2 + 2*(39*b^5*c - 4*a^2*b^3*d)*n)*x^3 + (a*b^4*c*n^4 + 10*a*b^4*c*n^3 + (29*a*b^4*c + 12*a^3*b^2*d)*n^2 + 4*(5*a*b^4*c + 3*a^3*b^2*d)*n)*x^2 - 2*(a^2*b^3*c*n^3 + 9*a^2*b^3*c*n^2 + 4*(5*a^2*b^3*c + 3*a^4*b*d)*n)*x)*(b*x + a)^n/(b^5*n^5 + 15*b^5*n^4 + 85*b^5*n^3 + 225*b^5*n^2 + 274*b^5*n + 120*b^5)","B",0
352,1,250,0,0.414279," ","integrate(x*(b*x+a)^n*(d*x^2+c),x, algorithm=""fricas"")","-\frac{{\left(a^{2} b^{2} c n^{2} + 7 \, a^{2} b^{2} c n + 12 \, a^{2} b^{2} c + 6 \, a^{4} d - {\left(b^{4} d n^{3} + 6 \, b^{4} d n^{2} + 11 \, b^{4} d n + 6 \, b^{4} d\right)} x^{4} - {\left(a b^{3} d n^{3} + 3 \, a b^{3} d n^{2} + 2 \, a b^{3} d n\right)} x^{3} - {\left(b^{4} c n^{3} + 12 \, b^{4} c + {\left(8 \, b^{4} c - 3 \, a^{2} b^{2} d\right)} n^{2} + {\left(19 \, b^{4} c - 3 \, a^{2} b^{2} d\right)} n\right)} x^{2} - {\left(a b^{3} c n^{3} + 7 \, a b^{3} c n^{2} + 6 \, {\left(2 \, a b^{3} c + a^{3} b d\right)} n\right)} x\right)} {\left(b x + a\right)}^{n}}{b^{4} n^{4} + 10 \, b^{4} n^{3} + 35 \, b^{4} n^{2} + 50 \, b^{4} n + 24 \, b^{4}}"," ",0,"-(a^2*b^2*c*n^2 + 7*a^2*b^2*c*n + 12*a^2*b^2*c + 6*a^4*d - (b^4*d*n^3 + 6*b^4*d*n^2 + 11*b^4*d*n + 6*b^4*d)*x^4 - (a*b^3*d*n^3 + 3*a*b^3*d*n^2 + 2*a*b^3*d*n)*x^3 - (b^4*c*n^3 + 12*b^4*c + (8*b^4*c - 3*a^2*b^2*d)*n^2 + (19*b^4*c - 3*a^2*b^2*d)*n)*x^2 - (a*b^3*c*n^3 + 7*a*b^3*c*n^2 + 6*(2*a*b^3*c + a^3*b*d)*n)*x)*(b*x + a)^n/(b^4*n^4 + 10*b^4*n^3 + 35*b^4*n^2 + 50*b^4*n + 24*b^4)","B",0
353,1,148,0,0.410669," ","integrate((b*x+a)^n*(d*x^2+c),x, algorithm=""fricas"")","\frac{{\left(a b^{2} c n^{2} + 5 \, a b^{2} c n + 6 \, a b^{2} c + 2 \, a^{3} d + {\left(b^{3} d n^{2} + 3 \, b^{3} d n + 2 \, b^{3} d\right)} x^{3} + {\left(a b^{2} d n^{2} + a b^{2} d n\right)} x^{2} + {\left(b^{3} c n^{2} + 6 \, b^{3} c + {\left(5 \, b^{3} c - 2 \, a^{2} b d\right)} n\right)} x\right)} {\left(b x + a\right)}^{n}}{b^{3} n^{3} + 6 \, b^{3} n^{2} + 11 \, b^{3} n + 6 \, b^{3}}"," ",0,"(a*b^2*c*n^2 + 5*a*b^2*c*n + 6*a*b^2*c + 2*a^3*d + (b^3*d*n^2 + 3*b^3*d*n + 2*b^3*d)*x^3 + (a*b^2*d*n^2 + a*b^2*d*n)*x^2 + (b^3*c*n^2 + 6*b^3*c + (5*b^3*c - 2*a^2*b*d)*n)*x)*(b*x + a)^n/(b^3*n^3 + 6*b^3*n^2 + 11*b^3*n + 6*b^3)","B",0
354,0,0,0,0.400733," ","integrate((b*x+a)^n*(d*x^2+c)/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d x^{2} + c\right)} {\left(b x + a\right)}^{n}}{x}, x\right)"," ",0,"integral((d*x^2 + c)*(b*x + a)^n/x, x)","F",0
355,1,1027,0,0.434970," ","integrate(x^2*(b*x+a)^n*(d*x^2+c)^2,x, algorithm=""fricas"")","\frac{{\left(2 \, a^{3} b^{4} c^{2} n^{4} + 44 \, a^{3} b^{4} c^{2} n^{3} + 1680 \, a^{3} b^{4} c^{2} + 2016 \, a^{5} b^{2} c d + 720 \, a^{7} d^{2} + {\left(b^{7} d^{2} n^{6} + 21 \, b^{7} d^{2} n^{5} + 175 \, b^{7} d^{2} n^{4} + 735 \, b^{7} d^{2} n^{3} + 1624 \, b^{7} d^{2} n^{2} + 1764 \, b^{7} d^{2} n + 720 \, b^{7} d^{2}\right)} x^{7} + {\left(a b^{6} d^{2} n^{6} + 15 \, a b^{6} d^{2} n^{5} + 85 \, a b^{6} d^{2} n^{4} + 225 \, a b^{6} d^{2} n^{3} + 274 \, a b^{6} d^{2} n^{2} + 120 \, a b^{6} d^{2} n\right)} x^{6} + 2 \, {\left(b^{7} c d n^{6} + 1008 \, b^{7} c d + {\left(23 \, b^{7} c d - 3 \, a^{2} b^{5} d^{2}\right)} n^{5} + 3 \, {\left(69 \, b^{7} c d - 10 \, a^{2} b^{5} d^{2}\right)} n^{4} + 5 \, {\left(185 \, b^{7} c d - 21 \, a^{2} b^{5} d^{2}\right)} n^{3} + 2 \, {\left(1072 \, b^{7} c d - 75 \, a^{2} b^{5} d^{2}\right)} n^{2} + 36 \, {\left(67 \, b^{7} c d - 2 \, a^{2} b^{5} d^{2}\right)} n\right)} x^{5} + 2 \, {\left(a b^{6} c d n^{6} + 19 \, a b^{6} c d n^{5} + {\left(131 \, a b^{6} c d + 15 \, a^{3} b^{4} d^{2}\right)} n^{4} + {\left(401 \, a b^{6} c d + 90 \, a^{3} b^{4} d^{2}\right)} n^{3} + 15 \, {\left(36 \, a b^{6} c d + 11 \, a^{3} b^{4} d^{2}\right)} n^{2} + 18 \, {\left(14 \, a b^{6} c d + 5 \, a^{3} b^{4} d^{2}\right)} n\right)} x^{4} + {\left(b^{7} c^{2} n^{6} + 1680 \, b^{7} c^{2} + {\left(25 \, b^{7} c^{2} - 8 \, a^{2} b^{5} c d\right)} n^{5} + {\left(247 \, b^{7} c^{2} - 128 \, a^{2} b^{5} c d\right)} n^{4} + {\left(1219 \, b^{7} c^{2} - 664 \, a^{2} b^{5} c d - 120 \, a^{4} b^{3} d^{2}\right)} n^{3} + 8 \, {\left(389 \, b^{7} c^{2} - 152 \, a^{2} b^{5} c d - 45 \, a^{4} b^{3} d^{2}\right)} n^{2} + 4 \, {\left(949 \, b^{7} c^{2} - 168 \, a^{2} b^{5} c d - 60 \, a^{4} b^{3} d^{2}\right)} n\right)} x^{3} + 2 \, {\left(179 \, a^{3} b^{4} c^{2} + 24 \, a^{5} b^{2} c d\right)} n^{2} + {\left(a b^{6} c^{2} n^{6} + 23 \, a b^{6} c^{2} n^{5} + 3 \, {\left(67 \, a b^{6} c^{2} + 8 \, a^{3} b^{4} c d\right)} n^{4} + {\left(817 \, a b^{6} c^{2} + 336 \, a^{3} b^{4} c d\right)} n^{3} + 2 \, {\left(739 \, a b^{6} c^{2} + 660 \, a^{3} b^{4} c d + 180 \, a^{5} b^{2} d^{2}\right)} n^{2} + 24 \, {\left(35 \, a b^{6} c^{2} + 42 \, a^{3} b^{4} c d + 15 \, a^{5} b^{2} d^{2}\right)} n\right)} x^{2} + 4 \, {\left(319 \, a^{3} b^{4} c^{2} + 156 \, a^{5} b^{2} c d\right)} n - 2 \, {\left(a^{2} b^{5} c^{2} n^{5} + 22 \, a^{2} b^{5} c^{2} n^{4} + {\left(179 \, a^{2} b^{5} c^{2} + 24 \, a^{4} b^{3} c d\right)} n^{3} + 2 \, {\left(319 \, a^{2} b^{5} c^{2} + 156 \, a^{4} b^{3} c d\right)} n^{2} + 24 \, {\left(35 \, a^{2} b^{5} c^{2} + 42 \, a^{4} b^{3} c d + 15 \, a^{6} b d^{2}\right)} n\right)} x\right)} {\left(b x + a\right)}^{n}}{b^{7} n^{7} + 28 \, b^{7} n^{6} + 322 \, b^{7} n^{5} + 1960 \, b^{7} n^{4} + 6769 \, b^{7} n^{3} + 13132 \, b^{7} n^{2} + 13068 \, b^{7} n + 5040 \, b^{7}}"," ",0,"(2*a^3*b^4*c^2*n^4 + 44*a^3*b^4*c^2*n^3 + 1680*a^3*b^4*c^2 + 2016*a^5*b^2*c*d + 720*a^7*d^2 + (b^7*d^2*n^6 + 21*b^7*d^2*n^5 + 175*b^7*d^2*n^4 + 735*b^7*d^2*n^3 + 1624*b^7*d^2*n^2 + 1764*b^7*d^2*n + 720*b^7*d^2)*x^7 + (a*b^6*d^2*n^6 + 15*a*b^6*d^2*n^5 + 85*a*b^6*d^2*n^4 + 225*a*b^6*d^2*n^3 + 274*a*b^6*d^2*n^2 + 120*a*b^6*d^2*n)*x^6 + 2*(b^7*c*d*n^6 + 1008*b^7*c*d + (23*b^7*c*d - 3*a^2*b^5*d^2)*n^5 + 3*(69*b^7*c*d - 10*a^2*b^5*d^2)*n^4 + 5*(185*b^7*c*d - 21*a^2*b^5*d^2)*n^3 + 2*(1072*b^7*c*d - 75*a^2*b^5*d^2)*n^2 + 36*(67*b^7*c*d - 2*a^2*b^5*d^2)*n)*x^5 + 2*(a*b^6*c*d*n^6 + 19*a*b^6*c*d*n^5 + (131*a*b^6*c*d + 15*a^3*b^4*d^2)*n^4 + (401*a*b^6*c*d + 90*a^3*b^4*d^2)*n^3 + 15*(36*a*b^6*c*d + 11*a^3*b^4*d^2)*n^2 + 18*(14*a*b^6*c*d + 5*a^3*b^4*d^2)*n)*x^4 + (b^7*c^2*n^6 + 1680*b^7*c^2 + (25*b^7*c^2 - 8*a^2*b^5*c*d)*n^5 + (247*b^7*c^2 - 128*a^2*b^5*c*d)*n^4 + (1219*b^7*c^2 - 664*a^2*b^5*c*d - 120*a^4*b^3*d^2)*n^3 + 8*(389*b^7*c^2 - 152*a^2*b^5*c*d - 45*a^4*b^3*d^2)*n^2 + 4*(949*b^7*c^2 - 168*a^2*b^5*c*d - 60*a^4*b^3*d^2)*n)*x^3 + 2*(179*a^3*b^4*c^2 + 24*a^5*b^2*c*d)*n^2 + (a*b^6*c^2*n^6 + 23*a*b^6*c^2*n^5 + 3*(67*a*b^6*c^2 + 8*a^3*b^4*c*d)*n^4 + (817*a*b^6*c^2 + 336*a^3*b^4*c*d)*n^3 + 2*(739*a*b^6*c^2 + 660*a^3*b^4*c*d + 180*a^5*b^2*d^2)*n^2 + 24*(35*a*b^6*c^2 + 42*a^3*b^4*c*d + 15*a^5*b^2*d^2)*n)*x^2 + 4*(319*a^3*b^4*c^2 + 156*a^5*b^2*c*d)*n - 2*(a^2*b^5*c^2*n^5 + 22*a^2*b^5*c^2*n^4 + (179*a^2*b^5*c^2 + 24*a^4*b^3*c*d)*n^3 + 2*(319*a^2*b^5*c^2 + 156*a^4*b^3*c*d)*n^2 + 24*(35*a^2*b^5*c^2 + 42*a^4*b^3*c*d + 15*a^6*b*d^2)*n)*x)*(b*x + a)^n/(b^7*n^7 + 28*b^7*n^6 + 322*b^7*n^5 + 1960*b^7*n^4 + 6769*b^7*n^3 + 13132*b^7*n^2 + 13068*b^7*n + 5040*b^7)","B",0
356,1,757,0,0.424438," ","integrate(x*(b*x+a)^n*(d*x^2+c)^2,x, algorithm=""fricas"")","-\frac{{\left(a^{2} b^{4} c^{2} n^{4} + 18 \, a^{2} b^{4} c^{2} n^{3} + 360 \, a^{2} b^{4} c^{2} + 360 \, a^{4} b^{2} c d + 120 \, a^{6} d^{2} - {\left(b^{6} d^{2} n^{5} + 15 \, b^{6} d^{2} n^{4} + 85 \, b^{6} d^{2} n^{3} + 225 \, b^{6} d^{2} n^{2} + 274 \, b^{6} d^{2} n + 120 \, b^{6} d^{2}\right)} x^{6} - {\left(a b^{5} d^{2} n^{5} + 10 \, a b^{5} d^{2} n^{4} + 35 \, a b^{5} d^{2} n^{3} + 50 \, a b^{5} d^{2} n^{2} + 24 \, a b^{5} d^{2} n\right)} x^{5} - {\left(2 \, b^{6} c d n^{5} + 360 \, b^{6} c d + {\left(34 \, b^{6} c d - 5 \, a^{2} b^{4} d^{2}\right)} n^{4} + 2 \, {\left(107 \, b^{6} c d - 15 \, a^{2} b^{4} d^{2}\right)} n^{3} + {\left(614 \, b^{6} c d - 55 \, a^{2} b^{4} d^{2}\right)} n^{2} + 6 \, {\left(132 \, b^{6} c d - 5 \, a^{2} b^{4} d^{2}\right)} n\right)} x^{4} - 2 \, {\left(a b^{5} c d n^{5} + 14 \, a b^{5} c d n^{4} + 5 \, {\left(13 \, a b^{5} c d + 2 \, a^{3} b^{3} d^{2}\right)} n^{3} + 2 \, {\left(56 \, a b^{5} c d + 15 \, a^{3} b^{3} d^{2}\right)} n^{2} + 20 \, {\left(3 \, a b^{5} c d + a^{3} b^{3} d^{2}\right)} n\right)} x^{3} + {\left(119 \, a^{2} b^{4} c^{2} + 12 \, a^{4} b^{2} c d\right)} n^{2} - {\left(b^{6} c^{2} n^{5} + 360 \, b^{6} c^{2} + {\left(19 \, b^{6} c^{2} - 6 \, a^{2} b^{4} c d\right)} n^{4} + {\left(137 \, b^{6} c^{2} - 72 \, a^{2} b^{4} c d\right)} n^{3} + {\left(461 \, b^{6} c^{2} - 246 \, a^{2} b^{4} c d - 60 \, a^{4} b^{2} d^{2}\right)} n^{2} + 6 \, {\left(117 \, b^{6} c^{2} - 30 \, a^{2} b^{4} c d - 10 \, a^{4} b^{2} d^{2}\right)} n\right)} x^{2} + 6 \, {\left(57 \, a^{2} b^{4} c^{2} + 22 \, a^{4} b^{2} c d\right)} n - {\left(a b^{5} c^{2} n^{5} + 18 \, a b^{5} c^{2} n^{4} + {\left(119 \, a b^{5} c^{2} + 12 \, a^{3} b^{3} c d\right)} n^{3} + 6 \, {\left(57 \, a b^{5} c^{2} + 22 \, a^{3} b^{3} c d\right)} n^{2} + 120 \, {\left(3 \, a b^{5} c^{2} + 3 \, a^{3} b^{3} c d + a^{5} b d^{2}\right)} n\right)} x\right)} {\left(b x + a\right)}^{n}}{b^{6} n^{6} + 21 \, b^{6} n^{5} + 175 \, b^{6} n^{4} + 735 \, b^{6} n^{3} + 1624 \, b^{6} n^{2} + 1764 \, b^{6} n + 720 \, b^{6}}"," ",0,"-(a^2*b^4*c^2*n^4 + 18*a^2*b^4*c^2*n^3 + 360*a^2*b^4*c^2 + 360*a^4*b^2*c*d + 120*a^6*d^2 - (b^6*d^2*n^5 + 15*b^6*d^2*n^4 + 85*b^6*d^2*n^3 + 225*b^6*d^2*n^2 + 274*b^6*d^2*n + 120*b^6*d^2)*x^6 - (a*b^5*d^2*n^5 + 10*a*b^5*d^2*n^4 + 35*a*b^5*d^2*n^3 + 50*a*b^5*d^2*n^2 + 24*a*b^5*d^2*n)*x^5 - (2*b^6*c*d*n^5 + 360*b^6*c*d + (34*b^6*c*d - 5*a^2*b^4*d^2)*n^4 + 2*(107*b^6*c*d - 15*a^2*b^4*d^2)*n^3 + (614*b^6*c*d - 55*a^2*b^4*d^2)*n^2 + 6*(132*b^6*c*d - 5*a^2*b^4*d^2)*n)*x^4 - 2*(a*b^5*c*d*n^5 + 14*a*b^5*c*d*n^4 + 5*(13*a*b^5*c*d + 2*a^3*b^3*d^2)*n^3 + 2*(56*a*b^5*c*d + 15*a^3*b^3*d^2)*n^2 + 20*(3*a*b^5*c*d + a^3*b^3*d^2)*n)*x^3 + (119*a^2*b^4*c^2 + 12*a^4*b^2*c*d)*n^2 - (b^6*c^2*n^5 + 360*b^6*c^2 + (19*b^6*c^2 - 6*a^2*b^4*c*d)*n^4 + (137*b^6*c^2 - 72*a^2*b^4*c*d)*n^3 + (461*b^6*c^2 - 246*a^2*b^4*c*d - 60*a^4*b^2*d^2)*n^2 + 6*(117*b^6*c^2 - 30*a^2*b^4*c*d - 10*a^4*b^2*d^2)*n)*x^2 + 6*(57*a^2*b^4*c^2 + 22*a^4*b^2*c*d)*n - (a*b^5*c^2*n^5 + 18*a*b^5*c^2*n^4 + (119*a*b^5*c^2 + 12*a^3*b^3*c*d)*n^3 + 6*(57*a*b^5*c^2 + 22*a^3*b^3*c*d)*n^2 + 120*(3*a*b^5*c^2 + 3*a^3*b^3*c*d + a^5*b*d^2)*n)*x)*(b*x + a)^n/(b^6*n^6 + 21*b^6*n^5 + 175*b^6*n^4 + 735*b^6*n^3 + 1624*b^6*n^2 + 1764*b^6*n + 720*b^6)","B",0
357,1,519,0,0.417884," ","integrate((b*x+a)^n*(d*x^2+c)^2,x, algorithm=""fricas"")","\frac{{\left(a b^{4} c^{2} n^{4} + 14 \, a b^{4} c^{2} n^{3} + 120 \, a b^{4} c^{2} + 80 \, a^{3} b^{2} c d + 24 \, a^{5} d^{2} + {\left(b^{5} d^{2} n^{4} + 10 \, b^{5} d^{2} n^{3} + 35 \, b^{5} d^{2} n^{2} + 50 \, b^{5} d^{2} n + 24 \, b^{5} d^{2}\right)} x^{5} + {\left(a b^{4} d^{2} n^{4} + 6 \, a b^{4} d^{2} n^{3} + 11 \, a b^{4} d^{2} n^{2} + 6 \, a b^{4} d^{2} n\right)} x^{4} + 2 \, {\left(b^{5} c d n^{4} + 40 \, b^{5} c d + 2 \, {\left(6 \, b^{5} c d - a^{2} b^{3} d^{2}\right)} n^{3} + {\left(49 \, b^{5} c d - 6 \, a^{2} b^{3} d^{2}\right)} n^{2} + 2 \, {\left(39 \, b^{5} c d - 2 \, a^{2} b^{3} d^{2}\right)} n\right)} x^{3} + {\left(71 \, a b^{4} c^{2} + 4 \, a^{3} b^{2} c d\right)} n^{2} + 2 \, {\left(a b^{4} c d n^{4} + 10 \, a b^{4} c d n^{3} + {\left(29 \, a b^{4} c d + 6 \, a^{3} b^{2} d^{2}\right)} n^{2} + 2 \, {\left(10 \, a b^{4} c d + 3 \, a^{3} b^{2} d^{2}\right)} n\right)} x^{2} + 2 \, {\left(77 \, a b^{4} c^{2} + 18 \, a^{3} b^{2} c d\right)} n + {\left(b^{5} c^{2} n^{4} + 120 \, b^{5} c^{2} + 2 \, {\left(7 \, b^{5} c^{2} - 2 \, a^{2} b^{3} c d\right)} n^{3} + {\left(71 \, b^{5} c^{2} - 36 \, a^{2} b^{3} c d\right)} n^{2} + 2 \, {\left(77 \, b^{5} c^{2} - 40 \, a^{2} b^{3} c d - 12 \, a^{4} b d^{2}\right)} n\right)} x\right)} {\left(b x + a\right)}^{n}}{b^{5} n^{5} + 15 \, b^{5} n^{4} + 85 \, b^{5} n^{3} + 225 \, b^{5} n^{2} + 274 \, b^{5} n + 120 \, b^{5}}"," ",0,"(a*b^4*c^2*n^4 + 14*a*b^4*c^2*n^3 + 120*a*b^4*c^2 + 80*a^3*b^2*c*d + 24*a^5*d^2 + (b^5*d^2*n^4 + 10*b^5*d^2*n^3 + 35*b^5*d^2*n^2 + 50*b^5*d^2*n + 24*b^5*d^2)*x^5 + (a*b^4*d^2*n^4 + 6*a*b^4*d^2*n^3 + 11*a*b^4*d^2*n^2 + 6*a*b^4*d^2*n)*x^4 + 2*(b^5*c*d*n^4 + 40*b^5*c*d + 2*(6*b^5*c*d - a^2*b^3*d^2)*n^3 + (49*b^5*c*d - 6*a^2*b^3*d^2)*n^2 + 2*(39*b^5*c*d - 2*a^2*b^3*d^2)*n)*x^3 + (71*a*b^4*c^2 + 4*a^3*b^2*c*d)*n^2 + 2*(a*b^4*c*d*n^4 + 10*a*b^4*c*d*n^3 + (29*a*b^4*c*d + 6*a^3*b^2*d^2)*n^2 + 2*(10*a*b^4*c*d + 3*a^3*b^2*d^2)*n)*x^2 + 2*(77*a*b^4*c^2 + 18*a^3*b^2*c*d)*n + (b^5*c^2*n^4 + 120*b^5*c^2 + 2*(7*b^5*c^2 - 2*a^2*b^3*c*d)*n^3 + (71*b^5*c^2 - 36*a^2*b^3*c*d)*n^2 + 2*(77*b^5*c^2 - 40*a^2*b^3*c*d - 12*a^4*b*d^2)*n)*x)*(b*x + a)^n/(b^5*n^5 + 15*b^5*n^4 + 85*b^5*n^3 + 225*b^5*n^2 + 274*b^5*n + 120*b^5)","B",0
358,0,0,0,0.415005," ","integrate((b*x+a)^n*(d*x^2+c)^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d^{2} x^{4} + 2 \, c d x^{2} + c^{2}\right)} {\left(b x + a\right)}^{n}}{x}, x\right)"," ",0,"integral((d^2*x^4 + 2*c*d*x^2 + c^2)*(b*x + a)^n/x, x)","F",0
359,1,2165,0,0.448587," ","integrate(x^2*(b*x+a)^n*(d*x^2+c)^3,x, algorithm=""fricas"")","\frac{{\left(2 \, a^{3} b^{6} c^{3} n^{6} + 78 \, a^{3} b^{6} c^{3} n^{5} + 120960 \, a^{3} b^{6} c^{3} + 217728 \, a^{5} b^{4} c^{2} d + 155520 \, a^{7} b^{2} c d^{2} + 40320 \, a^{9} d^{3} + {\left(b^{9} d^{3} n^{8} + 36 \, b^{9} d^{3} n^{7} + 546 \, b^{9} d^{3} n^{6} + 4536 \, b^{9} d^{3} n^{5} + 22449 \, b^{9} d^{3} n^{4} + 67284 \, b^{9} d^{3} n^{3} + 118124 \, b^{9} d^{3} n^{2} + 109584 \, b^{9} d^{3} n + 40320 \, b^{9} d^{3}\right)} x^{9} + {\left(a b^{8} d^{3} n^{8} + 28 \, a b^{8} d^{3} n^{7} + 322 \, a b^{8} d^{3} n^{6} + 1960 \, a b^{8} d^{3} n^{5} + 6769 \, a b^{8} d^{3} n^{4} + 13132 \, a b^{8} d^{3} n^{3} + 13068 \, a b^{8} d^{3} n^{2} + 5040 \, a b^{8} d^{3} n\right)} x^{8} + {\left(3 \, b^{9} c d^{2} n^{8} + 155520 \, b^{9} c d^{2} + 2 \, {\left(57 \, b^{9} c d^{2} - 4 \, a^{2} b^{7} d^{3}\right)} n^{7} + 12 \, {\left(151 \, b^{9} c d^{2} - 14 \, a^{2} b^{7} d^{3}\right)} n^{6} + 14 \, {\left(1119 \, b^{9} c d^{2} - 100 \, a^{2} b^{7} d^{3}\right)} n^{5} + 21 \, {\left(3817 \, b^{9} c d^{2} - 280 \, a^{2} b^{7} d^{3}\right)} n^{4} + 28 \, {\left(8817 \, b^{9} c d^{2} - 464 \, a^{2} b^{7} d^{3}\right)} n^{3} + 36 \, {\left(12303 \, b^{9} c d^{2} - 392 \, a^{2} b^{7} d^{3}\right)} n^{2} + 144 \, {\left(2901 \, b^{9} c d^{2} - 40 \, a^{2} b^{7} d^{3}\right)} n\right)} x^{7} + {\left(3 \, a b^{8} c d^{2} n^{8} + 96 \, a b^{8} c d^{2} n^{7} + 4 \, {\left(309 \, a b^{8} c d^{2} + 14 \, a^{3} b^{6} d^{3}\right)} n^{6} + 30 \, {\left(275 \, a b^{8} c d^{2} + 28 \, a^{3} b^{6} d^{3}\right)} n^{5} + {\left(30657 \, a b^{8} c d^{2} + 4760 \, a^{3} b^{6} d^{3}\right)} n^{4} + 6 \, {\left(10489 \, a b^{8} c d^{2} + 2100 \, a^{3} b^{6} d^{3}\right)} n^{3} + 8 \, {\left(8163 \, a b^{8} c d^{2} + 1918 \, a^{3} b^{6} d^{3}\right)} n^{2} + 960 \, {\left(27 \, a b^{8} c d^{2} + 7 \, a^{3} b^{6} d^{3}\right)} n\right)} x^{6} + 3 \, {\left(b^{9} c^{2} d n^{8} + 72576 \, b^{9} c^{2} d + 2 \, {\left(20 \, b^{9} c^{2} d - 3 \, a^{2} b^{7} c d^{2}\right)} n^{7} + 2 \, {\left(335 \, b^{9} c^{2} d - 81 \, a^{2} b^{7} c d^{2}\right)} n^{6} + 2 \, {\left(3050 \, b^{9} c^{2} d - 831 \, a^{2} b^{7} c d^{2} - 56 \, a^{4} b^{5} d^{3}\right)} n^{5} + {\left(32773 \, b^{9} c^{2} d - 8190 \, a^{2} b^{7} c d^{2} - 1120 \, a^{4} b^{5} d^{3}\right)} n^{4} + 4 \, {\left(26365 \, b^{9} c^{2} d - 5091 \, a^{2} b^{7} c d^{2} - 980 \, a^{4} b^{5} d^{3}\right)} n^{3} + 4 \, {\left(49095 \, b^{9} c^{2} d - 6012 \, a^{2} b^{7} c d^{2} - 1400 \, a^{4} b^{5} d^{3}\right)} n^{2} + 48 \, {\left(3975 \, b^{9} c^{2} d - 216 \, a^{2} b^{7} c d^{2} - 56 \, a^{4} b^{5} d^{3}\right)} n\right)} x^{5} + 2 \, {\left(625 \, a^{3} b^{6} c^{3} + 36 \, a^{5} b^{4} c^{2} d\right)} n^{4} + 3 \, {\left(a b^{8} c^{2} d n^{8} + 36 \, a b^{8} c^{2} d n^{7} + 2 \, {\left(263 \, a b^{8} c^{2} d + 15 \, a^{3} b^{6} c d^{2}\right)} n^{6} + 6 \, {\left(666 \, a b^{8} c^{2} d + 115 \, a^{3} b^{6} c d^{2}\right)} n^{5} + {\left(16789 \, a b^{8} c^{2} d + 5550 \, a^{3} b^{6} c d^{2} + 560 \, a^{5} b^{4} d^{3}\right)} n^{4} + 6 \, {\left(6384 \, a b^{8} c^{2} d + 3125 \, a^{3} b^{6} c d^{2} + 560 \, a^{5} b^{4} d^{3}\right)} n^{3} + 4 \, {\left(10791 \, a b^{8} c^{2} d + 6705 \, a^{3} b^{6} c d^{2} + 1540 \, a^{5} b^{4} d^{3}\right)} n^{2} + 96 \, {\left(189 \, a b^{8} c^{2} d + 135 \, a^{3} b^{6} c d^{2} + 35 \, a^{5} b^{4} d^{3}\right)} n\right)} x^{4} + 270 \, {\left(39 \, a^{3} b^{6} c^{3} + 8 \, a^{5} b^{4} c^{2} d\right)} n^{3} + {\left(b^{9} c^{3} n^{8} + 120960 \, b^{9} c^{3} + 6 \, {\left(7 \, b^{9} c^{3} - 2 \, a^{2} b^{7} c^{2} d\right)} n^{7} + 12 \, {\left(62 \, b^{9} c^{3} - 33 \, a^{2} b^{7} c^{2} d\right)} n^{6} + 6 \, {\left(1203 \, b^{9} c^{3} - 854 \, a^{2} b^{7} c^{2} d - 60 \, a^{4} b^{5} c d^{2}\right)} n^{5} + 3 \, {\left(13873 \, b^{9} c^{3} - 10860 \, a^{2} b^{7} c^{2} d - 2400 \, a^{4} b^{5} c d^{2}\right)} n^{4} + 12 \, {\left(12039 \, b^{9} c^{3} - 8644 \, a^{2} b^{7} c^{2} d - 3750 \, a^{4} b^{5} c d^{2} - 560 \, a^{6} b^{3} d^{3}\right)} n^{3} + 4 \, {\left(72569 \, b^{9} c^{3} - 37116 \, a^{2} b^{7} c^{2} d - 22500 \, a^{4} b^{5} c d^{2} - 5040 \, a^{6} b^{3} d^{3}\right)} n^{2} + 48 \, {\left(6289 \, b^{9} c^{3} - 1512 \, a^{2} b^{7} c^{2} d - 1080 \, a^{4} b^{5} c d^{2} - 280 \, a^{6} b^{3} d^{3}\right)} n\right)} x^{3} + 4 \, {\left(12287 \, a^{3} b^{6} c^{3} + 6030 \, a^{5} b^{4} c^{2} d + 540 \, a^{7} b^{2} c d^{2}\right)} n^{2} + {\left(a b^{8} c^{3} n^{8} + 40 \, a b^{8} c^{3} n^{7} + 4 \, {\left(166 \, a b^{8} c^{3} + 9 \, a^{3} b^{6} c^{2} d\right)} n^{6} + 62 \, {\left(95 \, a b^{8} c^{3} + 18 \, a^{3} b^{6} c^{2} d\right)} n^{5} + {\left(29839 \, a b^{8} c^{3} + 13140 \, a^{3} b^{6} c^{2} d + 1080 \, a^{5} b^{4} c d^{2}\right)} n^{4} + 10 \, {\left(8479 \, a b^{8} c^{3} + 7146 \, a^{3} b^{6} c^{2} d + 1944 \, a^{5} b^{4} c d^{2}\right)} n^{3} + 24 \, {\left(5029 \, a b^{8} c^{3} + 7011 \, a^{3} b^{6} c^{2} d + 4005 \, a^{5} b^{4} c d^{2} + 840 \, a^{7} b^{2} d^{3}\right)} n^{2} + 576 \, {\left(105 \, a b^{8} c^{3} + 189 \, a^{3} b^{6} c^{2} d + 135 \, a^{5} b^{4} c d^{2} + 35 \, a^{7} b^{2} d^{3}\right)} n\right)} x^{2} + 48 \, {\left(2509 \, a^{3} b^{6} c^{3} + 2475 \, a^{5} b^{4} c^{2} d + 765 \, a^{7} b^{2} c d^{2}\right)} n - 2 \, {\left(a^{2} b^{7} c^{3} n^{7} + 39 \, a^{2} b^{7} c^{3} n^{6} + {\left(625 \, a^{2} b^{7} c^{3} + 36 \, a^{4} b^{5} c^{2} d\right)} n^{5} + 135 \, {\left(39 \, a^{2} b^{7} c^{3} + 8 \, a^{4} b^{5} c^{2} d\right)} n^{4} + 2 \, {\left(12287 \, a^{2} b^{7} c^{3} + 6030 \, a^{4} b^{5} c^{2} d + 540 \, a^{6} b^{3} c d^{2}\right)} n^{3} + 24 \, {\left(2509 \, a^{2} b^{7} c^{3} + 2475 \, a^{4} b^{5} c^{2} d + 765 \, a^{6} b^{3} c d^{2}\right)} n^{2} + 576 \, {\left(105 \, a^{2} b^{7} c^{3} + 189 \, a^{4} b^{5} c^{2} d + 135 \, a^{6} b^{3} c d^{2} + 35 \, a^{8} b d^{3}\right)} n\right)} x\right)} {\left(b x + a\right)}^{n}}{b^{9} n^{9} + 45 \, b^{9} n^{8} + 870 \, b^{9} n^{7} + 9450 \, b^{9} n^{6} + 63273 \, b^{9} n^{5} + 269325 \, b^{9} n^{4} + 723680 \, b^{9} n^{3} + 1172700 \, b^{9} n^{2} + 1026576 \, b^{9} n + 362880 \, b^{9}}"," ",0,"(2*a^3*b^6*c^3*n^6 + 78*a^3*b^6*c^3*n^5 + 120960*a^3*b^6*c^3 + 217728*a^5*b^4*c^2*d + 155520*a^7*b^2*c*d^2 + 40320*a^9*d^3 + (b^9*d^3*n^8 + 36*b^9*d^3*n^7 + 546*b^9*d^3*n^6 + 4536*b^9*d^3*n^5 + 22449*b^9*d^3*n^4 + 67284*b^9*d^3*n^3 + 118124*b^9*d^3*n^2 + 109584*b^9*d^3*n + 40320*b^9*d^3)*x^9 + (a*b^8*d^3*n^8 + 28*a*b^8*d^3*n^7 + 322*a*b^8*d^3*n^6 + 1960*a*b^8*d^3*n^5 + 6769*a*b^8*d^3*n^4 + 13132*a*b^8*d^3*n^3 + 13068*a*b^8*d^3*n^2 + 5040*a*b^8*d^3*n)*x^8 + (3*b^9*c*d^2*n^8 + 155520*b^9*c*d^2 + 2*(57*b^9*c*d^2 - 4*a^2*b^7*d^3)*n^7 + 12*(151*b^9*c*d^2 - 14*a^2*b^7*d^3)*n^6 + 14*(1119*b^9*c*d^2 - 100*a^2*b^7*d^3)*n^5 + 21*(3817*b^9*c*d^2 - 280*a^2*b^7*d^3)*n^4 + 28*(8817*b^9*c*d^2 - 464*a^2*b^7*d^3)*n^3 + 36*(12303*b^9*c*d^2 - 392*a^2*b^7*d^3)*n^2 + 144*(2901*b^9*c*d^2 - 40*a^2*b^7*d^3)*n)*x^7 + (3*a*b^8*c*d^2*n^8 + 96*a*b^8*c*d^2*n^7 + 4*(309*a*b^8*c*d^2 + 14*a^3*b^6*d^3)*n^6 + 30*(275*a*b^8*c*d^2 + 28*a^3*b^6*d^3)*n^5 + (30657*a*b^8*c*d^2 + 4760*a^3*b^6*d^3)*n^4 + 6*(10489*a*b^8*c*d^2 + 2100*a^3*b^6*d^3)*n^3 + 8*(8163*a*b^8*c*d^2 + 1918*a^3*b^6*d^3)*n^2 + 960*(27*a*b^8*c*d^2 + 7*a^3*b^6*d^3)*n)*x^6 + 3*(b^9*c^2*d*n^8 + 72576*b^9*c^2*d + 2*(20*b^9*c^2*d - 3*a^2*b^7*c*d^2)*n^7 + 2*(335*b^9*c^2*d - 81*a^2*b^7*c*d^2)*n^6 + 2*(3050*b^9*c^2*d - 831*a^2*b^7*c*d^2 - 56*a^4*b^5*d^3)*n^5 + (32773*b^9*c^2*d - 8190*a^2*b^7*c*d^2 - 1120*a^4*b^5*d^3)*n^4 + 4*(26365*b^9*c^2*d - 5091*a^2*b^7*c*d^2 - 980*a^4*b^5*d^3)*n^3 + 4*(49095*b^9*c^2*d - 6012*a^2*b^7*c*d^2 - 1400*a^4*b^5*d^3)*n^2 + 48*(3975*b^9*c^2*d - 216*a^2*b^7*c*d^2 - 56*a^4*b^5*d^3)*n)*x^5 + 2*(625*a^3*b^6*c^3 + 36*a^5*b^4*c^2*d)*n^4 + 3*(a*b^8*c^2*d*n^8 + 36*a*b^8*c^2*d*n^7 + 2*(263*a*b^8*c^2*d + 15*a^3*b^6*c*d^2)*n^6 + 6*(666*a*b^8*c^2*d + 115*a^3*b^6*c*d^2)*n^5 + (16789*a*b^8*c^2*d + 5550*a^3*b^6*c*d^2 + 560*a^5*b^4*d^3)*n^4 + 6*(6384*a*b^8*c^2*d + 3125*a^3*b^6*c*d^2 + 560*a^5*b^4*d^3)*n^3 + 4*(10791*a*b^8*c^2*d + 6705*a^3*b^6*c*d^2 + 1540*a^5*b^4*d^3)*n^2 + 96*(189*a*b^8*c^2*d + 135*a^3*b^6*c*d^2 + 35*a^5*b^4*d^3)*n)*x^4 + 270*(39*a^3*b^6*c^3 + 8*a^5*b^4*c^2*d)*n^3 + (b^9*c^3*n^8 + 120960*b^9*c^3 + 6*(7*b^9*c^3 - 2*a^2*b^7*c^2*d)*n^7 + 12*(62*b^9*c^3 - 33*a^2*b^7*c^2*d)*n^6 + 6*(1203*b^9*c^3 - 854*a^2*b^7*c^2*d - 60*a^4*b^5*c*d^2)*n^5 + 3*(13873*b^9*c^3 - 10860*a^2*b^7*c^2*d - 2400*a^4*b^5*c*d^2)*n^4 + 12*(12039*b^9*c^3 - 8644*a^2*b^7*c^2*d - 3750*a^4*b^5*c*d^2 - 560*a^6*b^3*d^3)*n^3 + 4*(72569*b^9*c^3 - 37116*a^2*b^7*c^2*d - 22500*a^4*b^5*c*d^2 - 5040*a^6*b^3*d^3)*n^2 + 48*(6289*b^9*c^3 - 1512*a^2*b^7*c^2*d - 1080*a^4*b^5*c*d^2 - 280*a^6*b^3*d^3)*n)*x^3 + 4*(12287*a^3*b^6*c^3 + 6030*a^5*b^4*c^2*d + 540*a^7*b^2*c*d^2)*n^2 + (a*b^8*c^3*n^8 + 40*a*b^8*c^3*n^7 + 4*(166*a*b^8*c^3 + 9*a^3*b^6*c^2*d)*n^6 + 62*(95*a*b^8*c^3 + 18*a^3*b^6*c^2*d)*n^5 + (29839*a*b^8*c^3 + 13140*a^3*b^6*c^2*d + 1080*a^5*b^4*c*d^2)*n^4 + 10*(8479*a*b^8*c^3 + 7146*a^3*b^6*c^2*d + 1944*a^5*b^4*c*d^2)*n^3 + 24*(5029*a*b^8*c^3 + 7011*a^3*b^6*c^2*d + 4005*a^5*b^4*c*d^2 + 840*a^7*b^2*d^3)*n^2 + 576*(105*a*b^8*c^3 + 189*a^3*b^6*c^2*d + 135*a^5*b^4*c*d^2 + 35*a^7*b^2*d^3)*n)*x^2 + 48*(2509*a^3*b^6*c^3 + 2475*a^5*b^4*c^2*d + 765*a^7*b^2*c*d^2)*n - 2*(a^2*b^7*c^3*n^7 + 39*a^2*b^7*c^3*n^6 + (625*a^2*b^7*c^3 + 36*a^4*b^5*c^2*d)*n^5 + 135*(39*a^2*b^7*c^3 + 8*a^4*b^5*c^2*d)*n^4 + 2*(12287*a^2*b^7*c^3 + 6030*a^4*b^5*c^2*d + 540*a^6*b^3*c*d^2)*n^3 + 24*(2509*a^2*b^7*c^3 + 2475*a^4*b^5*c^2*d + 765*a^6*b^3*c*d^2)*n^2 + 576*(105*a^2*b^7*c^3 + 189*a^4*b^5*c^2*d + 135*a^6*b^3*c*d^2 + 35*a^8*b*d^3)*n)*x)*(b*x + a)^n/(b^9*n^9 + 45*b^9*n^8 + 870*b^9*n^7 + 9450*b^9*n^6 + 63273*b^9*n^5 + 269325*b^9*n^4 + 723680*b^9*n^3 + 1172700*b^9*n^2 + 1026576*b^9*n + 362880*b^9)","B",0
360,1,1675,0,0.445628," ","integrate(x*(b*x+a)^n*(d*x^2+c)^3,x, algorithm=""fricas"")","-\frac{{\left(a^{2} b^{6} c^{3} n^{6} + 33 \, a^{2} b^{6} c^{3} n^{5} + 20160 \, a^{2} b^{6} c^{3} + 30240 \, a^{4} b^{4} c^{2} d + 20160 \, a^{6} b^{2} c d^{2} + 5040 \, a^{8} d^{3} - {\left(b^{8} d^{3} n^{7} + 28 \, b^{8} d^{3} n^{6} + 322 \, b^{8} d^{3} n^{5} + 1960 \, b^{8} d^{3} n^{4} + 6769 \, b^{8} d^{3} n^{3} + 13132 \, b^{8} d^{3} n^{2} + 13068 \, b^{8} d^{3} n + 5040 \, b^{8} d^{3}\right)} x^{8} - {\left(a b^{7} d^{3} n^{7} + 21 \, a b^{7} d^{3} n^{6} + 175 \, a b^{7} d^{3} n^{5} + 735 \, a b^{7} d^{3} n^{4} + 1624 \, a b^{7} d^{3} n^{3} + 1764 \, a b^{7} d^{3} n^{2} + 720 \, a b^{7} d^{3} n\right)} x^{7} - {\left(3 \, b^{8} c d^{2} n^{7} + 20160 \, b^{8} c d^{2} + {\left(90 \, b^{8} c d^{2} - 7 \, a^{2} b^{6} d^{3}\right)} n^{6} + 3 \, {\left(366 \, b^{8} c d^{2} - 35 \, a^{2} b^{6} d^{3}\right)} n^{5} + 5 \, {\left(1404 \, b^{8} c d^{2} - 119 \, a^{2} b^{6} d^{3}\right)} n^{4} + 9 \, {\left(2803 \, b^{8} c d^{2} - 175 \, a^{2} b^{6} d^{3}\right)} n^{3} + 2 \, {\left(25245 \, b^{8} c d^{2} - 959 \, a^{2} b^{6} d^{3}\right)} n^{2} + 24 \, {\left(2143 \, b^{8} c d^{2} - 35 \, a^{2} b^{6} d^{3}\right)} n\right)} x^{6} - 3 \, {\left(a b^{7} c d^{2} n^{7} + 25 \, a b^{7} c d^{2} n^{6} + {\left(241 \, a b^{7} c d^{2} + 14 \, a^{3} b^{5} d^{3}\right)} n^{5} + 5 \, {\left(227 \, a b^{7} c d^{2} + 28 \, a^{3} b^{5} d^{3}\right)} n^{4} + 2 \, {\left(1367 \, a b^{7} c d^{2} + 245 \, a^{3} b^{5} d^{3}\right)} n^{3} + 20 \, {\left(158 \, a b^{7} c d^{2} + 35 \, a^{3} b^{5} d^{3}\right)} n^{2} + 336 \, {\left(4 \, a b^{7} c d^{2} + a^{3} b^{5} d^{3}\right)} n\right)} x^{5} + {\left(445 \, a^{2} b^{6} c^{3} + 18 \, a^{4} b^{4} c^{2} d\right)} n^{4} - 3 \, {\left(b^{8} c^{2} d n^{7} + 10080 \, b^{8} c^{2} d + {\left(32 \, b^{8} c^{2} d - 5 \, a^{2} b^{6} c d^{2}\right)} n^{6} + {\left(418 \, b^{8} c^{2} d - 105 \, a^{2} b^{6} c d^{2}\right)} n^{5} + {\left(2864 \, b^{8} c^{2} d - 785 \, a^{2} b^{6} c d^{2} - 70 \, a^{4} b^{4} d^{3}\right)} n^{4} + {\left(10993 \, b^{8} c^{2} d - 2535 \, a^{2} b^{6} c d^{2} - 420 \, a^{4} b^{4} d^{3}\right)} n^{3} + 2 \, {\left(11656 \, b^{8} c^{2} d - 1765 \, a^{2} b^{6} c d^{2} - 385 \, a^{4} b^{4} d^{3}\right)} n^{2} + 12 \, {\left(2073 \, b^{8} c^{2} d - 140 \, a^{2} b^{6} c d^{2} - 35 \, a^{4} b^{4} d^{3}\right)} n\right)} x^{4} + 3 \, {\left(1045 \, a^{2} b^{6} c^{3} + 156 \, a^{4} b^{4} c^{2} d\right)} n^{3} - 3 \, {\left(a b^{7} c^{2} d n^{7} + 29 \, a b^{7} c^{2} d n^{6} + {\left(331 \, a b^{7} c^{2} d + 20 \, a^{3} b^{5} c d^{2}\right)} n^{5} + {\left(1871 \, a b^{7} c^{2} d + 360 \, a^{3} b^{5} c d^{2}\right)} n^{4} + 20 \, {\left(269 \, a b^{7} c^{2} d + 103 \, a^{3} b^{5} c d^{2} + 14 \, a^{5} b^{3} d^{3}\right)} n^{3} + 4 \, {\left(1793 \, a b^{7} c^{2} d + 990 \, a^{3} b^{5} c d^{2} + 210 \, a^{5} b^{3} d^{3}\right)} n^{2} + 560 \, {\left(6 \, a b^{7} c^{2} d + 4 \, a^{3} b^{5} c d^{2} + a^{5} b^{3} d^{3}\right)} n\right)} x^{3} + 2 \, {\left(6077 \, a^{2} b^{6} c^{3} + 2259 \, a^{4} b^{4} c^{2} d + 180 \, a^{6} b^{2} c d^{2}\right)} n^{2} - {\left(b^{8} c^{3} n^{7} + 20160 \, b^{8} c^{3} + {\left(34 \, b^{8} c^{3} - 9 \, a^{2} b^{6} c^{2} d\right)} n^{6} + {\left(478 \, b^{8} c^{3} - 243 \, a^{2} b^{6} c^{2} d\right)} n^{5} + {\left(3580 \, b^{8} c^{3} - 2493 \, a^{2} b^{6} c^{2} d - 180 \, a^{4} b^{4} c d^{2}\right)} n^{4} + {\left(15289 \, b^{8} c^{3} - 11853 \, a^{2} b^{6} c^{2} d - 2880 \, a^{4} b^{4} c d^{2}\right)} n^{3} + 2 \, {\left(18353 \, b^{8} c^{3} - 12357 \, a^{2} b^{6} c^{2} d - 6390 \, a^{4} b^{4} c d^{2} - 1260 \, a^{6} b^{2} d^{3}\right)} n^{2} + 72 \, {\left(621 \, b^{8} c^{3} - 210 \, a^{2} b^{6} c^{2} d - 140 \, a^{4} b^{4} c d^{2} - 35 \, a^{6} b^{2} d^{3}\right)} n\right)} x^{2} + 36 \, {\left(682 \, a^{2} b^{6} c^{3} + 533 \, a^{4} b^{4} c^{2} d + 150 \, a^{6} b^{2} c d^{2}\right)} n - {\left(a b^{7} c^{3} n^{7} + 33 \, a b^{7} c^{3} n^{6} + {\left(445 \, a b^{7} c^{3} + 18 \, a^{3} b^{5} c^{2} d\right)} n^{5} + 3 \, {\left(1045 \, a b^{7} c^{3} + 156 \, a^{3} b^{5} c^{2} d\right)} n^{4} + 2 \, {\left(6077 \, a b^{7} c^{3} + 2259 \, a^{3} b^{5} c^{2} d + 180 \, a^{5} b^{3} c d^{2}\right)} n^{3} + 36 \, {\left(682 \, a b^{7} c^{3} + 533 \, a^{3} b^{5} c^{2} d + 150 \, a^{5} b^{3} c d^{2}\right)} n^{2} + 5040 \, {\left(4 \, a b^{7} c^{3} + 6 \, a^{3} b^{5} c^{2} d + 4 \, a^{5} b^{3} c d^{2} + a^{7} b d^{3}\right)} n\right)} x\right)} {\left(b x + a\right)}^{n}}{b^{8} n^{8} + 36 \, b^{8} n^{7} + 546 \, b^{8} n^{6} + 4536 \, b^{8} n^{5} + 22449 \, b^{8} n^{4} + 67284 \, b^{8} n^{3} + 118124 \, b^{8} n^{2} + 109584 \, b^{8} n + 40320 \, b^{8}}"," ",0,"-(a^2*b^6*c^3*n^6 + 33*a^2*b^6*c^3*n^5 + 20160*a^2*b^6*c^3 + 30240*a^4*b^4*c^2*d + 20160*a^6*b^2*c*d^2 + 5040*a^8*d^3 - (b^8*d^3*n^7 + 28*b^8*d^3*n^6 + 322*b^8*d^3*n^5 + 1960*b^8*d^3*n^4 + 6769*b^8*d^3*n^3 + 13132*b^8*d^3*n^2 + 13068*b^8*d^3*n + 5040*b^8*d^3)*x^8 - (a*b^7*d^3*n^7 + 21*a*b^7*d^3*n^6 + 175*a*b^7*d^3*n^5 + 735*a*b^7*d^3*n^4 + 1624*a*b^7*d^3*n^3 + 1764*a*b^7*d^3*n^2 + 720*a*b^7*d^3*n)*x^7 - (3*b^8*c*d^2*n^7 + 20160*b^8*c*d^2 + (90*b^8*c*d^2 - 7*a^2*b^6*d^3)*n^6 + 3*(366*b^8*c*d^2 - 35*a^2*b^6*d^3)*n^5 + 5*(1404*b^8*c*d^2 - 119*a^2*b^6*d^3)*n^4 + 9*(2803*b^8*c*d^2 - 175*a^2*b^6*d^3)*n^3 + 2*(25245*b^8*c*d^2 - 959*a^2*b^6*d^3)*n^2 + 24*(2143*b^8*c*d^2 - 35*a^2*b^6*d^3)*n)*x^6 - 3*(a*b^7*c*d^2*n^7 + 25*a*b^7*c*d^2*n^6 + (241*a*b^7*c*d^2 + 14*a^3*b^5*d^3)*n^5 + 5*(227*a*b^7*c*d^2 + 28*a^3*b^5*d^3)*n^4 + 2*(1367*a*b^7*c*d^2 + 245*a^3*b^5*d^3)*n^3 + 20*(158*a*b^7*c*d^2 + 35*a^3*b^5*d^3)*n^2 + 336*(4*a*b^7*c*d^2 + a^3*b^5*d^3)*n)*x^5 + (445*a^2*b^6*c^3 + 18*a^4*b^4*c^2*d)*n^4 - 3*(b^8*c^2*d*n^7 + 10080*b^8*c^2*d + (32*b^8*c^2*d - 5*a^2*b^6*c*d^2)*n^6 + (418*b^8*c^2*d - 105*a^2*b^6*c*d^2)*n^5 + (2864*b^8*c^2*d - 785*a^2*b^6*c*d^2 - 70*a^4*b^4*d^3)*n^4 + (10993*b^8*c^2*d - 2535*a^2*b^6*c*d^2 - 420*a^4*b^4*d^3)*n^3 + 2*(11656*b^8*c^2*d - 1765*a^2*b^6*c*d^2 - 385*a^4*b^4*d^3)*n^2 + 12*(2073*b^8*c^2*d - 140*a^2*b^6*c*d^2 - 35*a^4*b^4*d^3)*n)*x^4 + 3*(1045*a^2*b^6*c^3 + 156*a^4*b^4*c^2*d)*n^3 - 3*(a*b^7*c^2*d*n^7 + 29*a*b^7*c^2*d*n^6 + (331*a*b^7*c^2*d + 20*a^3*b^5*c*d^2)*n^5 + (1871*a*b^7*c^2*d + 360*a^3*b^5*c*d^2)*n^4 + 20*(269*a*b^7*c^2*d + 103*a^3*b^5*c*d^2 + 14*a^5*b^3*d^3)*n^3 + 4*(1793*a*b^7*c^2*d + 990*a^3*b^5*c*d^2 + 210*a^5*b^3*d^3)*n^2 + 560*(6*a*b^7*c^2*d + 4*a^3*b^5*c*d^2 + a^5*b^3*d^3)*n)*x^3 + 2*(6077*a^2*b^6*c^3 + 2259*a^4*b^4*c^2*d + 180*a^6*b^2*c*d^2)*n^2 - (b^8*c^3*n^7 + 20160*b^8*c^3 + (34*b^8*c^3 - 9*a^2*b^6*c^2*d)*n^6 + (478*b^8*c^3 - 243*a^2*b^6*c^2*d)*n^5 + (3580*b^8*c^3 - 2493*a^2*b^6*c^2*d - 180*a^4*b^4*c*d^2)*n^4 + (15289*b^8*c^3 - 11853*a^2*b^6*c^2*d - 2880*a^4*b^4*c*d^2)*n^3 + 2*(18353*b^8*c^3 - 12357*a^2*b^6*c^2*d - 6390*a^4*b^4*c*d^2 - 1260*a^6*b^2*d^3)*n^2 + 72*(621*b^8*c^3 - 210*a^2*b^6*c^2*d - 140*a^4*b^4*c*d^2 - 35*a^6*b^2*d^3)*n)*x^2 + 36*(682*a^2*b^6*c^3 + 533*a^4*b^4*c^2*d + 150*a^6*b^2*c*d^2)*n - (a*b^7*c^3*n^7 + 33*a*b^7*c^3*n^6 + (445*a*b^7*c^3 + 18*a^3*b^5*c^2*d)*n^5 + 3*(1045*a*b^7*c^3 + 156*a^3*b^5*c^2*d)*n^4 + 2*(6077*a*b^7*c^3 + 2259*a^3*b^5*c^2*d + 180*a^5*b^3*c*d^2)*n^3 + 36*(682*a*b^7*c^3 + 533*a^3*b^5*c^2*d + 150*a^5*b^3*c*d^2)*n^2 + 5040*(4*a*b^7*c^3 + 6*a^3*b^5*c^2*d + 4*a^5*b^3*c*d^2 + a^7*b*d^3)*n)*x)*(b*x + a)^n/(b^8*n^8 + 36*b^8*n^7 + 546*b^8*n^6 + 4536*b^8*n^5 + 22449*b^8*n^4 + 67284*b^8*n^3 + 118124*b^8*n^2 + 109584*b^8*n + 40320*b^8)","B",0
361,1,1244,0,0.414452," ","integrate((b*x+a)^n*(d*x^2+c)^3,x, algorithm=""fricas"")","\frac{{\left(a b^{6} c^{3} n^{6} + 27 \, a b^{6} c^{3} n^{5} + 5040 \, a b^{6} c^{3} + 5040 \, a^{3} b^{4} c^{2} d + 3024 \, a^{5} b^{2} c d^{2} + 720 \, a^{7} d^{3} + {\left(b^{7} d^{3} n^{6} + 21 \, b^{7} d^{3} n^{5} + 175 \, b^{7} d^{3} n^{4} + 735 \, b^{7} d^{3} n^{3} + 1624 \, b^{7} d^{3} n^{2} + 1764 \, b^{7} d^{3} n + 720 \, b^{7} d^{3}\right)} x^{7} + {\left(a b^{6} d^{3} n^{6} + 15 \, a b^{6} d^{3} n^{5} + 85 \, a b^{6} d^{3} n^{4} + 225 \, a b^{6} d^{3} n^{3} + 274 \, a b^{6} d^{3} n^{2} + 120 \, a b^{6} d^{3} n\right)} x^{6} + 3 \, {\left(b^{7} c d^{2} n^{6} + 1008 \, b^{7} c d^{2} + {\left(23 \, b^{7} c d^{2} - 2 \, a^{2} b^{5} d^{3}\right)} n^{5} + {\left(207 \, b^{7} c d^{2} - 20 \, a^{2} b^{5} d^{3}\right)} n^{4} + 5 \, {\left(185 \, b^{7} c d^{2} - 14 \, a^{2} b^{5} d^{3}\right)} n^{3} + 4 \, {\left(536 \, b^{7} c d^{2} - 25 \, a^{2} b^{5} d^{3}\right)} n^{2} + 12 \, {\left(201 \, b^{7} c d^{2} - 4 \, a^{2} b^{5} d^{3}\right)} n\right)} x^{5} + {\left(295 \, a b^{6} c^{3} + 6 \, a^{3} b^{4} c^{2} d\right)} n^{4} + 3 \, {\left(a b^{6} c d^{2} n^{6} + 19 \, a b^{6} c d^{2} n^{5} + {\left(131 \, a b^{6} c d^{2} + 10 \, a^{3} b^{4} d^{3}\right)} n^{4} + {\left(401 \, a b^{6} c d^{2} + 60 \, a^{3} b^{4} d^{3}\right)} n^{3} + 10 \, {\left(54 \, a b^{6} c d^{2} + 11 \, a^{3} b^{4} d^{3}\right)} n^{2} + 12 \, {\left(21 \, a b^{6} c d^{2} + 5 \, a^{3} b^{4} d^{3}\right)} n\right)} x^{4} + 3 \, {\left(555 \, a b^{6} c^{3} + 44 \, a^{3} b^{4} c^{2} d\right)} n^{3} + 3 \, {\left(b^{7} c^{2} d n^{6} + 1680 \, b^{7} c^{2} d + {\left(25 \, b^{7} c^{2} d - 4 \, a^{2} b^{5} c d^{2}\right)} n^{5} + {\left(247 \, b^{7} c^{2} d - 64 \, a^{2} b^{5} c d^{2}\right)} n^{4} + {\left(1219 \, b^{7} c^{2} d - 332 \, a^{2} b^{5} c d^{2} - 40 \, a^{4} b^{3} d^{3}\right)} n^{3} + 8 \, {\left(389 \, b^{7} c^{2} d - 76 \, a^{2} b^{5} c d^{2} - 15 \, a^{4} b^{3} d^{3}\right)} n^{2} + 4 \, {\left(949 \, b^{7} c^{2} d - 84 \, a^{2} b^{5} c d^{2} - 20 \, a^{4} b^{3} d^{3}\right)} n\right)} x^{3} + 2 \, {\left(2552 \, a b^{6} c^{3} + 537 \, a^{3} b^{4} c^{2} d + 36 \, a^{5} b^{2} c d^{2}\right)} n^{2} + 3 \, {\left(a b^{6} c^{2} d n^{6} + 23 \, a b^{6} c^{2} d n^{5} + 3 \, {\left(67 \, a b^{6} c^{2} d + 4 \, a^{3} b^{4} c d^{2}\right)} n^{4} + {\left(817 \, a b^{6} c^{2} d + 168 \, a^{3} b^{4} c d^{2}\right)} n^{3} + 2 \, {\left(739 \, a b^{6} c^{2} d + 330 \, a^{3} b^{4} c d^{2} + 60 \, a^{5} b^{2} d^{3}\right)} n^{2} + 24 \, {\left(35 \, a b^{6} c^{2} d + 21 \, a^{3} b^{4} c d^{2} + 5 \, a^{5} b^{2} d^{3}\right)} n\right)} x^{2} + 12 \, {\left(669 \, a b^{6} c^{3} + 319 \, a^{3} b^{4} c^{2} d + 78 \, a^{5} b^{2} c d^{2}\right)} n + {\left(b^{7} c^{3} n^{6} + 5040 \, b^{7} c^{3} + 3 \, {\left(9 \, b^{7} c^{3} - 2 \, a^{2} b^{5} c^{2} d\right)} n^{5} + {\left(295 \, b^{7} c^{3} - 132 \, a^{2} b^{5} c^{2} d\right)} n^{4} + 3 \, {\left(555 \, b^{7} c^{3} - 358 \, a^{2} b^{5} c^{2} d - 24 \, a^{4} b^{3} c d^{2}\right)} n^{3} + 4 \, {\left(1276 \, b^{7} c^{3} - 957 \, a^{2} b^{5} c^{2} d - 234 \, a^{4} b^{3} c d^{2}\right)} n^{2} + 36 \, {\left(223 \, b^{7} c^{3} - 140 \, a^{2} b^{5} c^{2} d - 84 \, a^{4} b^{3} c d^{2} - 20 \, a^{6} b d^{3}\right)} n\right)} x\right)} {\left(b x + a\right)}^{n}}{b^{7} n^{7} + 28 \, b^{7} n^{6} + 322 \, b^{7} n^{5} + 1960 \, b^{7} n^{4} + 6769 \, b^{7} n^{3} + 13132 \, b^{7} n^{2} + 13068 \, b^{7} n + 5040 \, b^{7}}"," ",0,"(a*b^6*c^3*n^6 + 27*a*b^6*c^3*n^5 + 5040*a*b^6*c^3 + 5040*a^3*b^4*c^2*d + 3024*a^5*b^2*c*d^2 + 720*a^7*d^3 + (b^7*d^3*n^6 + 21*b^7*d^3*n^5 + 175*b^7*d^3*n^4 + 735*b^7*d^3*n^3 + 1624*b^7*d^3*n^2 + 1764*b^7*d^3*n + 720*b^7*d^3)*x^7 + (a*b^6*d^3*n^6 + 15*a*b^6*d^3*n^5 + 85*a*b^6*d^3*n^4 + 225*a*b^6*d^3*n^3 + 274*a*b^6*d^3*n^2 + 120*a*b^6*d^3*n)*x^6 + 3*(b^7*c*d^2*n^6 + 1008*b^7*c*d^2 + (23*b^7*c*d^2 - 2*a^2*b^5*d^3)*n^5 + (207*b^7*c*d^2 - 20*a^2*b^5*d^3)*n^4 + 5*(185*b^7*c*d^2 - 14*a^2*b^5*d^3)*n^3 + 4*(536*b^7*c*d^2 - 25*a^2*b^5*d^3)*n^2 + 12*(201*b^7*c*d^2 - 4*a^2*b^5*d^3)*n)*x^5 + (295*a*b^6*c^3 + 6*a^3*b^4*c^2*d)*n^4 + 3*(a*b^6*c*d^2*n^6 + 19*a*b^6*c*d^2*n^5 + (131*a*b^6*c*d^2 + 10*a^3*b^4*d^3)*n^4 + (401*a*b^6*c*d^2 + 60*a^3*b^4*d^3)*n^3 + 10*(54*a*b^6*c*d^2 + 11*a^3*b^4*d^3)*n^2 + 12*(21*a*b^6*c*d^2 + 5*a^3*b^4*d^3)*n)*x^4 + 3*(555*a*b^6*c^3 + 44*a^3*b^4*c^2*d)*n^3 + 3*(b^7*c^2*d*n^6 + 1680*b^7*c^2*d + (25*b^7*c^2*d - 4*a^2*b^5*c*d^2)*n^5 + (247*b^7*c^2*d - 64*a^2*b^5*c*d^2)*n^4 + (1219*b^7*c^2*d - 332*a^2*b^5*c*d^2 - 40*a^4*b^3*d^3)*n^3 + 8*(389*b^7*c^2*d - 76*a^2*b^5*c*d^2 - 15*a^4*b^3*d^3)*n^2 + 4*(949*b^7*c^2*d - 84*a^2*b^5*c*d^2 - 20*a^4*b^3*d^3)*n)*x^3 + 2*(2552*a*b^6*c^3 + 537*a^3*b^4*c^2*d + 36*a^5*b^2*c*d^2)*n^2 + 3*(a*b^6*c^2*d*n^6 + 23*a*b^6*c^2*d*n^5 + 3*(67*a*b^6*c^2*d + 4*a^3*b^4*c*d^2)*n^4 + (817*a*b^6*c^2*d + 168*a^3*b^4*c*d^2)*n^3 + 2*(739*a*b^6*c^2*d + 330*a^3*b^4*c*d^2 + 60*a^5*b^2*d^3)*n^2 + 24*(35*a*b^6*c^2*d + 21*a^3*b^4*c*d^2 + 5*a^5*b^2*d^3)*n)*x^2 + 12*(669*a*b^6*c^3 + 319*a^3*b^4*c^2*d + 78*a^5*b^2*c*d^2)*n + (b^7*c^3*n^6 + 5040*b^7*c^3 + 3*(9*b^7*c^3 - 2*a^2*b^5*c^2*d)*n^5 + (295*b^7*c^3 - 132*a^2*b^5*c^2*d)*n^4 + 3*(555*b^7*c^3 - 358*a^2*b^5*c^2*d - 24*a^4*b^3*c*d^2)*n^3 + 4*(1276*b^7*c^3 - 957*a^2*b^5*c^2*d - 234*a^4*b^3*c*d^2)*n^2 + 36*(223*b^7*c^3 - 140*a^2*b^5*c^2*d - 84*a^4*b^3*c*d^2 - 20*a^6*b*d^3)*n)*x)*(b*x + a)^n/(b^7*n^7 + 28*b^7*n^6 + 322*b^7*n^5 + 1960*b^7*n^4 + 6769*b^7*n^3 + 13132*b^7*n^2 + 13068*b^7*n + 5040*b^7)","B",0
362,0,0,0,0.395326," ","integrate((b*x+a)^n*(d*x^2+c)^3/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d^{3} x^{6} + 3 \, c d^{2} x^{4} + 3 \, c^{2} d x^{2} + c^{3}\right)} {\left(b x + a\right)}^{n}}{x}, x\right)"," ",0,"integral((d^3*x^6 + 3*c*d^2*x^4 + 3*c^2*d*x^2 + c^3)*(b*x + a)^n/x, x)","F",0
363,0,0,0,0.420808," ","integrate(x^4*(e*x+d)^n/(c*x^2+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)}^{n} x^{4}}{c x^{2} + a}, x\right)"," ",0,"integral((e*x + d)^n*x^4/(c*x^2 + a), x)","F",0
364,0,0,0,0.411353," ","integrate(x^3*(e*x+d)^n/(c*x^2+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)}^{n} x^{3}}{c x^{2} + a}, x\right)"," ",0,"integral((e*x + d)^n*x^3/(c*x^2 + a), x)","F",0
365,0,0,0,0.411863," ","integrate(x^2*(e*x+d)^n/(c*x^2+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)}^{n} x^{2}}{c x^{2} + a}, x\right)"," ",0,"integral((e*x + d)^n*x^2/(c*x^2 + a), x)","F",0
366,0,0,0,0.418276," ","integrate(x*(e*x+d)^n/(c*x^2+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)}^{n} x}{c x^{2} + a}, x\right)"," ",0,"integral((e*x + d)^n*x/(c*x^2 + a), x)","F",0
367,0,0,0,0.438239," ","integrate((e*x+d)^n/(c*x^2+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)}^{n}}{c x^{2} + a}, x\right)"," ",0,"integral((e*x + d)^n/(c*x^2 + a), x)","F",0
368,0,0,0,0.450177," ","integrate((e*x+d)^n/x/(c*x^2+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)}^{n}}{c x^{3} + a x}, x\right)"," ",0,"integral((e*x + d)^n/(c*x^3 + a*x), x)","F",0
369,0,0,0,0.458448," ","integrate((e*x+d)^n/x^2/(c*x^2+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)}^{n}}{c x^{4} + a x^{2}}, x\right)"," ",0,"integral((e*x + d)^n/(c*x^4 + a*x^2), x)","F",0
370,0,0,0,0.473960," ","integrate(x^4*(e*x+d)^n/(c*x^2+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)}^{n} x^{4}}{c^{2} x^{4} + 2 \, a c x^{2} + a^{2}}, x\right)"," ",0,"integral((e*x + d)^n*x^4/(c^2*x^4 + 2*a*c*x^2 + a^2), x)","F",0
371,0,0,0,0.433910," ","integrate(x^3*(e*x+d)^n/(c*x^2+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)}^{n} x^{3}}{c^{2} x^{4} + 2 \, a c x^{2} + a^{2}}, x\right)"," ",0,"integral((e*x + d)^n*x^3/(c^2*x^4 + 2*a*c*x^2 + a^2), x)","F",0
372,0,0,0,0.451072," ","integrate(x^2*(e*x+d)^n/(c*x^2+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)}^{n} x^{2}}{c^{2} x^{4} + 2 \, a c x^{2} + a^{2}}, x\right)"," ",0,"integral((e*x + d)^n*x^2/(c^2*x^4 + 2*a*c*x^2 + a^2), x)","F",0
373,0,0,0,0.452339," ","integrate(x*(e*x+d)^n/(c*x^2+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)}^{n} x}{c^{2} x^{4} + 2 \, a c x^{2} + a^{2}}, x\right)"," ",0,"integral((e*x + d)^n*x/(c^2*x^4 + 2*a*c*x^2 + a^2), x)","F",0
374,0,0,0,0.432464," ","integrate((e*x+d)^n/(c*x^2+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)}^{n}}{c^{2} x^{4} + 2 \, a c x^{2} + a^{2}}, x\right)"," ",0,"integral((e*x + d)^n/(c^2*x^4 + 2*a*c*x^2 + a^2), x)","F",0
375,0,0,0,0.435512," ","integrate((e*x+d)^n/x/(c*x^2+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)}^{n}}{c^{2} x^{5} + 2 \, a c x^{3} + a^{2} x}, x\right)"," ",0,"integral((e*x + d)^n/(c^2*x^5 + 2*a*c*x^3 + a^2*x), x)","F",0
376,0,0,0,0.446122," ","integrate((e*x+d)^n/x^2/(c*x^2+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)}^{n}}{c^{2} x^{6} + 2 \, a c x^{4} + a^{2} x^{2}}, x\right)"," ",0,"integral((e*x + d)^n/(c^2*x^6 + 2*a*c*x^4 + a^2*x^2), x)","F",0
377,0,0,0,0.420148," ","integrate((g*x)^m*(e*x+d)^n*(c*x^2+a)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(c^{2} x^{4} + 2 \, a c x^{2} + a^{2}\right)} {\left(e x + d\right)}^{n} \left(g x\right)^{m}, x\right)"," ",0,"integral((c^2*x^4 + 2*a*c*x^2 + a^2)*(e*x + d)^n*(g*x)^m, x)","F",0
378,0,0,0,0.426825," ","integrate((g*x)^m*(e*x+d)^n*(c*x^2+a),x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{2} + a\right)} {\left(e x + d\right)}^{n} \left(g x\right)^{m}, x\right)"," ",0,"integral((c*x^2 + a)*(e*x + d)^n*(g*x)^m, x)","F",0
379,0,0,0,0.409050," ","integrate((g*x)^m*(e*x+d)^n/(c*x^2+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)}^{n} \left(g x\right)^{m}}{c x^{2} + a}, x\right)"," ",0,"integral((e*x + d)^n*(g*x)^m/(c*x^2 + a), x)","F",0
380,0,0,0,0.469227," ","integrate((g*x)^m*(e*x+d)^n/(c*x^2+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)}^{n} \left(g x\right)^{m}}{c^{2} x^{4} + 2 \, a c x^{2} + a^{2}}, x\right)"," ",0,"integral((e*x + d)^n*(g*x)^m/(c^2*x^4 + 2*a*c*x^2 + a^2), x)","F",0
381,0,0,0,0.416635," ","integrate(x^5*(e*x+d)*(b*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e x^{6} + d x^{5}\right)} {\left(b x^{2} + a\right)}^{p}, x\right)"," ",0,"integral((e*x^6 + d*x^5)*(b*x^2 + a)^p, x)","F",0
382,0,0,0,0.411184," ","integrate(x^4*(e*x+d)*(b*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e x^{5} + d x^{4}\right)} {\left(b x^{2} + a\right)}^{p}, x\right)"," ",0,"integral((e*x^5 + d*x^4)*(b*x^2 + a)^p, x)","F",0
383,0,0,0,0.414184," ","integrate(x^3*(e*x+d)*(b*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e x^{4} + d x^{3}\right)} {\left(b x^{2} + a\right)}^{p}, x\right)"," ",0,"integral((e*x^4 + d*x^3)*(b*x^2 + a)^p, x)","F",0
384,0,0,0,0.397532," ","integrate(x^2*(e*x+d)*(b*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e x^{3} + d x^{2}\right)} {\left(b x^{2} + a\right)}^{p}, x\right)"," ",0,"integral((e*x^3 + d*x^2)*(b*x^2 + a)^p, x)","F",0
385,0,0,0,0.411976," ","integrate(x*(e*x+d)*(b*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e x^{2} + d x\right)} {\left(b x^{2} + a\right)}^{p}, x\right)"," ",0,"integral((e*x^2 + d*x)*(b*x^2 + a)^p, x)","F",0
386,0,0,0,0.409156," ","integrate((e*x+d)*(b*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e x + d\right)} {\left(b x^{2} + a\right)}^{p}, x\right)"," ",0,"integral((e*x + d)*(b*x^2 + a)^p, x)","F",0
387,0,0,0,0.413872," ","integrate((e*x+d)*(b*x^2+a)^p/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)} {\left(b x^{2} + a\right)}^{p}}{x}, x\right)"," ",0,"integral((e*x + d)*(b*x^2 + a)^p/x, x)","F",0
388,0,0,0,0.416001," ","integrate((e*x+d)*(b*x^2+a)^p/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)} {\left(b x^{2} + a\right)}^{p}}{x^{2}}, x\right)"," ",0,"integral((e*x + d)*(b*x^2 + a)^p/x^2, x)","F",0
389,0,0,0,0.406594," ","integrate((e*x+d)*(b*x^2+a)^p/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)} {\left(b x^{2} + a\right)}^{p}}{x^{3}}, x\right)"," ",0,"integral((e*x + d)*(b*x^2 + a)^p/x^3, x)","F",0
390,0,0,0,0.421381," ","integrate(x^5*(e*x+d)^2*(b*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{2} x^{7} + 2 \, d e x^{6} + d^{2} x^{5}\right)} {\left(b x^{2} + a\right)}^{p}, x\right)"," ",0,"integral((e^2*x^7 + 2*d*e*x^6 + d^2*x^5)*(b*x^2 + a)^p, x)","F",0
391,0,0,0,0.393973," ","integrate(x^4*(e*x+d)^2*(b*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{2} x^{6} + 2 \, d e x^{5} + d^{2} x^{4}\right)} {\left(b x^{2} + a\right)}^{p}, x\right)"," ",0,"integral((e^2*x^6 + 2*d*e*x^5 + d^2*x^4)*(b*x^2 + a)^p, x)","F",0
392,0,0,0,0.407612," ","integrate(x^3*(e*x+d)^2*(b*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{2} x^{5} + 2 \, d e x^{4} + d^{2} x^{3}\right)} {\left(b x^{2} + a\right)}^{p}, x\right)"," ",0,"integral((e^2*x^5 + 2*d*e*x^4 + d^2*x^3)*(b*x^2 + a)^p, x)","F",0
393,0,0,0,0.400343," ","integrate(x^2*(e*x+d)^2*(b*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{2} x^{4} + 2 \, d e x^{3} + d^{2} x^{2}\right)} {\left(b x^{2} + a\right)}^{p}, x\right)"," ",0,"integral((e^2*x^4 + 2*d*e*x^3 + d^2*x^2)*(b*x^2 + a)^p, x)","F",0
394,0,0,0,0.400438," ","integrate(x*(e*x+d)^2*(b*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{2} x^{3} + 2 \, d e x^{2} + d^{2} x\right)} {\left(b x^{2} + a\right)}^{p}, x\right)"," ",0,"integral((e^2*x^3 + 2*d*e*x^2 + d^2*x)*(b*x^2 + a)^p, x)","F",0
395,0,0,0,0.412383," ","integrate((e*x+d)^2*(b*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{2} x^{2} + 2 \, d e x + d^{2}\right)} {\left(b x^{2} + a\right)}^{p}, x\right)"," ",0,"integral((e^2*x^2 + 2*d*e*x + d^2)*(b*x^2 + a)^p, x)","F",0
396,0,0,0,0.410600," ","integrate((e*x+d)^2*(b*x^2+a)^p/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{2} x^{2} + 2 \, d e x + d^{2}\right)} {\left(b x^{2} + a\right)}^{p}}{x}, x\right)"," ",0,"integral((e^2*x^2 + 2*d*e*x + d^2)*(b*x^2 + a)^p/x, x)","F",0
397,0,0,0,0.402669," ","integrate((e*x+d)^2*(b*x^2+a)^p/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{2} x^{2} + 2 \, d e x + d^{2}\right)} {\left(b x^{2} + a\right)}^{p}}{x^{2}}, x\right)"," ",0,"integral((e^2*x^2 + 2*d*e*x + d^2)*(b*x^2 + a)^p/x^2, x)","F",0
398,0,0,0,0.415634," ","integrate((e*x+d)^2*(b*x^2+a)^p/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{2} x^{2} + 2 \, d e x + d^{2}\right)} {\left(b x^{2} + a\right)}^{p}}{x^{3}}, x\right)"," ",0,"integral((e^2*x^2 + 2*d*e*x + d^2)*(b*x^2 + a)^p/x^3, x)","F",0
399,0,0,0,0.400604," ","integrate(x^5*(e*x+d)^3*(b*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{3} x^{8} + 3 \, d e^{2} x^{7} + 3 \, d^{2} e x^{6} + d^{3} x^{5}\right)} {\left(b x^{2} + a\right)}^{p}, x\right)"," ",0,"integral((e^3*x^8 + 3*d*e^2*x^7 + 3*d^2*e*x^6 + d^3*x^5)*(b*x^2 + a)^p, x)","F",0
400,0,0,0,0.405450," ","integrate(x^4*(e*x+d)^3*(b*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{3} x^{7} + 3 \, d e^{2} x^{6} + 3 \, d^{2} e x^{5} + d^{3} x^{4}\right)} {\left(b x^{2} + a\right)}^{p}, x\right)"," ",0,"integral((e^3*x^7 + 3*d*e^2*x^6 + 3*d^2*e*x^5 + d^3*x^4)*(b*x^2 + a)^p, x)","F",0
401,0,0,0,0.405968," ","integrate(x^3*(e*x+d)^3*(b*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{3} x^{6} + 3 \, d e^{2} x^{5} + 3 \, d^{2} e x^{4} + d^{3} x^{3}\right)} {\left(b x^{2} + a\right)}^{p}, x\right)"," ",0,"integral((e^3*x^6 + 3*d*e^2*x^5 + 3*d^2*e*x^4 + d^3*x^3)*(b*x^2 + a)^p, x)","F",0
402,0,0,0,0.412161," ","integrate(x^2*(e*x+d)^3*(b*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{3} x^{5} + 3 \, d e^{2} x^{4} + 3 \, d^{2} e x^{3} + d^{3} x^{2}\right)} {\left(b x^{2} + a\right)}^{p}, x\right)"," ",0,"integral((e^3*x^5 + 3*d*e^2*x^4 + 3*d^2*e*x^3 + d^3*x^2)*(b*x^2 + a)^p, x)","F",0
403,0,0,0,0.415006," ","integrate(x*(e*x+d)^3*(b*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{3} x^{4} + 3 \, d e^{2} x^{3} + 3 \, d^{2} e x^{2} + d^{3} x\right)} {\left(b x^{2} + a\right)}^{p}, x\right)"," ",0,"integral((e^3*x^4 + 3*d*e^2*x^3 + 3*d^2*e*x^2 + d^3*x)*(b*x^2 + a)^p, x)","F",0
404,0,0,0,0.412521," ","integrate((e*x+d)^3*(b*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}\right)} {\left(b x^{2} + a\right)}^{p}, x\right)"," ",0,"integral((e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)*(b*x^2 + a)^p, x)","F",0
405,0,0,0,0.412922," ","integrate((e*x+d)^3*(b*x^2+a)^p/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}\right)} {\left(b x^{2} + a\right)}^{p}}{x}, x\right)"," ",0,"integral((e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)*(b*x^2 + a)^p/x, x)","F",0
406,0,0,0,0.405103," ","integrate((e*x+d)^3*(b*x^2+a)^p/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}\right)} {\left(b x^{2} + a\right)}^{p}}{x^{2}}, x\right)"," ",0,"integral((e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)*(b*x^2 + a)^p/x^2, x)","F",0
407,0,0,0,0.413113," ","integrate((e*x+d)^3*(b*x^2+a)^p/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}\right)} {\left(b x^{2} + a\right)}^{p}}{x^{3}}, x\right)"," ",0,"integral((e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)*(b*x^2 + a)^p/x^3, x)","F",0
408,0,0,0,0.412162," ","integrate(x^4*(b*x^2+a)^p/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)}^{p} x^{4}}{e x + d}, x\right)"," ",0,"integral((b*x^2 + a)^p*x^4/(e*x + d), x)","F",0
409,0,0,0,0.393976," ","integrate(x^3*(b*x^2+a)^p/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)}^{p} x^{3}}{e x + d}, x\right)"," ",0,"integral((b*x^2 + a)^p*x^3/(e*x + d), x)","F",0
410,0,0,0,0.415711," ","integrate(x^2*(b*x^2+a)^p/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)}^{p} x^{2}}{e x + d}, x\right)"," ",0,"integral((b*x^2 + a)^p*x^2/(e*x + d), x)","F",0
411,0,0,0,0.412603," ","integrate(x*(b*x^2+a)^p/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)}^{p} x}{e x + d}, x\right)"," ",0,"integral((b*x^2 + a)^p*x/(e*x + d), x)","F",0
412,0,0,0,0.415550," ","integrate((b*x^2+a)^p/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)}^{p}}{e x + d}, x\right)"," ",0,"integral((b*x^2 + a)^p/(e*x + d), x)","F",0
413,0,0,0,0.418922," ","integrate((b*x^2+a)^p/x/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)}^{p}}{e x^{2} + d x}, x\right)"," ",0,"integral((b*x^2 + a)^p/(e*x^2 + d*x), x)","F",0
414,0,0,0,0.405031," ","integrate((b*x^2+a)^p/x^2/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)}^{p}}{e x^{3} + d x^{2}}, x\right)"," ",0,"integral((b*x^2 + a)^p/(e*x^3 + d*x^2), x)","F",0
415,0,0,0,0.415319," ","integrate((b*x^2+a)^p/x^3/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)}^{p}}{e x^{4} + d x^{3}}, x\right)"," ",0,"integral((b*x^2 + a)^p/(e*x^4 + d*x^3), x)","F",0
416,0,0,0,0.421355," ","integrate(x^4*(b*x^2+a)^p/(e*x+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)}^{p} x^{4}}{e^{2} x^{2} + 2 \, d e x + d^{2}}, x\right)"," ",0,"integral((b*x^2 + a)^p*x^4/(e^2*x^2 + 2*d*e*x + d^2), x)","F",0
417,0,0,0,0.430439," ","integrate(x^3*(b*x^2+a)^p/(e*x+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)}^{p} x^{3}}{e^{2} x^{2} + 2 \, d e x + d^{2}}, x\right)"," ",0,"integral((b*x^2 + a)^p*x^3/(e^2*x^2 + 2*d*e*x + d^2), x)","F",0
418,0,0,0,0.430917," ","integrate(x^2*(b*x^2+a)^p/(e*x+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)}^{p} x^{2}}{e^{2} x^{2} + 2 \, d e x + d^{2}}, x\right)"," ",0,"integral((b*x^2 + a)^p*x^2/(e^2*x^2 + 2*d*e*x + d^2), x)","F",0
419,0,0,0,0.405982," ","integrate(x*(b*x^2+a)^p/(e*x+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)}^{p} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}, x\right)"," ",0,"integral((b*x^2 + a)^p*x/(e^2*x^2 + 2*d*e*x + d^2), x)","F",0
420,0,0,0,0.406300," ","integrate((b*x^2+a)^p/(e*x+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)}^{p}}{e^{2} x^{2} + 2 \, d e x + d^{2}}, x\right)"," ",0,"integral((b*x^2 + a)^p/(e^2*x^2 + 2*d*e*x + d^2), x)","F",0
421,0,0,0,0.437132," ","integrate((b*x^2+a)^p/x/(e*x+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)}^{p}}{e^{2} x^{3} + 2 \, d e x^{2} + d^{2} x}, x\right)"," ",0,"integral((b*x^2 + a)^p/(e^2*x^3 + 2*d*e*x^2 + d^2*x), x)","F",0
422,0,0,0,0.448129," ","integrate((b*x^2+a)^p/x^2/(e*x+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)}^{p}}{e^{2} x^{4} + 2 \, d e x^{3} + d^{2} x^{2}}, x\right)"," ",0,"integral((b*x^2 + a)^p/(e^2*x^4 + 2*d*e*x^3 + d^2*x^2), x)","F",0
423,0,0,0,0.428593," ","integrate(x^4*(b*x^2+a)^p/(e*x+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)}^{p} x^{4}}{e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}}, x\right)"," ",0,"integral((b*x^2 + a)^p*x^4/(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3), x)","F",0
424,0,0,0,0.433728," ","integrate(x^3*(b*x^2+a)^p/(e*x+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)}^{p} x^{3}}{e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}}, x\right)"," ",0,"integral((b*x^2 + a)^p*x^3/(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3), x)","F",0
425,0,0,0,0.430217," ","integrate(x^2*(b*x^2+a)^p/(e*x+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)}^{p} x^{2}}{e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}}, x\right)"," ",0,"integral((b*x^2 + a)^p*x^2/(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3), x)","F",0
426,0,0,0,0.409522," ","integrate(x*(b*x^2+a)^p/(e*x+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)}^{p} x}{e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}}, x\right)"," ",0,"integral((b*x^2 + a)^p*x/(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3), x)","F",0
427,0,0,0,0.418424," ","integrate((b*x^2+a)^p/(e*x+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)}^{p}}{e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}}, x\right)"," ",0,"integral((b*x^2 + a)^p/(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3), x)","F",0
428,0,0,0,0.420389," ","integrate((b*x^2+a)^p/x/(e*x+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)}^{p}}{e^{3} x^{4} + 3 \, d e^{2} x^{3} + 3 \, d^{2} e x^{2} + d^{3} x}, x\right)"," ",0,"integral((b*x^2 + a)^p/(e^3*x^4 + 3*d*e^2*x^3 + 3*d^2*e*x^2 + d^3*x), x)","F",0
429,0,0,0,0.492321," ","integrate((b*x^2+a)^p/x^2/(e*x+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)}^{p}}{e^{3} x^{5} + 3 \, d e^{2} x^{4} + 3 \, d^{2} e x^{3} + d^{3} x^{2}}, x\right)"," ",0,"integral((b*x^2 + a)^p/(e^3*x^5 + 3*d*e^2*x^4 + 3*d^2*e*x^3 + d^3*x^2), x)","F",0
430,0,0,0,0.418831," ","integrate((g*x)^m*(e*x+d)^3*(c*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}\right)} {\left(c x^{2} + a\right)}^{p} \left(g x\right)^{m}, x\right)"," ",0,"integral((e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)*(c*x^2 + a)^p*(g*x)^m, x)","F",0
431,0,0,0,0.432053," ","integrate((g*x)^m*(e*x+d)^2*(c*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{2} x^{2} + 2 \, d e x + d^{2}\right)} {\left(c x^{2} + a\right)}^{p} \left(g x\right)^{m}, x\right)"," ",0,"integral((e^2*x^2 + 2*d*e*x + d^2)*(c*x^2 + a)^p*(g*x)^m, x)","F",0
432,0,0,0,0.409405," ","integrate((g*x)^m*(e*x+d)*(c*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e x + d\right)} {\left(c x^{2} + a\right)}^{p} \left(g x\right)^{m}, x\right)"," ",0,"integral((e*x + d)*(c*x^2 + a)^p*(g*x)^m, x)","F",0
433,0,0,0,0.418396," ","integrate((g*x)^m*(c*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{2} + a\right)}^{p} \left(g x\right)^{m}, x\right)"," ",0,"integral((c*x^2 + a)^p*(g*x)^m, x)","F",0
434,0,0,0,0.430911," ","integrate((g*x)^m*(c*x^2+a)^p/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2} + a\right)}^{p} \left(g x\right)^{m}}{e x + d}, x\right)"," ",0,"integral((c*x^2 + a)^p*(g*x)^m/(e*x + d), x)","F",0
435,0,0,0,0.436807," ","integrate((g*x)^m*(c*x^2+a)^p/(e*x+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2} + a\right)}^{p} \left(g x\right)^{m}}{e^{2} x^{2} + 2 \, d e x + d^{2}}, x\right)"," ",0,"integral((c*x^2 + a)^p*(g*x)^m/(e^2*x^2 + 2*d*e*x + d^2), x)","F",0
436,0,0,0,0.488768," ","integrate((g*x)^m*(c*x^2+a)^p/(e*x+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2} + a\right)}^{p} \left(g x\right)^{m}}{e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}}, x\right)"," ",0,"integral((c*x^2 + a)^p*(g*x)^m/(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3), x)","F",0
437,1,678,0,0.574041," ","integrate(x^3*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)/(e*x+d),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(35 \, c^{4} d^{8} - 20 \, a c^{3} d^{6} e^{2} - 6 \, a^{2} c^{2} d^{4} e^{4} - 4 \, a^{3} c d^{2} e^{6} - 5 \, a^{4} e^{8}\right)} \sqrt{c d e} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) - 4 \, {\left(48 \, c^{4} d^{4} e^{4} x^{3} - 105 \, c^{4} d^{7} e + 25 \, a c^{3} d^{5} e^{3} + 17 \, a^{2} c^{2} d^{3} e^{5} + 15 \, a^{3} c d e^{7} - 8 \, {\left(7 \, c^{4} d^{5} e^{3} - a c^{3} d^{3} e^{5}\right)} x^{2} + 2 \, {\left(35 \, c^{4} d^{6} e^{2} - 6 \, a c^{3} d^{4} e^{4} - 5 \, a^{2} c^{2} d^{2} e^{6}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{768 \, c^{4} d^{4} e^{5}}, -\frac{3 \, {\left(35 \, c^{4} d^{8} - 20 \, a c^{3} d^{6} e^{2} - 6 \, a^{2} c^{2} d^{4} e^{4} - 4 \, a^{3} c d^{2} e^{6} - 5 \, a^{4} e^{8}\right)} \sqrt{-c d e} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right) - 2 \, {\left(48 \, c^{4} d^{4} e^{4} x^{3} - 105 \, c^{4} d^{7} e + 25 \, a c^{3} d^{5} e^{3} + 17 \, a^{2} c^{2} d^{3} e^{5} + 15 \, a^{3} c d e^{7} - 8 \, {\left(7 \, c^{4} d^{5} e^{3} - a c^{3} d^{3} e^{5}\right)} x^{2} + 2 \, {\left(35 \, c^{4} d^{6} e^{2} - 6 \, a c^{3} d^{4} e^{4} - 5 \, a^{2} c^{2} d^{2} e^{6}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{384 \, c^{4} d^{4} e^{5}}\right]"," ",0,"[-1/768*(3*(35*c^4*d^8 - 20*a*c^3*d^6*e^2 - 6*a^2*c^2*d^4*e^4 - 4*a^3*c*d^2*e^6 - 5*a^4*e^8)*sqrt(c*d*e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) - 4*(48*c^4*d^4*e^4*x^3 - 105*c^4*d^7*e + 25*a*c^3*d^5*e^3 + 17*a^2*c^2*d^3*e^5 + 15*a^3*c*d*e^7 - 8*(7*c^4*d^5*e^3 - a*c^3*d^3*e^5)*x^2 + 2*(35*c^4*d^6*e^2 - 6*a*c^3*d^4*e^4 - 5*a^2*c^2*d^2*e^6)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^4*d^4*e^5), -1/384*(3*(35*c^4*d^8 - 20*a*c^3*d^6*e^2 - 6*a^2*c^2*d^4*e^4 - 4*a^3*c*d^2*e^6 - 5*a^4*e^8)*sqrt(-c*d*e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)) - 2*(48*c^4*d^4*e^4*x^3 - 105*c^4*d^7*e + 25*a*c^3*d^5*e^3 + 17*a^2*c^2*d^3*e^5 + 15*a^3*c*d*e^7 - 8*(7*c^4*d^5*e^3 - a*c^3*d^3*e^5)*x^2 + 2*(35*c^4*d^6*e^2 - 6*a*c^3*d^4*e^4 - 5*a^2*c^2*d^2*e^6)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^4*d^4*e^5)]","A",0
438,1,536,0,0.472061," ","integrate(x^2*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)/(e*x+d),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, c^{3} d^{6} - 3 \, a c^{2} d^{4} e^{2} - a^{2} c d^{2} e^{4} - a^{3} e^{6}\right)} \sqrt{c d e} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) - 4 \, {\left(8 \, c^{3} d^{3} e^{3} x^{2} + 15 \, c^{3} d^{5} e - 4 \, a c^{2} d^{3} e^{3} - 3 \, a^{2} c d e^{5} - 2 \, {\left(5 \, c^{3} d^{4} e^{2} - a c^{2} d^{2} e^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{96 \, c^{3} d^{3} e^{4}}, \frac{3 \, {\left(5 \, c^{3} d^{6} - 3 \, a c^{2} d^{4} e^{2} - a^{2} c d^{2} e^{4} - a^{3} e^{6}\right)} \sqrt{-c d e} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right) + 2 \, {\left(8 \, c^{3} d^{3} e^{3} x^{2} + 15 \, c^{3} d^{5} e - 4 \, a c^{2} d^{3} e^{3} - 3 \, a^{2} c d e^{5} - 2 \, {\left(5 \, c^{3} d^{4} e^{2} - a c^{2} d^{2} e^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{48 \, c^{3} d^{3} e^{4}}\right]"," ",0,"[-1/96*(3*(5*c^3*d^6 - 3*a*c^2*d^4*e^2 - a^2*c*d^2*e^4 - a^3*e^6)*sqrt(c*d*e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) - 4*(8*c^3*d^3*e^3*x^2 + 15*c^3*d^5*e - 4*a*c^2*d^3*e^3 - 3*a^2*c*d*e^5 - 2*(5*c^3*d^4*e^2 - a*c^2*d^2*e^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^3*d^3*e^4), 1/48*(3*(5*c^3*d^6 - 3*a*c^2*d^4*e^2 - a^2*c*d^2*e^4 - a^3*e^6)*sqrt(-c*d*e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)) + 2*(8*c^3*d^3*e^3*x^2 + 15*c^3*d^5*e - 4*a*c^2*d^3*e^3 - 3*a^2*c*d*e^5 - 2*(5*c^3*d^4*e^2 - a*c^2*d^2*e^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^3*d^3*e^4)]","A",0
439,1,418,0,0.433610," ","integrate(x*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)/(e*x+d),x, algorithm=""fricas"")","\left[-\frac{{\left(3 \, c^{2} d^{4} - 2 \, a c d^{2} e^{2} - a^{2} e^{4}\right)} \sqrt{c d e} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) - 4 \, {\left(2 \, c^{2} d^{2} e^{2} x - 3 \, c^{2} d^{3} e + a c d e^{3}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{16 \, c^{2} d^{2} e^{3}}, -\frac{{\left(3 \, c^{2} d^{4} - 2 \, a c d^{2} e^{2} - a^{2} e^{4}\right)} \sqrt{-c d e} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right) - 2 \, {\left(2 \, c^{2} d^{2} e^{2} x - 3 \, c^{2} d^{3} e + a c d e^{3}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{8 \, c^{2} d^{2} e^{3}}\right]"," ",0,"[-1/16*((3*c^2*d^4 - 2*a*c*d^2*e^2 - a^2*e^4)*sqrt(c*d*e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) - 4*(2*c^2*d^2*e^2*x - 3*c^2*d^3*e + a*c*d*e^3)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^2*d^2*e^3), -1/8*((3*c^2*d^4 - 2*a*c*d^2*e^2 - a^2*e^4)*sqrt(-c*d*e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)) - 2*(2*c^2*d^2*e^2*x - 3*c^2*d^3*e + a*c*d*e^3)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^2*d^2*e^3)]","A",0
440,1,337,0,0.435642," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)/(e*x+d),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} c d e - {\left(c d^{2} - a e^{2}\right)} \sqrt{c d e} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}{4 \, c d e^{2}}, \frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} c d e + {\left(c d^{2} - a e^{2}\right)} \sqrt{-c d e} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right)}{2 \, c d e^{2}}\right]"," ",0,"[1/4*(4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*c*d*e - (c*d^2 - a*e^2)*sqrt(c*d*e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x))/(c*d*e^2), 1/2*(2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*c*d*e + (c*d^2 - a*e^2)*sqrt(-c*d*e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)))/(c*d*e^2)]","A",0
441,1,947,0,0.655334," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)/x/(e*x+d),x, algorithm=""fricas"")","\left[\frac{1}{2} \, \sqrt{\frac{c d}{e}} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} + 4 \, {\left(2 \, c d e^{2} x + c d^{2} e + a e^{3}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{\frac{c d}{e}} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) + \frac{1}{2} \, \sqrt{\frac{a e}{d}} \log\left(\frac{8 \, a^{2} d^{2} e^{2} + {\left(c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} x^{2} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d^{2} e + {\left(c d^{3} + a d e^{2}\right)} x\right)} \sqrt{\frac{a e}{d}} + 8 \, {\left(a c d^{3} e + a^{2} d e^{3}\right)} x}{x^{2}}\right), -\sqrt{-\frac{c d}{e}} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-\frac{c d}{e}}}{2 \, {\left(c^{2} d^{2} e x^{2} + a c d^{2} e + {\left(c^{2} d^{3} + a c d e^{2}\right)} x\right)}}\right) + \frac{1}{2} \, \sqrt{\frac{a e}{d}} \log\left(\frac{8 \, a^{2} d^{2} e^{2} + {\left(c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} x^{2} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d^{2} e + {\left(c d^{3} + a d e^{2}\right)} x\right)} \sqrt{\frac{a e}{d}} + 8 \, {\left(a c d^{3} e + a^{2} d e^{3}\right)} x}{x^{2}}\right), \sqrt{-\frac{a e}{d}} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{-\frac{a e}{d}}}{2 \, {\left(a c d e^{2} x^{2} + a^{2} d e^{2} + {\left(a c d^{2} e + a^{2} e^{3}\right)} x\right)}}\right) + \frac{1}{2} \, \sqrt{\frac{c d}{e}} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} + 4 \, {\left(2 \, c d e^{2} x + c d^{2} e + a e^{3}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{\frac{c d}{e}} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right), -\sqrt{-\frac{c d}{e}} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-\frac{c d}{e}}}{2 \, {\left(c^{2} d^{2} e x^{2} + a c d^{2} e + {\left(c^{2} d^{3} + a c d e^{2}\right)} x\right)}}\right) + \sqrt{-\frac{a e}{d}} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{-\frac{a e}{d}}}{2 \, {\left(a c d e^{2} x^{2} + a^{2} d e^{2} + {\left(a c d^{2} e + a^{2} e^{3}\right)} x\right)}}\right)\right]"," ",0,"[1/2*sqrt(c*d/e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 + 4*(2*c*d*e^2*x + c*d^2*e + a*e^3)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(c*d/e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) + 1/2*sqrt(a*e/d)*log((8*a^2*d^2*e^2 + (c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4)*x^2 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d^2*e + (c*d^3 + a*d*e^2)*x)*sqrt(a*e/d) + 8*(a*c*d^3*e + a^2*d*e^3)*x)/x^2), -sqrt(-c*d/e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d/e)/(c^2*d^2*e*x^2 + a*c*d^2*e + (c^2*d^3 + a*c*d*e^2)*x)) + 1/2*sqrt(a*e/d)*log((8*a^2*d^2*e^2 + (c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4)*x^2 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d^2*e + (c*d^3 + a*d*e^2)*x)*sqrt(a*e/d) + 8*(a*c*d^3*e + a^2*d*e^3)*x)/x^2), sqrt(-a*e/d)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-a*e/d)/(a*c*d*e^2*x^2 + a^2*d*e^2 + (a*c*d^2*e + a^2*e^3)*x)) + 1/2*sqrt(c*d/e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 + 4*(2*c*d*e^2*x + c*d^2*e + a*e^3)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(c*d/e) + 8*(c^2*d^3*e + a*c*d*e^3)*x), -sqrt(-c*d/e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d/e)/(c^2*d^2*e*x^2 + a*c*d^2*e + (c^2*d^3 + a*c*d*e^2)*x)) + sqrt(-a*e/d)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-a*e/d)/(a*c*d*e^2*x^2 + a^2*d*e^2 + (a*c*d^2*e + a^2*e^3)*x))]","A",0
442,1,355,0,0.519126," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)/x^2/(e*x+d),x, algorithm=""fricas"")","\left[-\frac{4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} a d e + {\left(c d^{2} - a e^{2}\right)} \sqrt{a d e} x \log\left(\frac{8 \, a^{2} d^{2} e^{2} + {\left(c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} x^{2} + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{a d e} + 8 \, {\left(a c d^{3} e + a^{2} d e^{3}\right)} x}{x^{2}}\right)}{4 \, a d^{2} e x}, -\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} a d e - {\left(c d^{2} - a e^{2}\right)} \sqrt{-a d e} x \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{-a d e}}{2 \, {\left(a c d^{2} e^{2} x^{2} + a^{2} d^{2} e^{2} + {\left(a c d^{3} e + a^{2} d e^{3}\right)} x\right)}}\right)}{2 \, a d^{2} e x}\right]"," ",0,"[-1/4*(4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*a*d*e + (c*d^2 - a*e^2)*sqrt(a*d*e)*x*log((8*a^2*d^2*e^2 + (c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4)*x^2 + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(a*d*e) + 8*(a*c*d^3*e + a^2*d*e^3)*x)/x^2))/(a*d^2*e*x), -1/2*(2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*a*d*e - (c*d^2 - a*e^2)*sqrt(-a*d*e)*x*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-a*d*e)/(a*c*d^2*e^2*x^2 + a^2*d^2*e^2 + (a*c*d^3*e + a^2*d*e^3)*x)))/(a*d^2*e*x)]","A",0
443,1,442,0,0.914426," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)/x^3/(e*x+d),x, algorithm=""fricas"")","\left[-\frac{{\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} - 3 \, a^{2} e^{4}\right)} \sqrt{a d e} x^{2} \log\left(\frac{8 \, a^{2} d^{2} e^{2} + {\left(c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} x^{2} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{a d e} + 8 \, {\left(a c d^{3} e + a^{2} d e^{3}\right)} x}{x^{2}}\right) + 4 \, {\left(2 \, a^{2} d^{2} e^{2} + {\left(a c d^{3} e - 3 \, a^{2} d e^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{16 \, a^{2} d^{3} e^{2} x^{2}}, -\frac{{\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} - 3 \, a^{2} e^{4}\right)} \sqrt{-a d e} x^{2} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{-a d e}}{2 \, {\left(a c d^{2} e^{2} x^{2} + a^{2} d^{2} e^{2} + {\left(a c d^{3} e + a^{2} d e^{3}\right)} x\right)}}\right) + 2 \, {\left(2 \, a^{2} d^{2} e^{2} + {\left(a c d^{3} e - 3 \, a^{2} d e^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{8 \, a^{2} d^{3} e^{2} x^{2}}\right]"," ",0,"[-1/16*((c^2*d^4 + 2*a*c*d^2*e^2 - 3*a^2*e^4)*sqrt(a*d*e)*x^2*log((8*a^2*d^2*e^2 + (c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4)*x^2 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(a*d*e) + 8*(a*c*d^3*e + a^2*d*e^3)*x)/x^2) + 4*(2*a^2*d^2*e^2 + (a*c*d^3*e - 3*a^2*d*e^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(a^2*d^3*e^2*x^2), -1/8*((c^2*d^4 + 2*a*c*d^2*e^2 - 3*a^2*e^4)*sqrt(-a*d*e)*x^2*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-a*d*e)/(a*c*d^2*e^2*x^2 + a^2*d^2*e^2 + (a*c*d^3*e + a^2*d*e^3)*x)) + 2*(2*a^2*d^2*e^2 + (a*c*d^3*e - 3*a^2*d*e^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(a^2*d^3*e^2*x^2)]","A",0
444,1,558,0,2.116346," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)/x^4/(e*x+d),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(c^{3} d^{6} + a c^{2} d^{4} e^{2} + 3 \, a^{2} c d^{2} e^{4} - 5 \, a^{3} e^{6}\right)} \sqrt{a d e} x^{3} \log\left(\frac{8 \, a^{2} d^{2} e^{2} + {\left(c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} x^{2} + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{a d e} + 8 \, {\left(a c d^{3} e + a^{2} d e^{3}\right)} x}{x^{2}}\right) + 4 \, {\left(8 \, a^{3} d^{3} e^{3} - {\left(3 \, a c^{2} d^{5} e + 4 \, a^{2} c d^{3} e^{3} - 15 \, a^{3} d e^{5}\right)} x^{2} + 2 \, {\left(a^{2} c d^{4} e^{2} - 5 \, a^{3} d^{2} e^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{96 \, a^{3} d^{4} e^{3} x^{3}}, \frac{3 \, {\left(c^{3} d^{6} + a c^{2} d^{4} e^{2} + 3 \, a^{2} c d^{2} e^{4} - 5 \, a^{3} e^{6}\right)} \sqrt{-a d e} x^{3} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{-a d e}}{2 \, {\left(a c d^{2} e^{2} x^{2} + a^{2} d^{2} e^{2} + {\left(a c d^{3} e + a^{2} d e^{3}\right)} x\right)}}\right) - 2 \, {\left(8 \, a^{3} d^{3} e^{3} - {\left(3 \, a c^{2} d^{5} e + 4 \, a^{2} c d^{3} e^{3} - 15 \, a^{3} d e^{5}\right)} x^{2} + 2 \, {\left(a^{2} c d^{4} e^{2} - 5 \, a^{3} d^{2} e^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{48 \, a^{3} d^{4} e^{3} x^{3}}\right]"," ",0,"[-1/96*(3*(c^3*d^6 + a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 - 5*a^3*e^6)*sqrt(a*d*e)*x^3*log((8*a^2*d^2*e^2 + (c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4)*x^2 + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(a*d*e) + 8*(a*c*d^3*e + a^2*d*e^3)*x)/x^2) + 4*(8*a^3*d^3*e^3 - (3*a*c^2*d^5*e + 4*a^2*c*d^3*e^3 - 15*a^3*d*e^5)*x^2 + 2*(a^2*c*d^4*e^2 - 5*a^3*d^2*e^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(a^3*d^4*e^3*x^3), 1/48*(3*(c^3*d^6 + a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 - 5*a^3*e^6)*sqrt(-a*d*e)*x^3*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-a*d*e)/(a*c*d^2*e^2*x^2 + a^2*d^2*e^2 + (a*c*d^3*e + a^2*d*e^3)*x)) - 2*(8*a^3*d^3*e^3 - (3*a*c^2*d^5*e + 4*a^2*c*d^3*e^3 - 15*a^3*d*e^5)*x^2 + 2*(a^2*c*d^4*e^2 - 5*a^3*d^2*e^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(a^3*d^4*e^3*x^3)]","A",0
445,1,702,0,9.698631," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)/x^5/(e*x+d),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, c^{4} d^{8} + 4 \, a c^{3} d^{6} e^{2} + 6 \, a^{2} c^{2} d^{4} e^{4} + 20 \, a^{3} c d^{2} e^{6} - 35 \, a^{4} e^{8}\right)} \sqrt{a d e} x^{4} \log\left(\frac{8 \, a^{2} d^{2} e^{2} + {\left(c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} x^{2} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{a d e} + 8 \, {\left(a c d^{3} e + a^{2} d e^{3}\right)} x}{x^{2}}\right) + 4 \, {\left(48 \, a^{4} d^{4} e^{4} + {\left(15 \, a c^{3} d^{7} e + 17 \, a^{2} c^{2} d^{5} e^{3} + 25 \, a^{3} c d^{3} e^{5} - 105 \, a^{4} d e^{7}\right)} x^{3} - 2 \, {\left(5 \, a^{2} c^{2} d^{6} e^{2} + 6 \, a^{3} c d^{4} e^{4} - 35 \, a^{4} d^{2} e^{6}\right)} x^{2} + 8 \, {\left(a^{3} c d^{5} e^{3} - 7 \, a^{4} d^{3} e^{5}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{768 \, a^{4} d^{5} e^{4} x^{4}}, -\frac{3 \, {\left(5 \, c^{4} d^{8} + 4 \, a c^{3} d^{6} e^{2} + 6 \, a^{2} c^{2} d^{4} e^{4} + 20 \, a^{3} c d^{2} e^{6} - 35 \, a^{4} e^{8}\right)} \sqrt{-a d e} x^{4} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{-a d e}}{2 \, {\left(a c d^{2} e^{2} x^{2} + a^{2} d^{2} e^{2} + {\left(a c d^{3} e + a^{2} d e^{3}\right)} x\right)}}\right) + 2 \, {\left(48 \, a^{4} d^{4} e^{4} + {\left(15 \, a c^{3} d^{7} e + 17 \, a^{2} c^{2} d^{5} e^{3} + 25 \, a^{3} c d^{3} e^{5} - 105 \, a^{4} d e^{7}\right)} x^{3} - 2 \, {\left(5 \, a^{2} c^{2} d^{6} e^{2} + 6 \, a^{3} c d^{4} e^{4} - 35 \, a^{4} d^{2} e^{6}\right)} x^{2} + 8 \, {\left(a^{3} c d^{5} e^{3} - 7 \, a^{4} d^{3} e^{5}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{384 \, a^{4} d^{5} e^{4} x^{4}}\right]"," ",0,"[-1/768*(3*(5*c^4*d^8 + 4*a*c^3*d^6*e^2 + 6*a^2*c^2*d^4*e^4 + 20*a^3*c*d^2*e^6 - 35*a^4*e^8)*sqrt(a*d*e)*x^4*log((8*a^2*d^2*e^2 + (c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4)*x^2 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(a*d*e) + 8*(a*c*d^3*e + a^2*d*e^3)*x)/x^2) + 4*(48*a^4*d^4*e^4 + (15*a*c^3*d^7*e + 17*a^2*c^2*d^5*e^3 + 25*a^3*c*d^3*e^5 - 105*a^4*d*e^7)*x^3 - 2*(5*a^2*c^2*d^6*e^2 + 6*a^3*c*d^4*e^4 - 35*a^4*d^2*e^6)*x^2 + 8*(a^3*c*d^5*e^3 - 7*a^4*d^3*e^5)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(a^4*d^5*e^4*x^4), -1/384*(3*(5*c^4*d^8 + 4*a*c^3*d^6*e^2 + 6*a^2*c^2*d^4*e^4 + 20*a^3*c*d^2*e^6 - 35*a^4*e^8)*sqrt(-a*d*e)*x^4*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-a*d*e)/(a*c*d^2*e^2*x^2 + a^2*d^2*e^2 + (a*c*d^3*e + a^2*d*e^3)*x)) + 2*(48*a^4*d^4*e^4 + (15*a*c^3*d^7*e + 17*a^2*c^2*d^5*e^3 + 25*a^3*c*d^3*e^5 - 105*a^4*d*e^7)*x^3 - 2*(5*a^2*c^2*d^6*e^2 + 6*a^3*c*d^4*e^4 - 35*a^4*d^2*e^6)*x^2 + 8*(a^3*c*d^5*e^3 - 7*a^4*d^3*e^5)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(a^4*d^5*e^4*x^4)]","A",0
446,1,1044,0,0.508076," ","integrate(x^3*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/(e*x+d),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(21 \, c^{6} d^{12} - 42 \, a c^{5} d^{10} e^{2} + 15 \, a^{2} c^{4} d^{8} e^{4} + 4 \, a^{3} c^{3} d^{6} e^{6} + 3 \, a^{4} c^{2} d^{4} e^{8} + 6 \, a^{5} c d^{2} e^{10} - 7 \, a^{6} e^{12}\right)} \sqrt{c d e} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) - 4 \, {\left(1280 \, c^{6} d^{6} e^{6} x^{5} + 315 \, c^{6} d^{11} e - 525 \, a c^{5} d^{9} e^{3} + 78 \, a^{2} c^{4} d^{7} e^{5} + 54 \, a^{3} c^{3} d^{5} e^{7} + 55 \, a^{4} c^{2} d^{3} e^{9} - 105 \, a^{5} c d e^{11} + 128 \, {\left(c^{6} d^{7} e^{5} + 13 \, a c^{5} d^{5} e^{7}\right)} x^{4} - 16 \, {\left(9 \, c^{6} d^{8} e^{4} - 14 \, a c^{5} d^{6} e^{6} - 3 \, a^{2} c^{4} d^{4} e^{8}\right)} x^{3} + 8 \, {\left(21 \, c^{6} d^{9} e^{3} - 33 \, a c^{5} d^{7} e^{5} + 3 \, a^{2} c^{4} d^{5} e^{7} - 7 \, a^{3} c^{3} d^{3} e^{9}\right)} x^{2} - 2 \, {\left(105 \, c^{6} d^{10} e^{2} - 168 \, a c^{5} d^{8} e^{4} + 18 \, a^{2} c^{4} d^{6} e^{6} + 16 \, a^{3} c^{3} d^{4} e^{8} - 35 \, a^{4} c^{2} d^{2} e^{10}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{30720 \, c^{5} d^{5} e^{6}}, \frac{15 \, {\left(21 \, c^{6} d^{12} - 42 \, a c^{5} d^{10} e^{2} + 15 \, a^{2} c^{4} d^{8} e^{4} + 4 \, a^{3} c^{3} d^{6} e^{6} + 3 \, a^{4} c^{2} d^{4} e^{8} + 6 \, a^{5} c d^{2} e^{10} - 7 \, a^{6} e^{12}\right)} \sqrt{-c d e} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right) + 2 \, {\left(1280 \, c^{6} d^{6} e^{6} x^{5} + 315 \, c^{6} d^{11} e - 525 \, a c^{5} d^{9} e^{3} + 78 \, a^{2} c^{4} d^{7} e^{5} + 54 \, a^{3} c^{3} d^{5} e^{7} + 55 \, a^{4} c^{2} d^{3} e^{9} - 105 \, a^{5} c d e^{11} + 128 \, {\left(c^{6} d^{7} e^{5} + 13 \, a c^{5} d^{5} e^{7}\right)} x^{4} - 16 \, {\left(9 \, c^{6} d^{8} e^{4} - 14 \, a c^{5} d^{6} e^{6} - 3 \, a^{2} c^{4} d^{4} e^{8}\right)} x^{3} + 8 \, {\left(21 \, c^{6} d^{9} e^{3} - 33 \, a c^{5} d^{7} e^{5} + 3 \, a^{2} c^{4} d^{5} e^{7} - 7 \, a^{3} c^{3} d^{3} e^{9}\right)} x^{2} - 2 \, {\left(105 \, c^{6} d^{10} e^{2} - 168 \, a c^{5} d^{8} e^{4} + 18 \, a^{2} c^{4} d^{6} e^{6} + 16 \, a^{3} c^{3} d^{4} e^{8} - 35 \, a^{4} c^{2} d^{2} e^{10}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{15360 \, c^{5} d^{5} e^{6}}\right]"," ",0,"[-1/30720*(15*(21*c^6*d^12 - 42*a*c^5*d^10*e^2 + 15*a^2*c^4*d^8*e^4 + 4*a^3*c^3*d^6*e^6 + 3*a^4*c^2*d^4*e^8 + 6*a^5*c*d^2*e^10 - 7*a^6*e^12)*sqrt(c*d*e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) - 4*(1280*c^6*d^6*e^6*x^5 + 315*c^6*d^11*e - 525*a*c^5*d^9*e^3 + 78*a^2*c^4*d^7*e^5 + 54*a^3*c^3*d^5*e^7 + 55*a^4*c^2*d^3*e^9 - 105*a^5*c*d*e^11 + 128*(c^6*d^7*e^5 + 13*a*c^5*d^5*e^7)*x^4 - 16*(9*c^6*d^8*e^4 - 14*a*c^5*d^6*e^6 - 3*a^2*c^4*d^4*e^8)*x^3 + 8*(21*c^6*d^9*e^3 - 33*a*c^5*d^7*e^5 + 3*a^2*c^4*d^5*e^7 - 7*a^3*c^3*d^3*e^9)*x^2 - 2*(105*c^6*d^10*e^2 - 168*a*c^5*d^8*e^4 + 18*a^2*c^4*d^6*e^6 + 16*a^3*c^3*d^4*e^8 - 35*a^4*c^2*d^2*e^10)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^5*d^5*e^6), 1/15360*(15*(21*c^6*d^12 - 42*a*c^5*d^10*e^2 + 15*a^2*c^4*d^8*e^4 + 4*a^3*c^3*d^6*e^6 + 3*a^4*c^2*d^4*e^8 + 6*a^5*c*d^2*e^10 - 7*a^6*e^12)*sqrt(-c*d*e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)) + 2*(1280*c^6*d^6*e^6*x^5 + 315*c^6*d^11*e - 525*a*c^5*d^9*e^3 + 78*a^2*c^4*d^7*e^5 + 54*a^3*c^3*d^5*e^7 + 55*a^4*c^2*d^3*e^9 - 105*a^5*c*d*e^11 + 128*(c^6*d^7*e^5 + 13*a*c^5*d^5*e^7)*x^4 - 16*(9*c^6*d^8*e^4 - 14*a*c^5*d^6*e^6 - 3*a^2*c^4*d^4*e^8)*x^3 + 8*(21*c^6*d^9*e^3 - 33*a*c^5*d^7*e^5 + 3*a^2*c^4*d^5*e^7 - 7*a^3*c^3*d^3*e^9)*x^2 - 2*(105*c^6*d^10*e^2 - 168*a*c^5*d^8*e^4 + 18*a^2*c^4*d^6*e^6 + 16*a^3*c^3*d^4*e^8 - 35*a^4*c^2*d^2*e^10)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^5*d^5*e^6)]","A",0
447,1,846,0,0.459047," ","integrate(x^2*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/(e*x+d),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(7 \, c^{5} d^{10} - 15 \, a c^{4} d^{8} e^{2} + 6 \, a^{2} c^{3} d^{6} e^{4} + 2 \, a^{3} c^{2} d^{4} e^{6} + 3 \, a^{4} c d^{2} e^{8} - 3 \, a^{5} e^{10}\right)} \sqrt{c d e} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) - 4 \, {\left(384 \, c^{5} d^{5} e^{5} x^{4} - 105 \, c^{5} d^{9} e + 190 \, a c^{4} d^{7} e^{3} - 36 \, a^{2} c^{3} d^{5} e^{5} - 30 \, a^{3} c^{2} d^{3} e^{7} + 45 \, a^{4} c d e^{9} + 48 \, {\left(c^{5} d^{6} e^{4} + 11 \, a c^{4} d^{4} e^{6}\right)} x^{3} - 8 \, {\left(7 \, c^{5} d^{7} e^{3} - 12 \, a c^{4} d^{5} e^{5} - 3 \, a^{2} c^{3} d^{3} e^{7}\right)} x^{2} + 2 \, {\left(35 \, c^{5} d^{8} e^{2} - 61 \, a c^{4} d^{6} e^{4} + 9 \, a^{2} c^{3} d^{4} e^{6} - 15 \, a^{3} c^{2} d^{2} e^{8}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{7680 \, c^{4} d^{4} e^{5}}, -\frac{15 \, {\left(7 \, c^{5} d^{10} - 15 \, a c^{4} d^{8} e^{2} + 6 \, a^{2} c^{3} d^{6} e^{4} + 2 \, a^{3} c^{2} d^{4} e^{6} + 3 \, a^{4} c d^{2} e^{8} - 3 \, a^{5} e^{10}\right)} \sqrt{-c d e} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right) - 2 \, {\left(384 \, c^{5} d^{5} e^{5} x^{4} - 105 \, c^{5} d^{9} e + 190 \, a c^{4} d^{7} e^{3} - 36 \, a^{2} c^{3} d^{5} e^{5} - 30 \, a^{3} c^{2} d^{3} e^{7} + 45 \, a^{4} c d e^{9} + 48 \, {\left(c^{5} d^{6} e^{4} + 11 \, a c^{4} d^{4} e^{6}\right)} x^{3} - 8 \, {\left(7 \, c^{5} d^{7} e^{3} - 12 \, a c^{4} d^{5} e^{5} - 3 \, a^{2} c^{3} d^{3} e^{7}\right)} x^{2} + 2 \, {\left(35 \, c^{5} d^{8} e^{2} - 61 \, a c^{4} d^{6} e^{4} + 9 \, a^{2} c^{3} d^{4} e^{6} - 15 \, a^{3} c^{2} d^{2} e^{8}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{3840 \, c^{4} d^{4} e^{5}}\right]"," ",0,"[-1/7680*(15*(7*c^5*d^10 - 15*a*c^4*d^8*e^2 + 6*a^2*c^3*d^6*e^4 + 2*a^3*c^2*d^4*e^6 + 3*a^4*c*d^2*e^8 - 3*a^5*e^10)*sqrt(c*d*e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) - 4*(384*c^5*d^5*e^5*x^4 - 105*c^5*d^9*e + 190*a*c^4*d^7*e^3 - 36*a^2*c^3*d^5*e^5 - 30*a^3*c^2*d^3*e^7 + 45*a^4*c*d*e^9 + 48*(c^5*d^6*e^4 + 11*a*c^4*d^4*e^6)*x^3 - 8*(7*c^5*d^7*e^3 - 12*a*c^4*d^5*e^5 - 3*a^2*c^3*d^3*e^7)*x^2 + 2*(35*c^5*d^8*e^2 - 61*a*c^4*d^6*e^4 + 9*a^2*c^3*d^4*e^6 - 15*a^3*c^2*d^2*e^8)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^4*d^4*e^5), -1/3840*(15*(7*c^5*d^10 - 15*a*c^4*d^8*e^2 + 6*a^2*c^3*d^6*e^4 + 2*a^3*c^2*d^4*e^6 + 3*a^4*c*d^2*e^8 - 3*a^5*e^10)*sqrt(-c*d*e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)) - 2*(384*c^5*d^5*e^5*x^4 - 105*c^5*d^9*e + 190*a*c^4*d^7*e^3 - 36*a^2*c^3*d^5*e^5 - 30*a^3*c^2*d^3*e^7 + 45*a^4*c*d*e^9 + 48*(c^5*d^6*e^4 + 11*a*c^4*d^4*e^6)*x^3 - 8*(7*c^5*d^7*e^3 - 12*a*c^4*d^5*e^5 - 3*a^2*c^3*d^3*e^7)*x^2 + 2*(35*c^5*d^8*e^2 - 61*a*c^4*d^6*e^4 + 9*a^2*c^3*d^4*e^6 - 15*a^3*c^2*d^2*e^8)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^4*d^4*e^5)]","A",0
448,1,676,0,0.459018," ","integrate(x*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/(e*x+d),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, c^{4} d^{8} - 12 \, a c^{3} d^{6} e^{2} + 6 \, a^{2} c^{2} d^{4} e^{4} + 4 \, a^{3} c d^{2} e^{6} - 3 \, a^{4} e^{8}\right)} \sqrt{c d e} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) - 4 \, {\left(48 \, c^{4} d^{4} e^{4} x^{3} + 15 \, c^{4} d^{7} e - 31 \, a c^{3} d^{5} e^{3} + 9 \, a^{2} c^{2} d^{3} e^{5} - 9 \, a^{3} c d e^{7} + 8 \, {\left(c^{4} d^{5} e^{3} + 9 \, a c^{3} d^{3} e^{5}\right)} x^{2} - 2 \, {\left(5 \, c^{4} d^{6} e^{2} - 10 \, a c^{3} d^{4} e^{4} - 3 \, a^{2} c^{2} d^{2} e^{6}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{768 \, c^{3} d^{3} e^{4}}, \frac{3 \, {\left(5 \, c^{4} d^{8} - 12 \, a c^{3} d^{6} e^{2} + 6 \, a^{2} c^{2} d^{4} e^{4} + 4 \, a^{3} c d^{2} e^{6} - 3 \, a^{4} e^{8}\right)} \sqrt{-c d e} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right) + 2 \, {\left(48 \, c^{4} d^{4} e^{4} x^{3} + 15 \, c^{4} d^{7} e - 31 \, a c^{3} d^{5} e^{3} + 9 \, a^{2} c^{2} d^{3} e^{5} - 9 \, a^{3} c d e^{7} + 8 \, {\left(c^{4} d^{5} e^{3} + 9 \, a c^{3} d^{3} e^{5}\right)} x^{2} - 2 \, {\left(5 \, c^{4} d^{6} e^{2} - 10 \, a c^{3} d^{4} e^{4} - 3 \, a^{2} c^{2} d^{2} e^{6}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{384 \, c^{3} d^{3} e^{4}}\right]"," ",0,"[-1/768*(3*(5*c^4*d^8 - 12*a*c^3*d^6*e^2 + 6*a^2*c^2*d^4*e^4 + 4*a^3*c*d^2*e^6 - 3*a^4*e^8)*sqrt(c*d*e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) - 4*(48*c^4*d^4*e^4*x^3 + 15*c^4*d^7*e - 31*a*c^3*d^5*e^3 + 9*a^2*c^2*d^3*e^5 - 9*a^3*c*d*e^7 + 8*(c^4*d^5*e^3 + 9*a*c^3*d^3*e^5)*x^2 - 2*(5*c^4*d^6*e^2 - 10*a*c^3*d^4*e^4 - 3*a^2*c^2*d^2*e^6)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^3*d^3*e^4), 1/384*(3*(5*c^4*d^8 - 12*a*c^3*d^6*e^2 + 6*a^2*c^2*d^4*e^4 + 4*a^3*c*d^2*e^6 - 3*a^4*e^8)*sqrt(-c*d*e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)) + 2*(48*c^4*d^4*e^4*x^3 + 15*c^4*d^7*e - 31*a*c^3*d^5*e^3 + 9*a^2*c^2*d^3*e^5 - 9*a^3*c*d*e^7 + 8*(c^4*d^5*e^3 + 9*a*c^3*d^3*e^5)*x^2 - 2*(5*c^4*d^6*e^2 - 10*a*c^3*d^4*e^4 - 3*a^2*c^2*d^2*e^6)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^3*d^3*e^4)]","A",0
449,1,532,0,0.428185," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/(e*x+d),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(c^{3} d^{6} - 3 \, a c^{2} d^{4} e^{2} + 3 \, a^{2} c d^{2} e^{4} - a^{3} e^{6}\right)} \sqrt{c d e} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) - 4 \, {\left(8 \, c^{3} d^{3} e^{3} x^{2} - 3 \, c^{3} d^{5} e + 8 \, a c^{2} d^{3} e^{3} + 3 \, a^{2} c d e^{5} + 2 \, {\left(c^{3} d^{4} e^{2} + 7 \, a c^{2} d^{2} e^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{96 \, c^{2} d^{2} e^{3}}, -\frac{3 \, {\left(c^{3} d^{6} - 3 \, a c^{2} d^{4} e^{2} + 3 \, a^{2} c d^{2} e^{4} - a^{3} e^{6}\right)} \sqrt{-c d e} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right) - 2 \, {\left(8 \, c^{3} d^{3} e^{3} x^{2} - 3 \, c^{3} d^{5} e + 8 \, a c^{2} d^{3} e^{3} + 3 \, a^{2} c d e^{5} + 2 \, {\left(c^{3} d^{4} e^{2} + 7 \, a c^{2} d^{2} e^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{48 \, c^{2} d^{2} e^{3}}\right]"," ",0,"[-1/96*(3*(c^3*d^6 - 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 - a^3*e^6)*sqrt(c*d*e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) - 4*(8*c^3*d^3*e^3*x^2 - 3*c^3*d^5*e + 8*a*c^2*d^3*e^3 + 3*a^2*c*d*e^5 + 2*(c^3*d^4*e^2 + 7*a*c^2*d^2*e^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^2*d^2*e^3), -1/48*(3*(c^3*d^6 - 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 - a^3*e^6)*sqrt(-c*d*e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)) - 2*(8*c^3*d^3*e^3*x^2 - 3*c^3*d^5*e + 8*a*c^2*d^3*e^3 + 3*a^2*c*d*e^5 + 2*(c^3*d^4*e^2 + 7*a*c^2*d^2*e^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^2*d^2*e^3)]","A",0
450,1,1327,0,4.404270," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/x/(e*x+d),x, algorithm=""fricas"")","\left[\frac{8 \, \sqrt{a d e} a c d e^{3} \log\left(\frac{8 \, a^{2} d^{2} e^{2} + {\left(c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} x^{2} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{a d e} + 8 \, {\left(a c d^{3} e + a^{2} d e^{3}\right)} x}{x^{2}}\right) - {\left(c^{2} d^{4} - 6 \, a c d^{2} e^{2} - 3 \, a^{2} e^{4}\right)} \sqrt{c d e} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) + 4 \, {\left(2 \, c^{2} d^{2} e^{2} x + c^{2} d^{3} e + 5 \, a c d e^{3}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{16 \, c d e^{2}}, \frac{4 \, \sqrt{a d e} a c d e^{3} \log\left(\frac{8 \, a^{2} d^{2} e^{2} + {\left(c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} x^{2} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{a d e} + 8 \, {\left(a c d^{3} e + a^{2} d e^{3}\right)} x}{x^{2}}\right) + {\left(c^{2} d^{4} - 6 \, a c d^{2} e^{2} - 3 \, a^{2} e^{4}\right)} \sqrt{-c d e} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right) + 2 \, {\left(2 \, c^{2} d^{2} e^{2} x + c^{2} d^{3} e + 5 \, a c d e^{3}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{8 \, c d e^{2}}, \frac{16 \, \sqrt{-a d e} a c d e^{3} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{-a d e}}{2 \, {\left(a c d^{2} e^{2} x^{2} + a^{2} d^{2} e^{2} + {\left(a c d^{3} e + a^{2} d e^{3}\right)} x\right)}}\right) - {\left(c^{2} d^{4} - 6 \, a c d^{2} e^{2} - 3 \, a^{2} e^{4}\right)} \sqrt{c d e} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) + 4 \, {\left(2 \, c^{2} d^{2} e^{2} x + c^{2} d^{3} e + 5 \, a c d e^{3}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{16 \, c d e^{2}}, \frac{8 \, \sqrt{-a d e} a c d e^{3} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{-a d e}}{2 \, {\left(a c d^{2} e^{2} x^{2} + a^{2} d^{2} e^{2} + {\left(a c d^{3} e + a^{2} d e^{3}\right)} x\right)}}\right) + {\left(c^{2} d^{4} - 6 \, a c d^{2} e^{2} - 3 \, a^{2} e^{4}\right)} \sqrt{-c d e} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right) + 2 \, {\left(2 \, c^{2} d^{2} e^{2} x + c^{2} d^{3} e + 5 \, a c d e^{3}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{8 \, c d e^{2}}\right]"," ",0,"[1/16*(8*sqrt(a*d*e)*a*c*d*e^3*log((8*a^2*d^2*e^2 + (c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4)*x^2 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(a*d*e) + 8*(a*c*d^3*e + a^2*d*e^3)*x)/x^2) - (c^2*d^4 - 6*a*c*d^2*e^2 - 3*a^2*e^4)*sqrt(c*d*e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) + 4*(2*c^2*d^2*e^2*x + c^2*d^3*e + 5*a*c*d*e^3)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c*d*e^2), 1/8*(4*sqrt(a*d*e)*a*c*d*e^3*log((8*a^2*d^2*e^2 + (c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4)*x^2 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(a*d*e) + 8*(a*c*d^3*e + a^2*d*e^3)*x)/x^2) + (c^2*d^4 - 6*a*c*d^2*e^2 - 3*a^2*e^4)*sqrt(-c*d*e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)) + 2*(2*c^2*d^2*e^2*x + c^2*d^3*e + 5*a*c*d*e^3)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c*d*e^2), 1/16*(16*sqrt(-a*d*e)*a*c*d*e^3*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-a*d*e)/(a*c*d^2*e^2*x^2 + a^2*d^2*e^2 + (a*c*d^3*e + a^2*d*e^3)*x)) - (c^2*d^4 - 6*a*c*d^2*e^2 - 3*a^2*e^4)*sqrt(c*d*e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) + 4*(2*c^2*d^2*e^2*x + c^2*d^3*e + 5*a*c*d*e^3)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c*d*e^2), 1/8*(8*sqrt(-a*d*e)*a*c*d*e^3*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-a*d*e)/(a*c*d^2*e^2*x^2 + a^2*d^2*e^2 + (a*c*d^3*e + a^2*d*e^3)*x)) + (c^2*d^4 - 6*a*c*d^2*e^2 - 3*a^2*e^4)*sqrt(-c*d*e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)) + 2*(2*c^2*d^2*e^2*x + c^2*d^3*e + 5*a*c*d*e^3)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c*d*e^2)]","A",0
451,1,1221,0,1.800907," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/x^2/(e*x+d),x, algorithm=""fricas"")","\left[\frac{{\left(c d^{2} + 3 \, a e^{2}\right)} \sqrt{\frac{c d}{e}} x \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} + 4 \, {\left(2 \, c d e^{2} x + c d^{2} e + a e^{3}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{\frac{c d}{e}} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) + {\left(3 \, c d^{2} + a e^{2}\right)} \sqrt{\frac{a e}{d}} x \log\left(\frac{8 \, a^{2} d^{2} e^{2} + {\left(c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} x^{2} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d^{2} e + {\left(c d^{3} + a d e^{2}\right)} x\right)} \sqrt{\frac{a e}{d}} + 8 \, {\left(a c d^{3} e + a^{2} d e^{3}\right)} x}{x^{2}}\right) + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d x - a e\right)}}{4 \, x}, -\frac{2 \, {\left(c d^{2} + 3 \, a e^{2}\right)} \sqrt{-\frac{c d}{e}} x \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-\frac{c d}{e}}}{2 \, {\left(c^{2} d^{2} e x^{2} + a c d^{2} e + {\left(c^{2} d^{3} + a c d e^{2}\right)} x\right)}}\right) - {\left(3 \, c d^{2} + a e^{2}\right)} \sqrt{\frac{a e}{d}} x \log\left(\frac{8 \, a^{2} d^{2} e^{2} + {\left(c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} x^{2} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d^{2} e + {\left(c d^{3} + a d e^{2}\right)} x\right)} \sqrt{\frac{a e}{d}} + 8 \, {\left(a c d^{3} e + a^{2} d e^{3}\right)} x}{x^{2}}\right) - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d x - a e\right)}}{4 \, x}, \frac{2 \, {\left(3 \, c d^{2} + a e^{2}\right)} \sqrt{-\frac{a e}{d}} x \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{-\frac{a e}{d}}}{2 \, {\left(a c d e^{2} x^{2} + a^{2} d e^{2} + {\left(a c d^{2} e + a^{2} e^{3}\right)} x\right)}}\right) + {\left(c d^{2} + 3 \, a e^{2}\right)} \sqrt{\frac{c d}{e}} x \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} + 4 \, {\left(2 \, c d e^{2} x + c d^{2} e + a e^{3}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{\frac{c d}{e}} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d x - a e\right)}}{4 \, x}, -\frac{{\left(c d^{2} + 3 \, a e^{2}\right)} \sqrt{-\frac{c d}{e}} x \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-\frac{c d}{e}}}{2 \, {\left(c^{2} d^{2} e x^{2} + a c d^{2} e + {\left(c^{2} d^{3} + a c d e^{2}\right)} x\right)}}\right) - {\left(3 \, c d^{2} + a e^{2}\right)} \sqrt{-\frac{a e}{d}} x \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{-\frac{a e}{d}}}{2 \, {\left(a c d e^{2} x^{2} + a^{2} d e^{2} + {\left(a c d^{2} e + a^{2} e^{3}\right)} x\right)}}\right) - 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d x - a e\right)}}{2 \, x}\right]"," ",0,"[1/4*((c*d^2 + 3*a*e^2)*sqrt(c*d/e)*x*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 + 4*(2*c*d*e^2*x + c*d^2*e + a*e^3)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(c*d/e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) + (3*c*d^2 + a*e^2)*sqrt(a*e/d)*x*log((8*a^2*d^2*e^2 + (c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4)*x^2 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d^2*e + (c*d^3 + a*d*e^2)*x)*sqrt(a*e/d) + 8*(a*c*d^3*e + a^2*d*e^3)*x)/x^2) + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d*x - a*e))/x, -1/4*(2*(c*d^2 + 3*a*e^2)*sqrt(-c*d/e)*x*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d/e)/(c^2*d^2*e*x^2 + a*c*d^2*e + (c^2*d^3 + a*c*d*e^2)*x)) - (3*c*d^2 + a*e^2)*sqrt(a*e/d)*x*log((8*a^2*d^2*e^2 + (c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4)*x^2 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d^2*e + (c*d^3 + a*d*e^2)*x)*sqrt(a*e/d) + 8*(a*c*d^3*e + a^2*d*e^3)*x)/x^2) - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d*x - a*e))/x, 1/4*(2*(3*c*d^2 + a*e^2)*sqrt(-a*e/d)*x*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-a*e/d)/(a*c*d*e^2*x^2 + a^2*d*e^2 + (a*c*d^2*e + a^2*e^3)*x)) + (c*d^2 + 3*a*e^2)*sqrt(c*d/e)*x*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 + 4*(2*c*d*e^2*x + c*d^2*e + a*e^3)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(c*d/e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d*x - a*e))/x, -1/2*((c*d^2 + 3*a*e^2)*sqrt(-c*d/e)*x*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d/e)/(c^2*d^2*e*x^2 + a*c*d^2*e + (c^2*d^3 + a*c*d*e^2)*x)) - (3*c*d^2 + a*e^2)*sqrt(-a*e/d)*x*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-a*e/d)/(a*c*d*e^2*x^2 + a^2*d*e^2 + (a*c*d^2*e + a^2*e^3)*x)) - 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d*x - a*e))/x]","A",0
452,1,1375,0,2.313925," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/x^3/(e*x+d),x, algorithm=""fricas"")","\left[\frac{8 \, \sqrt{c d e} a c d^{3} e x^{2} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) - {\left(3 \, c^{2} d^{4} + 6 \, a c d^{2} e^{2} - a^{2} e^{4}\right)} \sqrt{a d e} x^{2} \log\left(\frac{8 \, a^{2} d^{2} e^{2} + {\left(c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} x^{2} + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{a d e} + 8 \, {\left(a c d^{3} e + a^{2} d e^{3}\right)} x}{x^{2}}\right) - 4 \, {\left(2 \, a^{2} d^{2} e^{2} + {\left(5 \, a c d^{3} e + a^{2} d e^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{16 \, a d^{2} e x^{2}}, -\frac{16 \, \sqrt{-c d e} a c d^{3} e x^{2} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right) + {\left(3 \, c^{2} d^{4} + 6 \, a c d^{2} e^{2} - a^{2} e^{4}\right)} \sqrt{a d e} x^{2} \log\left(\frac{8 \, a^{2} d^{2} e^{2} + {\left(c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} x^{2} + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{a d e} + 8 \, {\left(a c d^{3} e + a^{2} d e^{3}\right)} x}{x^{2}}\right) + 4 \, {\left(2 \, a^{2} d^{2} e^{2} + {\left(5 \, a c d^{3} e + a^{2} d e^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{16 \, a d^{2} e x^{2}}, \frac{4 \, \sqrt{c d e} a c d^{3} e x^{2} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) + {\left(3 \, c^{2} d^{4} + 6 \, a c d^{2} e^{2} - a^{2} e^{4}\right)} \sqrt{-a d e} x^{2} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{-a d e}}{2 \, {\left(a c d^{2} e^{2} x^{2} + a^{2} d^{2} e^{2} + {\left(a c d^{3} e + a^{2} d e^{3}\right)} x\right)}}\right) - 2 \, {\left(2 \, a^{2} d^{2} e^{2} + {\left(5 \, a c d^{3} e + a^{2} d e^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{8 \, a d^{2} e x^{2}}, -\frac{8 \, \sqrt{-c d e} a c d^{3} e x^{2} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right) - {\left(3 \, c^{2} d^{4} + 6 \, a c d^{2} e^{2} - a^{2} e^{4}\right)} \sqrt{-a d e} x^{2} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{-a d e}}{2 \, {\left(a c d^{2} e^{2} x^{2} + a^{2} d^{2} e^{2} + {\left(a c d^{3} e + a^{2} d e^{3}\right)} x\right)}}\right) + 2 \, {\left(2 \, a^{2} d^{2} e^{2} + {\left(5 \, a c d^{3} e + a^{2} d e^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{8 \, a d^{2} e x^{2}}\right]"," ",0,"[1/16*(8*sqrt(c*d*e)*a*c*d^3*e*x^2*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) - (3*c^2*d^4 + 6*a*c*d^2*e^2 - a^2*e^4)*sqrt(a*d*e)*x^2*log((8*a^2*d^2*e^2 + (c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4)*x^2 + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(a*d*e) + 8*(a*c*d^3*e + a^2*d*e^3)*x)/x^2) - 4*(2*a^2*d^2*e^2 + (5*a*c*d^3*e + a^2*d*e^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(a*d^2*e*x^2), -1/16*(16*sqrt(-c*d*e)*a*c*d^3*e*x^2*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)) + (3*c^2*d^4 + 6*a*c*d^2*e^2 - a^2*e^4)*sqrt(a*d*e)*x^2*log((8*a^2*d^2*e^2 + (c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4)*x^2 + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(a*d*e) + 8*(a*c*d^3*e + a^2*d*e^3)*x)/x^2) + 4*(2*a^2*d^2*e^2 + (5*a*c*d^3*e + a^2*d*e^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(a*d^2*e*x^2), 1/8*(4*sqrt(c*d*e)*a*c*d^3*e*x^2*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) + (3*c^2*d^4 + 6*a*c*d^2*e^2 - a^2*e^4)*sqrt(-a*d*e)*x^2*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-a*d*e)/(a*c*d^2*e^2*x^2 + a^2*d^2*e^2 + (a*c*d^3*e + a^2*d*e^3)*x)) - 2*(2*a^2*d^2*e^2 + (5*a*c*d^3*e + a^2*d*e^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(a*d^2*e*x^2), -1/8*(8*sqrt(-c*d*e)*a*c*d^3*e*x^2*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)) - (3*c^2*d^4 + 6*a*c*d^2*e^2 - a^2*e^4)*sqrt(-a*d*e)*x^2*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-a*d*e)/(a*c*d^2*e^2*x^2 + a^2*d^2*e^2 + (a*c*d^3*e + a^2*d*e^3)*x)) + 2*(2*a^2*d^2*e^2 + (5*a*c*d^3*e + a^2*d*e^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(a*d^2*e*x^2)]","A",0
453,1,558,0,1.554127," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/x^4/(e*x+d),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(c^{3} d^{6} - 3 \, a c^{2} d^{4} e^{2} + 3 \, a^{2} c d^{2} e^{4} - a^{3} e^{6}\right)} \sqrt{a d e} x^{3} \log\left(\frac{8 \, a^{2} d^{2} e^{2} + {\left(c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} x^{2} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{a d e} + 8 \, {\left(a c d^{3} e + a^{2} d e^{3}\right)} x}{x^{2}}\right) + 4 \, {\left(8 \, a^{3} d^{3} e^{3} + {\left(3 \, a c^{2} d^{5} e + 8 \, a^{2} c d^{3} e^{3} - 3 \, a^{3} d e^{5}\right)} x^{2} + 2 \, {\left(7 \, a^{2} c d^{4} e^{2} + a^{3} d^{2} e^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{96 \, a^{2} d^{3} e^{2} x^{3}}, -\frac{3 \, {\left(c^{3} d^{6} - 3 \, a c^{2} d^{4} e^{2} + 3 \, a^{2} c d^{2} e^{4} - a^{3} e^{6}\right)} \sqrt{-a d e} x^{3} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{-a d e}}{2 \, {\left(a c d^{2} e^{2} x^{2} + a^{2} d^{2} e^{2} + {\left(a c d^{3} e + a^{2} d e^{3}\right)} x\right)}}\right) + 2 \, {\left(8 \, a^{3} d^{3} e^{3} + {\left(3 \, a c^{2} d^{5} e + 8 \, a^{2} c d^{3} e^{3} - 3 \, a^{3} d e^{5}\right)} x^{2} + 2 \, {\left(7 \, a^{2} c d^{4} e^{2} + a^{3} d^{2} e^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{48 \, a^{2} d^{3} e^{2} x^{3}}\right]"," ",0,"[-1/96*(3*(c^3*d^6 - 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 - a^3*e^6)*sqrt(a*d*e)*x^3*log((8*a^2*d^2*e^2 + (c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4)*x^2 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(a*d*e) + 8*(a*c*d^3*e + a^2*d*e^3)*x)/x^2) + 4*(8*a^3*d^3*e^3 + (3*a*c^2*d^5*e + 8*a^2*c*d^3*e^3 - 3*a^3*d*e^5)*x^2 + 2*(7*a^2*c*d^4*e^2 + a^3*d^2*e^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(a^2*d^3*e^2*x^3), -1/48*(3*(c^3*d^6 - 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 - a^3*e^6)*sqrt(-a*d*e)*x^3*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-a*d*e)/(a*c*d^2*e^2*x^2 + a^2*d^2*e^2 + (a*c*d^3*e + a^2*d*e^3)*x)) + 2*(8*a^3*d^3*e^3 + (3*a*c^2*d^5*e + 8*a^2*c*d^3*e^3 - 3*a^3*d*e^5)*x^2 + 2*(7*a^2*c*d^4*e^2 + a^3*d^2*e^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(a^2*d^3*e^2*x^3)]","A",0
454,1,704,0,8.658581," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/x^5/(e*x+d),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(3 \, c^{4} d^{8} - 4 \, a c^{3} d^{6} e^{2} - 6 \, a^{2} c^{2} d^{4} e^{4} + 12 \, a^{3} c d^{2} e^{6} - 5 \, a^{4} e^{8}\right)} \sqrt{a d e} x^{4} \log\left(\frac{8 \, a^{2} d^{2} e^{2} + {\left(c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} x^{2} + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{a d e} + 8 \, {\left(a c d^{3} e + a^{2} d e^{3}\right)} x}{x^{2}}\right) + 4 \, {\left(48 \, a^{4} d^{4} e^{4} - {\left(9 \, a c^{3} d^{7} e - 9 \, a^{2} c^{2} d^{5} e^{3} + 31 \, a^{3} c d^{3} e^{5} - 15 \, a^{4} d e^{7}\right)} x^{3} + 2 \, {\left(3 \, a^{2} c^{2} d^{6} e^{2} + 10 \, a^{3} c d^{4} e^{4} - 5 \, a^{4} d^{2} e^{6}\right)} x^{2} + 8 \, {\left(9 \, a^{3} c d^{5} e^{3} + a^{4} d^{3} e^{5}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{768 \, a^{3} d^{4} e^{3} x^{4}}, \frac{3 \, {\left(3 \, c^{4} d^{8} - 4 \, a c^{3} d^{6} e^{2} - 6 \, a^{2} c^{2} d^{4} e^{4} + 12 \, a^{3} c d^{2} e^{6} - 5 \, a^{4} e^{8}\right)} \sqrt{-a d e} x^{4} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{-a d e}}{2 \, {\left(a c d^{2} e^{2} x^{2} + a^{2} d^{2} e^{2} + {\left(a c d^{3} e + a^{2} d e^{3}\right)} x\right)}}\right) - 2 \, {\left(48 \, a^{4} d^{4} e^{4} - {\left(9 \, a c^{3} d^{7} e - 9 \, a^{2} c^{2} d^{5} e^{3} + 31 \, a^{3} c d^{3} e^{5} - 15 \, a^{4} d e^{7}\right)} x^{3} + 2 \, {\left(3 \, a^{2} c^{2} d^{6} e^{2} + 10 \, a^{3} c d^{4} e^{4} - 5 \, a^{4} d^{2} e^{6}\right)} x^{2} + 8 \, {\left(9 \, a^{3} c d^{5} e^{3} + a^{4} d^{3} e^{5}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{384 \, a^{3} d^{4} e^{3} x^{4}}\right]"," ",0,"[-1/768*(3*(3*c^4*d^8 - 4*a*c^3*d^6*e^2 - 6*a^2*c^2*d^4*e^4 + 12*a^3*c*d^2*e^6 - 5*a^4*e^8)*sqrt(a*d*e)*x^4*log((8*a^2*d^2*e^2 + (c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4)*x^2 + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(a*d*e) + 8*(a*c*d^3*e + a^2*d*e^3)*x)/x^2) + 4*(48*a^4*d^4*e^4 - (9*a*c^3*d^7*e - 9*a^2*c^2*d^5*e^3 + 31*a^3*c*d^3*e^5 - 15*a^4*d*e^7)*x^3 + 2*(3*a^2*c^2*d^6*e^2 + 10*a^3*c*d^4*e^4 - 5*a^4*d^2*e^6)*x^2 + 8*(9*a^3*c*d^5*e^3 + a^4*d^3*e^5)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(a^3*d^4*e^3*x^4), 1/384*(3*(3*c^4*d^8 - 4*a*c^3*d^6*e^2 - 6*a^2*c^2*d^4*e^4 + 12*a^3*c*d^2*e^6 - 5*a^4*e^8)*sqrt(-a*d*e)*x^4*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-a*d*e)/(a*c*d^2*e^2*x^2 + a^2*d^2*e^2 + (a*c*d^3*e + a^2*d*e^3)*x)) - 2*(48*a^4*d^4*e^4 - (9*a*c^3*d^7*e - 9*a^2*c^2*d^5*e^3 + 31*a^3*c*d^3*e^5 - 15*a^4*d*e^7)*x^3 + 2*(3*a^2*c^2*d^6*e^2 + 10*a^3*c*d^4*e^4 - 5*a^4*d^2*e^6)*x^2 + 8*(9*a^3*c*d^5*e^3 + a^4*d^3*e^5)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(a^3*d^4*e^3*x^4)]","A",0
455,1,872,0,20.244570," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/x^6/(e*x+d),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(3 \, c^{5} d^{10} - 3 \, a c^{4} d^{8} e^{2} - 2 \, a^{2} c^{3} d^{6} e^{4} - 6 \, a^{3} c^{2} d^{4} e^{6} + 15 \, a^{4} c d^{2} e^{8} - 7 \, a^{5} e^{10}\right)} \sqrt{a d e} x^{5} \log\left(\frac{8 \, a^{2} d^{2} e^{2} + {\left(c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} x^{2} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{a d e} + 8 \, {\left(a c d^{3} e + a^{2} d e^{3}\right)} x}{x^{2}}\right) + 4 \, {\left(384 \, a^{5} d^{5} e^{5} + {\left(45 \, a c^{4} d^{9} e - 30 \, a^{2} c^{3} d^{7} e^{3} - 36 \, a^{3} c^{2} d^{5} e^{5} + 190 \, a^{4} c d^{3} e^{7} - 105 \, a^{5} d e^{9}\right)} x^{4} - 2 \, {\left(15 \, a^{2} c^{3} d^{8} e^{2} - 9 \, a^{3} c^{2} d^{6} e^{4} + 61 \, a^{4} c d^{4} e^{6} - 35 \, a^{5} d^{2} e^{8}\right)} x^{3} + 8 \, {\left(3 \, a^{3} c^{2} d^{7} e^{3} + 12 \, a^{4} c d^{5} e^{5} - 7 \, a^{5} d^{3} e^{7}\right)} x^{2} + 48 \, {\left(11 \, a^{4} c d^{6} e^{4} + a^{5} d^{4} e^{6}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{7680 \, a^{4} d^{5} e^{4} x^{5}}, -\frac{15 \, {\left(3 \, c^{5} d^{10} - 3 \, a c^{4} d^{8} e^{2} - 2 \, a^{2} c^{3} d^{6} e^{4} - 6 \, a^{3} c^{2} d^{4} e^{6} + 15 \, a^{4} c d^{2} e^{8} - 7 \, a^{5} e^{10}\right)} \sqrt{-a d e} x^{5} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{-a d e}}{2 \, {\left(a c d^{2} e^{2} x^{2} + a^{2} d^{2} e^{2} + {\left(a c d^{3} e + a^{2} d e^{3}\right)} x\right)}}\right) + 2 \, {\left(384 \, a^{5} d^{5} e^{5} + {\left(45 \, a c^{4} d^{9} e - 30 \, a^{2} c^{3} d^{7} e^{3} - 36 \, a^{3} c^{2} d^{5} e^{5} + 190 \, a^{4} c d^{3} e^{7} - 105 \, a^{5} d e^{9}\right)} x^{4} - 2 \, {\left(15 \, a^{2} c^{3} d^{8} e^{2} - 9 \, a^{3} c^{2} d^{6} e^{4} + 61 \, a^{4} c d^{4} e^{6} - 35 \, a^{5} d^{2} e^{8}\right)} x^{3} + 8 \, {\left(3 \, a^{3} c^{2} d^{7} e^{3} + 12 \, a^{4} c d^{5} e^{5} - 7 \, a^{5} d^{3} e^{7}\right)} x^{2} + 48 \, {\left(11 \, a^{4} c d^{6} e^{4} + a^{5} d^{4} e^{6}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{3840 \, a^{4} d^{5} e^{4} x^{5}}\right]"," ",0,"[-1/7680*(15*(3*c^5*d^10 - 3*a*c^4*d^8*e^2 - 2*a^2*c^3*d^6*e^4 - 6*a^3*c^2*d^4*e^6 + 15*a^4*c*d^2*e^8 - 7*a^5*e^10)*sqrt(a*d*e)*x^5*log((8*a^2*d^2*e^2 + (c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4)*x^2 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(a*d*e) + 8*(a*c*d^3*e + a^2*d*e^3)*x)/x^2) + 4*(384*a^5*d^5*e^5 + (45*a*c^4*d^9*e - 30*a^2*c^3*d^7*e^3 - 36*a^3*c^2*d^5*e^5 + 190*a^4*c*d^3*e^7 - 105*a^5*d*e^9)*x^4 - 2*(15*a^2*c^3*d^8*e^2 - 9*a^3*c^2*d^6*e^4 + 61*a^4*c*d^4*e^6 - 35*a^5*d^2*e^8)*x^3 + 8*(3*a^3*c^2*d^7*e^3 + 12*a^4*c*d^5*e^5 - 7*a^5*d^3*e^7)*x^2 + 48*(11*a^4*c*d^6*e^4 + a^5*d^4*e^6)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(a^4*d^5*e^4*x^5), -1/3840*(15*(3*c^5*d^10 - 3*a*c^4*d^8*e^2 - 2*a^2*c^3*d^6*e^4 - 6*a^3*c^2*d^4*e^6 + 15*a^4*c*d^2*e^8 - 7*a^5*e^10)*sqrt(-a*d*e)*x^5*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-a*d*e)/(a*c*d^2*e^2*x^2 + a^2*d^2*e^2 + (a*c*d^3*e + a^2*d*e^3)*x)) + 2*(384*a^5*d^5*e^5 + (45*a*c^4*d^9*e - 30*a^2*c^3*d^7*e^3 - 36*a^3*c^2*d^5*e^5 + 190*a^4*c*d^3*e^7 - 105*a^5*d*e^9)*x^4 - 2*(15*a^2*c^3*d^8*e^2 - 9*a^3*c^2*d^6*e^4 + 61*a^4*c*d^4*e^6 - 35*a^5*d^2*e^8)*x^3 + 8*(3*a^3*c^2*d^7*e^3 + 12*a^4*c*d^5*e^5 - 7*a^5*d^3*e^7)*x^2 + 48*(11*a^4*c*d^6*e^4 + a^5*d^4*e^6)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(a^4*d^5*e^4*x^5)]","A",0
456,1,1072,0,55.727800," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/x^7/(e*x+d),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(7 \, c^{6} d^{12} - 6 \, a c^{5} d^{10} e^{2} - 3 \, a^{2} c^{4} d^{8} e^{4} - 4 \, a^{3} c^{3} d^{6} e^{6} - 15 \, a^{4} c^{2} d^{4} e^{8} + 42 \, a^{5} c d^{2} e^{10} - 21 \, a^{6} e^{12}\right)} \sqrt{a d e} x^{6} \log\left(\frac{8 \, a^{2} d^{2} e^{2} + {\left(c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} x^{2} + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{a d e} + 8 \, {\left(a c d^{3} e + a^{2} d e^{3}\right)} x}{x^{2}}\right) + 4 \, {\left(1280 \, a^{6} d^{6} e^{6} - {\left(105 \, a c^{5} d^{11} e - 55 \, a^{2} c^{4} d^{9} e^{3} - 54 \, a^{3} c^{3} d^{7} e^{5} - 78 \, a^{4} c^{2} d^{5} e^{7} + 525 \, a^{5} c d^{3} e^{9} - 315 \, a^{6} d e^{11}\right)} x^{5} + 2 \, {\left(35 \, a^{2} c^{4} d^{10} e^{2} - 16 \, a^{3} c^{3} d^{8} e^{4} - 18 \, a^{4} c^{2} d^{6} e^{6} + 168 \, a^{5} c d^{4} e^{8} - 105 \, a^{6} d^{2} e^{10}\right)} x^{4} - 8 \, {\left(7 \, a^{3} c^{3} d^{9} e^{3} - 3 \, a^{4} c^{2} d^{7} e^{5} + 33 \, a^{5} c d^{5} e^{7} - 21 \, a^{6} d^{3} e^{9}\right)} x^{3} + 16 \, {\left(3 \, a^{4} c^{2} d^{8} e^{4} + 14 \, a^{5} c d^{6} e^{6} - 9 \, a^{6} d^{4} e^{8}\right)} x^{2} + 128 \, {\left(13 \, a^{5} c d^{7} e^{5} + a^{6} d^{5} e^{7}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{30720 \, a^{5} d^{6} e^{5} x^{6}}, \frac{15 \, {\left(7 \, c^{6} d^{12} - 6 \, a c^{5} d^{10} e^{2} - 3 \, a^{2} c^{4} d^{8} e^{4} - 4 \, a^{3} c^{3} d^{6} e^{6} - 15 \, a^{4} c^{2} d^{4} e^{8} + 42 \, a^{5} c d^{2} e^{10} - 21 \, a^{6} e^{12}\right)} \sqrt{-a d e} x^{6} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{-a d e}}{2 \, {\left(a c d^{2} e^{2} x^{2} + a^{2} d^{2} e^{2} + {\left(a c d^{3} e + a^{2} d e^{3}\right)} x\right)}}\right) - 2 \, {\left(1280 \, a^{6} d^{6} e^{6} - {\left(105 \, a c^{5} d^{11} e - 55 \, a^{2} c^{4} d^{9} e^{3} - 54 \, a^{3} c^{3} d^{7} e^{5} - 78 \, a^{4} c^{2} d^{5} e^{7} + 525 \, a^{5} c d^{3} e^{9} - 315 \, a^{6} d e^{11}\right)} x^{5} + 2 \, {\left(35 \, a^{2} c^{4} d^{10} e^{2} - 16 \, a^{3} c^{3} d^{8} e^{4} - 18 \, a^{4} c^{2} d^{6} e^{6} + 168 \, a^{5} c d^{4} e^{8} - 105 \, a^{6} d^{2} e^{10}\right)} x^{4} - 8 \, {\left(7 \, a^{3} c^{3} d^{9} e^{3} - 3 \, a^{4} c^{2} d^{7} e^{5} + 33 \, a^{5} c d^{5} e^{7} - 21 \, a^{6} d^{3} e^{9}\right)} x^{3} + 16 \, {\left(3 \, a^{4} c^{2} d^{8} e^{4} + 14 \, a^{5} c d^{6} e^{6} - 9 \, a^{6} d^{4} e^{8}\right)} x^{2} + 128 \, {\left(13 \, a^{5} c d^{7} e^{5} + a^{6} d^{5} e^{7}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{15360 \, a^{5} d^{6} e^{5} x^{6}}\right]"," ",0,"[-1/30720*(15*(7*c^6*d^12 - 6*a*c^5*d^10*e^2 - 3*a^2*c^4*d^8*e^4 - 4*a^3*c^3*d^6*e^6 - 15*a^4*c^2*d^4*e^8 + 42*a^5*c*d^2*e^10 - 21*a^6*e^12)*sqrt(a*d*e)*x^6*log((8*a^2*d^2*e^2 + (c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4)*x^2 + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(a*d*e) + 8*(a*c*d^3*e + a^2*d*e^3)*x)/x^2) + 4*(1280*a^6*d^6*e^6 - (105*a*c^5*d^11*e - 55*a^2*c^4*d^9*e^3 - 54*a^3*c^3*d^7*e^5 - 78*a^4*c^2*d^5*e^7 + 525*a^5*c*d^3*e^9 - 315*a^6*d*e^11)*x^5 + 2*(35*a^2*c^4*d^10*e^2 - 16*a^3*c^3*d^8*e^4 - 18*a^4*c^2*d^6*e^6 + 168*a^5*c*d^4*e^8 - 105*a^6*d^2*e^10)*x^4 - 8*(7*a^3*c^3*d^9*e^3 - 3*a^4*c^2*d^7*e^5 + 33*a^5*c*d^5*e^7 - 21*a^6*d^3*e^9)*x^3 + 16*(3*a^4*c^2*d^8*e^4 + 14*a^5*c*d^6*e^6 - 9*a^6*d^4*e^8)*x^2 + 128*(13*a^5*c*d^7*e^5 + a^6*d^5*e^7)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(a^5*d^6*e^5*x^6), 1/15360*(15*(7*c^6*d^12 - 6*a*c^5*d^10*e^2 - 3*a^2*c^4*d^8*e^4 - 4*a^3*c^3*d^6*e^6 - 15*a^4*c^2*d^4*e^8 + 42*a^5*c*d^2*e^10 - 21*a^6*e^12)*sqrt(-a*d*e)*x^6*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-a*d*e)/(a*c*d^2*e^2*x^2 + a^2*d^2*e^2 + (a*c*d^3*e + a^2*d*e^3)*x)) - 2*(1280*a^6*d^6*e^6 - (105*a*c^5*d^11*e - 55*a^2*c^4*d^9*e^3 - 54*a^3*c^3*d^7*e^5 - 78*a^4*c^2*d^5*e^7 + 525*a^5*c*d^3*e^9 - 315*a^6*d*e^11)*x^5 + 2*(35*a^2*c^4*d^10*e^2 - 16*a^3*c^3*d^8*e^4 - 18*a^4*c^2*d^6*e^6 + 168*a^5*c*d^4*e^8 - 105*a^6*d^2*e^10)*x^4 - 8*(7*a^3*c^3*d^9*e^3 - 3*a^4*c^2*d^7*e^5 + 33*a^5*c*d^5*e^7 - 21*a^6*d^3*e^9)*x^3 + 16*(3*a^4*c^2*d^8*e^4 + 14*a^5*c*d^6*e^6 - 9*a^6*d^4*e^8)*x^2 + 128*(13*a^5*c*d^7*e^5 + a^6*d^5*e^7)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(a^5*d^6*e^5*x^6)]","A",0
457,1,1524,0,0.573736," ","integrate(x^3*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(33 \, c^{8} d^{16} - 120 \, a c^{7} d^{14} e^{2} + 140 \, a^{2} c^{6} d^{12} e^{4} - 40 \, a^{3} c^{5} d^{10} e^{6} - 10 \, a^{4} c^{4} d^{8} e^{8} - 8 \, a^{5} c^{3} d^{6} e^{10} - 20 \, a^{6} c^{2} d^{4} e^{12} + 40 \, a^{7} c d^{2} e^{14} - 15 \, a^{8} e^{16}\right)} \sqrt{c d e} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) + 4 \, {\left(71680 \, c^{8} d^{8} e^{8} x^{7} - 3465 \, c^{8} d^{15} e + 11445 \, a c^{7} d^{13} e^{3} - 11193 \, a^{2} c^{6} d^{11} e^{5} + 1325 \, a^{3} c^{5} d^{9} e^{7} + 925 \, a^{4} c^{4} d^{7} e^{9} + 1015 \, a^{5} c^{3} d^{5} e^{11} - 3675 \, a^{6} c^{2} d^{3} e^{13} + 1575 \, a^{7} c d e^{15} + 5120 \, {\left(17 \, c^{8} d^{9} e^{7} + 33 \, a c^{7} d^{7} e^{9}\right)} x^{6} + 1280 \, {\left(c^{8} d^{10} e^{6} + 166 \, a c^{7} d^{8} e^{8} + 81 \, a^{2} c^{6} d^{6} e^{10}\right)} x^{5} - 128 \, {\left(11 \, c^{8} d^{11} e^{5} - 35 \, a c^{7} d^{9} e^{7} - 1075 \, a^{2} c^{6} d^{7} e^{9} - 5 \, a^{3} c^{5} d^{5} e^{11}\right)} x^{4} + 16 \, {\left(99 \, c^{8} d^{12} e^{4} - 316 \, a c^{7} d^{10} e^{6} + 290 \, a^{2} c^{6} d^{8} e^{8} + 100 \, a^{3} c^{5} d^{6} e^{10} - 45 \, a^{4} c^{4} d^{4} e^{12}\right)} x^{3} - 8 \, {\left(231 \, c^{8} d^{13} e^{3} - 741 \, a c^{7} d^{11} e^{5} + 686 \, a^{2} c^{6} d^{9} e^{7} - 50 \, a^{3} c^{5} d^{7} e^{9} + 235 \, a^{4} c^{4} d^{5} e^{11} - 105 \, a^{5} c^{3} d^{3} e^{13}\right)} x^{2} + 2 \, {\left(1155 \, c^{8} d^{14} e^{2} - 3738 \, a c^{7} d^{12} e^{4} + 3517 \, a^{2} c^{6} d^{10} e^{6} - 300 \, a^{3} c^{5} d^{8} e^{8} - 275 \, a^{4} c^{4} d^{6} e^{10} + 1190 \, a^{5} c^{3} d^{4} e^{12} - 525 \, a^{6} c^{2} d^{2} e^{14}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{2293760 \, c^{6} d^{6} e^{7}}, -\frac{105 \, {\left(33 \, c^{8} d^{16} - 120 \, a c^{7} d^{14} e^{2} + 140 \, a^{2} c^{6} d^{12} e^{4} - 40 \, a^{3} c^{5} d^{10} e^{6} - 10 \, a^{4} c^{4} d^{8} e^{8} - 8 \, a^{5} c^{3} d^{6} e^{10} - 20 \, a^{6} c^{2} d^{4} e^{12} + 40 \, a^{7} c d^{2} e^{14} - 15 \, a^{8} e^{16}\right)} \sqrt{-c d e} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right) - 2 \, {\left(71680 \, c^{8} d^{8} e^{8} x^{7} - 3465 \, c^{8} d^{15} e + 11445 \, a c^{7} d^{13} e^{3} - 11193 \, a^{2} c^{6} d^{11} e^{5} + 1325 \, a^{3} c^{5} d^{9} e^{7} + 925 \, a^{4} c^{4} d^{7} e^{9} + 1015 \, a^{5} c^{3} d^{5} e^{11} - 3675 \, a^{6} c^{2} d^{3} e^{13} + 1575 \, a^{7} c d e^{15} + 5120 \, {\left(17 \, c^{8} d^{9} e^{7} + 33 \, a c^{7} d^{7} e^{9}\right)} x^{6} + 1280 \, {\left(c^{8} d^{10} e^{6} + 166 \, a c^{7} d^{8} e^{8} + 81 \, a^{2} c^{6} d^{6} e^{10}\right)} x^{5} - 128 \, {\left(11 \, c^{8} d^{11} e^{5} - 35 \, a c^{7} d^{9} e^{7} - 1075 \, a^{2} c^{6} d^{7} e^{9} - 5 \, a^{3} c^{5} d^{5} e^{11}\right)} x^{4} + 16 \, {\left(99 \, c^{8} d^{12} e^{4} - 316 \, a c^{7} d^{10} e^{6} + 290 \, a^{2} c^{6} d^{8} e^{8} + 100 \, a^{3} c^{5} d^{6} e^{10} - 45 \, a^{4} c^{4} d^{4} e^{12}\right)} x^{3} - 8 \, {\left(231 \, c^{8} d^{13} e^{3} - 741 \, a c^{7} d^{11} e^{5} + 686 \, a^{2} c^{6} d^{9} e^{7} - 50 \, a^{3} c^{5} d^{7} e^{9} + 235 \, a^{4} c^{4} d^{5} e^{11} - 105 \, a^{5} c^{3} d^{3} e^{13}\right)} x^{2} + 2 \, {\left(1155 \, c^{8} d^{14} e^{2} - 3738 \, a c^{7} d^{12} e^{4} + 3517 \, a^{2} c^{6} d^{10} e^{6} - 300 \, a^{3} c^{5} d^{8} e^{8} - 275 \, a^{4} c^{4} d^{6} e^{10} + 1190 \, a^{5} c^{3} d^{4} e^{12} - 525 \, a^{6} c^{2} d^{2} e^{14}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{1146880 \, c^{6} d^{6} e^{7}}\right]"," ",0,"[1/2293760*(105*(33*c^8*d^16 - 120*a*c^7*d^14*e^2 + 140*a^2*c^6*d^12*e^4 - 40*a^3*c^5*d^10*e^6 - 10*a^4*c^4*d^8*e^8 - 8*a^5*c^3*d^6*e^10 - 20*a^6*c^2*d^4*e^12 + 40*a^7*c*d^2*e^14 - 15*a^8*e^16)*sqrt(c*d*e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) + 4*(71680*c^8*d^8*e^8*x^7 - 3465*c^8*d^15*e + 11445*a*c^7*d^13*e^3 - 11193*a^2*c^6*d^11*e^5 + 1325*a^3*c^5*d^9*e^7 + 925*a^4*c^4*d^7*e^9 + 1015*a^5*c^3*d^5*e^11 - 3675*a^6*c^2*d^3*e^13 + 1575*a^7*c*d*e^15 + 5120*(17*c^8*d^9*e^7 + 33*a*c^7*d^7*e^9)*x^6 + 1280*(c^8*d^10*e^6 + 166*a*c^7*d^8*e^8 + 81*a^2*c^6*d^6*e^10)*x^5 - 128*(11*c^8*d^11*e^5 - 35*a*c^7*d^9*e^7 - 1075*a^2*c^6*d^7*e^9 - 5*a^3*c^5*d^5*e^11)*x^4 + 16*(99*c^8*d^12*e^4 - 316*a*c^7*d^10*e^6 + 290*a^2*c^6*d^8*e^8 + 100*a^3*c^5*d^6*e^10 - 45*a^4*c^4*d^4*e^12)*x^3 - 8*(231*c^8*d^13*e^3 - 741*a*c^7*d^11*e^5 + 686*a^2*c^6*d^9*e^7 - 50*a^3*c^5*d^7*e^9 + 235*a^4*c^4*d^5*e^11 - 105*a^5*c^3*d^3*e^13)*x^2 + 2*(1155*c^8*d^14*e^2 - 3738*a*c^7*d^12*e^4 + 3517*a^2*c^6*d^10*e^6 - 300*a^3*c^5*d^8*e^8 - 275*a^4*c^4*d^6*e^10 + 1190*a^5*c^3*d^4*e^12 - 525*a^6*c^2*d^2*e^14)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^6*d^6*e^7), -1/1146880*(105*(33*c^8*d^16 - 120*a*c^7*d^14*e^2 + 140*a^2*c^6*d^12*e^4 - 40*a^3*c^5*d^10*e^6 - 10*a^4*c^4*d^8*e^8 - 8*a^5*c^3*d^6*e^10 - 20*a^6*c^2*d^4*e^12 + 40*a^7*c*d^2*e^14 - 15*a^8*e^16)*sqrt(-c*d*e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)) - 2*(71680*c^8*d^8*e^8*x^7 - 3465*c^8*d^15*e + 11445*a*c^7*d^13*e^3 - 11193*a^2*c^6*d^11*e^5 + 1325*a^3*c^5*d^9*e^7 + 925*a^4*c^4*d^7*e^9 + 1015*a^5*c^3*d^5*e^11 - 3675*a^6*c^2*d^3*e^13 + 1575*a^7*c*d*e^15 + 5120*(17*c^8*d^9*e^7 + 33*a*c^7*d^7*e^9)*x^6 + 1280*(c^8*d^10*e^6 + 166*a*c^7*d^8*e^8 + 81*a^2*c^6*d^6*e^10)*x^5 - 128*(11*c^8*d^11*e^5 - 35*a*c^7*d^9*e^7 - 1075*a^2*c^6*d^7*e^9 - 5*a^3*c^5*d^5*e^11)*x^4 + 16*(99*c^8*d^12*e^4 - 316*a*c^7*d^10*e^6 + 290*a^2*c^6*d^8*e^8 + 100*a^3*c^5*d^6*e^10 - 45*a^4*c^4*d^4*e^12)*x^3 - 8*(231*c^8*d^13*e^3 - 741*a*c^7*d^11*e^5 + 686*a^2*c^6*d^9*e^7 - 50*a^3*c^5*d^7*e^9 + 235*a^4*c^4*d^5*e^11 - 105*a^5*c^3*d^3*e^13)*x^2 + 2*(1155*c^8*d^14*e^2 - 3738*a*c^7*d^12*e^4 + 3517*a^2*c^6*d^10*e^6 - 300*a^3*c^5*d^8*e^8 - 275*a^4*c^4*d^6*e^10 + 1190*a^5*c^3*d^4*e^12 - 525*a^6*c^2*d^2*e^14)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^6*d^6*e^7)]","A",0
458,1,1272,0,0.507158," ","integrate(x^2*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(9 \, c^{7} d^{14} - 35 \, a c^{6} d^{12} e^{2} + 45 \, a^{2} c^{5} d^{10} e^{4} - 15 \, a^{3} c^{4} d^{8} e^{6} - 5 \, a^{4} c^{3} d^{6} e^{8} - 9 \, a^{5} c^{2} d^{4} e^{10} + 15 \, a^{6} c d^{2} e^{12} - 5 \, a^{7} e^{14}\right)} \sqrt{c d e} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) - 4 \, {\left(15360 \, c^{7} d^{7} e^{7} x^{6} + 945 \, c^{7} d^{13} e - 3360 \, a c^{6} d^{11} e^{3} + 3689 \, a^{2} c^{5} d^{9} e^{5} - 600 \, a^{3} c^{4} d^{7} e^{7} - 525 \, a^{4} c^{3} d^{5} e^{9} + 1400 \, a^{5} c^{2} d^{3} e^{11} - 525 \, a^{6} c d e^{13} + 1280 \, {\left(15 \, c^{7} d^{8} e^{6} + 29 \, a c^{6} d^{6} e^{8}\right)} x^{5} + 128 \, {\left(3 \, c^{7} d^{9} e^{5} + 380 \, a c^{6} d^{7} e^{7} + 185 \, a^{2} c^{5} d^{5} e^{9}\right)} x^{4} - 16 \, {\left(27 \, c^{7} d^{10} e^{4} - 93 \, a c^{6} d^{8} e^{6} - 2095 \, a^{2} c^{5} d^{6} e^{8} - 15 \, a^{3} c^{4} d^{4} e^{10}\right)} x^{3} + 8 \, {\left(63 \, c^{7} d^{11} e^{3} - 218 \, a c^{6} d^{9} e^{5} + 228 \, a^{2} c^{5} d^{7} e^{7} + 90 \, a^{3} c^{4} d^{5} e^{9} - 35 \, a^{4} c^{3} d^{3} e^{11}\right)} x^{2} - 2 \, {\left(315 \, c^{7} d^{12} e^{2} - 1099 \, a c^{6} d^{10} e^{4} + 1166 \, a^{2} c^{5} d^{8} e^{6} - 150 \, a^{3} c^{4} d^{6} e^{8} + 455 \, a^{4} c^{3} d^{4} e^{10} - 175 \, a^{5} c^{2} d^{2} e^{12}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{430080 \, c^{5} d^{5} e^{6}}, \frac{105 \, {\left(9 \, c^{7} d^{14} - 35 \, a c^{6} d^{12} e^{2} + 45 \, a^{2} c^{5} d^{10} e^{4} - 15 \, a^{3} c^{4} d^{8} e^{6} - 5 \, a^{4} c^{3} d^{6} e^{8} - 9 \, a^{5} c^{2} d^{4} e^{10} + 15 \, a^{6} c d^{2} e^{12} - 5 \, a^{7} e^{14}\right)} \sqrt{-c d e} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right) + 2 \, {\left(15360 \, c^{7} d^{7} e^{7} x^{6} + 945 \, c^{7} d^{13} e - 3360 \, a c^{6} d^{11} e^{3} + 3689 \, a^{2} c^{5} d^{9} e^{5} - 600 \, a^{3} c^{4} d^{7} e^{7} - 525 \, a^{4} c^{3} d^{5} e^{9} + 1400 \, a^{5} c^{2} d^{3} e^{11} - 525 \, a^{6} c d e^{13} + 1280 \, {\left(15 \, c^{7} d^{8} e^{6} + 29 \, a c^{6} d^{6} e^{8}\right)} x^{5} + 128 \, {\left(3 \, c^{7} d^{9} e^{5} + 380 \, a c^{6} d^{7} e^{7} + 185 \, a^{2} c^{5} d^{5} e^{9}\right)} x^{4} - 16 \, {\left(27 \, c^{7} d^{10} e^{4} - 93 \, a c^{6} d^{8} e^{6} - 2095 \, a^{2} c^{5} d^{6} e^{8} - 15 \, a^{3} c^{4} d^{4} e^{10}\right)} x^{3} + 8 \, {\left(63 \, c^{7} d^{11} e^{3} - 218 \, a c^{6} d^{9} e^{5} + 228 \, a^{2} c^{5} d^{7} e^{7} + 90 \, a^{3} c^{4} d^{5} e^{9} - 35 \, a^{4} c^{3} d^{3} e^{11}\right)} x^{2} - 2 \, {\left(315 \, c^{7} d^{12} e^{2} - 1099 \, a c^{6} d^{10} e^{4} + 1166 \, a^{2} c^{5} d^{8} e^{6} - 150 \, a^{3} c^{4} d^{6} e^{8} + 455 \, a^{4} c^{3} d^{4} e^{10} - 175 \, a^{5} c^{2} d^{2} e^{12}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{215040 \, c^{5} d^{5} e^{6}}\right]"," ",0,"[-1/430080*(105*(9*c^7*d^14 - 35*a*c^6*d^12*e^2 + 45*a^2*c^5*d^10*e^4 - 15*a^3*c^4*d^8*e^6 - 5*a^4*c^3*d^6*e^8 - 9*a^5*c^2*d^4*e^10 + 15*a^6*c*d^2*e^12 - 5*a^7*e^14)*sqrt(c*d*e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) - 4*(15360*c^7*d^7*e^7*x^6 + 945*c^7*d^13*e - 3360*a*c^6*d^11*e^3 + 3689*a^2*c^5*d^9*e^5 - 600*a^3*c^4*d^7*e^7 - 525*a^4*c^3*d^5*e^9 + 1400*a^5*c^2*d^3*e^11 - 525*a^6*c*d*e^13 + 1280*(15*c^7*d^8*e^6 + 29*a*c^6*d^6*e^8)*x^5 + 128*(3*c^7*d^9*e^5 + 380*a*c^6*d^7*e^7 + 185*a^2*c^5*d^5*e^9)*x^4 - 16*(27*c^7*d^10*e^4 - 93*a*c^6*d^8*e^6 - 2095*a^2*c^5*d^6*e^8 - 15*a^3*c^4*d^4*e^10)*x^3 + 8*(63*c^7*d^11*e^3 - 218*a*c^6*d^9*e^5 + 228*a^2*c^5*d^7*e^7 + 90*a^3*c^4*d^5*e^9 - 35*a^4*c^3*d^3*e^11)*x^2 - 2*(315*c^7*d^12*e^2 - 1099*a*c^6*d^10*e^4 + 1166*a^2*c^5*d^8*e^6 - 150*a^3*c^4*d^6*e^8 + 455*a^4*c^3*d^4*e^10 - 175*a^5*c^2*d^2*e^12)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^5*d^5*e^6), 1/215040*(105*(9*c^7*d^14 - 35*a*c^6*d^12*e^2 + 45*a^2*c^5*d^10*e^4 - 15*a^3*c^4*d^8*e^6 - 5*a^4*c^3*d^6*e^8 - 9*a^5*c^2*d^4*e^10 + 15*a^6*c*d^2*e^12 - 5*a^7*e^14)*sqrt(-c*d*e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)) + 2*(15360*c^7*d^7*e^7*x^6 + 945*c^7*d^13*e - 3360*a*c^6*d^11*e^3 + 3689*a^2*c^5*d^9*e^5 - 600*a^3*c^4*d^7*e^7 - 525*a^4*c^3*d^5*e^9 + 1400*a^5*c^2*d^3*e^11 - 525*a^6*c*d*e^13 + 1280*(15*c^7*d^8*e^6 + 29*a*c^6*d^6*e^8)*x^5 + 128*(3*c^7*d^9*e^5 + 380*a*c^6*d^7*e^7 + 185*a^2*c^5*d^5*e^9)*x^4 - 16*(27*c^7*d^10*e^4 - 93*a*c^6*d^8*e^6 - 2095*a^2*c^5*d^6*e^8 - 15*a^3*c^4*d^4*e^10)*x^3 + 8*(63*c^7*d^11*e^3 - 218*a*c^6*d^9*e^5 + 228*a^2*c^5*d^7*e^7 + 90*a^3*c^4*d^5*e^9 - 35*a^4*c^3*d^3*e^11)*x^2 - 2*(315*c^7*d^12*e^2 - 1099*a*c^6*d^10*e^4 + 1166*a^2*c^5*d^8*e^6 - 150*a^3*c^4*d^6*e^8 + 455*a^4*c^3*d^4*e^10 - 175*a^5*c^2*d^2*e^12)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^5*d^5*e^6)]","A",0
459,1,1046,0,0.490770," ","integrate(x*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(7 \, c^{6} d^{12} - 30 \, a c^{5} d^{10} e^{2} + 45 \, a^{2} c^{4} d^{8} e^{4} - 20 \, a^{3} c^{3} d^{6} e^{6} - 15 \, a^{4} c^{2} d^{4} e^{8} + 18 \, a^{5} c d^{2} e^{10} - 5 \, a^{6} e^{12}\right)} \sqrt{c d e} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) - 4 \, {\left(1280 \, c^{6} d^{6} e^{6} x^{5} - 105 \, c^{6} d^{11} e + 415 \, a c^{5} d^{9} e^{3} - 546 \, a^{2} c^{4} d^{7} e^{5} + 150 \, a^{3} c^{3} d^{5} e^{7} - 245 \, a^{4} c^{2} d^{3} e^{9} + 75 \, a^{5} c d e^{11} + 128 \, {\left(13 \, c^{6} d^{7} e^{5} + 25 \, a c^{5} d^{5} e^{7}\right)} x^{4} + 16 \, {\left(3 \, c^{6} d^{8} e^{4} + 278 \, a c^{5} d^{6} e^{6} + 135 \, a^{2} c^{4} d^{4} e^{8}\right)} x^{3} - 8 \, {\left(7 \, c^{6} d^{9} e^{3} - 27 \, a c^{5} d^{7} e^{5} - 423 \, a^{2} c^{4} d^{5} e^{7} - 5 \, a^{3} c^{3} d^{3} e^{9}\right)} x^{2} + 2 \, {\left(35 \, c^{6} d^{10} e^{2} - 136 \, a c^{5} d^{8} e^{4} + 174 \, a^{2} c^{4} d^{6} e^{6} + 80 \, a^{3} c^{3} d^{4} e^{8} - 25 \, a^{4} c^{2} d^{2} e^{10}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{30720 \, c^{4} d^{4} e^{5}}, -\frac{15 \, {\left(7 \, c^{6} d^{12} - 30 \, a c^{5} d^{10} e^{2} + 45 \, a^{2} c^{4} d^{8} e^{4} - 20 \, a^{3} c^{3} d^{6} e^{6} - 15 \, a^{4} c^{2} d^{4} e^{8} + 18 \, a^{5} c d^{2} e^{10} - 5 \, a^{6} e^{12}\right)} \sqrt{-c d e} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right) - 2 \, {\left(1280 \, c^{6} d^{6} e^{6} x^{5} - 105 \, c^{6} d^{11} e + 415 \, a c^{5} d^{9} e^{3} - 546 \, a^{2} c^{4} d^{7} e^{5} + 150 \, a^{3} c^{3} d^{5} e^{7} - 245 \, a^{4} c^{2} d^{3} e^{9} + 75 \, a^{5} c d e^{11} + 128 \, {\left(13 \, c^{6} d^{7} e^{5} + 25 \, a c^{5} d^{5} e^{7}\right)} x^{4} + 16 \, {\left(3 \, c^{6} d^{8} e^{4} + 278 \, a c^{5} d^{6} e^{6} + 135 \, a^{2} c^{4} d^{4} e^{8}\right)} x^{3} - 8 \, {\left(7 \, c^{6} d^{9} e^{3} - 27 \, a c^{5} d^{7} e^{5} - 423 \, a^{2} c^{4} d^{5} e^{7} - 5 \, a^{3} c^{3} d^{3} e^{9}\right)} x^{2} + 2 \, {\left(35 \, c^{6} d^{10} e^{2} - 136 \, a c^{5} d^{8} e^{4} + 174 \, a^{2} c^{4} d^{6} e^{6} + 80 \, a^{3} c^{3} d^{4} e^{8} - 25 \, a^{4} c^{2} d^{2} e^{10}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{15360 \, c^{4} d^{4} e^{5}}\right]"," ",0,"[-1/30720*(15*(7*c^6*d^12 - 30*a*c^5*d^10*e^2 + 45*a^2*c^4*d^8*e^4 - 20*a^3*c^3*d^6*e^6 - 15*a^4*c^2*d^4*e^8 + 18*a^5*c*d^2*e^10 - 5*a^6*e^12)*sqrt(c*d*e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) - 4*(1280*c^6*d^6*e^6*x^5 - 105*c^6*d^11*e + 415*a*c^5*d^9*e^3 - 546*a^2*c^4*d^7*e^5 + 150*a^3*c^3*d^5*e^7 - 245*a^4*c^2*d^3*e^9 + 75*a^5*c*d*e^11 + 128*(13*c^6*d^7*e^5 + 25*a*c^5*d^5*e^7)*x^4 + 16*(3*c^6*d^8*e^4 + 278*a*c^5*d^6*e^6 + 135*a^2*c^4*d^4*e^8)*x^3 - 8*(7*c^6*d^9*e^3 - 27*a*c^5*d^7*e^5 - 423*a^2*c^4*d^5*e^7 - 5*a^3*c^3*d^3*e^9)*x^2 + 2*(35*c^6*d^10*e^2 - 136*a*c^5*d^8*e^4 + 174*a^2*c^4*d^6*e^6 + 80*a^3*c^3*d^4*e^8 - 25*a^4*c^2*d^2*e^10)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^4*d^4*e^5), -1/15360*(15*(7*c^6*d^12 - 30*a*c^5*d^10*e^2 + 45*a^2*c^4*d^8*e^4 - 20*a^3*c^3*d^6*e^6 - 15*a^4*c^2*d^4*e^8 + 18*a^5*c*d^2*e^10 - 5*a^6*e^12)*sqrt(-c*d*e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)) - 2*(1280*c^6*d^6*e^6*x^5 - 105*c^6*d^11*e + 415*a*c^5*d^9*e^3 - 546*a^2*c^4*d^7*e^5 + 150*a^3*c^3*d^5*e^7 - 245*a^4*c^2*d^3*e^9 + 75*a^5*c*d*e^11 + 128*(13*c^6*d^7*e^5 + 25*a*c^5*d^5*e^7)*x^4 + 16*(3*c^6*d^8*e^4 + 278*a*c^5*d^6*e^6 + 135*a^2*c^4*d^4*e^8)*x^3 - 8*(7*c^6*d^9*e^3 - 27*a*c^5*d^7*e^5 - 423*a^2*c^4*d^5*e^7 - 5*a^3*c^3*d^3*e^9)*x^2 + 2*(35*c^6*d^10*e^2 - 136*a*c^5*d^8*e^4 + 174*a^2*c^4*d^6*e^6 + 80*a^3*c^3*d^4*e^8 - 25*a^4*c^2*d^2*e^10)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^4*d^4*e^5)]","A",0
460,1,844,0,0.460536," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(c^{5} d^{10} - 5 \, a c^{4} d^{8} e^{2} + 10 \, a^{2} c^{3} d^{6} e^{4} - 10 \, a^{3} c^{2} d^{4} e^{6} + 5 \, a^{4} c d^{2} e^{8} - a^{5} e^{10}\right)} \sqrt{c d e} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) + 4 \, {\left(128 \, c^{5} d^{5} e^{5} x^{4} + 15 \, c^{5} d^{9} e - 70 \, a c^{4} d^{7} e^{3} + 128 \, a^{2} c^{3} d^{5} e^{5} + 70 \, a^{3} c^{2} d^{3} e^{7} - 15 \, a^{4} c d e^{9} + 16 \, {\left(11 \, c^{5} d^{6} e^{4} + 21 \, a c^{4} d^{4} e^{6}\right)} x^{3} + 8 \, {\left(c^{5} d^{7} e^{3} + 64 \, a c^{4} d^{5} e^{5} + 31 \, a^{2} c^{3} d^{3} e^{7}\right)} x^{2} - 2 \, {\left(5 \, c^{5} d^{8} e^{2} - 23 \, a c^{4} d^{6} e^{4} - 233 \, a^{2} c^{3} d^{4} e^{6} - 5 \, a^{3} c^{2} d^{2} e^{8}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{2560 \, c^{3} d^{3} e^{4}}, \frac{15 \, {\left(c^{5} d^{10} - 5 \, a c^{4} d^{8} e^{2} + 10 \, a^{2} c^{3} d^{6} e^{4} - 10 \, a^{3} c^{2} d^{4} e^{6} + 5 \, a^{4} c d^{2} e^{8} - a^{5} e^{10}\right)} \sqrt{-c d e} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right) + 2 \, {\left(128 \, c^{5} d^{5} e^{5} x^{4} + 15 \, c^{5} d^{9} e - 70 \, a c^{4} d^{7} e^{3} + 128 \, a^{2} c^{3} d^{5} e^{5} + 70 \, a^{3} c^{2} d^{3} e^{7} - 15 \, a^{4} c d e^{9} + 16 \, {\left(11 \, c^{5} d^{6} e^{4} + 21 \, a c^{4} d^{4} e^{6}\right)} x^{3} + 8 \, {\left(c^{5} d^{7} e^{3} + 64 \, a c^{4} d^{5} e^{5} + 31 \, a^{2} c^{3} d^{3} e^{7}\right)} x^{2} - 2 \, {\left(5 \, c^{5} d^{8} e^{2} - 23 \, a c^{4} d^{6} e^{4} - 233 \, a^{2} c^{3} d^{4} e^{6} - 5 \, a^{3} c^{2} d^{2} e^{8}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{1280 \, c^{3} d^{3} e^{4}}\right]"," ",0,"[1/2560*(15*(c^5*d^10 - 5*a*c^4*d^8*e^2 + 10*a^2*c^3*d^6*e^4 - 10*a^3*c^2*d^4*e^6 + 5*a^4*c*d^2*e^8 - a^5*e^10)*sqrt(c*d*e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) + 4*(128*c^5*d^5*e^5*x^4 + 15*c^5*d^9*e - 70*a*c^4*d^7*e^3 + 128*a^2*c^3*d^5*e^5 + 70*a^3*c^2*d^3*e^7 - 15*a^4*c*d*e^9 + 16*(11*c^5*d^6*e^4 + 21*a*c^4*d^4*e^6)*x^3 + 8*(c^5*d^7*e^3 + 64*a*c^4*d^5*e^5 + 31*a^2*c^3*d^3*e^7)*x^2 - 2*(5*c^5*d^8*e^2 - 23*a*c^4*d^6*e^4 - 233*a^2*c^3*d^4*e^6 - 5*a^3*c^2*d^2*e^8)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^3*d^3*e^4), 1/1280*(15*(c^5*d^10 - 5*a*c^4*d^8*e^2 + 10*a^2*c^3*d^6*e^4 - 10*a^3*c^2*d^4*e^6 + 5*a^4*c*d^2*e^8 - a^5*e^10)*sqrt(-c*d*e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)) + 2*(128*c^5*d^5*e^5*x^4 + 15*c^5*d^9*e - 70*a*c^4*d^7*e^3 + 128*a^2*c^3*d^5*e^5 + 70*a^3*c^2*d^3*e^7 - 15*a^4*c*d*e^9 + 16*(11*c^5*d^6*e^4 + 21*a*c^4*d^4*e^6)*x^3 + 8*(c^5*d^7*e^3 + 64*a*c^4*d^5*e^5 + 31*a^2*c^3*d^3*e^7)*x^2 - 2*(5*c^5*d^8*e^2 - 23*a*c^4*d^6*e^4 - 233*a^2*c^3*d^4*e^6 - 5*a^3*c^2*d^2*e^8)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^3*d^3*e^4)]","A",0
461,1,1873,0,45.740614," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/x/(e*x+d),x, algorithm=""fricas"")","\left[\frac{384 \, \sqrt{a d e} a^{2} c^{2} d^{3} e^{5} \log\left(\frac{8 \, a^{2} d^{2} e^{2} + {\left(c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} x^{2} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{a d e} + 8 \, {\left(a c d^{3} e + a^{2} d e^{3}\right)} x}{x^{2}}\right) - 3 \, {\left(3 \, c^{4} d^{8} - 20 \, a c^{3} d^{6} e^{2} + 90 \, a^{2} c^{2} d^{4} e^{4} + 60 \, a^{3} c d^{2} e^{6} - 5 \, a^{4} e^{8}\right)} \sqrt{c d e} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) + 4 \, {\left(48 \, c^{4} d^{4} e^{4} x^{3} - 9 \, c^{4} d^{7} e + 57 \, a c^{3} d^{5} e^{3} + 337 \, a^{2} c^{2} d^{3} e^{5} + 15 \, a^{3} c d e^{7} + 8 \, {\left(9 \, c^{4} d^{5} e^{3} + 17 \, a c^{3} d^{3} e^{5}\right)} x^{2} + 2 \, {\left(3 \, c^{4} d^{6} e^{2} + 122 \, a c^{3} d^{4} e^{4} + 59 \, a^{2} c^{2} d^{2} e^{6}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{768 \, c^{2} d^{2} e^{3}}, \frac{192 \, \sqrt{a d e} a^{2} c^{2} d^{3} e^{5} \log\left(\frac{8 \, a^{2} d^{2} e^{2} + {\left(c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} x^{2} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{a d e} + 8 \, {\left(a c d^{3} e + a^{2} d e^{3}\right)} x}{x^{2}}\right) - 3 \, {\left(3 \, c^{4} d^{8} - 20 \, a c^{3} d^{6} e^{2} + 90 \, a^{2} c^{2} d^{4} e^{4} + 60 \, a^{3} c d^{2} e^{6} - 5 \, a^{4} e^{8}\right)} \sqrt{-c d e} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right) + 2 \, {\left(48 \, c^{4} d^{4} e^{4} x^{3} - 9 \, c^{4} d^{7} e + 57 \, a c^{3} d^{5} e^{3} + 337 \, a^{2} c^{2} d^{3} e^{5} + 15 \, a^{3} c d e^{7} + 8 \, {\left(9 \, c^{4} d^{5} e^{3} + 17 \, a c^{3} d^{3} e^{5}\right)} x^{2} + 2 \, {\left(3 \, c^{4} d^{6} e^{2} + 122 \, a c^{3} d^{4} e^{4} + 59 \, a^{2} c^{2} d^{2} e^{6}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{384 \, c^{2} d^{2} e^{3}}, \frac{768 \, \sqrt{-a d e} a^{2} c^{2} d^{3} e^{5} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{-a d e}}{2 \, {\left(a c d^{2} e^{2} x^{2} + a^{2} d^{2} e^{2} + {\left(a c d^{3} e + a^{2} d e^{3}\right)} x\right)}}\right) - 3 \, {\left(3 \, c^{4} d^{8} - 20 \, a c^{3} d^{6} e^{2} + 90 \, a^{2} c^{2} d^{4} e^{4} + 60 \, a^{3} c d^{2} e^{6} - 5 \, a^{4} e^{8}\right)} \sqrt{c d e} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) + 4 \, {\left(48 \, c^{4} d^{4} e^{4} x^{3} - 9 \, c^{4} d^{7} e + 57 \, a c^{3} d^{5} e^{3} + 337 \, a^{2} c^{2} d^{3} e^{5} + 15 \, a^{3} c d e^{7} + 8 \, {\left(9 \, c^{4} d^{5} e^{3} + 17 \, a c^{3} d^{3} e^{5}\right)} x^{2} + 2 \, {\left(3 \, c^{4} d^{6} e^{2} + 122 \, a c^{3} d^{4} e^{4} + 59 \, a^{2} c^{2} d^{2} e^{6}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{768 \, c^{2} d^{2} e^{3}}, \frac{384 \, \sqrt{-a d e} a^{2} c^{2} d^{3} e^{5} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{-a d e}}{2 \, {\left(a c d^{2} e^{2} x^{2} + a^{2} d^{2} e^{2} + {\left(a c d^{3} e + a^{2} d e^{3}\right)} x\right)}}\right) - 3 \, {\left(3 \, c^{4} d^{8} - 20 \, a c^{3} d^{6} e^{2} + 90 \, a^{2} c^{2} d^{4} e^{4} + 60 \, a^{3} c d^{2} e^{6} - 5 \, a^{4} e^{8}\right)} \sqrt{-c d e} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right) + 2 \, {\left(48 \, c^{4} d^{4} e^{4} x^{3} - 9 \, c^{4} d^{7} e + 57 \, a c^{3} d^{5} e^{3} + 337 \, a^{2} c^{2} d^{3} e^{5} + 15 \, a^{3} c d e^{7} + 8 \, {\left(9 \, c^{4} d^{5} e^{3} + 17 \, a c^{3} d^{3} e^{5}\right)} x^{2} + 2 \, {\left(3 \, c^{4} d^{6} e^{2} + 122 \, a c^{3} d^{4} e^{4} + 59 \, a^{2} c^{2} d^{2} e^{6}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{384 \, c^{2} d^{2} e^{3}}\right]"," ",0,"[1/768*(384*sqrt(a*d*e)*a^2*c^2*d^3*e^5*log((8*a^2*d^2*e^2 + (c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4)*x^2 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(a*d*e) + 8*(a*c*d^3*e + a^2*d*e^3)*x)/x^2) - 3*(3*c^4*d^8 - 20*a*c^3*d^6*e^2 + 90*a^2*c^2*d^4*e^4 + 60*a^3*c*d^2*e^6 - 5*a^4*e^8)*sqrt(c*d*e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) + 4*(48*c^4*d^4*e^4*x^3 - 9*c^4*d^7*e + 57*a*c^3*d^5*e^3 + 337*a^2*c^2*d^3*e^5 + 15*a^3*c*d*e^7 + 8*(9*c^4*d^5*e^3 + 17*a*c^3*d^3*e^5)*x^2 + 2*(3*c^4*d^6*e^2 + 122*a*c^3*d^4*e^4 + 59*a^2*c^2*d^2*e^6)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^2*d^2*e^3), 1/384*(192*sqrt(a*d*e)*a^2*c^2*d^3*e^5*log((8*a^2*d^2*e^2 + (c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4)*x^2 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(a*d*e) + 8*(a*c*d^3*e + a^2*d*e^3)*x)/x^2) - 3*(3*c^4*d^8 - 20*a*c^3*d^6*e^2 + 90*a^2*c^2*d^4*e^4 + 60*a^3*c*d^2*e^6 - 5*a^4*e^8)*sqrt(-c*d*e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)) + 2*(48*c^4*d^4*e^4*x^3 - 9*c^4*d^7*e + 57*a*c^3*d^5*e^3 + 337*a^2*c^2*d^3*e^5 + 15*a^3*c*d*e^7 + 8*(9*c^4*d^5*e^3 + 17*a*c^3*d^3*e^5)*x^2 + 2*(3*c^4*d^6*e^2 + 122*a*c^3*d^4*e^4 + 59*a^2*c^2*d^2*e^6)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^2*d^2*e^3), 1/768*(768*sqrt(-a*d*e)*a^2*c^2*d^3*e^5*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-a*d*e)/(a*c*d^2*e^2*x^2 + a^2*d^2*e^2 + (a*c*d^3*e + a^2*d*e^3)*x)) - 3*(3*c^4*d^8 - 20*a*c^3*d^6*e^2 + 90*a^2*c^2*d^4*e^4 + 60*a^3*c*d^2*e^6 - 5*a^4*e^8)*sqrt(c*d*e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) + 4*(48*c^4*d^4*e^4*x^3 - 9*c^4*d^7*e + 57*a*c^3*d^5*e^3 + 337*a^2*c^2*d^3*e^5 + 15*a^3*c*d*e^7 + 8*(9*c^4*d^5*e^3 + 17*a*c^3*d^3*e^5)*x^2 + 2*(3*c^4*d^6*e^2 + 122*a*c^3*d^4*e^4 + 59*a^2*c^2*d^2*e^6)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^2*d^2*e^3), 1/384*(384*sqrt(-a*d*e)*a^2*c^2*d^3*e^5*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-a*d*e)/(a*c*d^2*e^2*x^2 + a^2*d^2*e^2 + (a*c*d^3*e + a^2*d*e^3)*x)) - 3*(3*c^4*d^8 - 20*a*c^3*d^6*e^2 + 90*a^2*c^2*d^4*e^4 + 60*a^3*c*d^2*e^6 - 5*a^4*e^8)*sqrt(-c*d*e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)) + 2*(48*c^4*d^4*e^4*x^3 - 9*c^4*d^7*e + 57*a*c^3*d^5*e^3 + 337*a^2*c^2*d^3*e^5 + 15*a^3*c*d*e^7 + 8*(9*c^4*d^5*e^3 + 17*a*c^3*d^3*e^5)*x^2 + 2*(3*c^4*d^6*e^2 + 122*a*c^3*d^4*e^4 + 59*a^2*c^2*d^2*e^6)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^2*d^2*e^3)]","A",0
462,1,1717,0,15.202034," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/x^2/(e*x+d),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(c^{3} d^{6} - 15 \, a c^{2} d^{4} e^{2} - 45 \, a^{2} c d^{2} e^{4} - 5 \, a^{3} e^{6}\right)} \sqrt{c d e} x \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) - 24 \, {\left(5 \, a c^{2} d^{3} e^{3} + 3 \, a^{2} c d e^{5}\right)} \sqrt{a d e} x \log\left(\frac{8 \, a^{2} d^{2} e^{2} + {\left(c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} x^{2} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{a d e} + 8 \, {\left(a c d^{3} e + a^{2} d e^{3}\right)} x}{x^{2}}\right) - 4 \, {\left(8 \, c^{3} d^{3} e^{3} x^{3} - 24 \, a^{2} c d^{2} e^{4} + 2 \, {\left(7 \, c^{3} d^{4} e^{2} + 13 \, a c^{2} d^{2} e^{4}\right)} x^{2} + {\left(3 \, c^{3} d^{5} e + 68 \, a c^{2} d^{3} e^{3} + 33 \, a^{2} c d e^{5}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{96 \, c d e^{2} x}, \frac{3 \, {\left(c^{3} d^{6} - 15 \, a c^{2} d^{4} e^{2} - 45 \, a^{2} c d^{2} e^{4} - 5 \, a^{3} e^{6}\right)} \sqrt{-c d e} x \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right) + 12 \, {\left(5 \, a c^{2} d^{3} e^{3} + 3 \, a^{2} c d e^{5}\right)} \sqrt{a d e} x \log\left(\frac{8 \, a^{2} d^{2} e^{2} + {\left(c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} x^{2} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{a d e} + 8 \, {\left(a c d^{3} e + a^{2} d e^{3}\right)} x}{x^{2}}\right) + 2 \, {\left(8 \, c^{3} d^{3} e^{3} x^{3} - 24 \, a^{2} c d^{2} e^{4} + 2 \, {\left(7 \, c^{3} d^{4} e^{2} + 13 \, a c^{2} d^{2} e^{4}\right)} x^{2} + {\left(3 \, c^{3} d^{5} e + 68 \, a c^{2} d^{3} e^{3} + 33 \, a^{2} c d e^{5}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{48 \, c d e^{2} x}, \frac{48 \, {\left(5 \, a c^{2} d^{3} e^{3} + 3 \, a^{2} c d e^{5}\right)} \sqrt{-a d e} x \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{-a d e}}{2 \, {\left(a c d^{2} e^{2} x^{2} + a^{2} d^{2} e^{2} + {\left(a c d^{3} e + a^{2} d e^{3}\right)} x\right)}}\right) - 3 \, {\left(c^{3} d^{6} - 15 \, a c^{2} d^{4} e^{2} - 45 \, a^{2} c d^{2} e^{4} - 5 \, a^{3} e^{6}\right)} \sqrt{c d e} x \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) + 4 \, {\left(8 \, c^{3} d^{3} e^{3} x^{3} - 24 \, a^{2} c d^{2} e^{4} + 2 \, {\left(7 \, c^{3} d^{4} e^{2} + 13 \, a c^{2} d^{2} e^{4}\right)} x^{2} + {\left(3 \, c^{3} d^{5} e + 68 \, a c^{2} d^{3} e^{3} + 33 \, a^{2} c d e^{5}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{96 \, c d e^{2} x}, \frac{24 \, {\left(5 \, a c^{2} d^{3} e^{3} + 3 \, a^{2} c d e^{5}\right)} \sqrt{-a d e} x \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{-a d e}}{2 \, {\left(a c d^{2} e^{2} x^{2} + a^{2} d^{2} e^{2} + {\left(a c d^{3} e + a^{2} d e^{3}\right)} x\right)}}\right) + 3 \, {\left(c^{3} d^{6} - 15 \, a c^{2} d^{4} e^{2} - 45 \, a^{2} c d^{2} e^{4} - 5 \, a^{3} e^{6}\right)} \sqrt{-c d e} x \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right) + 2 \, {\left(8 \, c^{3} d^{3} e^{3} x^{3} - 24 \, a^{2} c d^{2} e^{4} + 2 \, {\left(7 \, c^{3} d^{4} e^{2} + 13 \, a c^{2} d^{2} e^{4}\right)} x^{2} + {\left(3 \, c^{3} d^{5} e + 68 \, a c^{2} d^{3} e^{3} + 33 \, a^{2} c d e^{5}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{48 \, c d e^{2} x}\right]"," ",0,"[-1/96*(3*(c^3*d^6 - 15*a*c^2*d^4*e^2 - 45*a^2*c*d^2*e^4 - 5*a^3*e^6)*sqrt(c*d*e)*x*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) - 24*(5*a*c^2*d^3*e^3 + 3*a^2*c*d*e^5)*sqrt(a*d*e)*x*log((8*a^2*d^2*e^2 + (c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4)*x^2 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(a*d*e) + 8*(a*c*d^3*e + a^2*d*e^3)*x)/x^2) - 4*(8*c^3*d^3*e^3*x^3 - 24*a^2*c*d^2*e^4 + 2*(7*c^3*d^4*e^2 + 13*a*c^2*d^2*e^4)*x^2 + (3*c^3*d^5*e + 68*a*c^2*d^3*e^3 + 33*a^2*c*d*e^5)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c*d*e^2*x), 1/48*(3*(c^3*d^6 - 15*a*c^2*d^4*e^2 - 45*a^2*c*d^2*e^4 - 5*a^3*e^6)*sqrt(-c*d*e)*x*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)) + 12*(5*a*c^2*d^3*e^3 + 3*a^2*c*d*e^5)*sqrt(a*d*e)*x*log((8*a^2*d^2*e^2 + (c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4)*x^2 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(a*d*e) + 8*(a*c*d^3*e + a^2*d*e^3)*x)/x^2) + 2*(8*c^3*d^3*e^3*x^3 - 24*a^2*c*d^2*e^4 + 2*(7*c^3*d^4*e^2 + 13*a*c^2*d^2*e^4)*x^2 + (3*c^3*d^5*e + 68*a*c^2*d^3*e^3 + 33*a^2*c*d*e^5)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c*d*e^2*x), 1/96*(48*(5*a*c^2*d^3*e^3 + 3*a^2*c*d*e^5)*sqrt(-a*d*e)*x*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-a*d*e)/(a*c*d^2*e^2*x^2 + a^2*d^2*e^2 + (a*c*d^3*e + a^2*d*e^3)*x)) - 3*(c^3*d^6 - 15*a*c^2*d^4*e^2 - 45*a^2*c*d^2*e^4 - 5*a^3*e^6)*sqrt(c*d*e)*x*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) + 4*(8*c^3*d^3*e^3*x^3 - 24*a^2*c*d^2*e^4 + 2*(7*c^3*d^4*e^2 + 13*a*c^2*d^2*e^4)*x^2 + (3*c^3*d^5*e + 68*a*c^2*d^3*e^3 + 33*a^2*c*d*e^5)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c*d*e^2*x), 1/48*(24*(5*a*c^2*d^3*e^3 + 3*a^2*c*d*e^5)*sqrt(-a*d*e)*x*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-a*d*e)/(a*c*d^2*e^2*x^2 + a^2*d^2*e^2 + (a*c*d^3*e + a^2*d*e^3)*x)) + 3*(c^3*d^6 - 15*a*c^2*d^4*e^2 - 45*a^2*c*d^2*e^4 - 5*a^3*e^6)*sqrt(-c*d*e)*x*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)) + 2*(8*c^3*d^3*e^3*x^3 - 24*a^2*c*d^2*e^4 + 2*(7*c^3*d^4*e^2 + 13*a*c^2*d^2*e^4)*x^2 + (3*c^3*d^5*e + 68*a*c^2*d^3*e^3 + 33*a^2*c*d*e^5)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c*d*e^2*x)]","A",0
463,1,1569,0,7.419348," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/x^3/(e*x+d),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(c^{2} d^{4} + 10 \, a c d^{2} e^{2} + 5 \, a^{2} e^{4}\right)} \sqrt{\frac{c d}{e}} x^{2} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} + 4 \, {\left(2 \, c d e^{2} x + c d^{2} e + a e^{3}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{\frac{c d}{e}} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) + 3 \, {\left(5 \, c^{2} d^{4} + 10 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \sqrt{\frac{a e}{d}} x^{2} \log\left(\frac{8 \, a^{2} d^{2} e^{2} + {\left(c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} x^{2} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d^{2} e + {\left(c d^{3} + a d e^{2}\right)} x\right)} \sqrt{\frac{a e}{d}} + 8 \, {\left(a c d^{3} e + a^{2} d e^{3}\right)} x}{x^{2}}\right) + 4 \, {\left(2 \, c^{2} d^{2} e x^{3} - 2 \, a^{2} d e^{2} + {\left(5 \, c^{2} d^{3} + 9 \, a c d e^{2}\right)} x^{2} - {\left(9 \, a c d^{2} e + 5 \, a^{2} e^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{16 \, x^{2}}, -\frac{6 \, {\left(c^{2} d^{4} + 10 \, a c d^{2} e^{2} + 5 \, a^{2} e^{4}\right)} \sqrt{-\frac{c d}{e}} x^{2} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-\frac{c d}{e}}}{2 \, {\left(c^{2} d^{2} e x^{2} + a c d^{2} e + {\left(c^{2} d^{3} + a c d e^{2}\right)} x\right)}}\right) - 3 \, {\left(5 \, c^{2} d^{4} + 10 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \sqrt{\frac{a e}{d}} x^{2} \log\left(\frac{8 \, a^{2} d^{2} e^{2} + {\left(c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} x^{2} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d^{2} e + {\left(c d^{3} + a d e^{2}\right)} x\right)} \sqrt{\frac{a e}{d}} + 8 \, {\left(a c d^{3} e + a^{2} d e^{3}\right)} x}{x^{2}}\right) - 4 \, {\left(2 \, c^{2} d^{2} e x^{3} - 2 \, a^{2} d e^{2} + {\left(5 \, c^{2} d^{3} + 9 \, a c d e^{2}\right)} x^{2} - {\left(9 \, a c d^{2} e + 5 \, a^{2} e^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{16 \, x^{2}}, \frac{6 \, {\left(5 \, c^{2} d^{4} + 10 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \sqrt{-\frac{a e}{d}} x^{2} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{-\frac{a e}{d}}}{2 \, {\left(a c d e^{2} x^{2} + a^{2} d e^{2} + {\left(a c d^{2} e + a^{2} e^{3}\right)} x\right)}}\right) + 3 \, {\left(c^{2} d^{4} + 10 \, a c d^{2} e^{2} + 5 \, a^{2} e^{4}\right)} \sqrt{\frac{c d}{e}} x^{2} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} + 4 \, {\left(2 \, c d e^{2} x + c d^{2} e + a e^{3}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{\frac{c d}{e}} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) + 4 \, {\left(2 \, c^{2} d^{2} e x^{3} - 2 \, a^{2} d e^{2} + {\left(5 \, c^{2} d^{3} + 9 \, a c d e^{2}\right)} x^{2} - {\left(9 \, a c d^{2} e + 5 \, a^{2} e^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{16 \, x^{2}}, -\frac{3 \, {\left(c^{2} d^{4} + 10 \, a c d^{2} e^{2} + 5 \, a^{2} e^{4}\right)} \sqrt{-\frac{c d}{e}} x^{2} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-\frac{c d}{e}}}{2 \, {\left(c^{2} d^{2} e x^{2} + a c d^{2} e + {\left(c^{2} d^{3} + a c d e^{2}\right)} x\right)}}\right) - 3 \, {\left(5 \, c^{2} d^{4} + 10 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \sqrt{-\frac{a e}{d}} x^{2} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{-\frac{a e}{d}}}{2 \, {\left(a c d e^{2} x^{2} + a^{2} d e^{2} + {\left(a c d^{2} e + a^{2} e^{3}\right)} x\right)}}\right) - 2 \, {\left(2 \, c^{2} d^{2} e x^{3} - 2 \, a^{2} d e^{2} + {\left(5 \, c^{2} d^{3} + 9 \, a c d e^{2}\right)} x^{2} - {\left(9 \, a c d^{2} e + 5 \, a^{2} e^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{8 \, x^{2}}\right]"," ",0,"[1/16*(3*(c^2*d^4 + 10*a*c*d^2*e^2 + 5*a^2*e^4)*sqrt(c*d/e)*x^2*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 + 4*(2*c*d*e^2*x + c*d^2*e + a*e^3)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(c*d/e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) + 3*(5*c^2*d^4 + 10*a*c*d^2*e^2 + a^2*e^4)*sqrt(a*e/d)*x^2*log((8*a^2*d^2*e^2 + (c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4)*x^2 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d^2*e + (c*d^3 + a*d*e^2)*x)*sqrt(a*e/d) + 8*(a*c*d^3*e + a^2*d*e^3)*x)/x^2) + 4*(2*c^2*d^2*e*x^3 - 2*a^2*d*e^2 + (5*c^2*d^3 + 9*a*c*d*e^2)*x^2 - (9*a*c*d^2*e + 5*a^2*e^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/x^2, -1/16*(6*(c^2*d^4 + 10*a*c*d^2*e^2 + 5*a^2*e^4)*sqrt(-c*d/e)*x^2*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d/e)/(c^2*d^2*e*x^2 + a*c*d^2*e + (c^2*d^3 + a*c*d*e^2)*x)) - 3*(5*c^2*d^4 + 10*a*c*d^2*e^2 + a^2*e^4)*sqrt(a*e/d)*x^2*log((8*a^2*d^2*e^2 + (c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4)*x^2 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d^2*e + (c*d^3 + a*d*e^2)*x)*sqrt(a*e/d) + 8*(a*c*d^3*e + a^2*d*e^3)*x)/x^2) - 4*(2*c^2*d^2*e*x^3 - 2*a^2*d*e^2 + (5*c^2*d^3 + 9*a*c*d*e^2)*x^2 - (9*a*c*d^2*e + 5*a^2*e^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/x^2, 1/16*(6*(5*c^2*d^4 + 10*a*c*d^2*e^2 + a^2*e^4)*sqrt(-a*e/d)*x^2*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-a*e/d)/(a*c*d*e^2*x^2 + a^2*d*e^2 + (a*c*d^2*e + a^2*e^3)*x)) + 3*(c^2*d^4 + 10*a*c*d^2*e^2 + 5*a^2*e^4)*sqrt(c*d/e)*x^2*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 + 4*(2*c*d*e^2*x + c*d^2*e + a*e^3)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(c*d/e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) + 4*(2*c^2*d^2*e*x^3 - 2*a^2*d*e^2 + (5*c^2*d^3 + 9*a*c*d*e^2)*x^2 - (9*a*c*d^2*e + 5*a^2*e^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/x^2, -1/8*(3*(c^2*d^4 + 10*a*c*d^2*e^2 + 5*a^2*e^4)*sqrt(-c*d/e)*x^2*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d/e)/(c^2*d^2*e*x^2 + a*c*d^2*e + (c^2*d^3 + a*c*d*e^2)*x)) - 3*(5*c^2*d^4 + 10*a*c*d^2*e^2 + a^2*e^4)*sqrt(-a*e/d)*x^2*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-a*e/d)/(a*c*d*e^2*x^2 + a^2*d*e^2 + (a*c*d^2*e + a^2*e^3)*x)) - 2*(2*c^2*d^2*e*x^3 - 2*a^2*d*e^2 + (5*c^2*d^3 + 9*a*c*d*e^2)*x^2 - (9*a*c*d^2*e + 5*a^2*e^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/x^2]","A",0
464,1,1741,0,8.715100," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/x^4/(e*x+d),x, algorithm=""fricas"")","\left[\frac{24 \, {\left(3 \, a c^{2} d^{5} e + 5 \, a^{2} c d^{3} e^{3}\right)} \sqrt{c d e} x^{3} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) - 3 \, {\left(5 \, c^{3} d^{6} + 45 \, a c^{2} d^{4} e^{2} + 15 \, a^{2} c d^{2} e^{4} - a^{3} e^{6}\right)} \sqrt{a d e} x^{3} \log\left(\frac{8 \, a^{2} d^{2} e^{2} + {\left(c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} x^{2} + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{a d e} + 8 \, {\left(a c d^{3} e + a^{2} d e^{3}\right)} x}{x^{2}}\right) + 4 \, {\left(24 \, a c^{2} d^{4} e^{2} x^{3} - 8 \, a^{3} d^{3} e^{3} - {\left(33 \, a c^{2} d^{5} e + 68 \, a^{2} c d^{3} e^{3} + 3 \, a^{3} d e^{5}\right)} x^{2} - 2 \, {\left(13 \, a^{2} c d^{4} e^{2} + 7 \, a^{3} d^{2} e^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{96 \, a d^{2} e x^{3}}, -\frac{48 \, {\left(3 \, a c^{2} d^{5} e + 5 \, a^{2} c d^{3} e^{3}\right)} \sqrt{-c d e} x^{3} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right) + 3 \, {\left(5 \, c^{3} d^{6} + 45 \, a c^{2} d^{4} e^{2} + 15 \, a^{2} c d^{2} e^{4} - a^{3} e^{6}\right)} \sqrt{a d e} x^{3} \log\left(\frac{8 \, a^{2} d^{2} e^{2} + {\left(c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} x^{2} + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{a d e} + 8 \, {\left(a c d^{3} e + a^{2} d e^{3}\right)} x}{x^{2}}\right) - 4 \, {\left(24 \, a c^{2} d^{4} e^{2} x^{3} - 8 \, a^{3} d^{3} e^{3} - {\left(33 \, a c^{2} d^{5} e + 68 \, a^{2} c d^{3} e^{3} + 3 \, a^{3} d e^{5}\right)} x^{2} - 2 \, {\left(13 \, a^{2} c d^{4} e^{2} + 7 \, a^{3} d^{2} e^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{96 \, a d^{2} e x^{3}}, \frac{3 \, {\left(5 \, c^{3} d^{6} + 45 \, a c^{2} d^{4} e^{2} + 15 \, a^{2} c d^{2} e^{4} - a^{3} e^{6}\right)} \sqrt{-a d e} x^{3} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{-a d e}}{2 \, {\left(a c d^{2} e^{2} x^{2} + a^{2} d^{2} e^{2} + {\left(a c d^{3} e + a^{2} d e^{3}\right)} x\right)}}\right) + 12 \, {\left(3 \, a c^{2} d^{5} e + 5 \, a^{2} c d^{3} e^{3}\right)} \sqrt{c d e} x^{3} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) + 2 \, {\left(24 \, a c^{2} d^{4} e^{2} x^{3} - 8 \, a^{3} d^{3} e^{3} - {\left(33 \, a c^{2} d^{5} e + 68 \, a^{2} c d^{3} e^{3} + 3 \, a^{3} d e^{5}\right)} x^{2} - 2 \, {\left(13 \, a^{2} c d^{4} e^{2} + 7 \, a^{3} d^{2} e^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{48 \, a d^{2} e x^{3}}, \frac{3 \, {\left(5 \, c^{3} d^{6} + 45 \, a c^{2} d^{4} e^{2} + 15 \, a^{2} c d^{2} e^{4} - a^{3} e^{6}\right)} \sqrt{-a d e} x^{3} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{-a d e}}{2 \, {\left(a c d^{2} e^{2} x^{2} + a^{2} d^{2} e^{2} + {\left(a c d^{3} e + a^{2} d e^{3}\right)} x\right)}}\right) - 24 \, {\left(3 \, a c^{2} d^{5} e + 5 \, a^{2} c d^{3} e^{3}\right)} \sqrt{-c d e} x^{3} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right) + 2 \, {\left(24 \, a c^{2} d^{4} e^{2} x^{3} - 8 \, a^{3} d^{3} e^{3} - {\left(33 \, a c^{2} d^{5} e + 68 \, a^{2} c d^{3} e^{3} + 3 \, a^{3} d e^{5}\right)} x^{2} - 2 \, {\left(13 \, a^{2} c d^{4} e^{2} + 7 \, a^{3} d^{2} e^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{48 \, a d^{2} e x^{3}}\right]"," ",0,"[1/96*(24*(3*a*c^2*d^5*e + 5*a^2*c*d^3*e^3)*sqrt(c*d*e)*x^3*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) - 3*(5*c^3*d^6 + 45*a*c^2*d^4*e^2 + 15*a^2*c*d^2*e^4 - a^3*e^6)*sqrt(a*d*e)*x^3*log((8*a^2*d^2*e^2 + (c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4)*x^2 + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(a*d*e) + 8*(a*c*d^3*e + a^2*d*e^3)*x)/x^2) + 4*(24*a*c^2*d^4*e^2*x^3 - 8*a^3*d^3*e^3 - (33*a*c^2*d^5*e + 68*a^2*c*d^3*e^3 + 3*a^3*d*e^5)*x^2 - 2*(13*a^2*c*d^4*e^2 + 7*a^3*d^2*e^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(a*d^2*e*x^3), -1/96*(48*(3*a*c^2*d^5*e + 5*a^2*c*d^3*e^3)*sqrt(-c*d*e)*x^3*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)) + 3*(5*c^3*d^6 + 45*a*c^2*d^4*e^2 + 15*a^2*c*d^2*e^4 - a^3*e^6)*sqrt(a*d*e)*x^3*log((8*a^2*d^2*e^2 + (c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4)*x^2 + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(a*d*e) + 8*(a*c*d^3*e + a^2*d*e^3)*x)/x^2) - 4*(24*a*c^2*d^4*e^2*x^3 - 8*a^3*d^3*e^3 - (33*a*c^2*d^5*e + 68*a^2*c*d^3*e^3 + 3*a^3*d*e^5)*x^2 - 2*(13*a^2*c*d^4*e^2 + 7*a^3*d^2*e^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(a*d^2*e*x^3), 1/48*(3*(5*c^3*d^6 + 45*a*c^2*d^4*e^2 + 15*a^2*c*d^2*e^4 - a^3*e^6)*sqrt(-a*d*e)*x^3*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-a*d*e)/(a*c*d^2*e^2*x^2 + a^2*d^2*e^2 + (a*c*d^3*e + a^2*d*e^3)*x)) + 12*(3*a*c^2*d^5*e + 5*a^2*c*d^3*e^3)*sqrt(c*d*e)*x^3*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) + 2*(24*a*c^2*d^4*e^2*x^3 - 8*a^3*d^3*e^3 - (33*a*c^2*d^5*e + 68*a^2*c*d^3*e^3 + 3*a^3*d*e^5)*x^2 - 2*(13*a^2*c*d^4*e^2 + 7*a^3*d^2*e^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(a*d^2*e*x^3), 1/48*(3*(5*c^3*d^6 + 45*a*c^2*d^4*e^2 + 15*a^2*c*d^2*e^4 - a^3*e^6)*sqrt(-a*d*e)*x^3*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-a*d*e)/(a*c*d^2*e^2*x^2 + a^2*d^2*e^2 + (a*c*d^3*e + a^2*d*e^3)*x)) - 24*(3*a*c^2*d^5*e + 5*a^2*c*d^3*e^3)*sqrt(-c*d*e)*x^3*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)) + 2*(24*a*c^2*d^4*e^2*x^3 - 8*a^3*d^3*e^3 - (33*a*c^2*d^5*e + 68*a^2*c*d^3*e^3 + 3*a^3*d*e^5)*x^2 - 2*(13*a^2*c*d^4*e^2 + 7*a^3*d^2*e^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(a*d^2*e*x^3)]","A",0
465,1,1917,0,24.350780," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/x^5/(e*x+d),x, algorithm=""fricas"")","\left[\frac{384 \, \sqrt{c d e} a^{2} c^{2} d^{5} e^{3} x^{4} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) - 3 \, {\left(5 \, c^{4} d^{8} - 60 \, a c^{3} d^{6} e^{2} - 90 \, a^{2} c^{2} d^{4} e^{4} + 20 \, a^{3} c d^{2} e^{6} - 3 \, a^{4} e^{8}\right)} \sqrt{a d e} x^{4} \log\left(\frac{8 \, a^{2} d^{2} e^{2} + {\left(c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} x^{2} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{a d e} + 8 \, {\left(a c d^{3} e + a^{2} d e^{3}\right)} x}{x^{2}}\right) - 4 \, {\left(48 \, a^{4} d^{4} e^{4} + {\left(15 \, a c^{3} d^{7} e + 337 \, a^{2} c^{2} d^{5} e^{3} + 57 \, a^{3} c d^{3} e^{5} - 9 \, a^{4} d e^{7}\right)} x^{3} + 2 \, {\left(59 \, a^{2} c^{2} d^{6} e^{2} + 122 \, a^{3} c d^{4} e^{4} + 3 \, a^{4} d^{2} e^{6}\right)} x^{2} + 8 \, {\left(17 \, a^{3} c d^{5} e^{3} + 9 \, a^{4} d^{3} e^{5}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{768 \, a^{2} d^{3} e^{2} x^{4}}, -\frac{768 \, \sqrt{-c d e} a^{2} c^{2} d^{5} e^{3} x^{4} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right) + 3 \, {\left(5 \, c^{4} d^{8} - 60 \, a c^{3} d^{6} e^{2} - 90 \, a^{2} c^{2} d^{4} e^{4} + 20 \, a^{3} c d^{2} e^{6} - 3 \, a^{4} e^{8}\right)} \sqrt{a d e} x^{4} \log\left(\frac{8 \, a^{2} d^{2} e^{2} + {\left(c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} x^{2} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{a d e} + 8 \, {\left(a c d^{3} e + a^{2} d e^{3}\right)} x}{x^{2}}\right) + 4 \, {\left(48 \, a^{4} d^{4} e^{4} + {\left(15 \, a c^{3} d^{7} e + 337 \, a^{2} c^{2} d^{5} e^{3} + 57 \, a^{3} c d^{3} e^{5} - 9 \, a^{4} d e^{7}\right)} x^{3} + 2 \, {\left(59 \, a^{2} c^{2} d^{6} e^{2} + 122 \, a^{3} c d^{4} e^{4} + 3 \, a^{4} d^{2} e^{6}\right)} x^{2} + 8 \, {\left(17 \, a^{3} c d^{5} e^{3} + 9 \, a^{4} d^{3} e^{5}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{768 \, a^{2} d^{3} e^{2} x^{4}}, \frac{192 \, \sqrt{c d e} a^{2} c^{2} d^{5} e^{3} x^{4} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) - 3 \, {\left(5 \, c^{4} d^{8} - 60 \, a c^{3} d^{6} e^{2} - 90 \, a^{2} c^{2} d^{4} e^{4} + 20 \, a^{3} c d^{2} e^{6} - 3 \, a^{4} e^{8}\right)} \sqrt{-a d e} x^{4} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{-a d e}}{2 \, {\left(a c d^{2} e^{2} x^{2} + a^{2} d^{2} e^{2} + {\left(a c d^{3} e + a^{2} d e^{3}\right)} x\right)}}\right) - 2 \, {\left(48 \, a^{4} d^{4} e^{4} + {\left(15 \, a c^{3} d^{7} e + 337 \, a^{2} c^{2} d^{5} e^{3} + 57 \, a^{3} c d^{3} e^{5} - 9 \, a^{4} d e^{7}\right)} x^{3} + 2 \, {\left(59 \, a^{2} c^{2} d^{6} e^{2} + 122 \, a^{3} c d^{4} e^{4} + 3 \, a^{4} d^{2} e^{6}\right)} x^{2} + 8 \, {\left(17 \, a^{3} c d^{5} e^{3} + 9 \, a^{4} d^{3} e^{5}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{384 \, a^{2} d^{3} e^{2} x^{4}}, -\frac{384 \, \sqrt{-c d e} a^{2} c^{2} d^{5} e^{3} x^{4} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right) + 3 \, {\left(5 \, c^{4} d^{8} - 60 \, a c^{3} d^{6} e^{2} - 90 \, a^{2} c^{2} d^{4} e^{4} + 20 \, a^{3} c d^{2} e^{6} - 3 \, a^{4} e^{8}\right)} \sqrt{-a d e} x^{4} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{-a d e}}{2 \, {\left(a c d^{2} e^{2} x^{2} + a^{2} d^{2} e^{2} + {\left(a c d^{3} e + a^{2} d e^{3}\right)} x\right)}}\right) + 2 \, {\left(48 \, a^{4} d^{4} e^{4} + {\left(15 \, a c^{3} d^{7} e + 337 \, a^{2} c^{2} d^{5} e^{3} + 57 \, a^{3} c d^{3} e^{5} - 9 \, a^{4} d e^{7}\right)} x^{3} + 2 \, {\left(59 \, a^{2} c^{2} d^{6} e^{2} + 122 \, a^{3} c d^{4} e^{4} + 3 \, a^{4} d^{2} e^{6}\right)} x^{2} + 8 \, {\left(17 \, a^{3} c d^{5} e^{3} + 9 \, a^{4} d^{3} e^{5}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{384 \, a^{2} d^{3} e^{2} x^{4}}\right]"," ",0,"[1/768*(384*sqrt(c*d*e)*a^2*c^2*d^5*e^3*x^4*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) - 3*(5*c^4*d^8 - 60*a*c^3*d^6*e^2 - 90*a^2*c^2*d^4*e^4 + 20*a^3*c*d^2*e^6 - 3*a^4*e^8)*sqrt(a*d*e)*x^4*log((8*a^2*d^2*e^2 + (c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4)*x^2 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(a*d*e) + 8*(a*c*d^3*e + a^2*d*e^3)*x)/x^2) - 4*(48*a^4*d^4*e^4 + (15*a*c^3*d^7*e + 337*a^2*c^2*d^5*e^3 + 57*a^3*c*d^3*e^5 - 9*a^4*d*e^7)*x^3 + 2*(59*a^2*c^2*d^6*e^2 + 122*a^3*c*d^4*e^4 + 3*a^4*d^2*e^6)*x^2 + 8*(17*a^3*c*d^5*e^3 + 9*a^4*d^3*e^5)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(a^2*d^3*e^2*x^4), -1/768*(768*sqrt(-c*d*e)*a^2*c^2*d^5*e^3*x^4*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)) + 3*(5*c^4*d^8 - 60*a*c^3*d^6*e^2 - 90*a^2*c^2*d^4*e^4 + 20*a^3*c*d^2*e^6 - 3*a^4*e^8)*sqrt(a*d*e)*x^4*log((8*a^2*d^2*e^2 + (c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4)*x^2 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(a*d*e) + 8*(a*c*d^3*e + a^2*d*e^3)*x)/x^2) + 4*(48*a^4*d^4*e^4 + (15*a*c^3*d^7*e + 337*a^2*c^2*d^5*e^3 + 57*a^3*c*d^3*e^5 - 9*a^4*d*e^7)*x^3 + 2*(59*a^2*c^2*d^6*e^2 + 122*a^3*c*d^4*e^4 + 3*a^4*d^2*e^6)*x^2 + 8*(17*a^3*c*d^5*e^3 + 9*a^4*d^3*e^5)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(a^2*d^3*e^2*x^4), 1/384*(192*sqrt(c*d*e)*a^2*c^2*d^5*e^3*x^4*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) - 3*(5*c^4*d^8 - 60*a*c^3*d^6*e^2 - 90*a^2*c^2*d^4*e^4 + 20*a^3*c*d^2*e^6 - 3*a^4*e^8)*sqrt(-a*d*e)*x^4*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-a*d*e)/(a*c*d^2*e^2*x^2 + a^2*d^2*e^2 + (a*c*d^3*e + a^2*d*e^3)*x)) - 2*(48*a^4*d^4*e^4 + (15*a*c^3*d^7*e + 337*a^2*c^2*d^5*e^3 + 57*a^3*c*d^3*e^5 - 9*a^4*d*e^7)*x^3 + 2*(59*a^2*c^2*d^6*e^2 + 122*a^3*c*d^4*e^4 + 3*a^4*d^2*e^6)*x^2 + 8*(17*a^3*c*d^5*e^3 + 9*a^4*d^3*e^5)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(a^2*d^3*e^2*x^4), -1/384*(384*sqrt(-c*d*e)*a^2*c^2*d^5*e^3*x^4*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)) + 3*(5*c^4*d^8 - 60*a*c^3*d^6*e^2 - 90*a^2*c^2*d^4*e^4 + 20*a^3*c*d^2*e^6 - 3*a^4*e^8)*sqrt(-a*d*e)*x^4*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-a*d*e)/(a*c*d^2*e^2*x^2 + a^2*d^2*e^2 + (a*c*d^3*e + a^2*d*e^3)*x)) + 2*(48*a^4*d^4*e^4 + (15*a*c^3*d^7*e + 337*a^2*c^2*d^5*e^3 + 57*a^3*c*d^3*e^5 - 9*a^4*d*e^7)*x^3 + 2*(59*a^2*c^2*d^6*e^2 + 122*a^3*c*d^4*e^4 + 3*a^4*d^2*e^6)*x^2 + 8*(17*a^3*c*d^5*e^3 + 9*a^4*d^3*e^5)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(a^2*d^3*e^2*x^4)]","A",0
466,1,872,0,19.496073," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/x^6/(e*x+d),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(c^{5} d^{10} - 5 \, a c^{4} d^{8} e^{2} + 10 \, a^{2} c^{3} d^{6} e^{4} - 10 \, a^{3} c^{2} d^{4} e^{6} + 5 \, a^{4} c d^{2} e^{8} - a^{5} e^{10}\right)} \sqrt{a d e} x^{5} \log\left(\frac{8 \, a^{2} d^{2} e^{2} + {\left(c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} x^{2} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{a d e} + 8 \, {\left(a c d^{3} e + a^{2} d e^{3}\right)} x}{x^{2}}\right) - 4 \, {\left(128 \, a^{5} d^{5} e^{5} - {\left(15 \, a c^{4} d^{9} e - 70 \, a^{2} c^{3} d^{7} e^{3} - 128 \, a^{3} c^{2} d^{5} e^{5} + 70 \, a^{4} c d^{3} e^{7} - 15 \, a^{5} d e^{9}\right)} x^{4} + 2 \, {\left(5 \, a^{2} c^{3} d^{8} e^{2} + 233 \, a^{3} c^{2} d^{6} e^{4} + 23 \, a^{4} c d^{4} e^{6} - 5 \, a^{5} d^{2} e^{8}\right)} x^{3} + 8 \, {\left(31 \, a^{3} c^{2} d^{7} e^{3} + 64 \, a^{4} c d^{5} e^{5} + a^{5} d^{3} e^{7}\right)} x^{2} + 16 \, {\left(21 \, a^{4} c d^{6} e^{4} + 11 \, a^{5} d^{4} e^{6}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{2560 \, a^{3} d^{4} e^{3} x^{5}}, \frac{15 \, {\left(c^{5} d^{10} - 5 \, a c^{4} d^{8} e^{2} + 10 \, a^{2} c^{3} d^{6} e^{4} - 10 \, a^{3} c^{2} d^{4} e^{6} + 5 \, a^{4} c d^{2} e^{8} - a^{5} e^{10}\right)} \sqrt{-a d e} x^{5} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{-a d e}}{2 \, {\left(a c d^{2} e^{2} x^{2} + a^{2} d^{2} e^{2} + {\left(a c d^{3} e + a^{2} d e^{3}\right)} x\right)}}\right) - 2 \, {\left(128 \, a^{5} d^{5} e^{5} - {\left(15 \, a c^{4} d^{9} e - 70 \, a^{2} c^{3} d^{7} e^{3} - 128 \, a^{3} c^{2} d^{5} e^{5} + 70 \, a^{4} c d^{3} e^{7} - 15 \, a^{5} d e^{9}\right)} x^{4} + 2 \, {\left(5 \, a^{2} c^{3} d^{8} e^{2} + 233 \, a^{3} c^{2} d^{6} e^{4} + 23 \, a^{4} c d^{4} e^{6} - 5 \, a^{5} d^{2} e^{8}\right)} x^{3} + 8 \, {\left(31 \, a^{3} c^{2} d^{7} e^{3} + 64 \, a^{4} c d^{5} e^{5} + a^{5} d^{3} e^{7}\right)} x^{2} + 16 \, {\left(21 \, a^{4} c d^{6} e^{4} + 11 \, a^{5} d^{4} e^{6}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{1280 \, a^{3} d^{4} e^{3} x^{5}}\right]"," ",0,"[1/2560*(15*(c^5*d^10 - 5*a*c^4*d^8*e^2 + 10*a^2*c^3*d^6*e^4 - 10*a^3*c^2*d^4*e^6 + 5*a^4*c*d^2*e^8 - a^5*e^10)*sqrt(a*d*e)*x^5*log((8*a^2*d^2*e^2 + (c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4)*x^2 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(a*d*e) + 8*(a*c*d^3*e + a^2*d*e^3)*x)/x^2) - 4*(128*a^5*d^5*e^5 - (15*a*c^4*d^9*e - 70*a^2*c^3*d^7*e^3 - 128*a^3*c^2*d^5*e^5 + 70*a^4*c*d^3*e^7 - 15*a^5*d*e^9)*x^4 + 2*(5*a^2*c^3*d^8*e^2 + 233*a^3*c^2*d^6*e^4 + 23*a^4*c*d^4*e^6 - 5*a^5*d^2*e^8)*x^3 + 8*(31*a^3*c^2*d^7*e^3 + 64*a^4*c*d^5*e^5 + a^5*d^3*e^7)*x^2 + 16*(21*a^4*c*d^6*e^4 + 11*a^5*d^4*e^6)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(a^3*d^4*e^3*x^5), 1/1280*(15*(c^5*d^10 - 5*a*c^4*d^8*e^2 + 10*a^2*c^3*d^6*e^4 - 10*a^3*c^2*d^4*e^6 + 5*a^4*c*d^2*e^8 - a^5*e^10)*sqrt(-a*d*e)*x^5*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-a*d*e)/(a*c*d^2*e^2*x^2 + a^2*d^2*e^2 + (a*c*d^3*e + a^2*d*e^3)*x)) - 2*(128*a^5*d^5*e^5 - (15*a*c^4*d^9*e - 70*a^2*c^3*d^7*e^3 - 128*a^3*c^2*d^5*e^5 + 70*a^4*c*d^3*e^7 - 15*a^5*d*e^9)*x^4 + 2*(5*a^2*c^3*d^8*e^2 + 233*a^3*c^2*d^6*e^4 + 23*a^4*c*d^4*e^6 - 5*a^5*d^2*e^8)*x^3 + 8*(31*a^3*c^2*d^7*e^3 + 64*a^4*c*d^5*e^5 + a^5*d^3*e^7)*x^2 + 16*(21*a^4*c*d^6*e^4 + 11*a^5*d^4*e^6)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(a^3*d^4*e^3*x^5)]","A",0
467,1,1072,0,60.752240," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/x^7/(e*x+d),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(5 \, c^{6} d^{12} - 18 \, a c^{5} d^{10} e^{2} + 15 \, a^{2} c^{4} d^{8} e^{4} + 20 \, a^{3} c^{3} d^{6} e^{6} - 45 \, a^{4} c^{2} d^{4} e^{8} + 30 \, a^{5} c d^{2} e^{10} - 7 \, a^{6} e^{12}\right)} \sqrt{a d e} x^{6} \log\left(\frac{8 \, a^{2} d^{2} e^{2} + {\left(c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} x^{2} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{a d e} + 8 \, {\left(a c d^{3} e + a^{2} d e^{3}\right)} x}{x^{2}}\right) + 4 \, {\left(1280 \, a^{6} d^{6} e^{6} + {\left(75 \, a c^{5} d^{11} e - 245 \, a^{2} c^{4} d^{9} e^{3} + 150 \, a^{3} c^{3} d^{7} e^{5} - 546 \, a^{4} c^{2} d^{5} e^{7} + 415 \, a^{5} c d^{3} e^{9} - 105 \, a^{6} d e^{11}\right)} x^{5} - 2 \, {\left(25 \, a^{2} c^{4} d^{10} e^{2} - 80 \, a^{3} c^{3} d^{8} e^{4} - 174 \, a^{4} c^{2} d^{6} e^{6} + 136 \, a^{5} c d^{4} e^{8} - 35 \, a^{6} d^{2} e^{10}\right)} x^{4} + 8 \, {\left(5 \, a^{3} c^{3} d^{9} e^{3} + 423 \, a^{4} c^{2} d^{7} e^{5} + 27 \, a^{5} c d^{5} e^{7} - 7 \, a^{6} d^{3} e^{9}\right)} x^{3} + 16 \, {\left(135 \, a^{4} c^{2} d^{8} e^{4} + 278 \, a^{5} c d^{6} e^{6} + 3 \, a^{6} d^{4} e^{8}\right)} x^{2} + 128 \, {\left(25 \, a^{5} c d^{7} e^{5} + 13 \, a^{6} d^{5} e^{7}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{30720 \, a^{4} d^{5} e^{4} x^{6}}, -\frac{15 \, {\left(5 \, c^{6} d^{12} - 18 \, a c^{5} d^{10} e^{2} + 15 \, a^{2} c^{4} d^{8} e^{4} + 20 \, a^{3} c^{3} d^{6} e^{6} - 45 \, a^{4} c^{2} d^{4} e^{8} + 30 \, a^{5} c d^{2} e^{10} - 7 \, a^{6} e^{12}\right)} \sqrt{-a d e} x^{6} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{-a d e}}{2 \, {\left(a c d^{2} e^{2} x^{2} + a^{2} d^{2} e^{2} + {\left(a c d^{3} e + a^{2} d e^{3}\right)} x\right)}}\right) + 2 \, {\left(1280 \, a^{6} d^{6} e^{6} + {\left(75 \, a c^{5} d^{11} e - 245 \, a^{2} c^{4} d^{9} e^{3} + 150 \, a^{3} c^{3} d^{7} e^{5} - 546 \, a^{4} c^{2} d^{5} e^{7} + 415 \, a^{5} c d^{3} e^{9} - 105 \, a^{6} d e^{11}\right)} x^{5} - 2 \, {\left(25 \, a^{2} c^{4} d^{10} e^{2} - 80 \, a^{3} c^{3} d^{8} e^{4} - 174 \, a^{4} c^{2} d^{6} e^{6} + 136 \, a^{5} c d^{4} e^{8} - 35 \, a^{6} d^{2} e^{10}\right)} x^{4} + 8 \, {\left(5 \, a^{3} c^{3} d^{9} e^{3} + 423 \, a^{4} c^{2} d^{7} e^{5} + 27 \, a^{5} c d^{5} e^{7} - 7 \, a^{6} d^{3} e^{9}\right)} x^{3} + 16 \, {\left(135 \, a^{4} c^{2} d^{8} e^{4} + 278 \, a^{5} c d^{6} e^{6} + 3 \, a^{6} d^{4} e^{8}\right)} x^{2} + 128 \, {\left(25 \, a^{5} c d^{7} e^{5} + 13 \, a^{6} d^{5} e^{7}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{15360 \, a^{4} d^{5} e^{4} x^{6}}\right]"," ",0,"[-1/30720*(15*(5*c^6*d^12 - 18*a*c^5*d^10*e^2 + 15*a^2*c^4*d^8*e^4 + 20*a^3*c^3*d^6*e^6 - 45*a^4*c^2*d^4*e^8 + 30*a^5*c*d^2*e^10 - 7*a^6*e^12)*sqrt(a*d*e)*x^6*log((8*a^2*d^2*e^2 + (c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4)*x^2 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(a*d*e) + 8*(a*c*d^3*e + a^2*d*e^3)*x)/x^2) + 4*(1280*a^6*d^6*e^6 + (75*a*c^5*d^11*e - 245*a^2*c^4*d^9*e^3 + 150*a^3*c^3*d^7*e^5 - 546*a^4*c^2*d^5*e^7 + 415*a^5*c*d^3*e^9 - 105*a^6*d*e^11)*x^5 - 2*(25*a^2*c^4*d^10*e^2 - 80*a^3*c^3*d^8*e^4 - 174*a^4*c^2*d^6*e^6 + 136*a^5*c*d^4*e^8 - 35*a^6*d^2*e^10)*x^4 + 8*(5*a^3*c^3*d^9*e^3 + 423*a^4*c^2*d^7*e^5 + 27*a^5*c*d^5*e^7 - 7*a^6*d^3*e^9)*x^3 + 16*(135*a^4*c^2*d^8*e^4 + 278*a^5*c*d^6*e^6 + 3*a^6*d^4*e^8)*x^2 + 128*(25*a^5*c*d^7*e^5 + 13*a^6*d^5*e^7)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(a^4*d^5*e^4*x^6), -1/15360*(15*(5*c^6*d^12 - 18*a*c^5*d^10*e^2 + 15*a^2*c^4*d^8*e^4 + 20*a^3*c^3*d^6*e^6 - 45*a^4*c^2*d^4*e^8 + 30*a^5*c*d^2*e^10 - 7*a^6*e^12)*sqrt(-a*d*e)*x^6*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-a*d*e)/(a*c*d^2*e^2*x^2 + a^2*d^2*e^2 + (a*c*d^3*e + a^2*d*e^3)*x)) + 2*(1280*a^6*d^6*e^6 + (75*a*c^5*d^11*e - 245*a^2*c^4*d^9*e^3 + 150*a^3*c^3*d^7*e^5 - 546*a^4*c^2*d^5*e^7 + 415*a^5*c*d^3*e^9 - 105*a^6*d*e^11)*x^5 - 2*(25*a^2*c^4*d^10*e^2 - 80*a^3*c^3*d^8*e^4 - 174*a^4*c^2*d^6*e^6 + 136*a^5*c*d^4*e^8 - 35*a^6*d^2*e^10)*x^4 + 8*(5*a^3*c^3*d^9*e^3 + 423*a^4*c^2*d^7*e^5 + 27*a^5*c*d^5*e^7 - 7*a^6*d^3*e^9)*x^3 + 16*(135*a^4*c^2*d^8*e^4 + 278*a^5*c*d^6*e^6 + 3*a^6*d^4*e^8)*x^2 + 128*(25*a^5*c*d^7*e^5 + 13*a^6*d^5*e^7)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(a^4*d^5*e^4*x^6)]","A",0
468,1,1300,0,124.863903," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/x^8/(e*x+d),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(5 \, c^{7} d^{14} - 15 \, a c^{6} d^{12} e^{2} + 9 \, a^{2} c^{5} d^{10} e^{4} + 5 \, a^{3} c^{4} d^{8} e^{6} + 15 \, a^{4} c^{3} d^{6} e^{8} - 45 \, a^{5} c^{2} d^{4} e^{10} + 35 \, a^{6} c d^{2} e^{12} - 9 \, a^{7} e^{14}\right)} \sqrt{a d e} x^{7} \log\left(\frac{8 \, a^{2} d^{2} e^{2} + {\left(c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} x^{2} + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{a d e} + 8 \, {\left(a c d^{3} e + a^{2} d e^{3}\right)} x}{x^{2}}\right) + 4 \, {\left(15360 \, a^{7} d^{7} e^{7} - {\left(525 \, a c^{6} d^{13} e - 1400 \, a^{2} c^{5} d^{11} e^{3} + 525 \, a^{3} c^{4} d^{9} e^{5} + 600 \, a^{4} c^{3} d^{7} e^{7} - 3689 \, a^{5} c^{2} d^{5} e^{9} + 3360 \, a^{6} c d^{3} e^{11} - 945 \, a^{7} d e^{13}\right)} x^{6} + 2 \, {\left(175 \, a^{2} c^{5} d^{12} e^{2} - 455 \, a^{3} c^{4} d^{10} e^{4} + 150 \, a^{4} c^{3} d^{8} e^{6} - 1166 \, a^{5} c^{2} d^{6} e^{8} + 1099 \, a^{6} c d^{4} e^{10} - 315 \, a^{7} d^{2} e^{12}\right)} x^{5} - 8 \, {\left(35 \, a^{3} c^{4} d^{11} e^{3} - 90 \, a^{4} c^{3} d^{9} e^{5} - 228 \, a^{5} c^{2} d^{7} e^{7} + 218 \, a^{6} c d^{5} e^{9} - 63 \, a^{7} d^{3} e^{11}\right)} x^{4} + 16 \, {\left(15 \, a^{4} c^{3} d^{10} e^{4} + 2095 \, a^{5} c^{2} d^{8} e^{6} + 93 \, a^{6} c d^{6} e^{8} - 27 \, a^{7} d^{4} e^{10}\right)} x^{3} + 128 \, {\left(185 \, a^{5} c^{2} d^{9} e^{5} + 380 \, a^{6} c d^{7} e^{7} + 3 \, a^{7} d^{5} e^{9}\right)} x^{2} + 1280 \, {\left(29 \, a^{6} c d^{8} e^{6} + 15 \, a^{7} d^{6} e^{8}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{430080 \, a^{5} d^{6} e^{5} x^{7}}, \frac{105 \, {\left(5 \, c^{7} d^{14} - 15 \, a c^{6} d^{12} e^{2} + 9 \, a^{2} c^{5} d^{10} e^{4} + 5 \, a^{3} c^{4} d^{8} e^{6} + 15 \, a^{4} c^{3} d^{6} e^{8} - 45 \, a^{5} c^{2} d^{4} e^{10} + 35 \, a^{6} c d^{2} e^{12} - 9 \, a^{7} e^{14}\right)} \sqrt{-a d e} x^{7} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{-a d e}}{2 \, {\left(a c d^{2} e^{2} x^{2} + a^{2} d^{2} e^{2} + {\left(a c d^{3} e + a^{2} d e^{3}\right)} x\right)}}\right) - 2 \, {\left(15360 \, a^{7} d^{7} e^{7} - {\left(525 \, a c^{6} d^{13} e - 1400 \, a^{2} c^{5} d^{11} e^{3} + 525 \, a^{3} c^{4} d^{9} e^{5} + 600 \, a^{4} c^{3} d^{7} e^{7} - 3689 \, a^{5} c^{2} d^{5} e^{9} + 3360 \, a^{6} c d^{3} e^{11} - 945 \, a^{7} d e^{13}\right)} x^{6} + 2 \, {\left(175 \, a^{2} c^{5} d^{12} e^{2} - 455 \, a^{3} c^{4} d^{10} e^{4} + 150 \, a^{4} c^{3} d^{8} e^{6} - 1166 \, a^{5} c^{2} d^{6} e^{8} + 1099 \, a^{6} c d^{4} e^{10} - 315 \, a^{7} d^{2} e^{12}\right)} x^{5} - 8 \, {\left(35 \, a^{3} c^{4} d^{11} e^{3} - 90 \, a^{4} c^{3} d^{9} e^{5} - 228 \, a^{5} c^{2} d^{7} e^{7} + 218 \, a^{6} c d^{5} e^{9} - 63 \, a^{7} d^{3} e^{11}\right)} x^{4} + 16 \, {\left(15 \, a^{4} c^{3} d^{10} e^{4} + 2095 \, a^{5} c^{2} d^{8} e^{6} + 93 \, a^{6} c d^{6} e^{8} - 27 \, a^{7} d^{4} e^{10}\right)} x^{3} + 128 \, {\left(185 \, a^{5} c^{2} d^{9} e^{5} + 380 \, a^{6} c d^{7} e^{7} + 3 \, a^{7} d^{5} e^{9}\right)} x^{2} + 1280 \, {\left(29 \, a^{6} c d^{8} e^{6} + 15 \, a^{7} d^{6} e^{8}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{215040 \, a^{5} d^{6} e^{5} x^{7}}\right]"," ",0,"[-1/430080*(105*(5*c^7*d^14 - 15*a*c^6*d^12*e^2 + 9*a^2*c^5*d^10*e^4 + 5*a^3*c^4*d^8*e^6 + 15*a^4*c^3*d^6*e^8 - 45*a^5*c^2*d^4*e^10 + 35*a^6*c*d^2*e^12 - 9*a^7*e^14)*sqrt(a*d*e)*x^7*log((8*a^2*d^2*e^2 + (c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4)*x^2 + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(a*d*e) + 8*(a*c*d^3*e + a^2*d*e^3)*x)/x^2) + 4*(15360*a^7*d^7*e^7 - (525*a*c^6*d^13*e - 1400*a^2*c^5*d^11*e^3 + 525*a^3*c^4*d^9*e^5 + 600*a^4*c^3*d^7*e^7 - 3689*a^5*c^2*d^5*e^9 + 3360*a^6*c*d^3*e^11 - 945*a^7*d*e^13)*x^6 + 2*(175*a^2*c^5*d^12*e^2 - 455*a^3*c^4*d^10*e^4 + 150*a^4*c^3*d^8*e^6 - 1166*a^5*c^2*d^6*e^8 + 1099*a^6*c*d^4*e^10 - 315*a^7*d^2*e^12)*x^5 - 8*(35*a^3*c^4*d^11*e^3 - 90*a^4*c^3*d^9*e^5 - 228*a^5*c^2*d^7*e^7 + 218*a^6*c*d^5*e^9 - 63*a^7*d^3*e^11)*x^4 + 16*(15*a^4*c^3*d^10*e^4 + 2095*a^5*c^2*d^8*e^6 + 93*a^6*c*d^6*e^8 - 27*a^7*d^4*e^10)*x^3 + 128*(185*a^5*c^2*d^9*e^5 + 380*a^6*c*d^7*e^7 + 3*a^7*d^5*e^9)*x^2 + 1280*(29*a^6*c*d^8*e^6 + 15*a^7*d^6*e^8)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(a^5*d^6*e^5*x^7), 1/215040*(105*(5*c^7*d^14 - 15*a*c^6*d^12*e^2 + 9*a^2*c^5*d^10*e^4 + 5*a^3*c^4*d^8*e^6 + 15*a^4*c^3*d^6*e^8 - 45*a^5*c^2*d^4*e^10 + 35*a^6*c*d^2*e^12 - 9*a^7*e^14)*sqrt(-a*d*e)*x^7*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-a*d*e)/(a*c*d^2*e^2*x^2 + a^2*d^2*e^2 + (a*c*d^3*e + a^2*d*e^3)*x)) - 2*(15360*a^7*d^7*e^7 - (525*a*c^6*d^13*e - 1400*a^2*c^5*d^11*e^3 + 525*a^3*c^4*d^9*e^5 + 600*a^4*c^3*d^7*e^7 - 3689*a^5*c^2*d^5*e^9 + 3360*a^6*c*d^3*e^11 - 945*a^7*d*e^13)*x^6 + 2*(175*a^2*c^5*d^12*e^2 - 455*a^3*c^4*d^10*e^4 + 150*a^4*c^3*d^8*e^6 - 1166*a^5*c^2*d^6*e^8 + 1099*a^6*c*d^4*e^10 - 315*a^7*d^2*e^12)*x^5 - 8*(35*a^3*c^4*d^11*e^3 - 90*a^4*c^3*d^9*e^5 - 228*a^5*c^2*d^7*e^7 + 218*a^6*c*d^5*e^9 - 63*a^7*d^3*e^11)*x^4 + 16*(15*a^4*c^3*d^10*e^4 + 2095*a^5*c^2*d^8*e^6 + 93*a^6*c*d^6*e^8 - 27*a^7*d^4*e^10)*x^3 + 128*(185*a^5*c^2*d^9*e^5 + 380*a^6*c*d^7*e^7 + 3*a^7*d^5*e^9)*x^2 + 1280*(29*a^6*c*d^8*e^6 + 15*a^7*d^6*e^8)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(a^5*d^6*e^5*x^7)]","A",0
469,-1,0,0,0.000000," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/x^9/(e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
470,1,758,0,0.902939," ","integrate(x^3/(e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(5 \, c^{3} d^{7} - 3 \, a c^{2} d^{5} e^{2} - a^{2} c d^{3} e^{4} - a^{3} d e^{6} + {\left(5 \, c^{3} d^{6} e - 3 \, a c^{2} d^{4} e^{3} - a^{2} c d^{2} e^{5} - a^{3} e^{7}\right)} x\right)} \sqrt{c d e} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) - 4 \, {\left(15 \, c^{3} d^{6} e - 4 \, a c^{2} d^{4} e^{3} - 3 \, a^{2} c d^{2} e^{5} - 2 \, {\left(c^{3} d^{4} e^{3} - a c^{2} d^{2} e^{5}\right)} x^{2} + {\left(5 \, c^{3} d^{5} e^{2} - 2 \, a c^{2} d^{3} e^{4} - 3 \, a^{2} c d e^{6}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{16 \, {\left(c^{4} d^{6} e^{4} - a c^{3} d^{4} e^{6} + {\left(c^{4} d^{5} e^{5} - a c^{3} d^{3} e^{7}\right)} x\right)}}, -\frac{3 \, {\left(5 \, c^{3} d^{7} - 3 \, a c^{2} d^{5} e^{2} - a^{2} c d^{3} e^{4} - a^{3} d e^{6} + {\left(5 \, c^{3} d^{6} e - 3 \, a c^{2} d^{4} e^{3} - a^{2} c d^{2} e^{5} - a^{3} e^{7}\right)} x\right)} \sqrt{-c d e} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right) + 2 \, {\left(15 \, c^{3} d^{6} e - 4 \, a c^{2} d^{4} e^{3} - 3 \, a^{2} c d^{2} e^{5} - 2 \, {\left(c^{3} d^{4} e^{3} - a c^{2} d^{2} e^{5}\right)} x^{2} + {\left(5 \, c^{3} d^{5} e^{2} - 2 \, a c^{2} d^{3} e^{4} - 3 \, a^{2} c d e^{6}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{8 \, {\left(c^{4} d^{6} e^{4} - a c^{3} d^{4} e^{6} + {\left(c^{4} d^{5} e^{5} - a c^{3} d^{3} e^{7}\right)} x\right)}}\right]"," ",0,"[1/16*(3*(5*c^3*d^7 - 3*a*c^2*d^5*e^2 - a^2*c*d^3*e^4 - a^3*d*e^6 + (5*c^3*d^6*e - 3*a*c^2*d^4*e^3 - a^2*c*d^2*e^5 - a^3*e^7)*x)*sqrt(c*d*e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) - 4*(15*c^3*d^6*e - 4*a*c^2*d^4*e^3 - 3*a^2*c*d^2*e^5 - 2*(c^3*d^4*e^3 - a*c^2*d^2*e^5)*x^2 + (5*c^3*d^5*e^2 - 2*a*c^2*d^3*e^4 - 3*a^2*c*d*e^6)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^4*d^6*e^4 - a*c^3*d^4*e^6 + (c^4*d^5*e^5 - a*c^3*d^3*e^7)*x), -1/8*(3*(5*c^3*d^7 - 3*a*c^2*d^5*e^2 - a^2*c*d^3*e^4 - a^3*d*e^6 + (5*c^3*d^6*e - 3*a*c^2*d^4*e^3 - a^2*c*d^2*e^5 - a^3*e^7)*x)*sqrt(-c*d*e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)) + 2*(15*c^3*d^6*e - 4*a*c^2*d^4*e^3 - 3*a^2*c*d^2*e^5 - 2*(c^3*d^4*e^3 - a*c^2*d^2*e^5)*x^2 + (5*c^3*d^5*e^2 - 2*a*c^2*d^3*e^4 - 3*a^2*c*d*e^6)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^4*d^6*e^4 - a*c^3*d^4*e^6 + (c^4*d^5*e^5 - a*c^3*d^3*e^7)*x)]","A",0
471,1,586,0,0.567642," ","integrate(x^2/(e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(3 \, c^{2} d^{5} - 2 \, a c d^{3} e^{2} - a^{2} d e^{4} + {\left(3 \, c^{2} d^{4} e - 2 \, a c d^{2} e^{3} - a^{2} e^{5}\right)} x\right)} \sqrt{c d e} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) + 4 \, {\left(3 \, c^{2} d^{4} e - a c d^{2} e^{3} + {\left(c^{2} d^{3} e^{2} - a c d e^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{4 \, {\left(c^{3} d^{5} e^{3} - a c^{2} d^{3} e^{5} + {\left(c^{3} d^{4} e^{4} - a c^{2} d^{2} e^{6}\right)} x\right)}}, \frac{{\left(3 \, c^{2} d^{5} - 2 \, a c d^{3} e^{2} - a^{2} d e^{4} + {\left(3 \, c^{2} d^{4} e - 2 \, a c d^{2} e^{3} - a^{2} e^{5}\right)} x\right)} \sqrt{-c d e} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right) + 2 \, {\left(3 \, c^{2} d^{4} e - a c d^{2} e^{3} + {\left(c^{2} d^{3} e^{2} - a c d e^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{2 \, {\left(c^{3} d^{5} e^{3} - a c^{2} d^{3} e^{5} + {\left(c^{3} d^{4} e^{4} - a c^{2} d^{2} e^{6}\right)} x\right)}}\right]"," ",0,"[1/4*((3*c^2*d^5 - 2*a*c*d^3*e^2 - a^2*d*e^4 + (3*c^2*d^4*e - 2*a*c*d^2*e^3 - a^2*e^5)*x)*sqrt(c*d*e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) + 4*(3*c^2*d^4*e - a*c*d^2*e^3 + (c^2*d^3*e^2 - a*c*d*e^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^3*d^5*e^3 - a*c^2*d^3*e^5 + (c^3*d^4*e^4 - a*c^2*d^2*e^6)*x), 1/2*((3*c^2*d^5 - 2*a*c*d^3*e^2 - a^2*d*e^4 + (3*c^2*d^4*e - 2*a*c*d^2*e^3 - a^2*e^5)*x)*sqrt(-c*d*e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)) + 2*(3*c^2*d^4*e - a*c*d^2*e^3 + (c^2*d^3*e^2 - a*c*d*e^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^3*d^5*e^3 - a*c^2*d^3*e^5 + (c^3*d^4*e^4 - a*c^2*d^2*e^6)*x)]","A",0
472,1,443,0,0.550605," ","integrate(x/(e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} c d^{2} e - {\left(c d^{3} - a d e^{2} + {\left(c d^{2} e - a e^{3}\right)} x\right)} \sqrt{c d e} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}{2 \, {\left(c^{2} d^{4} e^{2} - a c d^{2} e^{4} + {\left(c^{2} d^{3} e^{3} - a c d e^{5}\right)} x\right)}}, -\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} c d^{2} e + {\left(c d^{3} - a d e^{2} + {\left(c d^{2} e - a e^{3}\right)} x\right)} \sqrt{-c d e} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right)}{c^{2} d^{4} e^{2} - a c d^{2} e^{4} + {\left(c^{2} d^{3} e^{3} - a c d e^{5}\right)} x}\right]"," ",0,"[-1/2*(4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*c*d^2*e - (c*d^3 - a*d*e^2 + (c*d^2*e - a*e^3)*x)*sqrt(c*d*e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x))/(c^2*d^4*e^2 - a*c*d^2*e^4 + (c^2*d^3*e^3 - a*c*d*e^5)*x), -(2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*c*d^2*e + (c*d^3 - a*d*e^2 + (c*d^2*e - a*e^3)*x)*sqrt(-c*d*e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)))/(c^2*d^4*e^2 - a*c*d^2*e^4 + (c^2*d^3*e^3 - a*c*d*e^5)*x)]","A",0
473,1,59,0,0.475259," ","integrate(1/(e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{c d^{3} - a d e^{2} + {\left(c d^{2} e - a e^{3}\right)} x}"," ",0,"2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)/(c*d^3 - a*d*e^2 + (c*d^2*e - a*e^3)*x)","A",0
474,1,454,0,0.772681," ","integrate(1/x/(e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} a d e^{2} - {\left(c d^{3} - a d e^{2} + {\left(c d^{2} e - a e^{3}\right)} x\right)} \sqrt{a d e} \log\left(\frac{8 \, a^{2} d^{2} e^{2} + {\left(c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} x^{2} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{a d e} + 8 \, {\left(a c d^{3} e + a^{2} d e^{3}\right)} x}{x^{2}}\right)}{2 \, {\left(a c d^{5} e - a^{2} d^{3} e^{3} + {\left(a c d^{4} e^{2} - a^{2} d^{2} e^{4}\right)} x\right)}}, -\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} a d e^{2} - {\left(c d^{3} - a d e^{2} + {\left(c d^{2} e - a e^{3}\right)} x\right)} \sqrt{-a d e} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{-a d e}}{2 \, {\left(a c d^{2} e^{2} x^{2} + a^{2} d^{2} e^{2} + {\left(a c d^{3} e + a^{2} d e^{3}\right)} x\right)}}\right)}{a c d^{5} e - a^{2} d^{3} e^{3} + {\left(a c d^{4} e^{2} - a^{2} d^{2} e^{4}\right)} x}\right]"," ",0,"[-1/2*(4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*a*d*e^2 - (c*d^3 - a*d*e^2 + (c*d^2*e - a*e^3)*x)*sqrt(a*d*e)*log((8*a^2*d^2*e^2 + (c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4)*x^2 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(a*d*e) + 8*(a*c*d^3*e + a^2*d*e^3)*x)/x^2))/(a*c*d^5*e - a^2*d^3*e^3 + (a*c*d^4*e^2 - a^2*d^2*e^4)*x), -(2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*a*d*e^2 - (c*d^3 - a*d*e^2 + (c*d^2*e - a*e^3)*x)*sqrt(-a*d*e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-a*d*e)/(a*c*d^2*e^2*x^2 + a^2*d^2*e^2 + (a*c*d^3*e + a^2*d*e^3)*x)))/(a*c*d^5*e - a^2*d^3*e^3 + (a*c*d^4*e^2 - a^2*d^2*e^4)*x)]","A",0
475,1,610,0,1.537765," ","integrate(1/x^2/(e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a d e} {\left({\left(c^{2} d^{4} e + 2 \, a c d^{2} e^{3} - 3 \, a^{2} e^{5}\right)} x^{2} + {\left(c^{2} d^{5} + 2 \, a c d^{3} e^{2} - 3 \, a^{2} d e^{4}\right)} x\right)} \log\left(\frac{8 \, a^{2} d^{2} e^{2} + {\left(c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} x^{2} + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{a d e} + 8 \, {\left(a c d^{3} e + a^{2} d e^{3}\right)} x}{x^{2}}\right) - 4 \, {\left(a c d^{4} e - a^{2} d^{2} e^{3} + {\left(a c d^{3} e^{2} - 3 \, a^{2} d e^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{4 \, {\left({\left(a^{2} c d^{5} e^{3} - a^{3} d^{3} e^{5}\right)} x^{2} + {\left(a^{2} c d^{6} e^{2} - a^{3} d^{4} e^{4}\right)} x\right)}}, -\frac{\sqrt{-a d e} {\left({\left(c^{2} d^{4} e + 2 \, a c d^{2} e^{3} - 3 \, a^{2} e^{5}\right)} x^{2} + {\left(c^{2} d^{5} + 2 \, a c d^{3} e^{2} - 3 \, a^{2} d e^{4}\right)} x\right)} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{-a d e}}{2 \, {\left(a c d^{2} e^{2} x^{2} + a^{2} d^{2} e^{2} + {\left(a c d^{3} e + a^{2} d e^{3}\right)} x\right)}}\right) + 2 \, {\left(a c d^{4} e - a^{2} d^{2} e^{3} + {\left(a c d^{3} e^{2} - 3 \, a^{2} d e^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{2 \, {\left({\left(a^{2} c d^{5} e^{3} - a^{3} d^{3} e^{5}\right)} x^{2} + {\left(a^{2} c d^{6} e^{2} - a^{3} d^{4} e^{4}\right)} x\right)}}\right]"," ",0,"[1/4*(sqrt(a*d*e)*((c^2*d^4*e + 2*a*c*d^2*e^3 - 3*a^2*e^5)*x^2 + (c^2*d^5 + 2*a*c*d^3*e^2 - 3*a^2*d*e^4)*x)*log((8*a^2*d^2*e^2 + (c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4)*x^2 + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(a*d*e) + 8*(a*c*d^3*e + a^2*d*e^3)*x)/x^2) - 4*(a*c*d^4*e - a^2*d^2*e^3 + (a*c*d^3*e^2 - 3*a^2*d*e^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/((a^2*c*d^5*e^3 - a^3*d^3*e^5)*x^2 + (a^2*c*d^6*e^2 - a^3*d^4*e^4)*x), -1/2*(sqrt(-a*d*e)*((c^2*d^4*e + 2*a*c*d^2*e^3 - 3*a^2*e^5)*x^2 + (c^2*d^5 + 2*a*c*d^3*e^2 - 3*a^2*d*e^4)*x)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-a*d*e)/(a*c*d^2*e^2*x^2 + a^2*d^2*e^2 + (a*c*d^3*e + a^2*d*e^3)*x)) + 2*(a*c*d^4*e - a^2*d^2*e^3 + (a*c*d^3*e^2 - 3*a^2*d*e^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/((a^2*c*d^5*e^3 - a^3*d^3*e^5)*x^2 + (a^2*c*d^6*e^2 - a^3*d^4*e^4)*x)]","A",0
476,1,792,0,3.715510," ","integrate(1/x^3/(e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(c^{3} d^{6} e + a c^{2} d^{4} e^{3} + 3 \, a^{2} c d^{2} e^{5} - 5 \, a^{3} e^{7}\right)} x^{3} + {\left(c^{3} d^{7} + a c^{2} d^{5} e^{2} + 3 \, a^{2} c d^{3} e^{4} - 5 \, a^{3} d e^{6}\right)} x^{2}\right)} \sqrt{a d e} \log\left(\frac{8 \, a^{2} d^{2} e^{2} + {\left(c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} x^{2} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{a d e} + 8 \, {\left(a c d^{3} e + a^{2} d e^{3}\right)} x}{x^{2}}\right) - 4 \, {\left(2 \, a^{2} c d^{5} e^{2} - 2 \, a^{3} d^{3} e^{4} - {\left(3 \, a c^{2} d^{5} e^{2} + 4 \, a^{2} c d^{3} e^{4} - 15 \, a^{3} d e^{6}\right)} x^{2} - {\left(3 \, a c^{2} d^{6} e + 2 \, a^{2} c d^{4} e^{3} - 5 \, a^{3} d^{2} e^{5}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{16 \, {\left({\left(a^{3} c d^{6} e^{4} - a^{4} d^{4} e^{6}\right)} x^{3} + {\left(a^{3} c d^{7} e^{3} - a^{4} d^{5} e^{5}\right)} x^{2}\right)}}, \frac{3 \, {\left({\left(c^{3} d^{6} e + a c^{2} d^{4} e^{3} + 3 \, a^{2} c d^{2} e^{5} - 5 \, a^{3} e^{7}\right)} x^{3} + {\left(c^{3} d^{7} + a c^{2} d^{5} e^{2} + 3 \, a^{2} c d^{3} e^{4} - 5 \, a^{3} d e^{6}\right)} x^{2}\right)} \sqrt{-a d e} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{-a d e}}{2 \, {\left(a c d^{2} e^{2} x^{2} + a^{2} d^{2} e^{2} + {\left(a c d^{3} e + a^{2} d e^{3}\right)} x\right)}}\right) - 2 \, {\left(2 \, a^{2} c d^{5} e^{2} - 2 \, a^{3} d^{3} e^{4} - {\left(3 \, a c^{2} d^{5} e^{2} + 4 \, a^{2} c d^{3} e^{4} - 15 \, a^{3} d e^{6}\right)} x^{2} - {\left(3 \, a c^{2} d^{6} e + 2 \, a^{2} c d^{4} e^{3} - 5 \, a^{3} d^{2} e^{5}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{8 \, {\left({\left(a^{3} c d^{6} e^{4} - a^{4} d^{4} e^{6}\right)} x^{3} + {\left(a^{3} c d^{7} e^{3} - a^{4} d^{5} e^{5}\right)} x^{2}\right)}}\right]"," ",0,"[1/16*(3*((c^3*d^6*e + a*c^2*d^4*e^3 + 3*a^2*c*d^2*e^5 - 5*a^3*e^7)*x^3 + (c^3*d^7 + a*c^2*d^5*e^2 + 3*a^2*c*d^3*e^4 - 5*a^3*d*e^6)*x^2)*sqrt(a*d*e)*log((8*a^2*d^2*e^2 + (c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4)*x^2 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(a*d*e) + 8*(a*c*d^3*e + a^2*d*e^3)*x)/x^2) - 4*(2*a^2*c*d^5*e^2 - 2*a^3*d^3*e^4 - (3*a*c^2*d^5*e^2 + 4*a^2*c*d^3*e^4 - 15*a^3*d*e^6)*x^2 - (3*a*c^2*d^6*e + 2*a^2*c*d^4*e^3 - 5*a^3*d^2*e^5)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/((a^3*c*d^6*e^4 - a^4*d^4*e^6)*x^3 + (a^3*c*d^7*e^3 - a^4*d^5*e^5)*x^2), 1/8*(3*((c^3*d^6*e + a*c^2*d^4*e^3 + 3*a^2*c*d^2*e^5 - 5*a^3*e^7)*x^3 + (c^3*d^7 + a*c^2*d^5*e^2 + 3*a^2*c*d^3*e^4 - 5*a^3*d*e^6)*x^2)*sqrt(-a*d*e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-a*d*e)/(a*c*d^2*e^2*x^2 + a^2*d^2*e^2 + (a*c*d^3*e + a^2*d*e^3)*x)) - 2*(2*a^2*c*d^5*e^2 - 2*a^3*d^3*e^4 - (3*a*c^2*d^5*e^2 + 4*a^2*c*d^3*e^4 - 15*a^3*d*e^6)*x^2 - (3*a*c^2*d^6*e + 2*a^2*c*d^4*e^3 - 5*a^3*d^2*e^5)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/((a^3*c*d^6*e^4 - a^4*d^4*e^6)*x^3 + (a^3*c*d^7*e^3 - a^4*d^5*e^5)*x^2)]","A",0
477,1,2120,0,6.648260," ","integrate(x^5/(e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(7 \, a c^{5} d^{12} e - 15 \, a^{2} c^{4} d^{10} e^{3} + 6 \, a^{3} c^{3} d^{8} e^{5} + 2 \, a^{4} c^{2} d^{6} e^{7} + 3 \, a^{5} c d^{4} e^{9} - 3 \, a^{6} d^{2} e^{11} + {\left(7 \, c^{6} d^{11} e^{2} - 15 \, a c^{5} d^{9} e^{4} + 6 \, a^{2} c^{4} d^{7} e^{6} + 2 \, a^{3} c^{3} d^{5} e^{8} + 3 \, a^{4} c^{2} d^{3} e^{10} - 3 \, a^{5} c d e^{12}\right)} x^{3} + {\left(14 \, c^{6} d^{12} e - 23 \, a c^{5} d^{10} e^{3} - 3 \, a^{2} c^{4} d^{8} e^{5} + 10 \, a^{3} c^{3} d^{6} e^{7} + 8 \, a^{4} c^{2} d^{4} e^{9} - 3 \, a^{5} c d^{2} e^{11} - 3 \, a^{6} e^{13}\right)} x^{2} + {\left(7 \, c^{6} d^{13} - a c^{5} d^{11} e^{2} - 24 \, a^{2} c^{4} d^{9} e^{4} + 14 \, a^{3} c^{3} d^{7} e^{6} + 7 \, a^{4} c^{2} d^{5} e^{8} + 3 \, a^{5} c d^{3} e^{10} - 6 \, a^{6} d e^{12}\right)} x\right)} \sqrt{c d e} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) - 4 \, {\left(105 \, a c^{5} d^{11} e^{2} - 190 \, a^{2} c^{4} d^{9} e^{4} + 36 \, a^{3} c^{3} d^{7} e^{6} + 30 \, a^{4} c^{2} d^{5} e^{8} - 45 \, a^{5} c d^{3} e^{10} - 6 \, {\left(c^{6} d^{9} e^{4} - 3 \, a c^{5} d^{7} e^{6} + 3 \, a^{2} c^{4} d^{5} e^{8} - a^{3} c^{3} d^{3} e^{10}\right)} x^{4} + 3 \, {\left(7 \, c^{6} d^{10} e^{3} - 16 \, a c^{5} d^{8} e^{5} + 6 \, a^{2} c^{4} d^{6} e^{7} + 8 \, a^{3} c^{3} d^{4} e^{9} - 5 \, a^{4} c^{2} d^{2} e^{11}\right)} x^{3} + {\left(140 \, c^{6} d^{11} e^{2} - 237 \, a c^{5} d^{9} e^{4} + 12 \, a^{2} c^{4} d^{7} e^{6} + 66 \, a^{3} c^{3} d^{5} e^{8} - 45 \, a^{5} c d e^{12}\right)} x^{2} + {\left(105 \, c^{6} d^{12} e - 50 \, a c^{5} d^{10} e^{3} - 222 \, a^{2} c^{4} d^{8} e^{5} + 84 \, a^{3} c^{3} d^{6} e^{7} + 45 \, a^{4} c^{2} d^{4} e^{9} - 90 \, a^{5} c d^{2} e^{11}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{48 \, {\left(a c^{7} d^{12} e^{6} - 3 \, a^{2} c^{6} d^{10} e^{8} + 3 \, a^{3} c^{5} d^{8} e^{10} - a^{4} c^{4} d^{6} e^{12} + {\left(c^{8} d^{11} e^{7} - 3 \, a c^{7} d^{9} e^{9} + 3 \, a^{2} c^{6} d^{7} e^{11} - a^{3} c^{5} d^{5} e^{13}\right)} x^{3} + {\left(2 \, c^{8} d^{12} e^{6} - 5 \, a c^{7} d^{10} e^{8} + 3 \, a^{2} c^{6} d^{8} e^{10} + a^{3} c^{5} d^{6} e^{12} - a^{4} c^{4} d^{4} e^{14}\right)} x^{2} + {\left(c^{8} d^{13} e^{5} - a c^{7} d^{11} e^{7} - 3 \, a^{2} c^{6} d^{9} e^{9} + 5 \, a^{3} c^{5} d^{7} e^{11} - 2 \, a^{4} c^{4} d^{5} e^{13}\right)} x\right)}}, -\frac{15 \, {\left(7 \, a c^{5} d^{12} e - 15 \, a^{2} c^{4} d^{10} e^{3} + 6 \, a^{3} c^{3} d^{8} e^{5} + 2 \, a^{4} c^{2} d^{6} e^{7} + 3 \, a^{5} c d^{4} e^{9} - 3 \, a^{6} d^{2} e^{11} + {\left(7 \, c^{6} d^{11} e^{2} - 15 \, a c^{5} d^{9} e^{4} + 6 \, a^{2} c^{4} d^{7} e^{6} + 2 \, a^{3} c^{3} d^{5} e^{8} + 3 \, a^{4} c^{2} d^{3} e^{10} - 3 \, a^{5} c d e^{12}\right)} x^{3} + {\left(14 \, c^{6} d^{12} e - 23 \, a c^{5} d^{10} e^{3} - 3 \, a^{2} c^{4} d^{8} e^{5} + 10 \, a^{3} c^{3} d^{6} e^{7} + 8 \, a^{4} c^{2} d^{4} e^{9} - 3 \, a^{5} c d^{2} e^{11} - 3 \, a^{6} e^{13}\right)} x^{2} + {\left(7 \, c^{6} d^{13} - a c^{5} d^{11} e^{2} - 24 \, a^{2} c^{4} d^{9} e^{4} + 14 \, a^{3} c^{3} d^{7} e^{6} + 7 \, a^{4} c^{2} d^{5} e^{8} + 3 \, a^{5} c d^{3} e^{10} - 6 \, a^{6} d e^{12}\right)} x\right)} \sqrt{-c d e} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right) + 2 \, {\left(105 \, a c^{5} d^{11} e^{2} - 190 \, a^{2} c^{4} d^{9} e^{4} + 36 \, a^{3} c^{3} d^{7} e^{6} + 30 \, a^{4} c^{2} d^{5} e^{8} - 45 \, a^{5} c d^{3} e^{10} - 6 \, {\left(c^{6} d^{9} e^{4} - 3 \, a c^{5} d^{7} e^{6} + 3 \, a^{2} c^{4} d^{5} e^{8} - a^{3} c^{3} d^{3} e^{10}\right)} x^{4} + 3 \, {\left(7 \, c^{6} d^{10} e^{3} - 16 \, a c^{5} d^{8} e^{5} + 6 \, a^{2} c^{4} d^{6} e^{7} + 8 \, a^{3} c^{3} d^{4} e^{9} - 5 \, a^{4} c^{2} d^{2} e^{11}\right)} x^{3} + {\left(140 \, c^{6} d^{11} e^{2} - 237 \, a c^{5} d^{9} e^{4} + 12 \, a^{2} c^{4} d^{7} e^{6} + 66 \, a^{3} c^{3} d^{5} e^{8} - 45 \, a^{5} c d e^{12}\right)} x^{2} + {\left(105 \, c^{6} d^{12} e - 50 \, a c^{5} d^{10} e^{3} - 222 \, a^{2} c^{4} d^{8} e^{5} + 84 \, a^{3} c^{3} d^{6} e^{7} + 45 \, a^{4} c^{2} d^{4} e^{9} - 90 \, a^{5} c d^{2} e^{11}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{24 \, {\left(a c^{7} d^{12} e^{6} - 3 \, a^{2} c^{6} d^{10} e^{8} + 3 \, a^{3} c^{5} d^{8} e^{10} - a^{4} c^{4} d^{6} e^{12} + {\left(c^{8} d^{11} e^{7} - 3 \, a c^{7} d^{9} e^{9} + 3 \, a^{2} c^{6} d^{7} e^{11} - a^{3} c^{5} d^{5} e^{13}\right)} x^{3} + {\left(2 \, c^{8} d^{12} e^{6} - 5 \, a c^{7} d^{10} e^{8} + 3 \, a^{2} c^{6} d^{8} e^{10} + a^{3} c^{5} d^{6} e^{12} - a^{4} c^{4} d^{4} e^{14}\right)} x^{2} + {\left(c^{8} d^{13} e^{5} - a c^{7} d^{11} e^{7} - 3 \, a^{2} c^{6} d^{9} e^{9} + 5 \, a^{3} c^{5} d^{7} e^{11} - 2 \, a^{4} c^{4} d^{5} e^{13}\right)} x\right)}}\right]"," ",0,"[1/48*(15*(7*a*c^5*d^12*e - 15*a^2*c^4*d^10*e^3 + 6*a^3*c^3*d^8*e^5 + 2*a^4*c^2*d^6*e^7 + 3*a^5*c*d^4*e^9 - 3*a^6*d^2*e^11 + (7*c^6*d^11*e^2 - 15*a*c^5*d^9*e^4 + 6*a^2*c^4*d^7*e^6 + 2*a^3*c^3*d^5*e^8 + 3*a^4*c^2*d^3*e^10 - 3*a^5*c*d*e^12)*x^3 + (14*c^6*d^12*e - 23*a*c^5*d^10*e^3 - 3*a^2*c^4*d^8*e^5 + 10*a^3*c^3*d^6*e^7 + 8*a^4*c^2*d^4*e^9 - 3*a^5*c*d^2*e^11 - 3*a^6*e^13)*x^2 + (7*c^6*d^13 - a*c^5*d^11*e^2 - 24*a^2*c^4*d^9*e^4 + 14*a^3*c^3*d^7*e^6 + 7*a^4*c^2*d^5*e^8 + 3*a^5*c*d^3*e^10 - 6*a^6*d*e^12)*x)*sqrt(c*d*e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) - 4*(105*a*c^5*d^11*e^2 - 190*a^2*c^4*d^9*e^4 + 36*a^3*c^3*d^7*e^6 + 30*a^4*c^2*d^5*e^8 - 45*a^5*c*d^3*e^10 - 6*(c^6*d^9*e^4 - 3*a*c^5*d^7*e^6 + 3*a^2*c^4*d^5*e^8 - a^3*c^3*d^3*e^10)*x^4 + 3*(7*c^6*d^10*e^3 - 16*a*c^5*d^8*e^5 + 6*a^2*c^4*d^6*e^7 + 8*a^3*c^3*d^4*e^9 - 5*a^4*c^2*d^2*e^11)*x^3 + (140*c^6*d^11*e^2 - 237*a*c^5*d^9*e^4 + 12*a^2*c^4*d^7*e^6 + 66*a^3*c^3*d^5*e^8 - 45*a^5*c*d*e^12)*x^2 + (105*c^6*d^12*e - 50*a*c^5*d^10*e^3 - 222*a^2*c^4*d^8*e^5 + 84*a^3*c^3*d^6*e^7 + 45*a^4*c^2*d^4*e^9 - 90*a^5*c*d^2*e^11)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(a*c^7*d^12*e^6 - 3*a^2*c^6*d^10*e^8 + 3*a^3*c^5*d^8*e^10 - a^4*c^4*d^6*e^12 + (c^8*d^11*e^7 - 3*a*c^7*d^9*e^9 + 3*a^2*c^6*d^7*e^11 - a^3*c^5*d^5*e^13)*x^3 + (2*c^8*d^12*e^6 - 5*a*c^7*d^10*e^8 + 3*a^2*c^6*d^8*e^10 + a^3*c^5*d^6*e^12 - a^4*c^4*d^4*e^14)*x^2 + (c^8*d^13*e^5 - a*c^7*d^11*e^7 - 3*a^2*c^6*d^9*e^9 + 5*a^3*c^5*d^7*e^11 - 2*a^4*c^4*d^5*e^13)*x), -1/24*(15*(7*a*c^5*d^12*e - 15*a^2*c^4*d^10*e^3 + 6*a^3*c^3*d^8*e^5 + 2*a^4*c^2*d^6*e^7 + 3*a^5*c*d^4*e^9 - 3*a^6*d^2*e^11 + (7*c^6*d^11*e^2 - 15*a*c^5*d^9*e^4 + 6*a^2*c^4*d^7*e^6 + 2*a^3*c^3*d^5*e^8 + 3*a^4*c^2*d^3*e^10 - 3*a^5*c*d*e^12)*x^3 + (14*c^6*d^12*e - 23*a*c^5*d^10*e^3 - 3*a^2*c^4*d^8*e^5 + 10*a^3*c^3*d^6*e^7 + 8*a^4*c^2*d^4*e^9 - 3*a^5*c*d^2*e^11 - 3*a^6*e^13)*x^2 + (7*c^6*d^13 - a*c^5*d^11*e^2 - 24*a^2*c^4*d^9*e^4 + 14*a^3*c^3*d^7*e^6 + 7*a^4*c^2*d^5*e^8 + 3*a^5*c*d^3*e^10 - 6*a^6*d*e^12)*x)*sqrt(-c*d*e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)) + 2*(105*a*c^5*d^11*e^2 - 190*a^2*c^4*d^9*e^4 + 36*a^3*c^3*d^7*e^6 + 30*a^4*c^2*d^5*e^8 - 45*a^5*c*d^3*e^10 - 6*(c^6*d^9*e^4 - 3*a*c^5*d^7*e^6 + 3*a^2*c^4*d^5*e^8 - a^3*c^3*d^3*e^10)*x^4 + 3*(7*c^6*d^10*e^3 - 16*a*c^5*d^8*e^5 + 6*a^2*c^4*d^6*e^7 + 8*a^3*c^3*d^4*e^9 - 5*a^4*c^2*d^2*e^11)*x^3 + (140*c^6*d^11*e^2 - 237*a*c^5*d^9*e^4 + 12*a^2*c^4*d^7*e^6 + 66*a^3*c^3*d^5*e^8 - 45*a^5*c*d*e^12)*x^2 + (105*c^6*d^12*e - 50*a*c^5*d^10*e^3 - 222*a^2*c^4*d^8*e^5 + 84*a^3*c^3*d^6*e^7 + 45*a^4*c^2*d^4*e^9 - 90*a^5*c*d^2*e^11)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(a*c^7*d^12*e^6 - 3*a^2*c^6*d^10*e^8 + 3*a^3*c^5*d^8*e^10 - a^4*c^4*d^6*e^12 + (c^8*d^11*e^7 - 3*a*c^7*d^9*e^9 + 3*a^2*c^6*d^7*e^11 - a^3*c^5*d^5*e^13)*x^3 + (2*c^8*d^12*e^6 - 5*a*c^7*d^10*e^8 + 3*a^2*c^6*d^8*e^10 + a^3*c^5*d^6*e^12 - a^4*c^4*d^4*e^14)*x^2 + (c^8*d^13*e^5 - a*c^7*d^11*e^7 - 3*a^2*c^6*d^9*e^9 + 5*a^3*c^5*d^7*e^11 - 2*a^4*c^4*d^5*e^13)*x)]","B",0
