1,1,211,0,1.495859," ","integrate((e*x+d)^2*(C*x^2+B*x+A)*(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","-\frac{30 \, {\left(3 \, C d^{6} + 4 \, B d^{5} e + 10 \, A d^{4} e^{2}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) - {\left(40 \, C e^{5} x^{5} - 64 \, C d^{5} - 112 \, B d^{4} e - 160 \, A d^{3} e^{2} + 48 \, {\left(2 \, C d e^{4} + B e^{5}\right)} x^{4} + 10 \, {\left(5 \, C d^{2} e^{3} + 12 \, B d e^{4} + 6 \, A e^{5}\right)} x^{3} - 32 \, {\left(C d^{3} e^{2} - 2 \, B d^{2} e^{3} - 5 \, A d e^{4}\right)} x^{2} - 15 \, {\left(3 \, C d^{4} e + 4 \, B d^{3} e^{2} - 6 \, A d^{2} e^{3}\right)} x\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{240 \, e^{3}}"," ",0,"-1/240*(30*(3*C*d^6 + 4*B*d^5*e + 10*A*d^4*e^2)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) - (40*C*e^5*x^5 - 64*C*d^5 - 112*B*d^4*e - 160*A*d^3*e^2 + 48*(2*C*d*e^4 + B*e^5)*x^4 + 10*(5*C*d^2*e^3 + 12*B*d*e^4 + 6*A*e^5)*x^3 - 32*(C*d^3*e^2 - 2*B*d^2*e^3 - 5*A*d*e^4)*x^2 - 15*(3*C*d^4*e + 4*B*d^3*e^2 - 6*A*d^2*e^3)*x)*sqrt(-e^2*x^2 + d^2))/e^3","A",0
2,1,173,0,1.105382," ","integrate((e*x+d)*(C*x^2+B*x+A)*(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","-\frac{30 \, {\left(C d^{5} + B d^{4} e + 4 \, A d^{3} e^{2}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) - {\left(24 \, C e^{4} x^{4} - 16 \, C d^{4} - 40 \, B d^{3} e - 40 \, A d^{2} e^{2} + 30 \, {\left(C d e^{3} + B e^{4}\right)} x^{3} - 8 \, {\left(C d^{2} e^{2} - 5 \, B d e^{3} - 5 \, A e^{4}\right)} x^{2} - 15 \, {\left(C d^{3} e + B d^{2} e^{2} - 4 \, A d e^{3}\right)} x\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{120 \, e^{3}}"," ",0,"-1/120*(30*(C*d^5 + B*d^4*e + 4*A*d^3*e^2)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) - (24*C*e^4*x^4 - 16*C*d^4 - 40*B*d^3*e - 40*A*d^2*e^2 + 30*(C*d*e^3 + B*e^4)*x^3 - 8*(C*d^2*e^2 - 5*B*d*e^3 - 5*A*e^4)*x^2 - 15*(C*d^3*e + B*d^2*e^2 - 4*A*d*e^3)*x)*sqrt(-e^2*x^2 + d^2))/e^3","A",0
3,1,108,0,1.468239," ","integrate((C*x^2+B*x+A)*(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","-\frac{6 \, {\left(C d^{4} + 4 \, A d^{2} e^{2}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) - {\left(6 \, C e^{3} x^{3} + 8 \, B e^{3} x^{2} - 8 \, B d^{2} e - 3 \, {\left(C d^{2} e - 4 \, A e^{3}\right)} x\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{24 \, e^{3}}"," ",0,"-1/24*(6*(C*d^4 + 4*A*d^2*e^2)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) - (6*C*e^3*x^3 + 8*B*e^3*x^2 - 8*B*d^2*e - 3*(C*d^2*e - 4*A*e^3)*x)*sqrt(-e^2*x^2 + d^2))/e^3","A",0
4,1,112,0,1.436321," ","integrate((C*x^2+B*x+A)*(-e^2*x^2+d^2)^(1/2)/(e*x+d),x, algorithm=""fricas"")","-\frac{6 \, {\left(C d^{3} - B d^{2} e + 2 \, A d e^{2}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) - {\left(2 \, C e^{2} x^{2} + 4 \, C d^{2} - 6 \, B d e + 6 \, A e^{2} - 3 \, {\left(C d e - B e^{2}\right)} x\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{6 \, e^{3}}"," ",0,"-1/6*(6*(C*d^3 - B*d^2*e + 2*A*d*e^2)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) - (2*C*e^2*x^2 + 4*C*d^2 - 6*B*d*e + 6*A*e^2 - 3*(C*d*e - B*e^2)*x)*sqrt(-e^2*x^2 + d^2))/e^3","A",0
5,1,190,0,1.413165," ","integrate((C*x^2+B*x+A)*(-e^2*x^2+d^2)^(1/2)/(e*x+d)^2,x, algorithm=""fricas"")","-\frac{8 \, C d^{3} - 6 \, B d^{2} e + 4 \, A d e^{2} + 2 \, {\left(4 \, C d^{2} e - 3 \, B d e^{2} + 2 \, A e^{3}\right)} x - 2 \, {\left(5 \, C d^{3} - 4 \, B d^{2} e + 2 \, A d e^{2} + {\left(5 \, C d^{2} e - 4 \, B d e^{2} + 2 \, A e^{3}\right)} x\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) - {\left(C e^{2} x^{2} - 8 \, C d^{2} + 6 \, B d e - 4 \, A e^{2} - {\left(3 \, C d e - 2 \, B e^{2}\right)} x\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{2 \, {\left(e^{4} x + d e^{3}\right)}}"," ",0,"-1/2*(8*C*d^3 - 6*B*d^2*e + 4*A*d*e^2 + 2*(4*C*d^2*e - 3*B*d*e^2 + 2*A*e^3)*x - 2*(5*C*d^3 - 4*B*d^2*e + 2*A*d*e^2 + (5*C*d^2*e - 4*B*d*e^2 + 2*A*e^3)*x)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) - (C*e^2*x^2 - 8*C*d^2 + 6*B*d*e - 4*A*e^2 - (3*C*d*e - 2*B*e^2)*x)*sqrt(-e^2*x^2 + d^2))/(e^4*x + d*e^3)","A",0
6,1,258,0,1.000685," ","integrate((C*x^2+B*x+A)*(-e^2*x^2+d^2)^(1/2)/(e*x+d)^3,x, algorithm=""fricas"")","\frac{14 \, C d^{4} - 5 \, B d^{3} e - A d^{2} e^{2} + {\left(14 \, C d^{2} e^{2} - 5 \, B d e^{3} - A e^{4}\right)} x^{2} + 2 \, {\left(14 \, C d^{3} e - 5 \, B d^{2} e^{2} - A d e^{3}\right)} x - 6 \, {\left(3 \, C d^{4} - B d^{3} e + {\left(3 \, C d^{2} e^{2} - B d e^{3}\right)} x^{2} + 2 \, {\left(3 \, C d^{3} e - B d^{2} e^{2}\right)} x\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(3 \, C d e^{2} x^{2} + 14 \, C d^{3} - 5 \, B d^{2} e - A d e^{2} + {\left(19 \, C d^{2} e - 7 \, B d e^{2} + A e^{3}\right)} x\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{3 \, {\left(d e^{5} x^{2} + 2 \, d^{2} e^{4} x + d^{3} e^{3}\right)}}"," ",0,"1/3*(14*C*d^4 - 5*B*d^3*e - A*d^2*e^2 + (14*C*d^2*e^2 - 5*B*d*e^3 - A*e^4)*x^2 + 2*(14*C*d^3*e - 5*B*d^2*e^2 - A*d*e^3)*x - 6*(3*C*d^4 - B*d^3*e + (3*C*d^2*e^2 - B*d*e^3)*x^2 + 2*(3*C*d^3*e - B*d^2*e^2)*x)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (3*C*d*e^2*x^2 + 14*C*d^3 - 5*B*d^2*e - A*d*e^2 + (19*C*d^2*e - 7*B*d*e^2 + A*e^3)*x)*sqrt(-e^2*x^2 + d^2))/(d*e^5*x^2 + 2*d^2*e^4*x + d^3*e^3)","A",0
7,1,304,0,0.996702," ","integrate((C*x^2+B*x+A)*(-e^2*x^2+d^2)^(1/2)/(e*x+d)^4,x, algorithm=""fricas"")","-\frac{24 \, C d^{5} + B d^{4} e + 4 \, A d^{3} e^{2} + {\left(24 \, C d^{2} e^{3} + B d e^{4} + 4 \, A e^{5}\right)} x^{3} + 3 \, {\left(24 \, C d^{3} e^{2} + B d^{2} e^{3} + 4 \, A d e^{4}\right)} x^{2} + 3 \, {\left(24 \, C d^{4} e + B d^{3} e^{2} + 4 \, A d^{2} e^{3}\right)} x - 30 \, {\left(C d^{2} e^{3} x^{3} + 3 \, C d^{3} e^{2} x^{2} + 3 \, C d^{4} e x + C d^{5}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(24 \, C d^{4} + B d^{3} e + 4 \, A d^{2} e^{2} + {\left(39 \, C d^{2} e^{2} - 4 \, B d e^{3} - A e^{4}\right)} x^{2} + 3 \, {\left(19 \, C d^{3} e + B d^{2} e^{2} - A d e^{3}\right)} x\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(d^{2} e^{6} x^{3} + 3 \, d^{3} e^{5} x^{2} + 3 \, d^{4} e^{4} x + d^{5} e^{3}\right)}}"," ",0,"-1/15*(24*C*d^5 + B*d^4*e + 4*A*d^3*e^2 + (24*C*d^2*e^3 + B*d*e^4 + 4*A*e^5)*x^3 + 3*(24*C*d^3*e^2 + B*d^2*e^3 + 4*A*d*e^4)*x^2 + 3*(24*C*d^4*e + B*d^3*e^2 + 4*A*d^2*e^3)*x - 30*(C*d^2*e^3*x^3 + 3*C*d^3*e^2*x^2 + 3*C*d^4*e*x + C*d^5)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (24*C*d^4 + B*d^3*e + 4*A*d^2*e^2 + (39*C*d^2*e^2 - 4*B*d*e^3 - A*e^4)*x^2 + 3*(19*C*d^3*e + B*d^2*e^2 - A*d*e^3)*x)*sqrt(-e^2*x^2 + d^2))/(d^2*e^6*x^3 + 3*d^3*e^5*x^2 + 3*d^4*e^4*x + d^5*e^3)","A",0
8,1,320,0,0.785111," ","integrate((C*x^2+B*x+A)*(-e^2*x^2+d^2)^(1/2)/(e*x+d)^5,x, algorithm=""fricas"")","-\frac{2 \, C d^{6} + 5 \, B d^{5} e + 23 \, A d^{4} e^{2} + {\left(2 \, C d^{2} e^{4} + 5 \, B d e^{5} + 23 \, A e^{6}\right)} x^{4} + 4 \, {\left(2 \, C d^{3} e^{3} + 5 \, B d^{2} e^{4} + 23 \, A d e^{5}\right)} x^{3} + 6 \, {\left(2 \, C d^{4} e^{2} + 5 \, B d^{3} e^{3} + 23 \, A d^{2} e^{4}\right)} x^{2} + 4 \, {\left(2 \, C d^{5} e + 5 \, B d^{4} e^{2} + 23 \, A d^{3} e^{3}\right)} x + {\left(2 \, C d^{5} + 5 \, B d^{4} e + 23 \, A d^{3} e^{2} - {\left(23 \, C d^{2} e^{3} + 5 \, B d e^{4} + 2 \, A e^{5}\right)} x^{3} + {\left(13 \, C d^{3} e^{2} - 20 \, B d^{2} e^{3} - 8 \, A d e^{4}\right)} x^{2} + {\left(8 \, C d^{4} e + 20 \, B d^{3} e^{2} - 13 \, A d^{2} e^{3}\right)} x\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{105 \, {\left(d^{3} e^{7} x^{4} + 4 \, d^{4} e^{6} x^{3} + 6 \, d^{5} e^{5} x^{2} + 4 \, d^{6} e^{4} x + d^{7} e^{3}\right)}}"," ",0,"-1/105*(2*C*d^6 + 5*B*d^5*e + 23*A*d^4*e^2 + (2*C*d^2*e^4 + 5*B*d*e^5 + 23*A*e^6)*x^4 + 4*(2*C*d^3*e^3 + 5*B*d^2*e^4 + 23*A*d*e^5)*x^3 + 6*(2*C*d^4*e^2 + 5*B*d^3*e^3 + 23*A*d^2*e^4)*x^2 + 4*(2*C*d^5*e + 5*B*d^4*e^2 + 23*A*d^3*e^3)*x + (2*C*d^5 + 5*B*d^4*e + 23*A*d^3*e^2 - (23*C*d^2*e^3 + 5*B*d*e^4 + 2*A*e^5)*x^3 + (13*C*d^3*e^2 - 20*B*d^2*e^3 - 8*A*d*e^4)*x^2 + (8*C*d^4*e + 20*B*d^3*e^2 - 13*A*d^2*e^3)*x)*sqrt(-e^2*x^2 + d^2))/(d^3*e^7*x^4 + 4*d^4*e^6*x^3 + 6*d^5*e^5*x^2 + 4*d^6*e^4*x + d^7*e^3)","A",0
9,1,399,0,1.017504," ","integrate((C*x^2+B*x+A)*(-e^2*x^2+d^2)^(1/2)/(e*x+d)^6,x, algorithm=""fricas"")","-\frac{4 \, C d^{7} + 11 \, B d^{6} e + 58 \, A d^{5} e^{2} + {\left(4 \, C d^{2} e^{5} + 11 \, B d e^{6} + 58 \, A e^{7}\right)} x^{5} + 5 \, {\left(4 \, C d^{3} e^{4} + 11 \, B d^{2} e^{5} + 58 \, A d e^{6}\right)} x^{4} + 10 \, {\left(4 \, C d^{4} e^{3} + 11 \, B d^{3} e^{4} + 58 \, A d^{2} e^{5}\right)} x^{3} + 10 \, {\left(4 \, C d^{5} e^{2} + 11 \, B d^{4} e^{3} + 58 \, A d^{3} e^{4}\right)} x^{2} + 5 \, {\left(4 \, C d^{6} e + 11 \, B d^{5} e^{2} + 58 \, A d^{4} e^{3}\right)} x + {\left(4 \, C d^{6} + 11 \, B d^{5} e + 58 \, A d^{4} e^{2} - {\left(11 \, C d^{2} e^{4} + 4 \, B d e^{5} + 2 \, A e^{6}\right)} x^{4} - 5 \, {\left(11 \, C d^{3} e^{3} + 4 \, B d^{2} e^{4} + 2 \, A d e^{5}\right)} x^{3} + 21 \, {\left(2 \, C d^{4} e^{2} - 2 \, B d^{3} e^{3} - A d^{2} e^{4}\right)} x^{2} + 5 \, {\left(4 \, C d^{5} e + 11 \, B d^{4} e^{2} - 5 \, A d^{3} e^{3}\right)} x\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{315 \, {\left(d^{4} e^{8} x^{5} + 5 \, d^{5} e^{7} x^{4} + 10 \, d^{6} e^{6} x^{3} + 10 \, d^{7} e^{5} x^{2} + 5 \, d^{8} e^{4} x + d^{9} e^{3}\right)}}"," ",0,"-1/315*(4*C*d^7 + 11*B*d^6*e + 58*A*d^5*e^2 + (4*C*d^2*e^5 + 11*B*d*e^6 + 58*A*e^7)*x^5 + 5*(4*C*d^3*e^4 + 11*B*d^2*e^5 + 58*A*d*e^6)*x^4 + 10*(4*C*d^4*e^3 + 11*B*d^3*e^4 + 58*A*d^2*e^5)*x^3 + 10*(4*C*d^5*e^2 + 11*B*d^4*e^3 + 58*A*d^3*e^4)*x^2 + 5*(4*C*d^6*e + 11*B*d^5*e^2 + 58*A*d^4*e^3)*x + (4*C*d^6 + 11*B*d^5*e + 58*A*d^4*e^2 - (11*C*d^2*e^4 + 4*B*d*e^5 + 2*A*e^6)*x^4 - 5*(11*C*d^3*e^3 + 4*B*d^2*e^4 + 2*A*d*e^5)*x^3 + 21*(2*C*d^4*e^2 - 2*B*d^3*e^3 - A*d^2*e^4)*x^2 + 5*(4*C*d^5*e + 11*B*d^4*e^2 - 5*A*d^3*e^3)*x)*sqrt(-e^2*x^2 + d^2))/(d^4*e^8*x^5 + 5*d^5*e^7*x^4 + 10*d^6*e^6*x^3 + 10*d^7*e^5*x^2 + 5*d^8*e^4*x + d^9*e^3)","A",0
10,1,178,0,0.867425," ","integrate((e*x+d)^3*(C*x^2+B*x+A)/(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","-\frac{30 \, {\left(13 \, C d^{5} + 15 \, B d^{4} e + 20 \, A d^{3} e^{2}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(24 \, C e^{4} x^{4} + 304 \, C d^{4} + 360 \, B d^{3} e + 440 \, A d^{2} e^{2} + 30 \, {\left(3 \, C d e^{3} + B e^{4}\right)} x^{3} + 8 \, {\left(19 \, C d^{2} e^{2} + 15 \, B d e^{3} + 5 \, A e^{4}\right)} x^{2} + 15 \, {\left(13 \, C d^{3} e + 15 \, B d^{2} e^{2} + 12 \, A d e^{3}\right)} x\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{120 \, e^{3}}"," ",0,"-1/120*(30*(13*C*d^5 + 15*B*d^4*e + 20*A*d^3*e^2)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (24*C*e^4*x^4 + 304*C*d^4 + 360*B*d^3*e + 440*A*d^2*e^2 + 30*(3*C*d*e^3 + B*e^4)*x^3 + 8*(19*C*d^2*e^2 + 15*B*d*e^3 + 5*A*e^4)*x^2 + 15*(13*C*d^3*e + 15*B*d^2*e^2 + 12*A*d*e^3)*x)*sqrt(-e^2*x^2 + d^2))/e^3","A",0
11,1,145,0,1.137442," ","integrate((e*x+d)^2*(C*x^2+B*x+A)/(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","-\frac{6 \, {\left(7 \, C d^{4} + 8 \, B d^{3} e + 12 \, A d^{2} e^{2}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(6 \, C e^{3} x^{3} + 32 \, C d^{3} + 40 \, B d^{2} e + 48 \, A d e^{2} + 8 \, {\left(2 \, C d e^{2} + B e^{3}\right)} x^{2} + 3 \, {\left(7 \, C d^{2} e + 8 \, B d e^{2} + 4 \, A e^{3}\right)} x\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{24 \, e^{3}}"," ",0,"-1/24*(6*(7*C*d^4 + 8*B*d^3*e + 12*A*d^2*e^2)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (6*C*e^3*x^3 + 32*C*d^3 + 40*B*d^2*e + 48*A*d*e^2 + 8*(2*C*d*e^2 + B*e^3)*x^2 + 3*(7*C*d^2*e + 8*B*d*e^2 + 4*A*e^3)*x)*sqrt(-e^2*x^2 + d^2))/e^3","A",0
12,1,109,0,0.788743," ","integrate((e*x+d)*(C*x^2+B*x+A)/(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","-\frac{6 \, {\left(C d^{3} + B d^{2} e + 2 \, A d e^{2}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(2 \, C e^{2} x^{2} + 4 \, C d^{2} + 6 \, B d e + 6 \, A e^{2} + 3 \, {\left(C d e + B e^{2}\right)} x\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{6 \, e^{3}}"," ",0,"-1/6*(6*(C*d^3 + B*d^2*e + 2*A*d*e^2)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (2*C*e^2*x^2 + 4*C*d^2 + 6*B*d*e + 6*A*e^2 + 3*(C*d*e + B*e^2)*x)*sqrt(-e^2*x^2 + d^2))/e^3","A",0
13,1,71,0,1.037453," ","integrate((C*x^2+B*x+A)/(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(C d^{2} + 2 \, A e^{2}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + \sqrt{-e^{2} x^{2} + d^{2}} {\left(C e x + 2 \, B e\right)}}{2 \, e^{3}}"," ",0,"-1/2*(2*(C*d^2 + 2*A*e^2)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + sqrt(-e^2*x^2 + d^2)*(C*e*x + 2*B*e))/e^3","A",0
14,1,155,0,0.720550," ","integrate((C*x^2+B*x+A)/(e*x+d)/(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, C d^{3} - B d^{2} e + A d e^{2} + {\left(2 \, C d^{2} e - B d e^{2} + A e^{3}\right)} x - 2 \, {\left(C d^{3} - B d^{2} e + {\left(C d^{2} e - B d e^{2}\right)} x\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(C d e x + 2 \, C d^{2} - B d e + A e^{2}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{d e^{4} x + d^{2} e^{3}}"," ",0,"-(2*C*d^3 - B*d^2*e + A*d*e^2 + (2*C*d^2*e - B*d*e^2 + A*e^3)*x - 2*(C*d^3 - B*d^2*e + (C*d^2*e - B*d*e^2)*x)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (C*d*e*x + 2*C*d^2 - B*d*e + A*e^2)*sqrt(-e^2*x^2 + d^2))/(d*e^4*x + d^2*e^3)","A",0
15,1,221,0,0.984986," ","integrate((C*x^2+B*x+A)/(e*x+d)^2/(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","\frac{4 \, C d^{4} - B d^{3} e - 2 \, A d^{2} e^{2} + {\left(4 \, C d^{2} e^{2} - B d e^{3} - 2 \, A e^{4}\right)} x^{2} + 2 \, {\left(4 \, C d^{3} e - B d^{2} e^{2} - 2 \, A d e^{3}\right)} x - 6 \, {\left(C d^{2} e^{2} x^{2} + 2 \, C d^{3} e x + C d^{4}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(4 \, C d^{3} - B d^{2} e - 2 \, A d e^{2} + {\left(5 \, C d^{2} e - 2 \, B d e^{2} - A e^{3}\right)} x\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{3 \, {\left(d^{2} e^{5} x^{2} + 2 \, d^{3} e^{4} x + d^{4} e^{3}\right)}}"," ",0,"1/3*(4*C*d^4 - B*d^3*e - 2*A*d^2*e^2 + (4*C*d^2*e^2 - B*d*e^3 - 2*A*e^4)*x^2 + 2*(4*C*d^3*e - B*d^2*e^2 - 2*A*d*e^3)*x - 6*(C*d^2*e^2*x^2 + 2*C*d^3*e*x + C*d^4)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (4*C*d^3 - B*d^2*e - 2*A*d*e^2 + (5*C*d^2*e - 2*B*d*e^2 - A*e^3)*x)*sqrt(-e^2*x^2 + d^2))/(d^2*e^5*x^2 + 2*d^3*e^4*x + d^4*e^3)","A",0
16,1,244,0,1.744446," ","integrate((C*x^2+B*x+A)/(e*x+d)^3/(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, C d^{5} + 3 \, B d^{4} e + 7 \, A d^{3} e^{2} + {\left(2 \, C d^{2} e^{3} + 3 \, B d e^{4} + 7 \, A e^{5}\right)} x^{3} + 3 \, {\left(2 \, C d^{3} e^{2} + 3 \, B d^{2} e^{3} + 7 \, A d e^{4}\right)} x^{2} + 3 \, {\left(2 \, C d^{4} e + 3 \, B d^{3} e^{2} + 7 \, A d^{2} e^{3}\right)} x + {\left(2 \, C d^{4} + 3 \, B d^{3} e + 7 \, A d^{2} e^{2} + {\left(7 \, C d^{2} e^{2} + 3 \, B d e^{3} + 2 \, A e^{4}\right)} x^{2} + 3 \, {\left(2 \, C d^{3} e + 3 \, B d^{2} e^{2} + 2 \, A d e^{3}\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*(2*C*d^5 + 3*B*d^4*e + 7*A*d^3*e^2 + (2*C*d^2*e^3 + 3*B*d*e^4 + 7*A*e^5)*x^3 + 3*(2*C*d^3*e^2 + 3*B*d^2*e^3 + 7*A*d*e^4)*x^2 + 3*(2*C*d^4*e + 3*B*d^3*e^2 + 7*A*d^2*e^3)*x + (2*C*d^4 + 3*B*d^3*e + 7*A*d^2*e^2 + (7*C*d^2*e^2 + 3*B*d*e^3 + 2*A*e^4)*x^2 + 3*(2*C*d^3*e + 3*B*d^2*e^2 + 2*A*d*e^3)*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)","A",0
17,1,320,0,1.183536," ","integrate((C*x^2+B*x+A)/(e*x+d)^4/(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","-\frac{8 \, C d^{6} + 13 \, B d^{5} e + 36 \, A d^{4} e^{2} + {\left(8 \, C d^{2} e^{4} + 13 \, B d e^{5} + 36 \, A e^{6}\right)} x^{4} + 4 \, {\left(8 \, C d^{3} e^{3} + 13 \, B d^{2} e^{4} + 36 \, A d e^{5}\right)} x^{3} + 6 \, {\left(8 \, C d^{4} e^{2} + 13 \, B d^{3} e^{3} + 36 \, A d^{2} e^{4}\right)} x^{2} + 4 \, {\left(8 \, C d^{5} e + 13 \, B d^{4} e^{2} + 36 \, A d^{3} e^{3}\right)} x + {\left(8 \, C d^{5} + 13 \, B d^{4} e + 36 \, A d^{3} e^{2} + {\left(13 \, C d^{2} e^{3} + 8 \, B d e^{4} + 6 \, A e^{5}\right)} x^{3} + 4 \, {\left(13 \, C d^{3} e^{2} + 8 \, B d^{2} e^{3} + 6 \, A d e^{4}\right)} x^{2} + {\left(32 \, C d^{4} e + 52 \, B d^{3} e^{2} + 39 \, A d^{2} e^{3}\right)} x\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{105 \, {\left(d^{4} e^{7} x^{4} + 4 \, d^{5} e^{6} x^{3} + 6 \, d^{6} e^{5} x^{2} + 4 \, d^{7} e^{4} x + d^{8} e^{3}\right)}}"," ",0,"-1/105*(8*C*d^6 + 13*B*d^5*e + 36*A*d^4*e^2 + (8*C*d^2*e^4 + 13*B*d*e^5 + 36*A*e^6)*x^4 + 4*(8*C*d^3*e^3 + 13*B*d^2*e^4 + 36*A*d*e^5)*x^3 + 6*(8*C*d^4*e^2 + 13*B*d^3*e^3 + 36*A*d^2*e^4)*x^2 + 4*(8*C*d^5*e + 13*B*d^4*e^2 + 36*A*d^3*e^3)*x + (8*C*d^5 + 13*B*d^4*e + 36*A*d^3*e^2 + (13*C*d^2*e^3 + 8*B*d*e^4 + 6*A*e^5)*x^3 + 4*(13*C*d^3*e^2 + 8*B*d^2*e^3 + 6*A*d*e^4)*x^2 + (32*C*d^4*e + 52*B*d^3*e^2 + 39*A*d^2*e^3)*x)*sqrt(-e^2*x^2 + d^2))/(d^4*e^7*x^4 + 4*d^5*e^6*x^3 + 6*d^6*e^5*x^2 + 4*d^7*e^4*x + d^8*e^3)","A",0
18,1,248,0,0.937297," ","integrate((e*x+d)^3*(c*x^2+a)*(C*x^2+B*x+A),x, algorithm=""fricas"")","\frac{1}{8} x^{8} e^{3} c C + \frac{3}{7} x^{7} e^{2} d c C + \frac{1}{7} x^{7} e^{3} c B + \frac{1}{2} x^{6} e d^{2} c C + \frac{1}{6} x^{6} e^{3} a C + \frac{1}{2} x^{6} e^{2} d c B + \frac{1}{6} x^{6} e^{3} c A + \frac{1}{5} x^{5} d^{3} c C + \frac{3}{5} x^{5} e^{2} d a C + \frac{3}{5} x^{5} e d^{2} c B + \frac{1}{5} x^{5} e^{3} a B + \frac{3}{5} x^{5} e^{2} d c A + \frac{3}{4} x^{4} e d^{2} a C + \frac{1}{4} x^{4} d^{3} c B + \frac{3}{4} x^{4} e^{2} d a B + \frac{3}{4} x^{4} e d^{2} c A + \frac{1}{4} x^{4} e^{3} a A + \frac{1}{3} x^{3} d^{3} a C + x^{3} e d^{2} a B + \frac{1}{3} x^{3} d^{3} c A + x^{3} e^{2} d a A + \frac{1}{2} x^{2} d^{3} a B + \frac{3}{2} x^{2} e d^{2} a A + x d^{3} a A"," ",0,"1/8*x^8*e^3*c*C + 3/7*x^7*e^2*d*c*C + 1/7*x^7*e^3*c*B + 1/2*x^6*e*d^2*c*C + 1/6*x^6*e^3*a*C + 1/2*x^6*e^2*d*c*B + 1/6*x^6*e^3*c*A + 1/5*x^5*d^3*c*C + 3/5*x^5*e^2*d*a*C + 3/5*x^5*e*d^2*c*B + 1/5*x^5*e^3*a*B + 3/5*x^5*e^2*d*c*A + 3/4*x^4*e*d^2*a*C + 1/4*x^4*d^3*c*B + 3/4*x^4*e^2*d*a*B + 3/4*x^4*e*d^2*c*A + 1/4*x^4*e^3*a*A + 1/3*x^3*d^3*a*C + x^3*e*d^2*a*B + 1/3*x^3*d^3*c*A + x^3*e^2*d*a*A + 1/2*x^2*d^3*a*B + 3/2*x^2*e*d^2*a*A + x*d^3*a*A","A",0
19,1,171,0,0.966060," ","integrate((e*x+d)^2*(c*x^2+a)*(C*x^2+B*x+A),x, algorithm=""fricas"")","\frac{1}{7} x^{7} e^{2} c C + \frac{1}{3} x^{6} e d c C + \frac{1}{6} x^{6} e^{2} c B + \frac{1}{5} x^{5} d^{2} c C + \frac{1}{5} x^{5} e^{2} a C + \frac{2}{5} x^{5} e d c B + \frac{1}{5} x^{5} e^{2} c A + \frac{1}{2} x^{4} e d a C + \frac{1}{4} x^{4} d^{2} c B + \frac{1}{4} x^{4} e^{2} a B + \frac{1}{2} x^{4} e d c A + \frac{1}{3} x^{3} d^{2} a C + \frac{2}{3} x^{3} e d a B + \frac{1}{3} x^{3} d^{2} c A + \frac{1}{3} x^{3} e^{2} a A + \frac{1}{2} x^{2} d^{2} a B + x^{2} e d a A + x d^{2} a A"," ",0,"1/7*x^7*e^2*c*C + 1/3*x^6*e*d*c*C + 1/6*x^6*e^2*c*B + 1/5*x^5*d^2*c*C + 1/5*x^5*e^2*a*C + 2/5*x^5*e*d*c*B + 1/5*x^5*e^2*c*A + 1/2*x^4*e*d*a*C + 1/4*x^4*d^2*c*B + 1/4*x^4*e^2*a*B + 1/2*x^4*e*d*c*A + 1/3*x^3*d^2*a*C + 2/3*x^3*e*d*a*B + 1/3*x^3*d^2*c*A + 1/3*x^3*e^2*a*A + 1/2*x^2*d^2*a*B + x^2*e*d*a*A + x*d^2*a*A","A",0
20,1,94,0,0.832047," ","integrate((e*x+d)*(c*x^2+a)*(C*x^2+B*x+A),x, algorithm=""fricas"")","\frac{1}{6} x^{6} e c C + \frac{1}{5} x^{5} d c C + \frac{1}{5} x^{5} e c B + \frac{1}{4} x^{4} e a C + \frac{1}{4} x^{4} d c B + \frac{1}{4} x^{4} e c A + \frac{1}{3} x^{3} d a C + \frac{1}{3} x^{3} e a B + \frac{1}{3} x^{3} d c A + \frac{1}{2} x^{2} d a B + \frac{1}{2} x^{2} e a A + x d a A"," ",0,"1/6*x^6*e*c*C + 1/5*x^5*d*c*C + 1/5*x^5*e*c*B + 1/4*x^4*e*a*C + 1/4*x^4*d*c*B + 1/4*x^4*e*c*A + 1/3*x^3*d*a*C + 1/3*x^3*e*a*B + 1/3*x^3*d*c*A + 1/2*x^2*d*a*B + 1/2*x^2*e*a*A + x*d*a*A","A",0
21,1,40,0,1.261619," ","integrate((c*x^2+a)*(C*x^2+B*x+A),x, algorithm=""fricas"")","\frac{1}{5} x^{5} c C + \frac{1}{4} x^{4} c B + \frac{1}{3} x^{3} a C + \frac{1}{3} x^{3} c A + \frac{1}{2} x^{2} a B + x a A"," ",0,"1/5*x^5*c*C + 1/4*x^4*c*B + 1/3*x^3*a*C + 1/3*x^3*c*A + 1/2*x^2*a*B + x*a*A","A",0
22,1,161,0,1.078431," ","integrate((c*x^2+a)*(C*x^2+B*x+A)/(e*x+d),x, algorithm=""fricas"")","\frac{3 \, C c e^{4} x^{4} - 4 \, {\left(C c d e^{3} - B c e^{4}\right)} x^{3} + 6 \, {\left(C c d^{2} e^{2} - B c d e^{3} + {\left(C a + A c\right)} e^{4}\right)} x^{2} - 12 \, {\left(C c d^{3} e - B c d^{2} e^{2} - B a e^{4} + {\left(C a + A c\right)} d e^{3}\right)} x + 12 \, {\left(C c d^{4} - B c d^{3} e - B a d e^{3} + A a e^{4} + {\left(C a + A c\right)} d^{2} e^{2}\right)} \log\left(e x + d\right)}{12 \, e^{5}}"," ",0,"1/12*(3*C*c*e^4*x^4 - 4*(C*c*d*e^3 - B*c*e^4)*x^3 + 6*(C*c*d^2*e^2 - B*c*d*e^3 + (C*a + A*c)*e^4)*x^2 - 12*(C*c*d^3*e - B*c*d^2*e^2 - B*a*e^4 + (C*a + A*c)*d*e^3)*x + 12*(C*c*d^4 - B*c*d^3*e - B*a*d*e^3 + A*a*e^4 + (C*a + A*c)*d^2*e^2)*log(e*x + d))/e^5","A",0
23,1,250,0,0.825965," ","integrate((c*x^2+a)*(C*x^2+B*x+A)/(e*x+d)^2,x, algorithm=""fricas"")","\frac{2 \, C c e^{4} x^{4} - 6 \, C c d^{4} + 6 \, B c d^{3} e + 6 \, B a d e^{3} - 6 \, A a e^{4} - 6 \, {\left(C a + A c\right)} d^{2} e^{2} - {\left(4 \, C c d e^{3} - 3 \, B c e^{4}\right)} x^{3} + 3 \, {\left(4 \, C c d^{2} e^{2} - 3 \, B c d e^{3} + 2 \, {\left(C a + A c\right)} e^{4}\right)} x^{2} + 6 \, {\left(3 \, C c d^{3} e - 2 \, B c d^{2} e^{2} + {\left(C a + A c\right)} d e^{3}\right)} x - 6 \, {\left(4 \, C c d^{4} - 3 \, B c d^{3} e - B a d e^{3} + 2 \, {\left(C a + A c\right)} d^{2} e^{2} + {\left(4 \, C c d^{3} e - 3 \, B c d^{2} e^{2} - B a e^{4} + 2 \, {\left(C a + A c\right)} d e^{3}\right)} x\right)} \log\left(e x + d\right)}{6 \, {\left(e^{6} x + d e^{5}\right)}}"," ",0,"1/6*(2*C*c*e^4*x^4 - 6*C*c*d^4 + 6*B*c*d^3*e + 6*B*a*d*e^3 - 6*A*a*e^4 - 6*(C*a + A*c)*d^2*e^2 - (4*C*c*d*e^3 - 3*B*c*e^4)*x^3 + 3*(4*C*c*d^2*e^2 - 3*B*c*d*e^3 + 2*(C*a + A*c)*e^4)*x^2 + 6*(3*C*c*d^3*e - 2*B*c*d^2*e^2 + (C*a + A*c)*d*e^3)*x - 6*(4*C*c*d^4 - 3*B*c*d^3*e - B*a*d*e^3 + 2*(C*a + A*c)*d^2*e^2 + (4*C*c*d^3*e - 3*B*c*d^2*e^2 - B*a*e^4 + 2*(C*a + A*c)*d*e^3)*x)*log(e*x + d))/(e^6*x + d*e^5)","A",0
24,1,273,0,0.919590," ","integrate((c*x^2+a)*(C*x^2+B*x+A)/(e*x+d)^3,x, algorithm=""fricas"")","\frac{C c e^{4} x^{4} + 7 \, C c d^{4} - 5 \, B c d^{3} e - B a d e^{3} - A a e^{4} + 3 \, {\left(C a + A c\right)} d^{2} e^{2} - 2 \, {\left(2 \, C c d e^{3} - B c e^{4}\right)} x^{3} - {\left(11 \, C c d^{2} e^{2} - 4 \, B c d e^{3}\right)} x^{2} + 2 \, {\left(C c d^{3} e - 2 \, B c d^{2} e^{2} - B a e^{4} + 2 \, {\left(C a + A c\right)} d e^{3}\right)} x + 2 \, {\left(6 \, C c d^{4} - 3 \, B c d^{3} e + {\left(C a + A c\right)} d^{2} e^{2} + {\left(6 \, C c d^{2} e^{2} - 3 \, B c d e^{3} + {\left(C a + A c\right)} e^{4}\right)} x^{2} + 2 \, {\left(6 \, C c d^{3} e - 3 \, B c d^{2} e^{2} + {\left(C a + A c\right)} d e^{3}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(e^{7} x^{2} + 2 \, d e^{6} x + d^{2} e^{5}\right)}}"," ",0,"1/2*(C*c*e^4*x^4 + 7*C*c*d^4 - 5*B*c*d^3*e - B*a*d*e^3 - A*a*e^4 + 3*(C*a + A*c)*d^2*e^2 - 2*(2*C*c*d*e^3 - B*c*e^4)*x^3 - (11*C*c*d^2*e^2 - 4*B*c*d*e^3)*x^2 + 2*(C*c*d^3*e - 2*B*c*d^2*e^2 - B*a*e^4 + 2*(C*a + A*c)*d*e^3)*x + 2*(6*C*c*d^4 - 3*B*c*d^3*e + (C*a + A*c)*d^2*e^2 + (6*C*c*d^2*e^2 - 3*B*c*d*e^3 + (C*a + A*c)*e^4)*x^2 + 2*(6*C*c*d^3*e - 3*B*c*d^2*e^2 + (C*a + A*c)*d*e^3)*x)*log(e*x + d))/(e^7*x^2 + 2*d*e^6*x + d^2*e^5)","A",0
25,1,432,0,0.750699," ","integrate((e*x+d)^3*(c*x^2+a)^2*(C*x^2+B*x+A),x, algorithm=""fricas"")","\frac{1}{10} x^{10} e^{3} c^{2} C + \frac{1}{3} x^{9} e^{2} d c^{2} C + \frac{1}{9} x^{9} e^{3} c^{2} B + \frac{3}{8} x^{8} e d^{2} c^{2} C + \frac{1}{4} x^{8} e^{3} c a C + \frac{3}{8} x^{8} e^{2} d c^{2} B + \frac{1}{8} x^{8} e^{3} c^{2} A + \frac{1}{7} x^{7} d^{3} c^{2} C + \frac{6}{7} x^{7} e^{2} d c a C + \frac{3}{7} x^{7} e d^{2} c^{2} B + \frac{2}{7} x^{7} e^{3} c a B + \frac{3}{7} x^{7} e^{2} d c^{2} A + x^{6} e d^{2} c a C + \frac{1}{6} x^{6} e^{3} a^{2} C + \frac{1}{6} x^{6} d^{3} c^{2} B + x^{6} e^{2} d c a B + \frac{1}{2} x^{6} e d^{2} c^{2} A + \frac{1}{3} x^{6} e^{3} c a A + \frac{2}{5} x^{5} d^{3} c a C + \frac{3}{5} x^{5} e^{2} d a^{2} C + \frac{6}{5} x^{5} e d^{2} c a B + \frac{1}{5} x^{5} e^{3} a^{2} B + \frac{1}{5} x^{5} d^{3} c^{2} A + \frac{6}{5} x^{5} e^{2} d c a A + \frac{3}{4} x^{4} e d^{2} a^{2} C + \frac{1}{2} x^{4} d^{3} c a B + \frac{3}{4} x^{4} e^{2} d a^{2} B + \frac{3}{2} x^{4} e d^{2} c a A + \frac{1}{4} x^{4} e^{3} a^{2} A + \frac{1}{3} x^{3} d^{3} a^{2} C + x^{3} e d^{2} a^{2} B + \frac{2}{3} x^{3} d^{3} c a A + x^{3} e^{2} d a^{2} A + \frac{1}{2} x^{2} d^{3} a^{2} B + \frac{3}{2} x^{2} e d^{2} a^{2} A + x d^{3} a^{2} A"," ",0,"1/10*x^10*e^3*c^2*C + 1/3*x^9*e^2*d*c^2*C + 1/9*x^9*e^3*c^2*B + 3/8*x^8*e*d^2*c^2*C + 1/4*x^8*e^3*c*a*C + 3/8*x^8*e^2*d*c^2*B + 1/8*x^8*e^3*c^2*A + 1/7*x^7*d^3*c^2*C + 6/7*x^7*e^2*d*c*a*C + 3/7*x^7*e*d^2*c^2*B + 2/7*x^7*e^3*c*a*B + 3/7*x^7*e^2*d*c^2*A + x^6*e*d^2*c*a*C + 1/6*x^6*e^3*a^2*C + 1/6*x^6*d^3*c^2*B + x^6*e^2*d*c*a*B + 1/2*x^6*e*d^2*c^2*A + 1/3*x^6*e^3*c*a*A + 2/5*x^5*d^3*c*a*C + 3/5*x^5*e^2*d*a^2*C + 6/5*x^5*e*d^2*c*a*B + 1/5*x^5*e^3*a^2*B + 1/5*x^5*d^3*c^2*A + 6/5*x^5*e^2*d*c*a*A + 3/4*x^4*e*d^2*a^2*C + 1/2*x^4*d^3*c*a*B + 3/4*x^4*e^2*d*a^2*B + 3/2*x^4*e*d^2*c*a*A + 1/4*x^4*e^3*a^2*A + 1/3*x^3*d^3*a^2*C + x^3*e*d^2*a^2*B + 2/3*x^3*d^3*c*a*A + x^3*e^2*d*a^2*A + 1/2*x^2*d^3*a^2*B + 3/2*x^2*e*d^2*a^2*A + x*d^3*a^2*A","A",0
26,1,302,0,0.846284," ","integrate((e*x+d)^2*(c*x^2+a)^2*(C*x^2+B*x+A),x, algorithm=""fricas"")","\frac{1}{9} x^{9} e^{2} c^{2} C + \frac{1}{4} x^{8} e d c^{2} C + \frac{1}{8} x^{8} e^{2} c^{2} B + \frac{1}{7} x^{7} d^{2} c^{2} C + \frac{2}{7} x^{7} e^{2} c a C + \frac{2}{7} x^{7} e d c^{2} B + \frac{1}{7} x^{7} e^{2} c^{2} A + \frac{2}{3} x^{6} e d c a C + \frac{1}{6} x^{6} d^{2} c^{2} B + \frac{1}{3} x^{6} e^{2} c a B + \frac{1}{3} x^{6} e d c^{2} A + \frac{2}{5} x^{5} d^{2} c a C + \frac{1}{5} x^{5} e^{2} a^{2} C + \frac{4}{5} x^{5} e d c a B + \frac{1}{5} x^{5} d^{2} c^{2} A + \frac{2}{5} x^{5} e^{2} c a A + \frac{1}{2} x^{4} e d a^{2} C + \frac{1}{2} x^{4} d^{2} c a B + \frac{1}{4} x^{4} e^{2} a^{2} B + x^{4} e d c a A + \frac{1}{3} x^{3} d^{2} a^{2} C + \frac{2}{3} x^{3} e d a^{2} B + \frac{2}{3} x^{3} d^{2} c a A + \frac{1}{3} x^{3} e^{2} a^{2} A + \frac{1}{2} x^{2} d^{2} a^{2} B + x^{2} e d a^{2} A + x d^{2} a^{2} A"," ",0,"1/9*x^9*e^2*c^2*C + 1/4*x^8*e*d*c^2*C + 1/8*x^8*e^2*c^2*B + 1/7*x^7*d^2*c^2*C + 2/7*x^7*e^2*c*a*C + 2/7*x^7*e*d*c^2*B + 1/7*x^7*e^2*c^2*A + 2/3*x^6*e*d*c*a*C + 1/6*x^6*d^2*c^2*B + 1/3*x^6*e^2*c*a*B + 1/3*x^6*e*d*c^2*A + 2/5*x^5*d^2*c*a*C + 1/5*x^5*e^2*a^2*C + 4/5*x^5*e*d*c*a*B + 1/5*x^5*d^2*c^2*A + 2/5*x^5*e^2*c*a*A + 1/2*x^4*e*d*a^2*C + 1/2*x^4*d^2*c*a*B + 1/4*x^4*e^2*a^2*B + x^4*e*d*c*a*A + 1/3*x^3*d^2*a^2*C + 2/3*x^3*e*d*a^2*B + 2/3*x^3*d^2*c*a*A + 1/3*x^3*e^2*a^2*A + 1/2*x^2*d^2*a^2*B + x^2*e*d*a^2*A + x*d^2*a^2*A","A",0
27,1,172,0,0.882347," ","integrate((e*x+d)*(c*x^2+a)^2*(C*x^2+B*x+A),x, algorithm=""fricas"")","\frac{1}{8} x^{8} e c^{2} C + \frac{1}{7} x^{7} d c^{2} C + \frac{1}{7} x^{7} e c^{2} B + \frac{1}{3} x^{6} e c a C + \frac{1}{6} x^{6} d c^{2} B + \frac{1}{6} x^{6} e c^{2} A + \frac{2}{5} x^{5} d c a C + \frac{2}{5} x^{5} e c a B + \frac{1}{5} x^{5} d c^{2} A + \frac{1}{4} x^{4} e a^{2} C + \frac{1}{2} x^{4} d c a B + \frac{1}{2} x^{4} e c a A + \frac{1}{3} x^{3} d a^{2} C + \frac{1}{3} x^{3} e a^{2} B + \frac{2}{3} x^{3} d c a A + \frac{1}{2} x^{2} d a^{2} B + \frac{1}{2} x^{2} e a^{2} A + x d a^{2} A"," ",0,"1/8*x^8*e*c^2*C + 1/7*x^7*d*c^2*C + 1/7*x^7*e*c^2*B + 1/3*x^6*e*c*a*C + 1/6*x^6*d*c^2*B + 1/6*x^6*e*c^2*A + 2/5*x^5*d*c*a*C + 2/5*x^5*e*c*a*B + 1/5*x^5*d*c^2*A + 1/4*x^4*e*a^2*C + 1/2*x^4*d*c*a*B + 1/2*x^4*e*c*a*A + 1/3*x^3*d*a^2*C + 1/3*x^3*e*a^2*B + 2/3*x^3*d*c*a*A + 1/2*x^2*d*a^2*B + 1/2*x^2*e*a^2*A + x*d*a^2*A","A",0
28,1,76,0,0.618063," ","integrate((c*x^2+a)^2*(C*x^2+B*x+A),x, algorithm=""fricas"")","\frac{1}{7} x^{7} c^{2} C + \frac{1}{6} x^{6} c^{2} B + \frac{2}{5} x^{5} c a C + \frac{1}{5} x^{5} c^{2} A + \frac{1}{2} x^{4} c a B + \frac{1}{3} x^{3} a^{2} C + \frac{2}{3} x^{3} c a A + \frac{1}{2} x^{2} a^{2} B + x a^{2} A"," ",0,"1/7*x^7*c^2*C + 1/6*x^6*c^2*B + 2/5*x^5*c*a*C + 1/5*x^5*c^2*A + 1/2*x^4*c*a*B + 1/3*x^3*a^2*C + 2/3*x^3*c*a*A + 1/2*x^2*a^2*B + x*a^2*A","A",0
29,1,379,0,1.014639," ","integrate((c*x^2+a)^2*(C*x^2+B*x+A)/(e*x+d),x, algorithm=""fricas"")","\frac{10 \, C c^{2} e^{6} x^{6} - 12 \, {\left(C c^{2} d e^{5} - B c^{2} e^{6}\right)} x^{5} + 15 \, {\left(C c^{2} d^{2} e^{4} - B c^{2} d e^{5} + {\left(2 \, C a c + A c^{2}\right)} e^{6}\right)} x^{4} - 20 \, {\left(C c^{2} d^{3} e^{3} - B c^{2} d^{2} e^{4} - 2 \, B a c e^{6} + {\left(2 \, C a c + A c^{2}\right)} d e^{5}\right)} x^{3} + 30 \, {\left(C c^{2} d^{4} e^{2} - B c^{2} d^{3} e^{3} - 2 \, B a c d e^{5} + {\left(2 \, C a c + A c^{2}\right)} d^{2} e^{4} + {\left(C a^{2} + 2 \, A a c\right)} e^{6}\right)} x^{2} - 60 \, {\left(C c^{2} d^{5} e - B c^{2} d^{4} e^{2} - 2 \, B a c d^{2} e^{4} - B a^{2} e^{6} + {\left(2 \, C a c + A c^{2}\right)} d^{3} e^{3} + {\left(C a^{2} + 2 \, A a c\right)} d e^{5}\right)} x + 60 \, {\left(C c^{2} d^{6} - B c^{2} d^{5} e - 2 \, B a c d^{3} e^{3} - B a^{2} d e^{5} + A a^{2} e^{6} + {\left(2 \, C a c + A c^{2}\right)} d^{4} e^{2} + {\left(C a^{2} + 2 \, A a c\right)} d^{2} e^{4}\right)} \log\left(e x + d\right)}{60 \, e^{7}}"," ",0,"1/60*(10*C*c^2*e^6*x^6 - 12*(C*c^2*d*e^5 - B*c^2*e^6)*x^5 + 15*(C*c^2*d^2*e^4 - B*c^2*d*e^5 + (2*C*a*c + A*c^2)*e^6)*x^4 - 20*(C*c^2*d^3*e^3 - B*c^2*d^2*e^4 - 2*B*a*c*e^6 + (2*C*a*c + A*c^2)*d*e^5)*x^3 + 30*(C*c^2*d^4*e^2 - B*c^2*d^3*e^3 - 2*B*a*c*d*e^5 + (2*C*a*c + A*c^2)*d^2*e^4 + (C*a^2 + 2*A*a*c)*e^6)*x^2 - 60*(C*c^2*d^5*e - B*c^2*d^4*e^2 - 2*B*a*c*d^2*e^4 - B*a^2*e^6 + (2*C*a*c + A*c^2)*d^3*e^3 + (C*a^2 + 2*A*a*c)*d*e^5)*x + 60*(C*c^2*d^6 - B*c^2*d^5*e - 2*B*a*c*d^3*e^3 - B*a^2*d*e^5 + A*a^2*e^6 + (2*C*a*c + A*c^2)*d^4*e^2 + (C*a^2 + 2*A*a*c)*d^2*e^4)*log(e*x + d))/e^7","A",0
30,1,553,0,1.611453," ","integrate((c*x^2+a)^2*(C*x^2+B*x+A)/(e*x+d)^2,x, algorithm=""fricas"")","\frac{12 \, C c^{2} e^{6} x^{6} - 60 \, C c^{2} d^{6} + 60 \, B c^{2} d^{5} e + 120 \, B a c d^{3} e^{3} + 60 \, B a^{2} d e^{5} - 60 \, A a^{2} e^{6} - 60 \, {\left(2 \, C a c + A c^{2}\right)} d^{4} e^{2} - 60 \, {\left(C a^{2} + 2 \, A a c\right)} d^{2} e^{4} - 3 \, {\left(6 \, C c^{2} d e^{5} - 5 \, B c^{2} e^{6}\right)} x^{5} + 5 \, {\left(6 \, C c^{2} d^{2} e^{4} - 5 \, B c^{2} d e^{5} + 4 \, {\left(2 \, C a c + A c^{2}\right)} e^{6}\right)} x^{4} - 10 \, {\left(6 \, C c^{2} d^{3} e^{3} - 5 \, B c^{2} d^{2} e^{4} - 6 \, B a c e^{6} + 4 \, {\left(2 \, C a c + A c^{2}\right)} d e^{5}\right)} x^{3} + 30 \, {\left(6 \, C c^{2} d^{4} e^{2} - 5 \, B c^{2} d^{3} e^{3} - 6 \, B a c d e^{5} + 4 \, {\left(2 \, C a c + A c^{2}\right)} d^{2} e^{4} + 2 \, {\left(C a^{2} + 2 \, A a c\right)} e^{6}\right)} x^{2} + 60 \, {\left(5 \, C c^{2} d^{5} e - 4 \, B c^{2} d^{4} e^{2} - 4 \, B a c d^{2} e^{4} + 3 \, {\left(2 \, C a c + A c^{2}\right)} d^{3} e^{3} + {\left(C a^{2} + 2 \, A a c\right)} d e^{5}\right)} x - 60 \, {\left(6 \, C c^{2} d^{6} - 5 \, B c^{2} d^{5} e - 6 \, B a c d^{3} e^{3} - B a^{2} d e^{5} + 4 \, {\left(2 \, C a c + A c^{2}\right)} d^{4} e^{2} + 2 \, {\left(C a^{2} + 2 \, A a c\right)} d^{2} e^{4} + {\left(6 \, C c^{2} d^{5} e - 5 \, B c^{2} d^{4} e^{2} - 6 \, B a c d^{2} e^{4} - B a^{2} e^{6} + 4 \, {\left(2 \, C a c + A c^{2}\right)} d^{3} e^{3} + 2 \, {\left(C a^{2} + 2 \, A a c\right)} d e^{5}\right)} x\right)} \log\left(e x + d\right)}{60 \, {\left(e^{8} x + d e^{7}\right)}}"," ",0,"1/60*(12*C*c^2*e^6*x^6 - 60*C*c^2*d^6 + 60*B*c^2*d^5*e + 120*B*a*c*d^3*e^3 + 60*B*a^2*d*e^5 - 60*A*a^2*e^6 - 60*(2*C*a*c + A*c^2)*d^4*e^2 - 60*(C*a^2 + 2*A*a*c)*d^2*e^4 - 3*(6*C*c^2*d*e^5 - 5*B*c^2*e^6)*x^5 + 5*(6*C*c^2*d^2*e^4 - 5*B*c^2*d*e^5 + 4*(2*C*a*c + A*c^2)*e^6)*x^4 - 10*(6*C*c^2*d^3*e^3 - 5*B*c^2*d^2*e^4 - 6*B*a*c*e^6 + 4*(2*C*a*c + A*c^2)*d*e^5)*x^3 + 30*(6*C*c^2*d^4*e^2 - 5*B*c^2*d^3*e^3 - 6*B*a*c*d*e^5 + 4*(2*C*a*c + A*c^2)*d^2*e^4 + 2*(C*a^2 + 2*A*a*c)*e^6)*x^2 + 60*(5*C*c^2*d^5*e - 4*B*c^2*d^4*e^2 - 4*B*a*c*d^2*e^4 + 3*(2*C*a*c + A*c^2)*d^3*e^3 + (C*a^2 + 2*A*a*c)*d*e^5)*x - 60*(6*C*c^2*d^6 - 5*B*c^2*d^5*e - 6*B*a*c*d^3*e^3 - B*a^2*d*e^5 + 4*(2*C*a*c + A*c^2)*d^4*e^2 + 2*(C*a^2 + 2*A*a*c)*d^2*e^4 + (6*C*c^2*d^5*e - 5*B*c^2*d^4*e^2 - 6*B*a*c*d^2*e^4 - B*a^2*e^6 + 4*(2*C*a*c + A*c^2)*d^3*e^3 + 2*(C*a^2 + 2*A*a*c)*d*e^5)*x)*log(e*x + d))/(e^8*x + d*e^7)","A",0
31,1,608,0,0.628015," ","integrate((c*x^2+a)^2*(C*x^2+B*x+A)/(e*x+d)^3,x, algorithm=""fricas"")","\frac{3 \, C c^{2} e^{6} x^{6} + 66 \, C c^{2} d^{6} - 54 \, B c^{2} d^{5} e - 60 \, B a c d^{3} e^{3} - 6 \, B a^{2} d e^{5} - 6 \, A a^{2} e^{6} + 42 \, {\left(2 \, C a c + A c^{2}\right)} d^{4} e^{2} + 18 \, {\left(C a^{2} + 2 \, A a c\right)} d^{2} e^{4} - 2 \, {\left(3 \, C c^{2} d e^{5} - 2 \, B c^{2} e^{6}\right)} x^{5} + {\left(15 \, C c^{2} d^{2} e^{4} - 10 \, B c^{2} d e^{5} + 6 \, {\left(2 \, C a c + A c^{2}\right)} e^{6}\right)} x^{4} - 4 \, {\left(15 \, C c^{2} d^{3} e^{3} - 10 \, B c^{2} d^{2} e^{4} - 6 \, B a c e^{6} + 6 \, {\left(2 \, C a c + A c^{2}\right)} d e^{5}\right)} x^{3} - 6 \, {\left(34 \, C c^{2} d^{4} e^{2} - 21 \, B c^{2} d^{3} e^{3} - 8 \, B a c d e^{5} + 11 \, {\left(2 \, C a c + A c^{2}\right)} d^{2} e^{4}\right)} x^{2} - 12 \, {\left(4 \, C c^{2} d^{5} e - B c^{2} d^{4} e^{2} + 4 \, B a c d^{2} e^{4} + B a^{2} e^{6} - {\left(2 \, C a c + A c^{2}\right)} d^{3} e^{3} - 2 \, {\left(C a^{2} + 2 \, A a c\right)} d e^{5}\right)} x + 12 \, {\left(15 \, C c^{2} d^{6} - 10 \, B c^{2} d^{5} e - 6 \, B a c d^{3} e^{3} + 6 \, {\left(2 \, C a c + A c^{2}\right)} d^{4} e^{2} + {\left(C a^{2} + 2 \, A a c\right)} d^{2} e^{4} + {\left(15 \, C c^{2} d^{4} e^{2} - 10 \, B c^{2} d^{3} e^{3} - 6 \, B a c d e^{5} + 6 \, {\left(2 \, C a c + A c^{2}\right)} d^{2} e^{4} + {\left(C a^{2} + 2 \, A a c\right)} e^{6}\right)} x^{2} + 2 \, {\left(15 \, C c^{2} d^{5} e - 10 \, B c^{2} d^{4} e^{2} - 6 \, B a c d^{2} e^{4} + 6 \, {\left(2 \, C a c + A c^{2}\right)} d^{3} e^{3} + {\left(C a^{2} + 2 \, A a c\right)} d e^{5}\right)} x\right)} \log\left(e x + d\right)}{12 \, {\left(e^{9} x^{2} + 2 \, d e^{8} x + d^{2} e^{7}\right)}}"," ",0,"1/12*(3*C*c^2*e^6*x^6 + 66*C*c^2*d^6 - 54*B*c^2*d^5*e - 60*B*a*c*d^3*e^3 - 6*B*a^2*d*e^5 - 6*A*a^2*e^6 + 42*(2*C*a*c + A*c^2)*d^4*e^2 + 18*(C*a^2 + 2*A*a*c)*d^2*e^4 - 2*(3*C*c^2*d*e^5 - 2*B*c^2*e^6)*x^5 + (15*C*c^2*d^2*e^4 - 10*B*c^2*d*e^5 + 6*(2*C*a*c + A*c^2)*e^6)*x^4 - 4*(15*C*c^2*d^3*e^3 - 10*B*c^2*d^2*e^4 - 6*B*a*c*e^6 + 6*(2*C*a*c + A*c^2)*d*e^5)*x^3 - 6*(34*C*c^2*d^4*e^2 - 21*B*c^2*d^3*e^3 - 8*B*a*c*d*e^5 + 11*(2*C*a*c + A*c^2)*d^2*e^4)*x^2 - 12*(4*C*c^2*d^5*e - B*c^2*d^4*e^2 + 4*B*a*c*d^2*e^4 + B*a^2*e^6 - (2*C*a*c + A*c^2)*d^3*e^3 - 2*(C*a^2 + 2*A*a*c)*d*e^5)*x + 12*(15*C*c^2*d^6 - 10*B*c^2*d^5*e - 6*B*a*c*d^3*e^3 + 6*(2*C*a*c + A*c^2)*d^4*e^2 + (C*a^2 + 2*A*a*c)*d^2*e^4 + (15*C*c^2*d^4*e^2 - 10*B*c^2*d^3*e^3 - 6*B*a*c*d*e^5 + 6*(2*C*a*c + A*c^2)*d^2*e^4 + (C*a^2 + 2*A*a*c)*e^6)*x^2 + 2*(15*C*c^2*d^5*e - 10*B*c^2*d^4*e^2 - 6*B*a*c*d^2*e^4 + 6*(2*C*a*c + A*c^2)*d^3*e^3 + (C*a^2 + 2*A*a*c)*d*e^5)*x)*log(e*x + d))/(e^9*x^2 + 2*d*e^8*x + d^2*e^7)","B",0
32,1,618,0,0.632228," ","integrate((e*x+d)^3*(c*x^2+a)^3*(C*x^2+B*x+A),x, algorithm=""fricas"")","\frac{1}{12} x^{12} e^{3} c^{3} C + \frac{3}{11} x^{11} e^{2} d c^{3} C + \frac{1}{11} x^{11} e^{3} c^{3} B + \frac{3}{10} x^{10} e d^{2} c^{3} C + \frac{3}{10} x^{10} e^{3} c^{2} a C + \frac{3}{10} x^{10} e^{2} d c^{3} B + \frac{1}{10} x^{10} e^{3} c^{3} A + \frac{1}{9} x^{9} d^{3} c^{3} C + x^{9} e^{2} d c^{2} a C + \frac{1}{3} x^{9} e d^{2} c^{3} B + \frac{1}{3} x^{9} e^{3} c^{2} a B + \frac{1}{3} x^{9} e^{2} d c^{3} A + \frac{9}{8} x^{8} e d^{2} c^{2} a C + \frac{3}{8} x^{8} e^{3} c a^{2} C + \frac{1}{8} x^{8} d^{3} c^{3} B + \frac{9}{8} x^{8} e^{2} d c^{2} a B + \frac{3}{8} x^{8} e d^{2} c^{3} A + \frac{3}{8} x^{8} e^{3} c^{2} a A + \frac{3}{7} x^{7} d^{3} c^{2} a C + \frac{9}{7} x^{7} e^{2} d c a^{2} C + \frac{9}{7} x^{7} e d^{2} c^{2} a B + \frac{3}{7} x^{7} e^{3} c a^{2} B + \frac{1}{7} x^{7} d^{3} c^{3} A + \frac{9}{7} x^{7} e^{2} d c^{2} a A + \frac{3}{2} x^{6} e d^{2} c a^{2} C + \frac{1}{6} x^{6} e^{3} a^{3} C + \frac{1}{2} x^{6} d^{3} c^{2} a B + \frac{3}{2} x^{6} e^{2} d c a^{2} B + \frac{3}{2} x^{6} e d^{2} c^{2} a A + \frac{1}{2} x^{6} e^{3} c a^{2} A + \frac{3}{5} x^{5} d^{3} c a^{2} C + \frac{3}{5} x^{5} e^{2} d a^{3} C + \frac{9}{5} x^{5} e d^{2} c a^{2} B + \frac{1}{5} x^{5} e^{3} a^{3} B + \frac{3}{5} x^{5} d^{3} c^{2} a A + \frac{9}{5} x^{5} e^{2} d c a^{2} A + \frac{3}{4} x^{4} e d^{2} a^{3} C + \frac{3}{4} x^{4} d^{3} c a^{2} B + \frac{3}{4} x^{4} e^{2} d a^{3} B + \frac{9}{4} x^{4} e d^{2} c a^{2} A + \frac{1}{4} x^{4} e^{3} a^{3} A + \frac{1}{3} x^{3} d^{3} a^{3} C + x^{3} e d^{2} a^{3} B + x^{3} d^{3} c a^{2} A + x^{3} e^{2} d a^{3} A + \frac{1}{2} x^{2} d^{3} a^{3} B + \frac{3}{2} x^{2} e d^{2} a^{3} A + x d^{3} a^{3} A"," ",0,"1/12*x^12*e^3*c^3*C + 3/11*x^11*e^2*d*c^3*C + 1/11*x^11*e^3*c^3*B + 3/10*x^10*e*d^2*c^3*C + 3/10*x^10*e^3*c^2*a*C + 3/10*x^10*e^2*d*c^3*B + 1/10*x^10*e^3*c^3*A + 1/9*x^9*d^3*c^3*C + x^9*e^2*d*c^2*a*C + 1/3*x^9*e*d^2*c^3*B + 1/3*x^9*e^3*c^2*a*B + 1/3*x^9*e^2*d*c^3*A + 9/8*x^8*e*d^2*c^2*a*C + 3/8*x^8*e^3*c*a^2*C + 1/8*x^8*d^3*c^3*B + 9/8*x^8*e^2*d*c^2*a*B + 3/8*x^8*e*d^2*c^3*A + 3/8*x^8*e^3*c^2*a*A + 3/7*x^7*d^3*c^2*a*C + 9/7*x^7*e^2*d*c*a^2*C + 9/7*x^7*e*d^2*c^2*a*B + 3/7*x^7*e^3*c*a^2*B + 1/7*x^7*d^3*c^3*A + 9/7*x^7*e^2*d*c^2*a*A + 3/2*x^6*e*d^2*c*a^2*C + 1/6*x^6*e^3*a^3*C + 1/2*x^6*d^3*c^2*a*B + 3/2*x^6*e^2*d*c*a^2*B + 3/2*x^6*e*d^2*c^2*a*A + 1/2*x^6*e^3*c*a^2*A + 3/5*x^5*d^3*c*a^2*C + 3/5*x^5*e^2*d*a^3*C + 9/5*x^5*e*d^2*c*a^2*B + 1/5*x^5*e^3*a^3*B + 3/5*x^5*d^3*c^2*a*A + 9/5*x^5*e^2*d*c*a^2*A + 3/4*x^4*e*d^2*a^3*C + 3/4*x^4*d^3*c*a^2*B + 3/4*x^4*e^2*d*a^3*B + 9/4*x^4*e*d^2*c*a^2*A + 1/4*x^4*e^3*a^3*A + 1/3*x^3*d^3*a^3*C + x^3*e*d^2*a^3*B + x^3*d^3*c*a^2*A + x^3*e^2*d*a^3*A + 1/2*x^2*d^3*a^3*B + 3/2*x^2*e*d^2*a^3*A + x*d^3*a^3*A","A",0
33,1,432,0,0.905811," ","integrate((e*x+d)^2*(c*x^2+a)^3*(C*x^2+B*x+A),x, algorithm=""fricas"")","\frac{1}{11} x^{11} e^{2} c^{3} C + \frac{1}{5} x^{10} e d c^{3} C + \frac{1}{10} x^{10} e^{2} c^{3} B + \frac{1}{9} x^{9} d^{2} c^{3} C + \frac{1}{3} x^{9} e^{2} c^{2} a C + \frac{2}{9} x^{9} e d c^{3} B + \frac{1}{9} x^{9} e^{2} c^{3} A + \frac{3}{4} x^{8} e d c^{2} a C + \frac{1}{8} x^{8} d^{2} c^{3} B + \frac{3}{8} x^{8} e^{2} c^{2} a B + \frac{1}{4} x^{8} e d c^{3} A + \frac{3}{7} x^{7} d^{2} c^{2} a C + \frac{3}{7} x^{7} e^{2} c a^{2} C + \frac{6}{7} x^{7} e d c^{2} a B + \frac{1}{7} x^{7} d^{2} c^{3} A + \frac{3}{7} x^{7} e^{2} c^{2} a A + x^{6} e d c a^{2} C + \frac{1}{2} x^{6} d^{2} c^{2} a B + \frac{1}{2} x^{6} e^{2} c a^{2} B + x^{6} e d c^{2} a A + \frac{3}{5} x^{5} d^{2} c a^{2} C + \frac{1}{5} x^{5} e^{2} a^{3} C + \frac{6}{5} x^{5} e d c a^{2} B + \frac{3}{5} x^{5} d^{2} c^{2} a A + \frac{3}{5} x^{5} e^{2} c a^{2} A + \frac{1}{2} x^{4} e d a^{3} C + \frac{3}{4} x^{4} d^{2} c a^{2} B + \frac{1}{4} x^{4} e^{2} a^{3} B + \frac{3}{2} x^{4} e d c a^{2} A + \frac{1}{3} x^{3} d^{2} a^{3} C + \frac{2}{3} x^{3} e d a^{3} B + x^{3} d^{2} c a^{2} A + \frac{1}{3} x^{3} e^{2} a^{3} A + \frac{1}{2} x^{2} d^{2} a^{3} B + x^{2} e d a^{3} A + x d^{2} a^{3} A"," ",0,"1/11*x^11*e^2*c^3*C + 1/5*x^10*e*d*c^3*C + 1/10*x^10*e^2*c^3*B + 1/9*x^9*d^2*c^3*C + 1/3*x^9*e^2*c^2*a*C + 2/9*x^9*e*d*c^3*B + 1/9*x^9*e^2*c^3*A + 3/4*x^8*e*d*c^2*a*C + 1/8*x^8*d^2*c^3*B + 3/8*x^8*e^2*c^2*a*B + 1/4*x^8*e*d*c^3*A + 3/7*x^7*d^2*c^2*a*C + 3/7*x^7*e^2*c*a^2*C + 6/7*x^7*e*d*c^2*a*B + 1/7*x^7*d^2*c^3*A + 3/7*x^7*e^2*c^2*a*A + x^6*e*d*c*a^2*C + 1/2*x^6*d^2*c^2*a*B + 1/2*x^6*e^2*c*a^2*B + x^6*e*d*c^2*a*A + 3/5*x^5*d^2*c*a^2*C + 1/5*x^5*e^2*a^3*C + 6/5*x^5*e*d*c*a^2*B + 3/5*x^5*d^2*c^2*a*A + 3/5*x^5*e^2*c*a^2*A + 1/2*x^4*e*d*a^3*C + 3/4*x^4*d^2*c*a^2*B + 1/4*x^4*e^2*a^3*B + 3/2*x^4*e*d*c*a^2*A + 1/3*x^3*d^2*a^3*C + 2/3*x^3*e*d*a^3*B + x^3*d^2*c*a^2*A + 1/3*x^3*e^2*a^3*A + 1/2*x^2*d^2*a^3*B + x^2*e*d*a^3*A + x*d^2*a^3*A","A",0
34,1,249,0,0.695394," ","integrate((e*x+d)*(c*x^2+a)^3*(C*x^2+B*x+A),x, algorithm=""fricas"")","\frac{1}{10} x^{10} e c^{3} C + \frac{1}{9} x^{9} d c^{3} C + \frac{1}{9} x^{9} e c^{3} B + \frac{3}{8} x^{8} e c^{2} a C + \frac{1}{8} x^{8} d c^{3} B + \frac{1}{8} x^{8} e c^{3} A + \frac{3}{7} x^{7} d c^{2} a C + \frac{3}{7} x^{7} e c^{2} a B + \frac{1}{7} x^{7} d c^{3} A + \frac{1}{2} x^{6} e c a^{2} C + \frac{1}{2} x^{6} d c^{2} a B + \frac{1}{2} x^{6} e c^{2} a A + \frac{3}{5} x^{5} d c a^{2} C + \frac{3}{5} x^{5} e c a^{2} B + \frac{3}{5} x^{5} d c^{2} a A + \frac{1}{4} x^{4} e a^{3} C + \frac{3}{4} x^{4} d c a^{2} B + \frac{3}{4} x^{4} e c a^{2} A + \frac{1}{3} x^{3} d a^{3} C + \frac{1}{3} x^{3} e a^{3} B + x^{3} d c a^{2} A + \frac{1}{2} x^{2} d a^{3} B + \frac{1}{2} x^{2} e a^{3} A + x d a^{3} A"," ",0,"1/10*x^10*e*c^3*C + 1/9*x^9*d*c^3*C + 1/9*x^9*e*c^3*B + 3/8*x^8*e*c^2*a*C + 1/8*x^8*d*c^3*B + 1/8*x^8*e*c^3*A + 3/7*x^7*d*c^2*a*C + 3/7*x^7*e*c^2*a*B + 1/7*x^7*d*c^3*A + 1/2*x^6*e*c*a^2*C + 1/2*x^6*d*c^2*a*B + 1/2*x^6*e*c^2*a*A + 3/5*x^5*d*c*a^2*C + 3/5*x^5*e*c*a^2*B + 3/5*x^5*d*c^2*a*A + 1/4*x^4*e*a^3*C + 3/4*x^4*d*c*a^2*B + 3/4*x^4*e*c*a^2*A + 1/3*x^3*d*a^3*C + 1/3*x^3*e*a^3*B + x^3*d*c*a^2*A + 1/2*x^2*d*a^3*B + 1/2*x^2*e*a^3*A + x*d*a^3*A","A",0
35,1,111,0,0.689056," ","integrate((c*x^2+a)^3*(C*x^2+B*x+A),x, algorithm=""fricas"")","\frac{1}{9} x^{9} c^{3} C + \frac{1}{8} x^{8} c^{3} B + \frac{3}{7} x^{7} c^{2} a C + \frac{1}{7} x^{7} c^{3} A + \frac{1}{2} x^{6} c^{2} a B + \frac{3}{5} x^{5} c a^{2} C + \frac{3}{5} x^{5} c^{2} a A + \frac{3}{4} x^{4} c a^{2} B + \frac{1}{3} x^{3} a^{3} C + x^{3} c a^{2} A + \frac{1}{2} x^{2} a^{3} B + x a^{3} A"," ",0,"1/9*x^9*c^3*C + 1/8*x^8*c^3*B + 3/7*x^7*c^2*a*C + 1/7*x^7*c^3*A + 1/2*x^6*c^2*a*B + 3/5*x^5*c*a^2*C + 3/5*x^5*c^2*a*A + 3/4*x^4*c*a^2*B + 1/3*x^3*a^3*C + x^3*c*a^2*A + 1/2*x^2*a^3*B + x*a^3*A","A",0
36,1,674,0,1.411449," ","integrate((c*x^2+a)^3*(C*x^2+B*x+A)/(e*x+d),x, algorithm=""fricas"")","\frac{105 \, C c^{3} e^{8} x^{8} - 120 \, {\left(C c^{3} d e^{7} - B c^{3} e^{8}\right)} x^{7} + 140 \, {\left(C c^{3} d^{2} e^{6} - B c^{3} d e^{7} + {\left(3 \, C a c^{2} + A c^{3}\right)} e^{8}\right)} x^{6} - 168 \, {\left(C c^{3} d^{3} e^{5} - B c^{3} d^{2} e^{6} - 3 \, B a c^{2} e^{8} + {\left(3 \, C a c^{2} + A c^{3}\right)} d e^{7}\right)} x^{5} + 210 \, {\left(C c^{3} d^{4} e^{4} - B c^{3} d^{3} e^{5} - 3 \, B a c^{2} d e^{7} + {\left(3 \, C a c^{2} + A c^{3}\right)} d^{2} e^{6} + 3 \, {\left(C a^{2} c + A a c^{2}\right)} e^{8}\right)} x^{4} - 280 \, {\left(C c^{3} d^{5} e^{3} - B c^{3} d^{4} e^{4} - 3 \, B a c^{2} d^{2} e^{6} - 3 \, B a^{2} c e^{8} + {\left(3 \, C a c^{2} + A c^{3}\right)} d^{3} e^{5} + 3 \, {\left(C a^{2} c + A a c^{2}\right)} d e^{7}\right)} x^{3} + 420 \, {\left(C c^{3} d^{6} e^{2} - B c^{3} d^{5} e^{3} - 3 \, B a c^{2} d^{3} e^{5} - 3 \, B a^{2} c d e^{7} + {\left(3 \, C a c^{2} + A c^{3}\right)} d^{4} e^{4} + 3 \, {\left(C a^{2} c + A a c^{2}\right)} d^{2} e^{6} + {\left(C a^{3} + 3 \, A a^{2} c\right)} e^{8}\right)} x^{2} - 840 \, {\left(C c^{3} d^{7} e - B c^{3} d^{6} e^{2} - 3 \, B a c^{2} d^{4} e^{4} - 3 \, B a^{2} c d^{2} e^{6} - B a^{3} e^{8} + {\left(3 \, C a c^{2} + A c^{3}\right)} d^{5} e^{3} + 3 \, {\left(C a^{2} c + A a c^{2}\right)} d^{3} e^{5} + {\left(C a^{3} + 3 \, A a^{2} c\right)} d e^{7}\right)} x + 840 \, {\left(C c^{3} d^{8} - B c^{3} d^{7} e - 3 \, B a c^{2} d^{5} e^{3} - 3 \, B a^{2} c d^{3} e^{5} - B a^{3} d e^{7} + A a^{3} e^{8} + {\left(3 \, C a c^{2} + A c^{3}\right)} d^{6} e^{2} + 3 \, {\left(C a^{2} c + A a c^{2}\right)} d^{4} e^{4} + {\left(C a^{3} + 3 \, A a^{2} c\right)} d^{2} e^{6}\right)} \log\left(e x + d\right)}{840 \, e^{9}}"," ",0,"1/840*(105*C*c^3*e^8*x^8 - 120*(C*c^3*d*e^7 - B*c^3*e^8)*x^7 + 140*(C*c^3*d^2*e^6 - B*c^3*d*e^7 + (3*C*a*c^2 + A*c^3)*e^8)*x^6 - 168*(C*c^3*d^3*e^5 - B*c^3*d^2*e^6 - 3*B*a*c^2*e^8 + (3*C*a*c^2 + A*c^3)*d*e^7)*x^5 + 210*(C*c^3*d^4*e^4 - B*c^3*d^3*e^5 - 3*B*a*c^2*d*e^7 + (3*C*a*c^2 + A*c^3)*d^2*e^6 + 3*(C*a^2*c + A*a*c^2)*e^8)*x^4 - 280*(C*c^3*d^5*e^3 - B*c^3*d^4*e^4 - 3*B*a*c^2*d^2*e^6 - 3*B*a^2*c*e^8 + (3*C*a*c^2 + A*c^3)*d^3*e^5 + 3*(C*a^2*c + A*a*c^2)*d*e^7)*x^3 + 420*(C*c^3*d^6*e^2 - B*c^3*d^5*e^3 - 3*B*a*c^2*d^3*e^5 - 3*B*a^2*c*d*e^7 + (3*C*a*c^2 + A*c^3)*d^4*e^4 + 3*(C*a^2*c + A*a*c^2)*d^2*e^6 + (C*a^3 + 3*A*a^2*c)*e^8)*x^2 - 840*(C*c^3*d^7*e - B*c^3*d^6*e^2 - 3*B*a*c^2*d^4*e^4 - 3*B*a^2*c*d^2*e^6 - B*a^3*e^8 + (3*C*a*c^2 + A*c^3)*d^5*e^3 + 3*(C*a^2*c + A*a*c^2)*d^3*e^5 + (C*a^3 + 3*A*a^2*c)*d*e^7)*x + 840*(C*c^3*d^8 - B*c^3*d^7*e - 3*B*a*c^2*d^5*e^3 - 3*B*a^2*c*d^3*e^5 - B*a^3*d*e^7 + A*a^3*e^8 + (3*C*a*c^2 + A*c^3)*d^6*e^2 + 3*(C*a^2*c + A*a*c^2)*d^4*e^4 + (C*a^3 + 3*A*a^2*c)*d^2*e^6)*log(e*x + d))/e^9","A",0
37,1,932,0,0.995883," ","integrate((c*x^2+a)^3*(C*x^2+B*x+A)/(e*x+d)^2,x, algorithm=""fricas"")","\frac{60 \, C c^{3} e^{8} x^{8} - 420 \, C c^{3} d^{8} + 420 \, B c^{3} d^{7} e + 1260 \, B a c^{2} d^{5} e^{3} + 1260 \, B a^{2} c d^{3} e^{5} + 420 \, B a^{3} d e^{7} - 420 \, A a^{3} e^{8} - 420 \, {\left(3 \, C a c^{2} + A c^{3}\right)} d^{6} e^{2} - 1260 \, {\left(C a^{2} c + A a c^{2}\right)} d^{4} e^{4} - 420 \, {\left(C a^{3} + 3 \, A a^{2} c\right)} d^{2} e^{6} - 10 \, {\left(8 \, C c^{3} d e^{7} - 7 \, B c^{3} e^{8}\right)} x^{7} + 14 \, {\left(8 \, C c^{3} d^{2} e^{6} - 7 \, B c^{3} d e^{7} + 6 \, {\left(3 \, C a c^{2} + A c^{3}\right)} e^{8}\right)} x^{6} - 21 \, {\left(8 \, C c^{3} d^{3} e^{5} - 7 \, B c^{3} d^{2} e^{6} - 15 \, B a c^{2} e^{8} + 6 \, {\left(3 \, C a c^{2} + A c^{3}\right)} d e^{7}\right)} x^{5} + 35 \, {\left(8 \, C c^{3} d^{4} e^{4} - 7 \, B c^{3} d^{3} e^{5} - 15 \, B a c^{2} d e^{7} + 6 \, {\left(3 \, C a c^{2} + A c^{3}\right)} d^{2} e^{6} + 12 \, {\left(C a^{2} c + A a c^{2}\right)} e^{8}\right)} x^{4} - 70 \, {\left(8 \, C c^{3} d^{5} e^{3} - 7 \, B c^{3} d^{4} e^{4} - 15 \, B a c^{2} d^{2} e^{6} - 9 \, B a^{2} c e^{8} + 6 \, {\left(3 \, C a c^{2} + A c^{3}\right)} d^{3} e^{5} + 12 \, {\left(C a^{2} c + A a c^{2}\right)} d e^{7}\right)} x^{3} + 210 \, {\left(8 \, C c^{3} d^{6} e^{2} - 7 \, B c^{3} d^{5} e^{3} - 15 \, B a c^{2} d^{3} e^{5} - 9 \, B a^{2} c d e^{7} + 6 \, {\left(3 \, C a c^{2} + A c^{3}\right)} d^{4} e^{4} + 12 \, {\left(C a^{2} c + A a c^{2}\right)} d^{2} e^{6} + 2 \, {\left(C a^{3} + 3 \, A a^{2} c\right)} e^{8}\right)} x^{2} + 420 \, {\left(7 \, C c^{3} d^{7} e - 6 \, B c^{3} d^{6} e^{2} - 12 \, B a c^{2} d^{4} e^{4} - 6 \, B a^{2} c d^{2} e^{6} + 5 \, {\left(3 \, C a c^{2} + A c^{3}\right)} d^{5} e^{3} + 9 \, {\left(C a^{2} c + A a c^{2}\right)} d^{3} e^{5} + {\left(C a^{3} + 3 \, A a^{2} c\right)} d e^{7}\right)} x - 420 \, {\left(8 \, C c^{3} d^{8} - 7 \, B c^{3} d^{7} e - 15 \, B a c^{2} d^{5} e^{3} - 9 \, B a^{2} c d^{3} e^{5} - B a^{3} d e^{7} + 6 \, {\left(3 \, C a c^{2} + A c^{3}\right)} d^{6} e^{2} + 12 \, {\left(C a^{2} c + A a c^{2}\right)} d^{4} e^{4} + 2 \, {\left(C a^{3} + 3 \, A a^{2} c\right)} d^{2} e^{6} + {\left(8 \, C c^{3} d^{7} e - 7 \, B c^{3} d^{6} e^{2} - 15 \, B a c^{2} d^{4} e^{4} - 9 \, B a^{2} c d^{2} e^{6} - B a^{3} e^{8} + 6 \, {\left(3 \, C a c^{2} + A c^{3}\right)} d^{5} e^{3} + 12 \, {\left(C a^{2} c + A a c^{2}\right)} d^{3} e^{5} + 2 \, {\left(C a^{3} + 3 \, A a^{2} c\right)} d e^{7}\right)} x\right)} \log\left(e x + d\right)}{420 \, {\left(e^{10} x + d e^{9}\right)}}"," ",0,"1/420*(60*C*c^3*e^8*x^8 - 420*C*c^3*d^8 + 420*B*c^3*d^7*e + 1260*B*a*c^2*d^5*e^3 + 1260*B*a^2*c*d^3*e^5 + 420*B*a^3*d*e^7 - 420*A*a^3*e^8 - 420*(3*C*a*c^2 + A*c^3)*d^6*e^2 - 1260*(C*a^2*c + A*a*c^2)*d^4*e^4 - 420*(C*a^3 + 3*A*a^2*c)*d^2*e^6 - 10*(8*C*c^3*d*e^7 - 7*B*c^3*e^8)*x^7 + 14*(8*C*c^3*d^2*e^6 - 7*B*c^3*d*e^7 + 6*(3*C*a*c^2 + A*c^3)*e^8)*x^6 - 21*(8*C*c^3*d^3*e^5 - 7*B*c^3*d^2*e^6 - 15*B*a*c^2*e^8 + 6*(3*C*a*c^2 + A*c^3)*d*e^7)*x^5 + 35*(8*C*c^3*d^4*e^4 - 7*B*c^3*d^3*e^5 - 15*B*a*c^2*d*e^7 + 6*(3*C*a*c^2 + A*c^3)*d^2*e^6 + 12*(C*a^2*c + A*a*c^2)*e^8)*x^4 - 70*(8*C*c^3*d^5*e^3 - 7*B*c^3*d^4*e^4 - 15*B*a*c^2*d^2*e^6 - 9*B*a^2*c*e^8 + 6*(3*C*a*c^2 + A*c^3)*d^3*e^5 + 12*(C*a^2*c + A*a*c^2)*d*e^7)*x^3 + 210*(8*C*c^3*d^6*e^2 - 7*B*c^3*d^5*e^3 - 15*B*a*c^2*d^3*e^5 - 9*B*a^2*c*d*e^7 + 6*(3*C*a*c^2 + A*c^3)*d^4*e^4 + 12*(C*a^2*c + A*a*c^2)*d^2*e^6 + 2*(C*a^3 + 3*A*a^2*c)*e^8)*x^2 + 420*(7*C*c^3*d^7*e - 6*B*c^3*d^6*e^2 - 12*B*a*c^2*d^4*e^4 - 6*B*a^2*c*d^2*e^6 + 5*(3*C*a*c^2 + A*c^3)*d^5*e^3 + 9*(C*a^2*c + A*a*c^2)*d^3*e^5 + (C*a^3 + 3*A*a^2*c)*d*e^7)*x - 420*(8*C*c^3*d^8 - 7*B*c^3*d^7*e - 15*B*a*c^2*d^5*e^3 - 9*B*a^2*c*d^3*e^5 - B*a^3*d*e^7 + 6*(3*C*a*c^2 + A*c^3)*d^6*e^2 + 12*(C*a^2*c + A*a*c^2)*d^4*e^4 + 2*(C*a^3 + 3*A*a^2*c)*d^2*e^6 + (8*C*c^3*d^7*e - 7*B*c^3*d^6*e^2 - 15*B*a*c^2*d^4*e^4 - 9*B*a^2*c*d^2*e^6 - B*a^3*e^8 + 6*(3*C*a*c^2 + A*c^3)*d^5*e^3 + 12*(C*a^2*c + A*a*c^2)*d^3*e^5 + 2*(C*a^3 + 3*A*a^2*c)*d*e^7)*x)*log(e*x + d))/(e^10*x + d*e^9)","A",0
38,1,1025,0,0.874237," ","integrate((c*x^2+a)^3*(C*x^2+B*x+A)/(e*x+d)^3,x, algorithm=""fricas"")","\frac{10 \, C c^{3} e^{8} x^{8} + 450 \, C c^{3} d^{8} - 390 \, B c^{3} d^{7} e - 810 \, B a c^{2} d^{5} e^{3} - 450 \, B a^{2} c d^{3} e^{5} - 30 \, B a^{3} d e^{7} - 30 \, A a^{3} e^{8} + 330 \, {\left(3 \, C a c^{2} + A c^{3}\right)} d^{6} e^{2} + 630 \, {\left(C a^{2} c + A a c^{2}\right)} d^{4} e^{4} + 90 \, {\left(C a^{3} + 3 \, A a^{2} c\right)} d^{2} e^{6} - 4 \, {\left(4 \, C c^{3} d e^{7} - 3 \, B c^{3} e^{8}\right)} x^{7} + {\left(28 \, C c^{3} d^{2} e^{6} - 21 \, B c^{3} d e^{7} + 15 \, {\left(3 \, C a c^{2} + A c^{3}\right)} e^{8}\right)} x^{6} - 2 \, {\left(28 \, C c^{3} d^{3} e^{5} - 21 \, B c^{3} d^{2} e^{6} - 30 \, B a c^{2} e^{8} + 15 \, {\left(3 \, C a c^{2} + A c^{3}\right)} d e^{7}\right)} x^{5} + 5 \, {\left(28 \, C c^{3} d^{4} e^{4} - 21 \, B c^{3} d^{3} e^{5} - 30 \, B a c^{2} d e^{7} + 15 \, {\left(3 \, C a c^{2} + A c^{3}\right)} d^{2} e^{6} + 18 \, {\left(C a^{2} c + A a c^{2}\right)} e^{8}\right)} x^{4} - 20 \, {\left(28 \, C c^{3} d^{5} e^{3} - 21 \, B c^{3} d^{4} e^{4} - 30 \, B a c^{2} d^{2} e^{6} - 9 \, B a^{2} c e^{8} + 15 \, {\left(3 \, C a c^{2} + A c^{3}\right)} d^{3} e^{5} + 18 \, {\left(C a^{2} c + A a c^{2}\right)} d e^{7}\right)} x^{3} - 30 \, {\left(69 \, C c^{3} d^{6} e^{2} - 50 \, B c^{3} d^{5} e^{3} - 63 \, B a c^{2} d^{3} e^{5} - 12 \, B a^{2} c d e^{7} + 34 \, {\left(3 \, C a c^{2} + A c^{3}\right)} d^{4} e^{4} + 33 \, {\left(C a^{2} c + A a c^{2}\right)} d^{2} e^{6}\right)} x^{2} - 60 \, {\left(13 \, C c^{3} d^{7} e - 8 \, B c^{3} d^{6} e^{2} - 3 \, B a c^{2} d^{4} e^{4} + 6 \, B a^{2} c d^{2} e^{6} + B a^{3} e^{8} + 4 \, {\left(3 \, C a c^{2} + A c^{3}\right)} d^{5} e^{3} - 3 \, {\left(C a^{2} c + A a c^{2}\right)} d^{3} e^{5} - 2 \, {\left(C a^{3} + 3 \, A a^{2} c\right)} d e^{7}\right)} x + 60 \, {\left(28 \, C c^{3} d^{8} - 21 \, B c^{3} d^{7} e - 30 \, B a c^{2} d^{5} e^{3} - 9 \, B a^{2} c d^{3} e^{5} + 15 \, {\left(3 \, C a c^{2} + A c^{3}\right)} d^{6} e^{2} + 18 \, {\left(C a^{2} c + A a c^{2}\right)} d^{4} e^{4} + {\left(C a^{3} + 3 \, A a^{2} c\right)} d^{2} e^{6} + {\left(28 \, C c^{3} d^{6} e^{2} - 21 \, B c^{3} d^{5} e^{3} - 30 \, B a c^{2} d^{3} e^{5} - 9 \, B a^{2} c d e^{7} + 15 \, {\left(3 \, C a c^{2} + A c^{3}\right)} d^{4} e^{4} + 18 \, {\left(C a^{2} c + A a c^{2}\right)} d^{2} e^{6} + {\left(C a^{3} + 3 \, A a^{2} c\right)} e^{8}\right)} x^{2} + 2 \, {\left(28 \, C c^{3} d^{7} e - 21 \, B c^{3} d^{6} e^{2} - 30 \, B a c^{2} d^{4} e^{4} - 9 \, B a^{2} c d^{2} e^{6} + 15 \, {\left(3 \, C a c^{2} + A c^{3}\right)} d^{5} e^{3} + 18 \, {\left(C a^{2} c + A a c^{2}\right)} d^{3} e^{5} + {\left(C a^{3} + 3 \, A a^{2} c\right)} d e^{7}\right)} x\right)} \log\left(e x + d\right)}{60 \, {\left(e^{11} x^{2} + 2 \, d e^{10} x + d^{2} e^{9}\right)}}"," ",0,"1/60*(10*C*c^3*e^8*x^8 + 450*C*c^3*d^8 - 390*B*c^3*d^7*e - 810*B*a*c^2*d^5*e^3 - 450*B*a^2*c*d^3*e^5 - 30*B*a^3*d*e^7 - 30*A*a^3*e^8 + 330*(3*C*a*c^2 + A*c^3)*d^6*e^2 + 630*(C*a^2*c + A*a*c^2)*d^4*e^4 + 90*(C*a^3 + 3*A*a^2*c)*d^2*e^6 - 4*(4*C*c^3*d*e^7 - 3*B*c^3*e^8)*x^7 + (28*C*c^3*d^2*e^6 - 21*B*c^3*d*e^7 + 15*(3*C*a*c^2 + A*c^3)*e^8)*x^6 - 2*(28*C*c^3*d^3*e^5 - 21*B*c^3*d^2*e^6 - 30*B*a*c^2*e^8 + 15*(3*C*a*c^2 + A*c^3)*d*e^7)*x^5 + 5*(28*C*c^3*d^4*e^4 - 21*B*c^3*d^3*e^5 - 30*B*a*c^2*d*e^7 + 15*(3*C*a*c^2 + A*c^3)*d^2*e^6 + 18*(C*a^2*c + A*a*c^2)*e^8)*x^4 - 20*(28*C*c^3*d^5*e^3 - 21*B*c^3*d^4*e^4 - 30*B*a*c^2*d^2*e^6 - 9*B*a^2*c*e^8 + 15*(3*C*a*c^2 + A*c^3)*d^3*e^5 + 18*(C*a^2*c + A*a*c^2)*d*e^7)*x^3 - 30*(69*C*c^3*d^6*e^2 - 50*B*c^3*d^5*e^3 - 63*B*a*c^2*d^3*e^5 - 12*B*a^2*c*d*e^7 + 34*(3*C*a*c^2 + A*c^3)*d^4*e^4 + 33*(C*a^2*c + A*a*c^2)*d^2*e^6)*x^2 - 60*(13*C*c^3*d^7*e - 8*B*c^3*d^6*e^2 - 3*B*a*c^2*d^4*e^4 + 6*B*a^2*c*d^2*e^6 + B*a^3*e^8 + 4*(3*C*a*c^2 + A*c^3)*d^5*e^3 - 3*(C*a^2*c + A*a*c^2)*d^3*e^5 - 2*(C*a^3 + 3*A*a^2*c)*d*e^7)*x + 60*(28*C*c^3*d^8 - 21*B*c^3*d^7*e - 30*B*a*c^2*d^5*e^3 - 9*B*a^2*c*d^3*e^5 + 15*(3*C*a*c^2 + A*c^3)*d^6*e^2 + 18*(C*a^2*c + A*a*c^2)*d^4*e^4 + (C*a^3 + 3*A*a^2*c)*d^2*e^6 + (28*C*c^3*d^6*e^2 - 21*B*c^3*d^5*e^3 - 30*B*a*c^2*d^3*e^5 - 9*B*a^2*c*d*e^7 + 15*(3*C*a*c^2 + A*c^3)*d^4*e^4 + 18*(C*a^2*c + A*a*c^2)*d^2*e^6 + (C*a^3 + 3*A*a^2*c)*e^8)*x^2 + 2*(28*C*c^3*d^7*e - 21*B*c^3*d^6*e^2 - 30*B*a*c^2*d^4*e^4 - 9*B*a^2*c*d^2*e^6 + 15*(3*C*a*c^2 + A*c^3)*d^5*e^3 + 18*(C*a^2*c + A*a*c^2)*d^3*e^5 + (C*a^3 + 3*A*a^2*c)*d*e^7)*x)*log(e*x + d))/(e^11*x^2 + 2*d*e^10*x + d^2*e^9)","B",0
39,1,78,0,0.877317," ","integrate((b*x^2+a)*(3*b*d*x^2+4*b*c*x-a*d)/(d*x+c)^2,x, algorithm=""fricas"")","\frac{b^{2} d^{4} x^{4} + 2 \, a b d^{4} x^{2} + b^{2} c^{4} + 2 \, a b c^{2} d^{2} + a^{2} d^{4} + {\left(b^{2} c^{3} d + 2 \, a b c d^{3}\right)} x}{d^{5} x + c d^{4}}"," ",0,"(b^2*d^4*x^4 + 2*a*b*d^4*x^2 + b^2*c^4 + 2*a*b*c^2*d^2 + a^2*d^4 + (b^2*c^3*d + 2*a*b*c*d^3)*x)/(d^5*x + c*d^4)","B",0
40,1,78,0,0.777884," ","integrate((b*x^2+a)*(-a*d+b*x*(3*d*x+4*c))/(d*x+c)^2,x, algorithm=""fricas"")","\frac{b^{2} d^{4} x^{4} + 2 \, a b d^{4} x^{2} + b^{2} c^{4} + 2 \, a b c^{2} d^{2} + a^{2} d^{4} + {\left(b^{2} c^{3} d + 2 \, a b c d^{3}\right)} x}{d^{5} x + c d^{4}}"," ",0,"(b^2*d^4*x^4 + 2*a*b*d^4*x^2 + b^2*c^4 + 2*a*b*c^2*d^2 + a^2*d^4 + (b^2*c^3*d + 2*a*b*c*d^3)*x)/(d^5*x + c*d^4)","B",0
41,1,120,0,0.652065," ","integrate((b*x^2+a)^2*(5*b*d*x^2+6*b*c*x-a*d)/(d*x+c)^2,x, algorithm=""fricas"")","\frac{b^{3} d^{6} x^{6} + 3 \, a b^{2} d^{6} x^{4} + 3 \, a^{2} b d^{6} x^{2} + b^{3} c^{6} + 3 \, a b^{2} c^{4} d^{2} + 3 \, a^{2} b c^{2} d^{4} + a^{3} d^{6} + {\left(b^{3} c^{5} d + 3 \, a b^{2} c^{3} d^{3} + 3 \, a^{2} b c d^{5}\right)} x}{d^{7} x + c d^{6}}"," ",0,"(b^3*d^6*x^6 + 3*a*b^2*d^6*x^4 + 3*a^2*b*d^6*x^2 + b^3*c^6 + 3*a*b^2*c^4*d^2 + 3*a^2*b*c^2*d^4 + a^3*d^6 + (b^3*c^5*d + 3*a*b^2*c^3*d^3 + 3*a^2*b*c*d^5)*x)/(d^7*x + c*d^6)","B",0
42,1,120,0,1.000294," ","integrate((b*x^2+a)^2*(-a*d+b*x*(5*d*x+6*c))/(d*x+c)^2,x, algorithm=""fricas"")","\frac{b^{3} d^{6} x^{6} + 3 \, a b^{2} d^{6} x^{4} + 3 \, a^{2} b d^{6} x^{2} + b^{3} c^{6} + 3 \, a b^{2} c^{4} d^{2} + 3 \, a^{2} b c^{2} d^{4} + a^{3} d^{6} + {\left(b^{3} c^{5} d + 3 \, a b^{2} c^{3} d^{3} + 3 \, a^{2} b c d^{5}\right)} x}{d^{7} x + c d^{6}}"," ",0,"(b^3*d^6*x^6 + 3*a*b^2*d^6*x^4 + 3*a^2*b*d^6*x^2 + b^3*c^6 + 3*a*b^2*c^4*d^2 + 3*a^2*b*c^2*d^4 + a^3*d^6 + (b^3*c^5*d + 3*a*b^2*c^3*d^3 + 3*a^2*b*c*d^5)*x)/(d^7*x + c*d^6)","B",0
43,1,592,0,1.068502," ","integrate((e*x+d)^3*(C*x^2+B*x+A)/(c*x^2+a),x, algorithm=""fricas"")","\left[\frac{3 \, C a c^{2} e^{3} x^{4} + 4 \, {\left(3 \, C a c^{2} d e^{2} + B a c^{2} e^{3}\right)} x^{3} + 6 \, {\left(3 \, C a c^{2} d^{2} e + 3 \, B a c^{2} d e^{2} - {\left(C a^{2} c - A a c^{2}\right)} e^{3}\right)} x^{2} + 6 \, {\left(3 \, B a c d^{2} e - B a^{2} e^{3} + {\left(C a c - A c^{2}\right)} d^{3} - 3 \, {\left(C a^{2} - A a c\right)} d e^{2}\right)} \sqrt{-a c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right) + 12 \, {\left(C a c^{2} d^{3} + 3 \, B a c^{2} d^{2} e - B a^{2} c e^{3} - 3 \, {\left(C a^{2} c - A a c^{2}\right)} d e^{2}\right)} x + 6 \, {\left(B a c^{2} d^{3} - 3 \, B a^{2} c d e^{2} - 3 \, {\left(C a^{2} c - A a c^{2}\right)} d^{2} e + {\left(C a^{3} - A a^{2} c\right)} e^{3}\right)} \log\left(c x^{2} + a\right)}{12 \, a c^{3}}, \frac{3 \, C a c^{2} e^{3} x^{4} + 4 \, {\left(3 \, C a c^{2} d e^{2} + B a c^{2} e^{3}\right)} x^{3} + 6 \, {\left(3 \, C a c^{2} d^{2} e + 3 \, B a c^{2} d e^{2} - {\left(C a^{2} c - A a c^{2}\right)} e^{3}\right)} x^{2} - 12 \, {\left(3 \, B a c d^{2} e - B a^{2} e^{3} + {\left(C a c - A c^{2}\right)} d^{3} - 3 \, {\left(C a^{2} - A a c\right)} d e^{2}\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right) + 12 \, {\left(C a c^{2} d^{3} + 3 \, B a c^{2} d^{2} e - B a^{2} c e^{3} - 3 \, {\left(C a^{2} c - A a c^{2}\right)} d e^{2}\right)} x + 6 \, {\left(B a c^{2} d^{3} - 3 \, B a^{2} c d e^{2} - 3 \, {\left(C a^{2} c - A a c^{2}\right)} d^{2} e + {\left(C a^{3} - A a^{2} c\right)} e^{3}\right)} \log\left(c x^{2} + a\right)}{12 \, a c^{3}}\right]"," ",0,"[1/12*(3*C*a*c^2*e^3*x^4 + 4*(3*C*a*c^2*d*e^2 + B*a*c^2*e^3)*x^3 + 6*(3*C*a*c^2*d^2*e + 3*B*a*c^2*d*e^2 - (C*a^2*c - A*a*c^2)*e^3)*x^2 + 6*(3*B*a*c*d^2*e - B*a^2*e^3 + (C*a*c - A*c^2)*d^3 - 3*(C*a^2 - A*a*c)*d*e^2)*sqrt(-a*c)*log((c*x^2 - 2*sqrt(-a*c)*x - a)/(c*x^2 + a)) + 12*(C*a*c^2*d^3 + 3*B*a*c^2*d^2*e - B*a^2*c*e^3 - 3*(C*a^2*c - A*a*c^2)*d*e^2)*x + 6*(B*a*c^2*d^3 - 3*B*a^2*c*d*e^2 - 3*(C*a^2*c - A*a*c^2)*d^2*e + (C*a^3 - A*a^2*c)*e^3)*log(c*x^2 + a))/(a*c^3), 1/12*(3*C*a*c^2*e^3*x^4 + 4*(3*C*a*c^2*d*e^2 + B*a*c^2*e^3)*x^3 + 6*(3*C*a*c^2*d^2*e + 3*B*a*c^2*d*e^2 - (C*a^2*c - A*a*c^2)*e^3)*x^2 - 12*(3*B*a*c*d^2*e - B*a^2*e^3 + (C*a*c - A*c^2)*d^3 - 3*(C*a^2 - A*a*c)*d*e^2)*sqrt(a*c)*arctan(sqrt(a*c)*x/a) + 12*(C*a*c^2*d^3 + 3*B*a*c^2*d^2*e - B*a^2*c*e^3 - 3*(C*a^2*c - A*a*c^2)*d*e^2)*x + 6*(B*a*c^2*d^3 - 3*B*a^2*c*d*e^2 - 3*(C*a^2*c - A*a*c^2)*d^2*e + (C*a^3 - A*a^2*c)*e^3)*log(c*x^2 + a))/(a*c^3)]","A",0
44,1,404,0,1.021059," ","integrate((e*x+d)^2*(C*x^2+B*x+A)/(c*x^2+a),x, algorithm=""fricas"")","\left[\frac{2 \, C a c^{2} e^{2} x^{3} + 3 \, {\left(2 \, C a c^{2} d e + B a c^{2} e^{2}\right)} x^{2} - 3 \, {\left(2 \, B a c d e + {\left(C a c - A c^{2}\right)} d^{2} - {\left(C a^{2} - A a c\right)} e^{2}\right)} \sqrt{-a c} \log\left(\frac{c x^{2} + 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right) + 6 \, {\left(C a c^{2} d^{2} + 2 \, B a c^{2} d e - {\left(C a^{2} c - A a c^{2}\right)} e^{2}\right)} x + 3 \, {\left(B a c^{2} d^{2} - B a^{2} c e^{2} - 2 \, {\left(C a^{2} c - A a c^{2}\right)} d e\right)} \log\left(c x^{2} + a\right)}{6 \, a c^{3}}, \frac{2 \, C a c^{2} e^{2} x^{3} + 3 \, {\left(2 \, C a c^{2} d e + B a c^{2} e^{2}\right)} x^{2} - 6 \, {\left(2 \, B a c d e + {\left(C a c - A c^{2}\right)} d^{2} - {\left(C a^{2} - A a c\right)} e^{2}\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right) + 6 \, {\left(C a c^{2} d^{2} + 2 \, B a c^{2} d e - {\left(C a^{2} c - A a c^{2}\right)} e^{2}\right)} x + 3 \, {\left(B a c^{2} d^{2} - B a^{2} c e^{2} - 2 \, {\left(C a^{2} c - A a c^{2}\right)} d e\right)} \log\left(c x^{2} + a\right)}{6 \, a c^{3}}\right]"," ",0,"[1/6*(2*C*a*c^2*e^2*x^3 + 3*(2*C*a*c^2*d*e + B*a*c^2*e^2)*x^2 - 3*(2*B*a*c*d*e + (C*a*c - A*c^2)*d^2 - (C*a^2 - A*a*c)*e^2)*sqrt(-a*c)*log((c*x^2 + 2*sqrt(-a*c)*x - a)/(c*x^2 + a)) + 6*(C*a*c^2*d^2 + 2*B*a*c^2*d*e - (C*a^2*c - A*a*c^2)*e^2)*x + 3*(B*a*c^2*d^2 - B*a^2*c*e^2 - 2*(C*a^2*c - A*a*c^2)*d*e)*log(c*x^2 + a))/(a*c^3), 1/6*(2*C*a*c^2*e^2*x^3 + 3*(2*C*a*c^2*d*e + B*a*c^2*e^2)*x^2 - 6*(2*B*a*c*d*e + (C*a*c - A*c^2)*d^2 - (C*a^2 - A*a*c)*e^2)*sqrt(a*c)*arctan(sqrt(a*c)*x/a) + 6*(C*a*c^2*d^2 + 2*B*a*c^2*d*e - (C*a^2*c - A*a*c^2)*e^2)*x + 3*(B*a*c^2*d^2 - B*a^2*c*e^2 - 2*(C*a^2*c - A*a*c^2)*d*e)*log(c*x^2 + a))/(a*c^3)]","A",0
45,1,206,0,1.120421," ","integrate((e*x+d)*(C*x^2+B*x+A)/(c*x^2+a),x, algorithm=""fricas"")","\left[\frac{C a c e x^{2} - {\left(B a e + {\left(C a - A c\right)} d\right)} \sqrt{-a c} \log\left(\frac{c x^{2} + 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right) + 2 \, {\left(C a c d + B a c e\right)} x + {\left(B a c d - {\left(C a^{2} - A a c\right)} e\right)} \log\left(c x^{2} + a\right)}{2 \, a c^{2}}, \frac{C a c e x^{2} - 2 \, {\left(B a e + {\left(C a - A c\right)} d\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right) + 2 \, {\left(C a c d + B a c e\right)} x + {\left(B a c d - {\left(C a^{2} - A a c\right)} e\right)} \log\left(c x^{2} + a\right)}{2 \, a c^{2}}\right]"," ",0,"[1/2*(C*a*c*e*x^2 - (B*a*e + (C*a - A*c)*d)*sqrt(-a*c)*log((c*x^2 + 2*sqrt(-a*c)*x - a)/(c*x^2 + a)) + 2*(C*a*c*d + B*a*c*e)*x + (B*a*c*d - (C*a^2 - A*a*c)*e)*log(c*x^2 + a))/(a*c^2), 1/2*(C*a*c*e*x^2 - 2*(B*a*e + (C*a - A*c)*d)*sqrt(a*c)*arctan(sqrt(a*c)*x/a) + 2*(C*a*c*d + B*a*c*e)*x + (B*a*c*d - (C*a^2 - A*a*c)*e)*log(c*x^2 + a))/(a*c^2)]","A",0
46,1,125,0,1.162045," ","integrate((C*x^2+B*x+A)/(c*x^2+a),x, algorithm=""fricas"")","\left[\frac{2 \, C a c x + B a c \log\left(c x^{2} + a\right) + {\left(C a - A c\right)} \sqrt{-a c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right)}{2 \, a c^{2}}, \frac{2 \, C a c x + B a c \log\left(c x^{2} + a\right) - 2 \, {\left(C a - A c\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right)}{2 \, a c^{2}}\right]"," ",0,"[1/2*(2*C*a*c*x + B*a*c*log(c*x^2 + a) + (C*a - A*c)*sqrt(-a*c)*log((c*x^2 - 2*sqrt(-a*c)*x - a)/(c*x^2 + a)))/(a*c^2), 1/2*(2*C*a*c*x + B*a*c*log(c*x^2 + a) - 2*(C*a - A*c)*sqrt(a*c)*arctan(sqrt(a*c)*x/a))/(a*c^2)]","A",0
47,1,262,0,19.015425," ","integrate((C*x^2+B*x+A)/(e*x+d)/(c*x^2+a),x, algorithm=""fricas"")","\left[-\frac{{\left(B a e^{2} - {\left(C a - A c\right)} d e\right)} \sqrt{-a c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right) - {\left(B a c d e + {\left(C a^{2} - A a c\right)} e^{2}\right)} \log\left(c x^{2} + a\right) - 2 \, {\left(C a c d^{2} - B a c d e + A a c e^{2}\right)} \log\left(e x + d\right)}{2 \, {\left(a c^{2} d^{2} e + a^{2} c e^{3}\right)}}, \frac{2 \, {\left(B a e^{2} - {\left(C a - A c\right)} d e\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right) + {\left(B a c d e + {\left(C a^{2} - A a c\right)} e^{2}\right)} \log\left(c x^{2} + a\right) + 2 \, {\left(C a c d^{2} - B a c d e + A a c e^{2}\right)} \log\left(e x + d\right)}{2 \, {\left(a c^{2} d^{2} e + a^{2} c e^{3}\right)}}\right]"," ",0,"[-1/2*((B*a*e^2 - (C*a - A*c)*d*e)*sqrt(-a*c)*log((c*x^2 - 2*sqrt(-a*c)*x - a)/(c*x^2 + a)) - (B*a*c*d*e + (C*a^2 - A*a*c)*e^2)*log(c*x^2 + a) - 2*(C*a*c*d^2 - B*a*c*d*e + A*a*c*e^2)*log(e*x + d))/(a*c^2*d^2*e + a^2*c*e^3), 1/2*(2*(B*a*e^2 - (C*a - A*c)*d*e)*sqrt(a*c)*arctan(sqrt(a*c)*x/a) + (B*a*c*d*e + (C*a^2 - A*a*c)*e^2)*log(c*x^2 + a) + 2*(C*a*c*d^2 - B*a*c*d*e + A*a*c*e^2)*log(e*x + d))/(a*c^2*d^2*e + a^2*c*e^3)]","A",0
48,1,904,0,72.027489," ","integrate((C*x^2+B*x+A)/(e*x+d)^2/(c*x^2+a),x, algorithm=""fricas"")","\left[-\frac{2 \, C a c^{2} d^{4} - 2 \, B a c^{2} d^{3} e - 2 \, B a^{2} c d e^{3} + 2 \, A a^{2} c e^{4} + 2 \, {\left(C a^{2} c + A a c^{2}\right)} d^{2} e^{2} - {\left(2 \, B a c d^{2} e^{2} - {\left(C a c - A c^{2}\right)} d^{3} e + {\left(C a^{2} - A a c\right)} d e^{3} + {\left(2 \, B a c d e^{3} - {\left(C a c - A c^{2}\right)} d^{2} e^{2} + {\left(C a^{2} - A a c\right)} e^{4}\right)} x\right)} \sqrt{-a c} \log\left(\frac{c x^{2} + 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right) - {\left(B a c^{2} d^{3} e - B a^{2} c d e^{3} + 2 \, {\left(C a^{2} c - A a c^{2}\right)} d^{2} e^{2} + {\left(B a c^{2} d^{2} e^{2} - B a^{2} c e^{4} + 2 \, {\left(C a^{2} c - A a c^{2}\right)} d e^{3}\right)} x\right)} \log\left(c x^{2} + a\right) + 2 \, {\left(B a c^{2} d^{3} e - B a^{2} c d e^{3} + 2 \, {\left(C a^{2} c - A a c^{2}\right)} d^{2} e^{2} + {\left(B a c^{2} d^{2} e^{2} - B a^{2} c e^{4} + 2 \, {\left(C a^{2} c - A a c^{2}\right)} d e^{3}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(a c^{3} d^{5} e + 2 \, a^{2} c^{2} d^{3} e^{3} + a^{3} c d e^{5} + {\left(a c^{3} d^{4} e^{2} + 2 \, a^{2} c^{2} d^{2} e^{4} + a^{3} c e^{6}\right)} x\right)}}, -\frac{2 \, C a c^{2} d^{4} - 2 \, B a c^{2} d^{3} e - 2 \, B a^{2} c d e^{3} + 2 \, A a^{2} c e^{4} + 2 \, {\left(C a^{2} c + A a c^{2}\right)} d^{2} e^{2} - 2 \, {\left(2 \, B a c d^{2} e^{2} - {\left(C a c - A c^{2}\right)} d^{3} e + {\left(C a^{2} - A a c\right)} d e^{3} + {\left(2 \, B a c d e^{3} - {\left(C a c - A c^{2}\right)} d^{2} e^{2} + {\left(C a^{2} - A a c\right)} e^{4}\right)} x\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right) - {\left(B a c^{2} d^{3} e - B a^{2} c d e^{3} + 2 \, {\left(C a^{2} c - A a c^{2}\right)} d^{2} e^{2} + {\left(B a c^{2} d^{2} e^{2} - B a^{2} c e^{4} + 2 \, {\left(C a^{2} c - A a c^{2}\right)} d e^{3}\right)} x\right)} \log\left(c x^{2} + a\right) + 2 \, {\left(B a c^{2} d^{3} e - B a^{2} c d e^{3} + 2 \, {\left(C a^{2} c - A a c^{2}\right)} d^{2} e^{2} + {\left(B a c^{2} d^{2} e^{2} - B a^{2} c e^{4} + 2 \, {\left(C a^{2} c - A a c^{2}\right)} d e^{3}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(a c^{3} d^{5} e + 2 \, a^{2} c^{2} d^{3} e^{3} + a^{3} c d e^{5} + {\left(a c^{3} d^{4} e^{2} + 2 \, a^{2} c^{2} d^{2} e^{4} + a^{3} c e^{6}\right)} x\right)}}\right]"," ",0,"[-1/2*(2*C*a*c^2*d^4 - 2*B*a*c^2*d^3*e - 2*B*a^2*c*d*e^3 + 2*A*a^2*c*e^4 + 2*(C*a^2*c + A*a*c^2)*d^2*e^2 - (2*B*a*c*d^2*e^2 - (C*a*c - A*c^2)*d^3*e + (C*a^2 - A*a*c)*d*e^3 + (2*B*a*c*d*e^3 - (C*a*c - A*c^2)*d^2*e^2 + (C*a^2 - A*a*c)*e^4)*x)*sqrt(-a*c)*log((c*x^2 + 2*sqrt(-a*c)*x - a)/(c*x^2 + a)) - (B*a*c^2*d^3*e - B*a^2*c*d*e^3 + 2*(C*a^2*c - A*a*c^2)*d^2*e^2 + (B*a*c^2*d^2*e^2 - B*a^2*c*e^4 + 2*(C*a^2*c - A*a*c^2)*d*e^3)*x)*log(c*x^2 + a) + 2*(B*a*c^2*d^3*e - B*a^2*c*d*e^3 + 2*(C*a^2*c - A*a*c^2)*d^2*e^2 + (B*a*c^2*d^2*e^2 - B*a^2*c*e^4 + 2*(C*a^2*c - A*a*c^2)*d*e^3)*x)*log(e*x + d))/(a*c^3*d^5*e + 2*a^2*c^2*d^3*e^3 + a^3*c*d*e^5 + (a*c^3*d^4*e^2 + 2*a^2*c^2*d^2*e^4 + a^3*c*e^6)*x), -1/2*(2*C*a*c^2*d^4 - 2*B*a*c^2*d^3*e - 2*B*a^2*c*d*e^3 + 2*A*a^2*c*e^4 + 2*(C*a^2*c + A*a*c^2)*d^2*e^2 - 2*(2*B*a*c*d^2*e^2 - (C*a*c - A*c^2)*d^3*e + (C*a^2 - A*a*c)*d*e^3 + (2*B*a*c*d*e^3 - (C*a*c - A*c^2)*d^2*e^2 + (C*a^2 - A*a*c)*e^4)*x)*sqrt(a*c)*arctan(sqrt(a*c)*x/a) - (B*a*c^2*d^3*e - B*a^2*c*d*e^3 + 2*(C*a^2*c - A*a*c^2)*d^2*e^2 + (B*a*c^2*d^2*e^2 - B*a^2*c*e^4 + 2*(C*a^2*c - A*a*c^2)*d*e^3)*x)*log(c*x^2 + a) + 2*(B*a*c^2*d^3*e - B*a^2*c*d*e^3 + 2*(C*a^2*c - A*a*c^2)*d^2*e^2 + (B*a*c^2*d^2*e^2 - B*a^2*c*e^4 + 2*(C*a^2*c - A*a*c^2)*d*e^3)*x)*log(e*x + d))/(a*c^3*d^5*e + 2*a^2*c^2*d^3*e^3 + a^3*c*d*e^5 + (a*c^3*d^4*e^2 + 2*a^2*c^2*d^2*e^4 + a^3*c*e^6)*x)]","B",0
49,-1,0,0,0.000000," ","integrate((C*x^2+B*x+A)/(e*x+d)^3/(c*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
50,1,931,0,1.072099," ","integrate((e*x+d)^3*(C*x^2+B*x+A)/(c*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{2 \, C a^{2} c^{2} e^{3} x^{4} + 2 \, C a^{3} c e^{3} x^{2} - 2 \, B a^{2} c^{2} d^{3} + 6 \, B a^{3} c d e^{2} + 6 \, {\left(C a^{3} c - A a^{2} c^{2}\right)} d^{2} e - 2 \, {\left(C a^{4} - A a^{3} c\right)} e^{3} + 4 \, {\left(3 \, C a^{2} c^{2} d e^{2} + B a^{2} c^{2} e^{3}\right)} x^{3} + {\left(3 \, B a^{2} c d^{2} e - 3 \, B a^{3} e^{3} + {\left(C a^{2} c + A a c^{2}\right)} d^{3} - 3 \, {\left(3 \, C a^{3} - A a^{2} c\right)} d e^{2} + {\left(3 \, B a c^{2} d^{2} e - 3 \, B a^{2} c e^{3} + {\left(C a c^{2} + A c^{3}\right)} d^{3} - 3 \, {\left(3 \, C a^{2} c - A a c^{2}\right)} d e^{2}\right)} x^{2}\right)} \sqrt{-a c} \log\left(\frac{c x^{2} + 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right) - 2 \, {\left(3 \, B a^{2} c^{2} d^{2} e - 3 \, B a^{3} c e^{3} + {\left(C a^{2} c^{2} - A a c^{3}\right)} d^{3} - 3 \, {\left(3 \, C a^{3} c - A a^{2} c^{2}\right)} d e^{2}\right)} x + 2 \, {\left(3 \, C a^{3} c d^{2} e + 3 \, B a^{3} c d e^{2} - {\left(2 \, C a^{4} - A a^{3} c\right)} e^{3} + {\left(3 \, C a^{2} c^{2} d^{2} e + 3 \, B a^{2} c^{2} d e^{2} - {\left(2 \, C a^{3} c - A a^{2} c^{2}\right)} e^{3}\right)} x^{2}\right)} \log\left(c x^{2} + a\right)}{4 \, {\left(a^{2} c^{4} x^{2} + a^{3} c^{3}\right)}}, \frac{C a^{2} c^{2} e^{3} x^{4} + C a^{3} c e^{3} x^{2} - B a^{2} c^{2} d^{3} + 3 \, B a^{3} c d e^{2} + 3 \, {\left(C a^{3} c - A a^{2} c^{2}\right)} d^{2} e - {\left(C a^{4} - A a^{3} c\right)} e^{3} + 2 \, {\left(3 \, C a^{2} c^{2} d e^{2} + B a^{2} c^{2} e^{3}\right)} x^{3} + {\left(3 \, B a^{2} c d^{2} e - 3 \, B a^{3} e^{3} + {\left(C a^{2} c + A a c^{2}\right)} d^{3} - 3 \, {\left(3 \, C a^{3} - A a^{2} c\right)} d e^{2} + {\left(3 \, B a c^{2} d^{2} e - 3 \, B a^{2} c e^{3} + {\left(C a c^{2} + A c^{3}\right)} d^{3} - 3 \, {\left(3 \, C a^{2} c - A a c^{2}\right)} d e^{2}\right)} x^{2}\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right) - {\left(3 \, B a^{2} c^{2} d^{2} e - 3 \, B a^{3} c e^{3} + {\left(C a^{2} c^{2} - A a c^{3}\right)} d^{3} - 3 \, {\left(3 \, C a^{3} c - A a^{2} c^{2}\right)} d e^{2}\right)} x + {\left(3 \, C a^{3} c d^{2} e + 3 \, B a^{3} c d e^{2} - {\left(2 \, C a^{4} - A a^{3} c\right)} e^{3} + {\left(3 \, C a^{2} c^{2} d^{2} e + 3 \, B a^{2} c^{2} d e^{2} - {\left(2 \, C a^{3} c - A a^{2} c^{2}\right)} e^{3}\right)} x^{2}\right)} \log\left(c x^{2} + a\right)}{2 \, {\left(a^{2} c^{4} x^{2} + a^{3} c^{3}\right)}}\right]"," ",0,"[1/4*(2*C*a^2*c^2*e^3*x^4 + 2*C*a^3*c*e^3*x^2 - 2*B*a^2*c^2*d^3 + 6*B*a^3*c*d*e^2 + 6*(C*a^3*c - A*a^2*c^2)*d^2*e - 2*(C*a^4 - A*a^3*c)*e^3 + 4*(3*C*a^2*c^2*d*e^2 + B*a^2*c^2*e^3)*x^3 + (3*B*a^2*c*d^2*e - 3*B*a^3*e^3 + (C*a^2*c + A*a*c^2)*d^3 - 3*(3*C*a^3 - A*a^2*c)*d*e^2 + (3*B*a*c^2*d^2*e - 3*B*a^2*c*e^3 + (C*a*c^2 + A*c^3)*d^3 - 3*(3*C*a^2*c - A*a*c^2)*d*e^2)*x^2)*sqrt(-a*c)*log((c*x^2 + 2*sqrt(-a*c)*x - a)/(c*x^2 + a)) - 2*(3*B*a^2*c^2*d^2*e - 3*B*a^3*c*e^3 + (C*a^2*c^2 - A*a*c^3)*d^3 - 3*(3*C*a^3*c - A*a^2*c^2)*d*e^2)*x + 2*(3*C*a^3*c*d^2*e + 3*B*a^3*c*d*e^2 - (2*C*a^4 - A*a^3*c)*e^3 + (3*C*a^2*c^2*d^2*e + 3*B*a^2*c^2*d*e^2 - (2*C*a^3*c - A*a^2*c^2)*e^3)*x^2)*log(c*x^2 + a))/(a^2*c^4*x^2 + a^3*c^3), 1/2*(C*a^2*c^2*e^3*x^4 + C*a^3*c*e^3*x^2 - B*a^2*c^2*d^3 + 3*B*a^3*c*d*e^2 + 3*(C*a^3*c - A*a^2*c^2)*d^2*e - (C*a^4 - A*a^3*c)*e^3 + 2*(3*C*a^2*c^2*d*e^2 + B*a^2*c^2*e^3)*x^3 + (3*B*a^2*c*d^2*e - 3*B*a^3*e^3 + (C*a^2*c + A*a*c^2)*d^3 - 3*(3*C*a^3 - A*a^2*c)*d*e^2 + (3*B*a*c^2*d^2*e - 3*B*a^2*c*e^3 + (C*a*c^2 + A*c^3)*d^3 - 3*(3*C*a^2*c - A*a*c^2)*d*e^2)*x^2)*sqrt(a*c)*arctan(sqrt(a*c)*x/a) - (3*B*a^2*c^2*d^2*e - 3*B*a^3*c*e^3 + (C*a^2*c^2 - A*a*c^3)*d^3 - 3*(3*C*a^3*c - A*a^2*c^2)*d*e^2)*x + (3*C*a^3*c*d^2*e + 3*B*a^3*c*d*e^2 - (2*C*a^4 - A*a^3*c)*e^3 + (3*C*a^2*c^2*d^2*e + 3*B*a^2*c^2*d*e^2 - (2*C*a^3*c - A*a^2*c^2)*e^3)*x^2)*log(c*x^2 + a))/(a^2*c^4*x^2 + a^3*c^3)]","B",0
51,1,631,0,0.836286," ","integrate((e*x+d)^2*(C*x^2+B*x+A)/(c*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{4 \, C a^{2} c^{2} e^{2} x^{3} - 2 \, B a^{2} c^{2} d^{2} + 2 \, B a^{3} c e^{2} + 4 \, {\left(C a^{3} c - A a^{2} c^{2}\right)} d e - {\left(2 \, B a^{2} c d e + {\left(C a^{2} c + A a c^{2}\right)} d^{2} - {\left(3 \, C a^{3} - A a^{2} c\right)} e^{2} + {\left(2 \, B a c^{2} d e + {\left(C a c^{2} + A c^{3}\right)} d^{2} - {\left(3 \, C a^{2} c - A a c^{2}\right)} e^{2}\right)} x^{2}\right)} \sqrt{-a c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right) - 2 \, {\left(2 \, B a^{2} c^{2} d e + {\left(C a^{2} c^{2} - A a c^{3}\right)} d^{2} - {\left(3 \, C a^{3} c - A a^{2} c^{2}\right)} e^{2}\right)} x + 2 \, {\left(2 \, C a^{3} c d e + B a^{3} c e^{2} + {\left(2 \, C a^{2} c^{2} d e + B a^{2} c^{2} e^{2}\right)} x^{2}\right)} \log\left(c x^{2} + a\right)}{4 \, {\left(a^{2} c^{4} x^{2} + a^{3} c^{3}\right)}}, \frac{2 \, C a^{2} c^{2} e^{2} x^{3} - B a^{2} c^{2} d^{2} + B a^{3} c e^{2} + 2 \, {\left(C a^{3} c - A a^{2} c^{2}\right)} d e + {\left(2 \, B a^{2} c d e + {\left(C a^{2} c + A a c^{2}\right)} d^{2} - {\left(3 \, C a^{3} - A a^{2} c\right)} e^{2} + {\left(2 \, B a c^{2} d e + {\left(C a c^{2} + A c^{3}\right)} d^{2} - {\left(3 \, C a^{2} c - A a c^{2}\right)} e^{2}\right)} x^{2}\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right) - {\left(2 \, B a^{2} c^{2} d e + {\left(C a^{2} c^{2} - A a c^{3}\right)} d^{2} - {\left(3 \, C a^{3} c - A a^{2} c^{2}\right)} e^{2}\right)} x + {\left(2 \, C a^{3} c d e + B a^{3} c e^{2} + {\left(2 \, C a^{2} c^{2} d e + B a^{2} c^{2} e^{2}\right)} x^{2}\right)} \log\left(c x^{2} + a\right)}{2 \, {\left(a^{2} c^{4} x^{2} + a^{3} c^{3}\right)}}\right]"," ",0,"[1/4*(4*C*a^2*c^2*e^2*x^3 - 2*B*a^2*c^2*d^2 + 2*B*a^3*c*e^2 + 4*(C*a^3*c - A*a^2*c^2)*d*e - (2*B*a^2*c*d*e + (C*a^2*c + A*a*c^2)*d^2 - (3*C*a^3 - A*a^2*c)*e^2 + (2*B*a*c^2*d*e + (C*a*c^2 + A*c^3)*d^2 - (3*C*a^2*c - A*a*c^2)*e^2)*x^2)*sqrt(-a*c)*log((c*x^2 - 2*sqrt(-a*c)*x - a)/(c*x^2 + a)) - 2*(2*B*a^2*c^2*d*e + (C*a^2*c^2 - A*a*c^3)*d^2 - (3*C*a^3*c - A*a^2*c^2)*e^2)*x + 2*(2*C*a^3*c*d*e + B*a^3*c*e^2 + (2*C*a^2*c^2*d*e + B*a^2*c^2*e^2)*x^2)*log(c*x^2 + a))/(a^2*c^4*x^2 + a^3*c^3), 1/2*(2*C*a^2*c^2*e^2*x^3 - B*a^2*c^2*d^2 + B*a^3*c*e^2 + 2*(C*a^3*c - A*a^2*c^2)*d*e + (2*B*a^2*c*d*e + (C*a^2*c + A*a*c^2)*d^2 - (3*C*a^3 - A*a^2*c)*e^2 + (2*B*a*c^2*d*e + (C*a*c^2 + A*c^3)*d^2 - (3*C*a^2*c - A*a*c^2)*e^2)*x^2)*sqrt(a*c)*arctan(sqrt(a*c)*x/a) - (2*B*a^2*c^2*d*e + (C*a^2*c^2 - A*a*c^3)*d^2 - (3*C*a^3*c - A*a^2*c^2)*e^2)*x + (2*C*a^3*c*d*e + B*a^3*c*e^2 + (2*C*a^2*c^2*d*e + B*a^2*c^2*e^2)*x^2)*log(c*x^2 + a))/(a^2*c^4*x^2 + a^3*c^3)]","B",0
52,1,337,0,0.530839," ","integrate((e*x+d)*(C*x^2+B*x+A)/(c*x^2+a)^2,x, algorithm=""fricas"")","\left[-\frac{2 \, B a^{2} c d + {\left(B a^{2} e + {\left(B a c e + {\left(C a c + A c^{2}\right)} d\right)} x^{2} + {\left(C a^{2} + A a c\right)} d\right)} \sqrt{-a c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right) - 2 \, {\left(C a^{3} - A a^{2} c\right)} e + 2 \, {\left(B a^{2} c e + {\left(C a^{2} c - A a c^{2}\right)} d\right)} x - 2 \, {\left(C a^{2} c e x^{2} + C a^{3} e\right)} \log\left(c x^{2} + a\right)}{4 \, {\left(a^{2} c^{3} x^{2} + a^{3} c^{2}\right)}}, -\frac{B a^{2} c d - {\left(B a^{2} e + {\left(B a c e + {\left(C a c + A c^{2}\right)} d\right)} x^{2} + {\left(C a^{2} + A a c\right)} d\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right) - {\left(C a^{3} - A a^{2} c\right)} e + {\left(B a^{2} c e + {\left(C a^{2} c - A a c^{2}\right)} d\right)} x - {\left(C a^{2} c e x^{2} + C a^{3} e\right)} \log\left(c x^{2} + a\right)}{2 \, {\left(a^{2} c^{3} x^{2} + a^{3} c^{2}\right)}}\right]"," ",0,"[-1/4*(2*B*a^2*c*d + (B*a^2*e + (B*a*c*e + (C*a*c + A*c^2)*d)*x^2 + (C*a^2 + A*a*c)*d)*sqrt(-a*c)*log((c*x^2 - 2*sqrt(-a*c)*x - a)/(c*x^2 + a)) - 2*(C*a^3 - A*a^2*c)*e + 2*(B*a^2*c*e + (C*a^2*c - A*a*c^2)*d)*x - 2*(C*a^2*c*e*x^2 + C*a^3*e)*log(c*x^2 + a))/(a^2*c^3*x^2 + a^3*c^2), -1/2*(B*a^2*c*d - (B*a^2*e + (B*a*c*e + (C*a*c + A*c^2)*d)*x^2 + (C*a^2 + A*a*c)*d)*sqrt(a*c)*arctan(sqrt(a*c)*x/a) - (C*a^3 - A*a^2*c)*e + (B*a^2*c*e + (C*a^2*c - A*a*c^2)*d)*x - (C*a^2*c*e*x^2 + C*a^3*e)*log(c*x^2 + a))/(a^2*c^3*x^2 + a^3*c^2)]","A",0
53,1,195,0,2.998769," ","integrate((C*x^2+B*x+A)/(c*x^2+a)^2,x, algorithm=""fricas"")","\left[-\frac{2 \, B a^{2} c + {\left(C a^{2} + A a c + {\left(C a c + A c^{2}\right)} x^{2}\right)} \sqrt{-a c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right) + 2 \, {\left(C a^{2} c - A a c^{2}\right)} x}{4 \, {\left(a^{2} c^{3} x^{2} + a^{3} c^{2}\right)}}, -\frac{B a^{2} c - {\left(C a^{2} + A a c + {\left(C a c + A c^{2}\right)} x^{2}\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right) + {\left(C a^{2} c - A a c^{2}\right)} x}{2 \, {\left(a^{2} c^{3} x^{2} + a^{3} c^{2}\right)}}\right]"," ",0,"[-1/4*(2*B*a^2*c + (C*a^2 + A*a*c + (C*a*c + A*c^2)*x^2)*sqrt(-a*c)*log((c*x^2 - 2*sqrt(-a*c)*x - a)/(c*x^2 + a)) + 2*(C*a^2*c - A*a*c^2)*x)/(a^2*c^3*x^2 + a^3*c^2), -1/2*(B*a^2*c - (C*a^2 + A*a*c + (C*a*c + A*c^2)*x^2)*sqrt(a*c)*arctan(sqrt(a*c)*x/a) + (C*a^2*c - A*a*c^2)*x)/(a^2*c^3*x^2 + a^3*c^2)]","A",0
54,1,1024,0,83.521973," ","integrate((C*x^2+B*x+A)/(e*x+d)/(c*x^2+a)^2,x, algorithm=""fricas"")","\left[-\frac{2 \, B a^{2} c^{2} d^{3} + 2 \, B a^{3} c d e^{2} + 2 \, {\left(C a^{3} c - A a^{2} c^{2}\right)} d^{2} e + 2 \, {\left(C a^{4} - A a^{3} c\right)} e^{3} - {\left(B a^{2} c d^{2} e - B a^{3} e^{3} - {\left(C a^{2} c + A a c^{2}\right)} d^{3} + {\left(C a^{3} - 3 \, A a^{2} c\right)} d e^{2} + {\left(B a c^{2} d^{2} e - B a^{2} c e^{3} - {\left(C a c^{2} + A c^{3}\right)} d^{3} + {\left(C a^{2} c - 3 \, A a c^{2}\right)} d e^{2}\right)} x^{2}\right)} \sqrt{-a c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right) - 2 \, {\left(B a^{2} c^{2} d^{2} e + B a^{3} c e^{3} - {\left(C a^{2} c^{2} - A a c^{3}\right)} d^{3} - {\left(C a^{3} c - A a^{2} c^{2}\right)} d e^{2}\right)} x + 2 \, {\left(C a^{3} c d^{2} e - B a^{3} c d e^{2} + A a^{3} c e^{3} + {\left(C a^{2} c^{2} d^{2} e - B a^{2} c^{2} d e^{2} + A a^{2} c^{2} e^{3}\right)} x^{2}\right)} \log\left(c x^{2} + a\right) - 4 \, {\left(C a^{3} c d^{2} e - B a^{3} c d e^{2} + A a^{3} c e^{3} + {\left(C a^{2} c^{2} d^{2} e - B a^{2} c^{2} d e^{2} + A a^{2} c^{2} e^{3}\right)} x^{2}\right)} \log\left(e x + d\right)}{4 \, {\left(a^{3} c^{3} d^{4} + 2 \, a^{4} c^{2} d^{2} e^{2} + a^{5} c e^{4} + {\left(a^{2} c^{4} d^{4} + 2 \, a^{3} c^{3} d^{2} e^{2} + a^{4} c^{2} e^{4}\right)} x^{2}\right)}}, -\frac{B a^{2} c^{2} d^{3} + B a^{3} c d e^{2} + {\left(C a^{3} c - A a^{2} c^{2}\right)} d^{2} e + {\left(C a^{4} - A a^{3} c\right)} e^{3} + {\left(B a^{2} c d^{2} e - B a^{3} e^{3} - {\left(C a^{2} c + A a c^{2}\right)} d^{3} + {\left(C a^{3} - 3 \, A a^{2} c\right)} d e^{2} + {\left(B a c^{2} d^{2} e - B a^{2} c e^{3} - {\left(C a c^{2} + A c^{3}\right)} d^{3} + {\left(C a^{2} c - 3 \, A a c^{2}\right)} d e^{2}\right)} x^{2}\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right) - {\left(B a^{2} c^{2} d^{2} e + B a^{3} c e^{3} - {\left(C a^{2} c^{2} - A a c^{3}\right)} d^{3} - {\left(C a^{3} c - A a^{2} c^{2}\right)} d e^{2}\right)} x + {\left(C a^{3} c d^{2} e - B a^{3} c d e^{2} + A a^{3} c e^{3} + {\left(C a^{2} c^{2} d^{2} e - B a^{2} c^{2} d e^{2} + A a^{2} c^{2} e^{3}\right)} x^{2}\right)} \log\left(c x^{2} + a\right) - 2 \, {\left(C a^{3} c d^{2} e - B a^{3} c d e^{2} + A a^{3} c e^{3} + {\left(C a^{2} c^{2} d^{2} e - B a^{2} c^{2} d e^{2} + A a^{2} c^{2} e^{3}\right)} x^{2}\right)} \log\left(e x + d\right)}{2 \, {\left(a^{3} c^{3} d^{4} + 2 \, a^{4} c^{2} d^{2} e^{2} + a^{5} c e^{4} + {\left(a^{2} c^{4} d^{4} + 2 \, a^{3} c^{3} d^{2} e^{2} + a^{4} c^{2} e^{4}\right)} x^{2}\right)}}\right]"," ",0,"[-1/4*(2*B*a^2*c^2*d^3 + 2*B*a^3*c*d*e^2 + 2*(C*a^3*c - A*a^2*c^2)*d^2*e + 2*(C*a^4 - A*a^3*c)*e^3 - (B*a^2*c*d^2*e - B*a^3*e^3 - (C*a^2*c + A*a*c^2)*d^3 + (C*a^3 - 3*A*a^2*c)*d*e^2 + (B*a*c^2*d^2*e - B*a^2*c*e^3 - (C*a*c^2 + A*c^3)*d^3 + (C*a^2*c - 3*A*a*c^2)*d*e^2)*x^2)*sqrt(-a*c)*log((c*x^2 - 2*sqrt(-a*c)*x - a)/(c*x^2 + a)) - 2*(B*a^2*c^2*d^2*e + B*a^3*c*e^3 - (C*a^2*c^2 - A*a*c^3)*d^3 - (C*a^3*c - A*a^2*c^2)*d*e^2)*x + 2*(C*a^3*c*d^2*e - B*a^3*c*d*e^2 + A*a^3*c*e^3 + (C*a^2*c^2*d^2*e - B*a^2*c^2*d*e^2 + A*a^2*c^2*e^3)*x^2)*log(c*x^2 + a) - 4*(C*a^3*c*d^2*e - B*a^3*c*d*e^2 + A*a^3*c*e^3 + (C*a^2*c^2*d^2*e - B*a^2*c^2*d*e^2 + A*a^2*c^2*e^3)*x^2)*log(e*x + d))/(a^3*c^3*d^4 + 2*a^4*c^2*d^2*e^2 + a^5*c*e^4 + (a^2*c^4*d^4 + 2*a^3*c^3*d^2*e^2 + a^4*c^2*e^4)*x^2), -1/2*(B*a^2*c^2*d^3 + B*a^3*c*d*e^2 + (C*a^3*c - A*a^2*c^2)*d^2*e + (C*a^4 - A*a^3*c)*e^3 + (B*a^2*c*d^2*e - B*a^3*e^3 - (C*a^2*c + A*a*c^2)*d^3 + (C*a^3 - 3*A*a^2*c)*d*e^2 + (B*a*c^2*d^2*e - B*a^2*c*e^3 - (C*a*c^2 + A*c^3)*d^3 + (C*a^2*c - 3*A*a*c^2)*d*e^2)*x^2)*sqrt(a*c)*arctan(sqrt(a*c)*x/a) - (B*a^2*c^2*d^2*e + B*a^3*c*e^3 - (C*a^2*c^2 - A*a*c^3)*d^3 - (C*a^3*c - A*a^2*c^2)*d*e^2)*x + (C*a^3*c*d^2*e - B*a^3*c*d*e^2 + A*a^3*c*e^3 + (C*a^2*c^2*d^2*e - B*a^2*c^2*d*e^2 + A*a^2*c^2*e^3)*x^2)*log(c*x^2 + a) - 2*(C*a^3*c*d^2*e - B*a^3*c*d*e^2 + A*a^3*c*e^3 + (C*a^2*c^2*d^2*e - B*a^2*c^2*d*e^2 + A*a^2*c^2*e^3)*x^2)*log(e*x + d))/(a^3*c^3*d^4 + 2*a^4*c^2*d^2*e^2 + a^5*c*e^4 + (a^2*c^4*d^4 + 2*a^3*c^3*d^2*e^2 + a^4*c^2*e^4)*x^2)]","B",0
55,-1,0,0,0.000000," ","integrate((C*x^2+B*x+A)/(e*x+d)^2/(c*x^2+a)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
56,-1,0,0,0.000000," ","integrate((C*x^2+B*x+A)/(e*x+d)^3/(c*x^2+a)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
57,1,1138,0,1.056104," ","integrate((e*x+d)^3*(C*x^2+B*x+A)/(c*x^2+a)^3,x, algorithm=""fricas"")","\left[-\frac{4 \, B a^{3} c^{2} d^{3} + 12 \, B a^{4} c d e^{2} + 12 \, {\left(C a^{4} c + A a^{3} c^{2}\right)} d^{2} e - 4 \, {\left(3 \, C a^{5} - A a^{4} c\right)} e^{3} - 2 \, {\left(3 \, B a^{2} c^{3} d^{2} e - 5 \, B a^{3} c^{2} e^{3} + {\left(C a^{2} c^{3} + 3 \, A a c^{4}\right)} d^{3} - 3 \, {\left(5 \, C a^{3} c^{2} - A a^{2} c^{3}\right)} d e^{2}\right)} x^{3} + 8 \, {\left(3 \, C a^{3} c^{2} d^{2} e + 3 \, B a^{3} c^{2} d e^{2} - {\left(2 \, C a^{4} c - A a^{3} c^{2}\right)} e^{3}\right)} x^{2} + {\left(3 \, B a^{3} c d^{2} e + 3 \, B a^{4} e^{3} + {\left(3 \, B a c^{3} d^{2} e + 3 \, B a^{2} c^{2} e^{3} + {\left(C a c^{3} + 3 \, A c^{4}\right)} d^{3} + 3 \, {\left(3 \, C a^{2} c^{2} + A a c^{3}\right)} d e^{2}\right)} x^{4} + {\left(C a^{3} c + 3 \, A a^{2} c^{2}\right)} d^{3} + 3 \, {\left(3 \, C a^{4} + A a^{3} c\right)} d e^{2} + 2 \, {\left(3 \, B a^{2} c^{2} d^{2} e + 3 \, B a^{3} c e^{3} + {\left(C a^{2} c^{2} + 3 \, A a c^{3}\right)} d^{3} + 3 \, {\left(3 \, C a^{3} c + A a^{2} c^{2}\right)} d e^{2}\right)} x^{2}\right)} \sqrt{-a c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right) + 2 \, {\left(3 \, B a^{3} c^{2} d^{2} e + 3 \, B a^{4} c e^{3} + {\left(C a^{3} c^{2} - 5 \, A a^{2} c^{3}\right)} d^{3} + 3 \, {\left(3 \, C a^{4} c + A a^{3} c^{2}\right)} d e^{2}\right)} x - 8 \, {\left(C a^{3} c^{2} e^{3} x^{4} + 2 \, C a^{4} c e^{3} x^{2} + C a^{5} e^{3}\right)} \log\left(c x^{2} + a\right)}{16 \, {\left(a^{3} c^{5} x^{4} + 2 \, a^{4} c^{4} x^{2} + a^{5} c^{3}\right)}}, -\frac{2 \, B a^{3} c^{2} d^{3} + 6 \, B a^{4} c d e^{2} + 6 \, {\left(C a^{4} c + A a^{3} c^{2}\right)} d^{2} e - 2 \, {\left(3 \, C a^{5} - A a^{4} c\right)} e^{3} - {\left(3 \, B a^{2} c^{3} d^{2} e - 5 \, B a^{3} c^{2} e^{3} + {\left(C a^{2} c^{3} + 3 \, A a c^{4}\right)} d^{3} - 3 \, {\left(5 \, C a^{3} c^{2} - A a^{2} c^{3}\right)} d e^{2}\right)} x^{3} + 4 \, {\left(3 \, C a^{3} c^{2} d^{2} e + 3 \, B a^{3} c^{2} d e^{2} - {\left(2 \, C a^{4} c - A a^{3} c^{2}\right)} e^{3}\right)} x^{2} - {\left(3 \, B a^{3} c d^{2} e + 3 \, B a^{4} e^{3} + {\left(3 \, B a c^{3} d^{2} e + 3 \, B a^{2} c^{2} e^{3} + {\left(C a c^{3} + 3 \, A c^{4}\right)} d^{3} + 3 \, {\left(3 \, C a^{2} c^{2} + A a c^{3}\right)} d e^{2}\right)} x^{4} + {\left(C a^{3} c + 3 \, A a^{2} c^{2}\right)} d^{3} + 3 \, {\left(3 \, C a^{4} + A a^{3} c\right)} d e^{2} + 2 \, {\left(3 \, B a^{2} c^{2} d^{2} e + 3 \, B a^{3} c e^{3} + {\left(C a^{2} c^{2} + 3 \, A a c^{3}\right)} d^{3} + 3 \, {\left(3 \, C a^{3} c + A a^{2} c^{2}\right)} d e^{2}\right)} x^{2}\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right) + {\left(3 \, B a^{3} c^{2} d^{2} e + 3 \, B a^{4} c e^{3} + {\left(C a^{3} c^{2} - 5 \, A a^{2} c^{3}\right)} d^{3} + 3 \, {\left(3 \, C a^{4} c + A a^{3} c^{2}\right)} d e^{2}\right)} x - 4 \, {\left(C a^{3} c^{2} e^{3} x^{4} + 2 \, C a^{4} c e^{3} x^{2} + C a^{5} e^{3}\right)} \log\left(c x^{2} + a\right)}{8 \, {\left(a^{3} c^{5} x^{4} + 2 \, a^{4} c^{4} x^{2} + a^{5} c^{3}\right)}}\right]"," ",0,"[-1/16*(4*B*a^3*c^2*d^3 + 12*B*a^4*c*d*e^2 + 12*(C*a^4*c + A*a^3*c^2)*d^2*e - 4*(3*C*a^5 - A*a^4*c)*e^3 - 2*(3*B*a^2*c^3*d^2*e - 5*B*a^3*c^2*e^3 + (C*a^2*c^3 + 3*A*a*c^4)*d^3 - 3*(5*C*a^3*c^2 - A*a^2*c^3)*d*e^2)*x^3 + 8*(3*C*a^3*c^2*d^2*e + 3*B*a^3*c^2*d*e^2 - (2*C*a^4*c - A*a^3*c^2)*e^3)*x^2 + (3*B*a^3*c*d^2*e + 3*B*a^4*e^3 + (3*B*a*c^3*d^2*e + 3*B*a^2*c^2*e^3 + (C*a*c^3 + 3*A*c^4)*d^3 + 3*(3*C*a^2*c^2 + A*a*c^3)*d*e^2)*x^4 + (C*a^3*c + 3*A*a^2*c^2)*d^3 + 3*(3*C*a^4 + A*a^3*c)*d*e^2 + 2*(3*B*a^2*c^2*d^2*e + 3*B*a^3*c*e^3 + (C*a^2*c^2 + 3*A*a*c^3)*d^3 + 3*(3*C*a^3*c + A*a^2*c^2)*d*e^2)*x^2)*sqrt(-a*c)*log((c*x^2 - 2*sqrt(-a*c)*x - a)/(c*x^2 + a)) + 2*(3*B*a^3*c^2*d^2*e + 3*B*a^4*c*e^3 + (C*a^3*c^2 - 5*A*a^2*c^3)*d^3 + 3*(3*C*a^4*c + A*a^3*c^2)*d*e^2)*x - 8*(C*a^3*c^2*e^3*x^4 + 2*C*a^4*c*e^3*x^2 + C*a^5*e^3)*log(c*x^2 + a))/(a^3*c^5*x^4 + 2*a^4*c^4*x^2 + a^5*c^3), -1/8*(2*B*a^3*c^2*d^3 + 6*B*a^4*c*d*e^2 + 6*(C*a^4*c + A*a^3*c^2)*d^2*e - 2*(3*C*a^5 - A*a^4*c)*e^3 - (3*B*a^2*c^3*d^2*e - 5*B*a^3*c^2*e^3 + (C*a^2*c^3 + 3*A*a*c^4)*d^3 - 3*(5*C*a^3*c^2 - A*a^2*c^3)*d*e^2)*x^3 + 4*(3*C*a^3*c^2*d^2*e + 3*B*a^3*c^2*d*e^2 - (2*C*a^4*c - A*a^3*c^2)*e^3)*x^2 - (3*B*a^3*c*d^2*e + 3*B*a^4*e^3 + (3*B*a*c^3*d^2*e + 3*B*a^2*c^2*e^3 + (C*a*c^3 + 3*A*c^4)*d^3 + 3*(3*C*a^2*c^2 + A*a*c^3)*d*e^2)*x^4 + (C*a^3*c + 3*A*a^2*c^2)*d^3 + 3*(3*C*a^4 + A*a^3*c)*d*e^2 + 2*(3*B*a^2*c^2*d^2*e + 3*B*a^3*c*e^3 + (C*a^2*c^2 + 3*A*a*c^3)*d^3 + 3*(3*C*a^3*c + A*a^2*c^2)*d*e^2)*x^2)*sqrt(a*c)*arctan(sqrt(a*c)*x/a) + (3*B*a^3*c^2*d^2*e + 3*B*a^4*c*e^3 + (C*a^3*c^2 - 5*A*a^2*c^3)*d^3 + 3*(3*C*a^4*c + A*a^3*c^2)*d*e^2)*x - 4*(C*a^3*c^2*e^3*x^4 + 2*C*a^4*c*e^3*x^2 + C*a^5*e^3)*log(c*x^2 + a))/(a^3*c^5*x^4 + 2*a^4*c^4*x^2 + a^5*c^3)]","B",0
58,1,806,0,1.022226," ","integrate((e*x+d)^2*(C*x^2+B*x+A)/(c*x^2+a)^3,x, algorithm=""fricas"")","\left[-\frac{4 \, B a^{3} c^{2} d^{2} + 4 \, B a^{4} c e^{2} - 2 \, {\left(2 \, B a^{2} c^{3} d e + {\left(C a^{2} c^{3} + 3 \, A a c^{4}\right)} d^{2} - {\left(5 \, C a^{3} c^{2} - A a^{2} c^{3}\right)} e^{2}\right)} x^{3} + 8 \, {\left(C a^{4} c + A a^{3} c^{2}\right)} d e + 8 \, {\left(2 \, C a^{3} c^{2} d e + B a^{3} c^{2} e^{2}\right)} x^{2} + {\left(2 \, B a^{3} c d e + {\left(2 \, B a c^{3} d e + {\left(C a c^{3} + 3 \, A c^{4}\right)} d^{2} + {\left(3 \, C a^{2} c^{2} + A a c^{3}\right)} e^{2}\right)} x^{4} + {\left(C a^{3} c + 3 \, A a^{2} c^{2}\right)} d^{2} + {\left(3 \, C a^{4} + A a^{3} c\right)} e^{2} + 2 \, {\left(2 \, B a^{2} c^{2} d e + {\left(C a^{2} c^{2} + 3 \, A a c^{3}\right)} d^{2} + {\left(3 \, C a^{3} c + A a^{2} c^{2}\right)} e^{2}\right)} x^{2}\right)} \sqrt{-a c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right) + 2 \, {\left(2 \, B a^{3} c^{2} d e + {\left(C a^{3} c^{2} - 5 \, A a^{2} c^{3}\right)} d^{2} + {\left(3 \, C a^{4} c + A a^{3} c^{2}\right)} e^{2}\right)} x}{16 \, {\left(a^{3} c^{5} x^{4} + 2 \, a^{4} c^{4} x^{2} + a^{5} c^{3}\right)}}, -\frac{2 \, B a^{3} c^{2} d^{2} + 2 \, B a^{4} c e^{2} - {\left(2 \, B a^{2} c^{3} d e + {\left(C a^{2} c^{3} + 3 \, A a c^{4}\right)} d^{2} - {\left(5 \, C a^{3} c^{2} - A a^{2} c^{3}\right)} e^{2}\right)} x^{3} + 4 \, {\left(C a^{4} c + A a^{3} c^{2}\right)} d e + 4 \, {\left(2 \, C a^{3} c^{2} d e + B a^{3} c^{2} e^{2}\right)} x^{2} - {\left(2 \, B a^{3} c d e + {\left(2 \, B a c^{3} d e + {\left(C a c^{3} + 3 \, A c^{4}\right)} d^{2} + {\left(3 \, C a^{2} c^{2} + A a c^{3}\right)} e^{2}\right)} x^{4} + {\left(C a^{3} c + 3 \, A a^{2} c^{2}\right)} d^{2} + {\left(3 \, C a^{4} + A a^{3} c\right)} e^{2} + 2 \, {\left(2 \, B a^{2} c^{2} d e + {\left(C a^{2} c^{2} + 3 \, A a c^{3}\right)} d^{2} + {\left(3 \, C a^{3} c + A a^{2} c^{2}\right)} e^{2}\right)} x^{2}\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right) + {\left(2 \, B a^{3} c^{2} d e + {\left(C a^{3} c^{2} - 5 \, A a^{2} c^{3}\right)} d^{2} + {\left(3 \, C a^{4} c + A a^{3} c^{2}\right)} e^{2}\right)} x}{8 \, {\left(a^{3} c^{5} x^{4} + 2 \, a^{4} c^{4} x^{2} + a^{5} c^{3}\right)}}\right]"," ",0,"[-1/16*(4*B*a^3*c^2*d^2 + 4*B*a^4*c*e^2 - 2*(2*B*a^2*c^3*d*e + (C*a^2*c^3 + 3*A*a*c^4)*d^2 - (5*C*a^3*c^2 - A*a^2*c^3)*e^2)*x^3 + 8*(C*a^4*c + A*a^3*c^2)*d*e + 8*(2*C*a^3*c^2*d*e + B*a^3*c^2*e^2)*x^2 + (2*B*a^3*c*d*e + (2*B*a*c^3*d*e + (C*a*c^3 + 3*A*c^4)*d^2 + (3*C*a^2*c^2 + A*a*c^3)*e^2)*x^4 + (C*a^3*c + 3*A*a^2*c^2)*d^2 + (3*C*a^4 + A*a^3*c)*e^2 + 2*(2*B*a^2*c^2*d*e + (C*a^2*c^2 + 3*A*a*c^3)*d^2 + (3*C*a^3*c + A*a^2*c^2)*e^2)*x^2)*sqrt(-a*c)*log((c*x^2 - 2*sqrt(-a*c)*x - a)/(c*x^2 + a)) + 2*(2*B*a^3*c^2*d*e + (C*a^3*c^2 - 5*A*a^2*c^3)*d^2 + (3*C*a^4*c + A*a^3*c^2)*e^2)*x)/(a^3*c^5*x^4 + 2*a^4*c^4*x^2 + a^5*c^3), -1/8*(2*B*a^3*c^2*d^2 + 2*B*a^4*c*e^2 - (2*B*a^2*c^3*d*e + (C*a^2*c^3 + 3*A*a*c^4)*d^2 - (5*C*a^3*c^2 - A*a^2*c^3)*e^2)*x^3 + 4*(C*a^4*c + A*a^3*c^2)*d*e + 4*(2*C*a^3*c^2*d*e + B*a^3*c^2*e^2)*x^2 - (2*B*a^3*c*d*e + (2*B*a*c^3*d*e + (C*a*c^3 + 3*A*c^4)*d^2 + (3*C*a^2*c^2 + A*a*c^3)*e^2)*x^4 + (C*a^3*c + 3*A*a^2*c^2)*d^2 + (3*C*a^4 + A*a^3*c)*e^2 + 2*(2*B*a^2*c^2*d*e + (C*a^2*c^2 + 3*A*a*c^3)*d^2 + (3*C*a^3*c + A*a^2*c^2)*e^2)*x^2)*sqrt(a*c)*arctan(sqrt(a*c)*x/a) + (2*B*a^3*c^2*d*e + (C*a^3*c^2 - 5*A*a^2*c^3)*d^2 + (3*C*a^4*c + A*a^3*c^2)*e^2)*x)/(a^3*c^5*x^4 + 2*a^4*c^4*x^2 + a^5*c^3)]","B",0
59,1,470,0,0.902326," ","integrate((e*x+d)*(C*x^2+B*x+A)/(c*x^2+a)^3,x, algorithm=""fricas"")","\left[-\frac{8 \, C a^{3} c e x^{2} + 4 \, B a^{3} c d - 2 \, {\left(B a^{2} c^{2} e + {\left(C a^{2} c^{2} + 3 \, A a c^{3}\right)} d\right)} x^{3} + {\left(B a^{3} e + {\left(B a c^{2} e + {\left(C a c^{2} + 3 \, A c^{3}\right)} d\right)} x^{4} + 2 \, {\left(B a^{2} c e + {\left(C a^{2} c + 3 \, A a c^{2}\right)} d\right)} x^{2} + {\left(C a^{3} + 3 \, A a^{2} c\right)} d\right)} \sqrt{-a c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right) + 4 \, {\left(C a^{4} + A a^{3} c\right)} e + 2 \, {\left(B a^{3} c e + {\left(C a^{3} c - 5 \, A a^{2} c^{2}\right)} d\right)} x}{16 \, {\left(a^{3} c^{4} x^{4} + 2 \, a^{4} c^{3} x^{2} + a^{5} c^{2}\right)}}, -\frac{4 \, C a^{3} c e x^{2} + 2 \, B a^{3} c d - {\left(B a^{2} c^{2} e + {\left(C a^{2} c^{2} + 3 \, A a c^{3}\right)} d\right)} x^{3} - {\left(B a^{3} e + {\left(B a c^{2} e + {\left(C a c^{2} + 3 \, A c^{3}\right)} d\right)} x^{4} + 2 \, {\left(B a^{2} c e + {\left(C a^{2} c + 3 \, A a c^{2}\right)} d\right)} x^{2} + {\left(C a^{3} + 3 \, A a^{2} c\right)} d\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right) + 2 \, {\left(C a^{4} + A a^{3} c\right)} e + {\left(B a^{3} c e + {\left(C a^{3} c - 5 \, A a^{2} c^{2}\right)} d\right)} x}{8 \, {\left(a^{3} c^{4} x^{4} + 2 \, a^{4} c^{3} x^{2} + a^{5} c^{2}\right)}}\right]"," ",0,"[-1/16*(8*C*a^3*c*e*x^2 + 4*B*a^3*c*d - 2*(B*a^2*c^2*e + (C*a^2*c^2 + 3*A*a*c^3)*d)*x^3 + (B*a^3*e + (B*a*c^2*e + (C*a*c^2 + 3*A*c^3)*d)*x^4 + 2*(B*a^2*c*e + (C*a^2*c + 3*A*a*c^2)*d)*x^2 + (C*a^3 + 3*A*a^2*c)*d)*sqrt(-a*c)*log((c*x^2 - 2*sqrt(-a*c)*x - a)/(c*x^2 + a)) + 4*(C*a^4 + A*a^3*c)*e + 2*(B*a^3*c*e + (C*a^3*c - 5*A*a^2*c^2)*d)*x)/(a^3*c^4*x^4 + 2*a^4*c^3*x^2 + a^5*c^2), -1/8*(4*C*a^3*c*e*x^2 + 2*B*a^3*c*d - (B*a^2*c^2*e + (C*a^2*c^2 + 3*A*a*c^3)*d)*x^3 - (B*a^3*e + (B*a*c^2*e + (C*a*c^2 + 3*A*c^3)*d)*x^4 + 2*(B*a^2*c*e + (C*a^2*c + 3*A*a*c^2)*d)*x^2 + (C*a^3 + 3*A*a^2*c)*d)*sqrt(a*c)*arctan(sqrt(a*c)*x/a) + 2*(C*a^4 + A*a^3*c)*e + (B*a^3*c*e + (C*a^3*c - 5*A*a^2*c^2)*d)*x)/(a^3*c^4*x^4 + 2*a^4*c^3*x^2 + a^5*c^2)]","A",0
60,1,314,0,1.037565," ","integrate((C*x^2+B*x+A)/(c*x^2+a)^3,x, algorithm=""fricas"")","\left[-\frac{4 \, B a^{3} c - 2 \, {\left(C a^{2} c^{2} + 3 \, A a c^{3}\right)} x^{3} + {\left({\left(C a c^{2} + 3 \, A c^{3}\right)} x^{4} + C a^{3} + 3 \, A a^{2} c + 2 \, {\left(C a^{2} c + 3 \, A a c^{2}\right)} x^{2}\right)} \sqrt{-a c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right) + 2 \, {\left(C a^{3} c - 5 \, A a^{2} c^{2}\right)} x}{16 \, {\left(a^{3} c^{4} x^{4} + 2 \, a^{4} c^{3} x^{2} + a^{5} c^{2}\right)}}, -\frac{2 \, B a^{3} c - {\left(C a^{2} c^{2} + 3 \, A a c^{3}\right)} x^{3} - {\left({\left(C a c^{2} + 3 \, A c^{3}\right)} x^{4} + C a^{3} + 3 \, A a^{2} c + 2 \, {\left(C a^{2} c + 3 \, A a c^{2}\right)} x^{2}\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right) + {\left(C a^{3} c - 5 \, A a^{2} c^{2}\right)} x}{8 \, {\left(a^{3} c^{4} x^{4} + 2 \, a^{4} c^{3} x^{2} + a^{5} c^{2}\right)}}\right]"," ",0,"[-1/16*(4*B*a^3*c - 2*(C*a^2*c^2 + 3*A*a*c^3)*x^3 + ((C*a*c^2 + 3*A*c^3)*x^4 + C*a^3 + 3*A*a^2*c + 2*(C*a^2*c + 3*A*a*c^2)*x^2)*sqrt(-a*c)*log((c*x^2 - 2*sqrt(-a*c)*x - a)/(c*x^2 + a)) + 2*(C*a^3*c - 5*A*a^2*c^2)*x)/(a^3*c^4*x^4 + 2*a^4*c^3*x^2 + a^5*c^2), -1/8*(2*B*a^3*c - (C*a^2*c^2 + 3*A*a*c^3)*x^3 - ((C*a*c^2 + 3*A*c^3)*x^4 + C*a^3 + 3*A*a^2*c + 2*(C*a^2*c + 3*A*a*c^2)*x^2)*sqrt(a*c)*arctan(sqrt(a*c)*x/a) + (C*a^3*c - 5*A*a^2*c^2)*x)/(a^3*c^4*x^4 + 2*a^4*c^3*x^2 + a^5*c^2)]","A",0
