1,1,406,0,0.720844," ","integrate((f*x+e)^3*(C*x^2+B*x+A)*(-d*x+1)^(1/2)*(d*x+1)^(1/2),x, algorithm=""fricas"")","\frac{{\left(240 \, C d^{6} f^{3} x^{6} - 560 \, B d^{4} e^{3} - 672 \, B d^{2} e f^{2} + 280 \, {\left(3 \, C d^{6} e f^{2} + B d^{6} f^{3}\right)} x^{5} + 48 \, {\left(21 \, C d^{6} e^{2} f + 21 \, B d^{6} e f^{2} + {\left(7 \, A d^{6} - C d^{4}\right)} f^{3}\right)} x^{4} - 336 \, {\left(5 \, A d^{4} + 2 \, C d^{2}\right)} e^{2} f - 32 \, {\left(7 \, A d^{2} + 4 \, C\right)} f^{3} + 70 \, {\left(6 \, C d^{6} e^{3} + 18 \, B d^{6} e^{2} f - B d^{4} f^{3} + 3 \, {\left(6 \, A d^{6} - C d^{4}\right)} e f^{2}\right)} x^{3} + 16 \, {\left(35 \, B d^{6} e^{3} - 21 \, B d^{4} e f^{2} + 21 \, {\left(5 \, A d^{6} - C d^{4}\right)} e^{2} f - {\left(7 \, A d^{4} + 4 \, C d^{2}\right)} f^{3}\right)} x^{2} - 105 \, {\left(6 \, B d^{4} e^{2} f + B d^{2} f^{3} - 2 \, {\left(4 \, A d^{6} - C d^{4}\right)} e^{3} + 3 \, {\left(2 \, A d^{4} + C d^{2}\right)} e f^{2}\right)} x\right)} \sqrt{d x + 1} \sqrt{-d x + 1} - 210 \, {\left(6 \, B d^{3} e^{2} f + B d f^{3} + 2 \, {\left(4 \, A d^{5} + C d^{3}\right)} e^{3} + 3 \, {\left(2 \, A d^{3} + C d\right)} e f^{2}\right)} \arctan\left(\frac{\sqrt{d x + 1} \sqrt{-d x + 1} - 1}{d x}\right)}{1680 \, d^{6}}"," ",0,"1/1680*((240*C*d^6*f^3*x^6 - 560*B*d^4*e^3 - 672*B*d^2*e*f^2 + 280*(3*C*d^6*e*f^2 + B*d^6*f^3)*x^5 + 48*(21*C*d^6*e^2*f + 21*B*d^6*e*f^2 + (7*A*d^6 - C*d^4)*f^3)*x^4 - 336*(5*A*d^4 + 2*C*d^2)*e^2*f - 32*(7*A*d^2 + 4*C)*f^3 + 70*(6*C*d^6*e^3 + 18*B*d^6*e^2*f - B*d^4*f^3 + 3*(6*A*d^6 - C*d^4)*e*f^2)*x^3 + 16*(35*B*d^6*e^3 - 21*B*d^4*e*f^2 + 21*(5*A*d^6 - C*d^4)*e^2*f - (7*A*d^4 + 4*C*d^2)*f^3)*x^2 - 105*(6*B*d^4*e^2*f + B*d^2*f^3 - 2*(4*A*d^6 - C*d^4)*e^3 + 3*(2*A*d^4 + C*d^2)*e*f^2)*x)*sqrt(d*x + 1)*sqrt(-d*x + 1) - 210*(6*B*d^3*e^2*f + B*d*f^3 + 2*(4*A*d^5 + C*d^3)*e^3 + 3*(2*A*d^3 + C*d)*e*f^2)*arctan((sqrt(d*x + 1)*sqrt(-d*x + 1) - 1)/(d*x)))/d^6","A",0
2,1,279,0,0.864067," ","integrate((f*x+e)^2*(C*x^2+B*x+A)*(-d*x+1)^(1/2)*(d*x+1)^(1/2),x, algorithm=""fricas"")","\frac{{\left(40 \, C d^{5} f^{2} x^{5} - 80 \, B d^{3} e^{2} + 48 \, {\left(2 \, C d^{5} e f + B d^{5} f^{2}\right)} x^{4} - 32 \, B d f^{2} + 10 \, {\left(6 \, C d^{5} e^{2} + 12 \, B d^{5} e f + {\left(6 \, A d^{5} - C d^{3}\right)} f^{2}\right)} x^{3} - 32 \, {\left(5 \, A d^{3} + 2 \, C d\right)} e f + 16 \, {\left(5 \, B d^{5} e^{2} - B d^{3} f^{2} + 2 \, {\left(5 \, A d^{5} - C d^{3}\right)} e f\right)} x^{2} - 15 \, {\left(4 \, B d^{3} e f - 2 \, {\left(4 \, A d^{5} - C d^{3}\right)} e^{2} + {\left(2 \, A d^{3} + C d\right)} f^{2}\right)} x\right)} \sqrt{d x + 1} \sqrt{-d x + 1} - 30 \, {\left(4 \, B d^{2} e f + 2 \, {\left(4 \, A d^{4} + C d^{2}\right)} e^{2} + {\left(2 \, A d^{2} + C\right)} f^{2}\right)} \arctan\left(\frac{\sqrt{d x + 1} \sqrt{-d x + 1} - 1}{d x}\right)}{240 \, d^{5}}"," ",0,"1/240*((40*C*d^5*f^2*x^5 - 80*B*d^3*e^2 + 48*(2*C*d^5*e*f + B*d^5*f^2)*x^4 - 32*B*d*f^2 + 10*(6*C*d^5*e^2 + 12*B*d^5*e*f + (6*A*d^5 - C*d^3)*f^2)*x^3 - 32*(5*A*d^3 + 2*C*d)*e*f + 16*(5*B*d^5*e^2 - B*d^3*f^2 + 2*(5*A*d^5 - C*d^3)*e*f)*x^2 - 15*(4*B*d^3*e*f - 2*(4*A*d^5 - C*d^3)*e^2 + (2*A*d^3 + C*d)*f^2)*x)*sqrt(d*x + 1)*sqrt(-d*x + 1) - 30*(4*B*d^2*e*f + 2*(4*A*d^4 + C*d^2)*e^2 + (2*A*d^2 + C)*f^2)*arctan((sqrt(d*x + 1)*sqrt(-d*x + 1) - 1)/(d*x)))/d^5","A",0
3,1,170,0,0.927823," ","integrate((f*x+e)*(C*x^2+B*x+A)*(-d*x+1)^(1/2)*(d*x+1)^(1/2),x, algorithm=""fricas"")","\frac{{\left(24 \, C d^{4} f x^{4} - 40 \, B d^{2} e + 30 \, {\left(C d^{4} e + B d^{4} f\right)} x^{3} + 8 \, {\left(5 \, B d^{4} e + {\left(5 \, A d^{4} - C d^{2}\right)} f\right)} x^{2} - 8 \, {\left(5 \, A d^{2} + 2 \, C\right)} f - 15 \, {\left(B d^{2} f - {\left(4 \, A d^{4} - C d^{2}\right)} e\right)} x\right)} \sqrt{d x + 1} \sqrt{-d x + 1} - 30 \, {\left(B d f + {\left(4 \, A d^{3} + C d\right)} e\right)} \arctan\left(\frac{\sqrt{d x + 1} \sqrt{-d x + 1} - 1}{d x}\right)}{120 \, d^{4}}"," ",0,"1/120*((24*C*d^4*f*x^4 - 40*B*d^2*e + 30*(C*d^4*e + B*d^4*f)*x^3 + 8*(5*B*d^4*e + (5*A*d^4 - C*d^2)*f)*x^2 - 8*(5*A*d^2 + 2*C)*f - 15*(B*d^2*f - (4*A*d^4 - C*d^2)*e)*x)*sqrt(d*x + 1)*sqrt(-d*x + 1) - 30*(B*d*f + (4*A*d^3 + C*d)*e)*arctan((sqrt(d*x + 1)*sqrt(-d*x + 1) - 1)/(d*x)))/d^4","A",0
4,1,95,0,0.918374," ","integrate((C*x^2+B*x+A)*(-d*x+1)^(1/2)*(d*x+1)^(1/2),x, algorithm=""fricas"")","\frac{{\left(6 \, C d^{3} x^{3} + 8 \, B d^{3} x^{2} - 8 \, B d + 3 \, {\left(4 \, A d^{3} - C d\right)} x\right)} \sqrt{d x + 1} \sqrt{-d x + 1} - 6 \, {\left(4 \, A d^{2} + C\right)} \arctan\left(\frac{\sqrt{d x + 1} \sqrt{-d x + 1} - 1}{d x}\right)}{24 \, d^{3}}"," ",0,"1/24*((6*C*d^3*x^3 + 8*B*d^3*x^2 - 8*B*d + 3*(4*A*d^3 - C*d)*x)*sqrt(d*x + 1)*sqrt(-d*x + 1) - 6*(4*A*d^2 + C)*arctan((sqrt(d*x + 1)*sqrt(-d*x + 1) - 1)/(d*x)))/d^3","A",0