478,1,1782,0,2.662915," ","integrate(x^4/(e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(5 \, a c^{4} d^{10} e - 12 \, a^{2} c^{3} d^{8} e^{3} + 6 \, a^{3} c^{2} d^{6} e^{5} + 4 \, a^{4} c d^{4} e^{7} - 3 \, a^{5} d^{2} e^{9} + {\left(5 \, c^{5} d^{9} e^{2} - 12 \, a c^{4} d^{7} e^{4} + 6 \, a^{2} c^{3} d^{5} e^{6} + 4 \, a^{3} c^{2} d^{3} e^{8} - 3 \, a^{4} c d e^{10}\right)} x^{3} + {\left(10 \, c^{5} d^{10} e - 19 \, a c^{4} d^{8} e^{3} + 14 \, a^{3} c^{2} d^{4} e^{7} - 2 \, a^{4} c d^{2} e^{9} - 3 \, a^{5} e^{11}\right)} x^{2} + {\left(5 \, c^{5} d^{11} - 2 \, a c^{4} d^{9} e^{2} - 18 \, a^{2} c^{3} d^{7} e^{4} + 16 \, a^{3} c^{2} d^{5} e^{6} + 5 \, a^{4} c d^{3} e^{8} - 6 \, a^{5} d e^{10}\right)} x\right)} \sqrt{c d e} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) + 4 \, {\left(15 \, a c^{4} d^{9} e^{2} - 31 \, a^{2} c^{3} d^{7} e^{4} + 9 \, a^{3} c^{2} d^{5} e^{6} - 9 \, a^{4} c d^{3} e^{8} + 3 \, {\left(c^{5} d^{8} e^{3} - 3 \, a c^{4} d^{6} e^{5} + 3 \, a^{2} c^{3} d^{4} e^{7} - a^{3} c^{2} d^{2} e^{9}\right)} x^{3} + {\left(20 \, c^{5} d^{9} e^{2} - 39 \, a c^{4} d^{7} e^{4} + 9 \, a^{2} c^{3} d^{5} e^{6} + 3 \, a^{3} c^{2} d^{3} e^{8} - 9 \, a^{4} c d e^{10}\right)} x^{2} + {\left(15 \, c^{5} d^{10} e - 11 \, a c^{4} d^{8} e^{3} - 33 \, a^{2} c^{3} d^{6} e^{5} + 15 \, a^{3} c^{2} d^{4} e^{7} - 18 \, a^{4} c d^{2} e^{9}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{12 \, {\left(a c^{6} d^{11} e^{5} - 3 \, a^{2} c^{5} d^{9} e^{7} + 3 \, a^{3} c^{4} d^{7} e^{9} - a^{4} c^{3} d^{5} e^{11} + {\left(c^{7} d^{10} e^{6} - 3 \, a c^{6} d^{8} e^{8} + 3 \, a^{2} c^{5} d^{6} e^{10} - a^{3} c^{4} d^{4} e^{12}\right)} x^{3} + {\left(2 \, c^{7} d^{11} e^{5} - 5 \, a c^{6} d^{9} e^{7} + 3 \, a^{2} c^{5} d^{7} e^{9} + a^{3} c^{4} d^{5} e^{11} - a^{4} c^{3} d^{3} e^{13}\right)} x^{2} + {\left(c^{7} d^{12} e^{4} - a c^{6} d^{10} e^{6} - 3 \, a^{2} c^{5} d^{8} e^{8} + 5 \, a^{3} c^{4} d^{6} e^{10} - 2 \, a^{4} c^{3} d^{4} e^{12}\right)} x\right)}}, \frac{3 \, {\left(5 \, a c^{4} d^{10} e - 12 \, a^{2} c^{3} d^{8} e^{3} + 6 \, a^{3} c^{2} d^{6} e^{5} + 4 \, a^{4} c d^{4} e^{7} - 3 \, a^{5} d^{2} e^{9} + {\left(5 \, c^{5} d^{9} e^{2} - 12 \, a c^{4} d^{7} e^{4} + 6 \, a^{2} c^{3} d^{5} e^{6} + 4 \, a^{3} c^{2} d^{3} e^{8} - 3 \, a^{4} c d e^{10}\right)} x^{3} + {\left(10 \, c^{5} d^{10} e - 19 \, a c^{4} d^{8} e^{3} + 14 \, a^{3} c^{2} d^{4} e^{7} - 2 \, a^{4} c d^{2} e^{9} - 3 \, a^{5} e^{11}\right)} x^{2} + {\left(5 \, c^{5} d^{11} - 2 \, a c^{4} d^{9} e^{2} - 18 \, a^{2} c^{3} d^{7} e^{4} + 16 \, a^{3} c^{2} d^{5} e^{6} + 5 \, a^{4} c d^{3} e^{8} - 6 \, a^{5} d e^{10}\right)} x\right)} \sqrt{-c d e} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right) + 2 \, {\left(15 \, a c^{4} d^{9} e^{2} - 31 \, a^{2} c^{3} d^{7} e^{4} + 9 \, a^{3} c^{2} d^{5} e^{6} - 9 \, a^{4} c d^{3} e^{8} + 3 \, {\left(c^{5} d^{8} e^{3} - 3 \, a c^{4} d^{6} e^{5} + 3 \, a^{2} c^{3} d^{4} e^{7} - a^{3} c^{2} d^{2} e^{9}\right)} x^{3} + {\left(20 \, c^{5} d^{9} e^{2} - 39 \, a c^{4} d^{7} e^{4} + 9 \, a^{2} c^{3} d^{5} e^{6} + 3 \, a^{3} c^{2} d^{3} e^{8} - 9 \, a^{4} c d e^{10}\right)} x^{2} + {\left(15 \, c^{5} d^{10} e - 11 \, a c^{4} d^{8} e^{3} - 33 \, a^{2} c^{3} d^{6} e^{5} + 15 \, a^{3} c^{2} d^{4} e^{7} - 18 \, a^{4} c d^{2} e^{9}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{6 \, {\left(a c^{6} d^{11} e^{5} - 3 \, a^{2} c^{5} d^{9} e^{7} + 3 \, a^{3} c^{4} d^{7} e^{9} - a^{4} c^{3} d^{5} e^{11} + {\left(c^{7} d^{10} e^{6} - 3 \, a c^{6} d^{8} e^{8} + 3 \, a^{2} c^{5} d^{6} e^{10} - a^{3} c^{4} d^{4} e^{12}\right)} x^{3} + {\left(2 \, c^{7} d^{11} e^{5} - 5 \, a c^{6} d^{9} e^{7} + 3 \, a^{2} c^{5} d^{7} e^{9} + a^{3} c^{4} d^{5} e^{11} - a^{4} c^{3} d^{3} e^{13}\right)} x^{2} + {\left(c^{7} d^{12} e^{4} - a c^{6} d^{10} e^{6} - 3 \, a^{2} c^{5} d^{8} e^{8} + 5 \, a^{3} c^{4} d^{6} e^{10} - 2 \, a^{4} c^{3} d^{4} e^{12}\right)} x\right)}}\right]"," ",0,"[1/12*(3*(5*a*c^4*d^10*e - 12*a^2*c^3*d^8*e^3 + 6*a^3*c^2*d^6*e^5 + 4*a^4*c*d^4*e^7 - 3*a^5*d^2*e^9 + (5*c^5*d^9*e^2 - 12*a*c^4*d^7*e^4 + 6*a^2*c^3*d^5*e^6 + 4*a^3*c^2*d^3*e^8 - 3*a^4*c*d*e^10)*x^3 + (10*c^5*d^10*e - 19*a*c^4*d^8*e^3 + 14*a^3*c^2*d^4*e^7 - 2*a^4*c*d^2*e^9 - 3*a^5*e^11)*x^2 + (5*c^5*d^11 - 2*a*c^4*d^9*e^2 - 18*a^2*c^3*d^7*e^4 + 16*a^3*c^2*d^5*e^6 + 5*a^4*c*d^3*e^8 - 6*a^5*d*e^10)*x)*sqrt(c*d*e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) + 4*(15*a*c^4*d^9*e^2 - 31*a^2*c^3*d^7*e^4 + 9*a^3*c^2*d^5*e^6 - 9*a^4*c*d^3*e^8 + 3*(c^5*d^8*e^3 - 3*a*c^4*d^6*e^5 + 3*a^2*c^3*d^4*e^7 - a^3*c^2*d^2*e^9)*x^3 + (20*c^5*d^9*e^2 - 39*a*c^4*d^7*e^4 + 9*a^2*c^3*d^5*e^6 + 3*a^3*c^2*d^3*e^8 - 9*a^4*c*d*e^10)*x^2 + (15*c^5*d^10*e - 11*a*c^4*d^8*e^3 - 33*a^2*c^3*d^6*e^5 + 15*a^3*c^2*d^4*e^7 - 18*a^4*c*d^2*e^9)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(a*c^6*d^11*e^5 - 3*a^2*c^5*d^9*e^7 + 3*a^3*c^4*d^7*e^9 - a^4*c^3*d^5*e^11 + (c^7*d^10*e^6 - 3*a*c^6*d^8*e^8 + 3*a^2*c^5*d^6*e^10 - a^3*c^4*d^4*e^12)*x^3 + (2*c^7*d^11*e^5 - 5*a*c^6*d^9*e^7 + 3*a^2*c^5*d^7*e^9 + a^3*c^4*d^5*e^11 - a^4*c^3*d^3*e^13)*x^2 + (c^7*d^12*e^4 - a*c^6*d^10*e^6 - 3*a^2*c^5*d^8*e^8 + 5*a^3*c^4*d^6*e^10 - 2*a^4*c^3*d^4*e^12)*x), 1/6*(3*(5*a*c^4*d^10*e - 12*a^2*c^3*d^8*e^3 + 6*a^3*c^2*d^6*e^5 + 4*a^4*c*d^4*e^7 - 3*a^5*d^2*e^9 + (5*c^5*d^9*e^2 - 12*a*c^4*d^7*e^4 + 6*a^2*c^3*d^5*e^6 + 4*a^3*c^2*d^3*e^8 - 3*a^4*c*d*e^10)*x^3 + (10*c^5*d^10*e - 19*a*c^4*d^8*e^3 + 14*a^3*c^2*d^4*e^7 - 2*a^4*c*d^2*e^9 - 3*a^5*e^11)*x^2 + (5*c^5*d^11 - 2*a*c^4*d^9*e^2 - 18*a^2*c^3*d^7*e^4 + 16*a^3*c^2*d^5*e^6 + 5*a^4*c*d^3*e^8 - 6*a^5*d*e^10)*x)*sqrt(-c*d*e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)) + 2*(15*a*c^4*d^9*e^2 - 31*a^2*c^3*d^7*e^4 + 9*a^3*c^2*d^5*e^6 - 9*a^4*c*d^3*e^8 + 3*(c^5*d^8*e^3 - 3*a*c^4*d^6*e^5 + 3*a^2*c^3*d^4*e^7 - a^3*c^2*d^2*e^9)*x^3 + (20*c^5*d^9*e^2 - 39*a*c^4*d^7*e^4 + 9*a^2*c^3*d^5*e^6 + 3*a^3*c^2*d^3*e^8 - 9*a^4*c*d*e^10)*x^2 + (15*c^5*d^10*e - 11*a*c^4*d^8*e^3 - 33*a^2*c^3*d^6*e^5 + 15*a^3*c^2*d^4*e^7 - 18*a^4*c*d^2*e^9)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(a*c^6*d^11*e^5 - 3*a^2*c^5*d^9*e^7 + 3*a^3*c^4*d^7*e^9 - a^4*c^3*d^5*e^11 + (c^7*d^10*e^6 - 3*a*c^6*d^8*e^8 + 3*a^2*c^5*d^6*e^10 - a^3*c^4*d^4*e^12)*x^3 + (2*c^7*d^11*e^5 - 5*a*c^6*d^9*e^7 + 3*a^2*c^5*d^7*e^9 + a^3*c^4*d^5*e^11 - a^4*c^3*d^3*e^13)*x^2 + (c^7*d^12*e^4 - a*c^6*d^10*e^6 - 3*a^2*c^5*d^8*e^8 + 5*a^3*c^4*d^6*e^10 - 2*a^4*c^3*d^4*e^12)*x)]","B",0
479,1,1466,0,3.244254," ","integrate(x^3/(e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a c^{3} d^{8} e - 3 \, a^{2} c^{2} d^{6} e^{3} + 3 \, a^{3} c d^{4} e^{5} - a^{4} d^{2} e^{7} + {\left(c^{4} d^{7} e^{2} - 3 \, a c^{3} d^{5} e^{4} + 3 \, a^{2} c^{2} d^{3} e^{6} - a^{3} c d e^{8}\right)} x^{3} + {\left(2 \, c^{4} d^{8} e - 5 \, a c^{3} d^{6} e^{3} + 3 \, a^{2} c^{2} d^{4} e^{5} + a^{3} c d^{2} e^{7} - a^{4} e^{9}\right)} x^{2} + {\left(c^{4} d^{9} - a c^{3} d^{7} e^{2} - 3 \, a^{2} c^{2} d^{5} e^{4} + 5 \, a^{3} c d^{3} e^{6} - 2 \, a^{4} d e^{8}\right)} x\right)} \sqrt{c d e} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) - 4 \, {\left(3 \, a c^{3} d^{7} e^{2} - 8 \, a^{2} c^{2} d^{5} e^{4} - 3 \, a^{3} c d^{3} e^{6} + {\left(4 \, c^{4} d^{7} e^{2} - 9 \, a c^{3} d^{5} e^{4} - 3 \, a^{3} c d e^{8}\right)} x^{2} + {\left(3 \, c^{4} d^{8} e - 4 \, a c^{3} d^{6} e^{3} - 9 \, a^{2} c^{2} d^{4} e^{5} - 6 \, a^{3} c d^{2} e^{7}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{6 \, {\left(a c^{5} d^{10} e^{4} - 3 \, a^{2} c^{4} d^{8} e^{6} + 3 \, a^{3} c^{3} d^{6} e^{8} - a^{4} c^{2} d^{4} e^{10} + {\left(c^{6} d^{9} e^{5} - 3 \, a c^{5} d^{7} e^{7} + 3 \, a^{2} c^{4} d^{5} e^{9} - a^{3} c^{3} d^{3} e^{11}\right)} x^{3} + {\left(2 \, c^{6} d^{10} e^{4} - 5 \, a c^{5} d^{8} e^{6} + 3 \, a^{2} c^{4} d^{6} e^{8} + a^{3} c^{3} d^{4} e^{10} - a^{4} c^{2} d^{2} e^{12}\right)} x^{2} + {\left(c^{6} d^{11} e^{3} - a c^{5} d^{9} e^{5} - 3 \, a^{2} c^{4} d^{7} e^{7} + 5 \, a^{3} c^{3} d^{5} e^{9} - 2 \, a^{4} c^{2} d^{3} e^{11}\right)} x\right)}}, -\frac{3 \, {\left(a c^{3} d^{8} e - 3 \, a^{2} c^{2} d^{6} e^{3} + 3 \, a^{3} c d^{4} e^{5} - a^{4} d^{2} e^{7} + {\left(c^{4} d^{7} e^{2} - 3 \, a c^{3} d^{5} e^{4} + 3 \, a^{2} c^{2} d^{3} e^{6} - a^{3} c d e^{8}\right)} x^{3} + {\left(2 \, c^{4} d^{8} e - 5 \, a c^{3} d^{6} e^{3} + 3 \, a^{2} c^{2} d^{4} e^{5} + a^{3} c d^{2} e^{7} - a^{4} e^{9}\right)} x^{2} + {\left(c^{4} d^{9} - a c^{3} d^{7} e^{2} - 3 \, a^{2} c^{2} d^{5} e^{4} + 5 \, a^{3} c d^{3} e^{6} - 2 \, a^{4} d e^{8}\right)} x\right)} \sqrt{-c d e} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right) + 2 \, {\left(3 \, a c^{3} d^{7} e^{2} - 8 \, a^{2} c^{2} d^{5} e^{4} - 3 \, a^{3} c d^{3} e^{6} + {\left(4 \, c^{4} d^{7} e^{2} - 9 \, a c^{3} d^{5} e^{4} - 3 \, a^{3} c d e^{8}\right)} x^{2} + {\left(3 \, c^{4} d^{8} e - 4 \, a c^{3} d^{6} e^{3} - 9 \, a^{2} c^{2} d^{4} e^{5} - 6 \, a^{3} c d^{2} e^{7}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{3 \, {\left(a c^{5} d^{10} e^{4} - 3 \, a^{2} c^{4} d^{8} e^{6} + 3 \, a^{3} c^{3} d^{6} e^{8} - a^{4} c^{2} d^{4} e^{10} + {\left(c^{6} d^{9} e^{5} - 3 \, a c^{5} d^{7} e^{7} + 3 \, a^{2} c^{4} d^{5} e^{9} - a^{3} c^{3} d^{3} e^{11}\right)} x^{3} + {\left(2 \, c^{6} d^{10} e^{4} - 5 \, a c^{5} d^{8} e^{6} + 3 \, a^{2} c^{4} d^{6} e^{8} + a^{3} c^{3} d^{4} e^{10} - a^{4} c^{2} d^{2} e^{12}\right)} x^{2} + {\left(c^{6} d^{11} e^{3} - a c^{5} d^{9} e^{5} - 3 \, a^{2} c^{4} d^{7} e^{7} + 5 \, a^{3} c^{3} d^{5} e^{9} - 2 \, a^{4} c^{2} d^{3} e^{11}\right)} x\right)}}\right]"," ",0,"[1/6*(3*(a*c^3*d^8*e - 3*a^2*c^2*d^6*e^3 + 3*a^3*c*d^4*e^5 - a^4*d^2*e^7 + (c^4*d^7*e^2 - 3*a*c^3*d^5*e^4 + 3*a^2*c^2*d^3*e^6 - a^3*c*d*e^8)*x^3 + (2*c^4*d^8*e - 5*a*c^3*d^6*e^3 + 3*a^2*c^2*d^4*e^5 + a^3*c*d^2*e^7 - a^4*e^9)*x^2 + (c^4*d^9 - a*c^3*d^7*e^2 - 3*a^2*c^2*d^5*e^4 + 5*a^3*c*d^3*e^6 - 2*a^4*d*e^8)*x)*sqrt(c*d*e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) - 4*(3*a*c^3*d^7*e^2 - 8*a^2*c^2*d^5*e^4 - 3*a^3*c*d^3*e^6 + (4*c^4*d^7*e^2 - 9*a*c^3*d^5*e^4 - 3*a^3*c*d*e^8)*x^2 + (3*c^4*d^8*e - 4*a*c^3*d^6*e^3 - 9*a^2*c^2*d^4*e^5 - 6*a^3*c*d^2*e^7)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(a*c^5*d^10*e^4 - 3*a^2*c^4*d^8*e^6 + 3*a^3*c^3*d^6*e^8 - a^4*c^2*d^4*e^10 + (c^6*d^9*e^5 - 3*a*c^5*d^7*e^7 + 3*a^2*c^4*d^5*e^9 - a^3*c^3*d^3*e^11)*x^3 + (2*c^6*d^10*e^4 - 5*a*c^5*d^8*e^6 + 3*a^2*c^4*d^6*e^8 + a^3*c^3*d^4*e^10 - a^4*c^2*d^2*e^12)*x^2 + (c^6*d^11*e^3 - a*c^5*d^9*e^5 - 3*a^2*c^4*d^7*e^7 + 5*a^3*c^3*d^5*e^9 - 2*a^4*c^2*d^3*e^11)*x), -1/3*(3*(a*c^3*d^8*e - 3*a^2*c^2*d^6*e^3 + 3*a^3*c*d^4*e^5 - a^4*d^2*e^7 + (c^4*d^7*e^2 - 3*a*c^3*d^5*e^4 + 3*a^2*c^2*d^3*e^6 - a^3*c*d*e^8)*x^3 + (2*c^4*d^8*e - 5*a*c^3*d^6*e^3 + 3*a^2*c^2*d^4*e^5 + a^3*c*d^2*e^7 - a^4*e^9)*x^2 + (c^4*d^9 - a*c^3*d^7*e^2 - 3*a^2*c^2*d^5*e^4 + 5*a^3*c*d^3*e^6 - 2*a^4*d*e^8)*x)*sqrt(-c*d*e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)) + 2*(3*a*c^3*d^7*e^2 - 8*a^2*c^2*d^5*e^4 - 3*a^3*c*d^3*e^6 + (4*c^4*d^7*e^2 - 9*a*c^3*d^5*e^4 - 3*a^3*c*d*e^8)*x^2 + (3*c^4*d^8*e - 4*a*c^3*d^6*e^3 - 9*a^2*c^2*d^4*e^5 - 6*a^3*c*d^2*e^7)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(a*c^5*d^10*e^4 - 3*a^2*c^4*d^8*e^6 + 3*a^3*c^3*d^6*e^8 - a^4*c^2*d^4*e^10 + (c^6*d^9*e^5 - 3*a*c^5*d^7*e^7 + 3*a^2*c^4*d^5*e^9 - a^3*c^3*d^3*e^11)*x^3 + (2*c^6*d^10*e^4 - 5*a*c^5*d^8*e^6 + 3*a^2*c^4*d^6*e^8 + a^3*c^3*d^4*e^10 - a^4*c^2*d^2*e^12)*x^2 + (c^6*d^11*e^3 - a*c^5*d^9*e^5 - 3*a^2*c^4*d^7*e^7 + 5*a^3*c^3*d^5*e^9 - 2*a^4*c^2*d^3*e^11)*x)]","B",0
480,1,308,0,2.825285," ","integrate(x^2/(e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(8 \, a^{2} d^{2} e^{2} - {\left(c^{2} d^{4} - 6 \, a c d^{2} e^{2} - 3 \, a^{2} e^{4}\right)} x^{2} + 4 \, {\left(a c d^{3} e + 3 \, a^{2} d e^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{3 \, {\left(a c^{3} d^{8} e - 3 \, a^{2} c^{2} d^{6} e^{3} + 3 \, a^{3} c d^{4} e^{5} - a^{4} d^{2} e^{7} + {\left(c^{4} d^{7} e^{2} - 3 \, a c^{3} d^{5} e^{4} + 3 \, a^{2} c^{2} d^{3} e^{6} - a^{3} c d e^{8}\right)} x^{3} + {\left(2 \, c^{4} d^{8} e - 5 \, a c^{3} d^{6} e^{3} + 3 \, a^{2} c^{2} d^{4} e^{5} + a^{3} c d^{2} e^{7} - a^{4} e^{9}\right)} x^{2} + {\left(c^{4} d^{9} - a c^{3} d^{7} e^{2} - 3 \, a^{2} c^{2} d^{5} e^{4} + 5 \, a^{3} c d^{3} e^{6} - 2 \, a^{4} d e^{8}\right)} x\right)}}"," ",0,"-2/3*(8*a^2*d^2*e^2 - (c^2*d^4 - 6*a*c*d^2*e^2 - 3*a^2*e^4)*x^2 + 4*(a*c*d^3*e + 3*a^2*d*e^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)/(a*c^3*d^8*e - 3*a^2*c^2*d^6*e^3 + 3*a^3*c*d^4*e^5 - a^4*d^2*e^7 + (c^4*d^7*e^2 - 3*a*c^3*d^5*e^4 + 3*a^2*c^2*d^3*e^6 - a^3*c*d*e^8)*x^3 + (2*c^4*d^8*e - 5*a*c^3*d^6*e^3 + 3*a^2*c^2*d^4*e^5 + a^3*c*d^2*e^7 - a^4*e^9)*x^2 + (c^4*d^9 - a*c^3*d^7*e^2 - 3*a^2*c^2*d^5*e^4 + 5*a^3*c*d^3*e^6 - 2*a^4*d*e^8)*x)","B",0
481,1,314,0,2.718758," ","integrate(x/(e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(6 \, a c d^{3} e + 2 \, a^{2} d e^{3} + 2 \, {\left(c^{2} d^{3} e + 3 \, a c d e^{3}\right)} x^{2} + {\left(3 \, c^{2} d^{4} + 10 \, a c d^{2} e^{2} + 3 \, a^{2} e^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{3 \, {\left(a c^{3} d^{8} e - 3 \, a^{2} c^{2} d^{6} e^{3} + 3 \, a^{3} c d^{4} e^{5} - a^{4} d^{2} e^{7} + {\left(c^{4} d^{7} e^{2} - 3 \, a c^{3} d^{5} e^{4} + 3 \, a^{2} c^{2} d^{3} e^{6} - a^{3} c d e^{8}\right)} x^{3} + {\left(2 \, c^{4} d^{8} e - 5 \, a c^{3} d^{6} e^{3} + 3 \, a^{2} c^{2} d^{4} e^{5} + a^{3} c d^{2} e^{7} - a^{4} e^{9}\right)} x^{2} + {\left(c^{4} d^{9} - a c^{3} d^{7} e^{2} - 3 \, a^{2} c^{2} d^{5} e^{4} + 5 \, a^{3} c d^{3} e^{6} - 2 \, a^{4} d e^{8}\right)} x\right)}}"," ",0,"2/3*(6*a*c*d^3*e + 2*a^2*d*e^3 + 2*(c^2*d^3*e + 3*a*c*d*e^3)*x^2 + (3*c^2*d^4 + 10*a*c*d^2*e^2 + 3*a^2*e^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)/(a*c^3*d^8*e - 3*a^2*c^2*d^6*e^3 + 3*a^3*c*d^4*e^5 - a^4*d^2*e^7 + (c^4*d^7*e^2 - 3*a*c^3*d^5*e^4 + 3*a^2*c^2*d^3*e^6 - a^3*c*d*e^8)*x^3 + (2*c^4*d^8*e - 5*a*c^3*d^6*e^3 + 3*a^2*c^2*d^4*e^5 + a^3*c*d^2*e^7 - a^4*e^9)*x^2 + (c^4*d^9 - a*c^3*d^7*e^2 - 3*a^2*c^2*d^5*e^4 + 5*a^3*c*d^3*e^6 - 2*a^4*d*e^8)*x)","B",0
482,1,306,0,2.297036," ","integrate(1/(e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(8 \, c^{2} d^{2} e^{2} x^{2} + 3 \, c^{2} d^{4} + 6 \, a c d^{2} e^{2} - a^{2} e^{4} + 4 \, {\left(3 \, c^{2} d^{3} e + a c d e^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{3 \, {\left(a c^{3} d^{8} e - 3 \, a^{2} c^{2} d^{6} e^{3} + 3 \, a^{3} c d^{4} e^{5} - a^{4} d^{2} e^{7} + {\left(c^{4} d^{7} e^{2} - 3 \, a c^{3} d^{5} e^{4} + 3 \, a^{2} c^{2} d^{3} e^{6} - a^{3} c d e^{8}\right)} x^{3} + {\left(2 \, c^{4} d^{8} e - 5 \, a c^{3} d^{6} e^{3} + 3 \, a^{2} c^{2} d^{4} e^{5} + a^{3} c d^{2} e^{7} - a^{4} e^{9}\right)} x^{2} + {\left(c^{4} d^{9} - a c^{3} d^{7} e^{2} - 3 \, a^{2} c^{2} d^{5} e^{4} + 5 \, a^{3} c d^{3} e^{6} - 2 \, a^{4} d e^{8}\right)} x\right)}}"," ",0,"-2/3*(8*c^2*d^2*e^2*x^2 + 3*c^2*d^4 + 6*a*c*d^2*e^2 - a^2*e^4 + 4*(3*c^2*d^3*e + a*c*d*e^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)/(a*c^3*d^8*e - 3*a^2*c^2*d^6*e^3 + 3*a^3*c*d^4*e^5 - a^4*d^2*e^7 + (c^4*d^7*e^2 - 3*a*c^3*d^5*e^4 + 3*a^2*c^2*d^3*e^6 - a^3*c*d*e^8)*x^3 + (2*c^4*d^8*e - 5*a*c^3*d^6*e^3 + 3*a^2*c^2*d^4*e^5 + a^3*c*d^2*e^7 - a^4*e^9)*x^2 + (c^4*d^9 - a*c^3*d^7*e^2 - 3*a^2*c^2*d^5*e^4 + 5*a^3*c*d^3*e^6 - 2*a^4*d*e^8)*x)","B",0
483,1,1476,0,6.516270," ","integrate(1/x/(e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a c^{3} d^{8} e - 3 \, a^{2} c^{2} d^{6} e^{3} + 3 \, a^{3} c d^{4} e^{5} - a^{4} d^{2} e^{7} + {\left(c^{4} d^{7} e^{2} - 3 \, a c^{3} d^{5} e^{4} + 3 \, a^{2} c^{2} d^{3} e^{6} - a^{3} c d e^{8}\right)} x^{3} + {\left(2 \, c^{4} d^{8} e - 5 \, a c^{3} d^{6} e^{3} + 3 \, a^{2} c^{2} d^{4} e^{5} + a^{3} c d^{2} e^{7} - a^{4} e^{9}\right)} x^{2} + {\left(c^{4} d^{9} - a c^{3} d^{7} e^{2} - 3 \, a^{2} c^{2} d^{5} e^{4} + 5 \, a^{3} c d^{3} e^{6} - 2 \, a^{4} d e^{8}\right)} x\right)} \sqrt{a d e} \log\left(\frac{8 \, a^{2} d^{2} e^{2} + {\left(c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} x^{2} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{a d e} + 8 \, {\left(a c d^{3} e + a^{2} d e^{3}\right)} x}{x^{2}}\right) + 4 \, {\left(3 \, a c^{3} d^{8} e + 9 \, a^{3} c d^{4} e^{5} - 4 \, a^{4} d^{2} e^{7} + {\left(3 \, a c^{3} d^{6} e^{3} + 8 \, a^{2} c^{2} d^{4} e^{5} - 3 \, a^{3} c d^{2} e^{7}\right)} x^{2} + {\left(6 \, a c^{3} d^{7} e^{2} + 9 \, a^{2} c^{2} d^{5} e^{4} + 4 \, a^{3} c d^{3} e^{6} - 3 \, a^{4} d e^{8}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{6 \, {\left(a^{3} c^{3} d^{11} e^{3} - 3 \, a^{4} c^{2} d^{9} e^{5} + 3 \, a^{5} c d^{7} e^{7} - a^{6} d^{5} e^{9} + {\left(a^{2} c^{4} d^{10} e^{4} - 3 \, a^{3} c^{3} d^{8} e^{6} + 3 \, a^{4} c^{2} d^{6} e^{8} - a^{5} c d^{4} e^{10}\right)} x^{3} + {\left(2 \, a^{2} c^{4} d^{11} e^{3} - 5 \, a^{3} c^{3} d^{9} e^{5} + 3 \, a^{4} c^{2} d^{7} e^{7} + a^{5} c d^{5} e^{9} - a^{6} d^{3} e^{11}\right)} x^{2} + {\left(a^{2} c^{4} d^{12} e^{2} - a^{3} c^{3} d^{10} e^{4} - 3 \, a^{4} c^{2} d^{8} e^{6} + 5 \, a^{5} c d^{6} e^{8} - 2 \, a^{6} d^{4} e^{10}\right)} x\right)}}, \frac{3 \, {\left(a c^{3} d^{8} e - 3 \, a^{2} c^{2} d^{6} e^{3} + 3 \, a^{3} c d^{4} e^{5} - a^{4} d^{2} e^{7} + {\left(c^{4} d^{7} e^{2} - 3 \, a c^{3} d^{5} e^{4} + 3 \, a^{2} c^{2} d^{3} e^{6} - a^{3} c d e^{8}\right)} x^{3} + {\left(2 \, c^{4} d^{8} e - 5 \, a c^{3} d^{6} e^{3} + 3 \, a^{2} c^{2} d^{4} e^{5} + a^{3} c d^{2} e^{7} - a^{4} e^{9}\right)} x^{2} + {\left(c^{4} d^{9} - a c^{3} d^{7} e^{2} - 3 \, a^{2} c^{2} d^{5} e^{4} + 5 \, a^{3} c d^{3} e^{6} - 2 \, a^{4} d e^{8}\right)} x\right)} \sqrt{-a d e} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{-a d e}}{2 \, {\left(a c d^{2} e^{2} x^{2} + a^{2} d^{2} e^{2} + {\left(a c d^{3} e + a^{2} d e^{3}\right)} x\right)}}\right) + 2 \, {\left(3 \, a c^{3} d^{8} e + 9 \, a^{3} c d^{4} e^{5} - 4 \, a^{4} d^{2} e^{7} + {\left(3 \, a c^{3} d^{6} e^{3} + 8 \, a^{2} c^{2} d^{4} e^{5} - 3 \, a^{3} c d^{2} e^{7}\right)} x^{2} + {\left(6 \, a c^{3} d^{7} e^{2} + 9 \, a^{2} c^{2} d^{5} e^{4} + 4 \, a^{3} c d^{3} e^{6} - 3 \, a^{4} d e^{8}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{3 \, {\left(a^{3} c^{3} d^{11} e^{3} - 3 \, a^{4} c^{2} d^{9} e^{5} + 3 \, a^{5} c d^{7} e^{7} - a^{6} d^{5} e^{9} + {\left(a^{2} c^{4} d^{10} e^{4} - 3 \, a^{3} c^{3} d^{8} e^{6} + 3 \, a^{4} c^{2} d^{6} e^{8} - a^{5} c d^{4} e^{10}\right)} x^{3} + {\left(2 \, a^{2} c^{4} d^{11} e^{3} - 5 \, a^{3} c^{3} d^{9} e^{5} + 3 \, a^{4} c^{2} d^{7} e^{7} + a^{5} c d^{5} e^{9} - a^{6} d^{3} e^{11}\right)} x^{2} + {\left(a^{2} c^{4} d^{12} e^{2} - a^{3} c^{3} d^{10} e^{4} - 3 \, a^{4} c^{2} d^{8} e^{6} + 5 \, a^{5} c d^{6} e^{8} - 2 \, a^{6} d^{4} e^{10}\right)} x\right)}}\right]"," ",0,"[1/6*(3*(a*c^3*d^8*e - 3*a^2*c^2*d^6*e^3 + 3*a^3*c*d^4*e^5 - a^4*d^2*e^7 + (c^4*d^7*e^2 - 3*a*c^3*d^5*e^4 + 3*a^2*c^2*d^3*e^6 - a^3*c*d*e^8)*x^3 + (2*c^4*d^8*e - 5*a*c^3*d^6*e^3 + 3*a^2*c^2*d^4*e^5 + a^3*c*d^2*e^7 - a^4*e^9)*x^2 + (c^4*d^9 - a*c^3*d^7*e^2 - 3*a^2*c^2*d^5*e^4 + 5*a^3*c*d^3*e^6 - 2*a^4*d*e^8)*x)*sqrt(a*d*e)*log((8*a^2*d^2*e^2 + (c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4)*x^2 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(a*d*e) + 8*(a*c*d^3*e + a^2*d*e^3)*x)/x^2) + 4*(3*a*c^3*d^8*e + 9*a^3*c*d^4*e^5 - 4*a^4*d^2*e^7 + (3*a*c^3*d^6*e^3 + 8*a^2*c^2*d^4*e^5 - 3*a^3*c*d^2*e^7)*x^2 + (6*a*c^3*d^7*e^2 + 9*a^2*c^2*d^5*e^4 + 4*a^3*c*d^3*e^6 - 3*a^4*d*e^8)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(a^3*c^3*d^11*e^3 - 3*a^4*c^2*d^9*e^5 + 3*a^5*c*d^7*e^7 - a^6*d^5*e^9 + (a^2*c^4*d^10*e^4 - 3*a^3*c^3*d^8*e^6 + 3*a^4*c^2*d^6*e^8 - a^5*c*d^4*e^10)*x^3 + (2*a^2*c^4*d^11*e^3 - 5*a^3*c^3*d^9*e^5 + 3*a^4*c^2*d^7*e^7 + a^5*c*d^5*e^9 - a^6*d^3*e^11)*x^2 + (a^2*c^4*d^12*e^2 - a^3*c^3*d^10*e^4 - 3*a^4*c^2*d^8*e^6 + 5*a^5*c*d^6*e^8 - 2*a^6*d^4*e^10)*x), 1/3*(3*(a*c^3*d^8*e - 3*a^2*c^2*d^6*e^3 + 3*a^3*c*d^4*e^5 - a^4*d^2*e^7 + (c^4*d^7*e^2 - 3*a*c^3*d^5*e^4 + 3*a^2*c^2*d^3*e^6 - a^3*c*d*e^8)*x^3 + (2*c^4*d^8*e - 5*a*c^3*d^6*e^3 + 3*a^2*c^2*d^4*e^5 + a^3*c*d^2*e^7 - a^4*e^9)*x^2 + (c^4*d^9 - a*c^3*d^7*e^2 - 3*a^2*c^2*d^5*e^4 + 5*a^3*c*d^3*e^6 - 2*a^4*d*e^8)*x)*sqrt(-a*d*e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-a*d*e)/(a*c*d^2*e^2*x^2 + a^2*d^2*e^2 + (a*c*d^3*e + a^2*d*e^3)*x)) + 2*(3*a*c^3*d^8*e + 9*a^3*c*d^4*e^5 - 4*a^4*d^2*e^7 + (3*a*c^3*d^6*e^3 + 8*a^2*c^2*d^4*e^5 - 3*a^3*c*d^2*e^7)*x^2 + (6*a*c^3*d^7*e^2 + 9*a^2*c^2*d^5*e^4 + 4*a^3*c*d^3*e^6 - 3*a^4*d*e^8)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(a^3*c^3*d^11*e^3 - 3*a^4*c^2*d^9*e^5 + 3*a^5*c*d^7*e^7 - a^6*d^5*e^9 + (a^2*c^4*d^10*e^4 - 3*a^3*c^3*d^8*e^6 + 3*a^4*c^2*d^6*e^8 - a^5*c*d^4*e^10)*x^3 + (2*a^2*c^4*d^11*e^3 - 5*a^3*c^3*d^9*e^5 + 3*a^4*c^2*d^7*e^7 + a^5*c*d^5*e^9 - a^6*d^3*e^11)*x^2 + (a^2*c^4*d^12*e^2 - a^3*c^3*d^10*e^4 - 3*a^4*c^2*d^8*e^6 + 5*a^5*c*d^6*e^8 - 2*a^6*d^4*e^10)*x)]","B",0
484,1,1812,0,19.592993," ","integrate(1/x^2/(e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(3 \, c^{5} d^{9} e^{2} - 4 \, a c^{4} d^{7} e^{4} - 6 \, a^{2} c^{3} d^{5} e^{6} + 12 \, a^{3} c^{2} d^{3} e^{8} - 5 \, a^{4} c d e^{10}\right)} x^{4} + {\left(6 \, c^{5} d^{10} e - 5 \, a c^{4} d^{8} e^{3} - 16 \, a^{2} c^{3} d^{6} e^{5} + 18 \, a^{3} c^{2} d^{4} e^{7} + 2 \, a^{4} c d^{2} e^{9} - 5 \, a^{5} e^{11}\right)} x^{3} + {\left(3 \, c^{5} d^{11} + 2 \, a c^{4} d^{9} e^{2} - 14 \, a^{2} c^{3} d^{7} e^{4} + 19 \, a^{4} c d^{3} e^{8} - 10 \, a^{5} d e^{10}\right)} x^{2} + {\left(3 \, a c^{4} d^{10} e - 4 \, a^{2} c^{3} d^{8} e^{3} - 6 \, a^{3} c^{2} d^{6} e^{5} + 12 \, a^{4} c d^{4} e^{7} - 5 \, a^{5} d^{2} e^{9}\right)} x\right)} \sqrt{a d e} \log\left(\frac{8 \, a^{2} d^{2} e^{2} + {\left(c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} x^{2} + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{a d e} + 8 \, {\left(a c d^{3} e + a^{2} d e^{3}\right)} x}{x^{2}}\right) - 4 \, {\left(3 \, a^{2} c^{3} d^{9} e^{2} - 9 \, a^{3} c^{2} d^{7} e^{4} + 9 \, a^{4} c d^{5} e^{6} - 3 \, a^{5} d^{3} e^{8} + {\left(9 \, a c^{4} d^{8} e^{3} - 9 \, a^{2} c^{3} d^{6} e^{5} + 31 \, a^{3} c^{2} d^{4} e^{7} - 15 \, a^{4} c d^{2} e^{9}\right)} x^{3} + {\left(18 \, a c^{4} d^{9} e^{2} - 15 \, a^{2} c^{3} d^{7} e^{4} + 33 \, a^{3} c^{2} d^{5} e^{6} + 11 \, a^{4} c d^{3} e^{8} - 15 \, a^{5} d e^{10}\right)} x^{2} + {\left(9 \, a c^{4} d^{10} e - 3 \, a^{2} c^{3} d^{8} e^{3} - 9 \, a^{3} c^{2} d^{6} e^{5} + 39 \, a^{4} c d^{4} e^{7} - 20 \, a^{5} d^{2} e^{9}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{12 \, {\left({\left(a^{3} c^{4} d^{11} e^{5} - 3 \, a^{4} c^{3} d^{9} e^{7} + 3 \, a^{5} c^{2} d^{7} e^{9} - a^{6} c d^{5} e^{11}\right)} x^{4} + {\left(2 \, a^{3} c^{4} d^{12} e^{4} - 5 \, a^{4} c^{3} d^{10} e^{6} + 3 \, a^{5} c^{2} d^{8} e^{8} + a^{6} c d^{6} e^{10} - a^{7} d^{4} e^{12}\right)} x^{3} + {\left(a^{3} c^{4} d^{13} e^{3} - a^{4} c^{3} d^{11} e^{5} - 3 \, a^{5} c^{2} d^{9} e^{7} + 5 \, a^{6} c d^{7} e^{9} - 2 \, a^{7} d^{5} e^{11}\right)} x^{2} + {\left(a^{4} c^{3} d^{12} e^{4} - 3 \, a^{5} c^{2} d^{10} e^{6} + 3 \, a^{6} c d^{8} e^{8} - a^{7} d^{6} e^{10}\right)} x\right)}}, -\frac{3 \, {\left({\left(3 \, c^{5} d^{9} e^{2} - 4 \, a c^{4} d^{7} e^{4} - 6 \, a^{2} c^{3} d^{5} e^{6} + 12 \, a^{3} c^{2} d^{3} e^{8} - 5 \, a^{4} c d e^{10}\right)} x^{4} + {\left(6 \, c^{5} d^{10} e - 5 \, a c^{4} d^{8} e^{3} - 16 \, a^{2} c^{3} d^{6} e^{5} + 18 \, a^{3} c^{2} d^{4} e^{7} + 2 \, a^{4} c d^{2} e^{9} - 5 \, a^{5} e^{11}\right)} x^{3} + {\left(3 \, c^{5} d^{11} + 2 \, a c^{4} d^{9} e^{2} - 14 \, a^{2} c^{3} d^{7} e^{4} + 19 \, a^{4} c d^{3} e^{8} - 10 \, a^{5} d e^{10}\right)} x^{2} + {\left(3 \, a c^{4} d^{10} e - 4 \, a^{2} c^{3} d^{8} e^{3} - 6 \, a^{3} c^{2} d^{6} e^{5} + 12 \, a^{4} c d^{4} e^{7} - 5 \, a^{5} d^{2} e^{9}\right)} x\right)} \sqrt{-a d e} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{-a d e}}{2 \, {\left(a c d^{2} e^{2} x^{2} + a^{2} d^{2} e^{2} + {\left(a c d^{3} e + a^{2} d e^{3}\right)} x\right)}}\right) + 2 \, {\left(3 \, a^{2} c^{3} d^{9} e^{2} - 9 \, a^{3} c^{2} d^{7} e^{4} + 9 \, a^{4} c d^{5} e^{6} - 3 \, a^{5} d^{3} e^{8} + {\left(9 \, a c^{4} d^{8} e^{3} - 9 \, a^{2} c^{3} d^{6} e^{5} + 31 \, a^{3} c^{2} d^{4} e^{7} - 15 \, a^{4} c d^{2} e^{9}\right)} x^{3} + {\left(18 \, a c^{4} d^{9} e^{2} - 15 \, a^{2} c^{3} d^{7} e^{4} + 33 \, a^{3} c^{2} d^{5} e^{6} + 11 \, a^{4} c d^{3} e^{8} - 15 \, a^{5} d e^{10}\right)} x^{2} + {\left(9 \, a c^{4} d^{10} e - 3 \, a^{2} c^{3} d^{8} e^{3} - 9 \, a^{3} c^{2} d^{6} e^{5} + 39 \, a^{4} c d^{4} e^{7} - 20 \, a^{5} d^{2} e^{9}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{6 \, {\left({\left(a^{3} c^{4} d^{11} e^{5} - 3 \, a^{4} c^{3} d^{9} e^{7} + 3 \, a^{5} c^{2} d^{7} e^{9} - a^{6} c d^{5} e^{11}\right)} x^{4} + {\left(2 \, a^{3} c^{4} d^{12} e^{4} - 5 \, a^{4} c^{3} d^{10} e^{6} + 3 \, a^{5} c^{2} d^{8} e^{8} + a^{6} c d^{6} e^{10} - a^{7} d^{4} e^{12}\right)} x^{3} + {\left(a^{3} c^{4} d^{13} e^{3} - a^{4} c^{3} d^{11} e^{5} - 3 \, a^{5} c^{2} d^{9} e^{7} + 5 \, a^{6} c d^{7} e^{9} - 2 \, a^{7} d^{5} e^{11}\right)} x^{2} + {\left(a^{4} c^{3} d^{12} e^{4} - 3 \, a^{5} c^{2} d^{10} e^{6} + 3 \, a^{6} c d^{8} e^{8} - a^{7} d^{6} e^{10}\right)} x\right)}}\right]"," ",0,"[1/12*(3*((3*c^5*d^9*e^2 - 4*a*c^4*d^7*e^4 - 6*a^2*c^3*d^5*e^6 + 12*a^3*c^2*d^3*e^8 - 5*a^4*c*d*e^10)*x^4 + (6*c^5*d^10*e - 5*a*c^4*d^8*e^3 - 16*a^2*c^3*d^6*e^5 + 18*a^3*c^2*d^4*e^7 + 2*a^4*c*d^2*e^9 - 5*a^5*e^11)*x^3 + (3*c^5*d^11 + 2*a*c^4*d^9*e^2 - 14*a^2*c^3*d^7*e^4 + 19*a^4*c*d^3*e^8 - 10*a^5*d*e^10)*x^2 + (3*a*c^4*d^10*e - 4*a^2*c^3*d^8*e^3 - 6*a^3*c^2*d^6*e^5 + 12*a^4*c*d^4*e^7 - 5*a^5*d^2*e^9)*x)*sqrt(a*d*e)*log((8*a^2*d^2*e^2 + (c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4)*x^2 + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(a*d*e) + 8*(a*c*d^3*e + a^2*d*e^3)*x)/x^2) - 4*(3*a^2*c^3*d^9*e^2 - 9*a^3*c^2*d^7*e^4 + 9*a^4*c*d^5*e^6 - 3*a^5*d^3*e^8 + (9*a*c^4*d^8*e^3 - 9*a^2*c^3*d^6*e^5 + 31*a^3*c^2*d^4*e^7 - 15*a^4*c*d^2*e^9)*x^3 + (18*a*c^4*d^9*e^2 - 15*a^2*c^3*d^7*e^4 + 33*a^3*c^2*d^5*e^6 + 11*a^4*c*d^3*e^8 - 15*a^5*d*e^10)*x^2 + (9*a*c^4*d^10*e - 3*a^2*c^3*d^8*e^3 - 9*a^3*c^2*d^6*e^5 + 39*a^4*c*d^4*e^7 - 20*a^5*d^2*e^9)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/((a^3*c^4*d^11*e^5 - 3*a^4*c^3*d^9*e^7 + 3*a^5*c^2*d^7*e^9 - a^6*c*d^5*e^11)*x^4 + (2*a^3*c^4*d^12*e^4 - 5*a^4*c^3*d^10*e^6 + 3*a^5*c^2*d^8*e^8 + a^6*c*d^6*e^10 - a^7*d^4*e^12)*x^3 + (a^3*c^4*d^13*e^3 - a^4*c^3*d^11*e^5 - 3*a^5*c^2*d^9*e^7 + 5*a^6*c*d^7*e^9 - 2*a^7*d^5*e^11)*x^2 + (a^4*c^3*d^12*e^4 - 3*a^5*c^2*d^10*e^6 + 3*a^6*c*d^8*e^8 - a^7*d^6*e^10)*x), -1/6*(3*((3*c^5*d^9*e^2 - 4*a*c^4*d^7*e^4 - 6*a^2*c^3*d^5*e^6 + 12*a^3*c^2*d^3*e^8 - 5*a^4*c*d*e^10)*x^4 + (6*c^5*d^10*e - 5*a*c^4*d^8*e^3 - 16*a^2*c^3*d^6*e^5 + 18*a^3*c^2*d^4*e^7 + 2*a^4*c*d^2*e^9 - 5*a^5*e^11)*x^3 + (3*c^5*d^11 + 2*a*c^4*d^9*e^2 - 14*a^2*c^3*d^7*e^4 + 19*a^4*c*d^3*e^8 - 10*a^5*d*e^10)*x^2 + (3*a*c^4*d^10*e - 4*a^2*c^3*d^8*e^3 - 6*a^3*c^2*d^6*e^5 + 12*a^4*c*d^4*e^7 - 5*a^5*d^2*e^9)*x)*sqrt(-a*d*e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-a*d*e)/(a*c*d^2*e^2*x^2 + a^2*d^2*e^2 + (a*c*d^3*e + a^2*d*e^3)*x)) + 2*(3*a^2*c^3*d^9*e^2 - 9*a^3*c^2*d^7*e^4 + 9*a^4*c*d^5*e^6 - 3*a^5*d^3*e^8 + (9*a*c^4*d^8*e^3 - 9*a^2*c^3*d^6*e^5 + 31*a^3*c^2*d^4*e^7 - 15*a^4*c*d^2*e^9)*x^3 + (18*a*c^4*d^9*e^2 - 15*a^2*c^3*d^7*e^4 + 33*a^3*c^2*d^5*e^6 + 11*a^4*c*d^3*e^8 - 15*a^5*d*e^10)*x^2 + (9*a*c^4*d^10*e - 3*a^2*c^3*d^8*e^3 - 9*a^3*c^2*d^6*e^5 + 39*a^4*c*d^4*e^7 - 20*a^5*d^2*e^9)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/((a^3*c^4*d^11*e^5 - 3*a^4*c^3*d^9*e^7 + 3*a^5*c^2*d^7*e^9 - a^6*c*d^5*e^11)*x^4 + (2*a^3*c^4*d^12*e^4 - 5*a^4*c^3*d^10*e^6 + 3*a^5*c^2*d^8*e^8 + a^6*c*d^6*e^10 - a^7*d^4*e^12)*x^3 + (a^3*c^4*d^13*e^3 - a^4*c^3*d^11*e^5 - 3*a^5*c^2*d^9*e^7 + 5*a^6*c*d^7*e^9 - 2*a^7*d^5*e^11)*x^2 + (a^4*c^3*d^12*e^4 - 3*a^5*c^2*d^10*e^6 + 3*a^6*c*d^8*e^8 - a^7*d^6*e^10)*x)]","B",0
485,1,2162,0,42.287198," ","integrate(1/x^3/(e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left({\left(3 \, c^{6} d^{11} e^{2} - 3 \, a c^{5} d^{9} e^{4} - 2 \, a^{2} c^{4} d^{7} e^{6} - 6 \, a^{3} c^{3} d^{5} e^{8} + 15 \, a^{4} c^{2} d^{3} e^{10} - 7 \, a^{5} c d e^{12}\right)} x^{5} + {\left(6 \, c^{6} d^{12} e - 3 \, a c^{5} d^{10} e^{3} - 7 \, a^{2} c^{4} d^{8} e^{5} - 14 \, a^{3} c^{3} d^{6} e^{7} + 24 \, a^{4} c^{2} d^{4} e^{9} + a^{5} c d^{2} e^{11} - 7 \, a^{6} e^{13}\right)} x^{4} + {\left(3 \, c^{6} d^{13} + 3 \, a c^{5} d^{11} e^{2} - 8 \, a^{2} c^{4} d^{9} e^{4} - 10 \, a^{3} c^{3} d^{7} e^{6} + 3 \, a^{4} c^{2} d^{5} e^{8} + 23 \, a^{5} c d^{3} e^{10} - 14 \, a^{6} d e^{12}\right)} x^{3} + {\left(3 \, a c^{5} d^{12} e - 3 \, a^{2} c^{4} d^{10} e^{3} - 2 \, a^{3} c^{3} d^{8} e^{5} - 6 \, a^{4} c^{2} d^{6} e^{7} + 15 \, a^{5} c d^{4} e^{9} - 7 \, a^{6} d^{2} e^{11}\right)} x^{2}\right)} \sqrt{a d e} \log\left(\frac{8 \, a^{2} d^{2} e^{2} + {\left(c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} x^{2} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{a d e} + 8 \, {\left(a c d^{3} e + a^{2} d e^{3}\right)} x}{x^{2}}\right) - 4 \, {\left(6 \, a^{3} c^{3} d^{10} e^{3} - 18 \, a^{4} c^{2} d^{8} e^{5} + 18 \, a^{5} c d^{6} e^{7} - 6 \, a^{6} d^{4} e^{9} - {\left(45 \, a c^{5} d^{10} e^{3} - 30 \, a^{2} c^{4} d^{8} e^{5} - 36 \, a^{3} c^{3} d^{6} e^{7} + 190 \, a^{4} c^{2} d^{4} e^{9} - 105 \, a^{5} c d^{2} e^{11}\right)} x^{4} - {\left(90 \, a c^{5} d^{11} e^{2} - 45 \, a^{2} c^{4} d^{9} e^{4} - 84 \, a^{3} c^{3} d^{7} e^{6} + 222 \, a^{4} c^{2} d^{5} e^{8} + 50 \, a^{5} c d^{3} e^{10} - 105 \, a^{6} d e^{12}\right)} x^{3} - {\left(45 \, a c^{5} d^{12} e - 66 \, a^{3} c^{3} d^{8} e^{5} - 12 \, a^{4} c^{2} d^{6} e^{7} + 237 \, a^{5} c d^{4} e^{9} - 140 \, a^{6} d^{2} e^{11}\right)} x^{2} - 3 \, {\left(5 \, a^{2} c^{4} d^{11} e^{2} - 8 \, a^{3} c^{3} d^{9} e^{4} - 6 \, a^{4} c^{2} d^{7} e^{6} + 16 \, a^{5} c d^{5} e^{8} - 7 \, a^{6} d^{3} e^{10}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{48 \, {\left({\left(a^{4} c^{4} d^{12} e^{6} - 3 \, a^{5} c^{3} d^{10} e^{8} + 3 \, a^{6} c^{2} d^{8} e^{10} - a^{7} c d^{6} e^{12}\right)} x^{5} + {\left(2 \, a^{4} c^{4} d^{13} e^{5} - 5 \, a^{5} c^{3} d^{11} e^{7} + 3 \, a^{6} c^{2} d^{9} e^{9} + a^{7} c d^{7} e^{11} - a^{8} d^{5} e^{13}\right)} x^{4} + {\left(a^{4} c^{4} d^{14} e^{4} - a^{5} c^{3} d^{12} e^{6} - 3 \, a^{6} c^{2} d^{10} e^{8} + 5 \, a^{7} c d^{8} e^{10} - 2 \, a^{8} d^{6} e^{12}\right)} x^{3} + {\left(a^{5} c^{3} d^{13} e^{5} - 3 \, a^{6} c^{2} d^{11} e^{7} + 3 \, a^{7} c d^{9} e^{9} - a^{8} d^{7} e^{11}\right)} x^{2}\right)}}, \frac{15 \, {\left({\left(3 \, c^{6} d^{11} e^{2} - 3 \, a c^{5} d^{9} e^{4} - 2 \, a^{2} c^{4} d^{7} e^{6} - 6 \, a^{3} c^{3} d^{5} e^{8} + 15 \, a^{4} c^{2} d^{3} e^{10} - 7 \, a^{5} c d e^{12}\right)} x^{5} + {\left(6 \, c^{6} d^{12} e - 3 \, a c^{5} d^{10} e^{3} - 7 \, a^{2} c^{4} d^{8} e^{5} - 14 \, a^{3} c^{3} d^{6} e^{7} + 24 \, a^{4} c^{2} d^{4} e^{9} + a^{5} c d^{2} e^{11} - 7 \, a^{6} e^{13}\right)} x^{4} + {\left(3 \, c^{6} d^{13} + 3 \, a c^{5} d^{11} e^{2} - 8 \, a^{2} c^{4} d^{9} e^{4} - 10 \, a^{3} c^{3} d^{7} e^{6} + 3 \, a^{4} c^{2} d^{5} e^{8} + 23 \, a^{5} c d^{3} e^{10} - 14 \, a^{6} d e^{12}\right)} x^{3} + {\left(3 \, a c^{5} d^{12} e - 3 \, a^{2} c^{4} d^{10} e^{3} - 2 \, a^{3} c^{3} d^{8} e^{5} - 6 \, a^{4} c^{2} d^{6} e^{7} + 15 \, a^{5} c d^{4} e^{9} - 7 \, a^{6} d^{2} e^{11}\right)} x^{2}\right)} \sqrt{-a d e} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{-a d e}}{2 \, {\left(a c d^{2} e^{2} x^{2} + a^{2} d^{2} e^{2} + {\left(a c d^{3} e + a^{2} d e^{3}\right)} x\right)}}\right) - 2 \, {\left(6 \, a^{3} c^{3} d^{10} e^{3} - 18 \, a^{4} c^{2} d^{8} e^{5} + 18 \, a^{5} c d^{6} e^{7} - 6 \, a^{6} d^{4} e^{9} - {\left(45 \, a c^{5} d^{10} e^{3} - 30 \, a^{2} c^{4} d^{8} e^{5} - 36 \, a^{3} c^{3} d^{6} e^{7} + 190 \, a^{4} c^{2} d^{4} e^{9} - 105 \, a^{5} c d^{2} e^{11}\right)} x^{4} - {\left(90 \, a c^{5} d^{11} e^{2} - 45 \, a^{2} c^{4} d^{9} e^{4} - 84 \, a^{3} c^{3} d^{7} e^{6} + 222 \, a^{4} c^{2} d^{5} e^{8} + 50 \, a^{5} c d^{3} e^{10} - 105 \, a^{6} d e^{12}\right)} x^{3} - {\left(45 \, a c^{5} d^{12} e - 66 \, a^{3} c^{3} d^{8} e^{5} - 12 \, a^{4} c^{2} d^{6} e^{7} + 237 \, a^{5} c d^{4} e^{9} - 140 \, a^{6} d^{2} e^{11}\right)} x^{2} - 3 \, {\left(5 \, a^{2} c^{4} d^{11} e^{2} - 8 \, a^{3} c^{3} d^{9} e^{4} - 6 \, a^{4} c^{2} d^{7} e^{6} + 16 \, a^{5} c d^{5} e^{8} - 7 \, a^{6} d^{3} e^{10}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{24 \, {\left({\left(a^{4} c^{4} d^{12} e^{6} - 3 \, a^{5} c^{3} d^{10} e^{8} + 3 \, a^{6} c^{2} d^{8} e^{10} - a^{7} c d^{6} e^{12}\right)} x^{5} + {\left(2 \, a^{4} c^{4} d^{13} e^{5} - 5 \, a^{5} c^{3} d^{11} e^{7} + 3 \, a^{6} c^{2} d^{9} e^{9} + a^{7} c d^{7} e^{11} - a^{8} d^{5} e^{13}\right)} x^{4} + {\left(a^{4} c^{4} d^{14} e^{4} - a^{5} c^{3} d^{12} e^{6} - 3 \, a^{6} c^{2} d^{10} e^{8} + 5 \, a^{7} c d^{8} e^{10} - 2 \, a^{8} d^{6} e^{12}\right)} x^{3} + {\left(a^{5} c^{3} d^{13} e^{5} - 3 \, a^{6} c^{2} d^{11} e^{7} + 3 \, a^{7} c d^{9} e^{9} - a^{8} d^{7} e^{11}\right)} x^{2}\right)}}\right]"," ",0,"[1/48*(15*((3*c^6*d^11*e^2 - 3*a*c^5*d^9*e^4 - 2*a^2*c^4*d^7*e^6 - 6*a^3*c^3*d^5*e^8 + 15*a^4*c^2*d^3*e^10 - 7*a^5*c*d*e^12)*x^5 + (6*c^6*d^12*e - 3*a*c^5*d^10*e^3 - 7*a^2*c^4*d^8*e^5 - 14*a^3*c^3*d^6*e^7 + 24*a^4*c^2*d^4*e^9 + a^5*c*d^2*e^11 - 7*a^6*e^13)*x^4 + (3*c^6*d^13 + 3*a*c^5*d^11*e^2 - 8*a^2*c^4*d^9*e^4 - 10*a^3*c^3*d^7*e^6 + 3*a^4*c^2*d^5*e^8 + 23*a^5*c*d^3*e^10 - 14*a^6*d*e^12)*x^3 + (3*a*c^5*d^12*e - 3*a^2*c^4*d^10*e^3 - 2*a^3*c^3*d^8*e^5 - 6*a^4*c^2*d^6*e^7 + 15*a^5*c*d^4*e^9 - 7*a^6*d^2*e^11)*x^2)*sqrt(a*d*e)*log((8*a^2*d^2*e^2 + (c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4)*x^2 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(a*d*e) + 8*(a*c*d^3*e + a^2*d*e^3)*x)/x^2) - 4*(6*a^3*c^3*d^10*e^3 - 18*a^4*c^2*d^8*e^5 + 18*a^5*c*d^6*e^7 - 6*a^6*d^4*e^9 - (45*a*c^5*d^10*e^3 - 30*a^2*c^4*d^8*e^5 - 36*a^3*c^3*d^6*e^7 + 190*a^4*c^2*d^4*e^9 - 105*a^5*c*d^2*e^11)*x^4 - (90*a*c^5*d^11*e^2 - 45*a^2*c^4*d^9*e^4 - 84*a^3*c^3*d^7*e^6 + 222*a^4*c^2*d^5*e^8 + 50*a^5*c*d^3*e^10 - 105*a^6*d*e^12)*x^3 - (45*a*c^5*d^12*e - 66*a^3*c^3*d^8*e^5 - 12*a^4*c^2*d^6*e^7 + 237*a^5*c*d^4*e^9 - 140*a^6*d^2*e^11)*x^2 - 3*(5*a^2*c^4*d^11*e^2 - 8*a^3*c^3*d^9*e^4 - 6*a^4*c^2*d^7*e^6 + 16*a^5*c*d^5*e^8 - 7*a^6*d^3*e^10)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/((a^4*c^4*d^12*e^6 - 3*a^5*c^3*d^10*e^8 + 3*a^6*c^2*d^8*e^10 - a^7*c*d^6*e^12)*x^5 + (2*a^4*c^4*d^13*e^5 - 5*a^5*c^3*d^11*e^7 + 3*a^6*c^2*d^9*e^9 + a^7*c*d^7*e^11 - a^8*d^5*e^13)*x^4 + (a^4*c^4*d^14*e^4 - a^5*c^3*d^12*e^6 - 3*a^6*c^2*d^10*e^8 + 5*a^7*c*d^8*e^10 - 2*a^8*d^6*e^12)*x^3 + (a^5*c^3*d^13*e^5 - 3*a^6*c^2*d^11*e^7 + 3*a^7*c*d^9*e^9 - a^8*d^7*e^11)*x^2), 1/24*(15*((3*c^6*d^11*e^2 - 3*a*c^5*d^9*e^4 - 2*a^2*c^4*d^7*e^6 - 6*a^3*c^3*d^5*e^8 + 15*a^4*c^2*d^3*e^10 - 7*a^5*c*d*e^12)*x^5 + (6*c^6*d^12*e - 3*a*c^5*d^10*e^3 - 7*a^2*c^4*d^8*e^5 - 14*a^3*c^3*d^6*e^7 + 24*a^4*c^2*d^4*e^9 + a^5*c*d^2*e^11 - 7*a^6*e^13)*x^4 + (3*c^6*d^13 + 3*a*c^5*d^11*e^2 - 8*a^2*c^4*d^9*e^4 - 10*a^3*c^3*d^7*e^6 + 3*a^4*c^2*d^5*e^8 + 23*a^5*c*d^3*e^10 - 14*a^6*d*e^12)*x^3 + (3*a*c^5*d^12*e - 3*a^2*c^4*d^10*e^3 - 2*a^3*c^3*d^8*e^5 - 6*a^4*c^2*d^6*e^7 + 15*a^5*c*d^4*e^9 - 7*a^6*d^2*e^11)*x^2)*sqrt(-a*d*e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-a*d*e)/(a*c*d^2*e^2*x^2 + a^2*d^2*e^2 + (a*c*d^3*e + a^2*d*e^3)*x)) - 2*(6*a^3*c^3*d^10*e^3 - 18*a^4*c^2*d^8*e^5 + 18*a^5*c*d^6*e^7 - 6*a^6*d^4*e^9 - (45*a*c^5*d^10*e^3 - 30*a^2*c^4*d^8*e^5 - 36*a^3*c^3*d^6*e^7 + 190*a^4*c^2*d^4*e^9 - 105*a^5*c*d^2*e^11)*x^4 - (90*a*c^5*d^11*e^2 - 45*a^2*c^4*d^9*e^4 - 84*a^3*c^3*d^7*e^6 + 222*a^4*c^2*d^5*e^8 + 50*a^5*c*d^3*e^10 - 105*a^6*d*e^12)*x^3 - (45*a*c^5*d^12*e - 66*a^3*c^3*d^8*e^5 - 12*a^4*c^2*d^6*e^7 + 237*a^5*c*d^4*e^9 - 140*a^6*d^2*e^11)*x^2 - 3*(5*a^2*c^4*d^11*e^2 - 8*a^3*c^3*d^9*e^4 - 6*a^4*c^2*d^7*e^6 + 16*a^5*c*d^5*e^8 - 7*a^6*d^3*e^10)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/((a^4*c^4*d^12*e^6 - 3*a^5*c^3*d^10*e^8 + 3*a^6*c^2*d^8*e^10 - a^7*c*d^6*e^12)*x^5 + (2*a^4*c^4*d^13*e^5 - 5*a^5*c^3*d^11*e^7 + 3*a^6*c^2*d^9*e^9 + a^7*c*d^7*e^11 - a^8*d^5*e^13)*x^4 + (a^4*c^4*d^14*e^4 - a^5*c^3*d^12*e^6 - 3*a^6*c^2*d^10*e^8 + 5*a^7*c*d^8*e^10 - 2*a^8*d^6*e^12)*x^3 + (a^5*c^3*d^13*e^5 - 3*a^6*c^2*d^11*e^7 + 3*a^7*c*d^9*e^9 - a^8*d^7*e^11)*x^2)]","B",0
486,1,2526,0,93.160778," ","integrate(1/x^4/(e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left({\left(7 \, c^{7} d^{13} e^{2} - 6 \, a c^{6} d^{11} e^{4} - 3 \, a^{2} c^{5} d^{9} e^{6} - 4 \, a^{3} c^{4} d^{7} e^{8} - 15 \, a^{4} c^{3} d^{5} e^{10} + 42 \, a^{5} c^{2} d^{3} e^{12} - 21 \, a^{6} c d e^{14}\right)} x^{6} + {\left(14 \, c^{7} d^{14} e - 5 \, a c^{6} d^{12} e^{3} - 12 \, a^{2} c^{5} d^{10} e^{5} - 11 \, a^{3} c^{4} d^{8} e^{7} - 34 \, a^{4} c^{3} d^{6} e^{9} + 69 \, a^{5} c^{2} d^{4} e^{11} - 21 \, a^{7} e^{15}\right)} x^{5} + {\left(7 \, c^{7} d^{15} + 8 \, a c^{6} d^{13} e^{2} - 15 \, a^{2} c^{5} d^{11} e^{4} - 10 \, a^{3} c^{4} d^{9} e^{6} - 23 \, a^{4} c^{3} d^{7} e^{8} + 12 \, a^{5} c^{2} d^{5} e^{10} + 63 \, a^{6} c d^{3} e^{12} - 42 \, a^{7} d e^{14}\right)} x^{4} + {\left(7 \, a c^{6} d^{14} e - 6 \, a^{2} c^{5} d^{12} e^{3} - 3 \, a^{3} c^{4} d^{10} e^{5} - 4 \, a^{4} c^{3} d^{8} e^{7} - 15 \, a^{5} c^{2} d^{6} e^{9} + 42 \, a^{6} c d^{4} e^{11} - 21 \, a^{7} d^{2} e^{13}\right)} x^{3}\right)} \sqrt{a d e} \log\left(\frac{8 \, a^{2} d^{2} e^{2} + {\left(c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} x^{2} + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{a d e} + 8 \, {\left(a c d^{3} e + a^{2} d e^{3}\right)} x}{x^{2}}\right) - 4 \, {\left(8 \, a^{4} c^{3} d^{11} e^{4} - 24 \, a^{5} c^{2} d^{9} e^{6} + 24 \, a^{6} c d^{7} e^{8} - 8 \, a^{7} d^{5} e^{10} + {\left(105 \, a c^{6} d^{12} e^{3} - 55 \, a^{2} c^{5} d^{10} e^{5} - 54 \, a^{3} c^{4} d^{8} e^{7} - 78 \, a^{4} c^{3} d^{6} e^{9} + 525 \, a^{5} c^{2} d^{4} e^{11} - 315 \, a^{6} c d^{2} e^{13}\right)} x^{5} + {\left(210 \, a c^{6} d^{13} e^{2} - 75 \, a^{2} c^{5} d^{11} e^{4} - 131 \, a^{3} c^{4} d^{9} e^{6} - 174 \, a^{4} c^{3} d^{7} e^{8} + 636 \, a^{5} c^{2} d^{5} e^{10} + 105 \, a^{6} c d^{3} e^{12} - 315 \, a^{7} d e^{14}\right)} x^{4} + {\left(105 \, a c^{6} d^{14} e + 15 \, a^{2} c^{5} d^{12} e^{3} - 114 \, a^{3} c^{4} d^{10} e^{5} - 106 \, a^{4} c^{3} d^{8} e^{7} - 3 \, a^{5} c^{2} d^{6} e^{9} + 651 \, a^{6} c d^{4} e^{11} - 420 \, a^{7} d^{2} e^{13}\right)} x^{3} + {\left(35 \, a^{2} c^{5} d^{13} e^{2} - 51 \, a^{3} c^{4} d^{11} e^{4} + 6 \, a^{4} c^{3} d^{9} e^{6} - 62 \, a^{5} c^{2} d^{7} e^{8} + 135 \, a^{6} c d^{5} e^{10} - 63 \, a^{7} d^{3} e^{12}\right)} x^{2} - 2 \, {\left(7 \, a^{3} c^{4} d^{12} e^{3} - 12 \, a^{4} c^{3} d^{10} e^{5} - 6 \, a^{5} c^{2} d^{8} e^{7} + 20 \, a^{6} c d^{6} e^{9} - 9 \, a^{7} d^{4} e^{11}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{96 \, {\left({\left(a^{5} c^{4} d^{13} e^{7} - 3 \, a^{6} c^{3} d^{11} e^{9} + 3 \, a^{7} c^{2} d^{9} e^{11} - a^{8} c d^{7} e^{13}\right)} x^{6} + {\left(2 \, a^{5} c^{4} d^{14} e^{6} - 5 \, a^{6} c^{3} d^{12} e^{8} + 3 \, a^{7} c^{2} d^{10} e^{10} + a^{8} c d^{8} e^{12} - a^{9} d^{6} e^{14}\right)} x^{5} + {\left(a^{5} c^{4} d^{15} e^{5} - a^{6} c^{3} d^{13} e^{7} - 3 \, a^{7} c^{2} d^{11} e^{9} + 5 \, a^{8} c d^{9} e^{11} - 2 \, a^{9} d^{7} e^{13}\right)} x^{4} + {\left(a^{6} c^{3} d^{14} e^{6} - 3 \, a^{7} c^{2} d^{12} e^{8} + 3 \, a^{8} c d^{10} e^{10} - a^{9} d^{8} e^{12}\right)} x^{3}\right)}}, -\frac{15 \, {\left({\left(7 \, c^{7} d^{13} e^{2} - 6 \, a c^{6} d^{11} e^{4} - 3 \, a^{2} c^{5} d^{9} e^{6} - 4 \, a^{3} c^{4} d^{7} e^{8} - 15 \, a^{4} c^{3} d^{5} e^{10} + 42 \, a^{5} c^{2} d^{3} e^{12} - 21 \, a^{6} c d e^{14}\right)} x^{6} + {\left(14 \, c^{7} d^{14} e - 5 \, a c^{6} d^{12} e^{3} - 12 \, a^{2} c^{5} d^{10} e^{5} - 11 \, a^{3} c^{4} d^{8} e^{7} - 34 \, a^{4} c^{3} d^{6} e^{9} + 69 \, a^{5} c^{2} d^{4} e^{11} - 21 \, a^{7} e^{15}\right)} x^{5} + {\left(7 \, c^{7} d^{15} + 8 \, a c^{6} d^{13} e^{2} - 15 \, a^{2} c^{5} d^{11} e^{4} - 10 \, a^{3} c^{4} d^{9} e^{6} - 23 \, a^{4} c^{3} d^{7} e^{8} + 12 \, a^{5} c^{2} d^{5} e^{10} + 63 \, a^{6} c d^{3} e^{12} - 42 \, a^{7} d e^{14}\right)} x^{4} + {\left(7 \, a c^{6} d^{14} e - 6 \, a^{2} c^{5} d^{12} e^{3} - 3 \, a^{3} c^{4} d^{10} e^{5} - 4 \, a^{4} c^{3} d^{8} e^{7} - 15 \, a^{5} c^{2} d^{6} e^{9} + 42 \, a^{6} c d^{4} e^{11} - 21 \, a^{7} d^{2} e^{13}\right)} x^{3}\right)} \sqrt{-a d e} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{-a d e}}{2 \, {\left(a c d^{2} e^{2} x^{2} + a^{2} d^{2} e^{2} + {\left(a c d^{3} e + a^{2} d e^{3}\right)} x\right)}}\right) + 2 \, {\left(8 \, a^{4} c^{3} d^{11} e^{4} - 24 \, a^{5} c^{2} d^{9} e^{6} + 24 \, a^{6} c d^{7} e^{8} - 8 \, a^{7} d^{5} e^{10} + {\left(105 \, a c^{6} d^{12} e^{3} - 55 \, a^{2} c^{5} d^{10} e^{5} - 54 \, a^{3} c^{4} d^{8} e^{7} - 78 \, a^{4} c^{3} d^{6} e^{9} + 525 \, a^{5} c^{2} d^{4} e^{11} - 315 \, a^{6} c d^{2} e^{13}\right)} x^{5} + {\left(210 \, a c^{6} d^{13} e^{2} - 75 \, a^{2} c^{5} d^{11} e^{4} - 131 \, a^{3} c^{4} d^{9} e^{6} - 174 \, a^{4} c^{3} d^{7} e^{8} + 636 \, a^{5} c^{2} d^{5} e^{10} + 105 \, a^{6} c d^{3} e^{12} - 315 \, a^{7} d e^{14}\right)} x^{4} + {\left(105 \, a c^{6} d^{14} e + 15 \, a^{2} c^{5} d^{12} e^{3} - 114 \, a^{3} c^{4} d^{10} e^{5} - 106 \, a^{4} c^{3} d^{8} e^{7} - 3 \, a^{5} c^{2} d^{6} e^{9} + 651 \, a^{6} c d^{4} e^{11} - 420 \, a^{7} d^{2} e^{13}\right)} x^{3} + {\left(35 \, a^{2} c^{5} d^{13} e^{2} - 51 \, a^{3} c^{4} d^{11} e^{4} + 6 \, a^{4} c^{3} d^{9} e^{6} - 62 \, a^{5} c^{2} d^{7} e^{8} + 135 \, a^{6} c d^{5} e^{10} - 63 \, a^{7} d^{3} e^{12}\right)} x^{2} - 2 \, {\left(7 \, a^{3} c^{4} d^{12} e^{3} - 12 \, a^{4} c^{3} d^{10} e^{5} - 6 \, a^{5} c^{2} d^{8} e^{7} + 20 \, a^{6} c d^{6} e^{9} - 9 \, a^{7} d^{4} e^{11}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{48 \, {\left({\left(a^{5} c^{4} d^{13} e^{7} - 3 \, a^{6} c^{3} d^{11} e^{9} + 3 \, a^{7} c^{2} d^{9} e^{11} - a^{8} c d^{7} e^{13}\right)} x^{6} + {\left(2 \, a^{5} c^{4} d^{14} e^{6} - 5 \, a^{6} c^{3} d^{12} e^{8} + 3 \, a^{7} c^{2} d^{10} e^{10} + a^{8} c d^{8} e^{12} - a^{9} d^{6} e^{14}\right)} x^{5} + {\left(a^{5} c^{4} d^{15} e^{5} - a^{6} c^{3} d^{13} e^{7} - 3 \, a^{7} c^{2} d^{11} e^{9} + 5 \, a^{8} c d^{9} e^{11} - 2 \, a^{9} d^{7} e^{13}\right)} x^{4} + {\left(a^{6} c^{3} d^{14} e^{6} - 3 \, a^{7} c^{2} d^{12} e^{8} + 3 \, a^{8} c d^{10} e^{10} - a^{9} d^{8} e^{12}\right)} x^{3}\right)}}\right]"," ",0,"[1/96*(15*((7*c^7*d^13*e^2 - 6*a*c^6*d^11*e^4 - 3*a^2*c^5*d^9*e^6 - 4*a^3*c^4*d^7*e^8 - 15*a^4*c^3*d^5*e^10 + 42*a^5*c^2*d^3*e^12 - 21*a^6*c*d*e^14)*x^6 + (14*c^7*d^14*e - 5*a*c^6*d^12*e^3 - 12*a^2*c^5*d^10*e^5 - 11*a^3*c^4*d^8*e^7 - 34*a^4*c^3*d^6*e^9 + 69*a^5*c^2*d^4*e^11 - 21*a^7*e^15)*x^5 + (7*c^7*d^15 + 8*a*c^6*d^13*e^2 - 15*a^2*c^5*d^11*e^4 - 10*a^3*c^4*d^9*e^6 - 23*a^4*c^3*d^7*e^8 + 12*a^5*c^2*d^5*e^10 + 63*a^6*c*d^3*e^12 - 42*a^7*d*e^14)*x^4 + (7*a*c^6*d^14*e - 6*a^2*c^5*d^12*e^3 - 3*a^3*c^4*d^10*e^5 - 4*a^4*c^3*d^8*e^7 - 15*a^5*c^2*d^6*e^9 + 42*a^6*c*d^4*e^11 - 21*a^7*d^2*e^13)*x^3)*sqrt(a*d*e)*log((8*a^2*d^2*e^2 + (c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4)*x^2 + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(a*d*e) + 8*(a*c*d^3*e + a^2*d*e^3)*x)/x^2) - 4*(8*a^4*c^3*d^11*e^4 - 24*a^5*c^2*d^9*e^6 + 24*a^6*c*d^7*e^8 - 8*a^7*d^5*e^10 + (105*a*c^6*d^12*e^3 - 55*a^2*c^5*d^10*e^5 - 54*a^3*c^4*d^8*e^7 - 78*a^4*c^3*d^6*e^9 + 525*a^5*c^2*d^4*e^11 - 315*a^6*c*d^2*e^13)*x^5 + (210*a*c^6*d^13*e^2 - 75*a^2*c^5*d^11*e^4 - 131*a^3*c^4*d^9*e^6 - 174*a^4*c^3*d^7*e^8 + 636*a^5*c^2*d^5*e^10 + 105*a^6*c*d^3*e^12 - 315*a^7*d*e^14)*x^4 + (105*a*c^6*d^14*e + 15*a^2*c^5*d^12*e^3 - 114*a^3*c^4*d^10*e^5 - 106*a^4*c^3*d^8*e^7 - 3*a^5*c^2*d^6*e^9 + 651*a^6*c*d^4*e^11 - 420*a^7*d^2*e^13)*x^3 + (35*a^2*c^5*d^13*e^2 - 51*a^3*c^4*d^11*e^4 + 6*a^4*c^3*d^9*e^6 - 62*a^5*c^2*d^7*e^8 + 135*a^6*c*d^5*e^10 - 63*a^7*d^3*e^12)*x^2 - 2*(7*a^3*c^4*d^12*e^3 - 12*a^4*c^3*d^10*e^5 - 6*a^5*c^2*d^8*e^7 + 20*a^6*c*d^6*e^9 - 9*a^7*d^4*e^11)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/((a^5*c^4*d^13*e^7 - 3*a^6*c^3*d^11*e^9 + 3*a^7*c^2*d^9*e^11 - a^8*c*d^7*e^13)*x^6 + (2*a^5*c^4*d^14*e^6 - 5*a^6*c^3*d^12*e^8 + 3*a^7*c^2*d^10*e^10 + a^8*c*d^8*e^12 - a^9*d^6*e^14)*x^5 + (a^5*c^4*d^15*e^5 - a^6*c^3*d^13*e^7 - 3*a^7*c^2*d^11*e^9 + 5*a^8*c*d^9*e^11 - 2*a^9*d^7*e^13)*x^4 + (a^6*c^3*d^14*e^6 - 3*a^7*c^2*d^12*e^8 + 3*a^8*c*d^10*e^10 - a^9*d^8*e^12)*x^3), -1/48*(15*((7*c^7*d^13*e^2 - 6*a*c^6*d^11*e^4 - 3*a^2*c^5*d^9*e^6 - 4*a^3*c^4*d^7*e^8 - 15*a^4*c^3*d^5*e^10 + 42*a^5*c^2*d^3*e^12 - 21*a^6*c*d*e^14)*x^6 + (14*c^7*d^14*e - 5*a*c^6*d^12*e^3 - 12*a^2*c^5*d^10*e^5 - 11*a^3*c^4*d^8*e^7 - 34*a^4*c^3*d^6*e^9 + 69*a^5*c^2*d^4*e^11 - 21*a^7*e^15)*x^5 + (7*c^7*d^15 + 8*a*c^6*d^13*e^2 - 15*a^2*c^5*d^11*e^4 - 10*a^3*c^4*d^9*e^6 - 23*a^4*c^3*d^7*e^8 + 12*a^5*c^2*d^5*e^10 + 63*a^6*c*d^3*e^12 - 42*a^7*d*e^14)*x^4 + (7*a*c^6*d^14*e - 6*a^2*c^5*d^12*e^3 - 3*a^3*c^4*d^10*e^5 - 4*a^4*c^3*d^8*e^7 - 15*a^5*c^2*d^6*e^9 + 42*a^6*c*d^4*e^11 - 21*a^7*d^2*e^13)*x^3)*sqrt(-a*d*e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-a*d*e)/(a*c*d^2*e^2*x^2 + a^2*d^2*e^2 + (a*c*d^3*e + a^2*d*e^3)*x)) + 2*(8*a^4*c^3*d^11*e^4 - 24*a^5*c^2*d^9*e^6 + 24*a^6*c*d^7*e^8 - 8*a^7*d^5*e^10 + (105*a*c^6*d^12*e^3 - 55*a^2*c^5*d^10*e^5 - 54*a^3*c^4*d^8*e^7 - 78*a^4*c^3*d^6*e^9 + 525*a^5*c^2*d^4*e^11 - 315*a^6*c*d^2*e^13)*x^5 + (210*a*c^6*d^13*e^2 - 75*a^2*c^5*d^11*e^4 - 131*a^3*c^4*d^9*e^6 - 174*a^4*c^3*d^7*e^8 + 636*a^5*c^2*d^5*e^10 + 105*a^6*c*d^3*e^12 - 315*a^7*d*e^14)*x^4 + (105*a*c^6*d^14*e + 15*a^2*c^5*d^12*e^3 - 114*a^3*c^4*d^10*e^5 - 106*a^4*c^3*d^8*e^7 - 3*a^5*c^2*d^6*e^9 + 651*a^6*c*d^4*e^11 - 420*a^7*d^2*e^13)*x^3 + (35*a^2*c^5*d^13*e^2 - 51*a^3*c^4*d^11*e^4 + 6*a^4*c^3*d^9*e^6 - 62*a^5*c^2*d^7*e^8 + 135*a^6*c*d^5*e^10 - 63*a^7*d^3*e^12)*x^2 - 2*(7*a^3*c^4*d^12*e^3 - 12*a^4*c^3*d^10*e^5 - 6*a^5*c^2*d^8*e^7 + 20*a^6*c*d^6*e^9 - 9*a^7*d^4*e^11)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/((a^5*c^4*d^13*e^7 - 3*a^6*c^3*d^11*e^9 + 3*a^7*c^2*d^9*e^11 - a^8*c*d^7*e^13)*x^6 + (2*a^5*c^4*d^14*e^6 - 5*a^6*c^3*d^12*e^8 + 3*a^7*c^2*d^10*e^10 + a^8*c*d^8*e^12 - a^9*d^6*e^14)*x^5 + (a^5*c^4*d^15*e^5 - a^6*c^3*d^13*e^7 - 3*a^7*c^2*d^11*e^9 + 5*a^8*c*d^9*e^11 - 2*a^9*d^7*e^13)*x^4 + (a^6*c^3*d^14*e^6 - 3*a^7*c^2*d^12*e^8 + 3*a^8*c*d^10*e^10 - a^9*d^8*e^12)*x^3)]","B",0
487,1,820,0,27.129461," ","integrate(x^2/(e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(40 \, a^{2} c^{2} d^{6} e^{2} + 80 \, a^{3} c d^{4} e^{4} + 8 \, a^{4} d^{2} e^{6} + 8 \, {\left(c^{4} d^{6} e^{2} + 10 \, a c^{3} d^{4} e^{4} + 5 \, a^{2} c^{2} d^{2} e^{6}\right)} x^{4} + 4 \, {\left(5 \, c^{4} d^{7} e + 53 \, a c^{3} d^{5} e^{3} + 55 \, a^{2} c^{2} d^{3} e^{5} + 15 \, a^{3} c d e^{7}\right)} x^{3} + 3 \, {\left(5 \, c^{4} d^{8} + 60 \, a c^{3} d^{6} e^{2} + 126 \, a^{2} c^{2} d^{4} e^{4} + 60 \, a^{3} c d^{2} e^{6} + 5 \, a^{4} e^{8}\right)} x^{2} + 4 \, {\left(15 \, a c^{3} d^{7} e + 55 \, a^{2} c^{2} d^{5} e^{3} + 53 \, a^{3} c d^{3} e^{5} + 5 \, a^{4} d e^{7}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{15 \, {\left(a^{2} c^{5} d^{13} e^{2} - 5 \, a^{3} c^{4} d^{11} e^{4} + 10 \, a^{4} c^{3} d^{9} e^{6} - 10 \, a^{5} c^{2} d^{7} e^{8} + 5 \, a^{6} c d^{5} e^{10} - a^{7} d^{3} e^{12} + {\left(c^{7} d^{12} e^{3} - 5 \, a c^{6} d^{10} e^{5} + 10 \, a^{2} c^{5} d^{8} e^{7} - 10 \, a^{3} c^{4} d^{6} e^{9} + 5 \, a^{4} c^{3} d^{4} e^{11} - a^{5} c^{2} d^{2} e^{13}\right)} x^{5} + {\left(3 \, c^{7} d^{13} e^{2} - 13 \, a c^{6} d^{11} e^{4} + 20 \, a^{2} c^{5} d^{9} e^{6} - 10 \, a^{3} c^{4} d^{7} e^{8} - 5 \, a^{4} c^{3} d^{5} e^{10} + 7 \, a^{5} c^{2} d^{3} e^{12} - 2 \, a^{6} c d e^{14}\right)} x^{4} + {\left(3 \, c^{7} d^{14} e - 9 \, a c^{6} d^{12} e^{3} + a^{2} c^{5} d^{10} e^{5} + 25 \, a^{3} c^{4} d^{8} e^{7} - 35 \, a^{4} c^{3} d^{6} e^{9} + 17 \, a^{5} c^{2} d^{4} e^{11} - a^{6} c d^{2} e^{13} - a^{7} e^{15}\right)} x^{3} + {\left(c^{7} d^{15} + a c^{6} d^{13} e^{2} - 17 \, a^{2} c^{5} d^{11} e^{4} + 35 \, a^{3} c^{4} d^{9} e^{6} - 25 \, a^{4} c^{3} d^{7} e^{8} - a^{5} c^{2} d^{5} e^{10} + 9 \, a^{6} c d^{3} e^{12} - 3 \, a^{7} d e^{14}\right)} x^{2} + {\left(2 \, a c^{6} d^{14} e - 7 \, a^{2} c^{5} d^{12} e^{3} + 5 \, a^{3} c^{4} d^{10} e^{5} + 10 \, a^{4} c^{3} d^{8} e^{7} - 20 \, a^{5} c^{2} d^{6} e^{9} + 13 \, a^{6} c d^{4} e^{11} - 3 \, a^{7} d^{2} e^{13}\right)} x\right)}}"," ",0,"2/15*(40*a^2*c^2*d^6*e^2 + 80*a^3*c*d^4*e^4 + 8*a^4*d^2*e^6 + 8*(c^4*d^6*e^2 + 10*a*c^3*d^4*e^4 + 5*a^2*c^2*d^2*e^6)*x^4 + 4*(5*c^4*d^7*e + 53*a*c^3*d^5*e^3 + 55*a^2*c^2*d^3*e^5 + 15*a^3*c*d*e^7)*x^3 + 3*(5*c^4*d^8 + 60*a*c^3*d^6*e^2 + 126*a^2*c^2*d^4*e^4 + 60*a^3*c*d^2*e^6 + 5*a^4*e^8)*x^2 + 4*(15*a*c^3*d^7*e + 55*a^2*c^2*d^5*e^3 + 53*a^3*c*d^3*e^5 + 5*a^4*d*e^7)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)/(a^2*c^5*d^13*e^2 - 5*a^3*c^4*d^11*e^4 + 10*a^4*c^3*d^9*e^6 - 10*a^5*c^2*d^7*e^8 + 5*a^6*c*d^5*e^10 - a^7*d^3*e^12 + (c^7*d^12*e^3 - 5*a*c^6*d^10*e^5 + 10*a^2*c^5*d^8*e^7 - 10*a^3*c^4*d^6*e^9 + 5*a^4*c^3*d^4*e^11 - a^5*c^2*d^2*e^13)*x^5 + (3*c^7*d^13*e^2 - 13*a*c^6*d^11*e^4 + 20*a^2*c^5*d^9*e^6 - 10*a^3*c^4*d^7*e^8 - 5*a^4*c^3*d^5*e^10 + 7*a^5*c^2*d^3*e^12 - 2*a^6*c*d*e^14)*x^4 + (3*c^7*d^14*e - 9*a*c^6*d^12*e^3 + a^2*c^5*d^10*e^5 + 25*a^3*c^4*d^8*e^7 - 35*a^4*c^3*d^6*e^9 + 17*a^5*c^2*d^4*e^11 - a^6*c*d^2*e^13 - a^7*e^15)*x^3 + (c^7*d^15 + a*c^6*d^13*e^2 - 17*a^2*c^5*d^11*e^4 + 35*a^3*c^4*d^9*e^6 - 25*a^4*c^3*d^7*e^8 - a^5*c^2*d^5*e^10 + 9*a^6*c*d^3*e^12 - 3*a^7*d*e^14)*x^2 + (2*a*c^6*d^14*e - 7*a^2*c^5*d^12*e^3 + 5*a^3*c^4*d^10*e^5 + 10*a^4*c^3*d^8*e^7 - 20*a^5*c^2*d^6*e^9 + 13*a^6*c*d^4*e^11 - 3*a^7*d^2*e^13)*x)","B",0
488,1,1540,0,167.967356," ","integrate(x^2/(e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(7/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(56 \, a^{2} c^{4} d^{10} e^{2} + 1120 \, a^{3} c^{3} d^{8} e^{4} + 1680 \, a^{4} c^{2} d^{6} e^{6} + 224 \, a^{5} c d^{4} e^{8} - 8 \, a^{6} d^{2} e^{10} + 128 \, {\left(3 \, c^{6} d^{8} e^{4} + 14 \, a c^{5} d^{6} e^{6} + 7 \, a^{2} c^{4} d^{4} e^{8}\right)} x^{6} + 64 \, {\left(21 \, c^{6} d^{9} e^{3} + 113 \, a c^{5} d^{7} e^{5} + 119 \, a^{2} c^{4} d^{5} e^{7} + 35 \, a^{3} c^{3} d^{3} e^{9}\right)} x^{5} + 80 \, {\left(21 \, c^{6} d^{10} e^{2} + 140 \, a c^{5} d^{8} e^{4} + 254 \, a^{2} c^{4} d^{6} e^{6} + 140 \, a^{3} c^{3} d^{4} e^{8} + 21 \, a^{4} c^{2} d^{2} e^{10}\right)} x^{4} + 40 \, {\left(21 \, c^{6} d^{11} e + 203 \, a c^{5} d^{9} e^{3} + 602 \, a^{2} c^{4} d^{7} e^{5} + 542 \, a^{3} c^{3} d^{5} e^{7} + 161 \, a^{4} c^{2} d^{3} e^{9} + 7 \, a^{5} c d e^{11}\right)} x^{3} + 5 \, {\left(21 \, c^{6} d^{12} + 518 \, a c^{5} d^{10} e^{2} + 2639 \, a^{2} c^{4} d^{8} e^{4} + 4004 \, a^{3} c^{3} d^{6} e^{6} + 1859 \, a^{4} c^{2} d^{4} e^{8} + 182 \, a^{5} c d^{2} e^{10} - 7 \, a^{6} e^{12}\right)} x^{2} + 4 \, {\left(35 \, a c^{5} d^{11} e + 749 \, a^{2} c^{4} d^{9} e^{3} + 2030 \, a^{3} c^{3} d^{7} e^{5} + 1610 \, a^{4} c^{2} d^{5} e^{7} + 191 \, a^{5} c d^{3} e^{9} - 7 \, a^{6} d e^{11}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{105 \, {\left(a^{3} c^{7} d^{18} e^{3} - 7 \, a^{4} c^{6} d^{16} e^{5} + 21 \, a^{5} c^{5} d^{14} e^{7} - 35 \, a^{6} c^{4} d^{12} e^{9} + 35 \, a^{7} c^{3} d^{10} e^{11} - 21 \, a^{8} c^{2} d^{8} e^{13} + 7 \, a^{9} c d^{6} e^{15} - a^{10} d^{4} e^{17} + {\left(c^{10} d^{17} e^{4} - 7 \, a c^{9} d^{15} e^{6} + 21 \, a^{2} c^{8} d^{13} e^{8} - 35 \, a^{3} c^{7} d^{11} e^{10} + 35 \, a^{4} c^{6} d^{9} e^{12} - 21 \, a^{5} c^{5} d^{7} e^{14} + 7 \, a^{6} c^{4} d^{5} e^{16} - a^{7} c^{3} d^{3} e^{18}\right)} x^{7} + {\left(4 \, c^{10} d^{18} e^{3} - 25 \, a c^{9} d^{16} e^{5} + 63 \, a^{2} c^{8} d^{14} e^{7} - 77 \, a^{3} c^{7} d^{12} e^{9} + 35 \, a^{4} c^{6} d^{10} e^{11} + 21 \, a^{5} c^{5} d^{8} e^{13} - 35 \, a^{6} c^{4} d^{6} e^{15} + 17 \, a^{7} c^{3} d^{4} e^{17} - 3 \, a^{8} c^{2} d^{2} e^{19}\right)} x^{6} + 3 \, {\left(2 \, c^{10} d^{19} e^{2} - 10 \, a c^{9} d^{17} e^{4} + 15 \, a^{2} c^{8} d^{15} e^{6} + 7 \, a^{3} c^{7} d^{13} e^{8} - 49 \, a^{4} c^{6} d^{11} e^{10} + 63 \, a^{5} c^{5} d^{9} e^{12} - 35 \, a^{6} c^{4} d^{7} e^{14} + 5 \, a^{7} c^{3} d^{5} e^{16} + 3 \, a^{8} c^{2} d^{3} e^{18} - a^{9} c d e^{20}\right)} x^{5} + {\left(4 \, c^{10} d^{20} e - 10 \, a c^{9} d^{18} e^{3} - 30 \, a^{2} c^{8} d^{16} e^{5} + 155 \, a^{3} c^{7} d^{14} e^{7} - 245 \, a^{4} c^{6} d^{12} e^{9} + 147 \, a^{5} c^{5} d^{10} e^{11} + 35 \, a^{6} c^{4} d^{8} e^{13} - 95 \, a^{7} c^{3} d^{6} e^{15} + 45 \, a^{8} c^{2} d^{4} e^{17} - 5 \, a^{9} c d^{2} e^{19} - a^{10} e^{21}\right)} x^{4} + {\left(c^{10} d^{21} + 5 \, a c^{9} d^{19} e^{2} - 45 \, a^{2} c^{8} d^{17} e^{4} + 95 \, a^{3} c^{7} d^{15} e^{6} - 35 \, a^{4} c^{6} d^{13} e^{8} - 147 \, a^{5} c^{5} d^{11} e^{10} + 245 \, a^{6} c^{4} d^{9} e^{12} - 155 \, a^{7} c^{3} d^{7} e^{14} + 30 \, a^{8} c^{2} d^{5} e^{16} + 10 \, a^{9} c d^{3} e^{18} - 4 \, a^{10} d e^{20}\right)} x^{3} + 3 \, {\left(a c^{9} d^{20} e - 3 \, a^{2} c^{8} d^{18} e^{3} - 5 \, a^{3} c^{7} d^{16} e^{5} + 35 \, a^{4} c^{6} d^{14} e^{7} - 63 \, a^{5} c^{5} d^{12} e^{9} + 49 \, a^{6} c^{4} d^{10} e^{11} - 7 \, a^{7} c^{3} d^{8} e^{13} - 15 \, a^{8} c^{2} d^{6} e^{15} + 10 \, a^{9} c d^{4} e^{17} - 2 \, a^{10} d^{2} e^{19}\right)} x^{2} + {\left(3 \, a^{2} c^{8} d^{19} e^{2} - 17 \, a^{3} c^{7} d^{17} e^{4} + 35 \, a^{4} c^{6} d^{15} e^{6} - 21 \, a^{5} c^{5} d^{13} e^{8} - 35 \, a^{6} c^{4} d^{11} e^{10} + 77 \, a^{7} c^{3} d^{9} e^{12} - 63 \, a^{8} c^{2} d^{7} e^{14} + 25 \, a^{9} c d^{5} e^{16} - 4 \, a^{10} d^{3} e^{18}\right)} x\right)}}"," ",0,"-2/105*(56*a^2*c^4*d^10*e^2 + 1120*a^3*c^3*d^8*e^4 + 1680*a^4*c^2*d^6*e^6 + 224*a^5*c*d^4*e^8 - 8*a^6*d^2*e^10 + 128*(3*c^6*d^8*e^4 + 14*a*c^5*d^6*e^6 + 7*a^2*c^4*d^4*e^8)*x^6 + 64*(21*c^6*d^9*e^3 + 113*a*c^5*d^7*e^5 + 119*a^2*c^4*d^5*e^7 + 35*a^3*c^3*d^3*e^9)*x^5 + 80*(21*c^6*d^10*e^2 + 140*a*c^5*d^8*e^4 + 254*a^2*c^4*d^6*e^6 + 140*a^3*c^3*d^4*e^8 + 21*a^4*c^2*d^2*e^10)*x^4 + 40*(21*c^6*d^11*e + 203*a*c^5*d^9*e^3 + 602*a^2*c^4*d^7*e^5 + 542*a^3*c^3*d^5*e^7 + 161*a^4*c^2*d^3*e^9 + 7*a^5*c*d*e^11)*x^3 + 5*(21*c^6*d^12 + 518*a*c^5*d^10*e^2 + 2639*a^2*c^4*d^8*e^4 + 4004*a^3*c^3*d^6*e^6 + 1859*a^4*c^2*d^4*e^8 + 182*a^5*c*d^2*e^10 - 7*a^6*e^12)*x^2 + 4*(35*a*c^5*d^11*e + 749*a^2*c^4*d^9*e^3 + 2030*a^3*c^3*d^7*e^5 + 1610*a^4*c^2*d^5*e^7 + 191*a^5*c*d^3*e^9 - 7*a^6*d*e^11)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)/(a^3*c^7*d^18*e^3 - 7*a^4*c^6*d^16*e^5 + 21*a^5*c^5*d^14*e^7 - 35*a^6*c^4*d^12*e^9 + 35*a^7*c^3*d^10*e^11 - 21*a^8*c^2*d^8*e^13 + 7*a^9*c*d^6*e^15 - a^10*d^4*e^17 + (c^10*d^17*e^4 - 7*a*c^9*d^15*e^6 + 21*a^2*c^8*d^13*e^8 - 35*a^3*c^7*d^11*e^10 + 35*a^4*c^6*d^9*e^12 - 21*a^5*c^5*d^7*e^14 + 7*a^6*c^4*d^5*e^16 - a^7*c^3*d^3*e^18)*x^7 + (4*c^10*d^18*e^3 - 25*a*c^9*d^16*e^5 + 63*a^2*c^8*d^14*e^7 - 77*a^3*c^7*d^12*e^9 + 35*a^4*c^6*d^10*e^11 + 21*a^5*c^5*d^8*e^13 - 35*a^6*c^4*d^6*e^15 + 17*a^7*c^3*d^4*e^17 - 3*a^8*c^2*d^2*e^19)*x^6 + 3*(2*c^10*d^19*e^2 - 10*a*c^9*d^17*e^4 + 15*a^2*c^8*d^15*e^6 + 7*a^3*c^7*d^13*e^8 - 49*a^4*c^6*d^11*e^10 + 63*a^5*c^5*d^9*e^12 - 35*a^6*c^4*d^7*e^14 + 5*a^7*c^3*d^5*e^16 + 3*a^8*c^2*d^3*e^18 - a^9*c*d*e^20)*x^5 + (4*c^10*d^20*e - 10*a*c^9*d^18*e^3 - 30*a^2*c^8*d^16*e^5 + 155*a^3*c^7*d^14*e^7 - 245*a^4*c^6*d^12*e^9 + 147*a^5*c^5*d^10*e^11 + 35*a^6*c^4*d^8*e^13 - 95*a^7*c^3*d^6*e^15 + 45*a^8*c^2*d^4*e^17 - 5*a^9*c*d^2*e^19 - a^10*e^21)*x^4 + (c^10*d^21 + 5*a*c^9*d^19*e^2 - 45*a^2*c^8*d^17*e^4 + 95*a^3*c^7*d^15*e^6 - 35*a^4*c^6*d^13*e^8 - 147*a^5*c^5*d^11*e^10 + 245*a^6*c^4*d^9*e^12 - 155*a^7*c^3*d^7*e^14 + 30*a^8*c^2*d^5*e^16 + 10*a^9*c*d^3*e^18 - 4*a^10*d*e^20)*x^3 + 3*(a*c^9*d^20*e - 3*a^2*c^8*d^18*e^3 - 5*a^3*c^7*d^16*e^5 + 35*a^4*c^6*d^14*e^7 - 63*a^5*c^5*d^12*e^9 + 49*a^6*c^4*d^10*e^11 - 7*a^7*c^3*d^8*e^13 - 15*a^8*c^2*d^6*e^15 + 10*a^9*c*d^4*e^17 - 2*a^10*d^2*e^19)*x^2 + (3*a^2*c^8*d^19*e^2 - 17*a^3*c^7*d^17*e^4 + 35*a^4*c^6*d^15*e^6 - 21*a^5*c^5*d^13*e^8 - 35*a^6*c^4*d^11*e^10 + 77*a^7*c^3*d^9*e^12 - 63*a^8*c^2*d^7*e^14 + 25*a^9*c*d^5*e^16 - 4*a^10*d^3*e^18)*x)","B",0
489,0,0,0,0.403336," ","integrate(x^3*(1+x)^(1/2)*(x^2-x+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{x^{2} - x + 1} \sqrt{x + 1} x^{3}, x\right)"," ",0,"integral(sqrt(x^2 - x + 1)*sqrt(x + 1)*x^3, x)","F",0
490,1,22,0,0.383390," ","integrate(x^2*(1+x)^(1/2)*(x^2-x+1)^(1/2),x, algorithm=""fricas"")","\frac{2}{9} \, {\left(x^{3} + 1\right)} \sqrt{x^{2} - x + 1} \sqrt{x + 1}"," ",0,"2/9*(x^3 + 1)*sqrt(x^2 - x + 1)*sqrt(x + 1)","A",0
491,0,0,0,0.405990," ","integrate(x*(1+x)^(1/2)*(x^2-x+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{x^{2} - x + 1} \sqrt{x + 1} x, x\right)"," ",0,"integral(sqrt(x^2 - x + 1)*sqrt(x + 1)*x, x)","F",0
492,0,0,0,0.396616," ","integrate((1+x)^(1/2)*(x^2-x+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{x^{2} - x + 1} \sqrt{x + 1}, x\right)"," ",0,"integral(sqrt(x^2 - x + 1)*sqrt(x + 1), x)","F",0
493,1,60,0,0.400477," ","integrate((1+x)^(1/2)*(x^2-x+1)^(1/2)/x,x, algorithm=""fricas"")","\frac{2}{3} \, \sqrt{x^{2} - x + 1} \sqrt{x + 1} - \frac{1}{3} \, \log\left(\sqrt{x^{2} - x + 1} \sqrt{x + 1} + 1\right) + \frac{1}{3} \, \log\left(\sqrt{x^{2} - x + 1} \sqrt{x + 1} - 1\right)"," ",0,"2/3*sqrt(x^2 - x + 1)*sqrt(x + 1) - 1/3*log(sqrt(x^2 - x + 1)*sqrt(x + 1) + 1) + 1/3*log(sqrt(x^2 - x + 1)*sqrt(x + 1) - 1)","A",0
494,0,0,0,0.402325," ","integrate((1+x)^(1/2)*(x^2-x+1)^(1/2)/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{2} - x + 1} \sqrt{x + 1}}{x^{2}}, x\right)"," ",0,"integral(sqrt(x^2 - x + 1)*sqrt(x + 1)/x^2, x)","F",0
495,0,0,0,0.410853," ","integrate((1+x)^(1/2)*(x^2-x+1)^(1/2)/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{2} - x + 1} \sqrt{x + 1}}{x^{3}}, x\right)"," ",0,"integral(sqrt(x^2 - x + 1)*sqrt(x + 1)/x^3, x)","F",0
496,0,0,0,0.405525," ","integrate(x^3*(1+x)^(3/2)*(x^2-x+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(x^{6} + x^{3}\right)} \sqrt{x^{2} - x + 1} \sqrt{x + 1}, x\right)"," ",0,"integral((x^6 + x^3)*sqrt(x^2 - x + 1)*sqrt(x + 1), x)","F",0
497,1,27,0,0.386074," ","integrate(x^2*(1+x)^(3/2)*(x^2-x+1)^(3/2),x, algorithm=""fricas"")","\frac{2}{15} \, {\left(x^{6} + 2 \, x^{3} + 1\right)} \sqrt{x^{2} - x + 1} \sqrt{x + 1}"," ",0,"2/15*(x^6 + 2*x^3 + 1)*sqrt(x^2 - x + 1)*sqrt(x + 1)","A",0
498,0,0,0,0.407157," ","integrate(x*(1+x)^(3/2)*(x^2-x+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(x^{4} + x\right)} \sqrt{x^{2} - x + 1} \sqrt{x + 1}, x\right)"," ",0,"integral((x^4 + x)*sqrt(x^2 - x + 1)*sqrt(x + 1), x)","F",0
499,0,0,0,0.405705," ","integrate((1+x)^(3/2)*(x^2-x+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(x^{3} + 1\right)} \sqrt{x^{2} - x + 1} \sqrt{x + 1}, x\right)"," ",0,"integral((x^3 + 1)*sqrt(x^2 - x + 1)*sqrt(x + 1), x)","F",0
500,1,65,0,0.397570," ","integrate((1+x)^(3/2)*(x^2-x+1)^(3/2)/x,x, algorithm=""fricas"")","\frac{2}{9} \, {\left(x^{3} + 4\right)} \sqrt{x^{2} - x + 1} \sqrt{x + 1} - \frac{1}{3} \, \log\left(\sqrt{x^{2} - x + 1} \sqrt{x + 1} + 1\right) + \frac{1}{3} \, \log\left(\sqrt{x^{2} - x + 1} \sqrt{x + 1} - 1\right)"," ",0,"2/9*(x^3 + 4)*sqrt(x^2 - x + 1)*sqrt(x + 1) - 1/3*log(sqrt(x^2 - x + 1)*sqrt(x + 1) + 1) + 1/3*log(sqrt(x^2 - x + 1)*sqrt(x + 1) - 1)","A",0
501,0,0,0,0.406714," ","integrate((1+x)^(3/2)*(x^2-x+1)^(3/2)/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(x^{3} + 1\right)} \sqrt{x^{2} - x + 1} \sqrt{x + 1}}{x^{2}}, x\right)"," ",0,"integral((x^3 + 1)*sqrt(x^2 - x + 1)*sqrt(x + 1)/x^2, x)","F",0
502,0,0,0,0.398765," ","integrate((1+x)^(3/2)*(x^2-x+1)^(3/2)/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(x^{3} + 1\right)} \sqrt{x^{2} - x + 1} \sqrt{x + 1}}{x^{3}}, x\right)"," ",0,"integral((x^3 + 1)*sqrt(x^2 - x + 1)*sqrt(x + 1)/x^3, x)","F",0
503,0,0,0,0.408110," ","integrate(x^3/(1+x)^(1/2)/(x^2-x+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{2} - x + 1} \sqrt{x + 1} x^{3}}{x^{3} + 1}, x\right)"," ",0,"integral(sqrt(x^2 - x + 1)*sqrt(x + 1)*x^3/(x^3 + 1), x)","F",0
504,1,17,0,0.382680," ","integrate(x^2/(1+x)^(1/2)/(x^2-x+1)^(1/2),x, algorithm=""fricas"")","\frac{2}{3} \, \sqrt{x^{2} - x + 1} \sqrt{x + 1}"," ",0,"2/3*sqrt(x^2 - x + 1)*sqrt(x + 1)","A",0
505,0,0,0,0.395613," ","integrate(x/(1+x)^(1/2)/(x^2-x+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{2} - x + 1} \sqrt{x + 1} x}{x^{3} + 1}, x\right)"," ",0,"integral(sqrt(x^2 - x + 1)*sqrt(x + 1)*x/(x^3 + 1), x)","F",0
506,0,0,0,0.396450," ","integrate(1/(1+x)^(1/2)/(x^2-x+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{2} - x + 1} \sqrt{x + 1}}{x^{3} + 1}, x\right)"," ",0,"integral(sqrt(x^2 - x + 1)*sqrt(x + 1)/(x^3 + 1), x)","F",0
507,1,43,0,0.393827," ","integrate(1/x/(1+x)^(1/2)/(x^2-x+1)^(1/2),x, algorithm=""fricas"")","-\frac{1}{3} \, \log\left(\sqrt{x^{2} - x + 1} \sqrt{x + 1} + 1\right) + \frac{1}{3} \, \log\left(\sqrt{x^{2} - x + 1} \sqrt{x + 1} - 1\right)"," ",0,"-1/3*log(sqrt(x^2 - x + 1)*sqrt(x + 1) + 1) + 1/3*log(sqrt(x^2 - x + 1)*sqrt(x + 1) - 1)","A",0
508,0,0,0,0.410776," ","integrate(1/x^2/(1+x)^(1/2)/(x^2-x+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{2} - x + 1} \sqrt{x + 1}}{x^{5} + x^{2}}, x\right)"," ",0,"integral(sqrt(x^2 - x + 1)*sqrt(x + 1)/(x^5 + x^2), x)","F",0
509,0,0,0,0.401794," ","integrate(1/x^3/(1+x)^(1/2)/(x^2-x+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{2} - x + 1} \sqrt{x + 1}}{x^{6} + x^{3}}, x\right)"," ",0,"integral(sqrt(x^2 - x + 1)*sqrt(x + 1)/(x^6 + x^3), x)","F",0
510,0,0,0,0.411389," ","integrate(x^3/(1+x)^(3/2)/(x^2-x+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{2} - x + 1} \sqrt{x + 1} x^{3}}{x^{6} + 2 \, x^{3} + 1}, x\right)"," ",0,"integral(sqrt(x^2 - x + 1)*sqrt(x + 1)*x^3/(x^6 + 2*x^3 + 1), x)","F",0
511,1,24,0,0.376845," ","integrate(x^2/(1+x)^(3/2)/(x^2-x+1)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{x^{2} - x + 1} \sqrt{x + 1}}{3 \, {\left(x^{3} + 1\right)}}"," ",0,"-2/3*sqrt(x^2 - x + 1)*sqrt(x + 1)/(x^3 + 1)","A",0
512,0,0,0,0.403486," ","integrate(x/(1+x)^(3/2)/(x^2-x+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{2} - x + 1} \sqrt{x + 1} x}{x^{6} + 2 \, x^{3} + 1}, x\right)"," ",0,"integral(sqrt(x^2 - x + 1)*sqrt(x + 1)*x/(x^6 + 2*x^3 + 1), x)","F",0
513,0,0,0,0.399849," ","integrate(1/(1+x)^(3/2)/(x^2-x+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{2} - x + 1} \sqrt{x + 1}}{x^{6} + 2 \, x^{3} + 1}, x\right)"," ",0,"integral(sqrt(x^2 - x + 1)*sqrt(x + 1)/(x^6 + 2*x^3 + 1), x)","F",0
514,1,78,0,0.387544," ","integrate(1/x/(1+x)^(3/2)/(x^2-x+1)^(3/2),x, algorithm=""fricas"")","-\frac{{\left(x^{3} + 1\right)} \log\left(\sqrt{x^{2} - x + 1} \sqrt{x + 1} + 1\right) - {\left(x^{3} + 1\right)} \log\left(\sqrt{x^{2} - x + 1} \sqrt{x + 1} - 1\right) - 2 \, \sqrt{x^{2} - x + 1} \sqrt{x + 1}}{3 \, {\left(x^{3} + 1\right)}}"," ",0,"-1/3*((x^3 + 1)*log(sqrt(x^2 - x + 1)*sqrt(x + 1) + 1) - (x^3 + 1)*log(sqrt(x^2 - x + 1)*sqrt(x + 1) - 1) - 2*sqrt(x^2 - x + 1)*sqrt(x + 1))/(x^3 + 1)","A",0
515,0,0,0,0.397757," ","integrate(1/x^2/(1+x)^(3/2)/(x^2-x+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{2} - x + 1} \sqrt{x + 1}}{x^{8} + 2 \, x^{5} + x^{2}}, x\right)"," ",0,"integral(sqrt(x^2 - x + 1)*sqrt(x + 1)/(x^8 + 2*x^5 + x^2), x)","F",0
516,0,0,0,0.406316," ","integrate(1/x^3/(1+x)^(3/2)/(x^2-x+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{2} - x + 1} \sqrt{x + 1}}{x^{9} + 2 \, x^{6} + x^{3}}, x\right)"," ",0,"integral(sqrt(x^2 - x + 1)*sqrt(x + 1)/(x^9 + 2*x^6 + x^3), x)","F",0
517,0,0,0,0.402837," ","integrate(x^3/(1+x)^(5/2)/(x^2-x+1)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{2} - x + 1} \sqrt{x + 1} x^{3}}{x^{9} + 3 \, x^{6} + 3 \, x^{3} + 1}, x\right)"," ",0,"integral(sqrt(x^2 - x + 1)*sqrt(x + 1)*x^3/(x^9 + 3*x^6 + 3*x^3 + 1), x)","F",0
518,1,29,0,0.395620," ","integrate(x^2/(1+x)^(5/2)/(x^2-x+1)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{x^{2} - x + 1} \sqrt{x + 1}}{9 \, {\left(x^{6} + 2 \, x^{3} + 1\right)}}"," ",0,"-2/9*sqrt(x^2 - x + 1)*sqrt(x + 1)/(x^6 + 2*x^3 + 1)","A",0
519,0,0,0,0.411877," ","integrate(x/(1+x)^(5/2)/(x^2-x+1)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{2} - x + 1} \sqrt{x + 1} x}{x^{9} + 3 \, x^{6} + 3 \, x^{3} + 1}, x\right)"," ",0,"integral(sqrt(x^2 - x + 1)*sqrt(x + 1)*x/(x^9 + 3*x^6 + 3*x^3 + 1), x)","F",0
520,0,0,0,0.393359," ","integrate(1/(1+x)^(5/2)/(x^2-x+1)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{2} - x + 1} \sqrt{x + 1}}{x^{9} + 3 \, x^{6} + 3 \, x^{3} + 1}, x\right)"," ",0,"integral(sqrt(x^2 - x + 1)*sqrt(x + 1)/(x^9 + 3*x^6 + 3*x^3 + 1), x)","F",0
521,1,101,0,0.384851," ","integrate(1/x/(1+x)^(5/2)/(x^2-x+1)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, x^{3} + 4\right)} \sqrt{x^{2} - x + 1} \sqrt{x + 1} - 3 \, {\left(x^{6} + 2 \, x^{3} + 1\right)} \log\left(\sqrt{x^{2} - x + 1} \sqrt{x + 1} + 1\right) + 3 \, {\left(x^{6} + 2 \, x^{3} + 1\right)} \log\left(\sqrt{x^{2} - x + 1} \sqrt{x + 1} - 1\right)}{9 \, {\left(x^{6} + 2 \, x^{3} + 1\right)}}"," ",0,"1/9*(2*(3*x^3 + 4)*sqrt(x^2 - x + 1)*sqrt(x + 1) - 3*(x^6 + 2*x^3 + 1)*log(sqrt(x^2 - x + 1)*sqrt(x + 1) + 1) + 3*(x^6 + 2*x^3 + 1)*log(sqrt(x^2 - x + 1)*sqrt(x + 1) - 1))/(x^6 + 2*x^3 + 1)","A",0
522,0,0,0,0.406880," ","integrate(1/x^2/(1+x)^(5/2)/(x^2-x+1)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{2} - x + 1} \sqrt{x + 1}}{x^{11} + 3 \, x^{8} + 3 \, x^{5} + x^{2}}, x\right)"," ",0,"integral(sqrt(x^2 - x + 1)*sqrt(x + 1)/(x^11 + 3*x^8 + 3*x^5 + x^2), x)","F",0
523,0,0,0,0.388341," ","integrate(1/x^3/(1+x)^(5/2)/(x^2-x+1)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{2} - x + 1} \sqrt{x + 1}}{x^{12} + 3 \, x^{9} + 3 \, x^{6} + x^{3}}, x\right)"," ",0,"integral(sqrt(x^2 - x + 1)*sqrt(x + 1)/(x^12 + 3*x^9 + 3*x^6 + x^3), x)","F",0
524,1,134,0,0.391167," ","integrate(x/(-1+x)^3/(4*x^2+5*x+3)^2,x, algorithm=""fricas"")","\frac{214176 \, x^{3} + 12046 \, \sqrt{23} {\left(4 \, x^{4} - 3 \, x^{3} - 3 \, x^{2} - x + 3\right)} \arctan\left(\frac{1}{23} \, \sqrt{23} {\left(8 \, x + 5\right)}\right) - 224664 \, x^{2} - 5819 \, {\left(4 \, x^{4} - 3 \, x^{3} - 3 \, x^{2} - x + 3\right)} \log\left(4 \, x^{2} + 5 \, x + 3\right) + 11638 \, {\left(4 \, x^{4} - 3 \, x^{3} - 3 \, x^{2} - x + 3\right)} \log\left(x - 1\right) - 66240 \, x - 24840}{2437632 \, {\left(4 \, x^{4} - 3 \, x^{3} - 3 \, x^{2} - x + 3\right)}}"," ",0,"1/2437632*(214176*x^3 + 12046*sqrt(23)*(4*x^4 - 3*x^3 - 3*x^2 - x + 3)*arctan(1/23*sqrt(23)*(8*x + 5)) - 224664*x^2 - 5819*(4*x^4 - 3*x^3 - 3*x^2 - x + 3)*log(4*x^2 + 5*x + 3) + 11638*(4*x^4 - 3*x^3 - 3*x^2 - x + 3)*log(x - 1) - 66240*x - 24840)/(4*x^4 - 3*x^3 - 3*x^2 - x + 3)","A",0
525,1,5507,0,1.002903," ","integrate(x^4*(e*x+d)^(1/2)/(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{105 \, \sqrt{2} c^{4} e^{3} \sqrt{\frac{{\left(b^{8} c - 8 \, a b^{6} c^{2} + 20 \, a^{2} b^{4} c^{3} - 16 \, a^{3} b^{2} c^{4} + 2 \, a^{4} c^{5}\right)} d - {\left(b^{9} - 9 \, a b^{7} c + 27 \, a^{2} b^{5} c^{2} - 30 \, a^{3} b^{3} c^{3} + 9 \, a^{4} b c^{4}\right)} e + {\left(b^{2} c^{9} - 4 \, a c^{10}\right)} \sqrt{\frac{{\left(b^{14} c^{2} - 12 \, a b^{12} c^{3} + 56 \, a^{2} b^{10} c^{4} - 128 \, a^{3} b^{8} c^{5} + 148 \, a^{4} b^{6} c^{6} - 80 \, a^{5} b^{4} c^{7} + 16 \, a^{6} b^{2} c^{8}\right)} d^{2} - 2 \, {\left(b^{15} c - 13 \, a b^{13} c^{2} + 67 \, a^{2} b^{11} c^{3} - 174 \, a^{3} b^{9} c^{4} + 239 \, a^{4} b^{7} c^{5} - 166 \, a^{5} b^{5} c^{6} + 50 \, a^{6} b^{3} c^{7} - 4 \, a^{7} b c^{8}\right)} d e + {\left(b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}\right)} e^{2}}{b^{2} c^{18} - 4 \, a c^{19}}}}{b^{2} c^{9} - 4 \, a c^{10}}} \log\left(\sqrt{2} {\left({\left(b^{12} c - 12 \, a b^{10} c^{2} + 54 \, a^{2} b^{8} c^{3} - 112 \, a^{3} b^{6} c^{4} + 104 \, a^{4} b^{4} c^{5} - 32 \, a^{5} b^{2} c^{6}\right)} d - {\left(b^{13} - 13 \, a b^{11} c + 65 \, a^{2} b^{9} c^{2} - 156 \, a^{3} b^{7} c^{3} + 181 \, a^{4} b^{5} c^{4} - 86 \, a^{5} b^{3} c^{5} + 8 \, a^{6} b c^{6}\right)} e - {\left(b^{6} c^{9} - 8 \, a b^{4} c^{10} + 18 \, a^{2} b^{2} c^{11} - 8 \, a^{3} c^{12}\right)} \sqrt{\frac{{\left(b^{14} c^{2} - 12 \, a b^{12} c^{3} + 56 \, a^{2} b^{10} c^{4} - 128 \, a^{3} b^{8} c^{5} + 148 \, a^{4} b^{6} c^{6} - 80 \, a^{5} b^{4} c^{7} + 16 \, a^{6} b^{2} c^{8}\right)} d^{2} - 2 \, {\left(b^{15} c - 13 \, a b^{13} c^{2} + 67 \, a^{2} b^{11} c^{3} - 174 \, a^{3} b^{9} c^{4} + 239 \, a^{4} b^{7} c^{5} - 166 \, a^{5} b^{5} c^{6} + 50 \, a^{6} b^{3} c^{7} - 4 \, a^{7} b c^{8}\right)} d e + {\left(b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}\right)} e^{2}}{b^{2} c^{18} - 4 \, a c^{19}}}\right)} \sqrt{\frac{{\left(b^{8} c - 8 \, a b^{6} c^{2} + 20 \, a^{2} b^{4} c^{3} - 16 \, a^{3} b^{2} c^{4} + 2 \, a^{4} c^{5}\right)} d - {\left(b^{9} - 9 \, a b^{7} c + 27 \, a^{2} b^{5} c^{2} - 30 \, a^{3} b^{3} c^{3} + 9 \, a^{4} b c^{4}\right)} e + {\left(b^{2} c^{9} - 4 \, a c^{10}\right)} \sqrt{\frac{{\left(b^{14} c^{2} - 12 \, a b^{12} c^{3} + 56 \, a^{2} b^{10} c^{4} - 128 \, a^{3} b^{8} c^{5} + 148 \, a^{4} b^{6} c^{6} - 80 \, a^{5} b^{4} c^{7} + 16 \, a^{6} b^{2} c^{8}\right)} d^{2} - 2 \, {\left(b^{15} c - 13 \, a b^{13} c^{2} + 67 \, a^{2} b^{11} c^{3} - 174 \, a^{3} b^{9} c^{4} + 239 \, a^{4} b^{7} c^{5} - 166 \, a^{5} b^{5} c^{6} + 50 \, a^{6} b^{3} c^{7} - 4 \, a^{7} b c^{8}\right)} d e + {\left(b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}\right)} e^{2}}{b^{2} c^{18} - 4 \, a c^{19}}}}{b^{2} c^{9} - 4 \, a c^{10}}} - 4 \, {\left({\left(a^{4} b^{7} c - 6 \, a^{5} b^{5} c^{2} + 10 \, a^{6} b^{3} c^{3} - 4 \, a^{7} b c^{4}\right)} d - {\left(a^{4} b^{8} - 7 \, a^{5} b^{6} c + 15 \, a^{6} b^{4} c^{2} - 10 \, a^{7} b^{2} c^{3} + a^{8} c^{4}\right)} e\right)} \sqrt{e x + d}\right) - 105 \, \sqrt{2} c^{4} e^{3} \sqrt{\frac{{\left(b^{8} c - 8 \, a b^{6} c^{2} + 20 \, a^{2} b^{4} c^{3} - 16 \, a^{3} b^{2} c^{4} + 2 \, a^{4} c^{5}\right)} d - {\left(b^{9} - 9 \, a b^{7} c + 27 \, a^{2} b^{5} c^{2} - 30 \, a^{3} b^{3} c^{3} + 9 \, a^{4} b c^{4}\right)} e + {\left(b^{2} c^{9} - 4 \, a c^{10}\right)} \sqrt{\frac{{\left(b^{14} c^{2} - 12 \, a b^{12} c^{3} + 56 \, a^{2} b^{10} c^{4} - 128 \, a^{3} b^{8} c^{5} + 148 \, a^{4} b^{6} c^{6} - 80 \, a^{5} b^{4} c^{7} + 16 \, a^{6} b^{2} c^{8}\right)} d^{2} - 2 \, {\left(b^{15} c - 13 \, a b^{13} c^{2} + 67 \, a^{2} b^{11} c^{3} - 174 \, a^{3} b^{9} c^{4} + 239 \, a^{4} b^{7} c^{5} - 166 \, a^{5} b^{5} c^{6} + 50 \, a^{6} b^{3} c^{7} - 4 \, a^{7} b c^{8}\right)} d e + {\left(b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}\right)} e^{2}}{b^{2} c^{18} - 4 \, a c^{19}}}}{b^{2} c^{9} - 4 \, a c^{10}}} \log\left(-\sqrt{2} {\left({\left(b^{12} c - 12 \, a b^{10} c^{2} + 54 \, a^{2} b^{8} c^{3} - 112 \, a^{3} b^{6} c^{4} + 104 \, a^{4} b^{4} c^{5} - 32 \, a^{5} b^{2} c^{6}\right)} d - {\left(b^{13} - 13 \, a b^{11} c + 65 \, a^{2} b^{9} c^{2} - 156 \, a^{3} b^{7} c^{3} + 181 \, a^{4} b^{5} c^{4} - 86 \, a^{5} b^{3} c^{5} + 8 \, a^{6} b c^{6}\right)} e - {\left(b^{6} c^{9} - 8 \, a b^{4} c^{10} + 18 \, a^{2} b^{2} c^{11} - 8 \, a^{3} c^{12}\right)} \sqrt{\frac{{\left(b^{14} c^{2} - 12 \, a b^{12} c^{3} + 56 \, a^{2} b^{10} c^{4} - 128 \, a^{3} b^{8} c^{5} + 148 \, a^{4} b^{6} c^{6} - 80 \, a^{5} b^{4} c^{7} + 16 \, a^{6} b^{2} c^{8}\right)} d^{2} - 2 \, {\left(b^{15} c - 13 \, a b^{13} c^{2} + 67 \, a^{2} b^{11} c^{3} - 174 \, a^{3} b^{9} c^{4} + 239 \, a^{4} b^{7} c^{5} - 166 \, a^{5} b^{5} c^{6} + 50 \, a^{6} b^{3} c^{7} - 4 \, a^{7} b c^{8}\right)} d e + {\left(b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}\right)} e^{2}}{b^{2} c^{18} - 4 \, a c^{19}}}\right)} \sqrt{\frac{{\left(b^{8} c - 8 \, a b^{6} c^{2} + 20 \, a^{2} b^{4} c^{3} - 16 \, a^{3} b^{2} c^{4} + 2 \, a^{4} c^{5}\right)} d - {\left(b^{9} - 9 \, a b^{7} c + 27 \, a^{2} b^{5} c^{2} - 30 \, a^{3} b^{3} c^{3} + 9 \, a^{4} b c^{4}\right)} e + {\left(b^{2} c^{9} - 4 \, a c^{10}\right)} \sqrt{\frac{{\left(b^{14} c^{2} - 12 \, a b^{12} c^{3} + 56 \, a^{2} b^{10} c^{4} - 128 \, a^{3} b^{8} c^{5} + 148 \, a^{4} b^{6} c^{6} - 80 \, a^{5} b^{4} c^{7} + 16 \, a^{6} b^{2} c^{8}\right)} d^{2} - 2 \, {\left(b^{15} c - 13 \, a b^{13} c^{2} + 67 \, a^{2} b^{11} c^{3} - 174 \, a^{3} b^{9} c^{4} + 239 \, a^{4} b^{7} c^{5} - 166 \, a^{5} b^{5} c^{6} + 50 \, a^{6} b^{3} c^{7} - 4 \, a^{7} b c^{8}\right)} d e + {\left(b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}\right)} e^{2}}{b^{2} c^{18} - 4 \, a c^{19}}}}{b^{2} c^{9} - 4 \, a c^{10}}} - 4 \, {\left({\left(a^{4} b^{7} c - 6 \, a^{5} b^{5} c^{2} + 10 \, a^{6} b^{3} c^{3} - 4 \, a^{7} b c^{4}\right)} d - {\left(a^{4} b^{8} - 7 \, a^{5} b^{6} c + 15 \, a^{6} b^{4} c^{2} - 10 \, a^{7} b^{2} c^{3} + a^{8} c^{4}\right)} e\right)} \sqrt{e x + d}\right) + 105 \, \sqrt{2} c^{4} e^{3} \sqrt{\frac{{\left(b^{8} c - 8 \, a b^{6} c^{2} + 20 \, a^{2} b^{4} c^{3} - 16 \, a^{3} b^{2} c^{4} + 2 \, a^{4} c^{5}\right)} d - {\left(b^{9} - 9 \, a b^{7} c + 27 \, a^{2} b^{5} c^{2} - 30 \, a^{3} b^{3} c^{3} + 9 \, a^{4} b c^{4}\right)} e - {\left(b^{2} c^{9} - 4 \, a c^{10}\right)} \sqrt{\frac{{\left(b^{14} c^{2} - 12 \, a b^{12} c^{3} + 56 \, a^{2} b^{10} c^{4} - 128 \, a^{3} b^{8} c^{5} + 148 \, a^{4} b^{6} c^{6} - 80 \, a^{5} b^{4} c^{7} + 16 \, a^{6} b^{2} c^{8}\right)} d^{2} - 2 \, {\left(b^{15} c - 13 \, a b^{13} c^{2} + 67 \, a^{2} b^{11} c^{3} - 174 \, a^{3} b^{9} c^{4} + 239 \, a^{4} b^{7} c^{5} - 166 \, a^{5} b^{5} c^{6} + 50 \, a^{6} b^{3} c^{7} - 4 \, a^{7} b c^{8}\right)} d e + {\left(b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}\right)} e^{2}}{b^{2} c^{18} - 4 \, a c^{19}}}}{b^{2} c^{9} - 4 \, a c^{10}}} \log\left(\sqrt{2} {\left({\left(b^{12} c - 12 \, a b^{10} c^{2} + 54 \, a^{2} b^{8} c^{3} - 112 \, a^{3} b^{6} c^{4} + 104 \, a^{4} b^{4} c^{5} - 32 \, a^{5} b^{2} c^{6}\right)} d - {\left(b^{13} - 13 \, a b^{11} c + 65 \, a^{2} b^{9} c^{2} - 156 \, a^{3} b^{7} c^{3} + 181 \, a^{4} b^{5} c^{4} - 86 \, a^{5} b^{3} c^{5} + 8 \, a^{6} b c^{6}\right)} e + {\left(b^{6} c^{9} - 8 \, a b^{4} c^{10} + 18 \, a^{2} b^{2} c^{11} - 8 \, a^{3} c^{12}\right)} \sqrt{\frac{{\left(b^{14} c^{2} - 12 \, a b^{12} c^{3} + 56 \, a^{2} b^{10} c^{4} - 128 \, a^{3} b^{8} c^{5} + 148 \, a^{4} b^{6} c^{6} - 80 \, a^{5} b^{4} c^{7} + 16 \, a^{6} b^{2} c^{8}\right)} d^{2} - 2 \, {\left(b^{15} c - 13 \, a b^{13} c^{2} + 67 \, a^{2} b^{11} c^{3} - 174 \, a^{3} b^{9} c^{4} + 239 \, a^{4} b^{7} c^{5} - 166 \, a^{5} b^{5} c^{6} + 50 \, a^{6} b^{3} c^{7} - 4 \, a^{7} b c^{8}\right)} d e + {\left(b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}\right)} e^{2}}{b^{2} c^{18} - 4 \, a c^{19}}}\right)} \sqrt{\frac{{\left(b^{8} c - 8 \, a b^{6} c^{2} + 20 \, a^{2} b^{4} c^{3} - 16 \, a^{3} b^{2} c^{4} + 2 \, a^{4} c^{5}\right)} d - {\left(b^{9} - 9 \, a b^{7} c + 27 \, a^{2} b^{5} c^{2} - 30 \, a^{3} b^{3} c^{3} + 9 \, a^{4} b c^{4}\right)} e - {\left(b^{2} c^{9} - 4 \, a c^{10}\right)} \sqrt{\frac{{\left(b^{14} c^{2} - 12 \, a b^{12} c^{3} + 56 \, a^{2} b^{10} c^{4} - 128 \, a^{3} b^{8} c^{5} + 148 \, a^{4} b^{6} c^{6} - 80 \, a^{5} b^{4} c^{7} + 16 \, a^{6} b^{2} c^{8}\right)} d^{2} - 2 \, {\left(b^{15} c - 13 \, a b^{13} c^{2} + 67 \, a^{2} b^{11} c^{3} - 174 \, a^{3} b^{9} c^{4} + 239 \, a^{4} b^{7} c^{5} - 166 \, a^{5} b^{5} c^{6} + 50 \, a^{6} b^{3} c^{7} - 4 \, a^{7} b c^{8}\right)} d e + {\left(b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}\right)} e^{2}}{b^{2} c^{18} - 4 \, a c^{19}}}}{b^{2} c^{9} - 4 \, a c^{10}}} - 4 \, {\left({\left(a^{4} b^{7} c - 6 \, a^{5} b^{5} c^{2} + 10 \, a^{6} b^{3} c^{3} - 4 \, a^{7} b c^{4}\right)} d - {\left(a^{4} b^{8} - 7 \, a^{5} b^{6} c + 15 \, a^{6} b^{4} c^{2} - 10 \, a^{7} b^{2} c^{3} + a^{8} c^{4}\right)} e\right)} \sqrt{e x + d}\right) - 105 \, \sqrt{2} c^{4} e^{3} \sqrt{\frac{{\left(b^{8} c - 8 \, a b^{6} c^{2} + 20 \, a^{2} b^{4} c^{3} - 16 \, a^{3} b^{2} c^{4} + 2 \, a^{4} c^{5}\right)} d - {\left(b^{9} - 9 \, a b^{7} c + 27 \, a^{2} b^{5} c^{2} - 30 \, a^{3} b^{3} c^{3} + 9 \, a^{4} b c^{4}\right)} e - {\left(b^{2} c^{9} - 4 \, a c^{10}\right)} \sqrt{\frac{{\left(b^{14} c^{2} - 12 \, a b^{12} c^{3} + 56 \, a^{2} b^{10} c^{4} - 128 \, a^{3} b^{8} c^{5} + 148 \, a^{4} b^{6} c^{6} - 80 \, a^{5} b^{4} c^{7} + 16 \, a^{6} b^{2} c^{8}\right)} d^{2} - 2 \, {\left(b^{15} c - 13 \, a b^{13} c^{2} + 67 \, a^{2} b^{11} c^{3} - 174 \, a^{3} b^{9} c^{4} + 239 \, a^{4} b^{7} c^{5} - 166 \, a^{5} b^{5} c^{6} + 50 \, a^{6} b^{3} c^{7} - 4 \, a^{7} b c^{8}\right)} d e + {\left(b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}\right)} e^{2}}{b^{2} c^{18} - 4 \, a c^{19}}}}{b^{2} c^{9} - 4 \, a c^{10}}} \log\left(-\sqrt{2} {\left({\left(b^{12} c - 12 \, a b^{10} c^{2} + 54 \, a^{2} b^{8} c^{3} - 112 \, a^{3} b^{6} c^{4} + 104 \, a^{4} b^{4} c^{5} - 32 \, a^{5} b^{2} c^{6}\right)} d - {\left(b^{13} - 13 \, a b^{11} c + 65 \, a^{2} b^{9} c^{2} - 156 \, a^{3} b^{7} c^{3} + 181 \, a^{4} b^{5} c^{4} - 86 \, a^{5} b^{3} c^{5} + 8 \, a^{6} b c^{6}\right)} e + {\left(b^{6} c^{9} - 8 \, a b^{4} c^{10} + 18 \, a^{2} b^{2} c^{11} - 8 \, a^{3} c^{12}\right)} \sqrt{\frac{{\left(b^{14} c^{2} - 12 \, a b^{12} c^{3} + 56 \, a^{2} b^{10} c^{4} - 128 \, a^{3} b^{8} c^{5} + 148 \, a^{4} b^{6} c^{6} - 80 \, a^{5} b^{4} c^{7} + 16 \, a^{6} b^{2} c^{8}\right)} d^{2} - 2 \, {\left(b^{15} c - 13 \, a b^{13} c^{2} + 67 \, a^{2} b^{11} c^{3} - 174 \, a^{3} b^{9} c^{4} + 239 \, a^{4} b^{7} c^{5} - 166 \, a^{5} b^{5} c^{6} + 50 \, a^{6} b^{3} c^{7} - 4 \, a^{7} b c^{8}\right)} d e + {\left(b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}\right)} e^{2}}{b^{2} c^{18} - 4 \, a c^{19}}}\right)} \sqrt{\frac{{\left(b^{8} c - 8 \, a b^{6} c^{2} + 20 \, a^{2} b^{4} c^{3} - 16 \, a^{3} b^{2} c^{4} + 2 \, a^{4} c^{5}\right)} d - {\left(b^{9} - 9 \, a b^{7} c + 27 \, a^{2} b^{5} c^{2} - 30 \, a^{3} b^{3} c^{3} + 9 \, a^{4} b c^{4}\right)} e - {\left(b^{2} c^{9} - 4 \, a c^{10}\right)} \sqrt{\frac{{\left(b^{14} c^{2} - 12 \, a b^{12} c^{3} + 56 \, a^{2} b^{10} c^{4} - 128 \, a^{3} b^{8} c^{5} + 148 \, a^{4} b^{6} c^{6} - 80 \, a^{5} b^{4} c^{7} + 16 \, a^{6} b^{2} c^{8}\right)} d^{2} - 2 \, {\left(b^{15} c - 13 \, a b^{13} c^{2} + 67 \, a^{2} b^{11} c^{3} - 174 \, a^{3} b^{9} c^{4} + 239 \, a^{4} b^{7} c^{5} - 166 \, a^{5} b^{5} c^{6} + 50 \, a^{6} b^{3} c^{7} - 4 \, a^{7} b c^{8}\right)} d e + {\left(b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}\right)} e^{2}}{b^{2} c^{18} - 4 \, a c^{19}}}}{b^{2} c^{9} - 4 \, a c^{10}}} - 4 \, {\left({\left(a^{4} b^{7} c - 6 \, a^{5} b^{5} c^{2} + 10 \, a^{6} b^{3} c^{3} - 4 \, a^{7} b c^{4}\right)} d - {\left(a^{4} b^{8} - 7 \, a^{5} b^{6} c + 15 \, a^{6} b^{4} c^{2} - 10 \, a^{7} b^{2} c^{3} + a^{8} c^{4}\right)} e\right)} \sqrt{e x + d}\right) + 4 \, {\left(15 \, c^{3} e^{3} x^{3} + 8 \, c^{3} d^{3} + 14 \, b c^{2} d^{2} e + 35 \, {\left(b^{2} c - a c^{2}\right)} d e^{2} - 105 \, {\left(b^{3} - 2 \, a b c\right)} e^{3} + 3 \, {\left(c^{3} d e^{2} - 7 \, b c^{2} e^{3}\right)} x^{2} - {\left(4 \, c^{3} d^{2} e + 7 \, b c^{2} d e^{2} - 35 \, {\left(b^{2} c - a c^{2}\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{210 \, c^{4} e^{3}}"," ",0,"1/210*(105*sqrt(2)*c^4*e^3*sqrt(((b^8*c - 8*a*b^6*c^2 + 20*a^2*b^4*c^3 - 16*a^3*b^2*c^4 + 2*a^4*c^5)*d - (b^9 - 9*a*b^7*c + 27*a^2*b^5*c^2 - 30*a^3*b^3*c^3 + 9*a^4*b*c^4)*e + (b^2*c^9 - 4*a*c^10)*sqrt(((b^14*c^2 - 12*a*b^12*c^3 + 56*a^2*b^10*c^4 - 128*a^3*b^8*c^5 + 148*a^4*b^6*c^6 - 80*a^5*b^4*c^7 + 16*a^6*b^2*c^8)*d^2 - 2*(b^15*c - 13*a*b^13*c^2 + 67*a^2*b^11*c^3 - 174*a^3*b^9*c^4 + 239*a^4*b^7*c^5 - 166*a^5*b^5*c^6 + 50*a^6*b^3*c^7 - 4*a^7*b*c^8)*d*e + (b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)*e^2)/(b^2*c^18 - 4*a*c^19)))/(b^2*c^9 - 4*a*c^10))*log(sqrt(2)*((b^12*c - 12*a*b^10*c^2 + 54*a^2*b^8*c^3 - 112*a^3*b^6*c^4 + 104*a^4*b^4*c^5 - 32*a^5*b^2*c^6)*d - (b^13 - 13*a*b^11*c + 65*a^2*b^9*c^2 - 156*a^3*b^7*c^3 + 181*a^4*b^5*c^4 - 86*a^5*b^3*c^5 + 8*a^6*b*c^6)*e - (b^6*c^9 - 8*a*b^4*c^10 + 18*a^2*b^2*c^11 - 8*a^3*c^12)*sqrt(((b^14*c^2 - 12*a*b^12*c^3 + 56*a^2*b^10*c^4 - 128*a^3*b^8*c^5 + 148*a^4*b^6*c^6 - 80*a^5*b^4*c^7 + 16*a^6*b^2*c^8)*d^2 - 2*(b^15*c - 13*a*b^13*c^2 + 67*a^2*b^11*c^3 - 174*a^3*b^9*c^4 + 239*a^4*b^7*c^5 - 166*a^5*b^5*c^6 + 50*a^6*b^3*c^7 - 4*a^7*b*c^8)*d*e + (b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)*e^2)/(b^2*c^18 - 4*a*c^19)))*sqrt(((b^8*c - 8*a*b^6*c^2 + 20*a^2*b^4*c^3 - 16*a^3*b^2*c^4 + 2*a^4*c^5)*d - (b^9 - 9*a*b^7*c + 27*a^2*b^5*c^2 - 30*a^3*b^3*c^3 + 9*a^4*b*c^4)*e + (b^2*c^9 - 4*a*c^10)*sqrt(((b^14*c^2 - 12*a*b^12*c^3 + 56*a^2*b^10*c^4 - 128*a^3*b^8*c^5 + 148*a^4*b^6*c^6 - 80*a^5*b^4*c^7 + 16*a^6*b^2*c^8)*d^2 - 2*(b^15*c - 13*a*b^13*c^2 + 67*a^2*b^11*c^3 - 174*a^3*b^9*c^4 + 239*a^4*b^7*c^5 - 166*a^5*b^5*c^6 + 50*a^6*b^3*c^7 - 4*a^7*b*c^8)*d*e + (b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)*e^2)/(b^2*c^18 - 4*a*c^19)))/(b^2*c^9 - 4*a*c^10)) - 4*((a^4*b^7*c - 6*a^5*b^5*c^2 + 10*a^6*b^3*c^3 - 4*a^7*b*c^4)*d - (a^4*b^8 - 7*a^5*b^6*c + 15*a^6*b^4*c^2 - 10*a^7*b^2*c^3 + a^8*c^4)*e)*sqrt(e*x + d)) - 105*sqrt(2)*c^4*e^3*sqrt(((b^8*c - 8*a*b^6*c^2 + 20*a^2*b^4*c^3 - 16*a^3*b^2*c^4 + 2*a^4*c^5)*d - (b^9 - 9*a*b^7*c + 27*a^2*b^5*c^2 - 30*a^3*b^3*c^3 + 9*a^4*b*c^4)*e + (b^2*c^9 - 4*a*c^10)*sqrt(((b^14*c^2 - 12*a*b^12*c^3 + 56*a^2*b^10*c^4 - 128*a^3*b^8*c^5 + 148*a^4*b^6*c^6 - 80*a^5*b^4*c^7 + 16*a^6*b^2*c^8)*d^2 - 2*(b^15*c - 13*a*b^13*c^2 + 67*a^2*b^11*c^3 - 174*a^3*b^9*c^4 + 239*a^4*b^7*c^5 - 166*a^5*b^5*c^6 + 50*a^6*b^3*c^7 - 4*a^7*b*c^8)*d*e + (b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)*e^2)/(b^2*c^18 - 4*a*c^19)))/(b^2*c^9 - 4*a*c^10))*log(-sqrt(2)*((b^12*c - 12*a*b^10*c^2 + 54*a^2*b^8*c^3 - 112*a^3*b^6*c^4 + 104*a^4*b^4*c^5 - 32*a^5*b^2*c^6)*d - (b^13 - 13*a*b^11*c + 65*a^2*b^9*c^2 - 156*a^3*b^7*c^3 + 181*a^4*b^5*c^4 - 86*a^5*b^3*c^5 + 8*a^6*b*c^6)*e - (b^6*c^9 - 8*a*b^4*c^10 + 18*a^2*b^2*c^11 - 8*a^3*c^12)*sqrt(((b^14*c^2 - 12*a*b^12*c^3 + 56*a^2*b^10*c^4 - 128*a^3*b^8*c^5 + 148*a^4*b^6*c^6 - 80*a^5*b^4*c^7 + 16*a^6*b^2*c^8)*d^2 - 2*(b^15*c - 13*a*b^13*c^2 + 67*a^2*b^11*c^3 - 174*a^3*b^9*c^4 + 239*a^4*b^7*c^5 - 166*a^5*b^5*c^6 + 50*a^6*b^3*c^7 - 4*a^7*b*c^8)*d*e + (b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)*e^2)/(b^2*c^18 - 4*a*c^19)))*sqrt(((b^8*c - 8*a*b^6*c^2 + 20*a^2*b^4*c^3 - 16*a^3*b^2*c^4 + 2*a^4*c^5)*d - (b^9 - 9*a*b^7*c + 27*a^2*b^5*c^2 - 30*a^3*b^3*c^3 + 9*a^4*b*c^4)*e + (b^2*c^9 - 4*a*c^10)*sqrt(((b^14*c^2 - 12*a*b^12*c^3 + 56*a^2*b^10*c^4 - 128*a^3*b^8*c^5 + 148*a^4*b^6*c^6 - 80*a^5*b^4*c^7 + 16*a^6*b^2*c^8)*d^2 - 2*(b^15*c - 13*a*b^13*c^2 + 67*a^2*b^11*c^3 - 174*a^3*b^9*c^4 + 239*a^4*b^7*c^5 - 166*a^5*b^5*c^6 + 50*a^6*b^3*c^7 - 4*a^7*b*c^8)*d*e + (b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)*e^2)/(b^2*c^18 - 4*a*c^19)))/(b^2*c^9 - 4*a*c^10)) - 4*((a^4*b^7*c - 6*a^5*b^5*c^2 + 10*a^6*b^3*c^3 - 4*a^7*b*c^4)*d - (a^4*b^8 - 7*a^5*b^6*c + 15*a^6*b^4*c^2 - 10*a^7*b^2*c^3 + a^8*c^4)*e)*sqrt(e*x + d)) + 105*sqrt(2)*c^4*e^3*sqrt(((b^8*c - 8*a*b^6*c^2 + 20*a^2*b^4*c^3 - 16*a^3*b^2*c^4 + 2*a^4*c^5)*d - (b^9 - 9*a*b^7*c + 27*a^2*b^5*c^2 - 30*a^3*b^3*c^3 + 9*a^4*b*c^4)*e - (b^2*c^9 - 4*a*c^10)*sqrt(((b^14*c^2 - 12*a*b^12*c^3 + 56*a^2*b^10*c^4 - 128*a^3*b^8*c^5 + 148*a^4*b^6*c^6 - 80*a^5*b^4*c^7 + 16*a^6*b^2*c^8)*d^2 - 2*(b^15*c - 13*a*b^13*c^2 + 67*a^2*b^11*c^3 - 174*a^3*b^9*c^4 + 239*a^4*b^7*c^5 - 166*a^5*b^5*c^6 + 50*a^6*b^3*c^7 - 4*a^7*b*c^8)*d*e + (b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)*e^2)/(b^2*c^18 - 4*a*c^19)))/(b^2*c^9 - 4*a*c^10))*log(sqrt(2)*((b^12*c - 12*a*b^10*c^2 + 54*a^2*b^8*c^3 - 112*a^3*b^6*c^4 + 104*a^4*b^4*c^5 - 32*a^5*b^2*c^6)*d - (b^13 - 13*a*b^11*c + 65*a^2*b^9*c^2 - 156*a^3*b^7*c^3 + 181*a^4*b^5*c^4 - 86*a^5*b^3*c^5 + 8*a^6*b*c^6)*e + (b^6*c^9 - 8*a*b^4*c^10 + 18*a^2*b^2*c^11 - 8*a^3*c^12)*sqrt(((b^14*c^2 - 12*a*b^12*c^3 + 56*a^2*b^10*c^4 - 128*a^3*b^8*c^5 + 148*a^4*b^6*c^6 - 80*a^5*b^4*c^7 + 16*a^6*b^2*c^8)*d^2 - 2*(b^15*c - 13*a*b^13*c^2 + 67*a^2*b^11*c^3 - 174*a^3*b^9*c^4 + 239*a^4*b^7*c^5 - 166*a^5*b^5*c^6 + 50*a^6*b^3*c^7 - 4*a^7*b*c^8)*d*e + (b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)*e^2)/(b^2*c^18 - 4*a*c^19)))*sqrt(((b^8*c - 8*a*b^6*c^2 + 20*a^2*b^4*c^3 - 16*a^3*b^2*c^4 + 2*a^4*c^5)*d - (b^9 - 9*a*b^7*c + 27*a^2*b^5*c^2 - 30*a^3*b^3*c^3 + 9*a^4*b*c^4)*e - (b^2*c^9 - 4*a*c^10)*sqrt(((b^14*c^2 - 12*a*b^12*c^3 + 56*a^2*b^10*c^4 - 128*a^3*b^8*c^5 + 148*a^4*b^6*c^6 - 80*a^5*b^4*c^7 + 16*a^6*b^2*c^8)*d^2 - 2*(b^15*c - 13*a*b^13*c^2 + 67*a^2*b^11*c^3 - 174*a^3*b^9*c^4 + 239*a^4*b^7*c^5 - 166*a^5*b^5*c^6 + 50*a^6*b^3*c^7 - 4*a^7*b*c^8)*d*e + (b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)*e^2)/(b^2*c^18 - 4*a*c^19)))/(b^2*c^9 - 4*a*c^10)) - 4*((a^4*b^7*c - 6*a^5*b^5*c^2 + 10*a^6*b^3*c^3 - 4*a^7*b*c^4)*d - (a^4*b^8 - 7*a^5*b^6*c + 15*a^6*b^4*c^2 - 10*a^7*b^2*c^3 + a^8*c^4)*e)*sqrt(e*x + d)) - 105*sqrt(2)*c^4*e^3*sqrt(((b^8*c - 8*a*b^6*c^2 + 20*a^2*b^4*c^3 - 16*a^3*b^2*c^4 + 2*a^4*c^5)*d - (b^9 - 9*a*b^7*c + 27*a^2*b^5*c^2 - 30*a^3*b^3*c^3 + 9*a^4*b*c^4)*e - (b^2*c^9 - 4*a*c^10)*sqrt(((b^14*c^2 - 12*a*b^12*c^3 + 56*a^2*b^10*c^4 - 128*a^3*b^8*c^5 + 148*a^4*b^6*c^6 - 80*a^5*b^4*c^7 + 16*a^6*b^2*c^8)*d^2 - 2*(b^15*c - 13*a*b^13*c^2 + 67*a^2*b^11*c^3 - 174*a^3*b^9*c^4 + 239*a^4*b^7*c^5 - 166*a^5*b^5*c^6 + 50*a^6*b^3*c^7 - 4*a^7*b*c^8)*d*e + (b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)*e^2)/(b^2*c^18 - 4*a*c^19)))/(b^2*c^9 - 4*a*c^10))*log(-sqrt(2)*((b^12*c - 12*a*b^10*c^2 + 54*a^2*b^8*c^3 - 112*a^3*b^6*c^4 + 104*a^4*b^4*c^5 - 32*a^5*b^2*c^6)*d - (b^13 - 13*a*b^11*c + 65*a^2*b^9*c^2 - 156*a^3*b^7*c^3 + 181*a^4*b^5*c^4 - 86*a^5*b^3*c^5 + 8*a^6*b*c^6)*e + (b^6*c^9 - 8*a*b^4*c^10 + 18*a^2*b^2*c^11 - 8*a^3*c^12)*sqrt(((b^14*c^2 - 12*a*b^12*c^3 + 56*a^2*b^10*c^4 - 128*a^3*b^8*c^5 + 148*a^4*b^6*c^6 - 80*a^5*b^4*c^7 + 16*a^6*b^2*c^8)*d^2 - 2*(b^15*c - 13*a*b^13*c^2 + 67*a^2*b^11*c^3 - 174*a^3*b^9*c^4 + 239*a^4*b^7*c^5 - 166*a^5*b^5*c^6 + 50*a^6*b^3*c^7 - 4*a^7*b*c^8)*d*e + (b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)*e^2)/(b^2*c^18 - 4*a*c^19)))*sqrt(((b^8*c - 8*a*b^6*c^2 + 20*a^2*b^4*c^3 - 16*a^3*b^2*c^4 + 2*a^4*c^5)*d - (b^9 - 9*a*b^7*c + 27*a^2*b^5*c^2 - 30*a^3*b^3*c^3 + 9*a^4*b*c^4)*e - (b^2*c^9 - 4*a*c^10)*sqrt(((b^14*c^2 - 12*a*b^12*c^3 + 56*a^2*b^10*c^4 - 128*a^3*b^8*c^5 + 148*a^4*b^6*c^6 - 80*a^5*b^4*c^7 + 16*a^6*b^2*c^8)*d^2 - 2*(b^15*c - 13*a*b^13*c^2 + 67*a^2*b^11*c^3 - 174*a^3*b^9*c^4 + 239*a^4*b^7*c^5 - 166*a^5*b^5*c^6 + 50*a^6*b^3*c^7 - 4*a^7*b*c^8)*d*e + (b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)*e^2)/(b^2*c^18 - 4*a*c^19)))/(b^2*c^9 - 4*a*c^10)) - 4*((a^4*b^7*c - 6*a^5*b^5*c^2 + 10*a^6*b^3*c^3 - 4*a^7*b*c^4)*d - (a^4*b^8 - 7*a^5*b^6*c + 15*a^6*b^4*c^2 - 10*a^7*b^2*c^3 + a^8*c^4)*e)*sqrt(e*x + d)) + 4*(15*c^3*e^3*x^3 + 8*c^3*d^3 + 14*b*c^2*d^2*e + 35*(b^2*c - a*c^2)*d*e^2 - 105*(b^3 - 2*a*b*c)*e^3 + 3*(c^3*d*e^2 - 7*b*c^2*e^3)*x^2 - (4*c^3*d^2*e + 7*b*c^2*d*e^2 - 35*(b^2*c - a*c^2)*e^3)*x)*sqrt(e*x + d))/(c^4*e^3)","B",0
526,1,4245,0,0.717733," ","integrate(x^3*(e*x+d)^(1/2)/(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{15 \, \sqrt{2} c^{3} e^{2} \sqrt{\frac{{\left(b^{6} c - 6 \, a b^{4} c^{2} + 9 \, a^{2} b^{2} c^{3} - 2 \, a^{3} c^{4}\right)} d - {\left(b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3}\right)} e + {\left(b^{2} c^{7} - 4 \, a c^{8}\right)} \sqrt{\frac{{\left(b^{10} c^{2} - 8 \, a b^{8} c^{3} + 22 \, a^{2} b^{6} c^{4} - 24 \, a^{3} b^{4} c^{5} + 9 \, a^{4} b^{2} c^{6}\right)} d^{2} - 2 \, {\left(b^{11} c - 9 \, a b^{9} c^{2} + 29 \, a^{2} b^{7} c^{3} - 40 \, a^{3} b^{5} c^{4} + 22 \, a^{4} b^{3} c^{5} - 3 \, a^{5} b c^{6}\right)} d e + {\left(b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}\right)} e^{2}}{b^{2} c^{14} - 4 \, a c^{15}}}}{b^{2} c^{7} - 4 \, a c^{8}}} \log\left(\sqrt{2} {\left({\left(b^{9} c - 9 \, a b^{7} c^{2} + 27 \, a^{2} b^{5} c^{3} - 31 \, a^{3} b^{3} c^{4} + 12 \, a^{4} b c^{5}\right)} d - {\left(b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 51 \, a^{3} b^{4} c^{3} + 29 \, a^{4} b^{2} c^{4} - 4 \, a^{5} c^{5}\right)} e - {\left(b^{5} c^{7} - 7 \, a b^{3} c^{8} + 12 \, a^{2} b c^{9}\right)} \sqrt{\frac{{\left(b^{10} c^{2} - 8 \, a b^{8} c^{3} + 22 \, a^{2} b^{6} c^{4} - 24 \, a^{3} b^{4} c^{5} + 9 \, a^{4} b^{2} c^{6}\right)} d^{2} - 2 \, {\left(b^{11} c - 9 \, a b^{9} c^{2} + 29 \, a^{2} b^{7} c^{3} - 40 \, a^{3} b^{5} c^{4} + 22 \, a^{4} b^{3} c^{5} - 3 \, a^{5} b c^{6}\right)} d e + {\left(b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}\right)} e^{2}}{b^{2} c^{14} - 4 \, a c^{15}}}\right)} \sqrt{\frac{{\left(b^{6} c - 6 \, a b^{4} c^{2} + 9 \, a^{2} b^{2} c^{3} - 2 \, a^{3} c^{4}\right)} d - {\left(b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3}\right)} e + {\left(b^{2} c^{7} - 4 \, a c^{8}\right)} \sqrt{\frac{{\left(b^{10} c^{2} - 8 \, a b^{8} c^{3} + 22 \, a^{2} b^{6} c^{4} - 24 \, a^{3} b^{4} c^{5} + 9 \, a^{4} b^{2} c^{6}\right)} d^{2} - 2 \, {\left(b^{11} c - 9 \, a b^{9} c^{2} + 29 \, a^{2} b^{7} c^{3} - 40 \, a^{3} b^{5} c^{4} + 22 \, a^{4} b^{3} c^{5} - 3 \, a^{5} b c^{6}\right)} d e + {\left(b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}\right)} e^{2}}{b^{2} c^{14} - 4 \, a c^{15}}}}{b^{2} c^{7} - 4 \, a c^{8}}} + 4 \, {\left({\left(a^{3} b^{5} c - 4 \, a^{4} b^{3} c^{2} + 3 \, a^{5} b c^{3}\right)} d - {\left(a^{3} b^{6} - 5 \, a^{4} b^{4} c + 6 \, a^{5} b^{2} c^{2} - a^{6} c^{3}\right)} e\right)} \sqrt{e x + d}\right) - 15 \, \sqrt{2} c^{3} e^{2} \sqrt{\frac{{\left(b^{6} c - 6 \, a b^{4} c^{2} + 9 \, a^{2} b^{2} c^{3} - 2 \, a^{3} c^{4}\right)} d - {\left(b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3}\right)} e + {\left(b^{2} c^{7} - 4 \, a c^{8}\right)} \sqrt{\frac{{\left(b^{10} c^{2} - 8 \, a b^{8} c^{3} + 22 \, a^{2} b^{6} c^{4} - 24 \, a^{3} b^{4} c^{5} + 9 \, a^{4} b^{2} c^{6}\right)} d^{2} - 2 \, {\left(b^{11} c - 9 \, a b^{9} c^{2} + 29 \, a^{2} b^{7} c^{3} - 40 \, a^{3} b^{5} c^{4} + 22 \, a^{4} b^{3} c^{5} - 3 \, a^{5} b c^{6}\right)} d e + {\left(b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}\right)} e^{2}}{b^{2} c^{14} - 4 \, a c^{15}}}}{b^{2} c^{7} - 4 \, a c^{8}}} \log\left(-\sqrt{2} {\left({\left(b^{9} c - 9 \, a b^{7} c^{2} + 27 \, a^{2} b^{5} c^{3} - 31 \, a^{3} b^{3} c^{4} + 12 \, a^{4} b c^{5}\right)} d - {\left(b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 51 \, a^{3} b^{4} c^{3} + 29 \, a^{4} b^{2} c^{4} - 4 \, a^{5} c^{5}\right)} e - {\left(b^{5} c^{7} - 7 \, a b^{3} c^{8} + 12 \, a^{2} b c^{9}\right)} \sqrt{\frac{{\left(b^{10} c^{2} - 8 \, a b^{8} c^{3} + 22 \, a^{2} b^{6} c^{4} - 24 \, a^{3} b^{4} c^{5} + 9 \, a^{4} b^{2} c^{6}\right)} d^{2} - 2 \, {\left(b^{11} c - 9 \, a b^{9} c^{2} + 29 \, a^{2} b^{7} c^{3} - 40 \, a^{3} b^{5} c^{4} + 22 \, a^{4} b^{3} c^{5} - 3 \, a^{5} b c^{6}\right)} d e + {\left(b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}\right)} e^{2}}{b^{2} c^{14} - 4 \, a c^{15}}}\right)} \sqrt{\frac{{\left(b^{6} c - 6 \, a b^{4} c^{2} + 9 \, a^{2} b^{2} c^{3} - 2 \, a^{3} c^{4}\right)} d - {\left(b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3}\right)} e + {\left(b^{2} c^{7} - 4 \, a c^{8}\right)} \sqrt{\frac{{\left(b^{10} c^{2} - 8 \, a b^{8} c^{3} + 22 \, a^{2} b^{6} c^{4} - 24 \, a^{3} b^{4} c^{5} + 9 \, a^{4} b^{2} c^{6}\right)} d^{2} - 2 \, {\left(b^{11} c - 9 \, a b^{9} c^{2} + 29 \, a^{2} b^{7} c^{3} - 40 \, a^{3} b^{5} c^{4} + 22 \, a^{4} b^{3} c^{5} - 3 \, a^{5} b c^{6}\right)} d e + {\left(b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}\right)} e^{2}}{b^{2} c^{14} - 4 \, a c^{15}}}}{b^{2} c^{7} - 4 \, a c^{8}}} + 4 \, {\left({\left(a^{3} b^{5} c - 4 \, a^{4} b^{3} c^{2} + 3 \, a^{5} b c^{3}\right)} d - {\left(a^{3} b^{6} - 5 \, a^{4} b^{4} c + 6 \, a^{5} b^{2} c^{2} - a^{6} c^{3}\right)} e\right)} \sqrt{e x + d}\right) + 15 \, \sqrt{2} c^{3} e^{2} \sqrt{\frac{{\left(b^{6} c - 6 \, a b^{4} c^{2} + 9 \, a^{2} b^{2} c^{3} - 2 \, a^{3} c^{4}\right)} d - {\left(b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3}\right)} e - {\left(b^{2} c^{7} - 4 \, a c^{8}\right)} \sqrt{\frac{{\left(b^{10} c^{2} - 8 \, a b^{8} c^{3} + 22 \, a^{2} b^{6} c^{4} - 24 \, a^{3} b^{4} c^{5} + 9 \, a^{4} b^{2} c^{6}\right)} d^{2} - 2 \, {\left(b^{11} c - 9 \, a b^{9} c^{2} + 29 \, a^{2} b^{7} c^{3} - 40 \, a^{3} b^{5} c^{4} + 22 \, a^{4} b^{3} c^{5} - 3 \, a^{5} b c^{6}\right)} d e + {\left(b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}\right)} e^{2}}{b^{2} c^{14} - 4 \, a c^{15}}}}{b^{2} c^{7} - 4 \, a c^{8}}} \log\left(\sqrt{2} {\left({\left(b^{9} c - 9 \, a b^{7} c^{2} + 27 \, a^{2} b^{5} c^{3} - 31 \, a^{3} b^{3} c^{4} + 12 \, a^{4} b c^{5}\right)} d - {\left(b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 51 \, a^{3} b^{4} c^{3} + 29 \, a^{4} b^{2} c^{4} - 4 \, a^{5} c^{5}\right)} e + {\left(b^{5} c^{7} - 7 \, a b^{3} c^{8} + 12 \, a^{2} b c^{9}\right)} \sqrt{\frac{{\left(b^{10} c^{2} - 8 \, a b^{8} c^{3} + 22 \, a^{2} b^{6} c^{4} - 24 \, a^{3} b^{4} c^{5} + 9 \, a^{4} b^{2} c^{6}\right)} d^{2} - 2 \, {\left(b^{11} c - 9 \, a b^{9} c^{2} + 29 \, a^{2} b^{7} c^{3} - 40 \, a^{3} b^{5} c^{4} + 22 \, a^{4} b^{3} c^{5} - 3 \, a^{5} b c^{6}\right)} d e + {\left(b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}\right)} e^{2}}{b^{2} c^{14} - 4 \, a c^{15}}}\right)} \sqrt{\frac{{\left(b^{6} c - 6 \, a b^{4} c^{2} + 9 \, a^{2} b^{2} c^{3} - 2 \, a^{3} c^{4}\right)} d - {\left(b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3}\right)} e - {\left(b^{2} c^{7} - 4 \, a c^{8}\right)} \sqrt{\frac{{\left(b^{10} c^{2} - 8 \, a b^{8} c^{3} + 22 \, a^{2} b^{6} c^{4} - 24 \, a^{3} b^{4} c^{5} + 9 \, a^{4} b^{2} c^{6}\right)} d^{2} - 2 \, {\left(b^{11} c - 9 \, a b^{9} c^{2} + 29 \, a^{2} b^{7} c^{3} - 40 \, a^{3} b^{5} c^{4} + 22 \, a^{4} b^{3} c^{5} - 3 \, a^{5} b c^{6}\right)} d e + {\left(b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}\right)} e^{2}}{b^{2} c^{14} - 4 \, a c^{15}}}}{b^{2} c^{7} - 4 \, a c^{8}}} + 4 \, {\left({\left(a^{3} b^{5} c - 4 \, a^{4} b^{3} c^{2} + 3 \, a^{5} b c^{3}\right)} d - {\left(a^{3} b^{6} - 5 \, a^{4} b^{4} c + 6 \, a^{5} b^{2} c^{2} - a^{6} c^{3}\right)} e\right)} \sqrt{e x + d}\right) - 15 \, \sqrt{2} c^{3} e^{2} \sqrt{\frac{{\left(b^{6} c - 6 \, a b^{4} c^{2} + 9 \, a^{2} b^{2} c^{3} - 2 \, a^{3} c^{4}\right)} d - {\left(b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3}\right)} e - {\left(b^{2} c^{7} - 4 \, a c^{8}\right)} \sqrt{\frac{{\left(b^{10} c^{2} - 8 \, a b^{8} c^{3} + 22 \, a^{2} b^{6} c^{4} - 24 \, a^{3} b^{4} c^{5} + 9 \, a^{4} b^{2} c^{6}\right)} d^{2} - 2 \, {\left(b^{11} c - 9 \, a b^{9} c^{2} + 29 \, a^{2} b^{7} c^{3} - 40 \, a^{3} b^{5} c^{4} + 22 \, a^{4} b^{3} c^{5} - 3 \, a^{5} b c^{6}\right)} d e + {\left(b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}\right)} e^{2}}{b^{2} c^{14} - 4 \, a c^{15}}}}{b^{2} c^{7} - 4 \, a c^{8}}} \log\left(-\sqrt{2} {\left({\left(b^{9} c - 9 \, a b^{7} c^{2} + 27 \, a^{2} b^{5} c^{3} - 31 \, a^{3} b^{3} c^{4} + 12 \, a^{4} b c^{5}\right)} d - {\left(b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 51 \, a^{3} b^{4} c^{3} + 29 \, a^{4} b^{2} c^{4} - 4 \, a^{5} c^{5}\right)} e + {\left(b^{5} c^{7} - 7 \, a b^{3} c^{8} + 12 \, a^{2} b c^{9}\right)} \sqrt{\frac{{\left(b^{10} c^{2} - 8 \, a b^{8} c^{3} + 22 \, a^{2} b^{6} c^{4} - 24 \, a^{3} b^{4} c^{5} + 9 \, a^{4} b^{2} c^{6}\right)} d^{2} - 2 \, {\left(b^{11} c - 9 \, a b^{9} c^{2} + 29 \, a^{2} b^{7} c^{3} - 40 \, a^{3} b^{5} c^{4} + 22 \, a^{4} b^{3} c^{5} - 3 \, a^{5} b c^{6}\right)} d e + {\left(b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}\right)} e^{2}}{b^{2} c^{14} - 4 \, a c^{15}}}\right)} \sqrt{\frac{{\left(b^{6} c - 6 \, a b^{4} c^{2} + 9 \, a^{2} b^{2} c^{3} - 2 \, a^{3} c^{4}\right)} d - {\left(b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3}\right)} e - {\left(b^{2} c^{7} - 4 \, a c^{8}\right)} \sqrt{\frac{{\left(b^{10} c^{2} - 8 \, a b^{8} c^{3} + 22 \, a^{2} b^{6} c^{4} - 24 \, a^{3} b^{4} c^{5} + 9 \, a^{4} b^{2} c^{6}\right)} d^{2} - 2 \, {\left(b^{11} c - 9 \, a b^{9} c^{2} + 29 \, a^{2} b^{7} c^{3} - 40 \, a^{3} b^{5} c^{4} + 22 \, a^{4} b^{3} c^{5} - 3 \, a^{5} b c^{6}\right)} d e + {\left(b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}\right)} e^{2}}{b^{2} c^{14} - 4 \, a c^{15}}}}{b^{2} c^{7} - 4 \, a c^{8}}} + 4 \, {\left({\left(a^{3} b^{5} c - 4 \, a^{4} b^{3} c^{2} + 3 \, a^{5} b c^{3}\right)} d - {\left(a^{3} b^{6} - 5 \, a^{4} b^{4} c + 6 \, a^{5} b^{2} c^{2} - a^{6} c^{3}\right)} e\right)} \sqrt{e x + d}\right) + 4 \, {\left(3 \, c^{2} e^{2} x^{2} - 2 \, c^{2} d^{2} - 5 \, b c d e + 15 \, {\left(b^{2} - a c\right)} e^{2} + {\left(c^{2} d e - 5 \, b c e^{2}\right)} x\right)} \sqrt{e x + d}}{30 \, c^{3} e^{2}}"," ",0,"1/30*(15*sqrt(2)*c^3*e^2*sqrt(((b^6*c - 6*a*b^4*c^2 + 9*a^2*b^2*c^3 - 2*a^3*c^4)*d - (b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3)*e + (b^2*c^7 - 4*a*c^8)*sqrt(((b^10*c^2 - 8*a*b^8*c^3 + 22*a^2*b^6*c^4 - 24*a^3*b^4*c^5 + 9*a^4*b^2*c^6)*d^2 - 2*(b^11*c - 9*a*b^9*c^2 + 29*a^2*b^7*c^3 - 40*a^3*b^5*c^4 + 22*a^4*b^3*c^5 - 3*a^5*b*c^6)*d*e + (b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)*e^2)/(b^2*c^14 - 4*a*c^15)))/(b^2*c^7 - 4*a*c^8))*log(sqrt(2)*((b^9*c - 9*a*b^7*c^2 + 27*a^2*b^5*c^3 - 31*a^3*b^3*c^4 + 12*a^4*b*c^5)*d - (b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 51*a^3*b^4*c^3 + 29*a^4*b^2*c^4 - 4*a^5*c^5)*e - (b^5*c^7 - 7*a*b^3*c^8 + 12*a^2*b*c^9)*sqrt(((b^10*c^2 - 8*a*b^8*c^3 + 22*a^2*b^6*c^4 - 24*a^3*b^4*c^5 + 9*a^4*b^2*c^6)*d^2 - 2*(b^11*c - 9*a*b^9*c^2 + 29*a^2*b^7*c^3 - 40*a^3*b^5*c^4 + 22*a^4*b^3*c^5 - 3*a^5*b*c^6)*d*e + (b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)*e^2)/(b^2*c^14 - 4*a*c^15)))*sqrt(((b^6*c - 6*a*b^4*c^2 + 9*a^2*b^2*c^3 - 2*a^3*c^4)*d - (b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3)*e + (b^2*c^7 - 4*a*c^8)*sqrt(((b^10*c^2 - 8*a*b^8*c^3 + 22*a^2*b^6*c^4 - 24*a^3*b^4*c^5 + 9*a^4*b^2*c^6)*d^2 - 2*(b^11*c - 9*a*b^9*c^2 + 29*a^2*b^7*c^3 - 40*a^3*b^5*c^4 + 22*a^4*b^3*c^5 - 3*a^5*b*c^6)*d*e + (b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)*e^2)/(b^2*c^14 - 4*a*c^15)))/(b^2*c^7 - 4*a*c^8)) + 4*((a^3*b^5*c - 4*a^4*b^3*c^2 + 3*a^5*b*c^3)*d - (a^3*b^6 - 5*a^4*b^4*c + 6*a^5*b^2*c^2 - a^6*c^3)*e)*sqrt(e*x + d)) - 15*sqrt(2)*c^3*e^2*sqrt(((b^6*c - 6*a*b^4*c^2 + 9*a^2*b^2*c^3 - 2*a^3*c^4)*d - (b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3)*e + (b^2*c^7 - 4*a*c^8)*sqrt(((b^10*c^2 - 8*a*b^8*c^3 + 22*a^2*b^6*c^4 - 24*a^3*b^4*c^5 + 9*a^4*b^2*c^6)*d^2 - 2*(b^11*c - 9*a*b^9*c^2 + 29*a^2*b^7*c^3 - 40*a^3*b^5*c^4 + 22*a^4*b^3*c^5 - 3*a^5*b*c^6)*d*e + (b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)*e^2)/(b^2*c^14 - 4*a*c^15)))/(b^2*c^7 - 4*a*c^8))*log(-sqrt(2)*((b^9*c - 9*a*b^7*c^2 + 27*a^2*b^5*c^3 - 31*a^3*b^3*c^4 + 12*a^4*b*c^5)*d - (b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 51*a^3*b^4*c^3 + 29*a^4*b^2*c^4 - 4*a^5*c^5)*e - (b^5*c^7 - 7*a*b^3*c^8 + 12*a^2*b*c^9)*sqrt(((b^10*c^2 - 8*a*b^8*c^3 + 22*a^2*b^6*c^4 - 24*a^3*b^4*c^5 + 9*a^4*b^2*c^6)*d^2 - 2*(b^11*c - 9*a*b^9*c^2 + 29*a^2*b^7*c^3 - 40*a^3*b^5*c^4 + 22*a^4*b^3*c^5 - 3*a^5*b*c^6)*d*e + (b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)*e^2)/(b^2*c^14 - 4*a*c^15)))*sqrt(((b^6*c - 6*a*b^4*c^2 + 9*a^2*b^2*c^3 - 2*a^3*c^4)*d - (b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3)*e + (b^2*c^7 - 4*a*c^8)*sqrt(((b^10*c^2 - 8*a*b^8*c^3 + 22*a^2*b^6*c^4 - 24*a^3*b^4*c^5 + 9*a^4*b^2*c^6)*d^2 - 2*(b^11*c - 9*a*b^9*c^2 + 29*a^2*b^7*c^3 - 40*a^3*b^5*c^4 + 22*a^4*b^3*c^5 - 3*a^5*b*c^6)*d*e + (b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)*e^2)/(b^2*c^14 - 4*a*c^15)))/(b^2*c^7 - 4*a*c^8)) + 4*((a^3*b^5*c - 4*a^4*b^3*c^2 + 3*a^5*b*c^3)*d - (a^3*b^6 - 5*a^4*b^4*c + 6*a^5*b^2*c^2 - a^6*c^3)*e)*sqrt(e*x + d)) + 15*sqrt(2)*c^3*e^2*sqrt(((b^6*c - 6*a*b^4*c^2 + 9*a^2*b^2*c^3 - 2*a^3*c^4)*d - (b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3)*e - (b^2*c^7 - 4*a*c^8)*sqrt(((b^10*c^2 - 8*a*b^8*c^3 + 22*a^2*b^6*c^4 - 24*a^3*b^4*c^5 + 9*a^4*b^2*c^6)*d^2 - 2*(b^11*c - 9*a*b^9*c^2 + 29*a^2*b^7*c^3 - 40*a^3*b^5*c^4 + 22*a^4*b^3*c^5 - 3*a^5*b*c^6)*d*e + (b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)*e^2)/(b^2*c^14 - 4*a*c^15)))/(b^2*c^7 - 4*a*c^8))*log(sqrt(2)*((b^9*c - 9*a*b^7*c^2 + 27*a^2*b^5*c^3 - 31*a^3*b^3*c^4 + 12*a^4*b*c^5)*d - (b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 51*a^3*b^4*c^3 + 29*a^4*b^2*c^4 - 4*a^5*c^5)*e + (b^5*c^7 - 7*a*b^3*c^8 + 12*a^2*b*c^9)*sqrt(((b^10*c^2 - 8*a*b^8*c^3 + 22*a^2*b^6*c^4 - 24*a^3*b^4*c^5 + 9*a^4*b^2*c^6)*d^2 - 2*(b^11*c - 9*a*b^9*c^2 + 29*a^2*b^7*c^3 - 40*a^3*b^5*c^4 + 22*a^4*b^3*c^5 - 3*a^5*b*c^6)*d*e + (b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)*e^2)/(b^2*c^14 - 4*a*c^15)))*sqrt(((b^6*c - 6*a*b^4*c^2 + 9*a^2*b^2*c^3 - 2*a^3*c^4)*d - (b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3)*e - (b^2*c^7 - 4*a*c^8)*sqrt(((b^10*c^2 - 8*a*b^8*c^3 + 22*a^2*b^6*c^4 - 24*a^3*b^4*c^5 + 9*a^4*b^2*c^6)*d^2 - 2*(b^11*c - 9*a*b^9*c^2 + 29*a^2*b^7*c^3 - 40*a^3*b^5*c^4 + 22*a^4*b^3*c^5 - 3*a^5*b*c^6)*d*e + (b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)*e^2)/(b^2*c^14 - 4*a*c^15)))/(b^2*c^7 - 4*a*c^8)) + 4*((a^3*b^5*c - 4*a^4*b^3*c^2 + 3*a^5*b*c^3)*d - (a^3*b^6 - 5*a^4*b^4*c + 6*a^5*b^2*c^2 - a^6*c^3)*e)*sqrt(e*x + d)) - 15*sqrt(2)*c^3*e^2*sqrt(((b^6*c - 6*a*b^4*c^2 + 9*a^2*b^2*c^3 - 2*a^3*c^4)*d - (b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3)*e - (b^2*c^7 - 4*a*c^8)*sqrt(((b^10*c^2 - 8*a*b^8*c^3 + 22*a^2*b^6*c^4 - 24*a^3*b^4*c^5 + 9*a^4*b^2*c^6)*d^2 - 2*(b^11*c - 9*a*b^9*c^2 + 29*a^2*b^7*c^3 - 40*a^3*b^5*c^4 + 22*a^4*b^3*c^5 - 3*a^5*b*c^6)*d*e + (b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)*e^2)/(b^2*c^14 - 4*a*c^15)))/(b^2*c^7 - 4*a*c^8))*log(-sqrt(2)*((b^9*c - 9*a*b^7*c^2 + 27*a^2*b^5*c^3 - 31*a^3*b^3*c^4 + 12*a^4*b*c^5)*d - (b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 51*a^3*b^4*c^3 + 29*a^4*b^2*c^4 - 4*a^5*c^5)*e + (b^5*c^7 - 7*a*b^3*c^8 + 12*a^2*b*c^9)*sqrt(((b^10*c^2 - 8*a*b^8*c^3 + 22*a^2*b^6*c^4 - 24*a^3*b^4*c^5 + 9*a^4*b^2*c^6)*d^2 - 2*(b^11*c - 9*a*b^9*c^2 + 29*a^2*b^7*c^3 - 40*a^3*b^5*c^4 + 22*a^4*b^3*c^5 - 3*a^5*b*c^6)*d*e + (b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)*e^2)/(b^2*c^14 - 4*a*c^15)))*sqrt(((b^6*c - 6*a*b^4*c^2 + 9*a^2*b^2*c^3 - 2*a^3*c^4)*d - (b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3)*e - (b^2*c^7 - 4*a*c^8)*sqrt(((b^10*c^2 - 8*a*b^8*c^3 + 22*a^2*b^6*c^4 - 24*a^3*b^4*c^5 + 9*a^4*b^2*c^6)*d^2 - 2*(b^11*c - 9*a*b^9*c^2 + 29*a^2*b^7*c^3 - 40*a^3*b^5*c^4 + 22*a^4*b^3*c^5 - 3*a^5*b*c^6)*d*e + (b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)*e^2)/(b^2*c^14 - 4*a*c^15)))/(b^2*c^7 - 4*a*c^8)) + 4*((a^3*b^5*c - 4*a^4*b^3*c^2 + 3*a^5*b*c^3)*d - (a^3*b^6 - 5*a^4*b^4*c + 6*a^5*b^2*c^2 - a^6*c^3)*e)*sqrt(e*x + d)) + 4*(3*c^2*e^2*x^2 - 2*c^2*d^2 - 5*b*c*d*e + 15*(b^2 - a*c)*e^2 + (c^2*d*e - 5*b*c*e^2)*x)*sqrt(e*x + d))/(c^3*e^2)","B",0
527,1,2966,0,0.523571," ","integrate(x^2*(e*x+d)^(1/2)/(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{3 \, \sqrt{2} c^{2} e \sqrt{\frac{{\left(b^{4} c - 4 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d - {\left(b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}\right)} e + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{{\left(b^{6} c^{2} - 4 \, a b^{4} c^{3} + 4 \, a^{2} b^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{7} c - 5 \, a b^{5} c^{2} + 7 \, a^{2} b^{3} c^{3} - 2 \, a^{3} b c^{4}\right)} d e + {\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} e^{2}}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}} \log\left(\sqrt{2} {\left({\left(b^{6} c - 6 \, a b^{4} c^{2} + 8 \, a^{2} b^{2} c^{3}\right)} d - {\left(b^{7} - 7 \, a b^{5} c + 13 \, a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} e - {\left(b^{4} c^{5} - 6 \, a b^{2} c^{6} + 8 \, a^{2} c^{7}\right)} \sqrt{\frac{{\left(b^{6} c^{2} - 4 \, a b^{4} c^{3} + 4 \, a^{2} b^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{7} c - 5 \, a b^{5} c^{2} + 7 \, a^{2} b^{3} c^{3} - 2 \, a^{3} b c^{4}\right)} d e + {\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} e^{2}}{b^{2} c^{10} - 4 \, a c^{11}}}\right)} \sqrt{\frac{{\left(b^{4} c - 4 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d - {\left(b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}\right)} e + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{{\left(b^{6} c^{2} - 4 \, a b^{4} c^{3} + 4 \, a^{2} b^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{7} c - 5 \, a b^{5} c^{2} + 7 \, a^{2} b^{3} c^{3} - 2 \, a^{3} b c^{4}\right)} d e + {\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} e^{2}}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}} - 4 \, {\left({\left(a^{2} b^{3} c - 2 \, a^{3} b c^{2}\right)} d - {\left(a^{2} b^{4} - 3 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e\right)} \sqrt{e x + d}\right) - 3 \, \sqrt{2} c^{2} e \sqrt{\frac{{\left(b^{4} c - 4 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d - {\left(b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}\right)} e + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{{\left(b^{6} c^{2} - 4 \, a b^{4} c^{3} + 4 \, a^{2} b^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{7} c - 5 \, a b^{5} c^{2} + 7 \, a^{2} b^{3} c^{3} - 2 \, a^{3} b c^{4}\right)} d e + {\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} e^{2}}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}} \log\left(-\sqrt{2} {\left({\left(b^{6} c - 6 \, a b^{4} c^{2} + 8 \, a^{2} b^{2} c^{3}\right)} d - {\left(b^{7} - 7 \, a b^{5} c + 13 \, a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} e - {\left(b^{4} c^{5} - 6 \, a b^{2} c^{6} + 8 \, a^{2} c^{7}\right)} \sqrt{\frac{{\left(b^{6} c^{2} - 4 \, a b^{4} c^{3} + 4 \, a^{2} b^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{7} c - 5 \, a b^{5} c^{2} + 7 \, a^{2} b^{3} c^{3} - 2 \, a^{3} b c^{4}\right)} d e + {\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} e^{2}}{b^{2} c^{10} - 4 \, a c^{11}}}\right)} \sqrt{\frac{{\left(b^{4} c - 4 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d - {\left(b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}\right)} e + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{{\left(b^{6} c^{2} - 4 \, a b^{4} c^{3} + 4 \, a^{2} b^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{7} c - 5 \, a b^{5} c^{2} + 7 \, a^{2} b^{3} c^{3} - 2 \, a^{3} b c^{4}\right)} d e + {\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} e^{2}}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}} - 4 \, {\left({\left(a^{2} b^{3} c - 2 \, a^{3} b c^{2}\right)} d - {\left(a^{2} b^{4} - 3 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e\right)} \sqrt{e x + d}\right) + 3 \, \sqrt{2} c^{2} e \sqrt{\frac{{\left(b^{4} c - 4 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d - {\left(b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}\right)} e - {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{{\left(b^{6} c^{2} - 4 \, a b^{4} c^{3} + 4 \, a^{2} b^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{7} c - 5 \, a b^{5} c^{2} + 7 \, a^{2} b^{3} c^{3} - 2 \, a^{3} b c^{4}\right)} d e + {\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} e^{2}}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}} \log\left(\sqrt{2} {\left({\left(b^{6} c - 6 \, a b^{4} c^{2} + 8 \, a^{2} b^{2} c^{3}\right)} d - {\left(b^{7} - 7 \, a b^{5} c + 13 \, a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} e + {\left(b^{4} c^{5} - 6 \, a b^{2} c^{6} + 8 \, a^{2} c^{7}\right)} \sqrt{\frac{{\left(b^{6} c^{2} - 4 \, a b^{4} c^{3} + 4 \, a^{2} b^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{7} c - 5 \, a b^{5} c^{2} + 7 \, a^{2} b^{3} c^{3} - 2 \, a^{3} b c^{4}\right)} d e + {\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} e^{2}}{b^{2} c^{10} - 4 \, a c^{11}}}\right)} \sqrt{\frac{{\left(b^{4} c - 4 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d - {\left(b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}\right)} e - {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{{\left(b^{6} c^{2} - 4 \, a b^{4} c^{3} + 4 \, a^{2} b^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{7} c - 5 \, a b^{5} c^{2} + 7 \, a^{2} b^{3} c^{3} - 2 \, a^{3} b c^{4}\right)} d e + {\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} e^{2}}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}} - 4 \, {\left({\left(a^{2} b^{3} c - 2 \, a^{3} b c^{2}\right)} d - {\left(a^{2} b^{4} - 3 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e\right)} \sqrt{e x + d}\right) - 3 \, \sqrt{2} c^{2} e \sqrt{\frac{{\left(b^{4} c - 4 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d - {\left(b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}\right)} e - {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{{\left(b^{6} c^{2} - 4 \, a b^{4} c^{3} + 4 \, a^{2} b^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{7} c - 5 \, a b^{5} c^{2} + 7 \, a^{2} b^{3} c^{3} - 2 \, a^{3} b c^{4}\right)} d e + {\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} e^{2}}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}} \log\left(-\sqrt{2} {\left({\left(b^{6} c - 6 \, a b^{4} c^{2} + 8 \, a^{2} b^{2} c^{3}\right)} d - {\left(b^{7} - 7 \, a b^{5} c + 13 \, a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} e + {\left(b^{4} c^{5} - 6 \, a b^{2} c^{6} + 8 \, a^{2} c^{7}\right)} \sqrt{\frac{{\left(b^{6} c^{2} - 4 \, a b^{4} c^{3} + 4 \, a^{2} b^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{7} c - 5 \, a b^{5} c^{2} + 7 \, a^{2} b^{3} c^{3} - 2 \, a^{3} b c^{4}\right)} d e + {\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} e^{2}}{b^{2} c^{10} - 4 \, a c^{11}}}\right)} \sqrt{\frac{{\left(b^{4} c - 4 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d - {\left(b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}\right)} e - {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{{\left(b^{6} c^{2} - 4 \, a b^{4} c^{3} + 4 \, a^{2} b^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{7} c - 5 \, a b^{5} c^{2} + 7 \, a^{2} b^{3} c^{3} - 2 \, a^{3} b c^{4}\right)} d e + {\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} e^{2}}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}} - 4 \, {\left({\left(a^{2} b^{3} c - 2 \, a^{3} b c^{2}\right)} d - {\left(a^{2} b^{4} - 3 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e\right)} \sqrt{e x + d}\right) + 4 \, {\left(c e x + c d - 3 \, b e\right)} \sqrt{e x + d}}{6 \, c^{2} e}"," ",0,"1/6*(3*sqrt(2)*c^2*e*sqrt(((b^4*c - 4*a*b^2*c^2 + 2*a^2*c^3)*d - (b^5 - 5*a*b^3*c + 5*a^2*b*c^2)*e + (b^2*c^5 - 4*a*c^6)*sqrt(((b^6*c^2 - 4*a*b^4*c^3 + 4*a^2*b^2*c^4)*d^2 - 2*(b^7*c - 5*a*b^5*c^2 + 7*a^2*b^3*c^3 - 2*a^3*b*c^4)*d*e + (b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*e^2)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6))*log(sqrt(2)*((b^6*c - 6*a*b^4*c^2 + 8*a^2*b^2*c^3)*d - (b^7 - 7*a*b^5*c + 13*a^2*b^3*c^2 - 4*a^3*b*c^3)*e - (b^4*c^5 - 6*a*b^2*c^6 + 8*a^2*c^7)*sqrt(((b^6*c^2 - 4*a*b^4*c^3 + 4*a^2*b^2*c^4)*d^2 - 2*(b^7*c - 5*a*b^5*c^2 + 7*a^2*b^3*c^3 - 2*a^3*b*c^4)*d*e + (b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*e^2)/(b^2*c^10 - 4*a*c^11)))*sqrt(((b^4*c - 4*a*b^2*c^2 + 2*a^2*c^3)*d - (b^5 - 5*a*b^3*c + 5*a^2*b*c^2)*e + (b^2*c^5 - 4*a*c^6)*sqrt(((b^6*c^2 - 4*a*b^4*c^3 + 4*a^2*b^2*c^4)*d^2 - 2*(b^7*c - 5*a*b^5*c^2 + 7*a^2*b^3*c^3 - 2*a^3*b*c^4)*d*e + (b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*e^2)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6)) - 4*((a^2*b^3*c - 2*a^3*b*c^2)*d - (a^2*b^4 - 3*a^3*b^2*c + a^4*c^2)*e)*sqrt(e*x + d)) - 3*sqrt(2)*c^2*e*sqrt(((b^4*c - 4*a*b^2*c^2 + 2*a^2*c^3)*d - (b^5 - 5*a*b^3*c + 5*a^2*b*c^2)*e + (b^2*c^5 - 4*a*c^6)*sqrt(((b^6*c^2 - 4*a*b^4*c^3 + 4*a^2*b^2*c^4)*d^2 - 2*(b^7*c - 5*a*b^5*c^2 + 7*a^2*b^3*c^3 - 2*a^3*b*c^4)*d*e + (b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*e^2)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6))*log(-sqrt(2)*((b^6*c - 6*a*b^4*c^2 + 8*a^2*b^2*c^3)*d - (b^7 - 7*a*b^5*c + 13*a^2*b^3*c^2 - 4*a^3*b*c^3)*e - (b^4*c^5 - 6*a*b^2*c^6 + 8*a^2*c^7)*sqrt(((b^6*c^2 - 4*a*b^4*c^3 + 4*a^2*b^2*c^4)*d^2 - 2*(b^7*c - 5*a*b^5*c^2 + 7*a^2*b^3*c^3 - 2*a^3*b*c^4)*d*e + (b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*e^2)/(b^2*c^10 - 4*a*c^11)))*sqrt(((b^4*c - 4*a*b^2*c^2 + 2*a^2*c^3)*d - (b^5 - 5*a*b^3*c + 5*a^2*b*c^2)*e + (b^2*c^5 - 4*a*c^6)*sqrt(((b^6*c^2 - 4*a*b^4*c^3 + 4*a^2*b^2*c^4)*d^2 - 2*(b^7*c - 5*a*b^5*c^2 + 7*a^2*b^3*c^3 - 2*a^3*b*c^4)*d*e + (b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*e^2)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6)) - 4*((a^2*b^3*c - 2*a^3*b*c^2)*d - (a^2*b^4 - 3*a^3*b^2*c + a^4*c^2)*e)*sqrt(e*x + d)) + 3*sqrt(2)*c^2*e*sqrt(((b^4*c - 4*a*b^2*c^2 + 2*a^2*c^3)*d - (b^5 - 5*a*b^3*c + 5*a^2*b*c^2)*e - (b^2*c^5 - 4*a*c^6)*sqrt(((b^6*c^2 - 4*a*b^4*c^3 + 4*a^2*b^2*c^4)*d^2 - 2*(b^7*c - 5*a*b^5*c^2 + 7*a^2*b^3*c^3 - 2*a^3*b*c^4)*d*e + (b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*e^2)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6))*log(sqrt(2)*((b^6*c - 6*a*b^4*c^2 + 8*a^2*b^2*c^3)*d - (b^7 - 7*a*b^5*c + 13*a^2*b^3*c^2 - 4*a^3*b*c^3)*e + (b^4*c^5 - 6*a*b^2*c^6 + 8*a^2*c^7)*sqrt(((b^6*c^2 - 4*a*b^4*c^3 + 4*a^2*b^2*c^4)*d^2 - 2*(b^7*c - 5*a*b^5*c^2 + 7*a^2*b^3*c^3 - 2*a^3*b*c^4)*d*e + (b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*e^2)/(b^2*c^10 - 4*a*c^11)))*sqrt(((b^4*c - 4*a*b^2*c^2 + 2*a^2*c^3)*d - (b^5 - 5*a*b^3*c + 5*a^2*b*c^2)*e - (b^2*c^5 - 4*a*c^6)*sqrt(((b^6*c^2 - 4*a*b^4*c^3 + 4*a^2*b^2*c^4)*d^2 - 2*(b^7*c - 5*a*b^5*c^2 + 7*a^2*b^3*c^3 - 2*a^3*b*c^4)*d*e + (b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*e^2)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6)) - 4*((a^2*b^3*c - 2*a^3*b*c^2)*d - (a^2*b^4 - 3*a^3*b^2*c + a^4*c^2)*e)*sqrt(e*x + d)) - 3*sqrt(2)*c^2*e*sqrt(((b^4*c - 4*a*b^2*c^2 + 2*a^2*c^3)*d - (b^5 - 5*a*b^3*c + 5*a^2*b*c^2)*e - (b^2*c^5 - 4*a*c^6)*sqrt(((b^6*c^2 - 4*a*b^4*c^3 + 4*a^2*b^2*c^4)*d^2 - 2*(b^7*c - 5*a*b^5*c^2 + 7*a^2*b^3*c^3 - 2*a^3*b*c^4)*d*e + (b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*e^2)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6))*log(-sqrt(2)*((b^6*c - 6*a*b^4*c^2 + 8*a^2*b^2*c^3)*d - (b^7 - 7*a*b^5*c + 13*a^2*b^3*c^2 - 4*a^3*b*c^3)*e + (b^4*c^5 - 6*a*b^2*c^6 + 8*a^2*c^7)*sqrt(((b^6*c^2 - 4*a*b^4*c^3 + 4*a^2*b^2*c^4)*d^2 - 2*(b^7*c - 5*a*b^5*c^2 + 7*a^2*b^3*c^3 - 2*a^3*b*c^4)*d*e + (b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*e^2)/(b^2*c^10 - 4*a*c^11)))*sqrt(((b^4*c - 4*a*b^2*c^2 + 2*a^2*c^3)*d - (b^5 - 5*a*b^3*c + 5*a^2*b*c^2)*e - (b^2*c^5 - 4*a*c^6)*sqrt(((b^6*c^2 - 4*a*b^4*c^3 + 4*a^2*b^2*c^4)*d^2 - 2*(b^7*c - 5*a*b^5*c^2 + 7*a^2*b^3*c^3 - 2*a^3*b*c^4)*d*e + (b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*e^2)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6)) - 4*((a^2*b^3*c - 2*a^3*b*c^2)*d - (a^2*b^4 - 3*a^3*b^2*c + a^4*c^2)*e)*sqrt(e*x + d)) + 4*(c*e*x + c*d - 3*b*e)*sqrt(e*x + d))/(c^2*e)","B",0
528,1,1721,0,0.455431," ","integrate(x*(e*x+d)^(1/2)/(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{\sqrt{2} c \sqrt{\frac{{\left(b^{2} c - 2 \, a c^{2}\right)} d - {\left(b^{3} - 3 \, a b c\right)} e + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{2} c^{2} d^{2} - 2 \, {\left(b^{3} c - a b c^{2}\right)} d e + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} \log\left(\sqrt{2} {\left({\left(b^{3} c - 4 \, a b c^{2}\right)} d - {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} e - {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} \sqrt{\frac{b^{2} c^{2} d^{2} - 2 \, {\left(b^{3} c - a b c^{2}\right)} d e + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}\right)} \sqrt{\frac{{\left(b^{2} c - 2 \, a c^{2}\right)} d - {\left(b^{3} - 3 \, a b c\right)} e + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{2} c^{2} d^{2} - 2 \, {\left(b^{3} c - a b c^{2}\right)} d e + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} + 4 \, {\left(a b c d - {\left(a b^{2} - a^{2} c\right)} e\right)} \sqrt{e x + d}\right) - \sqrt{2} c \sqrt{\frac{{\left(b^{2} c - 2 \, a c^{2}\right)} d - {\left(b^{3} - 3 \, a b c\right)} e + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{2} c^{2} d^{2} - 2 \, {\left(b^{3} c - a b c^{2}\right)} d e + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} \log\left(-\sqrt{2} {\left({\left(b^{3} c - 4 \, a b c^{2}\right)} d - {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} e - {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} \sqrt{\frac{b^{2} c^{2} d^{2} - 2 \, {\left(b^{3} c - a b c^{2}\right)} d e + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}\right)} \sqrt{\frac{{\left(b^{2} c - 2 \, a c^{2}\right)} d - {\left(b^{3} - 3 \, a b c\right)} e + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{2} c^{2} d^{2} - 2 \, {\left(b^{3} c - a b c^{2}\right)} d e + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} + 4 \, {\left(a b c d - {\left(a b^{2} - a^{2} c\right)} e\right)} \sqrt{e x + d}\right) + \sqrt{2} c \sqrt{\frac{{\left(b^{2} c - 2 \, a c^{2}\right)} d - {\left(b^{3} - 3 \, a b c\right)} e - {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{2} c^{2} d^{2} - 2 \, {\left(b^{3} c - a b c^{2}\right)} d e + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} \log\left(\sqrt{2} {\left({\left(b^{3} c - 4 \, a b c^{2}\right)} d - {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} e + {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} \sqrt{\frac{b^{2} c^{2} d^{2} - 2 \, {\left(b^{3} c - a b c^{2}\right)} d e + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}\right)} \sqrt{\frac{{\left(b^{2} c - 2 \, a c^{2}\right)} d - {\left(b^{3} - 3 \, a b c\right)} e - {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{2} c^{2} d^{2} - 2 \, {\left(b^{3} c - a b c^{2}\right)} d e + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} + 4 \, {\left(a b c d - {\left(a b^{2} - a^{2} c\right)} e\right)} \sqrt{e x + d}\right) - \sqrt{2} c \sqrt{\frac{{\left(b^{2} c - 2 \, a c^{2}\right)} d - {\left(b^{3} - 3 \, a b c\right)} e - {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{2} c^{2} d^{2} - 2 \, {\left(b^{3} c - a b c^{2}\right)} d e + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} \log\left(-\sqrt{2} {\left({\left(b^{3} c - 4 \, a b c^{2}\right)} d - {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} e + {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} \sqrt{\frac{b^{2} c^{2} d^{2} - 2 \, {\left(b^{3} c - a b c^{2}\right)} d e + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}\right)} \sqrt{\frac{{\left(b^{2} c - 2 \, a c^{2}\right)} d - {\left(b^{3} - 3 \, a b c\right)} e - {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{2} c^{2} d^{2} - 2 \, {\left(b^{3} c - a b c^{2}\right)} d e + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} + 4 \, {\left(a b c d - {\left(a b^{2} - a^{2} c\right)} e\right)} \sqrt{e x + d}\right) + 4 \, \sqrt{e x + d}}{2 \, c}"," ",0,"1/2*(sqrt(2)*c*sqrt(((b^2*c - 2*a*c^2)*d - (b^3 - 3*a*b*c)*e + (b^2*c^3 - 4*a*c^4)*sqrt((b^2*c^2*d^2 - 2*(b^3*c - a*b*c^2)*d*e + (b^4 - 2*a*b^2*c + a^2*c^2)*e^2)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))*log(sqrt(2)*((b^3*c - 4*a*b*c^2)*d - (b^4 - 5*a*b^2*c + 4*a^2*c^2)*e - (b^3*c^3 - 4*a*b*c^4)*sqrt((b^2*c^2*d^2 - 2*(b^3*c - a*b*c^2)*d*e + (b^4 - 2*a*b^2*c + a^2*c^2)*e^2)/(b^2*c^6 - 4*a*c^7)))*sqrt(((b^2*c - 2*a*c^2)*d - (b^3 - 3*a*b*c)*e + (b^2*c^3 - 4*a*c^4)*sqrt((b^2*c^2*d^2 - 2*(b^3*c - a*b*c^2)*d*e + (b^4 - 2*a*b^2*c + a^2*c^2)*e^2)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4)) + 4*(a*b*c*d - (a*b^2 - a^2*c)*e)*sqrt(e*x + d)) - sqrt(2)*c*sqrt(((b^2*c - 2*a*c^2)*d - (b^3 - 3*a*b*c)*e + (b^2*c^3 - 4*a*c^4)*sqrt((b^2*c^2*d^2 - 2*(b^3*c - a*b*c^2)*d*e + (b^4 - 2*a*b^2*c + a^2*c^2)*e^2)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))*log(-sqrt(2)*((b^3*c - 4*a*b*c^2)*d - (b^4 - 5*a*b^2*c + 4*a^2*c^2)*e - (b^3*c^3 - 4*a*b*c^4)*sqrt((b^2*c^2*d^2 - 2*(b^3*c - a*b*c^2)*d*e + (b^4 - 2*a*b^2*c + a^2*c^2)*e^2)/(b^2*c^6 - 4*a*c^7)))*sqrt(((b^2*c - 2*a*c^2)*d - (b^3 - 3*a*b*c)*e + (b^2*c^3 - 4*a*c^4)*sqrt((b^2*c^2*d^2 - 2*(b^3*c - a*b*c^2)*d*e + (b^4 - 2*a*b^2*c + a^2*c^2)*e^2)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4)) + 4*(a*b*c*d - (a*b^2 - a^2*c)*e)*sqrt(e*x + d)) + sqrt(2)*c*sqrt(((b^2*c - 2*a*c^2)*d - (b^3 - 3*a*b*c)*e - (b^2*c^3 - 4*a*c^4)*sqrt((b^2*c^2*d^2 - 2*(b^3*c - a*b*c^2)*d*e + (b^4 - 2*a*b^2*c + a^2*c^2)*e^2)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))*log(sqrt(2)*((b^3*c - 4*a*b*c^2)*d - (b^4 - 5*a*b^2*c + 4*a^2*c^2)*e + (b^3*c^3 - 4*a*b*c^4)*sqrt((b^2*c^2*d^2 - 2*(b^3*c - a*b*c^2)*d*e + (b^4 - 2*a*b^2*c + a^2*c^2)*e^2)/(b^2*c^6 - 4*a*c^7)))*sqrt(((b^2*c - 2*a*c^2)*d - (b^3 - 3*a*b*c)*e - (b^2*c^3 - 4*a*c^4)*sqrt((b^2*c^2*d^2 - 2*(b^3*c - a*b*c^2)*d*e + (b^4 - 2*a*b^2*c + a^2*c^2)*e^2)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4)) + 4*(a*b*c*d - (a*b^2 - a^2*c)*e)*sqrt(e*x + d)) - sqrt(2)*c*sqrt(((b^2*c - 2*a*c^2)*d - (b^3 - 3*a*b*c)*e - (b^2*c^3 - 4*a*c^4)*sqrt((b^2*c^2*d^2 - 2*(b^3*c - a*b*c^2)*d*e + (b^4 - 2*a*b^2*c + a^2*c^2)*e^2)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))*log(-sqrt(2)*((b^3*c - 4*a*b*c^2)*d - (b^4 - 5*a*b^2*c + 4*a^2*c^2)*e + (b^3*c^3 - 4*a*b*c^4)*sqrt((b^2*c^2*d^2 - 2*(b^3*c - a*b*c^2)*d*e + (b^4 - 2*a*b^2*c + a^2*c^2)*e^2)/(b^2*c^6 - 4*a*c^7)))*sqrt(((b^2*c - 2*a*c^2)*d - (b^3 - 3*a*b*c)*e - (b^2*c^3 - 4*a*c^4)*sqrt((b^2*c^2*d^2 - 2*(b^3*c - a*b*c^2)*d*e + (b^4 - 2*a*b^2*c + a^2*c^2)*e^2)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4)) + 4*(a*b*c*d - (a*b^2 - a^2*c)*e)*sqrt(e*x + d)) + 4*sqrt(e*x + d))/c","B",0
529,1,715,0,0.422201," ","integrate((e*x+d)^(1/2)/(c*x^2+b*x+a),x, algorithm=""fricas"")","-\frac{1}{2} \, \sqrt{2} \sqrt{\frac{2 \, c d - b e + {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{e^{2}}{b^{2} c^{2} - 4 \, a c^{3}}}}{b^{2} c - 4 \, a c^{2}}} \log\left(\sqrt{2} {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{e^{2}}{b^{2} c^{2} - 4 \, a c^{3}}} \sqrt{\frac{2 \, c d - b e + {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{e^{2}}{b^{2} c^{2} - 4 \, a c^{3}}}}{b^{2} c - 4 \, a c^{2}}} + 2 \, \sqrt{e x + d} e\right) + \frac{1}{2} \, \sqrt{2} \sqrt{\frac{2 \, c d - b e + {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{e^{2}}{b^{2} c^{2} - 4 \, a c^{3}}}}{b^{2} c - 4 \, a c^{2}}} \log\left(-\sqrt{2} {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{e^{2}}{b^{2} c^{2} - 4 \, a c^{3}}} \sqrt{\frac{2 \, c d - b e + {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{e^{2}}{b^{2} c^{2} - 4 \, a c^{3}}}}{b^{2} c - 4 \, a c^{2}}} + 2 \, \sqrt{e x + d} e\right) + \frac{1}{2} \, \sqrt{2} \sqrt{\frac{2 \, c d - b e - {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{e^{2}}{b^{2} c^{2} - 4 \, a c^{3}}}}{b^{2} c - 4 \, a c^{2}}} \log\left(\sqrt{2} {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{e^{2}}{b^{2} c^{2} - 4 \, a c^{3}}} \sqrt{\frac{2 \, c d - b e - {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{e^{2}}{b^{2} c^{2} - 4 \, a c^{3}}}}{b^{2} c - 4 \, a c^{2}}} + 2 \, \sqrt{e x + d} e\right) - \frac{1}{2} \, \sqrt{2} \sqrt{\frac{2 \, c d - b e - {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{e^{2}}{b^{2} c^{2} - 4 \, a c^{3}}}}{b^{2} c - 4 \, a c^{2}}} \log\left(-\sqrt{2} {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{e^{2}}{b^{2} c^{2} - 4 \, a c^{3}}} \sqrt{\frac{2 \, c d - b e - {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{e^{2}}{b^{2} c^{2} - 4 \, a c^{3}}}}{b^{2} c - 4 \, a c^{2}}} + 2 \, \sqrt{e x + d} e\right)"," ",0,"-1/2*sqrt(2)*sqrt((2*c*d - b*e + (b^2*c - 4*a*c^2)*sqrt(e^2/(b^2*c^2 - 4*a*c^3)))/(b^2*c - 4*a*c^2))*log(sqrt(2)*(b^2*c - 4*a*c^2)*sqrt(e^2/(b^2*c^2 - 4*a*c^3))*sqrt((2*c*d - b*e + (b^2*c - 4*a*c^2)*sqrt(e^2/(b^2*c^2 - 4*a*c^3)))/(b^2*c - 4*a*c^2)) + 2*sqrt(e*x + d)*e) + 1/2*sqrt(2)*sqrt((2*c*d - b*e + (b^2*c - 4*a*c^2)*sqrt(e^2/(b^2*c^2 - 4*a*c^3)))/(b^2*c - 4*a*c^2))*log(-sqrt(2)*(b^2*c - 4*a*c^2)*sqrt(e^2/(b^2*c^2 - 4*a*c^3))*sqrt((2*c*d - b*e + (b^2*c - 4*a*c^2)*sqrt(e^2/(b^2*c^2 - 4*a*c^3)))/(b^2*c - 4*a*c^2)) + 2*sqrt(e*x + d)*e) + 1/2*sqrt(2)*sqrt((2*c*d - b*e - (b^2*c - 4*a*c^2)*sqrt(e^2/(b^2*c^2 - 4*a*c^3)))/(b^2*c - 4*a*c^2))*log(sqrt(2)*(b^2*c - 4*a*c^2)*sqrt(e^2/(b^2*c^2 - 4*a*c^3))*sqrt((2*c*d - b*e - (b^2*c - 4*a*c^2)*sqrt(e^2/(b^2*c^2 - 4*a*c^3)))/(b^2*c - 4*a*c^2)) + 2*sqrt(e*x + d)*e) - 1/2*sqrt(2)*sqrt((2*c*d - b*e - (b^2*c - 4*a*c^2)*sqrt(e^2/(b^2*c^2 - 4*a*c^3)))/(b^2*c - 4*a*c^2))*log(-sqrt(2)*(b^2*c - 4*a*c^2)*sqrt(e^2/(b^2*c^2 - 4*a*c^3))*sqrt((2*c*d - b*e - (b^2*c - 4*a*c^2)*sqrt(e^2/(b^2*c^2 - 4*a*c^3)))/(b^2*c - 4*a*c^2)) + 2*sqrt(e*x + d)*e)","B",0
530,1,2446,0,0.786095," ","integrate((e*x+d)^(1/2)/x/(c*x^2+b*x+a),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} a \sqrt{-\frac{a b e - {\left(b^{2} - 2 \, a c\right)} d + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} \sqrt{\frac{b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}}{a^{4} b^{2} - 4 \, a^{5} c}}}{a^{2} b^{2} - 4 \, a^{3} c}} \log\left(\sqrt{2} {\left({\left(b^{3} - 4 \, a b c\right)} d - {\left(a b^{2} - 4 \, a^{2} c\right)} e + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} \sqrt{\frac{b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}}{a^{4} b^{2} - 4 \, a^{5} c}}\right)} \sqrt{-\frac{a b e - {\left(b^{2} - 2 \, a c\right)} d + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} \sqrt{\frac{b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}}{a^{4} b^{2} - 4 \, a^{5} c}}}{a^{2} b^{2} - 4 \, a^{3} c}} - 4 \, {\left(b c d - a c e\right)} \sqrt{e x + d}\right) - \sqrt{2} a \sqrt{-\frac{a b e - {\left(b^{2} - 2 \, a c\right)} d + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} \sqrt{\frac{b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}}{a^{4} b^{2} - 4 \, a^{5} c}}}{a^{2} b^{2} - 4 \, a^{3} c}} \log\left(-\sqrt{2} {\left({\left(b^{3} - 4 \, a b c\right)} d - {\left(a b^{2} - 4 \, a^{2} c\right)} e + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} \sqrt{\frac{b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}}{a^{4} b^{2} - 4 \, a^{5} c}}\right)} \sqrt{-\frac{a b e - {\left(b^{2} - 2 \, a c\right)} d + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} \sqrt{\frac{b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}}{a^{4} b^{2} - 4 \, a^{5} c}}}{a^{2} b^{2} - 4 \, a^{3} c}} - 4 \, {\left(b c d - a c e\right)} \sqrt{e x + d}\right) + \sqrt{2} a \sqrt{-\frac{a b e - {\left(b^{2} - 2 \, a c\right)} d - {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} \sqrt{\frac{b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}}{a^{4} b^{2} - 4 \, a^{5} c}}}{a^{2} b^{2} - 4 \, a^{3} c}} \log\left(\sqrt{2} {\left({\left(b^{3} - 4 \, a b c\right)} d - {\left(a b^{2} - 4 \, a^{2} c\right)} e - {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} \sqrt{\frac{b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}}{a^{4} b^{2} - 4 \, a^{5} c}}\right)} \sqrt{-\frac{a b e - {\left(b^{2} - 2 \, a c\right)} d - {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} \sqrt{\frac{b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}}{a^{4} b^{2} - 4 \, a^{5} c}}}{a^{2} b^{2} - 4 \, a^{3} c}} - 4 \, {\left(b c d - a c e\right)} \sqrt{e x + d}\right) - \sqrt{2} a \sqrt{-\frac{a b e - {\left(b^{2} - 2 \, a c\right)} d - {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} \sqrt{\frac{b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}}{a^{4} b^{2} - 4 \, a^{5} c}}}{a^{2} b^{2} - 4 \, a^{3} c}} \log\left(-\sqrt{2} {\left({\left(b^{3} - 4 \, a b c\right)} d - {\left(a b^{2} - 4 \, a^{2} c\right)} e - {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} \sqrt{\frac{b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}}{a^{4} b^{2} - 4 \, a^{5} c}}\right)} \sqrt{-\frac{a b e - {\left(b^{2} - 2 \, a c\right)} d - {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} \sqrt{\frac{b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}}{a^{4} b^{2} - 4 \, a^{5} c}}}{a^{2} b^{2} - 4 \, a^{3} c}} - 4 \, {\left(b c d - a c e\right)} \sqrt{e x + d}\right) + 2 \, \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right)}{2 \, a}, \frac{\sqrt{2} a \sqrt{-\frac{a b e - {\left(b^{2} - 2 \, a c\right)} d + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} \sqrt{\frac{b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}}{a^{4} b^{2} - 4 \, a^{5} c}}}{a^{2} b^{2} - 4 \, a^{3} c}} \log\left(\sqrt{2} {\left({\left(b^{3} - 4 \, a b c\right)} d - {\left(a b^{2} - 4 \, a^{2} c\right)} e + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} \sqrt{\frac{b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}}{a^{4} b^{2} - 4 \, a^{5} c}}\right)} \sqrt{-\frac{a b e - {\left(b^{2} - 2 \, a c\right)} d + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} \sqrt{\frac{b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}}{a^{4} b^{2} - 4 \, a^{5} c}}}{a^{2} b^{2} - 4 \, a^{3} c}} - 4 \, {\left(b c d - a c e\right)} \sqrt{e x + d}\right) - \sqrt{2} a \sqrt{-\frac{a b e - {\left(b^{2} - 2 \, a c\right)} d + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} \sqrt{\frac{b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}}{a^{4} b^{2} - 4 \, a^{5} c}}}{a^{2} b^{2} - 4 \, a^{3} c}} \log\left(-\sqrt{2} {\left({\left(b^{3} - 4 \, a b c\right)} d - {\left(a b^{2} - 4 \, a^{2} c\right)} e + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} \sqrt{\frac{b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}}{a^{4} b^{2} - 4 \, a^{5} c}}\right)} \sqrt{-\frac{a b e - {\left(b^{2} - 2 \, a c\right)} d + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} \sqrt{\frac{b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}}{a^{4} b^{2} - 4 \, a^{5} c}}}{a^{2} b^{2} - 4 \, a^{3} c}} - 4 \, {\left(b c d - a c e\right)} \sqrt{e x + d}\right) + \sqrt{2} a \sqrt{-\frac{a b e - {\left(b^{2} - 2 \, a c\right)} d - {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} \sqrt{\frac{b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}}{a^{4} b^{2} - 4 \, a^{5} c}}}{a^{2} b^{2} - 4 \, a^{3} c}} \log\left(\sqrt{2} {\left({\left(b^{3} - 4 \, a b c\right)} d - {\left(a b^{2} - 4 \, a^{2} c\right)} e - {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} \sqrt{\frac{b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}}{a^{4} b^{2} - 4 \, a^{5} c}}\right)} \sqrt{-\frac{a b e - {\left(b^{2} - 2 \, a c\right)} d - {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} \sqrt{\frac{b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}}{a^{4} b^{2} - 4 \, a^{5} c}}}{a^{2} b^{2} - 4 \, a^{3} c}} - 4 \, {\left(b c d - a c e\right)} \sqrt{e x + d}\right) - \sqrt{2} a \sqrt{-\frac{a b e - {\left(b^{2} - 2 \, a c\right)} d - {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} \sqrt{\frac{b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}}{a^{4} b^{2} - 4 \, a^{5} c}}}{a^{2} b^{2} - 4 \, a^{3} c}} \log\left(-\sqrt{2} {\left({\left(b^{3} - 4 \, a b c\right)} d - {\left(a b^{2} - 4 \, a^{2} c\right)} e - {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} \sqrt{\frac{b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}}{a^{4} b^{2} - 4 \, a^{5} c}}\right)} \sqrt{-\frac{a b e - {\left(b^{2} - 2 \, a c\right)} d - {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} \sqrt{\frac{b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}}{a^{4} b^{2} - 4 \, a^{5} c}}}{a^{2} b^{2} - 4 \, a^{3} c}} - 4 \, {\left(b c d - a c e\right)} \sqrt{e x + d}\right) + 4 \, \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right)}{2 \, a}\right]"," ",0,"[1/2*(sqrt(2)*a*sqrt(-(a*b*e - (b^2 - 2*a*c)*d + (a^2*b^2 - 4*a^3*c)*sqrt((b^2*d^2 - 2*a*b*d*e + a^2*e^2)/(a^4*b^2 - 4*a^5*c)))/(a^2*b^2 - 4*a^3*c))*log(sqrt(2)*((b^3 - 4*a*b*c)*d - (a*b^2 - 4*a^2*c)*e + (a^2*b^3 - 4*a^3*b*c)*sqrt((b^2*d^2 - 2*a*b*d*e + a^2*e^2)/(a^4*b^2 - 4*a^5*c)))*sqrt(-(a*b*e - (b^2 - 2*a*c)*d + (a^2*b^2 - 4*a^3*c)*sqrt((b^2*d^2 - 2*a*b*d*e + a^2*e^2)/(a^4*b^2 - 4*a^5*c)))/(a^2*b^2 - 4*a^3*c)) - 4*(b*c*d - a*c*e)*sqrt(e*x + d)) - sqrt(2)*a*sqrt(-(a*b*e - (b^2 - 2*a*c)*d + (a^2*b^2 - 4*a^3*c)*sqrt((b^2*d^2 - 2*a*b*d*e + a^2*e^2)/(a^4*b^2 - 4*a^5*c)))/(a^2*b^2 - 4*a^3*c))*log(-sqrt(2)*((b^3 - 4*a*b*c)*d - (a*b^2 - 4*a^2*c)*e + (a^2*b^3 - 4*a^3*b*c)*sqrt((b^2*d^2 - 2*a*b*d*e + a^2*e^2)/(a^4*b^2 - 4*a^5*c)))*sqrt(-(a*b*e - (b^2 - 2*a*c)*d + (a^2*b^2 - 4*a^3*c)*sqrt((b^2*d^2 - 2*a*b*d*e + a^2*e^2)/(a^4*b^2 - 4*a^5*c)))/(a^2*b^2 - 4*a^3*c)) - 4*(b*c*d - a*c*e)*sqrt(e*x + d)) + sqrt(2)*a*sqrt(-(a*b*e - (b^2 - 2*a*c)*d - (a^2*b^2 - 4*a^3*c)*sqrt((b^2*d^2 - 2*a*b*d*e + a^2*e^2)/(a^4*b^2 - 4*a^5*c)))/(a^2*b^2 - 4*a^3*c))*log(sqrt(2)*((b^3 - 4*a*b*c)*d - (a*b^2 - 4*a^2*c)*e - (a^2*b^3 - 4*a^3*b*c)*sqrt((b^2*d^2 - 2*a*b*d*e + a^2*e^2)/(a^4*b^2 - 4*a^5*c)))*sqrt(-(a*b*e - (b^2 - 2*a*c)*d - (a^2*b^2 - 4*a^3*c)*sqrt((b^2*d^2 - 2*a*b*d*e + a^2*e^2)/(a^4*b^2 - 4*a^5*c)))/(a^2*b^2 - 4*a^3*c)) - 4*(b*c*d - a*c*e)*sqrt(e*x + d)) - sqrt(2)*a*sqrt(-(a*b*e - (b^2 - 2*a*c)*d - (a^2*b^2 - 4*a^3*c)*sqrt((b^2*d^2 - 2*a*b*d*e + a^2*e^2)/(a^4*b^2 - 4*a^5*c)))/(a^2*b^2 - 4*a^3*c))*log(-sqrt(2)*((b^3 - 4*a*b*c)*d - (a*b^2 - 4*a^2*c)*e - (a^2*b^3 - 4*a^3*b*c)*sqrt((b^2*d^2 - 2*a*b*d*e + a^2*e^2)/(a^4*b^2 - 4*a^5*c)))*sqrt(-(a*b*e - (b^2 - 2*a*c)*d - (a^2*b^2 - 4*a^3*c)*sqrt((b^2*d^2 - 2*a*b*d*e + a^2*e^2)/(a^4*b^2 - 4*a^5*c)))/(a^2*b^2 - 4*a^3*c)) - 4*(b*c*d - a*c*e)*sqrt(e*x + d)) + 2*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x))/a, 1/2*(sqrt(2)*a*sqrt(-(a*b*e - (b^2 - 2*a*c)*d + (a^2*b^2 - 4*a^3*c)*sqrt((b^2*d^2 - 2*a*b*d*e + a^2*e^2)/(a^4*b^2 - 4*a^5*c)))/(a^2*b^2 - 4*a^3*c))*log(sqrt(2)*((b^3 - 4*a*b*c)*d - (a*b^2 - 4*a^2*c)*e + (a^2*b^3 - 4*a^3*b*c)*sqrt((b^2*d^2 - 2*a*b*d*e + a^2*e^2)/(a^4*b^2 - 4*a^5*c)))*sqrt(-(a*b*e - (b^2 - 2*a*c)*d + (a^2*b^2 - 4*a^3*c)*sqrt((b^2*d^2 - 2*a*b*d*e + a^2*e^2)/(a^4*b^2 - 4*a^5*c)))/(a^2*b^2 - 4*a^3*c)) - 4*(b*c*d - a*c*e)*sqrt(e*x + d)) - sqrt(2)*a*sqrt(-(a*b*e - (b^2 - 2*a*c)*d + (a^2*b^2 - 4*a^3*c)*sqrt((b^2*d^2 - 2*a*b*d*e + a^2*e^2)/(a^4*b^2 - 4*a^5*c)))/(a^2*b^2 - 4*a^3*c))*log(-sqrt(2)*((b^3 - 4*a*b*c)*d - (a*b^2 - 4*a^2*c)*e + (a^2*b^3 - 4*a^3*b*c)*sqrt((b^2*d^2 - 2*a*b*d*e + a^2*e^2)/(a^4*b^2 - 4*a^5*c)))*sqrt(-(a*b*e - (b^2 - 2*a*c)*d + (a^2*b^2 - 4*a^3*c)*sqrt((b^2*d^2 - 2*a*b*d*e + a^2*e^2)/(a^4*b^2 - 4*a^5*c)))/(a^2*b^2 - 4*a^3*c)) - 4*(b*c*d - a*c*e)*sqrt(e*x + d)) + sqrt(2)*a*sqrt(-(a*b*e - (b^2 - 2*a*c)*d - (a^2*b^2 - 4*a^3*c)*sqrt((b^2*d^2 - 2*a*b*d*e + a^2*e^2)/(a^4*b^2 - 4*a^5*c)))/(a^2*b^2 - 4*a^3*c))*log(sqrt(2)*((b^3 - 4*a*b*c)*d - (a*b^2 - 4*a^2*c)*e - (a^2*b^3 - 4*a^3*b*c)*sqrt((b^2*d^2 - 2*a*b*d*e + a^2*e^2)/(a^4*b^2 - 4*a^5*c)))*sqrt(-(a*b*e - (b^2 - 2*a*c)*d - (a^2*b^2 - 4*a^3*c)*sqrt((b^2*d^2 - 2*a*b*d*e + a^2*e^2)/(a^4*b^2 - 4*a^5*c)))/(a^2*b^2 - 4*a^3*c)) - 4*(b*c*d - a*c*e)*sqrt(e*x + d)) - sqrt(2)*a*sqrt(-(a*b*e - (b^2 - 2*a*c)*d - (a^2*b^2 - 4*a^3*c)*sqrt((b^2*d^2 - 2*a*b*d*e + a^2*e^2)/(a^4*b^2 - 4*a^5*c)))/(a^2*b^2 - 4*a^3*c))*log(-sqrt(2)*((b^3 - 4*a*b*c)*d - (a*b^2 - 4*a^2*c)*e - (a^2*b^3 - 4*a^3*b*c)*sqrt((b^2*d^2 - 2*a*b*d*e + a^2*e^2)/(a^4*b^2 - 4*a^5*c)))*sqrt(-(a*b*e - (b^2 - 2*a*c)*d - (a^2*b^2 - 4*a^3*c)*sqrt((b^2*d^2 - 2*a*b*d*e + a^2*e^2)/(a^4*b^2 - 4*a^5*c)))/(a^2*b^2 - 4*a^3*c)) - 4*(b*c*d - a*c*e)*sqrt(e*x + d)) + 4*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d))/a]","B",0
531,1,4860,0,9.994719," ","integrate((e*x+d)^(1/2)/x^2/(c*x^2+b*x+a),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} a^{2} d x \sqrt{\frac{{\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} d - {\left(a b^{3} - 3 \, a^{2} b c\right)} e + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{\frac{{\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{5} - 3 \, a^{2} b^{3} c + 2 \, a^{3} b c^{2}\right)} d e + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{2}}{a^{8} b^{2} - 4 \, a^{9} c}}}{a^{4} b^{2} - 4 \, a^{5} c}} \log\left(\sqrt{2} {\left({\left(b^{6} - 6 \, a b^{4} c + 8 \, a^{2} b^{2} c^{2}\right)} d - {\left(a b^{5} - 5 \, a^{2} b^{3} c + 4 \, a^{3} b c^{2}\right)} e - {\left(a^{4} b^{4} - 6 \, a^{5} b^{2} c + 8 \, a^{6} c^{2}\right)} \sqrt{\frac{{\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{5} - 3 \, a^{2} b^{3} c + 2 \, a^{3} b c^{2}\right)} d e + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{2}}{a^{8} b^{2} - 4 \, a^{9} c}}\right)} \sqrt{\frac{{\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} d - {\left(a b^{3} - 3 \, a^{2} b c\right)} e + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{\frac{{\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{5} - 3 \, a^{2} b^{3} c + 2 \, a^{3} b c^{2}\right)} d e + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{2}}{a^{8} b^{2} - 4 \, a^{9} c}}}{a^{4} b^{2} - 4 \, a^{5} c}} + 4 \, {\left({\left(b^{3} c^{2} - 2 \, a b c^{3}\right)} d - {\left(a b^{2} c^{2} - a^{2} c^{3}\right)} e\right)} \sqrt{e x + d}\right) - \sqrt{2} a^{2} d x \sqrt{\frac{{\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} d - {\left(a b^{3} - 3 \, a^{2} b c\right)} e + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{\frac{{\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{5} - 3 \, a^{2} b^{3} c + 2 \, a^{3} b c^{2}\right)} d e + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{2}}{a^{8} b^{2} - 4 \, a^{9} c}}}{a^{4} b^{2} - 4 \, a^{5} c}} \log\left(-\sqrt{2} {\left({\left(b^{6} - 6 \, a b^{4} c + 8 \, a^{2} b^{2} c^{2}\right)} d - {\left(a b^{5} - 5 \, a^{2} b^{3} c + 4 \, a^{3} b c^{2}\right)} e - {\left(a^{4} b^{4} - 6 \, a^{5} b^{2} c + 8 \, a^{6} c^{2}\right)} \sqrt{\frac{{\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{5} - 3 \, a^{2} b^{3} c + 2 \, a^{3} b c^{2}\right)} d e + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{2}}{a^{8} b^{2} - 4 \, a^{9} c}}\right)} \sqrt{\frac{{\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} d - {\left(a b^{3} - 3 \, a^{2} b c\right)} e + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{\frac{{\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{5} - 3 \, a^{2} b^{3} c + 2 \, a^{3} b c^{2}\right)} d e + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{2}}{a^{8} b^{2} - 4 \, a^{9} c}}}{a^{4} b^{2} - 4 \, a^{5} c}} + 4 \, {\left({\left(b^{3} c^{2} - 2 \, a b c^{3}\right)} d - {\left(a b^{2} c^{2} - a^{2} c^{3}\right)} e\right)} \sqrt{e x + d}\right) + \sqrt{2} a^{2} d x \sqrt{\frac{{\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} d - {\left(a b^{3} - 3 \, a^{2} b c\right)} e - {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{\frac{{\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{5} - 3 \, a^{2} b^{3} c + 2 \, a^{3} b c^{2}\right)} d e + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{2}}{a^{8} b^{2} - 4 \, a^{9} c}}}{a^{4} b^{2} - 4 \, a^{5} c}} \log\left(\sqrt{2} {\left({\left(b^{6} - 6 \, a b^{4} c + 8 \, a^{2} b^{2} c^{2}\right)} d - {\left(a b^{5} - 5 \, a^{2} b^{3} c + 4 \, a^{3} b c^{2}\right)} e + {\left(a^{4} b^{4} - 6 \, a^{5} b^{2} c + 8 \, a^{6} c^{2}\right)} \sqrt{\frac{{\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{5} - 3 \, a^{2} b^{3} c + 2 \, a^{3} b c^{2}\right)} d e + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{2}}{a^{8} b^{2} - 4 \, a^{9} c}}\right)} \sqrt{\frac{{\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} d - {\left(a b^{3} - 3 \, a^{2} b c\right)} e - {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{\frac{{\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{5} - 3 \, a^{2} b^{3} c + 2 \, a^{3} b c^{2}\right)} d e + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{2}}{a^{8} b^{2} - 4 \, a^{9} c}}}{a^{4} b^{2} - 4 \, a^{5} c}} + 4 \, {\left({\left(b^{3} c^{2} - 2 \, a b c^{3}\right)} d - {\left(a b^{2} c^{2} - a^{2} c^{3}\right)} e\right)} \sqrt{e x + d}\right) - \sqrt{2} a^{2} d x \sqrt{\frac{{\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} d - {\left(a b^{3} - 3 \, a^{2} b c\right)} e - {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{\frac{{\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{5} - 3 \, a^{2} b^{3} c + 2 \, a^{3} b c^{2}\right)} d e + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{2}}{a^{8} b^{2} - 4 \, a^{9} c}}}{a^{4} b^{2} - 4 \, a^{5} c}} \log\left(-\sqrt{2} {\left({\left(b^{6} - 6 \, a b^{4} c + 8 \, a^{2} b^{2} c^{2}\right)} d - {\left(a b^{5} - 5 \, a^{2} b^{3} c + 4 \, a^{3} b c^{2}\right)} e + {\left(a^{4} b^{4} - 6 \, a^{5} b^{2} c + 8 \, a^{6} c^{2}\right)} \sqrt{\frac{{\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{5} - 3 \, a^{2} b^{3} c + 2 \, a^{3} b c^{2}\right)} d e + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{2}}{a^{8} b^{2} - 4 \, a^{9} c}}\right)} \sqrt{\frac{{\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} d - {\left(a b^{3} - 3 \, a^{2} b c\right)} e - {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{\frac{{\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{5} - 3 \, a^{2} b^{3} c + 2 \, a^{3} b c^{2}\right)} d e + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{2}}{a^{8} b^{2} - 4 \, a^{9} c}}}{a^{4} b^{2} - 4 \, a^{5} c}} + 4 \, {\left({\left(b^{3} c^{2} - 2 \, a b c^{3}\right)} d - {\left(a b^{2} c^{2} - a^{2} c^{3}\right)} e\right)} \sqrt{e x + d}\right) - {\left(2 \, b d - a e\right)} \sqrt{d} x \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) - 2 \, \sqrt{e x + d} a d}{2 \, a^{2} d x}, \frac{\sqrt{2} a^{2} d x \sqrt{\frac{{\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} d - {\left(a b^{3} - 3 \, a^{2} b c\right)} e + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{\frac{{\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{5} - 3 \, a^{2} b^{3} c + 2 \, a^{3} b c^{2}\right)} d e + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{2}}{a^{8} b^{2} - 4 \, a^{9} c}}}{a^{4} b^{2} - 4 \, a^{5} c}} \log\left(\sqrt{2} {\left({\left(b^{6} - 6 \, a b^{4} c + 8 \, a^{2} b^{2} c^{2}\right)} d - {\left(a b^{5} - 5 \, a^{2} b^{3} c + 4 \, a^{3} b c^{2}\right)} e - {\left(a^{4} b^{4} - 6 \, a^{5} b^{2} c + 8 \, a^{6} c^{2}\right)} \sqrt{\frac{{\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{5} - 3 \, a^{2} b^{3} c + 2 \, a^{3} b c^{2}\right)} d e + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{2}}{a^{8} b^{2} - 4 \, a^{9} c}}\right)} \sqrt{\frac{{\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} d - {\left(a b^{3} - 3 \, a^{2} b c\right)} e + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{\frac{{\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{5} - 3 \, a^{2} b^{3} c + 2 \, a^{3} b c^{2}\right)} d e + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{2}}{a^{8} b^{2} - 4 \, a^{9} c}}}{a^{4} b^{2} - 4 \, a^{5} c}} + 4 \, {\left({\left(b^{3} c^{2} - 2 \, a b c^{3}\right)} d - {\left(a b^{2} c^{2} - a^{2} c^{3}\right)} e\right)} \sqrt{e x + d}\right) - \sqrt{2} a^{2} d x \sqrt{\frac{{\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} d - {\left(a b^{3} - 3 \, a^{2} b c\right)} e + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{\frac{{\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{5} - 3 \, a^{2} b^{3} c + 2 \, a^{3} b c^{2}\right)} d e + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{2}}{a^{8} b^{2} - 4 \, a^{9} c}}}{a^{4} b^{2} - 4 \, a^{5} c}} \log\left(-\sqrt{2} {\left({\left(b^{6} - 6 \, a b^{4} c + 8 \, a^{2} b^{2} c^{2}\right)} d - {\left(a b^{5} - 5 \, a^{2} b^{3} c + 4 \, a^{3} b c^{2}\right)} e - {\left(a^{4} b^{4} - 6 \, a^{5} b^{2} c + 8 \, a^{6} c^{2}\right)} \sqrt{\frac{{\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{5} - 3 \, a^{2} b^{3} c + 2 \, a^{3} b c^{2}\right)} d e + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{2}}{a^{8} b^{2} - 4 \, a^{9} c}}\right)} \sqrt{\frac{{\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} d - {\left(a b^{3} - 3 \, a^{2} b c\right)} e + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{\frac{{\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{5} - 3 \, a^{2} b^{3} c + 2 \, a^{3} b c^{2}\right)} d e + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{2}}{a^{8} b^{2} - 4 \, a^{9} c}}}{a^{4} b^{2} - 4 \, a^{5} c}} + 4 \, {\left({\left(b^{3} c^{2} - 2 \, a b c^{3}\right)} d - {\left(a b^{2} c^{2} - a^{2} c^{3}\right)} e\right)} \sqrt{e x + d}\right) + \sqrt{2} a^{2} d x \sqrt{\frac{{\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} d - {\left(a b^{3} - 3 \, a^{2} b c\right)} e - {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{\frac{{\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{5} - 3 \, a^{2} b^{3} c + 2 \, a^{3} b c^{2}\right)} d e + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{2}}{a^{8} b^{2} - 4 \, a^{9} c}}}{a^{4} b^{2} - 4 \, a^{5} c}} \log\left(\sqrt{2} {\left({\left(b^{6} - 6 \, a b^{4} c + 8 \, a^{2} b^{2} c^{2}\right)} d - {\left(a b^{5} - 5 \, a^{2} b^{3} c + 4 \, a^{3} b c^{2}\right)} e + {\left(a^{4} b^{4} - 6 \, a^{5} b^{2} c + 8 \, a^{6} c^{2}\right)} \sqrt{\frac{{\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{5} - 3 \, a^{2} b^{3} c + 2 \, a^{3} b c^{2}\right)} d e + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{2}}{a^{8} b^{2} - 4 \, a^{9} c}}\right)} \sqrt{\frac{{\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} d - {\left(a b^{3} - 3 \, a^{2} b c\right)} e - {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{\frac{{\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{5} - 3 \, a^{2} b^{3} c + 2 \, a^{3} b c^{2}\right)} d e + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{2}}{a^{8} b^{2} - 4 \, a^{9} c}}}{a^{4} b^{2} - 4 \, a^{5} c}} + 4 \, {\left({\left(b^{3} c^{2} - 2 \, a b c^{3}\right)} d - {\left(a b^{2} c^{2} - a^{2} c^{3}\right)} e\right)} \sqrt{e x + d}\right) - \sqrt{2} a^{2} d x \sqrt{\frac{{\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} d - {\left(a b^{3} - 3 \, a^{2} b c\right)} e - {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{\frac{{\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{5} - 3 \, a^{2} b^{3} c + 2 \, a^{3} b c^{2}\right)} d e + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{2}}{a^{8} b^{2} - 4 \, a^{9} c}}}{a^{4} b^{2} - 4 \, a^{5} c}} \log\left(-\sqrt{2} {\left({\left(b^{6} - 6 \, a b^{4} c + 8 \, a^{2} b^{2} c^{2}\right)} d - {\left(a b^{5} - 5 \, a^{2} b^{3} c + 4 \, a^{3} b c^{2}\right)} e + {\left(a^{4} b^{4} - 6 \, a^{5} b^{2} c + 8 \, a^{6} c^{2}\right)} \sqrt{\frac{{\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{5} - 3 \, a^{2} b^{3} c + 2 \, a^{3} b c^{2}\right)} d e + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{2}}{a^{8} b^{2} - 4 \, a^{9} c}}\right)} \sqrt{\frac{{\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} d - {\left(a b^{3} - 3 \, a^{2} b c\right)} e - {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{\frac{{\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{5} - 3 \, a^{2} b^{3} c + 2 \, a^{3} b c^{2}\right)} d e + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{2}}{a^{8} b^{2} - 4 \, a^{9} c}}}{a^{4} b^{2} - 4 \, a^{5} c}} + 4 \, {\left({\left(b^{3} c^{2} - 2 \, a b c^{3}\right)} d - {\left(a b^{2} c^{2} - a^{2} c^{3}\right)} e\right)} \sqrt{e x + d}\right) - 2 \, {\left(2 \, b d - a e\right)} \sqrt{-d} x \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) - 2 \, \sqrt{e x + d} a d}{2 \, a^{2} d x}\right]"," ",0,"[1/2*(sqrt(2)*a^2*d*x*sqrt(((b^4 - 4*a*b^2*c + 2*a^2*c^2)*d - (a*b^3 - 3*a^2*b*c)*e + (a^4*b^2 - 4*a^5*c)*sqrt(((b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*d^2 - 2*(a*b^5 - 3*a^2*b^3*c + 2*a^3*b*c^2)*d*e + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^2)/(a^8*b^2 - 4*a^9*c)))/(a^4*b^2 - 4*a^5*c))*log(sqrt(2)*((b^6 - 6*a*b^4*c + 8*a^2*b^2*c^2)*d - (a*b^5 - 5*a^2*b^3*c + 4*a^3*b*c^2)*e - (a^4*b^4 - 6*a^5*b^2*c + 8*a^6*c^2)*sqrt(((b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*d^2 - 2*(a*b^5 - 3*a^2*b^3*c + 2*a^3*b*c^2)*d*e + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^2)/(a^8*b^2 - 4*a^9*c)))*sqrt(((b^4 - 4*a*b^2*c + 2*a^2*c^2)*d - (a*b^3 - 3*a^2*b*c)*e + (a^4*b^2 - 4*a^5*c)*sqrt(((b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*d^2 - 2*(a*b^5 - 3*a^2*b^3*c + 2*a^3*b*c^2)*d*e + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^2)/(a^8*b^2 - 4*a^9*c)))/(a^4*b^2 - 4*a^5*c)) + 4*((b^3*c^2 - 2*a*b*c^3)*d - (a*b^2*c^2 - a^2*c^3)*e)*sqrt(e*x + d)) - sqrt(2)*a^2*d*x*sqrt(((b^4 - 4*a*b^2*c + 2*a^2*c^2)*d - (a*b^3 - 3*a^2*b*c)*e + (a^4*b^2 - 4*a^5*c)*sqrt(((b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*d^2 - 2*(a*b^5 - 3*a^2*b^3*c + 2*a^3*b*c^2)*d*e + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^2)/(a^8*b^2 - 4*a^9*c)))/(a^4*b^2 - 4*a^5*c))*log(-sqrt(2)*((b^6 - 6*a*b^4*c + 8*a^2*b^2*c^2)*d - (a*b^5 - 5*a^2*b^3*c + 4*a^3*b*c^2)*e - (a^4*b^4 - 6*a^5*b^2*c + 8*a^6*c^2)*sqrt(((b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*d^2 - 2*(a*b^5 - 3*a^2*b^3*c + 2*a^3*b*c^2)*d*e + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^2)/(a^8*b^2 - 4*a^9*c)))*sqrt(((b^4 - 4*a*b^2*c + 2*a^2*c^2)*d - (a*b^3 - 3*a^2*b*c)*e + (a^4*b^2 - 4*a^5*c)*sqrt(((b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*d^2 - 2*(a*b^5 - 3*a^2*b^3*c + 2*a^3*b*c^2)*d*e + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^2)/(a^8*b^2 - 4*a^9*c)))/(a^4*b^2 - 4*a^5*c)) + 4*((b^3*c^2 - 2*a*b*c^3)*d - (a*b^2*c^2 - a^2*c^3)*e)*sqrt(e*x + d)) + sqrt(2)*a^2*d*x*sqrt(((b^4 - 4*a*b^2*c + 2*a^2*c^2)*d - (a*b^3 - 3*a^2*b*c)*e - (a^4*b^2 - 4*a^5*c)*sqrt(((b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*d^2 - 2*(a*b^5 - 3*a^2*b^3*c + 2*a^3*b*c^2)*d*e + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^2)/(a^8*b^2 - 4*a^9*c)))/(a^4*b^2 - 4*a^5*c))*log(sqrt(2)*((b^6 - 6*a*b^4*c + 8*a^2*b^2*c^2)*d - (a*b^5 - 5*a^2*b^3*c + 4*a^3*b*c^2)*e + (a^4*b^4 - 6*a^5*b^2*c + 8*a^6*c^2)*sqrt(((b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*d^2 - 2*(a*b^5 - 3*a^2*b^3*c + 2*a^3*b*c^2)*d*e + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^2)/(a^8*b^2 - 4*a^9*c)))*sqrt(((b^4 - 4*a*b^2*c + 2*a^2*c^2)*d - (a*b^3 - 3*a^2*b*c)*e - (a^4*b^2 - 4*a^5*c)*sqrt(((b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*d^2 - 2*(a*b^5 - 3*a^2*b^3*c + 2*a^3*b*c^2)*d*e + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^2)/(a^8*b^2 - 4*a^9*c)))/(a^4*b^2 - 4*a^5*c)) + 4*((b^3*c^2 - 2*a*b*c^3)*d - (a*b^2*c^2 - a^2*c^3)*e)*sqrt(e*x + d)) - sqrt(2)*a^2*d*x*sqrt(((b^4 - 4*a*b^2*c + 2*a^2*c^2)*d - (a*b^3 - 3*a^2*b*c)*e - (a^4*b^2 - 4*a^5*c)*sqrt(((b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*d^2 - 2*(a*b^5 - 3*a^2*b^3*c + 2*a^3*b*c^2)*d*e + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^2)/(a^8*b^2 - 4*a^9*c)))/(a^4*b^2 - 4*a^5*c))*log(-sqrt(2)*((b^6 - 6*a*b^4*c + 8*a^2*b^2*c^2)*d - (a*b^5 - 5*a^2*b^3*c + 4*a^3*b*c^2)*e + (a^4*b^4 - 6*a^5*b^2*c + 8*a^6*c^2)*sqrt(((b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*d^2 - 2*(a*b^5 - 3*a^2*b^3*c + 2*a^3*b*c^2)*d*e + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^2)/(a^8*b^2 - 4*a^9*c)))*sqrt(((b^4 - 4*a*b^2*c + 2*a^2*c^2)*d - (a*b^3 - 3*a^2*b*c)*e - (a^4*b^2 - 4*a^5*c)*sqrt(((b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*d^2 - 2*(a*b^5 - 3*a^2*b^3*c + 2*a^3*b*c^2)*d*e + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^2)/(a^8*b^2 - 4*a^9*c)))/(a^4*b^2 - 4*a^5*c)) + 4*((b^3*c^2 - 2*a*b*c^3)*d - (a*b^2*c^2 - a^2*c^3)*e)*sqrt(e*x + d)) - (2*b*d - a*e)*sqrt(d)*x*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) - 2*sqrt(e*x + d)*a*d)/(a^2*d*x), 1/2*(sqrt(2)*a^2*d*x*sqrt(((b^4 - 4*a*b^2*c + 2*a^2*c^2)*d - (a*b^3 - 3*a^2*b*c)*e + (a^4*b^2 - 4*a^5*c)*sqrt(((b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*d^2 - 2*(a*b^5 - 3*a^2*b^3*c + 2*a^3*b*c^2)*d*e + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^2)/(a^8*b^2 - 4*a^9*c)))/(a^4*b^2 - 4*a^5*c))*log(sqrt(2)*((b^6 - 6*a*b^4*c + 8*a^2*b^2*c^2)*d - (a*b^5 - 5*a^2*b^3*c + 4*a^3*b*c^2)*e - (a^4*b^4 - 6*a^5*b^2*c + 8*a^6*c^2)*sqrt(((b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*d^2 - 2*(a*b^5 - 3*a^2*b^3*c + 2*a^3*b*c^2)*d*e + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^2)/(a^8*b^2 - 4*a^9*c)))*sqrt(((b^4 - 4*a*b^2*c + 2*a^2*c^2)*d - (a*b^3 - 3*a^2*b*c)*e + (a^4*b^2 - 4*a^5*c)*sqrt(((b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*d^2 - 2*(a*b^5 - 3*a^2*b^3*c + 2*a^3*b*c^2)*d*e + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^2)/(a^8*b^2 - 4*a^9*c)))/(a^4*b^2 - 4*a^5*c)) + 4*((b^3*c^2 - 2*a*b*c^3)*d - (a*b^2*c^2 - a^2*c^3)*e)*sqrt(e*x + d)) - sqrt(2)*a^2*d*x*sqrt(((b^4 - 4*a*b^2*c + 2*a^2*c^2)*d - (a*b^3 - 3*a^2*b*c)*e + (a^4*b^2 - 4*a^5*c)*sqrt(((b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*d^2 - 2*(a*b^5 - 3*a^2*b^3*c + 2*a^3*b*c^2)*d*e + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^2)/(a^8*b^2 - 4*a^9*c)))/(a^4*b^2 - 4*a^5*c))*log(-sqrt(2)*((b^6 - 6*a*b^4*c + 8*a^2*b^2*c^2)*d - (a*b^5 - 5*a^2*b^3*c + 4*a^3*b*c^2)*e - (a^4*b^4 - 6*a^5*b^2*c + 8*a^6*c^2)*sqrt(((b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*d^2 - 2*(a*b^5 - 3*a^2*b^3*c + 2*a^3*b*c^2)*d*e + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^2)/(a^8*b^2 - 4*a^9*c)))*sqrt(((b^4 - 4*a*b^2*c + 2*a^2*c^2)*d - (a*b^3 - 3*a^2*b*c)*e + (a^4*b^2 - 4*a^5*c)*sqrt(((b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*d^2 - 2*(a*b^5 - 3*a^2*b^3*c + 2*a^3*b*c^2)*d*e + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^2)/(a^8*b^2 - 4*a^9*c)))/(a^4*b^2 - 4*a^5*c)) + 4*((b^3*c^2 - 2*a*b*c^3)*d - (a*b^2*c^2 - a^2*c^3)*e)*sqrt(e*x + d)) + sqrt(2)*a^2*d*x*sqrt(((b^4 - 4*a*b^2*c + 2*a^2*c^2)*d - (a*b^3 - 3*a^2*b*c)*e - (a^4*b^2 - 4*a^5*c)*sqrt(((b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*d^2 - 2*(a*b^5 - 3*a^2*b^3*c + 2*a^3*b*c^2)*d*e + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^2)/(a^8*b^2 - 4*a^9*c)))/(a^4*b^2 - 4*a^5*c))*log(sqrt(2)*((b^6 - 6*a*b^4*c + 8*a^2*b^2*c^2)*d - (a*b^5 - 5*a^2*b^3*c + 4*a^3*b*c^2)*e + (a^4*b^4 - 6*a^5*b^2*c + 8*a^6*c^2)*sqrt(((b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*d^2 - 2*(a*b^5 - 3*a^2*b^3*c + 2*a^3*b*c^2)*d*e + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^2)/(a^8*b^2 - 4*a^9*c)))*sqrt(((b^4 - 4*a*b^2*c + 2*a^2*c^2)*d - (a*b^3 - 3*a^2*b*c)*e - (a^4*b^2 - 4*a^5*c)*sqrt(((b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*d^2 - 2*(a*b^5 - 3*a^2*b^3*c + 2*a^3*b*c^2)*d*e + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^2)/(a^8*b^2 - 4*a^9*c)))/(a^4*b^2 - 4*a^5*c)) + 4*((b^3*c^2 - 2*a*b*c^3)*d - (a*b^2*c^2 - a^2*c^3)*e)*sqrt(e*x + d)) - sqrt(2)*a^2*d*x*sqrt(((b^4 - 4*a*b^2*c + 2*a^2*c^2)*d - (a*b^3 - 3*a^2*b*c)*e - (a^4*b^2 - 4*a^5*c)*sqrt(((b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*d^2 - 2*(a*b^5 - 3*a^2*b^3*c + 2*a^3*b*c^2)*d*e + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^2)/(a^8*b^2 - 4*a^9*c)))/(a^4*b^2 - 4*a^5*c))*log(-sqrt(2)*((b^6 - 6*a*b^4*c + 8*a^2*b^2*c^2)*d - (a*b^5 - 5*a^2*b^3*c + 4*a^3*b*c^2)*e + (a^4*b^4 - 6*a^5*b^2*c + 8*a^6*c^2)*sqrt(((b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*d^2 - 2*(a*b^5 - 3*a^2*b^3*c + 2*a^3*b*c^2)*d*e + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^2)/(a^8*b^2 - 4*a^9*c)))*sqrt(((b^4 - 4*a*b^2*c + 2*a^2*c^2)*d - (a*b^3 - 3*a^2*b*c)*e - (a^4*b^2 - 4*a^5*c)*sqrt(((b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*d^2 - 2*(a*b^5 - 3*a^2*b^3*c + 2*a^3*b*c^2)*d*e + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^2)/(a^8*b^2 - 4*a^9*c)))/(a^4*b^2 - 4*a^5*c)) + 4*((b^3*c^2 - 2*a*b*c^3)*d - (a*b^2*c^2 - a^2*c^3)*e)*sqrt(e*x + d)) - 2*(2*b*d - a*e)*sqrt(-d)*x*arctan(sqrt(e*x + d)*sqrt(-d)/d) - 2*sqrt(e*x + d)*a*d)/(a^2*d*x)]","B",0
532,1,7425,0,149.302769," ","integrate((e*x+d)^(1/2)/x^3/(c*x^2+b*x+a),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{2} a^{3} d^{2} x^{2} \sqrt{\frac{{\left(b^{6} - 6 \, a b^{4} c + 9 \, a^{2} b^{2} c^{2} - 2 \, a^{3} c^{3}\right)} d - {\left(a b^{5} - 5 \, a^{2} b^{3} c + 5 \, a^{3} b c^{2}\right)} e + {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} \sqrt{\frac{{\left(b^{10} - 8 \, a b^{8} c + 22 \, a^{2} b^{6} c^{2} - 24 \, a^{3} b^{4} c^{3} + 9 \, a^{4} b^{2} c^{4}\right)} d^{2} - 2 \, {\left(a b^{9} - 7 \, a^{2} b^{7} c + 16 \, a^{3} b^{5} c^{2} - 13 \, a^{4} b^{3} c^{3} + 3 \, a^{5} b c^{4}\right)} d e + {\left(a^{2} b^{8} - 6 \, a^{3} b^{6} c + 11 \, a^{4} b^{4} c^{2} - 6 \, a^{5} b^{2} c^{3} + a^{6} c^{4}\right)} e^{2}}{a^{12} b^{2} - 4 \, a^{13} c}}}{a^{6} b^{2} - 4 \, a^{7} c}} \log\left(\sqrt{2} {\left({\left(b^{9} - 9 \, a b^{7} c + 27 \, a^{2} b^{5} c^{2} - 31 \, a^{3} b^{3} c^{3} + 12 \, a^{4} b c^{4}\right)} d - {\left(a b^{8} - 8 \, a^{2} b^{6} c + 20 \, a^{3} b^{4} c^{2} - 17 \, a^{4} b^{2} c^{3} + 4 \, a^{5} c^{4}\right)} e - {\left(a^{6} b^{5} - 7 \, a^{7} b^{3} c + 12 \, a^{8} b c^{2}\right)} \sqrt{\frac{{\left(b^{10} - 8 \, a b^{8} c + 22 \, a^{2} b^{6} c^{2} - 24 \, a^{3} b^{4} c^{3} + 9 \, a^{4} b^{2} c^{4}\right)} d^{2} - 2 \, {\left(a b^{9} - 7 \, a^{2} b^{7} c + 16 \, a^{3} b^{5} c^{2} - 13 \, a^{4} b^{3} c^{3} + 3 \, a^{5} b c^{4}\right)} d e + {\left(a^{2} b^{8} - 6 \, a^{3} b^{6} c + 11 \, a^{4} b^{4} c^{2} - 6 \, a^{5} b^{2} c^{3} + a^{6} c^{4}\right)} e^{2}}{a^{12} b^{2} - 4 \, a^{13} c}}\right)} \sqrt{\frac{{\left(b^{6} - 6 \, a b^{4} c + 9 \, a^{2} b^{2} c^{2} - 2 \, a^{3} c^{3}\right)} d - {\left(a b^{5} - 5 \, a^{2} b^{3} c + 5 \, a^{3} b c^{2}\right)} e + {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} \sqrt{\frac{{\left(b^{10} - 8 \, a b^{8} c + 22 \, a^{2} b^{6} c^{2} - 24 \, a^{3} b^{4} c^{3} + 9 \, a^{4} b^{2} c^{4}\right)} d^{2} - 2 \, {\left(a b^{9} - 7 \, a^{2} b^{7} c + 16 \, a^{3} b^{5} c^{2} - 13 \, a^{4} b^{3} c^{3} + 3 \, a^{5} b c^{4}\right)} d e + {\left(a^{2} b^{8} - 6 \, a^{3} b^{6} c + 11 \, a^{4} b^{4} c^{2} - 6 \, a^{5} b^{2} c^{3} + a^{6} c^{4}\right)} e^{2}}{a^{12} b^{2} - 4 \, a^{13} c}}}{a^{6} b^{2} - 4 \, a^{7} c}} - 4 \, {\left({\left(b^{5} c^{3} - 4 \, a b^{3} c^{4} + 3 \, a^{2} b c^{5}\right)} d - {\left(a b^{4} c^{3} - 3 \, a^{2} b^{2} c^{4} + a^{3} c^{5}\right)} e\right)} \sqrt{e x + d}\right) - 4 \, \sqrt{2} a^{3} d^{2} x^{2} \sqrt{\frac{{\left(b^{6} - 6 \, a b^{4} c + 9 \, a^{2} b^{2} c^{2} - 2 \, a^{3} c^{3}\right)} d - {\left(a b^{5} - 5 \, a^{2} b^{3} c + 5 \, a^{3} b c^{2}\right)} e + {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} \sqrt{\frac{{\left(b^{10} - 8 \, a b^{8} c + 22 \, a^{2} b^{6} c^{2} - 24 \, a^{3} b^{4} c^{3} + 9 \, a^{4} b^{2} c^{4}\right)} d^{2} - 2 \, {\left(a b^{9} - 7 \, a^{2} b^{7} c + 16 \, a^{3} b^{5} c^{2} - 13 \, a^{4} b^{3} c^{3} + 3 \, a^{5} b c^{4}\right)} d e + {\left(a^{2} b^{8} - 6 \, a^{3} b^{6} c + 11 \, a^{4} b^{4} c^{2} - 6 \, a^{5} b^{2} c^{3} + a^{6} c^{4}\right)} e^{2}}{a^{12} b^{2} - 4 \, a^{13} c}}}{a^{6} b^{2} - 4 \, a^{7} c}} \log\left(-\sqrt{2} {\left({\left(b^{9} - 9 \, a b^{7} c + 27 \, a^{2} b^{5} c^{2} - 31 \, a^{3} b^{3} c^{3} + 12 \, a^{4} b c^{4}\right)} d - {\left(a b^{8} - 8 \, a^{2} b^{6} c + 20 \, a^{3} b^{4} c^{2} - 17 \, a^{4} b^{2} c^{3} + 4 \, a^{5} c^{4}\right)} e - {\left(a^{6} b^{5} - 7 \, a^{7} b^{3} c + 12 \, a^{8} b c^{2}\right)} \sqrt{\frac{{\left(b^{10} - 8 \, a b^{8} c + 22 \, a^{2} b^{6} c^{2} - 24 \, a^{3} b^{4} c^{3} + 9 \, a^{4} b^{2} c^{4}\right)} d^{2} - 2 \, {\left(a b^{9} - 7 \, a^{2} b^{7} c + 16 \, a^{3} b^{5} c^{2} - 13 \, a^{4} b^{3} c^{3} + 3 \, a^{5} b c^{4}\right)} d e + {\left(a^{2} b^{8} - 6 \, a^{3} b^{6} c + 11 \, a^{4} b^{4} c^{2} - 6 \, a^{5} b^{2} c^{3} + a^{6} c^{4}\right)} e^{2}}{a^{12} b^{2} - 4 \, a^{13} c}}\right)} \sqrt{\frac{{\left(b^{6} - 6 \, a b^{4} c + 9 \, a^{2} b^{2} c^{2} - 2 \, a^{3} c^{3}\right)} d - {\left(a b^{5} - 5 \, a^{2} b^{3} c + 5 \, a^{3} b c^{2}\right)} e + {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} \sqrt{\frac{{\left(b^{10} - 8 \, a b^{8} c + 22 \, a^{2} b^{6} c^{2} - 24 \, a^{3} b^{4} c^{3} + 9 \, a^{4} b^{2} c^{4}\right)} d^{2} - 2 \, {\left(a b^{9} - 7 \, a^{2} b^{7} c + 16 \, a^{3} b^{5} c^{2} - 13 \, a^{4} b^{3} c^{3} + 3 \, a^{5} b c^{4}\right)} d e + {\left(a^{2} b^{8} - 6 \, a^{3} b^{6} c + 11 \, a^{4} b^{4} c^{2} - 6 \, a^{5} b^{2} c^{3} + a^{6} c^{4}\right)} e^{2}}{a^{12} b^{2} - 4 \, a^{13} c}}}{a^{6} b^{2} - 4 \, a^{7} c}} - 4 \, {\left({\left(b^{5} c^{3} - 4 \, a b^{3} c^{4} + 3 \, a^{2} b c^{5}\right)} d - {\left(a b^{4} c^{3} - 3 \, a^{2} b^{2} c^{4} + a^{3} c^{5}\right)} e\right)} \sqrt{e x + d}\right) + 4 \, \sqrt{2} a^{3} d^{2} x^{2} \sqrt{\frac{{\left(b^{6} - 6 \, a b^{4} c + 9 \, a^{2} b^{2} c^{2} - 2 \, a^{3} c^{3}\right)} d - {\left(a b^{5} - 5 \, a^{2} b^{3} c + 5 \, a^{3} b c^{2}\right)} e - {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} \sqrt{\frac{{\left(b^{10} - 8 \, a b^{8} c + 22 \, a^{2} b^{6} c^{2} - 24 \, a^{3} b^{4} c^{3} + 9 \, a^{4} b^{2} c^{4}\right)} d^{2} - 2 \, {\left(a b^{9} - 7 \, a^{2} b^{7} c + 16 \, a^{3} b^{5} c^{2} - 13 \, a^{4} b^{3} c^{3} + 3 \, a^{5} b c^{4}\right)} d e + {\left(a^{2} b^{8} - 6 \, a^{3} b^{6} c + 11 \, a^{4} b^{4} c^{2} - 6 \, a^{5} b^{2} c^{3} + a^{6} c^{4}\right)} e^{2}}{a^{12} b^{2} - 4 \, a^{13} c}}}{a^{6} b^{2} - 4 \, a^{7} c}} \log\left(\sqrt{2} {\left({\left(b^{9} - 9 \, a b^{7} c + 27 \, a^{2} b^{5} c^{2} - 31 \, a^{3} b^{3} c^{3} + 12 \, a^{4} b c^{4}\right)} d - {\left(a b^{8} - 8 \, a^{2} b^{6} c + 20 \, a^{3} b^{4} c^{2} - 17 \, a^{4} b^{2} c^{3} + 4 \, a^{5} c^{4}\right)} e + {\left(a^{6} b^{5} - 7 \, a^{7} b^{3} c + 12 \, a^{8} b c^{2}\right)} \sqrt{\frac{{\left(b^{10} - 8 \, a b^{8} c + 22 \, a^{2} b^{6} c^{2} - 24 \, a^{3} b^{4} c^{3} + 9 \, a^{4} b^{2} c^{4}\right)} d^{2} - 2 \, {\left(a b^{9} - 7 \, a^{2} b^{7} c + 16 \, a^{3} b^{5} c^{2} - 13 \, a^{4} b^{3} c^{3} + 3 \, a^{5} b c^{4}\right)} d e + {\left(a^{2} b^{8} - 6 \, a^{3} b^{6} c + 11 \, a^{4} b^{4} c^{2} - 6 \, a^{5} b^{2} c^{3} + a^{6} c^{4}\right)} e^{2}}{a^{12} b^{2} - 4 \, a^{13} c}}\right)} \sqrt{\frac{{\left(b^{6} - 6 \, a b^{4} c + 9 \, a^{2} b^{2} c^{2} - 2 \, a^{3} c^{3}\right)} d - {\left(a b^{5} - 5 \, a^{2} b^{3} c + 5 \, a^{3} b c^{2}\right)} e - {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} \sqrt{\frac{{\left(b^{10} - 8 \, a b^{8} c + 22 \, a^{2} b^{6} c^{2} - 24 \, a^{3} b^{4} c^{3} + 9 \, a^{4} b^{2} c^{4}\right)} d^{2} - 2 \, {\left(a b^{9} - 7 \, a^{2} b^{7} c + 16 \, a^{3} b^{5} c^{2} - 13 \, a^{4} b^{3} c^{3} + 3 \, a^{5} b c^{4}\right)} d e + {\left(a^{2} b^{8} - 6 \, a^{3} b^{6} c + 11 \, a^{4} b^{4} c^{2} - 6 \, a^{5} b^{2} c^{3} + a^{6} c^{4}\right)} e^{2}}{a^{12} b^{2} - 4 \, a^{13} c}}}{a^{6} b^{2} - 4 \, a^{7} c}} - 4 \, {\left({\left(b^{5} c^{3} - 4 \, a b^{3} c^{4} + 3 \, a^{2} b c^{5}\right)} d - {\left(a b^{4} c^{3} - 3 \, a^{2} b^{2} c^{4} + a^{3} c^{5}\right)} e\right)} \sqrt{e x + d}\right) - 4 \, \sqrt{2} a^{3} d^{2} x^{2} \sqrt{\frac{{\left(b^{6} - 6 \, a b^{4} c + 9 \, a^{2} b^{2} c^{2} - 2 \, a^{3} c^{3}\right)} d - {\left(a b^{5} - 5 \, a^{2} b^{3} c + 5 \, a^{3} b c^{2}\right)} e - {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} \sqrt{\frac{{\left(b^{10} - 8 \, a b^{8} c + 22 \, a^{2} b^{6} c^{2} - 24 \, a^{3} b^{4} c^{3} + 9 \, a^{4} b^{2} c^{4}\right)} d^{2} - 2 \, {\left(a b^{9} - 7 \, a^{2} b^{7} c + 16 \, a^{3} b^{5} c^{2} - 13 \, a^{4} b^{3} c^{3} + 3 \, a^{5} b c^{4}\right)} d e + {\left(a^{2} b^{8} - 6 \, a^{3} b^{6} c + 11 \, a^{4} b^{4} c^{2} - 6 \, a^{5} b^{2} c^{3} + a^{6} c^{4}\right)} e^{2}}{a^{12} b^{2} - 4 \, a^{13} c}}}{a^{6} b^{2} - 4 \, a^{7} c}} \log\left(-\sqrt{2} {\left({\left(b^{9} - 9 \, a b^{7} c + 27 \, a^{2} b^{5} c^{2} - 31 \, a^{3} b^{3} c^{3} + 12 \, a^{4} b c^{4}\right)} d - {\left(a b^{8} - 8 \, a^{2} b^{6} c + 20 \, a^{3} b^{4} c^{2} - 17 \, a^{4} b^{2} c^{3} + 4 \, a^{5} c^{4}\right)} e + {\left(a^{6} b^{5} - 7 \, a^{7} b^{3} c + 12 \, a^{8} b c^{2}\right)} \sqrt{\frac{{\left(b^{10} - 8 \, a b^{8} c + 22 \, a^{2} b^{6} c^{2} - 24 \, a^{3} b^{4} c^{3} + 9 \, a^{4} b^{2} c^{4}\right)} d^{2} - 2 \, {\left(a b^{9} - 7 \, a^{2} b^{7} c + 16 \, a^{3} b^{5} c^{2} - 13 \, a^{4} b^{3} c^{3} + 3 \, a^{5} b c^{4}\right)} d e + {\left(a^{2} b^{8} - 6 \, a^{3} b^{6} c + 11 \, a^{4} b^{4} c^{2} - 6 \, a^{5} b^{2} c^{3} + a^{6} c^{4}\right)} e^{2}}{a^{12} b^{2} - 4 \, a^{13} c}}\right)} \sqrt{\frac{{\left(b^{6} - 6 \, a b^{4} c + 9 \, a^{2} b^{2} c^{2} - 2 \, a^{3} c^{3}\right)} d - {\left(a b^{5} - 5 \, a^{2} b^{3} c + 5 \, a^{3} b c^{2}\right)} e - {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} \sqrt{\frac{{\left(b^{10} - 8 \, a b^{8} c + 22 \, a^{2} b^{6} c^{2} - 24 \, a^{3} b^{4} c^{3} + 9 \, a^{4} b^{2} c^{4}\right)} d^{2} - 2 \, {\left(a b^{9} - 7 \, a^{2} b^{7} c + 16 \, a^{3} b^{5} c^{2} - 13 \, a^{4} b^{3} c^{3} + 3 \, a^{5} b c^{4}\right)} d e + {\left(a^{2} b^{8} - 6 \, a^{3} b^{6} c + 11 \, a^{4} b^{4} c^{2} - 6 \, a^{5} b^{2} c^{3} + a^{6} c^{4}\right)} e^{2}}{a^{12} b^{2} - 4 \, a^{13} c}}}{a^{6} b^{2} - 4 \, a^{7} c}} - 4 \, {\left({\left(b^{5} c^{3} - 4 \, a b^{3} c^{4} + 3 \, a^{2} b c^{5}\right)} d - {\left(a b^{4} c^{3} - 3 \, a^{2} b^{2} c^{4} + a^{3} c^{5}\right)} e\right)} \sqrt{e x + d}\right) + {\left(4 \, a b d e + a^{2} e^{2} - 8 \, {\left(b^{2} - a c\right)} d^{2}\right)} \sqrt{d} x^{2} \log\left(\frac{e x + 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) - 2 \, {\left(2 \, a^{2} d^{2} - {\left(4 \, a b d^{2} - a^{2} d e\right)} x\right)} \sqrt{e x + d}}{8 \, a^{3} d^{2} x^{2}}, \frac{2 \, \sqrt{2} a^{3} d^{2} x^{2} \sqrt{\frac{{\left(b^{6} - 6 \, a b^{4} c + 9 \, a^{2} b^{2} c^{2} - 2 \, a^{3} c^{3}\right)} d - {\left(a b^{5} - 5 \, a^{2} b^{3} c + 5 \, a^{3} b c^{2}\right)} e + {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} \sqrt{\frac{{\left(b^{10} - 8 \, a b^{8} c + 22 \, a^{2} b^{6} c^{2} - 24 \, a^{3} b^{4} c^{3} + 9 \, a^{4} b^{2} c^{4}\right)} d^{2} - 2 \, {\left(a b^{9} - 7 \, a^{2} b^{7} c + 16 \, a^{3} b^{5} c^{2} - 13 \, a^{4} b^{3} c^{3} + 3 \, a^{5} b c^{4}\right)} d e + {\left(a^{2} b^{8} - 6 \, a^{3} b^{6} c + 11 \, a^{4} b^{4} c^{2} - 6 \, a^{5} b^{2} c^{3} + a^{6} c^{4}\right)} e^{2}}{a^{12} b^{2} - 4 \, a^{13} c}}}{a^{6} b^{2} - 4 \, a^{7} c}} \log\left(\sqrt{2} {\left({\left(b^{9} - 9 \, a b^{7} c + 27 \, a^{2} b^{5} c^{2} - 31 \, a^{3} b^{3} c^{3} + 12 \, a^{4} b c^{4}\right)} d - {\left(a b^{8} - 8 \, a^{2} b^{6} c + 20 \, a^{3} b^{4} c^{2} - 17 \, a^{4} b^{2} c^{3} + 4 \, a^{5} c^{4}\right)} e - {\left(a^{6} b^{5} - 7 \, a^{7} b^{3} c + 12 \, a^{8} b c^{2}\right)} \sqrt{\frac{{\left(b^{10} - 8 \, a b^{8} c + 22 \, a^{2} b^{6} c^{2} - 24 \, a^{3} b^{4} c^{3} + 9 \, a^{4} b^{2} c^{4}\right)} d^{2} - 2 \, {\left(a b^{9} - 7 \, a^{2} b^{7} c + 16 \, a^{3} b^{5} c^{2} - 13 \, a^{4} b^{3} c^{3} + 3 \, a^{5} b c^{4}\right)} d e + {\left(a^{2} b^{8} - 6 \, a^{3} b^{6} c + 11 \, a^{4} b^{4} c^{2} - 6 \, a^{5} b^{2} c^{3} + a^{6} c^{4}\right)} e^{2}}{a^{12} b^{2} - 4 \, a^{13} c}}\right)} \sqrt{\frac{{\left(b^{6} - 6 \, a b^{4} c + 9 \, a^{2} b^{2} c^{2} - 2 \, a^{3} c^{3}\right)} d - {\left(a b^{5} - 5 \, a^{2} b^{3} c + 5 \, a^{3} b c^{2}\right)} e + {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} \sqrt{\frac{{\left(b^{10} - 8 \, a b^{8} c + 22 \, a^{2} b^{6} c^{2} - 24 \, a^{3} b^{4} c^{3} + 9 \, a^{4} b^{2} c^{4}\right)} d^{2} - 2 \, {\left(a b^{9} - 7 \, a^{2} b^{7} c + 16 \, a^{3} b^{5} c^{2} - 13 \, a^{4} b^{3} c^{3} + 3 \, a^{5} b c^{4}\right)} d e + {\left(a^{2} b^{8} - 6 \, a^{3} b^{6} c + 11 \, a^{4} b^{4} c^{2} - 6 \, a^{5} b^{2} c^{3} + a^{6} c^{4}\right)} e^{2}}{a^{12} b^{2} - 4 \, a^{13} c}}}{a^{6} b^{2} - 4 \, a^{7} c}} - 4 \, {\left({\left(b^{5} c^{3} - 4 \, a b^{3} c^{4} + 3 \, a^{2} b c^{5}\right)} d - {\left(a b^{4} c^{3} - 3 \, a^{2} b^{2} c^{4} + a^{3} c^{5}\right)} e\right)} \sqrt{e x + d}\right) - 2 \, \sqrt{2} a^{3} d^{2} x^{2} \sqrt{\frac{{\left(b^{6} - 6 \, a b^{4} c + 9 \, a^{2} b^{2} c^{2} - 2 \, a^{3} c^{3}\right)} d - {\left(a b^{5} - 5 \, a^{2} b^{3} c + 5 \, a^{3} b c^{2}\right)} e + {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} \sqrt{\frac{{\left(b^{10} - 8 \, a b^{8} c + 22 \, a^{2} b^{6} c^{2} - 24 \, a^{3} b^{4} c^{3} + 9 \, a^{4} b^{2} c^{4}\right)} d^{2} - 2 \, {\left(a b^{9} - 7 \, a^{2} b^{7} c + 16 \, a^{3} b^{5} c^{2} - 13 \, a^{4} b^{3} c^{3} + 3 \, a^{5} b c^{4}\right)} d e + {\left(a^{2} b^{8} - 6 \, a^{3} b^{6} c + 11 \, a^{4} b^{4} c^{2} - 6 \, a^{5} b^{2} c^{3} + a^{6} c^{4}\right)} e^{2}}{a^{12} b^{2} - 4 \, a^{13} c}}}{a^{6} b^{2} - 4 \, a^{7} c}} \log\left(-\sqrt{2} {\left({\left(b^{9} - 9 \, a b^{7} c + 27 \, a^{2} b^{5} c^{2} - 31 \, a^{3} b^{3} c^{3} + 12 \, a^{4} b c^{4}\right)} d - {\left(a b^{8} - 8 \, a^{2} b^{6} c + 20 \, a^{3} b^{4} c^{2} - 17 \, a^{4} b^{2} c^{3} + 4 \, a^{5} c^{4}\right)} e - {\left(a^{6} b^{5} - 7 \, a^{7} b^{3} c + 12 \, a^{8} b c^{2}\right)} \sqrt{\frac{{\left(b^{10} - 8 \, a b^{8} c + 22 \, a^{2} b^{6} c^{2} - 24 \, a^{3} b^{4} c^{3} + 9 \, a^{4} b^{2} c^{4}\right)} d^{2} - 2 \, {\left(a b^{9} - 7 \, a^{2} b^{7} c + 16 \, a^{3} b^{5} c^{2} - 13 \, a^{4} b^{3} c^{3} + 3 \, a^{5} b c^{4}\right)} d e + {\left(a^{2} b^{8} - 6 \, a^{3} b^{6} c + 11 \, a^{4} b^{4} c^{2} - 6 \, a^{5} b^{2} c^{3} + a^{6} c^{4}\right)} e^{2}}{a^{12} b^{2} - 4 \, a^{13} c}}\right)} \sqrt{\frac{{\left(b^{6} - 6 \, a b^{4} c + 9 \, a^{2} b^{2} c^{2} - 2 \, a^{3} c^{3}\right)} d - {\left(a b^{5} - 5 \, a^{2} b^{3} c + 5 \, a^{3} b c^{2}\right)} e + {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} \sqrt{\frac{{\left(b^{10} - 8 \, a b^{8} c + 22 \, a^{2} b^{6} c^{2} - 24 \, a^{3} b^{4} c^{3} + 9 \, a^{4} b^{2} c^{4}\right)} d^{2} - 2 \, {\left(a b^{9} - 7 \, a^{2} b^{7} c + 16 \, a^{3} b^{5} c^{2} - 13 \, a^{4} b^{3} c^{3} + 3 \, a^{5} b c^{4}\right)} d e + {\left(a^{2} b^{8} - 6 \, a^{3} b^{6} c + 11 \, a^{4} b^{4} c^{2} - 6 \, a^{5} b^{2} c^{3} + a^{6} c^{4}\right)} e^{2}}{a^{12} b^{2} - 4 \, a^{13} c}}}{a^{6} b^{2} - 4 \, a^{7} c}} - 4 \, {\left({\left(b^{5} c^{3} - 4 \, a b^{3} c^{4} + 3 \, a^{2} b c^{5}\right)} d - {\left(a b^{4} c^{3} - 3 \, a^{2} b^{2} c^{4} + a^{3} c^{5}\right)} e\right)} \sqrt{e x + d}\right) + 2 \, \sqrt{2} a^{3} d^{2} x^{2} \sqrt{\frac{{\left(b^{6} - 6 \, a b^{4} c + 9 \, a^{2} b^{2} c^{2} - 2 \, a^{3} c^{3}\right)} d - {\left(a b^{5} - 5 \, a^{2} b^{3} c + 5 \, a^{3} b c^{2}\right)} e - {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} \sqrt{\frac{{\left(b^{10} - 8 \, a b^{8} c + 22 \, a^{2} b^{6} c^{2} - 24 \, a^{3} b^{4} c^{3} + 9 \, a^{4} b^{2} c^{4}\right)} d^{2} - 2 \, {\left(a b^{9} - 7 \, a^{2} b^{7} c + 16 \, a^{3} b^{5} c^{2} - 13 \, a^{4} b^{3} c^{3} + 3 \, a^{5} b c^{4}\right)} d e + {\left(a^{2} b^{8} - 6 \, a^{3} b^{6} c + 11 \, a^{4} b^{4} c^{2} - 6 \, a^{5} b^{2} c^{3} + a^{6} c^{4}\right)} e^{2}}{a^{12} b^{2} - 4 \, a^{13} c}}}{a^{6} b^{2} - 4 \, a^{7} c}} \log\left(\sqrt{2} {\left({\left(b^{9} - 9 \, a b^{7} c + 27 \, a^{2} b^{5} c^{2} - 31 \, a^{3} b^{3} c^{3} + 12 \, a^{4} b c^{4}\right)} d - {\left(a b^{8} - 8 \, a^{2} b^{6} c + 20 \, a^{3} b^{4} c^{2} - 17 \, a^{4} b^{2} c^{3} + 4 \, a^{5} c^{4}\right)} e + {\left(a^{6} b^{5} - 7 \, a^{7} b^{3} c + 12 \, a^{8} b c^{2}\right)} \sqrt{\frac{{\left(b^{10} - 8 \, a b^{8} c + 22 \, a^{2} b^{6} c^{2} - 24 \, a^{3} b^{4} c^{3} + 9 \, a^{4} b^{2} c^{4}\right)} d^{2} - 2 \, {\left(a b^{9} - 7 \, a^{2} b^{7} c + 16 \, a^{3} b^{5} c^{2} - 13 \, a^{4} b^{3} c^{3} + 3 \, a^{5} b c^{4}\right)} d e + {\left(a^{2} b^{8} - 6 \, a^{3} b^{6} c + 11 \, a^{4} b^{4} c^{2} - 6 \, a^{5} b^{2} c^{3} + a^{6} c^{4}\right)} e^{2}}{a^{12} b^{2} - 4 \, a^{13} c}}\right)} \sqrt{\frac{{\left(b^{6} - 6 \, a b^{4} c + 9 \, a^{2} b^{2} c^{2} - 2 \, a^{3} c^{3}\right)} d - {\left(a b^{5} - 5 \, a^{2} b^{3} c + 5 \, a^{3} b c^{2}\right)} e - {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} \sqrt{\frac{{\left(b^{10} - 8 \, a b^{8} c + 22 \, a^{2} b^{6} c^{2} - 24 \, a^{3} b^{4} c^{3} + 9 \, a^{4} b^{2} c^{4}\right)} d^{2} - 2 \, {\left(a b^{9} - 7 \, a^{2} b^{7} c + 16 \, a^{3} b^{5} c^{2} - 13 \, a^{4} b^{3} c^{3} + 3 \, a^{5} b c^{4}\right)} d e + {\left(a^{2} b^{8} - 6 \, a^{3} b^{6} c + 11 \, a^{4} b^{4} c^{2} - 6 \, a^{5} b^{2} c^{3} + a^{6} c^{4}\right)} e^{2}}{a^{12} b^{2} - 4 \, a^{13} c}}}{a^{6} b^{2} - 4 \, a^{7} c}} - 4 \, {\left({\left(b^{5} c^{3} - 4 \, a b^{3} c^{4} + 3 \, a^{2} b c^{5}\right)} d - {\left(a b^{4} c^{3} - 3 \, a^{2} b^{2} c^{4} + a^{3} c^{5}\right)} e\right)} \sqrt{e x + d}\right) - 2 \, \sqrt{2} a^{3} d^{2} x^{2} \sqrt{\frac{{\left(b^{6} - 6 \, a b^{4} c + 9 \, a^{2} b^{2} c^{2} - 2 \, a^{3} c^{3}\right)} d - {\left(a b^{5} - 5 \, a^{2} b^{3} c + 5 \, a^{3} b c^{2}\right)} e - {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} \sqrt{\frac{{\left(b^{10} - 8 \, a b^{8} c + 22 \, a^{2} b^{6} c^{2} - 24 \, a^{3} b^{4} c^{3} + 9 \, a^{4} b^{2} c^{4}\right)} d^{2} - 2 \, {\left(a b^{9} - 7 \, a^{2} b^{7} c + 16 \, a^{3} b^{5} c^{2} - 13 \, a^{4} b^{3} c^{3} + 3 \, a^{5} b c^{4}\right)} d e + {\left(a^{2} b^{8} - 6 \, a^{3} b^{6} c + 11 \, a^{4} b^{4} c^{2} - 6 \, a^{5} b^{2} c^{3} + a^{6} c^{4}\right)} e^{2}}{a^{12} b^{2} - 4 \, a^{13} c}}}{a^{6} b^{2} - 4 \, a^{7} c}} \log\left(-\sqrt{2} {\left({\left(b^{9} - 9 \, a b^{7} c + 27 \, a^{2} b^{5} c^{2} - 31 \, a^{3} b^{3} c^{3} + 12 \, a^{4} b c^{4}\right)} d - {\left(a b^{8} - 8 \, a^{2} b^{6} c + 20 \, a^{3} b^{4} c^{2} - 17 \, a^{4} b^{2} c^{3} + 4 \, a^{5} c^{4}\right)} e + {\left(a^{6} b^{5} - 7 \, a^{7} b^{3} c + 12 \, a^{8} b c^{2}\right)} \sqrt{\frac{{\left(b^{10} - 8 \, a b^{8} c + 22 \, a^{2} b^{6} c^{2} - 24 \, a^{3} b^{4} c^{3} + 9 \, a^{4} b^{2} c^{4}\right)} d^{2} - 2 \, {\left(a b^{9} - 7 \, a^{2} b^{7} c + 16 \, a^{3} b^{5} c^{2} - 13 \, a^{4} b^{3} c^{3} + 3 \, a^{5} b c^{4}\right)} d e + {\left(a^{2} b^{8} - 6 \, a^{3} b^{6} c + 11 \, a^{4} b^{4} c^{2} - 6 \, a^{5} b^{2} c^{3} + a^{6} c^{4}\right)} e^{2}}{a^{12} b^{2} - 4 \, a^{13} c}}\right)} \sqrt{\frac{{\left(b^{6} - 6 \, a b^{4} c + 9 \, a^{2} b^{2} c^{2} - 2 \, a^{3} c^{3}\right)} d - {\left(a b^{5} - 5 \, a^{2} b^{3} c + 5 \, a^{3} b c^{2}\right)} e - {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} \sqrt{\frac{{\left(b^{10} - 8 \, a b^{8} c + 22 \, a^{2} b^{6} c^{2} - 24 \, a^{3} b^{4} c^{3} + 9 \, a^{4} b^{2} c^{4}\right)} d^{2} - 2 \, {\left(a b^{9} - 7 \, a^{2} b^{7} c + 16 \, a^{3} b^{5} c^{2} - 13 \, a^{4} b^{3} c^{3} + 3 \, a^{5} b c^{4}\right)} d e + {\left(a^{2} b^{8} - 6 \, a^{3} b^{6} c + 11 \, a^{4} b^{4} c^{2} - 6 \, a^{5} b^{2} c^{3} + a^{6} c^{4}\right)} e^{2}}{a^{12} b^{2} - 4 \, a^{13} c}}}{a^{6} b^{2} - 4 \, a^{7} c}} - 4 \, {\left({\left(b^{5} c^{3} - 4 \, a b^{3} c^{4} + 3 \, a^{2} b c^{5}\right)} d - {\left(a b^{4} c^{3} - 3 \, a^{2} b^{2} c^{4} + a^{3} c^{5}\right)} e\right)} \sqrt{e x + d}\right) - {\left(4 \, a b d e + a^{2} e^{2} - 8 \, {\left(b^{2} - a c\right)} d^{2}\right)} \sqrt{-d} x^{2} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) - {\left(2 \, a^{2} d^{2} - {\left(4 \, a b d^{2} - a^{2} d e\right)} x\right)} \sqrt{e x + d}}{4 \, a^{3} d^{2} x^{2}}\right]"," ",0,"[1/8*(4*sqrt(2)*a^3*d^2*x^2*sqrt(((b^6 - 6*a*b^4*c + 9*a^2*b^2*c^2 - 2*a^3*c^3)*d - (a*b^5 - 5*a^2*b^3*c + 5*a^3*b*c^2)*e + (a^6*b^2 - 4*a^7*c)*sqrt(((b^10 - 8*a*b^8*c + 22*a^2*b^6*c^2 - 24*a^3*b^4*c^3 + 9*a^4*b^2*c^4)*d^2 - 2*(a*b^9 - 7*a^2*b^7*c + 16*a^3*b^5*c^2 - 13*a^4*b^3*c^3 + 3*a^5*b*c^4)*d*e + (a^2*b^8 - 6*a^3*b^6*c + 11*a^4*b^4*c^2 - 6*a^5*b^2*c^3 + a^6*c^4)*e^2)/(a^12*b^2 - 4*a^13*c)))/(a^6*b^2 - 4*a^7*c))*log(sqrt(2)*((b^9 - 9*a*b^7*c + 27*a^2*b^5*c^2 - 31*a^3*b^3*c^3 + 12*a^4*b*c^4)*d - (a*b^8 - 8*a^2*b^6*c + 20*a^3*b^4*c^2 - 17*a^4*b^2*c^3 + 4*a^5*c^4)*e - (a^6*b^5 - 7*a^7*b^3*c + 12*a^8*b*c^2)*sqrt(((b^10 - 8*a*b^8*c + 22*a^2*b^6*c^2 - 24*a^3*b^4*c^3 + 9*a^4*b^2*c^4)*d^2 - 2*(a*b^9 - 7*a^2*b^7*c + 16*a^3*b^5*c^2 - 13*a^4*b^3*c^3 + 3*a^5*b*c^4)*d*e + (a^2*b^8 - 6*a^3*b^6*c + 11*a^4*b^4*c^2 - 6*a^5*b^2*c^3 + a^6*c^4)*e^2)/(a^12*b^2 - 4*a^13*c)))*sqrt(((b^6 - 6*a*b^4*c + 9*a^2*b^2*c^2 - 2*a^3*c^3)*d - (a*b^5 - 5*a^2*b^3*c + 5*a^3*b*c^2)*e + (a^6*b^2 - 4*a^7*c)*sqrt(((b^10 - 8*a*b^8*c + 22*a^2*b^6*c^2 - 24*a^3*b^4*c^3 + 9*a^4*b^2*c^4)*d^2 - 2*(a*b^9 - 7*a^2*b^7*c + 16*a^3*b^5*c^2 - 13*a^4*b^3*c^3 + 3*a^5*b*c^4)*d*e + (a^2*b^8 - 6*a^3*b^6*c + 11*a^4*b^4*c^2 - 6*a^5*b^2*c^3 + a^6*c^4)*e^2)/(a^12*b^2 - 4*a^13*c)))/(a^6*b^2 - 4*a^7*c)) - 4*((b^5*c^3 - 4*a*b^3*c^4 + 3*a^2*b*c^5)*d - (a*b^4*c^3 - 3*a^2*b^2*c^4 + a^3*c^5)*e)*sqrt(e*x + d)) - 4*sqrt(2)*a^3*d^2*x^2*sqrt(((b^6 - 6*a*b^4*c + 9*a^2*b^2*c^2 - 2*a^3*c^3)*d - (a*b^5 - 5*a^2*b^3*c + 5*a^3*b*c^2)*e + (a^6*b^2 - 4*a^7*c)*sqrt(((b^10 - 8*a*b^8*c + 22*a^2*b^6*c^2 - 24*a^3*b^4*c^3 + 9*a^4*b^2*c^4)*d^2 - 2*(a*b^9 - 7*a^2*b^7*c + 16*a^3*b^5*c^2 - 13*a^4*b^3*c^3 + 3*a^5*b*c^4)*d*e + (a^2*b^8 - 6*a^3*b^6*c + 11*a^4*b^4*c^2 - 6*a^5*b^2*c^3 + a^6*c^4)*e^2)/(a^12*b^2 - 4*a^13*c)))/(a^6*b^2 - 4*a^7*c))*log(-sqrt(2)*((b^9 - 9*a*b^7*c + 27*a^2*b^5*c^2 - 31*a^3*b^3*c^3 + 12*a^4*b*c^4)*d - (a*b^8 - 8*a^2*b^6*c + 20*a^3*b^4*c^2 - 17*a^4*b^2*c^3 + 4*a^5*c^4)*e - (a^6*b^5 - 7*a^7*b^3*c + 12*a^8*b*c^2)*sqrt(((b^10 - 8*a*b^8*c + 22*a^2*b^6*c^2 - 24*a^3*b^4*c^3 + 9*a^4*b^2*c^4)*d^2 - 2*(a*b^9 - 7*a^2*b^7*c + 16*a^3*b^5*c^2 - 13*a^4*b^3*c^3 + 3*a^5*b*c^4)*d*e + (a^2*b^8 - 6*a^3*b^6*c + 11*a^4*b^4*c^2 - 6*a^5*b^2*c^3 + a^6*c^4)*e^2)/(a^12*b^2 - 4*a^13*c)))*sqrt(((b^6 - 6*a*b^4*c + 9*a^2*b^2*c^2 - 2*a^3*c^3)*d - (a*b^5 - 5*a^2*b^3*c + 5*a^3*b*c^2)*e + (a^6*b^2 - 4*a^7*c)*sqrt(((b^10 - 8*a*b^8*c + 22*a^2*b^6*c^2 - 24*a^3*b^4*c^3 + 9*a^4*b^2*c^4)*d^2 - 2*(a*b^9 - 7*a^2*b^7*c + 16*a^3*b^5*c^2 - 13*a^4*b^3*c^3 + 3*a^5*b*c^4)*d*e + (a^2*b^8 - 6*a^3*b^6*c + 11*a^4*b^4*c^2 - 6*a^5*b^2*c^3 + a^6*c^4)*e^2)/(a^12*b^2 - 4*a^13*c)))/(a^6*b^2 - 4*a^7*c)) - 4*((b^5*c^3 - 4*a*b^3*c^4 + 3*a^2*b*c^5)*d - (a*b^4*c^3 - 3*a^2*b^2*c^4 + a^3*c^5)*e)*sqrt(e*x + d)) + 4*sqrt(2)*a^3*d^2*x^2*sqrt(((b^6 - 6*a*b^4*c + 9*a^2*b^2*c^2 - 2*a^3*c^3)*d - (a*b^5 - 5*a^2*b^3*c + 5*a^3*b*c^2)*e - (a^6*b^2 - 4*a^7*c)*sqrt(((b^10 - 8*a*b^8*c + 22*a^2*b^6*c^2 - 24*a^3*b^4*c^3 + 9*a^4*b^2*c^4)*d^2 - 2*(a*b^9 - 7*a^2*b^7*c + 16*a^3*b^5*c^2 - 13*a^4*b^3*c^3 + 3*a^5*b*c^4)*d*e + (a^2*b^8 - 6*a^3*b^6*c + 11*a^4*b^4*c^2 - 6*a^5*b^2*c^3 + a^6*c^4)*e^2)/(a^12*b^2 - 4*a^13*c)))/(a^6*b^2 - 4*a^7*c))*log(sqrt(2)*((b^9 - 9*a*b^7*c + 27*a^2*b^5*c^2 - 31*a^3*b^3*c^3 + 12*a^4*b*c^4)*d - (a*b^8 - 8*a^2*b^6*c + 20*a^3*b^4*c^2 - 17*a^4*b^2*c^3 + 4*a^5*c^4)*e + (a^6*b^5 - 7*a^7*b^3*c + 12*a^8*b*c^2)*sqrt(((b^10 - 8*a*b^8*c + 22*a^2*b^6*c^2 - 24*a^3*b^4*c^3 + 9*a^4*b^2*c^4)*d^2 - 2*(a*b^9 - 7*a^2*b^7*c + 16*a^3*b^5*c^2 - 13*a^4*b^3*c^3 + 3*a^5*b*c^4)*d*e + (a^2*b^8 - 6*a^3*b^6*c + 11*a^4*b^4*c^2 - 6*a^5*b^2*c^3 + a^6*c^4)*e^2)/(a^12*b^2 - 4*a^13*c)))*sqrt(((b^6 - 6*a*b^4*c + 9*a^2*b^2*c^2 - 2*a^3*c^3)*d - (a*b^5 - 5*a^2*b^3*c + 5*a^3*b*c^2)*e - (a^6*b^2 - 4*a^7*c)*sqrt(((b^10 - 8*a*b^8*c + 22*a^2*b^6*c^2 - 24*a^3*b^4*c^3 + 9*a^4*b^2*c^4)*d^2 - 2*(a*b^9 - 7*a^2*b^7*c + 16*a^3*b^5*c^2 - 13*a^4*b^3*c^3 + 3*a^5*b*c^4)*d*e + (a^2*b^8 - 6*a^3*b^6*c + 11*a^4*b^4*c^2 - 6*a^5*b^2*c^3 + a^6*c^4)*e^2)/(a^12*b^2 - 4*a^13*c)))/(a^6*b^2 - 4*a^7*c)) - 4*((b^5*c^3 - 4*a*b^3*c^4 + 3*a^2*b*c^5)*d - (a*b^4*c^3 - 3*a^2*b^2*c^4 + a^3*c^5)*e)*sqrt(e*x + d)) - 4*sqrt(2)*a^3*d^2*x^2*sqrt(((b^6 - 6*a*b^4*c + 9*a^2*b^2*c^2 - 2*a^3*c^3)*d - (a*b^5 - 5*a^2*b^3*c + 5*a^3*b*c^2)*e - (a^6*b^2 - 4*a^7*c)*sqrt(((b^10 - 8*a*b^8*c + 22*a^2*b^6*c^2 - 24*a^3*b^4*c^3 + 9*a^4*b^2*c^4)*d^2 - 2*(a*b^9 - 7*a^2*b^7*c + 16*a^3*b^5*c^2 - 13*a^4*b^3*c^3 + 3*a^5*b*c^4)*d*e + (a^2*b^8 - 6*a^3*b^6*c + 11*a^4*b^4*c^2 - 6*a^5*b^2*c^3 + a^6*c^4)*e^2)/(a^12*b^2 - 4*a^13*c)))/(a^6*b^2 - 4*a^7*c))*log(-sqrt(2)*((b^9 - 9*a*b^7*c + 27*a^2*b^5*c^2 - 31*a^3*b^3*c^3 + 12*a^4*b*c^4)*d - (a*b^8 - 8*a^2*b^6*c + 20*a^3*b^4*c^2 - 17*a^4*b^2*c^3 + 4*a^5*c^4)*e + (a^6*b^5 - 7*a^7*b^3*c + 12*a^8*b*c^2)*sqrt(((b^10 - 8*a*b^8*c + 22*a^2*b^6*c^2 - 24*a^3*b^4*c^3 + 9*a^4*b^2*c^4)*d^2 - 2*(a*b^9 - 7*a^2*b^7*c + 16*a^3*b^5*c^2 - 13*a^4*b^3*c^3 + 3*a^5*b*c^4)*d*e + (a^2*b^8 - 6*a^3*b^6*c + 11*a^4*b^4*c^2 - 6*a^5*b^2*c^3 + a^6*c^4)*e^2)/(a^12*b^2 - 4*a^13*c)))*sqrt(((b^6 - 6*a*b^4*c + 9*a^2*b^2*c^2 - 2*a^3*c^3)*d - (a*b^5 - 5*a^2*b^3*c + 5*a^3*b*c^2)*e - (a^6*b^2 - 4*a^7*c)*sqrt(((b^10 - 8*a*b^8*c + 22*a^2*b^6*c^2 - 24*a^3*b^4*c^3 + 9*a^4*b^2*c^4)*d^2 - 2*(a*b^9 - 7*a^2*b^7*c + 16*a^3*b^5*c^2 - 13*a^4*b^3*c^3 + 3*a^5*b*c^4)*d*e + (a^2*b^8 - 6*a^3*b^6*c + 11*a^4*b^4*c^2 - 6*a^5*b^2*c^3 + a^6*c^4)*e^2)/(a^12*b^2 - 4*a^13*c)))/(a^6*b^2 - 4*a^7*c)) - 4*((b^5*c^3 - 4*a*b^3*c^4 + 3*a^2*b*c^5)*d - (a*b^4*c^3 - 3*a^2*b^2*c^4 + a^3*c^5)*e)*sqrt(e*x + d)) + (4*a*b*d*e + a^2*e^2 - 8*(b^2 - a*c)*d^2)*sqrt(d)*x^2*log((e*x + 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) - 2*(2*a^2*d^2 - (4*a*b*d^2 - a^2*d*e)*x)*sqrt(e*x + d))/(a^3*d^2*x^2), 1/4*(2*sqrt(2)*a^3*d^2*x^2*sqrt(((b^6 - 6*a*b^4*c + 9*a^2*b^2*c^2 - 2*a^3*c^3)*d - (a*b^5 - 5*a^2*b^3*c + 5*a^3*b*c^2)*e + (a^6*b^2 - 4*a^7*c)*sqrt(((b^10 - 8*a*b^8*c + 22*a^2*b^6*c^2 - 24*a^3*b^4*c^3 + 9*a^4*b^2*c^4)*d^2 - 2*(a*b^9 - 7*a^2*b^7*c + 16*a^3*b^5*c^2 - 13*a^4*b^3*c^3 + 3*a^5*b*c^4)*d*e + (a^2*b^8 - 6*a^3*b^6*c + 11*a^4*b^4*c^2 - 6*a^5*b^2*c^3 + a^6*c^4)*e^2)/(a^12*b^2 - 4*a^13*c)))/(a^6*b^2 - 4*a^7*c))*log(sqrt(2)*((b^9 - 9*a*b^7*c + 27*a^2*b^5*c^2 - 31*a^3*b^3*c^3 + 12*a^4*b*c^4)*d - (a*b^8 - 8*a^2*b^6*c + 20*a^3*b^4*c^2 - 17*a^4*b^2*c^3 + 4*a^5*c^4)*e - (a^6*b^5 - 7*a^7*b^3*c + 12*a^8*b*c^2)*sqrt(((b^10 - 8*a*b^8*c + 22*a^2*b^6*c^2 - 24*a^3*b^4*c^3 + 9*a^4*b^2*c^4)*d^2 - 2*(a*b^9 - 7*a^2*b^7*c + 16*a^3*b^5*c^2 - 13*a^4*b^3*c^3 + 3*a^5*b*c^4)*d*e + (a^2*b^8 - 6*a^3*b^6*c + 11*a^4*b^4*c^2 - 6*a^5*b^2*c^3 + a^6*c^4)*e^2)/(a^12*b^2 - 4*a^13*c)))*sqrt(((b^6 - 6*a*b^4*c + 9*a^2*b^2*c^2 - 2*a^3*c^3)*d - (a*b^5 - 5*a^2*b^3*c + 5*a^3*b*c^2)*e + (a^6*b^2 - 4*a^7*c)*sqrt(((b^10 - 8*a*b^8*c + 22*a^2*b^6*c^2 - 24*a^3*b^4*c^3 + 9*a^4*b^2*c^4)*d^2 - 2*(a*b^9 - 7*a^2*b^7*c + 16*a^3*b^5*c^2 - 13*a^4*b^3*c^3 + 3*a^5*b*c^4)*d*e + (a^2*b^8 - 6*a^3*b^6*c + 11*a^4*b^4*c^2 - 6*a^5*b^2*c^3 + a^6*c^4)*e^2)/(a^12*b^2 - 4*a^13*c)))/(a^6*b^2 - 4*a^7*c)) - 4*((b^5*c^3 - 4*a*b^3*c^4 + 3*a^2*b*c^5)*d - (a*b^4*c^3 - 3*a^2*b^2*c^4 + a^3*c^5)*e)*sqrt(e*x + d)) - 2*sqrt(2)*a^3*d^2*x^2*sqrt(((b^6 - 6*a*b^4*c + 9*a^2*b^2*c^2 - 2*a^3*c^3)*d - (a*b^5 - 5*a^2*b^3*c + 5*a^3*b*c^2)*e + (a^6*b^2 - 4*a^7*c)*sqrt(((b^10 - 8*a*b^8*c + 22*a^2*b^6*c^2 - 24*a^3*b^4*c^3 + 9*a^4*b^2*c^4)*d^2 - 2*(a*b^9 - 7*a^2*b^7*c + 16*a^3*b^5*c^2 - 13*a^4*b^3*c^3 + 3*a^5*b*c^4)*d*e + (a^2*b^8 - 6*a^3*b^6*c + 11*a^4*b^4*c^2 - 6*a^5*b^2*c^3 + a^6*c^4)*e^2)/(a^12*b^2 - 4*a^13*c)))/(a^6*b^2 - 4*a^7*c))*log(-sqrt(2)*((b^9 - 9*a*b^7*c + 27*a^2*b^5*c^2 - 31*a^3*b^3*c^3 + 12*a^4*b*c^4)*d - (a*b^8 - 8*a^2*b^6*c + 20*a^3*b^4*c^2 - 17*a^4*b^2*c^3 + 4*a^5*c^4)*e - (a^6*b^5 - 7*a^7*b^3*c + 12*a^8*b*c^2)*sqrt(((b^10 - 8*a*b^8*c + 22*a^2*b^6*c^2 - 24*a^3*b^4*c^3 + 9*a^4*b^2*c^4)*d^2 - 2*(a*b^9 - 7*a^2*b^7*c + 16*a^3*b^5*c^2 - 13*a^4*b^3*c^3 + 3*a^5*b*c^4)*d*e + (a^2*b^8 - 6*a^3*b^6*c + 11*a^4*b^4*c^2 - 6*a^5*b^2*c^3 + a^6*c^4)*e^2)/(a^12*b^2 - 4*a^13*c)))*sqrt(((b^6 - 6*a*b^4*c + 9*a^2*b^2*c^2 - 2*a^3*c^3)*d - (a*b^5 - 5*a^2*b^3*c + 5*a^3*b*c^2)*e + (a^6*b^2 - 4*a^7*c)*sqrt(((b^10 - 8*a*b^8*c + 22*a^2*b^6*c^2 - 24*a^3*b^4*c^3 + 9*a^4*b^2*c^4)*d^2 - 2*(a*b^9 - 7*a^2*b^7*c + 16*a^3*b^5*c^2 - 13*a^4*b^3*c^3 + 3*a^5*b*c^4)*d*e + (a^2*b^8 - 6*a^3*b^6*c + 11*a^4*b^4*c^2 - 6*a^5*b^2*c^3 + a^6*c^4)*e^2)/(a^12*b^2 - 4*a^13*c)))/(a^6*b^2 - 4*a^7*c)) - 4*((b^5*c^3 - 4*a*b^3*c^4 + 3*a^2*b*c^5)*d - (a*b^4*c^3 - 3*a^2*b^2*c^4 + a^3*c^5)*e)*sqrt(e*x + d)) + 2*sqrt(2)*a^3*d^2*x^2*sqrt(((b^6 - 6*a*b^4*c + 9*a^2*b^2*c^2 - 2*a^3*c^3)*d - (a*b^5 - 5*a^2*b^3*c + 5*a^3*b*c^2)*e - (a^6*b^2 - 4*a^7*c)*sqrt(((b^10 - 8*a*b^8*c + 22*a^2*b^6*c^2 - 24*a^3*b^4*c^3 + 9*a^4*b^2*c^4)*d^2 - 2*(a*b^9 - 7*a^2*b^7*c + 16*a^3*b^5*c^2 - 13*a^4*b^3*c^3 + 3*a^5*b*c^4)*d*e + (a^2*b^8 - 6*a^3*b^6*c + 11*a^4*b^4*c^2 - 6*a^5*b^2*c^3 + a^6*c^4)*e^2)/(a^12*b^2 - 4*a^13*c)))/(a^6*b^2 - 4*a^7*c))*log(sqrt(2)*((b^9 - 9*a*b^7*c + 27*a^2*b^5*c^2 - 31*a^3*b^3*c^3 + 12*a^4*b*c^4)*d - (a*b^8 - 8*a^2*b^6*c + 20*a^3*b^4*c^2 - 17*a^4*b^2*c^3 + 4*a^5*c^4)*e + (a^6*b^5 - 7*a^7*b^3*c + 12*a^8*b*c^2)*sqrt(((b^10 - 8*a*b^8*c + 22*a^2*b^6*c^2 - 24*a^3*b^4*c^3 + 9*a^4*b^2*c^4)*d^2 - 2*(a*b^9 - 7*a^2*b^7*c + 16*a^3*b^5*c^2 - 13*a^4*b^3*c^3 + 3*a^5*b*c^4)*d*e + (a^2*b^8 - 6*a^3*b^6*c + 11*a^4*b^4*c^2 - 6*a^5*b^2*c^3 + a^6*c^4)*e^2)/(a^12*b^2 - 4*a^13*c)))*sqrt(((b^6 - 6*a*b^4*c + 9*a^2*b^2*c^2 - 2*a^3*c^3)*d - (a*b^5 - 5*a^2*b^3*c + 5*a^3*b*c^2)*e - (a^6*b^2 - 4*a^7*c)*sqrt(((b^10 - 8*a*b^8*c + 22*a^2*b^6*c^2 - 24*a^3*b^4*c^3 + 9*a^4*b^2*c^4)*d^2 - 2*(a*b^9 - 7*a^2*b^7*c + 16*a^3*b^5*c^2 - 13*a^4*b^3*c^3 + 3*a^5*b*c^4)*d*e + (a^2*b^8 - 6*a^3*b^6*c + 11*a^4*b^4*c^2 - 6*a^5*b^2*c^3 + a^6*c^4)*e^2)/(a^12*b^2 - 4*a^13*c)))/(a^6*b^2 - 4*a^7*c)) - 4*((b^5*c^3 - 4*a*b^3*c^4 + 3*a^2*b*c^5)*d - (a*b^4*c^3 - 3*a^2*b^2*c^4 + a^3*c^5)*e)*sqrt(e*x + d)) - 2*sqrt(2)*a^3*d^2*x^2*sqrt(((b^6 - 6*a*b^4*c + 9*a^2*b^2*c^2 - 2*a^3*c^3)*d - (a*b^5 - 5*a^2*b^3*c + 5*a^3*b*c^2)*e - (a^6*b^2 - 4*a^7*c)*sqrt(((b^10 - 8*a*b^8*c + 22*a^2*b^6*c^2 - 24*a^3*b^4*c^3 + 9*a^4*b^2*c^4)*d^2 - 2*(a*b^9 - 7*a^2*b^7*c + 16*a^3*b^5*c^2 - 13*a^4*b^3*c^3 + 3*a^5*b*c^4)*d*e + (a^2*b^8 - 6*a^3*b^6*c + 11*a^4*b^4*c^2 - 6*a^5*b^2*c^3 + a^6*c^4)*e^2)/(a^12*b^2 - 4*a^13*c)))/(a^6*b^2 - 4*a^7*c))*log(-sqrt(2)*((b^9 - 9*a*b^7*c + 27*a^2*b^5*c^2 - 31*a^3*b^3*c^3 + 12*a^4*b*c^4)*d - (a*b^8 - 8*a^2*b^6*c + 20*a^3*b^4*c^2 - 17*a^4*b^2*c^3 + 4*a^5*c^4)*e + (a^6*b^5 - 7*a^7*b^3*c + 12*a^8*b*c^2)*sqrt(((b^10 - 8*a*b^8*c + 22*a^2*b^6*c^2 - 24*a^3*b^4*c^3 + 9*a^4*b^2*c^4)*d^2 - 2*(a*b^9 - 7*a^2*b^7*c + 16*a^3*b^5*c^2 - 13*a^4*b^3*c^3 + 3*a^5*b*c^4)*d*e + (a^2*b^8 - 6*a^3*b^6*c + 11*a^4*b^4*c^2 - 6*a^5*b^2*c^3 + a^6*c^4)*e^2)/(a^12*b^2 - 4*a^13*c)))*sqrt(((b^6 - 6*a*b^4*c + 9*a^2*b^2*c^2 - 2*a^3*c^3)*d - (a*b^5 - 5*a^2*b^3*c + 5*a^3*b*c^2)*e - (a^6*b^2 - 4*a^7*c)*sqrt(((b^10 - 8*a*b^8*c + 22*a^2*b^6*c^2 - 24*a^3*b^4*c^3 + 9*a^4*b^2*c^4)*d^2 - 2*(a*b^9 - 7*a^2*b^7*c + 16*a^3*b^5*c^2 - 13*a^4*b^3*c^3 + 3*a^5*b*c^4)*d*e + (a^2*b^8 - 6*a^3*b^6*c + 11*a^4*b^4*c^2 - 6*a^5*b^2*c^3 + a^6*c^4)*e^2)/(a^12*b^2 - 4*a^13*c)))/(a^6*b^2 - 4*a^7*c)) - 4*((b^5*c^3 - 4*a*b^3*c^4 + 3*a^2*b*c^5)*d - (a*b^4*c^3 - 3*a^2*b^2*c^4 + a^3*c^5)*e)*sqrt(e*x + d)) - (4*a*b*d*e + a^2*e^2 - 8*(b^2 - a*c)*d^2)*sqrt(-d)*x^2*arctan(sqrt(e*x + d)*sqrt(-d)/d) - (2*a^2*d^2 - (4*a*b*d^2 - a^2*d*e)*x)*sqrt(e*x + d))/(a^3*d^2*x^2)]","B",0