61,-1,0,0,0.000000," ","integrate((C*x^2+B*x+A)/(e*x+d)/(c*x^2+a)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
62,-1,0,0,0.000000," ","integrate((C*x^2+B*x+A)/(e*x+d)^2/(c*x^2+a)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
63,-1,0,0,0.000000," ","integrate((C*x^2+B*x+A)/(e*x+d)^3/(c*x^2+a)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
64,1,1864,0,1.549940," ","integrate((e*x+d)^4*(C*x^2+B*x+A)/(c*x^2+a)^4,x, algorithm=""fricas"")","\left[-\frac{16 \, B a^{4} c^{3} d^{4} + 48 \, B a^{5} c^{2} d^{2} e^{2} + 16 \, B a^{6} c e^{4} - 6 \, {\left(4 \, B a^{2} c^{5} d^{3} e + 4 \, B a^{3} c^{4} d e^{3} + {\left(C a^{2} c^{5} + 5 \, A a c^{6}\right)} d^{4} + 6 \, {\left(C a^{3} c^{4} + A a^{2} c^{5}\right)} d^{2} e^{2} - {\left(11 \, C a^{4} c^{3} - A a^{3} c^{4}\right)} e^{4}\right)} x^{5} + 32 \, {\left(C a^{5} c^{2} + 2 \, A a^{4} c^{3}\right)} d^{3} e + 32 \, {\left(2 \, C a^{6} c + A a^{5} c^{2}\right)} d e^{3} + 48 \, {\left(4 \, C a^{4} c^{3} d e^{3} + B a^{4} c^{3} e^{4}\right)} x^{4} - 16 \, {\left(4 \, B a^{3} c^{4} d^{3} e - 4 \, B a^{4} c^{3} d e^{3} + {\left(C a^{3} c^{4} + 5 \, A a^{2} c^{5}\right)} d^{4} - 6 \, {\left(C a^{4} c^{3} - A a^{3} c^{4}\right)} d^{2} e^{2} - {\left(5 \, C a^{5} c^{2} + A a^{4} c^{3}\right)} e^{4}\right)} x^{3} + 48 \, {\left(2 \, C a^{4} c^{3} d^{3} e + 3 \, B a^{4} c^{3} d^{2} e^{2} + B a^{5} c^{2} e^{4} + 2 \, {\left(2 \, C a^{5} c^{2} + A a^{4} c^{3}\right)} d e^{3}\right)} x^{2} + 3 \, {\left(4 \, B a^{4} c^{2} d^{3} e + 4 \, B a^{5} c d e^{3} + {\left(4 \, B a c^{5} d^{3} e + 4 \, B a^{2} c^{4} d e^{3} + {\left(C a c^{5} + 5 \, A c^{6}\right)} d^{4} + 6 \, {\left(C a^{2} c^{4} + A a c^{5}\right)} d^{2} e^{2} + {\left(5 \, C a^{3} c^{3} + A a^{2} c^{4}\right)} e^{4}\right)} x^{6} + {\left(C a^{4} c^{2} + 5 \, A a^{3} c^{3}\right)} d^{4} + 6 \, {\left(C a^{5} c + A a^{4} c^{2}\right)} d^{2} e^{2} + {\left(5 \, C a^{6} + A a^{5} c\right)} e^{4} + 3 \, {\left(4 \, B a^{2} c^{4} d^{3} e + 4 \, B a^{3} c^{3} d e^{3} + {\left(C a^{2} c^{4} + 5 \, A a c^{5}\right)} d^{4} + 6 \, {\left(C a^{3} c^{3} + A a^{2} c^{4}\right)} d^{2} e^{2} + {\left(5 \, C a^{4} c^{2} + A a^{3} c^{3}\right)} e^{4}\right)} x^{4} + 3 \, {\left(4 \, B a^{3} c^{3} d^{3} e + 4 \, B a^{4} c^{2} d e^{3} + {\left(C a^{3} c^{3} + 5 \, A a^{2} c^{4}\right)} d^{4} + 6 \, {\left(C a^{4} c^{2} + A a^{3} c^{3}\right)} d^{2} e^{2} + {\left(5 \, C a^{5} c + A a^{4} c^{2}\right)} e^{4}\right)} x^{2}\right)} \sqrt{-a c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right) + 6 \, {\left(4 \, B a^{4} c^{3} d^{3} e + 4 \, B a^{5} c^{2} d e^{3} + {\left(C a^{4} c^{3} - 11 \, A a^{3} c^{4}\right)} d^{4} + 6 \, {\left(C a^{5} c^{2} + A a^{4} c^{3}\right)} d^{2} e^{2} + {\left(5 \, C a^{6} c + A a^{5} c^{2}\right)} e^{4}\right)} x}{96 \, {\left(a^{4} c^{7} x^{6} + 3 \, a^{5} c^{6} x^{4} + 3 \, a^{6} c^{5} x^{2} + a^{7} c^{4}\right)}}, -\frac{8 \, B a^{4} c^{3} d^{4} + 24 \, B a^{5} c^{2} d^{2} e^{2} + 8 \, B a^{6} c e^{4} - 3 \, {\left(4 \, B a^{2} c^{5} d^{3} e + 4 \, B a^{3} c^{4} d e^{3} + {\left(C a^{2} c^{5} + 5 \, A a c^{6}\right)} d^{4} + 6 \, {\left(C a^{3} c^{4} + A a^{2} c^{5}\right)} d^{2} e^{2} - {\left(11 \, C a^{4} c^{3} - A a^{3} c^{4}\right)} e^{4}\right)} x^{5} + 16 \, {\left(C a^{5} c^{2} + 2 \, A a^{4} c^{3}\right)} d^{3} e + 16 \, {\left(2 \, C a^{6} c + A a^{5} c^{2}\right)} d e^{3} + 24 \, {\left(4 \, C a^{4} c^{3} d e^{3} + B a^{4} c^{3} e^{4}\right)} x^{4} - 8 \, {\left(4 \, B a^{3} c^{4} d^{3} e - 4 \, B a^{4} c^{3} d e^{3} + {\left(C a^{3} c^{4} + 5 \, A a^{2} c^{5}\right)} d^{4} - 6 \, {\left(C a^{4} c^{3} - A a^{3} c^{4}\right)} d^{2} e^{2} - {\left(5 \, C a^{5} c^{2} + A a^{4} c^{3}\right)} e^{4}\right)} x^{3} + 24 \, {\left(2 \, C a^{4} c^{3} d^{3} e + 3 \, B a^{4} c^{3} d^{2} e^{2} + B a^{5} c^{2} e^{4} + 2 \, {\left(2 \, C a^{5} c^{2} + A a^{4} c^{3}\right)} d e^{3}\right)} x^{2} - 3 \, {\left(4 \, B a^{4} c^{2} d^{3} e + 4 \, B a^{5} c d e^{3} + {\left(4 \, B a c^{5} d^{3} e + 4 \, B a^{2} c^{4} d e^{3} + {\left(C a c^{5} + 5 \, A c^{6}\right)} d^{4} + 6 \, {\left(C a^{2} c^{4} + A a c^{5}\right)} d^{2} e^{2} + {\left(5 \, C a^{3} c^{3} + A a^{2} c^{4}\right)} e^{4}\right)} x^{6} + {\left(C a^{4} c^{2} + 5 \, A a^{3} c^{3}\right)} d^{4} + 6 \, {\left(C a^{5} c + A a^{4} c^{2}\right)} d^{2} e^{2} + {\left(5 \, C a^{6} + A a^{5} c\right)} e^{4} + 3 \, {\left(4 \, B a^{2} c^{4} d^{3} e + 4 \, B a^{3} c^{3} d e^{3} + {\left(C a^{2} c^{4} + 5 \, A a c^{5}\right)} d^{4} + 6 \, {\left(C a^{3} c^{3} + A a^{2} c^{4}\right)} d^{2} e^{2} + {\left(5 \, C a^{4} c^{2} + A a^{3} c^{3}\right)} e^{4}\right)} x^{4} + 3 \, {\left(4 \, B a^{3} c^{3} d^{3} e + 4 \, B a^{4} c^{2} d e^{3} + {\left(C a^{3} c^{3} + 5 \, A a^{2} c^{4}\right)} d^{4} + 6 \, {\left(C a^{4} c^{2} + A a^{3} c^{3}\right)} d^{2} e^{2} + {\left(5 \, C a^{5} c + A a^{4} c^{2}\right)} e^{4}\right)} x^{2}\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right) + 3 \, {\left(4 \, B a^{4} c^{3} d^{3} e + 4 \, B a^{5} c^{2} d e^{3} + {\left(C a^{4} c^{3} - 11 \, A a^{3} c^{4}\right)} d^{4} + 6 \, {\left(C a^{5} c^{2} + A a^{4} c^{3}\right)} d^{2} e^{2} + {\left(5 \, C a^{6} c + A a^{5} c^{2}\right)} e^{4}\right)} x}{48 \, {\left(a^{4} c^{7} x^{6} + 3 \, a^{5} c^{6} x^{4} + 3 \, a^{6} c^{5} x^{2} + a^{7} c^{4}\right)}}\right]"," ",0,"[-1/96*(16*B*a^4*c^3*d^4 + 48*B*a^5*c^2*d^2*e^2 + 16*B*a^6*c*e^4 - 6*(4*B*a^2*c^5*d^3*e + 4*B*a^3*c^4*d*e^3 + (C*a^2*c^5 + 5*A*a*c^6)*d^4 + 6*(C*a^3*c^4 + A*a^2*c^5)*d^2*e^2 - (11*C*a^4*c^3 - A*a^3*c^4)*e^4)*x^5 + 32*(C*a^5*c^2 + 2*A*a^4*c^3)*d^3*e + 32*(2*C*a^6*c + A*a^5*c^2)*d*e^3 + 48*(4*C*a^4*c^3*d*e^3 + B*a^4*c^3*e^4)*x^4 - 16*(4*B*a^3*c^4*d^3*e - 4*B*a^4*c^3*d*e^3 + (C*a^3*c^4 + 5*A*a^2*c^5)*d^4 - 6*(C*a^4*c^3 - A*a^3*c^4)*d^2*e^2 - (5*C*a^5*c^2 + A*a^4*c^3)*e^4)*x^3 + 48*(2*C*a^4*c^3*d^3*e + 3*B*a^4*c^3*d^2*e^2 + B*a^5*c^2*e^4 + 2*(2*C*a^5*c^2 + A*a^4*c^3)*d*e^3)*x^2 + 3*(4*B*a^4*c^2*d^3*e + 4*B*a^5*c*d*e^3 + (4*B*a*c^5*d^3*e + 4*B*a^2*c^4*d*e^3 + (C*a*c^5 + 5*A*c^6)*d^4 + 6*(C*a^2*c^4 + A*a*c^5)*d^2*e^2 + (5*C*a^3*c^3 + A*a^2*c^4)*e^4)*x^6 + (C*a^4*c^2 + 5*A*a^3*c^3)*d^4 + 6*(C*a^5*c + A*a^4*c^2)*d^2*e^2 + (5*C*a^6 + A*a^5*c)*e^4 + 3*(4*B*a^2*c^4*d^3*e + 4*B*a^3*c^3*d*e^3 + (C*a^2*c^4 + 5*A*a*c^5)*d^4 + 6*(C*a^3*c^3 + A*a^2*c^4)*d^2*e^2 + (5*C*a^4*c^2 + A*a^3*c^3)*e^4)*x^4 + 3*(4*B*a^3*c^3*d^3*e + 4*B*a^4*c^2*d*e^3 + (C*a^3*c^3 + 5*A*a^2*c^4)*d^4 + 6*(C*a^4*c^2 + A*a^3*c^3)*d^2*e^2 + (5*C*a^5*c + A*a^4*c^2)*e^4)*x^2)*sqrt(-a*c)*log((c*x^2 - 2*sqrt(-a*c)*x - a)/(c*x^2 + a)) + 6*(4*B*a^4*c^3*d^3*e + 4*B*a^5*c^2*d*e^3 + (C*a^4*c^3 - 11*A*a^3*c^4)*d^4 + 6*(C*a^5*c^2 + A*a^4*c^3)*d^2*e^2 + (5*C*a^6*c + A*a^5*c^2)*e^4)*x)/(a^4*c^7*x^6 + 3*a^5*c^6*x^4 + 3*a^6*c^5*x^2 + a^7*c^4), -1/48*(8*B*a^4*c^3*d^4 + 24*B*a^5*c^2*d^2*e^2 + 8*B*a^6*c*e^4 - 3*(4*B*a^2*c^5*d^3*e + 4*B*a^3*c^4*d*e^3 + (C*a^2*c^5 + 5*A*a*c^6)*d^4 + 6*(C*a^3*c^4 + A*a^2*c^5)*d^2*e^2 - (11*C*a^4*c^3 - A*a^3*c^4)*e^4)*x^5 + 16*(C*a^5*c^2 + 2*A*a^4*c^3)*d^3*e + 16*(2*C*a^6*c + A*a^5*c^2)*d*e^3 + 24*(4*C*a^4*c^3*d*e^3 + B*a^4*c^3*e^4)*x^4 - 8*(4*B*a^3*c^4*d^3*e - 4*B*a^4*c^3*d*e^3 + (C*a^3*c^4 + 5*A*a^2*c^5)*d^4 - 6*(C*a^4*c^3 - A*a^3*c^4)*d^2*e^2 - (5*C*a^5*c^2 + A*a^4*c^3)*e^4)*x^3 + 24*(2*C*a^4*c^3*d^3*e + 3*B*a^4*c^3*d^2*e^2 + B*a^5*c^2*e^4 + 2*(2*C*a^5*c^2 + A*a^4*c^3)*d*e^3)*x^2 - 3*(4*B*a^4*c^2*d^3*e + 4*B*a^5*c*d*e^3 + (4*B*a*c^5*d^3*e + 4*B*a^2*c^4*d*e^3 + (C*a*c^5 + 5*A*c^6)*d^4 + 6*(C*a^2*c^4 + A*a*c^5)*d^2*e^2 + (5*C*a^3*c^3 + A*a^2*c^4)*e^4)*x^6 + (C*a^4*c^2 + 5*A*a^3*c^3)*d^4 + 6*(C*a^5*c + A*a^4*c^2)*d^2*e^2 + (5*C*a^6 + A*a^5*c)*e^4 + 3*(4*B*a^2*c^4*d^3*e + 4*B*a^3*c^3*d*e^3 + (C*a^2*c^4 + 5*A*a*c^5)*d^4 + 6*(C*a^3*c^3 + A*a^2*c^4)*d^2*e^2 + (5*C*a^4*c^2 + A*a^3*c^3)*e^4)*x^4 + 3*(4*B*a^3*c^3*d^3*e + 4*B*a^4*c^2*d*e^3 + (C*a^3*c^3 + 5*A*a^2*c^4)*d^4 + 6*(C*a^4*c^2 + A*a^3*c^3)*d^2*e^2 + (5*C*a^5*c + A*a^4*c^2)*e^4)*x^2)*sqrt(a*c)*arctan(sqrt(a*c)*x/a) + 3*(4*B*a^4*c^3*d^3*e + 4*B*a^5*c^2*d*e^3 + (C*a^4*c^3 - 11*A*a^3*c^4)*d^4 + 6*(C*a^5*c^2 + A*a^4*c^3)*d^2*e^2 + (5*C*a^6*c + A*a^5*c^2)*e^4)*x)/(a^4*c^7*x^6 + 3*a^5*c^6*x^4 + 3*a^6*c^5*x^2 + a^7*c^4)]","B",0
65,1,1378,0,1.673490," ","integrate((e*x+d)^3*(C*x^2+B*x+A)/(c*x^2+a)^4,x, algorithm=""fricas"")","\left[-\frac{48 \, C a^{4} c^{2} e^{3} x^{4} + 16 \, B a^{4} c^{2} d^{3} + 24 \, B a^{5} c d e^{2} - 6 \, {\left(3 \, B a^{2} c^{4} d^{2} e + B a^{3} c^{3} e^{3} + {\left(C a^{2} c^{4} + 5 \, A a c^{5}\right)} d^{3} + 3 \, {\left(C a^{3} c^{3} + A a^{2} c^{4}\right)} d e^{2}\right)} x^{5} + 24 \, {\left(C a^{5} c + 2 \, A a^{4} c^{2}\right)} d^{2} e + 8 \, {\left(2 \, C a^{6} + A a^{5} c\right)} e^{3} - 16 \, {\left(3 \, B a^{3} c^{3} d^{2} e - B a^{4} c^{2} e^{3} + {\left(C a^{3} c^{3} + 5 \, A a^{2} c^{4}\right)} d^{3} - 3 \, {\left(C a^{4} c^{2} - A a^{3} c^{3}\right)} d e^{2}\right)} x^{3} + 24 \, {\left(3 \, C a^{4} c^{2} d^{2} e + 3 \, B a^{4} c^{2} d e^{2} + {\left(2 \, C a^{5} c + A a^{4} c^{2}\right)} e^{3}\right)} x^{2} + 3 \, {\left(3 \, B a^{4} c d^{2} e + B a^{5} e^{3} + {\left(3 \, B a c^{4} d^{2} e + B a^{2} c^{3} e^{3} + {\left(C a c^{4} + 5 \, A c^{5}\right)} d^{3} + 3 \, {\left(C a^{2} c^{3} + A a c^{4}\right)} d e^{2}\right)} x^{6} + 3 \, {\left(3 \, B a^{2} c^{3} d^{2} e + B a^{3} c^{2} e^{3} + {\left(C a^{2} c^{3} + 5 \, A a c^{4}\right)} d^{3} + 3 \, {\left(C a^{3} c^{2} + A a^{2} c^{3}\right)} d e^{2}\right)} x^{4} + {\left(C a^{4} c + 5 \, A a^{3} c^{2}\right)} d^{3} + 3 \, {\left(C a^{5} + A a^{4} c\right)} d e^{2} + 3 \, {\left(3 \, B a^{3} c^{2} d^{2} e + B a^{4} c e^{3} + {\left(C a^{3} c^{2} + 5 \, A a^{2} c^{3}\right)} d^{3} + 3 \, {\left(C a^{4} c + A a^{3} c^{2}\right)} d e^{2}\right)} x^{2}\right)} \sqrt{-a c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right) + 6 \, {\left(3 \, B a^{4} c^{2} d^{2} e + B a^{5} c e^{3} + {\left(C a^{4} c^{2} - 11 \, A a^{3} c^{3}\right)} d^{3} + 3 \, {\left(C a^{5} c + A a^{4} c^{2}\right)} d e^{2}\right)} x}{96 \, {\left(a^{4} c^{6} x^{6} + 3 \, a^{5} c^{5} x^{4} + 3 \, a^{6} c^{4} x^{2} + a^{7} c^{3}\right)}}, -\frac{24 \, C a^{4} c^{2} e^{3} x^{4} + 8 \, B a^{4} c^{2} d^{3} + 12 \, B a^{5} c d e^{2} - 3 \, {\left(3 \, B a^{2} c^{4} d^{2} e + B a^{3} c^{3} e^{3} + {\left(C a^{2} c^{4} + 5 \, A a c^{5}\right)} d^{3} + 3 \, {\left(C a^{3} c^{3} + A a^{2} c^{4}\right)} d e^{2}\right)} x^{5} + 12 \, {\left(C a^{5} c + 2 \, A a^{4} c^{2}\right)} d^{2} e + 4 \, {\left(2 \, C a^{6} + A a^{5} c\right)} e^{3} - 8 \, {\left(3 \, B a^{3} c^{3} d^{2} e - B a^{4} c^{2} e^{3} + {\left(C a^{3} c^{3} + 5 \, A a^{2} c^{4}\right)} d^{3} - 3 \, {\left(C a^{4} c^{2} - A a^{3} c^{3}\right)} d e^{2}\right)} x^{3} + 12 \, {\left(3 \, C a^{4} c^{2} d^{2} e + 3 \, B a^{4} c^{2} d e^{2} + {\left(2 \, C a^{5} c + A a^{4} c^{2}\right)} e^{3}\right)} x^{2} - 3 \, {\left(3 \, B a^{4} c d^{2} e + B a^{5} e^{3} + {\left(3 \, B a c^{4} d^{2} e + B a^{2} c^{3} e^{3} + {\left(C a c^{4} + 5 \, A c^{5}\right)} d^{3} + 3 \, {\left(C a^{2} c^{3} + A a c^{4}\right)} d e^{2}\right)} x^{6} + 3 \, {\left(3 \, B a^{2} c^{3} d^{2} e + B a^{3} c^{2} e^{3} + {\left(C a^{2} c^{3} + 5 \, A a c^{4}\right)} d^{3} + 3 \, {\left(C a^{3} c^{2} + A a^{2} c^{3}\right)} d e^{2}\right)} x^{4} + {\left(C a^{4} c + 5 \, A a^{3} c^{2}\right)} d^{3} + 3 \, {\left(C a^{5} + A a^{4} c\right)} d e^{2} + 3 \, {\left(3 \, B a^{3} c^{2} d^{2} e + B a^{4} c e^{3} + {\left(C a^{3} c^{2} + 5 \, A a^{2} c^{3}\right)} d^{3} + 3 \, {\left(C a^{4} c + A a^{3} c^{2}\right)} d e^{2}\right)} x^{2}\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right) + 3 \, {\left(3 \, B a^{4} c^{2} d^{2} e + B a^{5} c e^{3} + {\left(C a^{4} c^{2} - 11 \, A a^{3} c^{3}\right)} d^{3} + 3 \, {\left(C a^{5} c + A a^{4} c^{2}\right)} d e^{2}\right)} x}{48 \, {\left(a^{4} c^{6} x^{6} + 3 \, a^{5} c^{5} x^{4} + 3 \, a^{6} c^{4} x^{2} + a^{7} c^{3}\right)}}\right]"," ",0,"[-1/96*(48*C*a^4*c^2*e^3*x^4 + 16*B*a^4*c^2*d^3 + 24*B*a^5*c*d*e^2 - 6*(3*B*a^2*c^4*d^2*e + B*a^3*c^3*e^3 + (C*a^2*c^4 + 5*A*a*c^5)*d^3 + 3*(C*a^3*c^3 + A*a^2*c^4)*d*e^2)*x^5 + 24*(C*a^5*c + 2*A*a^4*c^2)*d^2*e + 8*(2*C*a^6 + A*a^5*c)*e^3 - 16*(3*B*a^3*c^3*d^2*e - B*a^4*c^2*e^3 + (C*a^3*c^3 + 5*A*a^2*c^4)*d^3 - 3*(C*a^4*c^2 - A*a^3*c^3)*d*e^2)*x^3 + 24*(3*C*a^4*c^2*d^2*e + 3*B*a^4*c^2*d*e^2 + (2*C*a^5*c + A*a^4*c^2)*e^3)*x^2 + 3*(3*B*a^4*c*d^2*e + B*a^5*e^3 + (3*B*a*c^4*d^2*e + B*a^2*c^3*e^3 + (C*a*c^4 + 5*A*c^5)*d^3 + 3*(C*a^2*c^3 + A*a*c^4)*d*e^2)*x^6 + 3*(3*B*a^2*c^3*d^2*e + B*a^3*c^2*e^3 + (C*a^2*c^3 + 5*A*a*c^4)*d^3 + 3*(C*a^3*c^2 + A*a^2*c^3)*d*e^2)*x^4 + (C*a^4*c + 5*A*a^3*c^2)*d^3 + 3*(C*a^5 + A*a^4*c)*d*e^2 + 3*(3*B*a^3*c^2*d^2*e + B*a^4*c*e^3 + (C*a^3*c^2 + 5*A*a^2*c^3)*d^3 + 3*(C*a^4*c + A*a^3*c^2)*d*e^2)*x^2)*sqrt(-a*c)*log((c*x^2 - 2*sqrt(-a*c)*x - a)/(c*x^2 + a)) + 6*(3*B*a^4*c^2*d^2*e + B*a^5*c*e^3 + (C*a^4*c^2 - 11*A*a^3*c^3)*d^3 + 3*(C*a^5*c + A*a^4*c^2)*d*e^2)*x)/(a^4*c^6*x^6 + 3*a^5*c^5*x^4 + 3*a^6*c^4*x^2 + a^7*c^3), -1/48*(24*C*a^4*c^2*e^3*x^4 + 8*B*a^4*c^2*d^3 + 12*B*a^5*c*d*e^2 - 3*(3*B*a^2*c^4*d^2*e + B*a^3*c^3*e^3 + (C*a^2*c^4 + 5*A*a*c^5)*d^3 + 3*(C*a^3*c^3 + A*a^2*c^4)*d*e^2)*x^5 + 12*(C*a^5*c + 2*A*a^4*c^2)*d^2*e + 4*(2*C*a^6 + A*a^5*c)*e^3 - 8*(3*B*a^3*c^3*d^2*e - B*a^4*c^2*e^3 + (C*a^3*c^3 + 5*A*a^2*c^4)*d^3 - 3*(C*a^4*c^2 - A*a^3*c^3)*d*e^2)*x^3 + 12*(3*C*a^4*c^2*d^2*e + 3*B*a^4*c^2*d*e^2 + (2*C*a^5*c + A*a^4*c^2)*e^3)*x^2 - 3*(3*B*a^4*c*d^2*e + B*a^5*e^3 + (3*B*a*c^4*d^2*e + B*a^2*c^3*e^3 + (C*a*c^4 + 5*A*c^5)*d^3 + 3*(C*a^2*c^3 + A*a*c^4)*d*e^2)*x^6 + 3*(3*B*a^2*c^3*d^2*e + B*a^3*c^2*e^3 + (C*a^2*c^3 + 5*A*a*c^4)*d^3 + 3*(C*a^3*c^2 + A*a^2*c^3)*d*e^2)*x^4 + (C*a^4*c + 5*A*a^3*c^2)*d^3 + 3*(C*a^5 + A*a^4*c)*d*e^2 + 3*(3*B*a^3*c^2*d^2*e + B*a^4*c*e^3 + (C*a^3*c^2 + 5*A*a^2*c^3)*d^3 + 3*(C*a^4*c + A*a^3*c^2)*d*e^2)*x^2)*sqrt(a*c)*arctan(sqrt(a*c)*x/a) + 3*(3*B*a^4*c^2*d^2*e + B*a^5*c*e^3 + (C*a^4*c^2 - 11*A*a^3*c^3)*d^3 + 3*(C*a^5*c + A*a^4*c^2)*d*e^2)*x)/(a^4*c^6*x^6 + 3*a^5*c^5*x^4 + 3*a^6*c^4*x^2 + a^7*c^3)]","B",0
66,1,1062,0,0.920961," ","integrate((e*x+d)^2*(C*x^2+B*x+A)/(c*x^2+a)^4,x, algorithm=""fricas"")","\left[-\frac{16 \, B a^{4} c^{2} d^{2} + 8 \, B a^{5} c e^{2} - 6 \, {\left(2 \, B a^{2} c^{4} d e + {\left(C a^{2} c^{4} + 5 \, A a c^{5}\right)} d^{2} + {\left(C a^{3} c^{3} + A a^{2} c^{4}\right)} e^{2}\right)} x^{5} - 16 \, {\left(2 \, B a^{3} c^{3} d e + {\left(C a^{3} c^{3} + 5 \, A a^{2} c^{4}\right)} d^{2} - {\left(C a^{4} c^{2} - A a^{3} c^{3}\right)} e^{2}\right)} x^{3} + 16 \, {\left(C a^{5} c + 2 \, A a^{4} c^{2}\right)} d e + 24 \, {\left(2 \, C a^{4} c^{2} d e + B a^{4} c^{2} e^{2}\right)} x^{2} + 3 \, {\left(2 \, B a^{4} c d e + {\left(2 \, B a c^{4} d e + {\left(C a c^{4} + 5 \, A c^{5}\right)} d^{2} + {\left(C a^{2} c^{3} + A a c^{4}\right)} e^{2}\right)} x^{6} + 3 \, {\left(2 \, B a^{2} c^{3} d e + {\left(C a^{2} c^{3} + 5 \, A a c^{4}\right)} d^{2} + {\left(C a^{3} c^{2} + A a^{2} c^{3}\right)} e^{2}\right)} x^{4} + {\left(C a^{4} c + 5 \, A a^{3} c^{2}\right)} d^{2} + {\left(C a^{5} + A a^{4} c\right)} e^{2} + 3 \, {\left(2 \, B a^{3} c^{2} d e + {\left(C a^{3} c^{2} + 5 \, A a^{2} c^{3}\right)} d^{2} + {\left(C a^{4} c + A a^{3} c^{2}\right)} e^{2}\right)} x^{2}\right)} \sqrt{-a c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right) + 6 \, {\left(2 \, B a^{4} c^{2} d e + {\left(C a^{4} c^{2} - 11 \, A a^{3} c^{3}\right)} d^{2} + {\left(C a^{5} c + A a^{4} c^{2}\right)} e^{2}\right)} x}{96 \, {\left(a^{4} c^{6} x^{6} + 3 \, a^{5} c^{5} x^{4} + 3 \, a^{6} c^{4} x^{2} + a^{7} c^{3}\right)}}, -\frac{8 \, B a^{4} c^{2} d^{2} + 4 \, B a^{5} c e^{2} - 3 \, {\left(2 \, B a^{2} c^{4} d e + {\left(C a^{2} c^{4} + 5 \, A a c^{5}\right)} d^{2} + {\left(C a^{3} c^{3} + A a^{2} c^{4}\right)} e^{2}\right)} x^{5} - 8 \, {\left(2 \, B a^{3} c^{3} d e + {\left(C a^{3} c^{3} + 5 \, A a^{2} c^{4}\right)} d^{2} - {\left(C a^{4} c^{2} - A a^{3} c^{3}\right)} e^{2}\right)} x^{3} + 8 \, {\left(C a^{5} c + 2 \, A a^{4} c^{2}\right)} d e + 12 \, {\left(2 \, C a^{4} c^{2} d e + B a^{4} c^{2} e^{2}\right)} x^{2} - 3 \, {\left(2 \, B a^{4} c d e + {\left(2 \, B a c^{4} d e + {\left(C a c^{4} + 5 \, A c^{5}\right)} d^{2} + {\left(C a^{2} c^{3} + A a c^{4}\right)} e^{2}\right)} x^{6} + 3 \, {\left(2 \, B a^{2} c^{3} d e + {\left(C a^{2} c^{3} + 5 \, A a c^{4}\right)} d^{2} + {\left(C a^{3} c^{2} + A a^{2} c^{3}\right)} e^{2}\right)} x^{4} + {\left(C a^{4} c + 5 \, A a^{3} c^{2}\right)} d^{2} + {\left(C a^{5} + A a^{4} c\right)} e^{2} + 3 \, {\left(2 \, B a^{3} c^{2} d e + {\left(C a^{3} c^{2} + 5 \, A a^{2} c^{3}\right)} d^{2} + {\left(C a^{4} c + A a^{3} c^{2}\right)} e^{2}\right)} x^{2}\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right) + 3 \, {\left(2 \, B a^{4} c^{2} d e + {\left(C a^{4} c^{2} - 11 \, A a^{3} c^{3}\right)} d^{2} + {\left(C a^{5} c + A a^{4} c^{2}\right)} e^{2}\right)} x}{48 \, {\left(a^{4} c^{6} x^{6} + 3 \, a^{5} c^{5} x^{4} + 3 \, a^{6} c^{4} x^{2} + a^{7} c^{3}\right)}}\right]"," ",0,"[-1/96*(16*B*a^4*c^2*d^2 + 8*B*a^5*c*e^2 - 6*(2*B*a^2*c^4*d*e + (C*a^2*c^4 + 5*A*a*c^5)*d^2 + (C*a^3*c^3 + A*a^2*c^4)*e^2)*x^5 - 16*(2*B*a^3*c^3*d*e + (C*a^3*c^3 + 5*A*a^2*c^4)*d^2 - (C*a^4*c^2 - A*a^3*c^3)*e^2)*x^3 + 16*(C*a^5*c + 2*A*a^4*c^2)*d*e + 24*(2*C*a^4*c^2*d*e + B*a^4*c^2*e^2)*x^2 + 3*(2*B*a^4*c*d*e + (2*B*a*c^4*d*e + (C*a*c^4 + 5*A*c^5)*d^2 + (C*a^2*c^3 + A*a*c^4)*e^2)*x^6 + 3*(2*B*a^2*c^3*d*e + (C*a^2*c^3 + 5*A*a*c^4)*d^2 + (C*a^3*c^2 + A*a^2*c^3)*e^2)*x^4 + (C*a^4*c + 5*A*a^3*c^2)*d^2 + (C*a^5 + A*a^4*c)*e^2 + 3*(2*B*a^3*c^2*d*e + (C*a^3*c^2 + 5*A*a^2*c^3)*d^2 + (C*a^4*c + A*a^3*c^2)*e^2)*x^2)*sqrt(-a*c)*log((c*x^2 - 2*sqrt(-a*c)*x - a)/(c*x^2 + a)) + 6*(2*B*a^4*c^2*d*e + (C*a^4*c^2 - 11*A*a^3*c^3)*d^2 + (C*a^5*c + A*a^4*c^2)*e^2)*x)/(a^4*c^6*x^6 + 3*a^5*c^5*x^4 + 3*a^6*c^4*x^2 + a^7*c^3), -1/48*(8*B*a^4*c^2*d^2 + 4*B*a^5*c*e^2 - 3*(2*B*a^2*c^4*d*e + (C*a^2*c^4 + 5*A*a*c^5)*d^2 + (C*a^3*c^3 + A*a^2*c^4)*e^2)*x^5 - 8*(2*B*a^3*c^3*d*e + (C*a^3*c^3 + 5*A*a^2*c^4)*d^2 - (C*a^4*c^2 - A*a^3*c^3)*e^2)*x^3 + 8*(C*a^5*c + 2*A*a^4*c^2)*d*e + 12*(2*C*a^4*c^2*d*e + B*a^4*c^2*e^2)*x^2 - 3*(2*B*a^4*c*d*e + (2*B*a*c^4*d*e + (C*a*c^4 + 5*A*c^5)*d^2 + (C*a^2*c^3 + A*a*c^4)*e^2)*x^6 + 3*(2*B*a^2*c^3*d*e + (C*a^2*c^3 + 5*A*a*c^4)*d^2 + (C*a^3*c^2 + A*a^2*c^3)*e^2)*x^4 + (C*a^4*c + 5*A*a^3*c^2)*d^2 + (C*a^5 + A*a^4*c)*e^2 + 3*(2*B*a^3*c^2*d*e + (C*a^3*c^2 + 5*A*a^2*c^3)*d^2 + (C*a^4*c + A*a^3*c^2)*e^2)*x^2)*sqrt(a*c)*arctan(sqrt(a*c)*x/a) + 3*(2*B*a^4*c^2*d*e + (C*a^4*c^2 - 11*A*a^3*c^3)*d^2 + (C*a^5*c + A*a^4*c^2)*e^2)*x)/(a^4*c^6*x^6 + 3*a^5*c^5*x^4 + 3*a^6*c^4*x^2 + a^7*c^3)]","B",0
67,1,636,0,0.595154," ","integrate((e*x+d)*(C*x^2+B*x+A)/(c*x^2+a)^4,x, algorithm=""fricas"")","\left[-\frac{24 \, C a^{4} c e x^{2} + 16 \, B a^{4} c d - 6 \, {\left(B a^{2} c^{3} e + {\left(C a^{2} c^{3} + 5 \, A a c^{4}\right)} d\right)} x^{5} - 16 \, {\left(B a^{3} c^{2} e + {\left(C a^{3} c^{2} + 5 \, A a^{2} c^{3}\right)} d\right)} x^{3} + 3 \, {\left({\left(B a c^{3} e + {\left(C a c^{3} + 5 \, A c^{4}\right)} d\right)} x^{6} + B a^{4} e + 3 \, {\left(B a^{2} c^{2} e + {\left(C a^{2} c^{2} + 5 \, A a c^{3}\right)} d\right)} x^{4} + 3 \, {\left(B a^{3} c e + {\left(C a^{3} c + 5 \, A a^{2} c^{2}\right)} d\right)} x^{2} + {\left(C a^{4} + 5 \, A a^{3} c\right)} d\right)} \sqrt{-a c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right) + 8 \, {\left(C a^{5} + 2 \, A a^{4} c\right)} e + 6 \, {\left(B a^{4} c e + {\left(C a^{4} c - 11 \, A a^{3} c^{2}\right)} d\right)} x}{96 \, {\left(a^{4} c^{5} x^{6} + 3 \, a^{5} c^{4} x^{4} + 3 \, a^{6} c^{3} x^{2} + a^{7} c^{2}\right)}}, -\frac{12 \, C a^{4} c e x^{2} + 8 \, B a^{4} c d - 3 \, {\left(B a^{2} c^{3} e + {\left(C a^{2} c^{3} + 5 \, A a c^{4}\right)} d\right)} x^{5} - 8 \, {\left(B a^{3} c^{2} e + {\left(C a^{3} c^{2} + 5 \, A a^{2} c^{3}\right)} d\right)} x^{3} - 3 \, {\left({\left(B a c^{3} e + {\left(C a c^{3} + 5 \, A c^{4}\right)} d\right)} x^{6} + B a^{4} e + 3 \, {\left(B a^{2} c^{2} e + {\left(C a^{2} c^{2} + 5 \, A a c^{3}\right)} d\right)} x^{4} + 3 \, {\left(B a^{3} c e + {\left(C a^{3} c + 5 \, A a^{2} c^{2}\right)} d\right)} x^{2} + {\left(C a^{4} + 5 \, A a^{3} c\right)} d\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right) + 4 \, {\left(C a^{5} + 2 \, A a^{4} c\right)} e + 3 \, {\left(B a^{4} c e + {\left(C a^{4} c - 11 \, A a^{3} c^{2}\right)} d\right)} x}{48 \, {\left(a^{4} c^{5} x^{6} + 3 \, a^{5} c^{4} x^{4} + 3 \, a^{6} c^{3} x^{2} + a^{7} c^{2}\right)}}\right]"," ",0,"[-1/96*(24*C*a^4*c*e*x^2 + 16*B*a^4*c*d - 6*(B*a^2*c^3*e + (C*a^2*c^3 + 5*A*a*c^4)*d)*x^5 - 16*(B*a^3*c^2*e + (C*a^3*c^2 + 5*A*a^2*c^3)*d)*x^3 + 3*((B*a*c^3*e + (C*a*c^3 + 5*A*c^4)*d)*x^6 + B*a^4*e + 3*(B*a^2*c^2*e + (C*a^2*c^2 + 5*A*a*c^3)*d)*x^4 + 3*(B*a^3*c*e + (C*a^3*c + 5*A*a^2*c^2)*d)*x^2 + (C*a^4 + 5*A*a^3*c)*d)*sqrt(-a*c)*log((c*x^2 - 2*sqrt(-a*c)*x - a)/(c*x^2 + a)) + 8*(C*a^5 + 2*A*a^4*c)*e + 6*(B*a^4*c*e + (C*a^4*c - 11*A*a^3*c^2)*d)*x)/(a^4*c^5*x^6 + 3*a^5*c^4*x^4 + 3*a^6*c^3*x^2 + a^7*c^2), -1/48*(12*C*a^4*c*e*x^2 + 8*B*a^4*c*d - 3*(B*a^2*c^3*e + (C*a^2*c^3 + 5*A*a*c^4)*d)*x^5 - 8*(B*a^3*c^2*e + (C*a^3*c^2 + 5*A*a^2*c^3)*d)*x^3 - 3*((B*a*c^3*e + (C*a*c^3 + 5*A*c^4)*d)*x^6 + B*a^4*e + 3*(B*a^2*c^2*e + (C*a^2*c^2 + 5*A*a*c^3)*d)*x^4 + 3*(B*a^3*c*e + (C*a^3*c + 5*A*a^2*c^2)*d)*x^2 + (C*a^4 + 5*A*a^3*c)*d)*sqrt(a*c)*arctan(sqrt(a*c)*x/a) + 4*(C*a^5 + 2*A*a^4*c)*e + 3*(B*a^4*c*e + (C*a^4*c - 11*A*a^3*c^2)*d)*x)/(a^4*c^5*x^6 + 3*a^5*c^4*x^4 + 3*a^6*c^3*x^2 + a^7*c^2)]","B",0
68,1,430,0,0.621917," ","integrate((C*x^2+B*x+A)/(c*x^2+a)^4,x, algorithm=""fricas"")","\left[-\frac{16 \, B a^{4} c - 6 \, {\left(C a^{2} c^{3} + 5 \, A a c^{4}\right)} x^{5} - 16 \, {\left(C a^{3} c^{2} + 5 \, A a^{2} c^{3}\right)} x^{3} + 3 \, {\left({\left(C a c^{3} + 5 \, A c^{4}\right)} x^{6} + C a^{4} + 5 \, A a^{3} c + 3 \, {\left(C a^{2} c^{2} + 5 \, A a c^{3}\right)} x^{4} + 3 \, {\left(C a^{3} c + 5 \, A a^{2} c^{2}\right)} x^{2}\right)} \sqrt{-a c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right) + 6 \, {\left(C a^{4} c - 11 \, A a^{3} c^{2}\right)} x}{96 \, {\left(a^{4} c^{5} x^{6} + 3 \, a^{5} c^{4} x^{4} + 3 \, a^{6} c^{3} x^{2} + a^{7} c^{2}\right)}}, -\frac{8 \, B a^{4} c - 3 \, {\left(C a^{2} c^{3} + 5 \, A a c^{4}\right)} x^{5} - 8 \, {\left(C a^{3} c^{2} + 5 \, A a^{2} c^{3}\right)} x^{3} - 3 \, {\left({\left(C a c^{3} + 5 \, A c^{4}\right)} x^{6} + C a^{4} + 5 \, A a^{3} c + 3 \, {\left(C a^{2} c^{2} + 5 \, A a c^{3}\right)} x^{4} + 3 \, {\left(C a^{3} c + 5 \, A a^{2} c^{2}\right)} x^{2}\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right) + 3 \, {\left(C a^{4} c - 11 \, A a^{3} c^{2}\right)} x}{48 \, {\left(a^{4} c^{5} x^{6} + 3 \, a^{5} c^{4} x^{4} + 3 \, a^{6} c^{3} x^{2} + a^{7} c^{2}\right)}}\right]"," ",0,"[-1/96*(16*B*a^4*c - 6*(C*a^2*c^3 + 5*A*a*c^4)*x^5 - 16*(C*a^3*c^2 + 5*A*a^2*c^3)*x^3 + 3*((C*a*c^3 + 5*A*c^4)*x^6 + C*a^4 + 5*A*a^3*c + 3*(C*a^2*c^2 + 5*A*a*c^3)*x^4 + 3*(C*a^3*c + 5*A*a^2*c^2)*x^2)*sqrt(-a*c)*log((c*x^2 - 2*sqrt(-a*c)*x - a)/(c*x^2 + a)) + 6*(C*a^4*c - 11*A*a^3*c^2)*x)/(a^4*c^5*x^6 + 3*a^5*c^4*x^4 + 3*a^6*c^3*x^2 + a^7*c^2), -1/48*(8*B*a^4*c - 3*(C*a^2*c^3 + 5*A*a*c^4)*x^5 - 8*(C*a^3*c^2 + 5*A*a^2*c^3)*x^3 - 3*((C*a*c^3 + 5*A*c^4)*x^6 + C*a^4 + 5*A*a^3*c + 3*(C*a^2*c^2 + 5*A*a*c^3)*x^4 + 3*(C*a^3*c + 5*A*a^2*c^2)*x^2)*sqrt(a*c)*arctan(sqrt(a*c)*x/a) + 3*(C*a^4*c - 11*A*a^3*c^2)*x)/(a^4*c^5*x^6 + 3*a^5*c^4*x^4 + 3*a^6*c^3*x^2 + a^7*c^2)]","A",0
69,1,46,0,0.916874," ","integrate(x^3*(x^2+x+1)/(x^2+1)^2,x, algorithm=""fricas"")","\frac{x^{4} + 2 \, x^{3} + x^{2} - 3 \, {\left(x^{2} + 1\right)} \arctan\left(x\right) - {\left(x^{2} + 1\right)} \log\left(x^{2} + 1\right) + 3 \, x}{2 \, {\left(x^{2} + 1\right)}}"," ",0,"1/2*(x^4 + 2*x^3 + x^2 - 3*(x^2 + 1)*arctan(x) - (x^2 + 1)*log(x^2 + 1) + 3*x)/(x^2 + 1)","A",0
70,1,40,0,0.603163," ","integrate(x^2*(x^2+x+1)/(x^2+1)^2,x, algorithm=""fricas"")","\frac{2 \, x^{3} - 2 \, {\left(x^{2} + 1\right)} \arctan\left(x\right) + {\left(x^{2} + 1\right)} \log\left(x^{2} + 1\right) + 2 \, x + 1}{2 \, {\left(x^{2} + 1\right)}}"," ",0,"1/2*(2*x^3 - 2*(x^2 + 1)*arctan(x) + (x^2 + 1)*log(x^2 + 1) + 2*x + 1)/(x^2 + 1)","A",0
71,1,33,0,0.590546," ","integrate(x*(x^2+x+1)/(x^2+1)^2,x, algorithm=""fricas"")","\frac{{\left(x^{2} + 1\right)} \arctan\left(x\right) + {\left(x^{2} + 1\right)} \log\left(x^{2} + 1\right) - x}{2 \, {\left(x^{2} + 1\right)}}"," ",0,"1/2*((x^2 + 1)*arctan(x) + (x^2 + 1)*log(x^2 + 1) - x)/(x^2 + 1)","A",0
72,1,20,0,0.731574," ","integrate((x^2+x+1)/(x^2+1)^2,x, algorithm=""fricas"")","\frac{2 \, {\left(x^{2} + 1\right)} \arctan\left(x\right) - 1}{2 \, {\left(x^{2} + 1\right)}}"," ",0,"1/2*(2*(x^2 + 1)*arctan(x) - 1)/(x^2 + 1)","A",0
73,1,41,0,1.084088," ","integrate((x^2+x+1)/x/(x^2+1)^2,x, algorithm=""fricas"")","\frac{{\left(x^{2} + 1\right)} \arctan\left(x\right) - {\left(x^{2} + 1\right)} \log\left(x^{2} + 1\right) + 2 \, {\left(x^{2} + 1\right)} \log\left(x\right) + x}{2 \, {\left(x^{2} + 1\right)}}"," ",0,"1/2*((x^2 + 1)*arctan(x) - (x^2 + 1)*log(x^2 + 1) + 2*(x^2 + 1)*log(x) + x)/(x^2 + 1)","A",0
74,1,49,0,2.965077," ","integrate((x^2+x+1)/x^2/(x^2+1)^2,x, algorithm=""fricas"")","-\frac{2 \, x^{2} + 2 \, {\left(x^{3} + x\right)} \arctan\left(x\right) + {\left(x^{3} + x\right)} \log\left(x^{2} + 1\right) - 2 \, {\left(x^{3} + x\right)} \log\left(x\right) - x + 2}{2 \, {\left(x^{3} + x\right)}}"," ",0,"-1/2*(2*x^2 + 2*(x^3 + x)*arctan(x) + (x^3 + x)*log(x^2 + 1) - 2*(x^3 + x)*log(x) - x + 2)/(x^3 + x)","A",0
75,1,61,0,0.606307," ","integrate((x^2+x+1)/x^3/(x^2+1)^2,x, algorithm=""fricas"")","-\frac{3 \, x^{3} + x^{2} + 3 \, {\left(x^{4} + x^{2}\right)} \arctan\left(x\right) - {\left(x^{4} + x^{2}\right)} \log\left(x^{2} + 1\right) + 2 \, {\left(x^{4} + x^{2}\right)} \log\left(x\right) + 2 \, x + 1}{2 \, {\left(x^{4} + x^{2}\right)}}"," ",0,"-1/2*(3*x^3 + x^2 + 3*(x^4 + x^2)*arctan(x) - (x^4 + x^2)*log(x^2 + 1) + 2*(x^4 + x^2)*log(x) + 2*x + 1)/(x^4 + x^2)","A",0
76,1,18,0,1.557057," ","integrate((x^2+2*x+1)/(x^2+1)^2,x, algorithm=""fricas"")","\frac{{\left(x^{2} + 1\right)} \arctan\left(x\right) - 1}{x^{2} + 1}"," ",0,"((x^2 + 1)*arctan(x) - 1)/(x^2 + 1)","A",0
77,1,25,0,0.957311," ","integrate((3*x^2+12*x+2)/(x^2+4)^2,x, algorithm=""fricas"")","\frac{7 \, {\left(x^{2} + 4\right)} \arctan\left(\frac{1}{2} \, x\right) - 10 \, x - 48}{8 \, {\left(x^{2} + 4\right)}}"," ",0,"1/8*(7*(x^2 + 4)*arctan(1/2*x) - 10*x - 48)/(x^2 + 4)","A",0
78,1,855,0,2.151785," ","integrate((h*x+g)^3*(f*x^2+e*x+d)*(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(6 \, a^{2} c e g^{2} h - a^{3} e h^{3} - 2 \, {\left(4 \, a c^{2} d - a^{2} c f\right)} g^{3} + 3 \, {\left(2 \, a^{2} c d - a^{3} f\right)} g h^{2}\right)} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) - 2 \, {\left(240 \, c^{3} f h^{3} x^{6} + 560 \, a c^{2} e g^{3} - 672 \, a^{2} c e g h^{2} + 280 \, {\left(3 \, c^{3} f g h^{2} + c^{3} e h^{3}\right)} x^{5} + 48 \, {\left(21 \, c^{3} f g^{2} h + 21 \, c^{3} e g h^{2} + {\left(7 \, c^{3} d + a c^{2} f\right)} h^{3}\right)} x^{4} + 336 \, {\left(5 \, a c^{2} d - 2 \, a^{2} c f\right)} g^{2} h - 32 \, {\left(7 \, a^{2} c d - 4 \, a^{3} f\right)} h^{3} + 70 \, {\left(6 \, c^{3} f g^{3} + 18 \, c^{3} e g^{2} h + a c^{2} e h^{3} + 3 \, {\left(6 \, c^{3} d + a c^{2} f\right)} g h^{2}\right)} x^{3} + 16 \, {\left(35 \, c^{3} e g^{3} + 21 \, a c^{2} e g h^{2} + 21 \, {\left(5 \, c^{3} d + a c^{2} f\right)} g^{2} h + {\left(7 \, a c^{2} d - 4 \, a^{2} c f\right)} h^{3}\right)} x^{2} + 105 \, {\left(6 \, a c^{2} e g^{2} h - a^{2} c e h^{3} + 2 \, {\left(4 \, c^{3} d + a c^{2} f\right)} g^{3} + 3 \, {\left(2 \, a c^{2} d - a^{2} c f\right)} g h^{2}\right)} x\right)} \sqrt{c x^{2} + a}}{3360 \, c^{3}}, \frac{105 \, {\left(6 \, a^{2} c e g^{2} h - a^{3} e h^{3} - 2 \, {\left(4 \, a c^{2} d - a^{2} c f\right)} g^{3} + 3 \, {\left(2 \, a^{2} c d - a^{3} f\right)} g h^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) + {\left(240 \, c^{3} f h^{3} x^{6} + 560 \, a c^{2} e g^{3} - 672 \, a^{2} c e g h^{2} + 280 \, {\left(3 \, c^{3} f g h^{2} + c^{3} e h^{3}\right)} x^{5} + 48 \, {\left(21 \, c^{3} f g^{2} h + 21 \, c^{3} e g h^{2} + {\left(7 \, c^{3} d + a c^{2} f\right)} h^{3}\right)} x^{4} + 336 \, {\left(5 \, a c^{2} d - 2 \, a^{2} c f\right)} g^{2} h - 32 \, {\left(7 \, a^{2} c d - 4 \, a^{3} f\right)} h^{3} + 70 \, {\left(6 \, c^{3} f g^{3} + 18 \, c^{3} e g^{2} h + a c^{2} e h^{3} + 3 \, {\left(6 \, c^{3} d + a c^{2} f\right)} g h^{2}\right)} x^{3} + 16 \, {\left(35 \, c^{3} e g^{3} + 21 \, a c^{2} e g h^{2} + 21 \, {\left(5 \, c^{3} d + a c^{2} f\right)} g^{2} h + {\left(7 \, a c^{2} d - 4 \, a^{2} c f\right)} h^{3}\right)} x^{2} + 105 \, {\left(6 \, a c^{2} e g^{2} h - a^{2} c e h^{3} + 2 \, {\left(4 \, c^{3} d + a c^{2} f\right)} g^{3} + 3 \, {\left(2 \, a c^{2} d - a^{2} c f\right)} g h^{2}\right)} x\right)} \sqrt{c x^{2} + a}}{1680 \, c^{3}}\right]"," ",0,"[-1/3360*(105*(6*a^2*c*e*g^2*h - a^3*e*h^3 - 2*(4*a*c^2*d - a^2*c*f)*g^3 + 3*(2*a^2*c*d - a^3*f)*g*h^2)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) - 2*(240*c^3*f*h^3*x^6 + 560*a*c^2*e*g^3 - 672*a^2*c*e*g*h^2 + 280*(3*c^3*f*g*h^2 + c^3*e*h^3)*x^5 + 48*(21*c^3*f*g^2*h + 21*c^3*e*g*h^2 + (7*c^3*d + a*c^2*f)*h^3)*x^4 + 336*(5*a*c^2*d - 2*a^2*c*f)*g^2*h - 32*(7*a^2*c*d - 4*a^3*f)*h^3 + 70*(6*c^3*f*g^3 + 18*c^3*e*g^2*h + a*c^2*e*h^3 + 3*(6*c^3*d + a*c^2*f)*g*h^2)*x^3 + 16*(35*c^3*e*g^3 + 21*a*c^2*e*g*h^2 + 21*(5*c^3*d + a*c^2*f)*g^2*h + (7*a*c^2*d - 4*a^2*c*f)*h^3)*x^2 + 105*(6*a*c^2*e*g^2*h - a^2*c*e*h^3 + 2*(4*c^3*d + a*c^2*f)*g^3 + 3*(2*a*c^2*d - a^2*c*f)*g*h^2)*x)*sqrt(c*x^2 + a))/c^3, 1/1680*(105*(6*a^2*c*e*g^2*h - a^3*e*h^3 - 2*(4*a*c^2*d - a^2*c*f)*g^3 + 3*(2*a^2*c*d - a^3*f)*g*h^2)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) + (240*c^3*f*h^3*x^6 + 560*a*c^2*e*g^3 - 672*a^2*c*e*g*h^2 + 280*(3*c^3*f*g*h^2 + c^3*e*h^3)*x^5 + 48*(21*c^3*f*g^2*h + 21*c^3*e*g*h^2 + (7*c^3*d + a*c^2*f)*h^3)*x^4 + 336*(5*a*c^2*d - 2*a^2*c*f)*g^2*h - 32*(7*a^2*c*d - 4*a^3*f)*h^3 + 70*(6*c^3*f*g^3 + 18*c^3*e*g^2*h + a*c^2*e*h^3 + 3*(6*c^3*d + a*c^2*f)*g*h^2)*x^3 + 16*(35*c^3*e*g^3 + 21*a*c^2*e*g*h^2 + 21*(5*c^3*d + a*c^2*f)*g^2*h + (7*a*c^2*d - 4*a^2*c*f)*h^3)*x^2 + 105*(6*a*c^2*e*g^2*h - a^2*c*e*h^3 + 2*(4*c^3*d + a*c^2*f)*g^3 + 3*(2*a*c^2*d - a^2*c*f)*g*h^2)*x)*sqrt(c*x^2 + a))/c^3]","A",0
79,1,595,0,0.799679," ","integrate((h*x+g)^2*(f*x^2+e*x+d)*(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(4 \, a^{2} c e g h - 2 \, {\left(4 \, a c^{2} d - a^{2} c f\right)} g^{2} + {\left(2 \, a^{2} c d - a^{3} f\right)} h^{2}\right)} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) - 2 \, {\left(40 \, c^{3} f h^{2} x^{5} + 80 \, a c^{2} e g^{2} - 32 \, a^{2} c e h^{2} + 48 \, {\left(2 \, c^{3} f g h + c^{3} e h^{2}\right)} x^{4} + 10 \, {\left(6 \, c^{3} f g^{2} + 12 \, c^{3} e g h + {\left(6 \, c^{3} d + a c^{2} f\right)} h^{2}\right)} x^{3} + 32 \, {\left(5 \, a c^{2} d - 2 \, a^{2} c f\right)} g h + 16 \, {\left(5 \, c^{3} e g^{2} + a c^{2} e h^{2} + 2 \, {\left(5 \, c^{3} d + a c^{2} f\right)} g h\right)} x^{2} + 15 \, {\left(4 \, a c^{2} e g h + 2 \, {\left(4 \, c^{3} d + a c^{2} f\right)} g^{2} + {\left(2 \, a c^{2} d - a^{2} c f\right)} h^{2}\right)} x\right)} \sqrt{c x^{2} + a}}{480 \, c^{3}}, \frac{15 \, {\left(4 \, a^{2} c e g h - 2 \, {\left(4 \, a c^{2} d - a^{2} c f\right)} g^{2} + {\left(2 \, a^{2} c d - a^{3} f\right)} h^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) + {\left(40 \, c^{3} f h^{2} x^{5} + 80 \, a c^{2} e g^{2} - 32 \, a^{2} c e h^{2} + 48 \, {\left(2 \, c^{3} f g h + c^{3} e h^{2}\right)} x^{4} + 10 \, {\left(6 \, c^{3} f g^{2} + 12 \, c^{3} e g h + {\left(6 \, c^{3} d + a c^{2} f\right)} h^{2}\right)} x^{3} + 32 \, {\left(5 \, a c^{2} d - 2 \, a^{2} c f\right)} g h + 16 \, {\left(5 \, c^{3} e g^{2} + a c^{2} e h^{2} + 2 \, {\left(5 \, c^{3} d + a c^{2} f\right)} g h\right)} x^{2} + 15 \, {\left(4 \, a c^{2} e g h + 2 \, {\left(4 \, c^{3} d + a c^{2} f\right)} g^{2} + {\left(2 \, a c^{2} d - a^{2} c f\right)} h^{2}\right)} x\right)} \sqrt{c x^{2} + a}}{240 \, c^{3}}\right]"," ",0,"[-1/480*(15*(4*a^2*c*e*g*h - 2*(4*a*c^2*d - a^2*c*f)*g^2 + (2*a^2*c*d - a^3*f)*h^2)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) - 2*(40*c^3*f*h^2*x^5 + 80*a*c^2*e*g^2 - 32*a^2*c*e*h^2 + 48*(2*c^3*f*g*h + c^3*e*h^2)*x^4 + 10*(6*c^3*f*g^2 + 12*c^3*e*g*h + (6*c^3*d + a*c^2*f)*h^2)*x^3 + 32*(5*a*c^2*d - 2*a^2*c*f)*g*h + 16*(5*c^3*e*g^2 + a*c^2*e*h^2 + 2*(5*c^3*d + a*c^2*f)*g*h)*x^2 + 15*(4*a*c^2*e*g*h + 2*(4*c^3*d + a*c^2*f)*g^2 + (2*a*c^2*d - a^2*c*f)*h^2)*x)*sqrt(c*x^2 + a))/c^3, 1/240*(15*(4*a^2*c*e*g*h - 2*(4*a*c^2*d - a^2*c*f)*g^2 + (2*a^2*c*d - a^3*f)*h^2)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) + (40*c^3*f*h^2*x^5 + 80*a*c^2*e*g^2 - 32*a^2*c*e*h^2 + 48*(2*c^3*f*g*h + c^3*e*h^2)*x^4 + 10*(6*c^3*f*g^2 + 12*c^3*e*g*h + (6*c^3*d + a*c^2*f)*h^2)*x^3 + 32*(5*a*c^2*d - 2*a^2*c*f)*g*h + 16*(5*c^3*e*g^2 + a*c^2*e*h^2 + 2*(5*c^3*d + a*c^2*f)*g*h)*x^2 + 15*(4*a*c^2*e*g*h + 2*(4*c^3*d + a*c^2*f)*g^2 + (2*a*c^2*d - a^2*c*f)*h^2)*x)*sqrt(c*x^2 + a))/c^3]","A",0
80,1,329,0,1.704925," ","integrate((h*x+g)*(f*x^2+e*x+d)*(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(a^{2} e h - {\left(4 \, a c d - a^{2} f\right)} g\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} f h x^{4} + 40 \, a c e g + 30 \, {\left(c^{2} f g + c^{2} e h\right)} x^{3} + 8 \, {\left(5 \, c^{2} e g + {\left(5 \, c^{2} d + a c f\right)} h\right)} x^{2} + 8 \, {\left(5 \, a c d - 2 \, a^{2} f\right)} h + 15 \, {\left(a c e h + {\left(4 \, c^{2} d + a c f\right)} g\right)} x\right)} \sqrt{c x^{2} + a}}{240 \, c^{2}}, \frac{15 \, {\left(a^{2} e h - {\left(4 \, a c d - a^{2} f\right)} g\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) + {\left(24 \, c^{2} f h x^{4} + 40 \, a c e g + 30 \, {\left(c^{2} f g + c^{2} e h\right)} x^{3} + 8 \, {\left(5 \, c^{2} e g + {\left(5 \, c^{2} d + a c f\right)} h\right)} x^{2} + 8 \, {\left(5 \, a c d - 2 \, a^{2} f\right)} h + 15 \, {\left(a c e h + {\left(4 \, c^{2} d + a c f\right)} g\right)} x\right)} \sqrt{c x^{2} + a}}{120 \, c^{2}}\right]"," ",0,"[1/240*(15*(a^2*e*h - (4*a*c*d - a^2*f)*g)*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(24*c^2*f*h*x^4 + 40*a*c*e*g + 30*(c^2*f*g + c^2*e*h)*x^3 + 8*(5*c^2*e*g + (5*c^2*d + a*c*f)*h)*x^2 + 8*(5*a*c*d - 2*a^2*f)*h + 15*(a*c*e*h + (4*c^2*d + a*c*f)*g)*x)*sqrt(c*x^2 + a))/c^2, 1/120*(15*(a^2*e*h - (4*a*c*d - a^2*f)*g)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) + (24*c^2*f*h*x^4 + 40*a*c*e*g + 30*(c^2*f*g + c^2*e*h)*x^3 + 8*(5*c^2*e*g + (5*c^2*d + a*c*f)*h)*x^2 + 8*(5*a*c*d - 2*a^2*f)*h + 15*(a*c*e*h + (4*c^2*d + a*c*f)*g)*x)*sqrt(c*x^2 + a))/c^2]","A",0
81,1,190,0,1.050714," ","integrate((f*x^2+e*x+d)*(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(4 \, a c d - a^{2} f\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} f x^{3} + 8 \, c^{2} e x^{2} + 8 \, a c e + 3 \, {\left(4 \, c^{2} d + a c f\right)} x\right)} \sqrt{c x^{2} + a}}{48 \, c^{2}}, -\frac{3 \, {\left(4 \, a c d - a^{2} f\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(6 \, c^{2} f x^{3} + 8 \, c^{2} e x^{2} + 8 \, a c e + 3 \, {\left(4 \, c^{2} d + a c f\right)} x\right)} \sqrt{c x^{2} + a}}{24 \, c^{2}}\right]"," ",0,"[-1/48*(3*(4*a*c*d - a^2*f)*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) - 2*(6*c^2*f*x^3 + 8*c^2*e*x^2 + 8*a*c*e + 3*(4*c^2*d + a*c*f)*x)*sqrt(c*x^2 + a))/c^2, -1/24*(3*(4*a*c*d - a^2*f)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (6*c^2*f*x^3 + 8*c^2*e*x^2 + 8*a*c*e + 3*(4*c^2*d + a*c*f)*x)*sqrt(c*x^2 + a))/c^2]","A",0
82,-1,0,0,0.000000," ","integrate((f*x^2+e*x+d)*(c*x^2+a)^(1/2)/(h*x+g),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
83,-1,0,0,0.000000," ","integrate((f*x^2+e*x+d)*(c*x^2+a)^(1/2)/(h*x+g)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
84,-1,0,0,0.000000," ","integrate((f*x^2+e*x+d)*(c*x^2+a)^(1/2)/(h*x+g)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
85,-1,0,0,0.000000," ","integrate((f*x^2+e*x+d)*(c*x^2+a)^(1/2)/(h*x+g)^4,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
86,-1,0,0,0.000000," ","integrate((f*x^2+e*x+d)*(c*x^2+a)^(1/2)/(h*x+g)^5,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
87,-1,0,0,0.000000," ","integrate((f*x^2+e*x+d)*(c*x^2+a)^(1/2)/(h*x+g)^6,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
88,1,1177,0,0.980593," ","integrate((h*x+g)^3*(c*x^2+a)^(3/2)*(f*x^2+e*x+d),x, algorithm=""fricas"")","\left[-\frac{315 \, {\left(24 \, a^{3} c e g^{2} h - 3 \, a^{4} e h^{3} - 8 \, {\left(6 \, a^{2} c^{2} d - a^{3} c f\right)} g^{3} + 3 \, {\left(8 \, a^{3} c d - 3 \, a^{4} f\right)} g h^{2}\right)} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) - 2 \, {\left(4480 \, c^{4} f h^{3} x^{8} + 8064 \, a^{2} c^{2} e g^{3} - 6912 \, a^{3} c e g h^{2} + 5040 \, {\left(3 \, c^{4} f g h^{2} + c^{4} e h^{3}\right)} x^{7} + 640 \, {\left(27 \, c^{4} f g^{2} h + 27 \, c^{4} e g h^{2} + {\left(9 \, c^{4} d + 10 \, a c^{3} f\right)} h^{3}\right)} x^{6} + 840 \, {\left(8 \, c^{4} f g^{3} + 24 \, c^{4} e g^{2} h + 9 \, a c^{3} e h^{3} + 3 \, {\left(8 \, c^{4} d + 9 \, a c^{3} f\right)} g h^{2}\right)} x^{5} + 384 \, {\left(21 \, c^{4} e g^{3} + 72 \, a c^{3} e g h^{2} + 9 \, {\left(7 \, c^{4} d + 8 \, a c^{3} f\right)} g^{2} h + {\left(24 \, a c^{3} d + a^{2} c^{2} f\right)} h^{3}\right)} x^{4} + 3456 \, {\left(7 \, a^{2} c^{2} d - 2 \, a^{3} c f\right)} g^{2} h - 256 \, {\left(9 \, a^{3} c d - 4 \, a^{4} f\right)} h^{3} + 210 \, {\left(168 \, a c^{3} e g^{2} h + 3 \, a^{2} c^{2} e h^{3} + 8 \, {\left(6 \, c^{4} d + 7 \, a c^{3} f\right)} g^{3} + 3 \, {\left(56 \, a c^{3} d + 3 \, a^{2} c^{2} f\right)} g h^{2}\right)} x^{3} + 128 \, {\left(126 \, a c^{3} e g^{3} + 27 \, a^{2} c^{2} e g h^{2} + 27 \, {\left(14 \, a c^{3} d + a^{2} c^{2} f\right)} g^{2} h + {\left(9 \, a^{2} c^{2} d - 4 \, a^{3} c f\right)} h^{3}\right)} x^{2} + 315 \, {\left(24 \, a^{2} c^{2} e g^{2} h - 3 \, a^{3} c e h^{3} + 8 \, {\left(10 \, a c^{3} d + a^{2} c^{2} f\right)} g^{3} + 3 \, {\left(8 \, a^{2} c^{2} d - 3 \, a^{3} c f\right)} g h^{2}\right)} x\right)} \sqrt{c x^{2} + a}}{80640 \, c^{3}}, \frac{315 \, {\left(24 \, a^{3} c e g^{2} h - 3 \, a^{4} e h^{3} - 8 \, {\left(6 \, a^{2} c^{2} d - a^{3} c f\right)} g^{3} + 3 \, {\left(8 \, a^{3} c d - 3 \, a^{4} f\right)} g h^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) + {\left(4480 \, c^{4} f h^{3} x^{8} + 8064 \, a^{2} c^{2} e g^{3} - 6912 \, a^{3} c e g h^{2} + 5040 \, {\left(3 \, c^{4} f g h^{2} + c^{4} e h^{3}\right)} x^{7} + 640 \, {\left(27 \, c^{4} f g^{2} h + 27 \, c^{4} e g h^{2} + {\left(9 \, c^{4} d + 10 \, a c^{3} f\right)} h^{3}\right)} x^{6} + 840 \, {\left(8 \, c^{4} f g^{3} + 24 \, c^{4} e g^{2} h + 9 \, a c^{3} e h^{3} + 3 \, {\left(8 \, c^{4} d + 9 \, a c^{3} f\right)} g h^{2}\right)} x^{5} + 384 \, {\left(21 \, c^{4} e g^{3} + 72 \, a c^{3} e g h^{2} + 9 \, {\left(7 \, c^{4} d + 8 \, a c^{3} f\right)} g^{2} h + {\left(24 \, a c^{3} d + a^{2} c^{2} f\right)} h^{3}\right)} x^{4} + 3456 \, {\left(7 \, a^{2} c^{2} d - 2 \, a^{3} c f\right)} g^{2} h - 256 \, {\left(9 \, a^{3} c d - 4 \, a^{4} f\right)} h^{3} + 210 \, {\left(168 \, a c^{3} e g^{2} h + 3 \, a^{2} c^{2} e h^{3} + 8 \, {\left(6 \, c^{4} d + 7 \, a c^{3} f\right)} g^{3} + 3 \, {\left(56 \, a c^{3} d + 3 \, a^{2} c^{2} f\right)} g h^{2}\right)} x^{3} + 128 \, {\left(126 \, a c^{3} e g^{3} + 27 \, a^{2} c^{2} e g h^{2} + 27 \, {\left(14 \, a c^{3} d + a^{2} c^{2} f\right)} g^{2} h + {\left(9 \, a^{2} c^{2} d - 4 \, a^{3} c f\right)} h^{3}\right)} x^{2} + 315 \, {\left(24 \, a^{2} c^{2} e g^{2} h - 3 \, a^{3} c e h^{3} + 8 \, {\left(10 \, a c^{3} d + a^{2} c^{2} f\right)} g^{3} + 3 \, {\left(8 \, a^{2} c^{2} d - 3 \, a^{3} c f\right)} g h^{2}\right)} x\right)} \sqrt{c x^{2} + a}}{40320 \, c^{3}}\right]"," ",0,"[-1/80640*(315*(24*a^3*c*e*g^2*h - 3*a^4*e*h^3 - 8*(6*a^2*c^2*d - a^3*c*f)*g^3 + 3*(8*a^3*c*d - 3*a^4*f)*g*h^2)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) - 2*(4480*c^4*f*h^3*x^8 + 8064*a^2*c^2*e*g^3 - 6912*a^3*c*e*g*h^2 + 5040*(3*c^4*f*g*h^2 + c^4*e*h^3)*x^7 + 640*(27*c^4*f*g^2*h + 27*c^4*e*g*h^2 + (9*c^4*d + 10*a*c^3*f)*h^3)*x^6 + 840*(8*c^4*f*g^3 + 24*c^4*e*g^2*h + 9*a*c^3*e*h^3 + 3*(8*c^4*d + 9*a*c^3*f)*g*h^2)*x^5 + 384*(21*c^4*e*g^3 + 72*a*c^3*e*g*h^2 + 9*(7*c^4*d + 8*a*c^3*f)*g^2*h + (24*a*c^3*d + a^2*c^2*f)*h^3)*x^4 + 3456*(7*a^2*c^2*d - 2*a^3*c*f)*g^2*h - 256*(9*a^3*c*d - 4*a^4*f)*h^3 + 210*(168*a*c^3*e*g^2*h + 3*a^2*c^2*e*h^3 + 8*(6*c^4*d + 7*a*c^3*f)*g^3 + 3*(56*a*c^3*d + 3*a^2*c^2*f)*g*h^2)*x^3 + 128*(126*a*c^3*e*g^3 + 27*a^2*c^2*e*g*h^2 + 27*(14*a*c^3*d + a^2*c^2*f)*g^2*h + (9*a^2*c^2*d - 4*a^3*c*f)*h^3)*x^2 + 315*(24*a^2*c^2*e*g^2*h - 3*a^3*c*e*h^3 + 8*(10*a*c^3*d + a^2*c^2*f)*g^3 + 3*(8*a^2*c^2*d - 3*a^3*c*f)*g*h^2)*x)*sqrt(c*x^2 + a))/c^3, 1/40320*(315*(24*a^3*c*e*g^2*h - 3*a^4*e*h^3 - 8*(6*a^2*c^2*d - a^3*c*f)*g^3 + 3*(8*a^3*c*d - 3*a^4*f)*g*h^2)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) + (4480*c^4*f*h^3*x^8 + 8064*a^2*c^2*e*g^3 - 6912*a^3*c*e*g*h^2 + 5040*(3*c^4*f*g*h^2 + c^4*e*h^3)*x^7 + 640*(27*c^4*f*g^2*h + 27*c^4*e*g*h^2 + (9*c^4*d + 10*a*c^3*f)*h^3)*x^6 + 840*(8*c^4*f*g^3 + 24*c^4*e*g^2*h + 9*a*c^3*e*h^3 + 3*(8*c^4*d + 9*a*c^3*f)*g*h^2)*x^5 + 384*(21*c^4*e*g^3 + 72*a*c^3*e*g*h^2 + 9*(7*c^4*d + 8*a*c^3*f)*g^2*h + (24*a*c^3*d + a^2*c^2*f)*h^3)*x^4 + 3456*(7*a^2*c^2*d - 2*a^3*c*f)*g^2*h - 256*(9*a^3*c*d - 4*a^4*f)*h^3 + 210*(168*a*c^3*e*g^2*h + 3*a^2*c^2*e*h^3 + 8*(6*c^4*d + 7*a*c^3*f)*g^3 + 3*(56*a*c^3*d + 3*a^2*c^2*f)*g*h^2)*x^3 + 128*(126*a*c^3*e*g^3 + 27*a^2*c^2*e*g*h^2 + 27*(14*a*c^3*d + a^2*c^2*f)*g^2*h + (9*a^2*c^2*d - 4*a^3*c*f)*h^3)*x^2 + 315*(24*a^2*c^2*e*g^2*h - 3*a^3*c*e*h^3 + 8*(10*a*c^3*d + a^2*c^2*f)*g^3 + 3*(8*a^2*c^2*d - 3*a^3*c*f)*g*h^2)*x)*sqrt(c*x^2 + a))/c^3]","A",0
89,1,831,0,1.107553," ","integrate((h*x+g)^2*(c*x^2+a)^(3/2)*(f*x^2+e*x+d),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(16 \, a^{3} c e g h - 8 \, {\left(6 \, a^{2} c^{2} d - a^{3} c f\right)} g^{2} + {\left(8 \, a^{3} c d - 3 \, a^{4} f\right)} h^{2}\right)} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) - 2 \, {\left(1680 \, c^{4} f h^{2} x^{7} + 2688 \, a^{2} c^{2} e g^{2} - 768 \, a^{3} c e h^{2} + 1920 \, {\left(2 \, c^{4} f g h + c^{4} e h^{2}\right)} x^{6} + 280 \, {\left(8 \, c^{4} f g^{2} + 16 \, c^{4} e g h + {\left(8 \, c^{4} d + 9 \, a c^{3} f\right)} h^{2}\right)} x^{5} + 384 \, {\left(7 \, c^{4} e g^{2} + 8 \, a c^{3} e h^{2} + 2 \, {\left(7 \, c^{4} d + 8 \, a c^{3} f\right)} g h\right)} x^{4} + 70 \, {\left(112 \, a c^{3} e g h + 8 \, {\left(6 \, c^{4} d + 7 \, a c^{3} f\right)} g^{2} + {\left(56 \, a c^{3} d + 3 \, a^{2} c^{2} f\right)} h^{2}\right)} x^{3} + 768 \, {\left(7 \, a^{2} c^{2} d - 2 \, a^{3} c f\right)} g h + 384 \, {\left(14 \, a c^{3} e g^{2} + a^{2} c^{2} e h^{2} + 2 \, {\left(14 \, a c^{3} d + a^{2} c^{2} f\right)} g h\right)} x^{2} + 105 \, {\left(16 \, a^{2} c^{2} e g h + 8 \, {\left(10 \, a c^{3} d + a^{2} c^{2} f\right)} g^{2} + {\left(8 \, a^{2} c^{2} d - 3 \, a^{3} c f\right)} h^{2}\right)} x\right)} \sqrt{c x^{2} + a}}{26880 \, c^{3}}, \frac{105 \, {\left(16 \, a^{3} c e g h - 8 \, {\left(6 \, a^{2} c^{2} d - a^{3} c f\right)} g^{2} + {\left(8 \, a^{3} c d - 3 \, a^{4} f\right)} h^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) + {\left(1680 \, c^{4} f h^{2} x^{7} + 2688 \, a^{2} c^{2} e g^{2} - 768 \, a^{3} c e h^{2} + 1920 \, {\left(2 \, c^{4} f g h + c^{4} e h^{2}\right)} x^{6} + 280 \, {\left(8 \, c^{4} f g^{2} + 16 \, c^{4} e g h + {\left(8 \, c^{4} d + 9 \, a c^{3} f\right)} h^{2}\right)} x^{5} + 384 \, {\left(7 \, c^{4} e g^{2} + 8 \, a c^{3} e h^{2} + 2 \, {\left(7 \, c^{4} d + 8 \, a c^{3} f\right)} g h\right)} x^{4} + 70 \, {\left(112 \, a c^{3} e g h + 8 \, {\left(6 \, c^{4} d + 7 \, a c^{3} f\right)} g^{2} + {\left(56 \, a c^{3} d + 3 \, a^{2} c^{2} f\right)} h^{2}\right)} x^{3} + 768 \, {\left(7 \, a^{2} c^{2} d - 2 \, a^{3} c f\right)} g h + 384 \, {\left(14 \, a c^{3} e g^{2} + a^{2} c^{2} e h^{2} + 2 \, {\left(14 \, a c^{3} d + a^{2} c^{2} f\right)} g h\right)} x^{2} + 105 \, {\left(16 \, a^{2} c^{2} e g h + 8 \, {\left(10 \, a c^{3} d + a^{2} c^{2} f\right)} g^{2} + {\left(8 \, a^{2} c^{2} d - 3 \, a^{3} c f\right)} h^{2}\right)} x\right)} \sqrt{c x^{2} + a}}{13440 \, c^{3}}\right]"," ",0,"[-1/26880*(105*(16*a^3*c*e*g*h - 8*(6*a^2*c^2*d - a^3*c*f)*g^2 + (8*a^3*c*d - 3*a^4*f)*h^2)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) - 2*(1680*c^4*f*h^2*x^7 + 2688*a^2*c^2*e*g^2 - 768*a^3*c*e*h^2 + 1920*(2*c^4*f*g*h + c^4*e*h^2)*x^6 + 280*(8*c^4*f*g^2 + 16*c^4*e*g*h + (8*c^4*d + 9*a*c^3*f)*h^2)*x^5 + 384*(7*c^4*e*g^2 + 8*a*c^3*e*h^2 + 2*(7*c^4*d + 8*a*c^3*f)*g*h)*x^4 + 70*(112*a*c^3*e*g*h + 8*(6*c^4*d + 7*a*c^3*f)*g^2 + (56*a*c^3*d + 3*a^2*c^2*f)*h^2)*x^3 + 768*(7*a^2*c^2*d - 2*a^3*c*f)*g*h + 384*(14*a*c^3*e*g^2 + a^2*c^2*e*h^2 + 2*(14*a*c^3*d + a^2*c^2*f)*g*h)*x^2 + 105*(16*a^2*c^2*e*g*h + 8*(10*a*c^3*d + a^2*c^2*f)*g^2 + (8*a^2*c^2*d - 3*a^3*c*f)*h^2)*x)*sqrt(c*x^2 + a))/c^3, 1/13440*(105*(16*a^3*c*e*g*h - 8*(6*a^2*c^2*d - a^3*c*f)*g^2 + (8*a^3*c*d - 3*a^4*f)*h^2)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) + (1680*c^4*f*h^2*x^7 + 2688*a^2*c^2*e*g^2 - 768*a^3*c*e*h^2 + 1920*(2*c^4*f*g*h + c^4*e*h^2)*x^6 + 280*(8*c^4*f*g^2 + 16*c^4*e*g*h + (8*c^4*d + 9*a*c^3*f)*h^2)*x^5 + 384*(7*c^4*e*g^2 + 8*a*c^3*e*h^2 + 2*(7*c^4*d + 8*a*c^3*f)*g*h)*x^4 + 70*(112*a*c^3*e*g*h + 8*(6*c^4*d + 7*a*c^3*f)*g^2 + (56*a*c^3*d + 3*a^2*c^2*f)*h^2)*x^3 + 768*(7*a^2*c^2*d - 2*a^3*c*f)*g*h + 384*(14*a*c^3*e*g^2 + a^2*c^2*e*h^2 + 2*(14*a*c^3*d + a^2*c^2*f)*g*h)*x^2 + 105*(16*a^2*c^2*e*g*h + 8*(10*a*c^3*d + a^2*c^2*f)*g^2 + (8*a^2*c^2*d - 3*a^3*c*f)*h^2)*x)*sqrt(c*x^2 + a))/c^3]","A",0
90,1,477,0,1.759712," ","integrate((h*x+g)*(c*x^2+a)^(3/2)*(f*x^2+e*x+d),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(a^{3} e h - {\left(6 \, a^{2} c d - a^{3} f\right)} g\right)} \sqrt{c} \log\left(-2 \, c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(240 \, c^{3} f h x^{6} + 280 \, {\left(c^{3} f g + c^{3} e h\right)} x^{5} + 336 \, a^{2} c e g + 48 \, {\left(7 \, c^{3} e g + {\left(7 \, c^{3} d + 8 \, a c^{2} f\right)} h\right)} x^{4} + 70 \, {\left(7 \, a c^{2} e h + {\left(6 \, c^{3} d + 7 \, a c^{2} f\right)} g\right)} x^{3} + 48 \, {\left(14 \, a c^{2} e g + {\left(14 \, a c^{2} d + a^{2} c f\right)} h\right)} x^{2} + 48 \, {\left(7 \, a^{2} c d - 2 \, a^{3} f\right)} h + 105 \, {\left(a^{2} c e h + {\left(10 \, a c^{2} d + a^{2} c f\right)} g\right)} x\right)} \sqrt{c x^{2} + a}}{3360 \, c^{2}}, \frac{105 \, {\left(a^{3} e h - {\left(6 \, a^{2} c d - a^{3} f\right)} g\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) + {\left(240 \, c^{3} f h x^{6} + 280 \, {\left(c^{3} f g + c^{3} e h\right)} x^{5} + 336 \, a^{2} c e g + 48 \, {\left(7 \, c^{3} e g + {\left(7 \, c^{3} d + 8 \, a c^{2} f\right)} h\right)} x^{4} + 70 \, {\left(7 \, a c^{2} e h + {\left(6 \, c^{3} d + 7 \, a c^{2} f\right)} g\right)} x^{3} + 48 \, {\left(14 \, a c^{2} e g + {\left(14 \, a c^{2} d + a^{2} c f\right)} h\right)} x^{2} + 48 \, {\left(7 \, a^{2} c d - 2 \, a^{3} f\right)} h + 105 \, {\left(a^{2} c e h + {\left(10 \, a c^{2} d + a^{2} c f\right)} g\right)} x\right)} \sqrt{c x^{2} + a}}{1680 \, c^{2}}\right]"," ",0,"[1/3360*(105*(a^3*e*h - (6*a^2*c*d - a^3*f)*g)*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(240*c^3*f*h*x^6 + 280*(c^3*f*g + c^3*e*h)*x^5 + 336*a^2*c*e*g + 48*(7*c^3*e*g + (7*c^3*d + 8*a*c^2*f)*h)*x^4 + 70*(7*a*c^2*e*h + (6*c^3*d + 7*a*c^2*f)*g)*x^3 + 48*(14*a*c^2*e*g + (14*a*c^2*d + a^2*c*f)*h)*x^2 + 48*(7*a^2*c*d - 2*a^3*f)*h + 105*(a^2*c*e*h + (10*a*c^2*d + a^2*c*f)*g)*x)*sqrt(c*x^2 + a))/c^2, 1/1680*(105*(a^3*e*h - (6*a^2*c*d - a^3*f)*g)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) + (240*c^3*f*h*x^6 + 280*(c^3*f*g + c^3*e*h)*x^5 + 336*a^2*c*e*g + 48*(7*c^3*e*g + (7*c^3*d + 8*a*c^2*f)*h)*x^4 + 70*(7*a*c^2*e*h + (6*c^3*d + 7*a*c^2*f)*g)*x^3 + 48*(14*a*c^2*e*g + (14*a*c^2*d + a^2*c*f)*h)*x^2 + 48*(7*a^2*c*d - 2*a^3*f)*h + 105*(a^2*c*e*h + (10*a*c^2*d + a^2*c*f)*g)*x)*sqrt(c*x^2 + a))/c^2]","A",0
91,1,262,0,1.283627," ","integrate((c*x^2+a)^(3/2)*(f*x^2+e*x+d),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(6 \, a^{2} c d - a^{3} f\right)} \sqrt{c} \log\left(-2 \, c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) - 2 \, {\left(40 \, c^{3} f x^{5} + 48 \, c^{3} e x^{4} + 96 \, a c^{2} e x^{2} + 48 \, a^{2} c e + 10 \, {\left(6 \, c^{3} d + 7 \, a c^{2} f\right)} x^{3} + 15 \, {\left(10 \, a c^{2} d + a^{2} c f\right)} x\right)} \sqrt{c x^{2} + a}}{480 \, c^{2}}, -\frac{15 \, {\left(6 \, a^{2} c d - a^{3} f\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(40 \, c^{3} f x^{5} + 48 \, c^{3} e x^{4} + 96 \, a c^{2} e x^{2} + 48 \, a^{2} c e + 10 \, {\left(6 \, c^{3} d + 7 \, a c^{2} f\right)} x^{3} + 15 \, {\left(10 \, a c^{2} d + a^{2} c f\right)} x\right)} \sqrt{c x^{2} + a}}{240 \, c^{2}}\right]"," ",0,"[-1/480*(15*(6*a^2*c*d - a^3*f)*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) - 2*(40*c^3*f*x^5 + 48*c^3*e*x^4 + 96*a*c^2*e*x^2 + 48*a^2*c*e + 10*(6*c^3*d + 7*a*c^2*f)*x^3 + 15*(10*a*c^2*d + a^2*c*f)*x)*sqrt(c*x^2 + a))/c^2, -1/240*(15*(6*a^2*c*d - a^3*f)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (40*c^3*f*x^5 + 48*c^3*e*x^4 + 96*a*c^2*e*x^2 + 48*a^2*c*e + 10*(6*c^3*d + 7*a*c^2*f)*x^3 + 15*(10*a*c^2*d + a^2*c*f)*x)*sqrt(c*x^2 + a))/c^2]","A",0
92,-1,0,0,0.000000," ","integrate((c*x^2+a)^(3/2)*(f*x^2+e*x+d)/(h*x+g),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
93,-1,0,0,0.000000," ","integrate((c*x^2+a)^(3/2)*(f*x^2+e*x+d)/(h*x+g)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
94,-1,0,0,0.000000," ","integrate((c*x^2+a)^(3/2)*(f*x^2+e*x+d)/(h*x+g)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
95,-1,0,0,0.000000," ","integrate((c*x^2+a)^(3/2)*(f*x^2+e*x+d)/(h*x+g)^4,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
96,-1,0,0,0.000000," ","integrate((c*x^2+a)^(3/2)*(f*x^2+e*x+d)/(h*x+g)^5,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
97,-1,0,0,0.000000," ","integrate((c*x^2+a)^(3/2)*(f*x^2+e*x+d)/(h*x+g)^6,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
98,-1,0,0,0.000000," ","integrate((c*x^2+a)^(3/2)*(f*x^2+e*x+d)/(h*x+g)^7,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
99,-1,0,0,0.000000," ","integrate((c*x^2+a)^(3/2)*(f*x^2+e*x+d)/(h*x+g)^8,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
100,1,333,0,1.203784," ","integrate((c*x^2+a)^(5/2)*(C*x^2+B*x+A),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(C a^{4} - 8 \, A a^{3} c\right)} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) - 2 \, {\left(336 \, C c^{4} x^{7} + 384 \, B c^{4} x^{6} + 1152 \, B a c^{3} x^{4} + 1152 \, B a^{2} c^{2} x^{2} + 56 \, {\left(17 \, C a c^{3} + 8 \, A c^{4}\right)} x^{5} + 384 \, B a^{3} c + 14 \, {\left(59 \, C a^{2} c^{2} + 104 \, A a c^{3}\right)} x^{3} + 21 \, {\left(5 \, C a^{3} c + 88 \, A a^{2} c^{2}\right)} x\right)} \sqrt{c x^{2} + a}}{5376 \, c^{2}}, \frac{105 \, {\left(C a^{4} - 8 \, A a^{3} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) + {\left(336 \, C c^{4} x^{7} + 384 \, B c^{4} x^{6} + 1152 \, B a c^{3} x^{4} + 1152 \, B a^{2} c^{2} x^{2} + 56 \, {\left(17 \, C a c^{3} + 8 \, A c^{4}\right)} x^{5} + 384 \, B a^{3} c + 14 \, {\left(59 \, C a^{2} c^{2} + 104 \, A a c^{3}\right)} x^{3} + 21 \, {\left(5 \, C a^{3} c + 88 \, A a^{2} c^{2}\right)} x\right)} \sqrt{c x^{2} + a}}{2688 \, c^{2}}\right]"," ",0,"[-1/5376*(105*(C*a^4 - 8*A*a^3*c)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) - 2*(336*C*c^4*x^7 + 384*B*c^4*x^6 + 1152*B*a*c^3*x^4 + 1152*B*a^2*c^2*x^2 + 56*(17*C*a*c^3 + 8*A*c^4)*x^5 + 384*B*a^3*c + 14*(59*C*a^2*c^2 + 104*A*a*c^3)*x^3 + 21*(5*C*a^3*c + 88*A*a^2*c^2)*x)*sqrt(c*x^2 + a))/c^2, 1/2688*(105*(C*a^4 - 8*A*a^3*c)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) + (336*C*c^4*x^7 + 384*B*c^4*x^6 + 1152*B*a*c^3*x^4 + 1152*B*a^2*c^2*x^2 + 56*(17*C*a*c^3 + 8*A*c^4)*x^5 + 384*B*a^3*c + 14*(59*C*a^2*c^2 + 104*A*a*c^3)*x^3 + 21*(5*C*a^3*c + 88*A*a^2*c^2)*x)*sqrt(c*x^2 + a))/c^2]","A",0
101,1,559,0,0.897151," ","integrate((h*x+g)^3*(f*x^2+e*x+d)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(12 \, a c e g^{2} h - 3 \, a^{2} e h^{3} - 4 \, {\left(2 \, c^{2} d - a c f\right)} g^{3} + 3 \, {\left(4 \, a c d - 3 \, a^{2} f\right)} g h^{2}\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} f h^{3} x^{4} + 120 \, c^{2} e g^{3} - 240 \, a c e g h^{2} + 120 \, {\left(3 \, c^{2} d - 2 \, a c f\right)} g^{2} h - 16 \, {\left(5 \, a c d - 4 \, a^{2} f\right)} h^{3} + 30 \, {\left(3 \, c^{2} f g h^{2} + c^{2} e h^{3}\right)} x^{3} + 8 \, {\left(15 \, c^{2} f g^{2} h + 15 \, c^{2} e g h^{2} + {\left(5 \, c^{2} d - 4 \, a c f\right)} h^{3}\right)} x^{2} + 15 \, {\left(4 \, c^{2} f g^{3} + 12 \, c^{2} e g^{2} h - 3 \, a c e h^{3} + 3 \, {\left(4 \, c^{2} d - 3 \, a c f\right)} g h^{2}\right)} x\right)} \sqrt{c x^{2} + a}}{240 \, c^{3}}, \frac{15 \, {\left(12 \, a c e g^{2} h - 3 \, a^{2} e h^{3} - 4 \, {\left(2 \, c^{2} d - a c f\right)} g^{3} + 3 \, {\left(4 \, a c d - 3 \, a^{2} f\right)} g h^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) + {\left(24 \, c^{2} f h^{3} x^{4} + 120 \, c^{2} e g^{3} - 240 \, a c e g h^{2} + 120 \, {\left(3 \, c^{2} d - 2 \, a c f\right)} g^{2} h - 16 \, {\left(5 \, a c d - 4 \, a^{2} f\right)} h^{3} + 30 \, {\left(3 \, c^{2} f g h^{2} + c^{2} e h^{3}\right)} x^{3} + 8 \, {\left(15 \, c^{2} f g^{2} h + 15 \, c^{2} e g h^{2} + {\left(5 \, c^{2} d - 4 \, a c f\right)} h^{3}\right)} x^{2} + 15 \, {\left(4 \, c^{2} f g^{3} + 12 \, c^{2} e g^{2} h - 3 \, a c e h^{3} + 3 \, {\left(4 \, c^{2} d - 3 \, a c f\right)} g h^{2}\right)} x\right)} \sqrt{c x^{2} + a}}{120 \, c^{3}}\right]"," ",0,"[-1/240*(15*(12*a*c*e*g^2*h - 3*a^2*e*h^3 - 4*(2*c^2*d - a*c*f)*g^3 + 3*(4*a*c*d - 3*a^2*f)*g*h^2)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) - 2*(24*c^2*f*h^3*x^4 + 120*c^2*e*g^3 - 240*a*c*e*g*h^2 + 120*(3*c^2*d - 2*a*c*f)*g^2*h - 16*(5*a*c*d - 4*a^2*f)*h^3 + 30*(3*c^2*f*g*h^2 + c^2*e*h^3)*x^3 + 8*(15*c^2*f*g^2*h + 15*c^2*e*g*h^2 + (5*c^2*d - 4*a*c*f)*h^3)*x^2 + 15*(4*c^2*f*g^3 + 12*c^2*e*g^2*h - 3*a*c*e*h^3 + 3*(4*c^2*d - 3*a*c*f)*g*h^2)*x)*sqrt(c*x^2 + a))/c^3, 1/120*(15*(12*a*c*e*g^2*h - 3*a^2*e*h^3 - 4*(2*c^2*d - a*c*f)*g^3 + 3*(4*a*c*d - 3*a^2*f)*g*h^2)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) + (24*c^2*f*h^3*x^4 + 120*c^2*e*g^3 - 240*a*c*e*g*h^2 + 120*(3*c^2*d - 2*a*c*f)*g^2*h - 16*(5*a*c*d - 4*a^2*f)*h^3 + 30*(3*c^2*f*g*h^2 + c^2*e*h^3)*x^3 + 8*(15*c^2*f*g^2*h + 15*c^2*e*g*h^2 + (5*c^2*d - 4*a*c*f)*h^3)*x^2 + 15*(4*c^2*f*g^3 + 12*c^2*e*g^2*h - 3*a*c*e*h^3 + 3*(4*c^2*d - 3*a*c*f)*g*h^2)*x)*sqrt(c*x^2 + a))/c^3]","A",0
102,1,381,0,0.829001," ","integrate((h*x+g)^2*(f*x^2+e*x+d)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(8 \, a c e g h - 4 \, {\left(2 \, c^{2} d - a c f\right)} g^{2} + {\left(4 \, a c d - 3 \, a^{2} f\right)} h^{2}\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} f h^{2} x^{3} + 24 \, c^{2} e g^{2} - 16 \, a c e h^{2} + 16 \, {\left(3 \, c^{2} d - 2 \, a c f\right)} g h + 8 \, {\left(2 \, c^{2} f g h + c^{2} e h^{2}\right)} x^{2} + 3 \, {\left(4 \, c^{2} f g^{2} + 8 \, c^{2} e g h + {\left(4 \, c^{2} d - 3 \, a c f\right)} h^{2}\right)} x\right)} \sqrt{c x^{2} + a}}{48 \, c^{3}}, \frac{3 \, {\left(8 \, a c e g h - 4 \, {\left(2 \, c^{2} d - a c f\right)} g^{2} + {\left(4 \, a c d - 3 \, a^{2} f\right)} h^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) + {\left(6 \, c^{2} f h^{2} x^{3} + 24 \, c^{2} e g^{2} - 16 \, a c e h^{2} + 16 \, {\left(3 \, c^{2} d - 2 \, a c f\right)} g h + 8 \, {\left(2 \, c^{2} f g h + c^{2} e h^{2}\right)} x^{2} + 3 \, {\left(4 \, c^{2} f g^{2} + 8 \, c^{2} e g h + {\left(4 \, c^{2} d - 3 \, a c f\right)} h^{2}\right)} x\right)} \sqrt{c x^{2} + a}}{24 \, c^{3}}\right]"," ",0,"[-1/48*(3*(8*a*c*e*g*h - 4*(2*c^2*d - a*c*f)*g^2 + (4*a*c*d - 3*a^2*f)*h^2)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) - 2*(6*c^2*f*h^2*x^3 + 24*c^2*e*g^2 - 16*a*c*e*h^2 + 16*(3*c^2*d - 2*a*c*f)*g*h + 8*(2*c^2*f*g*h + c^2*e*h^2)*x^2 + 3*(4*c^2*f*g^2 + 8*c^2*e*g*h + (4*c^2*d - 3*a*c*f)*h^2)*x)*sqrt(c*x^2 + a))/c^3, 1/24*(3*(8*a*c*e*g*h - 4*(2*c^2*d - a*c*f)*g^2 + (4*a*c*d - 3*a^2*f)*h^2)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) + (6*c^2*f*h^2*x^3 + 24*c^2*e*g^2 - 16*a*c*e*h^2 + 16*(3*c^2*d - 2*a*c*f)*g*h + 8*(2*c^2*f*g*h + c^2*e*h^2)*x^2 + 3*(4*c^2*f*g^2 + 8*c^2*e*g*h + (4*c^2*d - 3*a*c*f)*h^2)*x)*sqrt(c*x^2 + a))/c^3]","A",0
103,1,199,0,1.282239," ","integrate((h*x+g)*(f*x^2+e*x+d)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a e h - {\left(2 \, c d - a f\right)} g\right)} \sqrt{c} \log\left(-2 \, c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(2 \, c f h x^{2} + 6 \, c e g + 2 \, {\left(3 \, c d - 2 \, a f\right)} h + 3 \, {\left(c f g + c e h\right)} x\right)} \sqrt{c x^{2} + a}}{12 \, c^{2}}, \frac{3 \, {\left(a e h - {\left(2 \, c d - a f\right)} g\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) + {\left(2 \, c f h x^{2} + 6 \, c e g + 2 \, {\left(3 \, c d - 2 \, a f\right)} h + 3 \, {\left(c f g + c e h\right)} x\right)} \sqrt{c x^{2} + a}}{6 \, c^{2}}\right]"," ",0,"[1/12*(3*(a*e*h - (2*c*d - a*f)*g)*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(2*c*f*h*x^2 + 6*c*e*g + 2*(3*c*d - 2*a*f)*h + 3*(c*f*g + c*e*h)*x)*sqrt(c*x^2 + a))/c^2, 1/6*(3*(a*e*h - (2*c*d - a*f)*g)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) + (2*c*f*h*x^2 + 6*c*e*g + 2*(3*c*d - 2*a*f)*h + 3*(c*f*g + c*e*h)*x)*sqrt(c*x^2 + a))/c^2]","A",0
104,1,124,0,0.868485," ","integrate((f*x^2+e*x+d)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(2 \, c d - a f\right)} \sqrt{c} \log\left(-2 \, c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) - 2 \, {\left(c f x + 2 \, c e\right)} \sqrt{c x^{2} + a}}{4 \, c^{2}}, -\frac{{\left(2 \, c d - a f\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(c f x + 2 \, c e\right)} \sqrt{c x^{2} + a}}{2 \, c^{2}}\right]"," ",0,"[-1/4*((2*c*d - a*f)*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) - 2*(c*f*x + 2*c*e)*sqrt(c*x^2 + a))/c^2, -1/2*((2*c*d - a*f)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (c*f*x + 2*c*e)*sqrt(c*x^2 + a))/c^2]","A",0
105,-1,0,0,0.000000," ","integrate((f*x^2+e*x+d)/(h*x+g)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
106,-1,0,0,0.000000," ","integrate((f*x^2+e*x+d)/(h*x+g)^2/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
107,1,1088,0,18.245551," ","integrate((f*x^2+e*x+d)/(h*x+g)^3/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(3 \, a c e g^{3} h + {\left(2 \, c^{2} d - a c f\right)} g^{4} - {\left(a c d - 2 \, a^{2} f\right)} g^{2} h^{2} + {\left(3 \, a c e g h^{3} + {\left(2 \, c^{2} d - a c f\right)} g^{2} h^{2} - {\left(a c d - 2 \, a^{2} f\right)} h^{4}\right)} x^{2} + 2 \, {\left(3 \, a c e g^{2} h^{2} + {\left(2 \, c^{2} d - a c f\right)} g^{3} h - {\left(a c d - 2 \, a^{2} f\right)} g h^{3}\right)} x\right)} \sqrt{c g^{2} + a h^{2}} \log\left(\frac{2 \, a c g h x - a c g^{2} - 2 \, a^{2} h^{2} - {\left(2 \, c^{2} g^{2} + a c h^{2}\right)} x^{2} - 2 \, \sqrt{c g^{2} + a h^{2}} {\left(c g x - a h\right)} \sqrt{c x^{2} + a}}{h^{2} x^{2} + 2 \, g h x + g^{2}}\right) + 2 \, {\left(2 \, c^{2} e g^{5} + a c e g^{3} h^{2} - a^{2} e g h^{4} - a^{2} d h^{5} - {\left(4 \, c^{2} d - 3 \, a c f\right)} g^{4} h - {\left(5 \, a c d - 3 \, a^{2} f\right)} g^{2} h^{3} + {\left(c^{2} f g^{5} + c^{2} e g^{4} h - a c e g^{2} h^{3} - 2 \, a^{2} e h^{5} - {\left(3 \, c^{2} d - 5 \, a c f\right)} g^{3} h^{2} - {\left(3 \, a c d - 4 \, a^{2} f\right)} g h^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{4 \, {\left(c^{3} g^{8} + 3 \, a c^{2} g^{6} h^{2} + 3 \, a^{2} c g^{4} h^{4} + a^{3} g^{2} h^{6} + {\left(c^{3} g^{6} h^{2} + 3 \, a c^{2} g^{4} h^{4} + 3 \, a^{2} c g^{2} h^{6} + a^{3} h^{8}\right)} x^{2} + 2 \, {\left(c^{3} g^{7} h + 3 \, a c^{2} g^{5} h^{3} + 3 \, a^{2} c g^{3} h^{5} + a^{3} g h^{7}\right)} x\right)}}, -\frac{{\left(3 \, a c e g^{3} h + {\left(2 \, c^{2} d - a c f\right)} g^{4} - {\left(a c d - 2 \, a^{2} f\right)} g^{2} h^{2} + {\left(3 \, a c e g h^{3} + {\left(2 \, c^{2} d - a c f\right)} g^{2} h^{2} - {\left(a c d - 2 \, a^{2} f\right)} h^{4}\right)} x^{2} + 2 \, {\left(3 \, a c e g^{2} h^{2} + {\left(2 \, c^{2} d - a c f\right)} g^{3} h - {\left(a c d - 2 \, a^{2} f\right)} g h^{3}\right)} x\right)} \sqrt{-c g^{2} - a h^{2}} \arctan\left(\frac{\sqrt{-c g^{2} - a h^{2}} {\left(c g x - a h\right)} \sqrt{c x^{2} + a}}{a c g^{2} + a^{2} h^{2} + {\left(c^{2} g^{2} + a c h^{2}\right)} x^{2}}\right) - {\left(2 \, c^{2} e g^{5} + a c e g^{3} h^{2} - a^{2} e g h^{4} - a^{2} d h^{5} - {\left(4 \, c^{2} d - 3 \, a c f\right)} g^{4} h - {\left(5 \, a c d - 3 \, a^{2} f\right)} g^{2} h^{3} + {\left(c^{2} f g^{5} + c^{2} e g^{4} h - a c e g^{2} h^{3} - 2 \, a^{2} e h^{5} - {\left(3 \, c^{2} d - 5 \, a c f\right)} g^{3} h^{2} - {\left(3 \, a c d - 4 \, a^{2} f\right)} g h^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{2 \, {\left(c^{3} g^{8} + 3 \, a c^{2} g^{6} h^{2} + 3 \, a^{2} c g^{4} h^{4} + a^{3} g^{2} h^{6} + {\left(c^{3} g^{6} h^{2} + 3 \, a c^{2} g^{4} h^{4} + 3 \, a^{2} c g^{2} h^{6} + a^{3} h^{8}\right)} x^{2} + 2 \, {\left(c^{3} g^{7} h + 3 \, a c^{2} g^{5} h^{3} + 3 \, a^{2} c g^{3} h^{5} + a^{3} g h^{7}\right)} x\right)}}\right]"," ",0,"[1/4*((3*a*c*e*g^3*h + (2*c^2*d - a*c*f)*g^4 - (a*c*d - 2*a^2*f)*g^2*h^2 + (3*a*c*e*g*h^3 + (2*c^2*d - a*c*f)*g^2*h^2 - (a*c*d - 2*a^2*f)*h^4)*x^2 + 2*(3*a*c*e*g^2*h^2 + (2*c^2*d - a*c*f)*g^3*h - (a*c*d - 2*a^2*f)*g*h^3)*x)*sqrt(c*g^2 + a*h^2)*log((2*a*c*g*h*x - a*c*g^2 - 2*a^2*h^2 - (2*c^2*g^2 + a*c*h^2)*x^2 - 2*sqrt(c*g^2 + a*h^2)*(c*g*x - a*h)*sqrt(c*x^2 + a))/(h^2*x^2 + 2*g*h*x + g^2)) + 2*(2*c^2*e*g^5 + a*c*e*g^3*h^2 - a^2*e*g*h^4 - a^2*d*h^5 - (4*c^2*d - 3*a*c*f)*g^4*h - (5*a*c*d - 3*a^2*f)*g^2*h^3 + (c^2*f*g^5 + c^2*e*g^4*h - a*c*e*g^2*h^3 - 2*a^2*e*h^5 - (3*c^2*d - 5*a*c*f)*g^3*h^2 - (3*a*c*d - 4*a^2*f)*g*h^4)*x)*sqrt(c*x^2 + a))/(c^3*g^8 + 3*a*c^2*g^6*h^2 + 3*a^2*c*g^4*h^4 + a^3*g^2*h^6 + (c^3*g^6*h^2 + 3*a*c^2*g^4*h^4 + 3*a^2*c*g^2*h^6 + a^3*h^8)*x^2 + 2*(c^3*g^7*h + 3*a*c^2*g^5*h^3 + 3*a^2*c*g^3*h^5 + a^3*g*h^7)*x), -1/2*((3*a*c*e*g^3*h + (2*c^2*d - a*c*f)*g^4 - (a*c*d - 2*a^2*f)*g^2*h^2 + (3*a*c*e*g*h^3 + (2*c^2*d - a*c*f)*g^2*h^2 - (a*c*d - 2*a^2*f)*h^4)*x^2 + 2*(3*a*c*e*g^2*h^2 + (2*c^2*d - a*c*f)*g^3*h - (a*c*d - 2*a^2*f)*g*h^3)*x)*sqrt(-c*g^2 - a*h^2)*arctan(sqrt(-c*g^2 - a*h^2)*(c*g*x - a*h)*sqrt(c*x^2 + a)/(a*c*g^2 + a^2*h^2 + (c^2*g^2 + a*c*h^2)*x^2)) - (2*c^2*e*g^5 + a*c*e*g^3*h^2 - a^2*e*g*h^4 - a^2*d*h^5 - (4*c^2*d - 3*a*c*f)*g^4*h - (5*a*c*d - 3*a^2*f)*g^2*h^3 + (c^2*f*g^5 + c^2*e*g^4*h - a*c*e*g^2*h^3 - 2*a^2*e*h^5 - (3*c^2*d - 5*a*c*f)*g^3*h^2 - (3*a*c*d - 4*a^2*f)*g*h^4)*x)*sqrt(c*x^2 + a))/(c^3*g^8 + 3*a*c^2*g^6*h^2 + 3*a^2*c*g^4*h^4 + a^3*g^2*h^6 + (c^3*g^6*h^2 + 3*a*c^2*g^4*h^4 + 3*a^2*c*g^2*h^6 + a^3*h^8)*x^2 + 2*(c^3*g^7*h + 3*a*c^2*g^5*h^3 + 3*a^2*c*g^3*h^5 + a^3*g*h^7)*x)]","B",0
108,1,758,0,1.003825," ","integrate((h*x+g)^3*(f*x^2+e*x+d)/(c*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(2 \, a^{2} c f g^{3} + 6 \, a^{2} c e g^{2} h - 3 \, a^{3} e h^{3} + 3 \, {\left(2 \, a^{2} c d - 3 \, a^{3} f\right)} g h^{2} + {\left(2 \, a c^{2} f g^{3} + 6 \, a c^{2} e g^{2} h - 3 \, a^{2} c e h^{3} + 3 \, {\left(2 \, a c^{2} d - 3 \, a^{2} c f\right)} g h^{2}\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(2 \, a c^{2} f h^{3} x^{4} - 6 \, a c^{2} e g^{3} + 36 \, a^{2} c e g h^{2} - 18 \, {\left(a c^{2} d - 2 \, a^{2} c f\right)} g^{2} h + 4 \, {\left(3 \, a^{2} c d - 4 \, a^{3} f\right)} h^{3} + 3 \, {\left(3 \, a c^{2} f g h^{2} + a c^{2} e h^{3}\right)} x^{3} + 2 \, {\left(9 \, a c^{2} f g^{2} h + 9 \, a c^{2} e g h^{2} + {\left(3 \, a c^{2} d - 4 \, a^{2} c f\right)} h^{3}\right)} x^{2} - 3 \, {\left(6 \, a c^{2} e g^{2} h - 3 \, a^{2} c e h^{3} - 2 \, {\left(c^{3} d - a c^{2} f\right)} g^{3} + 3 \, {\left(2 \, a c^{2} d - 3 \, a^{2} c f\right)} g h^{2}\right)} x\right)} \sqrt{c x^{2} + a}}{12 \, {\left(a c^{4} x^{2} + a^{2} c^{3}\right)}}, -\frac{3 \, {\left(2 \, a^{2} c f g^{3} + 6 \, a^{2} c e g^{2} h - 3 \, a^{3} e h^{3} + 3 \, {\left(2 \, a^{2} c d - 3 \, a^{3} f\right)} g h^{2} + {\left(2 \, a c^{2} f g^{3} + 6 \, a c^{2} e g^{2} h - 3 \, a^{2} c e h^{3} + 3 \, {\left(2 \, a c^{2} d - 3 \, a^{2} c f\right)} g h^{2}\right)} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(2 \, a c^{2} f h^{3} x^{4} - 6 \, a c^{2} e g^{3} + 36 \, a^{2} c e g h^{2} - 18 \, {\left(a c^{2} d - 2 \, a^{2} c f\right)} g^{2} h + 4 \, {\left(3 \, a^{2} c d - 4 \, a^{3} f\right)} h^{3} + 3 \, {\left(3 \, a c^{2} f g h^{2} + a c^{2} e h^{3}\right)} x^{3} + 2 \, {\left(9 \, a c^{2} f g^{2} h + 9 \, a c^{2} e g h^{2} + {\left(3 \, a c^{2} d - 4 \, a^{2} c f\right)} h^{3}\right)} x^{2} - 3 \, {\left(6 \, a c^{2} e g^{2} h - 3 \, a^{2} c e h^{3} - 2 \, {\left(c^{3} d - a c^{2} f\right)} g^{3} + 3 \, {\left(2 \, a c^{2} d - 3 \, a^{2} c f\right)} g h^{2}\right)} x\right)} \sqrt{c x^{2} + a}}{6 \, {\left(a c^{4} x^{2} + a^{2} c^{3}\right)}}\right]"," ",0,"[-1/12*(3*(2*a^2*c*f*g^3 + 6*a^2*c*e*g^2*h - 3*a^3*e*h^3 + 3*(2*a^2*c*d - 3*a^3*f)*g*h^2 + (2*a*c^2*f*g^3 + 6*a*c^2*e*g^2*h - 3*a^2*c*e*h^3 + 3*(2*a*c^2*d - 3*a^2*c*f)*g*h^2)*x^2)*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) - 2*(2*a*c^2*f*h^3*x^4 - 6*a*c^2*e*g^3 + 36*a^2*c*e*g*h^2 - 18*(a*c^2*d - 2*a^2*c*f)*g^2*h + 4*(3*a^2*c*d - 4*a^3*f)*h^3 + 3*(3*a*c^2*f*g*h^2 + a*c^2*e*h^3)*x^3 + 2*(9*a*c^2*f*g^2*h + 9*a*c^2*e*g*h^2 + (3*a*c^2*d - 4*a^2*c*f)*h^3)*x^2 - 3*(6*a*c^2*e*g^2*h - 3*a^2*c*e*h^3 - 2*(c^3*d - a*c^2*f)*g^3 + 3*(2*a*c^2*d - 3*a^2*c*f)*g*h^2)*x)*sqrt(c*x^2 + a))/(a*c^4*x^2 + a^2*c^3), -1/6*(3*(2*a^2*c*f*g^3 + 6*a^2*c*e*g^2*h - 3*a^3*e*h^3 + 3*(2*a^2*c*d - 3*a^3*f)*g*h^2 + (2*a*c^2*f*g^3 + 6*a*c^2*e*g^2*h - 3*a^2*c*e*h^3 + 3*(2*a*c^2*d - 3*a^2*c*f)*g*h^2)*x^2)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (2*a*c^2*f*h^3*x^4 - 6*a*c^2*e*g^3 + 36*a^2*c*e*g*h^2 - 18*(a*c^2*d - 2*a^2*c*f)*g^2*h + 4*(3*a^2*c*d - 4*a^3*f)*h^3 + 3*(3*a*c^2*f*g*h^2 + a*c^2*e*h^3)*x^3 + 2*(9*a*c^2*f*g^2*h + 9*a*c^2*e*g*h^2 + (3*a*c^2*d - 4*a^2*c*f)*h^3)*x^2 - 3*(6*a*c^2*e*g^2*h - 3*a^2*c*e*h^3 - 2*(c^3*d - a*c^2*f)*g^3 + 3*(2*a*c^2*d - 3*a^2*c*f)*g*h^2)*x)*sqrt(c*x^2 + a))/(a*c^4*x^2 + a^2*c^3)]","A",0
109,1,530,0,0.860616," ","integrate((h*x+g)^2*(f*x^2+e*x+d)/(c*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left(2 \, a^{2} c f g^{2} + 4 \, a^{2} c e g h + {\left(2 \, a^{2} c d - 3 \, a^{3} f\right)} h^{2} + {\left(2 \, a c^{2} f g^{2} + 4 \, a c^{2} e g h + {\left(2 \, a c^{2} d - 3 \, a^{2} c f\right)} h^{2}\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} f h^{2} x^{3} - 2 \, a c^{2} e g^{2} + 4 \, a^{2} c e h^{2} - 4 \, {\left(a c^{2} d - 2 \, a^{2} c f\right)} g h + 2 \, {\left(2 \, a c^{2} f g h + a c^{2} e h^{2}\right)} x^{2} - {\left(4 \, a c^{2} e g h - 2 \, {\left(c^{3} d - a c^{2} f\right)} g^{2} + {\left(2 \, a c^{2} d - 3 \, a^{2} c f\right)} h^{2}\right)} x\right)} \sqrt{c x^{2} + a}}{4 \, {\left(a c^{4} x^{2} + a^{2} c^{3}\right)}}, -\frac{{\left(2 \, a^{2} c f g^{2} + 4 \, a^{2} c e g h + {\left(2 \, a^{2} c d - 3 \, a^{3} f\right)} h^{2} + {\left(2 \, a c^{2} f g^{2} + 4 \, a c^{2} e g h + {\left(2 \, a c^{2} d - 3 \, a^{2} c f\right)} h^{2}\right)} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(a c^{2} f h^{2} x^{3} - 2 \, a c^{2} e g^{2} + 4 \, a^{2} c e h^{2} - 4 \, {\left(a c^{2} d - 2 \, a^{2} c f\right)} g h + 2 \, {\left(2 \, a c^{2} f g h + a c^{2} e h^{2}\right)} x^{2} - {\left(4 \, a c^{2} e g h - 2 \, {\left(c^{3} d - a c^{2} f\right)} g^{2} + {\left(2 \, a c^{2} d - 3 \, a^{2} c f\right)} h^{2}\right)} x\right)} \sqrt{c x^{2} + a}}{2 \, {\left(a c^{4} x^{2} + a^{2} c^{3}\right)}}\right]"," ",0,"[-1/4*((2*a^2*c*f*g^2 + 4*a^2*c*e*g*h + (2*a^2*c*d - 3*a^3*f)*h^2 + (2*a*c^2*f*g^2 + 4*a*c^2*e*g*h + (2*a*c^2*d - 3*a^2*c*f)*h^2)*x^2)*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) - 2*(a*c^2*f*h^2*x^3 - 2*a*c^2*e*g^2 + 4*a^2*c*e*h^2 - 4*(a*c^2*d - 2*a^2*c*f)*g*h + 2*(2*a*c^2*f*g*h + a*c^2*e*h^2)*x^2 - (4*a*c^2*e*g*h - 2*(c^3*d - a*c^2*f)*g^2 + (2*a*c^2*d - 3*a^2*c*f)*h^2)*x)*sqrt(c*x^2 + a))/(a*c^4*x^2 + a^2*c^3), -1/2*((2*a^2*c*f*g^2 + 4*a^2*c*e*g*h + (2*a^2*c*d - 3*a^3*f)*h^2 + (2*a*c^2*f*g^2 + 4*a*c^2*e*g*h + (2*a*c^2*d - 3*a^2*c*f)*h^2)*x^2)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (a*c^2*f*h^2*x^3 - 2*a*c^2*e*g^2 + 4*a^2*c*e*h^2 - 4*(a*c^2*d - 2*a^2*c*f)*g*h + 2*(2*a*c^2*f*g*h + a*c^2*e*h^2)*x^2 - (4*a*c^2*e*g*h - 2*(c^3*d - a*c^2*f)*g^2 + (2*a*c^2*d - 3*a^2*c*f)*h^2)*x)*sqrt(c*x^2 + a))/(a*c^4*x^2 + a^2*c^3)]","A",0
110,1,278,0,1.024051," ","integrate((h*x+g)*(f*x^2+e*x+d)/(c*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(a^{2} f g + a^{2} e h + {\left(a c f g + a c e h\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 f h x^{2} - a c e g - {\left(a c d - 2 \, a^{2} f\right)} h - {\left(a c e h - {\left(c^{2} d - a c f\right)} g\right)} x\right)} \sqrt{c x^{2} + a}}{2 \, {\left(a c^{3} x^{2} + a^{2} c^{2}\right)}}, -\frac{{\left(a^{2} f g + a^{2} e h + {\left(a c f g + a c e h\right)} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(a c f h x^{2} - a c e g - {\left(a c d - 2 \, a^{2} f\right)} h - {\left(a c e h - {\left(c^{2} d - a c f\right)} g\right)} x\right)} \sqrt{c x^{2} + a}}{a c^{3} x^{2} + a^{2} c^{2}}\right]"," ",0,"[1/2*((a^2*f*g + a^2*e*h + (a*c*f*g + a*c*e*h)*x^2)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(a*c*f*h*x^2 - a*c*e*g - (a*c*d - 2*a^2*f)*h - (a*c*e*h - (c^2*d - a*c*f)*g)*x)*sqrt(c*x^2 + a))/(a*c^3*x^2 + a^2*c^2), -((a^2*f*g + a^2*e*h + (a*c*f*g + a*c*e*h)*x^2)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (a*c*f*h*x^2 - a*c*e*g - (a*c*d - 2*a^2*f)*h - (a*c*e*h - (c^2*d - a*c*f)*g)*x)*sqrt(c*x^2 + a))/(a*c^3*x^2 + a^2*c^2)]","A",0
111,1,181,0,0.929838," ","integrate((f*x^2+e*x+d)/(c*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(a c f x^{2} + a^{2} f\right)} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) - 2 \, {\left(a c e - {\left(c^{2} d - a c f\right)} x\right)} \sqrt{c x^{2} + a}}{2 \, {\left(a c^{3} x^{2} + a^{2} c^{2}\right)}}, -\frac{{\left(a c f x^{2} + a^{2} f\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) + {\left(a c e - {\left(c^{2} d - a c f\right)} x\right)} \sqrt{c x^{2} + a}}{a c^{3} x^{2} + a^{2} c^{2}}\right]"," ",0,"[1/2*((a*c*f*x^2 + a^2*f)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) - 2*(a*c*e - (c^2*d - a*c*f)*x)*sqrt(c*x^2 + a))/(a*c^3*x^2 + a^2*c^2), -((a*c*f*x^2 + a^2*f)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) + (a*c*e - (c^2*d - a*c*f)*x)*sqrt(c*x^2 + a))/(a*c^3*x^2 + a^2*c^2)]","A",0
112,1,721,0,3.202219," ","integrate((f*x^2+e*x+d)/(h*x+g)/(c*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(a^{2} c f g^{2} - a^{2} c e g h + a^{2} c d h^{2} + {\left(a c^{2} f g^{2} - a c^{2} e g h + a c^{2} d h^{2}\right)} x^{2}\right)} \sqrt{c g^{2} + a h^{2}} \log\left(\frac{2 \, a c g h x - a c g^{2} - 2 \, a^{2} h^{2} - {\left(2 \, c^{2} g^{2} + a c h^{2}\right)} x^{2} - 2 \, \sqrt{c g^{2} + a h^{2}} {\left(c g x - a h\right)} \sqrt{c x^{2} + a}}{h^{2} x^{2} + 2 \, g h x + g^{2}}\right) - 2 \, {\left(a c^{2} e g^{3} + a^{2} c e g h^{2} - {\left(a c^{2} d - a^{2} c f\right)} g^{2} h - {\left(a^{2} c d - a^{3} f\right)} h^{3} - {\left(a c^{2} e g^{2} h + a^{2} c e h^{3} + {\left(c^{3} d - a c^{2} f\right)} g^{3} + {\left(a c^{2} d - a^{2} c f\right)} g h^{2}\right)} x\right)} \sqrt{c x^{2} + a}}{2 \, {\left(a^{2} c^{3} g^{4} + 2 \, a^{3} c^{2} g^{2} h^{2} + a^{4} c h^{4} + {\left(a c^{4} g^{4} + 2 \, a^{2} c^{3} g^{2} h^{2} + a^{3} c^{2} h^{4}\right)} x^{2}\right)}}, -\frac{{\left(a^{2} c f g^{2} - a^{2} c e g h + a^{2} c d h^{2} + {\left(a c^{2} f g^{2} - a c^{2} e g h + a c^{2} d h^{2}\right)} x^{2}\right)} \sqrt{-c g^{2} - a h^{2}} \arctan\left(\frac{\sqrt{-c g^{2} - a h^{2}} {\left(c g x - a h\right)} \sqrt{c x^{2} + a}}{a c g^{2} + a^{2} h^{2} + {\left(c^{2} g^{2} + a c h^{2}\right)} x^{2}}\right) + {\left(a c^{2} e g^{3} + a^{2} c e g h^{2} - {\left(a c^{2} d - a^{2} c f\right)} g^{2} h - {\left(a^{2} c d - a^{3} f\right)} h^{3} - {\left(a c^{2} e g^{2} h + a^{2} c e h^{3} + {\left(c^{3} d - a c^{2} f\right)} g^{3} + {\left(a c^{2} d - a^{2} c f\right)} g h^{2}\right)} x\right)} \sqrt{c x^{2} + a}}{a^{2} c^{3} g^{4} + 2 \, a^{3} c^{2} g^{2} h^{2} + a^{4} c h^{4} + {\left(a c^{4} g^{4} + 2 \, a^{2} c^{3} g^{2} h^{2} + a^{3} c^{2} h^{4}\right)} x^{2}}\right]"," ",0,"[1/2*((a^2*c*f*g^2 - a^2*c*e*g*h + a^2*c*d*h^2 + (a*c^2*f*g^2 - a*c^2*e*g*h + a*c^2*d*h^2)*x^2)*sqrt(c*g^2 + a*h^2)*log((2*a*c*g*h*x - a*c*g^2 - 2*a^2*h^2 - (2*c^2*g^2 + a*c*h^2)*x^2 - 2*sqrt(c*g^2 + a*h^2)*(c*g*x - a*h)*sqrt(c*x^2 + a))/(h^2*x^2 + 2*g*h*x + g^2)) - 2*(a*c^2*e*g^3 + a^2*c*e*g*h^2 - (a*c^2*d - a^2*c*f)*g^2*h - (a^2*c*d - a^3*f)*h^3 - (a*c^2*e*g^2*h + a^2*c*e*h^3 + (c^3*d - a*c^2*f)*g^3 + (a*c^2*d - a^2*c*f)*g*h^2)*x)*sqrt(c*x^2 + a))/(a^2*c^3*g^4 + 2*a^3*c^2*g^2*h^2 + a^4*c*h^4 + (a*c^4*g^4 + 2*a^2*c^3*g^2*h^2 + a^3*c^2*h^4)*x^2), -((a^2*c*f*g^2 - a^2*c*e*g*h + a^2*c*d*h^2 + (a*c^2*f*g^2 - a*c^2*e*g*h + a*c^2*d*h^2)*x^2)*sqrt(-c*g^2 - a*h^2)*arctan(sqrt(-c*g^2 - a*h^2)*(c*g*x - a*h)*sqrt(c*x^2 + a)/(a*c*g^2 + a^2*h^2 + (c^2*g^2 + a*c*h^2)*x^2)) + (a*c^2*e*g^3 + a^2*c*e*g*h^2 - (a*c^2*d - a^2*c*f)*g^2*h - (a^2*c*d - a^3*f)*h^3 - (a*c^2*e*g^2*h + a^2*c*e*h^3 + (c^3*d - a*c^2*f)*g^3 + (a*c^2*d - a^2*c*f)*g*h^2)*x)*sqrt(c*x^2 + a))/(a^2*c^3*g^4 + 2*a^3*c^2*g^2*h^2 + a^4*c*h^4 + (a*c^4*g^4 + 2*a^2*c^3*g^2*h^2 + a^3*c^2*h^4)*x^2)]","B",0
113,1,1573,0,4.363303," ","integrate((f*x^2+e*x+d)/(h*x+g)^2/(c*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left(a^{2} c f g^{4} - 2 \, a^{2} c e g^{3} h + a^{3} e g h^{3} + {\left(3 \, a^{2} c d - 2 \, a^{3} f\right)} g^{2} h^{2} + {\left(a c^{2} f g^{3} h - 2 \, a c^{2} e g^{2} h^{2} + a^{2} c e h^{4} + {\left(3 \, a c^{2} d - 2 \, a^{2} c f\right)} g h^{3}\right)} x^{3} + {\left(a c^{2} f g^{4} - 2 \, a c^{2} e g^{3} h + a^{2} c e g h^{3} + {\left(3 \, a c^{2} d - 2 \, a^{2} c f\right)} g^{2} h^{2}\right)} x^{2} + {\left(a^{2} c f g^{3} h - 2 \, a^{2} c e g^{2} h^{2} + a^{3} e h^{4} + {\left(3 \, a^{2} c d - 2 \, a^{3} f\right)} g h^{3}\right)} x\right)} \sqrt{c g^{2} + a h^{2}} \log\left(\frac{2 \, a c g h x - a c g^{2} - 2 \, a^{2} h^{2} - {\left(2 \, c^{2} g^{2} + a c h^{2}\right)} x^{2} + 2 \, \sqrt{c g^{2} + a h^{2}} {\left(c g x - a h\right)} \sqrt{c x^{2} + a}}{h^{2} x^{2} + 2 \, g h x + g^{2}}\right) + 2 \, {\left(a c^{2} e g^{5} - a^{2} c e g^{3} h^{2} - 2 \, a^{3} e g h^{4} + a^{3} d h^{5} - {\left(2 \, a c^{2} d - 3 \, a^{2} c f\right)} g^{4} h - {\left(a^{2} c d - 3 \, a^{3} f\right)} g^{2} h^{3} - {\left(3 \, a c^{2} e g^{3} h^{2} + 3 \, a^{2} c e g h^{4} + {\left(c^{3} d - 2 \, a c^{2} f\right)} g^{4} h - {\left(a c^{2} d + a^{2} c f\right)} g^{2} h^{3} - {\left(2 \, a^{2} c d - a^{3} f\right)} h^{5}\right)} x^{2} - {\left(a c^{2} e g^{4} h + 2 \, a^{2} c e g^{2} h^{3} + a^{3} e h^{5} + {\left(c^{3} d - a c^{2} f\right)} g^{5} + 2 \, {\left(a c^{2} d - a^{2} c f\right)} g^{3} h^{2} + {\left(a^{2} c d - a^{3} f\right)} g h^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{2 \, {\left(a^{2} c^{3} g^{7} + 3 \, a^{3} c^{2} g^{5} h^{2} + 3 \, a^{4} c g^{3} h^{4} + a^{5} g h^{6} + {\left(a c^{4} g^{6} h + 3 \, a^{2} c^{3} g^{4} h^{3} + 3 \, a^{3} c^{2} g^{2} h^{5} + a^{4} c h^{7}\right)} x^{3} + {\left(a c^{4} g^{7} + 3 \, a^{2} c^{3} g^{5} h^{2} + 3 \, a^{3} c^{2} g^{3} h^{4} + a^{4} c g h^{6}\right)} x^{2} + {\left(a^{2} c^{3} g^{6} h + 3 \, a^{3} c^{2} g^{4} h^{3} + 3 \, a^{4} c g^{2} h^{5} + a^{5} h^{7}\right)} x\right)}}, -\frac{{\left(a^{2} c f g^{4} - 2 \, a^{2} c e g^{3} h + a^{3} e g h^{3} + {\left(3 \, a^{2} c d - 2 \, a^{3} f\right)} g^{2} h^{2} + {\left(a c^{2} f g^{3} h - 2 \, a c^{2} e g^{2} h^{2} + a^{2} c e h^{4} + {\left(3 \, a c^{2} d - 2 \, a^{2} c f\right)} g h^{3}\right)} x^{3} + {\left(a c^{2} f g^{4} - 2 \, a c^{2} e g^{3} h + a^{2} c e g h^{3} + {\left(3 \, a c^{2} d - 2 \, a^{2} c f\right)} g^{2} h^{2}\right)} x^{2} + {\left(a^{2} c f g^{3} h - 2 \, a^{2} c e g^{2} h^{2} + a^{3} e h^{4} + {\left(3 \, a^{2} c d - 2 \, a^{3} f\right)} g h^{3}\right)} x\right)} \sqrt{-c g^{2} - a h^{2}} \arctan\left(\frac{\sqrt{-c g^{2} - a h^{2}} {\left(c g x - a h\right)} \sqrt{c x^{2} + a}}{a c g^{2} + a^{2} h^{2} + {\left(c^{2} g^{2} + a c h^{2}\right)} x^{2}}\right) + {\left(a c^{2} e g^{5} - a^{2} c e g^{3} h^{2} - 2 \, a^{3} e g h^{4} + a^{3} d h^{5} - {\left(2 \, a c^{2} d - 3 \, a^{2} c f\right)} g^{4} h - {\left(a^{2} c d - 3 \, a^{3} f\right)} g^{2} h^{3} - {\left(3 \, a c^{2} e g^{3} h^{2} + 3 \, a^{2} c e g h^{4} + {\left(c^{3} d - 2 \, a c^{2} f\right)} g^{4} h - {\left(a c^{2} d + a^{2} c f\right)} g^{2} h^{3} - {\left(2 \, a^{2} c d - a^{3} f\right)} h^{5}\right)} x^{2} - {\left(a c^{2} e g^{4} h + 2 \, a^{2} c e g^{2} h^{3} + a^{3} e h^{5} + {\left(c^{3} d - a c^{2} f\right)} g^{5} + 2 \, {\left(a c^{2} d - a^{2} c f\right)} g^{3} h^{2} + {\left(a^{2} c d - a^{3} f\right)} g h^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{a^{2} c^{3} g^{7} + 3 \, a^{3} c^{2} g^{5} h^{2} + 3 \, a^{4} c g^{3} h^{4} + a^{5} g h^{6} + {\left(a c^{4} g^{6} h + 3 \, a^{2} c^{3} g^{4} h^{3} + 3 \, a^{3} c^{2} g^{2} h^{5} + a^{4} c h^{7}\right)} x^{3} + {\left(a c^{4} g^{7} + 3 \, a^{2} c^{3} g^{5} h^{2} + 3 \, a^{3} c^{2} g^{3} h^{4} + a^{4} c g h^{6}\right)} x^{2} + {\left(a^{2} c^{3} g^{6} h + 3 \, a^{3} c^{2} g^{4} h^{3} + 3 \, a^{4} c g^{2} h^{5} + a^{5} h^{7}\right)} x}\right]"," ",0,"[-1/2*((a^2*c*f*g^4 - 2*a^2*c*e*g^3*h + a^3*e*g*h^3 + (3*a^2*c*d - 2*a^3*f)*g^2*h^2 + (a*c^2*f*g^3*h - 2*a*c^2*e*g^2*h^2 + a^2*c*e*h^4 + (3*a*c^2*d - 2*a^2*c*f)*g*h^3)*x^3 + (a*c^2*f*g^4 - 2*a*c^2*e*g^3*h + a^2*c*e*g*h^3 + (3*a*c^2*d - 2*a^2*c*f)*g^2*h^2)*x^2 + (a^2*c*f*g^3*h - 2*a^2*c*e*g^2*h^2 + a^3*e*h^4 + (3*a^2*c*d - 2*a^3*f)*g*h^3)*x)*sqrt(c*g^2 + a*h^2)*log((2*a*c*g*h*x - a*c*g^2 - 2*a^2*h^2 - (2*c^2*g^2 + a*c*h^2)*x^2 + 2*sqrt(c*g^2 + a*h^2)*(c*g*x - a*h)*sqrt(c*x^2 + a))/(h^2*x^2 + 2*g*h*x + g^2)) + 2*(a*c^2*e*g^5 - a^2*c*e*g^3*h^2 - 2*a^3*e*g*h^4 + a^3*d*h^5 - (2*a*c^2*d - 3*a^2*c*f)*g^4*h - (a^2*c*d - 3*a^3*f)*g^2*h^3 - (3*a*c^2*e*g^3*h^2 + 3*a^2*c*e*g*h^4 + (c^3*d - 2*a*c^2*f)*g^4*h - (a*c^2*d + a^2*c*f)*g^2*h^3 - (2*a^2*c*d - a^3*f)*h^5)*x^2 - (a*c^2*e*g^4*h + 2*a^2*c*e*g^2*h^3 + a^3*e*h^5 + (c^3*d - a*c^2*f)*g^5 + 2*(a*c^2*d - a^2*c*f)*g^3*h^2 + (a^2*c*d - a^3*f)*g*h^4)*x)*sqrt(c*x^2 + a))/(a^2*c^3*g^7 + 3*a^3*c^2*g^5*h^2 + 3*a^4*c*g^3*h^4 + a^5*g*h^6 + (a*c^4*g^6*h + 3*a^2*c^3*g^4*h^3 + 3*a^3*c^2*g^2*h^5 + a^4*c*h^7)*x^3 + (a*c^4*g^7 + 3*a^2*c^3*g^5*h^2 + 3*a^3*c^2*g^3*h^4 + a^4*c*g*h^6)*x^2 + (a^2*c^3*g^6*h + 3*a^3*c^2*g^4*h^3 + 3*a^4*c*g^2*h^5 + a^5*h^7)*x), -((a^2*c*f*g^4 - 2*a^2*c*e*g^3*h + a^3*e*g*h^3 + (3*a^2*c*d - 2*a^3*f)*g^2*h^2 + (a*c^2*f*g^3*h - 2*a*c^2*e*g^2*h^2 + a^2*c*e*h^4 + (3*a*c^2*d - 2*a^2*c*f)*g*h^3)*x^3 + (a*c^2*f*g^4 - 2*a*c^2*e*g^3*h + a^2*c*e*g*h^3 + (3*a*c^2*d - 2*a^2*c*f)*g^2*h^2)*x^2 + (a^2*c*f*g^3*h - 2*a^2*c*e*g^2*h^2 + a^3*e*h^4 + (3*a^2*c*d - 2*a^3*f)*g*h^3)*x)*sqrt(-c*g^2 - a*h^2)*arctan(sqrt(-c*g^2 - a*h^2)*(c*g*x - a*h)*sqrt(c*x^2 + a)/(a*c*g^2 + a^2*h^2 + (c^2*g^2 + a*c*h^2)*x^2)) + (a*c^2*e*g^5 - a^2*c*e*g^3*h^2 - 2*a^3*e*g*h^4 + a^3*d*h^5 - (2*a*c^2*d - 3*a^2*c*f)*g^4*h - (a^2*c*d - 3*a^3*f)*g^2*h^3 - (3*a*c^2*e*g^3*h^2 + 3*a^2*c*e*g*h^4 + (c^3*d - 2*a*c^2*f)*g^4*h - (a*c^2*d + a^2*c*f)*g^2*h^3 - (2*a^2*c*d - a^3*f)*h^5)*x^2 - (a*c^2*e*g^4*h + 2*a^2*c*e*g^2*h^3 + a^3*e*h^5 + (c^3*d - a*c^2*f)*g^5 + 2*(a*c^2*d - a^2*c*f)*g^3*h^2 + (a^2*c*d - a^3*f)*g*h^4)*x)*sqrt(c*x^2 + a))/(a^2*c^3*g^7 + 3*a^3*c^2*g^5*h^2 + 3*a^4*c*g^3*h^4 + a^5*g*h^6 + (a*c^4*g^6*h + 3*a^2*c^3*g^4*h^3 + 3*a^3*c^2*g^2*h^5 + a^4*c*h^7)*x^3 + (a*c^4*g^7 + 3*a^2*c^3*g^5*h^2 + 3*a^3*c^2*g^3*h^4 + a^4*c*g*h^6)*x^2 + (a^2*c^3*g^6*h + 3*a^3*c^2*g^4*h^3 + 3*a^4*c*g^2*h^5 + a^5*h^7)*x)]","B",0
114,1,2853,0,21.945682," ","integrate((f*x^2+e*x+d)/(h*x+g)^3/(c*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(2 \, a^{2} c^{2} f g^{6} - 6 \, a^{2} c^{2} e g^{5} h + 9 \, a^{3} c e g^{3} h^{3} + {\left(12 \, a^{2} c^{2} d - 11 \, a^{3} c f\right)} g^{4} h^{2} - {\left(3 \, a^{3} c d - 2 \, a^{4} f\right)} g^{2} h^{4} + {\left(2 \, a c^{3} f g^{4} h^{2} - 6 \, a c^{3} e g^{3} h^{3} + 9 \, a^{2} c^{2} e g h^{5} + {\left(12 \, a c^{3} d - 11 \, a^{2} c^{2} f\right)} g^{2} h^{4} - {\left(3 \, a^{2} c^{2} d - 2 \, a^{3} c f\right)} h^{6}\right)} x^{4} + 2 \, {\left(2 \, a c^{3} f g^{5} h - 6 \, a c^{3} e g^{4} h^{2} + 9 \, a^{2} c^{2} e g^{2} h^{4} + {\left(12 \, a c^{3} d - 11 \, a^{2} c^{2} f\right)} g^{3} h^{3} - {\left(3 \, a^{2} c^{2} d - 2 \, a^{3} c f\right)} g h^{5}\right)} x^{3} + {\left(2 \, a c^{3} f g^{6} - 6 \, a c^{3} e g^{5} h + 3 \, a^{2} c^{2} e g^{3} h^{3} + 9 \, a^{3} c e g h^{5} + 3 \, {\left(4 \, a c^{3} d - 3 \, a^{2} c^{2} f\right)} g^{4} h^{2} + 9 \, {\left(a^{2} c^{2} d - a^{3} c f\right)} g^{2} h^{4} - {\left(3 \, a^{3} c d - 2 \, a^{4} f\right)} h^{6}\right)} x^{2} + 2 \, {\left(2 \, a^{2} c^{2} f g^{5} h - 6 \, a^{2} c^{2} e g^{4} h^{2} + 9 \, a^{3} c e g^{2} h^{4} + {\left(12 \, a^{2} c^{2} d - 11 \, a^{3} c f\right)} g^{3} h^{3} - {\left(3 \, a^{3} c d - 2 \, a^{4} f\right)} g h^{5}\right)} x\right)} \sqrt{c g^{2} + a h^{2}} \log\left(\frac{2 \, a c g h x - a c g^{2} - 2 \, a^{2} h^{2} - {\left(2 \, c^{2} g^{2} + a c h^{2}\right)} x^{2} - 2 \, \sqrt{c g^{2} + a h^{2}} {\left(c g x - a h\right)} \sqrt{c x^{2} + a}}{h^{2} x^{2} + 2 \, g h x + g^{2}}\right) - 2 \, {\left(2 \, a c^{3} e g^{7} - 10 \, a^{2} c^{2} e g^{5} h^{2} - 11 \, a^{3} c e g^{3} h^{4} + a^{4} e g h^{6} + a^{4} d h^{7} - 2 \, {\left(3 \, a c^{3} d - 5 \, a^{2} c^{2} f\right)} g^{6} h + {\left(4 \, a^{2} c^{2} d + 5 \, a^{3} c f\right)} g^{4} h^{3} + {\left(11 \, a^{3} c d - 5 \, a^{4} f\right)} g^{2} h^{5} - {\left(11 \, a c^{3} e g^{4} h^{3} + 7 \, a^{2} c^{2} e g^{2} h^{5} - 4 \, a^{3} c e h^{7} + {\left(2 \, c^{4} d - 5 \, a c^{3} f\right)} g^{5} h^{2} - {\left(11 \, a c^{3} d - 5 \, a^{2} c^{2} f\right)} g^{3} h^{4} - {\left(13 \, a^{2} c^{2} d - 10 \, a^{3} c f\right)} g h^{6}\right)} x^{3} - {\left(16 \, a c^{3} e g^{5} h^{2} + 17 \, a^{2} c^{2} e g^{3} h^{4} + a^{3} c e g h^{6} + 4 \, {\left(c^{4} d - 2 \, a c^{3} f\right)} g^{6} h - {\left(10 \, a c^{3} d - a^{2} c^{2} f\right)} g^{4} h^{3} - {\left(17 \, a^{2} c^{2} d - 11 \, a^{3} c f\right)} g^{2} h^{5} - {\left(3 \, a^{3} c d - 2 \, a^{4} f\right)} h^{7}\right)} x^{2} - {\left(2 \, a c^{3} e g^{6} h + 17 \, a^{2} c^{2} e g^{4} h^{3} + 13 \, a^{3} c e g^{2} h^{5} - 2 \, a^{4} e h^{7} + 2 \, {\left(c^{4} d - a c^{3} f\right)} g^{7} + {\left(8 \, a c^{3} d - 11 \, a^{2} c^{2} f\right)} g^{5} h^{2} - {\left(5 \, a^{2} c^{2} d + a^{3} c f\right)} g^{3} h^{4} - {\left(11 \, a^{3} c d - 8 \, a^{4} f\right)} g h^{6}\right)} x\right)} \sqrt{c x^{2} + a}}{4 \, {\left(a^{2} c^{4} g^{10} + 4 \, a^{3} c^{3} g^{8} h^{2} + 6 \, a^{4} c^{2} g^{6} h^{4} + 4 \, a^{5} c g^{4} h^{6} + a^{6} g^{2} h^{8} + {\left(a c^{5} g^{8} h^{2} + 4 \, a^{2} c^{4} g^{6} h^{4} + 6 \, a^{3} c^{3} g^{4} h^{6} + 4 \, a^{4} c^{2} g^{2} h^{8} + a^{5} c h^{10}\right)} x^{4} + 2 \, {\left(a c^{5} g^{9} h + 4 \, a^{2} c^{4} g^{7} h^{3} + 6 \, a^{3} c^{3} g^{5} h^{5} + 4 \, a^{4} c^{2} g^{3} h^{7} + a^{5} c g h^{9}\right)} x^{3} + {\left(a c^{5} g^{10} + 5 \, a^{2} c^{4} g^{8} h^{2} + 10 \, a^{3} c^{3} g^{6} h^{4} + 10 \, a^{4} c^{2} g^{4} h^{6} + 5 \, a^{5} c g^{2} h^{8} + a^{6} h^{10}\right)} x^{2} + 2 \, {\left(a^{2} c^{4} g^{9} h + 4 \, a^{3} c^{3} g^{7} h^{3} + 6 \, a^{4} c^{2} g^{5} h^{5} + 4 \, a^{5} c g^{3} h^{7} + a^{6} g h^{9}\right)} x\right)}}, -\frac{{\left(2 \, a^{2} c^{2} f g^{6} - 6 \, a^{2} c^{2} e g^{5} h + 9 \, a^{3} c e g^{3} h^{3} + {\left(12 \, a^{2} c^{2} d - 11 \, a^{3} c f\right)} g^{4} h^{2} - {\left(3 \, a^{3} c d - 2 \, a^{4} f\right)} g^{2} h^{4} + {\left(2 \, a c^{3} f g^{4} h^{2} - 6 \, a c^{3} e g^{3} h^{3} + 9 \, a^{2} c^{2} e g h^{5} + {\left(12 \, a c^{3} d - 11 \, a^{2} c^{2} f\right)} g^{2} h^{4} - {\left(3 \, a^{2} c^{2} d - 2 \, a^{3} c f\right)} h^{6}\right)} x^{4} + 2 \, {\left(2 \, a c^{3} f g^{5} h - 6 \, a c^{3} e g^{4} h^{2} + 9 \, a^{2} c^{2} e g^{2} h^{4} + {\left(12 \, a c^{3} d - 11 \, a^{2} c^{2} f\right)} g^{3} h^{3} - {\left(3 \, a^{2} c^{2} d - 2 \, a^{3} c f\right)} g h^{5}\right)} x^{3} + {\left(2 \, a c^{3} f g^{6} - 6 \, a c^{3} e g^{5} h + 3 \, a^{2} c^{2} e g^{3} h^{3} + 9 \, a^{3} c e g h^{5} + 3 \, {\left(4 \, a c^{3} d - 3 \, a^{2} c^{2} f\right)} g^{4} h^{2} + 9 \, {\left(a^{2} c^{2} d - a^{3} c f\right)} g^{2} h^{4} - {\left(3 \, a^{3} c d - 2 \, a^{4} f\right)} h^{6}\right)} x^{2} + 2 \, {\left(2 \, a^{2} c^{2} f g^{5} h - 6 \, a^{2} c^{2} e g^{4} h^{2} + 9 \, a^{3} c e g^{2} h^{4} + {\left(12 \, a^{2} c^{2} d - 11 \, a^{3} c f\right)} g^{3} h^{3} - {\left(3 \, a^{3} c d - 2 \, a^{4} f\right)} g h^{5}\right)} x\right)} \sqrt{-c g^{2} - a h^{2}} \arctan\left(\frac{\sqrt{-c g^{2} - a h^{2}} {\left(c g x - a h\right)} \sqrt{c x^{2} + a}}{a c g^{2} + a^{2} h^{2} + {\left(c^{2} g^{2} + a c h^{2}\right)} x^{2}}\right) + {\left(2 \, a c^{3} e g^{7} - 10 \, a^{2} c^{2} e g^{5} h^{2} - 11 \, a^{3} c e g^{3} h^{4} + a^{4} e g h^{6} + a^{4} d h^{7} - 2 \, {\left(3 \, a c^{3} d - 5 \, a^{2} c^{2} f\right)} g^{6} h + {\left(4 \, a^{2} c^{2} d + 5 \, a^{3} c f\right)} g^{4} h^{3} + {\left(11 \, a^{3} c d - 5 \, a^{4} f\right)} g^{2} h^{5} - {\left(11 \, a c^{3} e g^{4} h^{3} + 7 \, a^{2} c^{2} e g^{2} h^{5} - 4 \, a^{3} c e h^{7} + {\left(2 \, c^{4} d - 5 \, a c^{3} f\right)} g^{5} h^{2} - {\left(11 \, a c^{3} d - 5 \, a^{2} c^{2} f\right)} g^{3} h^{4} - {\left(13 \, a^{2} c^{2} d - 10 \, a^{3} c f\right)} g h^{6}\right)} x^{3} - {\left(16 \, a c^{3} e g^{5} h^{2} + 17 \, a^{2} c^{2} e g^{3} h^{4} + a^{3} c e g h^{6} + 4 \, {\left(c^{4} d - 2 \, a c^{3} f\right)} g^{6} h - {\left(10 \, a c^{3} d - a^{2} c^{2} f\right)} g^{4} h^{3} - {\left(17 \, a^{2} c^{2} d - 11 \, a^{3} c f\right)} g^{2} h^{5} - {\left(3 \, a^{3} c d - 2 \, a^{4} f\right)} h^{7}\right)} x^{2} - {\left(2 \, a c^{3} e g^{6} h + 17 \, a^{2} c^{2} e g^{4} h^{3} + 13 \, a^{3} c e g^{2} h^{5} - 2 \, a^{4} e h^{7} + 2 \, {\left(c^{4} d - a c^{3} f\right)} g^{7} + {\left(8 \, a c^{3} d - 11 \, a^{2} c^{2} f\right)} g^{5} h^{2} - {\left(5 \, a^{2} c^{2} d + a^{3} c f\right)} g^{3} h^{4} - {\left(11 \, a^{3} c d - 8 \, a^{4} f\right)} g h^{6}\right)} x\right)} \sqrt{c x^{2} + a}}{2 \, {\left(a^{2} c^{4} g^{10} + 4 \, a^{3} c^{3} g^{8} h^{2} + 6 \, a^{4} c^{2} g^{6} h^{4} + 4 \, a^{5} c g^{4} h^{6} + a^{6} g^{2} h^{8} + {\left(a c^{5} g^{8} h^{2} + 4 \, a^{2} c^{4} g^{6} h^{4} + 6 \, a^{3} c^{3} g^{4} h^{6} + 4 \, a^{4} c^{2} g^{2} h^{8} + a^{5} c h^{10}\right)} x^{4} + 2 \, {\left(a c^{5} g^{9} h + 4 \, a^{2} c^{4} g^{7} h^{3} + 6 \, a^{3} c^{3} g^{5} h^{5} + 4 \, a^{4} c^{2} g^{3} h^{7} + a^{5} c g h^{9}\right)} x^{3} + {\left(a c^{5} g^{10} + 5 \, a^{2} c^{4} g^{8} h^{2} + 10 \, a^{3} c^{3} g^{6} h^{4} + 10 \, a^{4} c^{2} g^{4} h^{6} + 5 \, a^{5} c g^{2} h^{8} + a^{6} h^{10}\right)} x^{2} + 2 \, {\left(a^{2} c^{4} g^{9} h + 4 \, a^{3} c^{3} g^{7} h^{3} + 6 \, a^{4} c^{2} g^{5} h^{5} + 4 \, a^{5} c g^{3} h^{7} + a^{6} g h^{9}\right)} x\right)}}\right]"," ",0,"[1/4*((2*a^2*c^2*f*g^6 - 6*a^2*c^2*e*g^5*h + 9*a^3*c*e*g^3*h^3 + (12*a^2*c^2*d - 11*a^3*c*f)*g^4*h^2 - (3*a^3*c*d - 2*a^4*f)*g^2*h^4 + (2*a*c^3*f*g^4*h^2 - 6*a*c^3*e*g^3*h^3 + 9*a^2*c^2*e*g*h^5 + (12*a*c^3*d - 11*a^2*c^2*f)*g^2*h^4 - (3*a^2*c^2*d - 2*a^3*c*f)*h^6)*x^4 + 2*(2*a*c^3*f*g^5*h - 6*a*c^3*e*g^4*h^2 + 9*a^2*c^2*e*g^2*h^4 + (12*a*c^3*d - 11*a^2*c^2*f)*g^3*h^3 - (3*a^2*c^2*d - 2*a^3*c*f)*g*h^5)*x^3 + (2*a*c^3*f*g^6 - 6*a*c^3*e*g^5*h + 3*a^2*c^2*e*g^3*h^3 + 9*a^3*c*e*g*h^5 + 3*(4*a*c^3*d - 3*a^2*c^2*f)*g^4*h^2 + 9*(a^2*c^2*d - a^3*c*f)*g^2*h^4 - (3*a^3*c*d - 2*a^4*f)*h^6)*x^2 + 2*(2*a^2*c^2*f*g^5*h - 6*a^2*c^2*e*g^4*h^2 + 9*a^3*c*e*g^2*h^4 + (12*a^2*c^2*d - 11*a^3*c*f)*g^3*h^3 - (3*a^3*c*d - 2*a^4*f)*g*h^5)*x)*sqrt(c*g^2 + a*h^2)*log((2*a*c*g*h*x - a*c*g^2 - 2*a^2*h^2 - (2*c^2*g^2 + a*c*h^2)*x^2 - 2*sqrt(c*g^2 + a*h^2)*(c*g*x - a*h)*sqrt(c*x^2 + a))/(h^2*x^2 + 2*g*h*x + g^2)) - 2*(2*a*c^3*e*g^7 - 10*a^2*c^2*e*g^5*h^2 - 11*a^3*c*e*g^3*h^4 + a^4*e*g*h^6 + a^4*d*h^7 - 2*(3*a*c^3*d - 5*a^2*c^2*f)*g^6*h + (4*a^2*c^2*d + 5*a^3*c*f)*g^4*h^3 + (11*a^3*c*d - 5*a^4*f)*g^2*h^5 - (11*a*c^3*e*g^4*h^3 + 7*a^2*c^2*e*g^2*h^5 - 4*a^3*c*e*h^7 + (2*c^4*d - 5*a*c^3*f)*g^5*h^2 - (11*a*c^3*d - 5*a^2*c^2*f)*g^3*h^4 - (13*a^2*c^2*d - 10*a^3*c*f)*g*h^6)*x^3 - (16*a*c^3*e*g^5*h^2 + 17*a^2*c^2*e*g^3*h^4 + a^3*c*e*g*h^6 + 4*(c^4*d - 2*a*c^3*f)*g^6*h - (10*a*c^3*d - a^2*c^2*f)*g^4*h^3 - (17*a^2*c^2*d - 11*a^3*c*f)*g^2*h^5 - (3*a^3*c*d - 2*a^4*f)*h^7)*x^2 - (2*a*c^3*e*g^6*h + 17*a^2*c^2*e*g^4*h^3 + 13*a^3*c*e*g^2*h^5 - 2*a^4*e*h^7 + 2*(c^4*d - a*c^3*f)*g^7 + (8*a*c^3*d - 11*a^2*c^2*f)*g^5*h^2 - (5*a^2*c^2*d + a^3*c*f)*g^3*h^4 - (11*a^3*c*d - 8*a^4*f)*g*h^6)*x)*sqrt(c*x^2 + a))/(a^2*c^4*g^10 + 4*a^3*c^3*g^8*h^2 + 6*a^4*c^2*g^6*h^4 + 4*a^5*c*g^4*h^6 + a^6*g^2*h^8 + (a*c^5*g^8*h^2 + 4*a^2*c^4*g^6*h^4 + 6*a^3*c^3*g^4*h^6 + 4*a^4*c^2*g^2*h^8 + a^5*c*h^10)*x^4 + 2*(a*c^5*g^9*h + 4*a^2*c^4*g^7*h^3 + 6*a^3*c^3*g^5*h^5 + 4*a^4*c^2*g^3*h^7 + a^5*c*g*h^9)*x^3 + (a*c^5*g^10 + 5*a^2*c^4*g^8*h^2 + 10*a^3*c^3*g^6*h^4 + 10*a^4*c^2*g^4*h^6 + 5*a^5*c*g^2*h^8 + a^6*h^10)*x^2 + 2*(a^2*c^4*g^9*h + 4*a^3*c^3*g^7*h^3 + 6*a^4*c^2*g^5*h^5 + 4*a^5*c*g^3*h^7 + a^6*g*h^9)*x), -1/2*((2*a^2*c^2*f*g^6 - 6*a^2*c^2*e*g^5*h + 9*a^3*c*e*g^3*h^3 + (12*a^2*c^2*d - 11*a^3*c*f)*g^4*h^2 - (3*a^3*c*d - 2*a^4*f)*g^2*h^4 + (2*a*c^3*f*g^4*h^2 - 6*a*c^3*e*g^3*h^3 + 9*a^2*c^2*e*g*h^5 + (12*a*c^3*d - 11*a^2*c^2*f)*g^2*h^4 - (3*a^2*c^2*d - 2*a^3*c*f)*h^6)*x^4 + 2*(2*a*c^3*f*g^5*h - 6*a*c^3*e*g^4*h^2 + 9*a^2*c^2*e*g^2*h^4 + (12*a*c^3*d - 11*a^2*c^2*f)*g^3*h^3 - (3*a^2*c^2*d - 2*a^3*c*f)*g*h^5)*x^3 + (2*a*c^3*f*g^6 - 6*a*c^3*e*g^5*h + 3*a^2*c^2*e*g^3*h^3 + 9*a^3*c*e*g*h^5 + 3*(4*a*c^3*d - 3*a^2*c^2*f)*g^4*h^2 + 9*(a^2*c^2*d - a^3*c*f)*g^2*h^4 - (3*a^3*c*d - 2*a^4*f)*h^6)*x^2 + 2*(2*a^2*c^2*f*g^5*h - 6*a^2*c^2*e*g^4*h^2 + 9*a^3*c*e*g^2*h^4 + (12*a^2*c^2*d - 11*a^3*c*f)*g^3*h^3 - (3*a^3*c*d - 2*a^4*f)*g*h^5)*x)*sqrt(-c*g^2 - a*h^2)*arctan(sqrt(-c*g^2 - a*h^2)*(c*g*x - a*h)*sqrt(c*x^2 + a)/(a*c*g^2 + a^2*h^2 + (c^2*g^2 + a*c*h^2)*x^2)) + (2*a*c^3*e*g^7 - 10*a^2*c^2*e*g^5*h^2 - 11*a^3*c*e*g^3*h^4 + a^4*e*g*h^6 + a^4*d*h^7 - 2*(3*a*c^3*d - 5*a^2*c^2*f)*g^6*h + (4*a^2*c^2*d + 5*a^3*c*f)*g^4*h^3 + (11*a^3*c*d - 5*a^4*f)*g^2*h^5 - (11*a*c^3*e*g^4*h^3 + 7*a^2*c^2*e*g^2*h^5 - 4*a^3*c*e*h^7 + (2*c^4*d - 5*a*c^3*f)*g^5*h^2 - (11*a*c^3*d - 5*a^2*c^2*f)*g^3*h^4 - (13*a^2*c^2*d - 10*a^3*c*f)*g*h^6)*x^3 - (16*a*c^3*e*g^5*h^2 + 17*a^2*c^2*e*g^3*h^4 + a^3*c*e*g*h^6 + 4*(c^4*d - 2*a*c^3*f)*g^6*h - (10*a*c^3*d - a^2*c^2*f)*g^4*h^3 - (17*a^2*c^2*d - 11*a^3*c*f)*g^2*h^5 - (3*a^3*c*d - 2*a^4*f)*h^7)*x^2 - (2*a*c^3*e*g^6*h + 17*a^2*c^2*e*g^4*h^3 + 13*a^3*c*e*g^2*h^5 - 2*a^4*e*h^7 + 2*(c^4*d - a*c^3*f)*g^7 + (8*a*c^3*d - 11*a^2*c^2*f)*g^5*h^2 - (5*a^2*c^2*d + a^3*c*f)*g^3*h^4 - (11*a^3*c*d - 8*a^4*f)*g*h^6)*x)*sqrt(c*x^2 + a))/(a^2*c^4*g^10 + 4*a^3*c^3*g^8*h^2 + 6*a^4*c^2*g^6*h^4 + 4*a^5*c*g^4*h^6 + a^6*g^2*h^8 + (a*c^5*g^8*h^2 + 4*a^2*c^4*g^6*h^4 + 6*a^3*c^3*g^4*h^6 + 4*a^4*c^2*g^2*h^8 + a^5*c*h^10)*x^4 + 2*(a*c^5*g^9*h + 4*a^2*c^4*g^7*h^3 + 6*a^3*c^3*g^5*h^5 + 4*a^4*c^2*g^3*h^7 + a^5*c*g*h^9)*x^3 + (a*c^5*g^10 + 5*a^2*c^4*g^8*h^2 + 10*a^3*c^3*g^6*h^4 + 10*a^4*c^2*g^4*h^6 + 5*a^5*c*g^2*h^8 + a^6*h^10)*x^2 + 2*(a^2*c^4*g^9*h + 4*a^3*c^3*g^7*h^3 + 6*a^4*c^2*g^5*h^5 + 4*a^5*c*g^3*h^7 + a^6*g*h^9)*x)]","B",0