5,1,493,0,15.664167," ","integrate((C*x^2+B*x+A)/(f*x+e)/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(C d^{2} e^{2} - B d^{2} e f + A d^{2} f^{2}\right)} \sqrt{-d^{2} e^{2} + f^{2}} \log\left(\frac{d^{2} e f x + f^{2} - \sqrt{-d^{2} e^{2} + f^{2}} {\left(d^{2} e x + f\right)} - {\left(\sqrt{-d^{2} e^{2} + f^{2}} \sqrt{-d x + 1} f + {\left(d^{2} e^{2} - f^{2}\right)} \sqrt{-d x + 1}\right)} \sqrt{d x + 1}}{f x + e}\right) + {\left(C d^{2} e^{2} f - C f^{3}\right)} \sqrt{d x + 1} \sqrt{-d x + 1} - 2 \, {\left(C d^{3} e^{3} - B d^{3} e^{2} f - C d e f^{2} + B d f^{3}\right)} \arctan\left(\frac{\sqrt{d x + 1} \sqrt{-d x + 1} - 1}{d x}\right)}{d^{4} e^{2} f^{2} - d^{2} f^{4}}, \frac{2 \, {\left(C d^{2} e^{2} - B d^{2} e f + A d^{2} f^{2}\right)} \sqrt{d^{2} e^{2} - f^{2}} \arctan\left(-\frac{\sqrt{d^{2} e^{2} - f^{2}} \sqrt{d x + 1} \sqrt{-d x + 1} e - \sqrt{d^{2} e^{2} - f^{2}} {\left(f x + e\right)}}{{\left(d^{2} e^{2} - f^{2}\right)} x}\right) - {\left(C d^{2} e^{2} f - C f^{3}\right)} \sqrt{d x + 1} \sqrt{-d x + 1} + 2 \, {\left(C d^{3} e^{3} - B d^{3} e^{2} f - C d e f^{2} + B d f^{3}\right)} \arctan\left(\frac{\sqrt{d x + 1} \sqrt{-d x + 1} - 1}{d x}\right)}{d^{4} e^{2} f^{2} - d^{2} f^{4}}\right]"," ",0,"[-((C*d^2*e^2 - B*d^2*e*f + A*d^2*f^2)*sqrt(-d^2*e^2 + f^2)*log((d^2*e*f*x + f^2 - sqrt(-d^2*e^2 + f^2)*(d^2*e*x + f) - (sqrt(-d^2*e^2 + f^2)*sqrt(-d*x + 1)*f + (d^2*e^2 - f^2)*sqrt(-d*x + 1))*sqrt(d*x + 1))/(f*x + e)) + (C*d^2*e^2*f - C*f^3)*sqrt(d*x + 1)*sqrt(-d*x + 1) - 2*(C*d^3*e^3 - B*d^3*e^2*f - C*d*e*f^2 + B*d*f^3)*arctan((sqrt(d*x + 1)*sqrt(-d*x + 1) - 1)/(d*x)))/(d^4*e^2*f^2 - d^2*f^4), (2*(C*d^2*e^2 - B*d^2*e*f + A*d^2*f^2)*sqrt(d^2*e^2 - f^2)*arctan(-(sqrt(d^2*e^2 - f^2)*sqrt(d*x + 1)*sqrt(-d*x + 1)*e - sqrt(d^2*e^2 - f^2)*(f*x + e))/((d^2*e^2 - f^2)*x)) - (C*d^2*e^2*f - C*f^3)*sqrt(d*x + 1)*sqrt(-d*x + 1) + 2*(C*d^3*e^3 - B*d^3*e^2*f - C*d*e*f^2 + B*d*f^3)*arctan((sqrt(d*x + 1)*sqrt(-d*x + 1) - 1)/(d*x)))/(d^4*e^2*f^2 - d^2*f^4)]","B",0
6,1,1025,0,72.527028," ","integrate((C*x^2+B*x+A)/(f*x+e)^2/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""fricas"")","\left[\frac{C d^{3} e^{5} f - B d^{3} e^{4} f^{2} + B d e^{2} f^{4} - A d e f^{5} + {\left(A d^{3} - C d\right)} e^{3} f^{3} - {\left(C d^{3} e^{5} + B d e^{2} f^{3} - {\left(A d^{3} + 2 \, C d\right)} e^{3} f^{2} + {\left(C d^{3} e^{4} f + B d e f^{4} - {\left(A d^{3} + 2 \, C d\right)} e^{2} f^{3}\right)} x\right)} \sqrt{-d^{2} e^{2} + f^{2}} \log\left(\frac{d^{2} e f x + f^{2} + \sqrt{-d^{2} e^{2} + f^{2}} {\left(d^{2} e x + f\right)} + {\left(\sqrt{-d^{2} e^{2} + f^{2}} \sqrt{-d x + 1} f - {\left(d^{2} e^{2} - f^{2}\right)} \sqrt{-d x + 1}\right)} \sqrt{d x + 1}}{f x + e}\right) + {\left(C d^{3} e^{5} f - B d^{3} e^{4} f^{2} + B d e^{2} f^{4} - A d e f^{5} + {\left(A d^{3} - C d\right)} e^{3} f^{3}\right)} \sqrt{d x + 1} \sqrt{-d x + 1} + {\left(C d^{3} e^{4} f^{2} - B d^{3} e^{3} f^{3} + B d e f^{5} - A d f^{6} + {\left(A d^{3} - C d\right)} e^{2} f^{4}\right)} x - 2 \, {\left(C d^{4} e^{6} - 2 \, C d^{2} e^{4} f^{2} + C e^{2} f^{4} + {\left(C d^{4} e^{5} f - 2 \, C d^{2} e^{3} f^{3} + C e f^{5}\right)} x\right)} \arctan\left(\frac{\sqrt{d x + 1} \sqrt{-d x + 1} - 1}{d x}\right)}{d^{5} e^{6} f^{2} - 2 \, d^{3} e^{4} f^{4} + d e^{2} f^{6} + {\left(d^{5} e^{5} f^{3} - 2 \, d^{3} e^{3} f^{5} + d e f^{7}\right)} x}, \frac{C d^{3} e^{5} f - B d^{3} e^{4} f^{2} + B d e^{2} f^{4} - A d e f^{5} + {\left(A d^{3} - C d\right)} e^{3} f^{3} - 2 \, {\left(C d^{3} e^{5} + B d e^{2} f^{3} - {\left(A d^{3} + 2 \, C d\right)} e^{3} f^{2} + {\left(C d^{3} e^{4} f + B d e f^{4} - {\left(A d^{3} + 2 \, C d\right)} e^{2} f^{3}\right)} x\right)} \sqrt{d^{2} e^{2} - f^{2}} \arctan\left(-\frac{\sqrt{d^{2} e^{2} - f^{2}} \sqrt{d x + 1} \sqrt{-d x + 1} e - \sqrt{d^{2} e^{2} - f^{2}} {\left(f x + e\right)}}{{\left(d^{2} e^{2} - f^{2}\right)} x}\right) + {\left(C d^{3} e^{5} f - B d^{3} e^{4} f^{2} + B d e^{2} f^{4} - A d e f^{5} + {\left(A d^{3} - C d\right)} e^{3} f^{3}\right)} \sqrt{d x + 1} \sqrt{-d x + 1} + {\left(C d^{3} e^{4} f^{2} - B d^{3} e^{3} f^{3} + B d e f^{5} - A d f^{6} + {\left(A d^{3} - C d\right)} e^{2} f^{4}\right)} x - 2 \, {\left(C d^{4} e^{6} - 2 \, C d^{2} e^{4} f^{2} + C e^{2} f^{4} + {\left(C d^{4} e^{5} f - 2 \, C d^{2} e^{3} f^{3} + C e f^{5}\right)} x\right)} \arctan\left(\frac{\sqrt{d x + 1} \sqrt{-d x + 1} - 1}{d x}\right)}{d^{5} e^{6} f^{2} - 2 \, d^{3} e^{4} f^{4} + d e^{2} f^{6} + {\left(d^{5} e^{5} f^{3} - 2 \, d^{3} e^{3} f^{5} + d e f^{7}\right)} x}\right]"," ",0,"[(C*d^3*e^5*f - B*d^3*e^4*f^2 + B*d*e^2*f^4 - A*d*e*f^5 + (A*d^3 - C*d)*e^3*f^3 - (C*d^3*e^5 + B*d*e^2*f^3 - (A*d^3 + 2*C*d)*e^3*f^2 + (C*d^3*e^4*f + B*d*e*f^4 - (A*d^3 + 2*C*d)*e^2*f^3)*x)*sqrt(-d^2*e^2 + f^2)*log((d^2*e*f*x + f^2 + sqrt(-d^2*e^2 + f^2)*(d^2*e*x + f) + (sqrt(-d^2*e^2 + f^2)*sqrt(-d*x + 1)*f - (d^2*e^2 - f^2)*sqrt(-d*x + 1))*sqrt(d*x + 1))/(f*x + e)) + (C*d^3*e^5*f - B*d^3*e^4*f^2 + B*d*e^2*f^4 - A*d*e*f^5 + (A*d^3 - C*d)*e^3*f^3)*sqrt(d*x + 1)*sqrt(-d*x + 1) + (C*d^3*e^4*f^2 - B*d^3*e^3*f^3 + B*d*e*f^5 - A*d*f^6 + (A*d^3 - C*d)*e^2*f^4)*x - 2*(C*d^4*e^6 - 2*C*d^2*e^4*f^2 + C*e^2*f^4 + (C*d^4*e^5*f - 2*C*d^2*e^3*f^3 + C*e*f^5)*x)*arctan((sqrt(d*x + 1)*sqrt(-d*x + 1) - 1)/(d*x)))/(d^5*e^6*f^2 - 2*d^3*e^4*f^4 + d*e^2*f^6 + (d^5*e^5*f^3 - 2*d^3*e^3*f^5 + d*e*f^7)*x), (C*d^3*e^5*f - B*d^3*e^4*f^2 + B*d*e^2*f^4 - A*d*e*f^5 + (A*d^3 - C*d)*e^3*f^3 - 2*(C*d^3*e^5 + B*d*e^2*f^3 - (A*d^3 + 2*C*d)*e^3*f^2 + (C*d^3*e^4*f + B*d*e*f^4 - (A*d^3 + 2*C*d)*e^2*f^3)*x)*sqrt(d^2*e^2 - f^2)*arctan(-(sqrt(d^2*e^2 - f^2)*sqrt(d*x + 1)*sqrt(-d*x + 1)*e - sqrt(d^2*e^2 - f^2)*(f*x + e))/((d^2*e^2 - f^2)*x)) + (C*d^3*e^5*f - B*d^3*e^4*f^2 + B*d*e^2*f^4 - A*d*e*f^5 + (A*d^3 - C*d)*e^3*f^3)*sqrt(d*x + 1)*sqrt(-d*x + 1) + (C*d^3*e^4*f^2 - B*d^3*e^3*f^3 + B*d*e*f^5 - A*d*f^6 + (A*d^3 - C*d)*e^2*f^4)*x - 2*(C*d^4*e^6 - 2*C*d^2*e^4*f^2 + C*e^2*f^4 + (C*d^4*e^5*f - 2*C*d^2*e^3*f^3 + C*e*f^5)*x)*arctan((sqrt(d*x + 1)*sqrt(-d*x + 1) - 1)/(d*x)))/(d^5*e^6*f^2 - 2*d^3*e^4*f^4 + d*e^2*f^6 + (d^5*e^5*f^3 - 2*d^3*e^3*f^5 + d*e*f^7)*x)]","B",0
7,1,1580,0,1.238498," ","integrate((C*x^2+B*x+A)/(f*x+e)^3/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""fricas"")","\left[-\frac{2 \, B d^{4} e^{7} - B d^{2} e^{5} f^{2} - {\left(4 \, A d^{4} + 3 \, C d^{2}\right)} e^{6} f + {\left(5 \, A d^{2} + 3 \, C\right)} e^{4} f^{3} - B e^{3} f^{4} - A e^{2} f^{5} + {\left(2 \, B d^{4} e^{5} f^{2} - B d^{2} e^{3} f^{4} - {\left(4 \, A d^{4} + 3 \, C d^{2}\right)} e^{4} f^{3} + {\left(5 \, A d^{2} + 3 \, C\right)} e^{2} f^{5} - B e f^{6} - A f^{7}\right)} x^{2} - {\left(3 \, B d^{2} e^{5} f - {\left(2 \, A d^{4} + C d^{2}\right)} e^{6} - {\left(A d^{2} + 2 \, C\right)} e^{4} f^{2} + {\left(3 \, B d^{2} e^{3} f^{3} - {\left(2 \, A d^{4} + C d^{2}\right)} e^{4} f^{2} - {\left(A d^{2} + 2 \, C\right)} e^{2} f^{4}\right)} x^{2} + 2 \, {\left(3 \, B d^{2} e^{4} f^{2} - {\left(2 \, A d^{4} + C d^{2}\right)} e^{5} f - {\left(A d^{2} + 2 \, C\right)} e^{3} f^{3}\right)} x\right)} \sqrt{-d^{2} e^{2} + f^{2}} \log\left(\frac{d^{2} e f x + f^{2} - \sqrt{-d^{2} e^{2} + f^{2}} {\left(d^{2} e x + f\right)} - {\left(\sqrt{-d^{2} e^{2} + f^{2}} \sqrt{-d x + 1} f + {\left(d^{2} e^{2} - f^{2}\right)} \sqrt{-d x + 1}\right)} \sqrt{d x + 1}}{f x + e}\right) + {\left(2 \, B d^{4} e^{7} - B d^{2} e^{5} f^{2} - {\left(4 \, A d^{4} + 3 \, C d^{2}\right)} e^{6} f + {\left(5 \, A d^{2} + 3 \, C\right)} e^{4} f^{3} - B e^{3} f^{4} - A e^{2} f^{5} + {\left(C d^{4} e^{7} + B d^{4} e^{6} f + B d^{2} e^{4} f^{3} - {\left(3 \, A d^{4} + 5 \, C d^{2}\right)} e^{5} f^{2} + {\left(3 \, A d^{2} + 4 \, C\right)} e^{3} f^{4} - 2 \, B e^{2} f^{5}\right)} x\right)} \sqrt{d x + 1} \sqrt{-d x + 1} + 2 \, {\left(2 \, B d^{4} e^{6} f - B d^{2} e^{4} f^{3} - {\left(4 \, A d^{4} + 3 \, C d^{2}\right)} e^{5} f^{2} + {\left(5 \, A d^{2} + 3 \, C\right)} e^{3} f^{4} - B e^{2} f^{5} - A e f^{6}\right)} x}{2 \, {\left(d^{6} e^{10} - 3 \, d^{4} e^{8} f^{2} + 3 \, d^{2} e^{6} f^{4} - e^{4} f^{6} + {\left(d^{6} e^{8} f^{2} - 3 \, d^{4} e^{6} f^{4} + 3 \, d^{2} e^{4} f^{6} - e^{2} f^{8}\right)} x^{2} + 2 \, {\left(d^{6} e^{9} f - 3 \, d^{4} e^{7} f^{3} + 3 \, d^{2} e^{5} f^{5} - e^{3} f^{7}\right)} x\right)}}, -\frac{2 \, B d^{4} e^{7} - B d^{2} e^{5} f^{2} - {\left(4 \, A d^{4} + 3 \, C d^{2}\right)} e^{6} f + {\left(5 \, A d^{2} + 3 \, C\right)} e^{4} f^{3} - B e^{3} f^{4} - A e^{2} f^{5} + {\left(2 \, B d^{4} e^{5} f^{2} - B d^{2} e^{3} f^{4} - {\left(4 \, A d^{4} + 3 \, C d^{2}\right)} e^{4} f^{3} + {\left(5 \, A d^{2} + 3 \, C\right)} e^{2} f^{5} - B e f^{6} - A f^{7}\right)} x^{2} + 2 \, {\left(3 \, B d^{2} e^{5} f - {\left(2 \, A d^{4} + C d^{2}\right)} e^{6} - {\left(A d^{2} + 2 \, C\right)} e^{4} f^{2} + {\left(3 \, B d^{2} e^{3} f^{3} - {\left(2 \, A d^{4} + C d^{2}\right)} e^{4} f^{2} - {\left(A d^{2} + 2 \, C\right)} e^{2} f^{4}\right)} x^{2} + 2 \, {\left(3 \, B d^{2} e^{4} f^{2} - {\left(2 \, A d^{4} + C d^{2}\right)} e^{5} f - {\left(A d^{2} + 2 \, C\right)} e^{3} f^{3}\right)} x\right)} \sqrt{d^{2} e^{2} - f^{2}} \arctan\left(-\frac{\sqrt{d^{2} e^{2} - f^{2}} \sqrt{d x + 1} \sqrt{-d x + 1} e - \sqrt{d^{2} e^{2} - f^{2}} {\left(f x + e\right)}}{{\left(d^{2} e^{2} - f^{2}\right)} x}\right) + {\left(2 \, B d^{4} e^{7} - B d^{2} e^{5} f^{2} - {\left(4 \, A d^{4} + 3 \, C d^{2}\right)} e^{6} f + {\left(5 \, A d^{2} + 3 \, C\right)} e^{4} f^{3} - B e^{3} f^{4} - A e^{2} f^{5} + {\left(C d^{4} e^{7} + B d^{4} e^{6} f + B d^{2} e^{4} f^{3} - {\left(3 \, A d^{4} + 5 \, C d^{2}\right)} e^{5} f^{2} + {\left(3 \, A d^{2} + 4 \, C\right)} e^{3} f^{4} - 2 \, B e^{2} f^{5}\right)} x\right)} \sqrt{d x + 1} \sqrt{-d x + 1} + 2 \, {\left(2 \, B d^{4} e^{6} f - B d^{2} e^{4} f^{3} - {\left(4 \, A d^{4} + 3 \, C