533,1,14340,0,11.223415," ","integrate(x^4*(e*x+d)^(3/2)/(c*x^2+b*x+a),x, algorithm=""fricas"")","-\frac{315 \, \sqrt{2} c^{5} e^{3} \sqrt{\frac{{\left(b^{8} c^{3} - 8 \, a b^{6} c^{4} + 20 \, a^{2} b^{4} c^{5} - 16 \, a^{3} b^{2} c^{6} + 2 \, a^{4} c^{7}\right)} d^{3} - 3 \, {\left(b^{9} c^{2} - 9 \, a b^{7} c^{3} + 27 \, a^{2} b^{5} c^{4} - 30 \, a^{3} b^{3} c^{5} + 9 \, a^{4} b c^{6}\right)} d^{2} e + 3 \, {\left(b^{10} c - 10 \, a b^{8} c^{2} + 35 \, a^{2} b^{6} c^{3} - 50 \, a^{3} b^{4} c^{4} + 25 \, a^{4} b^{2} c^{5} - 2 \, a^{5} c^{6}\right)} d e^{2} - {\left(b^{11} - 11 \, a b^{9} c + 44 \, a^{2} b^{7} c^{2} - 77 \, a^{3} b^{5} c^{3} + 55 \, a^{4} b^{3} c^{4} - 11 \, a^{5} b c^{5}\right)} e^{3} + {\left(b^{2} c^{11} - 4 \, a c^{12}\right)} \sqrt{\frac{{\left(b^{14} c^{6} - 12 \, a b^{12} c^{7} + 56 \, a^{2} b^{10} c^{8} - 128 \, a^{3} b^{8} c^{9} + 148 \, a^{4} b^{6} c^{10} - 80 \, a^{5} b^{4} c^{11} + 16 \, a^{6} b^{2} c^{12}\right)} d^{6} - 6 \, {\left(b^{15} c^{5} - 13 \, a b^{13} c^{6} + 67 \, a^{2} b^{11} c^{7} - 174 \, a^{3} b^{9} c^{8} + 239 \, a^{4} b^{7} c^{9} - 166 \, a^{5} b^{5} c^{10} + 50 \, a^{6} b^{3} c^{11} - 4 \, a^{7} b c^{12}\right)} d^{5} e + 3 \, {\left(5 \, b^{16} c^{4} - 70 \, a b^{14} c^{5} + 395 \, a^{2} b^{12} c^{6} - 1150 \, a^{3} b^{10} c^{7} + 1835 \, a^{4} b^{8} c^{8} - 1570 \, a^{5} b^{6} c^{9} + 650 \, a^{6} b^{4} c^{10} - 100 \, a^{7} b^{2} c^{11} + 3 \, a^{8} c^{12}\right)} d^{4} e^{2} - 2 \, {\left(10 \, b^{17} c^{3} - 150 \, a b^{15} c^{4} + 920 \, a^{2} b^{13} c^{5} - 2970 \, a^{3} b^{11} c^{6} + 5410 \, a^{4} b^{9} c^{7} - 5530 \, a^{5} b^{7} c^{8} + 2960 \, a^{6} b^{5} c^{9} - 700 \, a^{7} b^{3} c^{10} + 49 \, a^{8} b c^{11}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{18} c^{2} - 80 \, a b^{16} c^{3} + 530 \, a^{2} b^{14} c^{4} - 1880 \, a^{3} b^{12} c^{5} + 3855 \, a^{4} b^{10} c^{6} - 4600 \, a^{5} b^{8} c^{7} + 3050 \, a^{6} b^{6} c^{8} - 1000 \, a^{7} b^{4} c^{9} + 125 \, a^{8} b^{2} c^{10} - 2 \, a^{9} c^{11}\right)} d^{2} e^{4} - 6 \, {\left(b^{19} c - 17 \, a b^{17} c^{2} + 121 \, a^{2} b^{15} c^{3} - 468 \, a^{3} b^{13} c^{4} + 1068 \, a^{4} b^{11} c^{5} - 1461 \, a^{5} b^{9} c^{6} + 1163 \, a^{6} b^{7} c^{7} - 496 \, a^{7} b^{5} c^{8} + 95 \, a^{8} b^{3} c^{9} - 5 \, a^{9} b c^{10}\right)} d e^{5} + {\left(b^{20} - 18 \, a b^{18} c + 137 \, a^{2} b^{16} c^{2} - 574 \, a^{3} b^{14} c^{3} + 1444 \, a^{4} b^{12} c^{4} - 2232 \, a^{5} b^{10} c^{5} + 2083 \, a^{6} b^{8} c^{6} - 1106 \, a^{7} b^{6} c^{7} + 295 \, a^{8} b^{4} c^{8} - 30 \, a^{9} b^{2} c^{9} + a^{10} c^{10}\right)} e^{6}}{b^{2} c^{22} - 4 \, a c^{23}}}}{b^{2} c^{11} - 4 \, a c^{12}}} \log\left(\sqrt{2} {\left({\left(b^{12} c^{4} - 12 \, a b^{10} c^{5} + 54 \, a^{2} b^{8} c^{6} - 112 \, a^{3} b^{6} c^{7} + 104 \, a^{4} b^{4} c^{8} - 32 \, a^{5} b^{2} c^{9}\right)} d^{4} - {\left(4 \, b^{13} c^{3} - 52 \, a b^{11} c^{4} + 260 \, a^{2} b^{9} c^{5} - 624 \, a^{3} b^{7} c^{6} + 725 \, a^{4} b^{5} c^{7} - 350 \, a^{5} b^{3} c^{8} + 40 \, a^{6} b c^{9}\right)} d^{3} e + 3 \, {\left(2 \, b^{14} c^{2} - 28 \, a b^{12} c^{3} + 154 \, a^{2} b^{10} c^{4} - 420 \, a^{3} b^{8} c^{5} + 587 \, a^{4} b^{6} c^{6} - 387 \, a^{5} b^{4} c^{7} + 93 \, a^{6} b^{2} c^{8} - 4 \, a^{7} c^{9}\right)} d^{2} e^{2} - {\left(4 \, b^{15} c - 60 \, a b^{13} c^{2} + 360 \, a^{2} b^{11} c^{3} - 1100 \, a^{3} b^{9} c^{4} + 1799 \, a^{4} b^{7} c^{5} - 1508 \, a^{5} b^{5} c^{6} + 561 \, a^{6} b^{3} c^{7} - 68 \, a^{7} b c^{8}\right)} d e^{3} + {\left(b^{16} - 16 \, a b^{14} c + 104 \, a^{2} b^{12} c^{2} - 352 \, a^{3} b^{10} c^{3} + 660 \, a^{4} b^{8} c^{4} - 673 \, a^{5} b^{6} c^{5} + 342 \, a^{6} b^{4} c^{6} - 73 \, a^{7} b^{2} c^{7} + 4 \, a^{8} c^{8}\right)} e^{4} - {\left({\left(b^{6} c^{12} - 8 \, a b^{4} c^{13} + 18 \, a^{2} b^{2} c^{14} - 8 \, a^{3} c^{15}\right)} d - {\left(b^{7} c^{11} - 9 \, a b^{5} c^{12} + 25 \, a^{2} b^{3} c^{13} - 20 \, a^{3} b c^{14}\right)} e\right)} \sqrt{\frac{{\left(b^{14} c^{6} - 12 \, a b^{12} c^{7} + 56 \, a^{2} b^{10} c^{8} - 128 \, a^{3} b^{8} c^{9} + 148 \, a^{4} b^{6} c^{10} - 80 \, a^{5} b^{4} c^{11} + 16 \, a^{6} b^{2} c^{12}\right)} d^{6} - 6 \, {\left(b^{15} c^{5} - 13 \, a b^{13} c^{6} + 67 \, a^{2} b^{11} c^{7} - 174 \, a^{3} b^{9} c^{8} + 239 \, a^{4} b^{7} c^{9} - 166 \, a^{5} b^{5} c^{10} + 50 \, a^{6} b^{3} c^{11} - 4 \, a^{7} b c^{12}\right)} d^{5} e + 3 \, {\left(5 \, b^{16} c^{4} - 70 \, a b^{14} c^{5} + 395 \, a^{2} b^{12} c^{6} - 1150 \, a^{3} b^{10} c^{7} + 1835 \, a^{4} b^{8} c^{8} - 1570 \, a^{5} b^{6} c^{9} + 650 \, a^{6} b^{4} c^{10} - 100 \, a^{7} b^{2} c^{11} + 3 \, a^{8} c^{12}\right)} d^{4} e^{2} - 2 \, {\left(10 \, b^{17} c^{3} - 150 \, a b^{15} c^{4} + 920 \, a^{2} b^{13} c^{5} - 2970 \, a^{3} b^{11} c^{6} + 5410 \, a^{4} b^{9} c^{7} - 5530 \, a^{5} b^{7} c^{8} + 2960 \, a^{6} b^{5} c^{9} - 700 \, a^{7} b^{3} c^{10} + 49 \, a^{8} b c^{11}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{18} c^{2} - 80 \, a b^{16} c^{3} + 530 \, a^{2} b^{14} c^{4} - 1880 \, a^{3} b^{12} c^{5} + 3855 \, a^{4} b^{10} c^{6} - 4600 \, a^{5} b^{8} c^{7} + 3050 \, a^{6} b^{6} c^{8} - 1000 \, a^{7} b^{4} c^{9} + 125 \, a^{8} b^{2} c^{10} - 2 \, a^{9} c^{11}\right)} d^{2} e^{4} - 6 \, {\left(b^{19} c - 17 \, a b^{17} c^{2} + 121 \, a^{2} b^{15} c^{3} - 468 \, a^{3} b^{13} c^{4} + 1068 \, a^{4} b^{11} c^{5} - 1461 \, a^{5} b^{9} c^{6} + 1163 \, a^{6} b^{7} c^{7} - 496 \, a^{7} b^{5} c^{8} + 95 \, a^{8} b^{3} c^{9} - 5 \, a^{9} b c^{10}\right)} d e^{5} + {\left(b^{20} - 18 \, a b^{18} c + 137 \, a^{2} b^{16} c^{2} - 574 \, a^{3} b^{14} c^{3} + 1444 \, a^{4} b^{12} c^{4} - 2232 \, a^{5} b^{10} c^{5} + 2083 \, a^{6} b^{8} c^{6} - 1106 \, a^{7} b^{6} c^{7} + 295 \, a^{8} b^{4} c^{8} - 30 \, a^{9} b^{2} c^{9} + a^{10} c^{10}\right)} e^{6}}{b^{2} c^{22} - 4 \, a c^{23}}}\right)} \sqrt{\frac{{\left(b^{8} c^{3} - 8 \, a b^{6} c^{4} + 20 \, a^{2} b^{4} c^{5} - 16 \, a^{3} b^{2} c^{6} + 2 \, a^{4} c^{7}\right)} d^{3} - 3 \, {\left(b^{9} c^{2} - 9 \, a b^{7} c^{3} + 27 \, a^{2} b^{5} c^{4} - 30 \, a^{3} b^{3} c^{5} + 9 \, a^{4} b c^{6}\right)} d^{2} e + 3 \, {\left(b^{10} c - 10 \, a b^{8} c^{2} + 35 \, a^{2} b^{6} c^{3} - 50 \, a^{3} b^{4} c^{4} + 25 \, a^{4} b^{2} c^{5} - 2 \, a^{5} c^{6}\right)} d e^{2} - {\left(b^{11} - 11 \, a b^{9} c + 44 \, a^{2} b^{7} c^{2} - 77 \, a^{3} b^{5} c^{3} + 55 \, a^{4} b^{3} c^{4} - 11 \, a^{5} b c^{5}\right)} e^{3} + {\left(b^{2} c^{11} - 4 \, a c^{12}\right)} \sqrt{\frac{{\left(b^{14} c^{6} - 12 \, a b^{12} c^{7} + 56 \, a^{2} b^{10} c^{8} - 128 \, a^{3} b^{8} c^{9} + 148 \, a^{4} b^{6} c^{10} - 80 \, a^{5} b^{4} c^{11} + 16 \, a^{6} b^{2} c^{12}\right)} d^{6} - 6 \, {\left(b^{15} c^{5} - 13 \, a b^{13} c^{6} + 67 \, a^{2} b^{11} c^{7} - 174 \, a^{3} b^{9} c^{8} + 239 \, a^{4} b^{7} c^{9} - 166 \, a^{5} b^{5} c^{10} + 50 \, a^{6} b^{3} c^{11} - 4 \, a^{7} b c^{12}\right)} d^{5} e + 3 \, {\left(5 \, b^{16} c^{4} - 70 \, a b^{14} c^{5} + 395 \, a^{2} b^{12} c^{6} - 1150 \, a^{3} b^{10} c^{7} + 1835 \, a^{4} b^{8} c^{8} - 1570 \, a^{5} b^{6} c^{9} + 650 \, a^{6} b^{4} c^{10} - 100 \, a^{7} b^{2} c^{11} + 3 \, a^{8} c^{12}\right)} d^{4} e^{2} - 2 \, {\left(10 \, b^{17} c^{3} - 150 \, a b^{15} c^{4} + 920 \, a^{2} b^{13} c^{5} - 2970 \, a^{3} b^{11} c^{6} + 5410 \, a^{4} b^{9} c^{7} - 5530 \, a^{5} b^{7} c^{8} + 2960 \, a^{6} b^{5} c^{9} - 700 \, a^{7} b^{3} c^{10} + 49 \, a^{8} b c^{11}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{18} c^{2} - 80 \, a b^{16} c^{3} + 530 \, a^{2} b^{14} c^{4} - 1880 \, a^{3} b^{12} c^{5} + 3855 \, a^{4} b^{10} c^{6} - 4600 \, a^{5} b^{8} c^{7} + 3050 \, a^{6} b^{6} c^{8} - 1000 \, a^{7} b^{4} c^{9} + 125 \, a^{8} b^{2} c^{10} - 2 \, a^{9} c^{11}\right)} d^{2} e^{4} - 6 \, {\left(b^{19} c - 17 \, a b^{17} c^{2} + 121 \, a^{2} b^{15} c^{3} - 468 \, a^{3} b^{13} c^{4} + 1068 \, a^{4} b^{11} c^{5} - 1461 \, a^{5} b^{9} c^{6} + 1163 \, a^{6} b^{7} c^{7} - 496 \, a^{7} b^{5} c^{8} + 95 \, a^{8} b^{3} c^{9} - 5 \, a^{9} b c^{10}\right)} d e^{5} + {\left(b^{20} - 18 \, a b^{18} c + 137 \, a^{2} b^{16} c^{2} - 574 \, a^{3} b^{14} c^{3} + 1444 \, a^{4} b^{12} c^{4} - 2232 \, a^{5} b^{10} c^{5} + 2083 \, a^{6} b^{8} c^{6} - 1106 \, a^{7} b^{6} c^{7} + 295 \, a^{8} b^{4} c^{8} - 30 \, a^{9} b^{2} c^{9} + a^{10} c^{10}\right)} e^{6}}{b^{2} c^{22} - 4 \, a c^{23}}}}{b^{2} c^{11} - 4 \, a c^{12}}} + 4 \, {\left({\left(a^{4} b^{7} c^{4} - 6 \, a^{5} b^{5} c^{5} + 10 \, a^{6} b^{3} c^{6} - 4 \, a^{7} b c^{7}\right)} d^{5} - {\left(4 \, a^{4} b^{8} c^{3} - 27 \, a^{5} b^{6} c^{4} + 55 \, a^{6} b^{4} c^{5} - 34 \, a^{7} b^{2} c^{6} + 3 \, a^{8} c^{7}\right)} d^{4} e + 2 \, {\left(3 \, a^{4} b^{9} c^{2} - 22 \, a^{5} b^{7} c^{3} + 51 \, a^{6} b^{5} c^{4} - 40 \, a^{7} b^{3} c^{5} + 7 \, a^{8} b c^{6}\right)} d^{3} e^{2} - 2 \, {\left(2 \, a^{4} b^{10} c - 15 \, a^{5} b^{8} c^{2} + 35 \, a^{6} b^{6} c^{3} - 25 \, a^{7} b^{4} c^{4} + a^{9} c^{6}\right)} d^{2} e^{3} + {\left(a^{4} b^{11} - 6 \, a^{5} b^{9} c + 4 \, a^{6} b^{7} c^{2} + 28 \, a^{7} b^{5} c^{3} - 45 \, a^{8} b^{3} c^{4} + 14 \, a^{9} b c^{5}\right)} d e^{4} - {\left(a^{5} b^{10} - 9 \, a^{6} b^{8} c + 28 \, a^{7} b^{6} c^{2} - 35 \, a^{8} b^{4} c^{3} + 15 \, a^{9} b^{2} c^{4} - a^{10} c^{5}\right)} e^{5}\right)} \sqrt{e x + d}\right) - 315 \, \sqrt{2} c^{5} e^{3} \sqrt{\frac{{\left(b^{8} c^{3} - 8 \, a b^{6} c^{4} + 20 \, a^{2} b^{4} c^{5} - 16 \, a^{3} b^{2} c^{6} + 2 \, a^{4} c^{7}\right)} d^{3} - 3 \, {\left(b^{9} c^{2} - 9 \, a b^{7} c^{3} + 27 \, a^{2} b^{5} c^{4} - 30 \, a^{3} b^{3} c^{5} + 9 \, a^{4} b c^{6}\right)} d^{2} e + 3 \, {\left(b^{10} c - 10 \, a b^{8} c^{2} + 35 \, a^{2} b^{6} c^{3} - 50 \, a^{3} b^{4} c^{4} + 25 \, a^{4} b^{2} c^{5} - 2 \, a^{5} c^{6}\right)} d e^{2} - {\left(b^{11} - 11 \, a b^{9} c + 44 \, a^{2} b^{7} c^{2} - 77 \, a^{3} b^{5} c^{3} + 55 \, a^{4} b^{3} c^{4} - 11 \, a^{5} b c^{5}\right)} e^{3} + {\left(b^{2} c^{11} - 4 \, a c^{12}\right)} \sqrt{\frac{{\left(b^{14} c^{6} - 12 \, a b^{12} c^{7} + 56 \, a^{2} b^{10} c^{8} - 128 \, a^{3} b^{8} c^{9} + 148 \, a^{4} b^{6} c^{10} - 80 \, a^{5} b^{4} c^{11} + 16 \, a^{6} b^{2} c^{12}\right)} d^{6} - 6 \, {\left(b^{15} c^{5} - 13 \, a b^{13} c^{6} + 67 \, a^{2} b^{11} c^{7} - 174 \, a^{3} b^{9} c^{8} + 239 \, a^{4} b^{7} c^{9} - 166 \, a^{5} b^{5} c^{10} + 50 \, a^{6} b^{3} c^{11} - 4 \, a^{7} b c^{12}\right)} d^{5} e + 3 \, {\left(5 \, b^{16} c^{4} - 70 \, a b^{14} c^{5} + 395 \, a^{2} b^{12} c^{6} - 1150 \, a^{3} b^{10} c^{7} + 1835 \, a^{4} b^{8} c^{8} - 1570 \, a^{5} b^{6} c^{9} + 650 \, a^{6} b^{4} c^{10} - 100 \, a^{7} b^{2} c^{11} + 3 \, a^{8} c^{12}\right)} d^{4} e^{2} - 2 \, {\left(10 \, b^{17} c^{3} - 150 \, a b^{15} c^{4} + 920 \, a^{2} b^{13} c^{5} - 2970 \, a^{3} b^{11} c^{6} + 5410 \, a^{4} b^{9} c^{7} - 5530 \, a^{5} b^{7} c^{8} + 2960 \, a^{6} b^{5} c^{9} - 700 \, a^{7} b^{3} c^{10} + 49 \, a^{8} b c^{11}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{18} c^{2} - 80 \, a b^{16} c^{3} + 530 \, a^{2} b^{14} c^{4} - 1880 \, a^{3} b^{12} c^{5} + 3855 \, a^{4} b^{10} c^{6} - 4600 \, a^{5} b^{8} c^{7} + 3050 \, a^{6} b^{6} c^{8} - 1000 \, a^{7} b^{4} c^{9} + 125 \, a^{8} b^{2} c^{10} - 2 \, a^{9} c^{11}\right)} d^{2} e^{4} - 6 \, {\left(b^{19} c - 17 \, a b^{17} c^{2} + 121 \, a^{2} b^{15} c^{3} - 468 \, a^{3} b^{13} c^{4} + 1068 \, a^{4} b^{11} c^{5} - 1461 \, a^{5} b^{9} c^{6} + 1163 \, a^{6} b^{7} c^{7} - 496 \, a^{7} b^{5} c^{8} + 95 \, a^{8} b^{3} c^{9} - 5 \, a^{9} b c^{10}\right)} d e^{5} + {\left(b^{20} - 18 \, a b^{18} c + 137 \, a^{2} b^{16} c^{2} - 574 \, a^{3} b^{14} c^{3} + 1444 \, a^{4} b^{12} c^{4} - 2232 \, a^{5} b^{10} c^{5} + 2083 \, a^{6} b^{8} c^{6} - 1106 \, a^{7} b^{6} c^{7} + 295 \, a^{8} b^{4} c^{8} - 30 \, a^{9} b^{2} c^{9} + a^{10} c^{10}\right)} e^{6}}{b^{2} c^{22} - 4 \, a c^{23}}}}{b^{2} c^{11} - 4 \, a c^{12}}} \log\left(-\sqrt{2} {\left({\left(b^{12} c^{4} - 12 \, a b^{10} c^{5} + 54 \, a^{2} b^{8} c^{6} - 112 \, a^{3} b^{6} c^{7} + 104 \, a^{4} b^{4} c^{8} - 32 \, a^{5} b^{2} c^{9}\right)} d^{4} - {\left(4 \, b^{13} c^{3} - 52 \, a b^{11} c^{4} + 260 \, a^{2} b^{9} c^{5} - 624 \, a^{3} b^{7} c^{6} + 725 \, a^{4} b^{5} c^{7} - 350 \, a^{5} b^{3} c^{8} + 40 \, a^{6} b c^{9}\right)} d^{3} e + 3 \, {\left(2 \, b^{14} c^{2} - 28 \, a b^{12} c^{3} + 154 \, a^{2} b^{10} c^{4} - 420 \, a^{3} b^{8} c^{5} + 587 \, a^{4} b^{6} c^{6} - 387 \, a^{5} b^{4} c^{7} + 93 \, a^{6} b^{2} c^{8} - 4 \, a^{7} c^{9}\right)} d^{2} e^{2} - {\left(4 \, b^{15} c - 60 \, a b^{13} c^{2} + 360 \, a^{2} b^{11} c^{3} - 1100 \, a^{3} b^{9} c^{4} + 1799 \, a^{4} b^{7} c^{5} - 1508 \, a^{5} b^{5} c^{6} + 561 \, a^{6} b^{3} c^{7} - 68 \, a^{7} b c^{8}\right)} d e^{3} + {\left(b^{16} - 16 \, a b^{14} c + 104 \, a^{2} b^{12} c^{2} - 352 \, a^{3} b^{10} c^{3} + 660 \, a^{4} b^{8} c^{4} - 673 \, a^{5} b^{6} c^{5} + 342 \, a^{6} b^{4} c^{6} - 73 \, a^{7} b^{2} c^{7} + 4 \, a^{8} c^{8}\right)} e^{4} - {\left({\left(b^{6} c^{12} - 8 \, a b^{4} c^{13} + 18 \, a^{2} b^{2} c^{14} - 8 \, a^{3} c^{15}\right)} d - {\left(b^{7} c^{11} - 9 \, a b^{5} c^{12} + 25 \, a^{2} b^{3} c^{13} - 20 \, a^{3} b c^{14}\right)} e\right)} \sqrt{\frac{{\left(b^{14} c^{6} - 12 \, a b^{12} c^{7} + 56 \, a^{2} b^{10} c^{8} - 128 \, a^{3} b^{8} c^{9} + 148 \, a^{4} b^{6} c^{10} - 80 \, a^{5} b^{4} c^{11} + 16 \, a^{6} b^{2} c^{12}\right)} d^{6} - 6 \, {\left(b^{15} c^{5} - 13 \, a b^{13} c^{6} + 67 \, a^{2} b^{11} c^{7} - 174 \, a^{3} b^{9} c^{8} + 239 \, a^{4} b^{7} c^{9} - 166 \, a^{5} b^{5} c^{10} + 50 \, a^{6} b^{3} c^{11} - 4 \, a^{7} b c^{12}\right)} d^{5} e + 3 \, {\left(5 \, b^{16} c^{4} - 70 \, a b^{14} c^{5} + 395 \, a^{2} b^{12} c^{6} - 1150 \, a^{3} b^{10} c^{7} + 1835 \, a^{4} b^{8} c^{8} - 1570 \, a^{5} b^{6} c^{9} + 650 \, a^{6} b^{4} c^{10} - 100 \, a^{7} b^{2} c^{11} + 3 \, a^{8} c^{12}\right)} d^{4} e^{2} - 2 \, {\left(10 \, b^{17} c^{3} - 150 \, a b^{15} c^{4} + 920 \, a^{2} b^{13} c^{5} - 2970 \, a^{3} b^{11} c^{6} + 5410 \, a^{4} b^{9} c^{7} - 5530 \, a^{5} b^{7} c^{8} + 2960 \, a^{6} b^{5} c^{9} - 700 \, a^{7} b^{3} c^{10} + 49 \, a^{8} b c^{11}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{18} c^{2} - 80 \, a b^{16} c^{3} + 530 \, a^{2} b^{14} c^{4} - 1880 \, a^{3} b^{12} c^{5} + 3855 \, a^{4} b^{10} c^{6} - 4600 \, a^{5} b^{8} c^{7} + 3050 \, a^{6} b^{6} c^{8} - 1000 \, a^{7} b^{4} c^{9} + 125 \, a^{8} b^{2} c^{10} - 2 \, a^{9} c^{11}\right)} d^{2} e^{4} - 6 \, {\left(b^{19} c - 17 \, a b^{17} c^{2} + 121 \, a^{2} b^{15} c^{3} - 468 \, a^{3} b^{13} c^{4} + 1068 \, a^{4} b^{11} c^{5} - 1461 \, a^{5} b^{9} c^{6} + 1163 \, a^{6} b^{7} c^{7} - 496 \, a^{7} b^{5} c^{8} + 95 \, a^{8} b^{3} c^{9} - 5 \, a^{9} b c^{10}\right)} d e^{5} + {\left(b^{20} - 18 \, a b^{18} c + 137 \, a^{2} b^{16} c^{2} - 574 \, a^{3} b^{14} c^{3} + 1444 \, a^{4} b^{12} c^{4} - 2232 \, a^{5} b^{10} c^{5} + 2083 \, a^{6} b^{8} c^{6} - 1106 \, a^{7} b^{6} c^{7} + 295 \, a^{8} b^{4} c^{8} - 30 \, a^{9} b^{2} c^{9} + a^{10} c^{10}\right)} e^{6}}{b^{2} c^{22} - 4 \, a c^{23}}}\right)} \sqrt{\frac{{\left(b^{8} c^{3} - 8 \, a b^{6} c^{4} + 20 \, a^{2} b^{4} c^{5} - 16 \, a^{3} b^{2} c^{6} + 2 \, a^{4} c^{7}\right)} d^{3} - 3 \, {\left(b^{9} c^{2} - 9 \, a b^{7} c^{3} + 27 \, a^{2} b^{5} c^{4} - 30 \, a^{3} b^{3} c^{5} + 9 \, a^{4} b c^{6}\right)} d^{2} e + 3 \, {\left(b^{10} c - 10 \, a b^{8} c^{2} + 35 \, a^{2} b^{6} c^{3} - 50 \, a^{3} b^{4} c^{4} + 25 \, a^{4} b^{2} c^{5} - 2 \, a^{5} c^{6}\right)} d e^{2} - {\left(b^{11} - 11 \, a b^{9} c + 44 \, a^{2} b^{7} c^{2} - 77 \, a^{3} b^{5} c^{3} + 55 \, a^{4} b^{3} c^{4} - 11 \, a^{5} b c^{5}\right)} e^{3} + {\left(b^{2} c^{11} - 4 \, a c^{12}\right)} \sqrt{\frac{{\left(b^{14} c^{6} - 12 \, a b^{12} c^{7} + 56 \, a^{2} b^{10} c^{8} - 128 \, a^{3} b^{8} c^{9} + 148 \, a^{4} b^{6} c^{10} - 80 \, a^{5} b^{4} c^{11} + 16 \, a^{6} b^{2} c^{12}\right)} d^{6} - 6 \, {\left(b^{15} c^{5} - 13 \, a b^{13} c^{6} + 67 \, a^{2} b^{11} c^{7} - 174 \, a^{3} b^{9} c^{8} + 239 \, a^{4} b^{7} c^{9} - 166 \, a^{5} b^{5} c^{10} + 50 \, a^{6} b^{3} c^{11} - 4 \, a^{7} b c^{12}\right)} d^{5} e + 3 \, {\left(5 \, b^{16} c^{4} - 70 \, a b^{14} c^{5} + 395 \, a^{2} b^{12} c^{6} - 1150 \, a^{3} b^{10} c^{7} + 1835 \, a^{4} b^{8} c^{8} - 1570 \, a^{5} b^{6} c^{9} + 650 \, a^{6} b^{4} c^{10} - 100 \, a^{7} b^{2} c^{11} + 3 \, a^{8} c^{12}\right)} d^{4} e^{2} - 2 \, {\left(10 \, b^{17} c^{3} - 150 \, a b^{15} c^{4} + 920 \, a^{2} b^{13} c^{5} - 2970 \, a^{3} b^{11} c^{6} + 5410 \, a^{4} b^{9} c^{7} - 5530 \, a^{5} b^{7} c^{8} + 2960 \, a^{6} b^{5} c^{9} - 700 \, a^{7} b^{3} c^{10} + 49 \, a^{8} b c^{11}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{18} c^{2} - 80 \, a b^{16} c^{3} + 530 \, a^{2} b^{14} c^{4} - 1880 \, a^{3} b^{12} c^{5} + 3855 \, a^{4} b^{10} c^{6} - 4600 \, a^{5} b^{8} c^{7} + 3050 \, a^{6} b^{6} c^{8} - 1000 \, a^{7} b^{4} c^{9} + 125 \, a^{8} b^{2} c^{10} - 2 \, a^{9} c^{11}\right)} d^{2} e^{4} - 6 \, {\left(b^{19} c - 17 \, a b^{17} c^{2} + 121 \, a^{2} b^{15} c^{3} - 468 \, a^{3} b^{13} c^{4} + 1068 \, a^{4} b^{11} c^{5} - 1461 \, a^{5} b^{9} c^{6} + 1163 \, a^{6} b^{7} c^{7} - 496 \, a^{7} b^{5} c^{8} + 95 \, a^{8} b^{3} c^{9} - 5 \, a^{9} b c^{10}\right)} d e^{5} + {\left(b^{20} - 18 \, a b^{18} c + 137 \, a^{2} b^{16} c^{2} - 574 \, a^{3} b^{14} c^{3} + 1444 \, a^{4} b^{12} c^{4} - 2232 \, a^{5} b^{10} c^{5} + 2083 \, a^{6} b^{8} c^{6} - 1106 \, a^{7} b^{6} c^{7} + 295 \, a^{8} b^{4} c^{8} - 30 \, a^{9} b^{2} c^{9} + a^{10} c^{10}\right)} e^{6}}{b^{2} c^{22} - 4 \, a c^{23}}}}{b^{2} c^{11} - 4 \, a c^{12}}} + 4 \, {\left({\left(a^{4} b^{7} c^{4} - 6 \, a^{5} b^{5} c^{5} + 10 \, a^{6} b^{3} c^{6} - 4 \, a^{7} b c^{7}\right)} d^{5} - {\left(4 \, a^{4} b^{8} c^{3} - 27 \, a^{5} b^{6} c^{4} + 55 \, a^{6} b^{4} c^{5} - 34 \, a^{7} b^{2} c^{6} + 3 \, a^{8} c^{7}\right)} d^{4} e + 2 \, {\left(3 \, a^{4} b^{9} c^{2} - 22 \, a^{5} b^{7} c^{3} + 51 \, a^{6} b^{5} c^{4} - 40 \, a^{7} b^{3} c^{5} + 7 \, a^{8} b c^{6}\right)} d^{3} e^{2} - 2 \, {\left(2 \, a^{4} b^{10} c - 15 \, a^{5} b^{8} c^{2} + 35 \, a^{6} b^{6} c^{3} - 25 \, a^{7} b^{4} c^{4} + a^{9} c^{6}\right)} d^{2} e^{3} + {\left(a^{4} b^{11} - 6 \, a^{5} b^{9} c + 4 \, a^{6} b^{7} c^{2} + 28 \, a^{7} b^{5} c^{3} - 45 \, a^{8} b^{3} c^{4} + 14 \, a^{9} b c^{5}\right)} d e^{4} - {\left(a^{5} b^{10} - 9 \, a^{6} b^{8} c + 28 \, a^{7} b^{6} c^{2} - 35 \, a^{8} b^{4} c^{3} + 15 \, a^{9} b^{2} c^{4} - a^{10} c^{5}\right)} e^{5}\right)} \sqrt{e x + d}\right) + 315 \, \sqrt{2} c^{5} e^{3} \sqrt{\frac{{\left(b^{8} c^{3} - 8 \, a b^{6} c^{4} + 20 \, a^{2} b^{4} c^{5} - 16 \, a^{3} b^{2} c^{6} + 2 \, a^{4} c^{7}\right)} d^{3} - 3 \, {\left(b^{9} c^{2} - 9 \, a b^{7} c^{3} + 27 \, a^{2} b^{5} c^{4} - 30 \, a^{3} b^{3} c^{5} + 9 \, a^{4} b c^{6}\right)} d^{2} e + 3 \, {\left(b^{10} c - 10 \, a b^{8} c^{2} + 35 \, a^{2} b^{6} c^{3} - 50 \, a^{3} b^{4} c^{4} + 25 \, a^{4} b^{2} c^{5} - 2 \, a^{5} c^{6}\right)} d e^{2} - {\left(b^{11} - 11 \, a b^{9} c + 44 \, a^{2} b^{7} c^{2} - 77 \, a^{3} b^{5} c^{3} + 55 \, a^{4} b^{3} c^{4} - 11 \, a^{5} b c^{5}\right)} e^{3} - {\left(b^{2} c^{11} - 4 \, a c^{12}\right)} \sqrt{\frac{{\left(b^{14} c^{6} - 12 \, a b^{12} c^{7} + 56 \, a^{2} b^{10} c^{8} - 128 \, a^{3} b^{8} c^{9} + 148 \, a^{4} b^{6} c^{10} - 80 \, a^{5} b^{4} c^{11} + 16 \, a^{6} b^{2} c^{12}\right)} d^{6} - 6 \, {\left(b^{15} c^{5} - 13 \, a b^{13} c^{6} + 67 \, a^{2} b^{11} c^{7} - 174 \, a^{3} b^{9} c^{8} + 239 \, a^{4} b^{7} c^{9} - 166 \, a^{5} b^{5} c^{10} + 50 \, a^{6} b^{3} c^{11} - 4 \, a^{7} b c^{12}\right)} d^{5} e + 3 \, {\left(5 \, b^{16} c^{4} - 70 \, a b^{14} c^{5} + 395 \, a^{2} b^{12} c^{6} - 1150 \, a^{3} b^{10} c^{7} + 1835 \, a^{4} b^{8} c^{8} - 1570 \, a^{5} b^{6} c^{9} + 650 \, a^{6} b^{4} c^{10} - 100 \, a^{7} b^{2} c^{11} + 3 \, a^{8} c^{12}\right)} d^{4} e^{2} - 2 \, {\left(10 \, b^{17} c^{3} - 150 \, a b^{15} c^{4} + 920 \, a^{2} b^{13} c^{5} - 2970 \, a^{3} b^{11} c^{6} + 5410 \, a^{4} b^{9} c^{7} - 5530 \, a^{5} b^{7} c^{8} + 2960 \, a^{6} b^{5} c^{9} - 700 \, a^{7} b^{3} c^{10} + 49 \, a^{8} b c^{11}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{18} c^{2} - 80 \, a b^{16} c^{3} + 530 \, a^{2} b^{14} c^{4} - 1880 \, a^{3} b^{12} c^{5} + 3855 \, a^{4} b^{10} c^{6} - 4600 \, a^{5} b^{8} c^{7} + 3050 \, a^{6} b^{6} c^{8} - 1000 \, a^{7} b^{4} c^{9} + 125 \, a^{8} b^{2} c^{10} - 2 \, a^{9} c^{11}\right)} d^{2} e^{4} - 6 \, {\left(b^{19} c - 17 \, a b^{17} c^{2} + 121 \, a^{2} b^{15} c^{3} - 468 \, a^{3} b^{13} c^{4} + 1068 \, a^{4} b^{11} c^{5} - 1461 \, a^{5} b^{9} c^{6} + 1163 \, a^{6} b^{7} c^{7} - 496 \, a^{7} b^{5} c^{8} + 95 \, a^{8} b^{3} c^{9} - 5 \, a^{9} b c^{10}\right)} d e^{5} + {\left(b^{20} - 18 \, a b^{18} c + 137 \, a^{2} b^{16} c^{2} - 574 \, a^{3} b^{14} c^{3} + 1444 \, a^{4} b^{12} c^{4} - 2232 \, a^{5} b^{10} c^{5} + 2083 \, a^{6} b^{8} c^{6} - 1106 \, a^{7} b^{6} c^{7} + 295 \, a^{8} b^{4} c^{8} - 30 \, a^{9} b^{2} c^{9} + a^{10} c^{10}\right)} e^{6}}{b^{2} c^{22} - 4 \, a c^{23}}}}{b^{2} c^{11} - 4 \, a c^{12}}} \log\left(\sqrt{2} {\left({\left(b^{12} c^{4} - 12 \, a b^{10} c^{5} + 54 \, a^{2} b^{8} c^{6} - 112 \, a^{3} b^{6} c^{7} + 104 \, a^{4} b^{4} c^{8} - 32 \, a^{5} b^{2} c^{9}\right)} d^{4} - {\left(4 \, b^{13} c^{3} - 52 \, a b^{11} c^{4} + 260 \, a^{2} b^{9} c^{5} - 624 \, a^{3} b^{7} c^{6} + 725 \, a^{4} b^{5} c^{7} - 350 \, a^{5} b^{3} c^{8} + 40 \, a^{6} b c^{9}\right)} d^{3} e + 3 \, {\left(2 \, b^{14} c^{2} - 28 \, a b^{12} c^{3} + 154 \, a^{2} b^{10} c^{4} - 420 \, a^{3} b^{8} c^{5} + 587 \, a^{4} b^{6} c^{6} - 387 \, a^{5} b^{4} c^{7} + 93 \, a^{6} b^{2} c^{8} - 4 \, a^{7} c^{9}\right)} d^{2} e^{2} - {\left(4 \, b^{15} c - 60 \, a b^{13} c^{2} + 360 \, a^{2} b^{11} c^{3} - 1100 \, a^{3} b^{9} c^{4} + 1799 \, a^{4} b^{7} c^{5} - 1508 \, a^{5} b^{5} c^{6} + 561 \, a^{6} b^{3} c^{7} - 68 \, a^{7} b c^{8}\right)} d e^{3} + {\left(b^{16} - 16 \, a b^{14} c + 104 \, a^{2} b^{12} c^{2} - 352 \, a^{3} b^{10} c^{3} + 660 \, a^{4} b^{8} c^{4} - 673 \, a^{5} b^{6} c^{5} + 342 \, a^{6} b^{4} c^{6} - 73 \, a^{7} b^{2} c^{7} + 4 \, a^{8} c^{8}\right)} e^{4} + {\left({\left(b^{6} c^{12} - 8 \, a b^{4} c^{13} + 18 \, a^{2} b^{2} c^{14} - 8 \, a^{3} c^{15}\right)} d - {\left(b^{7} c^{11} - 9 \, a b^{5} c^{12} + 25 \, a^{2} b^{3} c^{13} - 20 \, a^{3} b c^{14}\right)} e\right)} \sqrt{\frac{{\left(b^{14} c^{6} - 12 \, a b^{12} c^{7} + 56 \, a^{2} b^{10} c^{8} - 128 \, a^{3} b^{8} c^{9} + 148 \, a^{4} b^{6} c^{10} - 80 \, a^{5} b^{4} c^{11} + 16 \, a^{6} b^{2} c^{12}\right)} d^{6} - 6 \, {\left(b^{15} c^{5} - 13 \, a b^{13} c^{6} + 67 \, a^{2} b^{11} c^{7} - 174 \, a^{3} b^{9} c^{8} + 239 \, a^{4} b^{7} c^{9} - 166 \, a^{5} b^{5} c^{10} + 50 \, a^{6} b^{3} c^{11} - 4 \, a^{7} b c^{12}\right)} d^{5} e + 3 \, {\left(5 \, b^{16} c^{4} - 70 \, a b^{14} c^{5} + 395 \, a^{2} b^{12} c^{6} - 1150 \, a^{3} b^{10} c^{7} + 1835 \, a^{4} b^{8} c^{8} - 1570 \, a^{5} b^{6} c^{9} + 650 \, a^{6} b^{4} c^{10} - 100 \, a^{7} b^{2} c^{11} + 3 \, a^{8} c^{12}\right)} d^{4} e^{2} - 2 \, {\left(10 \, b^{17} c^{3} - 150 \, a b^{15} c^{4} + 920 \, a^{2} b^{13} c^{5} - 2970 \, a^{3} b^{11} c^{6} + 5410 \, a^{4} b^{9} c^{7} - 5530 \, a^{5} b^{7} c^{8} + 2960 \, a^{6} b^{5} c^{9} - 700 \, a^{7} b^{3} c^{10} + 49 \, a^{8} b c^{11}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{18} c^{2} - 80 \, a b^{16} c^{3} + 530 \, a^{2} b^{14} c^{4} - 1880 \, a^{3} b^{12} c^{5} + 3855 \, a^{4} b^{10} c^{6} - 4600 \, a^{5} b^{8} c^{7} + 3050 \, a^{6} b^{6} c^{8} - 1000 \, a^{7} b^{4} c^{9} + 125 \, a^{8} b^{2} c^{10} - 2 \, a^{9} c^{11}\right)} d^{2} e^{4} - 6 \, {\left(b^{19} c - 17 \, a b^{17} c^{2} + 121 \, a^{2} b^{15} c^{3} - 468 \, a^{3} b^{13} c^{4} + 1068 \, a^{4} b^{11} c^{5} - 1461 \, a^{5} b^{9} c^{6} + 1163 \, a^{6} b^{7} c^{7} - 496 \, a^{7} b^{5} c^{8} + 95 \, a^{8} b^{3} c^{9} - 5 \, a^{9} b c^{10}\right)} d e^{5} + {\left(b^{20} - 18 \, a b^{18} c + 137 \, a^{2} b^{16} c^{2} - 574 \, a^{3} b^{14} c^{3} + 1444 \, a^{4} b^{12} c^{4} - 2232 \, a^{5} b^{10} c^{5} + 2083 \, a^{6} b^{8} c^{6} - 1106 \, a^{7} b^{6} c^{7} + 295 \, a^{8} b^{4} c^{8} - 30 \, a^{9} b^{2} c^{9} + a^{10} c^{10}\right)} e^{6}}{b^{2} c^{22} - 4 \, a c^{23}}}\right)} \sqrt{\frac{{\left(b^{8} c^{3} - 8 \, a b^{6} c^{4} + 20 \, a^{2} b^{4} c^{5} - 16 \, a^{3} b^{2} c^{6} + 2 \, a^{4} c^{7}\right)} d^{3} - 3 \, {\left(b^{9} c^{2} - 9 \, a b^{7} c^{3} + 27 \, a^{2} b^{5} c^{4} - 30 \, a^{3} b^{3} c^{5} + 9 \, a^{4} b c^{6}\right)} d^{2} e + 3 \, {\left(b^{10} c - 10 \, a b^{8} c^{2} + 35 \, a^{2} b^{6} c^{3} - 50 \, a^{3} b^{4} c^{4} + 25 \, a^{4} b^{2} c^{5} - 2 \, a^{5} c^{6}\right)} d e^{2} - {\left(b^{11} - 11 \, a b^{9} c + 44 \, a^{2} b^{7} c^{2} - 77 \, a^{3} b^{5} c^{3} + 55 \, a^{4} b^{3} c^{4} - 11 \, a^{5} b c^{5}\right)} e^{3} - {\left(b^{2} c^{11} - 4 \, a c^{12}\right)} \sqrt{\frac{{\left(b^{14} c^{6} - 12 \, a b^{12} c^{7} + 56 \, a^{2} b^{10} c^{8} - 128 \, a^{3} b^{8} c^{9} + 148 \, a^{4} b^{6} c^{10} - 80 \, a^{5} b^{4} c^{11} + 16 \, a^{6} b^{2} c^{12}\right)} d^{6} - 6 \, {\left(b^{15} c^{5} - 13 \, a b^{13} c^{6} + 67 \, a^{2} b^{11} c^{7} - 174 \, a^{3} b^{9} c^{8} + 239 \, a^{4} b^{7} c^{9} - 166 \, a^{5} b^{5} c^{10} + 50 \, a^{6} b^{3} c^{11} - 4 \, a^{7} b c^{12}\right)} d^{5} e + 3 \, {\left(5 \, b^{16} c^{4} - 70 \, a b^{14} c^{5} + 395 \, a^{2} b^{12} c^{6} - 1150 \, a^{3} b^{10} c^{7} + 1835 \, a^{4} b^{8} c^{8} - 1570 \, a^{5} b^{6} c^{9} + 650 \, a^{6} b^{4} c^{10} - 100 \, a^{7} b^{2} c^{11} + 3 \, a^{8} c^{12}\right)} d^{4} e^{2} - 2 \, {\left(10 \, b^{17} c^{3} - 150 \, a b^{15} c^{4} + 920 \, a^{2} b^{13} c^{5} - 2970 \, a^{3} b^{11} c^{6} + 5410 \, a^{4} b^{9} c^{7} - 5530 \, a^{5} b^{7} c^{8} + 2960 \, a^{6} b^{5} c^{9} - 700 \, a^{7} b^{3} c^{10} + 49 \, a^{8} b c^{11}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{18} c^{2} - 80 \, a b^{16} c^{3} + 530 \, a^{2} b^{14} c^{4} - 1880 \, a^{3} b^{12} c^{5} + 3855 \, a^{4} b^{10} c^{6} - 4600 \, a^{5} b^{8} c^{7} + 3050 \, a^{6} b^{6} c^{8} - 1000 \, a^{7} b^{4} c^{9} + 125 \, a^{8} b^{2} c^{10} - 2 \, a^{9} c^{11}\right)} d^{2} e^{4} - 6 \, {\left(b^{19} c - 17 \, a b^{17} c^{2} + 121 \, a^{2} b^{15} c^{3} - 468 \, a^{3} b^{13} c^{4} + 1068 \, a^{4} b^{11} c^{5} - 1461 \, a^{5} b^{9} c^{6} + 1163 \, a^{6} b^{7} c^{7} - 496 \, a^{7} b^{5} c^{8} + 95 \, a^{8} b^{3} c^{9} - 5 \, a^{9} b c^{10}\right)} d e^{5} + {\left(b^{20} - 18 \, a b^{18} c + 137 \, a^{2} b^{16} c^{2} - 574 \, a^{3} b^{14} c^{3} + 1444 \, a^{4} b^{12} c^{4} - 2232 \, a^{5} b^{10} c^{5} + 2083 \, a^{6} b^{8} c^{6} - 1106 \, a^{7} b^{6} c^{7} + 295 \, a^{8} b^{4} c^{8} - 30 \, a^{9} b^{2} c^{9} + a^{10} c^{10}\right)} e^{6}}{b^{2} c^{22} - 4 \, a c^{23}}}}{b^{2} c^{11} - 4 \, a c^{12}}} + 4 \, {\left({\left(a^{4} b^{7} c^{4} - 6 \, a^{5} b^{5} c^{5} + 10 \, a^{6} b^{3} c^{6} - 4 \, a^{7} b c^{7}\right)} d^{5} - {\left(4 \, a^{4} b^{8} c^{3} - 27 \, a^{5} b^{6} c^{4} + 55 \, a^{6} b^{4} c^{5} - 34 \, a^{7} b^{2} c^{6} + 3 \, a^{8} c^{7}\right)} d^{4} e + 2 \, {\left(3 \, a^{4} b^{9} c^{2} - 22 \, a^{5} b^{7} c^{3} + 51 \, a^{6} b^{5} c^{4} - 40 \, a^{7} b^{3} c^{5} + 7 \, a^{8} b c^{6}\right)} d^{3} e^{2} - 2 \, {\left(2 \, a^{4} b^{10} c - 15 \, a^{5} b^{8} c^{2} + 35 \, a^{6} b^{6} c^{3} - 25 \, a^{7} b^{4} c^{4} + a^{9} c^{6}\right)} d^{2} e^{3} + {\left(a^{4} b^{11} - 6 \, a^{5} b^{9} c + 4 \, a^{6} b^{7} c^{2} + 28 \, a^{7} b^{5} c^{3} - 45 \, a^{8} b^{3} c^{4} + 14 \, a^{9} b c^{5}\right)} d e^{4} - {\left(a^{5} b^{10} - 9 \, a^{6} b^{8} c + 28 \, a^{7} b^{6} c^{2} - 35 \, a^{8} b^{4} c^{3} + 15 \, a^{9} b^{2} c^{4} - a^{10} c^{5}\right)} e^{5}\right)} \sqrt{e x + d}\right) - 315 \, \sqrt{2} c^{5} e^{3} \sqrt{\frac{{\left(b^{8} c^{3} - 8 \, a b^{6} c^{4} + 20 \, a^{2} b^{4} c^{5} - 16 \, a^{3} b^{2} c^{6} + 2 \, a^{4} c^{7}\right)} d^{3} - 3 \, {\left(b^{9} c^{2} - 9 \, a b^{7} c^{3} + 27 \, a^{2} b^{5} c^{4} - 30 \, a^{3} b^{3} c^{5} + 9 \, a^{4} b c^{6}\right)} d^{2} e + 3 \, {\left(b^{10} c - 10 \, a b^{8} c^{2} + 35 \, a^{2} b^{6} c^{3} - 50 \, a^{3} b^{4} c^{4} + 25 \, a^{4} b^{2} c^{5} - 2 \, a^{5} c^{6}\right)} d e^{2} - {\left(b^{11} - 11 \, a b^{9} c + 44 \, a^{2} b^{7} c^{2} - 77 \, a^{3} b^{5} c^{3} + 55 \, a^{4} b^{3} c^{4} - 11 \, a^{5} b c^{5}\right)} e^{3} - {\left(b^{2} c^{11} - 4 \, a c^{12}\right)} \sqrt{\frac{{\left(b^{14} c^{6} - 12 \, a b^{12} c^{7} + 56 \, a^{2} b^{10} c^{8} - 128 \, a^{3} b^{8} c^{9} + 148 \, a^{4} b^{6} c^{10} - 80 \, a^{5} b^{4} c^{11} + 16 \, a^{6} b^{2} c^{12}\right)} d^{6} - 6 \, {\left(b^{15} c^{5} - 13 \, a b^{13} c^{6} + 67 \, a^{2} b^{11} c^{7} - 174 \, a^{3} b^{9} c^{8} + 239 \, a^{4} b^{7} c^{9} - 166 \, a^{5} b^{5} c^{10} + 50 \, a^{6} b^{3} c^{11} - 4 \, a^{7} b c^{12}\right)} d^{5} e + 3 \, {\left(5 \, b^{16} c^{4} - 70 \, a b^{14} c^{5} + 395 \, a^{2} b^{12} c^{6} - 1150 \, a^{3} b^{10} c^{7} + 1835 \, a^{4} b^{8} c^{8} - 1570 \, a^{5} b^{6} c^{9} + 650 \, a^{6} b^{4} c^{10} - 100 \, a^{7} b^{2} c^{11} + 3 \, a^{8} c^{12}\right)} d^{4} e^{2} - 2 \, {\left(10 \, b^{17} c^{3} - 150 \, a b^{15} c^{4} + 920 \, a^{2} b^{13} c^{5} - 2970 \, a^{3} b^{11} c^{6} + 5410 \, a^{4} b^{9} c^{7} - 5530 \, a^{5} b^{7} c^{8} + 2960 \, a^{6} b^{5} c^{9} - 700 \, a^{7} b^{3} c^{10} + 49 \, a^{8} b c^{11}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{18} c^{2} - 80 \, a b^{16} c^{3} + 530 \, a^{2} b^{14} c^{4} - 1880 \, a^{3} b^{12} c^{5} + 3855 \, a^{4} b^{10} c^{6} - 4600 \, a^{5} b^{8} c^{7} + 3050 \, a^{6} b^{6} c^{8} - 1000 \, a^{7} b^{4} c^{9} + 125 \, a^{8} b^{2} c^{10} - 2 \, a^{9} c^{11}\right)} d^{2} e^{4} - 6 \, {\left(b^{19} c - 17 \, a b^{17} c^{2} + 121 \, a^{2} b^{15} c^{3} - 468 \, a^{3} b^{13} c^{4} + 1068 \, a^{4} b^{11} c^{5} - 1461 \, a^{5} b^{9} c^{6} + 1163 \, a^{6} b^{7} c^{7} - 496 \, a^{7} b^{5} c^{8} + 95 \, a^{8} b^{3} c^{9} - 5 \, a^{9} b c^{10}\right)} d e^{5} + {\left(b^{20} - 18 \, a b^{18} c + 137 \, a^{2} b^{16} c^{2} - 574 \, a^{3} b^{14} c^{3} + 1444 \, a^{4} b^{12} c^{4} - 2232 \, a^{5} b^{10} c^{5} + 2083 \, a^{6} b^{8} c^{6} - 1106 \, a^{7} b^{6} c^{7} + 295 \, a^{8} b^{4} c^{8} - 30 \, a^{9} b^{2} c^{9} + a^{10} c^{10}\right)} e^{6}}{b^{2} c^{22} - 4 \, a c^{23}}}}{b^{2} c^{11} - 4 \, a c^{12}}} \log\left(-\sqrt{2} {\left({\left(b^{12} c^{4} - 12 \, a b^{10} c^{5} + 54 \, a^{2} b^{8} c^{6} - 112 \, a^{3} b^{6} c^{7} + 104 \, a^{4} b^{4} c^{8} - 32 \, a^{5} b^{2} c^{9}\right)} d^{4} - {\left(4 \, b^{13} c^{3} - 52 \, a b^{11} c^{4} + 260 \, a^{2} b^{9} c^{5} - 624 \, a^{3} b^{7} c^{6} + 725 \, a^{4} b^{5} c^{7} - 350 \, a^{5} b^{3} c^{8} + 40 \, a^{6} b c^{9}\right)} d^{3} e + 3 \, {\left(2 \, b^{14} c^{2} - 28 \, a b^{12} c^{3} + 154 \, a^{2} b^{10} c^{4} - 420 \, a^{3} b^{8} c^{5} + 587 \, a^{4} b^{6} c^{6} - 387 \, a^{5} b^{4} c^{7} + 93 \, a^{6} b^{2} c^{8} - 4 \, a^{7} c^{9}\right)} d^{2} e^{2} - {\left(4 \, b^{15} c - 60 \, a b^{13} c^{2} + 360 \, a^{2} b^{11} c^{3} - 1100 \, a^{3} b^{9} c^{4} + 1799 \, a^{4} b^{7} c^{5} - 1508 \, a^{5} b^{5} c^{6} + 561 \, a^{6} b^{3} c^{7} - 68 \, a^{7} b c^{8}\right)} d e^{3} + {\left(b^{16} - 16 \, a b^{14} c + 104 \, a^{2} b^{12} c^{2} - 352 \, a^{3} b^{10} c^{3} + 660 \, a^{4} b^{8} c^{4} - 673 \, a^{5} b^{6} c^{5} + 342 \, a^{6} b^{4} c^{6} - 73 \, a^{7} b^{2} c^{7} + 4 \, a^{8} c^{8}\right)} e^{4} + {\left({\left(b^{6} c^{12} - 8 \, a b^{4} c^{13} + 18 \, a^{2} b^{2} c^{14} - 8 \, a^{3} c^{15}\right)} d - {\left(b^{7} c^{11} - 9 \, a b^{5} c^{12} + 25 \, a^{2} b^{3} c^{13} - 20 \, a^{3} b c^{14}\right)} e\right)} \sqrt{\frac{{\left(b^{14} c^{6} - 12 \, a b^{12} c^{7} + 56 \, a^{2} b^{10} c^{8} - 128 \, a^{3} b^{8} c^{9} + 148 \, a^{4} b^{6} c^{10} - 80 \, a^{5} b^{4} c^{11} + 16 \, a^{6} b^{2} c^{12}\right)} d^{6} - 6 \, {\left(b^{15} c^{5} - 13 \, a b^{13} c^{6} + 67 \, a^{2} b^{11} c^{7} - 174 \, a^{3} b^{9} c^{8} + 239 \, a^{4} b^{7} c^{9} - 166 \, a^{5} b^{5} c^{10} + 50 \, a^{6} b^{3} c^{11} - 4 \, a^{7} b c^{12}\right)} d^{5} e + 3 \, {\left(5 \, b^{16} c^{4} - 70 \, a b^{14} c^{5} + 395 \, a^{2} b^{12} c^{6} - 1150 \, a^{3} b^{10} c^{7} + 1835 \, a^{4} b^{8} c^{8} - 1570 \, a^{5} b^{6} c^{9} + 650 \, a^{6} b^{4} c^{10} - 100 \, a^{7} b^{2} c^{11} + 3 \, a^{8} c^{12}\right)} d^{4} e^{2} - 2 \, {\left(10 \, b^{17} c^{3} - 150 \, a b^{15} c^{4} + 920 \, a^{2} b^{13} c^{5} - 2970 \, a^{3} b^{11} c^{6} + 5410 \, a^{4} b^{9} c^{7} - 5530 \, a^{5} b^{7} c^{8} + 2960 \, a^{6} b^{5} c^{9} - 700 \, a^{7} b^{3} c^{10} + 49 \, a^{8} b c^{11}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{18} c^{2} - 80 \, a b^{16} c^{3} + 530 \, a^{2} b^{14} c^{4} - 1880 \, a^{3} b^{12} c^{5} + 3855 \, a^{4} b^{10} c^{6} - 4600 \, a^{5} b^{8} c^{7} + 3050 \, a^{6} b^{6} c^{8} - 1000 \, a^{7} b^{4} c^{9} + 125 \, a^{8} b^{2} c^{10} - 2 \, a^{9} c^{11}\right)} d^{2} e^{4} - 6 \, {\left(b^{19} c - 17 \, a b^{17} c^{2} + 121 \, a^{2} b^{15} c^{3} - 468 \, a^{3} b^{13} c^{4} + 1068 \, a^{4} b^{11} c^{5} - 1461 \, a^{5} b^{9} c^{6} + 1163 \, a^{6} b^{7} c^{7} - 496 \, a^{7} b^{5} c^{8} + 95 \, a^{8} b^{3} c^{9} - 5 \, a^{9} b c^{10}\right)} d e^{5} + {\left(b^{20} - 18 \, a b^{18} c + 137 \, a^{2} b^{16} c^{2} - 574 \, a^{3} b^{14} c^{3} + 1444 \, a^{4} b^{12} c^{4} - 2232 \, a^{5} b^{10} c^{5} + 2083 \, a^{6} b^{8} c^{6} - 1106 \, a^{7} b^{6} c^{7} + 295 \, a^{8} b^{4} c^{8} - 30 \, a^{9} b^{2} c^{9} + a^{10} c^{10}\right)} e^{6}}{b^{2} c^{22} - 4 \, a c^{23}}}\right)} \sqrt{\frac{{\left(b^{8} c^{3} - 8 \, a b^{6} c^{4} + 20 \, a^{2} b^{4} c^{5} - 16 \, a^{3} b^{2} c^{6} + 2 \, a^{4} c^{7}\right)} d^{3} - 3 \, {\left(b^{9} c^{2} - 9 \, a b^{7} c^{3} + 27 \, a^{2} b^{5} c^{4} - 30 \, a^{3} b^{3} c^{5} + 9 \, a^{4} b c^{6}\right)} d^{2} e + 3 \, {\left(b^{10} c - 10 \, a b^{8} c^{2} + 35 \, a^{2} b^{6} c^{3} - 50 \, a^{3} b^{4} c^{4} + 25 \, a^{4} b^{2} c^{5} - 2 \, a^{5} c^{6}\right)} d e^{2} - {\left(b^{11} - 11 \, a b^{9} c + 44 \, a^{2} b^{7} c^{2} - 77 \, a^{3} b^{5} c^{3} + 55 \, a^{4} b^{3} c^{4} - 11 \, a^{5} b c^{5}\right)} e^{3} - {\left(b^{2} c^{11} - 4 \, a c^{12}\right)} \sqrt{\frac{{\left(b^{14} c^{6} - 12 \, a b^{12} c^{7} + 56 \, a^{2} b^{10} c^{8} - 128 \, a^{3} b^{8} c^{9} + 148 \, a^{4} b^{6} c^{10} - 80 \, a^{5} b^{4} c^{11} + 16 \, a^{6} b^{2} c^{12}\right)} d^{6} - 6 \, {\left(b^{15} c^{5} - 13 \, a b^{13} c^{6} + 67 \, a^{2} b^{11} c^{7} - 174 \, a^{3} b^{9} c^{8} + 239 \, a^{4} b^{7} c^{9} - 166 \, a^{5} b^{5} c^{10} + 50 \, a^{6} b^{3} c^{11} - 4 \, a^{7} b c^{12}\right)} d^{5} e + 3 \, {\left(5 \, b^{16} c^{4} - 70 \, a b^{14} c^{5} + 395 \, a^{2} b^{12} c^{6} - 1150 \, a^{3} b^{10} c^{7} + 1835 \, a^{4} b^{8} c^{8} - 1570 \, a^{5} b^{6} c^{9} + 650 \, a^{6} b^{4} c^{10} - 100 \, a^{7} b^{2} c^{11} + 3 \, a^{8} c^{12}\right)} d^{4} e^{2} - 2 \, {\left(10 \, b^{17} c^{3} - 150 \, a b^{15} c^{4} + 920 \, a^{2} b^{13} c^{5} - 2970 \, a^{3} b^{11} c^{6} + 5410 \, a^{4} b^{9} c^{7} - 5530 \, a^{5} b^{7} c^{8} + 2960 \, a^{6} b^{5} c^{9} - 700 \, a^{7} b^{3} c^{10} + 49 \, a^{8} b c^{11}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{18} c^{2} - 80 \, a b^{16} c^{3} + 530 \, a^{2} b^{14} c^{4} - 1880 \, a^{3} b^{12} c^{5} + 3855 \, a^{4} b^{10} c^{6} - 4600 \, a^{5} b^{8} c^{7} + 3050 \, a^{6} b^{6} c^{8} - 1000 \, a^{7} b^{4} c^{9} + 125 \, a^{8} b^{2} c^{10} - 2 \, a^{9} c^{11}\right)} d^{2} e^{4} - 6 \, {\left(b^{19} c - 17 \, a b^{17} c^{2} + 121 \, a^{2} b^{15} c^{3} - 468 \, a^{3} b^{13} c^{4} + 1068 \, a^{4} b^{11} c^{5} - 1461 \, a^{5} b^{9} c^{6} + 1163 \, a^{6} b^{7} c^{7} - 496 \, a^{7} b^{5} c^{8} + 95 \, a^{8} b^{3} c^{9} - 5 \, a^{9} b c^{10}\right)} d e^{5} + {\left(b^{20} - 18 \, a b^{18} c + 137 \, a^{2} b^{16} c^{2} - 574 \, a^{3} b^{14} c^{3} + 1444 \, a^{4} b^{12} c^{4} - 2232 \, a^{5} b^{10} c^{5} + 2083 \, a^{6} b^{8} c^{6} - 1106 \, a^{7} b^{6} c^{7} + 295 \, a^{8} b^{4} c^{8} - 30 \, a^{9} b^{2} c^{9} + a^{10} c^{10}\right)} e^{6}}{b^{2} c^{22} - 4 \, a c^{23}}}}{b^{2} c^{11} - 4 \, a c^{12}}} + 4 \, {\left({\left(a^{4} b^{7} c^{4} - 6 \, a^{5} b^{5} c^{5} + 10 \, a^{6} b^{3} c^{6} - 4 \, a^{7} b c^{7}\right)} d^{5} - {\left(4 \, a^{4} b^{8} c^{3} - 27 \, a^{5} b^{6} c^{4} + 55 \, a^{6} b^{4} c^{5} - 34 \, a^{7} b^{2} c^{6} + 3 \, a^{8} c^{7}\right)} d^{4} e + 2 \, {\left(3 \, a^{4} b^{9} c^{2} - 22 \, a^{5} b^{7} c^{3} + 51 \, a^{6} b^{5} c^{4} - 40 \, a^{7} b^{3} c^{5} + 7 \, a^{8} b c^{6}\right)} d^{3} e^{2} - 2 \, {\left(2 \, a^{4} b^{10} c - 15 \, a^{5} b^{8} c^{2} + 35 \, a^{6} b^{6} c^{3} - 25 \, a^{7} b^{4} c^{4} + a^{9} c^{6}\right)} d^{2} e^{3} + {\left(a^{4} b^{11} - 6 \, a^{5} b^{9} c + 4 \, a^{6} b^{7} c^{2} + 28 \, a^{7} b^{5} c^{3} - 45 \, a^{8} b^{3} c^{4} + 14 \, a^{9} b c^{5}\right)} d e^{4} - {\left(a^{5} b^{10} - 9 \, a^{6} b^{8} c + 28 \, a^{7} b^{6} c^{2} - 35 \, a^{8} b^{4} c^{3} + 15 \, a^{9} b^{2} c^{4} - a^{10} c^{5}\right)} e^{5}\right)} \sqrt{e x + d}\right) - 4 \, {\left(35 \, c^{4} e^{4} x^{4} + 8 \, c^{4} d^{4} + 18 \, b c^{3} d^{3} e + 63 \, {\left(b^{2} c^{2} - a c^{3}\right)} d^{2} e^{2} - 420 \, {\left(b^{3} c - 2 \, a b c^{2}\right)} d e^{3} + 315 \, {\left(b^{4} - 3 \, a b^{2} c + a^{2} c^{2}\right)} e^{4} + 5 \, {\left(10 \, c^{4} d e^{3} - 9 \, b c^{3} e^{4}\right)} x^{3} + 3 \, {\left(c^{4} d^{2} e^{2} - 24 \, b c^{3} d e^{3} + 21 \, {\left(b^{2} c^{2} - a c^{3}\right)} e^{4}\right)} x^{2} - {\left(4 \, c^{4} d^{3} e + 9 \, b c^{3} d^{2} e^{2} - 126 \, {\left(b^{2} c^{2} - a c^{3}\right)} d e^{3} + 105 \, {\left(b^{3} c - 2 \, a b c^{2}\right)} e^{4}\right)} x\right)} \sqrt{e x + d}}{630 \, c^{5} e^{3}}"," ",0,"-1/630*(315*sqrt(2)*c^5*e^3*sqrt(((b^8*c^3 - 8*a*b^6*c^4 + 20*a^2*b^4*c^5 - 16*a^3*b^2*c^6 + 2*a^4*c^7)*d^3 - 3*(b^9*c^2 - 9*a*b^7*c^3 + 27*a^2*b^5*c^4 - 30*a^3*b^3*c^5 + 9*a^4*b*c^6)*d^2*e + 3*(b^10*c - 10*a*b^8*c^2 + 35*a^2*b^6*c^3 - 50*a^3*b^4*c^4 + 25*a^4*b^2*c^5 - 2*a^5*c^6)*d*e^2 - (b^11 - 11*a*b^9*c + 44*a^2*b^7*c^2 - 77*a^3*b^5*c^3 + 55*a^4*b^3*c^4 - 11*a^5*b*c^5)*e^3 + (b^2*c^11 - 4*a*c^12)*sqrt(((b^14*c^6 - 12*a*b^12*c^7 + 56*a^2*b^10*c^8 - 128*a^3*b^8*c^9 + 148*a^4*b^6*c^10 - 80*a^5*b^4*c^11 + 16*a^6*b^2*c^12)*d^6 - 6*(b^15*c^5 - 13*a*b^13*c^6 + 67*a^2*b^11*c^7 - 174*a^3*b^9*c^8 + 239*a^4*b^7*c^9 - 166*a^5*b^5*c^10 + 50*a^6*b^3*c^11 - 4*a^7*b*c^12)*d^5*e + 3*(5*b^16*c^4 - 70*a*b^14*c^5 + 395*a^2*b^12*c^6 - 1150*a^3*b^10*c^7 + 1835*a^4*b^8*c^8 - 1570*a^5*b^6*c^9 + 650*a^6*b^4*c^10 - 100*a^7*b^2*c^11 + 3*a^8*c^12)*d^4*e^2 - 2*(10*b^17*c^3 - 150*a*b^15*c^4 + 920*a^2*b^13*c^5 - 2970*a^3*b^11*c^6 + 5410*a^4*b^9*c^7 - 5530*a^5*b^7*c^8 + 2960*a^6*b^5*c^9 - 700*a^7*b^3*c^10 + 49*a^8*b*c^11)*d^3*e^3 + 3*(5*b^18*c^2 - 80*a*b^16*c^3 + 530*a^2*b^14*c^4 - 1880*a^3*b^12*c^5 + 3855*a^4*b^10*c^6 - 4600*a^5*b^8*c^7 + 3050*a^6*b^6*c^8 - 1000*a^7*b^4*c^9 + 125*a^8*b^2*c^10 - 2*a^9*c^11)*d^2*e^4 - 6*(b^19*c - 17*a*b^17*c^2 + 121*a^2*b^15*c^3 - 468*a^3*b^13*c^4 + 1068*a^4*b^11*c^5 - 1461*a^5*b^9*c^6 + 1163*a^6*b^7*c^7 - 496*a^7*b^5*c^8 + 95*a^8*b^3*c^9 - 5*a^9*b*c^10)*d*e^5 + (b^20 - 18*a*b^18*c + 137*a^2*b^16*c^2 - 574*a^3*b^14*c^3 + 1444*a^4*b^12*c^4 - 2232*a^5*b^10*c^5 + 2083*a^6*b^8*c^6 - 1106*a^7*b^6*c^7 + 295*a^8*b^4*c^8 - 30*a^9*b^2*c^9 + a^10*c^10)*e^6)/(b^2*c^22 - 4*a*c^23)))/(b^2*c^11 - 4*a*c^12))*log(sqrt(2)*((b^12*c^4 - 12*a*b^10*c^5 + 54*a^2*b^8*c^6 - 112*a^3*b^6*c^7 + 104*a^4*b^4*c^8 - 32*a^5*b^2*c^9)*d^4 - (4*b^13*c^3 - 52*a*b^11*c^4 + 260*a^2*b^9*c^5 - 624*a^3*b^7*c^6 + 725*a^4*b^5*c^7 - 350*a^5*b^3*c^8 + 40*a^6*b*c^9)*d^3*e + 3*(2*b^14*c^2 - 28*a*b^12*c^3 + 154*a^2*b^10*c^4 - 420*a^3*b^8*c^5 + 587*a^4*b^6*c^6 - 387*a^5*b^4*c^7 + 93*a^6*b^2*c^8 - 4*a^7*c^9)*d^2*e^2 - (4*b^15*c - 60*a*b^13*c^2 + 360*a^2*b^11*c^3 - 1100*a^3*b^9*c^4 + 1799*a^4*b^7*c^5 - 1508*a^5*b^5*c^6 + 561*a^6*b^3*c^7 - 68*a^7*b*c^8)*d*e^3 + (b^16 - 16*a*b^14*c + 104*a^2*b^12*c^2 - 352*a^3*b^10*c^3 + 660*a^4*b^8*c^4 - 673*a^5*b^6*c^5 + 342*a^6*b^4*c^6 - 73*a^7*b^2*c^7 + 4*a^8*c^8)*e^4 - ((b^6*c^12 - 8*a*b^4*c^13 + 18*a^2*b^2*c^14 - 8*a^3*c^15)*d - (b^7*c^11 - 9*a*b^5*c^12 + 25*a^2*b^3*c^13 - 20*a^3*b*c^14)*e)*sqrt(((b^14*c^6 - 12*a*b^12*c^7 + 56*a^2*b^10*c^8 - 128*a^3*b^8*c^9 + 148*a^4*b^6*c^10 - 80*a^5*b^4*c^11 + 16*a^6*b^2*c^12)*d^6 - 6*(b^15*c^5 - 13*a*b^13*c^6 + 67*a^2*b^11*c^7 - 174*a^3*b^9*c^8 + 239*a^4*b^7*c^9 - 166*a^5*b^5*c^10 + 50*a^6*b^3*c^11 - 4*a^7*b*c^12)*d^5*e + 3*(5*b^16*c^4 - 70*a*b^14*c^5 + 395*a^2*b^12*c^6 - 1150*a^3*b^10*c^7 + 1835*a^4*b^8*c^8 - 1570*a^5*b^6*c^9 + 650*a^6*b^4*c^10 - 100*a^7*b^2*c^11 + 3*a^8*c^12)*d^4*e^2 - 2*(10*b^17*c^3 - 150*a*b^15*c^4 + 920*a^2*b^13*c^5 - 2970*a^3*b^11*c^6 + 5410*a^4*b^9*c^7 - 5530*a^5*b^7*c^8 + 2960*a^6*b^5*c^9 - 700*a^7*b^3*c^10 + 49*a^8*b*c^11)*d^3*e^3 + 3*(5*b^18*c^2 - 80*a*b^16*c^3 + 530*a^2*b^14*c^4 - 1880*a^3*b^12*c^5 + 3855*a^4*b^10*c^6 - 4600*a^5*b^8*c^7 + 3050*a^6*b^6*c^8 - 1000*a^7*b^4*c^9 + 125*a^8*b^2*c^10 - 2*a^9*c^11)*d^2*e^4 - 6*(b^19*c - 17*a*b^17*c^2 + 121*a^2*b^15*c^3 - 468*a^3*b^13*c^4 + 1068*a^4*b^11*c^5 - 1461*a^5*b^9*c^6 + 1163*a^6*b^7*c^7 - 496*a^7*b^5*c^8 + 95*a^8*b^3*c^9 - 5*a^9*b*c^10)*d*e^5 + (b^20 - 18*a*b^18*c + 137*a^2*b^16*c^2 - 574*a^3*b^14*c^3 + 1444*a^4*b^12*c^4 - 2232*a^5*b^10*c^5 + 2083*a^6*b^8*c^6 - 1106*a^7*b^6*c^7 + 295*a^8*b^4*c^8 - 30*a^9*b^2*c^9 + a^10*c^10)*e^6)/(b^2*c^22 - 4*a*c^23)))*sqrt(((b^8*c^3 - 8*a*b^6*c^4 + 20*a^2*b^4*c^5 - 16*a^3*b^2*c^6 + 2*a^4*c^7)*d^3 - 3*(b^9*c^2 - 9*a*b^7*c^3 + 27*a^2*b^5*c^4 - 30*a^3*b^3*c^5 + 9*a^4*b*c^6)*d^2*e + 3*(b^10*c - 10*a*b^8*c^2 + 35*a^2*b^6*c^3 - 50*a^3*b^4*c^4 + 25*a^4*b^2*c^5 - 2*a^5*c^6)*d*e^2 - (b^11 - 11*a*b^9*c + 44*a^2*b^7*c^2 - 77*a^3*b^5*c^3 + 55*a^4*b^3*c^4 - 11*a^5*b*c^5)*e^3 + (b^2*c^11 - 4*a*c^12)*sqrt(((b^14*c^6 - 12*a*b^12*c^7 + 56*a^2*b^10*c^8 - 128*a^3*b^8*c^9 + 148*a^4*b^6*c^10 - 80*a^5*b^4*c^11 + 16*a^6*b^2*c^12)*d^6 - 6*(b^15*c^5 - 13*a*b^13*c^6 + 67*a^2*b^11*c^7 - 174*a^3*b^9*c^8 + 239*a^4*b^7*c^9 - 166*a^5*b^5*c^10 + 50*a^6*b^3*c^11 - 4*a^7*b*c^12)*d^5*e + 3*(5*b^16*c^4 - 70*a*b^14*c^5 + 395*a^2*b^12*c^6 - 1150*a^3*b^10*c^7 + 1835*a^4*b^8*c^8 - 1570*a^5*b^6*c^9 + 650*a^6*b^4*c^10 - 100*a^7*b^2*c^11 + 3*a^8*c^12)*d^4*e^2 - 2*(10*b^17*c^3 - 150*a*b^15*c^4 + 920*a^2*b^13*c^5 - 2970*a^3*b^11*c^6 + 5410*a^4*b^9*c^7 - 5530*a^5*b^7*c^8 + 2960*a^6*b^5*c^9 - 700*a^7*b^3*c^10 + 49*a^8*b*c^11)*d^3*e^3 + 3*(5*b^18*c^2 - 80*a*b^16*c^3 + 530*a^2*b^14*c^4 - 1880*a^3*b^12*c^5 + 3855*a^4*b^10*c^6 - 4600*a^5*b^8*c^7 + 3050*a^6*b^6*c^8 - 1000*a^7*b^4*c^9 + 125*a^8*b^2*c^10 - 2*a^9*c^11)*d^2*e^4 - 6*(b^19*c - 17*a*b^17*c^2 + 121*a^2*b^15*c^3 - 468*a^3*b^13*c^4 + 1068*a^4*b^11*c^5 - 1461*a^5*b^9*c^6 + 1163*a^6*b^7*c^7 - 496*a^7*b^5*c^8 + 95*a^8*b^3*c^9 - 5*a^9*b*c^10)*d*e^5 + (b^20 - 18*a*b^18*c + 137*a^2*b^16*c^2 - 574*a^3*b^14*c^3 + 1444*a^4*b^12*c^4 - 2232*a^5*b^10*c^5 + 2083*a^6*b^8*c^6 - 1106*a^7*b^6*c^7 + 295*a^8*b^4*c^8 - 30*a^9*b^2*c^9 + a^10*c^10)*e^6)/(b^2*c^22 - 4*a*c^23)))/(b^2*c^11 - 4*a*c^12)) + 4*((a^4*b^7*c^4 - 6*a^5*b^5*c^5 + 10*a^6*b^3*c^6 - 4*a^7*b*c^7)*d^5 - (4*a^4*b^8*c^3 - 27*a^5*b^6*c^4 + 55*a^6*b^4*c^5 - 34*a^7*b^2*c^6 + 3*a^8*c^7)*d^4*e + 2*(3*a^4*b^9*c^2 - 22*a^5*b^7*c^3 + 51*a^6*b^5*c^4 - 40*a^7*b^3*c^5 + 7*a^8*b*c^6)*d^3*e^2 - 2*(2*a^4*b^10*c - 15*a^5*b^8*c^2 + 35*a^6*b^6*c^3 - 25*a^7*b^4*c^4 + a^9*c^6)*d^2*e^3 + (a^4*b^11 - 6*a^5*b^9*c + 4*a^6*b^7*c^2 + 28*a^7*b^5*c^3 - 45*a^8*b^3*c^4 + 14*a^9*b*c^5)*d*e^4 - (a^5*b^10 - 9*a^6*b^8*c + 28*a^7*b^6*c^2 - 35*a^8*b^4*c^3 + 15*a^9*b^2*c^4 - a^10*c^5)*e^5)*sqrt(e*x + d)) - 315*sqrt(2)*c^5*e^3*sqrt(((b^8*c^3 - 8*a*b^6*c^4 + 20*a^2*b^4*c^5 - 16*a^3*b^2*c^6 + 2*a^4*c^7)*d^3 - 3*(b^9*c^2 - 9*a*b^7*c^3 + 27*a^2*b^5*c^4 - 30*a^3*b^3*c^5 + 9*a^4*b*c^6)*d^2*e + 3*(b^10*c - 10*a*b^8*c^2 + 35*a^2*b^6*c^3 - 50*a^3*b^4*c^4 + 25*a^4*b^2*c^5 - 2*a^5*c^6)*d*e^2 - (b^11 - 11*a*b^9*c + 44*a^2*b^7*c^2 - 77*a^3*b^5*c^3 + 55*a^4*b^3*c^4 - 11*a^5*b*c^5)*e^3 + (b^2*c^11 - 4*a*c^12)*sqrt(((b^14*c^6 - 12*a*b^12*c^7 + 56*a^2*b^10*c^8 - 128*a^3*b^8*c^9 + 148*a^4*b^6*c^10 - 80*a^5*b^4*c^11 + 16*a^6*b^2*c^12)*d^6 - 6*(b^15*c^5 - 13*a*b^13*c^6 + 67*a^2*b^11*c^7 - 174*a^3*b^9*c^8 + 239*a^4*b^7*c^9 - 166*a^5*b^5*c^10 + 50*a^6*b^3*c^11 - 4*a^7*b*c^12)*d^5*e + 3*(5*b^16*c^4 - 70*a*b^14*c^5 + 395*a^2*b^12*c^6 - 1150*a^3*b^10*c^7 + 1835*a^4*b^8*c^8 - 1570*a^5*b^6*c^9 + 650*a^6*b^4*c^10 - 100*a^7*b^2*c^11 + 3*a^8*c^12)*d^4*e^2 - 2*(10*b^17*c^3 - 150*a*b^15*c^4 + 920*a^2*b^13*c^5 - 2970*a^3*b^11*c^6 + 5410*a^4*b^9*c^7 - 5530*a^5*b^7*c^8 + 2960*a^6*b^5*c^9 - 700*a^7*b^3*c^10 + 49*a^8*b*c^11)*d^3*e^3 + 3*(5*b^18*c^2 - 80*a*b^16*c^3 + 530*a^2*b^14*c^4 - 1880*a^3*b^12*c^5 + 3855*a^4*b^10*c^6 - 4600*a^5*b^8*c^7 + 3050*a^6*b^6*c^8 - 1000*a^7*b^4*c^9 + 125*a^8*b^2*c^10 - 2*a^9*c^11)*d^2*e^4 - 6*(b^19*c - 17*a*b^17*c^2 + 121*a^2*b^15*c^3 - 468*a^3*b^13*c^4 + 1068*a^4*b^11*c^5 - 1461*a^5*b^9*c^6 + 1163*a^6*b^7*c^7 - 496*a^7*b^5*c^8 + 95*a^8*b^3*c^9 - 5*a^9*b*c^10)*d*e^5 + (b^20 - 18*a*b^18*c + 137*a^2*b^16*c^2 - 574*a^3*b^14*c^3 + 1444*a^4*b^12*c^4 - 2232*a^5*b^10*c^5 + 2083*a^6*b^8*c^6 - 1106*a^7*b^6*c^7 + 295*a^8*b^4*c^8 - 30*a^9*b^2*c^9 + a^10*c^10)*e^6)/(b^2*c^22 - 4*a*c^23)))/(b^2*c^11 - 4*a*c^12))*log(-sqrt(2)*((b^12*c^4 - 12*a*b^10*c^5 + 54*a^2*b^8*c^6 - 112*a^3*b^6*c^7 + 104*a^4*b^4*c^8 - 32*a^5*b^2*c^9)*d^4 - (4*b^13*c^3 - 52*a*b^11*c^4 + 260*a^2*b^9*c^5 - 624*a^3*b^7*c^6 + 725*a^4*b^5*c^7 - 350*a^5*b^3*c^8 + 40*a^6*b*c^9)*d^3*e + 3*(2*b^14*c^2 - 28*a*b^12*c^3 + 154*a^2*b^10*c^4 - 420*a^3*b^8*c^5 + 587*a^4*b^6*c^6 - 387*a^5*b^4*c^7 + 93*a^6*b^2*c^8 - 4*a^7*c^9)*d^2*e^2 - (4*b^15*c - 60*a*b^13*c^2 + 360*a^2*b^11*c^3 - 1100*a^3*b^9*c^4 + 1799*a^4*b^7*c^5 - 1508*a^5*b^5*c^6 + 561*a^6*b^3*c^7 - 68*a^7*b*c^8)*d*e^3 + (b^16 - 16*a*b^14*c + 104*a^2*b^12*c^2 - 352*a^3*b^10*c^3 + 660*a^4*b^8*c^4 - 673*a^5*b^6*c^5 + 342*a^6*b^4*c^6 - 73*a^7*b^2*c^7 + 4*a^8*c^8)*e^4 - ((b^6*c^12 - 8*a*b^4*c^13 + 18*a^2*b^2*c^14 - 8*a^3*c^15)*d - (b^7*c^11 - 9*a*b^5*c^12 + 25*a^2*b^3*c^13 - 20*a^3*b*c^14)*e)*sqrt(((b^14*c^6 - 12*a*b^12*c^7 + 56*a^2*b^10*c^8 - 128*a^3*b^8*c^9 + 148*a^4*b^6*c^10 - 80*a^5*b^4*c^11 + 16*a^6*b^2*c^12)*d^6 - 6*(b^15*c^5 - 13*a*b^13*c^6 + 67*a^2*b^11*c^7 - 174*a^3*b^9*c^8 + 239*a^4*b^7*c^9 - 166*a^5*b^5*c^10 + 50*a^6*b^3*c^11 - 4*a^7*b*c^12)*d^5*e + 3*(5*b^16*c^4 - 70*a*b^14*c^5 + 395*a^2*b^12*c^6 - 1150*a^3*b^10*c^7 + 1835*a^4*b^8*c^8 - 1570*a^5*b^6*c^9 + 650*a^6*b^4*c^10 - 100*a^7*b^2*c^11 + 3*a^8*c^12)*d^4*e^2 - 2*(10*b^17*c^3 - 150*a*b^15*c^4 + 920*a^2*b^13*c^5 - 2970*a^3*b^11*c^6 + 5410*a^4*b^9*c^7 - 5530*a^5*b^7*c^8 + 2960*a^6*b^5*c^9 - 700*a^7*b^3*c^10 + 49*a^8*b*c^11)*d^3*e^3 + 3*(5*b^18*c^2 - 80*a*b^16*c^3 + 530*a^2*b^14*c^4 - 1880*a^3*b^12*c^5 + 3855*a^4*b^10*c^6 - 4600*a^5*b^8*c^7 + 3050*a^6*b^6*c^8 - 1000*a^7*b^4*c^9 + 125*a^8*b^2*c^10 - 2*a^9*c^11)*d^2*e^4 - 6*(b^19*c - 17*a*b^17*c^2 + 121*a^2*b^15*c^3 - 468*a^3*b^13*c^4 + 1068*a^4*b^11*c^5 - 1461*a^5*b^9*c^6 + 1163*a^6*b^7*c^7 - 496*a^7*b^5*c^8 + 95*a^8*b^3*c^9 - 5*a^9*b*c^10)*d*e^5 + (b^20 - 18*a*b^18*c + 137*a^2*b^16*c^2 - 574*a^3*b^14*c^3 + 1444*a^4*b^12*c^4 - 2232*a^5*b^10*c^5 + 2083*a^6*b^8*c^6 - 1106*a^7*b^6*c^7 + 295*a^8*b^4*c^8 - 30*a^9*b^2*c^9 + a^10*c^10)*e^6)/(b^2*c^22 - 4*a*c^23)))*sqrt(((b^8*c^3 - 8*a*b^6*c^4 + 20*a^2*b^4*c^5 - 16*a^3*b^2*c^6 + 2*a^4*c^7)*d^3 - 3*(b^9*c^2 - 9*a*b^7*c^3 + 27*a^2*b^5*c^4 - 30*a^3*b^3*c^5 + 9*a^4*b*c^6)*d^2*e + 3*(b^10*c - 10*a*b^8*c^2 + 35*a^2*b^6*c^3 - 50*a^3*b^4*c^4 + 25*a^4*b^2*c^5 - 2*a^5*c^6)*d*e^2 - (b^11 - 11*a*b^9*c + 44*a^2*b^7*c^2 - 77*a^3*b^5*c^3 + 55*a^4*b^3*c^4 - 11*a^5*b*c^5)*e^3 + (b^2*c^11 - 4*a*c^12)*sqrt(((b^14*c^6 - 12*a*b^12*c^7 + 56*a^2*b^10*c^8 - 128*a^3*b^8*c^9 + 148*a^4*b^6*c^10 - 80*a^5*b^4*c^11 + 16*a^6*b^2*c^12)*d^6 - 6*(b^15*c^5 - 13*a*b^13*c^6 + 67*a^2*b^11*c^7 - 174*a^3*b^9*c^8 + 239*a^4*b^7*c^9 - 166*a^5*b^5*c^10 + 50*a^6*b^3*c^11 - 4*a^7*b*c^12)*d^5*e + 3*(5*b^16*c^4 - 70*a*b^14*c^5 + 395*a^2*b^12*c^6 - 1150*a^3*b^10*c^7 + 1835*a^4*b^8*c^8 - 1570*a^5*b^6*c^9 + 650*a^6*b^4*c^10 - 100*a^7*b^2*c^11 + 3*a^8*c^12)*d^4*e^2 - 2*(10*b^17*c^3 - 150*a*b^15*c^4 + 920*a^2*b^13*c^5 - 2970*a^3*b^11*c^6 + 5410*a^4*b^9*c^7 - 5530*a^5*b^7*c^8 + 2960*a^6*b^5*c^9 - 700*a^7*b^3*c^10 + 49*a^8*b*c^11)*d^3*e^3 + 3*(5*b^18*c^2 - 80*a*b^16*c^3 + 530*a^2*b^14*c^4 - 1880*a^3*b^12*c^5 + 3855*a^4*b^10*c^6 - 4600*a^5*b^8*c^7 + 3050*a^6*b^6*c^8 - 1000*a^7*b^4*c^9 + 125*a^8*b^2*c^10 - 2*a^9*c^11)*d^2*e^4 - 6*(b^19*c - 17*a*b^17*c^2 + 121*a^2*b^15*c^3 - 468*a^3*b^13*c^4 + 1068*a^4*b^11*c^5 - 1461*a^5*b^9*c^6 + 1163*a^6*b^7*c^7 - 496*a^7*b^5*c^8 + 95*a^8*b^3*c^9 - 5*a^9*b*c^10)*d*e^5 + (b^20 - 18*a*b^18*c + 137*a^2*b^16*c^2 - 574*a^3*b^14*c^3 + 1444*a^4*b^12*c^4 - 2232*a^5*b^10*c^5 + 2083*a^6*b^8*c^6 - 1106*a^7*b^6*c^7 + 295*a^8*b^4*c^8 - 30*a^9*b^2*c^9 + a^10*c^10)*e^6)/(b^2*c^22 - 4*a*c^23)))/(b^2*c^11 - 4*a*c^12)) + 4*((a^4*b^7*c^4 - 6*a^5*b^5*c^5 + 10*a^6*b^3*c^6 - 4*a^7*b*c^7)*d^5 - (4*a^4*b^8*c^3 - 27*a^5*b^6*c^4 + 55*a^6*b^4*c^5 - 34*a^7*b^2*c^6 + 3*a^8*c^7)*d^4*e + 2*(3*a^4*b^9*c^2 - 22*a^5*b^7*c^3 + 51*a^6*b^5*c^4 - 40*a^7*b^3*c^5 + 7*a^8*b*c^6)*d^3*e^2 - 2*(2*a^4*b^10*c - 15*a^5*b^8*c^2 + 35*a^6*b^6*c^3 - 25*a^7*b^4*c^4 + a^9*c^6)*d^2*e^3 + (a^4*b^11 - 6*a^5*b^9*c + 4*a^6*b^7*c^2 + 28*a^7*b^5*c^3 - 45*a^8*b^3*c^4 + 14*a^9*b*c^5)*d*e^4 - (a^5*b^10 - 9*a^6*b^8*c + 28*a^7*b^6*c^2 - 35*a^8*b^4*c^3 + 15*a^9*b^2*c^4 - a^10*c^5)*e^5)*sqrt(e*x + d)) + 315*sqrt(2)*c^5*e^3*sqrt(((b^8*c^3 - 8*a*b^6*c^4 + 20*a^2*b^4*c^5 - 16*a^3*b^2*c^6 + 2*a^4*c^7)*d^3 - 3*(b^9*c^2 - 9*a*b^7*c^3 + 27*a^2*b^5*c^4 - 30*a^3*b^3*c^5 + 9*a^4*b*c^6)*d^2*e + 3*(b^10*c - 10*a*b^8*c^2 + 35*a^2*b^6*c^3 - 50*a^3*b^4*c^4 + 25*a^4*b^2*c^5 - 2*a^5*c^6)*d*e^2 - (b^11 - 11*a*b^9*c + 44*a^2*b^7*c^2 - 77*a^3*b^5*c^3 + 55*a^4*b^3*c^4 - 11*a^5*b*c^5)*e^3 - (b^2*c^11 - 4*a*c^12)*sqrt(((b^14*c^6 - 12*a*b^12*c^7 + 56*a^2*b^10*c^8 - 128*a^3*b^8*c^9 + 148*a^4*b^6*c^10 - 80*a^5*b^4*c^11 + 16*a^6*b^2*c^12)*d^6 - 6*(b^15*c^5 - 13*a*b^13*c^6 + 67*a^2*b^11*c^7 - 174*a^3*b^9*c^8 + 239*a^4*b^7*c^9 - 166*a^5*b^5*c^10 + 50*a^6*b^3*c^11 - 4*a^7*b*c^12)*d^5*e + 3*(5*b^16*c^4 - 70*a*b^14*c^5 + 395*a^2*b^12*c^6 - 1150*a^3*b^10*c^7 + 1835*a^4*b^8*c^8 - 1570*a^5*b^6*c^9 + 650*a^6*b^4*c^10 - 100*a^7*b^2*c^11 + 3*a^8*c^12)*d^4*e^2 - 2*(10*b^17*c^3 - 150*a*b^15*c^4 + 920*a^2*b^13*c^5 - 2970*a^3*b^11*c^6 + 5410*a^4*b^9*c^7 - 5530*a^5*b^7*c^8 + 2960*a^6*b^5*c^9 - 700*a^7*b^3*c^10 + 49*a^8*b*c^11)*d^3*e^3 + 3*(5*b^18*c^2 - 80*a*b^16*c^3 + 530*a^2*b^14*c^4 - 1880*a^3*b^12*c^5 + 3855*a^4*b^10*c^6 - 4600*a^5*b^8*c^7 + 3050*a^6*b^6*c^8 - 1000*a^7*b^4*c^9 + 125*a^8*b^2*c^10 - 2*a^9*c^11)*d^2*e^4 - 6*(b^19*c - 17*a*b^17*c^2 + 121*a^2*b^15*c^3 - 468*a^3*b^13*c^4 + 1068*a^4*b^11*c^5 - 1461*a^5*b^9*c^6 + 1163*a^6*b^7*c^7 - 496*a^7*b^5*c^8 + 95*a^8*b^3*c^9 - 5*a^9*b*c^10)*d*e^5 + (b^20 - 18*a*b^18*c + 137*a^2*b^16*c^2 - 574*a^3*b^14*c^3 + 1444*a^4*b^12*c^4 - 2232*a^5*b^10*c^5 + 2083*a^6*b^8*c^6 - 1106*a^7*b^6*c^7 + 295*a^8*b^4*c^8 - 30*a^9*b^2*c^9 + a^10*c^10)*e^6)/(b^2*c^22 - 4*a*c^23)))/(b^2*c^11 - 4*a*c^12))*log(sqrt(2)*((b^12*c^4 - 12*a*b^10*c^5 + 54*a^2*b^8*c^6 - 112*a^3*b^6*c^7 + 104*a^4*b^4*c^8 - 32*a^5*b^2*c^9)*d^4 - (4*b^13*c^3 - 52*a*b^11*c^4 + 260*a^2*b^9*c^5 - 624*a^3*b^7*c^6 + 725*a^4*b^5*c^7 - 350*a^5*b^3*c^8 + 40*a^6*b*c^9)*d^3*e + 3*(2*b^14*c^2 - 28*a*b^12*c^3 + 154*a^2*b^10*c^4 - 420*a^3*b^8*c^5 + 587*a^4*b^6*c^6 - 387*a^5*b^4*c^7 + 93*a^6*b^2*c^8 - 4*a^7*c^9)*d^2*e^2 - (4*b^15*c - 60*a*b^13*c^2 + 360*a^2*b^11*c^3 - 1100*a^3*b^9*c^4 + 1799*a^4*b^7*c^5 - 1508*a^5*b^5*c^6 + 561*a^6*b^3*c^7 - 68*a^7*b*c^8)*d*e^3 + (b^16 - 16*a*b^14*c + 104*a^2*b^12*c^2 - 352*a^3*b^10*c^3 + 660*a^4*b^8*c^4 - 673*a^5*b^6*c^5 + 342*a^6*b^4*c^6 - 73*a^7*b^2*c^7 + 4*a^8*c^8)*e^4 + ((b^6*c^12 - 8*a*b^4*c^13 + 18*a^2*b^2*c^14 - 8*a^3*c^15)*d - (b^7*c^11 - 9*a*b^5*c^12 + 25*a^2*b^3*c^13 - 20*a^3*b*c^14)*e)*sqrt(((b^14*c^6 - 12*a*b^12*c^7 + 56*a^2*b^10*c^8 - 128*a^3*b^8*c^9 + 148*a^4*b^6*c^10 - 80*a^5*b^4*c^11 + 16*a^6*b^2*c^12)*d^6 - 6*(b^15*c^5 - 13*a*b^13*c^6 + 67*a^2*b^11*c^7 - 174*a^3*b^9*c^8 + 239*a^4*b^7*c^9 - 166*a^5*b^5*c^10 + 50*a^6*b^3*c^11 - 4*a^7*b*c^12)*d^5*e + 3*(5*b^16*c^4 - 70*a*b^14*c^5 + 395*a^2*b^12*c^6 - 1150*a^3*b^10*c^7 + 1835*a^4*b^8*c^8 - 1570*a^5*b^6*c^9 + 650*a^6*b^4*c^10 - 100*a^7*b^2*c^11 + 3*a^8*c^12)*d^4*e^2 - 2*(10*b^17*c^3 - 150*a*b^15*c^4 + 920*a^2*b^13*c^5 - 2970*a^3*b^11*c^6 + 5410*a^4*b^9*c^7 - 5530*a^5*b^7*c^8 + 2960*a^6*b^5*c^9 - 700*a^7*b^3*c^10 + 49*a^8*b*c^11)*d^3*e^3 + 3*(5*b^18*c^2 - 80*a*b^16*c^3 + 530*a^2*b^14*c^4 - 1880*a^3*b^12*c^5 + 3855*a^4*b^10*c^6 - 4600*a^5*b^8*c^7 + 3050*a^6*b^6*c^8 - 1000*a^7*b^4*c^9 + 125*a^8*b^2*c^10 - 2*a^9*c^11)*d^2*e^4 - 6*(b^19*c - 17*a*b^17*c^2 + 121*a^2*b^15*c^3 - 468*a^3*b^13*c^4 + 1068*a^4*b^11*c^5 - 1461*a^5*b^9*c^6 + 1163*a^6*b^7*c^7 - 496*a^7*b^5*c^8 + 95*a^8*b^3*c^9 - 5*a^9*b*c^10)*d*e^5 + (b^20 - 18*a*b^18*c + 137*a^2*b^16*c^2 - 574*a^3*b^14*c^3 + 1444*a^4*b^12*c^4 - 2232*a^5*b^10*c^5 + 2083*a^6*b^8*c^6 - 1106*a^7*b^6*c^7 + 295*a^8*b^4*c^8 - 30*a^9*b^2*c^9 + a^10*c^10)*e^6)/(b^2*c^22 - 4*a*c^23)))*sqrt(((b^8*c^3 - 8*a*b^6*c^4 + 20*a^2*b^4*c^5 - 16*a^3*b^2*c^6 + 2*a^4*c^7)*d^3 - 3*(b^9*c^2 - 9*a*b^7*c^3 + 27*a^2*b^5*c^4 - 30*a^3*b^3*c^5 + 9*a^4*b*c^6)*d^2*e + 3*(b^10*c - 10*a*b^8*c^2 + 35*a^2*b^6*c^3 - 50*a^3*b^4*c^4 + 25*a^4*b^2*c^5 - 2*a^5*c^6)*d*e^2 - (b^11 - 11*a*b^9*c + 44*a^2*b^7*c^2 - 77*a^3*b^5*c^3 + 55*a^4*b^3*c^4 - 11*a^5*b*c^5)*e^3 - (b^2*c^11 - 4*a*c^12)*sqrt(((b^14*c^6 - 12*a*b^12*c^7 + 56*a^2*b^10*c^8 - 128*a^3*b^8*c^9 + 148*a^4*b^6*c^10 - 80*a^5*b^4*c^11 + 16*a^6*b^2*c^12)*d^6 - 6*(b^15*c^5 - 13*a*b^13*c^6 + 67*a^2*b^11*c^7 - 174*a^3*b^9*c^8 + 239*a^4*b^7*c^9 - 166*a^5*b^5*c^10 + 50*a^6*b^3*c^11 - 4*a^7*b*c^12)*d^5*e + 3*(5*b^16*c^4 - 70*a*b^14*c^5 + 395*a^2*b^12*c^6 - 1150*a^3*b^10*c^7 + 1835*a^4*b^8*c^8 - 1570*a^5*b^6*c^9 + 650*a^6*b^4*c^10 - 100*a^7*b^2*c^11 + 3*a^8*c^12)*d^4*e^2 - 2*(10*b^17*c^3 - 150*a*b^15*c^4 + 920*a^2*b^13*c^5 - 2970*a^3*b^11*c^6 + 5410*a^4*b^9*c^7 - 5530*a^5*b^7*c^8 + 2960*a^6*b^5*c^9 - 700*a^7*b^3*c^10 + 49*a^8*b*c^11)*d^3*e^3 + 3*(5*b^18*c^2 - 80*a*b^16*c^3 + 530*a^2*b^14*c^4 - 1880*a^3*b^12*c^5 + 3855*a^4*b^10*c^6 - 4600*a^5*b^8*c^7 + 3050*a^6*b^6*c^8 - 1000*a^7*b^4*c^9 + 125*a^8*b^2*c^10 - 2*a^9*c^11)*d^2*e^4 - 6*(b^19*c - 17*a*b^17*c^2 + 121*a^2*b^15*c^3 - 468*a^3*b^13*c^4 + 1068*a^4*b^11*c^5 - 1461*a^5*b^9*c^6 + 1163*a^6*b^7*c^7 - 496*a^7*b^5*c^8 + 95*a^8*b^3*c^9 - 5*a^9*b*c^10)*d*e^5 + (b^20 - 18*a*b^18*c + 137*a^2*b^16*c^2 - 574*a^3*b^14*c^3 + 1444*a^4*b^12*c^4 - 2232*a^5*b^10*c^5 + 2083*a^6*b^8*c^6 - 1106*a^7*b^6*c^7 + 295*a^8*b^4*c^8 - 30*a^9*b^2*c^9 + a^10*c^10)*e^6)/(b^2*c^22 - 4*a*c^23)))/(b^2*c^11 - 4*a*c^12)) + 4*((a^4*b^7*c^4 - 6*a^5*b^5*c^5 + 10*a^6*b^3*c^6 - 4*a^7*b*c^7)*d^5 - (4*a^4*b^8*c^3 - 27*a^5*b^6*c^4 + 55*a^6*b^4*c^5 - 34*a^7*b^2*c^6 + 3*a^8*c^7)*d^4*e + 2*(3*a^4*b^9*c^2 - 22*a^5*b^7*c^3 + 51*a^6*b^5*c^4 - 40*a^7*b^3*c^5 + 7*a^8*b*c^6)*d^3*e^2 - 2*(2*a^4*b^10*c - 15*a^5*b^8*c^2 + 35*a^6*b^6*c^3 - 25*a^7*b^4*c^4 + a^9*c^6)*d^2*e^3 + (a^4*b^11 - 6*a^5*b^9*c + 4*a^6*b^7*c^2 + 28*a^7*b^5*c^3 - 45*a^8*b^3*c^4 + 14*a^9*b*c^5)*d*e^4 - (a^5*b^10 - 9*a^6*b^8*c + 28*a^7*b^6*c^2 - 35*a^8*b^4*c^3 + 15*a^9*b^2*c^4 - a^10*c^5)*e^5)*sqrt(e*x + d)) - 315*sqrt(2)*c^5*e^3*sqrt(((b^8*c^3 - 8*a*b^6*c^4 + 20*a^2*b^4*c^5 - 16*a^3*b^2*c^6 + 2*a^4*c^7)*d^3 - 3*(b^9*c^2 - 9*a*b^7*c^3 + 27*a^2*b^5*c^4 - 30*a^3*b^3*c^5 + 9*a^4*b*c^6)*d^2*e + 3*(b^10*c - 10*a*b^8*c^2 + 35*a^2*b^6*c^3 - 50*a^3*b^4*c^4 + 25*a^4*b^2*c^5 - 2*a^5*c^6)*d*e^2 - (b^11 - 11*a*b^9*c + 44*a^2*b^7*c^2 - 77*a^3*b^5*c^3 + 55*a^4*b^3*c^4 - 11*a^5*b*c^5)*e^3 - (b^2*c^11 - 4*a*c^12)*sqrt(((b^14*c^6 - 12*a*b^12*c^7 + 56*a^2*b^10*c^8 - 128*a^3*b^8*c^9 + 148*a^4*b^6*c^10 - 80*a^5*b^4*c^11 + 16*a^6*b^2*c^12)*d^6 - 6*(b^15*c^5 - 13*a*b^13*c^6 + 67*a^2*b^11*c^7 - 174*a^3*b^9*c^8 + 239*a^4*b^7*c^9 - 166*a^5*b^5*c^10 + 50*a^6*b^3*c^11 - 4*a^7*b*c^12)*d^5*e + 3*(5*b^16*c^4 - 70*a*b^14*c^5 + 395*a^2*b^12*c^6 - 1150*a^3*b^10*c^7 + 1835*a^4*b^8*c^8 - 1570*a^5*b^6*c^9 + 650*a^6*b^4*c^10 - 100*a^7*b^2*c^11 + 3*a^8*c^12)*d^4*e^2 - 2*(10*b^17*c^3 - 150*a*b^15*c^4 + 920*a^2*b^13*c^5 - 2970*a^3*b^11*c^6 + 5410*a^4*b^9*c^7 - 5530*a^5*b^7*c^8 + 2960*a^6*b^5*c^9 - 700*a^7*b^3*c^10 + 49*a^8*b*c^11)*d^3*e^3 + 3*(5*b^18*c^2 - 80*a*b^16*c^3 + 530*a^2*b^14*c^4 - 1880*a^3*b^12*c^5 + 3855*a^4*b^10*c^6 - 4600*a^5*b^8*c^7 + 3050*a^6*b^6*c^8 - 1000*a^7*b^4*c^9 + 125*a^8*b^2*c^10 - 2*a^9*c^11)*d^2*e^4 - 6*(b^19*c - 17*a*b^17*c^2 + 121*a^2*b^15*c^3 - 468*a^3*b^13*c^4 + 1068*a^4*b^11*c^5 - 1461*a^5*b^9*c^6 + 1163*a^6*b^7*c^7 - 496*a^7*b^5*c^8 + 95*a^8*b^3*c^9 - 5*a^9*b*c^10)*d*e^5 + (b^20 - 18*a*b^18*c + 137*a^2*b^16*c^2 - 574*a^3*b^14*c^3 + 1444*a^4*b^12*c^4 - 2232*a^5*b^10*c^5 + 2083*a^6*b^8*c^6 - 1106*a^7*b^6*c^7 + 295*a^8*b^4*c^8 - 30*a^9*b^2*c^9 + a^10*c^10)*e^6)/(b^2*c^22 - 4*a*c^23)))/(b^2*c^11 - 4*a*c^12))*log(-sqrt(2)*((b^12*c^4 - 12*a*b^10*c^5 + 54*a^2*b^8*c^6 - 112*a^3*b^6*c^7 + 104*a^4*b^4*c^8 - 32*a^5*b^2*c^9)*d^4 - (4*b^13*c^3 - 52*a*b^11*c^4 + 260*a^2*b^9*c^5 - 624*a^3*b^7*c^6 + 725*a^4*b^5*c^7 - 350*a^5*b^3*c^8 + 40*a^6*b*c^9)*d^3*e + 3*(2*b^14*c^2 - 28*a*b^12*c^3 + 154*a^2*b^10*c^4 - 420*a^3*b^8*c^5 + 587*a^4*b^6*c^6 - 387*a^5*b^4*c^7 + 93*a^6*b^2*c^8 - 4*a^7*c^9)*d^2*e^2 - (4*b^15*c - 60*a*b^13*c^2 + 360*a^2*b^11*c^3 - 1100*a^3*b^9*c^4 + 1799*a^4*b^7*c^5 - 1508*a^5*b^5*c^6 + 561*a^6*b^3*c^7 - 68*a^7*b*c^8)*d*e^3 + (b^16 - 16*a*b^14*c + 104*a^2*b^12*c^2 - 352*a^3*b^10*c^3 + 660*a^4*b^8*c^4 - 673*a^5*b^6*c^5 + 342*a^6*b^4*c^6 - 73*a^7*b^2*c^7 + 4*a^8*c^8)*e^4 + ((b^6*c^12 - 8*a*b^4*c^13 + 18*a^2*b^2*c^14 - 8*a^3*c^15)*d - (b^7*c^11 - 9*a*b^5*c^12 + 25*a^2*b^3*c^13 - 20*a^3*b*c^14)*e)*sqrt(((b^14*c^6 - 12*a*b^12*c^7 + 56*a^2*b^10*c^8 - 128*a^3*b^8*c^9 + 148*a^4*b^6*c^10 - 80*a^5*b^4*c^11 + 16*a^6*b^2*c^12)*d^6 - 6*(b^15*c^5 - 13*a*b^13*c^6 + 67*a^2*b^11*c^7 - 174*a^3*b^9*c^8 + 239*a^4*b^7*c^9 - 166*a^5*b^5*c^10 + 50*a^6*b^3*c^11 - 4*a^7*b*c^12)*d^5*e + 3*(5*b^16*c^4 - 70*a*b^14*c^5 + 395*a^2*b^12*c^6 - 1150*a^3*b^10*c^7 + 1835*a^4*b^8*c^8 - 1570*a^5*b^6*c^9 + 650*a^6*b^4*c^10 - 100*a^7*b^2*c^11 + 3*a^8*c^12)*d^4*e^2 - 2*(10*b^17*c^3 - 150*a*b^15*c^4 + 920*a^2*b^13*c^5 - 2970*a^3*b^11*c^6 + 5410*a^4*b^9*c^7 - 5530*a^5*b^7*c^8 + 2960*a^6*b^5*c^9 - 700*a^7*b^3*c^10 + 49*a^8*b*c^11)*d^3*e^3 + 3*(5*b^18*c^2 - 80*a*b^16*c^3 + 530*a^2*b^14*c^4 - 1880*a^3*b^12*c^5 + 3855*a^4*b^10*c^6 - 4600*a^5*b^8*c^7 + 3050*a^6*b^6*c^8 - 1000*a^7*b^4*c^9 + 125*a^8*b^2*c^10 - 2*a^9*c^11)*d^2*e^4 - 6*(b^19*c - 17*a*b^17*c^2 + 121*a^2*b^15*c^3 - 468*a^3*b^13*c^4 + 1068*a^4*b^11*c^5 - 1461*a^5*b^9*c^6 + 1163*a^6*b^7*c^7 - 496*a^7*b^5*c^8 + 95*a^8*b^3*c^9 - 5*a^9*b*c^10)*d*e^5 + (b^20 - 18*a*b^18*c + 137*a^2*b^16*c^2 - 574*a^3*b^14*c^3 + 1444*a^4*b^12*c^4 - 2232*a^5*b^10*c^5 + 2083*a^6*b^8*c^6 - 1106*a^7*b^6*c^7 + 295*a^8*b^4*c^8 - 30*a^9*b^2*c^9 + a^10*c^10)*e^6)/(b^2*c^22 - 4*a*c^23)))*sqrt(((b^8*c^3 - 8*a*b^6*c^4 + 20*a^2*b^4*c^5 - 16*a^3*b^2*c^6 + 2*a^4*c^7)*d^3 - 3*(b^9*c^2 - 9*a*b^7*c^3 + 27*a^2*b^5*c^4 - 30*a^3*b^3*c^5 + 9*a^4*b*c^6)*d^2*e + 3*(b^10*c - 10*a*b^8*c^2 + 35*a^2*b^6*c^3 - 50*a^3*b^4*c^4 + 25*a^4*b^2*c^5 - 2*a^5*c^6)*d*e^2 - (b^11 - 11*a*b^9*c + 44*a^2*b^7*c^2 - 77*a^3*b^5*c^3 + 55*a^4*b^3*c^4 - 11*a^5*b*c^5)*e^3 - (b^2*c^11 - 4*a*c^12)*sqrt(((b^14*c^6 - 12*a*b^12*c^7 + 56*a^2*b^10*c^8 - 128*a^3*b^8*c^9 + 148*a^4*b^6*c^10 - 80*a^5*b^4*c^11 + 16*a^6*b^2*c^12)*d^6 - 6*(b^15*c^5 - 13*a*b^13*c^6 + 67*a^2*b^11*c^7 - 174*a^3*b^9*c^8 + 239*a^4*b^7*c^9 - 166*a^5*b^5*c^10 + 50*a^6*b^3*c^11 - 4*a^7*b*c^12)*d^5*e + 3*(5*b^16*c^4 - 70*a*b^14*c^5 + 395*a^2*b^12*c^6 - 1150*a^3*b^10*c^7 + 1835*a^4*b^8*c^8 - 1570*a^5*b^6*c^9 + 650*a^6*b^4*c^10 - 100*a^7*b^2*c^11 + 3*a^8*c^12)*d^4*e^2 - 2*(10*b^17*c^3 - 150*a*b^15*c^4 + 920*a^2*b^13*c^5 - 2970*a^3*b^11*c^6 + 5410*a^4*b^9*c^7 - 5530*a^5*b^7*c^8 + 2960*a^6*b^5*c^9 - 700*a^7*b^3*c^10 + 49*a^8*b*c^11)*d^3*e^3 + 3*(5*b^18*c^2 - 80*a*b^16*c^3 + 530*a^2*b^14*c^4 - 1880*a^3*b^12*c^5 + 3855*a^4*b^10*c^6 - 4600*a^5*b^8*c^7 + 3050*a^6*b^6*c^8 - 1000*a^7*b^4*c^9 + 125*a^8*b^2*c^10 - 2*a^9*c^11)*d^2*e^4 - 6*(b^19*c - 17*a*b^17*c^2 + 121*a^2*b^15*c^3 - 468*a^3*b^13*c^4 + 1068*a^4*b^11*c^5 - 1461*a^5*b^9*c^6 + 1163*a^6*b^7*c^7 - 496*a^7*b^5*c^8 + 95*a^8*b^3*c^9 - 5*a^9*b*c^10)*d*e^5 + (b^20 - 18*a*b^18*c + 137*a^2*b^16*c^2 - 574*a^3*b^14*c^3 + 1444*a^4*b^12*c^4 - 2232*a^5*b^10*c^5 + 2083*a^6*b^8*c^6 - 1106*a^7*b^6*c^7 + 295*a^8*b^4*c^8 - 30*a^9*b^2*c^9 + a^10*c^10)*e^6)/(b^2*c^22 - 4*a*c^23)))/(b^2*c^11 - 4*a*c^12)) + 4*((a^4*b^7*c^4 - 6*a^5*b^5*c^5 + 10*a^6*b^3*c^6 - 4*a^7*b*c^7)*d^5 - (4*a^4*b^8*c^3 - 27*a^5*b^6*c^4 + 55*a^6*b^4*c^5 - 34*a^7*b^2*c^6 + 3*a^8*c^7)*d^4*e + 2*(3*a^4*b^9*c^2 - 22*a^5*b^7*c^3 + 51*a^6*b^5*c^4 - 40*a^7*b^3*c^5 + 7*a^8*b*c^6)*d^3*e^2 - 2*(2*a^4*b^10*c - 15*a^5*b^8*c^2 + 35*a^6*b^6*c^3 - 25*a^7*b^4*c^4 + a^9*c^6)*d^2*e^3 + (a^4*b^11 - 6*a^5*b^9*c + 4*a^6*b^7*c^2 + 28*a^7*b^5*c^3 - 45*a^8*b^3*c^4 + 14*a^9*b*c^5)*d*e^4 - (a^5*b^10 - 9*a^6*b^8*c + 28*a^7*b^6*c^2 - 35*a^8*b^4*c^3 + 15*a^9*b^2*c^4 - a^10*c^5)*e^5)*sqrt(e*x + d)) - 4*(35*c^4*e^4*x^4 + 8*c^4*d^4 + 18*b*c^3*d^3*e + 63*(b^2*c^2 - a*c^3)*d^2*e^2 - 420*(b^3*c - 2*a*b*c^2)*d*e^3 + 315*(b^4 - 3*a*b^2*c + a^2*c^2)*e^4 + 5*(10*c^4*d*e^3 - 9*b*c^3*e^4)*x^3 + 3*(c^4*d^2*e^2 - 24*b*c^3*d*e^3 + 21*(b^2*c^2 - a*c^3)*e^4)*x^2 - (4*c^4*d^3*e + 9*b*c^3*d^2*e^2 - 126*(b^2*c^2 - a*c^3)*d*e^3 + 105*(b^3*c - 2*a*b*c^2)*e^4)*x)*sqrt(e*x + d))/(c^5*e^3)","B",0
534,1,11459,0,6.060631," ","integrate(x^3*(e*x+d)^(3/2)/(c*x^2+b*x+a),x, algorithm=""fricas"")","-\frac{105 \, \sqrt{2} c^{4} e^{2} \sqrt{\frac{{\left(b^{6} c^{3} - 6 \, a b^{4} c^{4} + 9 \, a^{2} b^{2} c^{5} - 2 \, a^{3} c^{6}\right)} d^{3} - 3 \, {\left(b^{7} c^{2} - 7 \, a b^{5} c^{3} + 14 \, a^{2} b^{3} c^{4} - 7 \, a^{3} b c^{5}\right)} d^{2} e + 3 \, {\left(b^{8} c - 8 \, a b^{6} c^{2} + 20 \, a^{2} b^{4} c^{3} - 16 \, a^{3} b^{2} c^{4} + 2 \, a^{4} c^{5}\right)} d e^{2} - {\left(b^{9} - 9 \, a b^{7} c + 27 \, a^{2} b^{5} c^{2} - 30 \, a^{3} b^{3} c^{3} + 9 \, a^{4} b c^{4}\right)} e^{3} + {\left(b^{2} c^{9} - 4 \, a c^{10}\right)} \sqrt{\frac{{\left(b^{10} c^{6} - 8 \, a b^{8} c^{7} + 22 \, a^{2} b^{6} c^{8} - 24 \, a^{3} b^{4} c^{9} + 9 \, a^{4} b^{2} c^{10}\right)} d^{6} - 6 \, {\left(b^{11} c^{5} - 9 \, a b^{9} c^{6} + 29 \, a^{2} b^{7} c^{7} - 40 \, a^{3} b^{5} c^{8} + 22 \, a^{4} b^{3} c^{9} - 3 \, a^{5} b c^{10}\right)} d^{5} e + 3 \, {\left(5 \, b^{12} c^{4} - 50 \, a b^{10} c^{5} + 185 \, a^{2} b^{8} c^{6} - 310 \, a^{3} b^{6} c^{7} + 230 \, a^{4} b^{4} c^{8} - 60 \, a^{5} b^{2} c^{9} + 3 \, a^{6} c^{10}\right)} d^{4} e^{2} - 2 \, {\left(10 \, b^{13} c^{3} - 110 \, a b^{11} c^{4} + 460 \, a^{2} b^{9} c^{5} - 910 \, a^{3} b^{7} c^{6} + 860 \, a^{4} b^{5} c^{7} - 340 \, a^{5} b^{3} c^{8} + 39 \, a^{6} b c^{9}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{14} c^{2} - 60 \, a b^{12} c^{3} + 280 \, a^{2} b^{10} c^{4} - 640 \, a^{3} b^{8} c^{5} + 740 \, a^{4} b^{6} c^{6} - 400 \, a^{5} b^{4} c^{7} + 80 \, a^{6} b^{2} c^{8} - 2 \, a^{7} c^{9}\right)} d^{2} e^{4} - 6 \, {\left(b^{15} c - 13 \, a b^{13} c^{2} + 67 \, a^{2} b^{11} c^{3} - 174 \, a^{3} b^{9} c^{4} + 239 \, a^{4} b^{7} c^{5} - 166 \, a^{5} b^{5} c^{6} + 50 \, a^{6} b^{3} c^{7} - 4 \, a^{7} b c^{8}\right)} d e^{5} + {\left(b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}\right)} e^{6}}{b^{2} c^{18} - 4 \, a c^{19}}}}{b^{2} c^{9} - 4 \, a c^{10}}} \log\left(\sqrt{2} {\left({\left(b^{9} c^{4} - 9 \, a b^{7} c^{5} + 27 \, a^{2} b^{5} c^{6} - 31 \, a^{3} b^{3} c^{7} + 12 \, a^{4} b c^{8}\right)} d^{4} - {\left(4 \, b^{10} c^{3} - 40 \, a b^{8} c^{4} + 140 \, a^{2} b^{6} c^{5} - 203 \, a^{3} b^{4} c^{6} + 111 \, a^{4} b^{2} c^{7} - 12 \, a^{5} c^{8}\right)} d^{3} e + 3 \, {\left(2 \, b^{11} c^{2} - 22 \, a b^{9} c^{3} + 88 \, a^{2} b^{7} c^{4} - 155 \, a^{3} b^{5} c^{5} + 114 \, a^{4} b^{3} c^{6} - 24 \, a^{5} b c^{7}\right)} d^{2} e^{2} - {\left(4 \, b^{12} c - 48 \, a b^{10} c^{2} + 216 \, a^{2} b^{8} c^{3} - 449 \, a^{3} b^{6} c^{4} + 423 \, a^{4} b^{4} c^{5} - 141 \, a^{5} b^{2} c^{6} + 4 \, a^{6} c^{7}\right)} d e^{3} + {\left(b^{13} - 13 \, a b^{11} c + 65 \, a^{2} b^{9} c^{2} - 156 \, a^{3} b^{7} c^{3} + 181 \, a^{4} b^{5} c^{4} - 86 \, a^{5} b^{3} c^{5} + 8 \, a^{6} b c^{6}\right)} e^{4} - {\left({\left(b^{5} c^{10} - 7 \, a b^{3} c^{11} + 12 \, a^{2} b c^{12}\right)} d - {\left(b^{6} c^{9} - 8 \, a b^{4} c^{10} + 18 \, a^{2} b^{2} c^{11} - 8 \, a^{3} c^{12}\right)} e\right)} \sqrt{\frac{{\left(b^{10} c^{6} - 8 \, a b^{8} c^{7} + 22 \, a^{2} b^{6} c^{8} - 24 \, a^{3} b^{4} c^{9} + 9 \, a^{4} b^{2} c^{10}\right)} d^{6} - 6 \, {\left(b^{11} c^{5} - 9 \, a b^{9} c^{6} + 29 \, a^{2} b^{7} c^{7} - 40 \, a^{3} b^{5} c^{8} + 22 \, a^{4} b^{3} c^{9} - 3 \, a^{5} b c^{10}\right)} d^{5} e + 3 \, {\left(5 \, b^{12} c^{4} - 50 \, a b^{10} c^{5} + 185 \, a^{2} b^{8} c^{6} - 310 \, a^{3} b^{6} c^{7} + 230 \, a^{4} b^{4} c^{8} - 60 \, a^{5} b^{2} c^{9} + 3 \, a^{6} c^{10}\right)} d^{4} e^{2} - 2 \, {\left(10 \, b^{13} c^{3} - 110 \, a b^{11} c^{4} + 460 \, a^{2} b^{9} c^{5} - 910 \, a^{3} b^{7} c^{6} + 860 \, a^{4} b^{5} c^{7} - 340 \, a^{5} b^{3} c^{8} + 39 \, a^{6} b c^{9}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{14} c^{2} - 60 \, a b^{12} c^{3} + 280 \, a^{2} b^{10} c^{4} - 640 \, a^{3} b^{8} c^{5} + 740 \, a^{4} b^{6} c^{6} - 400 \, a^{5} b^{4} c^{7} + 80 \, a^{6} b^{2} c^{8} - 2 \, a^{7} c^{9}\right)} d^{2} e^{4} - 6 \, {\left(b^{15} c - 13 \, a b^{13} c^{2} + 67 \, a^{2} b^{11} c^{3} - 174 \, a^{3} b^{9} c^{4} + 239 \, a^{4} b^{7} c^{5} - 166 \, a^{5} b^{5} c^{6} + 50 \, a^{6} b^{3} c^{7} - 4 \, a^{7} b c^{8}\right)} d e^{5} + {\left(b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}\right)} e^{6}}{b^{2} c^{18} - 4 \, a c^{19}}}\right)} \sqrt{\frac{{\left(b^{6} c^{3} - 6 \, a b^{4} c^{4} + 9 \, a^{2} b^{2} c^{5} - 2 \, a^{3} c^{6}\right)} d^{3} - 3 \, {\left(b^{7} c^{2} - 7 \, a b^{5} c^{3} + 14 \, a^{2} b^{3} c^{4} - 7 \, a^{3} b c^{5}\right)} d^{2} e + 3 \, {\left(b^{8} c - 8 \, a b^{6} c^{2} + 20 \, a^{2} b^{4} c^{3} - 16 \, a^{3} b^{2} c^{4} + 2 \, a^{4} c^{5}\right)} d e^{2} - {\left(b^{9} - 9 \, a b^{7} c + 27 \, a^{2} b^{5} c^{2} - 30 \, a^{3} b^{3} c^{3} + 9 \, a^{4} b c^{4}\right)} e^{3} + {\left(b^{2} c^{9} - 4 \, a c^{10}\right)} \sqrt{\frac{{\left(b^{10} c^{6} - 8 \, a b^{8} c^{7} + 22 \, a^{2} b^{6} c^{8} - 24 \, a^{3} b^{4} c^{9} + 9 \, a^{4} b^{2} c^{10}\right)} d^{6} - 6 \, {\left(b^{11} c^{5} - 9 \, a b^{9} c^{6} + 29 \, a^{2} b^{7} c^{7} - 40 \, a^{3} b^{5} c^{8} + 22 \, a^{4} b^{3} c^{9} - 3 \, a^{5} b c^{10}\right)} d^{5} e + 3 \, {\left(5 \, b^{12} c^{4} - 50 \, a b^{10} c^{5} + 185 \, a^{2} b^{8} c^{6} - 310 \, a^{3} b^{6} c^{7} + 230 \, a^{4} b^{4} c^{8} - 60 \, a^{5} b^{2} c^{9} + 3 \, a^{6} c^{10}\right)} d^{4} e^{2} - 2 \, {\left(10 \, b^{13} c^{3} - 110 \, a b^{11} c^{4} + 460 \, a^{2} b^{9} c^{5} - 910 \, a^{3} b^{7} c^{6} + 860 \, a^{4} b^{5} c^{7} - 340 \, a^{5} b^{3} c^{8} + 39 \, a^{6} b c^{9}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{14} c^{2} - 60 \, a b^{12} c^{3} + 280 \, a^{2} b^{10} c^{4} - 640 \, a^{3} b^{8} c^{5} + 740 \, a^{4} b^{6} c^{6} - 400 \, a^{5} b^{4} c^{7} + 80 \, a^{6} b^{2} c^{8} - 2 \, a^{7} c^{9}\right)} d^{2} e^{4} - 6 \, {\left(b^{15} c - 13 \, a b^{13} c^{2} + 67 \, a^{2} b^{11} c^{3} - 174 \, a^{3} b^{9} c^{4} + 239 \, a^{4} b^{7} c^{5} - 166 \, a^{5} b^{5} c^{6} + 50 \, a^{6} b^{3} c^{7} - 4 \, a^{7} b c^{8}\right)} d e^{5} + {\left(b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}\right)} e^{6}}{b^{2} c^{18} - 4 \, a c^{19}}}}{b^{2} c^{9} - 4 \, a c^{10}}} - 4 \, {\left({\left(a^{3} b^{5} c^{4} - 4 \, a^{4} b^{3} c^{5} + 3 \, a^{5} b c^{6}\right)} d^{5} - {\left(4 \, a^{3} b^{6} c^{3} - 19 \, a^{4} b^{4} c^{4} + 21 \, a^{5} b^{2} c^{5} - 3 \, a^{6} c^{6}\right)} d^{4} e + 2 \, {\left(3 \, a^{3} b^{7} c^{2} - 16 \, a^{4} b^{5} c^{3} + 22 \, a^{5} b^{3} c^{4} - 6 \, a^{6} b c^{5}\right)} d^{3} e^{2} - 2 \, {\left(2 \, a^{3} b^{8} c - 11 \, a^{4} b^{6} c^{2} + 15 \, a^{5} b^{4} c^{3} - 2 \, a^{6} b^{2} c^{4} - a^{7} c^{5}\right)} d^{2} e^{3} + {\left(a^{3} b^{9} - 4 \, a^{4} b^{7} c - 3 \, a^{5} b^{5} c^{2} + 20 \, a^{6} b^{3} c^{3} - 11 \, a^{7} b c^{4}\right)} d e^{4} - {\left(a^{4} b^{8} - 7 \, a^{5} b^{6} c + 15 \, a^{6} b^{4} c^{2} - 10 \, a^{7} b^{2} c^{3} + a^{8} c^{4}\right)} e^{5}\right)} \sqrt{e x + d}\right) - 105 \, \sqrt{2} c^{4} e^{2} \sqrt{\frac{{\left(b^{6} c^{3} - 6 \, a b^{4} c^{4} + 9 \, a^{2} b^{2} c^{5} - 2 \, a^{3} c^{6}\right)} d^{3} - 3 \, {\left(b^{7} c^{2} - 7 \, a b^{5} c^{3} + 14 \, a^{2} b^{3} c^{4} - 7 \, a^{3} b c^{5}\right)} d^{2} e + 3 \, {\left(b^{8} c - 8 \, a b^{6} c^{2} + 20 \, a^{2} b^{4} c^{3} - 16 \, a^{3} b^{2} c^{4} + 2 \, a^{4} c^{5}\right)} d e^{2} - {\left(b^{9} - 9 \, a b^{7} c + 27 \, a^{2} b^{5} c^{2} - 30 \, a^{3} b^{3} c^{3} + 9 \, a^{4} b c^{4}\right)} e^{3} + {\left(b^{2} c^{9} - 4 \, a c^{10}\right)} \sqrt{\frac{{\left(b^{10} c^{6} - 8 \, a b^{8} c^{7} + 22 \, a^{2} b^{6} c^{8} - 24 \, a^{3} b^{4} c^{9} + 9 \, a^{4} b^{2} c^{10}\right)} d^{6} - 6 \, {\left(b^{11} c^{5} - 9 \, a b^{9} c^{6} + 29 \, a^{2} b^{7} c^{7} - 40 \, a^{3} b^{5} c^{8} + 22 \, a^{4} b^{3} c^{9} - 3 \, a^{5} b c^{10}\right)} d^{5} e + 3 \, {\left(5 \, b^{12} c^{4} - 50 \, a b^{10} c^{5} + 185 \, a^{2} b^{8} c^{6} - 310 \, a^{3} b^{6} c^{7} + 230 \, a^{4} b^{4} c^{8} - 60 \, a^{5} b^{2} c^{9} + 3 \, a^{6} c^{10}\right)} d^{4} e^{2} - 2 \, {\left(10 \, b^{13} c^{3} - 110 \, a b^{11} c^{4} + 460 \, a^{2} b^{9} c^{5} - 910 \, a^{3} b^{7} c^{6} + 860 \, a^{4} b^{5} c^{7} - 340 \, a^{5} b^{3} c^{8} + 39 \, a^{6} b c^{9}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{14} c^{2} - 60 \, a b^{12} c^{3} + 280 \, a^{2} b^{10} c^{4} - 640 \, a^{3} b^{8} c^{5} + 740 \, a^{4} b^{6} c^{6} - 400 \, a^{5} b^{4} c^{7} + 80 \, a^{6} b^{2} c^{8} - 2 \, a^{7} c^{9}\right)} d^{2} e^{4} - 6 \, {\left(b^{15} c - 13 \, a b^{13} c^{2} + 67 \, a^{2} b^{11} c^{3} - 174 \, a^{3} b^{9} c^{4} + 239 \, a^{4} b^{7} c^{5} - 166 \, a^{5} b^{5} c^{6} + 50 \, a^{6} b^{3} c^{7} - 4 \, a^{7} b c^{8}\right)} d e^{5} + {\left(b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}\right)} e^{6}}{b^{2} c^{18} - 4 \, a c^{19}}}}{b^{2} c^{9} - 4 \, a c^{10}}} \log\left(-\sqrt{2} {\left({\left(b^{9} c^{4} - 9 \, a b^{7} c^{5} + 27 \, a^{2} b^{5} c^{6} - 31 \, a^{3} b^{3} c^{7} + 12 \, a^{4} b c^{8}\right)} d^{4} - {\left(4 \, b^{10} c^{3} - 40 \, a b^{8} c^{4} + 140 \, a^{2} b^{6} c^{5} - 203 \, a^{3} b^{4} c^{6} + 111 \, a^{4} b^{2} c^{7} - 12 \, a^{5} c^{8}\right)} d^{3} e + 3 \, {\left(2 \, b^{11} c^{2} - 22 \, a b^{9} c^{3} + 88 \, a^{2} b^{7} c^{4} - 155 \, a^{3} b^{5} c^{5} + 114 \, a^{4} b^{3} c^{6} - 24 \, a^{5} b c^{7}\right)} d^{2} e^{2} - {\left(4 \, b^{12} c - 48 \, a b^{10} c^{2} + 216 \, a^{2} b^{8} c^{3} - 449 \, a^{3} b^{6} c^{4} + 423 \, a^{4} b^{4} c^{5} - 141 \, a^{5} b^{2} c^{6} + 4 \, a^{6} c^{7}\right)} d e^{3} + {\left(b^{13} - 13 \, a b^{11} c + 65 \, a^{2} b^{9} c^{2} - 156 \, a^{3} b^{7} c^{3} + 181 \, a^{4} b^{5} c^{4} - 86 \, a^{5} b^{3} c^{5} + 8 \, a^{6} b c^{6}\right)} e^{4} - {\left({\left(b^{5} c^{10} - 7 \, a b^{3} c^{11} + 12 \, a^{2} b c^{12}\right)} d - {\left(b^{6} c^{9} - 8 \, a b^{4} c^{10} + 18 \, a^{2} b^{2} c^{11} - 8 \, a^{3} c^{12}\right)} e\right)} \sqrt{\frac{{\left(b^{10} c^{6} - 8 \, a b^{8} c^{7} + 22 \, a^{2} b^{6} c^{8} - 24 \, a^{3} b^{4} c^{9} + 9 \, a^{4} b^{2} c^{10}\right)} d^{6} - 6 \, {\left(b^{11} c^{5} - 9 \, a b^{9} c^{6} + 29 \, a^{2} b^{7} c^{7} - 40 \, a^{3} b^{5} c^{8} + 22 \, a^{4} b^{3} c^{9} - 3 \, a^{5} b c^{10}\right)} d^{5} e + 3 \, {\left(5 \, b^{12} c^{4} - 50 \, a b^{10} c^{5} + 185 \, a^{2} b^{8} c^{6} - 310 \, a^{3} b^{6} c^{7} + 230 \, a^{4} b^{4} c^{8} - 60 \, a^{5} b^{2} c^{9} + 3 \, a^{6} c^{10}\right)} d^{4} e^{2} - 2 \, {\left(10 \, b^{13} c^{3} - 110 \, a b^{11} c^{4} + 460 \, a^{2} b^{9} c^{5} - 910 \, a^{3} b^{7} c^{6} + 860 \, a^{4} b^{5} c^{7} - 340 \, a^{5} b^{3} c^{8} + 39 \, a^{6} b c^{9}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{14} c^{2} - 60 \, a b^{12} c^{3} + 280 \, a^{2} b^{10} c^{4} - 640 \, a^{3} b^{8} c^{5} + 740 \, a^{4} b^{6} c^{6} - 400 \, a^{5} b^{4} c^{7} + 80 \, a^{6} b^{2} c^{8} - 2 \, a^{7} c^{9}\right)} d^{2} e^{4} - 6 \, {\left(b^{15} c - 13 \, a b^{13} c^{2} + 67 \, a^{2} b^{11} c^{3} - 174 \, a^{3} b^{9} c^{4} + 239 \, a^{4} b^{7} c^{5} - 166 \, a^{5} b^{5} c^{6} + 50 \, a^{6} b^{3} c^{7} - 4 \, a^{7} b c^{8}\right)} d e^{5} + {\left(b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}\right)} e^{6}}{b^{2} c^{18} - 4 \, a c^{19}}}\right)} \sqrt{\frac{{\left(b^{6} c^{3} - 6 \, a b^{4} c^{4} + 9 \, a^{2} b^{2} c^{5} - 2 \, a^{3} c^{6}\right)} d^{3} - 3 \, {\left(b^{7} c^{2} - 7 \, a b^{5} c^{3} + 14 \, a^{2} b^{3} c^{4} - 7 \, a^{3} b c^{5}\right)} d^{2} e + 3 \, {\left(b^{8} c - 8 \, a b^{6} c^{2} + 20 \, a^{2} b^{4} c^{3} - 16 \, a^{3} b^{2} c^{4} + 2 \, a^{4} c^{5}\right)} d e^{2} - {\left(b^{9} - 9 \, a b^{7} c + 27 \, a^{2} b^{5} c^{2} - 30 \, a^{3} b^{3} c^{3} + 9 \, a^{4} b c^{4}\right)} e^{3} + {\left(b^{2} c^{9} - 4 \, a c^{10}\right)} \sqrt{\frac{{\left(b^{10} c^{6} - 8 \, a b^{8} c^{7} + 22 \, a^{2} b^{6} c^{8} - 24 \, a^{3} b^{4} c^{9} + 9 \, a^{4} b^{2} c^{10}\right)} d^{6} - 6 \, {\left(b^{11} c^{5} - 9 \, a b^{9} c^{6} + 29 \, a^{2} b^{7} c^{7} - 40 \, a^{3} b^{5} c^{8} + 22 \, a^{4} b^{3} c^{9} - 3 \, a^{5} b c^{10}\right)} d^{5} e + 3 \, {\left(5 \, b^{12} c^{4} - 50 \, a b^{10} c^{5} + 185 \, a^{2} b^{8} c^{6} - 310 \, a^{3} b^{6} c^{7} + 230 \, a^{4} b^{4} c^{8} - 60 \, a^{5} b^{2} c^{9} + 3 \, a^{6} c^{10}\right)} d^{4} e^{2} - 2 \, {\left(10 \, b^{13} c^{3} - 110 \, a b^{11} c^{4} + 460 \, a^{2} b^{9} c^{5} - 910 \, a^{3} b^{7} c^{6} + 860 \, a^{4} b^{5} c^{7} - 340 \, a^{5} b^{3} c^{8} + 39 \, a^{6} b c^{9}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{14} c^{2} - 60 \, a b^{12} c^{3} + 280 \, a^{2} b^{10} c^{4} - 640 \, a^{3} b^{8} c^{5} + 740 \, a^{4} b^{6} c^{6} - 400 \, a^{5} b^{4} c^{7} + 80 \, a^{6} b^{2} c^{8} - 2 \, a^{7} c^{9}\right)} d^{2} e^{4} - 6 \, {\left(b^{15} c - 13 \, a b^{13} c^{2} + 67 \, a^{2} b^{11} c^{3} - 174 \, a^{3} b^{9} c^{4} + 239 \, a^{4} b^{7} c^{5} - 166 \, a^{5} b^{5} c^{6} + 50 \, a^{6} b^{3} c^{7} - 4 \, a^{7} b c^{8}\right)} d e^{5} + {\left(b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}\right)} e^{6}}{b^{2} c^{18} - 4 \, a c^{19}}}}{b^{2} c^{9} - 4 \, a c^{10}}} - 4 \, {\left({\left(a^{3} b^{5} c^{4} - 4 \, a^{4} b^{3} c^{5} + 3 \, a^{5} b c^{6}\right)} d^{5} - {\left(4 \, a^{3} b^{6} c^{3} - 19 \, a^{4} b^{4} c^{4} + 21 \, a^{5} b^{2} c^{5} - 3 \, a^{6} c^{6}\right)} d^{4} e + 2 \, {\left(3 \, a^{3} b^{7} c^{2} - 16 \, a^{4} b^{5} c^{3} + 22 \, a^{5} b^{3} c^{4} - 6 \, a^{6} b c^{5}\right)} d^{3} e^{2} - 2 \, {\left(2 \, a^{3} b^{8} c - 11 \, a^{4} b^{6} c^{2} + 15 \, a^{5} b^{4} c^{3} - 2 \, a^{6} b^{2} c^{4} - a^{7} c^{5}\right)} d^{2} e^{3} + {\left(a^{3} b^{9} - 4 \, a^{4} b^{7} c - 3 \, a^{5} b^{5} c^{2} + 20 \, a^{6} b^{3} c^{3} - 11 \, a^{7} b c^{4}\right)} d e^{4} - {\left(a^{4} b^{8} - 7 \, a^{5} b^{6} c + 15 \, a^{6} b^{4} c^{2} - 10 \, a^{7} b^{2} c^{3} + a^{8} c^{4}\right)} e^{5}\right)} \sqrt{e x + d}\right) + 105 \, \sqrt{2} c^{4} e^{2} \sqrt{\frac{{\left(b^{6} c^{3} - 6 \, a b^{4} c^{4} + 9 \, a^{2} b^{2} c^{5} - 2 \, a^{3} c^{6}\right)} d^{3} - 3 \, {\left(b^{7} c^{2} - 7 \, a b^{5} c^{3} + 14 \, a^{2} b^{3} c^{4} - 7 \, a^{3} b c^{5}\right)} d^{2} e + 3 \, {\left(b^{8} c - 8 \, a b^{6} c^{2} + 20 \, a^{2} b^{4} c^{3} - 16 \, a^{3} b^{2} c^{4} + 2 \, a^{4} c^{5}\right)} d e^{2} - {\left(b^{9} - 9 \, a b^{7} c + 27 \, a^{2} b^{5} c^{2} - 30 \, a^{3} b^{3} c^{3} + 9 \, a^{4} b c^{4}\right)} e^{3} - {\left(b^{2} c^{9} - 4 \, a c^{10}\right)} \sqrt{\frac{{\left(b^{10} c^{6} - 8 \, a b^{8} c^{7} + 22 \, a^{2} b^{6} c^{8} - 24 \, a^{3} b^{4} c^{9} + 9 \, a^{4} b^{2} c^{10}\right)} d^{6} - 6 \, {\left(b^{11} c^{5} - 9 \, a b^{9} c^{6} + 29 \, a^{2} b^{7} c^{7} - 40 \, a^{3} b^{5} c^{8} + 22 \, a^{4} b^{3} c^{9} - 3 \, a^{5} b c^{10}\right)} d^{5} e + 3 \, {\left(5 \, b^{12} c^{4} - 50 \, a b^{10} c^{5} + 185 \, a^{2} b^{8} c^{6} - 310 \, a^{3} b^{6} c^{7} + 230 \, a^{4} b^{4} c^{8} - 60 \, a^{5} b^{2} c^{9} + 3 \, a^{6} c^{10}\right)} d^{4} e^{2} - 2 \, {\left(10 \, b^{13} c^{3} - 110 \, a b^{11} c^{4} + 460 \, a^{2} b^{9} c^{5} - 910 \, a^{3} b^{7} c^{6} + 860 \, a^{4} b^{5} c^{7} - 340 \, a^{5} b^{3} c^{8} + 39 \, a^{6} b c^{9}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{14} c^{2} - 60 \, a b^{12} c^{3} + 280 \, a^{2} b^{10} c^{4} - 640 \, a^{3} b^{8} c^{5} + 740 \, a^{4} b^{6} c^{6} - 400 \, a^{5} b^{4} c^{7} + 80 \, a^{6} b^{2} c^{8} - 2 \, a^{7} c^{9}\right)} d^{2} e^{4} - 6 \, {\left(b^{15} c - 13 \, a b^{13} c^{2} + 67 \, a^{2} b^{11} c^{3} - 174 \, a^{3} b^{9} c^{4} + 239 \, a^{4} b^{7} c^{5} - 166 \, a^{5} b^{5} c^{6} + 50 \, a^{6} b^{3} c^{7} - 4 \, a^{7} b c^{8}\right)} d e^{5} + {\left(b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}\right)} e^{6}}{b^{2} c^{18} - 4 \, a c^{19}}}}{b^{2} c^{9} - 4 \, a c^{10}}} \log\left(\sqrt{2} {\left({\left(b^{9} c^{4} - 9 \, a b^{7} c^{5} + 27 \, a^{2} b^{5} c^{6} - 31 \, a^{3} b^{3} c^{7} + 12 \, a^{4} b c^{8}\right)} d^{4} - {\left(4 \, b^{10} c^{3} - 40 \, a b^{8} c^{4} + 140 \, a^{2} b^{6} c^{5} - 203 \, a^{3} b^{4} c^{6} + 111 \, a^{4} b^{2} c^{7} - 12 \, a^{5} c^{8}\right)} d^{3} e + 3 \, {\left(2 \, b^{11} c^{2} - 22 \, a b^{9} c^{3} + 88 \, a^{2} b^{7} c^{4} - 155 \, a^{3} b^{5} c^{5} + 114 \, a^{4} b^{3} c^{6} - 24 \, a^{5} b c^{7}\right)} d^{2} e^{2} - {\left(4 \, b^{12} c - 48 \, a b^{10} c^{2} + 216 \, a^{2} b^{8} c^{3} - 449 \, a^{3} b^{6} c^{4} + 423 \, a^{4} b^{4} c^{5} - 141 \, a^{5} b^{2} c^{6} + 4 \, a^{6} c^{7}\right)} d e^{3} + {\left(b^{13} - 13 \, a b^{11} c + 65 \, a^{2} b^{9} c^{2} - 156 \, a^{3} b^{7} c^{3} + 181 \, a^{4} b^{5} c^{4} - 86 \, a^{5} b^{3} c^{5} + 8 \, a^{6} b c^{6}\right)} e^{4} + {\left({\left(b^{5} c^{10} - 7 \, a b^{3} c^{11} + 12 \, a^{2} b c^{12}\right)} d - {\left(b^{6} c^{9} - 8 \, a b^{4} c^{10} + 18 \, a^{2} b^{2} c^{11} - 8 \, a^{3} c^{12}\right)} e\right)} \sqrt{\frac{{\left(b^{10} c^{6} - 8 \, a b^{8} c^{7} + 22 \, a^{2} b^{6} c^{8} - 24 \, a^{3} b^{4} c^{9} + 9 \, a^{4} b^{2} c^{10}\right)} d^{6} - 6 \, {\left(b^{11} c^{5} - 9 \, a b^{9} c^{6} + 29 \, a^{2} b^{7} c^{7} - 40 \, a^{3} b^{5} c^{8} + 22 \, a^{4} b^{3} c^{9} - 3 \, a^{5} b c^{10}\right)} d^{5} e + 3 \, {\left(5 \, b^{12} c^{4} - 50 \, a b^{10} c^{5} + 185 \, a^{2} b^{8} c^{6} - 310 \, a^{3} b^{6} c^{7} + 230 \, a^{4} b^{4} c^{8} - 60 \, a^{5} b^{2} c^{9} + 3 \, a^{6} c^{10}\right)} d^{4} e^{2} - 2 \, {\left(10 \, b^{13} c^{3} - 110 \, a b^{11} c^{4} + 460 \, a^{2} b^{9} c^{5} - 910 \, a^{3} b^{7} c^{6} + 860 \, a^{4} b^{5} c^{7} - 340 \, a^{5} b^{3} c^{8} + 39 \, a^{6} b c^{9}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{14} c^{2} - 60 \, a b^{12} c^{3} + 280 \, a^{2} b^{10} c^{4} - 640 \, a^{3} b^{8} c^{5} + 740 \, a^{4} b^{6} c^{6} - 400 \, a^{5} b^{4} c^{7} + 80 \, a^{6} b^{2} c^{8} - 2 \, a^{7} c^{9}\right)} d^{2} e^{4} - 6 \, {\left(b^{15} c - 13 \, a b^{13} c^{2} + 67 \, a^{2} b^{11} c^{3} - 174 \, a^{3} b^{9} c^{4} + 239 \, a^{4} b^{7} c^{5} - 166 \, a^{5} b^{5} c^{6} + 50 \, a^{6} b^{3} c^{7} - 4 \, a^{7} b c^{8}\right)} d e^{5} + {\left(b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}\right)} e^{6}}{b^{2} c^{18} - 4 \, a c^{19}}}\right)} \sqrt{\frac{{\left(b^{6} c^{3} - 6 \, a b^{4} c^{4} + 9 \, a^{2} b^{2} c^{5} - 2 \, a^{3} c^{6}\right)} d^{3} - 3 \, {\left(b^{7} c^{2} - 7 \, a b^{5} c^{3} + 14 \, a^{2} b^{3} c^{4} - 7 \, a^{3} b c^{5}\right)} d^{2} e + 3 \, {\left(b^{8} c - 8 \, a b^{6} c^{2} + 20 \, a^{2} b^{4} c^{3} - 16 \, a^{3} b^{2} c^{4} + 2 \, a^{4} c^{5}\right)} d e^{2} - {\left(b^{9} - 9 \, a b^{7} c + 27 \, a^{2} b^{5} c^{2} - 30 \, a^{3} b^{3} c^{3} + 9 \, a^{4} b c^{4}\right)} e^{3} - {\left(b^{2} c^{9} - 4 \, a c^{10}\right)} \sqrt{\frac{{\left(b^{10} c^{6} - 8 \, a b^{8} c^{7} + 22 \, a^{2} b^{6} c^{8} - 24 \, a^{3} b^{4} c^{9} + 9 \, a^{4} b^{2} c^{10}\right)} d^{6} - 6 \, {\left(b^{11} c^{5} - 9 \, a b^{9} c^{6} + 29 \, a^{2} b^{7} c^{7} - 40 \, a^{3} b^{5} c^{8} + 22 \, a^{4} b^{3} c^{9} - 3 \, a^{5} b c^{10}\right)} d^{5} e + 3 \, {\left(5 \, b^{12} c^{4} - 50 \, a b^{10} c^{5} + 185 \, a^{2} b^{8} c^{6} - 310 \, a^{3} b^{6} c^{7} + 230 \, a^{4} b^{4} c^{8} - 60 \, a^{5} b^{2} c^{9} + 3 \, a^{6} c^{10}\right)} d^{4} e^{2} - 2 \, {\left(10 \, b^{13} c^{3} - 110 \, a b^{11} c^{4} + 460 \, a^{2} b^{9} c^{5} - 910 \, a^{3} b^{7} c^{6} + 860 \, a^{4} b^{5} c^{7} - 340 \, a^{5} b^{3} c^{8} + 39 \, a^{6} b c^{9}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{14} c^{2} - 60 \, a b^{12} c^{3} + 280 \, a^{2} b^{10} c^{4} - 640 \, a^{3} b^{8} c^{5} + 740 \, a^{4} b^{6} c^{6} - 400 \, a^{5} b^{4} c^{7} + 80 \, a^{6} b^{2} c^{8} - 2 \, a^{7} c^{9}\right)} d^{2} e^{4} - 6 \, {\left(b^{15} c - 13 \, a b^{13} c^{2} + 67 \, a^{2} b^{11} c^{3} - 174 \, a^{3} b^{9} c^{4} + 239 \, a^{4} b^{7} c^{5} - 166 \, a^{5} b^{5} c^{6} + 50 \, a^{6} b^{3} c^{7} - 4 \, a^{7} b c^{8}\right)} d e^{5} + {\left(b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}\right)} e^{6}}{b^{2} c^{18} - 4 \, a c^{19}}}}{b^{2} c^{9} - 4 \, a c^{10}}} - 4 \, {\left({\left(a^{3} b^{5} c^{4} - 4 \, a^{4} b^{3} c^{5} + 3 \, a^{5} b c^{6}\right)} d^{5} - {\left(4 \, a^{3} b^{6} c^{3} - 19 \, a^{4} b^{4} c^{4} + 21 \, a^{5} b^{2} c^{5} - 3 \, a^{6} c^{6}\right)} d^{4} e + 2 \, {\left(3 \, a^{3} b^{7} c^{2} - 16 \, a^{4} b^{5} c^{3} + 22 \, a^{5} b^{3} c^{4} - 6 \, a^{6} b c^{5}\right)} d^{3} e^{2} - 2 \, {\left(2 \, a^{3} b^{8} c - 11 \, a^{4} b^{6} c^{2} + 15 \, a^{5} b^{4} c^{3} - 2 \, a^{6} b^{2} c^{4} - a^{7} c^{5}\right)} d^{2} e^{3} + {\left(a^{3} b^{9} - 4 \, a^{4} b^{7} c - 3 \, a^{5} b^{5} c^{2} + 20 \, a^{6} b^{3} c^{3} - 11 \, a^{7} b c^{4}\right)} d e^{4} - {\left(a^{4} b^{8} - 7 \, a^{5} b^{6} c + 15 \, a^{6} b^{4} c^{2} - 10 \, a^{7} b^{2} c^{3} + a^{8} c^{4}\right)} e^{5}\right)} \sqrt{e x + d}\right) - 105 \, \sqrt{2} c^{4} e^{2} \sqrt{\frac{{\left(b^{6} c^{3} - 6 \, a b^{4} c^{4} + 9 \, a^{2} b^{2} c^{5} - 2 \, a^{3} c^{6}\right)} d^{3} - 3 \, {\left(b^{7} c^{2} - 7 \, a b^{5} c^{3} + 14 \, a^{2} b^{3} c^{4} - 7 \, a^{3} b c^{5}\right)} d^{2} e + 3 \, {\left(b^{8} c - 8 \, a b^{6} c^{2} + 20 \, a^{2} b^{4} c^{3} - 16 \, a^{3} b^{2} c^{4} + 2 \, a^{4} c^{5}\right)} d e^{2} - {\left(b^{9} - 9 \, a b^{7} c + 27 \, a^{2} b^{5} c^{2} - 30 \, a^{3} b^{3} c^{3} + 9 \, a^{4} b c^{4}\right)} e^{3} - {\left(b^{2} c^{9} - 4 \, a c^{10}\right)} \sqrt{\frac{{\left(b^{10} c^{6} - 8 \, a b^{8} c^{7} + 22 \, a^{2} b^{6} c^{8} - 24 \, a^{3} b^{4} c^{9} + 9 \, a^{4} b^{2} c^{10}\right)} d^{6} - 6 \, {\left(b^{11} c^{5} - 9 \, a b^{9} c^{6} + 29 \, a^{2} b^{7} c^{7} - 40 \, a^{3} b^{5} c^{8} + 22 \, a^{4} b^{3} c^{9} - 3 \, a^{5} b c^{10}\right)} d^{5} e + 3 \, {\left(5 \, b^{12} c^{4} - 50 \, a b^{10} c^{5} + 185 \, a^{2} b^{8} c^{6} - 310 \, a^{3} b^{6} c^{7} + 230 \, a^{4} b^{4} c^{8} - 60 \, a^{5} b^{2} c^{9} + 3 \, a^{6} c^{10}\right)} d^{4} e^{2} - 2 \, {\left(10 \, b^{13} c^{3} - 110 \, a b^{11} c^{4} + 460 \, a^{2} b^{9} c^{5} - 910 \, a^{3} b^{7} c^{6} + 860 \, a^{4} b^{5} c^{7} - 340 \, a^{5} b^{3} c^{8} + 39 \, a^{6} b c^{9}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{14} c^{2} - 60 \, a b^{12} c^{3} + 280 \, a^{2} b^{10} c^{4} - 640 \, a^{3} b^{8} c^{5} + 740 \, a^{4} b^{6} c^{6} - 400 \, a^{5} b^{4} c^{7} + 80 \, a^{6} b^{2} c^{8} - 2 \, a^{7} c^{9}\right)} d^{2} e^{4} - 6 \, {\left(b^{15} c - 13 \, a b^{13} c^{2} + 67 \, a^{2} b^{11} c^{3} - 174 \, a^{3} b^{9} c^{4} + 239 \, a^{4} b^{7} c^{5} - 166 \, a^{5} b^{5} c^{6} + 50 \, a^{6} b^{3} c^{7} - 4 \, a^{7} b c^{8}\right)} d e^{5} + {\left(b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}\right)} e^{6}}{b^{2} c^{18} - 4 \, a c^{19}}}}{b^{2} c^{9} - 4 \, a c^{10}}} \log\left(-\sqrt{2} {\left({\left(b^{9} c^{4} - 9 \, a b^{7} c^{5} + 27 \, a^{2} b^{5} c^{6} - 31 \, a^{3} b^{3} c^{7} + 12 \, a^{4} b c^{8}\right)} d^{4} - {\left(4 \, b^{10} c^{3} - 40 \, a b^{8} c^{4} + 140 \, a^{2} b^{6} c^{5} - 203 \, a^{3} b^{4} c^{6} + 111 \, a^{4} b^{2} c^{7} - 12 \, a^{5} c^{8}\right)} d^{3} e + 3 \, {\left(2 \, b^{11} c^{2} - 22 \, a b^{9} c^{3} + 88 \, a^{2} b^{7} c^{4} - 155 \, a^{3} b^{5} c^{5} + 114 \, a^{4} b^{3} c^{6} - 24 \, a^{5} b c^{7}\right)} d^{2} e^{2} - {\left(4 \, b^{12} c - 48 \, a b^{10} c^{2} + 216 \, a^{2} b^{8} c^{3} - 449 \, a^{3} b^{6} c^{4} + 423 \, a^{4} b^{4} c^{5} - 141 \, a^{5} b^{2} c^{6} + 4 \, a^{6} c^{7}\right)} d e^{3} + {\left(b^{13} - 13 \, a b^{11} c + 65 \, a^{2} b^{9} c^{2} - 156 \, a^{3} b^{7} c^{3} + 181 \, a^{4} b^{5} c^{4} - 86 \, a^{5} b^{3} c^{5} + 8 \, a^{6} b c^{6}\right)} e^{4} + {\left({\left(b^{5} c^{10} - 7 \, a b^{3} c^{11} + 12 \, a^{2} b c^{12}\right)} d - {\left(b^{6} c^{9} - 8 \, a b^{4} c^{10} + 18 \, a^{2} b^{2} c^{11} - 8 \, a^{3} c^{12}\right)} e\right)} \sqrt{\frac{{\left(b^{10} c^{6} - 8 \, a b^{8} c^{7} + 22 \, a^{2} b^{6} c^{8} - 24 \, a^{3} b^{4} c^{9} + 9 \, a^{4} b^{2} c^{10}\right)} d^{6} - 6 \, {\left(b^{11} c^{5} - 9 \, a b^{9} c^{6} + 29 \, a^{2} b^{7} c^{7} - 40 \, a^{3} b^{5} c^{8} + 22 \, a^{4} b^{3} c^{9} - 3 \, a^{5} b c^{10}\right)} d^{5} e + 3 \, {\left(5 \, b^{12} c^{4} - 50 \, a b^{10} c^{5} + 185 \, a^{2} b^{8} c^{6} - 310 \, a^{3} b^{6} c^{7} + 230 \, a^{4} b^{4} c^{8} - 60 \, a^{5} b^{2} c^{9} + 3 \, a^{6} c^{10}\right)} d^{4} e^{2} - 2 \, {\left(10 \, b^{13} c^{3} - 110 \, a b^{11} c^{4} + 460 \, a^{2} b^{9} c^{5} - 910 \, a^{3} b^{7} c^{6} + 860 \, a^{4} b^{5} c^{7} - 340 \, a^{5} b^{3} c^{8} + 39 \, a^{6} b c^{9}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{14} c^{2} - 60 \, a b^{12} c^{3} + 280 \, a^{2} b^{10} c^{4} - 640 \, a^{3} b^{8} c^{5} + 740 \, a^{4} b^{6} c^{6} - 400 \, a^{5} b^{4} c^{7} + 80 \, a^{6} b^{2} c^{8} - 2 \, a^{7} c^{9}\right)} d^{2} e^{4} - 6 \, {\left(b^{15} c - 13 \, a b^{13} c^{2} + 67 \, a^{2} b^{11} c^{3} - 174 \, a^{3} b^{9} c^{4} + 239 \, a^{4} b^{7} c^{5} - 166 \, a^{5} b^{5} c^{6} + 50 \, a^{6} b^{3} c^{7} - 4 \, a^{7} b c^{8}\right)} d e^{5} + {\left(b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}\right)} e^{6}}{b^{2} c^{18} - 4 \, a c^{19}}}\right)} \sqrt{\frac{{\left(b^{6} c^{3} - 6 \, a b^{4} c^{4} + 9 \, a^{2} b^{2} c^{5} - 2 \, a^{3} c^{6}\right)} d^{3} - 3 \, {\left(b^{7} c^{2} - 7 \, a b^{5} c^{3} + 14 \, a^{2} b^{3} c^{4} - 7 \, a^{3} b c^{5}\right)} d^{2} e + 3 \, {\left(b^{8} c - 8 \, a b^{6} c^{2} + 20 \, a^{2} b^{4} c^{3} - 16 \, a^{3} b^{2} c^{4} + 2 \, a^{4} c^{5}\right)} d e^{2} - {\left(b^{9} - 9 \, a b^{7} c + 27 \, a^{2} b^{5} c^{2} - 30 \, a^{3} b^{3} c^{3} + 9 \, a^{4} b c^{4}\right)} e^{3} - {\left(b^{2} c^{9} - 4 \, a c^{10}\right)} \sqrt{\frac{{\left(b^{10} c^{6} - 8 \, a b^{8} c^{7} + 22 \, a^{2} b^{6} c^{8} - 24 \, a^{3} b^{4} c^{9} + 9 \, a^{4} b^{2} c^{10}\right)} d^{6} - 6 \, {\left(b^{11} c^{5} - 9 \, a b^{9} c^{6} + 29 \, a^{2} b^{7} c^{7} - 40 \, a^{3} b^{5} c^{8} + 22 \, a^{4} b^{3} c^{9} - 3 \, a^{5} b c^{10}\right)} d^{5} e + 3 \, {\left(5 \, b^{12} c^{4} - 50 \, a b^{10} c^{5} + 185 \, a^{2} b^{8} c^{6} - 310 \, a^{3} b^{6} c^{7} + 230 \, a^{4} b^{4} c^{8} - 60 \, a^{5} b^{2} c^{9} + 3 \, a^{6} c^{10}\right)} d^{4} e^{2} - 2 \, {\left(10 \, b^{13} c^{3} - 110 \, a b^{11} c^{4} + 460 \, a^{2} b^{9} c^{5} - 910 \, a^{3} b^{7} c^{6} + 860 \, a^{4} b^{5} c^{7} - 340 \, a^{5} b^{3} c^{8} + 39 \, a^{6} b c^{9}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{14} c^{2} - 60 \, a b^{12} c^{3} + 280 \, a^{2} b^{10} c^{4} - 640 \, a^{3} b^{8} c^{5} + 740 \, a^{4} b^{6} c^{6} - 400 \, a^{5} b^{4} c^{7} + 80 \, a^{6} b^{2} c^{8} - 2 \, a^{7} c^{9}\right)} d^{2} e^{4} - 6 \, {\left(b^{15} c - 13 \, a b^{13} c^{2} + 67 \, a^{2} b^{11} c^{3} - 174 \, a^{3} b^{9} c^{4} + 239 \, a^{4} b^{7} c^{5} - 166 \, a^{5} b^{5} c^{6} + 50 \, a^{6} b^{3} c^{7} - 4 \, a^{7} b c^{8}\right)} d e^{5} + {\left(b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}\right)} e^{6}}{b^{2} c^{18} - 4 \, a c^{19}}}}{b^{2} c^{9} - 4 \, a c^{10}}} - 4 \, {\left({\left(a^{3} b^{5} c^{4} - 4 \, a^{4} b^{3} c^{5} + 3 \, a^{5} b c^{6}\right)} d^{5} - {\left(4 \, a^{3} b^{6} c^{3} - 19 \, a^{4} b^{4} c^{4} + 21 \, a^{5} b^{2} c^{5} - 3 \, a^{6} c^{6}\right)} d^{4} e + 2 \, {\left(3 \, a^{3} b^{7} c^{2} - 16 \, a^{4} b^{5} c^{3} + 22 \, a^{5} b^{3} c^{4} - 6 \, a^{6} b c^{5}\right)} d^{3} e^{2} - 2 \, {\left(2 \, a^{3} b^{8} c - 11 \, a^{4} b^{6} c^{2} + 15 \, a^{5} b^{4} c^{3} - 2 \, a^{6} b^{2} c^{4} - a^{7} c^{5}\right)} d^{2} e^{3} + {\left(a^{3} b^{9} - 4 \, a^{4} b^{7} c - 3 \, a^{5} b^{5} c^{2} + 20 \, a^{6} b^{3} c^{3} - 11 \, a^{7} b c^{4}\right)} d e^{4} - {\left(a^{4} b^{8} - 7 \, a^{5} b^{6} c + 15 \, a^{6} b^{4} c^{2} - 10 \, a^{7} b^{2} c^{3} + a^{8} c^{4}\right)} e^{5}\right)} \sqrt{e x + d}\right) - 4 \, {\left(15 \, c^{3} e^{3} x^{3} - 6 \, c^{3} d^{3} - 21 \, b c^{2} d^{2} e + 140 \, {\left(b^{2} c - a c^{2}\right)} d e^{2} - 105 \, {\left(b^{3} - 2 \, a b c\right)} e^{3} + 3 \, {\left(8 \, c^{3} d e^{2} - 7 \, b c^{2} e^{3}\right)} x^{2} + {\left(3 \, c^{3} d^{2} e - 42 \, b c^{2} d e^{2} + 35 \, {\left(b^{2} c - a c^{2}\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{210 \, c^{4} e^{2}}"," ",0,"-1/210*(105*sqrt(2)*c^4*e^2*sqrt(((b^6*c^3 - 6*a*b^4*c^4 + 9*a^2*b^2*c^5 - 2*a^3*c^6)*d^3 - 3*(b^7*c^2 - 7*a*b^5*c^3 + 14*a^2*b^3*c^4 - 7*a^3*b*c^5)*d^2*e + 3*(b^8*c - 8*a*b^6*c^2 + 20*a^2*b^4*c^3 - 16*a^3*b^2*c^4 + 2*a^4*c^5)*d*e^2 - (b^9 - 9*a*b^7*c + 27*a^2*b^5*c^2 - 30*a^3*b^3*c^3 + 9*a^4*b*c^4)*e^3 + (b^2*c^9 - 4*a*c^10)*sqrt(((b^10*c^6 - 8*a*b^8*c^7 + 22*a^2*b^6*c^8 - 24*a^3*b^4*c^9 + 9*a^4*b^2*c^10)*d^6 - 6*(b^11*c^5 - 9*a*b^9*c^6 + 29*a^2*b^7*c^7 - 40*a^3*b^5*c^8 + 22*a^4*b^3*c^9 - 3*a^5*b*c^10)*d^5*e + 3*(5*b^12*c^4 - 50*a*b^10*c^5 + 185*a^2*b^8*c^6 - 310*a^3*b^6*c^7 + 230*a^4*b^4*c^8 - 60*a^5*b^2*c^9 + 3*a^6*c^10)*d^4*e^2 - 2*(10*b^13*c^3 - 110*a*b^11*c^4 + 460*a^2*b^9*c^5 - 910*a^3*b^7*c^6 + 860*a^4*b^5*c^7 - 340*a^5*b^3*c^8 + 39*a^6*b*c^9)*d^3*e^3 + 3*(5*b^14*c^2 - 60*a*b^12*c^3 + 280*a^2*b^10*c^4 - 640*a^3*b^8*c^5 + 740*a^4*b^6*c^6 - 400*a^5*b^4*c^7 + 80*a^6*b^2*c^8 - 2*a^7*c^9)*d^2*e^4 - 6*(b^15*c - 13*a*b^13*c^2 + 67*a^2*b^11*c^3 - 174*a^3*b^9*c^4 + 239*a^4*b^7*c^5 - 166*a^5*b^5*c^6 + 50*a^6*b^3*c^7 - 4*a^7*b*c^8)*d*e^5 + (b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)*e^6)/(b^2*c^18 - 4*a*c^19)))/(b^2*c^9 - 4*a*c^10))*log(sqrt(2)*((b^9*c^4 - 9*a*b^7*c^5 + 27*a^2*b^5*c^6 - 31*a^3*b^3*c^7 + 12*a^4*b*c^8)*d^4 - (4*b^10*c^3 - 40*a*b^8*c^4 + 140*a^2*b^6*c^5 - 203*a^3*b^4*c^6 + 111*a^4*b^2*c^7 - 12*a^5*c^8)*d^3*e + 3*(2*b^11*c^2 - 22*a*b^9*c^3 + 88*a^2*b^7*c^4 - 155*a^3*b^5*c^5 + 114*a^4*b^3*c^6 - 24*a^5*b*c^7)*d^2*e^2 - (4*b^12*c - 48*a*b^10*c^2 + 216*a^2*b^8*c^3 - 449*a^3*b^6*c^4 + 423*a^4*b^4*c^5 - 141*a^5*b^2*c^6 + 4*a^6*c^7)*d*e^3 + (b^13 - 13*a*b^11*c + 65*a^2*b^9*c^2 - 156*a^3*b^7*c^3 + 181*a^4*b^5*c^4 - 86*a^5*b^3*c^5 + 8*a^6*b*c^6)*e^4 - ((b^5*c^10 - 7*a*b^3*c^11 + 12*a^2*b*c^12)*d - (b^6*c^9 - 8*a*b^4*c^10 + 18*a^2*b^2*c^11 - 8*a^3*c^12)*e)*sqrt(((b^10*c^6 - 8*a*b^8*c^7 + 22*a^2*b^6*c^8 - 24*a^3*b^4*c^9 + 9*a^4*b^2*c^10)*d^6 - 6*(b^11*c^5 - 9*a*b^9*c^6 + 29*a^2*b^7*c^7 - 40*a^3*b^5*c^8 + 22*a^4*b^3*c^9 - 3*a^5*b*c^10)*d^5*e + 3*(5*b^12*c^4 - 50*a*b^10*c^5 + 185*a^2*b^8*c^6 - 310*a^3*b^6*c^7 + 230*a^4*b^4*c^8 - 60*a^5*b^2*c^9 + 3*a^6*c^10)*d^4*e^2 - 2*(10*b^13*c^3 - 110*a*b^11*c^4 + 460*a^2*b^9*c^5 - 910*a^3*b^7*c^6 + 860*a^4*b^5*c^7 - 340*a^5*b^3*c^8 + 39*a^6*b*c^9)*d^3*e^3 + 3*(5*b^14*c^2 - 60*a*b^12*c^3 + 280*a^2*b^10*c^4 - 640*a^3*b^8*c^5 + 740*a^4*b^6*c^6 - 400*a^5*b^4*c^7 + 80*a^6*b^2*c^8 - 2*a^7*c^9)*d^2*e^4 - 6*(b^15*c - 13*a*b^13*c^2 + 67*a^2*b^11*c^3 - 174*a^3*b^9*c^4 + 239*a^4*b^7*c^5 - 166*a^5*b^5*c^6 + 50*a^6*b^3*c^7 - 4*a^7*b*c^8)*d*e^5 + (b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)*e^6)/(b^2*c^18 - 4*a*c^19)))*sqrt(((b^6*c^3 - 6*a*b^4*c^4 + 9*a^2*b^2*c^5 - 2*a^3*c^6)*d^3 - 3*(b^7*c^2 - 7*a*b^5*c^3 + 14*a^2*b^3*c^4 - 7*a^3*b*c^5)*d^2*e + 3*(b^8*c - 8*a*b^6*c^2 + 20*a^2*b^4*c^3 - 16*a^3*b^2*c^4 + 2*a^4*c^5)*d*e^2 - (b^9 - 9*a*b^7*c + 27*a^2*b^5*c^2 - 30*a^3*b^3*c^3 + 9*a^4*b*c^4)*e^3 + (b^2*c^9 - 4*a*c^10)*sqrt(((b^10*c^6 - 8*a*b^8*c^7 + 22*a^2*b^6*c^8 - 24*a^3*b^4*c^9 + 9*a^4*b^2*c^10)*d^6 - 6*(b^11*c^5 - 9*a*b^9*c^6 + 29*a^2*b^7*c^7 - 40*a^3*b^5*c^8 + 22*a^4*b^3*c^9 - 3*a^5*b*c^10)*d^5*e + 3*(5*b^12*c^4 - 50*a*b^10*c^5 + 185*a^2*b^8*c^6 - 310*a^3*b^6*c^7 + 230*a^4*b^4*c^8 - 60*a^5*b^2*c^9 + 3*a^6*c^10)*d^4*e^2 - 2*(10*b^13*c^3 - 110*a*b^11*c^4 + 460*a^2*b^9*c^5 - 910*a^3*b^7*c^6 + 860*a^4*b^5*c^7 - 340*a^5*b^3*c^8 + 39*a^6*b*c^9)*d^3*e^3 + 3*(5*b^14*c^2 - 60*a*b^12*c^3 + 280*a^2*b^10*c^4 - 640*a^3*b^8*c^5 + 740*a^4*b^6*c^6 - 400*a^5*b^4*c^7 + 80*a^6*b^2*c^8 - 2*a^7*c^9)*d^2*e^4 - 6*(b^15*c - 13*a*b^13*c^2 + 67*a^2*b^11*c^3 - 174*a^3*b^9*c^4 + 239*a^4*b^7*c^5 - 166*a^5*b^5*c^6 + 50*a^6*b^3*c^7 - 4*a^7*b*c^8)*d*e^5 + (b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)*e^6)/(b^2*c^18 - 4*a*c^19)))/(b^2*c^9 - 4*a*c^10)) - 4*((a^3*b^5*c^4 - 4*a^4*b^3*c^5 + 3*a^5*b*c^6)*d^5 - (4*a^3*b^6*c^3 - 19*a^4*b^4*c^4 + 21*a^5*b^2*c^5 - 3*a^6*c^6)*d^4*e + 2*(3*a^3*b^7*c^2 - 16*a^4*b^5*c^3 + 22*a^5*b^3*c^4 - 6*a^6*b*c^5)*d^3*e^2 - 2*(2*a^3*b^8*c - 11*a^4*b^6*c^2 + 15*a^5*b^4*c^3 - 2*a^6*b^2*c^4 - a^7*c^5)*d^2*e^3 + (a^3*b^9 - 4*a^4*b^7*c - 3*a^5*b^5*c^2 + 20*a^6*b^3*c^3 - 11*a^7*b*c^4)*d*e^4 - (a^4*b^8 - 7*a^5*b^6*c + 15*a^6*b^4*c^2 - 10*a^7*b^2*c^3 + a^8*c^4)*e^5)*sqrt(e*x + d)) - 105*sqrt(2)*c^4*e^2*sqrt(((b^6*c^3 - 6*a*b^4*c^4 + 9*a^2*b^2*c^5 - 2*a^3*c^6)*d^3 - 3*(b^7*c^2 - 7*a*b^5*c^3 + 14*a^2*b^3*c^4 - 7*a^3*b*c^5)*d^2*e + 3*(b^8*c - 8*a*b^6*c^2 + 20*a^2*b^4*c^3 - 16*a^3*b^2*c^4 + 2*a^4*c^5)*d*e^2 - (b^9 - 9*a*b^7*c + 27*a^2*b^5*c^2 - 30*a^3*b^3*c^3 + 9*a^4*b*c^4)*e^3 + (b^2*c^9 - 4*a*c^10)*sqrt(((b^10*c^6 - 8*a*b^8*c^7 + 22*a^2*b^6*c^8 - 24*a^3*b^4*c^9 + 9*a^4*b^2*c^10)*d^6 - 6*(b^11*c^5 - 9*a*b^9*c^6 + 29*a^2*b^7*c^7 - 40*a^3*b^5*c^8 + 22*a^4*b^3*c^9 - 3*a^5*b*c^10)*d^5*e + 3*(5*b^12*c^4 - 50*a*b^10*c^5 + 185*a^2*b^8*c^6 - 310*a^3*b^6*c^7 + 230*a^4*b^4*c^8 - 60*a^5*b^2*c^9 + 3*a^6*c^10)*d^4*e^2 - 2*(10*b^13*c^3 - 110*a*b^11*c^4 + 460*a^2*b^9*c^5 - 910*a^3*b^7*c^6 + 860*a^4*b^5*c^7 - 340*a^5*b^3*c^8 + 39*a^6*b*c^9)*d^3*e^3 + 3*(5*b^14*c^2 - 60*a*b^12*c^3 + 280*a^2*b^10*c^4 - 640*a^3*b^8*c^5 + 740*a^4*b^6*c^6 - 400*a^5*b^4*c^7 + 80*a^6*b^2*c^8 - 2*a^7*c^9)*d^2*e^4 - 6*(b^15*c - 13*a*b^13*c^2 + 67*a^2*b^11*c^3 - 174*a^3*b^9*c^4 + 239*a^4*b^7*c^5 - 166*a^5*b^5*c^6 + 50*a^6*b^3*c^7 - 4*a^7*b*c^8)*d*e^5 + (b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)*e^6)/(b^2*c^18 - 4*a*c^19)))/(b^2*c^9 - 4*a*c^10))*log(-sqrt(2)*((b^9*c^4 - 9*a*b^7*c^5 + 27*a^2*b^5*c^6 - 31*a^3*b^3*c^7 + 12*a^4*b*c^8)*d^4 - (4*b^10*c^3 - 40*a*b^8*c^4 + 140*a^2*b^6*c^5 - 203*a^3*b^4*c^6 + 111*a^4*b^2*c^7 - 12*a^5*c^8)*d^3*e + 3*(2*b^11*c^2 - 22*a*b^9*c^3 + 88*a^2*b^7*c^4 - 155*a^3*b^5*c^5 + 114*a^4*b^3*c^6 - 24*a^5*b*c^7)*d^2*e^2 - (4*b^12*c - 48*a*b^10*c^2 + 216*a^2*b^8*c^3 - 449*a^3*b^6*c^4 + 423*a^4*b^4*c^5 - 141*a^5*b^2*c^6 + 4*a^6*c^7)*d*e^3 + (b^13 - 13*a*b^11*c + 65*a^2*b^9*c^2 - 156*a^3*b^7*c^3 + 181*a^4*b^5*c^4 - 86*a^5*b^3*c^5 + 8*a^6*b*c^6)*e^4 - ((b^5*c^10 - 7*a*b^3*c^11 + 12*a^2*b*c^12)*d - (b^6*c^9 - 8*a*b^4*c^10 + 18*a^2*b^2*c^11 - 8*a^3*c^12)*e)*sqrt(((b^10*c^6 - 8*a*b^8*c^7 + 22*a^2*b^6*c^8 - 24*a^3*b^4*c^9 + 9*a^4*b^2*c^10)*d^6 - 6*(b^11*c^5 - 9*a*b^9*c^6 + 29*a^2*b^7*c^7 - 40*a^3*b^5*c^8 + 22*a^4*b^3*c^9 - 3*a^5*b*c^10)*d^5*e + 3*(5*b^12*c^4 - 50*a*b^10*c^5 + 185*a^2*b^8*c^6 - 310*a^3*b^6*c^7 + 230*a^4*b^4*c^8 - 60*a^5*b^2*c^9 + 3*a^6*c^10)*d^4*e^2 - 2*(10*b^13*c^3 - 110*a*b^11*c^4 + 460*a^2*b^9*c^5 - 910*a^3*b^7*c^6 + 860*a^4*b^5*c^7 - 340*a^5*b^3*c^8 + 39*a^6*b*c^9)*d^3*e^3 + 3*(5*b^14*c^2 - 60*a*b^12*c^3 + 280*a^2*b^10*c^4 - 640*a^3*b^8*c^5 + 740*a^4*b^6*c^6 - 400*a^5*b^4*c^7 + 80*a^6*b^2*c^8 - 2*a^7*c^9)*d^2*e^4 - 6*(b^15*c - 13*a*b^13*c^2 + 67*a^2*b^11*c^3 - 174*a^3*b^9*c^4 + 239*a^4*b^7*c^5 - 166*a^5*b^5*c^6 + 50*a^6*b^3*c^7 - 4*a^7*b*c^8)*d*e^5 + (b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)*e^6)/(b^2*c^18 - 4*a*c^19)))*sqrt(((b^6*c^3 - 6*a*b^4*c^4 + 9*a^2*b^2*c^5 - 2*a^3*c^6)*d^3 - 3*(b^7*c^2 - 7*a*b^5*c^3 + 14*a^2*b^3*c^4 - 7*a^3*b*c^5)*d^2*e + 3*(b^8*c - 8*a*b^6*c^2 + 20*a^2*b^4*c^3 - 16*a^3*b^2*c^4 + 2*a^4*c^5)*d*e^2 - (b^9 - 9*a*b^7*c + 27*a^2*b^5*c^2 - 30*a^3*b^3*c^3 + 9*a^4*b*c^4)*e^3 + (b^2*c^9 - 4*a*c^10)*sqrt(((b^10*c^6 - 8*a*b^8*c^7 + 22*a^2*b^6*c^8 - 24*a^3*b^4*c^9 + 9*a^4*b^2*c^10)*d^6 - 6*(b^11*c^5 - 9*a*b^9*c^6 + 29*a^2*b^7*c^7 - 40*a^3*b^5*c^8 + 22*a^4*b^3*c^9 - 3*a^5*b*c^10)*d^5*e + 3*(5*b^12*c^4 - 50*a*b^10*c^5 + 185*a^2*b^8*c^6 - 310*a^3*b^6*c^7 + 230*a^4*b^4*c^8 - 60*a^5*b^2*c^9 + 3*a^6*c^10)*d^4*e^2 - 2*(10*b^13*c^3 - 110*a*b^11*c^4 + 460*a^2*b^9*c^5 - 910*a^3*b^7*c^6 + 860*a^4*b^5*c^7 - 340*a^5*b^3*c^8 + 39*a^6*b*c^9)*d^3*e^3 + 3*(5*b^14*c^2 - 60*a*b^12*c^3 + 280*a^2*b^10*c^4 - 640*a^3*b^8*c^5 + 740*a^4*b^6*c^6 - 400*a^5*b^4*c^7 + 80*a^6*b^2*c^8 - 2*a^7*c^9)*d^2*e^4 - 6*(b^15*c - 13*a*b^13*c^2 + 67*a^2*b^11*c^3 - 174*a^3*b^9*c^4 + 239*a^4*b^7*c^5 - 166*a^5*b^5*c^6 + 50*a^6*b^3*c^7 - 4*a^7*b*c^8)*d*e^5 + (b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)*e^6)/(b^2*c^18 - 4*a*c^19)))/(b^2*c^9 - 4*a*c^10)) - 4*((a^3*b^5*c^4 - 4*a^4*b^3*c^5 + 3*a^5*b*c^6)*d^5 - (4*a^3*b^6*c^3 - 19*a^4*b^4*c^4 + 21*a^5*b^2*c^5 - 3*a^6*c^6)*d^4*e + 2*(3*a^3*b^7*c^2 - 16*a^4*b^5*c^3 + 22*a^5*b^3*c^4 - 6*a^6*b*c^5)*d^3*e^2 - 2*(2*a^3*b^8*c - 11*a^4*b^6*c^2 + 15*a^5*b^4*c^3 - 2*a^6*b^2*c^4 - a^7*c^5)*d^2*e^3 + (a^3*b^9 - 4*a^4*b^7*c - 3*a^5*b^5*c^2 + 20*a^6*b^3*c^3 - 11*a^7*b*c^4)*d*e^4 - (a^4*b^8 - 7*a^5*b^6*c + 15*a^6*b^4*c^2 - 10*a^7*b^2*c^3 + a^8*c^4)*e^5)*sqrt(e*x + d)) + 105*sqrt(2)*c^4*e^2*sqrt(((b^6*c^3 - 6*a*b^4*c^4 + 9*a^2*b^2*c^5 - 2*a^3*c^6)*d^3 - 3*(b^7*c^2 - 7*a*b^5*c^3 + 14*a^2*b^3*c^4 - 7*a^3*b*c^5)*d^2*e + 3*(b^8*c - 8*a*b^6*c^2 + 20*a^2*b^4*c^3 - 16*a^3*b^2*c^4 + 2*a^4*c^5)*d*e^2 - (b^9 - 9*a*b^7*c + 27*a^2*b^5*c^2 - 30*a^3*b^3*c^3 + 9*a^4*b*c^4)*e^3 - (b^2*c^9 - 4*a*c^10)*sqrt(((b^10*c^6 - 8*a*b^8*c^7 + 22*a^2*b^6*c^8 - 24*a^3*b^4*c^9 + 9*a^4*b^2*c^10)*d^6 - 6*(b^11*c^5 - 9*a*b^9*c^6 + 29*a^2*b^7*c^7 - 40*a^3*b^5*c^8 + 22*a^4*b^3*c^9 - 3*a^5*b*c^10)*d^5*e + 3*(5*b^12*c^4 - 50*a*b^10*c^5 + 185*a^2*b^8*c^6 - 310*a^3*b^6*c^7 + 230*a^4*b^4*c^8 - 60*a^5*b^2*c^9 + 3*a^6*c^10)*d^4*e^2 - 2*(10*b^13*c^3 - 110*a*b^11*c^4 + 460*a^2*b^9*c^5 - 910*a^3*b^7*c^6 + 860*a^4*b^5*c^7 - 340*a^5*b^3*c^8 + 39*a^6*b*c^9)*d^3*e^3 + 3*(5*b^14*c^2 - 60*a*b^12*c^3 + 280*a^2*b^10*c^4 - 640*a^3*b^8*c^5 + 740*a^4*b^6*c^6 - 400*a^5*b^4*c^7 + 80*a^6*b^2*c^8 - 2*a^7*c^9)*d^2*e^4 - 6*(b^15*c - 13*a*b^13*c^2 + 67*a^2*b^11*c^3 - 174*a^3*b^9*c^4 + 239*a^4*b^7*c^5 - 166*a^5*b^5*c^6 + 50*a^6*b^3*c^7 - 4*a^7*b*c^8)*d*e^5 + (b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)*e^6)/(b^2*c^18 - 4*a*c^19)))/(b^2*c^9 - 4*a*c^10))*log(sqrt(2)*((b^9*c^4 - 9*a*b^7*c^5 + 27*a^2*b^5*c^6 - 31*a^3*b^3*c^7 + 12*a^4*b*c^8)*d^4 - (4*b^10*c^3 - 40*a*b^8*c^4 + 140*a^2*b^6*c^5 - 203*a^3*b^4*c^6 + 111*a^4*b^2*c^7 - 12*a^5*c^8)*d^3*e + 3*(2*b^11*c^2 - 22*a*b^9*c^3 + 88*a^2*b^7*c^4 - 155*a^3*b^5*c^5 + 114*a^4*b^3*c^6 - 24*a^5*b*c^7)*d^2*e^2 - (4*b^12*c - 48*a*b^10*c^2 + 216*a^2*b^8*c^3 - 449*a^3*b^6*c^4 + 423*a^4*b^4*c^5 - 141*a^5*b^2*c^6 + 4*a^6*c^7)*d*e^3 + (b^13 - 13*a*b^11*c + 65*a^2*b^9*c^2 - 156*a^3*b^7*c^3 + 181*a^4*b^5*c^4 - 86*a^5*b^3*c^5 + 8*a^6*b*c^6)*e^4 + ((b^5*c^10 - 7*a*b^3*c^11 + 12*a^2*b*c^12)*d - (b^6*c^9 - 8*a*b^4*c^10 + 18*a^2*b^2*c^11 - 8*a^3*c^12)*e)*sqrt(((b^10*c^6 - 8*a*b^8*c^7 + 22*a^2*b^6*c^8 - 24*a^3*b^4*c^9 + 9*a^4*b^2*c^10)*d^6 - 6*(b^11*c^5 - 9*a*b^9*c^6 + 29*a^2*b^7*c^7 - 40*a^3*b^5*c^8 + 22*a^4*b^3*c^9 - 3*a^5*b*c^10)*d^5*e + 3*(5*b^12*c^4 - 50*a*b^10*c^5 + 185*a^2*b^8*c^6 - 310*a^3*b^6*c^7 + 230*a^4*b^4*c^8 - 60*a^5*b^2*c^9 + 3*a^6*c^10)*d^4*e^2 - 2*(10*b^13*c^3 - 110*a*b^11*c^4 + 460*a^2*b^9*c^5 - 910*a^3*b^7*c^6 + 860*a^4*b^5*c^7 - 340*a^5*b^3*c^8 + 39*a^6*b*c^9)*d^3*e^3 + 3*(5*b^14*c^2 - 60*a*b^12*c^3 + 280*a^2*b^10*c^4 - 640*a^3*b^8*c^5 + 740*a^4*b^6*c^6 - 400*a^5*b^4*c^7 + 80*a^6*b^2*c^8 - 2*a^7*c^9)*d^2*e^4 - 6*(b^15*c - 13*a*b^13*c^2 + 67*a^2*b^11*c^3 - 174*a^3*b^9*c^4 + 239*a^4*b^7*c^5 - 166*a^5*b^5*c^6 + 50*a^6*b^3*c^7 - 4*a^7*b*c^8)*d*e^5 + (b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)*e^6)/(b^2*c^18 - 4*a*c^19)))*sqrt(((b^6*c^3 - 6*a*b^4*c^4 + 9*a^2*b^2*c^5 - 2*a^3*c^6)*d^3 - 3*(b^7*c^2 - 7*a*b^5*c^3 + 14*a^2*b^3*c^4 - 7*a^3*b*c^5)*d^2*e + 3*(b^8*c - 8*a*b^6*c^2 + 20*a^2*b^4*c^3 - 16*a^3*b^2*c^4 + 2*a^4*c^5)*d*e^2 - (b^9 - 9*a*b^7*c + 27*a^2*b^5*c^2 - 30*a^3*b^3*c^3 + 9*a^4*b*c^4)*e^3 - (b^2*c^9 - 4*a*c^10)*sqrt(((b^10*c^6 - 8*a*b^8*c^7 + 22*a^2*b^6*c^8 - 24*a^3*b^4*c^9 + 9*a^4*b^2*c^10)*d^6 - 6*(b^11*c^5 - 9*a*b^9*c^6 + 29*a^2*b^7*c^7 - 40*a^3*b^5*c^8 + 22*a^4*b^3*c^9 - 3*a^5*b*c^10)*d^5*e + 3*(5*b^12*c^4 - 50*a*b^10*c^5 + 185*a^2*b^8*c^6 - 310*a^3*b^6*c^7 + 230*a^4*b^4*c^8 - 60*a^5*b^2*c^9 + 3*a^6*c^10)*d^4*e^2 - 2*(10*b^13*c^3 - 110*a*b^11*c^4 + 460*a^2*b^9*c^5 - 910*a^3*b^7*c^6 + 860*a^4*b^5*c^7 - 340*a^5*b^3*c^8 + 39*a^6*b*c^9)*d^3*e^3 + 3*(5*b^14*c^2 - 60*a*b^12*c^3 + 280*a^2*b^10*c^4 - 640*a^3*b^8*c^5 + 740*a^4*b^6*c^6 - 400*a^5*b^4*c^7 + 80*a^6*b^2*c^8 - 2*a^7*c^9)*d^2*e^4 - 6*(b^15*c - 13*a*b^13*c^2 + 67*a^2*b^11*c^3 - 174*a^3*b^9*c^4 + 239*a^4*b^7*c^5 - 166*a^5*b^5*c^6 + 50*a^6*b^3*c^7 - 4*a^7*b*c^8)*d*e^5 + (b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)*e^6)/(b^2*c^18 - 4*a*c^19)))/(b^2*c^9 - 4*a*c^10)) - 4*((a^3*b^5*c^4 - 4*a^4*b^3*c^5 + 3*a^5*b*c^6)*d^5 - (4*a^3*b^6*c^3 - 19*a^4*b^4*c^4 + 21*a^5*b^2*c^5 - 3*a^6*c^6)*d^4*e + 2*(3*a^3*b^7*c^2 - 16*a^4*b^5*c^3 + 22*a^5*b^3*c^4 - 6*a^6*b*c^5)*d^3*e^2 - 2*(2*a^3*b^8*c - 11*a^4*b^6*c^2 + 15*a^5*b^4*c^3 - 2*a^6*b^2*c^4 - a^7*c^5)*d^2*e^3 + (a^3*b^9 - 4*a^4*b^7*c - 3*a^5*b^5*c^2 + 20*a^6*b^3*c^3 - 11*a^7*b*c^4)*d*e^4 - (a^4*b^8 - 7*a^5*b^6*c + 15*a^6*b^4*c^2 - 10*a^7*b^2*c^3 + a^8*c^4)*e^5)*sqrt(e*x + d)) - 105*sqrt(2)*c^4*e^2*sqrt(((b^6*c^3 - 6*a*b^4*c^4 + 9*a^2*b^2*c^5 - 2*a^3*c^6)*d^3 - 3*(b^7*c^2 - 7*a*b^5*c^3 + 14*a^2*b^3*c^4 - 7*a^3*b*c^5)*d^2*e + 3*(b^8*c - 8*a*b^6*c^2 + 20*a^2*b^4*c^3 - 16*a^3*b^2*c^4 + 2*a^4*c^5)*d*e^2 - (b^9 - 9*a*b^7*c + 27*a^2*b^5*c^2 - 30*a^3*b^3*c^3 + 9*a^4*b*c^4)*e^3 - (b^2*c^9 - 4*a*c^10)*sqrt(((b^10*c^6 - 8*a*b^8*c^7 + 22*a^2*b^6*c^8 - 24*a^3*b^4*c^9 + 9*a^4*b^2*c^10)*d^6 - 6*(b^11*c^5 - 9*a*b^9*c^6 + 29*a^2*b^7*c^7 - 40*a^3*b^5*c^8 + 22*a^4*b^3*c^9 - 3*a^5*b*c^10)*d^5*e + 3*(5*b^12*c^4 - 50*a*b^10*c^5 + 185*a^2*b^8*c^6 - 310*a^3*b^6*c^7 + 230*a^4*b^4*c^8 - 60*a^5*b^2*c^9 + 3*a^6*c^10)*d^4*e^2 - 2*(10*b^13*c^3 - 110*a*b^11*c^4 + 460*a^2*b^9*c^5 - 910*a^3*b^7*c^6 + 860*a^4*b^5*c^7 - 340*a^5*b^3*c^8 + 39*a^6*b*c^9)*d^3*e^3 + 3*(5*b^14*c^2 - 60*a*b^12*c^3 + 280*a^2*b^10*c^4 - 640*a^3*b^8*c^5 + 740*a^4*b^6*c^6 - 400*a^5*b^4*c^7 + 80*a^6*b^2*c^8 - 2*a^7*c^9)*d^2*e^4 - 6*(b^15*c - 13*a*b^13*c^2 + 67*a^2*b^11*c^3 - 174*a^3*b^9*c^4 + 239*a^4*b^7*c^5 - 166*a^5*b^5*c^6 + 50*a^6*b^3*c^7 - 4*a^7*b*c^8)*d*e^5 + (b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)*e^6)/(b^2*c^18 - 4*a*c^19)))/(b^2*c^9 - 4*a*c^10))*log(-sqrt(2)*((b^9*c^4 - 9*a*b^7*c^5 + 27*a^2*b^5*c^6 - 31*a^3*b^3*c^7 + 12*a^4*b*c^8)*d^4 - (4*b^10*c^3 - 40*a*b^8*c^4 + 140*a^2*b^6*c^5 - 203*a^3*b^4*c^6 + 111*a^4*b^2*c^7 - 12*a^5*c^8)*d^3*e + 3*(2*b^11*c^2 - 22*a*b^9*c^3 + 88*a^2*b^7*c^4 - 155*a^3*b^5*c^5 + 114*a^4*b^3*c^6 - 24*a^5*b*c^7)*d^2*e^2 - (4*b^12*c - 48*a*b^10*c^2 + 216*a^2*b^8*c^3 - 449*a^3*b^6*c^4 + 423*a^4*b^4*c^5 - 141*a^5*b^2*c^6 + 4*a^6*c^7)*d*e^3 + (b^13 - 13*a*b^11*c + 65*a^2*b^9*c^2 - 156*a^3*b^7*c^3 + 181*a^4*b^5*c^4 - 86*a^5*b^3*c^5 + 8*a^6*b*c^6)*e^4 + ((b^5*c^10 - 7*a*b^3*c^11 + 12*a^2*b*c^12)*d - (b^6*c^9 - 8*a*b^4*c^10 + 18*a^2*b^2*c^11 - 8*a^3*c^12)*e)*sqrt(((b^10*c^6 - 8*a*b^8*c^7 + 22*a^2*b^6*c^8 - 24*a^3*b^4*c^9 + 9*a^4*b^2*c^10)*d^6 - 6*(b^11*c^5 - 9*a*b^9*c^6 + 29*a^2*b^7*c^7 - 40*a^3*b^5*c^8 + 22*a^4*b^3*c^9 - 3*a^5*b*c^10)*d^5*e + 3*(5*b^12*c^4 - 50*a*b^10*c^5 + 185*a^2*b^8*c^6 - 310*a^3*b^6*c^7 + 230*a^4*b^4*c^8 - 60*a^5*b^2*c^9 + 3*a^6*c^10)*d^4*e^2 - 2*(10*b^13*c^3 - 110*a*b^11*c^4 + 460*a^2*b^9*c^5 - 910*a^3*b^7*c^6 + 860*a^4*b^5*c^7 - 340*a^5*b^3*c^8 + 39*a^6*b*c^9)*d^3*e^3 + 3*(5*b^14*c^2 - 60*a*b^12*c^3 + 280*a^2*b^10*c^4 - 640*a^3*b^8*c^5 + 740*a^4*b^6*c^6 - 400*a^5*b^4*c^7 + 80*a^6*b^2*c^8 - 2*a^7*c^9)*d^2*e^4 - 6*(b^15*c - 13*a*b^13*c^2 + 67*a^2*b^11*c^3 - 174*a^3*b^9*c^4 + 239*a^4*b^7*c^5 - 166*a^5*b^5*c^6 + 50*a^6*b^3*c^7 - 4*a^7*b*c^8)*d*e^5 + (b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)*e^6)/(b^2*c^18 - 4*a*c^19)))*sqrt(((b^6*c^3 - 6*a*b^4*c^4 + 9*a^2*b^2*c^5 - 2*a^3*c^6)*d^3 - 3*(b^7*c^2 - 7*a*b^5*c^3 + 14*a^2*b^3*c^4 - 7*a^3*b*c^5)*d^2*e + 3*(b^8*c - 8*a*b^6*c^2 + 20*a^2*b^4*c^3 - 16*a^3*b^2*c^4 + 2*a^4*c^5)*d*e^2 - (b^9 - 9*a*b^7*c + 27*a^2*b^5*c^2 - 30*a^3*b^3*c^3 + 9*a^4*b*c^4)*e^3 - (b^2*c^9 - 4*a*c^10)*sqrt(((b^10*c^6 - 8*a*b^8*c^7 + 22*a^2*b^6*c^8 - 24*a^3*b^4*c^9 + 9*a^4*b^2*c^10)*d^6 - 6*(b^11*c^5 - 9*a*b^9*c^6 + 29*a^2*b^7*c^7 - 40*a^3*b^5*c^8 + 22*a^4*b^3*c^9 - 3*a^5*b*c^10)*d^5*e + 3*(5*b^12*c^4 - 50*a*b^10*c^5 + 185*a^2*b^8*c^6 - 310*a^3*b^6*c^7 + 230*a^4*b^4*c^8 - 60*a^5*b^2*c^9 + 3*a^6*c^10)*d^4*e^2 - 2*(10*b^13*c^3 - 110*a*b^11*c^4 + 460*a^2*b^9*c^5 - 910*a^3*b^7*c^6 + 860*a^4*b^5*c^7 - 340*a^5*b^3*c^8 + 39*a^6*b*c^9)*d^3*e^3 + 3*(5*b^14*c^2 - 60*a*b^12*c^3 + 280*a^2*b^10*c^4 - 640*a^3*b^8*c^5 + 740*a^4*b^6*c^6 - 400*a^5*b^4*c^7 + 80*a^6*b^2*c^8 - 2*a^7*c^9)*d^2*e^4 - 6*(b^15*c - 13*a*b^13*c^2 + 67*a^2*b^11*c^3 - 174*a^3*b^9*c^4 + 239*a^4*b^7*c^5 - 166*a^5*b^5*c^6 + 50*a^6*b^3*c^7 - 4*a^7*b*c^8)*d*e^5 + (b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)*e^6)/(b^2*c^18 - 4*a*c^19)))/(b^2*c^9 - 4*a*c^10)) - 4*((a^3*b^5*c^4 - 4*a^4*b^3*c^5 + 3*a^5*b*c^6)*d^5 - (4*a^3*b^6*c^3 - 19*a^4*b^4*c^4 + 21*a^5*b^2*c^5 - 3*a^6*c^6)*d^4*e + 2*(3*a^3*b^7*c^2 - 16*a^4*b^5*c^3 + 22*a^5*b^3*c^4 - 6*a^6*b*c^5)*d^3*e^2 - 2*(2*a^3*b^8*c - 11*a^4*b^6*c^2 + 15*a^5*b^4*c^3 - 2*a^6*b^2*c^4 - a^7*c^5)*d^2*e^3 + (a^3*b^9 - 4*a^4*b^7*c - 3*a^5*b^5*c^2 + 20*a^6*b^3*c^3 - 11*a^7*b*c^4)*d*e^4 - (a^4*b^8 - 7*a^5*b^6*c + 15*a^6*b^4*c^2 - 10*a^7*b^2*c^3 + a^8*c^4)*e^5)*sqrt(e*x + d)) - 4*(15*c^3*e^3*x^3 - 6*c^3*d^3 - 21*b*c^2*d^2*e + 140*(b^2*c - a*c^2)*d*e^2 - 105*(b^3 - 2*a*b*c)*e^3 + 3*(8*c^3*d*e^2 - 7*b*c^2*e^3)*x^2 + (3*c^3*d^2*e - 42*b*c^2*d*e^2 + 35*(b^2*c - a*c^2)*e^3)*x)*sqrt(e*x + d))/(c^4*e^2)","B",0
535,1,8530,0,2.404286," ","integrate(x^2*(e*x+d)^(3/2)/(c*x^2+b*x+a),x, algorithm=""fricas"")","-\frac{15 \, \sqrt{2} c^{3} e \sqrt{\frac{{\left(b^{4} c^{3} - 4 \, a b^{2} c^{4} + 2 \, a^{2} c^{5}\right)} d^{3} - 3 \, {\left(b^{5} c^{2} - 5 \, a b^{3} c^{3} + 5 \, a^{2} b c^{4}\right)} d^{2} e + 3 \, {\left(b^{6} c - 6 \, a b^{4} c^{2} + 9 \, a^{2} b^{2} c^{3} - 2 \, a^{3} c^{4}\right)} d e^{2} - {\left(b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3}\right)} e^{3} + {\left(b^{2} c^{7} - 4 \, a c^{8}\right)} \sqrt{\frac{{\left(b^{6} c^{6} - 4 \, a b^{4} c^{7} + 4 \, a^{2} b^{2} c^{8}\right)} d^{6} - 6 \, {\left(b^{7} c^{5} - 5 \, a b^{5} c^{6} + 7 \, a^{2} b^{3} c^{7} - 2 \, a^{3} b c^{8}\right)} d^{5} e + 3 \, {\left(5 \, b^{8} c^{4} - 30 \, a b^{6} c^{5} + 55 \, a^{2} b^{4} c^{6} - 30 \, a^{3} b^{2} c^{7} + 3 \, a^{4} c^{8}\right)} d^{4} e^{2} - 2 \, {\left(10 \, b^{9} c^{3} - 70 \, a b^{7} c^{4} + 160 \, a^{2} b^{5} c^{5} - 130 \, a^{3} b^{3} c^{6} + 29 \, a^{4} b c^{7}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{10} c^{2} - 40 \, a b^{8} c^{3} + 110 \, a^{2} b^{6} c^{4} - 120 \, a^{3} b^{4} c^{5} + 45 \, a^{4} b^{2} c^{6} - 2 \, a^{5} c^{7}\right)} d^{2} e^{4} - 6 \, {\left(b^{11} c - 9 \, a b^{9} c^{2} + 29 \, a^{2} b^{7} c^{3} - 40 \, a^{3} b^{5} c^{4} + 22 \, a^{4} b^{3} c^{5} - 3 \, a^{5} b c^{6}\right)} d e^{5} + {\left(b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}\right)} e^{6}}{b^{2} c^{14} - 4 \, a c^{15}}}}{b^{2} c^{7} - 4 \, a c^{8}}} \log\left(\sqrt{2} {\left({\left(b^{6} c^{4} - 6 \, a b^{4} c^{5} + 8 \, a^{2} b^{2} c^{6}\right)} d^{4} - {\left(4 \, b^{7} c^{3} - 28 \, a b^{5} c^{4} + 53 \, a^{2} b^{3} c^{5} - 20 \, a^{3} b c^{6}\right)} d^{3} e + 3 \, {\left(2 \, b^{8} c^{2} - 16 \, a b^{6} c^{3} + 39 \, a^{2} b^{4} c^{4} - 29 \, a^{3} b^{2} c^{5} + 4 \, a^{4} c^{6}\right)} d^{2} e^{2} - {\left(4 \, b^{9} c - 36 \, a b^{7} c^{2} + 107 \, a^{2} b^{5} c^{3} - 118 \, a^{3} b^{3} c^{4} + 40 \, a^{4} b c^{5}\right)} d e^{3} + {\left(b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 51 \, a^{3} b^{4} c^{3} + 29 \, a^{4} b^{2} c^{4} - 4 \, a^{5} c^{5}\right)} e^{4} - {\left({\left(b^{4} c^{8} - 6 \, a b^{2} c^{9} + 8 \, a^{2} c^{10}\right)} d - {\left(b^{5} c^{7} - 7 \, a b^{3} c^{8} + 12 \, a^{2} b c^{9}\right)} e\right)} \sqrt{\frac{{\left(b^{6} c^{6} - 4 \, a b^{4} c^{7} + 4 \, a^{2} b^{2} c^{8}\right)} d^{6} - 6 \, {\left(b^{7} c^{5} - 5 \, a b^{5} c^{6} + 7 \, a^{2} b^{3} c^{7} - 2 \, a^{3} b c^{8}\right)} d^{5} e + 3 \, {\left(5 \, b^{8} c^{4} - 30 \, a b^{6} c^{5} + 55 \, a^{2} b^{4} c^{6} - 30 \, a^{3} b^{2} c^{7} + 3 \, a^{4} c^{8}\right)} d^{4} e^{2} - 2 \, {\left(10 \, b^{9} c^{3} - 70 \, a b^{7} c^{4} + 160 \, a^{2} b^{5} c^{5} - 130 \, a^{3} b^{3} c^{6} + 29 \, a^{4} b c^{7}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{10} c^{2} - 40 \, a b^{8} c^{3} + 110 \, a^{2} b^{6} c^{4} - 120 \, a^{3} b^{4} c^{5} + 45 \, a^{4} b^{2} c^{6} - 2 \, a^{5} c^{7}\right)} d^{2} e^{4} - 6 \, {\left(b^{11} c - 9 \, a b^{9} c^{2} + 29 \, a^{2} b^{7} c^{3} - 40 \, a^{3} b^{5} c^{4} + 22 \, a^{4} b^{3} c^{5} - 3 \, a^{5} b c^{6}\right)} d e^{5} + {\left(b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}\right)} e^{6}}{b^{2} c^{14} - 4 \, a c^{15}}}\right)} \sqrt{\frac{{\left(b^{4} c^{3} - 4 \, a b^{2} c^{4} + 2 \, a^{2} c^{5}\right)} d^{3} - 3 \, {\left(b^{5} c^{2} - 5 \, a b^{3} c^{3} + 5 \, a^{2} b c^{4}\right)} d^{2} e + 3 \, {\left(b^{6} c - 6 \, a b^{4} c^{2} + 9 \, a^{2} b^{2} c^{3} - 2 \, a^{3} c^{4}\right)} d e^{2} - {\left(b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3}\right)} e^{3} + {\left(b^{2} c^{7} - 4 \, a c^{8}\right)} \sqrt{\frac{{\left(b^{6} c^{6} - 4 \, a b^{4} c^{7} + 4 \, a^{2} b^{2} c^{8}\right)} d^{6} - 6 \, {\left(b^{7} c^{5} - 5 \, a b^{5} c^{6} + 7 \, a^{2} b^{3} c^{7} - 2 \, a^{3} b c^{8}\right)} d^{5} e + 3 \, {\left(5 \, b^{8} c^{4} - 30 \, a b^{6} c^{5} + 55 \, a^{2} b^{4} c^{6} - 30 \, a^{3} b^{2} c^{7} + 3 \, a^{4} c^{8}\right)} d^{4} e^{2} - 2 \, {\left(10 \, b^{9} c^{3} - 70 \, a b^{7} c^{4} + 160 \, a^{2} b^{5} c^{5} - 130 \, a^{3} b^{3} c^{6} + 29 \, a^{4} b c^{7}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{10} c^{2} - 40 \, a b^{8} c^{3} + 110 \, a^{2} b^{6} c^{4} - 120 \, a^{3} b^{4} c^{5} + 45 \, a^{4} b^{2} c^{6} - 2 \, a^{5} c^{7}\right)} d^{2} e^{4} - 6 \, {\left(b^{11} c - 9 \, a b^{9} c^{2} + 29 \, a^{2} b^{7} c^{3} - 40 \, a^{3} b^{5} c^{4} + 22 \, a^{4} b^{3} c^{5} - 3 \, a^{5} b c^{6}\right)} d e^{5} + {\left(b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}\right)} e^{6}}{b^{2} c^{14} - 4 \, a c^{15}}}}{b^{2} c^{7} - 4 \, a c^{8}}} + 4 \, {\left({\left(a^{2} b^{3} c^{4} - 2 \, a^{3} b c^{5}\right)} d^{5} - {\left(4 \, a^{2} b^{4} c^{3} - 11 \, a^{3} b^{2} c^{4} + 3 \, a^{4} c^{5}\right)} d^{4} e + 2 \, {\left(3 \, a^{2} b^{5} c^{2} - 10 \, a^{3} b^{3} c^{3} + 5 \, a^{4} b c^{4}\right)} d^{3} e^{2} - 2 \, {\left(2 \, a^{2} b^{6} c - 7 \, a^{3} b^{4} c^{2} + 3 \, a^{4} b^{2} c^{3} + a^{5} c^{4}\right)} d^{2} e^{3} + {\left(a^{2} b^{7} - 2 \, a^{3} b^{5} c - 6 \, a^{4} b^{3} c^{2} + 8 \, a^{5} b c^{3}\right)} d e^{4} - {\left(a^{3} b^{6} - 5 \, a^{4} b^{4} c + 6 \, a^{5} b^{2} c^{2} - a^{6} c^{3}\right)} e^{5}\right)} \sqrt{e x + d}\right) - 15 \, \sqrt{2} c^{3} e \sqrt{\frac{{\left(b^{4} c^{3} - 4 \, a b^{2} c^{4} + 2 \, a^{2} c^{5}\right)} d^{3} - 3 \, {\left(b^{5} c^{2} - 5 \, a b^{3} c^{3} + 5 \, a^{2} b c^{4}\right)} d^{2} e + 3 \, {\left(b^{6} c - 6 \, a b^{4} c^{2} + 9 \, a^{2} b^{2} c^{3} - 2 \, a^{3} c^{4}\right)} d e^{2} - {\left(b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3}\right)} e^{3} + {\left(b^{2} c^{7} - 4 \, a c^{8}\right)} \sqrt{\frac{{\left(b^{6} c^{6} - 4 \, a b^{4} c^{7} + 4 \, a^{2} b^{2} c^{8}\right)} d^{6} - 6 \, {\left(b^{7} c^{5} - 5 \, a b^{5} c^{6} + 7 \, a^{2} b^{3} c^{7} - 2 \, a^{3} b c^{8}\right)} d^{5} e + 3 \, {\left(5 \, b^{8} c^{4} - 30 \, a b^{6} c^{5} + 55 \, a^{2} b^{4} c^{6} - 30 \, a^{3} b^{2} c^{7} + 3 \, a^{4} c^{8}\right)} d^{4} e^{2} - 2 \, {\left(10 \, b^{9} c^{3} - 70 \, a b^{7} c^{4} + 160 \, a^{2} b^{5} c^{5} - 130 \, a^{3} b^{3} c^{6} + 29 \, a^{4} b c^{7}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{10} c^{2} - 40 \, a b^{8} c^{3} + 110 \, a^{2} b^{6} c^{4} - 120 \, a^{3} b^{4} c^{5} + 45 \, a^{4} b^{2} c^{6} - 2 \, a^{5} c^{7}\right)} d^{2} e^{4} - 6 \, {\left(b^{11} c - 9 \, a b^{9} c^{2} + 29 \, a^{2} b^{7} c^{3} - 40 \, a^{3} b^{5} c^{4} + 22 \, a^{4} b^{3} c^{5} - 3 \, a^{5} b c^{6}\right)} d e^{5} + {\left(b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}\right)} e^{6}}{b^{2} c^{14} - 4 \, a c^{15}}}}{b^{2} c^{7} - 4 \, a c^{8}}} \log\left(-\sqrt{2} {\left({\left(b^{6} c^{4} - 6 \, a b^{4} c^{5} + 8 \, a^{2} b^{2} c^{6}\right)} d^{4} - {\left(4 \, b^{7} c^{3} - 28 \, a b^{5} c^{4} + 53 \, a^{2} b^{3} c^{5} - 20 \, a^{3} b c^{6}\right)} d^{3} e + 3 \, {\left(2 \, b^{8} c^{2} - 16 \, a b^{6} c^{3} + 39 \, a^{2} b^{4} c^{4} - 29 \, a^{3} b^{2} c^{5} + 4 \, a^{4} c^{6}\right)} d^{2} e^{2} - {\left(4 \, b^{9} c - 36 \, a b^{7} c^{2} + 107 \, a^{2} b^{5} c^{3} - 118 \, a^{3} b^{3} c^{4} + 40 \, a^{4} b c^{5}\right)} d e^{3} + {\left(b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 51 \, a^{3} b^{4} c^{3} + 29 \, a^{4} b^{2} c^{4} - 4 \, a^{5} c^{5}\right)} e^{4} - {\left({\left(b^{4} c^{8} - 6 \, a b^{2} c^{9} + 8 \, a^{2} c^{10}\right)} d - {\left(b^{5} c^{7} - 7 \, a b^{3} c^{8} + 12 \, a^{2} b c^{9}\right)} e\right)} \sqrt{\frac{{\left(b^{6} c^{6} - 4 \, a b^{4} c^{7} + 4 \, a^{2} b^{2} c^{8}\right)} d^{6} - 6 \, {\left(b^{7} c^{5} - 5 \, a b^{5} c^{6} + 7 \, a^{2} b^{3} c^{7} - 2 \, a^{3} b c^{8}\right)} d^{5} e + 3 \, {\left(5 \, b^{8} c^{4} - 30 \, a b^{6} c^{5} + 55 \, a^{2} b^{4} c^{6} - 30 \, a^{3} b^{2} c^{7} + 3 \, a^{4} c^{8}\right)} d^{4} e^{2} - 2 \, {\left(10 \, b^{9} c^{3} - 70 \, a b^{7} c^{4} + 160 \, a^{2} b^{5} c^{5} - 130 \, a^{3} b^{3} c^{6} + 29 \, a^{4} b c^{7}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{10} c^{2} - 40 \, a b^{8} c^{3} + 110 \, a^{2} b^{6} c^{4} - 120 \, a^{3} b^{4} c^{5} + 45 \, a^{4} b^{2} c^{6} - 2 \, a^{5} c^{7}\right)} d^{2} e^{4} - 6 \, {\left(b^{11} c - 9 \, a b^{9} c^{2} + 29 \, a^{2} b^{7} c^{3} - 40 \, a^{3} b^{5} c^{4} + 22 \, a^{4} b^{3} c^{5} - 3 \, a^{5} b c^{6}\right)} d e^{5} + {\left(b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}\right)} e^{6}}{b^{2} c^{14} - 4 \, a c^{15}}}\right)} \sqrt{\frac{{\left(b^{4} c^{3} - 4 \, a b^{2} c^{4} + 2 \, a^{2} c^{5}\right)} d^{3} - 3 \, {\left(b^{5} c^{2} - 5 \, a b^{3} c^{3} + 5 \, a^{2} b c^{4}\right)} d^{2} e + 3 \, {\left(b^{6} c - 6 \, a b^{4} c^{2} + 9 \, a^{2} b^{2} c^{3} - 2 \, a^{3} c^{4}\right)} d e^{2} - {\left(b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3}\right)} e^{3} + {\left(b^{2} c^{7} - 4 \, a c^{8}\right)} \sqrt{\frac{{\left(b^{6} c^{6} - 4 \, a b^{4} c^{7} + 4 \, a^{2} b^{2} c^{8}\right)} d^{6} - 6 \, {\left(b^{7} c^{5} - 5 \, a b^{5} c^{6} + 7 \, a^{2} b^{3} c^{7} - 2 \, a^{3} b c^{8}\right)} d^{5} e + 3 \, {\left(5 \, b^{8} c^{4} - 30 \, a b^{6} c^{5} + 55 \, a^{2} b^{4} c^{6} - 30 \, a^{3} b^{2} c^{7} + 3 \, a^{4} c^{8}\right)} d^{4} e^{2} - 2 \, {\left(10 \, b^{9} c^{3} - 70 \, a b^{7} c^{4} + 160 \, a^{2} b^{5} c^{5} - 130 \, a^{3} b^{3} c^{6} + 29 \, a^{4} b c^{7}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{10} c^{2} - 40 \, a b^{8} c^{3} + 110 \, a^{2} b^{6} c^{4} - 120 \, a^{3} b^{4} c^{5} + 45 \, a^{4} b^{2} c^{6} - 2 \, a^{5} c^{7}\right)} d^{2} e^{4} - 6 \, {\left(b^{11} c - 9 \, a b^{9} c^{2} + 29 \, a^{2} b^{7} c^{3} - 40 \, a^{3} b^{5} c^{4} + 22 \, a^{4} b^{3} c^{5} - 3 \, a^{5} b c^{6}\right)} d e^{5} + {\left(b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}\right)} e^{6}}{b^{2} c^{14} - 4 \, a c^{15}}}}{b^{2} c^{7} - 4 \, a c^{8}}} + 4 \, {\left({\left(a^{2} b^{3} c^{4} - 2 \, a^{3} b c^{5}\right)} d^{5} - {\left(4 \, a^{2} b^{4} c^{3} - 11 \, a^{3} b^{2} c^{4} + 3 \, a^{4} c^{5}\right)} d^{4} e + 2 \, {\left(3 \, a^{2} b^{5} c^{2} - 10 \, a^{3} b^{3} c^{3} + 5 \, a^{4} b c^{4}\right)} d^{3} e^{2} - 2 \, {\left(2 \, a^{2} b^{6} c - 7 \, a^{3} b^{4} c^{2} + 3 \, a^{4} b^{2} c^{3} + a^{5} c^{4}\right)} d^{2} e^{3} + {\left(a^{2} b^{7} - 2 \, a^{3} b^{5} c - 6 \, a^{4} b^{3} c^{2} + 8 \, a^{5} b c^{3}\right)} d e^{4} - {\left(a^{3} b^{6} - 5 \, a^{4} b^{4} c + 6 \, a^{5} b^{2} c^{2} - a^{6} c^{3}\right)} e^{5}\right)} \sqrt{e x + d}\right) + 15 \, \sqrt{2} c^{3} e \sqrt{\frac{{\left(b^{4} c^{3} - 4 \, a b^{2} c^{4} + 2 \, a^{2} c^{5}\right)} d^{3} - 3 \, {\left(b^{5} c^{2} - 5 \, a b^{3} c^{3} + 5 \, a^{2} b c^{4}\right)} d^{2} e + 3 \, {\left(b^{6} c - 6 \, a b^{4} c^{2} + 9 \, a^{2} b^{2} c^{3} - 2 \, a^{3} c^{4}\right)} d e^{2} - {\left(b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3}\right)} e^{3} - {\left(b^{2} c^{7} - 4 \, a c^{8}\right)} \sqrt{\frac{{\left(b^{6} c^{6} - 4 \, a b^{4} c^{7} + 4 \, a^{2} b^{2} c^{8}\right)} d^{6} - 6 \, {\left(b^{7} c^{5} - 5 \, a b^{5} c^{6} + 7 \, a^{2} b^{3} c^{7} - 2 \, a^{3} b c^{8}\right)} d^{5} e + 3 \, {\left(5 \, b^{8} c^{4} - 30 \, a b^{6} c^{5} + 55 \, a^{2} b^{4} c^{6} - 30 \, a^{3} b^{2} c^{7} + 3 \, a^{4} c^{8}\right)} d^{4} e^{2} - 2 \, {\left(10 \, b^{9} c^{3} - 70 \, a b^{7} c^{4} + 160 \, a^{2} b^{5} c^{5} - 130 \, a^{3} b^{3} c^{6} + 29 \, a^{4} b c^{7}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{10} c^{2} - 40 \, a b^{8} c^{3} + 110 \, a^{2} b^{6} c^{4} - 120 \, a^{3} b^{4} c^{5} + 45 \, a^{4} b^{2} c^{6} - 2 \, a^{5} c^{7}\right)} d^{2} e^{4} - 6 \, {\left(b^{11} c - 9 \, a b^{9} c^{2} + 29 \, a^{2} b^{7} c^{3} - 40 \, a^{3} b^{5} c^{4} + 22 \, a^{4} b^{3} c^{5} - 3 \, a^{5} b c^{6}\right)} d e^{5} + {\left(b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}\right)} e^{6}}{b^{2} c^{14} - 4 \, a c^{15}}}}{b^{2} c^{7} - 4 \, a c^{8}}} \log\left(\sqrt{2} {\left({\left(b^{6} c^{4} - 6 \, a b^{4} c^{5} + 8 \, a^{2} b^{2} c^{6}\right)} d^{4} - {\left(4 \, b^{7} c^{3} - 28 \, a b^{5} c^{4} + 53 \, a^{2} b^{3} c^{5} - 20 \, a^{3} b c^{6}\right)} d^{3} e + 3 \, {\left(2 \, b^{8} c^{2} - 16 \, a b^{6} c^{3} + 39 \, a^{2} b^{4} c^{4} - 29 \, a^{3} b^{2} c^{5} + 4 \, a^{4} c^{6}\right)} d^{2} e^{2} - {\left(4 \, b^{9} c - 36 \, a b^{7} c^{2} + 107 \, a^{2} b^{5} c^{3} - 118 \, a^{3} b^{3} c^{4} + 40 \, a^{4} b c^{5}\right)} d e^{3} + {\left(b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 51 \, a^{3} b^{4} c^{3} + 29 \, a^{4} b^{2} c^{4} - 4 \, a^{5} c^{5}\right)} e^{4} + {\left({\left(b^{4} c^{8} - 6 \, a b^{2} c^{9} + 8 \, a^{2} c^{10}\right)} d - {\left(b^{5} c^{7} - 7 \, a b^{3} c^{8} + 12 \, a^{2} b c^{9}\right)} e\right)} \sqrt{\frac{{\left(b^{6} c^{6} - 4 \, a b^{4} c^{7} + 4 \, a^{2} b^{2} c^{8}\right)} d^{6} - 6 \, {\left(b^{7} c^{5} - 5 \, a b^{5} c^{6} + 7 \, a^{2} b^{3} c^{7} - 2 \, a^{3} b c^{8}\right)} d^{5} e + 3 \, {\left(5 \, b^{8} c^{4} - 30 \, a b^{6} c^{5} + 55 \, a^{2} b^{4} c^{6} - 30 \, a^{3} b^{2} c^{7} + 3 \, a^{4} c^{8}\right)} d^{4} e^{2} - 2 \, {\left(10 \, b^{9} c^{3} - 70 \, a b^{7} c^{4} + 160 \, a^{2} b^{5} c^{5} - 130 \, a^{3} b^{3} c^{6} + 29 \, a^{4} b c^{7}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{10} c^{2} - 40 \, a b^{8} c^{3} + 110 \, a^{2} b^{6} c^{4} - 120 \, a^{3} b^{4} c^{5} + 45 \, a^{4} b^{2} c^{6} - 2 \, a^{5} c^{7}\right)} d^{2} e^{4} - 6 \, {\left(b^{11} c - 9 \, a b^{9} c^{2} + 29 \, a^{2} b^{7} c^{3} - 40 \, a^{3} b^{5} c^{4} + 22 \, a^{4} b^{3} c^{5} - 3 \, a^{5} b c^{6}\right)} d e^{5} + {\left(b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}\right)} e^{6}}{b^{2} c^{14} - 4 \, a c^{15}}}\right)} \sqrt{\frac{{\left(b^{4} c^{3} - 4 \, a b^{2} c^{4} + 2 \, a^{2} c^{5}\right)} d^{3} - 3 \, {\left(b^{5} c^{2} - 5 \, a b^{3} c^{3} + 5 \, a^{2} b c^{4}\right)} d^{2} e + 3 \, {\left(b^{6} c - 6 \, a b^{4} c^{2} + 9 \, a^{2} b^{2} c^{3} - 2 \, a^{3} c^{4}\right)} d e^{2} - {\left(b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3}\right)} e^{3} - {\left(b^{2} c^{7} - 4 \, a c^{8}\right)} \sqrt{\frac{{\left(b^{6} c^{6} - 4 \, a b^{4} c^{7} + 4 \, a^{2} b^{2} c^{8}\right)} d^{6} - 6 \, {\left(b^{7} c^{5} - 5 \, a b^{5} c^{6} + 7 \, a^{2} b^{3} c^{7} - 2 \, a^{3} b c^{8}\right)} d^{5} e + 3 \, {\left(5 \, b^{8} c^{4} - 30 \, a b^{6} c^{5} + 55 \, a^{2} b^{4} c^{6} - 30 \, a^{3} b^{2} c^{7} + 3 \, a^{4} c^{8}\right)} d^{4} e^{2} - 2 \, {\left(10 \, b^{9} c^{3} - 70 \, a b^{7} c^{4} + 160 \, a^{2} b^{5} c^{5} - 130 \, a^{3} b^{3} c^{6} + 29 \, a^{4} b c^{7}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{10} c^{2} - 40 \, a b^{8} c^{3} + 110 \, a^{2} b^{6} c^{4} - 120 \, a^{3} b^{4} c^{5} + 45 \, a^{4} b^{2} c^{6} - 2 \, a^{5} c^{7}\right)} d^{2} e^{4} - 6 \, {\left(b^{11} c - 9 \, a b^{9} c^{2} + 29 \, a^{2} b^{7} c^{3} - 40 \, a^{3} b^{5} c^{4} + 22 \, a^{4} b^{3} c^{5} - 3 \, a^{5} b c^{6}\right)} d e^{5} + {\left(b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}\right)} e^{6}}{b^{2} c^{14} - 4 \, a c^{15}}}}{b^{2} c^{7} - 4 \, a c^{8}}} + 4 \, {\left({\left(a^{2} b^{3} c^{4} - 2 \, a^{3} b c^{5}\right)} d^{5} - {\left(4 \, a^{2} b^{4} c^{3} - 11 \, a^{3} b^{2} c^{4} + 3 \, a^{4} c^{5}\right)} d^{4} e + 2 \, {\left(3 \, a^{2} b^{5} c^{2} - 10 \, a^{3} b^{3} c^{3} + 5 \, a^{4} b c^{4}\right)} d^{3} e^{2} - 2 \, {\left(2 \, a^{2} b^{6} c - 7 \, a^{3} b^{4} c^{2} + 3 \, a^{4} b^{2} c^{3} + a^{5} c^{4}\right)} d^{2} e^{3} + {\left(a^{2} b^{7} - 2 \, a^{3} b^{5} c - 6 \, a^{4} b^{3} c^{2} + 8 \, a^{5} b c^{3}\right)} d e^{4} - {\left(a^{3} b^{6} - 5 \, a^{4} b^{4} c + 6 \, a^{5} b^{2} c^{2} - a^{6} c^{3}\right)} e^{5}\right)} \sqrt{e x + d}\right) - 15 \, \sqrt{2} c^{3} e \sqrt{\frac{{\left(b^{4} c^{3} - 4 \, a b^{2} c^{4} + 2 \, a^{2} c^{5}\right)} d^{3} - 3 \, {\left(b^{5} c^{2} - 5 \, a b^{3} c^{3} + 5 \, a^{2} b c^{4}\right)} d^{2} e + 3 \, {\left(b^{6} c - 6 \, a b^{4} c^{2} + 9 \, a^{2} b^{2} c^{3} - 2 \, a^{3} c^{4}\right)} d e^{2} - {\left(b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3}\right)} e^{3} - {\left(b^{2} c^{7} - 4 \, a c^{8}\right)} \sqrt{\frac{{\left(b^{6} c^{6} - 4 \, a b^{4} c^{7} + 4 \, a^{2} b^{2} c^{8}\right)} d^{6} - 6 \, {\left(b^{7} c^{5} - 5 \, a b^{5} c^{6} + 7 \, a^{2} b^{3} c^{7} - 2 \, a^{3} b c^{8}\right)} d^{5} e + 3 \, {\left(5 \, b^{8} c^{4} - 30 \, a b^{6} c^{5} + 55 \, a^{2} b^{4} c^{6} - 30 \, a^{3} b^{2} c^{7} + 3 \, a^{4} c^{8}\right)} d^{4} e^{2} - 2 \, {\left(10 \, b^{9} c^{3} - 70 \, a b^{7} c^{4} + 160 \, a^{2} b^{5} c^{5} - 130 \, a^{3} b^{3} c^{6} + 29 \, a^{4} b c^{7}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{10} c^{2} - 40 \, a b^{8} c^{3} + 110 \, a^{2} b^{6} c^{4} - 120 \, a^{3} b^{4} c^{5} + 45 \, a^{4} b^{2} c^{6} - 2 \, a^{5} c^{7}\right)} d^{2} e^{4} - 6 \, {\left(b^{11} c - 9 \, a b^{9} c^{2} + 29 \, a^{2} b^{7} c^{3} - 40 \, a^{3} b^{5} c^{4} + 22 \, a^{4} b^{3} c^{5} - 3 \, a^{5} b c^{6}\right)} d e^{5} + {\left(b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}\right)} e^{6}}{b^{2} c^{14} - 4 \, a c^{15}}}}{b^{2} c^{7} - 4 \, a c^{8}}} \log\left(-\sqrt{2} {\left({\left(b^{6} c^{4} - 6 \, a b^{4} c^{5} + 8 \, a^{2} b^{2} c^{6}\right)} d^{4} - {\left(4 \, b^{7} c^{3} - 28 \, a b^{5} c^{4} + 53 \, a^{2} b^{3} c^{5} - 20 \, a^{3} b c^{6}\right)} d^{3} e + 3 \, {\left(2 \, b^{8} c^{2} - 16 \, a b^{6} c^{3} + 39 \, a^{2} b^{4} c^{4} - 29 \, a^{3} b^{2} c^{5} + 4 \, a^{4} c^{6}\right)} d^{2} e^{2} - {\left(4 \, b^{9} c - 36 \, a b^{7} c^{2} + 107 \, a^{2} b^{5} c^{3} - 118 \, a^{3} b^{3} c^{4} + 40 \, a^{4} b c^{5}\right)} d e^{3} + {\left(b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 51 \, a^{3} b^{4} c^{3} + 29 \, a^{4} b^{2} c^{4} - 4 \, a^{5} c^{5}\right)} e^{4} + {\left({\left(b^{4} c^{8} - 6 \, a b^{2} c^{9} + 8 \, a^{2} c^{10}\right)} d - {\left(b^{5} c^{7} - 7 \, a b^{3} c^{8} + 12 \, a^{2} b c^{9}\right)} e\right)} \sqrt{\frac{{\left(b^{6} c^{6} - 4 \, a b^{4} c^{7} + 4 \, a^{2} b^{2} c^{8}\right)} d^{6} - 6 \, {\left(b^{7} c^{5} - 5 \, a b^{5} c^{6} + 7 \, a^{2} b^{3} c^{7} - 2 \, a^{3} b c^{8}\right)} d^{5} e + 3 \, {\left(5 \, b^{8} c^{4} - 30 \, a b^{6} c^{5} + 55 \, a^{2} b^{4} c^{6} - 30 \, a^{3} b^{2} c^{7} + 3 \, a^{4} c^{8}\right)} d^{4} e^{2} - 2 \, {\left(10 \, b^{9} c^{3} - 70 \, a b^{7} c^{4} + 160 \, a^{2} b^{5} c^{5} - 130 \, a^{3} b^{3} c^{6} + 29 \, a^{4} b c^{7}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{10} c^{2} - 40 \, a b^{8} c^{3} + 110 \, a^{2} b^{6} c^{4} - 120 \, a^{3} b^{4} c^{5} + 45 \, a^{4} b^{2} c^{6} - 2 \, a^{5} c^{7}\right)} d^{2} e^{4} - 6 \, {\left(b^{11} c - 9 \, a b^{9} c^{2} + 29 \, a^{2} b^{7} c^{3} - 40 \, a^{3} b^{5} c^{4} + 22 \, a^{4} b^{3} c^{5} - 3 \, a^{5} b c^{6}\right)} d e^{5} + {\left(b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}\right)} e^{6}}{b^{2} c^{14} - 4 \, a c^{15}}}\right)} \sqrt{\frac{{\left(b^{4} c^{3} - 4 \, a b^{2} c^{4} + 2 \, a^{2} c^{5}\right)} d^{3} - 3 \, {\left(b^{5} c^{2} - 5 \, a b^{3} c^{3} + 5 \, a^{2} b c^{4}\right)} d^{2} e + 3 \, {\left(b^{6} c - 6 \, a b^{4} c^{2} + 9 \, a^{2} b^{2} c^{3} - 2 \, a^{3} c^{4}\right)} d e^{2} - {\left(b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3}\right)} e^{3} - {\left(b^{2} c^{7} - 4 \, a c^{8}\right)} \sqrt{\frac{{\left(b^{6} c^{6} - 4 \, a b^{4} c^{7} + 4 \, a^{2} b^{2} c^{8}\right)} d^{6} - 6 \, {\left(b^{7} c^{5} - 5 \, a b^{5} c^{6} + 7 \, a^{2} b^{3} c^{7} - 2 \, a^{3} b c^{8}\right)} d^{5} e + 3 \, {\left(5 \, b^{8} c^{4} - 30 \, a b^{6} c^{5} + 55 \, a^{2} b^{4} c^{6} - 30 \, a^{3} b^{2} c^{7} + 3 \, a^{4} c^{8}\right)} d^{4} e^{2} - 2 \, {\left(10 \, b^{9} c^{3} - 70 \, a b^{7} c^{4} + 160 \, a^{2} b^{5} c^{5} - 130 \, a^{3} b^{3} c^{6} + 29 \, a^{4} b c^{7}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{10} c^{2} - 40 \, a b^{8} c^{3} + 110 \, a^{2} b^{6} c^{4} - 120 \, a^{3} b^{4} c^{5} + 45 \, a^{4} b^{2} c^{6} - 2 \, a^{5} c^{7}\right)} d^{2} e^{4} - 6 \, {\left(b^{11} c - 9 \, a b^{9} c^{2} + 29 \, a^{2} b^{7} c^{3} - 40 \, a^{3} b^{5} c^{4} + 22 \, a^{4} b^{3} c^{5} - 3 \, a^{5} b c^{6}\right)} d e^{5} + {\left(b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}\right)} e^{6}}{b^{2} c^{14} - 4 \, a c^{15}}}}{b^{2} c^{7} - 4 \, a c^{8}}} + 4 \, {\left({\left(a^{2} b^{3} c^{4} - 2 \, a^{3} b c^{5}\right)} d^{5} - {\left(4 \, a^{2} b^{4} c^{3} - 11 \, a^{3} b^{2} c^{4} + 3 \, a^{4} c^{5}\right)} d^{4} e + 2 \, {\left(3 \, a^{2} b^{5} c^{2} - 10 \, a^{3} b^{3} c^{3} + 5 \, a^{4} b c^{4}\right)} d^{3} e^{2} - 2 \, {\left(2 \, a^{2} b^{6} c - 7 \, a^{3} b^{4} c^{2} + 3 \, a^{4} b^{2} c^{3} + a^{5} c^{4}\right)} d^{2} e^{3} + {\left(a^{2} b^{7} - 2 \, a^{3} b^{5} c - 6 \, a^{4} b^{3} c^{2} + 8 \, a^{5} b c^{3}\right)} d e^{4} - {\left(a^{3} b^{6} - 5 \, a^{4} b^{4} c + 6 \, a^{5} b^{2} c^{2} - a^{6} c^{3}\right)} e^{5}\right)} \sqrt{e x + d}\right) - 4 \, {\left(3 \, c^{2} e^{2} x^{2} + 3 \, c^{2} d^{2} - 20 \, b c d e + 15 \, {\left(b^{2} - a c\right)} e^{2} + {\left(6 \, c^{2} d e - 5 \, b c e^{2}\right)} x\right)} \sqrt{e x + d}}{30 \, c^{3} e}"," ",0,"-1/30*(15*sqrt(2)*c^3*e*sqrt(((b^4*c^3 - 4*a*b^2*c^4 + 2*a^2*c^5)*d^3 - 3*(b^5*c^2 - 5*a*b^3*c^3 + 5*a^2*b*c^4)*d^2*e + 3*(b^6*c - 6*a*b^4*c^2 + 9*a^2*b^2*c^3 - 2*a^3*c^4)*d*e^2 - (b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3)*e^3 + (b^2*c^7 - 4*a*c^8)*sqrt(((b^6*c^6 - 4*a*b^4*c^7 + 4*a^2*b^2*c^8)*d^6 - 6*(b^7*c^5 - 5*a*b^5*c^6 + 7*a^2*b^3*c^7 - 2*a^3*b*c^8)*d^5*e + 3*(5*b^8*c^4 - 30*a*b^6*c^5 + 55*a^2*b^4*c^6 - 30*a^3*b^2*c^7 + 3*a^4*c^8)*d^4*e^2 - 2*(10*b^9*c^3 - 70*a*b^7*c^4 + 160*a^2*b^5*c^5 - 130*a^3*b^3*c^6 + 29*a^4*b*c^7)*d^3*e^3 + 3*(5*b^10*c^2 - 40*a*b^8*c^3 + 110*a^2*b^6*c^4 - 120*a^3*b^4*c^5 + 45*a^4*b^2*c^6 - 2*a^5*c^7)*d^2*e^4 - 6*(b^11*c - 9*a*b^9*c^2 + 29*a^2*b^7*c^3 - 40*a^3*b^5*c^4 + 22*a^4*b^3*c^5 - 3*a^5*b*c^6)*d*e^5 + (b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)*e^6)/(b^2*c^14 - 4*a*c^15)))/(b^2*c^7 - 4*a*c^8))*log(sqrt(2)*((b^6*c^4 - 6*a*b^4*c^5 + 8*a^2*b^2*c^6)*d^4 - (4*b^7*c^3 - 28*a*b^5*c^4 + 53*a^2*b^3*c^5 - 20*a^3*b*c^6)*d^3*e + 3*(2*b^8*c^2 - 16*a*b^6*c^3 + 39*a^2*b^4*c^4 - 29*a^3*b^2*c^5 + 4*a^4*c^6)*d^2*e^2 - (4*b^9*c - 36*a*b^7*c^2 + 107*a^2*b^5*c^3 - 118*a^3*b^3*c^4 + 40*a^4*b*c^5)*d*e^3 + (b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 51*a^3*b^4*c^3 + 29*a^4*b^2*c^4 - 4*a^5*c^5)*e^4 - ((b^4*c^8 - 6*a*b^2*c^9 + 8*a^2*c^10)*d - (b^5*c^7 - 7*a*b^3*c^8 + 12*a^2*b*c^9)*e)*sqrt(((b^6*c^6 - 4*a*b^4*c^7 + 4*a^2*b^2*c^8)*d^6 - 6*(b^7*c^5 - 5*a*b^5*c^6 + 7*a^2*b^3*c^7 - 2*a^3*b*c^8)*d^5*e + 3*(5*b^8*c^4 - 30*a*b^6*c^5 + 55*a^2*b^4*c^6 - 30*a^3*b^2*c^7 + 3*a^4*c^8)*d^4*e^2 - 2*(10*b^9*c^3 - 70*a*b^7*c^4 + 160*a^2*b^5*c^5 - 130*a^3*b^3*c^6 + 29*a^4*b*c^7)*d^3*e^3 + 3*(5*b^10*c^2 - 40*a*b^8*c^3 + 110*a^2*b^6*c^4 - 120*a^3*b^4*c^5 + 45*a^4*b^2*c^6 - 2*a^5*c^7)*d^2*e^4 - 6*(b^11*c - 9*a*b^9*c^2 + 29*a^2*b^7*c^3 - 40*a^3*b^5*c^4 + 22*a^4*b^3*c^5 - 3*a^5*b*c^6)*d*e^5 + (b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)*e^6)/(b^2*c^14 - 4*a*c^15)))*sqrt(((b^4*c^3 - 4*a*b^2*c^4 + 2*a^2*c^5)*d^3 - 3*(b^5*c^2 - 5*a*b^3*c^3 + 5*a^2*b*c^4)*d^2*e + 3*(b^6*c - 6*a*b^4*c^2 + 9*a^2*b^2*c^3 - 2*a^3*c^4)*d*e^2 - (b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3)*e^3 + (b^2*c^7 - 4*a*c^8)*sqrt(((b^6*c^6 - 4*a*b^4*c^7 + 4*a^2*b^2*c^8)*d^6 - 6*(b^7*c^5 - 5*a*b^5*c^6 + 7*a^2*b^3*c^7 - 2*a^3*b*c^8)*d^5*e + 3*(5*b^8*c^4 - 30*a*b^6*c^5 + 55*a^2*b^4*c^6 - 30*a^3*b^2*c^7 + 3*a^4*c^8)*d^4*e^2 - 2*(10*b^9*c^3 - 70*a*b^7*c^4 + 160*a^2*b^5*c^5 - 130*a^3*b^3*c^6 + 29*a^4*b*c^7)*d^3*e^3 + 3*(5*b^10*c^2 - 40*a*b^8*c^3 + 110*a^2*b^6*c^4 - 120*a^3*b^4*c^5 + 45*a^4*b^2*c^6 - 2*a^5*c^7)*d^2*e^4 - 6*(b^11*c - 9*a*b^9*c^2 + 29*a^2*b^7*c^3 - 40*a^3*b^5*c^4 + 22*a^4*b^3*c^5 - 3*a^5*b*c^6)*d*e^5 + (b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)*e^6)/(b^2*c^14 - 4*a*c^15)))/(b^2*c^7 - 4*a*c^8)) + 4*((a^2*b^3*c^4 - 2*a^3*b*c^5)*d^5 - (4*a^2*b^4*c^3 - 11*a^3*b^2*c^4 + 3*a^4*c^5)*d^4*e + 2*(3*a^2*b^5*c^2 - 10*a^3*b^3*c^3 + 5*a^4*b*c^4)*d^3*e^2 - 2*(2*a^2*b^6*c - 7*a^3*b^4*c^2 + 3*a^4*b^2*c^3 + a^5*c^4)*d^2*e^3 + (a^2*b^7 - 2*a^3*b^5*c - 6*a^4*b^3*c^2 + 8*a^5*b*c^3)*d*e^4 - (a^3*b^6 - 5*a^4*b^4*c + 6*a^5*b^2*c^2 - a^6*c^3)*e^5)*sqrt(e*x + d)) - 15*sqrt(2)*c^3*e*sqrt(((b^4*c^3 - 4*a*b^2*c^4 + 2*a^2*c^5)*d^3 - 3*(b^5*c^2 - 5*a*b^3*c^3 + 5*a^2*b*c^4)*d^2*e + 3*(b^6*c - 6*a*b^4*c^2 + 9*a^2*b^2*c^3 - 2*a^3*c^4)*d*e^2 - (b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3)*e^3 + (b^2*c^7 - 4*a*c^8)*sqrt(((b^6*c^6 - 4*a*b^4*c^7 + 4*a^2*b^2*c^8)*d^6 - 6*(b^7*c^5 - 5*a*b^5*c^6 + 7*a^2*b^3*c^7 - 2*a^3*b*c^8)*d^5*e + 3*(5*b^8*c^4 - 30*a*b^6*c^5 + 55*a^2*b^4*c^6 - 30*a^3*b^2*c^7 + 3*a^4*c^8)*d^4*e^2 - 2*(10*b^9*c^3 - 70*a*b^7*c^4 + 160*a^2*b^5*c^5 - 130*a^3*b^3*c^6 + 29*a^4*b*c^7)*d^3*e^3 + 3*(5*b^10*c^2 - 40*a*b^8*c^3 + 110*a^2*b^6*c^4 - 120*a^3*b^4*c^5 + 45*a^4*b^2*c^6 - 2*a^5*c^7)*d^2*e^4 - 6*(b^11*c - 9*a*b^9*c^2 + 29*a^2*b^7*c^3 - 40*a^3*b^5*c^4 + 22*a^4*b^3*c^5 - 3*a^5*b*c^6)*d*e^5 + (b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)*e^6)/(b^2*c^14 - 4*a*c^15)))/(b^2*c^7 - 4*a*c^8))*log(-sqrt(2)*((b^6*c^4 - 6*a*b^4*c^5 + 8*a^2*b^2*c^6)*d^4 - (4*b^7*c^3 - 28*a*b^5*c^4 + 53*a^2*b^3*c^5 - 20*a^3*b*c^6)*d^3*e + 3*(2*b^8*c^2 - 16*a*b^6*c^3 + 39*a^2*b^4*c^4 - 29*a^3*b^2*c^5 + 4*a^4*c^6)*d^2*e^2 - (4*b^9*c - 36*a*b^7*c^2 + 107*a^2*b^5*c^3 - 118*a^3*b^3*c^4 + 40*a^4*b*c^5)*d*e^3 + (b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 51*a^3*b^4*c^3 + 29*a^4*b^2*c^4 - 4*a^5*c^5)*e^4 - ((b^4*c^8 - 6*a*b^2*c^9 + 8*a^2*c^10)*d - (b^5*c^7 - 7*a*b^3*c^8 + 12*a^2*b*c^9)*e)*sqrt(((b^6*c^6 - 4*a*b^4*c^7 + 4*a^2*b^2*c^8)*d^6 - 6*(b^7*c^5 - 5*a*b^5*c^6 + 7*a^2*b^3*c^7 - 2*a^3*b*c^8)*d^5*e + 3*(5*b^8*c^4 - 30*a*b^6*c^5 + 55*a^2*b^4*c^6 - 30*a^3*b^2*c^7 + 3*a^4*c^8)*d^4*e^2 - 2*(10*b^9*c^3 - 70*a*b^7*c^4 + 160*a^2*b^5*c^5 - 130*a^3*b^3*c^6 + 29*a^4*b*c^7)*d^3*e^3 + 3*(5*b^10*c^2 - 40*a*b^8*c^3 + 110*a^2*b^6*c^4 - 120*a^3*b^4*c^5 + 45*a^4*b^2*c^6 - 2*a^5*c^7)*d^2*e^4 - 6*(b^11*c - 9*a*b^9*c^2 + 29*a^2*b^7*c^3 - 40*a^3*b^5*c^4 + 22*a^4*b^3*c^5 - 3*a^5*b*c^6)*d*e^5 + (b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)*e^6)/(b^2*c^14 - 4*a*c^15)))*sqrt(((b^4*c^3 - 4*a*b^2*c^4 + 2*a^2*c^5)*d^3 - 3*(b^5*c^2 - 5*a*b^3*c^3 + 5*a^2*b*c^4)*d^2*e + 3*(b^6*c - 6*a*b^4*c^2 + 9*a^2*b^2*c^3 - 2*a^3*c^4)*d*e^2 - (b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3)*e^3 + (b^2*c^7 - 4*a*c^8)*sqrt(((b^6*c^6 - 4*a*b^4*c^7 + 4*a^2*b^2*c^8)*d^6 - 6*(b^7*c^5 - 5*a*b^5*c^6 + 7*a^2*b^3*c^7 - 2*a^3*b*c^8)*d^5*e + 3*(5*b^8*c^4 - 30*a*b^6*c^5 + 55*a^2*b^4*c^6 - 30*a^3*b^2*c^7 + 3*a^4*c^8)*d^4*e^2 - 2*(10*b^9*c^3 - 70*a*b^7*c^4 + 160*a^2*b^5*c^5 - 130*a^3*b^3*c^6 + 29*a^4*b*c^7)*d^3*e^3 + 3*(5*b^10*c^2 - 40*a*b^8*c^3 + 110*a^2*b^6*c^4 - 120*a^3*b^4*c^5 + 45*a^4*b^2*c^6 - 2*a^5*c^7)*d^2*e^4 - 6*(b^11*c - 9*a*b^9*c^2 + 29*a^2*b^7*c^3 - 40*a^3*b^5*c^4 + 22*a^4*b^3*c^5 - 3*a^5*b*c^6)*d*e^5 + (b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)*e^6)/(b^2*c^14 - 4*a*c^15)))/(b^2*c^7 - 4*a*c^8)) + 4*((a^2*b^3*c^4 - 2*a^3*b*c^5)*d^5 - (4*a^2*b^4*c^3 - 11*a^3*b^2*c^4 + 3*a^4*c^5)*d^4*e + 2*(3*a^2*b^5*c^2 - 10*a^3*b^3*c^3 + 5*a^4*b*c^4)*d^3*e^2 - 2*(2*a^2*b^6*c - 7*a^3*b^4*c^2 + 3*a^4*b^2*c^3 + a^5*c^4)*d^2*e^3 + (a^2*b^7 - 2*a^3*b^5*c - 6*a^4*b^3*c^2 + 8*a^5*b*c^3)*d*e^4 - (a^3*b^6 - 5*a^4*b^4*c + 6*a^5*b^2*c^2 - a^6*c^3)*e^5)*sqrt(e*x + d)) + 15*sqrt(2)*c^3*e*sqrt(((b^4*c^3 - 4*a*b^2*c^4 + 2*a^2*c^5)*d^3 - 3*(b^5*c^2 - 5*a*b^3*c^3 + 5*a^2*b*c^4)*d^2*e + 3*(b^6*c - 6*a*b^4*c^2 + 9*a^2*b^2*c^3 - 2*a^3*c^4)*d*e^2 - (b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3)*e^3 - (b^2*c^7 - 4*a*c^8)*sqrt(((b^6*c^6 - 4*a*b^4*c^7 + 4*a^2*b^2*c^8)*d^6 - 6*(b^7*c^5 - 5*a*b^5*c^6 + 7*a^2*b^3*c^7 - 2*a^3*b*c^8)*d^5*e + 3*(5*b^8*c^4 - 30*a*b^6*c^5 + 55*a^2*b^4*c^6 - 30*a^3*b^2*c^7 + 3*a^4*c^8)*d^4*e^2 - 2*(10*b^9*c^3 - 70*a*b^7*c^4 + 160*a^2*b^5*c^5 - 130*a^3*b^3*c^6 + 29*a^4*b*c^7)*d^3*e^3 + 3*(5*b^10*c^2 - 40*a*b^8*c^3 + 110*a^2*b^6*c^4 - 120*a^3*b^4*c^5 + 45*a^4*b^2*c^6 - 2*a^5*c^7)*d^2*e^4 - 6*(b^11*c - 9*a*b^9*c^2 + 29*a^2*b^7*c^3 - 40*a^3*b^5*c^4 + 22*a^4*b^3*c^5 - 3*a^5*b*c^6)*d*e^5 + (b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)*e^6)/(b^2*c^14 - 4*a*c^15)))/(b^2*c^7 - 4*a*c^8))*log(sqrt(2)*((b^6*c^4 - 6*a*b^4*c^5 + 8*a^2*b^2*c^6)*d^4 - (4*b^7*c^3 - 28*a*b^5*c^4 + 53*a^2*b^3*c^5 - 20*a^3*b*c^6)*d^3*e + 3*(2*b^8*c^2 - 16*a*b^6*c^3 + 39*a^2*b^4*c^4 - 29*a^3*b^2*c^5 + 4*a^4*c^6)*d^2*e^2 - (4*b^9*c - 36*a*b^7*c^2 + 107*a^2*b^5*c^3 - 118*a^3*b^3*c^4 + 40*a^4*b*c^5)*d*e^3 + (b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 51*a^3*b^4*c^3 + 29*a^4*b^2*c^4 - 4*a^5*c^5)*e^4 + ((b^4*c^8 - 6*a*b^2*c^9 + 8*a^2*c^10)*d - (b^5*c^7 - 7*a*b^3*c^8 + 12*a^2*b*c^9)*e)*sqrt(((b^6*c^6 - 4*a*b^4*c^7 + 4*a^2*b^2*c^8)*d^6 - 6*(b^7*c^5 - 5*a*b^5*c^6 + 7*a^2*b^3*c^7 - 2*a^3*b*c^8)*d^5*e + 3*(5*b^8*c^4 - 30*a*b^6*c^5 + 55*a^2*b^4*c^6 - 30*a^3*b^2*c^7 + 3*a^4*c^8)*d^4*e^2 - 2*(10*b^9*c^3 - 70*a*b^7*c^4 + 160*a^2*b^5*c^5 - 130*a^3*b^3*c^6 + 29*a^4*b*c^7)*d^3*e^3 + 3*(5*b^10*c^2 - 40*a*b^8*c^3 + 110*a^2*b^6*c^4 - 120*a^3*b^4*c^5 + 45*a^4*b^2*c^6 - 2*a^5*c^7)*d^2*e^4 - 6*(b^11*c - 9*a*b^9*c^2 + 29*a^2*b^7*c^3 - 40*a^3*b^5*c^4 + 22*a^4*b^3*c^5 - 3*a^5*b*c^6)*d*e^5 + (b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)*e^6)/(b^2*c^14 - 4*a*c^15)))*sqrt(((b^4*c^3 - 4*a*b^2*c^4 + 2*a^2*c^5)*d^3 - 3*(b^5*c^2 - 5*a*b^3*c^3 + 5*a^2*b*c^4)*d^2*e + 3*(b^6*c - 6*a*b^4*c^2 + 9*a^2*b^2*c^3 - 2*a^3*c^4)*d*e^2 - (b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3)*e^3 - (b^2*c^7 - 4*a*c^8)*sqrt(((b^6*c^6 - 4*a*b^4*c^7 + 4*a^2*b^2*c^8)*d^6 - 6*(b^7*c^5 - 5*a*b^5*c^6 + 7*a^2*b^3*c^7 - 2*a^3*b*c^8)*d^5*e + 3*(5*b^8*c^4 - 30*a*b^6*c^5 + 55*a^2*b^4*c^6 - 30*a^3*b^2*c^7 + 3*a^4*c^8)*d^4*e^2 - 2*(10*b^9*c^3 - 70*a*b^7*c^4 + 160*a^2*b^5*c^5 - 130*a^3*b^3*c^6 + 29*a^4*b*c^7)*d^3*e^3 + 3*(5*b^10*c^2 - 40*a*b^8*c^3 + 110*a^2*b^6*c^4 - 120*a^3*b^4*c^5 + 45*a^4*b^2*c^6 - 2*a^5*c^7)*d^2*e^4 - 6*(b^11*c - 9*a*b^9*c^2 + 29*a^2*b^7*c^3 - 40*a^3*b^5*c^4 + 22*a^4*b^3*c^5 - 3*a^5*b*c^6)*d*e^5 + (b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)*e^6)/(b^2*c^14 - 4*a*c^15)))/(b^2*c^7 - 4*a*c^8)) + 4*((a^2*b^3*c^4 - 2*a^3*b*c^5)*d^5 - (4*a^2*b^4*c^3 - 11*a^3*b^2*c^4 + 3*a^4*c^5)*d^4*e + 2*(3*a^2*b^5*c^2 - 10*a^3*b^3*c^3 + 5*a^4*b*c^4)*d^3*e^2 - 2*(2*a^2*b^6*c - 7*a^3*b^4*c^2 + 3*a^4*b^2*c^3 + a^5*c^4)*d^2*e^3 + (a^2*b^7 - 2*a^3*b^5*c - 6*a^4*b^3*c^2 + 8*a^5*b*c^3)*d*e^4 - (a^3*b^6 - 5*a^4*b^4*c + 6*a^5*b^2*c^2 - a^6*c^3)*e^5)*sqrt(e*x + d)) - 15*sqrt(2)*c^3*e*sqrt(((b^4*c^3 - 4*a*b^2*c^4 + 2*a^2*c^5)*d^3 - 3*(b^5*c^2 - 5*a*b^3*c^3 + 5*a^2*b*c^4)*d^2*e + 3*(b^6*c - 6*a*b^4*c^2 + 9*a^2*b^2*c^3 - 2*a^3*c^4)*d*e^2 - (b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3)*e^3 - (b^2*c^7 - 4*a*c^8)*sqrt(((b^6*c^6 - 4*a*b^4*c^7 + 4*a^2*b^2*c^8)*d^6 - 6*(b^7*c^5 - 5*a*b^5*c^6 + 7*a^2*b^3*c^7 - 2*a^3*b*c^8)*d^5*e + 3*(5*b^8*c^4 - 30*a*b^6*c^5 + 55*a^2*b^4*c^6 - 30*a^3*b^2*c^7 + 3*a^4*c^8)*d^4*e^2 - 2*(10*b^9*c^3 - 70*a*b^7*c^4 + 160*a^2*b^5*c^5 - 130*a^3*b^3*c^6 + 29*a^4*b*c^7)*d^3*e^3 + 3*(5*b^10*c^2 - 40*a*b^8*c^3 + 110*a^2*b^6*c^4 - 120*a^3*b^4*c^5 + 45*a^4*b^2*c^6 - 2*a^5*c^7)*d^2*e^4 - 6*(b^11*c - 9*a*b^9*c^2 + 29*a^2*b^7*c^3 - 40*a^3*b^5*c^4 + 22*a^4*b^3*c^5 - 3*a^5*b*c^6)*d*e^5 + (b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)*e^6)/(b^2*c^14 - 4*a*c^15)))/(b^2*c^7 - 4*a*c^8))*log(-sqrt(2)*((b^6*c^4 - 6*a*b^4*c^5 + 8*a^2*b^2*c^6)*d^4 - (4*b^7*c^3 - 28*a*b^5*c^4 + 53*a^2*b^3*c^5 - 20*a^3*b*c^6)*d^3*e + 3*(2*b^8*c^2 - 16*a*b^6*c^3 + 39*a^2*b^4*c^4 - 29*a^3*b^2*c^5 + 4*a^4*c^6)*d^2*e^2 - (4*b^9*c - 36*a*b^7*c^2 + 107*a^2*b^5*c^3 - 118*a^3*b^3*c^4 + 40*a^4*b*c^5)*d*e^3 + (b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 51*a^3*b^4*c^3 + 29*a^4*b^2*c^4 - 4*a^5*c^5)*e^4 + ((b^4*c^8 - 6*a*b^2*c^9 + 8*a^2*c^10)*d - (b^5*c^7 - 7*a*b^3*c^8 + 12*a^2*b*c^9)*e)*sqrt(((b^6*c^6 - 4*a*b^4*c^7 + 4*a^2*b^2*c^8)*d^6 - 6*(b^7*c^5 - 5*a*b^5*c^6 + 7*a^2*b^3*c^7 - 2*a^3*b*c^8)*d^5*e + 3*(5*b^8*c^4 - 30*a*b^6*c^5 + 55*a^2*b^4*c^6 - 30*a^3*b^2*c^7 + 3*a^4*c^8)*d^4*e^2 - 2*(10*b^9*c^3 - 70*a*b^7*c^4 + 160*a^2*b^5*c^5 - 130*a^3*b^3*c^6 + 29*a^4*b*c^7)*d^3*e^3 + 3*(5*b^10*c^2 - 40*a*b^8*c^3 + 110*a^2*b^6*c^4 - 120*a^3*b^4*c^5 + 45*a^4*b^2*c^6 - 2*a^5*c^7)*d^2*e^4 - 6*(b^11*c - 9*a*b^9*c^2 + 29*a^2*b^7*c^3 - 40*a^3*b^5*c^4 + 22*a^4*b^3*c^5 - 3*a^5*b*c^6)*d*e^5 + (b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)*e^6)/(b^2*c^14 - 4*a*c^15)))*sqrt(((b^4*c^3 - 4*a*b^2*c^4 + 2*a^2*c^5)*d^3 - 3*(b^5*c^2 - 5*a*b^3*c^3 + 5*a^2*b*c^4)*d^2*e + 3*(b^6*c - 6*a*b^4*c^2 + 9*a^2*b^2*c^3 - 2*a^3*c^4)*d*e^2 - (b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3)*e^3 - (b^2*c^7 - 4*a*c^8)*sqrt(((b^6*c^6 - 4*a*b^4*c^7 + 4*a^2*b^2*c^8)*d^6 - 6*(b^7*c^5 - 5*a*b^5*c^6 + 7*a^2*b^3*c^7 - 2*a^3*b*c^8)*d^5*e + 3*(5*b^8*c^4 - 30*a*b^6*c^5 + 55*a^2*b^4*c^6 - 30*a^3*b^2*c^7 + 3*a^4*c^8)*d^4*e^2 - 2*(10*b^9*c^3 - 70*a*b^7*c^4 + 160*a^2*b^5*c^5 - 130*a^3*b^3*c^6 + 29*a^4*b*c^7)*d^3*e^3 + 3*(5*b^10*c^2 - 40*a*b^8*c^3 + 110*a^2*b^6*c^4 - 120*a^3*b^4*c^5 + 45*a^4*b^2*c^6 - 2*a^5*c^7)*d^2*e^4 - 6*(b^11*c - 9*a*b^9*c^2 + 29*a^2*b^7*c^3 - 40*a^3*b^5*c^4 + 22*a^4*b^3*c^5 - 3*a^5*b*c^6)*d*e^5 + (b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)*e^6)/(b^2*c^14 - 4*a*c^15)))/(b^2*c^7 - 4*a*c^8)) + 4*((a^2*b^3*c^4 - 2*a^3*b*c^5)*d^5 - (4*a^2*b^4*c^3 - 11*a^3*b^2*c^4 + 3*a^4*c^5)*d^4*e + 2*(3*a^2*b^5*c^2 - 10*a^3*b^3*c^3 + 5*a^4*b*c^4)*d^3*e^2 - 2*(2*a^2*b^6*c - 7*a^3*b^4*c^2 + 3*a^4*b^2*c^3 + a^5*c^4)*d^2*e^3 + (a^2*b^7 - 2*a^3*b^5*c - 6*a^4*b^3*c^2 + 8*a^5*b*c^3)*d*e^4 - (a^3*b^6 - 5*a^4*b^4*c + 6*a^5*b^2*c^2 - a^6*c^3)*e^5)*sqrt(e*x + d)) - 4*(3*c^2*e^2*x^2 + 3*c^2*d^2 - 20*b*c*d*e + 15*(b^2 - a*c)*e^2 + (6*c^2*d*e - 5*b*c*e^2)*x)*sqrt(e*x + d))/(c^3*e)","B",0
536,1,5572,0,1.125927," ","integrate(x*(e*x+d)^(3/2)/(c*x^2+b*x+a),x, algorithm=""fricas"")","-\frac{3 \, \sqrt{2} c^{2} \sqrt{\frac{{\left(b^{2} c^{3} - 2 \, a c^{4}\right)} d^{3} - 3 \, {\left(b^{3} c^{2} - 3 \, a b c^{3}\right)} d^{2} e + 3 \, {\left(b^{4} c - 4 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d e^{2} - {\left(b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}\right)} e^{3} + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{b^{2} c^{6} d^{6} - 6 \, {\left(b^{3} c^{5} - a b c^{6}\right)} d^{5} e + 3 \, {\left(5 \, b^{4} c^{4} - 10 \, a b^{2} c^{5} + 3 \, a^{2} c^{6}\right)} d^{4} e^{2} - 2 \, {\left(10 \, b^{5} c^{3} - 30 \, a b^{3} c^{4} + 19 \, a^{2} b c^{5}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{6} c^{2} - 20 \, a b^{4} c^{3} + 20 \, a^{2} b^{2} c^{4} - 2 \, a^{3} c^{5}\right)} d^{2} e^{4} - 6 \, {\left(b^{7} c - 5 \, a b^{5} c^{2} + 7 \, a^{2} b^{3} c^{3} - 2 \, a^{3} b c^{4}\right)} d e^{5} + {\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} e^{6}}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}} \log\left(\sqrt{2} {\left({\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{4} - {\left(4 \, b^{4} c^{3} - 19 \, a b^{2} c^{4} + 12 \, a^{2} c^{5}\right)} d^{3} e + 3 \, {\left(2 \, b^{5} c^{2} - 11 \, a b^{3} c^{3} + 12 \, a^{2} b c^{4}\right)} d^{2} e^{2} - {\left(4 \, b^{6} c - 25 \, a b^{4} c^{2} + 37 \, a^{2} b^{2} c^{3} - 4 \, a^{3} c^{4}\right)} d e^{3} + {\left(b^{7} - 7 \, a b^{5} c + 13 \, a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} e^{4} - {\left({\left(b^{3} c^{6} - 4 \, a b c^{7}\right)} d - {\left(b^{4} c^{5} - 6 \, a b^{2} c^{6} + 8 \, a^{2} c^{7}\right)} e\right)} \sqrt{\frac{b^{2} c^{6} d^{6} - 6 \, {\left(b^{3} c^{5} - a b c^{6}\right)} d^{5} e + 3 \, {\left(5 \, b^{4} c^{4} - 10 \, a b^{2} c^{5} + 3 \, a^{2} c^{6}\right)} d^{4} e^{2} - 2 \, {\left(10 \, b^{5} c^{3} - 30 \, a b^{3} c^{4} + 19 \, a^{2} b c^{5}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{6} c^{2} - 20 \, a b^{4} c^{3} + 20 \, a^{2} b^{2} c^{4} - 2 \, a^{3} c^{5}\right)} d^{2} e^{4} - 6 \, {\left(b^{7} c - 5 \, a b^{5} c^{2} + 7 \, a^{2} b^{3} c^{3} - 2 \, a^{3} b c^{4}\right)} d e^{5} + {\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} e^{6}}{b^{2} c^{10} - 4 \, a c^{11}}}\right)} \sqrt{\frac{{\left(b^{2} c^{3} - 2 \, a c^{4}\right)} d^{3} - 3 \, {\left(b^{3} c^{2} - 3 \, a b c^{3}\right)} d^{2} e + 3 \, {\left(b^{4} c - 4 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d e^{2} - {\left(b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}\right)} e^{3} + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{b^{2} c^{6} d^{6} - 6 \, {\left(b^{3} c^{5} - a b c^{6}\right)} d^{5} e + 3 \, {\left(5 \, b^{4} c^{4} - 10 \, a b^{2} c^{5} + 3 \, a^{2} c^{6}\right)} d^{4} e^{2} - 2 \, {\left(10 \, b^{5} c^{3} - 30 \, a b^{3} c^{4} + 19 \, a^{2} b c^{5}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{6} c^{2} - 20 \, a b^{4} c^{3} + 20 \, a^{2} b^{2} c^{4} - 2 \, a^{3} c^{5}\right)} d^{2} e^{4} - 6 \, {\left(b^{7} c - 5 \, a b^{5} c^{2} + 7 \, a^{2} b^{3} c^{3} - 2 \, a^{3} b c^{4}\right)} d e^{5} + {\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} e^{6}}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}} - 4 \, {\left(a b c^{4} d^{5} - {\left(4 \, a b^{2} c^{3} - 3 \, a^{2} c^{4}\right)} d^{4} e + 2 \, {\left(3 \, a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{3} e^{2} - 2 \, {\left(2 \, a b^{4} c - 3 \, a^{2} b^{2} c^{2} - a^{3} c^{3}\right)} d^{2} e^{3} + {\left(a b^{5} - 5 \, a^{3} b c^{2}\right)} d e^{4} - {\left(a^{2} b^{4} - 3 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{5}\right)} \sqrt{e x + d}\right) - 3 \, \sqrt{2} c^{2} \sqrt{\frac{{\left(b^{2} c^{3} - 2 \, a c^{4}\right)} d^{3} - 3 \, {\left(b^{3} c^{2} - 3 \, a b c^{3}\right)} d^{2} e + 3 \, {\left(b^{4} c - 4 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d e^{2} - {\left(b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}\right)} e^{3} + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{b^{2} c^{6} d^{6} - 6 \, {\left(b^{3} c^{5} - a b c^{6}\right)} d^{5} e + 3 \, {\left(5 \, b^{4} c^{4} - 10 \, a b^{2} c^{5} + 3 \, a^{2} c^{6}\right)} d^{4} e^{2} - 2 \, {\left(10 \, b^{5} c^{3} - 30 \, a b^{3} c^{4} + 19 \, a^{2} b c^{5}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{6} c^{2} - 20 \, a b^{4} c^{3} + 20 \, a^{2} b^{2} c^{4} - 2 \, a^{3} c^{5}\right)} d^{2} e^{4} - 6 \, {\left(b^{7} c - 5 \, a b^{5} c^{2} + 7 \, a^{2} b^{3} c^{3} - 2 \, a^{3} b c^{4}\right)} d e^{5} + {\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} e^{6}}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}} \log\left(-\sqrt{2} {\left({\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{4} - {\left(4 \, b^{4} c^{3} - 19 \, a b^{2} c^{4} + 12 \, a^{2} c^{5}\right)} d^{3} e + 3 \, {\left(2 \, b^{5} c^{2} - 11 \, a b^{3} c^{3} + 12 \, a^{2} b c^{4}\right)} d^{2} e^{2} - {\left(4 \, b^{6} c - 25 \, a b^{4} c^{2} + 37 \, a^{2} b^{2} c^{3} - 4 \, a^{3} c^{4}\right)} d e^{3} + {\left(b^{7} - 7 \, a b^{5} c + 13 \, a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} e^{4} - {\left({\left(b^{3} c^{6} - 4 \, a b c^{7}\right)} d - {\left(b^{4} c^{5} - 6 \, a b^{2} c^{6} + 8 \, a^{2} c^{7}\right)} e\right)} \sqrt{\frac{b^{2} c^{6} d^{6} - 6 \, {\left(b^{3} c^{5} - a b c^{6}\right)} d^{5} e + 3 \, {\left(5 \, b^{4} c^{4} - 10 \, a b^{2} c^{5} + 3 \, a^{2} c^{6}\right)} d^{4} e^{2} - 2 \, {\left(10 \, b^{5} c^{3} - 30 \, a b^{3} c^{4} + 19 \, a^{2} b c^{5}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{6} c^{2} - 20 \, a b^{4} c^{3} + 20 \, a^{2} b^{2} c^{4} - 2 \, a^{3} c^{5}\right)} d^{2} e^{4} - 6 \, {\left(b^{7} c - 5 \, a b^{5} c^{2} + 7 \, a^{2} b^{3} c^{3} - 2 \, a^{3} b c^{4}\right)} d e^{5} + {\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} e^{6}}{b^{2} c^{10} - 4 \, a c^{11}}}\right)} \sqrt{\frac{{\left(b^{2} c^{3} - 2 \, a c^{4}\right)} d^{3} - 3 \, {\left(b^{3} c^{2} - 3 \, a b c^{3}\right)} d^{2} e + 3 \, {\left(b^{4} c - 4 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d e^{2} - {\left(b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}\right)} e^{3} + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{b^{2} c^{6} d^{6} - 6 \, {\left(b^{3} c^{5} - a b c^{6}\right)} d^{5} e + 3 \, {\left(5 \, b^{4} c^{4} - 10 \, a b^{2} c^{5} + 3 \, a^{2} c^{6}\right)} d^{4} e^{2} - 2 \, {\left(10 \, b^{5} c^{3} - 30 \, a b^{3} c^{4} + 19 \, a^{2} b c^{5}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{6} c^{2} - 20 \, a b^{4} c^{3} + 20 \, a^{2} b^{2} c^{4} - 2 \, a^{3} c^{5}\right)} d^{2} e^{4} - 6 \, {\left(b^{7} c - 5 \, a b^{5} c^{2} + 7 \, a^{2} b^{3} c^{3} - 2 \, a^{3} b c^{4}\right)} d e^{5} + {\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} e^{6}}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}} - 4 \, {\left(a b c^{4} d^{5} - {\left(4 \, a b^{2} c^{3} - 3 \, a^{2} c^{4}\right)} d^{4} e + 2 \, {\left(3 \, a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{3} e^{2} - 2 \, {\left(2 \, a b^{4} c - 3 \, a^{2} b^{2} c^{2} - a^{3} c^{3}\right)} d^{2} e^{3} + {\left(a b^{5} - 5 \, a^{3} b c^{2}\right)} d e^{4} - {\left(a^{2} b^{4} - 3 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{5}\right)} \sqrt{e x + d}\right) + 3 \, \sqrt{2} c^{2} \sqrt{\frac{{\left(b^{2} c^{3} - 2 \, a c^{4}\right)} d^{3} - 3 \, {\left(b^{3} c^{2} - 3 \, a b c^{3}\right)} d^{2} e + 3 \, {\left(b^{4} c - 4 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d e^{2} - {\left(b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}\right)} e^{3} - {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{b^{2} c^{6} d^{6} - 6 \, {\left(b^{3} c^{5} - a b c^{6}\right)} d^{5} e + 3 \, {\left(5 \, b^{4} c^{4} - 10 \, a b^{2} c^{5} + 3 \, a^{2} c^{6}\right)} d^{4} e^{2} - 2 \, {\left(10 \, b^{5} c^{3} - 30 \, a b^{3} c^{4} + 19 \, a^{2} b c^{5}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{6} c^{2} - 20 \, a b^{4} c^{3} + 20 \, a^{2} b^{2} c^{4} - 2 \, a^{3} c^{5}\right)} d^{2} e^{4} - 6 \, {\left(b^{7} c - 5 \, a b^{5} c^{2} + 7 \, a^{2} b^{3} c^{3} - 2 \, a^{3} b c^{4}\right)} d e^{5} + {\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} e^{6}}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}} \log\left(\sqrt{2} {\left({\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{4} - {\left(4 \, b^{4} c^{3} - 19 \, a b^{2} c^{4} + 12 \, a^{2} c^{5}\right)} d^{3} e + 3 \, {\left(2 \, b^{5} c^{2} - 11 \, a b^{3} c^{3} + 12 \, a^{2} b c^{4}\right)} d^{2} e^{2} - {\left(4 \, b^{6} c - 25 \, a b^{4} c^{2} + 37 \, a^{2} b^{2} c^{3} - 4 \, a^{3} c^{4}\right)} d e^{3} + {\left(b^{7} - 7 \, a b^{5} c + 13 \, a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} e^{4} + {\left({\left(b^{3} c^{6} - 4 \, a b c^{7}\right)} d - {\left(b^{4} c^{5} - 6 \, a b^{2} c^{6} + 8 \, a^{2} c^{7}\right)} e\right)} \sqrt{\frac{b^{2} c^{6} d^{6} - 6 \, {\left(b^{3} c^{5} - a b c^{6}\right)} d^{5} e + 3 \, {\left(5 \, b^{4} c^{4} - 10 \, a b^{2} c^{5} + 3 \, a^{2} c^{6}\right)} d^{4} e^{2} - 2 \, {\left(10 \, b^{5} c^{3} - 30 \, a b^{3} c^{4} + 19 \, a^{2} b c^{5}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{6} c^{2} - 20 \, a b^{4} c^{3} + 20 \, a^{2} b^{2} c^{4} - 2 \, a^{3} c^{5}\right)} d^{2} e^{4} - 6 \, {\left(b^{7} c - 5 \, a b^{5} c^{2} + 7 \, a^{2} b^{3} c^{3} - 2 \, a^{3} b c^{4}\right)} d e^{5} + {\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} e^{6}}{b^{2} c^{10} - 4 \, a c^{11}}}\right)} \sqrt{\frac{{\left(b^{2} c^{3} - 2 \, a c^{4}\right)} d^{3} - 3 \, {\left(b^{3} c^{2} - 3 \, a b c^{3}\right)} d^{2} e + 3 \, {\left(b^{4} c - 4 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d e^{2} - {\left(b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}\right)} e^{3} - {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{b^{2} c^{6} d^{6} - 6 \, {\left(b^{3} c^{5} - a b c^{6}\right)} d^{5} e + 3 \, {\left(5 \, b^{4} c^{4} - 10 \, a b^{2} c^{5} + 3 \, a^{2} c^{6}\right)} d^{4} e^{2} - 2 \, {\left(10 \, b^{5} c^{3} - 30 \, a b^{3} c^{4} + 19 \, a^{2} b c^{5}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{6} c^{2} - 20 \, a b^{4} c^{3} + 20 \, a^{2} b^{2} c^{4} - 2 \, a^{3} c^{5}\right)} d^{2} e^{4} - 6 \, {\left(b^{7} c - 5 \, a b^{5} c^{2} + 7 \, a^{2} b^{3} c^{3} - 2 \, a^{3} b c^{4}\right)} d e^{5} + {\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} e^{6}}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}} - 4 \, {\left(a b c^{4} d^{5} - {\left(4 \, a b^{2} c^{3} - 3 \, a^{2} c^{4}\right)} d^{4} e + 2 \, {\left(3 \, a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{3} e^{2} - 2 \, {\left(2 \, a b^{4} c - 3 \, a^{2} b^{2} c^{2} - a^{3} c^{3}\right)} d^{2} e^{3} + {\left(a b^{5} - 5 \, a^{3} b c^{2}\right)} d e^{4} - {\left(a^{2} b^{4} - 3 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{5}\right)} \sqrt{e x + d}\right) - 3 \, \sqrt{2} c^{2} \sqrt{\frac{{\left(b^{2} c^{3} - 2 \, a c^{4}\right)} d^{3} - 3 \, {\left(b^{3} c^{2} - 3 \, a b c^{3}\right)} d^{2} e + 3 \, {\left(b^{4} c - 4 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d e^{2} - {\left(b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}\right)} e^{3} - {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{b^{2} c^{6} d^{6} - 6 \, {\left(b^{3} c^{5} - a b c^{6}\right)} d^{5} e + 3 \, {\left(5 \, b^{4} c^{4} - 10 \, a b^{2} c^{5} + 3 \, a^{2} c^{6}\right)} d^{4} e^{2} - 2 \, {\left(10 \, b^{5} c^{3} - 30 \, a b^{3} c^{4} + 19 \, a^{2} b c^{5}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{6} c^{2} - 20 \, a b^{4} c^{3} + 20 \, a^{2} b^{2} c^{4} - 2 \, a^{3} c^{5}\right)} d^{2} e^{4} - 6 \, {\left(b^{7} c - 5 \, a b^{5} c^{2} + 7 \, a^{2} b^{3} c^{3} - 2 \, a^{3} b c^{4}\right)} d e^{5} + {\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} e^{6}}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}} \log\left(-\sqrt{2} {\left({\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{4} - {\left(4 \, b^{4} c^{3} - 19 \, a b^{2} c^{4} + 12 \, a^{2} c^{5}\right)} d^{3} e + 3 \, {\left(2 \, b^{5} c^{2} - 11 \, a b^{3} c^{3} + 12 \, a^{2} b c^{4}\right)} d^{2} e^{2} - {\left(4 \, b^{6} c - 25 \, a b^{4} c^{2} + 37 \, a^{2} b^{2} c^{3} - 4 \, a^{3} c^{4}\right)} d e^{3} + {\left(b^{7} - 7 \, a b^{5} c + 13 \, a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} e^{4} + {\left({\left(b^{3} c^{6} - 4 \, a b c^{7}\right)} d - {\left(b^{4} c^{5} - 6 \, a b^{2} c^{6} + 8 \, a^{2} c^{7}\right)} e\right)} \sqrt{\frac{b^{2} c^{6} d^{6} - 6 \, {\left(b^{3} c^{5} - a b c^{6}\right)} d^{5} e + 3 \, {\left(5 \, b^{4} c^{4} - 10 \, a b^{2} c^{5} + 3 \, a^{2} c^{6}\right)} d^{4} e^{2} - 2 \, {\left(10 \, b^{5} c^{3} - 30 \, a b^{3} c^{4} + 19 \, a^{2} b c^{5}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{6} c^{2} - 20 \, a b^{4} c^{3} + 20 \, a^{2} b^{2} c^{4} - 2 \, a^{3} c^{5}\right)} d^{2} e^{4} - 6 \, {\left(b^{7} c - 5 \, a b^{5} c^{2} + 7 \, a^{2} b^{3} c^{3} - 2 \, a^{3} b c^{4}\right)} d e^{5} + {\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} e^{6}}{b^{2} c^{10} - 4 \, a c^{11}}}\right)} \sqrt{\frac{{\left(b^{2} c^{3} - 2 \, a c^{4}\right)} d^{3} - 3 \, {\left(b^{3} c^{2} - 3 \, a b c^{3}\right)} d^{2} e + 3 \, {\left(b^{4} c - 4 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d e^{2} - {\left(b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}\right)} e^{3} - {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{b^{2} c^{6} d^{6} - 6 \, {\left(b^{3} c^{5} - a b c^{6}\right)} d^{5} e + 3 \, {\left(5 \, b^{4} c^{4} - 10 \, a b^{2} c^{5} + 3 \, a^{2} c^{6}\right)} d^{4} e^{2} - 2 \, {\left(10 \, b^{5} c^{3} - 30 \, a b^{3} c^{4} + 19 \, a^{2} b c^{5}\right)} d^{3} e^{3} + 3 \, {\left(5 \, b^{6} c^{2} - 20 \, a b^{4} c^{3} + 20 \, a^{2} b^{2} c^{4} - 2 \, a^{3} c^{5}\right)} d^{2} e^{4} - 6 \, {\left(b^{7} c - 5 \, a b^{5} c^{2} + 7 \, a^{2} b^{3} c^{3} - 2 \, a^{3} b c^{4}\right)} d e^{5} + {\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} e^{6}}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}} - 4 \, {\left(a b c^{4} d^{5} - {\left(4 \, a b^{2} c^{3} - 3 \, a^{2} c^{4}\right)} d^{4} e + 2 \, {\left(3 \, a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{3} e^{2} - 2 \, {\left(2 \, a b^{4} c - 3 \, a^{2} b^{2} c^{2} - a^{3} c^{3}\right)} d^{2} e^{3} + {\left(a b^{5} - 5 \, a^{3} b c^{2}\right)} d e^{4} - {\left(a^{2} b^{4} - 3 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{5}\right)} \sqrt{e x + d}\right) - 4 \, {\left(c e x + 4 \, c d - 3 \, b e\right)} \sqrt{e x + d}}{6 \, c^{2}}"," ",0,"-1/6*(3*sqrt(2)*c^2*sqrt(((b^2*c^3 - 2*a*c^4)*d^3 - 3*(b^3*c^2 - 3*a*b*c^3)*d^2*e + 3*(b^4*c - 4*a*b^2*c^2 + 2*a^2*c^3)*d*e^2 - (b^5 - 5*a*b^3*c + 5*a^2*b*c^2)*e^3 + (b^2*c^5 - 4*a*c^6)*sqrt((b^2*c^6*d^6 - 6*(b^3*c^5 - a*b*c^6)*d^5*e + 3*(5*b^4*c^4 - 10*a*b^2*c^5 + 3*a^2*c^6)*d^4*e^2 - 2*(10*b^5*c^3 - 30*a*b^3*c^4 + 19*a^2*b*c^5)*d^3*e^3 + 3*(5*b^6*c^2 - 20*a*b^4*c^3 + 20*a^2*b^2*c^4 - 2*a^3*c^5)*d^2*e^4 - 6*(b^7*c - 5*a*b^5*c^2 + 7*a^2*b^3*c^3 - 2*a^3*b*c^4)*d*e^5 + (b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*e^6)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6))*log(sqrt(2)*((b^3*c^4 - 4*a*b*c^5)*d^4 - (4*b^4*c^3 - 19*a*b^2*c^4 + 12*a^2*c^5)*d^3*e + 3*(2*b^5*c^2 - 11*a*b^3*c^3 + 12*a^2*b*c^4)*d^2*e^2 - (4*b^6*c - 25*a*b^4*c^2 + 37*a^2*b^2*c^3 - 4*a^3*c^4)*d*e^3 + (b^7 - 7*a*b^5*c + 13*a^2*b^3*c^2 - 4*a^3*b*c^3)*e^4 - ((b^3*c^6 - 4*a*b*c^7)*d - (b^4*c^5 - 6*a*b^2*c^6 + 8*a^2*c^7)*e)*sqrt((b^2*c^6*d^6 - 6*(b^3*c^5 - a*b*c^6)*d^5*e + 3*(5*b^4*c^4 - 10*a*b^2*c^5 + 3*a^2*c^6)*d^4*e^2 - 2*(10*b^5*c^3 - 30*a*b^3*c^4 + 19*a^2*b*c^5)*d^3*e^3 + 3*(5*b^6*c^2 - 20*a*b^4*c^3 + 20*a^2*b^2*c^4 - 2*a^3*c^5)*d^2*e^4 - 6*(b^7*c - 5*a*b^5*c^2 + 7*a^2*b^3*c^3 - 2*a^3*b*c^4)*d*e^5 + (b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*e^6)/(b^2*c^10 - 4*a*c^11)))*sqrt(((b^2*c^3 - 2*a*c^4)*d^3 - 3*(b^3*c^2 - 3*a*b*c^3)*d^2*e + 3*(b^4*c - 4*a*b^2*c^2 + 2*a^2*c^3)*d*e^2 - (b^5 - 5*a*b^3*c + 5*a^2*b*c^2)*e^3 + (b^2*c^5 - 4*a*c^6)*sqrt((b^2*c^6*d^6 - 6*(b^3*c^5 - a*b*c^6)*d^5*e + 3*(5*b^4*c^4 - 10*a*b^2*c^5 + 3*a^2*c^6)*d^4*e^2 - 2*(10*b^5*c^3 - 30*a*b^3*c^4 + 19*a^2*b*c^5)*d^3*e^3 + 3*(5*b^6*c^2 - 20*a*b^4*c^3 + 20*a^2*b^2*c^4 - 2*a^3*c^5)*d^2*e^4 - 6*(b^7*c - 5*a*b^5*c^2 + 7*a^2*b^3*c^3 - 2*a^3*b*c^4)*d*e^5 + (b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*e^6)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6)) - 4*(a*b*c^4*d^5 - (4*a*b^2*c^3 - 3*a^2*c^4)*d^4*e + 2*(3*a*b^3*c^2 - 4*a^2*b*c^3)*d^3*e^2 - 2*(2*a*b^4*c - 3*a^2*b^2*c^2 - a^3*c^3)*d^2*e^3 + (a*b^5 - 5*a^3*b*c^2)*d*e^4 - (a^2*b^4 - 3*a^3*b^2*c + a^4*c^2)*e^5)*sqrt(e*x + d)) - 3*sqrt(2)*c^2*sqrt(((b^2*c^3 - 2*a*c^4)*d^3 - 3*(b^3*c^2 - 3*a*b*c^3)*d^2*e + 3*(b^4*c - 4*a*b^2*c^2 + 2*a^2*c^3)*d*e^2 - (b^5 - 5*a*b^3*c + 5*a^2*b*c^2)*e^3 + (b^2*c^5 - 4*a*c^6)*sqrt((b^2*c^6*d^6 - 6*(b^3*c^5 - a*b*c^6)*d^5*e + 3*(5*b^4*c^4 - 10*a*b^2*c^5 + 3*a^2*c^6)*d^4*e^2 - 2*(10*b^5*c^3 - 30*a*b^3*c^4 + 19*a^2*b*c^5)*d^3*e^3 + 3*(5*b^6*c^2 - 20*a*b^4*c^3 + 20*a^2*b^2*c^4 - 2*a^3*c^5)*d^2*e^4 - 6*(b^7*c - 5*a*b^5*c^2 + 7*a^2*b^3*c^3 - 2*a^3*b*c^4)*d*e^5 + (b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*e^6)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6))*log(-sqrt(2)*((b^3*c^4 - 4*a*b*c^5)*d^4 - (4*b^4*c^3 - 19*a*b^2*c^4 + 12*a^2*c^5)*d^3*e + 3*(2*b^5*c^2 - 11*a*b^3*c^3 + 12*a^2*b*c^4)*d^2*e^2 - (4*b^6*c - 25*a*b^4*c^2 + 37*a^2*b^2*c^3 - 4*a^3*c^4)*d*e^3 + (b^7 - 7*a*b^5*c + 13*a^2*b^3*c^2 - 4*a^3*b*c^3)*e^4 - ((b^3*c^6 - 4*a*b*c^7)*d - (b^4*c^5 - 6*a*b^2*c^6 + 8*a^2*c^7)*e)*sqrt((b^2*c^6*d^6 - 6*(b^3*c^5 - a*b*c^6)*d^5*e + 3*(5*b^4*c^4 - 10*a*b^2*c^5 + 3*a^2*c^6)*d^4*e^2 - 2*(10*b^5*c^3 - 30*a*b^3*c^4 + 19*a^2*b*c^5)*d^3*e^3 + 3*(5*b^6*c^2 - 20*a*b^4*c^3 + 20*a^2*b^2*c^4 - 2*a^3*c^5)*d^2*e^4 - 6*(b^7*c - 5*a*b^5*c^2 + 7*a^2*b^3*c^3 - 2*a^3*b*c^4)*d*e^5 + (b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*e^6)/(b^2*c^10 - 4*a*c^11)))*sqrt(((b^2*c^3 - 2*a*c^4)*d^3 - 3*(b^3*c^2 - 3*a*b*c^3)*d^2*e + 3*(b^4*c - 4*a*b^2*c^2 + 2*a^2*c^3)*d*e^2 - (b^5 - 5*a*b^3*c + 5*a^2*b*c^2)*e^3 + (b^2*c^5 - 4*a*c^6)*sqrt((b^2*c^6*d^6 - 6*(b^3*c^5 - a*b*c^6)*d^5*e + 3*(5*b^4*c^4 - 10*a*b^2*c^5 + 3*a^2*c^6)*d^4*e^2 - 2*(10*b^5*c^3 - 30*a*b^3*c^4 + 19*a^2*b*c^5)*d^3*e^3 + 3*(5*b^6*c^2 - 20*a*b^4*c^3 + 20*a^2*b^2*c^4 - 2*a^3*c^5)*d^2*e^4 - 6*(b^7*c - 5*a*b^5*c^2 + 7*a^2*b^3*c^3 - 2*a^3*b*c^4)*d*e^5 + (b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*e^6)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6)) - 4*(a*b*c^4*d^5 - (4*a*b^2*c^3 - 3*a^2*c^4)*d^4*e + 2*(3*a*b^3*c^2 - 4*a^2*b*c^3)*d^3*e^2 - 2*(2*a*b^4*c - 3*a^2*b^2*c^2 - a^3*c^3)*d^2*e^3 + (a*b^5 - 5*a^3*b*c^2)*d*e^4 - (a^2*b^4 - 3*a^3*b^2*c + a^4*c^2)*e^5)*sqrt(e*x + d)) + 3*sqrt(2)*c^2*sqrt(((b^2*c^3 - 2*a*c^4)*d^3 - 3*(b^3*c^2 - 3*a*b*c^3)*d^2*e + 3*(b^4*c - 4*a*b^2*c^2 + 2*a^2*c^3)*d*e^2 - (b^5 - 5*a*b^3*c + 5*a^2*b*c^2)*e^3 - (b^2*c^5 - 4*a*c^6)*sqrt((b^2*c^6*d^6 - 6*(b^3*c^5 - a*b*c^6)*d^5*e + 3*(5*b^4*c^4 - 10*a*b^2*c^5 + 3*a^2*c^6)*d^4*e^2 - 2*(10*b^5*c^3 - 30*a*b^3*c^4 + 19*a^2*b*c^5)*d^3*e^3 + 3*(5*b^6*c^2 - 20*a*b^4*c^3 + 20*a^2*b^2*c^4 - 2*a^3*c^5)*d^2*e^4 - 6*(b^7*c - 5*a*b^5*c^2 + 7*a^2*b^3*c^3 - 2*a^3*b*c^4)*d*e^5 + (b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*e^6)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6))*log(sqrt(2)*((b^3*c^4 - 4*a*b*c^5)*d^4 - (4*b^4*c^3 - 19*a*b^2*c^4 + 12*a^2*c^5)*d^3*e + 3*(2*b^5*c^2 - 11*a*b^3*c^3 + 12*a^2*b*c^4)*d^2*e^2 - (4*b^6*c - 25*a*b^4*c^2 + 37*a^2*b^2*c^3 - 4*a^3*c^4)*d*e^3 + (b^7 - 7*a*b^5*c + 13*a^2*b^3*c^2 - 4*a^3*b*c^3)*e^4 + ((b^3*c^6 - 4*a*b*c^7)*d - (b^4*c^5 - 6*a*b^2*c^6 + 8*a^2*c^7)*e)*sqrt((b^2*c^6*d^6 - 6*(b^3*c^5 - a*b*c^6)*d^5*e + 3*(5*b^4*c^4 - 10*a*b^2*c^5 + 3*a^2*c^6)*d^4*e^2 - 2*(10*b^5*c^3 - 30*a*b^3*c^4 + 19*a^2*b*c^5)*d^3*e^3 + 3*(5*b^6*c^2 - 20*a*b^4*c^3 + 20*a^2*b^2*c^4 - 2*a^3*c^5)*d^2*e^4 - 6*(b^7*c - 5*a*b^5*c^2 + 7*a^2*b^3*c^3 - 2*a^3*b*c^4)*d*e^5 + (b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*e^6)/(b^2*c^10 - 4*a*c^11)))*sqrt(((b^2*c^3 - 2*a*c^4)*d^3 - 3*(b^3*c^2 - 3*a*b*c^3)*d^2*e + 3*(b^4*c - 4*a*b^2*c^2 + 2*a^2*c^3)*d*e^2 - (b^5 - 5*a*b^3*c + 5*a^2*b*c^2)*e^3 - (b^2*c^5 - 4*a*c^6)*sqrt((b^2*c^6*d^6 - 6*(b^3*c^5 - a*b*c^6)*d^5*e + 3*(5*b^4*c^4 - 10*a*b^2*c^5 + 3*a^2*c^6)*d^4*e^2 - 2*(10*b^5*c^3 - 30*a*b^3*c^4 + 19*a^2*b*c^5)*d^3*e^3 + 3*(5*b^6*c^2 - 20*a*b^4*c^3 + 20*a^2*b^2*c^4 - 2*a^3*c^5)*d^2*e^4 - 6*(b^7*c - 5*a*b^5*c^2 + 7*a^2*b^3*c^3 - 2*a^3*b*c^4)*d*e^5 + (b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*e^6)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6)) - 4*(a*b*c^4*d^5 - (4*a*b^2*c^3 - 3*a^2*c^4)*d^4*e + 2*(3*a*b^3*c^2 - 4*a^2*b*c^3)*d^3*e^2 - 2*(2*a*b^4*c - 3*a^2*b^2*c^2 - a^3*c^3)*d^2*e^3 + (a*b^5 - 5*a^3*b*c^2)*d*e^4 - (a^2*b^4 - 3*a^3*b^2*c + a^4*c^2)*e^5)*sqrt(e*x + d)) - 3*sqrt(2)*c^2*sqrt(((b^2*c^3 - 2*a*c^4)*d^3 - 3*(b^3*c^2 - 3*a*b*c^3)*d^2*e + 3*(b^4*c - 4*a*b^2*c^2 + 2*a^2*c^3)*d*e^2 - (b^5 - 5*a*b^3*c + 5*a^2*b*c^2)*e^3 - (b^2*c^5 - 4*a*c^6)*sqrt((b^2*c^6*d^6 - 6*(b^3*c^5 - a*b*c^6)*d^5*e + 3*(5*b^4*c^4 - 10*a*b^2*c^5 + 3*a^2*c^6)*d^4*e^2 - 2*(10*b^5*c^3 - 30*a*b^3*c^4 + 19*a^2*b*c^5)*d^3*e^3 + 3*(5*b^6*c^2 - 20*a*b^4*c^3 + 20*a^2*b^2*c^4 - 2*a^3*c^5)*d^2*e^4 - 6*(b^7*c - 5*a*b^5*c^2 + 7*a^2*b^3*c^3 - 2*a^3*b*c^4)*d*e^5 + (b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*e^6)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6))*log(-sqrt(2)*((b^3*c^4 - 4*a*b*c^5)*d^4 - (4*b^4*c^3 - 19*a*b^2*c^4 + 12*a^2*c^5)*d^3*e + 3*(2*b^5*c^2 - 11*a*b^3*c^3 + 12*a^2*b*c^4)*d^2*e^2 - (4*b^6*c - 25*a*b^4*c^2 + 37*a^2*b^2*c^3 - 4*a^3*c^4)*d*e^3 + (b^7 - 7*a*b^5*c + 13*a^2*b^3*c^2 - 4*a^3*b*c^3)*e^4 + ((b^3*c^6 - 4*a*b*c^7)*d - (b^4*c^5 - 6*a*b^2*c^6 + 8*a^2*c^7)*e)*sqrt((b^2*c^6*d^6 - 6*(b^3*c^5 - a*b*c^6)*d^5*e + 3*(5*b^4*c^4 - 10*a*b^2*c^5 + 3*a^2*c^6)*d^4*e^2 - 2*(10*b^5*c^3 - 30*a*b^3*c^4 + 19*a^2*b*c^5)*d^3*e^3 + 3*(5*b^6*c^2 - 20*a*b^4*c^3 + 20*a^2*b^2*c^4 - 2*a^3*c^5)*d^2*e^4 - 6*(b^7*c - 5*a*b^5*c^2 + 7*a^2*b^3*c^3 - 2*a^3*b*c^4)*d*e^5 + (b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*e^6)/(b^2*c^10 - 4*a*c^11)))*sqrt(((b^2*c^3 - 2*a*c^4)*d^3 - 3*(b^3*c^2 - 3*a*b*c^3)*d^2*e + 3*(b^4*c - 4*a*b^2*c^2 + 2*a^2*c^3)*d*e^2 - (b^5 - 5*a*b^3*c + 5*a^2*b*c^2)*e^3 - (b^2*c^5 - 4*a*c^6)*sqrt((b^2*c^6*d^6 - 6*(b^3*c^5 - a*b*c^6)*d^5*e + 3*(5*b^4*c^4 - 10*a*b^2*c^5 + 3*a^2*c^6)*d^4*e^2 - 2*(10*b^5*c^3 - 30*a*b^3*c^4 + 19*a^2*b*c^5)*d^3*e^3 + 3*(5*b^6*c^2 - 20*a*b^4*c^3 + 20*a^2*b^2*c^4 - 2*a^3*c^5)*d^2*e^4 - 6*(b^7*c - 5*a*b^5*c^2 + 7*a^2*b^3*c^3 - 2*a^3*b*c^4)*d*e^5 + (b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*e^6)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6)) - 4*(a*b*c^4*d^5 - (4*a*b^2*c^3 - 3*a^2*c^4)*d^4*e + 2*(3*a*b^3*c^2 - 4*a^2*b*c^3)*d^3*e^2 - 2*(2*a*b^4*c - 3*a^2*b^2*c^2 - a^3*c^3)*d^2*e^3 + (a*b^5 - 5*a^3*b*c^2)*d*e^4 - (a^2*b^4 - 3*a^3*b^2*c + a^4*c^2)*e^5)*sqrt(e*x + d)) - 4*(c*e*x + 4*c*d - 3*b*e)*sqrt(e*x + d))/c^2","B",0
537,1,2770,0,0.543073," ","integrate((e*x+d)^(3/2)/(c*x^2+b*x+a),x, algorithm=""fricas"")","-\frac{\sqrt{2} c \sqrt{\frac{2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{2} - {\left(b^{3} - 3 \, a b c\right)} e^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{2} - 18 \, b c^{3} d^{3} e^{3} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{4} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{5} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{6}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} \log\left(\sqrt{2} {\left(3 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} e^{2} - 3 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d e^{3} + {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} e^{4} - {\left(2 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d - {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} e\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{2} - 18 \, b c^{3} d^{3} e^{3} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{4} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{5} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{6}}{b^{2} c^{6} - 4 \, a c^{7}}}\right)} \sqrt{\frac{2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{2} - {\left(b^{3} - 3 \, a b c\right)} e^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{2} - 18 \, b c^{3} d^{3} e^{3} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{4} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{5} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{6}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} - 4 \, {\left(3 \, c^{3} d^{4} e - 6 \, b c^{2} d^{3} e^{2} + 2 \, {\left(2 \, b^{2} c + a c^{2}\right)} d^{2} e^{3} - {\left(b^{3} + 2 \, a b c\right)} d e^{4} + {\left(a b^{2} - a^{2} c\right)} e^{5}\right)} \sqrt{e x + d}\right) - \sqrt{2} c \sqrt{\frac{2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{2} - {\left(b^{3} - 3 \, a b c\right)} e^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{2} - 18 \, b c^{3} d^{3} e^{3} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{4} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{5} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{6}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} \log\left(-\sqrt{2} {\left(3 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} e^{2} - 3 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d e^{3} + {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} e^{4} - {\left(2 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d - {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} e\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{2} - 18 \, b c^{3} d^{3} e^{3} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{4} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{5} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{6}}{b^{2} c^{6} - 4 \, a c^{7}}}\right)} \sqrt{\frac{2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{2} - {\left(b^{3} - 3 \, a b c\right)} e^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{2} - 18 \, b c^{3} d^{3} e^{3} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{4} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{5} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{6}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} - 4 \, {\left(3 \, c^{3} d^{4} e - 6 \, b c^{2} d^{3} e^{2} + 2 \, {\left(2 \, b^{2} c + a c^{2}\right)} d^{2} e^{3} - {\left(b^{3} + 2 \, a b c\right)} d e^{4} + {\left(a b^{2} - a^{2} c\right)} e^{5}\right)} \sqrt{e x + d}\right) + \sqrt{2} c \sqrt{\frac{2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{2} - {\left(b^{3} - 3 \, a b c\right)} e^{3} - {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{2} - 18 \, b c^{3} d^{3} e^{3} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{4} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{5} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{6}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} \log\left(\sqrt{2} {\left(3 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} e^{2} - 3 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d e^{3} + {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} e^{4} + {\left(2 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d - {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} e\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{2} - 18 \, b c^{3} d^{3} e^{3} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{4} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{5} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{6}}{b^{2} c^{6} - 4 \, a c^{7}}}\right)} \sqrt{\frac{2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{2} - {\left(b^{3} - 3 \, a b c\right)} e^{3} - {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{2} - 18 \, b c^{3} d^{3} e^{3} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{4} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{5} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{6}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} - 4 \, {\left(3 \, c^{3} d^{4} e - 6 \, b c^{2} d^{3} e^{2} + 2 \, {\left(2 \, b^{2} c + a c^{2}\right)} d^{2} e^{3} - {\left(b^{3} + 2 \, a b c\right)} d e^{4} + {\left(a b^{2} - a^{2} c\right)} e^{5}\right)} \sqrt{e x + d}\right) - \sqrt{2} c \sqrt{\frac{2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{2} - {\left(b^{3} - 3 \, a b c\right)} e^{3} - {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{2} - 18 \, b c^{3} d^{3} e^{3} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{4} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{5} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{6}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} \log\left(-\sqrt{2} {\left(3 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} e^{2} - 3 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d e^{3} + {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} e^{4} + {\left(2 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d - {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} e\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{2} - 18 \, b c^{3} d^{3} e^{3} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{4} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{5} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{6}}{b^{2} c^{6} - 4 \, a c^{7}}}\right)} \sqrt{\frac{2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{2} - {\left(b^{3} - 3 \, a b c\right)} e^{3} - {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{2} - 18 \, b c^{3} d^{3} e^{3} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{4} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{5} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{6}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} - 4 \, {\left(3 \, c^{3} d^{4} e - 6 \, b c^{2} d^{3} e^{2} + 2 \, {\left(2 \, b^{2} c + a c^{2}\right)} d^{2} e^{3} - {\left(b^{3} + 2 \, a b c\right)} d e^{4} + {\left(a b^{2} - a^{2} c\right)} e^{5}\right)} \sqrt{e x + d}\right) - 4 \, \sqrt{e x + d} e}{2 \, c}"," ",0,"-1/2*(sqrt(2)*c*sqrt((2*c^3*d^3 - 3*b*c^2*d^2*e + 3*(b^2*c - 2*a*c^2)*d*e^2 - (b^3 - 3*a*b*c)*e^3 + (b^2*c^3 - 4*a*c^4)*sqrt((9*c^4*d^4*e^2 - 18*b*c^3*d^3*e^3 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^4 - 6*(b^3*c - a*b*c^2)*d*e^5 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^6)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))*log(sqrt(2)*(3*(b^2*c^2 - 4*a*c^3)*d^2*e^2 - 3*(b^3*c - 4*a*b*c^2)*d*e^3 + (b^4 - 5*a*b^2*c + 4*a^2*c^2)*e^4 - (2*(b^2*c^4 - 4*a*c^5)*d - (b^3*c^3 - 4*a*b*c^4)*e)*sqrt((9*c^4*d^4*e^2 - 18*b*c^3*d^3*e^3 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^4 - 6*(b^3*c - a*b*c^2)*d*e^5 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^6)/(b^2*c^6 - 4*a*c^7)))*sqrt((2*c^3*d^3 - 3*b*c^2*d^2*e + 3*(b^2*c - 2*a*c^2)*d*e^2 - (b^3 - 3*a*b*c)*e^3 + (b^2*c^3 - 4*a*c^4)*sqrt((9*c^4*d^4*e^2 - 18*b*c^3*d^3*e^3 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^4 - 6*(b^3*c - a*b*c^2)*d*e^5 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^6)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4)) - 4*(3*c^3*d^4*e - 6*b*c^2*d^3*e^2 + 2*(2*b^2*c + a*c^2)*d^2*e^3 - (b^3 + 2*a*b*c)*d*e^4 + (a*b^2 - a^2*c)*e^5)*sqrt(e*x + d)) - sqrt(2)*c*sqrt((2*c^3*d^3 - 3*b*c^2*d^2*e + 3*(b^2*c - 2*a*c^2)*d*e^2 - (b^3 - 3*a*b*c)*e^3 + (b^2*c^3 - 4*a*c^4)*sqrt((9*c^4*d^4*e^2 - 18*b*c^3*d^3*e^3 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^4 - 6*(b^3*c - a*b*c^2)*d*e^5 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^6)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))*log(-sqrt(2)*(3*(b^2*c^2 - 4*a*c^3)*d^2*e^2 - 3*(b^3*c - 4*a*b*c^2)*d*e^3 + (b^4 - 5*a*b^2*c + 4*a^2*c^2)*e^4 - (2*(b^2*c^4 - 4*a*c^5)*d - (b^3*c^3 - 4*a*b*c^4)*e)*sqrt((9*c^4*d^4*e^2 - 18*b*c^3*d^3*e^3 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^4 - 6*(b^3*c - a*b*c^2)*d*e^5 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^6)/(b^2*c^6 - 4*a*c^7)))*sqrt((2*c^3*d^3 - 3*b*c^2*d^2*e + 3*(b^2*c - 2*a*c^2)*d*e^2 - (b^3 - 3*a*b*c)*e^3 + (b^2*c^3 - 4*a*c^4)*sqrt((9*c^4*d^4*e^2 - 18*b*c^3*d^3*e^3 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^4 - 6*(b^3*c - a*b*c^2)*d*e^5 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^6)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4)) - 4*(3*c^3*d^4*e - 6*b*c^2*d^3*e^2 + 2*(2*b^2*c + a*c^2)*d^2*e^3 - (b^3 + 2*a*b*c)*d*e^4 + (a*b^2 - a^2*c)*e^5)*sqrt(e*x + d)) + sqrt(2)*c*sqrt((2*c^3*d^3 - 3*b*c^2*d^2*e + 3*(b^2*c - 2*a*c^2)*d*e^2 - (b^3 - 3*a*b*c)*e^3 - (b^2*c^3 - 4*a*c^4)*sqrt((9*c^4*d^4*e^2 - 18*b*c^3*d^3*e^3 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^4 - 6*(b^3*c - a*b*c^2)*d*e^5 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^6)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))*log(sqrt(2)*(3*(b^2*c^2 - 4*a*c^3)*d^2*e^2 - 3*(b^3*c - 4*a*b*c^2)*d*e^3 + (b^4 - 5*a*b^2*c + 4*a^2*c^2)*e^4 + (2*(b^2*c^4 - 4*a*c^5)*d - (b^3*c^3 - 4*a*b*c^4)*e)*sqrt((9*c^4*d^4*e^2 - 18*b*c^3*d^3*e^3 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^4 - 6*(b^3*c - a*b*c^2)*d*e^5 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^6)/(b^2*c^6 - 4*a*c^7)))*sqrt((2*c^3*d^3 - 3*b*c^2*d^2*e + 3*(b^2*c - 2*a*c^2)*d*e^2 - (b^3 - 3*a*b*c)*e^3 - (b^2*c^3 - 4*a*c^4)*sqrt((9*c^4*d^4*e^2 - 18*b*c^3*d^3*e^3 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^4 - 6*(b^3*c - a*b*c^2)*d*e^5 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^6)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4)) - 4*(3*c^3*d^4*e - 6*b*c^2*d^3*e^2 + 2*(2*b^2*c + a*c^2)*d^2*e^3 - (b^3 + 2*a*b*c)*d*e^4 + (a*b^2 - a^2*c)*e^5)*sqrt(e*x + d)) - sqrt(2)*c*sqrt((2*c^3*d^3 - 3*b*c^2*d^2*e + 3*(b^2*c - 2*a*c^2)*d*e^2 - (b^3 - 3*a*b*c)*e^3 - (b^2*c^3 - 4*a*c^4)*sqrt((9*c^4*d^4*e^2 - 18*b*c^3*d^3*e^3 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^4 - 6*(b^3*c - a*b*c^2)*d*e^5 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^6)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))*log(-sqrt(2)*(3*(b^2*c^2 - 4*a*c^3)*d^2*e^2 - 3*(b^3*c - 4*a*b*c^2)*d*e^3 + (b^4 - 5*a*b^2*c + 4*a^2*c^2)*e^4 + (2*(b^2*c^4 - 4*a*c^5)*d - (b^3*c^3 - 4*a*b*c^4)*e)*sqrt((9*c^4*d^4*e^2 - 18*b*c^3*d^3*e^3 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^4 - 6*(b^3*c - a*b*c^2)*d*e^5 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^6)/(b^2*c^6 - 4*a*c^7)))*sqrt((2*c^3*d^3 - 3*b*c^2*d^2*e + 3*(b^2*c - 2*a*c^2)*d*e^2 - (b^3 - 3*a*b*c)*e^3 - (b^2*c^3 - 4*a*c^4)*sqrt((9*c^4*d^4*e^2 - 18*b*c^3*d^3*e^3 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^4 - 6*(b^3*c - a*b*c^2)*d*e^5 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^6)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4)) - 4*(3*c^3*d^4*e - 6*b*c^2*d^3*e^2 + 2*(2*b^2*c + a*c^2)*d^2*e^3 - (b^3 + 2*a*b*c)*d*e^4 + (a*b^2 - a^2*c)*e^5)*sqrt(e*x + d)) - 4*sqrt(e*x + d)*e)/c","B",0
538,1,5167,0,7.611387," ","integrate((e*x+d)^(3/2)/x/(c*x^2+b*x+a),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} a \sqrt{-\frac{3 \, a b c d^{2} e - 6 \, a^{2} c d e^{2} + a^{2} b e^{3} - {\left(b^{2} c - 2 \, a c^{2}\right)} d^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} \sqrt{\frac{b^{2} c^{2} d^{6} - 6 \, a b c^{2} d^{5} e + 9 \, a^{2} c^{2} d^{4} e^{2} + 2 \, a^{2} b c d^{3} e^{3} - 6 \, a^{3} c d^{2} e^{4} + a^{4} e^{6}}{a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}}}}{a^{2} b^{2} c - 4 \, a^{3} c^{2}}} \log\left(\sqrt{2} {\left({\left(b^{3} c - 4 \, a b c^{2}\right)} d^{4} - 3 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{3} e + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d e^{3} + {\left({\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d - 2 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} e\right)} \sqrt{\frac{b^{2} c^{2} d^{6} - 6 \, a b c^{2} d^{5} e + 9 \, a^{2} c^{2} d^{4} e^{2} + 2 \, a^{2} b c d^{3} e^{3} - 6 \, a^{3} c d^{2} e^{4} + a^{4} e^{6}}{a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}}}\right)} \sqrt{-\frac{3 \, a b c d^{2} e - 6 \, a^{2} c d e^{2} + a^{2} b e^{3} - {\left(b^{2} c - 2 \, a c^{2}\right)} d^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} \sqrt{\frac{b^{2} c^{2} d^{6} - 6 \, a b c^{2} d^{5} e + 9 \, a^{2} c^{2} d^{4} e^{2} + 2 \, a^{2} b c d^{3} e^{3} - 6 \, a^{3} c d^{2} e^{4} + a^{4} e^{6}}{a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}}}}{a^{2} b^{2} c - 4 \, a^{3} c^{2}}} + 4 \, {\left(b c^{2} d^{5} + 4 \, a b c d^{3} e^{2} - 2 \, a^{2} c d^{2} e^{3} - a^{2} b d e^{4} + a^{3} e^{5} - {\left(b^{2} c + 3 \, a c^{2}\right)} d^{4} e\right)} \sqrt{e x + d}\right) - \sqrt{2} a \sqrt{-\frac{3 \, a b c d^{2} e - 6 \, a^{2} c d e^{2} + a^{2} b e^{3} - {\left(b^{2} c - 2 \, a c^{2}\right)} d^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} \sqrt{\frac{b^{2} c^{2} d^{6} - 6 \, a b c^{2} d^{5} e + 9 \, a^{2} c^{2} d^{4} e^{2} + 2 \, a^{2} b c d^{3} e^{3} - 6 \, a^{3} c d^{2} e^{4} + a^{4} e^{6}}{a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}}}}{a^{2} b^{2} c - 4 \, a^{3} c^{2}}} \log\left(-\sqrt{2} {\left({\left(b^{3} c - 4 \, a b c^{2}\right)} d^{4} - 3 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{3} e + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d e^{3} + {\left({\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d - 2 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} e\right)} \sqrt{\frac{b^{2} c^{2} d^{6} - 6 \, a b c^{2} d^{5} e + 9 \, a^{2} c^{2} d^{4} e^{2} + 2 \, a^{2} b c d^{3} e^{3} - 6 \, a^{3} c d^{2} e^{4} + a^{4} e^{6}}{a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}}}\right)} \sqrt{-\frac{3 \, a b c d^{2} e - 6 \, a^{2} c d e^{2} + a^{2} b e^{3} - {\left(b^{2} c - 2 \, a c^{2}\right)} d^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} \sqrt{\frac{b^{2} c^{2} d^{6} - 6 \, a b c^{2} d^{5} e + 9 \, a^{2} c^{2} d^{4} e^{2} + 2 \, a^{2} b c d^{3} e^{3} - 6 \, a^{3} c d^{2} e^{4} + a^{4} e^{6}}{a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}}}}{a^{2} b^{2} c - 4 \, a^{3} c^{2}}} + 4 \, {\left(b c^{2} d^{5} + 4 \, a b c d^{3} e^{2} - 2 \, a^{2} c d^{2} e^{3} - a^{2} b d e^{4} + a^{3} e^{5} - {\left(b^{2} c + 3 \, a c^{2}\right)} d^{4} e\right)} \sqrt{e x + d}\right) + \sqrt{2} a \sqrt{-\frac{3 \, a b c d^{2} e - 6 \, a^{2} c d e^{2} + a^{2} b e^{3} - {\left(b^{2} c - 2 \, a c^{2}\right)} d^{3} - {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} \sqrt{\frac{b^{2} c^{2} d^{6} - 6 \, a b c^{2} d^{5} e + 9 \, a^{2} c^{2} d^{4} e^{2} + 2 \, a^{2} b c d^{3} e^{3} - 6 \, a^{3} c d^{2} e^{4} + a^{4} e^{6}}{a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}}}}{a^{2} b^{2} c - 4 \, a^{3} c^{2}}} \log\left(\sqrt{2} {\left({\left(b^{3} c - 4 \, a b c^{2}\right)} d^{4} - 3 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{3} e + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d e^{3} - {\left({\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d - 2 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} e\right)} \sqrt{\frac{b^{2} c^{2} d^{6} - 6 \, a b c^{2} d^{5} e + 9 \, a^{2} c^{2} d^{4} e^{2} + 2 \, a^{2} b c d^{3} e^{3} - 6 \, a^{3} c d^{2} e^{4} + a^{4} e^{6}}{a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}}}\right)} \sqrt{-\frac{3 \, a b c d^{2} e - 6 \, a^{2} c d e^{2} + a^{2} b e^{3} - {\left(b^{2} c - 2 \, a c^{2}\right)} d^{3} - {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} \sqrt{\frac{b^{2} c^{2} d^{6} - 6 \, a b c^{2} d^{5} e + 9 \, a^{2} c^{2} d^{4} e^{2} + 2 \, a^{2} b c d^{3} e^{3} - 6 \, a^{3} c d^{2} e^{4} + a^{4} e^{6}}{a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}}}}{a^{2} b^{2} c - 4 \, a^{3} c^{2}}} + 4 \, {\left(b c^{2} d^{5} + 4 \, a b c d^{3} e^{2} - 2 \, a^{2} c d^{2} e^{3} - a^{2} b d e^{4} + a^{3} e^{5} - {\left(b^{2} c + 3 \, a c^{2}\right)} d^{4} e\right)} \sqrt{e x + d}\right) - \sqrt{2} a \sqrt{-\frac{3 \, a b c d^{2} e - 6 \, a^{2} c d e^{2} + a^{2} b e^{3} - {\left(b^{2} c - 2 \, a c^{2}\right)} d^{3} - {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} \sqrt{\frac{b^{2} c^{2} d^{6} - 6 \, a b c^{2} d^{5} e + 9 \, a^{2} c^{2} d^{4} e^{2} + 2 \, a^{2} b c d^{3} e^{3} - 6 \, a^{3} c d^{2} e^{4} + a^{4} e^{6}}{a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}}}}{a^{2} b^{2} c - 4 \, a^{3} c^{2}}} \log\left(-\sqrt{2} {\left({\left(b^{3} c - 4 \, a b c^{2}\right)} d^{4} - 3 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{3} e + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d e^{3} - {\left({\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d - 2 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} e\right)} \sqrt{\frac{b^{2} c^{2} d^{6} - 6 \, a b c^{2} d^{5} e + 9 \, a^{2} c^{2} d^{4} e^{2} + 2 \, a^{2} b c d^{3} e^{3} - 6 \, a^{3} c d^{2} e^{4} + a^{4} e^{6}}{a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}}}\right)} \sqrt{-\frac{3 \, a b c d^{2} e - 6 \, a^{2} c d e^{2} + a^{2} b e^{3} - {\left(b^{2} c - 2 \, a c^{2}\right)} d^{3} - {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} \sqrt{\frac{b^{2} c^{2} d^{6} - 6 \, a b c^{2} d^{5} e + 9 \, a^{2} c^{2} d^{4} e^{2} + 2 \, a^{2} b c d^{3} e^{3} - 6 \, a^{3} c d^{2} e^{4} + a^{4} e^{6}}{a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}}}}{a^{2} b^{2} c - 4 \, a^{3} c^{2}}} + 4 \, {\left(b c^{2} d^{5} + 4 \, a b c d^{3} e^{2} - 2 \, a^{2} c d^{2} e^{3} - a^{2} b d e^{4} + a^{3} e^{5} - {\left(b^{2} c + 3 \, a c^{2}\right)} d^{4} e\right)} \sqrt{e x + d}\right) - 2 \, d^{\frac{3}{2}} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right)}{2 \, a}, -\frac{\sqrt{2} a \sqrt{-\frac{3 \, a b c d^{2} e - 6 \, a^{2} c d e^{2} + a^{2} b e^{3} - {\left(b^{2} c - 2 \, a c^{2}\right)} d^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} \sqrt{\frac{b^{2} c^{2} d^{6} - 6 \, a b c^{2} d^{5} e + 9 \, a^{2} c^{2} d^{4} e^{2} + 2 \, a^{2} b c d^{3} e^{3} - 6 \, a^{3} c d^{2} e^{4} + a^{4} e^{6}}{a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}}}}{a^{2} b^{2} c - 4 \, a^{3} c^{2}}} \log\left(\sqrt{2} {\left({\left(b^{3} c - 4 \, a b c^{2}\right)} d^{4} - 3 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{3} e + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d e^{3} + {\left({\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d - 2 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} e\right)} \sqrt{\frac{b^{2} c^{2} d^{6} - 6 \, a b c^{2} d^{5} e + 9 \, a^{2} c^{2} d^{4} e^{2} + 2 \, a^{2} b c d^{3} e^{3} - 6 \, a^{3} c d^{2} e^{4} + a^{4} e^{6}}{a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}}}\right)} \sqrt{-\frac{3 \, a b c d^{2} e - 6 \, a^{2} c d e^{2} + a^{2} b e^{3} - {\left(b^{2} c - 2 \, a c^{2}\right)} d^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} \sqrt{\frac{b^{2} c^{2} d^{6} - 6 \, a b c^{2} d^{5} e + 9 \, a^{2} c^{2} d^{4} e^{2} + 2 \, a^{2} b c d^{3} e^{3} - 6 \, a^{3} c d^{2} e^{4} + a^{4} e^{6}}{a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}}}}{a^{2} b^{2} c - 4 \, a^{3} c^{2}}} + 4 \, {\left(b c^{2} d^{5} + 4 \, a b c d^{3} e^{2} - 2 \, a^{2} c d^{2} e^{3} - a^{2} b d e^{4} + a^{3} e^{5} - {\left(b^{2} c + 3 \, a c^{2}\right)} d^{4} e\right)} \sqrt{e x + d}\right) - \sqrt{2} a \sqrt{-\frac{3 \, a b c d^{2} e - 6 \, a^{2} c d e^{2} + a^{2} b e^{3} - {\left(b^{2} c - 2 \, a c^{2}\right)} d^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} \sqrt{\frac{b^{2} c^{2} d^{6} - 6 \, a b c^{2} d^{5} e + 9 \, a^{2} c^{2} d^{4} e^{2} + 2 \, a^{2} b c d^{3} e^{3} - 6 \, a^{3} c d^{2} e^{4} + a^{4} e^{6}}{a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}}}}{a^{2} b^{2} c - 4 \, a^{3} c^{2}}} \log\left(-\sqrt{2} {\left({\left(b^{3} c - 4 \, a b c^{2}\right)} d^{4} - 3 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{3} e + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d e^{3} + {\left({\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d - 2 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} e\right)} \sqrt{\frac{b^{2} c^{2} d^{6} - 6 \, a b c^{2} d^{5} e + 9 \, a^{2} c^{2} d^{4} e^{2} + 2 \, a^{2} b c d^{3} e^{3} - 6 \, a^{3} c d^{2} e^{4} + a^{4} e^{6}}{a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}}}\right)} \sqrt{-\frac{3 \, a b c d^{2} e - 6 \, a^{2} c d e^{2} + a^{2} b e^{3} - {\left(b^{2} c - 2 \, a c^{2}\right)} d^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} \sqrt{\frac{b^{2} c^{2} d^{6} - 6 \, a b c^{2} d^{5} e + 9 \, a^{2} c^{2} d^{4} e^{2} + 2 \, a^{2} b c d^{3} e^{3} - 6 \, a^{3} c d^{2} e^{4} + a^{4} e^{6}}{a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}}}}{a^{2} b^{2} c - 4 \, a^{3} c^{2}}} + 4 \, {\left(b c^{2} d^{5} + 4 \, a b c d^{3} e^{2} - 2 \, a^{2} c d^{2} e^{3} - a^{2} b d e^{4} + a^{3} e^{5} - {\left(b^{2} c + 3 \, a c^{2}\right)} d^{4} e\right)} \sqrt{e x + d}\right) + \sqrt{2} a \sqrt{-\frac{3 \, a b c d^{2} e - 6 \, a^{2} c d e^{2} + a^{2} b e^{3} - {\left(b^{2} c - 2 \, a c^{2}\right)} d^{3} - {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} \sqrt{\frac{b^{2} c^{2} d^{6} - 6 \, a b c^{2} d^{5} e + 9 \, a^{2} c^{2} d^{4} e^{2} + 2 \, a^{2} b c d^{3} e^{3} - 6 \, a^{3} c d^{2} e^{4} + a^{4} e^{6}}{a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}}}}{a^{2} b^{2} c - 4 \, a^{3} c^{2}}} \log\left(\sqrt{2} {\left({\left(b^{3} c - 4 \, a b c^{2}\right)} d^{4} - 3 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{3} e + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d e^{3} - {\left({\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d - 2 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} e\right)} \sqrt{\frac{b^{2} c^{2} d^{6} - 6 \, a b c^{2} d^{5} e + 9 \, a^{2} c^{2} d^{4} e^{2} + 2 \, a^{2} b c d^{3} e^{3} - 6 \, a^{3} c d^{2} e^{4} + a^{4} e^{6}}{a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}}}\right)} \sqrt{-\frac{3 \, a b c d^{2} e - 6 \, a^{2} c d e^{2} + a^{2} b e^{3} - {\left(b^{2} c - 2 \, a c^{2}\right)} d^{3} - {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} \sqrt{\frac{b^{2} c^{2} d^{6} - 6 \, a b c^{2} d^{5} e + 9 \, a^{2} c^{2} d^{4} e^{2} + 2 \, a^{2} b c d^{3} e^{3} - 6 \, a^{3} c d^{2} e^{4} + a^{4} e^{6}}{a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}}}}{a^{2} b^{2} c - 4 \, a^{3} c^{2}}} + 4 \, {\left(b c^{2} d^{5} + 4 \, a b c d^{3} e^{2} - 2 \, a^{2} c d^{2} e^{3} - a^{2} b d e^{4} + a^{3} e^{5} - {\left(b^{2} c + 3 \, a c^{2}\right)} d^{4} e\right)} \sqrt{e x + d}\right) - \sqrt{2} a \sqrt{-\frac{3 \, a b c d^{2} e - 6 \, a^{2} c d e^{2} + a^{2} b e^{3} - {\left(b^{2} c - 2 \, a c^{2}\right)} d^{3} - {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} \sqrt{\frac{b^{2} c^{2} d^{6} - 6 \, a b c^{2} d^{5} e + 9 \, a^{2} c^{2} d^{4} e^{2} + 2 \, a^{2} b c d^{3} e^{3} - 6 \, a^{3} c d^{2} e^{4} + a^{4} e^{6}}{a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}}}}{a^{2} b^{2} c - 4 \, a^{3} c^{2}}} \log\left(-\sqrt{2} {\left({\left(b^{3} c - 4 \, a b c^{2}\right)} d^{4} - 3 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{3} e + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d e^{3} - {\left({\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d - 2 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} e\right)} \sqrt{\frac{b^{2} c^{2} d^{6} - 6 \, a b c^{2} d^{5} e + 9 \, a^{2} c^{2} d^{4} e^{2} + 2 \, a^{2} b c d^{3} e^{3} - 6 \, a^{3} c d^{2} e^{4} + a^{4} e^{6}}{a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}}}\right)} \sqrt{-\frac{3 \, a b c d^{2} e - 6 \, a^{2} c d e^{2} + a^{2} b e^{3} - {\left(b^{2} c - 2 \, a c^{2}\right)} d^{3} - {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} \sqrt{\frac{b^{2} c^{2} d^{6} - 6 \, a b c^{2} d^{5} e + 9 \, a^{2} c^{2} d^{4} e^{2} + 2 \, a^{2} b c d^{3} e^{3} - 6 \, a^{3} c d^{2} e^{4} + a^{4} e^{6}}{a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}}}}{a^{2} b^{2} c - 4 \, a^{3} c^{2}}} + 4 \, {\left(b c^{2} d^{5} + 4 \, a b c d^{3} e^{2} - 2 \, a^{2} c d^{2} e^{3} - a^{2} b d e^{4} + a^{3} e^{5} - {\left(b^{2} c + 3 \, a c^{2}\right)} d^{4} e\right)} \sqrt{e x + d}\right) - 4 \, \sqrt{-d} d \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right)}{2 \, a}\right]"," ",0,"[-1/2*(sqrt(2)*a*sqrt(-(3*a*b*c*d^2*e - 6*a^2*c*d*e^2 + a^2*b*e^3 - (b^2*c - 2*a*c^2)*d^3 + (a^2*b^2*c - 4*a^3*c^2)*sqrt((b^2*c^2*d^6 - 6*a*b*c^2*d^5*e + 9*a^2*c^2*d^4*e^2 + 2*a^2*b*c*d^3*e^3 - 6*a^3*c*d^2*e^4 + a^4*e^6)/(a^4*b^2*c^2 - 4*a^5*c^3)))/(a^2*b^2*c - 4*a^3*c^2))*log(sqrt(2)*((b^3*c - 4*a*b*c^2)*d^4 - 3*(a*b^2*c - 4*a^2*c^2)*d^3*e + (a^2*b^2 - 4*a^3*c)*d*e^3 + ((a^2*b^3*c - 4*a^3*b*c^2)*d - 2*(a^3*b^2*c - 4*a^4*c^2)*e)*sqrt((b^2*c^2*d^6 - 6*a*b*c^2*d^5*e + 9*a^2*c^2*d^4*e^2 + 2*a^2*b*c*d^3*e^3 - 6*a^3*c*d^2*e^4 + a^4*e^6)/(a^4*b^2*c^2 - 4*a^5*c^3)))*sqrt(-(3*a*b*c*d^2*e - 6*a^2*c*d*e^2 + a^2*b*e^3 - (b^2*c - 2*a*c^2)*d^3 + (a^2*b^2*c - 4*a^3*c^2)*sqrt((b^2*c^2*d^6 - 6*a*b*c^2*d^5*e + 9*a^2*c^2*d^4*e^2 + 2*a^2*b*c*d^3*e^3 - 6*a^3*c*d^2*e^4 + a^4*e^6)/(a^4*b^2*c^2 - 4*a^5*c^3)))/(a^2*b^2*c - 4*a^3*c^2)) + 4*(b*c^2*d^5 + 4*a*b*c*d^3*e^2 - 2*a^2*c*d^2*e^3 - a^2*b*d*e^4 + a^3*e^5 - (b^2*c + 3*a*c^2)*d^4*e)*sqrt(e*x + d)) - sqrt(2)*a*sqrt(-(3*a*b*c*d^2*e - 6*a^2*c*d*e^2 + a^2*b*e^3 - (b^2*c - 2*a*c^2)*d^3 + (a^2*b^2*c - 4*a^3*c^2)*sqrt((b^2*c^2*d^6 - 6*a*b*c^2*d^5*e + 9*a^2*c^2*d^4*e^2 + 2*a^2*b*c*d^3*e^3 - 6*a^3*c*d^2*e^4 + a^4*e^6)/(a^4*b^2*c^2 - 4*a^5*c^3)))/(a^2*b^2*c - 4*a^3*c^2))*log(-sqrt(2)*((b^3*c - 4*a*b*c^2)*d^4 - 3*(a*b^2*c - 4*a^2*c^2)*d^3*e + (a^2*b^2 - 4*a^3*c)*d*e^3 + ((a^2*b^3*c - 4*a^3*b*c^2)*d - 2*(a^3*b^2*c - 4*a^4*c^2)*e)*sqrt((b^2*c^2*d^6 - 6*a*b*c^2*d^5*e + 9*a^2*c^2*d^4*e^2 + 2*a^2*b*c*d^3*e^3 - 6*a^3*c*d^2*e^4 + a^4*e^6)/(a^4*b^2*c^2 - 4*a^5*c^3)))*sqrt(-(3*a*b*c*d^2*e - 6*a^2*c*d*e^2 + a^2*b*e^3 - (b^2*c - 2*a*c^2)*d^3 + (a^2*b^2*c - 4*a^3*c^2)*sqrt((b^2*c^2*d^6 - 6*a*b*c^2*d^5*e + 9*a^2*c^2*d^4*e^2 + 2*a^2*b*c*d^3*e^3 - 6*a^3*c*d^2*e^4 + a^4*e^6)/(a^4*b^2*c^2 - 4*a^5*c^3)))/(a^2*b^2*c - 4*a^3*c^2)) + 4*(b*c^2*d^5 + 4*a*b*c*d^3*e^2 - 2*a^2*c*d^2*e^3 - a^2*b*d*e^4 + a^3*e^5 - (b^2*c + 3*a*c^2)*d^4*e)*sqrt(e*x + d)) + sqrt(2)*a*sqrt(-(3*a*b*c*d^2*e - 6*a^2*c*d*e^2 + a^2*b*e^3 - (b^2*c - 2*a*c^2)*d^3 - (a^2*b^2*c - 4*a^3*c^2)*sqrt((b^2*c^2*d^6 - 6*a*b*c^2*d^5*e + 9*a^2*c^2*d^4*e^2 + 2*a^2*b*c*d^3*e^3 - 6*a^3*c*d^2*e^4 + a^4*e^6)/(a^4*b^2*c^2 - 4*a^5*c^3)))/(a^2*b^2*c - 4*a^3*c^2))*log(sqrt(2)*((b^3*c - 4*a*b*c^2)*d^4 - 3*(a*b^2*c - 4*a^2*c^2)*d^3*e + (a^2*b^2 - 4*a^3*c)*d*e^3 - ((a^2*b^3*c - 4*a^3*b*c^2)*d - 2*(a^3*b^2*c - 4*a^4*c^2)*e)*sqrt((b^2*c^2*d^6 - 6*a*b*c^2*d^5*e + 9*a^2*c^2*d^4*e^2 + 2*a^2*b*c*d^3*e^3 - 6*a^3*c*d^2*e^4 + a^4*e^6)/(a^4*b^2*c^2 - 4*a^5*c^3)))*sqrt(-(3*a*b*c*d^2*e - 6*a^2*c*d*e^2 + a^2*b*e^3 - (b^2*c - 2*a*c^2)*d^3 - (a^2*b^2*c - 4*a^3*c^2)*sqrt((b^2*c^2*d^6 - 6*a*b*c^2*d^5*e + 9*a^2*c^2*d^4*e^2 + 2*a^2*b*c*d^3*e^3 - 6*a^3*c*d^2*e^4 + a^4*e^6)/(a^4*b^2*c^2 - 4*a^5*c^3)))/(a^2*b^2*c - 4*a^3*c^2)) + 4*(b*c^2*d^5 + 4*a*b*c*d^3*e^2 - 2*a^2*c*d^2*e^3 - a^2*b*d*e^4 + a^3*e^5 - (b^2*c + 3*a*c^2)*d^4*e)*sqrt(e*x + d)) - sqrt(2)*a*sqrt(-(3*a*b*c*d^2*e - 6*a^2*c*d*e^2 + a^2*b*e^3 - (b^2*c - 2*a*c^2)*d^3 - (a^2*b^2*c - 4*a^3*c^2)*sqrt((b^2*c^2*d^6 - 6*a*b*c^2*d^5*e + 9*a^2*c^2*d^4*e^2 + 2*a^2*b*c*d^3*e^3 - 6*a^3*c*d^2*e^4 + a^4*e^6)/(a^4*b^2*c^2 - 4*a^5*c^3)))/(a^2*b^2*c - 4*a^3*c^2))*log(-sqrt(2)*((b^3*c - 4*a*b*c^2)*d^4 - 3*(a*b^2*c - 4*a^2*c^2)*d^3*e + (a^2*b^2 - 4*a^3*c)*d*e^3 - ((a^2*b^3*c - 4*a^3*b*c^2)*d - 2*(a^3*b^2*c - 4*a^4*c^2)*e)*sqrt((b^2*c^2*d^6 - 6*a*b*c^2*d^5*e + 9*a^2*c^2*d^4*e^2 + 2*a^2*b*c*d^3*e^3 - 6*a^3*c*d^2*e^4 + a^4*e^6)/(a^4*b^2*c^2 - 4*a^5*c^3)))*sqrt(-(3*a*b*c*d^2*e - 6*a^2*c*d*e^2 + a^2*b*e^3 - (b^2*c - 2*a*c^2)*d^3 - (a^2*b^2*c - 4*a^3*c^2)*sqrt((b^2*c^2*d^6 - 6*a*b*c^2*d^5*e + 9*a^2*c^2*d^4*e^2 + 2*a^2*b*c*d^3*e^3 - 6*a^3*c*d^2*e^4 + a^4*e^6)/(a^4*b^2*c^2 - 4*a^5*c^3)))/(a^2*b^2*c - 4*a^3*c^2)) + 4*(b*c^2*d^5 + 4*a*b*c*d^3*e^2 - 2*a^2*c*d^2*e^3 - a^2*b*d*e^4 + a^3*e^5 - (b^2*c + 3*a*c^2)*d^4*e)*sqrt(e*x + d)) - 2*d^(3/2)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x))/a, -1/2*(sqrt(2)*a*sqrt(-(3*a*b*c*d^2*e - 6*a^2*c*d*e^2 + a^2*b*e^3 - (b^2*c - 2*a*c^2)*d^3 + (a^2*b^2*c - 4*a^3*c^2)*sqrt((b^2*c^2*d^6 - 6*a*b*c^2*d^5*e + 9*a^2*c^2*d^4*e^2 + 2*a^2*b*c*d^3*e^3 - 6*a^3*c*d^2*e^4 + a^4*e^6)/(a^4*b^2*c^2 - 4*a^5*c^3)))/(a^2*b^2*c - 4*a^3*c^2))*log(sqrt(2)*((b^3*c - 4*a*b*c^2)*d^4 - 3*(a*b^2*c - 4*a^2*c^2)*d^3*e + (a^2*b^2 - 4*a^3*c)*d*e^3 + ((a^2*b^3*c - 4*a^3*b*c^2)*d - 2*(a^3*b^2*c - 4*a^4*c^2)*e)*sqrt((b^2*c^2*d^6 - 6*a*b*c^2*d^5*e + 9*a^2*c^2*d^4*e^2 + 2*a^2*b*c*d^3*e^3 - 6*a^3*c*d^2*e^4 + a^4*e^6)/(a^4*b^2*c^2 - 4*a^5*c^3)))*sqrt(-(3*a*b*c*d^2*e - 6*a^2*c*d*e^2 + a^2*b*e^3 - (b^2*c - 2*a*c^2)*d^3 + (a^2*b^2*c - 4*a^3*c^2)*sqrt((b^2*c^2*d^6 - 6*a*b*c^2*d^5*e + 9*a^2*c^2*d^4*e^2 + 2*a^2*b*c*d^3*e^3 - 6*a^3*c*d^2*e^4 + a^4*e^6)/(a^4*b^2*c^2 - 4*a^5*c^3)))/(a^2*b^2*c - 4*a^3*c^2)) + 4*(b*c^2*d^5 + 4*a*b*c*d^3*e^2 - 2*a^2*c*d^2*e^3 - a^2*b*d*e^4 + a^3*e^5 - (b^2*c + 3*a*c^2)*d^4*e)*sqrt(e*x + d)) - sqrt(2)*a*sqrt(-(3*a*b*c*d^2*e - 6*a^2*c*d*e^2 + a^2*b*e^3 - (b^2*c - 2*a*c^2)*d^3 + (a^2*b^2*c - 4*a^3*c^2)*sqrt((b^2*c^2*d^6 - 6*a*b*c^2*d^5*e + 9*a^2*c^2*d^4*e^2 + 2*a^2*b*c*d^3*e^3 - 6*a^3*c*d^2*e^4 + a^4*e^6)/(a^4*b^2*c^2 - 4*a^5*c^3)))/(a^2*b^2*c - 4*a^3*c^2))*log(-sqrt(2)*((b^3*c - 4*a*b*c^2)*d^4 - 3*(a*b^2*c - 4*a^2*c^2)*d^3*e + (a^2*b^2 - 4*a^3*c)*d*e^3 + ((a^2*b^3*c - 4*a^3*b*c^2)*d - 2*(a^3*b^2*c - 4*a^4*c^2)*e)*sqrt((b^2*c^2*d^6 - 6*a*b*c^2*d^5*e + 9*a^2*c^2*d^4*e^2 + 2*a^2*b*c*d^3*e^3 - 6*a^3*c*d^2*e^4 + a^4*e^6)/(a^4*b^2*c^2 - 4*a^5*c^3)))*sqrt(-(3*a*b*c*d^2*e - 6*a^2*c*d*e^2 + a^2*b*e^3 - (b^2*c - 2*a*c^2)*d^3 + (a^2*b^2*c - 4*a^3*c^2)*sqrt((b^2*c^2*d^6 - 6*a*b*c^2*d^5*e + 9*a^2*c^2*d^4*e^2 + 2*a^2*b*c*d^3*e^3 - 6*a^3*c*d^2*e^4 + a^4*e^6)/(a^4*b^2*c^2 - 4*a^5*c^3)))/(a^2*b^2*c - 4*a^3*c^2)) + 4*(b*c^2*d^5 + 4*a*b*c*d^3*e^2 - 2*a^2*c*d^2*e^3 - a^2*b*d*e^4 + a^3*e^5 - (b^2*c + 3*a*c^2)*d^4*e)*sqrt(e*x + d)) + sqrt(2)*a*sqrt(-(3*a*b*c*d^2*e - 6*a^2*c*d*e^2 + a^2*b*e^3 - (b^2*c - 2*a*c^2)*d^3 - (a^2*b^2*c - 4*a^3*c^2)*sqrt((b^2*c^2*d^6 - 6*a*b*c^2*d^5*e + 9*a^2*c^2*d^4*e^2 + 2*a^2*b*c*d^3*e^3 - 6*a^3*c*d^2*e^4 + a^4*e^6)/(a^4*b^2*c^2 - 4*a^5*c^3)))/(a^2*b^2*c - 4*a^3*c^2))*log(sqrt(2)*((b^3*c - 4*a*b*c^2)*d^4 - 3*(a*b^2*c - 4*a^2*c^2)*d^3*e + (a^2*b^2 - 4*a^3*c)*d*e^3 - ((a^2*b^3*c - 4*a^3*b*c^2)*d - 2*(a^3*b^2*c - 4*a^4*c^2)*e)*sqrt((b^2*c^2*d^6 - 6*a*b*c^2*d^5*e + 9*a^2*c^2*d^4*e^2 + 2*a^2*b*c*d^3*e^3 - 6*a^3*c*d^2*e^4 + a^4*e^6)/(a^4*b^2*c^2 - 4*a^5*c^3)))*sqrt(-(3*a*b*c*d^2*e - 6*a^2*c*d*e^2 + a^2*b*e^3 - (b^2*c - 2*a*c^2)*d^3 - (a^2*b^2*c - 4*a^3*c^2)*sqrt((b^2*c^2*d^6 - 6*a*b*c^2*d^5*e + 9*a^2*c^2*d^4*e^2 + 2*a^2*b*c*d^3*e^3 - 6*a^3*c*d^2*e^4 + a^4*e^6)/(a^4*b^2*c^2 - 4*a^5*c^3)))/(a^2*b^2*c - 4*a^3*c^2)) + 4*(b*c^2*d^5 + 4*a*b*c*d^3*e^2 - 2*a^2*c*d^2*e^3 - a^2*b*d*e^4 + a^3*e^5 - (b^2*c + 3*a*c^2)*d^4*e)*sqrt(e*x + d)) - sqrt(2)*a*sqrt(-(3*a*b*c*d^2*e - 6*a^2*c*d*e^2 + a^2*b*e^3 - (b^2*c - 2*a*c^2)*d^3 - (a^2*b^2*c - 4*a^3*c^2)*sqrt((b^2*c^2*d^6 - 6*a*b*c^2*d^5*e + 9*a^2*c^2*d^4*e^2 + 2*a^2*b*c*d^3*e^3 - 6*a^3*c*d^2*e^4 + a^4*e^6)/(a^4*b^2*c^2 - 4*a^5*c^3)))/(a^2*b^2*c - 4*a^3*c^2))*log(-sqrt(2)*((b^3*c - 4*a*b*c^2)*d^4 - 3*(a*b^2*c - 4*a^2*c^2)*d^3*e + (a^2*b^2 - 4*a^3*c)*d*e^3 - ((a^2*b^3*c - 4*a^3*b*c^2)*d - 2*(a^3*b^2*c - 4*a^4*c^2)*e)*sqrt((b^2*c^2*d^6 - 6*a*b*c^2*d^5*e + 9*a^2*c^2*d^4*e^2 + 2*a^2*b*c*d^3*e^3 - 6*a^3*c*d^2*e^4 + a^4*e^6)/(a^4*b^2*c^2 - 4*a^5*c^3)))*sqrt(-(3*a*b*c*d^2*e - 6*a^2*c*d*e^2 + a^2*b*e^3 - (b^2*c - 2*a*c^2)*d^3 - (a^2*b^2*c - 4*a^3*c^2)*sqrt((b^2*c^2*d^6 - 6*a*b*c^2*d^5*e + 9*a^2*c^2*d^4*e^2 + 2*a^2*b*c*d^3*e^3 - 6*a^3*c*d^2*e^4 + a^4*e^6)/(a^4*b^2*c^2 - 4*a^5*c^3)))/(a^2*b^2*c - 4*a^3*c^2)) + 4*(b*c^2*d^5 + 4*a*b*c*d^3*e^2 - 2*a^2*c*d^2*e^3 - a^2*b*d*e^4 + a^3*e^5 - (b^2*c + 3*a*c^2)*d^4*e)*sqrt(e*x + d)) - 4*sqrt(-d)*d*arctan(sqrt(e*x + d)*sqrt(-d)/d))/a]","B",0