115,1,68,0,0.745655," ","integrate((C*x^2+B*x+A)/(c*x^2+a)^(5/2),x, algorithm=""fricas"")","\frac{{\left(3 \, A a c x + {\left(C a c + 2 \, A c^{2}\right)} x^{3} - B a^{2}\right)} \sqrt{c x^{2} + a}}{3 \, {\left(a^{2} c^{3} x^{4} + 2 \, a^{3} c^{2} x^{2} + a^{4} c\right)}}"," ",0,"1/3*(3*A*a*c*x + (C*a*c + 2*A*c^2)*x^3 - B*a^2)*sqrt(c*x^2 + a)/(a^2*c^3*x^4 + 2*a^3*c^2*x^2 + a^4*c)","A",0
116,1,103,0,0.800159," ","integrate((C*x^2+B*x+A)/(c*x^2+a)^(7/2),x, algorithm=""fricas"")","\frac{{\left(2 \, {\left(C a c^{2} + 4 \, A c^{3}\right)} x^{5} + 15 \, A a^{2} c x - 3 \, B a^{3} + 5 \, {\left(C a^{2} c + 4 \, A a c^{2}\right)} x^{3}\right)} \sqrt{c x^{2} + a}}{15 \, {\left(a^{3} c^{4} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{5} c^{2} x^{2} + a^{6} c\right)}}"," ",0,"1/15*(2*(C*a*c^2 + 4*A*c^3)*x^5 + 15*A*a^2*c*x - 3*B*a^3 + 5*(C*a^2*c + 4*A*a*c^2)*x^3)*sqrt(c*x^2 + a)/(a^3*c^4*x^6 + 3*a^4*c^3*x^4 + 3*a^5*c^2*x^2 + a^6*c)","A",0
117,1,137,0,0.708726," ","integrate((C*x^2+B*x+A)/(c*x^2+a)^(9/2),x, algorithm=""fricas"")","\frac{{\left(8 \, {\left(C a c^{3} + 6 \, A c^{4}\right)} x^{7} + 105 \, A a^{3} c x + 28 \, {\left(C a^{2} c^{2} + 6 \, A a c^{3}\right)} x^{5} - 15 \, B a^{4} + 35 \, {\left(C a^{3} c + 6 \, A a^{2} c^{2}\right)} x^{3}\right)} \sqrt{c x^{2} + a}}{105 \, {\left(a^{4} c^{5} x^{8} + 4 \, a^{5} c^{4} x^{6} + 6 \, a^{6} c^{3} x^{4} + 4 \, a^{7} c^{2} x^{2} + a^{8} c\right)}}"," ",0,"1/105*(8*(C*a*c^3 + 6*A*c^4)*x^7 + 105*A*a^3*c*x + 28*(C*a^2*c^2 + 6*A*a*c^3)*x^5 - 15*B*a^4 + 35*(C*a^3*c + 6*A*a^2*c^2)*x^3)*sqrt(c*x^2 + a)/(a^4*c^5*x^8 + 4*a^5*c^4*x^6 + 6*a^6*c^3*x^4 + 4*a^7*c^2*x^2 + a^8*c)","A",0
118,1,60,0,0.579176," ","integrate((1+2*x)^3*(4*x^2+3*x+1)/(3*x^2+2)^(1/2),x, algorithm=""fricas"")","\frac{1}{405} \, {\left(864 \, x^{4} + 2430 \, x^{3} + 2292 \, x^{2} - 135 \, x - 1841\right)} \sqrt{3 \, x^{2} + 2} + \frac{5}{18} \, \sqrt{3} \log\left(-\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right)"," ",0,"1/405*(864*x^4 + 2430*x^3 + 2292*x^2 - 135*x - 1841)*sqrt(3*x^2 + 2) + 5/18*sqrt(3)*log(-sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1)","A",0
119,1,54,0,0.667718," ","integrate((1+2*x)^2*(4*x^2+3*x+1)/(3*x^2+2)^(1/2),x, algorithm=""fricas"")","\frac{1}{27} \, {\left(36 \, x^{3} + 84 \, x^{2} + 54 \, x - 49\right)} \sqrt{3 \, x^{2} + 2} + \frac{1}{2} \, \sqrt{3} \log\left(\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right)"," ",0,"1/27*(36*x^3 + 84*x^2 + 54*x - 49)*sqrt(3*x^2 + 2) + 1/2*sqrt(3)*log(sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1)","A",0
120,1,49,0,0.719243," ","integrate((1+2*x)*(4*x^2+3*x+1)/(3*x^2+2)^(1/2),x, algorithm=""fricas"")","\frac{1}{27} \, {\left(24 \, x^{2} + 45 \, x + 13\right)} \sqrt{3 \, x^{2} + 2} + \frac{7}{18} \, \sqrt{3} \log\left(\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right)"," ",0,"1/27*(24*x^2 + 45*x + 13)*sqrt(3*x^2 + 2) + 7/18*sqrt(3)*log(sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1)","A",0
121,1,88,0,0.753134," ","integrate((4*x^2+3*x+1)/(1+2*x)/(3*x^2+2)^(1/2),x, algorithm=""fricas"")","\frac{1}{12} \, \sqrt{3} \log\left(-\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right) + \frac{1}{44} \, \sqrt{11} \log\left(-\frac{\sqrt{11} \sqrt{3 \, x^{2} + 2} {\left(3 \, x - 4\right)} + 21 \, x^{2} - 12 \, x + 19}{4 \, x^{2} + 4 \, x + 1}\right) + \frac{2}{3} \, \sqrt{3 \, x^{2} + 2}"," ",0,"1/12*sqrt(3)*log(-sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1) + 1/44*sqrt(11)*log(-(sqrt(11)*sqrt(3*x^2 + 2)*(3*x - 4) + 21*x^2 - 12*x + 19)/(4*x^2 + 4*x + 1)) + 2/3*sqrt(3*x^2 + 2)","A",0
122,1,106,0,0.753118," ","integrate((4*x^2+3*x+1)/(1+2*x)^2/(3*x^2+2)^(1/2),x, algorithm=""fricas"")","\frac{121 \, \sqrt{3} {\left(2 \, x + 1\right)} \log\left(-\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right) + 12 \, \sqrt{11} {\left(2 \, x + 1\right)} \log\left(\frac{\sqrt{11} \sqrt{3 \, x^{2} + 2} {\left(3 \, x - 4\right)} - 21 \, x^{2} + 12 \, x - 19}{4 \, x^{2} + 4 \, x + 1}\right) - 66 \, \sqrt{3 \, x^{2} + 2}}{726 \, {\left(2 \, x + 1\right)}}"," ",0,"1/726*(121*sqrt(3)*(2*x + 1)*log(-sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1) + 12*sqrt(11)*(2*x + 1)*log((sqrt(11)*sqrt(3*x^2 + 2)*(3*x - 4) - 21*x^2 + 12*x - 19)/(4*x^2 + 4*x + 1)) - 66*sqrt(3*x^2 + 2))/(2*x + 1)","A",0
123,1,89,0,0.643171," ","integrate((4*x^2+3*x+1)/(1+2*x)^3/(3*x^2+2)^(1/2),x, algorithm=""fricas"")","\frac{103 \, \sqrt{11} {\left(4 \, x^{2} + 4 \, x + 1\right)} \log\left(-\frac{\sqrt{11} \sqrt{3 \, x^{2} + 2} {\left(3 \, x - 4\right)} + 21 \, x^{2} - 12 \, x + 19}{4 \, x^{2} + 4 \, x + 1}\right) + 22 \, \sqrt{3 \, x^{2} + 2} {\left(13 \, x + 1\right)}}{2662 \, {\left(4 \, x^{2} + 4 \, x + 1\right)}}"," ",0,"1/2662*(103*sqrt(11)*(4*x^2 + 4*x + 1)*log(-(sqrt(11)*sqrt(3*x^2 + 2)*(3*x - 4) + 21*x^2 - 12*x + 19)/(4*x^2 + 4*x + 1)) + 22*sqrt(3*x^2 + 2)*(13*x + 1))/(4*x^2 + 4*x + 1)","A",0
124,1,76,0,0.805925," ","integrate((1+2*x)^3*(4*x^2+3*x+1)/(3*x^2+2)^(3/2),x, algorithm=""fricas"")","\frac{342 \, \sqrt{3} {\left(3 \, x^{2} + 2\right)} \log\left(\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right) + {\left(576 \, x^{4} + 1944 \, x^{3} + 2136 \, x^{2} + 2133 \, x + 2362\right)} \sqrt{3 \, x^{2} + 2}}{162 \, {\left(3 \, x^{2} + 2\right)}}"," ",0,"1/162*(342*sqrt(3)*(3*x^2 + 2)*log(sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1) + (576*x^4 + 1944*x^3 + 2136*x^2 + 2133*x + 2362)*sqrt(3*x^2 + 2))/(3*x^2 + 2)","A",0
125,1,72,0,0.516267," ","integrate((1+2*x)^2*(4*x^2+3*x+1)/(3*x^2+2)^(3/2),x, algorithm=""fricas"")","\frac{4 \, \sqrt{3} {\left(3 \, x^{2} + 2\right)} \log\left(-\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right) + {\left(48 \, x^{3} + 168 \, x^{2} - 15 \, x + 182\right)} \sqrt{3 \, x^{2} + 2}}{18 \, {\left(3 \, x^{2} + 2\right)}}"," ",0,"1/18*(4*sqrt(3)*(3*x^2 + 2)*log(-sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1) + (48*x^3 + 168*x^2 - 15*x + 182)*sqrt(3*x^2 + 2))/(3*x^2 + 2)","A",0
126,1,67,0,0.975924," ","integrate((1+2*x)*(4*x^2+3*x+1)/(3*x^2+2)^(3/2),x, algorithm=""fricas"")","\frac{10 \, \sqrt{3} {\left(3 \, x^{2} + 2\right)} \log\left(-\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right) + {\left(48 \, x^{2} - 51 \, x + 34\right)} \sqrt{3 \, x^{2} + 2}}{18 \, {\left(3 \, x^{2} + 2\right)}}"," ",0,"1/18*(10*sqrt(3)*(3*x^2 + 2)*log(-sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1) + (48*x^2 - 51*x + 34)*sqrt(3*x^2 + 2))/(3*x^2 + 2)","A",0
127,1,83,0,0.541592," ","integrate((4*x^2+3*x+1)/(1+2*x)/(3*x^2+2)^(3/2),x, algorithm=""fricas"")","\frac{6 \, \sqrt{11} {\left(3 \, x^{2} + 2\right)} \log\left(-\frac{\sqrt{11} \sqrt{3 \, x^{2} + 2} {\left(3 \, x - 4\right)} + 21 \, x^{2} - 12 \, x + 19}{4 \, x^{2} + 4 \, x + 1}\right) + 11 \, \sqrt{3 \, x^{2} + 2} {\left(21 \, x - 38\right)}}{726 \, {\left(3 \, x^{2} + 2\right)}}"," ",0,"1/726*(6*sqrt(11)*(3*x^2 + 2)*log(-(sqrt(11)*sqrt(3*x^2 + 2)*(3*x - 4) + 21*x^2 - 12*x + 19)/(4*x^2 + 4*x + 1)) + 11*sqrt(3*x^2 + 2)*(21*x - 38))/(3*x^2 + 2)","A",0
128,1,103,0,0.838165," ","integrate((4*x^2+3*x+1)/(1+2*x)^2/(3*x^2+2)^(3/2),x, algorithm=""fricas"")","\frac{4 \, \sqrt{11} {\left(6 \, x^{3} + 3 \, x^{2} + 4 \, x + 2\right)} \log\left(\frac{\sqrt{11} \sqrt{3 \, x^{2} + 2} {\left(3 \, x - 4\right)} - 21 \, x^{2} + 12 \, x - 19}{4 \, x^{2} + 4 \, x + 1}\right) + 11 \, {\left(170 \, x^{2} + 77 \, x - 26\right)} \sqrt{3 \, x^{2} + 2}}{2662 \, {\left(6 \, x^{3} + 3 \, x^{2} + 4 \, x + 2\right)}}"," ",0,"1/2662*(4*sqrt(11)*(6*x^3 + 3*x^2 + 4*x + 2)*log((sqrt(11)*sqrt(3*x^2 + 2)*(3*x - 4) - 21*x^2 + 12*x - 19)/(4*x^2 + 4*x + 1)) + 11*(170*x^2 + 77*x - 26)*sqrt(3*x^2 + 2))/(6*x^3 + 3*x^2 + 4*x + 2)","A",0
129,1,119,0,0.724119," ","integrate((4*x^2+3*x+1)/(1+2*x)^3/(3*x^2+2)^(3/2),x, algorithm=""fricas"")","\frac{322 \, \sqrt{11} {\left(12 \, x^{4} + 12 \, x^{3} + 11 \, x^{2} + 8 \, x + 2\right)} \log\left(-\frac{\sqrt{11} \sqrt{3 \, x^{2} + 2} {\left(3 \, x - 4\right)} + 21 \, x^{2} - 12 \, x + 19}{4 \, x^{2} + 4 \, x + 1}\right) + 11 \, {\left(1428 \, x^{3} + 2716 \, x^{2} + 1799 \, x + 278\right)} \sqrt{3 \, x^{2} + 2}}{29282 \, {\left(12 \, x^{4} + 12 \, x^{3} + 11 \, x^{2} + 8 \, x + 2\right)}}"," ",0,"1/29282*(322*sqrt(11)*(12*x^4 + 12*x^3 + 11*x^2 + 8*x + 2)*log(-(sqrt(11)*sqrt(3*x^2 + 2)*(3*x - 4) + 21*x^2 - 12*x + 19)/(4*x^2 + 4*x + 1)) + 11*(1428*x^3 + 2716*x^2 + 1799*x + 278)*sqrt(3*x^2 + 2))/(12*x^4 + 12*x^3 + 11*x^2 + 8*x + 2)","A",0
130,1,87,0,0.464653," ","integrate((1+2*x)^3*(4*x^2+3*x+1)/(3*x^2+2)^(5/2),x, algorithm=""fricas"")","\frac{216 \, \sqrt{3} {\left(9 \, x^{4} + 12 \, x^{2} + 4\right)} \log\left(-\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right) + {\left(1728 \, x^{4} - 4185 \, x^{3} + 936 \, x^{2} - 2511 \, x + 254\right)} \sqrt{3 \, x^{2} + 2}}{162 \, {\left(9 \, x^{4} + 12 \, x^{2} + 4\right)}}"," ",0,"1/162*(216*sqrt(3)*(9*x^4 + 12*x^2 + 4)*log(-sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1) + (1728*x^4 - 4185*x^3 + 936*x^2 - 2511*x + 254)*sqrt(3*x^2 + 2))/(9*x^4 + 12*x^2 + 4)","A",0
131,1,83,0,0.653561," ","integrate((1+2*x)^2*(4*x^2+3*x+1)/(3*x^2+2)^(5/2),x, algorithm=""fricas"")","\frac{16 \, \sqrt{3} {\left(9 \, x^{4} + 12 \, x^{2} + 4\right)} \log\left(-\sqrt{3} \sqrt{3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right) - {\left(177 \, x^{3} + 504 \, x^{2} + 165 \, x + 266\right)} \sqrt{3 \, x^{2} + 2}}{54 \, {\left(9 \, x^{4} + 12 \, x^{2} + 4\right)}}"," ",0,"1/54*(16*sqrt(3)*(9*x^4 + 12*x^2 + 4)*log(-sqrt(3)*sqrt(3*x^2 + 2)*x - 3*x^2 - 1) - (177*x^3 + 504*x^2 + 165*x + 266)*sqrt(3*x^2 + 2))/(9*x^4 + 12*x^2 + 4)","A",0
132,1,40,0,0.954479," ","integrate((1+2*x)*(4*x^2+3*x+1)/(3*x^2+2)^(5/2),x, algorithm=""fricas"")","\frac{{\left(117 \, x^{3} - 144 \, x^{2} + 27 \, x - 94\right)} \sqrt{3 \, x^{2} + 2}}{54 \, {\left(9 \, x^{4} + 12 \, x^{2} + 4\right)}}"," ",0,"1/54*(117*x^3 - 144*x^2 + 27*x - 94)*sqrt(3*x^2 + 2)/(9*x^4 + 12*x^2 + 4)","A",0
133,1,103,0,0.985216," ","integrate((4*x^2+3*x+1)/(1+2*x)/(3*x^2+2)^(5/2),x, algorithm=""fricas"")","\frac{72 \, \sqrt{11} {\left(9 \, x^{4} + 12 \, x^{2} + 4\right)} \log\left(-\frac{\sqrt{11} \sqrt{3 \, x^{2} + 2} {\left(3 \, x - 4\right)} + 21 \, x^{2} - 12 \, x + 19}{4 \, x^{2} + 4 \, x + 1}\right) + 11 \, {\left(855 \, x^{3} + 216 \, x^{2} + 801 \, x - 274\right)} \sqrt{3 \, x^{2} + 2}}{23958 \, {\left(9 \, x^{4} + 12 \, x^{2} + 4\right)}}"," ",0,"1/23958*(72*sqrt(11)*(9*x^4 + 12*x^2 + 4)*log(-(sqrt(11)*sqrt(3*x^2 + 2)*(3*x - 4) + 21*x^2 - 12*x + 19)/(4*x^2 + 4*x + 1)) + 11*(855*x^3 + 216*x^2 + 801*x - 274)*sqrt(3*x^2 + 2))/(9*x^4 + 12*x^2 + 4)","A",0
134,1,134,0,0.562069," ","integrate((4*x^2+3*x+1)/(1+2*x)^2/(3*x^2+2)^(5/2),x, algorithm=""fricas"")","\frac{96 \, \sqrt{11} {\left(18 \, x^{5} + 9 \, x^{4} + 24 \, x^{3} + 12 \, x^{2} + 8 \, x + 4\right)} \log\left(-\frac{\sqrt{11} \sqrt{3 \, x^{2} + 2} {\left(3 \, x - 4\right)} + 21 \, x^{2} - 12 \, x + 19}{4 \, x^{2} + 4 \, x + 1}\right) + 11 \, {\left(4458 \, x^{4} + 2805 \, x^{3} + 4602 \, x^{2} + 2717 \, x - 446\right)} \sqrt{3 \, x^{2} + 2}}{87846 \, {\left(18 \, x^{5} + 9 \, x^{4} + 24 \, x^{3} + 12 \, x^{2} + 8 \, x + 4\right)}}"," ",0,"1/87846*(96*sqrt(11)*(18*x^5 + 9*x^4 + 24*x^3 + 12*x^2 + 8*x + 4)*log(-(sqrt(11)*sqrt(3*x^2 + 2)*(3*x - 4) + 21*x^2 - 12*x + 19)/(4*x^2 + 4*x + 1)) + 11*(4458*x^4 + 2805*x^3 + 4602*x^2 + 2717*x - 446)*sqrt(3*x^2 + 2))/(18*x^5 + 9*x^4 + 24*x^3 + 12*x^2 + 8*x + 4)","A",0
135,1,149,0,0.936711," ","integrate((4*x^2+3*x+1)/(1+2*x)^3/(3*x^2+2)^(5/2),x, algorithm=""fricas"")","\frac{3648 \, \sqrt{11} {\left(36 \, x^{6} + 36 \, x^{5} + 57 \, x^{4} + 48 \, x^{3} + 28 \, x^{2} + 16 \, x + 4\right)} \log\left(-\frac{\sqrt{11} \sqrt{3 \, x^{2} + 2} {\left(3 \, x - 4\right)} + 21 \, x^{2} - 12 \, x + 19}{4 \, x^{2} + 4 \, x + 1}\right) + 11 \, {\left(67284 \, x^{5} + 111060 \, x^{4} + 116937 \, x^{3} + 109844 \, x^{2} + 57371 \, x + 7010\right)} \sqrt{3 \, x^{2} + 2}}{966306 \, {\left(36 \, x^{6} + 36 \, x^{5} + 57 \, x^{4} + 48 \, x^{3} + 28 \, x^{2} + 16 \, x + 4\right)}}"," ",0,"1/966306*(3648*sqrt(11)*(36*x^6 + 36*x^5 + 57*x^4 + 48*x^3 + 28*x^2 + 16*x + 4)*log(-(sqrt(11)*sqrt(3*x^2 + 2)*(3*x - 4) + 21*x^2 - 12*x + 19)/(4*x^2 + 4*x + 1)) + 11*(67284*x^5 + 111060*x^4 + 116937*x^3 + 109844*x^2 + 57371*x + 7010)*sqrt(3*x^2 + 2))/(36*x^6 + 36*x^5 + 57*x^4 + 48*x^3 + 28*x^2 + 16*x + 4)","A",0
136,0,0,0,0.580888," ","integrate((h*x+g)^m*(c*x^2+a)^p*(f*x^2+e*x+d),x, algorithm=""fricas"")","{\rm integral}\left({\left(f x^{2} + e x + d\right)} {\left(c x^{2} + a\right)}^{p} {\left(h x + g\right)}^{m}, x\right)"," ",0,"integral((f*x^2 + e*x + d)*(c*x^2 + a)^p*(h*x + g)^m, x)","F",0
137,0,0,0,0.963240," ","integrate((h*x+g)^m*(f*x^2+e*x+d)*(c*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{2} + a} {\left(f x^{2} + e x + d\right)} {\left(h x + g\right)}^{m}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*(f*x^2 + e*x + d)*(h*x + g)^m, x)","F",0
138,0,0,0,0.773395," ","integrate((h*x+g)^(-3-2*p)*(c*x^2+a)^p*(f*x^2+e*x+d),x, algorithm=""fricas"")","{\rm integral}\left({\left(f x^{2} + e x + d\right)} {\left(c x^{2} + a\right)}^{p} {\left(h x + g\right)}^{-2 \, p - 3}, x\right)"," ",0,"integral((f*x^2 + e*x + d)*(c*x^2 + a)^p*(h*x + g)^(-2*p - 3), x)","F",0
139,0,0,0,0.800106," ","integrate((e*x+d)^m*(c*e^2*x^2+b*e^2*x+b*d*e-c*d^2)^p*(-(-b*e+c*d)*f+(b*e*g-c*d*g+c*e*f)*x+c*e*g*x^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(c e g x^{2} - {\left(c d - b e\right)} f + {\left(c e f - {\left(c d - b e\right)} g\right)} x\right)} {\left(c e^{2} x^{2} + b e^{2} x - c d^{2} + b d e\right)}^{p} {\left(e x + d\right)}^{m}, x\right)"," ",0,"integral((c*e*g*x^2 - (c*d - b*e)*f + (c*e*f - (c*d - b*e)*g)*x)*(c*e^2*x^2 + b*e^2*x - c*d^2 + b*d*e)^p*(e*x + d)^m, x)","F",0
140,1,308,0,0.541885," ","integrate((c*x^2+b*x+a)^4*(C*x^2+A),x, algorithm=""fricas"")","\frac{1}{11} x^{11} c^{4} C + \frac{2}{5} x^{10} c^{3} b C + \frac{2}{3} x^{9} c^{2} b^{2} C + \frac{4}{9} x^{9} c^{3} a C + \frac{1}{9} x^{9} c^{4} A + \frac{1}{2} x^{8} c b^{3} C + \frac{3}{2} x^{8} c^{2} b a C + \frac{1}{2} x^{8} c^{3} b A + \frac{1}{7} x^{7} b^{4} C + \frac{12}{7} x^{7} c b^{2} a C + \frac{6}{7} x^{7} c^{2} a^{2} C + \frac{6}{7} x^{7} c^{2} b^{2} A + \frac{4}{7} x^{7} c^{3} a A + \frac{2}{3} x^{6} b^{3} a C + 2 x^{6} c b a^{2} C + \frac{2}{3} x^{6} c b^{3} A + 2 x^{6} c^{2} b a A + \frac{6}{5} x^{5} b^{2} a^{2} C + \frac{4}{5} x^{5} c a^{3} C + \frac{1}{5} x^{5} b^{4} A + \frac{12}{5} x^{5} c b^{2} a A + \frac{6}{5} x^{5} c^{2} a^{2} A + x^{4} b a^{3} C + x^{4} b^{3} a A + 3 x^{4} c b a^{2} A + \frac{1}{3} x^{3} a^{4} C + 2 x^{3} b^{2} a^{2} A + \frac{4}{3} x^{3} c a^{3} A + 2 x^{2} b a^{3} A + x a^{4} A"," ",0,"1/11*x^11*c^4*C + 2/5*x^10*c^3*b*C + 2/3*x^9*c^2*b^2*C + 4/9*x^9*c^3*a*C + 1/9*x^9*c^4*A + 1/2*x^8*c*b^3*C + 3/2*x^8*c^2*b*a*C + 1/2*x^8*c^3*b*A + 1/7*x^7*b^4*C + 12/7*x^7*c*b^2*a*C + 6/7*x^7*c^2*a^2*C + 6/7*x^7*c^2*b^2*A + 4/7*x^7*c^3*a*A + 2/3*x^6*b^3*a*C + 2*x^6*c*b*a^2*C + 2/3*x^6*c*b^3*A + 2*x^6*c^2*b*a*A + 6/5*x^5*b^2*a^2*C + 4/5*x^5*c*a^3*C + 1/5*x^5*b^4*A + 12/5*x^5*c*b^2*a*A + 6/5*x^5*c^2*a^2*A + x^4*b*a^3*C + x^4*b^3*a*A + 3*x^4*c*b*a^2*A + 1/3*x^3*a^4*C + 2*x^3*b^2*a^2*A + 4/3*x^3*c*a^3*A + 2*x^2*b*a^3*A + x*a^4*A","A",0
141,1,187,0,0.429527," ","integrate((c*x^2+b*x+a)^3*(C*x^2+A),x, algorithm=""fricas"")","\frac{1}{9} x^{9} c^{3} C + \frac{3}{8} x^{8} c^{2} b C + \frac{3}{7} x^{7} c b^{2} C + \frac{3}{7} x^{7} c^{2} a C + \frac{1}{7} x^{7} c^{3} A + \frac{1}{6} x^{6} b^{3} C + x^{6} c b a C + \frac{1}{2} x^{6} c^{2} b A + \frac{3}{5} x^{5} b^{2} a C + \frac{3}{5} x^{5} c a^{2} C + \frac{3}{5} x^{5} c b^{2} A + \frac{3}{5} x^{5} c^{2} a A + \frac{3}{4} x^{4} b a^{2} C + \frac{1}{4} x^{4} b^{3} A + \frac{3}{2} x^{4} c b a A + \frac{1}{3} x^{3} a^{3} C + x^{3} b^{2} a A + x^{3} c a^{2} A + \frac{3}{2} x^{2} b a^{2} A + x a^{3} A"," ",0,"1/9*x^9*c^3*C + 3/8*x^8*c^2*b*C + 3/7*x^7*c*b^2*C + 3/7*x^7*c^2*a*C + 1/7*x^7*c^3*A + 1/6*x^6*b^3*C + x^6*c*b*a*C + 1/2*x^6*c^2*b*A + 3/5*x^5*b^2*a*C + 3/5*x^5*c*a^2*C + 3/5*x^5*c*b^2*A + 3/5*x^5*c^2*a*A + 3/4*x^4*b*a^2*C + 1/4*x^4*b^3*A + 3/2*x^4*c*b*a*A + 1/3*x^3*a^3*C + x^3*b^2*a*A + x^3*c*a^2*A + 3/2*x^2*b*a^2*A + x*a^3*A","A",0
142,1,99,0,0.985007," ","integrate((c*x^2+b*x+a)^2*(C*x^2+A),x, algorithm=""fricas"")","\frac{1}{7} x^{7} c^{2} C + \frac{1}{3} x^{6} c b C + \frac{1}{5} x^{5} b^{2} C + \frac{2}{5} x^{5} c a C + \frac{1}{5} x^{5} c^{2} A + \frac{1}{2} x^{4} b a C + \frac{1}{2} x^{4} c b A + \frac{1}{3} x^{3} a^{2} C + \frac{1}{3} x^{3} b^{2} A + \frac{2}{3} x^{3} c a A + x^{2} b a A + x a^{2} A"," ",0,"1/7*x^7*c^2*C + 1/3*x^6*c*b*C + 1/5*x^5*b^2*C + 2/5*x^5*c*a*C + 1/5*x^5*c^2*A + 1/2*x^4*b*a*C + 1/2*x^4*c*b*A + 1/3*x^3*a^2*C + 1/3*x^3*b^2*A + 2/3*x^3*c*a*A + x^2*b*a*A + x*a^2*A","A",0
143,1,40,0,0.339875," ","integrate((c*x^2+b*x+a)*(C*x^2+A),x, algorithm=""fricas"")","\frac{1}{5} x^{5} c C + \frac{1}{4} x^{4} b C + \frac{1}{3} x^{3} a C + \frac{1}{3} x^{3} c A + \frac{1}{2} x^{2} b A + x a A"," ",0,"1/5*x^5*c*C + 1/4*x^4*b*C + 1/3*x^3*a*C + 1/3*x^3*c*A + 1/2*x^2*b*A + x*a*A","A",0
144,1,265,0,0.769105," ","integrate((C*x^2+A)/(c*x^2+b*x+a),x, algorithm=""fricas"")","\left[\frac{{\left(C b^{2} - 2 \, C a c + 2 \, A c^{2}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 2 \, {\left(C b^{2} c - 4 \, C a c^{2}\right)} x - {\left(C b^{3} - 4 \, C a b c\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}}, -\frac{2 \, {\left(C b^{2} - 2 \, C a c + 2 \, A c^{2}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - 2 \, {\left(C b^{2} c - 4 \, C a c^{2}\right)} x + {\left(C b^{3} - 4 \, C a b c\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}}\right]"," ",0,"[1/2*((C*b^2 - 2*C*a*c + 2*A*c^2)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 2*(C*b^2*c - 4*C*a*c^2)*x - (C*b^3 - 4*C*a*b*c)*log(c*x^2 + b*x + a))/(b^2*c^2 - 4*a*c^3), -1/2*(2*(C*b^2 - 2*C*a*c + 2*A*c^2)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - 2*(C*b^2*c - 4*C*a*c^2)*x + (C*b^3 - 4*C*a*b*c)*log(c*x^2 + b*x + a))/(b^2*c^2 - 4*a*c^3)]","A",0
145,1,511,0,0.671366," ","integrate((C*x^2+A)/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\left[-\frac{C a b^{3} - 4 \, A a b c^{2} + 2 \, {\left(C a^{2} c + A a c^{2} + {\left(C a c^{2} + A c^{3}\right)} x^{2} + {\left(C a b c + A b c^{2}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - {\left(4 \, C a^{2} b - A b^{3}\right)} c + {\left(C b^{4} - 6 \, C a b^{2} c - 8 \, A a c^{3} + 2 \, {\left(4 \, C a^{2} + A b^{2}\right)} c^{2}\right)} x}{a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3} + {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{2} + {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x}, -\frac{C a b^{3} - 4 \, A a b c^{2} - 4 \, {\left(C a^{2} c + A a c^{2} + {\left(C a c^{2} + A c^{3}\right)} x^{2} + {\left(C a b c + A b c^{2}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - {\left(4 \, C a^{2} b - A b^{3}\right)} c + {\left(C b^{4} - 6 \, C a b^{2} c - 8 \, A a c^{3} + 2 \, {\left(4 \, C a^{2} + A b^{2}\right)} c^{2}\right)} x}{a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3} + {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{2} + {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x}\right]"," ",0,"[-(C*a*b^3 - 4*A*a*b*c^2 + 2*(C*a^2*c + A*a*c^2 + (C*a*c^2 + A*c^3)*x^2 + (C*a*b*c + A*b*c^2)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - (4*C*a^2*b - A*b^3)*c + (C*b^4 - 6*C*a*b^2*c - 8*A*a*c^3 + 2*(4*C*a^2 + A*b^2)*c^2)*x)/(a*b^4*c - 8*a^2*b^2*c^2 + 16*a^3*c^3 + (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^2 + (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x), -(C*a*b^3 - 4*A*a*b*c^2 - 4*(C*a^2*c + A*a*c^2 + (C*a*c^2 + A*c^3)*x^2 + (C*a*b*c + A*b*c^2)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - (4*C*a^2*b - A*b^3)*c + (C*b^4 - 6*C*a*b^2*c - 8*A*a*c^3 + 2*(4*C*a^2 + A*b^2)*c^2)*x)/(a*b^4*c - 8*a^2*b^2*c^2 + 16*a^3*c^3 + (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^2 + (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x)]","B",0
146,1,1199,0,0.603430," ","integrate((C*x^2+A)/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\left[\frac{6 \, C a^{2} b^{3} - A b^{5} - 40 \, A a^{2} b c^{2} + 2 \, {\left(C b^{4} c - 2 \, C a b^{2} c^{2} - 24 \, A a c^{4} - 2 \, {\left(4 \, C a^{2} - 3 \, A b^{2}\right)} c^{3}\right)} x^{3} + 3 \, {\left(C b^{5} - 2 \, C a b^{3} c - 24 \, A a b c^{3} - 2 \, {\left(4 \, C a^{2} b - 3 \, A b^{3}\right)} c^{2}\right)} x^{2} + 2 \, {\left(C a^{2} b^{2} + 2 \, C a^{3} c + 6 \, A a^{2} c^{2} + {\left(C b^{2} c^{2} + 2 \, C a c^{3} + 6 \, A c^{4}\right)} x^{4} + 2 \, {\left(C b^{3} c + 2 \, C a b c^{2} + 6 \, A b c^{3}\right)} x^{3} + {\left(C b^{4} + 4 \, C a b^{2} c + 12 \, A a c^{3} + 2 \, {\left(2 \, C a^{2} + 3 \, A b^{2}\right)} c^{2}\right)} x^{2} + 2 \, {\left(C a b^{3} + 2 \, C a^{2} b c + 6 \, A a b c^{2}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - 2 \, {\left(12 \, C a^{3} b - 7 \, A a b^{3}\right)} c + 2 \, {\left(5 \, C a b^{4} - 40 \, A a^{2} c^{3} + 2 \, {\left(4 \, C a^{3} + A a b^{2}\right)} c^{2} - 2 \, {\left(11 \, C a^{2} b^{2} - A b^{4}\right)} c\right)} x}{2 \, {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3} + {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} x^{4} + 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} x^{3} + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} x^{2} + 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} x\right)}}, \frac{6 \, C a^{2} b^{3} - A b^{5} - 40 \, A a^{2} b c^{2} + 2 \, {\left(C b^{4} c - 2 \, C a b^{2} c^{2} - 24 \, A a c^{4} - 2 \, {\left(4 \, C a^{2} - 3 \, A b^{2}\right)} c^{3}\right)} x^{3} + 3 \, {\left(C b^{5} - 2 \, C a b^{3} c - 24 \, A a b c^{3} - 2 \, {\left(4 \, C a^{2} b - 3 \, A b^{3}\right)} c^{2}\right)} x^{2} - 4 \, {\left(C a^{2} b^{2} + 2 \, C a^{3} c + 6 \, A a^{2} c^{2} + {\left(C b^{2} c^{2} + 2 \, C a c^{3} + 6 \, A c^{4}\right)} x^{4} + 2 \, {\left(C b^{3} c + 2 \, C a b c^{2} + 6 \, A b c^{3}\right)} x^{3} + {\left(C b^{4} + 4 \, C a b^{2} c + 12 \, A a c^{3} + 2 \, {\left(2 \, C a^{2} + 3 \, A b^{2}\right)} c^{2}\right)} x^{2} + 2 \, {\left(C a b^{3} + 2 \, C a^{2} b c + 6 \, A a b c^{2}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - 2 \, {\left(12 \, C a^{3} b - 7 \, A a b^{3}\right)} c + 2 \, {\left(5 \, C a b^{4} - 40 \, A a^{2} c^{3} + 2 \, {\left(4 \, C a^{3} + A a b^{2}\right)} c^{2} - 2 \, {\left(11 \, C a^{2} b^{2} - A b^{4}\right)} c\right)} x}{2 \, {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3} + {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} x^{4} + 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} x^{3} + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} x^{2} + 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} x\right)}}\right]"," ",0,"[1/2*(6*C*a^2*b^3 - A*b^5 - 40*A*a^2*b*c^2 + 2*(C*b^4*c - 2*C*a*b^2*c^2 - 24*A*a*c^4 - 2*(4*C*a^2 - 3*A*b^2)*c^3)*x^3 + 3*(C*b^5 - 2*C*a*b^3*c - 24*A*a*b*c^3 - 2*(4*C*a^2*b - 3*A*b^3)*c^2)*x^2 + 2*(C*a^2*b^2 + 2*C*a^3*c + 6*A*a^2*c^2 + (C*b^2*c^2 + 2*C*a*c^3 + 6*A*c^4)*x^4 + 2*(C*b^3*c + 2*C*a*b*c^2 + 6*A*b*c^3)*x^3 + (C*b^4 + 4*C*a*b^2*c + 12*A*a*c^3 + 2*(2*C*a^2 + 3*A*b^2)*c^2)*x^2 + 2*(C*a*b^3 + 2*C*a^2*b*c + 6*A*a*b*c^2)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - 2*(12*C*a^3*b - 7*A*a*b^3)*c + 2*(5*C*a*b^4 - 40*A*a^2*c^3 + 2*(4*C*a^3 + A*a*b^2)*c^2 - 2*(11*C*a^2*b^2 - A*b^4)*c)*x)/(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3 + (b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*x^4 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*x^3 + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*x^2 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*x), 1/2*(6*C*a^2*b^3 - A*b^5 - 40*A*a^2*b*c^2 + 2*(C*b^4*c - 2*C*a*b^2*c^2 - 24*A*a*c^4 - 2*(4*C*a^2 - 3*A*b^2)*c^3)*x^3 + 3*(C*b^5 - 2*C*a*b^3*c - 24*A*a*b*c^3 - 2*(4*C*a^2*b - 3*A*b^3)*c^2)*x^2 - 4*(C*a^2*b^2 + 2*C*a^3*c + 6*A*a^2*c^2 + (C*b^2*c^2 + 2*C*a*c^3 + 6*A*c^4)*x^4 + 2*(C*b^3*c + 2*C*a*b*c^2 + 6*A*b*c^3)*x^3 + (C*b^4 + 4*C*a*b^2*c + 12*A*a*c^3 + 2*(2*C*a^2 + 3*A*b^2)*c^2)*x^2 + 2*(C*a*b^3 + 2*C*a^2*b*c + 6*A*a*b*c^2)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - 2*(12*C*a^3*b - 7*A*a*b^3)*c + 2*(5*C*a*b^4 - 40*A*a^2*c^3 + 2*(4*C*a^3 + A*a*b^2)*c^2 - 2*(11*C*a^2*b^2 - A*b^4)*c)*x)/(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3 + (b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*x^4 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*x^3 + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*x^2 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*x)]","B",0
147,1,2103,0,0.865922," ","integrate((C*x^2+A)/(c*x^2+b*x+a)^4,x, algorithm=""fricas"")","\left[-\frac{C a^{2} b^{5} + A b^{7} - 264 \, A a^{3} b c^{3} + 12 \, {\left(C b^{4} c^{3} - 3 \, C a b^{2} c^{4} - 20 \, A a c^{6} - {\left(4 \, C a^{2} - 5 \, A b^{2}\right)} c^{5}\right)} x^{5} + 30 \, {\left(C b^{5} c^{2} - 3 \, C a b^{3} c^{3} - 20 \, A a b c^{5} - {\left(4 \, C a^{2} b - 5 \, A b^{3}\right)} c^{4}\right)} x^{4} + 2 \, {\left(11 \, C b^{6} c - 17 \, C a b^{4} c^{2} - 320 \, A a^{2} c^{5} - 4 \, {\left(16 \, C a^{3} + 35 \, A a b^{2}\right)} c^{4} - {\left(92 \, C a^{2} b^{2} - 55 \, A b^{4}\right)} c^{3}\right)} x^{3} - 2 \, {\left(52 \, C a^{4} b - 59 \, A a^{2} b^{3}\right)} c^{2} + 3 \, {\left(C b^{7} + 13 \, C a b^{5} c - 320 \, A a^{2} b c^{4} - 4 \, {\left(16 \, C a^{3} b - 15 \, A a b^{3}\right)} c^{3} - {\left(52 \, C a^{2} b^{3} - 5 \, A b^{5}\right)} c^{2}\right)} x^{2} + 12 \, {\left(C a^{3} b^{2} c + C a^{4} c^{2} + 5 \, A a^{3} c^{3} + {\left(C b^{2} c^{4} + C a c^{5} + 5 \, A c^{6}\right)} x^{6} + 3 \, {\left(C b^{3} c^{3} + C a b c^{4} + 5 \, A b c^{5}\right)} x^{5} + 3 \, {\left(C b^{4} c^{2} + 2 \, C a b^{2} c^{3} + 5 \, A a c^{5} + {\left(C a^{2} + 5 \, A b^{2}\right)} c^{4}\right)} x^{4} + {\left(C b^{5} c + 7 \, C a b^{3} c^{2} + 30 \, A a b c^{4} + {\left(6 \, C a^{2} b + 5 \, A b^{3}\right)} c^{3}\right)} x^{3} + 3 \, {\left(C a b^{4} c + 2 \, C a^{2} b^{2} c^{2} + 5 \, A a^{2} c^{4} + {\left(C a^{3} + 5 \, A a b^{2}\right)} c^{3}\right)} x^{2} + 3 \, {\left(C a^{2} b^{3} c + C a^{3} b c^{2} + 5 \, A a^{2} b c^{3}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + {\left(22 \, C a^{3} b^{3} - 17 \, A a b^{5}\right)} c + 3 \, {\left(C a b^{6} - 176 \, A a^{3} c^{4} + 4 \, {\left(4 \, C a^{4} - 7 \, A a^{2} b^{2}\right)} c^{3} - 2 \, {\left(46 \, C a^{3} b^{2} - 11 \, A a b^{4}\right)} c^{2} + {\left(18 \, C a^{2} b^{4} - A b^{6}\right)} c\right)} x}{3 \, {\left(a^{3} b^{8} - 16 \, a^{4} b^{6} c + 96 \, a^{5} b^{4} c^{2} - 256 \, a^{6} b^{2} c^{3} + 256 \, a^{7} c^{4} + {\left(b^{8} c^{3} - 16 \, a b^{6} c^{4} + 96 \, a^{2} b^{4} c^{5} - 256 \, a^{3} b^{2} c^{6} + 256 \, a^{4} c^{7}\right)} x^{6} + 3 \, {\left(b^{9} c^{2} - 16 \, a b^{7} c^{3} + 96 \, a^{2} b^{5} c^{4} - 256 \, a^{3} b^{3} c^{5} + 256 \, a^{4} b c^{6}\right)} x^{5} + 3 \, {\left(b^{10} c - 15 \, a b^{8} c^{2} + 80 \, a^{2} b^{6} c^{3} - 160 \, a^{3} b^{4} c^{4} + 256 \, a^{5} c^{6}\right)} x^{4} + {\left(b^{11} - 10 \, a b^{9} c + 320 \, a^{3} b^{5} c^{3} - 1280 \, a^{4} b^{3} c^{4} + 1536 \, a^{5} b c^{5}\right)} x^{3} + 3 \, {\left(a b^{10} - 15 \, a^{2} b^{8} c + 80 \, a^{3} b^{6} c^{2} - 160 \, a^{4} b^{4} c^{3} + 256 \, a^{6} c^{5}\right)} x^{2} + 3 \, {\left(a^{2} b^{9} - 16 \, a^{3} b^{7} c + 96 \, a^{4} b^{5} c^{2} - 256 \, a^{5} b^{3} c^{3} + 256 \, a^{6} b c^{4}\right)} x\right)}}, -\frac{C a^{2} b^{5} + A b^{7} - 264 \, A a^{3} b c^{3} + 12 \, {\left(C b^{4} c^{3} - 3 \, C a b^{2} c^{4} - 20 \, A a c^{6} - {\left(4 \, C a^{2} - 5 \, A b^{2}\right)} c^{5}\right)} x^{5} + 30 \, {\left(C b^{5} c^{2} - 3 \, C a b^{3} c^{3} - 20 \, A a b c^{5} - {\left(4 \, C a^{2} b - 5 \, A b^{3}\right)} c^{4}\right)} x^{4} + 2 \, {\left(11 \, C b^{6} c - 17 \, C a b^{4} c^{2} - 320 \, A a^{2} c^{5} - 4 \, {\left(16 \, C a^{3} + 35 \, A a b^{2}\right)} c^{4} - {\left(92 \, C a^{2} b^{2} - 55 \, A b^{4}\right)} c^{3}\right)} x^{3} - 2 \, {\left(52 \, C a^{4} b - 59 \, A a^{2} b^{3}\right)} c^{2} + 3 \, {\left(C b^{7} + 13 \, C a b^{5} c - 320 \, A a^{2} b c^{4} - 4 \, {\left(16 \, C a^{3} b - 15 \, A a b^{3}\right)} c^{3} - {\left(52 \, C a^{2} b^{3} - 5 \, A b^{5}\right)} c^{2}\right)} x^{2} - 24 \, {\left(C a^{3} b^{2} c + C a^{4} c^{2} + 5 \, A a^{3} c^{3} + {\left(C b^{2} c^{4} + C a c^{5} + 5 \, A c^{6}\right)} x^{6} + 3 \, {\left(C b^{3} c^{3} + C a b c^{4} + 5 \, A b c^{5}\right)} x^{5} + 3 \, {\left(C b^{4} c^{2} + 2 \, C a b^{2} c^{3} + 5 \, A a c^{5} + {\left(C a^{2} + 5 \, A b^{2}\right)} c^{4}\right)} x^{4} + {\left(C b^{5} c + 7 \, C a b^{3} c^{2} + 30 \, A a b c^{4} + {\left(6 \, C a^{2} b + 5 \, A b^{3}\right)} c^{3}\right)} x^{3} + 3 \, {\left(C a b^{4} c + 2 \, C a^{2} b^{2} c^{2} + 5 \, A a^{2} c^{4} + {\left(C a^{3} + 5 \, A a b^{2}\right)} c^{3}\right)} x^{2} + 3 \, {\left(C a^{2} b^{3} c + C a^{3} b c^{2} + 5 \, A a^{2} b c^{3}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + {\left(22 \, C a^{3} b^{3} - 17 \, A a b^{5}\right)} c + 3 \, {\left(C a b^{6} - 176 \, A a^{3} c^{4} + 4 \, {\left(4 \, C a^{4} - 7 \, A a^{2} b^{2}\right)} c^{3} - 2 \, {\left(46 \, C a^{3} b^{2} - 11 \, A a b^{4}\right)} c^{2} + {\left(18 \, C a^{2} b^{4} - A b^{6}\right)} c\right)} x}{3 \, {\left(a^{3} b^{8} - 16 \, a^{4} b^{6} c + 96 \, a^{5} b^{4} c^{2} - 256 \, a^{6} b^{2} c^{3} + 256 \, a^{7} c^{4} + {\left(b^{8} c^{3} - 16 \, a b^{6} c^{4} + 96 \, a^{2} b^{4} c^{5} - 256 \, a^{3} b^{2} c^{6} + 256 \, a^{4} c^{7}\right)} x^{6} + 3 \, {\left(b^{9} c^{2} - 16 \, a b^{7} c^{3} + 96 \, a^{2} b^{5} c^{4} - 256 \, a^{3} b^{3} c^{5} + 256 \, a^{4} b c^{6}\right)} x^{5} + 3 \, {\left(b^{10} c - 15 \, a b^{8} c^{2} + 80 \, a^{2} b^{6} c^{3} - 160 \, a^{3} b^{4} c^{4} + 256 \, a^{5} c^{6}\right)} x^{4} + {\left(b^{11} - 10 \, a b^{9} c + 320 \, a^{3} b^{5} c^{3} - 1280 \, a^{4} b^{3} c^{4} + 1536 \, a^{5} b c^{5}\right)} x^{3} + 3 \, {\left(a b^{10} - 15 \, a^{2} b^{8} c + 80 \, a^{3} b^{6} c^{2} - 160 \, a^{4} b^{4} c^{3} + 256 \, a^{6} c^{5}\right)} x^{2} + 3 \, {\left(a^{2} b^{9} - 16 \, a^{3} b^{7} c + 96 \, a^{4} b^{5} c^{2} - 256 \, a^{5} b^{3} c^{3} + 256 \, a^{6} b c^{4}\right)} x\right)}}\right]"," ",0,"[-1/3*(C*a^2*b^5 + A*b^7 - 264*A*a^3*b*c^3 + 12*(C*b^4*c^3 - 3*C*a*b^2*c^4 - 20*A*a*c^6 - (4*C*a^2 - 5*A*b^2)*c^5)*x^5 + 30*(C*b^5*c^2 - 3*C*a*b^3*c^3 - 20*A*a*b*c^5 - (4*C*a^2*b - 5*A*b^3)*c^4)*x^4 + 2*(11*C*b^6*c - 17*C*a*b^4*c^2 - 320*A*a^2*c^5 - 4*(16*C*a^3 + 35*A*a*b^2)*c^4 - (92*C*a^2*b^2 - 55*A*b^4)*c^3)*x^3 - 2*(52*C*a^4*b - 59*A*a^2*b^3)*c^2 + 3*(C*b^7 + 13*C*a*b^5*c - 320*A*a^2*b*c^4 - 4*(16*C*a^3*b - 15*A*a*b^3)*c^3 - (52*C*a^2*b^3 - 5*A*b^5)*c^2)*x^2 + 12*(C*a^3*b^2*c + C*a^4*c^2 + 5*A*a^3*c^3 + (C*b^2*c^4 + C*a*c^5 + 5*A*c^6)*x^6 + 3*(C*b^3*c^3 + C*a*b*c^4 + 5*A*b*c^5)*x^5 + 3*(C*b^4*c^2 + 2*C*a*b^2*c^3 + 5*A*a*c^5 + (C*a^2 + 5*A*b^2)*c^4)*x^4 + (C*b^5*c + 7*C*a*b^3*c^2 + 30*A*a*b*c^4 + (6*C*a^2*b + 5*A*b^3)*c^3)*x^3 + 3*(C*a*b^4*c + 2*C*a^2*b^2*c^2 + 5*A*a^2*c^4 + (C*a^3 + 5*A*a*b^2)*c^3)*x^2 + 3*(C*a^2*b^3*c + C*a^3*b*c^2 + 5*A*a^2*b*c^3)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + (22*C*a^3*b^3 - 17*A*a*b^5)*c + 3*(C*a*b^6 - 176*A*a^3*c^4 + 4*(4*C*a^4 - 7*A*a^2*b^2)*c^3 - 2*(46*C*a^3*b^2 - 11*A*a*b^4)*c^2 + (18*C*a^2*b^4 - A*b^6)*c)*x)/(a^3*b^8 - 16*a^4*b^6*c + 96*a^5*b^4*c^2 - 256*a^6*b^2*c^3 + 256*a^7*c^4 + (b^8*c^3 - 16*a*b^6*c^4 + 96*a^2*b^4*c^5 - 256*a^3*b^2*c^6 + 256*a^4*c^7)*x^6 + 3*(b^9*c^2 - 16*a*b^7*c^3 + 96*a^2*b^5*c^4 - 256*a^3*b^3*c^5 + 256*a^4*b*c^6)*x^5 + 3*(b^10*c - 15*a*b^8*c^2 + 80*a^2*b^6*c^3 - 160*a^3*b^4*c^4 + 256*a^5*c^6)*x^4 + (b^11 - 10*a*b^9*c + 320*a^3*b^5*c^3 - 1280*a^4*b^3*c^4 + 1536*a^5*b*c^5)*x^3 + 3*(a*b^10 - 15*a^2*b^8*c + 80*a^3*b^6*c^2 - 160*a^4*b^4*c^3 + 256*a^6*c^5)*x^2 + 3*(a^2*b^9 - 16*a^3*b^7*c + 96*a^4*b^5*c^2 - 256*a^5*b^3*c^3 + 256*a^6*b*c^4)*x), -1/3*(C*a^2*b^5 + A*b^7 - 264*A*a^3*b*c^3 + 12*(C*b^4*c^3 - 3*C*a*b^2*c^4 - 20*A*a*c^6 - (4*C*a^2 - 5*A*b^2)*c^5)*x^5 + 30*(C*b^5*c^2 - 3*C*a*b^3*c^3 - 20*A*a*b*c^5 - (4*C*a^2*b - 5*A*b^3)*c^4)*x^4 + 2*(11*C*b^6*c - 17*C*a*b^4*c^2 - 320*A*a^2*c^5 - 4*(16*C*a^3 + 35*A*a*b^2)*c^4 - (92*C*a^2*b^2 - 55*A*b^4)*c^3)*x^3 - 2*(52*C*a^4*b - 59*A*a^2*b^3)*c^2 + 3*(C*b^7 + 13*C*a*b^5*c - 320*A*a^2*b*c^4 - 4*(16*C*a^3*b - 15*A*a*b^3)*c^3 - (52*C*a^2*b^3 - 5*A*b^5)*c^2)*x^2 - 24*(C*a^3*b^2*c + C*a^4*c^2 + 5*A*a^3*c^3 + (C*b^2*c^4 + C*a*c^5 + 5*A*c^6)*x^6 + 3*(C*b^3*c^3 + C*a*b*c^4 + 5*A*b*c^5)*x^5 + 3*(C*b^4*c^2 + 2*C*a*b^2*c^3 + 5*A*a*c^5 + (C*a^2 + 5*A*b^2)*c^4)*x^4 + (C*b^5*c + 7*C*a*b^3*c^2 + 30*A*a*b*c^4 + (6*C*a^2*b + 5*A*b^3)*c^3)*x^3 + 3*(C*a*b^4*c + 2*C*a^2*b^2*c^2 + 5*A*a^2*c^4 + (C*a^3 + 5*A*a*b^2)*c^3)*x^2 + 3*(C*a^2*b^3*c + C*a^3*b*c^2 + 5*A*a^2*b*c^3)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + (22*C*a^3*b^3 - 17*A*a*b^5)*c + 3*(C*a*b^6 - 176*A*a^3*c^4 + 4*(4*C*a^4 - 7*A*a^2*b^2)*c^3 - 2*(46*C*a^3*b^2 - 11*A*a*b^4)*c^2 + (18*C*a^2*b^4 - A*b^6)*c)*x)/(a^3*b^8 - 16*a^4*b^6*c + 96*a^5*b^4*c^2 - 256*a^6*b^2*c^3 + 256*a^7*c^4 + (b^8*c^3 - 16*a*b^6*c^4 + 96*a^2*b^4*c^5 - 256*a^3*b^2*c^6 + 256*a^4*c^7)*x^6 + 3*(b^9*c^2 - 16*a*b^7*c^3 + 96*a^2*b^5*c^4 - 256*a^3*b^3*c^5 + 256*a^4*b*c^6)*x^5 + 3*(b^10*c - 15*a*b^8*c^2 + 80*a^2*b^6*c^3 - 160*a^3*b^4*c^4 + 256*a^5*c^6)*x^4 + (b^11 - 10*a*b^9*c + 320*a^3*b^5*c^3 - 1280*a^4*b^3*c^4 + 1536*a^5*b*c^5)*x^3 + 3*(a*b^10 - 15*a^2*b^8*c + 80*a^3*b^6*c^2 - 160*a^4*b^4*c^3 + 256*a^6*c^5)*x^2 + 3*(a^2*b^9 - 16*a^3*b^7*c + 96*a^4*b^5*c^2 - 256*a^5*b^3*c^3 + 256*a^6*b*c^4)*x)]","B",0
148,1,2150,0,2.520304," ","integrate((e*x+d)^3*(h*x^2+g*x+f)/(c*x^2+b*x+a),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} e^{3} h x^{4} + 4 \, {\left({\left(b^{2} c^{4} - 4 \, a c^{5}\right)} e^{3} g + {\left(3 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d e^{2} - {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} e^{3}\right)} h\right)} x^{3} + 6 \, {\left({\left(b^{2} c^{4} - 4 \, a c^{5}\right)} e^{3} f + {\left(3 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d e^{2} - {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} e^{3}\right)} g + {\left(3 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{2} e - 3 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d e^{2} + {\left(b^{4} c^{2} - 5 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} e^{3}\right)} h\right)} x^{2} - 6 \, \sqrt{b^{2} - 4 \, a c} {\left({\left(2 \, c^{5} d^{3} - 3 \, b c^{4} d^{2} e + 3 \, {\left(b^{2} c^{3} - 2 \, a c^{4}\right)} d e^{2} - {\left(b^{3} c^{2} - 3 \, a b c^{3}\right)} e^{3}\right)} f - {\left(b c^{4} d^{3} - 3 \, {\left(b^{2} c^{3} - 2 \, a c^{4}\right)} d^{2} e + 3 \, {\left(b^{3} c^{2} - 3 \, a b c^{3}\right)} d e^{2} - {\left(b^{4} c - 4 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} e^{3}\right)} g + {\left({\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}\right)} h\right)} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 12 \, {\left({\left(3 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d e^{2} - {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} e^{3}\right)} f + {\left(3 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{2} e - 3 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d e^{2} + {\left(b^{4} c^{2} - 5 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} e^{3}\right)} g + {\left({\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{3} - 3 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{2} e + 3 \, {\left(b^{4} c^{2} - 5 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d e^{2} - {\left(b^{5} c - 6 \, a b^{3} c^{2} + 8 \, a^{2} b c^{3}\right)} e^{3}\right)} h\right)} x + 6 \, {\left({\left(3 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{2} e - 3 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d e^{2} + {\left(b^{4} c^{2} - 5 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} e^{3}\right)} f + {\left({\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{3} - 3 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{2} e + 3 \, {\left(b^{4} c^{2} - 5 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d e^{2} - {\left(b^{5} c - 6 \, a b^{3} c^{2} + 8 \, a^{2} b c^{3}\right)} e^{3}\right)} g - {\left({\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{3} - 3 \, {\left(b^{4} c^{2} - 5 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{2} e + 3 \, {\left(b^{5} c - 6 \, a b^{3} c^{2} + 8 \, a^{2} b c^{3}\right)} d e^{2} - {\left(b^{6} - 7 \, a b^{4} c + 13 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} e^{3}\right)} h\right)} \log\left(c x^{2} + b x + a\right)}{12 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)}}, \frac{3 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} e^{3} h x^{4} + 4 \, {\left({\left(b^{2} c^{4} - 4 \, a c^{5}\right)} e^{3} g + {\left(3 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d e^{2} - {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} e^{3}\right)} h\right)} x^{3} + 6 \, {\left({\left(b^{2} c^{4} - 4 \, a c^{5}\right)} e^{3} f + {\left(3 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d e^{2} - {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} e^{3}\right)} g + {\left(3 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{2} e - 3 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d e^{2} + {\left(b^{4} c^{2} - 5 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} e^{3}\right)} h\right)} x^{2} - 12 \, \sqrt{-b^{2} + 4 \, a c} {\left({\left(2 \, c^{5} d^{3} - 3 \, b c^{4} d^{2} e + 3 \, {\left(b^{2} c^{3} - 2 \, a c^{4}\right)} d e^{2} - {\left(b^{3} c^{2} - 3 \, a b c^{3}\right)} e^{3}\right)} f - {\left(b c^{4} d^{3} - 3 \, {\left(b^{2} c^{3} - 2 \, a c^{4}\right)} d^{2} e + 3 \, {\left(b^{3} c^{2} - 3 \, a b c^{3}\right)} d e^{2} - {\left(b^{4} c - 4 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} e^{3}\right)} g + {\left({\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}\right)} h\right)} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 12 \, {\left({\left(3 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d e^{2} - {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} e^{3}\right)} f + {\left(3 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{2} e - 3 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d e^{2} + {\left(b^{4} c^{2} - 5 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} e^{3}\right)} g + {\left({\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{3} - 3 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{2} e + 3 \, {\left(b^{4} c^{2} - 5 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d e^{2} - {\left(b^{5} c - 6 \, a b^{3} c^{2} + 8 \, a^{2} b c^{3}\right)} e^{3}\right)} h\right)} x + 6 \, {\left({\left(3 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{2} e - 3 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d e^{2} + {\left(b^{4} c^{2} - 5 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} e^{3}\right)} f + {\left({\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{3} - 3 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{2} e + 3 \, {\left(b^{4} c^{2} - 5 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d e^{2} - {\left(b^{5} c - 6 \, a b^{3} c^{2} + 8 \, a^{2} b c^{3}\right)} e^{3}\right)} g - {\left({\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{3} - 3 \, {\left(b^{4} c^{2} - 5 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{2} e + 3 \, {\left(b^{5} c - 6 \, a b^{3} c^{2} + 8 \, a^{2} b c^{3}\right)} d e^{2} - {\left(b^{6} - 7 \, a b^{4} c + 13 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} e^{3}\right)} h\right)} \log\left(c x^{2} + b x + a\right)}{12 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)}}\right]"," ",0,"[1/12*(3*(b^2*c^4 - 4*a*c^5)*e^3*h*x^4 + 4*((b^2*c^4 - 4*a*c^5)*e^3*g + (3*(b^2*c^4 - 4*a*c^5)*d*e^2 - (b^3*c^3 - 4*a*b*c^4)*e^3)*h)*x^3 + 6*((b^2*c^4 - 4*a*c^5)*e^3*f + (3*(b^2*c^4 - 4*a*c^5)*d*e^2 - (b^3*c^3 - 4*a*b*c^4)*e^3)*g + (3*(b^2*c^4 - 4*a*c^5)*d^2*e - 3*(b^3*c^3 - 4*a*b*c^4)*d*e^2 + (b^4*c^2 - 5*a*b^2*c^3 + 4*a^2*c^4)*e^3)*h)*x^2 - 6*sqrt(b^2 - 4*a*c)*((2*c^5*d^3 - 3*b*c^4*d^2*e + 3*(b^2*c^3 - 2*a*c^4)*d*e^2 - (b^3*c^2 - 3*a*b*c^3)*e^3)*f - (b*c^4*d^3 - 3*(b^2*c^3 - 2*a*c^4)*d^2*e + 3*(b^3*c^2 - 3*a*b*c^3)*d*e^2 - (b^4*c - 4*a*b^2*c^2 + 2*a^2*c^3)*e^3)*g + ((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)*h)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 12*((3*(b^2*c^4 - 4*a*c^5)*d*e^2 - (b^3*c^3 - 4*a*b*c^4)*e^3)*f + (3*(b^2*c^4 - 4*a*c^5)*d^2*e - 3*(b^3*c^3 - 4*a*b*c^4)*d*e^2 + (b^4*c^2 - 5*a*b^2*c^3 + 4*a^2*c^4)*e^3)*g + ((b^2*c^4 - 4*a*c^5)*d^3 - 3*(b^3*c^3 - 4*a*b*c^4)*d^2*e + 3*(b^4*c^2 - 5*a*b^2*c^3 + 4*a^2*c^4)*d*e^2 - (b^5*c - 6*a*b^3*c^2 + 8*a^2*b*c^3)*e^3)*h)*x + 6*((3*(b^2*c^4 - 4*a*c^5)*d^2*e - 3*(b^3*c^3 - 4*a*b*c^4)*d*e^2 + (b^4*c^2 - 5*a*b^2*c^3 + 4*a^2*c^4)*e^3)*f + ((b^2*c^4 - 4*a*c^5)*d^3 - 3*(b^3*c^3 - 4*a*b*c^4)*d^2*e + 3*(b^4*c^2 - 5*a*b^2*c^3 + 4*a^2*c^4)*d*e^2 - (b^5*c - 6*a*b^3*c^2 + 8*a^2*b*c^3)*e^3)*g - ((b^3*c^3 - 4*a*b*c^4)*d^3 - 3*(b^4*c^2 - 5*a*b^2*c^3 + 4*a^2*c^4)*d^2*e + 3*(b^5*c - 6*a*b^3*c^2 + 8*a^2*b*c^3)*d*e^2 - (b^6 - 7*a*b^4*c + 13*a^2*b^2*c^2 - 4*a^3*c^3)*e^3)*h)*log(c*x^2 + b*x + a))/(b^2*c^5 - 4*a*c^6), 1/12*(3*(b^2*c^4 - 4*a*c^5)*e^3*h*x^4 + 4*((b^2*c^4 - 4*a*c^5)*e^3*g + (3*(b^2*c^4 - 4*a*c^5)*d*e^2 - (b^3*c^3 - 4*a*b*c^4)*e^3)*h)*x^3 + 6*((b^2*c^4 - 4*a*c^5)*e^3*f + (3*(b^2*c^4 - 4*a*c^5)*d*e^2 - (b^3*c^3 - 4*a*b*c^4)*e^3)*g + (3*(b^2*c^4 - 4*a*c^5)*d^2*e - 3*(b^3*c^3 - 4*a*b*c^4)*d*e^2 + (b^4*c^2 - 5*a*b^2*c^3 + 4*a^2*c^4)*e^3)*h)*x^2 - 12*sqrt(-b^2 + 4*a*c)*((2*c^5*d^3 - 3*b*c^4*d^2*e + 3*(b^2*c^3 - 2*a*c^4)*d*e^2 - (b^3*c^2 - 3*a*b*c^3)*e^3)*f - (b*c^4*d^3 - 3*(b^2*c^3 - 2*a*c^4)*d^2*e + 3*(b^3*c^2 - 3*a*b*c^3)*d*e^2 - (b^4*c - 4*a*b^2*c^2 + 2*a^2*c^3)*e^3)*g + ((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)*h)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 12*((3*(b^2*c^4 - 4*a*c^5)*d*e^2 - (b^3*c^3 - 4*a*b*c^4)*e^3)*f + (3*(b^2*c^4 - 4*a*c^5)*d^2*e - 3*(b^3*c^3 - 4*a*b*c^4)*d*e^2 + (b^4*c^2 - 5*a*b^2*c^3 + 4*a^2*c^4)*e^3)*g + ((b^2*c^4 - 4*a*c^5)*d^3 - 3*(b^3*c^3 - 4*a*b*c^4)*d^2*e + 3*(b^4*c^2 - 5*a*b^2*c^3 + 4*a^2*c^4)*d*e^2 - (b^5*c - 6*a*b^3*c^2 + 8*a^2*b*c^3)*e^3)*h)*x + 6*((3*(b^2*c^4 - 4*a*c^5)*d^2*e - 3*(b^3*c^3 - 4*a*b*c^4)*d*e^2 + (b^4*c^2 - 5*a*b^2*c^3 + 4*a^2*c^4)*e^3)*f + ((b^2*c^4 - 4*a*c^5)*d^3 - 3*(b^3*c^3 - 4*a*b*c^4)*d^2*e + 3*(b^4*c^2 - 5*a*b^2*c^3 + 4*a^2*c^4)*d*e^2 - (b^5*c - 6*a*b^3*c^2 + 8*a^2*b*c^3)*e^3)*g - ((b^3*c^3 - 4*a*b*c^4)*d^3 - 3*(b^4*c^2 - 5*a*b^2*c^3 + 4*a^2*c^4)*d^2*e + 3*(b^5*c - 6*a*b^3*c^2 + 8*a^2*b*c^3)*d*e^2 - (b^6 - 7*a*b^4*c + 13*a^2*b^2*c^2 - 4*a^3*c^3)*e^3)*h)*log(c*x^2 + b*x + a))/(b^2*c^5 - 4*a*c^6)]","A",0
149,1,1273,0,1.202744," ","integrate((e*x+d)^2*(h*x^2+g*x+f)/(c*x^2+b*x+a),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e^{2} h x^{3} + 3 \, {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e^{2} g + {\left(2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d e - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} e^{2}\right)} h\right)} x^{2} + 3 \, \sqrt{b^{2} - 4 \, a c} {\left({\left(2 \, c^{4} d^{2} - 2 \, b c^{3} d e + {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} e^{2}\right)} f - {\left(b c^{3} d^{2} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d e + {\left(b^{3} c - 3 \, a b c^{2}\right)} e^{2}\right)} g + {\left({\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} - 2 \, {\left(b^{3} c - 3 \, a b c^{2}\right)} d e + {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} e^{2}\right)} h\right)} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 6 \, {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e^{2} f + {\left(2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d e - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} e^{2}\right)} g + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e + {\left(b^{4} c - 5 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} e^{2}\right)} h\right)} x + 3 \, {\left({\left(2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d e - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} e^{2}\right)} f + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e + {\left(b^{4} c - 5 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} e^{2}\right)} g - {\left({\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{2} - 2 \, {\left(b^{4} c - 5 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} d e + {\left(b^{5} - 6 \, a b^{3} c + 8 \, a^{2} b c^{2}\right)} e^{2}\right)} h\right)} \log\left(c x^{2} + b x + a\right)}{6 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)}}, \frac{2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e^{2} h x^{3} + 3 \, {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e^{2} g + {\left(2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d e - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} e^{2}\right)} h\right)} x^{2} - 6 \, \sqrt{-b^{2} + 4 \, a c} {\left({\left(2 \, c^{4} d^{2} - 2 \, b c^{3} d e + {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} e^{2}\right)} f - {\left(b c^{3} d^{2} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d e + {\left(b^{3} c - 3 \, a b c^{2}\right)} e^{2}\right)} g + {\left({\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} - 2 \, {\left(b^{3} c - 3 \, a b c^{2}\right)} d e + {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} e^{2}\right)} h\right)} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 6 \, {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e^{2} f + {\left(2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d e - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} e^{2}\right)} g + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e + {\left(b^{4} c - 5 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} e^{2}\right)} h\right)} x + 3 \, {\left({\left(2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d e - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} e^{2}\right)} f + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e + {\left(b^{4} c - 5 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} e^{2}\right)} g - {\left({\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{2} - 2 \, {\left(b^{4} c - 5 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} d e + {\left(b^{5} - 6 \, a b^{3} c + 8 \, a^{2} b c^{2}\right)} e^{2}\right)} h\right)} \log\left(c x^{2} + b x + a\right)}{6 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)}}\right]"," ",0,"[1/6*(2*(b^2*c^3 - 4*a*c^4)*e^2*h*x^3 + 3*((b^2*c^3 - 4*a*c^4)*e^2*g + (2*(b^2*c^3 - 4*a*c^4)*d*e - (b^3*c^2 - 4*a*b*c^3)*e^2)*h)*x^2 + 3*sqrt(b^2 - 4*a*c)*((2*c^4*d^2 - 2*b*c^3*d*e + (b^2*c^2 - 2*a*c^3)*e^2)*f - (b*c^3*d^2 - 2*(b^2*c^2 - 2*a*c^3)*d*e + (b^3*c - 3*a*b*c^2)*e^2)*g + ((b^2*c^2 - 2*a*c^3)*d^2 - 2*(b^3*c - 3*a*b*c^2)*d*e + (b^4 - 4*a*b^2*c + 2*a^2*c^2)*e^2)*h)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 6*((b^2*c^3 - 4*a*c^4)*e^2*f + (2*(b^2*c^3 - 4*a*c^4)*d*e - (b^3*c^2 - 4*a*b*c^3)*e^2)*g + ((b^2*c^3 - 4*a*c^4)*d^2 - 2*(b^3*c^2 - 4*a*b*c^3)*d*e + (b^4*c - 5*a*b^2*c^2 + 4*a^2*c^3)*e^2)*h)*x + 3*((2*(b^2*c^3 - 4*a*c^4)*d*e - (b^3*c^2 - 4*a*b*c^3)*e^2)*f + ((b^2*c^3 - 4*a*c^4)*d^2 - 2*(b^3*c^2 - 4*a*b*c^3)*d*e + (b^4*c - 5*a*b^2*c^2 + 4*a^2*c^3)*e^2)*g - ((b^3*c^2 - 4*a*b*c^3)*d^2 - 2*(b^4*c - 5*a*b^2*c^2 + 4*a^2*c^3)*d*e + (b^5 - 6*a*b^3*c + 8*a^2*b*c^2)*e^2)*h)*log(c*x^2 + b*x + a))/(b^2*c^4 - 4*a*c^5), 1/6*(2*(b^2*c^3 - 4*a*c^4)*e^2*h*x^3 + 3*((b^2*c^3 - 4*a*c^4)*e^2*g + (2*(b^2*c^3 - 4*a*c^4)*d*e - (b^3*c^2 - 4*a*b*c^3)*e^2)*h)*x^2 - 6*sqrt(-b^2 + 4*a*c)*((2*c^4*d^2 - 2*b*c^3*d*e + (b^2*c^2 - 2*a*c^3)*e^2)*f - (b*c^3*d^2 - 2*(b^2*c^2 - 2*a*c^3)*d*e + (b^3*c - 3*a*b*c^2)*e^2)*g + ((b^2*c^2 - 2*a*c^3)*d^2 - 2*(b^3*c - 3*a*b*c^2)*d*e + (b^4 - 4*a*b^2*c + 2*a^2*c^2)*e^2)*h)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 6*((b^2*c^3 - 4*a*c^4)*e^2*f + (2*(b^2*c^3 - 4*a*c^4)*d*e - (b^3*c^2 - 4*a*b*c^3)*e^2)*g + ((b^2*c^3 - 4*a*c^4)*d^2 - 2*(b^3*c^2 - 4*a*b*c^3)*d*e + (b^4*c - 5*a*b^2*c^2 + 4*a^2*c^3)*e^2)*h)*x + 3*((2*(b^2*c^3 - 4*a*c^4)*d*e - (b^3*c^2 - 4*a*b*c^3)*e^2)*f + ((b^2*c^3 - 4*a*c^4)*d^2 - 2*(b^3*c^2 - 4*a*b*c^3)*d*e + (b^4*c - 5*a*b^2*c^2 + 4*a^2*c^3)*e^2)*g - ((b^3*c^2 - 4*a*b*c^3)*d^2 - 2*(b^4*c - 5*a*b^2*c^2 + 4*a^2*c^3)*d*e + (b^5 - 6*a*b^3*c + 8*a^2*b*c^2)*e^2)*h)*log(c*x^2 + b*x + a))/(b^2*c^4 - 4*a*c^5)]","A",0
150,1,654,0,0.752471," ","integrate((e*x+d)*(h*x^2+g*x+f)/(c*x^2+b*x+a),x, algorithm=""fricas"")","\left[\frac{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e h x^{2} + \sqrt{b^{2} - 4 \, a c} {\left({\left(2 \, c^{3} d - b c^{2} e\right)} f - {\left(b c^{2} d - {\left(b^{2} c - 2 \, a c^{2}\right)} e\right)} g + {\left({\left(b^{2} c - 2 \, a c^{2}\right)} d - {\left(b^{3} - 3 \, a b c\right)} e\right)} h\right)} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 2 \, {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e g + {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d - {\left(b^{3} c - 4 \, a b c^{2}\right)} e\right)} h\right)} x + {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e f + {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d - {\left(b^{3} c - 4 \, a b c^{2}\right)} e\right)} g - {\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\right)} h\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)}}, \frac{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e h x^{2} - 2 \, \sqrt{-b^{2} + 4 \, a c} {\left({\left(2 \, c^{3} d - b c^{2} e\right)} f - {\left(b c^{2} d - {\left(b^{2} c - 2 \, a c^{2}\right)} e\right)} g + {\left({\left(b^{2} c - 2 \, a c^{2}\right)} d - {\left(b^{3} - 3 \, a b c\right)} e\right)} h\right)} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 2 \, {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e g + {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d - {\left(b^{3} c - 4 \, a b c^{2}\right)} e\right)} h\right)} x + {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e f + {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d - {\left(b^{3} c - 4 \, a b c^{2}\right)} e\right)} g - {\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\right)} h\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)}}\right]"," ",0,"[1/2*((b^2*c^2 - 4*a*c^3)*e*h*x^2 + sqrt(b^2 - 4*a*c)*((2*c^3*d - b*c^2*e)*f - (b*c^2*d - (b^2*c - 2*a*c^2)*e)*g + ((b^2*c - 2*a*c^2)*d - (b^3 - 3*a*b*c)*e)*h)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 2*((b^2*c^2 - 4*a*c^3)*e*g + ((b^2*c^2 - 4*a*c^3)*d - (b^3*c - 4*a*b*c^2)*e)*h)*x + ((b^2*c^2 - 4*a*c^3)*e*f + ((b^2*c^2 - 4*a*c^3)*d - (b^3*c - 4*a*b*c^2)*e)*g - ((b^3*c - 4*a*b*c^2)*d - (b^4 - 5*a*b^2*c + 4*a^2*c^2)*e)*h)*log(c*x^2 + b*x + a))/(b^2*c^3 - 4*a*c^4), 1/2*((b^2*c^2 - 4*a*c^3)*e*h*x^2 - 2*sqrt(-b^2 + 4*a*c)*((2*c^3*d - b*c^2*e)*f - (b*c^2*d - (b^2*c - 2*a*c^2)*e)*g + ((b^2*c - 2*a*c^2)*d - (b^3 - 3*a*b*c)*e)*h)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 2*((b^2*c^2 - 4*a*c^3)*e*g + ((b^2*c^2 - 4*a*c^3)*d - (b^3*c - 4*a*b*c^2)*e)*h)*x + ((b^2*c^2 - 4*a*c^3)*e*f + ((b^2*c^2 - 4*a*c^3)*d - (b^3*c - 4*a*b*c^2)*e)*g - ((b^3*c - 4*a*b*c^2)*d - (b^4 - 5*a*b^2*c + 4*a^2*c^2)*e)*h)*log(c*x^2 + b*x + a))/(b^2*c^3 - 4*a*c^4)]","A",0
151,1,302,0,0.743137," ","integrate((h*x^2+g*x+f)/(c*x^2+b*x+a),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} h x - {\left(2 \, c^{2} f - b c g + {\left(b^{2} - 2 \, a c\right)} h\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} g - {\left(b^{3} - 4 \, a b c\right)} h\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}}, \frac{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} h x - 2 \, {\left(2 \, c^{2} f - b c g + {\left(b^{2} - 2 \, a c\right)} h\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} g - {\left(b^{3} - 4 \, a b c\right)} h\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}}\right]"," ",0,"[1/2*(2*(b^2*c - 4*a*c^2)*h*x - (2*c^2*f - b*c*g + (b^2 - 2*a*c)*h)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + ((b^2*c - 4*a*c^2)*g - (b^3 - 4*a*b*c)*h)*log(c*x^2 + b*x + a))/(b^2*c^2 - 4*a*c^3), 1/2*(2*(b^2*c - 4*a*c^2)*h*x - 2*(2*c^2*f - b*c*g + (b^2 - 2*a*c)*h)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + ((b^2*c - 4*a*c^2)*g - (b^3 - 4*a*b*c)*h)*log(c*x^2 + b*x + a))/(b^2*c^2 - 4*a*c^3)]","A",0
152,1,625,0,89.668344," ","integrate((h*x^2+g*x+f)/(e*x+d)/(c*x^2+b*x+a),x, algorithm=""fricas"")","\left[-\frac{\sqrt{b^{2} - 4 \, a c} {\left({\left(2 \, c^{2} d e - b c e^{2}\right)} f - {\left(b c d e - 2 \, a c e^{2}\right)} g - {\left(a b e^{2} - {\left(b^{2} - 2 \, a c\right)} d e\right)} h\right)} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + {\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 + {\left({\left(b^{3} - 4 \, a b c\right)} d e - {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}\right)} h\right)} \log\left(c x^{2} + b x + a\right) - 2 \, {\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 + {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} h\right)} \log\left(e x + d\right)}{2 \, {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} e - {\left(b^{3} c - 4 \, a b c^{2}\right)} d e^{2} + {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} e^{3}\right)}}, -\frac{2 \, \sqrt{-b^{2} + 4 \, a c} {\left({\left(2 \, c^{2} d e - b c e^{2}\right)} f - {\left(b c d e - 2 \, a c e^{2}\right)} g - {\left(a b e^{2} - {\left(b^{2} - 2 \, a c\right)} d e\right)} h\right)} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + {\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 + {\left({\left(b^{3} - 4 \, a b c\right)} d e - {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}\right)} h\right)} \log\left(c x^{2} + b x + a\right) - 2 \, {\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 + {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} h\right)} \log\left(e x + d\right)}{2 \, {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} e - {\left(b^{3} c - 4 \, a b c^{2}\right)} d e^{2} + {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} e^{3}\right)}}\right]"," ",0,"[-1/2*(sqrt(b^2 - 4*a*c)*((2*c^2*d*e - b*c*e^2)*f - (b*c*d*e - 2*a*c*e^2)*g - (a*b*e^2 - (b^2 - 2*a*c)*d*e)*h)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + ((b^2*c - 4*a*c^2)*e^2*f - (b^2*c - 4*a*c^2)*d*e*g + ((b^3 - 4*a*b*c)*d*e - (a*b^2 - 4*a^2*c)*e^2)*h)*log(c*x^2 + b*x + a) - 2*((b^2*c - 4*a*c^2)*e^2*f - (b^2*c - 4*a*c^2)*d*e*g + (b^2*c - 4*a*c^2)*d^2*h)*log(e*x + d))/((b^2*c^2 - 4*a*c^3)*d^2*e - (b^3*c - 4*a*b*c^2)*d*e^2 + (a*b^2*c - 4*a^2*c^2)*e^3), -1/2*(2*sqrt(-b^2 + 4*a*c)*((2*c^2*d*e - b*c*e^2)*f - (b*c*d*e - 2*a*c*e^2)*g - (a*b*e^2 - (b^2 - 2*a*c)*d*e)*h)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + ((b^2*c - 4*a*c^2)*e^2*f - (b^2*c - 4*a*c^2)*d*e*g + ((b^3 - 4*a*b*c)*d*e - (a*b^2 - 4*a^2*c)*e^2)*h)*log(c*x^2 + b*x + a) - 2*((b^2*c - 4*a*c^2)*e^2*f - (b^2*c - 4*a*c^2)*d*e*g + (b^2*c - 4*a*c^2)*d^2*h)*log(e*x + d))/((b^2*c^2 - 4*a*c^3)*d^2*e - (b^3*c - 4*a*b*c^2)*d*e^2 + (a*b^2*c - 4*a^2*c^2)*e^3)]","A",0
153,-1,0,0,0.000000," ","integrate((h*x^2+g*x+f)/(e*x+d)^2/(c*x^2+b*x+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
154,-1,0,0,0.000000," ","integrate((h*x^2+g*x+f)/(e*x+d)^3/(c*x^2+b*x+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
155,1,2771,0,1.749185," ","integrate((e*x+d)^2*(h*x^2+g*x+f)/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} e^{2} h x^{3} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} e^{2} h x^{2} + {\left({\left(4 \, {\left(c^{5} d^{2} - b c^{4} d e + a c^{4} e^{2}\right)} f - {\left(2 \, b c^{4} d^{2} - 8 \, a c^{4} d e - {\left(b^{3} c^{2} - 6 \, a b c^{3}\right)} e^{2}\right)} g + 2 \, {\left(2 \, a c^{4} d^{2} + {\left(b^{3} c^{2} - 6 \, a b c^{3}\right)} d e - {\left(b^{4} c - 6 \, a b^{2} c^{2} + 6 \, a^{2} c^{3}\right)} e^{2}\right)} h\right)} x^{2} + 4 \, {\left(a c^{4} d^{2} - a b c^{3} d e + a^{2} c^{3} e^{2}\right)} f - {\left(2 \, a b c^{3} d^{2} - 8 \, a^{2} c^{3} d e - {\left(a b^{3} c - 6 \, a^{2} b c^{2}\right)} e^{2}\right)} g + 2 \, {\left(2 \, a^{2} c^{3} d^{2} + {\left(a b^{3} c - 6 \, a^{2} b c^{2}\right)} d e - {\left(a b^{4} - 6 \, a^{2} b^{2} c + 6 \, a^{3} c^{2}\right)} e^{2}\right)} h + {\left(4 \, {\left(b c^{4} d^{2} - b^{2} c^{3} d e + a b c^{3} e^{2}\right)} f - {\left(2 \, b^{2} c^{3} d^{2} - 8 \, a b c^{3} d e - {\left(b^{4} c - 6 \, a b^{2} c^{2}\right)} e^{2}\right)} g + 2 \, {\left(2 \, a b c^{3} d^{2} + {\left(b^{4} c - 6 \, a b^{2} c^{2}\right)} d e - {\left(b^{5} - 6 \, a b^{3} c + 6 \, a^{2} b c^{2}\right)} e^{2}\right)} h\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - 2 \, {\left({\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{2} - 4 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d e + {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} e^{2}\right)} f + 2 \, {\left(2 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{2} - 2 \, {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d e + {\left(a b^{4} c - 6 \, a^{2} b^{2} c^{2} + 8 \, a^{3} c^{3}\right)} e^{2}\right)} g - 2 \, {\left({\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{2} - 2 \, {\left(a b^{4} c - 6 \, a^{2} b^{2} c^{2} + 8 \, a^{3} c^{3}\right)} d e + {\left(a b^{5} - 7 \, a^{2} b^{3} c + 12 \, a^{3} b c^{2}\right)} e^{2}\right)} h - 2 \, {\left({\left(2 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{2} - 2 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d e + {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} e^{2}\right)} f - {\left({\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{2} - 2 \, {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d e + {\left(b^{5} c - 7 \, a b^{3} c^{2} + 12 \, a^{2} b c^{3}\right)} e^{2}\right)} g + {\left({\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{5} c - 7 \, a b^{3} c^{2} + 12 \, a^{2} b c^{3}\right)} d e + {\left(b^{6} - 9 \, a b^{4} c + 26 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} e^{2}\right)} h\right)} x + {\left({\left(a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3}\right)} e^{2} g + {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} e^{2} g + 2 \, {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d e - {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} e^{2}\right)} h\right)} x^{2} + 2 \, {\left({\left(a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3}\right)} d e - {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} e^{2}\right)} h + {\left({\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} e^{2} g + 2 \, {\left({\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d e - {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} e^{2}\right)} h\right)} x\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5} + {\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} x^{2} + {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} x\right)}}, \frac{2 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} e^{2} h x^{3} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} e^{2} h x^{2} + 2 \, {\left({\left(4 \, {\left(c^{5} d^{2} - b c^{4} d e + a c^{4} e^{2}\right)} f - {\left(2 \, b c^{4} d^{2} - 8 \, a c^{4} d e - {\left(b^{3} c^{2} - 6 \, a b c^{3}\right)} e^{2}\right)} g + 2 \, {\left(2 \, a c^{4} d^{2} + {\left(b^{3} c^{2} - 6 \, a b c^{3}\right)} d e - {\left(b^{4} c - 6 \, a b^{2} c^{2} + 6 \, a^{2} c^{3}\right)} e^{2}\right)} h\right)} x^{2} + 4 \, {\left(a c^{4} d^{2} - a b c^{3} d e + a^{2} c^{3} e^{2}\right)} f - {\left(2 \, a b c^{3} d^{2} - 8 \, a^{2} c^{3} d e - {\left(a b^{3} c - 6 \, a^{2} b c^{2}\right)} e^{2}\right)} g + 2 \, {\left(2 \, a^{2} c^{3} d^{2} + {\left(a b^{3} c - 6 \, a^{2} b c^{2}\right)} d e - {\left(a b^{4} - 6 \, a^{2} b^{2} c + 6 \, a^{3} c^{2}\right)} e^{2}\right)} h + {\left(4 \, {\left(b c^{4} d^{2} - b^{2} c^{3} d e + a b c^{3} e^{2}\right)} f - {\left(2 \, b^{2} c^{3} d^{2} - 8 \, a b c^{3} d e - {\left(b^{4} c - 6 \, a b^{2} c^{2}\right)} e^{2}\right)} g + 2 \, {\left(2 \, a b c^{3} d^{2} + {\left(b^{4} c - 6 \, a b^{2} c^{2}\right)} d e - {\left(b^{5} - 6 \, a b^{3} c + 6 \, a^{2} b c^{2}\right)} e^{2}\right)} h\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - 2 \, {\left({\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{2} - 4 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d e + {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} e^{2}\right)} f + 2 \, {\left(2 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{2} - 2 \, {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d e + {\left(a b^{4} c - 6 \, a^{2} b^{2} c^{2} + 8 \, a^{3} c^{3}\right)} e^{2}\right)} g - 2 \, {\left({\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{2} - 2 \, {\left(a b^{4} c - 6 \, a^{2} b^{2} c^{2} + 8 \, a^{3} c^{3}\right)} d e + {\left(a b^{5} - 7 \, a^{2} b^{3} c + 12 \, a^{3} b c^{2}\right)} e^{2}\right)} h - 2 \, {\left({\left(2 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{2} - 2 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d e + {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} e^{2}\right)} f - {\left({\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{2} - 2 \, {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d e + {\left(b^{5} c - 7 \, a b^{3} c^{2} + 12 \, a^{2} b c^{3}\right)} e^{2}\right)} g + {\left({\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{5} c - 7 \, a b^{3} c^{2} + 12 \, a^{2} b c^{3}\right)} d e + {\left(b^{6} - 9 \, a b^{4} c + 26 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} e^{2}\right)} h\right)} x + {\left({\left(a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3}\right)} e^{2} g + {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} e^{2} g + 2 \, {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d e - {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} e^{2}\right)} h\right)} x^{2} + 2 \, {\left({\left(a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3}\right)} d e - {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} e^{2}\right)} h + {\left({\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} e^{2} g + 2 \, {\left({\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d e - {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} e^{2}\right)} h\right)} x\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5} + {\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} x^{2} + {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} x\right)}}\right]"," ",0,"[1/2*(2*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*e^2*h*x^3 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*e^2*h*x^2 + ((4*(c^5*d^2 - b*c^4*d*e + a*c^4*e^2)*f - (2*b*c^4*d^2 - 8*a*c^4*d*e - (b^3*c^2 - 6*a*b*c^3)*e^2)*g + 2*(2*a*c^4*d^2 + (b^3*c^2 - 6*a*b*c^3)*d*e - (b^4*c - 6*a*b^2*c^2 + 6*a^2*c^3)*e^2)*h)*x^2 + 4*(a*c^4*d^2 - a*b*c^3*d*e + a^2*c^3*e^2)*f - (2*a*b*c^3*d^2 - 8*a^2*c^3*d*e - (a*b^3*c - 6*a^2*b*c^2)*e^2)*g + 2*(2*a^2*c^3*d^2 + (a*b^3*c - 6*a^2*b*c^2)*d*e - (a*b^4 - 6*a^2*b^2*c + 6*a^3*c^2)*e^2)*h + (4*(b*c^4*d^2 - b^2*c^3*d*e + a*b*c^3*e^2)*f - (2*b^2*c^3*d^2 - 8*a*b*c^3*d*e - (b^4*c - 6*a*b^2*c^2)*e^2)*g + 2*(2*a*b*c^3*d^2 + (b^4*c - 6*a*b^2*c^2)*d*e - (b^5 - 6*a*b^3*c + 6*a^2*b*c^2)*e^2)*h)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - 2*((b^3*c^3 - 4*a*b*c^4)*d^2 - 4*(a*b^2*c^3 - 4*a^2*c^4)*d*e + (a*b^3*c^2 - 4*a^2*b*c^3)*e^2)*f + 2*(2*(a*b^2*c^3 - 4*a^2*c^4)*d^2 - 2*(a*b^3*c^2 - 4*a^2*b*c^3)*d*e + (a*b^4*c - 6*a^2*b^2*c^2 + 8*a^3*c^3)*e^2)*g - 2*((a*b^3*c^2 - 4*a^2*b*c^3)*d^2 - 2*(a*b^4*c - 6*a^2*b^2*c^2 + 8*a^3*c^3)*d*e + (a*b^5 - 7*a^2*b^3*c + 12*a^3*b*c^2)*e^2)*h - 2*((2*(b^2*c^4 - 4*a*c^5)*d^2 - 2*(b^3*c^3 - 4*a*b*c^4)*d*e + (b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*e^2)*f - ((b^3*c^3 - 4*a*b*c^4)*d^2 - 2*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d*e + (b^5*c - 7*a*b^3*c^2 + 12*a^2*b*c^3)*e^2)*g + ((b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^2 - 2*(b^5*c - 7*a*b^3*c^2 + 12*a^2*b*c^3)*d*e + (b^6 - 9*a*b^4*c + 26*a^2*b^2*c^2 - 24*a^3*c^3)*e^2)*h)*x + ((a*b^4*c - 8*a^2*b^2*c^2 + 16*a^3*c^3)*e^2*g + ((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*e^2*g + 2*((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d*e - (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*e^2)*h)*x^2 + 2*((a*b^4*c - 8*a^2*b^2*c^2 + 16*a^3*c^3)*d*e - (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*e^2)*h + ((b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*e^2*g + 2*((b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d*e - (b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*e^2)*h)*x)*log(c*x^2 + b*x + a))/(a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5 + (b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*x^2 + (b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*x), 1/2*(2*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*e^2*h*x^3 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*e^2*h*x^2 + 2*((4*(c^5*d^2 - b*c^4*d*e + a*c^4*e^2)*f - (2*b*c^4*d^2 - 8*a*c^4*d*e - (b^3*c^2 - 6*a*b*c^3)*e^2)*g + 2*(2*a*c^4*d^2 + (b^3*c^2 - 6*a*b*c^3)*d*e - (b^4*c - 6*a*b^2*c^2 + 6*a^2*c^3)*e^2)*h)*x^2 + 4*(a*c^4*d^2 - a*b*c^3*d*e + a^2*c^3*e^2)*f - (2*a*b*c^3*d^2 - 8*a^2*c^3*d*e - (a*b^3*c - 6*a^2*b*c^2)*e^2)*g + 2*(2*a^2*c^3*d^2 + (a*b^3*c - 6*a^2*b*c^2)*d*e - (a*b^4 - 6*a^2*b^2*c + 6*a^3*c^2)*e^2)*h + (4*(b*c^4*d^2 - b^2*c^3*d*e + a*b*c^3*e^2)*f - (2*b^2*c^3*d^2 - 8*a*b*c^3*d*e - (b^4*c - 6*a*b^2*c^2)*e^2)*g + 2*(2*a*b*c^3*d^2 + (b^4*c - 6*a*b^2*c^2)*d*e - (b^5 - 6*a*b^3*c + 6*a^2*b*c^2)*e^2)*h)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - 2*((b^3*c^3 - 4*a*b*c^4)*d^2 - 4*(a*b^2*c^3 - 4*a^2*c^4)*d*e + (a*b^3*c^2 - 4*a^2*b*c^3)*e^2)*f + 2*(2*(a*b^2*c^3 - 4*a^2*c^4)*d^2 - 2*(a*b^3*c^2 - 4*a^2*b*c^3)*d*e + (a*b^4*c - 6*a^2*b^2*c^2 + 8*a^3*c^3)*e^2)*g - 2*((a*b^3*c^2 - 4*a^2*b*c^3)*d^2 - 2*(a*b^4*c - 6*a^2*b^2*c^2 + 8*a^3*c^3)*d*e + (a*b^5 - 7*a^2*b^3*c + 12*a^3*b*c^2)*e^2)*h - 2*((2*(b^2*c^4 - 4*a*c^5)*d^2 - 2*(b^3*c^3 - 4*a*b*c^4)*d*e + (b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*e^2)*f - ((b^3*c^3 - 4*a*b*c^4)*d^2 - 2*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d*e + (b^5*c - 7*a*b^3*c^2 + 12*a^2*b*c^3)*e^2)*g + ((b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^2 - 2*(b^5*c - 7*a*b^3*c^2 + 12*a^2*b*c^3)*d*e + (b^6 - 9*a*b^4*c + 26*a^2*b^2*c^2 - 24*a^3*c^3)*e^2)*h)*x + ((a*b^4*c - 8*a^2*b^2*c^2 + 16*a^3*c^3)*e^2*g + ((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*e^2*g + 2*((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d*e - (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*e^2)*h)*x^2 + 2*((a*b^4*c - 8*a^2*b^2*c^2 + 16*a^3*c^3)*d*e - (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*e^2)*h + ((b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*e^2*g + 2*((b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d*e - (b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*e^2)*h)*x)*log(c*x^2 + b*x + a))/(a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5 + (b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*x^2 + (b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*x)]","B",0
156,1,1413,0,1.565783," ","integrate((e*x+d)*(h*x^2+g*x+f)/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\left[\frac{{\left({\left(2 \, {\left(2 \, c^{4} d - b c^{3} e\right)} f - 2 \, {\left(b c^{3} d - 2 \, a c^{3} e\right)} g + {\left(4 \, a c^{3} d + {\left(b^{3} c - 6 \, a b c^{2}\right)} e\right)} h\right)} x^{2} + 2 \, {\left(2 \, a c^{3} d - a b c^{2} e\right)} f - 2 \, {\left(a b c^{2} d - 2 \, a^{2} c^{2} e\right)} g + {\left(4 \, a^{2} c^{2} d + {\left(a b^{3} - 6 \, a^{2} b c\right)} e\right)} h + {\left(2 \, {\left(2 \, b c^{3} d - b^{2} c^{2} e\right)} f - 2 \, {\left(b^{2} c^{2} d - 2 \, a b c^{2} e\right)} g + {\left(4 \, a b c^{2} d + {\left(b^{4} - 6 \, a b^{2} c\right)} e\right)} h\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - 2 \, {\left({\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d - 2 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} e\right)} f + 2 \, {\left(2 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d - {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} e\right)} g - 2 \, {\left({\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d - {\left(a b^{4} - 6 \, a^{2} b^{2} c + 8 \, a^{3} c^{2}\right)} e\right)} h - 2 \, {\left({\left(2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} e\right)} f - {\left({\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d - {\left(b^{4} c - 6 \, a b^{2} c^{2} + 8 \, a^{2} c^{3}\right)} e\right)} g + {\left({\left(b^{4} c - 6 \, a b^{2} c^{2} + 8 \, a^{2} c^{3}\right)} d - {\left(b^{5} - 7 \, a b^{3} c + 12 \, a^{2} b c^{2}\right)} e\right)} h\right)} x + {\left({\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} e h x^{2} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} e h x + {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} e h\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4} + {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} x^{2} + {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} x\right)}}, \frac{2 \, {\left({\left(2 \, {\left(2 \, c^{4} d - b c^{3} e\right)} f - 2 \, {\left(b c^{3} d - 2 \, a c^{3} e\right)} g + {\left(4 \, a c^{3} d + {\left(b^{3} c - 6 \, a b c^{2}\right)} e\right)} h\right)} x^{2} + 2 \, {\left(2 \, a c^{3} d - a b c^{2} e\right)} f - 2 \, {\left(a b c^{2} d - 2 \, a^{2} c^{2} e\right)} g + {\left(4 \, a^{2} c^{2} d + {\left(a b^{3} - 6 \, a^{2} b c\right)} e\right)} h + {\left(2 \, {\left(2 \, b c^{3} d - b^{2} c^{2} e\right)} f - 2 \, {\left(b^{2} c^{2} d - 2 \, a b c^{2} e\right)} g + {\left(4 \, a b c^{2} d + {\left(b^{4} - 6 \, a b^{2} c\right)} e\right)} h\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - 2 \, {\left({\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d - 2 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} e\right)} f + 2 \, {\left(2 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d - {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} e\right)} g - 2 \, {\left({\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d - {\left(a b^{4} - 6 \, a^{2} b^{2} c + 8 \, a^{3} c^{2}\right)} e\right)} h - 2 \, {\left({\left(2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} e\right)} f - {\left({\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d - {\left(b^{4} c - 6 \, a b^{2} c^{2} + 8 \, a^{2} c^{3}\right)} e\right)} g + {\left({\left(b^{4} c - 6 \, a b^{2} c^{2} + 8 \, a^{2} c^{3}\right)} d - {\left(b^{5} - 7 \, a b^{3} c + 12 \, a^{2} b c^{2}\right)} e\right)} h\right)} x + {\left({\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} e h x^{2} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} e h x + {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} e h\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4} + {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} x^{2} + {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} x\right)}}\right]"," ",0,"[1/2*(((2*(2*c^4*d - b*c^3*e)*f - 2*(b*c^3*d - 2*a*c^3*e)*g + (4*a*c^3*d + (b^3*c - 6*a*b*c^2)*e)*h)*x^2 + 2*(2*a*c^3*d - a*b*c^2*e)*f - 2*(a*b*c^2*d - 2*a^2*c^2*e)*g + (4*a^2*c^2*d + (a*b^3 - 6*a^2*b*c)*e)*h + (2*(2*b*c^3*d - b^2*c^2*e)*f - 2*(b^2*c^2*d - 2*a*b*c^2*e)*g + (4*a*b*c^2*d + (b^4 - 6*a*b^2*c)*e)*h)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - 2*((b^3*c^2 - 4*a*b*c^3)*d - 2*(a*b^2*c^2 - 4*a^2*c^3)*e)*f + 2*(2*(a*b^2*c^2 - 4*a^2*c^3)*d - (a*b^3*c - 4*a^2*b*c^2)*e)*g - 2*((a*b^3*c - 4*a^2*b*c^2)*d - (a*b^4 - 6*a^2*b^2*c + 8*a^3*c^2)*e)*h - 2*((2*(b^2*c^3 - 4*a*c^4)*d - (b^3*c^2 - 4*a*b*c^3)*e)*f - ((b^3*c^2 - 4*a*b*c^3)*d - (b^4*c - 6*a*b^2*c^2 + 8*a^2*c^3)*e)*g + ((b^4*c - 6*a*b^2*c^2 + 8*a^2*c^3)*d - (b^5 - 7*a*b^3*c + 12*a^2*b*c^2)*e)*h)*x + ((b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*e*h*x^2 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*e*h*x + (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)*e*h)*log(c*x^2 + b*x + a))/(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4 + (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*x^2 + (b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*x), 1/2*(2*((2*(2*c^4*d - b*c^3*e)*f - 2*(b*c^3*d - 2*a*c^3*e)*g + (4*a*c^3*d + (b^3*c - 6*a*b*c^2)*e)*h)*x^2 + 2*(2*a*c^3*d - a*b*c^2*e)*f - 2*(a*b*c^2*d - 2*a^2*c^2*e)*g + (4*a^2*c^2*d + (a*b^3 - 6*a^2*b*c)*e)*h + (2*(2*b*c^3*d - b^2*c^2*e)*f - 2*(b^2*c^2*d - 2*a*b*c^2*e)*g + (4*a*b*c^2*d + (b^4 - 6*a*b^2*c)*e)*h)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - 2*((b^3*c^2 - 4*a*b*c^3)*d - 2*(a*b^2*c^2 - 4*a^2*c^3)*e)*f + 2*(2*(a*b^2*c^2 - 4*a^2*c^3)*d - (a*b^3*c - 4*a^2*b*c^2)*e)*g - 2*((a*b^3*c - 4*a^2*b*c^2)*d - (a*b^4 - 6*a^2*b^2*c + 8*a^3*c^2)*e)*h - 2*((2*(b^2*c^3 - 4*a*c^4)*d - (b^3*c^2 - 4*a*b*c^3)*e)*f - ((b^3*c^2 - 4*a*b*c^3)*d - (b^4*c - 6*a*b^2*c^2 + 8*a^2*c^3)*e)*g + ((b^4*c - 6*a*b^2*c^2 + 8*a^2*c^3)*d - (b^5 - 7*a*b^3*c + 12*a^2*b*c^2)*e)*h)*x + ((b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*e*h*x^2 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*e*h*x + (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)*e*h)*log(c*x^2 + b*x + a))/(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4 + (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*x^2 + (b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*x)]","B",0
157,1,632,0,1.063206," ","integrate((h*x^2+g*x+f)/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\left[-\frac{{\left(2 \, a c^{2} f - a b c g + 2 \, a^{2} c h + {\left(2 \, c^{3} f - b c^{2} g + 2 \, a c^{2} h\right)} x^{2} + {\left(2 \, b c^{2} f - b^{2} c g + 2 \, a b c h\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + {\left(b^{3} c - 4 \, a b c^{2}\right)} f - 2 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} g + {\left(a b^{3} - 4 \, a^{2} b c\right)} h + {\left(2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} f - {\left(b^{3} c - 4 \, a b c^{2}\right)} g + {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} h\right)} x}{a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3} + {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{2} + {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x}, \frac{2 \, {\left(2 \, a c^{2} f - a b c g + 2 \, a^{2} c h + {\left(2 \, c^{3} f - b c^{2} g + 2 \, a c^{2} h\right)} x^{2} + {\left(2 \, b c^{2} f - b^{2} c g + 2 \, a b c h\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - {\left(b^{3} c - 4 \, a b c^{2}\right)} f + 2 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} g - {\left(a b^{3} - 4 \, a^{2} b c\right)} h - {\left(2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} f - {\left(b^{3} c - 4 \, a b c^{2}\right)} g + {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} h\right)} x}{a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3} + {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{2} + {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x}\right]"," ",0,"[-((2*a*c^2*f - a*b*c*g + 2*a^2*c*h + (2*c^3*f - b*c^2*g + 2*a*c^2*h)*x^2 + (2*b*c^2*f - b^2*c*g + 2*a*b*c*h)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + (b^3*c - 4*a*b*c^2)*f - 2*(a*b^2*c - 4*a^2*c^2)*g + (a*b^3 - 4*a^2*b*c)*h + (2*(b^2*c^2 - 4*a*c^3)*f - (b^3*c - 4*a*b*c^2)*g + (b^4 - 6*a*b^2*c + 8*a^2*c^2)*h)*x)/(a*b^4*c - 8*a^2*b^2*c^2 + 16*a^3*c^3 + (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^2 + (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x), (2*(2*a*c^2*f - a*b*c*g + 2*a^2*c*h + (2*c^3*f - b*c^2*g + 2*a*c^2*h)*x^2 + (2*b*c^2*f - b^2*c*g + 2*a*b*c*h)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - (b^3*c - 4*a*b*c^2)*f + 2*(a*b^2*c - 4*a^2*c^2)*g - (a*b^3 - 4*a^2*b*c)*h - (2*(b^2*c^2 - 4*a*c^3)*f - (b^3*c - 4*a*b*c^2)*g + (b^4 - 6*a*b^2*c + 8*a^2*c^2)*h)*x)/(a*b^4*c - 8*a^2*b^2*c^2 + 16*a^3*c^3 + (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^2 + (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x)]","B",0
158,-1,0,0,0.000000," ","integrate((h*x^2+g*x+f)/(e*x+d)/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
159,-1,0,0,0.000000," ","integrate((h*x^2+g*x+f)/(e*x+d)^2/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
160,1,75,0,1.927500," ","integrate(x^3*(x^2+x+1)/(x^2-x+1)^2,x, algorithm=""fricas"")","\frac{9 \, x^{4} + 45 \, x^{3} - 20 \, \sqrt{3} {\left(x^{2} - x + 1\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) - 45 \, x^{2} + 36 \, {\left(x^{2} - x + 1\right)} \log\left(x^{2} - x + 1\right) + 42 \, x + 24}{18 \, {\left(x^{2} - x + 1\right)}}"," ",0,"1/18*(9*x^4 + 45*x^3 - 20*sqrt(3)*(x^2 - x + 1)*arctan(1/3*sqrt(3)*(2*x - 1)) - 45*x^2 + 36*(x^2 - x + 1)*log(x^2 - x + 1) + 42*x + 24)/(x^2 - x + 1)","A",0
161,1,70,0,0.693471," ","integrate(x^2*(x^2+x+1)/(x^2-x+1)^2,x, algorithm=""fricas"")","\frac{18 \, x^{3} + 14 \, \sqrt{3} {\left(x^{2} - x + 1\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) - 18 \, x^{2} + 27 \, {\left(x^{2} - x + 1\right)} \log\left(x^{2} - x + 1\right) - 6 \, x + 12}{18 \, {\left(x^{2} - x + 1\right)}}"," ",0,"1/18*(18*x^3 + 14*sqrt(3)*(x^2 - x + 1)*arctan(1/3*sqrt(3)*(2*x - 1)) - 18*x^2 + 27*(x^2 - x + 1)*log(x^2 - x + 1) - 6*x + 12)/(x^2 - x + 1)","A",0
162,1,60,0,1.041244," ","integrate(x*(x^2+x+1)/(x^2-x+1)^2,x, algorithm=""fricas"")","\frac{22 \, \sqrt{3} {\left(x^{2} - x + 1\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + 9 \, {\left(x^{2} - x + 1\right)} \log\left(x^{2} - x + 1\right) - 12 \, x - 12}{18 \, {\left(x^{2} - x + 1\right)}}"," ",0,"1/18*(22*sqrt(3)*(x^2 - x + 1)*arctan(1/3*sqrt(3)*(2*x - 1)) + 9*(x^2 - x + 1)*log(x^2 - x + 1) - 12*x - 12)/(x^2 - x + 1)","A",0
163,1,41,0,0.613505," ","integrate((x^2+x+1)/(x^2-x+1)^2,x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, \sqrt{3} {\left(x^{2} - x + 1\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + 3 \, x - 6\right)}}{9 \, {\left(x^{2} - x + 1\right)}}"," ",0,"2/9*(5*sqrt(3)*(x^2 - x + 1)*arctan(1/3*sqrt(3)*(2*x - 1)) + 3*x - 6)/(x^2 - x + 1)","A",0
164,1,72,0,1.088766," ","integrate((x^2+x+1)/x/(x^2-x+1)^2,x, algorithm=""fricas"")","\frac{22 \, \sqrt{3} {\left(x^{2} - x + 1\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) - 9 \, {\left(x^{2} - x + 1\right)} \log\left(x^{2} - x + 1\right) + 18 \, {\left(x^{2} - x + 1\right)} \log\left(x\right) + 24 \, x - 12}{18 \, {\left(x^{2} - x + 1\right)}}"," ",0,"1/18*(22*sqrt(3)*(x^2 - x + 1)*arctan(1/3*sqrt(3)*(2*x - 1)) - 9*(x^2 - x + 1)*log(x^2 - x + 1) + 18*(x^2 - x + 1)*log(x) + 24*x - 12)/(x^2 - x + 1)","A",0
165,1,85,0,1.249704," ","integrate((x^2+x+1)/x^2/(x^2-x+1)^2,x, algorithm=""fricas"")","\frac{14 \, \sqrt{3} {\left(x^{3} - x^{2} + x\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) - 6 \, x^{2} - 27 \, {\left(x^{3} - x^{2} + x\right)} \log\left(x^{2} - x + 1\right) + 54 \, {\left(x^{3} - x^{2} + x\right)} \log\left(x\right) + 30 \, x - 18}{18 \, {\left(x^{3} - x^{2} + x\right)}}"," ",0,"1/18*(14*sqrt(3)*(x^3 - x^2 + x)*arctan(1/3*sqrt(3)*(2*x - 1)) - 6*x^2 - 27*(x^3 - x^2 + x)*log(x^2 - x + 1) + 54*(x^3 - x^2 + x)*log(x) + 30*x - 18)/(x^3 - x^2 + x)","A",0
166,1,98,0,1.689441," ","integrate((x^2+x+1)/x^3/(x^2-x+1)^2,x, algorithm=""fricas"")","-\frac{66 \, x^{3} + 20 \, \sqrt{3} {\left(x^{4} - x^{3} + x^{2}\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) - 69 \, x^{2} + 36 \, {\left(x^{4} - x^{3} + x^{2}\right)} \log\left(x^{2} - x + 1\right) - 72 \, {\left(x^{4} - x^{3} + x^{2}\right)} \log\left(x\right) + 45 \, x + 9}{18 \, {\left(x^{4} - x^{3} + x^{2}\right)}}"," ",0,"-1/18*(66*x^3 + 20*sqrt(3)*(x^4 - x^3 + x^2)*arctan(1/3*sqrt(3)*(2*x - 1)) - 69*x^2 + 36*(x^4 - x^3 + x^2)*log(x^2 - x + 1) - 72*(x^4 - x^3 + x^2)*log(x) + 45*x + 9)/(x^4 - x^3 + x^2)","A",0
167,1,10,0,1.111732," ","integrate((-x^2+1)/(x^2+x+1)^2,x, algorithm=""fricas"")","\frac{x}{x^{2} + x + 1}"," ",0,"x/(x^2 + x + 1)","A",0
168,1,27,0,1.953726," ","integrate((x^2+1)/(x^2+x+1),x, algorithm=""fricas"")","\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + x - \frac{1}{2} \, \log\left(x^{2} + x + 1\right)"," ",0,"1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) + x - 1/2*log(x^2 + x + 1)","A",0
169,1,21,0,1.580808," ","integrate((x^2-1)/(x^2-6*x+25),x, algorithm=""fricas"")","x - 2 \, \arctan\left(\frac{1}{4} \, x - \frac{3}{4}\right) + 3 \, \log\left(x^{2} - 6 \, x + 25\right)"," ",0,"x - 2*arctan(1/4*x - 3/4) + 3*log(x^2 - 6*x + 25)","A",0
170,1,25,0,3.097744," ","integrate((3*x^2-10)/(x^2-4*x+4),x, algorithm=""fricas"")","\frac{3 \, x^{2} + 12 \, {\left(x - 2\right)} \log\left(x - 2\right) - 6 \, x - 2}{x - 2}"," ",0,"(3*x^2 + 12*(x - 2)*log(x - 2) - 6*x - 2)/(x - 2)","A",0
171,1,14,0,1.070256," ","integrate((x^2+8)/(x^2-5*x+6),x, algorithm=""fricas"")","x - 12 \, \log\left(x - 2\right) + 17 \, \log\left(x - 3\right)"," ",0,"x - 12*log(x - 2) + 17*log(x - 3)","A",0
172,1,12,0,0.743924," ","integrate((x^2+3*x-4)/(x^2-2*x-8),x, algorithm=""fricas"")","x + \log\left(x + 2\right) + 4 \, \log\left(x - 4\right)"," ",0,"x + log(x + 2) + 4*log(x - 4)","A",0
173,1,21,0,0.799011," ","integrate((4*x^2+5*x+7)/(4*x^2+4*x+5),x, algorithm=""fricas"")","x + \frac{3}{8} \, \arctan\left(x + \frac{1}{2}\right) + \frac{1}{8} \, \log\left(4 \, x^{2} + 4 \, x + 5\right)"," ",0,"x + 3/8*arctan(x + 1/2) + 1/8*log(4*x^2 + 4*x + 5)","A",0
174,1,55,0,0.742372," ","integrate((x^2-x+2)/(x^2+2*x-5),x, algorithm=""fricas"")","\frac{5}{6} \, \sqrt{3} \sqrt{2} \log\left(-\frac{2 \, \sqrt{3} \sqrt{2} {\left(x + 1\right)} - x^{2} - 2 \, x - 7}{x^{2} + 2 \, x - 5}\right) + x - \frac{3}{2} \, \log\left(x^{2} + 2 \, x - 5\right)"," ",0,"5/6*sqrt(3)*sqrt(2)*log(-(2*sqrt(3)*sqrt(2)*(x + 1) - x^2 - 2*x - 7)/(x^2 + 2*x - 5)) + x - 3/2*log(x^2 + 2*x - 5)","A",0
175,1,19,0,0.782540," ","integrate((3*x^2+4*x+1)/(2*x^2+7*x+4)^2,x, algorithm=""fricas"")","-\frac{3 \, x + 2}{2 \, {\left(2 \, x^{2} + 7 \, x + 4\right)}}"," ",0,"-1/2*(3*x + 2)/(2*x^2 + 7*x + 4)","A",0
176,1,39,0,0.862544," ","integrate((x^2+x+1)/(x^2+2*x+3)^2,x, algorithm=""fricas"")","\frac{3 \, \sqrt{2} {\left(x^{2} + 2 \, x + 3\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(x + 1\right)}\right) - 2 \, x + 2}{8 \, {\left(x^{2} + 2 \, x + 3\right)}}"," ",0,"1/8*(3*sqrt(2)*(x^2 + 2*x + 3)*arctan(1/2*sqrt(2)*(x + 1)) - 2*x + 2)/(x^2 + 2*x + 3)","A",0
177,1,33,0,0.816248," ","integrate((5*x^2+2*x-1)/(x^2+x+1)^4,x, algorithm=""fricas"")","-\frac{x}{x^{6} + 3 \, x^{5} + 6 \, x^{4} + 7 \, x^{3} + 6 \, x^{2} + 3 \, x + 1}"," ",0,"-x/(x^6 + 3*x^5 + 6*x^4 + 7*x^3 + 6*x^2 + 3*x + 1)","B",0
178,1,953,0,1.661312," ","integrate((c*x^2+b*x+a)^(5/2)*(C*x^2+A),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(9 \, C b^{8} - 112 \, C a b^{6} c - 2048 \, A a^{3} c^{5} + 256 \, {\left(C a^{4} + 6 \, A a^{2} b^{2}\right)} c^{4} - 384 \, {\left(2 \, C a^{3} b^{2} + A a b^{4}\right)} c^{3} + 32 \, {\left(15 \, C a^{2} b^{4} + A b^{6}\right)} c^{2}\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 \, {\left(43008 \, C c^{8} x^{7} + 101376 \, C b c^{7} x^{6} + 945 \, C b^{7} c - 10500 \, C a b^{5} c^{2} + 118272 \, A a^{2} b c^{5} + 256 \, {\left(243 \, C b^{2} c^{6} + 476 \, C a c^{7} + 224 \, A c^{8}\right)} x^{5} - 64 \, {\left(663 \, C a^{3} b + 560 \, A a b^{3}\right)} c^{4} + 128 \, {\left(3 \, C b^{3} c^{5} + 1228 \, C a b c^{6} + 1120 \, A b c^{7}\right)} x^{4} + 112 \, {\left(337 \, C a^{2} b^{3} + 30 \, A b^{5}\right)} c^{3} - 16 \, {\left(27 \, C b^{4} c^{4} - 216 \, C a b^{2} c^{5} - 11648 \, A a c^{7} - 112 \, {\left(59 \, C a^{2} + 54 \, A b^{2}\right)} c^{6}\right)} x^{3} + 8 \, {\left(63 \, C b^{5} c^{3} - 568 \, C a b^{3} c^{4} + 34944 \, A a b c^{6} + 16 \, {\left(87 \, C a^{2} b + 14 \, A b^{3}\right)} c^{5}\right)} x^{2} - 2 \, {\left(315 \, C b^{6} c^{2} - 3164 \, C a b^{4} c^{3} - 118272 \, A a^{2} c^{6} - 1344 \, {\left(5 \, C a^{3} + 8 \, A a b^{2}\right)} c^{5} + 16 \, {\left(597 \, C a^{2} b^{2} + 70 \, A b^{4}\right)} c^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{1376256 \, c^{6}}, \frac{105 \, {\left(9 \, C b^{8} - 112 \, C a b^{6} c - 2048 \, A a^{3} c^{5} + 256 \, {\left(C a^{4} + 6 \, A a^{2} b^{2}\right)} c^{4} - 384 \, {\left(2 \, C a^{3} b^{2} + A a b^{4}\right)} c^{3} + 32 \, {\left(15 \, C a^{2} b^{4} + A b^{6}\right)} c^{2}\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 \, {\left(43008 \, C c^{8} x^{7} + 101376 \, C b c^{7} x^{6} + 945 \, C b^{7} c - 10500 \, C a b^{5} c^{2} + 118272 \, A a^{2} b c^{5} + 256 \, {\left(243 \, C b^{2} c^{6} + 476 \, C a c^{7} + 224 \, A c^{8}\right)} x^{5} - 64 \, {\left(663 \, C a^{3} b + 560 \, A a b^{3}\right)} c^{4} + 128 \, {\left(3 \, C b^{3} c^{5} + 1228 \, C a b c^{6} + 1120 \, A b c^{7}\right)} x^{4} + 112 \, {\left(337 \, C a^{2} b^{3} + 30 \, A b^{5}\right)} c^{3} - 16 \, {\left(27 \, C b^{4} c^{4} - 216 \, C a b^{2} c^{5} - 11648 \, A a c^{7} - 112 \, {\left(59 \, C a^{2} + 54 \, A b^{2}\right)} c^{6}\right)} x^{3} + 8 \, {\left(63 \, C b^{5} c^{3} - 568 \, C a b^{3} c^{4} + 34944 \, A a b c^{6} + 16 \, {\left(87 \, C a^{2} b + 14 \, A b^{3}\right)} c^{5}\right)} x^{2} - 2 \, {\left(315 \, C b^{6} c^{2} - 3164 \, C a b^{4} c^{3} - 118272 \, A a^{2} c^{6} - 1344 \, {\left(5 \, C a^{3} + 8 \, A a b^{2}\right)} c^{5} + 16 \, {\left(597 \, C a^{2} b^{2} + 70 \, A b^{4}\right)} c^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{688128 \, c^{6}}\right]"," ",0,"[1/1376256*(105*(9*C*b^8 - 112*C*a*b^6*c - 2048*A*a^3*c^5 + 256*(C*a^4 + 6*A*a^2*b^2)*c^4 - 384*(2*C*a^3*b^2 + A*a*b^4)*c^3 + 32*(15*C*a^2*b^4 + A*b^6)*c^2)*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) + 4*(43008*C*c^8*x^7 + 101376*C*b*c^7*x^6 + 945*C*b^7*c - 10500*C*a*b^5*c^2 + 118272*A*a^2*b*c^5 + 256*(243*C*b^2*c^6 + 476*C*a*c^7 + 224*A*c^8)*x^5 - 64*(663*C*a^3*b + 560*A*a*b^3)*c^4 + 128*(3*C*b^3*c^5 + 1228*C*a*b*c^6 + 1120*A*b*c^7)*x^4 + 112*(337*C*a^2*b^3 + 30*A*b^5)*c^3 - 16*(27*C*b^4*c^4 - 216*C*a*b^2*c^5 - 11648*A*a*c^7 - 112*(59*C*a^2 + 54*A*b^2)*c^6)*x^3 + 8*(63*C*b^5*c^3 - 568*C*a*b^3*c^4 + 34944*A*a*b*c^6 + 16*(87*C*a^2*b + 14*A*b^3)*c^5)*x^2 - 2*(315*C*b^6*c^2 - 3164*C*a*b^4*c^3 - 118272*A*a^2*c^6 - 1344*(5*C*a^3 + 8*A*a*b^2)*c^5 + 16*(597*C*a^2*b^2 + 70*A*b^4)*c^4)*x)*sqrt(c*x^2 + b*x + a))/c^6, 1/688128*(105*(9*C*b^8 - 112*C*a*b^6*c - 2048*A*a^3*c^5 + 256*(C*a^4 + 6*A*a^2*b^2)*c^4 - 384*(2*C*a^3*b^2 + A*a*b^4)*c^3 + 32*(15*C*a^2*b^4 + A*b^6)*c^2)*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)) + 2*(43008*C*c^8*x^7 + 101376*C*b*c^7*x^6 + 945*C*b^7*c - 10500*C*a*b^5*c^2 + 118272*A*a^2*b*c^5 + 256*(243*C*b^2*c^6 + 476*C*a*c^7 + 224*A*c^8)*x^5 - 64*(663*C*a^3*b + 560*A*a*b^3)*c^4 + 128*(3*C*b^3*c^5 + 1228*C*a*b*c^6 + 1120*A*b*c^7)*x^4 + 112*(337*C*a^2*b^3 + 30*A*b^5)*c^3 - 16*(27*C*b^4*c^4 - 216*C*a*b^2*c^5 - 11648*A*a*c^7 - 112*(59*C*a^2 + 54*A*b^2)*c^6)*x^3 + 8*(63*C*b^5*c^3 - 568*C*a*b^3*c^4 + 34944*A*a*b*c^6 + 16*(87*C*a^2*b + 14*A*b^3)*c^5)*x^2 - 2*(315*C*b^6*c^2 - 3164*C*a*b^4*c^3 - 118272*A*a^2*c^6 - 1344*(5*C*a^3 + 8*A*a*b^2)*c^5 + 16*(597*C*a^2*b^2 + 70*A*b^4)*c^4)*x)*sqrt(c*x^2 + b*x + a))/c^6]","B",0
179,1,605,0,0.925466," ","integrate((c*x^2+b*x+a)^(3/2)*(C*x^2+A),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(7 \, C b^{6} - 60 \, C a b^{4} c + 384 \, A a^{2} c^{4} - 64 \, {\left(C a^{3} + 3 \, A a b^{2}\right)} c^{3} + 24 \, {\left(6 \, C a^{2} b^{2} + A b^{4}\right)} c^{2}\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 \, {\left(1280 \, C c^{6} x^{5} + 1664 \, C b c^{5} x^{4} - 105 \, C b^{5} c + 760 \, C a b^{3} c^{2} + 2400 \, A a b c^{4} - 72 \, {\left(18 \, C a^{2} b + 5 \, A b^{3}\right)} c^{3} + 16 \, {\left(3 \, C b^{2} c^{4} + 140 \, C a c^{5} + 120 \, A c^{6}\right)} x^{3} - 8 \, {\left(7 \, C b^{3} c^{3} - 36 \, C a b c^{4} - 360 \, A b c^{5}\right)} x^{2} + 2 \, {\left(35 \, C b^{4} c^{2} - 216 \, C a b^{2} c^{3} + 2400 \, A a c^{5} + 120 \, {\left(2 \, C a^{2} + A b^{2}\right)} c^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{30720 \, c^{5}}, -\frac{15 \, {\left(7 \, C b^{6} - 60 \, C a b^{4} c + 384 \, A a^{2} c^{4} - 64 \, {\left(C a^{3} + 3 \, A a b^{2}\right)} c^{3} + 24 \, {\left(6 \, C a^{2} b^{2} + A b^{4}\right)} c^{2}\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 \, {\left(1280 \, C c^{6} x^{5} + 1664 \, C b c^{5} x^{4} - 105 \, C b^{5} c + 760 \, C a b^{3} c^{2} + 2400 \, A a b c^{4} - 72 \, {\left(18 \, C a^{2} b + 5 \, A b^{3}\right)} c^{3} + 16 \, {\left(3 \, C b^{2} c^{4} + 140 \, C a c^{5} + 120 \, A c^{6}\right)} x^{3} - 8 \, {\left(7 \, C b^{3} c^{3} - 36 \, C a b c^{4} - 360 \, A b c^{5}\right)} x^{2} + 2 \, {\left(35 \, C b^{4} c^{2} - 216 \, C a b^{2} c^{3} + 2400 \, A a c^{5} + 120 \, {\left(2 \, C a^{2} + A b^{2}\right)} c^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{15360 \, c^{5}}\right]"," ",0,"[1/30720*(15*(7*C*b^6 - 60*C*a*b^4*c + 384*A*a^2*c^4 - 64*(C*a^3 + 3*A*a*b^2)*c^3 + 24*(6*C*a^2*b^2 + A*b^4)*c^2)*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) + 4*(1280*C*c^6*x^5 + 1664*C*b*c^5*x^4 - 105*C*b^5*c + 760*C*a*b^3*c^2 + 2400*A*a*b*c^4 - 72*(18*C*a^2*b + 5*A*b^3)*c^3 + 16*(3*C*b^2*c^4 + 140*C*a*c^5 + 120*A*c^6)*x^3 - 8*(7*C*b^3*c^3 - 36*C*a*b*c^4 - 360*A*b*c^5)*x^2 + 2*(35*C*b^4*c^2 - 216*C*a*b^2*c^3 + 2400*A*a*c^5 + 120*(2*C*a^2 + A*b^2)*c^4)*x)*sqrt(c*x^2 + b*x + a))/c^5, -1/15360*(15*(7*C*b^6 - 60*C*a*b^4*c + 384*A*a^2*c^4 - 64*(C*a^3 + 3*A*a*b^2)*c^3 + 24*(6*C*a^2*b^2 + A*b^4)*c^2)*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)) - 2*(1280*C*c^6*x^5 + 1664*C*b*c^5*x^4 - 105*C*b^5*c + 760*C*a*b^3*c^2 + 2400*A*a*b*c^4 - 72*(18*C*a^2*b + 5*A*b^3)*c^3 + 16*(3*C*b^2*c^4 + 140*C*a*c^5 + 120*A*c^6)*x^3 - 8*(7*C*b^3*c^3 - 36*C*a*b*c^4 - 360*A*b*c^5)*x^2 + 2*(35*C*b^4*c^2 - 216*C*a*b^2*c^3 + 2400*A*a*c^5 + 120*(2*C*a^2 + A*b^2)*c^4)*x)*sqrt(c*x^2 + b*x + a))/c^5]","A",0
180,1,355,0,0.793868," ","integrate((c*x^2+b*x+a)^(1/2)*(C*x^2+A),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, C b^{4} - 24 \, C a b^{2} c - 64 \, A a c^{3} + 16 \, {\left(C a^{2} + A b^{2}\right)} c^{2}\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 \, {\left(48 \, C c^{4} x^{3} + 8 \, C b c^{3} x^{2} + 15 \, C b^{3} c - 52 \, C a b c^{2} + 48 \, A b c^{3} - 2 \, {\left(5 \, C b^{2} c^{2} - 12 \, C a c^{3} - 48 \, A c^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{768 \, c^{4}}, \frac{3 \, {\left(5 \, C b^{4} - 24 \, C a b^{2} c - 64 \, A a c^{3} + 16 \, {\left(C a^{2} + A b^{2}\right)} c^{2}\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 \, {\left(48 \, C c^{4} x^{3} + 8 \, C b c^{3} x^{2} + 15 \, C b^{3} c - 52 \, C a b c^{2} + 48 \, A b c^{3} - 2 \, {\left(5 \, C b^{2} c^{2} - 12 \, C a c^{3} - 48 \, A c^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{384 \, c^{4}}\right]"," ",0,"[-1/768*(3*(5*C*b^4 - 24*C*a*b^2*c - 64*A*a*c^3 + 16*(C*a^2 + A*b^2)*c^2)*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) - 4*(48*C*c^4*x^3 + 8*C*b*c^3*x^2 + 15*C*b^3*c - 52*C*a*b*c^2 + 48*A*b*c^3 - 2*(5*C*b^2*c^2 - 12*C*a*c^3 - 48*A*c^4)*x)*sqrt(c*x^2 + b*x + a))/c^4, 1/384*(3*(5*C*b^4 - 24*C*a*b^2*c - 64*A*a*c^3 + 16*(C*a^2 + A*b^2)*c^2)*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)) + 2*(48*C*c^4*x^3 + 8*C*b*c^3*x^2 + 15*C*b^3*c - 52*C*a*b*c^2 + 48*A*b*c^3 - 2*(5*C*b^2*c^2 - 12*C*a*c^3 - 48*A*c^4)*x)*sqrt(c*x^2 + b*x + a))/c^4]","A",0