d^{2}\right)} e^{5} f^{2} + {\left(5 \, A d^{2} + 3 \, C\right)} e^{3} f^{4} - B e^{2} f^{5} - A e f^{6}\right)} x}{2 \, {\left(d^{6} e^{10} - 3 \, d^{4} e^{8} f^{2} + 3 \, d^{2} e^{6} f^{4} - e^{4} f^{6} + {\left(d^{6} e^{8} f^{2} - 3 \, d^{4} e^{6} f^{4} + 3 \, d^{2} e^{4} f^{6} - e^{2} f^{8}\right)} x^{2} + 2 \, {\left(d^{6} e^{9} f - 3 \, d^{4} e^{7} f^{3} + 3 \, d^{2} e^{5} f^{5} - e^{3} f^{7}\right)} x\right)}}\right]"," ",0,"[-1/2*(2*B*d^4*e^7 - B*d^2*e^5*f^2 - (4*A*d^4 + 3*C*d^2)*e^6*f + (5*A*d^2 + 3*C)*e^4*f^3 - B*e^3*f^4 - A*e^2*f^5 + (2*B*d^4*e^5*f^2 - B*d^2*e^3*f^4 - (4*A*d^4 + 3*C*d^2)*e^4*f^3 + (5*A*d^2 + 3*C)*e^2*f^5 - B*e*f^6 - A*f^7)*x^2 - (3*B*d^2*e^5*f - (2*A*d^4 + C*d^2)*e^6 - (A*d^2 + 2*C)*e^4*f^2 + (3*B*d^2*e^3*f^3 - (2*A*d^4 + C*d^2)*e^4*f^2 - (A*d^2 + 2*C)*e^2*f^4)*x^2 + 2*(3*B*d^2*e^4*f^2 - (2*A*d^4 + C*d^2)*e^5*f - (A*d^2 + 2*C)*e^3*f^3)*x)*sqrt(-d^2*e^2 + f^2)*log((d^2*e*f*x + f^2 - sqrt(-d^2*e^2 + f^2)*(d^2*e*x + f) - (sqrt(-d^2*e^2 + f^2)*sqrt(-d*x + 1)*f + (d^2*e^2 - f^2)*sqrt(-d*x + 1))*sqrt(d*x + 1))/(f*x + e)) + (2*B*d^4*e^7 - B*d^2*e^5*f^2 - (4*A*d^4 + 3*C*d^2)*e^6*f + (5*A*d^2 + 3*C)*e^4*f^3 - B*e^3*f^4 - A*e^2*f^5 + (C*d^4*e^7 + B*d^4*e^6*f + B*d^2*e^4*f^3 - (3*A*d^4 + 5*C*d^2)*e^5*f^2 + (3*A*d^2 + 4*C)*e^3*f^4 - 2*B*e^2*f^5)*x)*sqrt(d*x + 1)*sqrt(-d*x + 1) + 2*(2*B*d^4*e^6*f - B*d^2*e^4*f^3 - (4*A*d^4 + 3*C*d^2)*e^5*f^2 + (5*A*d^2 + 3*C)*e^3*f^4 - B*e^2*f^5 - A*e*f^6)*x)/(d^6*e^10 - 3*d^4*e^8*f^2 + 3*d^2*e^6*f^4 - e^4*f^6 + (d^6*e^8*f^2 - 3*d^4*e^6*f^4 + 3*d^2*e^4*f^6 - e^2*f^8)*x^2 + 2*(d^6*e^9*f - 3*d^4*e^7*f^3 + 3*d^2*e^5*f^5 - e^3*f^7)*x), -1/2*(2*B*d^4*e^7 - B*d^2*e^5*f^2 - (4*A*d^4 + 3*C*d^2)*e^6*f + (5*A*d^2 + 3*C)*e^4*f^3 - B*e^3*f^4 - A*e^2*f^5 + (2*B*d^4*e^5*f^2 - B*d^2*e^3*f^4 - (4*A*d^4 + 3*C*d^2)*e^4*f^3 + (5*A*d^2 + 3*C)*e^2*f^5 - B*e*f^6 - A*f^7)*x^2 + 2*(3*B*d^2*e^5*f - (2*A*d^4 + C*d^2)*e^6 - (A*d^2 + 2*C)*e^4*f^2 + (3*B*d^2*e^3*f^3 - (2*A*d^4 + C*d^2)*e^4*f^2 - (A*d^2 + 2*C)*e^2*f^4)*x^2 + 2*(3*B*d^2*e^4*f^2 - (2*A*d^4 + C*d^2)*e^5*f - (A*d^2 + 2*C)*e^3*f^3)*x)*sqrt(d^2*e^2 - f^2)*arctan(-(sqrt(d^2*e^2 - f^2)*sqrt(d*x + 1)*sqrt(-d*x + 1)*e - sqrt(d^2*e^2 - f^2)*(f*x + e))/((d^2*e^2 - f^2)*x)) + (2*B*d^4*e^7 - B*d^2*e^5*f^2 - (4*A*d^4 + 3*C*d^2)*e^6*f + (5*A*d^2 + 3*C)*e^4*f^3 - B*e^3*f^4 - A*e^2*f^5 + (C*d^4*e^7 + B*d^4*e^6*f + B*d^2*e^4*f^3 - (3*A*d^4 + 5*C*d^2)*e^5*f^2 + (3*A*d^2 + 4*C)*e^3*f^4 - 2*B*e^2*f^5)*x)*sqrt(d*x + 1)*sqrt(-d*x + 1) + 2*(2*B*d^4*e^6*f - B*d^2*e^4*f^3 - (4*A*d^4 + 3*C*d^2)*e^5*f^2 + (5*A*d^2 + 3*C)*e^3*f^4 - B*e^2*f^5 - A*e*f^6)*x)/(d^6*e^10 - 3*d^4*e^8*f^2 + 3*d^2*e^6*f^4 - e^4*f^6 + (d^6*e^8*f^2 - 3*d^4*e^6*f^4 + 3*d^2*e^4*f^6 - e^2*f^8)*x^2 + 2*(d^6*e^9*f - 3*d^4*e^7*f^3 + 3*d^2*e^5*f^5 - e^3*f^7)*x)]","B",0
8,1,286,0,1.228683," ","integrate((f*x+e)^3*(C*x^2+B*x+A)/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""fricas"")","-\frac{{\left(24 \, C d^{4} f^{3} x^{4} + 120 \, B d^{4} e^{3} + 240 \, B d^{2} e f^{2} + 120 \, {\left(3 \, A d^{4} + 2 \, C d^{2}\right)} e^{2} f + 16 \, {\left(5 \, A d^{2} + 4 \, C\right)} f^{3} + 30 \, {\left(3 \, C d^{4} e f^{2} + B d^{4} f^{3}\right)} x^{3} + 8 \, {\left(15 \, C d^{4} e^{2} f + 15 \, B d^{4} e f^{2} + {\left(5 \, A d^{4} + 4 \, C d^{2}\right)} f^{3}\right)} x^{2} + 15 \, {\left(4 \, C d^{4} e^{3} + 12 \, B d^{4} e^{2} f + 3 \, B d^{2} f^{3} + 3 \, {\left(4 \, A d^{4} + 3 \, C d^{2}\right)} e f^{2}\right)} x\right)} \sqrt{d x + 1} \sqrt{-d x + 1} + 30 \, {\left(12 \, B d^{3} e^{2} f + 3 \, B d f^{3} + 4 \, {\left(2 \, A d^{5} + C d^{3}\right)} e^{3} + 3 \, {\left(4 \, A d^{3} + 3 \, C d\right)} e f^{2}\right)} \arctan\left(\frac{\sqrt{d x + 1} \sqrt{-d x + 1} - 1}{d x}\right)}{120 \, d^{6}}"," ",0,"-1/120*((24*C*d^4*f^3*x^4 + 120*B*d^4*e^3 + 240*B*d^2*e*f^2 + 120*(3*A*d^4 + 2*C*d^2)*e^2*f + 16*(5*A*d^2 + 4*C)*f^3 + 30*(3*C*d^4*e*f^2 + B*d^4*f^3)*x^3 + 8*(15*C*d^4*e^2*f + 15*B*d^4*e*f^2 + (5*A*d^4 + 4*C*d^2)*f^3)*x^2 + 15*(4*C*d^4*e^3 + 12*B*d^4*e^2*f + 3*B*d^2*f^3 + 3*(4*A*d^4 + 3*C*d^2)*e*f^2)*x)*sqrt(d*x + 1)*sqrt(-d*x + 1) + 30*(12*B*d^3*e^2*f + 3*B*d*f^3 + 4*(2*A*d^5 + C*d^3)*e^3 + 3*(4*A*d^3 + 3*C*d)*e*f^2)*arctan((sqrt(d*x + 1)*sqrt(-d*x + 1) - 1)/(d*x)))/d^6","A",0
9,1,192,0,0.824438," ","integrate((f*x+e)^2*(C*x^2+B*x+A)/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""fricas"")","-\frac{{\left(6 \, C d^{3} f^{2} x^{3} + 24 \, B d^{3} e^{2} + 16 \, B d f^{2} + 16 \, {\left(3 \, A d^{3} + 2 \, C d\right)} e f + 8 \, {\left(2 \, C d^{3} e f + B d^{3} f^{2}\right)} x^{2} + 3 \, {\left(4 \, C d^{3} e^{2} + 8 \, B d^{3} e f + {\left(4 \, A d^{3} + 3 \, C d\right)} f^{2}\right)} x\right)} \sqrt{d x + 1} \sqrt{-d x + 1} + 6 \, {\left(8 \, B d^{2} e f + 4 \, {\left(2 \, A d^{4} + C d^{2}\right)} e^{2} + {\left(4 \, A d^{2} + 3 \, C\right)} f^{2}\right)} \arctan\left(\frac{\sqrt{d x + 1} \sqrt{-d x + 1} - 1}{d x}\right)}{24 \, d^{5}}"," ",0,"-1/24*((6*C*d^3*f^2*x^3 + 24*B*d^3*e^2 + 16*B*d*f^2 + 16*(3*A*d^3 + 2*C*d)*e*f + 8*(2*C*d^3*e*f + B*d^3*f^2)*x^2 + 3*(4*C*d^3*e^2 + 8*B*d^3*e*f + (4*A*d^3 + 3*C*d)*f^2)*x)*sqrt(d*x + 1)*sqrt(-d*x + 1) + 6*(8*B*d^2*e*f + 4*(2*A*d^4 + C*d^2)*e^2 + (4*A*d^2 + 3*C)*f^2)*arctan((sqrt(d*x + 1)*sqrt(-d*x + 1) - 1)/(d*x)))/d^5","A",0