539,1,8653,0,34.641600," ","integrate((e*x+d)^(3/2)/x^2/(c*x^2+b*x+a),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} a^{2} x \sqrt{-\frac{a^{3} b e^{3} - {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} d^{3} + 3 \, {\left(a b^{3} - 3 \, a^{2} b c\right)} d^{2} e - 3 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d e^{2} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{-\frac{6 \, a^{5} b d e^{5} - a^{6} e^{6} - {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} d^{6} + 6 \, {\left(a b^{5} - 3 \, a^{2} b^{3} c + 2 \, a^{3} b c^{2}\right)} d^{5} e - 3 \, {\left(5 \, a^{2} b^{4} - 10 \, a^{3} b^{2} c + 3 \, a^{4} c^{2}\right)} d^{4} e^{2} + 2 \, {\left(10 \, a^{3} b^{3} - 11 \, a^{4} b c\right)} d^{3} e^{3} - 3 \, {\left(5 \, a^{4} b^{2} - 2 \, a^{5} c\right)} d^{2} e^{4}}{a^{8} b^{2} - 4 \, a^{9} c}}}{a^{4} b^{2} - 4 \, a^{5} c}} \log\left(\sqrt{2} {\left({\left(b^{6} - 6 \, a b^{4} c + 8 \, a^{2} b^{2} c^{2}\right)} d^{4} - {\left(4 \, a b^{5} - 21 \, a^{2} b^{3} c + 20 \, a^{3} b c^{2}\right)} d^{3} e + 3 \, {\left(2 \, a^{2} b^{4} - 9 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} d^{2} e^{2} - 4 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{4} + {\left({\left(a^{4} b^{4} - 6 \, a^{5} b^{2} c + 8 \, a^{6} c^{2}\right)} d - {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} e\right)} \sqrt{-\frac{6 \, a^{5} b d e^{5} - a^{6} e^{6} - {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} d^{6} + 6 \, {\left(a b^{5} - 3 \, a^{2} b^{3} c + 2 \, a^{3} b c^{2}\right)} d^{5} e - 3 \, {\left(5 \, a^{2} b^{4} - 10 \, a^{3} b^{2} c + 3 \, a^{4} c^{2}\right)} d^{4} e^{2} + 2 \, {\left(10 \, a^{3} b^{3} - 11 \, a^{4} b c\right)} d^{3} e^{3} - 3 \, {\left(5 \, a^{4} b^{2} - 2 \, a^{5} c\right)} d^{2} e^{4}}{a^{8} b^{2} - 4 \, a^{9} c}}\right)} \sqrt{-\frac{a^{3} b e^{3} - {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} d^{3} + 3 \, {\left(a b^{3} - 3 \, a^{2} b c\right)} d^{2} e - 3 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d e^{2} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{-\frac{6 \, a^{5} b d e^{5} - a^{6} e^{6} - {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} d^{6} + 6 \, {\left(a b^{5} - 3 \, a^{2} b^{3} c + 2 \, a^{3} b c^{2}\right)} d^{5} e - 3 \, {\left(5 \, a^{2} b^{4} - 10 \, a^{3} b^{2} c + 3 \, a^{4} c^{2}\right)} d^{4} e^{2} + 2 \, {\left(10 \, a^{3} b^{3} - 11 \, a^{4} b c\right)} d^{3} e^{3} - 3 \, {\left(5 \, a^{4} b^{2} - 2 \, a^{5} c\right)} d^{2} e^{4}}{a^{8} b^{2} - 4 \, a^{9} c}}}{a^{4} b^{2} - 4 \, a^{5} c}} - 4 \, {\left(4 \, a^{3} b c d e^{4} - a^{4} c e^{5} + {\left(b^{3} c^{2} - 2 \, a b c^{3}\right)} d^{5} - {\left(b^{4} c + a b^{2} c^{2} - 3 \, a^{2} c^{3}\right)} d^{4} e + 2 \, {\left(2 \, a b^{3} c - a^{2} b c^{2}\right)} d^{3} e^{2} - 2 \, {\left(3 \, a^{2} b^{2} c - a^{3} c^{2}\right)} d^{2} e^{3}\right)} \sqrt{e x + d}\right) - \sqrt{2} a^{2} x \sqrt{-\frac{a^{3} b e^{3} - {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} d^{3} + 3 \, {\left(a b^{3} - 3 \, a^{2} b c\right)} d^{2} e - 3 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d e^{2} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{-\frac{6 \, a^{5} b d e^{5} - a^{6} e^{6} - {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} d^{6} + 6 \, {\left(a b^{5} - 3 \, a^{2} b^{3} c + 2 \, a^{3} b c^{2}\right)} d^{5} e - 3 \, {\left(5 \, a^{2} b^{4} - 10 \, a^{3} b^{2} c + 3 \, a^{4} c^{2}\right)} d^{4} e^{2} + 2 \, {\left(10 \, a^{3} b^{3} - 11 \, a^{4} b c\right)} d^{3} e^{3} - 3 \, {\left(5 \, a^{4} b^{2} - 2 \, a^{5} c\right)} d^{2} e^{4}}{a^{8} b^{2} - 4 \, a^{9} c}}}{a^{4} b^{2} - 4 \, a^{5} c}} \log\left(-\sqrt{2} {\left({\left(b^{6} - 6 \, a b^{4} c + 8 \, a^{2} b^{2} c^{2}\right)} d^{4} - {\left(4 \, a b^{5} - 21 \, a^{2} b^{3} c + 20 \, a^{3} b c^{2}\right)} d^{3} e + 3 \, {\left(2 \, a^{2} b^{4} - 9 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} d^{2} e^{2} - 4 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{4} + {\left({\left(a^{4} b^{4} - 6 \, a^{5} b^{2} c + 8 \, a^{6} c^{2}\right)} d - {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} e\right)} \sqrt{-\frac{6 \, a^{5} b d e^{5} - a^{6} e^{6} - {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} d^{6} + 6 \, {\left(a b^{5} - 3 \, a^{2} b^{3} c + 2 \, a^{3} b c^{2}\right)} d^{5} e - 3 \, {\left(5 \, a^{2} b^{4} - 10 \, a^{3} b^{2} c + 3 \, a^{4} c^{2}\right)} d^{4} e^{2} + 2 \, {\left(10 \, a^{3} b^{3} - 11 \, a^{4} b c\right)} d^{3} e^{3} - 3 \, {\left(5 \, a^{4} b^{2} - 2 \, a^{5} c\right)} d^{2} e^{4}}{a^{8} b^{2} - 4 \, a^{9} c}}\right)} \sqrt{-\frac{a^{3} b e^{3} - {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} d^{3} + 3 \, {\left(a b^{3} - 3 \, a^{2} b c\right)} d^{2} e - 3 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d e^{2} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{-\frac{6 \, a^{5} b d e^{5} - a^{6} e^{6} - {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} d^{6} + 6 \, {\left(a b^{5} - 3 \, a^{2} b^{3} c + 2 \, a^{3} b c^{2}\right)} d^{5} e - 3 \, {\left(5 \, a^{2} b^{4} - 10 \, a^{3} b^{2} c + 3 \, a^{4} c^{2}\right)} d^{4} e^{2} + 2 \, {\left(10 \, a^{3} b^{3} - 11 \, a^{4} b c\right)} d^{3} e^{3} - 3 \, {\left(5 \, a^{4} b^{2} - 2 \, a^{5} c\right)} d^{2} e^{4}}{a^{8} b^{2} - 4 \, a^{9} c}}}{a^{4} b^{2} - 4 \, a^{5} c}} - 4 \, {\left(4 \, a^{3} b c d e^{4} - a^{4} c e^{5} + {\left(b^{3} c^{2} - 2 \, a b c^{3}\right)} d^{5} - {\left(b^{4} c + a b^{2} c^{2} - 3 \, a^{2} c^{3}\right)} d^{4} e + 2 \, {\left(2 \, a b^{3} c - a^{2} b c^{2}\right)} d^{3} e^{2} - 2 \, {\left(3 \, a^{2} b^{2} c - a^{3} c^{2}\right)} d^{2} e^{3}\right)} \sqrt{e x + d}\right) + \sqrt{2} a^{2} x \sqrt{-\frac{a^{3} b e^{3} - {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} d^{3} + 3 \, {\left(a b^{3} - 3 \, a^{2} b c\right)} d^{2} e - 3 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d e^{2} - {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{-\frac{6 \, a^{5} b d e^{5} - a^{6} e^{6} - {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} d^{6} + 6 \, {\left(a b^{5} - 3 \, a^{2} b^{3} c + 2 \, a^{3} b c^{2}\right)} d^{5} e - 3 \, {\left(5 \, a^{2} b^{4} - 10 \, a^{3} b^{2} c + 3 \, a^{4} c^{2}\right)} d^{4} e^{2} + 2 \, {\left(10 \, a^{3} b^{3} - 11 \, a^{4} b c\right)} d^{3} e^{3} - 3 \, {\left(5 \, a^{4} b^{2} - 2 \, a^{5} c\right)} d^{2} e^{4}}{a^{8} b^{2} - 4 \, a^{9} c}}}{a^{4} b^{2} - 4 \, a^{5} c}} \log\left(\sqrt{2} {\left({\left(b^{6} - 6 \, a b^{4} c + 8 \, a^{2} b^{2} c^{2}\right)} d^{4} - {\left(4 \, a b^{5} - 21 \, a^{2} b^{3} c + 20 \, a^{3} b c^{2}\right)} d^{3} e + 3 \, {\left(2 \, a^{2} b^{4} - 9 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} d^{2} e^{2} - 4 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{4} - {\left({\left(a^{4} b^{4} - 6 \, a^{5} b^{2} c + 8 \, a^{6} c^{2}\right)} d - {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} e\right)} \sqrt{-\frac{6 \, a^{5} b d e^{5} - a^{6} e^{6} - {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} d^{6} + 6 \, {\left(a b^{5} - 3 \, a^{2} b^{3} c + 2 \, a^{3} b c^{2}\right)} d^{5} e - 3 \, {\left(5 \, a^{2} b^{4} - 10 \, a^{3} b^{2} c + 3 \, a^{4} c^{2}\right)} d^{4} e^{2} + 2 \, {\left(10 \, a^{3} b^{3} - 11 \, a^{4} b c\right)} d^{3} e^{3} - 3 \, {\left(5 \, a^{4} b^{2} - 2 \, a^{5} c\right)} d^{2} e^{4}}{a^{8} b^{2} - 4 \, a^{9} c}}\right)} \sqrt{-\frac{a^{3} b e^{3} - {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} d^{3} + 3 \, {\left(a b^{3} - 3 \, a^{2} b c\right)} d^{2} e - 3 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d e^{2} - {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{-\frac{6 \, a^{5} b d e^{5} - a^{6} e^{6} - {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} d^{6} + 6 \, {\left(a b^{5} - 3 \, a^{2} b^{3} c + 2 \, a^{3} b c^{2}\right)} d^{5} e - 3 \, {\left(5 \, a^{2} b^{4} - 10 \, a^{3} b^{2} c + 3 \, a^{4} c^{2}\right)} d^{4} e^{2} + 2 \, {\left(10 \, a^{3} b^{3} - 11 \, a^{4} b c\right)} d^{3} e^{3} - 3 \, {\left(5 \, a^{4} b^{2} - 2 \, a^{5} c\right)} d^{2} e^{4}}{a^{8} b^{2} - 4 \, a^{9} c}}}{a^{4} b^{2} - 4 \, a^{5} c}} - 4 \, {\left(4 \, a^{3} b c d e^{4} - a^{4} c e^{5} + {\left(b^{3} c^{2} - 2 \, a b c^{3}\right)} d^{5} - {\left(b^{4} c + a b^{2} c^{2} - 3 \, a^{2} c^{3}\right)} d^{4} e + 2 \, {\left(2 \, a b^{3} c - a^{2} b c^{2}\right)} d^{3} e^{2} - 2 \, {\left(3 \, a^{2} b^{2} c - a^{3} c^{2}\right)} d^{2} e^{3}\right)} \sqrt{e x + d}\right) - \sqrt{2} a^{2} x \sqrt{-\frac{a^{3} b e^{3} - {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} d^{3} + 3 \, {\left(a b^{3} - 3 \, a^{2} b c\right)} d^{2} e - 3 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d e^{2} - {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{-\frac{6 \, a^{5} b d e^{5} - a^{6} e^{6} - {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} d^{6} + 6 \, {\left(a b^{5} - 3 \, a^{2} b^{3} c + 2 \, a^{3} b c^{2}\right)} d^{5} e - 3 \, {\left(5 \, a^{2} b^{4} - 10 \, a^{3} b^{2} c + 3 \, a^{4} c^{2}\right)} d^{4} e^{2} + 2 \, {\left(10 \, a^{3} b^{3} - 11 \, a^{4} b c\right)} d^{3} e^{3} - 3 \, {\left(5 \, a^{4} b^{2} - 2 \, a^{5} c\right)} d^{2} e^{4}}{a^{8} b^{2} - 4 \, a^{9} c}}}{a^{4} b^{2} - 4 \, a^{5} c}} \log\left(-\sqrt{2} {\left({\left(b^{6} - 6 \, a b^{4} c + 8 \, a^{2} b^{2} c^{2}\right)} d^{4} - {\left(4 \, a b^{5} - 21 \, a^{2} b^{3} c + 20 \, a^{3} b c^{2}\right)} d^{3} e + 3 \, {\left(2 \, a^{2} b^{4} - 9 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} d^{2} e^{2} - 4 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{4} - {\left({\left(a^{4} b^{4} - 6 \, a^{5} b^{2} c + 8 \, a^{6} c^{2}\right)} d - {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} e\right)} \sqrt{-\frac{6 \, a^{5} b d e^{5} - a^{6} e^{6} - {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} d^{6} + 6 \, {\left(a b^{5} - 3 \, a^{2} b^{3} c + 2 \, a^{3} b c^{2}\right)} d^{5} e - 3 \, {\left(5 \, a^{2} b^{4} - 10 \, a^{3} b^{2} c + 3 \, a^{4} c^{2}\right)} d^{4} e^{2} + 2 \, {\left(10 \, a^{3} b^{3} - 11 \, a^{4} b c\right)} d^{3} e^{3} - 3 \, {\left(5 \, a^{4} b^{2} - 2 \, a^{5} c\right)} d^{2} e^{4}}{a^{8} b^{2} - 4 \, a^{9} c}}\right)} \sqrt{-\frac{a^{3} b e^{3} - {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} d^{3} + 3 \, {\left(a b^{3} - 3 \, a^{2} b c\right)} d^{2} e - 3 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d e^{2} - {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{-\frac{6 \, a^{5} b d e^{5} - a^{6} e^{6} - {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} d^{6} + 6 \, {\left(a b^{5} - 3 \, a^{2} b^{3} c + 2 \, a^{3} b c^{2}\right)} d^{5} e - 3 \, {\left(5 \, a^{2} b^{4} - 10 \, a^{3} b^{2} c + 3 \, a^{4} c^{2}\right)} d^{4} e^{2} + 2 \, {\left(10 \, a^{3} b^{3} - 11 \, a^{4} b c\right)} d^{3} e^{3} - 3 \, {\left(5 \, a^{4} b^{2} - 2 \, a^{5} c\right)} d^{2} e^{4}}{a^{8} b^{2} - 4 \, a^{9} c}}}{a^{4} b^{2} - 4 \, a^{5} c}} - 4 \, {\left(4 \, a^{3} b c d e^{4} - a^{4} c e^{5} + {\left(b^{3} c^{2} - 2 \, a b c^{3}\right)} d^{5} - {\left(b^{4} c + a b^{2} c^{2} - 3 \, a^{2} c^{3}\right)} d^{4} e + 2 \, {\left(2 \, a b^{3} c - a^{2} b c^{2}\right)} d^{3} e^{2} - 2 \, {\left(3 \, a^{2} b^{2} c - a^{3} c^{2}\right)} d^{2} e^{3}\right)} \sqrt{e x + d}\right) + {\left(2 \, b d - 3 \, a e\right)} \sqrt{d} x \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) + 2 \, \sqrt{e x + d} a d}{2 \, a^{2} x}, -\frac{\sqrt{2} a^{2} x \sqrt{-\frac{a^{3} b e^{3} - {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} d^{3} + 3 \, {\left(a b^{3} - 3 \, a^{2} b c\right)} d^{2} e - 3 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d e^{2} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{-\frac{6 \, a^{5} b d e^{5} - a^{6} e^{6} - {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} d^{6} + 6 \, {\left(a b^{5} - 3 \, a^{2} b^{3} c + 2 \, a^{3} b c^{2}\right)} d^{5} e - 3 \, {\left(5 \, a^{2} b^{4} - 10 \, a^{3} b^{2} c + 3 \, a^{4} c^{2}\right)} d^{4} e^{2} + 2 \, {\left(10 \, a^{3} b^{3} - 11 \, a^{4} b c\right)} d^{3} e^{3} - 3 \, {\left(5 \, a^{4} b^{2} - 2 \, a^{5} c\right)} d^{2} e^{4}}{a^{8} b^{2} - 4 \, a^{9} c}}}{a^{4} b^{2} - 4 \, a^{5} c}} \log\left(\sqrt{2} {\left({\left(b^{6} - 6 \, a b^{4} c + 8 \, a^{2} b^{2} c^{2}\right)} d^{4} - {\left(4 \, a b^{5} - 21 \, a^{2} b^{3} c + 20 \, a^{3} b c^{2}\right)} d^{3} e + 3 \, {\left(2 \, a^{2} b^{4} - 9 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} d^{2} e^{2} - 4 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{4} + {\left({\left(a^{4} b^{4} - 6 \, a^{5} b^{2} c + 8 \, a^{6} c^{2}\right)} d - {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} e\right)} \sqrt{-\frac{6 \, a^{5} b d e^{5} - a^{6} e^{6} - {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} d^{6} + 6 \, {\left(a b^{5} - 3 \, a^{2} b^{3} c + 2 \, a^{3} b c^{2}\right)} d^{5} e - 3 \, {\left(5 \, a^{2} b^{4} - 10 \, a^{3} b^{2} c + 3 \, a^{4} c^{2}\right)} d^{4} e^{2} + 2 \, {\left(10 \, a^{3} b^{3} - 11 \, a^{4} b c\right)} d^{3} e^{3} - 3 \, {\left(5 \, a^{4} b^{2} - 2 \, a^{5} c\right)} d^{2} e^{4}}{a^{8} b^{2} - 4 \, a^{9} c}}\right)} \sqrt{-\frac{a^{3} b e^{3} - {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} d^{3} + 3 \, {\left(a b^{3} - 3 \, a^{2} b c\right)} d^{2} e - 3 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d e^{2} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{-\frac{6 \, a^{5} b d e^{5} - a^{6} e^{6} - {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} d^{6} + 6 \, {\left(a b^{5} - 3 \, a^{2} b^{3} c + 2 \, a^{3} b c^{2}\right)} d^{5} e - 3 \, {\left(5 \, a^{2} b^{4} - 10 \, a^{3} b^{2} c + 3 \, a^{4} c^{2}\right)} d^{4} e^{2} + 2 \, {\left(10 \, a^{3} b^{3} - 11 \, a^{4} b c\right)} d^{3} e^{3} - 3 \, {\left(5 \, a^{4} b^{2} - 2 \, a^{5} c\right)} d^{2} e^{4}}{a^{8} b^{2} - 4 \, a^{9} c}}}{a^{4} b^{2} - 4 \, a^{5} c}} - 4 \, {\left(4 \, a^{3} b c d e^{4} - a^{4} c e^{5} + {\left(b^{3} c^{2} - 2 \, a b c^{3}\right)} d^{5} - {\left(b^{4} c + a b^{2} c^{2} - 3 \, a^{2} c^{3}\right)} d^{4} e + 2 \, {\left(2 \, a b^{3} c - a^{2} b c^{2}\right)} d^{3} e^{2} - 2 \, {\left(3 \, a^{2} b^{2} c - a^{3} c^{2}\right)} d^{2} e^{3}\right)} \sqrt{e x + d}\right) - \sqrt{2} a^{2} x \sqrt{-\frac{a^{3} b e^{3} - {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} d^{3} + 3 \, {\left(a b^{3} - 3 \, a^{2} b c\right)} d^{2} e - 3 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d e^{2} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{-\frac{6 \, a^{5} b d e^{5} - a^{6} e^{6} - {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} d^{6} + 6 \, {\left(a b^{5} - 3 \, a^{2} b^{3} c + 2 \, a^{3} b c^{2}\right)} d^{5} e - 3 \, {\left(5 \, a^{2} b^{4} - 10 \, a^{3} b^{2} c + 3 \, a^{4} c^{2}\right)} d^{4} e^{2} + 2 \, {\left(10 \, a^{3} b^{3} - 11 \, a^{4} b c\right)} d^{3} e^{3} - 3 \, {\left(5 \, a^{4} b^{2} - 2 \, a^{5} c\right)} d^{2} e^{4}}{a^{8} b^{2} - 4 \, a^{9} c}}}{a^{4} b^{2} - 4 \, a^{5} c}} \log\left(-\sqrt{2} {\left({\left(b^{6} - 6 \, a b^{4} c + 8 \, a^{2} b^{2} c^{2}\right)} d^{4} - {\left(4 \, a b^{5} - 21 \, a^{2} b^{3} c + 20 \, a^{3} b c^{2}\right)} d^{3} e + 3 \, {\left(2 \, a^{2} b^{4} - 9 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} d^{2} e^{2} - 4 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{4} + {\left({\left(a^{4} b^{4} - 6 \, a^{5} b^{2} c + 8 \, a^{6} c^{2}\right)} d - {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} e\right)} \sqrt{-\frac{6 \, a^{5} b d e^{5} - a^{6} e^{6} - {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} d^{6} + 6 \, {\left(a b^{5} - 3 \, a^{2} b^{3} c + 2 \, a^{3} b c^{2}\right)} d^{5} e - 3 \, {\left(5 \, a^{2} b^{4} - 10 \, a^{3} b^{2} c + 3 \, a^{4} c^{2}\right)} d^{4} e^{2} + 2 \, {\left(10 \, a^{3} b^{3} - 11 \, a^{4} b c\right)} d^{3} e^{3} - 3 \, {\left(5 \, a^{4} b^{2} - 2 \, a^{5} c\right)} d^{2} e^{4}}{a^{8} b^{2} - 4 \, a^{9} c}}\right)} \sqrt{-\frac{a^{3} b e^{3} - {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} d^{3} + 3 \, {\left(a b^{3} - 3 \, a^{2} b c\right)} d^{2} e - 3 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d e^{2} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{-\frac{6 \, a^{5} b d e^{5} - a^{6} e^{6} - {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} d^{6} + 6 \, {\left(a b^{5} - 3 \, a^{2} b^{3} c + 2 \, a^{3} b c^{2}\right)} d^{5} e - 3 \, {\left(5 \, a^{2} b^{4} - 10 \, a^{3} b^{2} c + 3 \, a^{4} c^{2}\right)} d^{4} e^{2} + 2 \, {\left(10 \, a^{3} b^{3} - 11 \, a^{4} b c\right)} d^{3} e^{3} - 3 \, {\left(5 \, a^{4} b^{2} - 2 \, a^{5} c\right)} d^{2} e^{4}}{a^{8} b^{2} - 4 \, a^{9} c}}}{a^{4} b^{2} - 4 \, a^{5} c}} - 4 \, {\left(4 \, a^{3} b c d e^{4} - a^{4} c e^{5} + {\left(b^{3} c^{2} - 2 \, a b c^{3}\right)} d^{5} - {\left(b^{4} c + a b^{2} c^{2} - 3 \, a^{2} c^{3}\right)} d^{4} e + 2 \, {\left(2 \, a b^{3} c - a^{2} b c^{2}\right)} d^{3} e^{2} - 2 \, {\left(3 \, a^{2} b^{2} c - a^{3} c^{2}\right)} d^{2} e^{3}\right)} \sqrt{e x + d}\right) + \sqrt{2} a^{2} x \sqrt{-\frac{a^{3} b e^{3} - {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} d^{3} + 3 \, {\left(a b^{3} - 3 \, a^{2} b c\right)} d^{2} e - 3 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d e^{2} - {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{-\frac{6 \, a^{5} b d e^{5} - a^{6} e^{6} - {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} d^{6} + 6 \, {\left(a b^{5} - 3 \, a^{2} b^{3} c + 2 \, a^{3} b c^{2}\right)} d^{5} e - 3 \, {\left(5 \, a^{2} b^{4} - 10 \, a^{3} b^{2} c + 3 \, a^{4} c^{2}\right)} d^{4} e^{2} + 2 \, {\left(10 \, a^{3} b^{3} - 11 \, a^{4} b c\right)} d^{3} e^{3} - 3 \, {\left(5 \, a^{4} b^{2} - 2 \, a^{5} c\right)} d^{2} e^{4}}{a^{8} b^{2} - 4 \, a^{9} c}}}{a^{4} b^{2} - 4 \, a^{5} c}} \log\left(\sqrt{2} {\left({\left(b^{6} - 6 \, a b^{4} c + 8 \, a^{2} b^{2} c^{2}\right)} d^{4} - {\left(4 \, a b^{5} - 21 \, a^{2} b^{3} c + 20 \, a^{3} b c^{2}\right)} d^{3} e + 3 \, {\left(2 \, a^{2} b^{4} - 9 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} d^{2} e^{2} - 4 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{4} - {\left({\left(a^{4} b^{4} - 6 \, a^{5} b^{2} c + 8 \, a^{6} c^{2}\right)} d - {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} e\right)} \sqrt{-\frac{6 \, a^{5} b d e^{5} - a^{6} e^{6} - {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} d^{6} + 6 \, {\left(a b^{5} - 3 \, a^{2} b^{3} c + 2 \, a^{3} b c^{2}\right)} d^{5} e - 3 \, {\left(5 \, a^{2} b^{4} - 10 \, a^{3} b^{2} c + 3 \, a^{4} c^{2}\right)} d^{4} e^{2} + 2 \, {\left(10 \, a^{3} b^{3} - 11 \, a^{4} b c\right)} d^{3} e^{3} - 3 \, {\left(5 \, a^{4} b^{2} - 2 \, a^{5} c\right)} d^{2} e^{4}}{a^{8} b^{2} - 4 \, a^{9} c}}\right)} \sqrt{-\frac{a^{3} b e^{3} - {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} d^{3} + 3 \, {\left(a b^{3} - 3 \, a^{2} b c\right)} d^{2} e - 3 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d e^{2} - {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{-\frac{6 \, a^{5} b d e^{5} - a^{6} e^{6} - {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} d^{6} + 6 \, {\left(a b^{5} - 3 \, a^{2} b^{3} c + 2 \, a^{3} b c^{2}\right)} d^{5} e - 3 \, {\left(5 \, a^{2} b^{4} - 10 \, a^{3} b^{2} c + 3 \, a^{4} c^{2}\right)} d^{4} e^{2} + 2 \, {\left(10 \, a^{3} b^{3} - 11 \, a^{4} b c\right)} d^{3} e^{3} - 3 \, {\left(5 \, a^{4} b^{2} - 2 \, a^{5} c\right)} d^{2} e^{4}}{a^{8} b^{2} - 4 \, a^{9} c}}}{a^{4} b^{2} - 4 \, a^{5} c}} - 4 \, {\left(4 \, a^{3} b c d e^{4} - a^{4} c e^{5} + {\left(b^{3} c^{2} - 2 \, a b c^{3}\right)} d^{5} - {\left(b^{4} c + a b^{2} c^{2} - 3 \, a^{2} c^{3}\right)} d^{4} e + 2 \, {\left(2 \, a b^{3} c - a^{2} b c^{2}\right)} d^{3} e^{2} - 2 \, {\left(3 \, a^{2} b^{2} c - a^{3} c^{2}\right)} d^{2} e^{3}\right)} \sqrt{e x + d}\right) - \sqrt{2} a^{2} x \sqrt{-\frac{a^{3} b e^{3} - {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} d^{3} + 3 \, {\left(a b^{3} - 3 \, a^{2} b c\right)} d^{2} e - 3 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d e^{2} - {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{-\frac{6 \, a^{5} b d e^{5} - a^{6} e^{6} - {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} d^{6} + 6 \, {\left(a b^{5} - 3 \, a^{2} b^{3} c + 2 \, a^{3} b c^{2}\right)} d^{5} e - 3 \, {\left(5 \, a^{2} b^{4} - 10 \, a^{3} b^{2} c + 3 \, a^{4} c^{2}\right)} d^{4} e^{2} + 2 \, {\left(10 \, a^{3} b^{3} - 11 \, a^{4} b c\right)} d^{3} e^{3} - 3 \, {\left(5 \, a^{4} b^{2} - 2 \, a^{5} c\right)} d^{2} e^{4}}{a^{8} b^{2} - 4 \, a^{9} c}}}{a^{4} b^{2} - 4 \, a^{5} c}} \log\left(-\sqrt{2} {\left({\left(b^{6} - 6 \, a b^{4} c + 8 \, a^{2} b^{2} c^{2}\right)} d^{4} - {\left(4 \, a b^{5} - 21 \, a^{2} b^{3} c + 20 \, a^{3} b c^{2}\right)} d^{3} e + 3 \, {\left(2 \, a^{2} b^{4} - 9 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} d^{2} e^{2} - 4 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{4} - {\left({\left(a^{4} b^{4} - 6 \, a^{5} b^{2} c + 8 \, a^{6} c^{2}\right)} d - {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} e\right)} \sqrt{-\frac{6 \, a^{5} b d e^{5} - a^{6} e^{6} - {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} d^{6} + 6 \, {\left(a b^{5} - 3 \, a^{2} b^{3} c + 2 \, a^{3} b c^{2}\right)} d^{5} e - 3 \, {\left(5 \, a^{2} b^{4} - 10 \, a^{3} b^{2} c + 3 \, a^{4} c^{2}\right)} d^{4} e^{2} + 2 \, {\left(10 \, a^{3} b^{3} - 11 \, a^{4} b c\right)} d^{3} e^{3} - 3 \, {\left(5 \, a^{4} b^{2} - 2 \, a^{5} c\right)} d^{2} e^{4}}{a^{8} b^{2} - 4 \, a^{9} c}}\right)} \sqrt{-\frac{a^{3} b e^{3} - {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} d^{3} + 3 \, {\left(a b^{3} - 3 \, a^{2} b c\right)} d^{2} e - 3 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d e^{2} - {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{-\frac{6 \, a^{5} b d e^{5} - a^{6} e^{6} - {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} d^{6} + 6 \, {\left(a b^{5} - 3 \, a^{2} b^{3} c + 2 \, a^{3} b c^{2}\right)} d^{5} e - 3 \, {\left(5 \, a^{2} b^{4} - 10 \, a^{3} b^{2} c + 3 \, a^{4} c^{2}\right)} d^{4} e^{2} + 2 \, {\left(10 \, a^{3} b^{3} - 11 \, a^{4} b c\right)} d^{3} e^{3} - 3 \, {\left(5 \, a^{4} b^{2} - 2 \, a^{5} c\right)} d^{2} e^{4}}{a^{8} b^{2} - 4 \, a^{9} c}}}{a^{4} b^{2} - 4 \, a^{5} c}} - 4 \, {\left(4 \, a^{3} b c d e^{4} - a^{4} c e^{5} + {\left(b^{3} c^{2} - 2 \, a b c^{3}\right)} d^{5} - {\left(b^{4} c + a b^{2} c^{2} - 3 \, a^{2} c^{3}\right)} d^{4} e + 2 \, {\left(2 \, a b^{3} c - a^{2} b c^{2}\right)} d^{3} e^{2} - 2 \, {\left(3 \, a^{2} b^{2} c - a^{3} c^{2}\right)} d^{2} e^{3}\right)} \sqrt{e x + d}\right) + 2 \, {\left(2 \, b d - 3 \, a e\right)} \sqrt{-d} x \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) + 2 \, \sqrt{e x + d} a d}{2 \, a^{2} x}\right]"," ",0,"[-1/2*(sqrt(2)*a^2*x*sqrt(-(a^3*b*e^3 - (b^4 - 4*a*b^2*c + 2*a^2*c^2)*d^3 + 3*(a*b^3 - 3*a^2*b*c)*d^2*e - 3*(a^2*b^2 - 2*a^3*c)*d*e^2 + (a^4*b^2 - 4*a^5*c)*sqrt(-(6*a^5*b*d*e^5 - a^6*e^6 - (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*d^6 + 6*(a*b^5 - 3*a^2*b^3*c + 2*a^3*b*c^2)*d^5*e - 3*(5*a^2*b^4 - 10*a^3*b^2*c + 3*a^4*c^2)*d^4*e^2 + 2*(10*a^3*b^3 - 11*a^4*b*c)*d^3*e^3 - 3*(5*a^4*b^2 - 2*a^5*c)*d^2*e^4)/(a^8*b^2 - 4*a^9*c)))/(a^4*b^2 - 4*a^5*c))*log(sqrt(2)*((b^6 - 6*a*b^4*c + 8*a^2*b^2*c^2)*d^4 - (4*a*b^5 - 21*a^2*b^3*c + 20*a^3*b*c^2)*d^3*e + 3*(2*a^2*b^4 - 9*a^3*b^2*c + 4*a^4*c^2)*d^2*e^2 - 4*(a^3*b^3 - 4*a^4*b*c)*d*e^3 + (a^4*b^2 - 4*a^5*c)*e^4 + ((a^4*b^4 - 6*a^5*b^2*c + 8*a^6*c^2)*d - (a^5*b^3 - 4*a^6*b*c)*e)*sqrt(-(6*a^5*b*d*e^5 - a^6*e^6 - (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*d^6 + 6*(a*b^5 - 3*a^2*b^3*c + 2*a^3*b*c^2)*d^5*e - 3*(5*a^2*b^4 - 10*a^3*b^2*c + 3*a^4*c^2)*d^4*e^2 + 2*(10*a^3*b^3 - 11*a^4*b*c)*d^3*e^3 - 3*(5*a^4*b^2 - 2*a^5*c)*d^2*e^4)/(a^8*b^2 - 4*a^9*c)))*sqrt(-(a^3*b*e^3 - (b^4 - 4*a*b^2*c + 2*a^2*c^2)*d^3 + 3*(a*b^3 - 3*a^2*b*c)*d^2*e - 3*(a^2*b^2 - 2*a^3*c)*d*e^2 + (a^4*b^2 - 4*a^5*c)*sqrt(-(6*a^5*b*d*e^5 - a^6*e^6 - (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*d^6 + 6*(a*b^5 - 3*a^2*b^3*c + 2*a^3*b*c^2)*d^5*e - 3*(5*a^2*b^4 - 10*a^3*b^2*c + 3*a^4*c^2)*d^4*e^2 + 2*(10*a^3*b^3 - 11*a^4*b*c)*d^3*e^3 - 3*(5*a^4*b^2 - 2*a^5*c)*d^2*e^4)/(a^8*b^2 - 4*a^9*c)))/(a^4*b^2 - 4*a^5*c)) - 4*(4*a^3*b*c*d*e^4 - a^4*c*e^5 + (b^3*c^2 - 2*a*b*c^3)*d^5 - (b^4*c + a*b^2*c^2 - 3*a^2*c^3)*d^4*e + 2*(2*a*b^3*c - a^2*b*c^2)*d^3*e^2 - 2*(3*a^2*b^2*c - a^3*c^2)*d^2*e^3)*sqrt(e*x + d)) - sqrt(2)*a^2*x*sqrt(-(a^3*b*e^3 - (b^4 - 4*a*b^2*c + 2*a^2*c^2)*d^3 + 3*(a*b^3 - 3*a^2*b*c)*d^2*e - 3*(a^2*b^2 - 2*a^3*c)*d*e^2 + (a^4*b^2 - 4*a^5*c)*sqrt(-(6*a^5*b*d*e^5 - a^6*e^6 - (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*d^6 + 6*(a*b^5 - 3*a^2*b^3*c + 2*a^3*b*c^2)*d^5*e - 3*(5*a^2*b^4 - 10*a^3*b^2*c + 3*a^4*c^2)*d^4*e^2 + 2*(10*a^3*b^3 - 11*a^4*b*c)*d^3*e^3 - 3*(5*a^4*b^2 - 2*a^5*c)*d^2*e^4)/(a^8*b^2 - 4*a^9*c)))/(a^4*b^2 - 4*a^5*c))*log(-sqrt(2)*((b^6 - 6*a*b^4*c + 8*a^2*b^2*c^2)*d^4 - (4*a*b^5 - 21*a^2*b^3*c + 20*a^3*b*c^2)*d^3*e + 3*(2*a^2*b^4 - 9*a^3*b^2*c + 4*a^4*c^2)*d^2*e^2 - 4*(a^3*b^3 - 4*a^4*b*c)*d*e^3 + (a^4*b^2 - 4*a^5*c)*e^4 + ((a^4*b^4 - 6*a^5*b^2*c + 8*a^6*c^2)*d - (a^5*b^3 - 4*a^6*b*c)*e)*sqrt(-(6*a^5*b*d*e^5 - a^6*e^6 - (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*d^6 + 6*(a*b^5 - 3*a^2*b^3*c + 2*a^3*b*c^2)*d^5*e - 3*(5*a^2*b^4 - 10*a^3*b^2*c + 3*a^4*c^2)*d^4*e^2 + 2*(10*a^3*b^3 - 11*a^4*b*c)*d^3*e^3 - 3*(5*a^4*b^2 - 2*a^5*c)*d^2*e^4)/(a^8*b^2 - 4*a^9*c)))*sqrt(-(a^3*b*e^3 - (b^4 - 4*a*b^2*c + 2*a^2*c^2)*d^3 + 3*(a*b^3 - 3*a^2*b*c)*d^2*e - 3*(a^2*b^2 - 2*a^3*c)*d*e^2 + (a^4*b^2 - 4*a^5*c)*sqrt(-(6*a^5*b*d*e^5 - a^6*e^6 - (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*d^6 + 6*(a*b^5 - 3*a^2*b^3*c + 2*a^3*b*c^2)*d^5*e - 3*(5*a^2*b^4 - 10*a^3*b^2*c + 3*a^4*c^2)*d^4*e^2 + 2*(10*a^3*b^3 - 11*a^4*b*c)*d^3*e^3 - 3*(5*a^4*b^2 - 2*a^5*c)*d^2*e^4)/(a^8*b^2 - 4*a^9*c)))/(a^4*b^2 - 4*a^5*c)) - 4*(4*a^3*b*c*d*e^4 - a^4*c*e^5 + (b^3*c^2 - 2*a*b*c^3)*d^5 - (b^4*c + a*b^2*c^2 - 3*a^2*c^3)*d^4*e + 2*(2*a*b^3*c - a^2*b*c^2)*d^3*e^2 - 2*(3*a^2*b^2*c - a^3*c^2)*d^2*e^3)*sqrt(e*x + d)) + sqrt(2)*a^2*x*sqrt(-(a^3*b*e^3 - (b^4 - 4*a*b^2*c + 2*a^2*c^2)*d^3 + 3*(a*b^3 - 3*a^2*b*c)*d^2*e - 3*(a^2*b^2 - 2*a^3*c)*d*e^2 - (a^4*b^2 - 4*a^5*c)*sqrt(-(6*a^5*b*d*e^5 - a^6*e^6 - (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*d^6 + 6*(a*b^5 - 3*a^2*b^3*c + 2*a^3*b*c^2)*d^5*e - 3*(5*a^2*b^4 - 10*a^3*b^2*c + 3*a^4*c^2)*d^4*e^2 + 2*(10*a^3*b^3 - 11*a^4*b*c)*d^3*e^3 - 3*(5*a^4*b^2 - 2*a^5*c)*d^2*e^4)/(a^8*b^2 - 4*a^9*c)))/(a^4*b^2 - 4*a^5*c))*log(sqrt(2)*((b^6 - 6*a*b^4*c + 8*a^2*b^2*c^2)*d^4 - (4*a*b^5 - 21*a^2*b^3*c + 20*a^3*b*c^2)*d^3*e + 3*(2*a^2*b^4 - 9*a^3*b^2*c + 4*a^4*c^2)*d^2*e^2 - 4*(a^3*b^3 - 4*a^4*b*c)*d*e^3 + (a^4*b^2 - 4*a^5*c)*e^4 - ((a^4*b^4 - 6*a^5*b^2*c + 8*a^6*c^2)*d - (a^5*b^3 - 4*a^6*b*c)*e)*sqrt(-(6*a^5*b*d*e^5 - a^6*e^6 - (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*d^6 + 6*(a*b^5 - 3*a^2*b^3*c + 2*a^3*b*c^2)*d^5*e - 3*(5*a^2*b^4 - 10*a^3*b^2*c + 3*a^4*c^2)*d^4*e^2 + 2*(10*a^3*b^3 - 11*a^4*b*c)*d^3*e^3 - 3*(5*a^4*b^2 - 2*a^5*c)*d^2*e^4)/(a^8*b^2 - 4*a^9*c)))*sqrt(-(a^3*b*e^3 - (b^4 - 4*a*b^2*c + 2*a^2*c^2)*d^3 + 3*(a*b^3 - 3*a^2*b*c)*d^2*e - 3*(a^2*b^2 - 2*a^3*c)*d*e^2 - (a^4*b^2 - 4*a^5*c)*sqrt(-(6*a^5*b*d*e^5 - a^6*e^6 - (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*d^6 + 6*(a*b^5 - 3*a^2*b^3*c + 2*a^3*b*c^2)*d^5*e - 3*(5*a^2*b^4 - 10*a^3*b^2*c + 3*a^4*c^2)*d^4*e^2 + 2*(10*a^3*b^3 - 11*a^4*b*c)*d^3*e^3 - 3*(5*a^4*b^2 - 2*a^5*c)*d^2*e^4)/(a^8*b^2 - 4*a^9*c)))/(a^4*b^2 - 4*a^5*c)) - 4*(4*a^3*b*c*d*e^4 - a^4*c*e^5 + (b^3*c^2 - 2*a*b*c^3)*d^5 - (b^4*c + a*b^2*c^2 - 3*a^2*c^3)*d^4*e + 2*(2*a*b^3*c - a^2*b*c^2)*d^3*e^2 - 2*(3*a^2*b^2*c - a^3*c^2)*d^2*e^3)*sqrt(e*x + d)) - sqrt(2)*a^2*x*sqrt(-(a^3*b*e^3 - (b^4 - 4*a*b^2*c + 2*a^2*c^2)*d^3 + 3*(a*b^3 - 3*a^2*b*c)*d^2*e - 3*(a^2*b^2 - 2*a^3*c)*d*e^2 - (a^4*b^2 - 4*a^5*c)*sqrt(-(6*a^5*b*d*e^5 - a^6*e^6 - (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*d^6 + 6*(a*b^5 - 3*a^2*b^3*c + 2*a^3*b*c^2)*d^5*e - 3*(5*a^2*b^4 - 10*a^3*b^2*c + 3*a^4*c^2)*d^4*e^2 + 2*(10*a^3*b^3 - 11*a^4*b*c)*d^3*e^3 - 3*(5*a^4*b^2 - 2*a^5*c)*d^2*e^4)/(a^8*b^2 - 4*a^9*c)))/(a^4*b^2 - 4*a^5*c))*log(-sqrt(2)*((b^6 - 6*a*b^4*c + 8*a^2*b^2*c^2)*d^4 - (4*a*b^5 - 21*a^2*b^3*c + 20*a^3*b*c^2)*d^3*e + 3*(2*a^2*b^4 - 9*a^3*b^2*c + 4*a^4*c^2)*d^2*e^2 - 4*(a^3*b^3 - 4*a^4*b*c)*d*e^3 + (a^4*b^2 - 4*a^5*c)*e^4 - ((a^4*b^4 - 6*a^5*b^2*c + 8*a^6*c^2)*d - (a^5*b^3 - 4*a^6*b*c)*e)*sqrt(-(6*a^5*b*d*e^5 - a^6*e^6 - (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*d^6 + 6*(a*b^5 - 3*a^2*b^3*c + 2*a^3*b*c^2)*d^5*e - 3*(5*a^2*b^4 - 10*a^3*b^2*c + 3*a^4*c^2)*d^4*e^2 + 2*(10*a^3*b^3 - 11*a^4*b*c)*d^3*e^3 - 3*(5*a^4*b^2 - 2*a^5*c)*d^2*e^4)/(a^8*b^2 - 4*a^9*c)))*sqrt(-(a^3*b*e^3 - (b^4 - 4*a*b^2*c + 2*a^2*c^2)*d^3 + 3*(a*b^3 - 3*a^2*b*c)*d^2*e - 3*(a^2*b^2 - 2*a^3*c)*d*e^2 - (a^4*b^2 - 4*a^5*c)*sqrt(-(6*a^5*b*d*e^5 - a^6*e^6 - (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*d^6 + 6*(a*b^5 - 3*a^2*b^3*c + 2*a^3*b*c^2)*d^5*e - 3*(5*a^2*b^4 - 10*a^3*b^2*c + 3*a^4*c^2)*d^4*e^2 + 2*(10*a^3*b^3 - 11*a^4*b*c)*d^3*e^3 - 3*(5*a^4*b^2 - 2*a^5*c)*d^2*e^4)/(a^8*b^2 - 4*a^9*c)))/(a^4*b^2 - 4*a^5*c)) - 4*(4*a^3*b*c*d*e^4 - a^4*c*e^5 + (b^3*c^2 - 2*a*b*c^3)*d^5 - (b^4*c + a*b^2*c^2 - 3*a^2*c^3)*d^4*e + 2*(2*a*b^3*c - a^2*b*c^2)*d^3*e^2 - 2*(3*a^2*b^2*c - a^3*c^2)*d^2*e^3)*sqrt(e*x + d)) + (2*b*d - 3*a*e)*sqrt(d)*x*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) + 2*sqrt(e*x + d)*a*d)/(a^2*x), -1/2*(sqrt(2)*a^2*x*sqrt(-(a^3*b*e^3 - (b^4 - 4*a*b^2*c + 2*a^2*c^2)*d^3 + 3*(a*b^3 - 3*a^2*b*c)*d^2*e - 3*(a^2*b^2 - 2*a^3*c)*d*e^2 + (a^4*b^2 - 4*a^5*c)*sqrt(-(6*a^5*b*d*e^5 - a^6*e^6 - (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*d^6 + 6*(a*b^5 - 3*a^2*b^3*c + 2*a^3*b*c^2)*d^5*e - 3*(5*a^2*b^4 - 10*a^3*b^2*c + 3*a^4*c^2)*d^4*e^2 + 2*(10*a^3*b^3 - 11*a^4*b*c)*d^3*e^3 - 3*(5*a^4*b^2 - 2*a^5*c)*d^2*e^4)/(a^8*b^2 - 4*a^9*c)))/(a^4*b^2 - 4*a^5*c))*log(sqrt(2)*((b^6 - 6*a*b^4*c + 8*a^2*b^2*c^2)*d^4 - (4*a*b^5 - 21*a^2*b^3*c + 20*a^3*b*c^2)*d^3*e + 3*(2*a^2*b^4 - 9*a^3*b^2*c + 4*a^4*c^2)*d^2*e^2 - 4*(a^3*b^3 - 4*a^4*b*c)*d*e^3 + (a^4*b^2 - 4*a^5*c)*e^4 + ((a^4*b^4 - 6*a^5*b^2*c + 8*a^6*c^2)*d - (a^5*b^3 - 4*a^6*b*c)*e)*sqrt(-(6*a^5*b*d*e^5 - a^6*e^6 - (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*d^6 + 6*(a*b^5 - 3*a^2*b^3*c + 2*a^3*b*c^2)*d^5*e - 3*(5*a^2*b^4 - 10*a^3*b^2*c + 3*a^4*c^2)*d^4*e^2 + 2*(10*a^3*b^3 - 11*a^4*b*c)*d^3*e^3 - 3*(5*a^4*b^2 - 2*a^5*c)*d^2*e^4)/(a^8*b^2 - 4*a^9*c)))*sqrt(-(a^3*b*e^3 - (b^4 - 4*a*b^2*c + 2*a^2*c^2)*d^3 + 3*(a*b^3 - 3*a^2*b*c)*d^2*e - 3*(a^2*b^2 - 2*a^3*c)*d*e^2 + (a^4*b^2 - 4*a^5*c)*sqrt(-(6*a^5*b*d*e^5 - a^6*e^6 - (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*d^6 + 6*(a*b^5 - 3*a^2*b^3*c + 2*a^3*b*c^2)*d^5*e - 3*(5*a^2*b^4 - 10*a^3*b^2*c + 3*a^4*c^2)*d^4*e^2 + 2*(10*a^3*b^3 - 11*a^4*b*c)*d^3*e^3 - 3*(5*a^4*b^2 - 2*a^5*c)*d^2*e^4)/(a^8*b^2 - 4*a^9*c)))/(a^4*b^2 - 4*a^5*c)) - 4*(4*a^3*b*c*d*e^4 - a^4*c*e^5 + (b^3*c^2 - 2*a*b*c^3)*d^5 - (b^4*c + a*b^2*c^2 - 3*a^2*c^3)*d^4*e + 2*(2*a*b^3*c - a^2*b*c^2)*d^3*e^2 - 2*(3*a^2*b^2*c - a^3*c^2)*d^2*e^3)*sqrt(e*x + d)) - sqrt(2)*a^2*x*sqrt(-(a^3*b*e^3 - (b^4 - 4*a*b^2*c + 2*a^2*c^2)*d^3 + 3*(a*b^3 - 3*a^2*b*c)*d^2*e - 3*(a^2*b^2 - 2*a^3*c)*d*e^2 + (a^4*b^2 - 4*a^5*c)*sqrt(-(6*a^5*b*d*e^5 - a^6*e^6 - (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*d^6 + 6*(a*b^5 - 3*a^2*b^3*c + 2*a^3*b*c^2)*d^5*e - 3*(5*a^2*b^4 - 10*a^3*b^2*c + 3*a^4*c^2)*d^4*e^2 + 2*(10*a^3*b^3 - 11*a^4*b*c)*d^3*e^3 - 3*(5*a^4*b^2 - 2*a^5*c)*d^2*e^4)/(a^8*b^2 - 4*a^9*c)))/(a^4*b^2 - 4*a^5*c))*log(-sqrt(2)*((b^6 - 6*a*b^4*c + 8*a^2*b^2*c^2)*d^4 - (4*a*b^5 - 21*a^2*b^3*c + 20*a^3*b*c^2)*d^3*e + 3*(2*a^2*b^4 - 9*a^3*b^2*c + 4*a^4*c^2)*d^2*e^2 - 4*(a^3*b^3 - 4*a^4*b*c)*d*e^3 + (a^4*b^2 - 4*a^5*c)*e^4 + ((a^4*b^4 - 6*a^5*b^2*c + 8*a^6*c^2)*d - (a^5*b^3 - 4*a^6*b*c)*e)*sqrt(-(6*a^5*b*d*e^5 - a^6*e^6 - (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*d^6 + 6*(a*b^5 - 3*a^2*b^3*c + 2*a^3*b*c^2)*d^5*e - 3*(5*a^2*b^4 - 10*a^3*b^2*c + 3*a^4*c^2)*d^4*e^2 + 2*(10*a^3*b^3 - 11*a^4*b*c)*d^3*e^3 - 3*(5*a^4*b^2 - 2*a^5*c)*d^2*e^4)/(a^8*b^2 - 4*a^9*c)))*sqrt(-(a^3*b*e^3 - (b^4 - 4*a*b^2*c + 2*a^2*c^2)*d^3 + 3*(a*b^3 - 3*a^2*b*c)*d^2*e - 3*(a^2*b^2 - 2*a^3*c)*d*e^2 + (a^4*b^2 - 4*a^5*c)*sqrt(-(6*a^5*b*d*e^5 - a^6*e^6 - (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*d^6 + 6*(a*b^5 - 3*a^2*b^3*c + 2*a^3*b*c^2)*d^5*e - 3*(5*a^2*b^4 - 10*a^3*b^2*c + 3*a^4*c^2)*d^4*e^2 + 2*(10*a^3*b^3 - 11*a^4*b*c)*d^3*e^3 - 3*(5*a^4*b^2 - 2*a^5*c)*d^2*e^4)/(a^8*b^2 - 4*a^9*c)))/(a^4*b^2 - 4*a^5*c)) - 4*(4*a^3*b*c*d*e^4 - a^4*c*e^5 + (b^3*c^2 - 2*a*b*c^3)*d^5 - (b^4*c + a*b^2*c^2 - 3*a^2*c^3)*d^4*e + 2*(2*a*b^3*c - a^2*b*c^2)*d^3*e^2 - 2*(3*a^2*b^2*c - a^3*c^2)*d^2*e^3)*sqrt(e*x + d)) + sqrt(2)*a^2*x*sqrt(-(a^3*b*e^3 - (b^4 - 4*a*b^2*c + 2*a^2*c^2)*d^3 + 3*(a*b^3 - 3*a^2*b*c)*d^2*e - 3*(a^2*b^2 - 2*a^3*c)*d*e^2 - (a^4*b^2 - 4*a^5*c)*sqrt(-(6*a^5*b*d*e^5 - a^6*e^6 - (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*d^6 + 6*(a*b^5 - 3*a^2*b^3*c + 2*a^3*b*c^2)*d^5*e - 3*(5*a^2*b^4 - 10*a^3*b^2*c + 3*a^4*c^2)*d^4*e^2 + 2*(10*a^3*b^3 - 11*a^4*b*c)*d^3*e^3 - 3*(5*a^4*b^2 - 2*a^5*c)*d^2*e^4)/(a^8*b^2 - 4*a^9*c)))/(a^4*b^2 - 4*a^5*c))*log(sqrt(2)*((b^6 - 6*a*b^4*c + 8*a^2*b^2*c^2)*d^4 - (4*a*b^5 - 21*a^2*b^3*c + 20*a^3*b*c^2)*d^3*e + 3*(2*a^2*b^4 - 9*a^3*b^2*c + 4*a^4*c^2)*d^2*e^2 - 4*(a^3*b^3 - 4*a^4*b*c)*d*e^3 + (a^4*b^2 - 4*a^5*c)*e^4 - ((a^4*b^4 - 6*a^5*b^2*c + 8*a^6*c^2)*d - (a^5*b^3 - 4*a^6*b*c)*e)*sqrt(-(6*a^5*b*d*e^5 - a^6*e^6 - (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*d^6 + 6*(a*b^5 - 3*a^2*b^3*c + 2*a^3*b*c^2)*d^5*e - 3*(5*a^2*b^4 - 10*a^3*b^2*c + 3*a^4*c^2)*d^4*e^2 + 2*(10*a^3*b^3 - 11*a^4*b*c)*d^3*e^3 - 3*(5*a^4*b^2 - 2*a^5*c)*d^2*e^4)/(a^8*b^2 - 4*a^9*c)))*sqrt(-(a^3*b*e^3 - (b^4 - 4*a*b^2*c + 2*a^2*c^2)*d^3 + 3*(a*b^3 - 3*a^2*b*c)*d^2*e - 3*(a^2*b^2 - 2*a^3*c)*d*e^2 - (a^4*b^2 - 4*a^5*c)*sqrt(-(6*a^5*b*d*e^5 - a^6*e^6 - (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*d^6 + 6*(a*b^5 - 3*a^2*b^3*c + 2*a^3*b*c^2)*d^5*e - 3*(5*a^2*b^4 - 10*a^3*b^2*c + 3*a^4*c^2)*d^4*e^2 + 2*(10*a^3*b^3 - 11*a^4*b*c)*d^3*e^3 - 3*(5*a^4*b^2 - 2*a^5*c)*d^2*e^4)/(a^8*b^2 - 4*a^9*c)))/(a^4*b^2 - 4*a^5*c)) - 4*(4*a^3*b*c*d*e^4 - a^4*c*e^5 + (b^3*c^2 - 2*a*b*c^3)*d^5 - (b^4*c + a*b^2*c^2 - 3*a^2*c^3)*d^4*e + 2*(2*a*b^3*c - a^2*b*c^2)*d^3*e^2 - 2*(3*a^2*b^2*c - a^3*c^2)*d^2*e^3)*sqrt(e*x + d)) - sqrt(2)*a^2*x*sqrt(-(a^3*b*e^3 - (b^4 - 4*a*b^2*c + 2*a^2*c^2)*d^3 + 3*(a*b^3 - 3*a^2*b*c)*d^2*e - 3*(a^2*b^2 - 2*a^3*c)*d*e^2 - (a^4*b^2 - 4*a^5*c)*sqrt(-(6*a^5*b*d*e^5 - a^6*e^6 - (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*d^6 + 6*(a*b^5 - 3*a^2*b^3*c + 2*a^3*b*c^2)*d^5*e - 3*(5*a^2*b^4 - 10*a^3*b^2*c + 3*a^4*c^2)*d^4*e^2 + 2*(10*a^3*b^3 - 11*a^4*b*c)*d^3*e^3 - 3*(5*a^4*b^2 - 2*a^5*c)*d^2*e^4)/(a^8*b^2 - 4*a^9*c)))/(a^4*b^2 - 4*a^5*c))*log(-sqrt(2)*((b^6 - 6*a*b^4*c + 8*a^2*b^2*c^2)*d^4 - (4*a*b^5 - 21*a^2*b^3*c + 20*a^3*b*c^2)*d^3*e + 3*(2*a^2*b^4 - 9*a^3*b^2*c + 4*a^4*c^2)*d^2*e^2 - 4*(a^3*b^3 - 4*a^4*b*c)*d*e^3 + (a^4*b^2 - 4*a^5*c)*e^4 - ((a^4*b^4 - 6*a^5*b^2*c + 8*a^6*c^2)*d - (a^5*b^3 - 4*a^6*b*c)*e)*sqrt(-(6*a^5*b*d*e^5 - a^6*e^6 - (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*d^6 + 6*(a*b^5 - 3*a^2*b^3*c + 2*a^3*b*c^2)*d^5*e - 3*(5*a^2*b^4 - 10*a^3*b^2*c + 3*a^4*c^2)*d^4*e^2 + 2*(10*a^3*b^3 - 11*a^4*b*c)*d^3*e^3 - 3*(5*a^4*b^2 - 2*a^5*c)*d^2*e^4)/(a^8*b^2 - 4*a^9*c)))*sqrt(-(a^3*b*e^3 - (b^4 - 4*a*b^2*c + 2*a^2*c^2)*d^3 + 3*(a*b^3 - 3*a^2*b*c)*d^2*e - 3*(a^2*b^2 - 2*a^3*c)*d*e^2 - (a^4*b^2 - 4*a^5*c)*sqrt(-(6*a^5*b*d*e^5 - a^6*e^6 - (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*d^6 + 6*(a*b^5 - 3*a^2*b^3*c + 2*a^3*b*c^2)*d^5*e - 3*(5*a^2*b^4 - 10*a^3*b^2*c + 3*a^4*c^2)*d^4*e^2 + 2*(10*a^3*b^3 - 11*a^4*b*c)*d^3*e^3 - 3*(5*a^4*b^2 - 2*a^5*c)*d^2*e^4)/(a^8*b^2 - 4*a^9*c)))/(a^4*b^2 - 4*a^5*c)) - 4*(4*a^3*b*c*d*e^4 - a^4*c*e^5 + (b^3*c^2 - 2*a*b*c^3)*d^5 - (b^4*c + a*b^2*c^2 - 3*a^2*c^3)*d^4*e + 2*(2*a*b^3*c - a^2*b*c^2)*d^3*e^2 - 2*(3*a^2*b^2*c - a^3*c^2)*d^2*e^3)*sqrt(e*x + d)) + 2*(2*b*d - 3*a*e)*sqrt(-d)*x*arctan(sqrt(e*x + d)*sqrt(-d)/d) + 2*sqrt(e*x + d)*a*d)/(a^2*x)]","B",0
540,-1,0,0,0.000000," ","integrate((e*x+d)^(3/2)/x^3/(c*x^2+b*x+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
541,0,0,0,0.426696," ","integrate(x^m*(f*x+e)^n/(c*x^2+b*x+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(f x + e\right)}^{n} x^{m}}{c x^{2} + b x + a}, x\right)"," ",0,"integral((f*x + e)^n*x^m/(c*x^2 + b*x + a), x)","F",0
542,0,0,0,0.427217," ","integrate(x^3*(f*x+e)^n/(c*x^2+b*x+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(f x + e\right)}^{n} x^{3}}{c x^{2} + b x + a}, x\right)"," ",0,"integral((f*x + e)^n*x^3/(c*x^2 + b*x + a), x)","F",0
543,0,0,0,0.412539," ","integrate(x^2*(f*x+e)^n/(c*x^2+b*x+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(f x + e\right)}^{n} x^{2}}{c x^{2} + b x + a}, x\right)"," ",0,"integral((f*x + e)^n*x^2/(c*x^2 + b*x + a), x)","F",0
544,0,0,0,0.413552," ","integrate(x*(f*x+e)^n/(c*x^2+b*x+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(f x + e\right)}^{n} x}{c x^{2} + b x + a}, x\right)"," ",0,"integral((f*x + e)^n*x/(c*x^2 + b*x + a), x)","F",0
545,0,0,0,0.410618," ","integrate((f*x+e)^n/(c*x^2+b*x+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(f x + e\right)}^{n}}{c x^{2} + b x + a}, x\right)"," ",0,"integral((f*x + e)^n/(c*x^2 + b*x + a), x)","F",0
546,0,0,0,0.427450," ","integrate((f*x+e)^n/x/(c*x^2+b*x+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(f x + e\right)}^{n}}{c x^{3} + b x^{2} + a x}, x\right)"," ",0,"integral((f*x + e)^n/(c*x^3 + b*x^2 + a*x), x)","F",0
547,0,0,0,0.407320," ","integrate((f*x+e)^n/x^2/(c*x^2+b*x+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(f x + e\right)}^{n}}{c x^{4} + b x^{3} + a x^{2}}, x\right)"," ",0,"integral((f*x + e)^n/(c*x^4 + b*x^3 + a*x^2), x)","F",0
548,1,176,0,0.385620," ","integrate((e*x+d)^4*(g*x+f)^2/(-e^2*x^2+d^2),x, algorithm=""fricas"")","-\frac{6 \, e^{5} g^{2} x^{5} + 15 \, {\left(e^{5} f g + 2 \, d e^{4} g^{2}\right)} x^{4} + 10 \, {\left(e^{5} f^{2} + 8 \, d e^{4} f g + 7 \, d^{2} e^{3} g^{2}\right)} x^{3} + 30 \, {\left(2 \, d e^{4} f^{2} + 7 \, d^{2} e^{3} f g + 4 \, d^{3} e^{2} g^{2}\right)} x^{2} + 30 \, {\left(7 \, d^{2} e^{3} f^{2} + 16 \, d^{3} e^{2} f g + 8 \, d^{4} e g^{2}\right)} x + 240 \, {\left(d^{3} e^{2} f^{2} + 2 \, d^{4} e f g + d^{5} g^{2}\right)} \log\left(e x - d\right)}{30 \, e^{3}}"," ",0,"-1/30*(6*e^5*g^2*x^5 + 15*(e^5*f*g + 2*d*e^4*g^2)*x^4 + 10*(e^5*f^2 + 8*d*e^4*f*g + 7*d^2*e^3*g^2)*x^3 + 30*(2*d*e^4*f^2 + 7*d^2*e^3*f*g + 4*d^3*e^2*g^2)*x^2 + 30*(7*d^2*e^3*f^2 + 16*d^3*e^2*f*g + 8*d^4*e*g^2)*x + 240*(d^3*e^2*f^2 + 2*d^4*e*f*g + d^5*g^2)*log(e*x - d))/e^3","A",0
549,1,139,0,0.409579," ","integrate((e*x+d)^3*(g*x+f)^2/(-e^2*x^2+d^2),x, algorithm=""fricas"")","-\frac{3 \, e^{4} g^{2} x^{4} + 4 \, {\left(2 \, e^{4} f g + 3 \, d e^{3} g^{2}\right)} x^{3} + 6 \, {\left(e^{4} f^{2} + 6 \, d e^{3} f g + 4 \, d^{2} e^{2} g^{2}\right)} x^{2} + 12 \, {\left(3 \, d e^{3} f^{2} + 8 \, d^{2} e^{2} f g + 4 \, d^{3} e g^{2}\right)} x + 48 \, {\left(d^{2} e^{2} f^{2} + 2 \, d^{3} e f g + d^{4} g^{2}\right)} \log\left(e x - d\right)}{12 \, e^{3}}"," ",0,"-1/12*(3*e^4*g^2*x^4 + 4*(2*e^4*f*g + 3*d*e^3*g^2)*x^3 + 6*(e^4*f^2 + 6*d*e^3*f*g + 4*d^2*e^2*g^2)*x^2 + 12*(3*d*e^3*f^2 + 8*d^2*e^2*f*g + 4*d^3*e*g^2)*x + 48*(d^2*e^2*f^2 + 2*d^3*e*f*g + d^4*g^2)*log(e*x - d))/e^3","A",0
550,1,98,0,0.388374," ","integrate((e*x+d)^2*(g*x+f)^2/(-e^2*x^2+d^2),x, algorithm=""fricas"")","-\frac{e^{3} g^{2} x^{3} + 3 \, {\left(e^{3} f g + d e^{2} g^{2}\right)} x^{2} + 3 \, {\left(e^{3} f^{2} + 4 \, d e^{2} f g + 2 \, d^{2} e g^{2}\right)} x + 6 \, {\left(d e^{2} f^{2} + 2 \, d^{2} e f g + d^{3} g^{2}\right)} \log\left(e x - d\right)}{3 \, e^{3}}"," ",0,"-1/3*(e^3*g^2*x^3 + 3*(e^3*f*g + d*e^2*g^2)*x^2 + 3*(e^3*f^2 + 4*d*e^2*f*g + 2*d^2*e*g^2)*x + 6*(d*e^2*f^2 + 2*d^2*e*f*g + d^3*g^2)*log(e*x - d))/e^3","A",0
551,1,64,0,0.390481," ","integrate((e*x+d)*(g*x+f)^2/(-e^2*x^2+d^2),x, algorithm=""fricas"")","-\frac{e^{2} g^{2} x^{2} + 2 \, {\left(2 \, e^{2} f g + d e g^{2}\right)} x + 2 \, {\left(e^{2} f^{2} + 2 \, d e f g + d^{2} g^{2}\right)} \log\left(e x - d\right)}{2 \, e^{3}}"," ",0,"-1/2*(e^2*g^2*x^2 + 2*(2*e^2*f*g + d*e*g^2)*x + 2*(e^2*f^2 + 2*d*e*f*g + d^2*g^2)*log(e*x - d))/e^3","A",0
552,1,76,0,0.407409," ","integrate((g*x+f)^2/(-e^2*x^2+d^2),x, algorithm=""fricas"")","-\frac{2 \, d e g^{2} x - {\left(e^{2} f^{2} - 2 \, d e f g + d^{2} g^{2}\right)} \log\left(e x + d\right) + {\left(e^{2} f^{2} + 2 \, d e f g + d^{2} g^{2}\right)} \log\left(e x - d\right)}{2 \, d e^{3}}"," ",0,"-1/2*(2*d*e*g^2*x - (e^2*f^2 - 2*d*e*f*g + d^2*g^2)*log(e*x + d) + (e^2*f^2 + 2*d*e*f*g + d^2*g^2)*log(e*x - d))/(d*e^3)","A",0
553,1,165,0,0.395584," ","integrate((g*x+f)^2/(e*x+d)/(-e^2*x^2+d^2),x, algorithm=""fricas"")","-\frac{2 \, d e^{2} f^{2} - 4 \, d^{2} e f g + 2 \, d^{3} g^{2} - {\left(d e^{2} f^{2} + 2 \, d^{2} e f g - 3 \, d^{3} g^{2} + {\left(e^{3} f^{2} + 2 \, d e^{2} f g - 3 \, d^{2} e g^{2}\right)} x\right)} \log\left(e x + d\right) + {\left(d e^{2} f^{2} + 2 \, d^{2} e f g + d^{3} g^{2} + {\left(e^{3} f^{2} + 2 \, d e^{2} f g + d^{2} e g^{2}\right)} x\right)} \log\left(e x - d\right)}{4 \, {\left(d^{2} e^{4} x + d^{3} e^{3}\right)}}"," ",0,"-1/4*(2*d*e^2*f^2 - 4*d^2*e*f*g + 2*d^3*g^2 - (d*e^2*f^2 + 2*d^2*e*f*g - 3*d^3*g^2 + (e^3*f^2 + 2*d*e^2*f*g - 3*d^2*e*g^2)*x)*log(e*x + d) + (d*e^2*f^2 + 2*d^2*e*f*g + d^3*g^2 + (e^3*f^2 + 2*d*e^2*f*g + d^2*e*g^2)*x)*log(e*x - d))/(d^2*e^4*x + d^3*e^3)","B",0
554,1,271,0,0.405003," ","integrate((g*x+f)^2/(e*x+d)^2/(-e^2*x^2+d^2),x, algorithm=""fricas"")","-\frac{4 \, d^{2} e^{2} f^{2} - 4 \, d^{4} g^{2} + 2 \, {\left(d e^{3} f^{2} + 2 \, d^{2} e^{2} f g - 3 \, d^{3} e g^{2}\right)} x - {\left(d^{2} e^{2} f^{2} + 2 \, d^{3} e f g + d^{4} g^{2} + {\left(e^{4} f^{2} + 2 \, d e^{3} f g + d^{2} e^{2} g^{2}\right)} x^{2} + 2 \, {\left(d e^{3} f^{2} + 2 \, d^{2} e^{2} f g + d^{3} e g^{2}\right)} x\right)} \log\left(e x + d\right) + {\left(d^{2} e^{2} f^{2} + 2 \, d^{3} e f g + d^{4} g^{2} + {\left(e^{4} f^{2} + 2 \, d e^{3} f g + d^{2} e^{2} g^{2}\right)} x^{2} + 2 \, {\left(d e^{3} f^{2} + 2 \, d^{2} e^{2} f g + d^{3} e g^{2}\right)} x\right)} \log\left(e x - d\right)}{8 \, {\left(d^{3} e^{5} x^{2} + 2 \, d^{4} e^{4} x + d^{5} e^{3}\right)}}"," ",0,"-1/8*(4*d^2*e^2*f^2 - 4*d^4*g^2 + 2*(d*e^3*f^2 + 2*d^2*e^2*f*g - 3*d^3*e*g^2)*x - (d^2*e^2*f^2 + 2*d^3*e*f*g + d^4*g^2 + (e^4*f^2 + 2*d*e^3*f*g + d^2*e^2*g^2)*x^2 + 2*(d*e^3*f^2 + 2*d^2*e^2*f*g + d^3*e*g^2)*x)*log(e*x + d) + (d^2*e^2*f^2 + 2*d^3*e*f*g + d^4*g^2 + (e^4*f^2 + 2*d*e^3*f*g + d^2*e^2*g^2)*x^2 + 2*(d*e^3*f^2 + 2*d^2*e^2*f*g + d^3*e*g^2)*x)*log(e*x - d))/(d^3*e^5*x^2 + 2*d^4*e^4*x + d^5*e^3)","B",0
555,1,400,0,0.386555," ","integrate((g*x+f)^2/(e*x+d)^3/(-e^2*x^2+d^2),x, algorithm=""fricas"")","-\frac{20 \, d^{3} e^{2} f^{2} + 8 \, d^{4} e f g - 4 \, d^{5} g^{2} + 6 \, {\left(d e^{4} f^{2} + 2 \, d^{2} e^{3} f g + d^{3} e^{2} g^{2}\right)} x^{2} + 6 \, {\left(3 \, d^{2} e^{3} f^{2} + 6 \, d^{3} e^{2} f g - d^{4} e g^{2}\right)} x - 3 \, {\left(d^{3} e^{2} f^{2} + 2 \, d^{4} e f g + d^{5} g^{2} + {\left(e^{5} f^{2} + 2 \, d e^{4} f g + d^{2} e^{3} g^{2}\right)} x^{3} + 3 \, {\left(d e^{4} f^{2} + 2 \, d^{2} e^{3} f g + d^{3} e^{2} g^{2}\right)} x^{2} + 3 \, {\left(d^{2} e^{3} f^{2} + 2 \, d^{3} e^{2} f g + d^{4} e g^{2}\right)} x\right)} \log\left(e x + d\right) + 3 \, {\left(d^{3} e^{2} f^{2} + 2 \, d^{4} e f g + d^{5} g^{2} + {\left(e^{5} f^{2} + 2 \, d e^{4} f g + d^{2} e^{3} g^{2}\right)} x^{3} + 3 \, {\left(d e^{4} f^{2} + 2 \, d^{2} e^{3} f g + d^{3} e^{2} g^{2}\right)} x^{2} + 3 \, {\left(d^{2} e^{3} f^{2} + 2 \, d^{3} e^{2} f g + d^{4} e g^{2}\right)} x\right)} \log\left(e x - d\right)}{48 \, {\left(d^{4} e^{6} x^{3} + 3 \, d^{5} e^{5} x^{2} + 3 \, d^{6} e^{4} x + d^{7} e^{3}\right)}}"," ",0,"-1/48*(20*d^3*e^2*f^2 + 8*d^4*e*f*g - 4*d^5*g^2 + 6*(d*e^4*f^2 + 2*d^2*e^3*f*g + d^3*e^2*g^2)*x^2 + 6*(3*d^2*e^3*f^2 + 6*d^3*e^2*f*g - d^4*e*g^2)*x - 3*(d^3*e^2*f^2 + 2*d^4*e*f*g + d^5*g^2 + (e^5*f^2 + 2*d*e^4*f*g + d^2*e^3*g^2)*x^3 + 3*(d*e^4*f^2 + 2*d^2*e^3*f*g + d^3*e^2*g^2)*x^2 + 3*(d^2*e^3*f^2 + 2*d^3*e^2*f*g + d^4*e*g^2)*x)*log(e*x + d) + 3*(d^3*e^2*f^2 + 2*d^4*e*f*g + d^5*g^2 + (e^5*f^2 + 2*d*e^4*f*g + d^2*e^3*g^2)*x^3 + 3*(d*e^4*f^2 + 2*d^2*e^3*f*g + d^3*e^2*g^2)*x^2 + 3*(d^2*e^3*f^2 + 2*d^3*e^2*f*g + d^4*e*g^2)*x)*log(e*x - d))/(d^4*e^6*x^3 + 3*d^5*e^5*x^2 + 3*d^6*e^4*x + d^7*e^3)","B",0
556,1,511,0,0.421762," ","integrate((g*x+f)^2/(e*x+d)^4/(-e^2*x^2+d^2),x, algorithm=""fricas"")","-\frac{32 \, d^{4} e^{2} f^{2} + 16 \, d^{5} e f g + 6 \, {\left(d e^{5} f^{2} + 2 \, d^{2} e^{4} f g + d^{3} e^{3} g^{2}\right)} x^{3} + 24 \, {\left(d^{2} e^{4} f^{2} + 2 \, d^{3} e^{3} f g + d^{4} e^{2} g^{2}\right)} x^{2} + 2 \, {\left(19 \, d^{3} e^{3} f^{2} + 38 \, d^{4} e^{2} f g + 3 \, d^{5} e g^{2}\right)} x - 3 \, {\left(d^{4} e^{2} f^{2} + 2 \, d^{5} e f g + d^{6} g^{2} + {\left(e^{6} f^{2} + 2 \, d e^{5} f g + d^{2} e^{4} g^{2}\right)} x^{4} + 4 \, {\left(d e^{5} f^{2} + 2 \, d^{2} e^{4} f g + d^{3} e^{3} g^{2}\right)} x^{3} + 6 \, {\left(d^{2} e^{4} f^{2} + 2 \, d^{3} e^{3} f g + d^{4} e^{2} g^{2}\right)} x^{2} + 4 \, {\left(d^{3} e^{3} f^{2} + 2 \, d^{4} e^{2} f g + d^{5} e g^{2}\right)} x\right)} \log\left(e x + d\right) + 3 \, {\left(d^{4} e^{2} f^{2} + 2 \, d^{5} e f g + d^{6} g^{2} + {\left(e^{6} f^{2} + 2 \, d e^{5} f g + d^{2} e^{4} g^{2}\right)} x^{4} + 4 \, {\left(d e^{5} f^{2} + 2 \, d^{2} e^{4} f g + d^{3} e^{3} g^{2}\right)} x^{3} + 6 \, {\left(d^{2} e^{4} f^{2} + 2 \, d^{3} e^{3} f g + d^{4} e^{2} g^{2}\right)} x^{2} + 4 \, {\left(d^{3} e^{3} f^{2} + 2 \, d^{4} e^{2} f g + d^{5} e g^{2}\right)} x\right)} \log\left(e x - d\right)}{96 \, {\left(d^{5} e^{7} x^{4} + 4 \, d^{6} e^{6} x^{3} + 6 \, d^{7} e^{5} x^{2} + 4 \, d^{8} e^{4} x + d^{9} e^{3}\right)}}"," ",0,"-1/96*(32*d^4*e^2*f^2 + 16*d^5*e*f*g + 6*(d*e^5*f^2 + 2*d^2*e^4*f*g + d^3*e^3*g^2)*x^3 + 24*(d^2*e^4*f^2 + 2*d^3*e^3*f*g + d^4*e^2*g^2)*x^2 + 2*(19*d^3*e^3*f^2 + 38*d^4*e^2*f*g + 3*d^5*e*g^2)*x - 3*(d^4*e^2*f^2 + 2*d^5*e*f*g + d^6*g^2 + (e^6*f^2 + 2*d*e^5*f*g + d^2*e^4*g^2)*x^4 + 4*(d*e^5*f^2 + 2*d^2*e^4*f*g + d^3*e^3*g^2)*x^3 + 6*(d^2*e^4*f^2 + 2*d^3*e^3*f*g + d^4*e^2*g^2)*x^2 + 4*(d^3*e^3*f^2 + 2*d^4*e^2*f*g + d^5*e*g^2)*x)*log(e*x + d) + 3*(d^4*e^2*f^2 + 2*d^5*e*f*g + d^6*g^2 + (e^6*f^2 + 2*d*e^5*f*g + d^2*e^4*g^2)*x^4 + 4*(d*e^5*f^2 + 2*d^2*e^4*f*g + d^3*e^3*g^2)*x^3 + 6*(d^2*e^4*f^2 + 2*d^3*e^3*f*g + d^4*e^2*g^2)*x^2 + 4*(d^3*e^3*f^2 + 2*d^4*e^2*f*g + d^5*e*g^2)*x)*log(e*x - d))/(d^5*e^7*x^4 + 4*d^6*e^6*x^3 + 6*d^7*e^5*x^2 + 4*d^8*e^4*x + d^9*e^3)","B",0
557,1,328,0,0.415037," ","integrate((e*x+d)^7*(g*x+f)^2/(-e^2*x^2+d^2)^2,x, algorithm=""fricas"")","\frac{10 \, e^{7} g^{2} x^{7} - 1920 \, d^{5} e^{2} f^{2} - 3840 \, d^{6} e f g - 1920 \, d^{7} g^{2} + 2 \, {\left(12 \, e^{7} f g + 37 \, d e^{6} g^{2}\right)} x^{6} + 3 \, {\left(5 \, e^{7} f^{2} + 62 \, d e^{6} f g + 87 \, d^{2} e^{5} g^{2}\right)} x^{5} + 5 \, {\left(25 \, d e^{6} f^{2} + 142 \, d^{2} e^{5} f g + 127 \, d^{3} e^{4} g^{2}\right)} x^{4} + 10 \, {\left(55 \, d^{2} e^{5} f^{2} + 202 \, d^{3} e^{4} f g + 142 \, d^{4} e^{3} g^{2}\right)} x^{3} + 90 \, {\left(25 \, d^{3} e^{4} f^{2} + 74 \, d^{4} e^{3} f g + 48 \, d^{5} e^{2} g^{2}\right)} x^{2} - 60 \, {\left(49 \, d^{4} e^{3} f^{2} + 160 \, d^{5} e^{2} f g + 112 \, d^{6} e g^{2}\right)} x - 960 \, {\left(5 \, d^{5} e^{2} f^{2} + 14 \, d^{6} e f g + 9 \, d^{7} g^{2} - {\left(5 \, d^{4} e^{3} f^{2} + 14 \, d^{5} e^{2} f g + 9 \, d^{6} e g^{2}\right)} x\right)} \log\left(e x - d\right)}{60 \, {\left(e^{4} x - d e^{3}\right)}}"," ",0,"1/60*(10*e^7*g^2*x^7 - 1920*d^5*e^2*f^2 - 3840*d^6*e*f*g - 1920*d^7*g^2 + 2*(12*e^7*f*g + 37*d*e^6*g^2)*x^6 + 3*(5*e^7*f^2 + 62*d*e^6*f*g + 87*d^2*e^5*g^2)*x^5 + 5*(25*d*e^6*f^2 + 142*d^2*e^5*f*g + 127*d^3*e^4*g^2)*x^4 + 10*(55*d^2*e^5*f^2 + 202*d^3*e^4*f*g + 142*d^4*e^3*g^2)*x^3 + 90*(25*d^3*e^4*f^2 + 74*d^4*e^3*f*g + 48*d^5*e^2*g^2)*x^2 - 60*(49*d^4*e^3*f^2 + 160*d^5*e^2*f*g + 112*d^6*e*g^2)*x - 960*(5*d^5*e^2*f^2 + 14*d^6*e*f*g + 9*d^7*g^2 - (5*d^4*e^3*f^2 + 14*d^5*e^2*f*g + 9*d^6*e*g^2)*x)*log(e*x - d))/(e^4*x - d*e^3)","A",0
558,1,288,0,0.391637," ","integrate((e*x+d)^6*(g*x+f)^2/(-e^2*x^2+d^2)^2,x, algorithm=""fricas"")","\frac{6 \, e^{6} g^{2} x^{6} - 480 \, d^{4} e^{2} f^{2} - 960 \, d^{5} e f g - 480 \, d^{6} g^{2} + 3 \, {\left(5 \, e^{6} f g + 13 \, d e^{5} g^{2}\right)} x^{5} + 5 \, {\left(2 \, e^{6} f^{2} + 21 \, d e^{5} f g + 25 \, d^{2} e^{4} g^{2}\right)} x^{4} + 10 \, {\left(8 \, d e^{5} f^{2} + 39 \, d^{2} e^{4} f g + 31 \, d^{3} e^{3} g^{2}\right)} x^{3} + 30 \, {\left(14 \, d^{2} e^{4} f^{2} + 47 \, d^{3} e^{3} f g + 32 \, d^{4} e^{2} g^{2}\right)} x^{2} - 30 \, {\left(17 \, d^{3} e^{3} f^{2} + 64 \, d^{4} e^{2} f g + 48 \, d^{5} e g^{2}\right)} x - 960 \, {\left(d^{4} e^{2} f^{2} + 3 \, d^{5} e f g + 2 \, d^{6} g^{2} - {\left(d^{3} e^{3} f^{2} + 3 \, d^{4} e^{2} f g + 2 \, d^{5} e g^{2}\right)} x\right)} \log\left(e x - d\right)}{30 \, {\left(e^{4} x - d e^{3}\right)}}"," ",0,"1/30*(6*e^6*g^2*x^6 - 480*d^4*e^2*f^2 - 960*d^5*e*f*g - 480*d^6*g^2 + 3*(5*e^6*f*g + 13*d*e^5*g^2)*x^5 + 5*(2*e^6*f^2 + 21*d*e^5*f*g + 25*d^2*e^4*g^2)*x^4 + 10*(8*d*e^5*f^2 + 39*d^2*e^4*f*g + 31*d^3*e^3*g^2)*x^3 + 30*(14*d^2*e^4*f^2 + 47*d^3*e^3*f*g + 32*d^4*e^2*g^2)*x^2 - 30*(17*d^3*e^3*f^2 + 64*d^4*e^2*f*g + 48*d^5*e*g^2)*x - 960*(d^4*e^2*f^2 + 3*d^5*e*f*g + 2*d^6*g^2 - (d^3*e^3*f^2 + 3*d^4*e^2*f*g + 2*d^5*e*g^2)*x)*log(e*x - d))/(e^4*x - d*e^3)","A",0
559,1,251,0,0.400154," ","integrate((e*x+d)^5*(g*x+f)^2/(-e^2*x^2+d^2)^2,x, algorithm=""fricas"")","\frac{3 \, e^{5} g^{2} x^{5} - 96 \, d^{3} e^{2} f^{2} - 192 \, d^{4} e f g - 96 \, d^{5} g^{2} + {\left(8 \, e^{5} f g + 17 \, d e^{4} g^{2}\right)} x^{4} + 2 \, {\left(3 \, e^{5} f^{2} + 26 \, d e^{4} f g + 26 \, d^{2} e^{3} g^{2}\right)} x^{3} + 6 \, {\left(9 \, d e^{4} f^{2} + 38 \, d^{2} e^{3} f g + 28 \, d^{3} e^{2} g^{2}\right)} x^{2} - 12 \, {\left(5 \, d^{2} e^{3} f^{2} + 24 \, d^{3} e^{2} f g + 20 \, d^{4} e g^{2}\right)} x - 48 \, {\left(3 \, d^{3} e^{2} f^{2} + 10 \, d^{4} e f g + 7 \, d^{5} g^{2} - {\left(3 \, d^{2} e^{3} f^{2} + 10 \, d^{3} e^{2} f g + 7 \, d^{4} e g^{2}\right)} x\right)} \log\left(e x - d\right)}{12 \, {\left(e^{4} x - d e^{3}\right)}}"," ",0,"1/12*(3*e^5*g^2*x^5 - 96*d^3*e^2*f^2 - 192*d^4*e*f*g - 96*d^5*g^2 + (8*e^5*f*g + 17*d*e^4*g^2)*x^4 + 2*(3*e^5*f^2 + 26*d*e^4*f*g + 26*d^2*e^3*g^2)*x^3 + 6*(9*d*e^4*f^2 + 38*d^2*e^3*f*g + 28*d^3*e^2*g^2)*x^2 - 12*(5*d^2*e^3*f^2 + 24*d^3*e^2*f*g + 20*d^4*e*g^2)*x - 48*(3*d^3*e^2*f^2 + 10*d^4*e*f*g + 7*d^5*g^2 - (3*d^2*e^3*f^2 + 10*d^3*e^2*f*g + 7*d^4*e*g^2)*x)*log(e*x - d))/(e^4*x - d*e^3)","A",0
560,1,206,0,0.386376," ","integrate((e*x+d)^4*(g*x+f)^2/(-e^2*x^2+d^2)^2,x, algorithm=""fricas"")","\frac{e^{4} g^{2} x^{4} - 12 \, d^{2} e^{2} f^{2} - 24 \, d^{3} e f g - 12 \, d^{4} g^{2} + {\left(3 \, e^{4} f g + 5 \, d e^{3} g^{2}\right)} x^{3} + 3 \, {\left(e^{4} f^{2} + 7 \, d e^{3} f g + 6 \, d^{2} e^{2} g^{2}\right)} x^{2} - 3 \, {\left(d e^{3} f^{2} + 8 \, d^{2} e^{2} f g + 8 \, d^{3} e g^{2}\right)} x - 12 \, {\left(d^{2} e^{2} f^{2} + 4 \, d^{3} e f g + 3 \, d^{4} g^{2} - {\left(d e^{3} f^{2} + 4 \, d^{2} e^{2} f g + 3 \, d^{3} e g^{2}\right)} x\right)} \log\left(e x - d\right)}{3 \, {\left(e^{4} x - d e^{3}\right)}}"," ",0,"1/3*(e^4*g^2*x^4 - 12*d^2*e^2*f^2 - 24*d^3*e*f*g - 12*d^4*g^2 + (3*e^4*f*g + 5*d*e^3*g^2)*x^3 + 3*(e^4*f^2 + 7*d*e^3*f*g + 6*d^2*e^2*g^2)*x^2 - 3*(d*e^3*f^2 + 8*d^2*e^2*f*g + 8*d^3*e*g^2)*x - 12*(d^2*e^2*f^2 + 4*d^3*e*f*g + 3*d^4*g^2 - (d*e^3*f^2 + 4*d^2*e^2*f*g + 3*d^3*e*g^2)*x)*log(e*x - d))/(e^4*x - d*e^3)","A",0
561,1,157,0,0.385391," ","integrate((e*x+d)^3*(g*x+f)^2/(-e^2*x^2+d^2)^2,x, algorithm=""fricas"")","\frac{e^{3} g^{2} x^{3} - 4 \, d e^{2} f^{2} - 8 \, d^{2} e f g - 4 \, d^{3} g^{2} + {\left(4 \, e^{3} f g + 5 \, d e^{2} g^{2}\right)} x^{2} - 2 \, {\left(2 \, d e^{2} f g + 3 \, d^{2} e g^{2}\right)} x - 2 \, {\left(d e^{2} f^{2} + 6 \, d^{2} e f g + 5 \, d^{3} g^{2} - {\left(e^{3} f^{2} + 6 \, d e^{2} f g + 5 \, d^{2} e g^{2}\right)} x\right)} \log\left(e x - d\right)}{2 \, {\left(e^{4} x - d e^{3}\right)}}"," ",0,"1/2*(e^3*g^2*x^3 - 4*d*e^2*f^2 - 8*d^2*e*f*g - 4*d^3*g^2 + (4*e^3*f*g + 5*d*e^2*g^2)*x^2 - 2*(2*d*e^2*f*g + 3*d^2*e*g^2)*x - 2*(d*e^2*f^2 + 6*d^2*e*f*g + 5*d^3*g^2 - (e^3*f^2 + 6*d*e^2*f*g + 5*d^2*e*g^2)*x)*log(e*x - d))/(e^4*x - d*e^3)","B",0
562,1,95,0,0.378372," ","integrate((e*x+d)^2*(g*x+f)^2/(-e^2*x^2+d^2)^2,x, algorithm=""fricas"")","\frac{e^{2} g^{2} x^{2} - d e g^{2} x - e^{2} f^{2} - 2 \, d e f g - d^{2} g^{2} - 2 \, {\left(d e f g + d^{2} g^{2} - {\left(e^{2} f g + d e g^{2}\right)} x\right)} \log\left(e x - d\right)}{e^{4} x - d e^{3}}"," ",0,"(e^2*g^2*x^2 - d*e*g^2*x - e^2*f^2 - 2*d*e*f*g - d^2*g^2 - 2*(d*e*f*g + d^2*g^2 - (e^2*f*g + d*e*g^2)*x)*log(e*x - d))/(e^4*x - d*e^3)","A",0
563,1,168,0,0.386906," ","integrate((e*x+d)*(g*x+f)^2/(-e^2*x^2+d^2)^2,x, algorithm=""fricas"")","-\frac{2 \, d e^{2} f^{2} + 4 \, d^{2} e f g + 2 \, d^{3} g^{2} + {\left(d e^{2} f^{2} - 2 \, d^{2} e f g + d^{3} g^{2} - {\left(e^{3} f^{2} - 2 \, d e^{2} f g + d^{2} e g^{2}\right)} x\right)} \log\left(e x + d\right) - {\left(d e^{2} f^{2} - 2 \, d^{2} e f g - 3 \, d^{3} g^{2} - {\left(e^{3} f^{2} - 2 \, d e^{2} f g - 3 \, d^{2} e g^{2}\right)} x\right)} \log\left(e x - d\right)}{4 \, {\left(d^{2} e^{4} x - d^{3} e^{3}\right)}}"," ",0,"-1/4*(2*d*e^2*f^2 + 4*d^2*e*f*g + 2*d^3*g^2 + (d*e^2*f^2 - 2*d^2*e*f*g + d^3*g^2 - (e^3*f^2 - 2*d*e^2*f*g + d^2*e*g^2)*x)*log(e*x + d) - (d*e^2*f^2 - 2*d^2*e*f*g - 3*d^3*g^2 - (e^3*f^2 - 2*d*e^2*f*g - 3*d^2*e*g^2)*x)*log(e*x - d))/(d^2*e^4*x - d^3*e^3)","B",0
564,1,155,0,0.408056," ","integrate((g*x+f)^2/(-e^2*x^2+d^2)^2,x, algorithm=""fricas"")","-\frac{4 \, d^{3} e f g + 2 \, {\left(d e^{3} f^{2} + d^{3} e g^{2}\right)} x + {\left(d^{2} e^{2} f^{2} - d^{4} g^{2} - {\left(e^{4} f^{2} - d^{2} e^{2} g^{2}\right)} x^{2}\right)} \log\left(e x + d\right) - {\left(d^{2} e^{2} f^{2} - d^{4} g^{2} - {\left(e^{4} f^{2} - d^{2} e^{2} g^{2}\right)} x^{2}\right)} \log\left(e x - d\right)}{4 \, {\left(d^{3} e^{5} x^{2} - d^{5} e^{3}\right)}}"," ",0,"-1/4*(4*d^3*e*f*g + 2*(d*e^3*f^2 + d^3*e*g^2)*x + (d^2*e^2*f^2 - d^4*g^2 - (e^4*f^2 - d^2*e^2*g^2)*x^2)*log(e*x + d) - (d^2*e^2*f^2 - d^4*g^2 - (e^4*f^2 - d^2*e^2*g^2)*x^2)*log(e*x - d))/(d^3*e^5*x^2 - d^5*e^3)","B",0
565,1,417,0,0.383939," ","integrate((g*x+f)^2/(e*x+d)/(-e^2*x^2+d^2)^2,x, algorithm=""fricas"")","\frac{4 \, d^{3} e^{2} f^{2} - 8 \, d^{4} e f g - 4 \, d^{5} g^{2} - 2 \, {\left(3 \, d e^{4} f^{2} + 2 \, d^{2} e^{3} f g - d^{3} e^{2} g^{2}\right)} x^{2} - 2 \, {\left(3 \, d^{2} e^{3} f^{2} + 2 \, d^{3} e^{2} f g + 3 \, d^{4} e g^{2}\right)} x - {\left(3 \, d^{3} e^{2} f^{2} + 2 \, d^{4} e f g - d^{5} g^{2} - {\left(3 \, e^{5} f^{2} + 2 \, d e^{4} f g - d^{2} e^{3} g^{2}\right)} x^{3} - {\left(3 \, d e^{4} f^{2} + 2 \, d^{2} e^{3} f g - d^{3} e^{2} g^{2}\right)} x^{2} + {\left(3 \, d^{2} e^{3} f^{2} + 2 \, d^{3} e^{2} f g - d^{4} e g^{2}\right)} x\right)} \log\left(e x + d\right) + {\left(3 \, d^{3} e^{2} f^{2} + 2 \, d^{4} e f g - d^{5} g^{2} - {\left(3 \, e^{5} f^{2} + 2 \, d e^{4} f g - d^{2} e^{3} g^{2}\right)} x^{3} - {\left(3 \, d e^{4} f^{2} + 2 \, d^{2} e^{3} f g - d^{3} e^{2} g^{2}\right)} x^{2} + {\left(3 \, d^{2} e^{3} f^{2} + 2 \, d^{3} e^{2} f g - d^{4} e g^{2}\right)} x\right)} \log\left(e x - d\right)}{16 \, {\left(d^{4} e^{6} x^{3} + d^{5} e^{5} x^{2} - d^{6} e^{4} x - d^{7} e^{3}\right)}}"," ",0,"1/16*(4*d^3*e^2*f^2 - 8*d^4*e*f*g - 4*d^5*g^2 - 2*(3*d*e^4*f^2 + 2*d^2*e^3*f*g - d^3*e^2*g^2)*x^2 - 2*(3*d^2*e^3*f^2 + 2*d^3*e^2*f*g + 3*d^4*e*g^2)*x - (3*d^3*e^2*f^2 + 2*d^4*e*f*g - d^5*g^2 - (3*e^5*f^2 + 2*d*e^4*f*g - d^2*e^3*g^2)*x^3 - (3*d*e^4*f^2 + 2*d^2*e^3*f*g - d^3*e^2*g^2)*x^2 + (3*d^2*e^3*f^2 + 2*d^3*e^2*f*g - d^4*e*g^2)*x)*log(e*x + d) + (3*d^3*e^2*f^2 + 2*d^4*e*f*g - d^5*g^2 - (3*e^5*f^2 + 2*d*e^4*f*g - d^2*e^3*g^2)*x^3 - (3*d*e^4*f^2 + 2*d^2*e^3*f*g - d^3*e^2*g^2)*x^2 + (3*d^2*e^3*f^2 + 2*d^3*e^2*f*g - d^4*e*g^2)*x)*log(e*x - d))/(d^4*e^6*x^3 + d^5*e^5*x^2 - d^6*e^4*x - d^7*e^3)","B",0
566,1,337,0,0.384108," ","integrate((g*x+f)^2/(e*x+d)^2/(-e^2*x^2+d^2)^2,x, algorithm=""fricas"")","\frac{8 \, d^{4} e^{2} f^{2} - 4 \, d^{5} e f g - 4 \, d^{6} g^{2} - 6 \, {\left(d e^{5} f^{2} + d^{2} e^{4} f g\right)} x^{3} - 12 \, {\left(d^{2} e^{4} f^{2} + d^{3} e^{3} f g\right)} x^{2} - 2 \, {\left(d^{3} e^{3} f^{2} + d^{4} e^{2} f g + 4 \, d^{5} e g^{2}\right)} x - 3 \, {\left(d^{4} e^{2} f^{2} + d^{5} e f g - {\left(e^{6} f^{2} + d e^{5} f g\right)} x^{4} - 2 \, {\left(d e^{5} f^{2} + d^{2} e^{4} f g\right)} x^{3} + 2 \, {\left(d^{3} e^{3} f^{2} + d^{4} e^{2} f g\right)} x\right)} \log\left(e x + d\right) + 3 \, {\left(d^{4} e^{2} f^{2} + d^{5} e f g - {\left(e^{6} f^{2} + d e^{5} f g\right)} x^{4} - 2 \, {\left(d e^{5} f^{2} + d^{2} e^{4} f g\right)} x^{3} + 2 \, {\left(d^{3} e^{3} f^{2} + d^{4} e^{2} f g\right)} x\right)} \log\left(e x - d\right)}{24 \, {\left(d^{5} e^{7} x^{4} + 2 \, d^{6} e^{6} x^{3} - 2 \, d^{8} e^{4} x - d^{9} e^{3}\right)}}"," ",0,"1/24*(8*d^4*e^2*f^2 - 4*d^5*e*f*g - 4*d^6*g^2 - 6*(d*e^5*f^2 + d^2*e^4*f*g)*x^3 - 12*(d^2*e^4*f^2 + d^3*e^3*f*g)*x^2 - 2*(d^3*e^3*f^2 + d^4*e^2*f*g + 4*d^5*e*g^2)*x - 3*(d^4*e^2*f^2 + d^5*e*f*g - (e^6*f^2 + d*e^5*f*g)*x^4 - 2*(d*e^5*f^2 + d^2*e^4*f*g)*x^3 + 2*(d^3*e^3*f^2 + d^4*e^2*f*g)*x)*log(e*x + d) + 3*(d^4*e^2*f^2 + d^5*e*f*g - (e^6*f^2 + d*e^5*f*g)*x^4 - 2*(d*e^5*f^2 + d^2*e^4*f*g)*x^3 + 2*(d^3*e^3*f^2 + d^4*e^2*f*g)*x)*log(e*x - d))/(d^5*e^7*x^4 + 2*d^6*e^6*x^3 - 2*d^8*e^4*x - d^9*e^3)","B",0
567,1,648,0,0.403103," ","integrate((g*x+f)^2/(e*x+d)^3/(-e^2*x^2+d^2)^2,x, algorithm=""fricas"")","\frac{64 \, d^{5} e^{2} f^{2} - 16 \, d^{7} g^{2} - 6 \, {\left(5 \, d e^{6} f^{2} + 6 \, d^{2} e^{5} f g + d^{3} e^{4} g^{2}\right)} x^{4} - 18 \, {\left(5 \, d^{2} e^{5} f^{2} + 6 \, d^{3} e^{4} f g + d^{4} e^{3} g^{2}\right)} x^{3} - 14 \, {\left(5 \, d^{3} e^{4} f^{2} + 6 \, d^{4} e^{3} f g + d^{5} e^{2} g^{2}\right)} x^{2} + 6 \, {\left(5 \, d^{4} e^{3} f^{2} + 6 \, d^{5} e^{2} f g - 7 \, d^{6} e g^{2}\right)} x - 3 \, {\left(5 \, d^{5} e^{2} f^{2} + 6 \, d^{6} e f g + d^{7} g^{2} - {\left(5 \, e^{7} f^{2} + 6 \, d e^{6} f g + d^{2} e^{5} g^{2}\right)} x^{5} - 3 \, {\left(5 \, d e^{6} f^{2} + 6 \, d^{2} e^{5} f g + d^{3} e^{4} g^{2}\right)} x^{4} - 2 \, {\left(5 \, d^{2} e^{5} f^{2} + 6 \, d^{3} e^{4} f g + d^{4} e^{3} g^{2}\right)} x^{3} + 2 \, {\left(5 \, d^{3} e^{4} f^{2} + 6 \, d^{4} e^{3} f g + d^{5} e^{2} g^{2}\right)} x^{2} + 3 \, {\left(5 \, d^{4} e^{3} f^{2} + 6 \, d^{5} e^{2} f g + d^{6} e g^{2}\right)} x\right)} \log\left(e x + d\right) + 3 \, {\left(5 \, d^{5} e^{2} f^{2} + 6 \, d^{6} e f g + d^{7} g^{2} - {\left(5 \, e^{7} f^{2} + 6 \, d e^{6} f g + d^{2} e^{5} g^{2}\right)} x^{5} - 3 \, {\left(5 \, d e^{6} f^{2} + 6 \, d^{2} e^{5} f g + d^{3} e^{4} g^{2}\right)} x^{4} - 2 \, {\left(5 \, d^{2} e^{5} f^{2} + 6 \, d^{3} e^{4} f g + d^{4} e^{3} g^{2}\right)} x^{3} + 2 \, {\left(5 \, d^{3} e^{4} f^{2} + 6 \, d^{4} e^{3} f g + d^{5} e^{2} g^{2}\right)} x^{2} + 3 \, {\left(5 \, d^{4} e^{3} f^{2} + 6 \, d^{5} e^{2} f g + d^{6} e g^{2}\right)} x\right)} \log\left(e x - d\right)}{192 \, {\left(d^{6} e^{8} x^{5} + 3 \, d^{7} e^{7} x^{4} + 2 \, d^{8} e^{6} x^{3} - 2 \, d^{9} e^{5} x^{2} - 3 \, d^{10} e^{4} x - d^{11} e^{3}\right)}}"," ",0,"1/192*(64*d^5*e^2*f^2 - 16*d^7*g^2 - 6*(5*d*e^6*f^2 + 6*d^2*e^5*f*g + d^3*e^4*g^2)*x^4 - 18*(5*d^2*e^5*f^2 + 6*d^3*e^4*f*g + d^4*e^3*g^2)*x^3 - 14*(5*d^3*e^4*f^2 + 6*d^4*e^3*f*g + d^5*e^2*g^2)*x^2 + 6*(5*d^4*e^3*f^2 + 6*d^5*e^2*f*g - 7*d^6*e*g^2)*x - 3*(5*d^5*e^2*f^2 + 6*d^6*e*f*g + d^7*g^2 - (5*e^7*f^2 + 6*d*e^6*f*g + d^2*e^5*g^2)*x^5 - 3*(5*d*e^6*f^2 + 6*d^2*e^5*f*g + d^3*e^4*g^2)*x^4 - 2*(5*d^2*e^5*f^2 + 6*d^3*e^4*f*g + d^4*e^3*g^2)*x^3 + 2*(5*d^3*e^4*f^2 + 6*d^4*e^3*f*g + d^5*e^2*g^2)*x^2 + 3*(5*d^4*e^3*f^2 + 6*d^5*e^2*f*g + d^6*e*g^2)*x)*log(e*x + d) + 3*(5*d^5*e^2*f^2 + 6*d^6*e*f*g + d^7*g^2 - (5*e^7*f^2 + 6*d*e^6*f*g + d^2*e^5*g^2)*x^5 - 3*(5*d*e^6*f^2 + 6*d^2*e^5*f*g + d^3*e^4*g^2)*x^4 - 2*(5*d^2*e^5*f^2 + 6*d^3*e^4*f*g + d^4*e^3*g^2)*x^3 + 2*(5*d^3*e^4*f^2 + 6*d^4*e^3*f*g + d^5*e^2*g^2)*x^2 + 3*(5*d^4*e^3*f^2 + 6*d^5*e^2*f*g + d^6*e*g^2)*x)*log(e*x - d))/(d^6*e^8*x^5 + 3*d^7*e^7*x^4 + 2*d^8*e^6*x^3 - 2*d^9*e^5*x^2 - 3*d^10*e^4*x - d^11*e^3)","B",0
568,1,693,0,0.397729," ","integrate((g*x+f)^2/(e*x+d)^4/(-e^2*x^2+d^2)^2,x, algorithm=""fricas"")","\frac{288 \, d^{6} e^{2} f^{2} + 64 \, d^{7} e f g - 32 \, d^{8} g^{2} - 30 \, {\left(3 \, d e^{7} f^{2} + 4 \, d^{2} e^{6} f g + d^{3} e^{5} g^{2}\right)} x^{5} - 120 \, {\left(3 \, d^{2} e^{6} f^{2} + 4 \, d^{3} e^{5} f g + d^{4} e^{4} g^{2}\right)} x^{4} - 160 \, {\left(3 \, d^{3} e^{5} f^{2} + 4 \, d^{4} e^{4} f g + d^{5} e^{3} g^{2}\right)} x^{3} - 40 \, {\left(3 \, d^{4} e^{4} f^{2} + 4 \, d^{5} e^{3} f g + d^{6} e^{2} g^{2}\right)} x^{2} + 2 \, {\left(141 \, d^{5} e^{3} f^{2} + 188 \, d^{6} e^{2} f g - 49 \, d^{7} e g^{2}\right)} x - 15 \, {\left(3 \, d^{6} e^{2} f^{2} + 4 \, d^{7} e f g + d^{8} g^{2} - {\left(3 \, e^{8} f^{2} + 4 \, d e^{7} f g + d^{2} e^{6} g^{2}\right)} x^{6} - 4 \, {\left(3 \, d e^{7} f^{2} + 4 \, d^{2} e^{6} f g + d^{3} e^{5} g^{2}\right)} x^{5} - 5 \, {\left(3 \, d^{2} e^{6} f^{2} + 4 \, d^{3} e^{5} f g + d^{4} e^{4} g^{2}\right)} x^{4} + 5 \, {\left(3 \, d^{4} e^{4} f^{2} + 4 \, d^{5} e^{3} f g + d^{6} e^{2} g^{2}\right)} x^{2} + 4 \, {\left(3 \, d^{5} e^{3} f^{2} + 4 \, d^{6} e^{2} f g + d^{7} e g^{2}\right)} x\right)} \log\left(e x + d\right) + 15 \, {\left(3 \, d^{6} e^{2} f^{2} + 4 \, d^{7} e f g + d^{8} g^{2} - {\left(3 \, e^{8} f^{2} + 4 \, d e^{7} f g + d^{2} e^{6} g^{2}\right)} x^{6} - 4 \, {\left(3 \, d e^{7} f^{2} + 4 \, d^{2} e^{6} f g + d^{3} e^{5} g^{2}\right)} x^{5} - 5 \, {\left(3 \, d^{2} e^{6} f^{2} + 4 \, d^{3} e^{5} f g + d^{4} e^{4} g^{2}\right)} x^{4} + 5 \, {\left(3 \, d^{4} e^{4} f^{2} + 4 \, d^{5} e^{3} f g + d^{6} e^{2} g^{2}\right)} x^{2} + 4 \, {\left(3 \, d^{5} e^{3} f^{2} + 4 \, d^{6} e^{2} f g + d^{7} e g^{2}\right)} x\right)} \log\left(e x - d\right)}{960 \, {\left(d^{7} e^{9} x^{6} + 4 \, d^{8} e^{8} x^{5} + 5 \, d^{9} e^{7} x^{4} - 5 \, d^{11} e^{5} x^{2} - 4 \, d^{12} e^{4} x - d^{13} e^{3}\right)}}"," ",0,"1/960*(288*d^6*e^2*f^2 + 64*d^7*e*f*g - 32*d^8*g^2 - 30*(3*d*e^7*f^2 + 4*d^2*e^6*f*g + d^3*e^5*g^2)*x^5 - 120*(3*d^2*e^6*f^2 + 4*d^3*e^5*f*g + d^4*e^4*g^2)*x^4 - 160*(3*d^3*e^5*f^2 + 4*d^4*e^4*f*g + d^5*e^3*g^2)*x^3 - 40*(3*d^4*e^4*f^2 + 4*d^5*e^3*f*g + d^6*e^2*g^2)*x^2 + 2*(141*d^5*e^3*f^2 + 188*d^6*e^2*f*g - 49*d^7*e*g^2)*x - 15*(3*d^6*e^2*f^2 + 4*d^7*e*f*g + d^8*g^2 - (3*e^8*f^2 + 4*d*e^7*f*g + d^2*e^6*g^2)*x^6 - 4*(3*d*e^7*f^2 + 4*d^2*e^6*f*g + d^3*e^5*g^2)*x^5 - 5*(3*d^2*e^6*f^2 + 4*d^3*e^5*f*g + d^4*e^4*g^2)*x^4 + 5*(3*d^4*e^4*f^2 + 4*d^5*e^3*f*g + d^6*e^2*g^2)*x^2 + 4*(3*d^5*e^3*f^2 + 4*d^6*e^2*f*g + d^7*e*g^2)*x)*log(e*x + d) + 15*(3*d^6*e^2*f^2 + 4*d^7*e*f*g + d^8*g^2 - (3*e^8*f^2 + 4*d*e^7*f*g + d^2*e^6*g^2)*x^6 - 4*(3*d*e^7*f^2 + 4*d^2*e^6*f*g + d^3*e^5*g^2)*x^5 - 5*(3*d^2*e^6*f^2 + 4*d^3*e^5*f*g + d^4*e^4*g^2)*x^4 + 5*(3*d^4*e^4*f^2 + 4*d^5*e^3*f*g + d^6*e^2*g^2)*x^2 + 4*(3*d^5*e^3*f^2 + 4*d^6*e^2*f*g + d^7*e*g^2)*x)*log(e*x - d))/(d^7*e^9*x^6 + 4*d^8*e^8*x^5 + 5*d^9*e^7*x^4 - 5*d^11*e^5*x^2 - 4*d^12*e^4*x - d^13*e^3)","B",0
569,1,336,0,0.382346," ","integrate((e*x+d)^7*(g*x+f)^2/(-e^2*x^2+d^2)^3,x, algorithm=""fricas"")","-\frac{3 \, e^{6} g^{2} x^{6} + 288 \, d^{4} e^{2} f^{2} + 960 \, d^{5} e f g + 672 \, d^{6} g^{2} + 2 \, {\left(4 \, e^{6} f g + 11 \, d e^{5} g^{2}\right)} x^{5} + {\left(6 \, e^{6} f^{2} + 68 \, d e^{5} f g + 91 \, d^{2} e^{4} g^{2}\right)} x^{4} + 4 \, {\left(18 \, d e^{5} f^{2} + 104 \, d^{2} e^{4} f g + 103 \, d^{3} e^{3} g^{2}\right)} x^{3} - 6 \, {\left(27 \, d^{2} e^{4} f^{2} + 178 \, d^{3} e^{3} f g + 200 \, d^{4} e^{2} g^{2}\right)} x^{2} - 12 \, {\left(25 \, d^{3} e^{3} f^{2} + 48 \, d^{4} e^{2} f g + 8 \, d^{5} e g^{2}\right)} x + 96 \, {\left(3 \, d^{4} e^{2} f^{2} + 14 \, d^{5} e f g + 13 \, d^{6} g^{2} + {\left(3 \, d^{2} e^{4} f^{2} + 14 \, d^{3} e^{3} f g + 13 \, d^{4} e^{2} g^{2}\right)} x^{2} - 2 \, {\left(3 \, d^{3} e^{3} f^{2} + 14 \, d^{4} e^{2} f g + 13 \, d^{5} e g^{2}\right)} x\right)} \log\left(e x - d\right)}{12 \, {\left(e^{5} x^{2} - 2 \, d e^{4} x + d^{2} e^{3}\right)}}"," ",0,"-1/12*(3*e^6*g^2*x^6 + 288*d^4*e^2*f^2 + 960*d^5*e*f*g + 672*d^6*g^2 + 2*(4*e^6*f*g + 11*d*e^5*g^2)*x^5 + (6*e^6*f^2 + 68*d*e^5*f*g + 91*d^2*e^4*g^2)*x^4 + 4*(18*d*e^5*f^2 + 104*d^2*e^4*f*g + 103*d^3*e^3*g^2)*x^3 - 6*(27*d^2*e^4*f^2 + 178*d^3*e^3*f*g + 200*d^4*e^2*g^2)*x^2 - 12*(25*d^3*e^3*f^2 + 48*d^4*e^2*f*g + 8*d^5*e*g^2)*x + 96*(3*d^4*e^2*f^2 + 14*d^5*e*f*g + 13*d^6*g^2 + (3*d^2*e^4*f^2 + 14*d^3*e^3*f*g + 13*d^4*e^2*g^2)*x^2 - 2*(3*d^3*e^3*f^2 + 14*d^4*e^2*f*g + 13*d^5*e*g^2)*x)*log(e*x - d))/(e^5*x^2 - 2*d*e^4*x + d^2*e^3)","A",0
570,1,294,0,0.379648," ","integrate((e*x+d)^6*(g*x+f)^2/(-e^2*x^2+d^2)^3,x, algorithm=""fricas"")","-\frac{e^{5} g^{2} x^{5} + 24 \, d^{3} e^{2} f^{2} + 96 \, d^{4} e f g + 72 \, d^{5} g^{2} + {\left(3 \, e^{5} f g + 7 \, d e^{4} g^{2}\right)} x^{4} + {\left(3 \, e^{5} f^{2} + 30 \, d e^{4} f g + 37 \, d^{2} e^{3} g^{2}\right)} x^{3} - 3 \, {\left(2 \, d e^{4} f^{2} + 23 \, d^{2} e^{3} f g + 33 \, d^{3} e^{2} g^{2}\right)} x^{2} - 3 \, {\left(11 \, d^{2} e^{3} f^{2} + 28 \, d^{3} e^{2} f g + 10 \, d^{4} e g^{2}\right)} x + 6 \, {\left(3 \, d^{3} e^{2} f^{2} + 18 \, d^{4} e f g + 19 \, d^{5} g^{2} + {\left(3 \, d e^{4} f^{2} + 18 \, d^{2} e^{3} f g + 19 \, d^{3} e^{2} g^{2}\right)} x^{2} - 2 \, {\left(3 \, d^{2} e^{3} f^{2} + 18 \, d^{3} e^{2} f g + 19 \, d^{4} e g^{2}\right)} x\right)} \log\left(e x - d\right)}{3 \, {\left(e^{5} x^{2} - 2 \, d e^{4} x + d^{2} e^{3}\right)}}"," ",0,"-1/3*(e^5*g^2*x^5 + 24*d^3*e^2*f^2 + 96*d^4*e*f*g + 72*d^5*g^2 + (3*e^5*f*g + 7*d*e^4*g^2)*x^4 + (3*e^5*f^2 + 30*d*e^4*f*g + 37*d^2*e^3*g^2)*x^3 - 3*(2*d*e^4*f^2 + 23*d^2*e^3*f*g + 33*d^3*e^2*g^2)*x^2 - 3*(11*d^2*e^3*f^2 + 28*d^3*e^2*f*g + 10*d^4*e*g^2)*x + 6*(3*d^3*e^2*f^2 + 18*d^4*e*f*g + 19*d^5*g^2 + (3*d*e^4*f^2 + 18*d^2*e^3*f*g + 19*d^3*e^2*g^2)*x^2 - 2*(3*d^2*e^3*f^2 + 18*d^3*e^2*f*g + 19*d^4*e*g^2)*x)*log(e*x - d))/(e^5*x^2 - 2*d*e^4*x + d^2*e^3)","A",0
571,1,241,0,0.387761," ","integrate((e*x+d)^5*(g*x+f)^2/(-e^2*x^2+d^2)^3,x, algorithm=""fricas"")","-\frac{e^{4} g^{2} x^{4} + 4 \, d^{2} e^{2} f^{2} + 24 \, d^{3} e f g + 20 \, d^{4} g^{2} + 4 \, {\left(e^{4} f g + 2 \, d e^{3} g^{2}\right)} x^{3} - {\left(8 \, d e^{3} f g + 19 \, d^{2} e^{2} g^{2}\right)} x^{2} - 2 \, {\left(4 \, d e^{3} f^{2} + 14 \, d^{2} e^{2} f g + 7 \, d^{3} e g^{2}\right)} x + 2 \, {\left(d^{2} e^{2} f^{2} + 10 \, d^{3} e f g + 13 \, d^{4} g^{2} + {\left(e^{4} f^{2} + 10 \, d e^{3} f g + 13 \, d^{2} e^{2} g^{2}\right)} x^{2} - 2 \, {\left(d e^{3} f^{2} + 10 \, d^{2} e^{2} f g + 13 \, d^{3} e g^{2}\right)} x\right)} \log\left(e x - d\right)}{2 \, {\left(e^{5} x^{2} - 2 \, d e^{4} x + d^{2} e^{3}\right)}}"," ",0,"-1/2*(e^4*g^2*x^4 + 4*d^2*e^2*f^2 + 24*d^3*e*f*g + 20*d^4*g^2 + 4*(e^4*f*g + 2*d*e^3*g^2)*x^3 - (8*d*e^3*f*g + 19*d^2*e^2*g^2)*x^2 - 2*(4*d*e^3*f^2 + 14*d^2*e^2*f*g + 7*d^3*e*g^2)*x + 2*(d^2*e^2*f^2 + 10*d^3*e*f*g + 13*d^4*g^2 + (e^4*f^2 + 10*d*e^3*f*g + 13*d^2*e^2*g^2)*x^2 - 2*(d*e^3*f^2 + 10*d^2*e^2*f*g + 13*d^3*e*g^2)*x)*log(e*x - d))/(e^5*x^2 - 2*d*e^4*x + d^2*e^3)","B",0
572,1,159,0,0.402411," ","integrate((e*x+d)^4*(g*x+f)^2/(-e^2*x^2+d^2)^3,x, algorithm=""fricas"")","-\frac{e^{3} g^{2} x^{3} - 2 \, d e^{2} g^{2} x^{2} + 4 \, d^{2} e f g + 4 \, d^{3} g^{2} - {\left(e^{3} f^{2} + 6 \, d e^{2} f g + 4 \, d^{2} e g^{2}\right)} x + 2 \, {\left(d^{2} e f g + 2 \, d^{3} g^{2} + {\left(e^{3} f g + 2 \, d e^{2} g^{2}\right)} x^{2} - 2 \, {\left(d e^{2} f g + 2 \, d^{2} e g^{2}\right)} x\right)} \log\left(e x - d\right)}{e^{5} x^{2} - 2 \, d e^{4} x + d^{2} e^{3}}"," ",0,"-(e^3*g^2*x^3 - 2*d*e^2*g^2*x^2 + 4*d^2*e*f*g + 4*d^3*g^2 - (e^3*f^2 + 6*d*e^2*f*g + 4*d^2*e*g^2)*x + 2*(d^2*e*f*g + 2*d^3*g^2 + (e^3*f*g + 2*d*e^2*g^2)*x^2 - 2*(d*e^2*f*g + 2*d^2*e*g^2)*x)*log(e*x - d))/(e^5*x^2 - 2*d*e^4*x + d^2*e^3)","A",0
573,1,100,0,0.382150," ","integrate((e*x+d)^3*(g*x+f)^2/(-e^2*x^2+d^2)^3,x, algorithm=""fricas"")","\frac{e^{2} f^{2} - 2 \, d e f g - 3 \, d^{2} g^{2} + 4 \, {\left(e^{2} f g + d e g^{2}\right)} x - 2 \, {\left(e^{2} g^{2} x^{2} - 2 \, d e g^{2} x + d^{2} g^{2}\right)} \log\left(e x - d\right)}{2 \, {\left(e^{5} x^{2} - 2 \, d e^{4} x + d^{2} e^{3}\right)}}"," ",0,"1/2*(e^2*f^2 - 2*d*e*f*g - 3*d^2*g^2 + 4*(e^2*f*g + d*e*g^2)*x - 2*(e^2*g^2*x^2 - 2*d*e*g^2*x + d^2*g^2)*log(e*x - d))/(e^5*x^2 - 2*d*e^4*x + d^2*e^3)","A",0
574,1,271,0,0.405502," ","integrate((e*x+d)^2*(g*x+f)^2/(-e^2*x^2+d^2)^3,x, algorithm=""fricas"")","\frac{4 \, d^{2} e^{2} f^{2} - 4 \, d^{4} g^{2} - 2 \, {\left(d e^{3} f^{2} - 2 \, d^{2} e^{2} f g - 3 \, d^{3} e g^{2}\right)} x + {\left(d^{2} e^{2} f^{2} - 2 \, d^{3} e f g + d^{4} g^{2} + {\left(e^{4} f^{2} - 2 \, d e^{3} f g + d^{2} e^{2} g^{2}\right)} x^{2} - 2 \, {\left(d e^{3} f^{2} - 2 \, d^{2} e^{2} f g + d^{3} e g^{2}\right)} x\right)} \log\left(e x + d\right) - {\left(d^{2} e^{2} f^{2} - 2 \, d^{3} e f g + d^{4} g^{2} + {\left(e^{4} f^{2} - 2 \, d e^{3} f g + d^{2} e^{2} g^{2}\right)} x^{2} - 2 \, {\left(d e^{3} f^{2} - 2 \, d^{2} e^{2} f g + d^{3} e g^{2}\right)} x\right)} \log\left(e x - d\right)}{8 \, {\left(d^{3} e^{5} x^{2} - 2 \, d^{4} e^{4} x + d^{5} e^{3}\right)}}"," ",0,"1/8*(4*d^2*e^2*f^2 - 4*d^4*g^2 - 2*(d*e^3*f^2 - 2*d^2*e^2*f*g - 3*d^3*e*g^2)*x + (d^2*e^2*f^2 - 2*d^3*e*f*g + d^4*g^2 + (e^4*f^2 - 2*d*e^3*f*g + d^2*e^2*g^2)*x^2 - 2*(d*e^3*f^2 - 2*d^2*e^2*f*g + d^3*e*g^2)*x)*log(e*x + d) - (d^2*e^2*f^2 - 2*d^3*e*f*g + d^4*g^2 + (e^4*f^2 - 2*d*e^3*f*g + d^2*e^2*g^2)*x^2 - 2*(d*e^3*f^2 - 2*d^2*e^2*f*g + d^3*e*g^2)*x)*log(e*x - d))/(d^3*e^5*x^2 - 2*d^4*e^4*x + d^5*e^3)","B",0
575,1,417,0,0.398084," ","integrate((e*x+d)*(g*x+f)^2/(-e^2*x^2+d^2)^3,x, algorithm=""fricas"")","\frac{4 \, d^{3} e^{2} f^{2} + 8 \, d^{4} e f g - 4 \, d^{5} g^{2} - 2 \, {\left(3 \, d e^{4} f^{2} - 2 \, d^{2} e^{3} f g - d^{3} e^{2} g^{2}\right)} x^{2} + 2 \, {\left(3 \, d^{2} e^{3} f^{2} - 2 \, d^{3} e^{2} f g + 3 \, d^{4} e g^{2}\right)} x + {\left(3 \, d^{3} e^{2} f^{2} - 2 \, d^{4} e f g - d^{5} g^{2} + {\left(3 \, e^{5} f^{2} - 2 \, d e^{4} f g - d^{2} e^{3} g^{2}\right)} x^{3} - {\left(3 \, d e^{4} f^{2} - 2 \, d^{2} e^{3} f g - d^{3} e^{2} g^{2}\right)} x^{2} - {\left(3 \, d^{2} e^{3} f^{2} - 2 \, d^{3} e^{2} f g - d^{4} e g^{2}\right)} x\right)} \log\left(e x + d\right) - {\left(3 \, d^{3} e^{2} f^{2} - 2 \, d^{4} e f g - d^{5} g^{2} + {\left(3 \, e^{5} f^{2} - 2 \, d e^{4} f g - d^{2} e^{3} g^{2}\right)} x^{3} - {\left(3 \, d e^{4} f^{2} - 2 \, d^{2} e^{3} f g - d^{3} e^{2} g^{2}\right)} x^{2} - {\left(3 \, d^{2} e^{3} f^{2} - 2 \, d^{3} e^{2} f g - d^{4} e g^{2}\right)} x\right)} \log\left(e x - d\right)}{16 \, {\left(d^{4} e^{6} x^{3} - d^{5} e^{5} x^{2} - d^{6} e^{4} x + d^{7} e^{3}\right)}}"," ",0,"1/16*(4*d^3*e^2*f^2 + 8*d^4*e*f*g - 4*d^5*g^2 - 2*(3*d*e^4*f^2 - 2*d^2*e^3*f*g - d^3*e^2*g^2)*x^2 + 2*(3*d^2*e^3*f^2 - 2*d^3*e^2*f*g + 3*d^4*e*g^2)*x + (3*d^3*e^2*f^2 - 2*d^4*e*f*g - d^5*g^2 + (3*e^5*f^2 - 2*d*e^4*f*g - d^2*e^3*g^2)*x^3 - (3*d*e^4*f^2 - 2*d^2*e^3*f*g - d^3*e^2*g^2)*x^2 - (3*d^2*e^3*f^2 - 2*d^3*e^2*f*g - d^4*e*g^2)*x)*log(e*x + d) - (3*d^3*e^2*f^2 - 2*d^4*e*f*g - d^5*g^2 + (3*e^5*f^2 - 2*d*e^4*f*g - d^2*e^3*g^2)*x^3 - (3*d*e^4*f^2 - 2*d^2*e^3*f*g - d^3*e^2*g^2)*x^2 - (3*d^2*e^3*f^2 - 2*d^3*e^2*f*g - d^4*e*g^2)*x)*log(e*x - d))/(d^4*e^6*x^3 - d^5*e^5*x^2 - d^6*e^4*x + d^7*e^3)","B",0
576,1,252,0,0.401941," ","integrate((g*x+f)^2/(-e^2*x^2+d^2)^3,x, algorithm=""fricas"")","\frac{8 \, d^{5} e f g - 2 \, {\left(3 \, d e^{5} f^{2} - d^{3} e^{3} g^{2}\right)} x^{3} + 2 \, {\left(5 \, d^{3} e^{3} f^{2} + d^{5} e g^{2}\right)} x + {\left(3 \, d^{4} e^{2} f^{2} - d^{6} g^{2} + {\left(3 \, e^{6} f^{2} - d^{2} e^{4} g^{2}\right)} x^{4} - 2 \, {\left(3 \, d^{2} e^{4} f^{2} - d^{4} e^{2} g^{2}\right)} x^{2}\right)} \log\left(e x + d\right) - {\left(3 \, d^{4} e^{2} f^{2} - d^{6} g^{2} + {\left(3 \, e^{6} f^{2} - d^{2} e^{4} g^{2}\right)} x^{4} - 2 \, {\left(3 \, d^{2} e^{4} f^{2} - d^{4} e^{2} g^{2}\right)} x^{2}\right)} \log\left(e x - d\right)}{16 \, {\left(d^{5} e^{7} x^{4} - 2 \, d^{7} e^{5} x^{2} + d^{9} e^{3}\right)}}"," ",0,"1/16*(8*d^5*e*f*g - 2*(3*d*e^5*f^2 - d^3*e^3*g^2)*x^3 + 2*(5*d^3*e^3*f^2 + d^5*e*g^2)*x + (3*d^4*e^2*f^2 - d^6*g^2 + (3*e^6*f^2 - d^2*e^4*g^2)*x^4 - 2*(3*d^2*e^4*f^2 - d^4*e^2*g^2)*x^2)*log(e*x + d) - (3*d^4*e^2*f^2 - d^6*g^2 + (3*e^6*f^2 - d^2*e^4*g^2)*x^4 - 2*(3*d^2*e^4*f^2 - d^4*e^2*g^2)*x^2)*log(e*x - d))/(d^5*e^7*x^4 - 2*d^7*e^5*x^2 + d^9*e^3)","B",0
577,1,662,0,0.401284," ","integrate((g*x+f)^2/(e*x+d)/(-e^2*x^2+d^2)^3,x, algorithm=""fricas"")","-\frac{16 \, d^{5} e^{2} f^{2} - 32 \, d^{6} e f g - 8 \, d^{7} g^{2} + 6 \, {\left(5 \, d e^{6} f^{2} + 2 \, d^{2} e^{5} f g - d^{3} e^{4} g^{2}\right)} x^{4} + 6 \, {\left(5 \, d^{2} e^{5} f^{2} + 2 \, d^{3} e^{4} f g - d^{4} e^{3} g^{2}\right)} x^{3} - 10 \, {\left(5 \, d^{3} e^{4} f^{2} + 2 \, d^{4} e^{3} f g - d^{5} e^{2} g^{2}\right)} x^{2} - 2 \, {\left(25 \, d^{4} e^{3} f^{2} + 10 \, d^{5} e^{2} f g + 7 \, d^{6} e g^{2}\right)} x - 3 \, {\left(5 \, d^{5} e^{2} f^{2} + 2 \, d^{6} e f g - d^{7} g^{2} + {\left(5 \, e^{7} f^{2} + 2 \, d e^{6} f g - d^{2} e^{5} g^{2}\right)} x^{5} + {\left(5 \, d e^{6} f^{2} + 2 \, d^{2} e^{5} f g - d^{3} e^{4} g^{2}\right)} x^{4} - 2 \, {\left(5 \, d^{2} e^{5} f^{2} + 2 \, d^{3} e^{4} f g - d^{4} e^{3} g^{2}\right)} x^{3} - 2 \, {\left(5 \, d^{3} e^{4} f^{2} + 2 \, d^{4} e^{3} f g - d^{5} e^{2} g^{2}\right)} x^{2} + {\left(5 \, d^{4} e^{3} f^{2} + 2 \, d^{5} e^{2} f g - d^{6} e g^{2}\right)} x\right)} \log\left(e x + d\right) + 3 \, {\left(5 \, d^{5} e^{2} f^{2} + 2 \, d^{6} e f g - d^{7} g^{2} + {\left(5 \, e^{7} f^{2} + 2 \, d e^{6} f g - d^{2} e^{5} g^{2}\right)} x^{5} + {\left(5 \, d e^{6} f^{2} + 2 \, d^{2} e^{5} f g - d^{3} e^{4} g^{2}\right)} x^{4} - 2 \, {\left(5 \, d^{2} e^{5} f^{2} + 2 \, d^{3} e^{4} f g - d^{4} e^{3} g^{2}\right)} x^{3} - 2 \, {\left(5 \, d^{3} e^{4} f^{2} + 2 \, d^{4} e^{3} f g - d^{5} e^{2} g^{2}\right)} x^{2} + {\left(5 \, d^{4} e^{3} f^{2} + 2 \, d^{5} e^{2} f g - d^{6} e g^{2}\right)} x\right)} \log\left(e x - d\right)}{96 \, {\left(d^{6} e^{8} x^{5} + d^{7} e^{7} x^{4} - 2 \, d^{8} e^{6} x^{3} - 2 \, d^{9} e^{5} x^{2} + d^{10} e^{4} x + d^{11} e^{3}\right)}}"," ",0,"-1/96*(16*d^5*e^2*f^2 - 32*d^6*e*f*g - 8*d^7*g^2 + 6*(5*d*e^6*f^2 + 2*d^2*e^5*f*g - d^3*e^4*g^2)*x^4 + 6*(5*d^2*e^5*f^2 + 2*d^3*e^4*f*g - d^4*e^3*g^2)*x^3 - 10*(5*d^3*e^4*f^2 + 2*d^4*e^3*f*g - d^5*e^2*g^2)*x^2 - 2*(25*d^4*e^3*f^2 + 10*d^5*e^2*f*g + 7*d^6*e*g^2)*x - 3*(5*d^5*e^2*f^2 + 2*d^6*e*f*g - d^7*g^2 + (5*e^7*f^2 + 2*d*e^6*f*g - d^2*e^5*g^2)*x^5 + (5*d*e^6*f^2 + 2*d^2*e^5*f*g - d^3*e^4*g^2)*x^4 - 2*(5*d^2*e^5*f^2 + 2*d^3*e^4*f*g - d^4*e^3*g^2)*x^3 - 2*(5*d^3*e^4*f^2 + 2*d^4*e^3*f*g - d^5*e^2*g^2)*x^2 + (5*d^4*e^3*f^2 + 2*d^5*e^2*f*g - d^6*e*g^2)*x)*log(e*x + d) + 3*(5*d^5*e^2*f^2 + 2*d^6*e*f*g - d^7*g^2 + (5*e^7*f^2 + 2*d*e^6*f*g - d^2*e^5*g^2)*x^5 + (5*d*e^6*f^2 + 2*d^2*e^5*f*g - d^3*e^4*g^2)*x^4 - 2*(5*d^2*e^5*f^2 + 2*d^3*e^4*f*g - d^4*e^3*g^2)*x^3 - 2*(5*d^3*e^4*f^2 + 2*d^4*e^3*f*g - d^5*e^2*g^2)*x^2 + (5*d^4*e^3*f^2 + 2*d^5*e^2*f*g - d^6*e*g^2)*x)*log(e*x - d))/(d^6*e^8*x^5 + d^7*e^7*x^4 - 2*d^8*e^6*x^3 - 2*d^9*e^5*x^2 + d^10*e^4*x + d^11*e^3)","B",0
578,1,793,0,0.405351," ","integrate((g*x+f)^2/(e*x+d)^2/(-e^2*x^2+d^2)^3,x, algorithm=""fricas"")","-\frac{96 \, d^{6} e^{2} f^{2} - 64 \, d^{7} e f g - 32 \, d^{8} g^{2} + 6 \, {\left(15 \, d e^{7} f^{2} + 10 \, d^{2} e^{6} f g - d^{3} e^{5} g^{2}\right)} x^{5} + 12 \, {\left(15 \, d^{2} e^{6} f^{2} + 10 \, d^{3} e^{5} f g - d^{4} e^{4} g^{2}\right)} x^{4} - 4 \, {\left(15 \, d^{3} e^{5} f^{2} + 10 \, d^{4} e^{4} f g - d^{5} e^{3} g^{2}\right)} x^{3} - 20 \, {\left(15 \, d^{4} e^{4} f^{2} + 10 \, d^{5} e^{3} f g - d^{6} e^{2} g^{2}\right)} x^{2} - 2 \, {\left(51 \, d^{5} e^{3} f^{2} + 34 \, d^{6} e^{2} f g + 35 \, d^{7} e g^{2}\right)} x - 3 \, {\left(15 \, d^{6} e^{2} f^{2} + 10 \, d^{7} e f g - d^{8} g^{2} + {\left(15 \, e^{8} f^{2} + 10 \, d e^{7} f g - d^{2} e^{6} g^{2}\right)} x^{6} + 2 \, {\left(15 \, d e^{7} f^{2} + 10 \, d^{2} e^{6} f g - d^{3} e^{5} g^{2}\right)} x^{5} - {\left(15 \, d^{2} e^{6} f^{2} + 10 \, d^{3} e^{5} f g - d^{4} e^{4} g^{2}\right)} x^{4} - 4 \, {\left(15 \, d^{3} e^{5} f^{2} + 10 \, d^{4} e^{4} f g - d^{5} e^{3} g^{2}\right)} x^{3} - {\left(15 \, d^{4} e^{4} f^{2} + 10 \, d^{5} e^{3} f g - d^{6} e^{2} g^{2}\right)} x^{2} + 2 \, {\left(15 \, d^{5} e^{3} f^{2} + 10 \, d^{6} e^{2} f g - d^{7} e g^{2}\right)} x\right)} \log\left(e x + d\right) + 3 \, {\left(15 \, d^{6} e^{2} f^{2} + 10 \, d^{7} e f g - d^{8} g^{2} + {\left(15 \, e^{8} f^{2} + 10 \, d e^{7} f g - d^{2} e^{6} g^{2}\right)} x^{6} + 2 \, {\left(15 \, d e^{7} f^{2} + 10 \, d^{2} e^{6} f g - d^{3} e^{5} g^{2}\right)} x^{5} - {\left(15 \, d^{2} e^{6} f^{2} + 10 \, d^{3} e^{5} f g - d^{4} e^{4} g^{2}\right)} x^{4} - 4 \, {\left(15 \, d^{3} e^{5} f^{2} + 10 \, d^{4} e^{4} f g - d^{5} e^{3} g^{2}\right)} x^{3} - {\left(15 \, d^{4} e^{4} f^{2} + 10 \, d^{5} e^{3} f g - d^{6} e^{2} g^{2}\right)} x^{2} + 2 \, {\left(15 \, d^{5} e^{3} f^{2} + 10 \, d^{6} e^{2} f g - d^{7} e g^{2}\right)} x\right)} \log\left(e x - d\right)}{384 \, {\left(d^{7} e^{9} x^{6} + 2 \, d^{8} e^{8} x^{5} - d^{9} e^{7} x^{4} - 4 \, d^{10} e^{6} x^{3} - d^{11} e^{5} x^{2} + 2 \, d^{12} e^{4} x + d^{13} e^{3}\right)}}"," ",0,"-1/384*(96*d^6*e^2*f^2 - 64*d^7*e*f*g - 32*d^8*g^2 + 6*(15*d*e^7*f^2 + 10*d^2*e^6*f*g - d^3*e^5*g^2)*x^5 + 12*(15*d^2*e^6*f^2 + 10*d^3*e^5*f*g - d^4*e^4*g^2)*x^4 - 4*(15*d^3*e^5*f^2 + 10*d^4*e^4*f*g - d^5*e^3*g^2)*x^3 - 20*(15*d^4*e^4*f^2 + 10*d^5*e^3*f*g - d^6*e^2*g^2)*x^2 - 2*(51*d^5*e^3*f^2 + 34*d^6*e^2*f*g + 35*d^7*e*g^2)*x - 3*(15*d^6*e^2*f^2 + 10*d^7*e*f*g - d^8*g^2 + (15*e^8*f^2 + 10*d*e^7*f*g - d^2*e^6*g^2)*x^6 + 2*(15*d*e^7*f^2 + 10*d^2*e^6*f*g - d^3*e^5*g^2)*x^5 - (15*d^2*e^6*f^2 + 10*d^3*e^5*f*g - d^4*e^4*g^2)*x^4 - 4*(15*d^3*e^5*f^2 + 10*d^4*e^4*f*g - d^5*e^3*g^2)*x^3 - (15*d^4*e^4*f^2 + 10*d^5*e^3*f*g - d^6*e^2*g^2)*x^2 + 2*(15*d^5*e^3*f^2 + 10*d^6*e^2*f*g - d^7*e*g^2)*x)*log(e*x + d) + 3*(15*d^6*e^2*f^2 + 10*d^7*e*f*g - d^8*g^2 + (15*e^8*f^2 + 10*d*e^7*f*g - d^2*e^6*g^2)*x^6 + 2*(15*d*e^7*f^2 + 10*d^2*e^6*f*g - d^3*e^5*g^2)*x^5 - (15*d^2*e^6*f^2 + 10*d^3*e^5*f*g - d^4*e^4*g^2)*x^4 - 4*(15*d^3*e^5*f^2 + 10*d^4*e^4*f*g - d^5*e^3*g^2)*x^3 - (15*d^4*e^4*f^2 + 10*d^5*e^3*f*g - d^6*e^2*g^2)*x^2 + 2*(15*d^5*e^3*f^2 + 10*d^6*e^2*f*g - d^7*e*g^2)*x)*log(e*x - d))/(d^7*e^9*x^6 + 2*d^8*e^8*x^5 - d^9*e^7*x^4 - 4*d^10*e^6*x^3 - d^11*e^5*x^2 + 2*d^12*e^4*x + d^13*e^3)","B",0
579,1,807,0,0.494423," ","integrate((e*x+d)^3*(g*x+f)^5/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","-\frac{14 \, d^{3} e^{5} f^{5} - 30 \, d^{4} e^{4} f^{4} g + 40 \, d^{5} e^{3} f^{3} g^{2} + 440 \, d^{6} e^{2} f^{2} g^{3} + 720 \, d^{7} e f g^{4} + 304 \, d^{8} g^{5} - 2 \, {\left(7 \, e^{8} f^{5} - 15 \, d e^{7} f^{4} g + 20 \, d^{2} e^{6} f^{3} g^{2} + 220 \, d^{3} e^{5} f^{2} g^{3} + 360 \, d^{4} e^{4} f g^{4} + 152 \, d^{5} e^{3} g^{5}\right)} x^{3} + 6 \, {\left(7 \, d e^{7} f^{5} - 15 \, d^{2} e^{6} f^{4} g + 20 \, d^{3} e^{5} f^{3} g^{2} + 220 \, d^{4} e^{4} f^{2} g^{3} + 360 \, d^{5} e^{3} f g^{4} + 152 \, d^{6} e^{2} g^{5}\right)} x^{2} - 6 \, {\left(7 \, d^{2} e^{6} f^{5} - 15 \, d^{3} e^{5} f^{4} g + 20 \, d^{4} e^{4} f^{3} g^{2} + 220 \, d^{5} e^{3} f^{2} g^{3} + 360 \, d^{6} e^{2} f g^{4} + 152 \, d^{7} e g^{5}\right)} x + 30 \, {\left(20 \, d^{6} e^{2} f^{2} g^{3} + 30 \, d^{7} e f g^{4} + 13 \, d^{8} g^{5} - {\left(20 \, d^{3} e^{5} f^{2} g^{3} + 30 \, d^{4} e^{4} f g^{4} + 13 \, d^{5} e^{3} g^{5}\right)} x^{3} + 3 \, {\left(20 \, d^{4} e^{4} f^{2} g^{3} + 30 \, d^{5} e^{3} f g^{4} + 13 \, d^{6} e^{2} g^{5}\right)} x^{2} - 3 \, {\left(20 \, d^{5} e^{3} f^{2} g^{3} + 30 \, d^{6} e^{2} f g^{4} + 13 \, d^{7} e g^{5}\right)} x\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) - {\left(15 \, d^{3} e^{4} g^{5} x^{4} - 14 \, d^{2} e^{5} f^{5} + 30 \, d^{3} e^{4} f^{4} g - 40 \, d^{4} e^{3} f^{3} g^{2} - 440 \, d^{5} e^{2} f^{2} g^{3} - 720 \, d^{6} e f g^{4} - 304 \, d^{7} g^{5} + 15 \, {\left(10 \, d^{3} e^{4} f g^{4} + 3 \, d^{4} e^{3} g^{5}\right)} x^{3} - {\left(4 \, e^{7} f^{5} - 30 \, d e^{6} f^{4} g + 140 \, d^{2} e^{5} f^{3} g^{2} + 640 \, d^{3} e^{4} f^{2} g^{3} + 1170 \, d^{4} e^{3} f g^{4} + 479 \, d^{5} e^{2} g^{5}\right)} x^{2} + 3 \, {\left(4 \, d e^{6} f^{5} - 30 \, d^{2} e^{5} f^{4} g + 40 \, d^{3} e^{4} f^{3} g^{2} + 340 \, d^{4} e^{3} f^{2} g^{3} + 570 \, d^{5} e^{2} f g^{4} + 239 \, d^{6} e g^{5}\right)} x\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{30 \, {\left(d^{3} e^{9} x^{3} - 3 \, d^{4} e^{8} x^{2} + 3 \, d^{5} e^{7} x - d^{6} e^{6}\right)}}"," ",0,"-1/30*(14*d^3*e^5*f^5 - 30*d^4*e^4*f^4*g + 40*d^5*e^3*f^3*g^2 + 440*d^6*e^2*f^2*g^3 + 720*d^7*e*f*g^4 + 304*d^8*g^5 - 2*(7*e^8*f^5 - 15*d*e^7*f^4*g + 20*d^2*e^6*f^3*g^2 + 220*d^3*e^5*f^2*g^3 + 360*d^4*e^4*f*g^4 + 152*d^5*e^3*g^5)*x^3 + 6*(7*d*e^7*f^5 - 15*d^2*e^6*f^4*g + 20*d^3*e^5*f^3*g^2 + 220*d^4*e^4*f^2*g^3 + 360*d^5*e^3*f*g^4 + 152*d^6*e^2*g^5)*x^2 - 6*(7*d^2*e^6*f^5 - 15*d^3*e^5*f^4*g + 20*d^4*e^4*f^3*g^2 + 220*d^5*e^3*f^2*g^3 + 360*d^6*e^2*f*g^4 + 152*d^7*e*g^5)*x + 30*(20*d^6*e^2*f^2*g^3 + 30*d^7*e*f*g^4 + 13*d^8*g^5 - (20*d^3*e^5*f^2*g^3 + 30*d^4*e^4*f*g^4 + 13*d^5*e^3*g^5)*x^3 + 3*(20*d^4*e^4*f^2*g^3 + 30*d^5*e^3*f*g^4 + 13*d^6*e^2*g^5)*x^2 - 3*(20*d^5*e^3*f^2*g^3 + 30*d^6*e^2*f*g^4 + 13*d^7*e*g^5)*x)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) - (15*d^3*e^4*g^5*x^4 - 14*d^2*e^5*f^5 + 30*d^3*e^4*f^4*g - 40*d^4*e^3*f^3*g^2 - 440*d^5*e^2*f^2*g^3 - 720*d^6*e*f*g^4 - 304*d^7*g^5 + 15*(10*d^3*e^4*f*g^4 + 3*d^4*e^3*g^5)*x^3 - (4*e^7*f^5 - 30*d*e^6*f^4*g + 140*d^2*e^5*f^3*g^2 + 640*d^3*e^4*f^2*g^3 + 1170*d^4*e^3*f*g^4 + 479*d^5*e^2*g^5)*x^2 + 3*(4*d*e^6*f^5 - 30*d^2*e^5*f^4*g + 40*d^3*e^4*f^3*g^2 + 340*d^4*e^3*f^2*g^3 + 570*d^5*e^2*f*g^4 + 239*d^6*e*g^5)*x)*sqrt(-e^2*x^2 + d^2))/(d^3*e^9*x^3 - 3*d^4*e^8*x^2 + 3*d^5*e^7*x - d^6*e^6)","B",0
580,1,624,0,0.572650," ","integrate((e*x+d)^3*(g*x+f)^4/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","-\frac{7 \, d^{3} e^{4} f^{4} - 12 \, d^{4} e^{3} f^{3} g + 12 \, d^{5} e^{2} f^{2} g^{2} + 88 \, d^{6} e f g^{3} + 72 \, d^{7} g^{4} - {\left(7 \, e^{7} f^{4} - 12 \, d e^{6} f^{3} g + 12 \, d^{2} e^{5} f^{2} g^{2} + 88 \, d^{3} e^{4} f g^{3} + 72 \, d^{4} e^{3} g^{4}\right)} x^{3} + 3 \, {\left(7 \, d e^{6} f^{4} - 12 \, d^{2} e^{5} f^{3} g + 12 \, d^{3} e^{4} f^{2} g^{2} + 88 \, d^{4} e^{3} f g^{3} + 72 \, d^{5} e^{2} g^{4}\right)} x^{2} - 3 \, {\left(7 \, d^{2} e^{5} f^{4} - 12 \, d^{3} e^{4} f^{3} g + 12 \, d^{4} e^{3} f^{2} g^{2} + 88 \, d^{5} e^{2} f g^{3} + 72 \, d^{6} e g^{4}\right)} x + 30 \, {\left(4 \, d^{6} e f g^{3} + 3 \, d^{7} g^{4} - {\left(4 \, d^{3} e^{4} f g^{3} + 3 \, d^{4} e^{3} g^{4}\right)} x^{3} + 3 \, {\left(4 \, d^{4} e^{3} f g^{3} + 3 \, d^{5} e^{2} g^{4}\right)} x^{2} - 3 \, {\left(4 \, d^{5} e^{2} f g^{3} + 3 \, d^{6} e g^{4}\right)} x\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) - {\left(15 \, d^{3} e^{3} g^{4} x^{3} - 7 \, d^{2} e^{4} f^{4} + 12 \, d^{3} e^{3} f^{3} g - 12 \, d^{4} e^{2} f^{2} g^{2} - 88 \, d^{5} e f g^{3} - 72 \, d^{6} g^{4} - {\left(2 \, e^{6} f^{4} - 12 \, d e^{5} f^{3} g + 42 \, d^{2} e^{4} f^{2} g^{2} + 128 \, d^{3} e^{3} f g^{3} + 117 \, d^{4} e^{2} g^{4}\right)} x^{2} + 3 \, {\left(2 \, d e^{5} f^{4} - 12 \, d^{2} e^{4} f^{3} g + 12 \, d^{3} e^{3} f^{2} g^{2} + 68 \, d^{4} e^{2} f g^{3} + 57 \, d^{5} e g^{4}\right)} x\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(d^{3} e^{8} x^{3} - 3 \, d^{4} e^{7} x^{2} + 3 \, d^{5} e^{6} x - d^{6} e^{5}\right)}}"," ",0,"-1/15*(7*d^3*e^4*f^4 - 12*d^4*e^3*f^3*g + 12*d^5*e^2*f^2*g^2 + 88*d^6*e*f*g^3 + 72*d^7*g^4 - (7*e^7*f^4 - 12*d*e^6*f^3*g + 12*d^2*e^5*f^2*g^2 + 88*d^3*e^4*f*g^3 + 72*d^4*e^3*g^4)*x^3 + 3*(7*d*e^6*f^4 - 12*d^2*e^5*f^3*g + 12*d^3*e^4*f^2*g^2 + 88*d^4*e^3*f*g^3 + 72*d^5*e^2*g^4)*x^2 - 3*(7*d^2*e^5*f^4 - 12*d^3*e^4*f^3*g + 12*d^4*e^3*f^2*g^2 + 88*d^5*e^2*f*g^3 + 72*d^6*e*g^4)*x + 30*(4*d^6*e*f*g^3 + 3*d^7*g^4 - (4*d^3*e^4*f*g^3 + 3*d^4*e^3*g^4)*x^3 + 3*(4*d^4*e^3*f*g^3 + 3*d^5*e^2*g^4)*x^2 - 3*(4*d^5*e^2*f*g^3 + 3*d^6*e*g^4)*x)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) - (15*d^3*e^3*g^4*x^3 - 7*d^2*e^4*f^4 + 12*d^3*e^3*f^3*g - 12*d^4*e^2*f^2*g^2 - 88*d^5*e*f*g^3 - 72*d^6*g^4 - (2*e^6*f^4 - 12*d*e^5*f^3*g + 42*d^2*e^4*f^2*g^2 + 128*d^3*e^3*f*g^3 + 117*d^4*e^2*g^4)*x^2 + 3*(2*d*e^5*f^4 - 12*d^2*e^4*f^3*g + 12*d^3*e^3*f^2*g^2 + 68*d^4*e^2*f*g^3 + 57*d^5*e*g^4)*x)*sqrt(-e^2*x^2 + d^2))/(d^3*e^8*x^3 - 3*d^4*e^7*x^2 + 3*d^5*e^6*x - d^6*e^5)","B",0
581,1,454,0,0.440197," ","integrate((e*x+d)^3*(g*x+f)^3/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","-\frac{7 \, d^{3} e^{3} f^{3} - 9 \, d^{4} e^{2} f^{2} g + 6 \, d^{5} e f g^{2} + 22 \, d^{6} g^{3} - {\left(7 \, e^{6} f^{3} - 9 \, d e^{5} f^{2} g + 6 \, d^{2} e^{4} f g^{2} + 22 \, d^{3} e^{3} g^{3}\right)} x^{3} + 3 \, {\left(7 \, d e^{5} f^{3} - 9 \, d^{2} e^{4} f^{2} g + 6 \, d^{3} e^{3} f g^{2} + 22 \, d^{4} e^{2} g^{3}\right)} x^{2} - 3 \, {\left(7 \, d^{2} e^{4} f^{3} - 9 \, d^{3} e^{3} f^{2} g + 6 \, d^{4} e^{2} f g^{2} + 22 \, d^{5} e g^{3}\right)} x - 30 \, {\left(d^{3} e^{3} g^{3} x^{3} - 3 \, d^{4} e^{2} g^{3} x^{2} + 3 \, d^{5} e g^{3} x - d^{6} g^{3}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(7 \, d^{2} e^{3} f^{3} - 9 \, d^{3} e^{2} f^{2} g + 6 \, d^{4} e f g^{2} + 22 \, d^{5} g^{3} + {\left(2 \, e^{5} f^{3} - 9 \, d e^{4} f^{2} g + 21 \, d^{2} e^{3} f g^{2} + 32 \, d^{3} e^{2} g^{3}\right)} x^{2} - 3 \, {\left(2 \, d e^{4} f^{3} - 9 \, d^{2} e^{3} f^{2} g + 6 \, d^{3} e^{2} f g^{2} + 17 \, d^{4} e g^{3}\right)} x\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(d^{3} e^{7} x^{3} - 3 \, d^{4} e^{6} x^{2} + 3 \, d^{5} e^{5} x - d^{6} e^{4}\right)}}"," ",0,"-1/15*(7*d^3*e^3*f^3 - 9*d^4*e^2*f^2*g + 6*d^5*e*f*g^2 + 22*d^6*g^3 - (7*e^6*f^3 - 9*d*e^5*f^2*g + 6*d^2*e^4*f*g^2 + 22*d^3*e^3*g^3)*x^3 + 3*(7*d*e^5*f^3 - 9*d^2*e^4*f^2*g + 6*d^3*e^3*f*g^2 + 22*d^4*e^2*g^3)*x^2 - 3*(7*d^2*e^4*f^3 - 9*d^3*e^3*f^2*g + 6*d^4*e^2*f*g^2 + 22*d^5*e*g^3)*x - 30*(d^3*e^3*g^3*x^3 - 3*d^4*e^2*g^3*x^2 + 3*d^5*e*g^3*x - d^6*g^3)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (7*d^2*e^3*f^3 - 9*d^3*e^2*f^2*g + 6*d^4*e*f*g^2 + 22*d^5*g^3 + (2*e^5*f^3 - 9*d*e^4*f^2*g + 21*d^2*e^3*f*g^2 + 32*d^3*e^2*g^3)*x^2 - 3*(2*d*e^4*f^3 - 9*d^2*e^3*f^2*g + 6*d^3*e^2*f*g^2 + 17*d^4*e*g^3)*x)*sqrt(-e^2*x^2 + d^2))/(d^3*e^7*x^3 - 3*d^4*e^6*x^2 + 3*d^5*e^5*x - d^6*e^4)","B",0
582,1,279,0,0.417568," ","integrate((e*x+d)^3*(g*x+f)^2/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","-\frac{7 \, d^{3} e^{2} f^{2} - 6 \, d^{4} e f g + 2 \, d^{5} g^{2} - {\left(7 \, e^{5} f^{2} - 6 \, d e^{4} f g + 2 \, d^{2} e^{3} g^{2}\right)} x^{3} + 3 \, {\left(7 \, d e^{4} f^{2} - 6 \, d^{2} e^{3} f g + 2 \, d^{3} e^{2} g^{2}\right)} x^{2} - 3 \, {\left(7 \, d^{2} e^{3} f^{2} - 6 \, d^{3} e^{2} f g + 2 \, d^{4} e g^{2}\right)} x + {\left(7 \, d^{2} e^{2} f^{2} - 6 \, d^{3} e f g + 2 \, d^{4} g^{2} + {\left(2 \, e^{4} f^{2} - 6 \, d e^{3} f g + 7 \, d^{2} e^{2} g^{2}\right)} x^{2} - 6 \, {\left(d e^{3} f^{2} - 3 \, d^{2} e^{2} f g + d^{3} e g^{2}\right)} x\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(d^{3} e^{6} x^{3} - 3 \, d^{4} e^{5} x^{2} + 3 \, d^{5} e^{4} x - d^{6} e^{3}\right)}}"," ",0,"-1/15*(7*d^3*e^2*f^2 - 6*d^4*e*f*g + 2*d^5*g^2 - (7*e^5*f^2 - 6*d*e^4*f*g + 2*d^2*e^3*g^2)*x^3 + 3*(7*d*e^4*f^2 - 6*d^2*e^3*f*g + 2*d^3*e^2*g^2)*x^2 - 3*(7*d^2*e^3*f^2 - 6*d^3*e^2*f*g + 2*d^4*e*g^2)*x + (7*d^2*e^2*f^2 - 6*d^3*e*f*g + 2*d^4*g^2 + (2*e^4*f^2 - 6*d*e^3*f*g + 7*d^2*e^2*g^2)*x^2 - 6*(d*e^3*f^2 - 3*d^2*e^2*f*g + d^3*e*g^2)*x)*sqrt(-e^2*x^2 + d^2))/(d^3*e^6*x^3 - 3*d^4*e^5*x^2 + 3*d^5*e^4*x - d^6*e^3)","B",0
583,1,183,0,0.390205," ","integrate((e*x+d)^3*(g*x+f)/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","-\frac{7 \, d^{3} e f - 3 \, d^{4} g - {\left(7 \, e^{4} f - 3 \, d e^{3} g\right)} x^{3} + 3 \, {\left(7 \, d e^{3} f - 3 \, d^{2} e^{2} g\right)} x^{2} - 3 \, {\left(7 \, d^{2} e^{2} f - 3 \, d^{3} e g\right)} x + {\left(7 \, d^{2} e f - 3 \, d^{3} g + {\left(2 \, e^{3} f - 3 \, d e^{2} g\right)} x^{2} - 3 \, {\left(2 \, d e^{2} f - 3 \, d^{2} e g\right)} x\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(d^{3} e^{5} x^{3} - 3 \, d^{4} e^{4} x^{2} + 3 \, d^{5} e^{3} x - d^{6} e^{2}\right)}}"," ",0,"-1/15*(7*d^3*e*f - 3*d^4*g - (7*e^4*f - 3*d*e^3*g)*x^3 + 3*(7*d*e^3*f - 3*d^2*e^2*g)*x^2 - 3*(7*d^2*e^2*f - 3*d^3*e*g)*x + (7*d^2*e*f - 3*d^3*g + (2*e^3*f - 3*d*e^2*g)*x^2 - 3*(2*d*e^2*f - 3*d^2*e*g)*x)*sqrt(-e^2*x^2 + d^2))/(d^3*e^5*x^3 - 3*d^4*e^4*x^2 + 3*d^5*e^3*x - d^6*e^2)","A",0
584,1,106,0,0.400769," ","integrate((e*x+d)^3/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","\frac{7 \, e^{3} x^{3} - 21 \, d e^{2} x^{2} + 21 \, d^{2} e x - 7 \, d^{3} - {\left(2 \, e^{2} x^{2} - 6 \, d e x + 7 \, d^{2}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(d^{3} e^{4} x^{3} - 3 \, d^{4} e^{3} x^{2} + 3 \, d^{5} e^{2} x - d^{6} e\right)}}"," ",0,"1/15*(7*e^3*x^3 - 21*d*e^2*x^2 + 21*d^2*e*x - 7*d^3 - (2*e^2*x^2 - 6*d*e*x + 7*d^2)*sqrt(-e^2*x^2 + d^2))/(d^3*e^4*x^3 - 3*d^4*e^3*x^2 + 3*d^5*e^2*x - d^6*e)","A",0
585,1,1767,0,0.480736," ","integrate((e*x+d)^3/(g*x+f)/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","\left[\frac{7 \, d^{3} e^{4} f^{4} + 24 \, d^{4} e^{3} f^{3} g + 25 \, d^{5} e^{2} f^{2} g^{2} - 24 \, d^{6} e f g^{3} - 32 \, d^{7} g^{4} - {\left(7 \, e^{7} f^{4} + 24 \, d e^{6} f^{3} g + 25 \, d^{2} e^{5} f^{2} g^{2} - 24 \, d^{3} e^{4} f g^{3} - 32 \, d^{4} e^{3} g^{4}\right)} x^{3} + 3 \, {\left(7 \, d e^{6} f^{4} + 24 \, d^{2} e^{5} f^{3} g + 25 \, d^{3} e^{4} f^{2} g^{2} - 24 \, d^{4} e^{3} f g^{3} - 32 \, d^{5} e^{2} g^{4}\right)} x^{2} + 15 \, {\left(d^{3} e^{3} g^{3} x^{3} - 3 \, d^{4} e^{2} g^{3} x^{2} + 3 \, d^{5} e g^{3} x - d^{6} g^{3}\right)} \sqrt{-e^{2} f^{2} + d^{2} g^{2}} \log\left(\frac{d e^{2} f g x + d^{3} g^{2} - \sqrt{-e^{2} f^{2} + d^{2} g^{2}} {\left(e^{2} f x + d^{2} g + \sqrt{-e^{2} x^{2} + d^{2}} d g\right)} - {\left(e^{2} f^{2} - d^{2} g^{2}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{g x + f}\right) - 3 \, {\left(7 \, d^{2} e^{5} f^{4} + 24 \, d^{3} e^{4} f^{3} g + 25 \, d^{4} e^{3} f^{2} g^{2} - 24 \, d^{5} e^{2} f g^{3} - 32 \, d^{6} e g^{4}\right)} x + {\left(7 \, d^{2} e^{4} f^{4} + 24 \, d^{3} e^{3} f^{3} g + 25 \, d^{4} e^{2} f^{2} g^{2} - 24 \, d^{5} e f g^{3} - 32 \, d^{6} g^{4} + {\left(2 \, e^{6} f^{4} + 9 \, d e^{5} f^{3} g + 20 \, d^{2} e^{4} f^{2} g^{2} - 9 \, d^{3} e^{3} f g^{3} - 22 \, d^{4} e^{2} g^{4}\right)} x^{2} - 3 \, {\left(2 \, d e^{5} f^{4} + 9 \, d^{2} e^{4} f^{3} g + 15 \, d^{3} e^{3} f^{2} g^{2} - 9 \, d^{4} e^{2} f g^{3} - 17 \, d^{5} e g^{4}\right)} x\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(d^{6} e^{5} f^{5} + 3 \, d^{7} e^{4} f^{4} g + 2 \, d^{8} e^{3} f^{3} g^{2} - 2 \, d^{9} e^{2} f^{2} g^{3} - 3 \, d^{10} e f g^{4} - d^{11} g^{5} - {\left(d^{3} e^{8} f^{5} + 3 \, d^{4} e^{7} f^{4} g + 2 \, d^{5} e^{6} f^{3} g^{2} - 2 \, d^{6} e^{5} f^{2} g^{3} - 3 \, d^{7} e^{4} f g^{4} - d^{8} e^{3} g^{5}\right)} x^{3} + 3 \, {\left(d^{4} e^{7} f^{5} + 3 \, d^{5} e^{6} f^{4} g + 2 \, d^{6} e^{5} f^{3} g^{2} - 2 \, d^{7} e^{4} f^{2} g^{3} - 3 \, d^{8} e^{3} f g^{4} - d^{9} e^{2} g^{5}\right)} x^{2} - 3 \, {\left(d^{5} e^{6} f^{5} + 3 \, d^{6} e^{5} f^{4} g + 2 \, d^{7} e^{4} f^{3} g^{2} - 2 \, d^{8} e^{3} f^{2} g^{3} - 3 \, d^{9} e^{2} f g^{4} - d^{10} e g^{5}\right)} x\right)}}, \frac{7 \, d^{3} e^{4} f^{4} + 24 \, d^{4} e^{3} f^{3} g + 25 \, d^{5} e^{2} f^{2} g^{2} - 24 \, d^{6} e f g^{3} - 32 \, d^{7} g^{4} - {\left(7 \, e^{7} f^{4} + 24 \, d e^{6} f^{3} g + 25 \, d^{2} e^{5} f^{2} g^{2} - 24 \, d^{3} e^{4} f g^{3} - 32 \, d^{4} e^{3} g^{4}\right)} x^{3} + 3 \, {\left(7 \, d e^{6} f^{4} + 24 \, d^{2} e^{5} f^{3} g + 25 \, d^{3} e^{4} f^{2} g^{2} - 24 \, d^{4} e^{3} f g^{3} - 32 \, d^{5} e^{2} g^{4}\right)} x^{2} - 30 \, {\left(d^{3} e^{3} g^{3} x^{3} - 3 \, d^{4} e^{2} g^{3} x^{2} + 3 \, d^{5} e g^{3} x - d^{6} g^{3}\right)} \sqrt{e^{2} f^{2} - d^{2} g^{2}} \arctan\left(\frac{d g x + d f - \sqrt{-e^{2} x^{2} + d^{2}} f}{\sqrt{e^{2} f^{2} - d^{2} g^{2}} x}\right) - 3 \, {\left(7 \, d^{2} e^{5} f^{4} + 24 \, d^{3} e^{4} f^{3} g + 25 \, d^{4} e^{3} f^{2} g^{2} - 24 \, d^{5} e^{2} f g^{3} - 32 \, d^{6} e g^{4}\right)} x + {\left(7 \, d^{2} e^{4} f^{4} + 24 \, d^{3} e^{3} f^{3} g + 25 \, d^{4} e^{2} f^{2} g^{2} - 24 \, d^{5} e f g^{3} - 32 \, d^{6} g^{4} + {\left(2 \, e^{6} f^{4} + 9 \, d e^{5} f^{3} g + 20 \, d^{2} e^{4} f^{2} g^{2} - 9 \, d^{3} e^{3} f g^{3} - 22 \, d^{4} e^{2} g^{4}\right)} x^{2} - 3 \, {\left(2 \, d e^{5} f^{4} + 9 \, d^{2} e^{4} f^{3} g + 15 \, d^{3} e^{3} f^{2} g^{2} - 9 \, d^{4} e^{2} f g^{3} - 17 \, d^{5} e g^{4}\right)} x\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(d^{6} e^{5} f^{5} + 3 \, d^{7} e^{4} f^{4} g + 2 \, d^{8} e^{3} f^{3} g^{2} - 2 \, d^{9} e^{2} f^{2} g^{3} - 3 \, d^{10} e f g^{4} - d^{11} g^{5} - {\left(d^{3} e^{8} f^{5} + 3 \, d^{4} e^{7} f^{4} g + 2 \, d^{5} e^{6} f^{3} g^{2} - 2 \, d^{6} e^{5} f^{2} g^{3} - 3 \, d^{7} e^{4} f g^{4} - d^{8} e^{3} g^{5}\right)} x^{3} + 3 \, {\left(d^{4} e^{7} f^{5} + 3 \, d^{5} e^{6} f^{4} g + 2 \, d^{6} e^{5} f^{3} g^{2} - 2 \, d^{7} e^{4} f^{2} g^{3} - 3 \, d^{8} e^{3} f g^{4} - d^{9} e^{2} g^{5}\right)} x^{2} - 3 \, {\left(d^{5} e^{6} f^{5} + 3 \, d^{6} e^{5} f^{4} g + 2 \, d^{7} e^{4} f^{3} g^{2} - 2 \, d^{8} e^{3} f^{2} g^{3} - 3 \, d^{9} e^{2} f g^{4} - d^{10} e g^{5}\right)} x\right)}}\right]"," ",0,"[1/15*(7*d^3*e^4*f^4 + 24*d^4*e^3*f^3*g + 25*d^5*e^2*f^2*g^2 - 24*d^6*e*f*g^3 - 32*d^7*g^4 - (7*e^7*f^4 + 24*d*e^6*f^3*g + 25*d^2*e^5*f^2*g^2 - 24*d^3*e^4*f*g^3 - 32*d^4*e^3*g^4)*x^3 + 3*(7*d*e^6*f^4 + 24*d^2*e^5*f^3*g + 25*d^3*e^4*f^2*g^2 - 24*d^4*e^3*f*g^3 - 32*d^5*e^2*g^4)*x^2 + 15*(d^3*e^3*g^3*x^3 - 3*d^4*e^2*g^3*x^2 + 3*d^5*e*g^3*x - d^6*g^3)*sqrt(-e^2*f^2 + d^2*g^2)*log((d*e^2*f*g*x + d^3*g^2 - sqrt(-e^2*f^2 + d^2*g^2)*(e^2*f*x + d^2*g + sqrt(-e^2*x^2 + d^2)*d*g) - (e^2*f^2 - d^2*g^2)*sqrt(-e^2*x^2 + d^2))/(g*x + f)) - 3*(7*d^2*e^5*f^4 + 24*d^3*e^4*f^3*g + 25*d^4*e^3*f^2*g^2 - 24*d^5*e^2*f*g^3 - 32*d^6*e*g^4)*x + (7*d^2*e^4*f^4 + 24*d^3*e^3*f^3*g + 25*d^4*e^2*f^2*g^2 - 24*d^5*e*f*g^3 - 32*d^6*g^4 + (2*e^6*f^4 + 9*d*e^5*f^3*g + 20*d^2*e^4*f^2*g^2 - 9*d^3*e^3*f*g^3 - 22*d^4*e^2*g^4)*x^2 - 3*(2*d*e^5*f^4 + 9*d^2*e^4*f^3*g + 15*d^3*e^3*f^2*g^2 - 9*d^4*e^2*f*g^3 - 17*d^5*e*g^4)*x)*sqrt(-e^2*x^2 + d^2))/(d^6*e^5*f^5 + 3*d^7*e^4*f^4*g + 2*d^8*e^3*f^3*g^2 - 2*d^9*e^2*f^2*g^3 - 3*d^10*e*f*g^4 - d^11*g^5 - (d^3*e^8*f^5 + 3*d^4*e^7*f^4*g + 2*d^5*e^6*f^3*g^2 - 2*d^6*e^5*f^2*g^3 - 3*d^7*e^4*f*g^4 - d^8*e^3*g^5)*x^3 + 3*(d^4*e^7*f^5 + 3*d^5*e^6*f^4*g + 2*d^6*e^5*f^3*g^2 - 2*d^7*e^4*f^2*g^3 - 3*d^8*e^3*f*g^4 - d^9*e^2*g^5)*x^2 - 3*(d^5*e^6*f^5 + 3*d^6*e^5*f^4*g + 2*d^7*e^4*f^3*g^2 - 2*d^8*e^3*f^2*g^3 - 3*d^9*e^2*f*g^4 - d^10*e*g^5)*x), 1/15*(7*d^3*e^4*f^4 + 24*d^4*e^3*f^3*g + 25*d^5*e^2*f^2*g^2 - 24*d^6*e*f*g^3 - 32*d^7*g^4 - (7*e^7*f^4 + 24*d*e^6*f^3*g + 25*d^2*e^5*f^2*g^2 - 24*d^3*e^4*f*g^3 - 32*d^4*e^3*g^4)*x^3 + 3*(7*d*e^6*f^4 + 24*d^2*e^5*f^3*g + 25*d^3*e^4*f^2*g^2 - 24*d^4*e^3*f*g^3 - 32*d^5*e^2*g^4)*x^2 - 30*(d^3*e^3*g^3*x^3 - 3*d^4*e^2*g^3*x^2 + 3*d^5*e*g^3*x - d^6*g^3)*sqrt(e^2*f^2 - d^2*g^2)*arctan((d*g*x + d*f - sqrt(-e^2*x^2 + d^2)*f)/(sqrt(e^2*f^2 - d^2*g^2)*x)) - 3*(7*d^2*e^5*f^4 + 24*d^3*e^4*f^3*g + 25*d^4*e^3*f^2*g^2 - 24*d^5*e^2*f*g^3 - 32*d^6*e*g^4)*x + (7*d^2*e^4*f^4 + 24*d^3*e^3*f^3*g + 25*d^4*e^2*f^2*g^2 - 24*d^5*e*f*g^3 - 32*d^6*g^4 + (2*e^6*f^4 + 9*d*e^5*f^3*g + 20*d^2*e^4*f^2*g^2 - 9*d^3*e^3*f*g^3 - 22*d^4*e^2*g^4)*x^2 - 3*(2*d*e^5*f^4 + 9*d^2*e^4*f^3*g + 15*d^3*e^3*f^2*g^2 - 9*d^4*e^2*f*g^3 - 17*d^5*e*g^4)*x)*sqrt(-e^2*x^2 + d^2))/(d^6*e^5*f^5 + 3*d^7*e^4*f^4*g + 2*d^8*e^3*f^3*g^2 - 2*d^9*e^2*f^2*g^3 - 3*d^10*e*f*g^4 - d^11*g^5 - (d^3*e^8*f^5 + 3*d^4*e^7*f^4*g + 2*d^5*e^6*f^3*g^2 - 2*d^6*e^5*f^2*g^3 - 3*d^7*e^4*f*g^4 - d^8*e^3*g^5)*x^3 + 3*(d^4*e^7*f^5 + 3*d^5*e^6*f^4*g + 2*d^6*e^5*f^3*g^2 - 2*d^7*e^4*f^2*g^3 - 3*d^8*e^3*f*g^4 - d^9*e^2*g^5)*x^2 - 3*(d^5*e^6*f^5 + 3*d^6*e^5*f^4*g + 2*d^7*e^4*f^3*g^2 - 2*d^8*e^3*f^2*g^3 - 3*d^9*e^2*f*g^4 - d^10*e*g^5)*x)]","B",0
586,1,3305,0,1.017170," ","integrate((e*x+d)^3/(g*x+f)^2/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","\left[\frac{7 \, d^{3} e^{6} f^{7} + 27 \, d^{4} e^{5} f^{6} g + 31 \, d^{5} e^{4} f^{5} g^{2} - 99 \, d^{6} e^{3} f^{4} g^{3} - 23 \, d^{7} e^{2} f^{3} g^{4} + 72 \, d^{8} e f^{2} g^{5} - 15 \, d^{9} f g^{6} - {\left(7 \, e^{9} f^{6} g + 27 \, d e^{8} f^{5} g^{2} + 31 \, d^{2} e^{7} f^{4} g^{3} - 99 \, d^{3} e^{6} f^{3} g^{4} - 23 \, d^{4} e^{5} f^{2} g^{5} + 72 \, d^{5} e^{4} f g^{6} - 15 \, d^{6} e^{3} g^{7}\right)} x^{4} - {\left(7 \, e^{9} f^{7} + 6 \, d e^{8} f^{6} g - 50 \, d^{2} e^{7} f^{5} g^{2} - 192 \, d^{3} e^{6} f^{4} g^{3} + 274 \, d^{4} e^{5} f^{3} g^{4} + 141 \, d^{5} e^{4} f^{2} g^{5} - 231 \, d^{6} e^{3} f g^{6} + 45 \, d^{7} e^{2} g^{7}\right)} x^{3} + 3 \, {\left(7 \, d e^{8} f^{7} + 20 \, d^{2} e^{7} f^{6} g + 4 \, d^{3} e^{6} f^{5} g^{2} - 130 \, d^{4} e^{5} f^{4} g^{3} + 76 \, d^{5} e^{4} f^{3} g^{4} + 95 \, d^{6} e^{3} f^{2} g^{5} - 87 \, d^{7} e^{2} f g^{6} + 15 \, d^{8} e g^{7}\right)} x^{2} - 15 \, {\left(4 \, d^{6} e^{2} f^{3} g^{3} - 3 \, d^{7} e f^{2} g^{4} - {\left(4 \, d^{3} e^{5} f^{2} g^{4} - 3 \, d^{4} e^{4} f g^{5}\right)} x^{4} - {\left(4 \, d^{3} e^{5} f^{3} g^{3} - 15 \, d^{4} e^{4} f^{2} g^{4} + 9 \, d^{5} e^{3} f g^{5}\right)} x^{3} + 3 \, {\left(4 \, d^{4} e^{4} f^{3} g^{3} - 7 \, d^{5} e^{3} f^{2} g^{4} + 3 \, d^{6} e^{2} f g^{5}\right)} x^{2} - {\left(12 \, d^{5} e^{3} f^{3} g^{3} - 13 \, d^{6} e^{2} f^{2} g^{4} + 3 \, d^{7} e f g^{5}\right)} x\right)} \sqrt{-e^{2} f^{2} + d^{2} g^{2}} \log\left(\frac{d e^{2} f g x + d^{3} g^{2} - \sqrt{-e^{2} f^{2} + d^{2} g^{2}} {\left(e^{2} f x + d^{2} g + \sqrt{-e^{2} x^{2} + d^{2}} d g\right)} - {\left(e^{2} f^{2} - d^{2} g^{2}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{g x + f}\right) - {\left(21 \, d^{2} e^{7} f^{7} + 74 \, d^{3} e^{6} f^{6} g + 66 \, d^{4} e^{5} f^{5} g^{2} - 328 \, d^{5} e^{4} f^{4} g^{3} + 30 \, d^{6} e^{3} f^{3} g^{4} + 239 \, d^{7} e^{2} f^{2} g^{5} - 117 \, d^{8} e f g^{6} + 15 \, d^{9} g^{7}\right)} x + {\left(7 \, d^{2} e^{6} f^{7} + 27 \, d^{3} e^{5} f^{6} g + 31 \, d^{4} e^{4} f^{5} g^{2} - 99 \, d^{5} e^{3} f^{4} g^{3} - 23 \, d^{6} e^{2} f^{3} g^{4} + 72 \, d^{7} e f^{2} g^{5} - 15 \, d^{8} f g^{6} + {\left(2 \, e^{8} f^{6} g + 12 \, d e^{7} f^{5} g^{2} + 41 \, d^{2} e^{6} f^{4} g^{3} - 84 \, d^{3} e^{5} f^{3} g^{4} - 43 \, d^{4} e^{4} f^{2} g^{5} + 72 \, d^{5} e^{3} f g^{6}\right)} x^{3} + {\left(2 \, e^{8} f^{7} + 6 \, d e^{7} f^{6} g + 5 \, d^{2} e^{6} f^{5} g^{2} - 147 \, d^{3} e^{5} f^{4} g^{3} + 164 \, d^{4} e^{4} f^{3} g^{4} + 141 \, d^{5} e^{3} f^{2} g^{5} - 171 \, d^{6} e^{2} f g^{6}\right)} x^{2} - {\left(6 \, d e^{7} f^{7} + 29 \, d^{2} e^{6} f^{6} g + 51 \, d^{3} e^{5} f^{5} g^{2} - 193 \, d^{4} e^{4} f^{4} g^{3} + 60 \, d^{5} e^{3} f^{3} g^{4} + 164 \, d^{6} e^{2} f^{2} g^{5} - 117 \, d^{7} e f g^{6}\right)} x\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(d^{6} e^{7} f^{9} + 3 \, d^{7} e^{6} f^{8} g + d^{8} e^{5} f^{7} g^{2} - 5 \, d^{9} e^{4} f^{6} g^{3} - 5 \, d^{10} e^{3} f^{5} g^{4} + d^{11} e^{2} f^{4} g^{5} + 3 \, d^{12} e f^{3} g^{6} + d^{13} f^{2} g^{7} - {\left(d^{3} e^{10} f^{8} g + 3 \, d^{4} e^{9} f^{7} g^{2} + d^{5} e^{8} f^{6} g^{3} - 5 \, d^{6} e^{7} f^{5} g^{4} - 5 \, d^{7} e^{6} f^{4} g^{5} + d^{8} e^{5} f^{3} g^{6} + 3 \, d^{9} e^{4} f^{2} g^{7} + d^{10} e^{3} f g^{8}\right)} x^{4} - {\left(d^{3} e^{10} f^{9} - 8 \, d^{5} e^{8} f^{7} g^{2} - 8 \, d^{6} e^{7} f^{6} g^{3} + 10 \, d^{7} e^{6} f^{5} g^{4} + 16 \, d^{8} e^{5} f^{4} g^{5} - 8 \, d^{10} e^{3} f^{2} g^{7} - 3 \, d^{11} e^{2} f g^{8}\right)} x^{3} + 3 \, {\left(d^{4} e^{9} f^{9} + 2 \, d^{5} e^{8} f^{8} g - 2 \, d^{6} e^{7} f^{7} g^{2} - 6 \, d^{7} e^{6} f^{6} g^{3} + 6 \, d^{9} e^{4} f^{4} g^{5} + 2 \, d^{10} e^{3} f^{3} g^{6} - 2 \, d^{11} e^{2} f^{2} g^{7} - d^{12} e f g^{8}\right)} x^{2} - {\left(3 \, d^{5} e^{8} f^{9} + 8 \, d^{6} e^{7} f^{8} g - 16 \, d^{8} e^{5} f^{6} g^{3} - 10 \, d^{9} e^{4} f^{5} g^{4} + 8 \, d^{10} e^{3} f^{4} g^{5} + 8 \, d^{11} e^{2} f^{3} g^{6} - d^{13} f g^{8}\right)} x\right)}}, \frac{7 \, d^{3} e^{6} f^{7} + 27 \, d^{4} e^{5} f^{6} g + 31 \, d^{5} e^{4} f^{5} g^{2} - 99 \, d^{6} e^{3} f^{4} g^{3} - 23 \, d^{7} e^{2} f^{3} g^{4} + 72 \, d^{8} e f^{2} g^{5} - 15 \, d^{9} f g^{6} - {\left(7 \, e^{9} f^{6} g + 27 \, d e^{8} f^{5} g^{2} + 31 \, d^{2} e^{7} f^{4} g^{3} - 99 \, d^{3} e^{6} f^{3} g^{4} - 23 \, d^{4} e^{5} f^{2} g^{5} + 72 \, d^{5} e^{4} f g^{6} - 15 \, d^{6} e^{3} g^{7}\right)} x^{4} - {\left(7 \, e^{9} f^{7} + 6 \, d e^{8} f^{6} g - 50 \, d^{2} e^{7} f^{5} g^{2} - 192 \, d^{3} e^{6} f^{4} g^{3} + 274 \, d^{4} e^{5} f^{3} g^{4} + 141 \, d^{5} e^{4} f^{2} g^{5} - 231 \, d^{6} e^{3} f g^{6} + 45 \, d^{7} e^{2} g^{7}\right)} x^{3} + 3 \, {\left(7 \, d e^{8} f^{7} + 20 \, d^{2} e^{7} f^{6} g + 4 \, d^{3} e^{6} f^{5} g^{2} - 130 \, d^{4} e^{5} f^{4} g^{3} + 76 \, d^{5} e^{4} f^{3} g^{4} + 95 \, d^{6} e^{3} f^{2} g^{5} - 87 \, d^{7} e^{2} f g^{6} + 15 \, d^{8} e g^{7}\right)} x^{2} + 30 \, {\left(4 \, d^{6} e^{2} f^{3} g^{3} - 3 \, d^{7} e f^{2} g^{4} - {\left(4 \, d^{3} e^{5} f^{2} g^{4} - 3 \, d^{4} e^{4} f g^{5}\right)} x^{4} - {\left(4 \, d^{3} e^{5} f^{3} g^{3} - 15 \, d^{4} e^{4} f^{2} g^{4} + 9 \, d^{5} e^{3} f g^{5}\right)} x^{3} + 3 \, {\left(4 \, d^{4} e^{4} f^{3} g^{3} - 7 \, d^{5} e^{3} f^{2} g^{4} + 3 \, d^{6} e^{2} f g^{5}\right)} x^{2} - {\left(12 \, d^{5} e^{3} f^{3} g^{3} - 13 \, d^{6} e^{2} f^{2} g^{4} + 3 \, d^{7} e f g^{5}\right)} x\right)} \sqrt{e^{2} f^{2} - d^{2} g^{2}} \arctan\left(\frac{d g x + d f - \sqrt{-e^{2} x^{2} + d^{2}} f}{\sqrt{e^{2} f^{2} - d^{2} g^{2}} x}\right) - {\left(21 \, d^{2} e^{7} f^{7} + 74 \, d^{3} e^{6} f^{6} g + 66 \, d^{4} e^{5} f^{5} g^{2} - 328 \, d^{5} e^{4} f^{4} g^{3} + 30 \, d^{6} e^{3} f^{3} g^{4} + 239 \, d^{7} e^{2} f^{2} g^{5} - 117 \, d^{8} e f g^{6} + 15 \, d^{9} g^{7}\right)} x + {\left(7 \, d^{2} e^{6} f^{7} + 27 \, d^{3} e^{5} f^{6} g + 31 \, d^{4} e^{4} f^{5} g^{2} - 99 \, d^{5} e^{3} f^{4} g^{3} - 23 \, d^{6} e^{2} f^{3} g^{4} + 72 \, d^{7} e f^{2} g^{5} - 15 \, d^{8} f g^{6} + {\left(2 \, e^{8} f^{6} g + 12 \, d e^{7} f^{5} g^{2} + 41 \, d^{2} e^{6} f^{4} g^{3} - 84 \, d^{3} e^{5} f^{3} g^{4} - 43 \, d^{4} e^{4} f^{2} g^{5} + 72 \, d^{5} e^{3} f g^{6}\right)} x^{3} + {\left(2 \, e^{8} f^{7} + 6 \, d e^{7} f^{6} g + 5 \, d^{2} e^{6} f^{5} g^{2} - 147 \, d^{3} e^{5} f^{4} g^{3} + 164 \, d^{4} e^{4} f^{3} g^{4} + 141 \, d^{5} e^{3} f^{2} g^{5} - 171 \, d^{6} e^{2} f g^{6}\right)} x^{2} - {\left(6 \, d e^{7} f^{7} + 29 \, d^{2} e^{6} f^{6} g + 51 \, d^{3} e^{5} f^{5} g^{2} - 193 \, d^{4} e^{4} f^{4} g^{3} + 60 \, d^{5} e^{3} f^{3} g^{4} + 164 \, d^{6} e^{2} f^{2} g^{5} - 117 \, d^{7} e f g^{6}\right)} x\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(d^{6} e^{7} f^{9} + 3 \, d^{7} e^{6} f^{8} g + d^{8} e^{5} f^{7} g^{2} - 5 \, d^{9} e^{4} f^{6} g^{3} - 5 \, d^{10} e^{3} f^{5} g^{4} + d^{11} e^{2} f^{4} g^{5} + 3 \, d^{12} e f^{3} g^{6} + d^{13} f^{2} g^{7} - {\left(d^{3} e^{10} f^{8} g + 3 \, d^{4} e^{9} f^{7} g^{2} + d^{5} e^{8} f^{6} g^{3} - 5 \, d^{6} e^{7} f^{5} g^{4} - 5 \, d^{7} e^{6} f^{4} g^{5} + d^{8} e^{5} f^{3} g^{6} + 3 \, d^{9} e^{4} f^{2} g^{7} + d^{10} e^{3} f g^{8}\right)} x^{4} - {\left(d^{3} e^{10} f^{9} - 8 \, d^{5} e^{8} f^{7} g^{2} - 8 \, d^{6} e^{7} f^{6} g^{3} + 10 \, d^{7} e^{6} f^{5} g^{4} + 16 \, d^{8} e^{5} f^{4} g^{5} - 8 \, d^{10} e^{3} f^{2} g^{7} - 3 \, d^{11} e^{2} f g^{8}\right)} x^{3} + 3 \, {\left(d^{4} e^{9} f^{9} + 2 \, d^{5} e^{8} f^{8} g - 2 \, d^{6} e^{7} f^{7} g^{2} - 6 \, d^{7} e^{6} f^{6} g^{3} + 6 \, d^{9} e^{4} f^{4} g^{5} + 2 \, d^{10} e^{3} f^{3} g^{6} - 2 \, d^{11} e^{2} f^{2} g^{7} - d^{12} e f g^{8}\right)} x^{2} - {\left(3 \, d^{5} e^{8} f^{9} + 8 \, d^{6} e^{7} f^{8} g - 16 \, d^{8} e^{5} f^{6} g^{3} - 10 \, d^{9} e^{4} f^{5} g^{4} + 8 \, d^{10} e^{3} f^{4} g^{5} + 8 \, d^{11} e^{2} f^{3} g^{6} - d^{13} f g^{8}\right)} x\right)}}\right]"," ",0,"[1/15*(7*d^3*e^6*f^7 + 27*d^4*e^5*f^6*g + 31*d^5*e^4*f^5*g^2 - 99*d^6*e^3*f^4*g^3 - 23*d^7*e^2*f^3*g^4 + 72*d^8*e*f^2*g^5 - 15*d^9*f*g^6 - (7*e^9*f^6*g + 27*d*e^8*f^5*g^2 + 31*d^2*e^7*f^4*g^3 - 99*d^3*e^6*f^3*g^4 - 23*d^4*e^5*f^2*g^5 + 72*d^5*e^4*f*g^6 - 15*d^6*e^3*g^7)*x^4 - (7*e^9*f^7 + 6*d*e^8*f^6*g - 50*d^2*e^7*f^5*g^2 - 192*d^3*e^6*f^4*g^3 + 274*d^4*e^5*f^3*g^4 + 141*d^5*e^4*f^2*g^5 - 231*d^6*e^3*f*g^6 + 45*d^7*e^2*g^7)*x^3 + 3*(7*d*e^8*f^7 + 20*d^2*e^7*f^6*g + 4*d^3*e^6*f^5*g^2 - 130*d^4*e^5*f^4*g^3 + 76*d^5*e^4*f^3*g^4 + 95*d^6*e^3*f^2*g^5 - 87*d^7*e^2*f*g^6 + 15*d^8*e*g^7)*x^2 - 15*(4*d^6*e^2*f^3*g^3 - 3*d^7*e*f^2*g^4 - (4*d^3*e^5*f^2*g^4 - 3*d^4*e^4*f*g^5)*x^4 - (4*d^3*e^5*f^3*g^3 - 15*d^4*e^4*f^2*g^4 + 9*d^5*e^3*f*g^5)*x^3 + 3*(4*d^4*e^4*f^3*g^3 - 7*d^5*e^3*f^2*g^4 + 3*d^6*e^2*f*g^5)*x^2 - (12*d^5*e^3*f^3*g^3 - 13*d^6*e^2*f^2*g^4 + 3*d^7*e*f*g^5)*x)*sqrt(-e^2*f^2 + d^2*g^2)*log((d*e^2*f*g*x + d^3*g^2 - sqrt(-e^2*f^2 + d^2*g^2)*(e^2*f*x + d^2*g + sqrt(-e^2*x^2 + d^2)*d*g) - (e^2*f^2 - d^2*g^2)*sqrt(-e^2*x^2 + d^2))/(g*x + f)) - (21*d^2*e^7*f^7 + 74*d^3*e^6*f^6*g + 66*d^4*e^5*f^5*g^2 - 328*d^5*e^4*f^4*g^3 + 30*d^6*e^3*f^3*g^4 + 239*d^7*e^2*f^2*g^5 - 117*d^8*e*f*g^6 + 15*d^9*g^7)*x + (7*d^2*e^6*f^7 + 27*d^3*e^5*f^6*g + 31*d^4*e^4*f^5*g^2 - 99*d^5*e^3*f^4*g^3 - 23*d^6*e^2*f^3*g^4 + 72*d^7*e*f^2*g^5 - 15*d^8*f*g^6 + (2*e^8*f^6*g + 12*d*e^7*f^5*g^2 + 41*d^2*e^6*f^4*g^3 - 84*d^3*e^5*f^3*g^4 - 43*d^4*e^4*f^2*g^5 + 72*d^5*e^3*f*g^6)*x^3 + (2*e^8*f^7 + 6*d*e^7*f^6*g + 5*d^2*e^6*f^5*g^2 - 147*d^3*e^5*f^4*g^3 + 164*d^4*e^4*f^3*g^4 + 141*d^5*e^3*f^2*g^5 - 171*d^6*e^2*f*g^6)*x^2 - (6*d*e^7*f^7 + 29*d^2*e^6*f^6*g + 51*d^3*e^5*f^5*g^2 - 193*d^4*e^4*f^4*g^3 + 60*d^5*e^3*f^3*g^4 + 164*d^6*e^2*f^2*g^5 - 117*d^7*e*f*g^6)*x)*sqrt(-e^2*x^2 + d^2))/(d^6*e^7*f^9 + 3*d^7*e^6*f^8*g + d^8*e^5*f^7*g^2 - 5*d^9*e^4*f^6*g^3 - 5*d^10*e^3*f^5*g^4 + d^11*e^2*f^4*g^5 + 3*d^12*e*f^3*g^6 + d^13*f^2*g^7 - (d^3*e^10*f^8*g + 3*d^4*e^9*f^7*g^2 + d^5*e^8*f^6*g^3 - 5*d^6*e^7*f^5*g^4 - 5*d^7*e^6*f^4*g^5 + d^8*e^5*f^3*g^6 + 3*d^9*e^4*f^2*g^7 + d^10*e^3*f*g^8)*x^4 - (d^3*e^10*f^9 - 8*d^5*e^8*f^7*g^2 - 8*d^6*e^7*f^6*g^3 + 10*d^7*e^6*f^5*g^4 + 16*d^8*e^5*f^4*g^5 - 8*d^10*e^3*f^2*g^7 - 3*d^11*e^2*f*g^8)*x^3 + 3*(d^4*e^9*f^9 + 2*d^5*e^8*f^8*g - 2*d^6*e^7*f^7*g^2 - 6*d^7*e^6*f^6*g^3 + 6*d^9*e^4*f^4*g^5 + 2*d^10*e^3*f^3*g^6 - 2*d^11*e^2*f^2*g^7 - d^12*e*f*g^8)*x^2 - (3*d^5*e^8*f^9 + 8*d^6*e^7*f^8*g - 16*d^8*e^5*f^6*g^3 - 10*d^9*e^4*f^5*g^4 + 8*d^10*e^3*f^4*g^5 + 8*d^11*e^2*f^3*g^6 - d^13*f*g^8)*x), 1/15*(7*d^3*e^6*f^7 + 27*d^4*e^5*f^6*g + 31*d^5*e^4*f^5*g^2 - 99*d^6*e^3*f^4*g^3 - 23*d^7*e^2*f^3*g^4 + 72*d^8*e*f^2*g^5 - 15*d^9*f*g^6 - (7*e^9*f^6*g + 27*d*e^8*f^5*g^2 + 31*d^2*e^7*f^4*g^3 - 99*d^3*e^6*f^3*g^4 - 23*d^4*e^5*f^2*g^5 + 72*d^5*e^4*f*g^6 - 15*d^6*e^3*g^7)*x^4 - (7*e^9*f^7 + 6*d*e^8*f^6*g - 50*d^2*e^7*f^5*g^2 - 192*d^3*e^6*f^4*g^3 + 274*d^4*e^5*f^3*g^4 + 141*d^5*e^4*f^2*g^5 - 231*d^6*e^3*f*g^6 + 45*d^7*e^2*g^7)*x^3 + 3*(7*d*e^8*f^7 + 20*d^2*e^7*f^6*g + 4*d^3*e^6*f^5*g^2 - 130*d^4*e^5*f^4*g^3 + 76*d^5*e^4*f^3*g^4 + 95*d^6*e^3*f^2*g^5 - 87*d^7*e^2*f*g^6 + 15*d^8*e*g^7)*x^2 + 30*(4*d^6*e^2*f^3*g^3 - 3*d^7*e*f^2*g^4 - (4*d^3*e^5*f^2*g^4 - 3*d^4*e^4*f*g^5)*x^4 - (4*d^3*e^5*f^3*g^3 - 15*d^4*e^4*f^2*g^4 + 9*d^5*e^3*f*g^5)*x^3 + 3*(4*d^4*e^4*f^3*g^3 - 7*d^5*e^3*f^2*g^4 + 3*d^6*e^2*f*g^5)*x^2 - (12*d^5*e^3*f^3*g^3 - 13*d^6*e^2*f^2*g^4 + 3*d^7*e*f*g^5)*x)*sqrt(e^2*f^2 - d^2*g^2)*arctan((d*g*x + d*f - sqrt(-e^2*x^2 + d^2)*f)/(sqrt(e^2*f^2 - d^2*g^2)*x)) - (21*d^2*e^7*f^7 + 74*d^3*e^6*f^6*g + 66*d^4*e^5*f^5*g^2 - 328*d^5*e^4*f^4*g^3 + 30*d^6*e^3*f^3*g^4 + 239*d^7*e^2*f^2*g^5 - 117*d^8*e*f*g^6 + 15*d^9*g^7)*x + (7*d^2*e^6*f^7 + 27*d^3*e^5*f^6*g + 31*d^4*e^4*f^5*g^2 - 99*d^5*e^3*f^4*g^3 - 23*d^6*e^2*f^3*g^4 + 72*d^7*e*f^2*g^5 - 15*d^8*f*g^6 + (2*e^8*f^6*g + 12*d*e^7*f^5*g^2 + 41*d^2*e^6*f^4*g^3 - 84*d^3*e^5*f^3*g^4 - 43*d^4*e^4*f^2*g^5 + 72*d^5*e^3*f*g^6)*x^3 + (2*e^8*f^7 + 6*d*e^7*f^6*g + 5*d^2*e^6*f^5*g^2 - 147*d^3*e^5*f^4*g^3 + 164*d^4*e^4*f^3*g^4 + 141*d^5*e^3*f^2*g^5 - 171*d^6*e^2*f*g^6)*x^2 - (6*d*e^7*f^7 + 29*d^2*e^6*f^6*g + 51*d^3*e^5*f^5*g^2 - 193*d^4*e^4*f^4*g^3 + 60*d^5*e^3*f^3*g^4 + 164*d^6*e^2*f^2*g^5 - 117*d^7*e*f*g^6)*x)*sqrt(-e^2*x^2 + d^2))/(d^6*e^7*f^9 + 3*d^7*e^6*f^8*g + d^8*e^5*f^7*g^2 - 5*d^9*e^4*f^6*g^3 - 5*d^10*e^3*f^5*g^4 + d^11*e^2*f^4*g^5 + 3*d^12*e*f^3*g^6 + d^13*f^2*g^7 - (d^3*e^10*f^8*g + 3*d^4*e^9*f^7*g^2 + d^5*e^8*f^6*g^3 - 5*d^6*e^7*f^5*g^4 - 5*d^7*e^6*f^4*g^5 + d^8*e^5*f^3*g^6 + 3*d^9*e^4*f^2*g^7 + d^10*e^3*f*g^8)*x^4 - (d^3*e^10*f^9 - 8*d^5*e^8*f^7*g^2 - 8*d^6*e^7*f^6*g^3 + 10*d^7*e^6*f^5*g^4 + 16*d^8*e^5*f^4*g^5 - 8*d^10*e^3*f^2*g^7 - 3*d^11*e^2*f*g^8)*x^3 + 3*(d^4*e^9*f^9 + 2*d^5*e^8*f^8*g - 2*d^6*e^7*f^7*g^2 - 6*d^7*e^6*f^6*g^3 + 6*d^9*e^4*f^4*g^5 + 2*d^10*e^3*f^3*g^6 - 2*d^11*e^2*f^2*g^7 - d^12*e*f*g^8)*x^2 - (3*d^5*e^8*f^9 + 8*d^6*e^7*f^8*g - 16*d^8*e^5*f^6*g^3 - 10*d^9*e^4*f^5*g^4 + 8*d^10*e^3*f^4*g^5 + 8*d^11*e^2*f^3*g^6 - d^13*f*g^8)*x)]","B",0
587,1,5361,0,3.547239," ","integrate((e*x+d)^3/(g*x+f)^3/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","\left[\frac{14 \, d^{3} e^{8} f^{10} + 60 \, d^{4} e^{7} f^{9} g + 78 \, d^{5} e^{6} f^{8} g^{2} - 480 \, d^{6} e^{5} f^{7} g^{3} + 312 \, d^{7} e^{4} f^{6} g^{4} + 330 \, d^{8} e^{3} f^{5} g^{5} - 419 \, d^{9} e^{2} f^{4} g^{6} + 90 \, d^{10} e f^{3} g^{7} + 15 \, d^{11} f^{2} g^{8} - {\left(14 \, e^{11} f^{8} g^{2} + 60 \, d e^{10} f^{7} g^{3} + 78 \, d^{2} e^{9} f^{6} g^{4} - 480 \, d^{3} e^{8} f^{5} g^{5} + 312 \, d^{4} e^{7} f^{4} g^{6} + 330 \, d^{5} e^{6} f^{3} g^{7} - 419 \, d^{6} e^{5} f^{2} g^{8} + 90 \, d^{7} e^{4} f g^{9} + 15 \, d^{8} e^{3} g^{10}\right)} x^{5} - {\left(28 \, e^{11} f^{9} g + 78 \, d e^{10} f^{8} g^{2} - 24 \, d^{2} e^{9} f^{7} g^{3} - 1194 \, d^{3} e^{8} f^{6} g^{4} + 2064 \, d^{4} e^{7} f^{5} g^{5} - 276 \, d^{5} e^{6} f^{4} g^{6} - 1828 \, d^{6} e^{5} f^{3} g^{7} + 1437 \, d^{7} e^{4} f^{2} g^{8} - 240 \, d^{8} e^{3} f g^{9} - 45 \, d^{9} e^{2} g^{10}\right)} x^{4} - {\left(14 \, e^{11} f^{10} - 24 \, d e^{10} f^{9} g - 240 \, d^{2} e^{9} f^{8} g^{2} - 768 \, d^{3} e^{8} f^{7} g^{3} + 3426 \, d^{4} e^{7} f^{6} g^{4} - 2982 \, d^{5} e^{6} f^{5} g^{5} - 1463 \, d^{6} e^{5} f^{4} g^{6} + 3594 \, d^{7} e^{4} f^{3} g^{7} - 1782 \, d^{8} e^{3} f^{2} g^{8} + 180 \, d^{9} e^{2} f g^{9} + 45 \, d^{10} e g^{10}\right)} x^{3} + {\left(42 \, d e^{10} f^{10} + 96 \, d^{2} e^{9} f^{9} g - 112 \, d^{3} e^{8} f^{8} g^{2} - 1848 \, d^{4} e^{7} f^{7} g^{3} + 3894 \, d^{5} e^{6} f^{6} g^{4} - 1362 \, d^{6} e^{5} f^{5} g^{5} - 2925 \, d^{7} e^{4} f^{4} g^{6} + 3114 \, d^{8} e^{3} f^{3} g^{7} - 914 \, d^{9} e^{2} f^{2} g^{8} + 15 \, d^{11} g^{10}\right)} x^{2} - 15 \, {\left(20 \, d^{6} e^{4} f^{6} g^{3} - 30 \, d^{7} e^{3} f^{5} g^{4} + 13 \, d^{8} e^{2} f^{4} g^{5} - {\left(20 \, d^{3} e^{7} f^{4} g^{5} - 30 \, d^{4} e^{6} f^{3} g^{6} + 13 \, d^{5} e^{5} f^{2} g^{7}\right)} x^{5} - {\left(40 \, d^{3} e^{7} f^{5} g^{4} - 120 \, d^{4} e^{6} f^{4} g^{5} + 116 \, d^{5} e^{5} f^{3} g^{6} - 39 \, d^{6} e^{4} f^{2} g^{7}\right)} x^{4} - {\left(20 \, d^{3} e^{7} f^{6} g^{3} - 150 \, d^{4} e^{6} f^{5} g^{4} + 253 \, d^{5} e^{5} f^{4} g^{5} - 168 \, d^{6} e^{4} f^{3} g^{6} + 39 \, d^{7} e^{3} f^{2} g^{7}\right)} x^{3} + {\left(60 \, d^{4} e^{6} f^{6} g^{3} - 210 \, d^{5} e^{5} f^{5} g^{4} + 239 \, d^{6} e^{4} f^{4} g^{5} - 108 \, d^{7} e^{3} f^{3} g^{6} + 13 \, d^{8} e^{2} f^{2} g^{7}\right)} x^{2} - {\left(60 \, d^{5} e^{5} f^{6} g^{3} - 130 \, d^{6} e^{4} f^{5} g^{4} + 99 \, d^{7} e^{3} f^{4} g^{5} - 26 \, d^{8} e^{2} f^{3} g^{6}\right)} x\right)} \sqrt{-e^{2} f^{2} + d^{2} g^{2}} \log\left(\frac{d e^{2} f g x + d^{3} g^{2} - \sqrt{-e^{2} f^{2} + d^{2} g^{2}} {\left(e^{2} f x + d^{2} g + \sqrt{-e^{2} x^{2} + d^{2}} d g\right)} - {\left(e^{2} f^{2} - d^{2} g^{2}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{g x + f}\right) - {\left(42 \, d^{2} e^{9} f^{10} + 152 \, d^{3} e^{8} f^{9} g + 114 \, d^{4} e^{7} f^{8} g^{2} - 1596 \, d^{5} e^{6} f^{7} g^{3} + 1896 \, d^{6} e^{5} f^{6} g^{4} + 366 \, d^{7} e^{4} f^{5} g^{5} - 1917 \, d^{8} e^{3} f^{4} g^{6} + 1108 \, d^{9} e^{2} f^{3} g^{7} - 135 \, d^{10} e f^{2} g^{8} - 30 \, d^{11} f g^{9}\right)} x + {\left(14 \, d^{2} e^{8} f^{10} + 60 \, d^{3} e^{7} f^{9} g + 78 \, d^{4} e^{6} f^{8} g^{2} - 480 \, d^{5} e^{5} f^{7} g^{3} + 312 \, d^{6} e^{4} f^{6} g^{4} + 330 \, d^{7} e^{3} f^{5} g^{5} - 419 \, d^{8} e^{2} f^{4} g^{6} + 90 \, d^{9} e f^{3} g^{7} + 15 \, d^{10} f^{2} g^{8} + {\left(4 \, e^{10} f^{8} g^{2} + 30 \, d e^{9} f^{7} g^{3} + 138 \, d^{2} e^{8} f^{6} g^{4} - 555 \, d^{3} e^{7} f^{5} g^{5} + 162 \, d^{4} e^{6} f^{4} g^{6} + 525 \, d^{5} e^{5} f^{3} g^{7} - 304 \, d^{6} e^{4} f^{2} g^{8}\right)} x^{4} + {\left(8 \, e^{10} f^{9} g + 48 \, d e^{9} f^{8} g^{2} + 186 \, d^{2} e^{8} f^{7} g^{3} - 1224 \, d^{3} e^{7} f^{6} g^{4} + 1539 \, d^{4} e^{6} f^{5} g^{5} + 459 \, d^{5} e^{5} f^{4} g^{6} - 1733 \, d^{6} e^{4} f^{3} g^{7} + 717 \, d^{7} e^{3} f^{2} g^{8}\right)} x^{3} + {\left(4 \, e^{10} f^{10} + 6 \, d e^{9} f^{9} g - 28 \, d^{2} e^{8} f^{8} g^{2} - 828 \, d^{3} e^{7} f^{7} g^{3} + 2400 \, d^{4} e^{6} f^{6} g^{4} - 1197 \, d^{5} e^{5} f^{5} g^{5} - 1897 \, d^{6} e^{4} f^{4} g^{6} + 2019 \, d^{7} e^{3} f^{3} g^{7} - 479 \, d^{8} e^{2} f^{2} g^{8}\right)} x^{2} - {\left(12 \, d e^{9} f^{10} + 62 \, d^{2} e^{8} f^{9} g + 114 \, d^{3} e^{7} f^{8} g^{2} - 1056 \, d^{4} e^{6} f^{7} g^{3} + 1626 \, d^{5} e^{5} f^{6} g^{4} + 81 \, d^{6} e^{4} f^{5} g^{5} - 1707 \, d^{7} e^{3} f^{4} g^{6} + 913 \, d^{8} e^{2} f^{3} g^{7} - 45 \, d^{9} e f^{2} g^{8}\right)} x\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{30 \, {\left(d^{6} e^{9} f^{13} + 3 \, d^{7} e^{8} f^{12} g - 8 \, d^{9} e^{6} f^{10} g^{3} - 6 \, d^{10} e^{5} f^{9} g^{4} + 6 \, d^{11} e^{4} f^{8} g^{5} + 8 \, d^{12} e^{3} f^{7} g^{6} - 3 \, d^{14} e f^{5} g^{8} - d^{15} f^{4} g^{9} - {\left(d^{3} e^{12} f^{11} g^{2} + 3 \, d^{4} e^{11} f^{10} g^{3} - 8 \, d^{6} e^{9} f^{8} g^{5} - 6 \, d^{7} e^{8} f^{7} g^{6} + 6 \, d^{8} e^{7} f^{6} g^{7} + 8 \, d^{9} e^{6} f^{5} g^{8} - 3 \, d^{11} e^{4} f^{3} g^{10} - d^{12} e^{3} f^{2} g^{11}\right)} x^{5} - {\left(2 \, d^{3} e^{12} f^{12} g + 3 \, d^{4} e^{11} f^{11} g^{2} - 9 \, d^{5} e^{10} f^{10} g^{3} - 16 \, d^{6} e^{9} f^{9} g^{4} + 12 \, d^{7} e^{8} f^{8} g^{5} + 30 \, d^{8} e^{7} f^{7} g^{6} - 2 \, d^{9} e^{6} f^{6} g^{7} - 24 \, d^{10} e^{5} f^{5} g^{8} - 6 \, d^{11} e^{4} f^{4} g^{9} + 7 \, d^{12} e^{3} f^{3} g^{10} + 3 \, d^{13} e^{2} f^{2} g^{11}\right)} x^{4} - {\left(d^{3} e^{12} f^{13} - 3 \, d^{4} e^{11} f^{12} g - 15 \, d^{5} e^{10} f^{11} g^{2} + d^{6} e^{9} f^{10} g^{3} + 42 \, d^{7} e^{8} f^{9} g^{4} + 18 \, d^{8} e^{7} f^{8} g^{5} - 46 \, d^{9} e^{6} f^{7} g^{6} - 30 \, d^{10} e^{5} f^{6} g^{7} + 21 \, d^{11} e^{4} f^{5} g^{8} + 17 \, d^{12} e^{3} f^{4} g^{9} - 3 \, d^{13} e^{2} f^{3} g^{10} - 3 \, d^{14} e f^{2} g^{11}\right)} x^{3} + {\left(3 \, d^{4} e^{11} f^{13} + 3 \, d^{5} e^{10} f^{12} g - 17 \, d^{6} e^{9} f^{11} g^{2} - 21 \, d^{7} e^{8} f^{10} g^{3} + 30 \, d^{8} e^{7} f^{9} g^{4} + 46 \, d^{9} e^{6} f^{8} g^{5} - 18 \, d^{10} e^{5} f^{7} g^{6} - 42 \, d^{11} e^{4} f^{6} g^{7} - d^{12} e^{3} f^{5} g^{8} + 15 \, d^{13} e^{2} f^{4} g^{9} + 3 \, d^{14} e f^{3} g^{10} - d^{15} f^{2} g^{11}\right)} x^{2} - {\left(3 \, d^{5} e^{10} f^{13} + 7 \, d^{6} e^{9} f^{12} g - 6 \, d^{7} e^{8} f^{11} g^{2} - 24 \, d^{8} e^{7} f^{10} g^{3} - 2 \, d^{9} e^{6} f^{9} g^{4} + 30 \, d^{10} e^{5} f^{8} g^{5} + 12 \, d^{11} e^{4} f^{7} g^{6} - 16 \, d^{12} e^{3} f^{6} g^{7} - 9 \, d^{13} e^{2} f^{5} g^{8} + 3 \, d^{14} e f^{4} g^{9} + 2 \, d^{15} f^{3} g^{10}\right)} x\right)}}, \frac{14 \, d^{3} e^{8} f^{10} + 60 \, d^{4} e^{7} f^{9} g + 78 \, d^{5} e^{6} f^{8} g^{2} - 480 \, d^{6} e^{5} f^{7} g^{3} + 312 \, d^{7} e^{4} f^{6} g^{4} + 330 \, d^{8} e^{3} f^{5} g^{5} - 419 \, d^{9} e^{2} f^{4} g^{6} + 90 \, d^{10} e f^{3} g^{7} + 15 \, d^{11} f^{2} g^{8} - {\left(14 \, e^{11} f^{8} g^{2} + 60 \, d e^{10} f^{7} g^{3} + 78 \, d^{2} e^{9} f^{6} g^{4} - 480 \, d^{3} e^{8} f^{5} g^{5} + 312 \, d^{4} e^{7} f^{4} g^{6} + 330 \, d^{5} e^{6} f^{3} g^{7} - 419 \, d^{6} e^{5} f^{2} g^{8} + 90 \, d^{7} e^{4} f g^{9} + 15 \, d^{8} e^{3} g^{10}\right)} x^{5} - {\left(28 \, e^{11} f^{9} g + 78 \, d e^{10} f^{8} g^{2} - 24 \, d^{2} e^{9} f^{7} g^{3} - 1194 \, d^{3} e^{8} f^{6} g^{4} + 2064 \, d^{4} e^{7} f^{5} g^{5} - 276 \, d^{5} e^{6} f^{4} g^{6} - 1828 \, d^{6} e^{5} f^{3} g^{7} + 1437 \, d^{7} e^{4} f^{2} g^{8} - 240 \, d^{8} e^{3} f g^{9} - 45 \, d^{9} e^{2} g^{10}\right)} x^{4} - {\left(14 \, e^{11} f^{10} - 24 \, d e^{10} f^{9} g - 240 \, d^{2} e^{9} f^{8} g^{2} - 768 \, d^{3} e^{8} f^{7} g^{3} + 3426 \, d^{4} e^{7} f^{6} g^{4} - 2982 \, d^{5} e^{6} f^{5} g^{5} - 1463 \, d^{6} e^{5} f^{4} g^{6} + 3594 \, d^{7} e^{4} f^{3} g^{7} - 1782 \, d^{8} e^{3} f^{2} g^{8} + 180 \, d^{9} e^{2} f g^{9} + 45 \, d^{10} e g^{10}\right)} x^{3} + {\left(42 \, d e^{10} f^{10} + 96 \, d^{2} e^{9} f^{9} g - 112 \, d^{3} e^{8} f^{8} g^{2} - 1848 \, d^{4} e^{7} f^{7} g^{3} + 3894 \, d^{5} e^{6} f^{6} g^{4} - 1362 \, d^{6} e^{5} f^{5} g^{5} - 2925 \, d^{7} e^{4} f^{4} g^{6} + 3114 \, d^{8} e^{3} f^{3} g^{7} - 914 \, d^{9} e^{2} f^{2} g^{8} + 15 \, d^{11} g^{10}\right)} x^{2} + 30 \, {\left(20 \, d^{6} e^{4} f^{6} g^{3} - 30 \, d^{7} e^{3} f^{5} g^{4} + 13 \, d^{8} e^{2} f^{4} g^{5} - {\left(20 \, d^{3} e^{7} f^{4} g^{5} - 30 \, d^{4} e^{6} f^{3} g^{6} + 13 \, d^{5} e^{5} f^{2} g^{7}\right)} x^{5} - {\left(40 \, d^{3} e^{7} f^{5} g^{4} - 120 \, d^{4} e^{6} f^{4} g^{5} + 116 \, d^{5} e^{5} f^{3} g^{6} - 39 \, d^{6} e^{4} f^{2} g^{7}\right)} x^{4} - {\left(20 \, d^{3} e^{7} f^{6} g^{3} - 150 \, d^{4} e^{6} f^{5} g^{4} + 253 \, d^{5} e^{5} f^{4} g^{5} - 168 \, d^{6} e^{4} f^{3} g^{6} + 39 \, d^{7} e^{3} f^{2} g^{7}\right)} x^{3} + {\left(60 \, d^{4} e^{6} f^{6} g^{3} - 210 \, d^{5} e^{5} f^{5} g^{4} + 239 \, d^{6} e^{4} f^{4} g^{5} - 108 \, d^{7} e^{3} f^{3} g^{6} + 13 \, d^{8} e^{2} f^{2} g^{7}\right)} x^{2} - {\left(60 \, d^{5} e^{5} f^{6} g^{3} - 130 \, d^{6} e^{4} f^{5} g^{4} + 99 \, d^{7} e^{3} f^{4} g^{5} - 26 \, d^{8} e^{2} f^{3} g^{6}\right)} x\right)} \sqrt{e^{2} f^{2} - d^{2} g^{2}} \arctan\left(\frac{d g x + d f - \sqrt{-e^{2} x^{2} + d^{2}} f}{\sqrt{e^{2} f^{2} - d^{2} g^{2}} x}\right) - {\left(42 \, d^{2} e^{9} f^{10} + 152 \, d^{3} e^{8} f^{9} g + 114 \, d^{4} e^{7} f^{8} g^{2} - 1596 \, d^{5} e^{6} f^{7} g^{3} + 1896 \, d^{6} e^{5} f^{6} g^{4} + 366 \, d^{7} e^{4} f^{5} g^{5} - 1917 \, d^{8} e^{3} f^{4} g^{6} + 1108 \, d^{9} e^{2} f^{3} g^{7} - 135 \, d^{10} e f^{2} g^{8} - 30 \, d^{11} f g^{9}\right)} x + {\left(14 \, d^{2} e^{8} f^{10} + 60 \, d^{3} e^{7} f^{9} g + 78 \, d^{4} e^{6} f^{8} g^{2} - 480 \, d^{5} e^{5} f^{7} g^{3} + 312 \, d^{6} e^{4} f^{6} g^{4} + 330 \, d^{7} e^{3} f^{5} g^{5} - 419 \, d^{8} e^{2} f^{4} g^{6} + 90 \, d^{9} e f^{3} g^{7} + 15 \, d^{10} f^{2} g^{8} + {\left(4 \, e^{10} f^{8} g^{2} + 30 \, d e^{9} f^{7} g^{3} + 138 \, d^{2} e^{8} f^{6} g^{4} - 555 \, d^{3} e^{7} f^{5} g^{5} + 162 \, d^{4} e^{6} f^{4} g^{6} + 525 \, d^{5} e^{5} f^{3} g^{7} - 304 \, d^{6} e^{4} f^{2} g^{8}\right)} x^{4} + {\left(8 \, e^{10} f^{9} g + 48 \, d e^{9} f^{8} g^{2} + 186 \, d^{2} e^{8} f^{7} g^{3} - 1224 \, d^{3} e^{7} f^{6} g^{4} + 1539 \, d^{4} e^{6} f^{5} g^{5} + 459 \, d^{5} e^{5} f^{4} g^{6} - 1733 \, d^{6} e^{4} f^{3} g^{7} + 717 \, d^{7} e^{3} f^{2} g^{8}\right)} x^{3} + {\left(4 \, e^{10} f^{10} + 6 \, d e^{9} f^{9} g - 28 \, d^{2} e^{8} f^{8} g^{2} - 828 \, d^{3} e^{7} f^{7} g^{3} + 2400 \, d^{4} e^{6} f^{6} g^{4} - 1197 \, d^{5} e^{5} f^{5} g^{5} - 1897 \, d^{6} e^{4} f^{4} g^{6} + 2019 \, d^{7} e^{3} f^{3} g^{7} - 479 \, d^{8} e^{2} f^{2} g^{8}\right)} x^{2} - {\left(12 \, d e^{9} f^{10} + 62 \, d^{2} e^{8} f^{9} g + 114 \, d^{3} e^{7} f^{8} g^{2} - 1056 \, d^{4} e^{6} f^{7} g^{3} + 1626 \, d^{5} e^{5} f^{6} g^{4} + 81 \, d^{6} e^{4} f^{5} g^{5} - 1707 \, d^{7} e^{3} f^{4} g^{6} + 913 \, d^{8} e^{2} f^{3} g^{7} - 45 \, d^{9} e f^{2} g^{8}\right)} x\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{30 \, {\left(d^{6} e^{9} f^{13} + 3 \, d^{7} e^{8} f^{12} g - 8 \, d^{9} e^{6} f^{10} g^{3} - 6 \, d^{10} e^{5} f^{9} g^{4} + 6 \, d^{11} e^{4} f^{8} g^{5} + 8 \, d^{12} e^{3} f^{7} g^{6} - 3 \, d^{14} e f^{5} g^{8} - d^{15} f^{4} g^{9} - {\left(d^{3} e^{12} f^{11} g^{2} + 3 \, d^{4} e^{11} f^{10} g^{3} - 8 \, d^{6} e^{9} f^{8} g^{5} - 6 \, d^{7} e^{8} f^{7} g^{6} + 6 \, d^{8} e^{7} f^{6} g^{7} + 8 \, d^{9} e^{6} f^{5} g^{8} - 3 \, d^{11} e^{4} f^{3} g^{10} - d^{12} e^{3} f^{2} g^{11}\right)} x^{5} - {\left(2 \, d^{3} e^{12} f^{12} g + 3 \, d^{4} e^{11} f^{11} g^{2} - 9 \, d^{5} e^{10} f^{10} g^{3} - 16 \, d^{6} e^{9} f^{9} g^{4} + 12 \, d^{7} e^{8} f^{8} g^{5} + 30 \, d^{8} e^{7} f^{7} g^{6} - 2 \, d^{9} e^{6} f^{6} g^{7} - 24 \, d^{10} e^{5} f^{5} g^{8} - 6 \, d^{11} e^{4} f^{4} g^{9} + 7 \, d^{12} e^{3} f^{3} g^{10} + 3 \, d^{13} e^{2} f^{2} g^{11}\right)} x^{4} - {\left(d^{3} e^{12} f^{13} - 3 \, d^{4} e^{11} f^{12} g - 15 \, d^{5} e^{10} f^{11} g^{2} + d^{6} e^{9} f^{10} g^{3} + 42 \, d^{7} e^{8} f^{9} g^{4} + 18 \, d^{8} e^{7} f^{8} g^{5} - 46 \, d^{9} e^{6} f^{7} g^{6} - 30 \, d^{10} e^{5} f^{6} g^{7} + 21 \, d^{11} e^{4} f^{5} g^{8} + 17 \, d^{12} e^{3} f^{4} g^{9} - 3 \, d^{13} e^{2} f^{3} g^{10} - 3 \, d^{14} e f^{2} g^{11}\right)} x^{3} + {\left(3 \, d^{4} e^{11} f^{13} + 3 \, d^{5} e^{10} f^{12} g - 17 \, d^{6} e^{9} f^{11} g^{2} - 21 \, d^{7} e^{8} f^{10} g^{3} + 30 \, d^{8} e^{7} f^{9} g^{4} + 46 \, d^{9} e^{6} f^{8} g^{5} - 18 \, d^{10} e^{5} f^{7} g^{6} - 42 \, d^{11} e^{4} f^{6} g^{7} - d^{12} e^{3} f^{5} g^{8} + 15 \, d^{13} e^{2} f^{4} g^{9} + 3 \, d^{14} e f^{3} g^{10} - d^{15} f^{2} g^{11}\right)} x^{2} - {\left(3 \, d^{5} e^{10} f^{13} + 7 \, d^{6} e^{9} f^{12} g - 6 \, d^{7} e^{8} f^{11} g^{2} - 24 \, d^{8} e^{7} f^{10} g^{3} - 2 \, d^{9} e^{6} f^{9} g^{4} + 30 \, d^{10} e^{5} f^{8} g^{5} + 12 \, d^{11} e^{4} f^{7} g^{6} - 16 \, d^{12} e^{3} f^{6} g^{7} - 9 \, d^{13} e^{2} f^{5} g^{8} + 3 \, d^{14} e f^{4} g^{9} + 2 \, d^{15} f^{3} g^{10}\right)} x\right)}}\right]"," ",0,"[1/30*(14*d^3*e^8*f^10 + 60*d^4*e^7*f^9*g + 78*d^5*e^6*f^8*g^2 - 480*d^6*e^5*f^7*g^3 + 312*d^7*e^4*f^6*g^4 + 330*d^8*e^3*f^5*g^5 - 419*d^9*e^2*f^4*g^6 + 90*d^10*e*f^3*g^7 + 15*d^11*f^2*g^8 - (14*e^11*f^8*g^2 + 60*d*e^10*f^7*g^3 + 78*d^2*e^9*f^6*g^4 - 480*d^3*e^8*f^5*g^5 + 312*d^4*e^7*f^4*g^6 + 330*d^5*e^6*f^3*g^7 - 419*d^6*e^5*f^2*g^8 + 90*d^7*e^4*f*g^9 + 15*d^8*e^3*g^10)*x^5 - (28*e^11*f^9*g + 78*d*e^10*f^8*g^2 - 24*d^2*e^9*f^7*g^3 - 1194*d^3*e^8*f^6*g^4 + 2064*d^4*e^7*f^5*g^5 - 276*d^5*e^6*f^4*g^6 - 1828*d^6*e^5*f^3*g^7 + 1437*d^7*e^4*f^2*g^8 - 240*d^8*e^3*f*g^9 - 45*d^9*e^2*g^10)*x^4 - (14*e^11*f^10 - 24*d*e^10*f^9*g - 240*d^2*e^9*f^8*g^2 - 768*d^3*e^8*f^7*g^3 + 3426*d^4*e^7*f^6*g^4 - 2982*d^5*e^6*f^5*g^5 - 1463*d^6*e^5*f^4*g^6 + 3594*d^7*e^4*f^3*g^7 - 1782*d^8*e^3*f^2*g^8 + 180*d^9*e^2*f*g^9 + 45*d^10*e*g^10)*x^3 + (42*d*e^10*f^10 + 96*d^2*e^9*f^9*g - 112*d^3*e^8*f^8*g^2 - 1848*d^4*e^7*f^7*g^3 + 3894*d^5*e^6*f^6*g^4 - 1362*d^6*e^5*f^5*g^5 - 2925*d^7*e^4*f^4*g^6 + 3114*d^8*e^3*f^3*g^7 - 914*d^9*e^2*f^2*g^8 + 15*d^11*g^10)*x^2 - 15*(20*d^6*e^4*f^6*g^3 - 30*d^7*e^3*f^5*g^4 + 13*d^8*e^2*f^4*g^5 - (20*d^3*e^7*f^4*g^5 - 30*d^4*e^6*f^3*g^6 + 13*d^5*e^5*f^2*g^7)*x^5 - (40*d^3*e^7*f^5*g^4 - 120*d^4*e^6*f^4*g^5 + 116*d^5*e^5*f^3*g^6 - 39*d^6*e^4*f^2*g^7)*x^4 - (20*d^3*e^7*f^6*g^3 - 150*d^4*e^6*f^5*g^4 + 253*d^5*e^5*f^4*g^5 - 168*d^6*e^4*f^3*g^6 + 39*d^7*e^3*f^2*g^7)*x^3 + (60*d^4*e^6*f^6*g^3 - 210*d^5*e^5*f^5*g^4 + 239*d^6*e^4*f^4*g^5 - 108*d^7*e^3*f^3*g^6 + 13*d^8*e^2*f^2*g^7)*x^2 - (60*d^5*e^5*f^6*g^3 - 130*d^6*e^4*f^5*g^4 + 99*d^7*e^3*f^4*g^5 - 26*d^8*e^2*f^3*g^6)*x)*sqrt(-e^2*f^2 + d^2*g^2)*log((d*e^2*f*g*x + d^3*g^2 - sqrt(-e^2*f^2 + d^2*g^2)*(e^2*f*x + d^2*g + sqrt(-e^2*x^2 + d^2)*d*g) - (e^2*f^2 - d^2*g^2)*sqrt(-e^2*x^2 + d^2))/(g*x + f)) - (42*d^2*e^9*f^10 + 152*d^3*e^8*f^9*g + 114*d^4*e^7*f^8*g^2 - 1596*d^5*e^6*f^7*g^3 + 1896*d^6*e^5*f^6*g^4 + 366*d^7*e^4*f^5*g^5 - 1917*d^8*e^3*f^4*g^6 + 1108*d^9*e^2*f^3*g^7 - 135*d^10*e*f^2*g^8 - 30*d^11*f*g^9)*x + (14*d^2*e^8*f^10 + 60*d^3*e^7*f^9*g + 78*d^4*e^6*f^8*g^2 - 480*d^5*e^5*f^7*g^3 + 312*d^6*e^4*f^6*g^4 + 330*d^7*e^3*f^5*g^5 - 419*d^8*e^2*f^4*g^6 + 90*d^9*e*f^3*g^7 + 15*d^10*f^2*g^8 + (4*e^10*f^8*g^2 + 30*d*e^9*f^7*g^3 + 138*d^2*e^8*f^6*g^4 - 555*d^3*e^7*f^5*g^5 + 162*d^4*e^6*f^4*g^6 + 525*d^5*e^5*f^3*g^7 - 304*d^6*e^4*f^2*g^8)*x^4 + (8*e^10*f^9*g + 48*d*e^9*f^8*g^2 + 186*d^2*e^8*f^7*g^3 - 1224*d^3*e^7*f^6*g^4 + 1539*d^4*e^6*f^5*g^5 + 459*d^5*e^5*f^4*g^6 - 1733*d^6*e^4*f^3*g^7 + 717*d^7*e^3*f^2*g^8)*x^3 + (4*e^10*f^10 + 6*d*e^9*f^9*g - 28*d^2*e^8*f^8*g^2 - 828*d^3*e^7*f^7*g^3 + 2400*d^4*e^6*f^6*g^4 - 1197*d^5*e^5*f^5*g^5 - 1897*d^6*e^4*f^4*g^6 + 2019*d^7*e^3*f^3*g^7 - 479*d^8*e^2*f^2*g^8)*x^2 - (12*d*e^9*f^10 + 62*d^2*e^8*f^9*g + 114*d^3*e^7*f^8*g^2 - 1056*d^4*e^6*f^7*g^3 + 1626*d^5*e^5*f^6*g^4 + 81*d^6*e^4*f^5*g^5 - 1707*d^7*e^3*f^4*g^6 + 913*d^8*e^2*f^3*g^7 - 45*d^9*e*f^2*g^8)*x)*sqrt(-e^2*x^2 + d^2))/(d^6*e^9*f^13 + 3*d^7*e^8*f^12*g - 8*d^9*e^6*f^10*g^3 - 6*d^10*e^5*f^9*g^4 + 6*d^11*e^4*f^8*g^5 + 8*d^12*e^3*f^7*g^6 - 3*d^14*e*f^5*g^8 - d^15*f^4*g^9 - (d^3*e^12*f^11*g^2 + 3*d^4*e^11*f^10*g^3 - 8*d^6*e^9*f^8*g^5 - 6*d^7*e^8*f^7*g^6 + 6*d^8*e^7*f^6*g^7 + 8*d^9*e^6*f^5*g^8 - 3*d^11*e^4*f^3*g^10 - d^12*e^3*f^2*g^11)*x^5 - (2*d^3*e^12*f^12*g + 3*d^4*e^11*f^11*g^2 - 9*d^5*e^10*f^10*g^3 - 16*d^6*e^9*f^9*g^4 + 12*d^7*e^8*f^8*g^5 + 30*d^8*e^7*f^7*g^6 - 2*d^9*e^6*f^6*g^7 - 24*d^10*e^5*f^5*g^8 - 6*d^11*e^4*f^4*g^9 + 7*d^12*e^3*f^3*g^10 + 3*d^13*e^2*f^2*g^11)*x^4 - (d^3*e^12*f^13 - 3*d^4*e^11*f^12*g - 15*d^5*e^10*f^11*g^2 + d^6*e^9*f^10*g^3 + 42*d^7*e^8*f^9*g^4 + 18*d^8*e^7*f^8*g^5 - 46*d^9*e^6*f^7*g^6 - 30*d^10*e^5*f^6*g^7 + 21*d^11*e^4*f^5*g^8 + 17*d^12*e^3*f^4*g^9 - 3*d^13*e^2*f^3*g^10 - 3*d^14*e*f^2*g^11)*x^3 + (3*d^4*e^11*f^13 + 3*d^5*e^10*f^12*g - 17*d^6*e^9*f^11*g^2 - 21*d^7*e^8*f^10*g^3 + 30*d^8*e^7*f^9*g^4 + 46*d^9*e^6*f^8*g^5 - 18*d^10*e^5*f^7*g^6 - 42*d^11*e^4*f^6*g^7 - d^12*e^3*f^5*g^8 + 15*d^13*e^2*f^4*g^9 + 3*d^14*e*f^3*g^10 - d^15*f^2*g^11)*x^2 - (3*d^5*e^10*f^13 + 7*d^6*e^9*f^12*g - 6*d^7*e^8*f^11*g^2 - 24*d^8*e^7*f^10*g^3 - 2*d^9*e^6*f^9*g^4 + 30*d^10*e^5*f^8*g^5 + 12*d^11*e^4*f^7*g^6 - 16*d^12*e^3*f^6*g^7 - 9*d^13*e^2*f^5*g^8 + 3*d^14*e*f^4*g^9 + 2*d^15*f^3*g^10)*x), 1/30*(14*d^3*e^8*f^10 + 60*d^4*e^7*f^9*g + 78*d^5*e^6*f^8*g^2 - 480*d^6*e^5*f^7*g^3 + 312*d^7*e^4*f^6*g^4 + 330*d^8*e^3*f^5*g^5 - 419*d^9*e^2*f^4*g^6 + 90*d^10*e*f^3*g^7 + 15*d^11*f^2*g^8 - (14*e^11*f^8*g^2 + 60*d*e^10*f^7*g^3 + 78*d^2*e^9*f^6*g^4 - 480*d^3*e^8*f^5*g^5 + 312*d^4*e^7*f^4*g^6 + 330*d^5*e^6*f^3*g^7 - 419*d^6*e^5*f^2*g^8 + 90*d^7*e^4*f*g^9 + 15*d^8*e^3*g^10)*x^5 - (28*e^11*f^9*g + 78*d*e^10*f^8*g^2 - 24*d^2*e^9*f^7*g^3 - 1194*d^3*e^8*f^6*g^4 + 2064*d^4*e^7*f^5*g^5 - 276*d^5*e^6*f^4*g^6 - 1828*d^6*e^5*f^3*g^7 + 1437*d^7*e^4*f^2*g^8 - 240*d^8*e^3*f*g^9 - 45*d^9*e^2*g^10)*x^4 - (14*e^11*f^10 - 24*d*e^10*f^9*g - 240*d^2*e^9*f^8*g^2 - 768*d^3*e^8*f^7*g^3 + 3426*d^4*e^7*f^6*g^4 - 2982*d^5*e^6*f^5*g^5 - 1463*d^6*e^5*f^4*g^6 + 3594*d^7*e^4*f^3*g^7 - 1782*d^8*e^3*f^2*g^8 + 180*d^9*e^2*f*g^9 + 45*d^10*e*g^10)*x^3 + (42*d*e^10*f^10 + 96*d^2*e^9*f^9*g - 112*d^3*e^8*f^8*g^2 - 1848*d^4*e^7*f^7*g^3 + 3894*d^5*e^6*f^6*g^4 - 1362*d^6*e^5*f^5*g^5 - 2925*d^7*e^4*f^4*g^6 + 3114*d^8*e^3*f^3*g^7 - 914*d^9*e^2*f^2*g^8 + 15*d^11*g^10)*x^2 + 30*(20*d^6*e^4*f^6*g^3 - 30*d^7*e^3*f^5*g^4 + 13*d^8*e^2*f^4*g^5 - (20*d^3*e^7*f^4*g^5 - 30*d^4*e^6*f^3*g^6 + 13*d^5*e^5*f^2*g^7)*x^5 - (40*d^3*e^7*f^5*g^4 - 120*d^4*e^6*f^4*g^5 + 116*d^5*e^5*f^3*g^6 - 39*d^6*e^4*f^2*g^7)*x^4 - (20*d^3*e^7*f^6*g^3 - 150*d^4*e^6*f^5*g^4 + 253*d^5*e^5*f^4*g^5 - 168*d^6*e^4*f^3*g^6 + 39*d^7*e^3*f^2*g^7)*x^3 + (60*d^4*e^6*f^6*g^3 - 210*d^5*e^5*f^5*g^4 + 239*d^6*e^4*f^4*g^5 - 108*d^7*e^3*f^3*g^6 + 13*d^8*e^2*f^2*g^7)*x^2 - (60*d^5*e^5*f^6*g^3 - 130*d^6*e^4*f^5*g^4 + 99*d^7*e^3*f^4*g^5 - 26*d^8*e^2*f^3*g^6)*x)*sqrt(e^2*f^2 - d^2*g^2)*arctan((d*g*x + d*f - sqrt(-e^2*x^2 + d^2)*f)/(sqrt(e^2*f^2 - d^2*g^2)*x)) - (42*d^2*e^9*f^10 + 152*d^3*e^8*f^9*g + 114*d^4*e^7*f^8*g^2 - 1596*d^5*e^6*f^7*g^3 + 1896*d^6*e^5*f^6*g^4 + 366*d^7*e^4*f^5*g^5 - 1917*d^8*e^3*f^4*g^6 + 1108*d^9*e^2*f^3*g^7 - 135*d^10*e*f^2*g^8 - 30*d^11*f*g^9)*x + (14*d^2*e^8*f^10 + 60*d^3*e^7*f^9*g + 78*d^4*e^6*f^8*g^2 - 480*d^5*e^5*f^7*g^3 + 312*d^6*e^4*f^6*g^4 + 330*d^7*e^3*f^5*g^5 - 419*d^8*e^2*f^4*g^6 + 90*d^9*e*f^3*g^7 + 15*d^10*f^2*g^8 + (4*e^10*f^8*g^2 + 30*d*e^9*f^7*g^3 + 138*d^2*e^8*f^6*g^4 - 555*d^3*e^7*f^5*g^5 + 162*d^4*e^6*f^4*g^6 + 525*d^5*e^5*f^3*g^7 - 304*d^6*e^4*f^2*g^8)*x^4 + (8*e^10*f^9*g + 48*d*e^9*f^8*g^2 + 186*d^2*e^8*f^7*g^3 - 1224*d^3*e^7*f^6*g^4 + 1539*d^4*e^6*f^5*g^5 + 459*d^5*e^5*f^4*g^6 - 1733*d^6*e^4*f^3*g^7 + 717*d^7*e^3*f^2*g^8)*x^3 + (4*e^10*f^10 + 6*d*e^9*f^9*g - 28*d^2*e^8*f^8*g^2 - 828*d^3*e^7*f^7*g^3 + 2400*d^4*e^6*f^6*g^4 - 1197*d^5*e^5*f^5*g^5 - 1897*d^6*e^4*f^4*g^6 + 2019*d^7*e^3*f^3*g^7 - 479*d^8*e^2*f^2*g^8)*x^2 - (12*d*e^9*f^10 + 62*d^2*e^8*f^9*g + 114*d^3*e^7*f^8*g^2 - 1056*d^4*e^6*f^7*g^3 + 1626*d^5*e^5*f^6*g^4 + 81*d^6*e^4*f^5*g^5 - 1707*d^7*e^3*f^4*g^6 + 913*d^8*e^2*f^3*g^7 - 45*d^9*e*f^2*g^8)*x)*sqrt(-e^2*x^2 + d^2))/(d^6*e^9*f^13 + 3*d^7*e^8*f^12*g - 8*d^9*e^6*f^10*g^3 - 6*d^10*e^5*f^9*g^4 + 6*d^11*e^4*f^8*g^5 + 8*d^12*e^3*f^7*g^6 - 3*d^14*e*f^5*g^8 - d^15*f^4*g^9 - (d^3*e^12*f^11*g^2 + 3*d^4*e^11*f^10*g^3 - 8*d^6*e^9*f^8*g^5 - 6*d^7*e^8*f^7*g^6 + 6*d^8*e^7*f^6*g^7 + 8*d^9*e^6*f^5*g^8 - 3*d^11*e^4*f^3*g^10 - d^12*e^3*f^2*g^11)*x^5 - (2*d^3*e^12*f^12*g + 3*d^4*e^11*f^11*g^2 - 9*d^5*e^10*f^10*g^3 - 16*d^6*e^9*f^9*g^4 + 12*d^7*e^8*f^8*g^5 + 30*d^8*e^7*f^7*g^6 - 2*d^9*e^6*f^6*g^7 - 24*d^10*e^5*f^5*g^8 - 6*d^11*e^4*f^4*g^9 + 7*d^12*e^3*f^3*g^10 + 3*d^13*e^2*f^2*g^11)*x^4 - (d^3*e^12*f^13 - 3*d^4*e^11*f^12*g - 15*d^5*e^10*f^11*g^2 + d^6*e^9*f^10*g^3 + 42*d^7*e^8*f^9*g^4 + 18*d^8*e^7*f^8*g^5 - 46*d^9*e^6*f^7*g^6 - 30*d^10*e^5*f^6*g^7 + 21*d^11*e^4*f^5*g^8 + 17*d^12*e^3*f^4*g^9 - 3*d^13*e^2*f^3*g^10 - 3*d^14*e*f^2*g^11)*x^3 + (3*d^4*e^11*f^13 + 3*d^5*e^10*f^12*g - 17*d^6*e^9*f^11*g^2 - 21*d^7*e^8*f^10*g^3 + 30*d^8*e^7*f^9*g^4 + 46*d^9*e^6*f^8*g^5 - 18*d^10*e^5*f^7*g^6 - 42*d^11*e^4*f^6*g^7 - d^12*e^3*f^5*g^8 + 15*d^13*e^2*f^4*g^9 + 3*d^14*e*f^3*g^10 - d^15*f^2*g^11)*x^2 - (3*d^5*e^10*f^13 + 7*d^6*e^9*f^12*g - 6*d^7*e^8*f^11*g^2 - 24*d^8*e^7*f^10*g^3 - 2*d^9*e^6*f^9*g^4 + 30*d^10*e^5*f^8*g^5 + 12*d^11*e^4*f^7*g^6 - 16*d^12*e^3*f^6*g^7 - 9*d^13*e^2*f^5*g^8 + 3*d^14*e*f^4*g^9 + 2*d^15*f^3*g^10)*x)]","B",0
588,1,499,0,0.433654," ","integrate((c*x^2+a)/(e*x+d)^(3/2)/(g*x+f),x, algorithm=""fricas"")","\left[\frac{{\left(c d e^{2} f^{2} + a d e^{2} g^{2} + {\left(c e^{3} f^{2} + a e^{3} g^{2}\right)} x\right)} \sqrt{-e f g + d g^{2}} \log\left(\frac{e g x - e f + 2 \, d g - 2 \, \sqrt{-e f g + d g^{2}} \sqrt{e x + d}}{g x + f}\right) + 2 \, {\left(c d e^{2} f^{2} g - {\left(3 \, c d^{2} e + a e^{3}\right)} f g^{2} + {\left(2 \, c d^{3} + a d e^{2}\right)} g^{3} + {\left(c e^{3} f^{2} g - 2 \, c d e^{2} f g^{2} + c d^{2} e g^{3}\right)} x\right)} \sqrt{e x + d}}{d e^{4} f^{2} g^{2} - 2 \, d^{2} e^{3} f g^{3} + d^{3} e^{2} g^{4} + {\left(e^{5} f^{2} g^{2} - 2 \, d e^{4} f g^{3} + d^{2} e^{3} g^{4}\right)} x}, \frac{2 \, {\left({\left(c d e^{2} f^{2} + a d e^{2} g^{2} + {\left(c e^{3} f^{2} + a e^{3} g^{2}\right)} x\right)} \sqrt{e f g - d g^{2}} \arctan\left(\frac{\sqrt{e f g - d g^{2}} \sqrt{e x + d}}{e g x + d g}\right) + {\left(c d e^{2} f^{2} g - {\left(3 \, c d^{2} e + a e^{3}\right)} f g^{2} + {\left(2 \, c d^{3} + a d e^{2}\right)} g^{3} + {\left(c e^{3} f^{2} g - 2 \, c d e^{2} f g^{2} + c d^{2} e g^{3}\right)} x\right)} \sqrt{e x + d}\right)}}{d e^{4} f^{2} g^{2} - 2 \, d^{2} e^{3} f g^{3} + d^{3} e^{2} g^{4} + {\left(e^{5} f^{2} g^{2} - 2 \, d e^{4} f g^{3} + d^{2} e^{3} g^{4}\right)} x}\right]"," ",0,"[((c*d*e^2*f^2 + a*d*e^2*g^2 + (c*e^3*f^2 + a*e^3*g^2)*x)*sqrt(-e*f*g + d*g^2)*log((e*g*x - e*f + 2*d*g - 2*sqrt(-e*f*g + d*g^2)*sqrt(e*x + d))/(g*x + f)) + 2*(c*d*e^2*f^2*g - (3*c*d^2*e + a*e^3)*f*g^2 + (2*c*d^3 + a*d*e^2)*g^3 + (c*e^3*f^2*g - 2*c*d*e^2*f*g^2 + c*d^2*e*g^3)*x)*sqrt(e*x + d))/(d*e^4*f^2*g^2 - 2*d^2*e^3*f*g^3 + d^3*e^2*g^4 + (e^5*f^2*g^2 - 2*d*e^4*f*g^3 + d^2*e^3*g^4)*x), 2*((c*d*e^2*f^2 + a*d*e^2*g^2 + (c*e^3*f^2 + a*e^3*g^2)*x)*sqrt(e*f*g - d*g^2)*arctan(sqrt(e*f*g - d*g^2)*sqrt(e*x + d)/(e*g*x + d*g)) + (c*d*e^2*f^2*g - (3*c*d^2*e + a*e^3)*f*g^2 + (2*c*d^3 + a*d*e^2)*g^3 + (c*e^3*f^2*g - 2*c*d*e^2*f*g^2 + c*d^2*e*g^3)*x)*sqrt(e*x + d))/(d*e^4*f^2*g^2 - 2*d^2*e^3*f*g^3 + d^3*e^2*g^4 + (e^5*f^2*g^2 - 2*d*e^4*f*g^3 + d^2*e^3*g^4)*x)]","B",0
589,1,324,0,0.400486," ","integrate((e*x+d)^3*(c*x^2+a)/(g*x+f)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(315 \, c e^{3} g^{5} x^{5} - 1280 \, c e^{3} f^{5} + 4224 \, c d e^{2} f^{4} g - 6930 \, a d^{2} e f g^{4} + 3465 \, a d^{3} g^{5} - 1584 \, {\left(3 \, c d^{2} e + a e^{3}\right)} f^{3} g^{2} + 1848 \, {\left(c d^{3} + 3 \, a d e^{2}\right)} f^{2} g^{3} - 35 \, {\left(10 \, c e^{3} f g^{4} - 33 \, c d e^{2} g^{5}\right)} x^{4} + 5 \, {\left(80 \, c e^{3} f^{2} g^{3} - 264 \, c d e^{2} f g^{4} + 99 \, {\left(3 \, c d^{2} e + a e^{3}\right)} g^{5}\right)} x^{3} - 3 \, {\left(160 \, c e^{3} f^{3} g^{2} - 528 \, c d e^{2} f^{2} g^{3} + 198 \, {\left(3 \, c d^{2} e + a e^{3}\right)} f g^{4} - 231 \, {\left(c d^{3} + 3 \, a d e^{2}\right)} g^{5}\right)} x^{2} + {\left(640 \, c e^{3} f^{4} g - 2112 \, c d e^{2} f^{3} g^{2} + 3465 \, a d^{2} e g^{5} + 792 \, {\left(3 \, c d^{2} e + a e^{3}\right)} f^{2} g^{3} - 924 \, {\left(c d^{3} + 3 \, a d e^{2}\right)} f g^{4}\right)} x\right)} \sqrt{g x + f}}{3465 \, g^{6}}"," ",0,"2/3465*(315*c*e^3*g^5*x^5 - 1280*c*e^3*f^5 + 4224*c*d*e^2*f^4*g - 6930*a*d^2*e*f*g^4 + 3465*a*d^3*g^5 - 1584*(3*c*d^2*e + a*e^3)*f^3*g^2 + 1848*(c*d^3 + 3*a*d*e^2)*f^2*g^3 - 35*(10*c*e^3*f*g^4 - 33*c*d*e^2*g^5)*x^4 + 5*(80*c*e^3*f^2*g^3 - 264*c*d*e^2*f*g^4 + 99*(3*c*d^2*e + a*e^3)*g^5)*x^3 - 3*(160*c*e^3*f^3*g^2 - 528*c*d*e^2*f^2*g^3 + 198*(3*c*d^2*e + a*e^3)*f*g^4 - 231*(c*d^3 + 3*a*d*e^2)*g^5)*x^2 + (640*c*e^3*f^4*g - 2112*c*d*e^2*f^3*g^2 + 3465*a*d^2*e*g^5 + 792*(3*c*d^2*e + a*e^3)*f^2*g^3 - 924*(c*d^3 + 3*a*d*e^2)*f*g^4)*x)*sqrt(g*x + f)/g^6","A",0
590,1,197,0,0.394014," ","integrate((e*x+d)^2*(c*x^2+a)/(g*x+f)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, c e^{2} g^{4} x^{4} + 128 \, c e^{2} f^{4} - 288 \, c d e f^{3} g - 420 \, a d e f g^{3} + 315 \, a d^{2} g^{4} + 168 \, {\left(c d^{2} + a e^{2}\right)} f^{2} g^{2} - 10 \, {\left(4 \, c e^{2} f g^{3} - 9 \, c d e g^{4}\right)} x^{3} + 3 \, {\left(16 \, c e^{2} f^{2} g^{2} - 36 \, c d e f g^{3} + 21 \, {\left(c d^{2} + a e^{2}\right)} g^{4}\right)} x^{2} - 2 \, {\left(32 \, c e^{2} f^{3} g - 72 \, c d e f^{2} g^{2} - 105 \, a d e g^{4} + 42 \, {\left(c d^{2} + a e^{2}\right)} f g^{3}\right)} x\right)} \sqrt{g x + f}}{315 \, g^{5}}"," ",0,"2/315*(35*c*e^2*g^4*x^4 + 128*c*e^2*f^4 - 288*c*d*e*f^3*g - 420*a*d*e*f*g^3 + 315*a*d^2*g^4 + 168*(c*d^2 + a*e^2)*f^2*g^2 - 10*(4*c*e^2*f*g^3 - 9*c*d*e*g^4)*x^3 + 3*(16*c*e^2*f^2*g^2 - 36*c*d*e*f*g^3 + 21*(c*d^2 + a*e^2)*g^4)*x^2 - 2*(32*c*e^2*f^3*g - 72*c*d*e*f^2*g^2 - 105*a*d*e*g^4 + 42*(c*d^2 + a*e^2)*f*g^3)*x)*sqrt(g*x + f)/g^5","A",0
591,1,100,0,0.387699," ","integrate((e*x+d)*(c*x^2+a)/(g*x+f)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, c e g^{3} x^{3} - 48 \, c e f^{3} + 56 \, c d f^{2} g - 70 \, a e f g^{2} + 105 \, a d g^{3} - 3 \, {\left(6 \, c e f g^{2} - 7 \, c d g^{3}\right)} x^{2} + {\left(24 \, c e f^{2} g - 28 \, c d f g^{2} + 35 \, a e g^{3}\right)} x\right)} \sqrt{g x + f}}{105 \, g^{4}}"," ",0,"2/105*(15*c*e*g^3*x^3 - 48*c*e*f^3 + 56*c*d*f^2*g - 70*a*e*f*g^2 + 105*a*d*g^3 - 3*(6*c*e*f*g^2 - 7*c*d*g^3)*x^2 + (24*c*e*f^2*g - 28*c*d*f*g^2 + 35*a*e*g^3)*x)*sqrt(g*x + f)/g^4","A",0
592,1,40,0,0.399573," ","integrate((c*x^2+a)/(g*x+f)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, c g^{2} x^{2} - 4 \, c f g x + 8 \, c f^{2} + 15 \, a g^{2}\right)} \sqrt{g x + f}}{15 \, g^{3}}"," ",0,"2/15*(3*c*g^2*x^2 - 4*c*f*g*x + 8*c*f^2 + 15*a*g^2)*sqrt(g*x + f)/g^3","A",0
593,1,297,0,0.414517," ","integrate((c*x^2+a)/(e*x+d)/(g*x+f)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(c d^{2} + a e^{2}\right)} \sqrt{e^{2} f - d e g} g^{2} \log\left(\frac{e g x + 2 \, e f - d g - 2 \, \sqrt{e^{2} f - d e g} \sqrt{g x + f}}{e x + d}\right) - 2 \, {\left(2 \, c e^{3} f^{2} + c d e^{2} f g - 3 \, c d^{2} e g^{2} - {\left(c e^{3} f g - c d e^{2} g^{2}\right)} x\right)} \sqrt{g x + f}}{3 \, {\left(e^{4} f g^{2} - d e^{3} g^{3}\right)}}, \frac{2 \, {\left(3 \, {\left(c d^{2} + a e^{2}\right)} \sqrt{-e^{2} f + d e g} g^{2} \arctan\left(\frac{\sqrt{-e^{2} f + d e g} \sqrt{g x + f}}{e g x + e f}\right) - {\left(2 \, c e^{3} f^{2} + c d e^{2} f g - 3 \, c d^{2} e g^{2} - {\left(c e^{3} f g - c d e^{2} g^{2}\right)} x\right)} \sqrt{g x + f}\right)}}{3 \, {\left(e^{4} f g^{2} - d e^{3} g^{3}\right)}}\right]"," ",0,"[1/3*(3*(c*d^2 + a*e^2)*sqrt(e^2*f - d*e*g)*g^2*log((e*g*x + 2*e*f - d*g - 2*sqrt(e^2*f - d*e*g)*sqrt(g*x + f))/(e*x + d)) - 2*(2*c*e^3*f^2 + c*d*e^2*f*g - 3*c*d^2*e*g^2 - (c*e^3*f*g - c*d*e^2*g^2)*x)*sqrt(g*x + f))/(e^4*f*g^2 - d*e^3*g^3), 2/3*(3*(c*d^2 + a*e^2)*sqrt(-e^2*f + d*e*g)*g^2*arctan(sqrt(-e^2*f + d*e*g)*sqrt(g*x + f)/(e*g*x + e*f)) - (2*c*e^3*f^2 + c*d*e^2*f*g - 3*c*d^2*e*g^2 - (c*e^3*f*g - c*d*e^2*g^2)*x)*sqrt(g*x + f))/(e^4*f*g^2 - d*e^3*g^3)]","A",0
594,1,539,0,0.409459," ","integrate((c*x^2+a)/(e*x+d)^2/(g*x+f)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(4 \, c d^{2} e f g - {\left(3 \, c d^{3} - a d e^{2}\right)} g^{2} + {\left(4 \, c d e^{2} f g - {\left(3 \, c d^{2} e - a e^{3}\right)} g^{2}\right)} x\right)} \sqrt{e^{2} f - d e g} \log\left(\frac{e g x + 2 \, e f - d g - 2 \, \sqrt{e^{2} f - d e g} \sqrt{g x + f}}{e x + d}\right) - 2 \, {\left(2 \, c d e^{3} f^{2} - {\left(5 \, c d^{2} e^{2} + a e^{4}\right)} f g + {\left(3 \, c d^{3} e + a d e^{3}\right)} g^{2} + 2 \, {\left(c e^{4} f^{2} - 2 \, c d e^{3} f g + c d^{2} e^{2} g^{2}\right)} x\right)} \sqrt{g x + f}}{2 \, {\left(d e^{5} f^{2} g - 2 \, d^{2} e^{4} f g^{2} + d^{3} e^{3} g^{3} + {\left(e^{6} f^{2} g - 2 \, d e^{5} f g^{2} + d^{2} e^{4} g^{3}\right)} x\right)}}, -\frac{{\left(4 \, c d^{2} e f g - {\left(3 \, c d^{3} - a d e^{2}\right)} g^{2} + {\left(4 \, c d e^{2} f g - {\left(3 \, c d^{2} e - a e^{3}\right)} g^{2}\right)} x\right)} \sqrt{-e^{2} f + d e g} \arctan\left(\frac{\sqrt{-e^{2} f + d e g} \sqrt{g x + f}}{e g x + e f}\right) - {\left(2 \, c d e^{3} f^{2} - {\left(5 \, c d^{2} e^{2} + a e^{4}\right)} f g + {\left(3 \, c d^{3} e + a d e^{3}\right)} g^{2} + 2 \, {\left(c e^{4} f^{2} - 2 \, c d e^{3} f g + c d^{2} e^{2} g^{2}\right)} x\right)} \sqrt{g x + f}}{d e^{5} f^{2} g - 2 \, d^{2} e^{4} f g^{2} + d^{3} e^{3} g^{3} + {\left(e^{6} f^{2} g - 2 \, d e^{5} f g^{2} + d^{2} e^{4} g^{3}\right)} x}\right]"," ",0,"[-1/2*((4*c*d^2*e*f*g - (3*c*d^3 - a*d*e^2)*g^2 + (4*c*d*e^2*f*g - (3*c*d^2*e - a*e^3)*g^2)*x)*sqrt(e^2*f - d*e*g)*log((e*g*x + 2*e*f - d*g - 2*sqrt(e^2*f - d*e*g)*sqrt(g*x + f))/(e*x + d)) - 2*(2*c*d*e^3*f^2 - (5*c*d^2*e^2 + a*e^4)*f*g + (3*c*d^3*e + a*d*e^3)*g^2 + 2*(c*e^4*f^2 - 2*c*d*e^3*f*g + c*d^2*e^2*g^2)*x)*sqrt(g*x + f))/(d*e^5*f^2*g - 2*d^2*e^4*f*g^2 + d^3*e^3*g^3 + (e^6*f^2*g - 2*d*e^5*f*g^2 + d^2*e^4*g^3)*x), -((4*c*d^2*e*f*g - (3*c*d^3 - a*d*e^2)*g^2 + (4*c*d*e^2*f*g - (3*c*d^2*e - a*e^3)*g^2)*x)*sqrt(-e^2*f + d*e*g)*arctan(sqrt(-e^2*f + d*e*g)*sqrt(g*x + f)/(e*g*x + e*f)) - (2*c*d*e^3*f^2 - (5*c*d^2*e^2 + a*e^4)*f*g + (3*c*d^3*e + a*d*e^3)*g^2 + 2*(c*e^4*f^2 - 2*c*d*e^3*f*g + c*d^2*e^2*g^2)*x)*sqrt(g*x + f))/(d*e^5*f^2*g - 2*d^2*e^4*f*g^2 + d^3*e^3*g^3 + (e^6*f^2*g - 2*d*e^5*f*g^2 + d^2*e^4*g^3)*x)]","B",0
595,1,896,0,0.428112," ","integrate((c*x^2+a)/(e*x+d)^3/(g*x+f)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(8 \, c d^{2} e^{2} f^{2} - 8 \, c d^{3} e f g + 3 \, {\left(c d^{4} + a d^{2} e^{2}\right)} g^{2} + {\left(8 \, c e^{4} f^{2} - 8 \, c d e^{3} f g + 3 \, {\left(c d^{2} e^{2} + a e^{4}\right)} g^{2}\right)} x^{2} + 2 \, {\left(8 \, c d e^{3} f^{2} - 8 \, c d^{2} e^{2} f g + 3 \, {\left(c d^{3} e + a d e^{3}\right)} g^{2}\right)} x\right)} \sqrt{e^{2} f - d e g} \log\left(\frac{e g x + 2 \, e f - d g - 2 \, \sqrt{e^{2} f - d e g} \sqrt{g x + f}}{e x + d}\right) + 2 \, {\left(2 \, {\left(3 \, c d^{2} e^{3} - a e^{5}\right)} f^{2} - {\left(9 \, c d^{3} e^{2} - 7 \, a d e^{4}\right)} f g + {\left(3 \, c d^{4} e - 5 \, a d^{2} e^{3}\right)} g^{2} + {\left(8 \, c d e^{4} f^{2} - {\left(13 \, c d^{2} e^{3} - 3 \, a e^{5}\right)} f g + {\left(5 \, c d^{3} e^{2} - 3 \, a d e^{4}\right)} g^{2}\right)} x\right)} \sqrt{g x + f}}{8 \, {\left(d^{2} e^{6} f^{3} - 3 \, d^{3} e^{5} f^{2} g + 3 \, d^{4} e^{4} f g^{2} - d^{5} e^{3} g^{3} + {\left(e^{8} f^{3} - 3 \, d e^{7} f^{2} g + 3 \, d^{2} e^{6} f g^{2} - d^{3} e^{5} g^{3}\right)} x^{2} + 2 \, {\left(d e^{7} f^{3} - 3 \, d^{2} e^{6} f^{2} g + 3 \, d^{3} e^{5} f g^{2} - d^{4} e^{4} g^{3}\right)} x\right)}}, \frac{{\left(8 \, c d^{2} e^{2} f^{2} - 8 \, c d^{3} e f g + 3 \, {\left(c d^{4} + a d^{2} e^{2}\right)} g^{2} + {\left(8 \, c e^{4} f^{2} - 8 \, c d e^{3} f g + 3 \, {\left(c d^{2} e^{2} + a e^{4}\right)} g^{2}\right)} x^{2} + 2 \, {\left(8 \, c d e^{3} f^{2} - 8 \, c d^{2} e^{2} f g + 3 \, {\left(c d^{3} e + a d e^{3}\right)} g^{2}\right)} x\right)} \sqrt{-e^{2} f + d e g} \arctan\left(\frac{\sqrt{-e^{2} f + d e g} \sqrt{g x + f}}{e g x + e f}\right) + {\left(2 \, {\left(3 \, c d^{2} e^{3} - a e^{5}\right)} f^{2} - {\left(9 \, c d^{3} e^{2} - 7 \, a d e^{4}\right)} f g + {\left(3 \, c d^{4} e - 5 \, a d^{2} e^{3}\right)} g^{2} + {\left(8 \, c d e^{4} f^{2} - {\left(13 \, c d^{2} e^{3} - 3 \, a e^{5}\right)} f g + {\left(5 \, c d^{3} e^{2} - 3 \, a d e^{4}\right)} g^{2}\right)} x\right)} \sqrt{g x + f}}{4 \, {\left(d^{2} e^{6} f^{3} - 3 \, d^{3} e^{5} f^{2} g + 3 \, d^{4} e^{4} f g^{2} - d^{5} e^{3} g^{3} + {\left(e^{8} f^{3} - 3 \, d e^{7} f^{2} g + 3 \, d^{2} e^{6} f g^{2} - d^{3} e^{5} g^{3}\right)} x^{2} + 2 \, {\left(d e^{7} f^{3} - 3 \, d^{2} e^{6} f^{2} g + 3 \, d^{3} e^{5} f g^{2} - d^{4} e^{4} g^{3}\right)} x\right)}}\right]"," ",0,"[1/8*((8*c*d^2*e^2*f^2 - 8*c*d^3*e*f*g + 3*(c*d^4 + a*d^2*e^2)*g^2 + (8*c*e^4*f^2 - 8*c*d*e^3*f*g + 3*(c*d^2*e^2 + a*e^4)*g^2)*x^2 + 2*(8*c*d*e^3*f^2 - 8*c*d^2*e^2*f*g + 3*(c*d^3*e + a*d*e^3)*g^2)*x)*sqrt(e^2*f - d*e*g)*log((e*g*x + 2*e*f - d*g - 2*sqrt(e^2*f - d*e*g)*sqrt(g*x + f))/(e*x + d)) + 2*(2*(3*c*d^2*e^3 - a*e^5)*f^2 - (9*c*d^3*e^2 - 7*a*d*e^4)*f*g + (3*c*d^4*e - 5*a*d^2*e^3)*g^2 + (8*c*d*e^4*f^2 - (13*c*d^2*e^3 - 3*a*e^5)*f*g + (5*c*d^3*e^2 - 3*a*d*e^4)*g^2)*x)*sqrt(g*x + f))/(d^2*e^6*f^3 - 3*d^3*e^5*f^2*g + 3*d^4*e^4*f*g^2 - d^5*e^3*g^3 + (e^8*f^3 - 3*d*e^7*f^2*g + 3*d^2*e^6*f*g^2 - d^3*e^5*g^3)*x^2 + 2*(d*e^7*f^3 - 3*d^2*e^6*f^2*g + 3*d^3*e^5*f*g^2 - d^4*e^4*g^3)*x), 1/4*((8*c*d^2*e^2*f^2 - 8*c*d^3*e*f*g + 3*(c*d^4 + a*d^2*e^2)*g^2 + (8*c*e^4*f^2 - 8*c*d*e^3*f*g + 3*(c*d^2*e^2 + a*e^4)*g^2)*x^2 + 2*(8*c*d*e^3*f^2 - 8*c*d^2*e^2*f*g + 3*(c*d^3*e + a*d*e^3)*g^2)*x)*sqrt(-e^2*f + d*e*g)*arctan(sqrt(-e^2*f + d*e*g)*sqrt(g*x + f)/(e*g*x + e*f)) + (2*(3*c*d^2*e^3 - a*e^5)*f^2 - (9*c*d^3*e^2 - 7*a*d*e^4)*f*g + (3*c*d^4*e - 5*a*d^2*e^3)*g^2 + (8*c*d*e^4*f^2 - (13*c*d^2*e^3 - 3*a*e^5)*f*g + (5*c*d^3*e^2 - 3*a*d*e^4)*g^2)*x)*sqrt(g*x + f))/(d^2*e^6*f^3 - 3*d^3*e^5*f^2*g + 3*d^4*e^4*f*g^2 - d^5*e^3*g^3 + (e^8*f^3 - 3*d*e^7*f^2*g + 3*d^2*e^6*f*g^2 - d^3*e^5*g^3)*x^2 + 2*(d*e^7*f^3 - 3*d^2*e^6*f^2*g + 3*d^3*e^5*f*g^2 - d^4*e^4*g^3)*x)]","B",0
596,1,333,0,0.393190," ","integrate((e*x+d)^3*(c*x^2+a)/(g*x+f)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, c e^{3} g^{5} x^{5} + 1280 \, c e^{3} f^{5} - 3456 \, c d e^{2} f^{4} g + 1890 \, a d^{2} e f g^{4} - 315 \, a d^{3} g^{5} + 1008 \, {\left(3 \, c d^{2} e + a e^{3}\right)} f^{3} g^{2} - 840 \, {\left(c d^{3} + 3 \, a d e^{2}\right)} f^{2} g^{3} - 5 \, {\left(10 \, c e^{3} f g^{4} - 27 \, c d e^{2} g^{5}\right)} x^{4} + {\left(80 \, c e^{3} f^{2} g^{3} - 216 \, c d e^{2} f g^{4} + 63 \, {\left(3 \, c d^{2} e + a e^{3}\right)} g^{5}\right)} x^{3} - {\left(160 \, c e^{3} f^{3} g^{2} - 432 \, c d e^{2} f^{2} g^{3} + 126 \, {\left(3 \, c d^{2} e + a e^{3}\right)} f g^{4} - 105 \, {\left(c d^{3} + 3 \, a d e^{2}\right)} g^{5}\right)} x^{2} + {\left(640 \, c e^{3} f^{4} g - 1728 \, c d e^{2} f^{3} g^{2} + 945 \, a d^{2} e g^{5} + 504 \, {\left(3 \, c d^{2} e + a e^{3}\right)} f^{2} g^{3} - 420 \, {\left(c d^{3} + 3 \, a d e^{2}\right)} f g^{4}\right)} x\right)} \sqrt{g x + f}}{315 \, {\left(g^{7} x + f g^{6}\right)}}"," ",0,"2/315*(35*c*e^3*g^5*x^5 + 1280*c*e^3*f^5 - 3456*c*d*e^2*f^4*g + 1890*a*d^2*e*f*g^4 - 315*a*d^3*g^5 + 1008*(3*c*d^2*e + a*e^3)*f^3*g^2 - 840*(c*d^3 + 3*a*d*e^2)*f^2*g^3 - 5*(10*c*e^3*f*g^4 - 27*c*d*e^2*g^5)*x^4 + (80*c*e^3*f^2*g^3 - 216*c*d*e^2*f*g^4 + 63*(3*c*d^2*e + a*e^3)*g^5)*x^3 - (160*c*e^3*f^3*g^2 - 432*c*d*e^2*f^2*g^3 + 126*(3*c*d^2*e + a*e^3)*f*g^4 - 105*(c*d^3 + 3*a*d*e^2)*g^5)*x^2 + (640*c*e^3*f^4*g - 1728*c*d*e^2*f^3*g^2 + 945*a*d^2*e*g^5 + 504*(3*c*d^2*e + a*e^3)*f^2*g^3 - 420*(c*d^3 + 3*a*d*e^2)*f*g^4)*x)*sqrt(g*x + f)/(g^7*x + f*g^6)","A",0
597,1,206,0,0.381747," ","integrate((e*x+d)^2*(c*x^2+a)/(g*x+f)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, c e^{2} g^{4} x^{4} - 384 \, c e^{2} f^{4} + 672 \, c d e f^{3} g + 420 \, a d e f g^{3} - 105 \, a d^{2} g^{4} - 280 \, {\left(c d^{2} + a e^{2}\right)} f^{2} g^{2} - 6 \, {\left(4 \, c e^{2} f g^{3} - 7 \, c d e g^{4}\right)} x^{3} + {\left(48 \, c e^{2} f^{2} g^{2} - 84 \, c d e f g^{3} + 35 \, {\left(c d^{2} + a e^{2}\right)} g^{4}\right)} x^{2} - 2 \, {\left(96 \, c e^{2} f^{3} g - 168 \, c d e f^{2} g^{2} - 105 \, a d e g^{4} + 70 \, {\left(c d^{2} + a e^{2}\right)} f g^{3}\right)} x\right)} \sqrt{g x + f}}{105 \, {\left(g^{6} x + f g^{5}\right)}}"," ",0,"2/105*(15*c*e^2*g^4*x^4 - 384*c*e^2*f^4 + 672*c*d*e*f^3*g + 420*a*d*e*f*g^3 - 105*a*d^2*g^4 - 280*(c*d^2 + a*e^2)*f^2*g^2 - 6*(4*c*e^2*f*g^3 - 7*c*d*e*g^4)*x^3 + (48*c*e^2*f^2*g^2 - 84*c*d*e*f*g^3 + 35*(c*d^2 + a*e^2)*g^4)*x^2 - 2*(96*c*e^2*f^3*g - 168*c*d*e*f^2*g^2 - 105*a*d*e*g^4 + 70*(c*d^2 + a*e^2)*f*g^3)*x)*sqrt(g*x + f)/(g^6*x + f*g^5)","A",0
598,1,110,0,0.395731," ","integrate((e*x+d)*(c*x^2+a)/(g*x+f)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, c e g^{3} x^{3} + 48 \, c e f^{3} - 40 \, c d f^{2} g + 30 \, a e f g^{2} - 15 \, a d g^{3} - {\left(6 \, c e f g^{2} - 5 \, c d g^{3}\right)} x^{2} + {\left(24 \, c e f^{2} g - 20 \, c d f g^{2} + 15 \, a e g^{3}\right)} x\right)} \sqrt{g x + f}}{15 \, {\left(g^{5} x + f g^{4}\right)}}"," ",0,"2/15*(3*c*e*g^3*x^3 + 48*c*e*f^3 - 40*c*d*f^2*g + 30*a*e*f*g^2 - 15*a*d*g^3 - (6*c*e*f*g^2 - 5*c*d*g^3)*x^2 + (24*c*e*f^2*g - 20*c*d*f*g^2 + 15*a*e*g^3)*x)*sqrt(g*x + f)/(g^5*x + f*g^4)","A",0
599,1,49,0,0.378766," ","integrate((c*x^2+a)/(g*x+f)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(c g^{2} x^{2} - 4 \, c f g x - 8 \, c f^{2} - 3 \, a g^{2}\right)} \sqrt{g x + f}}{3 \, {\left(g^{4} x + f g^{3}\right)}}"," ",0,"2/3*(c*g^2*x^2 - 4*c*f*g*x - 8*c*f^2 - 3*a*g^2)*sqrt(g*x + f)/(g^4*x + f*g^3)","A",0
600,1,492,0,0.424871," ","integrate((c*x^2+a)/(e*x+d)/(g*x+f)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left({\left(c d^{2} + a e^{2}\right)} g^{3} x + {\left(c d^{2} + a e^{2}\right)} f g^{2}\right)} \sqrt{e^{2} f - d e g} \log\left(\frac{e g x + 2 \, e f - d g + 2 \, \sqrt{e^{2} f - d e g} \sqrt{g x + f}}{e x + d}\right) - 2 \, {\left(2 \, c e^{3} f^{3} - 3 \, c d e^{2} f^{2} g - a d e^{2} g^{3} + {\left(c d^{2} e + a e^{3}\right)} f g^{2} + {\left(c e^{3} f^{2} g - 2 \, c d e^{2} f g^{2} + c d^{2} e g^{3}\right)} x\right)} \sqrt{g x + f}}{e^{4} f^{3} g^{2} - 2 \, d e^{3} f^{2} g^{3} + d^{2} e^{2} f g^{4} + {\left(e^{4} f^{2} g^{3} - 2 \, d e^{3} f g^{4} + d^{2} e^{2} g^{5}\right)} x}, \frac{2 \, {\left({\left({\left(c d^{2} + a e^{2}\right)} g^{3} x + {\left(c d^{2} + a e^{2}\right)} f g^{2}\right)} \sqrt{-e^{2} f + d e g} \arctan\left(\frac{\sqrt{-e^{2} f + d e g} \sqrt{g x + f}}{e g x + e f}\right) + {\left(2 \, c e^{3} f^{3} - 3 \, c d e^{2} f^{2} g - a d e^{2} g^{3} + {\left(c d^{2} e + a e^{3}\right)} f g^{2} + {\left(c e^{3} f^{2} g - 2 \, c d e^{2} f g^{2} + c d^{2} e g^{3}\right)} x\right)} \sqrt{g x + f}\right)}}{e^{4} f^{3} g^{2} - 2 \, d e^{3} f^{2} g^{3} + d^{2} e^{2} f g^{4} + {\left(e^{4} f^{2} g^{3} - 2 \, d e^{3} f g^{4} + d^{2} e^{2} g^{5}\right)} x}\right]"," ",0,"[-(((c*d^2 + a*e^2)*g^3*x + (c*d^2 + a*e^2)*f*g^2)*sqrt(e^2*f - d*e*g)*log((e*g*x + 2*e*f - d*g + 2*sqrt(e^2*f - d*e*g)*sqrt(g*x + f))/(e*x + d)) - 2*(2*c*e^3*f^3 - 3*c*d*e^2*f^2*g - a*d*e^2*g^3 + (c*d^2*e + a*e^3)*f*g^2 + (c*e^3*f^2*g - 2*c*d*e^2*f*g^2 + c*d^2*e*g^3)*x)*sqrt(g*x + f))/(e^4*f^3*g^2 - 2*d*e^3*f^2*g^3 + d^2*e^2*f*g^4 + (e^4*f^2*g^3 - 2*d*e^3*f*g^4 + d^2*e^2*g^5)*x), 2*(((c*d^2 + a*e^2)*g^3*x + (c*d^2 + a*e^2)*f*g^2)*sqrt(-e^2*f + d*e*g)*arctan(sqrt(-e^2*f + d*e*g)*sqrt(g*x + f)/(e*g*x + e*f)) + (2*c*e^3*f^3 - 3*c*d*e^2*f^2*g - a*d*e^2*g^3 + (c*d^2*e + a*e^3)*f*g^2 + (c*e^3*f^2*g - 2*c*d*e^2*f*g^2 + c*d^2*e*g^3)*x)*sqrt(g*x + f))/(e^4*f^3*g^2 - 2*d*e^3*f^2*g^3 + d^2*e^2*f*g^4 + (e^4*f^2*g^3 - 2*d*e^3*f*g^4 + d^2*e^2*g^5)*x)]","B",0
601,1,906,0,0.432652," ","integrate((c*x^2+a)/(e*x+d)^2/(g*x+f)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(4 \, c d^{2} e f^{2} g - {\left(c d^{3} - 3 \, a d e^{2}\right)} f g^{2} + {\left(4 \, c d e^{2} f g^{2} - {\left(c d^{2} e - 3 \, a e^{3}\right)} g^{3}\right)} x^{2} + {\left(4 \, c d e^{2} f^{2} g + 3 \, {\left(c d^{2} e + a e^{3}\right)} f g^{2} - {\left(c d^{3} - 3 \, a d e^{2}\right)} g^{3}\right)} x\right)} \sqrt{e^{2} f - d e g} \log\left(\frac{e g x + 2 \, e f - d g + 2 \, \sqrt{e^{2} f - d e g} \sqrt{g x + f}}{e x + d}\right) - 2 \, {\left(2 \, c d e^{3} f^{3} - 2 \, a d^{2} e^{2} g^{3} - {\left(c d^{2} e^{2} - a e^{4}\right)} f^{2} g - {\left(c d^{3} e - a d e^{3}\right)} f g^{2} + {\left(2 \, c e^{4} f^{3} - 2 \, c d e^{3} f^{2} g + {\left(c d^{2} e^{2} + 3 \, a e^{4}\right)} f g^{2} - {\left(c d^{3} e + 3 \, a d e^{3}\right)} g^{3}\right)} x\right)} \sqrt{g x + f}}{2 \, {\left(d e^{5} f^{4} g - 3 \, d^{2} e^{4} f^{3} g^{2} + 3 \, d^{3} e^{3} f^{2} g^{3} - d^{4} e^{2} f g^{4} + {\left(e^{6} f^{3} g^{2} - 3 \, d e^{5} f^{2} g^{3} + 3 \, d^{2} e^{4} f g^{4} - d^{3} e^{3} g^{5}\right)} x^{2} + {\left(e^{6} f^{4} g - 2 \, d e^{5} f^{3} g^{2} + 2 \, d^{3} e^{3} f g^{4} - d^{4} e^{2} g^{5}\right)} x\right)}}, -\frac{{\left(4 \, c d^{2} e f^{2} g - {\left(c d^{3} - 3 \, a d e^{2}\right)} f g^{2} + {\left(4 \, c d e^{2} f g^{2} - {\left(c d^{2} e - 3 \, a e^{3}\right)} g^{3}\right)} x^{2} + {\left(4 \, c d e^{2} f^{2} g + 3 \, {\left(c d^{2} e + a e^{3}\right)} f g^{2} - {\left(c d^{3} - 3 \, a d e^{2}\right)} g^{3}\right)} x\right)} \sqrt{-e^{2} f + d e g} \arctan\left(\frac{\sqrt{-e^{2} f + d e g} \sqrt{g x + f}}{e g x + e f}\right) + {\left(2 \, c d e^{3} f^{3} - 2 \, a d^{2} e^{2} g^{3} - {\left(c d^{2} e^{2} - a e^{4}\right)} f^{2} g - {\left(c d^{3} e - a d e^{3}\right)} f g^{2} + {\left(2 \, c e^{4} f^{3} - 2 \, c d e^{3} f^{2} g + {\left(c d^{2} e^{2} + 3 \, a e^{4}\right)} f g^{2} - {\left(c d^{3} e + 3 \, a d e^{3}\right)} g^{3}\right)} x\right)} \sqrt{g x + f}}{d e^{5} f^{4} g - 3 \, d^{2} e^{4} f^{3} g^{2} + 3 \, d^{3} e^{3} f^{2} g^{3} - d^{4} e^{2} f g^{4} + {\left(e^{6} f^{3} g^{2} - 3 \, d e^{5} f^{2} g^{3} + 3 \, d^{2} e^{4} f g^{4} - d^{3} e^{3} g^{5}\right)} x^{2} + {\left(e^{6} f^{4} g - 2 \, d e^{5} f^{3} g^{2} + 2 \, d^{3} e^{3} f g^{4} - d^{4} e^{2} g^{5}\right)} x}\right]"," ",0,"[1/2*((4*c*d^2*e*f^2*g - (c*d^3 - 3*a*d*e^2)*f*g^2 + (4*c*d*e^2*f*g^2 - (c*d^2*e - 3*a*e^3)*g^3)*x^2 + (4*c*d*e^2*f^2*g + 3*(c*d^2*e + a*e^3)*f*g^2 - (c*d^3 - 3*a*d*e^2)*g^3)*x)*sqrt(e^2*f - d*e*g)*log((e*g*x + 2*e*f - d*g + 2*sqrt(e^2*f - d*e*g)*sqrt(g*x + f))/(e*x + d)) - 2*(2*c*d*e^3*f^3 - 2*a*d^2*e^2*g^3 - (c*d^2*e^2 - a*e^4)*f^2*g - (c*d^3*e - a*d*e^3)*f*g^2 + (2*c*e^4*f^3 - 2*c*d*e^3*f^2*g + (c*d^2*e^2 + 3*a*e^4)*f*g^2 - (c*d^3*e + 3*a*d*e^3)*g^3)*x)*sqrt(g*x + f))/(d*e^5*f^4*g - 3*d^2*e^4*f^3*g^2 + 3*d^3*e^3*f^2*g^3 - d^4*e^2*f*g^4 + (e^6*f^3*g^2 - 3*d*e^5*f^2*g^3 + 3*d^2*e^4*f*g^4 - d^3*e^3*g^5)*x^2 + (e^6*f^4*g - 2*d*e^5*f^3*g^2 + 2*d^3*e^3*f*g^4 - d^4*e^2*g^5)*x), -((4*c*d^2*e*f^2*g - (c*d^3 - 3*a*d*e^2)*f*g^2 + (4*c*d*e^2*f*g^2 - (c*d^2*e - 3*a*e^3)*g^3)*x^2 + (4*c*d*e^2*f^2*g + 3*(c*d^2*e + a*e^3)*f*g^2 - (c*d^3 - 3*a*d*e^2)*g^3)*x)*sqrt(-e^2*f + d*e*g)*arctan(sqrt(-e^2*f + d*e*g)*sqrt(g*x + f)/(e*g*x + e*f)) + (2*c*d*e^3*f^3 - 2*a*d^2*e^2*g^3 - (c*d^2*e^2 - a*e^4)*f^2*g - (c*d^3*e - a*d*e^3)*f*g^2 + (2*c*e^4*f^3 - 2*c*d*e^3*f^2*g + (c*d^2*e^2 + 3*a*e^4)*f*g^2 - (c*d^3*e + 3*a*d*e^3)*g^3)*x)*sqrt(g*x + f))/(d*e^5*f^4*g - 3*d^2*e^4*f^3*g^2 + 3*d^3*e^3*f^2*g^3 - d^4*e^2*f*g^4 + (e^6*f^3*g^2 - 3*d*e^5*f^2*g^3 + 3*d^2*e^4*f*g^4 - d^3*e^3*g^5)*x^2 + (e^6*f^4*g - 2*d*e^5*f^3*g^2 + 2*d^3*e^3*f*g^4 - d^4*e^2*g^5)*x)]","B",0
602,1,1539,0,0.447997," ","integrate((c*x^2+a)/(e*x+d)^3/(g*x+f)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left(8 \, c d^{2} e^{2} f^{3} + 8 \, c d^{3} e f^{2} g - {\left(c d^{4} - 15 \, a d^{2} e^{2}\right)} f g^{2} + {\left(8 \, c e^{4} f^{2} g + 8 \, c d e^{3} f g^{2} - {\left(c d^{2} e^{2} - 15 \, a e^{4}\right)} g^{3}\right)} x^{3} + {\left(8 \, c e^{4} f^{3} + 24 \, c d e^{3} f^{2} g + 15 \, {\left(c d^{2} e^{2} + a e^{4}\right)} f g^{2} - 2 \, {\left(c d^{3} e - 15 \, a d e^{3}\right)} g^{3}\right)} x^{2} + {\left(16 \, c d e^{3} f^{3} + 24 \, c d^{2} e^{2} f^{2} g + 6 \, {\left(c d^{3} e + 5 \, a d e^{3}\right)} f g^{2} - {\left(c d^{4} - 15 \, a d^{2} e^{2}\right)} g^{3}\right)} x\right)} \sqrt{e^{2} f - d e g} \log\left(\frac{e g x + 2 \, e f - d g + 2 \, \sqrt{e^{2} f - d e g} \sqrt{g x + f}}{e x + d}\right) + 2 \, {\left(8 \, a d^{3} e^{2} g^{3} - 2 \, {\left(7 \, c d^{2} e^{3} - a e^{5}\right)} f^{3} + {\left(13 \, c d^{3} e^{2} - 11 \, a d e^{4}\right)} f^{2} g + {\left(c d^{4} e + a d^{2} e^{3}\right)} f g^{2} - {\left(8 \, c e^{5} f^{3} - 3 \, {\left(3 \, c d^{2} e^{3} - 5 \, a e^{5}\right)} f g^{2} + {\left(c d^{3} e^{2} - 15 \, a d e^{4}\right)} g^{3}\right)} x^{2} - {\left(24 \, c d e^{4} f^{3} - {\left(19 \, c d^{2} e^{3} - 5 \, a e^{5}\right)} f^{2} g - 4 \, {\left(c d^{3} e^{2} - 5 \, a d e^{4}\right)} f g^{2} - {\left(c d^{4} e + 25 \, a d^{2} e^{3}\right)} g^{3}\right)} x\right)} \sqrt{g x + f}}{8 \, {\left(d^{2} e^{6} f^{5} - 4 \, d^{3} e^{5} f^{4} g + 6 \, d^{4} e^{4} f^{3} g^{2} - 4 \, d^{5} e^{3} f^{2} g^{3} + d^{6} e^{2} f g^{4} + {\left(e^{8} f^{4} g - 4 \, d e^{7} f^{3} g^{2} + 6 \, d^{2} e^{6} f^{2} g^{3} - 4 \, d^{3} e^{5} f g^{4} + d^{4} e^{4} g^{5}\right)} x^{3} + {\left(e^{8} f^{5} - 2 \, d e^{7} f^{4} g - 2 \, d^{2} e^{6} f^{3} g^{2} + 8 \, d^{3} e^{5} f^{2} g^{3} - 7 \, d^{4} e^{4} f g^{4} + 2 \, d^{5} e^{3} g^{5}\right)} x^{2} + {\left(2 \, d e^{7} f^{5} - 7 \, d^{2} e^{6} f^{4} g + 8 \, d^{3} e^{5} f^{3} g^{2} - 2 \, d^{4} e^{4} f^{2} g^{3} - 2 \, d^{5} e^{3} f g^{4} + d^{6} e^{2} g^{5}\right)} x\right)}}, \frac{{\left(8 \, c d^{2} e^{2} f^{3} + 8 \, c d^{3} e f^{2} g - {\left(c d^{4} - 15 \, a d^{2} e^{2}\right)} f g^{2} + {\left(8 \, c e^{4} f^{2} g + 8 \, c d e^{3} f g^{2} - {\left(c d^{2} e^{2} - 15 \, a e^{4}\right)} g^{3}\right)} x^{3} + {\left(8 \, c e^{4} f^{3} + 24 \, c d e^{3} f^{2} g + 15 \, {\left(c d^{2} e^{2} + a e^{4}\right)} f g^{2} - 2 \, {\left(c d^{3} e - 15 \, a d e^{3}\right)} g^{3}\right)} x^{2} + {\left(16 \, c d e^{3} f^{3} + 24 \, c d^{2} e^{2} f^{2} g + 6 \, {\left(c d^{3} e + 5 \, a d e^{3}\right)} f g^{2} - {\left(c d^{4} - 15 \, a d^{2} e^{2}\right)} g^{3}\right)} x\right)} \sqrt{-e^{2} f + d e g} \arctan\left(\frac{\sqrt{-e^{2} f + d e g} \sqrt{g x + f}}{e g x + e f}\right) - {\left(8 \, a d^{3} e^{2} g^{3} - 2 \, {\left(7 \, c d^{2} e^{3} - a e^{5}\right)} f^{3} + {\left(13 \, c d^{3} e^{2} - 11 \, a d e^{4}\right)} f^{2} g + {\left(c d^{4} e + a d^{2} e^{3}\right)} f g^{2} - {\left(8 \, c e^{5} f^{3} - 3 \, {\left(3 \, c d^{2} e^{3} - 5 \, a e^{5}\right)} f g^{2} + {\left(c d^{3} e^{2} - 15 \, a d e^{4}\right)} g^{3}\right)} x^{2} - {\left(24 \, c d e^{4} f^{3} - {\left(19 \, c d^{2} e^{3} - 5 \, a e^{5}\right)} f^{2} g - 4 \, {\left(c d^{3} e^{2} - 5 \, a d e^{4}\right)} f g^{2} - {\left(c d^{4} e + 25 \, a d^{2} e^{3}\right)} g^{3}\right)} x\right)} \sqrt{g x + f}}{4 \, {\left(d^{2} e^{6} f^{5} - 4 \, d^{3} e^{5} f^{4} g + 6 \, d^{4} e^{4} f^{3} g^{2} - 4 \, d^{5} e^{3} f^{2} g^{3} + d^{6} e^{2} f g^{4} + {\left(e^{8} f^{4} g - 4 \, d e^{7} f^{3} g^{2} + 6 \, d^{2} e^{6} f^{2} g^{3} - 4 \, d^{3} e^{5} f g^{4} + d^{4} e^{4} g^{5}\right)} x^{3} + {\left(e^{8} f^{5} - 2 \, d e^{7} f^{4} g - 2 \, d^{2} e^{6} f^{3} g^{2} + 8 \, d^{3} e^{5} f^{2} g^{3} - 7 \, d^{4} e^{4} f g^{4} + 2 \, d^{5} e^{3} g^{5}\right)} x^{2} + {\left(2 \, d e^{7} f^{5} - 7 \, d^{2} e^{6} f^{4} g + 8 \, d^{3} e^{5} f^{3} g^{2} - 2 \, d^{4} e^{4} f^{2} g^{3} - 2 \, d^{5} e^{3} f g^{4} + d^{6} e^{2} g^{5}\right)} x\right)}}\right]"," ",0,"[-1/8*((8*c*d^2*e^2*f^3 + 8*c*d^3*e*f^2*g - (c*d^4 - 15*a*d^2*e^2)*f*g^2 + (8*c*e^4*f^2*g + 8*c*d*e^3*f*g^2 - (c*d^2*e^2 - 15*a*e^4)*g^3)*x^3 + (8*c*e^4*f^3 + 24*c*d*e^3*f^2*g + 15*(c*d^2*e^2 + a*e^4)*f*g^2 - 2*(c*d^3*e - 15*a*d*e^3)*g^3)*x^2 + (16*c*d*e^3*f^3 + 24*c*d^2*e^2*f^2*g + 6*(c*d^3*e + 5*a*d*e^3)*f*g^2 - (c*d^4 - 15*a*d^2*e^2)*g^3)*x)*sqrt(e^2*f - d*e*g)*log((e*g*x + 2*e*f - d*g + 2*sqrt(e^2*f - d*e*g)*sqrt(g*x + f))/(e*x + d)) + 2*(8*a*d^3*e^2*g^3 - 2*(7*c*d^2*e^3 - a*e^5)*f^3 + (13*c*d^3*e^2 - 11*a*d*e^4)*f^2*g + (c*d^4*e + a*d^2*e^3)*f*g^2 - (8*c*e^5*f^3 - 3*(3*c*d^2*e^3 - 5*a*e^5)*f*g^2 + (c*d^3*e^2 - 15*a*d*e^4)*g^3)*x^2 - (24*c*d*e^4*f^3 - (19*c*d^2*e^3 - 5*a*e^5)*f^2*g - 4*(c*d^3*e^2 - 5*a*d*e^4)*f*g^2 - (c*d^4*e + 25*a*d^2*e^3)*g^3)*x)*sqrt(g*x + f))/(d^2*e^6*f^5 - 4*d^3*e^5*f^4*g + 6*d^4*e^4*f^3*g^2 - 4*d^5*e^3*f^2*g^3 + d^6*e^2*f*g^4 + (e^8*f^4*g - 4*d*e^7*f^3*g^2 + 6*d^2*e^6*f^2*g^3 - 4*d^3*e^5*f*g^4 + d^4*e^4*g^5)*x^3 + (e^8*f^5 - 2*d*e^7*f^4*g - 2*d^2*e^6*f^3*g^2 + 8*d^3*e^5*f^2*g^3 - 7*d^4*e^4*f*g^4 + 2*d^5*e^3*g^5)*x^2 + (2*d*e^7*f^5 - 7*d^2*e^6*f^4*g + 8*d^3*e^5*f^3*g^2 - 2*d^4*e^4*f^2*g^3 - 2*d^5*e^3*f*g^4 + d^6*e^2*g^5)*x), 1/4*((8*c*d^2*e^2*f^3 + 8*c*d^3*e*f^2*g - (c*d^4 - 15*a*d^2*e^2)*f*g^2 + (8*c*e^4*f^2*g + 8*c*d*e^3*f*g^2 - (c*d^2*e^2 - 15*a*e^4)*g^3)*x^3 + (8*c*e^4*f^3 + 24*c*d*e^3*f^2*g + 15*(c*d^2*e^2 + a*e^4)*f*g^2 - 2*(c*d^3*e - 15*a*d*e^3)*g^3)*x^2 + (16*c*d*e^3*f^3 + 24*c*d^2*e^2*f^2*g + 6*(c*d^3*e + 5*a*d*e^3)*f*g^2 - (c*d^4 - 15*a*d^2*e^2)*g^3)*x)*sqrt(-e^2*f + d*e*g)*arctan(sqrt(-e^2*f + d*e*g)*sqrt(g*x + f)/(e*g*x + e*f)) - (8*a*d^3*e^2*g^3 - 2*(7*c*d^2*e^3 - a*e^5)*f^3 + (13*c*d^3*e^2 - 11*a*d*e^4)*f^2*g + (c*d^4*e + a*d^2*e^3)*f*g^2 - (8*c*e^5*f^3 - 3*(3*c*d^2*e^3 - 5*a*e^5)*f*g^2 + (c*d^3*e^2 - 15*a*d*e^4)*g^3)*x^2 - (24*c*d*e^4*f^3 - (19*c*d^2*e^3 - 5*a*e^5)*f^2*g - 4*(c*d^3*e^2 - 5*a*d*e^4)*f*g^2 - (c*d^4*e + 25*a*d^2*e^3)*g^3)*x)*sqrt(g*x + f))/(d^2*e^6*f^5 - 4*d^3*e^5*f^4*g + 6*d^4*e^4*f^3*g^2 - 4*d^5*e^3*f^2*g^3 + d^6*e^2*f*g^4 + (e^8*f^4*g - 4*d*e^7*f^3*g^2 + 6*d^2*e^6*f^2*g^3 - 4*d^3*e^5*f*g^4 + d^4*e^4*g^5)*x^3 + (e^8*f^5 - 2*d*e^7*f^4*g - 2*d^2*e^6*f^3*g^2 + 8*d^3*e^5*f^2*g^3 - 7*d^4*e^4*f*g^4 + 2*d^5*e^3*g^5)*x^2 + (2*d*e^7*f^5 - 7*d^2*e^6*f^4*g + 8*d^3*e^5*f^3*g^2 - 2*d^4*e^4*f^2*g^3 - 2*d^5*e^3*f*g^4 + d^6*e^2*g^5)*x)]","B",0
603,1,336,0,0.469803," ","integrate((c*x^2+a)/(e*x+d)^(1/2)/(g*x+f)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(3 \, c e^{2} f^{2} + 2 \, c d e f g + {\left(3 \, c d^{2} + 8 \, a e^{2}\right)} g^{2}\right)} \sqrt{e g} \log\left(8 \, e^{2} g^{2} x^{2} + e^{2} f^{2} + 6 \, d e f g + d^{2} g^{2} + 4 \, {\left(2 \, e g x + e f + d g\right)} \sqrt{e g} \sqrt{e x + d} \sqrt{g x + f} + 8 \, {\left(e^{2} f g + d e g^{2}\right)} x\right) + 4 \, {\left(2 \, c e^{2} g^{2} x - 3 \, c e^{2} f g - 3 \, c d e g^{2}\right)} \sqrt{e x + d} \sqrt{g x + f}}{16 \, e^{3} g^{3}}, -\frac{{\left(3 \, c e^{2} f^{2} + 2 \, c d e f g + {\left(3 \, c d^{2} + 8 \, a e^{2}\right)} g^{2}\right)} \sqrt{-e g} \arctan\left(\frac{{\left(2 \, e g x + e f + d g\right)} \sqrt{-e g} \sqrt{e x + d} \sqrt{g x + f}}{2 \, {\left(e^{2} g^{2} x^{2} + d e f g + {\left(e^{2} f g + d e g^{2}\right)} x\right)}}\right) - 2 \, {\left(2 \, c e^{2} g^{2} x - 3 \, c e^{2} f g - 3 \, c d e g^{2}\right)} \sqrt{e x + d} \sqrt{g x + f}}{8 \, e^{3} g^{3}}\right]"," ",0,"[1/16*((3*c*e^2*f^2 + 2*c*d*e*f*g + (3*c*d^2 + 8*a*e^2)*g^2)*sqrt(e*g)*log(8*e^2*g^2*x^2 + e^2*f^2 + 6*d*e*f*g + d^2*g^2 + 4*(2*e*g*x + e*f + d*g)*sqrt(e*g)*sqrt(e*x + d)*sqrt(g*x + f) + 8*(e^2*f*g + d*e*g^2)*x) + 4*(2*c*e^2*g^2*x - 3*c*e^2*f*g - 3*c*d*e*g^2)*sqrt(e*x + d)*sqrt(g*x + f))/(e^3*g^3), -1/8*((3*c*e^2*f^2 + 2*c*d*e*f*g + (3*c*d^2 + 8*a*e^2)*g^2)*sqrt(-e*g)*arctan(1/2*(2*e*g*x + e*f + d*g)*sqrt(-e*g)*sqrt(e*x + d)*sqrt(g*x + f)/(e^2*g^2*x^2 + d*e*f*g + (e^2*f*g + d*e*g^2)*x)) - 2*(2*c*e^2*g^2*x - 3*c*e^2*f*g - 3*c*d*e*g^2)*sqrt(e*x + d)*sqrt(g*x + f))/(e^3*g^3)]","A",0
604,1,12,0,0.391769," ","integrate((2*x^2-1)/(-1+x)^(1/2)/(1+x)^(1/2),x, algorithm=""fricas"")","\sqrt{x + 1} \sqrt{x - 1} x"," ",0,"sqrt(x + 1)*sqrt(x - 1)*x","A",0
605,-1,0,0,0.000000," ","integrate((e*x+d)^(3/2)*(g*x+f)^(1/2)/(c*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
606,-1,0,0,0.000000," ","integrate((e*x+d)^(1/2)*(g*x+f)^(1/2)/(c*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
607,1,1921,0,10.389959," ","integrate((g*x+f)^(1/2)/(e*x+d)^(1/2)/(c*x^2+a),x, algorithm=""fricas"")","-\frac{1}{4} \, \sqrt{-\frac{c d f + a e g + {\left(a c^{2} d^{2} + a^{2} c e^{2}\right)} \sqrt{-\frac{e^{2} f^{2} - 2 \, d e f g + d^{2} g^{2}}{a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}}}}{a c^{2} d^{2} + a^{2} c e^{2}}} \log\left(-\frac{e^{2} f^{2} - d^{2} g^{2} + 2 \, {\left(c d e f - c d^{2} g - {\left(a c^{2} d^{2} e + a^{2} c e^{3}\right)} \sqrt{-\frac{e^{2} f^{2} - 2 \, d e f g + d^{2} g^{2}}{a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}}}\right)} \sqrt{e x + d} \sqrt{g x + f} \sqrt{-\frac{c d f + a e g + {\left(a c^{2} d^{2} + a^{2} c e^{2}\right)} \sqrt{-\frac{e^{2} f^{2} - 2 \, d e f g + d^{2} g^{2}}{a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}}}}{a c^{2} d^{2} + a^{2} c e^{2}}} + 2 \, {\left(e^{2} f g - d e g^{2}\right)} x + {\left(2 \, {\left(c^{2} d^{3} + a c d e^{2}\right)} f + {\left({\left(c^{2} d^{2} e + a c e^{3}\right)} f + {\left(c^{2} d^{3} + a c d e^{2}\right)} g\right)} x\right)} \sqrt{-\frac{e^{2} f^{2} - 2 \, d e f g + d^{2} g^{2}}{a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}}}}{x}\right) + \frac{1}{4} \, \sqrt{-\frac{c d f + a e g + {\left(a c^{2} d^{2} + a^{2} c e^{2}\right)} \sqrt{-\frac{e^{2} f^{2} - 2 \, d e f g + d^{2} g^{2}}{a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}}}}{a c^{2} d^{2} + a^{2} c e^{2}}} \log\left(-\frac{e^{2} f^{2} - d^{2} g^{2} - 2 \, {\left(c d e f - c d^{2} g - {\left(a c^{2} d^{2} e + a^{2} c e^{3}\right)} \sqrt{-\frac{e^{2} f^{2} - 2 \, d e f g + d^{2} g^{2}}{a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}}}\right)} \sqrt{e x + d} \sqrt{g x + f} \sqrt{-\frac{c d f + a e g + {\left(a c^{2} d^{2} + a^{2} c e^{2}\right)} \sqrt{-\frac{e^{2} f^{2} - 2 \, d e f g + d^{2} g^{2}}{a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}}}}{a c^{2} d^{2} + a^{2} c e^{2}}} + 2 \, {\left(e^{2} f g - d e g^{2}\right)} x + {\left(2 \, {\left(c^{2} d^{3} + a c d e^{2}\right)} f + {\left({\left(c^{2} d^{2} e + a c e^{3}\right)} f + {\left(c^{2} d^{3} + a c d e^{2}\right)} g\right)} x\right)} \sqrt{-\frac{e^{2} f^{2} - 2 \, d e f g + d^{2} g^{2}}{a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}}}}{x}\right) - \frac{1}{4} \, \sqrt{-\frac{c d f + a e g - {\left(a c^{2} d^{2} + a^{2} c e^{2}\right)} \sqrt{-\frac{e^{2} f^{2} - 2 \, d e f g + d^{2} g^{2}}{a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}}}}{a c^{2} d^{2} + a^{2} c e^{2}}} \log\left(-\frac{e^{2} f^{2} - d^{2} g^{2} + 2 \, {\left(c d e f - c d^{2} g + {\left(a c^{2} d^{2} e + a^{2} c e^{3}\right)} \sqrt{-\frac{e^{2} f^{2} - 2 \, d e f g + d^{2} g^{2}}{a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}}}\right)} \sqrt{e x + d} \sqrt{g x + f} \sqrt{-\frac{c d f + a e g - {\left(a c^{2} d^{2} + a^{2} c e^{2}\right)} \sqrt{-\frac{e^{2} f^{2} - 2 \, d e f g + d^{2} g^{2}}{a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}}}}{a c^{2} d^{2} + a^{2} c e^{2}}} + 2 \, {\left(e^{2} f g - d e g^{2}\right)} x - {\left(2 \, {\left(c^{2} d^{3} + a c d e^{2}\right)} f + {\left({\left(c^{2} d^{2} e + a c e^{3}\right)} f + {\left(c^{2} d^{3} + a c d e^{2}\right)} g\right)} x\right)} \sqrt{-\frac{e^{2} f^{2} - 2 \, d e f g + d^{2} g^{2}}{a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}}}}{x}\right) + \frac{1}{4} \, \sqrt{-\frac{c d f + a e g - {\left(a c^{2} d^{2} + a^{2} c e^{2}\right)} \sqrt{-\frac{e^{2} f^{2} - 2 \, d e f g + d^{2} g^{2}}{a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}}}}{a c^{2} d^{2} + a^{2} c e^{2}}} \log\left(-\frac{e^{2} f^{2} - d^{2} g^{2} - 2 \, {\left(c d e f - c d^{2} g + {\left(a c^{2} d^{2} e + a^{2} c e^{3}\right)} \sqrt{-\frac{e^{2} f^{2} - 2 \, d e f g + d^{2} g^{2}}{a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}}}\right)} \sqrt{e x + d} \sqrt{g x + f} \sqrt{-\frac{c d f + a e g - {\left(a c^{2} d^{2} + a^{2} c e^{2}\right)} \sqrt{-\frac{e^{2} f^{2} - 2 \, d e f g + d^{2} g^{2}}{a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}}}}{a c^{2} d^{2} + a^{2} c e^{2}}} + 2 \, {\left(e^{2} f g - d e g^{2}\right)} x - {\left(2 \, {\left(c^{2} d^{3} + a c d e^{2}\right)} f + {\left({\left(c^{2} d^{2} e + a c e^{3}\right)} f + {\left(c^{2} d^{3} + a c d e^{2}\right)} g\right)} x\right)} \sqrt{-\frac{e^{2} f^{2} - 2 \, d e f g + d^{2} g^{2}}{a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}}}}{x}\right)"," ",0,"-1/4*sqrt(-(c*d*f + a*e*g + (a*c^2*d^2 + a^2*c*e^2)*sqrt(-(e^2*f^2 - 2*d*e*f*g + d^2*g^2)/(a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)))/(a*c^2*d^2 + a^2*c*e^2))*log(-(e^2*f^2 - d^2*g^2 + 2*(c*d*e*f - c*d^2*g - (a*c^2*d^2*e + a^2*c*e^3)*sqrt(-(e^2*f^2 - 2*d*e*f*g + d^2*g^2)/(a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)))*sqrt(e*x + d)*sqrt(g*x + f)*sqrt(-(c*d*f + a*e*g + (a*c^2*d^2 + a^2*c*e^2)*sqrt(-(e^2*f^2 - 2*d*e*f*g + d^2*g^2)/(a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)))/(a*c^2*d^2 + a^2*c*e^2)) + 2*(e^2*f*g - d*e*g^2)*x + (2*(c^2*d^3 + a*c*d*e^2)*f + ((c^2*d^2*e + a*c*e^3)*f + (c^2*d^3 + a*c*d*e^2)*g)*x)*sqrt(-(e^2*f^2 - 2*d*e*f*g + d^2*g^2)/(a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)))/x) + 1/4*sqrt(-(c*d*f + a*e*g + (a*c^2*d^2 + a^2*c*e^2)*sqrt(-(e^2*f^2 - 2*d*e*f*g + d^2*g^2)/(a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)))/(a*c^2*d^2 + a^2*c*e^2))*log(-(e^2*f^2 - d^2*g^2 - 2*(c*d*e*f - c*d^2*g - (a*c^2*d^2*e + a^2*c*e^3)*sqrt(-(e^2*f^2 - 2*d*e*f*g + d^2*g^2)/(a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)))*sqrt(e*x + d)*sqrt(g*x + f)*sqrt(-(c*d*f + a*e*g + (a*c^2*d^2 + a^2*c*e^2)*sqrt(-(e^2*f^2 - 2*d*e*f*g + d^2*g^2)/(a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)))/(a*c^2*d^2 + a^2*c*e^2)) + 2*(e^2*f*g - d*e*g^2)*x + (2*(c^2*d^3 + a*c*d*e^2)*f + ((c^2*d^2*e + a*c*e^3)*f + (c^2*d^3 + a*c*d*e^2)*g)*x)*sqrt(-(e^2*f^2 - 2*d*e*f*g + d^2*g^2)/(a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)))/x) - 1/4*sqrt(-(c*d*f + a*e*g - (a*c^2*d^2 + a^2*c*e^2)*sqrt(-(e^2*f^2 - 2*d*e*f*g + d^2*g^2)/(a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)))/(a*c^2*d^2 + a^2*c*e^2))*log(-(e^2*f^2 - d^2*g^2 + 2*(c*d*e*f - c*d^2*g + (a*c^2*d^2*e + a^2*c*e^3)*sqrt(-(e^2*f^2 - 2*d*e*f*g + d^2*g^2)/(a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)))*sqrt(e*x + d)*sqrt(g*x + f)*sqrt(-(c*d*f + a*e*g - (a*c^2*d^2 + a^2*c*e^2)*sqrt(-(e^2*f^2 - 2*d*e*f*g + d^2*g^2)/(a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)))/(a*c^2*d^2 + a^2*c*e^2)) + 2*(e^2*f*g - d*e*g^2)*x - (2*(c^2*d^3 + a*c*d*e^2)*f + ((c^2*d^2*e + a*c*e^3)*f + (c^2*d^3 + a*c*d*e^2)*g)*x)*sqrt(-(e^2*f^2 - 2*d*e*f*g + d^2*g^2)/(a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)))/x) + 1/4*sqrt(-(c*d*f + a*e*g - (a*c^2*d^2 + a^2*c*e^2)*sqrt(-(e^2*f^2 - 2*d*e*f*g + d^2*g^2)/(a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)))/(a*c^2*d^2 + a^2*c*e^2))*log(-(e^2*f^2 - d^2*g^2 - 2*(c*d*e*f - c*d^2*g + (a*c^2*d^2*e + a^2*c*e^3)*sqrt(-(e^2*f^2 - 2*d*e*f*g + d^2*g^2)/(a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)))*sqrt(e*x + d)*sqrt(g*x + f)*sqrt(-(c*d*f + a*e*g - (a*c^2*d^2 + a^2*c*e^2)*sqrt(-(e^2*f^2 - 2*d*e*f*g + d^2*g^2)/(a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)))/(a*c^2*d^2 + a^2*c*e^2)) + 2*(e^2*f*g - d*e*g^2)*x - (2*(c^2*d^3 + a*c*d*e^2)*f + ((c^2*d^2*e + a*c*e^3)*f + (c^2*d^3 + a*c*d*e^2)*g)*x)*sqrt(-(e^2*f^2 - 2*d*e*f*g + d^2*g^2)/(a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)))/x)","B",0
608,1,5816,0,52.327600," ","integrate((g*x+f)^(1/2)/(e*x+d)^(3/2)/(c*x^2+a),x, algorithm=""fricas"")","-\frac{{\left(c d^{3} + a d e^{2} + {\left(c d^{2} e + a e^{3}\right)} x\right)} \sqrt{-\frac{{\left(c^{2} d^{3} - 3 \, a c d e^{2}\right)} f + {\left(3 \, a c d^{2} e - a^{2} e^{3}\right)} g + {\left(a c^{3} d^{6} + 3 \, a^{2} c^{2} d^{4} e^{2} + 3 \, a^{3} c d^{2} e^{4} + a^{4} e^{6}\right)} \sqrt{-\frac{{\left(9 \, c^{3} d^{4} e^{2} - 6 \, a c^{2} d^{2} e^{4} + a^{2} c e^{6}\right)} f^{2} - 2 \, {\left(3 \, c^{3} d^{5} e - 10 \, a c^{2} d^{3} e^{3} + 3 \, a^{2} c d e^{5}\right)} f g + {\left(c^{3} d^{6} - 6 \, a c^{2} d^{4} e^{2} + 9 \, a^{2} c d^{2} e^{4}\right)} g^{2}}{a c^{6} d^{12} + 6 \, a^{2} c^{5} d^{10} e^{2} + 15 \, a^{3} c^{4} d^{8} e^{4} + 20 \, a^{4} c^{3} d^{6} e^{6} + 15 \, a^{5} c^{2} d^{4} e^{8} + 6 \, a^{6} c d^{2} e^{10} + a^{7} e^{12}}}}{a c^{3} d^{6} + 3 \, a^{2} c^{2} d^{4} e^{2} + 3 \, a^{3} c d^{2} e^{4} + a^{4} e^{6}}} \log\left(\frac{{\left(3 \, c d^{2} e^{2} - a e^{4}\right)} f^{2} + 2 \, {\left(c d^{3} e + a d e^{3}\right)} f g - {\left(c d^{4} - 3 \, a d^{2} e^{2}\right)} g^{2} + 2 \, {\left({\left(3 \, c^{2} d^{4} e - 4 \, a c d^{2} e^{3} + a^{2} e^{5}\right)} f - {\left(c^{2} d^{5} - 4 \, a c d^{3} e^{2} + 3 \, a^{2} d e^{4}\right)} g - 2 \, {\left(a c^{3} d^{7} e + 3 \, a^{2} c^{2} d^{5} e^{3} + 3 \, a^{3} c d^{3} e^{5} + a^{4} d e^{7}\right)} \sqrt{-\frac{{\left(9 \, c^{3} d^{4} e^{2} - 6 \, a c^{2} d^{2} e^{4} + a^{2} c e^{6}\right)} f^{2} - 2 \, {\left(3 \, c^{3} d^{5} e - 10 \, a c^{2} d^{3} e^{3} + 3 \, a^{2} c d e^{5}\right)} f g + {\left(c^{3} d^{6} - 6 \, a c^{2} d^{4} e^{2} + 9 \, a^{2} c d^{2} e^{4}\right)} g^{2}}{a c^{6} d^{12} + 6 \, a^{2} c^{5} d^{10} e^{2} + 15 \, a^{3} c^{4} d^{8} e^{4} + 20 \, a^{4} c^{3} d^{6} e^{6} + 15 \, a^{5} c^{2} d^{4} e^{8} + 6 \, a^{6} c d^{2} e^{10} + a^{7} e^{12}}}\right)} \sqrt{e x + d} \sqrt{g x + f} \sqrt{-\frac{{\left(c^{2} d^{3} - 3 \, a c d e^{2}\right)} f + {\left(3 \, a c d^{2} e - a^{2} e^{3}\right)} g + {\left(a c^{3} d^{6} + 3 \, a^{2} c^{2} d^{4} e^{2} + 3 \, a^{3} c d^{2} e^{4} + a^{4} e^{6}\right)} \sqrt{-\frac{{\left(9 \, c^{3} d^{4} e^{2} - 6 \, a c^{2} d^{2} e^{4} + a^{2} c e^{6}\right)} f^{2} - 2 \, {\left(3 \, c^{3} d^{5} e - 10 \, a c^{2} d^{3} e^{3} + 3 \, a^{2} c d e^{5}\right)} f g + {\left(c^{3} d^{6} - 6 \, a c^{2} d^{4} e^{2} + 9 \, a^{2} c d^{2} e^{4}\right)} g^{2}}{a c^{6} d^{12} + 6 \, a^{2} c^{5} d^{10} e^{2} + 15 \, a^{3} c^{4} d^{8} e^{4} + 20 \, a^{4} c^{3} d^{6} e^{6} + 15 \, a^{5} c^{2} d^{4} e^{8} + 6 \, a^{6} c d^{2} e^{10} + a^{7} e^{12}}}}{a c^{3} d^{6} + 3 \, a^{2} c^{2} d^{4} e^{2} + 3 \, a^{3} c d^{2} e^{4} + a^{4} e^{6}}} + 2 \, {\left({\left(3 \, c d^{2} e^{2} - a e^{4}\right)} f g - {\left(c d^{3} e - 3 \, a d e^{3}\right)} g^{2}\right)} x + {\left(2 \, {\left(c^{3} d^{7} + 3 \, a c^{2} d^{5} e^{2} + 3 \, a^{2} c d^{3} e^{4} + a^{3} d e^{6}\right)} f + {\left({\left(c^{3} d^{6} e + 3 \, a c^{2} d^{4} e^{3} + 3 \, a^{2} c d^{2} e^{5} + a^{3} e^{7}\right)} f + {\left(c^{3} d^{7} + 3 \, a c^{2} d^{5} e^{2} + 3 \, a^{2} c d^{3} e^{4} + a^{3} d e^{6}\right)} g\right)} x\right)} \sqrt{-\frac{{\left(9 \, c^{3} d^{4} e^{2} - 6 \, a c^{2} d^{2} e^{4} + a^{2} c e^{6}\right)} f^{2} - 2 \, {\left(3 \, c^{3} d^{5} e - 10 \, a c^{2} d^{3} e^{3} + 3 \, a^{2} c d e^{5}\right)} f g + {\left(c^{3} d^{6} - 6 \, a c^{2} d^{4} e^{2} + 9 \, a^{2} c d^{2} e^{4}\right)} g^{2}}{a c^{6} d^{12} + 6 \, a^{2} c^{5} d^{10} e^{2} + 15 \, a^{3} c^{4} d^{8} e^{4} + 20 \, a^{4} c^{3} d^{6} e^{6} + 15 \, a^{5} c^{2} d^{4} e^{8} + 6 \, a^{6} c d^{2} e^{10} + a^{7} e^{12}}}}{x}\right) - {\left(c d^{3} + a d e^{2} + {\left(c d^{2} e + a e^{3}\right)} x\right)} \sqrt{-\frac{{\left(c^{2} d^{3} - 3 \, a c d e^{2}\right)} f + {\left(3 \, a c d^{2} e - a^{2} e^{3}\right)} g + {\left(a c^{3} d^{6} + 3 \, a^{2} c^{2} d^{4} e^{2} + 3 \, a^{3} c d^{2} e^{4} + a^{4} e^{6}\right)} \sqrt{-\frac{{\left(9 \, c^{3} d^{4} e^{2} - 6 \, a c^{2} d^{2} e^{4} + a^{2} c e^{6}\right)} f^{2} - 2 \, {\left(3 \, c^{3} d^{5} e - 10 \, a c^{2} d^{3} e^{3} + 3 \, a^{2} c d e^{5}\right)} f g + {\left(c^{3} d^{6} - 6 \, a c^{2} d^{4} e^{2} + 9 \, a^{2} c d^{2} e^{4}\right)} g^{2}}{a c^{6} d^{12} + 6 \, a^{2} c^{5} d^{10} e^{2} + 15 \, a^{3} c^{4} d^{8} e^{4} + 20 \, a^{4} c^{3} d^{6} e^{6} + 15 \, a^{5} c^{2} d^{4} e^{8} + 6 \, a^{6} c d^{2} e^{10} + a^{7} e^{12}}}}{a c^{3} d^{6} + 3 \, a^{2} c^{2} d^{4} e^{2} + 3 \, a^{3} c d^{2} e^{4} + a^{4} e^{6}}} \log\left(\frac{{\left(3 \, c d^{2} e^{2} - a e^{4}\right)} f^{2} + 2 \, {\left(c d^{3} e + a d e^{3}\right)} f g - {\left(c d^{4} - 3 \, a d^{2} e^{2}\right)} g^{2} - 2 \, {\left({\left(3 \, c^{2} d^{4} e - 4 \, a c d^{2} e^{3} + a^{2} e^{5}\right)} f - {\left(c^{2} d^{5} - 4 \, a c d^{3} e^{2} + 3 \, a^{2} d e^{4}\right)} g - 2 \, {\left(a c^{3} d^{7} e + 3 \, a^{2} c^{2} d^{5} e^{3} + 3 \, a^{3} c d^{3} e^{5} + a^{4} d e^{7}\right)} \sqrt{-\frac{{\left(9 \, c^{3} d^{4} e^{2} - 6 \, a c^{2} d^{2} e^{4} + a^{2} c e^{6}\right)} f^{2} - 2 \, {\left(3 \, c^{3} d^{5} e - 10 \, a c^{2} d^{3} e^{3} + 3 \, a^{2} c d e^{5}\right)} f g + {\left(c^{3} d^{6} - 6 \, a c^{2} d^{4} e^{2} + 9 \, a^{2} c d^{2} e^{4}\right)} g^{2}}{a c^{6} d^{12} + 6 \, a^{2} c^{5} d^{10} e^{2} + 15 \, a^{3} c^{4} d^{8} e^{4} + 20 \, a^{4} c^{3} d^{6} e^{6} + 15 \, a^{5} c^{2} d^{4} e^{8} + 6 \, a^{6} c d^{2} e^{10} + a^{7} e^{12}}}\right)} \sqrt{e x + d} \sqrt{g x + f} \sqrt{-\frac{{\left(c^{2} d^{3} - 3 \, a c d e^{2}\right)} f + {\left(3 \, a c d^{2} e - a^{2} e^{3}\right)} g + {\left(a c^{3} d^{6} + 3 \, a^{2} c^{2} d^{4} e^{2} + 3 \, a^{3} c d^{2} e^{4} + a^{4} e^{6}\right)} \sqrt{-\frac{{\left(9 \, c^{3} d^{4} e^{2} - 6 \, a c^{2} d^{2} e^{4} + a^{2} c e^{6}\right)} f^{2} - 2 \, {\left(3 \, c^{3} d^{5} e - 10 \, a c^{2} d^{3} e^{3} + 3 \, a^{2} c d e^{5}\right)} f g + {\left(c^{3} d^{6} - 6 \, a c^{2} d^{4} e^{2} + 9 \, a^{2} c d^{2} e^{4}\right)} g^{2}}{a c^{6} d^{12} + 6 \, a^{2} c^{5} d^{10} e^{2} + 15 \, a^{3} c^{4} d^{8} e^{4} + 20 \, a^{4} c^{3} d^{6} e^{6} + 15 \, a^{5} c^{2} d^{4} e^{8} + 6 \, a^{6} c d^{2} e^{10} + a^{7} e^{12}}}}{a c^{3} d^{6} + 3 \, a^{2} c^{2} d^{4} e^{2} + 3 \, a^{3} c d^{2} e^{4} + a^{4} e^{6}}} + 2 \, {\left({\left(3 \, c d^{2} e^{2} - a e^{4}\right)} f g - {\left(c d^{3} e - 3 \, a d e^{3}\right)} g^{2}\right)} x + {\left(2 \, {\left(c^{3} d^{7} + 3 \, a c^{2} d^{5} e^{2} + 3 \, a^{2} c d^{3} e^{4} + a^{3} d e^{6}\right)} f + {\left({\left(c^{3} d^{6} e + 3 \, a c^{2} d^{4} e^{3} + 3 \, a^{2} c d^{2} e^{5} + a^{3} e^{7}\right)} f + {\left(c^{3} d^{7} + 3 \, a c^{2} d^{5} e^{2} + 3 \, a^{2} c d^{3} e^{4} + a^{3} d e^{6}\right)} g\right)} x\right)} \sqrt{-\frac{{\left(9 \, c^{3} d^{4} e^{2} - 6 \, a c^{2} d^{2} e^{4} + a^{2} c e^{6}\right)} f^{2} - 2 \, {\left(3 \, c^{3} d^{5} e - 10 \, a c^{2} d^{3} e^{3} + 3 \, a^{2} c d e^{5}\right)} f g + {\left(c^{3} d^{6} - 6 \, a c^{2} d^{4} e^{2} + 9 \, a^{2} c d^{2} e^{4}\right)} g^{2}}{a c^{6} d^{12} + 6 \, a^{2} c^{5} d^{10} e^{2} + 15 \, a^{3} c^{4} d^{8} e^{4} + 20 \, a^{4} c^{3} d^{6} e^{6} + 15 \, a^{5} c^{2} d^{4} e^{8} + 6 \, a^{6} c d^{2} e^{10} + a^{7} e^{12}}}}{x}\right) + {\left(c d^{3} + a d e^{2} + {\left(c d^{2} e + a e^{3}\right)} x\right)} \sqrt{-\frac{{\left(c^{2} d^{3} - 3 \, a c d e^{2}\right)} f + {\left(3 \, a c d^{2} e - a^{2} e^{3}\right)} g - {\left(a c^{3} d^{6} + 3 \, a^{2} c^{2} d^{4} e^{2} + 3 \, a^{3} c d^{2} e^{4} + a^{4} e^{6}\right)} \sqrt{-\frac{{\left(9 \, c^{3} d^{4} e^{2} - 6 \, a c^{2} d^{2} e^{4} + a^{2} c e^{6}\right)} f^{2} - 2 \, {\left(3 \, c^{3} d^{5} e - 10 \, a c^{2} d^{3} e^{3} + 3 \, a^{2} c d e^{5}\right)} f g + {\left(c^{3} d^{6} - 6 \, a c^{2} d^{4} e^{2} + 9 \, a^{2} c d^{2} e^{4}\right)} g^{2}}{a c^{6} d^{12} + 6 \, a^{2} c^{5} d^{10} e^{2} + 15 \, a^{3} c^{4} d^{8} e^{4} + 20 \, a^{4} c^{3} d^{6} e^{6} + 15 \, a^{5} c^{2} d^{4} e^{8} + 6 \, a^{6} c d^{2} e^{10} + a^{7} e^{12}}}}{a c^{3} d^{6} + 3 \, a^{2} c^{2} d^{4} e^{2} + 3 \, a^{3} c d^{2} e^{4} + a^{4} e^{6}}} \log\left(\frac{{\left(3 \, c d^{2} e^{2} - a e^{4}\right)} f^{2} + 2 \, {\left(c d^{3} e + a d e^{3}\right)} f g - {\left(c d^{4} - 3 \, a d^{2} e^{2}\right)} g^{2} + 2 \, {\left({\left(3 \, c^{2} d^{4} e - 4 \, a c d^{2} e^{3} + a^{2} e^{5}\right)} f - {\left(c^{2} d^{5} - 4 \, a c d^{3} e^{2} + 3 \, a^{2} d e^{4}\right)} g + 2 \, {\left(a c^{3} d^{7} e + 3 \, a^{2} c^{2} d^{5} e^{3} + 3 \, a^{3} c d^{3} e^{5} + a^{4} d e^{7}\right)} \sqrt{-\frac{{\left(9 \, c^{3} d^{4} e^{2} - 6 \, a c^{2} d^{2} e^{4} + a^{2} c e^{6}\right)} f^{2} - 2 \, {\left(3 \, c^{3} d^{5} e - 10 \, a c^{2} d^{3} e^{3} + 3 \, a^{2} c d e^{5}\right)} f g + {\left(c^{3} d^{6} - 6 \, a c^{2} d^{4} e^{2} + 9 \, a^{2} c d^{2} e^{4}\right)} g^{2}}{a c^{6} d^{12} + 6 \, a^{2} c^{5} d^{10} e^{2} + 15 \, a^{3} c^{4} d^{8} e^{4} + 20 \, a^{4} c^{3} d^{6} e^{6} + 15 \, a^{5} c^{2} d^{4} e^{8} + 6 \, a^{6} c d^{2} e^{10} + a^{7} e^{12}}}\right)} \sqrt{e x + d} \sqrt{g x + f} \sqrt{-\frac{{\left(c^{2} d^{3} - 3 \, a c d e^{2}\right)} f + {\left(3 \, a c d^{2} e - a^{2} e^{3}\right)} g - {\left(a c^{3} d^{6} + 3 \, a^{2} c^{2} d^{4} e^{2} + 3 \, a^{3} c d^{2} e^{4} + a^{4} e^{6}\right)} \sqrt{-\frac{{\left(9 \, c^{3} d^{4} e^{2} - 6 \, a c^{2} d^{2} e^{4} + a^{2} c e^{6}\right)} f^{2} - 2 \, {\left(3 \, c^{3} d^{5} e - 10 \, a c^{2} d^{3} e^{3} + 3 \, a^{2} c d e^{5}\right)} f g + {\left(c^{3} d^{6} - 6 \, a c^{2} d^{4} e^{2} + 9 \, a^{2} c d^{2} e^{4}\right)} g^{2}}{a c^{6} d^{12} + 6 \, a^{2} c^{5} d^{10} e^{2} + 15 \, a^{3} c^{4} d^{8} e^{4} + 20 \, a^{4} c^{3} d^{6} e^{6} + 15 \, a^{5} c^{2} d^{4} e^{8} + 6 \, a^{6} c d^{2} e^{10} + a^{7} e^{12}}}}{a c^{3} d^{6} + 3 \, a^{2} c^{2} d^{4} e^{2} + 3 \, a^{3} c d^{2} e^{4} + a^{4} e^{6}}} + 2 \, {\left({\left(3 \, c d^{2} e^{2} - a e^{4}\right)} f g - {\left(c d^{3} e - 3 \, a d e^{3}\right)} g^{2}\right)} x - {\left(2 \, {\left(c^{3} d^{7} + 3 \, a c^{2} d^{5} e^{2} + 3 \, a^{2} c d^{3} e^{4} + a^{3} d e^{6}\right)} f + {\left({\left(c^{3} d^{6} e + 3 \, a c^{2} d^{4} e^{3} + 3 \, a^{2} c d^{2} e^{5} + a^{3} e^{7}\right)} f + {\left(c^{3} d^{7} + 3 \, a c^{2} d^{5} e^{2} + 3 \, a^{2} c d^{3} e^{4} + a^{3} d e^{6}\right)} g\right)} x\right)} \sqrt{-\frac{{\left(9 \, c^{3} d^{4} e^{2} - 6 \, a c^{2} d^{2} e^{4} + a^{2} c e^{6}\right)} f^{2} - 2 \, {\left(3 \, c^{3} d^{5} e - 10 \, a c^{2} d^{3} e^{3} + 3 \, a^{2} c d e^{5}\right)} f g + {\left(c^{3} d^{6} - 6 \, a c^{2} d^{4} e^{2} + 9 \, a^{2} c d^{2} e^{4}\right)} g^{2}}{a c^{6} d^{12} + 6 \, a^{2} c^{5} d^{10} e^{2} + 15 \, a^{3} c^{4} d^{8} e^{4} + 20 \, a^{4} c^{3} d^{6} e^{6} + 15 \, a^{5} c^{2} d^{4} e^{8} + 6 \, a^{6} c d^{2} e^{10} + a^{7} e^{12}}}}{x}\right) - {\left(c d^{3} + a d e^{2} + {\left(c d^{2} e + a e^{3}\right)} x\right)} \sqrt{-\frac{{\left(c^{2} d^{3} - 3 \, a c d e^{2}\right)} f + {\left(3 \, a c d^{2} e - a^{2} e^{3}\right)} g - {\left(a c^{3} d^{6} + 3 \, a^{2} c^{2} d^{4} e^{2} + 3 \, a^{3} c d^{2} e^{4} + a^{4} e^{6}\right)} \sqrt{-\frac{{\left(9 \, c^{3} d^{4} e^{2} - 6 \, a c^{2} d^{2} e^{4} + a^{2} c e^{6}\right)} f^{2} - 2 \, {\left(3 \, c^{3} d^{5} e - 10 \, a c^{2} d^{3} e^{3} + 3 \, a^{2} c d e^{5}\right)} f g + {\left(c^{3} d^{6} - 6 \, a c^{2} d^{4} e^{2} + 9 \, a^{2} c d^{2} e^{4}\right)} g^{2}}{a c^{6} d^{12} + 6 \, a^{2} c^{5} d^{10} e^{2} + 15 \, a^{3} c^{4} d^{8} e^{4} + 20 \, a^{4} c^{3} d^{6} e^{6} + 15 \, a^{5} c^{2} d^{4} e^{8} + 6 \, a^{6} c d^{2} e^{10} + a^{7} e^{12}}}}{a c^{3} d^{6} + 3 \, a^{2} c^{2} d^{4} e^{2} + 3 \, a^{3} c d^{2} e^{4} + a^{4} e^{6}}} \log\left(\frac{{\left(3 \, c d^{2} e^{2} - a e^{4}\right)} f^{2} + 2 \, {\left(c d^{3} e + a d e^{3}\right)} f g - {\left(c d^{4} - 3 \, a d^{2} e^{2}\right)} g^{2} - 2 \, {\left({\left(3 \, c^{2} d^{4} e - 4 \, a c d^{2} e^{3} + a^{2} e^{5}\right)} f - {\left(c^{2} d^{5} - 4 \, a c d^{3} e^{2} + 3 \, a^{2} d e^{4}\right)} g + 2 \, {\left(a c^{3} d^{7} e + 3 \, a^{2} c^{2} d^{5} e^{3} + 3 \, a^{3} c d^{3} e^{5} + a^{4} d e^{7}\right)} \sqrt{-\frac{{\left(9 \, c^{3} d^{4} e^{2} - 6 \, a c^{2} d^{2} e^{4} + a^{2} c e^{6}\right)} f^{2} - 2 \, {\left(3 \, c^{3} d^{5} e - 10 \, a c^{2} d^{3} e^{3} + 3 \, a^{2} c d e^{5}\right)} f g + {\left(c^{3} d^{6} - 6 \, a c^{2} d^{4} e^{2} + 9 \, a^{2} c d^{2} e^{4}\right)} g^{2}}{a c^{6} d^{12} + 6 \, a^{2} c^{5} d^{10} e^{2} + 15 \, a^{3} c^{4} d^{8} e^{4} + 20 \, a^{4} c^{3} d^{6} e^{6} + 15 \, a^{5} c^{2} d^{4} e^{8} + 6 \, a^{6} c d^{2} e^{10} + a^{7} e^{12}}}\right)} \sqrt{e x + d} \sqrt{g x + f} \sqrt{-\frac{{\left(c^{2} d^{3} - 3 \, a c d e^{2}\right)} f + {\left(3 \, a c d^{2} e - a^{2} e^{3}\right)} g - {\left(a c^{3} d^{6} + 3 \, a^{2} c^{2} d^{4} e^{2} + 3 \, a^{3} c d^{2} e^{4} + a^{4} e^{6}\right)} \sqrt{-\frac{{\left(9 \, c^{3} d^{4} e^{2} - 6 \, a c^{2} d^{2} e^{4} + a^{2} c e^{6}\right)} f^{2} - 2 \, {\left(3 \, c^{3} d^{5} e - 10 \, a c^{2} d^{3} e^{3} + 3 \, a^{2} c d e^{5}\right)} f g + {\left(c^{3} d^{6} - 6 \, a c^{2} d^{4} e^{2} + 9 \, a^{2} c d^{2} e^{4}\right)} g^{2}}{a c^{6} d^{12} + 6 \, a^{2} c^{5} d^{10} e^{2} + 15 \, a^{3} c^{4} d^{8} e^{4} + 20 \, a^{4} c^{3} d^{6} e^{6} + 15 \, a^{5} c^{2} d^{4} e^{8} + 6 \, a^{6} c d^{2} e^{10} + a^{7} e^{12}}}}{a c^{3} d^{6} + 3 \, a^{2} c^{2} d^{4} e^{2} + 3 \, a^{3} c d^{2} e^{4} + a^{4} e^{6}}} + 2 \, {\left({\left(3 \, c d^{2} e^{2} - a e^{4}\right)} f g - {\left(c d^{3} e - 3 \, a d e^{3}\right)} g^{2}\right)} x - {\left(2 \, {\left(c^{3} d^{7} + 3 \, a c^{2} d^{5} e^{2} + 3 \, a^{2} c d^{3} e^{4} + a^{3} d e^{6}\right)} f + {\left({\left(c^{3} d^{6} e + 3 \, a c^{2} d^{4} e^{3} + 3 \, a^{2} c d^{2} e^{5} + a^{3} e^{7}\right)} f + {\left(c^{3} d^{7} + 3 \, a c^{2} d^{5} e^{2} + 3 \, a^{2} c d^{3} e^{4} + a^{3} d e^{6}\right)} g\right)} x\right)} \sqrt{-\frac{{\left(9 \, c^{3} d^{4} e^{2} - 6 \, a c^{2} d^{2} e^{4} + a^{2} c e^{6}\right)} f^{2} - 2 \, {\left(3 \, c^{3} d^{5} e - 10 \, a c^{2} d^{3} e^{3} + 3 \, a^{2} c d e^{5}\right)} f g + {\left(c^{3} d^{6} - 6 \, a c^{2} d^{4} e^{2} + 9 \, a^{2} c d^{2} e^{4}\right)} g^{2}}{a c^{6} d^{12} + 6 \, a^{2} c^{5} d^{10} e^{2} + 15 \, a^{3} c^{4} d^{8} e^{4} + 20 \, a^{4} c^{3} d^{6} e^{6} + 15 \, a^{5} c^{2} d^{4} e^{8} + 6 \, a^{6} c d^{2} e^{10} + a^{7} e^{12}}}}{x}\right) + 8 \, \sqrt{e x + d} \sqrt{g x + f} e}{4 \, {\left(c d^{3} + a d e^{2} + {\left(c d^{2} e + a e^{3}\right)} x\right)}}"," ",0,"-1/4*((c*d^3 + a*d*e^2 + (c*d^2*e + a*e^3)*x)*sqrt(-((c^2*d^3 - 3*a*c*d*e^2)*f + (3*a*c*d^2*e - a^2*e^3)*g + (a*c^3*d^6 + 3*a^2*c^2*d^4*e^2 + 3*a^3*c*d^2*e^4 + a^4*e^6)*sqrt(-((9*c^3*d^4*e^2 - 6*a*c^2*d^2*e^4 + a^2*c*e^6)*f^2 - 2*(3*c^3*d^5*e - 10*a*c^2*d^3*e^3 + 3*a^2*c*d*e^5)*f*g + (c^3*d^6 - 6*a*c^2*d^4*e^2 + 9*a^2*c*d^2*e^4)*g^2)/(a*c^6*d^12 + 6*a^2*c^5*d^10*e^2 + 15*a^3*c^4*d^8*e^4 + 20*a^4*c^3*d^6*e^6 + 15*a^5*c^2*d^4*e^8 + 6*a^6*c*d^2*e^10 + a^7*e^12)))/(a*c^3*d^6 + 3*a^2*c^2*d^4*e^2 + 3*a^3*c*d^2*e^4 + a^4*e^6))*log(((3*c*d^2*e^2 - a*e^4)*f^2 + 2*(c*d^3*e + a*d*e^3)*f*g - (c*d^4 - 3*a*d^2*e^2)*g^2 + 2*((3*c^2*d^4*e - 4*a*c*d^2*e^3 + a^2*e^5)*f - (c^2*d^5 - 4*a*c*d^3*e^2 + 3*a^2*d*e^4)*g - 2*(a*c^3*d^7*e + 3*a^2*c^2*d^5*e^3 + 3*a^3*c*d^3*e^5 + a^4*d*e^7)*sqrt(-((9*c^3*d^4*e^2 - 6*a*c^2*d^2*e^4 + a^2*c*e^6)*f^2 - 2*(3*c^3*d^5*e - 10*a*c^2*d^3*e^3 + 3*a^2*c*d*e^5)*f*g + (c^3*d^6 - 6*a*c^2*d^4*e^2 + 9*a^2*c*d^2*e^4)*g^2)/(a*c^6*d^12 + 6*a^2*c^5*d^10*e^2 + 15*a^3*c^4*d^8*e^4 + 20*a^4*c^3*d^6*e^6 + 15*a^5*c^2*d^4*e^8 + 6*a^6*c*d^2*e^10 + a^7*e^12)))*sqrt(e*x + d)*sqrt(g*x + f)*sqrt(-((c^2*d^3 - 3*a*c*d*e^2)*f + (3*a*c*d^2*e - a^2*e^3)*g + (a*c^3*d^6 + 3*a^2*c^2*d^4*e^2 + 3*a^3*c*d^2*e^4 + a^4*e^6)*sqrt(-((9*c^3*d^4*e^2 - 6*a*c^2*d^2*e^4 + a^2*c*e^6)*f^2 - 2*(3*c^3*d^5*e - 10*a*c^2*d^3*e^3 + 3*a^2*c*d*e^5)*f*g + (c^3*d^6 - 6*a*c^2*d^4*e^2 + 9*a^2*c*d^2*e^4)*g^2)/(a*c^6*d^12 + 6*a^2*c^5*d^10*e^2 + 15*a^3*c^4*d^8*e^4 + 20*a^4*c^3*d^6*e^6 + 15*a^5*c^2*d^4*e^8 + 6*a^6*c*d^2*e^10 + a^7*e^12)))/(a*c^3*d^6 + 3*a^2*c^2*d^4*e^2 + 3*a^3*c*d^2*e^4 + a^4*e^6)) + 2*((3*c*d^2*e^2 - a*e^4)*f*g - (c*d^3*e - 3*a*d*e^3)*g^2)*x + (2*(c^3*d^7 + 3*a*c^2*d^5*e^2 + 3*a^2*c*d^3*e^4 + a^3*d*e^6)*f + ((c^3*d^6*e + 3*a*c^2*d^4*e^3 + 3*a^2*c*d^2*e^5 + a^3*e^7)*f + (c^3*d^7 + 3*a*c^2*d^5*e^2 + 3*a^2*c*d^3*e^4 + a^3*d*e^6)*g)*x)*sqrt(-((9*c^3*d^4*e^2 - 6*a*c^2*d^2*e^4 + a^2*c*e^6)*f^2 - 2*(3*c^3*d^5*e - 10*a*c^2*d^3*e^3 + 3*a^2*c*d*e^5)*f*g + (c^3*d^6 - 6*a*c^2*d^4*e^2 + 9*a^2*c*d^2*e^4)*g^2)/(a*c^6*d^12 + 6*a^2*c^5*d^10*e^2 + 15*a^3*c^4*d^8*e^4 + 20*a^4*c^3*d^6*e^6 + 15*a^5*c^2*d^4*e^8 + 6*a^6*c*d^2*e^10 + a^7*e^12)))/x) - (c*d^3 + a*d*e^2 + (c*d^2*e + a*e^3)*x)*sqrt(-((c^2*d^3 - 3*a*c*d*e^2)*f + (3*a*c*d^2*e - a^2*e^3)*g + (a*c^3*d^6 + 3*a^2*c^2*d^4*e^2 + 3*a^3*c*d^2*e^4 + a^4*e^6)*sqrt(-((9*c^3*d^4*e^2 - 6*a*c^2*d^2*e^4 + a^2*c*e^6)*f^2 - 2*(3*c^3*d^5*e - 10*a*c^2*d^3*e^3 + 3*a^2*c*d*e^5)*f*g + (c^3*d^6 - 6*a*c^2*d^4*e^2 + 9*a^2*c*d^2*e^4)*g^2)/(a*c^6*d^12 + 6*a^2*c^5*d^10*e^2 + 15*a^3*c^4*d^8*e^4 + 20*a^4*c^3*d^6*e^6 + 15*a^5*c^2*d^4*e^8 + 6*a^6*c*d^2*e^10 + a^7*e^12)))/(a*c^3*d^6 + 3*a^2*c^2*d^4*e^2 + 3*a^3*c*d^2*e^4 + a^4*e^6))*log(((3*c*d^2*e^2 - a*e^4)*f^2 + 2*(c*d^3*e + a*d*e^3)*f*g - (c*d^4 - 3*a*d^2*e^2)*g^2 - 2*((3*c^2*d^4*e - 4*a*c*d^2*e^3 + a^2*e^5)*f - (c^2*d^5 - 4*a*c*d^3*e^2 + 3*a^2*d*e^4)*g - 2*(a*c^3*d^7*e + 3*a^2*c^2*d^5*e^3 + 3*a^3*c*d^3*e^5 + a^4*d*e^7)*sqrt(-((9*c^3*d^4*e^2 - 6*a*c^2*d^2*e^4 + a^2*c*e^6)*f^2 - 2*(3*c^3*d^5*e - 10*a*c^2*d^3*e^3 + 3*a^2*c*d*e^5)*f*g + (c^3*d^6 - 6*a*c^2*d^4*e^2 + 9*a^2*c*d^2*e^4)*g^2)/(a*c^6*d^12 + 6*a^2*c^5*d^10*e^2 + 15*a^3*c^4*d^8*e^4 + 20*a^4*c^3*d^6*e^6 + 15*a^5*c^2*d^4*e^8 + 6*a^6*c*d^2*e^10 + a^7*e^12)))*sqrt(e*x + d)*sqrt(g*x + f)*sqrt(-((c^2*d^3 - 3*a*c*d*e^2)*f + (3*a*c*d^2*e - a^2*e^3)*g + (a*c^3*d^6 + 3*a^2*c^2*d^4*e^2 + 3*a^3*c*d^2*e^4 + a^4*e^6)*sqrt(-((9*c^3*d^4*e^2 - 6*a*c^2*d^2*e^4 + a^2*c*e^6)*f^2 - 2*(3*c^3*d^5*e - 10*a*c^2*d^3*e^3 + 3*a^2*c*d*e^5)*f*g + (c^3*d^6 - 6*a*c^2*d^4*e^2 + 9*a^2*c*d^2*e^4)*g^2)/(a*c^6*d^12 + 6*a^2*c^5*d^10*e^2 + 15*a^3*c^4*d^8*e^4 + 20*a^4*c^3*d^6*e^6 + 15*a^5*c^2*d^4*e^8 + 6*a^6*c*d^2*e^10 + a^7*e^12)))/(a*c^3*d^6 + 3*a^2*c^2*d^4*e^2 + 3*a^3*c*d^2*e^4 + a^4*e^6)) + 2*((3*c*d^2*e^2 - a*e^4)*f*g - (c*d^3*e - 3*a*d*e^3)*g^2)*x + (2*(c^3*d^7 + 3*a*c^2*d^5*e^2 + 3*a^2*c*d^3*e^4 + a^3*d*e^6)*f + ((c^3*d^6*e + 3*a*c^2*d^4*e^3 + 3*a^2*c*d^2*e^5 + a^3*e^7)*f + (c^3*d^7 + 3*a*c^2*d^5*e^2 + 3*a^2*c*d^3*e^4 + a^3*d*e^6)*g)*x)*sqrt(-((9*c^3*d^4*e^2 - 6*a*c^2*d^2*e^4 + a^2*c*e^6)*f^2 - 2*(3*c^3*d^5*e - 10*a*c^2*d^3*e^3 + 3*a^2*c*d*e^5)*f*g + (c^3*d^6 - 6*a*c^2*d^4*e^2 + 9*a^2*c*d^2*e^4)*g^2)/(a*c^6*d^12 + 6*a^2*c^5*d^10*e^2 + 15*a^3*c^4*d^8*e^4 + 20*a^4*c^3*d^6*e^6 + 15*a^5*c^2*d^4*e^8 + 6*a^6*c*d^2*e^10 + a^7*e^12)))/x) + (c*d^3 + a*d*e^2 + (c*d^2*e + a*e^3)*x)*sqrt(-((c^2*d^3 - 3*a*c*d*e^2)*f + (3*a*c*d^2*e - a^2*e^3)*g - (a*c^3*d^6 + 3*a^2*c^2*d^4*e^2 + 3*a^3*c*d^2*e^4 + a^4*e^6)*sqrt(-((9*c^3*d^4*e^2 - 6*a*c^2*d^2*e^4 + a^2*c*e^6)*f^2 - 2*(3*c^3*d^5*e - 10*a*c^2*d^3*e^3 + 3*a^2*c*d*e^5)*f*g + (c^3*d^6 - 6*a*c^2*d^4*e^2 + 9*a^2*c*d^2*e^4)*g^2)/(a*c^6*d^12 + 6*a^2*c^5*d^10*e^2 + 15*a^3*c^4*d^8*e^4 + 20*a^4*c^3*d^6*e^6 + 15*a^5*c^2*d^4*e^8 + 6*a^6*c*d^2*e^10 + a^7*e^12)))/(a*c^3*d^6 + 3*a^2*c^2*d^4*e^2 + 3*a^3*c*d^2*e^4 + a^4*e^6))*log(((3*c*d^2*e^2 - a*e^4)*f^2 + 2*(c*d^3*e + a*d*e^3)*f*g - (c*d^4 - 3*a*d^2*e^2)*g^2 + 2*((3*c^2*d^4*e - 4*a*c*d^2*e^3 + a^2*e^5)*f - (c^2*d^5 - 4*a*c*d^3*e^2 + 3*a^2*d*e^4)*g + 2*(a*c^3*d^7*e + 3*a^2*c^2*d^5*e^3 + 3*a^3*c*d^3*e^5 + a^4*d*e^7)*sqrt(-((9*c^3*d^4*e^2 - 6*a*c^2*d^2*e^4 + a^2*c*e^6)*f^2 - 2*(3*c^3*d^5*e - 10*a*c^2*d^3*e^3 + 3*a^2*c*d*e^5)*f*g + (c^3*d^6 - 6*a*c^2*d^4*e^2 + 9*a^2*c*d^2*e^4)*g^2)/(a*c^6*d^12 + 6*a^2*c^5*d^10*e^2 + 15*a^3*c^4*d^8*e^4 + 20*a^4*c^3*d^6*e^6 + 15*a^5*c^2*d^4*e^8 + 6*a^6*c*d^2*e^10 + a^7*e^12)))*sqrt(e*x + d)*sqrt(g*x + f)*sqrt(-((c^2*d^3 - 3*a*c*d*e^2)*f + (3*a*c*d^2*e - a^2*e^3)*g - (a*c^3*d^6 + 3*a^2*c^2*d^4*e^2 + 3*a^3*c*d^2*e^4 + a^4*e^6)*sqrt(-((9*c^3*d^4*e^2 - 6*a*c^2*d^2*e^4 + a^2*c*e^6)*f^2 - 2*(3*c^3*d^5*e - 10*a*c^2*d^3*e^3 + 3*a^2*c*d*e^5)*f*g + (c^3*d^6 - 6*a*c^2*d^4*e^2 + 9*a^2*c*d^2*e^4)*g^2)/(a*c^6*d^12 + 6*a^2*c^5*d^10*e^2 + 15*a^3*c^4*d^8*e^4 + 20*a^4*c^3*d^6*e^6 + 15*a^5*c^2*d^4*e^8 + 6*a^6*c*d^2*e^10 + a^7*e^12)))/(a*c^3*d^6 + 3*a^2*c^2*d^4*e^2 + 3*a^3*c*d^2*e^4 + a^4*e^6)) + 2*((3*c*d^2*e^2 - a*e^4)*f*g - (c*d^3*e - 3*a*d*e^3)*g^2)*x - (2*(c^3*d^7 + 3*a*c^2*d^5*e^2 + 3*a^2*c*d^3*e^4 + a^3*d*e^6)*f + ((c^3*d^6*e + 3*a*c^2*d^4*e^3 + 3*a^2*c*d^2*e^5 + a^3*e^7)*f + (c^3*d^7 + 3*a*c^2*d^5*e^2 + 3*a^2*c*d^3*e^4 + a^3*d*e^6)*g)*x)*sqrt(-((9*c^3*d^4*e^2 - 6*a*c^2*d^2*e^4 + a^2*c*e^6)*f^2 - 2*(3*c^3*d^5*e - 10*a*c^2*d^3*e^3 + 3*a^2*c*d*e^5)*f*g + (c^3*d^6 - 6*a*c^2*d^4*e^2 + 9*a^2*c*d^2*e^4)*g^2)/(a*c^6*d^12 + 6*a^2*c^5*d^10*e^2 + 15*a^3*c^4*d^8*e^4 + 20*a^4*c^3*d^6*e^6 + 15*a^5*c^2*d^4*e^8 + 6*a^6*c*d^2*e^10 + a^7*e^12)))/x) - (c*d^3 + a*d*e^2 + (c*d^2*e + a*e^3)*x)*sqrt(-((c^2*d^3 - 3*a*c*d*e^2)*f + (3*a*c*d^2*e - a^2*e^3)*g - (a*c^3*d^6 + 3*a^2*c^2*d^4*e^2 + 3*a^3*c*d^2*e^4 + a^4*e^6)*sqrt(-((9*c^3*d^4*e^2 - 6*a*c^2*d^2*e^4 + a^2*c*e^6)*f^2 - 2*(3*c^3*d^5*e - 10*a*c^2*d^3*e^3 + 3*a^2*c*d*e^5)*f*g + (c^3*d^6 - 6*a*c^2*d^4*e^2 + 9*a^2*c*d^2*e^4)*g^2)/(a*c^6*d^12 + 6*a^2*c^5*d^10*e^2 + 15*a^3*c^4*d^8*e^4 + 20*a^4*c^3*d^6*e^6 + 15*a^5*c^2*d^4*e^8 + 6*a^6*c*d^2*e^10 + a^7*e^12)))/(a*c^3*d^6 + 3*a^2*c^2*d^4*e^2 + 3*a^3*c*d^2*e^4 + a^4*e^6))*log(((3*c*d^2*e^2 - a*e^4)*f^2 + 2*(c*d^3*e + a*d*e^3)*f*g - (c*d^4 - 3*a*d^2*e^2)*g^2 - 2*((3*c^2*d^4*e - 4*a*c*d^2*e^3 + a^2*e^5)*f - (c^2*d^5 - 4*a*c*d^3*e^2 + 3*a^2*d*e^4)*g + 2*(a*c^3*d^7*e + 3*a^2*c^2*d^5*e^3 + 3*a^3*c*d^3*e^5 + a^4*d*e^7)*sqrt(-((9*c^3*d^4*e^2 - 6*a*c^2*d^2*e^4 + a^2*c*e^6)*f^2 - 2*(3*c^3*d^5*e - 10*a*c^2*d^3*e^3 + 3*a^2*c*d*e^5)*f*g + (c^3*d^6 - 6*a*c^2*d^4*e^2 + 9*a^2*c*d^2*e^4)*g^2)/(a*c^6*d^12 + 6*a^2*c^5*d^10*e^2 + 15*a^3*c^4*d^8*e^4 + 20*a^4*c^3*d^6*e^6 + 15*a^5*c^2*d^4*e^8 + 6*a^6*c*d^2*e^10 + a^7*e^12)))*sqrt(e*x + d)*sqrt(g*x + f)*sqrt(-((c^2*d^3 - 3*a*c*d*e^2)*f + (3*a*c*d^2*e - a^2*e^3)*g - (a*c^3*d^6 + 3*a^2*c^2*d^4*e^2 + 3*a^3*c*d^2*e^4 + a^4*e^6)*sqrt(-((9*c^3*d^4*e^2 - 6*a*c^2*d^2*e^4 + a^2*c*e^6)*f^2 - 2*(3*c^3*d^5*e - 10*a*c^2*d^3*e^3 + 3*a^2*c*d*e^5)*f*g + (c^3*d^6 - 6*a*c^2*d^4*e^2 + 9*a^2*c*d^2*e^4)*g^2)/(a*c^6*d^12 + 6*a^2*c^5*d^10*e^2 + 15*a^3*c^4*d^8*e^4 + 20*a^4*c^3*d^6*e^6 + 15*a^5*c^2*d^4*e^8 + 6*a^6*c*d^2*e^10 + a^7*e^12)))/(a*c^3*d^6 + 3*a^2*c^2*d^4*e^2 + 3*a^3*c*d^2*e^4 + a^4*e^6)) + 2*((3*c*d^2*e^2 - a*e^4)*f*g - (c*d^3*e - 3*a*d*e^3)*g^2)*x - (2*(c^3*d^7 + 3*a*c^2*d^5*e^2 + 3*a^2*c*d^3*e^4 + a^3*d*e^6)*f + ((c^3*d^6*e + 3*a*c^2*d^4*e^3 + 3*a^2*c*d^2*e^5 + a^3*e^7)*f + (c^3*d^7 + 3*a*c^2*d^5*e^2 + 3*a^2*c*d^3*e^4 + a^3*d*e^6)*g)*x)*sqrt(-((9*c^3*d^4*e^2 - 6*a*c^2*d^2*e^4 + a^2*c*e^6)*f^2 - 2*(3*c^3*d^5*e - 10*a*c^2*d^3*e^3 + 3*a^2*c*d*e^5)*f*g + (c^3*d^6 - 6*a*c^2*d^4*e^2 + 9*a^2*c*d^2*e^4)*g^2)/(a*c^6*d^12 + 6*a^2*c^5*d^10*e^2 + 15*a^3*c^4*d^8*e^4 + 20*a^4*c^3*d^6*e^6 + 15*a^5*c^2*d^4*e^8 + 6*a^6*c*d^2*e^10 + a^7*e^12)))/x) + 8*sqrt(e*x + d)*sqrt(g*x + f)*e)/(c*d^3 + a*d*e^2 + (c*d^2*e + a*e^3)*x)","B",0