181,1,203,0,0.942480," ","integrate((C*x^2+A)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(3 \, C b^{2} - 4 \, C a c + 8 \, A c^{2}\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 \, {\left(2 \, C c^{2} x - 3 \, C b c\right)} \sqrt{c x^{2} + b x + a}}{16 \, c^{3}}, -\frac{{\left(3 \, C b^{2} - 4 \, C a c + 8 \, A c^{2}\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 \, {\left(2 \, C c^{2} x - 3 \, C b c\right)} \sqrt{c x^{2} + b x + a}}{8 \, c^{3}}\right]"," ",0,"[1/16*((3*C*b^2 - 4*C*a*c + 8*A*c^2)*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) + 4*(2*C*c^2*x - 3*C*b*c)*sqrt(c*x^2 + b*x + a))/c^3, -1/8*((3*C*b^2 - 4*C*a*c + 8*A*c^2)*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)) - 2*(2*C*c^2*x - 3*C*b*c)*sqrt(c*x^2 + b*x + a))/c^3]","A",0
182,1,403,0,1.729891," ","integrate((C*x^2+A)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(C a b^{2} - 4 \, C a^{2} c + {\left(C b^{2} c - 4 \, C a c^{2}\right)} x^{2} + {\left(C b^{3} - 4 \, C a b c\right)} x\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 \, {\left(C a b c + A b c^{2} + {\left(C b^{2} c - 2 \, C a c^{2} + 2 \, A c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{2 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{2} + {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x\right)}}, -\frac{{\left(C a b^{2} - 4 \, C a^{2} c + {\left(C b^{2} c - 4 \, C a c^{2}\right)} x^{2} + {\left(C b^{3} - 4 \, C a b c\right)} x\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 \, {\left(C a b c + A b c^{2} + {\left(C b^{2} c - 2 \, C a c^{2} + 2 \, A c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{a b^{2} c^{2} - 4 \, a^{2} c^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{2} + {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x}\right]"," ",0,"[1/2*((C*a*b^2 - 4*C*a^2*c + (C*b^2*c - 4*C*a*c^2)*x^2 + (C*b^3 - 4*C*a*b*c)*x)*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) - 4*(C*a*b*c + A*b*c^2 + (C*b^2*c - 2*C*a*c^2 + 2*A*c^3)*x)*sqrt(c*x^2 + b*x + a))/(a*b^2*c^2 - 4*a^2*c^3 + (b^2*c^3 - 4*a*c^4)*x^2 + (b^3*c^2 - 4*a*b*c^3)*x), -((C*a*b^2 - 4*C*a^2*c + (C*b^2*c - 4*C*a*c^2)*x^2 + (C*b^3 - 4*C*a*b*c)*x)*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)) + 2*(C*a*b*c + A*b*c^2 + (C*b^2*c - 2*C*a*c^2 + 2*A*c^3)*x)*sqrt(c*x^2 + b*x + a))/(a*b^2*c^2 - 4*a^2*c^3 + (b^2*c^3 - 4*a*c^4)*x^2 + (b^3*c^2 - 4*a*b*c^3)*x)]","B",0
183,1,242,0,2.067998," ","integrate((C*x^2+A)/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, C a^{2} b - A b^{3} + 12 \, A a b c + 2 \, {\left(C b^{2} c + 4 \, C a c^{2} + 8 \, A c^{3}\right)} x^{3} + 3 \, {\left(C b^{3} + 4 \, C a b c + 8 \, A b c^{2}\right)} x^{2} + 6 \, {\left(2 \, C a b^{2} + A b^{2} c + 4 \, A a c^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{3 \, {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x\right)}}"," ",0,"2/3*(8*C*a^2*b - A*b^3 + 12*A*a*b*c + 2*(C*b^2*c + 4*C*a*c^2 + 8*A*c^3)*x^3 + 3*(C*b^3 + 4*C*a*b*c + 8*A*b*c^2)*x^2 + 6*(2*C*a*b^2 + A*b^2*c + 4*A*a*c^2)*x)*sqrt(c*x^2 + b*x + a)/(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x)","B",0
184,1,563,0,17.197079," ","integrate((C*x^2+A)/(c*x^2+b*x+a)^(7/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(8 \, C a^{2} b^{3} + 3 \, A b^{5} + 240 \, A a^{2} b c^{2} + 16 \, {\left(3 \, C b^{2} c^{3} + 4 \, C a c^{4} + 16 \, A c^{5}\right)} x^{5} + 40 \, {\left(3 \, C b^{3} c^{2} + 4 \, C a b c^{3} + 16 \, A b c^{4}\right)} x^{4} + 10 \, {\left(9 \, C b^{4} c + 24 \, C a b^{2} c^{2} + 64 \, A a c^{4} + 16 \, {\left(C a^{2} + 3 \, A b^{2}\right)} c^{3}\right)} x^{3} + 5 \, {\left(3 \, C b^{5} + 40 \, C a b^{3} c + 192 \, A a b c^{3} + 16 \, {\left(3 \, C a^{2} b + A b^{3}\right)} c^{2}\right)} x^{2} + 8 \, {\left(12 \, C a^{3} b - 5 \, A a b^{3}\right)} c + 10 \, {\left(2 \, C a b^{4} + 24 \, A a b^{2} c^{2} + 48 \, A a^{2} c^{3} + {\left(24 \, C a^{2} b^{2} - A b^{4}\right)} c\right)} x\right)} \sqrt{c x^{2} + b x + a}}{15 \, {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3} + {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} x^{6} + 3 \, {\left(b^{7} c^{2} - 12 \, a b^{5} c^{3} + 48 \, a^{2} b^{3} c^{4} - 64 \, a^{3} b c^{5}\right)} x^{5} + 3 \, {\left(b^{8} c - 11 \, a b^{6} c^{2} + 36 \, a^{2} b^{4} c^{3} - 16 \, a^{3} b^{2} c^{4} - 64 \, a^{4} c^{5}\right)} x^{4} + {\left(b^{9} - 6 \, a b^{7} c - 24 \, a^{2} b^{5} c^{2} + 224 \, a^{3} b^{3} c^{3} - 384 \, a^{4} b c^{4}\right)} x^{3} + 3 \, {\left(a b^{8} - 11 \, a^{2} b^{6} c + 36 \, a^{3} b^{4} c^{2} - 16 \, a^{4} b^{2} c^{3} - 64 \, a^{5} c^{4}\right)} x^{2} + 3 \, {\left(a^{2} b^{7} - 12 \, a^{3} b^{5} c + 48 \, a^{4} b^{3} c^{2} - 64 \, a^{5} b c^{3}\right)} x\right)}}"," ",0,"-2/15*(8*C*a^2*b^3 + 3*A*b^5 + 240*A*a^2*b*c^2 + 16*(3*C*b^2*c^3 + 4*C*a*c^4 + 16*A*c^5)*x^5 + 40*(3*C*b^3*c^2 + 4*C*a*b*c^3 + 16*A*b*c^4)*x^4 + 10*(9*C*b^4*c + 24*C*a*b^2*c^2 + 64*A*a*c^4 + 16*(C*a^2 + 3*A*b^2)*c^3)*x^3 + 5*(3*C*b^5 + 40*C*a*b^3*c + 192*A*a*b*c^3 + 16*(3*C*a^2*b + A*b^3)*c^2)*x^2 + 8*(12*C*a^3*b - 5*A*a*b^3)*c + 10*(2*C*a*b^4 + 24*A*a*b^2*c^2 + 48*A*a^2*c^3 + (24*C*a^2*b^2 - A*b^4)*c)*x)*sqrt(c*x^2 + b*x + a)/(a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3 + (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*x^6 + 3*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*x^5 + 3*(b^8*c - 11*a*b^6*c^2 + 36*a^2*b^4*c^3 - 16*a^3*b^2*c^4 - 64*a^4*c^5)*x^4 + (b^9 - 6*a*b^7*c - 24*a^2*b^5*c^2 + 224*a^3*b^3*c^3 - 384*a^4*b*c^4)*x^3 + 3*(a*b^8 - 11*a^2*b^6*c + 36*a^3*b^4*c^2 - 16*a^4*b^2*c^3 - 64*a^5*c^4)*x^2 + 3*(a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3)*x)","B",0
185,1,978,0,49.880579," ","integrate((C*x^2+A)/(c*x^2+b*x+a)^(9/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(8 \, C a^{2} b^{5} + 15 \, A b^{7} - 6720 \, A a^{3} b c^{3} - 256 \, {\left(5 \, C b^{2} c^{5} + 4 \, C a c^{6} + 24 \, A c^{7}\right)} x^{7} - 896 \, {\left(5 \, C b^{3} c^{4} + 4 \, C a b c^{5} + 24 \, A b c^{6}\right)} x^{6} - 224 \, {\left(25 \, C b^{4} c^{3} + 40 \, C a b^{2} c^{4} + 96 \, A a c^{6} + 8 \, {\left(2 \, C a^{2} + 15 \, A b^{2}\right)} c^{5}\right)} x^{5} - 560 \, {\left(5 \, C b^{5} c^{2} + 24 \, C a b^{3} c^{3} + 96 \, A a b c^{5} + 8 \, {\left(2 \, C a^{2} b + 3 \, A b^{3}\right)} c^{4}\right)} x^{4} - 70 \, {\left(5 \, C b^{6} c + 124 \, C a b^{4} c^{2} + 384 \, A a^{2} c^{5} + 64 \, {\left(C a^{3} + 9 \, A a b^{2}\right)} c^{4} + 8 \, {\left(22 \, C a^{2} b^{2} + 3 \, A b^{4}\right)} c^{3}\right)} x^{3} - 240 \, {\left(8 \, C a^{4} b - 7 \, A a^{2} b^{3}\right)} c^{2} + 7 \, {\left(5 \, C b^{7} - 196 \, C a b^{5} c - 5760 \, A a^{2} b c^{4} - 960 \, {\left(C a^{3} b + A a b^{3}\right)} c^{3} - 8 \, {\left(170 \, C a^{2} b^{3} - 3 \, A b^{5}\right)} c^{2}\right)} x^{2} - 4 \, {\left(80 \, C a^{3} b^{3} + 63 \, A a b^{5}\right)} c + 14 \, {\left(2 \, C a b^{6} - 720 \, A a^{2} b^{2} c^{3} - 960 \, A a^{3} c^{4} - 60 \, {\left(8 \, C a^{3} b^{2} - A a b^{4}\right)} c^{2} - {\left(80 \, C a^{2} b^{4} + 3 \, A b^{6}\right)} c\right)} x\right)} \sqrt{c x^{2} + b x + a}}{105 \, {\left(a^{4} b^{8} - 16 \, a^{5} b^{6} c + 96 \, a^{6} b^{4} c^{2} - 256 \, a^{7} b^{2} c^{3} + 256 \, a^{8} c^{4} + {\left(b^{8} c^{4} - 16 \, a b^{6} c^{5} + 96 \, a^{2} b^{4} c^{6} - 256 \, a^{3} b^{2} c^{7} + 256 \, a^{4} c^{8}\right)} x^{8} + 4 \, {\left(b^{9} c^{3} - 16 \, a b^{7} c^{4} + 96 \, a^{2} b^{5} c^{5} - 256 \, a^{3} b^{3} c^{6} + 256 \, a^{4} b c^{7}\right)} x^{7} + 2 \, {\left(3 \, b^{10} c^{2} - 46 \, a b^{8} c^{3} + 256 \, a^{2} b^{6} c^{4} - 576 \, a^{3} b^{4} c^{5} + 256 \, a^{4} b^{2} c^{6} + 512 \, a^{5} c^{7}\right)} x^{6} + 4 \, {\left(b^{11} c - 13 \, a b^{9} c^{2} + 48 \, a^{2} b^{7} c^{3} + 32 \, a^{3} b^{5} c^{4} - 512 \, a^{4} b^{3} c^{5} + 768 \, a^{5} b c^{6}\right)} x^{5} + {\left(b^{12} - 4 \, a b^{10} c - 90 \, a^{2} b^{8} c^{2} + 800 \, a^{3} b^{6} c^{3} - 2240 \, a^{4} b^{4} c^{4} + 1536 \, a^{5} b^{2} c^{5} + 1536 \, a^{6} c^{6}\right)} x^{4} + 4 \, {\left(a b^{11} - 13 \, a^{2} b^{9} c + 48 \, a^{3} b^{7} c^{2} + 32 \, a^{4} b^{5} c^{3} - 512 \, a^{5} b^{3} c^{4} + 768 \, a^{6} b c^{5}\right)} x^{3} + 2 \, {\left(3 \, a^{2} b^{10} - 46 \, a^{3} b^{8} c + 256 \, a^{4} b^{6} c^{2} - 576 \, a^{5} b^{4} c^{3} + 256 \, a^{6} b^{2} c^{4} + 512 \, a^{7} c^{5}\right)} x^{2} + 4 \, {\left(a^{3} b^{9} - 16 \, a^{4} b^{7} c + 96 \, a^{5} b^{5} c^{2} - 256 \, a^{6} b^{3} c^{3} + 256 \, a^{7} b c^{4}\right)} x\right)}}"," ",0,"-2/105*(8*C*a^2*b^5 + 15*A*b^7 - 6720*A*a^3*b*c^3 - 256*(5*C*b^2*c^5 + 4*C*a*c^6 + 24*A*c^7)*x^7 - 896*(5*C*b^3*c^4 + 4*C*a*b*c^5 + 24*A*b*c^6)*x^6 - 224*(25*C*b^4*c^3 + 40*C*a*b^2*c^4 + 96*A*a*c^6 + 8*(2*C*a^2 + 15*A*b^2)*c^5)*x^5 - 560*(5*C*b^5*c^2 + 24*C*a*b^3*c^3 + 96*A*a*b*c^5 + 8*(2*C*a^2*b + 3*A*b^3)*c^4)*x^4 - 70*(5*C*b^6*c + 124*C*a*b^4*c^2 + 384*A*a^2*c^5 + 64*(C*a^3 + 9*A*a*b^2)*c^4 + 8*(22*C*a^2*b^2 + 3*A*b^4)*c^3)*x^3 - 240*(8*C*a^4*b - 7*A*a^2*b^3)*c^2 + 7*(5*C*b^7 - 196*C*a*b^5*c - 5760*A*a^2*b*c^4 - 960*(C*a^3*b + A*a*b^3)*c^3 - 8*(170*C*a^2*b^3 - 3*A*b^5)*c^2)*x^2 - 4*(80*C*a^3*b^3 + 63*A*a*b^5)*c + 14*(2*C*a*b^6 - 720*A*a^2*b^2*c^3 - 960*A*a^3*c^4 - 60*(8*C*a^3*b^2 - A*a*b^4)*c^2 - (80*C*a^2*b^4 + 3*A*b^6)*c)*x)*sqrt(c*x^2 + b*x + a)/(a^4*b^8 - 16*a^5*b^6*c + 96*a^6*b^4*c^2 - 256*a^7*b^2*c^3 + 256*a^8*c^4 + (b^8*c^4 - 16*a*b^6*c^5 + 96*a^2*b^4*c^6 - 256*a^3*b^2*c^7 + 256*a^4*c^8)*x^8 + 4*(b^9*c^3 - 16*a*b^7*c^4 + 96*a^2*b^5*c^5 - 256*a^3*b^3*c^6 + 256*a^4*b*c^7)*x^7 + 2*(3*b^10*c^2 - 46*a*b^8*c^3 + 256*a^2*b^6*c^4 - 576*a^3*b^4*c^5 + 256*a^4*b^2*c^6 + 512*a^5*c^7)*x^6 + 4*(b^11*c - 13*a*b^9*c^2 + 48*a^2*b^7*c^3 + 32*a^3*b^5*c^4 - 512*a^4*b^3*c^5 + 768*a^5*b*c^6)*x^5 + (b^12 - 4*a*b^10*c - 90*a^2*b^8*c^2 + 800*a^3*b^6*c^3 - 2240*a^4*b^4*c^4 + 1536*a^5*b^2*c^5 + 1536*a^6*c^6)*x^4 + 4*(a*b^11 - 13*a^2*b^9*c + 48*a^3*b^7*c^2 + 32*a^4*b^5*c^3 - 512*a^5*b^3*c^4 + 768*a^6*b*c^5)*x^3 + 2*(3*a^2*b^10 - 46*a^3*b^8*c + 256*a^4*b^6*c^2 - 576*a^5*b^4*c^3 + 256*a^6*b^2*c^4 + 512*a^7*c^5)*x^2 + 4*(a^3*b^9 - 16*a^4*b^7*c + 96*a^5*b^5*c^2 - 256*a^6*b^3*c^3 + 256*a^7*b*c^4)*x)","B",0
186,1,2817,0,3.619848," ","integrate((h*x+g)^3*(f*x^2+e*x+d)*(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(16 \, {\left(16 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d - 8 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} e + {\left(5 \, b^{4} c^{3} - 24 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} f\right)} g^{3} - 24 \, {\left(16 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d - 2 \, {\left(5 \, b^{4} c^{3} - 24 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} e + {\left(7 \, b^{5} c^{2} - 40 \, a b^{3} c^{3} + 48 \, a^{2} b c^{4}\right)} f\right)} g^{2} h + 6 \, {\left(8 \, {\left(5 \, b^{4} c^{3} - 24 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d - 4 \, {\left(7 \, b^{5} c^{2} - 40 \, a b^{3} c^{3} + 48 \, a^{2} b c^{4}\right)} e + {\left(21 \, b^{6} c - 140 \, a b^{4} c^{2} + 240 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} f\right)} g h^{2} - {\left(8 \, {\left(7 \, b^{5} c^{2} - 40 \, a b^{3} c^{3} + 48 \, a^{2} b c^{4}\right)} d - 2 \, {\left(21 \, b^{6} c - 140 \, a b^{4} c^{2} + 240 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} e + {\left(33 \, b^{7} - 252 \, a b^{5} c + 560 \, a^{2} b^{3} c^{2} - 320 \, a^{3} b c^{3}\right)} f\right)} h^{3}\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 \, {\left(15360 \, c^{7} f h^{3} x^{6} + 1280 \, {\left(42 \, c^{7} f g h^{2} + {\left(14 \, c^{7} e + b c^{6} f\right)} h^{3}\right)} x^{5} + 128 \, {\left(504 \, c^{7} f g^{2} h + 42 \, {\left(12 \, c^{7} e + b c^{6} f\right)} g h^{2} + {\left(168 \, c^{7} d + 14 \, b c^{6} e - {\left(11 \, b^{2} c^{5} - 24 \, a c^{6}\right)} f\right)} h^{3}\right)} x^{4} + 560 \, {\left(48 \, b c^{6} d - 8 \, {\left(3 \, b^{2} c^{5} - 8 \, a c^{6}\right)} e + {\left(15 \, b^{3} c^{4} - 52 \, a b c^{5}\right)} f\right)} g^{3} - 168 \, {\left(80 \, {\left(3 \, b^{2} c^{5} - 8 \, a c^{6}\right)} d - 10 \, {\left(15 \, b^{3} c^{4} - 52 \, a b c^{5}\right)} e + {\left(105 \, b^{4} c^{3} - 460 \, a b^{2} c^{4} + 256 \, a^{2} c^{5}\right)} f\right)} g^{2} h + 42 \, {\left(40 \, {\left(15 \, b^{3} c^{4} - 52 \, a b c^{5}\right)} d - 4 \, {\left(105 \, b^{4} c^{3} - 460 \, a b^{2} c^{4} + 256 \, a^{2} c^{5}\right)} e + {\left(315 \, b^{5} c^{2} - 1680 \, a b^{3} c^{3} + 1808 \, a^{2} b c^{4}\right)} f\right)} g h^{2} - {\left(56 \, {\left(105 \, b^{4} c^{3} - 460 \, a b^{2} c^{4} + 256 \, a^{2} c^{5}\right)} d - 14 \, {\left(315 \, b^{5} c^{2} - 1680 \, a b^{3} c^{3} + 1808 \, a^{2} b c^{4}\right)} e + {\left(3465 \, b^{6} c - 21840 \, a b^{4} c^{2} + 34608 \, a^{2} b^{2} c^{3} - 8192 \, a^{3} c^{4}\right)} f\right)} h^{3} + 16 \, {\left(1680 \, c^{7} f g^{3} + 504 \, {\left(10 \, c^{7} e + b c^{6} f\right)} g^{2} h + 42 \, {\left(120 \, c^{7} d + 12 \, b c^{6} e - {\left(9 \, b^{2} c^{5} - 20 \, a c^{6}\right)} f\right)} g h^{2} + {\left(168 \, b c^{6} d - 14 \, {\left(9 \, b^{2} c^{5} - 20 \, a c^{6}\right)} e + {\left(99 \, b^{3} c^{4} - 316 \, a b c^{5}\right)} f\right)} h^{3}\right)} x^{3} + 8 \, {\left(560 \, {\left(8 \, c^{7} e + b c^{6} f\right)} g^{3} + 168 \, {\left(80 \, c^{7} d + 10 \, b c^{6} e - {\left(7 \, b^{2} c^{5} - 16 \, a c^{6}\right)} f\right)} g^{2} h + 42 \, {\left(40 \, b c^{6} d - 4 \, {\left(7 \, b^{2} c^{5} - 16 \, a c^{6}\right)} e + {\left(21 \, b^{3} c^{4} - 68 \, a b c^{5}\right)} f\right)} g h^{2} - {\left(56 \, {\left(7 \, b^{2} c^{5} - 16 \, a c^{6}\right)} d - 14 \, {\left(21 \, b^{3} c^{4} - 68 \, a b c^{5}\right)} e + {\left(231 \, b^{4} c^{3} - 972 \, a b^{2} c^{4} + 512 \, a^{2} c^{5}\right)} f\right)} h^{3}\right)} x^{2} + 2 \, {\left(560 \, {\left(48 \, c^{7} d + 8 \, b c^{6} e - {\left(5 \, b^{2} c^{5} - 12 \, a c^{6}\right)} f\right)} g^{3} + 168 \, {\left(80 \, b c^{6} d - 10 \, {\left(5 \, b^{2} c^{5} - 12 \, a c^{6}\right)} e + {\left(35 \, b^{3} c^{4} - 116 \, a b c^{5}\right)} f\right)} g^{2} h - 42 \, {\left(40 \, {\left(5 \, b^{2} c^{5} - 12 \, a c^{6}\right)} d - 4 \, {\left(35 \, b^{3} c^{4} - 116 \, a b c^{5}\right)} e + {\left(105 \, b^{4} c^{3} - 448 \, a b^{2} c^{4} + 240 \, a^{2} c^{5}\right)} f\right)} g h^{2} + {\left(56 \, {\left(35 \, b^{3} c^{4} - 116 \, a b c^{5}\right)} d - 14 \, {\left(105 \, b^{4} c^{3} - 448 \, a b^{2} c^{4} + 240 \, a^{2} c^{5}\right)} e + {\left(1155 \, b^{5} c^{2} - 6048 \, a b^{3} c^{3} + 6352 \, a^{2} b c^{4}\right)} f\right)} h^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{430080 \, c^{7}}, \frac{105 \, {\left(16 \, {\left(16 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d - 8 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} e + {\left(5 \, b^{4} c^{3} - 24 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} f\right)} g^{3} - 24 \, {\left(16 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d - 2 \, {\left(5 \, b^{4} c^{3} - 24 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} e + {\left(7 \, b^{5} c^{2} - 40 \, a b^{3} c^{3} + 48 \, a^{2} b c^{4}\right)} f\right)} g^{2} h + 6 \, {\left(8 \, {\left(5 \, b^{4} c^{3} - 24 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d - 4 \, {\left(7 \, b^{5} c^{2} - 40 \, a b^{3} c^{3} + 48 \, a^{2} b c^{4}\right)} e + {\left(21 \, b^{6} c - 140 \, a b^{4} c^{2} + 240 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} f\right)} g h^{2} - {\left(8 \, {\left(7 \, b^{5} c^{2} - 40 \, a b^{3} c^{3} + 48 \, a^{2} b c^{4}\right)} d - 2 \, {\left(21 \, b^{6} c - 140 \, a b^{4} c^{2} + 240 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} e + {\left(33 \, b^{7} - 252 \, a b^{5} c + 560 \, a^{2} b^{3} c^{2} - 320 \, a^{3} b c^{3}\right)} f\right)} h^{3}\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 \, {\left(15360 \, c^{7} f h^{3} x^{6} + 1280 \, {\left(42 \, c^{7} f g h^{2} + {\left(14 \, c^{7} e + b c^{6} f\right)} h^{3}\right)} x^{5} + 128 \, {\left(504 \, c^{7} f g^{2} h + 42 \, {\left(12 \, c^{7} e + b c^{6} f\right)} g h^{2} + {\left(168 \, c^{7} d + 14 \, b c^{6} e - {\left(11 \, b^{2} c^{5} - 24 \, a c^{6}\right)} f\right)} h^{3}\right)} x^{4} + 560 \, {\left(48 \, b c^{6} d - 8 \, {\left(3 \, b^{2} c^{5} - 8 \, a c^{6}\right)} e + {\left(15 \, b^{3} c^{4} - 52 \, a b c^{5}\right)} f\right)} g^{3} - 168 \, {\left(80 \, {\left(3 \, b^{2} c^{5} - 8 \, a c^{6}\right)} d - 10 \, {\left(15 \, b^{3} c^{4} - 52 \, a b c^{5}\right)} e + {\left(105 \, b^{4} c^{3} - 460 \, a b^{2} c^{4} + 256 \, a^{2} c^{5}\right)} f\right)} g^{2} h + 42 \, {\left(40 \, {\left(15 \, b^{3} c^{4} - 52 \, a b c^{5}\right)} d - 4 \, {\left(105 \, b^{4} c^{3} - 460 \, a b^{2} c^{4} + 256 \, a^{2} c^{5}\right)} e + {\left(315 \, b^{5} c^{2} - 1680 \, a b^{3} c^{3} + 1808 \, a^{2} b c^{4}\right)} f\right)} g h^{2} - {\left(56 \, {\left(105 \, b^{4} c^{3} - 460 \, a b^{2} c^{4} + 256 \, a^{2} c^{5}\right)} d - 14 \, {\left(315 \, b^{5} c^{2} - 1680 \, a b^{3} c^{3} + 1808 \, a^{2} b c^{4}\right)} e + {\left(3465 \, b^{6} c - 21840 \, a b^{4} c^{2} + 34608 \, a^{2} b^{2} c^{3} - 8192 \, a^{3} c^{4}\right)} f\right)} h^{3} + 16 \, {\left(1680 \, c^{7} f g^{3} + 504 \, {\left(10 \, c^{7} e + b c^{6} f\right)} g^{2} h + 42 \, {\left(120 \, c^{7} d + 12 \, b c^{6} e - {\left(9 \, b^{2} c^{5} - 20 \, a c^{6}\right)} f\right)} g h^{2} + {\left(168 \, b c^{6} d - 14 \, {\left(9 \, b^{2} c^{5} - 20 \, a c^{6}\right)} e + {\left(99 \, b^{3} c^{4} - 316 \, a b c^{5}\right)} f\right)} h^{3}\right)} x^{3} + 8 \, {\left(560 \, {\left(8 \, c^{7} e + b c^{6} f\right)} g^{3} + 168 \, {\left(80 \, c^{7} d + 10 \, b c^{6} e - {\left(7 \, b^{2} c^{5} - 16 \, a c^{6}\right)} f\right)} g^{2} h + 42 \, {\left(40 \, b c^{6} d - 4 \, {\left(7 \, b^{2} c^{5} - 16 \, a c^{6}\right)} e + {\left(21 \, b^{3} c^{4} - 68 \, a b c^{5}\right)} f\right)} g h^{2} - {\left(56 \, {\left(7 \, b^{2} c^{5} - 16 \, a c^{6}\right)} d - 14 \, {\left(21 \, b^{3} c^{4} - 68 \, a b c^{5}\right)} e + {\left(231 \, b^{4} c^{3} - 972 \, a b^{2} c^{4} + 512 \, a^{2} c^{5}\right)} f\right)} h^{3}\right)} x^{2} + 2 \, {\left(560 \, {\left(48 \, c^{7} d + 8 \, b c^{6} e - {\left(5 \, b^{2} c^{5} - 12 \, a c^{6}\right)} f\right)} g^{3} + 168 \, {\left(80 \, b c^{6} d - 10 \, {\left(5 \, b^{2} c^{5} - 12 \, a c^{6}\right)} e + {\left(35 \, b^{3} c^{4} - 116 \, a b c^{5}\right)} f\right)} g^{2} h - 42 \, {\left(40 \, {\left(5 \, b^{2} c^{5} - 12 \, a c^{6}\right)} d - 4 \, {\left(35 \, b^{3} c^{4} - 116 \, a b c^{5}\right)} e + {\left(105 \, b^{4} c^{3} - 448 \, a b^{2} c^{4} + 240 \, a^{2} c^{5}\right)} f\right)} g h^{2} + {\left(56 \, {\left(35 \, b^{3} c^{4} - 116 \, a b c^{5}\right)} d - 14 \, {\left(105 \, b^{4} c^{3} - 448 \, a b^{2} c^{4} + 240 \, a^{2} c^{5}\right)} e + {\left(1155 \, b^{5} c^{2} - 6048 \, a b^{3} c^{3} + 6352 \, a^{2} b c^{4}\right)} f\right)} h^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{215040 \, c^{7}}\right]"," ",0,"[1/430080*(105*(16*(16*(b^2*c^5 - 4*a*c^6)*d - 8*(b^3*c^4 - 4*a*b*c^5)*e + (5*b^4*c^3 - 24*a*b^2*c^4 + 16*a^2*c^5)*f)*g^3 - 24*(16*(b^3*c^4 - 4*a*b*c^5)*d - 2*(5*b^4*c^3 - 24*a*b^2*c^4 + 16*a^2*c^5)*e + (7*b^5*c^2 - 40*a*b^3*c^3 + 48*a^2*b*c^4)*f)*g^2*h + 6*(8*(5*b^4*c^3 - 24*a*b^2*c^4 + 16*a^2*c^5)*d - 4*(7*b^5*c^2 - 40*a*b^3*c^3 + 48*a^2*b*c^4)*e + (21*b^6*c - 140*a*b^4*c^2 + 240*a^2*b^2*c^3 - 64*a^3*c^4)*f)*g*h^2 - (8*(7*b^5*c^2 - 40*a*b^3*c^3 + 48*a^2*b*c^4)*d - 2*(21*b^6*c - 140*a*b^4*c^2 + 240*a^2*b^2*c^3 - 64*a^3*c^4)*e + (33*b^7 - 252*a*b^5*c + 560*a^2*b^3*c^2 - 320*a^3*b*c^3)*f)*h^3)*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) + 4*(15360*c^7*f*h^3*x^6 + 1280*(42*c^7*f*g*h^2 + (14*c^7*e + b*c^6*f)*h^3)*x^5 + 128*(504*c^7*f*g^2*h + 42*(12*c^7*e + b*c^6*f)*g*h^2 + (168*c^7*d + 14*b*c^6*e - (11*b^2*c^5 - 24*a*c^6)*f)*h^3)*x^4 + 560*(48*b*c^6*d - 8*(3*b^2*c^5 - 8*a*c^6)*e + (15*b^3*c^4 - 52*a*b*c^5)*f)*g^3 - 168*(80*(3*b^2*c^5 - 8*a*c^6)*d - 10*(15*b^3*c^4 - 52*a*b*c^5)*e + (105*b^4*c^3 - 460*a*b^2*c^4 + 256*a^2*c^5)*f)*g^2*h + 42*(40*(15*b^3*c^4 - 52*a*b*c^5)*d - 4*(105*b^4*c^3 - 460*a*b^2*c^4 + 256*a^2*c^5)*e + (315*b^5*c^2 - 1680*a*b^3*c^3 + 1808*a^2*b*c^4)*f)*g*h^2 - (56*(105*b^4*c^3 - 460*a*b^2*c^4 + 256*a^2*c^5)*d - 14*(315*b^5*c^2 - 1680*a*b^3*c^3 + 1808*a^2*b*c^4)*e + (3465*b^6*c - 21840*a*b^4*c^2 + 34608*a^2*b^2*c^3 - 8192*a^3*c^4)*f)*h^3 + 16*(1680*c^7*f*g^3 + 504*(10*c^7*e + b*c^6*f)*g^2*h + 42*(120*c^7*d + 12*b*c^6*e - (9*b^2*c^5 - 20*a*c^6)*f)*g*h^2 + (168*b*c^6*d - 14*(9*b^2*c^5 - 20*a*c^6)*e + (99*b^3*c^4 - 316*a*b*c^5)*f)*h^3)*x^3 + 8*(560*(8*c^7*e + b*c^6*f)*g^3 + 168*(80*c^7*d + 10*b*c^6*e - (7*b^2*c^5 - 16*a*c^6)*f)*g^2*h + 42*(40*b*c^6*d - 4*(7*b^2*c^5 - 16*a*c^6)*e + (21*b^3*c^4 - 68*a*b*c^5)*f)*g*h^2 - (56*(7*b^2*c^5 - 16*a*c^6)*d - 14*(21*b^3*c^4 - 68*a*b*c^5)*e + (231*b^4*c^3 - 972*a*b^2*c^4 + 512*a^2*c^5)*f)*h^3)*x^2 + 2*(560*(48*c^7*d + 8*b*c^6*e - (5*b^2*c^5 - 12*a*c^6)*f)*g^3 + 168*(80*b*c^6*d - 10*(5*b^2*c^5 - 12*a*c^6)*e + (35*b^3*c^4 - 116*a*b*c^5)*f)*g^2*h - 42*(40*(5*b^2*c^5 - 12*a*c^6)*d - 4*(35*b^3*c^4 - 116*a*b*c^5)*e + (105*b^4*c^3 - 448*a*b^2*c^4 + 240*a^2*c^5)*f)*g*h^2 + (56*(35*b^3*c^4 - 116*a*b*c^5)*d - 14*(105*b^4*c^3 - 448*a*b^2*c^4 + 240*a^2*c^5)*e + (1155*b^5*c^2 - 6048*a*b^3*c^3 + 6352*a^2*b*c^4)*f)*h^3)*x)*sqrt(c*x^2 + b*x + a))/c^7, 1/215040*(105*(16*(16*(b^2*c^5 - 4*a*c^6)*d - 8*(b^3*c^4 - 4*a*b*c^5)*e + (5*b^4*c^3 - 24*a*b^2*c^4 + 16*a^2*c^5)*f)*g^3 - 24*(16*(b^3*c^4 - 4*a*b*c^5)*d - 2*(5*b^4*c^3 - 24*a*b^2*c^4 + 16*a^2*c^5)*e + (7*b^5*c^2 - 40*a*b^3*c^3 + 48*a^2*b*c^4)*f)*g^2*h + 6*(8*(5*b^4*c^3 - 24*a*b^2*c^4 + 16*a^2*c^5)*d - 4*(7*b^5*c^2 - 40*a*b^3*c^3 + 48*a^2*b*c^4)*e + (21*b^6*c - 140*a*b^4*c^2 + 240*a^2*b^2*c^3 - 64*a^3*c^4)*f)*g*h^2 - (8*(7*b^5*c^2 - 40*a*b^3*c^3 + 48*a^2*b*c^4)*d - 2*(21*b^6*c - 140*a*b^4*c^2 + 240*a^2*b^2*c^3 - 64*a^3*c^4)*e + (33*b^7 - 252*a*b^5*c + 560*a^2*b^3*c^2 - 320*a^3*b*c^3)*f)*h^3)*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)) + 2*(15360*c^7*f*h^3*x^6 + 1280*(42*c^7*f*g*h^2 + (14*c^7*e + b*c^6*f)*h^3)*x^5 + 128*(504*c^7*f*g^2*h + 42*(12*c^7*e + b*c^6*f)*g*h^2 + (168*c^7*d + 14*b*c^6*e - (11*b^2*c^5 - 24*a*c^6)*f)*h^3)*x^4 + 560*(48*b*c^6*d - 8*(3*b^2*c^5 - 8*a*c^6)*e + (15*b^3*c^4 - 52*a*b*c^5)*f)*g^3 - 168*(80*(3*b^2*c^5 - 8*a*c^6)*d - 10*(15*b^3*c^4 - 52*a*b*c^5)*e + (105*b^4*c^3 - 460*a*b^2*c^4 + 256*a^2*c^5)*f)*g^2*h + 42*(40*(15*b^3*c^4 - 52*a*b*c^5)*d - 4*(105*b^4*c^3 - 460*a*b^2*c^4 + 256*a^2*c^5)*e + (315*b^5*c^2 - 1680*a*b^3*c^3 + 1808*a^2*b*c^4)*f)*g*h^2 - (56*(105*b^4*c^3 - 460*a*b^2*c^4 + 256*a^2*c^5)*d - 14*(315*b^5*c^2 - 1680*a*b^3*c^3 + 1808*a^2*b*c^4)*e + (3465*b^6*c - 21840*a*b^4*c^2 + 34608*a^2*b^2*c^3 - 8192*a^3*c^4)*f)*h^3 + 16*(1680*c^7*f*g^3 + 504*(10*c^7*e + b*c^6*f)*g^2*h + 42*(120*c^7*d + 12*b*c^6*e - (9*b^2*c^5 - 20*a*c^6)*f)*g*h^2 + (168*b*c^6*d - 14*(9*b^2*c^5 - 20*a*c^6)*e + (99*b^3*c^4 - 316*a*b*c^5)*f)*h^3)*x^3 + 8*(560*(8*c^7*e + b*c^6*f)*g^3 + 168*(80*c^7*d + 10*b*c^6*e - (7*b^2*c^5 - 16*a*c^6)*f)*g^2*h + 42*(40*b*c^6*d - 4*(7*b^2*c^5 - 16*a*c^6)*e + (21*b^3*c^4 - 68*a*b*c^5)*f)*g*h^2 - (56*(7*b^2*c^5 - 16*a*c^6)*d - 14*(21*b^3*c^4 - 68*a*b*c^5)*e + (231*b^4*c^3 - 972*a*b^2*c^4 + 512*a^2*c^5)*f)*h^3)*x^2 + 2*(560*(48*c^7*d + 8*b*c^6*e - (5*b^2*c^5 - 12*a*c^6)*f)*g^3 + 168*(80*b*c^6*d - 10*(5*b^2*c^5 - 12*a*c^6)*e + (35*b^3*c^4 - 116*a*b*c^5)*f)*g^2*h - 42*(40*(5*b^2*c^5 - 12*a*c^6)*d - 4*(35*b^3*c^4 - 116*a*b*c^5)*e + (105*b^4*c^3 - 448*a*b^2*c^4 + 240*a^2*c^5)*f)*g*h^2 + (56*(35*b^3*c^4 - 116*a*b*c^5)*d - 14*(105*b^4*c^3 - 448*a*b^2*c^4 + 240*a^2*c^5)*e + (1155*b^5*c^2 - 6048*a*b^3*c^3 + 6352*a^2*b*c^4)*f)*h^3)*x)*sqrt(c*x^2 + b*x + a))/c^7]","A",0
187,1,1791,0,2.058819," ","integrate((h*x+g)^2*(f*x^2+e*x+d)*(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(8 \, {\left(16 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d - 8 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} e + {\left(5 \, b^{4} c^{2} - 24 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} f\right)} g^{2} - 8 \, {\left(16 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d - 2 \, {\left(5 \, b^{4} c^{2} - 24 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} e + {\left(7 \, b^{5} c - 40 \, a b^{3} c^{2} + 48 \, a^{2} b c^{3}\right)} f\right)} g h + {\left(8 \, {\left(5 \, b^{4} c^{2} - 24 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d - 4 \, {\left(7 \, b^{5} c - 40 \, a b^{3} c^{2} + 48 \, a^{2} b c^{3}\right)} e + {\left(21 \, b^{6} - 140 \, a b^{4} c + 240 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} f\right)} h^{2}\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 \, {\left(1280 \, c^{6} f h^{2} x^{5} + 128 \, {\left(24 \, c^{6} f g h + {\left(12 \, c^{6} e + b c^{5} f\right)} h^{2}\right)} x^{4} + 16 \, {\left(120 \, c^{6} f g^{2} + 24 \, {\left(10 \, c^{6} e + b c^{5} f\right)} g h + {\left(120 \, c^{6} d + 12 \, b c^{5} e - {\left(9 \, b^{2} c^{4} - 20 \, a c^{5}\right)} f\right)} h^{2}\right)} x^{3} + 40 \, {\left(48 \, b c^{5} d - 8 \, {\left(3 \, b^{2} c^{4} - 8 \, a c^{5}\right)} e + {\left(15 \, b^{3} c^{3} - 52 \, a b c^{4}\right)} f\right)} g^{2} - 8 \, {\left(80 \, {\left(3 \, b^{2} c^{4} - 8 \, a c^{5}\right)} d - 10 \, {\left(15 \, b^{3} c^{3} - 52 \, a b c^{4}\right)} e + {\left(105 \, b^{4} c^{2} - 460 \, a b^{2} c^{3} + 256 \, a^{2} c^{4}\right)} f\right)} g h + {\left(40 \, {\left(15 \, b^{3} c^{3} - 52 \, a b c^{4}\right)} d - 4 \, {\left(105 \, b^{4} c^{2} - 460 \, a b^{2} c^{3} + 256 \, a^{2} c^{4}\right)} e + {\left(315 \, b^{5} c - 1680 \, a b^{3} c^{2} + 1808 \, a^{2} b c^{3}\right)} f\right)} h^{2} + 8 \, {\left(40 \, {\left(8 \, c^{6} e + b c^{5} f\right)} g^{2} + 8 \, {\left(80 \, c^{6} d + 10 \, b c^{5} e - {\left(7 \, b^{2} c^{4} - 16 \, a c^{5}\right)} f\right)} g h + {\left(40 \, b c^{5} d - 4 \, {\left(7 \, b^{2} c^{4} - 16 \, a c^{5}\right)} e + {\left(21 \, b^{3} c^{3} - 68 \, a b c^{4}\right)} f\right)} h^{2}\right)} x^{2} + 2 \, {\left(40 \, {\left(48 \, c^{6} d + 8 \, b c^{5} e - {\left(5 \, b^{2} c^{4} - 12 \, a c^{5}\right)} f\right)} g^{2} + 8 \, {\left(80 \, b c^{5} d - 10 \, {\left(5 \, b^{2} c^{4} - 12 \, a c^{5}\right)} e + {\left(35 \, b^{3} c^{3} - 116 \, a b c^{4}\right)} f\right)} g h - {\left(40 \, {\left(5 \, b^{2} c^{4} - 12 \, a c^{5}\right)} d - 4 \, {\left(35 \, b^{3} c^{3} - 116 \, a b c^{4}\right)} e + {\left(105 \, b^{4} c^{2} - 448 \, a b^{2} c^{3} + 240 \, a^{2} c^{4}\right)} f\right)} h^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{30720 \, c^{6}}, \frac{15 \, {\left(8 \, {\left(16 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d - 8 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} e + {\left(5 \, b^{4} c^{2} - 24 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} f\right)} g^{2} - 8 \, {\left(16 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d - 2 \, {\left(5 \, b^{4} c^{2} - 24 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} e + {\left(7 \, b^{5} c - 40 \, a b^{3} c^{2} + 48 \, a^{2} b c^{3}\right)} f\right)} g h + {\left(8 \, {\left(5 \, b^{4} c^{2} - 24 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d - 4 \, {\left(7 \, b^{5} c - 40 \, a b^{3} c^{2} + 48 \, a^{2} b c^{3}\right)} e + {\left(21 \, b^{6} - 140 \, a b^{4} c + 240 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} f\right)} h^{2}\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 \, {\left(1280 \, c^{6} f h^{2} x^{5} + 128 \, {\left(24 \, c^{6} f g h + {\left(12 \, c^{6} e + b c^{5} f\right)} h^{2}\right)} x^{4} + 16 \, {\left(120 \, c^{6} f g^{2} + 24 \, {\left(10 \, c^{6} e + b c^{5} f\right)} g h + {\left(120 \, c^{6} d + 12 \, b c^{5} e - {\left(9 \, b^{2} c^{4} - 20 \, a c^{5}\right)} f\right)} h^{2}\right)} x^{3} + 40 \, {\left(48 \, b c^{5} d - 8 \, {\left(3 \, b^{2} c^{4} - 8 \, a c^{5}\right)} e + {\left(15 \, b^{3} c^{3} - 52 \, a b c^{4}\right)} f\right)} g^{2} - 8 \, {\left(80 \, {\left(3 \, b^{2} c^{4} - 8 \, a c^{5}\right)} d - 10 \, {\left(15 \, b^{3} c^{3} - 52 \, a b c^{4}\right)} e + {\left(105 \, b^{4} c^{2} - 460 \, a b^{2} c^{3} + 256 \, a^{2} c^{4}\right)} f\right)} g h + {\left(40 \, {\left(15 \, b^{3} c^{3} - 52 \, a b c^{4}\right)} d - 4 \, {\left(105 \, b^{4} c^{2} - 460 \, a b^{2} c^{3} + 256 \, a^{2} c^{4}\right)} e + {\left(315 \, b^{5} c - 1680 \, a b^{3} c^{2} + 1808 \, a^{2} b c^{3}\right)} f\right)} h^{2} + 8 \, {\left(40 \, {\left(8 \, c^{6} e + b c^{5} f\right)} g^{2} + 8 \, {\left(80 \, c^{6} d + 10 \, b c^{5} e - {\left(7 \, b^{2} c^{4} - 16 \, a c^{5}\right)} f\right)} g h + {\left(40 \, b c^{5} d - 4 \, {\left(7 \, b^{2} c^{4} - 16 \, a c^{5}\right)} e + {\left(21 \, b^{3} c^{3} - 68 \, a b c^{4}\right)} f\right)} h^{2}\right)} x^{2} + 2 \, {\left(40 \, {\left(48 \, c^{6} d + 8 \, b c^{5} e - {\left(5 \, b^{2} c^{4} - 12 \, a c^{5}\right)} f\right)} g^{2} + 8 \, {\left(80 \, b c^{5} d - 10 \, {\left(5 \, b^{2} c^{4} - 12 \, a c^{5}\right)} e + {\left(35 \, b^{3} c^{3} - 116 \, a b c^{4}\right)} f\right)} g h - {\left(40 \, {\left(5 \, b^{2} c^{4} - 12 \, a c^{5}\right)} d - 4 \, {\left(35 \, b^{3} c^{3} - 116 \, a b c^{4}\right)} e + {\left(105 \, b^{4} c^{2} - 448 \, a b^{2} c^{3} + 240 \, a^{2} c^{4}\right)} f\right)} h^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{15360 \, c^{6}}\right]"," ",0,"[-1/30720*(15*(8*(16*(b^2*c^4 - 4*a*c^5)*d - 8*(b^3*c^3 - 4*a*b*c^4)*e + (5*b^4*c^2 - 24*a*b^2*c^3 + 16*a^2*c^4)*f)*g^2 - 8*(16*(b^3*c^3 - 4*a*b*c^4)*d - 2*(5*b^4*c^2 - 24*a*b^2*c^3 + 16*a^2*c^4)*e + (7*b^5*c - 40*a*b^3*c^2 + 48*a^2*b*c^3)*f)*g*h + (8*(5*b^4*c^2 - 24*a*b^2*c^3 + 16*a^2*c^4)*d - 4*(7*b^5*c - 40*a*b^3*c^2 + 48*a^2*b*c^3)*e + (21*b^6 - 140*a*b^4*c + 240*a^2*b^2*c^2 - 64*a^3*c^3)*f)*h^2)*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) - 4*(1280*c^6*f*h^2*x^5 + 128*(24*c^6*f*g*h + (12*c^6*e + b*c^5*f)*h^2)*x^4 + 16*(120*c^6*f*g^2 + 24*(10*c^6*e + b*c^5*f)*g*h + (120*c^6*d + 12*b*c^5*e - (9*b^2*c^4 - 20*a*c^5)*f)*h^2)*x^3 + 40*(48*b*c^5*d - 8*(3*b^2*c^4 - 8*a*c^5)*e + (15*b^3*c^3 - 52*a*b*c^4)*f)*g^2 - 8*(80*(3*b^2*c^4 - 8*a*c^5)*d - 10*(15*b^3*c^3 - 52*a*b*c^4)*e + (105*b^4*c^2 - 460*a*b^2*c^3 + 256*a^2*c^4)*f)*g*h + (40*(15*b^3*c^3 - 52*a*b*c^4)*d - 4*(105*b^4*c^2 - 460*a*b^2*c^3 + 256*a^2*c^4)*e + (315*b^5*c - 1680*a*b^3*c^2 + 1808*a^2*b*c^3)*f)*h^2 + 8*(40*(8*c^6*e + b*c^5*f)*g^2 + 8*(80*c^6*d + 10*b*c^5*e - (7*b^2*c^4 - 16*a*c^5)*f)*g*h + (40*b*c^5*d - 4*(7*b^2*c^4 - 16*a*c^5)*e + (21*b^3*c^3 - 68*a*b*c^4)*f)*h^2)*x^2 + 2*(40*(48*c^6*d + 8*b*c^5*e - (5*b^2*c^4 - 12*a*c^5)*f)*g^2 + 8*(80*b*c^5*d - 10*(5*b^2*c^4 - 12*a*c^5)*e + (35*b^3*c^3 - 116*a*b*c^4)*f)*g*h - (40*(5*b^2*c^4 - 12*a*c^5)*d - 4*(35*b^3*c^3 - 116*a*b*c^4)*e + (105*b^4*c^2 - 448*a*b^2*c^3 + 240*a^2*c^4)*f)*h^2)*x)*sqrt(c*x^2 + b*x + a))/c^6, 1/15360*(15*(8*(16*(b^2*c^4 - 4*a*c^5)*d - 8*(b^3*c^3 - 4*a*b*c^4)*e + (5*b^4*c^2 - 24*a*b^2*c^3 + 16*a^2*c^4)*f)*g^2 - 8*(16*(b^3*c^3 - 4*a*b*c^4)*d - 2*(5*b^4*c^2 - 24*a*b^2*c^3 + 16*a^2*c^4)*e + (7*b^5*c - 40*a*b^3*c^2 + 48*a^2*b*c^3)*f)*g*h + (8*(5*b^4*c^2 - 24*a*b^2*c^3 + 16*a^2*c^4)*d - 4*(7*b^5*c - 40*a*b^3*c^2 + 48*a^2*b*c^3)*e + (21*b^6 - 140*a*b^4*c + 240*a^2*b^2*c^2 - 64*a^3*c^3)*f)*h^2)*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)) + 2*(1280*c^6*f*h^2*x^5 + 128*(24*c^6*f*g*h + (12*c^6*e + b*c^5*f)*h^2)*x^4 + 16*(120*c^6*f*g^2 + 24*(10*c^6*e + b*c^5*f)*g*h + (120*c^6*d + 12*b*c^5*e - (9*b^2*c^4 - 20*a*c^5)*f)*h^2)*x^3 + 40*(48*b*c^5*d - 8*(3*b^2*c^4 - 8*a*c^5)*e + (15*b^3*c^3 - 52*a*b*c^4)*f)*g^2 - 8*(80*(3*b^2*c^4 - 8*a*c^5)*d - 10*(15*b^3*c^3 - 52*a*b*c^4)*e + (105*b^4*c^2 - 460*a*b^2*c^3 + 256*a^2*c^4)*f)*g*h + (40*(15*b^3*c^3 - 52*a*b*c^4)*d - 4*(105*b^4*c^2 - 460*a*b^2*c^3 + 256*a^2*c^4)*e + (315*b^5*c - 1680*a*b^3*c^2 + 1808*a^2*b*c^3)*f)*h^2 + 8*(40*(8*c^6*e + b*c^5*f)*g^2 + 8*(80*c^6*d + 10*b*c^5*e - (7*b^2*c^4 - 16*a*c^5)*f)*g*h + (40*b*c^5*d - 4*(7*b^2*c^4 - 16*a*c^5)*e + (21*b^3*c^3 - 68*a*b*c^4)*f)*h^2)*x^2 + 2*(40*(48*c^6*d + 8*b*c^5*e - (5*b^2*c^4 - 12*a*c^5)*f)*g^2 + 8*(80*b*c^5*d - 10*(5*b^2*c^4 - 12*a*c^5)*e + (35*b^3*c^3 - 116*a*b*c^4)*f)*g*h - (40*(5*b^2*c^4 - 12*a*c^5)*d - 4*(35*b^3*c^3 - 116*a*b*c^4)*e + (105*b^4*c^2 - 448*a*b^2*c^3 + 240*a^2*c^4)*f)*h^2)*x)*sqrt(c*x^2 + b*x + a))/c^6]","A",0
188,1,1009,0,2.762941," ","integrate((h*x+g)*(f*x^2+e*x+d)*(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(2 \, {\left(16 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d - 8 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} e + {\left(5 \, b^{4} c - 24 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} f\right)} g - {\left(16 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d - 2 \, {\left(5 \, b^{4} c - 24 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} e + {\left(7 \, b^{5} - 40 \, a b^{3} c + 48 \, a^{2} b c^{2}\right)} f\right)} h\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 \, {\left(384 \, c^{5} f h x^{4} + 48 \, {\left(10 \, c^{5} f g + {\left(10 \, c^{5} e + b c^{4} f\right)} h\right)} x^{3} + 8 \, {\left(10 \, {\left(8 \, c^{5} e + b c^{4} f\right)} g + {\left(80 \, c^{5} d + 10 \, b c^{4} e - {\left(7 \, b^{2} c^{3} - 16 \, a c^{4}\right)} f\right)} h\right)} x^{2} + 10 \, {\left(48 \, b c^{4} d - 8 \, {\left(3 \, b^{2} c^{3} - 8 \, a c^{4}\right)} e + {\left(15 \, b^{3} c^{2} - 52 \, a b c^{3}\right)} f\right)} g - {\left(80 \, {\left(3 \, b^{2} c^{3} - 8 \, a c^{4}\right)} d - 10 \, {\left(15 \, b^{3} c^{2} - 52 \, a b c^{3}\right)} e + {\left(105 \, b^{4} c - 460 \, a b^{2} c^{2} + 256 \, a^{2} c^{3}\right)} f\right)} h + 2 \, {\left(10 \, {\left(48 \, c^{5} d + 8 \, b c^{4} e - {\left(5 \, b^{2} c^{3} - 12 \, a c^{4}\right)} f\right)} g + {\left(80 \, b c^{4} d - 10 \, {\left(5 \, b^{2} c^{3} - 12 \, a c^{4}\right)} e + {\left(35 \, b^{3} c^{2} - 116 \, a b c^{3}\right)} f\right)} h\right)} x\right)} \sqrt{c x^{2} + b x + a}}{7680 \, c^{5}}, \frac{15 \, {\left(2 \, {\left(16 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d - 8 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} e + {\left(5 \, b^{4} c - 24 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} f\right)} g - {\left(16 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d - 2 \, {\left(5 \, b^{4} c - 24 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} e + {\left(7 \, b^{5} - 40 \, a b^{3} c + 48 \, a^{2} b c^{2}\right)} f\right)} h\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 \, {\left(384 \, c^{5} f h x^{4} + 48 \, {\left(10 \, c^{5} f g + {\left(10 \, c^{5} e + b c^{4} f\right)} h\right)} x^{3} + 8 \, {\left(10 \, {\left(8 \, c^{5} e + b c^{4} f\right)} g + {\left(80 \, c^{5} d + 10 \, b c^{4} e - {\left(7 \, b^{2} c^{3} - 16 \, a c^{4}\right)} f\right)} h\right)} x^{2} + 10 \, {\left(48 \, b c^{4} d - 8 \, {\left(3 \, b^{2} c^{3} - 8 \, a c^{4}\right)} e + {\left(15 \, b^{3} c^{2} - 52 \, a b c^{3}\right)} f\right)} g - {\left(80 \, {\left(3 \, b^{2} c^{3} - 8 \, a c^{4}\right)} d - 10 \, {\left(15 \, b^{3} c^{2} - 52 \, a b c^{3}\right)} e + {\left(105 \, b^{4} c - 460 \, a b^{2} c^{2} + 256 \, a^{2} c^{3}\right)} f\right)} h + 2 \, {\left(10 \, {\left(48 \, c^{5} d + 8 \, b c^{4} e - {\left(5 \, b^{2} c^{3} - 12 \, a c^{4}\right)} f\right)} g + {\left(80 \, b c^{4} d - 10 \, {\left(5 \, b^{2} c^{3} - 12 \, a c^{4}\right)} e + {\left(35 \, b^{3} c^{2} - 116 \, a b c^{3}\right)} f\right)} h\right)} x\right)} \sqrt{c x^{2} + b x + a}}{3840 \, c^{5}}\right]"," ",0,"[-1/7680*(15*(2*(16*(b^2*c^3 - 4*a*c^4)*d - 8*(b^3*c^2 - 4*a*b*c^3)*e + (5*b^4*c - 24*a*b^2*c^2 + 16*a^2*c^3)*f)*g - (16*(b^3*c^2 - 4*a*b*c^3)*d - 2*(5*b^4*c - 24*a*b^2*c^2 + 16*a^2*c^3)*e + (7*b^5 - 40*a*b^3*c + 48*a^2*b*c^2)*f)*h)*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) - 4*(384*c^5*f*h*x^4 + 48*(10*c^5*f*g + (10*c^5*e + b*c^4*f)*h)*x^3 + 8*(10*(8*c^5*e + b*c^4*f)*g + (80*c^5*d + 10*b*c^4*e - (7*b^2*c^3 - 16*a*c^4)*f)*h)*x^2 + 10*(48*b*c^4*d - 8*(3*b^2*c^3 - 8*a*c^4)*e + (15*b^3*c^2 - 52*a*b*c^3)*f)*g - (80*(3*b^2*c^3 - 8*a*c^4)*d - 10*(15*b^3*c^2 - 52*a*b*c^3)*e + (105*b^4*c - 460*a*b^2*c^2 + 256*a^2*c^3)*f)*h + 2*(10*(48*c^5*d + 8*b*c^4*e - (5*b^2*c^3 - 12*a*c^4)*f)*g + (80*b*c^4*d - 10*(5*b^2*c^3 - 12*a*c^4)*e + (35*b^3*c^2 - 116*a*b*c^3)*f)*h)*x)*sqrt(c*x^2 + b*x + a))/c^5, 1/3840*(15*(2*(16*(b^2*c^3 - 4*a*c^4)*d - 8*(b^3*c^2 - 4*a*b*c^3)*e + (5*b^4*c - 24*a*b^2*c^2 + 16*a^2*c^3)*f)*g - (16*(b^3*c^2 - 4*a*b*c^3)*d - 2*(5*b^4*c - 24*a*b^2*c^2 + 16*a^2*c^3)*e + (7*b^5 - 40*a*b^3*c + 48*a^2*b*c^2)*f)*h)*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)) + 2*(384*c^5*f*h*x^4 + 48*(10*c^5*f*g + (10*c^5*e + b*c^4*f)*h)*x^3 + 8*(10*(8*c^5*e + b*c^4*f)*g + (80*c^5*d + 10*b*c^4*e - (7*b^2*c^3 - 16*a*c^4)*f)*h)*x^2 + 10*(48*b*c^4*d - 8*(3*b^2*c^3 - 8*a*c^4)*e + (15*b^3*c^2 - 52*a*b*c^3)*f)*g - (80*(3*b^2*c^3 - 8*a*c^4)*d - 10*(15*b^3*c^2 - 52*a*b*c^3)*e + (105*b^4*c - 460*a*b^2*c^2 + 256*a^2*c^3)*f)*h + 2*(10*(48*c^5*d + 8*b*c^4*e - (5*b^2*c^3 - 12*a*c^4)*f)*g + (80*b*c^4*d - 10*(5*b^2*c^3 - 12*a*c^4)*e + (35*b^3*c^2 - 116*a*b*c^3)*f)*h)*x)*sqrt(c*x^2 + b*x + a))/c^5]","A",0
189,1,465,0,1.147712," ","integrate((c*x^2+b*x+a)^(1/2)*(f*x^2+e*x+d),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(16 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d - 8 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} e + {\left(5 \, b^{4} - 24 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} f\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 \, {\left(48 \, c^{4} f x^{3} + 48 \, b c^{3} d + 8 \, {\left(8 \, c^{4} e + b c^{3} f\right)} x^{2} - 8 \, {\left(3 \, b^{2} c^{2} - 8 \, a c^{3}\right)} e + {\left(15 \, b^{3} c - 52 \, a b c^{2}\right)} f + 2 \, {\left(48 \, c^{4} d + 8 \, b c^{3} e - {\left(5 \, b^{2} c^{2} - 12 \, a c^{3}\right)} f\right)} x\right)} \sqrt{c x^{2} + b x + a}}{768 \, c^{4}}, \frac{3 \, {\left(16 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d - 8 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} e + {\left(5 \, b^{4} - 24 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} f\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 \, {\left(48 \, c^{4} f x^{3} + 48 \, b c^{3} d + 8 \, {\left(8 \, c^{4} e + b c^{3} f\right)} x^{2} - 8 \, {\left(3 \, b^{2} c^{2} - 8 \, a c^{3}\right)} e + {\left(15 \, b^{3} c - 52 \, a b c^{2}\right)} f + 2 \, {\left(48 \, c^{4} d + 8 \, b c^{3} e - {\left(5 \, b^{2} c^{2} - 12 \, a c^{3}\right)} f\right)} x\right)} \sqrt{c x^{2} + b x + a}}{384 \, c^{4}}\right]"," ",0,"[1/768*(3*(16*(b^2*c^2 - 4*a*c^3)*d - 8*(b^3*c - 4*a*b*c^2)*e + (5*b^4 - 24*a*b^2*c + 16*a^2*c^2)*f)*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) + 4*(48*c^4*f*x^3 + 48*b*c^3*d + 8*(8*c^4*e + b*c^3*f)*x^2 - 8*(3*b^2*c^2 - 8*a*c^3)*e + (15*b^3*c - 52*a*b*c^2)*f + 2*(48*c^4*d + 8*b*c^3*e - (5*b^2*c^2 - 12*a*c^3)*f)*x)*sqrt(c*x^2 + b*x + a))/c^4, 1/384*(3*(16*(b^2*c^2 - 4*a*c^3)*d - 8*(b^3*c - 4*a*b*c^2)*e + (5*b^4 - 24*a*b^2*c + 16*a^2*c^2)*f)*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)) + 2*(48*c^4*f*x^3 + 48*b*c^3*d + 8*(8*c^4*e + b*c^3*f)*x^2 - 8*(3*b^2*c^2 - 8*a*c^3)*e + (15*b^3*c - 52*a*b*c^2)*f + 2*(48*c^4*d + 8*b*c^3*e - (5*b^2*c^2 - 12*a*c^3)*f)*x)*sqrt(c*x^2 + b*x + a))/c^4]","A",0
190,-1,0,0,0.000000," ","integrate((f*x^2+e*x+d)*(c*x^2+b*x+a)^(1/2)/(h*x+g),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
191,-1,0,0,0.000000," ","integrate((f*x^2+e*x+d)*(c*x^2+b*x+a)^(1/2)/(h*x+g)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
192,-1,0,0,0.000000," ","integrate((f*x^2+e*x+d)*(c*x^2+b*x+a)^(1/2)/(h*x+g)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
193,-1,0,0,0.000000," ","integrate((f*x^2+e*x+d)*(c*x^2+b*x+a)^(1/2)/(h*x+g)^4,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
194,-1,0,0,0.000000," ","integrate((f*x^2+e*x+d)*(c*x^2+b*x+a)^(1/2)/(h*x+g)^5,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
195,-1,0,0,0.000000," ","integrate((f*x^2+e*x+d)*(c*x^2+b*x+a)^(1/2)/(h*x+g)^6,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
196,1,4751,0,14.763143," ","integrate((h*x+g)^3*(c*x^2+b*x+a)^(3/2)*(f*x^2+e*x+d),x, algorithm=""fricas"")","\left[-\frac{315 \, {\left(64 \, {\left(24 \, {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} d - 12 \, {\left(b^{5} c^{4} - 8 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6}\right)} e + {\left(7 \, b^{6} c^{3} - 60 \, a b^{4} c^{4} + 144 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} f\right)} g^{3} - 96 \, {\left(24 \, {\left(b^{5} c^{4} - 8 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6}\right)} d - 2 \, {\left(7 \, b^{6} c^{3} - 60 \, a b^{4} c^{4} + 144 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} e + 3 \, {\left(3 \, b^{7} c^{2} - 28 \, a b^{5} c^{3} + 80 \, a^{2} b^{3} c^{4} - 64 \, a^{3} b c^{5}\right)} f\right)} g^{2} h + 6 \, {\left(32 \, {\left(7 \, b^{6} c^{3} - 60 \, a b^{4} c^{4} + 144 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} d - 48 \, {\left(3 \, b^{7} c^{2} - 28 \, a b^{5} c^{3} + 80 \, a^{2} b^{3} c^{4} - 64 \, a^{3} b c^{5}\right)} e + 3 \, {\left(33 \, b^{8} c - 336 \, a b^{6} c^{2} + 1120 \, a^{2} b^{4} c^{3} - 1280 \, a^{3} b^{2} c^{4} + 256 \, a^{4} c^{5}\right)} f\right)} g h^{2} - {\left(96 \, {\left(3 \, b^{7} c^{2} - 28 \, a b^{5} c^{3} + 80 \, a^{2} b^{3} c^{4} - 64 \, a^{3} b c^{5}\right)} d - 6 \, {\left(33 \, b^{8} c - 336 \, a b^{6} c^{2} + 1120 \, a^{2} b^{4} c^{3} - 1280 \, a^{3} b^{2} c^{4} + 256 \, a^{4} c^{5}\right)} e + {\left(143 \, b^{9} - 1584 \, a b^{7} c + 6048 \, a^{2} b^{5} c^{2} - 8960 \, a^{3} b^{3} c^{3} + 3840 \, a^{4} b c^{4}\right)} f\right)} h^{3}\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 \, {\left(1146880 \, c^{9} f h^{3} x^{8} + 71680 \, {\left(54 \, c^{9} f g h^{2} + {\left(18 \, c^{9} e + 19 \, b c^{8} f\right)} h^{3}\right)} x^{7} + 5120 \, {\left(864 \, c^{9} f g^{2} h + 54 \, {\left(16 \, c^{9} e + 17 \, b c^{8} f\right)} g h^{2} + {\left(288 \, c^{9} d + 306 \, b c^{8} e + {\left(3 \, b^{2} c^{7} + 320 \, a c^{8}\right)} f\right)} h^{3}\right)} x^{6} + 1280 \, {\left(1344 \, c^{9} f g^{3} + 288 \, {\left(14 \, c^{9} e + 15 \, b c^{8} f\right)} g^{2} h + 18 \, {\left(224 \, c^{9} d + 240 \, b c^{8} e + 3 \, {\left(b^{2} c^{7} + 84 \, a c^{8}\right)} f\right)} g h^{2} + {\left(1440 \, b c^{8} d + 18 \, {\left(b^{2} c^{7} + 84 \, a c^{8}\right)} e - {\left(13 \, b^{3} c^{6} - 60 \, a b c^{7}\right)} f\right)} h^{3}\right)} x^{5} + 128 \, {\left(1344 \, {\left(12 \, c^{9} e + 13 \, b c^{8} f\right)} g^{3} + 288 \, {\left(168 \, c^{9} d + 182 \, b c^{8} e + 3 \, {\left(b^{2} c^{7} + 64 \, a c^{8}\right)} f\right)} g^{2} h + 18 \, {\left(2912 \, b c^{8} d + 48 \, {\left(b^{2} c^{7} + 64 \, a c^{8}\right)} e - 3 \, {\left(11 \, b^{3} c^{6} - 52 \, a b c^{7}\right)} f\right)} g h^{2} + {\left(288 \, {\left(b^{2} c^{7} + 64 \, a c^{8}\right)} d - 18 \, {\left(11 \, b^{3} c^{6} - 52 \, a b c^{7}\right)} e + {\left(143 \, b^{4} c^{5} - 804 \, a b^{2} c^{6} + 768 \, a^{2} c^{7}\right)} f\right)} h^{3}\right)} x^{4} - 1344 \, {\left(120 \, {\left(3 \, b^{3} c^{6} - 20 \, a b c^{7}\right)} d - 12 \, {\left(15 \, b^{4} c^{5} - 100 \, a b^{2} c^{6} + 128 \, a^{2} c^{7}\right)} e + {\left(105 \, b^{5} c^{4} - 760 \, a b^{3} c^{5} + 1296 \, a^{2} b c^{6}\right)} f\right)} g^{3} + 288 \, {\left(168 \, {\left(15 \, b^{4} c^{5} - 100 \, a b^{2} c^{6} + 128 \, a^{2} c^{7}\right)} d - 14 \, {\left(105 \, b^{5} c^{4} - 760 \, a b^{3} c^{5} + 1296 \, a^{2} b c^{6}\right)} e + 3 \, {\left(315 \, b^{6} c^{3} - 2520 \, a b^{4} c^{4} + 5488 \, a^{2} b^{2} c^{5} - 2048 \, a^{3} c^{6}\right)} f\right)} g^{2} h - 18 \, {\left(224 \, {\left(105 \, b^{5} c^{4} - 760 \, a b^{3} c^{5} + 1296 \, a^{2} b c^{6}\right)} d - 48 \, {\left(315 \, b^{6} c^{3} - 2520 \, a b^{4} c^{4} + 5488 \, a^{2} b^{2} c^{5} - 2048 \, a^{3} c^{6}\right)} e + 3 \, {\left(3465 \, b^{7} c^{2} - 30660 \, a b^{5} c^{3} + 81648 \, a^{2} b^{3} c^{4} - 58816 \, a^{3} b c^{5}\right)} f\right)} g h^{2} + {\left(288 \, {\left(315 \, b^{6} c^{3} - 2520 \, a b^{4} c^{4} + 5488 \, a^{2} b^{2} c^{5} - 2048 \, a^{3} c^{6}\right)} d - 18 \, {\left(3465 \, b^{7} c^{2} - 30660 \, a b^{5} c^{3} + 81648 \, a^{2} b^{3} c^{4} - 58816 \, a^{3} b c^{5}\right)} e + {\left(45045 \, b^{8} c - 438900 \, a b^{6} c^{2} + 1383984 \, a^{2} b^{4} c^{3} - 1467072 \, a^{3} b^{2} c^{4} + 262144 \, a^{4} c^{5}\right)} f\right)} h^{3} + 16 \, {\left(1344 \, {\left(120 \, c^{9} d + 132 \, b c^{8} e + {\left(3 \, b^{2} c^{7} + 140 \, a c^{8}\right)} f\right)} g^{3} + 288 \, {\left(1848 \, b c^{8} d + 14 \, {\left(3 \, b^{2} c^{7} + 140 \, a c^{8}\right)} e - 3 \, {\left(9 \, b^{3} c^{6} - 44 \, a b c^{7}\right)} f\right)} g^{2} h + 18 \, {\left(224 \, {\left(3 \, b^{2} c^{7} + 140 \, a c^{8}\right)} d - 48 \, {\left(9 \, b^{3} c^{6} - 44 \, a b c^{7}\right)} e + 3 \, {\left(99 \, b^{4} c^{5} - 568 \, a b^{2} c^{6} + 560 \, a^{2} c^{7}\right)} f\right)} g h^{2} - {\left(288 \, {\left(9 \, b^{3} c^{6} - 44 \, a b c^{7}\right)} d - 18 \, {\left(99 \, b^{4} c^{5} - 568 \, a b^{2} c^{6} + 560 \, a^{2} c^{7}\right)} e + {\left(1287 \, b^{5} c^{4} - 8536 \, a b^{3} c^{5} + 12912 \, a^{2} b c^{6}\right)} f\right)} h^{3}\right)} x^{3} + 8 \, {\left(1344 \, {\left(360 \, b c^{8} d + 12 \, {\left(b^{2} c^{7} + 32 \, a c^{8}\right)} e - {\left(7 \, b^{3} c^{6} - 36 \, a b c^{7}\right)} f\right)} g^{3} + 288 \, {\left(168 \, {\left(b^{2} c^{7} + 32 \, a c^{8}\right)} d - 14 \, {\left(7 \, b^{3} c^{6} - 36 \, a b c^{7}\right)} e + 3 \, {\left(21 \, b^{4} c^{5} - 124 \, a b^{2} c^{6} + 128 \, a^{2} c^{7}\right)} f\right)} g^{2} h - 18 \, {\left(224 \, {\left(7 \, b^{3} c^{6} - 36 \, a b c^{7}\right)} d - 48 \, {\left(21 \, b^{4} c^{5} - 124 \, a b^{2} c^{6} + 128 \, a^{2} c^{7}\right)} e + 3 \, {\left(231 \, b^{5} c^{4} - 1560 \, a b^{3} c^{5} + 2416 \, a^{2} b c^{6}\right)} f\right)} g h^{2} + {\left(288 \, {\left(21 \, b^{4} c^{5} - 124 \, a b^{2} c^{6} + 128 \, a^{2} c^{7}\right)} d - 18 \, {\left(231 \, b^{5} c^{4} - 1560 \, a b^{3} c^{5} + 2416 \, a^{2} b c^{6}\right)} e + {\left(3003 \, b^{6} c^{3} - 22968 \, a b^{4} c^{4} + 47280 \, a^{2} b^{2} c^{5} - 16384 \, a^{3} c^{6}\right)} f\right)} h^{3}\right)} x^{2} + 2 \, {\left(1344 \, {\left(120 \, {\left(b^{2} c^{7} + 20 \, a c^{8}\right)} d - 12 \, {\left(5 \, b^{3} c^{6} - 28 \, a b c^{7}\right)} e + {\left(35 \, b^{4} c^{5} - 216 \, a b^{2} c^{6} + 240 \, a^{2} c^{7}\right)} f\right)} g^{3} - 288 \, {\left(168 \, {\left(5 \, b^{3} c^{6} - 28 \, a b c^{7}\right)} d - 14 \, {\left(35 \, b^{4} c^{5} - 216 \, a b^{2} c^{6} + 240 \, a^{2} c^{7}\right)} e + 3 \, {\left(105 \, b^{5} c^{4} - 728 \, a b^{3} c^{5} + 1168 \, a^{2} b c^{6}\right)} f\right)} g^{2} h + 18 \, {\left(224 \, {\left(35 \, b^{4} c^{5} - 216 \, a b^{2} c^{6} + 240 \, a^{2} c^{7}\right)} d - 48 \, {\left(105 \, b^{5} c^{4} - 728 \, a b^{3} c^{5} + 1168 \, a^{2} b c^{6}\right)} e + 3 \, {\left(1155 \, b^{6} c^{3} - 8988 \, a b^{4} c^{4} + 18896 \, a^{2} b^{2} c^{5} - 6720 \, a^{3} c^{6}\right)} f\right)} g h^{2} - {\left(288 \, {\left(105 \, b^{5} c^{4} - 728 \, a b^{3} c^{5} + 1168 \, a^{2} b c^{6}\right)} d - 18 \, {\left(1155 \, b^{6} c^{3} - 8988 \, a b^{4} c^{4} + 18896 \, a^{2} b^{2} c^{5} - 6720 \, a^{3} c^{6}\right)} e + {\left(15015 \, b^{7} c^{2} - 130284 \, a b^{5} c^{3} + 338832 \, a^{2} b^{3} c^{4} - 236864 \, a^{3} b c^{5}\right)} f\right)} h^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{41287680 \, c^{8}}, -\frac{315 \, {\left(64 \, {\left(24 \, {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} d - 12 \, {\left(b^{5} c^{4} - 8 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6}\right)} e + {\left(7 \, b^{6} c^{3} - 60 \, a b^{4} c^{4} + 144 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} f\right)} g^{3} - 96 \, {\left(24 \, {\left(b^{5} c^{4} - 8 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6}\right)} d - 2 \, {\left(7 \, b^{6} c^{3} - 60 \, a b^{4} c^{4} + 144 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} e + 3 \, {\left(3 \, b^{7} c^{2} - 28 \, a b^{5} c^{3} + 80 \, a^{2} b^{3} c^{4} - 64 \, a^{3} b c^{5}\right)} f\right)} g^{2} h + 6 \, {\left(32 \, {\left(7 \, b^{6} c^{3} - 60 \, a b^{4} c^{4} + 144 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} d - 48 \, {\left(3 \, b^{7} c^{2} - 28 \, a b^{5} c^{3} + 80 \, a^{2} b^{3} c^{4} - 64 \, a^{3} b c^{5}\right)} e + 3 \, {\left(33 \, b^{8} c - 336 \, a b^{6} c^{2} + 1120 \, a^{2} b^{4} c^{3} - 1280 \, a^{3} b^{2} c^{4} + 256 \, a^{4} c^{5}\right)} f\right)} g h^{2} - {\left(96 \, {\left(3 \, b^{7} c^{2} - 28 \, a b^{5} c^{3} + 80 \, a^{2} b^{3} c^{4} - 64 \, a^{3} b c^{5}\right)} d - 6 \, {\left(33 \, b^{8} c - 336 \, a b^{6} c^{2} + 1120 \, a^{2} b^{4} c^{3} - 1280 \, a^{3} b^{2} c^{4} + 256 \, a^{4} c^{5}\right)} e + {\left(143 \, b^{9} - 1584 \, a b^{7} c + 6048 \, a^{2} b^{5} c^{2} - 8960 \, a^{3} b^{3} c^{3} + 3840 \, a^{4} b c^{4}\right)} f\right)} h^{3}\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 \, {\left(1146880 \, c^{9} f h^{3} x^{8} + 71680 \, {\left(54 \, c^{9} f g h^{2} + {\left(18 \, c^{9} e + 19 \, b c^{8} f\right)} h^{3}\right)} x^{7} + 5120 \, {\left(864 \, c^{9} f g^{2} h + 54 \, {\left(16 \, c^{9} e + 17 \, b c^{8} f\right)} g h^{2} + {\left(288 \, c^{9} d + 306 \, b c^{8} e + {\left(3 \, b^{2} c^{7} + 320 \, a c^{8}\right)} f\right)} h^{3}\right)} x^{6} + 1280 \, {\left(1344 \, c^{9} f g^{3} + 288 \, {\left(14 \, c^{9} e + 15 \, b c^{8} f\right)} g^{2} h + 18 \, {\left(224 \, c^{9} d + 240 \, b c^{8} e + 3 \, {\left(b^{2} c^{7} + 84 \, a c^{8}\right)} f\right)} g h^{2} + {\left(1440 \, b c^{8} d + 18 \, {\left(b^{2} c^{7} + 84 \, a c^{8}\right)} e - {\left(13 \, b^{3} c^{6} - 60 \, a b c^{7}\right)} f\right)} h^{3}\right)} x^{5} + 128 \, {\left(1344 \, {\left(12 \, c^{9} e + 13 \, b c^{8} f\right)} g^{3} + 288 \, {\left(168 \, c^{9} d + 182 \, b c^{8} e + 3 \, {\left(b^{2} c^{7} + 64 \, a c^{8}\right)} f\right)} g^{2} h + 18 \, {\left(2912 \, b c^{8} d + 48 \, {\left(b^{2} c^{7} + 64 \, a c^{8}\right)} e - 3 \, {\left(11 \, b^{3} c^{6} - 52 \, a b c^{7}\right)} f\right)} g h^{2} + {\left(288 \, {\left(b^{2} c^{7} + 64 \, a c^{8}\right)} d - 18 \, {\left(11 \, b^{3} c^{6} - 52 \, a b c^{7}\right)} e + {\left(143 \, b^{4} c^{5} - 804 \, a b^{2} c^{6} + 768 \, a^{2} c^{7}\right)} f\right)} h^{3}\right)} x^{4} - 1344 \, {\left(120 \, {\left(3 \, b^{3} c^{6} - 20 \, a b c^{7}\right)} d - 12 \, {\left(15 \, b^{4} c^{5} - 100 \, a b^{2} c^{6} + 128 \, a^{2} c^{7}\right)} e + {\left(105 \, b^{5} c^{4} - 760 \, a b^{3} c^{5} + 1296 \, a^{2} b c^{6}\right)} f\right)} g^{3} + 288 \, {\left(168 \, {\left(15 \, b^{4} c^{5} - 100 \, a b^{2} c^{6} + 128 \, a^{2} c^{7}\right)} d - 14 \, {\left(105 \, b^{5} c^{4} - 760 \, a b^{3} c^{5} + 1296 \, a^{2} b c^{6}\right)} e + 3 \, {\left(315 \, b^{6} c^{3} - 2520 \, a b^{4} c^{4} + 5488 \, a^{2} b^{2} c^{5} - 2048 \, a^{3} c^{6}\right)} f\right)} g^{2} h - 18 \, {\left(224 \, {\left(105 \, b^{5} c^{4} - 760 \, a b^{3} c^{5} + 1296 \, a^{2} b c^{6}\right)} d - 48 \, {\left(315 \, b^{6} c^{3} - 2520 \, a b^{4} c^{4} + 5488 \, a^{2} b^{2} c^{5} - 2048 \, a^{3} c^{6}\right)} e + 3 \, {\left(3465 \, b^{7} c^{2} - 30660 \, a b^{5} c^{3} + 81648 \, a^{2} b^{3} c^{4} - 58816 \, a^{3} b c^{5}\right)} f\right)} g h^{2} + {\left(288 \, {\left(315 \, b^{6} c^{3} - 2520 \, a b^{4} c^{4} + 5488 \, a^{2} b^{2} c^{5} - 2048 \, a^{3} c^{6}\right)} d - 18 \, {\left(3465 \, b^{7} c^{2} - 30660 \, a b^{5} c^{3} + 81648 \, a^{2} b^{3} c^{4} - 58816 \, a^{3} b c^{5}\right)} e + {\left(45045 \, b^{8} c - 438900 \, a b^{6} c^{2} + 1383984 \, a^{2} b^{4} c^{3} - 1467072 \, a^{3} b^{2} c^{4} + 262144 \, a^{4} c^{5}\right)} f\right)} h^{3} + 16 \, {\left(1344 \, {\left(120 \, c^{9} d + 132 \, b c^{8} e + {\left(3 \, b^{2} c^{7} + 140 \, a c^{8}\right)} f\right)} g^{3} + 288 \, {\left(1848 \, b c^{8} d + 14 \, {\left(3 \, b^{2} c^{7} + 140 \, a c^{8}\right)} e - 3 \, {\left(9 \, b^{3} c^{6} - 44 \, a b c^{7}\right)} f\right)} g^{2} h + 18 \, {\left(224 \, {\left(3 \, b^{2} c^{7} + 140 \, a c^{8}\right)} d - 48 \, {\left(9 \, b^{3} c^{6} - 44 \, a b c^{7}\right)} e + 3 \, {\left(99 \, b^{4} c^{5} - 568 \, a b^{2} c^{6} + 560 \, a^{2} c^{7}\right)} f\right)} g h^{2} - {\left(288 \, {\left(9 \, b^{3} c^{6} - 44 \, a b c^{7}\right)} d - 18 \, {\left(99 \, b^{4} c^{5} - 568 \, a b^{2} c^{6} + 560 \, a^{2} c^{7}\right)} e + {\left(1287 \, b^{5} c^{4} - 8536 \, a b^{3} c^{5} + 12912 \, a^{2} b c^{6}\right)} f\right)} h^{3}\right)} x^{3} + 8 \, {\left(1344 \, {\left(360 \, b c^{8} d + 12 \, {\left(b^{2} c^{7} + 32 \, a c^{8}\right)} e - {\left(7 \, b^{3} c^{6} - 36 \, a b c^{7}\right)} f\right)} g^{3} + 288 \, {\left(168 \, {\left(b^{2} c^{7} + 32 \, a c^{8}\right)} d - 14 \, {\left(7 \, b^{3} c^{6} - 36 \, a b c^{7}\right)} e + 3 \, {\left(21 \, b^{4} c^{5} - 124 \, a b^{2} c^{6} + 128 \, a^{2} c^{7}\right)} f\right)} g^{2} h - 18 \, {\left(224 \, {\left(7 \, b^{3} c^{6} - 36 \, a b c^{7}\right)} d - 48 \, {\left(21 \, b^{4} c^{5} - 124 \, a b^{2} c^{6} + 128 \, a^{2} c^{7}\right)} e + 3 \, {\left(231 \, b^{5} c^{4} - 1560 \, a b^{3} c^{5} + 2416 \, a^{2} b c^{6}\right)} f\right)} g h^{2} + {\left(288 \, {\left(21 \, b^{4} c^{5} - 124 \, a b^{2} c^{6} + 128 \, a^{2} c^{7}\right)} d - 18 \, {\left(231 \, b^{5} c^{4} - 1560 \, a b^{3} c^{5} + 2416 \, a^{2} b c^{6}\right)} e + {\left(3003 \, b^{6} c^{3} - 22968 \, a b^{4} c^{4} + 47280 \, a^{2} b^{2} c^{5} - 16384 \, a^{3} c^{6}\right)} f\right)} h^{3}\right)} x^{2} + 2 \, {\left(1344 \, {\left(120 \, {\left(b^{2} c^{7} + 20 \, a c^{8}\right)} d - 12 \, {\left(5 \, b^{3} c^{6} - 28 \, a b c^{7}\right)} e + {\left(35 \, b^{4} c^{5} - 216 \, a b^{2} c^{6} + 240 \, a^{2} c^{7}\right)} f\right)} g^{3} - 288 \, {\left(168 \, {\left(5 \, b^{3} c^{6} - 28 \, a b c^{7}\right)} d - 14 \, {\left(35 \, b^{4} c^{5} - 216 \, a b^{2} c^{6} + 240 \, a^{2} c^{7}\right)} e + 3 \, {\left(105 \, b^{5} c^{4} - 728 \, a b^{3} c^{5} + 1168 \, a^{2} b c^{6}\right)} f\right)} g^{2} h + 18 \, {\left(224 \, {\left(35 \, b^{4} c^{5} - 216 \, a b^{2} c^{6} + 240 \, a^{2} c^{7}\right)} d - 48 \, {\left(105 \, b^{5} c^{4} - 728 \, a b^{3} c^{5} + 1168 \, a^{2} b c^{6}\right)} e + 3 \, {\left(1155 \, b^{6} c^{3} - 8988 \, a b^{4} c^{4} + 18896 \, a^{2} b^{2} c^{5} - 6720 \, a^{3} c^{6}\right)} f\right)} g h^{2} - {\left(288 \, {\left(105 \, b^{5} c^{4} - 728 \, a b^{3} c^{5} + 1168 \, a^{2} b c^{6}\right)} d - 18 \, {\left(1155 \, b^{6} c^{3} - 8988 \, a b^{4} c^{4} + 18896 \, a^{2} b^{2} c^{5} - 6720 \, a^{3} c^{6}\right)} e + {\left(15015 \, b^{7} c^{2} - 130284 \, a b^{5} c^{3} + 338832 \, a^{2} b^{3} c^{4} - 236864 \, a^{3} b c^{5}\right)} f\right)} h^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{20643840 \, c^{8}}\right]"," ",0,"[-1/41287680*(315*(64*(24*(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*d - 12*(b^5*c^4 - 8*a*b^3*c^5 + 16*a^2*b*c^6)*e + (7*b^6*c^3 - 60*a*b^4*c^4 + 144*a^2*b^2*c^5 - 64*a^3*c^6)*f)*g^3 - 96*(24*(b^5*c^4 - 8*a*b^3*c^5 + 16*a^2*b*c^6)*d - 2*(7*b^6*c^3 - 60*a*b^4*c^4 + 144*a^2*b^2*c^5 - 64*a^3*c^6)*e + 3*(3*b^7*c^2 - 28*a*b^5*c^3 + 80*a^2*b^3*c^4 - 64*a^3*b*c^5)*f)*g^2*h + 6*(32*(7*b^6*c^3 - 60*a*b^4*c^4 + 144*a^2*b^2*c^5 - 64*a^3*c^6)*d - 48*(3*b^7*c^2 - 28*a*b^5*c^3 + 80*a^2*b^3*c^4 - 64*a^3*b*c^5)*e + 3*(33*b^8*c - 336*a*b^6*c^2 + 1120*a^2*b^4*c^3 - 1280*a^3*b^2*c^4 + 256*a^4*c^5)*f)*g*h^2 - (96*(3*b^7*c^2 - 28*a*b^5*c^3 + 80*a^2*b^3*c^4 - 64*a^3*b*c^5)*d - 6*(33*b^8*c - 336*a*b^6*c^2 + 1120*a^2*b^4*c^3 - 1280*a^3*b^2*c^4 + 256*a^4*c^5)*e + (143*b^9 - 1584*a*b^7*c + 6048*a^2*b^5*c^2 - 8960*a^3*b^3*c^3 + 3840*a^4*b*c^4)*f)*h^3)*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) - 4*(1146880*c^9*f*h^3*x^8 + 71680*(54*c^9*f*g*h^2 + (18*c^9*e + 19*b*c^8*f)*h^3)*x^7 + 5120*(864*c^9*f*g^2*h + 54*(16*c^9*e + 17*b*c^8*f)*g*h^2 + (288*c^9*d + 306*b*c^8*e + (3*b^2*c^7 + 320*a*c^8)*f)*h^3)*x^6 + 1280*(1344*c^9*f*g^3 + 288*(14*c^9*e + 15*b*c^8*f)*g^2*h + 18*(224*c^9*d + 240*b*c^8*e + 3*(b^2*c^7 + 84*a*c^8)*f)*g*h^2 + (1440*b*c^8*d + 18*(b^2*c^7 + 84*a*c^8)*e - (13*b^3*c^6 - 60*a*b*c^7)*f)*h^3)*x^5 + 128*(1344*(12*c^9*e + 13*b*c^8*f)*g^3 + 288*(168*c^9*d + 182*b*c^8*e + 3*(b^2*c^7 + 64*a*c^8)*f)*g^2*h + 18*(2912*b*c^8*d + 48*(b^2*c^7 + 64*a*c^8)*e - 3*(11*b^3*c^6 - 52*a*b*c^7)*f)*g*h^2 + (288*(b^2*c^7 + 64*a*c^8)*d - 18*(11*b^3*c^6 - 52*a*b*c^7)*e + (143*b^4*c^5 - 804*a*b^2*c^6 + 768*a^2*c^7)*f)*h^3)*x^4 - 1344*(120*(3*b^3*c^6 - 20*a*b*c^7)*d - 12*(15*b^4*c^5 - 100*a*b^2*c^6 + 128*a^2*c^7)*e + (105*b^5*c^4 - 760*a*b^3*c^5 + 1296*a^2*b*c^6)*f)*g^3 + 288*(168*(15*b^4*c^5 - 100*a*b^2*c^6 + 128*a^2*c^7)*d - 14*(105*b^5*c^4 - 760*a*b^3*c^5 + 1296*a^2*b*c^6)*e + 3*(315*b^6*c^3 - 2520*a*b^4*c^4 + 5488*a^2*b^2*c^5 - 2048*a^3*c^6)*f)*g^2*h - 18*(224*(105*b^5*c^4 - 760*a*b^3*c^5 + 1296*a^2*b*c^6)*d - 48*(315*b^6*c^3 - 2520*a*b^4*c^4 + 5488*a^2*b^2*c^5 - 2048*a^3*c^6)*e + 3*(3465*b^7*c^2 - 30660*a*b^5*c^3 + 81648*a^2*b^3*c^4 - 58816*a^3*b*c^5)*f)*g*h^2 + (288*(315*b^6*c^3 - 2520*a*b^4*c^4 + 5488*a^2*b^2*c^5 - 2048*a^3*c^6)*d - 18*(3465*b^7*c^2 - 30660*a*b^5*c^3 + 81648*a^2*b^3*c^4 - 58816*a^3*b*c^5)*e + (45045*b^8*c - 438900*a*b^6*c^2 + 1383984*a^2*b^4*c^3 - 1467072*a^3*b^2*c^4 + 262144*a^4*c^5)*f)*h^3 + 16*(1344*(120*c^9*d + 132*b*c^8*e + (3*b^2*c^7 + 140*a*c^8)*f)*g^3 + 288*(1848*b*c^8*d + 14*(3*b^2*c^7 + 140*a*c^8)*e - 3*(9*b^3*c^6 - 44*a*b*c^7)*f)*g^2*h + 18*(224*(3*b^2*c^7 + 140*a*c^8)*d - 48*(9*b^3*c^6 - 44*a*b*c^7)*e + 3*(99*b^4*c^5 - 568*a*b^2*c^6 + 560*a^2*c^7)*f)*g*h^2 - (288*(9*b^3*c^6 - 44*a*b*c^7)*d - 18*(99*b^4*c^5 - 568*a*b^2*c^6 + 560*a^2*c^7)*e + (1287*b^5*c^4 - 8536*a*b^3*c^5 + 12912*a^2*b*c^6)*f)*h^3)*x^3 + 8*(1344*(360*b*c^8*d + 12*(b^2*c^7 + 32*a*c^8)*e - (7*b^3*c^6 - 36*a*b*c^7)*f)*g^3 + 288*(168*(b^2*c^7 + 32*a*c^8)*d - 14*(7*b^3*c^6 - 36*a*b*c^7)*e + 3*(21*b^4*c^5 - 124*a*b^2*c^6 + 128*a^2*c^7)*f)*g^2*h - 18*(224*(7*b^3*c^6 - 36*a*b*c^7)*d - 48*(21*b^4*c^5 - 124*a*b^2*c^6 + 128*a^2*c^7)*e + 3*(231*b^5*c^4 - 1560*a*b^3*c^5 + 2416*a^2*b*c^6)*f)*g*h^2 + (288*(21*b^4*c^5 - 124*a*b^2*c^6 + 128*a^2*c^7)*d - 18*(231*b^5*c^4 - 1560*a*b^3*c^5 + 2416*a^2*b*c^6)*e + (3003*b^6*c^3 - 22968*a*b^4*c^4 + 47280*a^2*b^2*c^5 - 16384*a^3*c^6)*f)*h^3)*x^2 + 2*(1344*(120*(b^2*c^7 + 20*a*c^8)*d - 12*(5*b^3*c^6 - 28*a*b*c^7)*e + (35*b^4*c^5 - 216*a*b^2*c^6 + 240*a^2*c^7)*f)*g^3 - 288*(168*(5*b^3*c^6 - 28*a*b*c^7)*d - 14*(35*b^4*c^5 - 216*a*b^2*c^6 + 240*a^2*c^7)*e + 3*(105*b^5*c^4 - 728*a*b^3*c^5 + 1168*a^2*b*c^6)*f)*g^2*h + 18*(224*(35*b^4*c^5 - 216*a*b^2*c^6 + 240*a^2*c^7)*d - 48*(105*b^5*c^4 - 728*a*b^3*c^5 + 1168*a^2*b*c^6)*e + 3*(1155*b^6*c^3 - 8988*a*b^4*c^4 + 18896*a^2*b^2*c^5 - 6720*a^3*c^6)*f)*g*h^2 - (288*(105*b^5*c^4 - 728*a*b^3*c^5 + 1168*a^2*b*c^6)*d - 18*(1155*b^6*c^3 - 8988*a*b^4*c^4 + 18896*a^2*b^2*c^5 - 6720*a^3*c^6)*e + (15015*b^7*c^2 - 130284*a*b^5*c^3 + 338832*a^2*b^3*c^4 - 236864*a^3*b*c^5)*f)*h^3)*x)*sqrt(c*x^2 + b*x + a))/c^8, -1/20643840*(315*(64*(24*(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*d - 12*(b^5*c^4 - 8*a*b^3*c^5 + 16*a^2*b*c^6)*e + (7*b^6*c^3 - 60*a*b^4*c^4 + 144*a^2*b^2*c^5 - 64*a^3*c^6)*f)*g^3 - 96*(24*(b^5*c^4 - 8*a*b^3*c^5 + 16*a^2*b*c^6)*d - 2*(7*b^6*c^3 - 60*a*b^4*c^4 + 144*a^2*b^2*c^5 - 64*a^3*c^6)*e + 3*(3*b^7*c^2 - 28*a*b^5*c^3 + 80*a^2*b^3*c^4 - 64*a^3*b*c^5)*f)*g^2*h + 6*(32*(7*b^6*c^3 - 60*a*b^4*c^4 + 144*a^2*b^2*c^5 - 64*a^3*c^6)*d - 48*(3*b^7*c^2 - 28*a*b^5*c^3 + 80*a^2*b^3*c^4 - 64*a^3*b*c^5)*e + 3*(33*b^8*c - 336*a*b^6*c^2 + 1120*a^2*b^4*c^3 - 1280*a^3*b^2*c^4 + 256*a^4*c^5)*f)*g*h^2 - (96*(3*b^7*c^2 - 28*a*b^5*c^3 + 80*a^2*b^3*c^4 - 64*a^3*b*c^5)*d - 6*(33*b^8*c - 336*a*b^6*c^2 + 1120*a^2*b^4*c^3 - 1280*a^3*b^2*c^4 + 256*a^4*c^5)*e + (143*b^9 - 1584*a*b^7*c + 6048*a^2*b^5*c^2 - 8960*a^3*b^3*c^3 + 3840*a^4*b*c^4)*f)*h^3)*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)) - 2*(1146880*c^9*f*h^3*x^8 + 71680*(54*c^9*f*g*h^2 + (18*c^9*e + 19*b*c^8*f)*h^3)*x^7 + 5120*(864*c^9*f*g^2*h + 54*(16*c^9*e + 17*b*c^8*f)*g*h^2 + (288*c^9*d + 306*b*c^8*e + (3*b^2*c^7 + 320*a*c^8)*f)*h^3)*x^6 + 1280*(1344*c^9*f*g^3 + 288*(14*c^9*e + 15*b*c^8*f)*g^2*h + 18*(224*c^9*d + 240*b*c^8*e + 3*(b^2*c^7 + 84*a*c^8)*f)*g*h^2 + (1440*b*c^8*d + 18*(b^2*c^7 + 84*a*c^8)*e - (13*b^3*c^6 - 60*a*b*c^7)*f)*h^3)*x^5 + 128*(1344*(12*c^9*e + 13*b*c^8*f)*g^3 + 288*(168*c^9*d + 182*b*c^8*e + 3*(b^2*c^7 + 64*a*c^8)*f)*g^2*h + 18*(2912*b*c^8*d + 48*(b^2*c^7 + 64*a*c^8)*e - 3*(11*b^3*c^6 - 52*a*b*c^7)*f)*g*h^2 + (288*(b^2*c^7 + 64*a*c^8)*d - 18*(11*b^3*c^6 - 52*a*b*c^7)*e + (143*b^4*c^5 - 804*a*b^2*c^6 + 768*a^2*c^7)*f)*h^3)*x^4 - 1344*(120*(3*b^3*c^6 - 20*a*b*c^7)*d - 12*(15*b^4*c^5 - 100*a*b^2*c^6 + 128*a^2*c^7)*e + (105*b^5*c^4 - 760*a*b^3*c^5 + 1296*a^2*b*c^6)*f)*g^3 + 288*(168*(15*b^4*c^5 - 100*a*b^2*c^6 + 128*a^2*c^7)*d - 14*(105*b^5*c^4 - 760*a*b^3*c^5 + 1296*a^2*b*c^6)*e + 3*(315*b^6*c^3 - 2520*a*b^4*c^4 + 5488*a^2*b^2*c^5 - 2048*a^3*c^6)*f)*g^2*h - 18*(224*(105*b^5*c^4 - 760*a*b^3*c^5 + 1296*a^2*b*c^6)*d - 48*(315*b^6*c^3 - 2520*a*b^4*c^4 + 5488*a^2*b^2*c^5 - 2048*a^3*c^6)*e + 3*(3465*b^7*c^2 - 30660*a*b^5*c^3 + 81648*a^2*b^3*c^4 - 58816*a^3*b*c^5)*f)*g*h^2 + (288*(315*b^6*c^3 - 2520*a*b^4*c^4 + 5488*a^2*b^2*c^5 - 2048*a^3*c^6)*d - 18*(3465*b^7*c^2 - 30660*a*b^5*c^3 + 81648*a^2*b^3*c^4 - 58816*a^3*b*c^5)*e + (45045*b^8*c - 438900*a*b^6*c^2 + 1383984*a^2*b^4*c^3 - 1467072*a^3*b^2*c^4 + 262144*a^4*c^5)*f)*h^3 + 16*(1344*(120*c^9*d + 132*b*c^8*e + (3*b^2*c^7 + 140*a*c^8)*f)*g^3 + 288*(1848*b*c^8*d + 14*(3*b^2*c^7 + 140*a*c^8)*e - 3*(9*b^3*c^6 - 44*a*b*c^7)*f)*g^2*h + 18*(224*(3*b^2*c^7 + 140*a*c^8)*d - 48*(9*b^3*c^6 - 44*a*b*c^7)*e + 3*(99*b^4*c^5 - 568*a*b^2*c^6 + 560*a^2*c^7)*f)*g*h^2 - (288*(9*b^3*c^6 - 44*a*b*c^7)*d - 18*(99*b^4*c^5 - 568*a*b^2*c^6 + 560*a^2*c^7)*e + (1287*b^5*c^4 - 8536*a*b^3*c^5 + 12912*a^2*b*c^6)*f)*h^3)*x^3 + 8*(1344*(360*b*c^8*d + 12*(b^2*c^7 + 32*a*c^8)*e - (7*b^3*c^6 - 36*a*b*c^7)*f)*g^3 + 288*(168*(b^2*c^7 + 32*a*c^8)*d - 14*(7*b^3*c^6 - 36*a*b*c^7)*e + 3*(21*b^4*c^5 - 124*a*b^2*c^6 + 128*a^2*c^7)*f)*g^2*h - 18*(224*(7*b^3*c^6 - 36*a*b*c^7)*d - 48*(21*b^4*c^5 - 124*a*b^2*c^6 + 128*a^2*c^7)*e + 3*(231*b^5*c^4 - 1560*a*b^3*c^5 + 2416*a^2*b*c^6)*f)*g*h^2 + (288*(21*b^4*c^5 - 124*a*b^2*c^6 + 128*a^2*c^7)*d - 18*(231*b^5*c^4 - 1560*a*b^3*c^5 + 2416*a^2*b*c^6)*e + (3003*b^6*c^3 - 22968*a*b^4*c^4 + 47280*a^2*b^2*c^5 - 16384*a^3*c^6)*f)*h^3)*x^2 + 2*(1344*(120*(b^2*c^7 + 20*a*c^8)*d - 12*(5*b^3*c^6 - 28*a*b*c^7)*e + (35*b^4*c^5 - 216*a*b^2*c^6 + 240*a^2*c^7)*f)*g^3 - 288*(168*(5*b^3*c^6 - 28*a*b*c^7)*d - 14*(35*b^4*c^5 - 216*a*b^2*c^6 + 240*a^2*c^7)*e + 3*(105*b^5*c^4 - 728*a*b^3*c^5 + 1168*a^2*b*c^6)*f)*g^2*h + 18*(224*(35*b^4*c^5 - 216*a*b^2*c^6 + 240*a^2*c^7)*d - 48*(105*b^5*c^4 - 728*a*b^3*c^5 + 1168*a^2*b*c^6)*e + 3*(1155*b^6*c^3 - 8988*a*b^4*c^4 + 18896*a^2*b^2*c^5 - 6720*a^3*c^6)*f)*g*h^2 - (288*(105*b^5*c^4 - 728*a*b^3*c^5 + 1168*a^2*b*c^6)*d - 18*(1155*b^6*c^3 - 8988*a*b^4*c^4 + 18896*a^2*b^2*c^5 - 6720*a^3*c^6)*e + (15015*b^7*c^2 - 130284*a*b^5*c^3 + 338832*a^2*b^3*c^4 - 236864*a^3*b*c^5)*f)*h^3)*x)*sqrt(c*x^2 + b*x + a))/c^8]","B",0
197,1,3145,0,7.903457," ","integrate((h*x+g)^2*(c*x^2+b*x+a)^(3/2)*(f*x^2+e*x+d),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(32 \, {\left(24 \, {\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} d - 12 \, {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} e + {\left(7 \, b^{6} c^{2} - 60 \, a b^{4} c^{3} + 144 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} f\right)} g^{2} - 32 \, {\left(24 \, {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} d - 2 \, {\left(7 \, b^{6} c^{2} - 60 \, a b^{4} c^{3} + 144 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} e + 3 \, {\left(3 \, b^{7} c - 28 \, a b^{5} c^{2} + 80 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} f\right)} g h + {\left(32 \, {\left(7 \, b^{6} c^{2} - 60 \, a b^{4} c^{3} + 144 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d - 48 \, {\left(3 \, b^{7} c - 28 \, a b^{5} c^{2} + 80 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} e + 3 \, {\left(33 \, b^{8} - 336 \, a b^{6} c + 1120 \, a^{2} b^{4} c^{2} - 1280 \, a^{3} b^{2} c^{3} + 256 \, a^{4} c^{4}\right)} f\right)} h^{2}\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 \, {\left(215040 \, c^{8} f h^{2} x^{7} + 15360 \, {\left(32 \, c^{8} f g h + {\left(16 \, c^{8} e + 17 \, b c^{7} f\right)} h^{2}\right)} x^{6} + 1280 \, {\left(224 \, c^{8} f g^{2} + 32 \, {\left(14 \, c^{8} e + 15 \, b c^{7} f\right)} g h + {\left(224 \, c^{8} d + 240 \, b c^{7} e + 3 \, {\left(b^{2} c^{6} + 84 \, a c^{7}\right)} f\right)} h^{2}\right)} x^{5} + 128 \, {\left(224 \, {\left(12 \, c^{8} e + 13 \, b c^{7} f\right)} g^{2} + 32 \, {\left(168 \, c^{8} d + 182 \, b c^{7} e + 3 \, {\left(b^{2} c^{6} + 64 \, a c^{7}\right)} f\right)} g h + {\left(2912 \, b c^{7} d + 48 \, {\left(b^{2} c^{6} + 64 \, a c^{7}\right)} e - 3 \, {\left(11 \, b^{3} c^{5} - 52 \, a b c^{6}\right)} f\right)} h^{2}\right)} x^{4} + 16 \, {\left(224 \, {\left(120 \, c^{8} d + 132 \, b c^{7} e + {\left(3 \, b^{2} c^{6} + 140 \, a c^{7}\right)} f\right)} g^{2} + 32 \, {\left(1848 \, b c^{7} d + 14 \, {\left(3 \, b^{2} c^{6} + 140 \, a c^{7}\right)} e - 3 \, {\left(9 \, b^{3} c^{5} - 44 \, a b c^{6}\right)} f\right)} g h + {\left(224 \, {\left(3 \, b^{2} c^{6} + 140 \, a c^{7}\right)} d - 48 \, {\left(9 \, b^{3} c^{5} - 44 \, a b c^{6}\right)} e + 3 \, {\left(99 \, b^{4} c^{4} - 568 \, a b^{2} c^{5} + 560 \, a^{2} c^{6}\right)} f\right)} h^{2}\right)} x^{3} - 224 \, {\left(120 \, {\left(3 \, b^{3} c^{5} - 20 \, a b c^{6}\right)} d - 12 \, {\left(15 \, b^{4} c^{4} - 100 \, a b^{2} c^{5} + 128 \, a^{2} c^{6}\right)} e + {\left(105 \, b^{5} c^{3} - 760 \, a b^{3} c^{4} + 1296 \, a^{2} b c^{5}\right)} f\right)} g^{2} + 32 \, {\left(168 \, {\left(15 \, b^{4} c^{4} - 100 \, a b^{2} c^{5} + 128 \, a^{2} c^{6}\right)} d - 14 \, {\left(105 \, b^{5} c^{3} - 760 \, a b^{3} c^{4} + 1296 \, a^{2} b c^{5}\right)} e + 3 \, {\left(315 \, b^{6} c^{2} - 2520 \, a b^{4} c^{3} + 5488 \, a^{2} b^{2} c^{4} - 2048 \, a^{3} c^{5}\right)} f\right)} g h - {\left(224 \, {\left(105 \, b^{5} c^{3} - 760 \, a b^{3} c^{4} + 1296 \, a^{2} b c^{5}\right)} d - 48 \, {\left(315 \, b^{6} c^{2} - 2520 \, a b^{4} c^{3} + 5488 \, a^{2} b^{2} c^{4} - 2048 \, a^{3} c^{5}\right)} e + 3 \, {\left(3465 \, b^{7} c - 30660 \, a b^{5} c^{2} + 81648 \, a^{2} b^{3} c^{3} - 58816 \, a^{3} b c^{4}\right)} f\right)} h^{2} + 8 \, {\left(224 \, {\left(360 \, b c^{7} d + 12 \, {\left(b^{2} c^{6} + 32 \, a c^{7}\right)} e - {\left(7 \, b^{3} c^{5} - 36 \, a b c^{6}\right)} f\right)} g^{2} + 32 \, {\left(168 \, {\left(b^{2} c^{6} + 32 \, a c^{7}\right)} d - 14 \, {\left(7 \, b^{3} c^{5} - 36 \, a b c^{6}\right)} e + 3 \, {\left(21 \, b^{4} c^{4} - 124 \, a b^{2} c^{5} + 128 \, a^{2} c^{6}\right)} f\right)} g h - {\left(224 \, {\left(7 \, b^{3} c^{5} - 36 \, a b c^{6}\right)} d - 48 \, {\left(21 \, b^{4} c^{4} - 124 \, a b^{2} c^{5} + 128 \, a^{2} c^{6}\right)} e + 3 \, {\left(231 \, b^{5} c^{3} - 1560 \, a b^{3} c^{4} + 2416 \, a^{2} b c^{5}\right)} f\right)} h^{2}\right)} x^{2} + 2 \, {\left(224 \, {\left(120 \, {\left(b^{2} c^{6} + 20 \, a c^{7}\right)} d - 12 \, {\left(5 \, b^{3} c^{5} - 28 \, a b c^{6}\right)} e + {\left(35 \, b^{4} c^{4} - 216 \, a b^{2} c^{5} + 240 \, a^{2} c^{6}\right)} f\right)} g^{2} - 32 \, {\left(168 \, {\left(5 \, b^{3} c^{5} - 28 \, a b c^{6}\right)} d - 14 \, {\left(35 \, b^{4} c^{4} - 216 \, a b^{2} c^{5} + 240 \, a^{2} c^{6}\right)} e + 3 \, {\left(105 \, b^{5} c^{3} - 728 \, a b^{3} c^{4} + 1168 \, a^{2} b c^{5}\right)} f\right)} g h + {\left(224 \, {\left(35 \, b^{4} c^{4} - 216 \, a b^{2} c^{5} + 240 \, a^{2} c^{6}\right)} d - 48 \, {\left(105 \, b^{5} c^{3} - 728 \, a b^{3} c^{4} + 1168 \, a^{2} b c^{5}\right)} e + 3 \, {\left(1155 \, b^{6} c^{2} - 8988 \, a b^{4} c^{3} + 18896 \, a^{2} b^{2} c^{4} - 6720 \, a^{3} c^{5}\right)} f\right)} h^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{6881280 \, c^{7}}, -\frac{105 \, {\left(32 \, {\left(24 \, {\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} d - 12 \, {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} e + {\left(7 \, b^{6} c^{2} - 60 \, a b^{4} c^{3} + 144 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} f\right)} g^{2} - 32 \, {\left(24 \, {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} d - 2 \, {\left(7 \, b^{6} c^{2} - 60 \, a b^{4} c^{3} + 144 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} e + 3 \, {\left(3 \, b^{7} c - 28 \, a b^{5} c^{2} + 80 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} f\right)} g h + {\left(32 \, {\left(7 \, b^{6} c^{2} - 60 \, a b^{4} c^{3} + 144 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d - 48 \, {\left(3 \, b^{7} c - 28 \, a b^{5} c^{2} + 80 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} e + 3 \, {\left(33 \, b^{8} - 336 \, a b^{6} c + 1120 \, a^{2} b^{4} c^{2} - 1280 \, a^{3} b^{2} c^{3} + 256 \, a^{4} c^{4}\right)} f\right)} h^{2}\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 \, {\left(215040 \, c^{8} f h^{2} x^{7} + 15360 \, {\left(32 \, c^{8} f g h + {\left(16 \, c^{8} e + 17 \, b c^{7} f\right)} h^{2}\right)} x^{6} + 1280 \, {\left(224 \, c^{8} f g^{2} + 32 \, {\left(14 \, c^{8} e + 15 \, b c^{7} f\right)} g h + {\left(224 \, c^{8} d + 240 \, b c^{7} e + 3 \, {\left(b^{2} c^{6} + 84 \, a c^{7}\right)} f\right)} h^{2}\right)} x^{5} + 128 \, {\left(224 \, {\left(12 \, c^{8} e + 13 \, b c^{7} f\right)} g^{2} + 32 \, {\left(168 \, c^{8} d + 182 \, b c^{7} e + 3 \, {\left(b^{2} c^{6} + 64 \, a c^{7}\right)} f\right)} g h + {\left(2912 \, b c^{7} d + 48 \, {\left(b^{2} c^{6} + 64 \, a c^{7}\right)} e - 3 \, {\left(11 \, b^{3} c^{5} - 52 \, a b c^{6}\right)} f\right)} h^{2}\right)} x^{4} + 16 \, {\left(224 \, {\left(120 \, c^{8} d + 132 \, b c^{7} e + {\left(3 \, b^{2} c^{6} + 140 \, a c^{7}\right)} f\right)} g^{2} + 32 \, {\left(1848 \, b c^{7} d + 14 \, {\left(3 \, b^{2} c^{6} + 140 \, a c^{7}\right)} e - 3 \, {\left(9 \, b^{3} c^{5} - 44 \, a b c^{6}\right)} f\right)} g h + {\left(224 \, {\left(3 \, b^{2} c^{6} + 140 \, a c^{7}\right)} d - 48 \, {\left(9 \, b^{3} c^{5} - 44 \, a b c^{6}\right)} e + 3 \, {\left(99 \, b^{4} c^{4} - 568 \, a b^{2} c^{5} + 560 \, a^{2} c^{6}\right)} f\right)} h^{2}\right)} x^{3} - 224 \, {\left(120 \, {\left(3 \, b^{3} c^{5} - 20 \, a b c^{6}\right)} d - 12 \, {\left(15 \, b^{4} c^{4} - 100 \, a b^{2} c^{5} + 128 \, a^{2} c^{6}\right)} e + {\left(105 \, b^{5} c^{3} - 760 \, a b^{3} c^{4} + 1296 \, a^{2} b c^{5}\right)} f\right)} g^{2} + 32 \, {\left(168 \, {\left(15 \, b^{4} c^{4} - 100 \, a b^{2} c^{5} + 128 \, a^{2} c^{6}\right)} d - 14 \, {\left(105 \, b^{5} c^{3} - 760 \, a b^{3} c^{4} + 1296 \, a^{2} b c^{5}\right)} e + 3 \, {\left(315 \, b^{6} c^{2} - 2520 \, a b^{4} c^{3} + 5488 \, a^{2} b^{2} c^{4} - 2048 \, a^{3} c^{5}\right)} f\right)} g h - {\left(224 \, {\left(105 \, b^{5} c^{3} - 760 \, a b^{3} c^{4} + 1296 \, a^{2} b c^{5}\right)} d - 48 \, {\left(315 \, b^{6} c^{2} - 2520 \, a b^{4} c^{3} + 5488 \, a^{2} b^{2} c^{4} - 2048 \, a^{3} c^{5}\right)} e + 3 \, {\left(3465 \, b^{7} c - 30660 \, a b^{5} c^{2} + 81648 \, a^{2} b^{3} c^{3} - 58816 \, a^{3} b c^{4}\right)} f\right)} h^{2} + 8 \, {\left(224 \, {\left(360 \, b c^{7} d + 12 \, {\left(b^{2} c^{6} + 32 \, a c^{7}\right)} e - {\left(7 \, b^{3} c^{5} - 36 \, a b c^{6}\right)} f\right)} g^{2} + 32 \, {\left(168 \, {\left(b^{2} c^{6} + 32 \, a c^{7}\right)} d - 14 \, {\left(7 \, b^{3} c^{5} - 36 \, a b c^{6}\right)} e + 3 \, {\left(21 \, b^{4} c^{4} - 124 \, a b^{2} c^{5} + 128 \, a^{2} c^{6}\right)} f\right)} g h - {\left(224 \, {\left(7 \, b^{3} c^{5} - 36 \, a b c^{6}\right)} d - 48 \, {\left(21 \, b^{4} c^{4} - 124 \, a b^{2} c^{5} + 128 \, a^{2} c^{6}\right)} e + 3 \, {\left(231 \, b^{5} c^{3} - 1560 \, a b^{3} c^{4} + 2416 \, a^{2} b c^{5}\right)} f\right)} h^{2}\right)} x^{2} + 2 \, {\left(224 \, {\left(120 \, {\left(b^{2} c^{6} + 20 \, a c^{7}\right)} d - 12 \, {\left(5 \, b^{3} c^{5} - 28 \, a b c^{6}\right)} e + {\left(35 \, b^{4} c^{4} - 216 \, a b^{2} c^{5} + 240 \, a^{2} c^{6}\right)} f\right)} g^{2} - 32 \, {\left(168 \, {\left(5 \, b^{3} c^{5} - 28 \, a b c^{6}\right)} d - 14 \, {\left(35 \, b^{4} c^{4} - 216 \, a b^{2} c^{5} + 240 \, a^{2} c^{6}\right)} e + 3 \, {\left(105 \, b^{5} c^{3} - 728 \, a b^{3} c^{4} + 1168 \, a^{2} b c^{5}\right)} f\right)} g h + {\left(224 \, {\left(35 \, b^{4} c^{4} - 216 \, a b^{2} c^{5} + 240 \, a^{2} c^{6}\right)} d - 48 \, {\left(105 \, b^{5} c^{3} - 728 \, a b^{3} c^{4} + 1168 \, a^{2} b c^{5}\right)} e + 3 \, {\left(1155 \, b^{6} c^{2} - 8988 \, a b^{4} c^{3} + 18896 \, a^{2} b^{2} c^{4} - 6720 \, a^{3} c^{5}\right)} f\right)} h^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{3440640 \, c^{7}}\right]"," ",0,"[1/6881280*(105*(32*(24*(b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*d - 12*(b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*e + (7*b^6*c^2 - 60*a*b^4*c^3 + 144*a^2*b^2*c^4 - 64*a^3*c^5)*f)*g^2 - 32*(24*(b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*d - 2*(7*b^6*c^2 - 60*a*b^4*c^3 + 144*a^2*b^2*c^4 - 64*a^3*c^5)*e + 3*(3*b^7*c - 28*a*b^5*c^2 + 80*a^2*b^3*c^3 - 64*a^3*b*c^4)*f)*g*h + (32*(7*b^6*c^2 - 60*a*b^4*c^3 + 144*a^2*b^2*c^4 - 64*a^3*c^5)*d - 48*(3*b^7*c - 28*a*b^5*c^2 + 80*a^2*b^3*c^3 - 64*a^3*b*c^4)*e + 3*(33*b^8 - 336*a*b^6*c + 1120*a^2*b^4*c^2 - 1280*a^3*b^2*c^3 + 256*a^4*c^4)*f)*h^2)*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) + 4*(215040*c^8*f*h^2*x^7 + 15360*(32*c^8*f*g*h + (16*c^8*e + 17*b*c^7*f)*h^2)*x^6 + 1280*(224*c^8*f*g^2 + 32*(14*c^8*e + 15*b*c^7*f)*g*h + (224*c^8*d + 240*b*c^7*e + 3*(b^2*c^6 + 84*a*c^7)*f)*h^2)*x^5 + 128*(224*(12*c^8*e + 13*b*c^7*f)*g^2 + 32*(168*c^8*d + 182*b*c^7*e + 3*(b^2*c^6 + 64*a*c^7)*f)*g*h + (2912*b*c^7*d + 48*(b^2*c^6 + 64*a*c^7)*e - 3*(11*b^3*c^5 - 52*a*b*c^6)*f)*h^2)*x^4 + 16*(224*(120*c^8*d + 132*b*c^7*e + (3*b^2*c^6 + 140*a*c^7)*f)*g^2 + 32*(1848*b*c^7*d + 14*(3*b^2*c^6 + 140*a*c^7)*e - 3*(9*b^3*c^5 - 44*a*b*c^6)*f)*g*h + (224*(3*b^2*c^6 + 140*a*c^7)*d - 48*(9*b^3*c^5 - 44*a*b*c^6)*e + 3*(99*b^4*c^4 - 568*a*b^2*c^5 + 560*a^2*c^6)*f)*h^2)*x^3 - 224*(120*(3*b^3*c^5 - 20*a*b*c^6)*d - 12*(15*b^4*c^4 - 100*a*b^2*c^5 + 128*a^2*c^6)*e + (105*b^5*c^3 - 760*a*b^3*c^4 + 1296*a^2*b*c^5)*f)*g^2 + 32*(168*(15*b^4*c^4 - 100*a*b^2*c^5 + 128*a^2*c^6)*d - 14*(105*b^5*c^3 - 760*a*b^3*c^4 + 1296*a^2*b*c^5)*e + 3*(315*b^6*c^2 - 2520*a*b^4*c^3 + 5488*a^2*b^2*c^4 - 2048*a^3*c^5)*f)*g*h - (224*(105*b^5*c^3 - 760*a*b^3*c^4 + 1296*a^2*b*c^5)*d - 48*(315*b^6*c^2 - 2520*a*b^4*c^3 + 5488*a^2*b^2*c^4 - 2048*a^3*c^5)*e + 3*(3465*b^7*c - 30660*a*b^5*c^2 + 81648*a^2*b^3*c^3 - 58816*a^3*b*c^4)*f)*h^2 + 8*(224*(360*b*c^7*d + 12*(b^2*c^6 + 32*a*c^7)*e - (7*b^3*c^5 - 36*a*b*c^6)*f)*g^2 + 32*(168*(b^2*c^6 + 32*a*c^7)*d - 14*(7*b^3*c^5 - 36*a*b*c^6)*e + 3*(21*b^4*c^4 - 124*a*b^2*c^5 + 128*a^2*c^6)*f)*g*h - (224*(7*b^3*c^5 - 36*a*b*c^6)*d - 48*(21*b^4*c^4 - 124*a*b^2*c^5 + 128*a^2*c^6)*e + 3*(231*b^5*c^3 - 1560*a*b^3*c^4 + 2416*a^2*b*c^5)*f)*h^2)*x^2 + 2*(224*(120*(b^2*c^6 + 20*a*c^7)*d - 12*(5*b^3*c^5 - 28*a*b*c^6)*e + (35*b^4*c^4 - 216*a*b^2*c^5 + 240*a^2*c^6)*f)*g^2 - 32*(168*(5*b^3*c^5 - 28*a*b*c^6)*d - 14*(35*b^4*c^4 - 216*a*b^2*c^5 + 240*a^2*c^6)*e + 3*(105*b^5*c^3 - 728*a*b^3*c^4 + 1168*a^2*b*c^5)*f)*g*h + (224*(35*b^4*c^4 - 216*a*b^2*c^5 + 240*a^2*c^6)*d - 48*(105*b^5*c^3 - 728*a*b^3*c^4 + 1168*a^2*b*c^5)*e + 3*(1155*b^6*c^2 - 8988*a*b^4*c^3 + 18896*a^2*b^2*c^4 - 6720*a^3*c^5)*f)*h^2)*x)*sqrt(c*x^2 + b*x + a))/c^7, -1/3440640*(105*(32*(24*(b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*d - 12*(b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*e + (7*b^6*c^2 - 60*a*b^4*c^3 + 144*a^2*b^2*c^4 - 64*a^3*c^5)*f)*g^2 - 32*(24*(b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*d - 2*(7*b^6*c^2 - 60*a*b^4*c^3 + 144*a^2*b^2*c^4 - 64*a^3*c^5)*e + 3*(3*b^7*c - 28*a*b^5*c^2 + 80*a^2*b^3*c^3 - 64*a^3*b*c^4)*f)*g*h + (32*(7*b^6*c^2 - 60*a*b^4*c^3 + 144*a^2*b^2*c^4 - 64*a^3*c^5)*d - 48*(3*b^7*c - 28*a*b^5*c^2 + 80*a^2*b^3*c^3 - 64*a^3*b*c^4)*e + 3*(33*b^8 - 336*a*b^6*c + 1120*a^2*b^4*c^2 - 1280*a^3*b^2*c^3 + 256*a^4*c^4)*f)*h^2)*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)) - 2*(215040*c^8*f*h^2*x^7 + 15360*(32*c^8*f*g*h + (16*c^8*e + 17*b*c^7*f)*h^2)*x^6 + 1280*(224*c^8*f*g^2 + 32*(14*c^8*e + 15*b*c^7*f)*g*h + (224*c^8*d + 240*b*c^7*e + 3*(b^2*c^6 + 84*a*c^7)*f)*h^2)*x^5 + 128*(224*(12*c^8*e + 13*b*c^7*f)*g^2 + 32*(168*c^8*d + 182*b*c^7*e + 3*(b^2*c^6 + 64*a*c^7)*f)*g*h + (2912*b*c^7*d + 48*(b^2*c^6 + 64*a*c^7)*e - 3*(11*b^3*c^5 - 52*a*b*c^6)*f)*h^2)*x^4 + 16*(224*(120*c^8*d + 132*b*c^7*e + (3*b^2*c^6 + 140*a*c^7)*f)*g^2 + 32*(1848*b*c^7*d + 14*(3*b^2*c^6 + 140*a*c^7)*e - 3*(9*b^3*c^5 - 44*a*b*c^6)*f)*g*h + (224*(3*b^2*c^6 + 140*a*c^7)*d - 48*(9*b^3*c^5 - 44*a*b*c^6)*e + 3*(99*b^4*c^4 - 568*a*b^2*c^5 + 560*a^2*c^6)*f)*h^2)*x^3 - 224*(120*(3*b^3*c^5 - 20*a*b*c^6)*d - 12*(15*b^4*c^4 - 100*a*b^2*c^5 + 128*a^2*c^6)*e + (105*b^5*c^3 - 760*a*b^3*c^4 + 1296*a^2*b*c^5)*f)*g^2 + 32*(168*(15*b^4*c^4 - 100*a*b^2*c^5 + 128*a^2*c^6)*d - 14*(105*b^5*c^3 - 760*a*b^3*c^4 + 1296*a^2*b*c^5)*e + 3*(315*b^6*c^2 - 2520*a*b^4*c^3 + 5488*a^2*b^2*c^4 - 2048*a^3*c^5)*f)*g*h - (224*(105*b^5*c^3 - 760*a*b^3*c^4 + 1296*a^2*b*c^5)*d - 48*(315*b^6*c^2 - 2520*a*b^4*c^3 + 5488*a^2*b^2*c^4 - 2048*a^3*c^5)*e + 3*(3465*b^7*c - 30660*a*b^5*c^2 + 81648*a^2*b^3*c^3 - 58816*a^3*b*c^4)*f)*h^2 + 8*(224*(360*b*c^7*d + 12*(b^2*c^6 + 32*a*c^7)*e - (7*b^3*c^5 - 36*a*b*c^6)*f)*g^2 + 32*(168*(b^2*c^6 + 32*a*c^7)*d - 14*(7*b^3*c^5 - 36*a*b*c^6)*e + 3*(21*b^4*c^4 - 124*a*b^2*c^5 + 128*a^2*c^6)*f)*g*h - (224*(7*b^3*c^5 - 36*a*b*c^6)*d - 48*(21*b^4*c^4 - 124*a*b^2*c^5 + 128*a^2*c^6)*e + 3*(231*b^5*c^3 - 1560*a*b^3*c^4 + 2416*a^2*b*c^5)*f)*h^2)*x^2 + 2*(224*(120*(b^2*c^6 + 20*a*c^7)*d - 12*(5*b^3*c^5 - 28*a*b*c^6)*e + (35*b^4*c^4 - 216*a*b^2*c^5 + 240*a^2*c^6)*f)*g^2 - 32*(168*(5*b^3*c^5 - 28*a*b*c^6)*d - 14*(35*b^4*c^4 - 216*a*b^2*c^5 + 240*a^2*c^6)*e + 3*(105*b^5*c^3 - 728*a*b^3*c^4 + 1168*a^2*b*c^5)*f)*g*h + (224*(35*b^4*c^4 - 216*a*b^2*c^5 + 240*a^2*c^6)*d - 48*(105*b^5*c^3 - 728*a*b^3*c^4 + 1168*a^2*b*c^5)*e + 3*(1155*b^6*c^2 - 8988*a*b^4*c^3 + 18896*a^2*b^2*c^4 - 6720*a^3*c^5)*f)*h^2)*x)*sqrt(c*x^2 + b*x + a))/c^7]","B",0
198,1,1833,0,1.908499," ","integrate((h*x+g)*(c*x^2+b*x+a)^(3/2)*(f*x^2+e*x+d),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(2 \, {\left(24 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d - 12 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} e + {\left(7 \, b^{6} c - 60 \, a b^{4} c^{2} + 144 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} f\right)} g - {\left(24 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d - 2 \, {\left(7 \, b^{6} c - 60 \, a b^{4} c^{2} + 144 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} e + 3 \, {\left(3 \, b^{7} - 28 \, a b^{5} c + 80 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} f\right)} h\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 \, {\left(15360 \, c^{7} f h x^{6} + 1280 \, {\left(14 \, c^{7} f g + {\left(14 \, c^{7} e + 15 \, b c^{6} f\right)} h\right)} x^{5} + 128 \, {\left(14 \, {\left(12 \, c^{7} e + 13 \, b c^{6} f\right)} g + {\left(168 \, c^{7} d + 182 \, b c^{6} e + 3 \, {\left(b^{2} c^{5} + 64 \, a c^{6}\right)} f\right)} h\right)} x^{4} + 16 \, {\left(14 \, {\left(120 \, c^{7} d + 132 \, b c^{6} e + {\left(3 \, b^{2} c^{5} + 140 \, a c^{6}\right)} f\right)} g + {\left(1848 \, b c^{6} d + 14 \, {\left(3 \, b^{2} c^{5} + 140 \, a c^{6}\right)} e - 3 \, {\left(9 \, b^{3} c^{4} - 44 \, a b c^{5}\right)} f\right)} h\right)} x^{3} + 8 \, {\left(14 \, {\left(360 \, b c^{6} d + 12 \, {\left(b^{2} c^{5} + 32 \, a c^{6}\right)} e - {\left(7 \, b^{3} c^{4} - 36 \, a b c^{5}\right)} f\right)} g + {\left(168 \, {\left(b^{2} c^{5} + 32 \, a c^{6}\right)} d - 14 \, {\left(7 \, b^{3} c^{4} - 36 \, a b c^{5}\right)} e + 3 \, {\left(21 \, b^{4} c^{3} - 124 \, a b^{2} c^{4} + 128 \, a^{2} c^{5}\right)} f\right)} h\right)} x^{2} - 14 \, {\left(120 \, {\left(3 \, b^{3} c^{4} - 20 \, a b c^{5}\right)} d - 12 \, {\left(15 \, b^{4} c^{3} - 100 \, a b^{2} c^{4} + 128 \, a^{2} c^{5}\right)} e + {\left(105 \, b^{5} c^{2} - 760 \, a b^{3} c^{3} + 1296 \, a^{2} b c^{4}\right)} f\right)} g + {\left(168 \, {\left(15 \, b^{4} c^{3} - 100 \, a b^{2} c^{4} + 128 \, a^{2} c^{5}\right)} d - 14 \, {\left(105 \, b^{5} c^{2} - 760 \, a b^{3} c^{3} + 1296 \, a^{2} b c^{4}\right)} e + 3 \, {\left(315 \, b^{6} c - 2520 \, a b^{4} c^{2} + 5488 \, a^{2} b^{2} c^{3} - 2048 \, a^{3} c^{4}\right)} f\right)} h + 2 \, {\left(14 \, {\left(120 \, {\left(b^{2} c^{5} + 20 \, a c^{6}\right)} d - 12 \, {\left(5 \, b^{3} c^{4} - 28 \, a b c^{5}\right)} e + {\left(35 \, b^{4} c^{3} - 216 \, a b^{2} c^{4} + 240 \, a^{2} c^{5}\right)} f\right)} g - {\left(168 \, {\left(5 \, b^{3} c^{4} - 28 \, a b c^{5}\right)} d - 14 \, {\left(35 \, b^{4} c^{3} - 216 \, a b^{2} c^{4} + 240 \, a^{2} c^{5}\right)} e + 3 \, {\left(105 \, b^{5} c^{2} - 728 \, a b^{3} c^{3} + 1168 \, a^{2} b c^{4}\right)} f\right)} h\right)} x\right)} \sqrt{c x^{2} + b x + a}}{430080 \, c^{6}}, -\frac{105 \, {\left(2 \, {\left(24 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d - 12 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} e + {\left(7 \, b^{6} c - 60 \, a b^{4} c^{2} + 144 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} f\right)} g - {\left(24 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d - 2 \, {\left(7 \, b^{6} c - 60 \, a b^{4} c^{2} + 144 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} e + 3 \, {\left(3 \, b^{7} - 28 \, a b^{5} c + 80 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} f\right)} h\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 \, {\left(15360 \, c^{7} f h x^{6} + 1280 \, {\left(14 \, c^{7} f g + {\left(14 \, c^{7} e + 15 \, b c^{6} f\right)} h\right)} x^{5} + 128 \, {\left(14 \, {\left(12 \, c^{7} e + 13 \, b c^{6} f\right)} g + {\left(168 \, c^{7} d + 182 \, b c^{6} e + 3 \, {\left(b^{2} c^{5} + 64 \, a c^{6}\right)} f\right)} h\right)} x^{4} + 16 \, {\left(14 \, {\left(120 \, c^{7} d + 132 \, b c^{6} e + {\left(3 \, b^{2} c^{5} + 140 \, a c^{6}\right)} f\right)} g + {\left(1848 \, b c^{6} d + 14 \, {\left(3 \, b^{2} c^{5} + 140 \, a c^{6}\right)} e - 3 \, {\left(9 \, b^{3} c^{4} - 44 \, a b c^{5}\right)} f\right)} h\right)} x^{3} + 8 \, {\left(14 \, {\left(360 \, b c^{6} d + 12 \, {\left(b^{2} c^{5} + 32 \, a c^{6}\right)} e - {\left(7 \, b^{3} c^{4} - 36 \, a b c^{5}\right)} f\right)} g + {\left(168 \, {\left(b^{2} c^{5} + 32 \, a c^{6}\right)} d - 14 \, {\left(7 \, b^{3} c^{4} - 36 \, a b c^{5}\right)} e + 3 \, {\left(21 \, b^{4} c^{3} - 124 \, a b^{2} c^{4} + 128 \, a^{2} c^{5}\right)} f\right)} h\right)} x^{2} - 14 \, {\left(120 \, {\left(3 \, b^{3} c^{4} - 20 \, a b c^{5}\right)} d - 12 \, {\left(15 \, b^{4} c^{3} - 100 \, a b^{2} c^{4} + 128 \, a^{2} c^{5}\right)} e + {\left(105 \, b^{5} c^{2} - 760 \, a b^{3} c^{3} + 1296 \, a^{2} b c^{4}\right)} f\right)} g + {\left(168 \, {\left(15 \, b^{4} c^{3} - 100 \, a b^{2} c^{4} + 128 \, a^{2} c^{5}\right)} d - 14 \, {\left(105 \, b^{5} c^{2} - 760 \, a b^{3} c^{3} + 1296 \, a^{2} b c^{4}\right)} e + 3 \, {\left(315 \, b^{6} c - 2520 \, a b^{4} c^{2} + 5488 \, a^{2} b^{2} c^{3} - 2048 \, a^{3} c^{4}\right)} f\right)} h + 2 \, {\left(14 \, {\left(120 \, {\left(b^{2} c^{5} + 20 \, a c^{6}\right)} d - 12 \, {\left(5 \, b^{3} c^{4} - 28 \, a b c^{5}\right)} e + {\left(35 \, b^{4} c^{3} - 216 \, a b^{2} c^{4} + 240 \, a^{2} c^{5}\right)} f\right)} g - {\left(168 \, {\left(5 \, b^{3} c^{4} - 28 \, a b c^{5}\right)} d - 14 \, {\left(35 \, b^{4} c^{3} - 216 \, a b^{2} c^{4} + 240 \, a^{2} c^{5}\right)} e + 3 \, {\left(105 \, b^{5} c^{2} - 728 \, a b^{3} c^{3} + 1168 \, a^{2} b c^{4}\right)} f\right)} h\right)} x\right)} \sqrt{c x^{2} + b x + a}}{215040 \, c^{6}}\right]"," ",0,"[1/430080*(105*(2*(24*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*d - 12*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*e + (7*b^6*c - 60*a*b^4*c^2 + 144*a^2*b^2*c^3 - 64*a^3*c^4)*f)*g - (24*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d - 2*(7*b^6*c - 60*a*b^4*c^2 + 144*a^2*b^2*c^3 - 64*a^3*c^4)*e + 3*(3*b^7 - 28*a*b^5*c + 80*a^2*b^3*c^2 - 64*a^3*b*c^3)*f)*h)*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) + 4*(15360*c^7*f*h*x^6 + 1280*(14*c^7*f*g + (14*c^7*e + 15*b*c^6*f)*h)*x^5 + 128*(14*(12*c^7*e + 13*b*c^6*f)*g + (168*c^7*d + 182*b*c^6*e + 3*(b^2*c^5 + 64*a*c^6)*f)*h)*x^4 + 16*(14*(120*c^7*d + 132*b*c^6*e + (3*b^2*c^5 + 140*a*c^6)*f)*g + (1848*b*c^6*d + 14*(3*b^2*c^5 + 140*a*c^6)*e - 3*(9*b^3*c^4 - 44*a*b*c^5)*f)*h)*x^3 + 8*(14*(360*b*c^6*d + 12*(b^2*c^5 + 32*a*c^6)*e - (7*b^3*c^4 - 36*a*b*c^5)*f)*g + (168*(b^2*c^5 + 32*a*c^6)*d - 14*(7*b^3*c^4 - 36*a*b*c^5)*e + 3*(21*b^4*c^3 - 124*a*b^2*c^4 + 128*a^2*c^5)*f)*h)*x^2 - 14*(120*(3*b^3*c^4 - 20*a*b*c^5)*d - 12*(15*b^4*c^3 - 100*a*b^2*c^4 + 128*a^2*c^5)*e + (105*b^5*c^2 - 760*a*b^3*c^3 + 1296*a^2*b*c^4)*f)*g + (168*(15*b^4*c^3 - 100*a*b^2*c^4 + 128*a^2*c^5)*d - 14*(105*b^5*c^2 - 760*a*b^3*c^3 + 1296*a^2*b*c^4)*e + 3*(315*b^6*c - 2520*a*b^4*c^2 + 5488*a^2*b^2*c^3 - 2048*a^3*c^4)*f)*h + 2*(14*(120*(b^2*c^5 + 20*a*c^6)*d - 12*(5*b^3*c^4 - 28*a*b*c^5)*e + (35*b^4*c^3 - 216*a*b^2*c^4 + 240*a^2*c^5)*f)*g - (168*(5*b^3*c^4 - 28*a*b*c^5)*d - 14*(35*b^4*c^3 - 216*a*b^2*c^4 + 240*a^2*c^5)*e + 3*(105*b^5*c^2 - 728*a*b^3*c^3 + 1168*a^2*b*c^4)*f)*h)*x)*sqrt(c*x^2 + b*x + a))/c^6, -1/215040*(105*(2*(24*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*d - 12*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*e + (7*b^6*c - 60*a*b^4*c^2 + 144*a^2*b^2*c^3 - 64*a^3*c^4)*f)*g - (24*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d - 2*(7*b^6*c - 60*a*b^4*c^2 + 144*a^2*b^2*c^3 - 64*a^3*c^4)*e + 3*(3*b^7 - 28*a*b^5*c + 80*a^2*b^3*c^2 - 64*a^3*b*c^3)*f)*h)*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)) - 2*(15360*c^7*f*h*x^6 + 1280*(14*c^7*f*g + (14*c^7*e + 15*b*c^6*f)*h)*x^5 + 128*(14*(12*c^7*e + 13*b*c^6*f)*g + (168*c^7*d + 182*b*c^6*e + 3*(b^2*c^5 + 64*a*c^6)*f)*h)*x^4 + 16*(14*(120*c^7*d + 132*b*c^6*e + (3*b^2*c^5 + 140*a*c^6)*f)*g + (1848*b*c^6*d + 14*(3*b^2*c^5 + 140*a*c^6)*e - 3*(9*b^3*c^4 - 44*a*b*c^5)*f)*h)*x^3 + 8*(14*(360*b*c^6*d + 12*(b^2*c^5 + 32*a*c^6)*e - (7*b^3*c^4 - 36*a*b*c^5)*f)*g + (168*(b^2*c^5 + 32*a*c^6)*d - 14*(7*b^3*c^4 - 36*a*b*c^5)*e + 3*(21*b^4*c^3 - 124*a*b^2*c^4 + 128*a^2*c^5)*f)*h)*x^2 - 14*(120*(3*b^3*c^4 - 20*a*b*c^5)*d - 12*(15*b^4*c^3 - 100*a*b^2*c^4 + 128*a^2*c^5)*e + (105*b^5*c^2 - 760*a*b^3*c^3 + 1296*a^2*b*c^4)*f)*g + (168*(15*b^4*c^3 - 100*a*b^2*c^4 + 128*a^2*c^5)*d - 14*(105*b^5*c^2 - 760*a*b^3*c^3 + 1296*a^2*b*c^4)*e + 3*(315*b^6*c - 2520*a*b^4*c^2 + 5488*a^2*b^2*c^3 - 2048*a^3*c^4)*f)*h + 2*(14*(120*(b^2*c^5 + 20*a*c^6)*d - 12*(5*b^3*c^4 - 28*a*b*c^5)*e + (35*b^4*c^3 - 216*a*b^2*c^4 + 240*a^2*c^5)*f)*g - (168*(5*b^3*c^4 - 28*a*b*c^5)*d - 14*(35*b^4*c^3 - 216*a*b^2*c^4 + 240*a^2*c^5)*e + 3*(105*b^5*c^2 - 728*a*b^3*c^3 + 1168*a^2*b*c^4)*f)*h)*x)*sqrt(c*x^2 + b*x + a))/c^6]","B",0
199,1,839,0,1.024743," ","integrate((c*x^2+b*x+a)^(3/2)*(f*x^2+e*x+d),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(24 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d - 12 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} e + {\left(7 \, b^{6} - 60 \, a b^{4} c + 144 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} f\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 \, {\left(1280 \, c^{6} f x^{5} + 128 \, {\left(12 \, c^{6} e + 13 \, b c^{5} f\right)} x^{4} + 16 \, {\left(120 \, c^{6} d + 132 \, b c^{5} e + {\left(3 \, b^{2} c^{4} + 140 \, a c^{5}\right)} f\right)} x^{3} + 8 \, {\left(360 \, b c^{5} d + 12 \, {\left(b^{2} c^{4} + 32 \, a c^{5}\right)} e - {\left(7 \, b^{3} c^{3} - 36 \, a b c^{4}\right)} f\right)} x^{2} - 120 \, {\left(3 \, b^{3} c^{3} - 20 \, a b c^{4}\right)} d + 12 \, {\left(15 \, b^{4} c^{2} - 100 \, a b^{2} c^{3} + 128 \, a^{2} c^{4}\right)} e - {\left(105 \, b^{5} c - 760 \, a b^{3} c^{2} + 1296 \, a^{2} b c^{3}\right)} f + 2 \, {\left(120 \, {\left(b^{2} c^{4} + 20 \, a c^{5}\right)} d - 12 \, {\left(5 \, b^{3} c^{3} - 28 \, a b c^{4}\right)} e + {\left(35 \, b^{4} c^{2} - 216 \, a b^{2} c^{3} + 240 \, a^{2} c^{4}\right)} f\right)} x\right)} \sqrt{c x^{2} + b x + a}}{30720 \, c^{5}}, -\frac{15 \, {\left(24 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d - 12 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} e + {\left(7 \, b^{6} - 60 \, a b^{4} c + 144 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} f\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 \, {\left(1280 \, c^{6} f x^{5} + 128 \, {\left(12 \, c^{6} e + 13 \, b c^{5} f\right)} x^{4} + 16 \, {\left(120 \, c^{6} d + 132 \, b c^{5} e + {\left(3 \, b^{2} c^{4} + 140 \, a c^{5}\right)} f\right)} x^{3} + 8 \, {\left(360 \, b c^{5} d + 12 \, {\left(b^{2} c^{4} + 32 \, a c^{5}\right)} e - {\left(7 \, b^{3} c^{3} - 36 \, a b c^{4}\right)} f\right)} x^{2} - 120 \, {\left(3 \, b^{3} c^{3} - 20 \, a b c^{4}\right)} d + 12 \, {\left(15 \, b^{4} c^{2} - 100 \, a b^{2} c^{3} + 128 \, a^{2} c^{4}\right)} e - {\left(105 \, b^{5} c - 760 \, a b^{3} c^{2} + 1296 \, a^{2} b c^{3}\right)} f + 2 \, {\left(120 \, {\left(b^{2} c^{4} + 20 \, a c^{5}\right)} d - 12 \, {\left(5 \, b^{3} c^{3} - 28 \, a b c^{4}\right)} e + {\left(35 \, b^{4} c^{2} - 216 \, a b^{2} c^{3} + 240 \, a^{2} c^{4}\right)} f\right)} x\right)} \sqrt{c x^{2} + b x + a}}{15360 \, c^{5}}\right]"," ",0,"[-1/30720*(15*(24*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d - 12*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*e + (7*b^6 - 60*a*b^4*c + 144*a^2*b^2*c^2 - 64*a^3*c^3)*f)*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) - 4*(1280*c^6*f*x^5 + 128*(12*c^6*e + 13*b*c^5*f)*x^4 + 16*(120*c^6*d + 132*b*c^5*e + (3*b^2*c^4 + 140*a*c^5)*f)*x^3 + 8*(360*b*c^5*d + 12*(b^2*c^4 + 32*a*c^5)*e - (7*b^3*c^3 - 36*a*b*c^4)*f)*x^2 - 120*(3*b^3*c^3 - 20*a*b*c^4)*d + 12*(15*b^4*c^2 - 100*a*b^2*c^3 + 128*a^2*c^4)*e - (105*b^5*c - 760*a*b^3*c^2 + 1296*a^2*b*c^3)*f + 2*(120*(b^2*c^4 + 20*a*c^5)*d - 12*(5*b^3*c^3 - 28*a*b*c^4)*e + (35*b^4*c^2 - 216*a*b^2*c^3 + 240*a^2*c^4)*f)*x)*sqrt(c*x^2 + b*x + a))/c^5, -1/15360*(15*(24*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d - 12*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*e + (7*b^6 - 60*a*b^4*c + 144*a^2*b^2*c^2 - 64*a^3*c^3)*f)*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)) - 2*(1280*c^6*f*x^5 + 128*(12*c^6*e + 13*b*c^5*f)*x^4 + 16*(120*c^6*d + 132*b*c^5*e + (3*b^2*c^4 + 140*a*c^5)*f)*x^3 + 8*(360*b*c^5*d + 12*(b^2*c^4 + 32*a*c^5)*e - (7*b^3*c^3 - 36*a*b*c^4)*f)*x^2 - 120*(3*b^3*c^3 - 20*a*b*c^4)*d + 12*(15*b^4*c^2 - 100*a*b^2*c^3 + 128*a^2*c^4)*e - (105*b^5*c - 760*a*b^3*c^2 + 1296*a^2*b*c^3)*f + 2*(120*(b^2*c^4 + 20*a*c^5)*d - 12*(5*b^3*c^3 - 28*a*b*c^4)*e + (35*b^4*c^2 - 216*a*b^2*c^3 + 240*a^2*c^4)*f)*x)*sqrt(c*x^2 + b*x + a))/c^5]","A",0
200,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)*(f*x^2+e*x+d)/(h*x+g),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
201,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)*(f*x^2+e*x+d)/(h*x+g)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
202,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)*(f*x^2+e*x+d)/(h*x+g)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
203,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)*(f*x^2+e*x+d)/(h*x+g)^4,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
204,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)*(f*x^2+e*x+d)/(h*x+g)^5,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