10,1,114,0,0.963597," ","integrate((f*x+e)*(C*x^2+B*x+A)/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""fricas"")","-\frac{{\left(2 \, C d^{2} f x^{2} + 6 \, B d^{2} e + 2 \, {\left(3 \, A d^{2} + 2 \, C\right)} f + 3 \, {\left(C d^{2} e + B d^{2} f\right)} x\right)} \sqrt{d x + 1} \sqrt{-d x + 1} + 6 \, {\left(B d f + {\left(2 \, A d^{3} + C d\right)} e\right)} \arctan\left(\frac{\sqrt{d x + 1} \sqrt{-d x + 1} - 1}{d x}\right)}{6 \, d^{4}}"," ",0,"-1/6*((2*C*d^2*f*x^2 + 6*B*d^2*e + 2*(3*A*d^2 + 2*C)*f + 3*(C*d^2*e + B*d^2*f)*x)*sqrt(d*x + 1)*sqrt(-d*x + 1) + 6*(B*d*f + (2*A*d^3 + C*d)*e)*arctan((sqrt(d*x + 1)*sqrt(-d*x + 1) - 1)/(d*x)))/d^4","A",0
11,1,67,0,1.451463," ","integrate((C*x^2+B*x+A)/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""fricas"")","-\frac{{\left(C d x + 2 \, B d\right)} \sqrt{d x + 1} \sqrt{-d x + 1} + 2 \, {\left(2 \, A d^{2} + C\right)} \arctan\left(\frac{\sqrt{d x + 1} \sqrt{-d x + 1} - 1}{d x}\right)}{2 \, d^{3}}"," ",0,"-1/2*((C*d*x + 2*B*d)*sqrt(d*x + 1)*sqrt(-d*x + 1) + 2*(2*A*d^2 + C)*arctan((sqrt(d*x + 1)*sqrt(-d*x + 1) - 1)/(d*x)))/d^3","A",0
12,1,493,0,19.358815," ","integrate((C*x^2+B*x+A)/(f*x+e)/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(C d^{2} e^{2} - B d^{2} e f + A d^{2} f^{2}\right)} \sqrt{-d^{2} e^{2} + f^{2}} \log\left(\frac{d^{2} e f x + f^{2} - \sqrt{-d^{2} e^{2} + f^{2}} {\left(d^{2} e x + f\right)} - {\left(\sqrt{-d^{2} e^{2} + f^{2}} \sqrt{-d x + 1} f + {\left(d^{2} e^{2} - f^{2}\right)} \sqrt{-d x + 1}\right)} \sqrt{d x + 1}}{f x + e}\right) + {\left(C d^{2} e^{2} f - C f^{3}\right)} \sqrt{d x + 1} \sqrt{-d x + 1} - 2 \, {\left(C d^{3} e^{3} - B d^{3} e^{2} f - C d e f^{2} + B d f^{3}\right)} \arctan\left(\frac{\sqrt{d x + 1} \sqrt{-d x + 1} - 1}{d x}\right)}{d^{4} e^{2} f^{2} - d^{2} f^{4}}, \frac{2 \, {\left(C d^{2} e^{2} - B d^{2} e f + A d^{2} f^{2}\right)} \sqrt{d^{2} e^{2} - f^{2}} \arctan\left(-\frac{\sqrt{d^{2} e^{2} - f^{2}} \sqrt{d x + 1} \sqrt{-d x + 1} e - \sqrt{d^{2} e^{2} - f^{2}} {\left(f x + e\right)}}{{\left(d^{2} e^{2} - f^{2}\right)} x}\right) - {\left(C d^{2} e^{2} f - C f^{3}\right)} \sqrt{d x + 1} \sqrt{-d x + 1} + 2 \, {\left(C d^{3} e^{3} - B d^{3} e^{2} f - C d e f^{2} + B d f^{3}\right)} \arctan\left(\frac{\sqrt{d x + 1} \sqrt{-d x + 1} - 1}{d x}\right)}{d^{4} e^{2} f^{2} - d^{2} f^{4}}\right]"," ",0,"[-((C*d^2*e^2 - B*d^2*e*f + A*d^2*f^2)*sqrt(-d^2*e^2 + f^2)*log((d^2*e*f*x + f^2 - sqrt(-d^2*e^2 + f^2)*(d^2*e*x + f) - (sqrt(-d^2*e^2 + f^2)*sqrt(-d*x + 1)*f + (d^2*e^2 - f^2)*sqrt(-d*x + 1))*sqrt(d*x + 1))/(f*x + e)) + (C*d^2*e^2*f - C*f^3)*sqrt(d*x + 1)*sqrt(-d*x + 1) - 2*(C*d^3*e^3 - B*d^3*e^2*f - C*d*e*f^2 + B*d*f^3)*arctan((sqrt(d*x + 1)*sqrt(-d*x + 1) - 1)/(d*x)))/(d^4*e^2*f^2 - d^2*f^4), (2*(C*d^2*e^2 - B*d^2*e*f + A*d^2*f^2)*sqrt(d^2*e^2 - f^2)*arctan(-(sqrt(d^2*e^2 - f^2)*sqrt(d*x + 1)*sqrt(-d*x + 1)*e - sqrt(d^2*e^2 - f^2)*(f*x + e))/((d^2*e^2 - f^2)*x)) - (C*d^2*e^2*f - C*f^3)*sqrt(d*x + 1)*sqrt(-d*x + 1) + 2*(C*d^3*e^3 - B*d^3*e^2*f - C*d*e*f^2 + B*d*f^3)*arctan((sqrt(d*x + 1)*sqrt(-d*x + 1) - 1)/(d*x)))/(d^4*e^2*f^2 - d^2*f^4)]","B",0
13,1,1025,0,76.120038," ","integrate((C*x^2+B*x+A)/(f*x+e)^2/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""fricas"")","\left[\frac{C d^{3} e^{5} f - B d^{3} e^{4} f^{2} + B d e^{2} f^{4} - A d e f^{5} + {\left(A d^{3} - C d\right)} e^{3} f^{3} - {\left(C d^{3} e^{5} + B d e^{2} f^{3} - {\left(A d^{3} + 2 \, C d\right)} e^{3} f^{2} + {\left(C d^{3} e^{4} f + B d e f^{4} - {\left(A d^{3} + 2 \, C d\right)} e^{2} f^{3}\right)} x\right)} \sqrt{-d^{2} e^{2} + f^{2}} \log\left(\frac{d^{2} e f x + f^{2} + \sqrt{-d^{2} e^{2} + f^{2}} {\left(d^{2} e x + f\right)} + {\left(\sqrt{-d^{2} e^{2} + f^{2}} \sqrt{-d x + 1} f - {\left(d^{2} e^{2} - f^{2}\right)} \sqrt{-d x + 1}\right)} \sqrt{d x + 1}}{f x + e}\right) + {\left(C d^{3} e^{5} f - B d^{3} e^{4} f^{2} + B d e^{2} f^{4} - A d e f^{5} + {\left(A d^{3} - C d\right)} e^{3} f^{3}\right)} \sqrt{d x + 1} \sqrt{-d x + 1} + {\left(C d^{3} e^{4} f^{2} - B d^{3} e^{3} f^{3} + B d e f^{5} - A d f^{6} + {\left(A d^{3} - C d\right)} e^{2} f^{4}\right)} x - 2 \, {\left(C d^{4} e^{6} - 2 \, C d^{2} e^{4} f^{2} + C e^{2} f^{4} + {\left(C d^{4} e^{5} f - 2 \, C d^{2} e^{3} f^{3} + C e f^{5}\right)} x\right)} \arctan\left(\frac{\sqrt{d x + 1} \sqrt{-d x + 1} - 1}{d x}\right)}{d^{5} e^{6} f^{2} - 2 \, d^{3} e^{4} f^{4} + d e^{2} f^{6} + {\left(d^{5} e^{5} f^{3} - 2 \, d^{3} e^{3} f^{5} + d e f^{7}\right)} x}, \frac{C d^{3} e^{5} f - B d^{3} e^{4} f^{2} + B