609,-1,0,0,0.000000," ","integrate((g*x+f)^(1/2)/(e*x+d)^(5/2)/(c*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
610,-1,0,0,0.000000," ","integrate((e*x+d)^(3/2)/(c*x^2+a)/(g*x+f)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
611,1,1913,0,9.630174," ","integrate((e*x+d)^(1/2)/(c*x^2+a)/(g*x+f)^(1/2),x, algorithm=""fricas"")","-\frac{1}{4} \, \sqrt{-\frac{c d f + a e g + {\left(a c^{2} f^{2} + a^{2} c g^{2}\right)} \sqrt{-\frac{e^{2} f^{2} - 2 \, d e f g + d^{2} g^{2}}{a c^{3} f^{4} + 2 \, a^{2} c^{2} f^{2} g^{2} + a^{3} c g^{4}}}}{a c^{2} f^{2} + a^{2} c g^{2}}} \log\left(-\frac{e^{2} f^{2} - d^{2} g^{2} + 2 \, {\left(c e f^{2} - c d f g + {\left(a c^{2} f^{2} g + a^{2} c g^{3}\right)} \sqrt{-\frac{e^{2} f^{2} - 2 \, d e f g + d^{2} g^{2}}{a c^{3} f^{4} + 2 \, a^{2} c^{2} f^{2} g^{2} + a^{3} c g^{4}}}\right)} \sqrt{e x + d} \sqrt{g x + f} \sqrt{-\frac{c d f + a e g + {\left(a c^{2} f^{2} + a^{2} c g^{2}\right)} \sqrt{-\frac{e^{2} f^{2} - 2 \, d e f g + d^{2} g^{2}}{a c^{3} f^{4} + 2 \, a^{2} c^{2} f^{2} g^{2} + a^{3} c g^{4}}}}{a c^{2} f^{2} + a^{2} c g^{2}}} + 2 \, {\left(e^{2} f g - d e g^{2}\right)} x - {\left(2 \, c^{2} d f^{3} + 2 \, a c d f g^{2} + {\left(c^{2} e f^{3} + c^{2} d f^{2} g + a c e f g^{2} + a c d g^{3}\right)} x\right)} \sqrt{-\frac{e^{2} f^{2} - 2 \, d e f g + d^{2} g^{2}}{a c^{3} f^{4} + 2 \, a^{2} c^{2} f^{2} g^{2} + a^{3} c g^{4}}}}{x}\right) + \frac{1}{4} \, \sqrt{-\frac{c d f + a e g + {\left(a c^{2} f^{2} + a^{2} c g^{2}\right)} \sqrt{-\frac{e^{2} f^{2} - 2 \, d e f g + d^{2} g^{2}}{a c^{3} f^{4} + 2 \, a^{2} c^{2} f^{2} g^{2} + a^{3} c g^{4}}}}{a c^{2} f^{2} + a^{2} c g^{2}}} \log\left(-\frac{e^{2} f^{2} - d^{2} g^{2} - 2 \, {\left(c e f^{2} - c d f g + {\left(a c^{2} f^{2} g + a^{2} c g^{3}\right)} \sqrt{-\frac{e^{2} f^{2} - 2 \, d e f g + d^{2} g^{2}}{a c^{3} f^{4} + 2 \, a^{2} c^{2} f^{2} g^{2} + a^{3} c g^{4}}}\right)} \sqrt{e x + d} \sqrt{g x + f} \sqrt{-\frac{c d f + a e g + {\left(a c^{2} f^{2} + a^{2} c g^{2}\right)} \sqrt{-\frac{e^{2} f^{2} - 2 \, d e f g + d^{2} g^{2}}{a c^{3} f^{4} + 2 \, a^{2} c^{2} f^{2} g^{2} + a^{3} c g^{4}}}}{a c^{2} f^{2} + a^{2} c g^{2}}} + 2 \, {\left(e^{2} f g - d e g^{2}\right)} x - {\left(2 \, c^{2} d f^{3} + 2 \, a c d f g^{2} + {\left(c^{2} e f^{3} + c^{2} d f^{2} g + a c e f g^{2} + a c d g^{3}\right)} x\right)} \sqrt{-\frac{e^{2} f^{2} - 2 \, d e f g + d^{2} g^{2}}{a c^{3} f^{4} + 2 \, a^{2} c^{2} f^{2} g^{2} + a^{3} c g^{4}}}}{x}\right) - \frac{1}{4} \, \sqrt{-\frac{c d f + a e g - {\left(a c^{2} f^{2} + a^{2} c g^{2}\right)} \sqrt{-\frac{e^{2} f^{2} - 2 \, d e f g + d^{2} g^{2}}{a c^{3} f^{4} + 2 \, a^{2} c^{2} f^{2} g^{2} + a^{3} c g^{4}}}}{a c^{2} f^{2} + a^{2} c g^{2}}} \log\left(-\frac{e^{2} f^{2} - d^{2} g^{2} + 2 \, {\left(c e f^{2} - c d f g - {\left(a c^{2} f^{2} g + a^{2} c g^{3}\right)} \sqrt{-\frac{e^{2} f^{2} - 2 \, d e f g + d^{2} g^{2}}{a c^{3} f^{4} + 2 \, a^{2} c^{2} f^{2} g^{2} + a^{3} c g^{4}}}\right)} \sqrt{e x + d} \sqrt{g x + f} \sqrt{-\frac{c d f + a e g - {\left(a c^{2} f^{2} + a^{2} c g^{2}\right)} \sqrt{-\frac{e^{2} f^{2} - 2 \, d e f g + d^{2} g^{2}}{a c^{3} f^{4} + 2 \, a^{2} c^{2} f^{2} g^{2} + a^{3} c g^{4}}}}{a c^{2} f^{2} + a^{2} c g^{2}}} + 2 \, {\left(e^{2} f g - d e g^{2}\right)} x + {\left(2 \, c^{2} d f^{3} + 2 \, a c d f g^{2} + {\left(c^{2} e f^{3} + c^{2} d f^{2} g + a c e f g^{2} + a c d g^{3}\right)} x\right)} \sqrt{-\frac{e^{2} f^{2} - 2 \, d e f g + d^{2} g^{2}}{a c^{3} f^{4} + 2 \, a^{2} c^{2} f^{2} g^{2} + a^{3} c g^{4}}}}{x}\right) + \frac{1}{4} \, \sqrt{-\frac{c d f + a e g - {\left(a c^{2} f^{2} + a^{2} c g^{2}\right)} \sqrt{-\frac{e^{2} f^{2} - 2 \, d e f g + d^{2} g^{2}}{a c^{3} f^{4} + 2 \, a^{2} c^{2} f^{2} g^{2} + a^{3} c g^{4}}}}{a c^{2} f^{2} + a^{2} c g^{2}}} \log\left(-\frac{e^{2} f^{2} - d^{2} g^{2} - 2 \, {\left(c e f^{2} - c d f g - {\left(a c^{2} f^{2} g + a^{2} c g^{3}\right)} \sqrt{-\frac{e^{2} f^{2} - 2 \, d e f g + d^{2} g^{2}}{a c^{3} f^{4} + 2 \, a^{2} c^{2} f^{2} g^{2} + a^{3} c g^{4}}}\right)} \sqrt{e x + d} \sqrt{g x + f} \sqrt{-\frac{c d f + a e g - {\left(a c^{2} f^{2} + a^{2} c g^{2}\right)} \sqrt{-\frac{e^{2} f^{2} - 2 \, d e f g + d^{2} g^{2}}{a c^{3} f^{4} + 2 \, a^{2} c^{2} f^{2} g^{2} + a^{3} c g^{4}}}}{a c^{2} f^{2} + a^{2} c g^{2}}} + 2 \, {\left(e^{2} f g - d e g^{2}\right)} x + {\left(2 \, c^{2} d f^{3} + 2 \, a c d f g^{2} + {\left(c^{2} e f^{3} + c^{2} d f^{2} g + a c e f g^{2} + a c d g^{3}\right)} x\right)} \sqrt{-\frac{e^{2} f^{2} - 2 \, d e f g + d^{2} g^{2}}{a c^{3} f^{4} + 2 \, a^{2} c^{2} f^{2} g^{2} + a^{3} c g^{4}}}}{x}\right)"," ",0,"-1/4*sqrt(-(c*d*f + a*e*g + (a*c^2*f^2 + a^2*c*g^2)*sqrt(-(e^2*f^2 - 2*d*e*f*g + d^2*g^2)/(a*c^3*f^4 + 2*a^2*c^2*f^2*g^2 + a^3*c*g^4)))/(a*c^2*f^2 + a^2*c*g^2))*log(-(e^2*f^2 - d^2*g^2 + 2*(c*e*f^2 - c*d*f*g + (a*c^2*f^2*g + a^2*c*g^3)*sqrt(-(e^2*f^2 - 2*d*e*f*g + d^2*g^2)/(a*c^3*f^4 + 2*a^2*c^2*f^2*g^2 + a^3*c*g^4)))*sqrt(e*x + d)*sqrt(g*x + f)*sqrt(-(c*d*f + a*e*g + (a*c^2*f^2 + a^2*c*g^2)*sqrt(-(e^2*f^2 - 2*d*e*f*g + d^2*g^2)/(a*c^3*f^4 + 2*a^2*c^2*f^2*g^2 + a^3*c*g^4)))/(a*c^2*f^2 + a^2*c*g^2)) + 2*(e^2*f*g - d*e*g^2)*x - (2*c^2*d*f^3 + 2*a*c*d*f*g^2 + (c^2*e*f^3 + c^2*d*f^2*g + a*c*e*f*g^2 + a*c*d*g^3)*x)*sqrt(-(e^2*f^2 - 2*d*e*f*g + d^2*g^2)/(a*c^3*f^4 + 2*a^2*c^2*f^2*g^2 + a^3*c*g^4)))/x) + 1/4*sqrt(-(c*d*f + a*e*g + (a*c^2*f^2 + a^2*c*g^2)*sqrt(-(e^2*f^2 - 2*d*e*f*g + d^2*g^2)/(a*c^3*f^4 + 2*a^2*c^2*f^2*g^2 + a^3*c*g^4)))/(a*c^2*f^2 + a^2*c*g^2))*log(-(e^2*f^2 - d^2*g^2 - 2*(c*e*f^2 - c*d*f*g + (a*c^2*f^2*g + a^2*c*g^3)*sqrt(-(e^2*f^2 - 2*d*e*f*g + d^2*g^2)/(a*c^3*f^4 + 2*a^2*c^2*f^2*g^2 + a^3*c*g^4)))*sqrt(e*x + d)*sqrt(g*x + f)*sqrt(-(c*d*f + a*e*g + (a*c^2*f^2 + a^2*c*g^2)*sqrt(-(e^2*f^2 - 2*d*e*f*g + d^2*g^2)/(a*c^3*f^4 + 2*a^2*c^2*f^2*g^2 + a^3*c*g^4)))/(a*c^2*f^2 + a^2*c*g^2)) + 2*(e^2*f*g - d*e*g^2)*x - (2*c^2*d*f^3 + 2*a*c*d*f*g^2 + (c^2*e*f^3 + c^2*d*f^2*g + a*c*e*f*g^2 + a*c*d*g^3)*x)*sqrt(-(e^2*f^2 - 2*d*e*f*g + d^2*g^2)/(a*c^3*f^4 + 2*a^2*c^2*f^2*g^2 + a^3*c*g^4)))/x) - 1/4*sqrt(-(c*d*f + a*e*g - (a*c^2*f^2 + a^2*c*g^2)*sqrt(-(e^2*f^2 - 2*d*e*f*g + d^2*g^2)/(a*c^3*f^4 + 2*a^2*c^2*f^2*g^2 + a^3*c*g^4)))/(a*c^2*f^2 + a^2*c*g^2))*log(-(e^2*f^2 - d^2*g^2 + 2*(c*e*f^2 - c*d*f*g - (a*c^2*f^2*g + a^2*c*g^3)*sqrt(-(e^2*f^2 - 2*d*e*f*g + d^2*g^2)/(a*c^3*f^4 + 2*a^2*c^2*f^2*g^2 + a^3*c*g^4)))*sqrt(e*x + d)*sqrt(g*x + f)*sqrt(-(c*d*f + a*e*g - (a*c^2*f^2 + a^2*c*g^2)*sqrt(-(e^2*f^2 - 2*d*e*f*g + d^2*g^2)/(a*c^3*f^4 + 2*a^2*c^2*f^2*g^2 + a^3*c*g^4)))/(a*c^2*f^2 + a^2*c*g^2)) + 2*(e^2*f*g - d*e*g^2)*x + (2*c^2*d*f^3 + 2*a*c*d*f*g^2 + (c^2*e*f^3 + c^2*d*f^2*g + a*c*e*f*g^2 + a*c*d*g^3)*x)*sqrt(-(e^2*f^2 - 2*d*e*f*g + d^2*g^2)/(a*c^3*f^4 + 2*a^2*c^2*f^2*g^2 + a^3*c*g^4)))/x) + 1/4*sqrt(-(c*d*f + a*e*g - (a*c^2*f^2 + a^2*c*g^2)*sqrt(-(e^2*f^2 - 2*d*e*f*g + d^2*g^2)/(a*c^3*f^4 + 2*a^2*c^2*f^2*g^2 + a^3*c*g^4)))/(a*c^2*f^2 + a^2*c*g^2))*log(-(e^2*f^2 - d^2*g^2 - 2*(c*e*f^2 - c*d*f*g - (a*c^2*f^2*g + a^2*c*g^3)*sqrt(-(e^2*f^2 - 2*d*e*f*g + d^2*g^2)/(a*c^3*f^4 + 2*a^2*c^2*f^2*g^2 + a^3*c*g^4)))*sqrt(e*x + d)*sqrt(g*x + f)*sqrt(-(c*d*f + a*e*g - (a*c^2*f^2 + a^2*c*g^2)*sqrt(-(e^2*f^2 - 2*d*e*f*g + d^2*g^2)/(a*c^3*f^4 + 2*a^2*c^2*f^2*g^2 + a^3*c*g^4)))/(a*c^2*f^2 + a^2*c*g^2)) + 2*(e^2*f*g - d*e*g^2)*x + (2*c^2*d*f^3 + 2*a*c*d*f*g^2 + (c^2*e*f^3 + c^2*d*f^2*g + a*c*e*f*g^2 + a*c*d*g^3)*x)*sqrt(-(e^2*f^2 - 2*d*e*f*g + d^2*g^2)/(a*c^3*f^4 + 2*a^2*c^2*f^2*g^2 + a^3*c*g^4)))/x)","B",0
612,1,4325,0,23.237742," ","integrate(1/(e*x+d)^(1/2)/(c*x^2+a)/(g*x+f)^(1/2),x, algorithm=""fricas"")","-\frac{1}{4} \, \sqrt{-\frac{c d f - a e g + {\left({\left(a c^{2} d^{2} + a^{2} c e^{2}\right)} f^{2} + {\left(a^{2} c d^{2} + a^{3} e^{2}\right)} g^{2}\right)} \sqrt{-\frac{c e^{2} f^{2} + 2 \, c d e f g + c d^{2} g^{2}}{{\left(a c^{4} d^{4} + 2 \, a^{2} c^{3} d^{2} e^{2} + a^{3} c^{2} e^{4}\right)} f^{4} + 2 \, {\left(a^{2} c^{3} d^{4} + 2 \, a^{3} c^{2} d^{2} e^{2} + a^{4} c e^{4}\right)} f^{2} g^{2} + {\left(a^{3} c^{2} d^{4} + 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}\right)} g^{4}}}}{{\left(a c^{2} d^{2} + a^{2} c e^{2}\right)} f^{2} + {\left(a^{2} c d^{2} + a^{3} e^{2}\right)} g^{2}}} \log\left(\frac{e^{2} f^{2} + 2 \, d e f g + d^{2} g^{2} + 2 \, {\left(c d e f^{2} - a d e g^{2} + {\left(c d^{2} - a e^{2}\right)} f g - {\left({\left(a c^{2} d^{2} e + a^{2} c e^{3}\right)} f^{3} + {\left(a c^{2} d^{3} + a^{2} c d e^{2}\right)} f^{2} g + {\left(a^{2} c d^{2} e + a^{3} e^{3}\right)} f g^{2} + {\left(a^{2} c d^{3} + a^{3} d e^{2}\right)} g^{3}\right)} \sqrt{-\frac{c e^{2} f^{2} + 2 \, c d e f g + c d^{2} g^{2}}{{\left(a c^{4} d^{4} + 2 \, a^{2} c^{3} d^{2} e^{2} + a^{3} c^{2} e^{4}\right)} f^{4} + 2 \, {\left(a^{2} c^{3} d^{4} + 2 \, a^{3} c^{2} d^{2} e^{2} + a^{4} c e^{4}\right)} f^{2} g^{2} + {\left(a^{3} c^{2} d^{4} + 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}\right)} g^{4}}}\right)} \sqrt{e x + d} \sqrt{g x + f} \sqrt{-\frac{c d f - a e g + {\left({\left(a c^{2} d^{2} + a^{2} c e^{2}\right)} f^{2} + {\left(a^{2} c d^{2} + a^{3} e^{2}\right)} g^{2}\right)} \sqrt{-\frac{c e^{2} f^{2} + 2 \, c d e f g + c d^{2} g^{2}}{{\left(a c^{4} d^{4} + 2 \, a^{2} c^{3} d^{2} e^{2} + a^{3} c^{2} e^{4}\right)} f^{4} + 2 \, {\left(a^{2} c^{3} d^{4} + 2 \, a^{3} c^{2} d^{2} e^{2} + a^{4} c e^{4}\right)} f^{2} g^{2} + {\left(a^{3} c^{2} d^{4} + 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}\right)} g^{4}}}}{{\left(a c^{2} d^{2} + a^{2} c e^{2}\right)} f^{2} + {\left(a^{2} c d^{2} + a^{3} e^{2}\right)} g^{2}}} + 2 \, {\left(e^{2} f g + d e g^{2}\right)} x + {\left(2 \, {\left(c^{2} d^{3} + a c d e^{2}\right)} f^{3} + 2 \, {\left(a c d^{3} + a^{2} d e^{2}\right)} f g^{2} + {\left({\left(c^{2} d^{2} e + a c e^{3}\right)} f^{3} + {\left(c^{2} d^{3} + a c d e^{2}\right)} f^{2} g + {\left(a c d^{2} e + a^{2} e^{3}\right)} f g^{2} + {\left(a c d^{3} + a^{2} d e^{2}\right)} g^{3}\right)} x\right)} \sqrt{-\frac{c e^{2} f^{2} + 2 \, c d e f g + c d^{2} g^{2}}{{\left(a c^{4} d^{4} + 2 \, a^{2} c^{3} d^{2} e^{2} + a^{3} c^{2} e^{4}\right)} f^{4} + 2 \, {\left(a^{2} c^{3} d^{4} + 2 \, a^{3} c^{2} d^{2} e^{2} + a^{4} c e^{4}\right)} f^{2} g^{2} + {\left(a^{3} c^{2} d^{4} + 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}\right)} g^{4}}}}{x}\right) + \frac{1}{4} \, \sqrt{-\frac{c d f - a e g + {\left({\left(a c^{2} d^{2} + a^{2} c e^{2}\right)} f^{2} + {\left(a^{2} c d^{2} + a^{3} e^{2}\right)} g^{2}\right)} \sqrt{-\frac{c e^{2} f^{2} + 2 \, c d e f g + c d^{2} g^{2}}{{\left(a c^{4} d^{4} + 2 \, a^{2} c^{3} d^{2} e^{2} + a^{3} c^{2} e^{4}\right)} f^{4} + 2 \, {\left(a^{2} c^{3} d^{4} + 2 \, a^{3} c^{2} d^{2} e^{2} + a^{4} c e^{4}\right)} f^{2} g^{2} + {\left(a^{3} c^{2} d^{4} + 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}\right)} g^{4}}}}{{\left(a c^{2} d^{2} + a^{2} c e^{2}\right)} f^{2} + {\left(a^{2} c d^{2} + a^{3} e^{2}\right)} g^{2}}} \log\left(\frac{e^{2} f^{2} + 2 \, d e f g + d^{2} g^{2} - 2 \, {\left(c d e f^{2} - a d e g^{2} + {\left(c d^{2} - a e^{2}\right)} f g - {\left({\left(a c^{2} d^{2} e + a^{2} c e^{3}\right)} f^{3} + {\left(a c^{2} d^{3} + a^{2} c d e^{2}\right)} f^{2} g + {\left(a^{2} c d^{2} e + a^{3} e^{3}\right)} f g^{2} + {\left(a^{2} c d^{3} + a^{3} d e^{2}\right)} g^{3}\right)} \sqrt{-\frac{c e^{2} f^{2} + 2 \, c d e f g + c d^{2} g^{2}}{{\left(a c^{4} d^{4} + 2 \, a^{2} c^{3} d^{2} e^{2} + a^{3} c^{2} e^{4}\right)} f^{4} + 2 \, {\left(a^{2} c^{3} d^{4} + 2 \, a^{3} c^{2} d^{2} e^{2} + a^{4} c e^{4}\right)} f^{2} g^{2} + {\left(a^{3} c^{2} d^{4} + 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}\right)} g^{4}}}\right)} \sqrt{e x + d} \sqrt{g x + f} \sqrt{-\frac{c d f - a e g + {\left({\left(a c^{2} d^{2} + a^{2} c e^{2}\right)} f^{2} + {\left(a^{2} c d^{2} + a^{3} e^{2}\right)} g^{2}\right)} \sqrt{-\frac{c e^{2} f^{2} + 2 \, c d e f g + c d^{2} g^{2}}{{\left(a c^{4} d^{4} + 2 \, a^{2} c^{3} d^{2} e^{2} + a^{3} c^{2} e^{4}\right)} f^{4} + 2 \, {\left(a^{2} c^{3} d^{4} + 2 \, a^{3} c^{2} d^{2} e^{2} + a^{4} c e^{4}\right)} f^{2} g^{2} + {\left(a^{3} c^{2} d^{4} + 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}\right)} g^{4}}}}{{\left(a c^{2} d^{2} + a^{2} c e^{2}\right)} f^{2} + {\left(a^{2} c d^{2} + a^{3} e^{2}\right)} g^{2}}} + 2 \, {\left(e^{2} f g + d e g^{2}\right)} x + {\left(2 \, {\left(c^{2} d^{3} + a c d e^{2}\right)} f^{3} + 2 \, {\left(a c d^{3} + a^{2} d e^{2}\right)} f g^{2} + {\left({\left(c^{2} d^{2} e + a c e^{3}\right)} f^{3} + {\left(c^{2} d^{3} + a c d e^{2}\right)} f^{2} g + {\left(a c d^{2} e + a^{2} e^{3}\right)} f g^{2} + {\left(a c d^{3} + a^{2} d e^{2}\right)} g^{3}\right)} x\right)} \sqrt{-\frac{c e^{2} f^{2} + 2 \, c d e f g + c d^{2} g^{2}}{{\left(a c^{4} d^{4} + 2 \, a^{2} c^{3} d^{2} e^{2} + a^{3} c^{2} e^{4}\right)} f^{4} + 2 \, {\left(a^{2} c^{3} d^{4} + 2 \, a^{3} c^{2} d^{2} e^{2} + a^{4} c e^{4}\right)} f^{2} g^{2} + {\left(a^{3} c^{2} d^{4} + 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}\right)} g^{4}}}}{x}\right) - \frac{1}{4} \, \sqrt{-\frac{c d f - a e g - {\left({\left(a c^{2} d^{2} + a^{2} c e^{2}\right)} f^{2} + {\left(a^{2} c d^{2} + a^{3} e^{2}\right)} g^{2}\right)} \sqrt{-\frac{c e^{2} f^{2} + 2 \, c d e f g + c d^{2} g^{2}}{{\left(a c^{4} d^{4} + 2 \, a^{2} c^{3} d^{2} e^{2} + a^{3} c^{2} e^{4}\right)} f^{4} + 2 \, {\left(a^{2} c^{3} d^{4} + 2 \, a^{3} c^{2} d^{2} e^{2} + a^{4} c e^{4}\right)} f^{2} g^{2} + {\left(a^{3} c^{2} d^{4} + 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}\right)} g^{4}}}}{{\left(a c^{2} d^{2} + a^{2} c e^{2}\right)} f^{2} + {\left(a^{2} c d^{2} + a^{3} e^{2}\right)} g^{2}}} \log\left(\frac{e^{2} f^{2} + 2 \, d e f g + d^{2} g^{2} + 2 \, {\left(c d e f^{2} - a d e g^{2} + {\left(c d^{2} - a e^{2}\right)} f g + {\left({\left(a c^{2} d^{2} e + a^{2} c e^{3}\right)} f^{3} + {\left(a c^{2} d^{3} + a^{2} c d e^{2}\right)} f^{2} g + {\left(a^{2} c d^{2} e + a^{3} e^{3}\right)} f g^{2} + {\left(a^{2} c d^{3} + a^{3} d e^{2}\right)} g^{3}\right)} \sqrt{-\frac{c e^{2} f^{2} + 2 \, c d e f g + c d^{2} g^{2}}{{\left(a c^{4} d^{4} + 2 \, a^{2} c^{3} d^{2} e^{2} + a^{3} c^{2} e^{4}\right)} f^{4} + 2 \, {\left(a^{2} c^{3} d^{4} + 2 \, a^{3} c^{2} d^{2} e^{2} + a^{4} c e^{4}\right)} f^{2} g^{2} + {\left(a^{3} c^{2} d^{4} + 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}\right)} g^{4}}}\right)} \sqrt{e x + d} \sqrt{g x + f} \sqrt{-\frac{c d f - a e g - {\left({\left(a c^{2} d^{2} + a^{2} c e^{2}\right)} f^{2} + {\left(a^{2} c d^{2} + a^{3} e^{2}\right)} g^{2}\right)} \sqrt{-\frac{c e^{2} f^{2} + 2 \, c d e f g + c d^{2} g^{2}}{{\left(a c^{4} d^{4} + 2 \, a^{2} c^{3} d^{2} e^{2} + a^{3} c^{2} e^{4}\right)} f^{4} + 2 \, {\left(a^{2} c^{3} d^{4} + 2 \, a^{3} c^{2} d^{2} e^{2} + a^{4} c e^{4}\right)} f^{2} g^{2} + {\left(a^{3} c^{2} d^{4} + 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}\right)} g^{4}}}}{{\left(a c^{2} d^{2} + a^{2} c e^{2}\right)} f^{2} + {\left(a^{2} c d^{2} + a^{3} e^{2}\right)} g^{2}}} + 2 \, {\left(e^{2} f g + d e g^{2}\right)} x - {\left(2 \, {\left(c^{2} d^{3} + a c d e^{2}\right)} f^{3} + 2 \, {\left(a c d^{3} + a^{2} d e^{2}\right)} f g^{2} + {\left({\left(c^{2} d^{2} e + a c e^{3}\right)} f^{3} + {\left(c^{2} d^{3} + a c d e^{2}\right)} f^{2} g + {\left(a c d^{2} e + a^{2} e^{3}\right)} f g^{2} + {\left(a c d^{3} + a^{2} d e^{2}\right)} g^{3}\right)} x\right)} \sqrt{-\frac{c e^{2} f^{2} + 2 \, c d e f g + c d^{2} g^{2}}{{\left(a c^{4} d^{4} + 2 \, a^{2} c^{3} d^{2} e^{2} + a^{3} c^{2} e^{4}\right)} f^{4} + 2 \, {\left(a^{2} c^{3} d^{4} + 2 \, a^{3} c^{2} d^{2} e^{2} + a^{4} c e^{4}\right)} f^{2} g^{2} + {\left(a^{3} c^{2} d^{4} + 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}\right)} g^{4}}}}{x}\right) + \frac{1}{4} \, \sqrt{-\frac{c d f - a e g - {\left({\left(a c^{2} d^{2} + a^{2} c e^{2}\right)} f^{2} + {\left(a^{2} c d^{2} + a^{3} e^{2}\right)} g^{2}\right)} \sqrt{-\frac{c e^{2} f^{2} + 2 \, c d e f g + c d^{2} g^{2}}{{\left(a c^{4} d^{4} + 2 \, a^{2} c^{3} d^{2} e^{2} + a^{3} c^{2} e^{4}\right)} f^{4} + 2 \, {\left(a^{2} c^{3} d^{4} + 2 \, a^{3} c^{2} d^{2} e^{2} + a^{4} c e^{4}\right)} f^{2} g^{2} + {\left(a^{3} c^{2} d^{4} + 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}\right)} g^{4}}}}{{\left(a c^{2} d^{2} + a^{2} c e^{2}\right)} f^{2} + {\left(a^{2} c d^{2} + a^{3} e^{2}\right)} g^{2}}} \log\left(\frac{e^{2} f^{2} + 2 \, d e f g + d^{2} g^{2} - 2 \, {\left(c d e f^{2} - a d e g^{2} + {\left(c d^{2} - a e^{2}\right)} f g + {\left({\left(a c^{2} d^{2} e + a^{2} c e^{3}\right)} f^{3} + {\left(a c^{2} d^{3} + a^{2} c d e^{2}\right)} f^{2} g + {\left(a^{2} c d^{2} e + a^{3} e^{3}\right)} f g^{2} + {\left(a^{2} c d^{3} + a^{3} d e^{2}\right)} g^{3}\right)} \sqrt{-\frac{c e^{2} f^{2} + 2 \, c d e f g + c d^{2} g^{2}}{{\left(a c^{4} d^{4} + 2 \, a^{2} c^{3} d^{2} e^{2} + a^{3} c^{2} e^{4}\right)} f^{4} + 2 \, {\left(a^{2} c^{3} d^{4} + 2 \, a^{3} c^{2} d^{2} e^{2} + a^{4} c e^{4}\right)} f^{2} g^{2} + {\left(a^{3} c^{2} d^{4} + 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}\right)} g^{4}}}\right)} \sqrt{e x + d} \sqrt{g x + f} \sqrt{-\frac{c d f - a e g - {\left({\left(a c^{2} d^{2} + a^{2} c e^{2}\right)} f^{2} + {\left(a^{2} c d^{2} + a^{3} e^{2}\right)} g^{2}\right)} \sqrt{-\frac{c e^{2} f^{2} + 2 \, c d e f g + c d^{2} g^{2}}{{\left(a c^{4} d^{4} + 2 \, a^{2} c^{3} d^{2} e^{2} + a^{3} c^{2} e^{4}\right)} f^{4} + 2 \, {\left(a^{2} c^{3} d^{4} + 2 \, a^{3} c^{2} d^{2} e^{2} + a^{4} c e^{4}\right)} f^{2} g^{2} + {\left(a^{3} c^{2} d^{4} + 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}\right)} g^{4}}}}{{\left(a c^{2} d^{2} + a^{2} c e^{2}\right)} f^{2} + {\left(a^{2} c d^{2} + a^{3} e^{2}\right)} g^{2}}} + 2 \, {\left(e^{2} f g + d e g^{2}\right)} x - {\left(2 \, {\left(c^{2} d^{3} + a c d e^{2}\right)} f^{3} + 2 \, {\left(a c d^{3} + a^{2} d e^{2}\right)} f g^{2} + {\left({\left(c^{2} d^{2} e + a c e^{3}\right)} f^{3} + {\left(c^{2} d^{3} + a c d e^{2}\right)} f^{2} g + {\left(a c d^{2} e + a^{2} e^{3}\right)} f g^{2} + {\left(a c d^{3} + a^{2} d e^{2}\right)} g^{3}\right)} x\right)} \sqrt{-\frac{c e^{2} f^{2} + 2 \, c d e f g + c d^{2} g^{2}}{{\left(a c^{4} d^{4} + 2 \, a^{2} c^{3} d^{2} e^{2} + a^{3} c^{2} e^{4}\right)} f^{4} + 2 \, {\left(a^{2} c^{3} d^{4} + 2 \, a^{3} c^{2} d^{2} e^{2} + a^{4} c e^{4}\right)} f^{2} g^{2} + {\left(a^{3} c^{2} d^{4} + 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}\right)} g^{4}}}}{x}\right)"," ",0,"-1/4*sqrt(-(c*d*f - a*e*g + ((a*c^2*d^2 + a^2*c*e^2)*f^2 + (a^2*c*d^2 + a^3*e^2)*g^2)*sqrt(-(c*e^2*f^2 + 2*c*d*e*f*g + c*d^2*g^2)/((a*c^4*d^4 + 2*a^2*c^3*d^2*e^2 + a^3*c^2*e^4)*f^4 + 2*(a^2*c^3*d^4 + 2*a^3*c^2*d^2*e^2 + a^4*c*e^4)*f^2*g^2 + (a^3*c^2*d^4 + 2*a^4*c*d^2*e^2 + a^5*e^4)*g^4)))/((a*c^2*d^2 + a^2*c*e^2)*f^2 + (a^2*c*d^2 + a^3*e^2)*g^2))*log((e^2*f^2 + 2*d*e*f*g + d^2*g^2 + 2*(c*d*e*f^2 - a*d*e*g^2 + (c*d^2 - a*e^2)*f*g - ((a*c^2*d^2*e + a^2*c*e^3)*f^3 + (a*c^2*d^3 + a^2*c*d*e^2)*f^2*g + (a^2*c*d^2*e + a^3*e^3)*f*g^2 + (a^2*c*d^3 + a^3*d*e^2)*g^3)*sqrt(-(c*e^2*f^2 + 2*c*d*e*f*g + c*d^2*g^2)/((a*c^4*d^4 + 2*a^2*c^3*d^2*e^2 + a^3*c^2*e^4)*f^4 + 2*(a^2*c^3*d^4 + 2*a^3*c^2*d^2*e^2 + a^4*c*e^4)*f^2*g^2 + (a^3*c^2*d^4 + 2*a^4*c*d^2*e^2 + a^5*e^4)*g^4)))*sqrt(e*x + d)*sqrt(g*x + f)*sqrt(-(c*d*f - a*e*g + ((a*c^2*d^2 + a^2*c*e^2)*f^2 + (a^2*c*d^2 + a^3*e^2)*g^2)*sqrt(-(c*e^2*f^2 + 2*c*d*e*f*g + c*d^2*g^2)/((a*c^4*d^4 + 2*a^2*c^3*d^2*e^2 + a^3*c^2*e^4)*f^4 + 2*(a^2*c^3*d^4 + 2*a^3*c^2*d^2*e^2 + a^4*c*e^4)*f^2*g^2 + (a^3*c^2*d^4 + 2*a^4*c*d^2*e^2 + a^5*e^4)*g^4)))/((a*c^2*d^2 + a^2*c*e^2)*f^2 + (a^2*c*d^2 + a^3*e^2)*g^2)) + 2*(e^2*f*g + d*e*g^2)*x + (2*(c^2*d^3 + a*c*d*e^2)*f^3 + 2*(a*c*d^3 + a^2*d*e^2)*f*g^2 + ((c^2*d^2*e + a*c*e^3)*f^3 + (c^2*d^3 + a*c*d*e^2)*f^2*g + (a*c*d^2*e + a^2*e^3)*f*g^2 + (a*c*d^3 + a^2*d*e^2)*g^3)*x)*sqrt(-(c*e^2*f^2 + 2*c*d*e*f*g + c*d^2*g^2)/((a*c^4*d^4 + 2*a^2*c^3*d^2*e^2 + a^3*c^2*e^4)*f^4 + 2*(a^2*c^3*d^4 + 2*a^3*c^2*d^2*e^2 + a^4*c*e^4)*f^2*g^2 + (a^3*c^2*d^4 + 2*a^4*c*d^2*e^2 + a^5*e^4)*g^4)))/x) + 1/4*sqrt(-(c*d*f - a*e*g + ((a*c^2*d^2 + a^2*c*e^2)*f^2 + (a^2*c*d^2 + a^3*e^2)*g^2)*sqrt(-(c*e^2*f^2 + 2*c*d*e*f*g + c*d^2*g^2)/((a*c^4*d^4 + 2*a^2*c^3*d^2*e^2 + a^3*c^2*e^4)*f^4 + 2*(a^2*c^3*d^4 + 2*a^3*c^2*d^2*e^2 + a^4*c*e^4)*f^2*g^2 + (a^3*c^2*d^4 + 2*a^4*c*d^2*e^2 + a^5*e^4)*g^4)))/((a*c^2*d^2 + a^2*c*e^2)*f^2 + (a^2*c*d^2 + a^3*e^2)*g^2))*log((e^2*f^2 + 2*d*e*f*g + d^2*g^2 - 2*(c*d*e*f^2 - a*d*e*g^2 + (c*d^2 - a*e^2)*f*g - ((a*c^2*d^2*e + a^2*c*e^3)*f^3 + (a*c^2*d^3 + a^2*c*d*e^2)*f^2*g + (a^2*c*d^2*e + a^3*e^3)*f*g^2 + (a^2*c*d^3 + a^3*d*e^2)*g^3)*sqrt(-(c*e^2*f^2 + 2*c*d*e*f*g + c*d^2*g^2)/((a*c^4*d^4 + 2*a^2*c^3*d^2*e^2 + a^3*c^2*e^4)*f^4 + 2*(a^2*c^3*d^4 + 2*a^3*c^2*d^2*e^2 + a^4*c*e^4)*f^2*g^2 + (a^3*c^2*d^4 + 2*a^4*c*d^2*e^2 + a^5*e^4)*g^4)))*sqrt(e*x + d)*sqrt(g*x + f)*sqrt(-(c*d*f - a*e*g + ((a*c^2*d^2 + a^2*c*e^2)*f^2 + (a^2*c*d^2 + a^3*e^2)*g^2)*sqrt(-(c*e^2*f^2 + 2*c*d*e*f*g + c*d^2*g^2)/((a*c^4*d^4 + 2*a^2*c^3*d^2*e^2 + a^3*c^2*e^4)*f^4 + 2*(a^2*c^3*d^4 + 2*a^3*c^2*d^2*e^2 + a^4*c*e^4)*f^2*g^2 + (a^3*c^2*d^4 + 2*a^4*c*d^2*e^2 + a^5*e^4)*g^4)))/((a*c^2*d^2 + a^2*c*e^2)*f^2 + (a^2*c*d^2 + a^3*e^2)*g^2)) + 2*(e^2*f*g + d*e*g^2)*x + (2*(c^2*d^3 + a*c*d*e^2)*f^3 + 2*(a*c*d^3 + a^2*d*e^2)*f*g^2 + ((c^2*d^2*e + a*c*e^3)*f^3 + (c^2*d^3 + a*c*d*e^2)*f^2*g + (a*c*d^2*e + a^2*e^3)*f*g^2 + (a*c*d^3 + a^2*d*e^2)*g^3)*x)*sqrt(-(c*e^2*f^2 + 2*c*d*e*f*g + c*d^2*g^2)/((a*c^4*d^4 + 2*a^2*c^3*d^2*e^2 + a^3*c^2*e^4)*f^4 + 2*(a^2*c^3*d^4 + 2*a^3*c^2*d^2*e^2 + a^4*c*e^4)*f^2*g^2 + (a^3*c^2*d^4 + 2*a^4*c*d^2*e^2 + a^5*e^4)*g^4)))/x) - 1/4*sqrt(-(c*d*f - a*e*g - ((a*c^2*d^2 + a^2*c*e^2)*f^2 + (a^2*c*d^2 + a^3*e^2)*g^2)*sqrt(-(c*e^2*f^2 + 2*c*d*e*f*g + c*d^2*g^2)/((a*c^4*d^4 + 2*a^2*c^3*d^2*e^2 + a^3*c^2*e^4)*f^4 + 2*(a^2*c^3*d^4 + 2*a^3*c^2*d^2*e^2 + a^4*c*e^4)*f^2*g^2 + (a^3*c^2*d^4 + 2*a^4*c*d^2*e^2 + a^5*e^4)*g^4)))/((a*c^2*d^2 + a^2*c*e^2)*f^2 + (a^2*c*d^2 + a^3*e^2)*g^2))*log((e^2*f^2 + 2*d*e*f*g + d^2*g^2 + 2*(c*d*e*f^2 - a*d*e*g^2 + (c*d^2 - a*e^2)*f*g + ((a*c^2*d^2*e + a^2*c*e^3)*f^3 + (a*c^2*d^3 + a^2*c*d*e^2)*f^2*g + (a^2*c*d^2*e + a^3*e^3)*f*g^2 + (a^2*c*d^3 + a^3*d*e^2)*g^3)*sqrt(-(c*e^2*f^2 + 2*c*d*e*f*g + c*d^2*g^2)/((a*c^4*d^4 + 2*a^2*c^3*d^2*e^2 + a^3*c^2*e^4)*f^4 + 2*(a^2*c^3*d^4 + 2*a^3*c^2*d^2*e^2 + a^4*c*e^4)*f^2*g^2 + (a^3*c^2*d^4 + 2*a^4*c*d^2*e^2 + a^5*e^4)*g^4)))*sqrt(e*x + d)*sqrt(g*x + f)*sqrt(-(c*d*f - a*e*g - ((a*c^2*d^2 + a^2*c*e^2)*f^2 + (a^2*c*d^2 + a^3*e^2)*g^2)*sqrt(-(c*e^2*f^2 + 2*c*d*e*f*g + c*d^2*g^2)/((a*c^4*d^4 + 2*a^2*c^3*d^2*e^2 + a^3*c^2*e^4)*f^4 + 2*(a^2*c^3*d^4 + 2*a^3*c^2*d^2*e^2 + a^4*c*e^4)*f^2*g^2 + (a^3*c^2*d^4 + 2*a^4*c*d^2*e^2 + a^5*e^4)*g^4)))/((a*c^2*d^2 + a^2*c*e^2)*f^2 + (a^2*c*d^2 + a^3*e^2)*g^2)) + 2*(e^2*f*g + d*e*g^2)*x - (2*(c^2*d^3 + a*c*d*e^2)*f^3 + 2*(a*c*d^3 + a^2*d*e^2)*f*g^2 + ((c^2*d^2*e + a*c*e^3)*f^3 + (c^2*d^3 + a*c*d*e^2)*f^2*g + (a*c*d^2*e + a^2*e^3)*f*g^2 + (a*c*d^3 + a^2*d*e^2)*g^3)*x)*sqrt(-(c*e^2*f^2 + 2*c*d*e*f*g + c*d^2*g^2)/((a*c^4*d^4 + 2*a^2*c^3*d^2*e^2 + a^3*c^2*e^4)*f^4 + 2*(a^2*c^3*d^4 + 2*a^3*c^2*d^2*e^2 + a^4*c*e^4)*f^2*g^2 + (a^3*c^2*d^4 + 2*a^4*c*d^2*e^2 + a^5*e^4)*g^4)))/x) + 1/4*sqrt(-(c*d*f - a*e*g - ((a*c^2*d^2 + a^2*c*e^2)*f^2 + (a^2*c*d^2 + a^3*e^2)*g^2)*sqrt(-(c*e^2*f^2 + 2*c*d*e*f*g + c*d^2*g^2)/((a*c^4*d^4 + 2*a^2*c^3*d^2*e^2 + a^3*c^2*e^4)*f^4 + 2*(a^2*c^3*d^4 + 2*a^3*c^2*d^2*e^2 + a^4*c*e^4)*f^2*g^2 + (a^3*c^2*d^4 + 2*a^4*c*d^2*e^2 + a^5*e^4)*g^4)))/((a*c^2*d^2 + a^2*c*e^2)*f^2 + (a^2*c*d^2 + a^3*e^2)*g^2))*log((e^2*f^2 + 2*d*e*f*g + d^2*g^2 - 2*(c*d*e*f^2 - a*d*e*g^2 + (c*d^2 - a*e^2)*f*g + ((a*c^2*d^2*e + a^2*c*e^3)*f^3 + (a*c^2*d^3 + a^2*c*d*e^2)*f^2*g + (a^2*c*d^2*e + a^3*e^3)*f*g^2 + (a^2*c*d^3 + a^3*d*e^2)*g^3)*sqrt(-(c*e^2*f^2 + 2*c*d*e*f*g + c*d^2*g^2)/((a*c^4*d^4 + 2*a^2*c^3*d^2*e^2 + a^3*c^2*e^4)*f^4 + 2*(a^2*c^3*d^4 + 2*a^3*c^2*d^2*e^2 + a^4*c*e^4)*f^2*g^2 + (a^3*c^2*d^4 + 2*a^4*c*d^2*e^2 + a^5*e^4)*g^4)))*sqrt(e*x + d)*sqrt(g*x + f)*sqrt(-(c*d*f - a*e*g - ((a*c^2*d^2 + a^2*c*e^2)*f^2 + (a^2*c*d^2 + a^3*e^2)*g^2)*sqrt(-(c*e^2*f^2 + 2*c*d*e*f*g + c*d^2*g^2)/((a*c^4*d^4 + 2*a^2*c^3*d^2*e^2 + a^3*c^2*e^4)*f^4 + 2*(a^2*c^3*d^4 + 2*a^3*c^2*d^2*e^2 + a^4*c*e^4)*f^2*g^2 + (a^3*c^2*d^4 + 2*a^4*c*d^2*e^2 + a^5*e^4)*g^4)))/((a*c^2*d^2 + a^2*c*e^2)*f^2 + (a^2*c*d^2 + a^3*e^2)*g^2)) + 2*(e^2*f*g + d*e*g^2)*x - (2*(c^2*d^3 + a*c*d*e^2)*f^3 + 2*(a*c*d^3 + a^2*d*e^2)*f*g^2 + ((c^2*d^2*e + a*c*e^3)*f^3 + (c^2*d^3 + a*c*d*e^2)*f^2*g + (a*c*d^2*e + a^2*e^3)*f*g^2 + (a*c*d^3 + a^2*d*e^2)*g^3)*x)*sqrt(-(c*e^2*f^2 + 2*c*d*e*f*g + c*d^2*g^2)/((a*c^4*d^4 + 2*a^2*c^3*d^2*e^2 + a^3*c^2*e^4)*f^4 + 2*(a^2*c^3*d^4 + 2*a^3*c^2*d^2*e^2 + a^4*c*e^4)*f^2*g^2 + (a^3*c^2*d^4 + 2*a^4*c*d^2*e^2 + a^5*e^4)*g^4)))/x)","B",0
613,1,11846,0,80.356381," ","integrate(1/(e*x+d)^(3/2)/(c*x^2+a)/(g*x+f)^(1/2),x, algorithm=""fricas"")","-\frac{8 \, \sqrt{e x + d} \sqrt{g x + f} e^{2} + {\left({\left(c d^{3} e + a d e^{3}\right)} f - {\left(c d^{4} + a d^{2} e^{2}\right)} g + {\left({\left(c d^{2} e^{2} + a e^{4}\right)} f - {\left(c d^{3} e + a d e^{3}\right)} g\right)} x\right)} \sqrt{-\frac{{\left(c^{3} d^{3} - 3 \, a c^{2} d e^{2}\right)} f - {\left(3 \, a c^{2} d^{2} e - a^{2} c e^{3}\right)} g + {\left({\left(a c^{4} d^{6} + 3 \, a^{2} c^{3} d^{4} e^{2} + 3 \, a^{3} c^{2} d^{2} e^{4} + a^{4} c e^{6}\right)} f^{2} + {\left(a^{2} c^{3} d^{6} + 3 \, a^{3} c^{2} d^{4} e^{2} + 3 \, a^{4} c d^{2} e^{4} + a^{5} e^{6}\right)} g^{2}\right)} \sqrt{-\frac{{\left(9 \, c^{5} d^{4} e^{2} - 6 \, a c^{4} d^{2} e^{4} + a^{2} c^{3} e^{6}\right)} f^{2} + 2 \, {\left(3 \, c^{5} d^{5} e - 10 \, a c^{4} d^{3} e^{3} + 3 \, a^{2} c^{3} d e^{5}\right)} f g + {\left(c^{5} d^{6} - 6 \, a c^{4} d^{4} e^{2} + 9 \, a^{2} c^{3} d^{2} e^{4}\right)} g^{2}}{{\left(a c^{8} d^{12} + 6 \, a^{2} c^{7} d^{10} e^{2} + 15 \, a^{3} c^{6} d^{8} e^{4} + 20 \, a^{4} c^{5} d^{6} e^{6} + 15 \, a^{5} c^{4} d^{4} e^{8} + 6 \, a^{6} c^{3} d^{2} e^{10} + a^{7} c^{2} e^{12}\right)} f^{4} + 2 \, {\left(a^{2} c^{7} d^{12} + 6 \, a^{3} c^{6} d^{10} e^{2} + 15 \, a^{4} c^{5} d^{8} e^{4} + 20 \, a^{5} c^{4} d^{6} e^{6} + 15 \, a^{6} c^{3} d^{4} e^{8} + 6 \, a^{7} c^{2} d^{2} e^{10} + a^{8} c e^{12}\right)} f^{2} g^{2} + {\left(a^{3} c^{6} d^{12} + 6 \, a^{4} c^{5} d^{10} e^{2} + 15 \, a^{5} c^{4} d^{8} e^{4} + 20 \, a^{6} c^{3} d^{6} e^{6} + 15 \, a^{7} c^{2} d^{4} e^{8} + 6 \, a^{8} c d^{2} e^{10} + a^{9} e^{12}\right)} g^{4}}}}{{\left(a c^{4} d^{6} + 3 \, a^{2} c^{3} d^{4} e^{2} + 3 \, a^{3} c^{2} d^{2} e^{4} + a^{4} c e^{6}\right)} f^{2} + {\left(a^{2} c^{3} d^{6} + 3 \, a^{3} c^{2} d^{4} e^{2} + 3 \, a^{4} c d^{2} e^{4} + a^{5} e^{6}\right)} g^{2}}} \log\left(-\frac{{\left(3 \, c^{3} d^{2} e^{2} - a c^{2} e^{4}\right)} f^{2} + 4 \, {\left(c^{3} d^{3} e - a c^{2} d e^{3}\right)} f g + {\left(c^{3} d^{4} - 3 \, a c^{2} d^{2} e^{2}\right)} g^{2} + 2 \, {\left({\left(3 \, c^{4} d^{4} e - 4 \, a c^{3} d^{2} e^{3} + a^{2} c^{2} e^{5}\right)} f^{2} + {\left(c^{4} d^{5} - 10 \, a c^{3} d^{3} e^{2} + 5 \, a^{2} c^{2} d e^{4}\right)} f g - 2 \, {\left(a c^{3} d^{4} e - 3 \, a^{2} c^{2} d^{2} e^{3}\right)} g^{2} - {\left(2 \, {\left(a c^{5} d^{7} e + 3 \, a^{2} c^{4} d^{5} e^{3} + 3 \, a^{3} c^{3} d^{3} e^{5} + a^{4} c^{2} d e^{7}\right)} f^{3} + {\left(a c^{5} d^{8} + 2 \, a^{2} c^{4} d^{6} e^{2} - 2 \, a^{4} c^{2} d^{2} e^{6} - a^{5} c e^{8}\right)} f^{2} g + 2 \, {\left(a^{2} c^{4} d^{7} e + 3 \, a^{3} c^{3} d^{5} e^{3} + 3 \, a^{4} c^{2} d^{3} e^{5} + a^{5} c d e^{7}\right)} f g^{2} + {\left(a^{2} c^{4} d^{8} + 2 \, a^{3} c^{3} d^{6} e^{2} - 2 \, a^{5} c d^{2} e^{6} - a^{6} e^{8}\right)} g^{3}\right)} \sqrt{-\frac{{\left(9 \, c^{5} d^{4} e^{2} - 6 \, a c^{4} d^{2} e^{4} + a^{2} c^{3} e^{6}\right)} f^{2} + 2 \, {\left(3 \, c^{5} d^{5} e - 10 \, a c^{4} d^{3} e^{3} + 3 \, a^{2} c^{3} d e^{5}\right)} f g + {\left(c^{5} d^{6} - 6 \, a c^{4} d^{4} e^{2} + 9 \, a^{2} c^{3} d^{2} e^{4}\right)} g^{2}}{{\left(a c^{8} d^{12} + 6 \, a^{2} c^{7} d^{10} e^{2} + 15 \, a^{3} c^{6} d^{8} e^{4} + 20 \, a^{4} c^{5} d^{6} e^{6} + 15 \, a^{5} c^{4} d^{4} e^{8} + 6 \, a^{6} c^{3} d^{2} e^{10} + a^{7} c^{2} e^{12}\right)} f^{4} + 2 \, {\left(a^{2} c^{7} d^{12} + 6 \, a^{3} c^{6} d^{10} e^{2} + 15 \, a^{4} c^{5} d^{8} e^{4} + 20 \, a^{5} c^{4} d^{6} e^{6} + 15 \, a^{6} c^{3} d^{4} e^{8} + 6 \, a^{7} c^{2} d^{2} e^{10} + a^{8} c e^{12}\right)} f^{2} g^{2} + {\left(a^{3} c^{6} d^{12} + 6 \, a^{4} c^{5} d^{10} e^{2} + 15 \, a^{5} c^{4} d^{8} e^{4} + 20 \, a^{6} c^{3} d^{6} e^{6} + 15 \, a^{7} c^{2} d^{4} e^{8} + 6 \, a^{8} c d^{2} e^{10} + a^{9} e^{12}\right)} g^{4}}}\right)} \sqrt{e x + d} \sqrt{g x + f} \sqrt{-\frac{{\left(c^{3} d^{3} - 3 \, a c^{2} d e^{2}\right)} f - {\left(3 \, a c^{2} d^{2} e - a^{2} c e^{3}\right)} g + {\left({\left(a c^{4} d^{6} + 3 \, a^{2} c^{3} d^{4} e^{2} + 3 \, a^{3} c^{2} d^{2} e^{4} + a^{4} c e^{6}\right)} f^{2} + {\left(a^{2} c^{3} d^{6} + 3 \, a^{3} c^{2} d^{4} e^{2} + 3 \, a^{4} c d^{2} e^{4} + a^{5} e^{6}\right)} g^{2}\right)} \sqrt{-\frac{{\left(9 \, c^{5} d^{4} e^{2} - 6 \, a c^{4} d^{2} e^{4} + a^{2} c^{3} e^{6}\right)} f^{2} + 2 \, {\left(3 \, c^{5} d^{5} e - 10 \, a c^{4} d^{3} e^{3} + 3 \, a^{2} c^{3} d e^{5}\right)} f g + {\left(c^{5} d^{6} - 6 \, a c^{4} d^{4} e^{2} + 9 \, a^{2} c^{3} d^{2} e^{4}\right)} g^{2}}{{\left(a c^{8} d^{12} + 6 \, a^{2} c^{7} d^{10} e^{2} + 15 \, a^{3} c^{6} d^{8} e^{4} + 20 \, a^{4} c^{5} d^{6} e^{6} + 15 \, a^{5} c^{4} d^{4} e^{8} + 6 \, a^{6} c^{3} d^{2} e^{10} + a^{7} c^{2} e^{12}\right)} f^{4} + 2 \, {\left(a^{2} c^{7} d^{12} + 6 \, a^{3} c^{6} d^{10} e^{2} + 15 \, a^{4} c^{5} d^{8} e^{4} + 20 \, a^{5} c^{4} d^{6} e^{6} + 15 \, a^{6} c^{3} d^{4} e^{8} + 6 \, a^{7} c^{2} d^{2} e^{10} + a^{8} c e^{12}\right)} f^{2} g^{2} + {\left(a^{3} c^{6} d^{12} + 6 \, a^{4} c^{5} d^{10} e^{2} + 15 \, a^{5} c^{4} d^{8} e^{4} + 20 \, a^{6} c^{3} d^{6} e^{6} + 15 \, a^{7} c^{2} d^{4} e^{8} + 6 \, a^{8} c d^{2} e^{10} + a^{9} e^{12}\right)} g^{4}}}}{{\left(a c^{4} d^{6} + 3 \, a^{2} c^{3} d^{4} e^{2} + 3 \, a^{3} c^{2} d^{2} e^{4} + a^{4} c e^{6}\right)} f^{2} + {\left(a^{2} c^{3} d^{6} + 3 \, a^{3} c^{2} d^{4} e^{2} + 3 \, a^{4} c d^{2} e^{4} + a^{5} e^{6}\right)} g^{2}}} + 2 \, {\left({\left(3 \, c^{3} d^{2} e^{2} - a c^{2} e^{4}\right)} f g + {\left(c^{3} d^{3} e - 3 \, a c^{2} d e^{3}\right)} g^{2}\right)} x + {\left(2 \, {\left(c^{5} d^{7} + 3 \, a c^{4} d^{5} e^{2} + 3 \, a^{2} c^{3} d^{3} e^{4} + a^{3} c^{2} d e^{6}\right)} f^{3} + 2 \, {\left(a c^{4} d^{7} + 3 \, a^{2} c^{3} d^{5} e^{2} + 3 \, a^{3} c^{2} d^{3} e^{4} + a^{4} c d e^{6}\right)} f g^{2} + {\left({\left(c^{5} d^{6} e + 3 \, a c^{4} d^{4} e^{3} + 3 \, a^{2} c^{3} d^{2} e^{5} + a^{3} c^{2} e^{7}\right)} f^{3} + {\left(c^{5} d^{7} + 3 \, a c^{4} d^{5} e^{2} + 3 \, a^{2} c^{3} d^{3} e^{4} + a^{3} c^{2} d e^{6}\right)} f^{2} g + {\left(a c^{4} d^{6} e + 3 \, a^{2} c^{3} d^{4} e^{3} + 3 \, a^{3} c^{2} d^{2} e^{5} + a^{4} c e^{7}\right)} f g^{2} + {\left(a c^{4} d^{7} + 3 \, a^{2} c^{3} d^{5} e^{2} + 3 \, a^{3} c^{2} d^{3} e^{4} + a^{4} c d e^{6}\right)} g^{3}\right)} x\right)} \sqrt{-\frac{{\left(9 \, c^{5} d^{4} e^{2} - 6 \, a c^{4} d^{2} e^{4} + a^{2} c^{3} e^{6}\right)} f^{2} + 2 \, {\left(3 \, c^{5} d^{5} e - 10 \, a c^{4} d^{3} e^{3} + 3 \, a^{2} c^{3} d e^{5}\right)} f g + {\left(c^{5} d^{6} - 6 \, a c^{4} d^{4} e^{2} + 9 \, a^{2} c^{3} d^{2} e^{4}\right)} g^{2}}{{\left(a c^{8} d^{12} + 6 \, a^{2} c^{7} d^{10} e^{2} + 15 \, a^{3} c^{6} d^{8} e^{4} + 20 \, a^{4} c^{5} d^{6} e^{6} + 15 \, a^{5} c^{4} d^{4} e^{8} + 6 \, a^{6} c^{3} d^{2} e^{10} + a^{7} c^{2} e^{12}\right)} f^{4} + 2 \, {\left(a^{2} c^{7} d^{12} + 6 \, a^{3} c^{6} d^{10} e^{2} + 15 \, a^{4} c^{5} d^{8} e^{4} + 20 \, a^{5} c^{4} d^{6} e^{6} + 15 \, a^{6} c^{3} d^{4} e^{8} + 6 \, a^{7} c^{2} d^{2} e^{10} + a^{8} c e^{12}\right)} f^{2} g^{2} + {\left(a^{3} c^{6} d^{12} + 6 \, a^{4} c^{5} d^{10} e^{2} + 15 \, a^{5} c^{4} d^{8} e^{4} + 20 \, a^{6} c^{3} d^{6} e^{6} + 15 \, a^{7} c^{2} d^{4} e^{8} + 6 \, a^{8} c d^{2} e^{10} + a^{9} e^{12}\right)} g^{4}}}}{x}\right) - {\left({\left(c d^{3} e + a d e^{3}\right)} f - {\left(c d^{4} + a d^{2} e^{2}\right)} g + {\left({\left(c d^{2} e^{2} + a e^{4}\right)} f - {\left(c d^{3} e + a d e^{3}\right)} g\right)} x\right)} \sqrt{-\frac{{\left(c^{3} d^{3} - 3 \, a c^{2} d e^{2}\right)} f - {\left(3 \, a c^{2} d^{2} e - a^{2} c e^{3}\right)} g + {\left({\left(a c^{4} d^{6} + 3 \, a^{2} c^{3} d^{4} e^{2} + 3 \, a^{3} c^{2} d^{2} e^{4} + a^{4} c e^{6}\right)} f^{2} + {\left(a^{2} c^{3} d^{6} + 3 \, a^{3} c^{2} d^{4} e^{2} + 3 \, a^{4} c d^{2} e^{4} + a^{5} e^{6}\right)} g^{2}\right)} \sqrt{-\frac{{\left(9 \, c^{5} d^{4} e^{2} - 6 \, a c^{4} d^{2} e^{4} + a^{2} c^{3} e^{6}\right)} f^{2} + 2 \, {\left(3 \, c^{5} d^{5} e - 10 \, a c^{4} d^{3} e^{3} + 3 \, a^{2} c^{3} d e^{5}\right)} f g + {\left(c^{5} d^{6} - 6 \, a c^{4} d^{4} e^{2} + 9 \, a^{2} c^{3} d^{2} e^{4}\right)} g^{2}}{{\left(a c^{8} d^{12} + 6 \, a^{2} c^{7} d^{10} e^{2} + 15 \, a^{3} c^{6} d^{8} e^{4} + 20 \, a^{4} c^{5} d^{6} e^{6} + 15 \, a^{5} c^{4} d^{4} e^{8} + 6 \, a^{6} c^{3} d^{2} e^{10} + a^{7} c^{2} e^{12}\right)} f^{4} + 2 \, {\left(a^{2} c^{7} d^{12} + 6 \, a^{3} c^{6} d^{10} e^{2} + 15 \, a^{4} c^{5} d^{8} e^{4} + 20 \, a^{5} c^{4} d^{6} e^{6} + 15 \, a^{6} c^{3} d^{4} e^{8} + 6 \, a^{7} c^{2} d^{2} e^{10} + a^{8} c e^{12}\right)} f^{2} g^{2} + {\left(a^{3} c^{6} d^{12} + 6 \, a^{4} c^{5} d^{10} e^{2} + 15 \, a^{5} c^{4} d^{8} e^{4} + 20 \, a^{6} c^{3} d^{6} e^{6} + 15 \, a^{7} c^{2} d^{4} e^{8} + 6 \, a^{8} c d^{2} e^{10} + a^{9} e^{12}\right)} g^{4}}}}{{\left(a c^{4} d^{6} + 3 \, a^{2} c^{3} d^{4} e^{2} + 3 \, a^{3} c^{2} d^{2} e^{4} + a^{4} c e^{6}\right)} f^{2} + {\left(a^{2} c^{3} d^{6} + 3 \, a^{3} c^{2} d^{4} e^{2} + 3 \, a^{4} c d^{2} e^{4} + a^{5} e^{6}\right)} g^{2}}} \log\left(-\frac{{\left(3 \, c^{3} d^{2} e^{2} - a c^{2} e^{4}\right)} f^{2} + 4 \, {\left(c^{3} d^{3} e - a c^{2} d e^{3}\right)} f g + {\left(c^{3} d^{4} - 3 \, a c^{2} d^{2} e^{2}\right)} g^{2} - 2 \, {\left({\left(3 \, c^{4} d^{4} e - 4 \, a c^{3} d^{2} e^{3} + a^{2} c^{2} e^{5}\right)} f^{2} + {\left(c^{4} d^{5} - 10 \, a c^{3} d^{3} e^{2} + 5 \, a^{2} c^{2} d e^{4}\right)} f g - 2 \, {\left(a c^{3} d^{4} e - 3 \, a^{2} c^{2} d^{2} e^{3}\right)} g^{2} - {\left(2 \, {\left(a c^{5} d^{7} e + 3 \, a^{2} c^{4} d^{5} e^{3} + 3 \, a^{3} c^{3} d^{3} e^{5} + a^{4} c^{2} d e^{7}\right)} f^{3} + {\left(a c^{5} d^{8} + 2 \, a^{2} c^{4} d^{6} e^{2} - 2 \, a^{4} c^{2} d^{2} e^{6} - a^{5} c e^{8}\right)} f^{2} g + 2 \, {\left(a^{2} c^{4} d^{7} e + 3 \, a^{3} c^{3} d^{5} e^{3} + 3 \, a^{4} c^{2} d^{3} e^{5} + a^{5} c d e^{7}\right)} f g^{2} + {\left(a^{2} c^{4} d^{8} + 2 \, a^{3} c^{3} d^{6} e^{2} - 2 \, a^{5} c d^{2} e^{6} - a^{6} e^{8}\right)} g^{3}\right)} \sqrt{-\frac{{\left(9 \, c^{5} d^{4} e^{2} - 6 \, a c^{4} d^{2} e^{4} + a^{2} c^{3} e^{6}\right)} f^{2} + 2 \, {\left(3 \, c^{5} d^{5} e - 10 \, a c^{4} d^{3} e^{3} + 3 \, a^{2} c^{3} d e^{5}\right)} f g + {\left(c^{5} d^{6} - 6 \, a c^{4} d^{4} e^{2} + 9 \, a^{2} c^{3} d^{2} e^{4}\right)} g^{2}}{{\left(a c^{8} d^{12} + 6 \, a^{2} c^{7} d^{10} e^{2} + 15 \, a^{3} c^{6} d^{8} e^{4} + 20 \, a^{4} c^{5} d^{6} e^{6} + 15 \, a^{5} c^{4} d^{4} e^{8} + 6 \, a^{6} c^{3} d^{2} e^{10} + a^{7} c^{2} e^{12}\right)} f^{4} + 2 \, {\left(a^{2} c^{7} d^{12} + 6 \, a^{3} c^{6} d^{10} e^{2} + 15 \, a^{4} c^{5} d^{8} e^{4} + 20 \, a^{5} c^{4} d^{6} e^{6} + 15 \, a^{6} c^{3} d^{4} e^{8} + 6 \, a^{7} c^{2} d^{2} e^{10} + a^{8} c e^{12}\right)} f^{2} g^{2} + {\left(a^{3} c^{6} d^{12} + 6 \, a^{4} c^{5} d^{10} e^{2} + 15 \, a^{5} c^{4} d^{8} e^{4} + 20 \, a^{6} c^{3} d^{6} e^{6} + 15 \, a^{7} c^{2} d^{4} e^{8} + 6 \, a^{8} c d^{2} e^{10} + a^{9} e^{12}\right)} g^{4}}}\right)} \sqrt{e x + d} \sqrt{g x + f} \sqrt{-\frac{{\left(c^{3} d^{3} - 3 \, a c^{2} d e^{2}\right)} f - {\left(3 \, a c^{2} d^{2} e - a^{2} c e^{3}\right)} g + {\left({\left(a c^{4} d^{6} + 3 \, a^{2} c^{3} d^{4} e^{2} + 3 \, a^{3} c^{2} d^{2} e^{4} + a^{4} c e^{6}\right)} f^{2} + {\left(a^{2} c^{3} d^{6} + 3 \, a^{3} c^{2} d^{4} e^{2} + 3 \, a^{4} c d^{2} e^{4} + a^{5} e^{6}\right)} g^{2}\right)} \sqrt{-\frac{{\left(9 \, c^{5} d^{4} e^{2} - 6 \, a c^{4} d^{2} e^{4} + a^{2} c^{3} e^{6}\right)} f^{2} + 2 \, {\left(3 \, c^{5} d^{5} e - 10 \, a c^{4} d^{3} e^{3} + 3 \, a^{2} c^{3} d e^{5}\right)} f g + {\left(c^{5} d^{6} - 6 \, a c^{4} d^{4} e^{2} + 9 \, a^{2} c^{3} d^{2} e^{4}\right)} g^{2}}{{\left(a c^{8} d^{12} + 6 \, a^{2} c^{7} d^{10} e^{2} + 15 \, a^{3} c^{6} d^{8} e^{4} + 20 \, a^{4} c^{5} d^{6} e^{6} + 15 \, a^{5} c^{4} d^{4} e^{8} + 6 \, a^{6} c^{3} d^{2} e^{10} + a^{7} c^{2} e^{12}\right)} f^{4} + 2 \, {\left(a^{2} c^{7} d^{12} + 6 \, a^{3} c^{6} d^{10} e^{2} + 15 \, a^{4} c^{5} d^{8} e^{4} + 20 \, a^{5} c^{4} d^{6} e^{6} + 15 \, a^{6} c^{3} d^{4} e^{8} + 6 \, a^{7} c^{2} d^{2} e^{10} + a^{8} c e^{12}\right)} f^{2} g^{2} + {\left(a^{3} c^{6} d^{12} + 6 \, a^{4} c^{5} d^{10} e^{2} + 15 \, a^{5} c^{4} d^{8} e^{4} + 20 \, a^{6} c^{3} d^{6} e^{6} + 15 \, a^{7} c^{2} d^{4} e^{8} + 6 \, a^{8} c d^{2} e^{10} + a^{9} e^{12}\right)} g^{4}}}}{{\left(a c^{4} d^{6} + 3 \, a^{2} c^{3} d^{4} e^{2} + 3 \, a^{3} c^{2} d^{2} e^{4} + a^{4} c e^{6}\right)} f^{2} + {\left(a^{2} c^{3} d^{6} + 3 \, a^{3} c^{2} d^{4} e^{2} + 3 \, a^{4} c d^{2} e^{4} + a^{5} e^{6}\right)} g^{2}}} + 2 \, {\left({\left(3 \, c^{3} d^{2} e^{2} - a c^{2} e^{4}\right)} f g + {\left(c^{3} d^{3} e - 3 \, a c^{2} d e^{3}\right)} g^{2}\right)} x + {\left(2 \, {\left(c^{5} d^{7} + 3 \, a c^{4} d^{5} e^{2} + 3 \, a^{2} c^{3} d^{3} e^{4} + a^{3} c^{2} d e^{6}\right)} f^{3} + 2 \, {\left(a c^{4} d^{7} + 3 \, a^{2} c^{3} d^{5} e^{2} + 3 \, a^{3} c^{2} d^{3} e^{4} + a^{4} c d e^{6}\right)} f g^{2} + {\left({\left(c^{5} d^{6} e + 3 \, a c^{4} d^{4} e^{3} + 3 \, a^{2} c^{3} d^{2} e^{5} + a^{3} c^{2} e^{7}\right)} f^{3} + {\left(c^{5} d^{7} + 3 \, a c^{4} d^{5} e^{2} + 3 \, a^{2} c^{3} d^{3} e^{4} + a^{3} c^{2} d e^{6}\right)} f^{2} g + {\left(a c^{4} d^{6} e + 3 \, a^{2} c^{3} d^{4} e^{3} + 3 \, a^{3} c^{2} d^{2} e^{5} + a^{4} c e^{7}\right)} f g^{2} + {\left(a c^{4} d^{7} + 3 \, a^{2} c^{3} d^{5} e^{2} + 3 \, a^{3} c^{2} d^{3} e^{4} + a^{4} c d e^{6}\right)} g^{3}\right)} x\right)} \sqrt{-\frac{{\left(9 \, c^{5} d^{4} e^{2} - 6 \, a c^{4} d^{2} e^{4} + a^{2} c^{3} e^{6}\right)} f^{2} + 2 \, {\left(3 \, c^{5} d^{5} e - 10 \, a c^{4} d^{3} e^{3} + 3 \, a^{2} c^{3} d e^{5}\right)} f g + {\left(c^{5} d^{6} - 6 \, a c^{4} d^{4} e^{2} + 9 \, a^{2} c^{3} d^{2} e^{4}\right)} g^{2}}{{\left(a c^{8} d^{12} + 6 \, a^{2} c^{7} d^{10} e^{2} + 15 \, a^{3} c^{6} d^{8} e^{4} + 20 \, a^{4} c^{5} d^{6} e^{6} + 15 \, a^{5} c^{4} d^{4} e^{8} + 6 \, a^{6} c^{3} d^{2} e^{10} + a^{7} c^{2} e^{12}\right)} f^{4} + 2 \, {\left(a^{2} c^{7} d^{12} + 6 \, a^{3} c^{6} d^{10} e^{2} + 15 \, a^{4} c^{5} d^{8} e^{4} + 20 \, a^{5} c^{4} d^{6} e^{6} + 15 \, a^{6} c^{3} d^{4} e^{8} + 6 \, a^{7} c^{2} d^{2} e^{10} + a^{8} c e^{12}\right)} f^{2} g^{2} + {\left(a^{3} c^{6} d^{12} + 6 \, a^{4} c^{5} d^{10} e^{2} + 15 \, a^{5} c^{4} d^{8} e^{4} + 20 \, a^{6} c^{3} d^{6} e^{6} + 15 \, a^{7} c^{2} d^{4} e^{8} + 6 \, a^{8} c d^{2} e^{10} + a^{9} e^{12}\right)} g^{4}}}}{x}\right) + {\left({\left(c d^{3} e + a d e^{3}\right)} f - {\left(c d^{4} + a d^{2} e^{2}\right)} g + {\left({\left(c d^{2} e^{2} + a e^{4}\right)} f - {\left(c d^{3} e + a d e^{3}\right)} g\right)} x\right)} \sqrt{-\frac{{\left(c^{3} d^{3} - 3 \, a c^{2} d e^{2}\right)} f - {\left(3 \, a c^{2} d^{2} e - a^{2} c e^{3}\right)} g - {\left({\left(a c^{4} d^{6} + 3 \, a^{2} c^{3} d^{4} e^{2} + 3 \, a^{3} c^{2} d^{2} e^{4} + a^{4} c e^{6}\right)} f^{2} + {\left(a^{2} c^{3} d^{6} + 3 \, a^{3} c^{2} d^{4} e^{2} + 3 \, a^{4} c d^{2} e^{4} + a^{5} e^{6}\right)} g^{2}\right)} \sqrt{-\frac{{\left(9 \, c^{5} d^{4} e^{2} - 6 \, a c^{4} d^{2} e^{4} + a^{2} c^{3} e^{6}\right)} f^{2} + 2 \, {\left(3 \, c^{5} d^{5} e - 10 \, a c^{4} d^{3} e^{3} + 3 \, a^{2} c^{3} d e^{5}\right)} f g + {\left(c^{5} d^{6} - 6 \, a c^{4} d^{4} e^{2} + 9 \, a^{2} c^{3} d^{2} e^{4}\right)} g^{2}}{{\left(a c^{8} d^{12} + 6 \, a^{2} c^{7} d^{10} e^{2} + 15 \, a^{3} c^{6} d^{8} e^{4} + 20 \, a^{4} c^{5} d^{6} e^{6} + 15 \, a^{5} c^{4} d^{4} e^{8} + 6 \, a^{6} c^{3} d^{2} e^{10} + a^{7} c^{2} e^{12}\right)} f^{4} + 2 \, {\left(a^{2} c^{7} d^{12} + 6 \, a^{3} c^{6} d^{10} e^{2} + 15 \, a^{4} c^{5} d^{8} e^{4} + 20 \, a^{5} c^{4} d^{6} e^{6} + 15 \, a^{6} c^{3} d^{4} e^{8} + 6 \, a^{7} c^{2} d^{2} e^{10} + a^{8} c e^{12}\right)} f^{2} g^{2} + {\left(a^{3} c^{6} d^{12} + 6 \, a^{4} c^{5} d^{10} e^{2} + 15 \, a^{5} c^{4} d^{8} e^{4} + 20 \, a^{6} c^{3} d^{6} e^{6} + 15 \, a^{7} c^{2} d^{4} e^{8} + 6 \, a^{8} c d^{2} e^{10} + a^{9} e^{12}\right)} g^{4}}}}{{\left(a c^{4} d^{6} + 3 \, a^{2} c^{3} d^{4} e^{2} + 3 \, a^{3} c^{2} d^{2} e^{4} + a^{4} c e^{6}\right)} f^{2} + {\left(a^{2} c^{3} d^{6} + 3 \, a^{3} c^{2} d^{4} e^{2} + 3 \, a^{4} c d^{2} e^{4} + a^{5} e^{6}\right)} g^{2}}} \log\left(-\frac{{\left(3 \, c^{3} d^{2} e^{2} - a c^{2} e^{4}\right)} f^{2} + 4 \, {\left(c^{3} d^{3} e - a c^{2} d e^{3}\right)} f g + {\left(c^{3} d^{4} - 3 \, a c^{2} d^{2} e^{2}\right)} g^{2} + 2 \, {\left({\left(3 \, c^{4} d^{4} e - 4 \, a c^{3} d^{2} e^{3} + a^{2} c^{2} e^{5}\right)} f^{2} + {\left(c^{4} d^{5} - 10 \, a c^{3} d^{3} e^{2} + 5 \, a^{2} c^{2} d e^{4}\right)} f g - 2 \, {\left(a c^{3} d^{4} e - 3 \, a^{2} c^{2} d^{2} e^{3}\right)} g^{2} + {\left(2 \, {\left(a c^{5} d^{7} e + 3 \, a^{2} c^{4} d^{5} e^{3} + 3 \, a^{3} c^{3} d^{3} e^{5} + a^{4} c^{2} d e^{7}\right)} f^{3} + {\left(a c^{5} d^{8} + 2 \, a^{2} c^{4} d^{6} e^{2} - 2 \, a^{4} c^{2} d^{2} e^{6} - a^{5} c e^{8}\right)} f^{2} g + 2 \, {\left(a^{2} c^{4} d^{7} e + 3 \, a^{3} c^{3} d^{5} e^{3} + 3 \, a^{4} c^{2} d^{3} e^{5} + a^{5} c d e^{7}\right)} f g^{2} + {\left(a^{2} c^{4} d^{8} + 2 \, a^{3} c^{3} d^{6} e^{2} - 2 \, a^{5} c d^{2} e^{6} - a^{6} e^{8}\right)} g^{3}\right)} \sqrt{-\frac{{\left(9 \, c^{5} d^{4} e^{2} - 6 \, a c^{4} d^{2} e^{4} + a^{2} c^{3} e^{6}\right)} f^{2} + 2 \, {\left(3 \, c^{5} d^{5} e - 10 \, a c^{4} d^{3} e^{3} + 3 \, a^{2} c^{3} d e^{5}\right)} f g + {\left(c^{5} d^{6} - 6 \, a c^{4} d^{4} e^{2} + 9 \, a^{2} c^{3} d^{2} e^{4}\right)} g^{2}}{{\left(a c^{8} d^{12} + 6 \, a^{2} c^{7} d^{10} e^{2} + 15 \, a^{3} c^{6} d^{8} e^{4} + 20 \, a^{4} c^{5} d^{6} e^{6} + 15 \, a^{5} c^{4} d^{4} e^{8} + 6 \, a^{6} c^{3} d^{2} e^{10} + a^{7} c^{2} e^{12}\right)} f^{4} + 2 \, {\left(a^{2} c^{7} d^{12} + 6 \, a^{3} c^{6} d^{10} e^{2} + 15 \, a^{4} c^{5} d^{8} e^{4} + 20 \, a^{5} c^{4} d^{6} e^{6} + 15 \, a^{6} c^{3} d^{4} e^{8} + 6 \, a^{7} c^{2} d^{2} e^{10} + a^{8} c e^{12}\right)} f^{2} g^{2} + {\left(a^{3} c^{6} d^{12} + 6 \, a^{4} c^{5} d^{10} e^{2} + 15 \, a^{5} c^{4} d^{8} e^{4} + 20 \, a^{6} c^{3} d^{6} e^{6} + 15 \, a^{7} c^{2} d^{4} e^{8} + 6 \, a^{8} c d^{2} e^{10} + a^{9} e^{12}\right)} g^{4}}}\right)} \sqrt{e x + d} \sqrt{g x + f} \sqrt{-\frac{{\left(c^{3} d^{3} - 3 \, a c^{2} d e^{2}\right)} f - {\left(3 \, a c^{2} d^{2} e - a^{2} c e^{3}\right)} g - {\left({\left(a c^{4} d^{6} + 3 \, a^{2} c^{3} d^{4} e^{2} + 3 \, a^{3} c^{2} d^{2} e^{4} + a^{4} c e^{6}\right)} f^{2} + {\left(a^{2} c^{3} d^{6} + 3 \, a^{3} c^{2} d^{4} e^{2} + 3 \, a^{4} c d^{2} e^{4} + a^{5} e^{6}\right)} g^{2}\right)} \sqrt{-\frac{{\left(9 \, c^{5} d^{4} e^{2} - 6 \, a c^{4} d^{2} e^{4} + a^{2} c^{3} e^{6}\right)} f^{2} + 2 \, {\left(3 \, c^{5} d^{5} e - 10 \, a c^{4} d^{3} e^{3} + 3 \, a^{2} c^{3} d e^{5}\right)} f g + {\left(c^{5} d^{6} - 6 \, a c^{4} d^{4} e^{2} + 9 \, a^{2} c^{3} d^{2} e^{4}\right)} g^{2}}{{\left(a c^{8} d^{12} + 6 \, a^{2} c^{7} d^{10} e^{2} + 15 \, a^{3} c^{6} d^{8} e^{4} + 20 \, a^{4} c^{5} d^{6} e^{6} + 15 \, a^{5} c^{4} d^{4} e^{8} + 6 \, a^{6} c^{3} d^{2} e^{10} + a^{7} c^{2} e^{12}\right)} f^{4} + 2 \, {\left(a^{2} c^{7} d^{12} + 6 \, a^{3} c^{6} d^{10} e^{2} + 15 \, a^{4} c^{5} d^{8} e^{4} + 20 \, a^{5} c^{4} d^{6} e^{6} + 15 \, a^{6} c^{3} d^{4} e^{8} + 6 \, a^{7} c^{2} d^{2} e^{10} + a^{8} c e^{12}\right)} f^{2} g^{2} + {\left(a^{3} c^{6} d^{12} + 6 \, a^{4} c^{5} d^{10} e^{2} + 15 \, a^{5} c^{4} d^{8} e^{4} + 20 \, a^{6} c^{3} d^{6} e^{6} + 15 \, a^{7} c^{2} d^{4} e^{8} + 6 \, a^{8} c d^{2} e^{10} + a^{9} e^{12}\right)} g^{4}}}}{{\left(a c^{4} d^{6} + 3 \, a^{2} c^{3} d^{4} e^{2} + 3 \, a^{3} c^{2} d^{2} e^{4} + a^{4} c e^{6}\right)} f^{2} + {\left(a^{2} c^{3} d^{6} + 3 \, a^{3} c^{2} d^{4} e^{2} + 3 \, a^{4} c d^{2} e^{4} + a^{5} e^{6}\right)} g^{2}}} + 2 \, {\left({\left(3 \, c^{3} d^{2} e^{2} - a c^{2} e^{4}\right)} f g + {\left(c^{3} d^{3} e - 3 \, a c^{2} d e^{3}\right)} g^{2}\right)} x - {\left(2 \, {\left(c^{5} d^{7} + 3 \, a c^{4} d^{5} e^{2} + 3 \, a^{2} c^{3} d^{3} e^{4} + a^{3} c^{2} d e^{6}\right)} f^{3} + 2 \, {\left(a c^{4} d^{7} + 3 \, a^{2} c^{3} d^{5} e^{2} + 3 \, a^{3} c^{2} d^{3} e^{4} + a^{4} c d e^{6}\right)} f g^{2} + {\left({\left(c^{5} d^{6} e + 3 \, a c^{4} d^{4} e^{3} + 3 \, a^{2} c^{3} d^{2} e^{5} + a^{3} c^{2} e^{7}\right)} f^{3} + {\left(c^{5} d^{7} + 3 \, a c^{4} d^{5} e^{2} + 3 \, a^{2} c^{3} d^{3} e^{4} + a^{3} c^{2} d e^{6}\right)} f^{2} g + {\left(a c^{4} d^{6} e + 3 \, a^{2} c^{3} d^{4} e^{3} + 3 \, a^{3} c^{2} d^{2} e^{5} + a^{4} c e^{7}\right)} f g^{2} + {\left(a c^{4} d^{7} + 3 \, a^{2} c^{3} d^{5} e^{2} + 3 \, a^{3} c^{2} d^{3} e^{4} + a^{4} c d e^{6}\right)} g^{3}\right)} x\right)} \sqrt{-\frac{{\left(9 \, c^{5} d^{4} e^{2} - 6 \, a c^{4} d^{2} e^{4} + a^{2} c^{3} e^{6}\right)} f^{2} + 2 \, {\left(3 \, c^{5} d^{5} e - 10 \, a c^{4} d^{3} e^{3} + 3 \, a^{2} c^{3} d e^{5}\right)} f g + {\left(c^{5} d^{6} - 6 \, a c^{4} d^{4} e^{2} + 9 \, a^{2} c^{3} d^{2} e^{4}\right)} g^{2}}{{\left(a c^{8} d^{12} + 6 \, a^{2} c^{7} d^{10} e^{2} + 15 \, a^{3} c^{6} d^{8} e^{4} + 20 \, a^{4} c^{5} d^{6} e^{6} + 15 \, a^{5} c^{4} d^{4} e^{8} + 6 \, a^{6} c^{3} d^{2} e^{10} + a^{7} c^{2} e^{12}\right)} f^{4} + 2 \, {\left(a^{2} c^{7} d^{12} + 6 \, a^{3} c^{6} d^{10} e^{2} + 15 \, a^{4} c^{5} d^{8} e^{4} + 20 \, a^{5} c^{4} d^{6} e^{6} + 15 \, a^{6} c^{3} d^{4} e^{8} + 6 \, a^{7} c^{2} d^{2} e^{10} + a^{8} c e^{12}\right)} f^{2} g^{2} + {\left(a^{3} c^{6} d^{12} + 6 \, a^{4} c^{5} d^{10} e^{2} + 15 \, a^{5} c^{4} d^{8} e^{4} + 20 \, a^{6} c^{3} d^{6} e^{6} + 15 \, a^{7} c^{2} d^{4} e^{8} + 6 \, a^{8} c d^{2} e^{10} + a^{9} e^{12}\right)} g^{4}}}}{x}\right) - {\left({\left(c d^{3} e + a d e^{3}\right)} f - {\left(c d^{4} + a d^{2} e^{2}\right)} g + {\left({\left(c d^{2} e^{2} + a e^{4}\right)} f - {\left(c d^{3} e + a d e^{3}\right)} g\right)} x\right)} \sqrt{-\frac{{\left(c^{3} d^{3} - 3 \, a c^{2} d e^{2}\right)} f - {\left(3 \, a c^{2} d^{2} e - a^{2} c e^{3}\right)} g - {\left({\left(a c^{4} d^{6} + 3 \, a^{2} c^{3} d^{4} e^{2} + 3 \, a^{3} c^{2} d^{2} e^{4} + a^{4} c e^{6}\right)} f^{2} + {\left(a^{2} c^{3} d^{6} + 3 \, a^{3} c^{2} d^{4} e^{2} + 3 \, a^{4} c d^{2} e^{4} + a^{5} e^{6}\right)} g^{2}\right)} \sqrt{-\frac{{\left(9 \, c^{5} d^{4} e^{2} - 6 \, a c^{4} d^{2} e^{4} + a^{2} c^{3} e^{6}\right)} f^{2} + 2 \, {\left(3 \, c^{5} d^{5} e - 10 \, a c^{4} d^{3} e^{3} + 3 \, a^{2} c^{3} d e^{5}\right)} f g + {\left(c^{5} d^{6} - 6 \, a c^{4} d^{4} e^{2} + 9 \, a^{2} c^{3} d^{2} e^{4}\right)} g^{2}}{{\left(a c^{8} d^{12} + 6 \, a^{2} c^{7} d^{10} e^{2} + 15 \, a^{3} c^{6} d^{8} e^{4} + 20 \, a^{4} c^{5} d^{6} e^{6} + 15 \, a^{5} c^{4} d^{4} e^{8} + 6 \, a^{6} c^{3} d^{2} e^{10} + a^{7} c^{2} e^{12}\right)} f^{4} + 2 \, {\left(a^{2} c^{7} d^{12} + 6 \, a^{3} c^{6} d^{10} e^{2} + 15 \, a^{4} c^{5} d^{8} e^{4} + 20 \, a^{5} c^{4} d^{6} e^{6} + 15 \, a^{6} c^{3} d^{4} e^{8} + 6 \, a^{7} c^{2} d^{2} e^{10} + a^{8} c e^{12}\right)} f^{2} g^{2} + {\left(a^{3} c^{6} d^{12} + 6 \, a^{4} c^{5} d^{10} e^{2} + 15 \, a^{5} c^{4} d^{8} e^{4} + 20 \, a^{6} c^{3} d^{6} e^{6} + 15 \, a^{7} c^{2} d^{4} e^{8} + 6 \, a^{8} c d^{2} e^{10} + a^{9} e^{12}\right)} g^{4}}}}{{\left(a c^{4} d^{6} + 3 \, a^{2} c^{3} d^{4} e^{2} + 3 \, a^{3} c^{2} d^{2} e^{4} + a^{4} c e^{6}\right)} f^{2} + {\left(a^{2} c^{3} d^{6} + 3 \, a^{3} c^{2} d^{4} e^{2} + 3 \, a^{4} c d^{2} e^{4} + a^{5} e^{6}\right)} g^{2}}} \log\left(-\frac{{\left(3 \, c^{3} d^{2} e^{2} - a c^{2} e^{4}\right)} f^{2} + 4 \, {\left(c^{3} d^{3} e - a c^{2} d e^{3}\right)} f g + {\left(c^{3} d^{4} - 3 \, a c^{2} d^{2} e^{2}\right)} g^{2} - 2 \, {\left({\left(3 \, c^{4} d^{4} e - 4 \, a c^{3} d^{2} e^{3} + a^{2} c^{2} e^{5}\right)} f^{2} + {\left(c^{4} d^{5} - 10 \, a c^{3} d^{3} e^{2} + 5 \, a^{2} c^{2} d e^{4}\right)} f g - 2 \, {\left(a c^{3} d^{4} e - 3 \, a^{2} c^{2} d^{2} e^{3}\right)} g^{2} + {\left(2 \, {\left(a c^{5} d^{7} e + 3 \, a^{2} c^{4} d^{5} e^{3} + 3 \, a^{3} c^{3} d^{3} e^{5} + a^{4} c^{2} d e^{7}\right)} f^{3} + {\left(a c^{5} d^{8} + 2 \, a^{2} c^{4} d^{6} e^{2} - 2 \, a^{4} c^{2} d^{2} e^{6} - a^{5} c e^{8}\right)} f^{2} g + 2 \, {\left(a^{2} c^{4} d^{7} e + 3 \, a^{3} c^{3} d^{5} e^{3} + 3 \, a^{4} c^{2} d^{3} e^{5} + a^{5} c d e^{7}\right)} f g^{2} + {\left(a^{2} c^{4} d^{8} + 2 \, a^{3} c^{3} d^{6} e^{2} - 2 \, a^{5} c d^{2} e^{6} - a^{6} e^{8}\right)} g^{3}\right)} \sqrt{-\frac{{\left(9 \, c^{5} d^{4} e^{2} - 6 \, a c^{4} d^{2} e^{4} + a^{2} c^{3} e^{6}\right)} f^{2} + 2 \, {\left(3 \, c^{5} d^{5} e - 10 \, a c^{4} d^{3} e^{3} + 3 \, a^{2} c^{3} d e^{5}\right)} f g + {\left(c^{5} d^{6} - 6 \, a c^{4} d^{4} e^{2} + 9 \, a^{2} c^{3} d^{2} e^{4}\right)} g^{2}}{{\left(a c^{8} d^{12} + 6 \, a^{2} c^{7} d^{10} e^{2} + 15 \, a^{3} c^{6} d^{8} e^{4} + 20 \, a^{4} c^{5} d^{6} e^{6} + 15 \, a^{5} c^{4} d^{4} e^{8} + 6 \, a^{6} c^{3} d^{2} e^{10} + a^{7} c^{2} e^{12}\right)} f^{4} + 2 \, {\left(a^{2} c^{7} d^{12} + 6 \, a^{3} c^{6} d^{10} e^{2} + 15 \, a^{4} c^{5} d^{8} e^{4} + 20 \, a^{5} c^{4} d^{6} e^{6} + 15 \, a^{6} c^{3} d^{4} e^{8} + 6 \, a^{7} c^{2} d^{2} e^{10} + a^{8} c e^{12}\right)} f^{2} g^{2} + {\left(a^{3} c^{6} d^{12} + 6 \, a^{4} c^{5} d^{10} e^{2} + 15 \, a^{5} c^{4} d^{8} e^{4} + 20 \, a^{6} c^{3} d^{6} e^{6} + 15 \, a^{7} c^{2} d^{4} e^{8} + 6 \, a^{8} c d^{2} e^{10} + a^{9} e^{12}\right)} g^{4}}}\right)} \sqrt{e x + d} \sqrt{g x + f} \sqrt{-\frac{{\left(c^{3} d^{3} - 3 \, a c^{2} d e^{2}\right)} f - {\left(3 \, a c^{2} d^{2} e - a^{2} c e^{3}\right)} g - {\left({\left(a c^{4} d^{6} + 3 \, a^{2} c^{3} d^{4} e^{2} + 3 \, a^{3} c^{2} d^{2} e^{4} + a^{4} c e^{6}\right)} f^{2} + {\left(a^{2} c^{3} d^{6} + 3 \, a^{3} c^{2} d^{4} e^{2} + 3 \, a^{4} c d^{2} e^{4} + a^{5} e^{6}\right)} g^{2}\right)} \sqrt{-\frac{{\left(9 \, c^{5} d^{4} e^{2} - 6 \, a c^{4} d^{2} e^{4} + a^{2} c^{3} e^{6}\right)} f^{2} + 2 \, {\left(3 \, c^{5} d^{5} e - 10 \, a c^{4} d^{3} e^{3} + 3 \, a^{2} c^{3} d e^{5}\right)} f g + {\left(c^{5} d^{6} - 6 \, a c^{4} d^{4} e^{2} + 9 \, a^{2} c^{3} d^{2} e^{4}\right)} g^{2}}{{\left(a c^{8} d^{12} + 6 \, a^{2} c^{7} d^{10} e^{2} + 15 \, a^{3} c^{6} d^{8} e^{4} + 20 \, a^{4} c^{5} d^{6} e^{6} + 15 \, a^{5} c^{4} d^{4} e^{8} + 6 \, a^{6} c^{3} d^{2} e^{10} + a^{7} c^{2} e^{12}\right)} f^{4} + 2 \, {\left(a^{2} c^{7} d^{12} + 6 \, a^{3} c^{6} d^{10} e^{2} + 15 \, a^{4} c^{5} d^{8} e^{4} + 20 \, a^{5} c^{4} d^{6} e^{6} + 15 \, a^{6} c^{3} d^{4} e^{8} + 6 \, a^{7} c^{2} d^{2} e^{10} + a^{8} c e^{12}\right)} f^{2} g^{2} + {\left(a^{3} c^{6} d^{12} + 6 \, a^{4} c^{5} d^{10} e^{2} + 15 \, a^{5} c^{4} d^{8} e^{4} + 20 \, a^{6} c^{3} d^{6} e^{6} + 15 \, a^{7} c^{2} d^{4} e^{8} + 6 \, a^{8} c d^{2} e^{10} + a^{9} e^{12}\right)} g^{4}}}}{{\left(a c^{4} d^{6} + 3 \, a^{2} c^{3} d^{4} e^{2} + 3 \, a^{3} c^{2} d^{2} e^{4} + a^{4} c e^{6}\right)} f^{2} + {\left(a^{2} c^{3} d^{6} + 3 \, a^{3} c^{2} d^{4} e^{2} + 3 \, a^{4} c d^{2} e^{4} + a^{5} e^{6}\right)} g^{2}}} + 2 \, {\left({\left(3 \, c^{3} d^{2} e^{2} - a c^{2} e^{4}\right)} f g + {\left(c^{3} d^{3} e - 3 \, a c^{2} d e^{3}\right)} g^{2}\right)} x - {\left(2 \, {\left(c^{5} d^{7} + 3 \, a c^{4} d^{5} e^{2} + 3 \, a^{2} c^{3} d^{3} e^{4} + a^{3} c^{2} d e^{6}\right)} f^{3} + 2 \, {\left(a c^{4} d^{7} + 3 \, a^{2} c^{3} d^{5} e^{2} + 3 \, a^{3} c^{2} d^{3} e^{4} + a^{4} c d e^{6}\right)} f g^{2} + {\left({\left(c^{5} d^{6} e + 3 \, a c^{4} d^{4} e^{3} + 3 \, a^{2} c^{3} d^{2} e^{5} + a^{3} c^{2} e^{7}\right)} f^{3} + {\left(c^{5} d^{7} + 3 \, a c^{4} d^{5} e^{2} + 3 \, a^{2} c^{3} d^{3} e^{4} + a^{3} c^{2} d e^{6}\right)} f^{2} g + {\left(a c^{4} d^{6} e + 3 \, a^{2} c^{3} d^{4} e^{3} + 3 \, a^{3} c^{2} d^{2} e^{5} + a^{4} c e^{7}\right)} f g^{2} + {\left(a c^{4} d^{7} + 3 \, a^{2} c^{3} d^{5} e^{2} + 3 \, a^{3} c^{2} d^{3} e^{4} + a^{4} c d e^{6}\right)} g^{3}\right)} x\right)} \sqrt{-\frac{{\left(9 \, c^{5} d^{4} e^{2} - 6 \, a c^{4} d^{2} e^{4} + a^{2} c^{3} e^{6}\right)} f^{2} + 2 \, {\left(3 \, c^{5} d^{5} e - 10 \, a c^{4} d^{3} e^{3} + 3 \, a^{2} c^{3} d e^{5}\right)} f g + {\left(c^{5} d^{6} - 6 \, a c^{4} d^{4} e^{2} + 9 \, a^{2} c^{3} d^{2} e^{4}\right)} g^{2}}{{\left(a c^{8} d^{12} + 6 \, a^{2} c^{7} d^{10} e^{2} + 15 \, a^{3} c^{6} d^{8} e^{4} + 20 \, a^{4} c^{5} d^{6} e^{6} + 15 \, a^{5} c^{4} d^{4} e^{8} + 6 \, a^{6} c^{3} d^{2} e^{10} + a^{7} c^{2} e^{12}\right)} f^{4} + 2 \, {\left(a^{2} c^{7} d^{12} + 6 \, a^{3} c^{6} d^{10} e^{2} + 15 \, a^{4} c^{5} d^{8} e^{4} + 20 \, a^{5} c^{4} d^{6} e^{6} + 15 \, a^{6} c^{3} d^{4} e^{8} + 6 \, a^{7} c^{2} d^{2} e^{10} + a^{8} c e^{12}\right)} f^{2} g^{2} + {\left(a^{3} c^{6} d^{12} + 6 \, a^{4} c^{5} d^{10} e^{2} + 15 \, a^{5} c^{4} d^{8} e^{4} + 20 \, a^{6} c^{3} d^{6} e^{6} + 15 \, a^{7} c^{2} d^{4} e^{8} + 6 \, a^{8} c d^{2} e^{10} + a^{9} e^{12}\right)} g^{4}}}}{x}\right)}{4 \, {\left({\left(c d^{3} e + a d e^{3}\right)} f - {\left(c d^{4} + a d^{2} e^{2}\right)} g + {\left({\left(c d^{2} e^{2} + a e^{4}\right)} f - {\left(c d^{3} e + a d e^{3}\right)} g\right)} x\right)}}"," ",0,"-1/4*(8*sqrt(e*x + d)*sqrt(g*x + f)*e^2 + ((c*d^3*e + a*d*e^3)*f - (c*d^4 + a*d^2*e^2)*g + ((c*d^2*e^2 + a*e^4)*f - (c*d^3*e + a*d*e^3)*g)*x)*sqrt(-((c^3*d^3 - 3*a*c^2*d*e^2)*f - (3*a*c^2*d^2*e - a^2*c*e^3)*g + ((a*c^4*d^6 + 3*a^2*c^3*d^4*e^2 + 3*a^3*c^2*d^2*e^4 + a^4*c*e^6)*f^2 + (a^2*c^3*d^6 + 3*a^3*c^2*d^4*e^2 + 3*a^4*c*d^2*e^4 + a^5*e^6)*g^2)*sqrt(-((9*c^5*d^4*e^2 - 6*a*c^4*d^2*e^4 + a^2*c^3*e^6)*f^2 + 2*(3*c^5*d^5*e - 10*a*c^4*d^3*e^3 + 3*a^2*c^3*d*e^5)*f*g + (c^5*d^6 - 6*a*c^4*d^4*e^2 + 9*a^2*c^3*d^2*e^4)*g^2)/((a*c^8*d^12 + 6*a^2*c^7*d^10*e^2 + 15*a^3*c^6*d^8*e^4 + 20*a^4*c^5*d^6*e^6 + 15*a^5*c^4*d^4*e^8 + 6*a^6*c^3*d^2*e^10 + a^7*c^2*e^12)*f^4 + 2*(a^2*c^7*d^12 + 6*a^3*c^6*d^10*e^2 + 15*a^4*c^5*d^8*e^4 + 20*a^5*c^4*d^6*e^6 + 15*a^6*c^3*d^4*e^8 + 6*a^7*c^2*d^2*e^10 + a^8*c*e^12)*f^2*g^2 + (a^3*c^6*d^12 + 6*a^4*c^5*d^10*e^2 + 15*a^5*c^4*d^8*e^4 + 20*a^6*c^3*d^6*e^6 + 15*a^7*c^2*d^4*e^8 + 6*a^8*c*d^2*e^10 + a^9*e^12)*g^4)))/((a*c^4*d^6 + 3*a^2*c^3*d^4*e^2 + 3*a^3*c^2*d^2*e^4 + a^4*c*e^6)*f^2 + (a^2*c^3*d^6 + 3*a^3*c^2*d^4*e^2 + 3*a^4*c*d^2*e^4 + a^5*e^6)*g^2))*log(-((3*c^3*d^2*e^2 - a*c^2*e^4)*f^2 + 4*(c^3*d^3*e - a*c^2*d*e^3)*f*g + (c^3*d^4 - 3*a*c^2*d^2*e^2)*g^2 + 2*((3*c^4*d^4*e - 4*a*c^3*d^2*e^3 + a^2*c^2*e^5)*f^2 + (c^4*d^5 - 10*a*c^3*d^3*e^2 + 5*a^2*c^2*d*e^4)*f*g - 2*(a*c^3*d^4*e - 3*a^2*c^2*d^2*e^3)*g^2 - (2*(a*c^5*d^7*e + 3*a^2*c^4*d^5*e^3 + 3*a^3*c^3*d^3*e^5 + a^4*c^2*d*e^7)*f^3 + (a*c^5*d^8 + 2*a^2*c^4*d^6*e^2 - 2*a^4*c^2*d^2*e^6 - a^5*c*e^8)*f^2*g + 2*(a^2*c^4*d^7*e + 3*a^3*c^3*d^5*e^3 + 3*a^4*c^2*d^3*e^5 + a^5*c*d*e^7)*f*g^2 + (a^2*c^4*d^8 + 2*a^3*c^3*d^6*e^2 - 2*a^5*c*d^2*e^6 - a^6*e^8)*g^3)*sqrt(-((9*c^5*d^4*e^2 - 6*a*c^4*d^2*e^4 + a^2*c^3*e^6)*f^2 + 2*(3*c^5*d^5*e - 10*a*c^4*d^3*e^3 + 3*a^2*c^3*d*e^5)*f*g + (c^5*d^6 - 6*a*c^4*d^4*e^2 + 9*a^2*c^3*d^2*e^4)*g^2)/((a*c^8*d^12 + 6*a^2*c^7*d^10*e^2 + 15*a^3*c^6*d^8*e^4 + 20*a^4*c^5*d^6*e^6 + 15*a^5*c^4*d^4*e^8 + 6*a^6*c^3*d^2*e^10 + a^7*c^2*e^12)*f^4 + 2*(a^2*c^7*d^12 + 6*a^3*c^6*d^10*e^2 + 15*a^4*c^5*d^8*e^4 + 20*a^5*c^4*d^6*e^6 + 15*a^6*c^3*d^4*e^8 + 6*a^7*c^2*d^2*e^10 + a^8*c*e^12)*f^2*g^2 + (a^3*c^6*d^12 + 6*a^4*c^5*d^10*e^2 + 15*a^5*c^4*d^8*e^4 + 20*a^6*c^3*d^6*e^6 + 15*a^7*c^2*d^4*e^8 + 6*a^8*c*d^2*e^10 + a^9*e^12)*g^4)))*sqrt(e*x + d)*sqrt(g*x + f)*sqrt(-((c^3*d^3 - 3*a*c^2*d*e^2)*f - (3*a*c^2*d^2*e - a^2*c*e^3)*g + ((a*c^4*d^6 + 3*a^2*c^3*d^4*e^2 + 3*a^3*c^2*d^2*e^4 + a^4*c*e^6)*f^2 + (a^2*c^3*d^6 + 3*a^3*c^2*d^4*e^2 + 3*a^4*c*d^2*e^4 + a^5*e^6)*g^2)*sqrt(-((9*c^5*d^4*e^2 - 6*a*c^4*d^2*e^4 + a^2*c^3*e^6)*f^2 + 2*(3*c^5*d^5*e - 10*a*c^4*d^3*e^3 + 3*a^2*c^3*d*e^5)*f*g + (c^5*d^6 - 6*a*c^4*d^4*e^2 + 9*a^2*c^3*d^2*e^4)*g^2)/((a*c^8*d^12 + 6*a^2*c^7*d^10*e^2 + 15*a^3*c^6*d^8*e^4 + 20*a^4*c^5*d^6*e^6 + 15*a^5*c^4*d^4*e^8 + 6*a^6*c^3*d^2*e^10 + a^7*c^2*e^12)*f^4 + 2*(a^2*c^7*d^12 + 6*a^3*c^6*d^10*e^2 + 15*a^4*c^5*d^8*e^4 + 20*a^5*c^4*d^6*e^6 + 15*a^6*c^3*d^4*e^8 + 6*a^7*c^2*d^2*e^10 + a^8*c*e^12)*f^2*g^2 + (a^3*c^6*d^12 + 6*a^4*c^5*d^10*e^2 + 15*a^5*c^4*d^8*e^4 + 20*a^6*c^3*d^6*e^6 + 15*a^7*c^2*d^4*e^8 + 6*a^8*c*d^2*e^10 + a^9*e^12)*g^4)))/((a*c^4*d^6 + 3*a^2*c^3*d^4*e^2 + 3*a^3*c^2*d^2*e^4 + a^4*c*e^6)*f^2 + (a^2*c^3*d^6 + 3*a^3*c^2*d^4*e^2 + 3*a^4*c*d^2*e^4 + a^5*e^6)*g^2)) + 2*((3*c^3*d^2*e^2 - a*c^2*e^4)*f*g + (c^3*d^3*e - 3*a*c^2*d*e^3)*g^2)*x + (2*(c^5*d^7 + 3*a*c^4*d^5*e^2 + 3*a^2*c^3*d^3*e^4 + a^3*c^2*d*e^6)*f^3 + 2*(a*c^4*d^7 + 3*a^2*c^3*d^5*e^2 + 3*a^3*c^2*d^3*e^4 + a^4*c*d*e^6)*f*g^2 + ((c^5*d^6*e + 3*a*c^4*d^4*e^3 + 3*a^2*c^3*d^2*e^5 + a^3*c^2*e^7)*f^3 + (c^5*d^7 + 3*a*c^4*d^5*e^2 + 3*a^2*c^3*d^3*e^4 + a^3*c^2*d*e^6)*f^2*g + (a*c^4*d^6*e + 3*a^2*c^3*d^4*e^3 + 3*a^3*c^2*d^2*e^5 + a^4*c*e^7)*f*g^2 + (a*c^4*d^7 + 3*a^2*c^3*d^5*e^2 + 3*a^3*c^2*d^3*e^4 + a^4*c*d*e^6)*g^3)*x)*sqrt(-((9*c^5*d^4*e^2 - 6*a*c^4*d^2*e^4 + a^2*c^3*e^6)*f^2 + 2*(3*c^5*d^5*e - 10*a*c^4*d^3*e^3 + 3*a^2*c^3*d*e^5)*f*g + (c^5*d^6 - 6*a*c^4*d^4*e^2 + 9*a^2*c^3*d^2*e^4)*g^2)/((a*c^8*d^12 + 6*a^2*c^7*d^10*e^2 + 15*a^3*c^6*d^8*e^4 + 20*a^4*c^5*d^6*e^6 + 15*a^5*c^4*d^4*e^8 + 6*a^6*c^3*d^2*e^10 + a^7*c^2*e^12)*f^4 + 2*(a^2*c^7*d^12 + 6*a^3*c^6*d^10*e^2 + 15*a^4*c^5*d^8*e^4 + 20*a^5*c^4*d^6*e^6 + 15*a^6*c^3*d^4*e^8 + 6*a^7*c^2*d^2*e^10 + a^8*c*e^12)*f^2*g^2 + (a^3*c^6*d^12 + 6*a^4*c^5*d^10*e^2 + 15*a^5*c^4*d^8*e^4 + 20*a^6*c^3*d^6*e^6 + 15*a^7*c^2*d^4*e^8 + 6*a^8*c*d^2*e^10 + a^9*e^12)*g^4)))/x) - ((c*d^3*e + a*d*e^3)*f - (c*d^4 + a*d^2*e^2)*g + ((c*d^2*e^2 + a*e^4)*f - (c*d^3*e + a*d*e^3)*g)*x)*sqrt(-((c^3*d^3 - 3*a*c^2*d*e^2)*f - (3*a*c^2*d^2*e - a^2*c*e^3)*g + ((a*c^4*d^6 + 3*a^2*c^3*d^4*e^2 + 3*a^3*c^2*d^2*e^4 + a^4*c*e^6)*f^2 + (a^2*c^3*d^6 + 3*a^3*c^2*d^4*e^2 + 3*a^4*c*d^2*e^4 + a^5*e^6)*g^2)*sqrt(-((9*c^5*d^4*e^2 - 6*a*c^4*d^2*e^4 + a^2*c^3*e^6)*f^2 + 2*(3*c^5*d^5*e - 10*a*c^4*d^3*e^3 + 3*a^2*c^3*d*e^5)*f*g + (c^5*d^6 - 6*a*c^4*d^4*e^2 + 9*a^2*c^3*d^2*e^4)*g^2)/((a*c^8*d^12 + 6*a^2*c^7*d^10*e^2 + 15*a^3*c^6*d^8*e^4 + 20*a^4*c^5*d^6*e^6 + 15*a^5*c^4*d^4*e^8 + 6*a^6*c^3*d^2*e^10 + a^7*c^2*e^12)*f^4 + 2*(a^2*c^7*d^12 + 6*a^3*c^6*d^10*e^2 + 15*a^4*c^5*d^8*e^4 + 20*a^5*c^4*d^6*e^6 + 15*a^6*c^3*d^4*e^8 + 6*a^7*c^2*d^2*e^10 + a^8*c*e^12)*f^2*g^2 + (a^3*c^6*d^12 + 6*a^4*c^5*d^10*e^2 + 15*a^5*c^4*d^8*e^4 + 20*a^6*c^3*d^6*e^6 + 15*a^7*c^2*d^4*e^8 + 6*a^8*c*d^2*e^10 + a^9*e^12)*g^4)))/((a*c^4*d^6 + 3*a^2*c^3*d^4*e^2 + 3*a^3*c^2*d^2*e^4 + a^4*c*e^6)*f^2 + (a^2*c^3*d^6 + 3*a^3*c^2*d^4*e^2 + 3*a^4*c*d^2*e^4 + a^5*e^6)*g^2))*log(-((3*c^3*d^2*e^2 - a*c^2*e^4)*f^2 + 4*(c^3*d^3*e - a*c^2*d*e^3)*f*g + (c^3*d^4 - 3*a*c^2*d^2*e^2)*g^2 - 2*((3*c^4*d^4*e - 4*a*c^3*d^2*e^3 + a^2*c^2*e^5)*f^2 + (c^4*d^5 - 10*a*c^3*d^3*e^2 + 5*a^2*c^2*d*e^4)*f*g - 2*(a*c^3*d^4*e - 3*a^2*c^2*d^2*e^3)*g^2 - (2*(a*c^5*d^7*e + 3*a^2*c^4*d^5*e^3 + 3*a^3*c^3*d^3*e^5 + a^4*c^2*d*e^7)*f^3 + (a*c^5*d^8 + 2*a^2*c^4*d^6*e^2 - 2*a^4*c^2*d^2*e^6 - a^5*c*e^8)*f^2*g + 2*(a^2*c^4*d^7*e + 3*a^3*c^3*d^5*e^3 + 3*a^4*c^2*d^3*e^5 + a^5*c*d*e^7)*f*g^2 + (a^2*c^4*d^8 + 2*a^3*c^3*d^6*e^2 - 2*a^5*c*d^2*e^6 - a^6*e^8)*g^3)*sqrt(-((9*c^5*d^4*e^2 - 6*a*c^4*d^2*e^4 + a^2*c^3*e^6)*f^2 + 2*(3*c^5*d^5*e - 10*a*c^4*d^3*e^3 + 3*a^2*c^3*d*e^5)*f*g + (c^5*d^6 - 6*a*c^4*d^4*e^2 + 9*a^2*c^3*d^2*e^4)*g^2)/((a*c^8*d^12 + 6*a^2*c^7*d^10*e^2 + 15*a^3*c^6*d^8*e^4 + 20*a^4*c^5*d^6*e^6 + 15*a^5*c^4*d^4*e^8 + 6*a^6*c^3*d^2*e^10 + a^7*c^2*e^12)*f^4 + 2*(a^2*c^7*d^12 + 6*a^3*c^6*d^10*e^2 + 15*a^4*c^5*d^8*e^4 + 20*a^5*c^4*d^6*e^6 + 15*a^6*c^3*d^4*e^8 + 6*a^7*c^2*d^2*e^10 + a^8*c*e^12)*f^2*g^2 + (a^3*c^6*d^12 + 6*a^4*c^5*d^10*e^2 + 15*a^5*c^4*d^8*e^4 + 20*a^6*c^3*d^6*e^6 + 15*a^7*c^2*d^4*e^8 + 6*a^8*c*d^2*e^10 + a^9*e^12)*g^4)))*sqrt(e*x + d)*sqrt(g*x + f)*sqrt(-((c^3*d^3 - 3*a*c^2*d*e^2)*f - (3*a*c^2*d^2*e - a^2*c*e^3)*g + ((a*c^4*d^6 + 3*a^2*c^3*d^4*e^2 + 3*a^3*c^2*d^2*e^4 + a^4*c*e^6)*f^2 + (a^2*c^3*d^6 + 3*a^3*c^2*d^4*e^2 + 3*a^4*c*d^2*e^4 + a^5*e^6)*g^2)*sqrt(-((9*c^5*d^4*e^2 - 6*a*c^4*d^2*e^4 + a^2*c^3*e^6)*f^2 + 2*(3*c^5*d^5*e - 10*a*c^4*d^3*e^3 + 3*a^2*c^3*d*e^5)*f*g + (c^5*d^6 - 6*a*c^4*d^4*e^2 + 9*a^2*c^3*d^2*e^4)*g^2)/((a*c^8*d^12 + 6*a^2*c^7*d^10*e^2 + 15*a^3*c^6*d^8*e^4 + 20*a^4*c^5*d^6*e^6 + 15*a^5*c^4*d^4*e^8 + 6*a^6*c^3*d^2*e^10 + a^7*c^2*e^12)*f^4 + 2*(a^2*c^7*d^12 + 6*a^3*c^6*d^10*e^2 + 15*a^4*c^5*d^8*e^4 + 20*a^5*c^4*d^6*e^6 + 15*a^6*c^3*d^4*e^8 + 6*a^7*c^2*d^2*e^10 + a^8*c*e^12)*f^2*g^2 + (a^3*c^6*d^12 + 6*a^4*c^5*d^10*e^2 + 15*a^5*c^4*d^8*e^4 + 20*a^6*c^3*d^6*e^6 + 15*a^7*c^2*d^4*e^8 + 6*a^8*c*d^2*e^10 + a^9*e^12)*g^4)))/((a*c^4*d^6 + 3*a^2*c^3*d^4*e^2 + 3*a^3*c^2*d^2*e^4 + a^4*c*e^6)*f^2 + (a^2*c^3*d^6 + 3*a^3*c^2*d^4*e^2 + 3*a^4*c*d^2*e^4 + a^5*e^6)*g^2)) + 2*((3*c^3*d^2*e^2 - a*c^2*e^4)*f*g + (c^3*d^3*e - 3*a*c^2*d*e^3)*g^2)*x + (2*(c^5*d^7 + 3*a*c^4*d^5*e^2 + 3*a^2*c^3*d^3*e^4 + a^3*c^2*d*e^6)*f^3 + 2*(a*c^4*d^7 + 3*a^2*c^3*d^5*e^2 + 3*a^3*c^2*d^3*e^4 + a^4*c*d*e^6)*f*g^2 + ((c^5*d^6*e + 3*a*c^4*d^4*e^3 + 3*a^2*c^3*d^2*e^5 + a^3*c^2*e^7)*f^3 + (c^5*d^7 + 3*a*c^4*d^5*e^2 + 3*a^2*c^3*d^3*e^4 + a^3*c^2*d*e^6)*f^2*g + (a*c^4*d^6*e + 3*a^2*c^3*d^4*e^3 + 3*a^3*c^2*d^2*e^5 + a^4*c*e^7)*f*g^2 + (a*c^4*d^7 + 3*a^2*c^3*d^5*e^2 + 3*a^3*c^2*d^3*e^4 + a^4*c*d*e^6)*g^3)*x)*sqrt(-((9*c^5*d^4*e^2 - 6*a*c^4*d^2*e^4 + a^2*c^3*e^6)*f^2 + 2*(3*c^5*d^5*e - 10*a*c^4*d^3*e^3 + 3*a^2*c^3*d*e^5)*f*g + (c^5*d^6 - 6*a*c^4*d^4*e^2 + 9*a^2*c^3*d^2*e^4)*g^2)/((a*c^8*d^12 + 6*a^2*c^7*d^10*e^2 + 15*a^3*c^6*d^8*e^4 + 20*a^4*c^5*d^6*e^6 + 15*a^5*c^4*d^4*e^8 + 6*a^6*c^3*d^2*e^10 + a^7*c^2*e^12)*f^4 + 2*(a^2*c^7*d^12 + 6*a^3*c^6*d^10*e^2 + 15*a^4*c^5*d^8*e^4 + 20*a^5*c^4*d^6*e^6 + 15*a^6*c^3*d^4*e^8 + 6*a^7*c^2*d^2*e^10 + a^8*c*e^12)*f^2*g^2 + (a^3*c^6*d^12 + 6*a^4*c^5*d^10*e^2 + 15*a^5*c^4*d^8*e^4 + 20*a^6*c^3*d^6*e^6 + 15*a^7*c^2*d^4*e^8 + 6*a^8*c*d^2*e^10 + a^9*e^12)*g^4)))/x) + ((c*d^3*e + a*d*e^3)*f - (c*d^4 + a*d^2*e^2)*g + ((c*d^2*e^2 + a*e^4)*f - (c*d^3*e + a*d*e^3)*g)*x)*sqrt(-((c^3*d^3 - 3*a*c^2*d*e^2)*f - (3*a*c^2*d^2*e - a^2*c*e^3)*g - ((a*c^4*d^6 + 3*a^2*c^3*d^4*e^2 + 3*a^3*c^2*d^2*e^4 + a^4*c*e^6)*f^2 + (a^2*c^3*d^6 + 3*a^3*c^2*d^4*e^2 + 3*a^4*c*d^2*e^4 + a^5*e^6)*g^2)*sqrt(-((9*c^5*d^4*e^2 - 6*a*c^4*d^2*e^4 + a^2*c^3*e^6)*f^2 + 2*(3*c^5*d^5*e - 10*a*c^4*d^3*e^3 + 3*a^2*c^3*d*e^5)*f*g + (c^5*d^6 - 6*a*c^4*d^4*e^2 + 9*a^2*c^3*d^2*e^4)*g^2)/((a*c^8*d^12 + 6*a^2*c^7*d^10*e^2 + 15*a^3*c^6*d^8*e^4 + 20*a^4*c^5*d^6*e^6 + 15*a^5*c^4*d^4*e^8 + 6*a^6*c^3*d^2*e^10 + a^7*c^2*e^12)*f^4 + 2*(a^2*c^7*d^12 + 6*a^3*c^6*d^10*e^2 + 15*a^4*c^5*d^8*e^4 + 20*a^5*c^4*d^6*e^6 + 15*a^6*c^3*d^4*e^8 + 6*a^7*c^2*d^2*e^10 + a^8*c*e^12)*f^2*g^2 + (a^3*c^6*d^12 + 6*a^4*c^5*d^10*e^2 + 15*a^5*c^4*d^8*e^4 + 20*a^6*c^3*d^6*e^6 + 15*a^7*c^2*d^4*e^8 + 6*a^8*c*d^2*e^10 + a^9*e^12)*g^4)))/((a*c^4*d^6 + 3*a^2*c^3*d^4*e^2 + 3*a^3*c^2*d^2*e^4 + a^4*c*e^6)*f^2 + (a^2*c^3*d^6 + 3*a^3*c^2*d^4*e^2 + 3*a^4*c*d^2*e^4 + a^5*e^6)*g^2))*log(-((3*c^3*d^2*e^2 - a*c^2*e^4)*f^2 + 4*(c^3*d^3*e - a*c^2*d*e^3)*f*g + (c^3*d^4 - 3*a*c^2*d^2*e^2)*g^2 + 2*((3*c^4*d^4*e - 4*a*c^3*d^2*e^3 + a^2*c^2*e^5)*f^2 + (c^4*d^5 - 10*a*c^3*d^3*e^2 + 5*a^2*c^2*d*e^4)*f*g - 2*(a*c^3*d^4*e - 3*a^2*c^2*d^2*e^3)*g^2 + (2*(a*c^5*d^7*e + 3*a^2*c^4*d^5*e^3 + 3*a^3*c^3*d^3*e^5 + a^4*c^2*d*e^7)*f^3 + (a*c^5*d^8 + 2*a^2*c^4*d^6*e^2 - 2*a^4*c^2*d^2*e^6 - a^5*c*e^8)*f^2*g + 2*(a^2*c^4*d^7*e + 3*a^3*c^3*d^5*e^3 + 3*a^4*c^2*d^3*e^5 + a^5*c*d*e^7)*f*g^2 + (a^2*c^4*d^8 + 2*a^3*c^3*d^6*e^2 - 2*a^5*c*d^2*e^6 - a^6*e^8)*g^3)*sqrt(-((9*c^5*d^4*e^2 - 6*a*c^4*d^2*e^4 + a^2*c^3*e^6)*f^2 + 2*(3*c^5*d^5*e - 10*a*c^4*d^3*e^3 + 3*a^2*c^3*d*e^5)*f*g + (c^5*d^6 - 6*a*c^4*d^4*e^2 + 9*a^2*c^3*d^2*e^4)*g^2)/((a*c^8*d^12 + 6*a^2*c^7*d^10*e^2 + 15*a^3*c^6*d^8*e^4 + 20*a^4*c^5*d^6*e^6 + 15*a^5*c^4*d^4*e^8 + 6*a^6*c^3*d^2*e^10 + a^7*c^2*e^12)*f^4 + 2*(a^2*c^7*d^12 + 6*a^3*c^6*d^10*e^2 + 15*a^4*c^5*d^8*e^4 + 20*a^5*c^4*d^6*e^6 + 15*a^6*c^3*d^4*e^8 + 6*a^7*c^2*d^2*e^10 + a^8*c*e^12)*f^2*g^2 + (a^3*c^6*d^12 + 6*a^4*c^5*d^10*e^2 + 15*a^5*c^4*d^8*e^4 + 20*a^6*c^3*d^6*e^6 + 15*a^7*c^2*d^4*e^8 + 6*a^8*c*d^2*e^10 + a^9*e^12)*g^4)))*sqrt(e*x + d)*sqrt(g*x + f)*sqrt(-((c^3*d^3 - 3*a*c^2*d*e^2)*f - (3*a*c^2*d^2*e - a^2*c*e^3)*g - ((a*c^4*d^6 + 3*a^2*c^3*d^4*e^2 + 3*a^3*c^2*d^2*e^4 + a^4*c*e^6)*f^2 + (a^2*c^3*d^6 + 3*a^3*c^2*d^4*e^2 + 3*a^4*c*d^2*e^4 + a^5*e^6)*g^2)*sqrt(-((9*c^5*d^4*e^2 - 6*a*c^4*d^2*e^4 + a^2*c^3*e^6)*f^2 + 2*(3*c^5*d^5*e - 10*a*c^4*d^3*e^3 + 3*a^2*c^3*d*e^5)*f*g + (c^5*d^6 - 6*a*c^4*d^4*e^2 + 9*a^2*c^3*d^2*e^4)*g^2)/((a*c^8*d^12 + 6*a^2*c^7*d^10*e^2 + 15*a^3*c^6*d^8*e^4 + 20*a^4*c^5*d^6*e^6 + 15*a^5*c^4*d^4*e^8 + 6*a^6*c^3*d^2*e^10 + a^7*c^2*e^12)*f^4 + 2*(a^2*c^7*d^12 + 6*a^3*c^6*d^10*e^2 + 15*a^4*c^5*d^8*e^4 + 20*a^5*c^4*d^6*e^6 + 15*a^6*c^3*d^4*e^8 + 6*a^7*c^2*d^2*e^10 + a^8*c*e^12)*f^2*g^2 + (a^3*c^6*d^12 + 6*a^4*c^5*d^10*e^2 + 15*a^5*c^4*d^8*e^4 + 20*a^6*c^3*d^6*e^6 + 15*a^7*c^2*d^4*e^8 + 6*a^8*c*d^2*e^10 + a^9*e^12)*g^4)))/((a*c^4*d^6 + 3*a^2*c^3*d^4*e^2 + 3*a^3*c^2*d^2*e^4 + a^4*c*e^6)*f^2 + (a^2*c^3*d^6 + 3*a^3*c^2*d^4*e^2 + 3*a^4*c*d^2*e^4 + a^5*e^6)*g^2)) + 2*((3*c^3*d^2*e^2 - a*c^2*e^4)*f*g + (c^3*d^3*e - 3*a*c^2*d*e^3)*g^2)*x - (2*(c^5*d^7 + 3*a*c^4*d^5*e^2 + 3*a^2*c^3*d^3*e^4 + a^3*c^2*d*e^6)*f^3 + 2*(a*c^4*d^7 + 3*a^2*c^3*d^5*e^2 + 3*a^3*c^2*d^3*e^4 + a^4*c*d*e^6)*f*g^2 + ((c^5*d^6*e + 3*a*c^4*d^4*e^3 + 3*a^2*c^3*d^2*e^5 + a^3*c^2*e^7)*f^3 + (c^5*d^7 + 3*a*c^4*d^5*e^2 + 3*a^2*c^3*d^3*e^4 + a^3*c^2*d*e^6)*f^2*g + (a*c^4*d^6*e + 3*a^2*c^3*d^4*e^3 + 3*a^3*c^2*d^2*e^5 + a^4*c*e^7)*f*g^2 + (a*c^4*d^7 + 3*a^2*c^3*d^5*e^2 + 3*a^3*c^2*d^3*e^4 + a^4*c*d*e^6)*g^3)*x)*sqrt(-((9*c^5*d^4*e^2 - 6*a*c^4*d^2*e^4 + a^2*c^3*e^6)*f^2 + 2*(3*c^5*d^5*e - 10*a*c^4*d^3*e^3 + 3*a^2*c^3*d*e^5)*f*g + (c^5*d^6 - 6*a*c^4*d^4*e^2 + 9*a^2*c^3*d^2*e^4)*g^2)/((a*c^8*d^12 + 6*a^2*c^7*d^10*e^2 + 15*a^3*c^6*d^8*e^4 + 20*a^4*c^5*d^6*e^6 + 15*a^5*c^4*d^4*e^8 + 6*a^6*c^3*d^2*e^10 + a^7*c^2*e^12)*f^4 + 2*(a^2*c^7*d^12 + 6*a^3*c^6*d^10*e^2 + 15*a^4*c^5*d^8*e^4 + 20*a^5*c^4*d^6*e^6 + 15*a^6*c^3*d^4*e^8 + 6*a^7*c^2*d^2*e^10 + a^8*c*e^12)*f^2*g^2 + (a^3*c^6*d^12 + 6*a^4*c^5*d^10*e^2 + 15*a^5*c^4*d^8*e^4 + 20*a^6*c^3*d^6*e^6 + 15*a^7*c^2*d^4*e^8 + 6*a^8*c*d^2*e^10 + a^9*e^12)*g^4)))/x) - ((c*d^3*e + a*d*e^3)*f - (c*d^4 + a*d^2*e^2)*g + ((c*d^2*e^2 + a*e^4)*f - (c*d^3*e + a*d*e^3)*g)*x)*sqrt(-((c^3*d^3 - 3*a*c^2*d*e^2)*f - (3*a*c^2*d^2*e - a^2*c*e^3)*g - ((a*c^4*d^6 + 3*a^2*c^3*d^4*e^2 + 3*a^3*c^2*d^2*e^4 + a^4*c*e^6)*f^2 + (a^2*c^3*d^6 + 3*a^3*c^2*d^4*e^2 + 3*a^4*c*d^2*e^4 + a^5*e^6)*g^2)*sqrt(-((9*c^5*d^4*e^2 - 6*a*c^4*d^2*e^4 + a^2*c^3*e^6)*f^2 + 2*(3*c^5*d^5*e - 10*a*c^4*d^3*e^3 + 3*a^2*c^3*d*e^5)*f*g + (c^5*d^6 - 6*a*c^4*d^4*e^2 + 9*a^2*c^3*d^2*e^4)*g^2)/((a*c^8*d^12 + 6*a^2*c^7*d^10*e^2 + 15*a^3*c^6*d^8*e^4 + 20*a^4*c^5*d^6*e^6 + 15*a^5*c^4*d^4*e^8 + 6*a^6*c^3*d^2*e^10 + a^7*c^2*e^12)*f^4 + 2*(a^2*c^7*d^12 + 6*a^3*c^6*d^10*e^2 + 15*a^4*c^5*d^8*e^4 + 20*a^5*c^4*d^6*e^6 + 15*a^6*c^3*d^4*e^8 + 6*a^7*c^2*d^2*e^10 + a^8*c*e^12)*f^2*g^2 + (a^3*c^6*d^12 + 6*a^4*c^5*d^10*e^2 + 15*a^5*c^4*d^8*e^4 + 20*a^6*c^3*d^6*e^6 + 15*a^7*c^2*d^4*e^8 + 6*a^8*c*d^2*e^10 + a^9*e^12)*g^4)))/((a*c^4*d^6 + 3*a^2*c^3*d^4*e^2 + 3*a^3*c^2*d^2*e^4 + a^4*c*e^6)*f^2 + (a^2*c^3*d^6 + 3*a^3*c^2*d^4*e^2 + 3*a^4*c*d^2*e^4 + a^5*e^6)*g^2))*log(-((3*c^3*d^2*e^2 - a*c^2*e^4)*f^2 + 4*(c^3*d^3*e - a*c^2*d*e^3)*f*g + (c^3*d^4 - 3*a*c^2*d^2*e^2)*g^2 - 2*((3*c^4*d^4*e - 4*a*c^3*d^2*e^3 + a^2*c^2*e^5)*f^2 + (c^4*d^5 - 10*a*c^3*d^3*e^2 + 5*a^2*c^2*d*e^4)*f*g - 2*(a*c^3*d^4*e - 3*a^2*c^2*d^2*e^3)*g^2 + (2*(a*c^5*d^7*e + 3*a^2*c^4*d^5*e^3 + 3*a^3*c^3*d^3*e^5 + a^4*c^2*d*e^7)*f^3 + (a*c^5*d^8 + 2*a^2*c^4*d^6*e^2 - 2*a^4*c^2*d^2*e^6 - a^5*c*e^8)*f^2*g + 2*(a^2*c^4*d^7*e + 3*a^3*c^3*d^5*e^3 + 3*a^4*c^2*d^3*e^5 + a^5*c*d*e^7)*f*g^2 + (a^2*c^4*d^8 + 2*a^3*c^3*d^6*e^2 - 2*a^5*c*d^2*e^6 - a^6*e^8)*g^3)*sqrt(-((9*c^5*d^4*e^2 - 6*a*c^4*d^2*e^4 + a^2*c^3*e^6)*f^2 + 2*(3*c^5*d^5*e - 10*a*c^4*d^3*e^3 + 3*a^2*c^3*d*e^5)*f*g + (c^5*d^6 - 6*a*c^4*d^4*e^2 + 9*a^2*c^3*d^2*e^4)*g^2)/((a*c^8*d^12 + 6*a^2*c^7*d^10*e^2 + 15*a^3*c^6*d^8*e^4 + 20*a^4*c^5*d^6*e^6 + 15*a^5*c^4*d^4*e^8 + 6*a^6*c^3*d^2*e^10 + a^7*c^2*e^12)*f^4 + 2*(a^2*c^7*d^12 + 6*a^3*c^6*d^10*e^2 + 15*a^4*c^5*d^8*e^4 + 20*a^5*c^4*d^6*e^6 + 15*a^6*c^3*d^4*e^8 + 6*a^7*c^2*d^2*e^10 + a^8*c*e^12)*f^2*g^2 + (a^3*c^6*d^12 + 6*a^4*c^5*d^10*e^2 + 15*a^5*c^4*d^8*e^4 + 20*a^6*c^3*d^6*e^6 + 15*a^7*c^2*d^4*e^8 + 6*a^8*c*d^2*e^10 + a^9*e^12)*g^4)))*sqrt(e*x + d)*sqrt(g*x + f)*sqrt(-((c^3*d^3 - 3*a*c^2*d*e^2)*f - (3*a*c^2*d^2*e - a^2*c*e^3)*g - ((a*c^4*d^6 + 3*a^2*c^3*d^4*e^2 + 3*a^3*c^2*d^2*e^4 + a^4*c*e^6)*f^2 + (a^2*c^3*d^6 + 3*a^3*c^2*d^4*e^2 + 3*a^4*c*d^2*e^4 + a^5*e^6)*g^2)*sqrt(-((9*c^5*d^4*e^2 - 6*a*c^4*d^2*e^4 + a^2*c^3*e^6)*f^2 + 2*(3*c^5*d^5*e - 10*a*c^4*d^3*e^3 + 3*a^2*c^3*d*e^5)*f*g + (c^5*d^6 - 6*a*c^4*d^4*e^2 + 9*a^2*c^3*d^2*e^4)*g^2)/((a*c^8*d^12 + 6*a^2*c^7*d^10*e^2 + 15*a^3*c^6*d^8*e^4 + 20*a^4*c^5*d^6*e^6 + 15*a^5*c^4*d^4*e^8 + 6*a^6*c^3*d^2*e^10 + a^7*c^2*e^12)*f^4 + 2*(a^2*c^7*d^12 + 6*a^3*c^6*d^10*e^2 + 15*a^4*c^5*d^8*e^4 + 20*a^5*c^4*d^6*e^6 + 15*a^6*c^3*d^4*e^8 + 6*a^7*c^2*d^2*e^10 + a^8*c*e^12)*f^2*g^2 + (a^3*c^6*d^12 + 6*a^4*c^5*d^10*e^2 + 15*a^5*c^4*d^8*e^4 + 20*a^6*c^3*d^6*e^6 + 15*a^7*c^2*d^4*e^8 + 6*a^8*c*d^2*e^10 + a^9*e^12)*g^4)))/((a*c^4*d^6 + 3*a^2*c^3*d^4*e^2 + 3*a^3*c^2*d^2*e^4 + a^4*c*e^6)*f^2 + (a^2*c^3*d^6 + 3*a^3*c^2*d^4*e^2 + 3*a^4*c*d^2*e^4 + a^5*e^6)*g^2)) + 2*((3*c^3*d^2*e^2 - a*c^2*e^4)*f*g + (c^3*d^3*e - 3*a*c^2*d*e^3)*g^2)*x - (2*(c^5*d^7 + 3*a*c^4*d^5*e^2 + 3*a^2*c^3*d^3*e^4 + a^3*c^2*d*e^6)*f^3 + 2*(a*c^4*d^7 + 3*a^2*c^3*d^5*e^2 + 3*a^3*c^2*d^3*e^4 + a^4*c*d*e^6)*f*g^2 + ((c^5*d^6*e + 3*a*c^4*d^4*e^3 + 3*a^2*c^3*d^2*e^5 + a^3*c^2*e^7)*f^3 + (c^5*d^7 + 3*a*c^4*d^5*e^2 + 3*a^2*c^3*d^3*e^4 + a^3*c^2*d*e^6)*f^2*g + (a*c^4*d^6*e + 3*a^2*c^3*d^4*e^3 + 3*a^3*c^2*d^2*e^5 + a^4*c*e^7)*f*g^2 + (a*c^4*d^7 + 3*a^2*c^3*d^5*e^2 + 3*a^3*c^2*d^3*e^4 + a^4*c*d*e^6)*g^3)*x)*sqrt(-((9*c^5*d^4*e^2 - 6*a*c^4*d^2*e^4 + a^2*c^3*e^6)*f^2 + 2*(3*c^5*d^5*e - 10*a*c^4*d^3*e^3 + 3*a^2*c^3*d*e^5)*f*g + (c^5*d^6 - 6*a*c^4*d^4*e^2 + 9*a^2*c^3*d^2*e^4)*g^2)/((a*c^8*d^12 + 6*a^2*c^7*d^10*e^2 + 15*a^3*c^6*d^8*e^4 + 20*a^4*c^5*d^6*e^6 + 15*a^5*c^4*d^4*e^8 + 6*a^6*c^3*d^2*e^10 + a^7*c^2*e^12)*f^4 + 2*(a^2*c^7*d^12 + 6*a^3*c^6*d^10*e^2 + 15*a^4*c^5*d^8*e^4 + 20*a^5*c^4*d^6*e^6 + 15*a^6*c^3*d^4*e^8 + 6*a^7*c^2*d^2*e^10 + a^8*c*e^12)*f^2*g^2 + (a^3*c^6*d^12 + 6*a^4*c^5*d^10*e^2 + 15*a^5*c^4*d^8*e^4 + 20*a^6*c^3*d^6*e^6 + 15*a^7*c^2*d^4*e^8 + 6*a^8*c*d^2*e^10 + a^9*e^12)*g^4)))/x))/((c*d^3*e + a*d*e^3)*f - (c*d^4 + a*d^2*e^2)*g + ((c*d^2*e^2 + a*e^4)*f - (c*d^3*e + a*d*e^3)*g)*x)","B",0
614,-1,0,0,0.000000," ","integrate((e*x+d)^(3/2)/(g*x+f)^(3/2)/(c*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
615,1,5844,0,66.392324," ","integrate((e*x+d)^(1/2)/(g*x+f)^(3/2)/(c*x^2+a),x, algorithm=""fricas"")","-\frac{{\left(c f^{3} + a f g^{2} + {\left(c f^{2} g + a g^{3}\right)} x\right)} \sqrt{-\frac{c^{2} d f^{3} + 3 \, a c e f^{2} g - 3 \, a c d f g^{2} - a^{2} e g^{3} + {\left(a c^{3} f^{6} + 3 \, a^{2} c^{2} f^{4} g^{2} + 3 \, a^{3} c f^{2} g^{4} + a^{4} g^{6}\right)} \sqrt{-\frac{c^{3} e^{2} f^{6} - 6 \, c^{3} d e f^{5} g + 20 \, a c^{2} d e f^{3} g^{3} - 6 \, a^{2} c d e f g^{5} + a^{2} c d^{2} g^{6} + 3 \, {\left(3 \, c^{3} d^{2} - 2 \, a c^{2} e^{2}\right)} f^{4} g^{2} - 3 \, {\left(2 \, a c^{2} d^{2} - 3 \, a^{2} c e^{2}\right)} f^{2} g^{4}}{a c^{6} f^{12} + 6 \, a^{2} c^{5} f^{10} g^{2} + 15 \, a^{3} c^{4} f^{8} g^{4} + 20 \, a^{4} c^{3} f^{6} g^{6} + 15 \, a^{5} c^{2} f^{4} g^{8} + 6 \, a^{6} c f^{2} g^{10} + a^{7} g^{12}}}}{a c^{3} f^{6} + 3 \, a^{2} c^{2} f^{4} g^{2} + 3 \, a^{3} c f^{2} g^{4} + a^{4} g^{6}}} \log\left(\frac{c e^{2} f^{4} - 2 \, c d e f^{3} g - 2 \, a d e f g^{3} + a d^{2} g^{4} - 3 \, {\left(c d^{2} + a e^{2}\right)} f^{2} g^{2} + 2 \, {\left(c^{2} e f^{5} - 3 \, c^{2} d f^{4} g - 4 \, a c e f^{3} g^{2} + 4 \, a c d f^{2} g^{3} + 3 \, a^{2} e f g^{4} - a^{2} d g^{5} + 2 \, {\left(a c^{3} f^{7} g + 3 \, a^{2} c^{2} f^{5} g^{3} + 3 \, a^{3} c f^{3} g^{5} + a^{4} f g^{7}\right)} \sqrt{-\frac{c^{3} e^{2} f^{6} - 6 \, c^{3} d e f^{5} g + 20 \, a c^{2} d e f^{3} g^{3} - 6 \, a^{2} c d e f g^{5} + a^{2} c d^{2} g^{6} + 3 \, {\left(3 \, c^{3} d^{2} - 2 \, a c^{2} e^{2}\right)} f^{4} g^{2} - 3 \, {\left(2 \, a c^{2} d^{2} - 3 \, a^{2} c e^{2}\right)} f^{2} g^{4}}{a c^{6} f^{12} + 6 \, a^{2} c^{5} f^{10} g^{2} + 15 \, a^{3} c^{4} f^{8} g^{4} + 20 \, a^{4} c^{3} f^{6} g^{6} + 15 \, a^{5} c^{2} f^{4} g^{8} + 6 \, a^{6} c f^{2} g^{10} + a^{7} g^{12}}}\right)} \sqrt{e x + d} \sqrt{g x + f} \sqrt{-\frac{c^{2} d f^{3} + 3 \, a c e f^{2} g - 3 \, a c d f g^{2} - a^{2} e g^{3} + {\left(a c^{3} f^{6} + 3 \, a^{2} c^{2} f^{4} g^{2} + 3 \, a^{3} c f^{2} g^{4} + a^{4} g^{6}\right)} \sqrt{-\frac{c^{3} e^{2} f^{6} - 6 \, c^{3} d e f^{5} g + 20 \, a c^{2} d e f^{3} g^{3} - 6 \, a^{2} c d e f g^{5} + a^{2} c d^{2} g^{6} + 3 \, {\left(3 \, c^{3} d^{2} - 2 \, a c^{2} e^{2}\right)} f^{4} g^{2} - 3 \, {\left(2 \, a c^{2} d^{2} - 3 \, a^{2} c e^{2}\right)} f^{2} g^{4}}{a c^{6} f^{12} + 6 \, a^{2} c^{5} f^{10} g^{2} + 15 \, a^{3} c^{4} f^{8} g^{4} + 20 \, a^{4} c^{3} f^{6} g^{6} + 15 \, a^{5} c^{2} f^{4} g^{8} + 6 \, a^{6} c f^{2} g^{10} + a^{7} g^{12}}}}{a c^{3} f^{6} + 3 \, a^{2} c^{2} f^{4} g^{2} + 3 \, a^{3} c f^{2} g^{4} + a^{4} g^{6}}} + 2 \, {\left(c e^{2} f^{3} g - 3 \, c d e f^{2} g^{2} - 3 \, a e^{2} f g^{3} + a d e g^{4}\right)} x - {\left(2 \, c^{3} d f^{7} + 6 \, a c^{2} d f^{5} g^{2} + 6 \, a^{2} c d f^{3} g^{4} + 2 \, a^{3} d f g^{6} + {\left(c^{3} e f^{7} + c^{3} d f^{6} g + 3 \, a c^{2} e f^{5} g^{2} + 3 \, a c^{2} d f^{4} g^{3} + 3 \, a^{2} c e f^{3} g^{4} + 3 \, a^{2} c d f^{2} g^{5} + a^{3} e f g^{6} + a^{3} d g^{7}\right)} x\right)} \sqrt{-\frac{c^{3} e^{2} f^{6} - 6 \, c^{3} d e f^{5} g + 20 \, a c^{2} d e f^{3} g^{3} - 6 \, a^{2} c d e f g^{5} + a^{2} c d^{2} g^{6} + 3 \, {\left(3 \, c^{3} d^{2} - 2 \, a c^{2} e^{2}\right)} f^{4} g^{2} - 3 \, {\left(2 \, a c^{2} d^{2} - 3 \, a^{2} c e^{2}\right)} f^{2} g^{4}}{a c^{6} f^{12} + 6 \, a^{2} c^{5} f^{10} g^{2} + 15 \, a^{3} c^{4} f^{8} g^{4} + 20 \, a^{4} c^{3} f^{6} g^{6} + 15 \, a^{5} c^{2} f^{4} g^{8} + 6 \, a^{6} c f^{2} g^{10} + a^{7} g^{12}}}}{x}\right) - {\left(c f^{3} + a f g^{2} + {\left(c f^{2} g + a g^{3}\right)} x\right)} \sqrt{-\frac{c^{2} d f^{3} + 3 \, a c e f^{2} g - 3 \, a c d f g^{2} - a^{2} e g^{3} + {\left(a c^{3} f^{6} + 3 \, a^{2} c^{2} f^{4} g^{2} + 3 \, a^{3} c f^{2} g^{4} + a^{4} g^{6}\right)} \sqrt{-\frac{c^{3} e^{2} f^{6} - 6 \, c^{3} d e f^{5} g + 20 \, a c^{2} d e f^{3} g^{3} - 6 \, a^{2} c d e f g^{5} + a^{2} c d^{2} g^{6} + 3 \, {\left(3 \, c^{3} d^{2} - 2 \, a c^{2} e^{2}\right)} f^{4} g^{2} - 3 \, {\left(2 \, a c^{2} d^{2} - 3 \, a^{2} c e^{2}\right)} f^{2} g^{4}}{a c^{6} f^{12} + 6 \, a^{2} c^{5} f^{10} g^{2} + 15 \, a^{3} c^{4} f^{8} g^{4} + 20 \, a^{4} c^{3} f^{6} g^{6} + 15 \, a^{5} c^{2} f^{4} g^{8} + 6 \, a^{6} c f^{2} g^{10} + a^{7} g^{12}}}}{a c^{3} f^{6} + 3 \, a^{2} c^{2} f^{4} g^{2} + 3 \, a^{3} c f^{2} g^{4} + a^{4} g^{6}}} \log\left(\frac{c e^{2} f^{4} - 2 \, c d e f^{3} g - 2 \, a d e f g^{3} + a d^{2} g^{4} - 3 \, {\left(c d^{2} + a e^{2}\right)} f^{2} g^{2} - 2 \, {\left(c^{2} e f^{5} - 3 \, c^{2} d f^{4} g - 4 \, a c e f^{3} g^{2} + 4 \, a c d f^{2} g^{3} + 3 \, a^{2} e f g^{4} - a^{2} d g^{5} + 2 \, {\left(a c^{3} f^{7} g + 3 \, a^{2} c^{2} f^{5} g^{3} + 3 \, a^{3} c f^{3} g^{5} + a^{4} f g^{7}\right)} \sqrt{-\frac{c^{3} e^{2} f^{6} - 6 \, c^{3} d e f^{5} g + 20 \, a c^{2} d e f^{3} g^{3} - 6 \, a^{2} c d e f g^{5} + a^{2} c d^{2} g^{6} + 3 \, {\left(3 \, c^{3} d^{2} - 2 \, a c^{2} e^{2}\right)} f^{4} g^{2} - 3 \, {\left(2 \, a c^{2} d^{2} - 3 \, a^{2} c e^{2}\right)} f^{2} g^{4}}{a c^{6} f^{12} + 6 \, a^{2} c^{5} f^{10} g^{2} + 15 \, a^{3} c^{4} f^{8} g^{4} + 20 \, a^{4} c^{3} f^{6} g^{6} + 15 \, a^{5} c^{2} f^{4} g^{8} + 6 \, a^{6} c f^{2} g^{10} + a^{7} g^{12}}}\right)} \sqrt{e x + d} \sqrt{g x + f} \sqrt{-\frac{c^{2} d f^{3} + 3 \, a c e f^{2} g - 3 \, a c d f g^{2} - a^{2} e g^{3} + {\left(a c^{3} f^{6} + 3 \, a^{2} c^{2} f^{4} g^{2} + 3 \, a^{3} c f^{2} g^{4} + a^{4} g^{6}\right)} \sqrt{-\frac{c^{3} e^{2} f^{6} - 6 \, c^{3} d e f^{5} g + 20 \, a c^{2} d e f^{3} g^{3} - 6 \, a^{2} c d e f g^{5} + a^{2} c d^{2} g^{6} + 3 \, {\left(3 \, c^{3} d^{2} - 2 \, a c^{2} e^{2}\right)} f^{4} g^{2} - 3 \, {\left(2 \, a c^{2} d^{2} - 3 \, a^{2} c e^{2}\right)} f^{2} g^{4}}{a c^{6} f^{12} + 6 \, a^{2} c^{5} f^{10} g^{2} + 15 \, a^{3} c^{4} f^{8} g^{4} + 20 \, a^{4} c^{3} f^{6} g^{6} + 15 \, a^{5} c^{2} f^{4} g^{8} + 6 \, a^{6} c f^{2} g^{10} + a^{7} g^{12}}}}{a c^{3} f^{6} + 3 \, a^{2} c^{2} f^{4} g^{2} + 3 \, a^{3} c f^{2} g^{4} + a^{4} g^{6}}} + 2 \, {\left(c e^{2} f^{3} g - 3 \, c d e f^{2} g^{2} - 3 \, a e^{2} f g^{3} + a d e g^{4}\right)} x - {\left(2 \, c^{3} d f^{7} + 6 \, a c^{2} d f^{5} g^{2} + 6 \, a^{2} c d f^{3} g^{4} + 2 \, a^{3} d f g^{6} + {\left(c^{3} e f^{7} + c^{3} d f^{6} g + 3 \, a c^{2} e f^{5} g^{2} + 3 \, a c^{2} d f^{4} g^{3} + 3 \, a^{2} c e f^{3} g^{4} + 3 \, a^{2} c d f^{2} g^{5} + a^{3} e f g^{6} + a^{3} d g^{7}\right)} x\right)} \sqrt{-\frac{c^{3} e^{2} f^{6} - 6 \, c^{3} d e f^{5} g + 20 \, a c^{2} d e f^{3} g^{3} - 6 \, a^{2} c d e f g^{5} + a^{2} c d^{2} g^{6} + 3 \, {\left(3 \, c^{3} d^{2} - 2 \, a c^{2} e^{2}\right)} f^{4} g^{2} - 3 \, {\left(2 \, a c^{2} d^{2} - 3 \, a^{2} c e^{2}\right)} f^{2} g^{4}}{a c^{6} f^{12} + 6 \, a^{2} c^{5} f^{10} g^{2} + 15 \, a^{3} c^{4} f^{8} g^{4} + 20 \, a^{4} c^{3} f^{6} g^{6} + 15 \, a^{5} c^{2} f^{4} g^{8} + 6 \, a^{6} c f^{2} g^{10} + a^{7} g^{12}}}}{x}\right) + {\left(c f^{3} + a f g^{2} + {\left(c f^{2} g + a g^{3}\right)} x\right)} \sqrt{-\frac{c^{2} d f^{3} + 3 \, a c e f^{2} g - 3 \, a c d f g^{2} - a^{2} e g^{3} - {\left(a c^{3} f^{6} + 3 \, a^{2} c^{2} f^{4} g^{2} + 3 \, a^{3} c f^{2} g^{4} + a^{4} g^{6}\right)} \sqrt{-\frac{c^{3} e^{2} f^{6} - 6 \, c^{3} d e f^{5} g + 20 \, a c^{2} d e f^{3} g^{3} - 6 \, a^{2} c d e f g^{5} + a^{2} c d^{2} g^{6} + 3 \, {\left(3 \, c^{3} d^{2} - 2 \, a c^{2} e^{2}\right)} f^{4} g^{2} - 3 \, {\left(2 \, a c^{2} d^{2} - 3 \, a^{2} c e^{2}\right)} f^{2} g^{4}}{a c^{6} f^{12} + 6 \, a^{2} c^{5} f^{10} g^{2} + 15 \, a^{3} c^{4} f^{8} g^{4} + 20 \, a^{4} c^{3} f^{6} g^{6} + 15 \, a^{5} c^{2} f^{4} g^{8} + 6 \, a^{6} c f^{2} g^{10} + a^{7} g^{12}}}}{a c^{3} f^{6} + 3 \, a^{2} c^{2} f^{4} g^{2} + 3 \, a^{3} c f^{2} g^{4} + a^{4} g^{6}}} \log\left(\frac{c e^{2} f^{4} - 2 \, c d e f^{3} g - 2 \, a d e f g^{3} + a d^{2} g^{4} - 3 \, {\left(c d^{2} + a e^{2}\right)} f^{2} g^{2} + 2 \, {\left(c^{2} e f^{5} - 3 \, c^{2} d f^{4} g - 4 \, a c e f^{3} g^{2} + 4 \, a c d f^{2} g^{3} + 3 \, a^{2} e f g^{4} - a^{2} d g^{5} - 2 \, {\left(a c^{3} f^{7} g + 3 \, a^{2} c^{2} f^{5} g^{3} + 3 \, a^{3} c f^{3} g^{5} + a^{4} f g^{7}\right)} \sqrt{-\frac{c^{3} e^{2} f^{6} - 6 \, c^{3} d e f^{5} g + 20 \, a c^{2} d e f^{3} g^{3} - 6 \, a^{2} c d e f g^{5} + a^{2} c d^{2} g^{6} + 3 \, {\left(3 \, c^{3} d^{2} - 2 \, a c^{2} e^{2}\right)} f^{4} g^{2} - 3 \, {\left(2 \, a c^{2} d^{2} - 3 \, a^{2} c e^{2}\right)} f^{2} g^{4}}{a c^{6} f^{12} + 6 \, a^{2} c^{5} f^{10} g^{2} + 15 \, a^{3} c^{4} f^{8} g^{4} + 20 \, a^{4} c^{3} f^{6} g^{6} + 15 \, a^{5} c^{2} f^{4} g^{8} + 6 \, a^{6} c f^{2} g^{10} + a^{7} g^{12}}}\right)} \sqrt{e x + d} \sqrt{g x + f} \sqrt{-\frac{c^{2} d f^{3} + 3 \, a c e f^{2} g - 3 \, a c d f g^{2} - a^{2} e g^{3} - {\left(a c^{3} f^{6} + 3 \, a^{2} c^{2} f^{4} g^{2} + 3 \, a^{3} c f^{2} g^{4} + a^{4} g^{6}\right)} \sqrt{-\frac{c^{3} e^{2} f^{6} - 6 \, c^{3} d e f^{5} g + 20 \, a c^{2} d e f^{3} g^{3} - 6 \, a^{2} c d e f g^{5} + a^{2} c d^{2} g^{6} + 3 \, {\left(3 \, c^{3} d^{2} - 2 \, a c^{2} e^{2}\right)} f^{4} g^{2} - 3 \, {\left(2 \, a c^{2} d^{2} - 3 \, a^{2} c e^{2}\right)} f^{2} g^{4}}{a c^{6} f^{12} + 6 \, a^{2} c^{5} f^{10} g^{2} + 15 \, a^{3} c^{4} f^{8} g^{4} + 20 \, a^{4} c^{3} f^{6} g^{6} + 15 \, a^{5} c^{2} f^{4} g^{8} + 6 \, a^{6} c f^{2} g^{10} + a^{7} g^{12}}}}{a c^{3} f^{6} + 3 \, a^{2} c^{2} f^{4} g^{2} + 3 \, a^{3} c f^{2} g^{4} + a^{4} g^{6}}} + 2 \, {\left(c e^{2} f^{3} g - 3 \, c d e f^{2} g^{2} - 3 \, a e^{2} f g^{3} + a d e g^{4}\right)} x + {\left(2 \, c^{3} d f^{7} + 6 \, a c^{2} d f^{5} g^{2} + 6 \, a^{2} c d f^{3} g^{4} + 2 \, a^{3} d f g^{6} + {\left(c^{3} e f^{7} + c^{3} d f^{6} g + 3 \, a c^{2} e f^{5} g^{2} + 3 \, a c^{2} d f^{4} g^{3} + 3 \, a^{2} c e f^{3} g^{4} + 3 \, a^{2} c d f^{2} g^{5} + a^{3} e f g^{6} + a^{3} d g^{7}\right)} x\right)} \sqrt{-\frac{c^{3} e^{2} f^{6} - 6 \, c^{3} d e f^{5} g + 20 \, a c^{2} d e f^{3} g^{3} - 6 \, a^{2} c d e f g^{5} + a^{2} c d^{2} g^{6} + 3 \, {\left(3 \, c^{3} d^{2} - 2 \, a c^{2} e^{2}\right)} f^{4} g^{2} - 3 \, {\left(2 \, a c^{2} d^{2} - 3 \, a^{2} c e^{2}\right)} f^{2} g^{4}}{a c^{6} f^{12} + 6 \, a^{2} c^{5} f^{10} g^{2} + 15 \, a^{3} c^{4} f^{8} g^{4} + 20 \, a^{4} c^{3} f^{6} g^{6} + 15 \, a^{5} c^{2} f^{4} g^{8} + 6 \, a^{6} c f^{2} g^{10} + a^{7} g^{12}}}}{x}\right) - {\left(c f^{3} + a f g^{2} + {\left(c f^{2} g + a g^{3}\right)} x\right)} \sqrt{-\frac{c^{2} d f^{3} + 3 \, a c e f^{2} g - 3 \, a c d f g^{2} - a^{2} e g^{3} - {\left(a c^{3} f^{6} + 3 \, a^{2} c^{2} f^{4} g^{2} + 3 \, a^{3} c f^{2} g^{4} + a^{4} g^{6}\right)} \sqrt{-\frac{c^{3} e^{2} f^{6} - 6 \, c^{3} d e f^{5} g + 20 \, a c^{2} d e f^{3} g^{3} - 6 \, a^{2} c d e f g^{5} + a^{2} c d^{2} g^{6} + 3 \, {\left(3 \, c^{3} d^{2} - 2 \, a c^{2} e^{2}\right)} f^{4} g^{2} - 3 \, {\left(2 \, a c^{2} d^{2} - 3 \, a^{2} c e^{2}\right)} f^{2} g^{4}}{a c^{6} f^{12} + 6 \, a^{2} c^{5} f^{10} g^{2} + 15 \, a^{3} c^{4} f^{8} g^{4} + 20 \, a^{4} c^{3} f^{6} g^{6} + 15 \, a^{5} c^{2} f^{4} g^{8} + 6 \, a^{6} c f^{2} g^{10} + a^{7} g^{12}}}}{a c^{3} f^{6} + 3 \, a^{2} c^{2} f^{4} g^{2} + 3 \, a^{3} c f^{2} g^{4} + a^{4} g^{6}}} \log\left(\frac{c e^{2} f^{4} - 2 \, c d e f^{3} g - 2 \, a d e f g^{3} + a d^{2} g^{4} - 3 \, {\left(c d^{2} + a e^{2}\right)} f^{2} g^{2} - 2 \, {\left(c^{2} e f^{5} - 3 \, c^{2} d f^{4} g - 4 \, a c e f^{3} g^{2} + 4 \, a c d f^{2} g^{3} + 3 \, a^{2} e f g^{4} - a^{2} d g^{5} - 2 \, {\left(a c^{3} f^{7} g + 3 \, a^{2} c^{2} f^{5} g^{3} + 3 \, a^{3} c f^{3} g^{5} + a^{4} f g^{7}\right)} \sqrt{-\frac{c^{3} e^{2} f^{6} - 6 \, c^{3} d e f^{5} g + 20 \, a c^{2} d e f^{3} g^{3} - 6 \, a^{2} c d e f g^{5} + a^{2} c d^{2} g^{6} + 3 \, {\left(3 \, c^{3} d^{2} - 2 \, a c^{2} e^{2}\right)} f^{4} g^{2} - 3 \, {\left(2 \, a c^{2} d^{2} - 3 \, a^{2} c e^{2}\right)} f^{2} g^{4}}{a c^{6} f^{12} + 6 \, a^{2} c^{5} f^{10} g^{2} + 15 \, a^{3} c^{4} f^{8} g^{4} + 20 \, a^{4} c^{3} f^{6} g^{6} + 15 \, a^{5} c^{2} f^{4} g^{8} + 6 \, a^{6} c f^{2} g^{10} + a^{7} g^{12}}}\right)} \sqrt{e x + d} \sqrt{g x + f} \sqrt{-\frac{c^{2} d f^{3} + 3 \, a c e f^{2} g - 3 \, a c d f g^{2} - a^{2} e g^{3} - {\left(a c^{3} f^{6} + 3 \, a^{2} c^{2} f^{4} g^{2} + 3 \, a^{3} c f^{2} g^{4} + a^{4} g^{6}\right)} \sqrt{-\frac{c^{3} e^{2} f^{6} - 6 \, c^{3} d e f^{5} g + 20 \, a c^{2} d e f^{3} g^{3} - 6 \, a^{2} c d e f g^{5} + a^{2} c d^{2} g^{6} + 3 \, {\left(3 \, c^{3} d^{2} - 2 \, a c^{2} e^{2}\right)} f^{4} g^{2} - 3 \, {\left(2 \, a c^{2} d^{2} - 3 \, a^{2} c e^{2}\right)} f^{2} g^{4}}{a c^{6} f^{12} + 6 \, a^{2} c^{5} f^{10} g^{2} + 15 \, a^{3} c^{4} f^{8} g^{4} + 20 \, a^{4} c^{3} f^{6} g^{6} + 15 \, a^{5} c^{2} f^{4} g^{8} + 6 \, a^{6} c f^{2} g^{10} + a^{7} g^{12}}}}{a c^{3} f^{6} + 3 \, a^{2} c^{2} f^{4} g^{2} + 3 \, a^{3} c f^{2} g^{4} + a^{4} g^{6}}} + 2 \, {\left(c e^{2} f^{3} g - 3 \, c d e f^{2} g^{2} - 3 \, a e^{2} f g^{3} + a d e g^{4}\right)} x + {\left(2 \, c^{3} d f^{7} + 6 \, a c^{2} d f^{5} g^{2} + 6 \, a^{2} c d f^{3} g^{4} + 2 \, a^{3} d f g^{6} + {\left(c^{3} e f^{7} + c^{3} d f^{6} g + 3 \, a c^{2} e f^{5} g^{2} + 3 \, a c^{2} d f^{4} g^{3} + 3 \, a^{2} c e f^{3} g^{4} + 3 \, a^{2} c d f^{2} g^{5} + a^{3} e f g^{6} + a^{3} d g^{7}\right)} x\right)} \sqrt{-\frac{c^{3} e^{2} f^{6} - 6 \, c^{3} d e f^{5} g + 20 \, a c^{2} d e f^{3} g^{3} - 6 \, a^{2} c d e f g^{5} + a^{2} c d^{2} g^{6} + 3 \, {\left(3 \, c^{3} d^{2} - 2 \, a c^{2} e^{2}\right)} f^{4} g^{2} - 3 \, {\left(2 \, a c^{2} d^{2} - 3 \, a^{2} c e^{2}\right)} f^{2} g^{4}}{a c^{6} f^{12} + 6 \, a^{2} c^{5} f^{10} g^{2} + 15 \, a^{3} c^{4} f^{8} g^{4} + 20 \, a^{4} c^{3} f^{6} g^{6} + 15 \, a^{5} c^{2} f^{4} g^{8} + 6 \, a^{6} c f^{2} g^{10} + a^{7} g^{12}}}}{x}\right) + 8 \, \sqrt{e x + d} \sqrt{g x + f} g}{4 \, {\left(c f^{3} + a f g^{2} + {\left(c f^{2} g + a g^{3}\right)} x\right)}}"," ",0,"-1/4*((c*f^3 + a*f*g^2 + (c*f^2*g + a*g^3)*x)*sqrt(-(c^2*d*f^3 + 3*a*c*e*f^2*g - 3*a*c*d*f*g^2 - a^2*e*g^3 + (a*c^3*f^6 + 3*a^2*c^2*f^4*g^2 + 3*a^3*c*f^2*g^4 + a^4*g^6)*sqrt(-(c^3*e^2*f^6 - 6*c^3*d*e*f^5*g + 20*a*c^2*d*e*f^3*g^3 - 6*a^2*c*d*e*f*g^5 + a^2*c*d^2*g^6 + 3*(3*c^3*d^2 - 2*a*c^2*e^2)*f^4*g^2 - 3*(2*a*c^2*d^2 - 3*a^2*c*e^2)*f^2*g^4)/(a*c^6*f^12 + 6*a^2*c^5*f^10*g^2 + 15*a^3*c^4*f^8*g^4 + 20*a^4*c^3*f^6*g^6 + 15*a^5*c^2*f^4*g^8 + 6*a^6*c*f^2*g^10 + a^7*g^12)))/(a*c^3*f^6 + 3*a^2*c^2*f^4*g^2 + 3*a^3*c*f^2*g^4 + a^4*g^6))*log((c*e^2*f^4 - 2*c*d*e*f^3*g - 2*a*d*e*f*g^3 + a*d^2*g^4 - 3*(c*d^2 + a*e^2)*f^2*g^2 + 2*(c^2*e*f^5 - 3*c^2*d*f^4*g - 4*a*c*e*f^3*g^2 + 4*a*c*d*f^2*g^3 + 3*a^2*e*f*g^4 - a^2*d*g^5 + 2*(a*c^3*f^7*g + 3*a^2*c^2*f^5*g^3 + 3*a^3*c*f^3*g^5 + a^4*f*g^7)*sqrt(-(c^3*e^2*f^6 - 6*c^3*d*e*f^5*g + 20*a*c^2*d*e*f^3*g^3 - 6*a^2*c*d*e*f*g^5 + a^2*c*d^2*g^6 + 3*(3*c^3*d^2 - 2*a*c^2*e^2)*f^4*g^2 - 3*(2*a*c^2*d^2 - 3*a^2*c*e^2)*f^2*g^4)/(a*c^6*f^12 + 6*a^2*c^5*f^10*g^2 + 15*a^3*c^4*f^8*g^4 + 20*a^4*c^3*f^6*g^6 + 15*a^5*c^2*f^4*g^8 + 6*a^6*c*f^2*g^10 + a^7*g^12)))*sqrt(e*x + d)*sqrt(g*x + f)*sqrt(-(c^2*d*f^3 + 3*a*c*e*f^2*g - 3*a*c*d*f*g^2 - a^2*e*g^3 + (a*c^3*f^6 + 3*a^2*c^2*f^4*g^2 + 3*a^3*c*f^2*g^4 + a^4*g^6)*sqrt(-(c^3*e^2*f^6 - 6*c^3*d*e*f^5*g + 20*a*c^2*d*e*f^3*g^3 - 6*a^2*c*d*e*f*g^5 + a^2*c*d^2*g^6 + 3*(3*c^3*d^2 - 2*a*c^2*e^2)*f^4*g^2 - 3*(2*a*c^2*d^2 - 3*a^2*c*e^2)*f^2*g^4)/(a*c^6*f^12 + 6*a^2*c^5*f^10*g^2 + 15*a^3*c^4*f^8*g^4 + 20*a^4*c^3*f^6*g^6 + 15*a^5*c^2*f^4*g^8 + 6*a^6*c*f^2*g^10 + a^7*g^12)))/(a*c^3*f^6 + 3*a^2*c^2*f^4*g^2 + 3*a^3*c*f^2*g^4 + a^4*g^6)) + 2*(c*e^2*f^3*g - 3*c*d*e*f^2*g^2 - 3*a*e^2*f*g^3 + a*d*e*g^4)*x - (2*c^3*d*f^7 + 6*a*c^2*d*f^5*g^2 + 6*a^2*c*d*f^3*g^4 + 2*a^3*d*f*g^6 + (c^3*e*f^7 + c^3*d*f^6*g + 3*a*c^2*e*f^5*g^2 + 3*a*c^2*d*f^4*g^3 + 3*a^2*c*e*f^3*g^4 + 3*a^2*c*d*f^2*g^5 + a^3*e*f*g^6 + a^3*d*g^7)*x)*sqrt(-(c^3*e^2*f^6 - 6*c^3*d*e*f^5*g + 20*a*c^2*d*e*f^3*g^3 - 6*a^2*c*d*e*f*g^5 + a^2*c*d^2*g^6 + 3*(3*c^3*d^2 - 2*a*c^2*e^2)*f^4*g^2 - 3*(2*a*c^2*d^2 - 3*a^2*c*e^2)*f^2*g^4)/(a*c^6*f^12 + 6*a^2*c^5*f^10*g^2 + 15*a^3*c^4*f^8*g^4 + 20*a^4*c^3*f^6*g^6 + 15*a^5*c^2*f^4*g^8 + 6*a^6*c*f^2*g^10 + a^7*g^12)))/x) - (c*f^3 + a*f*g^2 + (c*f^2*g + a*g^3)*x)*sqrt(-(c^2*d*f^3 + 3*a*c*e*f^2*g - 3*a*c*d*f*g^2 - a^2*e*g^3 + (a*c^3*f^6 + 3*a^2*c^2*f^4*g^2 + 3*a^3*c*f^2*g^4 + a^4*g^6)*sqrt(-(c^3*e^2*f^6 - 6*c^3*d*e*f^5*g + 20*a*c^2*d*e*f^3*g^3 - 6*a^2*c*d*e*f*g^5 + a^2*c*d^2*g^6 + 3*(3*c^3*d^2 - 2*a*c^2*e^2)*f^4*g^2 - 3*(2*a*c^2*d^2 - 3*a^2*c*e^2)*f^2*g^4)/(a*c^6*f^12 + 6*a^2*c^5*f^10*g^2 + 15*a^3*c^4*f^8*g^4 + 20*a^4*c^3*f^6*g^6 + 15*a^5*c^2*f^4*g^8 + 6*a^6*c*f^2*g^10 + a^7*g^12)))/(a*c^3*f^6 + 3*a^2*c^2*f^4*g^2 + 3*a^3*c*f^2*g^4 + a^4*g^6))*log((c*e^2*f^4 - 2*c*d*e*f^3*g - 2*a*d*e*f*g^3 + a*d^2*g^4 - 3*(c*d^2 + a*e^2)*f^2*g^2 - 2*(c^2*e*f^5 - 3*c^2*d*f^4*g - 4*a*c*e*f^3*g^2 + 4*a*c*d*f^2*g^3 + 3*a^2*e*f*g^4 - a^2*d*g^5 + 2*(a*c^3*f^7*g + 3*a^2*c^2*f^5*g^3 + 3*a^3*c*f^3*g^5 + a^4*f*g^7)*sqrt(-(c^3*e^2*f^6 - 6*c^3*d*e*f^5*g + 20*a*c^2*d*e*f^3*g^3 - 6*a^2*c*d*e*f*g^5 + a^2*c*d^2*g^6 + 3*(3*c^3*d^2 - 2*a*c^2*e^2)*f^4*g^2 - 3*(2*a*c^2*d^2 - 3*a^2*c*e^2)*f^2*g^4)/(a*c^6*f^12 + 6*a^2*c^5*f^10*g^2 + 15*a^3*c^4*f^8*g^4 + 20*a^4*c^3*f^6*g^6 + 15*a^5*c^2*f^4*g^8 + 6*a^6*c*f^2*g^10 + a^7*g^12)))*sqrt(e*x + d)*sqrt(g*x + f)*sqrt(-(c^2*d*f^3 + 3*a*c*e*f^2*g - 3*a*c*d*f*g^2 - a^2*e*g^3 + (a*c^3*f^6 + 3*a^2*c^2*f^4*g^2 + 3*a^3*c*f^2*g^4 + a^4*g^6)*sqrt(-(c^3*e^2*f^6 - 6*c^3*d*e*f^5*g + 20*a*c^2*d*e*f^3*g^3 - 6*a^2*c*d*e*f*g^5 + a^2*c*d^2*g^6 + 3*(3*c^3*d^2 - 2*a*c^2*e^2)*f^4*g^2 - 3*(2*a*c^2*d^2 - 3*a^2*c*e^2)*f^2*g^4)/(a*c^6*f^12 + 6*a^2*c^5*f^10*g^2 + 15*a^3*c^4*f^8*g^4 + 20*a^4*c^3*f^6*g^6 + 15*a^5*c^2*f^4*g^8 + 6*a^6*c*f^2*g^10 + a^7*g^12)))/(a*c^3*f^6 + 3*a^2*c^2*f^4*g^2 + 3*a^3*c*f^2*g^4 + a^4*g^6)) + 2*(c*e^2*f^3*g - 3*c*d*e*f^2*g^2 - 3*a*e^2*f*g^3 + a*d*e*g^4)*x - (2*c^3*d*f^7 + 6*a*c^2*d*f^5*g^2 + 6*a^2*c*d*f^3*g^4 + 2*a^3*d*f*g^6 + (c^3*e*f^7 + c^3*d*f^6*g + 3*a*c^2*e*f^5*g^2 + 3*a*c^2*d*f^4*g^3 + 3*a^2*c*e*f^3*g^4 + 3*a^2*c*d*f^2*g^5 + a^3*e*f*g^6 + a^3*d*g^7)*x)*sqrt(-(c^3*e^2*f^6 - 6*c^3*d*e*f^5*g + 20*a*c^2*d*e*f^3*g^3 - 6*a^2*c*d*e*f*g^5 + a^2*c*d^2*g^6 + 3*(3*c^3*d^2 - 2*a*c^2*e^2)*f^4*g^2 - 3*(2*a*c^2*d^2 - 3*a^2*c*e^2)*f^2*g^4)/(a*c^6*f^12 + 6*a^2*c^5*f^10*g^2 + 15*a^3*c^4*f^8*g^4 + 20*a^4*c^3*f^6*g^6 + 15*a^5*c^2*f^4*g^8 + 6*a^6*c*f^2*g^10 + a^7*g^12)))/x) + (c*f^3 + a*f*g^2 + (c*f^2*g + a*g^3)*x)*sqrt(-(c^2*d*f^3 + 3*a*c*e*f^2*g - 3*a*c*d*f*g^2 - a^2*e*g^3 - (a*c^3*f^6 + 3*a^2*c^2*f^4*g^2 + 3*a^3*c*f^2*g^4 + a^4*g^6)*sqrt(-(c^3*e^2*f^6 - 6*c^3*d*e*f^5*g + 20*a*c^2*d*e*f^3*g^3 - 6*a^2*c*d*e*f*g^5 + a^2*c*d^2*g^6 + 3*(3*c^3*d^2 - 2*a*c^2*e^2)*f^4*g^2 - 3*(2*a*c^2*d^2 - 3*a^2*c*e^2)*f^2*g^4)/(a*c^6*f^12 + 6*a^2*c^5*f^10*g^2 + 15*a^3*c^4*f^8*g^4 + 20*a^4*c^3*f^6*g^6 + 15*a^5*c^2*f^4*g^8 + 6*a^6*c*f^2*g^10 + a^7*g^12)))/(a*c^3*f^6 + 3*a^2*c^2*f^4*g^2 + 3*a^3*c*f^2*g^4 + a^4*g^6))*log((c*e^2*f^4 - 2*c*d*e*f^3*g - 2*a*d*e*f*g^3 + a*d^2*g^4 - 3*(c*d^2 + a*e^2)*f^2*g^2 + 2*(c^2*e*f^5 - 3*c^2*d*f^4*g - 4*a*c*e*f^3*g^2 + 4*a*c*d*f^2*g^3 + 3*a^2*e*f*g^4 - a^2*d*g^5 - 2*(a*c^3*f^7*g + 3*a^2*c^2*f^5*g^3 + 3*a^3*c*f^3*g^5 + a^4*f*g^7)*sqrt(-(c^3*e^2*f^6 - 6*c^3*d*e*f^5*g + 20*a*c^2*d*e*f^3*g^3 - 6*a^2*c*d*e*f*g^5 + a^2*c*d^2*g^6 + 3*(3*c^3*d^2 - 2*a*c^2*e^2)*f^4*g^2 - 3*(2*a*c^2*d^2 - 3*a^2*c*e^2)*f^2*g^4)/(a*c^6*f^12 + 6*a^2*c^5*f^10*g^2 + 15*a^3*c^4*f^8*g^4 + 20*a^4*c^3*f^6*g^6 + 15*a^5*c^2*f^4*g^8 + 6*a^6*c*f^2*g^10 + a^7*g^12)))*sqrt(e*x + d)*sqrt(g*x + f)*sqrt(-(c^2*d*f^3 + 3*a*c*e*f^2*g - 3*a*c*d*f*g^2 - a^2*e*g^3 - (a*c^3*f^6 + 3*a^2*c^2*f^4*g^2 + 3*a^3*c*f^2*g^4 + a^4*g^6)*sqrt(-(c^3*e^2*f^6 - 6*c^3*d*e*f^5*g + 20*a*c^2*d*e*f^3*g^3 - 6*a^2*c*d*e*f*g^5 + a^2*c*d^2*g^6 + 3*(3*c^3*d^2 - 2*a*c^2*e^2)*f^4*g^2 - 3*(2*a*c^2*d^2 - 3*a^2*c*e^2)*f^2*g^4)/(a*c^6*f^12 + 6*a^2*c^5*f^10*g^2 + 15*a^3*c^4*f^8*g^4 + 20*a^4*c^3*f^6*g^6 + 15*a^5*c^2*f^4*g^8 + 6*a^6*c*f^2*g^10 + a^7*g^12)))/(a*c^3*f^6 + 3*a^2*c^2*f^4*g^2 + 3*a^3*c*f^2*g^4 + a^4*g^6)) + 2*(c*e^2*f^3*g - 3*c*d*e*f^2*g^2 - 3*a*e^2*f*g^3 + a*d*e*g^4)*x + (2*c^3*d*f^7 + 6*a*c^2*d*f^5*g^2 + 6*a^2*c*d*f^3*g^4 + 2*a^3*d*f*g^6 + (c^3*e*f^7 + c^3*d*f^6*g + 3*a*c^2*e*f^5*g^2 + 3*a*c^2*d*f^4*g^3 + 3*a^2*c*e*f^3*g^4 + 3*a^2*c*d*f^2*g^5 + a^3*e*f*g^6 + a^3*d*g^7)*x)*sqrt(-(c^3*e^2*f^6 - 6*c^3*d*e*f^5*g + 20*a*c^2*d*e*f^3*g^3 - 6*a^2*c*d*e*f*g^5 + a^2*c*d^2*g^6 + 3*(3*c^3*d^2 - 2*a*c^2*e^2)*f^4*g^2 - 3*(2*a*c^2*d^2 - 3*a^2*c*e^2)*f^2*g^4)/(a*c^6*f^12 + 6*a^2*c^5*f^10*g^2 + 15*a^3*c^4*f^8*g^4 + 20*a^4*c^3*f^6*g^6 + 15*a^5*c^2*f^4*g^8 + 6*a^6*c*f^2*g^10 + a^7*g^12)))/x) - (c*f^3 + a*f*g^2 + (c*f^2*g + a*g^3)*x)*sqrt(-(c^2*d*f^3 + 3*a*c*e*f^2*g - 3*a*c*d*f*g^2 - a^2*e*g^3 - (a*c^3*f^6 + 3*a^2*c^2*f^4*g^2 + 3*a^3*c*f^2*g^4 + a^4*g^6)*sqrt(-(c^3*e^2*f^6 - 6*c^3*d*e*f^5*g + 20*a*c^2*d*e*f^3*g^3 - 6*a^2*c*d*e*f*g^5 + a^2*c*d^2*g^6 + 3*(3*c^3*d^2 - 2*a*c^2*e^2)*f^4*g^2 - 3*(2*a*c^2*d^2 - 3*a^2*c*e^2)*f^2*g^4)/(a*c^6*f^12 + 6*a^2*c^5*f^10*g^2 + 15*a^3*c^4*f^8*g^4 + 20*a^4*c^3*f^6*g^6 + 15*a^5*c^2*f^4*g^8 + 6*a^6*c*f^2*g^10 + a^7*g^12)))/(a*c^3*f^6 + 3*a^2*c^2*f^4*g^2 + 3*a^3*c*f^2*g^4 + a^4*g^6))*log((c*e^2*f^4 - 2*c*d*e*f^3*g - 2*a*d*e*f*g^3 + a*d^2*g^4 - 3*(c*d^2 + a*e^2)*f^2*g^2 - 2*(c^2*e*f^5 - 3*c^2*d*f^4*g - 4*a*c*e*f^3*g^2 + 4*a*c*d*f^2*g^3 + 3*a^2*e*f*g^4 - a^2*d*g^5 - 2*(a*c^3*f^7*g + 3*a^2*c^2*f^5*g^3 + 3*a^3*c*f^3*g^5 + a^4*f*g^7)*sqrt(-(c^3*e^2*f^6 - 6*c^3*d*e*f^5*g + 20*a*c^2*d*e*f^3*g^3 - 6*a^2*c*d*e*f*g^5 + a^2*c*d^2*g^6 + 3*(3*c^3*d^2 - 2*a*c^2*e^2)*f^4*g^2 - 3*(2*a*c^2*d^2 - 3*a^2*c*e^2)*f^2*g^4)/(a*c^6*f^12 + 6*a^2*c^5*f^10*g^2 + 15*a^3*c^4*f^8*g^4 + 20*a^4*c^3*f^6*g^6 + 15*a^5*c^2*f^4*g^8 + 6*a^6*c*f^2*g^10 + a^7*g^12)))*sqrt(e*x + d)*sqrt(g*x + f)*sqrt(-(c^2*d*f^3 + 3*a*c*e*f^2*g - 3*a*c*d*f*g^2 - a^2*e*g^3 - (a*c^3*f^6 + 3*a^2*c^2*f^4*g^2 + 3*a^3*c*f^2*g^4 + a^4*g^6)*sqrt(-(c^3*e^2*f^6 - 6*c^3*d*e*f^5*g + 20*a*c^2*d*e*f^3*g^3 - 6*a^2*c*d*e*f*g^5 + a^2*c*d^2*g^6 + 3*(3*c^3*d^2 - 2*a*c^2*e^2)*f^4*g^2 - 3*(2*a*c^2*d^2 - 3*a^2*c*e^2)*f^2*g^4)/(a*c^6*f^12 + 6*a^2*c^5*f^10*g^2 + 15*a^3*c^4*f^8*g^4 + 20*a^4*c^3*f^6*g^6 + 15*a^5*c^2*f^4*g^8 + 6*a^6*c*f^2*g^10 + a^7*g^12)))/(a*c^3*f^6 + 3*a^2*c^2*f^4*g^2 + 3*a^3*c*f^2*g^4 + a^4*g^6)) + 2*(c*e^2*f^3*g - 3*c*d*e*f^2*g^2 - 3*a*e^2*f*g^3 + a*d*e*g^4)*x + (2*c^3*d*f^7 + 6*a*c^2*d*f^5*g^2 + 6*a^2*c*d*f^3*g^4 + 2*a^3*d*f*g^6 + (c^3*e*f^7 + c^3*d*f^6*g + 3*a*c^2*e*f^5*g^2 + 3*a*c^2*d*f^4*g^3 + 3*a^2*c*e*f^3*g^4 + 3*a^2*c*d*f^2*g^5 + a^3*e*f*g^6 + a^3*d*g^7)*x)*sqrt(-(c^3*e^2*f^6 - 6*c^3*d*e*f^5*g + 20*a*c^2*d*e*f^3*g^3 - 6*a^2*c*d*e*f*g^5 + a^2*c*d^2*g^6 + 3*(3*c^3*d^2 - 2*a*c^2*e^2)*f^4*g^2 - 3*(2*a*c^2*d^2 - 3*a^2*c*e^2)*f^2*g^4)/(a*c^6*f^12 + 6*a^2*c^5*f^10*g^2 + 15*a^3*c^4*f^8*g^4 + 20*a^4*c^3*f^6*g^6 + 15*a^5*c^2*f^4*g^8 + 6*a^6*c*f^2*g^10 + a^7*g^12)))/x) + 8*sqrt(e*x + d)*sqrt(g*x + f)*g)/(c*f^3 + a*f*g^2 + (c*f^2*g + a*g^3)*x)","B",0
616,1,12028,0,126.493876," ","integrate(1/(e*x+d)^(1/2)/(g*x+f)^(3/2)/(c*x^2+a),x, algorithm=""fricas"")","\frac{8 \, \sqrt{e x + d} \sqrt{g x + f} g^{2} - {\left(c e f^{4} - c d f^{3} g + a e f^{2} g^{2} - a d f g^{3} + {\left(c e f^{3} g - c d f^{2} g^{2} + a e f g^{3} - a d g^{4}\right)} x\right)} \sqrt{-\frac{c^{3} d f^{3} - 3 \, a c^{2} e f^{2} g - 3 \, a c^{2} d f g^{2} + a^{2} c e g^{3} + {\left({\left(a c^{4} d^{2} + a^{2} c^{3} e^{2}\right)} f^{6} + 3 \, {\left(a^{2} c^{3} d^{2} + a^{3} c^{2} e^{2}\right)} f^{4} g^{2} + 3 \, {\left(a^{3} c^{2} d^{2} + a^{4} c e^{2}\right)} f^{2} g^{4} + {\left(a^{4} c d^{2} + a^{5} e^{2}\right)} g^{6}\right)} \sqrt{-\frac{c^{5} e^{2} f^{6} + 6 \, c^{5} d e f^{5} g - 20 \, a c^{4} d e f^{3} g^{3} + 6 \, a^{2} c^{3} d e f g^{5} + a^{2} c^{3} d^{2} g^{6} + 3 \, {\left(3 \, c^{5} d^{2} - 2 \, a c^{4} e^{2}\right)} f^{4} g^{2} - 3 \, {\left(2 \, a c^{4} d^{2} - 3 \, a^{2} c^{3} e^{2}\right)} f^{2} g^{4}}{{\left(a c^{8} d^{4} + 2 \, a^{2} c^{7} d^{2} e^{2} + a^{3} c^{6} e^{4}\right)} f^{12} + 6 \, {\left(a^{2} c^{7} d^{4} + 2 \, a^{3} c^{6} d^{2} e^{2} + a^{4} c^{5} e^{4}\right)} f^{10} g^{2} + 15 \, {\left(a^{3} c^{6} d^{4} + 2 \, a^{4} c^{5} d^{2} e^{2} + a^{5} c^{4} e^{4}\right)} f^{8} g^{4} + 20 \, {\left(a^{4} c^{5} d^{4} + 2 \, a^{5} c^{4} d^{2} e^{2} + a^{6} c^{3} e^{4}\right)} f^{6} g^{6} + 15 \, {\left(a^{5} c^{4} d^{4} + 2 \, a^{6} c^{3} d^{2} e^{2} + a^{7} c^{2} e^{4}\right)} f^{4} g^{8} + 6 \, {\left(a^{6} c^{3} d^{4} + 2 \, a^{7} c^{2} d^{2} e^{2} + a^{8} c e^{4}\right)} f^{2} g^{10} + {\left(a^{7} c^{2} d^{4} + 2 \, a^{8} c d^{2} e^{2} + a^{9} e^{4}\right)} g^{12}}}}{{\left(a c^{4} d^{2} + a^{2} c^{3} e^{2}\right)} f^{6} + 3 \, {\left(a^{2} c^{3} d^{2} + a^{3} c^{2} e^{2}\right)} f^{4} g^{2} + 3 \, {\left(a^{3} c^{2} d^{2} + a^{4} c e^{2}\right)} f^{2} g^{4} + {\left(a^{4} c d^{2} + a^{5} e^{2}\right)} g^{6}}} \log\left(-\frac{c^{3} e^{2} f^{4} + 4 \, c^{3} d e f^{3} g - 4 \, a c^{2} d e f g^{3} - a c^{2} d^{2} g^{4} + 3 \, {\left(c^{3} d^{2} - a c^{2} e^{2}\right)} f^{2} g^{2} + 2 \, {\left(c^{4} d e f^{5} - 10 \, a c^{3} d e f^{3} g^{2} + 5 \, a^{2} c^{2} d e f g^{4} + a^{2} c^{2} d^{2} g^{5} + {\left(3 \, c^{4} d^{2} - 2 \, a c^{3} e^{2}\right)} f^{4} g - 2 \, {\left(2 \, a c^{3} d^{2} - 3 \, a^{2} c^{2} e^{2}\right)} f^{2} g^{3} - {\left({\left(a c^{5} d^{2} e + a^{2} c^{4} e^{3}\right)} f^{8} + 2 \, {\left(a c^{5} d^{3} + a^{2} c^{4} d e^{2}\right)} f^{7} g + 2 \, {\left(a^{2} c^{4} d^{2} e + a^{3} c^{3} e^{3}\right)} f^{6} g^{2} + 6 \, {\left(a^{2} c^{4} d^{3} + a^{3} c^{3} d e^{2}\right)} f^{5} g^{3} + 6 \, {\left(a^{3} c^{3} d^{3} + a^{4} c^{2} d e^{2}\right)} f^{3} g^{5} - 2 \, {\left(a^{4} c^{2} d^{2} e + a^{5} c e^{3}\right)} f^{2} g^{6} + 2 \, {\left(a^{4} c^{2} d^{3} + a^{5} c d e^{2}\right)} f g^{7} - {\left(a^{5} c d^{2} e + a^{6} e^{3}\right)} g^{8}\right)} \sqrt{-\frac{c^{5} e^{2} f^{6} + 6 \, c^{5} d e f^{5} g - 20 \, a c^{4} d e f^{3} g^{3} + 6 \, a^{2} c^{3} d e f g^{5} + a^{2} c^{3} d^{2} g^{6} + 3 \, {\left(3 \, c^{5} d^{2} - 2 \, a c^{4} e^{2}\right)} f^{4} g^{2} - 3 \, {\left(2 \, a c^{4} d^{2} - 3 \, a^{2} c^{3} e^{2}\right)} f^{2} g^{4}}{{\left(a c^{8} d^{4} + 2 \, a^{2} c^{7} d^{2} e^{2} + a^{3} c^{6} e^{4}\right)} f^{12} + 6 \, {\left(a^{2} c^{7} d^{4} + 2 \, a^{3} c^{6} d^{2} e^{2} + a^{4} c^{5} e^{4}\right)} f^{10} g^{2} + 15 \, {\left(a^{3} c^{6} d^{4} + 2 \, a^{4} c^{5} d^{2} e^{2} + a^{5} c^{4} e^{4}\right)} f^{8} g^{4} + 20 \, {\left(a^{4} c^{5} d^{4} + 2 \, a^{5} c^{4} d^{2} e^{2} + a^{6} c^{3} e^{4}\right)} f^{6} g^{6} + 15 \, {\left(a^{5} c^{4} d^{4} + 2 \, a^{6} c^{3} d^{2} e^{2} + a^{7} c^{2} e^{4}\right)} f^{4} g^{8} + 6 \, {\left(a^{6} c^{3} d^{4} + 2 \, a^{7} c^{2} d^{2} e^{2} + a^{8} c e^{4}\right)} f^{2} g^{10} + {\left(a^{7} c^{2} d^{4} + 2 \, a^{8} c d^{2} e^{2} + a^{9} e^{4}\right)} g^{12}}}\right)} \sqrt{e x + d} \sqrt{g x + f} \sqrt{-\frac{c^{3} d f^{3} - 3 \, a c^{2} e f^{2} g - 3 \, a c^{2} d f g^{2} + a^{2} c e g^{3} + {\left({\left(a c^{4} d^{2} + a^{2} c^{3} e^{2}\right)} f^{6} + 3 \, {\left(a^{2} c^{3} d^{2} + a^{3} c^{2} e^{2}\right)} f^{4} g^{2} + 3 \, {\left(a^{3} c^{2} d^{2} + a^{4} c e^{2}\right)} f^{2} g^{4} + {\left(a^{4} c d^{2} + a^{5} e^{2}\right)} g^{6}\right)} \sqrt{-\frac{c^{5} e^{2} f^{6} + 6 \, c^{5} d e f^{5} g - 20 \, a c^{4} d e f^{3} g^{3} + 6 \, a^{2} c^{3} d e f g^{5} + a^{2} c^{3} d^{2} g^{6} + 3 \, {\left(3 \, c^{5} d^{2} - 2 \, a c^{4} e^{2}\right)} f^{4} g^{2} - 3 \, {\left(2 \, a c^{4} d^{2} - 3 \, a^{2} c^{3} e^{2}\right)} f^{2} g^{4}}{{\left(a c^{8} d^{4} + 2 \, a^{2} c^{7} d^{2} e^{2} + a^{3} c^{6} e^{4}\right)} f^{12} + 6 \, {\left(a^{2} c^{7} d^{4} + 2 \, a^{3} c^{6} d^{2} e^{2} + a^{4} c^{5} e^{4}\right)} f^{10} g^{2} + 15 \, {\left(a^{3} c^{6} d^{4} + 2 \, a^{4} c^{5} d^{2} e^{2} + a^{5} c^{4} e^{4}\right)} f^{8} g^{4} + 20 \, {\left(a^{4} c^{5} d^{4} + 2 \, a^{5} c^{4} d^{2} e^{2} + a^{6} c^{3} e^{4}\right)} f^{6} g^{6} + 15 \, {\left(a^{5} c^{4} d^{4} + 2 \, a^{6} c^{3} d^{2} e^{2} + a^{7} c^{2} e^{4}\right)} f^{4} g^{8} + 6 \, {\left(a^{6} c^{3} d^{4} + 2 \, a^{7} c^{2} d^{2} e^{2} + a^{8} c e^{4}\right)} f^{2} g^{10} + {\left(a^{7} c^{2} d^{4} + 2 \, a^{8} c d^{2} e^{2} + a^{9} e^{4}\right)} g^{12}}}}{{\left(a c^{4} d^{2} + a^{2} c^{3} e^{2}\right)} f^{6} + 3 \, {\left(a^{2} c^{3} d^{2} + a^{3} c^{2} e^{2}\right)} f^{4} g^{2} + 3 \, {\left(a^{3} c^{2} d^{2} + a^{4} c e^{2}\right)} f^{2} g^{4} + {\left(a^{4} c d^{2} + a^{5} e^{2}\right)} g^{6}}} + 2 \, {\left(c^{3} e^{2} f^{3} g + 3 \, c^{3} d e f^{2} g^{2} - 3 \, a c^{2} e^{2} f g^{3} - a c^{2} d e g^{4}\right)} x + {\left(2 \, {\left(c^{5} d^{3} + a c^{4} d e^{2}\right)} f^{7} + 6 \, {\left(a c^{4} d^{3} + a^{2} c^{3} d e^{2}\right)} f^{5} g^{2} + 6 \, {\left(a^{2} c^{3} d^{3} + a^{3} c^{2} d e^{2}\right)} f^{3} g^{4} + 2 \, {\left(a^{3} c^{2} d^{3} + a^{4} c d e^{2}\right)} f g^{6} + {\left({\left(c^{5} d^{2} e + a c^{4} e^{3}\right)} f^{7} + {\left(c^{5} d^{3} + a c^{4} d e^{2}\right)} f^{6} g + 3 \, {\left(a c^{4} d^{2} e + a^{2} c^{3} e^{3}\right)} f^{5} g^{2} + 3 \, {\left(a c^{4} d^{3} + a^{2} c^{3} d e^{2}\right)} f^{4} g^{3} + 3 \, {\left(a^{2} c^{3} d^{2} e + a^{3} c^{2} e^{3}\right)} f^{3} g^{4} + 3 \, {\left(a^{2} c^{3} d^{3} + a^{3} c^{2} d e^{2}\right)} f^{2} g^{5} + {\left(a^{3} c^{2} d^{2} e + a^{4} c e^{3}\right)} f g^{6} + {\left(a^{3} c^{2} d^{3} + a^{4} c d e^{2}\right)} g^{7}\right)} x\right)} \sqrt{-\frac{c^{5} e^{2} f^{6} + 6 \, c^{5} d e f^{5} g - 20 \, a c^{4} d e f^{3} g^{3} + 6 \, a^{2} c^{3} d e f g^{5} + a^{2} c^{3} d^{2} g^{6} + 3 \, {\left(3 \, c^{5} d^{2} - 2 \, a c^{4} e^{2}\right)} f^{4} g^{2} - 3 \, {\left(2 \, a c^{4} d^{2} - 3 \, a^{2} c^{3} e^{2}\right)} f^{2} g^{4}}{{\left(a c^{8} d^{4} + 2 \, a^{2} c^{7} d^{2} e^{2} + a^{3} c^{6} e^{4}\right)} f^{12} + 6 \, {\left(a^{2} c^{7} d^{4} + 2 \, a^{3} c^{6} d^{2} e^{2} + a^{4} c^{5} e^{4}\right)} f^{10} g^{2} + 15 \, {\left(a^{3} c^{6} d^{4} + 2 \, a^{4} c^{5} d^{2} e^{2} + a^{5} c^{4} e^{4}\right)} f^{8} g^{4} + 20 \, {\left(a^{4} c^{5} d^{4} + 2 \, a^{5} c^{4} d^{2} e^{2} + a^{6} c^{3} e^{4}\right)} f^{6} g^{6} + 15 \, {\left(a^{5} c^{4} d^{4} + 2 \, a^{6} c^{3} d^{2} e^{2} + a^{7} c^{2} e^{4}\right)} f^{4} g^{8} + 6 \, {\left(a^{6} c^{3} d^{4} + 2 \, a^{7} c^{2} d^{2} e^{2} + a^{8} c e^{4}\right)} f^{2} g^{10} + {\left(a^{7} c^{2} d^{4} + 2 \, a^{8} c d^{2} e^{2} + a^{9} e^{4}\right)} g^{12}}}}{x}\right) + {\left(c e f^{4} - c d f^{3} g + a e f^{2} g^{2} - a d f g^{3} + {\left(c e f^{3} g - c d f^{2} g^{2} + a e f g^{3} - a d g^{4}\right)} x\right)} \sqrt{-\frac{c^{3} d f^{3} - 3 \, a c^{2} e f^{2} g - 3 \, a c^{2} d f g^{2} + a^{2} c e g^{3} + {\left({\left(a c^{4} d^{2} + a^{2} c^{3} e^{2}\right)} f^{6} + 3 \, {\left(a^{2} c^{3} d^{2} + a^{3} c^{2} e^{2}\right)} f^{4} g^{2} + 3 \, {\left(a^{3} c^{2} d^{2} + a^{4} c e^{2}\right)} f^{2} g^{4} + {\left(a^{4} c d^{2} + a^{5} e^{2}\right)} g^{6}\right)} \sqrt{-\frac{c^{5} e^{2} f^{6} + 6 \, c^{5} d e f^{5} g - 20 \, a c^{4} d e f^{3} g^{3} + 6 \, a^{2} c^{3} d e f g^{5} + a^{2} c^{3} d^{2} g^{6} + 3 \, {\left(3 \, c^{5} d^{2} - 2 \, a c^{4} e^{2}\right)} f^{4} g^{2} - 3 \, {\left(2 \, a c^{4} d^{2} - 3 \, a^{2} c^{3} e^{2}\right)} f^{2} g^{4}}{{\left(a c^{8} d^{4} + 2 \, a^{2} c^{7} d^{2} e^{2} + a^{3} c^{6} e^{4}\right)} f^{12} + 6 \, {\left(a^{2} c^{7} d^{4} + 2 \, a^{3} c^{6} d^{2} e^{2} + a^{4} c^{5} e^{4}\right)} f^{10} g^{2} + 15 \, {\left(a^{3} c^{6} d^{4} + 2 \, a^{4} c^{5} d^{2} e^{2} + a^{5} c^{4} e^{4}\right)} f^{8} g^{4} + 20 \, {\left(a^{4} c^{5} d^{4} + 2 \, a^{5} c^{4} d^{2} e^{2} + a^{6} c^{3} e^{4}\right)} f^{6} g^{6} + 15 \, {\left(a^{5} c^{4} d^{4} + 2 \, a^{6} c^{3} d^{2} e^{2} + a^{7} c^{2} e^{4}\right)} f^{4} g^{8} + 6 \, {\left(a^{6} c^{3} d^{4} + 2 \, a^{7} c^{2} d^{2} e^{2} + a^{8} c e^{4}\right)} f^{2} g^{10} + {\left(a^{7} c^{2} d^{4} + 2 \, a^{8} c d^{2} e^{2} + a^{9} e^{4}\right)} g^{12}}}}{{\left(a c^{4} d^{2} + a^{2} c^{3} e^{2}\right)} f^{6} + 3 \, {\left(a^{2} c^{3} d^{2} + a^{3} c^{2} e^{2}\right)} f^{4} g^{2} + 3 \, {\left(a^{3} c^{2} d^{2} + a^{4} c e^{2}\right)} f^{2} g^{4} + {\left(a^{4} c d^{2} + a^{5} e^{2}\right)} g^{6}}} \log\left(-\frac{c^{3} e^{2} f^{4} + 4 \, c^{3} d e f^{3} g - 4 \, a c^{2} d e f g^{3} - a c^{2} d^{2} g^{4} + 3 \, {\left(c^{3} d^{2} - a c^{2} e^{2}\right)} f^{2} g^{2} - 2 \, {\left(c^{4} d e f^{5} - 10 \, a c^{3} d e f^{3} g^{2} + 5 \, a^{2} c^{2} d e f g^{4} + a^{2} c^{2} d^{2} g^{5} + {\left(3 \, c^{4} d^{2} - 2 \, a c^{3} e^{2}\right)} f^{4} g - 2 \, {\left(2 \, a c^{3} d^{2} - 3 \, a^{2} c^{2} e^{2}\right)} f^{2} g^{3} - {\left({\left(a c^{5} d^{2} e + a^{2} c^{4} e^{3}\right)} f^{8} + 2 \, {\left(a c^{5} d^{3} + a^{2} c^{4} d e^{2}\right)} f^{7} g + 2 \, {\left(a^{2} c^{4} d^{2} e + a^{3} c^{3} e^{3}\right)} f^{6} g^{2} + 6 \, {\left(a^{2} c^{4} d^{3} + a^{3} c^{3} d e^{2}\right)} f^{5} g^{3} + 6 \, {\left(a^{3} c^{3} d^{3} + a^{4} c^{2} d e^{2}\right)} f^{3} g^{5} - 2 \, {\left(a^{4} c^{2} d^{2} e + a^{5} c e^{3}\right)} f^{2} g^{6} + 2 \, {\left(a^{4} c^{2} d^{3} + a^{5} c d e^{2}\right)} f g^{7} - {\left(a^{5} c d^{2} e + a^{6} e^{3}\right)} g^{8}\right)} \sqrt{-\frac{c^{5} e^{2} f^{6} + 6 \, c^{5} d e f^{5} g - 20 \, a c^{4} d e f^{3} g^{3} + 6 \, a^{2} c^{3} d e f g^{5} + a^{2} c^{3} d^{2} g^{6} + 3 \, {\left(3 \, c^{5} d^{2} - 2 \, a c^{4} e^{2}\right)} f^{4} g^{2} - 3 \, {\left(2 \, a c^{4} d^{2} - 3 \, a^{2} c^{3} e^{2}\right)} f^{2} g^{4}}{{\left(a c^{8} d^{4} + 2 \, a^{2} c^{7} d^{2} e^{2} + a^{3} c^{6} e^{4}\right)} f^{12} + 6 \, {\left(a^{2} c^{7} d^{4} + 2 \, a^{3} c^{6} d^{2} e^{2} + a^{4} c^{5} e^{4}\right)} f^{10} g^{2} + 15 \, {\left(a^{3} c^{6} d^{4} + 2 \, a^{4} c^{5} d^{2} e^{2} + a^{5} c^{4} e^{4}\right)} f^{8} g^{4} + 20 \, {\left(a^{4} c^{5} d^{4} + 2 \, a^{5} c^{4} d^{2} e^{2} + a^{6} c^{3} e^{4}\right)} f^{6} g^{6} + 15 \, {\left(a^{5} c^{4} d^{4} + 2 \, a^{6} c^{3} d^{2} e^{2} + a^{7} c^{2} e^{4}\right)} f^{4} g^{8} + 6 \, {\left(a^{6} c^{3} d^{4} + 2 \, a^{7} c^{2} d^{2} e^{2} + a^{8} c e^{4}\right)} f^{2} g^{10} + {\left(a^{7} c^{2} d^{4} + 2 \, a^{8} c d^{2} e^{2} + a^{9} e^{4}\right)} g^{12}}}\right)} \sqrt{e x + d} \sqrt{g x + f} \sqrt{-\frac{c^{3} d f^{3} - 3 \, a c^{2} e f^{2} g - 3 \, a c^{2} d f g^{2} + a^{2} c e g^{3} + {\left({\left(a c^{4} d^{2} + a^{2} c^{3} e^{2}\right)} f^{6} + 3 \, {\left(a^{2} c^{3} d^{2} + a^{3} c^{2} e^{2}\right)} f^{4} g^{2} + 3 \, {\left(a^{3} c^{2} d^{2} + a^{4} c e^{2}\right)} f^{2} g^{4} + {\left(a^{4} c d^{2} + a^{5} e^{2}\right)} g^{6}\right)} \sqrt{-\frac{c^{5} e^{2} f^{6} + 6 \, c^{5} d e f^{5} g - 20 \, a c^{4} d e f^{3} g^{3} + 6 \, a^{2} c^{3} d e f g^{5} + a^{2} c^{3} d^{2} g^{6} + 3 \, {\left(3 \, c^{5} d^{2} - 2 \, a c^{4} e^{2}\right)} f^{4} g^{2} - 3 \, {\left(2 \, a c^{4} d^{2} - 3 \, a^{2} c^{3} e^{2}\right)} f^{2} g^{4}}{{\left(a c^{8} d^{4} + 2 \, a^{2} c^{7} d^{2} e^{2} + a^{3} c^{6} e^{4}\right)} f^{12} + 6 \, {\left(a^{2} c^{7} d^{4} + 2 \, a^{3} c^{6} d^{2} e^{2} + a^{4} c^{5} e^{4}\right)} f^{10} g^{2} + 15 \, {\left(a^{3} c^{6} d^{4} + 2 \, a^{4} c^{5} d^{2} e^{2} + a^{5} c^{4} e^{4}\right)} f^{8} g^{4} + 20 \, {\left(a^{4} c^{5} d^{4} + 2 \, a^{5} c^{4} d^{2} e^{2} + a^{6} c^{3} e^{4}\right)} f^{6} g^{6} + 15 \, {\left(a^{5} c^{4} d^{4} + 2 \, a^{6} c^{3} d^{2} e^{2} + a^{7} c^{2} e^{4}\right)} f^{4} g^{8} + 6 \, {\left(a^{6} c^{3} d^{4} + 2 \, a^{7} c^{2} d^{2} e^{2} + a^{8} c e^{4}\right)} f^{2} g^{10} + {\left(a^{7} c^{2} d^{4} + 2 \, a^{8} c d^{2} e^{2} + a^{9} e^{4}\right)} g^{12}}}}{{\left(a c^{4} d^{2} + a^{2} c^{3} e^{2}\right)} f^{6} + 3 \, {\left(a^{2} c^{3} d^{2} + a^{3} c^{2} e^{2}\right)} f^{4} g^{2} + 3 \, {\left(a^{3} c^{2} d^{2} + a^{4} c e^{2}\right)} f^{2} g^{4} + {\left(a^{4} c d^{2} + a^{5} e^{2}\right)} g^{6}}} + 2 \, {\left(c^{3} e^{2} f^{3} g + 3 \, c^{3} d e f^{2} g^{2} - 3 \, a c^{2} e^{2} f g^{3} - a c^{2} d e g^{4}\right)} x + {\left(2 \, {\left(c^{5} d^{3} + a c^{4} d e^{2}\right)} f^{7} + 6 \, {\left(a c^{4} d^{3} + a^{2} c^{3} d e^{2}\right)} f^{5} g^{2} + 6 \, {\left(a^{2} c^{3} d^{3} + a^{3} c^{2} d e^{2}\right)} f^{3} g^{4} + 2 \, {\left(a^{3} c^{2} d^{3} + a^{4} c d e^{2}\right)} f g^{6} + {\left({\left(c^{5} d^{2} e + a c^{4} e^{3}\right)} f^{7} + {\left(c^{5} d^{3} + a c^{4} d e^{2}\right)} f^{6} g + 3 \, {\left(a c^{4} d^{2} e + a^{2} c^{3} e^{3}\right)} f^{5} g^{2} + 3 \, {\left(a c^{4} d^{3} + a^{2} c^{3} d e^{2}\right)} f^{4} g^{3} + 3 \, {\left(a^{2} c^{3} d^{2} e + a^{3} c^{2} e^{3}\right)} f^{3} g^{4} + 3 \, {\left(a^{2} c^{3} d^{3} + a^{3} c^{2} d e^{2}\right)} f^{2} g^{5} + {\left(a^{3} c^{2} d^{2} e + a^{4} c e^{3}\right)} f g^{6} + {\left(a^{3} c^{2} d^{3} + a^{4} c d e^{2}\right)} g^{7}\right)} x\right)} \sqrt{-\frac{c^{5} e^{2} f^{6} + 6 \, c^{5} d e f^{5} g - 20 \, a c^{4} d e f^{3} g^{3} + 6 \, a^{2} c^{3} d e f g^{5} + a^{2} c^{3} d^{2} g^{6} + 3 \, {\left(3 \, c^{5} d^{2} - 2 \, a c^{4} e^{2}\right)} f^{4} g^{2} - 3 \, {\left(2 \, a c^{4} d^{2} - 3 \, a^{2} c^{3} e^{2}\right)} f^{2} g^{4}}{{\left(a c^{8} d^{4} + 2 \, a^{2} c^{7} d^{2} e^{2} + a^{3} c^{6} e^{4}\right)} f^{12} + 6 \, {\left(a^{2} c^{7} d^{4} + 2 \, a^{3} c^{6} d^{2} e^{2} + a^{4} c^{5} e^{4}\right)} f^{10} g^{2} + 15 \, {\left(a^{3} c^{6} d^{4} + 2 \, a^{4} c^{5} d^{2} e^{2} + a^{5} c^{4} e^{4}\right)} f^{8} g^{4} + 20 \, {\left(a^{4} c^{5} d^{4} + 2 \, a^{5} c^{4} d^{2} e^{2} + a^{6} c^{3} e^{4}\right)} f^{6} g^{6} + 15 \, {\left(a^{5} c^{4} d^{4} + 2 \, a^{6} c^{3} d^{2} e^{2} + a^{7} c^{2} e^{4}\right)} f^{4} g^{8} + 6 \, {\left(a^{6} c^{3} d^{4} + 2 \, a^{7} c^{2} d^{2} e^{2} + a^{8} c e^{4}\right)} f^{2} g^{10} + {\left(a^{7} c^{2} d^{4} + 2 \, a^{8} c d^{2} e^{2} + a^{9} e^{4}\right)} g^{12}}}}{x}\right) - {\left(c e f^{4} - c d f^{3} g + a e f^{2} g^{2} - a d f g^{3} + {\left(c e f^{3} g - c d f^{2} g^{2} + a e f g^{3} - a d g^{4}\right)} x\right)} \sqrt{-\frac{c^{3} d f^{3} - 3 \, a c^{2} e f^{2} g - 3 \, a c^{2} d f g^{2} + a^{2} c e g^{3} - {\left({\left(a c^{4} d^{2} + a^{2} c^{3} e^{2}\right)} f^{6} + 3 \, {\left(a^{2} c^{3} d^{2} + a^{3} c^{2} e^{2}\right)} f^{4} g^{2} + 3 \, {\left(a^{3} c^{2} d^{2} + a^{4} c e^{2}\right)} f^{2} g^{4} + {\left(a^{4} c d^{2} + a^{5} e^{2}\right)} g^{6}\right)} \sqrt{-\frac{c^{5} e^{2} f^{6} + 6 \, c^{5} d e f^{5} g - 20 \, a c^{4} d e f^{3} g^{3} + 6 \, a^{2} c^{3} d e f g^{5} + a^{2} c^{3} d^{2} g^{6} + 3 \, {\left(3 \, c^{5} d^{2} - 2 \, a c^{4} e^{2}\right)} f^{4} g^{2} - 3 \, {\left(2 \, a c^{4} d^{2} - 3 \, a^{2} c^{3} e^{2}\right)} f^{2} g^{4}}{{\left(a c^{8} d^{4} + 2 \, a^{2} c^{7} d^{2} e^{2} + a^{3} c^{6} e^{4}\right)} f^{12} + 6 \, {\left(a^{2} c^{7} d^{4} + 2 \, a^{3} c^{6} d^{2} e^{2} + a^{4} c^{5} e^{4}\right)} f^{10} g^{2} + 15 \, {\left(a^{3} c^{6} d^{4} + 2 \, a^{4} c^{5} d^{2} e^{2} + a^{5} c^{4} e^{4}\right)} f^{8} g^{4} + 20 \, {\left(a^{4} c^{5} d^{4} + 2 \, a^{5} c^{4} d^{2} e^{2} + a^{6} c^{3} e^{4}\right)} f^{6} g^{6} + 15 \, {\left(a^{5} c^{4} d^{4} + 2 \, a^{6} c^{3} d^{2} e^{2} + a^{7} c^{2} e^{4}\right)} f^{4} g^{8} + 6 \, {\left(a^{6} c^{3} d^{4} + 2 \, a^{7} c^{2} d^{2} e^{2} + a^{8} c e^{4}\right)} f^{2} g^{10} + {\left(a^{7} c^{2} d^{4} + 2 \, a^{8} c d^{2} e^{2} + a^{9} e^{4}\right)} g^{12}}}}{{\left(a c^{4} d^{2} + a^{2} c^{3} e^{2}\right)} f^{6} + 3 \, {\left(a^{2} c^{3} d^{2} + a^{3} c^{2} e^{2}\right)} f^{4} g^{2} + 3 \, {\left(a^{3} c^{2} d^{2} + a^{4} c e^{2}\right)} f^{2} g^{4} + {\left(a^{4} c d^{2} + a^{5} e^{2}\right)} g^{6}}} \log\left(-\frac{c^{3} e^{2} f^{4} + 4 \, c^{3} d e f^{3} g - 4 \, a c^{2} d e f g^{3} - a c^{2} d^{2} g^{4} + 3 \, {\left(c^{3} d^{2} - a c^{2} e^{2}\right)} f^{2} g^{2} + 2 \, {\left(c^{4} d e f^{5} - 10 \, a c^{3} d e f^{3} g^{2} + 5 \, a^{2} c^{2} d e f g^{4} + a^{2} c^{2} d^{2} g^{5} + {\left(3 \, c^{4} d^{2} - 2 \, a c^{3} e^{2}\right)} f^{4} g - 2 \, {\left(2 \, a c^{3} d^{2} - 3 \, a^{2} c^{2} e^{2}\right)} f^{2} g^{3} + {\left({\left(a c^{5} d^{2} e + a^{2} c^{4} e^{3}\right)} f^{8} + 2 \, {\left(a c^{5} d^{3} + a^{2} c^{4} d e^{2}\right)} f^{7} g + 2 \, {\left(a^{2} c^{4} d^{2} e + a^{3} c^{3} e^{3}\right)} f^{6} g^{2} + 6 \, {\left(a^{2} c^{4} d^{3} + a^{3} c^{3} d e^{2}\right)} f^{5} g^{3} + 6 \, {\left(a^{3} c^{3} d^{3} + a^{4} c^{2} d e^{2}\right)} f^{3} g^{5} - 2 \, {\left(a^{4} c^{2} d^{2} e + a^{5} c e^{3}\right)} f^{2} g^{6} + 2 \, {\left(a^{4} c^{2} d^{3} + a^{5} c d e^{2}\right)} f g^{7} - {\left(a^{5} c d^{2} e + a^{6} e^{3}\right)} g^{8}\right)} \sqrt{-\frac{c^{5} e^{2} f^{6} + 6 \, c^{5} d e f^{5} g - 20 \, a c^{4} d e f^{3} g^{3} + 6 \, a^{2} c^{3} d e f g^{5} + a^{2} c^{3} d^{2} g^{6} + 3 \, {\left(3 \, c^{5} d^{2} - 2 \, a c^{4} e^{2}\right)} f^{4} g^{2} - 3 \, {\left(2 \, a c^{4} d^{2} - 3 \, a^{2} c^{3} e^{2}\right)} f^{2} g^{4}}{{\left(a c^{8} d^{4} + 2 \, a^{2} c^{7} d^{2} e^{2} + a^{3} c^{6} e^{4}\right)} f^{12} + 6 \, {\left(a^{2} c^{7} d^{4} + 2 \, a^{3} c^{6} d^{2} e^{2} + a^{4} c^{5} e^{4}\right)} f^{10} g^{2} + 15 \, {\left(a^{3} c^{6} d^{4} + 2 \, a^{4} c^{5} d^{2} e^{2} + a^{5} c^{4} e^{4}\right)} f^{8} g^{4} + 20 \, {\left(a^{4} c^{5} d^{4} + 2 \, a^{5} c^{4} d^{2} e^{2} + a^{6} c^{3} e^{4}\right)} f^{6} g^{6} + 15 \, {\left(a^{5} c^{4} d^{4} + 2 \, a^{6} c^{3} d^{2} e^{2} + a^{7} c^{2} e^{4}\right)} f^{4} g^{8} + 6 \, {\left(a^{6} c^{3} d^{4} + 2 \, a^{7} c^{2} d^{2} e^{2} + a^{8} c e^{4}\right)} f^{2} g^{10} + {\left(a^{7} c^{2} d^{4} + 2 \, a^{8} c d^{2} e^{2} + a^{9} e^{4}\right)} g^{12}}}\right)} \sqrt{e x + d} \sqrt{g x + f} \sqrt{-\frac{c^{3} d f^{3} - 3 \, a c^{2} e f^{2} g - 3 \, a c^{2} d f g^{2} + a^{2} c e g^{3} - {\left({\left(a c^{4} d^{2} + a^{2} c^{3} e^{2}\right)} f^{6} + 3 \, {\left(a^{2} c^{3} d^{2} + a^{3} c^{2} e^{2}\right)} f^{4} g^{2} + 3 \, {\left(a^{3} c^{2} d^{2} + a^{4} c e^{2}\right)} f^{2} g^{4} + {\left(a^{4} c d^{2} + a^{5} e^{2}\right)} g^{6}\right)} \sqrt{-\frac{c^{5} e^{2} f^{6} + 6 \, c^{5} d e f^{5} g - 20 \, a c^{4} d e f^{3} g^{3} + 6 \, a^{2} c^{3} d e f g^{5} + a^{2} c^{3} d^{2} g^{6} + 3 \, {\left(3 \, c^{5} d^{2} - 2 \, a c^{4} e^{2}\right)} f^{4} g^{2} - 3 \, {\left(2 \, a c^{4} d^{2} - 3 \, a^{2} c^{3} e^{2}\right)} f^{2} g^{4}}{{\left(a c^{8} d^{4} + 2 \, a^{2} c^{7} d^{2} e^{2} + a^{3} c^{6} e^{4}\right)} f^{12} + 6 \, {\left(a^{2} c^{7} d^{4} + 2 \, a^{3} c^{6} d^{2} e^{2} + a^{4} c^{5} e^{4}\right)} f^{10} g^{2} + 15 \, {\left(a^{3} c^{6} d^{4} + 2 \, a^{4} c^{5} d^{2} e^{2} + a^{5} c^{4} e^{4}\right)} f^{8} g^{4} + 20 \, {\left(a^{4} c^{5} d^{4} + 2 \, a^{5} c^{4} d^{2} e^{2} + a^{6} c^{3} e^{4}\right)} f^{6} g^{6} + 15 \, {\left(a^{5} c^{4} d^{4} + 2 \, a^{6} c^{3} d^{2} e^{2} + a^{7} c^{2} e^{4}\right)} f^{4} g^{8} + 6 \, {\left(a^{6} c^{3} d^{4} + 2 \, a^{7} c^{2} d^{2} e^{2} + a^{8} c e^{4}\right)} f^{2} g^{10} + {\left(a^{7} c^{2} d^{4} + 2 \, a^{8} c d^{2} e^{2} + a^{9} e^{4}\right)} g^{12}}}}{{\left(a c^{4} d^{2} + a^{2} c^{3} e^{2}\right)} f^{6} + 3 \, {\left(a^{2} c^{3} d^{2} + a^{3} c^{2} e^{2}\right)} f^{4} g^{2} + 3 \, {\left(a^{3} c^{2} d^{2} + a^{4} c e^{2}\right)} f^{2} g^{4} + {\left(a^{4} c d^{2} + a^{5} e^{2}\right)} g^{6}}} + 2 \, {\left(c^{3} e^{2} f^{3} g + 3 \, c^{3} d e f^{2} g^{2} - 3 \, a c^{2} e^{2} f g^{3} - a c^{2} d e g^{4}\right)} x - {\left(2 \, {\left(c^{5} d^{3} + a c^{4} d e^{2}\right)} f^{7} + 6 \, {\left(a c^{4} d^{3} + a^{2} c^{3} d e^{2}\right)} f^{5} g^{2} + 6 \, {\left(a^{2} c^{3} d^{3} + a^{3} c^{2} d e^{2}\right)} f^{3} g^{4} + 2 \, {\left(a^{3} c^{2} d^{3} + a^{4} c d e^{2}\right)} f g^{6} + {\left({\left(c^{5} d^{2} e + a c^{4} e^{3}\right)} f^{7} + {\left(c^{5} d^{3} + a c^{4} d e^{2}\right)} f^{6} g + 3 \, {\left(a c^{4} d^{2} e + a^{2} c^{3} e^{3}\right)} f^{5} g^{2} + 3 \, {\left(a c^{4} d^{3} + a^{2} c^{3} d e^{2}\right)} f^{4} g^{3} + 3 \, {\left(a^{2} c^{3} d^{2} e + a^{3} c^{2} e^{3}\right)} f^{3} g^{4} + 3 \, {\left(a^{2} c^{3} d^{3} + a^{3} c^{2} d e^{2}\right)} f^{2} g^{5} + {\left(a^{3} c^{2} d^{2} e + a^{4} c e^{3}\right)} f g^{6} + {\left(a^{3} c^{2} d^{3} + a^{4} c d e^{2}\right)} g^{7}\right)} x\right)} \sqrt{-\frac{c^{5} e^{2} f^{6} + 6 \, c^{5} d e f^{5} g - 20 \, a c^{4} d e f^{3} g^{3} + 6 \, a^{2} c^{3} d e f g^{5} + a^{2} c^{3} d^{2} g^{6} + 3 \, {\left(3 \, c^{5} d^{2} - 2 \, a c^{4} e^{2}\right)} f^{4} g^{2} - 3 \, {\left(2 \, a c^{4} d^{2} - 3 \, a^{2} c^{3} e^{2}\right)} f^{2} g^{4}}{{\left(a c^{8} d^{4} + 2 \, a^{2} c^{7} d^{2} e^{2} + a^{3} c^{6} e^{4}\right)} f^{12} + 6 \, {\left(a^{2} c^{7} d^{4} + 2 \, a^{3} c^{6} d^{2} e^{2} + a^{4} c^{5} e^{4}\right)} f^{10} g^{2} + 15 \, {\left(a^{3} c^{6} d^{4} + 2 \, a^{4} c^{5} d^{2} e^{2} + a^{5} c^{4} e^{4}\right)} f^{8} g^{4} + 20 \, {\left(a^{4} c^{5} d^{4} + 2 \, a^{5} c^{4} d^{2} e^{2} + a^{6} c^{3} e^{4}\right)} f^{6} g^{6} + 15 \, {\left(a^{5} c^{4} d^{4} + 2 \, a^{6} c^{3} d^{2} e^{2} + a^{7} c^{2} e^{4}\right)} f^{4} g^{8} + 6 \, {\left(a^{6} c^{3} d^{4} + 2 \, a^{7} c^{2} d^{2} e^{2} + a^{8} c e^{4}\right)} f^{2} g^{10} + {\left(a^{7} c^{2} d^{4} + 2 \, a^{8} c d^{2} e^{2} + a^{9} e^{4}\right)} g^{12}}}}{x}\right) + {\left(c e f^{4} - c d f^{3} g + a e f^{2} g^{2} - a d f g^{3} + {\left(c e f^{3} g - c d f^{2} g^{2} + a e f g^{3} - a d g^{4}\right)} x\right)} \sqrt{-\frac{c^{3} d f^{3} - 3 \, a c^{2} e f^{2} g - 3 \, a c^{2} d f g^{2} + a^{2} c e g^{3} - {\left({\left(a c^{4} d^{2} + a^{2} c^{3} e^{2}\right)} f^{6} + 3 \, {\left(a^{2} c^{3} d^{2} + a^{3} c^{2} e^{2}\right)} f^{4} g^{2} + 3 \, {\left(a^{3} c^{2} d^{2} + a^{4} c e^{2}\right)} f^{2} g^{4} + {\left(a^{4} c d^{2} + a^{5} e^{2}\right)} g^{6}\right)} \sqrt{-\frac{c^{5} e^{2} f^{6} + 6 \, c^{5} d e f^{5} g - 20 \, a c^{4} d e f^{3} g^{3} + 6 \, a^{2} c^{3} d e f g^{5} + a^{2} c^{3} d^{2} g^{6} + 3 \, {\left(3 \, c^{5} d^{2} - 2 \, a c^{4} e^{2}\right)} f^{4} g^{2} - 3 \, {\left(2 \, a c^{4} d^{2} - 3 \, a^{2} c^{3} e^{2}\right)} f^{2} g^{4}}{{\left(a c^{8} d^{4} + 2 \, a^{2} c^{7} d^{2} e^{2} + a^{3} c^{6} e^{4}\right)} f^{12} + 6 \, {\left(a^{2} c^{7} d^{4} + 2 \, a^{3} c^{6} d^{2} e^{2} + a^{4} c^{5} e^{4}\right)} f^{10} g^{2} + 15 \, {\left(a^{3} c^{6} d^{4} + 2 \, a^{4} c^{5} d^{2} e^{2} + a^{5} c^{4} e^{4}\right)} f^{8} g^{4} + 20 \, {\left(a^{4} c^{5} d^{4} + 2 \, a^{5} c^{4} d^{2} e^{2} + a^{6} c^{3} e^{4}\right)} f^{6} g^{6} + 15 \, {\left(a^{5} c^{4} d^{4} + 2 \, a^{6} c^{3} d^{2} e^{2} + a^{7} c^{2} e^{4}\right)} f^{4} g^{8} + 6 \, {\left(a^{6} c^{3} d^{4} + 2 \, a^{7} c^{2} d^{2} e^{2} + a^{8} c e^{4}\right)} f^{2} g^{10} + {\left(a^{7} c^{2} d^{4} + 2 \, a^{8} c d^{2} e^{2} + a^{9} e^{4}\right)} g^{12}}}}{{\left(a c^{4} d^{2} + a^{2} c^{3} e^{2}\right)} f^{6} + 3 \, {\left(a^{2} c^{3} d^{2} + a^{3} c^{2} e^{2}\right)} f^{4} g^{2} + 3 \, {\left(a^{3} c^{2} d^{2} + a^{4} c e^{2}\right)} f^{2} g^{4} + {\left(a^{4} c d^{2} + a^{5} e^{2}\right)} g^{6}}} \log\left(-\frac{c^{3} e^{2} f^{4} + 4 \, c^{3} d e f^{3} g - 4 \, a c^{2} d e f g^{3} - a c^{2} d^{2} g^{4} + 3 \, {\left(c^{3} d^{2} - a c^{2} e^{2}\right)} f^{2} g^{2} - 2 \, {\left(c^{4} d e f^{5} - 10 \, a c^{3} d e f^{3} g^{2} + 5 \, a^{2} c^{2} d e f g^{4} + a^{2} c^{2} d^{2} g^{5} + {\left(3 \, c^{4} d^{2} - 2 \, a c^{3} e^{2}\right)} f^{4} g - 2 \, {\left(2 \, a c^{3} d^{2} - 3 \, a^{2} c^{2} e^{2}\right)} f^{2} g^{3} + {\left({\left(a c^{5} d^{2} e + a^{2} c^{4} e^{3}\right)} f^{8} + 2 \, {\left(a c^{5} d^{3} + a^{2} c^{4} d e^{2}\right)} f^{7} g + 2 \, {\left(a^{2} c^{4} d^{2} e + a^{3} c^{3} e^{3}\right)} f^{6} g^{2} + 6 \, {\left(a^{2} c^{4} d^{3} + a^{3} c^{3} d e^{2}\right)} f^{5} g^{3} + 6 \, {\left(a^{3} c^{3} d^{3} + a^{4} c^{2} d e^{2}\right)} f^{3} g^{5} - 2 \, {\left(a^{4} c^{2} d^{2} e + a^{5} c e^{3}\right)} f^{2} g^{6} + 2 \, {\left(a^{4} c^{2} d^{3} + a^{5} c d e^{2}\right)} f g^{7} - {\left(a^{5} c d^{2} e + a^{6} e^{3}\right)} g^{8}\right)} \sqrt{-\frac{c^{5} e^{2} f^{6} + 6 \, c^{5} d e f^{5} g - 20 \, a c^{4} d e f^{3} g^{3} + 6 \, a^{2} c^{3} d e f g^{5} + a^{2} c^{3} d^{2} g^{6} + 3 \, {\left(3 \, c^{5} d^{2} - 2 \, a c^{4} e^{2}\right)} f^{4} g^{2} - 3 \, {\left(2 \, a c^{4} d^{2} - 3 \, a^{2} c^{3} e^{2}\right)} f^{2} g^{4}}{{\left(a c^{8} d^{4} + 2 \, a^{2} c^{7} d^{2} e^{2} + a^{3} c^{6} e^{4}\right)} f^{12} + 6 \, {\left(a^{2} c^{7} d^{4} + 2 \, a^{3} c^{6} d^{2} e^{2} + a^{4} c^{5} e^{4}\right)} f^{10} g^{2} + 15 \, {\left(a^{3} c^{6} d^{4} + 2 \, a^{4} c^{5} d^{2} e^{2} + a^{5} c^{4} e^{4}\right)} f^{8} g^{4} + 20 \, {\left(a^{4} c^{5} d^{4} + 2 \, a^{5} c^{4} d^{2} e^{2} + a^{6} c^{3} e^{4}\right)} f^{6} g^{6} + 15 \, {\left(a^{5} c^{4} d^{4} + 2 \, a^{6} c^{3} d^{2} e^{2} + a^{7} c^{2} e^{4}\right)} f^{4} g^{8} + 6 \, {\left(a^{6} c^{3} d^{4} + 2 \, a^{7} c^{2} d^{2} e^{2} + a^{8} c e^{4}\right)} f^{2} g^{10} + {\left(a^{7} c^{2} d^{4} + 2 \, a^{8} c d^{2} e^{2} + a^{9} e^{4}\right)} g^{12}}}\right)} \sqrt{e x + d} \sqrt{g x + f} \sqrt{-\frac{c^{3} d f^{3} - 3 \, a c^{2} e f^{2} g - 3 \, a c^{2} d f g^{2} + a^{2} c e g^{3} - {\left({\left(a c^{4} d^{2} + a^{2} c^{3} e^{2}\right)} f^{6} + 3 \, {\left(a^{2} c^{3} d^{2} + a^{3} c^{2} e^{2}\right)} f^{4} g^{2} + 3 \, {\left(a^{3} c^{2} d^{2} + a^{4} c e^{2}\right)} f^{2} g^{4} + {\left(a^{4} c d^{2} + a^{5} e^{2}\right)} g^{6}\right)} \sqrt{-\frac{c^{5} e^{2} f^{6} + 6 \, c^{5} d e f^{5} g - 20 \, a c^{4} d e f^{3} g^{3} + 6 \, a^{2} c^{3} d e f g^{5} + a^{2} c^{3} d^{2} g^{6} + 3 \, {\left(3 \, c^{5} d^{2} - 2 \, a c^{4} e^{2}\right)} f^{4} g^{2} - 3 \, {\left(2 \, a c^{4} d^{2} - 3 \, a^{2} c^{3} e^{2}\right)} f^{2} g^{4}}{{\left(a c^{8} d^{4} + 2 \, a^{2} c^{7} d^{2} e^{2} + a^{3} c^{6} e^{4}\right)} f^{12} + 6 \, {\left(a^{2} c^{7} d^{4} + 2 \, a^{3} c^{6} d^{2} e^{2} + a^{4} c^{5} e^{4}\right)} f^{10} g^{2} + 15 \, {\left(a^{3} c^{6} d^{4} + 2 \, a^{4} c^{5} d^{2} e^{2} + a^{5} c^{4} e^{4}\right)} f^{8} g^{4} + 20 \, {\left(a^{4} c^{5} d^{4} + 2 \, a^{5} c^{4} d^{2} e^{2} + a^{6} c^{3} e^{4}\right)} f^{6} g^{6} + 15 \, {\left(a^{5} c^{4} d^{4} + 2 \, a^{6} c^{3} d^{2} e^{2} + a^{7} c^{2} e^{4}\right)} f^{4} g^{8} + 6 \, {\left(a^{6} c^{3} d^{4} + 2 \, a^{7} c^{2} d^{2} e^{2} + a^{8} c e^{4}\right)} f^{2} g^{10} + {\left(a^{7} c^{2} d^{4} + 2 \, a^{8} c d^{2} e^{2} + a^{9} e^{4}\right)} g^{12}}}}{{\left(a c^{4} d^{2} + a^{2} c^{3} e^{2}\right)} f^{6} + 3 \, {\left(a^{2} c^{3} d^{2} + a^{3} c^{2} e^{2}\right)} f^{4} g^{2} + 3 \, {\left(a^{3} c^{2} d^{2} + a^{4} c e^{2}\right)} f^{2} g^{4} + {\left(a^{4} c d^{2} + a^{5} e^{2}\right)} g^{6}}} + 2 \, {\left(c^{3} e^{2} f^{3} g + 3 \, c^{3} d e f^{2} g^{2} - 3 \, a c^{2} e^{2} f g^{3} - a c^{2} d e g^{4}\right)} x - {\left(2 \, {\left(c^{5} d^{3} + a c^{4} d e^{2}\right)} f^{7} + 6 \, {\left(a c^{4} d^{3} + a^{2} c^{3} d e^{2}\right)} f^{5} g^{2} + 6 \, {\left(a^{2} c^{3} d^{3} + a^{3} c^{2} d e^{2}\right)} f^{3} g^{4} + 2 \, {\left(a^{3} c^{2} d^{3} + a^{4} c d e^{2}\right)} f g^{6} + {\left({\left(c^{5} d^{2} e + a c^{4} e^{3}\right)} f^{7} + {\left(c^{5} d^{3} + a c^{4} d e^{2}\right)} f^{6} g + 3 \, {\left(a c^{4} d^{2} e + a^{2} c^{3} e^{3}\right)} f^{5} g^{2} + 3 \, {\left(a c^{4} d^{3} + a^{2} c^{3} d e^{2}\right)} f^{4} g^{3} + 3 \, {\left(a^{2} c^{3} d^{2} e + a^{3} c^{2} e^{3}\right)} f^{3} g^{4} + 3 \, {\left(a^{2} c^{3} d^{3} + a^{3} c^{2} d e^{2}\right)} f^{2} g^{5} + {\left(a^{3} c^{2} d^{2} e + a^{4} c e^{3}\right)} f g^{6} + {\left(a^{3} c^{2} d^{3} + a^{4} c d e^{2}\right)} g^{7}\right)} x\right)} \sqrt{-\frac{c^{5} e^{2} f^{6} + 6 \, c^{5} d e f^{5} g - 20 \, a c^{4} d e f^{3} g^{3} + 6 \, a^{2} c^{3} d e f g^{5} + a^{2} c^{3} d^{2} g^{6} + 3 \, {\left(3 \, c^{5} d^{2} - 2 \, a c^{4} e^{2}\right)} f^{4} g^{2} - 3 \, {\left(2 \, a c^{4} d^{2} - 3 \, a^{2} c^{3} e^{2}\right)} f^{2} g^{4}}{{\left(a c^{8} d^{4} + 2 \, a^{2} c^{7} d^{2} e^{2} + a^{3} c^{6} e^{4}\right)} f^{12} + 6 \, {\left(a^{2} c^{7} d^{4} + 2 \, a^{3} c^{6} d^{2} e^{2} + a^{4} c^{5} e^{4}\right)} f^{10} g^{2} + 15 \, {\left(a^{3} c^{6} d^{4} + 2 \, a^{4} c^{5} d^{2} e^{2} + a^{5} c^{4} e^{4}\right)} f^{8} g^{4} + 20 \, {\left(a^{4} c^{5} d^{4} + 2 \, a^{5} c^{4} d^{2} e^{2} + a^{6} c^{3} e^{4}\right)} f^{6} g^{6} + 15 \, {\left(a^{5} c^{4} d^{4} + 2 \, a^{6} c^{3} d^{2} e^{2} + a^{7} c^{2} e^{4}\right)} f^{4} g^{8} + 6 \, {\left(a^{6} c^{3} d^{4} + 2 \, a^{7} c^{2} d^{2} e^{2} + a^{8} c e^{4}\right)} f^{2} g^{10} + {\left(a^{7} c^{2} d^{4} + 2 \, a^{8} c d^{2} e^{2} + a^{9} e^{4}\right)} g^{12}}}}{x}\right)}{4 \, {\left(c e f^{4} - c d f^{3} g + a e f^{2} g^{2} - a d f g^{3} + {\left(c e f^{3} g - c d f^{2} g^{2} + a e f g^{3} - a d g^{4}\right)} x\right)}}"," ",0,"1/4*(8*sqrt(e*x + d)*sqrt(g*x + f)*g^2 - (c*e*f^4 - c*d*f^3*g + a*e*f^2*g^2 - a*d*f*g^3 + (c*e*f^3*g - c*d*f^2*g^2 + a*e*f*g^3 - a*d*g^4)*x)*sqrt(-(c^3*d*f^3 - 3*a*c^2*e*f^2*g - 3*a*c^2*d*f*g^2 + a^2*c*e*g^3 + ((a*c^4*d^2 + a^2*c^3*e^2)*f^6 + 3*(a^2*c^3*d^2 + a^3*c^2*e^2)*f^4*g^2 + 3*(a^3*c^2*d^2 + a^4*c*e^2)*f^2*g^4 + (a^4*c*d^2 + a^5*e^2)*g^6)*sqrt(-(c^5*e^2*f^6 + 6*c^5*d*e*f^5*g - 20*a*c^4*d*e*f^3*g^3 + 6*a^2*c^3*d*e*f*g^5 + a^2*c^3*d^2*g^6 + 3*(3*c^5*d^2 - 2*a*c^4*e^2)*f^4*g^2 - 3*(2*a*c^4*d^2 - 3*a^2*c^3*e^2)*f^2*g^4)/((a*c^8*d^4 + 2*a^2*c^7*d^2*e^2 + a^3*c^6*e^4)*f^12 + 6*(a^2*c^7*d^4 + 2*a^3*c^6*d^2*e^2 + a^4*c^5*e^4)*f^10*g^2 + 15*(a^3*c^6*d^4 + 2*a^4*c^5*d^2*e^2 + a^5*c^4*e^4)*f^8*g^4 + 20*(a^4*c^5*d^4 + 2*a^5*c^4*d^2*e^2 + a^6*c^3*e^4)*f^6*g^6 + 15*(a^5*c^4*d^4 + 2*a^6*c^3*d^2*e^2 + a^7*c^2*e^4)*f^4*g^8 + 6*(a^6*c^3*d^4 + 2*a^7*c^2*d^2*e^2 + a^8*c*e^4)*f^2*g^10 + (a^7*c^2*d^4 + 2*a^8*c*d^2*e^2 + a^9*e^4)*g^12)))/((a*c^4*d^2 + a^2*c^3*e^2)*f^6 + 3*(a^2*c^3*d^2 + a^3*c^2*e^2)*f^4*g^2 + 3*(a^3*c^2*d^2 + a^4*c*e^2)*f^2*g^4 + (a^4*c*d^2 + a^5*e^2)*g^6))*log(-(c^3*e^2*f^4 + 4*c^3*d*e*f^3*g - 4*a*c^2*d*e*f*g^3 - a*c^2*d^2*g^4 + 3*(c^3*d^2 - a*c^2*e^2)*f^2*g^2 + 2*(c^4*d*e*f^5 - 10*a*c^3*d*e*f^3*g^2 + 5*a^2*c^2*d*e*f*g^4 + a^2*c^2*d^2*g^5 + (3*c^4*d^2 - 2*a*c^3*e^2)*f^4*g - 2*(2*a*c^3*d^2 - 3*a^2*c^2*e^2)*f^2*g^3 - ((a*c^5*d^2*e + a^2*c^4*e^3)*f^8 + 2*(a*c^5*d^3 + a^2*c^4*d*e^2)*f^7*g + 2*(a^2*c^4*d^2*e + a^3*c^3*e^3)*f^6*g^2 + 6*(a^2*c^4*d^3 + a^3*c^3*d*e^2)*f^5*g^3 + 6*(a^3*c^3*d^3 + a^4*c^2*d*e^2)*f^3*g^5 - 2*(a^4*c^2*d^2*e + a^5*c*e^3)*f^2*g^6 + 2*(a^4*c^2*d^3 + a^5*c*d*e^2)*f*g^7 - (a^5*c*d^2*e + a^6*e^3)*g^8)*sqrt(-(c^5*e^2*f^6 + 6*c^5*d*e*f^5*g - 20*a*c^4*d*e*f^3*g^3 + 6*a^2*c^3*d*e*f*g^5 + a^2*c^3*d^2*g^6 + 3*(3*c^5*d^2 - 2*a*c^4*e^2)*f^4*g^2 - 3*(2*a*c^4*d^2 - 3*a^2*c^3*e^2)*f^2*g^4)/((a*c^8*d^4 + 2*a^2*c^7*d^2*e^2 + a^3*c^6*e^4)*f^12 + 6*(a^2*c^7*d^4 + 2*a^3*c^6*d^2*e^2 + a^4*c^5*e^4)*f^10*g^2 + 15*(a^3*c^6*d^4 + 2*a^4*c^5*d^2*e^2 + a^5*c^4*e^4)*f^8*g^4 + 20*(a^4*c^5*d^4 + 2*a^5*c^4*d^2*e^2 + a^6*c^3*e^4)*f^6*g^6 + 15*(a^5*c^4*d^4 + 2*a^6*c^3*d^2*e^2 + a^7*c^2*e^4)*f^4*g^8 + 6*(a^6*c^3*d^4 + 2*a^7*c^2*d^2*e^2 + a^8*c*e^4)*f^2*g^10 + (a^7*c^2*d^4 + 2*a^8*c*d^2*e^2 + a^9*e^4)*g^12)))*sqrt(e*x + d)*sqrt(g*x + f)*sqrt(-(c^3*d*f^3 - 3*a*c^2*e*f^2*g - 3*a*c^2*d*f*g^2 + a^2*c*e*g^3 + ((a*c^4*d^2 + a^2*c^3*e^2)*f^6 + 3*(a^2*c^3*d^2 + a^3*c^2*e^2)*f^4*g^2 + 3*(a^3*c^2*d^2 + a^4*c*e^2)*f^2*g^4 + (a^4*c*d^2 + a^5*e^2)*g^6)*sqrt(-(c^5*e^2*f^6 + 6*c^5*d*e*f^5*g - 20*a*c^4*d*e*f^3*g^3 + 6*a^2*c^3*d*e*f*g^5 + a^2*c^3*d^2*g^6 + 3*(3*c^5*d^2 - 2*a*c^4*e^2)*f^4*g^2 - 3*(2*a*c^4*d^2 - 3*a^2*c^3*e^2)*f^2*g^4)/((a*c^8*d^4 + 2*a^2*c^7*d^2*e^2 + a^3*c^6*e^4)*f^12 + 6*(a^2*c^7*d^4 + 2*a^3*c^6*d^2*e^2 + a^4*c^5*e^4)*f^10*g^2 + 15*(a^3*c^6*d^4 + 2*a^4*c^5*d^2*e^2 + a^5*c^4*e^4)*f^8*g^4 + 20*(a^4*c^5*d^4 + 2*a^5*c^4*d^2*e^2 + a^6*c^3*e^4)*f^6*g^6 + 15*(a^5*c^4*d^4 + 2*a^6*c^3*d^2*e^2 + a^7*c^2*e^4)*f^4*g^8 + 6*(a^6*c^3*d^4 + 2*a^7*c^2*d^2*e^2 + a^8*c*e^4)*f^2*g^10 + (a^7*c^2*d^4 + 2*a^8*c*d^2*e^2 + a^9*e^4)*g^12)))/((a*c^4*d^2 + a^2*c^3*e^2)*f^6 + 3*(a^2*c^3*d^2 + a^3*c^2*e^2)*f^4*g^2 + 3*(a^3*c^2*d^2 + a^4*c*e^2)*f^2*g^4 + (a^4*c*d^2 + a^5*e^2)*g^6)) + 2*(c^3*e^2*f^3*g + 3*c^3*d*e*f^2*g^2 - 3*a*c^2*e^2*f*g^3 - a*c^2*d*e*g^4)*x + (2*(c^5*d^3 + a*c^4*d*e^2)*f^7 + 6*(a*c^4*d^3 + a^2*c^3*d*e^2)*f^5*g^2 + 6*(a^2*c^3*d^3 + a^3*c^2*d*e^2)*f^3*g^4 + 2*(a^3*c^2*d^3 + a^4*c*d*e^2)*f*g^6 + ((c^5*d^2*e + a*c^4*e^3)*f^7 + (c^5*d^3 + a*c^4*d*e^2)*f^6*g + 3*(a*c^4*d^2*e + a^2*c^3*e^3)*f^5*g^2 + 3*(a*c^4*d^3 + a^2*c^3*d*e^2)*f^4*g^3 + 3*(a^2*c^3*d^2*e + a^3*c^2*e^3)*f^3*g^4 + 3*(a^2*c^3*d^3 + a^3*c^2*d*e^2)*f^2*g^5 + (a^3*c^2*d^2*e + a^4*c*e^3)*f*g^6 + (a^3*c^2*d^3 + a^4*c*d*e^2)*g^7)*x)*sqrt(-(c^5*e^2*f^6 + 6*c^5*d*e*f^5*g - 20*a*c^4*d*e*f^3*g^3 + 6*a^2*c^3*d*e*f*g^5 + a^2*c^3*d^2*g^6 + 3*(3*c^5*d^2 - 2*a*c^4*e^2)*f^4*g^2 - 3*(2*a*c^4*d^2 - 3*a^2*c^3*e^2)*f^2*g^4)/((a*c^8*d^4 + 2*a^2*c^7*d^2*e^2 + a^3*c^6*e^4)*f^12 + 6*(a^2*c^7*d^4 + 2*a^3*c^6*d^2*e^2 + a^4*c^5*e^4)*f^10*g^2 + 15*(a^3*c^6*d^4 + 2*a^4*c^5*d^2*e^2 + a^5*c^4*e^4)*f^8*g^4 + 20*(a^4*c^5*d^4 + 2*a^5*c^4*d^2*e^2 + a^6*c^3*e^4)*f^6*g^6 + 15*(a^5*c^4*d^4 + 2*a^6*c^3*d^2*e^2 + a^7*c^2*e^4)*f^4*g^8 + 6*(a^6*c^3*d^4 + 2*a^7*c^2*d^2*e^2 + a^8*c*e^4)*f^2*g^10 + (a^7*c^2*d^4 + 2*a^8*c*d^2*e^2 + a^9*e^4)*g^12)))/x) + (c*e*f^4 - c*d*f^3*g + a*e*f^2*g^2 - a*d*f*g^3 + (c*e*f^3*g - c*d*f^2*g^2 + a*e*f*g^3 - a*d*g^4)*x)*sqrt(-(c^3*d*f^3 - 3*a*c^2*e*f^2*g - 3*a*c^2*d*f*g^2 + a^2*c*e*g^3 + ((a*c^4*d^2 + a^2*c^3*e^2)*f^6 + 3*(a^2*c^3*d^2 + a^3*c^2*e^2)*f^4*g^2 + 3*(a^3*c^2*d^2 + a^4*c*e^2)*f^2*g^4 + (a^4*c*d^2 + a^5*e^2)*g^6)*sqrt(-(c^5*e^2*f^6 + 6*c^5*d*e*f^5*g - 20*a*c^4*d*e*f^3*g^3 + 6*a^2*c^3*d*e*f*g^5 + a^2*c^3*d^2*g^6 + 3*(3*c^5*d^2 - 2*a*c^4*e^2)*f^4*g^2 - 3*(2*a*c^4*d^2 - 3*a^2*c^3*e^2)*f^2*g^4)/((a*c^8*d^4 + 2*a^2*c^7*d^2*e^2 + a^3*c^6*e^4)*f^12 + 6*(a^2*c^7*d^4 + 2*a^3*c^6*d^2*e^2 + a^4*c^5*e^4)*f^10*g^2 + 15*(a^3*c^6*d^4 + 2*a^4*c^5*d^2*e^2 + a^5*c^4*e^4)*f^8*g^4 + 20*(a^4*c^5*d^4 + 2*a^5*c^4*d^2*e^2 + a^6*c^3*e^4)*f^6*g^6 + 15*(a^5*c^4*d^4 + 2*a^6*c^3*d^2*e^2 + a^7*c^2*e^4)*f^4*g^8 + 6*(a^6*c^3*d^4 + 2*a^7*c^2*d^2*e^2 + a^8*c*e^4)*f^2*g^10 + (a^7*c^2*d^4 + 2*a^8*c*d^2*e^2 + a^9*e^4)*g^12)))/((a*c^4*d^2 + a^2*c^3*e^2)*f^6 + 3*(a^2*c^3*d^2 + a^3*c^2*e^2)*f^4*g^2 + 3*(a^3*c^2*d^2 + a^4*c*e^2)*f^2*g^4 + (a^4*c*d^2 + a^5*e^2)*g^6))*log(-(c^3*e^2*f^4 + 4*c^3*d*e*f^3*g - 4*a*c^2*d*e*f*g^3 - a*c^2*d^2*g^4 + 3*(c^3*d^2 - a*c^2*e^2)*f^2*g^2 - 2*(c^4*d*e*f^5 - 10*a*c^3*d*e*f^3*g^2 + 5*a^2*c^2*d*e*f*g^4 + a^2*c^2*d^2*g^5 + (3*c^4*d^2 - 2*a*c^3*e^2)*f^4*g - 2*(2*a*c^3*d^2 - 3*a^2*c^2*e^2)*f^2*g^3 - ((a*c^5*d^2*e + a^2*c^4*e^3)*f^8 + 2*(a*c^5*d^3 + a^2*c^4*d*e^2)*f^7*g + 2*(a^2*c^4*d^2*e + a^3*c^3*e^3)*f^6*g^2 + 6*(a^2*c^4*d^3 + a^3*c^3*d*e^2)*f^5*g^3 + 6*(a^3*c^3*d^3 + a^4*c^2*d*e^2)*f^3*g^5 - 2*(a^4*c^2*d^2*e + a^5*c*e^3)*f^2*g^6 + 2*(a^4*c^2*d^3 + a^5*c*d*e^2)*f*g^7 - (a^5*c*d^2*e + a^6*e^3)*g^8)*sqrt(-(c^5*e^2*f^6 + 6*c^5*d*e*f^5*g - 20*a*c^4*d*e*f^3*g^3 + 6*a^2*c^3*d*e*f*g^5 + a^2*c^3*d^2*g^6 + 3*(3*c^5*d^2 - 2*a*c^4*e^2)*f^4*g^2 - 3*(2*a*c^4*d^2 - 3*a^2*c^3*e^2)*f^2*g^4)/((a*c^8*d^4 + 2*a^2*c^7*d^2*e^2 + a^3*c^6*e^4)*f^12 + 6*(a^2*c^7*d^4 + 2*a^3*c^6*d^2*e^2 + a^4*c^5*e^4)*f^10*g^2 + 15*(a^3*c^6*d^4 + 2*a^4*c^5*d^2*e^2 + a^5*c^4*e^4)*f^8*g^4 + 20*(a^4*c^5*d^4 + 2*a^5*c^4*d^2*e^2 + a^6*c^3*e^4)*f^6*g^6 + 15*(a^5*c^4*d^4 + 2*a^6*c^3*d^2*e^2 + a^7*c^2*e^4)*f^4*g^8 + 6*(a^6*c^3*d^4 + 2*a^7*c^2*d^2*e^2 + a^8*c*e^4)*f^2*g^10 + (a^7*c^2*d^4 + 2*a^8*c*d^2*e^2 + a^9*e^4)*g^12)))*sqrt(e*x + d)*sqrt(g*x + f)*sqrt(-(c^3*d*f^3 - 3*a*c^2*e*f^2*g - 3*a*c^2*d*f*g^2 + a^2*c*e*g^3 + ((a*c^4*d^2 + a^2*c^3*e^2)*f^6 + 3*(a^2*c^3*d^2 + a^3*c^2*e^2)*f^4*g^2 + 3*(a^3*c^2*d^2 + a^4*c*e^2)*f^2*g^4 + (a^4*c*d^2 + a^5*e^2)*g^6)*sqrt(-(c^5*e^2*f^6 + 6*c^5*d*e*f^5*g - 20*a*c^4*d*e*f^3*g^3 + 6*a^2*c^3*d*e*f*g^5 + a^2*c^3*d^2*g^6 + 3*(3*c^5*d^2 - 2*a*c^4*e^2)*f^4*g^2 - 3*(2*a*c^4*d^2 - 3*a^2*c^3*e^2)*f^2*g^4)/((a*c^8*d^4 + 2*a^2*c^7*d^2*e^2 + a^3*c^6*e^4)*f^12 + 6*(a^2*c^7*d^4 + 2*a^3*c^6*d^2*e^2 + a^4*c^5*e^4)*f^10*g^2 + 15*(a^3*c^6*d^4 + 2*a^4*c^5*d^2*e^2 + a^5*c^4*e^4)*f^8*g^4 + 20*(a^4*c^5*d^4 + 2*a^5*c^4*d^2*e^2 + a^6*c^3*e^4)*f^6*g^6 + 15*(a^5*c^4*d^4 + 2*a^6*c^3*d^2*e^2 + a^7*c^2*e^4)*f^4*g^8 + 6*(a^6*c^3*d^4 + 2*a^7*c^2*d^2*e^2 + a^8*c*e^4)*f^2*g^10 + (a^7*c^2*d^4 + 2*a^8*c*d^2*e^2 + a^9*e^4)*g^12)))/((a*c^4*d^2 + a^2*c^3*e^2)*f^6 + 3*(a^2*c^3*d^2 + a^3*c^2*e^2)*f^4*g^2 + 3*(a^3*c^2*d^2 + a^4*c*e^2)*f^2*g^4 + (a^4*c*d^2 + a^5*e^2)*g^6)) + 2*(c^3*e^2*f^3*g + 3*c^3*d*e*f^2*g^2 - 3*a*c^2*e^2*f*g^3 - a*c^2*d*e*g^4)*x + (2*(c^5*d^3 + a*c^4*d*e^2)*f^7 + 6*(a*c^4*d^3 + a^2*c^3*d*e^2)*f^5*g^2 + 6*(a^2*c^3*d^3 + a^3*c^2*d*e^2)*f^3*g^4 + 2*(a^3*c^2*d^3 + a^4*c*d*e^2)*f*g^6 + ((c^5*d^2*e + a*c^4*e^3)*f^7 + (c^5*d^3 + a*c^4*d*e^2)*f^6*g + 3*(a*c^4*d^2*e + a^2*c^3*e^3)*f^5*g^2 + 3*(a*c^4*d^3 + a^2*c^3*d*e^2)*f^4*g^3 + 3*(a^2*c^3*d^2*e + a^3*c^2*e^3)*f^3*g^4 + 3*(a^2*c^3*d^3 + a^3*c^2*d*e^2)*f^2*g^5 + (a^3*c^2*d^2*e + a^4*c*e^3)*f*g^6 + (a^3*c^2*d^3 + a^4*c*d*e^2)*g^7)*x)*sqrt(-(c^5*e^2*f^6 + 6*c^5*d*e*f^5*g - 20*a*c^4*d*e*f^3*g^3 + 6*a^2*c^3*d*e*f*g^5 + a^2*c^3*d^2*g^6 + 3*(3*c^5*d^2 - 2*a*c^4*e^2)*f^4*g^2 - 3*(2*a*c^4*d^2 - 3*a^2*c^3*e^2)*f^2*g^4)/((a*c^8*d^4 + 2*a^2*c^7*d^2*e^2 + a^3*c^6*e^4)*f^12 + 6*(a^2*c^7*d^4 + 2*a^3*c^6*d^2*e^2 + a^4*c^5*e^4)*f^10*g^2 + 15*(a^3*c^6*d^4 + 2*a^4*c^5*d^2*e^2 + a^5*c^4*e^4)*f^8*g^4 + 20*(a^4*c^5*d^4 + 2*a^5*c^4*d^2*e^2 + a^6*c^3*e^4)*f^6*g^6 + 15*(a^5*c^4*d^4 + 2*a^6*c^3*d^2*e^2 + a^7*c^2*e^4)*f^4*g^8 + 6*(a^6*c^3*d^4 + 2*a^7*c^2*d^2*e^2 + a^8*c*e^4)*f^2*g^10 + (a^7*c^2*d^4 + 2*a^8*c*d^2*e^2 + a^9*e^4)*g^12)))/x) - (c*e*f^4 - c*d*f^3*g + a*e*f^2*g^2 - a*d*f*g^3 + (c*e*f^3*g - c*d*f^2*g^2 + a*e*f*g^3 - a*d*g^4)*x)*sqrt(-(c^3*d*f^3 - 3*a*c^2*e*f^2*g - 3*a*c^2*d*f*g^2 + a^2*c*e*g^3 - ((a*c^4*d^2 + a^2*c^3*e^2)*f^6 + 3*(a^2*c^3*d^2 + a^3*c^2*e^2)*f^4*g^2 + 3*(a^3*c^2*d^2 + a^4*c*e^2)*f^2*g^4 + (a^4*c*d^2 + a^5*e^2)*g^6)*sqrt(-(c^5*e^2*f^6 + 6*c^5*d*e*f^5*g - 20*a*c^4*d*e*f^3*g^3 + 6*a^2*c^3*d*e*f*g^5 + a^2*c^3*d^2*g^6 + 3*(3*c^5*d^2 - 2*a*c^4*e^2)*f^4*g^2 - 3*(2*a*c^4*d^2 - 3*a^2*c^3*e^2)*f^2*g^4)/((a*c^8*d^4 + 2*a^2*c^7*d^2*e^2 + a^3*c^6*e^4)*f^12 + 6*(a^2*c^7*d^4 + 2*a^3*c^6*d^2*e^2 + a^4*c^5*e^4)*f^10*g^2 + 15*(a^3*c^6*d^4 + 2*a^4*c^5*d^2*e^2 + a^5*c^4*e^4)*f^8*g^4 + 20*(a^4*c^5*d^4 + 2*a^5*c^4*d^2*e^2 + a^6*c^3*e^4)*f^6*g^6 + 15*(a^5*c^4*d^4 + 2*a^6*c^3*d^2*e^2 + a^7*c^2*e^4)*f^4*g^8 + 6*(a^6*c^3*d^4 + 2*a^7*c^2*d^2*e^2 + a^8*c*e^4)*f^2*g^10 + (a^7*c^2*d^4 + 2*a^8*c*d^2*e^2 + a^9*e^4)*g^12)))/((a*c^4*d^2 + a^2*c^3*e^2)*f^6 + 3*(a^2*c^3*d^2 + a^3*c^2*e^2)*f^4*g^2 + 3*(a^3*c^2*d^2 + a^4*c*e^2)*f^2*g^4 + (a^4*c*d^2 + a^5*e^2)*g^6))*log(-(c^3*e^2*f^4 + 4*c^3*d*e*f^3*g - 4*a*c^2*d*e*f*g^3 - a*c^2*d^2*g^4 + 3*(c^3*d^2 - a*c^2*e^2)*f^2*g^2 + 2*(c^4*d*e*f^5 - 10*a*c^3*d*e*f^3*g^2 + 5*a^2*c^2*d*e*f*g^4 + a^2*c^2*d^2*g^5 + (3*c^4*d^2 - 2*a*c^3*e^2)*f^4*g - 2*(2*a*c^3*d^2 - 3*a^2*c^2*e^2)*f^2*g^3 + ((a*c^5*d^2*e + a^2*c^4*e^3)*f^8 + 2*(a*c^5*d^3 + a^2*c^4*d*e^2)*f^7*g + 2*(a^2*c^4*d^2*e + a^3*c^3*e^3)*f^6*g^2 + 6*(a^2*c^4*d^3 + a^3*c^3*d*e^2)*f^5*g^3 + 6*(a^3*c^3*d^3 + a^4*c^2*d*e^2)*f^3*g^5 - 2*(a^4*c^2*d^2*e + a^5*c*e^3)*f^2*g^6 + 2*(a^4*c^2*d^3 + a^5*c*d*e^2)*f*g^7 - (a^5*c*d^2*e + a^6*e^3)*g^8)*sqrt(-(c^5*e^2*f^6 + 6*c^5*d*e*f^5*g - 20*a*c^4*d*e*f^3*g^3 + 6*a^2*c^3*d*e*f*g^5 + a^2*c^3*d^2*g^6 + 3*(3*c^5*d^2 - 2*a*c^4*e^2)*f^4*g^2 - 3*(2*a*c^4*d^2 - 3*a^2*c^3*e^2)*f^2*g^4)/((a*c^8*d^4 + 2*a^2*c^7*d^2*e^2 + a^3*c^6*e^4)*f^12 + 6*(a^2*c^7*d^4 + 2*a^3*c^6*d^2*e^2 + a^4*c^5*e^4)*f^10*g^2 + 15*(a^3*c^6*d^4 + 2*a^4*c^5*d^2*e^2 + a^5*c^4*e^4)*f^8*g^4 + 20*(a^4*c^5*d^4 + 2*a^5*c^4*d^2*e^2 + a^6*c^3*e^4)*f^6*g^6 + 15*(a^5*c^4*d^4 + 2*a^6*c^3*d^2*e^2 + a^7*c^2*e^4)*f^4*g^8 + 6*(a^6*c^3*d^4 + 2*a^7*c^2*d^2*e^2 + a^8*c*e^4)*f^2*g^10 + (a^7*c^2*d^4 + 2*a^8*c*d^2*e^2 + a^9*e^4)*g^12)))*sqrt(e*x + d)*sqrt(g*x + f)*sqrt(-(c^3*d*f^3 - 3*a*c^2*e*f^2*g - 3*a*c^2*d*f*g^2 + a^2*c*e*g^3 - ((a*c^4*d^2 + a^2*c^3*e^2)*f^6 + 3*(a^2*c^3*d^2 + a^3*c^2*e^2)*f^4*g^2 + 3*(a^3*c^2*d^2 + a^4*c*e^2)*f^2*g^4 + (a^4*c*d^2 + a^5*e^2)*g^6)*sqrt(-(c^5*e^2*f^6 + 6*c^5*d*e*f^5*g - 20*a*c^4*d*e*f^3*g^3 + 6*a^2*c^3*d*e*f*g^5 + a^2*c^3*d^2*g^6 + 3*(3*c^5*d^2 - 2*a*c^4*e^2)*f^4*g^2 - 3*(2*a*c^4*d^2 - 3*a^2*c^3*e^2)*f^2*g^4)/((a*c^8*d^4 + 2*a^2*c^7*d^2*e^2 + a^3*c^6*e^4)*f^12 + 6*(a^2*c^7*d^4 + 2*a^3*c^6*d^2*e^2 + a^4*c^5*e^4)*f^10*g^2 + 15*(a^3*c^6*d^4 + 2*a^4*c^5*d^2*e^2 + a^5*c^4*e^4)*f^8*g^4 + 20*(a^4*c^5*d^4 + 2*a^5*c^4*d^2*e^2 + a^6*c^3*e^4)*f^6*g^6 + 15*(a^5*c^4*d^4 + 2*a^6*c^3*d^2*e^2 + a^7*c^2*e^4)*f^4*g^8 + 6*(a^6*c^3*d^4 + 2*a^7*c^2*d^2*e^2 + a^8*c*e^4)*f^2*g^10 + (a^7*c^2*d^4 + 2*a^8*c*d^2*e^2 + a^9*e^4)*g^12)))/((a*c^4*d^2 + a^2*c^3*e^2)*f^6 + 3*(a^2*c^3*d^2 + a^3*c^2*e^2)*f^4*g^2 + 3*(a^3*c^2*d^2 + a^4*c*e^2)*f^2*g^4 + (a^4*c*d^2 + a^5*e^2)*g^6)) + 2*(c^3*e^2*f^3*g + 3*c^3*d*e*f^2*g^2 - 3*a*c^2*e^2*f*g^3 - a*c^2*d*e*g^4)*x - (2*(c^5*d^3 + a*c^4*d*e^2)*f^7 + 6*(a*c^4*d^3 + a^2*c^3*d*e^2)*f^5*g^2 + 6*(a^2*c^3*d^3 + a^3*c^2*d*e^2)*f^3*g^4 + 2*(a^3*c^2*d^3 + a^4*c*d*e^2)*f*g^6 + ((c^5*d^2*e + a*c^4*e^3)*f^7 + (c^5*d^3 + a*c^4*d*e^2)*f^6*g + 3*(a*c^4*d^2*e + a^2*c^3*e^3)*f^5*g^2 + 3*(a*c^4*d^3 + a^2*c^3*d*e^2)*f^4*g^3 + 3*(a^2*c^3*d^2*e + a^3*c^2*e^3)*f^3*g^4 + 3*(a^2*c^3*d^3 + a^3*c^2*d*e^2)*f^2*g^5 + (a^3*c^2*d^2*e + a^4*c*e^3)*f*g^6 + (a^3*c^2*d^3 + a^4*c*d*e^2)*g^7)*x)*sqrt(-(c^5*e^2*f^6 + 6*c^5*d*e*f^5*g - 20*a*c^4*d*e*f^3*g^3 + 6*a^2*c^3*d*e*f*g^5 + a^2*c^3*d^2*g^6 + 3*(3*c^5*d^2 - 2*a*c^4*e^2)*f^4*g^2 - 3*(2*a*c^4*d^2 - 3*a^2*c^3*e^2)*f^2*g^4)/((a*c^8*d^4 + 2*a^2*c^7*d^2*e^2 + a^3*c^6*e^4)*f^12 + 6*(a^2*c^7*d^4 + 2*a^3*c^6*d^2*e^2 + a^4*c^5*e^4)*f^10*g^2 + 15*(a^3*c^6*d^4 + 2*a^4*c^5*d^2*e^2 + a^5*c^4*e^4)*f^8*g^4 + 20*(a^4*c^5*d^4 + 2*a^5*c^4*d^2*e^2 + a^6*c^3*e^4)*f^6*g^6 + 15*(a^5*c^4*d^4 + 2*a^6*c^3*d^2*e^2 + a^7*c^2*e^4)*f^4*g^8 + 6*(a^6*c^3*d^4 + 2*a^7*c^2*d^2*e^2 + a^8*c*e^4)*f^2*g^10 + (a^7*c^2*d^4 + 2*a^8*c*d^2*e^2 + a^9*e^4)*g^12)))/x) + (c*e*f^4 - c*d*f^3*g + a*e*f^2*g^2 - a*d*f*g^3 + (c*e*f^3*g - c*d*f^2*g^2 + a*e*f*g^3 - a*d*g^4)*x)*sqrt(-(c^3*d*f^3 - 3*a*c^2*e*f^2*g - 3*a*c^2*d*f*g^2 + a^2*c*e*g^3 - ((a*c^4*d^2 + a^2*c^3*e^2)*f^6 + 3*(a^2*c^3*d^2 + a^3*c^2*e^2)*f^4*g^2 + 3*(a^3*c^2*d^2 + a^4*c*e^2)*f^2*g^4 + (a^4*c*d^2 + a^5*e^2)*g^6)*sqrt(-(c^5*e^2*f^6 + 6*c^5*d*e*f^5*g - 20*a*c^4*d*e*f^3*g^3 + 6*a^2*c^3*d*e*f*g^5 + a^2*c^3*d^2*g^6 + 3*(3*c^5*d^2 - 2*a*c^4*e^2)*f^4*g^2 - 3*(2*a*c^4*d^2 - 3*a^2*c^3*e^2)*f^2*g^4)/((a*c^8*d^4 + 2*a^2*c^7*d^2*e^2 + a^3*c^6*e^4)*f^12 + 6*(a^2*c^7*d^4 + 2*a^3*c^6*d^2*e^2 + a^4*c^5*e^4)*f^10*g^2 + 15*(a^3*c^6*d^4 + 2*a^4*c^5*d^2*e^2 + a^5*c^4*e^4)*f^8*g^4 + 20*(a^4*c^5*d^4 + 2*a^5*c^4*d^2*e^2 + a^6*c^3*e^4)*f^6*g^6 + 15*(a^5*c^4*d^4 + 2*a^6*c^3*d^2*e^2 + a^7*c^2*e^4)*f^4*g^8 + 6*(a^6*c^3*d^4 + 2*a^7*c^2*d^2*e^2 + a^8*c*e^4)*f^2*g^10 + (a^7*c^2*d^4 + 2*a^8*c*d^2*e^2 + a^9*e^4)*g^12)))/((a*c^4*d^2 + a^2*c^3*e^2)*f^6 + 3*(a^2*c^3*d^2 + a^3*c^2*e^2)*f^4*g^2 + 3*(a^3*c^2*d^2 + a^4*c*e^2)*f^2*g^4 + (a^4*c*d^2 + a^5*e^2)*g^6))*log(-(c^3*e^2*f^4 + 4*c^3*d*e*f^3*g - 4*a*c^2*d*e*f*g^3 - a*c^2*d^2*g^4 + 3*(c^3*d^2 - a*c^2*e^2)*f^2*g^2 - 2*(c^4*d*e*f^5 - 10*a*c^3*d*e*f^3*g^2 + 5*a^2*c^2*d*e*f*g^4 + a^2*c^2*d^2*g^5 + (3*c^4*d^2 - 2*a*c^3*e^2)*f^4*g - 2*(2*a*c^3*d^2 - 3*a^2*c^2*e^2)*f^2*g^3 + ((a*c^5*d^2*e + a^2*c^4*e^3)*f^8 + 2*(a*c^5*d^3 + a^2*c^4*d*e^2)*f^7*g + 2*(a^2*c^4*d^2*e + a^3*c^3*e^3)*f^6*g^2 + 6*(a^2*c^4*d^3 + a^3*c^3*d*e^2)*f^5*g^3 + 6*(a^3*c^3*d^3 + a^4*c^2*d*e^2)*f^3*g^5 - 2*(a^4*c^2*d^2*e + a^5*c*e^3)*f^2*g^6 + 2*(a^4*c^2*d^3 + a^5*c*d*e^2)*f*g^7 - (a^5*c*d^2*e + a^6*e^3)*g^8)*sqrt(-(c^5*e^2*f^6 + 6*c^5*d*e*f^5*g - 20*a*c^4*d*e*f^3*g^3 + 6*a^2*c^3*d*e*f*g^5 + a^2*c^3*d^2*g^6 + 3*(3*c^5*d^2 - 2*a*c^4*e^2)*f^4*g^2 - 3*(2*a*c^4*d^2 - 3*a^2*c^3*e^2)*f^2*g^4)/((a*c^8*d^4 + 2*a^2*c^7*d^2*e^2 + a^3*c^6*e^4)*f^12 + 6*(a^2*c^7*d^4 + 2*a^3*c^6*d^2*e^2 + a^4*c^5*e^4)*f^10*g^2 + 15*(a^3*c^6*d^4 + 2*a^4*c^5*d^2*e^2 + a^5*c^4*e^4)*f^8*g^4 + 20*(a^4*c^5*d^4 + 2*a^5*c^4*d^2*e^2 + a^6*c^3*e^4)*f^6*g^6 + 15*(a^5*c^4*d^4 + 2*a^6*c^3*d^2*e^2 + a^7*c^2*e^4)*f^4*g^8 + 6*(a^6*c^3*d^4 + 2*a^7*c^2*d^2*e^2 + a^8*c*e^4)*f^2*g^10 + (a^7*c^2*d^4 + 2*a^8*c*d^2*e^2 + a^9*e^4)*g^12)))*sqrt(e*x + d)*sqrt(g*x + f)*sqrt(-(c^3*d*f^3 - 3*a*c^2*e*f^2*g - 3*a*c^2*d*f*g^2 + a^2*c*e*g^3 - ((a*c^4*d^2 + a^2*c^3*e^2)*f^6 + 3*(a^2*c^3*d^2 + a^3*c^2*e^2)*f^4*g^2 + 3*(a^3*c^2*d^2 + a^4*c*e^2)*f^2*g^4 + (a^4*c*d^2 + a^5*e^2)*g^6)*sqrt(-(c^5*e^2*f^6 + 6*c^5*d*e*f^5*g - 20*a*c^4*d*e*f^3*g^3 + 6*a^2*c^3*d*e*f*g^5 + a^2*c^3*d^2*g^6 + 3*(3*c^5*d^2 - 2*a*c^4*e^2)*f^4*g^2 - 3*(2*a*c^4*d^2 - 3*a^2*c^3*e^2)*f^2*g^4)/((a*c^8*d^4 + 2*a^2*c^7*d^2*e^2 + a^3*c^6*e^4)*f^12 + 6*(a^2*c^7*d^4 + 2*a^3*c^6*d^2*e^2 + a^4*c^5*e^4)*f^10*g^2 + 15*(a^3*c^6*d^4 + 2*a^4*c^5*d^2*e^2 + a^5*c^4*e^4)*f^8*g^4 + 20*(a^4*c^5*d^4 + 2*a^5*c^4*d^2*e^2 + a^6*c^3*e^4)*f^6*g^6 + 15*(a^5*c^4*d^4 + 2*a^6*c^3*d^2*e^2 + a^7*c^2*e^4)*f^4*g^8 + 6*(a^6*c^3*d^4 + 2*a^7*c^2*d^2*e^2 + a^8*c*e^4)*f^2*g^10 + (a^7*c^2*d^4 + 2*a^8*c*d^2*e^2 + a^9*e^4)*g^12)))/((a*c^4*d^2 + a^2*c^3*e^2)*f^6 + 3*(a^2*c^3*d^2 + a^3*c^2*e^2)*f^4*g^2 + 3*(a^3*c^2*d^2 + a^4*c*e^2)*f^2*g^4 + (a^4*c*d^2 + a^5*e^2)*g^6)) + 2*(c^3*e^2*f^3*g + 3*c^3*d*e*f^2*g^2 - 3*a*c^2*e^2*f*g^3 - a*c^2*d*e*g^4)*x - (2*(c^5*d^3 + a*c^4*d*e^2)*f^7 + 6*(a*c^4*d^3 + a^2*c^3*d*e^2)*f^5*g^2 + 6*(a^2*c^3*d^3 + a^3*c^2*d*e^2)*f^3*g^4 + 2*(a^3*c^2*d^3 + a^4*c*d*e^2)*f*g^6 + ((c^5*d^2*e + a*c^4*e^3)*f^7 + (c^5*d^3 + a*c^4*d*e^2)*f^6*g + 3*(a*c^4*d^2*e + a^2*c^3*e^3)*f^5*g^2 + 3*(a*c^4*d^3 + a^2*c^3*d*e^2)*f^4*g^3 + 3*(a^2*c^3*d^2*e + a^3*c^2*e^3)*f^3*g^4 + 3*(a^2*c^3*d^3 + a^3*c^2*d*e^2)*f^2*g^5 + (a^3*c^2*d^2*e + a^4*c*e^3)*f*g^6 + (a^3*c^2*d^3 + a^4*c*d*e^2)*g^7)*x)*sqrt(-(c^5*e^2*f^6 + 6*c^5*d*e*f^5*g - 20*a*c^4*d*e*f^3*g^3 + 6*a^2*c^3*d*e*f*g^5 + a^2*c^3*d^2*g^6 + 3*(3*c^5*d^2 - 2*a*c^4*e^2)*f^4*g^2 - 3*(2*a*c^4*d^2 - 3*a^2*c^3*e^2)*f^2*g^4)/((a*c^8*d^4 + 2*a^2*c^7*d^2*e^2 + a^3*c^6*e^4)*f^12 + 6*(a^2*c^7*d^4 + 2*a^3*c^6*d^2*e^2 + a^4*c^5*e^4)*f^10*g^2 + 15*(a^3*c^6*d^4 + 2*a^4*c^5*d^2*e^2 + a^5*c^4*e^4)*f^8*g^4 + 20*(a^4*c^5*d^4 + 2*a^5*c^4*d^2*e^2 + a^6*c^3*e^4)*f^6*g^6 + 15*(a^5*c^4*d^4 + 2*a^6*c^3*d^2*e^2 + a^7*c^2*e^4)*f^4*g^8 + 6*(a^6*c^3*d^4 + 2*a^7*c^2*d^2*e^2 + a^8*c*e^4)*f^2*g^10 + (a^7*c^2*d^4 + 2*a^8*c*d^2*e^2 + a^9*e^4)*g^12)))/x))/(c*e*f^4 - c*d*f^3*g + a*e*f^2*g^2 - a*d*f*g^3 + (c*e*f^3*g - c*d*f^2*g^2 + a*e*f*g^3 - a*d*g^4)*x)","B",0
617,-1,0,0,0.000000," ","integrate(1/(e*x+d)^(3/2)/(g*x+f)^(3/2)/(c*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
618,1,744,0,0.479723," ","integrate(x^(1/2)/(x^2+1)/(1+x)^(1/2),x, algorithm=""fricas"")","\frac{1}{8} \cdot 2^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} + 4} {\left(\sqrt{2} - 1\right)} \log\left(-8 \, \sqrt{x + 1} x^{\frac{3}{2}} + 8 \, x^{2} + 2 \, {\left(2^{\frac{1}{4}} \sqrt{x + 1} \sqrt{x} {\left(\sqrt{2} - 2\right)} - 2^{\frac{1}{4}} {\left(\sqrt{2} {\left(x + 1\right)} - 2 \, x\right)}\right)} \sqrt{2 \, \sqrt{2} + 4} + 4 \, x + 4 \, \sqrt{2} + 4\right) - \frac{1}{8} \cdot 2^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} + 4} {\left(\sqrt{2} - 1\right)} \log\left(-8 \, \sqrt{x + 1} x^{\frac{3}{2}} + 8 \, x^{2} - 2 \, {\left(2^{\frac{1}{4}} \sqrt{x + 1} \sqrt{x} {\left(\sqrt{2} - 2\right)} - 2^{\frac{1}{4}} {\left(\sqrt{2} {\left(x + 1\right)} - 2 \, x\right)}\right)} \sqrt{2 \, \sqrt{2} + 4} + 4 \, x + 4 \, \sqrt{2} + 4\right) - \frac{1}{2} \cdot 2^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} + 4} \arctan\left(\frac{1}{7} \, {\left(\sqrt{2} {\left(5 \, \sqrt{2} + 6\right)} + 8 \, \sqrt{2} + 4\right)} \sqrt{x + 1} \sqrt{x} - \frac{1}{7} \, \sqrt{2} {\left(\sqrt{2} {\left(5 \, x + 1\right)} + 6 \, x + 4\right)} - \frac{1}{28} \, \sqrt{-8 \, \sqrt{x + 1} x^{\frac{3}{2}} + 8 \, x^{2} - 2 \, {\left(2^{\frac{1}{4}} \sqrt{x + 1} \sqrt{x} {\left(\sqrt{2} - 2\right)} - 2^{\frac{1}{4}} {\left(\sqrt{2} {\left(x + 1\right)} - 2 \, x\right)}\right)} \sqrt{2 \, \sqrt{2} + 4} + 4 \, x + 4 \, \sqrt{2} + 4} {\left(2 \, \sqrt{2} {\left(5 \, \sqrt{2} + 6\right)} - {\left(2^{\frac{3}{4}} {\left(3 \, \sqrt{2} + 5\right)} + 2 \cdot 2^{\frac{1}{4}} {\left(\sqrt{2} + 4\right)}\right)} \sqrt{2 \, \sqrt{2} + 4} + 16 \, \sqrt{2} + 8\right)} - \frac{1}{7} \, \sqrt{2} {\left(8 \, x + 3\right)} - \frac{1}{14} \, {\left({\left(2^{\frac{3}{4}} {\left(3 \, \sqrt{2} + 5\right)} + 2 \cdot 2^{\frac{1}{4}} {\left(\sqrt{2} + 4\right)}\right)} \sqrt{x + 1} \sqrt{x} - 2^{\frac{3}{4}} {\left(\sqrt{2} {\left(3 \, x + 2\right)} + 5 \, x + 1\right)} - 2 \cdot 2^{\frac{1}{4}} {\left(\sqrt{2} {\left(x + 3\right)} + 4 \, x - 2\right)}\right)} \sqrt{2 \, \sqrt{2} + 4} - \frac{4}{7} \, x - \frac{5}{7}\right) - \frac{1}{2} \cdot 2^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} + 4} \arctan\left(-\frac{1}{7} \, {\left(\sqrt{2} {\left(5 \, \sqrt{2} + 6\right)} + 8 \, \sqrt{2} + 4\right)} \sqrt{x + 1} \sqrt{x} + \frac{1}{7} \, \sqrt{2} {\left(\sqrt{2} {\left(5 \, x + 1\right)} + 6 \, x + 4\right)} + \frac{1}{28} \, \sqrt{-8 \, \sqrt{x + 1} x^{\frac{3}{2}} + 8 \, x^{2} + 2 \, {\left(2^{\frac{1}{4}} \sqrt{x + 1} \sqrt{x} {\left(\sqrt{2} - 2\right)} - 2^{\frac{1}{4}} {\left(\sqrt{2} {\left(x + 1\right)} - 2 \, x\right)}\right)} \sqrt{2 \, \sqrt{2} + 4} + 4 \, x + 4 \, \sqrt{2} + 4} {\left(2 \, \sqrt{2} {\left(5 \, \sqrt{2} + 6\right)} + {\left(2^{\frac{3}{4}} {\left(3 \, \sqrt{2} + 5\right)} + 2 \cdot 2^{\frac{1}{4}} {\left(\sqrt{2} + 4\right)}\right)} \sqrt{2 \, \sqrt{2} + 4} + 16 \, \sqrt{2} + 8\right)} + \frac{1}{7} \, \sqrt{2} {\left(8 \, x + 3\right)} - \frac{1}{14} \, {\left({\left(2^{\frac{3}{4}} {\left(3 \, \sqrt{2} + 5\right)} + 2 \cdot 2^{\frac{1}{4}} {\left(\sqrt{2} + 4\right)}\right)} \sqrt{x + 1} \sqrt{x} - 2^{\frac{3}{4}} {\left(\sqrt{2} {\left(3 \, x + 2\right)} + 5 \, x + 1\right)} - 2 \cdot 2^{\frac{1}{4}} {\left(\sqrt{2} {\left(x + 3\right)} + 4 \, x - 2\right)}\right)} \sqrt{2 \, \sqrt{2} + 4} + \frac{4}{7} \, x + \frac{5}{7}\right)"," ",0,"1/8*2^(1/4)*sqrt(2*sqrt(2) + 4)*(sqrt(2) - 1)*log(-8*sqrt(x + 1)*x^(3/2) + 8*x^2 + 2*(2^(1/4)*sqrt(x + 1)*sqrt(x)*(sqrt(2) - 2) - 2^(1/4)*(sqrt(2)*(x + 1) - 2*x))*sqrt(2*sqrt(2) + 4) + 4*x + 4*sqrt(2) + 4) - 1/8*2^(1/4)*sqrt(2*sqrt(2) + 4)*(sqrt(2) - 1)*log(-8*sqrt(x + 1)*x^(3/2) + 8*x^2 - 2*(2^(1/4)*sqrt(x + 1)*sqrt(x)*(sqrt(2) - 2) - 2^(1/4)*(sqrt(2)*(x + 1) - 2*x))*sqrt(2*sqrt(2) + 4) + 4*x + 4*sqrt(2) + 4) - 1/2*2^(1/4)*sqrt(2*sqrt(2) + 4)*arctan(1/7*(sqrt(2)*(5*sqrt(2) + 6) + 8*sqrt(2) + 4)*sqrt(x + 1)*sqrt(x) - 1/7*sqrt(2)*(sqrt(2)*(5*x + 1) + 6*x + 4) - 1/28*sqrt(-8*sqrt(x + 1)*x^(3/2) + 8*x^2 - 2*(2^(1/4)*sqrt(x + 1)*sqrt(x)*(sqrt(2) - 2) - 2^(1/4)*(sqrt(2)*(x + 1) - 2*x))*sqrt(2*sqrt(2) + 4) + 4*x + 4*sqrt(2) + 4)*(2*sqrt(2)*(5*sqrt(2) + 6) - (2^(3/4)*(3*sqrt(2) + 5) + 2*2^(1/4)*(sqrt(2) + 4))*sqrt(2*sqrt(2) + 4) + 16*sqrt(2) + 8) - 1/7*sqrt(2)*(8*x + 3) - 1/14*((2^(3/4)*(3*sqrt(2) + 5) + 2*2^(1/4)*(sqrt(2) + 4))*sqrt(x + 1)*sqrt(x) - 2^(3/4)*(sqrt(2)*(3*x + 2) + 5*x + 1) - 2*2^(1/4)*(sqrt(2)*(x + 3) + 4*x - 2))*sqrt(2*sqrt(2) + 4) - 4/7*x - 5/7) - 1/2*2^(1/4)*sqrt(2*sqrt(2) + 4)*arctan(-1/7*(sqrt(2)*(5*sqrt(2) + 6) + 8*sqrt(2) + 4)*sqrt(x + 1)*sqrt(x) + 1/7*sqrt(2)*(sqrt(2)*(5*x + 1) + 6*x + 4) + 1/28*sqrt(-8*sqrt(x + 1)*x^(3/2) + 8*x^2 + 2*(2^(1/4)*sqrt(x + 1)*sqrt(x)*(sqrt(2) - 2) - 2^(1/4)*(sqrt(2)*(x + 1) - 2*x))*sqrt(2*sqrt(2) + 4) + 4*x + 4*sqrt(2) + 4)*(2*sqrt(2)*(5*sqrt(2) + 6) + (2^(3/4)*(3*sqrt(2) + 5) + 2*2^(1/4)*(sqrt(2) + 4))*sqrt(2*sqrt(2) + 4) + 16*sqrt(2) + 8) + 1/7*sqrt(2)*(8*x + 3) - 1/14*((2^(3/4)*(3*sqrt(2) + 5) + 2*2^(1/4)*(sqrt(2) + 4))*sqrt(x + 1)*sqrt(x) - 2^(3/4)*(sqrt(2)*(3*x + 2) + 5*x + 1) - 2*2^(1/4)*(sqrt(2)*(x + 3) + 4*x - 2))*sqrt(2*sqrt(2) + 4) + 4/7*x + 5/7)","B",0
619,1,193,0,0.398659," ","integrate((g*x+f)^2*(-x^2+1)^(1/2)/(1-x)^4,x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, f^{2} - f g + 12 \, g^{2}\right)} x^{3} - 6 \, {\left(2 \, f^{2} - f g + 12 \, g^{2}\right)} x^{2} - 4 \, f^{2} + 2 \, f g - 24 \, g^{2} + 6 \, {\left(2 \, f^{2} - f g + 12 \, g^{2}\right)} x + 30 \, {\left(g^{2} x^{3} - 3 \, g^{2} x^{2} + 3 \, g^{2} x - g^{2}\right)} \arctan\left(\frac{\sqrt{-x^{2} + 1} - 1}{x}\right) + {\left({\left(f^{2} - 8 \, f g - 39 \, g^{2}\right)} x^{2} - 4 \, f^{2} + 2 \, f g - 24 \, g^{2} - 3 \, {\left(f^{2} + 2 \, f g - 19 \, g^{2}\right)} x\right)} \sqrt{-x^{2} + 1}}{15 \, {\left(x^{3} - 3 \, x^{2} + 3 \, x - 1\right)}}"," ",0,"1/15*(2*(2*f^2 - f*g + 12*g^2)*x^3 - 6*(2*f^2 - f*g + 12*g^2)*x^2 - 4*f^2 + 2*f*g - 24*g^2 + 6*(2*f^2 - f*g + 12*g^2)*x + 30*(g^2*x^3 - 3*g^2*x^2 + 3*g^2*x - g^2)*arctan((sqrt(-x^2 + 1) - 1)/x) + ((f^2 - 8*f*g - 39*g^2)*x^2 - 4*f^2 + 2*f*g - 24*g^2 - 3*(f^2 + 2*f*g - 19*g^2)*x)*sqrt(-x^2 + 1))/(x^3 - 3*x^2 + 3*x - 1)","B",0
620,1,318,0,0.543471," ","integrate((-a^2*x^2+1)^(3/2)/(-a*x+1)^2/(d*x+c),x, algorithm=""fricas"")","\left[-\frac{{\left(a c - d\right)} \sqrt{-\frac{a c - d}{a c + d}} \log\left(\frac{a^{2} c d x + d^{2} - {\left(a^{2} c^{2} - d^{2}\right)} \sqrt{-a^{2} x^{2} + 1} - {\left(a c d + d^{2} + {\left(a^{3} c^{2} + a^{2} c d\right)} x + \sqrt{-a^{2} x^{2} + 1} {\left(a c d + d^{2}\right)}\right)} \sqrt{-\frac{a c - d}{a c + d}}}{d x + c}\right) - 2 \, {\left(a c - 2 \, d\right)} \arctan\left(\frac{\sqrt{-a^{2} x^{2} + 1} - 1}{a x}\right) + \sqrt{-a^{2} x^{2} + 1} d}{d^{2}}, \frac{2 \, {\left(a c - d\right)} \sqrt{\frac{a c - d}{a c + d}} \arctan\left(\frac{{\left(d x - \sqrt{-a^{2} x^{2} + 1} c + c\right)} \sqrt{\frac{a c - d}{a c + d}}}{{\left(a c - d\right)} x}\right) + 2 \, {\left(a c - 2 \, d\right)} \arctan\left(\frac{\sqrt{-a^{2} x^{2} + 1} - 1}{a x}\right) - \sqrt{-a^{2} x^{2} + 1} d}{d^{2}}\right]"," ",0,"[-((a*c - d)*sqrt(-(a*c - d)/(a*c + d))*log((a^2*c*d*x + d^2 - (a^2*c^2 - d^2)*sqrt(-a^2*x^2 + 1) - (a*c*d + d^2 + (a^3*c^2 + a^2*c*d)*x + sqrt(-a^2*x^2 + 1)*(a*c*d + d^2))*sqrt(-(a*c - d)/(a*c + d)))/(d*x + c)) - 2*(a*c - 2*d)*arctan((sqrt(-a^2*x^2 + 1) - 1)/(a*x)) + sqrt(-a^2*x^2 + 1)*d)/d^2, (2*(a*c - d)*sqrt((a*c - d)/(a*c + d))*arctan((d*x - sqrt(-a^2*x^2 + 1)*c + c)*sqrt((a*c - d)/(a*c + d))/((a*c - d)*x)) + 2*(a*c - 2*d)*arctan((sqrt(-a^2*x^2 + 1) - 1)/(a*x)) - sqrt(-a^2*x^2 + 1)*d)/d^2]","A",0
621,1,318,0,0.558203," ","integrate((a*x+1)^2/(d*x+c)/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(a c - d\right)} \sqrt{-\frac{a c - d}{a c + d}} \log\left(\frac{a^{2} c d x + d^{2} - {\left(a^{2} c^{2} - d^{2}\right)} \sqrt{-a^{2} x^{2} + 1} - {\left(a c d + d^{2} + {\left(a^{3} c^{2} + a^{2} c d\right)} x + \sqrt{-a^{2} x^{2} + 1} {\left(a c d + d^{2}\right)}\right)} \sqrt{-\frac{a c - d}{a c + d}}}{d x + c}\right) - 2 \, {\left(a c - 2 \, d\right)} \arctan\left(\frac{\sqrt{-a^{2} x^{2} + 1} - 1}{a x}\right) + \sqrt{-a^{2} x^{2} + 1} d}{d^{2}}, \frac{2 \, {\left(a c - d\right)} \sqrt{\frac{a c - d}{a c + d}} \arctan\left(\frac{{\left(d x - \sqrt{-a^{2} x^{2} + 1} c + c\right)} \sqrt{\frac{a c - d}{a c + d}}}{{\left(a c - d\right)} x}\right) + 2 \, {\left(a c - 2 \, d\right)} \arctan\left(\frac{\sqrt{-a^{2} x^{2} + 1} - 1}{a x}\right) - \sqrt{-a^{2} x^{2} + 1} d}{d^{2}}\right]"," ",0,"[-((a*c - d)*sqrt(-(a*c - d)/(a*c + d))*log((a^2*c*d*x + d^2 - (a^2*c^2 - d^2)*sqrt(-a^2*x^2 + 1) - (a*c*d + d^2 + (a^3*c^2 + a^2*c*d)*x + sqrt(-a^2*x^2 + 1)*(a*c*d + d^2))*sqrt(-(a*c - d)/(a*c + d)))/(d*x + c)) - 2*(a*c - 2*d)*arctan((sqrt(-a^2*x^2 + 1) - 1)/(a*x)) + sqrt(-a^2*x^2 + 1)*d)/d^2, (2*(a*c - d)*sqrt((a*c - d)/(a*c + d))*arctan((d*x - sqrt(-a^2*x^2 + 1)*c + c)*sqrt((a*c - d)/(a*c + d))/((a*c - d)*x)) + 2*(a*c - 2*d)*arctan((sqrt(-a^2*x^2 + 1) - 1)/(a*x)) - sqrt(-a^2*x^2 + 1)*d)/d^2]","A",0
622,0,0,0,0.419148," ","integrate((e*x+d)^3*(g*x+f)^(1/2)*(c*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}\right)} \sqrt{c x^{2} + a} \sqrt{g x + f}, x\right)"," ",0,"integral((e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)*sqrt(c*x^2 + a)*sqrt(g*x + f), x)","F",0
623,0,0,0,0.426965," ","integrate((e*x+d)^2*(g*x+f)^(1/2)*(c*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{2} x^{2} + 2 \, d e x + d^{2}\right)} \sqrt{c x^{2} + a} \sqrt{g x + f}, x\right)"," ",0,"integral((e^2*x^2 + 2*d*e*x + d^2)*sqrt(c*x^2 + a)*sqrt(g*x + f), x)","F",0
624,0,0,0,0.421360," ","integrate((e*x+d)*(g*x+f)^(1/2)*(c*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{2} + a} {\left(e x + d\right)} \sqrt{g x + f}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*(e*x + d)*sqrt(g*x + f), x)","F",0
625,0,0,0,0.401694," ","integrate((g*x+f)^(1/2)*(c*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{2} + a} \sqrt{g x + f}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*sqrt(g*x + f), x)","F",0
626,-1,0,0,0.000000," ","integrate((g*x+f)^(1/2)*(c*x^2+a)^(1/2)/(e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
627,-1,0,0,0.000000," ","integrate((g*x+f)^(1/2)*(c*x^2+a)^(1/2)/(e*x+d)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
628,-1,0,0,0.000000," ","integrate((g*x+f)^(1/2)*(c*x^2+a)^(1/2)/(e*x+d)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
629,0,0,0,0.689997," ","integrate((e*x+d)^3*(c*x^2+a)^(1/2)/(g*x+f)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}\right)} \sqrt{c x^{2} + a}}{\sqrt{g x + f}}, x\right)"," ",0,"integral((e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)*sqrt(c*x^2 + a)/sqrt(g*x + f), x)","F",0
630,0,0,0,0.580418," ","integrate((e*x+d)^2*(c*x^2+a)^(1/2)/(g*x+f)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{2} x^{2} + 2 \, d e x + d^{2}\right)} \sqrt{c x^{2} + a}}{\sqrt{g x + f}}, x\right)"," ",0,"integral((e^2*x^2 + 2*d*e*x + d^2)*sqrt(c*x^2 + a)/sqrt(g*x + f), x)","F",0
631,0,0,0,0.655164," ","integrate((e*x+d)*(c*x^2+a)^(1/2)/(g*x+f)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + a} {\left(e x + d\right)}}{\sqrt{g x + f}}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*(e*x + d)/sqrt(g*x + f), x)","F",0
632,0,0,0,0.698407," ","integrate((c*x^2+a)^(1/2)/(g*x+f)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + a}}{\sqrt{g x + f}}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)/sqrt(g*x + f), x)","F",0
633,-1,0,0,0.000000," ","integrate((c*x^2+a)^(1/2)/(e*x+d)/(g*x+f)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
634,-1,0,0,0.000000," ","integrate((c*x^2+a)^(1/2)/(e*x+d)^2/(g*x+f)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
635,-1,0,0,0.000000," ","integrate((c*x^2+a)^(1/2)/(e*x+d)^3/(g*x+f)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
636,0,0,0,0.751927," ","integrate((e*x+d)^3*(g*x+f)^(1/2)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}\right)} \sqrt{g x + f}}{\sqrt{c x^{2} + a}}, x\right)"," ",0,"integral((e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)*sqrt(g*x + f)/sqrt(c*x^2 + a), x)","F",0
637,0,0,0,0.612558," ","integrate((e*x+d)^2*(g*x+f)^(1/2)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{2} x^{2} + 2 \, d e x + d^{2}\right)} \sqrt{g x + f}}{\sqrt{c x^{2} + a}}, x\right)"," ",0,"integral((e^2*x^2 + 2*d*e*x + d^2)*sqrt(g*x + f)/sqrt(c*x^2 + a), x)","F",0
638,0,0,0,0.487443," ","integrate((e*x+d)*(g*x+f)^(1/2)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)} \sqrt{g x + f}}{\sqrt{c x^{2} + a}}, x\right)"," ",0,"integral((e*x + d)*sqrt(g*x + f)/sqrt(c*x^2 + a), x)","F",0
639,0,0,0,0.426220," ","integrate((g*x+f)^(1/2)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{g x + f}}{\sqrt{c x^{2} + a}}, x\right)"," ",0,"integral(sqrt(g*x + f)/sqrt(c*x^2 + a), x)","F",0
640,-1,0,0,0.000000," ","integrate((g*x+f)^(1/2)/(e*x+d)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
641,-1,0,0,0.000000," ","integrate((g*x+f)^(1/2)/(e*x+d)^2/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
642,-1,0,0,0.000000," ","integrate((g*x+f)^(1/2)/(e*x+d)^3/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
643,-1,0,0,0.000000," ","integrate((g*x+f)^(5/2)/(e*x+d)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
644,-1,0,0,0.000000," ","integrate((g*x+f)^(3/2)/(e*x+d)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
645,0,0,0,0.585459," ","integrate((e*x+d)^3/(g*x+f)^(1/2)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}\right)} \sqrt{c x^{2} + a} \sqrt{g x + f}}{c g x^{3} + c f x^{2} + a g x + a f}, x\right)"," ",0,"integral((e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)*sqrt(c*x^2 + a)*sqrt(g*x + f)/(c*g*x^3 + c*f*x^2 + a*g*x + a*f), x)","F",0
646,0,0,0,0.435673," ","integrate((e*x+d)^2/(g*x+f)^(1/2)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{2} x^{2} + 2 \, d e x + d^{2}\right)} \sqrt{c x^{2} + a} \sqrt{g x + f}}{c g x^{3} + c f x^{2} + a g x + a f}, x\right)"," ",0,"integral((e^2*x^2 + 2*d*e*x + d^2)*sqrt(c*x^2 + a)*sqrt(g*x + f)/(c*g*x^3 + c*f*x^2 + a*g*x + a*f), x)","F",0
647,0,0,0,0.464938," ","integrate((e*x+d)/(g*x+f)^(1/2)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + a} {\left(e x + d\right)} \sqrt{g x + f}}{c g x^{3} + c f x^{2} + a g x + a f}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*(e*x + d)*sqrt(g*x + f)/(c*g*x^3 + c*f*x^2 + a*g*x + a*f), x)","F",0
648,0,0,0,0.423069," ","integrate(1/(g*x+f)^(1/2)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + a} \sqrt{g x + f}}{c g x^{3} + c f x^{2} + a g x + a f}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*sqrt(g*x + f)/(c*g*x^3 + c*f*x^2 + a*g*x + a*f), x)","F",0
649,-1,0,0,0.000000," ","integrate(1/(e*x+d)/(g*x+f)^(1/2)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
650,-1,0,0,0.000000," ","integrate(1/(e*x+d)^2/(g*x+f)^(1/2)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
651,-1,0,0,0.000000," ","integrate(1/(e*x+d)^3/(g*x+f)^(1/2)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
652,-1,0,0,0.000000," ","integrate(1/(e*x+d)/(g*x+f)^(3/2)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
653,-1,0,0,0.000000," ","integrate(1/(e*x+d)/(g*x+f)^(5/2)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
654,-1,0,0,0.000000," ","integrate(1/(e*x+d)/(g*x+f)^(1/2)/(c*x^2+1)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
655,0,0,0,0.796005," ","integrate(1/(e*x+d)^(1/2)/(g*x+f)^(1/2)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + a} \sqrt{e x + d} \sqrt{g x + f}}{c e g x^{4} + {\left(c e f + c d g\right)} x^{3} + a d f + {\left(c d f + a e g\right)} x^{2} + {\left(a e f + a d g\right)} x}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*sqrt(e*x + d)*sqrt(g*x + f)/(c*e*g*x^4 + (c*e*f + c*d*g)*x^3 + a*d*f + (c*d*f + a*e*g)*x^2 + (a*e*f + a*d*g)*x), x)","F",0
656,0,0,0,0.439318," ","integrate(1/(-1+x)^(1/2)/(1+x)^(1/2)/(2*x^2-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2 \, x^{2} - 1} \sqrt{x + 1} \sqrt{x - 1}}{2 \, x^{4} - 3 \, x^{2} + 1}, x\right)"," ",0,"integral(sqrt(2*x^2 - 1)*sqrt(x + 1)*sqrt(x - 1)/(2*x^4 - 3*x^2 + 1), x)","F",0
657,1,193,0,0.421340," ","integrate((g*x+f)^3*(e*x+d)^(1/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, c^{3} d^{3} g^{3} x^{3} + 35 \, c^{3} d^{3} f^{3} - 70 \, a c^{2} d^{2} e f^{2} g + 56 \, a^{2} c d e^{2} f g^{2} - 16 \, a^{3} e^{3} g^{3} + 3 \, {\left(7 \, c^{3} d^{3} f g^{2} - 2 \, a c^{2} d^{2} e g^{3}\right)} x^{2} + {\left(35 \, c^{3} d^{3} f^{2} g - 28 \, a c^{2} d^{2} e f g^{2} + 8 \, a^{2} c d e^{2} g^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{35 \, {\left(c^{4} d^{4} e x + c^{4} d^{5}\right)}}"," ",0,"2/35*(5*c^3*d^3*g^3*x^3 + 35*c^3*d^3*f^3 - 70*a*c^2*d^2*e*f^2*g + 56*a^2*c*d*e^2*f*g^2 - 16*a^3*e^3*g^3 + 3*(7*c^3*d^3*f*g^2 - 2*a*c^2*d^2*e*g^3)*x^2 + (35*c^3*d^3*f^2*g - 28*a*c^2*d^2*e*f*g^2 + 8*a^2*c*d*e^2*g^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)/(c^4*d^4*e*x + c^4*d^5)","A",0
658,1,123,0,0.440810," ","integrate((g*x+f)^2*(e*x+d)^(1/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, c^{2} d^{2} g^{2} x^{2} + 15 \, c^{2} d^{2} f^{2} - 20 \, a c d e f g + 8 \, a^{2} e^{2} g^{2} + 2 \, {\left(5 \, c^{2} d^{2} f g - 2 \, a c d e g^{2}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{15 \, {\left(c^{3} d^{3} e x + c^{3} d^{4}\right)}}"," ",0,"2/15*(3*c^2*d^2*g^2*x^2 + 15*c^2*d^2*f^2 - 20*a*c*d*e*f*g + 8*a^2*e^2*g^2 + 2*(5*c^2*d^2*f*g - 2*a*c*d*e*g^2)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)/(c^3*d^3*e*x + c^3*d^4)","A",0
659,1,71,0,0.399146," ","integrate((g*x+f)*(e*x+d)^(1/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d g x + 3 \, c d f - 2 \, a e g\right)} \sqrt{e x + d}}{3 \, {\left(c^{2} d^{2} e x + c^{2} d^{3}\right)}}"," ",0,"2/3*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d*g*x + 3*c*d*f - 2*a*e*g)*sqrt(e*x + d)/(c^2*d^2*e*x + c^2*d^3)","A",0
660,1,49,0,0.407220," ","integrate((e*x+d)^(1/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{c d e x + c d^{2}}"," ",0,"2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)/(c*d*e*x + c*d^2)","A",0
661,1,252,0,0.423655," ","integrate((e*x+d)^(1/2)/(g*x+f)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-c d f g + a e g^{2}} \log\left(-\frac{c d e g x^{2} - c d^{2} f + 2 \, a d e g - {\left(c d e f - {\left(c d^{2} + 2 \, a e^{2}\right)} g\right)} x - 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{-c d f g + a e g^{2}} \sqrt{e x + d}}{e g x^{2} + d f + {\left(e f + d g\right)} x}\right)}{c d f g - a e g^{2}}, -\frac{2 \, \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{c d f g - a e g^{2}} \sqrt{e x + d}}{c d e g x^{2} + a d e g + {\left(c d^{2} + a e^{2}\right)} g x}\right)}{\sqrt{c d f g - a e g^{2}}}\right]"," ",0,"[-sqrt(-c*d*f*g + a*e*g^2)*log(-(c*d*e*g*x^2 - c*d^2*f + 2*a*d*e*g - (c*d*e*f - (c*d^2 + 2*a*e^2)*g)*x - 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-c*d*f*g + a*e*g^2)*sqrt(e*x + d))/(e*g*x^2 + d*f + (e*f + d*g)*x))/(c*d*f*g - a*e*g^2), -2*arctan(sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(c*d*f*g - a*e*g^2)*sqrt(e*x + d)/(c*d*e*g*x^2 + a*d*e*g + (c*d^2 + a*e^2)*g*x))/sqrt(c*d*f*g - a*e*g^2)]","A",0
662,1,703,0,0.426453," ","integrate((e*x+d)^(1/2)/(g*x+f)^2/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(c d e g x^{2} + c d^{2} f + {\left(c d e f + c d^{2} g\right)} x\right)} \sqrt{-c d f g + a e g^{2}} \log\left(-\frac{c d e g x^{2} - c d^{2} f + 2 \, a d e g - {\left(c d e f - {\left(c d^{2} + 2 \, a e^{2}\right)} g\right)} x + 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{-c d f g + a e g^{2}} \sqrt{e x + d}}{e g x^{2} + d f + {\left(e f + d g\right)} x}\right) + 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d f g - a e g^{2}\right)} \sqrt{e x + d}}{2 \, {\left(c^{2} d^{3} f^{3} g - 2 \, a c d^{2} e f^{2} g^{2} + a^{2} d e^{2} f g^{3} + {\left(c^{2} d^{2} e f^{2} g^{2} - 2 \, a c d e^{2} f g^{3} + a^{2} e^{3} g^{4}\right)} x^{2} + {\left(c^{2} d^{2} e f^{3} g + a^{2} d e^{2} g^{4} + {\left(c^{2} d^{3} - 2 \, a c d e^{2}\right)} f^{2} g^{2} - {\left(2 \, a c d^{2} e - a^{2} e^{3}\right)} f g^{3}\right)} x\right)}}, -\frac{{\left(c d e g x^{2} + c d^{2} f + {\left(c d e f + c d^{2} g\right)} x\right)} \sqrt{c d f g - a e g^{2}} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{c d f g - a e g^{2}} \sqrt{e x + d}}{c d e g x^{2} + a d e g + {\left(c d^{2} + a e^{2}\right)} g x}\right) - \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d f g - a e g^{2}\right)} \sqrt{e x + d}}{c^{2} d^{3} f^{3} g - 2 \, a c d^{2} e f^{2} g^{2} + a^{2} d e^{2} f g^{3} + {\left(c^{2} d^{2} e f^{2} g^{2} - 2 \, a c d e^{2} f g^{3} + a^{2} e^{3} g^{4}\right)} x^{2} + {\left(c^{2} d^{2} e f^{3} g + a^{2} d e^{2} g^{4} + {\left(c^{2} d^{3} - 2 \, a c d e^{2}\right)} f^{2} g^{2} - {\left(2 \, a c d^{2} e - a^{2} e^{3}\right)} f g^{3}\right)} x}\right]"," ",0,"[1/2*((c*d*e*g*x^2 + c*d^2*f + (c*d*e*f + c*d^2*g)*x)*sqrt(-c*d*f*g + a*e*g^2)*log(-(c*d*e*g*x^2 - c*d^2*f + 2*a*d*e*g - (c*d*e*f - (c*d^2 + 2*a*e^2)*g)*x + 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-c*d*f*g + a*e*g^2)*sqrt(e*x + d))/(e*g*x^2 + d*f + (e*f + d*g)*x)) + 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d*f*g - a*e*g^2)*sqrt(e*x + d))/(c^2*d^3*f^3*g - 2*a*c*d^2*e*f^2*g^2 + a^2*d*e^2*f*g^3 + (c^2*d^2*e*f^2*g^2 - 2*a*c*d*e^2*f*g^3 + a^2*e^3*g^4)*x^2 + (c^2*d^2*e*f^3*g + a^2*d*e^2*g^4 + (c^2*d^3 - 2*a*c*d*e^2)*f^2*g^2 - (2*a*c*d^2*e - a^2*e^3)*f*g^3)*x), -((c*d*e*g*x^2 + c*d^2*f + (c*d*e*f + c*d^2*g)*x)*sqrt(c*d*f*g - a*e*g^2)*arctan(sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(c*d*f*g - a*e*g^2)*sqrt(e*x + d)/(c*d*e*g*x^2 + a*d*e*g + (c*d^2 + a*e^2)*g*x)) - sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d*f*g - a*e*g^2)*sqrt(e*x + d))/(c^2*d^3*f^3*g - 2*a*c*d^2*e*f^2*g^2 + a^2*d*e^2*f*g^3 + (c^2*d^2*e*f^2*g^2 - 2*a*c*d*e^2*f*g^3 + a^2*e^3*g^4)*x^2 + (c^2*d^2*e*f^3*g + a^2*d*e^2*g^4 + (c^2*d^3 - 2*a*c*d*e^2)*f^2*g^2 - (2*a*c*d^2*e - a^2*e^3)*f*g^3)*x)]","B",0
663,1,1283,0,0.446623," ","integrate((e*x+d)^(1/2)/(g*x+f)^3/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(c^{2} d^{2} e g^{2} x^{3} + c^{2} d^{3} f^{2} + {\left(2 \, c^{2} d^{2} e f g + c^{2} d^{3} g^{2}\right)} x^{2} + {\left(c^{2} d^{2} e f^{2} + 2 \, c^{2} d^{3} f g\right)} x\right)} \sqrt{-c d f g + a e g^{2}} \log\left(-\frac{c d e g x^{2} - c d^{2} f + 2 \, a d e g - {\left(c d e f - {\left(c d^{2} + 2 \, a e^{2}\right)} g\right)} x - 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{-c d f g + a e g^{2}} \sqrt{e x + d}}{e g x^{2} + d f + {\left(e f + d g\right)} x}\right) - 2 \, {\left(5 \, c^{2} d^{2} f^{2} g - 7 \, a c d e f g^{2} + 2 \, a^{2} e^{2} g^{3} + 3 \, {\left(c^{2} d^{2} f g^{2} - a c d e g^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{8 \, {\left(c^{3} d^{4} f^{5} g - 3 \, a c^{2} d^{3} e f^{4} g^{2} + 3 \, a^{2} c d^{2} e^{2} f^{3} g^{3} - a^{3} d e^{3} f^{2} g^{4} + {\left(c^{3} d^{3} e f^{3} g^{3} - 3 \, a c^{2} d^{2} e^{2} f^{2} g^{4} + 3 \, a^{2} c d e^{3} f g^{5} - a^{3} e^{4} g^{6}\right)} x^{3} + {\left(2 \, c^{3} d^{3} e f^{4} g^{2} - a^{3} d e^{3} g^{6} + {\left(c^{3} d^{4} - 6 \, a c^{2} d^{2} e^{2}\right)} f^{3} g^{3} - 3 \, {\left(a c^{2} d^{3} e - 2 \, a^{2} c d e^{3}\right)} f^{2} g^{4} + {\left(3 \, a^{2} c d^{2} e^{2} - 2 \, a^{3} e^{4}\right)} f g^{5}\right)} x^{2} + {\left(c^{3} d^{3} e f^{5} g - 2 \, a^{3} d e^{3} f g^{5} + {\left(2 \, c^{3} d^{4} - 3 \, a c^{2} d^{2} e^{2}\right)} f^{4} g^{2} - 3 \, {\left(2 \, a c^{2} d^{3} e - a^{2} c d e^{3}\right)} f^{3} g^{3} + {\left(6 \, a^{2} c d^{2} e^{2} - a^{3} e^{4}\right)} f^{2} g^{4}\right)} x\right)}}, -\frac{3 \, {\left(c^{2} d^{2} e g^{2} x^{3} + c^{2} d^{3} f^{2} + {\left(2 \, c^{2} d^{2} e f g + c^{2} d^{3} g^{2}\right)} x^{2} + {\left(c^{2} d^{2} e f^{2} + 2 \, c^{2} d^{3} f g\right)} x\right)} \sqrt{c d f g - a e g^{2}} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{c d f g - a e g^{2}} \sqrt{e x + d}}{c d e g x^{2} + a d e g + {\left(c d^{2} + a e^{2}\right)} g x}\right) - {\left(5 \, c^{2} d^{2} f^{2} g - 7 \, a c d e f g^{2} + 2 \, a^{2} e^{2} g^{3} + 3 \, {\left(c^{2} d^{2} f g^{2} - a c d e g^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{4 \, {\left(c^{3} d^{4} f^{5} g - 3 \, a c^{2} d^{3} e f^{4} g^{2} + 3 \, a^{2} c d^{2} e^{2} f^{3} g^{3} - a^{3} d e^{3} f^{2} g^{4} + {\left(c^{3} d^{3} e f^{3} g^{3} - 3 \, a c^{2} d^{2} e^{2} f^{2} g^{4} + 3 \, a^{2} c d e^{3} f g^{5} - a^{3} e^{4} g^{6}\right)} x^{3} + {\left(2 \, c^{3} d^{3} e f^{4} g^{2} - a^{3} d e^{3} g^{6} + {\left(c^{3} d^{4} - 6 \, a c^{2} d^{2} e^{2}\right)} f^{3} g^{3} - 3 \, {\left(a c^{2} d^{3} e - 2 \, a^{2} c d e^{3}\right)} f^{2} g^{4} + {\left(3 \, a^{2} c d^{2} e^{2} - 2 \, a^{3} e^{4}\right)} f g^{5}\right)} x^{2} + {\left(c^{3} d^{3} e f^{5} g - 2 \, a^{3} d e^{3} f g^{5} + {\left(2 \, c^{3} d^{4} - 3 \, a c^{2} d^{2} e^{2}\right)} f^{4} g^{2} - 3 \, {\left(2 \, a c^{2} d^{3} e - a^{2} c d e^{3}\right)} f^{3} g^{3} + {\left(6 \, a^{2} c d^{2} e^{2} - a^{3} e^{4}\right)} f^{2} g^{4}\right)} x\right)}}\right]"," ",0,"[-1/8*(3*(c^2*d^2*e*g^2*x^3 + c^2*d^3*f^2 + (2*c^2*d^2*e*f*g + c^2*d^3*g^2)*x^2 + (c^2*d^2*e*f^2 + 2*c^2*d^3*f*g)*x)*sqrt(-c*d*f*g + a*e*g^2)*log(-(c*d*e*g*x^2 - c*d^2*f + 2*a*d*e*g - (c*d*e*f - (c*d^2 + 2*a*e^2)*g)*x - 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-c*d*f*g + a*e*g^2)*sqrt(e*x + d))/(e*g*x^2 + d*f + (e*f + d*g)*x)) - 2*(5*c^2*d^2*f^2*g - 7*a*c*d*e*f*g^2 + 2*a^2*e^2*g^3 + 3*(c^2*d^2*f*g^2 - a*c*d*e*g^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c^3*d^4*f^5*g - 3*a*c^2*d^3*e*f^4*g^2 + 3*a^2*c*d^2*e^2*f^3*g^3 - a^3*d*e^3*f^2*g^4 + (c^3*d^3*e*f^3*g^3 - 3*a*c^2*d^2*e^2*f^2*g^4 + 3*a^2*c*d*e^3*f*g^5 - a^3*e^4*g^6)*x^3 + (2*c^3*d^3*e*f^4*g^2 - a^3*d*e^3*g^6 + (c^3*d^4 - 6*a*c^2*d^2*e^2)*f^3*g^3 - 3*(a*c^2*d^3*e - 2*a^2*c*d*e^3)*f^2*g^4 + (3*a^2*c*d^2*e^2 - 2*a^3*e^4)*f*g^5)*x^2 + (c^3*d^3*e*f^5*g - 2*a^3*d*e^3*f*g^5 + (2*c^3*d^4 - 3*a*c^2*d^2*e^2)*f^4*g^2 - 3*(2*a*c^2*d^3*e - a^2*c*d*e^3)*f^3*g^3 + (6*a^2*c*d^2*e^2 - a^3*e^4)*f^2*g^4)*x), -1/4*(3*(c^2*d^2*e*g^2*x^3 + c^2*d^3*f^2 + (2*c^2*d^2*e*f*g + c^2*d^3*g^2)*x^2 + (c^2*d^2*e*f^2 + 2*c^2*d^3*f*g)*x)*sqrt(c*d*f*g - a*e*g^2)*arctan(sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(c*d*f*g - a*e*g^2)*sqrt(e*x + d)/(c*d*e*g*x^2 + a*d*e*g + (c*d^2 + a*e^2)*g*x)) - (5*c^2*d^2*f^2*g - 7*a*c*d*e*f*g^2 + 2*a^2*e^2*g^3 + 3*(c^2*d^2*f*g^2 - a*c*d*e*g^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c^3*d^4*f^5*g - 3*a*c^2*d^3*e*f^4*g^2 + 3*a^2*c*d^2*e^2*f^3*g^3 - a^3*d*e^3*f^2*g^4 + (c^3*d^3*e*f^3*g^3 - 3*a*c^2*d^2*e^2*f^2*g^4 + 3*a^2*c*d*e^3*f*g^5 - a^3*e^4*g^6)*x^3 + (2*c^3*d^3*e*f^4*g^2 - a^3*d*e^3*g^6 + (c^3*d^4 - 6*a*c^2*d^2*e^2)*f^3*g^3 - 3*(a*c^2*d^3*e - 2*a^2*c*d*e^3)*f^2*g^4 + (3*a^2*c*d^2*e^2 - 2*a^3*e^4)*f*g^5)*x^2 + (c^3*d^3*e*f^5*g - 2*a^3*d*e^3*f*g^5 + (2*c^3*d^4 - 3*a*c^2*d^2*e^2)*f^4*g^2 - 3*(2*a*c^2*d^3*e - a^2*c*d*e^3)*f^3*g^3 + (6*a^2*c*d^2*e^2 - a^3*e^4)*f^2*g^4)*x)]","B",0
664,1,2027,0,0.471723," ","integrate((e*x+d)^(1/2)/(g*x+f)^4/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(c^{3} d^{3} e g^{3} x^{4} + c^{3} d^{4} f^{3} + {\left(3 \, c^{3} d^{3} e f g^{2} + c^{3} d^{4} g^{3}\right)} x^{3} + 3 \, {\left(c^{3} d^{3} e f^{2} g + c^{3} d^{4} f g^{2}\right)} x^{2} + {\left(c^{3} d^{3} e f^{3} + 3 \, c^{3} d^{4} f^{2} g\right)} x\right)} \sqrt{-c d f g + a e g^{2}} \log\left(-\frac{c d e g x^{2} - c d^{2} f + 2 \, a d e g - {\left(c d e f - {\left(c d^{2} + 2 \, a e^{2}\right)} g\right)} x + 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{-c d f g + a e g^{2}} \sqrt{e x + d}}{e g x^{2} + d f + {\left(e f + d g\right)} x}\right) + 2 \, {\left(33 \, c^{3} d^{3} f^{3} g - 59 \, a c^{2} d^{2} e f^{2} g^{2} + 34 \, a^{2} c d e^{2} f g^{3} - 8 \, a^{3} e^{3} g^{4} + 15 \, {\left(c^{3} d^{3} f g^{3} - a c^{2} d^{2} e g^{4}\right)} x^{2} + 10 \, {\left(4 \, c^{3} d^{3} f^{2} g^{2} - 5 \, a c^{2} d^{2} e f g^{3} + a^{2} c d e^{2} g^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{48 \, {\left(c^{4} d^{5} f^{7} g - 4 \, a c^{3} d^{4} e f^{6} g^{2} + 6 \, a^{2} c^{2} d^{3} e^{2} f^{5} g^{3} - 4 \, a^{3} c d^{2} e^{3} f^{4} g^{4} + a^{4} d e^{4} f^{3} g^{5} + {\left(c^{4} d^{4} e f^{4} g^{4} - 4 \, a c^{3} d^{3} e^{2} f^{3} g^{5} + 6 \, a^{2} c^{2} d^{2} e^{3} f^{2} g^{6} - 4 \, a^{3} c d e^{4} f g^{7} + a^{4} e^{5} g^{8}\right)} x^{4} + {\left(3 \, c^{4} d^{4} e f^{5} g^{3} + a^{4} d e^{4} g^{8} + {\left(c^{4} d^{5} - 12 \, a c^{3} d^{3} e^{2}\right)} f^{4} g^{4} - 2 \, {\left(2 \, a c^{3} d^{4} e - 9 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{3} g^{5} + 6 \, {\left(a^{2} c^{2} d^{3} e^{2} - 2 \, a^{3} c d e^{4}\right)} f^{2} g^{6} - {\left(4 \, a^{3} c d^{2} e^{3} - 3 \, a^{4} e^{5}\right)} f g^{7}\right)} x^{3} + 3 \, {\left(c^{4} d^{4} e f^{6} g^{2} + a^{4} d e^{4} f g^{7} + {\left(c^{4} d^{5} - 4 \, a c^{3} d^{3} e^{2}\right)} f^{5} g^{3} - 2 \, {\left(2 \, a c^{3} d^{4} e - 3 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{4} g^{4} + 2 \, {\left(3 \, a^{2} c^{2} d^{3} e^{2} - 2 \, a^{3} c d e^{4}\right)} f^{3} g^{5} - {\left(4 \, a^{3} c d^{2} e^{3} - a^{4} e^{5}\right)} f^{2} g^{6}\right)} x^{2} + {\left(c^{4} d^{4} e f^{7} g + 3 \, a^{4} d e^{4} f^{2} g^{6} + {\left(3 \, c^{4} d^{5} - 4 \, a c^{3} d^{3} e^{2}\right)} f^{6} g^{2} - 6 \, {\left(2 \, a c^{3} d^{4} e - a^{2} c^{2} d^{2} e^{3}\right)} f^{5} g^{3} + 2 \, {\left(9 \, a^{2} c^{2} d^{3} e^{2} - 2 \, a^{3} c d e^{4}\right)} f^{4} g^{4} - {\left(12 \, a^{3} c d^{2} e^{3} - a^{4} e^{5}\right)} f^{3} g^{5}\right)} x\right)}}, -\frac{15 \, {\left(c^{3} d^{3} e g^{3} x^{4} + c^{3} d^{4} f^{3} + {\left(3 \, c^{3} d^{3} e f g^{2} + c^{3} d^{4} g^{3}\right)} x^{3} + 3 \, {\left(c^{3} d^{3} e f^{2} g + c^{3} d^{4} f g^{2}\right)} x^{2} + {\left(c^{3} d^{3} e f^{3} + 3 \, c^{3} d^{4} f^{2} g\right)} x\right)} \sqrt{c d f g - a e g^{2}} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{c d f g - a e g^{2}} \sqrt{e x + d}}{c d e g x^{2} + a d e g + {\left(c d^{2} + a e^{2}\right)} g x}\right) - {\left(33 \, c^{3} d^{3} f^{3} g - 59 \, a c^{2} d^{2} e f^{2} g^{2} + 34 \, a^{2} c d e^{2} f g^{3} - 8 \, a^{3} e^{3} g^{4} + 15 \, {\left(c^{3} d^{3} f g^{3} - a c^{2} d^{2} e g^{4}\right)} x^{2} + 10 \, {\left(4 \, c^{3} d^{3} f^{2} g^{2} - 5 \, a c^{2} d^{2} e f g^{3} + a^{2} c d e^{2} g^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{24 \, {\left(c^{4} d^{5} f^{7} g - 4 \, a c^{3} d^{4} e f^{6} g^{2} + 6 \, a^{2} c^{2} d^{3} e^{2} f^{5} g^{3} - 4 \, a^{3} c d^{2} e^{3} f^{4} g^{4} + a^{4} d e^{4} f^{3} g^{5} + {\left(c^{4} d^{4} e f^{4} g^{4} - 4 \, a c^{3} d^{3} e^{2} f^{3} g^{5} + 6 \, a^{2} c^{2} d^{2} e^{3} f^{2} g^{6} - 4 \, a^{3} c d e^{4} f g^{7} + a^{4} e^{5} g^{8}\right)} x^{4} + {\left(3 \, c^{4} d^{4} e f^{5} g^{3} + a^{4} d e^{4} g^{8} + {\left(c^{4} d^{5} - 12 \, a c^{3} d^{3} e^{2}\right)} f^{4} g^{4} - 2 \, {\left(2 \, a c^{3} d^{4} e - 9 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{3} g^{5} + 6 \, {\left(a^{2} c^{2} d^{3} e^{2} - 2 \, a^{3} c d e^{4}\right)} f^{2} g^{6} - {\left(4 \, a^{3} c d^{2} e^{3} - 3 \, a^{4} e^{5}\right)} f g^{7}\right)} x^{3} + 3 \, {\left(c^{4} d^{4} e f^{6} g^{2} + a^{4} d e^{4} f g^{7} + {\left(c^{4} d^{5} - 4 \, a c^{3} d^{3} e^{2}\right)} f^{5} g^{3} - 2 \, {\left(2 \, a c^{3} d^{4} e - 3 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{4} g^{4} + 2 \, {\left(3 \, a^{2} c^{2} d^{3} e^{2} - 2 \, a^{3} c d e^{4}\right)} f^{3} g^{5} - {\left(4 \, a^{3} c d^{2} e^{3} - a^{4} e^{5}\right)} f^{2} g^{6}\right)} x^{2} + {\left(c^{4} d^{4} e f^{7} g + 3 \, a^{4} d e^{4} f^{2} g^{6} + {\left(3 \, c^{4} d^{5} - 4 \, a c^{3} d^{3} e^{2}\right)} f^{6} g^{2} - 6 \, {\left(2 \, a c^{3} d^{4} e - a^{2} c^{2} d^{2} e^{3}\right)} f^{5} g^{3} + 2 \, {\left(9 \, a^{2} c^{2} d^{3} e^{2} - 2 \, a^{3} c d e^{4}\right)} f^{4} g^{4} - {\left(12 \, a^{3} c d^{2} e^{3} - a^{4} e^{5}\right)} f^{3} g^{5}\right)} x\right)}}\right]"," ",0,"[1/48*(15*(c^3*d^3*e*g^3*x^4 + c^3*d^4*f^3 + (3*c^3*d^3*e*f*g^2 + c^3*d^4*g^3)*x^3 + 3*(c^3*d^3*e*f^2*g + c^3*d^4*f*g^2)*x^2 + (c^3*d^3*e*f^3 + 3*c^3*d^4*f^2*g)*x)*sqrt(-c*d*f*g + a*e*g^2)*log(-(c*d*e*g*x^2 - c*d^2*f + 2*a*d*e*g - (c*d*e*f - (c*d^2 + 2*a*e^2)*g)*x + 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-c*d*f*g + a*e*g^2)*sqrt(e*x + d))/(e*g*x^2 + d*f + (e*f + d*g)*x)) + 2*(33*c^3*d^3*f^3*g - 59*a*c^2*d^2*e*f^2*g^2 + 34*a^2*c*d*e^2*f*g^3 - 8*a^3*e^3*g^4 + 15*(c^3*d^3*f*g^3 - a*c^2*d^2*e*g^4)*x^2 + 10*(4*c^3*d^3*f^2*g^2 - 5*a*c^2*d^2*e*f*g^3 + a^2*c*d*e^2*g^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c^4*d^5*f^7*g - 4*a*c^3*d^4*e*f^6*g^2 + 6*a^2*c^2*d^3*e^2*f^5*g^3 - 4*a^3*c*d^2*e^3*f^4*g^4 + a^4*d*e^4*f^3*g^5 + (c^4*d^4*e*f^4*g^4 - 4*a*c^3*d^3*e^2*f^3*g^5 + 6*a^2*c^2*d^2*e^3*f^2*g^6 - 4*a^3*c*d*e^4*f*g^7 + a^4*e^5*g^8)*x^4 + (3*c^4*d^4*e*f^5*g^3 + a^4*d*e^4*g^8 + (c^4*d^5 - 12*a*c^3*d^3*e^2)*f^4*g^4 - 2*(2*a*c^3*d^4*e - 9*a^2*c^2*d^2*e^3)*f^3*g^5 + 6*(a^2*c^2*d^3*e^2 - 2*a^3*c*d*e^4)*f^2*g^6 - (4*a^3*c*d^2*e^3 - 3*a^4*e^5)*f*g^7)*x^3 + 3*(c^4*d^4*e*f^6*g^2 + a^4*d*e^4*f*g^7 + (c^4*d^5 - 4*a*c^3*d^3*e^2)*f^5*g^3 - 2*(2*a*c^3*d^4*e - 3*a^2*c^2*d^2*e^3)*f^4*g^4 + 2*(3*a^2*c^2*d^3*e^2 - 2*a^3*c*d*e^4)*f^3*g^5 - (4*a^3*c*d^2*e^3 - a^4*e^5)*f^2*g^6)*x^2 + (c^4*d^4*e*f^7*g + 3*a^4*d*e^4*f^2*g^6 + (3*c^4*d^5 - 4*a*c^3*d^3*e^2)*f^6*g^2 - 6*(2*a*c^3*d^4*e - a^2*c^2*d^2*e^3)*f^5*g^3 + 2*(9*a^2*c^2*d^3*e^2 - 2*a^3*c*d*e^4)*f^4*g^4 - (12*a^3*c*d^2*e^3 - a^4*e^5)*f^3*g^5)*x), -1/24*(15*(c^3*d^3*e*g^3*x^4 + c^3*d^4*f^3 + (3*c^3*d^3*e*f*g^2 + c^3*d^4*g^3)*x^3 + 3*(c^3*d^3*e*f^2*g + c^3*d^4*f*g^2)*x^2 + (c^3*d^3*e*f^3 + 3*c^3*d^4*f^2*g)*x)*sqrt(c*d*f*g - a*e*g^2)*arctan(sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(c*d*f*g - a*e*g^2)*sqrt(e*x + d)/(c*d*e*g*x^2 + a*d*e*g + (c*d^2 + a*e^2)*g*x)) - (33*c^3*d^3*f^3*g - 59*a*c^2*d^2*e*f^2*g^2 + 34*a^2*c*d*e^2*f*g^3 - 8*a^3*e^3*g^4 + 15*(c^3*d^3*f*g^3 - a*c^2*d^2*e*g^4)*x^2 + 10*(4*c^3*d^3*f^2*g^2 - 5*a*c^2*d^2*e*f*g^3 + a^2*c*d*e^2*g^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c^4*d^5*f^7*g - 4*a*c^3*d^4*e*f^6*g^2 + 6*a^2*c^2*d^3*e^2*f^5*g^3 - 4*a^3*c*d^2*e^3*f^4*g^4 + a^4*d*e^4*f^3*g^5 + (c^4*d^4*e*f^4*g^4 - 4*a*c^3*d^3*e^2*f^3*g^5 + 6*a^2*c^2*d^2*e^3*f^2*g^6 - 4*a^3*c*d*e^4*f*g^7 + a^4*e^5*g^8)*x^4 + (3*c^4*d^4*e*f^5*g^3 + a^4*d*e^4*g^8 + (c^4*d^5 - 12*a*c^3*d^3*e^2)*f^4*g^4 - 2*(2*a*c^3*d^4*e - 9*a^2*c^2*d^2*e^3)*f^3*g^5 + 6*(a^2*c^2*d^3*e^2 - 2*a^3*c*d*e^4)*f^2*g^6 - (4*a^3*c*d^2*e^3 - 3*a^4*e^5)*f*g^7)*x^3 + 3*(c^4*d^4*e*f^6*g^2 + a^4*d*e^4*f*g^7 + (c^4*d^5 - 4*a*c^3*d^3*e^2)*f^5*g^3 - 2*(2*a*c^3*d^4*e - 3*a^2*c^2*d^2*e^3)*f^4*g^4 + 2*(3*a^2*c^2*d^3*e^2 - 2*a^3*c*d*e^4)*f^3*g^5 - (4*a^3*c*d^2*e^3 - a^4*e^5)*f^2*g^6)*x^2 + (c^4*d^4*e*f^7*g + 3*a^4*d*e^4*f^2*g^6 + (3*c^4*d^5 - 4*a*c^3*d^3*e^2)*f^6*g^2 - 6*(2*a*c^3*d^4*e - a^2*c^2*d^2*e^3)*f^5*g^3 + 2*(9*a^2*c^2*d^3*e^2 - 2*a^3*c*d*e^4)*f^4*g^4 - (12*a^3*c*d^2*e^3 - a^4*e^5)*f^3*g^5)*x)]","B",0
665,1,216,0,0.417833," ","integrate((e*x+d)^(3/2)*(g*x+f)^3/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(c^{3} d^{3} g^{3} x^{3} - 5 \, c^{3} d^{3} f^{3} + 30 \, a c^{2} d^{2} e f^{2} g - 40 \, a^{2} c d e^{2} f g^{2} + 16 \, a^{3} e^{3} g^{3} + {\left(5 \, c^{3} d^{3} f g^{2} - 2 \, a c^{2} d^{2} e g^{3}\right)} x^{2} + {\left(15 \, c^{3} d^{3} f^{2} g - 20 \, a c^{2} d^{2} e f g^{2} + 8 \, a^{2} c d e^{2} g^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{5 \, {\left(c^{5} d^{5} e x^{2} + a c^{4} d^{5} e + {\left(c^{5} d^{6} + a c^{4} d^{4} e^{2}\right)} x\right)}}"," ",0,"2/5*(c^3*d^3*g^3*x^3 - 5*c^3*d^3*f^3 + 30*a*c^2*d^2*e*f^2*g - 40*a^2*c*d*e^2*f*g^2 + 16*a^3*e^3*g^3 + (5*c^3*d^3*f*g^2 - 2*a*c^2*d^2*e*g^3)*x^2 + (15*c^3*d^3*f^2*g - 20*a*c^2*d^2*e*f*g^2 + 8*a^2*c*d*e^2*g^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)/(c^5*d^5*e*x^2 + a*c^4*d^5*e + (c^5*d^6 + a*c^4*d^4*e^2)*x)","A",0
666,1,147,0,0.411253," ","integrate((e*x+d)^(3/2)*(g*x+f)^2/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(c^{2} d^{2} g^{2} x^{2} - 3 \, c^{2} d^{2} f^{2} + 12 \, a c d e f g - 8 \, a^{2} e^{2} g^{2} + 2 \, {\left(3 \, c^{2} d^{2} f g - 2 \, a c d e g^{2}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{3 \, {\left(c^{4} d^{4} e x^{2} + a c^{3} d^{4} e + {\left(c^{4} d^{5} + a c^{3} d^{3} e^{2}\right)} x\right)}}"," ",0,"2/3*(c^2*d^2*g^2*x^2 - 3*c^2*d^2*f^2 + 12*a*c*d*e*f*g - 8*a^2*e^2*g^2 + 2*(3*c^2*d^2*f*g - 2*a*c*d*e*g^2)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)/(c^4*d^4*e*x^2 + a*c^3*d^4*e + (c^4*d^5 + a*c^3*d^3*e^2)*x)","A",0
667,1,96,0,0.404263," ","integrate((e*x+d)^(3/2)*(g*x+f)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d g x - c d f + 2 \, a e g\right)} \sqrt{e x + d}}{c^{3} d^{3} e x^{2} + a c^{2} d^{3} e + {\left(c^{3} d^{4} + a c^{2} d^{2} e^{2}\right)} x}"," ",0,"2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d*g*x - c*d*f + 2*a*e*g)*sqrt(e*x + d)/(c^3*d^3*e*x^2 + a*c^2*d^3*e + (c^3*d^4 + a*c^2*d^2*e^2)*x)","A",0
668,1,74,0,0.413827," ","integrate((e*x+d)^(3/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{c^{2} d^{2} e x^{2} + a c d^{2} e + {\left(c^{2} d^{3} + a c d e^{2}\right)} x}"," ",0,"-2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)/(c^2*d^2*e*x^2 + a*c*d^2*e + (c^2*d^3 + a*c*d*e^2)*x)","A",0
669,1,553,0,0.435633," ","integrate((e*x+d)^(3/2)/(g*x+f)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{-\frac{g}{c d f - a e g}} \log\left(-\frac{c d e g x^{2} - c d^{2} f + 2 \, a d e g + 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d f - a e g\right)} \sqrt{e x + d} \sqrt{-\frac{g}{c d f - a e g}} - {\left(c d e f - {\left(c d^{2} + 2 \, a e^{2}\right)} g\right)} x}{e g x^{2} + d f + {\left(e f + d g\right)} x}\right) + 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{a c d^{2} e f - a^{2} d e^{2} g + {\left(c^{2} d^{2} e f - a c d e^{2} g\right)} x^{2} + {\left({\left(c^{2} d^{3} + a c d e^{2}\right)} f - {\left(a c d^{2} e + a^{2} e^{3}\right)} g\right)} x}, -\frac{2 \, {\left({\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{\frac{g}{c d f - a e g}} \arctan\left(-\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d f - a e g\right)} \sqrt{e x + d} \sqrt{\frac{g}{c d f - a e g}}}{c d e g x^{2} + a d e g + {\left(c d^{2} + a e^{2}\right)} g x}\right) + \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}\right)}}{a c d^{2} e f - a^{2} d e^{2} g + {\left(c^{2} d^{2} e f - a c d e^{2} g\right)} x^{2} + {\left({\left(c^{2} d^{3} + a c d e^{2}\right)} f - {\left(a c d^{2} e + a^{2} e^{3}\right)} g\right)} x}\right]"," ",0,"[-((c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-g/(c*d*f - a*e*g))*log(-(c*d*e*g*x^2 - c*d^2*f + 2*a*d*e*g + 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d*f - a*e*g)*sqrt(e*x + d)*sqrt(-g/(c*d*f - a*e*g)) - (c*d*e*f - (c*d^2 + 2*a*e^2)*g)*x)/(e*g*x^2 + d*f + (e*f + d*g)*x)) + 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(a*c*d^2*e*f - a^2*d*e^2*g + (c^2*d^2*e*f - a*c*d*e^2*g)*x^2 + ((c^2*d^3 + a*c*d*e^2)*f - (a*c*d^2*e + a^2*e^3)*g)*x), -2*((c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(g/(c*d*f - a*e*g))*arctan(-sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d*f - a*e*g)*sqrt(e*x + d)*sqrt(g/(c*d*f - a*e*g))/(c*d*e*g*x^2 + a*d*e*g + (c*d^2 + a*e^2)*g*x)) + sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(a*c*d^2*e*f - a^2*d*e^2*g + (c^2*d^2*e*f - a*c*d*e^2*g)*x^2 + ((c^2*d^3 + a*c*d*e^2)*f - (a*c*d^2*e + a^2*e^3)*g)*x)]","B",0
670,1,1067,0,0.447969," ","integrate((e*x+d)^(3/2)/(g*x+f)^2/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(c^{2} d^{2} e g x^{3} + a c d^{2} e f + {\left(c^{2} d^{2} e f + {\left(c^{2} d^{3} + a c d e^{2}\right)} g\right)} x^{2} + {\left(a c d^{2} e g + {\left(c^{2} d^{3} + a c d e^{2}\right)} f\right)} x\right)} \sqrt{-\frac{g}{c d f - a e g}} \log\left(-\frac{c d e g x^{2} - c d^{2} f + 2 \, a d e g - 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d f - a e g\right)} \sqrt{e x + d} \sqrt{-\frac{g}{c d f - a e g}} - {\left(c d e f - {\left(c d^{2} + 2 \, a e^{2}\right)} g\right)} x}{e g x^{2} + d f + {\left(e f + d g\right)} x}\right) - 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(3 \, c d g x + 2 \, c d f + a e g\right)} \sqrt{e x + d}}{2 \, {\left(a c^{2} d^{3} e f^{3} - 2 \, a^{2} c d^{2} e^{2} f^{2} g + a^{3} d e^{3} f g^{2} + {\left(c^{3} d^{3} e f^{2} g - 2 \, a c^{2} d^{2} e^{2} f g^{2} + a^{2} c d e^{3} g^{3}\right)} x^{3} + {\left(c^{3} d^{3} e f^{3} + {\left(c^{3} d^{4} - a c^{2} d^{2} e^{2}\right)} f^{2} g - {\left(2 \, a c^{2} d^{3} e + a^{2} c d e^{3}\right)} f g^{2} + {\left(a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} g^{3}\right)} x^{2} + {\left(a^{3} d e^{3} g^{3} + {\left(c^{3} d^{4} + a c^{2} d^{2} e^{2}\right)} f^{3} - {\left(a c^{2} d^{3} e + 2 \, a^{2} c d e^{3}\right)} f^{2} g - {\left(a^{2} c d^{2} e^{2} - a^{3} e^{4}\right)} f g^{2}\right)} x\right)}}, -\frac{3 \, {\left(c^{2} d^{2} e g x^{3} + a c d^{2} e f + {\left(c^{2} d^{2} e f + {\left(c^{2} d^{3} + a c d e^{2}\right)} g\right)} x^{2} + {\left(a c d^{2} e g + {\left(c^{2} d^{3} + a c d e^{2}\right)} f\right)} x\right)} \sqrt{\frac{g}{c d f - a e g}} \arctan\left(-\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d f - a e g\right)} \sqrt{e x + d} \sqrt{\frac{g}{c d f - a e g}}}{c d e g x^{2} + a d e g + {\left(c d^{2} + a e^{2}\right)} g x}\right) + \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(3 \, c d g x + 2 \, c d f + a e g\right)} \sqrt{e x + d}}{a c^{2} d^{3} e f^{3} - 2 \, a^{2} c d^{2} e^{2} f^{2} g + a^{3} d e^{3} f g^{2} + {\left(c^{3} d^{3} e f^{2} g - 2 \, a c^{2} d^{2} e^{2} f g^{2} + a^{2} c d e^{3} g^{3}\right)} x^{3} + {\left(c^{3} d^{3} e f^{3} + {\left(c^{3} d^{4} - a c^{2} d^{2} e^{2}\right)} f^{2} g - {\left(2 \, a c^{2} d^{3} e + a^{2} c d e^{3}\right)} f g^{2} + {\left(a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} g^{3}\right)} x^{2} + {\left(a^{3} d e^{3} g^{3} + {\left(c^{3} d^{4} + a c^{2} d^{2} e^{2}\right)} f^{3} - {\left(a c^{2} d^{3} e + 2 \, a^{2} c d e^{3}\right)} f^{2} g - {\left(a^{2} c d^{2} e^{2} - a^{3} e^{4}\right)} f g^{2}\right)} x}\right]"," ",0,"[1/2*(3*(c^2*d^2*e*g*x^3 + a*c*d^2*e*f + (c^2*d^2*e*f + (c^2*d^3 + a*c*d*e^2)*g)*x^2 + (a*c*d^2*e*g + (c^2*d^3 + a*c*d*e^2)*f)*x)*sqrt(-g/(c*d*f - a*e*g))*log(-(c*d*e*g*x^2 - c*d^2*f + 2*a*d*e*g - 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d*f - a*e*g)*sqrt(e*x + d)*sqrt(-g/(c*d*f - a*e*g)) - (c*d*e*f - (c*d^2 + 2*a*e^2)*g)*x)/(e*g*x^2 + d*f + (e*f + d*g)*x)) - 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(3*c*d*g*x + 2*c*d*f + a*e*g)*sqrt(e*x + d))/(a*c^2*d^3*e*f^3 - 2*a^2*c*d^2*e^2*f^2*g + a^3*d*e^3*f*g^2 + (c^3*d^3*e*f^2*g - 2*a*c^2*d^2*e^2*f*g^2 + a^2*c*d*e^3*g^3)*x^3 + (c^3*d^3*e*f^3 + (c^3*d^4 - a*c^2*d^2*e^2)*f^2*g - (2*a*c^2*d^3*e + a^2*c*d*e^3)*f*g^2 + (a^2*c*d^2*e^2 + a^3*e^4)*g^3)*x^2 + (a^3*d*e^3*g^3 + (c^3*d^4 + a*c^2*d^2*e^2)*f^3 - (a*c^2*d^3*e + 2*a^2*c*d*e^3)*f^2*g - (a^2*c*d^2*e^2 - a^3*e^4)*f*g^2)*x), -(3*(c^2*d^2*e*g*x^3 + a*c*d^2*e*f + (c^2*d^2*e*f + (c^2*d^3 + a*c*d*e^2)*g)*x^2 + (a*c*d^2*e*g + (c^2*d^3 + a*c*d*e^2)*f)*x)*sqrt(g/(c*d*f - a*e*g))*arctan(-sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d*f - a*e*g)*sqrt(e*x + d)*sqrt(g/(c*d*f - a*e*g))/(c*d*e*g*x^2 + a*d*e*g + (c*d^2 + a*e^2)*g*x)) + sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(3*c*d*g*x + 2*c*d*f + a*e*g)*sqrt(e*x + d))/(a*c^2*d^3*e*f^3 - 2*a^2*c*d^2*e^2*f^2*g + a^3*d*e^3*f*g^2 + (c^3*d^3*e*f^2*g - 2*a*c^2*d^2*e^2*f*g^2 + a^2*c*d*e^3*g^3)*x^3 + (c^3*d^3*e*f^3 + (c^3*d^4 - a*c^2*d^2*e^2)*f^2*g - (2*a*c^2*d^3*e + a^2*c*d*e^3)*f*g^2 + (a^2*c*d^2*e^2 + a^3*e^4)*g^3)*x^2 + (a^3*d*e^3*g^3 + (c^3*d^4 + a*c^2*d^2*e^2)*f^3 - (a*c^2*d^3*e + 2*a^2*c*d*e^3)*f^2*g - (a^2*c*d^2*e^2 - a^3*e^4)*f*g^2)*x)]","B",0
671,1,1863,0,0.470313," ","integrate((e*x+d)^(3/2)/(g*x+f)^3/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(c^{3} d^{3} e g^{2} x^{4} + a c^{2} d^{3} e f^{2} + {\left(2 \, c^{3} d^{3} e f g + {\left(c^{3} d^{4} + a c^{2} d^{2} e^{2}\right)} g^{2}\right)} x^{3} + {\left(c^{3} d^{3} e f^{2} + a c^{2} d^{3} e g^{2} + 2 \, {\left(c^{3} d^{4} + a c^{2} d^{2} e^{2}\right)} f g\right)} x^{2} + {\left(2 \, a c^{2} d^{3} e f g + {\left(c^{3} d^{4} + a c^{2} d^{2} e^{2}\right)} f^{2}\right)} x\right)} \sqrt{-\frac{g}{c d f - a e g}} \log\left(-\frac{c d e g x^{2} - c d^{2} f + 2 \, a d e g + 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d f - a e g\right)} \sqrt{e x + d} \sqrt{-\frac{g}{c d f - a e g}} - {\left(c d e f - {\left(c d^{2} + 2 \, a e^{2}\right)} g\right)} x}{e g x^{2} + d f + {\left(e f + d g\right)} x}\right) + 2 \, {\left(15 \, c^{2} d^{2} g^{2} x^{2} + 8 \, c^{2} d^{2} f^{2} + 9 \, a c d e f g - 2 \, a^{2} e^{2} g^{2} + 5 \, {\left(5 \, c^{2} d^{2} f g + a c d e g^{2}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{8 \, {\left(a c^{3} d^{4} e f^{5} - 3 \, a^{2} c^{2} d^{3} e^{2} f^{4} g + 3 \, a^{3} c d^{2} e^{3} f^{3} g^{2} - a^{4} d e^{4} f^{2} g^{3} + {\left(c^{4} d^{4} e f^{3} g^{2} - 3 \, a c^{3} d^{3} e^{2} f^{2} g^{3} + 3 \, a^{2} c^{2} d^{2} e^{3} f g^{4} - a^{3} c d e^{4} g^{5}\right)} x^{4} + {\left(2 \, c^{4} d^{4} e f^{4} g + {\left(c^{4} d^{5} - 5 \, a c^{3} d^{3} e^{2}\right)} f^{3} g^{2} - 3 \, {\left(a c^{3} d^{4} e - a^{2} c^{2} d^{2} e^{3}\right)} f^{2} g^{3} + {\left(3 \, a^{2} c^{2} d^{3} e^{2} + a^{3} c d e^{4}\right)} f g^{4} - {\left(a^{3} c d^{2} e^{3} + a^{4} e^{5}\right)} g^{5}\right)} x^{3} + {\left(c^{4} d^{4} e f^{5} - a^{4} d e^{4} g^{5} + {\left(2 \, c^{4} d^{5} - a c^{3} d^{3} e^{2}\right)} f^{4} g - {\left(5 \, a c^{3} d^{4} e + 3 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{3} g^{2} + {\left(3 \, a^{2} c^{2} d^{3} e^{2} + 5 \, a^{3} c d e^{4}\right)} f^{2} g^{3} + {\left(a^{3} c d^{2} e^{3} - 2 \, a^{4} e^{5}\right)} f g^{4}\right)} x^{2} - {\left(2 \, a^{4} d e^{4} f g^{4} - {\left(c^{4} d^{5} + a c^{3} d^{3} e^{2}\right)} f^{5} + {\left(a c^{3} d^{4} e + 3 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{4} g + 3 \, {\left(a^{2} c^{2} d^{3} e^{2} - a^{3} c d e^{4}\right)} f^{3} g^{2} - {\left(5 \, a^{3} c d^{2} e^{3} - a^{4} e^{5}\right)} f^{2} g^{3}\right)} x\right)}}, -\frac{15 \, {\left(c^{3} d^{3} e g^{2} x^{4} + a c^{2} d^{3} e f^{2} + {\left(2 \, c^{3} d^{3} e f g + {\left(c^{3} d^{4} + a c^{2} d^{2} e^{2}\right)} g^{2}\right)} x^{3} + {\left(c^{3} d^{3} e f^{2} + a c^{2} d^{3} e g^{2} + 2 \, {\left(c^{3} d^{4} + a c^{2} d^{2} e^{2}\right)} f g\right)} x^{2} + {\left(2 \, a c^{2} d^{3} e f g + {\left(c^{3} d^{4} + a c^{2} d^{2} e^{2}\right)} f^{2}\right)} x\right)} \sqrt{\frac{g}{c d f - a e g}} \arctan\left(-\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d f - a e g\right)} \sqrt{e x + d} \sqrt{\frac{g}{c d f - a e g}}}{c d e g x^{2} + a d e g + {\left(c d^{2} + a e^{2}\right)} g x}\right) + {\left(15 \, c^{2} d^{2} g^{2} x^{2} + 8 \, c^{2} d^{2} f^{2} + 9 \, a c d e f g - 2 \, a^{2} e^{2} g^{2} + 5 \, {\left(5 \, c^{2} d^{2} f g + a c d e g^{2}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{4 \, {\left(a c^{3} d^{4} e f^{5} - 3 \, a^{2} c^{2} d^{3} e^{2} f^{4} g + 3 \, a^{3} c d^{2} e^{3} f^{3} g^{2} - a^{4} d e^{4} f^{2} g^{3} + {\left(c^{4} d^{4} e f^{3} g^{2} - 3 \, a c^{3} d^{3} e^{2} f^{2} g^{3} + 3 \, a^{2} c^{2} d^{2} e^{3} f g^{4} - a^{3} c d e^{4} g^{5}\right)} x^{4} + {\left(2 \, c^{4} d^{4} e f^{4} g + {\left(c^{4} d^{5} - 5 \, a c^{3} d^{3} e^{2}\right)} f^{3} g^{2} - 3 \, {\left(a c^{3} d^{4} e - a^{2} c^{2} d^{2} e^{3}\right)} f^{2} g^{3} + {\left(3 \, a^{2} c^{2} d^{3} e^{2} + a^{3} c d e^{4}\right)} f g^{4} - {\left(a^{3} c d^{2} e^{3} + a^{4} e^{5}\right)} g^{5}\right)} x^{3} + {\left(c^{4} d^{4} e f^{5} - a^{4} d e^{4} g^{5} + {\left(2 \, c^{4} d^{5} - a c^{3} d^{3} e^{2}\right)} f^{4} g - {\left(5 \, a c^{3} d^{4} e + 3 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{3} g^{2} + {\left(3 \, a^{2} c^{2} d^{3} e^{2} + 5 \, a^{3} c d e^{4}\right)} f^{2} g^{3} + {\left(a^{3} c d^{2} e^{3} - 2 \, a^{4} e^{5}\right)} f g^{4}\right)} x^{2} - {\left(2 \, a^{4} d e^{4} f g^{4} - {\left(c^{4} d^{5} + a c^{3} d^{3} e^{2}\right)} f^{5} + {\left(a c^{3} d^{4} e + 3 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{4} g + 3 \, {\left(a^{2} c^{2} d^{3} e^{2} - a^{3} c d e^{4}\right)} f^{3} g^{2} - {\left(5 \, a^{3} c d^{2} e^{3} - a^{4} e^{5}\right)} f^{2} g^{3}\right)} x\right)}}\right]"," ",0,"[-1/8*(15*(c^3*d^3*e*g^2*x^4 + a*c^2*d^3*e*f^2 + (2*c^3*d^3*e*f*g + (c^3*d^4 + a*c^2*d^2*e^2)*g^2)*x^3 + (c^3*d^3*e*f^2 + a*c^2*d^3*e*g^2 + 2*(c^3*d^4 + a*c^2*d^2*e^2)*f*g)*x^2 + (2*a*c^2*d^3*e*f*g + (c^3*d^4 + a*c^2*d^2*e^2)*f^2)*x)*sqrt(-g/(c*d*f - a*e*g))*log(-(c*d*e*g*x^2 - c*d^2*f + 2*a*d*e*g + 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d*f - a*e*g)*sqrt(e*x + d)*sqrt(-g/(c*d*f - a*e*g)) - (c*d*e*f - (c*d^2 + 2*a*e^2)*g)*x)/(e*g*x^2 + d*f + (e*f + d*g)*x)) + 2*(15*c^2*d^2*g^2*x^2 + 8*c^2*d^2*f^2 + 9*a*c*d*e*f*g - 2*a^2*e^2*g^2 + 5*(5*c^2*d^2*f*g + a*c*d*e*g^2)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(a*c^3*d^4*e*f^5 - 3*a^2*c^2*d^3*e^2*f^4*g + 3*a^3*c*d^2*e^3*f^3*g^2 - a^4*d*e^4*f^2*g^3 + (c^4*d^4*e*f^3*g^2 - 3*a*c^3*d^3*e^2*f^2*g^3 + 3*a^2*c^2*d^2*e^3*f*g^4 - a^3*c*d*e^4*g^5)*x^4 + (2*c^4*d^4*e*f^4*g + (c^4*d^5 - 5*a*c^3*d^3*e^2)*f^3*g^2 - 3*(a*c^3*d^4*e - a^2*c^2*d^2*e^3)*f^2*g^3 + (3*a^2*c^2*d^3*e^2 + a^3*c*d*e^4)*f*g^4 - (a^3*c*d^2*e^3 + a^4*e^5)*g^5)*x^3 + (c^4*d^4*e*f^5 - a^4*d*e^4*g^5 + (2*c^4*d^5 - a*c^3*d^3*e^2)*f^4*g - (5*a*c^3*d^4*e + 3*a^2*c^2*d^2*e^3)*f^3*g^2 + (3*a^2*c^2*d^3*e^2 + 5*a^3*c*d*e^4)*f^2*g^3 + (a^3*c*d^2*e^3 - 2*a^4*e^5)*f*g^4)*x^2 - (2*a^4*d*e^4*f*g^4 - (c^4*d^5 + a*c^3*d^3*e^2)*f^5 + (a*c^3*d^4*e + 3*a^2*c^2*d^2*e^3)*f^4*g + 3*(a^2*c^2*d^3*e^2 - a^3*c*d*e^4)*f^3*g^2 - (5*a^3*c*d^2*e^3 - a^4*e^5)*f^2*g^3)*x), -1/4*(15*(c^3*d^3*e*g^2*x^4 + a*c^2*d^3*e*f^2 + (2*c^3*d^3*e*f*g + (c^3*d^4 + a*c^2*d^2*e^2)*g^2)*x^3 + (c^3*d^3*e*f^2 + a*c^2*d^3*e*g^2 + 2*(c^3*d^4 + a*c^2*d^2*e^2)*f*g)*x^2 + (2*a*c^2*d^3*e*f*g + (c^3*d^4 + a*c^2*d^2*e^2)*f^2)*x)*sqrt(g/(c*d*f - a*e*g))*arctan(-sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d*f - a*e*g)*sqrt(e*x + d)*sqrt(g/(c*d*f - a*e*g))/(c*d*e*g*x^2 + a*d*e*g + (c*d^2 + a*e^2)*g*x)) + (15*c^2*d^2*g^2*x^2 + 8*c^2*d^2*f^2 + 9*a*c*d*e*f*g - 2*a^2*e^2*g^2 + 5*(5*c^2*d^2*f*g + a*c*d*e*g^2)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(a*c^3*d^4*e*f^5 - 3*a^2*c^2*d^3*e^2*f^4*g + 3*a^3*c*d^2*e^3*f^3*g^2 - a^4*d*e^4*f^2*g^3 + (c^4*d^4*e*f^3*g^2 - 3*a*c^3*d^3*e^2*f^2*g^3 + 3*a^2*c^2*d^2*e^3*f*g^4 - a^3*c*d*e^4*g^5)*x^4 + (2*c^4*d^4*e*f^4*g + (c^4*d^5 - 5*a*c^3*d^3*e^2)*f^3*g^2 - 3*(a*c^3*d^4*e - a^2*c^2*d^2*e^3)*f^2*g^3 + (3*a^2*c^2*d^3*e^2 + a^3*c*d*e^4)*f*g^4 - (a^3*c*d^2*e^3 + a^4*e^5)*g^5)*x^3 + (c^4*d^4*e*f^5 - a^4*d*e^4*g^5 + (2*c^4*d^5 - a*c^3*d^3*e^2)*f^4*g - (5*a*c^3*d^4*e + 3*a^2*c^2*d^2*e^3)*f^3*g^2 + (3*a^2*c^2*d^3*e^2 + 5*a^3*c*d*e^4)*f^2*g^3 + (a^3*c*d^2*e^3 - 2*a^4*e^5)*f*g^4)*x^2 - (2*a^4*d*e^4*f*g^4 - (c^4*d^5 + a*c^3*d^3*e^2)*f^5 + (a*c^3*d^4*e + 3*a^2*c^2*d^2*e^3)*f^4*g + 3*(a^2*c^2*d^3*e^2 - a^3*c*d*e^4)*f^3*g^2 - (5*a^3*c*d^2*e^3 - a^4*e^5)*f^2*g^3)*x)]","B",0