205,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)*(f*x^2+e*x+d)/(h*x+g)^6,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
206,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)*(f*x^2+e*x+d)/(h*x+g)^7,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
207,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)*(f*x^2+e*x+d)/(h*x+g)^8,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
208,1,83,0,1.814578," ","integrate((1+2*x)^3*(4*x^2+3*x+1)*(3*x^2-x+2)^(1/2),x, algorithm=""fricas"")","\frac{1}{544320} \, {\left(2488320 \, x^{6} + 6462720 \, x^{5} + 7491456 \, x^{4} + 5497776 \, x^{3} + 3280872 \, x^{2} + 1493894 \, x - 543069\right)} \sqrt{3 \, x^{2} - x + 2} + \frac{124039}{186624} \, \sqrt{3} \log\left(4 \, \sqrt{3} \sqrt{3 \, x^{2} - x + 2} {\left(6 \, x - 1\right)} - 72 \, x^{2} + 24 \, x - 25\right)"," ",0,"1/544320*(2488320*x^6 + 6462720*x^5 + 7491456*x^4 + 5497776*x^3 + 3280872*x^2 + 1493894*x - 543069)*sqrt(3*x^2 - x + 2) + 124039/186624*sqrt(3)*log(4*sqrt(3)*sqrt(3*x^2 - x + 2)*(6*x - 1) - 72*x^2 + 24*x - 25)","A",0
209,1,78,0,0.754355," ","integrate((1+2*x)^2*(4*x^2+3*x+1)*(3*x^2-x+2)^(1/2),x, algorithm=""fricas"")","\frac{1}{6480} \, {\left(17280 \, x^{5} + 35712 \, x^{4} + 33552 \, x^{3} + 22344 \, x^{2} + 14638 \, x + 5607\right)} \sqrt{3 \, x^{2} - x + 2} + \frac{5405}{15552} \, \sqrt{3} \log\left(4 \, \sqrt{3} \sqrt{3 \, x^{2} - x + 2} {\left(6 \, x - 1\right)} - 72 \, x^{2} + 24 \, x - 25\right)"," ",0,"1/6480*(17280*x^5 + 35712*x^4 + 33552*x^3 + 22344*x^2 + 14638*x + 5607)*sqrt(3*x^2 - x + 2) + 5405/15552*sqrt(3)*log(4*sqrt(3)*sqrt(3*x^2 - x + 2)*(6*x - 1) - 72*x^2 + 24*x - 25)","A",0
210,1,73,0,0.858045," ","integrate((1+2*x)*(4*x^2+3*x+1)*(3*x^2-x+2)^(1/2),x, algorithm=""fricas"")","\frac{1}{12960} \, {\left(20736 \, x^{4} + 31536 \, x^{3} + 24072 \, x^{2} + 17374 \, x + 15471\right)} \sqrt{3 \, x^{2} - x + 2} + \frac{437}{31104} \, \sqrt{3} \log\left(4 \, \sqrt{3} \sqrt{3 \, x^{2} - x + 2} {\left(6 \, x - 1\right)} - 72 \, x^{2} + 24 \, x - 25\right)"," ",0,"1/12960*(20736*x^4 + 31536*x^3 + 24072*x^2 + 17374*x + 15471)*sqrt(3*x^2 - x + 2) + 437/31104*sqrt(3)*log(4*sqrt(3)*sqrt(3*x^2 - x + 2)*(6*x - 1) - 72*x^2 + 24*x - 25)","A",0
211,1,115,0,1.330849," ","integrate((4*x^2+3*x+1)*(3*x^2-x+2)^(1/2)/(1+2*x),x, algorithm=""fricas"")","\frac{1}{72} \, {\left(48 \, x^{2} + 14 \, x + 45\right)} \sqrt{3 \, x^{2} - x + 2} + \frac{43}{864} \, \sqrt{3} \log\left(-4 \, \sqrt{3} \sqrt{3 \, x^{2} - x + 2} {\left(6 \, x - 1\right)} - 72 \, x^{2} + 24 \, x - 25\right) + \frac{1}{16} \, \sqrt{13} \log\left(-\frac{4 \, \sqrt{13} \sqrt{3 \, x^{2} - x + 2} {\left(8 \, x - 9\right)} + 220 \, x^{2} - 196 \, x + 185}{4 \, x^{2} + 4 \, x + 1}\right)"," ",0,"1/72*(48*x^2 + 14*x + 45)*sqrt(3*x^2 - x + 2) + 43/864*sqrt(3)*log(-4*sqrt(3)*sqrt(3*x^2 - x + 2)*(6*x - 1) - 72*x^2 + 24*x - 25) + 1/16*sqrt(13)*log(-(4*sqrt(13)*sqrt(3*x^2 - x + 2)*(8*x - 9) + 220*x^2 - 196*x + 185)/(4*x^2 + 4*x + 1))","A",0
212,1,133,0,0.872742," ","integrate((4*x^2+3*x+1)*(3*x^2-x+2)^(1/2)/(1+2*x)^2,x, algorithm=""fricas"")","\frac{572 \, \sqrt{3} {\left(2 \, x + 1\right)} \log\left(-4 \, \sqrt{3} \sqrt{3 \, x^{2} - x + 2} {\left(6 \, x - 1\right)} - 72 \, x^{2} + 24 \, x - 25\right) + 153 \, \sqrt{13} {\left(2 \, x + 1\right)} \log\left(\frac{4 \, \sqrt{13} \sqrt{3 \, x^{2} - x + 2} {\left(8 \, x - 9\right)} - 220 \, x^{2} + 196 \, x - 185}{4 \, x^{2} + 4 \, x + 1}\right) + 156 \, {\left(12 \, x^{2} - 2 \, x - 7\right)} \sqrt{3 \, x^{2} - x + 2}}{1872 \, {\left(2 \, x + 1\right)}}"," ",0,"1/1872*(572*sqrt(3)*(2*x + 1)*log(-4*sqrt(3)*sqrt(3*x^2 - x + 2)*(6*x - 1) - 72*x^2 + 24*x - 25) + 153*sqrt(13)*(2*x + 1)*log((4*sqrt(13)*sqrt(3*x^2 - x + 2)*(8*x - 9) - 220*x^2 + 196*x - 185)/(4*x^2 + 4*x + 1)) + 156*(12*x^2 - 2*x - 7)*sqrt(3*x^2 - x + 2))/(2*x + 1)","A",0
213,1,149,0,1.392021," ","integrate((4*x^2+3*x+1)*(3*x^2-x+2)^(1/2)/(1+2*x)^3,x, algorithm=""fricas"")","\frac{3718 \, \sqrt{3} {\left(4 \, x^{2} + 4 \, x + 1\right)} \log\left(4 \, \sqrt{3} \sqrt{3 \, x^{2} - x + 2} {\left(6 \, x - 1\right)} - 72 \, x^{2} + 24 \, x - 25\right) + 2409 \, \sqrt{13} {\left(4 \, x^{2} + 4 \, x + 1\right)} \log\left(-\frac{4 \, \sqrt{13} \sqrt{3 \, x^{2} - x + 2} {\left(8 \, x - 9\right)} + 220 \, x^{2} - 196 \, x + 185}{4 \, x^{2} + 4 \, x + 1}\right) + 156 \, {\left(208 \, x^{2} + 268 \, x + 69\right)} \sqrt{3 \, x^{2} - x + 2}}{16224 \, {\left(4 \, x^{2} + 4 \, x + 1\right)}}"," ",0,"1/16224*(3718*sqrt(3)*(4*x^2 + 4*x + 1)*log(4*sqrt(3)*sqrt(3*x^2 - x + 2)*(6*x - 1) - 72*x^2 + 24*x - 25) + 2409*sqrt(13)*(4*x^2 + 4*x + 1)*log(-(4*sqrt(13)*sqrt(3*x^2 - x + 2)*(8*x - 9) + 220*x^2 - 196*x + 185)/(4*x^2 + 4*x + 1)) + 156*(208*x^2 + 268*x + 69)*sqrt(3*x^2 - x + 2))/(4*x^2 + 4*x + 1)","A",0
214,1,93,0,1.499577," ","integrate((1+2*x)^3*(3*x^2-x+2)^(3/2)*(4*x^2+3*x+1),x, algorithm=""fricas"")","\frac{1}{22394880} \, {\left(238878720 \, x^{8} + 510105600 \, x^{7} + 635765760 \, x^{6} + 711210240 \, x^{5} + 649452672 \, x^{4} + 421626672 \, x^{3} + 201289704 \, x^{2} + 84014278 \, x + 12499587\right)} \sqrt{3 \, x^{2} - x + 2} + \frac{28879697}{53747712} \, \sqrt{3} \log\left(4 \, \sqrt{3} \sqrt{3 \, x^{2} - x + 2} {\left(6 \, x - 1\right)} - 72 \, x^{2} + 24 \, x - 25\right)"," ",0,"1/22394880*(238878720*x^8 + 510105600*x^7 + 635765760*x^6 + 711210240*x^5 + 649452672*x^4 + 421626672*x^3 + 201289704*x^2 + 84014278*x + 12499587)*sqrt(3*x^2 - x + 2) + 28879697/53747712*sqrt(3)*log(4*sqrt(3)*sqrt(3*x^2 - x + 2)*(6*x - 1) - 72*x^2 + 24*x - 25)","A",0
215,1,88,0,1.264114," ","integrate((1+2*x)^2*(3*x^2-x+2)^(3/2)*(4*x^2+3*x+1),x, algorithm=""fricas"")","\frac{1}{967680} \, {\left(5806080 \, x^{7} + 9262080 \, x^{6} + 10656000 \, x^{5} + 12173952 \, x^{4} + 10119792 \, x^{3} + 5694024 \, x^{2} + 2735918 \, x + 1517367\right)} \sqrt{3 \, x^{2} - x + 2} + \frac{48139}{331776} \, \sqrt{3} \log\left(4 \, \sqrt{3} \sqrt{3 \, x^{2} - x + 2} {\left(6 \, x - 1\right)} - 72 \, x^{2} + 24 \, x - 25\right)"," ",0,"1/967680*(5806080*x^7 + 9262080*x^6 + 10656000*x^5 + 12173952*x^4 + 10119792*x^3 + 5694024*x^2 + 2735918*x + 1517367)*sqrt(3*x^2 - x + 2) + 48139/331776*sqrt(3)*log(4*sqrt(3)*sqrt(3*x^2 - x + 2)*(6*x - 1) - 72*x^2 + 24*x - 25)","A",0
216,1,83,0,2.011104," ","integrate((1+2*x)*(3*x^2-x+2)^(3/2)*(4*x^2+3*x+1),x, algorithm=""fricas"")","\frac{1}{145152} \, {\left(497664 \, x^{6} + 518400 \, x^{5} + 653184 \, x^{4} + 744336 \, x^{3} + 531384 \, x^{2} + 275410 \, x + 203337\right)} \sqrt{3 \, x^{2} - x + 2} + \frac{37559}{248832} \, \sqrt{3} \log\left(-4 \, \sqrt{3} \sqrt{3 \, x^{2} - x + 2} {\left(6 \, x - 1\right)} - 72 \, x^{2} + 24 \, x - 25\right)"," ",0,"1/145152*(497664*x^6 + 518400*x^5 + 653184*x^4 + 744336*x^3 + 531384*x^2 + 275410*x + 203337)*sqrt(3*x^2 - x + 2) + 37559/248832*sqrt(3)*log(-4*sqrt(3)*sqrt(3*x^2 - x + 2)*(6*x - 1) - 72*x^2 + 24*x - 25)","A",0
217,1,125,0,0.957911," ","integrate((3*x^2-x+2)^(3/2)*(4*x^2+3*x+1)/(1+2*x),x, algorithm=""fricas"")","\frac{1}{5760} \, {\left(6912 \, x^{4} - 1008 \, x^{3} + 9624 \, x^{2} + 1058 \, x + 7977\right)} \sqrt{3 \, x^{2} - x + 2} + \frac{2203}{13824} \, \sqrt{3} \log\left(4 \, \sqrt{3} \sqrt{3 \, x^{2} - x + 2} {\left(6 \, x - 1\right)} - 72 \, x^{2} + 24 \, x - 25\right) + \frac{13}{64} \, \sqrt{13} \log\left(-\frac{4 \, \sqrt{13} \sqrt{3 \, x^{2} - x + 2} {\left(8 \, x - 9\right)} + 220 \, x^{2} - 196 \, x + 185}{4 \, x^{2} + 4 \, x + 1}\right)"," ",0,"1/5760*(6912*x^4 - 1008*x^3 + 9624*x^2 + 1058*x + 7977)*sqrt(3*x^2 - x + 2) + 2203/13824*sqrt(3)*log(4*sqrt(3)*sqrt(3*x^2 - x + 2)*(6*x - 1) - 72*x^2 + 24*x - 25) + 13/64*sqrt(13)*log(-(4*sqrt(13)*sqrt(3*x^2 - x + 2)*(8*x - 9) + 220*x^2 - 196*x + 185)/(4*x^2 + 4*x + 1))","A",0
218,1,143,0,1.402715," ","integrate((3*x^2-x+2)^(3/2)*(4*x^2+3*x+1)/(1+2*x)^2,x, algorithm=""fricas"")","\frac{2327 \, \sqrt{3} {\left(2 \, x + 1\right)} \log\left(-4 \, \sqrt{3} \sqrt{3 \, x^{2} - x + 2} {\left(6 \, x - 1\right)} - 72 \, x^{2} + 24 \, x - 25\right) + 900 \, \sqrt{13} {\left(2 \, x + 1\right)} \log\left(\frac{4 \, \sqrt{13} \sqrt{3 \, x^{2} - x + 2} {\left(8 \, x - 9\right)} - 220 \, x^{2} + 196 \, x - 185}{4 \, x^{2} + 4 \, x + 1}\right) + 12 \, {\left(288 \, x^{4} - 96 \, x^{3} + 564 \, x^{2} - 332 \, x - 493\right)} \sqrt{3 \, x^{2} - x + 2}}{2304 \, {\left(2 \, x + 1\right)}}"," ",0,"1/2304*(2327*sqrt(3)*(2*x + 1)*log(-4*sqrt(3)*sqrt(3*x^2 - x + 2)*(6*x - 1) - 72*x^2 + 24*x - 25) + 900*sqrt(13)*(2*x + 1)*log((4*sqrt(13)*sqrt(3*x^2 - x + 2)*(8*x - 9) - 220*x^2 + 196*x - 185)/(4*x^2 + 4*x + 1)) + 12*(288*x^4 - 96*x^3 + 564*x^2 - 332*x - 493)*sqrt(3*x^2 - x + 2))/(2*x + 1)","A",0
219,1,159,0,0.808443," ","integrate((3*x^2-x+2)^(3/2)*(4*x^2+3*x+1)/(1+2*x)^3,x, algorithm=""fricas"")","\frac{19747 \, \sqrt{3} {\left(4 \, x^{2} + 4 \, x + 1\right)} \log\left(4 \, \sqrt{3} \sqrt{3 \, x^{2} - x + 2} {\left(6 \, x - 1\right)} - 72 \, x^{2} + 24 \, x - 25\right) + 10377 \, \sqrt{13} {\left(4 \, x^{2} + 4 \, x + 1\right)} \log\left(-\frac{4 \, \sqrt{13} \sqrt{3 \, x^{2} - x + 2} {\left(8 \, x - 9\right)} + 220 \, x^{2} - 196 \, x + 185}{4 \, x^{2} + 4 \, x + 1}\right) + 312 \, {\left(96 \, x^{4} - 68 \, x^{3} + 390 \, x^{2} + 627 \, x + 182\right)} \sqrt{3 \, x^{2} - x + 2}}{14976 \, {\left(4 \, x^{2} + 4 \, x + 1\right)}}"," ",0,"1/14976*(19747*sqrt(3)*(4*x^2 + 4*x + 1)*log(4*sqrt(3)*sqrt(3*x^2 - x + 2)*(6*x - 1) - 72*x^2 + 24*x - 25) + 10377*sqrt(13)*(4*x^2 + 4*x + 1)*log(-(4*sqrt(13)*sqrt(3*x^2 - x + 2)*(8*x - 9) + 220*x^2 - 196*x + 185)/(4*x^2 + 4*x + 1)) + 312*(96*x^4 - 68*x^3 + 390*x^2 + 627*x + 182)*sqrt(3*x^2 - x + 2))/(4*x^2 + 4*x + 1)","A",0
220,1,103,0,1.616441," ","integrate((1+2*x)^3*(3*x^2-x+2)^(5/2)*(4*x^2+3*x+1),x, algorithm=""fricas"")","\frac{1}{4598415360} \, {\left(120394874880 \, x^{10} + 207681159168 \, x^{9} + 308846297088 \, x^{8} + 419978151936 \, x^{7} + 415908006912 \, x^{6} + 347247744768 \, x^{5} + 263636134272 \, x^{4} + 161269204752 \, x^{3} + 72088585464 \, x^{2} + 26646633218 \, x + 9173509857\right)} \sqrt{3 \, x^{2} - x + 2} + \frac{61917863}{143327232} \, \sqrt{3} \log\left(4 \, \sqrt{3} \sqrt{3 \, x^{2} - x + 2} {\left(6 \, x - 1\right)} - 72 \, x^{2} + 24 \, x - 25\right)"," ",0,"1/4598415360*(120394874880*x^10 + 207681159168*x^9 + 308846297088*x^8 + 419978151936*x^7 + 415908006912*x^6 + 347247744768*x^5 + 263636134272*x^4 + 161269204752*x^3 + 72088585464*x^2 + 26646633218*x + 9173509857)*sqrt(3*x^2 - x + 2) + 61917863/143327232*sqrt(3)*log(4*sqrt(3)*sqrt(3*x^2 - x + 2)*(6*x - 1) - 72*x^2 + 24*x - 25)","A",0
221,1,98,0,1.079574," ","integrate((1+2*x)^2*(3*x^2-x+2)^(5/2)*(4*x^2+3*x+1),x, algorithm=""fricas"")","\frac{1}{156764160} \, {\left(2257403904 \, x^{9} + 2675441664 \, x^{8} + 4427716608 \, x^{7} + 5671627776 \, x^{6} + 4996802304 \, x^{5} + 4171579776 \, x^{4} + 3096104976 \, x^{3} + 1693765752 \, x^{2} + 692659234 \, x + 387182961\right)} \sqrt{3 \, x^{2} - x + 2} + \frac{3564931}{53747712} \, \sqrt{3} \log\left(-4 \, \sqrt{3} \sqrt{3 \, x^{2} - x + 2} {\left(6 \, x - 1\right)} - 72 \, x^{2} + 24 \, x - 25\right)"," ",0,"1/156764160*(2257403904*x^9 + 2675441664*x^8 + 4427716608*x^7 + 5671627776*x^6 + 4996802304*x^5 + 4171579776*x^4 + 3096104976*x^3 + 1693765752*x^2 + 692659234*x + 387182961)*sqrt(3*x^2 - x + 2) + 3564931/53747712*sqrt(3)*log(-4*sqrt(3)*sqrt(3*x^2 - x + 2)*(6*x - 1) - 72*x^2 + 24*x - 25)","A",0
222,1,93,0,1.091773," ","integrate((1+2*x)*(3*x^2-x+2)^(5/2)*(4*x^2+3*x+1),x, algorithm=""fricas"")","\frac{1}{5971968} \, {\left(47775744 \, x^{8} + 30357504 \, x^{7} + 79377408 \, x^{6} + 80034048 \, x^{5} + 66969216 \, x^{4} + 58946544 \, x^{3} + 41031048 \, x^{2} + 19860062 \, x + 10960335\right)} \sqrt{3 \, x^{2} - x + 2} + \frac{27071575}{71663616} \, \sqrt{3} \log\left(-4 \, \sqrt{3} \sqrt{3 \, x^{2} - x + 2} {\left(6 \, x - 1\right)} - 72 \, x^{2} + 24 \, x - 25\right)"," ",0,"1/5971968*(47775744*x^8 + 30357504*x^7 + 79377408*x^6 + 80034048*x^5 + 66969216*x^4 + 58946544*x^3 + 41031048*x^2 + 19860062*x + 10960335)*sqrt(3*x^2 - x + 2) + 27071575/71663616*sqrt(3)*log(-4*sqrt(3)*sqrt(3*x^2 - x + 2)*(6*x - 1) - 72*x^2 + 24*x - 25)","A",0
223,1,135,0,1.140184," ","integrate((3*x^2-x+2)^(5/2)*(4*x^2+3*x+1)/(1+2*x),x, algorithm=""fricas"")","\frac{1}{2903040} \, {\left(7464960 \, x^{6} - 3836160 \, x^{5} + 15700608 \, x^{4} - 3646512 \, x^{3} + 12466776 \, x^{2} - 2120998 \, x + 11665053\right)} \sqrt{3 \, x^{2} - x + 2} + \frac{944521}{995328} \, \sqrt{3} \log\left(4 \, \sqrt{3} \sqrt{3 \, x^{2} - x + 2} {\left(6 \, x - 1\right)} - 72 \, x^{2} + 24 \, x - 25\right) + \frac{169}{256} \, \sqrt{13} \log\left(-\frac{4 \, \sqrt{13} \sqrt{3 \, x^{2} - x + 2} {\left(8 \, x - 9\right)} + 220 \, x^{2} - 196 \, x + 185}{4 \, x^{2} + 4 \, x + 1}\right)"," ",0,"1/2903040*(7464960*x^6 - 3836160*x^5 + 15700608*x^4 - 3646512*x^3 + 12466776*x^2 - 2120998*x + 11665053)*sqrt(3*x^2 - x + 2) + 944521/995328*sqrt(3)*log(4*sqrt(3)*sqrt(3*x^2 - x + 2)*(6*x - 1) - 72*x^2 + 24*x - 25) + 169/256*sqrt(13)*log(-(4*sqrt(13)*sqrt(3*x^2 - x + 2)*(8*x - 9) + 220*x^2 - 196*x + 185)/(4*x^2 + 4*x + 1))","A",0
224,1,153,0,0.622305," ","integrate((3*x^2-x+2)^(5/2)*(4*x^2+3*x+1)/(1+2*x)^2,x, algorithm=""fricas"")","\frac{1578115 \, \sqrt{3} {\left(2 \, x + 1\right)} \log\left(-4 \, \sqrt{3} \sqrt{3 \, x^{2} - x + 2} {\left(6 \, x - 1\right)} - 72 \, x^{2} + 24 \, x - 25\right) + 694980 \, \sqrt{13} {\left(2 \, x + 1\right)} \log\left(\frac{4 \, \sqrt{13} \sqrt{3 \, x^{2} - x + 2} {\left(8 \, x - 9\right)} - 220 \, x^{2} + 196 \, x - 185}{4 \, x^{2} + 4 \, x + 1}\right) + 12 \, {\left(103680 \, x^{6} - 65664 \, x^{5} + 251424 \, x^{4} - 115680 \, x^{3} + 310660 \, x^{2} - 322972 \, x - 364257\right)} \sqrt{3 \, x^{2} - x + 2}}{414720 \, {\left(2 \, x + 1\right)}}"," ",0,"1/414720*(1578115*sqrt(3)*(2*x + 1)*log(-4*sqrt(3)*sqrt(3*x^2 - x + 2)*(6*x - 1) - 72*x^2 + 24*x - 25) + 694980*sqrt(13)*(2*x + 1)*log((4*sqrt(13)*sqrt(3*x^2 - x + 2)*(8*x - 9) - 220*x^2 + 196*x - 185)/(4*x^2 + 4*x + 1)) + 12*(103680*x^6 - 65664*x^5 + 251424*x^4 - 115680*x^3 + 310660*x^2 - 322972*x - 364257)*sqrt(3*x^2 - x + 2))/(2*x + 1)","A",0
225,1,169,0,1.111523," ","integrate((3*x^2-x+2)^(5/2)*(4*x^2+3*x+1)/(1+2*x)^3,x, algorithm=""fricas"")","\frac{592115 \, \sqrt{3} {\left(4 \, x^{2} + 4 \, x + 1\right)} \log\left(4 \, \sqrt{3} \sqrt{3 \, x^{2} - x + 2} {\left(6 \, x - 1\right)} - 72 \, x^{2} + 24 \, x - 25\right) + 293580 \, \sqrt{13} {\left(4 \, x^{2} + 4 \, x + 1\right)} \log\left(-\frac{4 \, \sqrt{13} \sqrt{3 \, x^{2} - x + 2} {\left(8 \, x - 9\right)} + 220 \, x^{2} - 196 \, x + 185}{4 \, x^{2} + 4 \, x + 1}\right) + 12 \, {\left(27648 \, x^{6} - 22464 \, x^{5} + 83616 \, x^{4} - 76200 \, x^{3} + 256564 \, x^{2} + 464446 \, x + 142057\right)} \sqrt{3 \, x^{2} - x + 2}}{92160 \, {\left(4 \, x^{2} + 4 \, x + 1\right)}}"," ",0,"1/92160*(592115*sqrt(3)*(4*x^2 + 4*x + 1)*log(4*sqrt(3)*sqrt(3*x^2 - x + 2)*(6*x - 1) - 72*x^2 + 24*x - 25) + 293580*sqrt(13)*(4*x^2 + 4*x + 1)*log(-(4*sqrt(13)*sqrt(3*x^2 - x + 2)*(8*x - 9) + 220*x^2 - 196*x + 185)/(4*x^2 + 4*x + 1)) + 12*(27648*x^6 - 22464*x^5 + 83616*x^4 - 76200*x^3 + 256564*x^2 + 464446*x + 142057)*sqrt(3*x^2 - x + 2))/(4*x^2 + 4*x + 1)","A",0
226,1,1435,0,2.303513," ","integrate((h*x+g)^3*(f*x^2+e*x+d)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(32 \, {\left(8 \, c^{5} d - 4 \, b c^{4} e + {\left(3 \, b^{2} c^{3} - 4 \, a c^{4}\right)} f\right)} g^{3} - 48 \, {\left(8 \, b c^{4} d - 2 \, {\left(3 \, b^{2} c^{3} - 4 \, a c^{4}\right)} e + {\left(5 \, b^{3} c^{2} - 12 \, a b c^{3}\right)} f\right)} g^{2} h + 6 \, {\left(16 \, {\left(3 \, b^{2} c^{3} - 4 \, a c^{4}\right)} d - 8 \, {\left(5 \, b^{3} c^{2} - 12 \, a b c^{3}\right)} e + {\left(35 \, b^{4} c - 120 \, a b^{2} c^{2} + 48 \, a^{2} c^{3}\right)} f\right)} g h^{2} - {\left(16 \, {\left(5 \, b^{3} c^{2} - 12 \, a b c^{3}\right)} d - 2 \, {\left(35 \, b^{4} c - 120 \, a b^{2} c^{2} + 48 \, a^{2} c^{3}\right)} e + {\left(63 \, b^{5} - 280 \, a b^{3} c + 240 \, a^{2} b c^{2}\right)} f\right)} h^{3}\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 \, {\left(384 \, c^{5} f h^{3} x^{4} + 480 \, {\left(4 \, c^{5} e - 3 \, b c^{4} f\right)} g^{3} + 240 \, {\left(24 \, c^{5} d - 18 \, b c^{4} e + {\left(15 \, b^{2} c^{3} - 16 \, a c^{4}\right)} f\right)} g^{2} h - 30 \, {\left(144 \, b c^{4} d - 8 \, {\left(15 \, b^{2} c^{3} - 16 \, a c^{4}\right)} e + 5 \, {\left(21 \, b^{3} c^{2} - 44 \, a b c^{3}\right)} f\right)} g h^{2} + {\left(80 \, {\left(15 \, b^{2} c^{3} - 16 \, a c^{4}\right)} d - 50 \, {\left(21 \, b^{3} c^{2} - 44 \, a b c^{3}\right)} e + {\left(945 \, b^{4} c - 2940 \, a b^{2} c^{2} + 1024 \, a^{2} c^{3}\right)} f\right)} h^{3} + 48 \, {\left(30 \, c^{5} f g h^{2} + {\left(10 \, c^{5} e - 9 \, b c^{4} f\right)} h^{3}\right)} x^{3} + 8 \, {\left(240 \, c^{5} f g^{2} h + 30 \, {\left(8 \, c^{5} e - 7 \, b c^{4} f\right)} g h^{2} + {\left(80 \, c^{5} d - 70 \, b c^{4} e + {\left(63 \, b^{2} c^{3} - 64 \, a c^{4}\right)} f\right)} h^{3}\right)} x^{2} + 2 \, {\left(480 \, c^{5} f g^{3} + 240 \, {\left(6 \, c^{5} e - 5 \, b c^{4} f\right)} g^{2} h + 30 \, {\left(48 \, c^{5} d - 40 \, b c^{4} e + {\left(35 \, b^{2} c^{3} - 36 \, a c^{4}\right)} f\right)} g h^{2} - {\left(400 \, b c^{4} d - 10 \, {\left(35 \, b^{2} c^{3} - 36 \, a c^{4}\right)} e + 7 \, {\left(45 \, b^{3} c^{2} - 92 \, a b c^{3}\right)} f\right)} h^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{7680 \, c^{6}}, -\frac{15 \, {\left(32 \, {\left(8 \, c^{5} d - 4 \, b c^{4} e + {\left(3 \, b^{2} c^{3} - 4 \, a c^{4}\right)} f\right)} g^{3} - 48 \, {\left(8 \, b c^{4} d - 2 \, {\left(3 \, b^{2} c^{3} - 4 \, a c^{4}\right)} e + {\left(5 \, b^{3} c^{2} - 12 \, a b c^{3}\right)} f\right)} g^{2} h + 6 \, {\left(16 \, {\left(3 \, b^{2} c^{3} - 4 \, a c^{4}\right)} d - 8 \, {\left(5 \, b^{3} c^{2} - 12 \, a b c^{3}\right)} e + {\left(35 \, b^{4} c - 120 \, a b^{2} c^{2} + 48 \, a^{2} c^{3}\right)} f\right)} g h^{2} - {\left(16 \, {\left(5 \, b^{3} c^{2} - 12 \, a b c^{3}\right)} d - 2 \, {\left(35 \, b^{4} c - 120 \, a b^{2} c^{2} + 48 \, a^{2} c^{3}\right)} e + {\left(63 \, b^{5} - 280 \, a b^{3} c + 240 \, a^{2} b c^{2}\right)} f\right)} h^{3}\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 \, {\left(384 \, c^{5} f h^{3} x^{4} + 480 \, {\left(4 \, c^{5} e - 3 \, b c^{4} f\right)} g^{3} + 240 \, {\left(24 \, c^{5} d - 18 \, b c^{4} e + {\left(15 \, b^{2} c^{3} - 16 \, a c^{4}\right)} f\right)} g^{2} h - 30 \, {\left(144 \, b c^{4} d - 8 \, {\left(15 \, b^{2} c^{3} - 16 \, a c^{4}\right)} e + 5 \, {\left(21 \, b^{3} c^{2} - 44 \, a b c^{3}\right)} f\right)} g h^{2} + {\left(80 \, {\left(15 \, b^{2} c^{3} - 16 \, a c^{4}\right)} d - 50 \, {\left(21 \, b^{3} c^{2} - 44 \, a b c^{3}\right)} e + {\left(945 \, b^{4} c - 2940 \, a b^{2} c^{2} + 1024 \, a^{2} c^{3}\right)} f\right)} h^{3} + 48 \, {\left(30 \, c^{5} f g h^{2} + {\left(10 \, c^{5} e - 9 \, b c^{4} f\right)} h^{3}\right)} x^{3} + 8 \, {\left(240 \, c^{5} f g^{2} h + 30 \, {\left(8 \, c^{5} e - 7 \, b c^{4} f\right)} g h^{2} + {\left(80 \, c^{5} d - 70 \, b c^{4} e + {\left(63 \, b^{2} c^{3} - 64 \, a c^{4}\right)} f\right)} h^{3}\right)} x^{2} + 2 \, {\left(480 \, c^{5} f g^{3} + 240 \, {\left(6 \, c^{5} e - 5 \, b c^{4} f\right)} g^{2} h + 30 \, {\left(48 \, c^{5} d - 40 \, b c^{4} e + {\left(35 \, b^{2} c^{3} - 36 \, a c^{4}\right)} f\right)} g h^{2} - {\left(400 \, b c^{4} d - 10 \, {\left(35 \, b^{2} c^{3} - 36 \, a c^{4}\right)} e + 7 \, {\left(45 \, b^{3} c^{2} - 92 \, a b c^{3}\right)} f\right)} h^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{3840 \, c^{6}}\right]"," ",0,"[-1/7680*(15*(32*(8*c^5*d - 4*b*c^4*e + (3*b^2*c^3 - 4*a*c^4)*f)*g^3 - 48*(8*b*c^4*d - 2*(3*b^2*c^3 - 4*a*c^4)*e + (5*b^3*c^2 - 12*a*b*c^3)*f)*g^2*h + 6*(16*(3*b^2*c^3 - 4*a*c^4)*d - 8*(5*b^3*c^2 - 12*a*b*c^3)*e + (35*b^4*c - 120*a*b^2*c^2 + 48*a^2*c^3)*f)*g*h^2 - (16*(5*b^3*c^2 - 12*a*b*c^3)*d - 2*(35*b^4*c - 120*a*b^2*c^2 + 48*a^2*c^3)*e + (63*b^5 - 280*a*b^3*c + 240*a^2*b*c^2)*f)*h^3)*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) - 4*(384*c^5*f*h^3*x^4 + 480*(4*c^5*e - 3*b*c^4*f)*g^3 + 240*(24*c^5*d - 18*b*c^4*e + (15*b^2*c^3 - 16*a*c^4)*f)*g^2*h - 30*(144*b*c^4*d - 8*(15*b^2*c^3 - 16*a*c^4)*e + 5*(21*b^3*c^2 - 44*a*b*c^3)*f)*g*h^2 + (80*(15*b^2*c^3 - 16*a*c^4)*d - 50*(21*b^3*c^2 - 44*a*b*c^3)*e + (945*b^4*c - 2940*a*b^2*c^2 + 1024*a^2*c^3)*f)*h^3 + 48*(30*c^5*f*g*h^2 + (10*c^5*e - 9*b*c^4*f)*h^3)*x^3 + 8*(240*c^5*f*g^2*h + 30*(8*c^5*e - 7*b*c^4*f)*g*h^2 + (80*c^5*d - 70*b*c^4*e + (63*b^2*c^3 - 64*a*c^4)*f)*h^3)*x^2 + 2*(480*c^5*f*g^3 + 240*(6*c^5*e - 5*b*c^4*f)*g^2*h + 30*(48*c^5*d - 40*b*c^4*e + (35*b^2*c^3 - 36*a*c^4)*f)*g*h^2 - (400*b*c^4*d - 10*(35*b^2*c^3 - 36*a*c^4)*e + 7*(45*b^3*c^2 - 92*a*b*c^3)*f)*h^3)*x)*sqrt(c*x^2 + b*x + a))/c^6, -1/3840*(15*(32*(8*c^5*d - 4*b*c^4*e + (3*b^2*c^3 - 4*a*c^4)*f)*g^3 - 48*(8*b*c^4*d - 2*(3*b^2*c^3 - 4*a*c^4)*e + (5*b^3*c^2 - 12*a*b*c^3)*f)*g^2*h + 6*(16*(3*b^2*c^3 - 4*a*c^4)*d - 8*(5*b^3*c^2 - 12*a*b*c^3)*e + (35*b^4*c - 120*a*b^2*c^2 + 48*a^2*c^3)*f)*g*h^2 - (16*(5*b^3*c^2 - 12*a*b*c^3)*d - 2*(35*b^4*c - 120*a*b^2*c^2 + 48*a^2*c^3)*e + (63*b^5 - 280*a*b^3*c + 240*a^2*b*c^2)*f)*h^3)*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)) - 2*(384*c^5*f*h^3*x^4 + 480*(4*c^5*e - 3*b*c^4*f)*g^3 + 240*(24*c^5*d - 18*b*c^4*e + (15*b^2*c^3 - 16*a*c^4)*f)*g^2*h - 30*(144*b*c^4*d - 8*(15*b^2*c^3 - 16*a*c^4)*e + 5*(21*b^3*c^2 - 44*a*b*c^3)*f)*g*h^2 + (80*(15*b^2*c^3 - 16*a*c^4)*d - 50*(21*b^3*c^2 - 44*a*b*c^3)*e + (945*b^4*c - 2940*a*b^2*c^2 + 1024*a^2*c^3)*f)*h^3 + 48*(30*c^5*f*g*h^2 + (10*c^5*e - 9*b*c^4*f)*h^3)*x^3 + 8*(240*c^5*f*g^2*h + 30*(8*c^5*e - 7*b*c^4*f)*g*h^2 + (80*c^5*d - 70*b*c^4*e + (63*b^2*c^3 - 64*a*c^4)*f)*h^3)*x^2 + 2*(480*c^5*f*g^3 + 240*(6*c^5*e - 5*b*c^4*f)*g^2*h + 30*(48*c^5*d - 40*b*c^4*e + (35*b^2*c^3 - 36*a*c^4)*f)*g*h^2 - (400*b*c^4*d - 10*(35*b^2*c^3 - 36*a*c^4)*e + 7*(45*b^3*c^2 - 92*a*b*c^3)*f)*h^3)*x)*sqrt(c*x^2 + b*x + a))/c^6]","A",0
227,1,861,0,1.983366," ","integrate((h*x+g)^2*(f*x^2+e*x+d)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(16 \, {\left(8 \, c^{4} d - 4 \, b c^{3} e + {\left(3 \, b^{2} c^{2} - 4 \, a c^{3}\right)} f\right)} g^{2} - 16 \, {\left(8 \, b c^{3} d - 2 \, {\left(3 \, b^{2} c^{2} - 4 \, a c^{3}\right)} e + {\left(5 \, b^{3} c - 12 \, a b c^{2}\right)} f\right)} g h + {\left(16 \, {\left(3 \, b^{2} c^{2} - 4 \, a c^{3}\right)} d - 8 \, {\left(5 \, b^{3} c - 12 \, a b c^{2}\right)} e + {\left(35 \, b^{4} - 120 \, a b^{2} c + 48 \, a^{2} c^{2}\right)} f\right)} h^{2}\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 \, {\left(48 \, c^{4} f h^{2} x^{3} + 48 \, {\left(4 \, c^{4} e - 3 \, b c^{3} f\right)} g^{2} + 16 \, {\left(24 \, c^{4} d - 18 \, b c^{3} e + {\left(15 \, b^{2} c^{2} - 16 \, a c^{3}\right)} f\right)} g h - {\left(144 \, b c^{3} d - 8 \, {\left(15 \, b^{2} c^{2} - 16 \, a c^{3}\right)} e + 5 \, {\left(21 \, b^{3} c - 44 \, a b c^{2}\right)} f\right)} h^{2} + 8 \, {\left(16 \, c^{4} f g h + {\left(8 \, c^{4} e - 7 \, b c^{3} f\right)} h^{2}\right)} x^{2} + 2 \, {\left(48 \, c^{4} f g^{2} + 16 \, {\left(6 \, c^{4} e - 5 \, b c^{3} f\right)} g h + {\left(48 \, c^{4} d - 40 \, b c^{3} e + {\left(35 \, b^{2} c^{2} - 36 \, a c^{3}\right)} f\right)} h^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{768 \, c^{5}}, -\frac{3 \, {\left(16 \, {\left(8 \, c^{4} d - 4 \, b c^{3} e + {\left(3 \, b^{2} c^{2} - 4 \, a c^{3}\right)} f\right)} g^{2} - 16 \, {\left(8 \, b c^{3} d - 2 \, {\left(3 \, b^{2} c^{2} - 4 \, a c^{3}\right)} e + {\left(5 \, b^{3} c - 12 \, a b c^{2}\right)} f\right)} g h + {\left(16 \, {\left(3 \, b^{2} c^{2} - 4 \, a c^{3}\right)} d - 8 \, {\left(5 \, b^{3} c - 12 \, a b c^{2}\right)} e + {\left(35 \, b^{4} - 120 \, a b^{2} c + 48 \, a^{2} c^{2}\right)} f\right)} h^{2}\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 \, {\left(48 \, c^{4} f h^{2} x^{3} + 48 \, {\left(4 \, c^{4} e - 3 \, b c^{3} f\right)} g^{2} + 16 \, {\left(24 \, c^{4} d - 18 \, b c^{3} e + {\left(15 \, b^{2} c^{2} - 16 \, a c^{3}\right)} f\right)} g h - {\left(144 \, b c^{3} d - 8 \, {\left(15 \, b^{2} c^{2} - 16 \, a c^{3}\right)} e + 5 \, {\left(21 \, b^{3} c - 44 \, a b c^{2}\right)} f\right)} h^{2} + 8 \, {\left(16 \, c^{4} f g h + {\left(8 \, c^{4} e - 7 \, b c^{3} f\right)} h^{2}\right)} x^{2} + 2 \, {\left(48 \, c^{4} f g^{2} + 16 \, {\left(6 \, c^{4} e - 5 \, b c^{3} f\right)} g h + {\left(48 \, c^{4} d - 40 \, b c^{3} e + {\left(35 \, b^{2} c^{2} - 36 \, a c^{3}\right)} f\right)} h^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{384 \, c^{5}}\right]"," ",0,"[1/768*(3*(16*(8*c^4*d - 4*b*c^3*e + (3*b^2*c^2 - 4*a*c^3)*f)*g^2 - 16*(8*b*c^3*d - 2*(3*b^2*c^2 - 4*a*c^3)*e + (5*b^3*c - 12*a*b*c^2)*f)*g*h + (16*(3*b^2*c^2 - 4*a*c^3)*d - 8*(5*b^3*c - 12*a*b*c^2)*e + (35*b^4 - 120*a*b^2*c + 48*a^2*c^2)*f)*h^2)*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) + 4*(48*c^4*f*h^2*x^3 + 48*(4*c^4*e - 3*b*c^3*f)*g^2 + 16*(24*c^4*d - 18*b*c^3*e + (15*b^2*c^2 - 16*a*c^3)*f)*g*h - (144*b*c^3*d - 8*(15*b^2*c^2 - 16*a*c^3)*e + 5*(21*b^3*c - 44*a*b*c^2)*f)*h^2 + 8*(16*c^4*f*g*h + (8*c^4*e - 7*b*c^3*f)*h^2)*x^2 + 2*(48*c^4*f*g^2 + 16*(6*c^4*e - 5*b*c^3*f)*g*h + (48*c^4*d - 40*b*c^3*e + (35*b^2*c^2 - 36*a*c^3)*f)*h^2)*x)*sqrt(c*x^2 + b*x + a))/c^5, -1/384*(3*(16*(8*c^4*d - 4*b*c^3*e + (3*b^2*c^2 - 4*a*c^3)*f)*g^2 - 16*(8*b*c^3*d - 2*(3*b^2*c^2 - 4*a*c^3)*e + (5*b^3*c - 12*a*b*c^2)*f)*g*h + (16*(3*b^2*c^2 - 4*a*c^3)*d - 8*(5*b^3*c - 12*a*b*c^2)*e + (35*b^4 - 120*a*b^2*c + 48*a^2*c^2)*f)*h^2)*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)) - 2*(48*c^4*f*h^2*x^3 + 48*(4*c^4*e - 3*b*c^3*f)*g^2 + 16*(24*c^4*d - 18*b*c^3*e + (15*b^2*c^2 - 16*a*c^3)*f)*g*h - (144*b*c^3*d - 8*(15*b^2*c^2 - 16*a*c^3)*e + 5*(21*b^3*c - 44*a*b*c^2)*f)*h^2 + 8*(16*c^4*f*g*h + (8*c^4*e - 7*b*c^3*f)*h^2)*x^2 + 2*(48*c^4*f*g^2 + 16*(6*c^4*e - 5*b*c^3*f)*g*h + (48*c^4*d - 40*b*c^3*e + (35*b^2*c^2 - 36*a*c^3)*f)*h^2)*x)*sqrt(c*x^2 + b*x + a))/c^5]","A",0
228,1,461,0,2.243991," ","integrate((h*x+g)*(f*x^2+e*x+d)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(2 \, {\left(8 \, c^{3} d - 4 \, b c^{2} e + {\left(3 \, b^{2} c - 4 \, a c^{2}\right)} f\right)} g - {\left(8 \, b c^{2} d - 2 \, {\left(3 \, b^{2} c - 4 \, a c^{2}\right)} e + {\left(5 \, b^{3} - 12 \, a b c\right)} f\right)} h\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 \, {\left(8 \, c^{3} f h x^{2} + 6 \, {\left(4 \, c^{3} e - 3 \, b c^{2} f\right)} g + {\left(24 \, c^{3} d - 18 \, b c^{2} e + {\left(15 \, b^{2} c - 16 \, a c^{2}\right)} f\right)} h + 2 \, {\left(6 \, c^{3} f g + {\left(6 \, c^{3} e - 5 \, b c^{2} f\right)} h\right)} x\right)} \sqrt{c x^{2} + b x + a}}{96 \, c^{4}}, -\frac{3 \, {\left(2 \, {\left(8 \, c^{3} d - 4 \, b c^{2} e + {\left(3 \, b^{2} c - 4 \, a c^{2}\right)} f\right)} g - {\left(8 \, b c^{2} d - 2 \, {\left(3 \, b^{2} c - 4 \, a c^{2}\right)} e + {\left(5 \, b^{3} - 12 \, a b c\right)} f\right)} h\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 \, {\left(8 \, c^{3} f h x^{2} + 6 \, {\left(4 \, c^{3} e - 3 \, b c^{2} f\right)} g + {\left(24 \, c^{3} d - 18 \, b c^{2} e + {\left(15 \, b^{2} c - 16 \, a c^{2}\right)} f\right)} h + 2 \, {\left(6 \, c^{3} f g + {\left(6 \, c^{3} e - 5 \, b c^{2} f\right)} h\right)} x\right)} \sqrt{c x^{2} + b x + a}}{48 \, c^{4}}\right]"," ",0,"[1/96*(3*(2*(8*c^3*d - 4*b*c^2*e + (3*b^2*c - 4*a*c^2)*f)*g - (8*b*c^2*d - 2*(3*b^2*c - 4*a*c^2)*e + (5*b^3 - 12*a*b*c)*f)*h)*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) + 4*(8*c^3*f*h*x^2 + 6*(4*c^3*e - 3*b*c^2*f)*g + (24*c^3*d - 18*b*c^2*e + (15*b^2*c - 16*a*c^2)*f)*h + 2*(6*c^3*f*g + (6*c^3*e - 5*b*c^2*f)*h)*x)*sqrt(c*x^2 + b*x + a))/c^4, -1/48*(3*(2*(8*c^3*d - 4*b*c^2*e + (3*b^2*c - 4*a*c^2)*f)*g - (8*b*c^2*d - 2*(3*b^2*c - 4*a*c^2)*e + (5*b^3 - 12*a*b*c)*f)*h)*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)) - 2*(8*c^3*f*h*x^2 + 6*(4*c^3*e - 3*b*c^2*f)*g + (24*c^3*d - 18*b*c^2*e + (15*b^2*c - 16*a*c^2)*f)*h + 2*(6*c^3*f*g + (6*c^3*e - 5*b*c^2*f)*h)*x)*sqrt(c*x^2 + b*x + a))/c^4]","A",0
229,1,227,0,2.725032," ","integrate((f*x^2+e*x+d)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(8 \, c^{2} d - 4 \, b c e + {\left(3 \, b^{2} - 4 \, a c\right)} f\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 \, {\left(2 \, c^{2} f x + 4 \, c^{2} e - 3 \, b c f\right)} \sqrt{c x^{2} + b x + a}}{16 \, c^{3}}, -\frac{{\left(8 \, c^{2} d - 4 \, b c e + {\left(3 \, b^{2} - 4 \, a c\right)} f\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 \, {\left(2 \, c^{2} f x + 4 \, c^{2} e - 3 \, b c f\right)} \sqrt{c x^{2} + b x + a}}{8 \, c^{3}}\right]"," ",0,"[-1/16*((8*c^2*d - 4*b*c*e + (3*b^2 - 4*a*c)*f)*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) - 4*(2*c^2*f*x + 4*c^2*e - 3*b*c*f)*sqrt(c*x^2 + b*x + a))/c^3, -1/8*((8*c^2*d - 4*b*c*e + (3*b^2 - 4*a*c)*f)*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)) - 2*(2*c^2*f*x + 4*c^2*e - 3*b*c*f)*sqrt(c*x^2 + b*x + a))/c^3]","A",0
230,-1,0,0,0.000000," ","integrate((f*x^2+e*x+d)/(h*x+g)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
231,-1,0,0,0.000000," ","integrate((f*x^2+e*x+d)/(h*x+g)^2/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
232,-1,0,0,0.000000," ","integrate((f*x^2+e*x+d)/(h*x+g)^3/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
233,1,2937,0,45.677662," ","integrate((h*x+g)^3*(f*x^2+e*x+d)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(16 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} f g^{3} + 24 \, {\left(2 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} e - 3 \, {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} f\right)} g^{2} h + 6 \, {\left(8 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d - 12 \, {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} e + 3 \, {\left(5 \, a b^{4} c - 24 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3}\right)} f\right)} g h^{2} - {\left(24 \, {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d - 6 \, {\left(5 \, a b^{4} c - 24 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3}\right)} e + 5 \, {\left(7 \, a b^{5} - 40 \, a^{2} b^{3} c + 48 \, a^{3} b c^{2}\right)} f\right)} h^{3} + {\left(16 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} f g^{3} + 24 \, {\left(2 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} e - 3 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} f\right)} g^{2} h + 6 \, {\left(8 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d - 12 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} e + 3 \, {\left(5 \, b^{4} c^{2} - 24 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} f\right)} g h^{2} - {\left(24 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d - 6 \, {\left(5 \, b^{4} c^{2} - 24 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} e + 5 \, {\left(7 \, b^{5} c - 40 \, a b^{3} c^{2} + 48 \, a^{2} b c^{3}\right)} f\right)} h^{3}\right)} x^{2} + {\left(16 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} f g^{3} + 24 \, {\left(2 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} e - 3 \, {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3}\right)} f\right)} g^{2} h + 6 \, {\left(8 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d - 12 \, {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3}\right)} e + 3 \, {\left(5 \, b^{5} c - 24 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} f\right)} g h^{2} - {\left(24 \, {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3}\right)} d - 6 \, {\left(5 \, b^{5} c - 24 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} e + 5 \, {\left(7 \, b^{6} - 40 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2}\right)} f\right)} h^{3}\right)} x\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 \, {\left(8 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} f h^{3} x^{4} - 48 \, {\left(b c^{5} d - 2 \, a c^{5} e + a b c^{4} f\right)} g^{3} + 72 \, {\left(4 \, a c^{5} d - 2 \, a b c^{4} e + {\left(3 \, a b^{2} c^{3} - 8 \, a^{2} c^{4}\right)} f\right)} g^{2} h - 18 \, {\left(8 \, a b c^{4} d - 4 \, {\left(3 \, a b^{2} c^{3} - 8 \, a^{2} c^{4}\right)} e + {\left(15 \, a b^{3} c^{2} - 52 \, a^{2} b c^{3}\right)} f\right)} g h^{2} + {\left(24 \, {\left(3 \, a b^{2} c^{3} - 8 \, a^{2} c^{4}\right)} d - 6 \, {\left(15 \, a b^{3} c^{2} - 52 \, a^{2} b c^{3}\right)} e + {\left(105 \, a b^{4} c - 460 \, a^{2} b^{2} c^{2} + 256 \, a^{3} c^{3}\right)} f\right)} h^{3} + 2 \, {\left(18 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} f g h^{2} + {\left(6 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} e - 7 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} f\right)} h^{3}\right)} x^{3} + {\left(72 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} f g^{2} h + 18 \, {\left(4 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} e - 5 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} f\right)} g h^{2} + {\left(24 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d - 30 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} e + {\left(35 \, b^{4} c^{2} - 172 \, a b^{2} c^{3} + 128 \, a^{2} c^{4}\right)} f\right)} h^{3}\right)} x^{2} - {\left(48 \, {\left(2 \, c^{6} d - b c^{5} e + {\left(b^{2} c^{4} - 2 \, a c^{5}\right)} f\right)} g^{3} - 72 \, {\left(2 \, b c^{5} d - 2 \, {\left(b^{2} c^{4} - 2 \, a c^{5}\right)} e + {\left(3 \, b^{3} c^{3} - 10 \, a b c^{4}\right)} f\right)} g^{2} h + 18 \, {\left(8 \, {\left(b^{2} c^{4} - 2 \, a c^{5}\right)} d - 4 \, {\left(3 \, b^{3} c^{3} - 10 \, a b c^{4}\right)} e + {\left(15 \, b^{4} c^{2} - 62 \, a b^{2} c^{3} + 24 \, a^{2} c^{4}\right)} f\right)} g h^{2} - {\left(24 \, {\left(3 \, b^{3} c^{3} - 10 \, a b c^{4}\right)} d - 6 \, {\left(15 \, b^{4} c^{2} - 62 \, a b^{2} c^{3} + 24 \, a^{2} c^{4}\right)} e + {\left(105 \, b^{5} c - 530 \, a b^{3} c^{2} + 488 \, a^{2} b c^{3}\right)} f\right)} h^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{96 \, {\left(a b^{2} c^{5} - 4 \, a^{2} c^{6} + {\left(b^{2} c^{6} - 4 \, a c^{7}\right)} x^{2} + {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} x\right)}}, -\frac{3 \, {\left(16 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} f g^{3} + 24 \, {\left(2 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} e - 3 \, {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} f\right)} g^{2} h + 6 \, {\left(8 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d - 12 \, {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} e + 3 \, {\left(5 \, a b^{4} c - 24 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3}\right)} f\right)} g h^{2} - {\left(24 \, {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d - 6 \, {\left(5 \, a b^{4} c - 24 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3}\right)} e + 5 \, {\left(7 \, a b^{5} - 40 \, a^{2} b^{3} c + 48 \, a^{3} b c^{2}\right)} f\right)} h^{3} + {\left(16 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} f g^{3} + 24 \, {\left(2 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} e - 3 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} f\right)} g^{2} h + 6 \, {\left(8 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d - 12 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} e + 3 \, {\left(5 \, b^{4} c^{2} - 24 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} f\right)} g h^{2} - {\left(24 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d - 6 \, {\left(5 \, b^{4} c^{2} - 24 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} e + 5 \, {\left(7 \, b^{5} c - 40 \, a b^{3} c^{2} + 48 \, a^{2} b c^{3}\right)} f\right)} h^{3}\right)} x^{2} + {\left(16 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} f g^{3} + 24 \, {\left(2 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} e - 3 \, {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3}\right)} f\right)} g^{2} h + 6 \, {\left(8 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d - 12 \, {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3}\right)} e + 3 \, {\left(5 \, b^{5} c - 24 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} f\right)} g h^{2} - {\left(24 \, {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3}\right)} d - 6 \, {\left(5 \, b^{5} c - 24 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} e + 5 \, {\left(7 \, b^{6} - 40 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2}\right)} f\right)} h^{3}\right)} x\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 \, {\left(8 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} f h^{3} x^{4} - 48 \, {\left(b c^{5} d - 2 \, a c^{5} e + a b c^{4} f\right)} g^{3} + 72 \, {\left(4 \, a c^{5} d - 2 \, a b c^{4} e + {\left(3 \, a b^{2} c^{3} - 8 \, a^{2} c^{4}\right)} f\right)} g^{2} h - 18 \, {\left(8 \, a b c^{4} d - 4 \, {\left(3 \, a b^{2} c^{3} - 8 \, a^{2} c^{4}\right)} e + {\left(15 \, a b^{3} c^{2} - 52 \, a^{2} b c^{3}\right)} f\right)} g h^{2} + {\left(24 \, {\left(3 \, a b^{2} c^{3} - 8 \, a^{2} c^{4}\right)} d - 6 \, {\left(15 \, a b^{3} c^{2} - 52 \, a^{2} b c^{3}\right)} e + {\left(105 \, a b^{4} c - 460 \, a^{2} b^{2} c^{2} + 256 \, a^{3} c^{3}\right)} f\right)} h^{3} + 2 \, {\left(18 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} f g h^{2} + {\left(6 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} e - 7 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} f\right)} h^{3}\right)} x^{3} + {\left(72 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} f g^{2} h + 18 \, {\left(4 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} e - 5 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} f\right)} g h^{2} + {\left(24 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d - 30 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} e + {\left(35 \, b^{4} c^{2} - 172 \, a b^{2} c^{3} + 128 \, a^{2} c^{4}\right)} f\right)} h^{3}\right)} x^{2} - {\left(48 \, {\left(2 \, c^{6} d - b c^{5} e + {\left(b^{2} c^{4} - 2 \, a c^{5}\right)} f\right)} g^{3} - 72 \, {\left(2 \, b c^{5} d - 2 \, {\left(b^{2} c^{4} - 2 \, a c^{5}\right)} e + {\left(3 \, b^{3} c^{3} - 10 \, a b c^{4}\right)} f\right)} g^{2} h + 18 \, {\left(8 \, {\left(b^{2} c^{4} - 2 \, a c^{5}\right)} d - 4 \, {\left(3 \, b^{3} c^{3} - 10 \, a b c^{4}\right)} e + {\left(15 \, b^{4} c^{2} - 62 \, a b^{2} c^{3} + 24 \, a^{2} c^{4}\right)} f\right)} g h^{2} - {\left(24 \, {\left(3 \, b^{3} c^{3} - 10 \, a b c^{4}\right)} d - 6 \, {\left(15 \, b^{4} c^{2} - 62 \, a b^{2} c^{3} + 24 \, a^{2} c^{4}\right)} e + {\left(105 \, b^{5} c - 530 \, a b^{3} c^{2} + 488 \, a^{2} b c^{3}\right)} f\right)} h^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{48 \, {\left(a b^{2} c^{5} - 4 \, a^{2} c^{6} + {\left(b^{2} c^{6} - 4 \, a c^{7}\right)} x^{2} + {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} x\right)}}\right]"," ",0,"[1/96*(3*(16*(a*b^2*c^3 - 4*a^2*c^4)*f*g^3 + 24*(2*(a*b^2*c^3 - 4*a^2*c^4)*e - 3*(a*b^3*c^2 - 4*a^2*b*c^3)*f)*g^2*h + 6*(8*(a*b^2*c^3 - 4*a^2*c^4)*d - 12*(a*b^3*c^2 - 4*a^2*b*c^3)*e + 3*(5*a*b^4*c - 24*a^2*b^2*c^2 + 16*a^3*c^3)*f)*g*h^2 - (24*(a*b^3*c^2 - 4*a^2*b*c^3)*d - 6*(5*a*b^4*c - 24*a^2*b^2*c^2 + 16*a^3*c^3)*e + 5*(7*a*b^5 - 40*a^2*b^3*c + 48*a^3*b*c^2)*f)*h^3 + (16*(b^2*c^4 - 4*a*c^5)*f*g^3 + 24*(2*(b^2*c^4 - 4*a*c^5)*e - 3*(b^3*c^3 - 4*a*b*c^4)*f)*g^2*h + 6*(8*(b^2*c^4 - 4*a*c^5)*d - 12*(b^3*c^3 - 4*a*b*c^4)*e + 3*(5*b^4*c^2 - 24*a*b^2*c^3 + 16*a^2*c^4)*f)*g*h^2 - (24*(b^3*c^3 - 4*a*b*c^4)*d - 6*(5*b^4*c^2 - 24*a*b^2*c^3 + 16*a^2*c^4)*e + 5*(7*b^5*c - 40*a*b^3*c^2 + 48*a^2*b*c^3)*f)*h^3)*x^2 + (16*(b^3*c^3 - 4*a*b*c^4)*f*g^3 + 24*(2*(b^3*c^3 - 4*a*b*c^4)*e - 3*(b^4*c^2 - 4*a*b^2*c^3)*f)*g^2*h + 6*(8*(b^3*c^3 - 4*a*b*c^4)*d - 12*(b^4*c^2 - 4*a*b^2*c^3)*e + 3*(5*b^5*c - 24*a*b^3*c^2 + 16*a^2*b*c^3)*f)*g*h^2 - (24*(b^4*c^2 - 4*a*b^2*c^3)*d - 6*(5*b^5*c - 24*a*b^3*c^2 + 16*a^2*b*c^3)*e + 5*(7*b^6 - 40*a*b^4*c + 48*a^2*b^2*c^2)*f)*h^3)*x)*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) + 4*(8*(b^2*c^4 - 4*a*c^5)*f*h^3*x^4 - 48*(b*c^5*d - 2*a*c^5*e + a*b*c^4*f)*g^3 + 72*(4*a*c^5*d - 2*a*b*c^4*e + (3*a*b^2*c^3 - 8*a^2*c^4)*f)*g^2*h - 18*(8*a*b*c^4*d - 4*(3*a*b^2*c^3 - 8*a^2*c^4)*e + (15*a*b^3*c^2 - 52*a^2*b*c^3)*f)*g*h^2 + (24*(3*a*b^2*c^3 - 8*a^2*c^4)*d - 6*(15*a*b^3*c^2 - 52*a^2*b*c^3)*e + (105*a*b^4*c - 460*a^2*b^2*c^2 + 256*a^3*c^3)*f)*h^3 + 2*(18*(b^2*c^4 - 4*a*c^5)*f*g*h^2 + (6*(b^2*c^4 - 4*a*c^5)*e - 7*(b^3*c^3 - 4*a*b*c^4)*f)*h^3)*x^3 + (72*(b^2*c^4 - 4*a*c^5)*f*g^2*h + 18*(4*(b^2*c^4 - 4*a*c^5)*e - 5*(b^3*c^3 - 4*a*b*c^4)*f)*g*h^2 + (24*(b^2*c^4 - 4*a*c^5)*d - 30*(b^3*c^3 - 4*a*b*c^4)*e + (35*b^4*c^2 - 172*a*b^2*c^3 + 128*a^2*c^4)*f)*h^3)*x^2 - (48*(2*c^6*d - b*c^5*e + (b^2*c^4 - 2*a*c^5)*f)*g^3 - 72*(2*b*c^5*d - 2*(b^2*c^4 - 2*a*c^5)*e + (3*b^3*c^3 - 10*a*b*c^4)*f)*g^2*h + 18*(8*(b^2*c^4 - 2*a*c^5)*d - 4*(3*b^3*c^3 - 10*a*b*c^4)*e + (15*b^4*c^2 - 62*a*b^2*c^3 + 24*a^2*c^4)*f)*g*h^2 - (24*(3*b^3*c^3 - 10*a*b*c^4)*d - 6*(15*b^4*c^2 - 62*a*b^2*c^3 + 24*a^2*c^4)*e + (105*b^5*c - 530*a*b^3*c^2 + 488*a^2*b*c^3)*f)*h^3)*x)*sqrt(c*x^2 + b*x + a))/(a*b^2*c^5 - 4*a^2*c^6 + (b^2*c^6 - 4*a*c^7)*x^2 + (b^3*c^5 - 4*a*b*c^6)*x), -1/48*(3*(16*(a*b^2*c^3 - 4*a^2*c^4)*f*g^3 + 24*(2*(a*b^2*c^3 - 4*a^2*c^4)*e - 3*(a*b^3*c^2 - 4*a^2*b*c^3)*f)*g^2*h + 6*(8*(a*b^2*c^3 - 4*a^2*c^4)*d - 12*(a*b^3*c^2 - 4*a^2*b*c^3)*e + 3*(5*a*b^4*c - 24*a^2*b^2*c^2 + 16*a^3*c^3)*f)*g*h^2 - (24*(a*b^3*c^2 - 4*a^2*b*c^3)*d - 6*(5*a*b^4*c - 24*a^2*b^2*c^2 + 16*a^3*c^3)*e + 5*(7*a*b^5 - 40*a^2*b^3*c + 48*a^3*b*c^2)*f)*h^3 + (16*(b^2*c^4 - 4*a*c^5)*f*g^3 + 24*(2*(b^2*c^4 - 4*a*c^5)*e - 3*(b^3*c^3 - 4*a*b*c^4)*f)*g^2*h + 6*(8*(b^2*c^4 - 4*a*c^5)*d - 12*(b^3*c^3 - 4*a*b*c^4)*e + 3*(5*b^4*c^2 - 24*a*b^2*c^3 + 16*a^2*c^4)*f)*g*h^2 - (24*(b^3*c^3 - 4*a*b*c^4)*d - 6*(5*b^4*c^2 - 24*a*b^2*c^3 + 16*a^2*c^4)*e + 5*(7*b^5*c - 40*a*b^3*c^2 + 48*a^2*b*c^3)*f)*h^3)*x^2 + (16*(b^3*c^3 - 4*a*b*c^4)*f*g^3 + 24*(2*(b^3*c^3 - 4*a*b*c^4)*e - 3*(b^4*c^2 - 4*a*b^2*c^3)*f)*g^2*h + 6*(8*(b^3*c^3 - 4*a*b*c^4)*d - 12*(b^4*c^2 - 4*a*b^2*c^3)*e + 3*(5*b^5*c - 24*a*b^3*c^2 + 16*a^2*b*c^3)*f)*g*h^2 - (24*(b^4*c^2 - 4*a*b^2*c^3)*d - 6*(5*b^5*c - 24*a*b^3*c^2 + 16*a^2*b*c^3)*e + 5*(7*b^6 - 40*a*b^4*c + 48*a^2*b^2*c^2)*f)*h^3)*x)*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)) - 2*(8*(b^2*c^4 - 4*a*c^5)*f*h^3*x^4 - 48*(b*c^5*d - 2*a*c^5*e + a*b*c^4*f)*g^3 + 72*(4*a*c^5*d - 2*a*b*c^4*e + (3*a*b^2*c^3 - 8*a^2*c^4)*f)*g^2*h - 18*(8*a*b*c^4*d - 4*(3*a*b^2*c^3 - 8*a^2*c^4)*e + (15*a*b^3*c^2 - 52*a^2*b*c^3)*f)*g*h^2 + (24*(3*a*b^2*c^3 - 8*a^2*c^4)*d - 6*(15*a*b^3*c^2 - 52*a^2*b*c^3)*e + (105*a*b^4*c - 460*a^2*b^2*c^2 + 256*a^3*c^3)*f)*h^3 + 2*(18*(b^2*c^4 - 4*a*c^5)*f*g*h^2 + (6*(b^2*c^4 - 4*a*c^5)*e - 7*(b^3*c^3 - 4*a*b*c^4)*f)*h^3)*x^3 + (72*(b^2*c^4 - 4*a*c^5)*f*g^2*h + 18*(4*(b^2*c^4 - 4*a*c^5)*e - 5*(b^3*c^3 - 4*a*b*c^4)*f)*g*h^2 + (24*(b^2*c^4 - 4*a*c^5)*d - 30*(b^3*c^3 - 4*a*b*c^4)*e + (35*b^4*c^2 - 172*a*b^2*c^3 + 128*a^2*c^4)*f)*h^3)*x^2 - (48*(2*c^6*d - b*c^5*e + (b^2*c^4 - 2*a*c^5)*f)*g^3 - 72*(2*b*c^5*d - 2*(b^2*c^4 - 2*a*c^5)*e + (3*b^3*c^3 - 10*a*b*c^4)*f)*g^2*h + 18*(8*(b^2*c^4 - 2*a*c^5)*d - 4*(3*b^3*c^3 - 10*a*b*c^4)*e + (15*b^4*c^2 - 62*a*b^2*c^3 + 24*a^2*c^4)*f)*g*h^2 - (24*(3*b^3*c^3 - 10*a*b*c^4)*d - 6*(15*b^4*c^2 - 62*a*b^2*c^3 + 24*a^2*c^4)*e + (105*b^5*c - 530*a*b^3*c^2 + 488*a^2*b*c^3)*f)*h^3)*x)*sqrt(c*x^2 + b*x + a))/(a*b^2*c^5 - 4*a^2*c^6 + (b^2*c^6 - 4*a*c^7)*x^2 + (b^3*c^5 - 4*a*b*c^6)*x)]","B",0
234,1,1769,0,28.874790," ","integrate((h*x+g)^2*(f*x^2+e*x+d)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left(8 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} f g^{2} + 8 \, {\left(2 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} e - 3 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} f\right)} g h + {\left(8 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d - 12 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} e + 3 \, {\left(5 \, a b^{4} - 24 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} f\right)} h^{2} + {\left(8 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} f g^{2} + 8 \, {\left(2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} f\right)} g h + {\left(8 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d - 12 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} e + 3 \, {\left(5 \, b^{4} c - 24 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} f\right)} h^{2}\right)} x^{2} + {\left(8 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} f g^{2} + 8 \, {\left(2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} e - 3 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} f\right)} g h + {\left(8 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d - 12 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} e + 3 \, {\left(5 \, b^{5} - 24 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} f\right)} h^{2}\right)} x\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 \, {\left(2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} f h^{2} x^{3} - 8 \, {\left(b c^{4} d - 2 \, a c^{4} e + a b c^{3} f\right)} g^{2} + 8 \, {\left(4 \, a c^{4} d - 2 \, a b c^{3} e + {\left(3 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} f\right)} g h - {\left(8 \, a b c^{3} d - 4 \, {\left(3 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} e + {\left(15 \, a b^{3} c - 52 \, a^{2} b c^{2}\right)} f\right)} h^{2} + {\left(8 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} f g h + {\left(4 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e - 5 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} f\right)} h^{2}\right)} x^{2} - {\left(8 \, {\left(2 \, c^{5} d - b c^{4} e + {\left(b^{2} c^{3} - 2 \, a c^{4}\right)} f\right)} g^{2} - 8 \, {\left(2 \, b c^{4} d - 2 \, {\left(b^{2} c^{3} - 2 \, a c^{4}\right)} e + {\left(3 \, b^{3} c^{2} - 10 \, a b c^{3}\right)} f\right)} g h + {\left(8 \, {\left(b^{2} c^{3} - 2 \, a c^{4}\right)} d - 4 \, {\left(3 \, b^{3} c^{2} - 10 \, a b c^{3}\right)} e + {\left(15 \, b^{4} c - 62 \, a b^{2} c^{2} + 24 \, a^{2} c^{3}\right)} f\right)} h^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{16 \, {\left(a b^{2} c^{4} - 4 \, a^{2} c^{5} + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} x^{2} + {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} x\right)}}, -\frac{{\left(8 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} f g^{2} + 8 \, {\left(2 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} e - 3 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} f\right)} g h + {\left(8 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d - 12 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} e + 3 \, {\left(5 \, a b^{4} - 24 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} f\right)} h^{2} + {\left(8 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} f g^{2} + 8 \, {\left(2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} f\right)} g h + {\left(8 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d - 12 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} e + 3 \, {\left(5 \, b^{4} c - 24 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} f\right)} h^{2}\right)} x^{2} + {\left(8 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} f g^{2} + 8 \, {\left(2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} e - 3 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} f\right)} g h + {\left(8 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d - 12 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} e + 3 \, {\left(5 \, b^{5} - 24 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} f\right)} h^{2}\right)} x\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 \, {\left(2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} f h^{2} x^{3} - 8 \, {\left(b c^{4} d - 2 \, a c^{4} e + a b c^{3} f\right)} g^{2} + 8 \, {\left(4 \, a c^{4} d - 2 \, a b c^{3} e + {\left(3 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} f\right)} g h - {\left(8 \, a b c^{3} d - 4 \, {\left(3 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} e + {\left(15 \, a b^{3} c - 52 \, a^{2} b c^{2}\right)} f\right)} h^{2} + {\left(8 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} f g h + {\left(4 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e - 5 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} f\right)} h^{2}\right)} x^{2} - {\left(8 \, {\left(2 \, c^{5} d - b c^{4} e + {\left(b^{2} c^{3} - 2 \, a c^{4}\right)} f\right)} g^{2} - 8 \, {\left(2 \, b c^{4} d - 2 \, {\left(b^{2} c^{3} - 2 \, a c^{4}\right)} e + {\left(3 \, b^{3} c^{2} - 10 \, a b c^{3}\right)} f\right)} g h + {\left(8 \, {\left(b^{2} c^{3} - 2 \, a c^{4}\right)} d - 4 \, {\left(3 \, b^{3} c^{2} - 10 \, a b c^{3}\right)} e + {\left(15 \, b^{4} c - 62 \, a b^{2} c^{2} + 24 \, a^{2} c^{3}\right)} f\right)} h^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{8 \, {\left(a b^{2} c^{4} - 4 \, a^{2} c^{5} + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} x^{2} + {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} x\right)}}\right]"," ",0,"[-1/16*((8*(a*b^2*c^2 - 4*a^2*c^3)*f*g^2 + 8*(2*(a*b^2*c^2 - 4*a^2*c^3)*e - 3*(a*b^3*c - 4*a^2*b*c^2)*f)*g*h + (8*(a*b^2*c^2 - 4*a^2*c^3)*d - 12*(a*b^3*c - 4*a^2*b*c^2)*e + 3*(5*a*b^4 - 24*a^2*b^2*c + 16*a^3*c^2)*f)*h^2 + (8*(b^2*c^3 - 4*a*c^4)*f*g^2 + 8*(2*(b^2*c^3 - 4*a*c^4)*e - 3*(b^3*c^2 - 4*a*b*c^3)*f)*g*h + (8*(b^2*c^3 - 4*a*c^4)*d - 12*(b^3*c^2 - 4*a*b*c^3)*e + 3*(5*b^4*c - 24*a*b^2*c^2 + 16*a^2*c^3)*f)*h^2)*x^2 + (8*(b^3*c^2 - 4*a*b*c^3)*f*g^2 + 8*(2*(b^3*c^2 - 4*a*b*c^3)*e - 3*(b^4*c - 4*a*b^2*c^2)*f)*g*h + (8*(b^3*c^2 - 4*a*b*c^3)*d - 12*(b^4*c - 4*a*b^2*c^2)*e + 3*(5*b^5 - 24*a*b^3*c + 16*a^2*b*c^2)*f)*h^2)*x)*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) - 4*(2*(b^2*c^3 - 4*a*c^4)*f*h^2*x^3 - 8*(b*c^4*d - 2*a*c^4*e + a*b*c^3*f)*g^2 + 8*(4*a*c^4*d - 2*a*b*c^3*e + (3*a*b^2*c^2 - 8*a^2*c^3)*f)*g*h - (8*a*b*c^3*d - 4*(3*a*b^2*c^2 - 8*a^2*c^3)*e + (15*a*b^3*c - 52*a^2*b*c^2)*f)*h^2 + (8*(b^2*c^3 - 4*a*c^4)*f*g*h + (4*(b^2*c^3 - 4*a*c^4)*e - 5*(b^3*c^2 - 4*a*b*c^3)*f)*h^2)*x^2 - (8*(2*c^5*d - b*c^4*e + (b^2*c^3 - 2*a*c^4)*f)*g^2 - 8*(2*b*c^4*d - 2*(b^2*c^3 - 2*a*c^4)*e + (3*b^3*c^2 - 10*a*b*c^3)*f)*g*h + (8*(b^2*c^3 - 2*a*c^4)*d - 4*(3*b^3*c^2 - 10*a*b*c^3)*e + (15*b^4*c - 62*a*b^2*c^2 + 24*a^2*c^3)*f)*h^2)*x)*sqrt(c*x^2 + b*x + a))/(a*b^2*c^4 - 4*a^2*c^5 + (b^2*c^5 - 4*a*c^6)*x^2 + (b^3*c^4 - 4*a*b*c^5)*x), -1/8*((8*(a*b^2*c^2 - 4*a^2*c^3)*f*g^2 + 8*(2*(a*b^2*c^2 - 4*a^2*c^3)*e - 3*(a*b^3*c - 4*a^2*b*c^2)*f)*g*h + (8*(a*b^2*c^2 - 4*a^2*c^3)*d - 12*(a*b^3*c - 4*a^2*b*c^2)*e + 3*(5*a*b^4 - 24*a^2*b^2*c + 16*a^3*c^2)*f)*h^2 + (8*(b^2*c^3 - 4*a*c^4)*f*g^2 + 8*(2*(b^2*c^3 - 4*a*c^4)*e - 3*(b^3*c^2 - 4*a*b*c^3)*f)*g*h + (8*(b^2*c^3 - 4*a*c^4)*d - 12*(b^3*c^2 - 4*a*b*c^3)*e + 3*(5*b^4*c - 24*a*b^2*c^2 + 16*a^2*c^3)*f)*h^2)*x^2 + (8*(b^3*c^2 - 4*a*b*c^3)*f*g^2 + 8*(2*(b^3*c^2 - 4*a*b*c^3)*e - 3*(b^4*c - 4*a*b^2*c^2)*f)*g*h + (8*(b^3*c^2 - 4*a*b*c^3)*d - 12*(b^4*c - 4*a*b^2*c^2)*e + 3*(5*b^5 - 24*a*b^3*c + 16*a^2*b*c^2)*f)*h^2)*x)*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)) - 2*(2*(b^2*c^3 - 4*a*c^4)*f*h^2*x^3 - 8*(b*c^4*d - 2*a*c^4*e + a*b*c^3*f)*g^2 + 8*(4*a*c^4*d - 2*a*b*c^3*e + (3*a*b^2*c^2 - 8*a^2*c^3)*f)*g*h - (8*a*b*c^3*d - 4*(3*a*b^2*c^2 - 8*a^2*c^3)*e + (15*a*b^3*c - 52*a^2*b*c^2)*f)*h^2 + (8*(b^2*c^3 - 4*a*c^4)*f*g*h + (4*(b^2*c^3 - 4*a*c^4)*e - 5*(b^3*c^2 - 4*a*b*c^3)*f)*h^2)*x^2 - (8*(2*c^5*d - b*c^4*e + (b^2*c^3 - 2*a*c^4)*f)*g^2 - 8*(2*b*c^4*d - 2*(b^2*c^3 - 2*a*c^4)*e + (3*b^3*c^2 - 10*a*b*c^3)*f)*g*h + (8*(b^2*c^3 - 2*a*c^4)*d - 4*(3*b^3*c^2 - 10*a*b*c^3)*e + (15*b^4*c - 62*a*b^2*c^2 + 24*a^2*c^3)*f)*h^2)*x)*sqrt(c*x^2 + b*x + a))/(a*b^2*c^4 - 4*a^2*c^5 + (b^2*c^5 - 4*a*c^6)*x^2 + (b^3*c^4 - 4*a*b*c^5)*x)]","B",0
235,1,905,0,19.703756," ","integrate((h*x+g)*(f*x^2+e*x+d)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left(2 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} f g + {\left(2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} f g + {\left(2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e - 3 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} f\right)} h\right)} x^{2} + {\left(2 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} e - 3 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} f\right)} h + {\left(2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} f g + {\left(2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} e - 3 \, {\left(b^{4} - 4 \, a b^{2} c\right)} f\right)} h\right)} x\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 \, {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} f h x^{2} - 2 \, {\left(b c^{3} d - 2 \, a c^{3} e + a b c^{2} f\right)} g + {\left(4 \, a c^{3} d - 2 \, a b c^{2} e + {\left(3 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} f\right)} h - {\left(2 \, {\left(2 \, c^{4} d - b c^{3} e + {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} f\right)} g - {\left(2 \, b c^{3} d - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} e + {\left(3 \, b^{3} c - 10 \, a b c^{2}\right)} f\right)} h\right)} x\right)} \sqrt{c x^{2} + b x + a}}{4 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4} + {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} x^{2} + {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} x\right)}}, -\frac{{\left(2 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} f g + {\left(2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} f g + {\left(2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e - 3 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} f\right)} h\right)} x^{2} + {\left(2 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} e - 3 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} f\right)} h + {\left(2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} f g + {\left(2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} e - 3 \, {\left(b^{4} - 4 \, a b^{2} c\right)} f\right)} h\right)} x\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 \, {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} f h x^{2} - 2 \, {\left(b c^{3} d - 2 \, a c^{3} e + a b c^{2} f\right)} g + {\left(4 \, a c^{3} d - 2 \, a b c^{2} e + {\left(3 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} f\right)} h - {\left(2 \, {\left(2 \, c^{4} d - b c^{3} e + {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} f\right)} g - {\left(2 \, b c^{3} d - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} e + {\left(3 \, b^{3} c - 10 \, a b c^{2}\right)} f\right)} h\right)} x\right)} \sqrt{c x^{2} + b x + a}}{2 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4} + {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} x^{2} + {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} x\right)}}\right]"," ",0,"[-1/4*((2*(a*b^2*c - 4*a^2*c^2)*f*g + (2*(b^2*c^2 - 4*a*c^3)*f*g + (2*(b^2*c^2 - 4*a*c^3)*e - 3*(b^3*c - 4*a*b*c^2)*f)*h)*x^2 + (2*(a*b^2*c - 4*a^2*c^2)*e - 3*(a*b^3 - 4*a^2*b*c)*f)*h + (2*(b^3*c - 4*a*b*c^2)*f*g + (2*(b^3*c - 4*a*b*c^2)*e - 3*(b^4 - 4*a*b^2*c)*f)*h)*x)*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) - 4*((b^2*c^2 - 4*a*c^3)*f*h*x^2 - 2*(b*c^3*d - 2*a*c^3*e + a*b*c^2*f)*g + (4*a*c^3*d - 2*a*b*c^2*e + (3*a*b^2*c - 8*a^2*c^2)*f)*h - (2*(2*c^4*d - b*c^3*e + (b^2*c^2 - 2*a*c^3)*f)*g - (2*b*c^3*d - 2*(b^2*c^2 - 2*a*c^3)*e + (3*b^3*c - 10*a*b*c^2)*f)*h)*x)*sqrt(c*x^2 + b*x + a))/(a*b^2*c^3 - 4*a^2*c^4 + (b^2*c^4 - 4*a*c^5)*x^2 + (b^3*c^3 - 4*a*b*c^4)*x), -1/2*((2*(a*b^2*c - 4*a^2*c^2)*f*g + (2*(b^2*c^2 - 4*a*c^3)*f*g + (2*(b^2*c^2 - 4*a*c^3)*e - 3*(b^3*c - 4*a*b*c^2)*f)*h)*x^2 + (2*(a*b^2*c - 4*a^2*c^2)*e - 3*(a*b^3 - 4*a^2*b*c)*f)*h + (2*(b^3*c - 4*a*b*c^2)*f*g + (2*(b^3*c - 4*a*b*c^2)*e - 3*(b^4 - 4*a*b^2*c)*f)*h)*x)*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)) - 2*((b^2*c^2 - 4*a*c^3)*f*h*x^2 - 2*(b*c^3*d - 2*a*c^3*e + a*b*c^2*f)*g + (4*a*c^3*d - 2*a*b*c^2*e + (3*a*b^2*c - 8*a^2*c^2)*f)*h - (2*(2*c^4*d - b*c^3*e + (b^2*c^2 - 2*a*c^3)*f)*g - (2*b*c^3*d - 2*(b^2*c^2 - 2*a*c^3)*e + (3*b^3*c - 10*a*b*c^2)*f)*h)*x)*sqrt(c*x^2 + b*x + a))/(a*b^2*c^3 - 4*a^2*c^4 + (b^2*c^4 - 4*a*c^5)*x^2 + (b^3*c^3 - 4*a*b*c^4)*x)]","B",0
236,1,429,0,2.453591," ","integrate((f*x^2+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)} f x^{2} + {\left(b^{3} - 4 \, a b c\right)} f x + {\left(a b^{2} - 4 \, a^{2} c\right)} f\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 \, {\left(b c^{2} d - 2 \, a c^{2} e + a b c f + {\left(2 \, c^{3} d - b c^{2} e + {\left(b^{2} c - 2 \, a c^{2}\right)} f\right)} x\right)} \sqrt{c x^{2} + b x + a}}{2 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{2} + {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x\right)}}, -\frac{{\left({\left(b^{2} c - 4 \, a c^{2}\right)} f x^{2} + {\left(b^{3} - 4 \, a b c\right)} f x + {\left(a b^{2} - 4 \, a^{2} c\right)} f\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 \, {\left(b c^{2} d - 2 \, a c^{2} e + a b c f + {\left(2 \, c^{3} d - b c^{2} e + {\left(b^{2} c - 2 \, a c^{2}\right)} f\right)} x\right)} \sqrt{c x^{2} + b x + a}}{a b^{2} c^{2} - 4 \, a^{2} c^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{2} + {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x}\right]"," ",0,"[1/2*(((b^2*c - 4*a*c^2)*f*x^2 + (b^3 - 4*a*b*c)*f*x + (a*b^2 - 4*a^2*c)*f)*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) - 4*(b*c^2*d - 2*a*c^2*e + a*b*c*f + (2*c^3*d - b*c^2*e + (b^2*c - 2*a*c^2)*f)*x)*sqrt(c*x^2 + b*x + a))/(a*b^2*c^2 - 4*a^2*c^3 + (b^2*c^3 - 4*a*c^4)*x^2 + (b^3*c^2 - 4*a*b*c^3)*x), -(((b^2*c - 4*a*c^2)*f*x^2 + (b^3 - 4*a*b*c)*f*x + (a*b^2 - 4*a^2*c)*f)*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)) + 2*(b*c^2*d - 2*a*c^2*e + a*b*c*f + (2*c^3*d - b*c^2*e + (b^2*c - 2*a*c^2)*f)*x)*sqrt(c*x^2 + b*x + a))/(a*b^2*c^2 - 4*a^2*c^3 + (b^2*c^3 - 4*a*c^4)*x^2 + (b^3*c^2 - 4*a*b*c^3)*x)]","B",0
237,1,1905,0,53.930731," ","integrate((f*x^2+e*x+d)/(h*x+g)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(a b^{2} - 4 \, a^{2} c\right)} f g^{2} - {\left(a b^{2} - 4 \, a^{2} c\right)} e g h + {\left(a b^{2} - 4 \, a^{2} c\right)} d h^{2} + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} f g^{2} - {\left(b^{2} c - 4 \, a c^{2}\right)} e g h + {\left(b^{2} c - 4 \, a c^{2}\right)} d h^{2}\right)} x^{2} + {\left({\left(b^{3} - 4 \, a b c\right)} f g^{2} - {\left(b^{3} - 4 \, a b c\right)} e g h + {\left(b^{3} - 4 \, a b c\right)} d h^{2}\right)} x\right)} \sqrt{c g^{2} - b g h + a h^{2}} \log\left(\frac{8 \, a b g h - 8 \, a^{2} h^{2} - {\left(b^{2} + 4 \, a c\right)} g^{2} - {\left(8 \, c^{2} g^{2} - 8 \, b c g h + {\left(b^{2} + 4 \, a c\right)} h^{2}\right)} x^{2} - 4 \, \sqrt{c g^{2} - b g h + a h^{2}} \sqrt{c x^{2} + b x + a} {\left(b g - 2 \, a h + {\left(2 \, c g - b h\right)} x\right)} - 2 \, {\left(4 \, b c g^{2} + 4 \, a b h^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} g h\right)} x}{h^{2} x^{2} + 2 \, g h x + g^{2}}\right) - 4 \, {\left({\left(b c^{2} d - 2 \, a c^{2} e + a b c f\right)} g^{3} + {\left(3 \, a b c e - 2 \, {\left(b^{2} c - a c^{2}\right)} d - {\left(a b^{2} + 2 \, a^{2} c\right)} f\right)} g^{2} h + {\left(3 \, a^{2} b f + {\left(b^{3} - a b c\right)} d - {\left(a b^{2} + 2 \, a^{2} c\right)} e\right)} g h^{2} + {\left(a^{2} b e - 2 \, a^{3} f - {\left(a b^{2} - 2 \, a^{2} c\right)} d\right)} h^{3} + {\left({\left(2 \, c^{3} d - b c^{2} e + {\left(b^{2} c - 2 \, a c^{2}\right)} f\right)} g^{3} - {\left(3 \, b c^{2} d - {\left(b^{2} c + 2 \, a c^{2}\right)} e + {\left(b^{3} - a b c\right)} f\right)} g^{2} h - {\left(3 \, a b c e - {\left(b^{2} c + 2 \, a c^{2}\right)} d - 2 \, {\left(a b^{2} - a^{2} c\right)} f\right)} g h^{2} - {\left(a b c d - 2 \, a^{2} c e + a^{2} b f\right)} h^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{2 \, {\left({\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} g^{4} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} g^{3} h + {\left(a b^{4} - 2 \, a^{2} b^{2} c - 8 \, a^{3} c^{2}\right)} g^{2} h^{2} - 2 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} g h^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} h^{4} + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} g^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} g^{3} h + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} g^{2} h^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} g h^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} h^{4}\right)} x^{2} + {\left({\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} g^{4} - 2 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} g^{3} h + {\left(b^{5} - 2 \, a b^{3} c - 8 \, a^{2} b c^{2}\right)} g^{2} h^{2} - 2 \, {\left(a b^{4} - 4 \, a^{2} b^{2} c\right)} g h^{3} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} h^{4}\right)} x\right)}}, \frac{{\left({\left(a b^{2} - 4 \, a^{2} c\right)} f g^{2} - {\left(a b^{2} - 4 \, a^{2} c\right)} e g h + {\left(a b^{2} - 4 \, a^{2} c\right)} d h^{2} + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} f g^{2} - {\left(b^{2} c - 4 \, a c^{2}\right)} e g h + {\left(b^{2} c - 4 \, a c^{2}\right)} d h^{2}\right)} x^{2} + {\left({\left(b^{3} - 4 \, a b c\right)} f g^{2} - {\left(b^{3} - 4 \, a b c\right)} e g h + {\left(b^{3} - 4 \, a b c\right)} d h^{2}\right)} x\right)} \sqrt{-c g^{2} + b g h - a h^{2}} \arctan\left(-\frac{\sqrt{-c g^{2} + b g h - a h^{2}} \sqrt{c x^{2} + b x + a} {\left(b g - 2 \, a h + {\left(2 \, c g - b h\right)} x\right)}}{2 \, {\left(a c g^{2} - a b g h + a^{2} h^{2} + {\left(c^{2} g^{2} - b c g h + a c h^{2}\right)} x^{2} + {\left(b c g^{2} - b^{2} g h + a b h^{2}\right)} x\right)}}\right) - 2 \, {\left({\left(b c^{2} d - 2 \, a c^{2} e + a b c f\right)} g^{3} + {\left(3 \, a b c e - 2 \, {\left(b^{2} c - a c^{2}\right)} d - {\left(a b^{2} + 2 \, a^{2} c\right)} f\right)} g^{2} h + {\left(3 \, a^{2} b f + {\left(b^{3} - a b c\right)} d - {\left(a b^{2} + 2 \, a^{2} c\right)} e\right)} g h^{2} + {\left(a^{2} b e - 2 \, a^{3} f - {\left(a b^{2} - 2 \, a^{2} c\right)} d\right)} h^{3} + {\left({\left(2 \, c^{3} d - b c^{2} e + {\left(b^{2} c - 2 \, a c^{2}\right)} f\right)} g^{3} - {\left(3 \, b c^{2} d - {\left(b^{2} c + 2 \, a c^{2}\right)} e + {\left(b^{3} - a b c\right)} f\right)} g^{2} h - {\left(3 \, a b c e - {\left(b^{2} c + 2 \, a c^{2}\right)} d - 2 \, {\left(a b^{2} - a^{2} c\right)} f\right)} g h^{2} - {\left(a b c d - 2 \, a^{2} c e + a^{2} b f\right)} h^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{{\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} g^{4} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} g^{3} h + {\left(a b^{4} - 2 \, a^{2} b^{2} c - 8 \, a^{3} c^{2}\right)} g^{2} h^{2} - 2 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} g h^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} h^{4} + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} g^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} g^{3} h + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} g^{2} h^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} g h^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} h^{4}\right)} x^{2} + {\left({\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} g^{4} - 2 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} g^{3} h + {\left(b^{5} - 2 \, a b^{3} c - 8 \, a^{2} b c^{2}\right)} g^{2} h^{2} - 2 \, {\left(a b^{4} - 4 \, a^{2} b^{2} c\right)} g h^{3} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} h^{4}\right)} x}\right]"," ",0,"[1/2*(((a*b^2 - 4*a^2*c)*f*g^2 - (a*b^2 - 4*a^2*c)*e*g*h + (a*b^2 - 4*a^2*c)*d*h^2 + ((b^2*c - 4*a*c^2)*f*g^2 - (b^2*c - 4*a*c^2)*e*g*h + (b^2*c - 4*a*c^2)*d*h^2)*x^2 + ((b^3 - 4*a*b*c)*f*g^2 - (b^3 - 4*a*b*c)*e*g*h + (b^3 - 4*a*b*c)*d*h^2)*x)*sqrt(c*g^2 - b*g*h + a*h^2)*log((8*a*b*g*h - 8*a^2*h^2 - (b^2 + 4*a*c)*g^2 - (8*c^2*g^2 - 8*b*c*g*h + (b^2 + 4*a*c)*h^2)*x^2 - 4*sqrt(c*g^2 - b*g*h + a*h^2)*sqrt(c*x^2 + b*x + a)*(b*g - 2*a*h + (2*c*g - b*h)*x) - 2*(4*b*c*g^2 + 4*a*b*h^2 - (3*b^2 + 4*a*c)*g*h)*x)/(h^2*x^2 + 2*g*h*x + g^2)) - 4*((b*c^2*d - 2*a*c^2*e + a*b*c*f)*g^3 + (3*a*b*c*e - 2*(b^2*c - a*c^2)*d - (a*b^2 + 2*a^2*c)*f)*g^2*h + (3*a^2*b*f + (b^3 - a*b*c)*d - (a*b^2 + 2*a^2*c)*e)*g*h^2 + (a^2*b*e - 2*a^3*f - (a*b^2 - 2*a^2*c)*d)*h^3 + ((2*c^3*d - b*c^2*e + (b^2*c - 2*a*c^2)*f)*g^3 - (3*b*c^2*d - (b^2*c + 2*a*c^2)*e + (b^3 - a*b*c)*f)*g^2*h - (3*a*b*c*e - (b^2*c + 2*a*c^2)*d - 2*(a*b^2 - a^2*c)*f)*g*h^2 - (a*b*c*d - 2*a^2*c*e + a^2*b*f)*h^3)*x)*sqrt(c*x^2 + b*x + a))/((a*b^2*c^2 - 4*a^2*c^3)*g^4 - 2*(a*b^3*c - 4*a^2*b*c^2)*g^3*h + (a*b^4 - 2*a^2*b^2*c - 8*a^3*c^2)*g^2*h^2 - 2*(a^2*b^3 - 4*a^3*b*c)*g*h^3 + (a^3*b^2 - 4*a^4*c)*h^4 + ((b^2*c^3 - 4*a*c^4)*g^4 - 2*(b^3*c^2 - 4*a*b*c^3)*g^3*h + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*g^2*h^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*g*h^3 + (a^2*b^2*c - 4*a^3*c^2)*h^4)*x^2 + ((b^3*c^2 - 4*a*b*c^3)*g^4 - 2*(b^4*c - 4*a*b^2*c^2)*g^3*h + (b^5 - 2*a*b^3*c - 8*a^2*b*c^2)*g^2*h^2 - 2*(a*b^4 - 4*a^2*b^2*c)*g*h^3 + (a^2*b^3 - 4*a^3*b*c)*h^4)*x), (((a*b^2 - 4*a^2*c)*f*g^2 - (a*b^2 - 4*a^2*c)*e*g*h + (a*b^2 - 4*a^2*c)*d*h^2 + ((b^2*c - 4*a*c^2)*f*g^2 - (b^2*c - 4*a*c^2)*e*g*h + (b^2*c - 4*a*c^2)*d*h^2)*x^2 + ((b^3 - 4*a*b*c)*f*g^2 - (b^3 - 4*a*b*c)*e*g*h + (b^3 - 4*a*b*c)*d*h^2)*x)*sqrt(-c*g^2 + b*g*h - a*h^2)*arctan(-1/2*sqrt(-c*g^2 + b*g*h - a*h^2)*sqrt(c*x^2 + b*x + a)*(b*g - 2*a*h + (2*c*g - b*h)*x)/(a*c*g^2 - a*b*g*h + a^2*h^2 + (c^2*g^2 - b*c*g*h + a*c*h^2)*x^2 + (b*c*g^2 - b^2*g*h + a*b*h^2)*x)) - 2*((b*c^2*d - 2*a*c^2*e + a*b*c*f)*g^3 + (3*a*b*c*e - 2*(b^2*c - a*c^2)*d - (a*b^2 + 2*a^2*c)*f)*g^2*h + (3*a^2*b*f + (b^3 - a*b*c)*d - (a*b^2 + 2*a^2*c)*e)*g*h^2 + (a^2*b*e - 2*a^3*f - (a*b^2 - 2*a^2*c)*d)*h^3 + ((2*c^3*d - b*c^2*e + (b^2*c - 2*a*c^2)*f)*g^3 - (3*b*c^2*d - (b^2*c + 2*a*c^2)*e + (b^3 - a*b*c)*f)*g^2*h - (3*a*b*c*e - (b^2*c + 2*a*c^2)*d - 2*(a*b^2 - a^2*c)*f)*g*h^2 - (a*b*c*d - 2*a^2*c*e + a^2*b*f)*h^3)*x)*sqrt(c*x^2 + b*x + a))/((a*b^2*c^2 - 4*a^2*c^3)*g^4 - 2*(a*b^3*c - 4*a^2*b*c^2)*g^3*h + (a*b^4 - 2*a^2*b^2*c - 8*a^3*c^2)*g^2*h^2 - 2*(a^2*b^3 - 4*a^3*b*c)*g*h^3 + (a^3*b^2 - 4*a^4*c)*h^4 + ((b^2*c^3 - 4*a*c^4)*g^4 - 2*(b^3*c^2 - 4*a*b*c^3)*g^3*h + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*g^2*h^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*g*h^3 + (a^2*b^2*c - 4*a^3*c^2)*h^4)*x^2 + ((b^3*c^2 - 4*a*b*c^3)*g^4 - 2*(b^4*c - 4*a*b^2*c^2)*g^3*h + (b^5 - 2*a*b^3*c - 8*a^2*b*c^2)*g^2*h^2 - 2*(a*b^4 - 4*a^2*b^2*c)*g*h^3 + (a^2*b^3 - 4*a^3*b*c)*h^4)*x)]","B",0
238,-1,0,0,0.000000," ","integrate((f*x^2+e*x+d)/(h*x+g)^2/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
239,-1,0,0,0.000000," ","integrate((f*x^2+e*x+d)/(h*x+g)^3/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
240,1,73,0,0.680434," ","integrate((1+2*x)^3*(4*x^2+3*x+1)/(3*x^2-x+2)^(1/2),x, algorithm=""fricas"")","\frac{1}{3240} \, {\left(6912 \, x^{4} + 22032 \, x^{3} + 26904 \, x^{2} + 7538 \, x - 22383\right)} \sqrt{3 \, x^{2} - x + 2} + \frac{9211}{7776} \, \sqrt{3} \log\left(4 \, \sqrt{3} \sqrt{3 \, x^{2} - x + 2} {\left(6 \, x - 1\right)} - 72 \, x^{2} + 24 \, x - 25\right)"," ",0,"1/3240*(6912*x^4 + 22032*x^3 + 26904*x^2 + 7538*x - 22383)*sqrt(3*x^2 - x + 2) + 9211/7776*sqrt(3)*log(4*sqrt(3)*sqrt(3*x^2 - x + 2)*(6*x - 1) - 72*x^2 + 24*x - 25)","A",0
241,1,68,0,1.493562," ","integrate((1+2*x)^2*(4*x^2+3*x+1)/(3*x^2-x+2)^(1/2),x, algorithm=""fricas"")","\frac{1}{324} \, {\left(432 \, x^{3} + 1176 \, x^{2} + 1138 \, x - 243\right)} \sqrt{3 \, x^{2} - x + 2} + \frac{4147}{3888} \, \sqrt{3} \log\left(4 \, \sqrt{3} \sqrt{3 \, x^{2} - x + 2} {\left(6 \, x - 1\right)} - 72 \, x^{2} + 24 \, x - 25\right)"," ",0,"1/324*(432*x^3 + 1176*x^2 + 1138*x - 243)*sqrt(3*x^2 - x + 2) + 4147/3888*sqrt(3)*log(4*sqrt(3)*sqrt(3*x^2 - x + 2)*(6*x - 1) - 72*x^2 + 24*x - 25)","A",0
242,1,63,0,0.691252," ","integrate((1+2*x)*(4*x^2+3*x+1)/(3*x^2-x+2)^(1/2),x, algorithm=""fricas"")","\frac{1}{54} \, {\left(48 \, x^{2} + 110 \, x + 81\right)} \sqrt{3 \, x^{2} - x + 2} + \frac{251}{648} \, \sqrt{3} \log\left(4 \, \sqrt{3} \sqrt{3 \, x^{2} - x + 2} {\left(6 \, x - 1\right)} - 72 \, x^{2} + 24 \, x - 25\right)"," ",0,"1/54*(48*x^2 + 110*x + 81)*sqrt(3*x^2 - x + 2) + 251/648*sqrt(3)*log(4*sqrt(3)*sqrt(3*x^2 - x + 2)*(6*x - 1) - 72*x^2 + 24*x - 25)","A",0
243,1,105,0,1.528633," ","integrate((4*x^2+3*x+1)/(1+2*x)/(3*x^2-x+2)^(1/2),x, algorithm=""fricas"")","\frac{5}{36} \, \sqrt{3} \log\left(-4 \, \sqrt{3} \sqrt{3 \, x^{2} - x + 2} {\left(6 \, x - 1\right)} - 72 \, x^{2} + 24 \, x - 25\right) + \frac{1}{52} \, \sqrt{13} \log\left(-\frac{4 \, \sqrt{13} \sqrt{3 \, x^{2} - x + 2} {\left(8 \, x - 9\right)} + 220 \, x^{2} - 196 \, x + 185}{4 \, x^{2} + 4 \, x + 1}\right) + \frac{2}{3} \, \sqrt{3 \, x^{2} - x + 2}"," ",0,"5/36*sqrt(3)*log(-4*sqrt(3)*sqrt(3*x^2 - x + 2)*(6*x - 1) - 72*x^2 + 24*x - 25) + 1/52*sqrt(13)*log(-(4*sqrt(13)*sqrt(3*x^2 - x + 2)*(8*x - 9) + 220*x^2 - 196*x + 185)/(4*x^2 + 4*x + 1)) + 2/3*sqrt(3*x^2 - x + 2)","A",0
244,1,123,0,0.991465," ","integrate((4*x^2+3*x+1)/(1+2*x)^2/(3*x^2-x+2)^(1/2),x, algorithm=""fricas"")","\frac{338 \, \sqrt{3} {\left(2 \, x + 1\right)} \log\left(-4 \, \sqrt{3} \sqrt{3 \, x^{2} - x + 2} {\left(6 \, x - 1\right)} - 72 \, x^{2} + 24 \, x - 25\right) + 27 \, \sqrt{13} {\left(2 \, x + 1\right)} \log\left(\frac{4 \, \sqrt{13} \sqrt{3 \, x^{2} - x + 2} {\left(8 \, x - 9\right)} - 220 \, x^{2} + 196 \, x - 185}{4 \, x^{2} + 4 \, x + 1}\right) - 156 \, \sqrt{3 \, x^{2} - x + 2}}{2028 \, {\left(2 \, x + 1\right)}}"," ",0,"1/2028*(338*sqrt(3)*(2*x + 1)*log(-4*sqrt(3)*sqrt(3*x^2 - x + 2)*(6*x - 1) - 72*x^2 + 24*x - 25) + 27*sqrt(13)*(2*x + 1)*log((4*sqrt(13)*sqrt(3*x^2 - x + 2)*(8*x - 9) - 220*x^2 + 196*x - 185)/(4*x^2 + 4*x + 1)) - 156*sqrt(3*x^2 - x + 2))/(2*x + 1)","A",0
245,1,96,0,1.497549," ","integrate((4*x^2+3*x+1)/(1+2*x)^3/(3*x^2-x+2)^(1/2),x, algorithm=""fricas"")","\frac{581 \, \sqrt{13} {\left(4 \, x^{2} + 4 \, x + 1\right)} \log\left(-\frac{4 \, \sqrt{13} \sqrt{3 \, x^{2} - x + 2} {\left(8 \, x - 9\right)} + 220 \, x^{2} - 196 \, x + 185}{4 \, x^{2} + 4 \, x + 1}\right) + 52 \, \sqrt{3 \, x^{2} - x + 2} {\left(28 \, x + 1\right)}}{17576 \, {\left(4 \, x^{2} + 4 \, x + 1\right)}}"," ",0,"1/17576*(581*sqrt(13)*(4*x^2 + 4*x + 1)*log(-(4*sqrt(13)*sqrt(3*x^2 - x + 2)*(8*x - 9) + 220*x^2 - 196*x + 185)/(4*x^2 + 4*x + 1)) + 52*sqrt(3*x^2 - x + 2)*(28*x + 1))/(4*x^2 + 4*x + 1)","A",0
246,1,97,0,0.865863," ","integrate((1+2*x)^3*(4*x^2+3*x+1)/(3*x^2-x+2)^(3/2),x, algorithm=""fricas"")","\frac{8119 \, \sqrt{3} {\left(3 \, x^{2} - x + 2\right)} \log\left(4 \, \sqrt{3} \sqrt{3 \, x^{2} - x + 2} {\left(6 \, x - 1\right)} - 72 \, x^{2} + 24 \, x - 25\right) + 12 \, {\left(3312 \, x^{4} + 13110 \, x^{3} + 23207 \, x^{2} - 2974 \, x + 29997\right)} \sqrt{3 \, x^{2} - x + 2}}{11178 \, {\left(3 \, x^{2} - x + 2\right)}}"," ",0,"1/11178*(8119*sqrt(3)*(3*x^2 - x + 2)*log(4*sqrt(3)*sqrt(3*x^2 - x + 2)*(6*x - 1) - 72*x^2 + 24*x - 25) + 12*(3312*x^4 + 13110*x^3 + 23207*x^2 - 2974*x + 29997)*sqrt(3*x^2 - x + 2))/(3*x^2 - x + 2)","A",0
247,1,92,0,1.433188," ","integrate((1+2*x)^2*(4*x^2+3*x+1)/(3*x^2-x+2)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(368 \, \sqrt{3} {\left(3 \, x^{2} - x + 2\right)} \log\left(-4 \, \sqrt{3} \sqrt{3 \, x^{2} - x + 2} {\left(6 \, x - 1\right)} - 72 \, x^{2} + 24 \, x - 25\right) + 3 \, {\left(276 \, x^{3} + 1196 \, x^{2} - 1003 \, x + 1275\right)} \sqrt{3 \, x^{2} - x + 2}\right)}}{621 \, {\left(3 \, x^{2} - x + 2\right)}}"," ",0,"2/621*(368*sqrt(3)*(3*x^2 - x + 2)*log(-4*sqrt(3)*sqrt(3*x^2 - x + 2)*(6*x - 1) - 72*x^2 + 24*x - 25) + 3*(276*x^3 + 1196*x^2 - 1003*x + 1275)*sqrt(3*x^2 - x + 2))/(3*x^2 - x + 2)","A",0
248,1,87,0,0.989752," ","integrate((1+2*x)*(4*x^2+3*x+1)/(3*x^2-x+2)^(3/2),x, algorithm=""fricas"")","\frac{161 \, \sqrt{3} {\left(3 \, x^{2} - x + 2\right)} \log\left(-4 \, \sqrt{3} \sqrt{3 \, x^{2} - x + 2} {\left(6 \, x - 1\right)} - 72 \, x^{2} + 24 \, x - 25\right) + 6 \, {\left(92 \, x^{2} - 153 \, x + 37\right)} \sqrt{3 \, x^{2} - x + 2}}{207 \, {\left(3 \, x^{2} - x + 2\right)}}"," ",0,"1/207*(161*sqrt(3)*(3*x^2 - x + 2)*log(-4*sqrt(3)*sqrt(3*x^2 - x + 2)*(6*x - 1) - 72*x^2 + 24*x - 25) + 6*(92*x^2 - 153*x + 37)*sqrt(3*x^2 - x + 2))/(3*x^2 - x + 2)","A",0
249,1,96,0,1.419894," ","integrate((4*x^2+3*x+1)/(1+2*x)/(3*x^2-x+2)^(3/2),x, algorithm=""fricas"")","\frac{23 \, \sqrt{13} {\left(3 \, x^{2} - x + 2\right)} \log\left(-\frac{4 \, \sqrt{13} \sqrt{3 \, x^{2} - x + 2} {\left(8 \, x - 9\right)} + 220 \, x^{2} - 196 \, x + 185}{4 \, x^{2} + 4 \, x + 1}\right) + 26 \, \sqrt{3 \, x^{2} - x + 2} {\left(77 \, x - 101\right)}}{3887 \, {\left(3 \, x^{2} - x + 2\right)}}"," ",0,"1/3887*(23*sqrt(13)*(3*x^2 - x + 2)*log(-(4*sqrt(13)*sqrt(3*x^2 - x + 2)*(8*x - 9) + 220*x^2 - 196*x + 185)/(4*x^2 + 4*x + 1)) + 26*sqrt(3*x^2 - x + 2)*(77*x - 101))/(3*x^2 - x + 2)","A",0
250,1,106,0,1.054990," ","integrate((4*x^2+3*x+1)/(1+2*x)^2/(3*x^2-x+2)^(3/2),x, algorithm=""fricas"")","\frac{23 \, \sqrt{13} {\left(6 \, x^{3} + x^{2} + 3 \, x + 2\right)} \log\left(\frac{4 \, \sqrt{13} \sqrt{3 \, x^{2} - x + 2} {\left(8 \, x - 9\right)} - 220 \, x^{2} + 196 \, x - 185}{4 \, x^{2} + 4 \, x + 1}\right) + 26 \, {\left(1536 \, x^{2} + 489 \, x - 289\right)} \sqrt{3 \, x^{2} - x + 2}}{50531 \, {\left(6 \, x^{3} + x^{2} + 3 \, x + 2\right)}}"," ",0,"1/50531*(23*sqrt(13)*(6*x^3 + x^2 + 3*x + 2)*log((4*sqrt(13)*sqrt(3*x^2 - x + 2)*(8*x - 9) - 220*x^2 + 196*x - 185)/(4*x^2 + 4*x + 1)) + 26*(1536*x^2 + 489*x - 289)*sqrt(3*x^2 - x + 2))/(6*x^3 + x^2 + 3*x + 2)","A",0
251,1,126,0,1.033048," ","integrate((4*x^2+3*x+1)/(1+2*x)^3/(3*x^2-x+2)^(3/2),x, algorithm=""fricas"")","\frac{11201 \, \sqrt{13} {\left(12 \, x^{4} + 8 \, x^{3} + 7 \, x^{2} + 7 \, x + 2\right)} \log\left(-\frac{4 \, \sqrt{13} \sqrt{3 \, x^{2} - x + 2} {\left(8 \, x - 9\right)} + 220 \, x^{2} - 196 \, x + 185}{4 \, x^{2} + 4 \, x + 1}\right) + 52 \, {\left(14496 \, x^{3} + 23281 \, x^{2} + 13306 \, x + 1673\right)} \sqrt{3 \, x^{2} - x + 2}}{1313806 \, {\left(12 \, x^{4} + 8 \, x^{3} + 7 \, x^{2} + 7 \, x + 2\right)}}"," ",0,"1/1313806*(11201*sqrt(13)*(12*x^4 + 8*x^3 + 7*x^2 + 7*x + 2)*log(-(4*sqrt(13)*sqrt(3*x^2 - x + 2)*(8*x - 9) + 220*x^2 - 196*x + 185)/(4*x^2 + 4*x + 1)) + 52*(14496*x^3 + 23281*x^2 + 13306*x + 1673)*sqrt(3*x^2 - x + 2))/(12*x^4 + 8*x^3 + 7*x^2 + 7*x + 2)","A",0
252,1,117,0,1.014335," ","integrate((1+2*x)^3*(4*x^2+3*x+1)/(3*x^2-x+2)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(39146 \, \sqrt{3} {\left(9 \, x^{4} - 6 \, x^{3} + 13 \, x^{2} - 4 \, x + 4\right)} \log\left(-4 \, \sqrt{3} \sqrt{3 \, x^{2} - x + 2} {\left(6 \, x - 1\right)} - 72 \, x^{2} + 24 \, x - 25\right) + 3 \, {\left(76176 \, x^{4} - 247904 \, x^{3} + 8630 \, x^{2} - 119459 \, x - 44739\right)} \sqrt{3 \, x^{2} - x + 2}\right)}}{42849 \, {\left(9 \, x^{4} - 6 \, x^{3} + 13 \, x^{2} - 4 \, x + 4\right)}}"," ",0,"2/42849*(39146*sqrt(3)*(9*x^4 - 6*x^3 + 13*x^2 - 4*x + 4)*log(-4*sqrt(3)*sqrt(3*x^2 - x + 2)*(6*x - 1) - 72*x^2 + 24*x - 25) + 3*(76176*x^4 - 247904*x^3 + 8630*x^2 - 119459*x - 44739)*sqrt(3*x^2 - x + 2))/(9*x^4 - 6*x^3 + 13*x^2 - 4*x + 4)","A",0
253,1,112,0,0.936039," ","integrate((1+2*x)^2*(4*x^2+3*x+1)/(3*x^2-x+2)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(2116 \, \sqrt{3} {\left(9 \, x^{4} - 6 \, x^{3} + 13 \, x^{2} - 4 \, x + 4\right)} \log\left(-4 \, \sqrt{3} \sqrt{3 \, x^{2} - x + 2} {\left(6 \, x - 1\right)} - 72 \, x^{2} + 24 \, x - 25\right) + 3 \, {\left(1964 \, x^{3} - 31664 \, x^{2} + 5837 \, x - 17481\right)} \sqrt{3 \, x^{2} - x + 2}\right)}}{14283 \, {\left(9 \, x^{4} - 6 \, x^{3} + 13 \, x^{2} - 4 \, x + 4\right)}}"," ",0,"2/14283*(2116*sqrt(3)*(9*x^4 - 6*x^3 + 13*x^2 - 4*x + 4)*log(-4*sqrt(3)*sqrt(3*x^2 - x + 2)*(6*x - 1) - 72*x^2 + 24*x - 25) + 3*(1964*x^3 - 31664*x^2 + 5837*x - 17481)*sqrt(3*x^2 - x + 2))/(9*x^4 - 6*x^3 + 13*x^2 - 4*x + 4)","B",0
254,1,51,0,1.196053," ","integrate((1+2*x)*(4*x^2+3*x+1)/(3*x^2-x+2)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(2860 \, x^{3} - 3546 \, x^{2} + 1833 \, x - 1915\right)} \sqrt{3 \, x^{2} - x + 2}}{1587 \, {\left(9 \, x^{4} - 6 \, x^{3} + 13 \, x^{2} - 4 \, x + 4\right)}}"," ",0,"2/1587*(2860*x^3 - 3546*x^2 + 1833*x - 1915)*sqrt(3*x^2 - x + 2)/(9*x^4 - 6*x^3 + 13*x^2 - 4*x + 4)","A",0
255,1,126,0,0.953833," ","integrate((4*x^2+3*x+1)/(1+2*x)/(3*x^2-x+2)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3174 \, \sqrt{13} {\left(9 \, x^{4} - 6 \, x^{3} + 13 \, x^{2} - 4 \, x + 4\right)} \log\left(-\frac{4 \, \sqrt{13} \sqrt{3 \, x^{2} - x + 2} {\left(8 \, x - 9\right)} + 220 \, x^{2} - 196 \, x + 185}{4 \, x^{2} + 4 \, x + 1}\right) + 13 \, {\left(82008 \, x^{3} - 31482 \, x^{2} + 79077 \, x - 32963\right)} \sqrt{3 \, x^{2} - x + 2}\right)}}{3486639 \, {\left(9 \, x^{4} - 6 \, x^{3} + 13 \, x^{2} - 4 \, x + 4\right)}}"," ",0,"2/3486639*(3174*sqrt(13)*(9*x^4 - 6*x^3 + 13*x^2 - 4*x + 4)*log(-(4*sqrt(13)*sqrt(3*x^2 - x + 2)*(8*x - 9) + 220*x^2 - 196*x + 185)/(4*x^2 + 4*x + 1)) + 13*(82008*x^3 - 31482*x^2 + 79077*x - 32963)*sqrt(3*x^2 - x + 2))/(9*x^4 - 6*x^3 + 13*x^2 - 4*x + 4)","A",0
256,1,141,0,0.742144," ","integrate((4*x^2+3*x+1)/(1+2*x)^2/(3*x^2-x+2)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(22218 \, \sqrt{13} {\left(18 \, x^{5} - 3 \, x^{4} + 20 \, x^{3} + 5 \, x^{2} + 4 \, x + 4\right)} \log\left(-\frac{4 \, \sqrt{13} \sqrt{3 \, x^{2} - x + 2} {\left(8 \, x - 9\right)} + 220 \, x^{2} - 196 \, x + 185}{4 \, x^{2} + 4 \, x + 1}\right) + 13 \, {\left(1318464 \, x^{4} + 133308 \, x^{3} + 1021566 \, x^{2} + 569989 \, x - 170239\right)} \sqrt{3 \, x^{2} - x + 2}\right)}}{45326307 \, {\left(18 \, x^{5} - 3 \, x^{4} + 20 \, x^{3} + 5 \, x^{2} + 4 \, x + 4\right)}}"," ",0,"2/45326307*(22218*sqrt(13)*(18*x^5 - 3*x^4 + 20*x^3 + 5*x^2 + 4*x + 4)*log(-(4*sqrt(13)*sqrt(3*x^2 - x + 2)*(8*x - 9) + 220*x^2 - 196*x + 185)/(4*x^2 + 4*x + 1)) + 13*(1318464*x^4 + 133308*x^3 + 1021566*x^2 + 569989*x - 170239)*sqrt(3*x^2 - x + 2))/(18*x^5 - 3*x^4 + 20*x^3 + 5*x^2 + 4*x + 4)","A",0
257,1,156,0,1.730356," ","integrate((4*x^2+3*x+1)/(1+2*x)^3/(3*x^2-x+2)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(826827 \, \sqrt{13} {\left(36 \, x^{6} + 12 \, x^{5} + 37 \, x^{4} + 30 \, x^{3} + 13 \, x^{2} + 12 \, x + 4\right)} \log\left(-\frac{4 \, \sqrt{13} \sqrt{3 \, x^{2} - x + 2} {\left(8 \, x - 9\right)} + 220 \, x^{2} - 196 \, x + 185}{4 \, x^{2} + 4 \, x + 1}\right) + 13 \, {\left(20304864 \, x^{5} + 20074356 \, x^{4} + 19381992 \, x^{3} + 21890266 \, x^{2} + 10777477 \, x + 847141\right)} \sqrt{3 \, x^{2} - x + 2}\right)}}{589241991 \, {\left(36 \, x^{6} + 12 \, x^{5} + 37 \, x^{4} + 30 \, x^{3} + 13 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"2/589241991*(826827*sqrt(13)*(36*x^6 + 12*x^5 + 37*x^4 + 30*x^3 + 13*x^2 + 12*x + 4)*log(-(4*sqrt(13)*sqrt(3*x^2 - x + 2)*(8*x - 9) + 220*x^2 - 196*x + 185)/(4*x^2 + 4*x + 1)) + 13*(20304864*x^5 + 20074356*x^4 + 19381992*x^3 + 21890266*x^2 + 10777477*x + 847141)*sqrt(3*x^2 - x + 2))/(36*x^6 + 12*x^5 + 37*x^4 + 30*x^3 + 13*x^2 + 12*x + 4)","A",0
258,1,465,0,60.068069," ","integrate((f*x^2+e*x+d)/(h*x+g)/(c*h^2*x^2+b*h^2*x+b*g*h-c*g^2)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, c^{2} f g^{4} - b^{2} d h^{4} + 4 \, {\left(c^{2} e - 4 \, b c f\right)} g^{3} h - 2 \, {\left(2 \, c^{2} d + b c e - 4 \, b^{2} f\right)} g^{2} h^{2} + 2 \, {\left(4 \, b c d - b^{2} e\right)} g h^{3} - {\left(4 \, c^{2} f g^{2} h^{2} - 4 \, c^{2} e g h^{3} - {\left(8 \, c^{2} d - 6 \, b c e + 3 \, b^{2} f\right)} h^{4}\right)} x^{2} + {\left(8 \, c^{2} f g^{3} h + 4 \, {\left(c^{2} e - 5 \, b c f\right)} g^{2} h^{2} + 4 \, {\left(2 \, c^{2} d - b c e + 3 \, b^{2} f\right)} g h^{3} + {\left(4 \, b c d - 3 \, b^{2} e\right)} h^{4}\right)} x\right)} \sqrt{c h^{2} x^{2} + b h^{2} x - c g^{2} + b g h}}{3 \, {\left(8 \, c^{4} g^{6} h^{3} - 20 \, b c^{3} g^{5} h^{4} + 18 \, b^{2} c^{2} g^{4} h^{5} - 7 \, b^{3} c g^{3} h^{6} + b^{4} g^{2} h^{7} - {\left(8 \, c^{4} g^{3} h^{6} - 12 \, b c^{3} g^{2} h^{7} + 6 \, b^{2} c^{2} g h^{8} - b^{3} c h^{9}\right)} x^{3} - {\left(8 \, c^{4} g^{4} h^{5} - 4 \, b c^{3} g^{3} h^{6} - 6 \, b^{2} c^{2} g^{2} h^{7} + 5 \, b^{3} c g h^{8} - b^{4} h^{9}\right)} x^{2} + {\left(8 \, c^{4} g^{5} h^{4} - 28 \, b c^{3} g^{4} h^{5} + 30 \, b^{2} c^{2} g^{3} h^{6} - 13 \, b^{3} c g^{2} h^{7} + 2 \, b^{4} g h^{8}\right)} x\right)}}"," ",0,"2/3*(8*c^2*f*g^4 - b^2*d*h^4 + 4*(c^2*e - 4*b*c*f)*g^3*h - 2*(2*c^2*d + b*c*e - 4*b^2*f)*g^2*h^2 + 2*(4*b*c*d - b^2*e)*g*h^3 - (4*c^2*f*g^2*h^2 - 4*c^2*e*g*h^3 - (8*c^2*d - 6*b*c*e + 3*b^2*f)*h^4)*x^2 + (8*c^2*f*g^3*h + 4*(c^2*e - 5*b*c*f)*g^2*h^2 + 4*(2*c^2*d - b*c*e + 3*b^2*f)*g*h^3 + (4*b*c*d - 3*b^2*e)*h^4)*x)*sqrt(c*h^2*x^2 + b*h^2*x - c*g^2 + b*g*h)/(8*c^4*g^6*h^3 - 20*b*c^3*g^5*h^4 + 18*b^2*c^2*g^4*h^5 - 7*b^3*c*g^3*h^6 + b^4*g^2*h^7 - (8*c^4*g^3*h^6 - 12*b*c^3*g^2*h^7 + 6*b^2*c^2*g*h^8 - b^3*c*h^9)*x^3 - (8*c^4*g^4*h^5 - 4*b*c^3*g^3*h^6 - 6*b^2*c^2*g^2*h^7 + 5*b^3*c*g*h^8 - b^4*h^9)*x^2 + (8*c^4*g^5*h^4 - 28*b*c^3*g^4*h^5 + 30*b^2*c^2*g^3*h^6 - 13*b^3*c*g^2*h^7 + 2*b^4*g*h^8)*x)","B",0
259,0,0,0,0.993504," ","integrate((e*x+d)^(1/2)*(C*x^2+B*x+A)*(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C x^{2} + B x + A\right)} \sqrt{c x^{2} + b x + a} \sqrt{e x + d}, x\right)"," ",0,"integral((C*x^2 + B*x + A)*sqrt(c*x^2 + b*x + a)*sqrt(e*x + d), x)","F",0
260,0,0,0,1.024122," ","integrate((C*x^2+B*x+A)*(c*x^2+b*x+a)^(1/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C x^{2} + B x + A\right)} \sqrt{c x^{2} + b x + a}}{\sqrt{e x + d}}, x\right)"," ",0,"integral((C*x^2 + B*x + A)*sqrt(c*x^2 + b*x + a)/sqrt(e*x + d), x)","F",0
261,0,0,0,1.022270," ","integrate((C*x^2+B*x+A)*(c*x^2+b*x+a)^(1/2)/(e*x+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C x^{2} + B x + A\right)} \sqrt{c x^{2} + b x + a} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}, x\right)"," ",0,"integral((C*x^2 + B*x + A)*sqrt(c*x^2 + b*x + a)*sqrt(e*x + d)/(e^2*x^2 + 2*d*e*x + d^2), x)","F",0
262,0,0,0,1.429048," ","integrate((C*x^2+B*x+A)*(c*x^2+b*x+a)^(1/2)/(e*x+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C x^{2} + B x + A\right)} \sqrt{c x^{2} + b x + a} \sqrt{e x + d}}{e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}}, x\right)"," ",0,"integral((C*x^2 + B*x + A)*sqrt(c*x^2 + b*x + a)*sqrt(e*x + d)/(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3), x)","F",0
263,0,0,0,1.157897," ","integrate((C*x^2+B*x+A)*(c*x^2+b*x+a)^(1/2)/(e*x+d)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C x^{2} + B x + A\right)} \sqrt{c x^{2} + b x + a} \sqrt{e x + d}}{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*x^2 + B*x + A)*sqrt(c*x^2 + b*x + a)*sqrt(e*x + d)/(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
264,0,0,0,0.858426," ","integrate((C*x^2+B*x+A)*(c*x^2+b*x+a)^(1/2)/(e*x+d)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C x^{2} + B x + A\right)} \sqrt{c x^{2} + b x + a} \sqrt{e x + d}}{e^{5} x^{5} + 5 \, d e^{4} x^{4} + 10 \, d^{2} e^{3} x^{3} + 10 \, d^{3} e^{2} x^{2} + 5 \, d^{4} e x + d^{5}}, x\right)"," ",0,"integral((C*x^2 + B*x + A)*sqrt(c*x^2 + b*x + a)*sqrt(e*x + d)/(e^5*x^5 + 5*d*e^4*x^4 + 10*d^2*e^3*x^3 + 10*d^3*e^2*x^2 + 5*d^4*e*x + d^5), x)","F",0
265,0,0,0,1.248077," ","integrate((C*x^2+B*x+A)*(c*x^2+b*x+a)^(1/2)/(e*x+d)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C x^{2} + B x + A\right)} \sqrt{c x^{2} + b x + a} \sqrt{e x + d}}{e^{6} x^{6} + 6 \, d e^{5} x^{5} + 15 \, 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 + d^{6}}, x\right)"," ",0,"integral((C*x^2 + B*x + A)*sqrt(c*x^2 + b*x + a)*sqrt(e*x + d)/(e^6*x^6 + 6*d*e^5*x^5 + 15*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 + d^6), x)","F",0
266,0,0,0,0.786657," ","integrate((e*x+d)^(3/2)*(C*x^2+B*x+A)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C e x^{3} + {\left(C d + B e\right)} x^{2} + A d + {\left(B d + A e\right)} x\right)} \sqrt{e x + d}}{\sqrt{c x^{2} + b x + a}}, x\right)"," ",0,"integral((C*e*x^3 + (C*d + B*e)*x^2 + A*d + (B*d + A*e)*x)*sqrt(e*x + d)/sqrt(c*x^2 + b*x + a), x)","F",0
267,0,0,0,1.343296," ","integrate((e*x+d)^(1/2)*(C*x^2+B*x+A)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C x^{2} + B x + A\right)} \sqrt{e x + d}}{\sqrt{c x^{2} + b x + a}}, x\right)"," ",0,"integral((C*x^2 + B*x + A)*sqrt(e*x + d)/sqrt(c*x^2 + b*x + a), x)","F",0
268,0,0,0,1.031480," ","integrate((C*x^2+B*x+A)/(e*x+d)^(1/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C x^{2} + B x + A\right)} \sqrt{c x^{2} + b x + a} \sqrt{e x + d}}{c e x^{3} + {\left(c d + b e\right)} x^{2} + a d + {\left(b d + a e\right)} x}, x\right)"," ",0,"integral((C*x^2 + B*x + A)*sqrt(c*x^2 + b*x + a)*sqrt(e*x + d)/(c*e*x^3 + (c*d + b*e)*x^2 + a*d + (b*d + a*e)*x), x)","F",0
269,0,0,0,1.270333," ","integrate((C*x^2+B*x+A)/(e*x+d)^(3/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C x^{2} + B x + A\right)} \sqrt{c x^{2} + b x + a} \sqrt{e x + d}}{c e^{2} x^{4} + {\left(2 \, c d e + b e^{2}\right)} x^{3} + a d^{2} + {\left(c d^{2} + 2 \, b d e + a e^{2}\right)} x^{2} + {\left(b d^{2} + 2 \, a d e\right)} x}, x\right)"," ",0,"integral((C*x^2 + B*x + A)*sqrt(c*x^2 + b*x + a)*sqrt(e*x + d)/(c*e^2*x^4 + (2*c*d*e + b*e^2)*x^3 + a*d^2 + (c*d^2 + 2*b*d*e + a*e^2)*x^2 + (b*d^2 + 2*a*d*e)*x), x)","F",0
270,0,0,0,1.020763," ","integrate((C*x^2+B*x+A)/(e*x+d)^(5/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C x^{2} + B x + A\right)} \sqrt{c x^{2} + b x + a} \sqrt{e x + d}}{c e^{3} x^{5} + {\left(3 \, c d e^{2} + b e^{3}\right)} x^{4} + a d^{3} + {\left(3 \, c d^{2} e + 3 \, b d e^{2} + a e^{3}\right)} x^{3} + {\left(c d^{3} + 3 \, b d^{2} e + 3 \, a d e^{2}\right)} x^{2} + {\left(b d^{3} + 3 \, a d^{2} e\right)} x}, x\right)"," ",0,"integral((C*x^2 + B*x + A)*sqrt(c*x^2 + b*x + a)*sqrt(e*x + d)/(c*e^3*x^5 + (3*c*d*e^2 + b*e^3)*x^4 + a*d^3 + (3*c*d^2*e + 3*b*d*e^2 + a*e^3)*x^3 + (c*d^3 + 3*b*d^2*e + 3*a*d*e^2)*x^2 + (b*d^3 + 3*a*d^2*e)*x), x)","F",0
271,0,0,0,1.253695," ","integrate((C*x^2+B*x+A)/(e*x+d)^(7/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C x^{2} + B x + A\right)} \sqrt{c x^{2} + b x + a} \sqrt{e x + d}}{c e^{4} x^{6} + {\left(4 \, c d e^{3} + b e^{4}\right)} x^{5} + a d^{4} + {\left(6 \, c d^{2} e^{2} + 4 \, b d e^{3} + a e^{4}\right)} x^{4} + 2 \, {\left(2 \, c d^{3} e + 3 \, b d^{2} e^{2} + 2 \, a d e^{3}\right)} x^{3} + {\left(c d^{4} + 4 \, b d^{3} e + 6 \, a d^{2} e^{2}\right)} x^{2} + {\left(b d^{4} + 4 \, a d^{3} e\right)} x}, x\right)"," ",0,"integral((C*x^2 + B*x + A)*sqrt(c*x^2 + b*x + a)*sqrt(e*x + d)/(c*e^4*x^6 + (4*c*d*e^3 + b*e^4)*x^5 + a*d^4 + (6*c*d^2*e^2 + 4*b*d*e^3 + a*e^4)*x^4 + 2*(2*c*d^3*e + 3*b*d^2*e^2 + 2*a*d*e^3)*x^3 + (c*d^4 + 4*b*d^3*e + 6*a*d^2*e^2)*x^2 + (b*d^4 + 4*a*d^3*e)*x), x)","F",0
272,0,0,0,1.400195," ","integrate((h*x+g)^m*(c*x^2+b*x+a)^p*(f*x^2+e*x+d),x, algorithm=""fricas"")","{\rm integral}\left({\left(f x^{2} + e x + d\right)} {\left(c x^{2} + b x + a\right)}^{p} {\left(h x + g\right)}^{m}, x\right)"," ",0,"integral((f*x^2 + e*x + d)*(c*x^2 + b*x + a)^p*(h*x + g)^m, x)","F",0
273,0,0,0,1.484385," ","integrate((h*x+g)^m*(f*x^2+e*x+d)*(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{2} + b x + a} {\left(f x^{2} + e x + d\right)} {\left(h x + g\right)}^{m}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*(f*x^2 + e*x + d)*(h*x + g)^m, x)","F",0
274,0,0,0,0.776782," ","integrate((h*x+g)^(-3-2*p)*(c*x^2+b*x+a)^p*(f*x^2+e*x+d),x, algorithm=""fricas"")","{\rm integral}\left({\left(f x^{2} + e x + d\right)} {\left(c x^{2} + b x + a\right)}^{p} {\left(h x + g\right)}^{-2 \, p - 3}, x\right)"," ",0,"integral((f*x^2 + e*x + d)*(c*x^2 + b*x + a)^p*(h*x + g)^(-2*p - 3), x)","F",0
275,1,75,0,0.892795," ","integrate((f*x^2+d)^p*(2*c*d*f+2*b*f^2*(3+2*p)*x+2*c*f^2*(3+2*p)*x^2),x, algorithm=""fricas"")","\frac{{\left(2 \, b d f p + 2 \, {\left(c f^{2} p + c f^{2}\right)} x^{3} + 3 \, b d f + {\left(2 \, b f^{2} p + 3 \, b f^{2}\right)} x^{2} + 2 \, {\left(c d f p + c d f\right)} x\right)} {\left(f x^{2} + d\right)}^{p}}{p + 1}"," ",0,"(2*b*d*f*p + 2*(c*f^2*p + c*f^2)*x^3 + 3*b*d*f + (2*b*f^2*p + 3*b*f^2)*x^2 + 2*(c*d*f*p + c*d*f)*x)*(f*x^2 + d)^p/(p + 1)","A",0
276,1,83,0,1.105701," ","integrate((f*x^2+e*x+d)^p*(-2*c*e^2+2*c*d*f-c*e^2*p+2*c*f^2*(3+2*p)*x^2),x, algorithm=""fricas"")","\frac{{\left(c e f p x^{2} - c d e p + 2 \, {\left(c f^{2} p + c f^{2}\right)} x^{3} - 2 \, c d e - {\left(2 \, c e^{2} - 2 \, c d f + {\left(c e^{2} - 2 \, c d f\right)} p\right)} x\right)} {\left(f x^{2} + e x + d\right)}^{p}}{p + 1}"," ",0,"(c*e*f*p*x^2 - c*d*e*p + 2*(c*f^2*p + c*f^2)*x^3 - 2*c*d*e - (2*c*e^2 - 2*c*d*f + (c*e^2 - 2*c*d*f)*p)*x)*(f*x^2 + e*x + d)^p/(p + 1)","A",0
277,1,123,0,0.807946," ","integrate((f*x^2+e*x+d)^p*(-2*c*e^2+2*c*d*f+3*b*e*f-c*e^2*p+2*b*e*f*p+2*b*f^2*(3+2*p)*x+2*c*f^2*(3+2*p)*x^2),x, algorithm=""fricas"")","\frac{{\left(2 \, {\left(c f^{2} p + c f^{2}\right)} x^{3} - 2 \, c d e + 3 \, b d f + {\left(3 \, b f^{2} + {\left(c e f + 2 \, b f^{2}\right)} p\right)} x^{2} - {\left(c d e - 2 \, b d f\right)} p - {\left(2 \, c e^{2} - {\left(2 \, c d + 3 \, b e\right)} f + {\left(c e^{2} - 2 \, {\left(c d + b e\right)} f\right)} p\right)} x\right)} {\left(f x^{2} + e x + d\right)}^{p}}{p + 1}"," ",0,"(2*(c*f^2*p + c*f^2)*x^3 - 2*c*d*e + 3*b*d*f + (3*b*f^2 + (c*e*f + 2*b*f^2)*p)*x^2 - (c*d*e - 2*b*d*f)*p - (2*c*e^2 - (2*c*d + 3*b*e)*f + (c*e^2 - 2*(c*d + b*e)*f)*p)*x)*(f*x^2 + e*x + d)^p/(p + 1)","B",0