d e^{2} f^{4} - A d e f^{5} + {\left(A d^{3} - C d\right)} e^{3} f^{3} - 2 \, {\left(C d^{3} e^{5} + B d e^{2} f^{3} - {\left(A d^{3} + 2 \, C d\right)} e^{3} f^{2} + {\left(C d^{3} e^{4} f + B d e f^{4} - {\left(A d^{3} + 2 \, C d\right)} e^{2} f^{3}\right)} x\right)} \sqrt{d^{2} e^{2} - f^{2}} \arctan\left(-\frac{\sqrt{d^{2} e^{2} - f^{2}} \sqrt{d x + 1} \sqrt{-d x + 1} e - \sqrt{d^{2} e^{2} - f^{2}} {\left(f x + e\right)}}{{\left(d^{2} e^{2} - f^{2}\right)} x}\right) + {\left(C d^{3} e^{5} f - B d^{3} e^{4} f^{2} + B d e^{2} f^{4} - A d e f^{5} + {\left(A d^{3} - C d\right)} e^{3} f^{3}\right)} \sqrt{d x + 1} \sqrt{-d x + 1} + {\left(C d^{3} e^{4} f^{2} - B d^{3} e^{3} f^{3} + B d e f^{5} - A d f^{6} + {\left(A d^{3} - C d\right)} e^{2} f^{4}\right)} x - 2 \, {\left(C d^{4} e^{6} - 2 \, C d^{2} e^{4} f^{2} + C e^{2} f^{4} + {\left(C d^{4} e^{5} f - 2 \, C d^{2} e^{3} f^{3} + C e f^{5}\right)} x\right)} \arctan\left(\frac{\sqrt{d x + 1} \sqrt{-d x + 1} - 1}{d x}\right)}{d^{5} e^{6} f^{2} - 2 \, d^{3} e^{4} f^{4} + d e^{2} f^{6} + {\left(d^{5} e^{5} f^{3} - 2 \, d^{3} e^{3} f^{5} + d e f^{7}\right)} x}\right]"," ",0,"[(C*d^3*e^5*f - B*d^3*e^4*f^2 + B*d*e^2*f^4 - A*d*e*f^5 + (A*d^3 - C*d)*e^3*f^3 - (C*d^3*e^5 + B*d*e^2*f^3 - (A*d^3 + 2*C*d)*e^3*f^2 + (C*d^3*e^4*f + B*d*e*f^4 - (A*d^3 + 2*C*d)*e^2*f^3)*x)*sqrt(-d^2*e^2 + f^2)*log((d^2*e*f*x + f^2 + sqrt(-d^2*e^2 + f^2)*(d^2*e*x + f) + (sqrt(-d^2*e^2 + f^2)*sqrt(-d*x + 1)*f - (d^2*e^2 - f^2)*sqrt(-d*x + 1))*sqrt(d*x + 1))/(f*x + e)) + (C*d^3*e^5*f - B*d^3*e^4*f^2 + B*d*e^2*f^4 - A*d*e*f^5 + (A*d^3 - C*d)*e^3*f^3)*sqrt(d*x + 1)*sqrt(-d*x + 1) + (C*d^3*e^4*f^2 - B*d^3*e^3*f^3 + B*d*e*f^5 - A*d*f^6 + (A*d^3 - C*d)*e^2*f^4)*x - 2*(C*d^4*e^6 - 2*C*d^2*e^4*f^2 + C*e^2*f^4 + (C*d^4*e^5*f - 2*C*d^2*e^3*f^3 + C*e*f^5)*x)*arctan((sqrt(d*x + 1)*sqrt(-d*x + 1) - 1)/(d*x)))/(d^5*e^6*f^2 - 2*d^3*e^4*f^4 + d*e^2*f^6 + (d^5*e^5*f^3 - 2*d^3*e^3*f^5 + d*e*f^7)*x), (C*d^3*e^5*f - B*d^3*e^4*f^2 + B*d*e^2*f^4 - A*d*e*f^5 + (A*d^3 - C*d)*e^3*f^3 - 2*(C*d^3*e^5 + B*d*e^2*f^3 - (A*d^3 + 2*C*d)*e^3*f^2 + (C*d^3*e^4*f + B*d*e*f^4 - (A*d^3 + 2*C*d)*e^2*f^3)*x)*sqrt(d^2*e^2 - f^2)*arctan(-(sqrt(d^2*e^2 - f^2)*sqrt(d*x + 1)*sqrt(-d*x + 1)*e - sqrt(d^2*e^2 - f^2)*(f*x + e))/((d^2*e^2 - f^2)*x)) + (C*d^3*e^5*f - B*d^3*e^4*f^2 + B*d*e^2*f^4 - A*d*e*f^5 + (A*d^3 - C*d)*e^3*f^3)*sqrt(d*x + 1)*sqrt(-d*x + 1) + (C*d^3*e^4*f^2 - B*d^3*e^3*f^3 + B*d*e*f^5 - A*d*f^6 + (A*d^3 - C*d)*e^2*f^4)*x - 2*(C*d^4*e^6 - 2*C*d^2*e^4*f^2 + C*e^2*f^4 + (C*d^4*e^5*f - 2*C*d^2*e^3*f^3 + C*e*f^5)*x)*arctan((sqrt(d*x + 1)*sqrt(-d*x + 1) - 1)/(d*x)))/(d^5*e^6*f^2 - 2*d^3*e^4*f^4 + d*e^2*f^6 + (d^5*e^5*f^3 - 2*d^3*e^3*f^5 + d*e*f^7)*x)]","B",0
14,1,1580,0,0.847685," ","integrate((C*x^2+B*x+A)/(f*x+e)^3/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""fricas"")","\left[-\frac{2 \, B d^{4} e^{7} - B d^{2} e^{5} f^{2} - {\left(4 \, A d^{4} + 3 \, C d^{2}\right)} e^{6} f + {\left(5 \, A d^{2} + 3 \, C\right)} e^{4} f^{3} - B e^{3} f^{4} - A e^{2} f^{5} + {\left(2 \, B d^{4} e^{5} f^{2} - B d^{2} e^{3} f^{4} - {\left(4 \, A d^{4} + 3 \, C d^{2}\right)} e^{4} f^{3} + {\left(5 \, A d^{2} + 3 \, C\right)} e^{2} f^{5} - B e f^{6} - A f^{7}\right)} x^{2} - {\left(3 \, B d^{2} e^{5} f - {\left(2 \, A d^{4} + C d^{2}\right)} e^{6} - {\left(A d^{2} + 2 \, C\right)} e^{4} f^{2} + {\left(3 \, B d^{2} e^{3} f^{3} - {\left(2 \, A d^{4} + C d^{2}\right)} e^{4} f^{2} - {\left(A d^{2} + 2 \, C\right)} e^{2} f^{4}\right)} x^{2} + 2 \, {\left(3 \, B d^{2} e^{4} f^{2} - {\left(2 \, A d^{4} + C d^{2}\right)} e^{5} f - {\left(A d^{2} + 2 \, C\right)} e^{3} f^{3}\right)} x\right)} \sqrt{-d^{2} e^{2} + f^{2}} \log\left(\frac{d^{2} e f x + f^{2} - \sqrt{-d^{2} e^{2} + f^{2}} {\left(d^{2} e x + f\right)} - {\left(\sqrt{-d^{2} e^{2} + f^{2}} \sqrt{-d x + 1} f + {\left(d^{2} e^{2} - f^{2}\right)} \sqrt{-d x + 1}\right)} \sqrt{d x + 1}}{f x + e}\right) + {\left(2 \, B d^{4} e^{7} - B d^{2} e^{5} f^{2} - {\left(4 \, A d^{4} + 3 \, C d^{2}\right)} e^{6} f + {\left(5 \, A d^{2} + 3 \, C\right)} e^{4} f^{3} - B e^{3} f^{4} - A e^{2} f^{5} + {\left(C d^{4} e^{7} + B d^{4} e^{6} f + B d^{2} e^{4} f^{3} - {\left(3 \, A d^{4} + 5 \, C d^{2}\right)} e^{5} f^{2} + {\left(3 \, A d^{2} + 4 \, C\right)} e^{3} f^{4} - 2 \, B e^{2} f^{5}\right)} x\right)} \sqrt{d x + 1} \sqrt{-d x + 1} + 2 \, {\left(2 \, B d^{4} e^{6} f - B d^{2} e^{4} f^{3} - {\left(4 \, A d^{4} + 3 \, C d^{2}\right)} e^{5} f^{2} + {\left(5 \, A d^{2} + 3 \, C\right)} e^{3} f^{4} - B e^{2} f^{5} - A e f^{6}\right)} x}{2 \, {\left(d^{6} e^{10} - 3 \, d^{4} e^{8} f^{2} + 3 \, d^{2} e^{6} f^{4} - e^{4} f^{6} + {\left(d^{6} e^{8} f^{2} - 3 \, d^{4} e^{6} f^{4} + 3 \, d^{2} e^{4} f^{6} - e^{2} f^{8}\right)} x^{2} + 2 \, {\left(d^{6} e^{9} f - 3 \, d^{4} e^{7} f^{3} + 3 \, d^{2} e^{5} f^{5} - e^{3} f^{7}\right)} x\right)}}, -\frac{2 \, B