672,1,251,0,0.419159," ","integrate((e*x+d)^(5/2)*(g*x+f)^3/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(c^{3} d^{3} g^{3} x^{3} - c^{3} d^{3} f^{3} - 6 \, a c^{2} d^{2} e f^{2} g + 24 \, a^{2} c d e^{2} f g^{2} - 16 \, a^{3} e^{3} g^{3} + 3 \, {\left(3 \, c^{3} d^{3} f g^{2} - 2 \, a c^{2} d^{2} e g^{3}\right)} x^{2} - 3 \, {\left(3 \, c^{3} d^{3} f^{2} g - 12 \, a c^{2} d^{2} e f g^{2} + 8 \, a^{2} c d e^{2} g^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{3 \, {\left(c^{6} d^{6} e x^{3} + a^{2} c^{4} d^{5} e^{2} + {\left(c^{6} d^{7} + 2 \, a c^{5} d^{5} e^{2}\right)} x^{2} + {\left(2 \, a c^{5} d^{6} e + a^{2} c^{4} d^{4} e^{3}\right)} x\right)}}"," ",0,"2/3*(c^3*d^3*g^3*x^3 - c^3*d^3*f^3 - 6*a*c^2*d^2*e*f^2*g + 24*a^2*c*d*e^2*f*g^2 - 16*a^3*e^3*g^3 + 3*(3*c^3*d^3*f*g^2 - 2*a*c^2*d^2*e*g^3)*x^2 - 3*(3*c^3*d^3*f^2*g - 12*a*c^2*d^2*e*f*g^2 + 8*a^2*c*d*e^2*g^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)/(c^6*d^6*e*x^3 + a^2*c^4*d^5*e^2 + (c^6*d^7 + 2*a*c^5*d^5*e^2)*x^2 + (2*a*c^5*d^6*e + a^2*c^4*d^4*e^3)*x)","A",0
673,1,180,0,0.407688," ","integrate((e*x+d)^(5/2)*(g*x+f)^2/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, c^{2} d^{2} g^{2} x^{2} - c^{2} d^{2} f^{2} - 4 \, a c d e f g + 8 \, a^{2} e^{2} g^{2} - 6 \, {\left(c^{2} d^{2} f g - 2 \, a c d e g^{2}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{3 \, {\left(c^{5} d^{5} e x^{3} + a^{2} c^{3} d^{4} e^{2} + {\left(c^{5} d^{6} + 2 \, a c^{4} d^{4} e^{2}\right)} x^{2} + {\left(2 \, a c^{4} d^{5} e + a^{2} c^{3} d^{3} e^{3}\right)} x\right)}}"," ",0,"2/3*(3*c^2*d^2*g^2*x^2 - c^2*d^2*f^2 - 4*a*c*d*e*f*g + 8*a^2*e^2*g^2 - 6*(c^2*d^2*f*g - 2*a*c*d*e*g^2)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)/(c^5*d^5*e*x^3 + a^2*c^3*d^4*e^2 + (c^5*d^6 + 2*a*c^4*d^4*e^2)*x^2 + (2*a*c^4*d^5*e + a^2*c^3*d^3*e^3)*x)","A",0
674,1,129,0,0.410923," ","integrate((e*x+d)^(5/2)*(g*x+f)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(3 \, c d g x + c d f + 2 \, a e g\right)} \sqrt{e x + d}}{3 \, {\left(c^{4} d^{4} e x^{3} + a^{2} c^{2} d^{3} e^{2} + {\left(c^{4} d^{5} + 2 \, a c^{3} d^{3} e^{2}\right)} x^{2} + {\left(2 \, a c^{3} d^{4} e + a^{2} c^{2} d^{2} e^{3}\right)} x\right)}}"," ",0,"-2/3*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(3*c*d*g*x + c*d*f + 2*a*e*g)*sqrt(e*x + d)/(c^4*d^4*e*x^3 + a^2*c^2*d^3*e^2 + (c^4*d^5 + 2*a*c^3*d^3*e^2)*x^2 + (2*a*c^3*d^4*e + a^2*c^2*d^2*e^3)*x)","A",0
675,1,107,0,0.407213," ","integrate((e*x+d)^(5/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{3 \, {\left(c^{3} d^{3} e x^{3} + a^{2} c d^{2} e^{2} + {\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2}\right)} x^{2} + {\left(2 \, a c^{2} d^{3} e + a^{2} c d e^{3}\right)} x\right)}}"," ",0,"-2/3*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)/(c^3*d^3*e*x^3 + a^2*c*d^2*e^2 + (c^3*d^4 + 2*a*c^2*d^2*e^2)*x^2 + (2*a*c^2*d^3*e + a^2*c*d*e^3)*x)","B",0
676,1,1015,0,0.430582," ","integrate((e*x+d)^(5/2)/(g*x+f)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(c^{2} d^{2} e g x^{3} + a^{2} d e^{2} g + {\left(c^{2} d^{3} + 2 \, a c d e^{2}\right)} g x^{2} + {\left(2 \, a c d^{2} e + a^{2} e^{3}\right)} g x\right)} \sqrt{-\frac{g}{c d f - a e g}} \log\left(-\frac{c d e g x^{2} - c d^{2} f + 2 \, a d e g + 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d f - a e g\right)} \sqrt{e x + d} \sqrt{-\frac{g}{c d f - a e g}} - {\left(c d e f - {\left(c d^{2} + 2 \, a e^{2}\right)} g\right)} x}{e g x^{2} + d f + {\left(e f + d g\right)} x}\right) + 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(3 \, c d g x - c d f + 4 \, a e g\right)} \sqrt{e x + d}}{3 \, {\left(a^{2} c^{2} d^{3} e^{2} f^{2} - 2 \, a^{3} c d^{2} e^{3} f g + a^{4} d e^{4} g^{2} + {\left(c^{4} d^{4} e f^{2} - 2 \, a c^{3} d^{3} e^{2} f g + a^{2} c^{2} d^{2} e^{3} g^{2}\right)} x^{3} + {\left({\left(c^{4} d^{5} + 2 \, a c^{3} d^{3} e^{2}\right)} f^{2} - 2 \, {\left(a c^{3} d^{4} e + 2 \, a^{2} c^{2} d^{2} e^{3}\right)} f g + {\left(a^{2} c^{2} d^{3} e^{2} + 2 \, a^{3} c d e^{4}\right)} g^{2}\right)} x^{2} + {\left({\left(2 \, a c^{3} d^{4} e + a^{2} c^{2} d^{2} e^{3}\right)} f^{2} - 2 \, {\left(2 \, a^{2} c^{2} d^{3} e^{2} + a^{3} c d e^{4}\right)} f g + {\left(2 \, a^{3} c d^{2} e^{3} + a^{4} e^{5}\right)} g^{2}\right)} x\right)}}, \frac{2 \, {\left(3 \, {\left(c^{2} d^{2} e g x^{3} + a^{2} d e^{2} g + {\left(c^{2} d^{3} + 2 \, a c d e^{2}\right)} g x^{2} + {\left(2 \, a c d^{2} e + a^{2} e^{3}\right)} g x\right)} \sqrt{\frac{g}{c d f - a e g}} \arctan\left(-\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d f - a e g\right)} \sqrt{e x + d} \sqrt{\frac{g}{c d f - a e g}}}{c d e g x^{2} + a d e g + {\left(c d^{2} + a e^{2}\right)} g x}\right) + \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(3 \, c d g x - c d f + 4 \, a e g\right)} \sqrt{e x + d}\right)}}{3 \, {\left(a^{2} c^{2} d^{3} e^{2} f^{2} - 2 \, a^{3} c d^{2} e^{3} f g + a^{4} d e^{4} g^{2} + {\left(c^{4} d^{4} e f^{2} - 2 \, a c^{3} d^{3} e^{2} f g + a^{2} c^{2} d^{2} e^{3} g^{2}\right)} x^{3} + {\left({\left(c^{4} d^{5} + 2 \, a c^{3} d^{3} e^{2}\right)} f^{2} - 2 \, {\left(a c^{3} d^{4} e + 2 \, a^{2} c^{2} d^{2} e^{3}\right)} f g + {\left(a^{2} c^{2} d^{3} e^{2} + 2 \, a^{3} c d e^{4}\right)} g^{2}\right)} x^{2} + {\left({\left(2 \, a c^{3} d^{4} e + a^{2} c^{2} d^{2} e^{3}\right)} f^{2} - 2 \, {\left(2 \, a^{2} c^{2} d^{3} e^{2} + a^{3} c d e^{4}\right)} f g + {\left(2 \, a^{3} c d^{2} e^{3} + a^{4} e^{5}\right)} g^{2}\right)} x\right)}}\right]"," ",0,"[1/3*(3*(c^2*d^2*e*g*x^3 + a^2*d*e^2*g + (c^2*d^3 + 2*a*c*d*e^2)*g*x^2 + (2*a*c*d^2*e + a^2*e^3)*g*x)*sqrt(-g/(c*d*f - a*e*g))*log(-(c*d*e*g*x^2 - c*d^2*f + 2*a*d*e*g + 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d*f - a*e*g)*sqrt(e*x + d)*sqrt(-g/(c*d*f - a*e*g)) - (c*d*e*f - (c*d^2 + 2*a*e^2)*g)*x)/(e*g*x^2 + d*f + (e*f + d*g)*x)) + 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(3*c*d*g*x - c*d*f + 4*a*e*g)*sqrt(e*x + d))/(a^2*c^2*d^3*e^2*f^2 - 2*a^3*c*d^2*e^3*f*g + a^4*d*e^4*g^2 + (c^4*d^4*e*f^2 - 2*a*c^3*d^3*e^2*f*g + a^2*c^2*d^2*e^3*g^2)*x^3 + ((c^4*d^5 + 2*a*c^3*d^3*e^2)*f^2 - 2*(a*c^3*d^4*e + 2*a^2*c^2*d^2*e^3)*f*g + (a^2*c^2*d^3*e^2 + 2*a^3*c*d*e^4)*g^2)*x^2 + ((2*a*c^3*d^4*e + a^2*c^2*d^2*e^3)*f^2 - 2*(2*a^2*c^2*d^3*e^2 + a^3*c*d*e^4)*f*g + (2*a^3*c*d^2*e^3 + a^4*e^5)*g^2)*x), 2/3*(3*(c^2*d^2*e*g*x^3 + a^2*d*e^2*g + (c^2*d^3 + 2*a*c*d*e^2)*g*x^2 + (2*a*c*d^2*e + a^2*e^3)*g*x)*sqrt(g/(c*d*f - a*e*g))*arctan(-sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d*f - a*e*g)*sqrt(e*x + d)*sqrt(g/(c*d*f - a*e*g))/(c*d*e*g*x^2 + a*d*e*g + (c*d^2 + a*e^2)*g*x)) + sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(3*c*d*g*x - c*d*f + 4*a*e*g)*sqrt(e*x + d))/(a^2*c^2*d^3*e^2*f^2 - 2*a^3*c*d^2*e^3*f*g + a^4*d*e^4*g^2 + (c^4*d^4*e*f^2 - 2*a*c^3*d^3*e^2*f*g + a^2*c^2*d^2*e^3*g^2)*x^3 + ((c^4*d^5 + 2*a*c^3*d^3*e^2)*f^2 - 2*(a*c^3*d^4*e + 2*a^2*c^2*d^2*e^3)*f*g + (a^2*c^2*d^3*e^2 + 2*a^3*c*d*e^4)*g^2)*x^2 + ((2*a*c^3*d^4*e + a^2*c^2*d^2*e^3)*f^2 - 2*(2*a^2*c^2*d^3*e^2 + a^3*c*d*e^4)*f*g + (2*a^3*c*d^2*e^3 + a^4*e^5)*g^2)*x)]","B",0
677,1,1907,0,0.481745," ","integrate((e*x+d)^(5/2)/(g*x+f)^2/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(c^{3} d^{3} e g^{2} x^{4} + a^{2} c d^{2} e^{2} f g + {\left(c^{3} d^{3} e f g + {\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2}\right)} g^{2}\right)} x^{3} + {\left({\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2}\right)} f g + {\left(2 \, a c^{2} d^{3} e + a^{2} c d e^{3}\right)} g^{2}\right)} x^{2} + {\left(a^{2} c d^{2} e^{2} g^{2} + {\left(2 \, a c^{2} d^{3} e + a^{2} c d e^{3}\right)} f g\right)} x\right)} \sqrt{-\frac{g}{c d f - a e g}} \log\left(-\frac{c d e g x^{2} - c d^{2} f + 2 \, a d e g - 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d f - a e g\right)} \sqrt{e x + d} \sqrt{-\frac{g}{c d f - a e g}} - {\left(c d e f - {\left(c d^{2} + 2 \, a e^{2}\right)} g\right)} x}{e g x^{2} + d f + {\left(e f + d g\right)} x}\right) - 2 \, {\left(15 \, c^{2} d^{2} g^{2} x^{2} - 2 \, c^{2} d^{2} f^{2} + 14 \, a c d e f g + 3 \, a^{2} e^{2} g^{2} + 10 \, {\left(c^{2} d^{2} f g + 2 \, a c d e g^{2}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{6 \, {\left(a^{2} c^{3} d^{4} e^{2} f^{4} - 3 \, a^{3} c^{2} d^{3} e^{3} f^{3} g + 3 \, a^{4} c d^{2} e^{4} f^{2} g^{2} - a^{5} d e^{5} f g^{3} + {\left(c^{5} d^{5} e f^{3} g - 3 \, a c^{4} d^{4} e^{2} f^{2} g^{2} + 3 \, a^{2} c^{3} d^{3} e^{3} f g^{3} - a^{3} c^{2} d^{2} e^{4} g^{4}\right)} x^{4} + {\left(c^{5} d^{5} e f^{4} + {\left(c^{5} d^{6} - a c^{4} d^{4} e^{2}\right)} f^{3} g - 3 \, {\left(a c^{4} d^{5} e + a^{2} c^{3} d^{3} e^{3}\right)} f^{2} g^{2} + {\left(3 \, a^{2} c^{3} d^{4} e^{2} + 5 \, a^{3} c^{2} d^{2} e^{4}\right)} f g^{3} - {\left(a^{3} c^{2} d^{3} e^{3} + 2 \, a^{4} c d e^{5}\right)} g^{4}\right)} x^{3} + {\left({\left(c^{5} d^{6} + 2 \, a c^{4} d^{4} e^{2}\right)} f^{4} - {\left(a c^{4} d^{5} e + 5 \, a^{2} c^{3} d^{3} e^{3}\right)} f^{3} g - 3 \, {\left(a^{2} c^{3} d^{4} e^{2} - a^{3} c^{2} d^{2} e^{4}\right)} f^{2} g^{2} + {\left(5 \, a^{3} c^{2} d^{3} e^{3} + a^{4} c d e^{5}\right)} f g^{3} - {\left(2 \, a^{4} c d^{2} e^{4} + a^{5} e^{6}\right)} g^{4}\right)} x^{2} - {\left(a^{5} d e^{5} g^{4} - {\left(2 \, a c^{4} d^{5} e + a^{2} c^{3} d^{3} e^{3}\right)} f^{4} + {\left(5 \, a^{2} c^{3} d^{4} e^{2} + 3 \, a^{3} c^{2} d^{2} e^{4}\right)} f^{3} g - 3 \, {\left(a^{3} c^{2} d^{3} e^{3} + a^{4} c d e^{5}\right)} f^{2} g^{2} - {\left(a^{4} c d^{2} e^{4} - a^{5} e^{6}\right)} f g^{3}\right)} x\right)}}, \frac{15 \, {\left(c^{3} d^{3} e g^{2} x^{4} + a^{2} c d^{2} e^{2} f g + {\left(c^{3} d^{3} e f g + {\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2}\right)} g^{2}\right)} x^{3} + {\left({\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2}\right)} f g + {\left(2 \, a c^{2} d^{3} e + a^{2} c d e^{3}\right)} g^{2}\right)} x^{2} + {\left(a^{2} c d^{2} e^{2} g^{2} + {\left(2 \, a c^{2} d^{3} e + a^{2} c d e^{3}\right)} f g\right)} x\right)} \sqrt{\frac{g}{c d f - a e g}} \arctan\left(-\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d f - a e g\right)} \sqrt{e x + d} \sqrt{\frac{g}{c d f - a e g}}}{c d e g x^{2} + a d e g + {\left(c d^{2} + a e^{2}\right)} g x}\right) + {\left(15 \, c^{2} d^{2} g^{2} x^{2} - 2 \, c^{2} d^{2} f^{2} + 14 \, a c d e f g + 3 \, a^{2} e^{2} g^{2} + 10 \, {\left(c^{2} d^{2} f g + 2 \, a c d e g^{2}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{3 \, {\left(a^{2} c^{3} d^{4} e^{2} f^{4} - 3 \, a^{3} c^{2} d^{3} e^{3} f^{3} g + 3 \, a^{4} c d^{2} e^{4} f^{2} g^{2} - a^{5} d e^{5} f g^{3} + {\left(c^{5} d^{5} e f^{3} g - 3 \, a c^{4} d^{4} e^{2} f^{2} g^{2} + 3 \, a^{2} c^{3} d^{3} e^{3} f g^{3} - a^{3} c^{2} d^{2} e^{4} g^{4}\right)} x^{4} + {\left(c^{5} d^{5} e f^{4} + {\left(c^{5} d^{6} - a c^{4} d^{4} e^{2}\right)} f^{3} g - 3 \, {\left(a c^{4} d^{5} e + a^{2} c^{3} d^{3} e^{3}\right)} f^{2} g^{2} + {\left(3 \, a^{2} c^{3} d^{4} e^{2} + 5 \, a^{3} c^{2} d^{2} e^{4}\right)} f g^{3} - {\left(a^{3} c^{2} d^{3} e^{3} + 2 \, a^{4} c d e^{5}\right)} g^{4}\right)} x^{3} + {\left({\left(c^{5} d^{6} + 2 \, a c^{4} d^{4} e^{2}\right)} f^{4} - {\left(a c^{4} d^{5} e + 5 \, a^{2} c^{3} d^{3} e^{3}\right)} f^{3} g - 3 \, {\left(a^{2} c^{3} d^{4} e^{2} - a^{3} c^{2} d^{2} e^{4}\right)} f^{2} g^{2} + {\left(5 \, a^{3} c^{2} d^{3} e^{3} + a^{4} c d e^{5}\right)} f g^{3} - {\left(2 \, a^{4} c d^{2} e^{4} + a^{5} e^{6}\right)} g^{4}\right)} x^{2} - {\left(a^{5} d e^{5} g^{4} - {\left(2 \, a c^{4} d^{5} e + a^{2} c^{3} d^{3} e^{3}\right)} f^{4} + {\left(5 \, a^{2} c^{3} d^{4} e^{2} + 3 \, a^{3} c^{2} d^{2} e^{4}\right)} f^{3} g - 3 \, {\left(a^{3} c^{2} d^{3} e^{3} + a^{4} c d e^{5}\right)} f^{2} g^{2} - {\left(a^{4} c d^{2} e^{4} - a^{5} e^{6}\right)} f g^{3}\right)} x\right)}}\right]"," ",0,"[-1/6*(15*(c^3*d^3*e*g^2*x^4 + a^2*c*d^2*e^2*f*g + (c^3*d^3*e*f*g + (c^3*d^4 + 2*a*c^2*d^2*e^2)*g^2)*x^3 + ((c^3*d^4 + 2*a*c^2*d^2*e^2)*f*g + (2*a*c^2*d^3*e + a^2*c*d*e^3)*g^2)*x^2 + (a^2*c*d^2*e^2*g^2 + (2*a*c^2*d^3*e + a^2*c*d*e^3)*f*g)*x)*sqrt(-g/(c*d*f - a*e*g))*log(-(c*d*e*g*x^2 - c*d^2*f + 2*a*d*e*g - 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d*f - a*e*g)*sqrt(e*x + d)*sqrt(-g/(c*d*f - a*e*g)) - (c*d*e*f - (c*d^2 + 2*a*e^2)*g)*x)/(e*g*x^2 + d*f + (e*f + d*g)*x)) - 2*(15*c^2*d^2*g^2*x^2 - 2*c^2*d^2*f^2 + 14*a*c*d*e*f*g + 3*a^2*e^2*g^2 + 10*(c^2*d^2*f*g + 2*a*c*d*e*g^2)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(a^2*c^3*d^4*e^2*f^4 - 3*a^3*c^2*d^3*e^3*f^3*g + 3*a^4*c*d^2*e^4*f^2*g^2 - a^5*d*e^5*f*g^3 + (c^5*d^5*e*f^3*g - 3*a*c^4*d^4*e^2*f^2*g^2 + 3*a^2*c^3*d^3*e^3*f*g^3 - a^3*c^2*d^2*e^4*g^4)*x^4 + (c^5*d^5*e*f^4 + (c^5*d^6 - a*c^4*d^4*e^2)*f^3*g - 3*(a*c^4*d^5*e + a^2*c^3*d^3*e^3)*f^2*g^2 + (3*a^2*c^3*d^4*e^2 + 5*a^3*c^2*d^2*e^4)*f*g^3 - (a^3*c^2*d^3*e^3 + 2*a^4*c*d*e^5)*g^4)*x^3 + ((c^5*d^6 + 2*a*c^4*d^4*e^2)*f^4 - (a*c^4*d^5*e + 5*a^2*c^3*d^3*e^3)*f^3*g - 3*(a^2*c^3*d^4*e^2 - a^3*c^2*d^2*e^4)*f^2*g^2 + (5*a^3*c^2*d^3*e^3 + a^4*c*d*e^5)*f*g^3 - (2*a^4*c*d^2*e^4 + a^5*e^6)*g^4)*x^2 - (a^5*d*e^5*g^4 - (2*a*c^4*d^5*e + a^2*c^3*d^3*e^3)*f^4 + (5*a^2*c^3*d^4*e^2 + 3*a^3*c^2*d^2*e^4)*f^3*g - 3*(a^3*c^2*d^3*e^3 + a^4*c*d*e^5)*f^2*g^2 - (a^4*c*d^2*e^4 - a^5*e^6)*f*g^3)*x), 1/3*(15*(c^3*d^3*e*g^2*x^4 + a^2*c*d^2*e^2*f*g + (c^3*d^3*e*f*g + (c^3*d^4 + 2*a*c^2*d^2*e^2)*g^2)*x^3 + ((c^3*d^4 + 2*a*c^2*d^2*e^2)*f*g + (2*a*c^2*d^3*e + a^2*c*d*e^3)*g^2)*x^2 + (a^2*c*d^2*e^2*g^2 + (2*a*c^2*d^3*e + a^2*c*d*e^3)*f*g)*x)*sqrt(g/(c*d*f - a*e*g))*arctan(-sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d*f - a*e*g)*sqrt(e*x + d)*sqrt(g/(c*d*f - a*e*g))/(c*d*e*g*x^2 + a*d*e*g + (c*d^2 + a*e^2)*g*x)) + (15*c^2*d^2*g^2*x^2 - 2*c^2*d^2*f^2 + 14*a*c*d*e*f*g + 3*a^2*e^2*g^2 + 10*(c^2*d^2*f*g + 2*a*c*d*e*g^2)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(a^2*c^3*d^4*e^2*f^4 - 3*a^3*c^2*d^3*e^3*f^3*g + 3*a^4*c*d^2*e^4*f^2*g^2 - a^5*d*e^5*f*g^3 + (c^5*d^5*e*f^3*g - 3*a*c^4*d^4*e^2*f^2*g^2 + 3*a^2*c^3*d^3*e^3*f*g^3 - a^3*c^2*d^2*e^4*g^4)*x^4 + (c^5*d^5*e*f^4 + (c^5*d^6 - a*c^4*d^4*e^2)*f^3*g - 3*(a*c^4*d^5*e + a^2*c^3*d^3*e^3)*f^2*g^2 + (3*a^2*c^3*d^4*e^2 + 5*a^3*c^2*d^2*e^4)*f*g^3 - (a^3*c^2*d^3*e^3 + 2*a^4*c*d*e^5)*g^4)*x^3 + ((c^5*d^6 + 2*a*c^4*d^4*e^2)*f^4 - (a*c^4*d^5*e + 5*a^2*c^3*d^3*e^3)*f^3*g - 3*(a^2*c^3*d^4*e^2 - a^3*c^2*d^2*e^4)*f^2*g^2 + (5*a^3*c^2*d^3*e^3 + a^4*c*d*e^5)*f*g^3 - (2*a^4*c*d^2*e^4 + a^5*e^6)*g^4)*x^2 - (a^5*d*e^5*g^4 - (2*a*c^4*d^5*e + a^2*c^3*d^3*e^3)*f^4 + (5*a^2*c^3*d^4*e^2 + 3*a^3*c^2*d^2*e^4)*f^3*g - 3*(a^3*c^2*d^3*e^3 + a^4*c*d*e^5)*f^2*g^2 - (a^4*c*d^2*e^4 - a^5*e^6)*f*g^3)*x)]","B",0
678,1,2935,0,0.490335," ","integrate((e*x+d)^(5/2)/(g*x+f)^3/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(c^{4} d^{4} e g^{3} x^{5} + a^{2} c^{2} d^{3} e^{2} f^{2} g + {\left(2 \, c^{4} d^{4} e f g^{2} + {\left(c^{4} d^{5} + 2 \, a c^{3} d^{3} e^{2}\right)} g^{3}\right)} x^{4} + {\left(c^{4} d^{4} e f^{2} g + 2 \, {\left(c^{4} d^{5} + 2 \, a c^{3} d^{3} e^{2}\right)} f g^{2} + {\left(2 \, a c^{3} d^{4} e + a^{2} c^{2} d^{2} e^{3}\right)} g^{3}\right)} x^{3} + {\left(a^{2} c^{2} d^{3} e^{2} g^{3} + {\left(c^{4} d^{5} + 2 \, a c^{3} d^{3} e^{2}\right)} f^{2} g + 2 \, {\left(2 \, a c^{3} d^{4} e + a^{2} c^{2} d^{2} e^{3}\right)} f g^{2}\right)} x^{2} + {\left(2 \, a^{2} c^{2} d^{3} e^{2} f g^{2} + {\left(2 \, a c^{3} d^{4} e + a^{2} c^{2} d^{2} e^{3}\right)} f^{2} g\right)} x\right)} \sqrt{-\frac{g}{c d f - a e g}} \log\left(-\frac{c d e g x^{2} - c d^{2} f + 2 \, a d e g + 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d f - a e g\right)} \sqrt{e x + d} \sqrt{-\frac{g}{c d f - a e g}} - {\left(c d e f - {\left(c d^{2} + 2 \, a e^{2}\right)} g\right)} x}{e g x^{2} + d f + {\left(e f + d g\right)} x}\right) + 2 \, {\left(105 \, c^{3} d^{3} g^{3} x^{3} - 8 \, c^{3} d^{3} f^{3} + 80 \, a c^{2} d^{2} e f^{2} g + 39 \, a^{2} c d e^{2} f g^{2} - 6 \, a^{3} e^{3} g^{3} + 35 \, {\left(5 \, c^{3} d^{3} f g^{2} + 4 \, a c^{2} d^{2} e g^{3}\right)} x^{2} + 7 \, {\left(8 \, c^{3} d^{3} f^{2} g + 34 \, a c^{2} d^{2} e f g^{2} + 3 \, a^{2} c d e^{2} g^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{24 \, {\left(a^{2} c^{4} d^{5} e^{2} f^{6} - 4 \, a^{3} c^{3} d^{4} e^{3} f^{5} g + 6 \, a^{4} c^{2} d^{3} e^{4} f^{4} g^{2} - 4 \, a^{5} c d^{2} e^{5} f^{3} g^{3} + a^{6} d e^{6} f^{2} g^{4} + {\left(c^{6} d^{6} e f^{4} g^{2} - 4 \, a c^{5} d^{5} e^{2} f^{3} g^{3} + 6 \, a^{2} c^{4} d^{4} e^{3} f^{2} g^{4} - 4 \, a^{3} c^{3} d^{3} e^{4} f g^{5} + a^{4} c^{2} d^{2} e^{5} g^{6}\right)} x^{5} + {\left(2 \, c^{6} d^{6} e f^{5} g + {\left(c^{6} d^{7} - 6 \, a c^{5} d^{5} e^{2}\right)} f^{4} g^{2} - 4 \, {\left(a c^{5} d^{6} e - a^{2} c^{4} d^{4} e^{3}\right)} f^{3} g^{3} + 2 \, {\left(3 \, a^{2} c^{4} d^{5} e^{2} + 2 \, a^{3} c^{3} d^{3} e^{4}\right)} f^{2} g^{4} - 2 \, {\left(2 \, a^{3} c^{3} d^{4} e^{3} + 3 \, a^{4} c^{2} d^{2} e^{5}\right)} f g^{5} + {\left(a^{4} c^{2} d^{3} e^{4} + 2 \, a^{5} c d e^{6}\right)} g^{6}\right)} x^{4} + {\left(c^{6} d^{6} e f^{6} + 2 \, c^{6} d^{7} f^{5} g - 6 \, a^{4} c^{2} d^{3} e^{4} f g^{5} - 3 \, {\left(2 \, a c^{5} d^{6} e + 3 \, a^{2} c^{4} d^{4} e^{3}\right)} f^{4} g^{2} + 4 \, {\left(a^{2} c^{4} d^{5} e^{2} + 4 \, a^{3} c^{3} d^{3} e^{4}\right)} f^{3} g^{3} + {\left(4 \, a^{3} c^{3} d^{4} e^{3} - 9 \, a^{4} c^{2} d^{2} e^{5}\right)} f^{2} g^{4} + {\left(2 \, a^{5} c d^{2} e^{5} + a^{6} e^{7}\right)} g^{6}\right)} x^{3} - {\left(6 \, a^{2} c^{4} d^{4} e^{3} f^{5} g - 2 \, a^{6} e^{7} f g^{5} - a^{6} d e^{6} g^{6} - {\left(c^{6} d^{7} + 2 \, a c^{5} d^{5} e^{2}\right)} f^{6} + {\left(9 \, a^{2} c^{4} d^{5} e^{2} - 4 \, a^{3} c^{3} d^{3} e^{4}\right)} f^{4} g^{2} - 4 \, {\left(4 \, a^{3} c^{3} d^{4} e^{3} + a^{4} c^{2} d^{2} e^{5}\right)} f^{3} g^{3} + 3 \, {\left(3 \, a^{4} c^{2} d^{3} e^{4} + 2 \, a^{5} c d e^{6}\right)} f^{2} g^{4}\right)} x^{2} + {\left(2 \, a^{6} d e^{6} f g^{5} + {\left(2 \, a c^{5} d^{6} e + a^{2} c^{4} d^{4} e^{3}\right)} f^{6} - 2 \, {\left(3 \, a^{2} c^{4} d^{5} e^{2} + 2 \, a^{3} c^{3} d^{3} e^{4}\right)} f^{5} g + 2 \, {\left(2 \, a^{3} c^{3} d^{4} e^{3} + 3 \, a^{4} c^{2} d^{2} e^{5}\right)} f^{4} g^{2} + 4 \, {\left(a^{4} c^{2} d^{3} e^{4} - a^{5} c d e^{6}\right)} f^{3} g^{3} - {\left(6 \, a^{5} c d^{2} e^{5} - a^{6} e^{7}\right)} f^{2} g^{4}\right)} x\right)}}, \frac{105 \, {\left(c^{4} d^{4} e g^{3} x^{5} + a^{2} c^{2} d^{3} e^{2} f^{2} g + {\left(2 \, c^{4} d^{4} e f g^{2} + {\left(c^{4} d^{5} + 2 \, a c^{3} d^{3} e^{2}\right)} g^{3}\right)} x^{4} + {\left(c^{4} d^{4} e f^{2} g + 2 \, {\left(c^{4} d^{5} + 2 \, a c^{3} d^{3} e^{2}\right)} f g^{2} + {\left(2 \, a c^{3} d^{4} e + a^{2} c^{2} d^{2} e^{3}\right)} g^{3}\right)} x^{3} + {\left(a^{2} c^{2} d^{3} e^{2} g^{3} + {\left(c^{4} d^{5} + 2 \, a c^{3} d^{3} e^{2}\right)} f^{2} g + 2 \, {\left(2 \, a c^{3} d^{4} e + a^{2} c^{2} d^{2} e^{3}\right)} f g^{2}\right)} x^{2} + {\left(2 \, a^{2} c^{2} d^{3} e^{2} f g^{2} + {\left(2 \, a c^{3} d^{4} e + a^{2} c^{2} d^{2} e^{3}\right)} f^{2} g\right)} x\right)} \sqrt{\frac{g}{c d f - a e g}} \arctan\left(-\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d f - a e g\right)} \sqrt{e x + d} \sqrt{\frac{g}{c d f - a e g}}}{c d e g x^{2} + a d e g + {\left(c d^{2} + a e^{2}\right)} g x}\right) + {\left(105 \, c^{3} d^{3} g^{3} x^{3} - 8 \, c^{3} d^{3} f^{3} + 80 \, a c^{2} d^{2} e f^{2} g + 39 \, a^{2} c d e^{2} f g^{2} - 6 \, a^{3} e^{3} g^{3} + 35 \, {\left(5 \, c^{3} d^{3} f g^{2} + 4 \, a c^{2} d^{2} e g^{3}\right)} x^{2} + 7 \, {\left(8 \, c^{3} d^{3} f^{2} g + 34 \, a c^{2} d^{2} e f g^{2} + 3 \, a^{2} c d e^{2} g^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{12 \, {\left(a^{2} c^{4} d^{5} e^{2} f^{6} - 4 \, a^{3} c^{3} d^{4} e^{3} f^{5} g + 6 \, a^{4} c^{2} d^{3} e^{4} f^{4} g^{2} - 4 \, a^{5} c d^{2} e^{5} f^{3} g^{3} + a^{6} d e^{6} f^{2} g^{4} + {\left(c^{6} d^{6} e f^{4} g^{2} - 4 \, a c^{5} d^{5} e^{2} f^{3} g^{3} + 6 \, a^{2} c^{4} d^{4} e^{3} f^{2} g^{4} - 4 \, a^{3} c^{3} d^{3} e^{4} f g^{5} + a^{4} c^{2} d^{2} e^{5} g^{6}\right)} x^{5} + {\left(2 \, c^{6} d^{6} e f^{5} g + {\left(c^{6} d^{7} - 6 \, a c^{5} d^{5} e^{2}\right)} f^{4} g^{2} - 4 \, {\left(a c^{5} d^{6} e - a^{2} c^{4} d^{4} e^{3}\right)} f^{3} g^{3} + 2 \, {\left(3 \, a^{2} c^{4} d^{5} e^{2} + 2 \, a^{3} c^{3} d^{3} e^{4}\right)} f^{2} g^{4} - 2 \, {\left(2 \, a^{3} c^{3} d^{4} e^{3} + 3 \, a^{4} c^{2} d^{2} e^{5}\right)} f g^{5} + {\left(a^{4} c^{2} d^{3} e^{4} + 2 \, a^{5} c d e^{6}\right)} g^{6}\right)} x^{4} + {\left(c^{6} d^{6} e f^{6} + 2 \, c^{6} d^{7} f^{5} g - 6 \, a^{4} c^{2} d^{3} e^{4} f g^{5} - 3 \, {\left(2 \, a c^{5} d^{6} e + 3 \, a^{2} c^{4} d^{4} e^{3}\right)} f^{4} g^{2} + 4 \, {\left(a^{2} c^{4} d^{5} e^{2} + 4 \, a^{3} c^{3} d^{3} e^{4}\right)} f^{3} g^{3} + {\left(4 \, a^{3} c^{3} d^{4} e^{3} - 9 \, a^{4} c^{2} d^{2} e^{5}\right)} f^{2} g^{4} + {\left(2 \, a^{5} c d^{2} e^{5} + a^{6} e^{7}\right)} g^{6}\right)} x^{3} - {\left(6 \, a^{2} c^{4} d^{4} e^{3} f^{5} g - 2 \, a^{6} e^{7} f g^{5} - a^{6} d e^{6} g^{6} - {\left(c^{6} d^{7} + 2 \, a c^{5} d^{5} e^{2}\right)} f^{6} + {\left(9 \, a^{2} c^{4} d^{5} e^{2} - 4 \, a^{3} c^{3} d^{3} e^{4}\right)} f^{4} g^{2} - 4 \, {\left(4 \, a^{3} c^{3} d^{4} e^{3} + a^{4} c^{2} d^{2} e^{5}\right)} f^{3} g^{3} + 3 \, {\left(3 \, a^{4} c^{2} d^{3} e^{4} + 2 \, a^{5} c d e^{6}\right)} f^{2} g^{4}\right)} x^{2} + {\left(2 \, a^{6} d e^{6} f g^{5} + {\left(2 \, a c^{5} d^{6} e + a^{2} c^{4} d^{4} e^{3}\right)} f^{6} - 2 \, {\left(3 \, a^{2} c^{4} d^{5} e^{2} + 2 \, a^{3} c^{3} d^{3} e^{4}\right)} f^{5} g + 2 \, {\left(2 \, a^{3} c^{3} d^{4} e^{3} + 3 \, a^{4} c^{2} d^{2} e^{5}\right)} f^{4} g^{2} + 4 \, {\left(a^{4} c^{2} d^{3} e^{4} - a^{5} c d e^{6}\right)} f^{3} g^{3} - {\left(6 \, a^{5} c d^{2} e^{5} - a^{6} e^{7}\right)} f^{2} g^{4}\right)} x\right)}}\right]"," ",0,"[1/24*(105*(c^4*d^4*e*g^3*x^5 + a^2*c^2*d^3*e^2*f^2*g + (2*c^4*d^4*e*f*g^2 + (c^4*d^5 + 2*a*c^3*d^3*e^2)*g^3)*x^4 + (c^4*d^4*e*f^2*g + 2*(c^4*d^5 + 2*a*c^3*d^3*e^2)*f*g^2 + (2*a*c^3*d^4*e + a^2*c^2*d^2*e^3)*g^3)*x^3 + (a^2*c^2*d^3*e^2*g^3 + (c^4*d^5 + 2*a*c^3*d^3*e^2)*f^2*g + 2*(2*a*c^3*d^4*e + a^2*c^2*d^2*e^3)*f*g^2)*x^2 + (2*a^2*c^2*d^3*e^2*f*g^2 + (2*a*c^3*d^4*e + a^2*c^2*d^2*e^3)*f^2*g)*x)*sqrt(-g/(c*d*f - a*e*g))*log(-(c*d*e*g*x^2 - c*d^2*f + 2*a*d*e*g + 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d*f - a*e*g)*sqrt(e*x + d)*sqrt(-g/(c*d*f - a*e*g)) - (c*d*e*f - (c*d^2 + 2*a*e^2)*g)*x)/(e*g*x^2 + d*f + (e*f + d*g)*x)) + 2*(105*c^3*d^3*g^3*x^3 - 8*c^3*d^3*f^3 + 80*a*c^2*d^2*e*f^2*g + 39*a^2*c*d*e^2*f*g^2 - 6*a^3*e^3*g^3 + 35*(5*c^3*d^3*f*g^2 + 4*a*c^2*d^2*e*g^3)*x^2 + 7*(8*c^3*d^3*f^2*g + 34*a*c^2*d^2*e*f*g^2 + 3*a^2*c*d*e^2*g^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(a^2*c^4*d^5*e^2*f^6 - 4*a^3*c^3*d^4*e^3*f^5*g + 6*a^4*c^2*d^3*e^4*f^4*g^2 - 4*a^5*c*d^2*e^5*f^3*g^3 + a^6*d*e^6*f^2*g^4 + (c^6*d^6*e*f^4*g^2 - 4*a*c^5*d^5*e^2*f^3*g^3 + 6*a^2*c^4*d^4*e^3*f^2*g^4 - 4*a^3*c^3*d^3*e^4*f*g^5 + a^4*c^2*d^2*e^5*g^6)*x^5 + (2*c^6*d^6*e*f^5*g + (c^6*d^7 - 6*a*c^5*d^5*e^2)*f^4*g^2 - 4*(a*c^5*d^6*e - a^2*c^4*d^4*e^3)*f^3*g^3 + 2*(3*a^2*c^4*d^5*e^2 + 2*a^3*c^3*d^3*e^4)*f^2*g^4 - 2*(2*a^3*c^3*d^4*e^3 + 3*a^4*c^2*d^2*e^5)*f*g^5 + (a^4*c^2*d^3*e^4 + 2*a^5*c*d*e^6)*g^6)*x^4 + (c^6*d^6*e*f^6 + 2*c^6*d^7*f^5*g - 6*a^4*c^2*d^3*e^4*f*g^5 - 3*(2*a*c^5*d^6*e + 3*a^2*c^4*d^4*e^3)*f^4*g^2 + 4*(a^2*c^4*d^5*e^2 + 4*a^3*c^3*d^3*e^4)*f^3*g^3 + (4*a^3*c^3*d^4*e^3 - 9*a^4*c^2*d^2*e^5)*f^2*g^4 + (2*a^5*c*d^2*e^5 + a^6*e^7)*g^6)*x^3 - (6*a^2*c^4*d^4*e^3*f^5*g - 2*a^6*e^7*f*g^5 - a^6*d*e^6*g^6 - (c^6*d^7 + 2*a*c^5*d^5*e^2)*f^6 + (9*a^2*c^4*d^5*e^2 - 4*a^3*c^3*d^3*e^4)*f^4*g^2 - 4*(4*a^3*c^3*d^4*e^3 + a^4*c^2*d^2*e^5)*f^3*g^3 + 3*(3*a^4*c^2*d^3*e^4 + 2*a^5*c*d*e^6)*f^2*g^4)*x^2 + (2*a^6*d*e^6*f*g^5 + (2*a*c^5*d^6*e + a^2*c^4*d^4*e^3)*f^6 - 2*(3*a^2*c^4*d^5*e^2 + 2*a^3*c^3*d^3*e^4)*f^5*g + 2*(2*a^3*c^3*d^4*e^3 + 3*a^4*c^2*d^2*e^5)*f^4*g^2 + 4*(a^4*c^2*d^3*e^4 - a^5*c*d*e^6)*f^3*g^3 - (6*a^5*c*d^2*e^5 - a^6*e^7)*f^2*g^4)*x), 1/12*(105*(c^4*d^4*e*g^3*x^5 + a^2*c^2*d^3*e^2*f^2*g + (2*c^4*d^4*e*f*g^2 + (c^4*d^5 + 2*a*c^3*d^3*e^2)*g^3)*x^4 + (c^4*d^4*e*f^2*g + 2*(c^4*d^5 + 2*a*c^3*d^3*e^2)*f*g^2 + (2*a*c^3*d^4*e + a^2*c^2*d^2*e^3)*g^3)*x^3 + (a^2*c^2*d^3*e^2*g^3 + (c^4*d^5 + 2*a*c^3*d^3*e^2)*f^2*g + 2*(2*a*c^3*d^4*e + a^2*c^2*d^2*e^3)*f*g^2)*x^2 + (2*a^2*c^2*d^3*e^2*f*g^2 + (2*a*c^3*d^4*e + a^2*c^2*d^2*e^3)*f^2*g)*x)*sqrt(g/(c*d*f - a*e*g))*arctan(-sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d*f - a*e*g)*sqrt(e*x + d)*sqrt(g/(c*d*f - a*e*g))/(c*d*e*g*x^2 + a*d*e*g + (c*d^2 + a*e^2)*g*x)) + (105*c^3*d^3*g^3*x^3 - 8*c^3*d^3*f^3 + 80*a*c^2*d^2*e*f^2*g + 39*a^2*c*d*e^2*f*g^2 - 6*a^3*e^3*g^3 + 35*(5*c^3*d^3*f*g^2 + 4*a*c^2*d^2*e*g^3)*x^2 + 7*(8*c^3*d^3*f^2*g + 34*a*c^2*d^2*e*f*g^2 + 3*a^2*c*d*e^2*g^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(a^2*c^4*d^5*e^2*f^6 - 4*a^3*c^3*d^4*e^3*f^5*g + 6*a^4*c^2*d^3*e^4*f^4*g^2 - 4*a^5*c*d^2*e^5*f^3*g^3 + a^6*d*e^6*f^2*g^4 + (c^6*d^6*e*f^4*g^2 - 4*a*c^5*d^5*e^2*f^3*g^3 + 6*a^2*c^4*d^4*e^3*f^2*g^4 - 4*a^3*c^3*d^3*e^4*f*g^5 + a^4*c^2*d^2*e^5*g^6)*x^5 + (2*c^6*d^6*e*f^5*g + (c^6*d^7 - 6*a*c^5*d^5*e^2)*f^4*g^2 - 4*(a*c^5*d^6*e - a^2*c^4*d^4*e^3)*f^3*g^3 + 2*(3*a^2*c^4*d^5*e^2 + 2*a^3*c^3*d^3*e^4)*f^2*g^4 - 2*(2*a^3*c^3*d^4*e^3 + 3*a^4*c^2*d^2*e^5)*f*g^5 + (a^4*c^2*d^3*e^4 + 2*a^5*c*d*e^6)*g^6)*x^4 + (c^6*d^6*e*f^6 + 2*c^6*d^7*f^5*g - 6*a^4*c^2*d^3*e^4*f*g^5 - 3*(2*a*c^5*d^6*e + 3*a^2*c^4*d^4*e^3)*f^4*g^2 + 4*(a^2*c^4*d^5*e^2 + 4*a^3*c^3*d^3*e^4)*f^3*g^3 + (4*a^3*c^3*d^4*e^3 - 9*a^4*c^2*d^2*e^5)*f^2*g^4 + (2*a^5*c*d^2*e^5 + a^6*e^7)*g^6)*x^3 - (6*a^2*c^4*d^4*e^3*f^5*g - 2*a^6*e^7*f*g^5 - a^6*d*e^6*g^6 - (c^6*d^7 + 2*a*c^5*d^5*e^2)*f^6 + (9*a^2*c^4*d^5*e^2 - 4*a^3*c^3*d^3*e^4)*f^4*g^2 - 4*(4*a^3*c^3*d^4*e^3 + a^4*c^2*d^2*e^5)*f^3*g^3 + 3*(3*a^4*c^2*d^3*e^4 + 2*a^5*c*d*e^6)*f^2*g^4)*x^2 + (2*a^6*d*e^6*f*g^5 + (2*a*c^5*d^6*e + a^2*c^4*d^4*e^3)*f^6 - 2*(3*a^2*c^4*d^5*e^2 + 2*a^3*c^3*d^3*e^4)*f^5*g + 2*(2*a^3*c^3*d^4*e^3 + 3*a^4*c^2*d^2*e^5)*f^4*g^2 + 4*(a^4*c^2*d^3*e^4 - a^5*c*d*e^6)*f^3*g^3 - (6*a^5*c*d^2*e^5 - a^6*e^7)*f^2*g^4)*x)]","B",0
679,1,375,0,0.402444," ","integrate((g*x+f)^4*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(315 \, c^{5} d^{5} g^{4} x^{5} + 1155 \, a c^{4} d^{4} e f^{4} - 1848 \, a^{2} c^{3} d^{3} e^{2} f^{3} g + 1584 \, a^{3} c^{2} d^{2} e^{3} f^{2} g^{2} - 704 \, a^{4} c d e^{4} f g^{3} + 128 \, a^{5} e^{5} g^{4} + 35 \, {\left(44 \, c^{5} d^{5} f g^{3} + a c^{4} d^{4} e g^{4}\right)} x^{4} + 10 \, {\left(297 \, c^{5} d^{5} f^{2} g^{2} + 22 \, a c^{4} d^{4} e f g^{3} - 4 \, a^{2} c^{3} d^{3} e^{2} g^{4}\right)} x^{3} + 6 \, {\left(462 \, c^{5} d^{5} f^{3} g + 99 \, a c^{4} d^{4} e f^{2} g^{2} - 44 \, a^{2} c^{3} d^{3} e^{2} f g^{3} + 8 \, a^{3} c^{2} d^{2} e^{3} g^{4}\right)} x^{2} + {\left(1155 \, c^{5} d^{5} f^{4} + 924 \, a c^{4} d^{4} e f^{3} g - 792 \, a^{2} c^{3} d^{3} e^{2} f^{2} g^{2} + 352 \, a^{3} c^{2} d^{2} e^{3} f g^{3} - 64 \, a^{4} c d e^{4} g^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{3465 \, {\left(c^{5} d^{5} e x + c^{5} d^{6}\right)}}"," ",0,"2/3465*(315*c^5*d^5*g^4*x^5 + 1155*a*c^4*d^4*e*f^4 - 1848*a^2*c^3*d^3*e^2*f^3*g + 1584*a^3*c^2*d^2*e^3*f^2*g^2 - 704*a^4*c*d*e^4*f*g^3 + 128*a^5*e^5*g^4 + 35*(44*c^5*d^5*f*g^3 + a*c^4*d^4*e*g^4)*x^4 + 10*(297*c^5*d^5*f^2*g^2 + 22*a*c^4*d^4*e*f*g^3 - 4*a^2*c^3*d^3*e^2*g^4)*x^3 + 6*(462*c^5*d^5*f^3*g + 99*a*c^4*d^4*e*f^2*g^2 - 44*a^2*c^3*d^3*e^2*f*g^3 + 8*a^3*c^2*d^2*e^3*g^4)*x^2 + (1155*c^5*d^5*f^4 + 924*a*c^4*d^4*e*f^3*g - 792*a^2*c^3*d^3*e^2*f^2*g^2 + 352*a^3*c^2*d^2*e^3*f*g^3 - 64*a^4*c*d*e^4*g^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)/(c^5*d^5*e*x + c^5*d^6)","A",0
680,1,264,0,0.414632," ","integrate((g*x+f)^3*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, c^{4} d^{4} g^{3} x^{4} + 105 \, a c^{3} d^{3} e f^{3} - 126 \, a^{2} c^{2} d^{2} e^{2} f^{2} g + 72 \, a^{3} c d e^{3} f g^{2} - 16 \, a^{4} e^{4} g^{3} + 5 \, {\left(27 \, c^{4} d^{4} f g^{2} + a c^{3} d^{3} e g^{3}\right)} x^{3} + 3 \, {\left(63 \, c^{4} d^{4} f^{2} g + 9 \, a c^{3} d^{3} e f g^{2} - 2 \, a^{2} c^{2} d^{2} e^{2} g^{3}\right)} x^{2} + {\left(105 \, c^{4} d^{4} f^{3} + 63 \, a c^{3} d^{3} e f^{2} g - 36 \, a^{2} c^{2} d^{2} e^{2} f g^{2} + 8 \, a^{3} c d e^{3} g^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{315 \, {\left(c^{4} d^{4} e x + c^{4} d^{5}\right)}}"," ",0,"2/315*(35*c^4*d^4*g^3*x^4 + 105*a*c^3*d^3*e*f^3 - 126*a^2*c^2*d^2*e^2*f^2*g + 72*a^3*c*d*e^3*f*g^2 - 16*a^4*e^4*g^3 + 5*(27*c^4*d^4*f*g^2 + a*c^3*d^3*e*g^3)*x^3 + 3*(63*c^4*d^4*f^2*g + 9*a*c^3*d^3*e*f*g^2 - 2*a^2*c^2*d^2*e^2*g^3)*x^2 + (105*c^4*d^4*f^3 + 63*a*c^3*d^3*e*f^2*g - 36*a^2*c^2*d^2*e^2*f*g^2 + 8*a^3*c*d*e^3*g^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)/(c^4*d^4*e*x + c^4*d^5)","A",0
681,1,173,0,0.414314," ","integrate((g*x+f)^2*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, c^{3} d^{3} g^{2} x^{3} + 35 \, a c^{2} d^{2} e f^{2} - 28 \, a^{2} c d e^{2} f g + 8 \, a^{3} e^{3} g^{2} + 3 \, {\left(14 \, c^{3} d^{3} f g + a c^{2} d^{2} e g^{2}\right)} x^{2} + {\left(35 \, c^{3} d^{3} f^{2} + 14 \, a c^{2} d^{2} e f g - 4 \, a^{2} c d e^{2} g^{2}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{105 \, {\left(c^{3} d^{3} e x + c^{3} d^{4}\right)}}"," ",0,"2/105*(15*c^3*d^3*g^2*x^3 + 35*a*c^2*d^2*e*f^2 - 28*a^2*c*d*e^2*f*g + 8*a^3*e^3*g^2 + 3*(14*c^3*d^3*f*g + a*c^2*d^2*e*g^2)*x^2 + (35*c^3*d^3*f^2 + 14*a*c^2*d^2*e*f*g - 4*a^2*c*d*e^2*g^2)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)/(c^3*d^3*e*x + c^3*d^4)","A",0
682,1,102,0,0.414820," ","integrate((g*x+f)*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, c^{2} d^{2} g x^{2} + 5 \, a c d e f - 2 \, a^{2} e^{2} g + {\left(5 \, c^{2} d^{2} f + a c d e g\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{15 \, {\left(c^{2} d^{2} e x + c^{2} d^{3}\right)}}"," ",0,"2/15*(3*c^2*d^2*g*x^2 + 5*a*c*d*e*f - 2*a^2*e^2*g + (5*c^2*d^2*f + a*c*d*e*g)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)/(c^2*d^2*e*x + c^2*d^3)","A",0
683,1,57,0,0.431360," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d x + a e\right)} \sqrt{e x + d}}{3 \, {\left(c d e x + c d^{2}\right)}}"," ",0,"2/3*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d*x + a*e)*sqrt(e*x + d)/(c*d*e*x + c*d^2)","A",0
684,1,318,0,0.441149," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)/(g*x+f)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(e x + d\right)} \sqrt{-\frac{c d f - a e g}{g}} \log\left(-\frac{c d e g x^{2} - c d^{2} f + 2 \, a d e g - 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} g \sqrt{-\frac{c d f - a e g}{g}} - {\left(c d e f - {\left(c d^{2} + 2 \, a e^{2}\right)} g\right)} x}{e g x^{2} + d f + {\left(e f + d g\right)} x}\right) + 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{e g x + d g}, \frac{2 \, {\left({\left(e x + d\right)} \sqrt{\frac{c d f - a e g}{g}} \arctan\left(\frac{\sqrt{e x + d} \sqrt{\frac{c d f - a e g}{g}}}{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}\right) + \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}\right)}}{e g x + d g}\right]"," ",0,"[((e*x + d)*sqrt(-(c*d*f - a*e*g)/g)*log(-(c*d*e*g*x^2 - c*d^2*f + 2*a*d*e*g - 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*g*sqrt(-(c*d*f - a*e*g)/g) - (c*d*e*f - (c*d^2 + 2*a*e^2)*g)*x)/(e*g*x^2 + d*f + (e*f + d*g)*x)) + 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(e*g*x + d*g), 2*((e*x + d)*sqrt((c*d*f - a*e*g)/g)*arctan(sqrt(e*x + d)*sqrt((c*d*f - a*e*g)/g)/sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)) + sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(e*g*x + d*g)]","A",0
685,1,562,0,0.451355," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)/(g*x+f)^2/(e*x+d)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(c d e g x^{2} + c d^{2} f + {\left(c d e f + c d^{2} g\right)} x\right)} \sqrt{-c d f g + a e g^{2}} \log\left(-\frac{c d e g x^{2} - c d^{2} f + 2 \, a d e g - {\left(c d e f - {\left(c d^{2} + 2 \, a e^{2}\right)} g\right)} x - 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{-c d f g + a e g^{2}} \sqrt{e x + d}}{e g x^{2} + d f + {\left(e f + d g\right)} x}\right) + 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d f g - a e g^{2}\right)} \sqrt{e x + d}}{2 \, {\left(c d^{2} f^{2} g^{2} - a d e f g^{3} + {\left(c d e f g^{3} - a e^{2} g^{4}\right)} x^{2} + {\left(c d e f^{2} g^{2} - a d e g^{4} + {\left(c d^{2} - a e^{2}\right)} f g^{3}\right)} x\right)}}, -\frac{{\left(c d e g x^{2} + c d^{2} f + {\left(c d e f + c d^{2} g\right)} x\right)} \sqrt{c d f g - a e g^{2}} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{c d f g - a e g^{2}} \sqrt{e x + d}}{c d e g x^{2} + a d e g + {\left(c d^{2} + a e^{2}\right)} g x}\right) + \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d f g - a e g^{2}\right)} \sqrt{e x + d}}{c d^{2} f^{2} g^{2} - a d e f g^{3} + {\left(c d e f g^{3} - a e^{2} g^{4}\right)} x^{2} + {\left(c d e f^{2} g^{2} - a d e g^{4} + {\left(c d^{2} - a e^{2}\right)} f g^{3}\right)} x}\right]"," ",0,"[-1/2*((c*d*e*g*x^2 + c*d^2*f + (c*d*e*f + c*d^2*g)*x)*sqrt(-c*d*f*g + a*e*g^2)*log(-(c*d*e*g*x^2 - c*d^2*f + 2*a*d*e*g - (c*d*e*f - (c*d^2 + 2*a*e^2)*g)*x - 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-c*d*f*g + a*e*g^2)*sqrt(e*x + d))/(e*g*x^2 + d*f + (e*f + d*g)*x)) + 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d*f*g - a*e*g^2)*sqrt(e*x + d))/(c*d^2*f^2*g^2 - a*d*e*f*g^3 + (c*d*e*f*g^3 - a*e^2*g^4)*x^2 + (c*d*e*f^2*g^2 - a*d*e*g^4 + (c*d^2 - a*e^2)*f*g^3)*x), -((c*d*e*g*x^2 + c*d^2*f + (c*d*e*f + c*d^2*g)*x)*sqrt(c*d*f*g - a*e*g^2)*arctan(sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(c*d*f*g - a*e*g^2)*sqrt(e*x + d)/(c*d*e*g*x^2 + a*d*e*g + (c*d^2 + a*e^2)*g*x)) + sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d*f*g - a*e*g^2)*sqrt(e*x + d))/(c*d^2*f^2*g^2 - a*d*e*f*g^3 + (c*d*e*f*g^3 - a*e^2*g^4)*x^2 + (c*d*e*f^2*g^2 - a*d*e*g^4 + (c*d^2 - a*e^2)*f*g^3)*x)]","B",0
686,1,1056,0,0.449965," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)/(g*x+f)^3/(e*x+d)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(c^{2} d^{2} e g^{2} x^{3} + c^{2} d^{3} f^{2} + {\left(2 \, c^{2} d^{2} e f g + c^{2} d^{3} g^{2}\right)} x^{2} + {\left(c^{2} d^{2} e f^{2} + 2 \, c^{2} d^{3} f g\right)} x\right)} \sqrt{-c d f g + a e g^{2}} \log\left(-\frac{c d e g x^{2} - c d^{2} f + 2 \, a d e g - {\left(c d e f - {\left(c d^{2} + 2 \, a e^{2}\right)} g\right)} x + 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{-c d f g + a e g^{2}} \sqrt{e x + d}}{e g x^{2} + d f + {\left(e f + d g\right)} x}\right) - 2 \, {\left(c^{2} d^{2} f^{2} g - 3 \, a c d e f g^{2} + 2 \, a^{2} e^{2} g^{3} - {\left(c^{2} d^{2} f g^{2} - a c d e g^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{8 \, {\left(c^{2} d^{3} f^{4} g^{2} - 2 \, a c d^{2} e f^{3} g^{3} + a^{2} d e^{2} f^{2} g^{4} + {\left(c^{2} d^{2} e f^{2} g^{4} - 2 \, a c d e^{2} f g^{5} + a^{2} e^{3} g^{6}\right)} x^{3} + {\left(2 \, c^{2} d^{2} e f^{3} g^{3} + a^{2} d e^{2} g^{6} + {\left(c^{2} d^{3} - 4 \, a c d e^{2}\right)} f^{2} g^{4} - 2 \, {\left(a c d^{2} e - a^{2} e^{3}\right)} f g^{5}\right)} x^{2} + {\left(c^{2} d^{2} e f^{4} g^{2} + 2 \, a^{2} d e^{2} f g^{5} + 2 \, {\left(c^{2} d^{3} - a c d e^{2}\right)} f^{3} g^{3} - {\left(4 \, a c d^{2} e - a^{2} e^{3}\right)} f^{2} g^{4}\right)} x\right)}}, -\frac{{\left(c^{2} d^{2} e g^{2} x^{3} + c^{2} d^{3} f^{2} + {\left(2 \, c^{2} d^{2} e f g + c^{2} d^{3} g^{2}\right)} x^{2} + {\left(c^{2} d^{2} e f^{2} + 2 \, c^{2} d^{3} f g\right)} x\right)} \sqrt{c d f g - a e g^{2}} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{c d f g - a e g^{2}} \sqrt{e x + d}}{c d e g x^{2} + a d e g + {\left(c d^{2} + a e^{2}\right)} g x}\right) + {\left(c^{2} d^{2} f^{2} g - 3 \, a c d e f g^{2} + 2 \, a^{2} e^{2} g^{3} - {\left(c^{2} d^{2} f g^{2} - a c d e g^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{4 \, {\left(c^{2} d^{3} f^{4} g^{2} - 2 \, a c d^{2} e f^{3} g^{3} + a^{2} d e^{2} f^{2} g^{4} + {\left(c^{2} d^{2} e f^{2} g^{4} - 2 \, a c d e^{2} f g^{5} + a^{2} e^{3} g^{6}\right)} x^{3} + {\left(2 \, c^{2} d^{2} e f^{3} g^{3} + a^{2} d e^{2} g^{6} + {\left(c^{2} d^{3} - 4 \, a c d e^{2}\right)} f^{2} g^{4} - 2 \, {\left(a c d^{2} e - a^{2} e^{3}\right)} f g^{5}\right)} x^{2} + {\left(c^{2} d^{2} e f^{4} g^{2} + 2 \, a^{2} d e^{2} f g^{5} + 2 \, {\left(c^{2} d^{3} - a c d e^{2}\right)} f^{3} g^{3} - {\left(4 \, a c d^{2} e - a^{2} e^{3}\right)} f^{2} g^{4}\right)} x\right)}}\right]"," ",0,"[1/8*((c^2*d^2*e*g^2*x^3 + c^2*d^3*f^2 + (2*c^2*d^2*e*f*g + c^2*d^3*g^2)*x^2 + (c^2*d^2*e*f^2 + 2*c^2*d^3*f*g)*x)*sqrt(-c*d*f*g + a*e*g^2)*log(-(c*d*e*g*x^2 - c*d^2*f + 2*a*d*e*g - (c*d*e*f - (c*d^2 + 2*a*e^2)*g)*x + 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-c*d*f*g + a*e*g^2)*sqrt(e*x + d))/(e*g*x^2 + d*f + (e*f + d*g)*x)) - 2*(c^2*d^2*f^2*g - 3*a*c*d*e*f*g^2 + 2*a^2*e^2*g^3 - (c^2*d^2*f*g^2 - a*c*d*e*g^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c^2*d^3*f^4*g^2 - 2*a*c*d^2*e*f^3*g^3 + a^2*d*e^2*f^2*g^4 + (c^2*d^2*e*f^2*g^4 - 2*a*c*d*e^2*f*g^5 + a^2*e^3*g^6)*x^3 + (2*c^2*d^2*e*f^3*g^3 + a^2*d*e^2*g^6 + (c^2*d^3 - 4*a*c*d*e^2)*f^2*g^4 - 2*(a*c*d^2*e - a^2*e^3)*f*g^5)*x^2 + (c^2*d^2*e*f^4*g^2 + 2*a^2*d*e^2*f*g^5 + 2*(c^2*d^3 - a*c*d*e^2)*f^3*g^3 - (4*a*c*d^2*e - a^2*e^3)*f^2*g^4)*x), -1/4*((c^2*d^2*e*g^2*x^3 + c^2*d^3*f^2 + (2*c^2*d^2*e*f*g + c^2*d^3*g^2)*x^2 + (c^2*d^2*e*f^2 + 2*c^2*d^3*f*g)*x)*sqrt(c*d*f*g - a*e*g^2)*arctan(sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(c*d*f*g - a*e*g^2)*sqrt(e*x + d)/(c*d*e*g*x^2 + a*d*e*g + (c*d^2 + a*e^2)*g*x)) + (c^2*d^2*f^2*g - 3*a*c*d*e*f*g^2 + 2*a^2*e^2*g^3 - (c^2*d^2*f*g^2 - a*c*d*e*g^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c^2*d^3*f^4*g^2 - 2*a*c*d^2*e*f^3*g^3 + a^2*d*e^2*f^2*g^4 + (c^2*d^2*e*f^2*g^4 - 2*a*c*d*e^2*f*g^5 + a^2*e^3*g^6)*x^3 + (2*c^2*d^2*e*f^3*g^3 + a^2*d*e^2*g^6 + (c^2*d^3 - 4*a*c*d*e^2)*f^2*g^4 - 2*(a*c*d^2*e - a^2*e^3)*f*g^5)*x^2 + (c^2*d^2*e*f^4*g^2 + 2*a^2*d*e^2*f*g^5 + 2*(c^2*d^3 - a*c*d*e^2)*f^3*g^3 - (4*a*c*d^2*e - a^2*e^3)*f^2*g^4)*x)]","B",0
687,1,1732,0,0.503619," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)/(g*x+f)^4/(e*x+d)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(c^{3} d^{3} e g^{3} x^{4} + c^{3} d^{4} f^{3} + {\left(3 \, c^{3} d^{3} e f g^{2} + c^{3} d^{4} g^{3}\right)} x^{3} + 3 \, {\left(c^{3} d^{3} e f^{2} g + c^{3} d^{4} f g^{2}\right)} x^{2} + {\left(c^{3} d^{3} e f^{3} + 3 \, c^{3} d^{4} f^{2} g\right)} x\right)} \sqrt{-c d f g + a e g^{2}} \log\left(-\frac{c d e g x^{2} - c d^{2} f + 2 \, a d e g - {\left(c d e f - {\left(c d^{2} + 2 \, a e^{2}\right)} g\right)} x - 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{-c d f g + a e g^{2}} \sqrt{e x + d}}{e g x^{2} + d f + {\left(e f + d g\right)} x}\right) + 2 \, {\left(3 \, c^{3} d^{3} f^{3} g - 17 \, a c^{2} d^{2} e f^{2} g^{2} + 22 \, a^{2} c d e^{2} f g^{3} - 8 \, a^{3} e^{3} g^{4} - 3 \, {\left(c^{3} d^{3} f g^{3} - a c^{2} d^{2} e g^{4}\right)} x^{2} - 2 \, {\left(4 \, c^{3} d^{3} f^{2} g^{2} - 5 \, a c^{2} d^{2} e f g^{3} + a^{2} c d e^{2} g^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{48 \, {\left(c^{3} d^{4} f^{6} g^{2} - 3 \, a c^{2} d^{3} e f^{5} g^{3} + 3 \, a^{2} c d^{2} e^{2} f^{4} g^{4} - a^{3} d e^{3} f^{3} g^{5} + {\left(c^{3} d^{3} e f^{3} g^{5} - 3 \, a c^{2} d^{2} e^{2} f^{2} g^{6} + 3 \, a^{2} c d e^{3} f g^{7} - a^{3} e^{4} g^{8}\right)} x^{4} + {\left(3 \, c^{3} d^{3} e f^{4} g^{4} - a^{3} d e^{3} g^{8} + {\left(c^{3} d^{4} - 9 \, a c^{2} d^{2} e^{2}\right)} f^{3} g^{5} - 3 \, {\left(a c^{2} d^{3} e - 3 \, a^{2} c d e^{3}\right)} f^{2} g^{6} + 3 \, {\left(a^{2} c d^{2} e^{2} - a^{3} e^{4}\right)} f g^{7}\right)} x^{3} + 3 \, {\left(c^{3} d^{3} e f^{5} g^{3} - a^{3} d e^{3} f g^{7} + {\left(c^{3} d^{4} - 3 \, a c^{2} d^{2} e^{2}\right)} f^{4} g^{4} - 3 \, {\left(a c^{2} d^{3} e - a^{2} c d e^{3}\right)} f^{3} g^{5} + {\left(3 \, a^{2} c d^{2} e^{2} - a^{3} e^{4}\right)} f^{2} g^{6}\right)} x^{2} + {\left(c^{3} d^{3} e f^{6} g^{2} - 3 \, a^{3} d e^{3} f^{2} g^{6} + 3 \, {\left(c^{3} d^{4} - a c^{2} d^{2} e^{2}\right)} f^{5} g^{3} - 3 \, {\left(3 \, a c^{2} d^{3} e - a^{2} c d e^{3}\right)} f^{4} g^{4} + {\left(9 \, a^{2} c d^{2} e^{2} - a^{3} e^{4}\right)} f^{3} g^{5}\right)} x\right)}}, -\frac{3 \, {\left(c^{3} d^{3} e g^{3} x^{4} + c^{3} d^{4} f^{3} + {\left(3 \, c^{3} d^{3} e f g^{2} + c^{3} d^{4} g^{3}\right)} x^{3} + 3 \, {\left(c^{3} d^{3} e f^{2} g + c^{3} d^{4} f g^{2}\right)} x^{2} + {\left(c^{3} d^{3} e f^{3} + 3 \, c^{3} d^{4} f^{2} g\right)} x\right)} \sqrt{c d f g - a e g^{2}} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{c d f g - a e g^{2}} \sqrt{e x + d}}{c d e g x^{2} + a d e g + {\left(c d^{2} + a e^{2}\right)} g x}\right) + {\left(3 \, c^{3} d^{3} f^{3} g - 17 \, a c^{2} d^{2} e f^{2} g^{2} + 22 \, a^{2} c d e^{2} f g^{3} - 8 \, a^{3} e^{3} g^{4} - 3 \, {\left(c^{3} d^{3} f g^{3} - a c^{2} d^{2} e g^{4}\right)} x^{2} - 2 \, {\left(4 \, c^{3} d^{3} f^{2} g^{2} - 5 \, a c^{2} d^{2} e f g^{3} + a^{2} c d e^{2} g^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{24 \, {\left(c^{3} d^{4} f^{6} g^{2} - 3 \, a c^{2} d^{3} e f^{5} g^{3} + 3 \, a^{2} c d^{2} e^{2} f^{4} g^{4} - a^{3} d e^{3} f^{3} g^{5} + {\left(c^{3} d^{3} e f^{3} g^{5} - 3 \, a c^{2} d^{2} e^{2} f^{2} g^{6} + 3 \, a^{2} c d e^{3} f g^{7} - a^{3} e^{4} g^{8}\right)} x^{4} + {\left(3 \, c^{3} d^{3} e f^{4} g^{4} - a^{3} d e^{3} g^{8} + {\left(c^{3} d^{4} - 9 \, a c^{2} d^{2} e^{2}\right)} f^{3} g^{5} - 3 \, {\left(a c^{2} d^{3} e - 3 \, a^{2} c d e^{3}\right)} f^{2} g^{6} + 3 \, {\left(a^{2} c d^{2} e^{2} - a^{3} e^{4}\right)} f g^{7}\right)} x^{3} + 3 \, {\left(c^{3} d^{3} e f^{5} g^{3} - a^{3} d e^{3} f g^{7} + {\left(c^{3} d^{4} - 3 \, a c^{2} d^{2} e^{2}\right)} f^{4} g^{4} - 3 \, {\left(a c^{2} d^{3} e - a^{2} c d e^{3}\right)} f^{3} g^{5} + {\left(3 \, a^{2} c d^{2} e^{2} - a^{3} e^{4}\right)} f^{2} g^{6}\right)} x^{2} + {\left(c^{3} d^{3} e f^{6} g^{2} - 3 \, a^{3} d e^{3} f^{2} g^{6} + 3 \, {\left(c^{3} d^{4} - a c^{2} d^{2} e^{2}\right)} f^{5} g^{3} - 3 \, {\left(3 \, a c^{2} d^{3} e - a^{2} c d e^{3}\right)} f^{4} g^{4} + {\left(9 \, a^{2} c d^{2} e^{2} - a^{3} e^{4}\right)} f^{3} g^{5}\right)} x\right)}}\right]"," ",0,"[-1/48*(3*(c^3*d^3*e*g^3*x^4 + c^3*d^4*f^3 + (3*c^3*d^3*e*f*g^2 + c^3*d^4*g^3)*x^3 + 3*(c^3*d^3*e*f^2*g + c^3*d^4*f*g^2)*x^2 + (c^3*d^3*e*f^3 + 3*c^3*d^4*f^2*g)*x)*sqrt(-c*d*f*g + a*e*g^2)*log(-(c*d*e*g*x^2 - c*d^2*f + 2*a*d*e*g - (c*d*e*f - (c*d^2 + 2*a*e^2)*g)*x - 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-c*d*f*g + a*e*g^2)*sqrt(e*x + d))/(e*g*x^2 + d*f + (e*f + d*g)*x)) + 2*(3*c^3*d^3*f^3*g - 17*a*c^2*d^2*e*f^2*g^2 + 22*a^2*c*d*e^2*f*g^3 - 8*a^3*e^3*g^4 - 3*(c^3*d^3*f*g^3 - a*c^2*d^2*e*g^4)*x^2 - 2*(4*c^3*d^3*f^2*g^2 - 5*a*c^2*d^2*e*f*g^3 + a^2*c*d*e^2*g^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c^3*d^4*f^6*g^2 - 3*a*c^2*d^3*e*f^5*g^3 + 3*a^2*c*d^2*e^2*f^4*g^4 - a^3*d*e^3*f^3*g^5 + (c^3*d^3*e*f^3*g^5 - 3*a*c^2*d^2*e^2*f^2*g^6 + 3*a^2*c*d*e^3*f*g^7 - a^3*e^4*g^8)*x^4 + (3*c^3*d^3*e*f^4*g^4 - a^3*d*e^3*g^8 + (c^3*d^4 - 9*a*c^2*d^2*e^2)*f^3*g^5 - 3*(a*c^2*d^3*e - 3*a^2*c*d*e^3)*f^2*g^6 + 3*(a^2*c*d^2*e^2 - a^3*e^4)*f*g^7)*x^3 + 3*(c^3*d^3*e*f^5*g^3 - a^3*d*e^3*f*g^7 + (c^3*d^4 - 3*a*c^2*d^2*e^2)*f^4*g^4 - 3*(a*c^2*d^3*e - a^2*c*d*e^3)*f^3*g^5 + (3*a^2*c*d^2*e^2 - a^3*e^4)*f^2*g^6)*x^2 + (c^3*d^3*e*f^6*g^2 - 3*a^3*d*e^3*f^2*g^6 + 3*(c^3*d^4 - a*c^2*d^2*e^2)*f^5*g^3 - 3*(3*a*c^2*d^3*e - a^2*c*d*e^3)*f^4*g^4 + (9*a^2*c*d^2*e^2 - a^3*e^4)*f^3*g^5)*x), -1/24*(3*(c^3*d^3*e*g^3*x^4 + c^3*d^4*f^3 + (3*c^3*d^3*e*f*g^2 + c^3*d^4*g^3)*x^3 + 3*(c^3*d^3*e*f^2*g + c^3*d^4*f*g^2)*x^2 + (c^3*d^3*e*f^3 + 3*c^3*d^4*f^2*g)*x)*sqrt(c*d*f*g - a*e*g^2)*arctan(sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(c*d*f*g - a*e*g^2)*sqrt(e*x + d)/(c*d*e*g*x^2 + a*d*e*g + (c*d^2 + a*e^2)*g*x)) + (3*c^3*d^3*f^3*g - 17*a*c^2*d^2*e*f^2*g^2 + 22*a^2*c*d*e^2*f*g^3 - 8*a^3*e^3*g^4 - 3*(c^3*d^3*f*g^3 - a*c^2*d^2*e*g^4)*x^2 - 2*(4*c^3*d^3*f^2*g^2 - 5*a*c^2*d^2*e*f*g^3 + a^2*c*d*e^2*g^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c^3*d^4*f^6*g^2 - 3*a*c^2*d^3*e*f^5*g^3 + 3*a^2*c*d^2*e^2*f^4*g^4 - a^3*d*e^3*f^3*g^5 + (c^3*d^3*e*f^3*g^5 - 3*a*c^2*d^2*e^2*f^2*g^6 + 3*a^2*c*d*e^3*f*g^7 - a^3*e^4*g^8)*x^4 + (3*c^3*d^3*e*f^4*g^4 - a^3*d*e^3*g^8 + (c^3*d^4 - 9*a*c^2*d^2*e^2)*f^3*g^5 - 3*(a*c^2*d^3*e - 3*a^2*c*d*e^3)*f^2*g^6 + 3*(a^2*c*d^2*e^2 - a^3*e^4)*f*g^7)*x^3 + 3*(c^3*d^3*e*f^5*g^3 - a^3*d*e^3*f*g^7 + (c^3*d^4 - 3*a*c^2*d^2*e^2)*f^4*g^4 - 3*(a*c^2*d^3*e - a^2*c*d*e^3)*f^3*g^5 + (3*a^2*c*d^2*e^2 - a^3*e^4)*f^2*g^6)*x^2 + (c^3*d^3*e*f^6*g^2 - 3*a^3*d*e^3*f^2*g^6 + 3*(c^3*d^4 - a*c^2*d^2*e^2)*f^5*g^3 - 3*(3*a*c^2*d^3*e - a^2*c*d*e^3)*f^4*g^4 + (9*a^2*c*d^2*e^2 - a^3*e^4)*f^3*g^5)*x)]","B",0
688,1,2610,0,0.475683," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)/(g*x+f)^5/(e*x+d)^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(c^{4} d^{4} e g^{4} x^{5} + c^{4} d^{5} f^{4} + {\left(4 \, c^{4} d^{4} e f g^{3} + c^{4} d^{5} g^{4}\right)} x^{4} + 2 \, {\left(3 \, c^{4} d^{4} e f^{2} g^{2} + 2 \, c^{4} d^{5} f g^{3}\right)} x^{3} + 2 \, {\left(2 \, c^{4} d^{4} e f^{3} g + 3 \, c^{4} d^{5} f^{2} g^{2}\right)} x^{2} + {\left(c^{4} d^{4} e f^{4} + 4 \, c^{4} d^{5} f^{3} g\right)} x\right)} \sqrt{-c d f g + a e g^{2}} \log\left(-\frac{c d e g x^{2} - c d^{2} f + 2 \, a d e g - {\left(c d e f - {\left(c d^{2} + 2 \, a e^{2}\right)} g\right)} x + 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{-c d f g + a e g^{2}} \sqrt{e x + d}}{e g x^{2} + d f + {\left(e f + d g\right)} x}\right) - 2 \, {\left(15 \, c^{4} d^{4} f^{4} g - 133 \, a c^{3} d^{3} e f^{3} g^{2} + 254 \, a^{2} c^{2} d^{2} e^{2} f^{2} g^{3} - 184 \, a^{3} c d e^{3} f g^{4} + 48 \, a^{4} e^{4} g^{5} - 15 \, {\left(c^{4} d^{4} f g^{4} - a c^{3} d^{3} e g^{5}\right)} x^{3} - 5 \, {\left(11 \, c^{4} d^{4} f^{2} g^{3} - 13 \, a c^{3} d^{3} e f g^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} g^{5}\right)} x^{2} - {\left(73 \, c^{4} d^{4} f^{3} g^{2} - 109 \, a c^{3} d^{3} e f^{2} g^{3} + 44 \, a^{2} c^{2} d^{2} e^{2} f g^{4} - 8 \, a^{3} c d e^{3} g^{5}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{384 \, {\left(c^{4} d^{5} f^{8} g^{2} - 4 \, a c^{3} d^{4} e f^{7} g^{3} + 6 \, a^{2} c^{2} d^{3} e^{2} f^{6} g^{4} - 4 \, a^{3} c d^{2} e^{3} f^{5} g^{5} + a^{4} d e^{4} f^{4} g^{6} + {\left(c^{4} d^{4} e f^{4} g^{6} - 4 \, a c^{3} d^{3} e^{2} f^{3} g^{7} + 6 \, a^{2} c^{2} d^{2} e^{3} f^{2} g^{8} - 4 \, a^{3} c d e^{4} f g^{9} + a^{4} e^{5} g^{10}\right)} x^{5} + {\left(4 \, c^{4} d^{4} e f^{5} g^{5} + a^{4} d e^{4} g^{10} + {\left(c^{4} d^{5} - 16 \, a c^{3} d^{3} e^{2}\right)} f^{4} g^{6} - 4 \, {\left(a c^{3} d^{4} e - 6 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{3} g^{7} + 2 \, {\left(3 \, a^{2} c^{2} d^{3} e^{2} - 8 \, a^{3} c d e^{4}\right)} f^{2} g^{8} - 4 \, {\left(a^{3} c d^{2} e^{3} - a^{4} e^{5}\right)} f g^{9}\right)} x^{4} + 2 \, {\left(3 \, c^{4} d^{4} e f^{6} g^{4} + 2 \, a^{4} d e^{4} f g^{9} + 2 \, {\left(c^{4} d^{5} - 6 \, a c^{3} d^{3} e^{2}\right)} f^{5} g^{5} - 2 \, {\left(4 \, a c^{3} d^{4} e - 9 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{4} g^{6} + 12 \, {\left(a^{2} c^{2} d^{3} e^{2} - a^{3} c d e^{4}\right)} f^{3} g^{7} - {\left(8 \, a^{3} c d^{2} e^{3} - 3 \, a^{4} e^{5}\right)} f^{2} g^{8}\right)} x^{3} + 2 \, {\left(2 \, c^{4} d^{4} e f^{7} g^{3} + 3 \, a^{4} d e^{4} f^{2} g^{8} + {\left(3 \, c^{4} d^{5} - 8 \, a c^{3} d^{3} e^{2}\right)} f^{6} g^{4} - 12 \, {\left(a c^{3} d^{4} e - a^{2} c^{2} d^{2} e^{3}\right)} f^{5} g^{5} + 2 \, {\left(9 \, a^{2} c^{2} d^{3} e^{2} - 4 \, a^{3} c d e^{4}\right)} f^{4} g^{6} - 2 \, {\left(6 \, a^{3} c d^{2} e^{3} - a^{4} e^{5}\right)} f^{3} g^{7}\right)} x^{2} + {\left(c^{4} d^{4} e f^{8} g^{2} + 4 \, a^{4} d e^{4} f^{3} g^{7} + 4 \, {\left(c^{4} d^{5} - a c^{3} d^{3} e^{2}\right)} f^{7} g^{3} - 2 \, {\left(8 \, a c^{3} d^{4} e - 3 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{6} g^{4} + 4 \, {\left(6 \, a^{2} c^{2} d^{3} e^{2} - a^{3} c d e^{4}\right)} f^{5} g^{5} - {\left(16 \, a^{3} c d^{2} e^{3} - a^{4} e^{5}\right)} f^{4} g^{6}\right)} x\right)}}, -\frac{15 \, {\left(c^{4} d^{4} e g^{4} x^{5} + c^{4} d^{5} f^{4} + {\left(4 \, c^{4} d^{4} e f g^{3} + c^{4} d^{5} g^{4}\right)} x^{4} + 2 \, {\left(3 \, c^{4} d^{4} e f^{2} g^{2} + 2 \, c^{4} d^{5} f g^{3}\right)} x^{3} + 2 \, {\left(2 \, c^{4} d^{4} e f^{3} g + 3 \, c^{4} d^{5} f^{2} g^{2}\right)} x^{2} + {\left(c^{4} d^{4} e f^{4} + 4 \, c^{4} d^{5} f^{3} g\right)} x\right)} \sqrt{c d f g - a e g^{2}} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{c d f g - a e g^{2}} \sqrt{e x + d}}{c d e g x^{2} + a d e g + {\left(c d^{2} + a e^{2}\right)} g x}\right) + {\left(15 \, c^{4} d^{4} f^{4} g - 133 \, a c^{3} d^{3} e f^{3} g^{2} + 254 \, a^{2} c^{2} d^{2} e^{2} f^{2} g^{3} - 184 \, a^{3} c d e^{3} f g^{4} + 48 \, a^{4} e^{4} g^{5} - 15 \, {\left(c^{4} d^{4} f g^{4} - a c^{3} d^{3} e g^{5}\right)} x^{3} - 5 \, {\left(11 \, c^{4} d^{4} f^{2} g^{3} - 13 \, a c^{3} d^{3} e f g^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} g^{5}\right)} x^{2} - {\left(73 \, c^{4} d^{4} f^{3} g^{2} - 109 \, a c^{3} d^{3} e f^{2} g^{3} + 44 \, a^{2} c^{2} d^{2} e^{2} f g^{4} - 8 \, a^{3} c d e^{3} g^{5}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{192 \, {\left(c^{4} d^{5} f^{8} g^{2} - 4 \, a c^{3} d^{4} e f^{7} g^{3} + 6 \, a^{2} c^{2} d^{3} e^{2} f^{6} g^{4} - 4 \, a^{3} c d^{2} e^{3} f^{5} g^{5} + a^{4} d e^{4} f^{4} g^{6} + {\left(c^{4} d^{4} e f^{4} g^{6} - 4 \, a c^{3} d^{3} e^{2} f^{3} g^{7} + 6 \, a^{2} c^{2} d^{2} e^{3} f^{2} g^{8} - 4 \, a^{3} c d e^{4} f g^{9} + a^{4} e^{5} g^{10}\right)} x^{5} + {\left(4 \, c^{4} d^{4} e f^{5} g^{5} + a^{4} d e^{4} g^{10} + {\left(c^{4} d^{5} - 16 \, a c^{3} d^{3} e^{2}\right)} f^{4} g^{6} - 4 \, {\left(a c^{3} d^{4} e - 6 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{3} g^{7} + 2 \, {\left(3 \, a^{2} c^{2} d^{3} e^{2} - 8 \, a^{3} c d e^{4}\right)} f^{2} g^{8} - 4 \, {\left(a^{3} c d^{2} e^{3} - a^{4} e^{5}\right)} f g^{9}\right)} x^{4} + 2 \, {\left(3 \, c^{4} d^{4} e f^{6} g^{4} + 2 \, a^{4} d e^{4} f g^{9} + 2 \, {\left(c^{4} d^{5} - 6 \, a c^{3} d^{3} e^{2}\right)} f^{5} g^{5} - 2 \, {\left(4 \, a c^{3} d^{4} e - 9 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{4} g^{6} + 12 \, {\left(a^{2} c^{2} d^{3} e^{2} - a^{3} c d e^{4}\right)} f^{3} g^{7} - {\left(8 \, a^{3} c d^{2} e^{3} - 3 \, a^{4} e^{5}\right)} f^{2} g^{8}\right)} x^{3} + 2 \, {\left(2 \, c^{4} d^{4} e f^{7} g^{3} + 3 \, a^{4} d e^{4} f^{2} g^{8} + {\left(3 \, c^{4} d^{5} - 8 \, a c^{3} d^{3} e^{2}\right)} f^{6} g^{4} - 12 \, {\left(a c^{3} d^{4} e - a^{2} c^{2} d^{2} e^{3}\right)} f^{5} g^{5} + 2 \, {\left(9 \, a^{2} c^{2} d^{3} e^{2} - 4 \, a^{3} c d e^{4}\right)} f^{4} g^{6} - 2 \, {\left(6 \, a^{3} c d^{2} e^{3} - a^{4} e^{5}\right)} f^{3} g^{7}\right)} x^{2} + {\left(c^{4} d^{4} e f^{8} g^{2} + 4 \, a^{4} d e^{4} f^{3} g^{7} + 4 \, {\left(c^{4} d^{5} - a c^{3} d^{3} e^{2}\right)} f^{7} g^{3} - 2 \, {\left(8 \, a c^{3} d^{4} e - 3 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{6} g^{4} + 4 \, {\left(6 \, a^{2} c^{2} d^{3} e^{2} - a^{3} c d e^{4}\right)} f^{5} g^{5} - {\left(16 \, a^{3} c d^{2} e^{3} - a^{4} e^{5}\right)} f^{4} g^{6}\right)} x\right)}}\right]"," ",0,"[1/384*(15*(c^4*d^4*e*g^4*x^5 + c^4*d^5*f^4 + (4*c^4*d^4*e*f*g^3 + c^4*d^5*g^4)*x^4 + 2*(3*c^4*d^4*e*f^2*g^2 + 2*c^4*d^5*f*g^3)*x^3 + 2*(2*c^4*d^4*e*f^3*g + 3*c^4*d^5*f^2*g^2)*x^2 + (c^4*d^4*e*f^4 + 4*c^4*d^5*f^3*g)*x)*sqrt(-c*d*f*g + a*e*g^2)*log(-(c*d*e*g*x^2 - c*d^2*f + 2*a*d*e*g - (c*d*e*f - (c*d^2 + 2*a*e^2)*g)*x + 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-c*d*f*g + a*e*g^2)*sqrt(e*x + d))/(e*g*x^2 + d*f + (e*f + d*g)*x)) - 2*(15*c^4*d^4*f^4*g - 133*a*c^3*d^3*e*f^3*g^2 + 254*a^2*c^2*d^2*e^2*f^2*g^3 - 184*a^3*c*d*e^3*f*g^4 + 48*a^4*e^4*g^5 - 15*(c^4*d^4*f*g^4 - a*c^3*d^3*e*g^5)*x^3 - 5*(11*c^4*d^4*f^2*g^3 - 13*a*c^3*d^3*e*f*g^4 + 2*a^2*c^2*d^2*e^2*g^5)*x^2 - (73*c^4*d^4*f^3*g^2 - 109*a*c^3*d^3*e*f^2*g^3 + 44*a^2*c^2*d^2*e^2*f*g^4 - 8*a^3*c*d*e^3*g^5)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c^4*d^5*f^8*g^2 - 4*a*c^3*d^4*e*f^7*g^3 + 6*a^2*c^2*d^3*e^2*f^6*g^4 - 4*a^3*c*d^2*e^3*f^5*g^5 + a^4*d*e^4*f^4*g^6 + (c^4*d^4*e*f^4*g^6 - 4*a*c^3*d^3*e^2*f^3*g^7 + 6*a^2*c^2*d^2*e^3*f^2*g^8 - 4*a^3*c*d*e^4*f*g^9 + a^4*e^5*g^10)*x^5 + (4*c^4*d^4*e*f^5*g^5 + a^4*d*e^4*g^10 + (c^4*d^5 - 16*a*c^3*d^3*e^2)*f^4*g^6 - 4*(a*c^3*d^4*e - 6*a^2*c^2*d^2*e^3)*f^3*g^7 + 2*(3*a^2*c^2*d^3*e^2 - 8*a^3*c*d*e^4)*f^2*g^8 - 4*(a^3*c*d^2*e^3 - a^4*e^5)*f*g^9)*x^4 + 2*(3*c^4*d^4*e*f^6*g^4 + 2*a^4*d*e^4*f*g^9 + 2*(c^4*d^5 - 6*a*c^3*d^3*e^2)*f^5*g^5 - 2*(4*a*c^3*d^4*e - 9*a^2*c^2*d^2*e^3)*f^4*g^6 + 12*(a^2*c^2*d^3*e^2 - a^3*c*d*e^4)*f^3*g^7 - (8*a^3*c*d^2*e^3 - 3*a^4*e^5)*f^2*g^8)*x^3 + 2*(2*c^4*d^4*e*f^7*g^3 + 3*a^4*d*e^4*f^2*g^8 + (3*c^4*d^5 - 8*a*c^3*d^3*e^2)*f^6*g^4 - 12*(a*c^3*d^4*e - a^2*c^2*d^2*e^3)*f^5*g^5 + 2*(9*a^2*c^2*d^3*e^2 - 4*a^3*c*d*e^4)*f^4*g^6 - 2*(6*a^3*c*d^2*e^3 - a^4*e^5)*f^3*g^7)*x^2 + (c^4*d^4*e*f^8*g^2 + 4*a^4*d*e^4*f^3*g^7 + 4*(c^4*d^5 - a*c^3*d^3*e^2)*f^7*g^3 - 2*(8*a*c^3*d^4*e - 3*a^2*c^2*d^2*e^3)*f^6*g^4 + 4*(6*a^2*c^2*d^3*e^2 - a^3*c*d*e^4)*f^5*g^5 - (16*a^3*c*d^2*e^3 - a^4*e^5)*f^4*g^6)*x), -1/192*(15*(c^4*d^4*e*g^4*x^5 + c^4*d^5*f^4 + (4*c^4*d^4*e*f*g^3 + c^4*d^5*g^4)*x^4 + 2*(3*c^4*d^4*e*f^2*g^2 + 2*c^4*d^5*f*g^3)*x^3 + 2*(2*c^4*d^4*e*f^3*g + 3*c^4*d^5*f^2*g^2)*x^2 + (c^4*d^4*e*f^4 + 4*c^4*d^5*f^3*g)*x)*sqrt(c*d*f*g - a*e*g^2)*arctan(sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(c*d*f*g - a*e*g^2)*sqrt(e*x + d)/(c*d*e*g*x^2 + a*d*e*g + (c*d^2 + a*e^2)*g*x)) + (15*c^4*d^4*f^4*g - 133*a*c^3*d^3*e*f^3*g^2 + 254*a^2*c^2*d^2*e^2*f^2*g^3 - 184*a^3*c*d*e^3*f*g^4 + 48*a^4*e^4*g^5 - 15*(c^4*d^4*f*g^4 - a*c^3*d^3*e*g^5)*x^3 - 5*(11*c^4*d^4*f^2*g^3 - 13*a*c^3*d^3*e*f*g^4 + 2*a^2*c^2*d^2*e^2*g^5)*x^2 - (73*c^4*d^4*f^3*g^2 - 109*a*c^3*d^3*e*f^2*g^3 + 44*a^2*c^2*d^2*e^2*f*g^4 - 8*a^3*c*d*e^3*g^5)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c^4*d^5*f^8*g^2 - 4*a*c^3*d^4*e*f^7*g^3 + 6*a^2*c^2*d^3*e^2*f^6*g^4 - 4*a^3*c*d^2*e^3*f^5*g^5 + a^4*d*e^4*f^4*g^6 + (c^4*d^4*e*f^4*g^6 - 4*a*c^3*d^3*e^2*f^3*g^7 + 6*a^2*c^2*d^2*e^3*f^2*g^8 - 4*a^3*c*d*e^4*f*g^9 + a^4*e^5*g^10)*x^5 + (4*c^4*d^4*e*f^5*g^5 + a^4*d*e^4*g^10 + (c^4*d^5 - 16*a*c^3*d^3*e^2)*f^4*g^6 - 4*(a*c^3*d^4*e - 6*a^2*c^2*d^2*e^3)*f^3*g^7 + 2*(3*a^2*c^2*d^3*e^2 - 8*a^3*c*d*e^4)*f^2*g^8 - 4*(a^3*c*d^2*e^3 - a^4*e^5)*f*g^9)*x^4 + 2*(3*c^4*d^4*e*f^6*g^4 + 2*a^4*d*e^4*f*g^9 + 2*(c^4*d^5 - 6*a*c^3*d^3*e^2)*f^5*g^5 - 2*(4*a*c^3*d^4*e - 9*a^2*c^2*d^2*e^3)*f^4*g^6 + 12*(a^2*c^2*d^3*e^2 - a^3*c*d*e^4)*f^3*g^7 - (8*a^3*c*d^2*e^3 - 3*a^4*e^5)*f^2*g^8)*x^3 + 2*(2*c^4*d^4*e*f^7*g^3 + 3*a^4*d*e^4*f^2*g^8 + (3*c^4*d^5 - 8*a*c^3*d^3*e^2)*f^6*g^4 - 12*(a*c^3*d^4*e - a^2*c^2*d^2*e^3)*f^5*g^5 + 2*(9*a^2*c^2*d^3*e^2 - 4*a^3*c*d*e^4)*f^4*g^6 - 2*(6*a^3*c*d^2*e^3 - a^4*e^5)*f^3*g^7)*x^2 + (c^4*d^4*e*f^8*g^2 + 4*a^4*d*e^4*f^3*g^7 + 4*(c^4*d^5 - a*c^3*d^3*e^2)*f^7*g^3 - 2*(8*a*c^3*d^4*e - 3*a^2*c^2*d^2*e^3)*f^6*g^4 + 4*(6*a^2*c^2*d^3*e^2 - a^3*c*d*e^4)*f^5*g^5 - (16*a^3*c*d^2*e^3 - a^4*e^5)*f^4*g^6)*x)]","B",0
689,1,472,0,0.429952," ","integrate((g*x+f)^4*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/(e*x+d)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(1155 \, c^{6} d^{6} g^{4} x^{6} + 3003 \, a^{2} c^{4} d^{4} e^{2} f^{4} - 3432 \, a^{3} c^{3} d^{3} e^{3} f^{3} g + 2288 \, a^{4} c^{2} d^{2} e^{4} f^{2} g^{2} - 832 \, a^{5} c d e^{5} f g^{3} + 128 \, a^{6} e^{6} g^{4} + 210 \, {\left(26 \, c^{6} d^{6} f g^{3} + 7 \, a c^{5} d^{5} e g^{4}\right)} x^{5} + 35 \, {\left(286 \, c^{6} d^{6} f^{2} g^{2} + 208 \, a c^{5} d^{5} e f g^{3} + a^{2} c^{4} d^{4} e^{2} g^{4}\right)} x^{4} + 20 \, {\left(429 \, c^{6} d^{6} f^{3} g + 715 \, a c^{5} d^{5} e f^{2} g^{2} + 13 \, a^{2} c^{4} d^{4} e^{2} f g^{3} - 2 \, a^{3} c^{3} d^{3} e^{3} g^{4}\right)} x^{3} + 3 \, {\left(1001 \, c^{6} d^{6} f^{4} + 4576 \, a c^{5} d^{5} e f^{3} g + 286 \, a^{2} c^{4} d^{4} e^{2} f^{2} g^{2} - 104 \, a^{3} c^{3} d^{3} e^{3} f g^{3} + 16 \, a^{4} c^{2} d^{2} e^{4} g^{4}\right)} x^{2} + 2 \, {\left(3003 \, a c^{5} d^{5} e f^{4} + 858 \, a^{2} c^{4} d^{4} e^{2} f^{3} g - 572 \, a^{3} c^{3} d^{3} e^{3} f^{2} g^{2} + 208 \, a^{4} c^{2} d^{2} e^{4} f g^{3} - 32 \, a^{5} c d e^{5} g^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{15015 \, {\left(c^{5} d^{5} e x + c^{5} d^{6}\right)}}"," ",0,"2/15015*(1155*c^6*d^6*g^4*x^6 + 3003*a^2*c^4*d^4*e^2*f^4 - 3432*a^3*c^3*d^3*e^3*f^3*g + 2288*a^4*c^2*d^2*e^4*f^2*g^2 - 832*a^5*c*d*e^5*f*g^3 + 128*a^6*e^6*g^4 + 210*(26*c^6*d^6*f*g^3 + 7*a*c^5*d^5*e*g^4)*x^5 + 35*(286*c^6*d^6*f^2*g^2 + 208*a*c^5*d^5*e*f*g^3 + a^2*c^4*d^4*e^2*g^4)*x^4 + 20*(429*c^6*d^6*f^3*g + 715*a*c^5*d^5*e*f^2*g^2 + 13*a^2*c^4*d^4*e^2*f*g^3 - 2*a^3*c^3*d^3*e^3*g^4)*x^3 + 3*(1001*c^6*d^6*f^4 + 4576*a*c^5*d^5*e*f^3*g + 286*a^2*c^4*d^4*e^2*f^2*g^2 - 104*a^3*c^3*d^3*e^3*f*g^3 + 16*a^4*c^2*d^2*e^4*g^4)*x^2 + 2*(3003*a*c^5*d^5*e*f^4 + 858*a^2*c^4*d^4*e^2*f^3*g - 572*a^3*c^3*d^3*e^3*f^2*g^2 + 208*a^4*c^2*d^2*e^4*f*g^3 - 32*a^5*c*d*e^5*g^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)/(c^5*d^5*e*x + c^5*d^6)","A",0
690,1,340,0,0.443259," ","integrate((g*x+f)^3*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/(e*x+d)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(105 \, c^{5} d^{5} g^{3} x^{5} + 231 \, a^{2} c^{3} d^{3} e^{2} f^{3} - 198 \, a^{3} c^{2} d^{2} e^{3} f^{2} g + 88 \, a^{4} c d e^{4} f g^{2} - 16 \, a^{5} e^{5} g^{3} + 35 \, {\left(11 \, c^{5} d^{5} f g^{2} + 4 \, a c^{4} d^{4} e g^{3}\right)} x^{4} + 5 \, {\left(99 \, c^{5} d^{5} f^{2} g + 110 \, a c^{4} d^{4} e f g^{2} + a^{2} c^{3} d^{3} e^{2} g^{3}\right)} x^{3} + 3 \, {\left(77 \, c^{5} d^{5} f^{3} + 264 \, a c^{4} d^{4} e f^{2} g + 11 \, a^{2} c^{3} d^{3} e^{2} f g^{2} - 2 \, a^{3} c^{2} d^{2} e^{3} g^{3}\right)} x^{2} + {\left(462 \, a c^{4} d^{4} e f^{3} + 99 \, a^{2} c^{3} d^{3} e^{2} f^{2} g - 44 \, a^{3} c^{2} d^{2} e^{3} f g^{2} + 8 \, a^{4} c d e^{4} g^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{1155 \, {\left(c^{4} d^{4} e x + c^{4} d^{5}\right)}}"," ",0,"2/1155*(105*c^5*d^5*g^3*x^5 + 231*a^2*c^3*d^3*e^2*f^3 - 198*a^3*c^2*d^2*e^3*f^2*g + 88*a^4*c*d*e^4*f*g^2 - 16*a^5*e^5*g^3 + 35*(11*c^5*d^5*f*g^2 + 4*a*c^4*d^4*e*g^3)*x^4 + 5*(99*c^5*d^5*f^2*g + 110*a*c^4*d^4*e*f*g^2 + a^2*c^3*d^3*e^2*g^3)*x^3 + 3*(77*c^5*d^5*f^3 + 264*a*c^4*d^4*e*f^2*g + 11*a^2*c^3*d^3*e^2*f*g^2 - 2*a^3*c^2*d^2*e^3*g^3)*x^2 + (462*a*c^4*d^4*e*f^3 + 99*a^2*c^3*d^3*e^2*f^2*g - 44*a^3*c^2*d^2*e^3*f*g^2 + 8*a^4*c*d*e^4*g^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)/(c^4*d^4*e*x + c^4*d^5)","A",0
691,1,230,0,0.418420," ","integrate((g*x+f)^2*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/(e*x+d)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, c^{4} d^{4} g^{2} x^{4} + 63 \, a^{2} c^{2} d^{2} e^{2} f^{2} - 36 \, a^{3} c d e^{3} f g + 8 \, a^{4} e^{4} g^{2} + 10 \, {\left(9 \, c^{4} d^{4} f g + 5 \, a c^{3} d^{3} e g^{2}\right)} x^{3} + 3 \, {\left(21 \, c^{4} d^{4} f^{2} + 48 \, a c^{3} d^{3} e f g + a^{2} c^{2} d^{2} e^{2} g^{2}\right)} x^{2} + 2 \, {\left(63 \, a c^{3} d^{3} e f^{2} + 9 \, a^{2} c^{2} d^{2} e^{2} f g - 2 \, a^{3} c d e^{3} g^{2}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{315 \, {\left(c^{3} d^{3} e x + c^{3} d^{4}\right)}}"," ",0,"2/315*(35*c^4*d^4*g^2*x^4 + 63*a^2*c^2*d^2*e^2*f^2 - 36*a^3*c*d*e^3*f*g + 8*a^4*e^4*g^2 + 10*(9*c^4*d^4*f*g + 5*a*c^3*d^3*e*g^2)*x^3 + 3*(21*c^4*d^4*f^2 + 48*a*c^3*d^3*e*f*g + a^2*c^2*d^2*e^2*g^2)*x^2 + 2*(63*a*c^3*d^3*e*f^2 + 9*a^2*c^2*d^2*e^2*f*g - 2*a^3*c*d*e^3*g^2)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)/(c^3*d^3*e*x + c^3*d^4)","A",0
692,1,137,0,0.413497," ","integrate((g*x+f)*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/(e*x+d)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, c^{3} d^{3} g x^{3} + 7 \, a^{2} c d e^{2} f - 2 \, a^{3} e^{3} g + {\left(7 \, c^{3} d^{3} f + 8 \, a c^{2} d^{2} e g\right)} x^{2} + {\left(14 \, a c^{2} d^{2} e f + a^{2} c d e^{2} g\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{35 \, {\left(c^{2} d^{2} e x + c^{2} d^{3}\right)}}"," ",0,"2/35*(5*c^3*d^3*g*x^3 + 7*a^2*c*d*e^2*f - 2*a^3*e^3*g + (7*c^3*d^3*f + 8*a*c^2*d^2*e*g)*x^2 + (14*a*c^2*d^2*e*f + a^2*c*d*e^2*g)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)/(c^2*d^2*e*x + c^2*d^3)","A",0
693,1,74,0,0.397082," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/(e*x+d)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(c^{2} d^{2} x^{2} + 2 \, a c d e x + a^{2} e^{2}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{5 \, {\left(c d e x + c d^{2}\right)}}"," ",0,"2/5*(c^2*d^2*x^2 + 2*a*c*d*e*x + a^2*e^2)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)/(c*d*e*x + c*d^2)","A",0
694,1,408,0,0.436161," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/(e*x+d)^(3/2)/(g*x+f),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(c d^{2} f - a d e g + {\left(c d e f - a e^{2} g\right)} x\right)} \sqrt{-\frac{c d f - a e g}{g}} \log\left(-\frac{c d e g x^{2} - c d^{2} f + 2 \, a d e g - 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} g \sqrt{-\frac{c d f - a e g}{g}} - {\left(c d e f - {\left(c d^{2} + 2 \, a e^{2}\right)} g\right)} x}{e g x^{2} + d f + {\left(e f + d g\right)} x}\right) - 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d g x - 3 \, c d f + 4 \, a e g\right)} \sqrt{e x + d}}{3 \, {\left(e g^{2} x + d g^{2}\right)}}, -\frac{2 \, {\left(3 \, {\left(c d^{2} f - a d e g + {\left(c d e f - a e^{2} g\right)} x\right)} \sqrt{\frac{c d f - a e g}{g}} \arctan\left(\frac{\sqrt{e x + d} \sqrt{\frac{c d f - a e g}{g}}}{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}\right) - \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d g x - 3 \, c d f + 4 \, a e g\right)} \sqrt{e x + d}\right)}}{3 \, {\left(e g^{2} x + d g^{2}\right)}}\right]"," ",0,"[-1/3*(3*(c*d^2*f - a*d*e*g + (c*d*e*f - a*e^2*g)*x)*sqrt(-(c*d*f - a*e*g)/g)*log(-(c*d*e*g*x^2 - c*d^2*f + 2*a*d*e*g - 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*g*sqrt(-(c*d*f - a*e*g)/g) - (c*d*e*f - (c*d^2 + 2*a*e^2)*g)*x)/(e*g*x^2 + d*f + (e*f + d*g)*x)) - 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d*g*x - 3*c*d*f + 4*a*e*g)*sqrt(e*x + d))/(e*g^2*x + d*g^2), -2/3*(3*(c*d^2*f - a*d*e*g + (c*d*e*f - a*e^2*g)*x)*sqrt((c*d*f - a*e*g)/g)*arctan(sqrt(e*x + d)*sqrt((c*d*f - a*e*g)/g)/sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)) - sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d*g*x - 3*c*d*f + 4*a*e*g)*sqrt(e*x + d))/(e*g^2*x + d*g^2)]","A",0
695,1,444,0,0.524499," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/(e*x+d)^(3/2)/(g*x+f)^2,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(c d e g x^{2} + c d^{2} f + {\left(c d e f + c d^{2} g\right)} x\right)} \sqrt{-\frac{c d f - a e g}{g}} \log\left(-\frac{c d e g x^{2} - c d^{2} f + 2 \, a d e g - 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} g \sqrt{-\frac{c d f - a e g}{g}} - {\left(c d e f - {\left(c d^{2} + 2 \, a e^{2}\right)} g\right)} x}{e g x^{2} + d f + {\left(e f + d g\right)} x}\right) + 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d g x + 3 \, c d f - a e g\right)} \sqrt{e x + d}}{2 \, {\left(e g^{3} x^{2} + d f g^{2} + {\left(e f g^{2} + d g^{3}\right)} x\right)}}, \frac{3 \, {\left(c d e g x^{2} + c d^{2} f + {\left(c d e f + c d^{2} g\right)} x\right)} \sqrt{\frac{c d f - a e g}{g}} \arctan\left(\frac{\sqrt{e x + d} \sqrt{\frac{c d f - a e g}{g}}}{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}\right) + \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d g x + 3 \, c d f - a e g\right)} \sqrt{e x + d}}{e g^{3} x^{2} + d f g^{2} + {\left(e f g^{2} + d g^{3}\right)} x}\right]"," ",0,"[1/2*(3*(c*d*e*g*x^2 + c*d^2*f + (c*d*e*f + c*d^2*g)*x)*sqrt(-(c*d*f - a*e*g)/g)*log(-(c*d*e*g*x^2 - c*d^2*f + 2*a*d*e*g - 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*g*sqrt(-(c*d*f - a*e*g)/g) - (c*d*e*f - (c*d^2 + 2*a*e^2)*g)*x)/(e*g*x^2 + d*f + (e*f + d*g)*x)) + 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*g*x + 3*c*d*f - a*e*g)*sqrt(e*x + d))/(e*g^3*x^2 + d*f*g^2 + (e*f*g^2 + d*g^3)*x), (3*(c*d*e*g*x^2 + c*d^2*f + (c*d*e*f + c*d^2*g)*x)*sqrt((c*d*f - a*e*g)/g)*arctan(sqrt(e*x + d)*sqrt((c*d*f - a*e*g)/g)/sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)) + sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*g*x + 3*c*d*f - a*e*g)*sqrt(e*x + d))/(e*g^3*x^2 + d*f*g^2 + (e*f*g^2 + d*g^3)*x)]","A",0
696,1,840,0,0.453204," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/(e*x+d)^(3/2)/(g*x+f)^3,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(c^{2} d^{2} e g^{2} x^{3} + c^{2} d^{3} f^{2} + {\left(2 \, c^{2} d^{2} e f g + c^{2} d^{3} g^{2}\right)} x^{2} + {\left(c^{2} d^{2} e f^{2} + 2 \, c^{2} d^{3} f g\right)} x\right)} \sqrt{-c d f g + a e g^{2}} \log\left(-\frac{c d e g x^{2} - c d^{2} f + 2 \, a d e g - {\left(c d e f - {\left(c d^{2} + 2 \, a e^{2}\right)} g\right)} x - 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{-c d f g + a e g^{2}} \sqrt{e x + d}}{e g x^{2} + d f + {\left(e f + d g\right)} x}\right) + 2 \, {\left(3 \, c^{2} d^{2} f^{2} g - a c d e f g^{2} - 2 \, a^{2} e^{2} g^{3} + 5 \, {\left(c^{2} d^{2} f g^{2} - a c d e g^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{8 \, {\left(c d^{2} f^{3} g^{3} - a d e f^{2} g^{4} + {\left(c d e f g^{5} - a e^{2} g^{6}\right)} x^{3} + {\left(2 \, c d e f^{2} g^{4} - a d e g^{6} + {\left(c d^{2} - 2 \, a e^{2}\right)} f g^{5}\right)} x^{2} + {\left(c d e f^{3} g^{3} - 2 \, a d e f g^{5} + {\left(2 \, c d^{2} - a e^{2}\right)} f^{2} g^{4}\right)} x\right)}}, -\frac{3 \, {\left(c^{2} d^{2} e g^{2} x^{3} + c^{2} d^{3} f^{2} + {\left(2 \, c^{2} d^{2} e f g + c^{2} d^{3} g^{2}\right)} x^{2} + {\left(c^{2} d^{2} e f^{2} + 2 \, c^{2} d^{3} f g\right)} x\right)} \sqrt{c d f g - a e g^{2}} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{c d f g - a e g^{2}} \sqrt{e x + d}}{c d e g x^{2} + a d e g + {\left(c d^{2} + a e^{2}\right)} g x}\right) + {\left(3 \, c^{2} d^{2} f^{2} g - a c d e f g^{2} - 2 \, a^{2} e^{2} g^{3} + 5 \, {\left(c^{2} d^{2} f g^{2} - a c d e g^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{4 \, {\left(c d^{2} f^{3} g^{3} - a d e f^{2} g^{4} + {\left(c d e f g^{5} - a e^{2} g^{6}\right)} x^{3} + {\left(2 \, c d e f^{2} g^{4} - a d e g^{6} + {\left(c d^{2} - 2 \, a e^{2}\right)} f g^{5}\right)} x^{2} + {\left(c d e f^{3} g^{3} - 2 \, a d e f g^{5} + {\left(2 \, c d^{2} - a e^{2}\right)} f^{2} g^{4}\right)} x\right)}}\right]"," ",0,"[-1/8*(3*(c^2*d^2*e*g^2*x^3 + c^2*d^3*f^2 + (2*c^2*d^2*e*f*g + c^2*d^3*g^2)*x^2 + (c^2*d^2*e*f^2 + 2*c^2*d^3*f*g)*x)*sqrt(-c*d*f*g + a*e*g^2)*log(-(c*d*e*g*x^2 - c*d^2*f + 2*a*d*e*g - (c*d*e*f - (c*d^2 + 2*a*e^2)*g)*x - 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-c*d*f*g + a*e*g^2)*sqrt(e*x + d))/(e*g*x^2 + d*f + (e*f + d*g)*x)) + 2*(3*c^2*d^2*f^2*g - a*c*d*e*f*g^2 - 2*a^2*e^2*g^3 + 5*(c^2*d^2*f*g^2 - a*c*d*e*g^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c*d^2*f^3*g^3 - a*d*e*f^2*g^4 + (c*d*e*f*g^5 - a*e^2*g^6)*x^3 + (2*c*d*e*f^2*g^4 - a*d*e*g^6 + (c*d^2 - 2*a*e^2)*f*g^5)*x^2 + (c*d*e*f^3*g^3 - 2*a*d*e*f*g^5 + (2*c*d^2 - a*e^2)*f^2*g^4)*x), -1/4*(3*(c^2*d^2*e*g^2*x^3 + c^2*d^3*f^2 + (2*c^2*d^2*e*f*g + c^2*d^3*g^2)*x^2 + (c^2*d^2*e*f^2 + 2*c^2*d^3*f*g)*x)*sqrt(c*d*f*g - a*e*g^2)*arctan(sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(c*d*f*g - a*e*g^2)*sqrt(e*x + d)/(c*d*e*g*x^2 + a*d*e*g + (c*d^2 + a*e^2)*g*x)) + (3*c^2*d^2*f^2*g - a*c*d*e*f*g^2 - 2*a^2*e^2*g^3 + 5*(c^2*d^2*f*g^2 - a*c*d*e*g^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c*d^2*f^3*g^3 - a*d*e*f^2*g^4 + (c*d*e*f*g^5 - a*e^2*g^6)*x^3 + (2*c*d*e*f^2*g^4 - a*d*e*g^6 + (c*d^2 - 2*a*e^2)*f*g^5)*x^2 + (c*d*e*f^3*g^3 - 2*a*d*e*f*g^5 + (2*c*d^2 - a*e^2)*f^2*g^4)*x)]","B",0
697,1,1434,0,0.467613," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/(e*x+d)^(3/2)/(g*x+f)^4,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(c^{3} d^{3} e g^{3} x^{4} + c^{3} d^{4} f^{3} + {\left(3 \, c^{3} d^{3} e f g^{2} + c^{3} d^{4} g^{3}\right)} x^{3} + 3 \, {\left(c^{3} d^{3} e f^{2} g + c^{3} d^{4} f g^{2}\right)} x^{2} + {\left(c^{3} d^{3} e f^{3} + 3 \, c^{3} d^{4} f^{2} g\right)} x\right)} \sqrt{-c d f g + a e g^{2}} \log\left(-\frac{c d e g x^{2} - c d^{2} f + 2 \, a d e g - {\left(c d e f - {\left(c d^{2} + 2 \, a e^{2}\right)} g\right)} x + 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{-c d f g + a e g^{2}} \sqrt{e x + d}}{e g x^{2} + d f + {\left(e f + d g\right)} x}\right) - 2 \, {\left(3 \, c^{3} d^{3} f^{3} g - a c^{2} d^{2} e f^{2} g^{2} - 10 \, a^{2} c d e^{2} f g^{3} + 8 \, a^{3} e^{3} g^{4} - 3 \, {\left(c^{3} d^{3} f g^{3} - a c^{2} d^{2} e g^{4}\right)} x^{2} + 2 \, {\left(4 \, c^{3} d^{3} f^{2} g^{2} - 11 \, a c^{2} d^{2} e f g^{3} + 7 \, a^{2} c d e^{2} g^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{48 \, {\left(c^{2} d^{3} f^{5} g^{3} - 2 \, a c d^{2} e f^{4} g^{4} + a^{2} d e^{2} f^{3} g^{5} + {\left(c^{2} d^{2} e f^{2} g^{6} - 2 \, a c d e^{2} f g^{7} + a^{2} e^{3} g^{8}\right)} x^{4} + {\left(3 \, c^{2} d^{2} e f^{3} g^{5} + a^{2} d e^{2} g^{8} + {\left(c^{2} d^{3} - 6 \, a c d e^{2}\right)} f^{2} g^{6} - {\left(2 \, a c d^{2} e - 3 \, a^{2} e^{3}\right)} f g^{7}\right)} x^{3} + 3 \, {\left(c^{2} d^{2} e f^{4} g^{4} + a^{2} d e^{2} f g^{7} + {\left(c^{2} d^{3} - 2 \, a c d e^{2}\right)} f^{3} g^{5} - {\left(2 \, a c d^{2} e - a^{2} e^{3}\right)} f^{2} g^{6}\right)} x^{2} + {\left(c^{2} d^{2} e f^{5} g^{3} + 3 \, a^{2} d e^{2} f^{2} g^{6} + {\left(3 \, c^{2} d^{3} - 2 \, a c d e^{2}\right)} f^{4} g^{4} - {\left(6 \, a c d^{2} e - a^{2} e^{3}\right)} f^{3} g^{5}\right)} x\right)}}, -\frac{3 \, {\left(c^{3} d^{3} e g^{3} x^{4} + c^{3} d^{4} f^{3} + {\left(3 \, c^{3} d^{3} e f g^{2} + c^{3} d^{4} g^{3}\right)} x^{3} + 3 \, {\left(c^{3} d^{3} e f^{2} g + c^{3} d^{4} f g^{2}\right)} x^{2} + {\left(c^{3} d^{3} e f^{3} + 3 \, c^{3} d^{4} f^{2} g\right)} x\right)} \sqrt{c d f g - a e g^{2}} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{c d f g - a e g^{2}} \sqrt{e x + d}}{c d e g x^{2} + a d e g + {\left(c d^{2} + a e^{2}\right)} g x}\right) + {\left(3 \, c^{3} d^{3} f^{3} g - a c^{2} d^{2} e f^{2} g^{2} - 10 \, a^{2} c d e^{2} f g^{3} + 8 \, a^{3} e^{3} g^{4} - 3 \, {\left(c^{3} d^{3} f g^{3} - a c^{2} d^{2} e g^{4}\right)} x^{2} + 2 \, {\left(4 \, c^{3} d^{3} f^{2} g^{2} - 11 \, a c^{2} d^{2} e f g^{3} + 7 \, a^{2} c d e^{2} g^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{24 \, {\left(c^{2} d^{3} f^{5} g^{3} - 2 \, a c d^{2} e f^{4} g^{4} + a^{2} d e^{2} f^{3} g^{5} + {\left(c^{2} d^{2} e f^{2} g^{6} - 2 \, a c d e^{2} f g^{7} + a^{2} e^{3} g^{8}\right)} x^{4} + {\left(3 \, c^{2} d^{2} e f^{3} g^{5} + a^{2} d e^{2} g^{8} + {\left(c^{2} d^{3} - 6 \, a c d e^{2}\right)} f^{2} g^{6} - {\left(2 \, a c d^{2} e - 3 \, a^{2} e^{3}\right)} f g^{7}\right)} x^{3} + 3 \, {\left(c^{2} d^{2} e f^{4} g^{4} + a^{2} d e^{2} f g^{7} + {\left(c^{2} d^{3} - 2 \, a c d e^{2}\right)} f^{3} g^{5} - {\left(2 \, a c d^{2} e - a^{2} e^{3}\right)} f^{2} g^{6}\right)} x^{2} + {\left(c^{2} d^{2} e f^{5} g^{3} + 3 \, a^{2} d e^{2} f^{2} g^{6} + {\left(3 \, c^{2} d^{3} - 2 \, a c d e^{2}\right)} f^{4} g^{4} - {\left(6 \, a c d^{2} e - a^{2} e^{3}\right)} f^{3} g^{5}\right)} x\right)}}\right]"," ",0,"[1/48*(3*(c^3*d^3*e*g^3*x^4 + c^3*d^4*f^3 + (3*c^3*d^3*e*f*g^2 + c^3*d^4*g^3)*x^3 + 3*(c^3*d^3*e*f^2*g + c^3*d^4*f*g^2)*x^2 + (c^3*d^3*e*f^3 + 3*c^3*d^4*f^2*g)*x)*sqrt(-c*d*f*g + a*e*g^2)*log(-(c*d*e*g*x^2 - c*d^2*f + 2*a*d*e*g - (c*d*e*f - (c*d^2 + 2*a*e^2)*g)*x + 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-c*d*f*g + a*e*g^2)*sqrt(e*x + d))/(e*g*x^2 + d*f + (e*f + d*g)*x)) - 2*(3*c^3*d^3*f^3*g - a*c^2*d^2*e*f^2*g^2 - 10*a^2*c*d*e^2*f*g^3 + 8*a^3*e^3*g^4 - 3*(c^3*d^3*f*g^3 - a*c^2*d^2*e*g^4)*x^2 + 2*(4*c^3*d^3*f^2*g^2 - 11*a*c^2*d^2*e*f*g^3 + 7*a^2*c*d*e^2*g^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c^2*d^3*f^5*g^3 - 2*a*c*d^2*e*f^4*g^4 + a^2*d*e^2*f^3*g^5 + (c^2*d^2*e*f^2*g^6 - 2*a*c*d*e^2*f*g^7 + a^2*e^3*g^8)*x^4 + (3*c^2*d^2*e*f^3*g^5 + a^2*d*e^2*g^8 + (c^2*d^3 - 6*a*c*d*e^2)*f^2*g^6 - (2*a*c*d^2*e - 3*a^2*e^3)*f*g^7)*x^3 + 3*(c^2*d^2*e*f^4*g^4 + a^2*d*e^2*f*g^7 + (c^2*d^3 - 2*a*c*d*e^2)*f^3*g^5 - (2*a*c*d^2*e - a^2*e^3)*f^2*g^6)*x^2 + (c^2*d^2*e*f^5*g^3 + 3*a^2*d*e^2*f^2*g^6 + (3*c^2*d^3 - 2*a*c*d*e^2)*f^4*g^4 - (6*a*c*d^2*e - a^2*e^3)*f^3*g^5)*x), -1/24*(3*(c^3*d^3*e*g^3*x^4 + c^3*d^4*f^3 + (3*c^3*d^3*e*f*g^2 + c^3*d^4*g^3)*x^3 + 3*(c^3*d^3*e*f^2*g + c^3*d^4*f*g^2)*x^2 + (c^3*d^3*e*f^3 + 3*c^3*d^4*f^2*g)*x)*sqrt(c*d*f*g - a*e*g^2)*arctan(sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(c*d*f*g - a*e*g^2)*sqrt(e*x + d)/(c*d*e*g*x^2 + a*d*e*g + (c*d^2 + a*e^2)*g*x)) + (3*c^3*d^3*f^3*g - a*c^2*d^2*e*f^2*g^2 - 10*a^2*c*d*e^2*f*g^3 + 8*a^3*e^3*g^4 - 3*(c^3*d^3*f*g^3 - a*c^2*d^2*e*g^4)*x^2 + 2*(4*c^3*d^3*f^2*g^2 - 11*a*c^2*d^2*e*f*g^3 + 7*a^2*c*d*e^2*g^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c^2*d^3*f^5*g^3 - 2*a*c*d^2*e*f^4*g^4 + a^2*d*e^2*f^3*g^5 + (c^2*d^2*e*f^2*g^6 - 2*a*c*d*e^2*f*g^7 + a^2*e^3*g^8)*x^4 + (3*c^2*d^2*e*f^3*g^5 + a^2*d*e^2*g^8 + (c^2*d^3 - 6*a*c*d*e^2)*f^2*g^6 - (2*a*c*d^2*e - 3*a^2*e^3)*f*g^7)*x^3 + 3*(c^2*d^2*e*f^4*g^4 + a^2*d*e^2*f*g^7 + (c^2*d^3 - 2*a*c*d*e^2)*f^3*g^5 - (2*a*c*d^2*e - a^2*e^3)*f^2*g^6)*x^2 + (c^2*d^2*e*f^5*g^3 + 3*a^2*d*e^2*f^2*g^6 + (3*c^2*d^3 - 2*a*c*d*e^2)*f^4*g^4 - (6*a*c*d^2*e - a^2*e^3)*f^3*g^5)*x)]","B",0
698,1,2238,0,0.484808," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/(e*x+d)^(3/2)/(g*x+f)^5,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(c^{4} d^{4} e g^{4} x^{5} + c^{4} d^{5} f^{4} + {\left(4 \, c^{4} d^{4} e f g^{3} + c^{4} d^{5} g^{4}\right)} x^{4} + 2 \, {\left(3 \, c^{4} d^{4} e f^{2} g^{2} + 2 \, c^{4} d^{5} f g^{3}\right)} x^{3} + 2 \, {\left(2 \, c^{4} d^{4} e f^{3} g + 3 \, c^{4} d^{5} f^{2} g^{2}\right)} x^{2} + {\left(c^{4} d^{4} e f^{4} + 4 \, c^{4} d^{5} f^{3} g\right)} x\right)} \sqrt{-c d f g + a e g^{2}} \log\left(-\frac{c d e g x^{2} - c d^{2} f + 2 \, a d e g - {\left(c d e f - {\left(c d^{2} + 2 \, a e^{2}\right)} g\right)} x - 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{-c d f g + a e g^{2}} \sqrt{e x + d}}{e g x^{2} + d f + {\left(e f + d g\right)} x}\right) + 2 \, {\left(3 \, c^{4} d^{4} f^{4} g - a c^{3} d^{3} e f^{3} g^{2} - 26 \, a^{2} c^{2} d^{2} e^{2} f^{2} g^{3} + 40 \, a^{3} c d e^{3} f g^{4} - 16 \, a^{4} e^{4} g^{5} - 3 \, {\left(c^{4} d^{4} f g^{4} - a c^{3} d^{3} e g^{5}\right)} x^{3} - {\left(11 \, c^{4} d^{4} f^{2} g^{3} - 13 \, a c^{3} d^{3} e f g^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} g^{5}\right)} x^{2} + {\left(11 \, c^{4} d^{4} f^{3} g^{2} - 55 \, a c^{3} d^{3} e f^{2} g^{3} + 68 \, a^{2} c^{2} d^{2} e^{2} f g^{4} - 24 \, a^{3} c d e^{3} g^{5}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{128 \, {\left(c^{3} d^{4} f^{7} g^{3} - 3 \, a c^{2} d^{3} e f^{6} g^{4} + 3 \, a^{2} c d^{2} e^{2} f^{5} g^{5} - a^{3} d e^{3} f^{4} g^{6} + {\left(c^{3} d^{3} e f^{3} g^{7} - 3 \, a c^{2} d^{2} e^{2} f^{2} g^{8} + 3 \, a^{2} c d e^{3} f g^{9} - a^{3} e^{4} g^{10}\right)} x^{5} + {\left(4 \, c^{3} d^{3} e f^{4} g^{6} - a^{3} d e^{3} g^{10} + {\left(c^{3} d^{4} - 12 \, a c^{2} d^{2} e^{2}\right)} f^{3} g^{7} - 3 \, {\left(a c^{2} d^{3} e - 4 \, a^{2} c d e^{3}\right)} f^{2} g^{8} + {\left(3 \, a^{2} c d^{2} e^{2} - 4 \, a^{3} e^{4}\right)} f g^{9}\right)} x^{4} + 2 \, {\left(3 \, c^{3} d^{3} e f^{5} g^{5} - 2 \, a^{3} d e^{3} f g^{9} + {\left(2 \, c^{3} d^{4} - 9 \, a c^{2} d^{2} e^{2}\right)} f^{4} g^{6} - 3 \, {\left(2 \, a c^{2} d^{3} e - 3 \, a^{2} c d e^{3}\right)} f^{3} g^{7} + 3 \, {\left(2 \, a^{2} c d^{2} e^{2} - a^{3} e^{4}\right)} f^{2} g^{8}\right)} x^{3} + 2 \, {\left(2 \, c^{3} d^{3} e f^{6} g^{4} - 3 \, a^{3} d e^{3} f^{2} g^{8} + 3 \, {\left(c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2}\right)} f^{5} g^{5} - 3 \, {\left(3 \, a c^{2} d^{3} e - 2 \, a^{2} c d e^{3}\right)} f^{4} g^{6} + {\left(9 \, a^{2} c d^{2} e^{2} - 2 \, a^{3} e^{4}\right)} f^{3} g^{7}\right)} x^{2} + {\left(c^{3} d^{3} e f^{7} g^{3} - 4 \, a^{3} d e^{3} f^{3} g^{7} + {\left(4 \, c^{3} d^{4} - 3 \, a c^{2} d^{2} e^{2}\right)} f^{6} g^{4} - 3 \, {\left(4 \, a c^{2} d^{3} e - a^{2} c d e^{3}\right)} f^{5} g^{5} + {\left(12 \, a^{2} c d^{2} e^{2} - a^{3} e^{4}\right)} f^{4} g^{6}\right)} x\right)}}, -\frac{3 \, {\left(c^{4} d^{4} e g^{4} x^{5} + c^{4} d^{5} f^{4} + {\left(4 \, c^{4} d^{4} e f g^{3} + c^{4} d^{5} g^{4}\right)} x^{4} + 2 \, {\left(3 \, c^{4} d^{4} e f^{2} g^{2} + 2 \, c^{4} d^{5} f g^{3}\right)} x^{3} + 2 \, {\left(2 \, c^{4} d^{4} e f^{3} g + 3 \, c^{4} d^{5} f^{2} g^{2}\right)} x^{2} + {\left(c^{4} d^{4} e f^{4} + 4 \, c^{4} d^{5} f^{3} g\right)} x\right)} \sqrt{c d f g - a e g^{2}} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{c d f g - a e g^{2}} \sqrt{e x + d}}{c d e g x^{2} + a d e g + {\left(c d^{2} + a e^{2}\right)} g x}\right) + {\left(3 \, c^{4} d^{4} f^{4} g - a c^{3} d^{3} e f^{3} g^{2} - 26 \, a^{2} c^{2} d^{2} e^{2} f^{2} g^{3} + 40 \, a^{3} c d e^{3} f g^{4} - 16 \, a^{4} e^{4} g^{5} - 3 \, {\left(c^{4} d^{4} f g^{4} - a c^{3} d^{3} e g^{5}\right)} x^{3} - {\left(11 \, c^{4} d^{4} f^{2} g^{3} - 13 \, a c^{3} d^{3} e f g^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} g^{5}\right)} x^{2} + {\left(11 \, c^{4} d^{4} f^{3} g^{2} - 55 \, a c^{3} d^{3} e f^{2} g^{3} + 68 \, a^{2} c^{2} d^{2} e^{2} f g^{4} - 24 \, a^{3} c d e^{3} g^{5}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{64 \, {\left(c^{3} d^{4} f^{7} g^{3} - 3 \, a c^{2} d^{3} e f^{6} g^{4} + 3 \, a^{2} c d^{2} e^{2} f^{5} g^{5} - a^{3} d e^{3} f^{4} g^{6} + {\left(c^{3} d^{3} e f^{3} g^{7} - 3 \, a c^{2} d^{2} e^{2} f^{2} g^{8} + 3 \, a^{2} c d e^{3} f g^{9} - a^{3} e^{4} g^{10}\right)} x^{5} + {\left(4 \, c^{3} d^{3} e f^{4} g^{6} - a^{3} d e^{3} g^{10} + {\left(c^{3} d^{4} - 12 \, a c^{2} d^{2} e^{2}\right)} f^{3} g^{7} - 3 \, {\left(a c^{2} d^{3} e - 4 \, a^{2} c d e^{3}\right)} f^{2} g^{8} + {\left(3 \, a^{2} c d^{2} e^{2} - 4 \, a^{3} e^{4}\right)} f g^{9}\right)} x^{4} + 2 \, {\left(3 \, c^{3} d^{3} e f^{5} g^{5} - 2 \, a^{3} d e^{3} f g^{9} + {\left(2 \, c^{3} d^{4} - 9 \, a c^{2} d^{2} e^{2}\right)} f^{4} g^{6} - 3 \, {\left(2 \, a c^{2} d^{3} e - 3 \, a^{2} c d e^{3}\right)} f^{3} g^{7} + 3 \, {\left(2 \, a^{2} c d^{2} e^{2} - a^{3} e^{4}\right)} f^{2} g^{8}\right)} x^{3} + 2 \, {\left(2 \, c^{3} d^{3} e f^{6} g^{4} - 3 \, a^{3} d e^{3} f^{2} g^{8} + 3 \, {\left(c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2}\right)} f^{5} g^{5} - 3 \, {\left(3 \, a c^{2} d^{3} e - 2 \, a^{2} c d e^{3}\right)} f^{4} g^{6} + {\left(9 \, a^{2} c d^{2} e^{2} - 2 \, a^{3} e^{4}\right)} f^{3} g^{7}\right)} x^{2} + {\left(c^{3} d^{3} e f^{7} g^{3} - 4 \, a^{3} d e^{3} f^{3} g^{7} + {\left(4 \, c^{3} d^{4} - 3 \, a c^{2} d^{2} e^{2}\right)} f^{6} g^{4} - 3 \, {\left(4 \, a c^{2} d^{3} e - a^{2} c d e^{3}\right)} f^{5} g^{5} + {\left(12 \, a^{2} c d^{2} e^{2} - a^{3} e^{4}\right)} f^{4} g^{6}\right)} x\right)}}\right]"," ",0,"[-1/128*(3*(c^4*d^4*e*g^4*x^5 + c^4*d^5*f^4 + (4*c^4*d^4*e*f*g^3 + c^4*d^5*g^4)*x^4 + 2*(3*c^4*d^4*e*f^2*g^2 + 2*c^4*d^5*f*g^3)*x^3 + 2*(2*c^4*d^4*e*f^3*g + 3*c^4*d^5*f^2*g^2)*x^2 + (c^4*d^4*e*f^4 + 4*c^4*d^5*f^3*g)*x)*sqrt(-c*d*f*g + a*e*g^2)*log(-(c*d*e*g*x^2 - c*d^2*f + 2*a*d*e*g - (c*d*e*f - (c*d^2 + 2*a*e^2)*g)*x - 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-c*d*f*g + a*e*g^2)*sqrt(e*x + d))/(e*g*x^2 + d*f + (e*f + d*g)*x)) + 2*(3*c^4*d^4*f^4*g - a*c^3*d^3*e*f^3*g^2 - 26*a^2*c^2*d^2*e^2*f^2*g^3 + 40*a^3*c*d*e^3*f*g^4 - 16*a^4*e^4*g^5 - 3*(c^4*d^4*f*g^4 - a*c^3*d^3*e*g^5)*x^3 - (11*c^4*d^4*f^2*g^3 - 13*a*c^3*d^3*e*f*g^4 + 2*a^2*c^2*d^2*e^2*g^5)*x^2 + (11*c^4*d^4*f^3*g^2 - 55*a*c^3*d^3*e*f^2*g^3 + 68*a^2*c^2*d^2*e^2*f*g^4 - 24*a^3*c*d*e^3*g^5)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c^3*d^4*f^7*g^3 - 3*a*c^2*d^3*e*f^6*g^4 + 3*a^2*c*d^2*e^2*f^5*g^5 - a^3*d*e^3*f^4*g^6 + (c^3*d^3*e*f^3*g^7 - 3*a*c^2*d^2*e^2*f^2*g^8 + 3*a^2*c*d*e^3*f*g^9 - a^3*e^4*g^10)*x^5 + (4*c^3*d^3*e*f^4*g^6 - a^3*d*e^3*g^10 + (c^3*d^4 - 12*a*c^2*d^2*e^2)*f^3*g^7 - 3*(a*c^2*d^3*e - 4*a^2*c*d*e^3)*f^2*g^8 + (3*a^2*c*d^2*e^2 - 4*a^3*e^4)*f*g^9)*x^4 + 2*(3*c^3*d^3*e*f^5*g^5 - 2*a^3*d*e^3*f*g^9 + (2*c^3*d^4 - 9*a*c^2*d^2*e^2)*f^4*g^6 - 3*(2*a*c^2*d^3*e - 3*a^2*c*d*e^3)*f^3*g^7 + 3*(2*a^2*c*d^2*e^2 - a^3*e^4)*f^2*g^8)*x^3 + 2*(2*c^3*d^3*e*f^6*g^4 - 3*a^3*d*e^3*f^2*g^8 + 3*(c^3*d^4 - 2*a*c^2*d^2*e^2)*f^5*g^5 - 3*(3*a*c^2*d^3*e - 2*a^2*c*d*e^3)*f^4*g^6 + (9*a^2*c*d^2*e^2 - 2*a^3*e^4)*f^3*g^7)*x^2 + (c^3*d^3*e*f^7*g^3 - 4*a^3*d*e^3*f^3*g^7 + (4*c^3*d^4 - 3*a*c^2*d^2*e^2)*f^6*g^4 - 3*(4*a*c^2*d^3*e - a^2*c*d*e^3)*f^5*g^5 + (12*a^2*c*d^2*e^2 - a^3*e^4)*f^4*g^6)*x), -1/64*(3*(c^4*d^4*e*g^4*x^5 + c^4*d^5*f^4 + (4*c^4*d^4*e*f*g^3 + c^4*d^5*g^4)*x^4 + 2*(3*c^4*d^4*e*f^2*g^2 + 2*c^4*d^5*f*g^3)*x^3 + 2*(2*c^4*d^4*e*f^3*g + 3*c^4*d^5*f^2*g^2)*x^2 + (c^4*d^4*e*f^4 + 4*c^4*d^5*f^3*g)*x)*sqrt(c*d*f*g - a*e*g^2)*arctan(sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(c*d*f*g - a*e*g^2)*sqrt(e*x + d)/(c*d*e*g*x^2 + a*d*e*g + (c*d^2 + a*e^2)*g*x)) + (3*c^4*d^4*f^4*g - a*c^3*d^3*e*f^3*g^2 - 26*a^2*c^2*d^2*e^2*f^2*g^3 + 40*a^3*c*d*e^3*f*g^4 - 16*a^4*e^4*g^5 - 3*(c^4*d^4*f*g^4 - a*c^3*d^3*e*g^5)*x^3 - (11*c^4*d^4*f^2*g^3 - 13*a*c^3*d^3*e*f*g^4 + 2*a^2*c^2*d^2*e^2*g^5)*x^2 + (11*c^4*d^4*f^3*g^2 - 55*a*c^3*d^3*e*f^2*g^3 + 68*a^2*c^2*d^2*e^2*f*g^4 - 24*a^3*c*d*e^3*g^5)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c^3*d^4*f^7*g^3 - 3*a*c^2*d^3*e*f^6*g^4 + 3*a^2*c*d^2*e^2*f^5*g^5 - a^3*d*e^3*f^4*g^6 + (c^3*d^3*e*f^3*g^7 - 3*a*c^2*d^2*e^2*f^2*g^8 + 3*a^2*c*d*e^3*f*g^9 - a^3*e^4*g^10)*x^5 + (4*c^3*d^3*e*f^4*g^6 - a^3*d*e^3*g^10 + (c^3*d^4 - 12*a*c^2*d^2*e^2)*f^3*g^7 - 3*(a*c^2*d^3*e - 4*a^2*c*d*e^3)*f^2*g^8 + (3*a^2*c*d^2*e^2 - 4*a^3*e^4)*f*g^9)*x^4 + 2*(3*c^3*d^3*e*f^5*g^5 - 2*a^3*d*e^3*f*g^9 + (2*c^3*d^4 - 9*a*c^2*d^2*e^2)*f^4*g^6 - 3*(2*a*c^2*d^3*e - 3*a^2*c*d*e^3)*f^3*g^7 + 3*(2*a^2*c*d^2*e^2 - a^3*e^4)*f^2*g^8)*x^3 + 2*(2*c^3*d^3*e*f^6*g^4 - 3*a^3*d*e^3*f^2*g^8 + 3*(c^3*d^4 - 2*a*c^2*d^2*e^2)*f^5*g^5 - 3*(3*a*c^2*d^3*e - 2*a^2*c*d*e^3)*f^4*g^6 + (9*a^2*c*d^2*e^2 - 2*a^3*e^4)*f^3*g^7)*x^2 + (c^3*d^3*e*f^7*g^3 - 4*a^3*d*e^3*f^3*g^7 + (4*c^3*d^4 - 3*a*c^2*d^2*e^2)*f^6*g^4 - 3*(4*a*c^2*d^3*e - a^2*c*d*e^3)*f^5*g^5 + (12*a^2*c*d^2*e^2 - a^3*e^4)*f^4*g^6)*x)]","B",0
699,1,3204,0,0.530836," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/(e*x+d)^(3/2)/(g*x+f)^6,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(c^{5} d^{5} e g^{5} x^{6} + c^{5} d^{6} f^{5} + {\left(5 \, c^{5} d^{5} e f g^{4} + c^{5} d^{6} g^{5}\right)} x^{5} + 5 \, {\left(2 \, c^{5} d^{5} e f^{2} g^{3} + c^{5} d^{6} f g^{4}\right)} x^{4} + 10 \, {\left(c^{5} d^{5} e f^{3} g^{2} + c^{5} d^{6} f^{2} g^{3}\right)} x^{3} + 5 \, {\left(c^{5} d^{5} e f^{4} g + 2 \, c^{5} d^{6} f^{3} g^{2}\right)} x^{2} + {\left(c^{5} d^{5} e f^{5} + 5 \, c^{5} d^{6} f^{4} g\right)} x\right)} \sqrt{-c d f g + a e g^{2}} \log\left(-\frac{c d e g x^{2} - c d^{2} f + 2 \, a d e g - {\left(c d e f - {\left(c d^{2} + 2 \, a e^{2}\right)} g\right)} x + 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{-c d f g + a e g^{2}} \sqrt{e x + d}}{e g x^{2} + d f + {\left(e f + d g\right)} x}\right) - 2 \, {\left(15 \, c^{5} d^{5} f^{5} g - 5 \, a c^{4} d^{4} e f^{4} g^{2} - 258 \, a^{2} c^{3} d^{3} e^{2} f^{3} g^{3} + 584 \, a^{3} c^{2} d^{2} e^{3} f^{2} g^{4} - 464 \, a^{4} c d e^{4} f g^{5} + 128 \, a^{5} e^{5} g^{6} - 15 \, {\left(c^{5} d^{5} f g^{5} - a c^{4} d^{4} e g^{6}\right)} x^{4} - 10 \, {\left(7 \, c^{5} d^{5} f^{2} g^{4} - 8 \, a c^{4} d^{4} e f g^{5} + a^{2} c^{3} d^{3} e^{2} g^{6}\right)} x^{3} - 2 \, {\left(64 \, c^{5} d^{5} f^{3} g^{3} - 87 \, a c^{4} d^{4} e f^{2} g^{4} + 27 \, a^{2} c^{3} d^{3} e^{2} f g^{5} - 4 \, a^{3} c^{2} d^{2} e^{3} g^{6}\right)} x^{2} + 2 \, {\left(35 \, c^{5} d^{5} f^{4} g^{2} - 268 \, a c^{4} d^{4} e f^{3} g^{3} + 489 \, a^{2} c^{3} d^{3} e^{2} f^{2} g^{4} - 344 \, a^{3} c^{2} d^{2} e^{3} f g^{5} + 88 \, a^{4} c d e^{4} g^{6}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{1280 \, {\left(c^{4} d^{5} f^{9} g^{3} - 4 \, a c^{3} d^{4} e f^{8} g^{4} + 6 \, a^{2} c^{2} d^{3} e^{2} f^{7} g^{5} - 4 \, a^{3} c d^{2} e^{3} f^{6} g^{6} + a^{4} d e^{4} f^{5} g^{7} + {\left(c^{4} d^{4} e f^{4} g^{8} - 4 \, a c^{3} d^{3} e^{2} f^{3} g^{9} + 6 \, a^{2} c^{2} d^{2} e^{3} f^{2} g^{10} - 4 \, a^{3} c d e^{4} f g^{11} + a^{4} e^{5} g^{12}\right)} x^{6} + {\left(5 \, c^{4} d^{4} e f^{5} g^{7} + a^{4} d e^{4} g^{12} + {\left(c^{4} d^{5} - 20 \, a c^{3} d^{3} e^{2}\right)} f^{4} g^{8} - 2 \, {\left(2 \, a c^{3} d^{4} e - 15 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{3} g^{9} + 2 \, {\left(3 \, a^{2} c^{2} d^{3} e^{2} - 10 \, a^{3} c d e^{4}\right)} f^{2} g^{10} - {\left(4 \, a^{3} c d^{2} e^{3} - 5 \, a^{4} e^{5}\right)} f g^{11}\right)} x^{5} + 5 \, {\left(2 \, c^{4} d^{4} e f^{6} g^{6} + a^{4} d e^{4} f g^{11} + {\left(c^{4} d^{5} - 8 \, a c^{3} d^{3} e^{2}\right)} f^{5} g^{7} - 4 \, {\left(a c^{3} d^{4} e - 3 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{4} g^{8} + 2 \, {\left(3 \, a^{2} c^{2} d^{3} e^{2} - 4 \, a^{3} c d e^{4}\right)} f^{3} g^{9} - 2 \, {\left(2 \, a^{3} c d^{2} e^{3} - a^{4} e^{5}\right)} f^{2} g^{10}\right)} x^{4} + 10 \, {\left(c^{4} d^{4} e f^{7} g^{5} + a^{4} d e^{4} f^{2} g^{10} + {\left(c^{4} d^{5} - 4 \, a c^{3} d^{3} e^{2}\right)} f^{6} g^{6} - 2 \, {\left(2 \, a c^{3} d^{4} e - 3 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{5} g^{7} + 2 \, {\left(3 \, a^{2} c^{2} d^{3} e^{2} - 2 \, a^{3} c d e^{4}\right)} f^{4} g^{8} - {\left(4 \, a^{3} c d^{2} e^{3} - a^{4} e^{5}\right)} f^{3} g^{9}\right)} x^{3} + 5 \, {\left(c^{4} d^{4} e f^{8} g^{4} + 2 \, a^{4} d e^{4} f^{3} g^{9} + 2 \, {\left(c^{4} d^{5} - 2 \, a c^{3} d^{3} e^{2}\right)} f^{7} g^{5} - 2 \, {\left(4 \, a c^{3} d^{4} e - 3 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{6} g^{6} + 4 \, {\left(3 \, a^{2} c^{2} d^{3} e^{2} - a^{3} c d e^{4}\right)} f^{5} g^{7} - {\left(8 \, a^{3} c d^{2} e^{3} - a^{4} e^{5}\right)} f^{4} g^{8}\right)} x^{2} + {\left(c^{4} d^{4} e f^{9} g^{3} + 5 \, a^{4} d e^{4} f^{4} g^{8} + {\left(5 \, c^{4} d^{5} - 4 \, a c^{3} d^{3} e^{2}\right)} f^{8} g^{4} - 2 \, {\left(10 \, a c^{3} d^{4} e - 3 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{7} g^{5} + 2 \, {\left(15 \, a^{2} c^{2} d^{3} e^{2} - 2 \, a^{3} c d e^{4}\right)} f^{6} g^{6} - {\left(20 \, a^{3} c d^{2} e^{3} - a^{4} e^{5}\right)} f^{5} g^{7}\right)} x\right)}}, -\frac{15 \, {\left(c^{5} d^{5} e g^{5} x^{6} + c^{5} d^{6} f^{5} + {\left(5 \, c^{5} d^{5} e f g^{4} + c^{5} d^{6} g^{5}\right)} x^{5} + 5 \, {\left(2 \, c^{5} d^{5} e f^{2} g^{3} + c^{5} d^{6} f g^{4}\right)} x^{4} + 10 \, {\left(c^{5} d^{5} e f^{3} g^{2} + c^{5} d^{6} f^{2} g^{3}\right)} x^{3} + 5 \, {\left(c^{5} d^{5} e f^{4} g + 2 \, c^{5} d^{6} f^{3} g^{2}\right)} x^{2} + {\left(c^{5} d^{5} e f^{5} + 5 \, c^{5} d^{6} f^{4} g\right)} x\right)} \sqrt{c d f g - a e g^{2}} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{c d f g - a e g^{2}} \sqrt{e x + d}}{c d e g x^{2} + a d e g + {\left(c d^{2} + a e^{2}\right)} g x}\right) + {\left(15 \, c^{5} d^{5} f^{5} g - 5 \, a c^{4} d^{4} e f^{4} g^{2} - 258 \, a^{2} c^{3} d^{3} e^{2} f^{3} g^{3} + 584 \, a^{3} c^{2} d^{2} e^{3} f^{2} g^{4} - 464 \, a^{4} c d e^{4} f g^{5} + 128 \, a^{5} e^{5} g^{6} - 15 \, {\left(c^{5} d^{5} f g^{5} - a c^{4} d^{4} e g^{6}\right)} x^{4} - 10 \, {\left(7 \, c^{5} d^{5} f^{2} g^{4} - 8 \, a c^{4} d^{4} e f g^{5} + a^{2} c^{3} d^{3} e^{2} g^{6}\right)} x^{3} - 2 \, {\left(64 \, c^{5} d^{5} f^{3} g^{3} - 87 \, a c^{4} d^{4} e f^{2} g^{4} + 27 \, a^{2} c^{3} d^{3} e^{2} f g^{5} - 4 \, a^{3} c^{2} d^{2} e^{3} g^{6}\right)} x^{2} + 2 \, {\left(35 \, c^{5} d^{5} f^{4} g^{2} - 268 \, a c^{4} d^{4} e f^{3} g^{3} + 489 \, a^{2} c^{3} d^{3} e^{2} f^{2} g^{4} - 344 \, a^{3} c^{2} d^{2} e^{3} f g^{5} + 88 \, a^{4} c d e^{4} g^{6}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{640 \, {\left(c^{4} d^{5} f^{9} g^{3} - 4 \, a c^{3} d^{4} e f^{8} g^{4} + 6 \, a^{2} c^{2} d^{3} e^{2} f^{7} g^{5} - 4 \, a^{3} c d^{2} e^{3} f^{6} g^{6} + a^{4} d e^{4} f^{5} g^{7} + {\left(c^{4} d^{4} e f^{4} g^{8} - 4 \, a c^{3} d^{3} e^{2} f^{3} g^{9} + 6 \, a^{2} c^{2} d^{2} e^{3} f^{2} g^{10} - 4 \, a^{3} c d e^{4} f g^{11} + a^{4} e^{5} g^{12}\right)} x^{6} + {\left(5 \, c^{4} d^{4} e f^{5} g^{7} + a^{4} d e^{4} g^{12} + {\left(c^{4} d^{5} - 20 \, a c^{3} d^{3} e^{2}\right)} f^{4} g^{8} - 2 \, {\left(2 \, a c^{3} d^{4} e - 15 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{3} g^{9} + 2 \, {\left(3 \, a^{2} c^{2} d^{3} e^{2} - 10 \, a^{3} c d e^{4}\right)} f^{2} g^{10} - {\left(4 \, a^{3} c d^{2} e^{3} - 5 \, a^{4} e^{5}\right)} f g^{11}\right)} x^{5} + 5 \, {\left(2 \, c^{4} d^{4} e f^{6} g^{6} + a^{4} d e^{4} f g^{11} + {\left(c^{4} d^{5} - 8 \, a c^{3} d^{3} e^{2}\right)} f^{5} g^{7} - 4 \, {\left(a c^{3} d^{4} e - 3 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{4} g^{8} + 2 \, {\left(3 \, a^{2} c^{2} d^{3} e^{2} - 4 \, a^{3} c d e^{4}\right)} f^{3} g^{9} - 2 \, {\left(2 \, a^{3} c d^{2} e^{3} - a^{4} e^{5}\right)} f^{2} g^{10}\right)} x^{4} + 10 \, {\left(c^{4} d^{4} e f^{7} g^{5} + a^{4} d e^{4} f^{2} g^{10} + {\left(c^{4} d^{5} - 4 \, a c^{3} d^{3} e^{2}\right)} f^{6} g^{6} - 2 \, {\left(2 \, a c^{3} d^{4} e - 3 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{5} g^{7} + 2 \, {\left(3 \, a^{2} c^{2} d^{3} e^{2} - 2 \, a^{3} c d e^{4}\right)} f^{4} g^{8} - {\left(4 \, a^{3} c d^{2} e^{3} - a^{4} e^{5}\right)} f^{3} g^{9}\right)} x^{3} + 5 \, {\left(c^{4} d^{4} e f^{8} g^{4} + 2 \, a^{4} d e^{4} f^{3} g^{9} + 2 \, {\left(c^{4} d^{5} - 2 \, a c^{3} d^{3} e^{2}\right)} f^{7} g^{5} - 2 \, {\left(4 \, a c^{3} d^{4} e - 3 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{6} g^{6} + 4 \, {\left(3 \, a^{2} c^{2} d^{3} e^{2} - a^{3} c d e^{4}\right)} f^{5} g^{7} - {\left(8 \, a^{3} c d^{2} e^{3} - a^{4} e^{5}\right)} f^{4} g^{8}\right)} x^{2} + {\left(c^{4} d^{4} e f^{9} g^{3} + 5 \, a^{4} d e^{4} f^{4} g^{8} + {\left(5 \, c^{4} d^{5} - 4 \, a c^{3} d^{3} e^{2}\right)} f^{8} g^{4} - 2 \, {\left(10 \, a c^{3} d^{4} e - 3 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{7} g^{5} + 2 \, {\left(15 \, a^{2} c^{2} d^{3} e^{2} - 2 \, a^{3} c d e^{4}\right)} f^{6} g^{6} - {\left(20 \, a^{3} c d^{2} e^{3} - a^{4} e^{5}\right)} f^{5} g^{7}\right)} x\right)}}\right]"," ",0,"[1/1280*(15*(c^5*d^5*e*g^5*x^6 + c^5*d^6*f^5 + (5*c^5*d^5*e*f*g^4 + c^5*d^6*g^5)*x^5 + 5*(2*c^5*d^5*e*f^2*g^3 + c^5*d^6*f*g^4)*x^4 + 10*(c^5*d^5*e*f^3*g^2 + c^5*d^6*f^2*g^3)*x^3 + 5*(c^5*d^5*e*f^4*g + 2*c^5*d^6*f^3*g^2)*x^2 + (c^5*d^5*e*f^5 + 5*c^5*d^6*f^4*g)*x)*sqrt(-c*d*f*g + a*e*g^2)*log(-(c*d*e*g*x^2 - c*d^2*f + 2*a*d*e*g - (c*d*e*f - (c*d^2 + 2*a*e^2)*g)*x + 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-c*d*f*g + a*e*g^2)*sqrt(e*x + d))/(e*g*x^2 + d*f + (e*f + d*g)*x)) - 2*(15*c^5*d^5*f^5*g - 5*a*c^4*d^4*e*f^4*g^2 - 258*a^2*c^3*d^3*e^2*f^3*g^3 + 584*a^3*c^2*d^2*e^3*f^2*g^4 - 464*a^4*c*d*e^4*f*g^5 + 128*a^5*e^5*g^6 - 15*(c^5*d^5*f*g^5 - a*c^4*d^4*e*g^6)*x^4 - 10*(7*c^5*d^5*f^2*g^4 - 8*a*c^4*d^4*e*f*g^5 + a^2*c^3*d^3*e^2*g^6)*x^3 - 2*(64*c^5*d^5*f^3*g^3 - 87*a*c^4*d^4*e*f^2*g^4 + 27*a^2*c^3*d^3*e^2*f*g^5 - 4*a^3*c^2*d^2*e^3*g^6)*x^2 + 2*(35*c^5*d^5*f^4*g^2 - 268*a*c^4*d^4*e*f^3*g^3 + 489*a^2*c^3*d^3*e^2*f^2*g^4 - 344*a^3*c^2*d^2*e^3*f*g^5 + 88*a^4*c*d*e^4*g^6)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c^4*d^5*f^9*g^3 - 4*a*c^3*d^4*e*f^8*g^4 + 6*a^2*c^2*d^3*e^2*f^7*g^5 - 4*a^3*c*d^2*e^3*f^6*g^6 + a^4*d*e^4*f^5*g^7 + (c^4*d^4*e*f^4*g^8 - 4*a*c^3*d^3*e^2*f^3*g^9 + 6*a^2*c^2*d^2*e^3*f^2*g^10 - 4*a^3*c*d*e^4*f*g^11 + a^4*e^5*g^12)*x^6 + (5*c^4*d^4*e*f^5*g^7 + a^4*d*e^4*g^12 + (c^4*d^5 - 20*a*c^3*d^3*e^2)*f^4*g^8 - 2*(2*a*c^3*d^4*e - 15*a^2*c^2*d^2*e^3)*f^3*g^9 + 2*(3*a^2*c^2*d^3*e^2 - 10*a^3*c*d*e^4)*f^2*g^10 - (4*a^3*c*d^2*e^3 - 5*a^4*e^5)*f*g^11)*x^5 + 5*(2*c^4*d^4*e*f^6*g^6 + a^4*d*e^4*f*g^11 + (c^4*d^5 - 8*a*c^3*d^3*e^2)*f^5*g^7 - 4*(a*c^3*d^4*e - 3*a^2*c^2*d^2*e^3)*f^4*g^8 + 2*(3*a^2*c^2*d^3*e^2 - 4*a^3*c*d*e^4)*f^3*g^9 - 2*(2*a^3*c*d^2*e^3 - a^4*e^5)*f^2*g^10)*x^4 + 10*(c^4*d^4*e*f^7*g^5 + a^4*d*e^4*f^2*g^10 + (c^4*d^5 - 4*a*c^3*d^3*e^2)*f^6*g^6 - 2*(2*a*c^3*d^4*e - 3*a^2*c^2*d^2*e^3)*f^5*g^7 + 2*(3*a^2*c^2*d^3*e^2 - 2*a^3*c*d*e^4)*f^4*g^8 - (4*a^3*c*d^2*e^3 - a^4*e^5)*f^3*g^9)*x^3 + 5*(c^4*d^4*e*f^8*g^4 + 2*a^4*d*e^4*f^3*g^9 + 2*(c^4*d^5 - 2*a*c^3*d^3*e^2)*f^7*g^5 - 2*(4*a*c^3*d^4*e - 3*a^2*c^2*d^2*e^3)*f^6*g^6 + 4*(3*a^2*c^2*d^3*e^2 - a^3*c*d*e^4)*f^5*g^7 - (8*a^3*c*d^2*e^3 - a^4*e^5)*f^4*g^8)*x^2 + (c^4*d^4*e*f^9*g^3 + 5*a^4*d*e^4*f^4*g^8 + (5*c^4*d^5 - 4*a*c^3*d^3*e^2)*f^8*g^4 - 2*(10*a*c^3*d^4*e - 3*a^2*c^2*d^2*e^3)*f^7*g^5 + 2*(15*a^2*c^2*d^3*e^2 - 2*a^3*c*d*e^4)*f^6*g^6 - (20*a^3*c*d^2*e^3 - a^4*e^5)*f^5*g^7)*x), -1/640*(15*(c^5*d^5*e*g^5*x^6 + c^5*d^6*f^5 + (5*c^5*d^5*e*f*g^4 + c^5*d^6*g^5)*x^5 + 5*(2*c^5*d^5*e*f^2*g^3 + c^5*d^6*f*g^4)*x^4 + 10*(c^5*d^5*e*f^3*g^2 + c^5*d^6*f^2*g^3)*x^3 + 5*(c^5*d^5*e*f^4*g + 2*c^5*d^6*f^3*g^2)*x^2 + (c^5*d^5*e*f^5 + 5*c^5*d^6*f^4*g)*x)*sqrt(c*d*f*g - a*e*g^2)*arctan(sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(c*d*f*g - a*e*g^2)*sqrt(e*x + d)/(c*d*e*g*x^2 + a*d*e*g + (c*d^2 + a*e^2)*g*x)) + (15*c^5*d^5*f^5*g - 5*a*c^4*d^4*e*f^4*g^2 - 258*a^2*c^3*d^3*e^2*f^3*g^3 + 584*a^3*c^2*d^2*e^3*f^2*g^4 - 464*a^4*c*d*e^4*f*g^5 + 128*a^5*e^5*g^6 - 15*(c^5*d^5*f*g^5 - a*c^4*d^4*e*g^6)*x^4 - 10*(7*c^5*d^5*f^2*g^4 - 8*a*c^4*d^4*e*f*g^5 + a^2*c^3*d^3*e^2*g^6)*x^3 - 2*(64*c^5*d^5*f^3*g^3 - 87*a*c^4*d^4*e*f^2*g^4 + 27*a^2*c^3*d^3*e^2*f*g^5 - 4*a^3*c^2*d^2*e^3*g^6)*x^2 + 2*(35*c^5*d^5*f^4*g^2 - 268*a*c^4*d^4*e*f^3*g^3 + 489*a^2*c^3*d^3*e^2*f^2*g^4 - 344*a^3*c^2*d^2*e^3*f*g^5 + 88*a^4*c*d*e^4*g^6)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c^4*d^5*f^9*g^3 - 4*a*c^3*d^4*e*f^8*g^4 + 6*a^2*c^2*d^3*e^2*f^7*g^5 - 4*a^3*c*d^2*e^3*f^6*g^6 + a^4*d*e^4*f^5*g^7 + (c^4*d^4*e*f^4*g^8 - 4*a*c^3*d^3*e^2*f^3*g^9 + 6*a^2*c^2*d^2*e^3*f^2*g^10 - 4*a^3*c*d*e^4*f*g^11 + a^4*e^5*g^12)*x^6 + (5*c^4*d^4*e*f^5*g^7 + a^4*d*e^4*g^12 + (c^4*d^5 - 20*a*c^3*d^3*e^2)*f^4*g^8 - 2*(2*a*c^3*d^4*e - 15*a^2*c^2*d^2*e^3)*f^3*g^9 + 2*(3*a^2*c^2*d^3*e^2 - 10*a^3*c*d*e^4)*f^2*g^10 - (4*a^3*c*d^2*e^3 - 5*a^4*e^5)*f*g^11)*x^5 + 5*(2*c^4*d^4*e*f^6*g^6 + a^4*d*e^4*f*g^11 + (c^4*d^5 - 8*a*c^3*d^3*e^2)*f^5*g^7 - 4*(a*c^3*d^4*e - 3*a^2*c^2*d^2*e^3)*f^4*g^8 + 2*(3*a^2*c^2*d^3*e^2 - 4*a^3*c*d*e^4)*f^3*g^9 - 2*(2*a^3*c*d^2*e^3 - a^4*e^5)*f^2*g^10)*x^4 + 10*(c^4*d^4*e*f^7*g^5 + a^4*d*e^4*f^2*g^10 + (c^4*d^5 - 4*a*c^3*d^3*e^2)*f^6*g^6 - 2*(2*a*c^3*d^4*e - 3*a^2*c^2*d^2*e^3)*f^5*g^7 + 2*(3*a^2*c^2*d^3*e^2 - 2*a^3*c*d*e^4)*f^4*g^8 - (4*a^3*c*d^2*e^3 - a^4*e^5)*f^3*g^9)*x^3 + 5*(c^4*d^4*e*f^8*g^4 + 2*a^4*d*e^4*f^3*g^9 + 2*(c^4*d^5 - 2*a*c^3*d^3*e^2)*f^7*g^5 - 2*(4*a*c^3*d^4*e - 3*a^2*c^2*d^2*e^3)*f^6*g^6 + 4*(3*a^2*c^2*d^3*e^2 - a^3*c*d*e^4)*f^5*g^7 - (8*a^3*c*d^2*e^3 - a^4*e^5)*f^4*g^8)*x^2 + (c^4*d^4*e*f^9*g^3 + 5*a^4*d*e^4*f^4*g^8 + (5*c^4*d^5 - 4*a*c^3*d^3*e^2)*f^8*g^4 - 2*(10*a*c^3*d^4*e - 3*a^2*c^2*d^2*e^3)*f^7*g^5 + 2*(15*a^2*c^2*d^3*e^2 - 2*a^3*c*d*e^4)*f^6*g^6 - (20*a^3*c*d^2*e^3 - a^4*e^5)*f^5*g^7)*x)]","B",0
700,1,567,0,0.418583," ","integrate((g*x+f)^4*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3003 \, c^{7} d^{7} g^{4} x^{7} + 6435 \, a^{3} c^{4} d^{4} e^{3} f^{4} - 5720 \, a^{4} c^{3} d^{3} e^{4} f^{3} g + 3120 \, a^{5} c^{2} d^{2} e^{5} f^{2} g^{2} - 960 \, a^{6} c d e^{6} f g^{3} + 128 \, a^{7} e^{7} g^{4} + 231 \, {\left(60 \, c^{7} d^{7} f g^{3} + 31 \, a c^{6} d^{6} e g^{4}\right)} x^{6} + 63 \, {\left(390 \, c^{7} d^{7} f^{2} g^{2} + 540 \, a c^{6} d^{6} e f g^{3} + 71 \, a^{2} c^{5} d^{5} e^{2} g^{4}\right)} x^{5} + 35 \, {\left(572 \, c^{7} d^{7} f^{3} g + 1794 \, a c^{6} d^{6} e f^{2} g^{2} + 636 \, a^{2} c^{5} d^{5} e^{2} f g^{3} + a^{3} c^{4} d^{4} e^{3} g^{4}\right)} x^{4} + 5 \, {\left(1287 \, c^{7} d^{7} f^{4} + 10868 \, a c^{6} d^{6} e f^{3} g + 8814 \, a^{2} c^{5} d^{5} e^{2} f^{2} g^{2} + 60 \, a^{3} c^{4} d^{4} e^{3} f g^{3} - 8 \, a^{4} c^{3} d^{3} e^{4} g^{4}\right)} x^{3} + 3 \, {\left(6435 \, a c^{6} d^{6} e f^{4} + 14300 \, a^{2} c^{5} d^{5} e^{2} f^{3} g + 390 \, a^{3} c^{4} d^{4} e^{3} f^{2} g^{2} - 120 \, a^{4} c^{3} d^{3} e^{4} f g^{3} + 16 \, a^{5} c^{2} d^{2} e^{5} g^{4}\right)} x^{2} + {\left(19305 \, a^{2} c^{5} d^{5} e^{2} f^{4} + 2860 \, a^{3} c^{4} d^{4} e^{3} f^{3} g - 1560 \, a^{4} c^{3} d^{3} e^{4} f^{2} g^{2} + 480 \, a^{5} c^{2} d^{2} e^{5} f g^{3} - 64 \, a^{6} c d e^{6} g^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{45045 \, {\left(c^{5} d^{5} e x + c^{5} d^{6}\right)}}"," ",0,"2/45045*(3003*c^7*d^7*g^4*x^7 + 6435*a^3*c^4*d^4*e^3*f^4 - 5720*a^4*c^3*d^3*e^4*f^3*g + 3120*a^5*c^2*d^2*e^5*f^2*g^2 - 960*a^6*c*d*e^6*f*g^3 + 128*a^7*e^7*g^4 + 231*(60*c^7*d^7*f*g^3 + 31*a*c^6*d^6*e*g^4)*x^6 + 63*(390*c^7*d^7*f^2*g^2 + 540*a*c^6*d^6*e*f*g^3 + 71*a^2*c^5*d^5*e^2*g^4)*x^5 + 35*(572*c^7*d^7*f^3*g + 1794*a*c^6*d^6*e*f^2*g^2 + 636*a^2*c^5*d^5*e^2*f*g^3 + a^3*c^4*d^4*e^3*g^4)*x^4 + 5*(1287*c^7*d^7*f^4 + 10868*a*c^6*d^6*e*f^3*g + 8814*a^2*c^5*d^5*e^2*f^2*g^2 + 60*a^3*c^4*d^4*e^3*f*g^3 - 8*a^4*c^3*d^3*e^4*g^4)*x^3 + 3*(6435*a*c^6*d^6*e*f^4 + 14300*a^2*c^5*d^5*e^2*f^3*g + 390*a^3*c^4*d^4*e^3*f^2*g^2 - 120*a^4*c^3*d^3*e^4*f*g^3 + 16*a^5*c^2*d^2*e^5*g^4)*x^2 + (19305*a^2*c^5*d^5*e^2*f^4 + 2860*a^3*c^4*d^4*e^3*f^3*g - 1560*a^4*c^3*d^3*e^4*f^2*g^2 + 480*a^5*c^2*d^2*e^5*f*g^3 - 64*a^6*c*d*e^6*g^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)/(c^5*d^5*e*x + c^5*d^6)","A",0
701,1,416,0,0.403748," ","integrate((g*x+f)^3*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(231 \, c^{6} d^{6} g^{3} x^{6} + 429 \, a^{3} c^{3} d^{3} e^{3} f^{3} - 286 \, a^{4} c^{2} d^{2} e^{4} f^{2} g + 104 \, a^{5} c d e^{5} f g^{2} - 16 \, a^{6} e^{6} g^{3} + 63 \, {\left(13 \, c^{6} d^{6} f g^{2} + 9 \, a c^{5} d^{5} e g^{3}\right)} x^{5} + 7 \, {\left(143 \, c^{6} d^{6} f^{2} g + 299 \, a c^{5} d^{5} e f g^{2} + 53 \, a^{2} c^{4} d^{4} e^{2} g^{3}\right)} x^{4} + {\left(429 \, c^{6} d^{6} f^{3} + 2717 \, a c^{5} d^{5} e f^{2} g + 1469 \, a^{2} c^{4} d^{4} e^{2} f g^{2} + 5 \, a^{3} c^{3} d^{3} e^{3} g^{3}\right)} x^{3} + 3 \, {\left(429 \, a c^{5} d^{5} e f^{3} + 715 \, a^{2} c^{4} d^{4} e^{2} f^{2} g + 13 \, a^{3} c^{3} d^{3} e^{3} f g^{2} - 2 \, a^{4} c^{2} d^{2} e^{4} g^{3}\right)} x^{2} + {\left(1287 \, a^{2} c^{4} d^{4} e^{2} f^{3} + 143 \, a^{3} c^{3} d^{3} e^{3} f^{2} g - 52 \, a^{4} c^{2} d^{2} e^{4} f g^{2} + 8 \, a^{5} c d e^{5} g^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{3003 \, {\left(c^{4} d^{4} e x + c^{4} d^{5}\right)}}"," ",0,"2/3003*(231*c^6*d^6*g^3*x^6 + 429*a^3*c^3*d^3*e^3*f^3 - 286*a^4*c^2*d^2*e^4*f^2*g + 104*a^5*c*d*e^5*f*g^2 - 16*a^6*e^6*g^3 + 63*(13*c^6*d^6*f*g^2 + 9*a*c^5*d^5*e*g^3)*x^5 + 7*(143*c^6*d^6*f^2*g + 299*a*c^5*d^5*e*f*g^2 + 53*a^2*c^4*d^4*e^2*g^3)*x^4 + (429*c^6*d^6*f^3 + 2717*a*c^5*d^5*e*f^2*g + 1469*a^2*c^4*d^4*e^2*f*g^2 + 5*a^3*c^3*d^3*e^3*g^3)*x^3 + 3*(429*a*c^5*d^5*e*f^3 + 715*a^2*c^4*d^4*e^2*f^2*g + 13*a^3*c^3*d^3*e^3*f*g^2 - 2*a^4*c^2*d^2*e^4*g^3)*x^2 + (1287*a^2*c^4*d^4*e^2*f^3 + 143*a^3*c^3*d^3*e^3*f^2*g - 52*a^4*c^2*d^2*e^4*f*g^2 + 8*a^5*c*d*e^5*g^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)/(c^4*d^4*e*x + c^4*d^5)","A",0
702,1,284,0,0.417791," ","integrate((g*x+f)^2*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(63 \, c^{5} d^{5} g^{2} x^{5} + 99 \, a^{3} c^{2} d^{2} e^{3} f^{2} - 44 \, a^{4} c d e^{4} f g + 8 \, a^{5} e^{5} g^{2} + 7 \, {\left(22 \, c^{5} d^{5} f g + 23 \, a c^{4} d^{4} e g^{2}\right)} x^{4} + {\left(99 \, c^{5} d^{5} f^{2} + 418 \, a c^{4} d^{4} e f g + 113 \, a^{2} c^{3} d^{3} e^{2} g^{2}\right)} x^{3} + 3 \, {\left(99 \, a c^{4} d^{4} e f^{2} + 110 \, a^{2} c^{3} d^{3} e^{2} f g + a^{3} c^{2} d^{2} e^{3} g^{2}\right)} x^{2} + {\left(297 \, a^{2} c^{3} d^{3} e^{2} f^{2} + 22 \, a^{3} c^{2} d^{2} e^{3} f g - 4 \, a^{4} c d e^{4} g^{2}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{693 \, {\left(c^{3} d^{3} e x + c^{3} d^{4}\right)}}"," ",0,"2/693*(63*c^5*d^5*g^2*x^5 + 99*a^3*c^2*d^2*e^3*f^2 - 44*a^4*c*d*e^4*f*g + 8*a^5*e^5*g^2 + 7*(22*c^5*d^5*f*g + 23*a*c^4*d^4*e*g^2)*x^4 + (99*c^5*d^5*f^2 + 418*a*c^4*d^4*e*f*g + 113*a^2*c^3*d^3*e^2*g^2)*x^3 + 3*(99*a*c^4*d^4*e*f^2 + 110*a^2*c^3*d^3*e^2*f*g + a^3*c^2*d^2*e^3*g^2)*x^2 + (297*a^2*c^3*d^3*e^2*f^2 + 22*a^3*c^2*d^2*e^3*f*g - 4*a^4*c*d*e^4*g^2)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)/(c^3*d^3*e*x + c^3*d^4)","A",0
703,1,173,0,0.422461," ","integrate((g*x+f)*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(7 \, c^{4} d^{4} g x^{4} + 9 \, a^{3} c d e^{3} f - 2 \, a^{4} e^{4} g + {\left(9 \, c^{4} d^{4} f + 19 \, a c^{3} d^{3} e g\right)} x^{3} + 3 \, {\left(9 \, a c^{3} d^{3} e f + 5 \, a^{2} c^{2} d^{2} e^{2} g\right)} x^{2} + {\left(27 \, a^{2} c^{2} d^{2} e^{2} f + a^{3} c d e^{3} g\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{63 \, {\left(c^{2} d^{2} e x + c^{2} d^{3}\right)}}"," ",0,"2/63*(7*c^4*d^4*g*x^4 + 9*a^3*c*d*e^3*f - 2*a^4*e^4*g + (9*c^4*d^4*f + 19*a*c^3*d^3*e*g)*x^3 + 3*(9*a*c^3*d^3*e*f + 5*a^2*c^2*d^2*e^2*g)*x^2 + (27*a^2*c^2*d^2*e^2*f + a^3*c*d*e^3*g)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)/(c^2*d^2*e*x + c^2*d^3)","A",0
704,1,91,0,0.406442," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(c^{3} d^{3} x^{3} + 3 \, a c^{2} d^{2} e x^{2} + 3 \, a^{2} c d e^{2} x + a^{3} e^{3}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{7 \, {\left(c d e x + c d^{2}\right)}}"," ",0,"2/7*(c^3*d^3*x^3 + 3*a*c^2*d^2*e*x^2 + 3*a^2*c*d*e^2*x + a^3*e^3)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)/(c*d*e*x + c*d^2)","B",0
705,1,587,0,0.443900," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^(5/2)/(g*x+f),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(c^{2} d^{3} f^{2} - 2 \, a c d^{2} e f g + a^{2} d e^{2} g^{2} + {\left(c^{2} d^{2} e f^{2} - 2 \, a c d e^{2} f g + a^{2} e^{3} g^{2}\right)} x\right)} \sqrt{-\frac{c d f - a e g}{g}} \log\left(-\frac{c d e g x^{2} - c d^{2} f + 2 \, a d e g - 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} g \sqrt{-\frac{c d f - a e g}{g}} - {\left(c d e f - {\left(c d^{2} + 2 \, a e^{2}\right)} g\right)} x}{e g x^{2} + d f + {\left(e f + d g\right)} x}\right) + 2 \, {\left(3 \, c^{2} d^{2} g^{2} x^{2} + 15 \, c^{2} d^{2} f^{2} - 35 \, a c d e f g + 23 \, a^{2} e^{2} g^{2} - {\left(5 \, c^{2} d^{2} f g - 11 \, a c d e g^{2}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{15 \, {\left(e g^{3} x + d g^{3}\right)}}, \frac{2 \, {\left(15 \, {\left(c^{2} d^{3} f^{2} - 2 \, a c d^{2} e f g + a^{2} d e^{2} g^{2} + {\left(c^{2} d^{2} e f^{2} - 2 \, a c d e^{2} f g + a^{2} e^{3} g^{2}\right)} x\right)} \sqrt{\frac{c d f - a e g}{g}} \arctan\left(\frac{\sqrt{e x + d} \sqrt{\frac{c d f - a e g}{g}}}{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}\right) + {\left(3 \, c^{2} d^{2} g^{2} x^{2} + 15 \, c^{2} d^{2} f^{2} - 35 \, a c d e f g + 23 \, a^{2} e^{2} g^{2} - {\left(5 \, c^{2} d^{2} f g - 11 \, a c d e g^{2}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}\right)}}{15 \, {\left(e g^{3} x + d g^{3}\right)}}\right]"," ",0,"[1/15*(15*(c^2*d^3*f^2 - 2*a*c*d^2*e*f*g + a^2*d*e^2*g^2 + (c^2*d^2*e*f^2 - 2*a*c*d*e^2*f*g + a^2*e^3*g^2)*x)*sqrt(-(c*d*f - a*e*g)/g)*log(-(c*d*e*g*x^2 - c*d^2*f + 2*a*d*e*g - 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*g*sqrt(-(c*d*f - a*e*g)/g) - (c*d*e*f - (c*d^2 + 2*a*e^2)*g)*x)/(e*g*x^2 + d*f + (e*f + d*g)*x)) + 2*(3*c^2*d^2*g^2*x^2 + 15*c^2*d^2*f^2 - 35*a*c*d*e*f*g + 23*a^2*e^2*g^2 - (5*c^2*d^2*f*g - 11*a*c*d*e*g^2)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(e*g^3*x + d*g^3), 2/15*(15*(c^2*d^3*f^2 - 2*a*c*d^2*e*f*g + a^2*d*e^2*g^2 + (c^2*d^2*e*f^2 - 2*a*c*d*e^2*f*g + a^2*e^3*g^2)*x)*sqrt((c*d*f - a*e*g)/g)*arctan(sqrt(e*x + d)*sqrt((c*d*f - a*e*g)/g)/sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)) + (3*c^2*d^2*g^2*x^2 + 15*c^2*d^2*f^2 - 35*a*c*d*e*f*g + 23*a^2*e^2*g^2 - (5*c^2*d^2*f*g - 11*a*c*d*e*g^2)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(e*g^3*x + d*g^3)]","A",0
706,1,672,0,0.486380," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^(5/2)/(g*x+f)^2,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(c^{2} d^{3} f^{2} - a c d^{2} e f g + {\left(c^{2} d^{2} e f g - a c d e^{2} g^{2}\right)} x^{2} + {\left(c^{2} d^{2} e f^{2} - a c d^{2} e g^{2} + {\left(c^{2} d^{3} - a c d e^{2}\right)} f g\right)} x\right)} \sqrt{-\frac{c d f - a e g}{g}} \log\left(-\frac{c d e g x^{2} - c d^{2} f + 2 \, a d e g - 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} g \sqrt{-\frac{c d f - a e g}{g}} - {\left(c d e f - {\left(c d^{2} + 2 \, a e^{2}\right)} g\right)} x}{e g x^{2} + d f + {\left(e f + d g\right)} x}\right) - 2 \, {\left(2 \, c^{2} d^{2} g^{2} x^{2} - 15 \, c^{2} d^{2} f^{2} + 20 \, a c d e f g - 3 \, a^{2} e^{2} g^{2} - 2 \, {\left(5 \, c^{2} d^{2} f g - 7 \, a c d e g^{2}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{6 \, {\left(e g^{4} x^{2} + d f g^{3} + {\left(e f g^{3} + d g^{4}\right)} x\right)}}, -\frac{15 \, {\left(c^{2} d^{3} f^{2} - a c d^{2} e f g + {\left(c^{2} d^{2} e f g - a c d e^{2} g^{2}\right)} x^{2} + {\left(c^{2} d^{2} e f^{2} - a c d^{2} e g^{2} + {\left(c^{2} d^{3} - a c d e^{2}\right)} f g\right)} x\right)} \sqrt{\frac{c d f - a e g}{g}} \arctan\left(\frac{\sqrt{e x + d} \sqrt{\frac{c d f - a e g}{g}}}{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}\right) - {\left(2 \, c^{2} d^{2} g^{2} x^{2} - 15 \, c^{2} d^{2} f^{2} + 20 \, a c d e f g - 3 \, a^{2} e^{2} g^{2} - 2 \, {\left(5 \, c^{2} d^{2} f g - 7 \, a c d e g^{2}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{3 \, {\left(e g^{4} x^{2} + d f g^{3} + {\left(e f g^{3} + d g^{4}\right)} x\right)}}\right]"," ",0,"[-1/6*(15*(c^2*d^3*f^2 - a*c*d^2*e*f*g + (c^2*d^2*e*f*g - a*c*d*e^2*g^2)*x^2 + (c^2*d^2*e*f^2 - a*c*d^2*e*g^2 + (c^2*d^3 - a*c*d*e^2)*f*g)*x)*sqrt(-(c*d*f - a*e*g)/g)*log(-(c*d*e*g*x^2 - c*d^2*f + 2*a*d*e*g - 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*g*sqrt(-(c*d*f - a*e*g)/g) - (c*d*e*f - (c*d^2 + 2*a*e^2)*g)*x)/(e*g*x^2 + d*f + (e*f + d*g)*x)) - 2*(2*c^2*d^2*g^2*x^2 - 15*c^2*d^2*f^2 + 20*a*c*d*e*f*g - 3*a^2*e^2*g^2 - 2*(5*c^2*d^2*f*g - 7*a*c*d*e*g^2)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(e*g^4*x^2 + d*f*g^3 + (e*f*g^3 + d*g^4)*x), -1/3*(15*(c^2*d^3*f^2 - a*c*d^2*e*f*g + (c^2*d^2*e*f*g - a*c*d*e^2*g^2)*x^2 + (c^2*d^2*e*f^2 - a*c*d^2*e*g^2 + (c^2*d^3 - a*c*d*e^2)*f*g)*x)*sqrt((c*d*f - a*e*g)/g)*arctan(sqrt(e*x + d)*sqrt((c*d*f - a*e*g)/g)/sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)) - (2*c^2*d^2*g^2*x^2 - 15*c^2*d^2*f^2 + 20*a*c*d*e*f*g - 3*a^2*e^2*g^2 - 2*(5*c^2*d^2*f*g - 7*a*c*d*e*g^2)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(e*g^4*x^2 + d*f*g^3 + (e*f*g^3 + d*g^4)*x)]","A",0
707,1,683,0,0.624196," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^(5/2)/(g*x+f)^3,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(c^{2} d^{2} e g^{2} x^{3} + c^{2} d^{3} f^{2} + {\left(2 \, c^{2} d^{2} e f g + c^{2} d^{3} g^{2}\right)} x^{2} + {\left(c^{2} d^{2} e f^{2} + 2 \, c^{2} d^{3} f g\right)} x\right)} \sqrt{-\frac{c d f - a e g}{g}} \log\left(-\frac{c d e g x^{2} - c d^{2} f + 2 \, a d e g - 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} g \sqrt{-\frac{c d f - a e g}{g}} - {\left(c d e f - {\left(c d^{2} + 2 \, a e^{2}\right)} g\right)} x}{e g x^{2} + d f + {\left(e f + d g\right)} x}\right) + 2 \, {\left(8 \, c^{2} d^{2} g^{2} x^{2} + 15 \, c^{2} d^{2} f^{2} - 5 \, a c d e f g - 2 \, a^{2} e^{2} g^{2} + {\left(25 \, c^{2} d^{2} f g - 9 \, a c d e g^{2}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{8 \, {\left(e g^{5} x^{3} + d f^{2} g^{3} + {\left(2 \, e f g^{4} + d g^{5}\right)} x^{2} + {\left(e f^{2} g^{3} + 2 \, d f g^{4}\right)} x\right)}}, \frac{15 \, {\left(c^{2} d^{2} e g^{2} x^{3} + c^{2} d^{3} f^{2} + {\left(2 \, c^{2} d^{2} e f g + c^{2} d^{3} g^{2}\right)} x^{2} + {\left(c^{2} d^{2} e f^{2} + 2 \, c^{2} d^{3} f g\right)} x\right)} \sqrt{\frac{c d f - a e g}{g}} \arctan\left(\frac{\sqrt{e x + d} \sqrt{\frac{c d f - a e g}{g}}}{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}\right) + {\left(8 \, c^{2} d^{2} g^{2} x^{2} + 15 \, c^{2} d^{2} f^{2} - 5 \, a c d e f g - 2 \, a^{2} e^{2} g^{2} + {\left(25 \, c^{2} d^{2} f g - 9 \, a c d e g^{2}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{4 \, {\left(e g^{5} x^{3} + d f^{2} g^{3} + {\left(2 \, e f g^{4} + d g^{5}\right)} x^{2} + {\left(e f^{2} g^{3} + 2 \, d f g^{4}\right)} x\right)}}\right]"," ",0,"[1/8*(15*(c^2*d^2*e*g^2*x^3 + c^2*d^3*f^2 + (2*c^2*d^2*e*f*g + c^2*d^3*g^2)*x^2 + (c^2*d^2*e*f^2 + 2*c^2*d^3*f*g)*x)*sqrt(-(c*d*f - a*e*g)/g)*log(-(c*d*e*g*x^2 - c*d^2*f + 2*a*d*e*g - 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*g*sqrt(-(c*d*f - a*e*g)/g) - (c*d*e*f - (c*d^2 + 2*a*e^2)*g)*x)/(e*g*x^2 + d*f + (e*f + d*g)*x)) + 2*(8*c^2*d^2*g^2*x^2 + 15*c^2*d^2*f^2 - 5*a*c*d*e*f*g - 2*a^2*e^2*g^2 + (25*c^2*d^2*f*g - 9*a*c*d*e*g^2)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(e*g^5*x^3 + d*f^2*g^3 + (2*e*f*g^4 + d*g^5)*x^2 + (e*f^2*g^3 + 2*d*f*g^4)*x), 1/4*(15*(c^2*d^2*e*g^2*x^3 + c^2*d^3*f^2 + (2*c^2*d^2*e*f*g + c^2*d^3*g^2)*x^2 + (c^2*d^2*e*f^2 + 2*c^2*d^3*f*g)*x)*sqrt((c*d*f - a*e*g)/g)*arctan(sqrt(e*x + d)*sqrt((c*d*f - a*e*g)/g)/sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)) + (8*c^2*d^2*g^2*x^2 + 15*c^2*d^2*f^2 - 5*a*c*d*e*f*g - 2*a^2*e^2*g^2 + (25*c^2*d^2*f*g - 9*a*c*d*e*g^2)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(e*g^5*x^3 + d*f^2*g^3 + (2*e*f*g^4 + d*g^5)*x^2 + (e*f^2*g^3 + 2*d*f*g^4)*x)]","A",0
708,1,1140,0,0.458793," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^(5/2)/(g*x+f)^4,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(c^{3} d^{3} e g^{3} x^{4} + c^{3} d^{4} f^{3} + {\left(3 \, c^{3} d^{3} e f g^{2} + c^{3} d^{4} g^{3}\right)} x^{3} + 3 \, {\left(c^{3} d^{3} e f^{2} g + c^{3} d^{4} f g^{2}\right)} x^{2} + {\left(c^{3} d^{3} e f^{3} + 3 \, c^{3} d^{4} f^{2} g\right)} x\right)} \sqrt{-c d f g + a e g^{2}} \log\left(-\frac{c d e g x^{2} - c d^{2} f + 2 \, a d e g - {\left(c d e f - {\left(c d^{2} + 2 \, a e^{2}\right)} g\right)} x - 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{-c d f g + a e g^{2}} \sqrt{e x + d}}{e g x^{2} + d f + {\left(e f + d g\right)} x}\right) + 2 \, {\left(15 \, c^{3} d^{3} f^{3} g - 5 \, a c^{2} d^{2} e f^{2} g^{2} - 2 \, a^{2} c d e^{2} f g^{3} - 8 \, a^{3} e^{3} g^{4} + 33 \, {\left(c^{3} d^{3} f g^{3} - a c^{2} d^{2} e g^{4}\right)} x^{2} + 2 \, {\left(20 \, c^{3} d^{3} f^{2} g^{2} - 7 \, a c^{2} d^{2} e f g^{3} - 13 \, a^{2} c d e^{2} g^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{48 \, {\left(c d^{2} f^{4} g^{4} - a d e f^{3} g^{5} + {\left(c d e f g^{7} - a e^{2} g^{8}\right)} x^{4} + {\left(3 \, c d e f^{2} g^{6} - a d e g^{8} + {\left(c d^{2} - 3 \, a e^{2}\right)} f g^{7}\right)} x^{3} + 3 \, {\left(c d e f^{3} g^{5} - a d e f g^{7} + {\left(c d^{2} - a e^{2}\right)} f^{2} g^{6}\right)} x^{2} + {\left(c d e f^{4} g^{4} - 3 \, a d e f^{2} g^{6} + {\left(3 \, c d^{2} - a e^{2}\right)} f^{3} g^{5}\right)} x\right)}}, -\frac{15 \, {\left(c^{3} d^{3} e g^{3} x^{4} + c^{3} d^{4} f^{3} + {\left(3 \, c^{3} d^{3} e f g^{2} + c^{3} d^{4} g^{3}\right)} x^{3} + 3 \, {\left(c^{3} d^{3} e f^{2} g + c^{3} d^{4} f g^{2}\right)} x^{2} + {\left(c^{3} d^{3} e f^{3} + 3 \, c^{3} d^{4} f^{2} g\right)} x\right)} \sqrt{c d f g - a e g^{2}} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{c d f g - a e g^{2}} \sqrt{e x + d}}{c d e g x^{2} + a d e g + {\left(c d^{2} + a e^{2}\right)} g x}\right) + {\left(15 \, c^{3} d^{3} f^{3} g - 5 \, a c^{2} d^{2} e f^{2} g^{2} - 2 \, a^{2} c d e^{2} f g^{3} - 8 \, a^{3} e^{3} g^{4} + 33 \, {\left(c^{3} d^{3} f g^{3} - a c^{2} d^{2} e g^{4}\right)} x^{2} + 2 \, {\left(20 \, c^{3} d^{3} f^{2} g^{2} - 7 \, a c^{2} d^{2} e f g^{3} - 13 \, a^{2} c d e^{2} g^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{24 \, {\left(c d^{2} f^{4} g^{4} - a d e f^{3} g^{5} + {\left(c d e f g^{7} - a e^{2} g^{8}\right)} x^{4} + {\left(3 \, c d e f^{2} g^{6} - a d e g^{8} + {\left(c d^{2} - 3 \, a e^{2}\right)} f g^{7}\right)} x^{3} + 3 \, {\left(c d e f^{3} g^{5} - a d e f g^{7} + {\left(c d^{2} - a e^{2}\right)} f^{2} g^{6}\right)} x^{2} + {\left(c d e f^{4} g^{4} - 3 \, a d e f^{2} g^{6} + {\left(3 \, c d^{2} - a e^{2}\right)} f^{3} g^{5}\right)} x\right)}}\right]"," ",0,"[-1/48*(15*(c^3*d^3*e*g^3*x^4 + c^3*d^4*f^3 + (3*c^3*d^3*e*f*g^2 + c^3*d^4*g^3)*x^3 + 3*(c^3*d^3*e*f^2*g + c^3*d^4*f*g^2)*x^2 + (c^3*d^3*e*f^3 + 3*c^3*d^4*f^2*g)*x)*sqrt(-c*d*f*g + a*e*g^2)*log(-(c*d*e*g*x^2 - c*d^2*f + 2*a*d*e*g - (c*d*e*f - (c*d^2 + 2*a*e^2)*g)*x - 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-c*d*f*g + a*e*g^2)*sqrt(e*x + d))/(e*g*x^2 + d*f + (e*f + d*g)*x)) + 2*(15*c^3*d^3*f^3*g - 5*a*c^2*d^2*e*f^2*g^2 - 2*a^2*c*d*e^2*f*g^3 - 8*a^3*e^3*g^4 + 33*(c^3*d^3*f*g^3 - a*c^2*d^2*e*g^4)*x^2 + 2*(20*c^3*d^3*f^2*g^2 - 7*a*c^2*d^2*e*f*g^3 - 13*a^2*c*d*e^2*g^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c*d^2*f^4*g^4 - a*d*e*f^3*g^5 + (c*d*e*f*g^7 - a*e^2*g^8)*x^4 + (3*c*d*e*f^2*g^6 - a*d*e*g^8 + (c*d^2 - 3*a*e^2)*f*g^7)*x^3 + 3*(c*d*e*f^3*g^5 - a*d*e*f*g^7 + (c*d^2 - a*e^2)*f^2*g^6)*x^2 + (c*d*e*f^4*g^4 - 3*a*d*e*f^2*g^6 + (3*c*d^2 - a*e^2)*f^3*g^5)*x), -1/24*(15*(c^3*d^3*e*g^3*x^4 + c^3*d^4*f^3 + (3*c^3*d^3*e*f*g^2 + c^3*d^4*g^3)*x^3 + 3*(c^3*d^3*e*f^2*g + c^3*d^4*f*g^2)*x^2 + (c^3*d^3*e*f^3 + 3*c^3*d^4*f^2*g)*x)*sqrt(c*d*f*g - a*e*g^2)*arctan(sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(c*d*f*g - a*e*g^2)*sqrt(e*x + d)/(c*d*e*g*x^2 + a*d*e*g + (c*d^2 + a*e^2)*g*x)) + (15*c^3*d^3*f^3*g - 5*a*c^2*d^2*e*f^2*g^2 - 2*a^2*c*d*e^2*f*g^3 - 8*a^3*e^3*g^4 + 33*(c^3*d^3*f*g^3 - a*c^2*d^2*e*g^4)*x^2 + 2*(20*c^3*d^3*f^2*g^2 - 7*a*c^2*d^2*e*f*g^3 - 13*a^2*c*d*e^2*g^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c*d^2*f^4*g^4 - a*d*e*f^3*g^5 + (c*d*e*f*g^7 - a*e^2*g^8)*x^4 + (3*c*d*e*f^2*g^6 - a*d*e*g^8 + (c*d^2 - 3*a*e^2)*f*g^7)*x^3 + 3*(c*d*e*f^3*g^5 - a*d*e*f*g^7 + (c*d^2 - a*e^2)*f^2*g^6)*x^2 + (c*d*e*f^4*g^4 - 3*a*d*e*f^2*g^6 + (3*c*d^2 - a*e^2)*f^3*g^5)*x)]","B",0
709,1,1862,0,0.476676," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^(5/2)/(g*x+f)^5,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(c^{4} d^{4} e g^{4} x^{5} + c^{4} d^{5} f^{4} + {\left(4 \, c^{4} d^{4} e f g^{3} + c^{4} d^{5} g^{4}\right)} x^{4} + 2 \, {\left(3 \, c^{4} d^{4} e f^{2} g^{2} + 2 \, c^{4} d^{5} f g^{3}\right)} x^{3} + 2 \, {\left(2 \, c^{4} d^{4} e f^{3} g + 3 \, c^{4} d^{5} f^{2} g^{2}\right)} x^{2} + {\left(c^{4} d^{4} e f^{4} + 4 \, c^{4} d^{5} f^{3} g\right)} x\right)} \sqrt{-c d f g + a e g^{2}} \log\left(-\frac{c d e g x^{2} - c d^{2} f + 2 \, a d e g - {\left(c d e f - {\left(c d^{2} + 2 \, a e^{2}\right)} g\right)} x + 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{-c d f g + a e g^{2}} \sqrt{e x + d}}{e g x^{2} + d f + {\left(e f + d g\right)} x}\right) - 2 \, {\left(15 \, c^{4} d^{4} f^{4} g - 5 \, a c^{3} d^{3} e f^{3} g^{2} - 2 \, a^{2} c^{2} d^{2} e^{2} f^{2} g^{3} - 56 \, a^{3} c d e^{3} f g^{4} + 48 \, a^{4} e^{4} g^{5} - 15 \, {\left(c^{4} d^{4} f g^{4} - a c^{3} d^{3} e g^{5}\right)} x^{3} + {\left(73 \, c^{4} d^{4} f^{2} g^{3} - 191 \, a c^{3} d^{3} e f g^{4} + 118 \, a^{2} c^{2} d^{2} e^{2} g^{5}\right)} x^{2} + {\left(55 \, c^{4} d^{4} f^{3} g^{2} - 19 \, a c^{3} d^{3} e f^{2} g^{3} - 172 \, a^{2} c^{2} d^{2} e^{2} f g^{4} + 136 \, a^{3} c d e^{3} g^{5}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{384 \, {\left(c^{2} d^{3} f^{6} g^{4} - 2 \, a c d^{2} e f^{5} g^{5} + a^{2} d e^{2} f^{4} g^{6} + {\left(c^{2} d^{2} e f^{2} g^{8} - 2 \, a c d e^{2} f g^{9} + a^{2} e^{3} g^{10}\right)} x^{5} + {\left(4 \, c^{2} d^{2} e f^{3} g^{7} + a^{2} d e^{2} g^{10} + {\left(c^{2} d^{3} - 8 \, a c d e^{2}\right)} f^{2} g^{8} - 2 \, {\left(a c d^{2} e - 2 \, a^{2} e^{3}\right)} f g^{9}\right)} x^{4} + 2 \, {\left(3 \, c^{2} d^{2} e f^{4} g^{6} + 2 \, a^{2} d e^{2} f g^{9} + 2 \, {\left(c^{2} d^{3} - 3 \, a c d e^{2}\right)} f^{3} g^{7} - {\left(4 \, a c d^{2} e - 3 \, a^{2} e^{3}\right)} f^{2} g^{8}\right)} x^{3} + 2 \, {\left(2 \, c^{2} d^{2} e f^{5} g^{5} + 3 \, a^{2} d e^{2} f^{2} g^{8} + {\left(3 \, c^{2} d^{3} - 4 \, a c d e^{2}\right)} f^{4} g^{6} - 2 \, {\left(3 \, a c d^{2} e - a^{2} e^{3}\right)} f^{3} g^{7}\right)} x^{2} + {\left(c^{2} d^{2} e f^{6} g^{4} + 4 \, a^{2} d e^{2} f^{3} g^{7} + 2 \, {\left(2 \, c^{2} d^{3} - a c d e^{2}\right)} f^{5} g^{5} - {\left(8 \, a c d^{2} e - a^{2} e^{3}\right)} f^{4} g^{6}\right)} x\right)}}, -\frac{15 \, {\left(c^{4} d^{4} e g^{4} x^{5} + c^{4} d^{5} f^{4} + {\left(4 \, c^{4} d^{4} e f g^{3} + c^{4} d^{5} g^{4}\right)} x^{4} + 2 \, {\left(3 \, c^{4} d^{4} e f^{2} g^{2} + 2 \, c^{4} d^{5} f g^{3}\right)} x^{3} + 2 \, {\left(2 \, c^{4} d^{4} e f^{3} g + 3 \, c^{4} d^{5} f^{2} g^{2}\right)} x^{2} + {\left(c^{4} d^{4} e f^{4} + 4 \, c^{4} d^{5} f^{3} g\right)} x\right)} \sqrt{c d f g - a e g^{2}} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{c d f g - a e g^{2}} \sqrt{e x + d}}{c d e g x^{2} + a d e g + {\left(c d^{2} + a e^{2}\right)} g x}\right) + {\left(15 \, c^{4} d^{4} f^{4} g - 5 \, a c^{3} d^{3} e f^{3} g^{2} - 2 \, a^{2} c^{2} d^{2} e^{2} f^{2} g^{3} - 56 \, a^{3} c d e^{3} f g^{4} + 48 \, a^{4} e^{4} g^{5} - 15 \, {\left(c^{4} d^{4} f g^{4} - a c^{3} d^{3} e g^{5}\right)} x^{3} + {\left(73 \, c^{4} d^{4} f^{2} g^{3} - 191 \, a c^{3} d^{3} e f g^{4} + 118 \, a^{2} c^{2} d^{2} e^{2} g^{5}\right)} x^{2} + {\left(55 \, c^{4} d^{4} f^{3} g^{2} - 19 \, a c^{3} d^{3} e f^{2} g^{3} - 172 \, a^{2} c^{2} d^{2} e^{2} f g^{4} + 136 \, a^{3} c d e^{3} g^{5}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{192 \, {\left(c^{2} d^{3} f^{6} g^{4} - 2 \, a c d^{2} e f^{5} g^{5} + a^{2} d e^{2} f^{4} g^{6} + {\left(c^{2} d^{2} e f^{2} g^{8} - 2 \, a c d e^{2} f g^{9} + a^{2} e^{3} g^{10}\right)} x^{5} + {\left(4 \, c^{2} d^{2} e f^{3} g^{7} + a^{2} d e^{2} g^{10} + {\left(c^{2} d^{3} - 8 \, a c d e^{2}\right)} f^{2} g^{8} - 2 \, {\left(a c d^{2} e - 2 \, a^{2} e^{3}\right)} f g^{9}\right)} x^{4} + 2 \, {\left(3 \, c^{2} d^{2} e f^{4} g^{6} + 2 \, a^{2} d e^{2} f g^{9} + 2 \, {\left(c^{2} d^{3} - 3 \, a c d e^{2}\right)} f^{3} g^{7} - {\left(4 \, a c d^{2} e - 3 \, a^{2} e^{3}\right)} f^{2} g^{8}\right)} x^{3} + 2 \, {\left(2 \, c^{2} d^{2} e f^{5} g^{5} + 3 \, a^{2} d e^{2} f^{2} g^{8} + {\left(3 \, c^{2} d^{3} - 4 \, a c d e^{2}\right)} f^{4} g^{6} - 2 \, {\left(3 \, a c d^{2} e - a^{2} e^{3}\right)} f^{3} g^{7}\right)} x^{2} + {\left(c^{2} d^{2} e f^{6} g^{4} + 4 \, a^{2} d e^{2} f^{3} g^{7} + 2 \, {\left(2 \, c^{2} d^{3} - a c d e^{2}\right)} f^{5} g^{5} - {\left(8 \, a c d^{2} e - a^{2} e^{3}\right)} f^{4} g^{6}\right)} x\right)}}\right]"," ",0,"[1/384*(15*(c^4*d^4*e*g^4*x^5 + c^4*d^5*f^4 + (4*c^4*d^4*e*f*g^3 + c^4*d^5*g^4)*x^4 + 2*(3*c^4*d^4*e*f^2*g^2 + 2*c^4*d^5*f*g^3)*x^3 + 2*(2*c^4*d^4*e*f^3*g + 3*c^4*d^5*f^2*g^2)*x^2 + (c^4*d^4*e*f^4 + 4*c^4*d^5*f^3*g)*x)*sqrt(-c*d*f*g + a*e*g^2)*log(-(c*d*e*g*x^2 - c*d^2*f + 2*a*d*e*g - (c*d*e*f - (c*d^2 + 2*a*e^2)*g)*x + 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-c*d*f*g + a*e*g^2)*sqrt(e*x + d))/(e*g*x^2 + d*f + (e*f + d*g)*x)) - 2*(15*c^4*d^4*f^4*g - 5*a*c^3*d^3*e*f^3*g^2 - 2*a^2*c^2*d^2*e^2*f^2*g^3 - 56*a^3*c*d*e^3*f*g^4 + 48*a^4*e^4*g^5 - 15*(c^4*d^4*f*g^4 - a*c^3*d^3*e*g^5)*x^3 + (73*c^4*d^4*f^2*g^3 - 191*a*c^3*d^3*e*f*g^4 + 118*a^2*c^2*d^2*e^2*g^5)*x^2 + (55*c^4*d^4*f^3*g^2 - 19*a*c^3*d^3*e*f^2*g^3 - 172*a^2*c^2*d^2*e^2*f*g^4 + 136*a^3*c*d*e^3*g^5)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c^2*d^3*f^6*g^4 - 2*a*c*d^2*e*f^5*g^5 + a^2*d*e^2*f^4*g^6 + (c^2*d^2*e*f^2*g^8 - 2*a*c*d*e^2*f*g^9 + a^2*e^3*g^10)*x^5 + (4*c^2*d^2*e*f^3*g^7 + a^2*d*e^2*g^10 + (c^2*d^3 - 8*a*c*d*e^2)*f^2*g^8 - 2*(a*c*d^2*e - 2*a^2*e^3)*f*g^9)*x^4 + 2*(3*c^2*d^2*e*f^4*g^6 + 2*a^2*d*e^2*f*g^9 + 2*(c^2*d^3 - 3*a*c*d*e^2)*f^3*g^7 - (4*a*c*d^2*e - 3*a^2*e^3)*f^2*g^8)*x^3 + 2*(2*c^2*d^2*e*f^5*g^5 + 3*a^2*d*e^2*f^2*g^8 + (3*c^2*d^3 - 4*a*c*d*e^2)*f^4*g^6 - 2*(3*a*c*d^2*e - a^2*e^3)*f^3*g^7)*x^2 + (c^2*d^2*e*f^6*g^4 + 4*a^2*d*e^2*f^3*g^7 + 2*(2*c^2*d^3 - a*c*d*e^2)*f^5*g^5 - (8*a*c*d^2*e - a^2*e^3)*f^4*g^6)*x), -1/192*(15*(c^4*d^4*e*g^4*x^5 + c^4*d^5*f^4 + (4*c^4*d^4*e*f*g^3 + c^4*d^5*g^4)*x^4 + 2*(3*c^4*d^4*e*f^2*g^2 + 2*c^4*d^5*f*g^3)*x^3 + 2*(2*c^4*d^4*e*f^3*g + 3*c^4*d^5*f^2*g^2)*x^2 + (c^4*d^4*e*f^4 + 4*c^4*d^5*f^3*g)*x)*sqrt(c*d*f*g - a*e*g^2)*arctan(sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(c*d*f*g - a*e*g^2)*sqrt(e*x + d)/(c*d*e*g*x^2 + a*d*e*g + (c*d^2 + a*e^2)*g*x)) + (15*c^4*d^4*f^4*g - 5*a*c^3*d^3*e*f^3*g^2 - 2*a^2*c^2*d^2*e^2*f^2*g^3 - 56*a^3*c*d*e^3*f*g^4 + 48*a^4*e^4*g^5 - 15*(c^4*d^4*f*g^4 - a*c^3*d^3*e*g^5)*x^3 + (73*c^4*d^4*f^2*g^3 - 191*a*c^3*d^3*e*f*g^4 + 118*a^2*c^2*d^2*e^2*g^5)*x^2 + (55*c^4*d^4*f^3*g^2 - 19*a*c^3*d^3*e*f^2*g^3 - 172*a^2*c^2*d^2*e^2*f*g^4 + 136*a^3*c*d*e^3*g^5)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c^2*d^3*f^6*g^4 - 2*a*c*d^2*e*f^5*g^5 + a^2*d*e^2*f^4*g^6 + (c^2*d^2*e*f^2*g^8 - 2*a*c*d*e^2*f*g^9 + a^2*e^3*g^10)*x^5 + (4*c^2*d^2*e*f^3*g^7 + a^2*d*e^2*g^10 + (c^2*d^3 - 8*a*c*d*e^2)*f^2*g^8 - 2*(a*c*d^2*e - 2*a^2*e^3)*f*g^9)*x^4 + 2*(3*c^2*d^2*e*f^4*g^6 + 2*a^2*d*e^2*f*g^9 + 2*(c^2*d^3 - 3*a*c*d*e^2)*f^3*g^7 - (4*a*c*d^2*e - 3*a^2*e^3)*f^2*g^8)*x^3 + 2*(2*c^2*d^2*e*f^5*g^5 + 3*a^2*d*e^2*f^2*g^8 + (3*c^2*d^3 - 4*a*c*d*e^2)*f^4*g^6 - 2*(3*a*c*d^2*e - a^2*e^3)*f^3*g^7)*x^2 + (c^2*d^2*e*f^6*g^4 + 4*a^2*d*e^2*f^3*g^7 + 2*(2*c^2*d^3 - a*c*d*e^2)*f^5*g^5 - (8*a*c*d^2*e - a^2*e^3)*f^4*g^6)*x)]","B",0
710,1,2750,0,0.530802," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^(5/2)/(g*x+f)^6,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(c^{5} d^{5} e g^{5} x^{6} + c^{5} d^{6} f^{5} + {\left(5 \, c^{5} d^{5} e f g^{4} + c^{5} d^{6} g^{5}\right)} x^{5} + 5 \, {\left(2 \, c^{5} d^{5} e f^{2} g^{3} + c^{5} d^{6} f g^{4}\right)} x^{4} + 10 \, {\left(c^{5} d^{5} e f^{3} g^{2} + c^{5} d^{6} f^{2} g^{3}\right)} x^{3} + 5 \, {\left(c^{5} d^{5} e f^{4} g + 2 \, c^{5} d^{6} f^{3} g^{2}\right)} x^{2} + {\left(c^{5} d^{5} e f^{5} + 5 \, c^{5} d^{6} f^{4} g\right)} x\right)} \sqrt{-c d f g + a e g^{2}} \log\left(-\frac{c d e g x^{2} - c d^{2} f + 2 \, a d e g - {\left(c d e f - {\left(c d^{2} + 2 \, a e^{2}\right)} g\right)} x - 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{-c d f g + a e g^{2}} \sqrt{e x + d}}{e g x^{2} + d f + {\left(e f + d g\right)} x}\right) + 2 \, {\left(15 \, c^{5} d^{5} f^{5} g - 5 \, a c^{4} d^{4} e f^{4} g^{2} - 2 \, a^{2} c^{3} d^{3} e^{2} f^{3} g^{3} - 184 \, a^{3} c^{2} d^{2} e^{3} f^{2} g^{4} + 304 \, a^{4} c d e^{4} f g^{5} - 128 \, a^{5} e^{5} g^{6} - 15 \, {\left(c^{5} d^{5} f g^{5} - a c^{4} d^{4} e g^{6}\right)} x^{4} - 10 \, {\left(7 \, c^{5} d^{5} f^{2} g^{4} - 8 \, a c^{4} d^{4} e f g^{5} + a^{2} c^{3} d^{3} e^{2} g^{6}\right)} x^{3} + 2 \, {\left(64 \, c^{5} d^{5} f^{3} g^{3} - 297 \, a c^{4} d^{4} e f^{2} g^{4} + 357 \, a^{2} c^{3} d^{3} e^{2} f g^{5} - 124 \, a^{3} c^{2} d^{2} e^{3} g^{6}\right)} x^{2} + 2 \, {\left(35 \, c^{5} d^{5} f^{4} g^{2} - 12 \, a c^{4} d^{4} e f^{3} g^{3} - 279 \, a^{2} c^{3} d^{3} e^{2} f^{2} g^{4} + 424 \, a^{3} c^{2} d^{2} e^{3} f g^{5} - 168 \, a^{4} c d e^{4} g^{6}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{1280 \, {\left(c^{3} d^{4} f^{8} g^{4} - 3 \, a c^{2} d^{3} e f^{7} g^{5} + 3 \, a^{2} c d^{2} e^{2} f^{6} g^{6} - a^{3} d e^{3} f^{5} g^{7} + {\left(c^{3} d^{3} e f^{3} g^{9} - 3 \, a c^{2} d^{2} e^{2} f^{2} g^{10} + 3 \, a^{2} c d e^{3} f g^{11} - a^{3} e^{4} g^{12}\right)} x^{6} + {\left(5 \, c^{3} d^{3} e f^{4} g^{8} - a^{3} d e^{3} g^{12} + {\left(c^{3} d^{4} - 15 \, a c^{2} d^{2} e^{2}\right)} f^{3} g^{9} - 3 \, {\left(a c^{2} d^{3} e - 5 \, a^{2} c d e^{3}\right)} f^{2} g^{10} + {\left(3 \, a^{2} c d^{2} e^{2} - 5 \, a^{3} e^{4}\right)} f g^{11}\right)} x^{5} + 5 \, {\left(2 \, c^{3} d^{3} e f^{5} g^{7} - a^{3} d e^{3} f g^{11} + {\left(c^{3} d^{4} - 6 \, a c^{2} d^{2} e^{2}\right)} f^{4} g^{8} - 3 \, {\left(a c^{2} d^{3} e - 2 \, a^{2} c d e^{3}\right)} f^{3} g^{9} + {\left(3 \, a^{2} c d^{2} e^{2} - 2 \, a^{3} e^{4}\right)} f^{2} g^{10}\right)} x^{4} + 10 \, {\left(c^{3} d^{3} e f^{6} g^{6} - a^{3} d e^{3} f^{2} g^{10} + {\left(c^{3} d^{4} - 3 \, a c^{2} d^{2} e^{2}\right)} f^{5} g^{7} - 3 \, {\left(a c^{2} d^{3} e - a^{2} c d e^{3}\right)} f^{4} g^{8} + {\left(3 \, a^{2} c d^{2} e^{2} - a^{3} e^{4}\right)} f^{3} g^{9}\right)} x^{3} + 5 \, {\left(c^{3} d^{3} e f^{7} g^{5} - 2 \, a^{3} d e^{3} f^{3} g^{9} + {\left(2 \, c^{3} d^{4} - 3 \, a c^{2} d^{2} e^{2}\right)} f^{6} g^{6} - 3 \, {\left(2 \, a c^{2} d^{3} e - a^{2} c d e^{3}\right)} f^{5} g^{7} + {\left(6 \, a^{2} c d^{2} e^{2} - a^{3} e^{4}\right)} f^{4} g^{8}\right)} x^{2} + {\left(c^{3} d^{3} e f^{8} g^{4} - 5 \, a^{3} d e^{3} f^{4} g^{8} + {\left(5 \, c^{3} d^{4} - 3 \, a c^{2} d^{2} e^{2}\right)} f^{7} g^{5} - 3 \, {\left(5 \, a c^{2} d^{3} e - a^{2} c d e^{3}\right)} f^{6} g^{6} + {\left(15 \, a^{2} c d^{2} e^{2} - a^{3} e^{4}\right)} f^{5} g^{7}\right)} x\right)}}, -\frac{15 \, {\left(c^{5} d^{5} e g^{5} x^{6} + c^{5} d^{6} f^{5} + {\left(5 \, c^{5} d^{5} e f g^{4} + c^{5} d^{6} g^{5}\right)} x^{5} + 5 \, {\left(2 \, c^{5} d^{5} e f^{2} g^{3} + c^{5} d^{6} f g^{4}\right)} x^{4} + 10 \, {\left(c^{5} d^{5} e f^{3} g^{2} + c^{5} d^{6} f^{2} g^{3}\right)} x^{3} + 5 \, {\left(c^{5} d^{5} e f^{4} g + 2 \, c^{5} d^{6} f^{3} g^{2}\right)} x^{2} + {\left(c^{5} d^{5} e f^{5} + 5 \, c^{5} d^{6} f^{4} g\right)} x\right)} \sqrt{c d f g - a e g^{2}} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{c d f g - a e g^{2}} \sqrt{e x + d}}{c d e g x^{2} + a d e g + {\left(c d^{2} + a e^{2}\right)} g x}\right) + {\left(15 \, c^{5} d^{5} f^{5} g - 5 \, a c^{4} d^{4} e f^{4} g^{2} - 2 \, a^{2} c^{3} d^{3} e^{2} f^{3} g^{3} - 184 \, a^{3} c^{2} d^{2} e^{3} f^{2} g^{4} + 304 \, a^{4} c d e^{4} f g^{5} - 128 \, a^{5} e^{5} g^{6} - 15 \, {\left(c^{5} d^{5} f g^{5} - a c^{4} d^{4} e g^{6}\right)} x^{4} - 10 \, {\left(7 \, c^{5} d^{5} f^{2} g^{4} - 8 \, a c^{4} d^{4} e f g^{5} + a^{2} c^{3} d^{3} e^{2} g^{6}\right)} x^{3} + 2 \, {\left(64 \, c^{5} d^{5} f^{3} g^{3} - 297 \, a c^{4} d^{4} e f^{2} g^{4} + 357 \, a^{2} c^{3} d^{3} e^{2} f g^{5} - 124 \, a^{3} c^{2} d^{2} e^{3} g^{6}\right)} x^{2} + 2 \, {\left(35 \, c^{5} d^{5} f^{4} g^{2} - 12 \, a c^{4} d^{4} e f^{3} g^{3} - 279 \, a^{2} c^{3} d^{3} e^{2} f^{2} g^{4} + 424 \, a^{3} c^{2} d^{2} e^{3} f g^{5} - 168 \, a^{4} c d e^{4} g^{6}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{640 \, {\left(c^{3} d^{4} f^{8} g^{4} - 3 \, a c^{2} d^{3} e f^{7} g^{5} + 3 \, a^{2} c d^{2} e^{2} f^{6} g^{6} - a^{3} d e^{3} f^{5} g^{7} + {\left(c^{3} d^{3} e f^{3} g^{9} - 3 \, a c^{2} d^{2} e^{2} f^{2} g^{10} + 3 \, a^{2} c d e^{3} f g^{11} - a^{3} e^{4} g^{12}\right)} x^{6} + {\left(5 \, c^{3} d^{3} e f^{4} g^{8} - a^{3} d e^{3} g^{12} + {\left(c^{3} d^{4} - 15 \, a c^{2} d^{2} e^{2}\right)} f^{3} g^{9} - 3 \, {\left(a c^{2} d^{3} e - 5 \, a^{2} c d e^{3}\right)} f^{2} g^{10} + {\left(3 \, a^{2} c d^{2} e^{2} - 5 \, a^{3} e^{4}\right)} f g^{11}\right)} x^{5} + 5 \, {\left(2 \, c^{3} d^{3} e f^{5} g^{7} - a^{3} d e^{3} f g^{11} + {\left(c^{3} d^{4} - 6 \, a c^{2} d^{2} e^{2}\right)} f^{4} g^{8} - 3 \, {\left(a c^{2} d^{3} e - 2 \, a^{2} c d e^{3}\right)} f^{3} g^{9} + {\left(3 \, a^{2} c d^{2} e^{2} - 2 \, a^{3} e^{4}\right)} f^{2} g^{10}\right)} x^{4} + 10 \, {\left(c^{3} d^{3} e f^{6} g^{6} - a^{3} d e^{3} f^{2} g^{10} + {\left(c^{3} d^{4} - 3 \, a c^{2} d^{2} e^{2}\right)} f^{5} g^{7} - 3 \, {\left(a c^{2} d^{3} e - a^{2} c d e^{3}\right)} f^{4} g^{8} + {\left(3 \, a^{2} c d^{2} e^{2} - a^{3} e^{4}\right)} f^{3} g^{9}\right)} x^{3} + 5 \, {\left(c^{3} d^{3} e f^{7} g^{5} - 2 \, a^{3} d e^{3} f^{3} g^{9} + {\left(2 \, c^{3} d^{4} - 3 \, a c^{2} d^{2} e^{2}\right)} f^{6} g^{6} - 3 \, {\left(2 \, a c^{2} d^{3} e - a^{2} c d e^{3}\right)} f^{5} g^{7} + {\left(6 \, a^{2} c d^{2} e^{2} - a^{3} e^{4}\right)} f^{4} g^{8}\right)} x^{2} + {\left(c^{3} d^{3} e f^{8} g^{4} - 5 \, a^{3} d e^{3} f^{4} g^{8} + {\left(5 \, c^{3} d^{4} - 3 \, a c^{2} d^{2} e^{2}\right)} f^{7} g^{5} - 3 \, {\left(5 \, a c^{2} d^{3} e - a^{2} c d e^{3}\right)} f^{6} g^{6} + {\left(15 \, a^{2} c d^{2} e^{2} - a^{3} e^{4}\right)} f^{5} g^{7}\right)} x\right)}}\right]"," ",0,"[-1/1280*(15*(c^5*d^5*e*g^5*x^6 + c^5*d^6*f^5 + (5*c^5*d^5*e*f*g^4 + c^5*d^6*g^5)*x^5 + 5*(2*c^5*d^5*e*f^2*g^3 + c^5*d^6*f*g^4)*x^4 + 10*(c^5*d^5*e*f^3*g^2 + c^5*d^6*f^2*g^3)*x^3 + 5*(c^5*d^5*e*f^4*g + 2*c^5*d^6*f^3*g^2)*x^2 + (c^5*d^5*e*f^5 + 5*c^5*d^6*f^4*g)*x)*sqrt(-c*d*f*g + a*e*g^2)*log(-(c*d*e*g*x^2 - c*d^2*f + 2*a*d*e*g - (c*d*e*f - (c*d^2 + 2*a*e^2)*g)*x - 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-c*d*f*g + a*e*g^2)*sqrt(e*x + d))/(e*g*x^2 + d*f + (e*f + d*g)*x)) + 2*(15*c^5*d^5*f^5*g - 5*a*c^4*d^4*e*f^4*g^2 - 2*a^2*c^3*d^3*e^2*f^3*g^3 - 184*a^3*c^2*d^2*e^3*f^2*g^4 + 304*a^4*c*d*e^4*f*g^5 - 128*a^5*e^5*g^6 - 15*(c^5*d^5*f*g^5 - a*c^4*d^4*e*g^6)*x^4 - 10*(7*c^5*d^5*f^2*g^4 - 8*a*c^4*d^4*e*f*g^5 + a^2*c^3*d^3*e^2*g^6)*x^3 + 2*(64*c^5*d^5*f^3*g^3 - 297*a*c^4*d^4*e*f^2*g^4 + 357*a^2*c^3*d^3*e^2*f*g^5 - 124*a^3*c^2*d^2*e^3*g^6)*x^2 + 2*(35*c^5*d^5*f^4*g^2 - 12*a*c^4*d^4*e*f^3*g^3 - 279*a^2*c^3*d^3*e^2*f^2*g^4 + 424*a^3*c^2*d^2*e^3*f*g^5 - 168*a^4*c*d*e^4*g^6)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c^3*d^4*f^8*g^4 - 3*a*c^2*d^3*e*f^7*g^5 + 3*a^2*c*d^2*e^2*f^6*g^6 - a^3*d*e^3*f^5*g^7 + (c^3*d^3*e*f^3*g^9 - 3*a*c^2*d^2*e^2*f^2*g^10 + 3*a^2*c*d*e^3*f*g^11 - a^3*e^4*g^12)*x^6 + (5*c^3*d^3*e*f^4*g^8 - a^3*d*e^3*g^12 + (c^3*d^4 - 15*a*c^2*d^2*e^2)*f^3*g^9 - 3*(a*c^2*d^3*e - 5*a^2*c*d*e^3)*f^2*g^10 + (3*a^2*c*d^2*e^2 - 5*a^3*e^4)*f*g^11)*x^5 + 5*(2*c^3*d^3*e*f^5*g^7 - a^3*d*e^3*f*g^11 + (c^3*d^4 - 6*a*c^2*d^2*e^2)*f^4*g^8 - 3*(a*c^2*d^3*e - 2*a^2*c*d*e^3)*f^3*g^9 + (3*a^2*c*d^2*e^2 - 2*a^3*e^4)*f^2*g^10)*x^4 + 10*(c^3*d^3*e*f^6*g^6 - a^3*d*e^3*f^2*g^10 + (c^3*d^4 - 3*a*c^2*d^2*e^2)*f^5*g^7 - 3*(a*c^2*d^3*e - a^2*c*d*e^3)*f^4*g^8 + (3*a^2*c*d^2*e^2 - a^3*e^4)*f^3*g^9)*x^3 + 5*(c^3*d^3*e*f^7*g^5 - 2*a^3*d*e^3*f^3*g^9 + (2*c^3*d^4 - 3*a*c^2*d^2*e^2)*f^6*g^6 - 3*(2*a*c^2*d^3*e - a^2*c*d*e^3)*f^5*g^7 + (6*a^2*c*d^2*e^2 - a^3*e^4)*f^4*g^8)*x^2 + (c^3*d^3*e*f^8*g^4 - 5*a^3*d*e^3*f^4*g^8 + (5*c^3*d^4 - 3*a*c^2*d^2*e^2)*f^7*g^5 - 3*(5*a*c^2*d^3*e - a^2*c*d*e^3)*f^6*g^6 + (15*a^2*c*d^2*e^2 - a^3*e^4)*f^5*g^7)*x), -1/640*(15*(c^5*d^5*e*g^5*x^6 + c^5*d^6*f^5 + (5*c^5*d^5*e*f*g^4 + c^5*d^6*g^5)*x^5 + 5*(2*c^5*d^5*e*f^2*g^3 + c^5*d^6*f*g^4)*x^4 + 10*(c^5*d^5*e*f^3*g^2 + c^5*d^6*f^2*g^3)*x^3 + 5*(c^5*d^5*e*f^4*g + 2*c^5*d^6*f^3*g^2)*x^2 + (c^5*d^5*e*f^5 + 5*c^5*d^6*f^4*g)*x)*sqrt(c*d*f*g - a*e*g^2)*arctan(sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(c*d*f*g - a*e*g^2)*sqrt(e*x + d)/(c*d*e*g*x^2 + a*d*e*g + (c*d^2 + a*e^2)*g*x)) + (15*c^5*d^5*f^5*g - 5*a*c^4*d^4*e*f^4*g^2 - 2*a^2*c^3*d^3*e^2*f^3*g^3 - 184*a^3*c^2*d^2*e^3*f^2*g^4 + 304*a^4*c*d*e^4*f*g^5 - 128*a^5*e^5*g^6 - 15*(c^5*d^5*f*g^5 - a*c^4*d^4*e*g^6)*x^4 - 10*(7*c^5*d^5*f^2*g^4 - 8*a*c^4*d^4*e*f*g^5 + a^2*c^3*d^3*e^2*g^6)*x^3 + 2*(64*c^5*d^5*f^3*g^3 - 297*a*c^4*d^4*e*f^2*g^4 + 357*a^2*c^3*d^3*e^2*f*g^5 - 124*a^3*c^2*d^2*e^3*g^6)*x^2 + 2*(35*c^5*d^5*f^4*g^2 - 12*a*c^4*d^4*e*f^3*g^3 - 279*a^2*c^3*d^3*e^2*f^2*g^4 + 424*a^3*c^2*d^2*e^3*f*g^5 - 168*a^4*c*d*e^4*g^6)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c^3*d^4*f^8*g^4 - 3*a*c^2*d^3*e*f^7*g^5 + 3*a^2*c*d^2*e^2*f^6*g^6 - a^3*d*e^3*f^5*g^7 + (c^3*d^3*e*f^3*g^9 - 3*a*c^2*d^2*e^2*f^2*g^10 + 3*a^2*c*d*e^3*f*g^11 - a^3*e^4*g^12)*x^6 + (5*c^3*d^3*e*f^4*g^8 - a^3*d*e^3*g^12 + (c^3*d^4 - 15*a*c^2*d^2*e^2)*f^3*g^9 - 3*(a*c^2*d^3*e - 5*a^2*c*d*e^3)*f^2*g^10 + (3*a^2*c*d^2*e^2 - 5*a^3*e^4)*f*g^11)*x^5 + 5*(2*c^3*d^3*e*f^5*g^7 - a^3*d*e^3*f*g^11 + (c^3*d^4 - 6*a*c^2*d^2*e^2)*f^4*g^8 - 3*(a*c^2*d^3*e - 2*a^2*c*d*e^3)*f^3*g^9 + (3*a^2*c*d^2*e^2 - 2*a^3*e^4)*f^2*g^10)*x^4 + 10*(c^3*d^3*e*f^6*g^6 - a^3*d*e^3*f^2*g^10 + (c^3*d^4 - 3*a*c^2*d^2*e^2)*f^5*g^7 - 3*(a*c^2*d^3*e - a^2*c*d*e^3)*f^4*g^8 + (3*a^2*c*d^2*e^2 - a^3*e^4)*f^3*g^9)*x^3 + 5*(c^3*d^3*e*f^7*g^5 - 2*a^3*d*e^3*f^3*g^9 + (2*c^3*d^4 - 3*a*c^2*d^2*e^2)*f^6*g^6 - 3*(2*a*c^2*d^3*e - a^2*c*d*e^3)*f^5*g^7 + (6*a^2*c*d^2*e^2 - a^3*e^4)*f^4*g^8)*x^2 + (c^3*d^3*e*f^8*g^4 - 5*a^3*d*e^3*f^4*g^8 + (5*c^3*d^4 - 3*a*c^2*d^2*e^2)*f^7*g^5 - 3*(5*a*c^2*d^3*e - a^2*c*d*e^3)*f^6*g^6 + (15*a^2*c*d^2*e^2 - a^3*e^4)*f^5*g^7)*x)]","B",0
711,1,3872,0,0.554955," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^(5/2)/(g*x+f)^7,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(c^{6} d^{6} e g^{6} x^{7} + c^{6} d^{7} f^{6} + {\left(6 \, c^{6} d^{6} e f g^{5} + c^{6} d^{7} g^{6}\right)} x^{6} + 3 \, {\left(5 \, c^{6} d^{6} e f^{2} g^{4} + 2 \, c^{6} d^{7} f g^{5}\right)} x^{5} + 5 \, {\left(4 \, c^{6} d^{6} e f^{3} g^{3} + 3 \, c^{6} d^{7} f^{2} g^{4}\right)} x^{4} + 5 \, {\left(3 \, c^{6} d^{6} e f^{4} g^{2} + 4 \, c^{6} d^{7} f^{3} g^{3}\right)} x^{3} + 3 \, {\left(2 \, c^{6} d^{6} e f^{5} g + 5 \, c^{6} d^{7} f^{4} g^{2}\right)} x^{2} + {\left(c^{6} d^{6} e f^{6} + 6 \, c^{6} d^{7} f^{5} g\right)} x\right)} \sqrt{-c d f g + a e g^{2}} \log\left(-\frac{c d e g x^{2} - c d^{2} f + 2 \, a d e g - {\left(c d e f - {\left(c d^{2} + 2 \, a e^{2}\right)} g\right)} x + 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{-c d f g + a e g^{2}} \sqrt{e x + d}}{e g x^{2} + d f + {\left(e f + d g\right)} x}\right) - 2 \, {\left(15 \, c^{6} d^{6} f^{6} g - 5 \, a c^{5} d^{5} e f^{5} g^{2} - 2 \, a^{2} c^{4} d^{4} e^{2} f^{4} g^{3} - 440 \, a^{3} c^{3} d^{3} e^{3} f^{3} g^{4} + 1072 \, a^{4} c^{2} d^{2} e^{4} f^{2} g^{5} - 896 \, a^{5} c d e^{5} f g^{6} + 256 \, a^{6} e^{6} g^{7} - 15 \, {\left(c^{6} d^{6} f g^{6} - a c^{5} d^{5} e g^{7}\right)} x^{5} - 5 \, {\left(17 \, c^{6} d^{6} f^{2} g^{5} - 19 \, a c^{5} d^{5} e f g^{6} + 2 \, a^{2} c^{4} d^{4} e^{2} g^{7}\right)} x^{4} - 2 \, {\left(99 \, c^{6} d^{6} f^{3} g^{4} - 127 \, a c^{5} d^{5} e f^{2} g^{5} + 32 \, a^{2} c^{4} d^{4} e^{2} f g^{6} - 4 \, a^{3} c^{3} d^{3} e^{3} g^{7}\right)} x^{3} + 6 \, {\left(33 \, c^{6} d^{6} f^{4} g^{3} - 231 \, a c^{5} d^{5} e f^{3} g^{4} + 410 \, a^{2} c^{4} d^{4} e^{2} f^{2} g^{5} - 284 \, a^{3} c^{3} d^{3} e^{3} f g^{6} + 72 \, a^{4} c^{2} d^{2} e^{4} g^{7}\right)} x^{2} + {\left(85 \, c^{6} d^{6} f^{5} g^{2} - 29 \, a c^{5} d^{5} e f^{4} g^{3} - 1328 \, a^{2} c^{4} d^{4} e^{2} f^{3} g^{4} + 2968 \, a^{3} c^{3} d^{3} e^{3} f^{2} g^{5} - 2336 \, a^{4} c^{2} d^{2} e^{4} f g^{6} + 640 \, a^{5} c d e^{5} g^{7}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{3072 \, {\left(c^{4} d^{5} f^{10} g^{4} - 4 \, a c^{3} d^{4} e f^{9} g^{5} + 6 \, a^{2} c^{2} d^{3} e^{2} f^{8} g^{6} - 4 \, a^{3} c d^{2} e^{3} f^{7} g^{7} + a^{4} d e^{4} f^{6} g^{8} + {\left(c^{4} d^{4} e f^{4} g^{10} - 4 \, a c^{3} d^{3} e^{2} f^{3} g^{11} + 6 \, a^{2} c^{2} d^{2} e^{3} f^{2} g^{12} - 4 \, a^{3} c d e^{4} f g^{13} + a^{4} e^{5} g^{14}\right)} x^{7} + {\left(6 \, c^{4} d^{4} e f^{5} g^{9} + a^{4} d e^{4} g^{14} + {\left(c^{4} d^{5} - 24 \, a c^{3} d^{3} e^{2}\right)} f^{4} g^{10} - 4 \, {\left(a c^{3} d^{4} e - 9 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{3} g^{11} + 6 \, {\left(a^{2} c^{2} d^{3} e^{2} - 4 \, a^{3} c d e^{4}\right)} f^{2} g^{12} - 2 \, {\left(2 \, a^{3} c d^{2} e^{3} - 3 \, a^{4} e^{5}\right)} f g^{13}\right)} x^{6} + 3 \, {\left(5 \, c^{4} d^{4} e f^{6} g^{8} + 2 \, a^{4} d e^{4} f g^{13} + 2 \, {\left(c^{4} d^{5} - 10 \, a c^{3} d^{3} e^{2}\right)} f^{5} g^{9} - 2 \, {\left(4 \, a c^{3} d^{4} e - 15 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{4} g^{10} + 4 \, {\left(3 \, a^{2} c^{2} d^{3} e^{2} - 5 \, a^{3} c d e^{4}\right)} f^{3} g^{11} - {\left(8 \, a^{3} c d^{2} e^{3} - 5 \, a^{4} e^{5}\right)} f^{2} g^{12}\right)} x^{5} + 5 \, {\left(4 \, c^{4} d^{4} e f^{7} g^{7} + 3 \, a^{4} d e^{4} f^{2} g^{12} + {\left(3 \, c^{4} d^{5} - 16 \, a c^{3} d^{3} e^{2}\right)} f^{6} g^{8} - 12 \, {\left(a c^{3} d^{4} e - 2 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{5} g^{9} + 2 \, {\left(9 \, a^{2} c^{2} d^{3} e^{2} - 8 \, a^{3} c d e^{4}\right)} f^{4} g^{10} - 4 \, {\left(3 \, a^{3} c d^{2} e^{3} - a^{4} e^{5}\right)} f^{3} g^{11}\right)} x^{4} + 5 \, {\left(3 \, c^{4} d^{4} e f^{8} g^{6} + 4 \, a^{4} d e^{4} f^{3} g^{11} + 4 \, {\left(c^{4} d^{5} - 3 \, a c^{3} d^{3} e^{2}\right)} f^{7} g^{7} - 2 \, {\left(8 \, a c^{3} d^{4} e - 9 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{6} g^{8} + 12 \, {\left(2 \, a^{2} c^{2} d^{3} e^{2} - a^{3} c d e^{4}\right)} f^{5} g^{9} - {\left(16 \, a^{3} c d^{2} e^{3} - 3 \, a^{4} e^{5}\right)} f^{4} g^{10}\right)} x^{3} + 3 \, {\left(2 \, c^{4} d^{4} e f^{9} g^{5} + 5 \, a^{4} d e^{4} f^{4} g^{10} + {\left(5 \, c^{4} d^{5} - 8 \, a c^{3} d^{3} e^{2}\right)} f^{8} g^{6} - 4 \, {\left(5 \, a c^{3} d^{4} e - 3 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{7} g^{7} + 2 \, {\left(15 \, a^{2} c^{2} d^{3} e^{2} - 4 \, a^{3} c d e^{4}\right)} f^{6} g^{8} - 2 \, {\left(10 \, a^{3} c d^{2} e^{3} - a^{4} e^{5}\right)} f^{5} g^{9}\right)} x^{2} + {\left(c^{4} d^{4} e f^{10} g^{4} + 6 \, a^{4} d e^{4} f^{5} g^{9} + 2 \, {\left(3 \, c^{4} d^{5} - 2 \, a c^{3} d^{3} e^{2}\right)} f^{9} g^{5} - 6 \, {\left(4 \, a c^{3} d^{4} e - a^{2} c^{2} d^{2} e^{3}\right)} f^{8} g^{6} + 4 \, {\left(9 \, a^{2} c^{2} d^{3} e^{2} - a^{3} c d e^{4}\right)} f^{7} g^{7} - {\left(24 \, a^{3} c d^{2} e^{3} - a^{4} e^{5}\right)} f^{6} g^{8}\right)} x\right)}}, -\frac{15 \, {\left(c^{6} d^{6} e g^{6} x^{7} + c^{6} d^{7} f^{6} + {\left(6 \, c^{6} d^{6} e f g^{5} + c^{6} d^{7} g^{6}\right)} x^{6} + 3 \, {\left(5 \, c^{6} d^{6} e f^{2} g^{4} + 2 \, c^{6} d^{7} f g^{5}\right)} x^{5} + 5 \, {\left(4 \, c^{6} d^{6} e f^{3} g^{3} + 3 \, c^{6} d^{7} f^{2} g^{4}\right)} x^{4} + 5 \, {\left(3 \, c^{6} d^{6} e f^{4} g^{2} + 4 \, c^{6} d^{7} f^{3} g^{3}\right)} x^{3} + 3 \, {\left(2 \, c^{6} d^{6} e f^{5} g + 5 \, c^{6} d^{7} f^{4} g^{2}\right)} x^{2} + {\left(c^{6} d^{6} e f^{6} + 6 \, c^{6} d^{7} f^{5} g\right)} x\right)} \sqrt{c d f g - a e g^{2}} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{c d f g - a e g^{2}} \sqrt{e x + d}}{c d e g x^{2} + a d e g + {\left(c d^{2} + a e^{2}\right)} g x}\right) + {\left(15 \, c^{6} d^{6} f^{6} g - 5 \, a c^{5} d^{5} e f^{5} g^{2} - 2 \, a^{2} c^{4} d^{4} e^{2} f^{4} g^{3} - 440 \, a^{3} c^{3} d^{3} e^{3} f^{3} g^{4} + 1072 \, a^{4} c^{2} d^{2} e^{4} f^{2} g^{5} - 896 \, a^{5} c d e^{5} f g^{6} + 256 \, a^{6} e^{6} g^{7} - 15 \, {\left(c^{6} d^{6} f g^{6} - a c^{5} d^{5} e g^{7}\right)} x^{5} - 5 \, {\left(17 \, c^{6} d^{6} f^{2} g^{5} - 19 \, a c^{5} d^{5} e f g^{6} + 2 \, a^{2} c^{4} d^{4} e^{2} g^{7}\right)} x^{4} - 2 \, {\left(99 \, c^{6} d^{6} f^{3} g^{4} - 127 \, a c^{5} d^{5} e f^{2} g^{5} + 32 \, a^{2} c^{4} d^{4} e^{2} f g^{6} - 4 \, a^{3} c^{3} d^{3} e^{3} g^{7}\right)} x^{3} + 6 \, {\left(33 \, c^{6} d^{6} f^{4} g^{3} - 231 \, a c^{5} d^{5} e f^{3} g^{4} + 410 \, a^{2} c^{4} d^{4} e^{2} f^{2} g^{5} - 284 \, a^{3} c^{3} d^{3} e^{3} f g^{6} + 72 \, a^{4} c^{2} d^{2} e^{4} g^{7}\right)} x^{2} + {\left(85 \, c^{6} d^{6} f^{5} g^{2} - 29 \, a c^{5} d^{5} e f^{4} g^{3} - 1328 \, a^{2} c^{4} d^{4} e^{2} f^{3} g^{4} + 2968 \, a^{3} c^{3} d^{3} e^{3} f^{2} g^{5} - 2336 \, a^{4} c^{2} d^{2} e^{4} f g^{6} + 640 \, a^{5} c d e^{5} g^{7}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{1536 \, {\left(c^{4} d^{5} f^{10} g^{4} - 4 \, a c^{3} d^{4} e f^{9} g^{5} + 6 \, a^{2} c^{2} d^{3} e^{2} f^{8} g^{6} - 4 \, a^{3} c d^{2} e^{3} f^{7} g^{7} + a^{4} d e^{4} f^{6} g^{8} + {\left(c^{4} d^{4} e f^{4} g^{10} - 4 \, a c^{3} d^{3} e^{2} f^{3} g^{11} + 6 \, a^{2} c^{2} d^{2} e^{3} f^{2} g^{12} - 4 \, a^{3} c d e^{4} f g^{13} + a^{4} e^{5} g^{14}\right)} x^{7} + {\left(6 \, c^{4} d^{4} e f^{5} g^{9} + a^{4} d e^{4} g^{14} + {\left(c^{4} d^{5} - 24 \, a c^{3} d^{3} e^{2}\right)} f^{4} g^{10} - 4 \, {\left(a c^{3} d^{4} e - 9 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{3} g^{11} + 6 \, {\left(a^{2} c^{2} d^{3} e^{2} - 4 \, a^{3} c d e^{4}\right)} f^{2} g^{12} - 2 \, {\left(2 \, a^{3} c d^{2} e^{3} - 3 \, a^{4} e^{5}\right)} f g^{13}\right)} x^{6} + 3 \, {\left(5 \, c^{4} d^{4} e f^{6} g^{8} + 2 \, a^{4} d e^{4} f g^{13} + 2 \, {\left(c^{4} d^{5} - 10 \, a c^{3} d^{3} e^{2}\right)} f^{5} g^{9} - 2 \, {\left(4 \, a c^{3} d^{4} e - 15 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{4} g^{10} + 4 \, {\left(3 \, a^{2} c^{2} d^{3} e^{2} - 5 \, a^{3} c d e^{4}\right)} f^{3} g^{11} - {\left(8 \, a^{3} c d^{2} e^{3} - 5 \, a^{4} e^{5}\right)} f^{2} g^{12}\right)} x^{5} + 5 \, {\left(4 \, c^{4} d^{4} e f^{7} g^{7} + 3 \, a^{4} d e^{4} f^{2} g^{12} + {\left(3 \, c^{4} d^{5} - 16 \, a c^{3} d^{3} e^{2}\right)} f^{6} g^{8} - 12 \, {\left(a c^{3} d^{4} e - 2 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{5} g^{9} + 2 \, {\left(9 \, a^{2} c^{2} d^{3} e^{2} - 8 \, a^{3} c d e^{4}\right)} f^{4} g^{10} - 4 \, {\left(3 \, a^{3} c d^{2} e^{3} - a^{4} e^{5}\right)} f^{3} g^{11}\right)} x^{4} + 5 \, {\left(3 \, c^{4} d^{4} e f^{8} g^{6} + 4 \, a^{4} d e^{4} f^{3} g^{11} + 4 \, {\left(c^{4} d^{5} - 3 \, a c^{3} d^{3} e^{2}\right)} f^{7} g^{7} - 2 \, {\left(8 \, a c^{3} d^{4} e - 9 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{6} g^{8} + 12 \, {\left(2 \, a^{2} c^{2} d^{3} e^{2} - a^{3} c d e^{4}\right)} f^{5} g^{9} - {\left(16 \, a^{3} c d^{2} e^{3} - 3 \, a^{4} e^{5}\right)} f^{4} g^{10}\right)} x^{3} + 3 \, {\left(2 \, c^{4} d^{4} e f^{9} g^{5} + 5 \, a^{4} d e^{4} f^{4} g^{10} + {\left(5 \, c^{4} d^{5} - 8 \, a c^{3} d^{3} e^{2}\right)} f^{8} g^{6} - 4 \, {\left(5 \, a c^{3} d^{4} e - 3 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{7} g^{7} + 2 \, {\left(15 \, a^{2} c^{2} d^{3} e^{2} - 4 \, a^{3} c d e^{4}\right)} f^{6} g^{8} - 2 \, {\left(10 \, a^{3} c d^{2} e^{3} - a^{4} e^{5}\right)} f^{5} g^{9}\right)} x^{2} + {\left(c^{4} d^{4} e f^{10} g^{4} + 6 \, a^{4} d e^{4} f^{5} g^{9} + 2 \, {\left(3 \, c^{4} d^{5} - 2 \, a c^{3} d^{3} e^{2}\right)} f^{9} g^{5} - 6 \, {\left(4 \, a c^{3} d^{4} e - a^{2} c^{2} d^{2} e^{3}\right)} f^{8} g^{6} + 4 \, {\left(9 \, a^{2} c^{2} d^{3} e^{2} - a^{3} c d e^{4}\right)} f^{7} g^{7} - {\left(24 \, a^{3} c d^{2} e^{3} - a^{4} e^{5}\right)} f^{6} g^{8}\right)} x\right)}}\right]"," ",0,"[1/3072*(15*(c^6*d^6*e*g^6*x^7 + c^6*d^7*f^6 + (6*c^6*d^6*e*f*g^5 + c^6*d^7*g^6)*x^6 + 3*(5*c^6*d^6*e*f^2*g^4 + 2*c^6*d^7*f*g^5)*x^5 + 5*(4*c^6*d^6*e*f^3*g^3 + 3*c^6*d^7*f^2*g^4)*x^4 + 5*(3*c^6*d^6*e*f^4*g^2 + 4*c^6*d^7*f^3*g^3)*x^3 + 3*(2*c^6*d^6*e*f^5*g + 5*c^6*d^7*f^4*g^2)*x^2 + (c^6*d^6*e*f^6 + 6*c^6*d^7*f^5*g)*x)*sqrt(-c*d*f*g + a*e*g^2)*log(-(c*d*e*g*x^2 - c*d^2*f + 2*a*d*e*g - (c*d*e*f - (c*d^2 + 2*a*e^2)*g)*x + 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-c*d*f*g + a*e*g^2)*sqrt(e*x + d))/(e*g*x^2 + d*f + (e*f + d*g)*x)) - 2*(15*c^6*d^6*f^6*g - 5*a*c^5*d^5*e*f^5*g^2 - 2*a^2*c^4*d^4*e^2*f^4*g^3 - 440*a^3*c^3*d^3*e^3*f^3*g^4 + 1072*a^4*c^2*d^2*e^4*f^2*g^5 - 896*a^5*c*d*e^5*f*g^6 + 256*a^6*e^6*g^7 - 15*(c^6*d^6*f*g^6 - a*c^5*d^5*e*g^7)*x^5 - 5*(17*c^6*d^6*f^2*g^5 - 19*a*c^5*d^5*e*f*g^6 + 2*a^2*c^4*d^4*e^2*g^7)*x^4 - 2*(99*c^6*d^6*f^3*g^4 - 127*a*c^5*d^5*e*f^2*g^5 + 32*a^2*c^4*d^4*e^2*f*g^6 - 4*a^3*c^3*d^3*e^3*g^7)*x^3 + 6*(33*c^6*d^6*f^4*g^3 - 231*a*c^5*d^5*e*f^3*g^4 + 410*a^2*c^4*d^4*e^2*f^2*g^5 - 284*a^3*c^3*d^3*e^3*f*g^6 + 72*a^4*c^2*d^2*e^4*g^7)*x^2 + (85*c^6*d^6*f^5*g^2 - 29*a*c^5*d^5*e*f^4*g^3 - 1328*a^2*c^4*d^4*e^2*f^3*g^4 + 2968*a^3*c^3*d^3*e^3*f^2*g^5 - 2336*a^4*c^2*d^2*e^4*f*g^6 + 640*a^5*c*d*e^5*g^7)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c^4*d^5*f^10*g^4 - 4*a*c^3*d^4*e*f^9*g^5 + 6*a^2*c^2*d^3*e^2*f^8*g^6 - 4*a^3*c*d^2*e^3*f^7*g^7 + a^4*d*e^4*f^6*g^8 + (c^4*d^4*e*f^4*g^10 - 4*a*c^3*d^3*e^2*f^3*g^11 + 6*a^2*c^2*d^2*e^3*f^2*g^12 - 4*a^3*c*d*e^4*f*g^13 + a^4*e^5*g^14)*x^7 + (6*c^4*d^4*e*f^5*g^9 + a^4*d*e^4*g^14 + (c^4*d^5 - 24*a*c^3*d^3*e^2)*f^4*g^10 - 4*(a*c^3*d^4*e - 9*a^2*c^2*d^2*e^3)*f^3*g^11 + 6*(a^2*c^2*d^3*e^2 - 4*a^3*c*d*e^4)*f^2*g^12 - 2*(2*a^3*c*d^2*e^3 - 3*a^4*e^5)*f*g^13)*x^6 + 3*(5*c^4*d^4*e*f^6*g^8 + 2*a^4*d*e^4*f*g^13 + 2*(c^4*d^5 - 10*a*c^3*d^3*e^2)*f^5*g^9 - 2*(4*a*c^3*d^4*e - 15*a^2*c^2*d^2*e^3)*f^4*g^10 + 4*(3*a^2*c^2*d^3*e^2 - 5*a^3*c*d*e^4)*f^3*g^11 - (8*a^3*c*d^2*e^3 - 5*a^4*e^5)*f^2*g^12)*x^5 + 5*(4*c^4*d^4*e*f^7*g^7 + 3*a^4*d*e^4*f^2*g^12 + (3*c^4*d^5 - 16*a*c^3*d^3*e^2)*f^6*g^8 - 12*(a*c^3*d^4*e - 2*a^2*c^2*d^2*e^3)*f^5*g^9 + 2*(9*a^2*c^2*d^3*e^2 - 8*a^3*c*d*e^4)*f^4*g^10 - 4*(3*a^3*c*d^2*e^3 - a^4*e^5)*f^3*g^11)*x^4 + 5*(3*c^4*d^4*e*f^8*g^6 + 4*a^4*d*e^4*f^3*g^11 + 4*(c^4*d^5 - 3*a*c^3*d^3*e^2)*f^7*g^7 - 2*(8*a*c^3*d^4*e - 9*a^2*c^2*d^2*e^3)*f^6*g^8 + 12*(2*a^2*c^2*d^3*e^2 - a^3*c*d*e^4)*f^5*g^9 - (16*a^3*c*d^2*e^3 - 3*a^4*e^5)*f^4*g^10)*x^3 + 3*(2*c^4*d^4*e*f^9*g^5 + 5*a^4*d*e^4*f^4*g^10 + (5*c^4*d^5 - 8*a*c^3*d^3*e^2)*f^8*g^6 - 4*(5*a*c^3*d^4*e - 3*a^2*c^2*d^2*e^3)*f^7*g^7 + 2*(15*a^2*c^2*d^3*e^2 - 4*a^3*c*d*e^4)*f^6*g^8 - 2*(10*a^3*c*d^2*e^3 - a^4*e^5)*f^5*g^9)*x^2 + (c^4*d^4*e*f^10*g^4 + 6*a^4*d*e^4*f^5*g^9 + 2*(3*c^4*d^5 - 2*a*c^3*d^3*e^2)*f^9*g^5 - 6*(4*a*c^3*d^4*e - a^2*c^2*d^2*e^3)*f^8*g^6 + 4*(9*a^2*c^2*d^3*e^2 - a^3*c*d*e^4)*f^7*g^7 - (24*a^3*c*d^2*e^3 - a^4*e^5)*f^6*g^8)*x), -1/1536*(15*(c^6*d^6*e*g^6*x^7 + c^6*d^7*f^6 + (6*c^6*d^6*e*f*g^5 + c^6*d^7*g^6)*x^6 + 3*(5*c^6*d^6*e*f^2*g^4 + 2*c^6*d^7*f*g^5)*x^5 + 5*(4*c^6*d^6*e*f^3*g^3 + 3*c^6*d^7*f^2*g^4)*x^4 + 5*(3*c^6*d^6*e*f^4*g^2 + 4*c^6*d^7*f^3*g^3)*x^3 + 3*(2*c^6*d^6*e*f^5*g + 5*c^6*d^7*f^4*g^2)*x^2 + (c^6*d^6*e*f^6 + 6*c^6*d^7*f^5*g)*x)*sqrt(c*d*f*g - a*e*g^2)*arctan(sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(c*d*f*g - a*e*g^2)*sqrt(e*x + d)/(c*d*e*g*x^2 + a*d*e*g + (c*d^2 + a*e^2)*g*x)) + (15*c^6*d^6*f^6*g - 5*a*c^5*d^5*e*f^5*g^2 - 2*a^2*c^4*d^4*e^2*f^4*g^3 - 440*a^3*c^3*d^3*e^3*f^3*g^4 + 1072*a^4*c^2*d^2*e^4*f^2*g^5 - 896*a^5*c*d*e^5*f*g^6 + 256*a^6*e^6*g^7 - 15*(c^6*d^6*f*g^6 - a*c^5*d^5*e*g^7)*x^5 - 5*(17*c^6*d^6*f^2*g^5 - 19*a*c^5*d^5*e*f*g^6 + 2*a^2*c^4*d^4*e^2*g^7)*x^4 - 2*(99*c^6*d^6*f^3*g^4 - 127*a*c^5*d^5*e*f^2*g^5 + 32*a^2*c^4*d^4*e^2*f*g^6 - 4*a^3*c^3*d^3*e^3*g^7)*x^3 + 6*(33*c^6*d^6*f^4*g^3 - 231*a*c^5*d^5*e*f^3*g^4 + 410*a^2*c^4*d^4*e^2*f^2*g^5 - 284*a^3*c^3*d^3*e^3*f*g^6 + 72*a^4*c^2*d^2*e^4*g^7)*x^2 + (85*c^6*d^6*f^5*g^2 - 29*a*c^5*d^5*e*f^4*g^3 - 1328*a^2*c^4*d^4*e^2*f^3*g^4 + 2968*a^3*c^3*d^3*e^3*f^2*g^5 - 2336*a^4*c^2*d^2*e^4*f*g^6 + 640*a^5*c*d*e^5*g^7)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c^4*d^5*f^10*g^4 - 4*a*c^3*d^4*e*f^9*g^5 + 6*a^2*c^2*d^3*e^2*f^8*g^6 - 4*a^3*c*d^2*e^3*f^7*g^7 + a^4*d*e^4*f^6*g^8 + (c^4*d^4*e*f^4*g^10 - 4*a*c^3*d^3*e^2*f^3*g^11 + 6*a^2*c^2*d^2*e^3*f^2*g^12 - 4*a^3*c*d*e^4*f*g^13 + a^4*e^5*g^14)*x^7 + (6*c^4*d^4*e*f^5*g^9 + a^4*d*e^4*g^14 + (c^4*d^5 - 24*a*c^3*d^3*e^2)*f^4*g^10 - 4*(a*c^3*d^4*e - 9*a^2*c^2*d^2*e^3)*f^3*g^11 + 6*(a^2*c^2*d^3*e^2 - 4*a^3*c*d*e^4)*f^2*g^12 - 2*(2*a^3*c*d^2*e^3 - 3*a^4*e^5)*f*g^13)*x^6 + 3*(5*c^4*d^4*e*f^6*g^8 + 2*a^4*d*e^4*f*g^13 + 2*(c^4*d^5 - 10*a*c^3*d^3*e^2)*f^5*g^9 - 2*(4*a*c^3*d^4*e - 15*a^2*c^2*d^2*e^3)*f^4*g^10 + 4*(3*a^2*c^2*d^3*e^2 - 5*a^3*c*d*e^4)*f^3*g^11 - (8*a^3*c*d^2*e^3 - 5*a^4*e^5)*f^2*g^12)*x^5 + 5*(4*c^4*d^4*e*f^7*g^7 + 3*a^4*d*e^4*f^2*g^12 + (3*c^4*d^5 - 16*a*c^3*d^3*e^2)*f^6*g^8 - 12*(a*c^3*d^4*e - 2*a^2*c^2*d^2*e^3)*f^5*g^9 + 2*(9*a^2*c^2*d^3*e^2 - 8*a^3*c*d*e^4)*f^4*g^10 - 4*(3*a^3*c*d^2*e^3 - a^4*e^5)*f^3*g^11)*x^4 + 5*(3*c^4*d^4*e*f^8*g^6 + 4*a^4*d*e^4*f^3*g^11 + 4*(c^4*d^5 - 3*a*c^3*d^3*e^2)*f^7*g^7 - 2*(8*a*c^3*d^4*e - 9*a^2*c^2*d^2*e^3)*f^6*g^8 + 12*(2*a^2*c^2*d^3*e^2 - a^3*c*d*e^4)*f^5*g^9 - (16*a^3*c*d^2*e^3 - 3*a^4*e^5)*f^4*g^10)*x^3 + 3*(2*c^4*d^4*e*f^9*g^5 + 5*a^4*d*e^4*f^4*g^10 + (5*c^4*d^5 - 8*a*c^3*d^3*e^2)*f^8*g^6 - 4*(5*a*c^3*d^4*e - 3*a^2*c^2*d^2*e^3)*f^7*g^7 + 2*(15*a^2*c^2*d^3*e^2 - 4*a^3*c*d*e^4)*f^6*g^8 - 2*(10*a^3*c*d^2*e^3 - a^4*e^5)*f^5*g^9)*x^2 + (c^4*d^4*e*f^10*g^4 + 6*a^4*d*e^4*f^5*g^9 + 2*(3*c^4*d^5 - 2*a*c^3*d^3*e^2)*f^9*g^5 - 6*(4*a*c^3*d^4*e - a^2*c^2*d^2*e^3)*f^8*g^6 + 4*(9*a^2*c^2*d^3*e^2 - a^3*c*d*e^4)*f^7*g^7 - (24*a^3*c*d^2*e^3 - a^4*e^5)*f^6*g^8)*x)]","B",0
712,1,841,0,1.559784," ","integrate((g*x+f)^(5/2)*(e*x+d)^(1/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(8 \, c^{3} d^{3} g^{3} x^{2} + 33 \, c^{3} d^{3} f^{2} g - 40 \, a c^{2} d^{2} e f g^{2} + 15 \, a^{2} c d e^{2} g^{3} + 2 \, {\left(13 \, c^{3} d^{3} f g^{2} - 5 \, a c^{2} d^{2} e g^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} - 15 \, {\left(c^{3} d^{4} f^{3} - 3 \, a c^{2} d^{3} e f^{2} g + 3 \, a^{2} c d^{2} e^{2} f g^{2} - a^{3} d e^{3} g^{3} + {\left(c^{3} d^{3} e f^{3} - 3 \, a c^{2} d^{2} e^{2} f^{2} g + 3 \, a^{2} c d e^{3} f g^{2} - a^{3} e^{4} g^{3}\right)} x\right)} \sqrt{c d g} \log\left(-\frac{8 \, c^{2} d^{2} e g^{2} x^{3} + c^{2} d^{3} f^{2} + 6 \, a c d^{2} e f g + a^{2} d e^{2} g^{2} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d g x + c d f + a e g\right)} \sqrt{c d g} \sqrt{e x + d} \sqrt{g x + f} + 8 \, {\left(c^{2} d^{2} e f g + {\left(c^{2} d^{3} + a c d e^{2}\right)} g^{2}\right)} x^{2} + {\left(c^{2} d^{2} e f^{2} + 2 \, {\left(4 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f g + {\left(8 \, a c d^{2} e + a^{2} e^{3}\right)} g^{2}\right)} x}{e x + d}\right)}{96 \, {\left(c^{4} d^{4} e g x + c^{4} d^{5} g\right)}}, \frac{2 \, {\left(8 \, c^{3} d^{3} g^{3} x^{2} + 33 \, c^{3} d^{3} f^{2} g - 40 \, a c^{2} d^{2} e f g^{2} + 15 \, a^{2} c d e^{2} g^{3} + 2 \, {\left(13 \, c^{3} d^{3} f g^{2} - 5 \, a c^{2} d^{2} e g^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} - 15 \, {\left(c^{3} d^{4} f^{3} - 3 \, a c^{2} d^{3} e f^{2} g + 3 \, a^{2} c d^{2} e^{2} f g^{2} - a^{3} d e^{3} g^{3} + {\left(c^{3} d^{3} e f^{3} - 3 \, a c^{2} d^{2} e^{2} f^{2} g + 3 \, a^{2} c d e^{3} f g^{2} - a^{3} e^{4} g^{3}\right)} x\right)} \sqrt{-c d g} \arctan\left(\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{-c d g} \sqrt{e x + d} \sqrt{g x + f}}{2 \, c d e g x^{2} + c d^{2} f + a d e g + {\left(c d e f + {\left(2 \, c d^{2} + a e^{2}\right)} g\right)} x}\right)}{48 \, {\left(c^{4} d^{4} e g x + c^{4} d^{5} g\right)}}\right]"," ",0,"[1/96*(4*(8*c^3*d^3*g^3*x^2 + 33*c^3*d^3*f^2*g - 40*a*c^2*d^2*e*f*g^2 + 15*a^2*c*d*e^2*g^3 + 2*(13*c^3*d^3*f*g^2 - 5*a*c^2*d^2*e*g^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f) - 15*(c^3*d^4*f^3 - 3*a*c^2*d^3*e*f^2*g + 3*a^2*c*d^2*e^2*f*g^2 - a^3*d*e^3*g^3 + (c^3*d^3*e*f^3 - 3*a*c^2*d^2*e^2*f^2*g + 3*a^2*c*d*e^3*f*g^2 - a^3*e^4*g^3)*x)*sqrt(c*d*g)*log(-(8*c^2*d^2*e*g^2*x^3 + c^2*d^3*f^2 + 6*a*c*d^2*e*f*g + a^2*d*e^2*g^2 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*g*x + c*d*f + a*e*g)*sqrt(c*d*g)*sqrt(e*x + d)*sqrt(g*x + f) + 8*(c^2*d^2*e*f*g + (c^2*d^3 + a*c*d*e^2)*g^2)*x^2 + (c^2*d^2*e*f^2 + 2*(4*c^2*d^3 + 3*a*c*d*e^2)*f*g + (8*a*c*d^2*e + a^2*e^3)*g^2)*x)/(e*x + d)))/(c^4*d^4*e*g*x + c^4*d^5*g), 1/48*(2*(8*c^3*d^3*g^3*x^2 + 33*c^3*d^3*f^2*g - 40*a*c^2*d^2*e*f*g^2 + 15*a^2*c*d*e^2*g^3 + 2*(13*c^3*d^3*f*g^2 - 5*a*c^2*d^2*e*g^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f) - 15*(c^3*d^4*f^3 - 3*a*c^2*d^3*e*f^2*g + 3*a^2*c*d^2*e^2*f*g^2 - a^3*d*e^3*g^3 + (c^3*d^3*e*f^3 - 3*a*c^2*d^2*e^2*f^2*g + 3*a^2*c*d*e^3*f*g^2 - a^3*e^4*g^3)*x)*sqrt(-c*d*g)*arctan(2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-c*d*g)*sqrt(e*x + d)*sqrt(g*x + f)/(2*c*d*e*g*x^2 + c*d^2*f + a*d*e*g + (c*d*e*f + (2*c*d^2 + a*e^2)*g)*x)))/(c^4*d^4*e*g*x + c^4*d^5*g)]","A",0
713,1,655,0,1.236018," ","integrate((g*x+f)^(3/2)*(e*x+d)^(1/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(2 \, c^{2} d^{2} g^{2} x + 5 \, c^{2} d^{2} f g - 3 \, a c d e g^{2}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} + 3 \, {\left(c^{2} d^{3} f^{2} - 2 \, a c d^{2} e f g + a^{2} d e^{2} g^{2} + {\left(c^{2} d^{2} e f^{2} - 2 \, a c d e^{2} f g + a^{2} e^{3} g^{2}\right)} x\right)} \sqrt{c d g} \log\left(-\frac{8 \, c^{2} d^{2} e g^{2} x^{3} + c^{2} d^{3} f^{2} + 6 \, a c d^{2} e f g + a^{2} d e^{2} g^{2} + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d g x + c d f + a e g\right)} \sqrt{c d g} \sqrt{e x + d} \sqrt{g x + f} + 8 \, {\left(c^{2} d^{2} e f g + {\left(c^{2} d^{3} + a c d e^{2}\right)} g^{2}\right)} x^{2} + {\left(c^{2} d^{2} e f^{2} + 2 \, {\left(4 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f g + {\left(8 \, a c d^{2} e + a^{2} e^{3}\right)} g^{2}\right)} x}{e x + d}\right)}{16 \, {\left(c^{3} d^{3} e g x + c^{3} d^{4} g\right)}}, \frac{2 \, {\left(2 \, c^{2} d^{2} g^{2} x + 5 \, c^{2} d^{2} f g - 3 \, a c d e g^{2}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} - 3 \, {\left(c^{2} d^{3} f^{2} - 2 \, a c d^{2} e f g + a^{2} d e^{2} g^{2} + {\left(c^{2} d^{2} e f^{2} - 2 \, a c d e^{2} f g + a^{2} e^{3} g^{2}\right)} x\right)} \sqrt{-c d g} \arctan\left(\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{-c d g} \sqrt{e x + d} \sqrt{g x + f}}{2 \, c d e g x^{2} + c d^{2} f + a d e g + {\left(c d e f + {\left(2 \, c d^{2} + a e^{2}\right)} g\right)} x}\right)}{8 \, {\left(c^{3} d^{3} e g x + c^{3} d^{4} g\right)}}\right]"," ",0,"[1/16*(4*(2*c^2*d^2*g^2*x + 5*c^2*d^2*f*g - 3*a*c*d*e*g^2)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f) + 3*(c^2*d^3*f^2 - 2*a*c*d^2*e*f*g + a^2*d*e^2*g^2 + (c^2*d^2*e*f^2 - 2*a*c*d*e^2*f*g + a^2*e^3*g^2)*x)*sqrt(c*d*g)*log(-(8*c^2*d^2*e*g^2*x^3 + c^2*d^3*f^2 + 6*a*c*d^2*e*f*g + a^2*d*e^2*g^2 + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*g*x + c*d*f + a*e*g)*sqrt(c*d*g)*sqrt(e*x + d)*sqrt(g*x + f) + 8*(c^2*d^2*e*f*g + (c^2*d^3 + a*c*d*e^2)*g^2)*x^2 + (c^2*d^2*e*f^2 + 2*(4*c^2*d^3 + 3*a*c*d*e^2)*f*g + (8*a*c*d^2*e + a^2*e^3)*g^2)*x)/(e*x + d)))/(c^3*d^3*e*g*x + c^3*d^4*g), 1/8*(2*(2*c^2*d^2*g^2*x + 5*c^2*d^2*f*g - 3*a*c*d*e*g^2)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f) - 3*(c^2*d^3*f^2 - 2*a*c*d^2*e*f*g + a^2*d*e^2*g^2 + (c^2*d^2*e*f^2 - 2*a*c*d*e^2*f*g + a^2*e^3*g^2)*x)*sqrt(-c*d*g)*arctan(2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-c*d*g)*sqrt(e*x + d)*sqrt(g*x + f)/(2*c*d*e*g*x^2 + c*d^2*f + a*d*e*g + (c*d*e*f + (2*c*d^2 + a*e^2)*g)*x)))/(c^3*d^3*e*g*x + c^3*d^4*g)]","A",0
714,1,521,0,1.145178," ","integrate((g*x+f)^(1/2)*(e*x+d)^(1/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} c d g - {\left(c d^{2} f - a d e g + {\left(c d e f - a e^{2} g\right)} x\right)} \sqrt{c d g} \log\left(-\frac{8 \, c^{2} d^{2} e g^{2} x^{3} + c^{2} d^{3} f^{2} + 6 \, a c d^{2} e f g + a^{2} d e^{2} g^{2} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d g x + c d f + a e g\right)} \sqrt{c d g} \sqrt{e x + d} \sqrt{g x + f} + 8 \, {\left(c^{2} d^{2} e f g + {\left(c^{2} d^{3} + a c d e^{2}\right)} g^{2}\right)} x^{2} + {\left(c^{2} d^{2} e f^{2} + 2 \, {\left(4 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f g + {\left(8 \, a c d^{2} e + a^{2} e^{3}\right)} g^{2}\right)} x}{e x + d}\right)}{4 \, {\left(c^{2} d^{2} e g x + c^{2} d^{3} g\right)}}, \frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} c d g - {\left(c d^{2} f - a d e g + {\left(c d e f - a e^{2} g\right)} x\right)} \sqrt{-c d g} \arctan\left(\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{-c d g} \sqrt{e x + d} \sqrt{g x + f}}{2 \, c d e g x^{2} + c d^{2} f + a d e g + {\left(c d e f + {\left(2 \, c d^{2} + a e^{2}\right)} g\right)} x}\right)}{2 \, {\left(c^{2} d^{2} e g x + c^{2} d^{3} g\right)}}\right]"," ",0,"[1/4*(4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f)*c*d*g - (c*d^2*f - a*d*e*g + (c*d*e*f - a*e^2*g)*x)*sqrt(c*d*g)*log(-(8*c^2*d^2*e*g^2*x^3 + c^2*d^3*f^2 + 6*a*c*d^2*e*f*g + a^2*d*e^2*g^2 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*g*x + c*d*f + a*e*g)*sqrt(c*d*g)*sqrt(e*x + d)*sqrt(g*x + f) + 8*(c^2*d^2*e*f*g + (c^2*d^3 + a*c*d*e^2)*g^2)*x^2 + (c^2*d^2*e*f^2 + 2*(4*c^2*d^3 + 3*a*c*d*e^2)*f*g + (8*a*c*d^2*e + a^2*e^3)*g^2)*x)/(e*x + d)))/(c^2*d^2*e*g*x + c^2*d^3*g), 1/2*(2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f)*c*d*g - (c*d^2*f - a*d*e*g + (c*d*e*f - a*e^2*g)*x)*sqrt(-c*d*g)*arctan(2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-c*d*g)*sqrt(e*x + d)*sqrt(g*x + f)/(2*c*d*e*g*x^2 + c*d^2*f + a*d*e*g + (c*d*e*f + (2*c*d^2 + a*e^2)*g)*x)))/(c^2*d^2*e*g*x + c^2*d^3*g)]","A",0
715,1,343,0,1.044274," ","integrate((e*x+d)^(1/2)/(g*x+f)^(1/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{c d g} \log\left(-\frac{8 \, c^{2} d^{2} e g^{2} x^{3} + c^{2} d^{3} f^{2} + 6 \, a c d^{2} e f g + a^{2} d e^{2} g^{2} + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d g x + c d f + a e g\right)} \sqrt{c d g} \sqrt{e x + d} \sqrt{g x + f} + 8 \, {\left(c^{2} d^{2} e f g + {\left(c^{2} d^{3} + a c d e^{2}\right)} g^{2}\right)} x^{2} + {\left(c^{2} d^{2} e f^{2} + 2 \, {\left(4 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f g + {\left(8 \, a c d^{2} e + a^{2} e^{3}\right)} g^{2}\right)} x}{e x + d}\right)}{2 \, c d g}, -\frac{\sqrt{-c d g} \arctan\left(\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{-c d g} \sqrt{e x + d} \sqrt{g x + f}}{2 \, c d e g x^{2} + c d^{2} f + a d e g + {\left(c d e f + {\left(2 \, c d^{2} + a e^{2}\right)} g\right)} x}\right)}{c d g}\right]"," ",0,"[1/2*sqrt(c*d*g)*log(-(8*c^2*d^2*e*g^2*x^3 + c^2*d^3*f^2 + 6*a*c*d^2*e*f*g + a^2*d*e^2*g^2 + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*g*x + c*d*f + a*e*g)*sqrt(c*d*g)*sqrt(e*x + d)*sqrt(g*x + f) + 8*(c^2*d^2*e*f*g + (c^2*d^3 + a*c*d*e^2)*g^2)*x^2 + (c^2*d^2*e*f^2 + 2*(4*c^2*d^3 + 3*a*c*d*e^2)*f*g + (8*a*c*d^2*e + a^2*e^3)*g^2)*x)/(e*x + d))/(c*d*g), -sqrt(-c*d*g)*arctan(2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-c*d*g)*sqrt(e*x + d)*sqrt(g*x + f)/(2*c*d*e*g*x^2 + c*d^2*f + a*d*e*g + (c*d*e*f + (2*c*d^2 + a*e^2)*g)*x))/(c*d*g)]","A",0
716,1,114,0,0.425649," ","integrate((e*x+d)^(1/2)/(g*x+f)^(3/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f}}{c d^{2} f^{2} - a d e f g + {\left(c d e f g - a e^{2} g^{2}\right)} x^{2} + {\left(c d e f^{2} - a d e g^{2} + {\left(c d^{2} - a e^{2}\right)} f g\right)} x}"," ",0,"2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f)/(c*d^2*f^2 - a*d*e*f*g + (c*d*e*f*g - a*e^2*g^2)*x^2 + (c*d*e*f^2 - a*d*e*g^2 + (c*d^2 - a*e^2)*f*g)*x)","B",0
717,1,288,0,0.419768," ","integrate((e*x+d)^(1/2)/(g*x+f)^(5/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d g x + 3 \, c d f - a e g\right)} \sqrt{e x + d} \sqrt{g x + f}}{3 \, {\left(c^{2} d^{3} f^{4} - 2 \, a c d^{2} e f^{3} g + a^{2} d e^{2} f^{2} g^{2} + {\left(c^{2} d^{2} e f^{2} g^{2} - 2 \, a c d e^{2} f g^{3} + a^{2} e^{3} g^{4}\right)} x^{3} + {\left(2 \, c^{2} d^{2} e f^{3} g + a^{2} d e^{2} g^{4} + {\left(c^{2} d^{3} - 4 \, a c d e^{2}\right)} f^{2} g^{2} - 2 \, {\left(a c d^{2} e - a^{2} e^{3}\right)} f g^{3}\right)} x^{2} + {\left(c^{2} d^{2} e f^{4} + 2 \, a^{2} d e^{2} f g^{3} + 2 \, {\left(c^{2} d^{3} - a c d e^{2}\right)} f^{3} g - {\left(4 \, a c d^{2} e - a^{2} e^{3}\right)} f^{2} g^{2}\right)} x\right)}}"," ",0,"2/3*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*g*x + 3*c*d*f - a*e*g)*sqrt(e*x + d)*sqrt(g*x + f)/(c^2*d^3*f^4 - 2*a*c*d^2*e*f^3*g + a^2*d*e^2*f^2*g^2 + (c^2*d^2*e*f^2*g^2 - 2*a*c*d*e^2*f*g^3 + a^2*e^3*g^4)*x^3 + (2*c^2*d^2*e*f^3*g + a^2*d*e^2*g^4 + (c^2*d^3 - 4*a*c*d*e^2)*f^2*g^2 - 2*(a*c*d^2*e - a^2*e^3)*f*g^3)*x^2 + (c^2*d^2*e*f^4 + 2*a^2*d*e^2*f*g^3 + 2*(c^2*d^3 - a*c*d*e^2)*f^3*g - (4*a*c*d^2*e - a^2*e^3)*f^2*g^2)*x)","B",0
718,1,572,0,0.449518," ","integrate((e*x+d)^(1/2)/(g*x+f)^(7/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, c^{2} d^{2} g^{2} x^{2} + 15 \, c^{2} d^{2} f^{2} - 10 \, a c d e f g + 3 \, a^{2} e^{2} g^{2} + 4 \, {\left(5 \, c^{2} d^{2} f g - a c d e g^{2}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f}}{15 \, {\left(c^{3} d^{4} f^{6} - 3 \, a c^{2} d^{3} e f^{5} g + 3 \, a^{2} c d^{2} e^{2} f^{4} g^{2} - a^{3} d e^{3} f^{3} g^{3} + {\left(c^{3} d^{3} e f^{3} g^{3} - 3 \, a c^{2} d^{2} e^{2} f^{2} g^{4} + 3 \, a^{2} c d e^{3} f g^{5} - a^{3} e^{4} g^{6}\right)} x^{4} + {\left(3 \, c^{3} d^{3} e f^{4} g^{2} - a^{3} d e^{3} g^{6} + {\left(c^{3} d^{4} - 9 \, a c^{2} d^{2} e^{2}\right)} f^{3} g^{3} - 3 \, {\left(a c^{2} d^{3} e - 3 \, a^{2} c d e^{3}\right)} f^{2} g^{4} + 3 \, {\left(a^{2} c d^{2} e^{2} - a^{3} e^{4}\right)} f g^{5}\right)} x^{3} + 3 \, {\left(c^{3} d^{3} e f^{5} g - a^{3} d e^{3} f g^{5} + {\left(c^{3} d^{4} - 3 \, a c^{2} d^{2} e^{2}\right)} f^{4} g^{2} - 3 \, {\left(a c^{2} d^{3} e - a^{2} c d e^{3}\right)} f^{3} g^{3} + {\left(3 \, a^{2} c d^{2} e^{2} - a^{3} e^{4}\right)} f^{2} g^{4}\right)} x^{2} + {\left(c^{3} d^{3} e f^{6} - 3 \, a^{3} d e^{3} f^{2} g^{4} + 3 \, {\left(c^{3} d^{4} - a c^{2} d^{2} e^{2}\right)} f^{5} g - 3 \, {\left(3 \, a c^{2} d^{3} e - a^{2} c d e^{3}\right)} f^{4} g^{2} + {\left(9 \, a^{2} c d^{2} e^{2} - a^{3} e^{4}\right)} f^{3} g^{3}\right)} x\right)}}"," ",0,"2/15*(8*c^2*d^2*g^2*x^2 + 15*c^2*d^2*f^2 - 10*a*c*d*e*f*g + 3*a^2*e^2*g^2 + 4*(5*c^2*d^2*f*g - a*c*d*e*g^2)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f)/(c^3*d^4*f^6 - 3*a*c^2*d^3*e*f^5*g + 3*a^2*c*d^2*e^2*f^4*g^2 - a^3*d*e^3*f^3*g^3 + (c^3*d^3*e*f^3*g^3 - 3*a*c^2*d^2*e^2*f^2*g^4 + 3*a^2*c*d*e^3*f*g^5 - a^3*e^4*g^6)*x^4 + (3*c^3*d^3*e*f^4*g^2 - a^3*d*e^3*g^6 + (c^3*d^4 - 9*a*c^2*d^2*e^2)*f^3*g^3 - 3*(a*c^2*d^3*e - 3*a^2*c*d*e^3)*f^2*g^4 + 3*(a^2*c*d^2*e^2 - a^3*e^4)*f*g^5)*x^3 + 3*(c^3*d^3*e*f^5*g - a^3*d*e^3*f*g^5 + (c^3*d^4 - 3*a*c^2*d^2*e^2)*f^4*g^2 - 3*(a*c^2*d^3*e - a^2*c*d*e^3)*f^3*g^3 + (3*a^2*c*d^2*e^2 - a^3*e^4)*f^2*g^4)*x^2 + (c^3*d^3*e*f^6 - 3*a^3*d*e^3*f^2*g^4 + 3*(c^3*d^4 - a*c^2*d^2*e^2)*f^5*g - 3*(3*a*c^2*d^3*e - a^2*c*d*e^3)*f^4*g^2 + (9*a^2*c*d^2*e^2 - a^3*e^4)*f^3*g^3)*x)","B",0
719,1,953,0,0.455851," ","integrate((e*x+d)^(1/2)/(g*x+f)^(9/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(16 \, c^{3} d^{3} g^{3} x^{3} + 35 \, c^{3} d^{3} f^{3} - 35 \, a c^{2} d^{2} e f^{2} g + 21 \, a^{2} c d e^{2} f g^{2} - 5 \, a^{3} e^{3} g^{3} + 8 \, {\left(7 \, c^{3} d^{3} f g^{2} - a c^{2} d^{2} e g^{3}\right)} x^{2} + 2 \, {\left(35 \, c^{3} d^{3} f^{2} g - 14 \, a c^{2} d^{2} e f g^{2} + 3 \, a^{2} c d e^{2} g^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f}}{35 \, {\left(c^{4} d^{5} f^{8} - 4 \, a c^{3} d^{4} e f^{7} g + 6 \, a^{2} c^{2} d^{3} e^{2} f^{6} g^{2} - 4 \, a^{3} c d^{2} e^{3} f^{5} g^{3} + a^{4} d e^{4} f^{4} g^{4} + {\left(c^{4} d^{4} e f^{4} g^{4} - 4 \, a c^{3} d^{3} e^{2} f^{3} g^{5} + 6 \, a^{2} c^{2} d^{2} e^{3} f^{2} g^{6} - 4 \, a^{3} c d e^{4} f g^{7} + a^{4} e^{5} g^{8}\right)} x^{5} + {\left(4 \, c^{4} d^{4} e f^{5} g^{3} + a^{4} d e^{4} g^{8} + {\left(c^{4} d^{5} - 16 \, a c^{3} d^{3} e^{2}\right)} f^{4} g^{4} - 4 \, {\left(a c^{3} d^{4} e - 6 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{3} g^{5} + 2 \, {\left(3 \, a^{2} c^{2} d^{3} e^{2} - 8 \, a^{3} c d e^{4}\right)} f^{2} g^{6} - 4 \, {\left(a^{3} c d^{2} e^{3} - a^{4} e^{5}\right)} f g^{7}\right)} x^{4} + 2 \, {\left(3 \, c^{4} d^{4} e f^{6} g^{2} + 2 \, a^{4} d e^{4} f g^{7} + 2 \, {\left(c^{4} d^{5} - 6 \, a c^{3} d^{3} e^{2}\right)} f^{5} g^{3} - 2 \, {\left(4 \, a c^{3} d^{4} e - 9 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{4} g^{4} + 12 \, {\left(a^{2} c^{2} d^{3} e^{2} - a^{3} c d e^{4}\right)} f^{3} g^{5} - {\left(8 \, a^{3} c d^{2} e^{3} - 3 \, a^{4} e^{5}\right)} f^{2} g^{6}\right)} x^{3} + 2 \, {\left(2 \, c^{4} d^{4} e f^{7} g + 3 \, a^{4} d e^{4} f^{2} g^{6} + {\left(3 \, c^{4} d^{5} - 8 \, a c^{3} d^{3} e^{2}\right)} f^{6} g^{2} - 12 \, {\left(a c^{3} d^{4} e - a^{2} c^{2} d^{2} e^{3}\right)} f^{5} g^{3} + 2 \, {\left(9 \, a^{2} c^{2} d^{3} e^{2} - 4 \, a^{3} c d e^{4}\right)} f^{4} g^{4} - 2 \, {\left(6 \, a^{3} c d^{2} e^{3} - a^{4} e^{5}\right)} f^{3} g^{5}\right)} x^{2} + {\left(c^{4} d^{4} e f^{8} + 4 \, a^{4} d e^{4} f^{3} g^{5} + 4 \, {\left(c^{4} d^{5} - a c^{3} d^{3} e^{2}\right)} f^{7} g - 2 \, {\left(8 \, a c^{3} d^{4} e - 3 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{6} g^{2} + 4 \, {\left(6 \, a^{2} c^{2} d^{3} e^{2} - a^{3} c d e^{4}\right)} f^{5} g^{3} - {\left(16 \, a^{3} c d^{2} e^{3} - a^{4} e^{5}\right)} f^{4} g^{4}\right)} x\right)}}"," ",0,"2/35*(16*c^3*d^3*g^3*x^3 + 35*c^3*d^3*f^3 - 35*a*c^2*d^2*e*f^2*g + 21*a^2*c*d*e^2*f*g^2 - 5*a^3*e^3*g^3 + 8*(7*c^3*d^3*f*g^2 - a*c^2*d^2*e*g^3)*x^2 + 2*(35*c^3*d^3*f^2*g - 14*a*c^2*d^2*e*f*g^2 + 3*a^2*c*d*e^2*g^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f)/(c^4*d^5*f^8 - 4*a*c^3*d^4*e*f^7*g + 6*a^2*c^2*d^3*e^2*f^6*g^2 - 4*a^3*c*d^2*e^3*f^5*g^3 + a^4*d*e^4*f^4*g^4 + (c^4*d^4*e*f^4*g^4 - 4*a*c^3*d^3*e^2*f^3*g^5 + 6*a^2*c^2*d^2*e^3*f^2*g^6 - 4*a^3*c*d*e^4*f*g^7 + a^4*e^5*g^8)*x^5 + (4*c^4*d^4*e*f^5*g^3 + a^4*d*e^4*g^8 + (c^4*d^5 - 16*a*c^3*d^3*e^2)*f^4*g^4 - 4*(a*c^3*d^4*e - 6*a^2*c^2*d^2*e^3)*f^3*g^5 + 2*(3*a^2*c^2*d^3*e^2 - 8*a^3*c*d*e^4)*f^2*g^6 - 4*(a^3*c*d^2*e^3 - a^4*e^5)*f*g^7)*x^4 + 2*(3*c^4*d^4*e*f^6*g^2 + 2*a^4*d*e^4*f*g^7 + 2*(c^4*d^5 - 6*a*c^3*d^3*e^2)*f^5*g^3 - 2*(4*a*c^3*d^4*e - 9*a^2*c^2*d^2*e^3)*f^4*g^4 + 12*(a^2*c^2*d^3*e^2 - a^3*c*d*e^4)*f^3*g^5 - (8*a^3*c*d^2*e^3 - 3*a^4*e^5)*f^2*g^6)*x^3 + 2*(2*c^4*d^4*e*f^7*g + 3*a^4*d*e^4*f^2*g^6 + (3*c^4*d^5 - 8*a*c^3*d^3*e^2)*f^6*g^2 - 12*(a*c^3*d^4*e - a^2*c^2*d^2*e^3)*f^5*g^3 + 2*(9*a^2*c^2*d^3*e^2 - 4*a^3*c*d*e^4)*f^4*g^4 - 2*(6*a^3*c*d^2*e^3 - a^4*e^5)*f^3*g^5)*x^2 + (c^4*d^4*e*f^8 + 4*a^4*d*e^4*f^3*g^5 + 4*(c^4*d^5 - a*c^3*d^3*e^2)*f^7*g - 2*(8*a*c^3*d^4*e - 3*a^2*c^2*d^2*e^3)*f^6*g^2 + 4*(6*a^2*c^2*d^3*e^2 - a^3*c*d*e^4)*f^5*g^3 - (16*a^3*c*d^2*e^3 - a^4*e^5)*f^4*g^4)*x)","B",0
720,1,971,0,1.225710," ","integrate((e*x+d)^(3/2)*(g*x+f)^(5/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(2 \, c^{2} d^{2} g^{2} x^{2} - 8 \, c^{2} d^{2} f^{2} + 25 \, a c d e f g - 15 \, a^{2} e^{2} g^{2} + {\left(9 \, c^{2} d^{2} f g - 5 \, a c d e g^{2}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} + 15 \, {\left(a c^{2} d^{3} e f^{2} - 2 \, a^{2} c d^{2} e^{2} f g + a^{3} d e^{3} g^{2} + {\left(c^{3} d^{3} e f^{2} - 2 \, a c^{2} d^{2} e^{2} f g + a^{2} c d e^{3} g^{2}\right)} x^{2} + {\left({\left(c^{3} d^{4} + a c^{2} d^{2} e^{2}\right)} f^{2} - 2 \, {\left(a c^{2} d^{3} e + a^{2} c d e^{3}\right)} f g + {\left(a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} g^{2}\right)} x\right)} \sqrt{\frac{g}{c d}} \log\left(-\frac{8 \, c^{2} d^{2} e g^{2} x^{3} + c^{2} d^{3} f^{2} + 6 \, a c d^{2} e f g + a^{2} d e^{2} g^{2} + 8 \, {\left(c^{2} d^{2} e f g + {\left(c^{2} d^{3} + a c d e^{2}\right)} g^{2}\right)} x^{2} + 4 \, {\left(2 \, c^{2} d^{2} g x + c^{2} d^{2} f + a c d e g\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} \sqrt{\frac{g}{c d}} + {\left(c^{2} d^{2} e f^{2} + 2 \, {\left(4 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f g + {\left(8 \, a c d^{2} e + a^{2} e^{3}\right)} g^{2}\right)} x}{e x + d}\right)}{16 \, {\left(c^{4} d^{4} e x^{2} + a c^{3} d^{4} e + {\left(c^{4} d^{5} + a c^{3} d^{3} e^{2}\right)} x\right)}}, \frac{2 \, {\left(2 \, c^{2} d^{2} g^{2} x^{2} - 8 \, c^{2} d^{2} f^{2} + 25 \, a c d e f g - 15 \, a^{2} e^{2} g^{2} + {\left(9 \, c^{2} d^{2} f g - 5 \, a c d e g^{2}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} - 15 \, {\left(a c^{2} d^{3} e f^{2} - 2 \, a^{2} c d^{2} e^{2} f g + a^{3} d e^{3} g^{2} + {\left(c^{3} d^{3} e f^{2} - 2 \, a c^{2} d^{2} e^{2} f g + a^{2} c d e^{3} g^{2}\right)} x^{2} + {\left({\left(c^{3} d^{4} + a c^{2} d^{2} e^{2}\right)} f^{2} - 2 \, {\left(a c^{2} d^{3} e + a^{2} c d e^{3}\right)} f g + {\left(a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} g^{2}\right)} x\right)} \sqrt{-\frac{g}{c d}} \arctan\left(\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} c d \sqrt{-\frac{g}{c d}}}{2 \, c d e g x^{2} + c d^{2} f + a d e g + {\left(c d e f + {\left(2 \, c d^{2} + a e^{2}\right)} g\right)} x}\right)}{8 \, {\left(c^{4} d^{4} e x^{2} + a c^{3} d^{4} e + {\left(c^{4} d^{5} + a c^{3} d^{3} e^{2}\right)} x\right)}}\right]"," ",0,"[1/16*(4*(2*c^2*d^2*g^2*x^2 - 8*c^2*d^2*f^2 + 25*a*c*d*e*f*g - 15*a^2*e^2*g^2 + (9*c^2*d^2*f*g - 5*a*c*d*e*g^2)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f) + 15*(a*c^2*d^3*e*f^2 - 2*a^2*c*d^2*e^2*f*g + a^3*d*e^3*g^2 + (c^3*d^3*e*f^2 - 2*a*c^2*d^2*e^2*f*g + a^2*c*d*e^3*g^2)*x^2 + ((c^3*d^4 + a*c^2*d^2*e^2)*f^2 - 2*(a*c^2*d^3*e + a^2*c*d*e^3)*f*g + (a^2*c*d^2*e^2 + a^3*e^4)*g^2)*x)*sqrt(g/(c*d))*log(-(8*c^2*d^2*e*g^2*x^3 + c^2*d^3*f^2 + 6*a*c*d^2*e*f*g + a^2*d*e^2*g^2 + 8*(c^2*d^2*e*f*g + (c^2*d^3 + a*c*d*e^2)*g^2)*x^2 + 4*(2*c^2*d^2*g*x + c^2*d^2*f + a*c*d*e*g)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f)*sqrt(g/(c*d)) + (c^2*d^2*e*f^2 + 2*(4*c^2*d^3 + 3*a*c*d*e^2)*f*g + (8*a*c*d^2*e + a^2*e^3)*g^2)*x)/(e*x + d)))/(c^4*d^4*e*x^2 + a*c^3*d^4*e + (c^4*d^5 + a*c^3*d^3*e^2)*x), 1/8*(2*(2*c^2*d^2*g^2*x^2 - 8*c^2*d^2*f^2 + 25*a*c*d*e*f*g - 15*a^2*e^2*g^2 + (9*c^2*d^2*f*g - 5*a*c*d*e*g^2)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f) - 15*(a*c^2*d^3*e*f^2 - 2*a^2*c*d^2*e^2*f*g + a^3*d*e^3*g^2 + (c^3*d^3*e*f^2 - 2*a*c^2*d^2*e^2*f*g + a^2*c*d*e^3*g^2)*x^2 + ((c^3*d^4 + a*c^2*d^2*e^2)*f^2 - 2*(a*c^2*d^3*e + a^2*c*d*e^3)*f*g + (a^2*c*d^2*e^2 + a^3*e^4)*g^2)*x)*sqrt(-g/(c*d))*arctan(2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f)*c*d*sqrt(-g/(c*d))/(2*c*d*e*g*x^2 + c*d^2*f + a*d*e*g + (c*d*e*f + (2*c*d^2 + a*e^2)*g)*x)))/(c^4*d^4*e*x^2 + a*c^3*d^4*e + (c^4*d^5 + a*c^3*d^3*e^2)*x)]","A",0
721,1,725,0,1.139231," ","integrate((e*x+d)^(3/2)*(g*x+f)^(3/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d g x - 2 \, c d f + 3 \, a e g\right)} \sqrt{e x + d} \sqrt{g x + f} - 3 \, {\left(a c d^{2} e f - a^{2} d e^{2} g + {\left(c^{2} d^{2} e f - a c d e^{2} g\right)} x^{2} + {\left({\left(c^{2} d^{3} + a c d e^{2}\right)} f - {\left(a c d^{2} e + a^{2} e^{3}\right)} g\right)} x\right)} \sqrt{\frac{g}{c d}} \log\left(-\frac{8 \, c^{2} d^{2} e g^{2} x^{3} + c^{2} d^{3} f^{2} + 6 \, a c d^{2} e f g + a^{2} d e^{2} g^{2} + 8 \, {\left(c^{2} d^{2} e f g + {\left(c^{2} d^{3} + a c d e^{2}\right)} g^{2}\right)} x^{2} - 4 \, {\left(2 \, c^{2} d^{2} g x + c^{2} d^{2} f + a c d e g\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} \sqrt{\frac{g}{c d}} + {\left(c^{2} d^{2} e f^{2} + 2 \, {\left(4 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f g + {\left(8 \, a c d^{2} e + a^{2} e^{3}\right)} g^{2}\right)} x}{e x + d}\right)}{4 \, {\left(c^{3} d^{3} e x^{2} + a c^{2} d^{3} e + {\left(c^{3} d^{4} + a c^{2} d^{2} e^{2}\right)} x\right)}}, \frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d g x - 2 \, c d f + 3 \, a e g\right)} \sqrt{e x + d} \sqrt{g x + f} - 3 \, {\left(a c d^{2} e f - a^{2} d e^{2} g + {\left(c^{2} d^{2} e f - a c d e^{2} g\right)} x^{2} + {\left({\left(c^{2} d^{3} + a c d e^{2}\right)} f - {\left(a c d^{2} e + a^{2} e^{3}\right)} g\right)} x\right)} \sqrt{-\frac{g}{c d}} \arctan\left(\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} c d \sqrt{-\frac{g}{c d}}}{2 \, c d e g x^{2} + c d^{2} f + a d e g + {\left(c d e f + {\left(2 \, c d^{2} + a e^{2}\right)} g\right)} x}\right)}{2 \, {\left(c^{3} d^{3} e x^{2} + a c^{2} d^{3} e + {\left(c^{3} d^{4} + a c^{2} d^{2} e^{2}\right)} x\right)}}\right]"," ",0,"[1/4*(4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d*g*x - 2*c*d*f + 3*a*e*g)*sqrt(e*x + d)*sqrt(g*x + f) - 3*(a*c*d^2*e*f - a^2*d*e^2*g + (c^2*d^2*e*f - a*c*d*e^2*g)*x^2 + ((c^2*d^3 + a*c*d*e^2)*f - (a*c*d^2*e + a^2*e^3)*g)*x)*sqrt(g/(c*d))*log(-(8*c^2*d^2*e*g^2*x^3 + c^2*d^3*f^2 + 6*a*c*d^2*e*f*g + a^2*d*e^2*g^2 + 8*(c^2*d^2*e*f*g + (c^2*d^3 + a*c*d*e^2)*g^2)*x^2 - 4*(2*c^2*d^2*g*x + c^2*d^2*f + a*c*d*e*g)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f)*sqrt(g/(c*d)) + (c^2*d^2*e*f^2 + 2*(4*c^2*d^3 + 3*a*c*d*e^2)*f*g + (8*a*c*d^2*e + a^2*e^3)*g^2)*x)/(e*x + d)))/(c^3*d^3*e*x^2 + a*c^2*d^3*e + (c^3*d^4 + a*c^2*d^2*e^2)*x), 1/2*(2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d*g*x - 2*c*d*f + 3*a*e*g)*sqrt(e*x + d)*sqrt(g*x + f) - 3*(a*c*d^2*e*f - a^2*d*e^2*g + (c^2*d^2*e*f - a*c*d*e^2*g)*x^2 + ((c^2*d^3 + a*c*d*e^2)*f - (a*c*d^2*e + a^2*e^3)*g)*x)*sqrt(-g/(c*d))*arctan(2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f)*c*d*sqrt(-g/(c*d))/(2*c*d*e*g*x^2 + c*d^2*f + a*d*e*g + (c*d*e*f + (2*c*d^2 + a*e^2)*g)*x)))/(c^3*d^3*e*x^2 + a*c^2*d^3*e + (c^3*d^4 + a*c^2*d^2*e^2)*x)]","A",0
722,1,569,0,1.100114," ","integrate((e*x+d)^(3/2)*(g*x+f)^(1/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{\frac{g}{c d}} \log\left(-\frac{8 \, c^{2} d^{2} e g^{2} x^{3} + c^{2} d^{3} f^{2} + 6 \, a c d^{2} e f g + a^{2} d e^{2} g^{2} + 8 \, {\left(c^{2} d^{2} e f g + {\left(c^{2} d^{3} + a c d e^{2}\right)} g^{2}\right)} x^{2} + 4 \, {\left(2 \, c^{2} d^{2} g x + c^{2} d^{2} f + a c d e g\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} \sqrt{\frac{g}{c d}} + {\left(c^{2} d^{2} e f^{2} + 2 \, {\left(4 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f g + {\left(8 \, a c d^{2} e + a^{2} e^{3}\right)} g^{2}\right)} x}{e x + d}\right) - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f}}{2 \, {\left(c^{2} d^{2} e x^{2} + a c d^{2} e + {\left(c^{2} d^{3} + a c d e^{2}\right)} x\right)}}, -\frac{{\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{-\frac{g}{c d}} \arctan\left(\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} c d \sqrt{-\frac{g}{c d}}}{2 \, c d e g x^{2} + c d^{2} f + a d e g + {\left(c d e f + {\left(2 \, c d^{2} + a e^{2}\right)} g\right)} x}\right) + 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f}}{c^{2} d^{2} e x^{2} + a c d^{2} e + {\left(c^{2} d^{3} + a c d e^{2}\right)} x}\right]"," ",0,"[1/2*((c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(g/(c*d))*log(-(8*c^2*d^2*e*g^2*x^3 + c^2*d^3*f^2 + 6*a*c*d^2*e*f*g + a^2*d*e^2*g^2 + 8*(c^2*d^2*e*f*g + (c^2*d^3 + a*c*d*e^2)*g^2)*x^2 + 4*(2*c^2*d^2*g*x + c^2*d^2*f + a*c*d*e*g)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f)*sqrt(g/(c*d)) + (c^2*d^2*e*f^2 + 2*(4*c^2*d^3 + 3*a*c*d*e^2)*f*g + (8*a*c*d^2*e + a^2*e^3)*g^2)*x)/(e*x + d)) - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f))/(c^2*d^2*e*x^2 + a*c*d^2*e + (c^2*d^3 + a*c*d*e^2)*x), -((c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-g/(c*d))*arctan(2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f)*c*d*sqrt(-g/(c*d))/(2*c*d*e*g*x^2 + c*d^2*f + a*d*e*g + (c*d*e*f + (2*c*d^2 + a*e^2)*g)*x)) + 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f))/(c^2*d^2*e*x^2 + a*c*d^2*e + (c^2*d^3 + a*c*d*e^2)*x)]","A",0
723,1,125,0,0.440924," ","integrate((e*x+d)^(3/2)/(g*x+f)^(1/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f}}{a c d^{2} e f - a^{2} d e^{2} g + {\left(c^{2} d^{2} e f - a c d e^{2} g\right)} x^{2} + {\left({\left(c^{2} d^{3} + a c d e^{2}\right)} f - {\left(a c d^{2} e + a^{2} e^{3}\right)} g\right)} x}"," ",0,"-2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f)/(a*c*d^2*e*f - a^2*d*e^2*g + (c^2*d^2*e*f - a*c*d*e^2*g)*x^2 + ((c^2*d^3 + a*c*d*e^2)*f - (a*c*d^2*e + a^2*e^3)*g)*x)","B",0
724,1,325,0,0.436237," ","integrate((e*x+d)^(3/2)/(g*x+f)^(3/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d g x + c d f + a e g\right)} \sqrt{e x + d} \sqrt{g x + f}}{a c^{2} d^{3} e f^{3} - 2 \, a^{2} c d^{2} e^{2} f^{2} g + a^{3} d e^{3} f g^{2} + {\left(c^{3} d^{3} e f^{2} g - 2 \, a c^{2} d^{2} e^{2} f g^{2} + a^{2} c d e^{3} g^{3}\right)} x^{3} + {\left(c^{3} d^{3} e f^{3} + {\left(c^{3} d^{4} - a c^{2} d^{2} e^{2}\right)} f^{2} g - {\left(2 \, a c^{2} d^{3} e + a^{2} c d e^{3}\right)} f g^{2} + {\left(a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} g^{3}\right)} x^{2} + {\left(a^{3} d e^{3} g^{3} + {\left(c^{3} d^{4} + a c^{2} d^{2} e^{2}\right)} f^{3} - {\left(a c^{2} d^{3} e + 2 \, a^{2} c d e^{3}\right)} f^{2} g - {\left(a^{2} c d^{2} e^{2} - a^{3} e^{4}\right)} f g^{2}\right)} x}"," ",0,"-2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*g*x + c*d*f + a*e*g)*sqrt(e*x + d)*sqrt(g*x + f)/(a*c^2*d^3*e*f^3 - 2*a^2*c*d^2*e^2*f^2*g + a^3*d*e^3*f*g^2 + (c^3*d^3*e*f^2*g - 2*a*c^2*d^2*e^2*f*g^2 + a^2*c*d*e^3*g^3)*x^3 + (c^3*d^3*e*f^3 + (c^3*d^4 - a*c^2*d^2*e^2)*f^2*g - (2*a*c^2*d^3*e + a^2*c*d*e^3)*f*g^2 + (a^2*c*d^2*e^2 + a^3*e^4)*g^3)*x^2 + (a^3*d*e^3*g^3 + (c^3*d^4 + a*c^2*d^2*e^2)*f^3 - (a*c^2*d^3*e + 2*a^2*c*d*e^3)*f^2*g - (a^2*c*d^2*e^2 - a^3*e^4)*f*g^2)*x)","B",0
725,1,649,0,0.457824," ","integrate((e*x+d)^(3/2)/(g*x+f)^(5/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(8 \, c^{2} d^{2} g^{2} x^{2} + 3 \, c^{2} d^{2} f^{2} + 6 \, a c d e f g - a^{2} e^{2} g^{2} + 4 \, {\left(3 \, c^{2} d^{2} f g + a c d e g^{2}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f}}{3 \, {\left(a c^{3} d^{4} e f^{5} - 3 \, a^{2} c^{2} d^{3} e^{2} f^{4} g + 3 \, a^{3} c d^{2} e^{3} f^{3} g^{2} - a^{4} d e^{4} f^{2} g^{3} + {\left(c^{4} d^{4} e f^{3} g^{2} - 3 \, a c^{3} d^{3} e^{2} f^{2} g^{3} + 3 \, a^{2} c^{2} d^{2} e^{3} f g^{4} - a^{3} c d e^{4} g^{5}\right)} x^{4} + {\left(2 \, c^{4} d^{4} e f^{4} g + {\left(c^{4} d^{5} - 5 \, a c^{3} d^{3} e^{2}\right)} f^{3} g^{2} - 3 \, {\left(a c^{3} d^{4} e - a^{2} c^{2} d^{2} e^{3}\right)} f^{2} g^{3} + {\left(3 \, a^{2} c^{2} d^{3} e^{2} + a^{3} c d e^{4}\right)} f g^{4} - {\left(a^{3} c d^{2} e^{3} + a^{4} e^{5}\right)} g^{5}\right)} x^{3} + {\left(c^{4} d^{4} e f^{5} - a^{4} d e^{4} g^{5} + {\left(2 \, c^{4} d^{5} - a c^{3} d^{3} e^{2}\right)} f^{4} g - {\left(5 \, a c^{3} d^{4} e + 3 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{3} g^{2} + {\left(3 \, a^{2} c^{2} d^{3} e^{2} + 5 \, a^{3} c d e^{4}\right)} f^{2} g^{3} + {\left(a^{3} c d^{2} e^{3} - 2 \, a^{4} e^{5}\right)} f g^{4}\right)} x^{2} - {\left(2 \, a^{4} d e^{4} f g^{4} - {\left(c^{4} d^{5} + a c^{3} d^{3} e^{2}\right)} f^{5} + {\left(a c^{3} d^{4} e + 3 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{4} g + 3 \, {\left(a^{2} c^{2} d^{3} e^{2} - a^{3} c d e^{4}\right)} f^{3} g^{2} - {\left(5 \, a^{3} c d^{2} e^{3} - a^{4} e^{5}\right)} f^{2} g^{3}\right)} x\right)}}"," ",0,"-2/3*(8*c^2*d^2*g^2*x^2 + 3*c^2*d^2*f^2 + 6*a*c*d*e*f*g - a^2*e^2*g^2 + 4*(3*c^2*d^2*f*g + a*c*d*e*g^2)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f)/(a*c^3*d^4*e*f^5 - 3*a^2*c^2*d^3*e^2*f^4*g + 3*a^3*c*d^2*e^3*f^3*g^2 - a^4*d*e^4*f^2*g^3 + (c^4*d^4*e*f^3*g^2 - 3*a*c^3*d^3*e^2*f^2*g^3 + 3*a^2*c^2*d^2*e^3*f*g^4 - a^3*c*d*e^4*g^5)*x^4 + (2*c^4*d^4*e*f^4*g + (c^4*d^5 - 5*a*c^3*d^3*e^2)*f^3*g^2 - 3*(a*c^3*d^4*e - a^2*c^2*d^2*e^3)*f^2*g^3 + (3*a^2*c^2*d^3*e^2 + a^3*c*d*e^4)*f*g^4 - (a^3*c*d^2*e^3 + a^4*e^5)*g^5)*x^3 + (c^4*d^4*e*f^5 - a^4*d*e^4*g^5 + (2*c^4*d^5 - a*c^3*d^3*e^2)*f^4*g - (5*a*c^3*d^4*e + 3*a^2*c^2*d^2*e^3)*f^3*g^2 + (3*a^2*c^2*d^3*e^2 + 5*a^3*c*d*e^4)*f^2*g^3 + (a^3*c*d^2*e^3 - 2*a^4*e^5)*f*g^4)*x^2 - (2*a^4*d*e^4*f*g^4 - (c^4*d^5 + a*c^3*d^3*e^2)*f^5 + (a*c^3*d^4*e + 3*a^2*c^2*d^2*e^3)*f^4*g + 3*(a^2*c^2*d^3*e^2 - a^3*c*d*e^4)*f^3*g^2 - (5*a^3*c*d^2*e^3 - a^4*e^5)*f^2*g^3)*x)","B",0
726,1,1062,0,0.512616," ","integrate((e*x+d)^(3/2)/(g*x+f)^(7/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(16 \, c^{3} d^{3} g^{3} x^{3} + 5 \, c^{3} d^{3} f^{3} + 15 \, a c^{2} d^{2} e f^{2} g - 5 \, a^{2} c d e^{2} f g^{2} + a^{3} e^{3} g^{3} + 8 \, {\left(5 \, c^{3} d^{3} f g^{2} + a c^{2} d^{2} e g^{3}\right)} x^{2} + 2 \, {\left(15 \, c^{3} d^{3} f^{2} g + 10 \, a c^{2} d^{2} e f g^{2} - a^{2} c d e^{2} g^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f}}{5 \, {\left(a c^{4} d^{5} e f^{7} - 4 \, a^{2} c^{3} d^{4} e^{2} f^{6} g + 6 \, a^{3} c^{2} d^{3} e^{3} f^{5} g^{2} - 4 \, a^{4} c d^{2} e^{4} f^{4} g^{3} + a^{5} d e^{5} f^{3} g^{4} + {\left(c^{5} d^{5} e f^{4} g^{3} - 4 \, a c^{4} d^{4} e^{2} f^{3} g^{4} + 6 \, a^{2} c^{3} d^{3} e^{3} f^{2} g^{5} - 4 \, a^{3} c^{2} d^{2} e^{4} f g^{6} + a^{4} c d e^{5} g^{7}\right)} x^{5} + {\left(3 \, c^{5} d^{5} e f^{5} g^{2} + {\left(c^{5} d^{6} - 11 \, a c^{4} d^{4} e^{2}\right)} f^{4} g^{3} - 2 \, {\left(2 \, a c^{4} d^{5} e - 7 \, a^{2} c^{3} d^{3} e^{3}\right)} f^{3} g^{4} + 6 \, {\left(a^{2} c^{3} d^{4} e^{2} - a^{3} c^{2} d^{2} e^{4}\right)} f^{2} g^{5} - {\left(4 \, a^{3} c^{2} d^{3} e^{3} + a^{4} c d e^{5}\right)} f g^{6} + {\left(a^{4} c d^{2} e^{4} + a^{5} e^{6}\right)} g^{7}\right)} x^{4} + {\left(3 \, c^{5} d^{5} e f^{6} g + a^{5} d e^{5} g^{7} + 3 \, {\left(c^{5} d^{6} - 3 \, a c^{4} d^{4} e^{2}\right)} f^{5} g^{2} - {\left(11 \, a c^{4} d^{5} e - 6 \, a^{2} c^{3} d^{3} e^{3}\right)} f^{4} g^{3} + 2 \, {\left(7 \, a^{2} c^{3} d^{4} e^{2} + 3 \, a^{3} c^{2} d^{2} e^{4}\right)} f^{3} g^{4} - 3 \, {\left(2 \, a^{3} c^{2} d^{3} e^{3} + 3 \, a^{4} c d e^{5}\right)} f^{2} g^{5} - {\left(a^{4} c d^{2} e^{4} - 3 \, a^{5} e^{6}\right)} f g^{6}\right)} x^{3} + {\left(c^{5} d^{5} e f^{7} + 3 \, a^{5} d e^{5} f g^{6} + {\left(3 \, c^{5} d^{6} - a c^{4} d^{4} e^{2}\right)} f^{6} g - 3 \, {\left(3 \, a c^{4} d^{5} e + 2 \, a^{2} c^{3} d^{3} e^{3}\right)} f^{5} g^{2} + 2 \, {\left(3 \, a^{2} c^{3} d^{4} e^{2} + 7 \, a^{3} c^{2} d^{2} e^{4}\right)} f^{4} g^{3} + {\left(6 \, a^{3} c^{2} d^{3} e^{3} - 11 \, a^{4} c d e^{5}\right)} f^{3} g^{4} - 3 \, {\left(3 \, a^{4} c d^{2} e^{4} - a^{5} e^{6}\right)} f^{2} g^{5}\right)} x^{2} + {\left(3 \, a^{5} d e^{5} f^{2} g^{5} + {\left(c^{5} d^{6} + a c^{4} d^{4} e^{2}\right)} f^{7} - {\left(a c^{4} d^{5} e + 4 \, a^{2} c^{3} d^{3} e^{3}\right)} f^{6} g - 6 \, {\left(a^{2} c^{3} d^{4} e^{2} - a^{3} c^{2} d^{2} e^{4}\right)} f^{5} g^{2} + 2 \, {\left(7 \, a^{3} c^{2} d^{3} e^{3} - 2 \, a^{4} c d e^{5}\right)} f^{4} g^{3} - {\left(11 \, a^{4} c d^{2} e^{4} - a^{5} e^{6}\right)} f^{3} g^{4}\right)} x\right)}}"," ",0,"-2/5*(16*c^3*d^3*g^3*x^3 + 5*c^3*d^3*f^3 + 15*a*c^2*d^2*e*f^2*g - 5*a^2*c*d*e^2*f*g^2 + a^3*e^3*g^3 + 8*(5*c^3*d^3*f*g^2 + a*c^2*d^2*e*g^3)*x^2 + 2*(15*c^3*d^3*f^2*g + 10*a*c^2*d^2*e*f*g^2 - a^2*c*d*e^2*g^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f)/(a*c^4*d^5*e*f^7 - 4*a^2*c^3*d^4*e^2*f^6*g + 6*a^3*c^2*d^3*e^3*f^5*g^2 - 4*a^4*c*d^2*e^4*f^4*g^3 + a^5*d*e^5*f^3*g^4 + (c^5*d^5*e*f^4*g^3 - 4*a*c^4*d^4*e^2*f^3*g^4 + 6*a^2*c^3*d^3*e^3*f^2*g^5 - 4*a^3*c^2*d^2*e^4*f*g^6 + a^4*c*d*e^5*g^7)*x^5 + (3*c^5*d^5*e*f^5*g^2 + (c^5*d^6 - 11*a*c^4*d^4*e^2)*f^4*g^3 - 2*(2*a*c^4*d^5*e - 7*a^2*c^3*d^3*e^3)*f^3*g^4 + 6*(a^2*c^3*d^4*e^2 - a^3*c^2*d^2*e^4)*f^2*g^5 - (4*a^3*c^2*d^3*e^3 + a^4*c*d*e^5)*f*g^6 + (a^4*c*d^2*e^4 + a^5*e^6)*g^7)*x^4 + (3*c^5*d^5*e*f^6*g + a^5*d*e^5*g^7 + 3*(c^5*d^6 - 3*a*c^4*d^4*e^2)*f^5*g^2 - (11*a*c^4*d^5*e - 6*a^2*c^3*d^3*e^3)*f^4*g^3 + 2*(7*a^2*c^3*d^4*e^2 + 3*a^3*c^2*d^2*e^4)*f^3*g^4 - 3*(2*a^3*c^2*d^3*e^3 + 3*a^4*c*d*e^5)*f^2*g^5 - (a^4*c*d^2*e^4 - 3*a^5*e^6)*f*g^6)*x^3 + (c^5*d^5*e*f^7 + 3*a^5*d*e^5*f*g^6 + (3*c^5*d^6 - a*c^4*d^4*e^2)*f^6*g - 3*(3*a*c^4*d^5*e + 2*a^2*c^3*d^3*e^3)*f^5*g^2 + 2*(3*a^2*c^3*d^4*e^2 + 7*a^3*c^2*d^2*e^4)*f^4*g^3 + (6*a^3*c^2*d^3*e^3 - 11*a^4*c*d*e^5)*f^3*g^4 - 3*(3*a^4*c*d^2*e^4 - a^5*e^6)*f^2*g^5)*x^2 + (3*a^5*d*e^5*f^2*g^5 + (c^5*d^6 + a*c^4*d^4*e^2)*f^7 - (a*c^4*d^5*e + 4*a^2*c^3*d^3*e^3)*f^6*g - 6*(a^2*c^3*d^4*e^2 - a^3*c^2*d^2*e^4)*f^5*g^2 + 2*(7*a^3*c^2*d^3*e^3 - 2*a^4*c*d*e^5)*f^4*g^3 - (11*a^4*c*d^2*e^4 - a^5*e^6)*f^3*g^4)*x)","B",0
727,1,1055,0,1.153049," ","integrate((e*x+d)^(5/2)*(g*x+f)^(5/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(3 \, c^{2} d^{2} g^{2} x^{2} - 2 \, c^{2} d^{2} f^{2} - 10 \, a c d e f g + 15 \, a^{2} e^{2} g^{2} - 2 \, {\left(7 \, c^{2} d^{2} f g - 10 \, a c d e g^{2}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} - 15 \, {\left(a^{2} c d^{2} e^{2} f g - a^{3} d e^{3} g^{2} + {\left(c^{3} d^{3} e f g - a c^{2} d^{2} e^{2} g^{2}\right)} x^{3} + {\left({\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2}\right)} f g - {\left(a c^{2} d^{3} e + 2 \, a^{2} c d e^{3}\right)} g^{2}\right)} x^{2} + {\left({\left(2 \, a c^{2} d^{3} e + a^{2} c d e^{3}\right)} f g - {\left(2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} g^{2}\right)} x\right)} \sqrt{\frac{g}{c d}} \log\left(-\frac{8 \, c^{2} d^{2} e g^{2} x^{3} + c^{2} d^{3} f^{2} + 6 \, a c d^{2} e f g + a^{2} d e^{2} g^{2} + 8 \, {\left(c^{2} d^{2} e f g + {\left(c^{2} d^{3} + a c d e^{2}\right)} g^{2}\right)} x^{2} - 4 \, {\left(2 \, c^{2} d^{2} g x + c^{2} d^{2} f + a c d e g\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} \sqrt{\frac{g}{c d}} + {\left(c^{2} d^{2} e f^{2} + 2 \, {\left(4 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f g + {\left(8 \, a c d^{2} e + a^{2} e^{3}\right)} g^{2}\right)} x}{e x + d}\right)}{12 \, {\left(c^{5} d^{5} e x^{3} + a^{2} c^{3} d^{4} e^{2} + {\left(c^{5} d^{6} + 2 \, a c^{4} d^{4} e^{2}\right)} x^{2} + {\left(2 \, a c^{4} d^{5} e + a^{2} c^{3} d^{3} e^{3}\right)} x\right)}}, \frac{2 \, {\left(3 \, c^{2} d^{2} g^{2} x^{2} - 2 \, c^{2} d^{2} f^{2} - 10 \, a c d e f g + 15 \, a^{2} e^{2} g^{2} - 2 \, {\left(7 \, c^{2} d^{2} f g - 10 \, a c d e g^{2}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} - 15 \, {\left(a^{2} c d^{2} e^{2} f g - a^{3} d e^{3} g^{2} + {\left(c^{3} d^{3} e f g - a c^{2} d^{2} e^{2} g^{2}\right)} x^{3} + {\left({\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2}\right)} f g - {\left(a c^{2} d^{3} e + 2 \, a^{2} c d e^{3}\right)} g^{2}\right)} x^{2} + {\left({\left(2 \, a c^{2} d^{3} e + a^{2} c d e^{3}\right)} f g - {\left(2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} g^{2}\right)} x\right)} \sqrt{-\frac{g}{c d}} \arctan\left(\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} c d \sqrt{-\frac{g}{c d}}}{2 \, c d e g x^{2} + c d^{2} f + a d e g + {\left(c d e f + {\left(2 \, c d^{2} + a e^{2}\right)} g\right)} x}\right)}{6 \, {\left(c^{5} d^{5} e x^{3} + a^{2} c^{3} d^{4} e^{2} + {\left(c^{5} d^{6} + 2 \, a c^{4} d^{4} e^{2}\right)} x^{2} + {\left(2 \, a c^{4} d^{5} e + a^{2} c^{3} d^{3} e^{3}\right)} x\right)}}\right]"," ",0,"[1/12*(4*(3*c^2*d^2*g^2*x^2 - 2*c^2*d^2*f^2 - 10*a*c*d*e*f*g + 15*a^2*e^2*g^2 - 2*(7*c^2*d^2*f*g - 10*a*c*d*e*g^2)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f) - 15*(a^2*c*d^2*e^2*f*g - a^3*d*e^3*g^2 + (c^3*d^3*e*f*g - a*c^2*d^2*e^2*g^2)*x^3 + ((c^3*d^4 + 2*a*c^2*d^2*e^2)*f*g - (a*c^2*d^3*e + 2*a^2*c*d*e^3)*g^2)*x^2 + ((2*a*c^2*d^3*e + a^2*c*d*e^3)*f*g - (2*a^2*c*d^2*e^2 + a^3*e^4)*g^2)*x)*sqrt(g/(c*d))*log(-(8*c^2*d^2*e*g^2*x^3 + c^2*d^3*f^2 + 6*a*c*d^2*e*f*g + a^2*d*e^2*g^2 + 8*(c^2*d^2*e*f*g + (c^2*d^3 + a*c*d*e^2)*g^2)*x^2 - 4*(2*c^2*d^2*g*x + c^2*d^2*f + a*c*d*e*g)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f)*sqrt(g/(c*d)) + (c^2*d^2*e*f^2 + 2*(4*c^2*d^3 + 3*a*c*d*e^2)*f*g + (8*a*c*d^2*e + a^2*e^3)*g^2)*x)/(e*x + d)))/(c^5*d^5*e*x^3 + a^2*c^3*d^4*e^2 + (c^5*d^6 + 2*a*c^4*d^4*e^2)*x^2 + (2*a*c^4*d^5*e + a^2*c^3*d^3*e^3)*x), 1/6*(2*(3*c^2*d^2*g^2*x^2 - 2*c^2*d^2*f^2 - 10*a*c*d*e*f*g + 15*a^2*e^2*g^2 - 2*(7*c^2*d^2*f*g - 10*a*c*d*e*g^2)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f) - 15*(a^2*c*d^2*e^2*f*g - a^3*d*e^3*g^2 + (c^3*d^3*e*f*g - a*c^2*d^2*e^2*g^2)*x^3 + ((c^3*d^4 + 2*a*c^2*d^2*e^2)*f*g - (a*c^2*d^3*e + 2*a^2*c*d*e^3)*g^2)*x^2 + ((2*a*c^2*d^3*e + a^2*c*d*e^3)*f*g - (2*a^2*c*d^2*e^2 + a^3*e^4)*g^2)*x)*sqrt(-g/(c*d))*arctan(2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f)*c*d*sqrt(-g/(c*d))/(2*c*d*e*g*x^2 + c*d^2*f + a*d*e*g + (c*d*e*f + (2*c*d^2 + a*e^2)*g)*x)))/(c^5*d^5*e*x^3 + a^2*c^3*d^4*e^2 + (c^5*d^6 + 2*a*c^4*d^4*e^2)*x^2 + (2*a*c^4*d^5*e + a^2*c^3*d^3*e^3)*x)]","A",0