278,1,2467,0,0.784847," ","integrate((e*x+d)^3*(c*x^2+b*x+a)^5*(d*(5*a*e+6*b*d)+(5*a*e^2+17*b*d*e+12*c*d^2)*x+e*(11*b*e+29*c*d)*x^2+17*c*e^2*x^3),x, algorithm=""fricas"")","x^{17} e^{5} c^{6} + 5 x^{16} e^{4} d c^{6} + 6 x^{16} e^{5} c^{5} b + 10 x^{15} e^{3} d^{2} c^{6} + 30 x^{15} e^{4} d c^{5} b + 15 x^{15} e^{5} c^{4} b^{2} + 6 x^{15} e^{5} c^{5} a + 10 x^{14} e^{2} d^{3} c^{6} + 60 x^{14} e^{3} d^{2} c^{5} b + 75 x^{14} e^{4} d c^{4} b^{2} + 20 x^{14} e^{5} c^{3} b^{3} + 30 x^{14} e^{4} d c^{5} a + 30 x^{14} e^{5} c^{4} b a + 5 x^{13} e d^{4} c^{6} + 60 x^{13} e^{2} d^{3} c^{5} b + 150 x^{13} e^{3} d^{2} c^{4} b^{2} + 100 x^{13} e^{4} d c^{3} b^{3} + 15 x^{13} e^{5} c^{2} b^{4} + 60 x^{13} e^{3} d^{2} c^{5} a + 150 x^{13} e^{4} d c^{4} b a + 60 x^{13} e^{5} c^{3} b^{2} a + 15 x^{13} e^{5} c^{4} a^{2} + x^{12} d^{5} c^{6} + 30 x^{12} e d^{4} c^{5} b + 150 x^{12} e^{2} d^{3} c^{4} b^{2} + 200 x^{12} e^{3} d^{2} c^{3} b^{3} + 75 x^{12} e^{4} d c^{2} b^{4} + 6 x^{12} e^{5} c b^{5} + 60 x^{12} e^{2} d^{3} c^{5} a + 300 x^{12} e^{3} d^{2} c^{4} b a + 300 x^{12} e^{4} d c^{3} b^{2} a + 60 x^{12} e^{5} c^{2} b^{3} a + 75 x^{12} e^{4} d c^{4} a^{2} + 60 x^{12} e^{5} c^{3} b a^{2} + 6 x^{11} d^{5} c^{5} b + 75 x^{11} e d^{4} c^{4} b^{2} + 200 x^{11} e^{2} d^{3} c^{3} b^{3} + 150 x^{11} e^{3} d^{2} c^{2} b^{4} + 30 x^{11} e^{4} d c b^{5} + x^{11} e^{5} b^{6} + 30 x^{11} e d^{4} c^{5} a + 300 x^{11} e^{2} d^{3} c^{4} b a + 600 x^{11} e^{3} d^{2} c^{3} b^{2} a + 300 x^{11} e^{4} d c^{2} b^{3} a + 30 x^{11} e^{5} c b^{4} a + 150 x^{11} e^{3} d^{2} c^{4} a^{2} + 300 x^{11} e^{4} d c^{3} b a^{2} + 90 x^{11} e^{5} c^{2} b^{2} a^{2} + 20 x^{11} e^{5} c^{3} a^{3} + 15 x^{10} d^{5} c^{4} b^{2} + 100 x^{10} e d^{4} c^{3} b^{3} + 150 x^{10} e^{2} d^{3} c^{2} b^{4} + 60 x^{10} e^{3} d^{2} c b^{5} + 5 x^{10} e^{4} d b^{6} + 6 x^{10} d^{5} c^{5} a + 150 x^{10} e d^{4} c^{4} b a + 600 x^{10} e^{2} d^{3} c^{3} b^{2} a + 600 x^{10} e^{3} d^{2} c^{2} b^{3} a + 150 x^{10} e^{4} d c b^{4} a + 6 x^{10} e^{5} b^{5} a + 150 x^{10} e^{2} d^{3} c^{4} a^{2} + 600 x^{10} e^{3} d^{2} c^{3} b a^{2} + 450 x^{10} e^{4} d c^{2} b^{2} a^{2} + 60 x^{10} e^{5} c b^{3} a^{2} + 100 x^{10} e^{4} d c^{3} a^{3} + 60 x^{10} e^{5} c^{2} b a^{3} + 20 x^{9} d^{5} c^{3} b^{3} + 75 x^{9} e d^{4} c^{2} b^{4} + 60 x^{9} e^{2} d^{3} c b^{5} + 10 x^{9} e^{3} d^{2} b^{6} + 30 x^{9} d^{5} c^{4} b a + 300 x^{9} e d^{4} c^{3} b^{2} a + 600 x^{9} e^{2} d^{3} c^{2} b^{3} a + 300 x^{9} e^{3} d^{2} c b^{4} a + 30 x^{9} e^{4} d b^{5} a + 75 x^{9} e d^{4} c^{4} a^{2} + 600 x^{9} e^{2} d^{3} c^{3} b a^{2} + 900 x^{9} e^{3} d^{2} c^{2} b^{2} a^{2} + 300 x^{9} e^{4} d c b^{3} a^{2} + 15 x^{9} e^{5} b^{4} a^{2} + 200 x^{9} e^{3} d^{2} c^{3} a^{3} + 300 x^{9} e^{4} d c^{2} b a^{3} + 60 x^{9} e^{5} c b^{2} a^{3} + 15 x^{9} e^{5} c^{2} a^{4} + 15 x^{8} d^{5} c^{2} b^{4} + 30 x^{8} e d^{4} c b^{5} + 10 x^{8} e^{2} d^{3} b^{6} + 60 x^{8} d^{5} c^{3} b^{2} a + 300 x^{8} e d^{4} c^{2} b^{3} a + 300 x^{8} e^{2} d^{3} c b^{4} a + 60 x^{8} e^{3} d^{2} b^{5} a + 15 x^{8} d^{5} c^{4} a^{2} + 300 x^{8} e d^{4} c^{3} b a^{2} + 900 x^{8} e^{2} d^{3} c^{2} b^{2} a^{2} + 600 x^{8} e^{3} d^{2} c b^{3} a^{2} + 75 x^{8} e^{4} d b^{4} a^{2} + 200 x^{8} e^{2} d^{3} c^{3} a^{3} + 600 x^{8} e^{3} d^{2} c^{2} b a^{3} + 300 x^{8} e^{4} d c b^{2} a^{3} + 20 x^{8} e^{5} b^{3} a^{3} + 75 x^{8} e^{4} d c^{2} a^{4} + 30 x^{8} e^{5} c b a^{4} + 6 x^{7} d^{5} c b^{5} + 5 x^{7} e d^{4} b^{6} + 60 x^{7} d^{5} c^{2} b^{3} a + 150 x^{7} e d^{4} c b^{4} a + 60 x^{7} e^{2} d^{3} b^{5} a + 60 x^{7} d^{5} c^{3} b a^{2} + 450 x^{7} e d^{4} c^{2} b^{2} a^{2} + 600 x^{7} e^{2} d^{3} c b^{3} a^{2} + 150 x^{7} e^{3} d^{2} b^{4} a^{2} + 100 x^{7} e d^{4} c^{3} a^{3} + 600 x^{7} e^{2} d^{3} c^{2} b a^{3} + 600 x^{7} e^{3} d^{2} c b^{2} a^{3} + 100 x^{7} e^{4} d b^{3} a^{3} + 150 x^{7} e^{3} d^{2} c^{2} a^{4} + 150 x^{7} e^{4} d c b a^{4} + 15 x^{7} e^{5} b^{2} a^{4} + 6 x^{7} e^{5} c a^{5} + x^{6} d^{5} b^{6} + 30 x^{6} d^{5} c b^{4} a + 30 x^{6} e d^{4} b^{5} a + 90 x^{6} d^{5} c^{2} b^{2} a^{2} + 300 x^{6} e d^{4} c b^{3} a^{2} + 150 x^{6} e^{2} d^{3} b^{4} a^{2} + 20 x^{6} d^{5} c^{3} a^{3} + 300 x^{6} e d^{4} c^{2} b a^{3} + 600 x^{6} e^{2} d^{3} c b^{2} a^{3} + 200 x^{6} e^{3} d^{2} b^{3} a^{3} + 150 x^{6} e^{2} d^{3} c^{2} a^{4} + 300 x^{6} e^{3} d^{2} c b a^{4} + 75 x^{6} e^{4} d b^{2} a^{4} + 30 x^{6} e^{4} d c a^{5} + 6 x^{6} e^{5} b a^{5} + 6 x^{5} d^{5} b^{5} a + 60 x^{5} d^{5} c b^{3} a^{2} + 75 x^{5} e d^{4} b^{4} a^{2} + 60 x^{5} d^{5} c^{2} b a^{3} + 300 x^{5} e d^{4} c b^{2} a^{3} + 200 x^{5} e^{2} d^{3} b^{3} a^{3} + 75 x^{5} e d^{4} c^{2} a^{4} + 300 x^{5} e^{2} d^{3} c b a^{4} + 150 x^{5} e^{3} d^{2} b^{2} a^{4} + 60 x^{5} e^{3} d^{2} c a^{5} + 30 x^{5} e^{4} d b a^{5} + x^{5} e^{5} a^{6} + 15 x^{4} d^{5} b^{4} a^{2} + 60 x^{4} d^{5} c b^{2} a^{3} + 100 x^{4} e d^{4} b^{3} a^{3} + 15 x^{4} d^{5} c^{2} a^{4} + 150 x^{4} e d^{4} c b a^{4} + 150 x^{4} e^{2} d^{3} b^{2} a^{4} + 60 x^{4} e^{2} d^{3} c a^{5} + 60 x^{4} e^{3} d^{2} b a^{5} + 5 x^{4} e^{4} d a^{6} + 20 x^{3} d^{5} b^{3} a^{3} + 30 x^{3} d^{5} c b a^{4} + 75 x^{3} e d^{4} b^{2} a^{4} + 30 x^{3} e d^{4} c a^{5} + 60 x^{3} e^{2} d^{3} b a^{5} + 10 x^{3} e^{3} d^{2} a^{6} + 15 x^{2} d^{5} b^{2} a^{4} + 6 x^{2} d^{5} c a^{5} + 30 x^{2} e d^{4} b a^{5} + 10 x^{2} e^{2} d^{3} a^{6} + 6 x d^{5} b a^{5} + 5 x e d^{4} a^{6}"," ",0,"x^17*e^5*c^6 + 5*x^16*e^4*d*c^6 + 6*x^16*e^5*c^5*b + 10*x^15*e^3*d^2*c^6 + 30*x^15*e^4*d*c^5*b + 15*x^15*e^5*c^4*b^2 + 6*x^15*e^5*c^5*a + 10*x^14*e^2*d^3*c^6 + 60*x^14*e^3*d^2*c^5*b + 75*x^14*e^4*d*c^4*b^2 + 20*x^14*e^5*c^3*b^3 + 30*x^14*e^4*d*c^5*a + 30*x^14*e^5*c^4*b*a + 5*x^13*e*d^4*c^6 + 60*x^13*e^2*d^3*c^5*b + 150*x^13*e^3*d^2*c^4*b^2 + 100*x^13*e^4*d*c^3*b^3 + 15*x^13*e^5*c^2*b^4 + 60*x^13*e^3*d^2*c^5*a + 150*x^13*e^4*d*c^4*b*a + 60*x^13*e^5*c^3*b^2*a + 15*x^13*e^5*c^4*a^2 + x^12*d^5*c^6 + 30*x^12*e*d^4*c^5*b + 150*x^12*e^2*d^3*c^4*b^2 + 200*x^12*e^3*d^2*c^3*b^3 + 75*x^12*e^4*d*c^2*b^4 + 6*x^12*e^5*c*b^5 + 60*x^12*e^2*d^3*c^5*a + 300*x^12*e^3*d^2*c^4*b*a + 300*x^12*e^4*d*c^3*b^2*a + 60*x^12*e^5*c^2*b^3*a + 75*x^12*e^4*d*c^4*a^2 + 60*x^12*e^5*c^3*b*a^2 + 6*x^11*d^5*c^5*b + 75*x^11*e*d^4*c^4*b^2 + 200*x^11*e^2*d^3*c^3*b^3 + 150*x^11*e^3*d^2*c^2*b^4 + 30*x^11*e^4*d*c*b^5 + x^11*e^5*b^6 + 30*x^11*e*d^4*c^5*a + 300*x^11*e^2*d^3*c^4*b*a + 600*x^11*e^3*d^2*c^3*b^2*a + 300*x^11*e^4*d*c^2*b^3*a + 30*x^11*e^5*c*b^4*a + 150*x^11*e^3*d^2*c^4*a^2 + 300*x^11*e^4*d*c^3*b*a^2 + 90*x^11*e^5*c^2*b^2*a^2 + 20*x^11*e^5*c^3*a^3 + 15*x^10*d^5*c^4*b^2 + 100*x^10*e*d^4*c^3*b^3 + 150*x^10*e^2*d^3*c^2*b^4 + 60*x^10*e^3*d^2*c*b^5 + 5*x^10*e^4*d*b^6 + 6*x^10*d^5*c^5*a + 150*x^10*e*d^4*c^4*b*a + 600*x^10*e^2*d^3*c^3*b^2*a + 600*x^10*e^3*d^2*c^2*b^3*a + 150*x^10*e^4*d*c*b^4*a + 6*x^10*e^5*b^5*a + 150*x^10*e^2*d^3*c^4*a^2 + 600*x^10*e^3*d^2*c^3*b*a^2 + 450*x^10*e^4*d*c^2*b^2*a^2 + 60*x^10*e^5*c*b^3*a^2 + 100*x^10*e^4*d*c^3*a^3 + 60*x^10*e^5*c^2*b*a^3 + 20*x^9*d^5*c^3*b^3 + 75*x^9*e*d^4*c^2*b^4 + 60*x^9*e^2*d^3*c*b^5 + 10*x^9*e^3*d^2*b^6 + 30*x^9*d^5*c^4*b*a + 300*x^9*e*d^4*c^3*b^2*a + 600*x^9*e^2*d^3*c^2*b^3*a + 300*x^9*e^3*d^2*c*b^4*a + 30*x^9*e^4*d*b^5*a + 75*x^9*e*d^4*c^4*a^2 + 600*x^9*e^2*d^3*c^3*b*a^2 + 900*x^9*e^3*d^2*c^2*b^2*a^2 + 300*x^9*e^4*d*c*b^3*a^2 + 15*x^9*e^5*b^4*a^2 + 200*x^9*e^3*d^2*c^3*a^3 + 300*x^9*e^4*d*c^2*b*a^3 + 60*x^9*e^5*c*b^2*a^3 + 15*x^9*e^5*c^2*a^4 + 15*x^8*d^5*c^2*b^4 + 30*x^8*e*d^4*c*b^5 + 10*x^8*e^2*d^3*b^6 + 60*x^8*d^5*c^3*b^2*a + 300*x^8*e*d^4*c^2*b^3*a + 300*x^8*e^2*d^3*c*b^4*a + 60*x^8*e^3*d^2*b^5*a + 15*x^8*d^5*c^4*a^2 + 300*x^8*e*d^4*c^3*b*a^2 + 900*x^8*e^2*d^3*c^2*b^2*a^2 + 600*x^8*e^3*d^2*c*b^3*a^2 + 75*x^8*e^4*d*b^4*a^2 + 200*x^8*e^2*d^3*c^3*a^3 + 600*x^8*e^3*d^2*c^2*b*a^3 + 300*x^8*e^4*d*c*b^2*a^3 + 20*x^8*e^5*b^3*a^3 + 75*x^8*e^4*d*c^2*a^4 + 30*x^8*e^5*c*b*a^4 + 6*x^7*d^5*c*b^5 + 5*x^7*e*d^4*b^6 + 60*x^7*d^5*c^2*b^3*a + 150*x^7*e*d^4*c*b^4*a + 60*x^7*e^2*d^3*b^5*a + 60*x^7*d^5*c^3*b*a^2 + 450*x^7*e*d^4*c^2*b^2*a^2 + 600*x^7*e^2*d^3*c*b^3*a^2 + 150*x^7*e^3*d^2*b^4*a^2 + 100*x^7*e*d^4*c^3*a^3 + 600*x^7*e^2*d^3*c^2*b*a^3 + 600*x^7*e^3*d^2*c*b^2*a^3 + 100*x^7*e^4*d*b^3*a^3 + 150*x^7*e^3*d^2*c^2*a^4 + 150*x^7*e^4*d*c*b*a^4 + 15*x^7*e^5*b^2*a^4 + 6*x^7*e^5*c*a^5 + x^6*d^5*b^6 + 30*x^6*d^5*c*b^4*a + 30*x^6*e*d^4*b^5*a + 90*x^6*d^5*c^2*b^2*a^2 + 300*x^6*e*d^4*c*b^3*a^2 + 150*x^6*e^2*d^3*b^4*a^2 + 20*x^6*d^5*c^3*a^3 + 300*x^6*e*d^4*c^2*b*a^3 + 600*x^6*e^2*d^3*c*b^2*a^3 + 200*x^6*e^3*d^2*b^3*a^3 + 150*x^6*e^2*d^3*c^2*a^4 + 300*x^6*e^3*d^2*c*b*a^4 + 75*x^6*e^4*d*b^2*a^4 + 30*x^6*e^4*d*c*a^5 + 6*x^6*e^5*b*a^5 + 6*x^5*d^5*b^5*a + 60*x^5*d^5*c*b^3*a^2 + 75*x^5*e*d^4*b^4*a^2 + 60*x^5*d^5*c^2*b*a^3 + 300*x^5*e*d^4*c*b^2*a^3 + 200*x^5*e^2*d^3*b^3*a^3 + 75*x^5*e*d^4*c^2*a^4 + 300*x^5*e^2*d^3*c*b*a^4 + 150*x^5*e^3*d^2*b^2*a^4 + 60*x^5*e^3*d^2*c*a^5 + 30*x^5*e^4*d*b*a^5 + x^5*e^5*a^6 + 15*x^4*d^5*b^4*a^2 + 60*x^4*d^5*c*b^2*a^3 + 100*x^4*e*d^4*b^3*a^3 + 15*x^4*d^5*c^2*a^4 + 150*x^4*e*d^4*c*b*a^4 + 150*x^4*e^2*d^3*b^2*a^4 + 60*x^4*e^2*d^3*c*a^5 + 60*x^4*e^3*d^2*b*a^5 + 5*x^4*e^4*d*a^6 + 20*x^3*d^5*b^3*a^3 + 30*x^3*d^5*c*b*a^4 + 75*x^3*e*d^4*b^2*a^4 + 30*x^3*e*d^4*c*a^5 + 60*x^3*e^2*d^3*b*a^5 + 10*x^3*e^3*d^2*a^6 + 15*x^2*d^5*b^2*a^4 + 6*x^2*d^5*c*a^5 + 30*x^2*e*d^4*b*a^5 + 10*x^2*e^2*d^3*a^6 + 6*x*d^5*b*a^5 + 5*x*e*d^4*a^6","B",0
279,1,18,0,0.596863," ","integrate((x^3+x^2)/(x^2+x-2),x, algorithm=""fricas"")","\frac{1}{2} \, x^{2} + \frac{4}{3} \, \log\left(x + 2\right) + \frac{2}{3} \, \log\left(x - 1\right)"," ",0,"1/2*x^2 + 4/3*log(x + 2) + 2/3*log(x - 1)","A",0
280,1,701,0,0.947964," ","integrate(x^2*(g*x^3+f*x^2+e*x+d)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(32 \, {\left(3 \, b^{2} c^{3} - 4 \, a c^{4}\right)} d - 16 \, {\left(5 \, b^{3} c^{2} - 12 \, a b c^{3}\right)} e + 2 \, {\left(35 \, b^{4} c - 120 \, a b^{2} c^{2} + 48 \, a^{2} c^{3}\right)} f - {\left(63 \, b^{5} - 280 \, a b^{3} c + 240 \, a^{2} b c^{2}\right)} g\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 \, {\left(384 \, c^{5} g x^{4} - 1440 \, b c^{4} d + 48 \, {\left(10 \, c^{5} f - 9 \, b c^{4} g\right)} x^{3} + 8 \, {\left(80 \, c^{5} e - 70 \, b c^{4} f + {\left(63 \, b^{2} c^{3} - 64 \, a c^{4}\right)} g\right)} x^{2} + 80 \, {\left(15 \, b^{2} c^{3} - 16 \, a c^{4}\right)} e - 50 \, {\left(21 \, b^{3} c^{2} - 44 \, a b c^{3}\right)} f + {\left(945 \, b^{4} c - 2940 \, a b^{2} c^{2} + 1024 \, a^{2} c^{3}\right)} g + 2 \, {\left(480 \, c^{5} d - 400 \, b c^{4} e + 10 \, {\left(35 \, b^{2} c^{3} - 36 \, a c^{4}\right)} f - 7 \, {\left(45 \, b^{3} c^{2} - 92 \, a b c^{3}\right)} g\right)} x\right)} \sqrt{c x^{2} + b x + a}}{7680 \, c^{6}}, -\frac{15 \, {\left(32 \, {\left(3 \, b^{2} c^{3} - 4 \, a c^{4}\right)} d - 16 \, {\left(5 \, b^{3} c^{2} - 12 \, a b c^{3}\right)} e + 2 \, {\left(35 \, b^{4} c - 120 \, a b^{2} c^{2} + 48 \, a^{2} c^{3}\right)} f - {\left(63 \, b^{5} - 280 \, a b^{3} c + 240 \, a^{2} b c^{2}\right)} g\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 \, {\left(384 \, c^{5} g x^{4} - 1440 \, b c^{4} d + 48 \, {\left(10 \, c^{5} f - 9 \, b c^{4} g\right)} x^{3} + 8 \, {\left(80 \, c^{5} e - 70 \, b c^{4} f + {\left(63 \, b^{2} c^{3} - 64 \, a c^{4}\right)} g\right)} x^{2} + 80 \, {\left(15 \, b^{2} c^{3} - 16 \, a c^{4}\right)} e - 50 \, {\left(21 \, b^{3} c^{2} - 44 \, a b c^{3}\right)} f + {\left(945 \, b^{4} c - 2940 \, a b^{2} c^{2} + 1024 \, a^{2} c^{3}\right)} g + 2 \, {\left(480 \, c^{5} d - 400 \, b c^{4} e + 10 \, {\left(35 \, b^{2} c^{3} - 36 \, a c^{4}\right)} f - 7 \, {\left(45 \, b^{3} c^{2} - 92 \, a b c^{3}\right)} g\right)} x\right)} \sqrt{c x^{2} + b x + a}}{3840 \, c^{6}}\right]"," ",0,"[-1/7680*(15*(32*(3*b^2*c^3 - 4*a*c^4)*d - 16*(5*b^3*c^2 - 12*a*b*c^3)*e + 2*(35*b^4*c - 120*a*b^2*c^2 + 48*a^2*c^3)*f - (63*b^5 - 280*a*b^3*c + 240*a^2*b*c^2)*g)*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) - 4*(384*c^5*g*x^4 - 1440*b*c^4*d + 48*(10*c^5*f - 9*b*c^4*g)*x^3 + 8*(80*c^5*e - 70*b*c^4*f + (63*b^2*c^3 - 64*a*c^4)*g)*x^2 + 80*(15*b^2*c^3 - 16*a*c^4)*e - 50*(21*b^3*c^2 - 44*a*b*c^3)*f + (945*b^4*c - 2940*a*b^2*c^2 + 1024*a^2*c^3)*g + 2*(480*c^5*d - 400*b*c^4*e + 10*(35*b^2*c^3 - 36*a*c^4)*f - 7*(45*b^3*c^2 - 92*a*b*c^3)*g)*x)*sqrt(c*x^2 + b*x + a))/c^6, -1/3840*(15*(32*(3*b^2*c^3 - 4*a*c^4)*d - 16*(5*b^3*c^2 - 12*a*b*c^3)*e + 2*(35*b^4*c - 120*a*b^2*c^2 + 48*a^2*c^3)*f - (63*b^5 - 280*a*b^3*c + 240*a^2*b*c^2)*g)*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)) - 2*(384*c^5*g*x^4 - 1440*b*c^4*d + 48*(10*c^5*f - 9*b*c^4*g)*x^3 + 8*(80*c^5*e - 70*b*c^4*f + (63*b^2*c^3 - 64*a*c^4)*g)*x^2 + 80*(15*b^2*c^3 - 16*a*c^4)*e - 50*(21*b^3*c^2 - 44*a*b*c^3)*f + (945*b^4*c - 2940*a*b^2*c^2 + 1024*a^2*c^3)*g + 2*(480*c^5*d - 400*b*c^4*e + 10*(35*b^2*c^3 - 36*a*c^4)*f - 7*(45*b^3*c^2 - 92*a*b*c^3)*g)*x)*sqrt(c*x^2 + b*x + a))/c^6]","A",0
281,1,499,0,0.763921," ","integrate(x*(g*x^3+f*x^2+e*x+d)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(64 \, b c^{3} d - 16 \, {\left(3 \, b^{2} c^{2} - 4 \, a c^{3}\right)} e + 8 \, {\left(5 \, b^{3} c - 12 \, a b c^{2}\right)} f - {\left(35 \, b^{4} - 120 \, a b^{2} c + 48 \, a^{2} c^{2}\right)} g\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 \, {\left(48 \, c^{4} g x^{3} + 192 \, c^{4} d - 144 \, b c^{3} e + 8 \, {\left(8 \, c^{4} f - 7 \, b c^{3} g\right)} x^{2} + 8 \, {\left(15 \, b^{2} c^{2} - 16 \, a c^{3}\right)} f - 5 \, {\left(21 \, b^{3} c - 44 \, a b c^{2}\right)} g + 2 \, {\left(48 \, c^{4} e - 40 \, b c^{3} f + {\left(35 \, b^{2} c^{2} - 36 \, a c^{3}\right)} g\right)} x\right)} \sqrt{c x^{2} + b x + a}}{768 \, c^{5}}, \frac{3 \, {\left(64 \, b c^{3} d - 16 \, {\left(3 \, b^{2} c^{2} - 4 \, a c^{3}\right)} e + 8 \, {\left(5 \, b^{3} c - 12 \, a b c^{2}\right)} f - {\left(35 \, b^{4} - 120 \, a b^{2} c + 48 \, a^{2} c^{2}\right)} g\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 \, {\left(48 \, c^{4} g x^{3} + 192 \, c^{4} d - 144 \, b c^{3} e + 8 \, {\left(8 \, c^{4} f - 7 \, b c^{3} g\right)} x^{2} + 8 \, {\left(15 \, b^{2} c^{2} - 16 \, a c^{3}\right)} f - 5 \, {\left(21 \, b^{3} c - 44 \, a b c^{2}\right)} g + 2 \, {\left(48 \, c^{4} e - 40 \, b c^{3} f + {\left(35 \, b^{2} c^{2} - 36 \, a c^{3}\right)} g\right)} x\right)} \sqrt{c x^{2} + b x + a}}{384 \, c^{5}}\right]"," ",0,"[-1/768*(3*(64*b*c^3*d - 16*(3*b^2*c^2 - 4*a*c^3)*e + 8*(5*b^3*c - 12*a*b*c^2)*f - (35*b^4 - 120*a*b^2*c + 48*a^2*c^2)*g)*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) - 4*(48*c^4*g*x^3 + 192*c^4*d - 144*b*c^3*e + 8*(8*c^4*f - 7*b*c^3*g)*x^2 + 8*(15*b^2*c^2 - 16*a*c^3)*f - 5*(21*b^3*c - 44*a*b*c^2)*g + 2*(48*c^4*e - 40*b*c^3*f + (35*b^2*c^2 - 36*a*c^3)*g)*x)*sqrt(c*x^2 + b*x + a))/c^5, 1/384*(3*(64*b*c^3*d - 16*(3*b^2*c^2 - 4*a*c^3)*e + 8*(5*b^3*c - 12*a*b*c^2)*f - (35*b^4 - 120*a*b^2*c + 48*a^2*c^2)*g)*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)) + 2*(48*c^4*g*x^3 + 192*c^4*d - 144*b*c^3*e + 8*(8*c^4*f - 7*b*c^3*g)*x^2 + 8*(15*b^2*c^2 - 16*a*c^3)*f - 5*(21*b^3*c - 44*a*b*c^2)*g + 2*(48*c^4*e - 40*b*c^3*f + (35*b^2*c^2 - 36*a*c^3)*g)*x)*sqrt(c*x^2 + b*x + a))/c^5]","A",0
282,1,341,0,1.040961," ","integrate((g*x^3+f*x^2+e*x+d)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(16 \, c^{3} d - 8 \, b c^{2} e + 2 \, {\left(3 \, b^{2} c - 4 \, a c^{2}\right)} f - {\left(5 \, b^{3} - 12 \, a b c\right)} g\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 \, {\left(8 \, c^{3} g x^{2} + 24 \, c^{3} e - 18 \, b c^{2} f + {\left(15 \, b^{2} c - 16 \, a c^{2}\right)} g + 2 \, {\left(6 \, c^{3} f - 5 \, b c^{2} g\right)} x\right)} \sqrt{c x^{2} + b x + a}}{96 \, c^{4}}, -\frac{3 \, {\left(16 \, c^{3} d - 8 \, b c^{2} e + 2 \, {\left(3 \, b^{2} c - 4 \, a c^{2}\right)} f - {\left(5 \, b^{3} - 12 \, a b c\right)} g\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 \, {\left(8 \, c^{3} g x^{2} + 24 \, c^{3} e - 18 \, b c^{2} f + {\left(15 \, b^{2} c - 16 \, a c^{2}\right)} g + 2 \, {\left(6 \, c^{3} f - 5 \, b c^{2} g\right)} x\right)} \sqrt{c x^{2} + b x + a}}{48 \, c^{4}}\right]"," ",0,"[1/96*(3*(16*c^3*d - 8*b*c^2*e + 2*(3*b^2*c - 4*a*c^2)*f - (5*b^3 - 12*a*b*c)*g)*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) + 4*(8*c^3*g*x^2 + 24*c^3*e - 18*b*c^2*f + (15*b^2*c - 16*a*c^2)*g + 2*(6*c^3*f - 5*b*c^2*g)*x)*sqrt(c*x^2 + b*x + a))/c^4, -1/48*(3*(16*c^3*d - 8*b*c^2*e + 2*(3*b^2*c - 4*a*c^2)*f - (5*b^3 - 12*a*b*c)*g)*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)) - 2*(8*c^3*g*x^2 + 24*c^3*e - 18*b*c^2*f + (15*b^2*c - 16*a*c^2)*g + 2*(6*c^3*f - 5*b*c^2*g)*x)*sqrt(c*x^2 + b*x + a))/c^4]","A",0
283,1,733,0,6.924691," ","integrate((g*x^3+f*x^2+e*x+d)/x/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{8 \, \sqrt{a} c^{3} d \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) - {\left(8 \, a c^{2} e - 4 \, a b c f + {\left(3 \, a b^{2} - 4 \, a^{2} c\right)} g\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 \, {\left(2 \, a c^{2} g x + 4 \, a c^{2} f - 3 \, a b c g\right)} \sqrt{c x^{2} + b x + a}}{16 \, a c^{3}}, \frac{4 \, \sqrt{a} c^{3} d \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) - {\left(8 \, a c^{2} e - 4 \, a b c f + {\left(3 \, a b^{2} - 4 \, a^{2} c\right)} g\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 \, {\left(2 \, a c^{2} g x + 4 \, a c^{2} f - 3 \, a b c g\right)} \sqrt{c x^{2} + b x + a}}{8 \, a c^{3}}, \frac{16 \, \sqrt{-a} c^{3} d \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) - {\left(8 \, a c^{2} e - 4 \, a b c f + {\left(3 \, a b^{2} - 4 \, a^{2} c\right)} g\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 \, {\left(2 \, a c^{2} g x + 4 \, a c^{2} f - 3 \, a b c g\right)} \sqrt{c x^{2} + b x + a}}{16 \, a c^{3}}, \frac{8 \, \sqrt{-a} c^{3} d \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) - {\left(8 \, a c^{2} e - 4 \, a b c f + {\left(3 \, a b^{2} - 4 \, a^{2} c\right)} g\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 \, {\left(2 \, a c^{2} g x + 4 \, a c^{2} f - 3 \, a b c g\right)} \sqrt{c x^{2} + b x + a}}{8 \, a c^{3}}\right]"," ",0,"[1/16*(8*sqrt(a)*c^3*d*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) - (8*a*c^2*e - 4*a*b*c*f + (3*a*b^2 - 4*a^2*c)*g)*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) + 4*(2*a*c^2*g*x + 4*a*c^2*f - 3*a*b*c*g)*sqrt(c*x^2 + b*x + a))/(a*c^3), 1/8*(4*sqrt(a)*c^3*d*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) - (8*a*c^2*e - 4*a*b*c*f + (3*a*b^2 - 4*a^2*c)*g)*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)) + 2*(2*a*c^2*g*x + 4*a*c^2*f - 3*a*b*c*g)*sqrt(c*x^2 + b*x + a))/(a*c^3), 1/16*(16*sqrt(-a)*c^3*d*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) - (8*a*c^2*e - 4*a*b*c*f + (3*a*b^2 - 4*a^2*c)*g)*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) + 4*(2*a*c^2*g*x + 4*a*c^2*f - 3*a*b*c*g)*sqrt(c*x^2 + b*x + a))/(a*c^3), 1/8*(8*sqrt(-a)*c^3*d*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) - (8*a*c^2*e - 4*a*b*c*f + (3*a*b^2 - 4*a^2*c)*g)*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)) + 2*(2*a*c^2*g*x + 4*a*c^2*f - 3*a*b*c*g)*sqrt(c*x^2 + b*x + a))/(a*c^3)]","A",0
284,1,703,0,6.163640," ","integrate((g*x^3+f*x^2+e*x+d)/x^2/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(2 \, a^{2} c f - a^{2} b g\right)} \sqrt{c} x \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) + {\left(b c^{2} d - 2 \, a c^{2} e\right)} \sqrt{a} x \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) - 4 \, {\left(a^{2} c g x - a c^{2} d\right)} \sqrt{c x^{2} + b x + a}}{4 \, a^{2} c^{2} x}, -\frac{2 \, {\left(2 \, a^{2} c f - a^{2} b g\right)} \sqrt{-c} x \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) + {\left(b c^{2} d - 2 \, a c^{2} e\right)} \sqrt{a} x \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) - 4 \, {\left(a^{2} c g x - a c^{2} d\right)} \sqrt{c x^{2} + b x + a}}{4 \, a^{2} c^{2} x}, -\frac{2 \, {\left(b c^{2} d - 2 \, a c^{2} e\right)} \sqrt{-a} x \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) + {\left(2 \, a^{2} c f - a^{2} b g\right)} \sqrt{c} x \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 \, {\left(a^{2} c g x - a c^{2} d\right)} \sqrt{c x^{2} + b x + a}}{4 \, a^{2} c^{2} x}, -\frac{{\left(b c^{2} d - 2 \, a c^{2} e\right)} \sqrt{-a} x \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) + {\left(2 \, a^{2} c f - a^{2} b g\right)} \sqrt{-c} x \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 \, {\left(a^{2} c g x - a c^{2} d\right)} \sqrt{c x^{2} + b x + a}}{2 \, a^{2} c^{2} x}\right]"," ",0,"[-1/4*((2*a^2*c*f - a^2*b*g)*sqrt(c)*x*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) + (b*c^2*d - 2*a*c^2*e)*sqrt(a)*x*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) - 4*(a^2*c*g*x - a*c^2*d)*sqrt(c*x^2 + b*x + a))/(a^2*c^2*x), -1/4*(2*(2*a^2*c*f - a^2*b*g)*sqrt(-c)*x*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)) + (b*c^2*d - 2*a*c^2*e)*sqrt(a)*x*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) - 4*(a^2*c*g*x - a*c^2*d)*sqrt(c*x^2 + b*x + a))/(a^2*c^2*x), -1/4*(2*(b*c^2*d - 2*a*c^2*e)*sqrt(-a)*x*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) + (2*a^2*c*f - a^2*b*g)*sqrt(c)*x*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) - 4*(a^2*c*g*x - a*c^2*d)*sqrt(c*x^2 + b*x + a))/(a^2*c^2*x), -1/2*((b*c^2*d - 2*a*c^2*e)*sqrt(-a)*x*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) + (2*a^2*c*f - a^2*b*g)*sqrt(-c)*x*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)) - 2*(a^2*c*g*x - a*c^2*d)*sqrt(c*x^2 + b*x + a))/(a^2*c^2*x)]","A",0
285,1,783,0,8.040895," ","integrate((g*x^3+f*x^2+e*x+d)/x^3/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{8 \, a^{3} \sqrt{c} g x^{2} \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) - {\left(4 \, a b c e - 8 \, a^{2} c f - {\left(3 \, b^{2} c - 4 \, a c^{2}\right)} d\right)} \sqrt{a} x^{2} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) - 4 \, {\left(2 \, a^{2} c d - {\left(3 \, a b c d - 4 \, a^{2} c e\right)} x\right)} \sqrt{c x^{2} + b x + a}}{16 \, a^{3} c x^{2}}, -\frac{16 \, a^{3} \sqrt{-c} g x^{2} \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) + {\left(4 \, a b c e - 8 \, a^{2} c f - {\left(3 \, b^{2} c - 4 \, a c^{2}\right)} d\right)} \sqrt{a} x^{2} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) + 4 \, {\left(2 \, a^{2} c d - {\left(3 \, a b c d - 4 \, a^{2} c e\right)} x\right)} \sqrt{c x^{2} + b x + a}}{16 \, a^{3} c x^{2}}, \frac{4 \, a^{3} \sqrt{c} g x^{2} \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) - {\left(4 \, a b c e - 8 \, a^{2} c f - {\left(3 \, b^{2} c - 4 \, a c^{2}\right)} d\right)} \sqrt{-a} x^{2} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) - 2 \, {\left(2 \, a^{2} c d - {\left(3 \, a b c d - 4 \, a^{2} c e\right)} x\right)} \sqrt{c x^{2} + b x + a}}{8 \, a^{3} c x^{2}}, -\frac{8 \, a^{3} \sqrt{-c} g x^{2} \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) + {\left(4 \, a b c e - 8 \, a^{2} c f - {\left(3 \, b^{2} c - 4 \, a c^{2}\right)} d\right)} \sqrt{-a} x^{2} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) + 2 \, {\left(2 \, a^{2} c d - {\left(3 \, a b c d - 4 \, a^{2} c e\right)} x\right)} \sqrt{c x^{2} + b x + a}}{8 \, a^{3} c x^{2}}\right]"," ",0,"[1/16*(8*a^3*sqrt(c)*g*x^2*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) - (4*a*b*c*e - 8*a^2*c*f - (3*b^2*c - 4*a*c^2)*d)*sqrt(a)*x^2*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) - 4*(2*a^2*c*d - (3*a*b*c*d - 4*a^2*c*e)*x)*sqrt(c*x^2 + b*x + a))/(a^3*c*x^2), -1/16*(16*a^3*sqrt(-c)*g*x^2*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)) + (4*a*b*c*e - 8*a^2*c*f - (3*b^2*c - 4*a*c^2)*d)*sqrt(a)*x^2*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) + 4*(2*a^2*c*d - (3*a*b*c*d - 4*a^2*c*e)*x)*sqrt(c*x^2 + b*x + a))/(a^3*c*x^2), 1/8*(4*a^3*sqrt(c)*g*x^2*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) - (4*a*b*c*e - 8*a^2*c*f - (3*b^2*c - 4*a*c^2)*d)*sqrt(-a)*x^2*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) - 2*(2*a^2*c*d - (3*a*b*c*d - 4*a^2*c*e)*x)*sqrt(c*x^2 + b*x + a))/(a^3*c*x^2), -1/8*(8*a^3*sqrt(-c)*g*x^2*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)) + (4*a*b*c*e - 8*a^2*c*f - (3*b^2*c - 4*a*c^2)*d)*sqrt(-a)*x^2*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) + 2*(2*a^2*c*d - (3*a*b*c*d - 4*a^2*c*e)*x)*sqrt(c*x^2 + b*x + a))/(a^3*c*x^2)]","A",0
286,1,365,0,7.645071," ","integrate((g*x^3+f*x^2+e*x+d)/x^4/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(8 \, a^{2} b f - 16 \, a^{3} g + {\left(5 \, b^{3} - 12 \, a b c\right)} d - 2 \, {\left(3 \, a b^{2} - 4 \, a^{2} c\right)} e\right)} \sqrt{a} x^{3} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) + 4 \, {\left(8 \, a^{3} d - {\left(18 \, a^{2} b e - 24 \, a^{3} f - {\left(15 \, a b^{2} - 16 \, a^{2} c\right)} d\right)} x^{2} - 2 \, {\left(5 \, a^{2} b d - 6 \, a^{3} e\right)} x\right)} \sqrt{c x^{2} + b x + a}}{96 \, a^{4} x^{3}}, -\frac{3 \, {\left(8 \, a^{2} b f - 16 \, a^{3} g + {\left(5 \, b^{3} - 12 \, a b c\right)} d - 2 \, {\left(3 \, a b^{2} - 4 \, a^{2} c\right)} e\right)} \sqrt{-a} x^{3} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) + 2 \, {\left(8 \, a^{3} d - {\left(18 \, a^{2} b e - 24 \, a^{3} f - {\left(15 \, a b^{2} - 16 \, a^{2} c\right)} d\right)} x^{2} - 2 \, {\left(5 \, a^{2} b d - 6 \, a^{3} e\right)} x\right)} \sqrt{c x^{2} + b x + a}}{48 \, a^{4} x^{3}}\right]"," ",0,"[-1/96*(3*(8*a^2*b*f - 16*a^3*g + (5*b^3 - 12*a*b*c)*d - 2*(3*a*b^2 - 4*a^2*c)*e)*sqrt(a)*x^3*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) + 4*(8*a^3*d - (18*a^2*b*e - 24*a^3*f - (15*a*b^2 - 16*a^2*c)*d)*x^2 - 2*(5*a^2*b*d - 6*a^3*e)*x)*sqrt(c*x^2 + b*x + a))/(a^4*x^3), -1/48*(3*(8*a^2*b*f - 16*a^3*g + (5*b^3 - 12*a*b*c)*d - 2*(3*a*b^2 - 4*a^2*c)*e)*sqrt(-a)*x^3*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) + 2*(8*a^3*d - (18*a^2*b*e - 24*a^3*f - (15*a*b^2 - 16*a^2*c)*d)*x^2 - 2*(5*a^2*b*d - 6*a^3*e)*x)*sqrt(c*x^2 + b*x + a))/(a^4*x^3)]","A",0
287,1,525,0,15.352680," ","integrate((g*x^3+f*x^2+e*x+d)/x^5/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(64 \, a^{3} b g - {\left(35 \, b^{4} - 120 \, a b^{2} c + 48 \, a^{2} c^{2}\right)} d + 8 \, {\left(5 \, a b^{3} - 12 \, a^{2} b c\right)} e - 16 \, {\left(3 \, a^{2} b^{2} - 4 \, a^{3} c\right)} f\right)} \sqrt{a} x^{4} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) - 4 \, {\left(48 \, a^{4} d - {\left(144 \, a^{3} b f - 192 \, a^{4} g + 5 \, {\left(21 \, a b^{3} - 44 \, a^{2} b c\right)} d - 8 \, {\left(15 \, a^{2} b^{2} - 16 \, a^{3} c\right)} e\right)} x^{3} - 2 \, {\left(40 \, a^{3} b e - 48 \, a^{4} f - {\left(35 \, a^{2} b^{2} - 36 \, a^{3} c\right)} d\right)} x^{2} - 8 \, {\left(7 \, a^{3} b d - 8 \, a^{4} e\right)} x\right)} \sqrt{c x^{2} + b x + a}}{768 \, a^{5} x^{4}}, -\frac{3 \, {\left(64 \, a^{3} b g - {\left(35 \, b^{4} - 120 \, a b^{2} c + 48 \, a^{2} c^{2}\right)} d + 8 \, {\left(5 \, a b^{3} - 12 \, a^{2} b c\right)} e - 16 \, {\left(3 \, a^{2} b^{2} - 4 \, a^{3} c\right)} f\right)} \sqrt{-a} x^{4} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) + 2 \, {\left(48 \, a^{4} d - {\left(144 \, a^{3} b f - 192 \, a^{4} g + 5 \, {\left(21 \, a b^{3} - 44 \, a^{2} b c\right)} d - 8 \, {\left(15 \, a^{2} b^{2} - 16 \, a^{3} c\right)} e\right)} x^{3} - 2 \, {\left(40 \, a^{3} b e - 48 \, a^{4} f - {\left(35 \, a^{2} b^{2} - 36 \, a^{3} c\right)} d\right)} x^{2} - 8 \, {\left(7 \, a^{3} b d - 8 \, a^{4} e\right)} x\right)} \sqrt{c x^{2} + b x + a}}{384 \, a^{5} x^{4}}\right]"," ",0,"[1/768*(3*(64*a^3*b*g - (35*b^4 - 120*a*b^2*c + 48*a^2*c^2)*d + 8*(5*a*b^3 - 12*a^2*b*c)*e - 16*(3*a^2*b^2 - 4*a^3*c)*f)*sqrt(a)*x^4*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 + 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) - 4*(48*a^4*d - (144*a^3*b*f - 192*a^4*g + 5*(21*a*b^3 - 44*a^2*b*c)*d - 8*(15*a^2*b^2 - 16*a^3*c)*e)*x^3 - 2*(40*a^3*b*e - 48*a^4*f - (35*a^2*b^2 - 36*a^3*c)*d)*x^2 - 8*(7*a^3*b*d - 8*a^4*e)*x)*sqrt(c*x^2 + b*x + a))/(a^5*x^4), -1/384*(3*(64*a^3*b*g - (35*b^4 - 120*a*b^2*c + 48*a^2*c^2)*d + 8*(5*a*b^3 - 12*a^2*b*c)*e - 16*(3*a^2*b^2 - 4*a^3*c)*f)*sqrt(-a)*x^4*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) + 2*(48*a^4*d - (144*a^3*b*f - 192*a^4*g + 5*(21*a*b^3 - 44*a^2*b*c)*d - 8*(15*a^2*b^2 - 16*a^3*c)*e)*x^3 - 2*(40*a^3*b*e - 48*a^4*f - (35*a^2*b^2 - 36*a^3*c)*d)*x^2 - 8*(7*a^3*b*d - 8*a^4*e)*x)*sqrt(c*x^2 + b*x + a))/(a^5*x^4)]","A",0
288,1,727,0,40.332934," ","integrate((g*x^3+f*x^2+e*x+d)/x^6/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left({\left(63 \, b^{5} - 280 \, a b^{3} c + 240 \, a^{2} b c^{2}\right)} d - 2 \, {\left(35 \, a b^{4} - 120 \, a^{2} b^{2} c + 48 \, a^{3} c^{2}\right)} e + 16 \, {\left(5 \, a^{2} b^{3} - 12 \, a^{3} b c\right)} f - 32 \, {\left(3 \, a^{3} b^{2} - 4 \, a^{4} c\right)} g\right)} \sqrt{a} x^{5} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) - 4 \, {\left(384 \, a^{5} d - {\left(1440 \, a^{4} b g - {\left(945 \, a b^{4} - 2940 \, a^{2} b^{2} c + 1024 \, a^{3} c^{2}\right)} d + 50 \, {\left(21 \, a^{2} b^{3} - 44 \, a^{3} b c\right)} e - 80 \, {\left(15 \, a^{3} b^{2} - 16 \, a^{4} c\right)} f\right)} x^{4} - 2 \, {\left(400 \, a^{4} b f - 480 \, a^{5} g + 7 \, {\left(45 \, a^{2} b^{3} - 92 \, a^{3} b c\right)} d - 10 \, {\left(35 \, a^{3} b^{2} - 36 \, a^{4} c\right)} e\right)} x^{3} - 8 \, {\left(70 \, a^{4} b e - 80 \, a^{5} f - {\left(63 \, a^{3} b^{2} - 64 \, a^{4} c\right)} d\right)} x^{2} - 48 \, {\left(9 \, a^{4} b d - 10 \, a^{5} e\right)} x\right)} \sqrt{c x^{2} + b x + a}}{7680 \, a^{6} x^{5}}, -\frac{15 \, {\left({\left(63 \, b^{5} - 280 \, a b^{3} c + 240 \, a^{2} b c^{2}\right)} d - 2 \, {\left(35 \, a b^{4} - 120 \, a^{2} b^{2} c + 48 \, a^{3} c^{2}\right)} e + 16 \, {\left(5 \, a^{2} b^{3} - 12 \, a^{3} b c\right)} f - 32 \, {\left(3 \, a^{3} b^{2} - 4 \, a^{4} c\right)} g\right)} \sqrt{-a} x^{5} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) + 2 \, {\left(384 \, a^{5} d - {\left(1440 \, a^{4} b g - {\left(945 \, a b^{4} - 2940 \, a^{2} b^{2} c + 1024 \, a^{3} c^{2}\right)} d + 50 \, {\left(21 \, a^{2} b^{3} - 44 \, a^{3} b c\right)} e - 80 \, {\left(15 \, a^{3} b^{2} - 16 \, a^{4} c\right)} f\right)} x^{4} - 2 \, {\left(400 \, a^{4} b f - 480 \, a^{5} g + 7 \, {\left(45 \, a^{2} b^{3} - 92 \, a^{3} b c\right)} d - 10 \, {\left(35 \, a^{3} b^{2} - 36 \, a^{4} c\right)} e\right)} x^{3} - 8 \, {\left(70 \, a^{4} b e - 80 \, a^{5} f - {\left(63 \, a^{3} b^{2} - 64 \, a^{4} c\right)} d\right)} x^{2} - 48 \, {\left(9 \, a^{4} b d - 10 \, a^{5} e\right)} x\right)} \sqrt{c x^{2} + b x + a}}{3840 \, a^{6} x^{5}}\right]"," ",0,"[1/7680*(15*((63*b^5 - 280*a*b^3*c + 240*a^2*b*c^2)*d - 2*(35*a*b^4 - 120*a^2*b^2*c + 48*a^3*c^2)*e + 16*(5*a^2*b^3 - 12*a^3*b*c)*f - 32*(3*a^3*b^2 - 4*a^4*c)*g)*sqrt(a)*x^5*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 + 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) - 4*(384*a^5*d - (1440*a^4*b*g - (945*a*b^4 - 2940*a^2*b^2*c + 1024*a^3*c^2)*d + 50*(21*a^2*b^3 - 44*a^3*b*c)*e - 80*(15*a^3*b^2 - 16*a^4*c)*f)*x^4 - 2*(400*a^4*b*f - 480*a^5*g + 7*(45*a^2*b^3 - 92*a^3*b*c)*d - 10*(35*a^3*b^2 - 36*a^4*c)*e)*x^3 - 8*(70*a^4*b*e - 80*a^5*f - (63*a^3*b^2 - 64*a^4*c)*d)*x^2 - 48*(9*a^4*b*d - 10*a^5*e)*x)*sqrt(c*x^2 + b*x + a))/(a^6*x^5), -1/3840*(15*((63*b^5 - 280*a*b^3*c + 240*a^2*b*c^2)*d - 2*(35*a*b^4 - 120*a^2*b^2*c + 48*a^3*c^2)*e + 16*(5*a^2*b^3 - 12*a^3*b*c)*f - 32*(3*a^3*b^2 - 4*a^4*c)*g)*sqrt(-a)*x^5*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) + 2*(384*a^5*d - (1440*a^4*b*g - (945*a*b^4 - 2940*a^2*b^2*c + 1024*a^3*c^2)*d + 50*(21*a^2*b^3 - 44*a^3*b*c)*e - 80*(15*a^3*b^2 - 16*a^4*c)*f)*x^4 - 2*(400*a^4*b*f - 480*a^5*g + 7*(45*a^2*b^3 - 92*a^3*b*c)*d - 10*(35*a^3*b^2 - 36*a^4*c)*e)*x^3 - 8*(70*a^4*b*e - 80*a^5*f - (63*a^3*b^2 - 64*a^4*c)*d)*x^2 - 48*(9*a^4*b*d - 10*a^5*e)*x)*sqrt(c*x^2 + b*x + a))/(a^6*x^5)]","A",0
289,1,237,0,0.742230," ","integrate((e*x+d)^3*(5*x^2+2*x+3)*(4*x^4-5*x^3+3*x^2+x+2),x, algorithm=""fricas"")","2 x^{10} e^{3} - \frac{17}{9} x^{9} e^{3} + \frac{20}{3} x^{9} e^{2} d + \frac{17}{8} x^{8} e^{3} - \frac{51}{8} x^{8} e^{2} d + \frac{15}{2} x^{8} e d^{2} - \frac{4}{7} x^{7} e^{3} + \frac{51}{7} x^{7} e^{2} d - \frac{51}{7} x^{7} e d^{2} + \frac{20}{7} x^{7} d^{3} + \frac{7}{2} x^{6} e^{3} - 2 x^{6} e^{2} d + \frac{17}{2} x^{6} e d^{2} - \frac{17}{6} x^{6} d^{3} + \frac{7}{5} x^{5} e^{3} + \frac{63}{5} x^{5} e^{2} d - \frac{12}{5} x^{5} e d^{2} + \frac{17}{5} x^{5} d^{3} + \frac{3}{2} x^{4} e^{3} + \frac{21}{4} x^{4} e^{2} d + \frac{63}{4} x^{4} e d^{2} - x^{4} d^{3} + 6 x^{3} e^{2} d + 7 x^{3} e d^{2} + 7 x^{3} d^{3} + 9 x^{2} e d^{2} + \frac{7}{2} x^{2} d^{3} + 6 x d^{3}"," ",0,"2*x^10*e^3 - 17/9*x^9*e^3 + 20/3*x^9*e^2*d + 17/8*x^8*e^3 - 51/8*x^8*e^2*d + 15/2*x^8*e*d^2 - 4/7*x^7*e^3 + 51/7*x^7*e^2*d - 51/7*x^7*e*d^2 + 20/7*x^7*d^3 + 7/2*x^6*e^3 - 2*x^6*e^2*d + 17/2*x^6*e*d^2 - 17/6*x^6*d^3 + 7/5*x^5*e^3 + 63/5*x^5*e^2*d - 12/5*x^5*e*d^2 + 17/5*x^5*d^3 + 3/2*x^4*e^3 + 21/4*x^4*e^2*d + 63/4*x^4*e*d^2 - x^4*d^3 + 6*x^3*e^2*d + 7*x^3*e*d^2 + 7*x^3*d^3 + 9*x^2*e*d^2 + 7/2*x^2*d^3 + 6*x*d^3","A",0
290,1,160,0,0.880752," ","integrate((e*x+d)^2*(5*x^2+2*x+3)*(4*x^4-5*x^3+3*x^2+x+2),x, algorithm=""fricas"")","\frac{20}{9} x^{9} e^{2} - \frac{17}{8} x^{8} e^{2} + 5 x^{8} e d + \frac{17}{7} x^{7} e^{2} - \frac{34}{7} x^{7} e d + \frac{20}{7} x^{7} d^{2} - \frac{2}{3} x^{6} e^{2} + \frac{17}{3} x^{6} e d - \frac{17}{6} x^{6} d^{2} + \frac{21}{5} x^{5} e^{2} - \frac{8}{5} x^{5} e d + \frac{17}{5} x^{5} d^{2} + \frac{7}{4} x^{4} e^{2} + \frac{21}{2} x^{4} e d - x^{4} d^{2} + 2 x^{3} e^{2} + \frac{14}{3} x^{3} e d + 7 x^{3} d^{2} + 6 x^{2} e d + \frac{7}{2} x^{2} d^{2} + 6 x d^{2}"," ",0,"20/9*x^9*e^2 - 17/8*x^8*e^2 + 5*x^8*e*d + 17/7*x^7*e^2 - 34/7*x^7*e*d + 20/7*x^7*d^2 - 2/3*x^6*e^2 + 17/3*x^6*e*d - 17/6*x^6*d^2 + 21/5*x^5*e^2 - 8/5*x^5*e*d + 17/5*x^5*d^2 + 7/4*x^4*e^2 + 21/2*x^4*e*d - x^4*d^2 + 2*x^3*e^2 + 14/3*x^3*e*d + 7*x^3*d^2 + 6*x^2*e*d + 7/2*x^2*d^2 + 6*x*d^2","A",0
291,1,83,0,0.761611," ","integrate((e*x+d)*(5*x^2+2*x+3)*(4*x^4-5*x^3+3*x^2+x+2),x, algorithm=""fricas"")","\frac{5}{2} x^{8} e - \frac{17}{7} x^{7} e + \frac{20}{7} x^{7} d + \frac{17}{6} x^{6} e - \frac{17}{6} x^{6} d - \frac{4}{5} x^{5} e + \frac{17}{5} x^{5} d + \frac{21}{4} x^{4} e - x^{4} d + \frac{7}{3} x^{3} e + 7 x^{3} d + 3 x^{2} e + \frac{7}{2} x^{2} d + 6 x d"," ",0,"5/2*x^8*e - 17/7*x^7*e + 20/7*x^7*d + 17/6*x^6*e - 17/6*x^6*d - 4/5*x^5*e + 17/5*x^5*d + 21/4*x^4*e - x^4*d + 7/3*x^3*e + 7*x^3*d + 3*x^2*e + 7/2*x^2*d + 6*x*d","A",0
292,1,34,0,0.630737," ","integrate((5*x^2+2*x+3)*(4*x^4-5*x^3+3*x^2+x+2),x, algorithm=""fricas"")","\frac{20}{7} x^{7} - \frac{17}{6} x^{6} + \frac{17}{5} x^{5} - x^{4} + 7 x^{3} + \frac{7}{2} x^{2} + 6 x"," ",0,"20/7*x^7 - 17/6*x^6 + 17/5*x^5 - x^4 + 7*x^3 + 7/2*x^2 + 6*x","A",0
293,1,230,0,0.733674," ","integrate((5*x^2+2*x+3)*(4*x^4-5*x^3+3*x^2+x+2)/(e*x+d),x, algorithm=""fricas"")","\frac{200 \, e^{6} x^{6} - 12 \, {\left(20 \, d e^{5} + 17 \, e^{6}\right)} x^{5} + 15 \, {\left(20 \, d^{2} e^{4} + 17 \, d e^{5} + 17 \, e^{6}\right)} x^{4} - 20 \, {\left(20 \, d^{3} e^{3} + 17 \, d^{2} e^{4} + 17 \, d e^{5} + 4 \, e^{6}\right)} x^{3} + 30 \, {\left(20 \, d^{4} e^{2} + 17 \, d^{3} e^{3} + 17 \, d^{2} e^{4} + 4 \, d e^{5} + 21 \, e^{6}\right)} x^{2} - 60 \, {\left(20 \, d^{5} e + 17 \, d^{4} e^{2} + 17 \, d^{3} e^{3} + 4 \, d^{2} e^{4} + 21 \, d e^{5} - 7 \, e^{6}\right)} x + 60 \, {\left(20 \, d^{6} + 17 \, d^{5} e + 17 \, d^{4} e^{2} + 4 \, d^{3} e^{3} + 21 \, d^{2} e^{4} - 7 \, d e^{5} + 6 \, e^{6}\right)} \log\left(e x + d\right)}{60 \, e^{7}}"," ",0,"1/60*(200*e^6*x^6 - 12*(20*d*e^5 + 17*e^6)*x^5 + 15*(20*d^2*e^4 + 17*d*e^5 + 17*e^6)*x^4 - 20*(20*d^3*e^3 + 17*d^2*e^4 + 17*d*e^5 + 4*e^6)*x^3 + 30*(20*d^4*e^2 + 17*d^3*e^3 + 17*d^2*e^4 + 4*d*e^5 + 21*e^6)*x^2 - 60*(20*d^5*e + 17*d^4*e^2 + 17*d^3*e^3 + 4*d^2*e^4 + 21*d*e^5 - 7*e^6)*x + 60*(20*d^6 + 17*d^5*e + 17*d^4*e^2 + 4*d^3*e^3 + 21*d^2*e^4 - 7*d*e^5 + 6*e^6)*log(e*x + d))/e^7","A",0
294,1,319,0,0.467194," ","integrate((5*x^2+2*x+3)*(4*x^4-5*x^3+3*x^2+x+2)/(e*x+d)^2,x, algorithm=""fricas"")","\frac{48 \, e^{6} x^{6} - 240 \, d^{6} - 204 \, d^{5} e - 204 \, d^{4} e^{2} - 48 \, d^{3} e^{3} - 252 \, d^{2} e^{4} + 84 \, d e^{5} - 72 \, e^{6} - 3 \, {\left(24 \, d e^{5} + 17 \, e^{6}\right)} x^{5} + {\left(120 \, d^{2} e^{4} + 85 \, d e^{5} + 68 \, e^{6}\right)} x^{4} - 2 \, {\left(120 \, d^{3} e^{3} + 85 \, d^{2} e^{4} + 68 \, d e^{5} + 12 \, e^{6}\right)} x^{3} + 6 \, {\left(120 \, d^{4} e^{2} + 85 \, d^{3} e^{3} + 68 \, d^{2} e^{4} + 12 \, d e^{5} + 42 \, e^{6}\right)} x^{2} + 12 \, {\left(100 \, d^{5} e + 68 \, d^{4} e^{2} + 51 \, d^{3} e^{3} + 8 \, d^{2} e^{4} + 21 \, d e^{5}\right)} x - 12 \, {\left(120 \, d^{6} + 85 \, d^{5} e + 68 \, d^{4} e^{2} + 12 \, d^{3} e^{3} + 42 \, d^{2} e^{4} - 7 \, d e^{5} + {\left(120 \, d^{5} e + 85 \, d^{4} e^{2} + 68 \, d^{3} e^{3} + 12 \, d^{2} e^{4} + 42 \, d e^{5} - 7 \, e^{6}\right)} x\right)} \log\left(e x + d\right)}{12 \, {\left(e^{8} x + d e^{7}\right)}}"," ",0,"1/12*(48*e^6*x^6 - 240*d^6 - 204*d^5*e - 204*d^4*e^2 - 48*d^3*e^3 - 252*d^2*e^4 + 84*d*e^5 - 72*e^6 - 3*(24*d*e^5 + 17*e^6)*x^5 + (120*d^2*e^4 + 85*d*e^5 + 68*e^6)*x^4 - 2*(120*d^3*e^3 + 85*d^2*e^4 + 68*d*e^5 + 12*e^6)*x^3 + 6*(120*d^4*e^2 + 85*d^3*e^3 + 68*d^2*e^4 + 12*d*e^5 + 42*e^6)*x^2 + 12*(100*d^5*e + 68*d^4*e^2 + 51*d^3*e^3 + 8*d^2*e^4 + 21*d*e^5)*x - 12*(120*d^6 + 85*d^5*e + 68*d^4*e^2 + 12*d^3*e^3 + 42*d^2*e^4 - 7*d*e^5 + (120*d^5*e + 85*d^4*e^2 + 68*d^3*e^3 + 12*d^2*e^4 + 42*d*e^5 - 7*e^6)*x)*log(e*x + d))/(e^8*x + d*e^7)","A",0
295,1,360,0,0.768287," ","integrate((5*x^2+2*x+3)*(4*x^4-5*x^3+3*x^2+x+2)/(e*x+d)^3,x, algorithm=""fricas"")","\frac{30 \, e^{6} x^{6} + 660 \, d^{6} + 459 \, d^{5} e + 357 \, d^{4} e^{2} + 60 \, d^{3} e^{3} + 189 \, d^{2} e^{4} - 21 \, d e^{5} - 18 \, e^{6} - 2 \, {\left(30 \, d e^{5} + 17 \, e^{6}\right)} x^{5} + {\left(150 \, d^{2} e^{4} + 85 \, d e^{5} + 51 \, e^{6}\right)} x^{4} - 4 \, {\left(150 \, d^{3} e^{3} + 85 \, d^{2} e^{4} + 51 \, d e^{5} + 6 \, e^{6}\right)} x^{3} - 3 \, {\left(680 \, d^{4} e^{2} + 357 \, d^{3} e^{3} + 187 \, d^{2} e^{4} + 16 \, d e^{5}\right)} x^{2} - 6 \, {\left(80 \, d^{5} e + 17 \, d^{4} e^{2} - 17 \, d^{3} e^{3} - 8 \, d^{2} e^{4} - 42 \, d e^{5} + 7 \, e^{6}\right)} x + 6 \, {\left(300 \, d^{6} + 170 \, d^{5} e + 102 \, d^{4} e^{2} + 12 \, d^{3} e^{3} + 21 \, d^{2} e^{4} + {\left(300 \, d^{4} e^{2} + 170 \, d^{3} e^{3} + 102 \, d^{2} e^{4} + 12 \, d e^{5} + 21 \, e^{6}\right)} x^{2} + 2 \, {\left(300 \, d^{5} e + 170 \, d^{4} e^{2} + 102 \, d^{3} e^{3} + 12 \, d^{2} e^{4} + 21 \, d e^{5}\right)} x\right)} \log\left(e x + d\right)}{6 \, {\left(e^{9} x^{2} + 2 \, d e^{8} x + d^{2} e^{7}\right)}}"," ",0,"1/6*(30*e^6*x^6 + 660*d^6 + 459*d^5*e + 357*d^4*e^2 + 60*d^3*e^3 + 189*d^2*e^4 - 21*d*e^5 - 18*e^6 - 2*(30*d*e^5 + 17*e^6)*x^5 + (150*d^2*e^4 + 85*d*e^5 + 51*e^6)*x^4 - 4*(150*d^3*e^3 + 85*d^2*e^4 + 51*d*e^5 + 6*e^6)*x^3 - 3*(680*d^4*e^2 + 357*d^3*e^3 + 187*d^2*e^4 + 16*d*e^5)*x^2 - 6*(80*d^5*e + 17*d^4*e^2 - 17*d^3*e^3 - 8*d^2*e^4 - 42*d*e^5 + 7*e^6)*x + 6*(300*d^6 + 170*d^5*e + 102*d^4*e^2 + 12*d^3*e^3 + 21*d^2*e^4 + (300*d^4*e^2 + 170*d^3*e^3 + 102*d^2*e^4 + 12*d*e^5 + 21*e^6)*x^2 + 2*(300*d^5*e + 170*d^4*e^2 + 102*d^3*e^3 + 12*d^2*e^4 + 21*d*e^5)*x)*log(e*x + d))/(e^9*x^2 + 2*d*e^8*x + d^2*e^7)","A",0
296,1,305,0,0.756399," ","integrate((e*x+d)^3*(5*x^2+2*x+3)^2*(4*x^4-5*x^3+3*x^2+x+2),x, algorithm=""fricas"")","\frac{25}{3} x^{12} e^{3} - \frac{45}{11} x^{11} e^{3} + \frac{300}{11} x^{11} e^{2} d + \frac{111}{10} x^{10} e^{3} - \frac{27}{2} x^{10} e^{2} d + 30 x^{10} e d^{2} - \frac{37}{9} x^{9} e^{3} + 37 x^{9} e^{2} d - 15 x^{9} e d^{2} + \frac{100}{9} x^{9} d^{3} + \frac{37}{2} x^{8} e^{3} - \frac{111}{8} x^{8} e^{2} d + \frac{333}{8} x^{8} e d^{2} - \frac{45}{8} x^{8} d^{3} + \frac{65}{7} x^{7} e^{3} + \frac{444}{7} x^{7} e^{2} d - \frac{111}{7} x^{7} e d^{2} + \frac{111}{7} x^{7} d^{3} + \frac{107}{6} x^{6} e^{3} + \frac{65}{2} x^{6} e^{2} d + 74 x^{6} e d^{2} - \frac{37}{6} x^{6} d^{3} + \frac{33}{5} x^{5} e^{3} + \frac{321}{5} x^{5} e^{2} d + 39 x^{5} e d^{2} + \frac{148}{5} x^{5} d^{3} + \frac{9}{2} x^{4} e^{3} + \frac{99}{4} x^{4} e^{2} d + \frac{321}{4} x^{4} e d^{2} + \frac{65}{4} x^{4} d^{3} + 18 x^{3} e^{2} d + 33 x^{3} e d^{2} + \frac{107}{3} x^{3} d^{3} + 27 x^{2} e d^{2} + \frac{33}{2} x^{2} d^{3} + 18 x d^{3}"," ",0,"25/3*x^12*e^3 - 45/11*x^11*e^3 + 300/11*x^11*e^2*d + 111/10*x^10*e^3 - 27/2*x^10*e^2*d + 30*x^10*e*d^2 - 37/9*x^9*e^3 + 37*x^9*e^2*d - 15*x^9*e*d^2 + 100/9*x^9*d^3 + 37/2*x^8*e^3 - 111/8*x^8*e^2*d + 333/8*x^8*e*d^2 - 45/8*x^8*d^3 + 65/7*x^7*e^3 + 444/7*x^7*e^2*d - 111/7*x^7*e*d^2 + 111/7*x^7*d^3 + 107/6*x^6*e^3 + 65/2*x^6*e^2*d + 74*x^6*e*d^2 - 37/6*x^6*d^3 + 33/5*x^5*e^3 + 321/5*x^5*e^2*d + 39*x^5*e*d^2 + 148/5*x^5*d^3 + 9/2*x^4*e^3 + 99/4*x^4*e^2*d + 321/4*x^4*e*d^2 + 65/4*x^4*d^3 + 18*x^3*e^2*d + 33*x^3*e*d^2 + 107/3*x^3*d^3 + 27*x^2*e*d^2 + 33/2*x^2*d^3 + 18*x*d^3","A",0
297,1,206,0,0.460073," ","integrate((e*x+d)^2*(5*x^2+2*x+3)^2*(4*x^4-5*x^3+3*x^2+x+2),x, algorithm=""fricas"")","\frac{100}{11} x^{11} e^{2} - \frac{9}{2} x^{10} e^{2} + 20 x^{10} e d + \frac{37}{3} x^{9} e^{2} - 10 x^{9} e d + \frac{100}{9} x^{9} d^{2} - \frac{37}{8} x^{8} e^{2} + \frac{111}{4} x^{8} e d - \frac{45}{8} x^{8} d^{2} + \frac{148}{7} x^{7} e^{2} - \frac{74}{7} x^{7} e d + \frac{111}{7} x^{7} d^{2} + \frac{65}{6} x^{6} e^{2} + \frac{148}{3} x^{6} e d - \frac{37}{6} x^{6} d^{2} + \frac{107}{5} x^{5} e^{2} + 26 x^{5} e d + \frac{148}{5} x^{5} d^{2} + \frac{33}{4} x^{4} e^{2} + \frac{107}{2} x^{4} e d + \frac{65}{4} x^{4} d^{2} + 6 x^{3} e^{2} + 22 x^{3} e d + \frac{107}{3} x^{3} d^{2} + 18 x^{2} e d + \frac{33}{2} x^{2} d^{2} + 18 x d^{2}"," ",0,"100/11*x^11*e^2 - 9/2*x^10*e^2 + 20*x^10*e*d + 37/3*x^9*e^2 - 10*x^9*e*d + 100/9*x^9*d^2 - 37/8*x^8*e^2 + 111/4*x^8*e*d - 45/8*x^8*d^2 + 148/7*x^7*e^2 - 74/7*x^7*e*d + 111/7*x^7*d^2 + 65/6*x^6*e^2 + 148/3*x^6*e*d - 37/6*x^6*d^2 + 107/5*x^5*e^2 + 26*x^5*e*d + 148/5*x^5*d^2 + 33/4*x^4*e^2 + 107/2*x^4*e*d + 65/4*x^4*d^2 + 6*x^3*e^2 + 22*x^3*e*d + 107/3*x^3*d^2 + 18*x^2*e*d + 33/2*x^2*d^2 + 18*x*d^2","A",0
298,1,107,0,0.806403," ","integrate((e*x+d)*(5*x^2+2*x+3)^2*(4*x^4-5*x^3+3*x^2+x+2),x, algorithm=""fricas"")","10 x^{10} e - 5 x^{9} e + \frac{100}{9} x^{9} d + \frac{111}{8} x^{8} e - \frac{45}{8} x^{8} d - \frac{37}{7} x^{7} e + \frac{111}{7} x^{7} d + \frac{74}{3} x^{6} e - \frac{37}{6} x^{6} d + 13 x^{5} e + \frac{148}{5} x^{5} d + \frac{107}{4} x^{4} e + \frac{65}{4} x^{4} d + 11 x^{3} e + \frac{107}{3} x^{3} d + 9 x^{2} e + \frac{33}{2} x^{2} d + 18 x d"," ",0,"10*x^10*e - 5*x^9*e + 100/9*x^9*d + 111/8*x^8*e - 45/8*x^8*d - 37/7*x^7*e + 111/7*x^7*d + 74/3*x^6*e - 37/6*x^6*d + 13*x^5*e + 148/5*x^5*d + 107/4*x^4*e + 65/4*x^4*d + 11*x^3*e + 107/3*x^3*d + 9*x^2*e + 33/2*x^2*d + 18*x*d","A",0
299,1,44,0,0.636450," ","integrate((5*x^2+2*x+3)^2*(4*x^4-5*x^3+3*x^2+x+2),x, algorithm=""fricas"")","\frac{100}{9} x^{9} - \frac{45}{8} x^{8} + \frac{111}{7} x^{7} - \frac{37}{6} x^{6} + \frac{148}{5} x^{5} + \frac{65}{4} x^{4} + \frac{107}{3} x^{3} + \frac{33}{2} x^{2} + 18 x"," ",0,"100/9*x^9 - 45/8*x^8 + 111/7*x^7 - 37/6*x^6 + 148/5*x^5 + 65/4*x^4 + 107/3*x^3 + 33/2*x^2 + 18*x","A",0
300,1,368,0,1.011634," ","integrate((5*x^2+2*x+3)^2*(4*x^4-5*x^3+3*x^2+x+2)/(e*x+d),x, algorithm=""fricas"")","\frac{5250 \, e^{8} x^{8} - 300 \, {\left(20 \, d e^{7} + 9 \, e^{8}\right)} x^{7} + 70 \, {\left(100 \, d^{2} e^{6} + 45 \, d e^{7} + 111 \, e^{8}\right)} x^{6} - 84 \, {\left(100 \, d^{3} e^{5} + 45 \, d^{2} e^{6} + 111 \, d e^{7} + 37 \, e^{8}\right)} x^{5} + 105 \, {\left(100 \, d^{4} e^{4} + 45 \, d^{3} e^{5} + 111 \, d^{2} e^{6} + 37 \, d e^{7} + 148 \, e^{8}\right)} x^{4} - 140 \, {\left(100 \, d^{5} e^{3} + 45 \, d^{4} e^{4} + 111 \, d^{3} e^{5} + 37 \, d^{2} e^{6} + 148 \, d e^{7} - 65 \, e^{8}\right)} x^{3} + 210 \, {\left(100 \, d^{6} e^{2} + 45 \, d^{5} e^{3} + 111 \, d^{4} e^{4} + 37 \, d^{3} e^{5} + 148 \, d^{2} e^{6} - 65 \, d e^{7} + 107 \, e^{8}\right)} x^{2} - 420 \, {\left(100 \, d^{7} e + 45 \, d^{6} e^{2} + 111 \, d^{5} e^{3} + 37 \, d^{4} e^{4} + 148 \, d^{3} e^{5} - 65 \, d^{2} e^{6} + 107 \, d e^{7} - 33 \, e^{8}\right)} x + 420 \, {\left(100 \, d^{8} + 45 \, d^{7} e + 111 \, d^{6} e^{2} + 37 \, d^{5} e^{3} + 148 \, d^{4} e^{4} - 65 \, d^{3} e^{5} + 107 \, d^{2} e^{6} - 33 \, d e^{7} + 18 \, e^{8}\right)} \log\left(e x + d\right)}{420 \, e^{9}}"," ",0,"1/420*(5250*e^8*x^8 - 300*(20*d*e^7 + 9*e^8)*x^7 + 70*(100*d^2*e^6 + 45*d*e^7 + 111*e^8)*x^6 - 84*(100*d^3*e^5 + 45*d^2*e^6 + 111*d*e^7 + 37*e^8)*x^5 + 105*(100*d^4*e^4 + 45*d^3*e^5 + 111*d^2*e^6 + 37*d*e^7 + 148*e^8)*x^4 - 140*(100*d^5*e^3 + 45*d^4*e^4 + 111*d^3*e^5 + 37*d^2*e^6 + 148*d*e^7 - 65*e^8)*x^3 + 210*(100*d^6*e^2 + 45*d^5*e^3 + 111*d^4*e^4 + 37*d^3*e^5 + 148*d^2*e^6 - 65*d*e^7 + 107*e^8)*x^2 - 420*(100*d^7*e + 45*d^6*e^2 + 111*d^5*e^3 + 37*d^4*e^4 + 148*d^3*e^5 - 65*d^2*e^6 + 107*d*e^7 - 33*e^8)*x + 420*(100*d^8 + 45*d^7*e + 111*d^6*e^2 + 37*d^5*e^3 + 148*d^4*e^4 - 65*d^3*e^5 + 107*d^2*e^6 - 33*d*e^7 + 18*e^8)*log(e*x + d))/e^9","A",0
301,1,490,0,0.880588," ","integrate((5*x^2+2*x+3)^2*(4*x^4-5*x^3+3*x^2+x+2)/(e*x+d)^2,x, algorithm=""fricas"")","\frac{6000 \, e^{8} x^{8} - 42000 \, d^{8} - 18900 \, d^{7} e - 46620 \, d^{6} e^{2} - 15540 \, d^{5} e^{3} - 62160 \, d^{4} e^{4} + 27300 \, d^{3} e^{5} - 44940 \, d^{2} e^{6} + 13860 \, d e^{7} - 7560 \, e^{8} - 50 \, {\left(160 \, d e^{7} + 63 \, e^{8}\right)} x^{7} + 14 \, {\left(800 \, d^{2} e^{6} + 315 \, d e^{7} + 666 \, e^{8}\right)} x^{6} - 21 \, {\left(800 \, d^{3} e^{5} + 315 \, d^{2} e^{6} + 666 \, d e^{7} + 185 \, e^{8}\right)} x^{5} + 35 \, {\left(800 \, d^{4} e^{4} + 315 \, d^{3} e^{5} + 666 \, d^{2} e^{6} + 185 \, d e^{7} + 592 \, e^{8}\right)} x^{4} - 70 \, {\left(800 \, d^{5} e^{3} + 315 \, d^{4} e^{4} + 666 \, d^{3} e^{5} + 185 \, d^{2} e^{6} + 592 \, d e^{7} - 195 \, e^{8}\right)} x^{3} + 210 \, {\left(800 \, d^{6} e^{2} + 315 \, d^{5} e^{3} + 666 \, d^{4} e^{4} + 185 \, d^{3} e^{5} + 592 \, d^{2} e^{6} - 195 \, d e^{7} + 214 \, e^{8}\right)} x^{2} + 420 \, {\left(700 \, d^{7} e + 270 \, d^{6} e^{2} + 555 \, d^{5} e^{3} + 148 \, d^{4} e^{4} + 444 \, d^{3} e^{5} - 130 \, d^{2} e^{6} + 107 \, d e^{7}\right)} x - 420 \, {\left(800 \, d^{8} + 315 \, d^{7} e + 666 \, d^{6} e^{2} + 185 \, d^{5} e^{3} + 592 \, d^{4} e^{4} - 195 \, d^{3} e^{5} + 214 \, d^{2} e^{6} - 33 \, d e^{7} + {\left(800 \, d^{7} e + 315 \, d^{6} e^{2} + 666 \, d^{5} e^{3} + 185 \, d^{4} e^{4} + 592 \, d^{3} e^{5} - 195 \, d^{2} e^{6} + 214 \, d e^{7} - 33 \, e^{8}\right)} x\right)} \log\left(e x + d\right)}{420 \, {\left(e^{10} x + d e^{9}\right)}}"," ",0,"1/420*(6000*e^8*x^8 - 42000*d^8 - 18900*d^7*e - 46620*d^6*e^2 - 15540*d^5*e^3 - 62160*d^4*e^4 + 27300*d^3*e^5 - 44940*d^2*e^6 + 13860*d*e^7 - 7560*e^8 - 50*(160*d*e^7 + 63*e^8)*x^7 + 14*(800*d^2*e^6 + 315*d*e^7 + 666*e^8)*x^6 - 21*(800*d^3*e^5 + 315*d^2*e^6 + 666*d*e^7 + 185*e^8)*x^5 + 35*(800*d^4*e^4 + 315*d^3*e^5 + 666*d^2*e^6 + 185*d*e^7 + 592*e^8)*x^4 - 70*(800*d^5*e^3 + 315*d^4*e^4 + 666*d^3*e^5 + 185*d^2*e^6 + 592*d*e^7 - 195*e^8)*x^3 + 210*(800*d^6*e^2 + 315*d^5*e^3 + 666*d^4*e^4 + 185*d^3*e^5 + 592*d^2*e^6 - 195*d*e^7 + 214*e^8)*x^2 + 420*(700*d^7*e + 270*d^6*e^2 + 555*d^5*e^3 + 148*d^4*e^4 + 444*d^3*e^5 - 130*d^2*e^6 + 107*d*e^7)*x - 420*(800*d^8 + 315*d^7*e + 666*d^6*e^2 + 185*d^5*e^3 + 592*d^4*e^4 - 195*d^3*e^5 + 214*d^2*e^6 - 33*d*e^7 + (800*d^7*e + 315*d^6*e^2 + 666*d^5*e^3 + 185*d^4*e^4 + 592*d^3*e^5 - 195*d^2*e^6 + 214*d*e^7 - 33*e^8)*x)*log(e*x + d))/(e^10*x + d*e^9)","A",0
302,1,545,0,1.564652," ","integrate((5*x^2+2*x+3)^2*(4*x^4-5*x^3+3*x^2+x+2)/(e*x+d)^3,x, algorithm=""fricas"")","\frac{200 \, e^{8} x^{8} + 9000 \, d^{8} + 3510 \, d^{7} e + 7326 \, d^{6} e^{2} + 1998 \, d^{5} e^{3} + 6216 \, d^{4} e^{4} - 1950 \, d^{3} e^{5} + 1926 \, d^{2} e^{6} - 198 \, d e^{7} - 108 \, e^{8} - 4 \, {\left(80 \, d e^{7} + 27 \, e^{8}\right)} x^{7} + {\left(560 \, d^{2} e^{6} + 189 \, d e^{7} + 333 \, e^{8}\right)} x^{6} - 2 \, {\left(560 \, d^{3} e^{5} + 189 \, d^{2} e^{6} + 333 \, d e^{7} + 74 \, e^{8}\right)} x^{5} + {\left(2800 \, d^{4} e^{4} + 945 \, d^{3} e^{5} + 1665 \, d^{2} e^{6} + 370 \, d e^{7} + 888 \, e^{8}\right)} x^{4} - 4 \, {\left(2800 \, d^{5} e^{3} + 945 \, d^{4} e^{4} + 1665 \, d^{3} e^{5} + 370 \, d^{2} e^{6} + 888 \, d e^{7} - 195 \, e^{8}\right)} x^{3} - 6 \, {\left(6900 \, d^{6} e^{2} + 2250 \, d^{5} e^{3} + 3774 \, d^{4} e^{4} + 777 \, d^{3} e^{5} + 1628 \, d^{2} e^{6} - 260 \, d e^{7}\right)} x^{2} - 12 \, {\left(1300 \, d^{7} e + 360 \, d^{6} e^{2} + 444 \, d^{5} e^{3} + 37 \, d^{4} e^{4} - 148 \, d^{3} e^{5} + 130 \, d^{2} e^{6} - 214 \, d e^{7} + 33 \, e^{8}\right)} x + 12 \, {\left(2800 \, d^{8} + 945 \, d^{7} e + 1665 \, d^{6} e^{2} + 370 \, d^{5} e^{3} + 888 \, d^{4} e^{4} - 195 \, d^{3} e^{5} + 107 \, d^{2} e^{6} + {\left(2800 \, d^{6} e^{2} + 945 \, d^{5} e^{3} + 1665 \, d^{4} e^{4} + 370 \, d^{3} e^{5} + 888 \, d^{2} e^{6} - 195 \, d e^{7} + 107 \, e^{8}\right)} x^{2} + 2 \, {\left(2800 \, d^{7} e + 945 \, d^{6} e^{2} + 1665 \, d^{5} e^{3} + 370 \, d^{4} e^{4} + 888 \, d^{3} e^{5} - 195 \, d^{2} e^{6} + 107 \, d e^{7}\right)} x\right)} \log\left(e x + d\right)}{12 \, {\left(e^{11} x^{2} + 2 \, d e^{10} x + d^{2} e^{9}\right)}}"," ",0,"1/12*(200*e^8*x^8 + 9000*d^8 + 3510*d^7*e + 7326*d^6*e^2 + 1998*d^5*e^3 + 6216*d^4*e^4 - 1950*d^3*e^5 + 1926*d^2*e^6 - 198*d*e^7 - 108*e^8 - 4*(80*d*e^7 + 27*e^8)*x^7 + (560*d^2*e^6 + 189*d*e^7 + 333*e^8)*x^6 - 2*(560*d^3*e^5 + 189*d^2*e^6 + 333*d*e^7 + 74*e^8)*x^5 + (2800*d^4*e^4 + 945*d^3*e^5 + 1665*d^2*e^6 + 370*d*e^7 + 888*e^8)*x^4 - 4*(2800*d^5*e^3 + 945*d^4*e^4 + 1665*d^3*e^5 + 370*d^2*e^6 + 888*d*e^7 - 195*e^8)*x^3 - 6*(6900*d^6*e^2 + 2250*d^5*e^3 + 3774*d^4*e^4 + 777*d^3*e^5 + 1628*d^2*e^6 - 260*d*e^7)*x^2 - 12*(1300*d^7*e + 360*d^6*e^2 + 444*d^5*e^3 + 37*d^4*e^4 - 148*d^3*e^5 + 130*d^2*e^6 - 214*d*e^7 + 33*e^8)*x + 12*(2800*d^8 + 945*d^7*e + 1665*d^6*e^2 + 370*d^5*e^3 + 888*d^4*e^4 - 195*d^3*e^5 + 107*d^2*e^6 + (2800*d^6*e^2 + 945*d^5*e^3 + 1665*d^4*e^4 + 370*d^3*e^5 + 888*d^2*e^6 - 195*d*e^7 + 107*e^8)*x^2 + 2*(2800*d^7*e + 945*d^6*e^2 + 1665*d^5*e^3 + 370*d^4*e^4 + 888*d^3*e^5 - 195*d^2*e^6 + 107*d*e^7)*x)*log(e*x + d))/(e^11*x^2 + 2*d*e^10*x + d^2*e^9)","A",0
303,1,587,0,0.931789," ","integrate((5*x^2+2*x+3)^2*(4*x^4-5*x^3+3*x^2+x+2)/(e*x+d)^4,x, algorithm=""fricas"")","\frac{240 \, e^{8} x^{8} - 29200 \, d^{8} - 9630 \, d^{7} e - 16428 \, d^{6} e^{2} - 3478 \, d^{5} e^{3} - 7696 \, d^{4} e^{4} + 1430 \, d^{3} e^{5} - 428 \, d^{2} e^{6} - 66 \, d e^{7} - 72 \, e^{8} - 15 \, {\left(32 \, d e^{7} + 9 \, e^{8}\right)} x^{7} + {\left(1120 \, d^{2} e^{6} + 315 \, d e^{7} + 444 \, e^{8}\right)} x^{6} - 3 \, {\left(1120 \, d^{3} e^{5} + 315 \, d^{2} e^{6} + 444 \, d e^{7} + 74 \, e^{8}\right)} x^{5} + 3 \, {\left(5600 \, d^{4} e^{4} + 1575 \, d^{3} e^{5} + 2220 \, d^{2} e^{6} + 370 \, d e^{7} + 592 \, e^{8}\right)} x^{4} + 2 \, {\left(47000 \, d^{5} e^{3} + 12510 \, d^{4} e^{4} + 16206 \, d^{3} e^{5} + 2331 \, d^{2} e^{6} + 2664 \, d e^{7}\right)} x^{3} + 6 \, {\left(13400 \, d^{6} e^{2} + 3060 \, d^{5} e^{3} + 2886 \, d^{4} e^{4} + 111 \, d^{3} e^{5} - 888 \, d^{2} e^{6} + 390 \, d e^{7} - 214 \, e^{8}\right)} x^{2} - 6 \, {\left(3400 \, d^{7} e + 1665 \, d^{6} e^{2} + 3774 \, d^{5} e^{3} + 999 \, d^{4} e^{4} + 2664 \, d^{3} e^{5} - 585 \, d^{2} e^{6} + 214 \, d e^{7} + 33 \, e^{8}\right)} x - 12 \, {\left(5600 \, d^{8} + 1575 \, d^{7} e + 2220 \, d^{6} e^{2} + 370 \, d^{5} e^{3} + 592 \, d^{4} e^{4} - 65 \, d^{3} e^{5} + {\left(5600 \, d^{5} e^{3} + 1575 \, d^{4} e^{4} + 2220 \, d^{3} e^{5} + 370 \, d^{2} e^{6} + 592 \, d e^{7} - 65 \, e^{8}\right)} x^{3} + 3 \, {\left(5600 \, d^{6} e^{2} + 1575 \, d^{5} e^{3} + 2220 \, d^{4} e^{4} + 370 \, d^{3} e^{5} + 592 \, d^{2} e^{6} - 65 \, d e^{7}\right)} x^{2} + 3 \, {\left(5600 \, d^{7} e + 1575 \, d^{6} e^{2} + 2220 \, d^{5} e^{3} + 370 \, d^{4} e^{4} + 592 \, d^{3} e^{5} - 65 \, d^{2} e^{6}\right)} x\right)} \log\left(e x + d\right)}{12 \, {\left(e^{12} x^{3} + 3 \, d e^{11} x^{2} + 3 \, d^{2} e^{10} x + d^{3} e^{9}\right)}}"," ",0,"1/12*(240*e^8*x^8 - 29200*d^8 - 9630*d^7*e - 16428*d^6*e^2 - 3478*d^5*e^3 - 7696*d^4*e^4 + 1430*d^3*e^5 - 428*d^2*e^6 - 66*d*e^7 - 72*e^8 - 15*(32*d*e^7 + 9*e^8)*x^7 + (1120*d^2*e^6 + 315*d*e^7 + 444*e^8)*x^6 - 3*(1120*d^3*e^5 + 315*d^2*e^6 + 444*d*e^7 + 74*e^8)*x^5 + 3*(5600*d^4*e^4 + 1575*d^3*e^5 + 2220*d^2*e^6 + 370*d*e^7 + 592*e^8)*x^4 + 2*(47000*d^5*e^3 + 12510*d^4*e^4 + 16206*d^3*e^5 + 2331*d^2*e^6 + 2664*d*e^7)*x^3 + 6*(13400*d^6*e^2 + 3060*d^5*e^3 + 2886*d^4*e^4 + 111*d^3*e^5 - 888*d^2*e^6 + 390*d*e^7 - 214*e^8)*x^2 - 6*(3400*d^7*e + 1665*d^6*e^2 + 3774*d^5*e^3 + 999*d^4*e^4 + 2664*d^3*e^5 - 585*d^2*e^6 + 214*d*e^7 + 33*e^8)*x - 12*(5600*d^8 + 1575*d^7*e + 2220*d^6*e^2 + 370*d^5*e^3 + 592*d^4*e^4 - 65*d^3*e^5 + (5600*d^5*e^3 + 1575*d^4*e^4 + 2220*d^3*e^5 + 370*d^2*e^6 + 592*d*e^7 - 65*e^8)*x^3 + 3*(5600*d^6*e^2 + 1575*d^5*e^3 + 2220*d^4*e^4 + 370*d^3*e^5 + 592*d^2*e^6 - 65*d*e^7)*x^2 + 3*(5600*d^7*e + 1575*d^6*e^2 + 2220*d^5*e^3 + 370*d^4*e^4 + 592*d^3*e^5 - 65*d^2*e^6)*x)*log(e*x + d))/(e^12*x^3 + 3*d*e^11*x^2 + 3*d^2*e^10*x + d^3*e^9)","A",0
304,1,206,0,0.767902," ","integrate((e*x+d)^3*(4*x^4-5*x^3+3*x^2+x+2)/(5*x^2+2*x+3),x, algorithm=""fricas"")","\frac{2}{15} \, e^{3} x^{6} + \frac{3}{125} \, {\left(20 \, d e^{2} - 11 \, e^{3}\right)} x^{5} + \frac{3}{500} \, {\left(100 \, d^{2} e - 165 \, d e^{2} + 27 \, e^{3}\right)} x^{4} + \frac{1}{1875} \, {\left(500 \, d^{3} - 2475 \, d^{2} e + 1215 \, d e^{2} + 458 \, e^{3}\right)} x^{3} - \frac{1}{6250} \, {\left(4125 \, d^{3} - 6075 \, d^{2} e - 6870 \, d e^{2} + 881 \, e^{3}\right)} x^{2} - \frac{1}{1093750} \, \sqrt{14} {\left(52875 \, d^{3} + 449175 \, d^{2} e - 274845 \, d e^{2} - 53189 \, e^{3}\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) + \frac{1}{15625} \, {\left(10125 \, d^{3} + 34350 \, d^{2} e - 13215 \, d e^{2} - 5108 \, e^{3}\right)} x + \frac{1}{156250} \, {\left(57250 \, d^{3} - 66075 \, d^{2} e - 76620 \, d e^{2} + 23431 \, e^{3}\right)} \log\left(5 \, x^{2} + 2 \, x + 3\right)"," ",0,"2/15*e^3*x^6 + 3/125*(20*d*e^2 - 11*e^3)*x^5 + 3/500*(100*d^2*e - 165*d*e^2 + 27*e^3)*x^4 + 1/1875*(500*d^3 - 2475*d^2*e + 1215*d*e^2 + 458*e^3)*x^3 - 1/6250*(4125*d^3 - 6075*d^2*e - 6870*d*e^2 + 881*e^3)*x^2 - 1/1093750*sqrt(14)*(52875*d^3 + 449175*d^2*e - 274845*d*e^2 - 53189*e^3)*arctan(1/14*sqrt(14)*(5*x + 1)) + 1/15625*(10125*d^3 + 34350*d^2*e - 13215*d*e^2 - 5108*e^3)*x + 1/156250*(57250*d^3 - 66075*d^2*e - 76620*d*e^2 + 23431*e^3)*log(5*x^2 + 2*x + 3)","A",0
305,1,141,0,0.776482," ","integrate((e*x+d)^2*(4*x^4-5*x^3+3*x^2+x+2)/(5*x^2+2*x+3),x, algorithm=""fricas"")","\frac{4}{25} \, e^{2} x^{5} + \frac{1}{100} \, {\left(40 \, d e - 33 \, e^{2}\right)} x^{4} + \frac{1}{375} \, {\left(100 \, d^{2} - 330 \, d e + 81 \, e^{2}\right)} x^{3} - \frac{1}{1250} \, {\left(825 \, d^{2} - 810 \, d e - 458 \, e^{2}\right)} x^{2} - \frac{1}{218750} \, \sqrt{14} {\left(10575 \, d^{2} + 59890 \, d e - 18323 \, e^{2}\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) + \frac{1}{3125} \, {\left(2025 \, d^{2} + 4580 \, d e - 881 \, e^{2}\right)} x + \frac{1}{15625} \, {\left(5725 \, d^{2} - 4405 \, d e - 2554 \, e^{2}\right)} \log\left(5 \, x^{2} + 2 \, x + 3\right)"," ",0,"4/25*e^2*x^5 + 1/100*(40*d*e - 33*e^2)*x^4 + 1/375*(100*d^2 - 330*d*e + 81*e^2)*x^3 - 1/1250*(825*d^2 - 810*d*e - 458*e^2)*x^2 - 1/218750*sqrt(14)*(10575*d^2 + 59890*d*e - 18323*e^2)*arctan(1/14*sqrt(14)*(5*x + 1)) + 1/3125*(2025*d^2 + 4580*d*e - 881*e^2)*x + 1/15625*(5725*d^2 - 4405*d*e - 2554*e^2)*log(5*x^2 + 2*x + 3)","A",0
306,1,84,0,0.800307," ","integrate((e*x+d)*(4*x^4-5*x^3+3*x^2+x+2)/(5*x^2+2*x+3),x, algorithm=""fricas"")","\frac{1}{5} \, e x^{4} + \frac{1}{75} \, {\left(20 \, d - 33 \, e\right)} x^{3} - \frac{3}{250} \, {\left(55 \, d - 27 \, e\right)} x^{2} - \frac{1}{43750} \, \sqrt{14} {\left(2115 \, d + 5989 \, e\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) + \frac{1}{625} \, {\left(405 \, d + 458 \, e\right)} x + \frac{1}{6250} \, {\left(2290 \, d - 881 \, e\right)} \log\left(5 \, x^{2} + 2 \, x + 3\right)"," ",0,"1/5*e*x^4 + 1/75*(20*d - 33*e)*x^3 - 3/250*(55*d - 27*e)*x^2 - 1/43750*sqrt(14)*(2115*d + 5989*e)*arctan(1/14*sqrt(14)*(5*x + 1)) + 1/625*(405*d + 458*e)*x + 1/6250*(2290*d - 881*e)*log(5*x^2 + 2*x + 3)","A",0
307,1,43,0,0.754082," ","integrate((4*x^4-5*x^3+3*x^2+x+2)/(5*x^2+2*x+3),x, algorithm=""fricas"")","\frac{4}{15} \, x^{3} - \frac{33}{50} \, x^{2} - \frac{423}{8750} \, \sqrt{14} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) + \frac{81}{125} \, x + \frac{229}{625} \, \log\left(5 \, x^{2} + 2 \, x + 3\right)"," ",0,"4/15*x^3 - 33/50*x^2 - 423/8750*sqrt(14)*arctan(1/14*sqrt(14)*(5*x + 1)) + 81/125*x + 229/625*log(5*x^2 + 2*x + 3)","A",0
308,1,171,0,0.799734," ","integrate((4*x^4-5*x^3+3*x^2+x+2)/(e*x+d)/(5*x^2+2*x+3),x, algorithm=""fricas"")","\frac{700 \, {\left(5 \, d^{2} e^{2} - 2 \, d e^{3} + 3 \, e^{4}\right)} x^{2} - \sqrt{14} {\left(423 \, d e^{3} - 1367 \, e^{4}\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) - 70 \, {\left(100 \, d^{3} e + 125 \, d^{2} e^{2} - 6 \, d e^{3} + 99 \, e^{4}\right)} x + 1750 \, {\left(4 \, d^{4} + 5 \, d^{3} e + 3 \, d^{2} e^{2} - d e^{3} + 2 \, e^{4}\right)} \log\left(e x + d\right) + 7 \, {\left(458 \, d e^{3} - 7 \, e^{4}\right)} \log\left(5 \, x^{2} + 2 \, x + 3\right)}{1750 \, {\left(5 \, d^{2} e^{3} - 2 \, d e^{4} + 3 \, e^{5}\right)}}"," ",0,"1/1750*(700*(5*d^2*e^2 - 2*d*e^3 + 3*e^4)*x^2 - sqrt(14)*(423*d*e^3 - 1367*e^4)*arctan(1/14*sqrt(14)*(5*x + 1)) - 70*(100*d^3*e + 125*d^2*e^2 - 6*d*e^3 + 99*e^4)*x + 1750*(4*d^4 + 5*d^3*e + 3*d^2*e^2 - d*e^3 + 2*e^4)*log(e*x + d) + 7*(458*d*e^3 - 7*e^4)*log(5*x^2 + 2*x + 3))/(5*d^2*e^3 - 2*d*e^4 + 3*e^5)","A",0
309,1,416,0,0.981893," ","integrate((4*x^4-5*x^3+3*x^2+x+2)/(e*x+d)^2/(5*x^2+2*x+3),x, algorithm=""fricas"")","-\frac{7000 \, d^{6} + 5950 \, d^{5} e + 5950 \, d^{4} e^{2} + 1400 \, d^{3} e^{3} + 7350 \, d^{2} e^{4} - 2450 \, d e^{5} + 2100 \, e^{6} - 280 \, {\left(25 \, d^{4} e^{2} - 20 \, d^{3} e^{3} + 34 \, d^{2} e^{4} - 12 \, d e^{5} + 9 \, e^{6}\right)} x^{2} + \sqrt{14} {\left(423 \, d^{3} e^{3} - 2734 \, d^{2} e^{4} + 293 \, d e^{5} + {\left(423 \, d^{2} e^{4} - 2734 \, d e^{5} + 293 \, e^{6}\right)} x\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) - 280 \, {\left(25 \, d^{5} e - 20 \, d^{4} e^{2} + 34 \, d^{3} e^{3} - 12 \, d^{2} e^{4} + 9 \, d e^{5}\right)} x + 350 \, {\left(40 \, d^{6} + d^{5} e + 28 \, d^{4} e^{2} + 44 \, d^{3} e^{3} - 2 \, d^{2} e^{4} + d e^{5} + {\left(40 \, d^{5} e + d^{4} e^{2} + 28 \, d^{3} e^{3} + 44 \, d^{2} e^{4} - 2 \, d e^{5} + e^{6}\right)} x\right)} \log\left(e x + d\right) - 14 \, {\left(229 \, d^{3} e^{3} - 7 \, d^{2} e^{4} - 136 \, d e^{5} + {\left(229 \, d^{2} e^{4} - 7 \, d e^{5} - 136 \, e^{6}\right)} x\right)} \log\left(5 \, x^{2} + 2 \, x + 3\right)}{350 \, {\left(25 \, d^{5} e^{3} - 20 \, d^{4} e^{4} + 34 \, d^{3} e^{5} - 12 \, d^{2} e^{6} + 9 \, d e^{7} + {\left(25 \, d^{4} e^{4} - 20 \, d^{3} e^{5} + 34 \, d^{2} e^{6} - 12 \, d e^{7} + 9 \, e^{8}\right)} x\right)}}"," ",0,"-1/350*(7000*d^6 + 5950*d^5*e + 5950*d^4*e^2 + 1400*d^3*e^3 + 7350*d^2*e^4 - 2450*d*e^5 + 2100*e^6 - 280*(25*d^4*e^2 - 20*d^3*e^3 + 34*d^2*e^4 - 12*d*e^5 + 9*e^6)*x^2 + sqrt(14)*(423*d^3*e^3 - 2734*d^2*e^4 + 293*d*e^5 + (423*d^2*e^4 - 2734*d*e^5 + 293*e^6)*x)*arctan(1/14*sqrt(14)*(5*x + 1)) - 280*(25*d^5*e - 20*d^4*e^2 + 34*d^3*e^3 - 12*d^2*e^4 + 9*d*e^5)*x + 350*(40*d^6 + d^5*e + 28*d^4*e^2 + 44*d^3*e^3 - 2*d^2*e^4 + d*e^5 + (40*d^5*e + d^4*e^2 + 28*d^3*e^3 + 44*d^2*e^4 - 2*d*e^5 + e^6)*x)*log(e*x + d) - 14*(229*d^3*e^3 - 7*d^2*e^4 - 136*d*e^5 + (229*d^2*e^4 - 7*d*e^5 - 136*e^6)*x)*log(5*x^2 + 2*x + 3))/(25*d^5*e^3 - 20*d^4*e^4 + 34*d^3*e^5 - 12*d^2*e^6 + 9*d*e^7 + (25*d^4*e^4 - 20*d^3*e^5 + 34*d^2*e^6 - 12*d*e^7 + 9*e^8)*x)","A",0
310,1,698,0,1.265325," ","integrate((4*x^4-5*x^3+3*x^2+x+2)/(e*x+d)^3/(5*x^2+2*x+3),x, algorithm=""fricas"")","\frac{10500 \, d^{8} - 6825 \, d^{7} e + 14175 \, d^{6} e^{2} + 10395 \, d^{5} e^{3} - 6160 \, d^{4} e^{4} + 12145 \, d^{3} e^{5} - 4305 \, d^{2} e^{6} + 1365 \, d e^{7} - 630 \, e^{8} - \sqrt{14} {\left(423 \, d^{5} e^{3} - 4101 \, d^{4} e^{4} + 879 \, d^{3} e^{5} + 703 \, d^{2} e^{6} + {\left(423 \, d^{3} e^{5} - 4101 \, d^{2} e^{6} + 879 \, d e^{7} + 703 \, e^{8}\right)} x^{2} + 2 \, {\left(423 \, d^{4} e^{4} - 4101 \, d^{3} e^{5} + 879 \, d^{2} e^{6} + 703 \, d e^{7}\right)} x\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) + 70 \, {\left(200 \, d^{7} e - 75 \, d^{6} e^{2} + 258 \, d^{5} e^{3} + 167 \, d^{4} e^{4} - 14 \, d^{3} e^{5} + 141 \, d^{2} e^{6} - 8 \, d e^{7} + 3 \, e^{8}\right)} x + 70 \, {\left(100 \, d^{8} - 120 \, d^{7} e + 228 \, d^{6} e^{2} - 242 \, d^{5} e^{3} + 141 \, d^{4} e^{4} + 120 \, d^{3} e^{5} - d^{2} e^{6} + {\left(100 \, d^{6} e^{2} - 120 \, d^{5} e^{3} + 228 \, d^{4} e^{4} - 242 \, d^{3} e^{5} + 141 \, d^{2} e^{6} + 120 \, d e^{7} - e^{8}\right)} x^{2} + 2 \, {\left(100 \, d^{7} e - 120 \, d^{6} e^{2} + 228 \, d^{5} e^{3} - 242 \, d^{4} e^{4} + 141 \, d^{3} e^{5} + 120 \, d^{2} e^{6} - d e^{7}\right)} x\right)} \log\left(e x + d\right) + 7 \, {\left(458 \, d^{5} e^{3} - 21 \, d^{4} e^{4} - 816 \, d^{3} e^{5} + 113 \, d^{2} e^{6} + {\left(458 \, d^{3} e^{5} - 21 \, d^{2} e^{6} - 816 \, d e^{7} + 113 \, e^{8}\right)} x^{2} + 2 \, {\left(458 \, d^{4} e^{4} - 21 \, d^{3} e^{5} - 816 \, d^{2} e^{6} + 113 \, d e^{7}\right)} x\right)} \log\left(5 \, x^{2} + 2 \, x + 3\right)}{70 \, {\left(125 \, d^{8} e^{3} - 150 \, d^{7} e^{4} + 285 \, d^{6} e^{5} - 188 \, d^{5} e^{6} + 171 \, d^{4} e^{7} - 54 \, d^{3} e^{8} + 27 \, d^{2} e^{9} + {\left(125 \, d^{6} e^{5} - 150 \, d^{5} e^{6} + 285 \, d^{4} e^{7} - 188 \, d^{3} e^{8} + 171 \, d^{2} e^{9} - 54 \, d e^{10} + 27 \, e^{11}\right)} x^{2} + 2 \, {\left(125 \, d^{7} e^{4} - 150 \, d^{6} e^{5} + 285 \, d^{5} e^{6} - 188 \, d^{4} e^{7} + 171 \, d^{3} e^{8} - 54 \, d^{2} e^{9} + 27 \, d e^{10}\right)} x\right)}}"," ",0,"1/70*(10500*d^8 - 6825*d^7*e + 14175*d^6*e^2 + 10395*d^5*e^3 - 6160*d^4*e^4 + 12145*d^3*e^5 - 4305*d^2*e^6 + 1365*d*e^7 - 630*e^8 - sqrt(14)*(423*d^5*e^3 - 4101*d^4*e^4 + 879*d^3*e^5 + 703*d^2*e^6 + (423*d^3*e^5 - 4101*d^2*e^6 + 879*d*e^7 + 703*e^8)*x^2 + 2*(423*d^4*e^4 - 4101*d^3*e^5 + 879*d^2*e^6 + 703*d*e^7)*x)*arctan(1/14*sqrt(14)*(5*x + 1)) + 70*(200*d^7*e - 75*d^6*e^2 + 258*d^5*e^3 + 167*d^4*e^4 - 14*d^3*e^5 + 141*d^2*e^6 - 8*d*e^7 + 3*e^8)*x + 70*(100*d^8 - 120*d^7*e + 228*d^6*e^2 - 242*d^5*e^3 + 141*d^4*e^4 + 120*d^3*e^5 - d^2*e^6 + (100*d^6*e^2 - 120*d^5*e^3 + 228*d^4*e^4 - 242*d^3*e^5 + 141*d^2*e^6 + 120*d*e^7 - e^8)*x^2 + 2*(100*d^7*e - 120*d^6*e^2 + 228*d^5*e^3 - 242*d^4*e^4 + 141*d^3*e^5 + 120*d^2*e^6 - d*e^7)*x)*log(e*x + d) + 7*(458*d^5*e^3 - 21*d^4*e^4 - 816*d^3*e^5 + 113*d^2*e^6 + (458*d^3*e^5 - 21*d^2*e^6 - 816*d*e^7 + 113*e^8)*x^2 + 2*(458*d^4*e^4 - 21*d^3*e^5 - 816*d^2*e^6 + 113*d*e^7)*x)*log(5*x^2 + 2*x + 3))/(125*d^8*e^3 - 150*d^7*e^4 + 285*d^6*e^5 - 188*d^5*e^6 + 171*d^4*e^7 - 54*d^3*e^8 + 27*d^2*e^9 + (125*d^6*e^5 - 150*d^5*e^6 + 285*d^4*e^7 - 188*d^3*e^8 + 171*d^2*e^9 - 54*d*e^10 + 27*e^11)*x^2 + 2*(125*d^7*e^4 - 150*d^6*e^5 + 285*d^5*e^6 - 188*d^4*e^7 + 171*d^3*e^8 - 54*d^2*e^9 + 27*d*e^10)*x)","B",0
311,1,350,0,0.594333," ","integrate((e*x+d)^3*(4*x^4-5*x^3+3*x^2+x+2)/(5*x^2+2*x+3)^2,x, algorithm=""fricas"")","\frac{3675000 \, e^{3} x^{6} + 1225000 \, {\left(12 \, d e^{2} - 7 \, e^{3}\right)} x^{5} + 122500 \, {\left(180 \, d^{2} e - 321 \, d e^{2} + 47 \, e^{3}\right)} x^{4} + 147000 \, {\left(100 \, d^{3} - 555 \, d^{2} e + 246 \, d e^{2} + 153 \, e^{3}\right)} x^{3} - 7176750 \, d^{3} + 3997350 \, d^{2} e + 11319210 \, d e^{2} - 2308698 \, e^{3} + 2940 \, {\left(2000 \, d^{3} - 7800 \, d^{2} e - 3045 \, d e^{2} + 5013 \, e^{3}\right)} x^{2} + 15 \, \sqrt{14} {\left(98475 \, d^{3} + 952695 \, d^{2} e - 664929 \, d e^{2} - 202497 \, e^{3} + 5 \, {\left(32825 \, d^{3} + 317565 \, d^{2} e - 221643 \, d e^{2} - 67499 \, e^{3}\right)} x^{2} + 2 \, {\left(32825 \, d^{3} + 317565 \, d^{2} e - 221643 \, d e^{2} - 67499 \, e^{3}\right)} x\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) + 42 \, {\left(157125 \, d^{3} - 1740675 \, d^{2} e + 923745 \, d e^{2} + 417329 \, e^{3}\right)} x - 2940 \, {\left(3075 \, d^{3} - 4635 \, d^{2} e - 7803 \, d e^{2} + 2496 \, e^{3} + 5 \, {\left(1025 \, d^{3} - 1545 \, d^{2} e - 2601 \, d e^{2} + 832 \, e^{3}\right)} x^{2} + 2 \, {\left(1025 \, d^{3} - 1545 \, d^{2} e - 2601 \, d e^{2} + 832 \, e^{3}\right)} x\right)} \log\left(5 \, x^{2} + 2 \, x + 3\right)}{18375000 \, {\left(5 \, x^{2} + 2 \, x + 3\right)}}"," ",0,"1/18375000*(3675000*e^3*x^6 + 1225000*(12*d*e^2 - 7*e^3)*x^5 + 122500*(180*d^2*e - 321*d*e^2 + 47*e^3)*x^4 + 147000*(100*d^3 - 555*d^2*e + 246*d*e^2 + 153*e^3)*x^3 - 7176750*d^3 + 3997350*d^2*e + 11319210*d*e^2 - 2308698*e^3 + 2940*(2000*d^3 - 7800*d^2*e - 3045*d*e^2 + 5013*e^3)*x^2 + 15*sqrt(14)*(98475*d^3 + 952695*d^2*e - 664929*d*e^2 - 202497*e^3 + 5*(32825*d^3 + 317565*d^2*e - 221643*d*e^2 - 67499*e^3)*x^2 + 2*(32825*d^3 + 317565*d^2*e - 221643*d*e^2 - 67499*e^3)*x)*arctan(1/14*sqrt(14)*(5*x + 1)) + 42*(157125*d^3 - 1740675*d^2*e + 923745*d*e^2 + 417329*e^3)*x - 2940*(3075*d^3 - 4635*d^2*e - 7803*d*e^2 + 2496*e^3 + 5*(1025*d^3 - 1545*d^2*e - 2601*d*e^2 + 832*e^3)*x^2 + 2*(1025*d^3 - 1545*d^2*e - 2601*d*e^2 + 832*e^3)*x)*log(5*x^2 + 2*x + 3))/(5*x^2 + 2*x + 3)","B",0
312,1,245,0,0.824947," ","integrate((e*x+d)^2*(4*x^4-5*x^3+3*x^2+x+2)/(5*x^2+2*x+3)^2,x, algorithm=""fricas"")","\frac{980000 \, e^{2} x^{5} + 24500 \, {\left(120 \, d e - 107 \, e^{2}\right)} x^{4} + 58800 \, {\left(50 \, d^{2} - 185 \, d e + 41 \, e^{2}\right)} x^{3} + 2940 \, {\left(400 \, d^{2} - 1040 \, d e - 203 \, e^{2}\right)} x^{2} + 3 \, \sqrt{14} {\left(5 \, {\left(32825 \, d^{2} + 211710 \, d e - 73881 \, e^{2}\right)} x^{2} + 98475 \, d^{2} + 635130 \, d e - 221643 \, e^{2} + 2 \, {\left(32825 \, d^{2} + 211710 \, d e - 73881 \, e^{2}\right)} x\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) - 1435350 \, d^{2} + 532980 \, d e + 754614 \, e^{2} + 42 \, {\left(31425 \, d^{2} - 232090 \, d e + 61583 \, e^{2}\right)} x - 588 \, {\left(5 \, {\left(1025 \, d^{2} - 1030 \, d e - 867 \, e^{2}\right)} x^{2} + 3075 \, d^{2} - 3090 \, d e - 2601 \, e^{2} + 2 \, {\left(1025 \, d^{2} - 1030 \, d e - 867 \, e^{2}\right)} x\right)} \log\left(5 \, x^{2} + 2 \, x + 3\right)}{3675000 \, {\left(5 \, x^{2} + 2 \, x + 3\right)}}"," ",0,"1/3675000*(980000*e^2*x^5 + 24500*(120*d*e - 107*e^2)*x^4 + 58800*(50*d^2 - 185*d*e + 41*e^2)*x^3 + 2940*(400*d^2 - 1040*d*e - 203*e^2)*x^2 + 3*sqrt(14)*(5*(32825*d^2 + 211710*d*e - 73881*e^2)*x^2 + 98475*d^2 + 635130*d*e - 221643*e^2 + 2*(32825*d^2 + 211710*d*e - 73881*e^2)*x)*arctan(1/14*sqrt(14)*(5*x + 1)) - 1435350*d^2 + 532980*d*e + 754614*e^2 + 42*(31425*d^2 - 232090*d*e + 61583*e^2)*x - 588*(5*(1025*d^2 - 1030*d*e - 867*e^2)*x^2 + 3075*d^2 - 3090*d*e - 2601*e^2 + 2*(1025*d^2 - 1030*d*e - 867*e^2)*x)*log(5*x^2 + 2*x + 3))/(5*x^2 + 2*x + 3)","A",0
313,1,147,0,0.630847," ","integrate((e*x+d)*(4*x^4-5*x^3+3*x^2+x+2)/(5*x^2+2*x+3)^2,x, algorithm=""fricas"")","\frac{98000 \, e x^{4} + 9800 \, {\left(20 \, d - 37 \, e\right)} x^{3} + 7840 \, {\left(10 \, d - 13 \, e\right)} x^{2} + \sqrt{14} {\left(5 \, {\left(6565 \, d + 21171 \, e\right)} x^{2} + 2 \, {\left(6565 \, d + 21171 \, e\right)} x + 19695 \, d + 63513 \, e\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) + 14 \, {\left(6285 \, d - 23209 \, e\right)} x - 196 \, {\left(5 \, {\left(205 \, d - 103 \, e\right)} x^{2} + 2 \, {\left(205 \, d - 103 \, e\right)} x + 615 \, d - 309 \, e\right)} \log\left(5 \, x^{2} + 2 \, x + 3\right) - 95690 \, d + 17766 \, e}{245000 \, {\left(5 \, x^{2} + 2 \, x + 3\right)}}"," ",0,"1/245000*(98000*e*x^4 + 9800*(20*d - 37*e)*x^3 + 7840*(10*d - 13*e)*x^2 + sqrt(14)*(5*(6565*d + 21171*e)*x^2 + 2*(6565*d + 21171*e)*x + 19695*d + 63513*e)*arctan(1/14*sqrt(14)*(5*x + 1)) + 14*(6285*d - 23209*e)*x - 196*(5*(205*d - 103*e)*x^2 + 2*(205*d - 103*e)*x + 615*d - 309*e)*log(5*x^2 + 2*x + 3) - 95690*d + 17766*e)/(5*x^2 + 2*x + 3)","A",0
314,1,78,0,0.386862," ","integrate((4*x^4-5*x^3+3*x^2+x+2)/(5*x^2+2*x+3)^2,x, algorithm=""fricas"")","\frac{39200 \, x^{3} + 1313 \, \sqrt{14} {\left(5 \, x^{2} + 2 \, x + 3\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) + 15680 \, x^{2} - 8036 \, {\left(5 \, x^{2} + 2 \, x + 3\right)} \log\left(5 \, x^{2} + 2 \, x + 3\right) + 17598 \, x - 19138}{49000 \, {\left(5 \, x^{2} + 2 \, x + 3\right)}}"," ",0,"1/49000*(39200*x^3 + 1313*sqrt(14)*(5*x^2 + 2*x + 3)*arctan(1/14*sqrt(14)*(5*x + 1)) + 15680*x^2 - 8036*(5*x^2 + 2*x + 3)*log(5*x^2 + 2*x + 3) + 17598*x - 19138)/(5*x^2 + 2*x + 3)","A",0
315,1,479,0,0.911997," ","integrate((4*x^4-5*x^3+3*x^2+x+2)/(e*x+d)/(5*x^2+2*x+3)^2,x, algorithm=""fricas"")","-\frac{95690 \, d^{3} e - 58786 \, d^{2} e^{2} + 65618 \, d e^{3} - 12306 \, e^{4} - \sqrt{14} {\left(19695 \, d^{3} e - 79269 \, d^{2} e^{2} + 33267 \, d e^{3} - 19869 \, e^{4} + 5 \, {\left(6565 \, d^{3} e - 26423 \, d^{2} e^{2} + 11089 \, d e^{3} - 6623 \, e^{4}\right)} x^{2} + 2 \, {\left(6565 \, d^{3} e - 26423 \, d^{2} e^{2} + 11089 \, d e^{3} - 6623 \, e^{4}\right)} x\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) + 14 \, {\left(2115 \, d^{3} e - 7681 \, d^{2} e^{2} + 4003 \, d e^{3} - 4101 \, e^{4}\right)} x - 9800 \, {\left(12 \, d^{4} + 15 \, d^{3} e + 9 \, d^{2} e^{2} - 3 \, d e^{3} + 6 \, e^{4} + 5 \, {\left(4 \, d^{4} + 5 \, d^{3} e + 3 \, d^{2} e^{2} - d e^{3} + 2 \, e^{4}\right)} x^{2} + 2 \, {\left(4 \, d^{4} + 5 \, d^{3} e + 3 \, d^{2} e^{2} - d e^{3} + 2 \, e^{4}\right)} x\right)} \log\left(e x + d\right) + 196 \, {\left(615 \, d^{3} e - 183 \, d^{2} e^{2} + 69 \, d e^{3} + 42 \, e^{4} + 5 \, {\left(205 \, d^{3} e - 61 \, d^{2} e^{2} + 23 \, d e^{3} + 14 \, e^{4}\right)} x^{2} + 2 \, {\left(205 \, d^{3} e - 61 \, d^{2} e^{2} + 23 \, d e^{3} + 14 \, e^{4}\right)} x\right)} \log\left(5 \, x^{2} + 2 \, x + 3\right)}{9800 \, {\left(75 \, d^{4} e - 60 \, d^{3} e^{2} + 102 \, d^{2} e^{3} - 36 \, d e^{4} + 27 \, e^{5} + 5 \, {\left(25 \, d^{4} e - 20 \, d^{3} e^{2} + 34 \, d^{2} e^{3} - 12 \, d e^{4} + 9 \, e^{5}\right)} x^{2} + 2 \, {\left(25 \, d^{4} e - 20 \, d^{3} e^{2} + 34 \, d^{2} e^{3} - 12 \, d e^{4} + 9 \, e^{5}\right)} x\right)}}"," ",0,"-1/9800*(95690*d^3*e - 58786*d^2*e^2 + 65618*d*e^3 - 12306*e^4 - sqrt(14)*(19695*d^3*e - 79269*d^2*e^2 + 33267*d*e^3 - 19869*e^4 + 5*(6565*d^3*e - 26423*d^2*e^2 + 11089*d*e^3 - 6623*e^4)*x^2 + 2*(6565*d^3*e - 26423*d^2*e^2 + 11089*d*e^3 - 6623*e^4)*x)*arctan(1/14*sqrt(14)*(5*x + 1)) + 14*(2115*d^3*e - 7681*d^2*e^2 + 4003*d*e^3 - 4101*e^4)*x - 9800*(12*d^4 + 15*d^3*e + 9*d^2*e^2 - 3*d*e^3 + 6*e^4 + 5*(4*d^4 + 5*d^3*e + 3*d^2*e^2 - d*e^3 + 2*e^4)*x^2 + 2*(4*d^4 + 5*d^3*e + 3*d^2*e^2 - d*e^3 + 2*e^4)*x)*log(e*x + d) + 196*(615*d^3*e - 183*d^2*e^2 + 69*d*e^3 + 42*e^4 + 5*(205*d^3*e - 61*d^2*e^2 + 23*d*e^3 + 14*e^4)*x^2 + 2*(205*d^3*e - 61*d^2*e^2 + 23*d*e^3 + 14*e^4)*x)*log(5*x^2 + 2*x + 3))/(75*d^4*e - 60*d^3*e^2 + 102*d^2*e^3 - 36*d*e^4 + 27*e^5 + 5*(25*d^4*e - 20*d^3*e^2 + 34*d^2*e^3 - 12*d*e^4 + 9*e^5)*x^2 + 2*(25*d^4*e - 20*d^3*e^2 + 34*d^2*e^3 - 12*d*e^4 + 9*e^5)*x)","B",0
316,1,910,0,1.099683," ","integrate((4*x^4-5*x^3+3*x^2+x+2)/(e*x+d)^2/(5*x^2+2*x+3)^2,x, algorithm=""fricas"")","-\frac{117600 \, d^{6} + 195650 \, d^{5} e + 20664 \, d^{4} e^{2} + 48132 \, d^{3} e^{3} + 118552 \, d^{2} e^{4} - 70686 \, d e^{5} + 35280 \, e^{6} + 14 \, {\left(14000 \, d^{6} + 11900 \, d^{5} e + 14015 \, d^{4} e^{2} - 11716 \, d^{3} e^{3} + 22902 \, d^{2} e^{4} - 13688 \, d e^{5} + 5079 \, e^{6}\right)} x^{2} - 5 \, \sqrt{14} {\left(3939 \, d^{5} e - 30132 \, d^{4} e^{2} + 12870 \, d^{3} e^{3} + 468 \, d^{2} e^{4} - 813 \, d e^{5} + 5 \, {\left(1313 \, d^{4} e^{2} - 10044 \, d^{3} e^{3} + 4290 \, d^{2} e^{4} + 156 \, d e^{5} - 271 \, e^{6}\right)} x^{3} + {\left(6565 \, d^{5} e - 47594 \, d^{4} e^{2} + 1362 \, d^{3} e^{3} + 9360 \, d^{2} e^{4} - 1043 \, d e^{5} - 542 \, e^{6}\right)} x^{2} + {\left(2626 \, d^{5} e - 16149 \, d^{4} e^{2} - 21552 \, d^{3} e^{3} + 13182 \, d^{2} e^{4} - 74 \, d e^{5} - 813 \, e^{6}\right)} x\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) + 14 \, {\left(5600 \, d^{6} + 6875 \, d^{5} e - 2921 \, d^{4} e^{2} + 3658 \, d^{3} e^{3} - 1150 \, d^{2} e^{4} - 1433 \, d e^{5} - 429 \, e^{6}\right)} x - 1960 \, {\left(123 \, d^{5} e - 24 \, d^{4} e^{2} - 180 \, d^{3} e^{3} + 72 \, d^{2} e^{4} - 15 \, d e^{5} + 5 \, {\left(41 \, d^{4} e^{2} - 8 \, d^{3} e^{3} - 60 \, d^{2} e^{4} + 24 \, d e^{5} - 5 \, e^{6}\right)} x^{3} + {\left(205 \, d^{5} e + 42 \, d^{4} e^{2} - 316 \, d^{3} e^{3} + 23 \, d e^{5} - 10 \, e^{6}\right)} x^{2} + {\left(82 \, d^{5} e + 107 \, d^{4} e^{2} - 144 \, d^{3} e^{3} - 132 \, d^{2} e^{4} + 62 \, d e^{5} - 15 \, e^{6}\right)} x\right)} \log\left(e x + d\right) + 980 \, {\left(123 \, d^{5} e - 24 \, d^{4} e^{2} - 180 \, d^{3} e^{3} + 72 \, d^{2} e^{4} - 15 \, d e^{5} + 5 \, {\left(41 \, d^{4} e^{2} - 8 \, d^{3} e^{3} - 60 \, d^{2} e^{4} + 24 \, d e^{5} - 5 \, e^{6}\right)} x^{3} + {\left(205 \, d^{5} e + 42 \, d^{4} e^{2} - 316 \, d^{3} e^{3} + 23 \, d e^{5} - 10 \, e^{6}\right)} x^{2} + {\left(82 \, d^{5} e + 107 \, d^{4} e^{2} - 144 \, d^{3} e^{3} - 132 \, d^{2} e^{4} + 62 \, d e^{5} - 15 \, e^{6}\right)} x\right)} \log\left(5 \, x^{2} + 2 \, x + 3\right)}{1960 \, {\left(375 \, d^{7} e - 450 \, d^{6} e^{2} + 855 \, d^{5} e^{3} - 564 \, d^{4} e^{4} + 513 \, d^{3} e^{5} - 162 \, d^{2} e^{6} + 81 \, d e^{7} + 5 \, {\left(125 \, d^{6} e^{2} - 150 \, d^{5} e^{3} + 285 \, d^{4} e^{4} - 188 \, d^{3} e^{5} + 171 \, d^{2} e^{6} - 54 \, d e^{7} + 27 \, e^{8}\right)} x^{3} + {\left(625 \, d^{7} e - 500 \, d^{6} e^{2} + 1125 \, d^{5} e^{3} - 370 \, d^{4} e^{4} + 479 \, d^{3} e^{5} + 72 \, d^{2} e^{6} + 27 \, d e^{7} + 54 \, e^{8}\right)} x^{2} + {\left(250 \, d^{7} e + 75 \, d^{6} e^{2} + 120 \, d^{5} e^{3} + 479 \, d^{4} e^{4} - 222 \, d^{3} e^{5} + 405 \, d^{2} e^{6} - 108 \, d e^{7} + 81 \, e^{8}\right)} x\right)}}"," ",0,"-1/1960*(117600*d^6 + 195650*d^5*e + 20664*d^4*e^2 + 48132*d^3*e^3 + 118552*d^2*e^4 - 70686*d*e^5 + 35280*e^6 + 14*(14000*d^6 + 11900*d^5*e + 14015*d^4*e^2 - 11716*d^3*e^3 + 22902*d^2*e^4 - 13688*d*e^5 + 5079*e^6)*x^2 - 5*sqrt(14)*(3939*d^5*e - 30132*d^4*e^2 + 12870*d^3*e^3 + 468*d^2*e^4 - 813*d*e^5 + 5*(1313*d^4*e^2 - 10044*d^3*e^3 + 4290*d^2*e^4 + 156*d*e^5 - 271*e^6)*x^3 + (6565*d^5*e - 47594*d^4*e^2 + 1362*d^3*e^3 + 9360*d^2*e^4 - 1043*d*e^5 - 542*e^6)*x^2 + (2626*d^5*e - 16149*d^4*e^2 - 21552*d^3*e^3 + 13182*d^2*e^4 - 74*d*e^5 - 813*e^6)*x)*arctan(1/14*sqrt(14)*(5*x + 1)) + 14*(5600*d^6 + 6875*d^5*e - 2921*d^4*e^2 + 3658*d^3*e^3 - 1150*d^2*e^4 - 1433*d*e^5 - 429*e^6)*x - 1960*(123*d^5*e - 24*d^4*e^2 - 180*d^3*e^3 + 72*d^2*e^4 - 15*d*e^5 + 5*(41*d^4*e^2 - 8*d^3*e^3 - 60*d^2*e^4 + 24*d*e^5 - 5*e^6)*x^3 + (205*d^5*e + 42*d^4*e^2 - 316*d^3*e^3 + 23*d*e^5 - 10*e^6)*x^2 + (82*d^5*e + 107*d^4*e^2 - 144*d^3*e^3 - 132*d^2*e^4 + 62*d*e^5 - 15*e^6)*x)*log(e*x + d) + 980*(123*d^5*e - 24*d^4*e^2 - 180*d^3*e^3 + 72*d^2*e^4 - 15*d*e^5 + 5*(41*d^4*e^2 - 8*d^3*e^3 - 60*d^2*e^4 + 24*d*e^5 - 5*e^6)*x^3 + (205*d^5*e + 42*d^4*e^2 - 316*d^3*e^3 + 23*d*e^5 - 10*e^6)*x^2 + (82*d^5*e + 107*d^4*e^2 - 144*d^3*e^3 - 132*d^2*e^4 + 62*d*e^5 - 15*e^6)*x)*log(5*x^2 + 2*x + 3))/(375*d^7*e - 450*d^6*e^2 + 855*d^5*e^3 - 564*d^4*e^4 + 513*d^3*e^5 - 162*d^2*e^6 + 81*d*e^7 + 5*(125*d^6*e^2 - 150*d^5*e^3 + 285*d^4*e^4 - 188*d^3*e^5 + 171*d^2*e^6 - 54*d*e^7 + 27*e^8)*x^3 + (625*d^7*e - 500*d^6*e^2 + 1125*d^5*e^3 - 370*d^4*e^4 + 479*d^3*e^5 + 72*d^2*e^6 + 27*d*e^7 + 54*e^8)*x^2 + (250*d^7*e + 75*d^6*e^2 + 120*d^5*e^3 + 479*d^4*e^4 - 222*d^3*e^5 + 405*d^2*e^6 - 108*d*e^7 + 81*e^8)*x)","B",0
317,1,1499,0,1.438621," ","integrate((4*x^4-5*x^3+3*x^2+x+2)/(e*x+d)^3/(5*x^2+2*x+3)^2,x, algorithm=""fricas"")","-\frac{58800 \, d^{8} + 363230 \, d^{7} e - 178010 \, d^{6} e^{2} - 233184 \, d^{5} e^{3} + 395164 \, d^{4} e^{4} - 437122 \, d^{3} e^{5} + 178542 \, d^{2} e^{6} - 37044 \, d e^{7} + 10584 \, e^{8} + 14 \, {\left(28700 \, d^{6} e^{2} - 14965 \, d^{5} e^{3} - 43891 \, d^{4} e^{4} + 44106 \, d^{3} e^{5} - 45966 \, d^{2} e^{6} + 12711 \, d e^{7} + 9 \, e^{8}\right)} x^{3} + 14 \, {\left(7000 \, d^{8} + 31850 \, d^{7} e + 6400 \, d^{6} e^{2} - 62649 \, d^{5} e^{3} + 52187 \, d^{4} e^{4} - 53652 \, d^{3} e^{5} + 11130 \, d^{2} e^{6} - 2841 \, d e^{7} + 1791 \, e^{8}\right)} x^{2} - \sqrt{14} {\left(19695 \, d^{7} e - 222051 \, d^{6} e^{2} + 105066 \, d^{5} e^{3} + 128574 \, d^{4} e^{4} - 51741 \, d^{3} e^{5} + 1737 \, d^{2} e^{6} + 5 \, {\left(6565 \, d^{5} e^{3} - 74017 \, d^{4} e^{4} + 35022 \, d^{3} e^{5} + 42858 \, d^{2} e^{6} - 17247 \, d e^{7} + 579 \, e^{8}\right)} x^{4} + 2 \, {\left(32825 \, d^{6} e^{2} - 363520 \, d^{5} e^{3} + 101093 \, d^{4} e^{4} + 249312 \, d^{3} e^{5} - 43377 \, d^{2} e^{6} - 14352 \, d e^{7} + 579 \, e^{8}\right)} x^{3} + {\left(32825 \, d^{7} e - 343825 \, d^{6} e^{2} - 101263 \, d^{5} e^{3} + 132327 \, d^{4} e^{4} + 190263 \, d^{3} e^{5} + 62481 \, d^{2} e^{6} - 49425 \, d e^{7} + 1737 \, e^{8}\right)} x^{2} + 2 \, {\left(6565 \, d^{7} e - 54322 \, d^{6} e^{2} - 187029 \, d^{5} e^{3} + 147924 \, d^{4} e^{4} + 111327 \, d^{3} e^{5} - 51162 \, d^{2} e^{6} + 1737 \, d e^{7}\right)} x\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) + 14 \, {\left(2800 \, d^{8} + 14855 \, d^{7} e + 5815 \, d^{6} e^{2} - 18620 \, d^{5} e^{3} - 17202 \, d^{4} e^{4} + 11119 \, d^{3} e^{5} - 26037 \, d^{2} e^{6} + 7866 \, d e^{7} - 756 \, e^{8}\right)} x - 392 \, {\left(615 \, d^{7} e - 57 \, d^{6} e^{2} - 2538 \, d^{5} e^{3} + 1188 \, d^{4} e^{4} + 171 \, d^{3} e^{5} - 63 \, d^{2} e^{6} + 5 \, {\left(205 \, d^{5} e^{3} - 19 \, d^{4} e^{4} - 846 \, d^{3} e^{5} + 396 \, d^{2} e^{6} + 57 \, d e^{7} - 21 \, e^{8}\right)} x^{4} + 2 \, {\left(1025 \, d^{6} e^{2} + 110 \, d^{5} e^{3} - 4249 \, d^{4} e^{4} + 1134 \, d^{3} e^{5} + 681 \, d^{2} e^{6} - 48 \, d e^{7} - 21 \, e^{8}\right)} x^{3} + {\left(1025 \, d^{7} e + 725 \, d^{6} e^{2} - 3691 \, d^{5} e^{3} - 1461 \, d^{4} e^{4} - 669 \, d^{3} e^{5} + 1311 \, d^{2} e^{6} + 87 \, d e^{7} - 63 \, e^{8}\right)} x^{2} + 2 \, {\left(205 \, d^{7} e + 596 \, d^{6} e^{2} - 903 \, d^{5} e^{3} - 2142 \, d^{4} e^{4} + 1245 \, d^{3} e^{5} + 150 \, d^{2} e^{6} - 63 \, d e^{7}\right)} x\right)} \log\left(e x + d\right) + 196 \, {\left(615 \, d^{7} e - 57 \, d^{6} e^{2} - 2538 \, d^{5} e^{3} + 1188 \, d^{4} e^{4} + 171 \, d^{3} e^{5} - 63 \, d^{2} e^{6} + 5 \, {\left(205 \, d^{5} e^{3} - 19 \, d^{4} e^{4} - 846 \, d^{3} e^{5} + 396 \, d^{2} e^{6} + 57 \, d e^{7} - 21 \, e^{8}\right)} x^{4} + 2 \, {\left(1025 \, d^{6} e^{2} + 110 \, d^{5} e^{3} - 4249 \, d^{4} e^{4} + 1134 \, d^{3} e^{5} + 681 \, d^{2} e^{6} - 48 \, d e^{7} - 21 \, e^{8}\right)} x^{3} + {\left(1025 \, d^{7} e + 725 \, d^{6} e^{2} - 3691 \, d^{5} e^{3} - 1461 \, d^{4} e^{4} - 669 \, d^{3} e^{5} + 1311 \, d^{2} e^{6} + 87 \, d e^{7} - 63 \, e^{8}\right)} x^{2} + 2 \, {\left(205 \, d^{7} e + 596 \, d^{6} e^{2} - 903 \, d^{5} e^{3} - 2142 \, d^{4} e^{4} + 1245 \, d^{3} e^{5} + 150 \, d^{2} e^{6} - 63 \, d e^{7}\right)} x\right)} \log\left(5 \, x^{2} + 2 \, x + 3\right)}{392 \, {\left(1875 \, d^{10} e - 3000 \, d^{9} e^{2} + 6300 \, d^{8} e^{3} - 5880 \, d^{7} e^{4} + 6258 \, d^{6} e^{5} - 3528 \, d^{5} e^{6} + 2268 \, d^{4} e^{7} - 648 \, d^{3} e^{8} + 243 \, d^{2} e^{9} + 5 \, {\left(625 \, d^{8} e^{3} - 1000 \, d^{7} e^{4} + 2100 \, d^{6} e^{5} - 1960 \, d^{5} e^{6} + 2086 \, d^{4} e^{7} - 1176 \, d^{3} e^{8} + 756 \, d^{2} e^{9} - 216 \, d e^{10} + 81 \, e^{11}\right)} x^{4} + 2 \, {\left(3125 \, d^{9} e^{2} - 4375 \, d^{8} e^{3} + 9500 \, d^{7} e^{4} - 7700 \, d^{6} e^{5} + 8470 \, d^{5} e^{6} - 3794 \, d^{4} e^{7} + 2604 \, d^{3} e^{8} - 324 \, d^{2} e^{9} + 189 \, d e^{10} + 81 \, e^{11}\right)} x^{3} + {\left(3125 \, d^{10} e - 2500 \, d^{9} e^{2} + 8375 \, d^{8} e^{3} - 4400 \, d^{7} e^{4} + 8890 \, d^{6} e^{5} - 3416 \, d^{5} e^{6} + 5334 \, d^{4} e^{7} - 1584 \, d^{3} e^{8} + 1809 \, d^{2} e^{9} - 324 \, d e^{10} + 243 \, e^{11}\right)} x^{2} + 2 \, {\left(625 \, d^{10} e + 875 \, d^{9} e^{2} - 900 \, d^{8} e^{3} + 4340 \, d^{7} e^{4} - 3794 \, d^{6} e^{5} + 5082 \, d^{5} e^{6} - 2772 \, d^{4} e^{7} + 2052 \, d^{3} e^{8} - 567 \, d^{2} e^{9} + 243 \, d e^{10}\right)} x\right)}}"," ",0,"-1/392*(58800*d^8 + 363230*d^7*e - 178010*d^6*e^2 - 233184*d^5*e^3 + 395164*d^4*e^4 - 437122*d^3*e^5 + 178542*d^2*e^6 - 37044*d*e^7 + 10584*e^8 + 14*(28700*d^6*e^2 - 14965*d^5*e^3 - 43891*d^4*e^4 + 44106*d^3*e^5 - 45966*d^2*e^6 + 12711*d*e^7 + 9*e^8)*x^3 + 14*(7000*d^8 + 31850*d^7*e + 6400*d^6*e^2 - 62649*d^5*e^3 + 52187*d^4*e^4 - 53652*d^3*e^5 + 11130*d^2*e^6 - 2841*d*e^7 + 1791*e^8)*x^2 - sqrt(14)*(19695*d^7*e - 222051*d^6*e^2 + 105066*d^5*e^3 + 128574*d^4*e^4 - 51741*d^3*e^5 + 1737*d^2*e^6 + 5*(6565*d^5*e^3 - 74017*d^4*e^4 + 35022*d^3*e^5 + 42858*d^2*e^6 - 17247*d*e^7 + 579*e^8)*x^4 + 2*(32825*d^6*e^2 - 363520*d^5*e^3 + 101093*d^4*e^4 + 249312*d^3*e^5 - 43377*d^2*e^6 - 14352*d*e^7 + 579*e^8)*x^3 + (32825*d^7*e - 343825*d^6*e^2 - 101263*d^5*e^3 + 132327*d^4*e^4 + 190263*d^3*e^5 + 62481*d^2*e^6 - 49425*d*e^7 + 1737*e^8)*x^2 + 2*(6565*d^7*e - 54322*d^6*e^2 - 187029*d^5*e^3 + 147924*d^4*e^4 + 111327*d^3*e^5 - 51162*d^2*e^6 + 1737*d*e^7)*x)*arctan(1/14*sqrt(14)*(5*x + 1)) + 14*(2800*d^8 + 14855*d^7*e + 5815*d^6*e^2 - 18620*d^5*e^3 - 17202*d^4*e^4 + 11119*d^3*e^5 - 26037*d^2*e^6 + 7866*d*e^7 - 756*e^8)*x - 392*(615*d^7*e - 57*d^6*e^2 - 2538*d^5*e^3 + 1188*d^4*e^4 + 171*d^3*e^5 - 63*d^2*e^6 + 5*(205*d^5*e^3 - 19*d^4*e^4 - 846*d^3*e^5 + 396*d^2*e^6 + 57*d*e^7 - 21*e^8)*x^4 + 2*(1025*d^6*e^2 + 110*d^5*e^3 - 4249*d^4*e^4 + 1134*d^3*e^5 + 681*d^2*e^6 - 48*d*e^7 - 21*e^8)*x^3 + (1025*d^7*e + 725*d^6*e^2 - 3691*d^5*e^3 - 1461*d^4*e^4 - 669*d^3*e^5 + 1311*d^2*e^6 + 87*d*e^7 - 63*e^8)*x^2 + 2*(205*d^7*e + 596*d^6*e^2 - 903*d^5*e^3 - 2142*d^4*e^4 + 1245*d^3*e^5 + 150*d^2*e^6 - 63*d*e^7)*x)*log(e*x + d) + 196*(615*d^7*e - 57*d^6*e^2 - 2538*d^5*e^3 + 1188*d^4*e^4 + 171*d^3*e^5 - 63*d^2*e^6 + 5*(205*d^5*e^3 - 19*d^4*e^4 - 846*d^3*e^5 + 396*d^2*e^6 + 57*d*e^7 - 21*e^8)*x^4 + 2*(1025*d^6*e^2 + 110*d^5*e^3 - 4249*d^4*e^4 + 1134*d^3*e^5 + 681*d^2*e^6 - 48*d*e^7 - 21*e^8)*x^3 + (1025*d^7*e + 725*d^6*e^2 - 3691*d^5*e^3 - 1461*d^4*e^4 - 669*d^3*e^5 + 1311*d^2*e^6 + 87*d*e^7 - 63*e^8)*x^2 + 2*(205*d^7*e + 596*d^6*e^2 - 903*d^5*e^3 - 2142*d^4*e^4 + 1245*d^3*e^5 + 150*d^2*e^6 - 63*d*e^7)*x)*log(5*x^2 + 2*x + 3))/(1875*d^10*e - 3000*d^9*e^2 + 6300*d^8*e^3 - 5880*d^7*e^4 + 6258*d^6*e^5 - 3528*d^5*e^6 + 2268*d^4*e^7 - 648*d^3*e^8 + 243*d^2*e^9 + 5*(625*d^8*e^3 - 1000*d^7*e^4 + 2100*d^6*e^5 - 1960*d^5*e^6 + 2086*d^4*e^7 - 1176*d^3*e^8 + 756*d^2*e^9 - 216*d*e^10 + 81*e^11)*x^4 + 2*(3125*d^9*e^2 - 4375*d^8*e^3 + 9500*d^7*e^4 - 7700*d^6*e^5 + 8470*d^5*e^6 - 3794*d^4*e^7 + 2604*d^3*e^8 - 324*d^2*e^9 + 189*d*e^10 + 81*e^11)*x^3 + (3125*d^10*e - 2500*d^9*e^2 + 8375*d^8*e^3 - 4400*d^7*e^4 + 8890*d^6*e^5 - 3416*d^5*e^6 + 5334*d^4*e^7 - 1584*d^3*e^8 + 1809*d^2*e^9 - 324*d*e^10 + 243*e^11)*x^2 + 2*(625*d^10*e + 875*d^9*e^2 - 900*d^8*e^3 + 4340*d^7*e^4 - 3794*d^6*e^5 + 5082*d^5*e^6 - 2772*d^4*e^7 + 2052*d^3*e^8 - 567*d^2*e^9 + 243*d*e^10)*x)","B",0
318,1,441,0,0.767401," ","integrate((e*x+d)^3*(4*x^4-5*x^3+3*x^2+x+2)/(5*x^2+2*x+3)^3,x, algorithm=""fricas"")","\frac{27440000 \, e^{3} x^{6} + 2744000 \, {\left(60 \, d e^{2} - 41 \, e^{3}\right)} x^{5} + 8780800 \, {\left(15 \, d e^{2} - 8 \, e^{3}\right)} x^{4} + 70 \, {\left(275375 \, d^{3} + 2726475 \, d^{2} e + 1257135 \, d e^{2} - 3045929 \, e^{3}\right)} x^{3} + 22667750 \, d^{3} - 20509650 \, d^{2} e - 80825850 \, d e^{2} + 17863398 \, e^{3} + 14 \, {\left(4844125 \, d^{3} + 2123025 \, d^{2} e - 10375875 \, d e^{2} - 2508283 \, e^{3}\right)} x^{2} + 3 \, \sqrt{14} {\left(25 \, {\left(353125 \, d^{3} - 855175 \, d^{2} e + 74085 \, d e^{2} + 556349 \, e^{3}\right)} x^{4} + 20 \, {\left(353125 \, d^{3} - 855175 \, d^{2} e + 74085 \, d e^{2} + 556349 \, e^{3}\right)} x^{3} + 3178125 \, d^{3} - 7696575 \, d^{2} e + 666765 \, d e^{2} + 5007141 \, e^{3} + 34 \, {\left(353125 \, d^{3} - 855175 \, d^{2} e + 74085 \, d e^{2} + 556349 \, e^{3}\right)} x^{2} + 12 \, {\left(353125 \, d^{3} - 855175 \, d^{2} e + 74085 \, d e^{2} + 556349 \, e^{3}\right)} x\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) + 42 \, {\left(749125 \, d^{3} + 1444025 \, d^{2} e - 1635675 \, d e^{2} - 1323043 \, e^{3}\right)} x + 32928 \, {\left(25 \, {\left(100 \, d^{2} e - 245 \, d e^{2} + 47 \, e^{3}\right)} x^{4} + 20 \, {\left(100 \, d^{2} e - 245 \, d e^{2} + 47 \, e^{3}\right)} x^{3} + 900 \, d^{2} e - 2205 \, d e^{2} + 423 \, e^{3} + 34 \, {\left(100 \, d^{2} e - 245 \, d e^{2} + 47 \, e^{3}\right)} x^{2} + 12 \, {\left(100 \, d^{2} e - 245 \, d e^{2} + 47 \, e^{3}\right)} x\right)} \log\left(5 \, x^{2} + 2 \, x + 3\right)}{68600000 \, {\left(25 \, x^{4} + 20 \, x^{3} + 34 \, x^{2} + 12 \, x + 9\right)}}"," ",0,"1/68600000*(27440000*e^3*x^6 + 2744000*(60*d*e^2 - 41*e^3)*x^5 + 8780800*(15*d*e^2 - 8*e^3)*x^4 + 70*(275375*d^3 + 2726475*d^2*e + 1257135*d*e^2 - 3045929*e^3)*x^3 + 22667750*d^3 - 20509650*d^2*e - 80825850*d*e^2 + 17863398*e^3 + 14*(4844125*d^3 + 2123025*d^2*e - 10375875*d*e^2 - 2508283*e^3)*x^2 + 3*sqrt(14)*(25*(353125*d^3 - 855175*d^2*e + 74085*d*e^2 + 556349*e^3)*x^4 + 20*(353125*d^3 - 855175*d^2*e + 74085*d*e^2 + 556349*e^3)*x^3 + 3178125*d^3 - 7696575*d^2*e + 666765*d*e^2 + 5007141*e^3 + 34*(353125*d^3 - 855175*d^2*e + 74085*d*e^2 + 556349*e^3)*x^2 + 12*(353125*d^3 - 855175*d^2*e + 74085*d*e^2 + 556349*e^3)*x)*arctan(1/14*sqrt(14)*(5*x + 1)) + 42*(749125*d^3 + 1444025*d^2*e - 1635675*d*e^2 - 1323043*e^3)*x + 32928*(25*(100*d^2*e - 245*d*e^2 + 47*e^3)*x^4 + 20*(100*d^2*e - 245*d*e^2 + 47*e^3)*x^3 + 900*d^2*e - 2205*d*e^2 + 423*e^3 + 34*(100*d^2*e - 245*d*e^2 + 47*e^3)*x^2 + 12*(100*d^2*e - 245*d*e^2 + 47*e^3)*x)*log(5*x^2 + 2*x + 3))/(25*x^4 + 20*x^3 + 34*x^2 + 12*x + 9)","B",0
319,1,302,0,0.806712," ","integrate((e*x+d)^2*(4*x^4-5*x^3+3*x^2+x+2)/(5*x^2+2*x+3)^3,x, algorithm=""fricas"")","\frac{10976000 \, e^{2} x^{5} + 8780800 \, e^{2} x^{4} + 70 \, {\left(55075 \, d^{2} + 363530 \, d e + 83809 \, e^{2}\right)} x^{3} + 70 \, {\left(193765 \, d^{2} + 56614 \, d e - 138345 \, e^{2}\right)} x^{2} + \sqrt{14} {\left(25 \, {\left(211875 \, d^{2} - 342070 \, d e + 14817 \, e^{2}\right)} x^{4} + 20 \, {\left(211875 \, d^{2} - 342070 \, d e + 14817 \, e^{2}\right)} x^{3} + 34 \, {\left(211875 \, d^{2} - 342070 \, d e + 14817 \, e^{2}\right)} x^{2} + 1906875 \, d^{2} - 3078630 \, d e + 133353 \, e^{2} + 12 \, {\left(211875 \, d^{2} - 342070 \, d e + 14817 \, e^{2}\right)} x\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) + 4533550 \, d^{2} - 2734620 \, d e - 5388390 \, e^{2} + 70 \, {\left(89895 \, d^{2} + 115522 \, d e - 65427 \, e^{2}\right)} x + 10976 \, {\left(25 \, {\left(40 \, d e - 49 \, e^{2}\right)} x^{4} + 20 \, {\left(40 \, d e - 49 \, e^{2}\right)} x^{3} + 34 \, {\left(40 \, d e - 49 \, e^{2}\right)} x^{2} + 360 \, d e - 441 \, e^{2} + 12 \, {\left(40 \, d e - 49 \, e^{2}\right)} x\right)} \log\left(5 \, x^{2} + 2 \, x + 3\right)}{13720000 \, {\left(25 \, x^{4} + 20 \, x^{3} + 34 \, x^{2} + 12 \, x + 9\right)}}"," ",0,"1/13720000*(10976000*e^2*x^5 + 8780800*e^2*x^4 + 70*(55075*d^2 + 363530*d*e + 83809*e^2)*x^3 + 70*(193765*d^2 + 56614*d*e - 138345*e^2)*x^2 + sqrt(14)*(25*(211875*d^2 - 342070*d*e + 14817*e^2)*x^4 + 20*(211875*d^2 - 342070*d*e + 14817*e^2)*x^3 + 34*(211875*d^2 - 342070*d*e + 14817*e^2)*x^2 + 1906875*d^2 - 3078630*d*e + 133353*e^2 + 12*(211875*d^2 - 342070*d*e + 14817*e^2)*x)*arctan(1/14*sqrt(14)*(5*x + 1)) + 4533550*d^2 - 2734620*d*e - 5388390*e^2 + 70*(89895*d^2 + 115522*d*e - 65427*e^2)*x + 10976*(25*(40*d*e - 49*e^2)*x^4 + 20*(40*d*e - 49*e^2)*x^3 + 34*(40*d*e - 49*e^2)*x^2 + 360*d*e - 441*e^2 + 12*(40*d*e - 49*e^2)*x)*log(5*x^2 + 2*x + 3))/(25*x^4 + 20*x^3 + 34*x^2 + 12*x + 9)","B",0
320,1,172,0,0.587090," ","integrate((e*x+d)*(4*x^4-5*x^3+3*x^2+x+2)/(5*x^2+2*x+3)^3,x, algorithm=""fricas"")","\frac{70 \, {\left(11015 \, d + 36353 \, e\right)} x^{3} + 14 \, {\left(193765 \, d + 28307 \, e\right)} x^{2} + \sqrt{14} {\left(25 \, {\left(42375 \, d - 34207 \, e\right)} x^{4} + 20 \, {\left(42375 \, d - 34207 \, e\right)} x^{3} + 34 \, {\left(42375 \, d - 34207 \, e\right)} x^{2} + 12 \, {\left(42375 \, d - 34207 \, e\right)} x + 381375 \, d - 307863 \, e\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) + 14 \, {\left(89895 \, d + 57761 \, e\right)} x + 43904 \, {\left(25 \, e x^{4} + 20 \, e x^{3} + 34 \, e x^{2} + 12 \, e x + 9 \, e\right)} \log\left(5 \, x^{2} + 2 \, x + 3\right) + 906710 \, d - 273462 \, e}{2744000 \, {\left(25 \, x^{4} + 20 \, x^{3} + 34 \, x^{2} + 12 \, x + 9\right)}}"," ",0,"1/2744000*(70*(11015*d + 36353*e)*x^3 + 14*(193765*d + 28307*e)*x^2 + sqrt(14)*(25*(42375*d - 34207*e)*x^4 + 20*(42375*d - 34207*e)*x^3 + 34*(42375*d - 34207*e)*x^2 + 12*(42375*d - 34207*e)*x + 381375*d - 307863*e)*arctan(1/14*sqrt(14)*(5*x + 1)) + 14*(89895*d + 57761*e)*x + 43904*(25*e*x^4 + 20*e*x^3 + 34*e*x^2 + 12*e*x + 9*e)*log(5*x^2 + 2*x + 3) + 906710*d - 273462*e)/(25*x^4 + 20*x^3 + 34*x^2 + 12*x + 9)","A",0
321,1,75,0,0.808980," ","integrate((4*x^4-5*x^3+3*x^2+x+2)/(5*x^2+2*x+3)^3,x, algorithm=""fricas"")","\frac{154210 \, x^{3} + 8475 \, \sqrt{14} {\left(25 \, x^{4} + 20 \, x^{3} + 34 \, x^{2} + 12 \, x + 9\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) + 542542 \, x^{2} + 251706 \, x + 181342}{548800 \, {\left(25 \, x^{4} + 20 \, x^{3} + 34 \, x^{2} + 12 \, x + 9\right)}}"," ",0,"1/548800*(154210*x^3 + 8475*sqrt(14)*(25*x^4 + 20*x^3 + 34*x^2 + 12*x + 9)*arctan(1/14*sqrt(14)*(5*x + 1)) + 542542*x^2 + 251706*x + 181342)/(25*x^4 + 20*x^3 + 34*x^2 + 12*x + 9)","A",0
322,1,1052,0,1.544895," ","integrate((4*x^4-5*x^3+3*x^2+x+2)/(e*x+d)/(5*x^2+2*x+3)^3,x, algorithm=""fricas"")","\frac{4533550 \, d^{5} - 4072950 \, d^{4} e + 3307332 \, d^{3} e^{2} - 807604 \, d^{2} e^{3} - 358554 \, d e^{4} + 252882 \, e^{5} + 350 \, {\left(11015 \, d^{5} - 49571 \, d^{4} e + 42850 \, d^{3} e^{2} - 43514 \, d^{2} e^{3} + 14563 \, d e^{4} - 5487 \, e^{5}\right)} x^{3} + 14 \, {\left(968825 \, d^{5} - 1304125 \, d^{4} e + 1310718 \, d^{3} e^{2} - 777366 \, d^{2} e^{3} + 250589 \, d e^{4} - 49377 \, e^{5}\right)} x^{2} + 5 \, \sqrt{14} {\left(381375 \, d^{5} - 149787 \, d^{4} e + 526770 \, d^{3} e^{2} - 504522 \, d^{2} e^{3} + 286299 \, d e^{4} - 77607 \, e^{5} + 25 \, {\left(42375 \, d^{5} - 16643 \, d^{4} e + 58530 \, d^{3} e^{2} - 56058 \, d^{2} e^{3} + 31811 \, d e^{4} - 8623 \, e^{5}\right)} x^{4} + 20 \, {\left(42375 \, d^{5} - 16643 \, d^{4} e + 58530 \, d^{3} e^{2} - 56058 \, d^{2} e^{3} + 31811 \, d e^{4} - 8623 \, e^{5}\right)} x^{3} + 34 \, {\left(42375 \, d^{5} - 16643 \, d^{4} e + 58530 \, d^{3} e^{2} - 56058 \, d^{2} e^{3} + 31811 \, d e^{4} - 8623 \, e^{5}\right)} x^{2} + 12 \, {\left(42375 \, d^{5} - 16643 \, d^{4} e + 58530 \, d^{3} e^{2} - 56058 \, d^{2} e^{3} + 31811 \, d e^{4} - 8623 \, e^{5}\right)} x\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) + 14 \, {\left(449475 \, d^{5} - 828175 \, d^{4} e + 761994 \, d^{3} e^{2} - 500898 \, d^{2} e^{3} + 147247 \, d e^{4} - 11211 \, e^{5}\right)} x + 109760 \, {\left(36 \, d^{4} e + 45 \, d^{3} e^{2} + 27 \, d^{2} e^{3} - 9 \, d e^{4} + 18 \, e^{5} + 25 \, {\left(4 \, d^{4} e + 5 \, d^{3} e^{2} + 3 \, d^{2} e^{3} - d e^{4} + 2 \, e^{5}\right)} x^{4} + 20 \, {\left(4 \, d^{4} e + 5 \, d^{3} e^{2} + 3 \, d^{2} e^{3} - d e^{4} + 2 \, e^{5}\right)} x^{3} + 34 \, {\left(4 \, d^{4} e + 5 \, d^{3} e^{2} + 3 \, d^{2} e^{3} - d e^{4} + 2 \, e^{5}\right)} x^{2} + 12 \, {\left(4 \, d^{4} e + 5 \, d^{3} e^{2} + 3 \, d^{2} e^{3} - d e^{4} + 2 \, e^{5}\right)} x\right)} \log\left(e x + d\right) - 54880 \, {\left(36 \, d^{4} e + 45 \, d^{3} e^{2} + 27 \, d^{2} e^{3} - 9 \, d e^{4} + 18 \, e^{5} + 25 \, {\left(4 \, d^{4} e + 5 \, d^{3} e^{2} + 3 \, d^{2} e^{3} - d e^{4} + 2 \, e^{5}\right)} x^{4} + 20 \, {\left(4 \, d^{4} e + 5 \, d^{3} e^{2} + 3 \, d^{2} e^{3} - d e^{4} + 2 \, e^{5}\right)} x^{3} + 34 \, {\left(4 \, d^{4} e + 5 \, d^{3} e^{2} + 3 \, d^{2} e^{3} - d e^{4} + 2 \, e^{5}\right)} x^{2} + 12 \, {\left(4 \, d^{4} e + 5 \, d^{3} e^{2} + 3 \, d^{2} e^{3} - d e^{4} + 2 \, e^{5}\right)} x\right)} \log\left(5 \, x^{2} + 2 \, x + 3\right)}{109760 \, {\left(1125 \, d^{6} - 1350 \, d^{5} e + 2565 \, d^{4} e^{2} - 1692 \, d^{3} e^{3} + 1539 \, d^{2} e^{4} - 486 \, d e^{5} + 243 \, e^{6} + 25 \, {\left(125 \, d^{6} - 150 \, d^{5} e + 285 \, d^{4} e^{2} - 188 \, d^{3} e^{3} + 171 \, d^{2} e^{4} - 54 \, d e^{5} + 27 \, e^{6}\right)} x^{4} + 20 \, {\left(125 \, d^{6} - 150 \, d^{5} e + 285 \, d^{4} e^{2} - 188 \, d^{3} e^{3} + 171 \, d^{2} e^{4} - 54 \, d e^{5} + 27 \, e^{6}\right)} x^{3} + 34 \, {\left(125 \, d^{6} - 150 \, d^{5} e + 285 \, d^{4} e^{2} - 188 \, d^{3} e^{3} + 171 \, d^{2} e^{4} - 54 \, d e^{5} + 27 \, e^{6}\right)} x^{2} + 12 \, {\left(125 \, d^{6} - 150 \, d^{5} e + 285 \, d^{4} e^{2} - 188 \, d^{3} e^{3} + 171 \, d^{2} e^{4} - 54 \, d e^{5} + 27 \, e^{6}\right)} x\right)}}"," ",0,"1/109760*(4533550*d^5 - 4072950*d^4*e + 3307332*d^3*e^2 - 807604*d^2*e^3 - 358554*d*e^4 + 252882*e^5 + 350*(11015*d^5 - 49571*d^4*e + 42850*d^3*e^2 - 43514*d^2*e^3 + 14563*d*e^4 - 5487*e^5)*x^3 + 14*(968825*d^5 - 1304125*d^4*e + 1310718*d^3*e^2 - 777366*d^2*e^3 + 250589*d*e^4 - 49377*e^5)*x^2 + 5*sqrt(14)*(381375*d^5 - 149787*d^4*e + 526770*d^3*e^2 - 504522*d^2*e^3 + 286299*d*e^4 - 77607*e^5 + 25*(42375*d^5 - 16643*d^4*e + 58530*d^3*e^2 - 56058*d^2*e^3 + 31811*d*e^4 - 8623*e^5)*x^4 + 20*(42375*d^5 - 16643*d^4*e + 58530*d^3*e^2 - 56058*d^2*e^3 + 31811*d*e^4 - 8623*e^5)*x^3 + 34*(42375*d^5 - 16643*d^4*e + 58530*d^3*e^2 - 56058*d^2*e^3 + 31811*d*e^4 - 8623*e^5)*x^2 + 12*(42375*d^5 - 16643*d^4*e + 58530*d^3*e^2 - 56058*d^2*e^3 + 31811*d*e^4 - 8623*e^5)*x)*arctan(1/14*sqrt(14)*(5*x + 1)) + 14*(449475*d^5 - 828175*d^4*e + 761994*d^3*e^2 - 500898*d^2*e^3 + 147247*d*e^4 - 11211*e^5)*x + 109760*(36*d^4*e + 45*d^3*e^2 + 27*d^2*e^3 - 9*d*e^4 + 18*e^5 + 25*(4*d^4*e + 5*d^3*e^2 + 3*d^2*e^3 - d*e^4 + 2*e^5)*x^4 + 20*(4*d^4*e + 5*d^3*e^2 + 3*d^2*e^3 - d*e^4 + 2*e^5)*x^3 + 34*(4*d^4*e + 5*d^3*e^2 + 3*d^2*e^3 - d*e^4 + 2*e^5)*x^2 + 12*(4*d^4*e + 5*d^3*e^2 + 3*d^2*e^3 - d*e^4 + 2*e^5)*x)*log(e*x + d) - 54880*(36*d^4*e + 45*d^3*e^2 + 27*d^2*e^3 - 9*d*e^4 + 18*e^5 + 25*(4*d^4*e + 5*d^3*e^2 + 3*d^2*e^3 - d*e^4 + 2*e^5)*x^4 + 20*(4*d^4*e + 5*d^3*e^2 + 3*d^2*e^3 - d*e^4 + 2*e^5)*x^3 + 34*(4*d^4*e + 5*d^3*e^2 + 3*d^2*e^3 - d*e^4 + 2*e^5)*x^2 + 12*(4*d^4*e + 5*d^3*e^2 + 3*d^2*e^3 - d*e^4 + 2*e^5)*x)*log(5*x^2 + 2*x + 3))/(1125*d^6 - 1350*d^5*e + 2565*d^4*e^2 - 1692*d^3*e^3 + 1539*d^2*e^4 - 486*d*e^5 + 243*e^6 + 25*(125*d^6 - 150*d^5*e + 285*d^4*e^2 - 188*d^3*e^3 + 171*d^2*e^4 - 54*d*e^5 + 27*e^6)*x^4 + 20*(125*d^6 - 150*d^5*e + 285*d^4*e^2 - 188*d^3*e^3 + 171*d^2*e^4 - 54*d*e^5 + 27*e^6)*x^3 + 34*(125*d^6 - 150*d^5*e + 285*d^4*e^2 - 188*d^3*e^3 + 171*d^2*e^4 - 54*d*e^5 + 27*e^6)*x^2 + 12*(125*d^6 - 150*d^5*e + 285*d^4*e^2 - 188*d^3*e^3 + 171*d^2*e^4 - 54*d*e^5 + 27*e^6)*x)","B",0