d^{4} e^{7} - B d^{2} e^{5} f^{2} - {\left(4 \, A d^{4} + 3 \, C d^{2}\right)} e^{6} f + {\left(5 \, A d^{2} + 3 \, C\right)} e^{4} f^{3} - B e^{3} f^{4} - A e^{2} f^{5} + {\left(2 \, B d^{4} e^{5} f^{2} - B d^{2} e^{3} f^{4} - {\left(4 \, A d^{4} + 3 \, C d^{2}\right)} e^{4} f^{3} + {\left(5 \, A d^{2} + 3 \, C\right)} e^{2} f^{5} - B e f^{6} - A f^{7}\right)} x^{2} + 2 \, {\left(3 \, B d^{2} e^{5} f - {\left(2 \, A d^{4} + C d^{2}\right)} e^{6} - {\left(A d^{2} + 2 \, C\right)} e^{4} f^{2} + {\left(3 \, B d^{2} e^{3} f^{3} - {\left(2 \, A d^{4} + C d^{2}\right)} e^{4} f^{2} - {\left(A d^{2} + 2 \, C\right)} e^{2} f^{4}\right)} x^{2} + 2 \, {\left(3 \, B d^{2} e^{4} f^{2} - {\left(2 \, A d^{4} + C d^{2}\right)} e^{5} f - {\left(A d^{2} + 2 \, C\right)} e^{3} f^{3}\right)} x\right)} \sqrt{d^{2} e^{2} - f^{2}} \arctan\left(-\frac{\sqrt{d^{2} e^{2} - f^{2}} \sqrt{d x + 1} \sqrt{-d x + 1} e - \sqrt{d^{2} e^{2} - f^{2}} {\left(f x + e\right)}}{{\left(d^{2} e^{2} - f^{2}\right)} x}\right) + {\left(2 \, B d^{4} e^{7} - B d^{2} e^{5} f^{2} - {\left(4 \, A d^{4} + 3 \, C d^{2}\right)} e^{6} f + {\left(5 \, A d^{2} + 3 \, C\right)} e^{4} f^{3} - B e^{3} f^{4} - A e^{2} f^{5} + {\left(C d^{4} e^{7} + B d^{4} e^{6} f + B d^{2} e^{4} f^{3} - {\left(3 \, A d^{4} + 5 \, C d^{2}\right)} e^{5} f^{2} + {\left(3 \, A d^{2} + 4 \, C\right)} e^{3} f^{4} - 2 \, B e^{2} f^{5}\right)} x\right)} \sqrt{d x + 1} \sqrt{-d x + 1} + 2 \, {\left(2 \, B d^{4} e^{6} f - B d^{2} e^{4} f^{3} - {\left(4 \, A d^{4} + 3 \, C d^{2}\right)} e^{5} f^{2} + {\left(5 \, A d^{2} + 3 \, C\right)} e^{3} f^{4} - B e^{2} f^{5} - A e f^{6}\right)} x}{2 \, {\left(d^{6} e^{10} - 3 \, d^{4} e^{8} f^{2} + 3 \, d^{2} e^{6} f^{4} - e^{4} f^{6} + {\left(d^{6} e^{8} f^{2} - 3 \, d^{4} e^{6} f^{4} + 3 \, d^{2} e^{4} f^{6} - e^{2} f^{8}\right)} x^{2} + 2 \, {\left(d^{6} e^{9} f - 3 \, d^{4} e^{7} f^{3} + 3 \, d^{2} e^{5} f^{5} - e^{3} f^{7}\right)} x\right)}}\right]"," ",0,"[-1/2*(2*B*d^4*e^7 - B*d^2*e^5*f^2 - (4*A*d^4 + 3*C*d^2)*e^6*f + (5*A*d^2 + 3*C)*e^4*f^3 - B*e^3*f^4 - A*e^2*f^5 + (2*B*d^4*e^5*f^2 - B*d^2*e^3*f^4 - (4*A*d^4 + 3*C*d^2)*e^4*f^3 + (5*A*d^2 + 3*C)*e^2*f^5 - B*e*f^6 - A*f^7)*x^2 - (3*B*d^2*e^5*f - (2*A*d^4 + C*d^2)*e^6 - (A*d^2 + 2*C)*e^4*f^2 + (3*B*d^2*e^3*f^3 - (2*A*d^4 + C*d^2)*e^4*f^2 - (A*d^2 + 2*C)*e^2*f^4)*x^2 + 2*(3*B*d^2*e^4*f^2 - (2*A*d^4 + C*d^2)*e^5*f - (A*d^2 + 2*C)*e^3*f^3)*x)*sqrt(-d^2*e^2 + f^2)*log((d^2*e*f*x + f^2 - sqrt(-d^2*e^2 + f^2)*(d^2*e*x + f) - (sqrt(-d^2*e^2 + f^2)*sqrt(-d*x + 1)*f + (d^2*e^2 - f^2)*sqrt(-d*x + 1))*sqrt(d*x + 1))/(f*x + e)) + (2*B*d^4*e^7 - B*d^2*e^5*f^2 - (4*A*d^4 + 3*C*d^2)*e^6*f + (5*A*d^2 + 3*C)*e^4*f^3 - B*e^3*f^4 - A*e^2*f^5 + (C*d^4*e^7 + B*d^4*e^6*f + B*d^2*e^4*f^3 - (3*A*d^4 + 5*C*d^2)*e^5*f^2 + (3*A*d^2 + 4*C)*e^3*f^4 - 2*B*e^2*f^5)*x)*sqrt(d*x + 1)*sqrt(-d*x + 1) + 2*(2*B*d^4*e^6*f - B*d^2*e^4*f^3 - (4*A*d^4 + 3*C*d^2)*e^5*f^2 + (5*A*d^2 + 3*C)*e^3*f^4 - B*e^2*f^5 - A*e*f^6)*x)/(d^6*e^10 - 3*d^4*e^8*f^2 + 3*d^2*e^6*f^4 - e^4*f^6 + (d^6*e^8*f^2 - 3*d^4*e^6*f^4 + 3*d^2*e^4*f^6 - e^2*f^8)*x^2 + 2*(d^6*e^9*f - 3*d^4*e^7*f^3 + 3*d^2*e^5*f^5 - e^3*f^7)*x), -1/2*(2*B*d^4*e^7 - B*d^2*e^5*f^2 - (4*A*d^4 + 3*C*d^2)*e^6*f + (5*A*d^2 + 3*C)*e^4*f^3 - B*e^3*f^4 - A*e^2*f^5 + (2*B*d^4*e^5*f^2 - B*d^2*e^3*f^4 - (4*A*d^4 + 3*C*d^2)*e^4*f^3 + (5*A*d^2 + 3*C)*e^2*f^5 - B*e*f^6 - A*f^7)*x^2 + 2*(3*B*d^2*e^5*f - (2*A*d^4 + C*d^2)*e^6 - (A*d^2 + 2*C)*e^4*f^2 + (3*B*d^2*e^3*f^3 - (2*A*d^4 + C*d^2)*e^4*f^2 - (A*d^2 + 2*C)*e^2*f^4)*x^2 + 2*(3*B*d^2*e^4*f^2 - (2*A*d^4 + C*d^2)*e^5*f - (A*d^2 + 2*C)*e^3*f^3)*x)*sqrt(d^2*e^2 - f^2)*arctan(-(sqrt(d^2*e^2 - f^2)*sqrt(d*x + 1)*sqrt(-d*x + 1)*e - sqrt(d^2*e^2 - f^2)*(f*x + e))/((d^2*e^2 - f^2)*x)) + (2*B*d^4*e^7 - B*d^2*e^5*f^2 - (4*A*d^4 + 3*C*d^2)*e^6*f + (5*A*d^2 + 3*C)*e^4*f^3 - B*e^3*f^4 - A*e^2*f^5 + (C*d^4*e^7 + B*d^4*e^6*f + B*d^2*e^4*f^3 - (3*A*d^4 + 5*C*d^2)*e^5*f^2 + (3*A*d^2 + 4*C)*e^3*f^4 - 2*B*e^2*f^5)*x)*sqrt(d*x + 1)*sqrt(-d*x + 1) + 2*(2*B*d^4*e^6*f - B*d^2*e^4*f^3 - (4*A*d^4 + 3*C*d^2)*e^5*f^2 + (5*A*d^2 + 3*C)*e^3*f^4 - B*e^2*f^5 - A*e*f^6)*x)/(d^6*e^10 - 3*d^4*e^8*f^2 + 3*d^2*e^6*f^4 - e^4*f^6 + (d^6*e^8*f^2 - 3*d^4*e^6*f^4 + 3*d^2*e^4*f^6 - e^2*f^8)*x^2 + 2*(d^6*e^9*f - 3*d^4*e^7*f^3 + 3*d^2*e^5*f^5 - e^3*f^7)*x)]","B",0
15,1,78,0,1.139492," ","integrate(x*(c*x^2+b*x+a)/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""fricas"")","-\frac{6 \, b d \arctan\left(\frac{\sqrt{d x + 1} \sqrt{-d x + 1} - 1}{d x}\right) + {\left(2 \, c d^{2} x^{2} + 3 \, b d^{2} x + 6 \, a d^{2} + 4 \, c\right)} \sqrt{d x + 1} \sqrt{-d x + 1}}{6 \, d^{4}}"," ",0,"-1/6*(6*b*d*arctan((sqrt(d*x + 1)*sqrt(-d*x + 1) - 1)/(d*x)) + (2*c*d^2*x^2 + 3*b*d^2*x + 6*a*d^2 + 4*c)*sqrt(d*x + 1)*sqrt(-d*x + 1))/d^4","A",0