728,1,755,0,1.125656," ","integrate((e*x+d)^(5/2)*(g*x+f)^(3/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""fricas"")","\left[-\frac{4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(4 \, c d g x + c d f + 3 \, a e g\right)} \sqrt{e x + d} \sqrt{g x + f} - 3 \, {\left(c^{2} d^{2} e g x^{3} + a^{2} d e^{2} g + {\left(c^{2} d^{3} + 2 \, a c d e^{2}\right)} g x^{2} + {\left(2 \, a c d^{2} e + a^{2} e^{3}\right)} g x\right)} \sqrt{\frac{g}{c d}} \log\left(-\frac{8 \, c^{2} d^{2} e g^{2} x^{3} + c^{2} d^{3} f^{2} + 6 \, a c d^{2} e f g + a^{2} d e^{2} g^{2} + 8 \, {\left(c^{2} d^{2} e f g + {\left(c^{2} d^{3} + a c d e^{2}\right)} g^{2}\right)} x^{2} + 4 \, {\left(2 \, c^{2} d^{2} g x + c^{2} d^{2} f + a c d e g\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} \sqrt{\frac{g}{c d}} + {\left(c^{2} d^{2} e f^{2} + 2 \, {\left(4 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f g + {\left(8 \, a c d^{2} e + a^{2} e^{3}\right)} g^{2}\right)} x}{e x + d}\right)}{6 \, {\left(c^{4} d^{4} e x^{3} + a^{2} c^{2} d^{3} e^{2} + {\left(c^{4} d^{5} + 2 \, a c^{3} d^{3} e^{2}\right)} x^{2} + {\left(2 \, a c^{3} d^{4} e + a^{2} c^{2} d^{2} e^{3}\right)} x\right)}}, -\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(4 \, c d g x + c d f + 3 \, a e g\right)} \sqrt{e x + d} \sqrt{g x + f} + 3 \, {\left(c^{2} d^{2} e g x^{3} + a^{2} d e^{2} g + {\left(c^{2} d^{3} + 2 \, a c d e^{2}\right)} g x^{2} + {\left(2 \, a c d^{2} e + a^{2} e^{3}\right)} g x\right)} \sqrt{-\frac{g}{c d}} \arctan\left(\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} c d \sqrt{-\frac{g}{c d}}}{2 \, c d e g x^{2} + c d^{2} f + a d e g + {\left(c d e f + {\left(2 \, c d^{2} + a e^{2}\right)} g\right)} x}\right)}{3 \, {\left(c^{4} d^{4} e x^{3} + a^{2} c^{2} d^{3} e^{2} + {\left(c^{4} d^{5} + 2 \, a c^{3} d^{3} e^{2}\right)} x^{2} + {\left(2 \, a c^{3} d^{4} e + a^{2} c^{2} d^{2} e^{3}\right)} x\right)}}\right]"," ",0,"[-1/6*(4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(4*c*d*g*x + c*d*f + 3*a*e*g)*sqrt(e*x + d)*sqrt(g*x + f) - 3*(c^2*d^2*e*g*x^3 + a^2*d*e^2*g + (c^2*d^3 + 2*a*c*d*e^2)*g*x^2 + (2*a*c*d^2*e + a^2*e^3)*g*x)*sqrt(g/(c*d))*log(-(8*c^2*d^2*e*g^2*x^3 + c^2*d^3*f^2 + 6*a*c*d^2*e*f*g + a^2*d*e^2*g^2 + 8*(c^2*d^2*e*f*g + (c^2*d^3 + a*c*d*e^2)*g^2)*x^2 + 4*(2*c^2*d^2*g*x + c^2*d^2*f + a*c*d*e*g)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f)*sqrt(g/(c*d)) + (c^2*d^2*e*f^2 + 2*(4*c^2*d^3 + 3*a*c*d*e^2)*f*g + (8*a*c*d^2*e + a^2*e^3)*g^2)*x)/(e*x + d)))/(c^4*d^4*e*x^3 + a^2*c^2*d^3*e^2 + (c^4*d^5 + 2*a*c^3*d^3*e^2)*x^2 + (2*a*c^3*d^4*e + a^2*c^2*d^2*e^3)*x), -1/3*(2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(4*c*d*g*x + c*d*f + 3*a*e*g)*sqrt(e*x + d)*sqrt(g*x + f) + 3*(c^2*d^2*e*g*x^3 + a^2*d*e^2*g + (c^2*d^3 + 2*a*c*d*e^2)*g*x^2 + (2*a*c*d^2*e + a^2*e^3)*g*x)*sqrt(-g/(c*d))*arctan(2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f)*c*d*sqrt(-g/(c*d))/(2*c*d*e*g*x^2 + c*d^2*f + a*d*e*g + (c*d*e*f + (2*c*d^2 + a*e^2)*g)*x)))/(c^4*d^4*e*x^3 + a^2*c^2*d^3*e^2 + (c^4*d^5 + 2*a*c^3*d^3*e^2)*x^2 + (2*a*c^3*d^4*e + a^2*c^2*d^2*e^3)*x)]","A",0
729,1,193,0,0.414402," ","integrate((e*x+d)^(5/2)*(g*x+f)^(1/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} {\left(g x + f\right)}^{\frac{3}{2}}}{3 \, {\left(a^{2} c d^{2} e^{2} f - a^{3} d e^{3} g + {\left(c^{3} d^{3} e f - a c^{2} d^{2} e^{2} g\right)} x^{3} + {\left({\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2}\right)} f - {\left(a c^{2} d^{3} e + 2 \, a^{2} c d e^{3}\right)} g\right)} x^{2} + {\left({\left(2 \, a c^{2} d^{3} e + a^{2} c d e^{3}\right)} f - {\left(2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} g\right)} x\right)}}"," ",0,"-2/3*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*(g*x + f)^(3/2)/(a^2*c*d^2*e^2*f - a^3*d*e^3*g + (c^3*d^3*e*f - a*c^2*d^2*e^2*g)*x^3 + ((c^3*d^4 + 2*a*c^2*d^2*e^2)*f - (a*c^2*d^3*e + 2*a^2*c*d*e^3)*g)*x^2 + ((2*a*c^2*d^3*e + a^2*c*d*e^3)*f - (2*a^2*c*d^2*e^2 + a^3*e^4)*g)*x)","B",0
730,1,318,0,0.453197," ","integrate((e*x+d)^(5/2)/(g*x+f)^(1/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d g x - c d f + 3 \, a e g\right)} \sqrt{e x + d} \sqrt{g x + f}}{3 \, {\left(a^{2} c^{2} d^{3} e^{2} f^{2} - 2 \, a^{3} c d^{2} e^{3} f g + a^{4} d e^{4} g^{2} + {\left(c^{4} d^{4} e f^{2} - 2 \, a c^{3} d^{3} e^{2} f g + a^{2} c^{2} d^{2} e^{3} g^{2}\right)} x^{3} + {\left({\left(c^{4} d^{5} + 2 \, a c^{3} d^{3} e^{2}\right)} f^{2} - 2 \, {\left(a c^{3} d^{4} e + 2 \, a^{2} c^{2} d^{2} e^{3}\right)} f g + {\left(a^{2} c^{2} d^{3} e^{2} + 2 \, a^{3} c d e^{4}\right)} g^{2}\right)} x^{2} + {\left({\left(2 \, a c^{3} d^{4} e + a^{2} c^{2} d^{2} e^{3}\right)} f^{2} - 2 \, {\left(2 \, a^{2} c^{2} d^{3} e^{2} + a^{3} c d e^{4}\right)} f g + {\left(2 \, a^{3} c d^{2} e^{3} + a^{4} e^{5}\right)} g^{2}\right)} x\right)}}"," ",0,"2/3*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*g*x - c*d*f + 3*a*e*g)*sqrt(e*x + d)*sqrt(g*x + f)/(a^2*c^2*d^3*e^2*f^2 - 2*a^3*c*d^2*e^3*f*g + a^4*d*e^4*g^2 + (c^4*d^4*e*f^2 - 2*a*c^3*d^3*e^2*f*g + a^2*c^2*d^2*e^3*g^2)*x^3 + ((c^4*d^5 + 2*a*c^3*d^3*e^2)*f^2 - 2*(a*c^3*d^4*e + 2*a^2*c^2*d^2*e^3)*f*g + (a^2*c^2*d^3*e^2 + 2*a^3*c*d*e^4)*g^2)*x^2 + ((2*a*c^3*d^4*e + a^2*c^2*d^2*e^3)*f^2 - 2*(2*a^2*c^2*d^3*e^2 + a^3*c*d*e^4)*f*g + (2*a^3*c*d^2*e^3 + a^4*e^5)*g^2)*x)","B",0
731,1,667,0,0.453105," ","integrate((e*x+d)^(5/2)/(g*x+f)^(3/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, c^{2} d^{2} g^{2} x^{2} - c^{2} d^{2} f^{2} + 6 \, a c d e f g + 3 \, a^{2} e^{2} g^{2} + 4 \, {\left(c^{2} d^{2} f g + 3 \, a c d e g^{2}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f}}{3 \, {\left(a^{2} c^{3} d^{4} e^{2} f^{4} - 3 \, a^{3} c^{2} d^{3} e^{3} f^{3} g + 3 \, a^{4} c d^{2} e^{4} f^{2} g^{2} - a^{5} d e^{5} f g^{3} + {\left(c^{5} d^{5} e f^{3} g - 3 \, a c^{4} d^{4} e^{2} f^{2} g^{2} + 3 \, a^{2} c^{3} d^{3} e^{3} f g^{3} - a^{3} c^{2} d^{2} e^{4} g^{4}\right)} x^{4} + {\left(c^{5} d^{5} e f^{4} + {\left(c^{5} d^{6} - a c^{4} d^{4} e^{2}\right)} f^{3} g - 3 \, {\left(a c^{4} d^{5} e + a^{2} c^{3} d^{3} e^{3}\right)} f^{2} g^{2} + {\left(3 \, a^{2} c^{3} d^{4} e^{2} + 5 \, a^{3} c^{2} d^{2} e^{4}\right)} f g^{3} - {\left(a^{3} c^{2} d^{3} e^{3} + 2 \, a^{4} c d e^{5}\right)} g^{4}\right)} x^{3} + {\left({\left(c^{5} d^{6} + 2 \, a c^{4} d^{4} e^{2}\right)} f^{4} - {\left(a c^{4} d^{5} e + 5 \, a^{2} c^{3} d^{3} e^{3}\right)} f^{3} g - 3 \, {\left(a^{2} c^{3} d^{4} e^{2} - a^{3} c^{2} d^{2} e^{4}\right)} f^{2} g^{2} + {\left(5 \, a^{3} c^{2} d^{3} e^{3} + a^{4} c d e^{5}\right)} f g^{3} - {\left(2 \, a^{4} c d^{2} e^{4} + a^{5} e^{6}\right)} g^{4}\right)} x^{2} - {\left(a^{5} d e^{5} g^{4} - {\left(2 \, a c^{4} d^{5} e + a^{2} c^{3} d^{3} e^{3}\right)} f^{4} + {\left(5 \, a^{2} c^{3} d^{4} e^{2} + 3 \, a^{3} c^{2} d^{2} e^{4}\right)} f^{3} g - 3 \, {\left(a^{3} c^{2} d^{3} e^{3} + a^{4} c d e^{5}\right)} f^{2} g^{2} - {\left(a^{4} c d^{2} e^{4} - a^{5} e^{6}\right)} f g^{3}\right)} x\right)}}"," ",0,"2/3*(8*c^2*d^2*g^2*x^2 - c^2*d^2*f^2 + 6*a*c*d*e*f*g + 3*a^2*e^2*g^2 + 4*(c^2*d^2*f*g + 3*a*c*d*e*g^2)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f)/(a^2*c^3*d^4*e^2*f^4 - 3*a^3*c^2*d^3*e^3*f^3*g + 3*a^4*c*d^2*e^4*f^2*g^2 - a^5*d*e^5*f*g^3 + (c^5*d^5*e*f^3*g - 3*a*c^4*d^4*e^2*f^2*g^2 + 3*a^2*c^3*d^3*e^3*f*g^3 - a^3*c^2*d^2*e^4*g^4)*x^4 + (c^5*d^5*e*f^4 + (c^5*d^6 - a*c^4*d^4*e^2)*f^3*g - 3*(a*c^4*d^5*e + a^2*c^3*d^3*e^3)*f^2*g^2 + (3*a^2*c^3*d^4*e^2 + 5*a^3*c^2*d^2*e^4)*f*g^3 - (a^3*c^2*d^3*e^3 + 2*a^4*c*d*e^5)*g^4)*x^3 + ((c^5*d^6 + 2*a*c^4*d^4*e^2)*f^4 - (a*c^4*d^5*e + 5*a^2*c^3*d^3*e^3)*f^3*g - 3*(a^2*c^3*d^4*e^2 - a^3*c^2*d^2*e^4)*f^2*g^2 + (5*a^3*c^2*d^3*e^3 + a^4*c*d*e^5)*f*g^3 - (2*a^4*c*d^2*e^4 + a^5*e^6)*g^4)*x^2 - (a^5*d*e^5*g^4 - (2*a*c^4*d^5*e + a^2*c^3*d^3*e^3)*f^4 + (5*a^2*c^3*d^4*e^2 + 3*a^3*c^2*d^2*e^4)*f^3*g - 3*(a^3*c^2*d^3*e^3 + a^4*c*d*e^5)*f^2*g^2 - (a^4*c*d^2*e^4 - a^5*e^6)*f*g^3)*x)","B",0
732,1,1065,0,0.509872," ","integrate((e*x+d)^(5/2)/(g*x+f)^(5/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(16 \, c^{3} d^{3} g^{3} x^{3} - c^{3} d^{3} f^{3} + 9 \, a c^{2} d^{2} e f^{2} g + 9 \, a^{2} c d e^{2} f g^{2} - a^{3} e^{3} g^{3} + 24 \, {\left(c^{3} d^{3} f g^{2} + a c^{2} d^{2} e g^{3}\right)} x^{2} + 6 \, {\left(c^{3} d^{3} f^{2} g + 6 \, a c^{2} d^{2} e f g^{2} + a^{2} c d e^{2} g^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f}}{3 \, {\left(a^{2} c^{4} d^{5} e^{2} f^{6} - 4 \, a^{3} c^{3} d^{4} e^{3} f^{5} g + 6 \, a^{4} c^{2} d^{3} e^{4} f^{4} g^{2} - 4 \, a^{5} c d^{2} e^{5} f^{3} g^{3} + a^{6} d e^{6} f^{2} g^{4} + {\left(c^{6} d^{6} e f^{4} g^{2} - 4 \, a c^{5} d^{5} e^{2} f^{3} g^{3} + 6 \, a^{2} c^{4} d^{4} e^{3} f^{2} g^{4} - 4 \, a^{3} c^{3} d^{3} e^{4} f g^{5} + a^{4} c^{2} d^{2} e^{5} g^{6}\right)} x^{5} + {\left(2 \, c^{6} d^{6} e f^{5} g + {\left(c^{6} d^{7} - 6 \, a c^{5} d^{5} e^{2}\right)} f^{4} g^{2} - 4 \, {\left(a c^{5} d^{6} e - a^{2} c^{4} d^{4} e^{3}\right)} f^{3} g^{3} + 2 \, {\left(3 \, a^{2} c^{4} d^{5} e^{2} + 2 \, a^{3} c^{3} d^{3} e^{4}\right)} f^{2} g^{4} - 2 \, {\left(2 \, a^{3} c^{3} d^{4} e^{3} + 3 \, a^{4} c^{2} d^{2} e^{5}\right)} f g^{5} + {\left(a^{4} c^{2} d^{3} e^{4} + 2 \, a^{5} c d e^{6}\right)} g^{6}\right)} x^{4} + {\left(c^{6} d^{6} e f^{6} + 2 \, c^{6} d^{7} f^{5} g - 6 \, a^{4} c^{2} d^{3} e^{4} f g^{5} - 3 \, {\left(2 \, a c^{5} d^{6} e + 3 \, a^{2} c^{4} d^{4} e^{3}\right)} f^{4} g^{2} + 4 \, {\left(a^{2} c^{4} d^{5} e^{2} + 4 \, a^{3} c^{3} d^{3} e^{4}\right)} f^{3} g^{3} + {\left(4 \, a^{3} c^{3} d^{4} e^{3} - 9 \, a^{4} c^{2} d^{2} e^{5}\right)} f^{2} g^{4} + {\left(2 \, a^{5} c d^{2} e^{5} + a^{6} e^{7}\right)} g^{6}\right)} x^{3} - {\left(6 \, a^{2} c^{4} d^{4} e^{3} f^{5} g - 2 \, a^{6} e^{7} f g^{5} - a^{6} d e^{6} g^{6} - {\left(c^{6} d^{7} + 2 \, a c^{5} d^{5} e^{2}\right)} f^{6} + {\left(9 \, a^{2} c^{4} d^{5} e^{2} - 4 \, a^{3} c^{3} d^{3} e^{4}\right)} f^{4} g^{2} - 4 \, {\left(4 \, a^{3} c^{3} d^{4} e^{3} + a^{4} c^{2} d^{2} e^{5}\right)} f^{3} g^{3} + 3 \, {\left(3 \, a^{4} c^{2} d^{3} e^{4} + 2 \, a^{5} c d e^{6}\right)} f^{2} g^{4}\right)} x^{2} + {\left(2 \, a^{6} d e^{6} f g^{5} + {\left(2 \, a c^{5} d^{6} e + a^{2} c^{4} d^{4} e^{3}\right)} f^{6} - 2 \, {\left(3 \, a^{2} c^{4} d^{5} e^{2} + 2 \, a^{3} c^{3} d^{3} e^{4}\right)} f^{5} g + 2 \, {\left(2 \, a^{3} c^{3} d^{4} e^{3} + 3 \, a^{4} c^{2} d^{2} e^{5}\right)} f^{4} g^{2} + 4 \, {\left(a^{4} c^{2} d^{3} e^{4} - a^{5} c d e^{6}\right)} f^{3} g^{3} - {\left(6 \, a^{5} c d^{2} e^{5} - a^{6} e^{7}\right)} f^{2} g^{4}\right)} x\right)}}"," ",0,"2/3*(16*c^3*d^3*g^3*x^3 - c^3*d^3*f^3 + 9*a*c^2*d^2*e*f^2*g + 9*a^2*c*d*e^2*f*g^2 - a^3*e^3*g^3 + 24*(c^3*d^3*f*g^2 + a*c^2*d^2*e*g^3)*x^2 + 6*(c^3*d^3*f^2*g + 6*a*c^2*d^2*e*f*g^2 + a^2*c*d*e^2*g^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f)/(a^2*c^4*d^5*e^2*f^6 - 4*a^3*c^3*d^4*e^3*f^5*g + 6*a^4*c^2*d^3*e^4*f^4*g^2 - 4*a^5*c*d^2*e^5*f^3*g^3 + a^6*d*e^6*f^2*g^4 + (c^6*d^6*e*f^4*g^2 - 4*a*c^5*d^5*e^2*f^3*g^3 + 6*a^2*c^4*d^4*e^3*f^2*g^4 - 4*a^3*c^3*d^3*e^4*f*g^5 + a^4*c^2*d^2*e^5*g^6)*x^5 + (2*c^6*d^6*e*f^5*g + (c^6*d^7 - 6*a*c^5*d^5*e^2)*f^4*g^2 - 4*(a*c^5*d^6*e - a^2*c^4*d^4*e^3)*f^3*g^3 + 2*(3*a^2*c^4*d^5*e^2 + 2*a^3*c^3*d^3*e^4)*f^2*g^4 - 2*(2*a^3*c^3*d^4*e^3 + 3*a^4*c^2*d^2*e^5)*f*g^5 + (a^4*c^2*d^3*e^4 + 2*a^5*c*d*e^6)*g^6)*x^4 + (c^6*d^6*e*f^6 + 2*c^6*d^7*f^5*g - 6*a^4*c^2*d^3*e^4*f*g^5 - 3*(2*a*c^5*d^6*e + 3*a^2*c^4*d^4*e^3)*f^4*g^2 + 4*(a^2*c^4*d^5*e^2 + 4*a^3*c^3*d^3*e^4)*f^3*g^3 + (4*a^3*c^3*d^4*e^3 - 9*a^4*c^2*d^2*e^5)*f^2*g^4 + (2*a^5*c*d^2*e^5 + a^6*e^7)*g^6)*x^3 - (6*a^2*c^4*d^4*e^3*f^5*g - 2*a^6*e^7*f*g^5 - a^6*d*e^6*g^6 - (c^6*d^7 + 2*a*c^5*d^5*e^2)*f^6 + (9*a^2*c^4*d^5*e^2 - 4*a^3*c^3*d^3*e^4)*f^4*g^2 - 4*(4*a^3*c^3*d^4*e^3 + a^4*c^2*d^2*e^5)*f^3*g^3 + 3*(3*a^4*c^2*d^3*e^4 + 2*a^5*c*d*e^6)*f^2*g^4)*x^2 + (2*a^6*d*e^6*f*g^5 + (2*a*c^5*d^6*e + a^2*c^4*d^4*e^3)*f^6 - 2*(3*a^2*c^4*d^5*e^2 + 2*a^3*c^3*d^3*e^4)*f^5*g + 2*(2*a^3*c^3*d^4*e^3 + 3*a^4*c^2*d^2*e^5)*f^4*g^2 + 4*(a^4*c^2*d^3*e^4 - a^5*c*d*e^6)*f^3*g^3 - (6*a^5*c*d^2*e^5 - a^6*e^7)*f^2*g^4)*x)","B",0
733,1,1065,0,2.691199," ","integrate((g*x+f)^(5/2)*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(48 \, c^{4} d^{4} g^{4} x^{3} + 15 \, c^{4} d^{4} f^{3} g + 73 \, a c^{3} d^{3} e f^{2} g^{2} - 55 \, a^{2} c^{2} d^{2} e^{2} f g^{3} + 15 \, a^{3} c d e^{3} g^{4} + 8 \, {\left(17 \, c^{4} d^{4} f g^{3} + a c^{3} d^{3} e g^{4}\right)} x^{2} + 2 \, {\left(59 \, c^{4} d^{4} f^{2} g^{2} + 18 \, a c^{3} d^{3} e f g^{3} - 5 \, a^{2} c^{2} d^{2} e^{2} g^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} + 15 \, {\left(c^{4} d^{5} f^{4} - 4 \, a c^{3} d^{4} e f^{3} g + 6 \, a^{2} c^{2} d^{3} e^{2} f^{2} g^{2} - 4 \, a^{3} c d^{2} e^{3} f g^{3} + a^{4} d e^{4} g^{4} + {\left(c^{4} d^{4} e f^{4} - 4 \, a c^{3} d^{3} e^{2} f^{3} g + 6 \, a^{2} c^{2} d^{2} e^{3} f^{2} g^{2} - 4 \, a^{3} c d e^{4} f g^{3} + a^{4} e^{5} g^{4}\right)} x\right)} \sqrt{c d g} \log\left(-\frac{8 \, c^{2} d^{2} e g^{2} x^{3} + c^{2} d^{3} f^{2} + 6 \, a c d^{2} e f g + a^{2} d e^{2} g^{2} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d g x + c d f + a e g\right)} \sqrt{c d g} \sqrt{e x + d} \sqrt{g x + f} + 8 \, {\left(c^{2} d^{2} e f g + {\left(c^{2} d^{3} + a c d e^{2}\right)} g^{2}\right)} x^{2} + {\left(c^{2} d^{2} e f^{2} + 2 \, {\left(4 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f g + {\left(8 \, a c d^{2} e + a^{2} e^{3}\right)} g^{2}\right)} x}{e x + d}\right)}{768 \, {\left(c^{4} d^{4} e g^{2} x + c^{4} d^{5} g^{2}\right)}}, \frac{2 \, {\left(48 \, c^{4} d^{4} g^{4} x^{3} + 15 \, c^{4} d^{4} f^{3} g + 73 \, a c^{3} d^{3} e f^{2} g^{2} - 55 \, a^{2} c^{2} d^{2} e^{2} f g^{3} + 15 \, a^{3} c d e^{3} g^{4} + 8 \, {\left(17 \, c^{4} d^{4} f g^{3} + a c^{3} d^{3} e g^{4}\right)} x^{2} + 2 \, {\left(59 \, c^{4} d^{4} f^{2} g^{2} + 18 \, a c^{3} d^{3} e f g^{3} - 5 \, a^{2} c^{2} d^{2} e^{2} g^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} + 15 \, {\left(c^{4} d^{5} f^{4} - 4 \, a c^{3} d^{4} e f^{3} g + 6 \, a^{2} c^{2} d^{3} e^{2} f^{2} g^{2} - 4 \, a^{3} c d^{2} e^{3} f g^{3} + a^{4} d e^{4} g^{4} + {\left(c^{4} d^{4} e f^{4} - 4 \, a c^{3} d^{3} e^{2} f^{3} g + 6 \, a^{2} c^{2} d^{2} e^{3} f^{2} g^{2} - 4 \, a^{3} c d e^{4} f g^{3} + a^{4} e^{5} g^{4}\right)} x\right)} \sqrt{-c d g} \arctan\left(\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{-c d g} \sqrt{e x + d} \sqrt{g x + f}}{2 \, c d e g x^{2} + c d^{2} f + a d e g + {\left(c d e f + {\left(2 \, c d^{2} + a e^{2}\right)} g\right)} x}\right)}{384 \, {\left(c^{4} d^{4} e g^{2} x + c^{4} d^{5} g^{2}\right)}}\right]"," ",0,"[1/768*(4*(48*c^4*d^4*g^4*x^3 + 15*c^4*d^4*f^3*g + 73*a*c^3*d^3*e*f^2*g^2 - 55*a^2*c^2*d^2*e^2*f*g^3 + 15*a^3*c*d*e^3*g^4 + 8*(17*c^4*d^4*f*g^3 + a*c^3*d^3*e*g^4)*x^2 + 2*(59*c^4*d^4*f^2*g^2 + 18*a*c^3*d^3*e*f*g^3 - 5*a^2*c^2*d^2*e^2*g^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f) + 15*(c^4*d^5*f^4 - 4*a*c^3*d^4*e*f^3*g + 6*a^2*c^2*d^3*e^2*f^2*g^2 - 4*a^3*c*d^2*e^3*f*g^3 + a^4*d*e^4*g^4 + (c^4*d^4*e*f^4 - 4*a*c^3*d^3*e^2*f^3*g + 6*a^2*c^2*d^2*e^3*f^2*g^2 - 4*a^3*c*d*e^4*f*g^3 + a^4*e^5*g^4)*x)*sqrt(c*d*g)*log(-(8*c^2*d^2*e*g^2*x^3 + c^2*d^3*f^2 + 6*a*c*d^2*e*f*g + a^2*d*e^2*g^2 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*g*x + c*d*f + a*e*g)*sqrt(c*d*g)*sqrt(e*x + d)*sqrt(g*x + f) + 8*(c^2*d^2*e*f*g + (c^2*d^3 + a*c*d*e^2)*g^2)*x^2 + (c^2*d^2*e*f^2 + 2*(4*c^2*d^3 + 3*a*c*d*e^2)*f*g + (8*a*c*d^2*e + a^2*e^3)*g^2)*x)/(e*x + d)))/(c^4*d^4*e*g^2*x + c^4*d^5*g^2), 1/384*(2*(48*c^4*d^4*g^4*x^3 + 15*c^4*d^4*f^3*g + 73*a*c^3*d^3*e*f^2*g^2 - 55*a^2*c^2*d^2*e^2*f*g^3 + 15*a^3*c*d*e^3*g^4 + 8*(17*c^4*d^4*f*g^3 + a*c^3*d^3*e*g^4)*x^2 + 2*(59*c^4*d^4*f^2*g^2 + 18*a*c^3*d^3*e*f*g^3 - 5*a^2*c^2*d^2*e^2*g^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f) + 15*(c^4*d^5*f^4 - 4*a*c^3*d^4*e*f^3*g + 6*a^2*c^2*d^3*e^2*f^2*g^2 - 4*a^3*c*d^2*e^3*f*g^3 + a^4*d*e^4*g^4 + (c^4*d^4*e*f^4 - 4*a*c^3*d^3*e^2*f^3*g + 6*a^2*c^2*d^2*e^3*f^2*g^2 - 4*a^3*c*d*e^4*f*g^3 + a^4*e^5*g^4)*x)*sqrt(-c*d*g)*arctan(2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-c*d*g)*sqrt(e*x + d)*sqrt(g*x + f)/(2*c*d*e*g*x^2 + c*d^2*f + a*d*e*g + (c*d*e*f + (2*c*d^2 + a*e^2)*g)*x)))/(c^4*d^4*e*g^2*x + c^4*d^5*g^2)]","A",0
734,1,847,0,1.500658," ","integrate((g*x+f)^(3/2)*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(8 \, c^{3} d^{3} g^{3} x^{2} + 3 \, c^{3} d^{3} f^{2} g + 8 \, a c^{2} d^{2} e f g^{2} - 3 \, a^{2} c d e^{2} g^{3} + 2 \, {\left(7 \, c^{3} d^{3} f g^{2} + a c^{2} d^{2} e g^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} - 3 \, {\left(c^{3} d^{4} f^{3} - 3 \, a c^{2} d^{3} e f^{2} g + 3 \, a^{2} c d^{2} e^{2} f g^{2} - a^{3} d e^{3} g^{3} + {\left(c^{3} d^{3} e f^{3} - 3 \, a c^{2} d^{2} e^{2} f^{2} g + 3 \, a^{2} c d e^{3} f g^{2} - a^{3} e^{4} g^{3}\right)} x\right)} \sqrt{c d g} \log\left(-\frac{8 \, c^{2} d^{2} e g^{2} x^{3} + c^{2} d^{3} f^{2} + 6 \, a c d^{2} e f g + a^{2} d e^{2} g^{2} + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d g x + c d f + a e g\right)} \sqrt{c d g} \sqrt{e x + d} \sqrt{g x + f} + 8 \, {\left(c^{2} d^{2} e f g + {\left(c^{2} d^{3} + a c d e^{2}\right)} g^{2}\right)} x^{2} + {\left(c^{2} d^{2} e f^{2} + 2 \, {\left(4 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f g + {\left(8 \, a c d^{2} e + a^{2} e^{3}\right)} g^{2}\right)} x}{e x + d}\right)}{96 \, {\left(c^{3} d^{3} e g^{2} x + c^{3} d^{4} g^{2}\right)}}, \frac{2 \, {\left(8 \, c^{3} d^{3} g^{3} x^{2} + 3 \, c^{3} d^{3} f^{2} g + 8 \, a c^{2} d^{2} e f g^{2} - 3 \, a^{2} c d e^{2} g^{3} + 2 \, {\left(7 \, c^{3} d^{3} f g^{2} + a c^{2} d^{2} e g^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} + 3 \, {\left(c^{3} d^{4} f^{3} - 3 \, a c^{2} d^{3} e f^{2} g + 3 \, a^{2} c d^{2} e^{2} f g^{2} - a^{3} d e^{3} g^{3} + {\left(c^{3} d^{3} e f^{3} - 3 \, a c^{2} d^{2} e^{2} f^{2} g + 3 \, a^{2} c d e^{3} f g^{2} - a^{3} e^{4} g^{3}\right)} x\right)} \sqrt{-c d g} \arctan\left(\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{-c d g} \sqrt{e x + d} \sqrt{g x + f}}{2 \, c d e g x^{2} + c d^{2} f + a d e g + {\left(c d e f + {\left(2 \, c d^{2} + a e^{2}\right)} g\right)} x}\right)}{48 \, {\left(c^{3} d^{3} e g^{2} x + c^{3} d^{4} g^{2}\right)}}\right]"," ",0,"[1/96*(4*(8*c^3*d^3*g^3*x^2 + 3*c^3*d^3*f^2*g + 8*a*c^2*d^2*e*f*g^2 - 3*a^2*c*d*e^2*g^3 + 2*(7*c^3*d^3*f*g^2 + a*c^2*d^2*e*g^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f) - 3*(c^3*d^4*f^3 - 3*a*c^2*d^3*e*f^2*g + 3*a^2*c*d^2*e^2*f*g^2 - a^3*d*e^3*g^3 + (c^3*d^3*e*f^3 - 3*a*c^2*d^2*e^2*f^2*g + 3*a^2*c*d*e^3*f*g^2 - a^3*e^4*g^3)*x)*sqrt(c*d*g)*log(-(8*c^2*d^2*e*g^2*x^3 + c^2*d^3*f^2 + 6*a*c*d^2*e*f*g + a^2*d*e^2*g^2 + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*g*x + c*d*f + a*e*g)*sqrt(c*d*g)*sqrt(e*x + d)*sqrt(g*x + f) + 8*(c^2*d^2*e*f*g + (c^2*d^3 + a*c*d*e^2)*g^2)*x^2 + (c^2*d^2*e*f^2 + 2*(4*c^2*d^3 + 3*a*c*d*e^2)*f*g + (8*a*c*d^2*e + a^2*e^3)*g^2)*x)/(e*x + d)))/(c^3*d^3*e*g^2*x + c^3*d^4*g^2), 1/48*(2*(8*c^3*d^3*g^3*x^2 + 3*c^3*d^3*f^2*g + 8*a*c^2*d^2*e*f*g^2 - 3*a^2*c*d*e^2*g^3 + 2*(7*c^3*d^3*f*g^2 + a*c^2*d^2*e*g^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f) + 3*(c^3*d^4*f^3 - 3*a*c^2*d^3*e*f^2*g + 3*a^2*c*d^2*e^2*f*g^2 - a^3*d*e^3*g^3 + (c^3*d^3*e*f^3 - 3*a*c^2*d^2*e^2*f^2*g + 3*a^2*c*d*e^3*f*g^2 - a^3*e^4*g^3)*x)*sqrt(-c*d*g)*arctan(2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-c*d*g)*sqrt(e*x + d)*sqrt(g*x + f)/(2*c*d*e*g*x^2 + c*d^2*f + a*d*e*g + (c*d*e*f + (2*c*d^2 + a*e^2)*g)*x)))/(c^3*d^3*e*g^2*x + c^3*d^4*g^2)]","A",0
735,1,657,0,1.201542," ","integrate((g*x+f)^(1/2)*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(2 \, c^{2} d^{2} g^{2} x + c^{2} d^{2} f g + a c d e g^{2}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} + {\left(c^{2} d^{3} f^{2} - 2 \, a c d^{2} e f g + a^{2} d e^{2} g^{2} + {\left(c^{2} d^{2} e f^{2} - 2 \, a c d e^{2} f g + a^{2} e^{3} g^{2}\right)} x\right)} \sqrt{c d g} \log\left(-\frac{8 \, c^{2} d^{2} e g^{2} x^{3} + c^{2} d^{3} f^{2} + 6 \, a c d^{2} e f g + a^{2} d e^{2} g^{2} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d g x + c d f + a e g\right)} \sqrt{c d g} \sqrt{e x + d} \sqrt{g x + f} + 8 \, {\left(c^{2} d^{2} e f g + {\left(c^{2} d^{3} + a c d e^{2}\right)} g^{2}\right)} x^{2} + {\left(c^{2} d^{2} e f^{2} + 2 \, {\left(4 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f g + {\left(8 \, a c d^{2} e + a^{2} e^{3}\right)} g^{2}\right)} x}{e x + d}\right)}{16 \, {\left(c^{2} d^{2} e g^{2} x + c^{2} d^{3} g^{2}\right)}}, \frac{2 \, {\left(2 \, c^{2} d^{2} g^{2} x + c^{2} d^{2} f g + a c d e g^{2}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} + {\left(c^{2} d^{3} f^{2} - 2 \, a c d^{2} e f g + a^{2} d e^{2} g^{2} + {\left(c^{2} d^{2} e f^{2} - 2 \, a c d e^{2} f g + a^{2} e^{3} g^{2}\right)} x\right)} \sqrt{-c d g} \arctan\left(\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{-c d g} \sqrt{e x + d} \sqrt{g x + f}}{2 \, c d e g x^{2} + c d^{2} f + a d e g + {\left(c d e f + {\left(2 \, c d^{2} + a e^{2}\right)} g\right)} x}\right)}{8 \, {\left(c^{2} d^{2} e g^{2} x + c^{2} d^{3} g^{2}\right)}}\right]"," ",0,"[1/16*(4*(2*c^2*d^2*g^2*x + c^2*d^2*f*g + a*c*d*e*g^2)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f) + (c^2*d^3*f^2 - 2*a*c*d^2*e*f*g + a^2*d*e^2*g^2 + (c^2*d^2*e*f^2 - 2*a*c*d*e^2*f*g + a^2*e^3*g^2)*x)*sqrt(c*d*g)*log(-(8*c^2*d^2*e*g^2*x^3 + c^2*d^3*f^2 + 6*a*c*d^2*e*f*g + a^2*d*e^2*g^2 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*g*x + c*d*f + a*e*g)*sqrt(c*d*g)*sqrt(e*x + d)*sqrt(g*x + f) + 8*(c^2*d^2*e*f*g + (c^2*d^3 + a*c*d*e^2)*g^2)*x^2 + (c^2*d^2*e*f^2 + 2*(4*c^2*d^3 + 3*a*c*d*e^2)*f*g + (8*a*c*d^2*e + a^2*e^3)*g^2)*x)/(e*x + d)))/(c^2*d^2*e*g^2*x + c^2*d^3*g^2), 1/8*(2*(2*c^2*d^2*g^2*x + c^2*d^2*f*g + a*c*d*e*g^2)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f) + (c^2*d^3*f^2 - 2*a*c*d^2*e*f*g + a^2*d*e^2*g^2 + (c^2*d^2*e*f^2 - 2*a*c*d*e^2*f*g + a^2*e^3*g^2)*x)*sqrt(-c*d*g)*arctan(2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-c*d*g)*sqrt(e*x + d)*sqrt(g*x + f)/(2*c*d*e*g*x^2 + c*d^2*f + a*d*e*g + (c*d*e*f + (2*c*d^2 + a*e^2)*g)*x)))/(c^2*d^2*e*g^2*x + c^2*d^3*g^2)]","A",0
736,1,516,0,1.139754," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)/(g*x+f)^(1/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} c d g - {\left(c d^{2} f - a d e g + {\left(c d e f - a e^{2} g\right)} x\right)} \sqrt{c d g} \log\left(-\frac{8 \, c^{2} d^{2} e g^{2} x^{3} + c^{2} d^{3} f^{2} + 6 \, a c d^{2} e f g + a^{2} d e^{2} g^{2} + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d g x + c d f + a e g\right)} \sqrt{c d g} \sqrt{e x + d} \sqrt{g x + f} + 8 \, {\left(c^{2} d^{2} e f g + {\left(c^{2} d^{3} + a c d e^{2}\right)} g^{2}\right)} x^{2} + {\left(c^{2} d^{2} e f^{2} + 2 \, {\left(4 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f g + {\left(8 \, a c d^{2} e + a^{2} e^{3}\right)} g^{2}\right)} x}{e x + d}\right)}{4 \, {\left(c d e g^{2} x + c d^{2} g^{2}\right)}}, \frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} c d g + {\left(c d^{2} f - a d e g + {\left(c d e f - a e^{2} g\right)} x\right)} \sqrt{-c d g} \arctan\left(\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{-c d g} \sqrt{e x + d} \sqrt{g x + f}}{2 \, c d e g x^{2} + c d^{2} f + a d e g + {\left(c d e f + {\left(2 \, c d^{2} + a e^{2}\right)} g\right)} x}\right)}{2 \, {\left(c d e g^{2} x + c d^{2} g^{2}\right)}}\right]"," ",0,"[1/4*(4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f)*c*d*g - (c*d^2*f - a*d*e*g + (c*d*e*f - a*e^2*g)*x)*sqrt(c*d*g)*log(-(8*c^2*d^2*e*g^2*x^3 + c^2*d^3*f^2 + 6*a*c*d^2*e*f*g + a^2*d*e^2*g^2 + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*g*x + c*d*f + a*e*g)*sqrt(c*d*g)*sqrt(e*x + d)*sqrt(g*x + f) + 8*(c^2*d^2*e*f*g + (c^2*d^3 + a*c*d*e^2)*g^2)*x^2 + (c^2*d^2*e*f^2 + 2*(4*c^2*d^3 + 3*a*c*d*e^2)*f*g + (8*a*c*d^2*e + a^2*e^3)*g^2)*x)/(e*x + d)))/(c*d*e*g^2*x + c*d^2*g^2), 1/2*(2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f)*c*d*g + (c*d^2*f - a*d*e*g + (c*d*e*f - a*e^2*g)*x)*sqrt(-c*d*g)*arctan(2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-c*d*g)*sqrt(e*x + d)*sqrt(g*x + f)/(2*c*d*e*g*x^2 + c*d^2*f + a*d*e*g + (c*d*e*f + (2*c*d^2 + a*e^2)*g)*x)))/(c*d*e*g^2*x + c*d^2*g^2)]","A",0
737,1,521,0,1.073424," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)/(g*x+f)^(3/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(e g x^{2} + d f + {\left(e f + d g\right)} x\right)} \sqrt{\frac{c d}{g}} \log\left(-\frac{8 \, c^{2} d^{2} e g^{2} x^{3} + c^{2} d^{3} f^{2} + 6 \, a c d^{2} e f g + a^{2} d e^{2} g^{2} + 4 \, {\left(2 \, c d g^{2} x + c d f g + a e g^{2}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} \sqrt{\frac{c d}{g}} + 8 \, {\left(c^{2} d^{2} e f g + {\left(c^{2} d^{3} + a c d e^{2}\right)} g^{2}\right)} x^{2} + {\left(c^{2} d^{2} e f^{2} + 2 \, {\left(4 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f g + {\left(8 \, a c d^{2} e + a^{2} e^{3}\right)} g^{2}\right)} x}{e x + d}\right) - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f}}{2 \, {\left(e g^{2} x^{2} + d f g + {\left(e f g + d g^{2}\right)} x\right)}}, -\frac{{\left(e g x^{2} + d f + {\left(e f + d g\right)} x\right)} \sqrt{-\frac{c d}{g}} \arctan\left(\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} \sqrt{-\frac{c d}{g}} g}{2 \, c d e g x^{2} + c d^{2} f + a d e g + {\left(c d e f + {\left(2 \, c d^{2} + a e^{2}\right)} g\right)} x}\right) + 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f}}{e g^{2} x^{2} + d f g + {\left(e f g + d g^{2}\right)} x}\right]"," ",0,"[1/2*((e*g*x^2 + d*f + (e*f + d*g)*x)*sqrt(c*d/g)*log(-(8*c^2*d^2*e*g^2*x^3 + c^2*d^3*f^2 + 6*a*c*d^2*e*f*g + a^2*d*e^2*g^2 + 4*(2*c*d*g^2*x + c*d*f*g + a*e*g^2)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f)*sqrt(c*d/g) + 8*(c^2*d^2*e*f*g + (c^2*d^3 + a*c*d*e^2)*g^2)*x^2 + (c^2*d^2*e*f^2 + 2*(4*c^2*d^3 + 3*a*c*d*e^2)*f*g + (8*a*c*d^2*e + a^2*e^3)*g^2)*x)/(e*x + d)) - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f))/(e*g^2*x^2 + d*f*g + (e*f*g + d*g^2)*x), -((e*g*x^2 + d*f + (e*f + d*g)*x)*sqrt(-c*d/g)*arctan(2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f)*sqrt(-c*d/g)*g/(2*c*d*e*g*x^2 + c*d^2*f + a*d*e*g + (c*d*e*f + (2*c*d^2 + a*e^2)*g)*x)) + 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f))/(e*g^2*x^2 + d*f*g + (e*f*g + d*g^2)*x)]","A",0
738,1,169,0,0.426766," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)/(g*x+f)^(5/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d x + a e\right)} \sqrt{e x + d} \sqrt{g x + f}}{3 \, {\left(c d^{2} f^{3} - a d e f^{2} g + {\left(c d e f g^{2} - a e^{2} g^{3}\right)} x^{3} + {\left(2 \, c d e f^{2} g - a d e g^{3} + {\left(c d^{2} - 2 \, a e^{2}\right)} f g^{2}\right)} x^{2} + {\left(c d e f^{3} - 2 \, a d e f g^{2} + {\left(2 \, c d^{2} - a e^{2}\right)} f^{2} g\right)} x\right)}}"," ",0,"2/3*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d*x + a*e)*sqrt(e*x + d)*sqrt(g*x + f)/(c*d^2*f^3 - a*d*e*f^2*g + (c*d*e*f*g^2 - a*e^2*g^3)*x^3 + (2*c*d*e*f^2*g - a*d*e*g^3 + (c*d^2 - 2*a*e^2)*f*g^2)*x^2 + (c*d*e*f^3 - 2*a*d*e*f*g^2 + (2*c*d^2 - a*e^2)*f^2*g)*x)","B",0
739,1,402,0,0.435083," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)/(g*x+f)^(7/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, c^{2} d^{2} g x^{2} + 5 \, a c d e f - 3 \, a^{2} e^{2} g + {\left(5 \, c^{2} d^{2} f - a c d e g\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f}}{15 \, {\left(c^{2} d^{3} f^{5} - 2 \, a c d^{2} e f^{4} g + a^{2} d e^{2} f^{3} g^{2} + {\left(c^{2} d^{2} e f^{2} g^{3} - 2 \, a c d e^{2} f g^{4} + a^{2} e^{3} g^{5}\right)} x^{4} + {\left(3 \, c^{2} d^{2} e f^{3} g^{2} + a^{2} d e^{2} g^{5} + {\left(c^{2} d^{3} - 6 \, a c d e^{2}\right)} f^{2} g^{3} - {\left(2 \, a c d^{2} e - 3 \, a^{2} e^{3}\right)} f g^{4}\right)} x^{3} + 3 \, {\left(c^{2} d^{2} e f^{4} g + a^{2} d e^{2} f g^{4} + {\left(c^{2} d^{3} - 2 \, a c d e^{2}\right)} f^{3} g^{2} - {\left(2 \, a c d^{2} e - a^{2} e^{3}\right)} f^{2} g^{3}\right)} x^{2} + {\left(c^{2} d^{2} e f^{5} + 3 \, a^{2} d e^{2} f^{2} g^{3} + {\left(3 \, c^{2} d^{3} - 2 \, a c d e^{2}\right)} f^{4} g - {\left(6 \, a c d^{2} e - a^{2} e^{3}\right)} f^{3} g^{2}\right)} x\right)}}"," ",0,"2/15*(2*c^2*d^2*g*x^2 + 5*a*c*d*e*f - 3*a^2*e^2*g + (5*c^2*d^2*f - a*c*d*e*g)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f)/(c^2*d^3*f^5 - 2*a*c*d^2*e*f^4*g + a^2*d*e^2*f^3*g^2 + (c^2*d^2*e*f^2*g^3 - 2*a*c*d*e^2*f*g^4 + a^2*e^3*g^5)*x^4 + (3*c^2*d^2*e*f^3*g^2 + a^2*d*e^2*g^5 + (c^2*d^3 - 6*a*c*d*e^2)*f^2*g^3 - (2*a*c*d^2*e - 3*a^2*e^3)*f*g^4)*x^3 + 3*(c^2*d^2*e*f^4*g + a^2*d*e^2*f*g^4 + (c^2*d^3 - 2*a*c*d*e^2)*f^3*g^2 - (2*a*c*d^2*e - a^2*e^3)*f^2*g^3)*x^2 + (c^2*d^2*e*f^5 + 3*a^2*d*e^2*f^2*g^3 + (3*c^2*d^3 - 2*a*c*d*e^2)*f^4*g - (6*a*c*d^2*e - a^2*e^3)*f^3*g^2)*x)","B",0
740,1,748,0,0.454548," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)/(g*x+f)^(9/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, c^{3} d^{3} g^{2} x^{3} + 35 \, a c^{2} d^{2} e f^{2} - 42 \, a^{2} c d e^{2} f g + 15 \, a^{3} e^{3} g^{2} + 4 \, {\left(7 \, c^{3} d^{3} f g - a c^{2} d^{2} e g^{2}\right)} x^{2} + {\left(35 \, c^{3} d^{3} f^{2} - 14 \, a c^{2} d^{2} e f g + 3 \, a^{2} c d e^{2} g^{2}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f}}{105 \, {\left(c^{3} d^{4} f^{7} - 3 \, a c^{2} d^{3} e f^{6} g + 3 \, a^{2} c d^{2} e^{2} f^{5} g^{2} - a^{3} d e^{3} f^{4} g^{3} + {\left(c^{3} d^{3} e f^{3} g^{4} - 3 \, a c^{2} d^{2} e^{2} f^{2} g^{5} + 3 \, a^{2} c d e^{3} f g^{6} - a^{3} e^{4} g^{7}\right)} x^{5} + {\left(4 \, c^{3} d^{3} e f^{4} g^{3} - a^{3} d e^{3} g^{7} + {\left(c^{3} d^{4} - 12 \, a c^{2} d^{2} e^{2}\right)} f^{3} g^{4} - 3 \, {\left(a c^{2} d^{3} e - 4 \, a^{2} c d e^{3}\right)} f^{2} g^{5} + {\left(3 \, a^{2} c d^{2} e^{2} - 4 \, a^{3} e^{4}\right)} f g^{6}\right)} x^{4} + 2 \, {\left(3 \, c^{3} d^{3} e f^{5} g^{2} - 2 \, a^{3} d e^{3} f g^{6} + {\left(2 \, c^{3} d^{4} - 9 \, a c^{2} d^{2} e^{2}\right)} f^{4} g^{3} - 3 \, {\left(2 \, a c^{2} d^{3} e - 3 \, a^{2} c d e^{3}\right)} f^{3} g^{4} + 3 \, {\left(2 \, a^{2} c d^{2} e^{2} - a^{3} e^{4}\right)} f^{2} g^{5}\right)} x^{3} + 2 \, {\left(2 \, c^{3} d^{3} e f^{6} g - 3 \, a^{3} d e^{3} f^{2} g^{5} + 3 \, {\left(c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2}\right)} f^{5} g^{2} - 3 \, {\left(3 \, a c^{2} d^{3} e - 2 \, a^{2} c d e^{3}\right)} f^{4} g^{3} + {\left(9 \, a^{2} c d^{2} e^{2} - 2 \, a^{3} e^{4}\right)} f^{3} g^{4}\right)} x^{2} + {\left(c^{3} d^{3} e f^{7} - 4 \, a^{3} d e^{3} f^{3} g^{4} + {\left(4 \, c^{3} d^{4} - 3 \, a c^{2} d^{2} e^{2}\right)} f^{6} g - 3 \, {\left(4 \, a c^{2} d^{3} e - a^{2} c d e^{3}\right)} f^{5} g^{2} + {\left(12 \, a^{2} c d^{2} e^{2} - a^{3} e^{4}\right)} f^{4} g^{3}\right)} x\right)}}"," ",0,"2/105*(8*c^3*d^3*g^2*x^3 + 35*a*c^2*d^2*e*f^2 - 42*a^2*c*d*e^2*f*g + 15*a^3*e^3*g^2 + 4*(7*c^3*d^3*f*g - a*c^2*d^2*e*g^2)*x^2 + (35*c^3*d^3*f^2 - 14*a*c^2*d^2*e*f*g + 3*a^2*c*d*e^2*g^2)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f)/(c^3*d^4*f^7 - 3*a*c^2*d^3*e*f^6*g + 3*a^2*c*d^2*e^2*f^5*g^2 - a^3*d*e^3*f^4*g^3 + (c^3*d^3*e*f^3*g^4 - 3*a*c^2*d^2*e^2*f^2*g^5 + 3*a^2*c*d*e^3*f*g^6 - a^3*e^4*g^7)*x^5 + (4*c^3*d^3*e*f^4*g^3 - a^3*d*e^3*g^7 + (c^3*d^4 - 12*a*c^2*d^2*e^2)*f^3*g^4 - 3*(a*c^2*d^3*e - 4*a^2*c*d*e^3)*f^2*g^5 + (3*a^2*c*d^2*e^2 - 4*a^3*e^4)*f*g^6)*x^4 + 2*(3*c^3*d^3*e*f^5*g^2 - 2*a^3*d*e^3*f*g^6 + (2*c^3*d^4 - 9*a*c^2*d^2*e^2)*f^4*g^3 - 3*(2*a*c^2*d^3*e - 3*a^2*c*d*e^3)*f^3*g^4 + 3*(2*a^2*c*d^2*e^2 - a^3*e^4)*f^2*g^5)*x^3 + 2*(2*c^3*d^3*e*f^6*g - 3*a^3*d*e^3*f^2*g^5 + 3*(c^3*d^4 - 2*a*c^2*d^2*e^2)*f^5*g^2 - 3*(3*a*c^2*d^3*e - 2*a^2*c*d*e^3)*f^4*g^3 + (9*a^2*c*d^2*e^2 - 2*a^3*e^4)*f^3*g^4)*x^2 + (c^3*d^3*e*f^7 - 4*a^3*d*e^3*f^3*g^4 + (4*c^3*d^4 - 3*a*c^2*d^2*e^2)*f^6*g - 3*(4*a*c^2*d^3*e - a^2*c*d*e^3)*f^5*g^2 + (12*a^2*c*d^2*e^2 - a^3*e^4)*f^4*g^3)*x)","B",0
741,1,1179,0,0.468362," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)/(g*x+f)^(11/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(16 \, c^{4} d^{4} g^{3} x^{4} + 105 \, a c^{3} d^{3} e f^{3} - 189 \, a^{2} c^{2} d^{2} e^{2} f^{2} g + 135 \, a^{3} c d e^{3} f g^{2} - 35 \, a^{4} e^{4} g^{3} + 8 \, {\left(9 \, c^{4} d^{4} f g^{2} - a c^{3} d^{3} e g^{3}\right)} x^{3} + 6 \, {\left(21 \, c^{4} d^{4} f^{2} g - 6 \, a c^{3} d^{3} e f g^{2} + a^{2} c^{2} d^{2} e^{2} g^{3}\right)} x^{2} + {\left(105 \, c^{4} d^{4} f^{3} - 63 \, a c^{3} d^{3} e f^{2} g + 27 \, a^{2} c^{2} d^{2} e^{2} f g^{2} - 5 \, a^{3} c d e^{3} g^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f}}{315 \, {\left(c^{4} d^{5} f^{9} - 4 \, a c^{3} d^{4} e f^{8} g + 6 \, a^{2} c^{2} d^{3} e^{2} f^{7} g^{2} - 4 \, a^{3} c d^{2} e^{3} f^{6} g^{3} + a^{4} d e^{4} f^{5} g^{4} + {\left(c^{4} d^{4} e f^{4} g^{5} - 4 \, a c^{3} d^{3} e^{2} f^{3} g^{6} + 6 \, a^{2} c^{2} d^{2} e^{3} f^{2} g^{7} - 4 \, a^{3} c d e^{4} f g^{8} + a^{4} e^{5} g^{9}\right)} x^{6} + {\left(5 \, c^{4} d^{4} e f^{5} g^{4} + a^{4} d e^{4} g^{9} + {\left(c^{4} d^{5} - 20 \, a c^{3} d^{3} e^{2}\right)} f^{4} g^{5} - 2 \, {\left(2 \, a c^{3} d^{4} e - 15 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{3} g^{6} + 2 \, {\left(3 \, a^{2} c^{2} d^{3} e^{2} - 10 \, a^{3} c d e^{4}\right)} f^{2} g^{7} - {\left(4 \, a^{3} c d^{2} e^{3} - 5 \, a^{4} e^{5}\right)} f g^{8}\right)} x^{5} + 5 \, {\left(2 \, c^{4} d^{4} e f^{6} g^{3} + a^{4} d e^{4} f g^{8} + {\left(c^{4} d^{5} - 8 \, a c^{3} d^{3} e^{2}\right)} f^{5} g^{4} - 4 \, {\left(a c^{3} d^{4} e - 3 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{4} g^{5} + 2 \, {\left(3 \, a^{2} c^{2} d^{3} e^{2} - 4 \, a^{3} c d e^{4}\right)} f^{3} g^{6} - 2 \, {\left(2 \, a^{3} c d^{2} e^{3} - a^{4} e^{5}\right)} f^{2} g^{7}\right)} x^{4} + 10 \, {\left(c^{4} d^{4} e f^{7} g^{2} + a^{4} d e^{4} f^{2} g^{7} + {\left(c^{4} d^{5} - 4 \, a c^{3} d^{3} e^{2}\right)} f^{6} g^{3} - 2 \, {\left(2 \, a c^{3} d^{4} e - 3 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{5} g^{4} + 2 \, {\left(3 \, a^{2} c^{2} d^{3} e^{2} - 2 \, a^{3} c d e^{4}\right)} f^{4} g^{5} - {\left(4 \, a^{3} c d^{2} e^{3} - a^{4} e^{5}\right)} f^{3} g^{6}\right)} x^{3} + 5 \, {\left(c^{4} d^{4} e f^{8} g + 2 \, a^{4} d e^{4} f^{3} g^{6} + 2 \, {\left(c^{4} d^{5} - 2 \, a c^{3} d^{3} e^{2}\right)} f^{7} g^{2} - 2 \, {\left(4 \, a c^{3} d^{4} e - 3 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{6} g^{3} + 4 \, {\left(3 \, a^{2} c^{2} d^{3} e^{2} - a^{3} c d e^{4}\right)} f^{5} g^{4} - {\left(8 \, a^{3} c d^{2} e^{3} - a^{4} e^{5}\right)} f^{4} g^{5}\right)} x^{2} + {\left(c^{4} d^{4} e f^{9} + 5 \, a^{4} d e^{4} f^{4} g^{5} + {\left(5 \, c^{4} d^{5} - 4 \, a c^{3} d^{3} e^{2}\right)} f^{8} g - 2 \, {\left(10 \, a c^{3} d^{4} e - 3 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{7} g^{2} + 2 \, {\left(15 \, a^{2} c^{2} d^{3} e^{2} - 2 \, a^{3} c d e^{4}\right)} f^{6} g^{3} - {\left(20 \, a^{3} c d^{2} e^{3} - a^{4} e^{5}\right)} f^{5} g^{4}\right)} x\right)}}"," ",0,"2/315*(16*c^4*d^4*g^3*x^4 + 105*a*c^3*d^3*e*f^3 - 189*a^2*c^2*d^2*e^2*f^2*g + 135*a^3*c*d*e^3*f*g^2 - 35*a^4*e^4*g^3 + 8*(9*c^4*d^4*f*g^2 - a*c^3*d^3*e*g^3)*x^3 + 6*(21*c^4*d^4*f^2*g - 6*a*c^3*d^3*e*f*g^2 + a^2*c^2*d^2*e^2*g^3)*x^2 + (105*c^4*d^4*f^3 - 63*a*c^3*d^3*e*f^2*g + 27*a^2*c^2*d^2*e^2*f*g^2 - 5*a^3*c*d*e^3*g^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f)/(c^4*d^5*f^9 - 4*a*c^3*d^4*e*f^8*g + 6*a^2*c^2*d^3*e^2*f^7*g^2 - 4*a^3*c*d^2*e^3*f^6*g^3 + a^4*d*e^4*f^5*g^4 + (c^4*d^4*e*f^4*g^5 - 4*a*c^3*d^3*e^2*f^3*g^6 + 6*a^2*c^2*d^2*e^3*f^2*g^7 - 4*a^3*c*d*e^4*f*g^8 + a^4*e^5*g^9)*x^6 + (5*c^4*d^4*e*f^5*g^4 + a^4*d*e^4*g^9 + (c^4*d^5 - 20*a*c^3*d^3*e^2)*f^4*g^5 - 2*(2*a*c^3*d^4*e - 15*a^2*c^2*d^2*e^3)*f^3*g^6 + 2*(3*a^2*c^2*d^3*e^2 - 10*a^3*c*d*e^4)*f^2*g^7 - (4*a^3*c*d^2*e^3 - 5*a^4*e^5)*f*g^8)*x^5 + 5*(2*c^4*d^4*e*f^6*g^3 + a^4*d*e^4*f*g^8 + (c^4*d^5 - 8*a*c^3*d^3*e^2)*f^5*g^4 - 4*(a*c^3*d^4*e - 3*a^2*c^2*d^2*e^3)*f^4*g^5 + 2*(3*a^2*c^2*d^3*e^2 - 4*a^3*c*d*e^4)*f^3*g^6 - 2*(2*a^3*c*d^2*e^3 - a^4*e^5)*f^2*g^7)*x^4 + 10*(c^4*d^4*e*f^7*g^2 + a^4*d*e^4*f^2*g^7 + (c^4*d^5 - 4*a*c^3*d^3*e^2)*f^6*g^3 - 2*(2*a*c^3*d^4*e - 3*a^2*c^2*d^2*e^3)*f^5*g^4 + 2*(3*a^2*c^2*d^3*e^2 - 2*a^3*c*d*e^4)*f^4*g^5 - (4*a^3*c*d^2*e^3 - a^4*e^5)*f^3*g^6)*x^3 + 5*(c^4*d^4*e*f^8*g + 2*a^4*d*e^4*f^3*g^6 + 2*(c^4*d^5 - 2*a*c^3*d^3*e^2)*f^7*g^2 - 2*(4*a*c^3*d^4*e - 3*a^2*c^2*d^2*e^3)*f^6*g^3 + 4*(3*a^2*c^2*d^3*e^2 - a^3*c*d*e^4)*f^5*g^4 - (8*a^3*c*d^2*e^3 - a^4*e^5)*f^4*g^5)*x^2 + (c^4*d^4*e*f^9 + 5*a^4*d*e^4*f^4*g^5 + (5*c^4*d^5 - 4*a*c^3*d^3*e^2)*f^8*g - 2*(10*a*c^3*d^4*e - 3*a^2*c^2*d^2*e^3)*f^7*g^2 + 2*(15*a^2*c^2*d^3*e^2 - 2*a^3*c*d*e^4)*f^6*g^3 - (20*a^3*c*d^2*e^3 - a^4*e^5)*f^5*g^4)*x)","B",0
742,1,1059,0,2.675649," ","integrate((g*x+f)^(3/2)*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/(e*x+d)^(3/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(16 \, c^{4} d^{4} g^{4} x^{3} - 3 \, c^{4} d^{4} f^{3} g + 11 \, a c^{3} d^{3} e f^{2} g^{2} + 11 \, a^{2} c^{2} d^{2} e^{2} f g^{3} - 3 \, a^{3} c d e^{3} g^{4} + 24 \, {\left(c^{4} d^{4} f g^{3} + a c^{3} d^{3} e g^{4}\right)} x^{2} + 2 \, {\left(c^{4} d^{4} f^{2} g^{2} + 22 \, a c^{3} d^{3} e f g^{3} + a^{2} c^{2} d^{2} e^{2} g^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} + 3 \, {\left(c^{4} d^{5} f^{4} - 4 \, a c^{3} d^{4} e f^{3} g + 6 \, a^{2} c^{2} d^{3} e^{2} f^{2} g^{2} - 4 \, a^{3} c d^{2} e^{3} f g^{3} + a^{4} d e^{4} g^{4} + {\left(c^{4} d^{4} e f^{4} - 4 \, a c^{3} d^{3} e^{2} f^{3} g + 6 \, a^{2} c^{2} d^{2} e^{3} f^{2} g^{2} - 4 \, a^{3} c d e^{4} f g^{3} + a^{4} e^{5} g^{4}\right)} x\right)} \sqrt{c d g} \log\left(-\frac{8 \, c^{2} d^{2} e g^{2} x^{3} + c^{2} d^{3} f^{2} + 6 \, a c d^{2} e f g + a^{2} d e^{2} g^{2} + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d g x + c d f + a e g\right)} \sqrt{c d g} \sqrt{e x + d} \sqrt{g x + f} + 8 \, {\left(c^{2} d^{2} e f g + {\left(c^{2} d^{3} + a c d e^{2}\right)} g^{2}\right)} x^{2} + {\left(c^{2} d^{2} e f^{2} + 2 \, {\left(4 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f g + {\left(8 \, a c d^{2} e + a^{2} e^{3}\right)} g^{2}\right)} x}{e x + d}\right)}{256 \, {\left(c^{3} d^{3} e g^{3} x + c^{3} d^{4} g^{3}\right)}}, \frac{2 \, {\left(16 \, c^{4} d^{4} g^{4} x^{3} - 3 \, c^{4} d^{4} f^{3} g + 11 \, a c^{3} d^{3} e f^{2} g^{2} + 11 \, a^{2} c^{2} d^{2} e^{2} f g^{3} - 3 \, a^{3} c d e^{3} g^{4} + 24 \, {\left(c^{4} d^{4} f g^{3} + a c^{3} d^{3} e g^{4}\right)} x^{2} + 2 \, {\left(c^{4} d^{4} f^{2} g^{2} + 22 \, a c^{3} d^{3} e f g^{3} + a^{2} c^{2} d^{2} e^{2} g^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} - 3 \, {\left(c^{4} d^{5} f^{4} - 4 \, a c^{3} d^{4} e f^{3} g + 6 \, a^{2} c^{2} d^{3} e^{2} f^{2} g^{2} - 4 \, a^{3} c d^{2} e^{3} f g^{3} + a^{4} d e^{4} g^{4} + {\left(c^{4} d^{4} e f^{4} - 4 \, a c^{3} d^{3} e^{2} f^{3} g + 6 \, a^{2} c^{2} d^{2} e^{3} f^{2} g^{2} - 4 \, a^{3} c d e^{4} f g^{3} + a^{4} e^{5} g^{4}\right)} x\right)} \sqrt{-c d g} \arctan\left(\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{-c d g} \sqrt{e x + d} \sqrt{g x + f}}{2 \, c d e g x^{2} + c d^{2} f + a d e g + {\left(c d e f + {\left(2 \, c d^{2} + a e^{2}\right)} g\right)} x}\right)}{128 \, {\left(c^{3} d^{3} e g^{3} x + c^{3} d^{4} g^{3}\right)}}\right]"," ",0,"[1/256*(4*(16*c^4*d^4*g^4*x^3 - 3*c^4*d^4*f^3*g + 11*a*c^3*d^3*e*f^2*g^2 + 11*a^2*c^2*d^2*e^2*f*g^3 - 3*a^3*c*d*e^3*g^4 + 24*(c^4*d^4*f*g^3 + a*c^3*d^3*e*g^4)*x^2 + 2*(c^4*d^4*f^2*g^2 + 22*a*c^3*d^3*e*f*g^3 + a^2*c^2*d^2*e^2*g^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f) + 3*(c^4*d^5*f^4 - 4*a*c^3*d^4*e*f^3*g + 6*a^2*c^2*d^3*e^2*f^2*g^2 - 4*a^3*c*d^2*e^3*f*g^3 + a^4*d*e^4*g^4 + (c^4*d^4*e*f^4 - 4*a*c^3*d^3*e^2*f^3*g + 6*a^2*c^2*d^2*e^3*f^2*g^2 - 4*a^3*c*d*e^4*f*g^3 + a^4*e^5*g^4)*x)*sqrt(c*d*g)*log(-(8*c^2*d^2*e*g^2*x^3 + c^2*d^3*f^2 + 6*a*c*d^2*e*f*g + a^2*d*e^2*g^2 + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*g*x + c*d*f + a*e*g)*sqrt(c*d*g)*sqrt(e*x + d)*sqrt(g*x + f) + 8*(c^2*d^2*e*f*g + (c^2*d^3 + a*c*d*e^2)*g^2)*x^2 + (c^2*d^2*e*f^2 + 2*(4*c^2*d^3 + 3*a*c*d*e^2)*f*g + (8*a*c*d^2*e + a^2*e^3)*g^2)*x)/(e*x + d)))/(c^3*d^3*e*g^3*x + c^3*d^4*g^3), 1/128*(2*(16*c^4*d^4*g^4*x^3 - 3*c^4*d^4*f^3*g + 11*a*c^3*d^3*e*f^2*g^2 + 11*a^2*c^2*d^2*e^2*f*g^3 - 3*a^3*c*d*e^3*g^4 + 24*(c^4*d^4*f*g^3 + a*c^3*d^3*e*g^4)*x^2 + 2*(c^4*d^4*f^2*g^2 + 22*a*c^3*d^3*e*f*g^3 + a^2*c^2*d^2*e^2*g^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f) - 3*(c^4*d^5*f^4 - 4*a*c^3*d^4*e*f^3*g + 6*a^2*c^2*d^3*e^2*f^2*g^2 - 4*a^3*c*d^2*e^3*f*g^3 + a^4*d*e^4*g^4 + (c^4*d^4*e*f^4 - 4*a*c^3*d^3*e^2*f^3*g + 6*a^2*c^2*d^2*e^3*f^2*g^2 - 4*a^3*c*d*e^4*f*g^3 + a^4*e^5*g^4)*x)*sqrt(-c*d*g)*arctan(2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-c*d*g)*sqrt(e*x + d)*sqrt(g*x + f)/(2*c*d*e*g*x^2 + c*d^2*f + a*d*e*g + (c*d*e*f + (2*c*d^2 + a*e^2)*g)*x)))/(c^3*d^3*e*g^3*x + c^3*d^4*g^3)]","A",0
743,1,847,0,1.513002," ","integrate((g*x+f)^(1/2)*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/(e*x+d)^(3/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(8 \, c^{3} d^{3} g^{3} x^{2} - 3 \, c^{3} d^{3} f^{2} g + 8 \, a c^{2} d^{2} e f g^{2} + 3 \, a^{2} c d e^{2} g^{3} + 2 \, {\left(c^{3} d^{3} f g^{2} + 7 \, a c^{2} d^{2} e g^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} - 3 \, {\left(c^{3} d^{4} f^{3} - 3 \, a c^{2} d^{3} e f^{2} g + 3 \, a^{2} c d^{2} e^{2} f g^{2} - a^{3} d e^{3} g^{3} + {\left(c^{3} d^{3} e f^{3} - 3 \, a c^{2} d^{2} e^{2} f^{2} g + 3 \, a^{2} c d e^{3} f g^{2} - a^{3} e^{4} g^{3}\right)} x\right)} \sqrt{c d g} \log\left(-\frac{8 \, c^{2} d^{2} e g^{2} x^{3} + c^{2} d^{3} f^{2} + 6 \, a c d^{2} e f g + a^{2} d e^{2} g^{2} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d g x + c d f + a e g\right)} \sqrt{c d g} \sqrt{e x + d} \sqrt{g x + f} + 8 \, {\left(c^{2} d^{2} e f g + {\left(c^{2} d^{3} + a c d e^{2}\right)} g^{2}\right)} x^{2} + {\left(c^{2} d^{2} e f^{2} + 2 \, {\left(4 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f g + {\left(8 \, a c d^{2} e + a^{2} e^{3}\right)} g^{2}\right)} x}{e x + d}\right)}{96 \, {\left(c^{2} d^{2} e g^{3} x + c^{2} d^{3} g^{3}\right)}}, \frac{2 \, {\left(8 \, c^{3} d^{3} g^{3} x^{2} - 3 \, c^{3} d^{3} f^{2} g + 8 \, a c^{2} d^{2} e f g^{2} + 3 \, a^{2} c d e^{2} g^{3} + 2 \, {\left(c^{3} d^{3} f g^{2} + 7 \, a c^{2} d^{2} e g^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} - 3 \, {\left(c^{3} d^{4} f^{3} - 3 \, a c^{2} d^{3} e f^{2} g + 3 \, a^{2} c d^{2} e^{2} f g^{2} - a^{3} d e^{3} g^{3} + {\left(c^{3} d^{3} e f^{3} - 3 \, a c^{2} d^{2} e^{2} f^{2} g + 3 \, a^{2} c d e^{3} f g^{2} - a^{3} e^{4} g^{3}\right)} x\right)} \sqrt{-c d g} \arctan\left(\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{-c d g} \sqrt{e x + d} \sqrt{g x + f}}{2 \, c d e g x^{2} + c d^{2} f + a d e g + {\left(c d e f + {\left(2 \, c d^{2} + a e^{2}\right)} g\right)} x}\right)}{48 \, {\left(c^{2} d^{2} e g^{3} x + c^{2} d^{3} g^{3}\right)}}\right]"," ",0,"[1/96*(4*(8*c^3*d^3*g^3*x^2 - 3*c^3*d^3*f^2*g + 8*a*c^2*d^2*e*f*g^2 + 3*a^2*c*d*e^2*g^3 + 2*(c^3*d^3*f*g^2 + 7*a*c^2*d^2*e*g^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f) - 3*(c^3*d^4*f^3 - 3*a*c^2*d^3*e*f^2*g + 3*a^2*c*d^2*e^2*f*g^2 - a^3*d*e^3*g^3 + (c^3*d^3*e*f^3 - 3*a*c^2*d^2*e^2*f^2*g + 3*a^2*c*d*e^3*f*g^2 - a^3*e^4*g^3)*x)*sqrt(c*d*g)*log(-(8*c^2*d^2*e*g^2*x^3 + c^2*d^3*f^2 + 6*a*c*d^2*e*f*g + a^2*d*e^2*g^2 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*g*x + c*d*f + a*e*g)*sqrt(c*d*g)*sqrt(e*x + d)*sqrt(g*x + f) + 8*(c^2*d^2*e*f*g + (c^2*d^3 + a*c*d*e^2)*g^2)*x^2 + (c^2*d^2*e*f^2 + 2*(4*c^2*d^3 + 3*a*c*d*e^2)*f*g + (8*a*c*d^2*e + a^2*e^3)*g^2)*x)/(e*x + d)))/(c^2*d^2*e*g^3*x + c^2*d^3*g^3), 1/48*(2*(8*c^3*d^3*g^3*x^2 - 3*c^3*d^3*f^2*g + 8*a*c^2*d^2*e*f*g^2 + 3*a^2*c*d*e^2*g^3 + 2*(c^3*d^3*f*g^2 + 7*a*c^2*d^2*e*g^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f) - 3*(c^3*d^4*f^3 - 3*a*c^2*d^3*e*f^2*g + 3*a^2*c*d^2*e^2*f*g^2 - a^3*d*e^3*g^3 + (c^3*d^3*e*f^3 - 3*a*c^2*d^2*e^2*f^2*g + 3*a^2*c*d*e^3*f*g^2 - a^3*e^4*g^3)*x)*sqrt(-c*d*g)*arctan(2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-c*d*g)*sqrt(e*x + d)*sqrt(g*x + f)/(2*c*d*e*g*x^2 + c*d^2*f + a*d*e*g + (c*d*e*f + (2*c*d^2 + a*e^2)*g)*x)))/(c^2*d^2*e*g^3*x + c^2*d^3*g^3)]","A",0
744,1,651,0,1.209456," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/(e*x+d)^(3/2)/(g*x+f)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(2 \, c^{2} d^{2} g^{2} x - 3 \, c^{2} d^{2} f g + 5 \, a c d e g^{2}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} + 3 \, {\left(c^{2} d^{3} f^{2} - 2 \, a c d^{2} e f g + a^{2} d e^{2} g^{2} + {\left(c^{2} d^{2} e f^{2} - 2 \, a c d e^{2} f g + a^{2} e^{3} g^{2}\right)} x\right)} \sqrt{c d g} \log\left(-\frac{8 \, c^{2} d^{2} e g^{2} x^{3} + c^{2} d^{3} f^{2} + 6 \, a c d^{2} e f g + a^{2} d e^{2} g^{2} + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d g x + c d f + a e g\right)} \sqrt{c d g} \sqrt{e x + d} \sqrt{g x + f} + 8 \, {\left(c^{2} d^{2} e f g + {\left(c^{2} d^{3} + a c d e^{2}\right)} g^{2}\right)} x^{2} + {\left(c^{2} d^{2} e f^{2} + 2 \, {\left(4 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f g + {\left(8 \, a c d^{2} e + a^{2} e^{3}\right)} g^{2}\right)} x}{e x + d}\right)}{16 \, {\left(c d e g^{3} x + c d^{2} g^{3}\right)}}, \frac{2 \, {\left(2 \, c^{2} d^{2} g^{2} x - 3 \, c^{2} d^{2} f g + 5 \, a c d e g^{2}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} - 3 \, {\left(c^{2} d^{3} f^{2} - 2 \, a c d^{2} e f g + a^{2} d e^{2} g^{2} + {\left(c^{2} d^{2} e f^{2} - 2 \, a c d e^{2} f g + a^{2} e^{3} g^{2}\right)} x\right)} \sqrt{-c d g} \arctan\left(\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{-c d g} \sqrt{e x + d} \sqrt{g x + f}}{2 \, c d e g x^{2} + c d^{2} f + a d e g + {\left(c d e f + {\left(2 \, c d^{2} + a e^{2}\right)} g\right)} x}\right)}{8 \, {\left(c d e g^{3} x + c d^{2} g^{3}\right)}}\right]"," ",0,"[1/16*(4*(2*c^2*d^2*g^2*x - 3*c^2*d^2*f*g + 5*a*c*d*e*g^2)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f) + 3*(c^2*d^3*f^2 - 2*a*c*d^2*e*f*g + a^2*d*e^2*g^2 + (c^2*d^2*e*f^2 - 2*a*c*d*e^2*f*g + a^2*e^3*g^2)*x)*sqrt(c*d*g)*log(-(8*c^2*d^2*e*g^2*x^3 + c^2*d^3*f^2 + 6*a*c*d^2*e*f*g + a^2*d*e^2*g^2 + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*g*x + c*d*f + a*e*g)*sqrt(c*d*g)*sqrt(e*x + d)*sqrt(g*x + f) + 8*(c^2*d^2*e*f*g + (c^2*d^3 + a*c*d*e^2)*g^2)*x^2 + (c^2*d^2*e*f^2 + 2*(4*c^2*d^3 + 3*a*c*d*e^2)*f*g + (8*a*c*d^2*e + a^2*e^3)*g^2)*x)/(e*x + d)))/(c*d*e*g^3*x + c*d^2*g^3), 1/8*(2*(2*c^2*d^2*g^2*x - 3*c^2*d^2*f*g + 5*a*c*d*e*g^2)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f) - 3*(c^2*d^3*f^2 - 2*a*c*d^2*e*f*g + a^2*d*e^2*g^2 + (c^2*d^2*e*f^2 - 2*a*c*d*e^2*f*g + a^2*e^3*g^2)*x)*sqrt(-c*d*g)*arctan(2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-c*d*g)*sqrt(e*x + d)*sqrt(g*x + f)/(2*c*d*e*g*x^2 + c*d^2*f + a*d*e*g + (c*d*e*f + (2*c*d^2 + a*e^2)*g)*x)))/(c*d*e*g^3*x + c*d^2*g^3)]","A",0
745,1,663,0,1.123740," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/(e*x+d)^(3/2)/(g*x+f)^(3/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d g x + 3 \, c d f - 2 \, a e g\right)} \sqrt{e x + d} \sqrt{g x + f} - 3 \, {\left(c d^{2} f^{2} - a d e f g + {\left(c d e f g - a e^{2} g^{2}\right)} x^{2} + {\left(c d e f^{2} - a d e g^{2} + {\left(c d^{2} - a e^{2}\right)} f g\right)} x\right)} \sqrt{\frac{c d}{g}} \log\left(-\frac{8 \, c^{2} d^{2} e g^{2} x^{3} + c^{2} d^{3} f^{2} + 6 \, a c d^{2} e f g + a^{2} d e^{2} g^{2} + 4 \, {\left(2 \, c d g^{2} x + c d f g + a e g^{2}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} \sqrt{\frac{c d}{g}} + 8 \, {\left(c^{2} d^{2} e f g + {\left(c^{2} d^{3} + a c d e^{2}\right)} g^{2}\right)} x^{2} + {\left(c^{2} d^{2} e f^{2} + 2 \, {\left(4 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f g + {\left(8 \, a c d^{2} e + a^{2} e^{3}\right)} g^{2}\right)} x}{e x + d}\right)}{4 \, {\left(e g^{3} x^{2} + d f g^{2} + {\left(e f g^{2} + d g^{3}\right)} x\right)}}, \frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d g x + 3 \, c d f - 2 \, a e g\right)} \sqrt{e x + d} \sqrt{g x + f} + 3 \, {\left(c d^{2} f^{2} - a d e f g + {\left(c d e f g - a e^{2} g^{2}\right)} x^{2} + {\left(c d e f^{2} - a d e g^{2} + {\left(c d^{2} - a e^{2}\right)} f g\right)} x\right)} \sqrt{-\frac{c d}{g}} \arctan\left(\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} \sqrt{-\frac{c d}{g}} g}{2 \, c d e g x^{2} + c d^{2} f + a d e g + {\left(c d e f + {\left(2 \, c d^{2} + a e^{2}\right)} g\right)} x}\right)}{2 \, {\left(e g^{3} x^{2} + d f g^{2} + {\left(e f g^{2} + d g^{3}\right)} x\right)}}\right]"," ",0,"[1/4*(4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d*g*x + 3*c*d*f - 2*a*e*g)*sqrt(e*x + d)*sqrt(g*x + f) - 3*(c*d^2*f^2 - a*d*e*f*g + (c*d*e*f*g - a*e^2*g^2)*x^2 + (c*d*e*f^2 - a*d*e*g^2 + (c*d^2 - a*e^2)*f*g)*x)*sqrt(c*d/g)*log(-(8*c^2*d^2*e*g^2*x^3 + c^2*d^3*f^2 + 6*a*c*d^2*e*f*g + a^2*d*e^2*g^2 + 4*(2*c*d*g^2*x + c*d*f*g + a*e*g^2)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f)*sqrt(c*d/g) + 8*(c^2*d^2*e*f*g + (c^2*d^3 + a*c*d*e^2)*g^2)*x^2 + (c^2*d^2*e*f^2 + 2*(4*c^2*d^3 + 3*a*c*d*e^2)*f*g + (8*a*c*d^2*e + a^2*e^3)*g^2)*x)/(e*x + d)))/(e*g^3*x^2 + d*f*g^2 + (e*f*g^2 + d*g^3)*x), 1/2*(2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d*g*x + 3*c*d*f - 2*a*e*g)*sqrt(e*x + d)*sqrt(g*x + f) + 3*(c*d^2*f^2 - a*d*e*f*g + (c*d*e*f*g - a*e^2*g^2)*x^2 + (c*d*e*f^2 - a*d*e*g^2 + (c*d^2 - a*e^2)*f*g)*x)*sqrt(-c*d/g)*arctan(2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f)*sqrt(-c*d/g)*g/(2*c*d*e*g*x^2 + c*d^2*f + a*d*e*g + (c*d*e*f + (2*c*d^2 + a*e^2)*g)*x)))/(e*g^3*x^2 + d*f*g^2 + (e*f*g^2 + d*g^3)*x)]","A",0
746,1,685,0,1.078144," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/(e*x+d)^(3/2)/(g*x+f)^(5/2),x, algorithm=""fricas"")","\left[-\frac{4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(4 \, c d g x + 3 \, c d f + a e g\right)} \sqrt{e x + d} \sqrt{g x + f} - 3 \, {\left(c d e g^{2} x^{3} + c d^{2} f^{2} + {\left(2 \, c d e f g + c d^{2} g^{2}\right)} x^{2} + {\left(c d e f^{2} + 2 \, c d^{2} f g\right)} x\right)} \sqrt{\frac{c d}{g}} \log\left(-\frac{8 \, c^{2} d^{2} e g^{2} x^{3} + c^{2} d^{3} f^{2} + 6 \, a c d^{2} e f g + a^{2} d e^{2} g^{2} + 4 \, {\left(2 \, c d g^{2} x + c d f g + a e g^{2}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} \sqrt{\frac{c d}{g}} + 8 \, {\left(c^{2} d^{2} e f g + {\left(c^{2} d^{3} + a c d e^{2}\right)} g^{2}\right)} x^{2} + {\left(c^{2} d^{2} e f^{2} + 2 \, {\left(4 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f g + {\left(8 \, a c d^{2} e + a^{2} e^{3}\right)} g^{2}\right)} x}{e x + d}\right)}{6 \, {\left(e g^{4} x^{3} + d f^{2} g^{2} + {\left(2 \, e f g^{3} + d g^{4}\right)} x^{2} + {\left(e f^{2} g^{2} + 2 \, d f g^{3}\right)} x\right)}}, -\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(4 \, c d g x + 3 \, c d f + a e g\right)} \sqrt{e x + d} \sqrt{g x + f} + 3 \, {\left(c d e g^{2} x^{3} + c d^{2} f^{2} + {\left(2 \, c d e f g + c d^{2} g^{2}\right)} x^{2} + {\left(c d e f^{2} + 2 \, c d^{2} f g\right)} x\right)} \sqrt{-\frac{c d}{g}} \arctan\left(\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} \sqrt{-\frac{c d}{g}} g}{2 \, c d e g x^{2} + c d^{2} f + a d e g + {\left(c d e f + {\left(2 \, c d^{2} + a e^{2}\right)} g\right)} x}\right)}{3 \, {\left(e g^{4} x^{3} + d f^{2} g^{2} + {\left(2 \, e f g^{3} + d g^{4}\right)} x^{2} + {\left(e f^{2} g^{2} + 2 \, d f g^{3}\right)} x\right)}}\right]"," ",0,"[-1/6*(4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(4*c*d*g*x + 3*c*d*f + a*e*g)*sqrt(e*x + d)*sqrt(g*x + f) - 3*(c*d*e*g^2*x^3 + c*d^2*f^2 + (2*c*d*e*f*g + c*d^2*g^2)*x^2 + (c*d*e*f^2 + 2*c*d^2*f*g)*x)*sqrt(c*d/g)*log(-(8*c^2*d^2*e*g^2*x^3 + c^2*d^3*f^2 + 6*a*c*d^2*e*f*g + a^2*d*e^2*g^2 + 4*(2*c*d*g^2*x + c*d*f*g + a*e*g^2)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f)*sqrt(c*d/g) + 8*(c^2*d^2*e*f*g + (c^2*d^3 + a*c*d*e^2)*g^2)*x^2 + (c^2*d^2*e*f^2 + 2*(4*c^2*d^3 + 3*a*c*d*e^2)*f*g + (8*a*c*d^2*e + a^2*e^3)*g^2)*x)/(e*x + d)))/(e*g^4*x^3 + d*f^2*g^2 + (2*e*f*g^3 + d*g^4)*x^2 + (e*f^2*g^2 + 2*d*f*g^3)*x), -1/3*(2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(4*c*d*g*x + 3*c*d*f + a*e*g)*sqrt(e*x + d)*sqrt(g*x + f) + 3*(c*d*e*g^2*x^3 + c*d^2*f^2 + (2*c*d*e*f*g + c*d^2*g^2)*x^2 + (c*d*e*f^2 + 2*c*d^2*f*g)*x)*sqrt(-c*d/g)*arctan(2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f)*sqrt(-c*d/g)*g/(2*c*d*e*g*x^2 + c*d^2*f + a*d*e*g + (c*d*e*f + (2*c*d^2 + a*e^2)*g)*x)))/(e*g^4*x^3 + d*f^2*g^2 + (2*e*f*g^3 + d*g^4)*x^2 + (e*f^2*g^2 + 2*d*f*g^3)*x)]","A",0
747,1,232,0,0.439293," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/(e*x+d)^(3/2)/(g*x+f)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(c^{2} d^{2} x^{2} + 2 \, a c d e x + a^{2} e^{2}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f}}{5 \, {\left(c d^{2} f^{4} - a d e f^{3} g + {\left(c d e f g^{3} - a e^{2} g^{4}\right)} x^{4} + {\left(3 \, c d e f^{2} g^{2} - a d e g^{4} + {\left(c d^{2} - 3 \, a e^{2}\right)} f g^{3}\right)} x^{3} + 3 \, {\left(c d e f^{3} g - a d e f g^{3} + {\left(c d^{2} - a e^{2}\right)} f^{2} g^{2}\right)} x^{2} + {\left(c d e f^{4} - 3 \, a d e f^{2} g^{2} + {\left(3 \, c d^{2} - a e^{2}\right)} f^{3} g\right)} x\right)}}"," ",0,"2/5*(c^2*d^2*x^2 + 2*a*c*d*e*x + a^2*e^2)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f)/(c*d^2*f^4 - a*d*e*f^3*g + (c*d*e*f*g^3 - a*e^2*g^4)*x^4 + (3*c*d*e*f^2*g^2 - a*d*e*g^4 + (c*d^2 - 3*a*e^2)*f*g^3)*x^3 + 3*(c*d*e*f^3*g - a*d*e*f*g^3 + (c*d^2 - a*e^2)*f^2*g^2)*x^2 + (c*d*e*f^4 - 3*a*d*e*f^2*g^2 + (3*c*d^2 - a*e^2)*f^3*g)*x)","B",0
748,1,526,0,0.465843," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/(e*x+d)^(3/2)/(g*x+f)^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, c^{3} d^{3} g x^{3} + 7 \, a^{2} c d e^{2} f - 5 \, a^{3} e^{3} g + {\left(7 \, c^{3} d^{3} f - a c^{2} d^{2} e g\right)} x^{2} + 2 \, {\left(7 \, a c^{2} d^{2} e f - 4 \, a^{2} c d e^{2} g\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f}}{35 \, {\left(c^{2} d^{3} f^{6} - 2 \, a c d^{2} e f^{5} g + a^{2} d e^{2} f^{4} g^{2} + {\left(c^{2} d^{2} e f^{2} g^{4} - 2 \, a c d e^{2} f g^{5} + a^{2} e^{3} g^{6}\right)} x^{5} + {\left(4 \, c^{2} d^{2} e f^{3} g^{3} + a^{2} d e^{2} g^{6} + {\left(c^{2} d^{3} - 8 \, a c d e^{2}\right)} f^{2} g^{4} - 2 \, {\left(a c d^{2} e - 2 \, a^{2} e^{3}\right)} f g^{5}\right)} x^{4} + 2 \, {\left(3 \, c^{2} d^{2} e f^{4} g^{2} + 2 \, a^{2} d e^{2} f g^{5} + 2 \, {\left(c^{2} d^{3} - 3 \, a c d e^{2}\right)} f^{3} g^{3} - {\left(4 \, a c d^{2} e - 3 \, a^{2} e^{3}\right)} f^{2} g^{4}\right)} x^{3} + 2 \, {\left(2 \, c^{2} d^{2} e f^{5} g + 3 \, a^{2} d e^{2} f^{2} g^{4} + {\left(3 \, c^{2} d^{3} - 4 \, a c d e^{2}\right)} f^{4} g^{2} - 2 \, {\left(3 \, a c d^{2} e - a^{2} e^{3}\right)} f^{3} g^{3}\right)} x^{2} + {\left(c^{2} d^{2} e f^{6} + 4 \, a^{2} d e^{2} f^{3} g^{3} + 2 \, {\left(2 \, c^{2} d^{3} - a c d e^{2}\right)} f^{5} g - {\left(8 \, a c d^{2} e - a^{2} e^{3}\right)} f^{4} g^{2}\right)} x\right)}}"," ",0,"2/35*(2*c^3*d^3*g*x^3 + 7*a^2*c*d*e^2*f - 5*a^3*e^3*g + (7*c^3*d^3*f - a*c^2*d^2*e*g)*x^2 + 2*(7*a*c^2*d^2*e*f - 4*a^2*c*d*e^2*g)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f)/(c^2*d^3*f^6 - 2*a*c*d^2*e*f^5*g + a^2*d*e^2*f^4*g^2 + (c^2*d^2*e*f^2*g^4 - 2*a*c*d*e^2*f*g^5 + a^2*e^3*g^6)*x^5 + (4*c^2*d^2*e*f^3*g^3 + a^2*d*e^2*g^6 + (c^2*d^3 - 8*a*c*d*e^2)*f^2*g^4 - 2*(a*c*d^2*e - 2*a^2*e^3)*f*g^5)*x^4 + 2*(3*c^2*d^2*e*f^4*g^2 + 2*a^2*d*e^2*f*g^5 + 2*(c^2*d^3 - 3*a*c*d*e^2)*f^3*g^3 - (4*a*c*d^2*e - 3*a^2*e^3)*f^2*g^4)*x^3 + 2*(2*c^2*d^2*e*f^5*g + 3*a^2*d*e^2*f^2*g^4 + (3*c^2*d^3 - 4*a*c*d*e^2)*f^4*g^2 - 2*(3*a*c*d^2*e - a^2*e^3)*f^3*g^3)*x^2 + (c^2*d^2*e*f^6 + 4*a^2*d*e^2*f^3*g^3 + 2*(2*c^2*d^3 - a*c*d*e^2)*f^5*g - (8*a*c*d^2*e - a^2*e^3)*f^4*g^2)*x)","B",0
749,1,918,0,0.464376," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/(e*x+d)^(3/2)/(g*x+f)^(11/2),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, c^{4} d^{4} g^{2} x^{4} + 63 \, a^{2} c^{2} d^{2} e^{2} f^{2} - 90 \, a^{3} c d e^{3} f g + 35 \, a^{4} e^{4} g^{2} + 4 \, {\left(9 \, c^{4} d^{4} f g - a c^{3} d^{3} e g^{2}\right)} x^{3} + 3 \, {\left(21 \, c^{4} d^{4} f^{2} - 6 \, a c^{3} d^{3} e f g + a^{2} c^{2} d^{2} e^{2} g^{2}\right)} x^{2} + 2 \, {\left(63 \, a c^{3} d^{3} e f^{2} - 72 \, a^{2} c^{2} d^{2} e^{2} f g + 25 \, a^{3} c d e^{3} g^{2}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f}}{315 \, {\left(c^{3} d^{4} f^{8} - 3 \, a c^{2} d^{3} e f^{7} g + 3 \, a^{2} c d^{2} e^{2} f^{6} g^{2} - a^{3} d e^{3} f^{5} g^{3} + {\left(c^{3} d^{3} e f^{3} g^{5} - 3 \, a c^{2} d^{2} e^{2} f^{2} g^{6} + 3 \, a^{2} c d e^{3} f g^{7} - a^{3} e^{4} g^{8}\right)} x^{6} + {\left(5 \, c^{3} d^{3} e f^{4} g^{4} - a^{3} d e^{3} g^{8} + {\left(c^{3} d^{4} - 15 \, a c^{2} d^{2} e^{2}\right)} f^{3} g^{5} - 3 \, {\left(a c^{2} d^{3} e - 5 \, a^{2} c d e^{3}\right)} f^{2} g^{6} + {\left(3 \, a^{2} c d^{2} e^{2} - 5 \, a^{3} e^{4}\right)} f g^{7}\right)} x^{5} + 5 \, {\left(2 \, c^{3} d^{3} e f^{5} g^{3} - a^{3} d e^{3} f g^{7} + {\left(c^{3} d^{4} - 6 \, a c^{2} d^{2} e^{2}\right)} f^{4} g^{4} - 3 \, {\left(a c^{2} d^{3} e - 2 \, a^{2} c d e^{3}\right)} f^{3} g^{5} + {\left(3 \, a^{2} c d^{2} e^{2} - 2 \, a^{3} e^{4}\right)} f^{2} g^{6}\right)} x^{4} + 10 \, {\left(c^{3} d^{3} e f^{6} g^{2} - a^{3} d e^{3} f^{2} g^{6} + {\left(c^{3} d^{4} - 3 \, a c^{2} d^{2} e^{2}\right)} f^{5} g^{3} - 3 \, {\left(a c^{2} d^{3} e - a^{2} c d e^{3}\right)} f^{4} g^{4} + {\left(3 \, a^{2} c d^{2} e^{2} - a^{3} e^{4}\right)} f^{3} g^{5}\right)} x^{3} + 5 \, {\left(c^{3} d^{3} e f^{7} g - 2 \, a^{3} d e^{3} f^{3} g^{5} + {\left(2 \, c^{3} d^{4} - 3 \, a c^{2} d^{2} e^{2}\right)} f^{6} g^{2} - 3 \, {\left(2 \, a c^{2} d^{3} e - a^{2} c d e^{3}\right)} f^{5} g^{3} + {\left(6 \, a^{2} c d^{2} e^{2} - a^{3} e^{4}\right)} f^{4} g^{4}\right)} x^{2} + {\left(c^{3} d^{3} e f^{8} - 5 \, a^{3} d e^{3} f^{4} g^{4} + {\left(5 \, c^{3} d^{4} - 3 \, a c^{2} d^{2} e^{2}\right)} f^{7} g - 3 \, {\left(5 \, a c^{2} d^{3} e - a^{2} c d e^{3}\right)} f^{6} g^{2} + {\left(15 \, a^{2} c d^{2} e^{2} - a^{3} e^{4}\right)} f^{5} g^{3}\right)} x\right)}}"," ",0,"2/315*(8*c^4*d^4*g^2*x^4 + 63*a^2*c^2*d^2*e^2*f^2 - 90*a^3*c*d*e^3*f*g + 35*a^4*e^4*g^2 + 4*(9*c^4*d^4*f*g - a*c^3*d^3*e*g^2)*x^3 + 3*(21*c^4*d^4*f^2 - 6*a*c^3*d^3*e*f*g + a^2*c^2*d^2*e^2*g^2)*x^2 + 2*(63*a*c^3*d^3*e*f^2 - 72*a^2*c^2*d^2*e^2*f*g + 25*a^3*c*d*e^3*g^2)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f)/(c^3*d^4*f^8 - 3*a*c^2*d^3*e*f^7*g + 3*a^2*c*d^2*e^2*f^6*g^2 - a^3*d*e^3*f^5*g^3 + (c^3*d^3*e*f^3*g^5 - 3*a*c^2*d^2*e^2*f^2*g^6 + 3*a^2*c*d*e^3*f*g^7 - a^3*e^4*g^8)*x^6 + (5*c^3*d^3*e*f^4*g^4 - a^3*d*e^3*g^8 + (c^3*d^4 - 15*a*c^2*d^2*e^2)*f^3*g^5 - 3*(a*c^2*d^3*e - 5*a^2*c*d*e^3)*f^2*g^6 + (3*a^2*c*d^2*e^2 - 5*a^3*e^4)*f*g^7)*x^5 + 5*(2*c^3*d^3*e*f^5*g^3 - a^3*d*e^3*f*g^7 + (c^3*d^4 - 6*a*c^2*d^2*e^2)*f^4*g^4 - 3*(a*c^2*d^3*e - 2*a^2*c*d*e^3)*f^3*g^5 + (3*a^2*c*d^2*e^2 - 2*a^3*e^4)*f^2*g^6)*x^4 + 10*(c^3*d^3*e*f^6*g^2 - a^3*d*e^3*f^2*g^6 + (c^3*d^4 - 3*a*c^2*d^2*e^2)*f^5*g^3 - 3*(a*c^2*d^3*e - a^2*c*d*e^3)*f^4*g^4 + (3*a^2*c*d^2*e^2 - a^3*e^4)*f^3*g^5)*x^3 + 5*(c^3*d^3*e*f^7*g - 2*a^3*d*e^3*f^3*g^5 + (2*c^3*d^4 - 3*a*c^2*d^2*e^2)*f^6*g^2 - 3*(2*a*c^2*d^3*e - a^2*c*d*e^3)*f^5*g^3 + (6*a^2*c*d^2*e^2 - a^3*e^4)*f^4*g^4)*x^2 + (c^3*d^3*e*f^8 - 5*a^3*d*e^3*f^4*g^4 + (5*c^3*d^4 - 3*a*c^2*d^2*e^2)*f^7*g - 3*(5*a*c^2*d^3*e - a^2*c*d*e^3)*f^6*g^2 + (15*a^2*c*d^2*e^2 - a^3*e^4)*f^5*g^3)*x)","B",0
750,1,1420,0,0.502973," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/(e*x+d)^(3/2)/(g*x+f)^(13/2),x, algorithm=""fricas"")","\frac{2 \, {\left(16 \, c^{5} d^{5} g^{3} x^{5} + 231 \, a^{2} c^{3} d^{3} e^{2} f^{3} - 495 \, a^{3} c^{2} d^{2} e^{3} f^{2} g + 385 \, a^{4} c d e^{4} f g^{2} - 105 \, a^{5} e^{5} g^{3} + 8 \, {\left(11 \, c^{5} d^{5} f g^{2} - a c^{4} d^{4} e g^{3}\right)} x^{4} + 2 \, {\left(99 \, c^{5} d^{5} f^{2} g - 22 \, a c^{4} d^{4} e f g^{2} + 3 \, a^{2} c^{3} d^{3} e^{2} g^{3}\right)} x^{3} + {\left(231 \, c^{5} d^{5} f^{3} - 99 \, a c^{4} d^{4} e f^{2} g + 33 \, a^{2} c^{3} d^{3} e^{2} f g^{2} - 5 \, a^{3} c^{2} d^{2} e^{3} g^{3}\right)} x^{2} + 2 \, {\left(231 \, a c^{4} d^{4} e f^{3} - 396 \, a^{2} c^{3} d^{3} e^{2} f^{2} g + 275 \, a^{3} c^{2} d^{2} e^{3} f g^{2} - 70 \, a^{4} c d e^{4} g^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f}}{1155 \, {\left(c^{4} d^{5} f^{10} - 4 \, a c^{3} d^{4} e f^{9} g + 6 \, a^{2} c^{2} d^{3} e^{2} f^{8} g^{2} - 4 \, a^{3} c d^{2} e^{3} f^{7} g^{3} + a^{4} d e^{4} f^{6} g^{4} + {\left(c^{4} d^{4} e f^{4} g^{6} - 4 \, a c^{3} d^{3} e^{2} f^{3} g^{7} + 6 \, a^{2} c^{2} d^{2} e^{3} f^{2} g^{8} - 4 \, a^{3} c d e^{4} f g^{9} + a^{4} e^{5} g^{10}\right)} x^{7} + {\left(6 \, c^{4} d^{4} e f^{5} g^{5} + a^{4} d e^{4} g^{10} + {\left(c^{4} d^{5} - 24 \, a c^{3} d^{3} e^{2}\right)} f^{4} g^{6} - 4 \, {\left(a c^{3} d^{4} e - 9 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{3} g^{7} + 6 \, {\left(a^{2} c^{2} d^{3} e^{2} - 4 \, a^{3} c d e^{4}\right)} f^{2} g^{8} - 2 \, {\left(2 \, a^{3} c d^{2} e^{3} - 3 \, a^{4} e^{5}\right)} f g^{9}\right)} x^{6} + 3 \, {\left(5 \, c^{4} d^{4} e f^{6} g^{4} + 2 \, a^{4} d e^{4} f g^{9} + 2 \, {\left(c^{4} d^{5} - 10 \, a c^{3} d^{3} e^{2}\right)} f^{5} g^{5} - 2 \, {\left(4 \, a c^{3} d^{4} e - 15 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{4} g^{6} + 4 \, {\left(3 \, a^{2} c^{2} d^{3} e^{2} - 5 \, a^{3} c d e^{4}\right)} f^{3} g^{7} - {\left(8 \, a^{3} c d^{2} e^{3} - 5 \, a^{4} e^{5}\right)} f^{2} g^{8}\right)} x^{5} + 5 \, {\left(4 \, c^{4} d^{4} e f^{7} g^{3} + 3 \, a^{4} d e^{4} f^{2} g^{8} + {\left(3 \, c^{4} d^{5} - 16 \, a c^{3} d^{3} e^{2}\right)} f^{6} g^{4} - 12 \, {\left(a c^{3} d^{4} e - 2 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{5} g^{5} + 2 \, {\left(9 \, a^{2} c^{2} d^{3} e^{2} - 8 \, a^{3} c d e^{4}\right)} f^{4} g^{6} - 4 \, {\left(3 \, a^{3} c d^{2} e^{3} - a^{4} e^{5}\right)} f^{3} g^{7}\right)} x^{4} + 5 \, {\left(3 \, c^{4} d^{4} e f^{8} g^{2} + 4 \, a^{4} d e^{4} f^{3} g^{7} + 4 \, {\left(c^{4} d^{5} - 3 \, a c^{3} d^{3} e^{2}\right)} f^{7} g^{3} - 2 \, {\left(8 \, a c^{3} d^{4} e - 9 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{6} g^{4} + 12 \, {\left(2 \, a^{2} c^{2} d^{3} e^{2} - a^{3} c d e^{4}\right)} f^{5} g^{5} - {\left(16 \, a^{3} c d^{2} e^{3} - 3 \, a^{4} e^{5}\right)} f^{4} g^{6}\right)} x^{3} + 3 \, {\left(2 \, c^{4} d^{4} e f^{9} g + 5 \, a^{4} d e^{4} f^{4} g^{6} + {\left(5 \, c^{4} d^{5} - 8 \, a c^{3} d^{3} e^{2}\right)} f^{8} g^{2} - 4 \, {\left(5 \, a c^{3} d^{4} e - 3 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{7} g^{3} + 2 \, {\left(15 \, a^{2} c^{2} d^{3} e^{2} - 4 \, a^{3} c d e^{4}\right)} f^{6} g^{4} - 2 \, {\left(10 \, a^{3} c d^{2} e^{3} - a^{4} e^{5}\right)} f^{5} g^{5}\right)} x^{2} + {\left(c^{4} d^{4} e f^{10} + 6 \, a^{4} d e^{4} f^{5} g^{5} + 2 \, {\left(3 \, c^{4} d^{5} - 2 \, a c^{3} d^{3} e^{2}\right)} f^{9} g - 6 \, {\left(4 \, a c^{3} d^{4} e - a^{2} c^{2} d^{2} e^{3}\right)} f^{8} g^{2} + 4 \, {\left(9 \, a^{2} c^{2} d^{3} e^{2} - a^{3} c d e^{4}\right)} f^{7} g^{3} - {\left(24 \, a^{3} c d^{2} e^{3} - a^{4} e^{5}\right)} f^{6} g^{4}\right)} x\right)}}"," ",0,"2/1155*(16*c^5*d^5*g^3*x^5 + 231*a^2*c^3*d^3*e^2*f^3 - 495*a^3*c^2*d^2*e^3*f^2*g + 385*a^4*c*d*e^4*f*g^2 - 105*a^5*e^5*g^3 + 8*(11*c^5*d^5*f*g^2 - a*c^4*d^4*e*g^3)*x^4 + 2*(99*c^5*d^5*f^2*g - 22*a*c^4*d^4*e*f*g^2 + 3*a^2*c^3*d^3*e^2*g^3)*x^3 + (231*c^5*d^5*f^3 - 99*a*c^4*d^4*e*f^2*g + 33*a^2*c^3*d^3*e^2*f*g^2 - 5*a^3*c^2*d^2*e^3*g^3)*x^2 + 2*(231*a*c^4*d^4*e*f^3 - 396*a^2*c^3*d^3*e^2*f^2*g + 275*a^3*c^2*d^2*e^3*f*g^2 - 70*a^4*c*d*e^4*g^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f)/(c^4*d^5*f^10 - 4*a*c^3*d^4*e*f^9*g + 6*a^2*c^2*d^3*e^2*f^8*g^2 - 4*a^3*c*d^2*e^3*f^7*g^3 + a^4*d*e^4*f^6*g^4 + (c^4*d^4*e*f^4*g^6 - 4*a*c^3*d^3*e^2*f^3*g^7 + 6*a^2*c^2*d^2*e^3*f^2*g^8 - 4*a^3*c*d*e^4*f*g^9 + a^4*e^5*g^10)*x^7 + (6*c^4*d^4*e*f^5*g^5 + a^4*d*e^4*g^10 + (c^4*d^5 - 24*a*c^3*d^3*e^2)*f^4*g^6 - 4*(a*c^3*d^4*e - 9*a^2*c^2*d^2*e^3)*f^3*g^7 + 6*(a^2*c^2*d^3*e^2 - 4*a^3*c*d*e^4)*f^2*g^8 - 2*(2*a^3*c*d^2*e^3 - 3*a^4*e^5)*f*g^9)*x^6 + 3*(5*c^4*d^4*e*f^6*g^4 + 2*a^4*d*e^4*f*g^9 + 2*(c^4*d^5 - 10*a*c^3*d^3*e^2)*f^5*g^5 - 2*(4*a*c^3*d^4*e - 15*a^2*c^2*d^2*e^3)*f^4*g^6 + 4*(3*a^2*c^2*d^3*e^2 - 5*a^3*c*d*e^4)*f^3*g^7 - (8*a^3*c*d^2*e^3 - 5*a^4*e^5)*f^2*g^8)*x^5 + 5*(4*c^4*d^4*e*f^7*g^3 + 3*a^4*d*e^4*f^2*g^8 + (3*c^4*d^5 - 16*a*c^3*d^3*e^2)*f^6*g^4 - 12*(a*c^3*d^4*e - 2*a^2*c^2*d^2*e^3)*f^5*g^5 + 2*(9*a^2*c^2*d^3*e^2 - 8*a^3*c*d*e^4)*f^4*g^6 - 4*(3*a^3*c*d^2*e^3 - a^4*e^5)*f^3*g^7)*x^4 + 5*(3*c^4*d^4*e*f^8*g^2 + 4*a^4*d*e^4*f^3*g^7 + 4*(c^4*d^5 - 3*a*c^3*d^3*e^2)*f^7*g^3 - 2*(8*a*c^3*d^4*e - 9*a^2*c^2*d^2*e^3)*f^6*g^4 + 12*(2*a^2*c^2*d^3*e^2 - a^3*c*d*e^4)*f^5*g^5 - (16*a^3*c*d^2*e^3 - 3*a^4*e^5)*f^4*g^6)*x^3 + 3*(2*c^4*d^4*e*f^9*g + 5*a^4*d*e^4*f^4*g^6 + (5*c^4*d^5 - 8*a*c^3*d^3*e^2)*f^8*g^2 - 4*(5*a*c^3*d^4*e - 3*a^2*c^2*d^2*e^3)*f^7*g^3 + 2*(15*a^2*c^2*d^3*e^2 - 4*a^3*c*d*e^4)*f^6*g^4 - 2*(10*a^3*c*d^2*e^3 - a^4*e^5)*f^5*g^5)*x^2 + (c^4*d^4*e*f^10 + 6*a^4*d*e^4*f^5*g^5 + 2*(3*c^4*d^5 - 2*a*c^3*d^3*e^2)*f^9*g - 6*(4*a*c^3*d^4*e - a^2*c^2*d^2*e^3)*f^8*g^2 + 4*(9*a^2*c^2*d^3*e^2 - a^3*c*d*e^4)*f^7*g^3 - (24*a^3*c*d^2*e^3 - a^4*e^5)*f^6*g^4)*x)","B",0
751,1,1331,0,5.787951," ","integrate((g*x+f)^(3/2)*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^(5/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(128 \, c^{5} d^{5} g^{5} x^{4} + 15 \, c^{5} d^{5} f^{4} g - 70 \, a c^{4} d^{4} e f^{3} g^{2} + 128 \, a^{2} c^{3} d^{3} e^{2} f^{2} g^{3} + 70 \, a^{3} c^{2} d^{2} e^{3} f g^{4} - 15 \, a^{4} c d e^{4} g^{5} + 16 \, {\left(11 \, c^{5} d^{5} f g^{4} + 21 \, a c^{4} d^{4} e g^{5}\right)} x^{3} + 8 \, {\left(c^{5} d^{5} f^{2} g^{3} + 64 \, a c^{4} d^{4} e f g^{4} + 31 \, a^{2} c^{3} d^{3} e^{2} g^{5}\right)} x^{2} - 2 \, {\left(5 \, c^{5} d^{5} f^{3} g^{2} - 23 \, a c^{4} d^{4} e f^{2} g^{3} - 233 \, a^{2} c^{3} d^{3} e^{2} f g^{4} - 5 \, a^{3} c^{2} d^{2} e^{3} g^{5}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} - 15 \, {\left(c^{5} d^{6} f^{5} - 5 \, a c^{4} d^{5} e f^{4} g + 10 \, a^{2} c^{3} d^{4} e^{2} f^{3} g^{2} - 10 \, a^{3} c^{2} d^{3} e^{3} f^{2} g^{3} + 5 \, a^{4} c d^{2} e^{4} f g^{4} - a^{5} d e^{5} g^{5} + {\left(c^{5} d^{5} e f^{5} - 5 \, a c^{4} d^{4} e^{2} f^{4} g + 10 \, a^{2} c^{3} d^{3} e^{3} f^{3} g^{2} - 10 \, a^{3} c^{2} d^{2} e^{4} f^{2} g^{3} + 5 \, a^{4} c d e^{5} f g^{4} - a^{5} e^{6} g^{5}\right)} x\right)} \sqrt{c d g} \log\left(-\frac{8 \, c^{2} d^{2} e g^{2} x^{3} + c^{2} d^{3} f^{2} + 6 \, a c d^{2} e f g + a^{2} d e^{2} g^{2} + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d g x + c d f + a e g\right)} \sqrt{c d g} \sqrt{e x + d} \sqrt{g x + f} + 8 \, {\left(c^{2} d^{2} e f g + {\left(c^{2} d^{3} + a c d e^{2}\right)} g^{2}\right)} x^{2} + {\left(c^{2} d^{2} e f^{2} + 2 \, {\left(4 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f g + {\left(8 \, a c d^{2} e + a^{2} e^{3}\right)} g^{2}\right)} x}{e x + d}\right)}{2560 \, {\left(c^{3} d^{3} e g^{4} x + c^{3} d^{4} g^{4}\right)}}, \frac{2 \, {\left(128 \, c^{5} d^{5} g^{5} x^{4} + 15 \, c^{5} d^{5} f^{4} g - 70 \, a c^{4} d^{4} e f^{3} g^{2} + 128 \, a^{2} c^{3} d^{3} e^{2} f^{2} g^{3} + 70 \, a^{3} c^{2} d^{2} e^{3} f g^{4} - 15 \, a^{4} c d e^{4} g^{5} + 16 \, {\left(11 \, c^{5} d^{5} f g^{4} + 21 \, a c^{4} d^{4} e g^{5}\right)} x^{3} + 8 \, {\left(c^{5} d^{5} f^{2} g^{3} + 64 \, a c^{4} d^{4} e f g^{4} + 31 \, a^{2} c^{3} d^{3} e^{2} g^{5}\right)} x^{2} - 2 \, {\left(5 \, c^{5} d^{5} f^{3} g^{2} - 23 \, a c^{4} d^{4} e f^{2} g^{3} - 233 \, a^{2} c^{3} d^{3} e^{2} f g^{4} - 5 \, a^{3} c^{2} d^{2} e^{3} g^{5}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} + 15 \, {\left(c^{5} d^{6} f^{5} - 5 \, a c^{4} d^{5} e f^{4} g + 10 \, a^{2} c^{3} d^{4} e^{2} f^{3} g^{2} - 10 \, a^{3} c^{2} d^{3} e^{3} f^{2} g^{3} + 5 \, a^{4} c d^{2} e^{4} f g^{4} - a^{5} d e^{5} g^{5} + {\left(c^{5} d^{5} e f^{5} - 5 \, a c^{4} d^{4} e^{2} f^{4} g + 10 \, a^{2} c^{3} d^{3} e^{3} f^{3} g^{2} - 10 \, a^{3} c^{2} d^{2} e^{4} f^{2} g^{3} + 5 \, a^{4} c d e^{5} f g^{4} - a^{5} e^{6} g^{5}\right)} x\right)} \sqrt{-c d g} \arctan\left(\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{-c d g} \sqrt{e x + d} \sqrt{g x + f}}{2 \, c d e g x^{2} + c d^{2} f + a d e g + {\left(c d e f + {\left(2 \, c d^{2} + a e^{2}\right)} g\right)} x}\right)}{1280 \, {\left(c^{3} d^{3} e g^{4} x + c^{3} d^{4} g^{4}\right)}}\right]"," ",0,"[1/2560*(4*(128*c^5*d^5*g^5*x^4 + 15*c^5*d^5*f^4*g - 70*a*c^4*d^4*e*f^3*g^2 + 128*a^2*c^3*d^3*e^2*f^2*g^3 + 70*a^3*c^2*d^2*e^3*f*g^4 - 15*a^4*c*d*e^4*g^5 + 16*(11*c^5*d^5*f*g^4 + 21*a*c^4*d^4*e*g^5)*x^3 + 8*(c^5*d^5*f^2*g^3 + 64*a*c^4*d^4*e*f*g^4 + 31*a^2*c^3*d^3*e^2*g^5)*x^2 - 2*(5*c^5*d^5*f^3*g^2 - 23*a*c^4*d^4*e*f^2*g^3 - 233*a^2*c^3*d^3*e^2*f*g^4 - 5*a^3*c^2*d^2*e^3*g^5)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f) - 15*(c^5*d^6*f^5 - 5*a*c^4*d^5*e*f^4*g + 10*a^2*c^3*d^4*e^2*f^3*g^2 - 10*a^3*c^2*d^3*e^3*f^2*g^3 + 5*a^4*c*d^2*e^4*f*g^4 - a^5*d*e^5*g^5 + (c^5*d^5*e*f^5 - 5*a*c^4*d^4*e^2*f^4*g + 10*a^2*c^3*d^3*e^3*f^3*g^2 - 10*a^3*c^2*d^2*e^4*f^2*g^3 + 5*a^4*c*d*e^5*f*g^4 - a^5*e^6*g^5)*x)*sqrt(c*d*g)*log(-(8*c^2*d^2*e*g^2*x^3 + c^2*d^3*f^2 + 6*a*c*d^2*e*f*g + a^2*d*e^2*g^2 + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*g*x + c*d*f + a*e*g)*sqrt(c*d*g)*sqrt(e*x + d)*sqrt(g*x + f) + 8*(c^2*d^2*e*f*g + (c^2*d^3 + a*c*d*e^2)*g^2)*x^2 + (c^2*d^2*e*f^2 + 2*(4*c^2*d^3 + 3*a*c*d*e^2)*f*g + (8*a*c*d^2*e + a^2*e^3)*g^2)*x)/(e*x + d)))/(c^3*d^3*e*g^4*x + c^3*d^4*g^4), 1/1280*(2*(128*c^5*d^5*g^5*x^4 + 15*c^5*d^5*f^4*g - 70*a*c^4*d^4*e*f^3*g^2 + 128*a^2*c^3*d^3*e^2*f^2*g^3 + 70*a^3*c^2*d^2*e^3*f*g^4 - 15*a^4*c*d*e^4*g^5 + 16*(11*c^5*d^5*f*g^4 + 21*a*c^4*d^4*e*g^5)*x^3 + 8*(c^5*d^5*f^2*g^3 + 64*a*c^4*d^4*e*f*g^4 + 31*a^2*c^3*d^3*e^2*g^5)*x^2 - 2*(5*c^5*d^5*f^3*g^2 - 23*a*c^4*d^4*e*f^2*g^3 - 233*a^2*c^3*d^3*e^2*f*g^4 - 5*a^3*c^2*d^2*e^3*g^5)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f) + 15*(c^5*d^6*f^5 - 5*a*c^4*d^5*e*f^4*g + 10*a^2*c^3*d^4*e^2*f^3*g^2 - 10*a^3*c^2*d^3*e^3*f^2*g^3 + 5*a^4*c*d^2*e^4*f*g^4 - a^5*d*e^5*g^5 + (c^5*d^5*e*f^5 - 5*a*c^4*d^4*e^2*f^4*g + 10*a^2*c^3*d^3*e^3*f^3*g^2 - 10*a^3*c^2*d^2*e^4*f^2*g^3 + 5*a^4*c*d*e^5*f*g^4 - a^5*e^6*g^5)*x)*sqrt(-c*d*g)*arctan(2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-c*d*g)*sqrt(e*x + d)*sqrt(g*x + f)/(2*c*d*e*g*x^2 + c*d^2*f + a*d*e*g + (c*d*e*f + (2*c*d^2 + a*e^2)*g)*x)))/(c^3*d^3*e*g^4*x + c^3*d^4*g^4)]","A",0
752,1,1065,0,2.711336," ","integrate((g*x+f)^(1/2)*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^(5/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(48 \, c^{4} d^{4} g^{4} x^{3} + 15 \, c^{4} d^{4} f^{3} g - 55 \, a c^{3} d^{3} e f^{2} g^{2} + 73 \, a^{2} c^{2} d^{2} e^{2} f g^{3} + 15 \, a^{3} c d e^{3} g^{4} + 8 \, {\left(c^{4} d^{4} f g^{3} + 17 \, a c^{3} d^{3} e g^{4}\right)} x^{2} - 2 \, {\left(5 \, c^{4} d^{4} f^{2} g^{2} - 18 \, a c^{3} d^{3} e f g^{3} - 59 \, a^{2} c^{2} d^{2} e^{2} g^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} + 15 \, {\left(c^{4} d^{5} f^{4} - 4 \, a c^{3} d^{4} e f^{3} g + 6 \, a^{2} c^{2} d^{3} e^{2} f^{2} g^{2} - 4 \, a^{3} c d^{2} e^{3} f g^{3} + a^{4} d e^{4} g^{4} + {\left(c^{4} d^{4} e f^{4} - 4 \, a c^{3} d^{3} e^{2} f^{3} g + 6 \, a^{2} c^{2} d^{2} e^{3} f^{2} g^{2} - 4 \, a^{3} c d e^{4} f g^{3} + a^{4} e^{5} g^{4}\right)} x\right)} \sqrt{c d g} \log\left(-\frac{8 \, c^{2} d^{2} e g^{2} x^{3} + c^{2} d^{3} f^{2} + 6 \, a c d^{2} e f g + a^{2} d e^{2} g^{2} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d g x + c d f + a e g\right)} \sqrt{c d g} \sqrt{e x + d} \sqrt{g x + f} + 8 \, {\left(c^{2} d^{2} e f g + {\left(c^{2} d^{3} + a c d e^{2}\right)} g^{2}\right)} x^{2} + {\left(c^{2} d^{2} e f^{2} + 2 \, {\left(4 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f g + {\left(8 \, a c d^{2} e + a^{2} e^{3}\right)} g^{2}\right)} x}{e x + d}\right)}{768 \, {\left(c^{2} d^{2} e g^{4} x + c^{2} d^{3} g^{4}\right)}}, \frac{2 \, {\left(48 \, c^{4} d^{4} g^{4} x^{3} + 15 \, c^{4} d^{4} f^{3} g - 55 \, a c^{3} d^{3} e f^{2} g^{2} + 73 \, a^{2} c^{2} d^{2} e^{2} f g^{3} + 15 \, a^{3} c d e^{3} g^{4} + 8 \, {\left(c^{4} d^{4} f g^{3} + 17 \, a c^{3} d^{3} e g^{4}\right)} x^{2} - 2 \, {\left(5 \, c^{4} d^{4} f^{2} g^{2} - 18 \, a c^{3} d^{3} e f g^{3} - 59 \, a^{2} c^{2} d^{2} e^{2} g^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} + 15 \, {\left(c^{4} d^{5} f^{4} - 4 \, a c^{3} d^{4} e f^{3} g + 6 \, a^{2} c^{2} d^{3} e^{2} f^{2} g^{2} - 4 \, a^{3} c d^{2} e^{3} f g^{3} + a^{4} d e^{4} g^{4} + {\left(c^{4} d^{4} e f^{4} - 4 \, a c^{3} d^{3} e^{2} f^{3} g + 6 \, a^{2} c^{2} d^{2} e^{3} f^{2} g^{2} - 4 \, a^{3} c d e^{4} f g^{3} + a^{4} e^{5} g^{4}\right)} x\right)} \sqrt{-c d g} \arctan\left(\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{-c d g} \sqrt{e x + d} \sqrt{g x + f}}{2 \, c d e g x^{2} + c d^{2} f + a d e g + {\left(c d e f + {\left(2 \, c d^{2} + a e^{2}\right)} g\right)} x}\right)}{384 \, {\left(c^{2} d^{2} e g^{4} x + c^{2} d^{3} g^{4}\right)}}\right]"," ",0,"[1/768*(4*(48*c^4*d^4*g^4*x^3 + 15*c^4*d^4*f^3*g - 55*a*c^3*d^3*e*f^2*g^2 + 73*a^2*c^2*d^2*e^2*f*g^3 + 15*a^3*c*d*e^3*g^4 + 8*(c^4*d^4*f*g^3 + 17*a*c^3*d^3*e*g^4)*x^2 - 2*(5*c^4*d^4*f^2*g^2 - 18*a*c^3*d^3*e*f*g^3 - 59*a^2*c^2*d^2*e^2*g^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f) + 15*(c^4*d^5*f^4 - 4*a*c^3*d^4*e*f^3*g + 6*a^2*c^2*d^3*e^2*f^2*g^2 - 4*a^3*c*d^2*e^3*f*g^3 + a^4*d*e^4*g^4 + (c^4*d^4*e*f^4 - 4*a*c^3*d^3*e^2*f^3*g + 6*a^2*c^2*d^2*e^3*f^2*g^2 - 4*a^3*c*d*e^4*f*g^3 + a^4*e^5*g^4)*x)*sqrt(c*d*g)*log(-(8*c^2*d^2*e*g^2*x^3 + c^2*d^3*f^2 + 6*a*c*d^2*e*f*g + a^2*d*e^2*g^2 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*g*x + c*d*f + a*e*g)*sqrt(c*d*g)*sqrt(e*x + d)*sqrt(g*x + f) + 8*(c^2*d^2*e*f*g + (c^2*d^3 + a*c*d*e^2)*g^2)*x^2 + (c^2*d^2*e*f^2 + 2*(4*c^2*d^3 + 3*a*c*d*e^2)*f*g + (8*a*c*d^2*e + a^2*e^3)*g^2)*x)/(e*x + d)))/(c^2*d^2*e*g^4*x + c^2*d^3*g^4), 1/384*(2*(48*c^4*d^4*g^4*x^3 + 15*c^4*d^4*f^3*g - 55*a*c^3*d^3*e*f^2*g^2 + 73*a^2*c^2*d^2*e^2*f*g^3 + 15*a^3*c*d*e^3*g^4 + 8*(c^4*d^4*f*g^3 + 17*a*c^3*d^3*e*g^4)*x^2 - 2*(5*c^4*d^4*f^2*g^2 - 18*a*c^3*d^3*e*f*g^3 - 59*a^2*c^2*d^2*e^2*g^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f) + 15*(c^4*d^5*f^4 - 4*a*c^3*d^4*e*f^3*g + 6*a^2*c^2*d^3*e^2*f^2*g^2 - 4*a^3*c*d^2*e^3*f*g^3 + a^4*d*e^4*g^4 + (c^4*d^4*e*f^4 - 4*a*c^3*d^3*e^2*f^3*g + 6*a^2*c^2*d^2*e^3*f^2*g^2 - 4*a^3*c*d*e^4*f*g^3 + a^4*e^5*g^4)*x)*sqrt(-c*d*g)*arctan(2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-c*d*g)*sqrt(e*x + d)*sqrt(g*x + f)/(2*c*d*e*g*x^2 + c*d^2*f + a*d*e*g + (c*d*e*f + (2*c*d^2 + a*e^2)*g)*x)))/(c^2*d^2*e*g^4*x + c^2*d^3*g^4)]","A",0
753,1,837,0,1.555120," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^(5/2)/(g*x+f)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(8 \, c^{3} d^{3} g^{3} x^{2} + 15 \, c^{3} d^{3} f^{2} g - 40 \, a c^{2} d^{2} e f g^{2} + 33 \, a^{2} c d e^{2} g^{3} - 2 \, {\left(5 \, c^{3} d^{3} f g^{2} - 13 \, a c^{2} d^{2} e g^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} - 15 \, {\left(c^{3} d^{4} f^{3} - 3 \, a c^{2} d^{3} e f^{2} g + 3 \, a^{2} c d^{2} e^{2} f g^{2} - a^{3} d e^{3} g^{3} + {\left(c^{3} d^{3} e f^{3} - 3 \, a c^{2} d^{2} e^{2} f^{2} g + 3 \, a^{2} c d e^{3} f g^{2} - a^{3} e^{4} g^{3}\right)} x\right)} \sqrt{c d g} \log\left(-\frac{8 \, c^{2} d^{2} e g^{2} x^{3} + c^{2} d^{3} f^{2} + 6 \, a c d^{2} e f g + a^{2} d e^{2} g^{2} + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d g x + c d f + a e g\right)} \sqrt{c d g} \sqrt{e x + d} \sqrt{g x + f} + 8 \, {\left(c^{2} d^{2} e f g + {\left(c^{2} d^{3} + a c d e^{2}\right)} g^{2}\right)} x^{2} + {\left(c^{2} d^{2} e f^{2} + 2 \, {\left(4 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f g + {\left(8 \, a c d^{2} e + a^{2} e^{3}\right)} g^{2}\right)} x}{e x + d}\right)}{96 \, {\left(c d e g^{4} x + c d^{2} g^{4}\right)}}, \frac{2 \, {\left(8 \, c^{3} d^{3} g^{3} x^{2} + 15 \, c^{3} d^{3} f^{2} g - 40 \, a c^{2} d^{2} e f g^{2} + 33 \, a^{2} c d e^{2} g^{3} - 2 \, {\left(5 \, c^{3} d^{3} f g^{2} - 13 \, a c^{2} d^{2} e g^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} + 15 \, {\left(c^{3} d^{4} f^{3} - 3 \, a c^{2} d^{3} e f^{2} g + 3 \, a^{2} c d^{2} e^{2} f g^{2} - a^{3} d e^{3} g^{3} + {\left(c^{3} d^{3} e f^{3} - 3 \, a c^{2} d^{2} e^{2} f^{2} g + 3 \, a^{2} c d e^{3} f g^{2} - a^{3} e^{4} g^{3}\right)} x\right)} \sqrt{-c d g} \arctan\left(\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{-c d g} \sqrt{e x + d} \sqrt{g x + f}}{2 \, c d e g x^{2} + c d^{2} f + a d e g + {\left(c d e f + {\left(2 \, c d^{2} + a e^{2}\right)} g\right)} x}\right)}{48 \, {\left(c d e g^{4} x + c d^{2} g^{4}\right)}}\right]"," ",0,"[1/96*(4*(8*c^3*d^3*g^3*x^2 + 15*c^3*d^3*f^2*g - 40*a*c^2*d^2*e*f*g^2 + 33*a^2*c*d*e^2*g^3 - 2*(5*c^3*d^3*f*g^2 - 13*a*c^2*d^2*e*g^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f) - 15*(c^3*d^4*f^3 - 3*a*c^2*d^3*e*f^2*g + 3*a^2*c*d^2*e^2*f*g^2 - a^3*d*e^3*g^3 + (c^3*d^3*e*f^3 - 3*a*c^2*d^2*e^2*f^2*g + 3*a^2*c*d*e^3*f*g^2 - a^3*e^4*g^3)*x)*sqrt(c*d*g)*log(-(8*c^2*d^2*e*g^2*x^3 + c^2*d^3*f^2 + 6*a*c*d^2*e*f*g + a^2*d*e^2*g^2 + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*g*x + c*d*f + a*e*g)*sqrt(c*d*g)*sqrt(e*x + d)*sqrt(g*x + f) + 8*(c^2*d^2*e*f*g + (c^2*d^3 + a*c*d*e^2)*g^2)*x^2 + (c^2*d^2*e*f^2 + 2*(4*c^2*d^3 + 3*a*c*d*e^2)*f*g + (8*a*c*d^2*e + a^2*e^3)*g^2)*x)/(e*x + d)))/(c*d*e*g^4*x + c*d^2*g^4), 1/48*(2*(8*c^3*d^3*g^3*x^2 + 15*c^3*d^3*f^2*g - 40*a*c^2*d^2*e*f*g^2 + 33*a^2*c*d*e^2*g^3 - 2*(5*c^3*d^3*f*g^2 - 13*a*c^2*d^2*e*g^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f) + 15*(c^3*d^4*f^3 - 3*a*c^2*d^3*e*f^2*g + 3*a^2*c*d^2*e^2*f*g^2 - a^3*d*e^3*g^3 + (c^3*d^3*e*f^3 - 3*a*c^2*d^2*e^2*f^2*g + 3*a^2*c*d*e^3*f*g^2 - a^3*e^4*g^3)*x)*sqrt(-c*d*g)*arctan(2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-c*d*g)*sqrt(e*x + d)*sqrt(g*x + f)/(2*c*d*e*g*x^2 + c*d^2*f + a*d*e*g + (c*d*e*f + (2*c*d^2 + a*e^2)*g)*x)))/(c*d*e*g^4*x + c*d^2*g^4)]","A",0
754,1,915,0,1.197425," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^(5/2)/(g*x+f)^(3/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(2 \, c^{2} d^{2} g^{2} x^{2} - 15 \, c^{2} d^{2} f^{2} + 25 \, a c d e f g - 8 \, a^{2} e^{2} g^{2} - {\left(5 \, c^{2} d^{2} f g - 9 \, a c d e g^{2}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} + 15 \, {\left(c^{2} d^{3} f^{3} - 2 \, a c d^{2} e f^{2} g + a^{2} d e^{2} f g^{2} + {\left(c^{2} d^{2} e f^{2} g - 2 \, a c d e^{2} f g^{2} + a^{2} e^{3} g^{3}\right)} x^{2} + {\left(c^{2} d^{2} e f^{3} + a^{2} d e^{2} g^{3} + {\left(c^{2} d^{3} - 2 \, a c d e^{2}\right)} f^{2} g - {\left(2 \, a c d^{2} e - a^{2} e^{3}\right)} f g^{2}\right)} x\right)} \sqrt{\frac{c d}{g}} \log\left(-\frac{8 \, c^{2} d^{2} e g^{2} x^{3} + c^{2} d^{3} f^{2} + 6 \, a c d^{2} e f g + a^{2} d e^{2} g^{2} + 4 \, {\left(2 \, c d g^{2} x + c d f g + a e g^{2}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} \sqrt{\frac{c d}{g}} + 8 \, {\left(c^{2} d^{2} e f g + {\left(c^{2} d^{3} + a c d e^{2}\right)} g^{2}\right)} x^{2} + {\left(c^{2} d^{2} e f^{2} + 2 \, {\left(4 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f g + {\left(8 \, a c d^{2} e + a^{2} e^{3}\right)} g^{2}\right)} x}{e x + d}\right)}{16 \, {\left(e g^{4} x^{2} + d f g^{3} + {\left(e f g^{3} + d g^{4}\right)} x\right)}}, \frac{2 \, {\left(2 \, c^{2} d^{2} g^{2} x^{2} - 15 \, c^{2} d^{2} f^{2} + 25 \, a c d e f g - 8 \, a^{2} e^{2} g^{2} - {\left(5 \, c^{2} d^{2} f g - 9 \, a c d e g^{2}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} - 15 \, {\left(c^{2} d^{3} f^{3} - 2 \, a c d^{2} e f^{2} g + a^{2} d e^{2} f g^{2} + {\left(c^{2} d^{2} e f^{2} g - 2 \, a c d e^{2} f g^{2} + a^{2} e^{3} g^{3}\right)} x^{2} + {\left(c^{2} d^{2} e f^{3} + a^{2} d e^{2} g^{3} + {\left(c^{2} d^{3} - 2 \, a c d e^{2}\right)} f^{2} g - {\left(2 \, a c d^{2} e - a^{2} e^{3}\right)} f g^{2}\right)} x\right)} \sqrt{-\frac{c d}{g}} \arctan\left(\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} \sqrt{-\frac{c d}{g}} g}{2 \, c d e g x^{2} + c d^{2} f + a d e g + {\left(c d e f + {\left(2 \, c d^{2} + a e^{2}\right)} g\right)} x}\right)}{8 \, {\left(e g^{4} x^{2} + d f g^{3} + {\left(e f g^{3} + d g^{4}\right)} x\right)}}\right]"," ",0,"[1/16*(4*(2*c^2*d^2*g^2*x^2 - 15*c^2*d^2*f^2 + 25*a*c*d*e*f*g - 8*a^2*e^2*g^2 - (5*c^2*d^2*f*g - 9*a*c*d*e*g^2)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f) + 15*(c^2*d^3*f^3 - 2*a*c*d^2*e*f^2*g + a^2*d*e^2*f*g^2 + (c^2*d^2*e*f^2*g - 2*a*c*d*e^2*f*g^2 + a^2*e^3*g^3)*x^2 + (c^2*d^2*e*f^3 + a^2*d*e^2*g^3 + (c^2*d^3 - 2*a*c*d*e^2)*f^2*g - (2*a*c*d^2*e - a^2*e^3)*f*g^2)*x)*sqrt(c*d/g)*log(-(8*c^2*d^2*e*g^2*x^3 + c^2*d^3*f^2 + 6*a*c*d^2*e*f*g + a^2*d*e^2*g^2 + 4*(2*c*d*g^2*x + c*d*f*g + a*e*g^2)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f)*sqrt(c*d/g) + 8*(c^2*d^2*e*f*g + (c^2*d^3 + a*c*d*e^2)*g^2)*x^2 + (c^2*d^2*e*f^2 + 2*(4*c^2*d^3 + 3*a*c*d*e^2)*f*g + (8*a*c*d^2*e + a^2*e^3)*g^2)*x)/(e*x + d)))/(e*g^4*x^2 + d*f*g^3 + (e*f*g^3 + d*g^4)*x), 1/8*(2*(2*c^2*d^2*g^2*x^2 - 15*c^2*d^2*f^2 + 25*a*c*d*e*f*g - 8*a^2*e^2*g^2 - (5*c^2*d^2*f*g - 9*a*c*d*e*g^2)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f) - 15*(c^2*d^3*f^3 - 2*a*c*d^2*e*f^2*g + a^2*d*e^2*f*g^2 + (c^2*d^2*e*f^2*g - 2*a*c*d*e^2*f*g^2 + a^2*e^3*g^3)*x^2 + (c^2*d^2*e*f^3 + a^2*d*e^2*g^3 + (c^2*d^3 - 2*a*c*d*e^2)*f^2*g - (2*a*c*d^2*e - a^2*e^3)*f*g^2)*x)*sqrt(-c*d/g)*arctan(2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f)*sqrt(-c*d/g)*g/(2*c*d*e*g*x^2 + c*d^2*f + a*d*e*g + (c*d*e*f + (2*c*d^2 + a*e^2)*g)*x)))/(e*g^4*x^2 + d*f*g^3 + (e*f*g^3 + d*g^4)*x)]","A",0
755,1,973,0,1.146013," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^(5/2)/(g*x+f)^(5/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(3 \, c^{2} d^{2} g^{2} x^{2} + 15 \, c^{2} d^{2} f^{2} - 10 \, a c d e f g - 2 \, a^{2} e^{2} g^{2} + 2 \, {\left(10 \, c^{2} d^{2} f g - 7 \, a c d e g^{2}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} - 15 \, {\left(c^{2} d^{3} f^{3} - a c d^{2} e f^{2} g + {\left(c^{2} d^{2} e f g^{2} - a c d e^{2} g^{3}\right)} x^{3} + {\left(2 \, c^{2} d^{2} e f^{2} g - a c d^{2} e g^{3} + {\left(c^{2} d^{3} - 2 \, a c d e^{2}\right)} f g^{2}\right)} x^{2} + {\left(c^{2} d^{2} e f^{3} - 2 \, a c d^{2} e f g^{2} + {\left(2 \, c^{2} d^{3} - a c d e^{2}\right)} f^{2} g\right)} x\right)} \sqrt{\frac{c d}{g}} \log\left(-\frac{8 \, c^{2} d^{2} e g^{2} x^{3} + c^{2} d^{3} f^{2} + 6 \, a c d^{2} e f g + a^{2} d e^{2} g^{2} + 4 \, {\left(2 \, c d g^{2} x + c d f g + a e g^{2}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} \sqrt{\frac{c d}{g}} + 8 \, {\left(c^{2} d^{2} e f g + {\left(c^{2} d^{3} + a c d e^{2}\right)} g^{2}\right)} x^{2} + {\left(c^{2} d^{2} e f^{2} + 2 \, {\left(4 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f g + {\left(8 \, a c d^{2} e + a^{2} e^{3}\right)} g^{2}\right)} x}{e x + d}\right)}{12 \, {\left(e g^{5} x^{3} + d f^{2} g^{3} + {\left(2 \, e f g^{4} + d g^{5}\right)} x^{2} + {\left(e f^{2} g^{3} + 2 \, d f g^{4}\right)} x\right)}}, \frac{2 \, {\left(3 \, c^{2} d^{2} g^{2} x^{2} + 15 \, c^{2} d^{2} f^{2} - 10 \, a c d e f g - 2 \, a^{2} e^{2} g^{2} + 2 \, {\left(10 \, c^{2} d^{2} f g - 7 \, a c d e g^{2}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} + 15 \, {\left(c^{2} d^{3} f^{3} - a c d^{2} e f^{2} g + {\left(c^{2} d^{2} e f g^{2} - a c d e^{2} g^{3}\right)} x^{3} + {\left(2 \, c^{2} d^{2} e f^{2} g - a c d^{2} e g^{3} + {\left(c^{2} d^{3} - 2 \, a c d e^{2}\right)} f g^{2}\right)} x^{2} + {\left(c^{2} d^{2} e f^{3} - 2 \, a c d^{2} e f g^{2} + {\left(2 \, c^{2} d^{3} - a c d e^{2}\right)} f^{2} g\right)} x\right)} \sqrt{-\frac{c d}{g}} \arctan\left(\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} \sqrt{-\frac{c d}{g}} g}{2 \, c d e g x^{2} + c d^{2} f + a d e g + {\left(c d e f + {\left(2 \, c d^{2} + a e^{2}\right)} g\right)} x}\right)}{6 \, {\left(e g^{5} x^{3} + d f^{2} g^{3} + {\left(2 \, e f g^{4} + d g^{5}\right)} x^{2} + {\left(e f^{2} g^{3} + 2 \, d f g^{4}\right)} x\right)}}\right]"," ",0,"[1/12*(4*(3*c^2*d^2*g^2*x^2 + 15*c^2*d^2*f^2 - 10*a*c*d*e*f*g - 2*a^2*e^2*g^2 + 2*(10*c^2*d^2*f*g - 7*a*c*d*e*g^2)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f) - 15*(c^2*d^3*f^3 - a*c*d^2*e*f^2*g + (c^2*d^2*e*f*g^2 - a*c*d*e^2*g^3)*x^3 + (2*c^2*d^2*e*f^2*g - a*c*d^2*e*g^3 + (c^2*d^3 - 2*a*c*d*e^2)*f*g^2)*x^2 + (c^2*d^2*e*f^3 - 2*a*c*d^2*e*f*g^2 + (2*c^2*d^3 - a*c*d*e^2)*f^2*g)*x)*sqrt(c*d/g)*log(-(8*c^2*d^2*e*g^2*x^3 + c^2*d^3*f^2 + 6*a*c*d^2*e*f*g + a^2*d*e^2*g^2 + 4*(2*c*d*g^2*x + c*d*f*g + a*e*g^2)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f)*sqrt(c*d/g) + 8*(c^2*d^2*e*f*g + (c^2*d^3 + a*c*d*e^2)*g^2)*x^2 + (c^2*d^2*e*f^2 + 2*(4*c^2*d^3 + 3*a*c*d*e^2)*f*g + (8*a*c*d^2*e + a^2*e^3)*g^2)*x)/(e*x + d)))/(e*g^5*x^3 + d*f^2*g^3 + (2*e*f*g^4 + d*g^5)*x^2 + (e*f^2*g^3 + 2*d*f*g^4)*x), 1/6*(2*(3*c^2*d^2*g^2*x^2 + 15*c^2*d^2*f^2 - 10*a*c*d*e*f*g - 2*a^2*e^2*g^2 + 2*(10*c^2*d^2*f*g - 7*a*c*d*e*g^2)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f) + 15*(c^2*d^3*f^3 - a*c*d^2*e*f^2*g + (c^2*d^2*e*f*g^2 - a*c*d*e^2*g^3)*x^3 + (2*c^2*d^2*e*f^2*g - a*c*d^2*e*g^3 + (c^2*d^3 - 2*a*c*d*e^2)*f*g^2)*x^2 + (c^2*d^2*e*f^3 - 2*a*c*d^2*e*f*g^2 + (2*c^2*d^3 - a*c*d*e^2)*f^2*g)*x)*sqrt(-c*d/g)*arctan(2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f)*sqrt(-c*d/g)*g/(2*c*d*e*g*x^2 + c*d^2*f + a*d*e*g + (c*d*e*f + (2*c*d^2 + a*e^2)*g)*x)))/(e*g^5*x^3 + d*f^2*g^3 + (2*e*f*g^4 + d*g^5)*x^2 + (e*f^2*g^3 + 2*d*f*g^4)*x)]","A",0
756,1,933,0,1.097234," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^(5/2)/(g*x+f)^(7/2),x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(23 \, c^{2} d^{2} g^{2} x^{2} + 15 \, c^{2} d^{2} f^{2} + 5 \, a c d e f g + 3 \, a^{2} e^{2} g^{2} + {\left(35 \, c^{2} d^{2} f g + 11 \, a c d e g^{2}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} - 15 \, {\left(c^{2} d^{2} e g^{3} x^{4} + c^{2} d^{3} f^{3} + {\left(3 \, c^{2} d^{2} e f g^{2} + c^{2} d^{3} g^{3}\right)} x^{3} + 3 \, {\left(c^{2} d^{2} e f^{2} g + c^{2} d^{3} f g^{2}\right)} x^{2} + {\left(c^{2} d^{2} e f^{3} + 3 \, c^{2} d^{3} f^{2} g\right)} x\right)} \sqrt{\frac{c d}{g}} \log\left(-\frac{8 \, c^{2} d^{2} e g^{2} x^{3} + c^{2} d^{3} f^{2} + 6 \, a c d^{2} e f g + a^{2} d e^{2} g^{2} + 4 \, {\left(2 \, c d g^{2} x + c d f g + a e g^{2}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} \sqrt{\frac{c d}{g}} + 8 \, {\left(c^{2} d^{2} e f g + {\left(c^{2} d^{3} + a c d e^{2}\right)} g^{2}\right)} x^{2} + {\left(c^{2} d^{2} e f^{2} + 2 \, {\left(4 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f g + {\left(8 \, a c d^{2} e + a^{2} e^{3}\right)} g^{2}\right)} x}{e x + d}\right)}{30 \, {\left(e g^{6} x^{4} + d f^{3} g^{3} + {\left(3 \, e f g^{5} + d g^{6}\right)} x^{3} + 3 \, {\left(e f^{2} g^{4} + d f g^{5}\right)} x^{2} + {\left(e f^{3} g^{3} + 3 \, d f^{2} g^{4}\right)} x\right)}}, -\frac{2 \, {\left(23 \, c^{2} d^{2} g^{2} x^{2} + 15 \, c^{2} d^{2} f^{2} + 5 \, a c d e f g + 3 \, a^{2} e^{2} g^{2} + {\left(35 \, c^{2} d^{2} f g + 11 \, a c d e g^{2}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} + 15 \, {\left(c^{2} d^{2} e g^{3} x^{4} + c^{2} d^{3} f^{3} + {\left(3 \, c^{2} d^{2} e f g^{2} + c^{2} d^{3} g^{3}\right)} x^{3} + 3 \, {\left(c^{2} d^{2} e f^{2} g + c^{2} d^{3} f g^{2}\right)} x^{2} + {\left(c^{2} d^{2} e f^{3} + 3 \, c^{2} d^{3} f^{2} g\right)} x\right)} \sqrt{-\frac{c d}{g}} \arctan\left(\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f} \sqrt{-\frac{c d}{g}} g}{2 \, c d e g x^{2} + c d^{2} f + a d e g + {\left(c d e f + {\left(2 \, c d^{2} + a e^{2}\right)} g\right)} x}\right)}{15 \, {\left(e g^{6} x^{4} + d f^{3} g^{3} + {\left(3 \, e f g^{5} + d g^{6}\right)} x^{3} + 3 \, {\left(e f^{2} g^{4} + d f g^{5}\right)} x^{2} + {\left(e f^{3} g^{3} + 3 \, d f^{2} g^{4}\right)} x\right)}}\right]"," ",0,"[-1/30*(4*(23*c^2*d^2*g^2*x^2 + 15*c^2*d^2*f^2 + 5*a*c*d*e*f*g + 3*a^2*e^2*g^2 + (35*c^2*d^2*f*g + 11*a*c*d*e*g^2)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f) - 15*(c^2*d^2*e*g^3*x^4 + c^2*d^3*f^3 + (3*c^2*d^2*e*f*g^2 + c^2*d^3*g^3)*x^3 + 3*(c^2*d^2*e*f^2*g + c^2*d^3*f*g^2)*x^2 + (c^2*d^2*e*f^3 + 3*c^2*d^3*f^2*g)*x)*sqrt(c*d/g)*log(-(8*c^2*d^2*e*g^2*x^3 + c^2*d^3*f^2 + 6*a*c*d^2*e*f*g + a^2*d*e^2*g^2 + 4*(2*c*d*g^2*x + c*d*f*g + a*e*g^2)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f)*sqrt(c*d/g) + 8*(c^2*d^2*e*f*g + (c^2*d^3 + a*c*d*e^2)*g^2)*x^2 + (c^2*d^2*e*f^2 + 2*(4*c^2*d^3 + 3*a*c*d*e^2)*f*g + (8*a*c*d^2*e + a^2*e^3)*g^2)*x)/(e*x + d)))/(e*g^6*x^4 + d*f^3*g^3 + (3*e*f*g^5 + d*g^6)*x^3 + 3*(e*f^2*g^4 + d*f*g^5)*x^2 + (e*f^3*g^3 + 3*d*f^2*g^4)*x), -1/15*(2*(23*c^2*d^2*g^2*x^2 + 15*c^2*d^2*f^2 + 5*a*c*d*e*f*g + 3*a^2*e^2*g^2 + (35*c^2*d^2*f*g + 11*a*c*d*e*g^2)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f) + 15*(c^2*d^2*e*g^3*x^4 + c^2*d^3*f^3 + (3*c^2*d^2*e*f*g^2 + c^2*d^3*g^3)*x^3 + 3*(c^2*d^2*e*f^2*g + c^2*d^3*f*g^2)*x^2 + (c^2*d^2*e*f^3 + 3*c^2*d^3*f^2*g)*x)*sqrt(-c*d/g)*arctan(2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f)*sqrt(-c*d/g)*g/(2*c*d*e*g*x^2 + c*d^2*f + a*d*e*g + (c*d*e*f + (2*c*d^2 + a*e^2)*g)*x)))/(e*g^6*x^4 + d*f^3*g^3 + (3*e*f*g^5 + d*g^6)*x^3 + 3*(e*f^2*g^4 + d*f*g^5)*x^2 + (e*f^3*g^3 + 3*d*f^2*g^4)*x)]","A",0
757,1,299,0,0.441923," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^(5/2)/(g*x+f)^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left(c^{3} d^{3} x^{3} + 3 \, a c^{2} d^{2} e x^{2} + 3 \, a^{2} c d e^{2} x + a^{3} e^{3}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f}}{7 \, {\left(c d^{2} f^{5} - a d e f^{4} g + {\left(c d e f g^{4} - a e^{2} g^{5}\right)} x^{5} + {\left(4 \, c d e f^{2} g^{3} - a d e g^{5} + {\left(c d^{2} - 4 \, a e^{2}\right)} f g^{4}\right)} x^{4} + 2 \, {\left(3 \, c d e f^{3} g^{2} - 2 \, a d e f g^{4} + {\left(2 \, c d^{2} - 3 \, a e^{2}\right)} f^{2} g^{3}\right)} x^{3} + 2 \, {\left(2 \, c d e f^{4} g - 3 \, a d e f^{2} g^{3} + {\left(3 \, c d^{2} - 2 \, a e^{2}\right)} f^{3} g^{2}\right)} x^{2} + {\left(c d e f^{5} - 4 \, a d e f^{3} g^{2} + {\left(4 \, c d^{2} - a e^{2}\right)} f^{4} g\right)} x\right)}}"," ",0,"2/7*(c^3*d^3*x^3 + 3*a*c^2*d^2*e*x^2 + 3*a^2*c*d*e^2*x + a^3*e^3)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f)/(c*d^2*f^5 - a*d*e*f^4*g + (c*d*e*f*g^4 - a*e^2*g^5)*x^5 + (4*c*d*e*f^2*g^3 - a*d*e*g^5 + (c*d^2 - 4*a*e^2)*f*g^4)*x^4 + 2*(3*c*d*e*f^3*g^2 - 2*a*d*e*f*g^4 + (2*c*d^2 - 3*a*e^2)*f^2*g^3)*x^3 + 2*(2*c*d*e*f^4*g - 3*a*d*e*f^2*g^3 + (3*c*d^2 - 2*a*e^2)*f^3*g^2)*x^2 + (c*d*e*f^5 - 4*a*d*e*f^3*g^2 + (4*c*d^2 - a*e^2)*f^4*g)*x)","B",0
758,1,639,0,0.470605," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^(5/2)/(g*x+f)^(11/2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, c^{4} d^{4} g x^{4} + 9 \, a^{3} c d e^{3} f - 7 \, a^{4} e^{4} g + {\left(9 \, c^{4} d^{4} f - a c^{3} d^{3} e g\right)} x^{3} + 3 \, {\left(9 \, a c^{3} d^{3} e f - 5 \, a^{2} c^{2} d^{2} e^{2} g\right)} x^{2} + {\left(27 \, a^{2} c^{2} d^{2} e^{2} f - 19 \, a^{3} c d e^{3} g\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f}}{63 \, {\left(c^{2} d^{3} f^{7} - 2 \, a c d^{2} e f^{6} g + a^{2} d e^{2} f^{5} g^{2} + {\left(c^{2} d^{2} e f^{2} g^{5} - 2 \, a c d e^{2} f g^{6} + a^{2} e^{3} g^{7}\right)} x^{6} + {\left(5 \, c^{2} d^{2} e f^{3} g^{4} + a^{2} d e^{2} g^{7} + {\left(c^{2} d^{3} - 10 \, a c d e^{2}\right)} f^{2} g^{5} - {\left(2 \, a c d^{2} e - 5 \, a^{2} e^{3}\right)} f g^{6}\right)} x^{5} + 5 \, {\left(2 \, c^{2} d^{2} e f^{4} g^{3} + a^{2} d e^{2} f g^{6} + {\left(c^{2} d^{3} - 4 \, a c d e^{2}\right)} f^{3} g^{4} - 2 \, {\left(a c d^{2} e - a^{2} e^{3}\right)} f^{2} g^{5}\right)} x^{4} + 10 \, {\left(c^{2} d^{2} e f^{5} g^{2} + a^{2} d e^{2} f^{2} g^{5} + {\left(c^{2} d^{3} - 2 \, a c d e^{2}\right)} f^{4} g^{3} - {\left(2 \, a c d^{2} e - a^{2} e^{3}\right)} f^{3} g^{4}\right)} x^{3} + 5 \, {\left(c^{2} d^{2} e f^{6} g + 2 \, a^{2} d e^{2} f^{3} g^{4} + 2 \, {\left(c^{2} d^{3} - a c d e^{2}\right)} f^{5} g^{2} - {\left(4 \, a c d^{2} e - a^{2} e^{3}\right)} f^{4} g^{3}\right)} x^{2} + {\left(c^{2} d^{2} e f^{7} + 5 \, a^{2} d e^{2} f^{4} g^{3} + {\left(5 \, c^{2} d^{3} - 2 \, a c d e^{2}\right)} f^{6} g - {\left(10 \, a c d^{2} e - a^{2} e^{3}\right)} f^{5} g^{2}\right)} x\right)}}"," ",0,"2/63*(2*c^4*d^4*g*x^4 + 9*a^3*c*d*e^3*f - 7*a^4*e^4*g + (9*c^4*d^4*f - a*c^3*d^3*e*g)*x^3 + 3*(9*a*c^3*d^3*e*f - 5*a^2*c^2*d^2*e^2*g)*x^2 + (27*a^2*c^2*d^2*e^2*f - 19*a^3*c*d*e^3*g)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f)/(c^2*d^3*f^7 - 2*a*c*d^2*e*f^6*g + a^2*d*e^2*f^5*g^2 + (c^2*d^2*e*f^2*g^5 - 2*a*c*d*e^2*f*g^6 + a^2*e^3*g^7)*x^6 + (5*c^2*d^2*e*f^3*g^4 + a^2*d*e^2*g^7 + (c^2*d^3 - 10*a*c*d*e^2)*f^2*g^5 - (2*a*c*d^2*e - 5*a^2*e^3)*f*g^6)*x^5 + 5*(2*c^2*d^2*e*f^4*g^3 + a^2*d*e^2*f*g^6 + (c^2*d^3 - 4*a*c*d*e^2)*f^3*g^4 - 2*(a*c*d^2*e - a^2*e^3)*f^2*g^5)*x^4 + 10*(c^2*d^2*e*f^5*g^2 + a^2*d*e^2*f^2*g^5 + (c^2*d^3 - 2*a*c*d*e^2)*f^4*g^3 - (2*a*c*d^2*e - a^2*e^3)*f^3*g^4)*x^3 + 5*(c^2*d^2*e*f^6*g + 2*a^2*d*e^2*f^3*g^4 + 2*(c^2*d^3 - a*c*d*e^2)*f^5*g^2 - (4*a*c*d^2*e - a^2*e^3)*f^4*g^3)*x^2 + (c^2*d^2*e*f^7 + 5*a^2*d*e^2*f^4*g^3 + (5*c^2*d^3 - 2*a*c*d*e^2)*f^6*g - (10*a*c*d^2*e - a^2*e^3)*f^5*g^2)*x)","B",0
759,1,1101,0,0.479093," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^(5/2)/(g*x+f)^(13/2),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, c^{5} d^{5} g^{2} x^{5} + 99 \, a^{3} c^{2} d^{2} e^{3} f^{2} - 154 \, a^{4} c d e^{4} f g + 63 \, a^{5} e^{5} g^{2} + 4 \, {\left(11 \, c^{5} d^{5} f g - a c^{4} d^{4} e g^{2}\right)} x^{4} + {\left(99 \, c^{5} d^{5} f^{2} - 22 \, a c^{4} d^{4} e f g + 3 \, a^{2} c^{3} d^{3} e^{2} g^{2}\right)} x^{3} + {\left(297 \, a c^{4} d^{4} e f^{2} - 330 \, a^{2} c^{3} d^{3} e^{2} f g + 113 \, a^{3} c^{2} d^{2} e^{3} g^{2}\right)} x^{2} + {\left(297 \, a^{2} c^{3} d^{3} e^{2} f^{2} - 418 \, a^{3} c^{2} d^{2} e^{3} f g + 161 \, a^{4} c d e^{4} g^{2}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f}}{693 \, {\left(c^{3} d^{4} f^{9} - 3 \, a c^{2} d^{3} e f^{8} g + 3 \, a^{2} c d^{2} e^{2} f^{7} g^{2} - a^{3} d e^{3} f^{6} g^{3} + {\left(c^{3} d^{3} e f^{3} g^{6} - 3 \, a c^{2} d^{2} e^{2} f^{2} g^{7} + 3 \, a^{2} c d e^{3} f g^{8} - a^{3} e^{4} g^{9}\right)} x^{7} + {\left(6 \, c^{3} d^{3} e f^{4} g^{5} - a^{3} d e^{3} g^{9} + {\left(c^{3} d^{4} - 18 \, a c^{2} d^{2} e^{2}\right)} f^{3} g^{6} - 3 \, {\left(a c^{2} d^{3} e - 6 \, a^{2} c d e^{3}\right)} f^{2} g^{7} + 3 \, {\left(a^{2} c d^{2} e^{2} - 2 \, a^{3} e^{4}\right)} f g^{8}\right)} x^{6} + 3 \, {\left(5 \, c^{3} d^{3} e f^{5} g^{4} - 2 \, a^{3} d e^{3} f g^{8} + {\left(2 \, c^{3} d^{4} - 15 \, a c^{2} d^{2} e^{2}\right)} f^{4} g^{5} - 3 \, {\left(2 \, a c^{2} d^{3} e - 5 \, a^{2} c d e^{3}\right)} f^{3} g^{6} + {\left(6 \, a^{2} c d^{2} e^{2} - 5 \, a^{3} e^{4}\right)} f^{2} g^{7}\right)} x^{5} + 5 \, {\left(4 \, c^{3} d^{3} e f^{6} g^{3} - 3 \, a^{3} d e^{3} f^{2} g^{7} + 3 \, {\left(c^{3} d^{4} - 4 \, a c^{2} d^{2} e^{2}\right)} f^{5} g^{4} - 3 \, {\left(3 \, a c^{2} d^{3} e - 4 \, a^{2} c d e^{3}\right)} f^{4} g^{5} + {\left(9 \, a^{2} c d^{2} e^{2} - 4 \, a^{3} e^{4}\right)} f^{3} g^{6}\right)} x^{4} + 5 \, {\left(3 \, c^{3} d^{3} e f^{7} g^{2} - 4 \, a^{3} d e^{3} f^{3} g^{6} + {\left(4 \, c^{3} d^{4} - 9 \, a c^{2} d^{2} e^{2}\right)} f^{6} g^{3} - 3 \, {\left(4 \, a c^{2} d^{3} e - 3 \, a^{2} c d e^{3}\right)} f^{5} g^{4} + 3 \, {\left(4 \, a^{2} c d^{2} e^{2} - a^{3} e^{4}\right)} f^{4} g^{5}\right)} x^{3} + 3 \, {\left(2 \, c^{3} d^{3} e f^{8} g - 5 \, a^{3} d e^{3} f^{4} g^{5} + {\left(5 \, c^{3} d^{4} - 6 \, a c^{2} d^{2} e^{2}\right)} f^{7} g^{2} - 3 \, {\left(5 \, a c^{2} d^{3} e - 2 \, a^{2} c d e^{3}\right)} f^{6} g^{3} + {\left(15 \, a^{2} c d^{2} e^{2} - 2 \, a^{3} e^{4}\right)} f^{5} g^{4}\right)} x^{2} + {\left(c^{3} d^{3} e f^{9} - 6 \, a^{3} d e^{3} f^{5} g^{4} + 3 \, {\left(2 \, c^{3} d^{4} - a c^{2} d^{2} e^{2}\right)} f^{8} g - 3 \, {\left(6 \, a c^{2} d^{3} e - a^{2} c d e^{3}\right)} f^{7} g^{2} + {\left(18 \, a^{2} c d^{2} e^{2} - a^{3} e^{4}\right)} f^{6} g^{3}\right)} x\right)}}"," ",0,"2/693*(8*c^5*d^5*g^2*x^5 + 99*a^3*c^2*d^2*e^3*f^2 - 154*a^4*c*d*e^4*f*g + 63*a^5*e^5*g^2 + 4*(11*c^5*d^5*f*g - a*c^4*d^4*e*g^2)*x^4 + (99*c^5*d^5*f^2 - 22*a*c^4*d^4*e*f*g + 3*a^2*c^3*d^3*e^2*g^2)*x^3 + (297*a*c^4*d^4*e*f^2 - 330*a^2*c^3*d^3*e^2*f*g + 113*a^3*c^2*d^2*e^3*g^2)*x^2 + (297*a^2*c^3*d^3*e^2*f^2 - 418*a^3*c^2*d^2*e^3*f*g + 161*a^4*c*d*e^4*g^2)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f)/(c^3*d^4*f^9 - 3*a*c^2*d^3*e*f^8*g + 3*a^2*c*d^2*e^2*f^7*g^2 - a^3*d*e^3*f^6*g^3 + (c^3*d^3*e*f^3*g^6 - 3*a*c^2*d^2*e^2*f^2*g^7 + 3*a^2*c*d*e^3*f*g^8 - a^3*e^4*g^9)*x^7 + (6*c^3*d^3*e*f^4*g^5 - a^3*d*e^3*g^9 + (c^3*d^4 - 18*a*c^2*d^2*e^2)*f^3*g^6 - 3*(a*c^2*d^3*e - 6*a^2*c*d*e^3)*f^2*g^7 + 3*(a^2*c*d^2*e^2 - 2*a^3*e^4)*f*g^8)*x^6 + 3*(5*c^3*d^3*e*f^5*g^4 - 2*a^3*d*e^3*f*g^8 + (2*c^3*d^4 - 15*a*c^2*d^2*e^2)*f^4*g^5 - 3*(2*a*c^2*d^3*e - 5*a^2*c*d*e^3)*f^3*g^6 + (6*a^2*c*d^2*e^2 - 5*a^3*e^4)*f^2*g^7)*x^5 + 5*(4*c^3*d^3*e*f^6*g^3 - 3*a^3*d*e^3*f^2*g^7 + 3*(c^3*d^4 - 4*a*c^2*d^2*e^2)*f^5*g^4 - 3*(3*a*c^2*d^3*e - 4*a^2*c*d*e^3)*f^4*g^5 + (9*a^2*c*d^2*e^2 - 4*a^3*e^4)*f^3*g^6)*x^4 + 5*(3*c^3*d^3*e*f^7*g^2 - 4*a^3*d*e^3*f^3*g^6 + (4*c^3*d^4 - 9*a*c^2*d^2*e^2)*f^6*g^3 - 3*(4*a*c^2*d^3*e - 3*a^2*c*d*e^3)*f^5*g^4 + 3*(4*a^2*c*d^2*e^2 - a^3*e^4)*f^4*g^5)*x^3 + 3*(2*c^3*d^3*e*f^8*g - 5*a^3*d*e^3*f^4*g^5 + (5*c^3*d^4 - 6*a*c^2*d^2*e^2)*f^7*g^2 - 3*(5*a*c^2*d^3*e - 2*a^2*c*d*e^3)*f^6*g^3 + (15*a^2*c*d^2*e^2 - 2*a^3*e^4)*f^5*g^4)*x^2 + (c^3*d^3*e*f^9 - 6*a^3*d*e^3*f^5*g^4 + 3*(2*c^3*d^4 - a*c^2*d^2*e^2)*f^8*g - 3*(6*a*c^2*d^3*e - a^2*c*d*e^3)*f^7*g^2 + (18*a^2*c*d^2*e^2 - a^3*e^4)*f^6*g^3)*x)","B",0
760,1,1648,0,0.536131," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^(5/2)/(g*x+f)^(15/2),x, algorithm=""fricas"")","\frac{2 \, {\left(16 \, c^{6} d^{6} g^{3} x^{6} + 429 \, a^{3} c^{3} d^{3} e^{3} f^{3} - 1001 \, a^{4} c^{2} d^{2} e^{4} f^{2} g + 819 \, a^{5} c d e^{5} f g^{2} - 231 \, a^{6} e^{6} g^{3} + 8 \, {\left(13 \, c^{6} d^{6} f g^{2} - a c^{5} d^{5} e g^{3}\right)} x^{5} + 2 \, {\left(143 \, c^{6} d^{6} f^{2} g - 26 \, a c^{5} d^{5} e f g^{2} + 3 \, a^{2} c^{4} d^{4} e^{2} g^{3}\right)} x^{4} + {\left(429 \, c^{6} d^{6} f^{3} - 143 \, a c^{5} d^{5} e f^{2} g + 39 \, a^{2} c^{4} d^{4} e^{2} f g^{2} - 5 \, a^{3} c^{3} d^{3} e^{3} g^{3}\right)} x^{3} + {\left(1287 \, a c^{5} d^{5} e f^{3} - 2145 \, a^{2} c^{4} d^{4} e^{2} f^{2} g + 1469 \, a^{3} c^{3} d^{3} e^{3} f g^{2} - 371 \, a^{4} c^{2} d^{2} e^{4} g^{3}\right)} x^{2} + {\left(1287 \, a^{2} c^{4} d^{4} e^{2} f^{3} - 2717 \, a^{3} c^{3} d^{3} e^{3} f^{2} g + 2093 \, a^{4} c^{2} d^{2} e^{4} f g^{2} - 567 \, a^{5} c d e^{5} g^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} \sqrt{g x + f}}{3003 \, {\left(c^{4} d^{5} f^{11} - 4 \, a c^{3} d^{4} e f^{10} g + 6 \, a^{2} c^{2} d^{3} e^{2} f^{9} g^{2} - 4 \, a^{3} c d^{2} e^{3} f^{8} g^{3} + a^{4} d e^{4} f^{7} g^{4} + {\left(c^{4} d^{4} e f^{4} g^{7} - 4 \, a c^{3} d^{3} e^{2} f^{3} g^{8} + 6 \, a^{2} c^{2} d^{2} e^{3} f^{2} g^{9} - 4 \, a^{3} c d e^{4} f g^{10} + a^{4} e^{5} g^{11}\right)} x^{8} + {\left(7 \, c^{4} d^{4} e f^{5} g^{6} + a^{4} d e^{4} g^{11} + {\left(c^{4} d^{5} - 28 \, a c^{3} d^{3} e^{2}\right)} f^{4} g^{7} - 2 \, {\left(2 \, a c^{3} d^{4} e - 21 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{3} g^{8} + 2 \, {\left(3 \, a^{2} c^{2} d^{3} e^{2} - 14 \, a^{3} c d e^{4}\right)} f^{2} g^{9} - {\left(4 \, a^{3} c d^{2} e^{3} - 7 \, a^{4} e^{5}\right)} f g^{10}\right)} x^{7} + 7 \, {\left(3 \, c^{4} d^{4} e f^{6} g^{5} + a^{4} d e^{4} f g^{10} + {\left(c^{4} d^{5} - 12 \, a c^{3} d^{3} e^{2}\right)} f^{5} g^{6} - 2 \, {\left(2 \, a c^{3} d^{4} e - 9 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{4} g^{7} + 6 \, {\left(a^{2} c^{2} d^{3} e^{2} - 2 \, a^{3} c d e^{4}\right)} f^{3} g^{8} - {\left(4 \, a^{3} c d^{2} e^{3} - 3 \, a^{4} e^{5}\right)} f^{2} g^{9}\right)} x^{6} + 7 \, {\left(5 \, c^{4} d^{4} e f^{7} g^{4} + 3 \, a^{4} d e^{4} f^{2} g^{9} + {\left(3 \, c^{4} d^{5} - 20 \, a c^{3} d^{3} e^{2}\right)} f^{6} g^{5} - 6 \, {\left(2 \, a c^{3} d^{4} e - 5 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{5} g^{6} + 2 \, {\left(9 \, a^{2} c^{2} d^{3} e^{2} - 10 \, a^{3} c d e^{4}\right)} f^{4} g^{7} - {\left(12 \, a^{3} c d^{2} e^{3} - 5 \, a^{4} e^{5}\right)} f^{3} g^{8}\right)} x^{5} + 35 \, {\left(c^{4} d^{4} e f^{8} g^{3} + a^{4} d e^{4} f^{3} g^{8} + {\left(c^{4} d^{5} - 4 \, a c^{3} d^{3} e^{2}\right)} f^{7} g^{4} - 2 \, {\left(2 \, a c^{3} d^{4} e - 3 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{6} g^{5} + 2 \, {\left(3 \, a^{2} c^{2} d^{3} e^{2} - 2 \, a^{3} c d e^{4}\right)} f^{5} g^{6} - {\left(4 \, a^{3} c d^{2} e^{3} - a^{4} e^{5}\right)} f^{4} g^{7}\right)} x^{4} + 7 \, {\left(3 \, c^{4} d^{4} e f^{9} g^{2} + 5 \, a^{4} d e^{4} f^{4} g^{7} + {\left(5 \, c^{4} d^{5} - 12 \, a c^{3} d^{3} e^{2}\right)} f^{8} g^{3} - 2 \, {\left(10 \, a c^{3} d^{4} e - 9 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{7} g^{4} + 6 \, {\left(5 \, a^{2} c^{2} d^{3} e^{2} - 2 \, a^{3} c d e^{4}\right)} f^{6} g^{5} - {\left(20 \, a^{3} c d^{2} e^{3} - 3 \, a^{4} e^{5}\right)} f^{5} g^{6}\right)} x^{3} + 7 \, {\left(c^{4} d^{4} e f^{10} g + 3 \, a^{4} d e^{4} f^{5} g^{6} + {\left(3 \, c^{4} d^{5} - 4 \, a c^{3} d^{3} e^{2}\right)} f^{9} g^{2} - 6 \, {\left(2 \, a c^{3} d^{4} e - a^{2} c^{2} d^{2} e^{3}\right)} f^{8} g^{3} + 2 \, {\left(9 \, a^{2} c^{2} d^{3} e^{2} - 2 \, a^{3} c d e^{4}\right)} f^{7} g^{4} - {\left(12 \, a^{3} c d^{2} e^{3} - a^{4} e^{5}\right)} f^{6} g^{5}\right)} x^{2} + {\left(c^{4} d^{4} e f^{11} + 7 \, a^{4} d e^{4} f^{6} g^{5} + {\left(7 \, c^{4} d^{5} - 4 \, a c^{3} d^{3} e^{2}\right)} f^{10} g - 2 \, {\left(14 \, a c^{3} d^{4} e - 3 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{9} g^{2} + 2 \, {\left(21 \, a^{2} c^{2} d^{3} e^{2} - 2 \, a^{3} c d e^{4}\right)} f^{8} g^{3} - {\left(28 \, a^{3} c d^{2} e^{3} - a^{4} e^{5}\right)} f^{7} g^{4}\right)} x\right)}}"," ",0,"2/3003*(16*c^6*d^6*g^3*x^6 + 429*a^3*c^3*d^3*e^3*f^3 - 1001*a^4*c^2*d^2*e^4*f^2*g + 819*a^5*c*d*e^5*f*g^2 - 231*a^6*e^6*g^3 + 8*(13*c^6*d^6*f*g^2 - a*c^5*d^5*e*g^3)*x^5 + 2*(143*c^6*d^6*f^2*g - 26*a*c^5*d^5*e*f*g^2 + 3*a^2*c^4*d^4*e^2*g^3)*x^4 + (429*c^6*d^6*f^3 - 143*a*c^5*d^5*e*f^2*g + 39*a^2*c^4*d^4*e^2*f*g^2 - 5*a^3*c^3*d^3*e^3*g^3)*x^3 + (1287*a*c^5*d^5*e*f^3 - 2145*a^2*c^4*d^4*e^2*f^2*g + 1469*a^3*c^3*d^3*e^3*f*g^2 - 371*a^4*c^2*d^2*e^4*g^3)*x^2 + (1287*a^2*c^4*d^4*e^2*f^3 - 2717*a^3*c^3*d^3*e^3*f^2*g + 2093*a^4*c^2*d^2*e^4*f*g^2 - 567*a^5*c*d*e^5*g^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*sqrt(g*x + f)/(c^4*d^5*f^11 - 4*a*c^3*d^4*e*f^10*g + 6*a^2*c^2*d^3*e^2*f^9*g^2 - 4*a^3*c*d^2*e^3*f^8*g^3 + a^4*d*e^4*f^7*g^4 + (c^4*d^4*e*f^4*g^7 - 4*a*c^3*d^3*e^2*f^3*g^8 + 6*a^2*c^2*d^2*e^3*f^2*g^9 - 4*a^3*c*d*e^4*f*g^10 + a^4*e^5*g^11)*x^8 + (7*c^4*d^4*e*f^5*g^6 + a^4*d*e^4*g^11 + (c^4*d^5 - 28*a*c^3*d^3*e^2)*f^4*g^7 - 2*(2*a*c^3*d^4*e - 21*a^2*c^2*d^2*e^3)*f^3*g^8 + 2*(3*a^2*c^2*d^3*e^2 - 14*a^3*c*d*e^4)*f^2*g^9 - (4*a^3*c*d^2*e^3 - 7*a^4*e^5)*f*g^10)*x^7 + 7*(3*c^4*d^4*e*f^6*g^5 + a^4*d*e^4*f*g^10 + (c^4*d^5 - 12*a*c^3*d^3*e^2)*f^5*g^6 - 2*(2*a*c^3*d^4*e - 9*a^2*c^2*d^2*e^3)*f^4*g^7 + 6*(a^2*c^2*d^3*e^2 - 2*a^3*c*d*e^4)*f^3*g^8 - (4*a^3*c*d^2*e^3 - 3*a^4*e^5)*f^2*g^9)*x^6 + 7*(5*c^4*d^4*e*f^7*g^4 + 3*a^4*d*e^4*f^2*g^9 + (3*c^4*d^5 - 20*a*c^3*d^3*e^2)*f^6*g^5 - 6*(2*a*c^3*d^4*e - 5*a^2*c^2*d^2*e^3)*f^5*g^6 + 2*(9*a^2*c^2*d^3*e^2 - 10*a^3*c*d*e^4)*f^4*g^7 - (12*a^3*c*d^2*e^3 - 5*a^4*e^5)*f^3*g^8)*x^5 + 35*(c^4*d^4*e*f^8*g^3 + a^4*d*e^4*f^3*g^8 + (c^4*d^5 - 4*a*c^3*d^3*e^2)*f^7*g^4 - 2*(2*a*c^3*d^4*e - 3*a^2*c^2*d^2*e^3)*f^6*g^5 + 2*(3*a^2*c^2*d^3*e^2 - 2*a^3*c*d*e^4)*f^5*g^6 - (4*a^3*c*d^2*e^3 - a^4*e^5)*f^4*g^7)*x^4 + 7*(3*c^4*d^4*e*f^9*g^2 + 5*a^4*d*e^4*f^4*g^7 + (5*c^4*d^5 - 12*a*c^3*d^3*e^2)*f^8*g^3 - 2*(10*a*c^3*d^4*e - 9*a^2*c^2*d^2*e^3)*f^7*g^4 + 6*(5*a^2*c^2*d^3*e^2 - 2*a^3*c*d*e^4)*f^6*g^5 - (20*a^3*c*d^2*e^3 - 3*a^4*e^5)*f^5*g^6)*x^3 + 7*(c^4*d^4*e*f^10*g + 3*a^4*d*e^4*f^5*g^6 + (3*c^4*d^5 - 4*a*c^3*d^3*e^2)*f^9*g^2 - 6*(2*a*c^3*d^4*e - a^2*c^2*d^2*e^3)*f^8*g^3 + 2*(9*a^2*c^2*d^3*e^2 - 2*a^3*c*d*e^4)*f^7*g^4 - (12*a^3*c*d^2*e^3 - a^4*e^5)*f^6*g^5)*x^2 + (c^4*d^4*e*f^11 + 7*a^4*d*e^4*f^6*g^5 + (7*c^4*d^5 - 4*a*c^3*d^3*e^2)*f^10*g - 2*(14*a*c^3*d^4*e - 3*a^2*c^2*d^2*e^3)*f^9*g^2 + 2*(21*a^2*c^2*d^3*e^2 - 2*a^3*c*d*e^4)*f^8*g^3 - (28*a^3*c*d^2*e^3 - a^4*e^5)*f^7*g^4)*x)","B",0
761,0,0,0,0.531623," ","integrate((e*x+d)^(5/2)*(g*x+f)^n/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} {\left(g x + f\right)}^{n}}{c^{3} d^{3} e x^{4} + a^{3} d e^{3} + {\left(c^{3} d^{4} + 3 \, a c^{2} d^{2} e^{2}\right)} x^{3} + 3 \, {\left(a c^{2} d^{3} e + a^{2} c d e^{3}\right)} x^{2} + {\left(3 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} x}, x\right)"," ",0,"integral(sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*(g*x + f)^n/(c^3*d^3*e*x^4 + a^3*d*e^3 + (c^3*d^4 + 3*a*c^2*d^2*e^2)*x^3 + 3*(a*c^2*d^3*e + a^2*c*d*e^3)*x^2 + (3*a^2*c*d^2*e^2 + a^3*e^4)*x), x)","F",0
762,0,0,0,0.474744," ","integrate((e*x+d)^(3/2)*(g*x+f)^n/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} {\left(g x + f\right)}^{n}}{c^{2} d^{2} e x^{3} + a^{2} d e^{2} + {\left(c^{2} d^{3} + 2 \, a c d e^{2}\right)} x^{2} + {\left(2 \, a c d^{2} e + a^{2} e^{3}\right)} x}, x\right)"," ",0,"integral(sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*(g*x + f)^n/(c^2*d^2*e*x^3 + a^2*d*e^2 + (c^2*d^3 + 2*a*c*d*e^2)*x^2 + (2*a*c*d^2*e + a^2*e^3)*x), x)","F",0
763,0,0,0,0.451082," ","integrate((e*x+d)^(1/2)*(g*x+f)^n/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x + d} {\left(g x + f\right)}^{n}}{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}, x\right)"," ",0,"integral(sqrt(e*x + d)*(g*x + f)^n/sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x), x)","F",0
764,0,0,0,0.460657," ","integrate((g*x+f)^n*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(g x + f\right)}^{n}}{\sqrt{e x + d}}, x\right)"," ",0,"integral(sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(g*x + f)^n/sqrt(e*x + d), x)","F",0
765,0,0,0,0.457173," ","integrate((g*x+f)^n*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/(e*x+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d x + a e\right)} {\left(g x + f\right)}^{n}}{\sqrt{e x + d}}, x\right)"," ",0,"integral(sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d*x + a*e)*(g*x + f)^n/sqrt(e*x + d), x)","F",0
766,0,0,0,0.452990," ","integrate((g*x+f)^n*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{2} d^{2} x^{2} + 2 \, a c d e x + a^{2} e^{2}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(g x + f\right)}^{n}}{\sqrt{e x + d}}, x\right)"," ",0,"integral((c^2*d^2*x^2 + 2*a*c*d*e*x + a^2*e^2)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(g*x + f)^n/sqrt(e*x + d), x)","F",0
767,0,0,0,0.444973," ","integrate((e*x+d)^m*(g*x+f)^n/((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^m),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)}^{m} {\left(g x + f\right)}^{n}}{{\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{m}}, x\right)"," ",0,"integral((e*x + d)^m*(g*x + f)^n/(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^m, x)","F",0
768,1,705,0,0.442429," ","integrate((e*x+d)^m*(g*x+f)^3/((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^m),x, algorithm=""fricas"")","-\frac{{\left(a c^{3} d^{3} e f^{3} m^{3} - 24 \, a c^{3} d^{3} e f^{3} + 36 \, a^{2} c^{2} d^{2} e^{2} f^{2} g - 24 \, a^{3} c d e^{3} f g^{2} + 6 \, a^{4} e^{4} g^{3} + {\left(c^{4} d^{4} g^{3} m^{3} - 6 \, c^{4} d^{4} g^{3} m^{2} + 11 \, c^{4} d^{4} g^{3} m - 6 \, c^{4} d^{4} g^{3}\right)} x^{4} - {\left(24 \, c^{4} d^{4} f g^{2} - {\left(3 \, c^{4} d^{4} f g^{2} + a c^{3} d^{3} e g^{3}\right)} m^{3} + 3 \, {\left(7 \, c^{4} d^{4} f g^{2} + a c^{3} d^{3} e g^{3}\right)} m^{2} - 2 \, {\left(21 \, c^{4} d^{4} f g^{2} + a c^{3} d^{3} e g^{3}\right)} m\right)} x^{3} - 3 \, {\left(3 \, a c^{3} d^{3} e f^{3} - a^{2} c^{2} d^{2} e^{2} f^{2} g\right)} m^{2} - 3 \, {\left(12 \, c^{4} d^{4} f^{2} g - {\left(c^{4} d^{4} f^{2} g + a c^{3} d^{3} e f g^{2}\right)} m^{3} + {\left(8 \, c^{4} d^{4} f^{2} g + 5 \, a c^{3} d^{3} e f g^{2} - a^{2} c^{2} d^{2} e^{2} g^{3}\right)} m^{2} - {\left(19 \, c^{4} d^{4} f^{2} g + 4 \, a c^{3} d^{3} e f g^{2} - a^{2} c^{2} d^{2} e^{2} g^{3}\right)} m\right)} x^{2} + {\left(26 \, a c^{3} d^{3} e f^{3} - 21 \, a^{2} c^{2} d^{2} e^{2} f^{2} g + 6 \, a^{3} c d e^{3} f g^{2}\right)} m - {\left(24 \, c^{4} d^{4} f^{3} - {\left(c^{4} d^{4} f^{3} + 3 \, a c^{3} d^{3} e f^{2} g\right)} m^{3} + 3 \, {\left(3 \, c^{4} d^{4} f^{3} + 7 \, a c^{3} d^{3} e f^{2} g - 2 \, a^{2} c^{2} d^{2} e^{2} f g^{2}\right)} m^{2} - 2 \, {\left(13 \, c^{4} d^{4} f^{3} + 18 \, a c^{3} d^{3} e f^{2} g - 12 \, a^{2} c^{2} d^{2} e^{2} f g^{2} + 3 \, a^{3} c d e^{3} g^{3}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{{\left(c^{4} d^{4} m^{4} - 10 \, c^{4} d^{4} m^{3} + 35 \, c^{4} d^{4} m^{2} - 50 \, c^{4} d^{4} m + 24 \, c^{4} d^{4}\right)} {\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{m}}"," ",0,"-(a*c^3*d^3*e*f^3*m^3 - 24*a*c^3*d^3*e*f^3 + 36*a^2*c^2*d^2*e^2*f^2*g - 24*a^3*c*d*e^3*f*g^2 + 6*a^4*e^4*g^3 + (c^4*d^4*g^3*m^3 - 6*c^4*d^4*g^3*m^2 + 11*c^4*d^4*g^3*m - 6*c^4*d^4*g^3)*x^4 - (24*c^4*d^4*f*g^2 - (3*c^4*d^4*f*g^2 + a*c^3*d^3*e*g^3)*m^3 + 3*(7*c^4*d^4*f*g^2 + a*c^3*d^3*e*g^3)*m^2 - 2*(21*c^4*d^4*f*g^2 + a*c^3*d^3*e*g^3)*m)*x^3 - 3*(3*a*c^3*d^3*e*f^3 - a^2*c^2*d^2*e^2*f^2*g)*m^2 - 3*(12*c^4*d^4*f^2*g - (c^4*d^4*f^2*g + a*c^3*d^3*e*f*g^2)*m^3 + (8*c^4*d^4*f^2*g + 5*a*c^3*d^3*e*f*g^2 - a^2*c^2*d^2*e^2*g^3)*m^2 - (19*c^4*d^4*f^2*g + 4*a*c^3*d^3*e*f*g^2 - a^2*c^2*d^2*e^2*g^3)*m)*x^2 + (26*a*c^3*d^3*e*f^3 - 21*a^2*c^2*d^2*e^2*f^2*g + 6*a^3*c*d*e^3*f*g^2)*m - (24*c^4*d^4*f^3 - (c^4*d^4*f^3 + 3*a*c^3*d^3*e*f^2*g)*m^3 + 3*(3*c^4*d^4*f^3 + 7*a*c^3*d^3*e*f^2*g - 2*a^2*c^2*d^2*e^2*f*g^2)*m^2 - 2*(13*c^4*d^4*f^3 + 18*a*c^3*d^3*e*f^2*g - 12*a^2*c^2*d^2*e^2*f*g^2 + 3*a^3*c*d*e^3*g^3)*m)*x)*(e*x + d)^m/((c^4*d^4*m^4 - 10*c^4*d^4*m^3 + 35*c^4*d^4*m^2 - 50*c^4*d^4*m + 24*c^4*d^4)*(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^m)","B",0
769,1,350,0,0.460426," ","integrate((e*x+d)^m*(g*x+f)^2/((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^m),x, algorithm=""fricas"")","-\frac{{\left(a c^{2} d^{2} e f^{2} m^{2} + 6 \, a c^{2} d^{2} e f^{2} - 6 \, a^{2} c d e^{2} f g + 2 \, a^{3} e^{3} g^{2} + {\left(c^{3} d^{3} g^{2} m^{2} - 3 \, c^{3} d^{3} g^{2} m + 2 \, c^{3} d^{3} g^{2}\right)} x^{3} + {\left(6 \, c^{3} d^{3} f g + {\left(2 \, c^{3} d^{3} f g + a c^{2} d^{2} e g^{2}\right)} m^{2} - {\left(8 \, c^{3} d^{3} f g + a c^{2} d^{2} e g^{2}\right)} m\right)} x^{2} - {\left(5 \, a c^{2} d^{2} e f^{2} - 2 \, a^{2} c d e^{2} f g\right)} m + {\left(6 \, c^{3} d^{3} f^{2} + {\left(c^{3} d^{3} f^{2} + 2 \, a c^{2} d^{2} e f g\right)} m^{2} - {\left(5 \, c^{3} d^{3} f^{2} + 6 \, a c^{2} d^{2} e f g - 2 \, a^{2} c d e^{2} g^{2}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{{\left(c^{3} d^{3} m^{3} - 6 \, c^{3} d^{3} m^{2} + 11 \, c^{3} d^{3} m - 6 \, c^{3} d^{3}\right)} {\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{m}}"," ",0,"-(a*c^2*d^2*e*f^2*m^2 + 6*a*c^2*d^2*e*f^2 - 6*a^2*c*d*e^2*f*g + 2*a^3*e^3*g^2 + (c^3*d^3*g^2*m^2 - 3*c^3*d^3*g^2*m + 2*c^3*d^3*g^2)*x^3 + (6*c^3*d^3*f*g + (2*c^3*d^3*f*g + a*c^2*d^2*e*g^2)*m^2 - (8*c^3*d^3*f*g + a*c^2*d^2*e*g^2)*m)*x^2 - (5*a*c^2*d^2*e*f^2 - 2*a^2*c*d*e^2*f*g)*m + (6*c^3*d^3*f^2 + (c^3*d^3*f^2 + 2*a*c^2*d^2*e*f*g)*m^2 - (5*c^3*d^3*f^2 + 6*a*c^2*d^2*e*f*g - 2*a^2*c*d*e^2*g^2)*m)*x)*(e*x + d)^m/((c^3*d^3*m^3 - 6*c^3*d^3*m^2 + 11*c^3*d^3*m - 6*c^3*d^3)*(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^m)","A",0
770,1,145,0,0.421999," ","integrate((e*x+d)^m*(g*x+f)/((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^m),x, algorithm=""fricas"")","-\frac{{\left(a c d e f m - 2 \, a c d e f + a^{2} e^{2} g + {\left(c^{2} d^{2} g m - c^{2} d^{2} g\right)} x^{2} - {\left(2 \, c^{2} d^{2} f - {\left(c^{2} d^{2} f + a c d e g\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{{\left(c^{2} d^{2} m^{2} - 3 \, c^{2} d^{2} m + 2 \, c^{2} d^{2}\right)} {\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{m}}"," ",0,"-(a*c*d*e*f*m - 2*a*c*d*e*f + a^2*e^2*g + (c^2*d^2*g*m - c^2*d^2*g)*x^2 - (2*c^2*d^2*f - (c^2*d^2*f + a*c*d*e*g)*m)*x)*(e*x + d)^m/((c^2*d^2*m^2 - 3*c^2*d^2*m + 2*c^2*d^2)*(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^m)","A",0
771,1,57,0,0.424209," ","integrate((e*x+d)^m/((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^m),x, algorithm=""fricas"")","-\frac{{\left(c d x + a e\right)} {\left(e x + d\right)}^{m}}{{\left(c d m - c d\right)} {\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{m}}"," ",0,"-(c*d*x + a*e)*(e*x + d)^m/((c*d*m - c*d)*(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^m)","A",0
772,0,0,0,0.434174," ","integrate((e*x+d)^m/(g*x+f)/((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^m),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)}^{m}}{{\left(g x + f\right)} {\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{m}}, x\right)"," ",0,"integral((e*x + d)^m/((g*x + f)*(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^m), x)","F",0
773,0,0,0,0.440727," ","integrate((e*x+d)^m/(g*x+f)^2/((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^m),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)}^{m}}{{\left(g^{2} x^{2} + 2 \, f g x + f^{2}\right)} {\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{m}}, x\right)"," ",0,"integral((e*x + d)^m/((g^2*x^2 + 2*f*g*x + f^2)*(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^m), x)","F",0
774,0,0,0,0.444929," ","integrate((e*x+d)^m/(g*x+f)^3/((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^m),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)}^{m}}{{\left(g^{3} x^{3} + 3 \, f g^{2} x^{2} + 3 \, f^{2} g x + f^{3}\right)} {\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{m}}, x\right)"," ",0,"integral((e*x + d)^m/((g^3*x^3 + 3*f*g^2*x^2 + 3*f^2*g*x + f^3)*(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^m), x)","F",0
775,0,0,0,0.441095," ","integrate((e*x+d)^m*(g*x+f)^(3/2)/((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^m),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(g x + f\right)}^{\frac{3}{2}} {\left(e x + d\right)}^{m}}{{\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{m}}, x\right)"," ",0,"integral((g*x + f)^(3/2)*(e*x + d)^m/(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^m, x)","F",0
776,0,0,0,0.453428," ","integrate((e*x+d)^m*(g*x+f)^(1/2)/((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^m),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{g x + f} {\left(e x + d\right)}^{m}}{{\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{m}}, x\right)"," ",0,"integral(sqrt(g*x + f)*(e*x + d)^m/(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^m, x)","F",0
777,0,0,0,0.429212," ","integrate((e*x+d)^m/(g*x+f)^(1/2)/((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^m),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)}^{m}}{\sqrt{g x + f} {\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{m}}, x\right)"," ",0,"integral((e*x + d)^m/(sqrt(g*x + f)*(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^m), x)","F",0
778,0,0,0,0.448163," ","integrate((e*x+d)^m/(g*x+f)^(3/2)/((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^m),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{g x + f} {\left(e x + d\right)}^{m}}{{\left(g^{2} x^{2} + 2 \, f g x + f^{2}\right)} {\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{m}}, x\right)"," ",0,"integral(sqrt(g*x + f)*(e*x + d)^m/((g^2*x^2 + 2*f*g*x + f^2)*(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^m), x)","F",0
779,0,0,0,0.447530," ","integrate((e*x+d)^m/(g*x+f)^(5/2)/((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^m),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{g x + f} {\left(e x + d\right)}^{m}}{{\left(g^{3} x^{3} + 3 \, f g^{2} x^{2} + 3 \, f^{2} g x + f^{3}\right)} {\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{m}}, x\right)"," ",0,"integral(sqrt(g*x + f)*(e*x + d)^m/((g^3*x^3 + 3*f*g^2*x^2 + 3*f^2*g*x + f^3)*(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^m), x)","F",0
780,1,66,0,0.420975," ","integrate((c*d*x+a*e)^n*(e*x+d)^m/((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^m),x, algorithm=""fricas"")","-\frac{{\left(c d x + a e\right)} {\left(c d x + a e\right)}^{n} {\left(e x + d\right)}^{m} e^{\left(-m \log\left(c d x + a e\right) - m \log\left(e x + d\right)\right)}}{c d m - c d n - c d}"," ",0,"-(c*d*x + a*e)*(c*d*x + a*e)^n*(e*x + d)^m*e^(-m*log(c*d*x + a*e) - m*log(e*x + d))/(c*d*m - c*d*n - c*d)","A",0
781,1,35,0,0.427925," ","integrate((e*x+d)^m*(c*d^2*e*g-e*(a*e^2+c*d^2)*g-c*d*e^2*g*x)^(-1+m)/((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^m),x, algorithm=""fricas"")","-\frac{\log\left(c d x + a e\right)}{c d e^{2} g \left(-\frac{1}{e^{2} g}\right)^{m}}"," ",0,"-log(c*d*x + a*e)/(c*d*e^2*g*(-1/(e^2*g))^m)","A",0
782,0,0,0,0.429925," ","integrate((e*x+d)^(3/2)*(g*x+f)^n/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} {\left(g x + f\right)}^{n}}{c d x + a e}, x\right)"," ",0,"integral(sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*(g*x + f)^n/(c*d*x + a*e), x)","F",0
783,1,597,0,0.422458," ","integrate((e*x+d)^(3/2)*(g*x+f)^4/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(315 \, c^{5} d^{5} e g^{4} x^{5} + 1155 \, {\left(3 \, c^{5} d^{6} - 2 \, a c^{4} d^{4} e^{2}\right)} f^{4} - 1848 \, {\left(5 \, a c^{4} d^{5} e - 4 \, a^{2} c^{3} d^{3} e^{3}\right)} f^{3} g + 1584 \, {\left(7 \, a^{2} c^{3} d^{4} e^{2} - 6 \, a^{3} c^{2} d^{2} e^{4}\right)} f^{2} g^{2} - 704 \, {\left(9 \, a^{3} c^{2} d^{3} e^{3} - 8 \, a^{4} c d e^{5}\right)} f g^{3} + 128 \, {\left(11 \, a^{4} c d^{2} e^{4} - 10 \, a^{5} e^{6}\right)} g^{4} + 35 \, {\left(44 \, c^{5} d^{5} e f g^{3} + {\left(11 \, c^{5} d^{6} - 10 \, a c^{4} d^{4} e^{2}\right)} g^{4}\right)} x^{4} + 10 \, {\left(297 \, c^{5} d^{5} e f^{2} g^{2} + 22 \, {\left(9 \, c^{5} d^{6} - 8 \, a c^{4} d^{4} e^{2}\right)} f g^{3} - 4 \, {\left(11 \, a c^{4} d^{5} e - 10 \, a^{2} c^{3} d^{3} e^{3}\right)} g^{4}\right)} x^{3} + 6 \, {\left(462 \, c^{5} d^{5} e f^{3} g + 99 \, {\left(7 \, c^{5} d^{6} - 6 \, a c^{4} d^{4} e^{2}\right)} f^{2} g^{2} - 44 \, {\left(9 \, a c^{4} d^{5} e - 8 \, a^{2} c^{3} d^{3} e^{3}\right)} f g^{3} + 8 \, {\left(11 \, a^{2} c^{3} d^{4} e^{2} - 10 \, a^{3} c^{2} d^{2} e^{4}\right)} g^{4}\right)} x^{2} + {\left(1155 \, c^{5} d^{5} e f^{4} + 924 \, {\left(5 \, c^{5} d^{6} - 4 \, a c^{4} d^{4} e^{2}\right)} f^{3} g - 792 \, {\left(7 \, a c^{4} d^{5} e - 6 \, a^{2} c^{3} d^{3} e^{3}\right)} f^{2} g^{2} + 352 \, {\left(9 \, a^{2} c^{3} d^{4} e^{2} - 8 \, a^{3} c^{2} d^{2} e^{4}\right)} f g^{3} - 64 \, {\left(11 \, a^{3} c^{2} d^{3} e^{3} - 10 \, a^{4} c d e^{5}\right)} g^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{3465 \, {\left(c^{6} d^{6} e x + c^{6} d^{7}\right)}}"," ",0,"2/3465*(315*c^5*d^5*e*g^4*x^5 + 1155*(3*c^5*d^6 - 2*a*c^4*d^4*e^2)*f^4 - 1848*(5*a*c^4*d^5*e - 4*a^2*c^3*d^3*e^3)*f^3*g + 1584*(7*a^2*c^3*d^4*e^2 - 6*a^3*c^2*d^2*e^4)*f^2*g^2 - 704*(9*a^3*c^2*d^3*e^3 - 8*a^4*c*d*e^5)*f*g^3 + 128*(11*a^4*c*d^2*e^4 - 10*a^5*e^6)*g^4 + 35*(44*c^5*d^5*e*f*g^3 + (11*c^5*d^6 - 10*a*c^4*d^4*e^2)*g^4)*x^4 + 10*(297*c^5*d^5*e*f^2*g^2 + 22*(9*c^5*d^6 - 8*a*c^4*d^4*e^2)*f*g^3 - 4*(11*a*c^4*d^5*e - 10*a^2*c^3*d^3*e^3)*g^4)*x^3 + 6*(462*c^5*d^5*e*f^3*g + 99*(7*c^5*d^6 - 6*a*c^4*d^4*e^2)*f^2*g^2 - 44*(9*a*c^4*d^5*e - 8*a^2*c^3*d^3*e^3)*f*g^3 + 8*(11*a^2*c^3*d^4*e^2 - 10*a^3*c^2*d^2*e^4)*g^4)*x^2 + (1155*c^5*d^5*e*f^4 + 924*(5*c^5*d^6 - 4*a*c^4*d^4*e^2)*f^3*g - 792*(7*a*c^4*d^5*e - 6*a^2*c^3*d^3*e^3)*f^2*g^2 + 352*(9*a^2*c^3*d^4*e^2 - 8*a^3*c^2*d^2*e^4)*f*g^3 - 64*(11*a^3*c^2*d^3*e^3 - 10*a^4*c*d*e^5)*g^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)/(c^6*d^6*e*x + c^6*d^7)","A",0
784,1,408,0,0.422705," ","integrate((e*x+d)^(3/2)*(g*x+f)^3/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, c^{4} d^{4} e g^{3} x^{4} + 105 \, {\left(3 \, c^{4} d^{5} - 2 \, a c^{3} d^{3} e^{2}\right)} f^{3} - 126 \, {\left(5 \, a c^{3} d^{4} e - 4 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{2} g + 72 \, {\left(7 \, a^{2} c^{2} d^{3} e^{2} - 6 \, a^{3} c d e^{4}\right)} f g^{2} - 16 \, {\left(9 \, a^{3} c d^{2} e^{3} - 8 \, a^{4} e^{5}\right)} g^{3} + 5 \, {\left(27 \, c^{4} d^{4} e f g^{2} + {\left(9 \, c^{4} d^{5} - 8 \, a c^{3} d^{3} e^{2}\right)} g^{3}\right)} x^{3} + 3 \, {\left(63 \, c^{4} d^{4} e f^{2} g + 9 \, {\left(7 \, c^{4} d^{5} - 6 \, a c^{3} d^{3} e^{2}\right)} f g^{2} - 2 \, {\left(9 \, a c^{3} d^{4} e - 8 \, a^{2} c^{2} d^{2} e^{3}\right)} g^{3}\right)} x^{2} + {\left(105 \, c^{4} d^{4} e f^{3} + 63 \, {\left(5 \, c^{4} d^{5} - 4 \, a c^{3} d^{3} e^{2}\right)} f^{2} g - 36 \, {\left(7 \, a c^{3} d^{4} e - 6 \, a^{2} c^{2} d^{2} e^{3}\right)} f g^{2} + 8 \, {\left(9 \, a^{2} c^{2} d^{3} e^{2} - 8 \, a^{3} c d e^{4}\right)} g^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{315 \, {\left(c^{5} d^{5} e x + c^{5} d^{6}\right)}}"," ",0,"2/315*(35*c^4*d^4*e*g^3*x^4 + 105*(3*c^4*d^5 - 2*a*c^3*d^3*e^2)*f^3 - 126*(5*a*c^3*d^4*e - 4*a^2*c^2*d^2*e^3)*f^2*g + 72*(7*a^2*c^2*d^3*e^2 - 6*a^3*c*d*e^4)*f*g^2 - 16*(9*a^3*c*d^2*e^3 - 8*a^4*e^5)*g^3 + 5*(27*c^4*d^4*e*f*g^2 + (9*c^4*d^5 - 8*a*c^3*d^3*e^2)*g^3)*x^3 + 3*(63*c^4*d^4*e*f^2*g + 9*(7*c^4*d^5 - 6*a*c^3*d^3*e^2)*f*g^2 - 2*(9*a*c^3*d^4*e - 8*a^2*c^2*d^2*e^3)*g^3)*x^2 + (105*c^4*d^4*e*f^3 + 63*(5*c^4*d^5 - 4*a*c^3*d^3*e^2)*f^2*g - 36*(7*a*c^3*d^4*e - 6*a^2*c^2*d^2*e^3)*f*g^2 + 8*(9*a^2*c^2*d^3*e^2 - 8*a^3*c*d*e^4)*g^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)/(c^5*d^5*e*x + c^5*d^6)","A",0
785,1,256,0,0.425775," ","integrate((e*x+d)^(3/2)*(g*x+f)^2/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, c^{3} d^{3} e g^{2} x^{3} + 35 \, {\left(3 \, c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2}\right)} f^{2} - 28 \, {\left(5 \, a c^{2} d^{3} e - 4 \, a^{2} c d e^{3}\right)} f g + 8 \, {\left(7 \, a^{2} c d^{2} e^{2} - 6 \, a^{3} e^{4}\right)} g^{2} + 3 \, {\left(14 \, c^{3} d^{3} e f g + {\left(7 \, c^{3} d^{4} - 6 \, a c^{2} d^{2} e^{2}\right)} g^{2}\right)} x^{2} + {\left(35 \, c^{3} d^{3} e f^{2} + 14 \, {\left(5 \, c^{3} d^{4} - 4 \, a c^{2} d^{2} e^{2}\right)} f g - 4 \, {\left(7 \, a c^{2} d^{3} e - 6 \, a^{2} c d e^{3}\right)} g^{2}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{105 \, {\left(c^{4} d^{4} e x + c^{4} d^{5}\right)}}"," ",0,"2/105*(15*c^3*d^3*e*g^2*x^3 + 35*(3*c^3*d^4 - 2*a*c^2*d^2*e^2)*f^2 - 28*(5*a*c^2*d^3*e - 4*a^2*c*d*e^3)*f*g + 8*(7*a^2*c*d^2*e^2 - 6*a^3*e^4)*g^2 + 3*(14*c^3*d^3*e*f*g + (7*c^3*d^4 - 6*a*c^2*d^2*e^2)*g^2)*x^2 + (35*c^3*d^3*e*f^2 + 14*(5*c^3*d^4 - 4*a*c^2*d^2*e^2)*f*g - 4*(7*a*c^2*d^3*e - 6*a^2*c*d*e^3)*g^2)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)/(c^4*d^4*e*x + c^4*d^5)","A",0
786,1,141,0,0.406325," ","integrate((e*x+d)^(3/2)*(g*x+f)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, c^{2} d^{2} e g x^{2} + 5 \, {\left(3 \, c^{2} d^{3} - 2 \, a c d e^{2}\right)} f - 2 \, {\left(5 \, a c d^{2} e - 4 \, a^{2} e^{3}\right)} g + {\left(5 \, c^{2} d^{2} e f + {\left(5 \, c^{2} d^{3} - 4 \, a c d e^{2}\right)} g\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{15 \, {\left(c^{3} d^{3} e x + c^{3} d^{4}\right)}}"," ",0,"2/15*(3*c^2*d^2*e*g*x^2 + 5*(3*c^2*d^3 - 2*a*c*d*e^2)*f - 2*(5*a*c*d^2*e - 4*a^2*e^3)*g + (5*c^2*d^2*e*f + (5*c^2*d^3 - 4*a*c*d*e^2)*g)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)/(c^3*d^3*e*x + c^3*d^4)","A",0
787,1,73,0,0.406460," ","integrate((e*x+d)^(3/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d e x + 3 \, c d^{2} - 2 \, a e^{2}\right)} \sqrt{e x + d}}{3 \, {\left(c^{2} d^{2} e x + c^{2} d^{3}\right)}}"," ",0,"2/3*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d*e*x + 3*c*d^2 - 2*a*e^2)*sqrt(e*x + d)/(c^2*d^2*e*x + c^2*d^3)","A",0
788,1,511,0,0.436144," ","integrate((e*x+d)^(3/2)/(g*x+f)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(c d^{2} e f - c d^{3} g + {\left(c d e^{2} f - c d^{2} e g\right)} x\right)} \sqrt{-c d f g + a e g^{2}} \log\left(-\frac{c d e g x^{2} - c d^{2} f + 2 \, a d e g - {\left(c d e f - {\left(c d^{2} + 2 \, a e^{2}\right)} g\right)} x - 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{-c d f g + a e g^{2}} \sqrt{e x + d}}{e g x^{2} + d f + {\left(e f + d g\right)} x}\right) + 2 \, {\left(c d e f g - a e^{2} g^{2}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{c^{2} d^{3} f g^{2} - a c d^{2} e g^{3} + {\left(c^{2} d^{2} e f g^{2} - a c d e^{2} g^{3}\right)} x}, \frac{2 \, {\left({\left(c d^{2} e f - c d^{3} g + {\left(c d e^{2} f - c d^{2} e g\right)} x\right)} \sqrt{c d f g - a e g^{2}} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{c d f g - a e g^{2}} \sqrt{e x + d}}{c d e g x^{2} + a d e g + {\left(c d^{2} + a e^{2}\right)} g x}\right) + {\left(c d e f g - a e^{2} g^{2}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}\right)}}{c^{2} d^{3} f g^{2} - a c d^{2} e g^{3} + {\left(c^{2} d^{2} e f g^{2} - a c d e^{2} g^{3}\right)} x}\right]"," ",0,"[((c*d^2*e*f - c*d^3*g + (c*d*e^2*f - c*d^2*e*g)*x)*sqrt(-c*d*f*g + a*e*g^2)*log(-(c*d*e*g*x^2 - c*d^2*f + 2*a*d*e*g - (c*d*e*f - (c*d^2 + 2*a*e^2)*g)*x - 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-c*d*f*g + a*e*g^2)*sqrt(e*x + d))/(e*g*x^2 + d*f + (e*f + d*g)*x)) + 2*(c*d*e*f*g - a*e^2*g^2)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c^2*d^3*f*g^2 - a*c*d^2*e*g^3 + (c^2*d^2*e*f*g^2 - a*c*d*e^2*g^3)*x), 2*((c*d^2*e*f - c*d^3*g + (c*d*e^2*f - c*d^2*e*g)*x)*sqrt(c*d*f*g - a*e*g^2)*arctan(sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(c*d*f*g - a*e*g^2)*sqrt(e*x + d)/(c*d*e*g*x^2 + a*d*e*g + (c*d^2 + a*e^2)*g*x)) + (c*d*e*f*g - a*e^2*g^2)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c^2*d^3*f*g^2 - a*c*d^2*e*g^3 + (c^2*d^2*e*f*g^2 - a*c*d*e^2*g^3)*x)]","A",0
789,1,896,0,0.443132," ","integrate((e*x+d)^(3/2)/(g*x+f)^2/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(c d^{2} e f^{2} + {\left(c d^{3} - 2 \, a d e^{2}\right)} f g + {\left(c d e^{2} f g + {\left(c d^{2} e - 2 \, a e^{3}\right)} g^{2}\right)} x^{2} + {\left(c d e^{2} f^{2} + 2 \, {\left(c d^{2} e - a e^{3}\right)} f g + {\left(c d^{3} - 2 \, a d e^{2}\right)} g^{2}\right)} x\right)} \sqrt{-c d f g + a e g^{2}} \log\left(-\frac{c d e g x^{2} - c d^{2} f + 2 \, a d e g - {\left(c d e f - {\left(c d^{2} + 2 \, a e^{2}\right)} g\right)} x - 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{-c d f g + a e g^{2}} \sqrt{e x + d}}{e g x^{2} + d f + {\left(e f + d g\right)} x}\right) + 2 \, {\left(c d e f^{2} g + a d e g^{3} - {\left(c d^{2} + a e^{2}\right)} f g^{2}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{2 \, {\left(c^{2} d^{3} f^{3} g^{2} - 2 \, a c d^{2} e f^{2} g^{3} + a^{2} d e^{2} f g^{4} + {\left(c^{2} d^{2} e f^{2} g^{3} - 2 \, a c d e^{2} f g^{4} + a^{2} e^{3} g^{5}\right)} x^{2} + {\left(c^{2} d^{2} e f^{3} g^{2} + a^{2} d e^{2} g^{5} + {\left(c^{2} d^{3} - 2 \, a c d e^{2}\right)} f^{2} g^{3} - {\left(2 \, a c d^{2} e - a^{2} e^{3}\right)} f g^{4}\right)} x\right)}}, -\frac{{\left(c d^{2} e f^{2} + {\left(c d^{3} - 2 \, a d e^{2}\right)} f g + {\left(c d e^{2} f g + {\left(c d^{2} e - 2 \, a e^{3}\right)} g^{2}\right)} x^{2} + {\left(c d e^{2} f^{2} + 2 \, {\left(c d^{2} e - a e^{3}\right)} f g + {\left(c d^{3} - 2 \, a d e^{2}\right)} g^{2}\right)} x\right)} \sqrt{c d f g - a e g^{2}} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{c d f g - a e g^{2}} \sqrt{e x + d}}{c d e g x^{2} + a d e g + {\left(c d^{2} + a e^{2}\right)} g x}\right) + {\left(c d e f^{2} g + a d e g^{3} - {\left(c d^{2} + a e^{2}\right)} f g^{2}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{c^{2} d^{3} f^{3} g^{2} - 2 \, a c d^{2} e f^{2} g^{3} + a^{2} d e^{2} f g^{4} + {\left(c^{2} d^{2} e f^{2} g^{3} - 2 \, a c d e^{2} f g^{4} + a^{2} e^{3} g^{5}\right)} x^{2} + {\left(c^{2} d^{2} e f^{3} g^{2} + a^{2} d e^{2} g^{5} + {\left(c^{2} d^{3} - 2 \, a c d e^{2}\right)} f^{2} g^{3} - {\left(2 \, a c d^{2} e - a^{2} e^{3}\right)} f g^{4}\right)} x}\right]"," ",0,"[-1/2*((c*d^2*e*f^2 + (c*d^3 - 2*a*d*e^2)*f*g + (c*d*e^2*f*g + (c*d^2*e - 2*a*e^3)*g^2)*x^2 + (c*d*e^2*f^2 + 2*(c*d^2*e - a*e^3)*f*g + (c*d^3 - 2*a*d*e^2)*g^2)*x)*sqrt(-c*d*f*g + a*e*g^2)*log(-(c*d*e*g*x^2 - c*d^2*f + 2*a*d*e*g - (c*d*e*f - (c*d^2 + 2*a*e^2)*g)*x - 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-c*d*f*g + a*e*g^2)*sqrt(e*x + d))/(e*g*x^2 + d*f + (e*f + d*g)*x)) + 2*(c*d*e*f^2*g + a*d*e*g^3 - (c*d^2 + a*e^2)*f*g^2)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c^2*d^3*f^3*g^2 - 2*a*c*d^2*e*f^2*g^3 + a^2*d*e^2*f*g^4 + (c^2*d^2*e*f^2*g^3 - 2*a*c*d*e^2*f*g^4 + a^2*e^3*g^5)*x^2 + (c^2*d^2*e*f^3*g^2 + a^2*d*e^2*g^5 + (c^2*d^3 - 2*a*c*d*e^2)*f^2*g^3 - (2*a*c*d^2*e - a^2*e^3)*f*g^4)*x), -((c*d^2*e*f^2 + (c*d^3 - 2*a*d*e^2)*f*g + (c*d*e^2*f*g + (c*d^2*e - 2*a*e^3)*g^2)*x^2 + (c*d*e^2*f^2 + 2*(c*d^2*e - a*e^3)*f*g + (c*d^3 - 2*a*d*e^2)*g^2)*x)*sqrt(c*d*f*g - a*e*g^2)*arctan(sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(c*d*f*g - a*e*g^2)*sqrt(e*x + d)/(c*d*e*g*x^2 + a*d*e*g + (c*d^2 + a*e^2)*g*x)) + (c*d*e*f^2*g + a*d*e*g^3 - (c*d^2 + a*e^2)*f*g^2)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c^2*d^3*f^3*g^2 - 2*a*c*d^2*e*f^2*g^3 + a^2*d*e^2*f*g^4 + (c^2*d^2*e*f^2*g^3 - 2*a*c*d*e^2*f*g^4 + a^2*e^3*g^5)*x^2 + (c^2*d^2*e*f^3*g^2 + a^2*d*e^2*g^5 + (c^2*d^3 - 2*a*c*d*e^2)*f^2*g^3 - (2*a*c*d^2*e - a^2*e^3)*f*g^4)*x)]","B",0
790,1,1704,0,0.470413," ","integrate((e*x+d)^(3/2)/(g*x+f)^3/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(c^{2} d^{3} e f^{3} + {\left(3 \, c^{2} d^{4} - 4 \, a c d^{2} e^{2}\right)} f^{2} g + {\left(c^{2} d^{2} e^{2} f g^{2} + {\left(3 \, c^{2} d^{3} e - 4 \, a c d e^{3}\right)} g^{3}\right)} x^{3} + {\left(2 \, c^{2} d^{2} e^{2} f^{2} g + {\left(7 \, c^{2} d^{3} e - 8 \, a c d e^{3}\right)} f g^{2} + {\left(3 \, c^{2} d^{4} - 4 \, a c d^{2} e^{2}\right)} g^{3}\right)} x^{2} + {\left(c^{2} d^{2} e^{2} f^{3} + {\left(5 \, c^{2} d^{3} e - 4 \, a c d e^{3}\right)} f^{2} g + 2 \, {\left(3 \, c^{2} d^{4} - 4 \, a c d^{2} e^{2}\right)} f g^{2}\right)} x\right)} \sqrt{-c d f g + a e g^{2}} \log\left(-\frac{c d e g x^{2} - c d^{2} f + 2 \, a d e g - {\left(c d e f - {\left(c d^{2} + 2 \, a e^{2}\right)} g\right)} x + 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{-c d f g + a e g^{2}} \sqrt{e x + d}}{e g x^{2} + d f + {\left(e f + d g\right)} x}\right) - 2 \, {\left(c^{2} d^{2} e f^{3} g - 2 \, a^{2} d e^{2} g^{4} - {\left(5 \, c^{2} d^{3} - a c d e^{2}\right)} f^{2} g^{2} + {\left(7 \, a c d^{2} e - 2 \, a^{2} e^{3}\right)} f g^{3} - {\left(c^{2} d^{2} e f^{2} g^{2} + {\left(3 \, c^{2} d^{3} - 5 \, a c d e^{2}\right)} f g^{3} - {\left(3 \, a c d^{2} e - 4 \, a^{2} e^{3}\right)} g^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{8 \, {\left(c^{3} d^{4} f^{5} g^{2} - 3 \, a c^{2} d^{3} e f^{4} g^{3} + 3 \, a^{2} c d^{2} e^{2} f^{3} g^{4} - a^{3} d e^{3} f^{2} g^{5} + {\left(c^{3} d^{3} e f^{3} g^{4} - 3 \, a c^{2} d^{2} e^{2} f^{2} g^{5} + 3 \, a^{2} c d e^{3} f g^{6} - a^{3} e^{4} g^{7}\right)} x^{3} + {\left(2 \, c^{3} d^{3} e f^{4} g^{3} - a^{3} d e^{3} g^{7} + {\left(c^{3} d^{4} - 6 \, a c^{2} d^{2} e^{2}\right)} f^{3} g^{4} - 3 \, {\left(a c^{2} d^{3} e - 2 \, a^{2} c d e^{3}\right)} f^{2} g^{5} + {\left(3 \, a^{2} c d^{2} e^{2} - 2 \, a^{3} e^{4}\right)} f g^{6}\right)} x^{2} + {\left(c^{3} d^{3} e f^{5} g^{2} - 2 \, a^{3} d e^{3} f g^{6} + {\left(2 \, c^{3} d^{4} - 3 \, a c^{2} d^{2} e^{2}\right)} f^{4} g^{3} - 3 \, {\left(2 \, a c^{2} d^{3} e - a^{2} c d e^{3}\right)} f^{3} g^{4} + {\left(6 \, a^{2} c d^{2} e^{2} - a^{3} e^{4}\right)} f^{2} g^{5}\right)} x\right)}}, -\frac{{\left(c^{2} d^{3} e f^{3} + {\left(3 \, c^{2} d^{4} - 4 \, a c d^{2} e^{2}\right)} f^{2} g + {\left(c^{2} d^{2} e^{2} f g^{2} + {\left(3 \, c^{2} d^{3} e - 4 \, a c d e^{3}\right)} g^{3}\right)} x^{3} + {\left(2 \, c^{2} d^{2} e^{2} f^{2} g + {\left(7 \, c^{2} d^{3} e - 8 \, a c d e^{3}\right)} f g^{2} + {\left(3 \, c^{2} d^{4} - 4 \, a c d^{2} e^{2}\right)} g^{3}\right)} x^{2} + {\left(c^{2} d^{2} e^{2} f^{3} + {\left(5 \, c^{2} d^{3} e - 4 \, a c d e^{3}\right)} f^{2} g + 2 \, {\left(3 \, c^{2} d^{4} - 4 \, a c d^{2} e^{2}\right)} f g^{2}\right)} x\right)} \sqrt{c d f g - a e g^{2}} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{c d f g - a e g^{2}} \sqrt{e x + d}}{c d e g x^{2} + a d e g + {\left(c d^{2} + a e^{2}\right)} g x}\right) + {\left(c^{2} d^{2} e f^{3} g - 2 \, a^{2} d e^{2} g^{4} - {\left(5 \, c^{2} d^{3} - a c d e^{2}\right)} f^{2} g^{2} + {\left(7 \, a c d^{2} e - 2 \, a^{2} e^{3}\right)} f g^{3} - {\left(c^{2} d^{2} e f^{2} g^{2} + {\left(3 \, c^{2} d^{3} - 5 \, a c d e^{2}\right)} f g^{3} - {\left(3 \, a c d^{2} e - 4 \, a^{2} e^{3}\right)} g^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{4 \, {\left(c^{3} d^{4} f^{5} g^{2} - 3 \, a c^{2} d^{3} e f^{4} g^{3} + 3 \, a^{2} c d^{2} e^{2} f^{3} g^{4} - a^{3} d e^{3} f^{2} g^{5} + {\left(c^{3} d^{3} e f^{3} g^{4} - 3 \, a c^{2} d^{2} e^{2} f^{2} g^{5} + 3 \, a^{2} c d e^{3} f g^{6} - a^{3} e^{4} g^{7}\right)} x^{3} + {\left(2 \, c^{3} d^{3} e f^{4} g^{3} - a^{3} d e^{3} g^{7} + {\left(c^{3} d^{4} - 6 \, a c^{2} d^{2} e^{2}\right)} f^{3} g^{4} - 3 \, {\left(a c^{2} d^{3} e - 2 \, a^{2} c d e^{3}\right)} f^{2} g^{5} + {\left(3 \, a^{2} c d^{2} e^{2} - 2 \, a^{3} e^{4}\right)} f g^{6}\right)} x^{2} + {\left(c^{3} d^{3} e f^{5} g^{2} - 2 \, a^{3} d e^{3} f g^{6} + {\left(2 \, c^{3} d^{4} - 3 \, a c^{2} d^{2} e^{2}\right)} f^{4} g^{3} - 3 \, {\left(2 \, a c^{2} d^{3} e - a^{2} c d e^{3}\right)} f^{3} g^{4} + {\left(6 \, a^{2} c d^{2} e^{2} - a^{3} e^{4}\right)} f^{2} g^{5}\right)} x\right)}}\right]"," ",0,"[1/8*((c^2*d^3*e*f^3 + (3*c^2*d^4 - 4*a*c*d^2*e^2)*f^2*g + (c^2*d^2*e^2*f*g^2 + (3*c^2*d^3*e - 4*a*c*d*e^3)*g^3)*x^3 + (2*c^2*d^2*e^2*f^2*g + (7*c^2*d^3*e - 8*a*c*d*e^3)*f*g^2 + (3*c^2*d^4 - 4*a*c*d^2*e^2)*g^3)*x^2 + (c^2*d^2*e^2*f^3 + (5*c^2*d^3*e - 4*a*c*d*e^3)*f^2*g + 2*(3*c^2*d^4 - 4*a*c*d^2*e^2)*f*g^2)*x)*sqrt(-c*d*f*g + a*e*g^2)*log(-(c*d*e*g*x^2 - c*d^2*f + 2*a*d*e*g - (c*d*e*f - (c*d^2 + 2*a*e^2)*g)*x + 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-c*d*f*g + a*e*g^2)*sqrt(e*x + d))/(e*g*x^2 + d*f + (e*f + d*g)*x)) - 2*(c^2*d^2*e*f^3*g - 2*a^2*d*e^2*g^4 - (5*c^2*d^3 - a*c*d*e^2)*f^2*g^2 + (7*a*c*d^2*e - 2*a^2*e^3)*f*g^3 - (c^2*d^2*e*f^2*g^2 + (3*c^2*d^3 - 5*a*c*d*e^2)*f*g^3 - (3*a*c*d^2*e - 4*a^2*e^3)*g^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c^3*d^4*f^5*g^2 - 3*a*c^2*d^3*e*f^4*g^3 + 3*a^2*c*d^2*e^2*f^3*g^4 - a^3*d*e^3*f^2*g^5 + (c^3*d^3*e*f^3*g^4 - 3*a*c^2*d^2*e^2*f^2*g^5 + 3*a^2*c*d*e^3*f*g^6 - a^3*e^4*g^7)*x^3 + (2*c^3*d^3*e*f^4*g^3 - a^3*d*e^3*g^7 + (c^3*d^4 - 6*a*c^2*d^2*e^2)*f^3*g^4 - 3*(a*c^2*d^3*e - 2*a^2*c*d*e^3)*f^2*g^5 + (3*a^2*c*d^2*e^2 - 2*a^3*e^4)*f*g^6)*x^2 + (c^3*d^3*e*f^5*g^2 - 2*a^3*d*e^3*f*g^6 + (2*c^3*d^4 - 3*a*c^2*d^2*e^2)*f^4*g^3 - 3*(2*a*c^2*d^3*e - a^2*c*d*e^3)*f^3*g^4 + (6*a^2*c*d^2*e^2 - a^3*e^4)*f^2*g^5)*x), -1/4*((c^2*d^3*e*f^3 + (3*c^2*d^4 - 4*a*c*d^2*e^2)*f^2*g + (c^2*d^2*e^2*f*g^2 + (3*c^2*d^3*e - 4*a*c*d*e^3)*g^3)*x^3 + (2*c^2*d^2*e^2*f^2*g + (7*c^2*d^3*e - 8*a*c*d*e^3)*f*g^2 + (3*c^2*d^4 - 4*a*c*d^2*e^2)*g^3)*x^2 + (c^2*d^2*e^2*f^3 + (5*c^2*d^3*e - 4*a*c*d*e^3)*f^2*g + 2*(3*c^2*d^4 - 4*a*c*d^2*e^2)*f*g^2)*x)*sqrt(c*d*f*g - a*e*g^2)*arctan(sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(c*d*f*g - a*e*g^2)*sqrt(e*x + d)/(c*d*e*g*x^2 + a*d*e*g + (c*d^2 + a*e^2)*g*x)) + (c^2*d^2*e*f^3*g - 2*a^2*d*e^2*g^4 - (5*c^2*d^3 - a*c*d*e^2)*f^2*g^2 + (7*a*c*d^2*e - 2*a^2*e^3)*f*g^3 - (c^2*d^2*e*f^2*g^2 + (3*c^2*d^3 - 5*a*c*d*e^2)*f*g^3 - (3*a*c*d^2*e - 4*a^2*e^3)*g^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c^3*d^4*f^5*g^2 - 3*a*c^2*d^3*e*f^4*g^3 + 3*a^2*c*d^2*e^2*f^3*g^4 - a^3*d*e^3*f^2*g^5 + (c^3*d^3*e*f^3*g^4 - 3*a*c^2*d^2*e^2*f^2*g^5 + 3*a^2*c*d*e^3*f*g^6 - a^3*e^4*g^7)*x^3 + (2*c^3*d^3*e*f^4*g^3 - a^3*d*e^3*g^7 + (c^3*d^4 - 6*a*c^2*d^2*e^2)*f^3*g^4 - 3*(a*c^2*d^3*e - 2*a^2*c*d*e^3)*f^2*g^5 + (3*a^2*c*d^2*e^2 - 2*a^3*e^4)*f*g^6)*x^2 + (c^3*d^3*e*f^5*g^2 - 2*a^3*d*e^3*f*g^6 + (2*c^3*d^4 - 3*a*c^2*d^2*e^2)*f^4*g^3 - 3*(2*a*c^2*d^3*e - a^2*c*d*e^3)*f^3*g^4 + (6*a^2*c*d^2*e^2 - a^3*e^4)*f^2*g^5)*x)]","B",0
791,1,2736,0,0.488975," ","integrate((e*x+d)^(3/2)/(g*x+f)^4/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(c^{3} d^{4} e f^{4} + {\left(5 \, c^{3} d^{5} - 6 \, a c^{2} d^{3} e^{2}\right)} f^{3} g + {\left(c^{3} d^{3} e^{2} f g^{3} + {\left(5 \, c^{3} d^{4} e - 6 \, a c^{2} d^{2} e^{3}\right)} g^{4}\right)} x^{4} + {\left(3 \, c^{3} d^{3} e^{2} f^{2} g^{2} + 2 \, {\left(8 \, c^{3} d^{4} e - 9 \, a c^{2} d^{2} e^{3}\right)} f g^{3} + {\left(5 \, c^{3} d^{5} - 6 \, a c^{2} d^{3} e^{2}\right)} g^{4}\right)} x^{3} + 3 \, {\left(c^{3} d^{3} e^{2} f^{3} g + 6 \, {\left(c^{3} d^{4} e - a c^{2} d^{2} e^{3}\right)} f^{2} g^{2} + {\left(5 \, c^{3} d^{5} - 6 \, a c^{2} d^{3} e^{2}\right)} f g^{3}\right)} x^{2} + {\left(c^{3} d^{3} e^{2} f^{4} + 2 \, {\left(4 \, c^{3} d^{4} e - 3 \, a c^{2} d^{2} e^{3}\right)} f^{3} g + 3 \, {\left(5 \, c^{3} d^{5} - 6 \, a c^{2} d^{3} e^{2}\right)} f^{2} g^{2}\right)} x\right)} \sqrt{-c d f g + a e g^{2}} \log\left(-\frac{c d e g x^{2} - c d^{2} f + 2 \, a d e g - {\left(c d e f - {\left(c d^{2} + 2 \, a e^{2}\right)} g\right)} x - 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{-c d f g + a e g^{2}} \sqrt{e x + d}}{e g x^{2} + d f + {\left(e f + d g\right)} x}\right) + 2 \, {\left(3 \, c^{3} d^{3} e f^{4} g + 8 \, a^{3} d e^{3} g^{5} - {\left(33 \, c^{3} d^{4} - 13 \, a c^{2} d^{2} e^{2}\right)} f^{3} g^{2} + {\left(59 \, a c^{2} d^{3} e - 20 \, a^{2} c d e^{3}\right)} f^{2} g^{3} - 2 \, {\left(17 \, a^{2} c d^{2} e^{2} - 2 \, a^{3} e^{4}\right)} f g^{4} - 3 \, {\left(c^{3} d^{3} e f^{2} g^{3} + {\left(5 \, c^{3} d^{4} - 7 \, a c^{2} d^{2} e^{2}\right)} f g^{4} - {\left(5 \, a c^{2} d^{3} e - 6 \, a^{2} c d e^{3}\right)} g^{5}\right)} x^{2} - 2 \, {\left(4 \, c^{3} d^{3} e f^{3} g^{2} + {\left(20 \, c^{3} d^{4} - 29 \, a c^{2} d^{2} e^{2}\right)} f^{2} g^{3} - {\left(25 \, a c^{2} d^{3} e - 31 \, a^{2} c d e^{3}\right)} f g^{4} + {\left(5 \, a^{2} c d^{2} e^{2} - 6 \, a^{3} e^{4}\right)} g^{5}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{48 \, {\left(c^{4} d^{5} f^{7} g^{2} - 4 \, a c^{3} d^{4} e f^{6} g^{3} + 6 \, a^{2} c^{2} d^{3} e^{2} f^{5} g^{4} - 4 \, a^{3} c d^{2} e^{3} f^{4} g^{5} + a^{4} d e^{4} f^{3} g^{6} + {\left(c^{4} d^{4} e f^{4} g^{5} - 4 \, a c^{3} d^{3} e^{2} f^{3} g^{6} + 6 \, a^{2} c^{2} d^{2} e^{3} f^{2} g^{7} - 4 \, a^{3} c d e^{4} f g^{8} + a^{4} e^{5} g^{9}\right)} x^{4} + {\left(3 \, c^{4} d^{4} e f^{5} g^{4} + a^{4} d e^{4} g^{9} + {\left(c^{4} d^{5} - 12 \, a c^{3} d^{3} e^{2}\right)} f^{4} g^{5} - 2 \, {\left(2 \, a c^{3} d^{4} e - 9 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{3} g^{6} + 6 \, {\left(a^{2} c^{2} d^{3} e^{2} - 2 \, a^{3} c d e^{4}\right)} f^{2} g^{7} - {\left(4 \, a^{3} c d^{2} e^{3} - 3 \, a^{4} e^{5}\right)} f g^{8}\right)} x^{3} + 3 \, {\left(c^{4} d^{4} e f^{6} g^{3} + a^{4} d e^{4} f g^{8} + {\left(c^{4} d^{5} - 4 \, a c^{3} d^{3} e^{2}\right)} f^{5} g^{4} - 2 \, {\left(2 \, a c^{3} d^{4} e - 3 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{4} g^{5} + 2 \, {\left(3 \, a^{2} c^{2} d^{3} e^{2} - 2 \, a^{3} c d e^{4}\right)} f^{3} g^{6} - {\left(4 \, a^{3} c d^{2} e^{3} - a^{4} e^{5}\right)} f^{2} g^{7}\right)} x^{2} + {\left(c^{4} d^{4} e f^{7} g^{2} + 3 \, a^{4} d e^{4} f^{2} g^{7} + {\left(3 \, c^{4} d^{5} - 4 \, a c^{3} d^{3} e^{2}\right)} f^{6} g^{3} - 6 \, {\left(2 \, a c^{3} d^{4} e - a^{2} c^{2} d^{2} e^{3}\right)} f^{5} g^{4} + 2 \, {\left(9 \, a^{2} c^{2} d^{3} e^{2} - 2 \, a^{3} c d e^{4}\right)} f^{4} g^{5} - {\left(12 \, a^{3} c d^{2} e^{3} - a^{4} e^{5}\right)} f^{3} g^{6}\right)} x\right)}}, -\frac{3 \, {\left(c^{3} d^{4} e f^{4} + {\left(5 \, c^{3} d^{5} - 6 \, a c^{2} d^{3} e^{2}\right)} f^{3} g + {\left(c^{3} d^{3} e^{2} f g^{3} + {\left(5 \, c^{3} d^{4} e - 6 \, a c^{2} d^{2} e^{3}\right)} g^{4}\right)} x^{4} + {\left(3 \, c^{3} d^{3} e^{2} f^{2} g^{2} + 2 \, {\left(8 \, c^{3} d^{4} e - 9 \, a c^{2} d^{2} e^{3}\right)} f g^{3} + {\left(5 \, c^{3} d^{5} - 6 \, a c^{2} d^{3} e^{2}\right)} g^{4}\right)} x^{3} + 3 \, {\left(c^{3} d^{3} e^{2} f^{3} g + 6 \, {\left(c^{3} d^{4} e - a c^{2} d^{2} e^{3}\right)} f^{2} g^{2} + {\left(5 \, c^{3} d^{5} - 6 \, a c^{2} d^{3} e^{2}\right)} f g^{3}\right)} x^{2} + {\left(c^{3} d^{3} e^{2} f^{4} + 2 \, {\left(4 \, c^{3} d^{4} e - 3 \, a c^{2} d^{2} e^{3}\right)} f^{3} g + 3 \, {\left(5 \, c^{3} d^{5} - 6 \, a c^{2} d^{3} e^{2}\right)} f^{2} g^{2}\right)} x\right)} \sqrt{c d f g - a e g^{2}} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{c d f g - a e g^{2}} \sqrt{e x + d}}{c d e g x^{2} + a d e g + {\left(c d^{2} + a e^{2}\right)} g x}\right) + {\left(3 \, c^{3} d^{3} e f^{4} g + 8 \, a^{3} d e^{3} g^{5} - {\left(33 \, c^{3} d^{4} - 13 \, a c^{2} d^{2} e^{2}\right)} f^{3} g^{2} + {\left(59 \, a c^{2} d^{3} e - 20 \, a^{2} c d e^{3}\right)} f^{2} g^{3} - 2 \, {\left(17 \, a^{2} c d^{2} e^{2} - 2 \, a^{3} e^{4}\right)} f g^{4} - 3 \, {\left(c^{3} d^{3} e f^{2} g^{3} + {\left(5 \, c^{3} d^{4} - 7 \, a c^{2} d^{2} e^{2}\right)} f g^{4} - {\left(5 \, a c^{2} d^{3} e - 6 \, a^{2} c d e^{3}\right)} g^{5}\right)} x^{2} - 2 \, {\left(4 \, c^{3} d^{3} e f^{3} g^{2} + {\left(20 \, c^{3} d^{4} - 29 \, a c^{2} d^{2} e^{2}\right)} f^{2} g^{3} - {\left(25 \, a c^{2} d^{3} e - 31 \, a^{2} c d e^{3}\right)} f g^{4} + {\left(5 \, a^{2} c d^{2} e^{2} - 6 \, a^{3} e^{4}\right)} g^{5}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{24 \, {\left(c^{4} d^{5} f^{7} g^{2} - 4 \, a c^{3} d^{4} e f^{6} g^{3} + 6 \, a^{2} c^{2} d^{3} e^{2} f^{5} g^{4} - 4 \, a^{3} c d^{2} e^{3} f^{4} g^{5} + a^{4} d e^{4} f^{3} g^{6} + {\left(c^{4} d^{4} e f^{4} g^{5} - 4 \, a c^{3} d^{3} e^{2} f^{3} g^{6} + 6 \, a^{2} c^{2} d^{2} e^{3} f^{2} g^{7} - 4 \, a^{3} c d e^{4} f g^{8} + a^{4} e^{5} g^{9}\right)} x^{4} + {\left(3 \, c^{4} d^{4} e f^{5} g^{4} + a^{4} d e^{4} g^{9} + {\left(c^{4} d^{5} - 12 \, a c^{3} d^{3} e^{2}\right)} f^{4} g^{5} - 2 \, {\left(2 \, a c^{3} d^{4} e - 9 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{3} g^{6} + 6 \, {\left(a^{2} c^{2} d^{3} e^{2} - 2 \, a^{3} c d e^{4}\right)} f^{2} g^{7} - {\left(4 \, a^{3} c d^{2} e^{3} - 3 \, a^{4} e^{5}\right)} f g^{8}\right)} x^{3} + 3 \, {\left(c^{4} d^{4} e f^{6} g^{3} + a^{4} d e^{4} f g^{8} + {\left(c^{4} d^{5} - 4 \, a c^{3} d^{3} e^{2}\right)} f^{5} g^{4} - 2 \, {\left(2 \, a c^{3} d^{4} e - 3 \, a^{2} c^{2} d^{2} e^{3}\right)} f^{4} g^{5} + 2 \, {\left(3 \, a^{2} c^{2} d^{3} e^{2} - 2 \, a^{3} c d e^{4}\right)} f^{3} g^{6} - {\left(4 \, a^{3} c d^{2} e^{3} - a^{4} e^{5}\right)} f^{2} g^{7}\right)} x^{2} + {\left(c^{4} d^{4} e f^{7} g^{2} + 3 \, a^{4} d e^{4} f^{2} g^{7} + {\left(3 \, c^{4} d^{5} - 4 \, a c^{3} d^{3} e^{2}\right)} f^{6} g^{3} - 6 \, {\left(2 \, a c^{3} d^{4} e - a^{2} c^{2} d^{2} e^{3}\right)} f^{5} g^{4} + 2 \, {\left(9 \, a^{2} c^{2} d^{3} e^{2} - 2 \, a^{3} c d e^{4}\right)} f^{4} g^{5} - {\left(12 \, a^{3} c d^{2} e^{3} - a^{4} e^{5}\right)} f^{3} g^{6}\right)} x\right)}}\right]"," ",0,"[-1/48*(3*(c^3*d^4*e*f^4 + (5*c^3*d^5 - 6*a*c^2*d^3*e^2)*f^3*g + (c^3*d^3*e^2*f*g^3 + (5*c^3*d^4*e - 6*a*c^2*d^2*e^3)*g^4)*x^4 + (3*c^3*d^3*e^2*f^2*g^2 + 2*(8*c^3*d^4*e - 9*a*c^2*d^2*e^3)*f*g^3 + (5*c^3*d^5 - 6*a*c^2*d^3*e^2)*g^4)*x^3 + 3*(c^3*d^3*e^2*f^3*g + 6*(c^3*d^4*e - a*c^2*d^2*e^3)*f^2*g^2 + (5*c^3*d^5 - 6*a*c^2*d^3*e^2)*f*g^3)*x^2 + (c^3*d^3*e^2*f^4 + 2*(4*c^3*d^4*e - 3*a*c^2*d^2*e^3)*f^3*g + 3*(5*c^3*d^5 - 6*a*c^2*d^3*e^2)*f^2*g^2)*x)*sqrt(-c*d*f*g + a*e*g^2)*log(-(c*d*e*g*x^2 - c*d^2*f + 2*a*d*e*g - (c*d*e*f - (c*d^2 + 2*a*e^2)*g)*x - 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-c*d*f*g + a*e*g^2)*sqrt(e*x + d))/(e*g*x^2 + d*f + (e*f + d*g)*x)) + 2*(3*c^3*d^3*e*f^4*g + 8*a^3*d*e^3*g^5 - (33*c^3*d^4 - 13*a*c^2*d^2*e^2)*f^3*g^2 + (59*a*c^2*d^3*e - 20*a^2*c*d*e^3)*f^2*g^3 - 2*(17*a^2*c*d^2*e^2 - 2*a^3*e^4)*f*g^4 - 3*(c^3*d^3*e*f^2*g^3 + (5*c^3*d^4 - 7*a*c^2*d^2*e^2)*f*g^4 - (5*a*c^2*d^3*e - 6*a^2*c*d*e^3)*g^5)*x^2 - 2*(4*c^3*d^3*e*f^3*g^2 + (20*c^3*d^4 - 29*a*c^2*d^2*e^2)*f^2*g^3 - (25*a*c^2*d^3*e - 31*a^2*c*d*e^3)*f*g^4 + (5*a^2*c*d^2*e^2 - 6*a^3*e^4)*g^5)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c^4*d^5*f^7*g^2 - 4*a*c^3*d^4*e*f^6*g^3 + 6*a^2*c^2*d^3*e^2*f^5*g^4 - 4*a^3*c*d^2*e^3*f^4*g^5 + a^4*d*e^4*f^3*g^6 + (c^4*d^4*e*f^4*g^5 - 4*a*c^3*d^3*e^2*f^3*g^6 + 6*a^2*c^2*d^2*e^3*f^2*g^7 - 4*a^3*c*d*e^4*f*g^8 + a^4*e^5*g^9)*x^4 + (3*c^4*d^4*e*f^5*g^4 + a^4*d*e^4*g^9 + (c^4*d^5 - 12*a*c^3*d^3*e^2)*f^4*g^5 - 2*(2*a*c^3*d^4*e - 9*a^2*c^2*d^2*e^3)*f^3*g^6 + 6*(a^2*c^2*d^3*e^2 - 2*a^3*c*d*e^4)*f^2*g^7 - (4*a^3*c*d^2*e^3 - 3*a^4*e^5)*f*g^8)*x^3 + 3*(c^4*d^4*e*f^6*g^3 + a^4*d*e^4*f*g^8 + (c^4*d^5 - 4*a*c^3*d^3*e^2)*f^5*g^4 - 2*(2*a*c^3*d^4*e - 3*a^2*c^2*d^2*e^3)*f^4*g^5 + 2*(3*a^2*c^2*d^3*e^2 - 2*a^3*c*d*e^4)*f^3*g^6 - (4*a^3*c*d^2*e^3 - a^4*e^5)*f^2*g^7)*x^2 + (c^4*d^4*e*f^7*g^2 + 3*a^4*d*e^4*f^2*g^7 + (3*c^4*d^5 - 4*a*c^3*d^3*e^2)*f^6*g^3 - 6*(2*a*c^3*d^4*e - a^2*c^2*d^2*e^3)*f^5*g^4 + 2*(9*a^2*c^2*d^3*e^2 - 2*a^3*c*d*e^4)*f^4*g^5 - (12*a^3*c*d^2*e^3 - a^4*e^5)*f^3*g^6)*x), -1/24*(3*(c^3*d^4*e*f^4 + (5*c^3*d^5 - 6*a*c^2*d^3*e^2)*f^3*g + (c^3*d^3*e^2*f*g^3 + (5*c^3*d^4*e - 6*a*c^2*d^2*e^3)*g^4)*x^4 + (3*c^3*d^3*e^2*f^2*g^2 + 2*(8*c^3*d^4*e - 9*a*c^2*d^2*e^3)*f*g^3 + (5*c^3*d^5 - 6*a*c^2*d^3*e^2)*g^4)*x^3 + 3*(c^3*d^3*e^2*f^3*g + 6*(c^3*d^4*e - a*c^2*d^2*e^3)*f^2*g^2 + (5*c^3*d^5 - 6*a*c^2*d^3*e^2)*f*g^3)*x^2 + (c^3*d^3*e^2*f^4 + 2*(4*c^3*d^4*e - 3*a*c^2*d^2*e^3)*f^3*g + 3*(5*c^3*d^5 - 6*a*c^2*d^3*e^2)*f^2*g^2)*x)*sqrt(c*d*f*g - a*e*g^2)*arctan(sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(c*d*f*g - a*e*g^2)*sqrt(e*x + d)/(c*d*e*g*x^2 + a*d*e*g + (c*d^2 + a*e^2)*g*x)) + (3*c^3*d^3*e*f^4*g + 8*a^3*d*e^3*g^5 - (33*c^3*d^4 - 13*a*c^2*d^2*e^2)*f^3*g^2 + (59*a*c^2*d^3*e - 20*a^2*c*d*e^3)*f^2*g^3 - 2*(17*a^2*c*d^2*e^2 - 2*a^3*e^4)*f*g^4 - 3*(c^3*d^3*e*f^2*g^3 + (5*c^3*d^4 - 7*a*c^2*d^2*e^2)*f*g^4 - (5*a*c^2*d^3*e - 6*a^2*c*d*e^3)*g^5)*x^2 - 2*(4*c^3*d^3*e*f^3*g^2 + (20*c^3*d^4 - 29*a*c^2*d^2*e^2)*f^2*g^3 - (25*a*c^2*d^3*e - 31*a^2*c*d*e^3)*f*g^4 + (5*a^2*c*d^2*e^2 - 6*a^3*e^4)*g^5)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c^4*d^5*f^7*g^2 - 4*a*c^3*d^4*e*f^6*g^3 + 6*a^2*c^2*d^3*e^2*f^5*g^4 - 4*a^3*c*d^2*e^3*f^4*g^5 + a^4*d*e^4*f^3*g^6 + (c^4*d^4*e*f^4*g^5 - 4*a*c^3*d^3*e^2*f^3*g^6 + 6*a^2*c^2*d^2*e^3*f^2*g^7 - 4*a^3*c*d*e^4*f*g^8 + a^4*e^5*g^9)*x^4 + (3*c^4*d^4*e*f^5*g^4 + a^4*d*e^4*g^9 + (c^4*d^5 - 12*a*c^3*d^3*e^2)*f^4*g^5 - 2*(2*a*c^3*d^4*e - 9*a^2*c^2*d^2*e^3)*f^3*g^6 + 6*(a^2*c^2*d^3*e^2 - 2*a^3*c*d*e^4)*f^2*g^7 - (4*a^3*c*d^2*e^3 - 3*a^4*e^5)*f*g^8)*x^3 + 3*(c^4*d^4*e*f^6*g^3 + a^4*d*e^4*f*g^8 + (c^4*d^5 - 4*a*c^3*d^3*e^2)*f^5*g^4 - 2*(2*a*c^3*d^4*e - 3*a^2*c^2*d^2*e^3)*f^4*g^5 + 2*(3*a^2*c^2*d^3*e^2 - 2*a^3*c*d*e^4)*f^3*g^6 - (4*a^3*c*d^2*e^3 - a^4*e^5)*f^2*g^7)*x^2 + (c^4*d^4*e*f^7*g^2 + 3*a^4*d*e^4*f^2*g^7 + (3*c^4*d^5 - 4*a*c^3*d^3*e^2)*f^6*g^3 - 6*(2*a*c^3*d^4*e - a^2*c^2*d^2*e^3)*f^5*g^4 + 2*(9*a^2*c^2*d^3*e^2 - 2*a^3*c*d*e^4)*f^4*g^5 - (12*a^3*c*d^2*e^3 - a^4*e^5)*f^3*g^6)*x)]","B",0
792,1,251,0,0.421117," ","integrate((c*x^2+b*x+a)^3/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""fricas"")","-\frac{{\left(40 \, c^{3} d^{5} x^{5} + 144 \, b c^{2} d^{5} x^{4} + 720 \, a^{2} b d^{5} + 384 \, b c^{2} d + 160 \, {\left(b^{3} + 6 \, a b c\right)} d^{3} + 10 \, {\left(5 \, c^{3} d^{3} + 18 \, {\left(b^{2} c + a c^{2}\right)} d^{5}\right)} x^{3} + 16 \, {\left(12 \, b c^{2} d^{3} + 5 \, {\left(b^{3} + 6 \, a b c\right)} d^{5}\right)} x^{2} + 15 \, {\left(24 \, {\left(a b^{2} + a^{2} c\right)} d^{5} + 5 \, c^{3} d + 18 \, {\left(b^{2} c + a c^{2}\right)} d^{3}\right)} x\right)} \sqrt{d x + 1} \sqrt{-d x + 1} + 30 \, {\left(16 \, a^{3} d^{6} + 24 \, {\left(a b^{2} + a^{2} c\right)} d^{4} + 5 \, c^{3} + 18 \, {\left(b^{2} c + a c^{2}\right)} d^{2}\right)} \arctan\left(\frac{\sqrt{d x + 1} \sqrt{-d x + 1} - 1}{d x}\right)}{240 \, d^{7}}"," ",0,"-1/240*((40*c^3*d^5*x^5 + 144*b*c^2*d^5*x^4 + 720*a^2*b*d^5 + 384*b*c^2*d + 160*(b^3 + 6*a*b*c)*d^3 + 10*(5*c^3*d^3 + 18*(b^2*c + a*c^2)*d^5)*x^3 + 16*(12*b*c^2*d^3 + 5*(b^3 + 6*a*b*c)*d^5)*x^2 + 15*(24*(a*b^2 + a^2*c)*d^5 + 5*c^3*d + 18*(b^2*c + a*c^2)*d^3)*x)*sqrt(d*x + 1)*sqrt(-d*x + 1) + 30*(16*a^3*d^6 + 24*(a*b^2 + a^2*c)*d^4 + 5*c^3 + 18*(b^2*c + a*c^2)*d^2)*arctan((sqrt(d*x + 1)*sqrt(-d*x + 1) - 1)/(d*x)))/d^7","A",0
793,1,134,0,0.423506," ","integrate((c*x^2+b*x+a)^2/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""fricas"")","-\frac{{\left(6 \, c^{2} d^{3} x^{3} + 16 \, b c d^{3} x^{2} + 48 \, a b d^{3} + 32 \, b c d + 3 \, {\left(4 \, {\left(b^{2} + 2 \, a c\right)} d^{3} + 3 \, c^{2} d\right)} x\right)} \sqrt{d x + 1} \sqrt{-d x + 1} + 6 \, {\left(8 \, a^{2} d^{4} + 4 \, {\left(b^{2} + 2 \, a c\right)} d^{2} + 3 \, c^{2}\right)} \arctan\left(\frac{\sqrt{d x + 1} \sqrt{-d x + 1} - 1}{d x}\right)}{24 \, d^{5}}"," ",0,"-1/24*((6*c^2*d^3*x^3 + 16*b*c*d^3*x^2 + 48*a*b*d^3 + 32*b*c*d + 3*(4*(b^2 + 2*a*c)*d^3 + 3*c^2*d)*x)*sqrt(d*x + 1)*sqrt(-d*x + 1) + 6*(8*a^2*d^4 + 4*(b^2 + 2*a*c)*d^2 + 3*c^2)*arctan((sqrt(d*x + 1)*sqrt(-d*x + 1) - 1)/(d*x)))/d^5","A",0
794,1,67,0,0.418539," ","integrate((c*x^2+b*x+a)/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""fricas"")","-\frac{{\left(c d x + 2 \, b d\right)} \sqrt{d x + 1} \sqrt{-d x + 1} + 2 \, {\left(2 \, a d^{2} + c\right)} \arctan\left(\frac{\sqrt{d x + 1} \sqrt{-d x + 1} - 1}{d x}\right)}{2 \, d^{3}}"," ",0,"-1/2*((c*d*x + 2*b*d)*sqrt(d*x + 1)*sqrt(-d*x + 1) + 2*(2*a*d^2 + c)*arctan((sqrt(d*x + 1)*sqrt(-d*x + 1) - 1)/(d*x)))/d^3","A",0
795,1,4313,0,0.614138," ","integrate(1/(c*x^2+b*x+a)/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{2} \sqrt{-\frac{{\left(b^{2} - 2 \, a c\right)} d^{2} - 2 \, c^{2} - {\left({\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d^{4} + b^{2} c^{2} - 4 \, a c^{3} - {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} d^{2}\right)} \sqrt{\frac{b^{2} d^{4}}{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d^{8} - 2 \, {\left(a^{2} b^{4} - 6 \, a^{3} b^{2} c + 8 \, a^{4} c^{2}\right)} d^{6} + b^{2} c^{4} - 4 \, a c^{5} + {\left(b^{6} - 8 \, a b^{4} c + 22 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{4} - 2 \, {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{2}}}}{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d^{4} + b^{2} c^{2} - 4 \, a c^{3} - {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} d^{2}}} \log\left(\frac{4 \, \sqrt{d x + 1} \sqrt{-d x + 1} a b c d^{2} - 2 \, b^{2} c d^{2} x - 4 \, a b c d^{2} + 2 \, {\left(b^{2} c^{3} - 4 \, a c^{4} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{4} - {\left(b^{4} c - 6 \, a b^{2} c^{2} + 8 \, a^{2} c^{3}\right)} d^{2}\right)} \sqrt{\frac{b^{2} d^{4}}{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d^{8} - 2 \, {\left(a^{2} b^{4} - 6 \, a^{3} b^{2} c + 8 \, a^{4} c^{2}\right)} d^{6} + b^{2} c^{4} - 4 \, a c^{5} + {\left(b^{6} - 8 \, a b^{4} c + 22 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{4} - 2 \, {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{2}}} x + \sqrt{2} {\left({\left({\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{6} - b^{3} c^{3} + 4 \, a b c^{4} - {\left(a b^{5} - 5 \, a^{2} b^{3} c + 4 \, a^{3} b c^{2}\right)} d^{4} + {\left(b^{5} c - 5 \, a b^{3} c^{2} + 4 \, a^{2} b c^{3}\right)} d^{2}\right)} \sqrt{\frac{b^{2} d^{4}}{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d^{8} - 2 \, {\left(a^{2} b^{4} - 6 \, a^{3} b^{2} c + 8 \, a^{4} c^{2}\right)} d^{6} + b^{2} c^{4} - 4 \, a c^{5} + {\left(b^{6} - 8 \, a b^{4} c + 22 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{4} - 2 \, {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{2}}} x + {\left({\left(a b^{3} - 4 \, a^{2} b c\right)} d^{4} + {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{2}\right)} x\right)} \sqrt{-\frac{{\left(b^{2} - 2 \, a c\right)} d^{2} - 2 \, c^{2} - {\left({\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d^{4} + b^{2} c^{2} - 4 \, a c^{3} - {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} d^{2}\right)} \sqrt{\frac{b^{2} d^{4}}{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d^{8} - 2 \, {\left(a^{2} b^{4} - 6 \, a^{3} b^{2} c + 8 \, a^{4} c^{2}\right)} d^{6} + b^{2} c^{4} - 4 \, a c^{5} + {\left(b^{6} - 8 \, a b^{4} c + 22 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{4} - 2 \, {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{2}}}}{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d^{4} + b^{2} c^{2} - 4 \, a c^{3} - {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} d^{2}}}}{x}\right) - \frac{1}{2} \, \sqrt{2} \sqrt{-\frac{{\left(b^{2} - 2 \, a c\right)} d^{2} - 2 \, c^{2} - {\left({\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d^{4} + b^{2} c^{2} - 4 \, a c^{3} - {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} d^{2}\right)} \sqrt{\frac{b^{2} d^{4}}{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d^{8} - 2 \, {\left(a^{2} b^{4} - 6 \, a^{3} b^{2} c + 8 \, a^{4} c^{2}\right)} d^{6} + b^{2} c^{4} - 4 \, a c^{5} + {\left(b^{6} - 8 \, a b^{4} c + 22 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{4} - 2 \, {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{2}}}}{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d^{4} + b^{2} c^{2} - 4 \, a c^{3} - {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} d^{2}}} \log\left(\frac{4 \, \sqrt{d x + 1} \sqrt{-d x + 1} a b c d^{2} - 2 \, b^{2} c d^{2} x - 4 \, a b c d^{2} + 2 \, {\left(b^{2} c^{3} - 4 \, a c^{4} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{4} - {\left(b^{4} c - 6 \, a b^{2} c^{2} + 8 \, a^{2} c^{3}\right)} d^{2}\right)} \sqrt{\frac{b^{2} d^{4}}{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d^{8} - 2 \, {\left(a^{2} b^{4} - 6 \, a^{3} b^{2} c + 8 \, a^{4} c^{2}\right)} d^{6} + b^{2} c^{4} - 4 \, a c^{5} + {\left(b^{6} - 8 \, a b^{4} c + 22 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{4} - 2 \, {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{2}}} x - \sqrt{2} {\left({\left({\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{6} - b^{3} c^{3} + 4 \, a b c^{4} - {\left(a b^{5} - 5 \, a^{2} b^{3} c + 4 \, a^{3} b c^{2}\right)} d^{4} + {\left(b^{5} c - 5 \, a b^{3} c^{2} + 4 \, a^{2} b c^{3}\right)} d^{2}\right)} \sqrt{\frac{b^{2} d^{4}}{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d^{8} - 2 \, {\left(a^{2} b^{4} - 6 \, a^{3} b^{2} c + 8 \, a^{4} c^{2}\right)} d^{6} + b^{2} c^{4} - 4 \, a c^{5} + {\left(b^{6} - 8 \, a b^{4} c + 22 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{4} - 2 \, {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{2}}} x + {\left({\left(a b^{3} - 4 \, a^{2} b c\right)} d^{4} + {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{2}\right)} x\right)} \sqrt{-\frac{{\left(b^{2} - 2 \, a c\right)} d^{2} - 2 \, c^{2} - {\left({\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d^{4} + b^{2} c^{2} - 4 \, a c^{3} - {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} d^{2}\right)} \sqrt{\frac{b^{2} d^{4}}{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d^{8} - 2 \, {\left(a^{2} b^{4} - 6 \, a^{3} b^{2} c + 8 \, a^{4} c^{2}\right)} d^{6} + b^{2} c^{4} - 4 \, a c^{5} + {\left(b^{6} - 8 \, a b^{4} c + 22 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{4} - 2 \, {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{2}}}}{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d^{4} + b^{2} c^{2} - 4 \, a c^{3} - {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} d^{2}}}}{x}\right) - \frac{1}{2} \, \sqrt{2} \sqrt{-\frac{{\left(b^{2} - 2 \, a c\right)} d^{2} - 2 \, c^{2} + {\left({\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d^{4} + b^{2} c^{2} - 4 \, a c^{3} - {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} d^{2}\right)} \sqrt{\frac{b^{2} d^{4}}{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d^{8} - 2 \, {\left(a^{2} b^{4} - 6 \, a^{3} b^{2} c + 8 \, a^{4} c^{2}\right)} d^{6} + b^{2} c^{4} - 4 \, a c^{5} + {\left(b^{6} - 8 \, a b^{4} c + 22 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{4} - 2 \, {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{2}}}}{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d^{4} + b^{2} c^{2} - 4 \, a c^{3} - {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} d^{2}}} \log\left(\frac{4 \, \sqrt{d x + 1} \sqrt{-d x + 1} a b c d^{2} - 2 \, b^{2} c d^{2} x - 4 \, a b c d^{2} - 2 \, {\left(b^{2} c^{3} - 4 \, a c^{4} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{4} - {\left(b^{4} c - 6 \, a b^{2} c^{2} + 8 \, a^{2} c^{3}\right)} d^{2}\right)} \sqrt{\frac{b^{2} d^{4}}{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d^{8} - 2 \, {\left(a^{2} b^{4} - 6 \, a^{3} b^{2} c + 8 \, a^{4} c^{2}\right)} d^{6} + b^{2} c^{4} - 4 \, a c^{5} + {\left(b^{6} - 8 \, a b^{4} c + 22 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{4} - 2 \, {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{2}}} x + \sqrt{2} {\left({\left({\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{6} - b^{3} c^{3} + 4 \, a b c^{4} - {\left(a b^{5} - 5 \, a^{2} b^{3} c + 4 \, a^{3} b c^{2}\right)} d^{4} + {\left(b^{5} c - 5 \, a b^{3} c^{2} + 4 \, a^{2} b c^{3}\right)} d^{2}\right)} \sqrt{\frac{b^{2} d^{4}}{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d^{8} - 2 \, {\left(a^{2} b^{4} - 6 \, a^{3} b^{2} c + 8 \, a^{4} c^{2}\right)} d^{6} + b^{2} c^{4} - 4 \, a c^{5} + {\left(b^{6} - 8 \, a b^{4} c + 22 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{4} - 2 \, {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{2}}} x - {\left({\left(a b^{3} - 4 \, a^{2} b c\right)} d^{4} + {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{2}\right)} x\right)} \sqrt{-\frac{{\left(b^{2} - 2 \, a c\right)} d^{2} - 2 \, c^{2} + {\left({\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d^{4} + b^{2} c^{2} - 4 \, a c^{3} - {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} d^{2}\right)} \sqrt{\frac{b^{2} d^{4}}{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d^{8} - 2 \, {\left(a^{2} b^{4} - 6 \, a^{3} b^{2} c + 8 \, a^{4} c^{2}\right)} d^{6} + b^{2} c^{4} - 4 \, a c^{5} + {\left(b^{6} - 8 \, a b^{4} c + 22 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{4} - 2 \, {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{2}}}}{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d^{4} + b^{2} c^{2} - 4 \, a c^{3} - {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} d^{2}}}}{x}\right) + \frac{1}{2} \, \sqrt{2} \sqrt{-\frac{{\left(b^{2} - 2 \, a c\right)} d^{2} - 2 \, c^{2} + {\left({\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d^{4} + b^{2} c^{2} - 4 \, a c^{3} - {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} d^{2}\right)} \sqrt{\frac{b^{2} d^{4}}{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d^{8} - 2 \, {\left(a^{2} b^{4} - 6 \, a^{3} b^{2} c + 8 \, a^{4} c^{2}\right)} d^{6} + b^{2} c^{4} - 4 \, a c^{5} + {\left(b^{6} - 8 \, a b^{4} c + 22 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{4} - 2 \, {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{2}}}}{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d^{4} + b^{2} c^{2} - 4 \, a c^{3} - {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} d^{2}}} \log\left(\frac{4 \, \sqrt{d x + 1} \sqrt{-d x + 1} a b c d^{2} - 2 \, b^{2} c d^{2} x - 4 \, a b c d^{2} - 2 \, {\left(b^{2} c^{3} - 4 \, a c^{4} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{4} - {\left(b^{4} c - 6 \, a b^{2} c^{2} + 8 \, a^{2} c^{3}\right)} d^{2}\right)} \sqrt{\frac{b^{2} d^{4}}{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d^{8} - 2 \, {\left(a^{2} b^{4} - 6 \, a^{3} b^{2} c + 8 \, a^{4} c^{2}\right)} d^{6} + b^{2} c^{4} - 4 \, a c^{5} + {\left(b^{6} - 8 \, a b^{4} c + 22 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{4} - 2 \, {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{2}}} x - \sqrt{2} {\left({\left({\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{6} - b^{3} c^{3} + 4 \, a b c^{4} - {\left(a b^{5} - 5 \, a^{2} b^{3} c + 4 \, a^{3} b c^{2}\right)} d^{4} + {\left(b^{5} c - 5 \, a b^{3} c^{2} + 4 \, a^{2} b c^{3}\right)} d^{2}\right)} \sqrt{\frac{b^{2} d^{4}}{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d^{8} - 2 \, {\left(a^{2} b^{4} - 6 \, a^{3} b^{2} c + 8 \, a^{4} c^{2}\right)} d^{6} + b^{2} c^{4} - 4 \, a c^{5} + {\left(b^{6} - 8 \, a b^{4} c + 22 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{4} - 2 \, {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{2}}} x - {\left({\left(a b^{3} - 4 \, a^{2} b c\right)} d^{4} + {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{2}\right)} x\right)} \sqrt{-\frac{{\left(b^{2} - 2 \, a c\right)} d^{2} - 2 \, c^{2} + {\left({\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d^{4} + b^{2} c^{2} - 4 \, a c^{3} - {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} d^{2}\right)} \sqrt{\frac{b^{2} d^{4}}{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d^{8} - 2 \, {\left(a^{2} b^{4} - 6 \, a^{3} b^{2} c + 8 \, a^{4} c^{2}\right)} d^{6} + b^{2} c^{4} - 4 \, a c^{5} + {\left(b^{6} - 8 \, a b^{4} c + 22 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{4} - 2 \, {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{2}}}}{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d^{4} + b^{2} c^{2} - 4 \, a c^{3} - {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} d^{2}}}}{x}\right)"," ",0,"1/2*sqrt(2)*sqrt(-((b^2 - 2*a*c)*d^2 - 2*c^2 - ((a^2*b^2 - 4*a^3*c)*d^4 + b^2*c^2 - 4*a*c^3 - (b^4 - 6*a*b^2*c + 8*a^2*c^2)*d^2)*sqrt(b^2*d^4/((a^4*b^2 - 4*a^5*c)*d^8 - 2*(a^2*b^4 - 6*a^3*b^2*c + 8*a^4*c^2)*d^6 + b^2*c^4 - 4*a*c^5 + (b^6 - 8*a*b^4*c + 22*a^2*b^2*c^2 - 24*a^3*c^3)*d^4 - 2*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^2)))/((a^2*b^2 - 4*a^3*c)*d^4 + b^2*c^2 - 4*a*c^3 - (b^4 - 6*a*b^2*c + 8*a^2*c^2)*d^2))*log((4*sqrt(d*x + 1)*sqrt(-d*x + 1)*a*b*c*d^2 - 2*b^2*c*d^2*x - 4*a*b*c*d^2 + 2*(b^2*c^3 - 4*a*c^4 + (a^2*b^2*c - 4*a^3*c^2)*d^4 - (b^4*c - 6*a*b^2*c^2 + 8*a^2*c^3)*d^2)*sqrt(b^2*d^4/((a^4*b^2 - 4*a^5*c)*d^8 - 2*(a^2*b^4 - 6*a^3*b^2*c + 8*a^4*c^2)*d^6 + b^2*c^4 - 4*a*c^5 + (b^6 - 8*a*b^4*c + 22*a^2*b^2*c^2 - 24*a^3*c^3)*d^4 - 2*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^2))*x + sqrt(2)*(((a^3*b^3 - 4*a^4*b*c)*d^6 - b^3*c^3 + 4*a*b*c^4 - (a*b^5 - 5*a^2*b^3*c + 4*a^3*b*c^2)*d^4 + (b^5*c - 5*a*b^3*c^2 + 4*a^2*b*c^3)*d^2)*sqrt(b^2*d^4/((a^4*b^2 - 4*a^5*c)*d^8 - 2*(a^2*b^4 - 6*a^3*b^2*c + 8*a^4*c^2)*d^6 + b^2*c^4 - 4*a*c^5 + (b^6 - 8*a*b^4*c + 22*a^2*b^2*c^2 - 24*a^3*c^3)*d^4 - 2*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^2))*x + ((a*b^3 - 4*a^2*b*c)*d^4 + (b^3*c - 4*a*b*c^2)*d^2)*x)*sqrt(-((b^2 - 2*a*c)*d^2 - 2*c^2 - ((a^2*b^2 - 4*a^3*c)*d^4 + b^2*c^2 - 4*a*c^3 - (b^4 - 6*a*b^2*c + 8*a^2*c^2)*d^2)*sqrt(b^2*d^4/((a^4*b^2 - 4*a^5*c)*d^8 - 2*(a^2*b^4 - 6*a^3*b^2*c + 8*a^4*c^2)*d^6 + b^2*c^4 - 4*a*c^5 + (b^6 - 8*a*b^4*c + 22*a^2*b^2*c^2 - 24*a^3*c^3)*d^4 - 2*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^2)))/((a^2*b^2 - 4*a^3*c)*d^4 + b^2*c^2 - 4*a*c^3 - (b^4 - 6*a*b^2*c + 8*a^2*c^2)*d^2)))/x) - 1/2*sqrt(2)*sqrt(-((b^2 - 2*a*c)*d^2 - 2*c^2 - ((a^2*b^2 - 4*a^3*c)*d^4 + b^2*c^2 - 4*a*c^3 - (b^4 - 6*a*b^2*c + 8*a^2*c^2)*d^2)*sqrt(b^2*d^4/((a^4*b^2 - 4*a^5*c)*d^8 - 2*(a^2*b^4 - 6*a^3*b^2*c + 8*a^4*c^2)*d^6 + b^2*c^4 - 4*a*c^5 + (b^6 - 8*a*b^4*c + 22*a^2*b^2*c^2 - 24*a^3*c^3)*d^4 - 2*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^2)))/((a^2*b^2 - 4*a^3*c)*d^4 + b^2*c^2 - 4*a*c^3 - (b^4 - 6*a*b^2*c + 8*a^2*c^2)*d^2))*log((4*sqrt(d*x + 1)*sqrt(-d*x + 1)*a*b*c*d^2 - 2*b^2*c*d^2*x - 4*a*b*c*d^2 + 2*(b^2*c^3 - 4*a*c^4 + (a^2*b^2*c - 4*a^3*c^2)*d^4 - (b^4*c - 6*a*b^2*c^2 + 8*a^2*c^3)*d^2)*sqrt(b^2*d^4/((a^4*b^2 - 4*a^5*c)*d^8 - 2*(a^2*b^4 - 6*a^3*b^2*c + 8*a^4*c^2)*d^6 + b^2*c^4 - 4*a*c^5 + (b^6 - 8*a*b^4*c + 22*a^2*b^2*c^2 - 24*a^3*c^3)*d^4 - 2*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^2))*x - sqrt(2)*(((a^3*b^3 - 4*a^4*b*c)*d^6 - b^3*c^3 + 4*a*b*c^4 - (a*b^5 - 5*a^2*b^3*c + 4*a^3*b*c^2)*d^4 + (b^5*c - 5*a*b^3*c^2 + 4*a^2*b*c^3)*d^2)*sqrt(b^2*d^4/((a^4*b^2 - 4*a^5*c)*d^8 - 2*(a^2*b^4 - 6*a^3*b^2*c + 8*a^4*c^2)*d^6 + b^2*c^4 - 4*a*c^5 + (b^6 - 8*a*b^4*c + 22*a^2*b^2*c^2 - 24*a^3*c^3)*d^4 - 2*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^2))*x + ((a*b^3 - 4*a^2*b*c)*d^4 + (b^3*c - 4*a*b*c^2)*d^2)*x)*sqrt(-((b^2 - 2*a*c)*d^2 - 2*c^2 - ((a^2*b^2 - 4*a^3*c)*d^4 + b^2*c^2 - 4*a*c^3 - (b^4 - 6*a*b^2*c + 8*a^2*c^2)*d^2)*sqrt(b^2*d^4/((a^4*b^2 - 4*a^5*c)*d^8 - 2*(a^2*b^4 - 6*a^3*b^2*c + 8*a^4*c^2)*d^6 + b^2*c^4 - 4*a*c^5 + (b^6 - 8*a*b^4*c + 22*a^2*b^2*c^2 - 24*a^3*c^3)*d^4 - 2*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^2)))/((a^2*b^2 - 4*a^3*c)*d^4 + b^2*c^2 - 4*a*c^3 - (b^4 - 6*a*b^2*c + 8*a^2*c^2)*d^2)))/x) - 1/2*sqrt(2)*sqrt(-((b^2 - 2*a*c)*d^2 - 2*c^2 + ((a^2*b^2 - 4*a^3*c)*d^4 + b^2*c^2 - 4*a*c^3 - (b^4 - 6*a*b^2*c + 8*a^2*c^2)*d^2)*sqrt(b^2*d^4/((a^4*b^2 - 4*a^5*c)*d^8 - 2*(a^2*b^4 - 6*a^3*b^2*c + 8*a^4*c^2)*d^6 + b^2*c^4 - 4*a*c^5 + (b^6 - 8*a*b^4*c + 22*a^2*b^2*c^2 - 24*a^3*c^3)*d^4 - 2*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^2)))/((a^2*b^2 - 4*a^3*c)*d^4 + b^2*c^2 - 4*a*c^3 - (b^4 - 6*a*b^2*c + 8*a^2*c^2)*d^2))*log((4*sqrt(d*x + 1)*sqrt(-d*x + 1)*a*b*c*d^2 - 2*b^2*c*d^2*x - 4*a*b*c*d^2 - 2*(b^2*c^3 - 4*a*c^4 + (a^2*b^2*c - 4*a^3*c^2)*d^4 - (b^4*c - 6*a*b^2*c^2 + 8*a^2*c^3)*d^2)*sqrt(b^2*d^4/((a^4*b^2 - 4*a^5*c)*d^8 - 2*(a^2*b^4 - 6*a^3*b^2*c + 8*a^4*c^2)*d^6 + b^2*c^4 - 4*a*c^5 + (b^6 - 8*a*b^4*c + 22*a^2*b^2*c^2 - 24*a^3*c^3)*d^4 - 2*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^2))*x + sqrt(2)*(((a^3*b^3 - 4*a^4*b*c)*d^6 - b^3*c^3 + 4*a*b*c^4 - (a*b^5 - 5*a^2*b^3*c + 4*a^3*b*c^2)*d^4 + (b^5*c - 5*a*b^3*c^2 + 4*a^2*b*c^3)*d^2)*sqrt(b^2*d^4/((a^4*b^2 - 4*a^5*c)*d^8 - 2*(a^2*b^4 - 6*a^3*b^2*c + 8*a^4*c^2)*d^6 + b^2*c^4 - 4*a*c^5 + (b^6 - 8*a*b^4*c + 22*a^2*b^2*c^2 - 24*a^3*c^3)*d^4 - 2*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^2))*x - ((a*b^3 - 4*a^2*b*c)*d^4 + (b^3*c - 4*a*b*c^2)*d^2)*x)*sqrt(-((b^2 - 2*a*c)*d^2 - 2*c^2 + ((a^2*b^2 - 4*a^3*c)*d^4 + b^2*c^2 - 4*a*c^3 - (b^4 - 6*a*b^2*c + 8*a^2*c^2)*d^2)*sqrt(b^2*d^4/((a^4*b^2 - 4*a^5*c)*d^8 - 2*(a^2*b^4 - 6*a^3*b^2*c + 8*a^4*c^2)*d^6 + b^2*c^4 - 4*a*c^5 + (b^6 - 8*a*b^4*c + 22*a^2*b^2*c^2 - 24*a^3*c^3)*d^4 - 2*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^2)))/((a^2*b^2 - 4*a^3*c)*d^4 + b^2*c^2 - 4*a*c^3 - (b^4 - 6*a*b^2*c + 8*a^2*c^2)*d^2)))/x) + 1/2*sqrt(2)*sqrt(-((b^2 - 2*a*c)*d^2 - 2*c^2 + ((a^2*b^2 - 4*a^3*c)*d^4 + b^2*c^2 - 4*a*c^3 - (b^4 - 6*a*b^2*c + 8*a^2*c^2)*d^2)*sqrt(b^2*d^4/((a^4*b^2 - 4*a^5*c)*d^8 - 2*(a^2*b^4 - 6*a^3*b^2*c + 8*a^4*c^2)*d^6 + b^2*c^4 - 4*a*c^5 + (b^6 - 8*a*b^4*c + 22*a^2*b^2*c^2 - 24*a^3*c^3)*d^4 - 2*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^2)))/((a^2*b^2 - 4*a^3*c)*d^4 + b^2*c^2 - 4*a*c^3 - (b^4 - 6*a*b^2*c + 8*a^2*c^2)*d^2))*log((4*sqrt(d*x + 1)*sqrt(-d*x + 1)*a*b*c*d^2 - 2*b^2*c*d^2*x - 4*a*b*c*d^2 - 2*(b^2*c^3 - 4*a*c^4 + (a^2*b^2*c - 4*a^3*c^2)*d^4 - (b^4*c - 6*a*b^2*c^2 + 8*a^2*c^3)*d^2)*sqrt(b^2*d^4/((a^4*b^2 - 4*a^5*c)*d^8 - 2*(a^2*b^4 - 6*a^3*b^2*c + 8*a^4*c^2)*d^6 + b^2*c^4 - 4*a*c^5 + (b^6 - 8*a*b^4*c + 22*a^2*b^2*c^2 - 24*a^3*c^3)*d^4 - 2*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^2))*x - sqrt(2)*(((a^3*b^3 - 4*a^4*b*c)*d^6 - b^3*c^3 + 4*a*b*c^4 - (a*b^5 - 5*a^2*b^3*c + 4*a^3*b*c^2)*d^4 + (b^5*c - 5*a*b^3*c^2 + 4*a^2*b*c^3)*d^2)*sqrt(b^2*d^4/((a^4*b^2 - 4*a^5*c)*d^8 - 2*(a^2*b^4 - 6*a^3*b^2*c + 8*a^4*c^2)*d^6 + b^2*c^4 - 4*a*c^5 + (b^6 - 8*a*b^4*c + 22*a^2*b^2*c^2 - 24*a^3*c^3)*d^4 - 2*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^2))*x - ((a*b^3 - 4*a^2*b*c)*d^4 + (b^3*c - 4*a*b*c^2)*d^2)*x)*sqrt(-((b^2 - 2*a*c)*d^2 - 2*c^2 + ((a^2*b^2 - 4*a^3*c)*d^4 + b^2*c^2 - 4*a*c^3 - (b^4 - 6*a*b^2*c + 8*a^2*c^2)*d^2)*sqrt(b^2*d^4/((a^4*b^2 - 4*a^5*c)*d^8 - 2*(a^2*b^4 - 6*a^3*b^2*c + 8*a^4*c^2)*d^6 + b^2*c^4 - 4*a*c^5 + (b^6 - 8*a*b^4*c + 22*a^2*b^2*c^2 - 24*a^3*c^3)*d^4 - 2*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^2)))/((a^2*b^2 - 4*a^3*c)*d^4 + b^2*c^2 - 4*a*c^3 - (b^4 - 6*a*b^2*c + 8*a^2*c^2)*d^2)))/x)","B",0
796,-1,0,0,0.000000," ","integrate(1/(c*x^2+b*x+a)^2/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
797,1,376,0,0.422272," ","integrate((c*x^2+b*x+a)^3/(-d*x+1)^(3/2)/(d*x+1)^(3/2),x, algorithm=""fricas"")","-\frac{24 \, a^{2} b d^{5} + 64 \, b c^{2} d + 16 \, {\left(b^{3} + 6 \, a b c\right)} d^{3} - 8 \, {\left(3 \, a^{2} b d^{7} + 8 \, b c^{2} d^{3} + 2 \, {\left(b^{3} + 6 \, a b c\right)} d^{5}\right)} x^{2} - {\left(2 \, c^{3} d^{5} x^{5} + 8 \, b c^{2} d^{5} x^{4} - 24 \, a^{2} b d^{5} - 64 \, b c^{2} d - 16 \, {\left(b^{3} + 6 \, a b c\right)} d^{3} + {\left(5 \, c^{3} d^{3} + 12 \, {\left(b^{2} c + a c^{2}\right)} d^{5}\right)} x^{3} + 8 \, {\left(4 \, b c^{2} d^{3} + {\left(b^{3} + 6 \, a b c\right)} d^{5}\right)} x^{2} - {\left(8 \, a^{3} d^{7} + 24 \, {\left(a b^{2} + a^{2} c\right)} d^{5} + 15 \, c^{3} d + 36 \, {\left(b^{2} c + a c^{2}\right)} d^{3}\right)} x\right)} \sqrt{d x + 1} \sqrt{-d x + 1} + 6 \, {\left(8 \, {\left(a b^{2} + a^{2} c\right)} d^{4} + 5 \, c^{3} + 12 \, {\left(b^{2} c + a c^{2}\right)} d^{2} - {\left(8 \, {\left(a b^{2} + a^{2} c\right)} d^{6} + 5 \, c^{3} d^{2} + 12 \, {\left(b^{2} c + a c^{2}\right)} d^{4}\right)} x^{2}\right)} \arctan\left(\frac{\sqrt{d x + 1} \sqrt{-d x + 1} - 1}{d x}\right)}{8 \, {\left(d^{9} x^{2} - d^{7}\right)}}"," ",0,"-1/8*(24*a^2*b*d^5 + 64*b*c^2*d + 16*(b^3 + 6*a*b*c)*d^3 - 8*(3*a^2*b*d^7 + 8*b*c^2*d^3 + 2*(b^3 + 6*a*b*c)*d^5)*x^2 - (2*c^3*d^5*x^5 + 8*b*c^2*d^5*x^4 - 24*a^2*b*d^5 - 64*b*c^2*d - 16*(b^3 + 6*a*b*c)*d^3 + (5*c^3*d^3 + 12*(b^2*c + a*c^2)*d^5)*x^3 + 8*(4*b*c^2*d^3 + (b^3 + 6*a*b*c)*d^5)*x^2 - (8*a^3*d^7 + 24*(a*b^2 + a^2*c)*d^5 + 15*c^3*d + 36*(b^2*c + a*c^2)*d^3)*x)*sqrt(d*x + 1)*sqrt(-d*x + 1) + 6*(8*(a*b^2 + a^2*c)*d^4 + 5*c^3 + 12*(b^2*c + a*c^2)*d^2 - (8*(a*b^2 + a^2*c)*d^6 + 5*c^3*d^2 + 12*(b^2*c + a*c^2)*d^4)*x^2)*arctan((sqrt(d*x + 1)*sqrt(-d*x + 1) - 1)/(d*x)))/(d^9*x^2 - d^7)","A",0
798,1,204,0,0.412224," ","integrate((c*x^2+b*x+a)^2/(-d*x+1)^(3/2)/(d*x+1)^(3/2),x, algorithm=""fricas"")","-\frac{4 \, a b d^{3} + 8 \, b c d - 4 \, {\left(a b d^{5} + 2 \, b c d^{3}\right)} x^{2} - {\left(c^{2} d^{3} x^{3} + 4 \, b c d^{3} x^{2} - 4 \, a b d^{3} - 8 \, b c d - {\left(2 \, a^{2} d^{5} + 2 \, {\left(b^{2} + 2 \, a c\right)} d^{3} + 3 \, c^{2} d\right)} x\right)} \sqrt{d x + 1} \sqrt{-d x + 1} + 2 \, {\left(2 \, {\left(b^{2} + 2 \, a c\right)} d^{2} - {\left(2 \, {\left(b^{2} + 2 \, a c\right)} d^{4} + 3 \, c^{2} d^{2}\right)} x^{2} + 3 \, c^{2}\right)} \arctan\left(\frac{\sqrt{d x + 1} \sqrt{-d x + 1} - 1}{d x}\right)}{2 \, {\left(d^{7} x^{2} - d^{5}\right)}}"," ",0,"-1/2*(4*a*b*d^3 + 8*b*c*d - 4*(a*b*d^5 + 2*b*c*d^3)*x^2 - (c^2*d^3*x^3 + 4*b*c*d^3*x^2 - 4*a*b*d^3 - 8*b*c*d - (2*a^2*d^5 + 2*(b^2 + 2*a*c)*d^3 + 3*c^2*d)*x)*sqrt(d*x + 1)*sqrt(-d*x + 1) + 2*(2*(b^2 + 2*a*c)*d^2 - (2*(b^2 + 2*a*c)*d^4 + 3*c^2*d^2)*x^2 + 3*c^2)*arctan((sqrt(d*x + 1)*sqrt(-d*x + 1) - 1)/(d*x)))/(d^7*x^2 - d^5)","A",0
799,1,101,0,0.422573," ","integrate((c*x^2+b*x+a)/(-d*x+1)^(3/2)/(d*x+1)^(3/2),x, algorithm=""fricas"")","\frac{b d^{3} x^{2} - {\left(b d + {\left(a d^{3} + c d\right)} x\right)} \sqrt{d x + 1} \sqrt{-d x + 1} - b d + 2 \, {\left(c d^{2} x^{2} - c\right)} \arctan\left(\frac{\sqrt{d x + 1} \sqrt{-d x + 1} - 1}{d x}\right)}{d^{5} x^{2} - d^{3}}"," ",0,"(b*d^3*x^2 - (b*d + (a*d^3 + c*d)*x)*sqrt(d*x + 1)*sqrt(-d*x + 1) - b*d + 2*(c*d^2*x^2 - c)*arctan((sqrt(d*x + 1)*sqrt(-d*x + 1) - 1)/(d*x)))/(d^5*x^2 - d^3)","B",0
800,-1,0,0,0.000000," ","integrate(1/(-d*x+1)^(3/2)/(d*x+1)^(3/2)/(c*x^2+b*x+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
801,-1,0,0,0.000000," ","integrate(1/(-d*x+1)^(3/2)/(d*x+1)^(3/2)/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
802,0,0,0,0.444782," ","integrate((-e*x+1)^m*(e*x+1)^m*(c*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{2} + a\right)}^{p} {\left(e x + 1\right)}^{m} {\left(-e x + 1\right)}^{m}, x\right)"," ",0,"integral((c*x^2 + a)^p*(e*x + 1)^m*(-e*x + 1)^m, x)","F",0
803,0,0,0,0.461822," ","integrate((-e*x+d)^m*(e*x+d)^m*(c*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{2} + a\right)}^{p} {\left(e x + d\right)}^{m} {\left(-e x + d\right)}^{m}, x\right)"," ",0,"integral((c*x^2 + a)^p*(e*x + d)^m*(-e*x + d)^m, x)","F",0
804,0,0,0,0.468413," ","integrate((e*x+d)^m*(-e*f*x+d*f)^m*(c*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(-e f x + d f\right)}^{m} {\left(c x^{2} + a\right)}^{p} {\left(e x + d\right)}^{m}, x\right)"," ",0,"integral((-e*f*x + d*f)^m*(c*x^2 + a)^p*(e*x + d)^m, x)","F",0
805,1,2032,0,0.481581," ","integrate((e*x+d)^3*(g*x+f)^n*(c*e*x^2+2*c*d*x+a),x, algorithm=""fricas"")","\frac{{\left(a d^{3} f g^{5} n^{5} - 120 \, c e^{4} f^{6} + 720 \, c d e^{3} f^{5} g + 720 \, a d^{3} f g^{5} - 180 \, {\left(9 \, c d^{2} e^{2} + a e^{3}\right)} f^{4} g^{2} + 240 \, {\left(7 \, c d^{3} e + 3 \, a d e^{2}\right)} f^{3} g^{3} - 360 \, {\left(2 \, c d^{4} + 3 \, a d^{2} e\right)} f^{2} g^{4} + {\left(c e^{4} g^{6} n^{5} + 15 \, c e^{4} g^{6} n^{4} + 85 \, c e^{4} g^{6} n^{3} + 225 \, c e^{4} g^{6} n^{2} + 274 \, c e^{4} g^{6} n + 120 \, c e^{4} g^{6}\right)} x^{6} + {\left(720 \, c d e^{3} g^{6} + {\left(c e^{4} f g^{5} + 5 \, c d e^{3} g^{6}\right)} n^{5} + 10 \, {\left(c e^{4} f g^{5} + 8 \, c d e^{3} g^{6}\right)} n^{4} + 5 \, {\left(7 \, c e^{4} f g^{5} + 95 \, c d e^{3} g^{6}\right)} n^{3} + 50 \, {\left(c e^{4} f g^{5} + 26 \, c d e^{3} g^{6}\right)} n^{2} + 12 \, {\left(2 \, c e^{4} f g^{5} + 135 \, c d e^{3} g^{6}\right)} n\right)} x^{5} + {\left(20 \, a d^{3} f g^{5} - {\left(2 \, c d^{4} + 3 \, a d^{2} e\right)} f^{2} g^{4}\right)} n^{4} + {\left(180 \, {\left(9 \, c d^{2} e^{2} + a e^{3}\right)} g^{6} + {\left(5 \, c d e^{3} f g^{5} + {\left(9 \, c d^{2} e^{2} + a e^{3}\right)} g^{6}\right)} n^{5} - {\left(5 \, c e^{4} f^{2} g^{4} - 60 \, c d e^{3} f g^{5} - 17 \, {\left(9 \, c d^{2} e^{2} + a e^{3}\right)} g^{6}\right)} n^{4} - {\left(30 \, c e^{4} f^{2} g^{4} - 235 \, c d e^{3} f g^{5} - 107 \, {\left(9 \, c d^{2} e^{2} + a e^{3}\right)} g^{6}\right)} n^{3} - {\left(55 \, c e^{4} f^{2} g^{4} - 360 \, c d e^{3} f g^{5} - 307 \, {\left(9 \, c d^{2} e^{2} + a e^{3}\right)} g^{6}\right)} n^{2} - 6 \, {\left(5 \, c e^{4} f^{2} g^{4} - 30 \, c d e^{3} f g^{5} - 66 \, {\left(9 \, c d^{2} e^{2} + a e^{3}\right)} g^{6}\right)} n\right)} x^{4} + {\left(155 \, a d^{3} f g^{5} + 2 \, {\left(7 \, c d^{3} e + 3 \, a d e^{2}\right)} f^{3} g^{3} - 18 \, {\left(2 \, c d^{4} + 3 \, a d^{2} e\right)} f^{2} g^{4}\right)} n^{3} + {\left(240 \, {\left(7 \, c d^{3} e + 3 \, a d e^{2}\right)} g^{6} + {\left({\left(9 \, c d^{2} e^{2} + a e^{3}\right)} f g^{5} + {\left(7 \, c d^{3} e + 3 \, a d e^{2}\right)} g^{6}\right)} n^{5} - 2 \, {\left(10 \, c d e^{3} f^{2} g^{4} - 7 \, {\left(9 \, c d^{2} e^{2} + a e^{3}\right)} f g^{5} - 9 \, {\left(7 \, c d^{3} e + 3 \, a d e^{2}\right)} g^{6}\right)} n^{4} + {\left(20 \, c e^{4} f^{3} g^{3} - 180 \, c d e^{3} f^{2} g^{4} + 65 \, {\left(9 \, c d^{2} e^{2} + a e^{3}\right)} f g^{5} + 121 \, {\left(7 \, c d^{3} e + 3 \, a d e^{2}\right)} g^{6}\right)} n^{3} + 4 \, {\left(15 \, c e^{4} f^{3} g^{3} - 100 \, c d e^{3} f^{2} g^{4} + 28 \, {\left(9 \, c d^{2} e^{2} + a e^{3}\right)} f g^{5} + 93 \, {\left(7 \, c d^{3} e + 3 \, a d e^{2}\right)} g^{6}\right)} n^{2} + 4 \, {\left(10 \, c e^{4} f^{3} g^{3} - 60 \, c d e^{3} f^{2} g^{4} + 15 \, {\left(9 \, c d^{2} e^{2} + a e^{3}\right)} f g^{5} + 127 \, {\left(7 \, c d^{3} e + 3 \, a d e^{2}\right)} g^{6}\right)} n\right)} x^{3} + {\left(580 \, a d^{3} f g^{5} - 6 \, {\left(9 \, c d^{2} e^{2} + a e^{3}\right)} f^{4} g^{2} + 30 \, {\left(7 \, c d^{3} e + 3 \, a d e^{2}\right)} f^{3} g^{3} - 119 \, {\left(2 \, c d^{4} + 3 \, a d^{2} e\right)} f^{2} g^{4}\right)} n^{2} + {\left(360 \, {\left(2 \, c d^{4} + 3 \, a d^{2} e\right)} g^{6} + {\left({\left(7 \, c d^{3} e + 3 \, a d e^{2}\right)} f g^{5} + {\left(2 \, c d^{4} + 3 \, a d^{2} e\right)} g^{6}\right)} n^{5} - {\left(3 \, {\left(9 \, c d^{2} e^{2} + a e^{3}\right)} f^{2} g^{4} - 16 \, {\left(7 \, c d^{3} e + 3 \, a d e^{2}\right)} f g^{5} - 19 \, {\left(2 \, c d^{4} + 3 \, a d^{2} e\right)} g^{6}\right)} n^{4} + {\left(60 \, c d e^{3} f^{3} g^{3} - 36 \, {\left(9 \, c d^{2} e^{2} + a e^{3}\right)} f^{2} g^{4} + 89 \, {\left(7 \, c d^{3} e + 3 \, a d e^{2}\right)} f g^{5} + 137 \, {\left(2 \, c d^{4} + 3 \, a d^{2} e\right)} g^{6}\right)} n^{3} - {\left(60 \, c e^{4} f^{4} g^{2} - 420 \, c d e^{3} f^{3} g^{3} + 123 \, {\left(9 \, c d^{2} e^{2} + a e^{3}\right)} f^{2} g^{4} - 194 \, {\left(7 \, c d^{3} e + 3 \, a d e^{2}\right)} f g^{5} - 461 \, {\left(2 \, c d^{4} + 3 \, a d^{2} e\right)} g^{6}\right)} n^{2} - 6 \, {\left(10 \, c e^{4} f^{4} g^{2} - 60 \, c d e^{3} f^{3} g^{3} + 15 \, {\left(9 \, c d^{2} e^{2} + a e^{3}\right)} f^{2} g^{4} - 20 \, {\left(7 \, c d^{3} e + 3 \, a d e^{2}\right)} f g^{5} - 117 \, {\left(2 \, c d^{4} + 3 \, a d^{2} e\right)} g^{6}\right)} n\right)} x^{2} + 2 \, {\left(60 \, c d e^{3} f^{5} g + 522 \, a d^{3} f g^{5} - 33 \, {\left(9 \, c d^{2} e^{2} + a e^{3}\right)} f^{4} g^{2} + 74 \, {\left(7 \, c d^{3} e + 3 \, a d e^{2}\right)} f^{3} g^{3} - 171 \, {\left(2 \, c d^{4} + 3 \, a d^{2} e\right)} f^{2} g^{4}\right)} n + {\left(720 \, a d^{3} g^{6} + {\left(a d^{3} g^{6} + {\left(2 \, c d^{4} + 3 \, a d^{2} e\right)} f g^{5}\right)} n^{5} + 2 \, {\left(10 \, a d^{3} g^{6} - {\left(7 \, c d^{3} e + 3 \, a d e^{2}\right)} f^{2} g^{4} + 9 \, {\left(2 \, c d^{4} + 3 \, a d^{2} e\right)} f g^{5}\right)} n^{4} + {\left(155 \, a d^{3} g^{6} + 6 \, {\left(9 \, c d^{2} e^{2} + a e^{3}\right)} f^{3} g^{3} - 30 \, {\left(7 \, c d^{3} e + 3 \, a d e^{2}\right)} f^{2} g^{4} + 119 \, {\left(2 \, c d^{4} + 3 \, a d^{2} e\right)} f g^{5}\right)} n^{3} - 2 \, {\left(60 \, c d e^{3} f^{4} g^{2} - 290 \, a d^{3} g^{6} - 33 \, {\left(9 \, c d^{2} e^{2} + a e^{3}\right)} f^{3} g^{3} + 74 \, {\left(7 \, c d^{3} e + 3 \, a d e^{2}\right)} f^{2} g^{4} - 171 \, {\left(2 \, c d^{4} + 3 \, a d^{2} e\right)} f g^{5}\right)} n^{2} + 12 \, {\left(10 \, c e^{4} f^{5} g - 60 \, c d e^{3} f^{4} g^{2} + 87 \, a d^{3} g^{6} + 15 \, {\left(9 \, c d^{2} e^{2} + a e^{3}\right)} f^{3} g^{3} - 20 \, {\left(7 \, c d^{3} e + 3 \, a d e^{2}\right)} f^{2} g^{4} + 30 \, {\left(2 \, c d^{4} + 3 \, a d^{2} e\right)} f g^{5}\right)} n\right)} x\right)} {\left(g x + f\right)}^{n}}{g^{6} n^{6} + 21 \, g^{6} n^{5} + 175 \, g^{6} n^{4} + 735 \, g^{6} n^{3} + 1624 \, g^{6} n^{2} + 1764 \, g^{6} n + 720 \, g^{6}}"," ",0,"(a*d^3*f*g^5*n^5 - 120*c*e^4*f^6 + 720*c*d*e^3*f^5*g + 720*a*d^3*f*g^5 - 180*(9*c*d^2*e^2 + a*e^3)*f^4*g^2 + 240*(7*c*d^3*e + 3*a*d*e^2)*f^3*g^3 - 360*(2*c*d^4 + 3*a*d^2*e)*f^2*g^4 + (c*e^4*g^6*n^5 + 15*c*e^4*g^6*n^4 + 85*c*e^4*g^6*n^3 + 225*c*e^4*g^6*n^2 + 274*c*e^4*g^6*n + 120*c*e^4*g^6)*x^6 + (720*c*d*e^3*g^6 + (c*e^4*f*g^5 + 5*c*d*e^3*g^6)*n^5 + 10*(c*e^4*f*g^5 + 8*c*d*e^3*g^6)*n^4 + 5*(7*c*e^4*f*g^5 + 95*c*d*e^3*g^6)*n^3 + 50*(c*e^4*f*g^5 + 26*c*d*e^3*g^6)*n^2 + 12*(2*c*e^4*f*g^5 + 135*c*d*e^3*g^6)*n)*x^5 + (20*a*d^3*f*g^5 - (2*c*d^4 + 3*a*d^2*e)*f^2*g^4)*n^4 + (180*(9*c*d^2*e^2 + a*e^3)*g^6 + (5*c*d*e^3*f*g^5 + (9*c*d^2*e^2 + a*e^3)*g^6)*n^5 - (5*c*e^4*f^2*g^4 - 60*c*d*e^3*f*g^5 - 17*(9*c*d^2*e^2 + a*e^3)*g^6)*n^4 - (30*c*e^4*f^2*g^4 - 235*c*d*e^3*f*g^5 - 107*(9*c*d^2*e^2 + a*e^3)*g^6)*n^3 - (55*c*e^4*f^2*g^4 - 360*c*d*e^3*f*g^5 - 307*(9*c*d^2*e^2 + a*e^3)*g^6)*n^2 - 6*(5*c*e^4*f^2*g^4 - 30*c*d*e^3*f*g^5 - 66*(9*c*d^2*e^2 + a*e^3)*g^6)*n)*x^4 + (155*a*d^3*f*g^5 + 2*(7*c*d^3*e + 3*a*d*e^2)*f^3*g^3 - 18*(2*c*d^4 + 3*a*d^2*e)*f^2*g^4)*n^3 + (240*(7*c*d^3*e + 3*a*d*e^2)*g^6 + ((9*c*d^2*e^2 + a*e^3)*f*g^5 + (7*c*d^3*e + 3*a*d*e^2)*g^6)*n^5 - 2*(10*c*d*e^3*f^2*g^4 - 7*(9*c*d^2*e^2 + a*e^3)*f*g^5 - 9*(7*c*d^3*e + 3*a*d*e^2)*g^6)*n^4 + (20*c*e^4*f^3*g^3 - 180*c*d*e^3*f^2*g^4 + 65*(9*c*d^2*e^2 + a*e^3)*f*g^5 + 121*(7*c*d^3*e + 3*a*d*e^2)*g^6)*n^3 + 4*(15*c*e^4*f^3*g^3 - 100*c*d*e^3*f^2*g^4 + 28*(9*c*d^2*e^2 + a*e^3)*f*g^5 + 93*(7*c*d^3*e + 3*a*d*e^2)*g^6)*n^2 + 4*(10*c*e^4*f^3*g^3 - 60*c*d*e^3*f^2*g^4 + 15*(9*c*d^2*e^2 + a*e^3)*f*g^5 + 127*(7*c*d^3*e + 3*a*d*e^2)*g^6)*n)*x^3 + (580*a*d^3*f*g^5 - 6*(9*c*d^2*e^2 + a*e^3)*f^4*g^2 + 30*(7*c*d^3*e + 3*a*d*e^2)*f^3*g^3 - 119*(2*c*d^4 + 3*a*d^2*e)*f^2*g^4)*n^2 + (360*(2*c*d^4 + 3*a*d^2*e)*g^6 + ((7*c*d^3*e + 3*a*d*e^2)*f*g^5 + (2*c*d^4 + 3*a*d^2*e)*g^6)*n^5 - (3*(9*c*d^2*e^2 + a*e^3)*f^2*g^4 - 16*(7*c*d^3*e + 3*a*d*e^2)*f*g^5 - 19*(2*c*d^4 + 3*a*d^2*e)*g^6)*n^4 + (60*c*d*e^3*f^3*g^3 - 36*(9*c*d^2*e^2 + a*e^3)*f^2*g^4 + 89*(7*c*d^3*e + 3*a*d*e^2)*f*g^5 + 137*(2*c*d^4 + 3*a*d^2*e)*g^6)*n^3 - (60*c*e^4*f^4*g^2 - 420*c*d*e^3*f^3*g^3 + 123*(9*c*d^2*e^2 + a*e^3)*f^2*g^4 - 194*(7*c*d^3*e + 3*a*d*e^2)*f*g^5 - 461*(2*c*d^4 + 3*a*d^2*e)*g^6)*n^2 - 6*(10*c*e^4*f^4*g^2 - 60*c*d*e^3*f^3*g^3 + 15*(9*c*d^2*e^2 + a*e^3)*f^2*g^4 - 20*(7*c*d^3*e + 3*a*d*e^2)*f*g^5 - 117*(2*c*d^4 + 3*a*d^2*e)*g^6)*n)*x^2 + 2*(60*c*d*e^3*f^5*g + 522*a*d^3*f*g^5 - 33*(9*c*d^2*e^2 + a*e^3)*f^4*g^2 + 74*(7*c*d^3*e + 3*a*d*e^2)*f^3*g^3 - 171*(2*c*d^4 + 3*a*d^2*e)*f^2*g^4)*n + (720*a*d^3*g^6 + (a*d^3*g^6 + (2*c*d^4 + 3*a*d^2*e)*f*g^5)*n^5 + 2*(10*a*d^3*g^6 - (7*c*d^3*e + 3*a*d*e^2)*f^2*g^4 + 9*(2*c*d^4 + 3*a*d^2*e)*f*g^5)*n^4 + (155*a*d^3*g^6 + 6*(9*c*d^2*e^2 + a*e^3)*f^3*g^3 - 30*(7*c*d^3*e + 3*a*d*e^2)*f^2*g^4 + 119*(2*c*d^4 + 3*a*d^2*e)*f*g^5)*n^3 - 2*(60*c*d*e^3*f^4*g^2 - 290*a*d^3*g^6 - 33*(9*c*d^2*e^2 + a*e^3)*f^3*g^3 + 74*(7*c*d^3*e + 3*a*d*e^2)*f^2*g^4 - 171*(2*c*d^4 + 3*a*d^2*e)*f*g^5)*n^2 + 12*(10*c*e^4*f^5*g - 60*c*d*e^3*f^4*g^2 + 87*a*d^3*g^6 + 15*(9*c*d^2*e^2 + a*e^3)*f^3*g^3 - 20*(7*c*d^3*e + 3*a*d*e^2)*f^2*g^4 + 30*(2*c*d^4 + 3*a*d^2*e)*f*g^5)*n)*x)*(g*x + f)^n/(g^6*n^6 + 21*g^6*n^5 + 175*g^6*n^4 + 735*g^6*n^3 + 1624*g^6*n^2 + 1764*g^6*n + 720*g^6)","B",0
806,1,1122,0,0.443062," ","integrate((e*x+d)^2*(g*x+f)^n*(c*e*x^2+2*c*d*x+a),x, algorithm=""fricas"")","\frac{{\left(a d^{2} f g^{4} n^{4} + 24 \, c e^{3} f^{5} - 120 \, c d e^{2} f^{4} g + 120 \, a d^{2} f g^{4} + 40 \, {\left(5 \, c d^{2} e + a e^{2}\right)} f^{3} g^{2} - 120 \, {\left(c d^{3} + a d e\right)} f^{2} g^{3} + {\left(c e^{3} g^{5} n^{4} + 10 \, c e^{3} g^{5} n^{3} + 35 \, c e^{3} g^{5} n^{2} + 50 \, c e^{3} g^{5} n + 24 \, c e^{3} g^{5}\right)} x^{5} + {\left(120 \, c d e^{2} g^{5} + {\left(c e^{3} f g^{4} + 4 \, c d e^{2} g^{5}\right)} n^{4} + 2 \, {\left(3 \, c e^{3} f g^{4} + 22 \, c d e^{2} g^{5}\right)} n^{3} + {\left(11 \, c e^{3} f g^{4} + 164 \, c d e^{2} g^{5}\right)} n^{2} + 2 \, {\left(3 \, c e^{3} f g^{4} + 122 \, c d e^{2} g^{5}\right)} n\right)} x^{4} + 2 \, {\left(7 \, a d^{2} f g^{4} - {\left(c d^{3} + a d e\right)} f^{2} g^{3}\right)} n^{3} + {\left(40 \, {\left(5 \, c d^{2} e + a e^{2}\right)} g^{5} + {\left(4 \, c d e^{2} f g^{4} + {\left(5 \, c d^{2} e + a e^{2}\right)} g^{5}\right)} n^{4} - 4 \, {\left(c e^{3} f^{2} g^{3} - 8 \, c d e^{2} f g^{4} - 3 \, {\left(5 \, c d^{2} e + a e^{2}\right)} g^{5}\right)} n^{3} - {\left(12 \, c e^{3} f^{2} g^{3} - 68 \, c d e^{2} f g^{4} - 49 \, {\left(5 \, c d^{2} e + a e^{2}\right)} g^{5}\right)} n^{2} - 2 \, {\left(4 \, c e^{3} f^{2} g^{3} - 20 \, c d e^{2} f g^{4} - 39 \, {\left(5 \, c d^{2} e + a e^{2}\right)} g^{5}\right)} n\right)} x^{3} + {\left(71 \, a d^{2} f g^{4} + 2 \, {\left(5 \, c d^{2} e + a e^{2}\right)} f^{3} g^{2} - 24 \, {\left(c d^{3} + a d e\right)} f^{2} g^{3}\right)} n^{2} + {\left(120 \, {\left(c d^{3} + a d e\right)} g^{5} + {\left({\left(5 \, c d^{2} e + a e^{2}\right)} f g^{4} + 2 \, {\left(c d^{3} + a d e\right)} g^{5}\right)} n^{4} - 2 \, {\left(6 \, c d e^{2} f^{2} g^{3} - 5 \, {\left(5 \, c d^{2} e + a e^{2}\right)} f g^{4} - 13 \, {\left(c d^{3} + a d e\right)} g^{5}\right)} n^{3} + {\left(12 \, c e^{3} f^{3} g^{2} - 72 \, c d e^{2} f^{2} g^{3} + 29 \, {\left(5 \, c d^{2} e + a e^{2}\right)} f g^{4} + 118 \, {\left(c d^{3} + a d e\right)} g^{5}\right)} n^{2} + 2 \, {\left(6 \, c e^{3} f^{3} g^{2} - 30 \, c d e^{2} f^{2} g^{3} + 10 \, {\left(5 \, c d^{2} e + a e^{2}\right)} f g^{4} + 107 \, {\left(c d^{3} + a d e\right)} g^{5}\right)} n\right)} x^{2} - 2 \, {\left(12 \, c d e^{2} f^{4} g - 77 \, a d^{2} f g^{4} - 9 \, {\left(5 \, c d^{2} e + a e^{2}\right)} f^{3} g^{2} + 47 \, {\left(c d^{3} + a d e\right)} f^{2} g^{3}\right)} n + {\left(120 \, a d^{2} g^{5} + {\left(a d^{2} g^{5} + 2 \, {\left(c d^{3} + a d e\right)} f g^{4}\right)} n^{4} + 2 \, {\left(7 \, a d^{2} g^{5} - {\left(5 \, c d^{2} e + a e^{2}\right)} f^{2} g^{3} + 12 \, {\left(c d^{3} + a d e\right)} f g^{4}\right)} n^{3} + {\left(24 \, c d e^{2} f^{3} g^{2} + 71 \, a d^{2} g^{5} - 18 \, {\left(5 \, c d^{2} e + a e^{2}\right)} f^{2} g^{3} + 94 \, {\left(c d^{3} + a d e\right)} f g^{4}\right)} n^{2} - 2 \, {\left(12 \, c e^{3} f^{4} g - 60 \, c d e^{2} f^{3} g^{2} - 77 \, a d^{2} g^{5} + 20 \, {\left(5 \, c d^{2} e + a e^{2}\right)} f^{2} g^{3} - 60 \, {\left(c d^{3} + a d e\right)} f g^{4}\right)} n\right)} x\right)} {\left(g x + f\right)}^{n}}{g^{5} n^{5} + 15 \, g^{5} n^{4} + 85 \, g^{5} n^{3} + 225 \, g^{5} n^{2} + 274 \, g^{5} n + 120 \, g^{5}}"," ",0,"(a*d^2*f*g^4*n^4 + 24*c*e^3*f^5 - 120*c*d*e^2*f^4*g + 120*a*d^2*f*g^4 + 40*(5*c*d^2*e + a*e^2)*f^3*g^2 - 120*(c*d^3 + a*d*e)*f^2*g^3 + (c*e^3*g^5*n^4 + 10*c*e^3*g^5*n^3 + 35*c*e^3*g^5*n^2 + 50*c*e^3*g^5*n + 24*c*e^3*g^5)*x^5 + (120*c*d*e^2*g^5 + (c*e^3*f*g^4 + 4*c*d*e^2*g^5)*n^4 + 2*(3*c*e^3*f*g^4 + 22*c*d*e^2*g^5)*n^3 + (11*c*e^3*f*g^4 + 164*c*d*e^2*g^5)*n^2 + 2*(3*c*e^3*f*g^4 + 122*c*d*e^2*g^5)*n)*x^4 + 2*(7*a*d^2*f*g^4 - (c*d^3 + a*d*e)*f^2*g^3)*n^3 + (40*(5*c*d^2*e + a*e^2)*g^5 + (4*c*d*e^2*f*g^4 + (5*c*d^2*e + a*e^2)*g^5)*n^4 - 4*(c*e^3*f^2*g^3 - 8*c*d*e^2*f*g^4 - 3*(5*c*d^2*e + a*e^2)*g^5)*n^3 - (12*c*e^3*f^2*g^3 - 68*c*d*e^2*f*g^4 - 49*(5*c*d^2*e + a*e^2)*g^5)*n^2 - 2*(4*c*e^3*f^2*g^3 - 20*c*d*e^2*f*g^4 - 39*(5*c*d^2*e + a*e^2)*g^5)*n)*x^3 + (71*a*d^2*f*g^4 + 2*(5*c*d^2*e + a*e^2)*f^3*g^2 - 24*(c*d^3 + a*d*e)*f^2*g^3)*n^2 + (120*(c*d^3 + a*d*e)*g^5 + ((5*c*d^2*e + a*e^2)*f*g^4 + 2*(c*d^3 + a*d*e)*g^5)*n^4 - 2*(6*c*d*e^2*f^2*g^3 - 5*(5*c*d^2*e + a*e^2)*f*g^4 - 13*(c*d^3 + a*d*e)*g^5)*n^3 + (12*c*e^3*f^3*g^2 - 72*c*d*e^2*f^2*g^3 + 29*(5*c*d^2*e + a*e^2)*f*g^4 + 118*(c*d^3 + a*d*e)*g^5)*n^2 + 2*(6*c*e^3*f^3*g^2 - 30*c*d*e^2*f^2*g^3 + 10*(5*c*d^2*e + a*e^2)*f*g^4 + 107*(c*d^3 + a*d*e)*g^5)*n)*x^2 - 2*(12*c*d*e^2*f^4*g - 77*a*d^2*f*g^4 - 9*(5*c*d^2*e + a*e^2)*f^3*g^2 + 47*(c*d^3 + a*d*e)*f^2*g^3)*n + (120*a*d^2*g^5 + (a*d^2*g^5 + 2*(c*d^3 + a*d*e)*f*g^4)*n^4 + 2*(7*a*d^2*g^5 - (5*c*d^2*e + a*e^2)*f^2*g^3 + 12*(c*d^3 + a*d*e)*f*g^4)*n^3 + (24*c*d*e^2*f^3*g^2 + 71*a*d^2*g^5 - 18*(5*c*d^2*e + a*e^2)*f^2*g^3 + 94*(c*d^3 + a*d*e)*f*g^4)*n^2 - 2*(12*c*e^3*f^4*g - 60*c*d*e^2*f^3*g^2 - 77*a*d^2*g^5 + 20*(5*c*d^2*e + a*e^2)*f^2*g^3 - 60*(c*d^3 + a*d*e)*f*g^4)*n)*x)*(g*x + f)^n/(g^5*n^5 + 15*g^5*n^4 + 85*g^5*n^3 + 225*g^5*n^2 + 274*g^5*n + 120*g^5)","B",0
807,1,549,0,0.429154," ","integrate((e*x+d)*(g*x+f)^n*(c*e*x^2+2*c*d*x+a),x, algorithm=""fricas"")","\frac{{\left(a d f g^{3} n^{3} - 6 \, c e^{2} f^{4} + 24 \, c d e f^{3} g + 24 \, a d f g^{3} - 12 \, {\left(2 \, c d^{2} + a e\right)} f^{2} g^{2} + {\left(c e^{2} g^{4} n^{3} + 6 \, c e^{2} g^{4} n^{2} + 11 \, c e^{2} g^{4} n + 6 \, c e^{2} g^{4}\right)} x^{4} + {\left(24 \, c d e g^{4} + {\left(c e^{2} f g^{3} + 3 \, c d e g^{4}\right)} n^{3} + 3 \, {\left(c e^{2} f g^{3} + 7 \, c d e g^{4}\right)} n^{2} + 2 \, {\left(c e^{2} f g^{3} + 21 \, c d e g^{4}\right)} n\right)} x^{3} + {\left(9 \, a d f g^{3} - {\left(2 \, c d^{2} + a e\right)} f^{2} g^{2}\right)} n^{2} + {\left(12 \, {\left(2 \, c d^{2} + a e\right)} g^{4} + {\left(3 \, c d e f g^{3} + {\left(2 \, c d^{2} + a e\right)} g^{4}\right)} n^{3} - {\left(3 \, c e^{2} f^{2} g^{2} - 15 \, c d e f g^{3} - 8 \, {\left(2 \, c d^{2} + a e\right)} g^{4}\right)} n^{2} - {\left(3 \, c e^{2} f^{2} g^{2} - 12 \, c d e f g^{3} - 19 \, {\left(2 \, c d^{2} + a e\right)} g^{4}\right)} n\right)} x^{2} + {\left(6 \, c d e f^{3} g + 26 \, a d f g^{3} - 7 \, {\left(2 \, c d^{2} + a e\right)} f^{2} g^{2}\right)} n + {\left(24 \, a d g^{4} + {\left(a d g^{4} + {\left(2 \, c d^{2} + a e\right)} f g^{3}\right)} n^{3} - {\left(6 \, c d e f^{2} g^{2} - 9 \, a d g^{4} - 7 \, {\left(2 \, c d^{2} + a e\right)} f g^{3}\right)} n^{2} + 2 \, {\left(3 \, c e^{2} f^{3} g - 12 \, c d e f^{2} g^{2} + 13 \, a d g^{4} + 6 \, {\left(2 \, c d^{2} + a e\right)} f g^{3}\right)} n\right)} x\right)} {\left(g x + f\right)}^{n}}{g^{4} n^{4} + 10 \, g^{4} n^{3} + 35 \, g^{4} n^{2} + 50 \, g^{4} n + 24 \, g^{4}}"," ",0,"(a*d*f*g^3*n^3 - 6*c*e^2*f^4 + 24*c*d*e*f^3*g + 24*a*d*f*g^3 - 12*(2*c*d^2 + a*e)*f^2*g^2 + (c*e^2*g^4*n^3 + 6*c*e^2*g^4*n^2 + 11*c*e^2*g^4*n + 6*c*e^2*g^4)*x^4 + (24*c*d*e*g^4 + (c*e^2*f*g^3 + 3*c*d*e*g^4)*n^3 + 3*(c*e^2*f*g^3 + 7*c*d*e*g^4)*n^2 + 2*(c*e^2*f*g^3 + 21*c*d*e*g^4)*n)*x^3 + (9*a*d*f*g^3 - (2*c*d^2 + a*e)*f^2*g^2)*n^2 + (12*(2*c*d^2 + a*e)*g^4 + (3*c*d*e*f*g^3 + (2*c*d^2 + a*e)*g^4)*n^3 - (3*c*e^2*f^2*g^2 - 15*c*d*e*f*g^3 - 8*(2*c*d^2 + a*e)*g^4)*n^2 - (3*c*e^2*f^2*g^2 - 12*c*d*e*f*g^3 - 19*(2*c*d^2 + a*e)*g^4)*n)*x^2 + (6*c*d*e*f^3*g + 26*a*d*f*g^3 - 7*(2*c*d^2 + a*e)*f^2*g^2)*n + (24*a*d*g^4 + (a*d*g^4 + (2*c*d^2 + a*e)*f*g^3)*n^3 - (6*c*d*e*f^2*g^2 - 9*a*d*g^4 - 7*(2*c*d^2 + a*e)*f*g^3)*n^2 + 2*(3*c*e^2*f^3*g - 12*c*d*e*f^2*g^2 + 13*a*d*g^4 + 6*(2*c*d^2 + a*e)*f*g^3)*n)*x)*(g*x + f)^n/(g^4*n^4 + 10*g^4*n^3 + 35*g^4*n^2 + 50*g^4*n + 24*g^4)","B",0
808,1,218,0,0.409158," ","integrate((g*x+f)^n*(c*e*x^2+2*c*d*x+a),x, algorithm=""fricas"")","\frac{{\left(a f g^{2} n^{2} + 2 \, c e f^{3} - 6 \, c d f^{2} g + 6 \, a f g^{2} + {\left(c e g^{3} n^{2} + 3 \, c e g^{3} n + 2 \, c e g^{3}\right)} x^{3} + {\left(6 \, c d g^{3} + {\left(c e f g^{2} + 2 \, c d g^{3}\right)} n^{2} + {\left(c e f g^{2} + 8 \, c d g^{3}\right)} n\right)} x^{2} - {\left(2 \, c d f^{2} g - 5 \, a f g^{2}\right)} n + {\left(6 \, a g^{3} + {\left(2 \, c d f g^{2} + a g^{3}\right)} n^{2} - {\left(2 \, c e f^{2} g - 6 \, c d f g^{2} - 5 \, a g^{3}\right)} n\right)} x\right)} {\left(g x + f\right)}^{n}}{g^{3} n^{3} + 6 \, g^{3} n^{2} + 11 \, g^{3} n + 6 \, g^{3}}"," ",0,"(a*f*g^2*n^2 + 2*c*e*f^3 - 6*c*d*f^2*g + 6*a*f*g^2 + (c*e*g^3*n^2 + 3*c*e*g^3*n + 2*c*e*g^3)*x^3 + (6*c*d*g^3 + (c*e*f*g^2 + 2*c*d*g^3)*n^2 + (c*e*f*g^2 + 8*c*d*g^3)*n)*x^2 - (2*c*d*f^2*g - 5*a*f*g^2)*n + (6*a*g^3 + (2*c*d*f*g^2 + a*g^3)*n^2 - (2*c*e*f^2*g - 6*c*d*f*g^2 - 5*a*g^3)*n)*x)*(g*x + f)^n/(g^3*n^3 + 6*g^3*n^2 + 11*g^3*n + 6*g^3)","B",0