323,1,1734,0,1.589415," ","integrate((4*x^4-5*x^3+3*x^2+x+2)/(e*x+d)^2/(5*x^2+2*x+3)^3,x, algorithm=""fricas"")","\frac{4533550 \, d^{7} - 8470420 \, d^{6} e - 8666490 \, d^{5} e^{2} + 3186008 \, d^{4} e^{3} - 8213198 \, d^{3} e^{4} - 1375668 \, d^{2} e^{5} + 1294650 \, d e^{6} - 1185408 \, e^{7} - 70 \, {\left(101725 \, d^{6} e + 584930 \, d^{5} e^{2} - 245103 \, d^{4} e^{3} + 306788 \, d^{3} e^{4} + 99187 \, d^{2} e^{5} - 93102 \, d e^{6} + 57807 \, e^{7}\right)} x^{4} + 14 \, {\left(275375 \, d^{7} - 1916625 \, d^{6} e - 474395 \, d^{5} e^{2} - 1406231 \, d^{4} e^{3} + 222261 \, d^{3} e^{4} - 1262851 \, d^{2} e^{5} + 601791 \, d e^{6} - 279261 \, e^{7}\right)} x^{3} + 14 \, {\left(968825 \, d^{7} - 2449955 \, d^{6} e - 1699045 \, d^{5} e^{2} - 279581 \, d^{4} e^{3} - 1024621 \, d^{3} e^{4} - 1118441 \, d^{2} e^{5} + 698097 \, d e^{6} - 394767 \, e^{7}\right)} x^{2} + \sqrt{14} {\left(1906875 \, d^{7} + 27630 \, d^{6} e + 1881351 \, d^{5} e^{2} - 8292996 \, d^{4} e^{3} + 3425589 \, d^{3} e^{4} - 446274 \, d^{2} e^{5} - 393255 \, d e^{6} + 25 \, {\left(211875 \, d^{6} e + 3070 \, d^{5} e^{2} + 209039 \, d^{4} e^{3} - 921444 \, d^{3} e^{4} + 380621 \, d^{2} e^{5} - 49586 \, d e^{6} - 43695 \, e^{7}\right)} x^{5} + 5 \, {\left(1059375 \, d^{7} + 862850 \, d^{6} e + 1057475 \, d^{5} e^{2} - 3771064 \, d^{4} e^{3} - 1782671 \, d^{3} e^{4} + 1274554 \, d^{2} e^{5} - 416819 \, d e^{6} - 174780 \, e^{7}\right)} x^{4} + 2 \, {\left(2118750 \, d^{7} + 3632575 \, d^{6} e + 2142580 \, d^{5} e^{2} - 5660777 \, d^{4} e^{3} - 11858338 \, d^{3} e^{4} + 5974697 \, d^{2} e^{5} - 1279912 \, d e^{6} - 742815 \, e^{7}\right)} x^{3} + 2 \, {\left(3601875 \, d^{7} + 1323440 \, d^{6} e + 3572083 \, d^{5} e^{2} - 14410314 \, d^{4} e^{3} + 941893 \, d^{3} e^{4} + 1440764 \, d^{2} e^{5} - 1040331 \, d e^{6} - 262170 \, e^{7}\right)} x^{2} + 3 \, {\left(847500 \, d^{7} + 647905 \, d^{6} e + 845366 \, d^{5} e^{2} - 3058659 \, d^{4} e^{3} - 1241848 \, d^{3} e^{4} + 943519 \, d^{2} e^{5} - 323538 \, d e^{6} - 131085 \, e^{7}\right)} x\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) + 42 \, {\left(149825 \, d^{7} - 449755 \, d^{6} e - 12125 \, d^{5} e^{2} - 238325 \, d^{4} e^{3} - 14261 \, d^{3} e^{4} - 169777 \, d^{2} e^{5} + 84969 \, d e^{6} - 39735 \, e^{7}\right)} x + 21952 \, {\left(360 \, d^{6} e + 747 \, d^{5} e^{2} + 108 \, d^{4} e^{3} - 684 \, d^{3} e^{4} + 414 \, d^{2} e^{5} - 81 \, d e^{6} + 25 \, {\left(40 \, d^{5} e^{2} + 83 \, d^{4} e^{3} + 12 \, d^{3} e^{4} - 76 \, d^{2} e^{5} + 46 \, d e^{6} - 9 \, e^{7}\right)} x^{5} + 5 \, {\left(200 \, d^{6} e + 575 \, d^{5} e^{2} + 392 \, d^{4} e^{3} - 332 \, d^{3} e^{4} - 74 \, d^{2} e^{5} + 139 \, d e^{6} - 36 \, e^{7}\right)} x^{4} + 2 \, {\left(400 \, d^{6} e + 1510 \, d^{5} e^{2} + 1531 \, d^{4} e^{3} - 556 \, d^{3} e^{4} - 832 \, d^{2} e^{5} + 692 \, d e^{6} - 153 \, e^{7}\right)} x^{3} + 2 \, {\left(680 \, d^{6} e + 1651 \, d^{5} e^{2} + 702 \, d^{4} e^{3} - 1220 \, d^{3} e^{4} + 326 \, d^{2} e^{5} + 123 \, d e^{6} - 54 \, e^{7}\right)} x^{2} + 3 \, {\left(160 \, d^{6} e + 452 \, d^{5} e^{2} + 297 \, d^{4} e^{3} - 268 \, d^{3} e^{4} - 44 \, d^{2} e^{5} + 102 \, d e^{6} - 27 \, e^{7}\right)} x\right)} \log\left(e x + d\right) - 10976 \, {\left(360 \, d^{6} e + 747 \, d^{5} e^{2} + 108 \, d^{4} e^{3} - 684 \, d^{3} e^{4} + 414 \, d^{2} e^{5} - 81 \, d e^{6} + 25 \, {\left(40 \, d^{5} e^{2} + 83 \, d^{4} e^{3} + 12 \, d^{3} e^{4} - 76 \, d^{2} e^{5} + 46 \, d e^{6} - 9 \, e^{7}\right)} x^{5} + 5 \, {\left(200 \, d^{6} e + 575 \, d^{5} e^{2} + 392 \, d^{4} e^{3} - 332 \, d^{3} e^{4} - 74 \, d^{2} e^{5} + 139 \, d e^{6} - 36 \, e^{7}\right)} x^{4} + 2 \, {\left(400 \, d^{6} e + 1510 \, d^{5} e^{2} + 1531 \, d^{4} e^{3} - 556 \, d^{3} e^{4} - 832 \, d^{2} e^{5} + 692 \, d e^{6} - 153 \, e^{7}\right)} x^{3} + 2 \, {\left(680 \, d^{6} e + 1651 \, d^{5} e^{2} + 702 \, d^{4} e^{3} - 1220 \, d^{3} e^{4} + 326 \, d^{2} e^{5} + 123 \, d e^{6} - 54 \, e^{7}\right)} x^{2} + 3 \, {\left(160 \, d^{6} e + 452 \, d^{5} e^{2} + 297 \, d^{4} e^{3} - 268 \, d^{3} e^{4} - 44 \, d^{2} e^{5} + 102 \, d e^{6} - 27 \, e^{7}\right)} x\right)} \log\left(5 \, x^{2} + 2 \, x + 3\right)}{21952 \, {\left(5625 \, d^{9} - 9000 \, d^{8} e + 18900 \, d^{7} e^{2} - 17640 \, d^{6} e^{3} + 18774 \, d^{5} e^{4} - 10584 \, d^{4} e^{5} + 6804 \, d^{3} e^{6} - 1944 \, d^{2} e^{7} + 729 \, d e^{8} + 25 \, {\left(625 \, d^{8} e - 1000 \, d^{7} e^{2} + 2100 \, d^{6} e^{3} - 1960 \, d^{5} e^{4} + 2086 \, d^{4} e^{5} - 1176 \, d^{3} e^{6} + 756 \, d^{2} e^{7} - 216 \, d e^{8} + 81 \, e^{9}\right)} x^{5} + 5 \, {\left(3125 \, d^{9} - 2500 \, d^{8} e + 6500 \, d^{7} e^{2} - 1400 \, d^{6} e^{3} + 2590 \, d^{5} e^{4} + 2464 \, d^{4} e^{5} - 924 \, d^{3} e^{6} + 1944 \, d^{2} e^{7} - 459 \, d e^{8} + 324 \, e^{9}\right)} x^{4} + 2 \, {\left(6250 \, d^{9} + 625 \, d^{8} e + 4000 \, d^{7} e^{2} + 16100 \, d^{6} e^{3} - 12460 \, d^{5} e^{4} + 23702 \, d^{4} e^{5} - 12432 \, d^{3} e^{6} + 10692 \, d^{2} e^{7} - 2862 \, d e^{8} + 1377 \, e^{9}\right)} x^{3} + 2 \, {\left(10625 \, d^{9} - 13250 \, d^{8} e + 29700 \, d^{7} e^{2} - 20720 \, d^{6} e^{3} + 23702 \, d^{5} e^{4} - 7476 \, d^{4} e^{5} + 5796 \, d^{3} e^{6} + 864 \, d^{2} e^{7} + 81 \, d e^{8} + 486 \, e^{9}\right)} x^{2} + 3 \, {\left(2500 \, d^{9} - 2125 \, d^{8} e + 5400 \, d^{7} e^{2} - 1540 \, d^{6} e^{3} + 2464 \, d^{5} e^{4} + 1554 \, d^{4} e^{5} - 504 \, d^{3} e^{6} + 1404 \, d^{2} e^{7} - 324 \, d e^{8} + 243 \, e^{9}\right)} x\right)}}"," ",0,"1/21952*(4533550*d^7 - 8470420*d^6*e - 8666490*d^5*e^2 + 3186008*d^4*e^3 - 8213198*d^3*e^4 - 1375668*d^2*e^5 + 1294650*d*e^6 - 1185408*e^7 - 70*(101725*d^6*e + 584930*d^5*e^2 - 245103*d^4*e^3 + 306788*d^3*e^4 + 99187*d^2*e^5 - 93102*d*e^6 + 57807*e^7)*x^4 + 14*(275375*d^7 - 1916625*d^6*e - 474395*d^5*e^2 - 1406231*d^4*e^3 + 222261*d^3*e^4 - 1262851*d^2*e^5 + 601791*d*e^6 - 279261*e^7)*x^3 + 14*(968825*d^7 - 2449955*d^6*e - 1699045*d^5*e^2 - 279581*d^4*e^3 - 1024621*d^3*e^4 - 1118441*d^2*e^5 + 698097*d*e^6 - 394767*e^7)*x^2 + sqrt(14)*(1906875*d^7 + 27630*d^6*e + 1881351*d^5*e^2 - 8292996*d^4*e^3 + 3425589*d^3*e^4 - 446274*d^2*e^5 - 393255*d*e^6 + 25*(211875*d^6*e + 3070*d^5*e^2 + 209039*d^4*e^3 - 921444*d^3*e^4 + 380621*d^2*e^5 - 49586*d*e^6 - 43695*e^7)*x^5 + 5*(1059375*d^7 + 862850*d^6*e + 1057475*d^5*e^2 - 3771064*d^4*e^3 - 1782671*d^3*e^4 + 1274554*d^2*e^5 - 416819*d*e^6 - 174780*e^7)*x^4 + 2*(2118750*d^7 + 3632575*d^6*e + 2142580*d^5*e^2 - 5660777*d^4*e^3 - 11858338*d^3*e^4 + 5974697*d^2*e^5 - 1279912*d*e^6 - 742815*e^7)*x^3 + 2*(3601875*d^7 + 1323440*d^6*e + 3572083*d^5*e^2 - 14410314*d^4*e^3 + 941893*d^3*e^4 + 1440764*d^2*e^5 - 1040331*d*e^6 - 262170*e^7)*x^2 + 3*(847500*d^7 + 647905*d^6*e + 845366*d^5*e^2 - 3058659*d^4*e^3 - 1241848*d^3*e^4 + 943519*d^2*e^5 - 323538*d*e^6 - 131085*e^7)*x)*arctan(1/14*sqrt(14)*(5*x + 1)) + 42*(149825*d^7 - 449755*d^6*e - 12125*d^5*e^2 - 238325*d^4*e^3 - 14261*d^3*e^4 - 169777*d^2*e^5 + 84969*d*e^6 - 39735*e^7)*x + 21952*(360*d^6*e + 747*d^5*e^2 + 108*d^4*e^3 - 684*d^3*e^4 + 414*d^2*e^5 - 81*d*e^6 + 25*(40*d^5*e^2 + 83*d^4*e^3 + 12*d^3*e^4 - 76*d^2*e^5 + 46*d*e^6 - 9*e^7)*x^5 + 5*(200*d^6*e + 575*d^5*e^2 + 392*d^4*e^3 - 332*d^3*e^4 - 74*d^2*e^5 + 139*d*e^6 - 36*e^7)*x^4 + 2*(400*d^6*e + 1510*d^5*e^2 + 1531*d^4*e^3 - 556*d^3*e^4 - 832*d^2*e^5 + 692*d*e^6 - 153*e^7)*x^3 + 2*(680*d^6*e + 1651*d^5*e^2 + 702*d^4*e^3 - 1220*d^3*e^4 + 326*d^2*e^5 + 123*d*e^6 - 54*e^7)*x^2 + 3*(160*d^6*e + 452*d^5*e^2 + 297*d^4*e^3 - 268*d^3*e^4 - 44*d^2*e^5 + 102*d*e^6 - 27*e^7)*x)*log(e*x + d) - 10976*(360*d^6*e + 747*d^5*e^2 + 108*d^4*e^3 - 684*d^3*e^4 + 414*d^2*e^5 - 81*d*e^6 + 25*(40*d^5*e^2 + 83*d^4*e^3 + 12*d^3*e^4 - 76*d^2*e^5 + 46*d*e^6 - 9*e^7)*x^5 + 5*(200*d^6*e + 575*d^5*e^2 + 392*d^4*e^3 - 332*d^3*e^4 - 74*d^2*e^5 + 139*d*e^6 - 36*e^7)*x^4 + 2*(400*d^6*e + 1510*d^5*e^2 + 1531*d^4*e^3 - 556*d^3*e^4 - 832*d^2*e^5 + 692*d*e^6 - 153*e^7)*x^3 + 2*(680*d^6*e + 1651*d^5*e^2 + 702*d^4*e^3 - 1220*d^3*e^4 + 326*d^2*e^5 + 123*d*e^6 - 54*e^7)*x^2 + 3*(160*d^6*e + 452*d^5*e^2 + 297*d^4*e^3 - 268*d^3*e^4 - 44*d^2*e^5 + 102*d*e^6 - 27*e^7)*x)*log(5*x^2 + 2*x + 3))/(5625*d^9 - 9000*d^8*e + 18900*d^7*e^2 - 17640*d^6*e^3 + 18774*d^5*e^4 - 10584*d^4*e^5 + 6804*d^3*e^6 - 1944*d^2*e^7 + 729*d*e^8 + 25*(625*d^8*e - 1000*d^7*e^2 + 2100*d^6*e^3 - 1960*d^5*e^4 + 2086*d^4*e^5 - 1176*d^3*e^6 + 756*d^2*e^7 - 216*d*e^8 + 81*e^9)*x^5 + 5*(3125*d^9 - 2500*d^8*e + 6500*d^7*e^2 - 1400*d^6*e^3 + 2590*d^5*e^4 + 2464*d^4*e^5 - 924*d^3*e^6 + 1944*d^2*e^7 - 459*d*e^8 + 324*e^9)*x^4 + 2*(6250*d^9 + 625*d^8*e + 4000*d^7*e^2 + 16100*d^6*e^3 - 12460*d^5*e^4 + 23702*d^4*e^5 - 12432*d^3*e^6 + 10692*d^2*e^7 - 2862*d*e^8 + 1377*e^9)*x^3 + 2*(10625*d^9 - 13250*d^8*e + 29700*d^7*e^2 - 20720*d^6*e^3 + 23702*d^5*e^4 - 7476*d^4*e^5 + 5796*d^3*e^6 + 864*d^2*e^7 + 81*d*e^8 + 486*e^9)*x^2 + 3*(2500*d^9 - 2125*d^8*e + 5400*d^7*e^2 - 1540*d^6*e^3 + 2464*d^5*e^4 + 1554*d^4*e^5 - 504*d^3*e^6 + 1404*d^2*e^7 - 324*d*e^8 + 243*e^9)*x)","B",0
324,1,83,0,0.864260," ","integrate((5+2*x)*(5*x^4-x^3+3*x^2+x+2)*(2*x^2-x+3)^(1/2),x, algorithm=""fricas"")","\frac{1}{3440640} \, {\left(4915200 \, x^{6} + 12984320 \, x^{5} + 1390592 \, x^{4} + 20304768 \, x^{3} + 11357024 \, x^{2} + 14742332 \, x + 6231117\right)} \sqrt{2 \, x^{2} - x + 3} + \frac{1183005}{262144} \, \sqrt{2} \log\left(-4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right)"," ",0,"1/3440640*(4915200*x^6 + 12984320*x^5 + 1390592*x^4 + 20304768*x^3 + 11357024*x^2 + 14742332*x + 6231117)*sqrt(2*x^2 - x + 3) + 1183005/262144*sqrt(2)*log(-4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25)","A",0
325,1,78,0,0.818800," ","integrate((5*x^4-x^3+3*x^2+x+2)*(2*x^2-x+3)^(1/2),x, algorithm=""fricas"")","\frac{1}{245760} \, {\left(204800 \, x^{5} - 59392 \, x^{4} + 258432 \, x^{3} + 105696 \, x^{2} + 221868 \, x - 27807\right)} \sqrt{2 \, x^{2} - x + 3} + \frac{106007}{131072} \, \sqrt{2} \log\left(-4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right)"," ",0,"1/245760*(204800*x^5 - 59392*x^4 + 258432*x^3 + 105696*x^2 + 221868*x - 27807)*sqrt(2*x^2 - x + 3) + 106007/131072*sqrt(2)*log(-4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25)","A",0
326,1,125,0,0.784097," ","integrate((5*x^4-x^3+3*x^2+x+2)*(2*x^2-x+3)^(1/2)/(5+2*x),x, algorithm=""fricas"")","\frac{1}{12288} \, {\left(6144 \, x^{4} - 21120 \, x^{3} + 79840 \, x^{2} - 300404 \, x + 1561161\right)} \sqrt{2 \, x^{2} - x + 3} + \frac{5627989}{32768} \, \sqrt{2} \log\left(4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right) + \frac{11001}{64} \, \sqrt{2} \log\left(-\frac{24 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(22 \, x - 17\right)} + 1060 \, x^{2} - 1036 \, x + 1153}{4 \, x^{2} + 20 \, x + 25}\right)"," ",0,"1/12288*(6144*x^4 - 21120*x^3 + 79840*x^2 - 300404*x + 1561161)*sqrt(2*x^2 - x + 3) + 5627989/32768*sqrt(2)*log(4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25) + 11001/64*sqrt(2)*log(-(24*sqrt(2)*sqrt(2*x^2 - x + 3)*(22*x - 17) + 1060*x^2 - 1036*x + 1153)/(4*x^2 + 20*x + 25))","A",0
327,1,143,0,0.866401," ","integrate((5*x^4-x^3+3*x^2+x+2)*(2*x^2-x+3)^(1/2)/(5+2*x)^2,x, algorithm=""fricas"")","\frac{7655541 \, \sqrt{2} {\left(2 \, x + 5\right)} \log\left(-4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right) + 7654432 \, \sqrt{2} {\left(2 \, x + 5\right)} \log\left(\frac{24 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(22 \, x - 17\right)} - 1060 \, x^{2} + 1036 \, x - 1153}{4 \, x^{2} + 20 \, x + 25}\right) + 8 \, {\left(3840 \, x^{4} - 17344 \, x^{3} + 94936 \, x^{2} - 728410 \, x - 3539439\right)} \sqrt{2 \, x^{2} - x + 3}}{49152 \, {\left(2 \, x + 5\right)}}"," ",0,"1/49152*(7655541*sqrt(2)*(2*x + 5)*log(-4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25) + 7654432*sqrt(2)*(2*x + 5)*log((24*sqrt(2)*sqrt(2*x^2 - x + 3)*(22*x - 17) - 1060*x^2 + 1036*x - 1153)/(4*x^2 + 20*x + 25)) + 8*(3840*x^4 - 17344*x^3 + 94936*x^2 - 728410*x - 3539439)*sqrt(2*x^2 - x + 3))/(2*x + 5)","A",0
328,1,159,0,0.812371," ","integrate((5*x^4-x^3+3*x^2+x+2)*(2*x^2-x+3)^(1/2)/(5+2*x)^3,x, algorithm=""fricas"")","\frac{12670020 \, \sqrt{2} {\left(4 \, x^{2} + 20 \, x + 25\right)} \log\left(4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right) + 12670805 \, \sqrt{2} {\left(4 \, x^{2} + 20 \, x + 25\right)} \log\left(-\frac{24 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(22 \, x - 17\right)} + 1060 \, x^{2} - 1036 \, x + 1153}{4 \, x^{2} + 20 \, x + 25}\right) + 48 \, {\left(3840 \, x^{4} - 25632 \, x^{3} + 272520 \, x^{2} + 2959330 \, x + 4880551\right)} \sqrt{2 \, x^{2} - x + 3}}{221184 \, {\left(4 \, x^{2} + 20 \, x + 25\right)}}"," ",0,"1/221184*(12670020*sqrt(2)*(4*x^2 + 20*x + 25)*log(4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25) + 12670805*sqrt(2)*(4*x^2 + 20*x + 25)*log(-(24*sqrt(2)*sqrt(2*x^2 - x + 3)*(22*x - 17) + 1060*x^2 - 1036*x + 1153)/(4*x^2 + 20*x + 25)) + 48*(3840*x^4 - 25632*x^3 + 272520*x^2 + 2959330*x + 4880551)*sqrt(2*x^2 - x + 3))/(4*x^2 + 20*x + 25)","A",0
329,1,173,0,0.833926," ","integrate((5*x^4-x^3+3*x^2+x+2)*(2*x^2-x+3)^(1/2)/(5+2*x)^4,x, algorithm=""fricas"")","\frac{170123328 \, \sqrt{2} {\left(8 \, x^{3} + 60 \, x^{2} + 150 \, x + 125\right)} \log\left(-4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right) + 170114729 \, \sqrt{2} {\left(8 \, x^{3} + 60 \, x^{2} + 150 \, x + 125\right)} \log\left(\frac{24 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(22 \, x - 17\right)} - 1060 \, x^{2} + 1036 \, x - 1153}{4 \, x^{2} + 20 \, x + 25}\right) + 48 \, {\left(414720 \, x^{4} - 5453568 \, x^{3} - 97682900 \, x^{2} - 329667508 \, x - 327735797\right)} \sqrt{2 \, x^{2} - x + 3}}{15925248 \, {\left(8 \, x^{3} + 60 \, x^{2} + 150 \, x + 125\right)}}"," ",0,"1/15925248*(170123328*sqrt(2)*(8*x^3 + 60*x^2 + 150*x + 125)*log(-4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25) + 170114729*sqrt(2)*(8*x^3 + 60*x^2 + 150*x + 125)*log((24*sqrt(2)*sqrt(2*x^2 - x + 3)*(22*x - 17) - 1060*x^2 + 1036*x - 1153)/(4*x^2 + 20*x + 25)) + 48*(414720*x^4 - 5453568*x^3 - 97682900*x^2 - 329667508*x - 327735797)*sqrt(2*x^2 - x + 3))/(8*x^3 + 60*x^2 + 150*x + 125)","A",0
330,1,189,0,1.214479," ","integrate((5*x^4-x^3+3*x^2+x+2)*(2*x^2-x+3)^(1/2)/(5+2*x)^5,x, algorithm=""fricas"")","\frac{4640219136 \, \sqrt{2} {\left(16 \, x^{4} + 160 \, x^{3} + 600 \, x^{2} + 1000 \, x + 625\right)} \log\left(4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right) + 4640586097 \, \sqrt{2} {\left(16 \, x^{4} + 160 \, x^{3} + 600 \, x^{2} + 1000 \, x + 625\right)} \log\left(-\frac{24 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(22 \, x - 17\right)} + 1060 \, x^{2} - 1036 \, x + 1153}{4 \, x^{2} + 20 \, x + 25}\right) + 48 \, {\left(238878720 \, x^{4} + 6105343976 \, x^{3} + 31323229164 \, x^{2} + 62847867486 \, x + 44676885233\right)} \sqrt{2 \, x^{2} - x + 3}}{4586471424 \, {\left(16 \, x^{4} + 160 \, x^{3} + 600 \, x^{2} + 1000 \, x + 625\right)}}"," ",0,"1/4586471424*(4640219136*sqrt(2)*(16*x^4 + 160*x^3 + 600*x^2 + 1000*x + 625)*log(4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25) + 4640586097*sqrt(2)*(16*x^4 + 160*x^3 + 600*x^2 + 1000*x + 625)*log(-(24*sqrt(2)*sqrt(2*x^2 - x + 3)*(22*x - 17) + 1060*x^2 - 1036*x + 1153)/(4*x^2 + 20*x + 25)) + 48*(238878720*x^4 + 6105343976*x^3 + 31323229164*x^2 + 62847867486*x + 44676885233)*sqrt(2*x^2 - x + 3))/(16*x^4 + 160*x^3 + 600*x^2 + 1000*x + 625)","A",0
331,1,203,0,1.073150," ","integrate((5*x^4-x^3+3*x^2+x+2)*(2*x^2-x+3)^(1/2)/(5+2*x)^6,x, algorithm=""fricas"")","\frac{64497254400 \, \sqrt{2} {\left(32 \, x^{5} + 400 \, x^{4} + 2000 \, x^{3} + 5000 \, x^{2} + 6250 \, x + 3125\right)} \log\left(-4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right) + 64477987315 \, \sqrt{2} {\left(32 \, x^{5} + 400 \, x^{4} + 2000 \, x^{3} + 5000 \, x^{2} + 6250 \, x + 3125\right)} \log\left(\frac{24 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(22 \, x - 17\right)} - 1060 \, x^{2} + 1036 \, x - 1153}{4 \, x^{2} + 20 \, x + 25}\right) - 48 \, {\left(186470433136 \, x^{4} + 1285267446304 \, x^{3} + 3919478861832 \, x^{2} + 5608297138216 \, x + 3110673952831\right)} \sqrt{2 \, x^{2} - x + 3}}{1651129712640 \, {\left(32 \, x^{5} + 400 \, x^{4} + 2000 \, x^{3} + 5000 \, x^{2} + 6250 \, x + 3125\right)}}"," ",0,"1/1651129712640*(64497254400*sqrt(2)*(32*x^5 + 400*x^4 + 2000*x^3 + 5000*x^2 + 6250*x + 3125)*log(-4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25) + 64477987315*sqrt(2)*(32*x^5 + 400*x^4 + 2000*x^3 + 5000*x^2 + 6250*x + 3125)*log((24*sqrt(2)*sqrt(2*x^2 - x + 3)*(22*x - 17) - 1060*x^2 + 1036*x - 1153)/(4*x^2 + 20*x + 25)) - 48*(186470433136*x^4 + 1285267446304*x^3 + 3919478861832*x^2 + 5608297138216*x + 3110673952831)*sqrt(2*x^2 - x + 3))/(32*x^5 + 400*x^4 + 2000*x^3 + 5000*x^2 + 6250*x + 3125)","A",0
332,1,156,0,0.530451," ","integrate((5*x^4-x^3+3*x^2+x+2)*(2*x^2-x+3)^(1/2)/(5+2*x)^7,x, algorithm=""fricas"")","\frac{134863375 \, \sqrt{2} {\left(64 \, x^{6} + 960 \, x^{5} + 6000 \, x^{4} + 20000 \, x^{3} + 37500 \, x^{2} + 37500 \, x + 15625\right)} \log\left(-\frac{24 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(22 \, x - 17\right)} + 1060 \, x^{2} - 1036 \, x + 1153}{4 \, x^{2} + 20 \, x + 25}\right) + 48 \, {\left(271409942624 \, x^{5} + 12256250416 \, x^{4} + 397498825328 \, x^{3} + 158340720344 \, x^{2} + 27245373694 \, x - 219337079305\right)} \sqrt{2 \, x^{2} - x + 3}}{79254226206720 \, {\left(64 \, x^{6} + 960 \, x^{5} + 6000 \, x^{4} + 20000 \, x^{3} + 37500 \, x^{2} + 37500 \, x + 15625\right)}}"," ",0,"1/79254226206720*(134863375*sqrt(2)*(64*x^6 + 960*x^5 + 6000*x^4 + 20000*x^3 + 37500*x^2 + 37500*x + 15625)*log(-(24*sqrt(2)*sqrt(2*x^2 - x + 3)*(22*x - 17) + 1060*x^2 - 1036*x + 1153)/(4*x^2 + 20*x + 25)) + 48*(271409942624*x^5 + 12256250416*x^4 + 397498825328*x^3 + 158340720344*x^2 + 27245373694*x - 219337079305)*sqrt(2*x^2 - x + 3))/(64*x^6 + 960*x^5 + 6000*x^4 + 20000*x^3 + 37500*x^2 + 37500*x + 15625)","A",0
333,1,171,0,0.898496," ","integrate((5*x^4-x^3+3*x^2+x+2)*(2*x^2-x+3)^(1/2)/(5+2*x)^8,x, algorithm=""fricas"")","\frac{2023498715 \, \sqrt{2} {\left(128 \, x^{7} + 2240 \, x^{6} + 16800 \, x^{5} + 70000 \, x^{4} + 175000 \, x^{3} + 262500 \, x^{2} + 218750 \, x + 78125\right)} \log\left(-\frac{24 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(22 \, x - 17\right)} + 1060 \, x^{2} - 1036 \, x + 1153}{4 \, x^{2} + 20 \, x + 25}\right) + 48 \, {\left(1574342277056 \, x^{6} + 27976951397184 \, x^{5} + 4982916071952 \, x^{4} + 41058010262368 \, x^{3} + 14716683780036 \, x^{2} + 590492177460 \, x - 20465234808721\right)} \sqrt{2 \, x^{2} - x + 3}}{7988826001637376 \, {\left(128 \, x^{7} + 2240 \, x^{6} + 16800 \, x^{5} + 70000 \, x^{4} + 175000 \, x^{3} + 262500 \, x^{2} + 218750 \, x + 78125\right)}}"," ",0,"1/7988826001637376*(2023498715*sqrt(2)*(128*x^7 + 2240*x^6 + 16800*x^5 + 70000*x^4 + 175000*x^3 + 262500*x^2 + 218750*x + 78125)*log(-(24*sqrt(2)*sqrt(2*x^2 - x + 3)*(22*x - 17) + 1060*x^2 - 1036*x + 1153)/(4*x^2 + 20*x + 25)) + 48*(1574342277056*x^6 + 27976951397184*x^5 + 4982916071952*x^4 + 41058010262368*x^3 + 14716683780036*x^2 + 590492177460*x - 20465234808721)*sqrt(2*x^2 - x + 3))/(128*x^7 + 2240*x^6 + 16800*x^5 + 70000*x^4 + 175000*x^3 + 262500*x^2 + 218750*x + 78125)","A",0
334,1,93,0,0.860992," ","integrate((5+2*x)*(2*x^2-x+3)^(3/2)*(5*x^4-x^3+3*x^2+x+2),x, algorithm=""fricas"")","\frac{1}{660602880} \, {\left(1468006400 \, x^{8} + 2926837760 \, x^{7} + 1033175040 \, x^{6} + 12117893120 \, x^{5} + 379086848 \, x^{4} + 12669290112 \, x^{3} + 4870637856 \, x^{2} + 12357760788 \, x + 1592737263\right)} \sqrt{2 \, x^{2} - x + 3} + \frac{147157749}{16777216} \, \sqrt{2} \log\left(-4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right)"," ",0,"1/660602880*(1468006400*x^8 + 2926837760*x^7 + 1033175040*x^6 + 12117893120*x^5 + 379086848*x^4 + 12669290112*x^3 + 4870637856*x^2 + 12357760788*x + 1592737263)*sqrt(2*x^2 - x + 3) + 147157749/16777216*sqrt(2)*log(-4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25)","A",0
335,1,88,0,0.876768," ","integrate((2*x^2-x+3)^(3/2)*(5*x^4-x^3+3*x^2+x+2),x, algorithm=""fricas"")","\frac{1}{7340032} \, {\left(9175040 \, x^{7} - 7667712 \, x^{6} + 29335552 \, x^{5} - 7497728 \, x^{4} + 27023744 \, x^{3} + 3845856 \, x^{2} + 27845612 \, x - 1663407\right)} \sqrt{2 \, x^{2} - x + 3} + \frac{13643439}{8388608} \, \sqrt{2} \log\left(-4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right)"," ",0,"1/7340032*(9175040*x^7 - 7667712*x^6 + 29335552*x^5 - 7497728*x^4 + 27023744*x^3 + 3845856*x^2 + 27845612*x - 1663407)*sqrt(2*x^2 - x + 3) + 13643439/8388608*sqrt(2)*log(-4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25)","A",0
336,1,135,0,0.826803," ","integrate((2*x^2-x+3)^(3/2)*(5*x^4-x^3+3*x^2+x+2)/(5+2*x),x, algorithm=""fricas"")","\frac{1}{1376256} \, {\left(983040 \, x^{6} - 3710976 \, x^{5} + 14493696 \, x^{4} - 46476672 \, x^{3} + 159973408 \, x^{2} - 609499532 \, x + 3149403255\right)} \sqrt{2 \, x^{2} - x + 3} + \frac{1622009981}{524288} \, \sqrt{2} \log\left(4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right) + \frac{99009}{32} \, \sqrt{2} \log\left(-\frac{24 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(22 \, x - 17\right)} + 1060 \, x^{2} - 1036 \, x + 1153}{4 \, x^{2} + 20 \, x + 25}\right)"," ",0,"1/1376256*(983040*x^6 - 3710976*x^5 + 14493696*x^4 - 46476672*x^3 + 159973408*x^2 - 609499532*x + 3149403255)*sqrt(2*x^2 - x + 3) + 1622009981/524288*sqrt(2)*log(4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25) + 99009/32*sqrt(2)*log(-(24*sqrt(2)*sqrt(2*x^2 - x + 3)*(22*x - 17) + 1060*x^2 - 1036*x + 1153)/(4*x^2 + 20*x + 25))","A",0
337,1,153,0,1.001875," ","integrate((2*x^2-x+3)^(3/2)*(5*x^4-x^3+3*x^2+x+2)/(5+2*x)^2,x, algorithm=""fricas"")","\frac{14740041885 \, \sqrt{2} {\left(2 \, x + 5\right)} \log\left(-4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right) + 14739840000 \, \sqrt{2} {\left(2 \, x + 5\right)} \log\left(\frac{24 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(22 \, x - 17\right)} - 1060 \, x^{2} + 1036 \, x - 1153}{4 \, x^{2} + 20 \, x + 25}\right) + 8 \, {\left(409600 \, x^{6} - 1798144 \, x^{5} + 8283904 \, x^{4} - 35369408 \, x^{3} + 182033816 \, x^{2} - 1404323114 \, x - 6814208295\right)} \sqrt{2 \, x^{2} - x + 3}}{3932160 \, {\left(2 \, x + 5\right)}}"," ",0,"1/3932160*(14740041885*sqrt(2)*(2*x + 5)*log(-4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25) + 14739840000*sqrt(2)*(2*x + 5)*log((24*sqrt(2)*sqrt(2*x^2 - x + 3)*(22*x - 17) - 1060*x^2 + 1036*x - 1153)/(4*x^2 + 20*x + 25)) + 8*(409600*x^6 - 1798144*x^5 + 8283904*x^4 - 35369408*x^3 + 182033816*x^2 - 1404323114*x - 6814208295)*sqrt(2*x^2 - x + 3))/(2*x + 5)","A",0
338,1,169,0,0.884916," ","integrate((2*x^2-x+3)^(3/2)*(5*x^4-x^3+3*x^2+x+2)/(5+2*x)^3,x, algorithm=""fricas"")","\frac{129342063 \, \sqrt{2} {\left(4 \, x^{2} + 20 \, x + 25\right)} \log\left(4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right) + 129342640 \, \sqrt{2} {\left(4 \, x^{2} + 20 \, x + 25\right)} \log\left(-\frac{24 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(22 \, x - 17\right)} + 1060 \, x^{2} - 1036 \, x + 1153}{4 \, x^{2} + 20 \, x + 25}\right) + 8 \, {\left(8192 \, x^{6} - 43520 \, x^{5} + 253312 \, x^{4} - 1620944 \, x^{3} + 16667188 \, x^{2} + 181223072 \, x + 298966737\right)} \sqrt{2 \, x^{2} - x + 3}}{65536 \, {\left(4 \, x^{2} + 20 \, x + 25\right)}}"," ",0,"1/65536*(129342063*sqrt(2)*(4*x^2 + 20*x + 25)*log(4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25) + 129342640*sqrt(2)*(4*x^2 + 20*x + 25)*log(-(24*sqrt(2)*sqrt(2*x^2 - x + 3)*(22*x - 17) + 1060*x^2 - 1036*x + 1153)/(4*x^2 + 20*x + 25)) + 8*(8192*x^6 - 43520*x^5 + 253312*x^4 - 1620944*x^3 + 16667188*x^2 + 181223072*x + 298966737)*sqrt(2*x^2 - x + 3))/(4*x^2 + 20*x + 25)","A",0
339,1,183,0,0.815873," ","integrate((2*x^2-x+3)^(3/2)*(5*x^4-x^3+3*x^2+x+2)/(5+2*x)^4,x, algorithm=""fricas"")","\frac{517763637 \, \sqrt{2} {\left(8 \, x^{3} + 60 \, x^{2} + 150 \, x + 125\right)} \log\left(-4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right) + 517762327 \, \sqrt{2} {\left(8 \, x^{3} + 60 \, x^{2} + 150 \, x + 125\right)} \log\left(\frac{24 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(22 \, x - 17\right)} - 1060 \, x^{2} + 1036 \, x - 1153}{4 \, x^{2} + 20 \, x + 25}\right) + 24 \, {\left(46080 \, x^{6} - 315648 \, x^{5} + 2626848 \, x^{4} - 33595416 \, x^{3} - 594798908 \, x^{2} - 2006873194 \, x - 1994650739\right)} \sqrt{2 \, x^{2} - x + 3}}{884736 \, {\left(8 \, x^{3} + 60 \, x^{2} + 150 \, x + 125\right)}}"," ",0,"1/884736*(517763637*sqrt(2)*(8*x^3 + 60*x^2 + 150*x + 125)*log(-4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25) + 517762327*sqrt(2)*(8*x^3 + 60*x^2 + 150*x + 125)*log((24*sqrt(2)*sqrt(2*x^2 - x + 3)*(22*x - 17) - 1060*x^2 + 1036*x - 1153)/(4*x^2 + 20*x + 25)) + 24*(46080*x^6 - 315648*x^5 + 2626848*x^4 - 33595416*x^3 - 594798908*x^2 - 2006873194*x - 1994650739)*sqrt(2*x^2 - x + 3))/(8*x^3 + 60*x^2 + 150*x + 125)","A",0
340,1,199,0,1.303098," ","integrate((2*x^2-x+3)^(3/2)*(5*x^4-x^3+3*x^2+x+2)/(5+2*x)^5,x, algorithm=""fricas"")","\frac{8969667840 \, \sqrt{2} {\left(16 \, x^{4} + 160 \, x^{3} + 600 \, x^{2} + 1000 \, x + 625\right)} \log\left(4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right) + 8969688643 \, \sqrt{2} {\left(16 \, x^{4} + 160 \, x^{3} + 600 \, x^{2} + 1000 \, x + 625\right)} \log\left(-\frac{24 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(22 \, x - 17\right)} + 1060 \, x^{2} - 1036 \, x + 1153}{4 \, x^{2} + 20 \, x + 25}\right) + 48 \, {\left(2949120 \, x^{6} - 29270016 \, x^{5} + 468043776 \, x^{4} + 11761910072 \, x^{3} + 60528581892 \, x^{2} + 121473790266 \, x + 86386856771\right)} \sqrt{2 \, x^{2} - x + 3}}{84934656 \, {\left(16 \, x^{4} + 160 \, x^{3} + 600 \, x^{2} + 1000 \, x + 625\right)}}"," ",0,"1/84934656*(8969667840*sqrt(2)*(16*x^4 + 160*x^3 + 600*x^2 + 1000*x + 625)*log(4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25) + 8969688643*sqrt(2)*(16*x^4 + 160*x^3 + 600*x^2 + 1000*x + 625)*log(-(24*sqrt(2)*sqrt(2*x^2 - x + 3)*(22*x - 17) + 1060*x^2 - 1036*x + 1153)/(4*x^2 + 20*x + 25)) + 48*(2949120*x^6 - 29270016*x^5 + 468043776*x^4 + 11761910072*x^3 + 60528581892*x^2 + 121473790266*x + 86386856771)*sqrt(2*x^2 - x + 3))/(16*x^4 + 160*x^3 + 600*x^2 + 1000*x + 625)","A",0
341,1,213,0,0.810443," ","integrate((2*x^2-x+3)^(3/2)*(5*x^4-x^3+3*x^2+x+2)/(5+2*x)^6,x, algorithm=""fricas"")","\frac{354958848000 \, \sqrt{2} {\left(32 \, x^{5} + 400 \, x^{4} + 2000 \, x^{3} + 5000 \, x^{2} + 6250 \, x + 3125\right)} \log\left(-4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right) + 354957625835 \, \sqrt{2} {\left(32 \, x^{5} + 400 \, x^{4} + 2000 \, x^{3} + 5000 \, x^{2} + 6250 \, x + 3125\right)} \log\left(\frac{24 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(22 \, x - 17\right)} - 1060 \, x^{2} + 1036 \, x - 1153}{4 \, x^{2} + 20 \, x + 25}\right) + 48 \, {\left(1592524800 \, x^{6} - 30496849920 \, x^{5} - 1023534029552 \, x^{4} - 7117092892448 \, x^{3} - 21590439797064 \, x^{2} - 30872393829992 \, x - 17093312738327\right)} \sqrt{2 \, x^{2} - x + 3}}{30576476160 \, {\left(32 \, x^{5} + 400 \, x^{4} + 2000 \, x^{3} + 5000 \, x^{2} + 6250 \, x + 3125\right)}}"," ",0,"1/30576476160*(354958848000*sqrt(2)*(32*x^5 + 400*x^4 + 2000*x^3 + 5000*x^2 + 6250*x + 3125)*log(-4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25) + 354957625835*sqrt(2)*(32*x^5 + 400*x^4 + 2000*x^3 + 5000*x^2 + 6250*x + 3125)*log((24*sqrt(2)*sqrt(2*x^2 - x + 3)*(22*x - 17) - 1060*x^2 + 1036*x - 1153)/(4*x^2 + 20*x + 25)) + 48*(1592524800*x^6 - 30496849920*x^5 - 1023534029552*x^4 - 7117092892448*x^3 - 21590439797064*x^2 - 30872393829992*x - 17093312738327)*sqrt(2*x^2 - x + 3))/(32*x^5 + 400*x^4 + 2000*x^3 + 5000*x^2 + 6250*x + 3125)","A",0
342,1,229,0,0.793210," ","integrate((2*x^2-x+3)^(3/2)*(5*x^4-x^3+3*x^2+x+2)/(5+2*x)^7,x, algorithm=""fricas"")","\frac{1903958949888 \, \sqrt{2} {\left(64 \, x^{6} + 960 \, x^{5} + 6000 \, x^{4} + 20000 \, x^{3} + 37500 \, x^{2} + 37500 \, x + 15625\right)} \log\left(4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right) + 1903976002333 \, \sqrt{2} {\left(64 \, x^{6} + 960 \, x^{5} + 6000 \, x^{4} + 20000 \, x^{3} + 37500 \, x^{2} + 37500 \, x + 15625\right)} \log\left(-\frac{24 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(22 \, x - 17\right)} + 1060 \, x^{2} - 1036 \, x + 1153}{4 \, x^{2} + 20 \, x + 25}\right) + 48 \, {\left(275188285440 \, x^{6} + 11854023276320 \, x^{5} + 103803827945872 \, x^{4} + 422554114856528 \, x^{3} + 910256842473992 \, x^{2} + 1011372787716826 \, x + 458411625354581\right)} \sqrt{2 \, x^{2} - x + 3}}{2641807540224 \, {\left(64 \, x^{6} + 960 \, x^{5} + 6000 \, x^{4} + 20000 \, x^{3} + 37500 \, x^{2} + 37500 \, x + 15625\right)}}"," ",0,"1/2641807540224*(1903958949888*sqrt(2)*(64*x^6 + 960*x^5 + 6000*x^4 + 20000*x^3 + 37500*x^2 + 37500*x + 15625)*log(4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25) + 1903976002333*sqrt(2)*(64*x^6 + 960*x^5 + 6000*x^4 + 20000*x^3 + 37500*x^2 + 37500*x + 15625)*log(-(24*sqrt(2)*sqrt(2*x^2 - x + 3)*(22*x - 17) + 1060*x^2 - 1036*x + 1153)/(4*x^2 + 20*x + 25)) + 48*(275188285440*x^6 + 11854023276320*x^5 + 103803827945872*x^4 + 422554114856528*x^3 + 910256842473992*x^2 + 1011372787716826*x + 458411625354581)*sqrt(2*x^2 - x + 3))/(64*x^6 + 960*x^5 + 6000*x^4 + 20000*x^3 + 37500*x^2 + 37500*x + 15625)","A",0
343,1,243,0,2.062557," ","integrate((2*x^2-x+3)^(3/2)*(5*x^4-x^3+3*x^2+x+2)/(5+2*x)^8,x, algorithm=""fricas"")","\frac{2889476997120 \, \sqrt{2} {\left(128 \, x^{7} + 2240 \, x^{6} + 16800 \, x^{5} + 70000 \, x^{4} + 175000 \, x^{3} + 262500 \, x^{2} + 218750 \, x + 78125\right)} \log\left(-4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right) + 2889323929457 \, \sqrt{2} {\left(128 \, x^{7} + 2240 \, x^{6} + 16800 \, x^{5} + 70000 \, x^{4} + 175000 \, x^{3} + 262500 \, x^{2} + 218750 \, x + 78125\right)} \log\left(\frac{24 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(22 \, x - 17\right)} - 1060 \, x^{2} + 1036 \, x - 1153}{4 \, x^{2} + 20 \, x + 25}\right) - 48 \, {\left(38463671680832 \, x^{6} + 402255822731712 \, x^{5} + 2069947287085104 \, x^{4} + 5966329646300704 \, x^{3} + 9976065367498188 \, x^{2} + 9065154700300572 \, x + 3479517268702637\right)} \sqrt{2 \, x^{2} - x + 3}}{147941222252544 \, {\left(128 \, x^{7} + 2240 \, x^{6} + 16800 \, x^{5} + 70000 \, x^{4} + 175000 \, x^{3} + 262500 \, x^{2} + 218750 \, x + 78125\right)}}"," ",0,"1/147941222252544*(2889476997120*sqrt(2)*(128*x^7 + 2240*x^6 + 16800*x^5 + 70000*x^4 + 175000*x^3 + 262500*x^2 + 218750*x + 78125)*log(-4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25) + 2889323929457*sqrt(2)*(128*x^7 + 2240*x^6 + 16800*x^5 + 70000*x^4 + 175000*x^3 + 262500*x^2 + 218750*x + 78125)*log((24*sqrt(2)*sqrt(2*x^2 - x + 3)*(22*x - 17) - 1060*x^2 + 1036*x - 1153)/(4*x^2 + 20*x + 25)) - 48*(38463671680832*x^6 + 402255822731712*x^5 + 2069947287085104*x^4 + 5966329646300704*x^3 + 9976065367498188*x^2 + 9065154700300572*x + 3479517268702637)*sqrt(2*x^2 - x + 3))/(128*x^7 + 2240*x^6 + 16800*x^5 + 70000*x^4 + 175000*x^3 + 262500*x^2 + 218750*x + 78125)","A",0
344,1,73,0,0.710260," ","integrate((5+2*x)*(5*x^4-x^3+3*x^2+x+2)/(2*x^2-x+3)^(1/2),x, algorithm=""fricas"")","\frac{1}{2048} \, {\left(2048 \, x^{4} + 7040 \, x^{3} + 352 \, x^{2} - 6916 \, x + 2973\right)} \sqrt{2 \, x^{2} - x + 3} + \frac{85429}{16384} \, \sqrt{2} \log\left(-4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right)"," ",0,"1/2048*(2048*x^4 + 7040*x^3 + 352*x^2 - 6916*x + 2973)*sqrt(2*x^2 - x + 3) + 85429/16384*sqrt(2)*log(-4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25)","A",0
345,1,68,0,0.678616," ","integrate((5*x^4-x^3+3*x^2+x+2)/(2*x^2-x+3)^(1/2),x, algorithm=""fricas"")","\frac{1}{3072} \, {\left(1920 \, x^{3} + 608 \, x^{2} - 1636 \, x - 1515\right)} \sqrt{2 \, x^{2} - x + 3} + \frac{6863}{8192} \, \sqrt{2} \log\left(-4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right)"," ",0,"1/3072*(1920*x^3 + 608*x^2 - 1636*x - 1515)*sqrt(2*x^2 - x + 3) + 6863/8192*sqrt(2)*log(-4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25)","A",0
346,1,115,0,0.841594," ","integrate((5*x^4-x^3+3*x^2+x+2)/(5+2*x)/(2*x^2-x+3)^(1/2),x, algorithm=""fricas"")","\frac{1}{384} \, {\left(160 \, x^{2} - 548 \, x + 2637\right)} \sqrt{2 \, x^{2} - x + 3} + \frac{9657}{1024} \, \sqrt{2} \log\left(4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right) + \frac{3667}{384} \, \sqrt{2} \log\left(-\frac{24 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(22 \, x - 17\right)} + 1060 \, x^{2} - 1036 \, x + 1153}{4 \, x^{2} + 20 \, x + 25}\right)"," ",0,"1/384*(160*x^2 - 548*x + 2637)*sqrt(2*x^2 - x + 3) + 9657/1024*sqrt(2)*log(4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25) + 3667/384*sqrt(2)*log(-(24*sqrt(2)*sqrt(2*x^2 - x + 3)*(22*x - 17) + 1060*x^2 - 1036*x + 1153)/(4*x^2 + 20*x + 25))","A",0
347,1,133,0,1.323179," ","integrate((5*x^4-x^3+3*x^2+x+2)/(5+2*x)^2/(2*x^2-x+3)^(1/2),x, algorithm=""fricas"")","\frac{158922 \, \sqrt{2} {\left(2 \, x + 5\right)} \log\left(-4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right) + 158527 \, \sqrt{2} {\left(2 \, x + 5\right)} \log\left(\frac{24 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(22 \, x - 17\right)} - 1060 \, x^{2} + 1036 \, x - 1153}{4 \, x^{2} + 20 \, x + 25}\right) + 96 \, {\left(180 \, x^{2} - 1287 \, x - 6176\right)} \sqrt{2 \, x^{2} - x + 3}}{27648 \, {\left(2 \, x + 5\right)}}"," ",0,"1/27648*(158922*sqrt(2)*(2*x + 5)*log(-4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25) + 158527*sqrt(2)*(2*x + 5)*log((24*sqrt(2)*sqrt(2*x^2 - x + 3)*(22*x - 17) - 1060*x^2 + 1036*x - 1153)/(4*x^2 + 20*x + 25)) + 96*(180*x^2 - 1287*x - 6176)*sqrt(2*x^2 - x + 3))/(2*x + 5)","A",0
348,1,149,0,1.513822," ","integrate((5*x^4-x^3+3*x^2+x+2)/(5+2*x)^3/(2*x^2-x+3)^(1/2),x, algorithm=""fricas"")","\frac{1544832 \, \sqrt{2} {\left(4 \, x^{2} + 20 \, x + 25\right)} \log\left(4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right) + 1546507 \, \sqrt{2} {\left(4 \, x^{2} + 20 \, x + 25\right)} \log\left(-\frac{24 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(22 \, x - 17\right)} + 1060 \, x^{2} - 1036 \, x + 1153}{4 \, x^{2} + 20 \, x + 25}\right) + 48 \, {\left(34560 \, x^{2} + 357278 \, x + 589187\right)} \sqrt{2 \, x^{2} - x + 3}}{1327104 \, {\left(4 \, x^{2} + 20 \, x + 25\right)}}"," ",0,"1/1327104*(1544832*sqrt(2)*(4*x^2 + 20*x + 25)*log(4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25) + 1546507*sqrt(2)*(4*x^2 + 20*x + 25)*log(-(24*sqrt(2)*sqrt(2*x^2 - x + 3)*(22*x - 17) + 1060*x^2 - 1036*x + 1153)/(4*x^2 + 20*x + 25)) + 48*(34560*x^2 + 357278*x + 589187)*sqrt(2*x^2 - x + 3))/(4*x^2 + 20*x + 25)","A",0
349,1,163,0,1.695559," ","integrate((5*x^4-x^3+3*x^2+x+2)/(5+2*x)^4/(2*x^2-x+3)^(1/2),x, algorithm=""fricas"")","\frac{22394880 \, \sqrt{2} {\left(8 \, x^{3} + 60 \, x^{2} + 150 \, x + 125\right)} \log\left(-4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right) + 22389491 \, \sqrt{2} {\left(8 \, x^{3} + 60 \, x^{2} + 150 \, x + 125\right)} \log\left(\frac{24 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(22 \, x - 17\right)} - 1060 \, x^{2} + 1036 \, x - 1153}{4 \, x^{2} + 20 \, x + 25}\right) - 48 \, {\left(12653660 \, x^{2} + 44312764 \, x + 44369687\right)} \sqrt{2 \, x^{2} - x + 3}}{286654464 \, {\left(8 \, x^{3} + 60 \, x^{2} + 150 \, x + 125\right)}}"," ",0,"1/286654464*(22394880*sqrt(2)*(8*x^3 + 60*x^2 + 150*x + 125)*log(-4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25) + 22389491*sqrt(2)*(8*x^3 + 60*x^2 + 150*x + 125)*log((24*sqrt(2)*sqrt(2*x^2 - x + 3)*(22*x - 17) - 1060*x^2 + 1036*x - 1153)/(4*x^2 + 20*x + 25)) - 48*(12653660*x^2 + 44312764*x + 44369687)*sqrt(2*x^2 - x + 3))/(8*x^3 + 60*x^2 + 150*x + 125)","A",0
350,1,125,0,0.859782," ","integrate((5*x^4-x^3+3*x^2+x+2)/(5+2*x)^5/(2*x^2-x+3)^(1/2),x, algorithm=""fricas"")","\frac{2053207 \, \sqrt{2} {\left(16 \, x^{4} + 160 \, x^{3} + 600 \, x^{2} + 1000 \, x + 625\right)} \log\left(\frac{24 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(22 \, x - 17\right)} - 1060 \, x^{2} + 1036 \, x - 1153}{4 \, x^{2} + 20 \, x + 25}\right) + 48 \, {\left(214400680 \, x^{3} + 43592076 \, x^{2} - 255525906 \, x - 298655447\right)} \sqrt{2 \, x^{2} - x + 3}}{82556485632 \, {\left(16 \, x^{4} + 160 \, x^{3} + 600 \, x^{2} + 1000 \, x + 625\right)}}"," ",0,"1/82556485632*(2053207*sqrt(2)*(16*x^4 + 160*x^3 + 600*x^2 + 1000*x + 625)*log((24*sqrt(2)*sqrt(2*x^2 - x + 3)*(22*x - 17) - 1060*x^2 + 1036*x - 1153)/(4*x^2 + 20*x + 25)) + 48*(214400680*x^3 + 43592076*x^2 - 255525906*x - 298655447)*sqrt(2*x^2 - x + 3))/(16*x^4 + 160*x^3 + 600*x^2 + 1000*x + 625)","A",0
351,1,102,0,0.936252," ","integrate((5+2*x)^2*(5*x^4-x^3+3*x^2+x+2)/(2*x^2-x+3)^(3/2),x, algorithm=""fricas"")","\frac{3316991 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} \log\left(4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right) + 8 \, {\left(29440 \, x^{5} + 210496 \, x^{4} + 418232 \, x^{3} - 510554 \, x^{2} + 2124123 \, x - 1616165\right)} \sqrt{2 \, x^{2} - x + 3}}{94208 \, {\left(2 \, x^{2} - x + 3\right)}}"," ",0,"1/94208*(3316991*sqrt(2)*(2*x^2 - x + 3)*log(4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25) + 8*(29440*x^5 + 210496*x^4 + 418232*x^3 - 510554*x^2 + 2124123*x - 1616165)*sqrt(2*x^2 - x + 3))/(2*x^2 - x + 3)","A",0
352,1,97,0,1.441950," ","integrate((5+2*x)*(5*x^4-x^3+3*x^2+x+2)/(2*x^2-x+3)^(3/2),x, algorithm=""fricas"")","\frac{214659 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} \log\left(4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right) + 8 \, {\left(7360 \, x^{4} + 31832 \, x^{3} - 2162 \, x^{2} + 122607 \, x - 3345\right)} \sqrt{2 \, x^{2} - x + 3}}{35328 \, {\left(2 \, x^{2} - x + 3\right)}}"," ",0,"1/35328*(214659*sqrt(2)*(2*x^2 - x + 3)*log(4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25) + 8*(7360*x^4 + 31832*x^3 - 2162*x^2 + 122607*x - 3345)*sqrt(2*x^2 - x + 3))/(2*x^2 - x + 3)","A",0
353,1,92,0,1.647027," ","integrate((5*x^4-x^3+3*x^2+x+2)/(2*x^2-x+3)^(3/2),x, algorithm=""fricas"")","\frac{4899 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} \log\left(4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right) + 8 \, {\left(920 \, x^{3} + 782 \, x^{2} + 2511 \, x + 2575\right)} \sqrt{2 \, x^{2} - x + 3}}{5888 \, {\left(2 \, x^{2} - x + 3\right)}}"," ",0,"1/5888*(4899*sqrt(2)*(2*x^2 - x + 3)*log(4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25) + 8*(920*x^3 + 782*x^2 + 2511*x + 2575)*sqrt(2*x^2 - x + 3))/(2*x^2 - x + 3)","A",0
354,1,149,0,1.166524," ","integrate((5*x^4-x^3+3*x^2+x+2)/(5+2*x)/(2*x^2-x+3)^(3/2),x, algorithm=""fricas"")","\frac{96876 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} \log\left(4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right) + 84341 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} \log\left(-\frac{24 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(22 \, x - 17\right)} + 1060 \, x^{2} - 1036 \, x + 1153}{4 \, x^{2} + 20 \, x + 25}\right) + 48 \, {\left(4140 \, x^{2} - 1153 \, x + 7401\right)} \sqrt{2 \, x^{2} - x + 3}}{158976 \, {\left(2 \, x^{2} - x + 3\right)}}"," ",0,"1/158976*(96876*sqrt(2)*(2*x^2 - x + 3)*log(4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25) + 84341*sqrt(2)*(2*x^2 - x + 3)*log(-(24*sqrt(2)*sqrt(2*x^2 - x + 3)*(22*x - 17) + 1060*x^2 - 1036*x + 1153)/(4*x^2 + 20*x + 25)) + 48*(4140*x^2 - 1153*x + 7401)*sqrt(2*x^2 - x + 3))/(2*x^2 - x + 3)","A",0
355,1,157,0,1.152601," ","integrate((5*x^4-x^3+3*x^2+x+2)/(5+2*x)^2/(2*x^2-x+3)^(3/2),x, algorithm=""fricas"")","\frac{596160 \, \sqrt{2} {\left(4 \, x^{3} + 8 \, x^{2} + x + 15\right)} \log\left(-4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right) + 596873 \, \sqrt{2} {\left(4 \, x^{3} + 8 \, x^{2} + x + 15\right)} \log\left(\frac{24 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(22 \, x - 17\right)} - 1060 \, x^{2} + 1036 \, x - 1153}{4 \, x^{2} + 20 \, x + 25}\right) - 48 \, {\left(53290 \, x^{2} - 48653 \, x + 51351\right)} \sqrt{2 \, x^{2} - x + 3}}{3815424 \, {\left(4 \, x^{3} + 8 \, x^{2} + x + 15\right)}}"," ",0,"1/3815424*(596160*sqrt(2)*(4*x^3 + 8*x^2 + x + 15)*log(-4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25) + 596873*sqrt(2)*(4*x^3 + 8*x^2 + x + 15)*log((24*sqrt(2)*sqrt(2*x^2 - x + 3)*(22*x - 17) - 1060*x^2 + 1036*x - 1153)/(4*x^2 + 20*x + 25)) - 48*(53290*x^2 - 48653*x + 51351)*sqrt(2*x^2 - x + 3))/(4*x^3 + 8*x^2 + x + 15)","A",0
356,1,126,0,1.198205," ","integrate((5*x^4-x^3+3*x^2+x+2)/(5+2*x)^3/(2*x^2-x+3)^(3/2),x, algorithm=""fricas"")","\frac{1210513 \, \sqrt{2} {\left(8 \, x^{4} + 36 \, x^{3} + 42 \, x^{2} + 35 \, x + 75\right)} \log\left(-\frac{24 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(22 \, x - 17\right)} + 1060 \, x^{2} - 1036 \, x + 1153}{4 \, x^{2} + 20 \, x + 25}\right) + 48 \, {\left(3444340 \, x^{3} + 3263288 \, x^{2} + 5842933 \, x + 11594283\right)} \sqrt{2 \, x^{2} - x + 3}}{549421056 \, {\left(8 \, x^{4} + 36 \, x^{3} + 42 \, x^{2} + 35 \, x + 75\right)}}"," ",0,"1/549421056*(1210513*sqrt(2)*(8*x^4 + 36*x^3 + 42*x^2 + 35*x + 75)*log(-(24*sqrt(2)*sqrt(2*x^2 - x + 3)*(22*x - 17) + 1060*x^2 - 1036*x + 1153)/(4*x^2 + 20*x + 25)) + 48*(3444340*x^3 + 3263288*x^2 + 5842933*x + 11594283)*sqrt(2*x^2 - x + 3))/(8*x^4 + 36*x^3 + 42*x^2 + 35*x + 75)","A",0
357,1,141,0,1.074580," ","integrate((5*x^4-x^3+3*x^2+x+2)/(5+2*x)^4/(2*x^2-x+3)^(3/2),x, algorithm=""fricas"")","\frac{80633837 \, \sqrt{2} {\left(16 \, x^{5} + 112 \, x^{4} + 264 \, x^{3} + 280 \, x^{2} + 325 \, x + 375\right)} \log\left(-\frac{24 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(22 \, x - 17\right)} + 1060 \, x^{2} - 1036 \, x + 1153}{4 \, x^{2} + 20 \, x + 25}\right) + 48 \, {\left(56754760 \, x^{4} + 572739684 \, x^{3} + 441046842 \, x^{2} + 1257975811 \, x + 1873786587\right)} \sqrt{2 \, x^{2} - x + 3}}{118674948096 \, {\left(16 \, x^{5} + 112 \, x^{4} + 264 \, x^{3} + 280 \, x^{2} + 325 \, x + 375\right)}}"," ",0,"1/118674948096*(80633837*sqrt(2)*(16*x^5 + 112*x^4 + 264*x^3 + 280*x^2 + 325*x + 375)*log(-(24*sqrt(2)*sqrt(2*x^2 - x + 3)*(22*x - 17) + 1060*x^2 - 1036*x + 1153)/(4*x^2 + 20*x + 25)) + 48*(56754760*x^4 + 572739684*x^3 + 441046842*x^2 + 1257975811*x + 1873786587)*sqrt(2*x^2 - x + 3))/(16*x^5 + 112*x^4 + 264*x^3 + 280*x^2 + 325*x + 375)","A",0
358,1,122,0,1.081252," ","integrate((5+2*x)^2*(5*x^4-x^3+3*x^2+x+2)/(2*x^2-x+3)^(5/2),x, algorithm=""fricas"")","\frac{2334477 \, \sqrt{2} {\left(4 \, x^{4} - 4 \, x^{3} + 13 \, x^{2} - 6 \, x + 9\right)} \log\left(-4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right) + 8 \, {\left(126960 \, x^{5} + 1440996 \, x^{4} - 3764360 \, x^{3} + 8639625 \, x^{2} - 6410082 \, x + 6663133\right)} \sqrt{2 \, x^{2} - x + 3}}{203136 \, {\left(4 \, x^{4} - 4 \, x^{3} + 13 \, x^{2} - 6 \, x + 9\right)}}"," ",0,"1/203136*(2334477*sqrt(2)*(4*x^4 - 4*x^3 + 13*x^2 - 6*x + 9)*log(-4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25) + 8*(126960*x^5 + 1440996*x^4 - 3764360*x^3 + 8639625*x^2 - 6410082*x + 6663133)*sqrt(2*x^2 - x + 3))/(4*x^4 - 4*x^3 + 13*x^2 - 6*x + 9)","A",0
359,1,117,0,0.922874," ","integrate((5+2*x)*(5*x^4-x^3+3*x^2+x+2)/(2*x^2-x+3)^(5/2),x, algorithm=""fricas"")","\frac{112677 \, \sqrt{2} {\left(4 \, x^{4} - 4 \, x^{3} + 13 \, x^{2} - 6 \, x + 9\right)} \log\left(-4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right) + 8 \, {\left(31740 \, x^{4} - 147664 \, x^{3} + 185337 \, x^{2} - 199290 \, x + 102869\right)} \sqrt{2 \, x^{2} - x + 3}}{50784 \, {\left(4 \, x^{4} - 4 \, x^{3} + 13 \, x^{2} - 6 \, x + 9\right)}}"," ",0,"1/50784*(112677*sqrt(2)*(4*x^4 - 4*x^3 + 13*x^2 - 6*x + 9)*log(-4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25) + 8*(31740*x^4 - 147664*x^3 + 185337*x^2 - 199290*x + 102869)*sqrt(2*x^2 - x + 3))/(4*x^4 - 4*x^3 + 13*x^2 - 6*x + 9)","A",0
360,1,112,0,0.933187," ","integrate((5*x^4-x^3+3*x^2+x+2)/(2*x^2-x+3)^(5/2),x, algorithm=""fricas"")","\frac{7935 \, \sqrt{2} {\left(4 \, x^{4} - 4 \, x^{3} + 13 \, x^{2} - 6 \, x + 9\right)} \log\left(-4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right) - 8 \, {\left(7812 \, x^{3} + 489 \, x^{2} + 7002 \, x + 5569\right)} \sqrt{2 \, x^{2} - x + 3}}{25392 \, {\left(4 \, x^{4} - 4 \, x^{3} + 13 \, x^{2} - 6 \, x + 9\right)}}"," ",0,"1/25392*(7935*sqrt(2)*(4*x^4 - 4*x^3 + 13*x^2 - 6*x + 9)*log(-4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25) - 8*(7812*x^3 + 489*x^2 + 7002*x + 5569)*sqrt(2*x^2 - x + 3))/(4*x^4 - 4*x^3 + 13*x^2 - 6*x + 9)","B",0
361,1,126,0,0.836409," ","integrate((5*x^4-x^3+3*x^2+x+2)/(5+2*x)/(2*x^2-x+3)^(5/2),x, algorithm=""fricas"")","\frac{1939843 \, \sqrt{2} {\left(4 \, x^{4} - 4 \, x^{3} + 13 \, x^{2} - 6 \, x + 9\right)} \log\left(-\frac{24 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(22 \, x - 17\right)} + 1060 \, x^{2} - 1036 \, x + 1153}{4 \, x^{2} + 20 \, x + 25}\right) - 48 \, {\left(293458 \, x^{3} + 523945 \, x^{2} - 21696 \, x + 841653\right)} \sqrt{2 \, x^{2} - x + 3}}{65816064 \, {\left(4 \, x^{4} - 4 \, x^{3} + 13 \, x^{2} - 6 \, x + 9\right)}}"," ",0,"1/65816064*(1939843*sqrt(2)*(4*x^4 - 4*x^3 + 13*x^2 - 6*x + 9)*log(-(24*sqrt(2)*sqrt(2*x^2 - x + 3)*(22*x - 17) + 1060*x^2 - 1036*x + 1153)/(4*x^2 + 20*x + 25)) - 48*(293458*x^3 + 523945*x^2 - 21696*x + 841653)*sqrt(2*x^2 - x + 3))/(4*x^4 - 4*x^3 + 13*x^2 - 6*x + 9)","A",0
362,1,141,0,1.237263," ","integrate((5*x^4-x^3+3*x^2+x+2)/(5+2*x)^2/(2*x^2-x+3)^(5/2),x, algorithm=""fricas"")","\frac{1492309 \, \sqrt{2} {\left(8 \, x^{5} + 12 \, x^{4} + 6 \, x^{3} + 53 \, x^{2} - 12 \, x + 45\right)} \log\left(-\frac{24 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(22 \, x - 17\right)} + 1060 \, x^{2} - 1036 \, x + 1153}{4 \, x^{2} + 20 \, x + 25}\right) - 48 \, {\left(6767036 \, x^{4} + 10350004 \, x^{3} + 63941915 \, x^{2} - 18840090 \, x + 79153407\right)} \sqrt{2 \, x^{2} - x + 3}}{4738756608 \, {\left(8 \, x^{5} + 12 \, x^{4} + 6 \, x^{3} + 53 \, x^{2} - 12 \, x + 45\right)}}"," ",0,"1/4738756608*(1492309*sqrt(2)*(8*x^5 + 12*x^4 + 6*x^3 + 53*x^2 - 12*x + 45)*log(-(24*sqrt(2)*sqrt(2*x^2 - x + 3)*(22*x - 17) + 1060*x^2 - 1036*x + 1153)/(4*x^2 + 20*x + 25)) - 48*(6767036*x^4 + 10350004*x^3 + 63941915*x^2 - 18840090*x + 79153407)*sqrt(2*x^2 - x + 3))/(8*x^5 + 12*x^4 + 6*x^3 + 53*x^2 - 12*x + 45)","A",0
363,1,155,0,1.099776," ","integrate((5*x^4-x^3+3*x^2+x+2)/(5+2*x)^3/(2*x^2-x+3)^(5/2),x, algorithm=""fricas"")","\frac{409487791 \, \sqrt{2} {\left(16 \, x^{6} + 64 \, x^{5} + 72 \, x^{4} + 136 \, x^{3} + 241 \, x^{2} + 30 \, x + 225\right)} \log\left(\frac{24 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(22 \, x - 17\right)} - 1060 \, x^{2} + 1036 \, x - 1153}{4 \, x^{2} + 20 \, x + 25}\right) + 48 \, {\left(217883368 \, x^{5} + 107028732 \, x^{4} - 1503926130 \, x^{3} - 5919924791 \, x^{2} + 2280511668 \, x - 8953831359\right)} \sqrt{2 \, x^{2} - x + 3}}{682380951552 \, {\left(16 \, x^{6} + 64 \, x^{5} + 72 \, x^{4} + 136 \, x^{3} + 241 \, x^{2} + 30 \, x + 225\right)}}"," ",0,"1/682380951552*(409487791*sqrt(2)*(16*x^6 + 64*x^5 + 72*x^4 + 136*x^3 + 241*x^2 + 30*x + 225)*log((24*sqrt(2)*sqrt(2*x^2 - x + 3)*(22*x - 17) - 1060*x^2 + 1036*x - 1153)/(4*x^2 + 20*x + 25)) + 48*(217883368*x^5 + 107028732*x^4 - 1503926130*x^3 - 5919924791*x^2 + 2280511668*x - 8953831359)*sqrt(2*x^2 - x + 3))/(16*x^6 + 64*x^5 + 72*x^4 + 136*x^3 + 241*x^2 + 30*x + 225)","A",0
364,1,170,0,0.722341," ","integrate((5*x^4-x^3+3*x^2+x+2)/(5+2*x)^4/(2*x^2-x+3)^(5/2),x, algorithm=""fricas"")","\frac{2527979381 \, \sqrt{2} {\left(32 \, x^{7} + 208 \, x^{6} + 464 \, x^{5} + 632 \, x^{4} + 1162 \, x^{3} + 1265 \, x^{2} + 600 \, x + 1125\right)} \log\left(\frac{24 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(22 \, x - 17\right)} - 1060 \, x^{2} + 1036 \, x - 1153}{4 \, x^{2} + 20 \, x + 25}\right) + 48 \, {\left(6664404208 \, x^{6} + 34872810880 \, x^{5} + 46210466520 \, x^{4} + 27484986184 \, x^{3} - 6702882569 \, x^{2} + 73621973154 \, x - 95241881529\right)} \sqrt{2 \, x^{2} - x + 3}}{16377142837248 \, {\left(32 \, x^{7} + 208 \, x^{6} + 464 \, x^{5} + 632 \, x^{4} + 1162 \, x^{3} + 1265 \, x^{2} + 600 \, x + 1125\right)}}"," ",0,"1/16377142837248*(2527979381*sqrt(2)*(32*x^7 + 208*x^6 + 464*x^5 + 632*x^4 + 1162*x^3 + 1265*x^2 + 600*x + 1125)*log((24*sqrt(2)*sqrt(2*x^2 - x + 3)*(22*x - 17) - 1060*x^2 + 1036*x - 1153)/(4*x^2 + 20*x + 25)) + 48*(6664404208*x^6 + 34872810880*x^5 + 46210466520*x^4 + 27484986184*x^3 - 6702882569*x^2 + 73621973154*x - 95241881529)*sqrt(2*x^2 - x + 3))/(32*x^7 + 208*x^6 + 464*x^5 + 632*x^4 + 1162*x^3 + 1265*x^2 + 600*x + 1125)","A",0
365,1,1373,0,95.074999," ","integrate((j*x^4+i*x^3+h*x^2+g*x+f)/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} j x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} j x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} j x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} j x + {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2}\right)} j\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 \, {\left(8 \, a^{2} b c^{3} h - 16 \, a^{3} c^{3} i + {\left(16 \, c^{6} f - 8 \, b c^{5} g + 2 \, {\left(b^{2} c^{4} + 4 \, a c^{5}\right)} h + {\left(b^{3} c^{3} - 12 \, a b c^{4}\right)} i - 4 \, {\left(b^{4} c^{2} - 7 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} j\right)} x^{3} + 3 \, {\left(8 \, b c^{5} f - 4 \, b^{2} c^{4} g + {\left(b^{3} c^{3} + 4 \, a b c^{4}\right)} h - 2 \, {\left(a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} i - {\left(b^{5} c - 6 \, a b^{3} c^{2}\right)} j\right)} x^{2} - {\left(b^{3} c^{3} - 12 \, a b c^{4}\right)} f - 2 \, {\left(a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} g - {\left(3 \, a^{2} b^{3} c - 20 \, a^{3} b c^{2}\right)} j + 3 \, {\left(4 \, a b^{2} c^{3} h - 8 \, a^{2} b c^{3} i + 2 \, {\left(b^{2} c^{4} + 4 \, a c^{5}\right)} f - {\left(b^{3} c^{3} + 4 \, a b c^{4}\right)} g - 2 \, {\left(a b^{4} c - 7 \, a^{2} b^{2} c^{2} + 4 \, a^{3} c^{3}\right)} j\right)} x\right)} \sqrt{c x^{2} + b x + a}}{6 \, {\left(a^{2} b^{4} c^{3} - 8 \, a^{3} b^{2} c^{4} + 16 \, a^{4} c^{5} + {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} x^{4} + 2 \, {\left(b^{5} c^{4} - 8 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6}\right)} x^{3} + {\left(b^{6} c^{3} - 6 \, a b^{4} c^{4} + 32 \, a^{3} c^{6}\right)} x^{2} + 2 \, {\left(a b^{5} c^{3} - 8 \, a^{2} b^{3} c^{4} + 16 \, a^{3} b c^{5}\right)} x\right)}}, -\frac{3 \, {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} j x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} j x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} j x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} j x + {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2}\right)} j\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 \, {\left(8 \, a^{2} b c^{3} h - 16 \, a^{3} c^{3} i + {\left(16 \, c^{6} f - 8 \, b c^{5} g + 2 \, {\left(b^{2} c^{4} + 4 \, a c^{5}\right)} h + {\left(b^{3} c^{3} - 12 \, a b c^{4}\right)} i - 4 \, {\left(b^{4} c^{2} - 7 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} j\right)} x^{3} + 3 \, {\left(8 \, b c^{5} f - 4 \, b^{2} c^{4} g + {\left(b^{3} c^{3} + 4 \, a b c^{4}\right)} h - 2 \, {\left(a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} i - {\left(b^{5} c - 6 \, a b^{3} c^{2}\right)} j\right)} x^{2} - {\left(b^{3} c^{3} - 12 \, a b c^{4}\right)} f - 2 \, {\left(a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} g - {\left(3 \, a^{2} b^{3} c - 20 \, a^{3} b c^{2}\right)} j + 3 \, {\left(4 \, a b^{2} c^{3} h - 8 \, a^{2} b c^{3} i + 2 \, {\left(b^{2} c^{4} + 4 \, a c^{5}\right)} f - {\left(b^{3} c^{3} + 4 \, a b c^{4}\right)} g - 2 \, {\left(a b^{4} c - 7 \, a^{2} b^{2} c^{2} + 4 \, a^{3} c^{3}\right)} j\right)} x\right)} \sqrt{c x^{2} + b x + a}}{3 \, {\left(a^{2} b^{4} c^{3} - 8 \, a^{3} b^{2} c^{4} + 16 \, a^{4} c^{5} + {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} x^{4} + 2 \, {\left(b^{5} c^{4} - 8 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6}\right)} x^{3} + {\left(b^{6} c^{3} - 6 \, a b^{4} c^{4} + 32 \, a^{3} c^{6}\right)} x^{2} + 2 \, {\left(a b^{5} c^{3} - 8 \, a^{2} b^{3} c^{4} + 16 \, a^{3} b c^{5}\right)} x\right)}}\right]"," ",0,"[1/6*(3*((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*j*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*j*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*j*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*j*x + (a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2)*j)*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) + 4*(8*a^2*b*c^3*h - 16*a^3*c^3*i + (16*c^6*f - 8*b*c^5*g + 2*(b^2*c^4 + 4*a*c^5)*h + (b^3*c^3 - 12*a*b*c^4)*i - 4*(b^4*c^2 - 7*a*b^2*c^3 + 8*a^2*c^4)*j)*x^3 + 3*(8*b*c^5*f - 4*b^2*c^4*g + (b^3*c^3 + 4*a*b*c^4)*h - 2*(a*b^2*c^3 + 4*a^2*c^4)*i - (b^5*c - 6*a*b^3*c^2)*j)*x^2 - (b^3*c^3 - 12*a*b*c^4)*f - 2*(a*b^2*c^3 + 4*a^2*c^4)*g - (3*a^2*b^3*c - 20*a^3*b*c^2)*j + 3*(4*a*b^2*c^3*h - 8*a^2*b*c^3*i + 2*(b^2*c^4 + 4*a*c^5)*f - (b^3*c^3 + 4*a*b*c^4)*g - 2*(a*b^4*c - 7*a^2*b^2*c^2 + 4*a^3*c^3)*j)*x)*sqrt(c*x^2 + b*x + a))/(a^2*b^4*c^3 - 8*a^3*b^2*c^4 + 16*a^4*c^5 + (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*x^4 + 2*(b^5*c^4 - 8*a*b^3*c^5 + 16*a^2*b*c^6)*x^3 + (b^6*c^3 - 6*a*b^4*c^4 + 32*a^3*c^6)*x^2 + 2*(a*b^5*c^3 - 8*a^2*b^3*c^4 + 16*a^3*b*c^5)*x), -1/3*(3*((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*j*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*j*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*j*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*j*x + (a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2)*j)*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)) - 2*(8*a^2*b*c^3*h - 16*a^3*c^3*i + (16*c^6*f - 8*b*c^5*g + 2*(b^2*c^4 + 4*a*c^5)*h + (b^3*c^3 - 12*a*b*c^4)*i - 4*(b^4*c^2 - 7*a*b^2*c^3 + 8*a^2*c^4)*j)*x^3 + 3*(8*b*c^5*f - 4*b^2*c^4*g + (b^3*c^3 + 4*a*b*c^4)*h - 2*(a*b^2*c^3 + 4*a^2*c^4)*i - (b^5*c - 6*a*b^3*c^2)*j)*x^2 - (b^3*c^3 - 12*a*b*c^4)*f - 2*(a*b^2*c^3 + 4*a^2*c^4)*g - (3*a^2*b^3*c - 20*a^3*b*c^2)*j + 3*(4*a*b^2*c^3*h - 8*a^2*b*c^3*i + 2*(b^2*c^4 + 4*a*c^5)*f - (b^3*c^3 + 4*a*b*c^4)*g - 2*(a*b^4*c - 7*a^2*b^2*c^2 + 4*a^3*c^3)*j)*x)*sqrt(c*x^2 + b*x + a))/(a^2*b^4*c^3 - 8*a^3*b^2*c^4 + 16*a^4*c^5 + (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*x^4 + 2*(b^5*c^4 - 8*a*b^3*c^5 + 16*a^2*b*c^6)*x^3 + (b^6*c^3 - 6*a*b^4*c^4 + 32*a^3*c^6)*x^2 + 2*(a*b^5*c^3 - 8*a^2*b^3*c^4 + 16*a^3*b*c^5)*x)]","B",0
366,1,1385,0,78.227454," ","integrate((j*x^4+i*x^3+h*x^2+g*x+f)/(-c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(b^{4} c^{2} + 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} j x^{4} - 2 \, {\left(b^{5} c + 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} j x^{3} + {\left(b^{6} + 6 \, a b^{4} c - 32 \, a^{3} c^{3}\right)} j x^{2} + 2 \, {\left(a b^{5} + 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} j x + {\left(a^{2} b^{4} + 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2}\right)} j\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 \, {\left(8 \, a^{2} b c^{3} h - 16 \, a^{3} c^{3} i - {\left(16 \, c^{6} f + 8 \, b c^{5} g + 2 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} h - {\left(b^{3} c^{3} + 12 \, a b c^{4}\right)} i - 4 \, {\left(b^{4} c^{2} + 7 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} j\right)} x^{3} + 3 \, {\left(8 \, b c^{5} f + 4 \, b^{2} c^{4} g + {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} h - 2 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} i - {\left(b^{5} c + 6 \, a b^{3} c^{2}\right)} j\right)} x^{2} - {\left(b^{3} c^{3} + 12 \, a b c^{4}\right)} f - 2 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} g - {\left(3 \, a^{2} b^{3} c + 20 \, a^{3} b c^{2}\right)} j + 3 \, {\left(4 \, a b^{2} c^{3} h - 8 \, a^{2} b c^{3} i - 2 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} f - {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} g - 2 \, {\left(a b^{4} c + 7 \, a^{2} b^{2} c^{2} + 4 \, a^{3} c^{3}\right)} j\right)} x\right)} \sqrt{-c x^{2} + b x + a}}{6 \, {\left(a^{2} b^{4} c^{3} + 8 \, a^{3} b^{2} c^{4} + 16 \, a^{4} c^{5} + {\left(b^{4} c^{5} + 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} x^{4} - 2 \, {\left(b^{5} c^{4} + 8 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6}\right)} x^{3} + {\left(b^{6} c^{3} + 6 \, a b^{4} c^{4} - 32 \, a^{3} c^{6}\right)} x^{2} + 2 \, {\left(a b^{5} c^{3} + 8 \, a^{2} b^{3} c^{4} + 16 \, a^{3} b c^{5}\right)} x\right)}}, -\frac{3 \, {\left({\left(b^{4} c^{2} + 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} j x^{4} - 2 \, {\left(b^{5} c + 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} j x^{3} + {\left(b^{6} + 6 \, a b^{4} c - 32 \, a^{3} c^{3}\right)} j x^{2} + 2 \, {\left(a b^{5} + 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} j x + {\left(a^{2} b^{4} + 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2}\right)} j\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 \, {\left(8 \, a^{2} b c^{3} h - 16 \, a^{3} c^{3} i - {\left(16 \, c^{6} f + 8 \, b c^{5} g + 2 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} h - {\left(b^{3} c^{3} + 12 \, a b c^{4}\right)} i - 4 \, {\left(b^{4} c^{2} + 7 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} j\right)} x^{3} + 3 \, {\left(8 \, b c^{5} f + 4 \, b^{2} c^{4} g + {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} h - 2 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} i - {\left(b^{5} c + 6 \, a b^{3} c^{2}\right)} j\right)} x^{2} - {\left(b^{3} c^{3} + 12 \, a b c^{4}\right)} f - 2 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} g - {\left(3 \, a^{2} b^{3} c + 20 \, a^{3} b c^{2}\right)} j + 3 \, {\left(4 \, a b^{2} c^{3} h - 8 \, a^{2} b c^{3} i - 2 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} f - {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} g - 2 \, {\left(a b^{4} c + 7 \, a^{2} b^{2} c^{2} + 4 \, a^{3} c^{3}\right)} j\right)} x\right)} \sqrt{-c x^{2} + b x + a}}{3 \, {\left(a^{2} b^{4} c^{3} + 8 \, a^{3} b^{2} c^{4} + 16 \, a^{4} c^{5} + {\left(b^{4} c^{5} + 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} x^{4} - 2 \, {\left(b^{5} c^{4} + 8 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6}\right)} x^{3} + {\left(b^{6} c^{3} + 6 \, a b^{4} c^{4} - 32 \, a^{3} c^{6}\right)} x^{2} + 2 \, {\left(a b^{5} c^{3} + 8 \, a^{2} b^{3} c^{4} + 16 \, a^{3} b c^{5}\right)} x\right)}}\right]"," ",0,"[-1/6*(3*((b^4*c^2 + 8*a*b^2*c^3 + 16*a^2*c^4)*j*x^4 - 2*(b^5*c + 8*a*b^3*c^2 + 16*a^2*b*c^3)*j*x^3 + (b^6 + 6*a*b^4*c - 32*a^3*c^3)*j*x^2 + 2*(a*b^5 + 8*a^2*b^3*c + 16*a^3*b*c^2)*j*x + (a^2*b^4 + 8*a^3*b^2*c + 16*a^4*c^2)*j)*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) - 4*(8*a^2*b*c^3*h - 16*a^3*c^3*i - (16*c^6*f + 8*b*c^5*g + 2*(b^2*c^4 - 4*a*c^5)*h - (b^3*c^3 + 12*a*b*c^4)*i - 4*(b^4*c^2 + 7*a*b^2*c^3 + 8*a^2*c^4)*j)*x^3 + 3*(8*b*c^5*f + 4*b^2*c^4*g + (b^3*c^3 - 4*a*b*c^4)*h - 2*(a*b^2*c^3 - 4*a^2*c^4)*i - (b^5*c + 6*a*b^3*c^2)*j)*x^2 - (b^3*c^3 + 12*a*b*c^4)*f - 2*(a*b^2*c^3 - 4*a^2*c^4)*g - (3*a^2*b^3*c + 20*a^3*b*c^2)*j + 3*(4*a*b^2*c^3*h - 8*a^2*b*c^3*i - 2*(b^2*c^4 - 4*a*c^5)*f - (b^3*c^3 - 4*a*b*c^4)*g - 2*(a*b^4*c + 7*a^2*b^2*c^2 + 4*a^3*c^3)*j)*x)*sqrt(-c*x^2 + b*x + a))/(a^2*b^4*c^3 + 8*a^3*b^2*c^4 + 16*a^4*c^5 + (b^4*c^5 + 8*a*b^2*c^6 + 16*a^2*c^7)*x^4 - 2*(b^5*c^4 + 8*a*b^3*c^5 + 16*a^2*b*c^6)*x^3 + (b^6*c^3 + 6*a*b^4*c^4 - 32*a^3*c^6)*x^2 + 2*(a*b^5*c^3 + 8*a^2*b^3*c^4 + 16*a^3*b*c^5)*x), -1/3*(3*((b^4*c^2 + 8*a*b^2*c^3 + 16*a^2*c^4)*j*x^4 - 2*(b^5*c + 8*a*b^3*c^2 + 16*a^2*b*c^3)*j*x^3 + (b^6 + 6*a*b^4*c - 32*a^3*c^3)*j*x^2 + 2*(a*b^5 + 8*a^2*b^3*c + 16*a^3*b*c^2)*j*x + (a^2*b^4 + 8*a^3*b^2*c + 16*a^4*c^2)*j)*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)) - 2*(8*a^2*b*c^3*h - 16*a^3*c^3*i - (16*c^6*f + 8*b*c^5*g + 2*(b^2*c^4 - 4*a*c^5)*h - (b^3*c^3 + 12*a*b*c^4)*i - 4*(b^4*c^2 + 7*a*b^2*c^3 + 8*a^2*c^4)*j)*x^3 + 3*(8*b*c^5*f + 4*b^2*c^4*g + (b^3*c^3 - 4*a*b*c^4)*h - 2*(a*b^2*c^3 - 4*a^2*c^4)*i - (b^5*c + 6*a*b^3*c^2)*j)*x^2 - (b^3*c^3 + 12*a*b*c^4)*f - 2*(a*b^2*c^3 - 4*a^2*c^4)*g - (3*a^2*b^3*c + 20*a^3*b*c^2)*j + 3*(4*a*b^2*c^3*h - 8*a^2*b*c^3*i - 2*(b^2*c^4 - 4*a*c^5)*f - (b^3*c^3 - 4*a*b*c^4)*g - 2*(a*b^4*c + 7*a^2*b^2*c^2 + 4*a^3*c^3)*j)*x)*sqrt(-c*x^2 + b*x + a))/(a^2*b^4*c^3 + 8*a^3*b^2*c^4 + 16*a^4*c^5 + (b^4*c^5 + 8*a*b^2*c^6 + 16*a^2*c^7)*x^4 - 2*(b^5*c^4 + 8*a*b^3*c^5 + 16*a^2*b*c^6)*x^3 + (b^6*c^3 + 6*a*b^4*c^4 - 32*a^3*c^6)*x^2 + 2*(a*b^5*c^3 + 8*a^2*b^3*c^4 + 16*a^3*b*c^5)*x)]","B",0
367,1,4795,0,0.939853," ","integrate((e*x+d)^m*(5*x^2+2*x+3)^3*(4*x^4-5*x^3+3*x^2+x+2),x, algorithm=""fricas"")","\frac{{\left(54 \, d e^{10} m^{10} + 500 \, {\left(e^{11} m^{10} + 55 \, e^{11} m^{9} + 1320 \, e^{11} m^{8} + 18150 \, e^{11} m^{7} + 157773 \, e^{11} m^{6} + 902055 \, e^{11} m^{5} + 3416930 \, e^{11} m^{4} + 8409500 \, e^{11} m^{3} + 12753576 \, e^{11} m^{2} + 10628640 \, e^{11} m + 3628800 \, e^{11}\right)} x^{11} + 1814400000 \, d^{11} + 99792000 \, d^{10} e + 3392928000 \, d^{9} e^{2} + 488980800 \, d^{8} e^{3} + 5696697600 \, d^{7} e^{4} - 3392928000 \, d^{6} e^{5} + 8853546240 \, d^{5} e^{6} - 5728060800 \, d^{4} e^{7} + 6346771200 \, d^{3} e^{8} - 2694384000 \, d^{2} e^{9} + 2155507200 \, d e^{10} - 25 \, {\left(3991680 \, e^{11} - {\left(20 \, d e^{10} - e^{11}\right)} m^{10} - 4 \, {\left(225 \, d e^{10} - 14 \, e^{11}\right)} m^{9} - 15 \, {\left(1160 \, d e^{10} - 91 \, e^{11}\right)} m^{8} - 60 \, {\left(3150 \, d e^{10} - 317 \, e^{11}\right)} m^{7} - 21 \, {\left(60260 \, d e^{10} - 7963 \, e^{11}\right)} m^{6} - 84 \, {\left(64125 \, d e^{10} - 11492 \, e^{11}\right)} m^{5} - 5 \, {\left(2894720 \, d e^{10} - 737251 \, e^{11}\right)} m^{4} - 20 \, {\left(1172700 \, d e^{10} - 456659 \, e^{11}\right)} m^{3} - 36 \, {\left(570320 \, d e^{10} - 386841 \, e^{11}\right)} m^{2} - 144 \, {\left(50400 \, d e^{10} - 80939 \, e^{11}\right)} m\right)} x^{10} - 135 \, {\left(d^{2} e^{9} - 26 \, d e^{10}\right)} m^{9} + 5 \, {\left(678585600 \, e^{11} - {\left(5 \, d e^{10} - 153 \, e^{11}\right)} m^{10} - {\left(1000 \, d^{2} e^{9} + 235 \, d e^{10} - 8721 \, e^{11}\right)} m^{9} - 6 \, {\left(6000 \, d^{2} e^{9} + 785 \, d e^{10} - 36006 \, e^{11}\right)} m^{8} - 6 \, {\left(91000 \, d^{2} e^{9} + 8785 \, d e^{10} - 509031 \, e^{11}\right)} m^{7} - 105 \, {\left(43200 \, d^{2} e^{9} + 3445 \, d e^{10} - 259029 \, e^{11}\right)} m^{6} - 21 \, {\left(1069000 \, d^{2} e^{9} + 74815 \, d e^{10} - 7560189 \, e^{11}\right)} m^{5} - 2 \, {\left(33642000 \, d^{2} e^{9} + 2145620 \, d e^{10} - 306036567 \, e^{11}\right)} m^{4} - 4 \, {\left(29531000 \, d^{2} e^{9} + 1761185 \, d e^{10} - 382172121 \, e^{11}\right)} m^{3} - 72 \, {\left(1522000 \, d^{2} e^{9} + 86510 \, d e^{10} - 32587351 \, e^{11}\right)} m^{2} - 1440 \, {\left(28000 \, d^{2} e^{9} + 1540 \, d e^{10} - 1370727 \, e^{11}\right)} m\right)} x^{9} + 9 \, {\left(106 \, d^{3} e^{8} - 945 \, d^{2} e^{9} + 11160 \, d e^{10}\right)} m^{8} - {\left(488980800 \, e^{11} - {\left(765 \, d e^{10} - 98 \, e^{11}\right)} m^{10} - {\left(225 \, d^{2} e^{9} + 37485 \, d e^{10} - 5684 \, e^{11}\right)} m^{9} - 3 \, {\left(15000 \, d^{3} e^{8} + 2925 \, d^{2} e^{9} + 260100 \, d e^{10} - 47726 \, e^{11}\right)} m^{8} - 42 \, {\left(30000 \, d^{3} e^{8} + 3375 \, d^{2} e^{9} + 214965 \, d e^{10} - 48958 \, e^{11}\right)} m^{7} - 63 \, {\left(230000 \, d^{3} e^{8} + 19650 \, d^{2} e^{9} + 1012095 \, d e^{10} - 294882 \, e^{11}\right)} m^{6} - 63 \, {\left(1400000 \, d^{3} e^{8} + 101175 \, d^{2} e^{9} + 4503555 \, d e^{10} - 1743812 \, e^{11}\right)} m^{5} - {\left(304605000 \, d^{3} e^{8} + 19707975 \, d^{2} e^{9} + 790573950 \, d e^{10} - 428393182 \, e^{11}\right)} m^{4} - 4 \, {\left(147735000 \, d^{3} e^{8} + 8860500 \, d^{2} e^{9} + 329712705 \, d e^{10} - 270109021 \, e^{11}\right)} m^{3} - 36 \, {\left(16335000 \, d^{3} e^{8} + 929925 \, d^{2} e^{9} + 32795550 \, d e^{10} - 46438966 \, e^{11}\right)} m^{2} - 5040 \, {\left(45000 \, d^{3} e^{8} + 2475 \, d^{2} e^{9} + 84150 \, d e^{10} - 280861 \, e^{11}\right)} m\right)} x^{8} - 6 \, {\left(574 \, d^{4} e^{7} - 9540 \, d^{3} e^{8} + 39015 \, d^{2} e^{9} - 277290 \, d e^{10}\right)} m^{7} + {\left(5696697600 \, e^{11} - {\left(98 \, d e^{10} - 999 \, e^{11}\right)} m^{10} - 3 \, {\left(2040 \, d^{2} e^{9} + 1666 \, d e^{10} - 19647 \, e^{11}\right)} m^{9} - 24 \, {\left(75 \, d^{3} e^{8} + 10710 \, d^{2} e^{9} + 4508 \, d e^{10} - 62937 \, e^{11}\right)} m^{8} - 6 \, {\left(60000 \, d^{4} e^{7} + 9600 \, d^{3} e^{8} + 740520 \, d^{2} e^{9} + 216482 \, d e^{10} - 3677319 \, e^{11}\right)} m^{7} - 3 \, {\left(2520000 \, d^{4} e^{7} + 243600 \, d^{3} e^{8} + 13708800 \, d^{2} e^{9} + 3161774 \, d e^{10} - 67539393 \, e^{11}\right)} m^{6} - 21 \, {\left(3000000 \, d^{4} e^{7} + 228000 \, d^{3} e^{8} + 10581480 \, d^{2} e^{9} + 2069662 \, d e^{10} - 57933009 \, e^{11}\right)} m^{5} - 2 \, {\left(132300000 \, d^{4} e^{7} + 8738100 \, d^{3} e^{8} + 357157080 \, d^{2} e^{9} + 62076434 \, d e^{10} - 2405021571 \, e^{11}\right)} m^{4} - 36 \, {\left(16240000 \, d^{4} e^{7} + 981400 \, d^{3} e^{8} + 36788680 \, d^{2} e^{9} + 5871278 \, d e^{10} - 341095341 \, e^{11}\right)} m^{3} - 72 \, {\left(8820000 \, d^{4} e^{7} + 503100 \, d^{3} e^{8} + 17778600 \, d^{2} e^{9} + 2670010 \, d e^{10} - 266622111 \, e^{11}\right)} m^{2} - 12960 \, {\left(20000 \, d^{4} e^{7} + 1100 \, d^{3} e^{8} + 37400 \, d^{2} e^{9} + 5390 \, d e^{10} - 1264623 \, e^{11}\right)} m\right)} x^{7} + 6 \, {\left(4436 \, d^{5} e^{6} - 32144 \, d^{4} e^{7} + 247086 \, d^{3} e^{8} - 615195 \, d^{2} e^{9} + 2939517 \, d e^{10}\right)} m^{6} + {\left(3392928000 \, e^{11} + 3 \, {\left(333 \, d e^{10} + 170 \, e^{11}\right)} m^{10} + {\left(686 \, d^{2} e^{9} + 52947 \, d e^{10} + 30600 \, e^{11}\right)} m^{9} + 6 \, {\left(7140 \, d^{3} e^{8} + 5145 \, d^{2} e^{9} + 198801 \, d e^{10} + 133025 \, e^{11}\right)} m^{8} + 6 \, {\left(2100 \, d^{4} e^{7} + 257040 \, d^{3} e^{8} + 95354 \, d^{2} e^{9} + 2484513 \, d e^{10} + 1978800 \, e^{11}\right)} m^{7} + 3 \, {\left(840000 \, d^{5} e^{6} + 109200 \, d^{4} e^{7} + 7282800 \, d^{3} e^{8} + 1886500 \, d^{2} e^{9} + 37725237 \, d e^{10} + 37016310 \, e^{11}\right)} m^{6} + 3 \, {\left(12600000 \, d^{5} e^{6} + 1050000 \, d^{4} e^{7} + 52264800 \, d^{3} e^{8} + 10813418 \, d^{2} e^{9} + 179179641 \, d e^{10} + 226287000 \, e^{11}\right)} m^{5} + 42 \, {\left(5100000 \, d^{5} e^{6} + 348000 \, d^{4} e^{7} + 14635980 \, d^{3} e^{8} + 2609495 \, d^{2} e^{9} + 37733562 \, d e^{10} + 64999925 \, e^{11}\right)} m^{4} + 4 \, {\left(141750000 \, d^{5} e^{6} + 8659350 \, d^{4} e^{7} + 327983040 \, d^{3} e^{8} + 52869334 \, d^{2} e^{9} + 692643663 \, d e^{10} + 1769460300 \, e^{11}\right)} m^{3} + 120 \, {\left(5754000 \, d^{5} e^{6} + 329070 \, d^{4} e^{7} + 11659620 \, d^{3} e^{8} + 1755817 \, d^{2} e^{9} + 21444534 \, d e^{10} + 93454763 \, e^{11}\right)} m^{2} + 7200 \, {\left(42000 \, d^{5} e^{6} + 2310 \, d^{4} e^{7} + 78540 \, d^{3} e^{8} + 11319 \, d^{2} e^{9} + 131868 \, d e^{10} + 1344547 \, e^{11}\right)} m\right)} x^{6} - 3 \, {\left(20400 \, d^{6} e^{5} - 452472 \, d^{5} e^{6} + 1526840 \, d^{4} e^{7} - 7212240 \, d^{3} e^{8} + 12236805 \, d^{2} e^{9} - 41597010 \, d e^{10}\right)} m^{5} + {\left(8853546240 \, e^{11} + {\left(510 \, d e^{10} + 1109 \, e^{11}\right)} m^{10} - {\left(5994 \, d^{2} e^{9} - 28050 \, d e^{10} - 67649 \, e^{11}\right)} m^{9} - 12 \, {\left(343 \, d^{3} e^{8} + 23976 \, d^{2} e^{9} - 54825 \, d e^{10} - 149715 \, e^{11}\right)} m^{8} - 6 \, {\left(42840 \, d^{4} e^{7} + 27440 \, d^{3} e^{8} + 953046 \, d^{2} e^{9} - 1430550 \, d e^{10} - 4541355 \, e^{11}\right)} m^{7} - 3 \, {\left(25200 \, d^{5} e^{6} + 2656080 \, d^{4} e^{7} + 869848 \, d^{3} e^{8} + 20283696 \, d^{2} e^{9} - 22710810 \, d e^{10} - 86713819 \, e^{11}\right)} m^{6} - 3 \, {\left(5040000 \, d^{6} e^{5} + 529200 \, d^{5} e^{6} + 30416400 \, d^{4} e^{7} + 6969760 \, d^{3} e^{8} + 124932942 \, d^{2} e^{9} - 112732950 \, d e^{10} - 541448179 \, e^{11}\right)} m^{5} - 2 \, {\left(75600000 \, d^{6} e^{5} + 5481000 \, d^{5} e^{6} + 242260200 \, d^{4} e^{7} + 45047562 \, d^{3} e^{8} + 675619704 \, d^{2} e^{9} - 519501300 \, d e^{10} - 3335910815 \, e^{11}\right)} m^{4} - 4 \, {\left(132300000 \, d^{6} e^{5} + 8221500 \, d^{5} e^{6} + 316416240 \, d^{4} e^{7} + 51779280 \, d^{3} e^{8} + 688165146 \, d^{2} e^{9} - 470707050 \, d e^{10} - 4412539105 \, e^{11}\right)} m^{3} - 72 \, {\left(10500000 \, d^{6} e^{5} + 602700 \, d^{5} e^{6} + 21434280 \, d^{4} e^{7} + 3239978 \, d^{3} e^{8} + 39724236 \, d^{2} e^{9} - 25005980 \, d e^{10} - 395561447 \, e^{11}\right)} m^{2} - 288 \, {\left(1260000 \, d^{6} e^{5} + 69300 \, d^{5} e^{6} + 2356200 \, d^{4} e^{7} + 339570 \, d^{3} e^{8} + 3956040 \, d^{2} e^{9} - 2356200 \, d e^{10} - 86687203 \, e^{11}\right)} m\right)} x^{5} + 3 \, {\left(239760 \, d^{7} e^{4} - 918000 \, d^{6} e^{5} + 9537400 \, d^{5} e^{6} - 19929280 \, d^{4} e^{7} + 64836702 \, d^{3} e^{8} - 79518915 \, d^{2} e^{9} + 198514620 \, d e^{10}\right)} m^{4} + {\left(5728060800 \, e^{11} + {\left(1109 \, d e^{10} + 574 \, e^{11}\right)} m^{10} - {\left(2550 \, d^{2} e^{9} - 63213 \, d e^{10} - 35588 \, e^{11}\right)} m^{9} + 6 \, {\left(4995 \, d^{3} e^{8} - 21675 \, d^{2} e^{9} + 257288 \, d e^{10} + 160433 \, e^{11}\right)} m^{8} + 6 \, {\left(3430 \, d^{4} e^{7} + 219780 \, d^{3} e^{8} - 461550 \, d^{2} e^{9} + 3512203 \, d e^{10} + 2483698 \, e^{11}\right)} m^{7} + 15 \, {\left(85680 \, d^{5} e^{6} + 49392 \, d^{4} e^{7} + 1554444 \, d^{3} e^{8} - 2122620 \, d^{2} e^{9} + 11723239 \, d e^{10} + 9703470 \, e^{11}\right)} m^{6} + 3 \, {\left(126000 \, d^{6} e^{5} + 11566800 \, d^{5} e^{6} + 3361400 \, d^{4} e^{7} + 70329600 \, d^{3} e^{8} - 71101650 \, d^{2} e^{9} + 306983399 \, d e^{10} + 310583364 \, e^{11}\right)} m^{5} + 2 \, {\left(37800000 \, d^{7} e^{4} + 3213000 \, d^{6} e^{5} + 158722200 \, d^{5} e^{6} + 32104800 \, d^{4} e^{7} + 515019465 \, d^{3} e^{8} - 418887225 \, d^{2} e^{9} + 1494010421 \, d e^{10} + 1964946361 \, e^{11}\right)} m^{4} + 4 \, {\left(113400000 \, d^{7} e^{4} + 7276500 \, d^{6} e^{5} + 288206100 \, d^{5} e^{6} + 48409305 \, d^{4} e^{7} + 659010330 \, d^{3} e^{8} - 460978800 \, d^{2} e^{9} + 1424518263 \, d e^{10} + 2670494533 \, e^{11}\right)} m^{3} + 72 \, {\left(11550000 \, d^{7} e^{4} + 666750 \, d^{6} e^{5} + 23847600 \, d^{5} e^{6} + 3625510 \, d^{4} e^{7} + 44710245 \, d^{3} e^{8} - 28312225 \, d^{2} e^{9} + 79001833 \, d e^{10} + 245697543 \, e^{11}\right)} m^{2} + 720 \, {\left(630000 \, d^{7} e^{4} + 34650 \, d^{6} e^{5} + 1178100 \, d^{5} e^{6} + 169785 \, d^{4} e^{7} + 1978020 \, d^{3} e^{8} - 1178100 \, d^{2} e^{9} + 3074148 \, d e^{10} + 22036147 \, e^{11}\right)} m\right)} x^{4} + 12 \, {\left(41160 \, d^{8} e^{3} + 2277720 \, d^{7} e^{4} - 4105500 \, d^{6} e^{5} + 26582730 \, d^{5} e^{6} - 38586863 \, d^{4} e^{7} + 91855890 \, d^{3} e^{8} - 84312180 \, d^{2} e^{9} + 157352130 \, d e^{10}\right)} m^{3} + {\left(6346771200 \, e^{11} + {\left(574 \, d e^{10} + 477 \, e^{11}\right)} m^{10} - {\left(4436 \, d^{2} e^{9} - 33866 \, d e^{10} - 30051 \, e^{11}\right)} m^{9} + 24 \, {\left(425 \, d^{3} e^{8} - 9981 \, d^{2} e^{9} + 35875 \, d e^{10} + 34503 \, e^{11}\right)} m^{8} - 6 \, {\left(19980 \, d^{4} e^{7} - 81600 \, d^{3} e^{8} + 909380 \, d^{2} e^{9} - 2053198 \, d e^{10} - 2183229 \, e^{11}\right)} m^{7} - 3 \, {\left(27440 \, d^{5} e^{6} + 1638360 \, d^{4} e^{7} - 3202800 \, d^{3} e^{8} + 22641344 \, d^{2} e^{9} - 36198162 \, d e^{10} - 43730883 \, e^{11}\right)} m^{6} - 3 \, {\left(1713600 \, d^{6} e^{5} + 905520 \, d^{5} e^{6} + 26173800 \, d^{4} e^{7} - 32844000 \, d^{3} e^{8} + 166540748 \, d^{2} e^{9} - 201988878 \, d e^{10} - 288179073 \, e^{11}\right)} m^{5} - 2 \, {\left(756000 \, d^{7} e^{4} + 61689600 \, d^{6} e^{5} + 16093560 \, d^{5} e^{6} + 304195500 \, d^{4} e^{7} - 278811900 \, d^{3} e^{8} + 1092467028 \, d^{2} e^{9} - 1055996410 \, d e^{10} - 1884673269 \, e^{11}\right)} m^{4} - 4 \, {\left(75600000 \, d^{8} e^{3} + 5292000 \, d^{7} e^{4} + 224910000 \, d^{6} e^{5} + 40069260 \, d^{5} e^{6} + 573745680 \, d^{4} e^{7} - 419556600 \, d^{3} e^{8} + 1349320300 \, d^{2} e^{9} - 1086499918 \, d e^{10} - 2657980899 \, e^{11}\right)} m^{3} - 24 \, {\left(37800000 \, d^{8} e^{3} + 2205000 \, d^{7} e^{4} + 79682400 \, d^{6} e^{5} + 12238240 \, d^{5} e^{6} + 152467380 \, d^{4} e^{7} - 97540900 \, d^{3} e^{8} + 275018692 \, d^{2} e^{9} - 193842670 \, d e^{10} - 763013811 \, e^{11}\right)} m^{2} - 4320 \, {\left(140000 \, d^{8} e^{3} + 7700 \, d^{7} e^{4} + 261800 \, d^{6} e^{5} + 37730 \, d^{5} e^{6} + 439560 \, d^{4} e^{7} - 261800 \, d^{3} e^{8} + 683144 \, d^{2} e^{9} - 441980 \, d e^{10} - 3946963 \, e^{11}\right)} m\right)} x^{3} + 12 \, {\left(2570400 \, d^{9} e^{2} + 1234800 \, d^{8} e^{3} + 32307660 \, d^{7} e^{4} - 36490500 \, d^{6} e^{5} + 165294232 \, d^{5} e^{6} - 177258088 \, d^{4} e^{7} + 320238402 \, d^{3} e^{8} - 224755965 \, d^{2} e^{9} + 316309212 \, d e^{10}\right)} m^{2} + 3 \, {\left(898128000 \, e^{11} + 3 \, {\left(53 \, d e^{10} + 15 \, e^{11}\right)} m^{10} - {\left(574 \, d^{2} e^{9} - 9699 \, d e^{10} - 2880 \, e^{11}\right)} m^{9} + {\left(4436 \, d^{3} e^{8} - 32718 \, d^{2} e^{9} + 256626 \, d e^{10} + 80865 \, e^{11}\right)} m^{8} - 2 \, {\left(5100 \, d^{4} e^{7} - 115336 \, d^{3} e^{8} + 397782 \, d^{2} e^{9} - 1926603 \, d e^{10} - 654210 \, e^{11}\right)} m^{7} + {\left(119880 \, d^{5} e^{6} - 469200 \, d^{4} e^{7} + 4994936 \, d^{3} e^{8} - 10728060 \, d^{2} e^{9} + 36024471 \, d e^{10} + 13467195 \, e^{11}\right)} m^{6} + {\left(82320 \, d^{6} e^{5} + 4675320 \, d^{5} e^{6} - 8670000 \, d^{4} e^{7} + 57934160 \, d^{3} e^{8} - 87138366 \, d^{2} e^{9} + 216130131 \, d e^{10} + 91755720 \, e^{11}\right)} m^{5} + {\left(5140800 \, d^{7} e^{4} + 2551920 \, d^{6} e^{5} + 69170760 \, d^{5} e^{6} - 81192000 \, d^{4} e^{7} + 383753924 \, d^{3} e^{8} - 431689902 \, d^{2} e^{9} + 824188584 \, d e^{10} + 416767635 \, e^{11}\right)} m^{4} + 4 \, {\left(378000 \, d^{8} e^{3} + 28274400 \, d^{7} e^{4} + 6770820 \, d^{6} e^{5} + 117512370 \, d^{5} e^{6} - 98809950 \, d^{4} e^{7} + 354356552 \, d^{3} e^{8} - 312153254 \, d^{2} e^{9} + 473899341 \, d e^{10} + 309068145 \, e^{11}\right)} m^{3} + 12 \, {\left(25200000 \, d^{9} e^{2} + 1512000 \, d^{8} e^{3} + 56120400 \, d^{7} e^{4} + 8842540 \, d^{6} e^{5} + 112906980 \, d^{5} e^{6} - 73978900 \, d^{4} e^{7} + 213535732 \, d^{3} e^{8} - 154064470 \, d^{2} e^{9} + 192742980 \, d e^{10} + 188672355 \, e^{11}\right)} m^{2} + 2160 \, {\left(140000 \, d^{9} e^{2} + 7700 \, d^{8} e^{3} + 261800 \, d^{7} e^{4} + 37730 \, d^{6} e^{5} + 439560 \, d^{5} e^{6} - 261800 \, d^{4} e^{7} + 683144 \, d^{3} e^{8} - 441980 \, d^{2} e^{9} + 489720 \, d e^{10} + 1047765 \, e^{11}\right)} m\right)} x^{2} + 144 \, {\left(63000 \, d^{10} e + 4498200 \, d^{9} e^{2} + 1025570 \, d^{8} e^{3} + 16893090 \, d^{7} e^{4} - 13427450 \, d^{6} e^{5} + 45284906 \, d^{5} e^{6} - 37254035 \, d^{4} e^{7} + 52296690 \, d^{3} e^{8} - 28438425 \, d^{2} e^{9} + 30235140 \, d e^{10}\right)} m + 3 \, {\left(718502400 \, e^{11} + 9 \, {\left(5 \, d e^{10} + 2 \, e^{11}\right)} m^{10} - 3 \, {\left(106 \, d^{2} e^{9} - 945 \, d e^{10} - 390 \, e^{11}\right)} m^{9} + 2 \, {\left(574 \, d^{3} e^{8} - 9540 \, d^{2} e^{9} + 39015 \, d e^{10} + 16740 \, e^{11}\right)} m^{8} - 2 \, {\left(4436 \, d^{4} e^{7} - 32144 \, d^{3} e^{8} + 247086 \, d^{2} e^{9} - 615195 \, d e^{10} - 277290 \, e^{11}\right)} m^{7} + {\left(20400 \, d^{5} e^{6} - 452472 \, d^{4} e^{7} + 1526840 \, d^{3} e^{8} - 7212240 \, d^{2} e^{9} + 12236805 \, d e^{10} + 5879034 \, e^{11}\right)} m^{6} - {\left(239760 \, d^{6} e^{5} - 918000 \, d^{5} e^{6} + 9537400 \, d^{4} e^{7} - 19929280 \, d^{3} e^{8} + 64836702 \, d^{2} e^{9} - 79518915 \, d e^{10} - 41597010 \, e^{11}\right)} m^{5} - 4 \, {\left(41160 \, d^{7} e^{4} + 2277720 \, d^{6} e^{5} - 4105500 \, d^{5} e^{6} + 26582730 \, d^{4} e^{7} - 38586863 \, d^{3} e^{8} + 91855890 \, d^{2} e^{9} - 84312180 \, d e^{10} - 49628655 \, e^{11}\right)} m^{4} - 4 \, {\left(2570400 \, d^{8} e^{3} + 1234800 \, d^{7} e^{4} + 32307660 \, d^{6} e^{5} - 36490500 \, d^{5} e^{6} + 165294232 \, d^{4} e^{7} - 177258088 \, d^{3} e^{8} + 320238402 \, d^{2} e^{9} - 224755965 \, d e^{10} - 157352130 \, e^{11}\right)} m^{3} - 48 \, {\left(63000 \, d^{9} e^{2} + 4498200 \, d^{8} e^{3} + 1025570 \, d^{7} e^{4} + 16893090 \, d^{6} e^{5} - 13427450 \, d^{5} e^{6} + 45284906 \, d^{4} e^{7} - 37254035 \, d^{3} e^{8} + 52296690 \, d^{2} e^{9} - 28438425 \, d e^{10} - 26359101 \, e^{11}\right)} m^{2} - 8640 \, {\left(70000 \, d^{10} e + 3850 \, d^{9} e^{2} + 130900 \, d^{8} e^{3} + 18865 \, d^{7} e^{4} + 219780 \, d^{6} e^{5} - 130900 \, d^{5} e^{6} + 341572 \, d^{4} e^{7} - 220990 \, d^{3} e^{8} + 244860 \, d^{2} e^{9} - 103950 \, d e^{10} - 167973 \, e^{11}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{11} m^{11} + 66 \, e^{11} m^{10} + 1925 \, e^{11} m^{9} + 32670 \, e^{11} m^{8} + 357423 \, e^{11} m^{7} + 2637558 \, e^{11} m^{6} + 13339535 \, e^{11} m^{5} + 45995730 \, e^{11} m^{4} + 105258076 \, e^{11} m^{3} + 150917976 \, e^{11} m^{2} + 120543840 \, e^{11} m + 39916800 \, e^{11}}"," ",0,"(54*d*e^10*m^10 + 500*(e^11*m^10 + 55*e^11*m^9 + 1320*e^11*m^8 + 18150*e^11*m^7 + 157773*e^11*m^6 + 902055*e^11*m^5 + 3416930*e^11*m^4 + 8409500*e^11*m^3 + 12753576*e^11*m^2 + 10628640*e^11*m + 3628800*e^11)*x^11 + 1814400000*d^11 + 99792000*d^10*e + 3392928000*d^9*e^2 + 488980800*d^8*e^3 + 5696697600*d^7*e^4 - 3392928000*d^6*e^5 + 8853546240*d^5*e^6 - 5728060800*d^4*e^7 + 6346771200*d^3*e^8 - 2694384000*d^2*e^9 + 2155507200*d*e^10 - 25*(3991680*e^11 - (20*d*e^10 - e^11)*m^10 - 4*(225*d*e^10 - 14*e^11)*m^9 - 15*(1160*d*e^10 - 91*e^11)*m^8 - 60*(3150*d*e^10 - 317*e^11)*m^7 - 21*(60260*d*e^10 - 7963*e^11)*m^6 - 84*(64125*d*e^10 - 11492*e^11)*m^5 - 5*(2894720*d*e^10 - 737251*e^11)*m^4 - 20*(1172700*d*e^10 - 456659*e^11)*m^3 - 36*(570320*d*e^10 - 386841*e^11)*m^2 - 144*(50400*d*e^10 - 80939*e^11)*m)*x^10 - 135*(d^2*e^9 - 26*d*e^10)*m^9 + 5*(678585600*e^11 - (5*d*e^10 - 153*e^11)*m^10 - (1000*d^2*e^9 + 235*d*e^10 - 8721*e^11)*m^9 - 6*(6000*d^2*e^9 + 785*d*e^10 - 36006*e^11)*m^8 - 6*(91000*d^2*e^9 + 8785*d*e^10 - 509031*e^11)*m^7 - 105*(43200*d^2*e^9 + 3445*d*e^10 - 259029*e^11)*m^6 - 21*(1069000*d^2*e^9 + 74815*d*e^10 - 7560189*e^11)*m^5 - 2*(33642000*d^2*e^9 + 2145620*d*e^10 - 306036567*e^11)*m^4 - 4*(29531000*d^2*e^9 + 1761185*d*e^10 - 382172121*e^11)*m^3 - 72*(1522000*d^2*e^9 + 86510*d*e^10 - 32587351*e^11)*m^2 - 1440*(28000*d^2*e^9 + 1540*d*e^10 - 1370727*e^11)*m)*x^9 + 9*(106*d^3*e^8 - 945*d^2*e^9 + 11160*d*e^10)*m^8 - (488980800*e^11 - (765*d*e^10 - 98*e^11)*m^10 - (225*d^2*e^9 + 37485*d*e^10 - 5684*e^11)*m^9 - 3*(15000*d^3*e^8 + 2925*d^2*e^9 + 260100*d*e^10 - 47726*e^11)*m^8 - 42*(30000*d^3*e^8 + 3375*d^2*e^9 + 214965*d*e^10 - 48958*e^11)*m^7 - 63*(230000*d^3*e^8 + 19650*d^2*e^9 + 1012095*d*e^10 - 294882*e^11)*m^6 - 63*(1400000*d^3*e^8 + 101175*d^2*e^9 + 4503555*d*e^10 - 1743812*e^11)*m^5 - (304605000*d^3*e^8 + 19707975*d^2*e^9 + 790573950*d*e^10 - 428393182*e^11)*m^4 - 4*(147735000*d^3*e^8 + 8860500*d^2*e^9 + 329712705*d*e^10 - 270109021*e^11)*m^3 - 36*(16335000*d^3*e^8 + 929925*d^2*e^9 + 32795550*d*e^10 - 46438966*e^11)*m^2 - 5040*(45000*d^3*e^8 + 2475*d^2*e^9 + 84150*d*e^10 - 280861*e^11)*m)*x^8 - 6*(574*d^4*e^7 - 9540*d^3*e^8 + 39015*d^2*e^9 - 277290*d*e^10)*m^7 + (5696697600*e^11 - (98*d*e^10 - 999*e^11)*m^10 - 3*(2040*d^2*e^9 + 1666*d*e^10 - 19647*e^11)*m^9 - 24*(75*d^3*e^8 + 10710*d^2*e^9 + 4508*d*e^10 - 62937*e^11)*m^8 - 6*(60000*d^4*e^7 + 9600*d^3*e^8 + 740520*d^2*e^9 + 216482*d*e^10 - 3677319*e^11)*m^7 - 3*(2520000*d^4*e^7 + 243600*d^3*e^8 + 13708800*d^2*e^9 + 3161774*d*e^10 - 67539393*e^11)*m^6 - 21*(3000000*d^4*e^7 + 228000*d^3*e^8 + 10581480*d^2*e^9 + 2069662*d*e^10 - 57933009*e^11)*m^5 - 2*(132300000*d^4*e^7 + 8738100*d^3*e^8 + 357157080*d^2*e^9 + 62076434*d*e^10 - 2405021571*e^11)*m^4 - 36*(16240000*d^4*e^7 + 981400*d^3*e^8 + 36788680*d^2*e^9 + 5871278*d*e^10 - 341095341*e^11)*m^3 - 72*(8820000*d^4*e^7 + 503100*d^3*e^8 + 17778600*d^2*e^9 + 2670010*d*e^10 - 266622111*e^11)*m^2 - 12960*(20000*d^4*e^7 + 1100*d^3*e^8 + 37400*d^2*e^9 + 5390*d*e^10 - 1264623*e^11)*m)*x^7 + 6*(4436*d^5*e^6 - 32144*d^4*e^7 + 247086*d^3*e^8 - 615195*d^2*e^9 + 2939517*d*e^10)*m^6 + (3392928000*e^11 + 3*(333*d*e^10 + 170*e^11)*m^10 + (686*d^2*e^9 + 52947*d*e^10 + 30600*e^11)*m^9 + 6*(7140*d^3*e^8 + 5145*d^2*e^9 + 198801*d*e^10 + 133025*e^11)*m^8 + 6*(2100*d^4*e^7 + 257040*d^3*e^8 + 95354*d^2*e^9 + 2484513*d*e^10 + 1978800*e^11)*m^7 + 3*(840000*d^5*e^6 + 109200*d^4*e^7 + 7282800*d^3*e^8 + 1886500*d^2*e^9 + 37725237*d*e^10 + 37016310*e^11)*m^6 + 3*(12600000*d^5*e^6 + 1050000*d^4*e^7 + 52264800*d^3*e^8 + 10813418*d^2*e^9 + 179179641*d*e^10 + 226287000*e^11)*m^5 + 42*(5100000*d^5*e^6 + 348000*d^4*e^7 + 14635980*d^3*e^8 + 2609495*d^2*e^9 + 37733562*d*e^10 + 64999925*e^11)*m^4 + 4*(141750000*d^5*e^6 + 8659350*d^4*e^7 + 327983040*d^3*e^8 + 52869334*d^2*e^9 + 692643663*d*e^10 + 1769460300*e^11)*m^3 + 120*(5754000*d^5*e^6 + 329070*d^4*e^7 + 11659620*d^3*e^8 + 1755817*d^2*e^9 + 21444534*d*e^10 + 93454763*e^11)*m^2 + 7200*(42000*d^5*e^6 + 2310*d^4*e^7 + 78540*d^3*e^8 + 11319*d^2*e^9 + 131868*d*e^10 + 1344547*e^11)*m)*x^6 - 3*(20400*d^6*e^5 - 452472*d^5*e^6 + 1526840*d^4*e^7 - 7212240*d^3*e^8 + 12236805*d^2*e^9 - 41597010*d*e^10)*m^5 + (8853546240*e^11 + (510*d*e^10 + 1109*e^11)*m^10 - (5994*d^2*e^9 - 28050*d*e^10 - 67649*e^11)*m^9 - 12*(343*d^3*e^8 + 23976*d^2*e^9 - 54825*d*e^10 - 149715*e^11)*m^8 - 6*(42840*d^4*e^7 + 27440*d^3*e^8 + 953046*d^2*e^9 - 1430550*d*e^10 - 4541355*e^11)*m^7 - 3*(25200*d^5*e^6 + 2656080*d^4*e^7 + 869848*d^3*e^8 + 20283696*d^2*e^9 - 22710810*d*e^10 - 86713819*e^11)*m^6 - 3*(5040000*d^6*e^5 + 529200*d^5*e^6 + 30416400*d^4*e^7 + 6969760*d^3*e^8 + 124932942*d^2*e^9 - 112732950*d*e^10 - 541448179*e^11)*m^5 - 2*(75600000*d^6*e^5 + 5481000*d^5*e^6 + 242260200*d^4*e^7 + 45047562*d^3*e^8 + 675619704*d^2*e^9 - 519501300*d*e^10 - 3335910815*e^11)*m^4 - 4*(132300000*d^6*e^5 + 8221500*d^5*e^6 + 316416240*d^4*e^7 + 51779280*d^3*e^8 + 688165146*d^2*e^9 - 470707050*d*e^10 - 4412539105*e^11)*m^3 - 72*(10500000*d^6*e^5 + 602700*d^5*e^6 + 21434280*d^4*e^7 + 3239978*d^3*e^8 + 39724236*d^2*e^9 - 25005980*d*e^10 - 395561447*e^11)*m^2 - 288*(1260000*d^6*e^5 + 69300*d^5*e^6 + 2356200*d^4*e^7 + 339570*d^3*e^8 + 3956040*d^2*e^9 - 2356200*d*e^10 - 86687203*e^11)*m)*x^5 + 3*(239760*d^7*e^4 - 918000*d^6*e^5 + 9537400*d^5*e^6 - 19929280*d^4*e^7 + 64836702*d^3*e^8 - 79518915*d^2*e^9 + 198514620*d*e^10)*m^4 + (5728060800*e^11 + (1109*d*e^10 + 574*e^11)*m^10 - (2550*d^2*e^9 - 63213*d*e^10 - 35588*e^11)*m^9 + 6*(4995*d^3*e^8 - 21675*d^2*e^9 + 257288*d*e^10 + 160433*e^11)*m^8 + 6*(3430*d^4*e^7 + 219780*d^3*e^8 - 461550*d^2*e^9 + 3512203*d*e^10 + 2483698*e^11)*m^7 + 15*(85680*d^5*e^6 + 49392*d^4*e^7 + 1554444*d^3*e^8 - 2122620*d^2*e^9 + 11723239*d*e^10 + 9703470*e^11)*m^6 + 3*(126000*d^6*e^5 + 11566800*d^5*e^6 + 3361400*d^4*e^7 + 70329600*d^3*e^8 - 71101650*d^2*e^9 + 306983399*d*e^10 + 310583364*e^11)*m^5 + 2*(37800000*d^7*e^4 + 3213000*d^6*e^5 + 158722200*d^5*e^6 + 32104800*d^4*e^7 + 515019465*d^3*e^8 - 418887225*d^2*e^9 + 1494010421*d*e^10 + 1964946361*e^11)*m^4 + 4*(113400000*d^7*e^4 + 7276500*d^6*e^5 + 288206100*d^5*e^6 + 48409305*d^4*e^7 + 659010330*d^3*e^8 - 460978800*d^2*e^9 + 1424518263*d*e^10 + 2670494533*e^11)*m^3 + 72*(11550000*d^7*e^4 + 666750*d^6*e^5 + 23847600*d^5*e^6 + 3625510*d^4*e^7 + 44710245*d^3*e^8 - 28312225*d^2*e^9 + 79001833*d*e^10 + 245697543*e^11)*m^2 + 720*(630000*d^7*e^4 + 34650*d^6*e^5 + 1178100*d^5*e^6 + 169785*d^4*e^7 + 1978020*d^3*e^8 - 1178100*d^2*e^9 + 3074148*d*e^10 + 22036147*e^11)*m)*x^4 + 12*(41160*d^8*e^3 + 2277720*d^7*e^4 - 4105500*d^6*e^5 + 26582730*d^5*e^6 - 38586863*d^4*e^7 + 91855890*d^3*e^8 - 84312180*d^2*e^9 + 157352130*d*e^10)*m^3 + (6346771200*e^11 + (574*d*e^10 + 477*e^11)*m^10 - (4436*d^2*e^9 - 33866*d*e^10 - 30051*e^11)*m^9 + 24*(425*d^3*e^8 - 9981*d^2*e^9 + 35875*d*e^10 + 34503*e^11)*m^8 - 6*(19980*d^4*e^7 - 81600*d^3*e^8 + 909380*d^2*e^9 - 2053198*d*e^10 - 2183229*e^11)*m^7 - 3*(27440*d^5*e^6 + 1638360*d^4*e^7 - 3202800*d^3*e^8 + 22641344*d^2*e^9 - 36198162*d*e^10 - 43730883*e^11)*m^6 - 3*(1713600*d^6*e^5 + 905520*d^5*e^6 + 26173800*d^4*e^7 - 32844000*d^3*e^8 + 166540748*d^2*e^9 - 201988878*d*e^10 - 288179073*e^11)*m^5 - 2*(756000*d^7*e^4 + 61689600*d^6*e^5 + 16093560*d^5*e^6 + 304195500*d^4*e^7 - 278811900*d^3*e^8 + 1092467028*d^2*e^9 - 1055996410*d*e^10 - 1884673269*e^11)*m^4 - 4*(75600000*d^8*e^3 + 5292000*d^7*e^4 + 224910000*d^6*e^5 + 40069260*d^5*e^6 + 573745680*d^4*e^7 - 419556600*d^3*e^8 + 1349320300*d^2*e^9 - 1086499918*d*e^10 - 2657980899*e^11)*m^3 - 24*(37800000*d^8*e^3 + 2205000*d^7*e^4 + 79682400*d^6*e^5 + 12238240*d^5*e^6 + 152467380*d^4*e^7 - 97540900*d^3*e^8 + 275018692*d^2*e^9 - 193842670*d*e^10 - 763013811*e^11)*m^2 - 4320*(140000*d^8*e^3 + 7700*d^7*e^4 + 261800*d^6*e^5 + 37730*d^5*e^6 + 439560*d^4*e^7 - 261800*d^3*e^8 + 683144*d^2*e^9 - 441980*d*e^10 - 3946963*e^11)*m)*x^3 + 12*(2570400*d^9*e^2 + 1234800*d^8*e^3 + 32307660*d^7*e^4 - 36490500*d^6*e^5 + 165294232*d^5*e^6 - 177258088*d^4*e^7 + 320238402*d^3*e^8 - 224755965*d^2*e^9 + 316309212*d*e^10)*m^2 + 3*(898128000*e^11 + 3*(53*d*e^10 + 15*e^11)*m^10 - (574*d^2*e^9 - 9699*d*e^10 - 2880*e^11)*m^9 + (4436*d^3*e^8 - 32718*d^2*e^9 + 256626*d*e^10 + 80865*e^11)*m^8 - 2*(5100*d^4*e^7 - 115336*d^3*e^8 + 397782*d^2*e^9 - 1926603*d*e^10 - 654210*e^11)*m^7 + (119880*d^5*e^6 - 469200*d^4*e^7 + 4994936*d^3*e^8 - 10728060*d^2*e^9 + 36024471*d*e^10 + 13467195*e^11)*m^6 + (82320*d^6*e^5 + 4675320*d^5*e^6 - 8670000*d^4*e^7 + 57934160*d^3*e^8 - 87138366*d^2*e^9 + 216130131*d*e^10 + 91755720*e^11)*m^5 + (5140800*d^7*e^4 + 2551920*d^6*e^5 + 69170760*d^5*e^6 - 81192000*d^4*e^7 + 383753924*d^3*e^8 - 431689902*d^2*e^9 + 824188584*d*e^10 + 416767635*e^11)*m^4 + 4*(378000*d^8*e^3 + 28274400*d^7*e^4 + 6770820*d^6*e^5 + 117512370*d^5*e^6 - 98809950*d^4*e^7 + 354356552*d^3*e^8 - 312153254*d^2*e^9 + 473899341*d*e^10 + 309068145*e^11)*m^3 + 12*(25200000*d^9*e^2 + 1512000*d^8*e^3 + 56120400*d^7*e^4 + 8842540*d^6*e^5 + 112906980*d^5*e^6 - 73978900*d^4*e^7 + 213535732*d^3*e^8 - 154064470*d^2*e^9 + 192742980*d*e^10 + 188672355*e^11)*m^2 + 2160*(140000*d^9*e^2 + 7700*d^8*e^3 + 261800*d^7*e^4 + 37730*d^6*e^5 + 439560*d^5*e^6 - 261800*d^4*e^7 + 683144*d^3*e^8 - 441980*d^2*e^9 + 489720*d*e^10 + 1047765*e^11)*m)*x^2 + 144*(63000*d^10*e + 4498200*d^9*e^2 + 1025570*d^8*e^3 + 16893090*d^7*e^4 - 13427450*d^6*e^5 + 45284906*d^5*e^6 - 37254035*d^4*e^7 + 52296690*d^3*e^8 - 28438425*d^2*e^9 + 30235140*d*e^10)*m + 3*(718502400*e^11 + 9*(5*d*e^10 + 2*e^11)*m^10 - 3*(106*d^2*e^9 - 945*d*e^10 - 390*e^11)*m^9 + 2*(574*d^3*e^8 - 9540*d^2*e^9 + 39015*d*e^10 + 16740*e^11)*m^8 - 2*(4436*d^4*e^7 - 32144*d^3*e^8 + 247086*d^2*e^9 - 615195*d*e^10 - 277290*e^11)*m^7 + (20400*d^5*e^6 - 452472*d^4*e^7 + 1526840*d^3*e^8 - 7212240*d^2*e^9 + 12236805*d*e^10 + 5879034*e^11)*m^6 - (239760*d^6*e^5 - 918000*d^5*e^6 + 9537400*d^4*e^7 - 19929280*d^3*e^8 + 64836702*d^2*e^9 - 79518915*d*e^10 - 41597010*e^11)*m^5 - 4*(41160*d^7*e^4 + 2277720*d^6*e^5 - 4105500*d^5*e^6 + 26582730*d^4*e^7 - 38586863*d^3*e^8 + 91855890*d^2*e^9 - 84312180*d*e^10 - 49628655*e^11)*m^4 - 4*(2570400*d^8*e^3 + 1234800*d^7*e^4 + 32307660*d^6*e^5 - 36490500*d^5*e^6 + 165294232*d^4*e^7 - 177258088*d^3*e^8 + 320238402*d^2*e^9 - 224755965*d*e^10 - 157352130*e^11)*m^3 - 48*(63000*d^9*e^2 + 4498200*d^8*e^3 + 1025570*d^7*e^4 + 16893090*d^6*e^5 - 13427450*d^5*e^6 + 45284906*d^4*e^7 - 37254035*d^3*e^8 + 52296690*d^2*e^9 - 28438425*d*e^10 - 26359101*e^11)*m^2 - 8640*(70000*d^10*e + 3850*d^9*e^2 + 130900*d^8*e^3 + 18865*d^7*e^4 + 219780*d^6*e^5 - 130900*d^5*e^6 + 341572*d^4*e^7 - 220990*d^3*e^8 + 244860*d^2*e^9 - 103950*d*e^10 - 167973*e^11)*m)*x)*(e*x + d)^m/(e^11*m^11 + 66*e^11*m^10 + 1925*e^11*m^9 + 32670*e^11*m^8 + 357423*e^11*m^7 + 2637558*e^11*m^6 + 13339535*e^11*m^5 + 45995730*e^11*m^4 + 105258076*e^11*m^3 + 150917976*e^11*m^2 + 120543840*e^11*m + 39916800*e^11)","B",0
368,1,2796,0,1.366759," ","integrate((e*x+d)^m*(5*x^2+2*x+3)^2*(4*x^4-5*x^3+3*x^2+x+2),x, algorithm=""fricas"")","\frac{{\left(18 \, d e^{8} m^{8} + 100 \, {\left(e^{9} m^{8} + 36 \, e^{9} m^{7} + 546 \, e^{9} m^{6} + 4536 \, e^{9} m^{5} + 22449 \, e^{9} m^{4} + 67284 \, e^{9} m^{3} + 118124 \, e^{9} m^{2} + 109584 \, e^{9} m + 40320 \, e^{9}\right)} x^{9} + 4032000 \, d^{9} + 2041200 \, d^{8} e + 5754240 \, d^{7} e^{2} + 2237760 \, d^{6} e^{3} + 10741248 \, d^{5} e^{4} - 5896800 \, d^{4} e^{5} + 12942720 \, d^{3} e^{6} - 5987520 \, d^{2} e^{7} + 6531840 \, d e^{8} - 5 \, {\left(408240 \, e^{9} - {\left(20 \, d e^{8} - 9 \, e^{9}\right)} m^{8} - {\left(560 \, d e^{8} - 333 \, e^{9}\right)} m^{7} - 14 \, {\left(460 \, d e^{8} - 369 \, e^{9}\right)} m^{6} - 14 \, {\left(2800 \, d e^{8} - 3123 \, e^{9}\right)} m^{5} - 7 \, {\left(19340 \, d e^{8} - 31383 \, e^{9}\right)} m^{4} - 7 \, {\left(37520 \, d e^{8} - 95211 \, e^{9}\right)} m^{3} - 216 \, {\left(1210 \, d e^{8} - 5469 \, e^{9}\right)} m^{2} - 36 \, {\left(2800 \, d e^{8} - 30663 \, e^{9}\right)} m\right)} x^{8} - 33 \, {\left(d^{2} e^{7} - 24 \, d e^{8}\right)} m^{7} + {\left(5754240 \, e^{9} - 3 \, {\left(15 \, d e^{8} - 37 \, e^{9}\right)} m^{8} - 2 \, {\left(400 \, d^{2} e^{7} + 675 \, d e^{8} - 2109 \, e^{9}\right)} m^{7} - 12 \, {\left(1400 \, d^{2} e^{7} + 1365 \, d e^{8} - 5587 \, e^{9}\right)} m^{6} - 14 \, {\left(10000 \, d^{2} e^{7} + 7425 \, d e^{8} - 41403 \, e^{9}\right)} m^{5} - 21 \, {\left(28000 \, d^{2} e^{7} + 17655 \, d e^{8} - 141229 \, e^{9}\right)} m^{4} - 28 \, {\left(46400 \, d^{2} e^{7} + 26325 \, d e^{8} - 326229 \, e^{9}\right)} m^{3} - 36 \, {\left(39200 \, d^{2} e^{7} + 20745 \, d e^{8} - 455211 \, e^{9}\right)} m^{2} - 144 \, {\left(4000 \, d^{2} e^{7} + 2025 \, d e^{8} - 107337 \, e^{9}\right)} m\right)} x^{7} + 2 \, {\left(107 \, d^{3} e^{6} - 693 \, d^{2} e^{7} + 7434 \, d e^{8}\right)} m^{6} - {\left(2237760 \, e^{9} - 37 \, {\left(3 \, d e^{8} - e^{9}\right)} m^{8} - 3 \, {\left(105 \, d^{2} e^{7} + 1184 \, d e^{8} - 481 \, e^{9}\right)} m^{7} - 4 \, {\left(1400 \, d^{3} e^{6} + 1890 \, d^{2} e^{7} + 11433 \, d e^{8} - 5883 \, e^{9}\right)} m^{6} - 6 \, {\left(14000 \, d^{3} e^{6} + 11550 \, d^{2} e^{7} + 50875 \, d e^{8} - 34743 \, e^{9}\right)} m^{5} - {\left(476000 \, d^{3} e^{6} + 311850 \, d^{2} e^{7} + 1134309 \, d e^{8} - 1090353 \, e^{9}\right)} m^{4} - 3 \, {\left(420000 \, d^{3} e^{6} + 241395 \, d^{2} e^{7} + 776186 \, d e^{8} - 1140969 \, e^{9}\right)} m^{3} - 2 \, {\left(767200 \, d^{3} e^{6} + 407295 \, d^{2} e^{7} + 1208124 \, d e^{8} - 3119359 \, e^{9}\right)} m^{2} - 24 \, {\left(28000 \, d^{3} e^{6} + 14175 \, d^{2} e^{7} + 39960 \, d e^{8} - 248233 \, e^{9}\right)} m\right)} x^{6} - 6 \, {\left(65 \, d^{4} e^{5} - 1391 \, d^{3} e^{6} + 4081 \, d^{2} e^{7} - 25872 \, d e^{8}\right)} m^{5} + {\left(10741248 \, e^{9} - 37 \, {\left(d e^{8} - 4 \, e^{9}\right)} m^{8} - 74 \, {\left(9 \, d^{2} e^{7} + 17 \, d e^{8} - 80 \, e^{9}\right)} m^{7} - 2 \, {\left(945 \, d^{3} e^{6} + 8991 \, d^{2} e^{7} + 8621 \, d e^{8} - 49580 \, e^{9}\right)} m^{6} - 2 \, {\left(16800 \, d^{4} e^{5} + 17955 \, d^{3} e^{6} + 92241 \, d^{2} e^{7} + 61124 \, d e^{8} - 451400 \, e^{9}\right)} m^{5} - {\left(336000 \, d^{4} e^{5} + 236250 \, d^{3} e^{6} + 909090 \, d^{2} e^{7} + 479113 \, d e^{8} - 4850404 \, e^{9}\right)} m^{4} - 2 \, {\left(588000 \, d^{4} e^{5} + 344925 \, d^{3} e^{6} + 1130202 \, d^{2} e^{7} + 513671 \, d e^{8} - 7804040 \, e^{9}\right)} m^{3} - 12 \, {\left(140000 \, d^{4} e^{5} + 74655 \, d^{3} e^{6} + 222444 \, d^{2} e^{7} + 91834 \, d e^{8} - 2422020 \, e^{9}\right)} m^{2} - 144 \, {\left(5600 \, d^{4} e^{5} + 2835 \, d^{3} e^{6} + 7992 \, d^{2} e^{7} + 3108 \, d e^{8} - 196100 \, e^{9}\right)} m\right)} x^{5} + 2 \, {\left(1776 \, d^{5} e^{4} - 6825 \, d^{4} e^{5} + 66875 \, d^{3} e^{6} - 117810 \, d^{2} e^{7} + 491841 \, d e^{8}\right)} m^{4} + {\left(5896800 \, e^{9} + {\left(148 \, d e^{8} + 65 \, e^{9}\right)} m^{8} + {\left(185 \, d^{2} e^{7} + 5328 \, d e^{8} + 2665 \, e^{9}\right)} m^{7} + 2 \, {\left(1665 \, d^{3} e^{6} + 2775 \, d^{2} e^{7} + 38924 \, d e^{8} + 22945 \, e^{9}\right)} m^{6} + 2 \, {\left(4725 \, d^{4} e^{5} + 38295 \, d^{3} e^{6} + 32005 \, d^{2} e^{7} + 295704 \, d e^{8} + 215345 \, e^{9}\right)} m^{5} + {\left(168000 \, d^{5} e^{4} + 141750 \, d^{4} e^{5} + 616050 \, d^{3} e^{6} + 355200 \, d^{2} e^{7} + 2484772 \, d e^{8} + 2389985 \, e^{9}\right)} m^{4} + {\left(1008000 \, d^{5} e^{4} + 614250 \, d^{4} e^{5} + 2081250 \, d^{3} e^{6} + 974765 \, d^{2} e^{7} + 5668992 \, d e^{8} + 7946185 \, e^{9}\right)} m^{3} + 6 \, {\left(308000 \, d^{5} e^{4} + 165375 \, d^{4} e^{5} + 496170 \, d^{3} e^{6} + 206275 \, d^{2} e^{7} + 1064712 \, d e^{8} + 2542410 \, e^{9}\right)} m^{2} + 36 \, {\left(28000 \, d^{5} e^{4} + 14175 \, d^{4} e^{5} + 39960 \, d^{3} e^{6} + 15540 \, d^{2} e^{7} + 74592 \, d e^{8} + 422435 \, e^{9}\right)} m\right)} x^{4} + 3 \, {\left(1480 \, d^{6} e^{3} + 35520 \, d^{5} e^{4} - 63050 \, d^{4} e^{5} + 375570 \, d^{3} e^{6} - 444059 \, d^{2} e^{7} + 1288056 \, d e^{8}\right)} m^{3} + {\left(12942720 \, e^{9} + {\left(65 \, d e^{8} + 107 \, e^{9}\right)} m^{8} - 2 \, {\left(296 \, d^{2} e^{7} - 1235 \, d e^{8} - 2247 \, e^{9}\right)} m^{7} - 4 \, {\left(185 \, d^{3} e^{6} + 4884 \, d^{2} e^{7} - 9620 \, d e^{8} - 19902 \, e^{9}\right)} m^{6} - 2 \, {\left(6660 \, d^{4} e^{5} + 9990 \, d^{3} e^{6} + 126392 \, d^{2} e^{7} - 157625 \, d e^{8} - 386163 \, e^{9}\right)} m^{5} - {\left(37800 \, d^{5} e^{4} + 266400 \, d^{4} e^{5} + 196100 \, d^{3} e^{6} + 1607280 \, d^{2} e^{7} - 1444235 \, d e^{8} - 4453233 \, e^{9}\right)} m^{4} - 4 \, {\left(168000 \, d^{6} e^{3} + 113400 \, d^{5} e^{4} + 416250 \, d^{4} e^{5} + 208125 \, d^{3} e^{6} + 1279312 \, d^{2} e^{7} - 903370 \, d e^{8} - 3864519 \, e^{9}\right)} m^{3} - 4 \, {\left(504000 \, d^{6} e^{3} + 274050 \, d^{5} e^{4} + 832500 \, d^{4} e^{5} + 350390 \, d^{3} e^{6} + 1831056 \, d^{2} e^{7} - 1103505 \, d e^{8} - 7764883 \, e^{9}\right)} m^{2} - 48 \, {\left(28000 \, d^{6} e^{3} + 14175 \, d^{5} e^{4} + 39960 \, d^{4} e^{5} + 15540 \, d^{3} e^{6} + 74592 \, d^{2} e^{7} - 40950 \, d e^{8} - 672923 \, e^{9}\right)} m\right)} x^{3} + 2 \, {\left(39960 \, d^{7} e^{2} + 53280 \, d^{6} e^{3} + 594960 \, d^{5} e^{4} - 648375 \, d^{4} e^{5} + 2629418 \, d^{3} e^{6} - 2209977 \, d^{2} e^{7} + 4581036 \, d e^{8}\right)} m^{2} + {\left(5987520 \, e^{9} + {\left(107 \, d e^{8} + 33 \, e^{9}\right)} m^{8} - {\left(195 \, d^{2} e^{7} - 4280 \, d e^{8} - 1419 \, e^{9}\right)} m^{7} + 4 \, {\left(444 \, d^{3} e^{6} - 1755 \, d^{2} e^{7} + 17762 \, d e^{8} + 6468 \, e^{9}\right)} m^{6} + 2 \, {\left(1110 \, d^{4} e^{5} + 27528 \, d^{3} e^{6} - 50700 \, d^{2} e^{7} + 315115 \, d e^{8} + 130053 \, e^{9}\right)} m^{5} + {\left(39960 \, d^{5} e^{4} + 55500 \, d^{4} e^{5} + 648240 \, d^{3} e^{6} - 742950 \, d^{2} e^{7} + 3192773 \, d e^{8} + 1567797 \, e^{9}\right)} m^{4} + {\left(113400 \, d^{6} e^{3} + 719280 \, d^{5} e^{4} + 477300 \, d^{4} e^{5} + 3525360 \, d^{3} e^{6} - 2846805 \, d^{2} e^{7} + 9072530 \, d e^{8} + 5752131 \, e^{9}\right)} m^{3} + 6 \, {\left(336000 \, d^{7} e^{2} + 189000 \, d^{6} e^{3} + 592740 \, d^{5} e^{4} + 257150 \, d^{4} e^{5} + 1383504 \, d^{3} e^{6} - 857805 \, d^{2} e^{7} + 2152412 \, d e^{8} + 2062863 \, e^{9}\right)} m^{2} + 72 \, {\left(28000 \, d^{7} e^{2} + 14175 \, d^{6} e^{3} + 39960 \, d^{5} e^{4} + 15540 \, d^{4} e^{5} + 74592 \, d^{3} e^{6} - 40950 \, d^{2} e^{7} + 89880 \, d e^{8} + 193677 \, e^{9}\right)} m\right)} x^{2} + 12 \, {\left(18900 \, d^{8} e + 113220 \, d^{7} e^{2} + 70670 \, d^{6} e^{3} + 488400 \, d^{5} e^{4} - 366405 \, d^{4} e^{5} + 1073852 \, d^{3} e^{6} - 663102 \, d^{2} e^{7} + 995544 \, d e^{8}\right)} m + {\left(6531840 \, e^{9} + 3 \, {\left(11 \, d e^{8} + 6 \, e^{9}\right)} m^{8} - 2 \, {\left(107 \, d^{2} e^{7} - 693 \, d e^{8} - 396 \, e^{9}\right)} m^{7} + 6 \, {\left(65 \, d^{3} e^{6} - 1391 \, d^{2} e^{7} + 4081 \, d e^{8} + 2478 \, e^{9}\right)} m^{6} - 2 \, {\left(1776 \, d^{4} e^{5} - 6825 \, d^{3} e^{6} + 66875 \, d^{2} e^{7} - 117810 \, d e^{8} - 77616 \, e^{9}\right)} m^{5} - 3 \, {\left(1480 \, d^{5} e^{4} + 35520 \, d^{4} e^{5} - 63050 \, d^{3} e^{6} + 375570 \, d^{2} e^{7} - 444059 \, d e^{8} - 327894 \, e^{9}\right)} m^{4} - 2 \, {\left(39960 \, d^{6} e^{3} + 53280 \, d^{5} e^{4} + 594960 \, d^{4} e^{5} - 648375 \, d^{3} e^{6} + 2629418 \, d^{2} e^{7} - 2209977 \, d e^{8} - 1932084 \, e^{9}\right)} m^{3} - 12 \, {\left(18900 \, d^{7} e^{2} + 113220 \, d^{6} e^{3} + 70670 \, d^{5} e^{4} + 488400 \, d^{4} e^{5} - 366405 \, d^{3} e^{6} + 1073852 \, d^{2} e^{7} - 663102 \, d e^{8} - 763506 \, e^{9}\right)} m^{2} - 144 \, {\left(28000 \, d^{8} e + 14175 \, d^{7} e^{2} + 39960 \, d^{6} e^{3} + 15540 \, d^{5} e^{4} + 74592 \, d^{4} e^{5} - 40950 \, d^{3} e^{6} + 89880 \, d^{2} e^{7} - 41580 \, d e^{8} - 82962 \, e^{9}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{9} m^{9} + 45 \, e^{9} m^{8} + 870 \, e^{9} m^{7} + 9450 \, e^{9} m^{6} + 63273 \, e^{9} m^{5} + 269325 \, e^{9} m^{4} + 723680 \, e^{9} m^{3} + 1172700 \, e^{9} m^{2} + 1026576 \, e^{9} m + 362880 \, e^{9}}"," ",0,"(18*d*e^8*m^8 + 100*(e^9*m^8 + 36*e^9*m^7 + 546*e^9*m^6 + 4536*e^9*m^5 + 22449*e^9*m^4 + 67284*e^9*m^3 + 118124*e^9*m^2 + 109584*e^9*m + 40320*e^9)*x^9 + 4032000*d^9 + 2041200*d^8*e + 5754240*d^7*e^2 + 2237760*d^6*e^3 + 10741248*d^5*e^4 - 5896800*d^4*e^5 + 12942720*d^3*e^6 - 5987520*d^2*e^7 + 6531840*d*e^8 - 5*(408240*e^9 - (20*d*e^8 - 9*e^9)*m^8 - (560*d*e^8 - 333*e^9)*m^7 - 14*(460*d*e^8 - 369*e^9)*m^6 - 14*(2800*d*e^8 - 3123*e^9)*m^5 - 7*(19340*d*e^8 - 31383*e^9)*m^4 - 7*(37520*d*e^8 - 95211*e^9)*m^3 - 216*(1210*d*e^8 - 5469*e^9)*m^2 - 36*(2800*d*e^8 - 30663*e^9)*m)*x^8 - 33*(d^2*e^7 - 24*d*e^8)*m^7 + (5754240*e^9 - 3*(15*d*e^8 - 37*e^9)*m^8 - 2*(400*d^2*e^7 + 675*d*e^8 - 2109*e^9)*m^7 - 12*(1400*d^2*e^7 + 1365*d*e^8 - 5587*e^9)*m^6 - 14*(10000*d^2*e^7 + 7425*d*e^8 - 41403*e^9)*m^5 - 21*(28000*d^2*e^7 + 17655*d*e^8 - 141229*e^9)*m^4 - 28*(46400*d^2*e^7 + 26325*d*e^8 - 326229*e^9)*m^3 - 36*(39200*d^2*e^7 + 20745*d*e^8 - 455211*e^9)*m^2 - 144*(4000*d^2*e^7 + 2025*d*e^8 - 107337*e^9)*m)*x^7 + 2*(107*d^3*e^6 - 693*d^2*e^7 + 7434*d*e^8)*m^6 - (2237760*e^9 - 37*(3*d*e^8 - e^9)*m^8 - 3*(105*d^2*e^7 + 1184*d*e^8 - 481*e^9)*m^7 - 4*(1400*d^3*e^6 + 1890*d^2*e^7 + 11433*d*e^8 - 5883*e^9)*m^6 - 6*(14000*d^3*e^6 + 11550*d^2*e^7 + 50875*d*e^8 - 34743*e^9)*m^5 - (476000*d^3*e^6 + 311850*d^2*e^7 + 1134309*d*e^8 - 1090353*e^9)*m^4 - 3*(420000*d^3*e^6 + 241395*d^2*e^7 + 776186*d*e^8 - 1140969*e^9)*m^3 - 2*(767200*d^3*e^6 + 407295*d^2*e^7 + 1208124*d*e^8 - 3119359*e^9)*m^2 - 24*(28000*d^3*e^6 + 14175*d^2*e^7 + 39960*d*e^8 - 248233*e^9)*m)*x^6 - 6*(65*d^4*e^5 - 1391*d^3*e^6 + 4081*d^2*e^7 - 25872*d*e^8)*m^5 + (10741248*e^9 - 37*(d*e^8 - 4*e^9)*m^8 - 74*(9*d^2*e^7 + 17*d*e^8 - 80*e^9)*m^7 - 2*(945*d^3*e^6 + 8991*d^2*e^7 + 8621*d*e^8 - 49580*e^9)*m^6 - 2*(16800*d^4*e^5 + 17955*d^3*e^6 + 92241*d^2*e^7 + 61124*d*e^8 - 451400*e^9)*m^5 - (336000*d^4*e^5 + 236250*d^3*e^6 + 909090*d^2*e^7 + 479113*d*e^8 - 4850404*e^9)*m^4 - 2*(588000*d^4*e^5 + 344925*d^3*e^6 + 1130202*d^2*e^7 + 513671*d*e^8 - 7804040*e^9)*m^3 - 12*(140000*d^4*e^5 + 74655*d^3*e^6 + 222444*d^2*e^7 + 91834*d*e^8 - 2422020*e^9)*m^2 - 144*(5600*d^4*e^5 + 2835*d^3*e^6 + 7992*d^2*e^7 + 3108*d*e^8 - 196100*e^9)*m)*x^5 + 2*(1776*d^5*e^4 - 6825*d^4*e^5 + 66875*d^3*e^6 - 117810*d^2*e^7 + 491841*d*e^8)*m^4 + (5896800*e^9 + (148*d*e^8 + 65*e^9)*m^8 + (185*d^2*e^7 + 5328*d*e^8 + 2665*e^9)*m^7 + 2*(1665*d^3*e^6 + 2775*d^2*e^7 + 38924*d*e^8 + 22945*e^9)*m^6 + 2*(4725*d^4*e^5 + 38295*d^3*e^6 + 32005*d^2*e^7 + 295704*d*e^8 + 215345*e^9)*m^5 + (168000*d^5*e^4 + 141750*d^4*e^5 + 616050*d^3*e^6 + 355200*d^2*e^7 + 2484772*d*e^8 + 2389985*e^9)*m^4 + (1008000*d^5*e^4 + 614250*d^4*e^5 + 2081250*d^3*e^6 + 974765*d^2*e^7 + 5668992*d*e^8 + 7946185*e^9)*m^3 + 6*(308000*d^5*e^4 + 165375*d^4*e^5 + 496170*d^3*e^6 + 206275*d^2*e^7 + 1064712*d*e^8 + 2542410*e^9)*m^2 + 36*(28000*d^5*e^4 + 14175*d^4*e^5 + 39960*d^3*e^6 + 15540*d^2*e^7 + 74592*d*e^8 + 422435*e^9)*m)*x^4 + 3*(1480*d^6*e^3 + 35520*d^5*e^4 - 63050*d^4*e^5 + 375570*d^3*e^6 - 444059*d^2*e^7 + 1288056*d*e^8)*m^3 + (12942720*e^9 + (65*d*e^8 + 107*e^9)*m^8 - 2*(296*d^2*e^7 - 1235*d*e^8 - 2247*e^9)*m^7 - 4*(185*d^3*e^6 + 4884*d^2*e^7 - 9620*d*e^8 - 19902*e^9)*m^6 - 2*(6660*d^4*e^5 + 9990*d^3*e^6 + 126392*d^2*e^7 - 157625*d*e^8 - 386163*e^9)*m^5 - (37800*d^5*e^4 + 266400*d^4*e^5 + 196100*d^3*e^6 + 1607280*d^2*e^7 - 1444235*d*e^8 - 4453233*e^9)*m^4 - 4*(168000*d^6*e^3 + 113400*d^5*e^4 + 416250*d^4*e^5 + 208125*d^3*e^6 + 1279312*d^2*e^7 - 903370*d*e^8 - 3864519*e^9)*m^3 - 4*(504000*d^6*e^3 + 274050*d^5*e^4 + 832500*d^4*e^5 + 350390*d^3*e^6 + 1831056*d^2*e^7 - 1103505*d*e^8 - 7764883*e^9)*m^2 - 48*(28000*d^6*e^3 + 14175*d^5*e^4 + 39960*d^4*e^5 + 15540*d^3*e^6 + 74592*d^2*e^7 - 40950*d*e^8 - 672923*e^9)*m)*x^3 + 2*(39960*d^7*e^2 + 53280*d^6*e^3 + 594960*d^5*e^4 - 648375*d^4*e^5 + 2629418*d^3*e^6 - 2209977*d^2*e^7 + 4581036*d*e^8)*m^2 + (5987520*e^9 + (107*d*e^8 + 33*e^9)*m^8 - (195*d^2*e^7 - 4280*d*e^8 - 1419*e^9)*m^7 + 4*(444*d^3*e^6 - 1755*d^2*e^7 + 17762*d*e^8 + 6468*e^9)*m^6 + 2*(1110*d^4*e^5 + 27528*d^3*e^6 - 50700*d^2*e^7 + 315115*d*e^8 + 130053*e^9)*m^5 + (39960*d^5*e^4 + 55500*d^4*e^5 + 648240*d^3*e^6 - 742950*d^2*e^7 + 3192773*d*e^8 + 1567797*e^9)*m^4 + (113400*d^6*e^3 + 719280*d^5*e^4 + 477300*d^4*e^5 + 3525360*d^3*e^6 - 2846805*d^2*e^7 + 9072530*d*e^8 + 5752131*e^9)*m^3 + 6*(336000*d^7*e^2 + 189000*d^6*e^3 + 592740*d^5*e^4 + 257150*d^4*e^5 + 1383504*d^3*e^6 - 857805*d^2*e^7 + 2152412*d*e^8 + 2062863*e^9)*m^2 + 72*(28000*d^7*e^2 + 14175*d^6*e^3 + 39960*d^5*e^4 + 15540*d^4*e^5 + 74592*d^3*e^6 - 40950*d^2*e^7 + 89880*d*e^8 + 193677*e^9)*m)*x^2 + 12*(18900*d^8*e + 113220*d^7*e^2 + 70670*d^6*e^3 + 488400*d^5*e^4 - 366405*d^4*e^5 + 1073852*d^3*e^6 - 663102*d^2*e^7 + 995544*d*e^8)*m + (6531840*e^9 + 3*(11*d*e^8 + 6*e^9)*m^8 - 2*(107*d^2*e^7 - 693*d*e^8 - 396*e^9)*m^7 + 6*(65*d^3*e^6 - 1391*d^2*e^7 + 4081*d*e^8 + 2478*e^9)*m^6 - 2*(1776*d^4*e^5 - 6825*d^3*e^6 + 66875*d^2*e^7 - 117810*d*e^8 - 77616*e^9)*m^5 - 3*(1480*d^5*e^4 + 35520*d^4*e^5 - 63050*d^3*e^6 + 375570*d^2*e^7 - 444059*d*e^8 - 327894*e^9)*m^4 - 2*(39960*d^6*e^3 + 53280*d^5*e^4 + 594960*d^4*e^5 - 648375*d^3*e^6 + 2629418*d^2*e^7 - 2209977*d*e^8 - 1932084*e^9)*m^3 - 12*(18900*d^7*e^2 + 113220*d^6*e^3 + 70670*d^5*e^4 + 488400*d^4*e^5 - 366405*d^3*e^6 + 1073852*d^2*e^7 - 663102*d*e^8 - 763506*e^9)*m^2 - 144*(28000*d^8*e + 14175*d^7*e^2 + 39960*d^6*e^3 + 15540*d^5*e^4 + 74592*d^4*e^5 - 40950*d^3*e^6 + 89880*d^2*e^7 - 41580*d*e^8 - 82962*e^9)*m)*x)*(e*x + d)^m/(e^9*m^9 + 45*e^9*m^8 + 870*e^9*m^7 + 9450*e^9*m^6 + 63273*e^9*m^5 + 269325*e^9*m^4 + 723680*e^9*m^3 + 1172700*e^9*m^2 + 1026576*e^9*m + 362880*e^9)","B",0
369,1,1448,0,0.782594," ","integrate((e*x+d)^m*(5*x^2+2*x+3)*(4*x^4-5*x^3+3*x^2+x+2),x, algorithm=""fricas"")","\frac{{\left(6 \, d e^{6} m^{6} + 20 \, {\left(e^{7} m^{6} + 21 \, e^{7} m^{5} + 175 \, e^{7} m^{4} + 735 \, e^{7} m^{3} + 1624 \, e^{7} m^{2} + 1764 \, e^{7} m + 720 \, e^{7}\right)} x^{7} + 14400 \, d^{7} + 14280 \, d^{6} e + 17136 \, d^{5} e^{2} + 5040 \, d^{4} e^{3} + 35280 \, d^{3} e^{4} - 17640 \, d^{2} e^{5} + 30240 \, d e^{6} - {\left(14280 \, e^{7} - {\left(20 \, d e^{6} - 17 \, e^{7}\right)} m^{6} - 2 \, {\left(150 \, d e^{6} - 187 \, e^{7}\right)} m^{5} - 170 \, {\left(10 \, d e^{6} - 19 \, e^{7}\right)} m^{4} - 20 \, {\left(225 \, d e^{6} - 697 \, e^{7}\right)} m^{3} - {\left(5480 \, d e^{6} - 31433 \, e^{7}\right)} m^{2} - 2 \, {\left(1200 \, d e^{6} - 17323 \, e^{7}\right)} m\right)} x^{6} - {\left(7 \, d^{2} e^{5} - 162 \, d e^{6}\right)} m^{5} + {\left(17136 \, e^{7} - 17 \, {\left(d e^{6} - e^{7}\right)} m^{6} - {\left(120 \, d^{2} e^{5} + 289 \, d e^{6} - 391 \, e^{7}\right)} m^{5} - 3 \, {\left(400 \, d^{2} e^{5} + 595 \, d e^{6} - 1173 \, e^{7}\right)} m^{4} - 5 \, {\left(840 \, d^{2} e^{5} + 1003 \, d e^{6} - 3145 \, e^{7}\right)} m^{3} - 2 \, {\left(3000 \, d^{2} e^{5} + 3179 \, d e^{6} - 18224 \, e^{7}\right)} m^{2} - 12 \, {\left(240 \, d^{2} e^{5} + 238 \, d e^{6} - 3417 \, e^{7}\right)} m\right)} x^{5} + {\left(42 \, d^{3} e^{4} - 175 \, d^{2} e^{5} + 1770 \, d e^{6}\right)} m^{4} - {\left(5040 \, e^{7} - {\left(17 \, d e^{6} - 4 \, e^{7}\right)} m^{6} - {\left(85 \, d^{2} e^{5} + 323 \, d e^{6} - 96 \, e^{7}\right)} m^{5} - {\left(600 \, d^{3} e^{4} + 1105 \, d^{2} e^{5} + 2227 \, d e^{6} - 904 \, e^{7}\right)} m^{4} - {\left(3600 \, d^{3} e^{4} + 4505 \, d^{2} e^{5} + 6817 \, d e^{6} - 4224 \, e^{7}\right)} m^{3} - 5 \, {\left(1320 \, d^{3} e^{4} + 1411 \, d^{2} e^{5} + 1836 \, d e^{6} - 2036 \, e^{7}\right)} m^{2} - 6 \, {\left(600 \, d^{3} e^{4} + 595 \, d^{2} e^{5} + 714 \, d e^{6} - 1968 \, e^{7}\right)} m\right)} x^{4} + {\left(24 \, d^{4} e^{3} + 924 \, d^{3} e^{4} - 1715 \, d^{2} e^{5} + 9990 \, d e^{6}\right)} m^{3} + {\left(35280 \, e^{7} - {\left(4 \, d e^{6} - 21 \, e^{7}\right)} m^{6} - {\left(68 \, d^{2} e^{5} + 84 \, d e^{6} - 525 \, e^{7}\right)} m^{5} - {\left(340 \, d^{3} e^{4} + 1088 \, d^{2} e^{5} + 652 \, d e^{6} - 5187 \, e^{7}\right)} m^{4} - {\left(2400 \, d^{4} e^{3} + 3400 \, d^{3} e^{4} + 5644 \, d^{2} e^{5} + 2268 \, d e^{6} - 25599 \, e^{7}\right)} m^{3} - 4 \, {\left(1800 \, d^{4} e^{3} + 1955 \, d^{3} e^{4} + 2584 \, d^{2} e^{5} + 844 \, d e^{6} - 16338 \, e^{7}\right)} m^{2} - 4 \, {\left(1200 \, d^{4} e^{3} + 1190 \, d^{3} e^{4} + 1428 \, d^{2} e^{5} + 420 \, d e^{6} - 19929 \, e^{7}\right)} m\right)} x^{3} + {\left(408 \, d^{5} e^{2} + 432 \, d^{4} e^{3} + 7518 \, d^{3} e^{4} - 8225 \, d^{2} e^{5} + 30624 \, d e^{6}\right)} m^{2} + {\left(17640 \, e^{7} + 7 \, {\left(3 \, d e^{6} + e^{7}\right)} m^{6} + {\left(12 \, d^{2} e^{5} + 483 \, d e^{6} + 182 \, e^{7}\right)} m^{5} + 3 \, {\left(68 \, d^{3} e^{4} + 76 \, d^{2} e^{5} + 1407 \, d e^{6} + 630 \, e^{7}\right)} m^{4} + {\left(1020 \, d^{4} e^{3} + 2856 \, d^{3} e^{4} + 1500 \, d^{2} e^{5} + 17157 \, d e^{6} + 9940 \, e^{7}\right)} m^{3} + {\left(7200 \, d^{5} e^{2} + 8160 \, d^{4} e^{3} + 11220 \, d^{3} e^{4} + 3804 \, d^{2} e^{5} + 31038 \, d e^{6} + 27503 \, e^{7}\right)} m^{2} + 6 \, {\left(1200 \, d^{5} e^{2} + 1190 \, d^{4} e^{3} + 1428 \, d^{3} e^{4} + 420 \, d^{2} e^{5} + 2940 \, d e^{6} + 6153 \, e^{7}\right)} m\right)} x^{2} + 6 \, {\left(340 \, d^{6} e + 884 \, d^{5} e^{2} + 428 \, d^{4} e^{3} + 4466 \, d^{3} e^{4} - 3213 \, d^{2} e^{5} + 8028 \, d e^{6}\right)} m + {\left(30240 \, e^{7} + {\left(7 \, d e^{6} + 6 \, e^{7}\right)} m^{6} - {\left(42 \, d^{2} e^{5} - 175 \, d e^{6} - 162 \, e^{7}\right)} m^{5} - {\left(24 \, d^{3} e^{4} + 924 \, d^{2} e^{5} - 1715 \, d e^{6} - 1770 \, e^{7}\right)} m^{4} - {\left(408 \, d^{4} e^{3} + 432 \, d^{3} e^{4} + 7518 \, d^{2} e^{5} - 8225 \, d e^{6} - 9990 \, e^{7}\right)} m^{3} - 6 \, {\left(340 \, d^{5} e^{2} + 884 \, d^{4} e^{3} + 428 \, d^{3} e^{4} + 4466 \, d^{2} e^{5} - 3213 \, d e^{6} - 5104 \, e^{7}\right)} m^{2} - 24 \, {\left(600 \, d^{6} e + 595 \, d^{5} e^{2} + 714 \, d^{4} e^{3} + 210 \, d^{3} e^{4} + 1470 \, d^{2} e^{5} - 735 \, d e^{6} - 2007 \, e^{7}\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,"(6*d*e^6*m^6 + 20*(e^7*m^6 + 21*e^7*m^5 + 175*e^7*m^4 + 735*e^7*m^3 + 1624*e^7*m^2 + 1764*e^7*m + 720*e^7)*x^7 + 14400*d^7 + 14280*d^6*e + 17136*d^5*e^2 + 5040*d^4*e^3 + 35280*d^3*e^4 - 17640*d^2*e^5 + 30240*d*e^6 - (14280*e^7 - (20*d*e^6 - 17*e^7)*m^6 - 2*(150*d*e^6 - 187*e^7)*m^5 - 170*(10*d*e^6 - 19*e^7)*m^4 - 20*(225*d*e^6 - 697*e^7)*m^3 - (5480*d*e^6 - 31433*e^7)*m^2 - 2*(1200*d*e^6 - 17323*e^7)*m)*x^6 - (7*d^2*e^5 - 162*d*e^6)*m^5 + (17136*e^7 - 17*(d*e^6 - e^7)*m^6 - (120*d^2*e^5 + 289*d*e^6 - 391*e^7)*m^5 - 3*(400*d^2*e^5 + 595*d*e^6 - 1173*e^7)*m^4 - 5*(840*d^2*e^5 + 1003*d*e^6 - 3145*e^7)*m^3 - 2*(3000*d^2*e^5 + 3179*d*e^6 - 18224*e^7)*m^2 - 12*(240*d^2*e^5 + 238*d*e^6 - 3417*e^7)*m)*x^5 + (42*d^3*e^4 - 175*d^2*e^5 + 1770*d*e^6)*m^4 - (5040*e^7 - (17*d*e^6 - 4*e^7)*m^6 - (85*d^2*e^5 + 323*d*e^6 - 96*e^7)*m^5 - (600*d^3*e^4 + 1105*d^2*e^5 + 2227*d*e^6 - 904*e^7)*m^4 - (3600*d^3*e^4 + 4505*d^2*e^5 + 6817*d*e^6 - 4224*e^7)*m^3 - 5*(1320*d^3*e^4 + 1411*d^2*e^5 + 1836*d*e^6 - 2036*e^7)*m^2 - 6*(600*d^3*e^4 + 595*d^2*e^5 + 714*d*e^6 - 1968*e^7)*m)*x^4 + (24*d^4*e^3 + 924*d^3*e^4 - 1715*d^2*e^5 + 9990*d*e^6)*m^3 + (35280*e^7 - (4*d*e^6 - 21*e^7)*m^6 - (68*d^2*e^5 + 84*d*e^6 - 525*e^7)*m^5 - (340*d^3*e^4 + 1088*d^2*e^5 + 652*d*e^6 - 5187*e^7)*m^4 - (2400*d^4*e^3 + 3400*d^3*e^4 + 5644*d^2*e^5 + 2268*d*e^6 - 25599*e^7)*m^3 - 4*(1800*d^4*e^3 + 1955*d^3*e^4 + 2584*d^2*e^5 + 844*d*e^6 - 16338*e^7)*m^2 - 4*(1200*d^4*e^3 + 1190*d^3*e^4 + 1428*d^2*e^5 + 420*d*e^6 - 19929*e^7)*m)*x^3 + (408*d^5*e^2 + 432*d^4*e^3 + 7518*d^3*e^4 - 8225*d^2*e^5 + 30624*d*e^6)*m^2 + (17640*e^7 + 7*(3*d*e^6 + e^7)*m^6 + (12*d^2*e^5 + 483*d*e^6 + 182*e^7)*m^5 + 3*(68*d^3*e^4 + 76*d^2*e^5 + 1407*d*e^6 + 630*e^7)*m^4 + (1020*d^4*e^3 + 2856*d^3*e^4 + 1500*d^2*e^5 + 17157*d*e^6 + 9940*e^7)*m^3 + (7200*d^5*e^2 + 8160*d^4*e^3 + 11220*d^3*e^4 + 3804*d^2*e^5 + 31038*d*e^6 + 27503*e^7)*m^2 + 6*(1200*d^5*e^2 + 1190*d^4*e^3 + 1428*d^3*e^4 + 420*d^2*e^5 + 2940*d*e^6 + 6153*e^7)*m)*x^2 + 6*(340*d^6*e + 884*d^5*e^2 + 428*d^4*e^3 + 4466*d^3*e^4 - 3213*d^2*e^5 + 8028*d*e^6)*m + (30240*e^7 + (7*d*e^6 + 6*e^7)*m^6 - (42*d^2*e^5 - 175*d*e^6 - 162*e^7)*m^5 - (24*d^3*e^4 + 924*d^2*e^5 - 1715*d*e^6 - 1770*e^7)*m^4 - (408*d^4*e^3 + 432*d^3*e^4 + 7518*d^2*e^5 - 8225*d*e^6 - 9990*e^7)*m^3 - 6*(340*d^5*e^2 + 884*d^4*e^3 + 428*d^3*e^4 + 4466*d^2*e^5 - 3213*d*e^6 - 5104*e^7)*m^2 - 24*(600*d^6*e + 595*d^5*e^2 + 714*d^4*e^3 + 210*d^3*e^4 + 1470*d^2*e^5 - 735*d*e^6 - 2007*e^7)*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
370,0,0,0,0.505208," ","integrate((e*x+d)^m*(4*x^4-5*x^3+3*x^2+x+2)/(5*x^2+2*x+3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(4 \, x^{4} - 5 \, x^{3} + 3 \, x^{2} + x + 2\right)} {\left(e x + d\right)}^{m}}{5 \, x^{2} + 2 \, x + 3}, x\right)"," ",0,"integral((4*x^4 - 5*x^3 + 3*x^2 + x + 2)*(e*x + d)^m/(5*x^2 + 2*x + 3), x)","F",0
371,0,0,0,0.549925," ","integrate((e*x+d)^m*(4*x^4-5*x^3+3*x^2+x+2)/(5*x^2+2*x+3)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(4 \, x^{4} - 5 \, x^{3} + 3 \, x^{2} + x + 2\right)} {\left(e x + d\right)}^{m}}{25 \, x^{4} + 20 \, x^{3} + 34 \, x^{2} + 12 \, x + 9}, x\right)"," ",0,"integral((4*x^4 - 5*x^3 + 3*x^2 + x + 2)*(e*x + d)^m/(25*x^4 + 20*x^3 + 34*x^2 + 12*x + 9), x)","F",0
372,1,3480,0,0.870171," ","integrate((i*x^5+h*x^4+g*x^3+f*x^2+e*x+d)/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(6 \, {\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d - 3 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} e + {\left(b^{4} c^{4} - 2 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} f - 3 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} g - {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 42 \, a^{2} b^{2} c^{4} - 40 \, a^{3} c^{5}\right)} h + {\left(2 \, b^{7} c - 23 \, a b^{5} c^{2} + 85 \, a^{2} b^{3} c^{3} - 100 \, a^{3} b c^{4}\right)} i\right)} x^{3} + {\left(18 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d - 9 \, {\left(b^{4} c^{4} - 4 \, a b^{2} c^{5}\right)} e + 3 \, {\left(b^{5} c^{3} - 2 \, a b^{3} c^{4} - 8 \, a^{2} b c^{5}\right)} f - {\left(b^{6} c^{2} - 3 \, a b^{4} c^{3} + 12 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} g - {\left(b^{7} c - 12 \, a b^{5} c^{2} + 30 \, a^{2} b^{3} c^{3} + 8 \, a^{3} b c^{4}\right)} h + {\left(3 \, b^{8} - 31 \, a b^{6} c + 87 \, a^{2} b^{4} c^{2} - 12 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} i\right)} x^{2} - {\left(12 \, a^{2} c^{5} d - 6 \, a^{2} b c^{4} e - 6 \, a^{3} b c^{3} g + 12 \, a^{4} c^{3} h + {\left(12 \, c^{7} d - 6 \, b c^{6} e - 6 \, a b c^{5} g + 12 \, a^{2} c^{5} h + 2 \, {\left(b^{2} c^{5} + 2 \, a c^{6}\right)} f - {\left(b^{5} c^{2} - 10 \, a b^{3} c^{3} + 30 \, a^{2} b c^{4}\right)} i\right)} x^{4} + 2 \, {\left(12 \, b c^{6} d - 6 \, b^{2} c^{5} e - 6 \, a b^{2} c^{4} g + 12 \, a^{2} b c^{4} h + 2 \, {\left(b^{3} c^{4} + 2 \, a b c^{5}\right)} f - {\left(b^{6} c - 10 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3}\right)} i\right)} x^{3} + {\left(12 \, {\left(b^{2} c^{5} + 2 \, a c^{6}\right)} d - 6 \, {\left(b^{3} c^{4} + 2 \, a b c^{5}\right)} e + 2 \, {\left(b^{4} c^{3} + 4 \, a b^{2} c^{4} + 4 \, a^{2} c^{5}\right)} f - 6 \, {\left(a b^{3} c^{3} + 2 \, a^{2} b c^{4}\right)} g + 12 \, {\left(a^{2} b^{2} c^{3} + 2 \, a^{3} c^{4}\right)} h - {\left(b^{7} - 8 \, a b^{5} c + 10 \, a^{2} b^{3} c^{2} + 60 \, a^{3} b c^{3}\right)} i\right)} x^{2} + 2 \, {\left(a^{2} b^{2} c^{3} + 2 \, a^{3} c^{4}\right)} f - {\left(a^{2} b^{5} - 10 \, a^{3} b^{3} c + 30 \, a^{4} b c^{2}\right)} i + 2 \, {\left(12 \, a b c^{5} d - 6 \, a b^{2} c^{4} e - 6 \, a^{2} b^{2} c^{3} g + 12 \, a^{3} b c^{3} h + 2 \, {\left(a b^{3} c^{3} + 2 \, a^{2} b c^{4}\right)} f - {\left(a b^{6} - 10 \, a^{2} b^{4} c + 30 \, a^{3} b^{2} c^{2}\right)} i\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - {\left(b^{5} c^{3} - 14 \, a b^{3} c^{4} + 40 \, a^{2} b c^{5}\right)} d - {\left(a b^{4} c^{3} + 4 \, a^{2} b^{2} c^{4} - 32 \, a^{3} c^{5}\right)} e + 6 \, {\left(a^{2} b^{3} c^{3} - 4 \, a^{3} b c^{4}\right)} f - {\left(a^{2} b^{4} c^{2} + 4 \, a^{3} b^{2} c^{3} - 32 \, a^{4} c^{4}\right)} g - {\left(a^{2} b^{5} c - 14 \, a^{3} b^{3} c^{2} + 40 \, a^{4} b c^{3}\right)} h + 3 \, {\left(a^{2} b^{6} - 11 \, a^{3} b^{4} c + 36 \, a^{4} b^{2} c^{2} - 32 \, a^{5} c^{3}\right)} i + 2 \, {\left(2 \, {\left(b^{4} c^{4} + a b^{2} c^{5} - 20 \, a^{2} c^{6}\right)} d - {\left(b^{5} c^{3} + a b^{3} c^{4} - 20 \, a^{2} b c^{5}\right)} e + {\left(5 \, a b^{4} c^{3} - 22 \, a^{2} b^{2} c^{4} + 8 \, a^{3} c^{5}\right)} f - {\left(a b^{5} c^{2} + a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} g - {\left(a b^{6} c - 14 \, a^{2} b^{4} c^{2} + 46 \, a^{3} b^{2} c^{3} - 24 \, a^{4} c^{4}\right)} h + {\left(3 \, a b^{7} - 34 \, a^{2} b^{5} c + 119 \, a^{3} b^{3} c^{2} - 124 \, a^{4} b c^{3}\right)} i\right)} x + {\left({\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} i x^{4} + 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} i x^{3} + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} i x^{2} + 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} i x + {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} i\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(a^{2} b^{6} c^{3} - 12 \, a^{3} b^{4} c^{4} + 48 \, a^{4} b^{2} c^{5} - 64 \, a^{5} c^{6} + {\left(b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}\right)} x^{4} + 2 \, {\left(b^{7} c^{4} - 12 \, a b^{5} c^{5} + 48 \, a^{2} b^{3} c^{6} - 64 \, a^{3} b c^{7}\right)} x^{3} + {\left(b^{8} c^{3} - 10 \, a b^{6} c^{4} + 24 \, a^{2} b^{4} c^{5} + 32 \, a^{3} b^{2} c^{6} - 128 \, a^{4} c^{7}\right)} x^{2} + 2 \, {\left(a b^{7} c^{3} - 12 \, a^{2} b^{5} c^{4} + 48 \, a^{3} b^{3} c^{5} - 64 \, a^{4} b c^{6}\right)} x\right)}}, \frac{2 \, {\left(6 \, {\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d - 3 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} e + {\left(b^{4} c^{4} - 2 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} f - 3 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} g - {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 42 \, a^{2} b^{2} c^{4} - 40 \, a^{3} c^{5}\right)} h + {\left(2 \, b^{7} c - 23 \, a b^{5} c^{2} + 85 \, a^{2} b^{3} c^{3} - 100 \, a^{3} b c^{4}\right)} i\right)} x^{3} + {\left(18 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d - 9 \, {\left(b^{4} c^{4} - 4 \, a b^{2} c^{5}\right)} e + 3 \, {\left(b^{5} c^{3} - 2 \, a b^{3} c^{4} - 8 \, a^{2} b c^{5}\right)} f - {\left(b^{6} c^{2} - 3 \, a b^{4} c^{3} + 12 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} g - {\left(b^{7} c - 12 \, a b^{5} c^{2} + 30 \, a^{2} b^{3} c^{3} + 8 \, a^{3} b c^{4}\right)} h + {\left(3 \, b^{8} - 31 \, a b^{6} c + 87 \, a^{2} b^{4} c^{2} - 12 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} i\right)} x^{2} - 2 \, {\left(12 \, a^{2} c^{5} d - 6 \, a^{2} b c^{4} e - 6 \, a^{3} b c^{3} g + 12 \, a^{4} c^{3} h + {\left(12 \, c^{7} d - 6 \, b c^{6} e - 6 \, a b c^{5} g + 12 \, a^{2} c^{5} h + 2 \, {\left(b^{2} c^{5} + 2 \, a c^{6}\right)} f - {\left(b^{5} c^{2} - 10 \, a b^{3} c^{3} + 30 \, a^{2} b c^{4}\right)} i\right)} x^{4} + 2 \, {\left(12 \, b c^{6} d - 6 \, b^{2} c^{5} e - 6 \, a b^{2} c^{4} g + 12 \, a^{2} b c^{4} h + 2 \, {\left(b^{3} c^{4} + 2 \, a b c^{5}\right)} f - {\left(b^{6} c - 10 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3}\right)} i\right)} x^{3} + {\left(12 \, {\left(b^{2} c^{5} + 2 \, a c^{6}\right)} d - 6 \, {\left(b^{3} c^{4} + 2 \, a b c^{5}\right)} e + 2 \, {\left(b^{4} c^{3} + 4 \, a b^{2} c^{4} + 4 \, a^{2} c^{5}\right)} f - 6 \, {\left(a b^{3} c^{3} + 2 \, a^{2} b c^{4}\right)} g + 12 \, {\left(a^{2} b^{2} c^{3} + 2 \, a^{3} c^{4}\right)} h - {\left(b^{7} - 8 \, a b^{5} c + 10 \, a^{2} b^{3} c^{2} + 60 \, a^{3} b c^{3}\right)} i\right)} x^{2} + 2 \, {\left(a^{2} b^{2} c^{3} + 2 \, a^{3} c^{4}\right)} f - {\left(a^{2} b^{5} - 10 \, a^{3} b^{3} c + 30 \, a^{4} b c^{2}\right)} i + 2 \, {\left(12 \, a b c^{5} d - 6 \, a b^{2} c^{4} e - 6 \, a^{2} b^{2} c^{3} g + 12 \, a^{3} b c^{3} h + 2 \, {\left(a b^{3} c^{3} + 2 \, a^{2} b c^{4}\right)} f - {\left(a b^{6} - 10 \, a^{2} b^{4} c + 30 \, a^{3} b^{2} c^{2}\right)} i\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - {\left(b^{5} c^{3} - 14 \, a b^{3} c^{4} + 40 \, a^{2} b c^{5}\right)} d - {\left(a b^{4} c^{3} + 4 \, a^{2} b^{2} c^{4} - 32 \, a^{3} c^{5}\right)} e + 6 \, {\left(a^{2} b^{3} c^{3} - 4 \, a^{3} b c^{4}\right)} f - {\left(a^{2} b^{4} c^{2} + 4 \, a^{3} b^{2} c^{3} - 32 \, a^{4} c^{4}\right)} g - {\left(a^{2} b^{5} c - 14 \, a^{3} b^{3} c^{2} + 40 \, a^{4} b c^{3}\right)} h + 3 \, {\left(a^{2} b^{6} - 11 \, a^{3} b^{4} c + 36 \, a^{4} b^{2} c^{2} - 32 \, a^{5} c^{3}\right)} i + 2 \, {\left(2 \, {\left(b^{4} c^{4} + a b^{2} c^{5} - 20 \, a^{2} c^{6}\right)} d - {\left(b^{5} c^{3} + a b^{3} c^{4} - 20 \, a^{2} b c^{5}\right)} e + {\left(5 \, a b^{4} c^{3} - 22 \, a^{2} b^{2} c^{4} + 8 \, a^{3} c^{5}\right)} f - {\left(a b^{5} c^{2} + a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} g - {\left(a b^{6} c - 14 \, a^{2} b^{4} c^{2} + 46 \, a^{3} b^{2} c^{3} - 24 \, a^{4} c^{4}\right)} h + {\left(3 \, a b^{7} - 34 \, a^{2} b^{5} c + 119 \, a^{3} b^{3} c^{2} - 124 \, a^{4} b c^{3}\right)} i\right)} x + {\left({\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} i x^{4} + 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} i x^{3} + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} i x^{2} + 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} i x + {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} i\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(a^{2} b^{6} c^{3} - 12 \, a^{3} b^{4} c^{4} + 48 \, a^{4} b^{2} c^{5} - 64 \, a^{5} c^{6} + {\left(b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}\right)} x^{4} + 2 \, {\left(b^{7} c^{4} - 12 \, a b^{5} c^{5} + 48 \, a^{2} b^{3} c^{6} - 64 \, a^{3} b c^{7}\right)} x^{3} + {\left(b^{8} c^{3} - 10 \, a b^{6} c^{4} + 24 \, a^{2} b^{4} c^{5} + 32 \, a^{3} b^{2} c^{6} - 128 \, a^{4} c^{7}\right)} x^{2} + 2 \, {\left(a b^{7} c^{3} - 12 \, a^{2} b^{5} c^{4} + 48 \, a^{3} b^{3} c^{5} - 64 \, a^{4} b c^{6}\right)} x\right)}}\right]"," ",0,"[1/2*(2*(6*(b^2*c^6 - 4*a*c^7)*d - 3*(b^3*c^5 - 4*a*b*c^6)*e + (b^4*c^4 - 2*a*b^2*c^5 - 8*a^2*c^6)*f - 3*(a*b^3*c^4 - 4*a^2*b*c^5)*g - (b^6*c^2 - 12*a*b^4*c^3 + 42*a^2*b^2*c^4 - 40*a^3*c^5)*h + (2*b^7*c - 23*a*b^5*c^2 + 85*a^2*b^3*c^3 - 100*a^3*b*c^4)*i)*x^3 + (18*(b^3*c^5 - 4*a*b*c^6)*d - 9*(b^4*c^4 - 4*a*b^2*c^5)*e + 3*(b^5*c^3 - 2*a*b^3*c^4 - 8*a^2*b*c^5)*f - (b^6*c^2 - 3*a*b^4*c^3 + 12*a^2*b^2*c^4 - 64*a^3*c^5)*g - (b^7*c - 12*a*b^5*c^2 + 30*a^2*b^3*c^3 + 8*a^3*b*c^4)*h + (3*b^8 - 31*a*b^6*c + 87*a^2*b^4*c^2 - 12*a^3*b^2*c^3 - 128*a^4*c^4)*i)*x^2 - (12*a^2*c^5*d - 6*a^2*b*c^4*e - 6*a^3*b*c^3*g + 12*a^4*c^3*h + (12*c^7*d - 6*b*c^6*e - 6*a*b*c^5*g + 12*a^2*c^5*h + 2*(b^2*c^5 + 2*a*c^6)*f - (b^5*c^2 - 10*a*b^3*c^3 + 30*a^2*b*c^4)*i)*x^4 + 2*(12*b*c^6*d - 6*b^2*c^5*e - 6*a*b^2*c^4*g + 12*a^2*b*c^4*h + 2*(b^3*c^4 + 2*a*b*c^5)*f - (b^6*c - 10*a*b^4*c^2 + 30*a^2*b^2*c^3)*i)*x^3 + (12*(b^2*c^5 + 2*a*c^6)*d - 6*(b^3*c^4 + 2*a*b*c^5)*e + 2*(b^4*c^3 + 4*a*b^2*c^4 + 4*a^2*c^5)*f - 6*(a*b^3*c^3 + 2*a^2*b*c^4)*g + 12*(a^2*b^2*c^3 + 2*a^3*c^4)*h - (b^7 - 8*a*b^5*c + 10*a^2*b^3*c^2 + 60*a^3*b*c^3)*i)*x^2 + 2*(a^2*b^2*c^3 + 2*a^3*c^4)*f - (a^2*b^5 - 10*a^3*b^3*c + 30*a^4*b*c^2)*i + 2*(12*a*b*c^5*d - 6*a*b^2*c^4*e - 6*a^2*b^2*c^3*g + 12*a^3*b*c^3*h + 2*(a*b^3*c^3 + 2*a^2*b*c^4)*f - (a*b^6 - 10*a^2*b^4*c + 30*a^3*b^2*c^2)*i)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - (b^5*c^3 - 14*a*b^3*c^4 + 40*a^2*b*c^5)*d - (a*b^4*c^3 + 4*a^2*b^2*c^4 - 32*a^3*c^5)*e + 6*(a^2*b^3*c^3 - 4*a^3*b*c^4)*f - (a^2*b^4*c^2 + 4*a^3*b^2*c^3 - 32*a^4*c^4)*g - (a^2*b^5*c - 14*a^3*b^3*c^2 + 40*a^4*b*c^3)*h + 3*(a^2*b^6 - 11*a^3*b^4*c + 36*a^4*b^2*c^2 - 32*a^5*c^3)*i + 2*(2*(b^4*c^4 + a*b^2*c^5 - 20*a^2*c^6)*d - (b^5*c^3 + a*b^3*c^4 - 20*a^2*b*c^5)*e + (5*a*b^4*c^3 - 22*a^2*b^2*c^4 + 8*a^3*c^5)*f - (a*b^5*c^2 + a^2*b^3*c^3 - 20*a^3*b*c^4)*g - (a*b^6*c - 14*a^2*b^4*c^2 + 46*a^3*b^2*c^3 - 24*a^4*c^4)*h + (3*a*b^7 - 34*a^2*b^5*c + 119*a^3*b^3*c^2 - 124*a^4*b*c^3)*i)*x + ((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*i*x^4 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*i*x^3 + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*i*x^2 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*i*x + (a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*i)*log(c*x^2 + b*x + a))/(a^2*b^6*c^3 - 12*a^3*b^4*c^4 + 48*a^4*b^2*c^5 - 64*a^5*c^6 + (b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)*x^4 + 2*(b^7*c^4 - 12*a*b^5*c^5 + 48*a^2*b^3*c^6 - 64*a^3*b*c^7)*x^3 + (b^8*c^3 - 10*a*b^6*c^4 + 24*a^2*b^4*c^5 + 32*a^3*b^2*c^6 - 128*a^4*c^7)*x^2 + 2*(a*b^7*c^3 - 12*a^2*b^5*c^4 + 48*a^3*b^3*c^5 - 64*a^4*b*c^6)*x), 1/2*(2*(6*(b^2*c^6 - 4*a*c^7)*d - 3*(b^3*c^5 - 4*a*b*c^6)*e + (b^4*c^4 - 2*a*b^2*c^5 - 8*a^2*c^6)*f - 3*(a*b^3*c^4 - 4*a^2*b*c^5)*g - (b^6*c^2 - 12*a*b^4*c^3 + 42*a^2*b^2*c^4 - 40*a^3*c^5)*h + (2*b^7*c - 23*a*b^5*c^2 + 85*a^2*b^3*c^3 - 100*a^3*b*c^4)*i)*x^3 + (18*(b^3*c^5 - 4*a*b*c^6)*d - 9*(b^4*c^4 - 4*a*b^2*c^5)*e + 3*(b^5*c^3 - 2*a*b^3*c^4 - 8*a^2*b*c^5)*f - (b^6*c^2 - 3*a*b^4*c^3 + 12*a^2*b^2*c^4 - 64*a^3*c^5)*g - (b^7*c - 12*a*b^5*c^2 + 30*a^2*b^3*c^3 + 8*a^3*b*c^4)*h + (3*b^8 - 31*a*b^6*c + 87*a^2*b^4*c^2 - 12*a^3*b^2*c^3 - 128*a^4*c^4)*i)*x^2 - 2*(12*a^2*c^5*d - 6*a^2*b*c^4*e - 6*a^3*b*c^3*g + 12*a^4*c^3*h + (12*c^7*d - 6*b*c^6*e - 6*a*b*c^5*g + 12*a^2*c^5*h + 2*(b^2*c^5 + 2*a*c^6)*f - (b^5*c^2 - 10*a*b^3*c^3 + 30*a^2*b*c^4)*i)*x^4 + 2*(12*b*c^6*d - 6*b^2*c^5*e - 6*a*b^2*c^4*g + 12*a^2*b*c^4*h + 2*(b^3*c^4 + 2*a*b*c^5)*f - (b^6*c - 10*a*b^4*c^2 + 30*a^2*b^2*c^3)*i)*x^3 + (12*(b^2*c^5 + 2*a*c^6)*d - 6*(b^3*c^4 + 2*a*b*c^5)*e + 2*(b^4*c^3 + 4*a*b^2*c^4 + 4*a^2*c^5)*f - 6*(a*b^3*c^3 + 2*a^2*b*c^4)*g + 12*(a^2*b^2*c^3 + 2*a^3*c^4)*h - (b^7 - 8*a*b^5*c + 10*a^2*b^3*c^2 + 60*a^3*b*c^3)*i)*x^2 + 2*(a^2*b^2*c^3 + 2*a^3*c^4)*f - (a^2*b^5 - 10*a^3*b^3*c + 30*a^4*b*c^2)*i + 2*(12*a*b*c^5*d - 6*a*b^2*c^4*e - 6*a^2*b^2*c^3*g + 12*a^3*b*c^3*h + 2*(a*b^3*c^3 + 2*a^2*b*c^4)*f - (a*b^6 - 10*a^2*b^4*c + 30*a^3*b^2*c^2)*i)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - (b^5*c^3 - 14*a*b^3*c^4 + 40*a^2*b*c^5)*d - (a*b^4*c^3 + 4*a^2*b^2*c^4 - 32*a^3*c^5)*e + 6*(a^2*b^3*c^3 - 4*a^3*b*c^4)*f - (a^2*b^4*c^2 + 4*a^3*b^2*c^3 - 32*a^4*c^4)*g - (a^2*b^5*c - 14*a^3*b^3*c^2 + 40*a^4*b*c^3)*h + 3*(a^2*b^6 - 11*a^3*b^4*c + 36*a^4*b^2*c^2 - 32*a^5*c^3)*i + 2*(2*(b^4*c^4 + a*b^2*c^5 - 20*a^2*c^6)*d - (b^5*c^3 + a*b^3*c^4 - 20*a^2*b*c^5)*e + (5*a*b^4*c^3 - 22*a^2*b^2*c^4 + 8*a^3*c^5)*f - (a*b^5*c^2 + a^2*b^3*c^3 - 20*a^3*b*c^4)*g - (a*b^6*c - 14*a^2*b^4*c^2 + 46*a^3*b^2*c^3 - 24*a^4*c^4)*h + (3*a*b^7 - 34*a^2*b^5*c + 119*a^3*b^3*c^2 - 124*a^4*b*c^3)*i)*x + ((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*i*x^4 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*i*x^3 + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*i*x^2 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*i*x + (a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*i)*log(c*x^2 + b*x + a))/(a^2*b^6*c^3 - 12*a^3*b^4*c^4 + 48*a^4*b^2*c^5 - 64*a^5*c^6 + (b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)*x^4 + 2*(b^7*c^4 - 12*a*b^5*c^5 + 48*a^2*b^3*c^6 - 64*a^3*b*c^7)*x^3 + (b^8*c^3 - 10*a*b^6*c^4 + 24*a^2*b^4*c^5 + 32*a^3*b^2*c^6 - 128*a^4*c^7)*x^2 + 2*(a*b^7*c^3 - 12*a^2*b^5*c^4 + 48*a^3*b^3*c^5 - 64*a^4*b*c^6)*x)]","B",0
373,1,2643,0,1.750249," ","integrate((m*x^8+l*x^7+k*x^6+j*x^5+h*x^4+g*x^3+f*x^2+e*x+d)/(c*x^2+b*x+a),x, algorithm=""fricas"")","\left[\frac{60 \, {\left(b^{2} c^{7} - 4 \, a c^{8}\right)} m x^{7} + 70 \, {\left({\left(b^{2} c^{7} - 4 \, a c^{8}\right)} l - {\left(b^{3} c^{6} - 4 \, a b c^{7}\right)} m\right)} x^{6} + 84 \, {\left({\left(b^{2} c^{7} - 4 \, a c^{8}\right)} k - {\left(b^{3} c^{6} - 4 \, a b c^{7}\right)} l + {\left(b^{4} c^{5} - 5 \, a b^{2} c^{6} + 4 \, a^{2} c^{7}\right)} m\right)} x^{5} + 105 \, {\left({\left(b^{2} c^{7} - 4 \, a c^{8}\right)} j - {\left(b^{3} c^{6} - 4 \, a b c^{7}\right)} k + {\left(b^{4} c^{5} - 5 \, a b^{2} c^{6} + 4 \, a^{2} c^{7}\right)} l - {\left(b^{5} c^{4} - 6 \, a b^{3} c^{5} + 8 \, a^{2} b c^{6}\right)} m\right)} x^{4} + 140 \, {\left({\left(b^{2} c^{7} - 4 \, a c^{8}\right)} h - {\left(b^{3} c^{6} - 4 \, a b c^{7}\right)} j + {\left(b^{4} c^{5} - 5 \, a b^{2} c^{6} + 4 \, a^{2} c^{7}\right)} k - {\left(b^{5} c^{4} - 6 \, a b^{3} c^{5} + 8 \, a^{2} b c^{6}\right)} l + {\left(b^{6} c^{3} - 7 \, a b^{4} c^{4} + 13 \, a^{2} b^{2} c^{5} - 4 \, a^{3} c^{6}\right)} m\right)} x^{3} + 210 \, {\left({\left(b^{2} c^{7} - 4 \, a c^{8}\right)} g - {\left(b^{3} c^{6} - 4 \, a b c^{7}\right)} h + {\left(b^{4} c^{5} - 5 \, a b^{2} c^{6} + 4 \, a^{2} c^{7}\right)} j - {\left(b^{5} c^{4} - 6 \, a b^{3} c^{5} + 8 \, a^{2} b c^{6}\right)} k + {\left(b^{6} c^{3} - 7 \, a b^{4} c^{4} + 13 \, a^{2} b^{2} c^{5} - 4 \, a^{3} c^{6}\right)} l - {\left(b^{7} c^{2} - 8 \, a b^{5} c^{3} + 19 \, a^{2} b^{3} c^{4} - 12 \, a^{3} b c^{5}\right)} m\right)} x^{2} + 210 \, {\left(2 \, c^{8} d - b c^{7} e + {\left(b^{2} c^{6} - 2 \, a c^{7}\right)} f - {\left(b^{3} c^{5} - 3 \, a b c^{6}\right)} g + {\left(b^{4} c^{4} - 4 \, a b^{2} c^{5} + 2 \, a^{2} c^{6}\right)} h - {\left(b^{5} c^{3} - 5 \, a b^{3} c^{4} + 5 \, a^{2} b c^{5}\right)} j + {\left(b^{6} c^{2} - 6 \, a b^{4} c^{3} + 9 \, a^{2} b^{2} c^{4} - 2 \, a^{3} c^{5}\right)} k - {\left(b^{7} c - 7 \, a b^{5} c^{2} + 14 \, a^{2} b^{3} c^{3} - 7 \, a^{3} b c^{4}\right)} l + {\left(b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 2 \, a^{4} c^{4}\right)} m\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 420 \, {\left({\left(b^{2} c^{7} - 4 \, a c^{8}\right)} f - {\left(b^{3} c^{6} - 4 \, a b c^{7}\right)} g + {\left(b^{4} c^{5} - 5 \, a b^{2} c^{6} + 4 \, a^{2} c^{7}\right)} h - {\left(b^{5} c^{4} - 6 \, a b^{3} c^{5} + 8 \, a^{2} b c^{6}\right)} j + {\left(b^{6} c^{3} - 7 \, a b^{4} c^{4} + 13 \, a^{2} b^{2} c^{5} - 4 \, a^{3} c^{6}\right)} k - {\left(b^{7} c^{2} - 8 \, a b^{5} c^{3} + 19 \, a^{2} b^{3} c^{4} - 12 \, a^{3} b c^{5}\right)} l + {\left(b^{8} c - 9 \, a b^{6} c^{2} + 26 \, a^{2} b^{4} c^{3} - 25 \, a^{3} b^{2} c^{4} + 4 \, a^{4} c^{5}\right)} m\right)} x + 210 \, {\left({\left(b^{2} c^{7} - 4 \, a c^{8}\right)} e - {\left(b^{3} c^{6} - 4 \, a b c^{7}\right)} f + {\left(b^{4} c^{5} - 5 \, a b^{2} c^{6} + 4 \, a^{2} c^{7}\right)} g - {\left(b^{5} c^{4} - 6 \, a b^{3} c^{5} + 8 \, a^{2} b c^{6}\right)} h + {\left(b^{6} c^{3} - 7 \, a b^{4} c^{4} + 13 \, a^{2} b^{2} c^{5} - 4 \, a^{3} c^{6}\right)} j - {\left(b^{7} c^{2} - 8 \, a b^{5} c^{3} + 19 \, a^{2} b^{3} c^{4} - 12 \, a^{3} b c^{5}\right)} k + {\left(b^{8} c - 9 \, a b^{6} c^{2} + 26 \, a^{2} b^{4} c^{3} - 25 \, a^{3} b^{2} c^{4} + 4 \, a^{4} c^{5}\right)} l - {\left(b^{9} - 10 \, a b^{7} c + 34 \, a^{2} b^{5} c^{2} - 44 \, a^{3} b^{3} c^{3} + 16 \, a^{4} b c^{4}\right)} m\right)} \log\left(c x^{2} + b x + a\right)}{420 \, {\left(b^{2} c^{8} - 4 \, a c^{9}\right)}}, \frac{60 \, {\left(b^{2} c^{7} - 4 \, a c^{8}\right)} m x^{7} + 70 \, {\left({\left(b^{2} c^{7} - 4 \, a c^{8}\right)} l - {\left(b^{3} c^{6} - 4 \, a b c^{7}\right)} m\right)} x^{6} + 84 \, {\left({\left(b^{2} c^{7} - 4 \, a c^{8}\right)} k - {\left(b^{3} c^{6} - 4 \, a b c^{7}\right)} l + {\left(b^{4} c^{5} - 5 \, a b^{2} c^{6} + 4 \, a^{2} c^{7}\right)} m\right)} x^{5} + 105 \, {\left({\left(b^{2} c^{7} - 4 \, a c^{8}\right)} j - {\left(b^{3} c^{6} - 4 \, a b c^{7}\right)} k + {\left(b^{4} c^{5} - 5 \, a b^{2} c^{6} + 4 \, a^{2} c^{7}\right)} l - {\left(b^{5} c^{4} - 6 \, a b^{3} c^{5} + 8 \, a^{2} b c^{6}\right)} m\right)} x^{4} + 140 \, {\left({\left(b^{2} c^{7} - 4 \, a c^{8}\right)} h - {\left(b^{3} c^{6} - 4 \, a b c^{7}\right)} j + {\left(b^{4} c^{5} - 5 \, a b^{2} c^{6} + 4 \, a^{2} c^{7}\right)} k - {\left(b^{5} c^{4} - 6 \, a b^{3} c^{5} + 8 \, a^{2} b c^{6}\right)} l + {\left(b^{6} c^{3} - 7 \, a b^{4} c^{4} + 13 \, a^{2} b^{2} c^{5} - 4 \, a^{3} c^{6}\right)} m\right)} x^{3} + 210 \, {\left({\left(b^{2} c^{7} - 4 \, a c^{8}\right)} g - {\left(b^{3} c^{6} - 4 \, a b c^{7}\right)} h + {\left(b^{4} c^{5} - 5 \, a b^{2} c^{6} + 4 \, a^{2} c^{7}\right)} j - {\left(b^{5} c^{4} - 6 \, a b^{3} c^{5} + 8 \, a^{2} b c^{6}\right)} k + {\left(b^{6} c^{3} - 7 \, a b^{4} c^{4} + 13 \, a^{2} b^{2} c^{5} - 4 \, a^{3} c^{6}\right)} l - {\left(b^{7} c^{2} - 8 \, a b^{5} c^{3} + 19 \, a^{2} b^{3} c^{4} - 12 \, a^{3} b c^{5}\right)} m\right)} x^{2} - 420 \, {\left(2 \, c^{8} d - b c^{7} e + {\left(b^{2} c^{6} - 2 \, a c^{7}\right)} f - {\left(b^{3} c^{5} - 3 \, a b c^{6}\right)} g + {\left(b^{4} c^{4} - 4 \, a b^{2} c^{5} + 2 \, a^{2} c^{6}\right)} h - {\left(b^{5} c^{3} - 5 \, a b^{3} c^{4} + 5 \, a^{2} b c^{5}\right)} j + {\left(b^{6} c^{2} - 6 \, a b^{4} c^{3} + 9 \, a^{2} b^{2} c^{4} - 2 \, a^{3} c^{5}\right)} k - {\left(b^{7} c - 7 \, a b^{5} c^{2} + 14 \, a^{2} b^{3} c^{3} - 7 \, a^{3} b c^{4}\right)} l + {\left(b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 2 \, a^{4} c^{4}\right)} m\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 420 \, {\left({\left(b^{2} c^{7} - 4 \, a c^{8}\right)} f - {\left(b^{3} c^{6} - 4 \, a b c^{7}\right)} g + {\left(b^{4} c^{5} - 5 \, a b^{2} c^{6} + 4 \, a^{2} c^{7}\right)} h - {\left(b^{5} c^{4} - 6 \, a b^{3} c^{5} + 8 \, a^{2} b c^{6}\right)} j + {\left(b^{6} c^{3} - 7 \, a b^{4} c^{4} + 13 \, a^{2} b^{2} c^{5} - 4 \, a^{3} c^{6}\right)} k - {\left(b^{7} c^{2} - 8 \, a b^{5} c^{3} + 19 \, a^{2} b^{3} c^{4} - 12 \, a^{3} b c^{5}\right)} l + {\left(b^{8} c - 9 \, a b^{6} c^{2} + 26 \, a^{2} b^{4} c^{3} - 25 \, a^{3} b^{2} c^{4} + 4 \, a^{4} c^{5}\right)} m\right)} x + 210 \, {\left({\left(b^{2} c^{7} - 4 \, a c^{8}\right)} e - {\left(b^{3} c^{6} - 4 \, a b c^{7}\right)} f + {\left(b^{4} c^{5} - 5 \, a b^{2} c^{6} + 4 \, a^{2} c^{7}\right)} g - {\left(b^{5} c^{4} - 6 \, a b^{3} c^{5} + 8 \, a^{2} b c^{6}\right)} h + {\left(b^{6} c^{3} - 7 \, a b^{4} c^{4} + 13 \, a^{2} b^{2} c^{5} - 4 \, a^{3} c^{6}\right)} j - {\left(b^{7} c^{2} - 8 \, a b^{5} c^{3} + 19 \, a^{2} b^{3} c^{4} - 12 \, a^{3} b c^{5}\right)} k + {\left(b^{8} c - 9 \, a b^{6} c^{2} + 26 \, a^{2} b^{4} c^{3} - 25 \, a^{3} b^{2} c^{4} + 4 \, a^{4} c^{5}\right)} l - {\left(b^{9} - 10 \, a b^{7} c + 34 \, a^{2} b^{5} c^{2} - 44 \, a^{3} b^{3} c^{3} + 16 \, a^{4} b c^{4}\right)} m\right)} \log\left(c x^{2} + b x + a\right)}{420 \, {\left(b^{2} c^{8} - 4 \, a c^{9}\right)}}\right]"," ",0,"[1/420*(60*(b^2*c^7 - 4*a*c^8)*m*x^7 + 70*((b^2*c^7 - 4*a*c^8)*l - (b^3*c^6 - 4*a*b*c^7)*m)*x^6 + 84*((b^2*c^7 - 4*a*c^8)*k - (b^3*c^6 - 4*a*b*c^7)*l + (b^4*c^5 - 5*a*b^2*c^6 + 4*a^2*c^7)*m)*x^5 + 105*((b^2*c^7 - 4*a*c^8)*j - (b^3*c^6 - 4*a*b*c^7)*k + (b^4*c^5 - 5*a*b^2*c^6 + 4*a^2*c^7)*l - (b^5*c^4 - 6*a*b^3*c^5 + 8*a^2*b*c^6)*m)*x^4 + 140*((b^2*c^7 - 4*a*c^8)*h - (b^3*c^6 - 4*a*b*c^7)*j + (b^4*c^5 - 5*a*b^2*c^6 + 4*a^2*c^7)*k - (b^5*c^4 - 6*a*b^3*c^5 + 8*a^2*b*c^6)*l + (b^6*c^3 - 7*a*b^4*c^4 + 13*a^2*b^2*c^5 - 4*a^3*c^6)*m)*x^3 + 210*((b^2*c^7 - 4*a*c^8)*g - (b^3*c^6 - 4*a*b*c^7)*h + (b^4*c^5 - 5*a*b^2*c^6 + 4*a^2*c^7)*j - (b^5*c^4 - 6*a*b^3*c^5 + 8*a^2*b*c^6)*k + (b^6*c^3 - 7*a*b^4*c^4 + 13*a^2*b^2*c^5 - 4*a^3*c^6)*l - (b^7*c^2 - 8*a*b^5*c^3 + 19*a^2*b^3*c^4 - 12*a^3*b*c^5)*m)*x^2 + 210*(2*c^8*d - b*c^7*e + (b^2*c^6 - 2*a*c^7)*f - (b^3*c^5 - 3*a*b*c^6)*g + (b^4*c^4 - 4*a*b^2*c^5 + 2*a^2*c^6)*h - (b^5*c^3 - 5*a*b^3*c^4 + 5*a^2*b*c^5)*j + (b^6*c^2 - 6*a*b^4*c^3 + 9*a^2*b^2*c^4 - 2*a^3*c^5)*k - (b^7*c - 7*a*b^5*c^2 + 14*a^2*b^3*c^3 - 7*a^3*b*c^4)*l + (b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 2*a^4*c^4)*m)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 420*((b^2*c^7 - 4*a*c^8)*f - (b^3*c^6 - 4*a*b*c^7)*g + (b^4*c^5 - 5*a*b^2*c^6 + 4*a^2*c^7)*h - (b^5*c^4 - 6*a*b^3*c^5 + 8*a^2*b*c^6)*j + (b^6*c^3 - 7*a*b^4*c^4 + 13*a^2*b^2*c^5 - 4*a^3*c^6)*k - (b^7*c^2 - 8*a*b^5*c^3 + 19*a^2*b^3*c^4 - 12*a^3*b*c^5)*l + (b^8*c - 9*a*b^6*c^2 + 26*a^2*b^4*c^3 - 25*a^3*b^2*c^4 + 4*a^4*c^5)*m)*x + 210*((b^2*c^7 - 4*a*c^8)*e - (b^3*c^6 - 4*a*b*c^7)*f + (b^4*c^5 - 5*a*b^2*c^6 + 4*a^2*c^7)*g - (b^5*c^4 - 6*a*b^3*c^5 + 8*a^2*b*c^6)*h + (b^6*c^3 - 7*a*b^4*c^4 + 13*a^2*b^2*c^5 - 4*a^3*c^6)*j - (b^7*c^2 - 8*a*b^5*c^3 + 19*a^2*b^3*c^4 - 12*a^3*b*c^5)*k + (b^8*c - 9*a*b^6*c^2 + 26*a^2*b^4*c^3 - 25*a^3*b^2*c^4 + 4*a^4*c^5)*l - (b^9 - 10*a*b^7*c + 34*a^2*b^5*c^2 - 44*a^3*b^3*c^3 + 16*a^4*b*c^4)*m)*log(c*x^2 + b*x + a))/(b^2*c^8 - 4*a*c^9), 1/420*(60*(b^2*c^7 - 4*a*c^8)*m*x^7 + 70*((b^2*c^7 - 4*a*c^8)*l - (b^3*c^6 - 4*a*b*c^7)*m)*x^6 + 84*((b^2*c^7 - 4*a*c^8)*k - (b^3*c^6 - 4*a*b*c^7)*l + (b^4*c^5 - 5*a*b^2*c^6 + 4*a^2*c^7)*m)*x^5 + 105*((b^2*c^7 - 4*a*c^8)*j - (b^3*c^6 - 4*a*b*c^7)*k + (b^4*c^5 - 5*a*b^2*c^6 + 4*a^2*c^7)*l - (b^5*c^4 - 6*a*b^3*c^5 + 8*a^2*b*c^6)*m)*x^4 + 140*((b^2*c^7 - 4*a*c^8)*h - (b^3*c^6 - 4*a*b*c^7)*j + (b^4*c^5 - 5*a*b^2*c^6 + 4*a^2*c^7)*k - (b^5*c^4 - 6*a*b^3*c^5 + 8*a^2*b*c^6)*l + (b^6*c^3 - 7*a*b^4*c^4 + 13*a^2*b^2*c^5 - 4*a^3*c^6)*m)*x^3 + 210*((b^2*c^7 - 4*a*c^8)*g - (b^3*c^6 - 4*a*b*c^7)*h + (b^4*c^5 - 5*a*b^2*c^6 + 4*a^2*c^7)*j - (b^5*c^4 - 6*a*b^3*c^5 + 8*a^2*b*c^6)*k + (b^6*c^3 - 7*a*b^4*c^4 + 13*a^2*b^2*c^5 - 4*a^3*c^6)*l - (b^7*c^2 - 8*a*b^5*c^3 + 19*a^2*b^3*c^4 - 12*a^3*b*c^5)*m)*x^2 - 420*(2*c^8*d - b*c^7*e + (b^2*c^6 - 2*a*c^7)*f - (b^3*c^5 - 3*a*b*c^6)*g + (b^4*c^4 - 4*a*b^2*c^5 + 2*a^2*c^6)*h - (b^5*c^3 - 5*a*b^3*c^4 + 5*a^2*b*c^5)*j + (b^6*c^2 - 6*a*b^4*c^3 + 9*a^2*b^2*c^4 - 2*a^3*c^5)*k - (b^7*c - 7*a*b^5*c^2 + 14*a^2*b^3*c^3 - 7*a^3*b*c^4)*l + (b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 2*a^4*c^4)*m)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 420*((b^2*c^7 - 4*a*c^8)*f - (b^3*c^6 - 4*a*b*c^7)*g + (b^4*c^5 - 5*a*b^2*c^6 + 4*a^2*c^7)*h - (b^5*c^4 - 6*a*b^3*c^5 + 8*a^2*b*c^6)*j + (b^6*c^3 - 7*a*b^4*c^4 + 13*a^2*b^2*c^5 - 4*a^3*c^6)*k - (b^7*c^2 - 8*a*b^5*c^3 + 19*a^2*b^3*c^4 - 12*a^3*b*c^5)*l + (b^8*c - 9*a*b^6*c^2 + 26*a^2*b^4*c^3 - 25*a^3*b^2*c^4 + 4*a^4*c^5)*m)*x + 210*((b^2*c^7 - 4*a*c^8)*e - (b^3*c^6 - 4*a*b*c^7)*f + (b^4*c^5 - 5*a*b^2*c^6 + 4*a^2*c^7)*g - (b^5*c^4 - 6*a*b^3*c^5 + 8*a^2*b*c^6)*h + (b^6*c^3 - 7*a*b^4*c^4 + 13*a^2*b^2*c^5 - 4*a^3*c^6)*j - (b^7*c^2 - 8*a*b^5*c^3 + 19*a^2*b^3*c^4 - 12*a^3*b*c^5)*k + (b^8*c - 9*a*b^6*c^2 + 26*a^2*b^4*c^3 - 25*a^3*b^2*c^4 + 4*a^4*c^5)*l - (b^9 - 10*a*b^7*c + 34*a^2*b^5*c^2 - 44*a^3*b^3*c^3 + 16*a^4*b*c^4)*m)*log(c*x^2 + b*x + a))/(b^2*c^8 - 4*a*c^9)]","A",0
374,1,97,0,0.760210," ","integrate((-7*x^2+4*x+1)^3*(x^2+5*x+2)*(5*x^2+2*x+3)^(1/2),x, algorithm=""fricas"")","-\frac{1}{1968750000} \, {\left(67528125000 \, x^{9} + 248031875000 \, x^{8} - 497593468750 \, x^{7} - 34674656250 \, x^{6} + 225922362500 \, x^{5} + 56757413000 \, x^{4} + 17642392275 \, x^{3} - 78839046795 \, x^{2} - 57768004650 \, x + 93436408944\right)} \sqrt{5 \, x^{2} + 2 \, x + 3} + \frac{540119881}{156250000} \, \sqrt{5} \log\left(\sqrt{5} \sqrt{5 \, x^{2} + 2 \, x + 3} {\left(5 \, x + 1\right)} - 25 \, x^{2} - 10 \, x - 8\right)"," ",0,"-1/1968750000*(67528125000*x^9 + 248031875000*x^8 - 497593468750*x^7 - 34674656250*x^6 + 225922362500*x^5 + 56757413000*x^4 + 17642392275*x^3 - 78839046795*x^2 - 57768004650*x + 93436408944)*sqrt(5*x^2 + 2*x + 3) + 540119881/156250000*sqrt(5)*log(sqrt(5)*sqrt(5*x^2 + 2*x + 3)*(5*x + 1) - 25*x^2 - 10*x - 8)","A",0
375,1,87,0,0.816816," ","integrate((-7*x^2+4*x+1)^2*(x^2+5*x+2)*(5*x^2+2*x+3)^(1/2),x, algorithm=""fricas"")","\frac{1}{3750000} \, {\left(22968750 \, x^{7} + 101906250 \, x^{6} - 107112500 \, x^{5} - 65693000 \, x^{4} + 15583725 \, x^{3} + 23531995 \, x^{2} + 44333650 \, x - 4588584\right)} \sqrt{5 \, x^{2} + 2 \, x + 3} + \frac{17652061}{6250000} \, \sqrt{5} \log\left(\sqrt{5} \sqrt{5 \, x^{2} + 2 \, x + 3} {\left(5 \, x + 1\right)} - 25 \, x^{2} - 10 \, x - 8\right)"," ",0,"1/3750000*(22968750*x^7 + 101906250*x^6 - 107112500*x^5 - 65693000*x^4 + 15583725*x^3 + 23531995*x^2 + 44333650*x - 4588584)*sqrt(5*x^2 + 2*x + 3) + 17652061/6250000*sqrt(5)*log(sqrt(5)*sqrt(5*x^2 + 2*x + 3)*(5*x + 1) - 25*x^2 - 10*x - 8)","A",0
376,1,77,0,0.651270," ","integrate((-7*x^2+4*x+1)*(x^2+5*x+2)*(5*x^2+2*x+3)^(1/2),x, algorithm=""fricas"")","-\frac{1}{37500} \, {\left(43750 \, x^{5} + 234250 \, x^{4} - 48225 \, x^{3} - 129895 \, x^{2} - 105400 \, x - 103386\right)} \sqrt{5 \, x^{2} + 2 \, x + 3} + \frac{32431}{62500} \, \sqrt{5} \log\left(\sqrt{5} \sqrt{5 \, x^{2} + 2 \, x + 3} {\left(5 \, x + 1\right)} - 25 \, x^{2} - 10 \, x - 8\right)"," ",0,"-1/37500*(43750*x^5 + 234250*x^4 - 48225*x^3 - 129895*x^2 - 105400*x - 103386)*sqrt(5*x^2 + 2*x + 3) + 32431/62500*sqrt(5)*log(sqrt(5)*sqrt(5*x^2 + 2*x + 3)*(5*x + 1) - 25*x^2 - 10*x - 8)","A",0
377,1,304,0,1.015516," ","integrate((x^2+5*x+2)*(5*x^2+2*x+3)^(1/2)/(-7*x^2+4*x+1),x, algorithm=""fricas"")","\frac{3}{7546} \, \sqrt{11} \sqrt{146555 \, \sqrt{11} + 497041} \log\left(\frac{6 \, {\left(\sqrt{5 \, x^{2} + 2 \, x + 3} \sqrt{146555 \, \sqrt{11} + 497041} {\left(87 \, \sqrt{11} - 265\right)} + 6517 \, \sqrt{11} {\left(x + 3\right)} + 19551 \, x - 32585\right)}}{x}\right) - \frac{3}{7546} \, \sqrt{11} \sqrt{146555 \, \sqrt{11} + 497041} \log\left(-\frac{6 \, {\left(\sqrt{5 \, x^{2} + 2 \, x + 3} \sqrt{146555 \, \sqrt{11} + 497041} {\left(87 \, \sqrt{11} - 265\right)} - 6517 \, \sqrt{11} {\left(x + 3\right)} - 19551 \, x + 32585\right)}}{x}\right) - \frac{1}{15092} \, \sqrt{11} \sqrt{-5275980 \, \sqrt{11} + 17893476} \log\left(-\frac{\sqrt{5 \, x^{2} + 2 \, x + 3} {\left(87 \, \sqrt{11} + 265\right)} \sqrt{-5275980 \, \sqrt{11} + 17893476} + 39102 \, \sqrt{11} {\left(x + 3\right)} - 117306 \, x + 195510}{x}\right) + \frac{1}{15092} \, \sqrt{11} \sqrt{-5275980 \, \sqrt{11} + 17893476} \log\left(\frac{\sqrt{5 \, x^{2} + 2 \, x + 3} {\left(87 \, \sqrt{11} + 265\right)} \sqrt{-5275980 \, \sqrt{11} + 17893476} - 39102 \, \sqrt{11} {\left(x + 3\right)} + 117306 \, x - 195510}{x}\right) - \frac{1}{490} \, \sqrt{5 \, x^{2} + 2 \, x + 3} {\left(35 \, x + 397\right)} + \frac{8233}{17150} \, \sqrt{5} \log\left(\sqrt{5} \sqrt{5 \, x^{2} + 2 \, x + 3} {\left(5 \, x + 1\right)} - 25 \, x^{2} - 10 \, x - 8\right)"," ",0,"3/7546*sqrt(11)*sqrt(146555*sqrt(11) + 497041)*log(6*(sqrt(5*x^2 + 2*x + 3)*sqrt(146555*sqrt(11) + 497041)*(87*sqrt(11) - 265) + 6517*sqrt(11)*(x + 3) + 19551*x - 32585)/x) - 3/7546*sqrt(11)*sqrt(146555*sqrt(11) + 497041)*log(-6*(sqrt(5*x^2 + 2*x + 3)*sqrt(146555*sqrt(11) + 497041)*(87*sqrt(11) - 265) - 6517*sqrt(11)*(x + 3) - 19551*x + 32585)/x) - 1/15092*sqrt(11)*sqrt(-5275980*sqrt(11) + 17893476)*log(-(sqrt(5*x^2 + 2*x + 3)*(87*sqrt(11) + 265)*sqrt(-5275980*sqrt(11) + 17893476) + 39102*sqrt(11)*(x + 3) - 117306*x + 195510)/x) + 1/15092*sqrt(11)*sqrt(-5275980*sqrt(11) + 17893476)*log((sqrt(5*x^2 + 2*x + 3)*(87*sqrt(11) + 265)*sqrt(-5275980*sqrt(11) + 17893476) - 39102*sqrt(11)*(x + 3) + 117306*x - 195510)/x) - 1/490*sqrt(5*x^2 + 2*x + 3)*(35*x + 397) + 8233/17150*sqrt(5)*log(sqrt(5)*sqrt(5*x^2 + 2*x + 3)*(5*x + 1) - 25*x^2 - 10*x - 8)","B",0
378,1,378,0,0.957980," ","integrate((x^2+5*x+2)*(5*x^2+2*x+3)^(1/2)/(-7*x^2+4*x+1)^2,x, algorithm=""fricas"")","-\frac{\sqrt{1397} {\left(7 \, x^{2} - 4 \, x - 1\right)} \sqrt{39132731 \, \sqrt{11} + 325022311} \log\left(-\frac{\sqrt{1397} \sqrt{5 \, x^{2} + 2 \, x + 3} \sqrt{39132731 \, \sqrt{11} + 325022311} {\left(16943 \, \sqrt{11} + 235367\right)} + 26119953475 \, \sqrt{11} {\left(x + 3\right)} - 78359860425 \, x + 130599767375}{x}\right) - \sqrt{1397} {\left(7 \, x^{2} - 4 \, x - 1\right)} \sqrt{39132731 \, \sqrt{11} + 325022311} \log\left(\frac{\sqrt{1397} \sqrt{5 \, x^{2} + 2 \, x + 3} \sqrt{39132731 \, \sqrt{11} + 325022311} {\left(16943 \, \sqrt{11} + 235367\right)} - 26119953475 \, \sqrt{11} {\left(x + 3\right)} + 78359860425 \, x - 130599767375}{x}\right) + \sqrt{1397} {\left(7 \, x^{2} - 4 \, x - 1\right)} \sqrt{-39132731 \, \sqrt{11} + 325022311} \log\left(\frac{\sqrt{1397} \sqrt{5 \, x^{2} + 2 \, x + 3} {\left(16943 \, \sqrt{11} - 235367\right)} \sqrt{-39132731 \, \sqrt{11} + 325022311} + 26119953475 \, \sqrt{11} {\left(x + 3\right)} + 78359860425 \, x - 130599767375}{x}\right) - \sqrt{1397} {\left(7 \, x^{2} - 4 \, x - 1\right)} \sqrt{-39132731 \, \sqrt{11} + 325022311} \log\left(-\frac{\sqrt{1397} \sqrt{5 \, x^{2} + 2 \, x + 3} {\left(16943 \, \sqrt{11} - 235367\right)} \sqrt{-39132731 \, \sqrt{11} + 325022311} - 26119953475 \, \sqrt{11} {\left(x + 3\right)} - 78359860425 \, x + 130599767375}{x}\right) - 61468 \, \sqrt{5} {\left(7 \, x^{2} - 4 \, x - 1\right)} \log\left(-\sqrt{5} \sqrt{5 \, x^{2} + 2 \, x + 3} {\left(5 \, x + 1\right)} - 25 \, x^{2} - 10 \, x - 8\right) + 117348 \, \sqrt{5 \, x^{2} + 2 \, x + 3} {\left(61 \, x + 3\right)}}{6023864 \, {\left(7 \, x^{2} - 4 \, x - 1\right)}}"," ",0,"-1/6023864*(sqrt(1397)*(7*x^2 - 4*x - 1)*sqrt(39132731*sqrt(11) + 325022311)*log(-(sqrt(1397)*sqrt(5*x^2 + 2*x + 3)*sqrt(39132731*sqrt(11) + 325022311)*(16943*sqrt(11) + 235367) + 26119953475*sqrt(11)*(x + 3) - 78359860425*x + 130599767375)/x) - sqrt(1397)*(7*x^2 - 4*x - 1)*sqrt(39132731*sqrt(11) + 325022311)*log((sqrt(1397)*sqrt(5*x^2 + 2*x + 3)*sqrt(39132731*sqrt(11) + 325022311)*(16943*sqrt(11) + 235367) - 26119953475*sqrt(11)*(x + 3) + 78359860425*x - 130599767375)/x) + sqrt(1397)*(7*x^2 - 4*x - 1)*sqrt(-39132731*sqrt(11) + 325022311)*log((sqrt(1397)*sqrt(5*x^2 + 2*x + 3)*(16943*sqrt(11) - 235367)*sqrt(-39132731*sqrt(11) + 325022311) + 26119953475*sqrt(11)*(x + 3) + 78359860425*x - 130599767375)/x) - sqrt(1397)*(7*x^2 - 4*x - 1)*sqrt(-39132731*sqrt(11) + 325022311)*log(-(sqrt(1397)*sqrt(5*x^2 + 2*x + 3)*(16943*sqrt(11) - 235367)*sqrt(-39132731*sqrt(11) + 325022311) - 26119953475*sqrt(11)*(x + 3) - 78359860425*x + 130599767375)/x) - 61468*sqrt(5)*(7*x^2 - 4*x - 1)*log(-sqrt(5)*sqrt(5*x^2 + 2*x + 3)*(5*x + 1) - 25*x^2 - 10*x - 8) + 117348*sqrt(5*x^2 + 2*x + 3)*(61*x + 3))/(7*x^2 - 4*x - 1)","B",0
379,1,390,0,0.992906," ","integrate((x^2+5*x+2)*(5*x^2+2*x+3)^(1/2)/(-7*x^2+4*x+1)^3,x, algorithm=""fricas"")","-\frac{\sqrt{1397} {\left(49 \, x^{4} - 56 \, x^{3} + 2 \, x^{2} + 8 \, x + 1\right)} \sqrt{11879169071 \, \sqrt{11} + 6492253020949} \log\left(\frac{\sqrt{1397} \sqrt{5 \, x^{2} + 2 \, x + 3} \sqrt{11879169071 \, \sqrt{11} + 6492253020949} {\left(4822219 \, \sqrt{11} - 37335441\right)} + 569071698870455 \, \sqrt{11} {\left(x + 3\right)} + 1707215096611365 \, x - 2845358494352275}{x}\right) - \sqrt{1397} {\left(49 \, x^{4} - 56 \, x^{3} + 2 \, x^{2} + 8 \, x + 1\right)} \sqrt{11879169071 \, \sqrt{11} + 6492253020949} \log\left(-\frac{\sqrt{1397} \sqrt{5 \, x^{2} + 2 \, x + 3} \sqrt{11879169071 \, \sqrt{11} + 6492253020949} {\left(4822219 \, \sqrt{11} - 37335441\right)} - 569071698870455 \, \sqrt{11} {\left(x + 3\right)} - 1707215096611365 \, x + 2845358494352275}{x}\right) + \sqrt{1397} {\left(49 \, x^{4} - 56 \, x^{3} + 2 \, x^{2} + 8 \, x + 1\right)} \sqrt{-11879169071 \, \sqrt{11} + 6492253020949} \log\left(-\frac{\sqrt{1397} \sqrt{5 \, x^{2} + 2 \, x + 3} {\left(4822219 \, \sqrt{11} + 37335441\right)} \sqrt{-11879169071 \, \sqrt{11} + 6492253020949} + 569071698870455 \, \sqrt{11} {\left(x + 3\right)} - 1707215096611365 \, x + 2845358494352275}{x}\right) - \sqrt{1397} {\left(49 \, x^{4} - 56 \, x^{3} + 2 \, x^{2} + 8 \, x + 1\right)} \sqrt{-11879169071 \, \sqrt{11} + 6492253020949} \log\left(\frac{\sqrt{1397} \sqrt{5 \, x^{2} + 2 \, x + 3} {\left(4822219 \, \sqrt{11} + 37335441\right)} \sqrt{-11879169071 \, \sqrt{11} + 6492253020949} - 569071698870455 \, \sqrt{11} {\left(x + 3\right)} + 1707215096611365 \, x - 2845358494352275}{x}\right) + 5588 \, {\left(813113 \, x^{3} - 737577 \, x^{2} - 106279 \, x + 31807\right)} \sqrt{5 \, x^{2} + 2 \, x + 3}}{1373932736 \, {\left(49 \, x^{4} - 56 \, x^{3} + 2 \, x^{2} + 8 \, x + 1\right)}}"," ",0,"-1/1373932736*(sqrt(1397)*(49*x^4 - 56*x^3 + 2*x^2 + 8*x + 1)*sqrt(11879169071*sqrt(11) + 6492253020949)*log((sqrt(1397)*sqrt(5*x^2 + 2*x + 3)*sqrt(11879169071*sqrt(11) + 6492253020949)*(4822219*sqrt(11) - 37335441) + 569071698870455*sqrt(11)*(x + 3) + 1707215096611365*x - 2845358494352275)/x) - sqrt(1397)*(49*x^4 - 56*x^3 + 2*x^2 + 8*x + 1)*sqrt(11879169071*sqrt(11) + 6492253020949)*log(-(sqrt(1397)*sqrt(5*x^2 + 2*x + 3)*sqrt(11879169071*sqrt(11) + 6492253020949)*(4822219*sqrt(11) - 37335441) - 569071698870455*sqrt(11)*(x + 3) - 1707215096611365*x + 2845358494352275)/x) + sqrt(1397)*(49*x^4 - 56*x^3 + 2*x^2 + 8*x + 1)*sqrt(-11879169071*sqrt(11) + 6492253020949)*log(-(sqrt(1397)*sqrt(5*x^2 + 2*x + 3)*(4822219*sqrt(11) + 37335441)*sqrt(-11879169071*sqrt(11) + 6492253020949) + 569071698870455*sqrt(11)*(x + 3) - 1707215096611365*x + 2845358494352275)/x) - sqrt(1397)*(49*x^4 - 56*x^3 + 2*x^2 + 8*x + 1)*sqrt(-11879169071*sqrt(11) + 6492253020949)*log((sqrt(1397)*sqrt(5*x^2 + 2*x + 3)*(4822219*sqrt(11) + 37335441)*sqrt(-11879169071*sqrt(11) + 6492253020949) - 569071698870455*sqrt(11)*(x + 3) + 1707215096611365*x - 2845358494352275)/x) + 5588*(813113*x^3 - 737577*x^2 - 106279*x + 31807)*sqrt(5*x^2 + 2*x + 3))/(49*x^4 - 56*x^3 + 2*x^2 + 8*x + 1)","B",0
380,1,107,0,0.865485," ","integrate((-7*x^2+4*x+1)^3*(x^2+5*x+2)*(5*x^2+2*x+3)^(3/2),x, algorithm=""fricas"")","-\frac{1}{216562500000} \, {\left(30950390625000 \, x^{11} + 125007421875000 \, x^{10} - 148393743750000 \, x^{9} - 30505457500000 \, x^{8} - 72918247281250 \, x^{7} + 52106830406250 \, x^{6} + 85130334087500 \, x^{5} - 2573089891000 \, x^{4} - 19041688239675 \, x^{3} - 15865844408685 \, x^{2} - 6352777129950 \, x + 10506617068392\right)} \sqrt{5 \, x^{2} + 2 \, x + 3} + \frac{3357568053}{1562500000} \, \sqrt{5} \log\left(\sqrt{5} \sqrt{5 \, x^{2} + 2 \, x + 3} {\left(5 \, x + 1\right)} - 25 \, x^{2} - 10 \, x - 8\right)"," ",0,"-1/216562500000*(30950390625000*x^11 + 125007421875000*x^10 - 148393743750000*x^9 - 30505457500000*x^8 - 72918247281250*x^7 + 52106830406250*x^6 + 85130334087500*x^5 - 2573089891000*x^4 - 19041688239675*x^3 - 15865844408685*x^2 - 6352777129950*x + 10506617068392)*sqrt(5*x^2 + 2*x + 3) + 3357568053/1562500000*sqrt(5)*log(sqrt(5)*sqrt(5*x^2 + 2*x + 3)*(5*x + 1) - 25*x^2 - 10*x - 8)","A",0
381,1,97,0,0.819339," ","integrate((-7*x^2+4*x+1)^2*(x^2+5*x+2)*(5*x^2+2*x+3)^(3/2),x, algorithm=""fricas"")","\frac{1}{131250000} \, {\left(3215625000 \, x^{9} + 15281875000 \, x^{8} - 5561281250 \, x^{7} - 4105593750 \, x^{6} - 12554262500 \, x^{5} - 3227597000 \, x^{4} + 5959365525 \, x^{3} + 3721040355 \, x^{2} + 2291675850 \, x - 249003936\right)} \sqrt{5 \, x^{2} + 2 \, x + 3} + \frac{101512467}{31250000} \, \sqrt{5} \log\left(\sqrt{5} \sqrt{5 \, x^{2} + 2 \, x + 3} {\left(5 \, x + 1\right)} - 25 \, x^{2} - 10 \, x - 8\right)"," ",0,"1/131250000*(3215625000*x^9 + 15281875000*x^8 - 5561281250*x^7 - 4105593750*x^6 - 12554262500*x^5 - 3227597000*x^4 + 5959365525*x^3 + 3721040355*x^2 + 2291675850*x - 249003936)*sqrt(5*x^2 + 2*x + 3) + 101512467/31250000*sqrt(5)*log(sqrt(5)*sqrt(5*x^2 + 2*x + 3)*(5*x + 1) - 25*x^2 - 10*x - 8)","A",0
382,1,87,0,0.817005," ","integrate((-7*x^2+4*x+1)*(x^2+5*x+2)*(5*x^2+2*x+3)^(3/2),x, algorithm=""fricas"")","-\frac{1}{5250000} \, {\left(22968750 \, x^{7} + 127406250 \, x^{6} + 48237500 \, x^{5} + 28373000 \, x^{4} - 78608475 \, x^{3} - 86464445 \, x^{2} - 36695150 \, x - 22275576\right)} \sqrt{5 \, x^{2} + 2 \, x + 3} + \frac{901453}{1250000} \, \sqrt{5} \log\left(\sqrt{5} \sqrt{5 \, x^{2} + 2 \, x + 3} {\left(5 \, x + 1\right)} - 25 \, x^{2} - 10 \, x - 8\right)"," ",0,"-1/5250000*(22968750*x^7 + 127406250*x^6 + 48237500*x^5 + 28373000*x^4 - 78608475*x^3 - 86464445*x^2 - 36695150*x - 22275576)*sqrt(5*x^2 + 2*x + 3) + 901453/1250000*sqrt(5)*log(sqrt(5)*sqrt(5*x^2 + 2*x + 3)*(5*x + 1) - 25*x^2 - 10*x - 8)","A",0
383,1,326,0,0.643715," ","integrate((x^2+5*x+2)*(5*x^2+2*x+3)^(3/2)/(-7*x^2+4*x+1),x, algorithm=""fricas"")","\frac{3}{184877} \, \sqrt{11} \sqrt{2} \sqrt{2434122235 \, \sqrt{11} + 8098902607} \log\left(\frac{12 \, {\left(\sqrt{2} \sqrt{5 \, x^{2} + 2 \, x + 3} \sqrt{2434122235 \, \sqrt{11} + 8098902607} {\left(7690 \, \sqrt{11} - 24697\right)} + 40555291 \, \sqrt{11} {\left(x + 3\right)} + 121665873 \, x - 202776455\right)}}{x}\right) - \frac{3}{184877} \, \sqrt{11} \sqrt{2} \sqrt{2434122235 \, \sqrt{11} + 8098902607} \log\left(-\frac{12 \, {\left(\sqrt{2} \sqrt{5 \, x^{2} + 2 \, x + 3} \sqrt{2434122235 \, \sqrt{11} + 8098902607} {\left(7690 \, \sqrt{11} - 24697\right)} - 40555291 \, \sqrt{11} {\left(x + 3\right)} - 121665873 \, x + 202776455\right)}}{x}\right) - \frac{1}{739508} \, \sqrt{11} \sqrt{-701027203680 \, \sqrt{11} + 2332483950816} \log\left(-\frac{\sqrt{5 \, x^{2} + 2 \, x + 3} {\left(7690 \, \sqrt{11} + 24697\right)} \sqrt{-701027203680 \, \sqrt{11} + 2332483950816} + 486663492 \, \sqrt{11} {\left(x + 3\right)} - 1459990476 \, x + 2433317460}{x}\right) + \frac{1}{739508} \, \sqrt{11} \sqrt{-701027203680 \, \sqrt{11} + 2332483950816} \log\left(\frac{\sqrt{5 \, x^{2} + 2 \, x + 3} {\left(7690 \, \sqrt{11} + 24697\right)} \sqrt{-701027203680 \, \sqrt{11} + 2332483950816} - 486663492 \, \sqrt{11} {\left(x + 3\right)} + 1459990476 \, x - 2433317460}{x}\right) - \frac{1}{240100} \, {\left(42875 \, x^{3} + 344225 \, x^{2} + 744870 \, x + 1911108\right)} \sqrt{5 \, x^{2} + 2 \, x + 3} + \frac{34425687}{8403500} \, \sqrt{5} \log\left(\sqrt{5} \sqrt{5 \, x^{2} + 2 \, x + 3} {\left(5 \, x + 1\right)} - 25 \, x^{2} - 10 \, x - 8\right)"," ",0,"3/184877*sqrt(11)*sqrt(2)*sqrt(2434122235*sqrt(11) + 8098902607)*log(12*(sqrt(2)*sqrt(5*x^2 + 2*x + 3)*sqrt(2434122235*sqrt(11) + 8098902607)*(7690*sqrt(11) - 24697) + 40555291*sqrt(11)*(x + 3) + 121665873*x - 202776455)/x) - 3/184877*sqrt(11)*sqrt(2)*sqrt(2434122235*sqrt(11) + 8098902607)*log(-12*(sqrt(2)*sqrt(5*x^2 + 2*x + 3)*sqrt(2434122235*sqrt(11) + 8098902607)*(7690*sqrt(11) - 24697) - 40555291*sqrt(11)*(x + 3) - 121665873*x + 202776455)/x) - 1/739508*sqrt(11)*sqrt(-701027203680*sqrt(11) + 2332483950816)*log(-(sqrt(5*x^2 + 2*x + 3)*(7690*sqrt(11) + 24697)*sqrt(-701027203680*sqrt(11) + 2332483950816) + 486663492*sqrt(11)*(x + 3) - 1459990476*x + 2433317460)/x) + 1/739508*sqrt(11)*sqrt(-701027203680*sqrt(11) + 2332483950816)*log((sqrt(5*x^2 + 2*x + 3)*(7690*sqrt(11) + 24697)*sqrt(-701027203680*sqrt(11) + 2332483950816) - 486663492*sqrt(11)*(x + 3) + 1459990476*x - 2433317460)/x) - 1/240100*(42875*x^3 + 344225*x^2 + 744870*x + 1911108)*sqrt(5*x^2 + 2*x + 3) + 34425687/8403500*sqrt(5)*log(sqrt(5)*sqrt(5*x^2 + 2*x + 3)*(5*x + 1) - 25*x^2 - 10*x - 8)","B",0
384,1,378,0,0.695027," ","integrate((x^2+5*x+2)*(5*x^2+2*x+3)^(3/2)/(-7*x^2+4*x+1)^2,x, algorithm=""fricas"")","\frac{5 \, \sqrt{11} {\left(7 \, x^{2} - 4 \, x - 1\right)} \sqrt{26310753062 \, \sqrt{11} + 104350800622} \log\left(\frac{\sqrt{5 \, x^{2} + 2 \, x + 3} \sqrt{26310753062 \, \sqrt{11} + 104350800622} {\left(16206 \, \sqrt{11} - 68441\right)} + 1795191685 \, \sqrt{11} {\left(x + 3\right)} + 5385575055 \, x - 8975958425}{x}\right) - 5 \, \sqrt{11} {\left(7 \, x^{2} - 4 \, x - 1\right)} \sqrt{26310753062 \, \sqrt{11} + 104350800622} \log\left(-\frac{\sqrt{5 \, x^{2} + 2 \, x + 3} \sqrt{26310753062 \, \sqrt{11} + 104350800622} {\left(16206 \, \sqrt{11} - 68441\right)} - 1795191685 \, \sqrt{11} {\left(x + 3\right)} - 5385575055 \, x + 8975958425}{x}\right) - 5 \, \sqrt{11} {\left(7 \, x^{2} - 4 \, x - 1\right)} \sqrt{-26310753062 \, \sqrt{11} + 104350800622} \log\left(-\frac{\sqrt{5 \, x^{2} + 2 \, x + 3} {\left(16206 \, \sqrt{11} + 68441\right)} \sqrt{-26310753062 \, \sqrt{11} + 104350800622} + 1795191685 \, \sqrt{11} {\left(x + 3\right)} - 5385575055 \, x + 8975958425}{x}\right) + 5 \, \sqrt{11} {\left(7 \, x^{2} - 4 \, x - 1\right)} \sqrt{-26310753062 \, \sqrt{11} + 104350800622} \log\left(\frac{\sqrt{5 \, x^{2} + 2 \, x + 3} {\left(16206 \, \sqrt{11} + 68441\right)} \sqrt{-26310753062 \, \sqrt{11} + 104350800622} - 1795191685 \, \sqrt{11} {\left(x + 3\right)} + 5385575055 \, x - 8975958425}{x}\right) + 4039222 \, \sqrt{5} {\left(7 \, x^{2} - 4 \, x - 1\right)} \log\left(-\sqrt{5} \sqrt{5 \, x^{2} + 2 \, x + 3} {\left(5 \, x + 1\right)} - 25 \, x^{2} - 10 \, x - 8\right) + 770 \, {\left(2695 \, x^{3} + 34265 \, x^{2} - 81181 \, x - 12975\right)} \sqrt{5 \, x^{2} + 2 \, x + 3}}{5810420 \, {\left(7 \, x^{2} - 4 \, x - 1\right)}}"," ",0,"1/5810420*(5*sqrt(11)*(7*x^2 - 4*x - 1)*sqrt(26310753062*sqrt(11) + 104350800622)*log((sqrt(5*x^2 + 2*x + 3)*sqrt(26310753062*sqrt(11) + 104350800622)*(16206*sqrt(11) - 68441) + 1795191685*sqrt(11)*(x + 3) + 5385575055*x - 8975958425)/x) - 5*sqrt(11)*(7*x^2 - 4*x - 1)*sqrt(26310753062*sqrt(11) + 104350800622)*log(-(sqrt(5*x^2 + 2*x + 3)*sqrt(26310753062*sqrt(11) + 104350800622)*(16206*sqrt(11) - 68441) - 1795191685*sqrt(11)*(x + 3) - 5385575055*x + 8975958425)/x) - 5*sqrt(11)*(7*x^2 - 4*x - 1)*sqrt(-26310753062*sqrt(11) + 104350800622)*log(-(sqrt(5*x^2 + 2*x + 3)*(16206*sqrt(11) + 68441)*sqrt(-26310753062*sqrt(11) + 104350800622) + 1795191685*sqrt(11)*(x + 3) - 5385575055*x + 8975958425)/x) + 5*sqrt(11)*(7*x^2 - 4*x - 1)*sqrt(-26310753062*sqrt(11) + 104350800622)*log((sqrt(5*x^2 + 2*x + 3)*(16206*sqrt(11) + 68441)*sqrt(-26310753062*sqrt(11) + 104350800622) - 1795191685*sqrt(11)*(x + 3) + 5385575055*x - 8975958425)/x) + 4039222*sqrt(5)*(7*x^2 - 4*x - 1)*log(-sqrt(5)*sqrt(5*x^2 + 2*x + 3)*(5*x + 1) - 25*x^2 - 10*x - 8) + 770*(2695*x^3 + 34265*x^2 - 81181*x - 12975)*sqrt(5*x^2 + 2*x + 3))/(7*x^2 - 4*x - 1)","B",0
385,1,447,0,0.741165," ","integrate((x^2+5*x+2)*(5*x^2+2*x+3)^(3/2)/(-7*x^2+4*x+1)^3,x, algorithm=""fricas"")","-\frac{\sqrt{2794} {\left(49 \, x^{4} - 56 \, x^{3} + 2 \, x^{2} + 8 \, x + 1\right)} \sqrt{2085440742055 \, \sqrt{11} + 62294197250171} \log\left(\frac{\sqrt{2794} \sqrt{5 \, x^{2} + 2 \, x + 3} \sqrt{2085440742055 \, \sqrt{11} + 62294197250171} {\left(11840590 \, \sqrt{11} - 83479737\right)} + 5426671202560069 \, \sqrt{11} {\left(x + 3\right)} + 16280013607680207 \, x - 27133356012800345}{x}\right) - \sqrt{2794} {\left(49 \, x^{4} - 56 \, x^{3} + 2 \, x^{2} + 8 \, x + 1\right)} \sqrt{2085440742055 \, \sqrt{11} + 62294197250171} \log\left(-\frac{\sqrt{2794} \sqrt{5 \, x^{2} + 2 \, x + 3} \sqrt{2085440742055 \, \sqrt{11} + 62294197250171} {\left(11840590 \, \sqrt{11} - 83479737\right)} - 5426671202560069 \, \sqrt{11} {\left(x + 3\right)} - 16280013607680207 \, x + 27133356012800345}{x}\right) + \sqrt{2794} {\left(49 \, x^{4} - 56 \, x^{3} + 2 \, x^{2} + 8 \, x + 1\right)} \sqrt{-2085440742055 \, \sqrt{11} + 62294197250171} \log\left(-\frac{\sqrt{2794} \sqrt{5 \, x^{2} + 2 \, x + 3} {\left(11840590 \, \sqrt{11} + 83479737\right)} \sqrt{-2085440742055 \, \sqrt{11} + 62294197250171} + 5426671202560069 \, \sqrt{11} {\left(x + 3\right)} - 16280013607680207 \, x + 27133356012800345}{x}\right) - \sqrt{2794} {\left(49 \, x^{4} - 56 \, x^{3} + 2 \, x^{2} + 8 \, x + 1\right)} \sqrt{-2085440742055 \, \sqrt{11} + 62294197250171} \log\left(\frac{\sqrt{2794} \sqrt{5 \, x^{2} + 2 \, x + 3} {\left(11840590 \, \sqrt{11} + 83479737\right)} \sqrt{-2085440742055 \, \sqrt{11} + 62294197250171} - 5426671202560069 \, \sqrt{11} {\left(x + 3\right)} + 16280013607680207 \, x - 27133356012800345}{x}\right) - 13522960 \, \sqrt{5} {\left(49 \, x^{4} - 56 \, x^{3} + 2 \, x^{2} + 8 \, x + 1\right)} \log\left(\sqrt{5} \sqrt{5 \, x^{2} + 2 \, x + 3} {\left(5 \, x + 1\right)} - 25 \, x^{2} - 10 \, x - 8\right) + 78232 \, {\left(189161 \, x^{3} - 246464 \, x^{2} - 42767 \, x + 7416\right)} \sqrt{5 \, x^{2} + 2 \, x + 3}}{1855350112 \, {\left(49 \, x^{4} - 56 \, x^{3} + 2 \, x^{2} + 8 \, x + 1\right)}}"," ",0,"-1/1855350112*(sqrt(2794)*(49*x^4 - 56*x^3 + 2*x^2 + 8*x + 1)*sqrt(2085440742055*sqrt(11) + 62294197250171)*log((sqrt(2794)*sqrt(5*x^2 + 2*x + 3)*sqrt(2085440742055*sqrt(11) + 62294197250171)*(11840590*sqrt(11) - 83479737) + 5426671202560069*sqrt(11)*(x + 3) + 16280013607680207*x - 27133356012800345)/x) - sqrt(2794)*(49*x^4 - 56*x^3 + 2*x^2 + 8*x + 1)*sqrt(2085440742055*sqrt(11) + 62294197250171)*log(-(sqrt(2794)*sqrt(5*x^2 + 2*x + 3)*sqrt(2085440742055*sqrt(11) + 62294197250171)*(11840590*sqrt(11) - 83479737) - 5426671202560069*sqrt(11)*(x + 3) - 16280013607680207*x + 27133356012800345)/x) + sqrt(2794)*(49*x^4 - 56*x^3 + 2*x^2 + 8*x + 1)*sqrt(-2085440742055*sqrt(11) + 62294197250171)*log(-(sqrt(2794)*sqrt(5*x^2 + 2*x + 3)*(11840590*sqrt(11) + 83479737)*sqrt(-2085440742055*sqrt(11) + 62294197250171) + 5426671202560069*sqrt(11)*(x + 3) - 16280013607680207*x + 27133356012800345)/x) - sqrt(2794)*(49*x^4 - 56*x^3 + 2*x^2 + 8*x + 1)*sqrt(-2085440742055*sqrt(11) + 62294197250171)*log((sqrt(2794)*sqrt(5*x^2 + 2*x + 3)*(11840590*sqrt(11) + 83479737)*sqrt(-2085440742055*sqrt(11) + 62294197250171) - 5426671202560069*sqrt(11)*(x + 3) + 16280013607680207*x - 27133356012800345)/x) - 13522960*sqrt(5)*(49*x^4 - 56*x^3 + 2*x^2 + 8*x + 1)*log(sqrt(5)*sqrt(5*x^2 + 2*x + 3)*(5*x + 1) - 25*x^2 - 10*x - 8) + 78232*(189161*x^3 - 246464*x^2 - 42767*x + 7416)*sqrt(5*x^2 + 2*x + 3))/(49*x^4 - 56*x^3 + 2*x^2 + 8*x + 1)","B",0
386,1,87,0,0.990816," ","integrate((-7*x^2+4*x+1)^3*(x^2+5*x+2)/(5*x^2+2*x+3)^(1/2),x, algorithm=""fricas"")","-\frac{1}{3750000} \, {\left(32156250 \, x^{7} + 106968750 \, x^{6} - 326987500 \, x^{5} + 47807000 \, x^{4} + 387039975 \, x^{3} - 203614255 \, x^{2} - 289653850 \, x + 396379416\right)} \sqrt{5 \, x^{2} + 2 \, x + 3} + \frac{77513689}{6250000} \, \sqrt{5} \log\left(\sqrt{5} \sqrt{5 \, x^{2} + 2 \, x + 3} {\left(5 \, x + 1\right)} - 25 \, x^{2} - 10 \, x - 8\right)"," ",0,"-1/3750000*(32156250*x^7 + 106968750*x^6 - 326987500*x^5 + 47807000*x^4 + 387039975*x^3 - 203614255*x^2 - 289653850*x + 396379416)*sqrt(5*x^2 + 2*x + 3) + 77513689/6250000*sqrt(5)*log(sqrt(5)*sqrt(5*x^2 + 2*x + 3)*(5*x + 1) - 25*x^2 - 10*x - 8)","A",0
387,1,77,0,0.694422," ","integrate((-7*x^2+4*x+1)^2*(x^2+5*x+2)/(5*x^2+2*x+3)^(1/2),x, algorithm=""fricas"")","\frac{1}{187500} \, {\left(306250 \, x^{5} + 1282750 \, x^{4} - 2494425 \, x^{3} - 1037135 \, x^{2} + 3607300 \, x - 132318\right)} \sqrt{5 \, x^{2} + 2 \, x + 3} + \frac{1719097}{312500} \, \sqrt{5} \log\left(\sqrt{5} \sqrt{5 \, x^{2} + 2 \, x + 3} {\left(5 \, x + 1\right)} - 25 \, x^{2} - 10 \, x - 8\right)"," ",0,"1/187500*(306250*x^5 + 1282750*x^4 - 2494425*x^3 - 1037135*x^2 + 3607300*x - 132318)*sqrt(5*x^2 + 2*x + 3) + 1719097/312500*sqrt(5)*log(sqrt(5)*sqrt(5*x^2 + 2*x + 3)*(5*x + 1) - 25*x^2 - 10*x - 8)","A",0
388,1,67,0,0.785212," ","integrate((-7*x^2+4*x+1)*(x^2+5*x+2)/(5*x^2+2*x+3)^(1/2),x, algorithm=""fricas"")","-\frac{1}{1500} \, {\left(525 \, x^{3} + 2855 \, x^{2} - 2950 \, x - 5556\right)} \sqrt{5 \, x^{2} + 2 \, x + 3} + \frac{1901}{2500} \, \sqrt{5} \log\left(\sqrt{5} \sqrt{5 \, x^{2} + 2 \, x + 3} {\left(5 \, x + 1\right)} - 25 \, x^{2} - 10 \, x - 8\right)"," ",0,"-1/1500*(525*x^3 + 2855*x^2 - 2950*x - 5556)*sqrt(5*x^2 + 2*x + 3) + 1901/2500*sqrt(5)*log(sqrt(5)*sqrt(5*x^2 + 2*x + 3)*(5*x + 1) - 25*x^2 - 10*x - 8)","A",0
389,1,297,0,0.414886," ","integrate((x^2+5*x+2)/(-7*x^2+4*x+1)/(5*x^2+2*x+3)^(1/2),x, algorithm=""fricas"")","-\frac{3}{78232} \, \sqrt{2794} \sqrt{1055 \, \sqrt{11} + 4091} \log\left(\frac{3 \, {\left(\sqrt{2794} \sqrt{5 \, x^{2} + 2 \, x + 3} \sqrt{1055 \, \sqrt{11} + 4091} {\left(172 \, \sqrt{11} - 715\right)} + 185801 \, \sqrt{11} {\left(x + 3\right)} + 557403 \, x - 929005\right)}}{x}\right) + \frac{3}{78232} \, \sqrt{2794} \sqrt{1055 \, \sqrt{11} + 4091} \log\left(-\frac{3 \, {\left(\sqrt{2794} \sqrt{5 \, x^{2} + 2 \, x + 3} \sqrt{1055 \, \sqrt{11} + 4091} {\left(172 \, \sqrt{11} - 715\right)} - 185801 \, \sqrt{11} {\left(x + 3\right)} - 557403 \, x + 929005\right)}}{x}\right) - \frac{1}{78232} \, \sqrt{2794} \sqrt{-9495 \, \sqrt{11} + 36819} \log\left(-\frac{\sqrt{2794} \sqrt{5 \, x^{2} + 2 \, x + 3} {\left(172 \, \sqrt{11} + 715\right)} \sqrt{-9495 \, \sqrt{11} + 36819} + 557403 \, \sqrt{11} {\left(x + 3\right)} - 1672209 \, x + 2787015}{x}\right) + \frac{1}{78232} \, \sqrt{2794} \sqrt{-9495 \, \sqrt{11} + 36819} \log\left(\frac{\sqrt{2794} \sqrt{5 \, x^{2} + 2 \, x + 3} {\left(172 \, \sqrt{11} + 715\right)} \sqrt{-9495 \, \sqrt{11} + 36819} - 557403 \, \sqrt{11} {\left(x + 3\right)} + 1672209 \, x - 2787015}{x}\right) + \frac{1}{70} \, \sqrt{5} \log\left(\sqrt{5} \sqrt{5 \, x^{2} + 2 \, x + 3} {\left(5 \, x + 1\right)} - 25 \, x^{2} - 10 \, x - 8\right)"," ",0,"-3/78232*sqrt(2794)*sqrt(1055*sqrt(11) + 4091)*log(3*(sqrt(2794)*sqrt(5*x^2 + 2*x + 3)*sqrt(1055*sqrt(11) + 4091)*(172*sqrt(11) - 715) + 185801*sqrt(11)*(x + 3) + 557403*x - 929005)/x) + 3/78232*sqrt(2794)*sqrt(1055*sqrt(11) + 4091)*log(-3*(sqrt(2794)*sqrt(5*x^2 + 2*x + 3)*sqrt(1055*sqrt(11) + 4091)*(172*sqrt(11) - 715) - 185801*sqrt(11)*(x + 3) - 557403*x + 929005)/x) - 1/78232*sqrt(2794)*sqrt(-9495*sqrt(11) + 36819)*log(-(sqrt(2794)*sqrt(5*x^2 + 2*x + 3)*(172*sqrt(11) + 715)*sqrt(-9495*sqrt(11) + 36819) + 557403*sqrt(11)*(x + 3) - 1672209*x + 2787015)/x) + 1/78232*sqrt(2794)*sqrt(-9495*sqrt(11) + 36819)*log((sqrt(2794)*sqrt(5*x^2 + 2*x + 3)*(172*sqrt(11) + 715)*sqrt(-9495*sqrt(11) + 36819) - 557403*sqrt(11)*(x + 3) + 1672209*x - 2787015)/x) + 1/70*sqrt(5)*log(sqrt(5)*sqrt(5*x^2 + 2*x + 3)*(5*x + 1) - 25*x^2 - 10*x - 8)","B",0
390,1,330,0,0.576191," ","integrate((x^2+5*x+2)/(-7*x^2+4*x+1)^2/(5*x^2+2*x+3)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{2794} {\left(7 \, x^{2} - 4 \, x - 1\right)} \sqrt{14035681 \, \sqrt{11} + 3027900955} \log\left(-\frac{\sqrt{2794} \sqrt{5 \, x^{2} + 2 \, x + 3} \sqrt{14035681 \, \sqrt{11} + 3027900955} {\left(71796 \, \sqrt{11} + 567523\right)} + 265381033753 \, \sqrt{11} {\left(x + 3\right)} - 796143101259 \, x + 1326905168765}{x}\right) - \sqrt{2794} {\left(7 \, x^{2} - 4 \, x - 1\right)} \sqrt{14035681 \, \sqrt{11} + 3027900955} \log\left(\frac{\sqrt{2794} \sqrt{5 \, x^{2} + 2 \, x + 3} \sqrt{14035681 \, \sqrt{11} + 3027900955} {\left(71796 \, \sqrt{11} + 567523\right)} - 265381033753 \, \sqrt{11} {\left(x + 3\right)} + 796143101259 \, x - 1326905168765}{x}\right) + \sqrt{2794} {\left(7 \, x^{2} - 4 \, x - 1\right)} \sqrt{-14035681 \, \sqrt{11} + 3027900955} \log\left(\frac{\sqrt{2794} \sqrt{5 \, x^{2} + 2 \, x + 3} {\left(71796 \, \sqrt{11} - 567523\right)} \sqrt{-14035681 \, \sqrt{11} + 3027900955} + 265381033753 \, \sqrt{11} {\left(x + 3\right)} + 796143101259 \, x - 1326905168765}{x}\right) - \sqrt{2794} {\left(7 \, x^{2} - 4 \, x - 1\right)} \sqrt{-14035681 \, \sqrt{11} + 3027900955} \log\left(-\frac{\sqrt{2794} \sqrt{5 \, x^{2} + 2 \, x + 3} {\left(71796 \, \sqrt{11} - 567523\right)} \sqrt{-14035681 \, \sqrt{11} + 3027900955} - 265381033753 \, \sqrt{11} {\left(x + 3\right)} - 796143101259 \, x + 1326905168765}{x}\right) + 33528 \, \sqrt{5 \, x^{2} + 2 \, x + 3} {\left(371 \, x - 40\right)}}{62451488 \, {\left(7 \, x^{2} - 4 \, x - 1\right)}}"," ",0,"-1/62451488*(sqrt(2794)*(7*x^2 - 4*x - 1)*sqrt(14035681*sqrt(11) + 3027900955)*log(-(sqrt(2794)*sqrt(5*x^2 + 2*x + 3)*sqrt(14035681*sqrt(11) + 3027900955)*(71796*sqrt(11) + 567523) + 265381033753*sqrt(11)*(x + 3) - 796143101259*x + 1326905168765)/x) - sqrt(2794)*(7*x^2 - 4*x - 1)*sqrt(14035681*sqrt(11) + 3027900955)*log((sqrt(2794)*sqrt(5*x^2 + 2*x + 3)*sqrt(14035681*sqrt(11) + 3027900955)*(71796*sqrt(11) + 567523) - 265381033753*sqrt(11)*(x + 3) + 796143101259*x - 1326905168765)/x) + sqrt(2794)*(7*x^2 - 4*x - 1)*sqrt(-14035681*sqrt(11) + 3027900955)*log((sqrt(2794)*sqrt(5*x^2 + 2*x + 3)*(71796*sqrt(11) - 567523)*sqrt(-14035681*sqrt(11) + 3027900955) + 265381033753*sqrt(11)*(x + 3) + 796143101259*x - 1326905168765)/x) - sqrt(2794)*(7*x^2 - 4*x - 1)*sqrt(-14035681*sqrt(11) + 3027900955)*log(-(sqrt(2794)*sqrt(5*x^2 + 2*x + 3)*(71796*sqrt(11) - 567523)*sqrt(-14035681*sqrt(11) + 3027900955) - 265381033753*sqrt(11)*(x + 3) - 796143101259*x + 1326905168765)/x) + 33528*sqrt(5*x^2 + 2*x + 3)*(371*x - 40))/(7*x^2 - 4*x - 1)","B",0
391,1,390,0,0.851189," ","integrate((x^2+5*x+2)/(-7*x^2+4*x+1)^3/(5*x^2+2*x+3)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{2794} {\left(49 \, x^{4} - 56 \, x^{3} + 2 \, x^{2} + 8 \, x + 1\right)} \sqrt{1283973697005131 \, \sqrt{11} + 82616280769148425} \log\left(-\frac{\sqrt{2794} \sqrt{5 \, x^{2} + 2 \, x + 3} \sqrt{1283973697005131 \, \sqrt{11} + 82616280769148425} {\left(358684877 \, \sqrt{11} + 2940638404\right)} + 7232150972206110797 \, \sqrt{11} {\left(x + 3\right)} - 21696452916618332391 \, x + 36160754861030553985}{x}\right) - \sqrt{2794} {\left(49 \, x^{4} - 56 \, x^{3} + 2 \, x^{2} + 8 \, x + 1\right)} \sqrt{1283973697005131 \, \sqrt{11} + 82616280769148425} \log\left(\frac{\sqrt{2794} \sqrt{5 \, x^{2} + 2 \, x + 3} \sqrt{1283973697005131 \, \sqrt{11} + 82616280769148425} {\left(358684877 \, \sqrt{11} + 2940638404\right)} - 7232150972206110797 \, \sqrt{11} {\left(x + 3\right)} + 21696452916618332391 \, x - 36160754861030553985}{x}\right) + \sqrt{2794} {\left(49 \, x^{4} - 56 \, x^{3} + 2 \, x^{2} + 8 \, x + 1\right)} \sqrt{-1283973697005131 \, \sqrt{11} + 82616280769148425} \log\left(\frac{\sqrt{2794} \sqrt{5 \, x^{2} + 2 \, x + 3} {\left(358684877 \, \sqrt{11} - 2940638404\right)} \sqrt{-1283973697005131 \, \sqrt{11} + 82616280769148425} + 7232150972206110797 \, \sqrt{11} {\left(x + 3\right)} + 21696452916618332391 \, x - 36160754861030553985}{x}\right) - \sqrt{2794} {\left(49 \, x^{4} - 56 \, x^{3} + 2 \, x^{2} + 8 \, x + 1\right)} \sqrt{-1283973697005131 \, \sqrt{11} + 82616280769148425} \log\left(-\frac{\sqrt{2794} \sqrt{5 \, x^{2} + 2 \, x + 3} {\left(358684877 \, \sqrt{11} - 2940638404\right)} \sqrt{-1283973697005131 \, \sqrt{11} + 82616280769148425} - 7232150972206110797 \, \sqrt{11} {\left(x + 3\right)} - 21696452916618332391 \, x + 36160754861030553985}{x}\right) + 11176 \, {\left(58279130 \, x^{3} - 53381041 \, x^{2} - 3071502 \, x + 3538943\right)} \sqrt{5 \, x^{2} + 2 \, x + 3}}{697957829888 \, {\left(49 \, x^{4} - 56 \, x^{3} + 2 \, x^{2} + 8 \, x + 1\right)}}"," ",0,"-1/697957829888*(sqrt(2794)*(49*x^4 - 56*x^3 + 2*x^2 + 8*x + 1)*sqrt(1283973697005131*sqrt(11) + 82616280769148425)*log(-(sqrt(2794)*sqrt(5*x^2 + 2*x + 3)*sqrt(1283973697005131*sqrt(11) + 82616280769148425)*(358684877*sqrt(11) + 2940638404) + 7232150972206110797*sqrt(11)*(x + 3) - 21696452916618332391*x + 36160754861030553985)/x) - sqrt(2794)*(49*x^4 - 56*x^3 + 2*x^2 + 8*x + 1)*sqrt(1283973697005131*sqrt(11) + 82616280769148425)*log((sqrt(2794)*sqrt(5*x^2 + 2*x + 3)*sqrt(1283973697005131*sqrt(11) + 82616280769148425)*(358684877*sqrt(11) + 2940638404) - 7232150972206110797*sqrt(11)*(x + 3) + 21696452916618332391*x - 36160754861030553985)/x) + sqrt(2794)*(49*x^4 - 56*x^3 + 2*x^2 + 8*x + 1)*sqrt(-1283973697005131*sqrt(11) + 82616280769148425)*log((sqrt(2794)*sqrt(5*x^2 + 2*x + 3)*(358684877*sqrt(11) - 2940638404)*sqrt(-1283973697005131*sqrt(11) + 82616280769148425) + 7232150972206110797*sqrt(11)*(x + 3) + 21696452916618332391*x - 36160754861030553985)/x) - sqrt(2794)*(49*x^4 - 56*x^3 + 2*x^2 + 8*x + 1)*sqrt(-1283973697005131*sqrt(11) + 82616280769148425)*log(-(sqrt(2794)*sqrt(5*x^2 + 2*x + 3)*(358684877*sqrt(11) - 2940638404)*sqrt(-1283973697005131*sqrt(11) + 82616280769148425) - 7232150972206110797*sqrt(11)*(x + 3) - 21696452916618332391*x + 36160754861030553985)/x) + 11176*(58279130*x^3 - 53381041*x^2 - 3071502*x + 3538943)*sqrt(5*x^2 + 2*x + 3))/(49*x^4 - 56*x^3 + 2*x^2 + 8*x + 1)","B",0
392,1,112,0,0.844597," ","integrate((-7*x^2+4*x+1)^3*(x^2+5*x+2)/(5*x^2+2*x+3)^(3/2),x, algorithm=""fricas"")","\frac{1051000797 \, \sqrt{5} {\left(5 \, x^{2} + 2 \, x + 3\right)} \log\left(-\sqrt{5} \sqrt{5 \, x^{2} + 2 \, x + 3} {\left(5 \, x + 1\right)} - 25 \, x^{2} - 10 \, x - 8\right) - 5 \, {\left(75031250 \, x^{7} + 256821250 \, x^{6} - 897612625 \, x^{5} + 174819575 \, x^{4} + 1795638985 \, x^{3} - 2135143465 \, x^{2} + 1045703388 \, x - 3155769618\right)} \sqrt{5 \, x^{2} + 2 \, x + 3}}{32812500 \, {\left(5 \, x^{2} + 2 \, x + 3\right)}}"," ",0,"1/32812500*(1051000797*sqrt(5)*(5*x^2 + 2*x + 3)*log(-sqrt(5)*sqrt(5*x^2 + 2*x + 3)*(5*x + 1) - 25*x^2 - 10*x - 8) - 5*(75031250*x^7 + 256821250*x^6 - 897612625*x^5 + 174819575*x^4 + 1795638985*x^3 - 2135143465*x^2 + 1045703388*x - 3155769618)*sqrt(5*x^2 + 2*x + 3))/(5*x^2 + 2*x + 3)","A",0
393,1,102,0,0.872268," ","integrate((-7*x^2+4*x+1)^2*(x^2+5*x+2)/(5*x^2+2*x+3)^(3/2),x, algorithm=""fricas"")","\frac{627081 \, \sqrt{5} {\left(5 \, x^{2} + 2 \, x + 3\right)} \log\left(-\sqrt{5} \sqrt{5 \, x^{2} + 2 \, x + 3} {\left(5 \, x + 1\right)} - 25 \, x^{2} - 10 \, x - 8\right) + 5 \, {\left(42875 \, x^{5} + 194775 \, x^{4} - 515655 \, x^{3} - 280805 \, x^{2} - 1298674 \, x - 168536\right)} \sqrt{5 \, x^{2} + 2 \, x + 3}}{87500 \, {\left(5 \, x^{2} + 2 \, x + 3\right)}}"," ",0,"1/87500*(627081*sqrt(5)*(5*x^2 + 2*x + 3)*log(-sqrt(5)*sqrt(5*x^2 + 2*x + 3)*(5*x + 1) - 25*x^2 - 10*x - 8) + 5*(42875*x^5 + 194775*x^4 - 515655*x^3 - 280805*x^2 - 1298674*x - 168536)*sqrt(5*x^2 + 2*x + 3))/(5*x^2 + 2*x + 3)","A",0
394,1,92,0,0.701134," ","integrate((-7*x^2+4*x+1)*(x^2+5*x+2)/(5*x^2+2*x+3)^(3/2),x, algorithm=""fricas"")","\frac{1043 \, \sqrt{5} {\left(5 \, x^{2} + 2 \, x + 3\right)} \log\left(-\sqrt{5} \sqrt{5 \, x^{2} + 2 \, x + 3} {\left(5 \, x + 1\right)} - 25 \, x^{2} - 10 \, x - 8\right) - 5 \, {\left(245 \, x^{3} + 1925 \, x^{2} + 2837 \, x + 2953\right)} \sqrt{5 \, x^{2} + 2 \, x + 3}}{1750 \, {\left(5 \, x^{2} + 2 \, x + 3\right)}}"," ",0,"1/1750*(1043*sqrt(5)*(5*x^2 + 2*x + 3)*log(-sqrt(5)*sqrt(5*x^2 + 2*x + 3)*(5*x + 1) - 25*x^2 - 10*x - 8) - 5*(245*x^3 + 1925*x^2 + 2837*x + 2953)*sqrt(5*x^2 + 2*x + 3))/(5*x^2 + 2*x + 3)","A",0
395,1,333,0,0.776337," ","integrate((x^2+5*x+2)/(-7*x^2+4*x+1)/(5*x^2+2*x+3)^(3/2),x, algorithm=""fricas"")","-\frac{21 \, \sqrt{1397} {\left(5 \, x^{2} + 2 \, x + 3\right)} \sqrt{25015 \, \sqrt{11} + 281693} \log\left(\frac{3 \, {\left(\sqrt{1397} \sqrt{5 \, x^{2} + 2 \, x + 3} \sqrt{25015 \, \sqrt{11} + 281693} {\left(1335 \, \sqrt{11} - 8173\right)} + 23596727 \, \sqrt{11} {\left(x + 3\right)} + 70790181 \, x - 117983635\right)}}{x}\right) - 21 \, \sqrt{1397} {\left(5 \, x^{2} + 2 \, x + 3\right)} \sqrt{25015 \, \sqrt{11} + 281693} \log\left(-\frac{3 \, {\left(\sqrt{1397} \sqrt{5 \, x^{2} + 2 \, x + 3} \sqrt{25015 \, \sqrt{11} + 281693} {\left(1335 \, \sqrt{11} - 8173\right)} - 23596727 \, \sqrt{11} {\left(x + 3\right)} - 70790181 \, x + 117983635\right)}}{x}\right) + 7 \, \sqrt{1397} {\left(5 \, x^{2} + 2 \, x + 3\right)} \sqrt{-225135 \, \sqrt{11} + 2535237} \log\left(-\frac{\sqrt{1397} \sqrt{5 \, x^{2} + 2 \, x + 3} {\left(1335 \, \sqrt{11} + 8173\right)} \sqrt{-225135 \, \sqrt{11} + 2535237} + 70790181 \, \sqrt{11} {\left(x + 3\right)} - 212370543 \, x + 353950905}{x}\right) - 7 \, \sqrt{1397} {\left(5 \, x^{2} + 2 \, x + 3\right)} \sqrt{-225135 \, \sqrt{11} + 2535237} \log\left(\frac{\sqrt{1397} \sqrt{5 \, x^{2} + 2 \, x + 3} {\left(1335 \, \sqrt{11} + 8173\right)} \sqrt{-225135 \, \sqrt{11} + 2535237} - 70790181 \, \sqrt{11} {\left(x + 3\right)} + 212370543 \, x - 353950905}{x}\right) - 5588 \, \sqrt{5 \, x^{2} + 2 \, x + 3} {\left(605 \, x - 131\right)}}{19870928 \, {\left(5 \, x^{2} + 2 \, x + 3\right)}}"," ",0,"-1/19870928*(21*sqrt(1397)*(5*x^2 + 2*x + 3)*sqrt(25015*sqrt(11) + 281693)*log(3*(sqrt(1397)*sqrt(5*x^2 + 2*x + 3)*sqrt(25015*sqrt(11) + 281693)*(1335*sqrt(11) - 8173) + 23596727*sqrt(11)*(x + 3) + 70790181*x - 117983635)/x) - 21*sqrt(1397)*(5*x^2 + 2*x + 3)*sqrt(25015*sqrt(11) + 281693)*log(-3*(sqrt(1397)*sqrt(5*x^2 + 2*x + 3)*sqrt(25015*sqrt(11) + 281693)*(1335*sqrt(11) - 8173) - 23596727*sqrt(11)*(x + 3) - 70790181*x + 117983635)/x) + 7*sqrt(1397)*(5*x^2 + 2*x + 3)*sqrt(-225135*sqrt(11) + 2535237)*log(-(sqrt(1397)*sqrt(5*x^2 + 2*x + 3)*(1335*sqrt(11) + 8173)*sqrt(-225135*sqrt(11) + 2535237) + 70790181*sqrt(11)*(x + 3) - 212370543*x + 353950905)/x) - 7*sqrt(1397)*(5*x^2 + 2*x + 3)*sqrt(-225135*sqrt(11) + 2535237)*log((sqrt(1397)*sqrt(5*x^2 + 2*x + 3)*(1335*sqrt(11) + 8173)*sqrt(-225135*sqrt(11) + 2535237) - 70790181*sqrt(11)*(x + 3) + 212370543*x - 353950905)/x) - 5588*sqrt(5*x^2 + 2*x + 3)*(605*x - 131))/(5*x^2 + 2*x + 3)","B",0
396,1,392,0,0.618332," ","integrate((x^2+5*x+2)/(-7*x^2+4*x+1)^2/(5*x^2+2*x+3)^(3/2),x, algorithm=""fricas"")","-\frac{7 \, \sqrt{1397} {\left(35 \, x^{4} - 6 \, x^{3} + 8 \, x^{2} - 14 \, x - 3\right)} \sqrt{4294093814065 \, \sqrt{11} + 35653135368317} \log\left(-\frac{\sqrt{1397} \sqrt{5 \, x^{2} + 2 \, x + 3} \sqrt{4294093814065 \, \sqrt{11} + 35653135368317} {\left(5609479 \, \sqrt{11} + 77949905\right)} + 2865029444171587 \, \sqrt{11} {\left(x + 3\right)} - 8595088332514761 \, x + 14325147220857935}{x}\right) - 7 \, \sqrt{1397} {\left(35 \, x^{4} - 6 \, x^{3} + 8 \, x^{2} - 14 \, x - 3\right)} \sqrt{4294093814065 \, \sqrt{11} + 35653135368317} \log\left(\frac{\sqrt{1397} \sqrt{5 \, x^{2} + 2 \, x + 3} \sqrt{4294093814065 \, \sqrt{11} + 35653135368317} {\left(5609479 \, \sqrt{11} + 77949905\right)} - 2865029444171587 \, \sqrt{11} {\left(x + 3\right)} + 8595088332514761 \, x - 14325147220857935}{x}\right) + 7 \, \sqrt{1397} {\left(35 \, x^{4} - 6 \, x^{3} + 8 \, x^{2} - 14 \, x - 3\right)} \sqrt{-4294093814065 \, \sqrt{11} + 35653135368317} \log\left(\frac{\sqrt{1397} \sqrt{5 \, x^{2} + 2 \, x + 3} {\left(5609479 \, \sqrt{11} - 77949905\right)} \sqrt{-4294093814065 \, \sqrt{11} + 35653135368317} + 2865029444171587 \, \sqrt{11} {\left(x + 3\right)} + 8595088332514761 \, x - 14325147220857935}{x}\right) - 7 \, \sqrt{1397} {\left(35 \, x^{4} - 6 \, x^{3} + 8 \, x^{2} - 14 \, x - 3\right)} \sqrt{-4294093814065 \, \sqrt{11} + 35653135368317} \log\left(-\frac{\sqrt{1397} \sqrt{5 \, x^{2} + 2 \, x + 3} {\left(5609479 \, \sqrt{11} - 77949905\right)} \sqrt{-4294093814065 \, \sqrt{11} + 35653135368317} - 2865029444171587 \, \sqrt{11} {\left(x + 3\right)} - 8595088332514761 \, x + 14325147220857935}{x}\right) + 5588 \, {\left(159285 \, x^{3} + 444949 \, x^{2} + 3628805 \, x - 503287\right)} \sqrt{5 \, x^{2} + 2 \, x + 3}}{111038745664 \, {\left(35 \, x^{4} - 6 \, x^{3} + 8 \, x^{2} - 14 \, x - 3\right)}}"," ",0,"-1/111038745664*(7*sqrt(1397)*(35*x^4 - 6*x^3 + 8*x^2 - 14*x - 3)*sqrt(4294093814065*sqrt(11) + 35653135368317)*log(-(sqrt(1397)*sqrt(5*x^2 + 2*x + 3)*sqrt(4294093814065*sqrt(11) + 35653135368317)*(5609479*sqrt(11) + 77949905) + 2865029444171587*sqrt(11)*(x + 3) - 8595088332514761*x + 14325147220857935)/x) - 7*sqrt(1397)*(35*x^4 - 6*x^3 + 8*x^2 - 14*x - 3)*sqrt(4294093814065*sqrt(11) + 35653135368317)*log((sqrt(1397)*sqrt(5*x^2 + 2*x + 3)*sqrt(4294093814065*sqrt(11) + 35653135368317)*(5609479*sqrt(11) + 77949905) - 2865029444171587*sqrt(11)*(x + 3) + 8595088332514761*x - 14325147220857935)/x) + 7*sqrt(1397)*(35*x^4 - 6*x^3 + 8*x^2 - 14*x - 3)*sqrt(-4294093814065*sqrt(11) + 35653135368317)*log((sqrt(1397)*sqrt(5*x^2 + 2*x + 3)*(5609479*sqrt(11) - 77949905)*sqrt(-4294093814065*sqrt(11) + 35653135368317) + 2865029444171587*sqrt(11)*(x + 3) + 8595088332514761*x - 14325147220857935)/x) - 7*sqrt(1397)*(35*x^4 - 6*x^3 + 8*x^2 - 14*x - 3)*sqrt(-4294093814065*sqrt(11) + 35653135368317)*log(-(sqrt(1397)*sqrt(5*x^2 + 2*x + 3)*(5609479*sqrt(11) - 77949905)*sqrt(-4294093814065*sqrt(11) + 35653135368317) - 2865029444171587*sqrt(11)*(x + 3) - 8595088332514761*x + 14325147220857935)/x) + 5588*(159285*x^3 + 444949*x^2 + 3628805*x - 503287)*sqrt(5*x^2 + 2*x + 3))/(35*x^4 - 6*x^3 + 8*x^2 - 14*x - 3)","B",0
397,1,452,0,1.169800," ","integrate((x^2+5*x+2)/(-7*x^2+4*x+1)^3/(5*x^2+2*x+3)^(3/2),x, algorithm=""fricas"")","-\frac{7 \, \sqrt{1397} {\left(245 \, x^{6} - 182 \, x^{5} + 45 \, x^{4} - 124 \, x^{3} + 27 \, x^{2} + 26 \, x + 3\right)} \sqrt{74693314710639641467 \, \sqrt{11} + 896266498377233657855} \log\left(-\frac{\sqrt{1397} \sqrt{5 \, x^{2} + 2 \, x + 3} \sqrt{74693314710639641467 \, \sqrt{11} + 896266498377233657855} {\left(37271563201 \, \sqrt{11} + 407780707037\right)} + 75502120686844055144479 \, \sqrt{11} {\left(x + 3\right)} - 226506362060532165433437 \, x + 377510603434220275722395}{x}\right) - 7 \, \sqrt{1397} {\left(245 \, x^{6} - 182 \, x^{5} + 45 \, x^{4} - 124 \, x^{3} + 27 \, x^{2} + 26 \, x + 3\right)} \sqrt{74693314710639641467 \, \sqrt{11} + 896266498377233657855} \log\left(\frac{\sqrt{1397} \sqrt{5 \, x^{2} + 2 \, x + 3} \sqrt{74693314710639641467 \, \sqrt{11} + 896266498377233657855} {\left(37271563201 \, \sqrt{11} + 407780707037\right)} - 75502120686844055144479 \, \sqrt{11} {\left(x + 3\right)} + 226506362060532165433437 \, x - 377510603434220275722395}{x}\right) + 7 \, \sqrt{1397} {\left(245 \, x^{6} - 182 \, x^{5} + 45 \, x^{4} - 124 \, x^{3} + 27 \, x^{2} + 26 \, x + 3\right)} \sqrt{-74693314710639641467 \, \sqrt{11} + 896266498377233657855} \log\left(\frac{\sqrt{1397} \sqrt{5 \, x^{2} + 2 \, x + 3} {\left(37271563201 \, \sqrt{11} - 407780707037\right)} \sqrt{-74693314710639641467 \, \sqrt{11} + 896266498377233657855} + 75502120686844055144479 \, \sqrt{11} {\left(x + 3\right)} + 226506362060532165433437 \, x - 377510603434220275722395}{x}\right) - 7 \, \sqrt{1397} {\left(245 \, x^{6} - 182 \, x^{5} + 45 \, x^{4} - 124 \, x^{3} + 27 \, x^{2} + 26 \, x + 3\right)} \sqrt{-74693314710639641467 \, \sqrt{11} + 896266498377233657855} \log\left(-\frac{\sqrt{1397} \sqrt{5 \, x^{2} + 2 \, x + 3} {\left(37271563201 \, \sqrt{11} - 407780707037\right)} \sqrt{-74693314710639641467 \, \sqrt{11} + 896266498377233657855} - 75502120686844055144479 \, \sqrt{11} {\left(x + 3\right)} - 226506362060532165433437 \, x + 377510603434220275722395}{x}\right) + 5588 \, {\left(274089186875 \, x^{5} - 200208943655 \, x^{4} + 109737266678 \, x^{3} - 148022158802 \, x^{2} + 7828199499 \, x + 14298727813\right)} \sqrt{5 \, x^{2} + 2 \, x + 3}}{1240969021540864 \, {\left(245 \, x^{6} - 182 \, x^{5} + 45 \, x^{4} - 124 \, x^{3} + 27 \, x^{2} + 26 \, x + 3\right)}}"," ",0,"-1/1240969021540864*(7*sqrt(1397)*(245*x^6 - 182*x^5 + 45*x^4 - 124*x^3 + 27*x^2 + 26*x + 3)*sqrt(74693314710639641467*sqrt(11) + 896266498377233657855)*log(-(sqrt(1397)*sqrt(5*x^2 + 2*x + 3)*sqrt(74693314710639641467*sqrt(11) + 896266498377233657855)*(37271563201*sqrt(11) + 407780707037) + 75502120686844055144479*sqrt(11)*(x + 3) - 226506362060532165433437*x + 377510603434220275722395)/x) - 7*sqrt(1397)*(245*x^6 - 182*x^5 + 45*x^4 - 124*x^3 + 27*x^2 + 26*x + 3)*sqrt(74693314710639641467*sqrt(11) + 896266498377233657855)*log((sqrt(1397)*sqrt(5*x^2 + 2*x + 3)*sqrt(74693314710639641467*sqrt(11) + 896266498377233657855)*(37271563201*sqrt(11) + 407780707037) - 75502120686844055144479*sqrt(11)*(x + 3) + 226506362060532165433437*x - 377510603434220275722395)/x) + 7*sqrt(1397)*(245*x^6 - 182*x^5 + 45*x^4 - 124*x^3 + 27*x^2 + 26*x + 3)*sqrt(-74693314710639641467*sqrt(11) + 896266498377233657855)*log((sqrt(1397)*sqrt(5*x^2 + 2*x + 3)*(37271563201*sqrt(11) - 407780707037)*sqrt(-74693314710639641467*sqrt(11) + 896266498377233657855) + 75502120686844055144479*sqrt(11)*(x + 3) + 226506362060532165433437*x - 377510603434220275722395)/x) - 7*sqrt(1397)*(245*x^6 - 182*x^5 + 45*x^4 - 124*x^3 + 27*x^2 + 26*x + 3)*sqrt(-74693314710639641467*sqrt(11) + 896266498377233657855)*log(-(sqrt(1397)*sqrt(5*x^2 + 2*x + 3)*(37271563201*sqrt(11) - 407780707037)*sqrt(-74693314710639641467*sqrt(11) + 896266498377233657855) - 75502120686844055144479*sqrt(11)*(x + 3) - 226506362060532165433437*x + 377510603434220275722395)/x) + 5588*(274089186875*x^5 - 200208943655*x^4 + 109737266678*x^3 - 148022158802*x^2 + 7828199499*x + 14298727813)*sqrt(5*x^2 + 2*x + 3))/(245*x^6 - 182*x^5 + 45*x^4 - 124*x^3 + 27*x^2 + 26*x + 3)","B",0
398,0,0,0,0.577029," ","integrate((c*x^2+a)^p*(C*x^2+A)*(f*x^2+d)^q,x, algorithm=""fricas"")","{\rm integral}\left({\left(C x^{2} + A\right)} {\left(c x^{2} + a\right)}^{p} {\left(f x^{2} + d\right)}^{q}, x\right)"," ",0,"integral((C*x^2 + A)*(c*x^2 + a)^p*(f*x^2 + d)^q, x)","F",0
399,0,0,0,0.860579," ","integrate((B*x+A)*(c*x^2+a)^p*(f*x^2+d)^q,x, algorithm=""fricas"")","{\rm integral}\left({\left(B x + A\right)} {\left(c x^{2} + a\right)}^{p} {\left(f x^{2} + d\right)}^{q}, x\right)"," ",0,"integral((B*x + A)*(c*x^2 + a)^p*(f*x^2 + d)^q, x)","F",0
400,0,0,0,0.522218," ","integrate((c*x^2+a)^p*(C*x^2+B*x+A)*(f*x^2+d)^q,x, algorithm=""fricas"")","{\rm integral}\left({\left(C x^{2} + B x + A\right)} {\left(c x^{2} + a\right)}^{p} {\left(f x^{2} + d\right)}^{q}, x\right)"," ",0,"integral((C*x^2 + B*x + A)*(c*x^2 + a)^p*(f*x^2 + d)^q, x)","F",0