809,0,0,0,0.436261," ","integrate((g*x+f)^n*(c*e*x^2+2*c*d*x+a)/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c e x^{2} + 2 \, c d x + a\right)} {\left(g x + f\right)}^{n}}{e x + d}, x\right)"," ",0,"integral((c*e*x^2 + 2*c*d*x + a)*(g*x + f)^n/(e*x + d), x)","F",0
810,0,0,0,0.433207," ","integrate((g*x+f)^n*(c*e*x^2+2*c*d*x+a)/(e*x+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c e x^{2} + 2 \, c d x + a\right)} {\left(g x + f\right)}^{n}}{e^{2} x^{2} + 2 \, d e x + d^{2}}, x\right)"," ",0,"integral((c*e*x^2 + 2*c*d*x + a)*(g*x + f)^n/(e^2*x^2 + 2*d*e*x + d^2), x)","F",0
811,0,0,0,0.427786," ","integrate((g*x+f)^n*(c*e*x^2+2*c*d*x+a)/(e*x+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c e x^{2} + 2 \, c d x + a\right)} {\left(g x + f\right)}^{n}}{e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}}, x\right)"," ",0,"integral((c*e*x^2 + 2*c*d*x + a)*(g*x + f)^n/(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3), x)","F",0
812,0,0,0,0.453530," ","integrate((g*x+f)^n*(c*e*x^2+2*c*d*x+a)/(e*x+d)^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c e x^{2} + 2 \, c d x + a\right)} {\left(g x + f\right)}^{n}}{e^{4} x^{4} + 4 \, d e^{3} x^{3} + 6 \, d^{2} e^{2} x^{2} + 4 \, d^{3} e x + d^{4}}, x\right)"," ",0,"integral((c*e*x^2 + 2*c*d*x + a)*(g*x + f)^n/(e^4*x^4 + 4*d*e^3*x^3 + 6*d^2*e^2*x^2 + 4*d^3*e*x + d^4), x)","F",0
813,0,0,0,0.443032," ","integrate((e*x+d)^m*(g*x+f)^n*(c*e*x^2+2*c*d*x+a),x, algorithm=""fricas"")","{\rm integral}\left({\left(c e x^{2} + 2 \, c d x + a\right)} {\left(e x + d\right)}^{m} {\left(g x + f\right)}^{n}, x\right)"," ",0,"integral((c*e*x^2 + 2*c*d*x + a)*(e*x + d)^m*(g*x + f)^n, x)","F",0
814,1,99,0,0.397626," ","integrate((c*x^2+b*x+a)/(e*x+d)/(g*x+f),x, algorithm=""fricas"")","\frac{{\left(c d^{2} - b d e + a e^{2}\right)} g^{2} \log\left(e x + d\right) + {\left(c e^{2} f g - c d e g^{2}\right)} x - {\left(c e^{2} f^{2} - b e^{2} f g + a e^{2} g^{2}\right)} \log\left(g x + f\right)}{e^{3} f g^{2} - d e^{2} g^{3}}"," ",0,"((c*d^2 - b*d*e + a*e^2)*g^2*log(e*x + d) + (c*e^2*f*g - c*d*e*g^2)*x - (c*e^2*f^2 - b*e^2*f*g + a*e^2*g^2)*log(g*x + f))/(e^3*f*g^2 - d*e^2*g^3)","A",0
815,1,313,0,0.712680," ","integrate((c*x^2+b*x+a)^2/(e*x+d)/(g*x+f),x, algorithm=""fricas"")","\frac{6 \, {\left(c^{2} d^{4} - 2 \, b c d^{3} e - 2 \, a b d e^{3} + a^{2} e^{4} + {\left(b^{2} + 2 \, a c\right)} d^{2} e^{2}\right)} g^{4} \log\left(e x + d\right) + 2 \, {\left(c^{2} e^{4} f g^{3} - c^{2} d e^{3} g^{4}\right)} x^{3} - 3 \, {\left(c^{2} e^{4} f^{2} g^{2} - 2 \, b c e^{4} f g^{3} - {\left(c^{2} d^{2} e^{2} - 2 \, b c d e^{3}\right)} g^{4}\right)} x^{2} + 6 \, {\left(c^{2} e^{4} f^{3} g - 2 \, b c e^{4} f^{2} g^{2} + {\left(b^{2} + 2 \, a c\right)} e^{4} f g^{3} - {\left(c^{2} d^{3} e - 2 \, b c d^{2} e^{2} + {\left(b^{2} + 2 \, a c\right)} d e^{3}\right)} g^{4}\right)} x - 6 \, {\left(c^{2} e^{4} f^{4} - 2 \, b c e^{4} f^{3} g - 2 \, a b e^{4} f g^{3} + a^{2} e^{4} g^{4} + {\left(b^{2} + 2 \, a c\right)} e^{4} f^{2} g^{2}\right)} \log\left(g x + f\right)}{6 \, {\left(e^{5} f g^{4} - d e^{4} g^{5}\right)}}"," ",0,"1/6*(6*(c^2*d^4 - 2*b*c*d^3*e - 2*a*b*d*e^3 + a^2*e^4 + (b^2 + 2*a*c)*d^2*e^2)*g^4*log(e*x + d) + 2*(c^2*e^4*f*g^3 - c^2*d*e^3*g^4)*x^3 - 3*(c^2*e^4*f^2*g^2 - 2*b*c*e^4*f*g^3 - (c^2*d^2*e^2 - 2*b*c*d*e^3)*g^4)*x^2 + 6*(c^2*e^4*f^3*g - 2*b*c*e^4*f^2*g^2 + (b^2 + 2*a*c)*e^4*f*g^3 - (c^2*d^3*e - 2*b*c*d^2*e^2 + (b^2 + 2*a*c)*d*e^3)*g^4)*x - 6*(c^2*e^4*f^4 - 2*b*c*e^4*f^3*g - 2*a*b*e^4*f*g^3 + a^2*e^4*g^4 + (b^2 + 2*a*c)*e^4*f^2*g^2)*log(g*x + f))/(e^5*f*g^4 - d*e^4*g^5)","A",0
816,1,736,0,3.897040," ","integrate((c*x^2+b*x+a)^3/(e*x+d)/(g*x+f),x, algorithm=""fricas"")","\frac{60 \, {\left(c^{3} d^{6} - 3 \, b c^{2} d^{5} e - 3 \, a^{2} b d e^{5} + a^{3} e^{6} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{2} - {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{4}\right)} g^{6} \log\left(e x + d\right) + 12 \, {\left(c^{3} e^{6} f g^{5} - c^{3} d e^{5} g^{6}\right)} x^{5} - 15 \, {\left(c^{3} e^{6} f^{2} g^{4} - 3 \, b c^{2} e^{6} f g^{5} - {\left(c^{3} d^{2} e^{4} - 3 \, b c^{2} d e^{5}\right)} g^{6}\right)} x^{4} + 20 \, {\left(c^{3} e^{6} f^{3} g^{3} - 3 \, b c^{2} e^{6} f^{2} g^{4} + 3 \, {\left(b^{2} c + a c^{2}\right)} e^{6} f g^{5} - {\left(c^{3} d^{3} e^{3} - 3 \, b c^{2} d^{2} e^{4} + 3 \, {\left(b^{2} c + a c^{2}\right)} d e^{5}\right)} g^{6}\right)} x^{3} - 30 \, {\left(c^{3} e^{6} f^{4} g^{2} - 3 \, b c^{2} e^{6} f^{3} g^{3} + 3 \, {\left(b^{2} c + a c^{2}\right)} e^{6} f^{2} g^{4} - {\left(b^{3} + 6 \, a b c\right)} e^{6} f g^{5} - {\left(c^{3} d^{4} e^{2} - 3 \, b c^{2} d^{3} e^{3} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{2} e^{4} - {\left(b^{3} + 6 \, a b c\right)} d e^{5}\right)} g^{6}\right)} x^{2} + 60 \, {\left(c^{3} e^{6} f^{5} g - 3 \, b c^{2} e^{6} f^{4} g^{2} + 3 \, {\left(b^{2} c + a c^{2}\right)} e^{6} f^{3} g^{3} - {\left(b^{3} + 6 \, a b c\right)} e^{6} f^{2} g^{4} + 3 \, {\left(a b^{2} + a^{2} c\right)} e^{6} f g^{5} - {\left(c^{3} d^{5} e - 3 \, b c^{2} d^{4} e^{2} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{3} e^{3} - {\left(b^{3} + 6 \, a b c\right)} d^{2} e^{4} + 3 \, {\left(a b^{2} + a^{2} c\right)} d e^{5}\right)} g^{6}\right)} x - 60 \, {\left(c^{3} e^{6} f^{6} - 3 \, b c^{2} e^{6} f^{5} g - 3 \, a^{2} b e^{6} f g^{5} + a^{3} e^{6} g^{6} + 3 \, {\left(b^{2} c + a c^{2}\right)} e^{6} f^{4} g^{2} - {\left(b^{3} + 6 \, a b c\right)} e^{6} f^{3} g^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} e^{6} f^{2} g^{4}\right)} \log\left(g x + f\right)}{60 \, {\left(e^{7} f g^{6} - d e^{6} g^{7}\right)}}"," ",0,"1/60*(60*(c^3*d^6 - 3*b*c^2*d^5*e - 3*a^2*b*d*e^5 + a^3*e^6 + 3*(b^2*c + a*c^2)*d^4*e^2 - (b^3 + 6*a*b*c)*d^3*e^3 + 3*(a*b^2 + a^2*c)*d^2*e^4)*g^6*log(e*x + d) + 12*(c^3*e^6*f*g^5 - c^3*d*e^5*g^6)*x^5 - 15*(c^3*e^6*f^2*g^4 - 3*b*c^2*e^6*f*g^5 - (c^3*d^2*e^4 - 3*b*c^2*d*e^5)*g^6)*x^4 + 20*(c^3*e^6*f^3*g^3 - 3*b*c^2*e^6*f^2*g^4 + 3*(b^2*c + a*c^2)*e^6*f*g^5 - (c^3*d^3*e^3 - 3*b*c^2*d^2*e^4 + 3*(b^2*c + a*c^2)*d*e^5)*g^6)*x^3 - 30*(c^3*e^6*f^4*g^2 - 3*b*c^2*e^6*f^3*g^3 + 3*(b^2*c + a*c^2)*e^6*f^2*g^4 - (b^3 + 6*a*b*c)*e^6*f*g^5 - (c^3*d^4*e^2 - 3*b*c^2*d^3*e^3 + 3*(b^2*c + a*c^2)*d^2*e^4 - (b^3 + 6*a*b*c)*d*e^5)*g^6)*x^2 + 60*(c^3*e^6*f^5*g - 3*b*c^2*e^6*f^4*g^2 + 3*(b^2*c + a*c^2)*e^6*f^3*g^3 - (b^3 + 6*a*b*c)*e^6*f^2*g^4 + 3*(a*b^2 + a^2*c)*e^6*f*g^5 - (c^3*d^5*e - 3*b*c^2*d^4*e^2 + 3*(b^2*c + a*c^2)*d^3*e^3 - (b^3 + 6*a*b*c)*d^2*e^4 + 3*(a*b^2 + a^2*c)*d*e^5)*g^6)*x - 60*(c^3*e^6*f^6 - 3*b*c^2*e^6*f^5*g - 3*a^2*b*e^6*f*g^5 + a^3*e^6*g^6 + 3*(b^2*c + a*c^2)*e^6*f^4*g^2 - (b^3 + 6*a*b*c)*e^6*f^3*g^3 + 3*(a*b^2 + a^2*c)*e^6*f^2*g^4)*log(g*x + f))/(e^7*f*g^6 - d*e^6*g^7)","A",0
817,-1,0,0,0.000000," ","integrate(1/(e*x+d)/(g*x+f)/(c*x^2+b*x+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
818,-1,0,0,0.000000," ","integrate(1/(e*x+d)/(g*x+f)/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
819,1,429,0,0.557722," ","integrate((e*x+d)^3*(c*x^2+b*x+a)/(g*x+f)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(315 \, c e^{3} g^{5} x^{5} - 1280 \, c e^{3} f^{5} + 3465 \, a d^{3} g^{5} + 1408 \, {\left(3 \, c d e^{2} + b e^{3}\right)} f^{4} g - 1584 \, {\left(3 \, c d^{2} e + 3 \, b d e^{2} + a e^{3}\right)} f^{3} g^{2} + 1848 \, {\left(c d^{3} + 3 \, b d^{2} e + 3 \, a d e^{2}\right)} f^{2} g^{3} - 2310 \, {\left(b d^{3} + 3 \, a d^{2} e\right)} f g^{4} - 35 \, {\left(10 \, c e^{3} f g^{4} - 11 \, {\left(3 \, c d e^{2} + b e^{3}\right)} g^{5}\right)} x^{4} + 5 \, {\left(80 \, c e^{3} f^{2} g^{3} - 88 \, {\left(3 \, c d e^{2} + b e^{3}\right)} f g^{4} + 99 \, {\left(3 \, c d^{2} e + 3 \, b d e^{2} + a e^{3}\right)} g^{5}\right)} x^{3} - 3 \, {\left(160 \, c e^{3} f^{3} g^{2} - 176 \, {\left(3 \, c d e^{2} + b e^{3}\right)} f^{2} g^{3} + 198 \, {\left(3 \, c d^{2} e + 3 \, b d e^{2} + a e^{3}\right)} f g^{4} - 231 \, {\left(c d^{3} + 3 \, b d^{2} e + 3 \, a d e^{2}\right)} g^{5}\right)} x^{2} + {\left(640 \, c e^{3} f^{4} g - 704 \, {\left(3 \, c d e^{2} + b e^{3}\right)} f^{3} g^{2} + 792 \, {\left(3 \, c d^{2} e + 3 \, b d e^{2} + a e^{3}\right)} f^{2} g^{3} - 924 \, {\left(c d^{3} + 3 \, b d^{2} e + 3 \, a d e^{2}\right)} f g^{4} + 1155 \, {\left(b d^{3} + 3 \, a d^{2} e\right)} g^{5}\right)} x\right)} \sqrt{g x + f}}{3465 \, g^{6}}"," ",0,"2/3465*(315*c*e^3*g^5*x^5 - 1280*c*e^3*f^5 + 3465*a*d^3*g^5 + 1408*(3*c*d*e^2 + b*e^3)*f^4*g - 1584*(3*c*d^2*e + 3*b*d*e^2 + a*e^3)*f^3*g^2 + 1848*(c*d^3 + 3*b*d^2*e + 3*a*d*e^2)*f^2*g^3 - 2310*(b*d^3 + 3*a*d^2*e)*f*g^4 - 35*(10*c*e^3*f*g^4 - 11*(3*c*d*e^2 + b*e^3)*g^5)*x^4 + 5*(80*c*e^3*f^2*g^3 - 88*(3*c*d*e^2 + b*e^3)*f*g^4 + 99*(3*c*d^2*e + 3*b*d*e^2 + a*e^3)*g^5)*x^3 - 3*(160*c*e^3*f^3*g^2 - 176*(3*c*d*e^2 + b*e^3)*f^2*g^3 + 198*(3*c*d^2*e + 3*b*d*e^2 + a*e^3)*f*g^4 - 231*(c*d^3 + 3*b*d^2*e + 3*a*d*e^2)*g^5)*x^2 + (640*c*e^3*f^4*g - 704*(3*c*d*e^2 + b*e^3)*f^3*g^2 + 792*(3*c*d^2*e + 3*b*d*e^2 + a*e^3)*f^2*g^3 - 924*(c*d^3 + 3*b*d^2*e + 3*a*d*e^2)*f*g^4 + 1155*(b*d^3 + 3*a*d^2*e)*g^5)*x)*sqrt(g*x + f)/g^6","A",0
820,1,260,0,0.540308," ","integrate((e*x+d)^2*(c*x^2+b*x+a)/(g*x+f)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, c e^{2} g^{4} x^{4} + 128 \, c e^{2} f^{4} + 315 \, a d^{2} g^{4} - 144 \, {\left(2 \, c d e + b e^{2}\right)} f^{3} g + 168 \, {\left(c d^{2} + 2 \, b d e + a e^{2}\right)} f^{2} g^{2} - 210 \, {\left(b d^{2} + 2 \, a d e\right)} f g^{3} - 5 \, {\left(8 \, c e^{2} f g^{3} - 9 \, {\left(2 \, c d e + b e^{2}\right)} g^{4}\right)} x^{3} + 3 \, {\left(16 \, c e^{2} f^{2} g^{2} - 18 \, {\left(2 \, c d e + b e^{2}\right)} f g^{3} + 21 \, {\left(c d^{2} + 2 \, b d e + a e^{2}\right)} g^{4}\right)} x^{2} - {\left(64 \, c e^{2} f^{3} g - 72 \, {\left(2 \, c d e + b e^{2}\right)} f^{2} g^{2} + 84 \, {\left(c d^{2} + 2 \, b d e + a e^{2}\right)} f g^{3} - 105 \, {\left(b d^{2} + 2 \, a d e\right)} g^{4}\right)} x\right)} \sqrt{g x + f}}{315 \, g^{5}}"," ",0,"2/315*(35*c*e^2*g^4*x^4 + 128*c*e^2*f^4 + 315*a*d^2*g^4 - 144*(2*c*d*e + b*e^2)*f^3*g + 168*(c*d^2 + 2*b*d*e + a*e^2)*f^2*g^2 - 210*(b*d^2 + 2*a*d*e)*f*g^3 - 5*(8*c*e^2*f*g^3 - 9*(2*c*d*e + b*e^2)*g^4)*x^3 + 3*(16*c*e^2*f^2*g^2 - 18*(2*c*d*e + b*e^2)*f*g^3 + 21*(c*d^2 + 2*b*d*e + a*e^2)*g^4)*x^2 - (64*c*e^2*f^3*g - 72*(2*c*d*e + b*e^2)*f^2*g^2 + 84*(c*d^2 + 2*b*d*e + a*e^2)*f*g^3 - 105*(b*d^2 + 2*a*d*e)*g^4)*x)*sqrt(g*x + f)/g^5","A",0
821,1,125,0,0.560794," ","integrate((e*x+d)*(c*x^2+b*x+a)/(g*x+f)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, c e g^{3} x^{3} - 48 \, c e f^{3} + 105 \, a d g^{3} + 56 \, {\left(c d + b e\right)} f^{2} g - 70 \, {\left(b d + a e\right)} f g^{2} - 3 \, {\left(6 \, c e f g^{2} - 7 \, {\left(c d + b e\right)} g^{3}\right)} x^{2} + {\left(24 \, c e f^{2} g - 28 \, {\left(c d + b e\right)} f g^{2} + 35 \, {\left(b d + a e\right)} g^{3}\right)} x\right)} \sqrt{g x + f}}{105 \, g^{4}}"," ",0,"2/105*(15*c*e*g^3*x^3 - 48*c*e*f^3 + 105*a*d*g^3 + 56*(c*d + b*e)*f^2*g - 70*(b*d + a*e)*f*g^2 - 3*(6*c*e*f*g^2 - 7*(c*d + b*e)*g^3)*x^2 + (24*c*e*f^2*g - 28*(c*d + b*e)*f*g^2 + 35*(b*d + a*e)*g^3)*x)*sqrt(g*x + f)/g^4","A",0
822,1,54,0,0.720521," ","integrate((c*x^2+b*x+a)/(g*x+f)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, c g^{2} x^{2} + 8 \, c f^{2} - 10 \, b f g + 15 \, a g^{2} - {\left(4 \, c f g - 5 \, b g^{2}\right)} x\right)} \sqrt{g x + f}}{15 \, g^{3}}"," ",0,"2/15*(3*c*g^2*x^2 + 8*c*f^2 - 10*b*f*g + 15*a*g^2 - (4*c*f*g - 5*b*g^2)*x)*sqrt(g*x + f)/g^3","A",0
823,1,341,0,0.565989," ","integrate((c*x^2+b*x+a)/(e*x+d)/(g*x+f)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{e^{2} f - d e g} g^{2} \log\left(\frac{e g x + 2 \, e f - d g - 2 \, \sqrt{e^{2} f - d e g} \sqrt{g x + f}}{e x + d}\right) - 2 \, {\left(2 \, c e^{3} f^{2} + {\left(c d e^{2} - 3 \, b e^{3}\right)} f g - 3 \, {\left(c d^{2} e - b d e^{2}\right)} g^{2} - {\left(c e^{3} f g - c d e^{2} g^{2}\right)} x\right)} \sqrt{g x + f}}{3 \, {\left(e^{4} f g^{2} - d e^{3} g^{3}\right)}}, \frac{2 \, {\left(3 \, {\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{-e^{2} f + d e g} g^{2} \arctan\left(\frac{\sqrt{-e^{2} f + d e g} \sqrt{g x + f}}{e g x + e f}\right) - {\left(2 \, c e^{3} f^{2} + {\left(c d e^{2} - 3 \, b e^{3}\right)} f g - 3 \, {\left(c d^{2} e - b d e^{2}\right)} g^{2} - {\left(c e^{3} f g - c d e^{2} g^{2}\right)} x\right)} \sqrt{g x + f}\right)}}{3 \, {\left(e^{4} f g^{2} - d e^{3} g^{3}\right)}}\right]"," ",0,"[1/3*(3*(c*d^2 - b*d*e + a*e^2)*sqrt(e^2*f - d*e*g)*g^2*log((e*g*x + 2*e*f - d*g - 2*sqrt(e^2*f - d*e*g)*sqrt(g*x + f))/(e*x + d)) - 2*(2*c*e^3*f^2 + (c*d*e^2 - 3*b*e^3)*f*g - 3*(c*d^2*e - b*d*e^2)*g^2 - (c*e^3*f*g - c*d*e^2*g^2)*x)*sqrt(g*x + f))/(e^4*f*g^2 - d*e^3*g^3), 2/3*(3*(c*d^2 - b*d*e + a*e^2)*sqrt(-e^2*f + d*e*g)*g^2*arctan(sqrt(-e^2*f + d*e*g)*sqrt(g*x + f)/(e*g*x + e*f)) - (2*c*e^3*f^2 + (c*d*e^2 - 3*b*e^3)*f*g - 3*(c*d^2*e - b*d*e^2)*g^2 - (c*e^3*f*g - c*d*e^2*g^2)*x)*sqrt(g*x + f))/(e^4*f*g^2 - d*e^3*g^3)]","A",0
824,1,637,0,0.651456," ","integrate((c*x^2+b*x+a)/(e*x+d)^2/(g*x+f)^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{e^{2} f - d e g} {\left(2 \, {\left(2 \, c d^{2} e - b d e^{2}\right)} f g - {\left(3 \, c d^{3} - b d^{2} e - a d e^{2}\right)} g^{2} + {\left(2 \, {\left(2 \, c d e^{2} - b e^{3}\right)} f g - {\left(3 \, c d^{2} e - b d e^{2} - a e^{3}\right)} g^{2}\right)} x\right)} \log\left(\frac{e g x + 2 \, e f - d g - 2 \, \sqrt{e^{2} f - d e g} \sqrt{g x + f}}{e x + d}\right) - 2 \, {\left(2 \, c d e^{3} f^{2} - {\left(5 \, c d^{2} e^{2} - b d e^{3} + a e^{4}\right)} f g + {\left(3 \, c d^{3} e - b d^{2} e^{2} + a d e^{3}\right)} g^{2} + 2 \, {\left(c e^{4} f^{2} - 2 \, c d e^{3} f g + c d^{2} e^{2} g^{2}\right)} x\right)} \sqrt{g x + f}}{2 \, {\left(d e^{5} f^{2} g - 2 \, d^{2} e^{4} f g^{2} + d^{3} e^{3} g^{3} + {\left(e^{6} f^{2} g - 2 \, d e^{5} f g^{2} + d^{2} e^{4} g^{3}\right)} x\right)}}, -\frac{\sqrt{-e^{2} f + d e g} {\left(2 \, {\left(2 \, c d^{2} e - b d e^{2}\right)} f g - {\left(3 \, c d^{3} - b d^{2} e - a d e^{2}\right)} g^{2} + {\left(2 \, {\left(2 \, c d e^{2} - b e^{3}\right)} f g - {\left(3 \, c d^{2} e - b d e^{2} - a e^{3}\right)} g^{2}\right)} x\right)} \arctan\left(\frac{\sqrt{-e^{2} f + d e g} \sqrt{g x + f}}{e g x + e f}\right) - {\left(2 \, c d e^{3} f^{2} - {\left(5 \, c d^{2} e^{2} - b d e^{3} + a e^{4}\right)} f g + {\left(3 \, c d^{3} e - b d^{2} e^{2} + a d e^{3}\right)} g^{2} + 2 \, {\left(c e^{4} f^{2} - 2 \, c d e^{3} f g + c d^{2} e^{2} g^{2}\right)} x\right)} \sqrt{g x + f}}{d e^{5} f^{2} g - 2 \, d^{2} e^{4} f g^{2} + d^{3} e^{3} g^{3} + {\left(e^{6} f^{2} g - 2 \, d e^{5} f g^{2} + d^{2} e^{4} g^{3}\right)} x}\right]"," ",0,"[-1/2*(sqrt(e^2*f - d*e*g)*(2*(2*c*d^2*e - b*d*e^2)*f*g - (3*c*d^3 - b*d^2*e - a*d*e^2)*g^2 + (2*(2*c*d*e^2 - b*e^3)*f*g - (3*c*d^2*e - b*d*e^2 - a*e^3)*g^2)*x)*log((e*g*x + 2*e*f - d*g - 2*sqrt(e^2*f - d*e*g)*sqrt(g*x + f))/(e*x + d)) - 2*(2*c*d*e^3*f^2 - (5*c*d^2*e^2 - b*d*e^3 + a*e^4)*f*g + (3*c*d^3*e - b*d^2*e^2 + a*d*e^3)*g^2 + 2*(c*e^4*f^2 - 2*c*d*e^3*f*g + c*d^2*e^2*g^2)*x)*sqrt(g*x + f))/(d*e^5*f^2*g - 2*d^2*e^4*f*g^2 + d^3*e^3*g^3 + (e^6*f^2*g - 2*d*e^5*f*g^2 + d^2*e^4*g^3)*x), -(sqrt(-e^2*f + d*e*g)*(2*(2*c*d^2*e - b*d*e^2)*f*g - (3*c*d^3 - b*d^2*e - a*d*e^2)*g^2 + (2*(2*c*d*e^2 - b*e^3)*f*g - (3*c*d^2*e - b*d*e^2 - a*e^3)*g^2)*x)*arctan(sqrt(-e^2*f + d*e*g)*sqrt(g*x + f)/(e*g*x + e*f)) - (2*c*d*e^3*f^2 - (5*c*d^2*e^2 - b*d*e^3 + a*e^4)*f*g + (3*c*d^3*e - b*d^2*e^2 + a*d*e^3)*g^2 + 2*(c*e^4*f^2 - 2*c*d*e^3*f*g + c*d^2*e^2*g^2)*x)*sqrt(g*x + f))/(d*e^5*f^2*g - 2*d^2*e^4*f*g^2 + d^3*e^3*g^3 + (e^6*f^2*g - 2*d*e^5*f*g^2 + d^2*e^4*g^3)*x)]","B",0
825,1,1096,0,0.661446," ","integrate((c*x^2+b*x+a)/(e*x+d)^3/(g*x+f)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(8 \, c d^{2} e^{2} f^{2} - 4 \, {\left(2 \, c d^{3} e + b d^{2} e^{2}\right)} f g + {\left(3 \, c d^{4} + b d^{3} e + 3 \, a d^{2} e^{2}\right)} g^{2} + {\left(8 \, c e^{4} f^{2} - 4 \, {\left(2 \, c d e^{3} + b e^{4}\right)} f g + {\left(3 \, c d^{2} e^{2} + b d e^{3} + 3 \, a e^{4}\right)} g^{2}\right)} x^{2} + 2 \, {\left(8 \, c d e^{3} f^{2} - 4 \, {\left(2 \, c d^{2} e^{2} + b d e^{3}\right)} f g + {\left(3 \, c d^{3} e + b d^{2} e^{2} + 3 \, a d e^{3}\right)} g^{2}\right)} x\right)} \sqrt{e^{2} f - d e g} \log\left(\frac{e g x + 2 \, e f - d g - 2 \, \sqrt{e^{2} f - d e g} \sqrt{g x + f}}{e x + d}\right) + 2 \, {\left(2 \, {\left(3 \, c d^{2} e^{3} - b d e^{4} - a e^{5}\right)} f^{2} - {\left(9 \, c d^{3} e^{2} - b d^{2} e^{3} - 7 \, a d e^{4}\right)} f g + {\left(3 \, c d^{4} e + b d^{3} e^{2} - 5 \, a d^{2} e^{3}\right)} g^{2} + {\left(4 \, {\left(2 \, c d e^{4} - b e^{5}\right)} f^{2} - {\left(13 \, c d^{2} e^{3} - 5 \, b d e^{4} - 3 \, a e^{5}\right)} f g + {\left(5 \, c d^{3} e^{2} - b d^{2} e^{3} - 3 \, a d e^{4}\right)} g^{2}\right)} x\right)} \sqrt{g x + f}}{8 \, {\left(d^{2} e^{6} f^{3} - 3 \, d^{3} e^{5} f^{2} g + 3 \, d^{4} e^{4} f g^{2} - d^{5} e^{3} g^{3} + {\left(e^{8} f^{3} - 3 \, d e^{7} f^{2} g + 3 \, d^{2} e^{6} f g^{2} - d^{3} e^{5} g^{3}\right)} x^{2} + 2 \, {\left(d e^{7} f^{3} - 3 \, d^{2} e^{6} f^{2} g + 3 \, d^{3} e^{5} f g^{2} - d^{4} e^{4} g^{3}\right)} x\right)}}, \frac{{\left(8 \, c d^{2} e^{2} f^{2} - 4 \, {\left(2 \, c d^{3} e + b d^{2} e^{2}\right)} f g + {\left(3 \, c d^{4} + b d^{3} e + 3 \, a d^{2} e^{2}\right)} g^{2} + {\left(8 \, c e^{4} f^{2} - 4 \, {\left(2 \, c d e^{3} + b e^{4}\right)} f g + {\left(3 \, c d^{2} e^{2} + b d e^{3} + 3 \, a e^{4}\right)} g^{2}\right)} x^{2} + 2 \, {\left(8 \, c d e^{3} f^{2} - 4 \, {\left(2 \, c d^{2} e^{2} + b d e^{3}\right)} f g + {\left(3 \, c d^{3} e + b d^{2} e^{2} + 3 \, a d e^{3}\right)} g^{2}\right)} x\right)} \sqrt{-e^{2} f + d e g} \arctan\left(\frac{\sqrt{-e^{2} f + d e g} \sqrt{g x + f}}{e g x + e f}\right) + {\left(2 \, {\left(3 \, c d^{2} e^{3} - b d e^{4} - a e^{5}\right)} f^{2} - {\left(9 \, c d^{3} e^{2} - b d^{2} e^{3} - 7 \, a d e^{4}\right)} f g + {\left(3 \, c d^{4} e + b d^{3} e^{2} - 5 \, a d^{2} e^{3}\right)} g^{2} + {\left(4 \, {\left(2 \, c d e^{4} - b e^{5}\right)} f^{2} - {\left(13 \, c d^{2} e^{3} - 5 \, b d e^{4} - 3 \, a e^{5}\right)} f g + {\left(5 \, c d^{3} e^{2} - b d^{2} e^{3} - 3 \, a d e^{4}\right)} g^{2}\right)} x\right)} \sqrt{g x + f}}{4 \, {\left(d^{2} e^{6} f^{3} - 3 \, d^{3} e^{5} f^{2} g + 3 \, d^{4} e^{4} f g^{2} - d^{5} e^{3} g^{3} + {\left(e^{8} f^{3} - 3 \, d e^{7} f^{2} g + 3 \, d^{2} e^{6} f g^{2} - d^{3} e^{5} g^{3}\right)} x^{2} + 2 \, {\left(d e^{7} f^{3} - 3 \, d^{2} e^{6} f^{2} g + 3 \, d^{3} e^{5} f g^{2} - d^{4} e^{4} g^{3}\right)} x\right)}}\right]"," ",0,"[1/8*((8*c*d^2*e^2*f^2 - 4*(2*c*d^3*e + b*d^2*e^2)*f*g + (3*c*d^4 + b*d^3*e + 3*a*d^2*e^2)*g^2 + (8*c*e^4*f^2 - 4*(2*c*d*e^3 + b*e^4)*f*g + (3*c*d^2*e^2 + b*d*e^3 + 3*a*e^4)*g^2)*x^2 + 2*(8*c*d*e^3*f^2 - 4*(2*c*d^2*e^2 + b*d*e^3)*f*g + (3*c*d^3*e + b*d^2*e^2 + 3*a*d*e^3)*g^2)*x)*sqrt(e^2*f - d*e*g)*log((e*g*x + 2*e*f - d*g - 2*sqrt(e^2*f - d*e*g)*sqrt(g*x + f))/(e*x + d)) + 2*(2*(3*c*d^2*e^3 - b*d*e^4 - a*e^5)*f^2 - (9*c*d^3*e^2 - b*d^2*e^3 - 7*a*d*e^4)*f*g + (3*c*d^4*e + b*d^3*e^2 - 5*a*d^2*e^3)*g^2 + (4*(2*c*d*e^4 - b*e^5)*f^2 - (13*c*d^2*e^3 - 5*b*d*e^4 - 3*a*e^5)*f*g + (5*c*d^3*e^2 - b*d^2*e^3 - 3*a*d*e^4)*g^2)*x)*sqrt(g*x + f))/(d^2*e^6*f^3 - 3*d^3*e^5*f^2*g + 3*d^4*e^4*f*g^2 - d^5*e^3*g^3 + (e^8*f^3 - 3*d*e^7*f^2*g + 3*d^2*e^6*f*g^2 - d^3*e^5*g^3)*x^2 + 2*(d*e^7*f^3 - 3*d^2*e^6*f^2*g + 3*d^3*e^5*f*g^2 - d^4*e^4*g^3)*x), 1/4*((8*c*d^2*e^2*f^2 - 4*(2*c*d^3*e + b*d^2*e^2)*f*g + (3*c*d^4 + b*d^3*e + 3*a*d^2*e^2)*g^2 + (8*c*e^4*f^2 - 4*(2*c*d*e^3 + b*e^4)*f*g + (3*c*d^2*e^2 + b*d*e^3 + 3*a*e^4)*g^2)*x^2 + 2*(8*c*d*e^3*f^2 - 4*(2*c*d^2*e^2 + b*d*e^3)*f*g + (3*c*d^3*e + b*d^2*e^2 + 3*a*d*e^3)*g^2)*x)*sqrt(-e^2*f + d*e*g)*arctan(sqrt(-e^2*f + d*e*g)*sqrt(g*x + f)/(e*g*x + e*f)) + (2*(3*c*d^2*e^3 - b*d*e^4 - a*e^5)*f^2 - (9*c*d^3*e^2 - b*d^2*e^3 - 7*a*d*e^4)*f*g + (3*c*d^4*e + b*d^3*e^2 - 5*a*d^2*e^3)*g^2 + (4*(2*c*d*e^4 - b*e^5)*f^2 - (13*c*d^2*e^3 - 5*b*d*e^4 - 3*a*e^5)*f*g + (5*c*d^3*e^2 - b*d^2*e^3 - 3*a*d*e^4)*g^2)*x)*sqrt(g*x + f))/(d^2*e^6*f^3 - 3*d^3*e^5*f^2*g + 3*d^4*e^4*f*g^2 - d^5*e^3*g^3 + (e^8*f^3 - 3*d*e^7*f^2*g + 3*d^2*e^6*f*g^2 - d^3*e^5*g^3)*x^2 + 2*(d*e^7*f^3 - 3*d^2*e^6*f^2*g + 3*d^3*e^5*f*g^2 - d^4*e^4*g^3)*x)]","B",0
826,1,438,0,0.620196," ","integrate((e*x+d)^3*(c*x^2+b*x+a)/(g*x+f)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, c e^{3} g^{5} x^{5} + 1280 \, c e^{3} f^{5} - 315 \, a d^{3} g^{5} - 1152 \, {\left(3 \, c d e^{2} + b e^{3}\right)} f^{4} g + 1008 \, {\left(3 \, c d^{2} e + 3 \, b d e^{2} + a e^{3}\right)} f^{3} g^{2} - 840 \, {\left(c d^{3} + 3 \, b d^{2} e + 3 \, a d e^{2}\right)} f^{2} g^{3} + 630 \, {\left(b d^{3} + 3 \, a d^{2} e\right)} f g^{4} - 5 \, {\left(10 \, c e^{3} f g^{4} - 9 \, {\left(3 \, c d e^{2} + b e^{3}\right)} g^{5}\right)} x^{4} + {\left(80 \, c e^{3} f^{2} g^{3} - 72 \, {\left(3 \, c d e^{2} + b e^{3}\right)} f g^{4} + 63 \, {\left(3 \, c d^{2} e + 3 \, b d e^{2} + a e^{3}\right)} g^{5}\right)} x^{3} - {\left(160 \, c e^{3} f^{3} g^{2} - 144 \, {\left(3 \, c d e^{2} + b e^{3}\right)} f^{2} g^{3} + 126 \, {\left(3 \, c d^{2} e + 3 \, b d e^{2} + a e^{3}\right)} f g^{4} - 105 \, {\left(c d^{3} + 3 \, b d^{2} e + 3 \, a d e^{2}\right)} g^{5}\right)} x^{2} + {\left(640 \, c e^{3} f^{4} g - 576 \, {\left(3 \, c d e^{2} + b e^{3}\right)} f^{3} g^{2} + 504 \, {\left(3 \, c d^{2} e + 3 \, b d e^{2} + a e^{3}\right)} f^{2} g^{3} - 420 \, {\left(c d^{3} + 3 \, b d^{2} e + 3 \, a d e^{2}\right)} f g^{4} + 315 \, {\left(b d^{3} + 3 \, a d^{2} e\right)} g^{5}\right)} x\right)} \sqrt{g x + f}}{315 \, {\left(g^{7} x + f g^{6}\right)}}"," ",0,"2/315*(35*c*e^3*g^5*x^5 + 1280*c*e^3*f^5 - 315*a*d^3*g^5 - 1152*(3*c*d*e^2 + b*e^3)*f^4*g + 1008*(3*c*d^2*e + 3*b*d*e^2 + a*e^3)*f^3*g^2 - 840*(c*d^3 + 3*b*d^2*e + 3*a*d*e^2)*f^2*g^3 + 630*(b*d^3 + 3*a*d^2*e)*f*g^4 - 5*(10*c*e^3*f*g^4 - 9*(3*c*d*e^2 + b*e^3)*g^5)*x^4 + (80*c*e^3*f^2*g^3 - 72*(3*c*d*e^2 + b*e^3)*f*g^4 + 63*(3*c*d^2*e + 3*b*d*e^2 + a*e^3)*g^5)*x^3 - (160*c*e^3*f^3*g^2 - 144*(3*c*d*e^2 + b*e^3)*f^2*g^3 + 126*(3*c*d^2*e + 3*b*d*e^2 + a*e^3)*f*g^4 - 105*(c*d^3 + 3*b*d^2*e + 3*a*d*e^2)*g^5)*x^2 + (640*c*e^3*f^4*g - 576*(3*c*d*e^2 + b*e^3)*f^3*g^2 + 504*(3*c*d^2*e + 3*b*d*e^2 + a*e^3)*f^2*g^3 - 420*(c*d^3 + 3*b*d^2*e + 3*a*d*e^2)*f*g^4 + 315*(b*d^3 + 3*a*d^2*e)*g^5)*x)*sqrt(g*x + f)/(g^7*x + f*g^6)","A",0
827,1,269,0,0.607942," ","integrate((e*x+d)^2*(c*x^2+b*x+a)/(g*x+f)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, c e^{2} g^{4} x^{4} - 384 \, c e^{2} f^{4} - 105 \, a d^{2} g^{4} + 336 \, {\left(2 \, c d e + b e^{2}\right)} f^{3} g - 280 \, {\left(c d^{2} + 2 \, b d e + a e^{2}\right)} f^{2} g^{2} + 210 \, {\left(b d^{2} + 2 \, a d e\right)} f g^{3} - 3 \, {\left(8 \, c e^{2} f g^{3} - 7 \, {\left(2 \, c d e + b e^{2}\right)} g^{4}\right)} x^{3} + {\left(48 \, c e^{2} f^{2} g^{2} - 42 \, {\left(2 \, c d e + b e^{2}\right)} f g^{3} + 35 \, {\left(c d^{2} + 2 \, b d e + a e^{2}\right)} g^{4}\right)} x^{2} - {\left(192 \, c e^{2} f^{3} g - 168 \, {\left(2 \, c d e + b e^{2}\right)} f^{2} g^{2} + 140 \, {\left(c d^{2} + 2 \, b d e + a e^{2}\right)} f g^{3} - 105 \, {\left(b d^{2} + 2 \, a d e\right)} g^{4}\right)} x\right)} \sqrt{g x + f}}{105 \, {\left(g^{6} x + f g^{5}\right)}}"," ",0,"2/105*(15*c*e^2*g^4*x^4 - 384*c*e^2*f^4 - 105*a*d^2*g^4 + 336*(2*c*d*e + b*e^2)*f^3*g - 280*(c*d^2 + 2*b*d*e + a*e^2)*f^2*g^2 + 210*(b*d^2 + 2*a*d*e)*f*g^3 - 3*(8*c*e^2*f*g^3 - 7*(2*c*d*e + b*e^2)*g^4)*x^3 + (48*c*e^2*f^2*g^2 - 42*(2*c*d*e + b*e^2)*f*g^3 + 35*(c*d^2 + 2*b*d*e + a*e^2)*g^4)*x^2 - (192*c*e^2*f^3*g - 168*(2*c*d*e + b*e^2)*f^2*g^2 + 140*(c*d^2 + 2*b*d*e + a*e^2)*f*g^3 - 105*(b*d^2 + 2*a*d*e)*g^4)*x)*sqrt(g*x + f)/(g^6*x + f*g^5)","A",0
828,1,135,0,0.392739," ","integrate((e*x+d)*(c*x^2+b*x+a)/(g*x+f)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, c e g^{3} x^{3} + 48 \, c e f^{3} - 15 \, a d g^{3} - 40 \, {\left(c d + b e\right)} f^{2} g + 30 \, {\left(b d + a e\right)} f g^{2} - {\left(6 \, c e f g^{2} - 5 \, {\left(c d + b e\right)} g^{3}\right)} x^{2} + {\left(24 \, c e f^{2} g - 20 \, {\left(c d + b e\right)} f g^{2} + 15 \, {\left(b d + a e\right)} g^{3}\right)} x\right)} \sqrt{g x + f}}{15 \, {\left(g^{5} x + f g^{4}\right)}}"," ",0,"2/15*(3*c*e*g^3*x^3 + 48*c*e*f^3 - 15*a*d*g^3 - 40*(c*d + b*e)*f^2*g + 30*(b*d + a*e)*f*g^2 - (6*c*e*f*g^2 - 5*(c*d + b*e)*g^3)*x^2 + (24*c*e*f^2*g - 20*(c*d + b*e)*f*g^2 + 15*(b*d + a*e)*g^3)*x)*sqrt(g*x + f)/(g^5*x + f*g^4)","A",0
829,1,63,0,0.397867," ","integrate((c*x^2+b*x+a)/(g*x+f)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(c g^{2} x^{2} - 8 \, c f^{2} + 6 \, b f g - 3 \, a g^{2} - {\left(4 \, c f g - 3 \, b g^{2}\right)} x\right)} \sqrt{g x + f}}{3 \, {\left(g^{4} x + f g^{3}\right)}}"," ",0,"2/3*(c*g^2*x^2 - 8*c*f^2 + 6*b*f*g - 3*a*g^2 - (4*c*f*g - 3*b*g^2)*x)*sqrt(g*x + f)/(g^4*x + f*g^3)","A",0
830,1,540,0,0.438998," ","integrate((c*x^2+b*x+a)/(e*x+d)/(g*x+f)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left({\left(c d^{2} - b d e + a e^{2}\right)} g^{3} x + {\left(c d^{2} - b d e + a e^{2}\right)} f g^{2}\right)} \sqrt{e^{2} f - d e g} \log\left(\frac{e g x + 2 \, e f - d g + 2 \, \sqrt{e^{2} f - d e g} \sqrt{g x + f}}{e x + d}\right) - 2 \, {\left(2 \, c e^{3} f^{3} - a d e^{2} g^{3} - {\left(3 \, c d e^{2} + b e^{3}\right)} f^{2} g + {\left(c d^{2} e + b d e^{2} + a e^{3}\right)} f g^{2} + {\left(c e^{3} f^{2} g - 2 \, c d e^{2} f g^{2} + c d^{2} e g^{3}\right)} x\right)} \sqrt{g x + f}}{e^{4} f^{3} g^{2} - 2 \, d e^{3} f^{2} g^{3} + d^{2} e^{2} f g^{4} + {\left(e^{4} f^{2} g^{3} - 2 \, d e^{3} f g^{4} + d^{2} e^{2} g^{5}\right)} x}, \frac{2 \, {\left({\left({\left(c d^{2} - b d e + a e^{2}\right)} g^{3} x + {\left(c d^{2} - b d e + a e^{2}\right)} f g^{2}\right)} \sqrt{-e^{2} f + d e g} \arctan\left(\frac{\sqrt{-e^{2} f + d e g} \sqrt{g x + f}}{e g x + e f}\right) + {\left(2 \, c e^{3} f^{3} - a d e^{2} g^{3} - {\left(3 \, c d e^{2} + b e^{3}\right)} f^{2} g + {\left(c d^{2} e + b d e^{2} + a e^{3}\right)} f g^{2} + {\left(c e^{3} f^{2} g - 2 \, c d e^{2} f g^{2} + c d^{2} e g^{3}\right)} x\right)} \sqrt{g x + f}\right)}}{e^{4} f^{3} g^{2} - 2 \, d e^{3} f^{2} g^{3} + d^{2} e^{2} f g^{4} + {\left(e^{4} f^{2} g^{3} - 2 \, d e^{3} f g^{4} + d^{2} e^{2} g^{5}\right)} x}\right]"," ",0,"[-(((c*d^2 - b*d*e + a*e^2)*g^3*x + (c*d^2 - b*d*e + a*e^2)*f*g^2)*sqrt(e^2*f - d*e*g)*log((e*g*x + 2*e*f - d*g + 2*sqrt(e^2*f - d*e*g)*sqrt(g*x + f))/(e*x + d)) - 2*(2*c*e^3*f^3 - a*d*e^2*g^3 - (3*c*d*e^2 + b*e^3)*f^2*g + (c*d^2*e + b*d*e^2 + a*e^3)*f*g^2 + (c*e^3*f^2*g - 2*c*d*e^2*f*g^2 + c*d^2*e*g^3)*x)*sqrt(g*x + f))/(e^4*f^3*g^2 - 2*d*e^3*f^2*g^3 + d^2*e^2*f*g^4 + (e^4*f^2*g^3 - 2*d*e^3*f*g^4 + d^2*e^2*g^5)*x), 2*(((c*d^2 - b*d*e + a*e^2)*g^3*x + (c*d^2 - b*d*e + a*e^2)*f*g^2)*sqrt(-e^2*f + d*e*g)*arctan(sqrt(-e^2*f + d*e*g)*sqrt(g*x + f)/(e*g*x + e*f)) + (2*c*e^3*f^3 - a*d*e^2*g^3 - (3*c*d*e^2 + b*e^3)*f^2*g + (c*d^2*e + b*d*e^2 + a*e^3)*f*g^2 + (c*e^3*f^2*g - 2*c*d*e^2*f*g^2 + c*d^2*e*g^3)*x)*sqrt(g*x + f))/(e^4*f^3*g^2 - 2*d*e^3*f^2*g^3 + d^2*e^2*f*g^4 + (e^4*f^2*g^3 - 2*d*e^3*f*g^4 + d^2*e^2*g^5)*x)]","B",0
831,1,1088,0,0.455627," ","integrate((c*x^2+b*x+a)/(e*x+d)^2/(g*x+f)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(2 \, {\left(2 \, c d^{2} e - b d e^{2}\right)} f^{2} g - {\left(c d^{3} + b d^{2} e - 3 \, a d e^{2}\right)} f g^{2} + {\left(2 \, {\left(2 \, c d e^{2} - b e^{3}\right)} f g^{2} - {\left(c d^{2} e + b d e^{2} - 3 \, a e^{3}\right)} g^{3}\right)} x^{2} + {\left(2 \, {\left(2 \, c d e^{2} - b e^{3}\right)} f^{2} g + 3 \, {\left(c d^{2} e - b d e^{2} + a e^{3}\right)} f g^{2} - {\left(c d^{3} + b d^{2} e - 3 \, a d e^{2}\right)} g^{3}\right)} x\right)} \sqrt{e^{2} f - d e g} \log\left(\frac{e g x + 2 \, e f - d g + 2 \, \sqrt{e^{2} f - d e g} \sqrt{g x + f}}{e x + d}\right) - 2 \, {\left(2 \, c d e^{3} f^{3} - 2 \, a d^{2} e^{2} g^{3} - {\left(c d^{2} e^{2} + 3 \, b d e^{3} - a e^{4}\right)} f^{2} g - {\left(c d^{3} e - 3 \, b d^{2} e^{2} - a d e^{3}\right)} f g^{2} + {\left(2 \, c e^{4} f^{3} - 2 \, {\left(c d e^{3} + b e^{4}\right)} f^{2} g + {\left(c d^{2} e^{2} + b d e^{3} + 3 \, a e^{4}\right)} f g^{2} - {\left(c d^{3} e - b d^{2} e^{2} + 3 \, a d e^{3}\right)} g^{3}\right)} x\right)} \sqrt{g x + f}}{2 \, {\left(d e^{5} f^{4} g - 3 \, d^{2} e^{4} f^{3} g^{2} + 3 \, d^{3} e^{3} f^{2} g^{3} - d^{4} e^{2} f g^{4} + {\left(e^{6} f^{3} g^{2} - 3 \, d e^{5} f^{2} g^{3} + 3 \, d^{2} e^{4} f g^{4} - d^{3} e^{3} g^{5}\right)} x^{2} + {\left(e^{6} f^{4} g - 2 \, d e^{5} f^{3} g^{2} + 2 \, d^{3} e^{3} f g^{4} - d^{4} e^{2} g^{5}\right)} x\right)}}, -\frac{{\left(2 \, {\left(2 \, c d^{2} e - b d e^{2}\right)} f^{2} g - {\left(c d^{3} + b d^{2} e - 3 \, a d e^{2}\right)} f g^{2} + {\left(2 \, {\left(2 \, c d e^{2} - b e^{3}\right)} f g^{2} - {\left(c d^{2} e + b d e^{2} - 3 \, a e^{3}\right)} g^{3}\right)} x^{2} + {\left(2 \, {\left(2 \, c d e^{2} - b e^{3}\right)} f^{2} g + 3 \, {\left(c d^{2} e - b d e^{2} + a e^{3}\right)} f g^{2} - {\left(c d^{3} + b d^{2} e - 3 \, a d e^{2}\right)} g^{3}\right)} x\right)} \sqrt{-e^{2} f + d e g} \arctan\left(\frac{\sqrt{-e^{2} f + d e g} \sqrt{g x + f}}{e g x + e f}\right) + {\left(2 \, c d e^{3} f^{3} - 2 \, a d^{2} e^{2} g^{3} - {\left(c d^{2} e^{2} + 3 \, b d e^{3} - a e^{4}\right)} f^{2} g - {\left(c d^{3} e - 3 \, b d^{2} e^{2} - a d e^{3}\right)} f g^{2} + {\left(2 \, c e^{4} f^{3} - 2 \, {\left(c d e^{3} + b e^{4}\right)} f^{2} g + {\left(c d^{2} e^{2} + b d e^{3} + 3 \, a e^{4}\right)} f g^{2} - {\left(c d^{3} e - b d^{2} e^{2} + 3 \, a d e^{3}\right)} g^{3}\right)} x\right)} \sqrt{g x + f}}{d e^{5} f^{4} g - 3 \, d^{2} e^{4} f^{3} g^{2} + 3 \, d^{3} e^{3} f^{2} g^{3} - d^{4} e^{2} f g^{4} + {\left(e^{6} f^{3} g^{2} - 3 \, d e^{5} f^{2} g^{3} + 3 \, d^{2} e^{4} f g^{4} - d^{3} e^{3} g^{5}\right)} x^{2} + {\left(e^{6} f^{4} g - 2 \, d e^{5} f^{3} g^{2} + 2 \, d^{3} e^{3} f g^{4} - d^{4} e^{2} g^{5}\right)} x}\right]"," ",0,"[1/2*((2*(2*c*d^2*e - b*d*e^2)*f^2*g - (c*d^3 + b*d^2*e - 3*a*d*e^2)*f*g^2 + (2*(2*c*d*e^2 - b*e^3)*f*g^2 - (c*d^2*e + b*d*e^2 - 3*a*e^3)*g^3)*x^2 + (2*(2*c*d*e^2 - b*e^3)*f^2*g + 3*(c*d^2*e - b*d*e^2 + a*e^3)*f*g^2 - (c*d^3 + b*d^2*e - 3*a*d*e^2)*g^3)*x)*sqrt(e^2*f - d*e*g)*log((e*g*x + 2*e*f - d*g + 2*sqrt(e^2*f - d*e*g)*sqrt(g*x + f))/(e*x + d)) - 2*(2*c*d*e^3*f^3 - 2*a*d^2*e^2*g^3 - (c*d^2*e^2 + 3*b*d*e^3 - a*e^4)*f^2*g - (c*d^3*e - 3*b*d^2*e^2 - a*d*e^3)*f*g^2 + (2*c*e^4*f^3 - 2*(c*d*e^3 + b*e^4)*f^2*g + (c*d^2*e^2 + b*d*e^3 + 3*a*e^4)*f*g^2 - (c*d^3*e - b*d^2*e^2 + 3*a*d*e^3)*g^3)*x)*sqrt(g*x + f))/(d*e^5*f^4*g - 3*d^2*e^4*f^3*g^2 + 3*d^3*e^3*f^2*g^3 - d^4*e^2*f*g^4 + (e^6*f^3*g^2 - 3*d*e^5*f^2*g^3 + 3*d^2*e^4*f*g^4 - d^3*e^3*g^5)*x^2 + (e^6*f^4*g - 2*d*e^5*f^3*g^2 + 2*d^3*e^3*f*g^4 - d^4*e^2*g^5)*x), -((2*(2*c*d^2*e - b*d*e^2)*f^2*g - (c*d^3 + b*d^2*e - 3*a*d*e^2)*f*g^2 + (2*(2*c*d*e^2 - b*e^3)*f*g^2 - (c*d^2*e + b*d*e^2 - 3*a*e^3)*g^3)*x^2 + (2*(2*c*d*e^2 - b*e^3)*f^2*g + 3*(c*d^2*e - b*d*e^2 + a*e^3)*f*g^2 - (c*d^3 + b*d^2*e - 3*a*d*e^2)*g^3)*x)*sqrt(-e^2*f + d*e*g)*arctan(sqrt(-e^2*f + d*e*g)*sqrt(g*x + f)/(e*g*x + e*f)) + (2*c*d*e^3*f^3 - 2*a*d^2*e^2*g^3 - (c*d^2*e^2 + 3*b*d*e^3 - a*e^4)*f^2*g - (c*d^3*e - 3*b*d^2*e^2 - a*d*e^3)*f*g^2 + (2*c*e^4*f^3 - 2*(c*d*e^3 + b*e^4)*f^2*g + (c*d^2*e^2 + b*d*e^3 + 3*a*e^4)*f*g^2 - (c*d^3*e - b*d^2*e^2 + 3*a*d*e^3)*g^3)*x)*sqrt(g*x + f))/(d*e^5*f^4*g - 3*d^2*e^4*f^3*g^2 + 3*d^3*e^3*f^2*g^3 - d^4*e^2*f*g^4 + (e^6*f^3*g^2 - 3*d*e^5*f^2*g^3 + 3*d^2*e^4*f*g^4 - d^3*e^3*g^5)*x^2 + (e^6*f^4*g - 2*d*e^5*f^3*g^2 + 2*d^3*e^3*f*g^4 - d^4*e^2*g^5)*x)]","B",0
832,1,1883,0,0.496704," ","integrate((c*x^2+b*x+a)/(e*x+d)^3/(g*x+f)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left(8 \, c d^{2} e^{2} f^{3} + 4 \, {\left(2 \, c d^{3} e - 3 \, b d^{2} e^{2}\right)} f^{2} g - {\left(c d^{4} + 3 \, b d^{3} e - 15 \, a d^{2} e^{2}\right)} f g^{2} + {\left(8 \, c e^{4} f^{2} g + 4 \, {\left(2 \, c d e^{3} - 3 \, b e^{4}\right)} f g^{2} - {\left(c d^{2} e^{2} + 3 \, b d e^{3} - 15 \, a e^{4}\right)} g^{3}\right)} x^{3} + {\left(8 \, c e^{4} f^{3} + 12 \, {\left(2 \, c d e^{3} - b e^{4}\right)} f^{2} g + 3 \, {\left(5 \, c d^{2} e^{2} - 9 \, b d e^{3} + 5 \, a e^{4}\right)} f g^{2} - 2 \, {\left(c d^{3} e + 3 \, b d^{2} e^{2} - 15 \, a d e^{3}\right)} g^{3}\right)} x^{2} + {\left(16 \, c d e^{3} f^{3} + 24 \, {\left(c d^{2} e^{2} - b d e^{3}\right)} f^{2} g + 6 \, {\left(c d^{3} e - 3 \, b d^{2} e^{2} + 5 \, a d e^{3}\right)} f g^{2} - {\left(c d^{4} + 3 \, b d^{3} e - 15 \, a d^{2} e^{2}\right)} g^{3}\right)} x\right)} \sqrt{e^{2} f - d e g} \log\left(\frac{e g x + 2 \, e f - d g + 2 \, \sqrt{e^{2} f - d e g} \sqrt{g x + f}}{e x + d}\right) + 2 \, {\left(8 \, a d^{3} e^{2} g^{3} - 2 \, {\left(7 \, c d^{2} e^{3} - b d e^{4} - a e^{5}\right)} f^{3} + {\left(13 \, c d^{3} e^{2} + 11 \, b d^{2} e^{3} - 11 \, a d e^{4}\right)} f^{2} g + {\left(c d^{4} e - 13 \, b d^{3} e^{2} + a d^{2} e^{3}\right)} f g^{2} - {\left(8 \, c e^{5} f^{3} - 12 \, b e^{5} f^{2} g - 3 \, {\left(3 \, c d^{2} e^{3} - 3 \, b d e^{4} - 5 \, a e^{5}\right)} f g^{2} + {\left(c d^{3} e^{2} + 3 \, b d^{2} e^{3} - 15 \, a d e^{4}\right)} g^{3}\right)} x^{2} - {\left(4 \, {\left(6 \, c d e^{4} - b e^{5}\right)} f^{3} - {\left(19 \, c d^{2} e^{3} + 17 \, b d e^{4} - 5 \, a e^{5}\right)} f^{2} g - 4 \, {\left(c d^{3} e^{2} - 4 \, b d^{2} e^{3} - 5 \, a d e^{4}\right)} f g^{2} - {\left(c d^{4} e - 5 \, b d^{3} e^{2} + 25 \, a d^{2} e^{3}\right)} g^{3}\right)} x\right)} \sqrt{g x + f}}{8 \, {\left(d^{2} e^{6} f^{5} - 4 \, d^{3} e^{5} f^{4} g + 6 \, d^{4} e^{4} f^{3} g^{2} - 4 \, d^{5} e^{3} f^{2} g^{3} + d^{6} e^{2} f g^{4} + {\left(e^{8} f^{4} g - 4 \, d e^{7} f^{3} g^{2} + 6 \, d^{2} e^{6} f^{2} g^{3} - 4 \, d^{3} e^{5} f g^{4} + d^{4} e^{4} g^{5}\right)} x^{3} + {\left(e^{8} f^{5} - 2 \, d e^{7} f^{4} g - 2 \, d^{2} e^{6} f^{3} g^{2} + 8 \, d^{3} e^{5} f^{2} g^{3} - 7 \, d^{4} e^{4} f g^{4} + 2 \, d^{5} e^{3} g^{5}\right)} x^{2} + {\left(2 \, d e^{7} f^{5} - 7 \, d^{2} e^{6} f^{4} g + 8 \, d^{3} e^{5} f^{3} g^{2} - 2 \, d^{4} e^{4} f^{2} g^{3} - 2 \, d^{5} e^{3} f g^{4} + d^{6} e^{2} g^{5}\right)} x\right)}}, \frac{{\left(8 \, c d^{2} e^{2} f^{3} + 4 \, {\left(2 \, c d^{3} e - 3 \, b d^{2} e^{2}\right)} f^{2} g - {\left(c d^{4} + 3 \, b d^{3} e - 15 \, a d^{2} e^{2}\right)} f g^{2} + {\left(8 \, c e^{4} f^{2} g + 4 \, {\left(2 \, c d e^{3} - 3 \, b e^{4}\right)} f g^{2} - {\left(c d^{2} e^{2} + 3 \, b d e^{3} - 15 \, a e^{4}\right)} g^{3}\right)} x^{3} + {\left(8 \, c e^{4} f^{3} + 12 \, {\left(2 \, c d e^{3} - b e^{4}\right)} f^{2} g + 3 \, {\left(5 \, c d^{2} e^{2} - 9 \, b d e^{3} + 5 \, a e^{4}\right)} f g^{2} - 2 \, {\left(c d^{3} e + 3 \, b d^{2} e^{2} - 15 \, a d e^{3}\right)} g^{3}\right)} x^{2} + {\left(16 \, c d e^{3} f^{3} + 24 \, {\left(c d^{2} e^{2} - b d e^{3}\right)} f^{2} g + 6 \, {\left(c d^{3} e - 3 \, b d^{2} e^{2} + 5 \, a d e^{3}\right)} f g^{2} - {\left(c d^{4} + 3 \, b d^{3} e - 15 \, a d^{2} e^{2}\right)} g^{3}\right)} x\right)} \sqrt{-e^{2} f + d e g} \arctan\left(\frac{\sqrt{-e^{2} f + d e g} \sqrt{g x + f}}{e g x + e f}\right) - {\left(8 \, a d^{3} e^{2} g^{3} - 2 \, {\left(7 \, c d^{2} e^{3} - b d e^{4} - a e^{5}\right)} f^{3} + {\left(13 \, c d^{3} e^{2} + 11 \, b d^{2} e^{3} - 11 \, a d e^{4}\right)} f^{2} g + {\left(c d^{4} e - 13 \, b d^{3} e^{2} + a d^{2} e^{3}\right)} f g^{2} - {\left(8 \, c e^{5} f^{3} - 12 \, b e^{5} f^{2} g - 3 \, {\left(3 \, c d^{2} e^{3} - 3 \, b d e^{4} - 5 \, a e^{5}\right)} f g^{2} + {\left(c d^{3} e^{2} + 3 \, b d^{2} e^{3} - 15 \, a d e^{4}\right)} g^{3}\right)} x^{2} - {\left(4 \, {\left(6 \, c d e^{4} - b e^{5}\right)} f^{3} - {\left(19 \, c d^{2} e^{3} + 17 \, b d e^{4} - 5 \, a e^{5}\right)} f^{2} g - 4 \, {\left(c d^{3} e^{2} - 4 \, b d^{2} e^{3} - 5 \, a d e^{4}\right)} f g^{2} - {\left(c d^{4} e - 5 \, b d^{3} e^{2} + 25 \, a d^{2} e^{3}\right)} g^{3}\right)} x\right)} \sqrt{g x + f}}{4 \, {\left(d^{2} e^{6} f^{5} - 4 \, d^{3} e^{5} f^{4} g + 6 \, d^{4} e^{4} f^{3} g^{2} - 4 \, d^{5} e^{3} f^{2} g^{3} + d^{6} e^{2} f g^{4} + {\left(e^{8} f^{4} g - 4 \, d e^{7} f^{3} g^{2} + 6 \, d^{2} e^{6} f^{2} g^{3} - 4 \, d^{3} e^{5} f g^{4} + d^{4} e^{4} g^{5}\right)} x^{3} + {\left(e^{8} f^{5} - 2 \, d e^{7} f^{4} g - 2 \, d^{2} e^{6} f^{3} g^{2} + 8 \, d^{3} e^{5} f^{2} g^{3} - 7 \, d^{4} e^{4} f g^{4} + 2 \, d^{5} e^{3} g^{5}\right)} x^{2} + {\left(2 \, d e^{7} f^{5} - 7 \, d^{2} e^{6} f^{4} g + 8 \, d^{3} e^{5} f^{3} g^{2} - 2 \, d^{4} e^{4} f^{2} g^{3} - 2 \, d^{5} e^{3} f g^{4} + d^{6} e^{2} g^{5}\right)} x\right)}}\right]"," ",0,"[-1/8*((8*c*d^2*e^2*f^3 + 4*(2*c*d^3*e - 3*b*d^2*e^2)*f^2*g - (c*d^4 + 3*b*d^3*e - 15*a*d^2*e^2)*f*g^2 + (8*c*e^4*f^2*g + 4*(2*c*d*e^3 - 3*b*e^4)*f*g^2 - (c*d^2*e^2 + 3*b*d*e^3 - 15*a*e^4)*g^3)*x^3 + (8*c*e^4*f^3 + 12*(2*c*d*e^3 - b*e^4)*f^2*g + 3*(5*c*d^2*e^2 - 9*b*d*e^3 + 5*a*e^4)*f*g^2 - 2*(c*d^3*e + 3*b*d^2*e^2 - 15*a*d*e^3)*g^3)*x^2 + (16*c*d*e^3*f^3 + 24*(c*d^2*e^2 - b*d*e^3)*f^2*g + 6*(c*d^3*e - 3*b*d^2*e^2 + 5*a*d*e^3)*f*g^2 - (c*d^4 + 3*b*d^3*e - 15*a*d^2*e^2)*g^3)*x)*sqrt(e^2*f - d*e*g)*log((e*g*x + 2*e*f - d*g + 2*sqrt(e^2*f - d*e*g)*sqrt(g*x + f))/(e*x + d)) + 2*(8*a*d^3*e^2*g^3 - 2*(7*c*d^2*e^3 - b*d*e^4 - a*e^5)*f^3 + (13*c*d^3*e^2 + 11*b*d^2*e^3 - 11*a*d*e^4)*f^2*g + (c*d^4*e - 13*b*d^3*e^2 + a*d^2*e^3)*f*g^2 - (8*c*e^5*f^3 - 12*b*e^5*f^2*g - 3*(3*c*d^2*e^3 - 3*b*d*e^4 - 5*a*e^5)*f*g^2 + (c*d^3*e^2 + 3*b*d^2*e^3 - 15*a*d*e^4)*g^3)*x^2 - (4*(6*c*d*e^4 - b*e^5)*f^3 - (19*c*d^2*e^3 + 17*b*d*e^4 - 5*a*e^5)*f^2*g - 4*(c*d^3*e^2 - 4*b*d^2*e^3 - 5*a*d*e^4)*f*g^2 - (c*d^4*e - 5*b*d^3*e^2 + 25*a*d^2*e^3)*g^3)*x)*sqrt(g*x + f))/(d^2*e^6*f^5 - 4*d^3*e^5*f^4*g + 6*d^4*e^4*f^3*g^2 - 4*d^5*e^3*f^2*g^3 + d^6*e^2*f*g^4 + (e^8*f^4*g - 4*d*e^7*f^3*g^2 + 6*d^2*e^6*f^2*g^3 - 4*d^3*e^5*f*g^4 + d^4*e^4*g^5)*x^3 + (e^8*f^5 - 2*d*e^7*f^4*g - 2*d^2*e^6*f^3*g^2 + 8*d^3*e^5*f^2*g^3 - 7*d^4*e^4*f*g^4 + 2*d^5*e^3*g^5)*x^2 + (2*d*e^7*f^5 - 7*d^2*e^6*f^4*g + 8*d^3*e^5*f^3*g^2 - 2*d^4*e^4*f^2*g^3 - 2*d^5*e^3*f*g^4 + d^6*e^2*g^5)*x), 1/4*((8*c*d^2*e^2*f^3 + 4*(2*c*d^3*e - 3*b*d^2*e^2)*f^2*g - (c*d^4 + 3*b*d^3*e - 15*a*d^2*e^2)*f*g^2 + (8*c*e^4*f^2*g + 4*(2*c*d*e^3 - 3*b*e^4)*f*g^2 - (c*d^2*e^2 + 3*b*d*e^3 - 15*a*e^4)*g^3)*x^3 + (8*c*e^4*f^3 + 12*(2*c*d*e^3 - b*e^4)*f^2*g + 3*(5*c*d^2*e^2 - 9*b*d*e^3 + 5*a*e^4)*f*g^2 - 2*(c*d^3*e + 3*b*d^2*e^2 - 15*a*d*e^3)*g^3)*x^2 + (16*c*d*e^3*f^3 + 24*(c*d^2*e^2 - b*d*e^3)*f^2*g + 6*(c*d^3*e - 3*b*d^2*e^2 + 5*a*d*e^3)*f*g^2 - (c*d^4 + 3*b*d^3*e - 15*a*d^2*e^2)*g^3)*x)*sqrt(-e^2*f + d*e*g)*arctan(sqrt(-e^2*f + d*e*g)*sqrt(g*x + f)/(e*g*x + e*f)) - (8*a*d^3*e^2*g^3 - 2*(7*c*d^2*e^3 - b*d*e^4 - a*e^5)*f^3 + (13*c*d^3*e^2 + 11*b*d^2*e^3 - 11*a*d*e^4)*f^2*g + (c*d^4*e - 13*b*d^3*e^2 + a*d^2*e^3)*f*g^2 - (8*c*e^5*f^3 - 12*b*e^5*f^2*g - 3*(3*c*d^2*e^3 - 3*b*d*e^4 - 5*a*e^5)*f*g^2 + (c*d^3*e^2 + 3*b*d^2*e^3 - 15*a*d*e^4)*g^3)*x^2 - (4*(6*c*d*e^4 - b*e^5)*f^3 - (19*c*d^2*e^3 + 17*b*d*e^4 - 5*a*e^5)*f^2*g - 4*(c*d^3*e^2 - 4*b*d^2*e^3 - 5*a*d*e^4)*f*g^2 - (c*d^4*e - 5*b*d^3*e^2 + 25*a*d^2*e^3)*g^3)*x)*sqrt(g*x + f))/(d^2*e^6*f^5 - 4*d^3*e^5*f^4*g + 6*d^4*e^4*f^3*g^2 - 4*d^5*e^3*f^2*g^3 + d^6*e^2*f*g^4 + (e^8*f^4*g - 4*d*e^7*f^3*g^2 + 6*d^2*e^6*f^2*g^3 - 4*d^3*e^5*f*g^4 + d^4*e^4*g^5)*x^3 + (e^8*f^5 - 2*d*e^7*f^4*g - 2*d^2*e^6*f^3*g^2 + 8*d^3*e^5*f^2*g^3 - 7*d^4*e^4*f*g^4 + 2*d^5*e^3*g^5)*x^2 + (2*d*e^7*f^5 - 7*d^2*e^6*f^4*g + 8*d^3*e^5*f^3*g^2 - 2*d^4*e^4*f^2*g^3 - 2*d^5*e^3*f*g^4 + d^6*e^2*g^5)*x)]","B",0
833,1,214,0,0.431949," ","integrate((-1+x)^(1/2)*(1+x)^(1/2)/(-x^2+x+1),x, algorithm=""fricas"")","\frac{2}{5} \, \sqrt{5} \sqrt{2 \, \sqrt{5} - 2} \arctan\left(\frac{1}{8} \, \sqrt{-4 \, {\left(2 \, x + \sqrt{5} - 1\right)} \sqrt{x + 1} \sqrt{x - 1} + 8 \, x^{2} + 4 \, \sqrt{5} x - 4 \, x} \sqrt{2 \, \sqrt{5} - 2} {\left(\sqrt{5} + 1\right)} - \frac{1}{4} \, {\left(\sqrt{x + 1} \sqrt{x - 1} {\left(\sqrt{5} + 1\right)} - \sqrt{5} x - x - 2\right)} \sqrt{2 \, \sqrt{5} - 2}\right) + \frac{1}{10} \, \sqrt{5} \sqrt{2 \, \sqrt{5} + 2} \log\left(2 \, \sqrt{x + 1} \sqrt{x - 1} - 2 \, x + \sqrt{5} + \sqrt{2 \, \sqrt{5} + 2} + 1\right) - \frac{1}{10} \, \sqrt{5} \sqrt{2 \, \sqrt{5} + 2} \log\left(2 \, \sqrt{x + 1} \sqrt{x - 1} - 2 \, x + \sqrt{5} - \sqrt{2 \, \sqrt{5} + 2} + 1\right) + \log\left(\sqrt{x + 1} \sqrt{x - 1} - x\right)"," ",0,"2/5*sqrt(5)*sqrt(2*sqrt(5) - 2)*arctan(1/8*sqrt(-4*(2*x + sqrt(5) - 1)*sqrt(x + 1)*sqrt(x - 1) + 8*x^2 + 4*sqrt(5)*x - 4*x)*sqrt(2*sqrt(5) - 2)*(sqrt(5) + 1) - 1/4*(sqrt(x + 1)*sqrt(x - 1)*(sqrt(5) + 1) - sqrt(5)*x - x - 2)*sqrt(2*sqrt(5) - 2)) + 1/10*sqrt(5)*sqrt(2*sqrt(5) + 2)*log(2*sqrt(x + 1)*sqrt(x - 1) - 2*x + sqrt(5) + sqrt(2*sqrt(5) + 2) + 1) - 1/10*sqrt(5)*sqrt(2*sqrt(5) + 2)*log(2*sqrt(x + 1)*sqrt(x - 1) - 2*x + sqrt(5) - sqrt(2*sqrt(5) + 2) + 1) + log(sqrt(x + 1)*sqrt(x - 1) - x)","B",0
834,1,380,0,0.497450," ","integrate((c*x^2+b*x+a)/(e*x+d)^(1/2)/(g*x+f)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(3 \, c e^{2} f^{2} + 2 \, {\left(c d e - 2 \, b e^{2}\right)} f g + {\left(3 \, c d^{2} - 4 \, b d e + 8 \, a e^{2}\right)} g^{2}\right)} \sqrt{e g} \log\left(8 \, e^{2} g^{2} x^{2} + e^{2} f^{2} + 6 \, d e f g + d^{2} g^{2} + 4 \, {\left(2 \, e g x + e f + d g\right)} \sqrt{e g} \sqrt{e x + d} \sqrt{g x + f} + 8 \, {\left(e^{2} f g + d e g^{2}\right)} x\right) + 4 \, {\left(2 \, c e^{2} g^{2} x - 3 \, c e^{2} f g - {\left(3 \, c d e - 4 \, b e^{2}\right)} g^{2}\right)} \sqrt{e x + d} \sqrt{g x + f}}{16 \, e^{3} g^{3}}, -\frac{{\left(3 \, c e^{2} f^{2} + 2 \, {\left(c d e - 2 \, b e^{2}\right)} f g + {\left(3 \, c d^{2} - 4 \, b d e + 8 \, a e^{2}\right)} g^{2}\right)} \sqrt{-e g} \arctan\left(\frac{{\left(2 \, e g x + e f + d g\right)} \sqrt{-e g} \sqrt{e x + d} \sqrt{g x + f}}{2 \, {\left(e^{2} g^{2} x^{2} + d e f g + {\left(e^{2} f g + d e g^{2}\right)} x\right)}}\right) - 2 \, {\left(2 \, c e^{2} g^{2} x - 3 \, c e^{2} f g - {\left(3 \, c d e - 4 \, b e^{2}\right)} g^{2}\right)} \sqrt{e x + d} \sqrt{g x + f}}{8 \, e^{3} g^{3}}\right]"," ",0,"[1/16*((3*c*e^2*f^2 + 2*(c*d*e - 2*b*e^2)*f*g + (3*c*d^2 - 4*b*d*e + 8*a*e^2)*g^2)*sqrt(e*g)*log(8*e^2*g^2*x^2 + e^2*f^2 + 6*d*e*f*g + d^2*g^2 + 4*(2*e*g*x + e*f + d*g)*sqrt(e*g)*sqrt(e*x + d)*sqrt(g*x + f) + 8*(e^2*f*g + d*e*g^2)*x) + 4*(2*c*e^2*g^2*x - 3*c*e^2*f*g - (3*c*d*e - 4*b*e^2)*g^2)*sqrt(e*x + d)*sqrt(g*x + f))/(e^3*g^3), -1/8*((3*c*e^2*f^2 + 2*(c*d*e - 2*b*e^2)*f*g + (3*c*d^2 - 4*b*d*e + 8*a*e^2)*g^2)*sqrt(-e*g)*arctan(1/2*(2*e*g*x + e*f + d*g)*sqrt(-e*g)*sqrt(e*x + d)*sqrt(g*x + f)/(e^2*g^2*x^2 + d*e*f*g + (e^2*f*g + d*e*g^2)*x)) - 2*(2*c*e^2*g^2*x - 3*c*e^2*f*g - (3*c*d*e - 4*b*e^2)*g^2)*sqrt(e*x + d)*sqrt(g*x + f))/(e^3*g^3)]","A",0
835,1,852,0,0.658039," ","integrate((e*x+d)^(3/2)*(c*x^2+b*x+a)/(g*x+f)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(35 \, c e^{4} f^{4} - 20 \, {\left(3 \, c d e^{3} + 2 \, b e^{4}\right)} f^{3} g + 6 \, {\left(3 \, c d^{2} e^{2} + 12 \, b d e^{3} + 8 \, a e^{4}\right)} f^{2} g^{2} + 4 \, {\left(c d^{3} e - 6 \, b d^{2} e^{2} - 24 \, a d e^{3}\right)} f g^{3} + {\left(3 \, c d^{4} - 8 \, b d^{3} e + 48 \, a d^{2} e^{2}\right)} g^{4}\right)} \sqrt{e g} \log\left(8 \, e^{2} g^{2} x^{2} + e^{2} f^{2} + 6 \, d e f g + d^{2} g^{2} + 4 \, {\left(2 \, e g x + e f + d g\right)} \sqrt{e g} \sqrt{e x + d} \sqrt{g x + f} + 8 \, {\left(e^{2} f g + d e g^{2}\right)} x\right) + 4 \, {\left(48 \, c e^{4} g^{4} x^{3} - 105 \, c e^{4} f^{3} g + 5 \, {\left(29 \, c d e^{3} + 24 \, b e^{4}\right)} f^{2} g^{2} - {\left(15 \, c d^{2} e^{2} + 176 \, b d e^{3} + 144 \, a e^{4}\right)} f g^{3} - 3 \, {\left(3 \, c d^{3} e - 8 \, b d^{2} e^{2} - 80 \, a d e^{3}\right)} g^{4} - 8 \, {\left(7 \, c e^{4} f g^{3} - {\left(9 \, c d e^{3} + 8 \, b e^{4}\right)} g^{4}\right)} x^{2} + 2 \, {\left(35 \, c e^{4} f^{2} g^{2} - 2 \, {\left(23 \, c d e^{3} + 20 \, b e^{4}\right)} f g^{3} + {\left(3 \, c d^{2} e^{2} + 56 \, b d e^{3} + 48 \, a e^{4}\right)} g^{4}\right)} x\right)} \sqrt{e x + d} \sqrt{g x + f}}{768 \, e^{3} g^{5}}, -\frac{3 \, {\left(35 \, c e^{4} f^{4} - 20 \, {\left(3 \, c d e^{3} + 2 \, b e^{4}\right)} f^{3} g + 6 \, {\left(3 \, c d^{2} e^{2} + 12 \, b d e^{3} + 8 \, a e^{4}\right)} f^{2} g^{2} + 4 \, {\left(c d^{3} e - 6 \, b d^{2} e^{2} - 24 \, a d e^{3}\right)} f g^{3} + {\left(3 \, c d^{4} - 8 \, b d^{3} e + 48 \, a d^{2} e^{2}\right)} g^{4}\right)} \sqrt{-e g} \arctan\left(\frac{{\left(2 \, e g x + e f + d g\right)} \sqrt{-e g} \sqrt{e x + d} \sqrt{g x + f}}{2 \, {\left(e^{2} g^{2} x^{2} + d e f g + {\left(e^{2} f g + d e g^{2}\right)} x\right)}}\right) - 2 \, {\left(48 \, c e^{4} g^{4} x^{3} - 105 \, c e^{4} f^{3} g + 5 \, {\left(29 \, c d e^{3} + 24 \, b e^{4}\right)} f^{2} g^{2} - {\left(15 \, c d^{2} e^{2} + 176 \, b d e^{3} + 144 \, a e^{4}\right)} f g^{3} - 3 \, {\left(3 \, c d^{3} e - 8 \, b d^{2} e^{2} - 80 \, a d e^{3}\right)} g^{4} - 8 \, {\left(7 \, c e^{4} f g^{3} - {\left(9 \, c d e^{3} + 8 \, b e^{4}\right)} g^{4}\right)} x^{2} + 2 \, {\left(35 \, c e^{4} f^{2} g^{2} - 2 \, {\left(23 \, c d e^{3} + 20 \, b e^{4}\right)} f g^{3} + {\left(3 \, c d^{2} e^{2} + 56 \, b d e^{3} + 48 \, a e^{4}\right)} g^{4}\right)} x\right)} \sqrt{e x + d} \sqrt{g x + f}}{384 \, e^{3} g^{5}}\right]"," ",0,"[1/768*(3*(35*c*e^4*f^4 - 20*(3*c*d*e^3 + 2*b*e^4)*f^3*g + 6*(3*c*d^2*e^2 + 12*b*d*e^3 + 8*a*e^4)*f^2*g^2 + 4*(c*d^3*e - 6*b*d^2*e^2 - 24*a*d*e^3)*f*g^3 + (3*c*d^4 - 8*b*d^3*e + 48*a*d^2*e^2)*g^4)*sqrt(e*g)*log(8*e^2*g^2*x^2 + e^2*f^2 + 6*d*e*f*g + d^2*g^2 + 4*(2*e*g*x + e*f + d*g)*sqrt(e*g)*sqrt(e*x + d)*sqrt(g*x + f) + 8*(e^2*f*g + d*e*g^2)*x) + 4*(48*c*e^4*g^4*x^3 - 105*c*e^4*f^3*g + 5*(29*c*d*e^3 + 24*b*e^4)*f^2*g^2 - (15*c*d^2*e^2 + 176*b*d*e^3 + 144*a*e^4)*f*g^3 - 3*(3*c*d^3*e - 8*b*d^2*e^2 - 80*a*d*e^3)*g^4 - 8*(7*c*e^4*f*g^3 - (9*c*d*e^3 + 8*b*e^4)*g^4)*x^2 + 2*(35*c*e^4*f^2*g^2 - 2*(23*c*d*e^3 + 20*b*e^4)*f*g^3 + (3*c*d^2*e^2 + 56*b*d*e^3 + 48*a*e^4)*g^4)*x)*sqrt(e*x + d)*sqrt(g*x + f))/(e^3*g^5), -1/384*(3*(35*c*e^4*f^4 - 20*(3*c*d*e^3 + 2*b*e^4)*f^3*g + 6*(3*c*d^2*e^2 + 12*b*d*e^3 + 8*a*e^4)*f^2*g^2 + 4*(c*d^3*e - 6*b*d^2*e^2 - 24*a*d*e^3)*f*g^3 + (3*c*d^4 - 8*b*d^3*e + 48*a*d^2*e^2)*g^4)*sqrt(-e*g)*arctan(1/2*(2*e*g*x + e*f + d*g)*sqrt(-e*g)*sqrt(e*x + d)*sqrt(g*x + f)/(e^2*g^2*x^2 + d*e*f*g + (e^2*f*g + d*e*g^2)*x)) - 2*(48*c*e^4*g^4*x^3 - 105*c*e^4*f^3*g + 5*(29*c*d*e^3 + 24*b*e^4)*f^2*g^2 - (15*c*d^2*e^2 + 176*b*d*e^3 + 144*a*e^4)*f*g^3 - 3*(3*c*d^3*e - 8*b*d^2*e^2 - 80*a*d*e^3)*g^4 - 8*(7*c*e^4*f*g^3 - (9*c*d*e^3 + 8*b*e^4)*g^4)*x^2 + 2*(35*c*e^4*f^2*g^2 - 2*(23*c*d*e^3 + 20*b*e^4)*f*g^3 + (3*c*d^2*e^2 + 56*b*d*e^3 + 48*a*e^4)*g^4)*x)*sqrt(e*x + d)*sqrt(g*x + f))/(e^3*g^5)]","A",0
836,1,576,0,0.521955," ","integrate((e*x+d)^(1/2)*(c*x^2+b*x+a)/(g*x+f)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, c e^{3} f^{3} - 3 \, {\left(c d e^{2} + 2 \, b e^{3}\right)} f^{2} g - {\left(c d^{2} e - 4 \, b d e^{2} - 8 \, a e^{3}\right)} f g^{2} - {\left(c d^{3} - 2 \, b d^{2} e + 8 \, a d e^{2}\right)} g^{3}\right)} \sqrt{e g} \log\left(8 \, e^{2} g^{2} x^{2} + e^{2} f^{2} + 6 \, d e f g + d^{2} g^{2} + 4 \, {\left(2 \, e g x + e f + d g\right)} \sqrt{e g} \sqrt{e x + d} \sqrt{g x + f} + 8 \, {\left(e^{2} f g + d e g^{2}\right)} x\right) - 4 \, {\left(8 \, c e^{3} g^{3} x^{2} + 15 \, c e^{3} f^{2} g - 2 \, {\left(2 \, c d e^{2} + 9 \, b e^{3}\right)} f g^{2} - 3 \, {\left(c d^{2} e - 2 \, b d e^{2} - 8 \, a e^{3}\right)} g^{3} - 2 \, {\left(5 \, c e^{3} f g^{2} - {\left(c d e^{2} + 6 \, b e^{3}\right)} g^{3}\right)} x\right)} \sqrt{e x + d} \sqrt{g x + f}}{96 \, e^{3} g^{4}}, \frac{3 \, {\left(5 \, c e^{3} f^{3} - 3 \, {\left(c d e^{2} + 2 \, b e^{3}\right)} f^{2} g - {\left(c d^{2} e - 4 \, b d e^{2} - 8 \, a e^{3}\right)} f g^{2} - {\left(c d^{3} - 2 \, b d^{2} e + 8 \, a d e^{2}\right)} g^{3}\right)} \sqrt{-e g} \arctan\left(\frac{{\left(2 \, e g x + e f + d g\right)} \sqrt{-e g} \sqrt{e x + d} \sqrt{g x + f}}{2 \, {\left(e^{2} g^{2} x^{2} + d e f g + {\left(e^{2} f g + d e g^{2}\right)} x\right)}}\right) + 2 \, {\left(8 \, c e^{3} g^{3} x^{2} + 15 \, c e^{3} f^{2} g - 2 \, {\left(2 \, c d e^{2} + 9 \, b e^{3}\right)} f g^{2} - 3 \, {\left(c d^{2} e - 2 \, b d e^{2} - 8 \, a e^{3}\right)} g^{3} - 2 \, {\left(5 \, c e^{3} f g^{2} - {\left(c d e^{2} + 6 \, b e^{3}\right)} g^{3}\right)} x\right)} \sqrt{e x + d} \sqrt{g x + f}}{48 \, e^{3} g^{4}}\right]"," ",0,"[-1/96*(3*(5*c*e^3*f^3 - 3*(c*d*e^2 + 2*b*e^3)*f^2*g - (c*d^2*e - 4*b*d*e^2 - 8*a*e^3)*f*g^2 - (c*d^3 - 2*b*d^2*e + 8*a*d*e^2)*g^3)*sqrt(e*g)*log(8*e^2*g^2*x^2 + e^2*f^2 + 6*d*e*f*g + d^2*g^2 + 4*(2*e*g*x + e*f + d*g)*sqrt(e*g)*sqrt(e*x + d)*sqrt(g*x + f) + 8*(e^2*f*g + d*e*g^2)*x) - 4*(8*c*e^3*g^3*x^2 + 15*c*e^3*f^2*g - 2*(2*c*d*e^2 + 9*b*e^3)*f*g^2 - 3*(c*d^2*e - 2*b*d*e^2 - 8*a*e^3)*g^3 - 2*(5*c*e^3*f*g^2 - (c*d*e^2 + 6*b*e^3)*g^3)*x)*sqrt(e*x + d)*sqrt(g*x + f))/(e^3*g^4), 1/48*(3*(5*c*e^3*f^3 - 3*(c*d*e^2 + 2*b*e^3)*f^2*g - (c*d^2*e - 4*b*d*e^2 - 8*a*e^3)*f*g^2 - (c*d^3 - 2*b*d^2*e + 8*a*d*e^2)*g^3)*sqrt(-e*g)*arctan(1/2*(2*e*g*x + e*f + d*g)*sqrt(-e*g)*sqrt(e*x + d)*sqrt(g*x + f)/(e^2*g^2*x^2 + d*e*f*g + (e^2*f*g + d*e*g^2)*x)) + 2*(8*c*e^3*g^3*x^2 + 15*c*e^3*f^2*g - 2*(2*c*d*e^2 + 9*b*e^3)*f*g^2 - 3*(c*d^2*e - 2*b*d*e^2 - 8*a*e^3)*g^3 - 2*(5*c*e^3*f*g^2 - (c*d*e^2 + 6*b*e^3)*g^3)*x)*sqrt(e*x + d)*sqrt(g*x + f))/(e^3*g^4)]","A",0
837,1,380,0,0.508922," ","integrate((c*x^2+b*x+a)/(e*x+d)^(1/2)/(g*x+f)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(3 \, c e^{2} f^{2} + 2 \, {\left(c d e - 2 \, b e^{2}\right)} f g + {\left(3 \, c d^{2} - 4 \, b d e + 8 \, a e^{2}\right)} g^{2}\right)} \sqrt{e g} \log\left(8 \, e^{2} g^{2} x^{2} + e^{2} f^{2} + 6 \, d e f g + d^{2} g^{2} + 4 \, {\left(2 \, e g x + e f + d g\right)} \sqrt{e g} \sqrt{e x + d} \sqrt{g x + f} + 8 \, {\left(e^{2} f g + d e g^{2}\right)} x\right) + 4 \, {\left(2 \, c e^{2} g^{2} x - 3 \, c e^{2} f g - {\left(3 \, c d e - 4 \, b e^{2}\right)} g^{2}\right)} \sqrt{e x + d} \sqrt{g x + f}}{16 \, e^{3} g^{3}}, -\frac{{\left(3 \, c e^{2} f^{2} + 2 \, {\left(c d e - 2 \, b e^{2}\right)} f g + {\left(3 \, c d^{2} - 4 \, b d e + 8 \, a e^{2}\right)} g^{2}\right)} \sqrt{-e g} \arctan\left(\frac{{\left(2 \, e g x + e f + d g\right)} \sqrt{-e g} \sqrt{e x + d} \sqrt{g x + f}}{2 \, {\left(e^{2} g^{2} x^{2} + d e f g + {\left(e^{2} f g + d e g^{2}\right)} x\right)}}\right) - 2 \, {\left(2 \, c e^{2} g^{2} x - 3 \, c e^{2} f g - {\left(3 \, c d e - 4 \, b e^{2}\right)} g^{2}\right)} \sqrt{e x + d} \sqrt{g x + f}}{8 \, e^{3} g^{3}}\right]"," ",0,"[1/16*((3*c*e^2*f^2 + 2*(c*d*e - 2*b*e^2)*f*g + (3*c*d^2 - 4*b*d*e + 8*a*e^2)*g^2)*sqrt(e*g)*log(8*e^2*g^2*x^2 + e^2*f^2 + 6*d*e*f*g + d^2*g^2 + 4*(2*e*g*x + e*f + d*g)*sqrt(e*g)*sqrt(e*x + d)*sqrt(g*x + f) + 8*(e^2*f*g + d*e*g^2)*x) + 4*(2*c*e^2*g^2*x - 3*c*e^2*f*g - (3*c*d*e - 4*b*e^2)*g^2)*sqrt(e*x + d)*sqrt(g*x + f))/(e^3*g^3), -1/8*((3*c*e^2*f^2 + 2*(c*d*e - 2*b*e^2)*f*g + (3*c*d^2 - 4*b*d*e + 8*a*e^2)*g^2)*sqrt(-e*g)*arctan(1/2*(2*e*g*x + e*f + d*g)*sqrt(-e*g)*sqrt(e*x + d)*sqrt(g*x + f)/(e^2*g^2*x^2 + d*e*f*g + (e^2*f*g + d*e*g^2)*x)) - 2*(2*c*e^2*g^2*x - 3*c*e^2*f*g - (3*c*d*e - 4*b*e^2)*g^2)*sqrt(e*x + d)*sqrt(g*x + f))/(e^3*g^3)]","A",0
838,1,588,0,1.435795," ","integrate((c*x^2+b*x+a)/(e*x+d)^(3/2)/(g*x+f)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(c d e^{2} f^{2} + 2 \, {\left(c d^{2} e - b d e^{2}\right)} f g - {\left(3 \, c d^{3} - 2 \, b d^{2} e\right)} g^{2} + {\left(c e^{3} f^{2} + 2 \, {\left(c d e^{2} - b e^{3}\right)} f g - {\left(3 \, c d^{2} e - 2 \, b d e^{2}\right)} g^{2}\right)} x\right)} \sqrt{e g} \log\left(8 \, e^{2} g^{2} x^{2} + e^{2} f^{2} + 6 \, d e f g + d^{2} g^{2} + 4 \, {\left(2 \, e g x + e f + d g\right)} \sqrt{e g} \sqrt{e x + d} \sqrt{g x + f} + 8 \, {\left(e^{2} f g + d e g^{2}\right)} x\right) - 4 \, {\left(c d e^{2} f g - {\left(3 \, c d^{2} e - 2 \, b d e^{2} + 2 \, a e^{3}\right)} g^{2} + {\left(c e^{3} f g - c d e^{2} g^{2}\right)} x\right)} \sqrt{e x + d} \sqrt{g x + f}}{4 \, {\left(d e^{4} f g^{2} - d^{2} e^{3} g^{3} + {\left(e^{5} f g^{2} - d e^{4} g^{3}\right)} x\right)}}, \frac{{\left(c d e^{2} f^{2} + 2 \, {\left(c d^{2} e - b d e^{2}\right)} f g - {\left(3 \, c d^{3} - 2 \, b d^{2} e\right)} g^{2} + {\left(c e^{3} f^{2} + 2 \, {\left(c d e^{2} - b e^{3}\right)} f g - {\left(3 \, c d^{2} e - 2 \, b d e^{2}\right)} g^{2}\right)} x\right)} \sqrt{-e g} \arctan\left(\frac{{\left(2 \, e g x + e f + d g\right)} \sqrt{-e g} \sqrt{e x + d} \sqrt{g x + f}}{2 \, {\left(e^{2} g^{2} x^{2} + d e f g + {\left(e^{2} f g + d e g^{2}\right)} x\right)}}\right) + 2 \, {\left(c d e^{2} f g - {\left(3 \, c d^{2} e - 2 \, b d e^{2} + 2 \, a e^{3}\right)} g^{2} + {\left(c e^{3} f g - c d e^{2} g^{2}\right)} x\right)} \sqrt{e x + d} \sqrt{g x + f}}{2 \, {\left(d e^{4} f g^{2} - d^{2} e^{3} g^{3} + {\left(e^{5} f g^{2} - d e^{4} g^{3}\right)} x\right)}}\right]"," ",0,"[-1/4*((c*d*e^2*f^2 + 2*(c*d^2*e - b*d*e^2)*f*g - (3*c*d^3 - 2*b*d^2*e)*g^2 + (c*e^3*f^2 + 2*(c*d*e^2 - b*e^3)*f*g - (3*c*d^2*e - 2*b*d*e^2)*g^2)*x)*sqrt(e*g)*log(8*e^2*g^2*x^2 + e^2*f^2 + 6*d*e*f*g + d^2*g^2 + 4*(2*e*g*x + e*f + d*g)*sqrt(e*g)*sqrt(e*x + d)*sqrt(g*x + f) + 8*(e^2*f*g + d*e*g^2)*x) - 4*(c*d*e^2*f*g - (3*c*d^2*e - 2*b*d*e^2 + 2*a*e^3)*g^2 + (c*e^3*f*g - c*d*e^2*g^2)*x)*sqrt(e*x + d)*sqrt(g*x + f))/(d*e^4*f*g^2 - d^2*e^3*g^3 + (e^5*f*g^2 - d*e^4*g^3)*x), 1/2*((c*d*e^2*f^2 + 2*(c*d^2*e - b*d*e^2)*f*g - (3*c*d^3 - 2*b*d^2*e)*g^2 + (c*e^3*f^2 + 2*(c*d*e^2 - b*e^3)*f*g - (3*c*d^2*e - 2*b*d*e^2)*g^2)*x)*sqrt(-e*g)*arctan(1/2*(2*e*g*x + e*f + d*g)*sqrt(-e*g)*sqrt(e*x + d)*sqrt(g*x + f)/(e^2*g^2*x^2 + d*e*f*g + (e^2*f*g + d*e*g^2)*x)) + 2*(c*d*e^2*f*g - (3*c*d^2*e - 2*b*d*e^2 + 2*a*e^3)*g^2 + (c*e^3*f*g - c*d*e^2*g^2)*x)*sqrt(e*x + d)*sqrt(g*x + f))/(d*e^4*f*g^2 - d^2*e^3*g^3 + (e^5*f*g^2 - d*e^4*g^3)*x)]","B",0
839,1,792,0,3.552552," ","integrate((c*x^2+b*x+a)/(e*x+d)^(5/2)/(g*x+f)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(c d^{2} e^{2} f^{2} - 2 \, c d^{3} e f g + c d^{4} g^{2} + {\left(c e^{4} f^{2} - 2 \, c d e^{3} f g + c d^{2} e^{2} g^{2}\right)} x^{2} + 2 \, {\left(c d e^{3} f^{2} - 2 \, c d^{2} e^{2} f g + c d^{3} e g^{2}\right)} x\right)} \sqrt{e g} \log\left(8 \, e^{2} g^{2} x^{2} + e^{2} f^{2} + 6 \, d e f g + d^{2} g^{2} + 4 \, {\left(2 \, e g x + e f + d g\right)} \sqrt{e g} \sqrt{e x + d} \sqrt{g x + f} + 8 \, {\left(e^{2} f g + d e g^{2}\right)} x\right) + 4 \, {\left({\left(5 \, c d^{2} e^{2} - 2 \, b d e^{3} - a e^{4}\right)} f g - 3 \, {\left(c d^{3} e - a d e^{3}\right)} g^{2} + {\left(3 \, {\left(2 \, c d e^{3} - b e^{4}\right)} f g - {\left(4 \, c d^{2} e^{2} - b d e^{3} - 2 \, a e^{4}\right)} g^{2}\right)} x\right)} \sqrt{e x + d} \sqrt{g x + f}}{6 \, {\left(d^{2} e^{5} f^{2} g - 2 \, d^{3} e^{4} f g^{2} + d^{4} e^{3} g^{3} + {\left(e^{7} f^{2} g - 2 \, d e^{6} f g^{2} + d^{2} e^{5} g^{3}\right)} x^{2} + 2 \, {\left(d e^{6} f^{2} g - 2 \, d^{2} e^{5} f g^{2} + d^{3} e^{4} g^{3}\right)} x\right)}}, -\frac{3 \, {\left(c d^{2} e^{2} f^{2} - 2 \, c d^{3} e f g + c d^{4} g^{2} + {\left(c e^{4} f^{2} - 2 \, c d e^{3} f g + c d^{2} e^{2} g^{2}\right)} x^{2} + 2 \, {\left(c d e^{3} f^{2} - 2 \, c d^{2} e^{2} f g + c d^{3} e g^{2}\right)} x\right)} \sqrt{-e g} \arctan\left(\frac{{\left(2 \, e g x + e f + d g\right)} \sqrt{-e g} \sqrt{e x + d} \sqrt{g x + f}}{2 \, {\left(e^{2} g^{2} x^{2} + d e f g + {\left(e^{2} f g + d e g^{2}\right)} x\right)}}\right) - 2 \, {\left({\left(5 \, c d^{2} e^{2} - 2 \, b d e^{3} - a e^{4}\right)} f g - 3 \, {\left(c d^{3} e - a d e^{3}\right)} g^{2} + {\left(3 \, {\left(2 \, c d e^{3} - b e^{4}\right)} f g - {\left(4 \, c d^{2} e^{2} - b d e^{3} - 2 \, a e^{4}\right)} g^{2}\right)} x\right)} \sqrt{e x + d} \sqrt{g x + f}}{3 \, {\left(d^{2} e^{5} f^{2} g - 2 \, d^{3} e^{4} f g^{2} + d^{4} e^{3} g^{3} + {\left(e^{7} f^{2} g - 2 \, d e^{6} f g^{2} + d^{2} e^{5} g^{3}\right)} x^{2} + 2 \, {\left(d e^{6} f^{2} g - 2 \, d^{2} e^{5} f g^{2} + d^{3} e^{4} g^{3}\right)} x\right)}}\right]"," ",0,"[1/6*(3*(c*d^2*e^2*f^2 - 2*c*d^3*e*f*g + c*d^4*g^2 + (c*e^4*f^2 - 2*c*d*e^3*f*g + c*d^2*e^2*g^2)*x^2 + 2*(c*d*e^3*f^2 - 2*c*d^2*e^2*f*g + c*d^3*e*g^2)*x)*sqrt(e*g)*log(8*e^2*g^2*x^2 + e^2*f^2 + 6*d*e*f*g + d^2*g^2 + 4*(2*e*g*x + e*f + d*g)*sqrt(e*g)*sqrt(e*x + d)*sqrt(g*x + f) + 8*(e^2*f*g + d*e*g^2)*x) + 4*((5*c*d^2*e^2 - 2*b*d*e^3 - a*e^4)*f*g - 3*(c*d^3*e - a*d*e^3)*g^2 + (3*(2*c*d*e^3 - b*e^4)*f*g - (4*c*d^2*e^2 - b*d*e^3 - 2*a*e^4)*g^2)*x)*sqrt(e*x + d)*sqrt(g*x + f))/(d^2*e^5*f^2*g - 2*d^3*e^4*f*g^2 + d^4*e^3*g^3 + (e^7*f^2*g - 2*d*e^6*f*g^2 + d^2*e^5*g^3)*x^2 + 2*(d*e^6*f^2*g - 2*d^2*e^5*f*g^2 + d^3*e^4*g^3)*x), -1/3*(3*(c*d^2*e^2*f^2 - 2*c*d^3*e*f*g + c*d^4*g^2 + (c*e^4*f^2 - 2*c*d*e^3*f*g + c*d^2*e^2*g^2)*x^2 + 2*(c*d*e^3*f^2 - 2*c*d^2*e^2*f*g + c*d^3*e*g^2)*x)*sqrt(-e*g)*arctan(1/2*(2*e*g*x + e*f + d*g)*sqrt(-e*g)*sqrt(e*x + d)*sqrt(g*x + f)/(e^2*g^2*x^2 + d*e*f*g + (e^2*f*g + d*e*g^2)*x)) - 2*((5*c*d^2*e^2 - 2*b*d*e^3 - a*e^4)*f*g - 3*(c*d^3*e - a*d*e^3)*g^2 + (3*(2*c*d*e^3 - b*e^4)*f*g - (4*c*d^2*e^2 - b*d*e^3 - 2*a*e^4)*g^2)*x)*sqrt(e*x + d)*sqrt(g*x + f))/(d^2*e^5*f^2*g - 2*d^3*e^4*f*g^2 + d^4*e^3*g^3 + (e^7*f^2*g - 2*d*e^6*f*g^2 + d^2*e^5*g^3)*x^2 + 2*(d*e^6*f^2*g - 2*d^2*e^5*f*g^2 + d^3*e^4*g^3)*x)]","B",0
840,1,353,0,10.805803," ","integrate((c*x^2+b*x+a)/(e*x+d)^(7/2)/(g*x+f)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(15 \, a d^{2} g^{2} + {\left(8 \, c d^{2} + 2 \, b d e + 3 \, a e^{2}\right)} f^{2} - 10 \, {\left(b d^{2} + a d e\right)} f g + {\left(15 \, c e^{2} f^{2} - 10 \, {\left(c d e + b e^{2}\right)} f g + {\left(3 \, c d^{2} + 2 \, b d e + 8 \, a e^{2}\right)} g^{2}\right)} x^{2} + {\left(5 \, {\left(4 \, c d e + b e^{2}\right)} f^{2} - 2 \, {\left(2 \, c d^{2} + 13 \, b d e + 2 \, a e^{2}\right)} f g + 5 \, {\left(b d^{2} + 4 \, a d e\right)} g^{2}\right)} x\right)} \sqrt{e x + d} \sqrt{g x + f}}{15 \, {\left(d^{3} e^{3} f^{3} - 3 \, d^{4} e^{2} f^{2} g + 3 \, d^{5} e f g^{2} - d^{6} g^{3} + {\left(e^{6} f^{3} - 3 \, d e^{5} f^{2} g + 3 \, d^{2} e^{4} f g^{2} - d^{3} e^{3} g^{3}\right)} x^{3} + 3 \, {\left(d e^{5} f^{3} - 3 \, d^{2} e^{4} f^{2} g + 3 \, d^{3} e^{3} f g^{2} - d^{4} e^{2} g^{3}\right)} x^{2} + 3 \, {\left(d^{2} e^{4} f^{3} - 3 \, d^{3} e^{3} f^{2} g + 3 \, d^{4} e^{2} f g^{2} - d^{5} e g^{3}\right)} x\right)}}"," ",0,"-2/15*(15*a*d^2*g^2 + (8*c*d^2 + 2*b*d*e + 3*a*e^2)*f^2 - 10*(b*d^2 + a*d*e)*f*g + (15*c*e^2*f^2 - 10*(c*d*e + b*e^2)*f*g + (3*c*d^2 + 2*b*d*e + 8*a*e^2)*g^2)*x^2 + (5*(4*c*d*e + b*e^2)*f^2 - 2*(2*c*d^2 + 13*b*d*e + 2*a*e^2)*f*g + 5*(b*d^2 + 4*a*d*e)*g^2)*x)*sqrt(e*x + d)*sqrt(g*x + f)/(d^3*e^3*f^3 - 3*d^4*e^2*f^2*g + 3*d^5*e*f*g^2 - d^6*g^3 + (e^6*f^3 - 3*d*e^5*f^2*g + 3*d^2*e^4*f*g^2 - d^3*e^3*g^3)*x^3 + 3*(d*e^5*f^3 - 3*d^2*e^4*f^2*g + 3*d^3*e^3*f*g^2 - d^4*e^2*g^3)*x^2 + 3*(d^2*e^4*f^3 - 3*d^3*e^3*f^2*g + 3*d^4*e^2*f*g^2 - d^5*e*g^3)*x)","A",0
841,1,641,0,36.000857," ","integrate((c*x^2+b*x+a)/(e*x+d)^(9/2)/(g*x+f)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(105 \, a d^{3} g^{3} - {\left(8 \, c d^{2} e + 6 \, b d e^{2} + 15 \, a e^{3}\right)} f^{3} + 7 \, {\left(8 \, c d^{3} + 4 \, b d^{2} e + 9 \, a d e^{2}\right)} f^{2} g - 35 \, {\left(2 \, b d^{3} + 3 \, a d^{2} e\right)} f g^{2} + 2 \, {\left(35 \, c e^{3} f^{2} g - 14 \, {\left(c d e^{2} + 2 \, b e^{3}\right)} f g^{2} + {\left(3 \, c d^{2} e + 4 \, b d e^{2} + 24 \, a e^{3}\right)} g^{3}\right)} x^{3} - {\left(35 \, c e^{3} f^{3} - 7 \, {\left(37 \, c d e^{2} + 4 \, b e^{3}\right)} f^{2} g + {\left(101 \, c d^{2} e + 200 \, b d e^{2} + 24 \, a e^{3}\right)} f g^{2} - 7 \, {\left(3 \, c d^{3} + 4 \, b d^{2} e + 24 \, a d e^{2}\right)} g^{3}\right)} x^{2} - {\left(7 \, {\left(4 \, c d e^{2} + 3 \, b e^{3}\right)} f^{3} - {\left(200 \, c d^{2} e + 101 \, b d e^{2} + 18 \, a e^{3}\right)} f^{2} g + 7 \, {\left(4 \, c d^{3} + 37 \, b d^{2} e + 12 \, a d e^{2}\right)} f g^{2} - 35 \, {\left(b d^{3} + 6 \, a d^{2} e\right)} g^{3}\right)} x\right)} \sqrt{e x + d} \sqrt{g x + f}}{105 \, {\left(d^{4} e^{4} f^{4} - 4 \, d^{5} e^{3} f^{3} g + 6 \, d^{6} e^{2} f^{2} g^{2} - 4 \, d^{7} e f g^{3} + d^{8} g^{4} + {\left(e^{8} f^{4} - 4 \, d e^{7} f^{3} g + 6 \, d^{2} e^{6} f^{2} g^{2} - 4 \, d^{3} e^{5} f g^{3} + d^{4} e^{4} g^{4}\right)} x^{4} + 4 \, {\left(d e^{7} f^{4} - 4 \, d^{2} e^{6} f^{3} g + 6 \, d^{3} e^{5} f^{2} g^{2} - 4 \, d^{4} e^{4} f g^{3} + d^{5} e^{3} g^{4}\right)} x^{3} + 6 \, {\left(d^{2} e^{6} f^{4} - 4 \, d^{3} e^{5} f^{3} g + 6 \, d^{4} e^{4} f^{2} g^{2} - 4 \, d^{5} e^{3} f g^{3} + d^{6} e^{2} g^{4}\right)} x^{2} + 4 \, {\left(d^{3} e^{5} f^{4} - 4 \, d^{4} e^{4} f^{3} g + 6 \, d^{5} e^{3} f^{2} g^{2} - 4 \, d^{6} e^{2} f g^{3} + d^{7} e g^{4}\right)} x\right)}}"," ",0,"2/105*(105*a*d^3*g^3 - (8*c*d^2*e + 6*b*d*e^2 + 15*a*e^3)*f^3 + 7*(8*c*d^3 + 4*b*d^2*e + 9*a*d*e^2)*f^2*g - 35*(2*b*d^3 + 3*a*d^2*e)*f*g^2 + 2*(35*c*e^3*f^2*g - 14*(c*d*e^2 + 2*b*e^3)*f*g^2 + (3*c*d^2*e + 4*b*d*e^2 + 24*a*e^3)*g^3)*x^3 - (35*c*e^3*f^3 - 7*(37*c*d*e^2 + 4*b*e^3)*f^2*g + (101*c*d^2*e + 200*b*d*e^2 + 24*a*e^3)*f*g^2 - 7*(3*c*d^3 + 4*b*d^2*e + 24*a*d*e^2)*g^3)*x^2 - (7*(4*c*d*e^2 + 3*b*e^3)*f^3 - (200*c*d^2*e + 101*b*d*e^2 + 18*a*e^3)*f^2*g + 7*(4*c*d^3 + 37*b*d^2*e + 12*a*d*e^2)*f*g^2 - 35*(b*d^3 + 6*a*d^2*e)*g^3)*x)*sqrt(e*x + d)*sqrt(g*x + f)/(d^4*e^4*f^4 - 4*d^5*e^3*f^3*g + 6*d^6*e^2*f^2*g^2 - 4*d^7*e*f*g^3 + d^8*g^4 + (e^8*f^4 - 4*d*e^7*f^3*g + 6*d^2*e^6*f^2*g^2 - 4*d^3*e^5*f*g^3 + d^4*e^4*g^4)*x^4 + 4*(d*e^7*f^4 - 4*d^2*e^6*f^3*g + 6*d^3*e^5*f^2*g^2 - 4*d^4*e^4*f*g^3 + d^5*e^3*g^4)*x^3 + 6*(d^2*e^6*f^4 - 4*d^3*e^5*f^3*g + 6*d^4*e^4*f^2*g^2 - 4*d^5*e^3*f*g^3 + d^6*e^2*g^4)*x^2 + 4*(d^3*e^5*f^4 - 4*d^4*e^4*f^3*g + 6*d^5*e^3*f^2*g^2 - 4*d^6*e^2*f*g^3 + d^7*e*g^4)*x)","B",0
842,1,580,0,0.980380," ","integrate((e*x+d)^(1/2)*(c*x^2+b*x+a)/(f*x+e)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(15 \, c e^{5} - {\left(c d^{2} e - 4 \, b d e^{2} - 8 \, a e^{3}\right)} f^{2} - 6 \, {\left(c d e^{3} + 2 \, b e^{4}\right)} f + {\left(15 \, c e^{4} f - {\left(c d^{2} - 4 \, b d e - 8 \, a e^{2}\right)} f^{3} - 6 \, {\left(c d e^{2} + 2 \, b e^{3}\right)} f^{2}\right)} x\right)} \sqrt{e f} \log\left(8 \, e^{2} f^{2} x^{2} + e^{4} + 6 \, d e^{2} f + d^{2} f^{2} + 4 \, {\left(2 \, e f x + e^{2} + d f\right)} \sqrt{e f} \sqrt{e x + d} \sqrt{f x + e} + 8 \, {\left(e^{3} f + d e f^{2}\right)} x\right) + 4 \, {\left(2 \, c e^{2} f^{3} x^{2} - 15 \, c e^{4} f - 8 \, a e^{2} f^{3} + {\left(c d e^{2} + 12 \, b e^{3}\right)} f^{2} - {\left(5 \, c e^{3} f^{2} - {\left(c d e + 4 \, b e^{2}\right)} f^{3}\right)} x\right)} \sqrt{e x + d} \sqrt{f x + e}}{16 \, {\left(e^{2} f^{5} x + e^{3} f^{4}\right)}}, -\frac{{\left(15 \, c e^{5} - {\left(c d^{2} e - 4 \, b d e^{2} - 8 \, a e^{3}\right)} f^{2} - 6 \, {\left(c d e^{3} + 2 \, b e^{4}\right)} f + {\left(15 \, c e^{4} f - {\left(c d^{2} - 4 \, b d e - 8 \, a e^{2}\right)} f^{3} - 6 \, {\left(c d e^{2} + 2 \, b e^{3}\right)} f^{2}\right)} x\right)} \sqrt{-e f} \arctan\left(\frac{{\left(2 \, e f x + e^{2} + d f\right)} \sqrt{-e f} \sqrt{e x + d} \sqrt{f x + e}}{2 \, {\left(e^{2} f^{2} x^{2} + d e^{2} f + {\left(e^{3} f + d e f^{2}\right)} x\right)}}\right) - 2 \, {\left(2 \, c e^{2} f^{3} x^{2} - 15 \, c e^{4} f - 8 \, a e^{2} f^{3} + {\left(c d e^{2} + 12 \, b e^{3}\right)} f^{2} - {\left(5 \, c e^{3} f^{2} - {\left(c d e + 4 \, b e^{2}\right)} f^{3}\right)} x\right)} \sqrt{e x + d} \sqrt{f x + e}}{8 \, {\left(e^{2} f^{5} x + e^{3} f^{4}\right)}}\right]"," ",0,"[1/16*((15*c*e^5 - (c*d^2*e - 4*b*d*e^2 - 8*a*e^3)*f^2 - 6*(c*d*e^3 + 2*b*e^4)*f + (15*c*e^4*f - (c*d^2 - 4*b*d*e - 8*a*e^2)*f^3 - 6*(c*d*e^2 + 2*b*e^3)*f^2)*x)*sqrt(e*f)*log(8*e^2*f^2*x^2 + e^4 + 6*d*e^2*f + d^2*f^2 + 4*(2*e*f*x + e^2 + d*f)*sqrt(e*f)*sqrt(e*x + d)*sqrt(f*x + e) + 8*(e^3*f + d*e*f^2)*x) + 4*(2*c*e^2*f^3*x^2 - 15*c*e^4*f - 8*a*e^2*f^3 + (c*d*e^2 + 12*b*e^3)*f^2 - (5*c*e^3*f^2 - (c*d*e + 4*b*e^2)*f^3)*x)*sqrt(e*x + d)*sqrt(f*x + e))/(e^2*f^5*x + e^3*f^4), -1/8*((15*c*e^5 - (c*d^2*e - 4*b*d*e^2 - 8*a*e^3)*f^2 - 6*(c*d*e^3 + 2*b*e^4)*f + (15*c*e^4*f - (c*d^2 - 4*b*d*e - 8*a*e^2)*f^3 - 6*(c*d*e^2 + 2*b*e^3)*f^2)*x)*sqrt(-e*f)*arctan(1/2*(2*e*f*x + e^2 + d*f)*sqrt(-e*f)*sqrt(e*x + d)*sqrt(f*x + e)/(e^2*f^2*x^2 + d*e^2*f + (e^3*f + d*e*f^2)*x)) - 2*(2*c*e^2*f^3*x^2 - 15*c*e^4*f - 8*a*e^2*f^3 + (c*d*e^2 + 12*b*e^3)*f^2 - (5*c*e^3*f^2 - (c*d*e + 4*b*e^2)*f^3)*x)*sqrt(e*x + d)*sqrt(f*x + e))/(e^2*f^5*x + e^3*f^4)]","A",0
843,1,546,0,0.463267," ","integrate((e*x+d)^(3/2)*(8*e^2*x^2+20*d*e*x+15*d^2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(73 \, b^{4} d^{4} - 236 \, a b^{3} d^{3} e + 288 \, a^{2} b^{2} d^{2} e^{2} - 160 \, a^{3} b d e^{3} + 35 \, a^{4} e^{4}\right)} \sqrt{b e} \log\left(8 \, b^{2} e^{2} x^{2} + b^{2} d^{2} + 6 \, a b d e + a^{2} e^{2} + 4 \, {\left(2 \, b e x + b d + a e\right)} \sqrt{b e} \sqrt{b x + a} \sqrt{e x + d} + 8 \, {\left(b^{2} d e + a b e^{2}\right)} x\right) + 4 \, {\left(48 \, b^{4} e^{4} x^{3} + 501 \, b^{4} d^{3} e - 725 \, a b^{3} d^{2} e^{2} + 445 \, a^{2} b^{2} d e^{3} - 105 \, a^{3} b e^{4} + 8 \, {\left(29 \, b^{4} d e^{3} - 7 \, a b^{3} e^{4}\right)} x^{2} + 2 \, {\left(233 \, b^{4} d^{2} e^{2} - 146 \, a b^{3} d e^{3} + 35 \, a^{2} b^{2} e^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{96 \, b^{5} e}, -\frac{3 \, {\left(73 \, b^{4} d^{4} - 236 \, a b^{3} d^{3} e + 288 \, a^{2} b^{2} d^{2} e^{2} - 160 \, a^{3} b d e^{3} + 35 \, a^{4} e^{4}\right)} \sqrt{-b e} \arctan\left(\frac{{\left(2 \, b e x + b d + a e\right)} \sqrt{-b e} \sqrt{b x + a} \sqrt{e x + d}}{2 \, {\left(b^{2} e^{2} x^{2} + a b d e + {\left(b^{2} d e + a b e^{2}\right)} x\right)}}\right) - 2 \, {\left(48 \, b^{4} e^{4} x^{3} + 501 \, b^{4} d^{3} e - 725 \, a b^{3} d^{2} e^{2} + 445 \, a^{2} b^{2} d e^{3} - 105 \, a^{3} b e^{4} + 8 \, {\left(29 \, b^{4} d e^{3} - 7 \, a b^{3} e^{4}\right)} x^{2} + 2 \, {\left(233 \, b^{4} d^{2} e^{2} - 146 \, a b^{3} d e^{3} + 35 \, a^{2} b^{2} e^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{48 \, b^{5} e}\right]"," ",0,"[1/96*(3*(73*b^4*d^4 - 236*a*b^3*d^3*e + 288*a^2*b^2*d^2*e^2 - 160*a^3*b*d*e^3 + 35*a^4*e^4)*sqrt(b*e)*log(8*b^2*e^2*x^2 + b^2*d^2 + 6*a*b*d*e + a^2*e^2 + 4*(2*b*e*x + b*d + a*e)*sqrt(b*e)*sqrt(b*x + a)*sqrt(e*x + d) + 8*(b^2*d*e + a*b*e^2)*x) + 4*(48*b^4*e^4*x^3 + 501*b^4*d^3*e - 725*a*b^3*d^2*e^2 + 445*a^2*b^2*d*e^3 - 105*a^3*b*e^4 + 8*(29*b^4*d*e^3 - 7*a*b^3*e^4)*x^2 + 2*(233*b^4*d^2*e^2 - 146*a*b^3*d*e^3 + 35*a^2*b^2*e^4)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b^5*e), -1/48*(3*(73*b^4*d^4 - 236*a*b^3*d^3*e + 288*a^2*b^2*d^2*e^2 - 160*a^3*b*d*e^3 + 35*a^4*e^4)*sqrt(-b*e)*arctan(1/2*(2*b*e*x + b*d + a*e)*sqrt(-b*e)*sqrt(b*x + a)*sqrt(e*x + d)/(b^2*e^2*x^2 + a*b*d*e + (b^2*d*e + a*b*e^2)*x)) - 2*(48*b^4*e^4*x^3 + 501*b^4*d^3*e - 725*a*b^3*d^2*e^2 + 445*a^2*b^2*d*e^3 - 105*a^3*b*e^4 + 8*(29*b^4*d*e^3 - 7*a*b^3*e^4)*x^2 + 2*(233*b^4*d^2*e^2 - 146*a*b^3*d*e^3 + 35*a^2*b^2*e^4)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b^5*e)]","A",0
844,1,414,0,0.457123," ","integrate((e*x+d)^(1/2)*(8*e^2*x^2+20*d*e*x+15*d^2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(11 \, b^{3} d^{3} - 24 \, a b^{2} d^{2} e + 18 \, a^{2} b d e^{2} - 5 \, a^{3} e^{3}\right)} \sqrt{b e} \log\left(8 \, b^{2} e^{2} x^{2} + b^{2} d^{2} + 6 \, a b d e + a^{2} e^{2} - 4 \, {\left(2 \, b e x + b d + a e\right)} \sqrt{b e} \sqrt{b x + a} \sqrt{e x + d} + 8 \, {\left(b^{2} d e + a b e^{2}\right)} x\right) - 4 \, {\left(8 \, b^{3} e^{3} x^{2} + 57 \, b^{3} d^{2} e - 49 \, a b^{2} d e^{2} + 15 \, a^{2} b e^{3} + 2 \, {\left(16 \, b^{3} d e^{2} - 5 \, a b^{2} e^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{12 \, b^{4} e}, -\frac{3 \, {\left(11 \, b^{3} d^{3} - 24 \, a b^{2} d^{2} e + 18 \, a^{2} b d e^{2} - 5 \, a^{3} e^{3}\right)} \sqrt{-b e} \arctan\left(\frac{{\left(2 \, b e x + b d + a e\right)} \sqrt{-b e} \sqrt{b x + a} \sqrt{e x + d}}{2 \, {\left(b^{2} e^{2} x^{2} + a b d e + {\left(b^{2} d e + a b e^{2}\right)} x\right)}}\right) - 2 \, {\left(8 \, b^{3} e^{3} x^{2} + 57 \, b^{3} d^{2} e - 49 \, a b^{2} d e^{2} + 15 \, a^{2} b e^{3} + 2 \, {\left(16 \, b^{3} d e^{2} - 5 \, a b^{2} e^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{6 \, b^{4} e}\right]"," ",0,"[-1/12*(3*(11*b^3*d^3 - 24*a*b^2*d^2*e + 18*a^2*b*d*e^2 - 5*a^3*e^3)*sqrt(b*e)*log(8*b^2*e^2*x^2 + b^2*d^2 + 6*a*b*d*e + a^2*e^2 - 4*(2*b*e*x + b*d + a*e)*sqrt(b*e)*sqrt(b*x + a)*sqrt(e*x + d) + 8*(b^2*d*e + a*b*e^2)*x) - 4*(8*b^3*e^3*x^2 + 57*b^3*d^2*e - 49*a*b^2*d*e^2 + 15*a^2*b*e^3 + 2*(16*b^3*d*e^2 - 5*a*b^2*e^3)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b^4*e), -1/6*(3*(11*b^3*d^3 - 24*a*b^2*d^2*e + 18*a^2*b*d*e^2 - 5*a^3*e^3)*sqrt(-b*e)*arctan(1/2*(2*b*e*x + b*d + a*e)*sqrt(-b*e)*sqrt(b*x + a)*sqrt(e*x + d)/(b^2*e^2*x^2 + a*b*d*e + (b^2*d*e + a*b*e^2)*x)) - 2*(8*b^3*e^3*x^2 + 57*b^3*d^2*e - 49*a*b^2*d*e^2 + 15*a^2*b*e^3 + 2*(16*b^3*d*e^2 - 5*a*b^2*e^3)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b^4*e)]","A",0
845,1,308,0,0.545486," ","integrate((8*e^2*x^2+20*d*e*x+15*d^2)/(e*x+d)^(1/2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(8 \, b^{2} d^{2} - 8 \, a b d e + 3 \, a^{2} e^{2}\right)} \sqrt{b e} \log\left(8 \, b^{2} e^{2} x^{2} + b^{2} d^{2} + 6 \, a b d e + a^{2} e^{2} + 4 \, {\left(2 \, b e x + b d + a e\right)} \sqrt{b e} \sqrt{b x + a} \sqrt{e x + d} + 8 \, {\left(b^{2} d e + a b e^{2}\right)} x\right) + 4 \, {\left(2 \, b^{2} e^{2} x + 7 \, b^{2} d e - 3 \, a b e^{2}\right)} \sqrt{b x + a} \sqrt{e x + d}}{2 \, b^{3} e}, -\frac{{\left(8 \, b^{2} d^{2} - 8 \, a b d e + 3 \, a^{2} e^{2}\right)} \sqrt{-b e} \arctan\left(\frac{{\left(2 \, b e x + b d + a e\right)} \sqrt{-b e} \sqrt{b x + a} \sqrt{e x + d}}{2 \, {\left(b^{2} e^{2} x^{2} + a b d e + {\left(b^{2} d e + a b e^{2}\right)} x\right)}}\right) - 2 \, {\left(2 \, b^{2} e^{2} x + 7 \, b^{2} d e - 3 \, a b e^{2}\right)} \sqrt{b x + a} \sqrt{e x + d}}{b^{3} e}\right]"," ",0,"[1/2*((8*b^2*d^2 - 8*a*b*d*e + 3*a^2*e^2)*sqrt(b*e)*log(8*b^2*e^2*x^2 + b^2*d^2 + 6*a*b*d*e + a^2*e^2 + 4*(2*b*e*x + b*d + a*e)*sqrt(b*e)*sqrt(b*x + a)*sqrt(e*x + d) + 8*(b^2*d*e + a*b*e^2)*x) + 4*(2*b^2*e^2*x + 7*b^2*d*e - 3*a*b*e^2)*sqrt(b*x + a)*sqrt(e*x + d))/(b^3*e), -((8*b^2*d^2 - 8*a*b*d*e + 3*a^2*e^2)*sqrt(-b*e)*arctan(1/2*(2*b*e*x + b*d + a*e)*sqrt(-b*e)*sqrt(b*x + a)*sqrt(e*x + d)/(b^2*e^2*x^2 + a*b*d*e + (b^2*d*e + a*b*e^2)*x)) - 2*(2*b^2*e^2*x + 7*b^2*d*e - 3*a*b*e^2)*sqrt(b*x + a)*sqrt(e*x + d))/(b^3*e)]","A",0
846,1,463,0,0.541217," ","integrate((8*e^2*x^2+20*d*e*x+15*d^2)/(e*x+d)^(3/2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{2 \, {\left({\left(2 \, b^{2} d^{3} - 3 \, a b d^{2} e + a^{2} d e^{2} + {\left(2 \, b^{2} d^{2} e - 3 \, a b d e^{2} + a^{2} e^{3}\right)} x\right)} \sqrt{b e} \log\left(8 \, b^{2} e^{2} x^{2} + b^{2} d^{2} + 6 \, a b d e + a^{2} e^{2} - 4 \, {\left(2 \, b e x + b d + a e\right)} \sqrt{b e} \sqrt{b x + a} \sqrt{e x + d} + 8 \, {\left(b^{2} d e + a b e^{2}\right)} x\right) - {\left(7 \, b^{2} d^{2} e - 4 \, a b d e^{2} + 4 \, {\left(b^{2} d e^{2} - a b e^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}\right)}}{b^{3} d^{2} e - a b^{2} d e^{2} + {\left(b^{3} d e^{2} - a b^{2} e^{3}\right)} x}, -\frac{2 \, {\left(2 \, {\left(2 \, b^{2} d^{3} - 3 \, a b d^{2} e + a^{2} d e^{2} + {\left(2 \, b^{2} d^{2} e - 3 \, a b d e^{2} + a^{2} e^{3}\right)} x\right)} \sqrt{-b e} \arctan\left(\frac{{\left(2 \, b e x + b d + a e\right)} \sqrt{-b e} \sqrt{b x + a} \sqrt{e x + d}}{2 \, {\left(b^{2} e^{2} x^{2} + a b d e + {\left(b^{2} d e + a b e^{2}\right)} x\right)}}\right) - {\left(7 \, b^{2} d^{2} e - 4 \, a b d e^{2} + 4 \, {\left(b^{2} d e^{2} - a b e^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}\right)}}{b^{3} d^{2} e - a b^{2} d e^{2} + {\left(b^{3} d e^{2} - a b^{2} e^{3}\right)} x}\right]"," ",0,"[-2*((2*b^2*d^3 - 3*a*b*d^2*e + a^2*d*e^2 + (2*b^2*d^2*e - 3*a*b*d*e^2 + a^2*e^3)*x)*sqrt(b*e)*log(8*b^2*e^2*x^2 + b^2*d^2 + 6*a*b*d*e + a^2*e^2 - 4*(2*b*e*x + b*d + a*e)*sqrt(b*e)*sqrt(b*x + a)*sqrt(e*x + d) + 8*(b^2*d*e + a*b*e^2)*x) - (7*b^2*d^2*e - 4*a*b*d*e^2 + 4*(b^2*d*e^2 - a*b*e^3)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b^3*d^2*e - a*b^2*d*e^2 + (b^3*d*e^2 - a*b^2*e^3)*x), -2*(2*(2*b^2*d^3 - 3*a*b*d^2*e + a^2*d*e^2 + (2*b^2*d^2*e - 3*a*b*d*e^2 + a^2*e^3)*x)*sqrt(-b*e)*arctan(1/2*(2*b*e*x + b*d + a*e)*sqrt(-b*e)*sqrt(b*x + a)*sqrt(e*x + d)/(b^2*e^2*x^2 + a*b*d*e + (b^2*d*e + a*b*e^2)*x)) - (7*b^2*d^2*e - 4*a*b*d*e^2 + 4*(b^2*d*e^2 - a*b*e^3)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b^3*d^2*e - a*b^2*d*e^2 + (b^3*d*e^2 - a*b^2*e^3)*x)]","B",0
847,1,665,0,0.603501," ","integrate((8*e^2*x^2+20*d*e*x+15*d^2)/(e*x+d)^(5/2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(2 \, {\left(b^{2} d^{4} - 2 \, a b d^{3} e + a^{2} d^{2} e^{2} + {\left(b^{2} d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4}\right)} x^{2} + 2 \, {\left(b^{2} d^{3} e - 2 \, a b d^{2} e^{2} + a^{2} d e^{3}\right)} x\right)} \sqrt{b e} \log\left(8 \, b^{2} e^{2} x^{2} + b^{2} d^{2} + 6 \, a b d e + a^{2} e^{2} + 4 \, {\left(2 \, b e x + b d + a e\right)} \sqrt{b e} \sqrt{b x + a} \sqrt{e x + d} + 8 \, {\left(b^{2} d e + a b e^{2}\right)} x\right) + {\left(7 \, b^{2} d^{3} e - 5 \, a b d^{2} e^{2} + 2 \, {\left(3 \, b^{2} d^{2} e^{2} - 2 \, a b d e^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}\right)}}{b^{3} d^{4} e - 2 \, a b^{2} d^{3} e^{2} + a^{2} b d^{2} e^{3} + {\left(b^{3} d^{2} e^{3} - 2 \, a b^{2} d e^{4} + a^{2} b e^{5}\right)} x^{2} + 2 \, {\left(b^{3} d^{3} e^{2} - 2 \, a b^{2} d^{2} e^{3} + a^{2} b d e^{4}\right)} x}, -\frac{2 \, {\left(4 \, {\left(b^{2} d^{4} - 2 \, a b d^{3} e + a^{2} d^{2} e^{2} + {\left(b^{2} d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4}\right)} x^{2} + 2 \, {\left(b^{2} d^{3} e - 2 \, a b d^{2} e^{2} + a^{2} d e^{3}\right)} x\right)} \sqrt{-b e} \arctan\left(\frac{{\left(2 \, b e x + b d + a e\right)} \sqrt{-b e} \sqrt{b x + a} \sqrt{e x + d}}{2 \, {\left(b^{2} e^{2} x^{2} + a b d e + {\left(b^{2} d e + a b e^{2}\right)} x\right)}}\right) - {\left(7 \, b^{2} d^{3} e - 5 \, a b d^{2} e^{2} + 2 \, {\left(3 \, b^{2} d^{2} e^{2} - 2 \, a b d e^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}\right)}}{b^{3} d^{4} e - 2 \, a b^{2} d^{3} e^{2} + a^{2} b d^{2} e^{3} + {\left(b^{3} d^{2} e^{3} - 2 \, a b^{2} d e^{4} + a^{2} b e^{5}\right)} x^{2} + 2 \, {\left(b^{3} d^{3} e^{2} - 2 \, a b^{2} d^{2} e^{3} + a^{2} b d e^{4}\right)} x}\right]"," ",0,"[2*(2*(b^2*d^4 - 2*a*b*d^3*e + a^2*d^2*e^2 + (b^2*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4)*x^2 + 2*(b^2*d^3*e - 2*a*b*d^2*e^2 + a^2*d*e^3)*x)*sqrt(b*e)*log(8*b^2*e^2*x^2 + b^2*d^2 + 6*a*b*d*e + a^2*e^2 + 4*(2*b*e*x + b*d + a*e)*sqrt(b*e)*sqrt(b*x + a)*sqrt(e*x + d) + 8*(b^2*d*e + a*b*e^2)*x) + (7*b^2*d^3*e - 5*a*b*d^2*e^2 + 2*(3*b^2*d^2*e^2 - 2*a*b*d*e^3)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b^3*d^4*e - 2*a*b^2*d^3*e^2 + a^2*b*d^2*e^3 + (b^3*d^2*e^3 - 2*a*b^2*d*e^4 + a^2*b*e^5)*x^2 + 2*(b^3*d^3*e^2 - 2*a*b^2*d^2*e^3 + a^2*b*d*e^4)*x), -2*(4*(b^2*d^4 - 2*a*b*d^3*e + a^2*d^2*e^2 + (b^2*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4)*x^2 + 2*(b^2*d^3*e - 2*a*b*d^2*e^2 + a^2*d*e^3)*x)*sqrt(-b*e)*arctan(1/2*(2*b*e*x + b*d + a*e)*sqrt(-b*e)*sqrt(b*x + a)*sqrt(e*x + d)/(b^2*e^2*x^2 + a*b*d*e + (b^2*d*e + a*b*e^2)*x)) - (7*b^2*d^3*e - 5*a*b*d^2*e^2 + 2*(3*b^2*d^2*e^2 - 2*a*b*d*e^3)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b^3*d^4*e - 2*a*b^2*d^3*e^2 + a^2*b*d^2*e^3 + (b^3*d^2*e^3 - 2*a*b^2*d*e^4 + a^2*b*e^5)*x^2 + 2*(b^3*d^3*e^2 - 2*a*b^2*d^2*e^3 + a^2*b*d*e^4)*x)]","B",0
848,1,293,0,1.054678," ","integrate((8*e^2*x^2+20*d*e*x+15*d^2)/(e*x+d)^(7/2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(225 \, b^{2} d^{4} - 350 \, a b d^{3} e + 149 \, a^{2} d^{2} e^{2} + 8 \, {\left(23 \, b^{2} d^{2} e^{2} - 35 \, a b d e^{3} + 15 \, a^{2} e^{4}\right)} x^{2} + 4 \, {\left(100 \, b^{2} d^{3} e - 153 \, a b d^{2} e^{2} + 65 \, a^{2} d e^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{15 \, {\left(b^{3} d^{6} - 3 \, a b^{2} d^{5} e + 3 \, a^{2} b d^{4} e^{2} - a^{3} d^{3} e^{3} + {\left(b^{3} d^{3} e^{3} - 3 \, a b^{2} d^{2} e^{4} + 3 \, a^{2} b d e^{5} - a^{3} e^{6}\right)} x^{3} + 3 \, {\left(b^{3} d^{4} e^{2} - 3 \, a b^{2} d^{3} e^{3} + 3 \, a^{2} b d^{2} e^{4} - a^{3} d e^{5}\right)} x^{2} + 3 \, {\left(b^{3} d^{5} e - 3 \, a b^{2} d^{4} e^{2} + 3 \, a^{2} b d^{3} e^{3} - a^{3} d^{2} e^{4}\right)} x\right)}}"," ",0,"2/15*(225*b^2*d^4 - 350*a*b*d^3*e + 149*a^2*d^2*e^2 + 8*(23*b^2*d^2*e^2 - 35*a*b*d*e^3 + 15*a^2*e^4)*x^2 + 4*(100*b^2*d^3*e - 153*a*b*d^2*e^2 + 65*a^2*d*e^3)*x)*sqrt(b*x + a)*sqrt(e*x + d)/(b^3*d^6 - 3*a*b^2*d^5*e + 3*a^2*b*d^4*e^2 - a^3*d^3*e^3 + (b^3*d^3*e^3 - 3*a*b^2*d^2*e^4 + 3*a^2*b*d*e^5 - a^3*e^6)*x^3 + 3*(b^3*d^4*e^2 - 3*a*b^2*d^3*e^3 + 3*a^2*b*d^2*e^4 - a^3*d*e^5)*x^2 + 3*(b^3*d^5*e - 3*a*b^2*d^4*e^2 + 3*a^2*b*d^3*e^3 - a^3*d^2*e^4)*x)","B",0
849,1,487,0,2.230083," ","integrate((8*e^2*x^2+20*d*e*x+15*d^2)/(e*x+d)^(9/2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(1575 \, b^{3} d^{5} - 2975 \, a b^{2} d^{4} e + 1953 \, a^{2} b d^{3} e^{2} - 409 \, a^{3} d^{2} e^{3} + 16 \, {\left(58 \, b^{3} d^{2} e^{3} - 84 \, a b^{2} d e^{4} + 35 \, a^{2} b e^{5}\right)} x^{3} + 8 \, {\left(406 \, b^{3} d^{3} e^{2} - 646 \, a b^{2} d^{2} e^{3} + 329 \, a^{2} b d e^{4} - 35 \, a^{3} e^{5}\right)} x^{2} + 2 \, {\left(1925 \, b^{3} d^{4} e - 3332 \, a b^{2} d^{3} e^{2} + 1945 \, a^{2} b d^{2} e^{3} - 322 \, a^{3} d e^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{105 \, {\left(b^{4} d^{8} - 4 \, a b^{3} d^{7} e + 6 \, a^{2} b^{2} d^{6} e^{2} - 4 \, a^{3} b d^{5} e^{3} + a^{4} d^{4} e^{4} + {\left(b^{4} d^{4} e^{4} - 4 \, a b^{3} d^{3} e^{5} + 6 \, a^{2} b^{2} d^{2} e^{6} - 4 \, a^{3} b d e^{7} + a^{4} e^{8}\right)} x^{4} + 4 \, {\left(b^{4} d^{5} e^{3} - 4 \, a b^{3} d^{4} e^{4} + 6 \, a^{2} b^{2} d^{3} e^{5} - 4 \, a^{3} b d^{2} e^{6} + a^{4} d e^{7}\right)} x^{3} + 6 \, {\left(b^{4} d^{6} e^{2} - 4 \, a b^{3} d^{5} e^{3} + 6 \, a^{2} b^{2} d^{4} e^{4} - 4 \, a^{3} b d^{3} e^{5} + a^{4} d^{2} e^{6}\right)} x^{2} + 4 \, {\left(b^{4} d^{7} e - 4 \, a b^{3} d^{6} e^{2} + 6 \, a^{2} b^{2} d^{5} e^{3} - 4 \, a^{3} b d^{4} e^{4} + a^{4} d^{3} e^{5}\right)} x\right)}}"," ",0,"2/105*(1575*b^3*d^5 - 2975*a*b^2*d^4*e + 1953*a^2*b*d^3*e^2 - 409*a^3*d^2*e^3 + 16*(58*b^3*d^2*e^3 - 84*a*b^2*d*e^4 + 35*a^2*b*e^5)*x^3 + 8*(406*b^3*d^3*e^2 - 646*a*b^2*d^2*e^3 + 329*a^2*b*d*e^4 - 35*a^3*e^5)*x^2 + 2*(1925*b^3*d^4*e - 3332*a*b^2*d^3*e^2 + 1945*a^2*b*d^2*e^3 - 322*a^3*d*e^4)*x)*sqrt(b*x + a)*sqrt(e*x + d)/(b^4*d^8 - 4*a*b^3*d^7*e + 6*a^2*b^2*d^6*e^2 - 4*a^3*b*d^5*e^3 + a^4*d^4*e^4 + (b^4*d^4*e^4 - 4*a*b^3*d^3*e^5 + 6*a^2*b^2*d^2*e^6 - 4*a^3*b*d*e^7 + a^4*e^8)*x^4 + 4*(b^4*d^5*e^3 - 4*a*b^3*d^4*e^4 + 6*a^2*b^2*d^3*e^5 - 4*a^3*b*d^2*e^6 + a^4*d*e^7)*x^3 + 6*(b^4*d^6*e^2 - 4*a*b^3*d^5*e^3 + 6*a^2*b^2*d^4*e^4 - 4*a^3*b*d^3*e^5 + a^4*d^2*e^6)*x^2 + 4*(b^4*d^7*e - 4*a*b^3*d^6*e^2 + 6*a^2*b^2*d^5*e^3 - 4*a^3*b*d^4*e^4 + a^4*d^3*e^5)*x)","B",0
850,-1,0,0,0.000000," ","integrate((e*x+d)^(3/2)/(c*x^2+b*x+a)/(g*x+f)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
851,1,4471,0,37.789962," ","integrate((e*x+d)^(1/2)/(c*x^2+b*x+a)/(g*x+f)^(1/2),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{2} \sqrt{\frac{{\left(2 \, c d - b e\right)} f - {\left(b d - 2 \, a e\right)} g + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} f^{2} - {\left(b^{3} - 4 \, a b c\right)} f g + {\left(a b^{2} - 4 \, a^{2} c\right)} g^{2}\right)} \sqrt{\frac{e^{2} f^{2} - 2 \, d e f g + d^{2} g^{2}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} f^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} f^{3} g + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} f^{2} g^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} f g^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} g^{4}}}}{{\left(b^{2} c - 4 \, a c^{2}\right)} f^{2} - {\left(b^{3} - 4 \, a b c\right)} f g + {\left(a b^{2} - 4 \, a^{2} c\right)} g^{2}}} \log\left(-\frac{2 \, b d^{2} f g - 2 \, a d^{2} g^{2} - 2 \, {\left(b d e - a e^{2}\right)} f^{2} + \sqrt{2} {\left({\left(b^{2} - 4 \, a c\right)} e f^{2} - {\left(b^{2} - 4 \, a c\right)} d f g + {\left({\left(b^{3} c - 4 \, a b c^{2}\right)} f^{3} - {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} f^{2} g + 3 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} f g^{2} - 2 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} g^{3}\right)} \sqrt{\frac{e^{2} f^{2} - 2 \, d e f g + d^{2} g^{2}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} f^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} f^{3} g + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} f^{2} g^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} f g^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} g^{4}}}\right)} \sqrt{e x + d} \sqrt{g x + f} \sqrt{\frac{{\left(2 \, c d - b e\right)} f - {\left(b d - 2 \, a e\right)} g + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} f^{2} - {\left(b^{3} - 4 \, a b c\right)} f g + {\left(a b^{2} - 4 \, a^{2} c\right)} g^{2}\right)} \sqrt{\frac{e^{2} f^{2} - 2 \, d e f g + d^{2} g^{2}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} f^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} f^{3} g + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} f^{2} g^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} f g^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} g^{4}}}}{{\left(b^{2} c - 4 \, a c^{2}\right)} f^{2} - {\left(b^{3} - 4 \, a b c\right)} f g + {\left(a b^{2} - 4 \, a^{2} c\right)} g^{2}}} - {\left(b e^{2} f^{2} - 4 \, a e^{2} f g - {\left(b d^{2} - 4 \, a d e\right)} g^{2}\right)} x - {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d f^{3} - 2 \, {\left(b^{3} - 4 \, a b c\right)} d f^{2} g + 2 \, {\left(a b^{2} - 4 \, a^{2} c\right)} d f g^{2} + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} e f^{3} + {\left(a b^{2} - 4 \, a^{2} c\right)} d g^{3} + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d - {\left(b^{3} - 4 \, a b c\right)} e\right)} f^{2} g - {\left({\left(b^{3} - 4 \, a b c\right)} d - {\left(a b^{2} - 4 \, a^{2} c\right)} e\right)} f g^{2}\right)} x\right)} \sqrt{\frac{e^{2} f^{2} - 2 \, d e f g + d^{2} g^{2}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} f^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} f^{3} g + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} f^{2} g^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} f g^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} g^{4}}}}{x}\right) - \frac{1}{4} \, \sqrt{2} \sqrt{\frac{{\left(2 \, c d - b e\right)} f - {\left(b d - 2 \, a e\right)} g + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} f^{2} - {\left(b^{3} - 4 \, a b c\right)} f g + {\left(a b^{2} - 4 \, a^{2} c\right)} g^{2}\right)} \sqrt{\frac{e^{2} f^{2} - 2 \, d e f g + d^{2} g^{2}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} f^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} f^{3} g + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} f^{2} g^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} f g^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} g^{4}}}}{{\left(b^{2} c - 4 \, a c^{2}\right)} f^{2} - {\left(b^{3} - 4 \, a b c\right)} f g + {\left(a b^{2} - 4 \, a^{2} c\right)} g^{2}}} \log\left(-\frac{2 \, b d^{2} f g - 2 \, a d^{2} g^{2} - 2 \, {\left(b d e - a e^{2}\right)} f^{2} - \sqrt{2} {\left({\left(b^{2} - 4 \, a c\right)} e f^{2} - {\left(b^{2} - 4 \, a c\right)} d f g + {\left({\left(b^{3} c - 4 \, a b c^{2}\right)} f^{3} - {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} f^{2} g + 3 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} f g^{2} - 2 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} g^{3}\right)} \sqrt{\frac{e^{2} f^{2} - 2 \, d e f g + d^{2} g^{2}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} f^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} f^{3} g + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} f^{2} g^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} f g^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} g^{4}}}\right)} \sqrt{e x + d} \sqrt{g x + f} \sqrt{\frac{{\left(2 \, c d - b e\right)} f - {\left(b d - 2 \, a e\right)} g + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} f^{2} - {\left(b^{3} - 4 \, a b c\right)} f g + {\left(a b^{2} - 4 \, a^{2} c\right)} g^{2}\right)} \sqrt{\frac{e^{2} f^{2} - 2 \, d e f g + d^{2} g^{2}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} f^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} f^{3} g + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} f^{2} g^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} f g^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} g^{4}}}}{{\left(b^{2} c - 4 \, a c^{2}\right)} f^{2} - {\left(b^{3} - 4 \, a b c\right)} f g + {\left(a b^{2} - 4 \, a^{2} c\right)} g^{2}}} - {\left(b e^{2} f^{2} - 4 \, a e^{2} f g - {\left(b d^{2} - 4 \, a d e\right)} g^{2}\right)} x - {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d f^{3} - 2 \, {\left(b^{3} - 4 \, a b c\right)} d f^{2} g + 2 \, {\left(a b^{2} - 4 \, a^{2} c\right)} d f g^{2} + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} e f^{3} + {\left(a b^{2} - 4 \, a^{2} c\right)} d g^{3} + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d - {\left(b^{3} - 4 \, a b c\right)} e\right)} f^{2} g - {\left({\left(b^{3} - 4 \, a b c\right)} d - {\left(a b^{2} - 4 \, a^{2} c\right)} e\right)} f g^{2}\right)} x\right)} \sqrt{\frac{e^{2} f^{2} - 2 \, d e f g + d^{2} g^{2}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} f^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} f^{3} g + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} f^{2} g^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} f g^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} g^{4}}}}{x}\right) + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{{\left(2 \, c d - b e\right)} f - {\left(b d - 2 \, a e\right)} g - {\left({\left(b^{2} c - 4 \, a c^{2}\right)} f^{2} - {\left(b^{3} - 4 \, a b c\right)} f g + {\left(a b^{2} - 4 \, a^{2} c\right)} g^{2}\right)} \sqrt{\frac{e^{2} f^{2} - 2 \, d e f g + d^{2} g^{2}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} f^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} f^{3} g + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} f^{2} g^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} f g^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} g^{4}}}}{{\left(b^{2} c - 4 \, a c^{2}\right)} f^{2} - {\left(b^{3} - 4 \, a b c\right)} f g + {\left(a b^{2} - 4 \, a^{2} c\right)} g^{2}}} \log\left(-\frac{2 \, b d^{2} f g - 2 \, a d^{2} g^{2} - 2 \, {\left(b d e - a e^{2}\right)} f^{2} + \sqrt{2} {\left({\left(b^{2} - 4 \, a c\right)} e f^{2} - {\left(b^{2} - 4 \, a c\right)} d f g - {\left({\left(b^{3} c - 4 \, a b c^{2}\right)} f^{3} - {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} f^{2} g + 3 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} f g^{2} - 2 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} g^{3}\right)} \sqrt{\frac{e^{2} f^{2} - 2 \, d e f g + d^{2} g^{2}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} f^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} f^{3} g + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} f^{2} g^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} f g^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} g^{4}}}\right)} \sqrt{e x + d} \sqrt{g x + f} \sqrt{\frac{{\left(2 \, c d - b e\right)} f - {\left(b d - 2 \, a e\right)} g - {\left({\left(b^{2} c - 4 \, a c^{2}\right)} f^{2} - {\left(b^{3} - 4 \, a b c\right)} f g + {\left(a b^{2} - 4 \, a^{2} c\right)} g^{2}\right)} \sqrt{\frac{e^{2} f^{2} - 2 \, d e f g + d^{2} g^{2}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} f^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} f^{3} g + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} f^{2} g^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} f g^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} g^{4}}}}{{\left(b^{2} c - 4 \, a c^{2}\right)} f^{2} - {\left(b^{3} - 4 \, a b c\right)} f g + {\left(a b^{2} - 4 \, a^{2} c\right)} g^{2}}} - {\left(b e^{2} f^{2} - 4 \, a e^{2} f g - {\left(b d^{2} - 4 \, a d e\right)} g^{2}\right)} x + {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d f^{3} - 2 \, {\left(b^{3} - 4 \, a b c\right)} d f^{2} g + 2 \, {\left(a b^{2} - 4 \, a^{2} c\right)} d f g^{2} + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} e f^{3} + {\left(a b^{2} - 4 \, a^{2} c\right)} d g^{3} + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d - {\left(b^{3} - 4 \, a b c\right)} e\right)} f^{2} g - {\left({\left(b^{3} - 4 \, a b c\right)} d - {\left(a b^{2} - 4 \, a^{2} c\right)} e\right)} f g^{2}\right)} x\right)} \sqrt{\frac{e^{2} f^{2} - 2 \, d e f g + d^{2} g^{2}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} f^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} f^{3} g + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} f^{2} g^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} f g^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} g^{4}}}}{x}\right) - \frac{1}{4} \, \sqrt{2} \sqrt{\frac{{\left(2 \, c d - b e\right)} f - {\left(b d - 2 \, a e\right)} g - {\left({\left(b^{2} c - 4 \, a c^{2}\right)} f^{2} - {\left(b^{3} - 4 \, a b c\right)} f g + {\left(a b^{2} - 4 \, a^{2} c\right)} g^{2}\right)} \sqrt{\frac{e^{2} f^{2} - 2 \, d e f g + d^{2} g^{2}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} f^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} f^{3} g + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} f^{2} g^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} f g^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} g^{4}}}}{{\left(b^{2} c - 4 \, a c^{2}\right)} f^{2} - {\left(b^{3} - 4 \, a b c\right)} f g + {\left(a b^{2} - 4 \, a^{2} c\right)} g^{2}}} \log\left(-\frac{2 \, b d^{2} f g - 2 \, a d^{2} g^{2} - 2 \, {\left(b d e - a e^{2}\right)} f^{2} - \sqrt{2} {\left({\left(b^{2} - 4 \, a c\right)} e f^{2} - {\left(b^{2} - 4 \, a c\right)} d f g - {\left({\left(b^{3} c - 4 \, a b c^{2}\right)} f^{3} - {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} f^{2} g + 3 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} f g^{2} - 2 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} g^{3}\right)} \sqrt{\frac{e^{2} f^{2} - 2 \, d e f g + d^{2} g^{2}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} f^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} f^{3} g + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} f^{2} g^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} f g^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} g^{4}}}\right)} \sqrt{e x + d} \sqrt{g x + f} \sqrt{\frac{{\left(2 \, c d - b e\right)} f - {\left(b d - 2 \, a e\right)} g - {\left({\left(b^{2} c - 4 \, a c^{2}\right)} f^{2} - {\left(b^{3} - 4 \, a b c\right)} f g + {\left(a b^{2} - 4 \, a^{2} c\right)} g^{2}\right)} \sqrt{\frac{e^{2} f^{2} - 2 \, d e f g + d^{2} g^{2}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} f^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} f^{3} g + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} f^{2} g^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} f g^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} g^{4}}}}{{\left(b^{2} c - 4 \, a c^{2}\right)} f^{2} - {\left(b^{3} - 4 \, a b c\right)} f g + {\left(a b^{2} - 4 \, a^{2} c\right)} g^{2}}} - {\left(b e^{2} f^{2} - 4 \, a e^{2} f g - {\left(b d^{2} - 4 \, a d e\right)} g^{2}\right)} x + {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d f^{3} - 2 \, {\left(b^{3} - 4 \, a b c\right)} d f^{2} g + 2 \, {\left(a b^{2} - 4 \, a^{2} c\right)} d f g^{2} + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} e f^{3} + {\left(a b^{2} - 4 \, a^{2} c\right)} d g^{3} + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d - {\left(b^{3} - 4 \, a b c\right)} e\right)} f^{2} g - {\left({\left(b^{3} - 4 \, a b c\right)} d - {\left(a b^{2} - 4 \, a^{2} c\right)} e\right)} f g^{2}\right)} x\right)} \sqrt{\frac{e^{2} f^{2} - 2 \, d e f g + d^{2} g^{2}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} f^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} f^{3} g + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} f^{2} g^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} f g^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} g^{4}}}}{x}\right)"," ",0,"1/4*sqrt(2)*sqrt(((2*c*d - b*e)*f - (b*d - 2*a*e)*g + ((b^2*c - 4*a*c^2)*f^2 - (b^3 - 4*a*b*c)*f*g + (a*b^2 - 4*a^2*c)*g^2)*sqrt((e^2*f^2 - 2*d*e*f*g + d^2*g^2)/((b^2*c^2 - 4*a*c^3)*f^4 - 2*(b^3*c - 4*a*b*c^2)*f^3*g + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*f^2*g^2 - 2*(a*b^3 - 4*a^2*b*c)*f*g^3 + (a^2*b^2 - 4*a^3*c)*g^4)))/((b^2*c - 4*a*c^2)*f^2 - (b^3 - 4*a*b*c)*f*g + (a*b^2 - 4*a^2*c)*g^2))*log(-(2*b*d^2*f*g - 2*a*d^2*g^2 - 2*(b*d*e - a*e^2)*f^2 + sqrt(2)*((b^2 - 4*a*c)*e*f^2 - (b^2 - 4*a*c)*d*f*g + ((b^3*c - 4*a*b*c^2)*f^3 - (b^4 - 2*a*b^2*c - 8*a^2*c^2)*f^2*g + 3*(a*b^3 - 4*a^2*b*c)*f*g^2 - 2*(a^2*b^2 - 4*a^3*c)*g^3)*sqrt((e^2*f^2 - 2*d*e*f*g + d^2*g^2)/((b^2*c^2 - 4*a*c^3)*f^4 - 2*(b^3*c - 4*a*b*c^2)*f^3*g + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*f^2*g^2 - 2*(a*b^3 - 4*a^2*b*c)*f*g^3 + (a^2*b^2 - 4*a^3*c)*g^4)))*sqrt(e*x + d)*sqrt(g*x + f)*sqrt(((2*c*d - b*e)*f - (b*d - 2*a*e)*g + ((b^2*c - 4*a*c^2)*f^2 - (b^3 - 4*a*b*c)*f*g + (a*b^2 - 4*a^2*c)*g^2)*sqrt((e^2*f^2 - 2*d*e*f*g + d^2*g^2)/((b^2*c^2 - 4*a*c^3)*f^4 - 2*(b^3*c - 4*a*b*c^2)*f^3*g + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*f^2*g^2 - 2*(a*b^3 - 4*a^2*b*c)*f*g^3 + (a^2*b^2 - 4*a^3*c)*g^4)))/((b^2*c - 4*a*c^2)*f^2 - (b^3 - 4*a*b*c)*f*g + (a*b^2 - 4*a^2*c)*g^2)) - (b*e^2*f^2 - 4*a*e^2*f*g - (b*d^2 - 4*a*d*e)*g^2)*x - (2*(b^2*c - 4*a*c^2)*d*f^3 - 2*(b^3 - 4*a*b*c)*d*f^2*g + 2*(a*b^2 - 4*a^2*c)*d*f*g^2 + ((b^2*c - 4*a*c^2)*e*f^3 + (a*b^2 - 4*a^2*c)*d*g^3 + ((b^2*c - 4*a*c^2)*d - (b^3 - 4*a*b*c)*e)*f^2*g - ((b^3 - 4*a*b*c)*d - (a*b^2 - 4*a^2*c)*e)*f*g^2)*x)*sqrt((e^2*f^2 - 2*d*e*f*g + d^2*g^2)/((b^2*c^2 - 4*a*c^3)*f^4 - 2*(b^3*c - 4*a*b*c^2)*f^3*g + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*f^2*g^2 - 2*(a*b^3 - 4*a^2*b*c)*f*g^3 + (a^2*b^2 - 4*a^3*c)*g^4)))/x) - 1/4*sqrt(2)*sqrt(((2*c*d - b*e)*f - (b*d - 2*a*e)*g + ((b^2*c - 4*a*c^2)*f^2 - (b^3 - 4*a*b*c)*f*g + (a*b^2 - 4*a^2*c)*g^2)*sqrt((e^2*f^2 - 2*d*e*f*g + d^2*g^2)/((b^2*c^2 - 4*a*c^3)*f^4 - 2*(b^3*c - 4*a*b*c^2)*f^3*g + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*f^2*g^2 - 2*(a*b^3 - 4*a^2*b*c)*f*g^3 + (a^2*b^2 - 4*a^3*c)*g^4)))/((b^2*c - 4*a*c^2)*f^2 - (b^3 - 4*a*b*c)*f*g + (a*b^2 - 4*a^2*c)*g^2))*log(-(2*b*d^2*f*g - 2*a*d^2*g^2 - 2*(b*d*e - a*e^2)*f^2 - sqrt(2)*((b^2 - 4*a*c)*e*f^2 - (b^2 - 4*a*c)*d*f*g + ((b^3*c - 4*a*b*c^2)*f^3 - (b^4 - 2*a*b^2*c - 8*a^2*c^2)*f^2*g + 3*(a*b^3 - 4*a^2*b*c)*f*g^2 - 2*(a^2*b^2 - 4*a^3*c)*g^3)*sqrt((e^2*f^2 - 2*d*e*f*g + d^2*g^2)/((b^2*c^2 - 4*a*c^3)*f^4 - 2*(b^3*c - 4*a*b*c^2)*f^3*g + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*f^2*g^2 - 2*(a*b^3 - 4*a^2*b*c)*f*g^3 + (a^2*b^2 - 4*a^3*c)*g^4)))*sqrt(e*x + d)*sqrt(g*x + f)*sqrt(((2*c*d - b*e)*f - (b*d - 2*a*e)*g + ((b^2*c - 4*a*c^2)*f^2 - (b^3 - 4*a*b*c)*f*g + (a*b^2 - 4*a^2*c)*g^2)*sqrt((e^2*f^2 - 2*d*e*f*g + d^2*g^2)/((b^2*c^2 - 4*a*c^3)*f^4 - 2*(b^3*c - 4*a*b*c^2)*f^3*g + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*f^2*g^2 - 2*(a*b^3 - 4*a^2*b*c)*f*g^3 + (a^2*b^2 - 4*a^3*c)*g^4)))/((b^2*c - 4*a*c^2)*f^2 - (b^3 - 4*a*b*c)*f*g + (a*b^2 - 4*a^2*c)*g^2)) - (b*e^2*f^2 - 4*a*e^2*f*g - (b*d^2 - 4*a*d*e)*g^2)*x - (2*(b^2*c - 4*a*c^2)*d*f^3 - 2*(b^3 - 4*a*b*c)*d*f^2*g + 2*(a*b^2 - 4*a^2*c)*d*f*g^2 + ((b^2*c - 4*a*c^2)*e*f^3 + (a*b^2 - 4*a^2*c)*d*g^3 + ((b^2*c - 4*a*c^2)*d - (b^3 - 4*a*b*c)*e)*f^2*g - ((b^3 - 4*a*b*c)*d - (a*b^2 - 4*a^2*c)*e)*f*g^2)*x)*sqrt((e^2*f^2 - 2*d*e*f*g + d^2*g^2)/((b^2*c^2 - 4*a*c^3)*f^4 - 2*(b^3*c - 4*a*b*c^2)*f^3*g + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*f^2*g^2 - 2*(a*b^3 - 4*a^2*b*c)*f*g^3 + (a^2*b^2 - 4*a^3*c)*g^4)))/x) + 1/4*sqrt(2)*sqrt(((2*c*d - b*e)*f - (b*d - 2*a*e)*g - ((b^2*c - 4*a*c^2)*f^2 - (b^3 - 4*a*b*c)*f*g + (a*b^2 - 4*a^2*c)*g^2)*sqrt((e^2*f^2 - 2*d*e*f*g + d^2*g^2)/((b^2*c^2 - 4*a*c^3)*f^4 - 2*(b^3*c - 4*a*b*c^2)*f^3*g + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*f^2*g^2 - 2*(a*b^3 - 4*a^2*b*c)*f*g^3 + (a^2*b^2 - 4*a^3*c)*g^4)))/((b^2*c - 4*a*c^2)*f^2 - (b^3 - 4*a*b*c)*f*g + (a*b^2 - 4*a^2*c)*g^2))*log(-(2*b*d^2*f*g - 2*a*d^2*g^2 - 2*(b*d*e - a*e^2)*f^2 + sqrt(2)*((b^2 - 4*a*c)*e*f^2 - (b^2 - 4*a*c)*d*f*g - ((b^3*c - 4*a*b*c^2)*f^3 - (b^4 - 2*a*b^2*c - 8*a^2*c^2)*f^2*g + 3*(a*b^3 - 4*a^2*b*c)*f*g^2 - 2*(a^2*b^2 - 4*a^3*c)*g^3)*sqrt((e^2*f^2 - 2*d*e*f*g + d^2*g^2)/((b^2*c^2 - 4*a*c^3)*f^4 - 2*(b^3*c - 4*a*b*c^2)*f^3*g + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*f^2*g^2 - 2*(a*b^3 - 4*a^2*b*c)*f*g^3 + (a^2*b^2 - 4*a^3*c)*g^4)))*sqrt(e*x + d)*sqrt(g*x + f)*sqrt(((2*c*d - b*e)*f - (b*d - 2*a*e)*g - ((b^2*c - 4*a*c^2)*f^2 - (b^3 - 4*a*b*c)*f*g + (a*b^2 - 4*a^2*c)*g^2)*sqrt((e^2*f^2 - 2*d*e*f*g + d^2*g^2)/((b^2*c^2 - 4*a*c^3)*f^4 - 2*(b^3*c - 4*a*b*c^2)*f^3*g + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*f^2*g^2 - 2*(a*b^3 - 4*a^2*b*c)*f*g^3 + (a^2*b^2 - 4*a^3*c)*g^4)))/((b^2*c - 4*a*c^2)*f^2 - (b^3 - 4*a*b*c)*f*g + (a*b^2 - 4*a^2*c)*g^2)) - (b*e^2*f^2 - 4*a*e^2*f*g - (b*d^2 - 4*a*d*e)*g^2)*x + (2*(b^2*c - 4*a*c^2)*d*f^3 - 2*(b^3 - 4*a*b*c)*d*f^2*g + 2*(a*b^2 - 4*a^2*c)*d*f*g^2 + ((b^2*c - 4*a*c^2)*e*f^3 + (a*b^2 - 4*a^2*c)*d*g^3 + ((b^2*c - 4*a*c^2)*d - (b^3 - 4*a*b*c)*e)*f^2*g - ((b^3 - 4*a*b*c)*d - (a*b^2 - 4*a^2*c)*e)*f*g^2)*x)*sqrt((e^2*f^2 - 2*d*e*f*g + d^2*g^2)/((b^2*c^2 - 4*a*c^3)*f^4 - 2*(b^3*c - 4*a*b*c^2)*f^3*g + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*f^2*g^2 - 2*(a*b^3 - 4*a^2*b*c)*f*g^3 + (a^2*b^2 - 4*a^3*c)*g^4)))/x) - 1/4*sqrt(2)*sqrt(((2*c*d - b*e)*f - (b*d - 2*a*e)*g - ((b^2*c - 4*a*c^2)*f^2 - (b^3 - 4*a*b*c)*f*g + (a*b^2 - 4*a^2*c)*g^2)*sqrt((e^2*f^2 - 2*d*e*f*g + d^2*g^2)/((b^2*c^2 - 4*a*c^3)*f^4 - 2*(b^3*c - 4*a*b*c^2)*f^3*g + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*f^2*g^2 - 2*(a*b^3 - 4*a^2*b*c)*f*g^3 + (a^2*b^2 - 4*a^3*c)*g^4)))/((b^2*c - 4*a*c^2)*f^2 - (b^3 - 4*a*b*c)*f*g + (a*b^2 - 4*a^2*c)*g^2))*log(-(2*b*d^2*f*g - 2*a*d^2*g^2 - 2*(b*d*e - a*e^2)*f^2 - sqrt(2)*((b^2 - 4*a*c)*e*f^2 - (b^2 - 4*a*c)*d*f*g - ((b^3*c - 4*a*b*c^2)*f^3 - (b^4 - 2*a*b^2*c - 8*a^2*c^2)*f^2*g + 3*(a*b^3 - 4*a^2*b*c)*f*g^2 - 2*(a^2*b^2 - 4*a^3*c)*g^3)*sqrt((e^2*f^2 - 2*d*e*f*g + d^2*g^2)/((b^2*c^2 - 4*a*c^3)*f^4 - 2*(b^3*c - 4*a*b*c^2)*f^3*g + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*f^2*g^2 - 2*(a*b^3 - 4*a^2*b*c)*f*g^3 + (a^2*b^2 - 4*a^3*c)*g^4)))*sqrt(e*x + d)*sqrt(g*x + f)*sqrt(((2*c*d - b*e)*f - (b*d - 2*a*e)*g - ((b^2*c - 4*a*c^2)*f^2 - (b^3 - 4*a*b*c)*f*g + (a*b^2 - 4*a^2*c)*g^2)*sqrt((e^2*f^2 - 2*d*e*f*g + d^2*g^2)/((b^2*c^2 - 4*a*c^3)*f^4 - 2*(b^3*c - 4*a*b*c^2)*f^3*g + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*f^2*g^2 - 2*(a*b^3 - 4*a^2*b*c)*f*g^3 + (a^2*b^2 - 4*a^3*c)*g^4)))/((b^2*c - 4*a*c^2)*f^2 - (b^3 - 4*a*b*c)*f*g + (a*b^2 - 4*a^2*c)*g^2)) - (b*e^2*f^2 - 4*a*e^2*f*g - (b*d^2 - 4*a*d*e)*g^2)*x + (2*(b^2*c - 4*a*c^2)*d*f^3 - 2*(b^3 - 4*a*b*c)*d*f^2*g + 2*(a*b^2 - 4*a^2*c)*d*f*g^2 + ((b^2*c - 4*a*c^2)*e*f^3 + (a*b^2 - 4*a^2*c)*d*g^3 + ((b^2*c - 4*a*c^2)*d - (b^3 - 4*a*b*c)*e)*f^2*g - ((b^3 - 4*a*b*c)*d - (a*b^2 - 4*a^2*c)*e)*f*g^2)*x)*sqrt((e^2*f^2 - 2*d*e*f*g + d^2*g^2)/((b^2*c^2 - 4*a*c^3)*f^4 - 2*(b^3*c - 4*a*b*c^2)*f^3*g + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*f^2*g^2 - 2*(a*b^3 - 4*a^2*b*c)*f*g^3 + (a^2*b^2 - 4*a^3*c)*g^4)))/x)","B",0
852,-1,0,0,0.000000," ","integrate(1/(e*x+d)^(1/2)/(c*x^2+b*x+a)/(g*x+f)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
853,-1,0,0,0.000000," ","integrate(1/(e*x+d)^(3/2)/(c*x^2+b*x+a)/(g*x+f)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
854,-1,0,0,0.000000," ","integrate((g*x+f)^3*(c*x^2+b*x+a)^(1/2)/(e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
855,-1,0,0,0.000000," ","integrate((g*x+f)^2*(c*x^2+b*x+a)^(1/2)/(e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
856,-1,0,0,0.000000," ","integrate((g*x+f)*(c*x^2+b*x+a)^(1/2)/(e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
857,1,992,0,1.983946," ","integrate((c*x^2+b*x+a)^(1/2)/(e*x+d),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{c x^{2} + b x + a} c e - {\left(2 \, c d - b e\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 2 \, \sqrt{c d^{2} - b d e + a e^{2}} c \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} - 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right)}{4 \, c e^{2}}, \frac{2 \, \sqrt{c x^{2} + b x + a} c e + {\left(2 \, c d - b e\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + \sqrt{c d^{2} - b d e + a e^{2}} c \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} - 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right)}{2 \, c e^{2}}, \frac{4 \, \sqrt{c x^{2} + b x + a} c e + 4 \, \sqrt{-c d^{2} + b d e - a e^{2}} c \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) - {\left(2 \, c d - b e\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right)}{4 \, c e^{2}}, \frac{2 \, \sqrt{c x^{2} + b x + a} c e + 2 \, \sqrt{-c d^{2} + b d e - a e^{2}} c \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) + {\left(2 \, c d - b e\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right)}{2 \, c e^{2}}\right]"," ",0,"[1/4*(4*sqrt(c*x^2 + b*x + a)*c*e - (2*c*d - b*e)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 2*sqrt(c*d^2 - b*d*e + a*e^2)*c*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 - 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)))/(c*e^2), 1/2*(2*sqrt(c*x^2 + b*x + a)*c*e + (2*c*d - b*e)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + sqrt(c*d^2 - b*d*e + a*e^2)*c*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 - 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)))/(c*e^2), 1/4*(4*sqrt(c*x^2 + b*x + a)*c*e + 4*sqrt(-c*d^2 + b*d*e - a*e^2)*c*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) - (2*c*d - b*e)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c))/(c*e^2), 1/2*(2*sqrt(c*x^2 + b*x + a)*c*e + 2*sqrt(-c*d^2 + b*d*e - a*e^2)*c*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) + (2*c*d - b*e)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)))/(c*e^2)]","A",0
858,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(1/2)/(e*x+d)/(g*x+f),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
859,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(1/2)/(e*x+d)/(g*x+f)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
860,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(1/2)/(e*x+d)/(g*x+f)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
861,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(1/2)/(e*x+d)/(g*x+f)^4,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
862,-1,0,0,0.000000," ","integrate((g*x+f)^3*(c*x^2+b*x+a)^(3/2)/(e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
863,-1,0,0,0.000000," ","integrate((g*x+f)^2*(c*x^2+b*x+a)^(3/2)/(e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
864,-1,0,0,0.000000," ","integrate((g*x+f)*(c*x^2+b*x+a)^(3/2)/(e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
865,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)/(e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
866,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)/(e*x+d)/(g*x+f),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
867,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)/(e*x+d)/(g*x+f)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
868,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)/(e*x+d)/(g*x+f)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
869,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(5/2)/(e*x+d)/(g*x+f),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
870,-1,0,0,0.000000," ","integrate((g*x+f)^4/(e*x+d)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
871,-1,0,0,0.000000," ","integrate((g*x+f)^3/(e*x+d)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
872,-1,0,0,0.000000," ","integrate((g*x+f)^2/(e*x+d)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
873,1,1071,0,31.643059," ","integrate((g*x+f)/(e*x+d)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{c} g \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - \sqrt{c d^{2} - b d e + a e^{2}} {\left(c e f - c d g\right)} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} + 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right)}{2 \, {\left(c^{2} d^{2} e - b c d e^{2} + a c e^{3}\right)}}, \frac{{\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{c} g \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 2 \, \sqrt{-c d^{2} + b d e - a e^{2}} {\left(c e f - c d g\right)} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right)}{2 \, {\left(c^{2} d^{2} e - b c d e^{2} + a c e^{3}\right)}}, -\frac{2 \, {\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{-c} g \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + \sqrt{c d^{2} - b d e + a e^{2}} {\left(c e f - c d g\right)} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} + 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right)}{2 \, {\left(c^{2} d^{2} e - b c d e^{2} + a c e^{3}\right)}}, -\frac{{\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{-c} g \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - \sqrt{-c d^{2} + b d e - a e^{2}} {\left(c e f - c d g\right)} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right)}{c^{2} d^{2} e - b c d e^{2} + a c e^{3}}\right]"," ",0,"[1/2*((c*d^2 - b*d*e + a*e^2)*sqrt(c)*g*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - sqrt(c*d^2 - b*d*e + a*e^2)*(c*e*f - c*d*g)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 + 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)))/(c^2*d^2*e - b*c*d*e^2 + a*c*e^3), 1/2*((c*d^2 - b*d*e + a*e^2)*sqrt(c)*g*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 2*sqrt(-c*d^2 + b*d*e - a*e^2)*(c*e*f - c*d*g)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)))/(c^2*d^2*e - b*c*d*e^2 + a*c*e^3), -1/2*(2*(c*d^2 - b*d*e + a*e^2)*sqrt(-c)*g*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + sqrt(c*d^2 - b*d*e + a*e^2)*(c*e*f - c*d*g)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 + 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)))/(c^2*d^2*e - b*c*d*e^2 + a*c*e^3), -((c*d^2 - b*d*e + a*e^2)*sqrt(-c)*g*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - sqrt(-c*d^2 + b*d*e - a*e^2)*(c*e*f - c*d*g)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)))/(c^2*d^2*e - b*c*d*e^2 + a*c*e^3)]","B",0
874,1,343,0,0.554355," ","integrate(1/(e*x+d)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} - 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right)}{2 \, \sqrt{c d^{2} - b d e + a e^{2}}}, \frac{\sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right)}{c d^{2} - b d e + a e^{2}}\right]"," ",0,"[1/2*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 - 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2))/sqrt(c*d^2 - b*d*e + a*e^2), sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x))/(c*d^2 - b*d*e + a*e^2)]","B",0
875,1,1952,0,123.751050," ","integrate(1/(e*x+d)/(g*x+f)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{c f^{2} - b f g + a g^{2}} g \log\left(\frac{8 \, a b f g - 8 \, a^{2} g^{2} - {\left(b^{2} + 4 \, a c\right)} f^{2} - {\left(8 \, c^{2} f^{2} - 8 \, b c f g + {\left(b^{2} + 4 \, a c\right)} g^{2}\right)} x^{2} - 4 \, \sqrt{c f^{2} - b f g + a g^{2}} \sqrt{c x^{2} + b x + a} {\left(b f - 2 \, a g + {\left(2 \, c f - b g\right)} x\right)} - 2 \, {\left(4 \, b c f^{2} + 4 \, a b g^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} f g\right)} x}{g^{2} x^{2} + 2 \, f g x + f^{2}}\right) + {\left(c e f^{2} - b e f g + a e g^{2}\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} + 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right)}{2 \, {\left({\left(c^{2} d^{2} e - b c d e^{2} + a c e^{3}\right)} f^{3} - {\left(c^{2} d^{3} + a b e^{3} - {\left(b^{2} - a c\right)} d e^{2}\right)} f^{2} g + {\left(b c d^{3} + a^{2} e^{3} - {\left(b^{2} - a c\right)} d^{2} e\right)} f g^{2} - {\left(a c d^{3} - a b d^{2} e + a^{2} d e^{2}\right)} g^{3}\right)}}, -\frac{2 \, {\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{-c f^{2} + b f g - a g^{2}} g \arctan\left(-\frac{\sqrt{-c f^{2} + b f g - a g^{2}} \sqrt{c x^{2} + b x + a} {\left(b f - 2 \, a g + {\left(2 \, c f - b g\right)} x\right)}}{2 \, {\left(a c f^{2} - a b f g + a^{2} g^{2} + {\left(c^{2} f^{2} - b c f g + a c g^{2}\right)} x^{2} + {\left(b c f^{2} - b^{2} f g + a b g^{2}\right)} x\right)}}\right) + {\left(c e f^{2} - b e f g + a e g^{2}\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} + 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right)}{2 \, {\left({\left(c^{2} d^{2} e - b c d e^{2} + a c e^{3}\right)} f^{3} - {\left(c^{2} d^{3} + a b e^{3} - {\left(b^{2} - a c\right)} d e^{2}\right)} f^{2} g + {\left(b c d^{3} + a^{2} e^{3} - {\left(b^{2} - a c\right)} d^{2} e\right)} f g^{2} - {\left(a c d^{3} - a b d^{2} e + a^{2} d e^{2}\right)} g^{3}\right)}}, -\frac{{\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{c f^{2} - b f g + a g^{2}} g \log\left(\frac{8 \, a b f g - 8 \, a^{2} g^{2} - {\left(b^{2} + 4 \, a c\right)} f^{2} - {\left(8 \, c^{2} f^{2} - 8 \, b c f g + {\left(b^{2} + 4 \, a c\right)} g^{2}\right)} x^{2} - 4 \, \sqrt{c f^{2} - b f g + a g^{2}} \sqrt{c x^{2} + b x + a} {\left(b f - 2 \, a g + {\left(2 \, c f - b g\right)} x\right)} - 2 \, {\left(4 \, b c f^{2} + 4 \, a b g^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} f g\right)} x}{g^{2} x^{2} + 2 \, f g x + f^{2}}\right) - 2 \, {\left(c e f^{2} - b e f g + a e g^{2}\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right)}{2 \, {\left({\left(c^{2} d^{2} e - b c d e^{2} + a c e^{3}\right)} f^{3} - {\left(c^{2} d^{3} + a b e^{3} - {\left(b^{2} - a c\right)} d e^{2}\right)} f^{2} g + {\left(b c d^{3} + a^{2} e^{3} - {\left(b^{2} - a c\right)} d^{2} e\right)} f g^{2} - {\left(a c d^{3} - a b d^{2} e + a^{2} d e^{2}\right)} g^{3}\right)}}, -\frac{{\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{-c f^{2} + b f g - a g^{2}} g \arctan\left(-\frac{\sqrt{-c f^{2} + b f g - a g^{2}} \sqrt{c x^{2} + b x + a} {\left(b f - 2 \, a g + {\left(2 \, c f - b g\right)} x\right)}}{2 \, {\left(a c f^{2} - a b f g + a^{2} g^{2} + {\left(c^{2} f^{2} - b c f g + a c g^{2}\right)} x^{2} + {\left(b c f^{2} - b^{2} f g + a b g^{2}\right)} x\right)}}\right) - {\left(c e f^{2} - b e f g + a e g^{2}\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right)}{{\left(c^{2} d^{2} e - b c d e^{2} + a c e^{3}\right)} f^{3} - {\left(c^{2} d^{3} + a b e^{3} - {\left(b^{2} - a c\right)} d e^{2}\right)} f^{2} g + {\left(b c d^{3} + a^{2} e^{3} - {\left(b^{2} - a c\right)} d^{2} e\right)} f g^{2} - {\left(a c d^{3} - a b d^{2} e + a^{2} d e^{2}\right)} g^{3}}\right]"," ",0,"[-1/2*((c*d^2 - b*d*e + a*e^2)*sqrt(c*f^2 - b*f*g + a*g^2)*g*log((8*a*b*f*g - 8*a^2*g^2 - (b^2 + 4*a*c)*f^2 - (8*c^2*f^2 - 8*b*c*f*g + (b^2 + 4*a*c)*g^2)*x^2 - 4*sqrt(c*f^2 - b*f*g + a*g^2)*sqrt(c*x^2 + b*x + a)*(b*f - 2*a*g + (2*c*f - b*g)*x) - 2*(4*b*c*f^2 + 4*a*b*g^2 - (3*b^2 + 4*a*c)*f*g)*x)/(g^2*x^2 + 2*f*g*x + f^2)) + (c*e*f^2 - b*e*f*g + a*e*g^2)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 + 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)))/((c^2*d^2*e - b*c*d*e^2 + a*c*e^3)*f^3 - (c^2*d^3 + a*b*e^3 - (b^2 - a*c)*d*e^2)*f^2*g + (b*c*d^3 + a^2*e^3 - (b^2 - a*c)*d^2*e)*f*g^2 - (a*c*d^3 - a*b*d^2*e + a^2*d*e^2)*g^3), -1/2*(2*(c*d^2 - b*d*e + a*e^2)*sqrt(-c*f^2 + b*f*g - a*g^2)*g*arctan(-1/2*sqrt(-c*f^2 + b*f*g - a*g^2)*sqrt(c*x^2 + b*x + a)*(b*f - 2*a*g + (2*c*f - b*g)*x)/(a*c*f^2 - a*b*f*g + a^2*g^2 + (c^2*f^2 - b*c*f*g + a*c*g^2)*x^2 + (b*c*f^2 - b^2*f*g + a*b*g^2)*x)) + (c*e*f^2 - b*e*f*g + a*e*g^2)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 + 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)))/((c^2*d^2*e - b*c*d*e^2 + a*c*e^3)*f^3 - (c^2*d^3 + a*b*e^3 - (b^2 - a*c)*d*e^2)*f^2*g + (b*c*d^3 + a^2*e^3 - (b^2 - a*c)*d^2*e)*f*g^2 - (a*c*d^3 - a*b*d^2*e + a^2*d*e^2)*g^3), -1/2*((c*d^2 - b*d*e + a*e^2)*sqrt(c*f^2 - b*f*g + a*g^2)*g*log((8*a*b*f*g - 8*a^2*g^2 - (b^2 + 4*a*c)*f^2 - (8*c^2*f^2 - 8*b*c*f*g + (b^2 + 4*a*c)*g^2)*x^2 - 4*sqrt(c*f^2 - b*f*g + a*g^2)*sqrt(c*x^2 + b*x + a)*(b*f - 2*a*g + (2*c*f - b*g)*x) - 2*(4*b*c*f^2 + 4*a*b*g^2 - (3*b^2 + 4*a*c)*f*g)*x)/(g^2*x^2 + 2*f*g*x + f^2)) - 2*(c*e*f^2 - b*e*f*g + a*e*g^2)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)))/((c^2*d^2*e - b*c*d*e^2 + a*c*e^3)*f^3 - (c^2*d^3 + a*b*e^3 - (b^2 - a*c)*d*e^2)*f^2*g + (b*c*d^3 + a^2*e^3 - (b^2 - a*c)*d^2*e)*f*g^2 - (a*c*d^3 - a*b*d^2*e + a^2*d*e^2)*g^3), -((c*d^2 - b*d*e + a*e^2)*sqrt(-c*f^2 + b*f*g - a*g^2)*g*arctan(-1/2*sqrt(-c*f^2 + b*f*g - a*g^2)*sqrt(c*x^2 + b*x + a)*(b*f - 2*a*g + (2*c*f - b*g)*x)/(a*c*f^2 - a*b*f*g + a^2*g^2 + (c^2*f^2 - b*c*f*g + a*c*g^2)*x^2 + (b*c*f^2 - b^2*f*g + a*b*g^2)*x)) - (c*e*f^2 - b*e*f*g + a*e*g^2)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)))/((c^2*d^2*e - b*c*d*e^2 + a*c*e^3)*f^3 - (c^2*d^3 + a*b*e^3 - (b^2 - a*c)*d*e^2)*f^2*g + (b*c*d^3 + a^2*e^3 - (b^2 - a*c)*d^2*e)*f*g^2 - (a*c*d^3 - a*b*d^2*e + a^2*d*e^2)*g^3)]","B",0
876,-1,0,0,0.000000," ","integrate(1/(e*x+d)/(g*x+f)^2/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
877,-1,0,0,0.000000," ","integrate(1/(e*x+d)/(g*x+f)^3/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
878,-1,0,0,0.000000," ","integrate((g*x+f)^4/(e*x+d)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
879,-1,0,0,0.000000," ","integrate((g*x+f)^3/(e*x+d)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
880,1,2023,0,7.789420," ","integrate((g*x+f)^2/(e*x+d)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(a b^{2} - 4 \, a^{2} c\right)} e^{2} f^{2} - 2 \, {\left(a b^{2} - 4 \, a^{2} c\right)} d e f g + {\left(a b^{2} - 4 \, a^{2} c\right)} d^{2} g^{2} + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} e^{2} f^{2} - 2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d e f g + {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} g^{2}\right)} x^{2} + {\left({\left(b^{3} - 4 \, a b c\right)} e^{2} f^{2} - 2 \, {\left(b^{3} - 4 \, a b c\right)} d e f g + {\left(b^{3} - 4 \, a b c\right)} d^{2} g^{2}\right)} x\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} - 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 4 \, {\left({\left(b c^{2} d^{3} - 2 \, {\left(b^{2} c - a c^{2}\right)} d^{2} e + {\left(b^{3} - a b c\right)} d e^{2} - {\left(a b^{2} - 2 \, a^{2} c\right)} e^{3}\right)} f^{2} - 2 \, {\left(2 \, a c^{2} d^{3} - 3 \, a b c d^{2} e - a^{2} b e^{3} + {\left(a b^{2} + 2 \, a^{2} c\right)} d e^{2}\right)} f g + {\left(a b c d^{3} + 3 \, a^{2} b d e^{2} - 2 \, a^{3} e^{3} - {\left(a b^{2} + 2 \, a^{2} c\right)} d^{2} e\right)} g^{2} + {\left({\left(2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e - a b c e^{3} + {\left(b^{2} c + 2 \, a c^{2}\right)} d e^{2}\right)} f^{2} - 2 \, {\left(b c^{2} d^{3} + 3 \, a b c d e^{2} - 2 \, a^{2} c e^{3} - {\left(b^{2} c + 2 \, a c^{2}\right)} d^{2} e\right)} f g - {\left(a^{2} b e^{3} - {\left(b^{2} c - 2 \, a c^{2}\right)} d^{3} + {\left(b^{3} - a b c\right)} d^{2} e - 2 \, {\left(a b^{2} - a^{2} c\right)} d e^{2}\right)} g^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{2 \, {\left({\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{3} e + {\left(a b^{4} - 2 \, a^{2} b^{2} c - 8 \, a^{3} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{4} + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}\right)} x^{2} + {\left({\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{4} - 2 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d^{3} e + {\left(b^{5} - 2 \, a b^{3} c - 8 \, a^{2} b c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{4} - 4 \, a^{2} b^{2} c\right)} d e^{3} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{4}\right)} x\right)}}, \frac{{\left({\left(a b^{2} - 4 \, a^{2} c\right)} e^{2} f^{2} - 2 \, {\left(a b^{2} - 4 \, a^{2} c\right)} d e f g + {\left(a b^{2} - 4 \, a^{2} c\right)} d^{2} g^{2} + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} e^{2} f^{2} - 2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d e f g + {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} g^{2}\right)} x^{2} + {\left({\left(b^{3} - 4 \, a b c\right)} e^{2} f^{2} - 2 \, {\left(b^{3} - 4 \, a b c\right)} d e f g + {\left(b^{3} - 4 \, a b c\right)} d^{2} g^{2}\right)} x\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) - 2 \, {\left({\left(b c^{2} d^{3} - 2 \, {\left(b^{2} c - a c^{2}\right)} d^{2} e + {\left(b^{3} - a b c\right)} d e^{2} - {\left(a b^{2} - 2 \, a^{2} c\right)} e^{3}\right)} f^{2} - 2 \, {\left(2 \, a c^{2} d^{3} - 3 \, a b c d^{2} e - a^{2} b e^{3} + {\left(a b^{2} + 2 \, a^{2} c\right)} d e^{2}\right)} f g + {\left(a b c d^{3} + 3 \, a^{2} b d e^{2} - 2 \, a^{3} e^{3} - {\left(a b^{2} + 2 \, a^{2} c\right)} d^{2} e\right)} g^{2} + {\left({\left(2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e - a b c e^{3} + {\left(b^{2} c + 2 \, a c^{2}\right)} d e^{2}\right)} f^{2} - 2 \, {\left(b c^{2} d^{3} + 3 \, a b c d e^{2} - 2 \, a^{2} c e^{3} - {\left(b^{2} c + 2 \, a c^{2}\right)} d^{2} e\right)} f g - {\left(a^{2} b e^{3} - {\left(b^{2} c - 2 \, a c^{2}\right)} d^{3} + {\left(b^{3} - a b c\right)} d^{2} e - 2 \, {\left(a b^{2} - a^{2} c\right)} d e^{2}\right)} g^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{{\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{3} e + {\left(a b^{4} - 2 \, a^{2} b^{2} c - 8 \, a^{3} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{4} + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}\right)} x^{2} + {\left({\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{4} - 2 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d^{3} e + {\left(b^{5} - 2 \, a b^{3} c - 8 \, a^{2} b c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{4} - 4 \, a^{2} b^{2} c\right)} d e^{3} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{4}\right)} x}\right]"," ",0,"[1/2*(((a*b^2 - 4*a^2*c)*e^2*f^2 - 2*(a*b^2 - 4*a^2*c)*d*e*f*g + (a*b^2 - 4*a^2*c)*d^2*g^2 + ((b^2*c - 4*a*c^2)*e^2*f^2 - 2*(b^2*c - 4*a*c^2)*d*e*f*g + (b^2*c - 4*a*c^2)*d^2*g^2)*x^2 + ((b^3 - 4*a*b*c)*e^2*f^2 - 2*(b^3 - 4*a*b*c)*d*e*f*g + (b^3 - 4*a*b*c)*d^2*g^2)*x)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 - 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)) - 4*((b*c^2*d^3 - 2*(b^2*c - a*c^2)*d^2*e + (b^3 - a*b*c)*d*e^2 - (a*b^2 - 2*a^2*c)*e^3)*f^2 - 2*(2*a*c^2*d^3 - 3*a*b*c*d^2*e - a^2*b*e^3 + (a*b^2 + 2*a^2*c)*d*e^2)*f*g + (a*b*c*d^3 + 3*a^2*b*d*e^2 - 2*a^3*e^3 - (a*b^2 + 2*a^2*c)*d^2*e)*g^2 + ((2*c^3*d^3 - 3*b*c^2*d^2*e - a*b*c*e^3 + (b^2*c + 2*a*c^2)*d*e^2)*f^2 - 2*(b*c^2*d^3 + 3*a*b*c*d*e^2 - 2*a^2*c*e^3 - (b^2*c + 2*a*c^2)*d^2*e)*f*g - (a^2*b*e^3 - (b^2*c - 2*a*c^2)*d^3 + (b^3 - a*b*c)*d^2*e - 2*(a*b^2 - a^2*c)*d*e^2)*g^2)*x)*sqrt(c*x^2 + b*x + a))/((a*b^2*c^2 - 4*a^2*c^3)*d^4 - 2*(a*b^3*c - 4*a^2*b*c^2)*d^3*e + (a*b^4 - 2*a^2*b^2*c - 8*a^3*c^2)*d^2*e^2 - 2*(a^2*b^3 - 4*a^3*b*c)*d*e^3 + (a^3*b^2 - 4*a^4*c)*e^4 + ((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4)*x^2 + ((b^3*c^2 - 4*a*b*c^3)*d^4 - 2*(b^4*c - 4*a*b^2*c^2)*d^3*e + (b^5 - 2*a*b^3*c - 8*a^2*b*c^2)*d^2*e^2 - 2*(a*b^4 - 4*a^2*b^2*c)*d*e^3 + (a^2*b^3 - 4*a^3*b*c)*e^4)*x), (((a*b^2 - 4*a^2*c)*e^2*f^2 - 2*(a*b^2 - 4*a^2*c)*d*e*f*g + (a*b^2 - 4*a^2*c)*d^2*g^2 + ((b^2*c - 4*a*c^2)*e^2*f^2 - 2*(b^2*c - 4*a*c^2)*d*e*f*g + (b^2*c - 4*a*c^2)*d^2*g^2)*x^2 + ((b^3 - 4*a*b*c)*e^2*f^2 - 2*(b^3 - 4*a*b*c)*d*e*f*g + (b^3 - 4*a*b*c)*d^2*g^2)*x)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) - 2*((b*c^2*d^3 - 2*(b^2*c - a*c^2)*d^2*e + (b^3 - a*b*c)*d*e^2 - (a*b^2 - 2*a^2*c)*e^3)*f^2 - 2*(2*a*c^2*d^3 - 3*a*b*c*d^2*e - a^2*b*e^3 + (a*b^2 + 2*a^2*c)*d*e^2)*f*g + (a*b*c*d^3 + 3*a^2*b*d*e^2 - 2*a^3*e^3 - (a*b^2 + 2*a^2*c)*d^2*e)*g^2 + ((2*c^3*d^3 - 3*b*c^2*d^2*e - a*b*c*e^3 + (b^2*c + 2*a*c^2)*d*e^2)*f^2 - 2*(b*c^2*d^3 + 3*a*b*c*d*e^2 - 2*a^2*c*e^3 - (b^2*c + 2*a*c^2)*d^2*e)*f*g - (a^2*b*e^3 - (b^2*c - 2*a*c^2)*d^3 + (b^3 - a*b*c)*d^2*e - 2*(a*b^2 - a^2*c)*d*e^2)*g^2)*x)*sqrt(c*x^2 + b*x + a))/((a*b^2*c^2 - 4*a^2*c^3)*d^4 - 2*(a*b^3*c - 4*a^2*b*c^2)*d^3*e + (a*b^4 - 2*a^2*b^2*c - 8*a^3*c^2)*d^2*e^2 - 2*(a^2*b^3 - 4*a^3*b*c)*d*e^3 + (a^3*b^2 - 4*a^4*c)*e^4 + ((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4)*x^2 + ((b^3*c^2 - 4*a*b*c^3)*d^4 - 2*(b^4*c - 4*a*b^2*c^2)*d^3*e + (b^5 - 2*a*b^3*c - 8*a^2*b*c^2)*d^2*e^2 - 2*(a*b^4 - 4*a^2*b^2*c)*d*e^3 + (a^2*b^3 - 4*a^3*b*c)*e^4)*x)]","B",0
881,1,1663,0,5.000305," ","integrate((g*x+f)/(e*x+d)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left({\left(a b^{2} - 4 \, a^{2} c\right)} e^{2} f - {\left(a b^{2} - 4 \, a^{2} c\right)} d e g + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} e^{2} f - {\left(b^{2} c - 4 \, a c^{2}\right)} d e g\right)} x^{2} + {\left({\left(b^{3} - 4 \, a b c\right)} e^{2} f - {\left(b^{3} - 4 \, a b c\right)} d e g\right)} x\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} + 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 4 \, \sqrt{c x^{2} + b x + a} {\left({\left(b c^{2} d^{3} - 2 \, {\left(b^{2} c - a c^{2}\right)} d^{2} e + {\left(b^{3} - a b c\right)} d e^{2} - {\left(a b^{2} - 2 \, a^{2} c\right)} e^{3}\right)} f - {\left(2 \, a c^{2} d^{3} - 3 \, a b c d^{2} e - a^{2} b e^{3} + {\left(a b^{2} + 2 \, a^{2} c\right)} d e^{2}\right)} g + {\left({\left(2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e - a b c e^{3} + {\left(b^{2} c + 2 \, a c^{2}\right)} d e^{2}\right)} f - {\left(b c^{2} d^{3} + 3 \, a b c d e^{2} - 2 \, a^{2} c e^{3} - {\left(b^{2} c + 2 \, a c^{2}\right)} d^{2} e\right)} g\right)} x\right)}}{2 \, {\left({\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{3} e + {\left(a b^{4} - 2 \, a^{2} b^{2} c - 8 \, a^{3} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{4} + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}\right)} x^{2} + {\left({\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{4} - 2 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d^{3} e + {\left(b^{5} - 2 \, a b^{3} c - 8 \, a^{2} b c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{4} - 4 \, a^{2} b^{2} c\right)} d e^{3} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{4}\right)} x\right)}}, \frac{{\left({\left(a b^{2} - 4 \, a^{2} c\right)} e^{2} f - {\left(a b^{2} - 4 \, a^{2} c\right)} d e g + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} e^{2} f - {\left(b^{2} c - 4 \, a c^{2}\right)} d e g\right)} x^{2} + {\left({\left(b^{3} - 4 \, a b c\right)} e^{2} f - {\left(b^{3} - 4 \, a b c\right)} d e g\right)} x\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) - 2 \, \sqrt{c x^{2} + b x + a} {\left({\left(b c^{2} d^{3} - 2 \, {\left(b^{2} c - a c^{2}\right)} d^{2} e + {\left(b^{3} - a b c\right)} d e^{2} - {\left(a b^{2} - 2 \, a^{2} c\right)} e^{3}\right)} f - {\left(2 \, a c^{2} d^{3} - 3 \, a b c d^{2} e - a^{2} b e^{3} + {\left(a b^{2} + 2 \, a^{2} c\right)} d e^{2}\right)} g + {\left({\left(2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e - a b c e^{3} + {\left(b^{2} c + 2 \, a c^{2}\right)} d e^{2}\right)} f - {\left(b c^{2} d^{3} + 3 \, a b c d e^{2} - 2 \, a^{2} c e^{3} - {\left(b^{2} c + 2 \, a c^{2}\right)} d^{2} e\right)} g\right)} x\right)}}{{\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{3} e + {\left(a b^{4} - 2 \, a^{2} b^{2} c - 8 \, a^{3} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{4} + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}\right)} x^{2} + {\left({\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{4} - 2 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d^{3} e + {\left(b^{5} - 2 \, a b^{3} c - 8 \, a^{2} b c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{4} - 4 \, a^{2} b^{2} c\right)} d e^{3} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{4}\right)} x}\right]"," ",0,"[-1/2*(((a*b^2 - 4*a^2*c)*e^2*f - (a*b^2 - 4*a^2*c)*d*e*g + ((b^2*c - 4*a*c^2)*e^2*f - (b^2*c - 4*a*c^2)*d*e*g)*x^2 + ((b^3 - 4*a*b*c)*e^2*f - (b^3 - 4*a*b*c)*d*e*g)*x)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 + 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)) + 4*sqrt(c*x^2 + b*x + a)*((b*c^2*d^3 - 2*(b^2*c - a*c^2)*d^2*e + (b^3 - a*b*c)*d*e^2 - (a*b^2 - 2*a^2*c)*e^3)*f - (2*a*c^2*d^3 - 3*a*b*c*d^2*e - a^2*b*e^3 + (a*b^2 + 2*a^2*c)*d*e^2)*g + ((2*c^3*d^3 - 3*b*c^2*d^2*e - a*b*c*e^3 + (b^2*c + 2*a*c^2)*d*e^2)*f - (b*c^2*d^3 + 3*a*b*c*d*e^2 - 2*a^2*c*e^3 - (b^2*c + 2*a*c^2)*d^2*e)*g)*x))/((a*b^2*c^2 - 4*a^2*c^3)*d^4 - 2*(a*b^3*c - 4*a^2*b*c^2)*d^3*e + (a*b^4 - 2*a^2*b^2*c - 8*a^3*c^2)*d^2*e^2 - 2*(a^2*b^3 - 4*a^3*b*c)*d*e^3 + (a^3*b^2 - 4*a^4*c)*e^4 + ((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4)*x^2 + ((b^3*c^2 - 4*a*b*c^3)*d^4 - 2*(b^4*c - 4*a*b^2*c^2)*d^3*e + (b^5 - 2*a*b^3*c - 8*a^2*b*c^2)*d^2*e^2 - 2*(a*b^4 - 4*a^2*b^2*c)*d*e^3 + (a^2*b^3 - 4*a^3*b*c)*e^4)*x), (((a*b^2 - 4*a^2*c)*e^2*f - (a*b^2 - 4*a^2*c)*d*e*g + ((b^2*c - 4*a*c^2)*e^2*f - (b^2*c - 4*a*c^2)*d*e*g)*x^2 + ((b^3 - 4*a*b*c)*e^2*f - (b^3 - 4*a*b*c)*d*e*g)*x)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) - 2*sqrt(c*x^2 + b*x + a)*((b*c^2*d^3 - 2*(b^2*c - a*c^2)*d^2*e + (b^3 - a*b*c)*d*e^2 - (a*b^2 - 2*a^2*c)*e^3)*f - (2*a*c^2*d^3 - 3*a*b*c*d^2*e - a^2*b*e^3 + (a*b^2 + 2*a^2*c)*d*e^2)*g + ((2*c^3*d^3 - 3*b*c^2*d^2*e - a*b*c*e^3 + (b^2*c + 2*a*c^2)*d*e^2)*f - (b*c^2*d^3 + 3*a*b*c*d*e^2 - 2*a^2*c*e^3 - (b^2*c + 2*a*c^2)*d^2*e)*g)*x))/((a*b^2*c^2 - 4*a^2*c^3)*d^4 - 2*(a*b^3*c - 4*a^2*b*c^2)*d^3*e + (a*b^4 - 2*a^2*b^2*c - 8*a^3*c^2)*d^2*e^2 - 2*(a^2*b^3 - 4*a^3*b*c)*d*e^3 + (a^3*b^2 - 4*a^4*c)*e^4 + ((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4)*x^2 + ((b^3*c^2 - 4*a*b*c^3)*d^4 - 2*(b^4*c - 4*a*b^2*c^2)*d^3*e + (b^5 - 2*a*b^3*c - 8*a^2*b*c^2)*d^2*e^2 - 2*(a*b^4 - 4*a^2*b^2*c)*d*e^3 + (a^2*b^3 - 4*a^3*b*c)*e^4)*x)]","B",0
882,1,1349,0,0.912451," ","integrate(1/(e*x+d)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(b^{2} c - 4 \, a c^{2}\right)} e^{2} x^{2} + {\left(b^{3} - 4 \, a b c\right)} e^{2} x + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} - 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 4 \, {\left(b c^{2} d^{3} - 2 \, {\left(b^{2} c - a c^{2}\right)} d^{2} e + {\left(b^{3} - a b c\right)} d e^{2} - {\left(a b^{2} - 2 \, a^{2} c\right)} e^{3} + {\left(2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e - a b c e^{3} + {\left(b^{2} c + 2 \, a c^{2}\right)} d e^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{2 \, {\left({\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{3} e + {\left(a b^{4} - 2 \, a^{2} b^{2} c - 8 \, a^{3} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{4} + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}\right)} x^{2} + {\left({\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{4} - 2 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d^{3} e + {\left(b^{5} - 2 \, a b^{3} c - 8 \, a^{2} b c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{4} - 4 \, a^{2} b^{2} c\right)} d e^{3} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{4}\right)} x\right)}}, \frac{{\left({\left(b^{2} c - 4 \, a c^{2}\right)} e^{2} x^{2} + {\left(b^{3} - 4 \, a b c\right)} e^{2} x + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) - 2 \, {\left(b c^{2} d^{3} - 2 \, {\left(b^{2} c - a c^{2}\right)} d^{2} e + {\left(b^{3} - a b c\right)} d e^{2} - {\left(a b^{2} - 2 \, a^{2} c\right)} e^{3} + {\left(2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e - a b c e^{3} + {\left(b^{2} c + 2 \, a c^{2}\right)} d e^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{{\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{3} e + {\left(a b^{4} - 2 \, a^{2} b^{2} c - 8 \, a^{3} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{4} + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}\right)} x^{2} + {\left({\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{4} - 2 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d^{3} e + {\left(b^{5} - 2 \, a b^{3} c - 8 \, a^{2} b c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{4} - 4 \, a^{2} b^{2} c\right)} d e^{3} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{4}\right)} x}\right]"," ",0,"[1/2*(((b^2*c - 4*a*c^2)*e^2*x^2 + (b^3 - 4*a*b*c)*e^2*x + (a*b^2 - 4*a^2*c)*e^2)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 - 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)) - 4*(b*c^2*d^3 - 2*(b^2*c - a*c^2)*d^2*e + (b^3 - a*b*c)*d*e^2 - (a*b^2 - 2*a^2*c)*e^3 + (2*c^3*d^3 - 3*b*c^2*d^2*e - a*b*c*e^3 + (b^2*c + 2*a*c^2)*d*e^2)*x)*sqrt(c*x^2 + b*x + a))/((a*b^2*c^2 - 4*a^2*c^3)*d^4 - 2*(a*b^3*c - 4*a^2*b*c^2)*d^3*e + (a*b^4 - 2*a^2*b^2*c - 8*a^3*c^2)*d^2*e^2 - 2*(a^2*b^3 - 4*a^3*b*c)*d*e^3 + (a^3*b^2 - 4*a^4*c)*e^4 + ((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4)*x^2 + ((b^3*c^2 - 4*a*b*c^3)*d^4 - 2*(b^4*c - 4*a*b^2*c^2)*d^3*e + (b^5 - 2*a*b^3*c - 8*a^2*b*c^2)*d^2*e^2 - 2*(a*b^4 - 4*a^2*b^2*c)*d*e^3 + (a^2*b^3 - 4*a^3*b*c)*e^4)*x), (((b^2*c - 4*a*c^2)*e^2*x^2 + (b^3 - 4*a*b*c)*e^2*x + (a*b^2 - 4*a^2*c)*e^2)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) - 2*(b*c^2*d^3 - 2*(b^2*c - a*c^2)*d^2*e + (b^3 - a*b*c)*d*e^2 - (a*b^2 - 2*a^2*c)*e^3 + (2*c^3*d^3 - 3*b*c^2*d^2*e - a*b*c*e^3 + (b^2*c + 2*a*c^2)*d*e^2)*x)*sqrt(c*x^2 + b*x + a))/((a*b^2*c^2 - 4*a^2*c^3)*d^4 - 2*(a*b^3*c - 4*a^2*b*c^2)*d^3*e + (a*b^4 - 2*a^2*b^2*c - 8*a^3*c^2)*d^2*e^2 - 2*(a^2*b^3 - 4*a^3*b*c)*d*e^3 + (a^3*b^2 - 4*a^4*c)*e^4 + ((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4)*x^2 + ((b^3*c^2 - 4*a*b*c^3)*d^4 - 2*(b^4*c - 4*a*b^2*c^2)*d^3*e + (b^5 - 2*a*b^3*c - 8*a^2*b*c^2)*d^2*e^2 - 2*(a*b^4 - 4*a^2*b^2*c)*d*e^3 + (a^2*b^3 - 4*a^3*b*c)*e^4)*x)]","B",0
883,-1,0,0,0.000000," ","integrate(1/(e*x+d)/(g*x+f)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
884,-1,0,0,0.000000," ","integrate(1/(e*x+d)/(g*x+f)^2/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
885,-1,0,0,0.000000," ","integrate(1/(e*x+d)/(g*x+f)^3/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
886,0,0,0,0.700020," ","integrate((e*x+d)^3*(g*x+f)^(1/2)*(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}\right)} \sqrt{c x^{2} + b x + a} \sqrt{g x + f}, x\right)"," ",0,"integral((e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)*sqrt(c*x^2 + b*x + a)*sqrt(g*x + f), x)","F",0
887,0,0,0,0.622820," ","integrate((e*x+d)^2*(g*x+f)^(1/2)*(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{2} x^{2} + 2 \, d e x + d^{2}\right)} \sqrt{c x^{2} + b x + a} \sqrt{g x + f}, x\right)"," ",0,"integral((e^2*x^2 + 2*d*e*x + d^2)*sqrt(c*x^2 + b*x + a)*sqrt(g*x + f), x)","F",0
888,0,0,0,0.709445," ","integrate((e*x+d)*(g*x+f)^(1/2)*(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{2} + b x + a} {\left(e x + d\right)} \sqrt{g x + f}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*(e*x + d)*sqrt(g*x + f), x)","F",0
889,0,0,0,0.662191," ","integrate((g*x+f)^(1/2)*(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{2} + b x + a} \sqrt{g x + f}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*sqrt(g*x + f), x)","F",0
890,-1,0,0,0.000000," ","integrate((g*x+f)^(1/2)*(c*x^2+b*x+a)^(1/2)/(e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
891,-1,0,0,0.000000," ","integrate((g*x+f)^(1/2)*(c*x^2+b*x+a)^(1/2)/(e*x+d)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
892,-1,0,0,0.000000," ","integrate((g*x+f)^(1/2)*(c*x^2+b*x+a)^(1/2)/(e*x+d)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
893,0,0,0,0.671249," ","integrate((e*x+d)^3*(c*x^2+b*x+a)^(1/2)/(g*x+f)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}\right)} \sqrt{c x^{2} + b x + a}}{\sqrt{g x + f}}, x\right)"," ",0,"integral((e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)*sqrt(c*x^2 + b*x + a)/sqrt(g*x + f), x)","F",0
894,0,0,0,0.607275," ","integrate((e*x+d)^2*(c*x^2+b*x+a)^(1/2)/(g*x+f)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{2} x^{2} + 2 \, d e x + d^{2}\right)} \sqrt{c x^{2} + b x + a}}{\sqrt{g x + f}}, x\right)"," ",0,"integral((e^2*x^2 + 2*d*e*x + d^2)*sqrt(c*x^2 + b*x + a)/sqrt(g*x + f), x)","F",0
895,0,0,0,0.768828," ","integrate((e*x+d)*(c*x^2+b*x+a)^(1/2)/(g*x+f)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} {\left(e x + d\right)}}{\sqrt{g x + f}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*(e*x + d)/sqrt(g*x + f), x)","F",0
896,0,0,0,0.607054," ","integrate((c*x^2+b*x+a)^(1/2)/(g*x+f)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a}}{\sqrt{g x + f}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)/sqrt(g*x + f), x)","F",0
897,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(1/2)/(e*x+d)/(g*x+f)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
898,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(1/2)/(e*x+d)^2/(g*x+f)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
899,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(1/2)/(e*x+d)^3/(g*x+f)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
900,0,0,0,0.698979," ","integrate((e*x+d)^3*(g*x+f)^(1/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}\right)} \sqrt{g x + f}}{\sqrt{c x^{2} + b x + a}}, x\right)"," ",0,"integral((e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)*sqrt(g*x + f)/sqrt(c*x^2 + b*x + a), x)","F",0
901,0,0,0,0.656108," ","integrate((e*x+d)^2*(g*x+f)^(1/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{2} x^{2} + 2 \, d e x + d^{2}\right)} \sqrt{g x + f}}{\sqrt{c x^{2} + b x + a}}, x\right)"," ",0,"integral((e^2*x^2 + 2*d*e*x + d^2)*sqrt(g*x + f)/sqrt(c*x^2 + b*x + a), x)","F",0
902,0,0,0,0.920478," ","integrate((e*x+d)*(g*x+f)^(1/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)} \sqrt{g x + f}}{\sqrt{c x^{2} + b x + a}}, x\right)"," ",0,"integral((e*x + d)*sqrt(g*x + f)/sqrt(c*x^2 + b*x + a), x)","F",0
903,0,0,0,0.800897," ","integrate((g*x+f)^(1/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{g x + f}}{\sqrt{c x^{2} + b x + a}}, x\right)"," ",0,"integral(sqrt(g*x + f)/sqrt(c*x^2 + b*x + a), x)","F",0
904,-1,0,0,0.000000," ","integrate((g*x+f)^(1/2)/(e*x+d)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
905,-1,0,0,0.000000," ","integrate((g*x+f)^(1/2)/(e*x+d)^2/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
906,-1,0,0,0.000000," ","integrate((g*x+f)^(1/2)/(e*x+d)^3/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
907,-1,0,0,0.000000," ","integrate((g*x+f)^(3/2)/(e*x+d)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
908,-1,0,0,0.000000," ","integrate((g*x+f)^(5/2)/(e*x+d)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
909,0,0,0,0.655008," ","integrate((e*x+d)^3/(g*x+f)^(1/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}\right)} \sqrt{c x^{2} + b x + a} \sqrt{g x + f}}{c g x^{3} + {\left(c f + b g\right)} x^{2} + a f + {\left(b f + a g\right)} x}, x\right)"," ",0,"integral((e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)*sqrt(c*x^2 + b*x + a)*sqrt(g*x + f)/(c*g*x^3 + (c*f + b*g)*x^2 + a*f + (b*f + a*g)*x), x)","F",0
910,0,0,0,0.809447," ","integrate((e*x+d)^2/(g*x+f)^(1/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{2} x^{2} + 2 \, d e x + d^{2}\right)} \sqrt{c x^{2} + b x + a} \sqrt{g x + f}}{c g x^{3} + {\left(c f + b g\right)} x^{2} + a f + {\left(b f + a g\right)} x}, x\right)"," ",0,"integral((e^2*x^2 + 2*d*e*x + d^2)*sqrt(c*x^2 + b*x + a)*sqrt(g*x + f)/(c*g*x^3 + (c*f + b*g)*x^2 + a*f + (b*f + a*g)*x), x)","F",0
911,0,0,0,0.660735," ","integrate((e*x+d)/(g*x+f)^(1/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} {\left(e x + d\right)} \sqrt{g x + f}}{c g x^{3} + {\left(c f + b g\right)} x^{2} + a f + {\left(b f + a g\right)} x}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*(e*x + d)*sqrt(g*x + f)/(c*g*x^3 + (c*f + b*g)*x^2 + a*f + (b*f + a*g)*x), x)","F",0
912,0,0,0,0.678683," ","integrate(1/(g*x+f)^(1/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} \sqrt{g x + f}}{c g x^{3} + {\left(c f + b g\right)} x^{2} + a f + {\left(b f + a g\right)} x}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*sqrt(g*x + f)/(c*g*x^3 + (c*f + b*g)*x^2 + a*f + (b*f + a*g)*x), x)","F",0
913,-1,0,0,0.000000," ","integrate(1/(e*x+d)/(g*x+f)^(1/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
914,-1,0,0,0.000000," ","integrate(1/(e*x+d)^2/(g*x+f)^(1/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
915,-1,0,0,0.000000," ","integrate(1/(e*x+d)^3/(g*x+f)^(1/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
916,-1,0,0,0.000000," ","integrate(1/(e*x+d)/(g*x+f)^(3/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
917,-1,0,0,0.000000," ","integrate(1/(e*x+d)/(g*x+f)^(5/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
918,-1,0,0,0.000000," ","integrate((e*x+d)^(1/2)/(g*x+f)^(1/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
919,0,0,0,1.015206," ","integrate(1/(e*x+d)^(1/2)/(g*x+f)^(1/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} \sqrt{e x + d} \sqrt{g x + f}}{c e g x^{4} + {\left(c e f + {\left(c d + b e\right)} g\right)} x^{3} + a d f + {\left({\left(c d + b e\right)} f + {\left(b d + a e\right)} g\right)} x^{2} + {\left(a d g + {\left(b d + a e\right)} f\right)} x}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*sqrt(e*x + d)*sqrt(g*x + f)/(c*e*g*x^4 + (c*e*f + (c*d + b*e)*g)*x^3 + a*d*f + ((c*d + b*e)*f + (b*d + a*e)*g)*x^2 + (a*d*g + (b*d + a*e)*f)*x), x)","F",0
920,1,1381,0,0.658030," ","integrate((e*x+d)^m*(g*x+f)^2*(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{{\left(a d e^{4} f^{2} m^{4} + {\left(c e^{5} g^{2} m^{4} + 10 \, c e^{5} g^{2} m^{3} + 35 \, c e^{5} g^{2} m^{2} + 50 \, c e^{5} g^{2} m + 24 \, c e^{5} g^{2}\right)} x^{5} + {\left(60 \, c e^{5} f g + 30 \, b e^{5} g^{2} + {\left(2 \, c e^{5} f g + {\left(c d e^{4} + b e^{5}\right)} g^{2}\right)} m^{4} + {\left(22 \, c e^{5} f g + {\left(6 \, c d e^{4} + 11 \, b e^{5}\right)} g^{2}\right)} m^{3} + {\left(82 \, c e^{5} f g + {\left(11 \, c d e^{4} + 41 \, b e^{5}\right)} g^{2}\right)} m^{2} + {\left(122 \, c e^{5} f g + {\left(6 \, c d e^{4} + 61 \, b e^{5}\right)} g^{2}\right)} m\right)} x^{4} - {\left(2 \, a d^{2} e^{3} f g + {\left(b d^{2} e^{3} - 14 \, a d e^{4}\right)} f^{2}\right)} m^{3} + {\left(40 \, c e^{5} f^{2} + 80 \, b e^{5} f g + 40 \, a e^{5} g^{2} + {\left(c e^{5} f^{2} + 2 \, {\left(c d e^{4} + b e^{5}\right)} f g + {\left(b d e^{4} + a e^{5}\right)} g^{2}\right)} m^{4} + 4 \, {\left(3 \, c e^{5} f^{2} + 2 \, {\left(2 \, c d e^{4} + 3 \, b e^{5}\right)} f g - {\left(c d^{2} e^{3} - 2 \, b d e^{4} - 3 \, a e^{5}\right)} g^{2}\right)} m^{3} + {\left(49 \, c e^{5} f^{2} + 2 \, {\left(17 \, c d e^{4} + 49 \, b e^{5}\right)} f g - {\left(12 \, c d^{2} e^{3} - 17 \, b d e^{4} - 49 \, a e^{5}\right)} g^{2}\right)} m^{2} + 2 \, {\left(39 \, c e^{5} f^{2} + 2 \, {\left(5 \, c d e^{4} + 39 \, b e^{5}\right)} f g - {\left(4 \, c d^{2} e^{3} - 5 \, b d e^{4} - 39 \, a e^{5}\right)} g^{2}\right)} m\right)} x^{3} + 20 \, {\left(2 \, c d^{3} e^{2} - 3 \, b d^{2} e^{3} + 6 \, a d e^{4}\right)} f^{2} - 20 \, {\left(3 \, c d^{4} e - 4 \, b d^{3} e^{2} + 6 \, a d^{2} e^{3}\right)} f g + 2 \, {\left(12 \, c d^{5} - 15 \, b d^{4} e + 20 \, a d^{3} e^{2}\right)} g^{2} + {\left(2 \, a d^{3} e^{2} g^{2} + {\left(2 \, c d^{3} e^{2} - 12 \, b d^{2} e^{3} + 71 \, a d e^{4}\right)} f^{2} + 4 \, {\left(b d^{3} e^{2} - 6 \, a d^{2} e^{3}\right)} f g\right)} m^{2} + {\left(60 \, b e^{5} f^{2} + 120 \, a e^{5} f g + {\left(a d e^{4} g^{2} + {\left(c d e^{4} + b e^{5}\right)} f^{2} + 2 \, {\left(b d e^{4} + a e^{5}\right)} f g\right)} m^{4} + {\left({\left(10 \, c d e^{4} + 13 \, b e^{5}\right)} f^{2} - 2 \, {\left(3 \, c d^{2} e^{3} - 10 \, b d e^{4} - 13 \, a e^{5}\right)} f g - {\left(3 \, b d^{2} e^{3} - 10 \, a d e^{4}\right)} g^{2}\right)} m^{3} + {\left({\left(29 \, c d e^{4} + 59 \, b e^{5}\right)} f^{2} - 2 \, {\left(18 \, c d^{2} e^{3} - 29 \, b d e^{4} - 59 \, a e^{5}\right)} f g + {\left(12 \, c d^{3} e^{2} - 18 \, b d^{2} e^{3} + 29 \, a d e^{4}\right)} g^{2}\right)} m^{2} + {\left({\left(20 \, c d e^{4} + 107 \, b e^{5}\right)} f^{2} - 2 \, {\left(15 \, c d^{2} e^{3} - 20 \, b d e^{4} - 107 \, a e^{5}\right)} f g + {\left(12 \, c d^{3} e^{2} - 15 \, b d^{2} e^{3} + 20 \, a d e^{4}\right)} g^{2}\right)} m\right)} x^{2} + {\left({\left(18 \, c d^{3} e^{2} - 47 \, b d^{2} e^{3} + 154 \, a d e^{4}\right)} f^{2} - 2 \, {\left(6 \, c d^{4} e - 18 \, b d^{3} e^{2} + 47 \, a d^{2} e^{3}\right)} f g - 6 \, {\left(b d^{4} e - 3 \, a d^{3} e^{2}\right)} g^{2}\right)} m + {\left(120 \, a e^{5} f^{2} + {\left(2 \, a d e^{4} f g + {\left(b d e^{4} + a e^{5}\right)} f^{2}\right)} m^{4} - 2 \, {\left(a d^{2} e^{3} g^{2} + {\left(c d^{2} e^{3} - 6 \, b d e^{4} - 7 \, a e^{5}\right)} f^{2} + 2 \, {\left(b d^{2} e^{3} - 6 \, a d e^{4}\right)} f g\right)} m^{3} - {\left({\left(18 \, c d^{2} e^{3} - 47 \, b d e^{4} - 71 \, a e^{5}\right)} f^{2} - 2 \, {\left(6 \, c d^{3} e^{2} - 18 \, b d^{2} e^{3} + 47 \, a d e^{4}\right)} f g - 6 \, {\left(b d^{3} e^{2} - 3 \, a d^{2} e^{3}\right)} g^{2}\right)} m^{2} - 2 \, {\left({\left(20 \, c d^{2} e^{3} - 30 \, b d e^{4} - 77 \, a e^{5}\right)} f^{2} - 10 \, {\left(3 \, c d^{3} e^{2} - 4 \, b d^{2} e^{3} + 6 \, a d e^{4}\right)} f g + {\left(12 \, c d^{4} e - 15 \, b d^{3} e^{2} + 20 \, a d^{2} e^{3}\right)} g^{2}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{5} m^{5} + 15 \, e^{5} m^{4} + 85 \, e^{5} m^{3} + 225 \, e^{5} m^{2} + 274 \, e^{5} m + 120 \, e^{5}}"," ",0,"(a*d*e^4*f^2*m^4 + (c*e^5*g^2*m^4 + 10*c*e^5*g^2*m^3 + 35*c*e^5*g^2*m^2 + 50*c*e^5*g^2*m + 24*c*e^5*g^2)*x^5 + (60*c*e^5*f*g + 30*b*e^5*g^2 + (2*c*e^5*f*g + (c*d*e^4 + b*e^5)*g^2)*m^4 + (22*c*e^5*f*g + (6*c*d*e^4 + 11*b*e^5)*g^2)*m^3 + (82*c*e^5*f*g + (11*c*d*e^4 + 41*b*e^5)*g^2)*m^2 + (122*c*e^5*f*g + (6*c*d*e^4 + 61*b*e^5)*g^2)*m)*x^4 - (2*a*d^2*e^3*f*g + (b*d^2*e^3 - 14*a*d*e^4)*f^2)*m^3 + (40*c*e^5*f^2 + 80*b*e^5*f*g + 40*a*e^5*g^2 + (c*e^5*f^2 + 2*(c*d*e^4 + b*e^5)*f*g + (b*d*e^4 + a*e^5)*g^2)*m^4 + 4*(3*c*e^5*f^2 + 2*(2*c*d*e^4 + 3*b*e^5)*f*g - (c*d^2*e^3 - 2*b*d*e^4 - 3*a*e^5)*g^2)*m^3 + (49*c*e^5*f^2 + 2*(17*c*d*e^4 + 49*b*e^5)*f*g - (12*c*d^2*e^3 - 17*b*d*e^4 - 49*a*e^5)*g^2)*m^2 + 2*(39*c*e^5*f^2 + 2*(5*c*d*e^4 + 39*b*e^5)*f*g - (4*c*d^2*e^3 - 5*b*d*e^4 - 39*a*e^5)*g^2)*m)*x^3 + 20*(2*c*d^3*e^2 - 3*b*d^2*e^3 + 6*a*d*e^4)*f^2 - 20*(3*c*d^4*e - 4*b*d^3*e^2 + 6*a*d^2*e^3)*f*g + 2*(12*c*d^5 - 15*b*d^4*e + 20*a*d^3*e^2)*g^2 + (2*a*d^3*e^2*g^2 + (2*c*d^3*e^2 - 12*b*d^2*e^3 + 71*a*d*e^4)*f^2 + 4*(b*d^3*e^2 - 6*a*d^2*e^3)*f*g)*m^2 + (60*b*e^5*f^2 + 120*a*e^5*f*g + (a*d*e^4*g^2 + (c*d*e^4 + b*e^5)*f^2 + 2*(b*d*e^4 + a*e^5)*f*g)*m^4 + ((10*c*d*e^4 + 13*b*e^5)*f^2 - 2*(3*c*d^2*e^3 - 10*b*d*e^4 - 13*a*e^5)*f*g - (3*b*d^2*e^3 - 10*a*d*e^4)*g^2)*m^3 + ((29*c*d*e^4 + 59*b*e^5)*f^2 - 2*(18*c*d^2*e^3 - 29*b*d*e^4 - 59*a*e^5)*f*g + (12*c*d^3*e^2 - 18*b*d^2*e^3 + 29*a*d*e^4)*g^2)*m^2 + ((20*c*d*e^4 + 107*b*e^5)*f^2 - 2*(15*c*d^2*e^3 - 20*b*d*e^4 - 107*a*e^5)*f*g + (12*c*d^3*e^2 - 15*b*d^2*e^3 + 20*a*d*e^4)*g^2)*m)*x^2 + ((18*c*d^3*e^2 - 47*b*d^2*e^3 + 154*a*d*e^4)*f^2 - 2*(6*c*d^4*e - 18*b*d^3*e^2 + 47*a*d^2*e^3)*f*g - 6*(b*d^4*e - 3*a*d^3*e^2)*g^2)*m + (120*a*e^5*f^2 + (2*a*d*e^4*f*g + (b*d*e^4 + a*e^5)*f^2)*m^4 - 2*(a*d^2*e^3*g^2 + (c*d^2*e^3 - 6*b*d*e^4 - 7*a*e^5)*f^2 + 2*(b*d^2*e^3 - 6*a*d*e^4)*f*g)*m^3 - ((18*c*d^2*e^3 - 47*b*d*e^4 - 71*a*e^5)*f^2 - 2*(6*c*d^3*e^2 - 18*b*d^2*e^3 + 47*a*d*e^4)*f*g - 6*(b*d^3*e^2 - 3*a*d^2*e^3)*g^2)*m^2 - 2*((20*c*d^2*e^3 - 30*b*d*e^4 - 77*a*e^5)*f^2 - 10*(3*c*d^3*e^2 - 4*b*d^2*e^3 + 6*a*d*e^4)*f*g + (12*c*d^4*e - 15*b*d^3*e^2 + 20*a*d^2*e^3)*g^2)*m)*x)*(e*x + d)^m/(e^5*m^5 + 15*e^5*m^4 + 85*e^5*m^3 + 225*e^5*m^2 + 274*e^5*m + 120*e^5)","B",0
921,1,613,0,0.429589," ","integrate((e*x+d)^m*(g*x+f)*(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{{\left(a d e^{3} f m^{3} + {\left(c e^{4} g m^{3} + 6 \, c e^{4} g m^{2} + 11 \, c e^{4} g m + 6 \, c e^{4} g\right)} x^{4} + {\left(8 \, c e^{4} f + 8 \, b e^{4} g + {\left(c e^{4} f + {\left(c d e^{3} + b e^{4}\right)} g\right)} m^{3} + {\left(7 \, c e^{4} f + {\left(3 \, c d e^{3} + 7 \, b e^{4}\right)} g\right)} m^{2} + 2 \, {\left(7 \, c e^{4} f + {\left(c d e^{3} + 7 \, b e^{4}\right)} g\right)} m\right)} x^{3} - {\left(a d^{2} e^{2} g + {\left(b d^{2} e^{2} - 9 \, a d e^{3}\right)} f\right)} m^{2} + {\left(12 \, b e^{4} f + 12 \, a e^{4} g + {\left({\left(c d e^{3} + b e^{4}\right)} f + {\left(b d e^{3} + a e^{4}\right)} g\right)} m^{3} + {\left({\left(5 \, c d e^{3} + 8 \, b e^{4}\right)} f - {\left(3 \, c d^{2} e^{2} - 5 \, b d e^{3} - 8 \, a e^{4}\right)} g\right)} m^{2} + {\left({\left(4 \, c d e^{3} + 19 \, b e^{4}\right)} f - {\left(3 \, c d^{2} e^{2} - 4 \, b d e^{3} - 19 \, a e^{4}\right)} g\right)} m\right)} x^{2} + 4 \, {\left(2 \, c d^{3} e - 3 \, b d^{2} e^{2} + 6 \, a d e^{3}\right)} f - 2 \, {\left(3 \, c d^{4} - 4 \, b d^{3} e + 6 \, a d^{2} e^{2}\right)} g + {\left({\left(2 \, c d^{3} e - 7 \, b d^{2} e^{2} + 26 \, a d e^{3}\right)} f + {\left(2 \, b d^{3} e - 7 \, a d^{2} e^{2}\right)} g\right)} m + {\left(24 \, a e^{4} f + {\left(a d e^{3} g + {\left(b d e^{3} + a e^{4}\right)} f\right)} m^{3} - {\left({\left(2 \, c d^{2} e^{2} - 7 \, b d e^{3} - 9 \, a e^{4}\right)} f + {\left(2 \, b d^{2} e^{2} - 7 \, a d e^{3}\right)} g\right)} m^{2} - 2 \, {\left({\left(4 \, c d^{2} e^{2} - 6 \, b d e^{3} - 13 \, a e^{4}\right)} f - {\left(3 \, c d^{3} e - 4 \, b d^{2} e^{2} + 6 \, a d e^{3}\right)} g\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{4} m^{4} + 10 \, e^{4} m^{3} + 35 \, e^{4} m^{2} + 50 \, e^{4} m + 24 \, e^{4}}"," ",0,"(a*d*e^3*f*m^3 + (c*e^4*g*m^3 + 6*c*e^4*g*m^2 + 11*c*e^4*g*m + 6*c*e^4*g)*x^4 + (8*c*e^4*f + 8*b*e^4*g + (c*e^4*f + (c*d*e^3 + b*e^4)*g)*m^3 + (7*c*e^4*f + (3*c*d*e^3 + 7*b*e^4)*g)*m^2 + 2*(7*c*e^4*f + (c*d*e^3 + 7*b*e^4)*g)*m)*x^3 - (a*d^2*e^2*g + (b*d^2*e^2 - 9*a*d*e^3)*f)*m^2 + (12*b*e^4*f + 12*a*e^4*g + ((c*d*e^3 + b*e^4)*f + (b*d*e^3 + a*e^4)*g)*m^3 + ((5*c*d*e^3 + 8*b*e^4)*f - (3*c*d^2*e^2 - 5*b*d*e^3 - 8*a*e^4)*g)*m^2 + ((4*c*d*e^3 + 19*b*e^4)*f - (3*c*d^2*e^2 - 4*b*d*e^3 - 19*a*e^4)*g)*m)*x^2 + 4*(2*c*d^3*e - 3*b*d^2*e^2 + 6*a*d*e^3)*f - 2*(3*c*d^4 - 4*b*d^3*e + 6*a*d^2*e^2)*g + ((2*c*d^3*e - 7*b*d^2*e^2 + 26*a*d*e^3)*f + (2*b*d^3*e - 7*a*d^2*e^2)*g)*m + (24*a*e^4*f + (a*d*e^3*g + (b*d*e^3 + a*e^4)*f)*m^3 - ((2*c*d^2*e^2 - 7*b*d*e^3 - 9*a*e^4)*f + (2*b*d^2*e^2 - 7*a*d*e^3)*g)*m^2 - 2*((4*c*d^2*e^2 - 6*b*d*e^3 - 13*a*e^4)*f - (3*c*d^3*e - 4*b*d^2*e^2 + 6*a*d*e^3)*g)*m)*x)*(e*x + d)^m/(e^4*m^4 + 10*e^4*m^3 + 35*e^4*m^2 + 50*e^4*m + 24*e^4)","B",0
922,0,0,0,0.420839," ","integrate((e*x+d)^m*(c*x^2+b*x+a)/(g*x+f),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2} + b x + a\right)} {\left(e x + d\right)}^{m}}{g x + f}, x\right)"," ",0,"integral((c*x^2 + b*x + a)*(e*x + d)^m/(g*x + f), x)","F",0
923,0,0,0,0.425576," ","integrate((e*x+d)^m*(c*x^2+b*x+a)/(g*x+f)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2} + b x + a\right)} {\left(e x + d\right)}^{m}}{g^{2} x^{2} + 2 \, f g x + f^{2}}, x\right)"," ",0,"integral((c*x^2 + b*x + a)*(e*x + d)^m/(g^2*x^2 + 2*f*g*x + f^2), x)","F",0
924,0,0,0,0.433560," ","integrate((e*x+d)^m*(c*x^2+b*x+a)/(g*x+f)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2} + b x + a\right)} {\left(e x + d\right)}^{m}}{g^{3} x^{3} + 3 \, f g^{2} x^{2} + 3 \, f^{2} g x + f^{3}}, x\right)"," ",0,"integral((c*x^2 + b*x + a)*(e*x + d)^m/(g^3*x^3 + 3*f*g^2*x^2 + 3*f^2*g*x + f^3), x)","F",0
925,1,4747,0,0.526091," ","integrate((e*x+d)^m*(g*x+f)^2*(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\frac{{\left(a^{2} d e^{6} f^{2} m^{6} + {\left(c^{2} e^{7} g^{2} m^{6} + 21 \, c^{2} e^{7} g^{2} m^{5} + 175 \, c^{2} e^{7} g^{2} m^{4} + 735 \, c^{2} e^{7} g^{2} m^{3} + 1624 \, c^{2} e^{7} g^{2} m^{2} + 1764 \, c^{2} e^{7} g^{2} m + 720 \, c^{2} e^{7} g^{2}\right)} x^{7} + {\left(1680 \, c^{2} e^{7} f g + 1680 \, b c e^{7} g^{2} + {\left(2 \, c^{2} e^{7} f g + {\left(c^{2} d e^{6} + 2 \, b c e^{7}\right)} g^{2}\right)} m^{6} + {\left(44 \, c^{2} e^{7} f g + {\left(15 \, c^{2} d e^{6} + 44 \, b c e^{7}\right)} g^{2}\right)} m^{5} + 5 \, {\left(76 \, c^{2} e^{7} f g + {\left(17 \, c^{2} d e^{6} + 76 \, b c e^{7}\right)} g^{2}\right)} m^{4} + 5 \, {\left(328 \, c^{2} e^{7} f g + {\left(45 \, c^{2} d e^{6} + 328 \, b c e^{7}\right)} g^{2}\right)} m^{3} + 2 \, {\left(1849 \, c^{2} e^{7} f g + {\left(137 \, c^{2} d e^{6} + 1849 \, b c e^{7}\right)} g^{2}\right)} m^{2} + 4 \, {\left(1019 \, c^{2} e^{7} f g + {\left(30 \, c^{2} d e^{6} + 1019 \, b c e^{7}\right)} g^{2}\right)} m\right)} x^{6} - {\left(2 \, a^{2} d^{2} e^{5} f g + {\left(2 \, a b d^{2} e^{5} - 27 \, a^{2} d e^{6}\right)} f^{2}\right)} m^{5} + {\left(1008 \, c^{2} e^{7} f^{2} + 4032 \, b c e^{7} f g + 1008 \, {\left(b^{2} + 2 \, a c\right)} e^{7} g^{2} + {\left(c^{2} e^{7} f^{2} + 2 \, {\left(c^{2} d e^{6} + 2 \, b c e^{7}\right)} f g + {\left(2 \, b c d e^{6} + {\left(b^{2} + 2 \, a c\right)} e^{7}\right)} g^{2}\right)} m^{6} + {\left(23 \, c^{2} e^{7} f^{2} + 2 \, {\left(17 \, c^{2} d e^{6} + 46 \, b c e^{7}\right)} f g - {\left(6 \, c^{2} d^{2} e^{5} - 34 \, b c d e^{6} - 23 \, {\left(b^{2} + 2 \, a c\right)} e^{7}\right)} g^{2}\right)} m^{5} + 3 \, {\left(69 \, c^{2} e^{7} f^{2} + 2 \, {\left(35 \, c^{2} d e^{6} + 138 \, b c e^{7}\right)} f g - {\left(20 \, c^{2} d^{2} e^{5} - 70 \, b c d e^{6} - 69 \, {\left(b^{2} + 2 \, a c\right)} e^{7}\right)} g^{2}\right)} m^{4} + 5 \, {\left(185 \, c^{2} e^{7} f^{2} + 2 \, {\left(59 \, c^{2} d e^{6} + 370 \, b c e^{7}\right)} f g - {\left(42 \, c^{2} d^{2} e^{5} - 118 \, b c d e^{6} - 185 \, {\left(b^{2} + 2 \, a c\right)} e^{7}\right)} g^{2}\right)} m^{3} + 4 \, {\left(536 \, c^{2} e^{7} f^{2} + {\left(187 \, c^{2} d e^{6} + 2144 \, b c e^{7}\right)} f g - {\left(75 \, c^{2} d^{2} e^{5} - 187 \, b c d e^{6} - 536 \, {\left(b^{2} + 2 \, a c\right)} e^{7}\right)} g^{2}\right)} m^{2} + 12 \, {\left(201 \, c^{2} e^{7} f^{2} + 4 \, {\left(7 \, c^{2} d e^{6} + 201 \, b c e^{7}\right)} f g - {\left(12 \, c^{2} d^{2} e^{5} - 28 \, b c d e^{6} - 201 \, {\left(b^{2} + 2 \, a c\right)} e^{7}\right)} g^{2}\right)} m\right)} x^{5} + {\left(2 \, a^{2} d^{3} e^{4} g^{2} - {\left(50 \, a b d^{2} e^{5} - 295 \, a^{2} d e^{6} - 2 \, {\left(b^{2} + 2 \, a c\right)} d^{3} e^{4}\right)} f^{2} + 2 \, {\left(4 \, a b d^{3} e^{4} - 25 \, a^{2} d^{2} e^{5}\right)} f g\right)} m^{4} + {\left(2520 \, b c e^{7} f^{2} + 2520 \, a b e^{7} g^{2} + 2520 \, {\left(b^{2} + 2 \, a c\right)} e^{7} f g + {\left({\left(c^{2} d e^{6} + 2 \, b c e^{7}\right)} f^{2} + 2 \, {\left(2 \, b c d e^{6} + {\left(b^{2} + 2 \, a c\right)} e^{7}\right)} f g + {\left(2 \, a b e^{7} + {\left(b^{2} + 2 \, a c\right)} d e^{6}\right)} g^{2}\right)} m^{6} + {\left({\left(19 \, c^{2} d e^{6} + 48 \, b c e^{7}\right)} f^{2} - 2 \, {\left(5 \, c^{2} d^{2} e^{5} - 38 \, b c d e^{6} - 24 \, {\left(b^{2} + 2 \, a c\right)} e^{7}\right)} f g - {\left(10 \, b c d^{2} e^{5} - 48 \, a b e^{7} - 19 \, {\left(b^{2} + 2 \, a c\right)} d e^{6}\right)} g^{2}\right)} m^{5} + {\left({\left(131 \, c^{2} d e^{6} + 452 \, b c e^{7}\right)} f^{2} - 2 \, {\left(65 \, c^{2} d^{2} e^{5} - 262 \, b c d e^{6} - 226 \, {\left(b^{2} + 2 \, a c\right)} e^{7}\right)} f g + {\left(30 \, c^{2} d^{3} e^{4} - 130 \, b c d^{2} e^{5} + 452 \, a b e^{7} + 131 \, {\left(b^{2} + 2 \, a c\right)} d e^{6}\right)} g^{2}\right)} m^{4} + {\left({\left(401 \, c^{2} d e^{6} + 2112 \, b c e^{7}\right)} f^{2} - 2 \, {\left(265 \, c^{2} d^{2} e^{5} - 802 \, b c d e^{6} - 1056 \, {\left(b^{2} + 2 \, a c\right)} e^{7}\right)} f g + {\left(180 \, c^{2} d^{3} e^{4} - 530 \, b c d^{2} e^{5} + 2112 \, a b e^{7} + 401 \, {\left(b^{2} + 2 \, a c\right)} d e^{6}\right)} g^{2}\right)} m^{3} + 10 \, {\left({\left(54 \, c^{2} d e^{6} + 509 \, b c e^{7}\right)} f^{2} - {\left(83 \, c^{2} d^{2} e^{5} - 216 \, b c d e^{6} - 509 \, {\left(b^{2} + 2 \, a c\right)} e^{7}\right)} f g + {\left(33 \, c^{2} d^{3} e^{4} - 83 \, b c d^{2} e^{5} + 509 \, a b e^{7} + 54 \, {\left(b^{2} + 2 \, a c\right)} d e^{6}\right)} g^{2}\right)} m^{2} + 12 \, {\left(3 \, {\left(7 \, c^{2} d e^{6} + 164 \, b c e^{7}\right)} f^{2} - {\left(35 \, c^{2} d^{2} e^{5} - 84 \, b c d e^{6} - 492 \, {\left(b^{2} + 2 \, a c\right)} e^{7}\right)} f g + {\left(15 \, c^{2} d^{3} e^{4} - 35 \, b c d^{2} e^{5} + 492 \, a b e^{7} + 21 \, {\left(b^{2} + 2 \, a c\right)} d e^{6}\right)} g^{2}\right)} m\right)} x^{4} - {\left({\left(12 \, b c d^{4} e^{3} + 490 \, a b d^{2} e^{5} - 1665 \, a^{2} d e^{6} - 44 \, {\left(b^{2} + 2 \, a c\right)} d^{3} e^{4}\right)} f^{2} - 2 \, {\left(88 \, a b d^{3} e^{4} - 245 \, a^{2} d^{2} e^{5} - 6 \, {\left(b^{2} + 2 \, a c\right)} d^{4} e^{3}\right)} f g + 4 \, {\left(3 \, a b d^{4} e^{3} - 11 \, a^{2} d^{3} e^{4}\right)} g^{2}\right)} m^{3} + {\left(6720 \, a b e^{7} f g + 1680 \, a^{2} e^{7} g^{2} + 1680 \, {\left(b^{2} + 2 \, a c\right)} e^{7} f^{2} + {\left({\left(2 \, b c d e^{6} + {\left(b^{2} + 2 \, a c\right)} e^{7}\right)} f^{2} + 2 \, {\left(2 \, a b e^{7} + {\left(b^{2} + 2 \, a c\right)} d e^{6}\right)} f g + {\left(2 \, a b d e^{6} + a^{2} e^{7}\right)} g^{2}\right)} m^{6} - {\left({\left(4 \, c^{2} d^{2} e^{5} - 42 \, b c d e^{6} - 25 \, {\left(b^{2} + 2 \, a c\right)} e^{7}\right)} f^{2} + 2 \, {\left(8 \, b c d^{2} e^{5} - 50 \, a b e^{7} - 21 \, {\left(b^{2} + 2 \, a c\right)} d e^{6}\right)} f g - {\left(42 \, a b d e^{6} + 25 \, a^{2} e^{7} - 4 \, {\left(b^{2} + 2 \, a c\right)} d^{2} e^{5}\right)} g^{2}\right)} m^{5} - {\left({\left(64 \, c^{2} d^{2} e^{5} - 326 \, b c d e^{6} - 247 \, {\left(b^{2} + 2 \, a c\right)} e^{7}\right)} f^{2} - 2 \, {\left(20 \, c^{2} d^{3} e^{4} - 128 \, b c d^{2} e^{5} + 494 \, a b e^{7} + 163 \, {\left(b^{2} + 2 \, a c\right)} d e^{6}\right)} f g - {\left(40 \, b c d^{3} e^{4} + 326 \, a b d e^{6} + 247 \, a^{2} e^{7} - 64 \, {\left(b^{2} + 2 \, a c\right)} d^{2} e^{5}\right)} g^{2}\right)} m^{4} - {\left({\left(332 \, c^{2} d^{2} e^{5} - 1134 \, b c d e^{6} - 1219 \, {\left(b^{2} + 2 \, a c\right)} e^{7}\right)} f^{2} - 2 \, {\left(200 \, c^{2} d^{3} e^{4} - 664 \, b c d^{2} e^{5} + 2438 \, a b e^{7} + 567 \, {\left(b^{2} + 2 \, a c\right)} d e^{6}\right)} f g + {\left(120 \, c^{2} d^{4} e^{3} - 400 \, b c d^{3} e^{4} - 1134 \, a b d e^{6} - 1219 \, a^{2} e^{7} + 332 \, {\left(b^{2} + 2 \, a c\right)} d^{2} e^{5}\right)} g^{2}\right)} m^{3} - 8 \, {\left({\left(76 \, c^{2} d^{2} e^{5} - 211 \, b c d e^{6} - 389 \, {\left(b^{2} + 2 \, a c\right)} e^{7}\right)} f^{2} - {\left(115 \, c^{2} d^{3} e^{4} - 304 \, b c d^{2} e^{5} + 1556 \, a b e^{7} + 211 \, {\left(b^{2} + 2 \, a c\right)} d e^{6}\right)} f g + {\left(45 \, c^{2} d^{4} e^{3} - 115 \, b c d^{3} e^{4} - 211 \, a b d e^{6} - 389 \, a^{2} e^{7} + 76 \, {\left(b^{2} + 2 \, a c\right)} d^{2} e^{5}\right)} g^{2}\right)} m^{2} - 4 \, {\left({\left(84 \, c^{2} d^{2} e^{5} - 210 \, b c d e^{6} - 949 \, {\left(b^{2} + 2 \, a c\right)} e^{7}\right)} f^{2} - 2 \, {\left(70 \, c^{2} d^{3} e^{4} - 168 \, b c d^{2} e^{5} + 1898 \, a b e^{7} + 105 \, {\left(b^{2} + 2 \, a c\right)} d e^{6}\right)} f g + {\left(60 \, c^{2} d^{4} e^{3} - 140 \, b c d^{3} e^{4} - 210 \, a b d e^{6} - 949 \, a^{2} e^{7} + 84 \, {\left(b^{2} + 2 \, a c\right)} d^{2} e^{5}\right)} g^{2}\right)} m\right)} x^{3} + 168 \, {\left(6 \, c^{2} d^{5} e^{2} - 15 \, b c d^{4} e^{3} - 30 \, a b d^{2} e^{5} + 30 \, a^{2} d e^{6} + 10 \, {\left(b^{2} + 2 \, a c\right)} d^{3} e^{4}\right)} f^{2} - 168 \, {\left(10 \, c^{2} d^{6} e - 24 \, b c d^{5} e^{2} - 40 \, a b d^{3} e^{4} + 30 \, a^{2} d^{2} e^{5} + 15 \, {\left(b^{2} + 2 \, a c\right)} d^{4} e^{3}\right)} f g + 24 \, {\left(30 \, c^{2} d^{7} - 70 \, b c d^{6} e - 105 \, a b d^{4} e^{3} + 70 \, a^{2} d^{3} e^{4} + 42 \, {\left(b^{2} + 2 \, a c\right)} d^{5} e^{2}\right)} g^{2} + 2 \, {\left({\left(12 \, c^{2} d^{5} e^{2} - 108 \, b c d^{4} e^{3} - 1175 \, a b d^{2} e^{5} + 2552 \, a^{2} d e^{6} + 179 \, {\left(b^{2} + 2 \, a c\right)} d^{3} e^{4}\right)} f^{2} + {\left(48 \, b c d^{5} e^{2} + 716 \, a b d^{3} e^{4} - 1175 \, a^{2} d^{2} e^{5} - 108 \, {\left(b^{2} + 2 \, a c\right)} d^{4} e^{3}\right)} f g - {\left(108 \, a b d^{4} e^{3} - 179 \, a^{2} d^{3} e^{4} - 12 \, {\left(b^{2} + 2 \, a c\right)} d^{5} e^{2}\right)} g^{2}\right)} m^{2} + {\left(5040 \, a b e^{7} f^{2} + 5040 \, a^{2} e^{7} f g + {\left(a^{2} d e^{6} g^{2} + {\left(2 \, a b e^{7} + {\left(b^{2} + 2 \, a c\right)} d e^{6}\right)} f^{2} + 2 \, {\left(2 \, a b d e^{6} + a^{2} e^{7}\right)} f g\right)} m^{6} - {\left({\left(6 \, b c d^{2} e^{5} - 52 \, a b e^{7} - 23 \, {\left(b^{2} + 2 \, a c\right)} d e^{6}\right)} f^{2} - 2 \, {\left(46 \, a b d e^{6} + 26 \, a^{2} e^{7} - 3 \, {\left(b^{2} + 2 \, a c\right)} d^{2} e^{5}\right)} f g + {\left(6 \, a b d^{2} e^{5} - 23 \, a^{2} d e^{6}\right)} g^{2}\right)} m^{5} + 3 \, {\left({\left(4 \, c^{2} d^{3} e^{4} - 38 \, b c d^{2} e^{5} + 180 \, a b e^{7} + 67 \, {\left(b^{2} + 2 \, a c\right)} d e^{6}\right)} f^{2} + 2 \, {\left(8 \, b c d^{3} e^{4} + 134 \, a b d e^{6} + 90 \, a^{2} e^{7} - 19 \, {\left(b^{2} + 2 \, a c\right)} d^{2} e^{5}\right)} f g - {\left(38 \, a b d^{2} e^{5} - 67 \, a^{2} d e^{6} - 4 \, {\left(b^{2} + 2 \, a c\right)} d^{3} e^{4}\right)} g^{2}\right)} m^{4} + {\left({\left(168 \, c^{2} d^{3} e^{4} - 750 \, b c d^{2} e^{5} + 2840 \, a b e^{7} + 817 \, {\left(b^{2} + 2 \, a c\right)} d e^{6}\right)} f^{2} - 2 \, {\left(60 \, c^{2} d^{4} e^{3} - 336 \, b c d^{3} e^{4} - 1634 \, a b d e^{6} - 1420 \, a^{2} e^{7} + 375 \, {\left(b^{2} + 2 \, a c\right)} d^{2} e^{5}\right)} f g - {\left(120 \, b c d^{4} e^{3} + 750 \, a b d^{2} e^{5} - 817 \, a^{2} d e^{6} - 168 \, {\left(b^{2} + 2 \, a c\right)} d^{3} e^{4}\right)} g^{2}\right)} m^{3} + 2 \, {\left({\left(330 \, c^{2} d^{3} e^{4} - 951 \, b c d^{2} e^{5} + 3929 \, a b e^{7} + 739 \, {\left(b^{2} + 2 \, a c\right)} d e^{6}\right)} f^{2} - {\left(480 \, c^{2} d^{4} e^{3} - 1320 \, b c d^{3} e^{4} - 2956 \, a b d e^{6} - 3929 \, a^{2} e^{7} + 951 \, {\left(b^{2} + 2 \, a c\right)} d^{2} e^{5}\right)} f g + {\left(180 \, c^{2} d^{5} e^{2} - 480 \, b c d^{4} e^{3} - 951 \, a b d^{2} e^{5} + 739 \, a^{2} d e^{6} + 330 \, {\left(b^{2} + 2 \, a c\right)} d^{3} e^{4}\right)} g^{2}\right)} m^{2} + 12 \, {\left({\left(42 \, c^{2} d^{3} e^{4} - 105 \, b c d^{2} e^{5} + 879 \, a b e^{7} + 70 \, {\left(b^{2} + 2 \, a c\right)} d e^{6}\right)} f^{2} - {\left(70 \, c^{2} d^{4} e^{3} - 168 \, b c d^{3} e^{4} - 280 \, a b d e^{6} - 879 \, a^{2} e^{7} + 105 \, {\left(b^{2} + 2 \, a c\right)} d^{2} e^{5}\right)} f g + {\left(30 \, c^{2} d^{5} e^{2} - 70 \, b c d^{4} e^{3} - 105 \, a b d^{2} e^{5} + 70 \, a^{2} d e^{6} + 42 \, {\left(b^{2} + 2 \, a c\right)} d^{3} e^{4}\right)} g^{2}\right)} m\right)} x^{2} + 4 \, {\left({\left(78 \, c^{2} d^{5} e^{2} - 321 \, b c d^{4} e^{3} - 1377 \, a b d^{2} e^{5} + 2007 \, a^{2} d e^{6} + 319 \, {\left(b^{2} + 2 \, a c\right)} d^{3} e^{4}\right)} f^{2} - {\left(60 \, c^{2} d^{6} e - 312 \, b c d^{5} e^{2} - 1276 \, a b d^{3} e^{4} + 1377 \, a^{2} d^{2} e^{5} + 321 \, {\left(b^{2} + 2 \, a c\right)} d^{4} e^{3}\right)} f g - {\left(60 \, b c d^{6} e + 321 \, a b d^{4} e^{3} - 319 \, a^{2} d^{3} e^{4} - 78 \, {\left(b^{2} + 2 \, a c\right)} d^{5} e^{2}\right)} g^{2}\right)} m + {\left(5040 \, a^{2} e^{7} f^{2} + {\left(2 \, a^{2} d e^{6} f g + {\left(2 \, a b d e^{6} + a^{2} e^{7}\right)} f^{2}\right)} m^{6} - {\left(2 \, a^{2} d^{2} e^{5} g^{2} - {\left(50 \, a b d e^{6} + 27 \, a^{2} e^{7} - 2 \, {\left(b^{2} + 2 \, a c\right)} d^{2} e^{5}\right)} f^{2} + 2 \, {\left(4 \, a b d^{2} e^{5} - 25 \, a^{2} d e^{6}\right)} f g\right)} m^{5} + {\left({\left(12 \, b c d^{3} e^{4} + 490 \, a b d e^{6} + 295 \, a^{2} e^{7} - 44 \, {\left(b^{2} + 2 \, a c\right)} d^{2} e^{5}\right)} f^{2} - 2 \, {\left(88 \, a b d^{2} e^{5} - 245 \, a^{2} d e^{6} - 6 \, {\left(b^{2} + 2 \, a c\right)} d^{3} e^{4}\right)} f g + 4 \, {\left(3 \, a b d^{3} e^{4} - 11 \, a^{2} d^{2} e^{5}\right)} g^{2}\right)} m^{4} - {\left({\left(24 \, c^{2} d^{4} e^{3} - 216 \, b c d^{3} e^{4} - 2350 \, a b d e^{6} - 1665 \, a^{2} e^{7} + 358 \, {\left(b^{2} + 2 \, a c\right)} d^{2} e^{5}\right)} f^{2} + 2 \, {\left(48 \, b c d^{4} e^{3} + 716 \, a b d^{2} e^{5} - 1175 \, a^{2} d e^{6} - 108 \, {\left(b^{2} + 2 \, a c\right)} d^{3} e^{4}\right)} f g - 2 \, {\left(108 \, a b d^{3} e^{4} - 179 \, a^{2} d^{2} e^{5} - 12 \, {\left(b^{2} + 2 \, a c\right)} d^{4} e^{3}\right)} g^{2}\right)} m^{3} - 4 \, {\left({\left(78 \, c^{2} d^{4} e^{3} - 321 \, b c d^{3} e^{4} - 1377 \, a b d e^{6} - 1276 \, a^{2} e^{7} + 319 \, {\left(b^{2} + 2 \, a c\right)} d^{2} e^{5}\right)} f^{2} - {\left(60 \, c^{2} d^{5} e^{2} - 312 \, b c d^{4} e^{3} - 1276 \, a b d^{2} e^{5} + 1377 \, a^{2} d e^{6} + 321 \, {\left(b^{2} + 2 \, a c\right)} d^{3} e^{4}\right)} f g - {\left(60 \, b c d^{5} e^{2} + 321 \, a b d^{3} e^{4} - 319 \, a^{2} d^{2} e^{5} - 78 \, {\left(b^{2} + 2 \, a c\right)} d^{4} e^{3}\right)} g^{2}\right)} m^{2} - 12 \, {\left({\left(84 \, c^{2} d^{4} e^{3} - 210 \, b c d^{3} e^{4} - 420 \, a b d e^{6} - 669 \, a^{2} e^{7} + 140 \, {\left(b^{2} + 2 \, a c\right)} d^{2} e^{5}\right)} f^{2} - 14 \, {\left(10 \, c^{2} d^{5} e^{2} - 24 \, b c d^{4} e^{3} - 40 \, a b d^{2} e^{5} + 30 \, a^{2} d e^{6} + 15 \, {\left(b^{2} + 2 \, a c\right)} d^{3} e^{4}\right)} f g + 2 \, {\left(30 \, c^{2} d^{6} e - 70 \, b c d^{5} e^{2} - 105 \, a b d^{3} e^{4} + 70 \, a^{2} d^{2} e^{5} + 42 \, {\left(b^{2} + 2 \, a c\right)} d^{4} e^{3}\right)} g^{2}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{7} m^{7} + 28 \, e^{7} m^{6} + 322 \, e^{7} m^{5} + 1960 \, e^{7} m^{4} + 6769 \, e^{7} m^{3} + 13132 \, e^{7} m^{2} + 13068 \, e^{7} m + 5040 \, e^{7}}"," ",0,"(a^2*d*e^6*f^2*m^6 + (c^2*e^7*g^2*m^6 + 21*c^2*e^7*g^2*m^5 + 175*c^2*e^7*g^2*m^4 + 735*c^2*e^7*g^2*m^3 + 1624*c^2*e^7*g^2*m^2 + 1764*c^2*e^7*g^2*m + 720*c^2*e^7*g^2)*x^7 + (1680*c^2*e^7*f*g + 1680*b*c*e^7*g^2 + (2*c^2*e^7*f*g + (c^2*d*e^6 + 2*b*c*e^7)*g^2)*m^6 + (44*c^2*e^7*f*g + (15*c^2*d*e^6 + 44*b*c*e^7)*g^2)*m^5 + 5*(76*c^2*e^7*f*g + (17*c^2*d*e^6 + 76*b*c*e^7)*g^2)*m^4 + 5*(328*c^2*e^7*f*g + (45*c^2*d*e^6 + 328*b*c*e^7)*g^2)*m^3 + 2*(1849*c^2*e^7*f*g + (137*c^2*d*e^6 + 1849*b*c*e^7)*g^2)*m^2 + 4*(1019*c^2*e^7*f*g + (30*c^2*d*e^6 + 1019*b*c*e^7)*g^2)*m)*x^6 - (2*a^2*d^2*e^5*f*g + (2*a*b*d^2*e^5 - 27*a^2*d*e^6)*f^2)*m^5 + (1008*c^2*e^7*f^2 + 4032*b*c*e^7*f*g + 1008*(b^2 + 2*a*c)*e^7*g^2 + (c^2*e^7*f^2 + 2*(c^2*d*e^6 + 2*b*c*e^7)*f*g + (2*b*c*d*e^6 + (b^2 + 2*a*c)*e^7)*g^2)*m^6 + (23*c^2*e^7*f^2 + 2*(17*c^2*d*e^6 + 46*b*c*e^7)*f*g - (6*c^2*d^2*e^5 - 34*b*c*d*e^6 - 23*(b^2 + 2*a*c)*e^7)*g^2)*m^5 + 3*(69*c^2*e^7*f^2 + 2*(35*c^2*d*e^6 + 138*b*c*e^7)*f*g - (20*c^2*d^2*e^5 - 70*b*c*d*e^6 - 69*(b^2 + 2*a*c)*e^7)*g^2)*m^4 + 5*(185*c^2*e^7*f^2 + 2*(59*c^2*d*e^6 + 370*b*c*e^7)*f*g - (42*c^2*d^2*e^5 - 118*b*c*d*e^6 - 185*(b^2 + 2*a*c)*e^7)*g^2)*m^3 + 4*(536*c^2*e^7*f^2 + (187*c^2*d*e^6 + 2144*b*c*e^7)*f*g - (75*c^2*d^2*e^5 - 187*b*c*d*e^6 - 536*(b^2 + 2*a*c)*e^7)*g^2)*m^2 + 12*(201*c^2*e^7*f^2 + 4*(7*c^2*d*e^6 + 201*b*c*e^7)*f*g - (12*c^2*d^2*e^5 - 28*b*c*d*e^6 - 201*(b^2 + 2*a*c)*e^7)*g^2)*m)*x^5 + (2*a^2*d^3*e^4*g^2 - (50*a*b*d^2*e^5 - 295*a^2*d*e^6 - 2*(b^2 + 2*a*c)*d^3*e^4)*f^2 + 2*(4*a*b*d^3*e^4 - 25*a^2*d^2*e^5)*f*g)*m^4 + (2520*b*c*e^7*f^2 + 2520*a*b*e^7*g^2 + 2520*(b^2 + 2*a*c)*e^7*f*g + ((c^2*d*e^6 + 2*b*c*e^7)*f^2 + 2*(2*b*c*d*e^6 + (b^2 + 2*a*c)*e^7)*f*g + (2*a*b*e^7 + (b^2 + 2*a*c)*d*e^6)*g^2)*m^6 + ((19*c^2*d*e^6 + 48*b*c*e^7)*f^2 - 2*(5*c^2*d^2*e^5 - 38*b*c*d*e^6 - 24*(b^2 + 2*a*c)*e^7)*f*g - (10*b*c*d^2*e^5 - 48*a*b*e^7 - 19*(b^2 + 2*a*c)*d*e^6)*g^2)*m^5 + ((131*c^2*d*e^6 + 452*b*c*e^7)*f^2 - 2*(65*c^2*d^2*e^5 - 262*b*c*d*e^6 - 226*(b^2 + 2*a*c)*e^7)*f*g + (30*c^2*d^3*e^4 - 130*b*c*d^2*e^5 + 452*a*b*e^7 + 131*(b^2 + 2*a*c)*d*e^6)*g^2)*m^4 + ((401*c^2*d*e^6 + 2112*b*c*e^7)*f^2 - 2*(265*c^2*d^2*e^5 - 802*b*c*d*e^6 - 1056*(b^2 + 2*a*c)*e^7)*f*g + (180*c^2*d^3*e^4 - 530*b*c*d^2*e^5 + 2112*a*b*e^7 + 401*(b^2 + 2*a*c)*d*e^6)*g^2)*m^3 + 10*((54*c^2*d*e^6 + 509*b*c*e^7)*f^2 - (83*c^2*d^2*e^5 - 216*b*c*d*e^6 - 509*(b^2 + 2*a*c)*e^7)*f*g + (33*c^2*d^3*e^4 - 83*b*c*d^2*e^5 + 509*a*b*e^7 + 54*(b^2 + 2*a*c)*d*e^6)*g^2)*m^2 + 12*(3*(7*c^2*d*e^6 + 164*b*c*e^7)*f^2 - (35*c^2*d^2*e^5 - 84*b*c*d*e^6 - 492*(b^2 + 2*a*c)*e^7)*f*g + (15*c^2*d^3*e^4 - 35*b*c*d^2*e^5 + 492*a*b*e^7 + 21*(b^2 + 2*a*c)*d*e^6)*g^2)*m)*x^4 - ((12*b*c*d^4*e^3 + 490*a*b*d^2*e^5 - 1665*a^2*d*e^6 - 44*(b^2 + 2*a*c)*d^3*e^4)*f^2 - 2*(88*a*b*d^3*e^4 - 245*a^2*d^2*e^5 - 6*(b^2 + 2*a*c)*d^4*e^3)*f*g + 4*(3*a*b*d^4*e^3 - 11*a^2*d^3*e^4)*g^2)*m^3 + (6720*a*b*e^7*f*g + 1680*a^2*e^7*g^2 + 1680*(b^2 + 2*a*c)*e^7*f^2 + ((2*b*c*d*e^6 + (b^2 + 2*a*c)*e^7)*f^2 + 2*(2*a*b*e^7 + (b^2 + 2*a*c)*d*e^6)*f*g + (2*a*b*d*e^6 + a^2*e^7)*g^2)*m^6 - ((4*c^2*d^2*e^5 - 42*b*c*d*e^6 - 25*(b^2 + 2*a*c)*e^7)*f^2 + 2*(8*b*c*d^2*e^5 - 50*a*b*e^7 - 21*(b^2 + 2*a*c)*d*e^6)*f*g - (42*a*b*d*e^6 + 25*a^2*e^7 - 4*(b^2 + 2*a*c)*d^2*e^5)*g^2)*m^5 - ((64*c^2*d^2*e^5 - 326*b*c*d*e^6 - 247*(b^2 + 2*a*c)*e^7)*f^2 - 2*(20*c^2*d^3*e^4 - 128*b*c*d^2*e^5 + 494*a*b*e^7 + 163*(b^2 + 2*a*c)*d*e^6)*f*g - (40*b*c*d^3*e^4 + 326*a*b*d*e^6 + 247*a^2*e^7 - 64*(b^2 + 2*a*c)*d^2*e^5)*g^2)*m^4 - ((332*c^2*d^2*e^5 - 1134*b*c*d*e^6 - 1219*(b^2 + 2*a*c)*e^7)*f^2 - 2*(200*c^2*d^3*e^4 - 664*b*c*d^2*e^5 + 2438*a*b*e^7 + 567*(b^2 + 2*a*c)*d*e^6)*f*g + (120*c^2*d^4*e^3 - 400*b*c*d^3*e^4 - 1134*a*b*d*e^6 - 1219*a^2*e^7 + 332*(b^2 + 2*a*c)*d^2*e^5)*g^2)*m^3 - 8*((76*c^2*d^2*e^5 - 211*b*c*d*e^6 - 389*(b^2 + 2*a*c)*e^7)*f^2 - (115*c^2*d^3*e^4 - 304*b*c*d^2*e^5 + 1556*a*b*e^7 + 211*(b^2 + 2*a*c)*d*e^6)*f*g + (45*c^2*d^4*e^3 - 115*b*c*d^3*e^4 - 211*a*b*d*e^6 - 389*a^2*e^7 + 76*(b^2 + 2*a*c)*d^2*e^5)*g^2)*m^2 - 4*((84*c^2*d^2*e^5 - 210*b*c*d*e^6 - 949*(b^2 + 2*a*c)*e^7)*f^2 - 2*(70*c^2*d^3*e^4 - 168*b*c*d^2*e^5 + 1898*a*b*e^7 + 105*(b^2 + 2*a*c)*d*e^6)*f*g + (60*c^2*d^4*e^3 - 140*b*c*d^3*e^4 - 210*a*b*d*e^6 - 949*a^2*e^7 + 84*(b^2 + 2*a*c)*d^2*e^5)*g^2)*m)*x^3 + 168*(6*c^2*d^5*e^2 - 15*b*c*d^4*e^3 - 30*a*b*d^2*e^5 + 30*a^2*d*e^6 + 10*(b^2 + 2*a*c)*d^3*e^4)*f^2 - 168*(10*c^2*d^6*e - 24*b*c*d^5*e^2 - 40*a*b*d^3*e^4 + 30*a^2*d^2*e^5 + 15*(b^2 + 2*a*c)*d^4*e^3)*f*g + 24*(30*c^2*d^7 - 70*b*c*d^6*e - 105*a*b*d^4*e^3 + 70*a^2*d^3*e^4 + 42*(b^2 + 2*a*c)*d^5*e^2)*g^2 + 2*((12*c^2*d^5*e^2 - 108*b*c*d^4*e^3 - 1175*a*b*d^2*e^5 + 2552*a^2*d*e^6 + 179*(b^2 + 2*a*c)*d^3*e^4)*f^2 + (48*b*c*d^5*e^2 + 716*a*b*d^3*e^4 - 1175*a^2*d^2*e^5 - 108*(b^2 + 2*a*c)*d^4*e^3)*f*g - (108*a*b*d^4*e^3 - 179*a^2*d^3*e^4 - 12*(b^2 + 2*a*c)*d^5*e^2)*g^2)*m^2 + (5040*a*b*e^7*f^2 + 5040*a^2*e^7*f*g + (a^2*d*e^6*g^2 + (2*a*b*e^7 + (b^2 + 2*a*c)*d*e^6)*f^2 + 2*(2*a*b*d*e^6 + a^2*e^7)*f*g)*m^6 - ((6*b*c*d^2*e^5 - 52*a*b*e^7 - 23*(b^2 + 2*a*c)*d*e^6)*f^2 - 2*(46*a*b*d*e^6 + 26*a^2*e^7 - 3*(b^2 + 2*a*c)*d^2*e^5)*f*g + (6*a*b*d^2*e^5 - 23*a^2*d*e^6)*g^2)*m^5 + 3*((4*c^2*d^3*e^4 - 38*b*c*d^2*e^5 + 180*a*b*e^7 + 67*(b^2 + 2*a*c)*d*e^6)*f^2 + 2*(8*b*c*d^3*e^4 + 134*a*b*d*e^6 + 90*a^2*e^7 - 19*(b^2 + 2*a*c)*d^2*e^5)*f*g - (38*a*b*d^2*e^5 - 67*a^2*d*e^6 - 4*(b^2 + 2*a*c)*d^3*e^4)*g^2)*m^4 + ((168*c^2*d^3*e^4 - 750*b*c*d^2*e^5 + 2840*a*b*e^7 + 817*(b^2 + 2*a*c)*d*e^6)*f^2 - 2*(60*c^2*d^4*e^3 - 336*b*c*d^3*e^4 - 1634*a*b*d*e^6 - 1420*a^2*e^7 + 375*(b^2 + 2*a*c)*d^2*e^5)*f*g - (120*b*c*d^4*e^3 + 750*a*b*d^2*e^5 - 817*a^2*d*e^6 - 168*(b^2 + 2*a*c)*d^3*e^4)*g^2)*m^3 + 2*((330*c^2*d^3*e^4 - 951*b*c*d^2*e^5 + 3929*a*b*e^7 + 739*(b^2 + 2*a*c)*d*e^6)*f^2 - (480*c^2*d^4*e^3 - 1320*b*c*d^3*e^4 - 2956*a*b*d*e^6 - 3929*a^2*e^7 + 951*(b^2 + 2*a*c)*d^2*e^5)*f*g + (180*c^2*d^5*e^2 - 480*b*c*d^4*e^3 - 951*a*b*d^2*e^5 + 739*a^2*d*e^6 + 330*(b^2 + 2*a*c)*d^3*e^4)*g^2)*m^2 + 12*((42*c^2*d^3*e^4 - 105*b*c*d^2*e^5 + 879*a*b*e^7 + 70*(b^2 + 2*a*c)*d*e^6)*f^2 - (70*c^2*d^4*e^3 - 168*b*c*d^3*e^4 - 280*a*b*d*e^6 - 879*a^2*e^7 + 105*(b^2 + 2*a*c)*d^2*e^5)*f*g + (30*c^2*d^5*e^2 - 70*b*c*d^4*e^3 - 105*a*b*d^2*e^5 + 70*a^2*d*e^6 + 42*(b^2 + 2*a*c)*d^3*e^4)*g^2)*m)*x^2 + 4*((78*c^2*d^5*e^2 - 321*b*c*d^4*e^3 - 1377*a*b*d^2*e^5 + 2007*a^2*d*e^6 + 319*(b^2 + 2*a*c)*d^3*e^4)*f^2 - (60*c^2*d^6*e - 312*b*c*d^5*e^2 - 1276*a*b*d^3*e^4 + 1377*a^2*d^2*e^5 + 321*(b^2 + 2*a*c)*d^4*e^3)*f*g - (60*b*c*d^6*e + 321*a*b*d^4*e^3 - 319*a^2*d^3*e^4 - 78*(b^2 + 2*a*c)*d^5*e^2)*g^2)*m + (5040*a^2*e^7*f^2 + (2*a^2*d*e^6*f*g + (2*a*b*d*e^6 + a^2*e^7)*f^2)*m^6 - (2*a^2*d^2*e^5*g^2 - (50*a*b*d*e^6 + 27*a^2*e^7 - 2*(b^2 + 2*a*c)*d^2*e^5)*f^2 + 2*(4*a*b*d^2*e^5 - 25*a^2*d*e^6)*f*g)*m^5 + ((12*b*c*d^3*e^4 + 490*a*b*d*e^6 + 295*a^2*e^7 - 44*(b^2 + 2*a*c)*d^2*e^5)*f^2 - 2*(88*a*b*d^2*e^5 - 245*a^2*d*e^6 - 6*(b^2 + 2*a*c)*d^3*e^4)*f*g + 4*(3*a*b*d^3*e^4 - 11*a^2*d^2*e^5)*g^2)*m^4 - ((24*c^2*d^4*e^3 - 216*b*c*d^3*e^4 - 2350*a*b*d*e^6 - 1665*a^2*e^7 + 358*(b^2 + 2*a*c)*d^2*e^5)*f^2 + 2*(48*b*c*d^4*e^3 + 716*a*b*d^2*e^5 - 1175*a^2*d*e^6 - 108*(b^2 + 2*a*c)*d^3*e^4)*f*g - 2*(108*a*b*d^3*e^4 - 179*a^2*d^2*e^5 - 12*(b^2 + 2*a*c)*d^4*e^3)*g^2)*m^3 - 4*((78*c^2*d^4*e^3 - 321*b*c*d^3*e^4 - 1377*a*b*d*e^6 - 1276*a^2*e^7 + 319*(b^2 + 2*a*c)*d^2*e^5)*f^2 - (60*c^2*d^5*e^2 - 312*b*c*d^4*e^3 - 1276*a*b*d^2*e^5 + 1377*a^2*d*e^6 + 321*(b^2 + 2*a*c)*d^3*e^4)*f*g - (60*b*c*d^5*e^2 + 321*a*b*d^3*e^4 - 319*a^2*d^2*e^5 - 78*(b^2 + 2*a*c)*d^4*e^3)*g^2)*m^2 - 12*((84*c^2*d^4*e^3 - 210*b*c*d^3*e^4 - 420*a*b*d*e^6 - 669*a^2*e^7 + 140*(b^2 + 2*a*c)*d^2*e^5)*f^2 - 14*(10*c^2*d^5*e^2 - 24*b*c*d^4*e^3 - 40*a*b*d^2*e^5 + 30*a^2*d*e^6 + 15*(b^2 + 2*a*c)*d^3*e^4)*f*g + 2*(30*c^2*d^6*e - 70*b*c*d^5*e^2 - 105*a*b*d^3*e^4 + 70*a^2*d^2*e^5 + 42*(b^2 + 2*a*c)*d^4*e^3)*g^2)*m)*x)*(e*x + d)^m/(e^7*m^7 + 28*e^7*m^6 + 322*e^7*m^5 + 1960*e^7*m^4 + 6769*e^7*m^3 + 13132*e^7*m^2 + 13068*e^7*m + 5040*e^7)","B",0
926,1,2368,0,0.453356," ","integrate((e*x+d)^m*(g*x+f)*(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\frac{{\left(a^{2} d e^{5} f m^{5} + {\left(c^{2} e^{6} g m^{5} + 15 \, c^{2} e^{6} g m^{4} + 85 \, c^{2} e^{6} g m^{3} + 225 \, c^{2} e^{6} g m^{2} + 274 \, c^{2} e^{6} g m + 120 \, c^{2} e^{6} g\right)} x^{6} + {\left(144 \, c^{2} e^{6} f + 288 \, b c e^{6} g + {\left(c^{2} e^{6} f + {\left(c^{2} d e^{5} + 2 \, b c e^{6}\right)} g\right)} m^{5} + 2 \, {\left(8 \, c^{2} e^{6} f + {\left(5 \, c^{2} d e^{5} + 16 \, b c e^{6}\right)} g\right)} m^{4} + 5 \, {\left(19 \, c^{2} e^{6} f + {\left(7 \, c^{2} d e^{5} + 38 \, b c e^{6}\right)} g\right)} m^{3} + 10 \, {\left(26 \, c^{2} e^{6} f + {\left(5 \, c^{2} d e^{5} + 52 \, b c e^{6}\right)} g\right)} m^{2} + 12 \, {\left(27 \, c^{2} e^{6} f + 2 \, {\left(c^{2} d e^{5} + 27 \, b c e^{6}\right)} g\right)} m\right)} x^{5} - {\left(a^{2} d^{2} e^{4} g + 2 \, {\left(a b d^{2} e^{4} - 10 \, a^{2} d e^{5}\right)} f\right)} m^{4} + {\left(360 \, b c e^{6} f + 180 \, {\left(b^{2} + 2 \, a c\right)} e^{6} g + {\left({\left(c^{2} d e^{5} + 2 \, b c e^{6}\right)} f + {\left(2 \, b c d e^{5} + {\left(b^{2} + 2 \, a c\right)} e^{6}\right)} g\right)} m^{5} + {\left(2 \, {\left(6 \, c^{2} d e^{5} + 17 \, b c e^{6}\right)} f - {\left(5 \, c^{2} d^{2} e^{4} - 24 \, b c d e^{5} - 17 \, {\left(b^{2} + 2 \, a c\right)} e^{6}\right)} g\right)} m^{4} + {\left({\left(47 \, c^{2} d e^{5} + 214 \, b c e^{6}\right)} f - {\left(30 \, c^{2} d^{2} e^{4} - 94 \, b c d e^{5} - 107 \, {\left(b^{2} + 2 \, a c\right)} e^{6}\right)} g\right)} m^{3} + {\left(2 \, {\left(36 \, c^{2} d e^{5} + 307 \, b c e^{6}\right)} f - {\left(55 \, c^{2} d^{2} e^{4} - 144 \, b c d e^{5} - 307 \, {\left(b^{2} + 2 \, a c\right)} e^{6}\right)} g\right)} m^{2} + 6 \, {\left(6 \, {\left(c^{2} d e^{5} + 22 \, b c e^{6}\right)} f - {\left(5 \, c^{2} d^{2} e^{4} - 12 \, b c d e^{5} - 66 \, {\left(b^{2} + 2 \, a c\right)} e^{6}\right)} g\right)} m\right)} x^{4} - {\left({\left(36 \, a b d^{2} e^{4} - 155 \, a^{2} d e^{5} - 2 \, {\left(b^{2} + 2 \, a c\right)} d^{3} e^{3}\right)} f - 2 \, {\left(2 \, a b d^{3} e^{3} - 9 \, a^{2} d^{2} e^{4}\right)} g\right)} m^{3} + {\left(480 \, a b e^{6} g + 240 \, {\left(b^{2} + 2 \, a c\right)} e^{6} f + {\left({\left(2 \, b c d e^{5} + {\left(b^{2} + 2 \, a c\right)} e^{6}\right)} f + {\left(2 \, a b e^{6} + {\left(b^{2} + 2 \, a c\right)} d e^{5}\right)} g\right)} m^{5} - 2 \, {\left({\left(2 \, c^{2} d^{2} e^{4} - 14 \, b c d e^{5} - 9 \, {\left(b^{2} + 2 \, a c\right)} e^{6}\right)} f + {\left(4 \, b c d^{2} e^{4} - 18 \, a b e^{6} - 7 \, {\left(b^{2} + 2 \, a c\right)} d e^{5}\right)} g\right)} m^{4} - {\left({\left(36 \, c^{2} d^{2} e^{4} - 130 \, b c d e^{5} - 121 \, {\left(b^{2} + 2 \, a c\right)} e^{6}\right)} f - {\left(20 \, c^{2} d^{3} e^{3} - 72 \, b c d^{2} e^{4} + 242 \, a b e^{6} + 65 \, {\left(b^{2} + 2 \, a c\right)} d e^{5}\right)} g\right)} m^{3} - 4 \, {\left({\left(20 \, c^{2} d^{2} e^{4} - 56 \, b c d e^{5} - 93 \, {\left(b^{2} + 2 \, a c\right)} e^{6}\right)} f - {\left(15 \, c^{2} d^{3} e^{3} - 40 \, b c d^{2} e^{4} + 186 \, a b e^{6} + 28 \, {\left(b^{2} + 2 \, a c\right)} d e^{5}\right)} g\right)} m^{2} - 4 \, {\left({\left(12 \, c^{2} d^{2} e^{4} - 30 \, b c d e^{5} - 127 \, {\left(b^{2} + 2 \, a c\right)} e^{6}\right)} f - {\left(10 \, c^{2} d^{3} e^{3} - 24 \, b c d^{2} e^{4} + 254 \, a b e^{6} + 15 \, {\left(b^{2} + 2 \, a c\right)} d e^{5}\right)} g\right)} m\right)} x^{3} - {\left(2 \, {\left(6 \, b c d^{4} e^{2} + 119 \, a b d^{2} e^{4} - 290 \, a^{2} d e^{5} - 15 \, {\left(b^{2} + 2 \, a c\right)} d^{3} e^{3}\right)} f - {\left(60 \, a b d^{3} e^{3} - 119 \, a^{2} d^{2} e^{4} - 6 \, {\left(b^{2} + 2 \, a c\right)} d^{4} e^{2}\right)} g\right)} m^{2} + {\left(720 \, a b e^{6} f + 360 \, a^{2} e^{6} g + {\left({\left(2 \, a b e^{6} + {\left(b^{2} + 2 \, a c\right)} d e^{5}\right)} f + {\left(2 \, a b d e^{5} + a^{2} e^{6}\right)} g\right)} m^{5} - {\left(2 \, {\left(3 \, b c d^{2} e^{4} - 19 \, a b e^{6} - 8 \, {\left(b^{2} + 2 \, a c\right)} d e^{5}\right)} f - {\left(32 \, a b d e^{5} + 19 \, a^{2} e^{6} - 3 \, {\left(b^{2} + 2 \, a c\right)} d^{2} e^{4}\right)} g\right)} m^{4} + {\left({\left(12 \, c^{2} d^{3} e^{3} - 72 \, b c d^{2} e^{4} + 274 \, a b e^{6} + 89 \, {\left(b^{2} + 2 \, a c\right)} d e^{5}\right)} f + {\left(24 \, b c d^{3} e^{3} + 178 \, a b d e^{5} + 137 \, a^{2} e^{6} - 36 \, {\left(b^{2} + 2 \, a c\right)} d^{2} e^{4}\right)} g\right)} m^{3} + {\left(2 \, {\left(42 \, c^{2} d^{3} e^{3} - 123 \, b c d^{2} e^{4} + 461 \, a b e^{6} + 97 \, {\left(b^{2} + 2 \, a c\right)} d e^{5}\right)} f - {\left(60 \, c^{2} d^{4} e^{2} - 168 \, b c d^{3} e^{3} - 388 \, a b d e^{5} - 461 \, a^{2} e^{6} + 123 \, {\left(b^{2} + 2 \, a c\right)} d^{2} e^{4}\right)} g\right)} m^{2} + 6 \, {\left(2 \, {\left(6 \, c^{2} d^{3} e^{3} - 15 \, b c d^{2} e^{4} + 117 \, a b e^{6} + 10 \, {\left(b^{2} + 2 \, a c\right)} d e^{5}\right)} f - {\left(10 \, c^{2} d^{4} e^{2} - 24 \, b c d^{3} e^{3} - 40 \, a b d e^{5} - 117 \, a^{2} e^{6} + 15 \, {\left(b^{2} + 2 \, a c\right)} d^{2} e^{4}\right)} g\right)} m\right)} x^{2} + 24 \, {\left(6 \, c^{2} d^{5} e - 15 \, b c d^{4} e^{2} - 30 \, a b d^{2} e^{4} + 30 \, a^{2} d e^{5} + 10 \, {\left(b^{2} + 2 \, a c\right)} d^{3} e^{3}\right)} f - 12 \, {\left(10 \, c^{2} d^{6} - 24 \, b c d^{5} e - 40 \, a b d^{3} e^{3} + 30 \, a^{2} d^{2} e^{4} + 15 \, {\left(b^{2} + 2 \, a c\right)} d^{4} e^{2}\right)} g + 2 \, {\left(2 \, {\left(6 \, c^{2} d^{5} e - 33 \, b c d^{4} e^{2} - 171 \, a b d^{2} e^{4} + 261 \, a^{2} d e^{5} + 37 \, {\left(b^{2} + 2 \, a c\right)} d^{3} e^{3}\right)} f + {\left(24 \, b c d^{5} e + 148 \, a b d^{3} e^{3} - 171 \, a^{2} d^{2} e^{4} - 33 \, {\left(b^{2} + 2 \, a c\right)} d^{4} e^{2}\right)} g\right)} m + {\left(720 \, a^{2} e^{6} f + {\left(a^{2} d e^{5} g + {\left(2 \, a b d e^{5} + a^{2} e^{6}\right)} f\right)} m^{5} + 2 \, {\left({\left(18 \, a b d e^{5} + 10 \, a^{2} e^{6} - {\left(b^{2} + 2 \, a c\right)} d^{2} e^{4}\right)} f - {\left(2 \, a b d^{2} e^{4} - 9 \, a^{2} d e^{5}\right)} g\right)} m^{4} + {\left({\left(12 \, b c d^{3} e^{3} + 238 \, a b d e^{5} + 155 \, a^{2} e^{6} - 30 \, {\left(b^{2} + 2 \, a c\right)} d^{2} e^{4}\right)} f - {\left(60 \, a b d^{2} e^{4} - 119 \, a^{2} d e^{5} - 6 \, {\left(b^{2} + 2 \, a c\right)} d^{3} e^{3}\right)} g\right)} m^{3} - 2 \, {\left(2 \, {\left(6 \, c^{2} d^{4} e^{2} - 33 \, b c d^{3} e^{3} - 171 \, a b d e^{5} - 145 \, a^{2} e^{6} + 37 \, {\left(b^{2} + 2 \, a c\right)} d^{2} e^{4}\right)} f + {\left(24 \, b c d^{4} e^{2} + 148 \, a b d^{2} e^{4} - 171 \, a^{2} d e^{5} - 33 \, {\left(b^{2} + 2 \, a c\right)} d^{3} e^{3}\right)} g\right)} m^{2} - 12 \, {\left({\left(12 \, c^{2} d^{4} e^{2} - 30 \, b c d^{3} e^{3} - 60 \, a b d e^{5} - 87 \, a^{2} e^{6} + 20 \, {\left(b^{2} + 2 \, a c\right)} d^{2} e^{4}\right)} f - {\left(10 \, c^{2} d^{5} e - 24 \, b c d^{4} e^{2} - 40 \, a b d^{2} e^{4} + 30 \, a^{2} d e^{5} + 15 \, {\left(b^{2} + 2 \, a c\right)} d^{3} e^{3}\right)} g\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{6} m^{6} + 21 \, e^{6} m^{5} + 175 \, e^{6} m^{4} + 735 \, e^{6} m^{3} + 1624 \, e^{6} m^{2} + 1764 \, e^{6} m + 720 \, e^{6}}"," ",0,"(a^2*d*e^5*f*m^5 + (c^2*e^6*g*m^5 + 15*c^2*e^6*g*m^4 + 85*c^2*e^6*g*m^3 + 225*c^2*e^6*g*m^2 + 274*c^2*e^6*g*m + 120*c^2*e^6*g)*x^6 + (144*c^2*e^6*f + 288*b*c*e^6*g + (c^2*e^6*f + (c^2*d*e^5 + 2*b*c*e^6)*g)*m^5 + 2*(8*c^2*e^6*f + (5*c^2*d*e^5 + 16*b*c*e^6)*g)*m^4 + 5*(19*c^2*e^6*f + (7*c^2*d*e^5 + 38*b*c*e^6)*g)*m^3 + 10*(26*c^2*e^6*f + (5*c^2*d*e^5 + 52*b*c*e^6)*g)*m^2 + 12*(27*c^2*e^6*f + 2*(c^2*d*e^5 + 27*b*c*e^6)*g)*m)*x^5 - (a^2*d^2*e^4*g + 2*(a*b*d^2*e^4 - 10*a^2*d*e^5)*f)*m^4 + (360*b*c*e^6*f + 180*(b^2 + 2*a*c)*e^6*g + ((c^2*d*e^5 + 2*b*c*e^6)*f + (2*b*c*d*e^5 + (b^2 + 2*a*c)*e^6)*g)*m^5 + (2*(6*c^2*d*e^5 + 17*b*c*e^6)*f - (5*c^2*d^2*e^4 - 24*b*c*d*e^5 - 17*(b^2 + 2*a*c)*e^6)*g)*m^4 + ((47*c^2*d*e^5 + 214*b*c*e^6)*f - (30*c^2*d^2*e^4 - 94*b*c*d*e^5 - 107*(b^2 + 2*a*c)*e^6)*g)*m^3 + (2*(36*c^2*d*e^5 + 307*b*c*e^6)*f - (55*c^2*d^2*e^4 - 144*b*c*d*e^5 - 307*(b^2 + 2*a*c)*e^6)*g)*m^2 + 6*(6*(c^2*d*e^5 + 22*b*c*e^6)*f - (5*c^2*d^2*e^4 - 12*b*c*d*e^5 - 66*(b^2 + 2*a*c)*e^6)*g)*m)*x^4 - ((36*a*b*d^2*e^4 - 155*a^2*d*e^5 - 2*(b^2 + 2*a*c)*d^3*e^3)*f - 2*(2*a*b*d^3*e^3 - 9*a^2*d^2*e^4)*g)*m^3 + (480*a*b*e^6*g + 240*(b^2 + 2*a*c)*e^6*f + ((2*b*c*d*e^5 + (b^2 + 2*a*c)*e^6)*f + (2*a*b*e^6 + (b^2 + 2*a*c)*d*e^5)*g)*m^5 - 2*((2*c^2*d^2*e^4 - 14*b*c*d*e^5 - 9*(b^2 + 2*a*c)*e^6)*f + (4*b*c*d^2*e^4 - 18*a*b*e^6 - 7*(b^2 + 2*a*c)*d*e^5)*g)*m^4 - ((36*c^2*d^2*e^4 - 130*b*c*d*e^5 - 121*(b^2 + 2*a*c)*e^6)*f - (20*c^2*d^3*e^3 - 72*b*c*d^2*e^4 + 242*a*b*e^6 + 65*(b^2 + 2*a*c)*d*e^5)*g)*m^3 - 4*((20*c^2*d^2*e^4 - 56*b*c*d*e^5 - 93*(b^2 + 2*a*c)*e^6)*f - (15*c^2*d^3*e^3 - 40*b*c*d^2*e^4 + 186*a*b*e^6 + 28*(b^2 + 2*a*c)*d*e^5)*g)*m^2 - 4*((12*c^2*d^2*e^4 - 30*b*c*d*e^5 - 127*(b^2 + 2*a*c)*e^6)*f - (10*c^2*d^3*e^3 - 24*b*c*d^2*e^4 + 254*a*b*e^6 + 15*(b^2 + 2*a*c)*d*e^5)*g)*m)*x^3 - (2*(6*b*c*d^4*e^2 + 119*a*b*d^2*e^4 - 290*a^2*d*e^5 - 15*(b^2 + 2*a*c)*d^3*e^3)*f - (60*a*b*d^3*e^3 - 119*a^2*d^2*e^4 - 6*(b^2 + 2*a*c)*d^4*e^2)*g)*m^2 + (720*a*b*e^6*f + 360*a^2*e^6*g + ((2*a*b*e^6 + (b^2 + 2*a*c)*d*e^5)*f + (2*a*b*d*e^5 + a^2*e^6)*g)*m^5 - (2*(3*b*c*d^2*e^4 - 19*a*b*e^6 - 8*(b^2 + 2*a*c)*d*e^5)*f - (32*a*b*d*e^5 + 19*a^2*e^6 - 3*(b^2 + 2*a*c)*d^2*e^4)*g)*m^4 + ((12*c^2*d^3*e^3 - 72*b*c*d^2*e^4 + 274*a*b*e^6 + 89*(b^2 + 2*a*c)*d*e^5)*f + (24*b*c*d^3*e^3 + 178*a*b*d*e^5 + 137*a^2*e^6 - 36*(b^2 + 2*a*c)*d^2*e^4)*g)*m^3 + (2*(42*c^2*d^3*e^3 - 123*b*c*d^2*e^4 + 461*a*b*e^6 + 97*(b^2 + 2*a*c)*d*e^5)*f - (60*c^2*d^4*e^2 - 168*b*c*d^3*e^3 - 388*a*b*d*e^5 - 461*a^2*e^6 + 123*(b^2 + 2*a*c)*d^2*e^4)*g)*m^2 + 6*(2*(6*c^2*d^3*e^3 - 15*b*c*d^2*e^4 + 117*a*b*e^6 + 10*(b^2 + 2*a*c)*d*e^5)*f - (10*c^2*d^4*e^2 - 24*b*c*d^3*e^3 - 40*a*b*d*e^5 - 117*a^2*e^6 + 15*(b^2 + 2*a*c)*d^2*e^4)*g)*m)*x^2 + 24*(6*c^2*d^5*e - 15*b*c*d^4*e^2 - 30*a*b*d^2*e^4 + 30*a^2*d*e^5 + 10*(b^2 + 2*a*c)*d^3*e^3)*f - 12*(10*c^2*d^6 - 24*b*c*d^5*e - 40*a*b*d^3*e^3 + 30*a^2*d^2*e^4 + 15*(b^2 + 2*a*c)*d^4*e^2)*g + 2*(2*(6*c^2*d^5*e - 33*b*c*d^4*e^2 - 171*a*b*d^2*e^4 + 261*a^2*d*e^5 + 37*(b^2 + 2*a*c)*d^3*e^3)*f + (24*b*c*d^5*e + 148*a*b*d^3*e^3 - 171*a^2*d^2*e^4 - 33*(b^2 + 2*a*c)*d^4*e^2)*g)*m + (720*a^2*e^6*f + (a^2*d*e^5*g + (2*a*b*d*e^5 + a^2*e^6)*f)*m^5 + 2*((18*a*b*d*e^5 + 10*a^2*e^6 - (b^2 + 2*a*c)*d^2*e^4)*f - (2*a*b*d^2*e^4 - 9*a^2*d*e^5)*g)*m^4 + ((12*b*c*d^3*e^3 + 238*a*b*d*e^5 + 155*a^2*e^6 - 30*(b^2 + 2*a*c)*d^2*e^4)*f - (60*a*b*d^2*e^4 - 119*a^2*d*e^5 - 6*(b^2 + 2*a*c)*d^3*e^3)*g)*m^3 - 2*(2*(6*c^2*d^4*e^2 - 33*b*c*d^3*e^3 - 171*a*b*d*e^5 - 145*a^2*e^6 + 37*(b^2 + 2*a*c)*d^2*e^4)*f + (24*b*c*d^4*e^2 + 148*a*b*d^2*e^4 - 171*a^2*d*e^5 - 33*(b^2 + 2*a*c)*d^3*e^3)*g)*m^2 - 12*((12*c^2*d^4*e^2 - 30*b*c*d^3*e^3 - 60*a*b*d*e^5 - 87*a^2*e^6 + 20*(b^2 + 2*a*c)*d^2*e^4)*f - (10*c^2*d^5*e - 24*b*c*d^4*e^2 - 40*a*b*d^2*e^4 + 30*a^2*d*e^5 + 15*(b^2 + 2*a*c)*d^3*e^3)*g)*m)*x)*(e*x + d)^m/(e^6*m^6 + 21*e^6*m^5 + 175*e^6*m^4 + 735*e^6*m^3 + 1624*e^6*m^2 + 1764*e^6*m + 720*e^6)","B",0
927,0,0,0,0.418928," ","integrate((e*x+d)^m*(c*x^2+b*x+a)^2/(g*x+f),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)} {\left(e x + d\right)}^{m}}{g x + f}, x\right)"," ",0,"integral((c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)*(e*x + d)^m/(g*x + f), x)","F",0
928,0,0,0,0.429937," ","integrate((e*x+d)^m*(c*x^2+b*x+a)^2/(g*x+f)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)} {\left(e x + d\right)}^{m}}{g^{2} x^{2} + 2 \, f g x + f^{2}}, x\right)"," ",0,"integral((c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)*(e*x + d)^m/(g^2*x^2 + 2*f*g*x + f^2), x)","F",0
929,0,0,0,0.431145," ","integrate((e*x+d)^m*(c*x^2+b*x+a)^2/(g*x+f)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)} {\left(e x + d\right)}^{m}}{g^{3} x^{3} + 3 \, f g^{2} x^{2} + 3 \, f^{2} g x + f^{3}}, x\right)"," ",0,"integral((c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)*(e*x + d)^m/(g^3*x^3 + 3*f*g^2*x^2 + 3*f^2*g*x + f^3), x)","F",0
930,0,0,0,0.419964," ","integrate((2+3*x)^4*(1+4*x)^m/(3*x^2-5*x+1),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} {\left(4 \, x + 1\right)}^{m}}{3 \, x^{2} - 5 \, x + 1}, x\right)"," ",0,"integral((81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*(4*x + 1)^m/(3*x^2 - 5*x + 1), x)","F",0
931,0,0,0,0.413803," ","integrate((2+3*x)^3*(1+4*x)^m/(3*x^2-5*x+1),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} {\left(4 \, x + 1\right)}^{m}}{3 \, x^{2} - 5 \, x + 1}, x\right)"," ",0,"integral((27*x^3 + 54*x^2 + 36*x + 8)*(4*x + 1)^m/(3*x^2 - 5*x + 1), x)","F",0
932,0,0,0,0.429410," ","integrate((2+3*x)^2*(1+4*x)^m/(3*x^2-5*x+1),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(9 \, x^{2} + 12 \, x + 4\right)} {\left(4 \, x + 1\right)}^{m}}{3 \, x^{2} - 5 \, x + 1}, x\right)"," ",0,"integral((9*x^2 + 12*x + 4)*(4*x + 1)^m/(3*x^2 - 5*x + 1), x)","F",0
933,0,0,0,0.416633," ","integrate((2+3*x)*(1+4*x)^m/(3*x^2-5*x+1),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(4 \, x + 1\right)}^{m} {\left(3 \, x + 2\right)}}{3 \, x^{2} - 5 \, x + 1}, x\right)"," ",0,"integral((4*x + 1)^m*(3*x + 2)/(3*x^2 - 5*x + 1), x)","F",0
934,0,0,0,0.436855," ","integrate((1+4*x)^m/(3*x^2-5*x+1),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(4 \, x + 1\right)}^{m}}{3 \, x^{2} - 5 \, x + 1}, x\right)"," ",0,"integral((4*x + 1)^m/(3*x^2 - 5*x + 1), x)","F",0
935,0,0,0,0.407453," ","integrate((1+4*x)^m/(2+3*x)/(3*x^2-5*x+1),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(4 \, x + 1\right)}^{m}}{9 \, x^{3} - 9 \, x^{2} - 7 \, x + 2}, x\right)"," ",0,"integral((4*x + 1)^m/(9*x^3 - 9*x^2 - 7*x + 2), x)","F",0
936,0,0,0,0.424713," ","integrate((1+4*x)^m/(2+3*x)^2/(3*x^2-5*x+1),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(4 \, x + 1\right)}^{m}}{27 \, x^{4} - 9 \, x^{3} - 39 \, x^{2} - 8 \, x + 4}, x\right)"," ",0,"integral((4*x + 1)^m/(27*x^4 - 9*x^3 - 39*x^2 - 8*x + 4), x)","F",0
937,0,0,0,0.423505," ","integrate((2+3*x)^4*(1+4*x)^m/(3*x^2-5*x+1)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} {\left(4 \, x + 1\right)}^{m}}{9 \, x^{4} - 30 \, x^{3} + 31 \, x^{2} - 10 \, x + 1}, x\right)"," ",0,"integral((81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*(4*x + 1)^m/(9*x^4 - 30*x^3 + 31*x^2 - 10*x + 1), x)","F",0
938,0,0,0,0.421687," ","integrate((2+3*x)^3*(1+4*x)^m/(3*x^2-5*x+1)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} {\left(4 \, x + 1\right)}^{m}}{9 \, x^{4} - 30 \, x^{3} + 31 \, x^{2} - 10 \, x + 1}, x\right)"," ",0,"integral((27*x^3 + 54*x^2 + 36*x + 8)*(4*x + 1)^m/(9*x^4 - 30*x^3 + 31*x^2 - 10*x + 1), x)","F",0
939,0,0,0,0.432426," ","integrate((2+3*x)^2*(1+4*x)^m/(3*x^2-5*x+1)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(9 \, x^{2} + 12 \, x + 4\right)} {\left(4 \, x + 1\right)}^{m}}{9 \, x^{4} - 30 \, x^{3} + 31 \, x^{2} - 10 \, x + 1}, x\right)"," ",0,"integral((9*x^2 + 12*x + 4)*(4*x + 1)^m/(9*x^4 - 30*x^3 + 31*x^2 - 10*x + 1), x)","F",0
940,0,0,0,0.414404," ","integrate((2+3*x)*(1+4*x)^m/(3*x^2-5*x+1)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(4 \, x + 1\right)}^{m} {\left(3 \, x + 2\right)}}{9 \, x^{4} - 30 \, x^{3} + 31 \, x^{2} - 10 \, x + 1}, x\right)"," ",0,"integral((4*x + 1)^m*(3*x + 2)/(9*x^4 - 30*x^3 + 31*x^2 - 10*x + 1), x)","F",0
941,0,0,0,0.427229," ","integrate((1+4*x)^m/(3*x^2-5*x+1)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(4 \, x + 1\right)}^{m}}{9 \, x^{4} - 30 \, x^{3} + 31 \, x^{2} - 10 \, x + 1}, x\right)"," ",0,"integral((4*x + 1)^m/(9*x^4 - 30*x^3 + 31*x^2 - 10*x + 1), x)","F",0
942,0,0,0,0.426039," ","integrate((1+4*x)^m/(2+3*x)/(3*x^2-5*x+1)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(4 \, x + 1\right)}^{m}}{27 \, x^{5} - 72 \, x^{4} + 33 \, x^{3} + 32 \, x^{2} - 17 \, x + 2}, x\right)"," ",0,"integral((4*x + 1)^m/(27*x^5 - 72*x^4 + 33*x^3 + 32*x^2 - 17*x + 2), x)","F",0
943,0,0,0,0.417042," ","integrate((1+4*x)^m/(2+3*x)^2/(3*x^2-5*x+1)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(4 \, x + 1\right)}^{m}}{81 \, x^{6} - 162 \, x^{5} - 45 \, x^{4} + 162 \, x^{3} + 13 \, x^{2} - 28 \, x + 4}, x\right)"," ",0,"integral((4*x + 1)^m/(81*x^6 - 162*x^5 - 45*x^4 + 162*x^3 + 13*x^2 - 28*x + 4), x)","F",0
944,0,0,0,0.440276," ","integrate((e*x+d)^m*(c*x^2+b*x+a)/(f*x+e)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2} + b x + a\right)} \sqrt{f x + e} {\left(e x + d\right)}^{m}}{f^{2} x^{2} + 2 \, e f x + e^{2}}, x\right)"," ",0,"integral((c*x^2 + b*x + a)*sqrt(f*x + e)*(e*x + d)^m/(f^2*x^2 + 2*e*f*x + e^2), x)","F",0
945,0,0,0,0.499087," ","integrate((e*x+d)^m*(g*x+f)^2*(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(g^{2} x^{2} + 2 \, f g x + f^{2}\right)} \sqrt{c x^{2} + b x + a} {\left(e x + d\right)}^{m}, x\right)"," ",0,"integral((g^2*x^2 + 2*f*g*x + f^2)*sqrt(c*x^2 + b*x + a)*(e*x + d)^m, x)","F",0
946,0,0,0,0.442263," ","integrate((e*x+d)^m*(g*x+f)*(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{2} + b x + a} {\left(g x + f\right)} {\left(e x + d\right)}^{m}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*(g*x + f)*(e*x + d)^m, x)","F",0
947,0,0,0,0.443676," ","integrate((e*x+d)^m*(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{2} + b x + a} {\left(e x + d\right)}^{m}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*(e*x + d)^m, x)","F",0
948,0,0,0,0.434673," ","integrate((e*x+d)^m*(c*x^2+b*x+a)^(1/2)/(g*x+f),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} {\left(e x + d\right)}^{m}}{g x + f}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*(e*x + d)^m/(g*x + f), x)","F",0
949,0,0,0,0.454191," ","integrate((e*x+d)^m*(g*x+f)^2/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(g^{2} x^{2} + 2 \, f g x + f^{2}\right)} {\left(e x + d\right)}^{m}}{\sqrt{c x^{2} + b x + a}}, x\right)"," ",0,"integral((g^2*x^2 + 2*f*g*x + f^2)*(e*x + d)^m/sqrt(c*x^2 + b*x + a), x)","F",0
950,0,0,0,0.449868," ","integrate((e*x+d)^m*(g*x+f)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(g x + f\right)} {\left(e x + d\right)}^{m}}{\sqrt{c x^{2} + b x + a}}, x\right)"," ",0,"integral((g*x + f)*(e*x + d)^m/sqrt(c*x^2 + b*x + a), x)","F",0
951,0,0,0,0.438994," ","integrate((e*x+d)^m/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)}^{m}}{\sqrt{c x^{2} + b x + a}}, x\right)"," ",0,"integral((e*x + d)^m/sqrt(c*x^2 + b*x + a), x)","F",0
952,0,0,0,0.440774," ","integrate((e*x+d)^m/(g*x+f)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} {\left(e x + d\right)}^{m}}{c g x^{3} + {\left(c f + b g\right)} x^{2} + a f + {\left(b f + a g\right)} x}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*(e*x + d)^m/(c*g*x^3 + (c*f + b*g)*x^2 + a*f + (b*f + a*g)*x), x)","F",0
953,0,0,0,0.443907," ","integrate((e*x+d)^m*(g*x+f)^n*(c*x^2+b*x+a),x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{2} + b x + a\right)} {\left(e x + d\right)}^{m} {\left(g x + f\right)}^{n}, x\right)"," ",0,"integral((c*x^2 + b*x + a)*(e*x + d)^m*(g*x + f)^n, x)","F",0
954,0,0,0,0.558152," ","integrate((e*x+d)^m*(g*x+f)^2*(c*x^2+b*x+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(g^{2} x^{2} + 2 \, f g x + f^{2}\right)} {\left(c x^{2} + b x + a\right)}^{p} {\left(e x + d\right)}^{m}, x\right)"," ",0,"integral((g^2*x^2 + 2*f*g*x + f^2)*(c*x^2 + b*x + a)^p*(e*x + d)^m, x)","F",0
955,0,0,0,0.465808," ","integrate((e*x+d)^m*(g*x+f)*(c*x^2+b*x+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(g x + f\right)} {\left(c x^{2} + b x + a\right)}^{p} {\left(e x + d\right)}^{m}, x\right)"," ",0,"integral((g*x + f)*(c*x^2 + b*x + a)^p*(e*x + d)^m, x)","F",0
956,0,0,0,0.453895," ","integrate((e*x+d)^m*(c*x^2+b*x+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{2} + b x + a\right)}^{p} {\left(e x + d\right)}^{m}, x\right)"," ",0,"integral((c*x^2 + b*x + a)^p*(e*x + d)^m, x)","F",0
957,0,0,0,0.454209," ","integrate((e*x+d)^m*(c*x^2+b*x+a)^p/(g*x+f),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2} + b x + a\right)}^{p} {\left(e x + d\right)}^{m}}{g x + f}, x\right)"," ",0,"integral((c*x^2 + b*x + a)^p*(e*x + d)^m/(g*x + f), x)","F",0
958,-1,0,0,0.000000," ","integrate(1/x^2/(1-1/c^2/x^2)^(1/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