16,1,67,0,0.974788," ","integrate((c*x^2+b*x+a)/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""fricas"")","-\frac{{\left(c d x + 2 \, b d\right)} \sqrt{d x + 1} \sqrt{-d x + 1} + 2 \, {\left(2 \, a d^{2} + c\right)} \arctan\left(\frac{\sqrt{d x + 1} \sqrt{-d x + 1} - 1}{d x}\right)}{2 \, d^{3}}"," ",0,"-1/2*((c*d*x + 2*b*d)*sqrt(d*x + 1)*sqrt(-d*x + 1) + 2*(2*a*d^2 + c)*arctan((sqrt(d*x + 1)*sqrt(-d*x + 1) - 1)/(d*x)))/d^3","A",0
17,1,81,0,0.998208," ","integrate((c*x^2+b*x+a)/x/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""fricas"")","\frac{a d^{2} \log\left(\frac{\sqrt{d x + 1} \sqrt{-d x + 1} - 1}{x}\right) - 2 \, b d \arctan\left(\frac{\sqrt{d x + 1} \sqrt{-d x + 1} - 1}{d x}\right) - \sqrt{d x + 1} \sqrt{-d x + 1} c}{d^{2}}"," ",0,"(a*d^2*log((sqrt(d*x + 1)*sqrt(-d*x + 1) - 1)/x) - 2*b*d*arctan((sqrt(d*x + 1)*sqrt(-d*x + 1) - 1)/(d*x)) - sqrt(d*x + 1)*sqrt(-d*x + 1)*c)/d^2","A",0
18,1,84,0,1.313836," ","integrate((c*x^2+b*x+a)/x^2/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""fricas"")","\frac{b d x \log\left(\frac{\sqrt{d x + 1} \sqrt{-d x + 1} - 1}{x}\right) - \sqrt{d x + 1} \sqrt{-d x + 1} a d - 2 \, c x \arctan\left(\frac{\sqrt{d x + 1} \sqrt{-d x + 1} - 1}{d x}\right)}{d x}"," ",0,"(b*d*x*log((sqrt(d*x + 1)*sqrt(-d*x + 1) - 1)/x) - sqrt(d*x + 1)*sqrt(-d*x + 1)*a*d - 2*c*x*arctan((sqrt(d*x + 1)*sqrt(-d*x + 1) - 1)/(d*x)))/(d*x)","A",0
19,1,65,0,0.882176," ","integrate((c*x^2+b*x+a)/x^3/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""fricas"")","\frac{{\left(a d^{2} + 2 \, c\right)} x^{2} \log\left(\frac{\sqrt{d x + 1} \sqrt{-d x + 1} - 1}{x}\right) - {\left(2 \, b x + a\right)} \sqrt{d x + 1} \sqrt{-d x + 1}}{2 \, x^{2}}"," ",0,"1/2*((a*d^2 + 2*c)*x^2*log((sqrt(d*x + 1)*sqrt(-d*x + 1) - 1)/x) - (2*b*x + a)*sqrt(d*x + 1)*sqrt(-d*x + 1))/x^2","A",0
20,1,1001,0,0.887502," ","integrate((f*x+e)^3*(C*x^2+B*x+A)*(b*x+a)^(1/2)*(-b*c*x+a*c)^(1/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(6 \, B a^{4} b^{3} e^{2} f + B a^{6} b f^{3} + 2 \, {\left(C a^{4} b^{3} + 4 \, A a^{2} b^{5}\right)} e^{3} + 3 \, {\left(C a^{6} b + 2 \, A a^{4} b^{3}\right)} e f^{2}\right)} \sqrt{-c} \log\left(2 \, b^{2} c x^{2} + 2 \, \sqrt{-b c x + a c} \sqrt{b x + a} b \sqrt{-c} x - a^{2} c\right) + 2 \, {\left(240 \, C b^{6} f^{3} x^{6} - 560 \, B a^{2} b^{4} e^{3} - 672 \, B a^{4} b^{2} e f^{2} + 280 \, {\left(3 \, C b^{6} e f^{2} + B b^{6} f^{3}\right)} x^{5} + 48 \, {\left(21 \, C b^{6} e^{2} f + 21 \, B b^{6} e f^{2} - {\left(C a^{2} b^{4} - 7 \, A b^{6}\right)} f^{3}\right)} x^{4} - 336 \, {\left(2 \, C a^{4} b^{2} + 5 \, A a^{2} b^{4}\right)} e^{2} f - 32 \, {\left(4 \, C a^{6} + 7 \, A a^{4} b^{2}\right)} f^{3} + 70 \, {\left(6 \, C b^{6} e^{3} + 18 \, B b^{6} e^{2} f - B a^{2} b^{4} f^{3} - 3 \, {\left(C a^{2} b^{4} - 6 \, A b^{6}\right)} e f^{2}\right)} x^{3} + 16 \, {\left(35 \, B b^{6} e^{3} - 21 \, B a^{2} b^{4} e f^{2} - 21 \, {\left(C a^{2} b^{4} - 5 \, A b^{6}\right)} e^{2} f - {\left(4 \, C a^{4} b^{2} + 7 \, A a^{2} b^{4}\right)} f^{3}\right)} x^{2} - 105 \, {\left(6 \, B a^{2} b^{4} e^{2} f + B a^{4} b^{2} f^{3} + 2 \, {\left(C a^{2} b^{4} - 4 \, A b^{6}\right)} e^{3} + 3 \, {\left(C a^{4} b^{2} + 2 \, A a^{2} b^{4}\right)} e f^{2}\right)} x\right)} \sqrt{-b c x + a c} \sqrt{b x + a}}{3360 \, b^{6}}, -\frac{105 \, {\left(6 \, B a^{4} b^{3} e^{2} f + B a^{6} b f^{3} + 2 \, {\left(C a^{4} b^{3} + 4 \, A a^{2} b^{5}\right)} e^{3} + 3 \, {\left(C a^{6} b + 2 \, A a^{4} b^{3}\right)} e f^{2}\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-b c x + a c} \sqrt{b x + a} b \sqrt{c} x}{b^{2} c x^{2} - a^{2} c}\right) - {\left(240 \, C b^{6} f^{3} x^{6} - 560 \, B a^{2} b^{4} e^{3} - 672 \, B a^{4} b^{2} e f^{2} + 280 \, {\left(3 \, C b^{6} e f^{2} + B b^{6} f^{3}\right)} x^{5} + 48 \, {\left(21 \, C b^{6} e^{2} f + 21 \, B b^{6} e f^{2} - {\left(C a^{2} b^{4} - 7 \, A b^{6}\right)} f^{3}\right)} x^{4} - 336 \, {\left(2 \, C a^{4} b^{2} + 5 \, A a^{2} b^{4}\right)} e^{2} f - 32 \, {\left(4 \, C a^{6} + 7 \, A a^{4} b^{2}\right)} f^{3} + 70 \, {\left(6 \, C b^{6} e^{3} + 18 \, B b^{6} e^{2} f - B a^{2} b^{4} f^{3} - 3 \, {\left(C a^{2} b^{4} - 6 \, A b^{6}\right)} e f^{2}\right)} x^{3} + 16 \, {\left(35 \, B b^{6} e^{3} - 21 \, B a^{2} b^{4} e f^{2} - 21 \, {\left(C a^{2} b^{4} - 5 \, A b^{6}\right)} e^{2} f - {\left(4 \, C a^{4} b^{2} + 7 \, A a^{2} b^{4}\right)} f^{3}\right)} x^{2} - 105 \, {\left(6 \, B a^{2} b^{4} e^{2} f + B a^{4} b^{2} f^{3} + 2 \, {\left(C a^{2} b^{4} - 4 \, A b^{6}\right)} e^{3} + 3 \, {\left(C a^{4} b^{2} + 2 \, A a^{2} b^{4}\right)} e f^{2}\right)} x\right)} \sqrt{-b c x + a c} \sqrt{b x + a}}{1680 \, b^{6}}\right]"," ",0,"[1/3360*(105*(6*B*a^4*b^3*e^2*f + B*a^6*b*f^3 + 2*(C*a^4*b^3 + 4*A*a^2*b^5)*e^3 + 3*(C*a^6*b + 2*A*a^4*b^3)*e*f^2)*sqrt(-c)*log(2*b^2*c*x^2 + 2*sqrt(-b*c*x + a*c)*sqrt(b*x + a)*b*sqrt(-c)*x - a^2*c) + 2*(240*C*b^6*f^3*x^6 - 560*B*a^2*b^4*e^3 - 672*B*a^4*b^2*e*f^2 + 280*(3*C*b^6*e*f^2 + B*b^6*f^3)*x^5 + 48*(21*C*b^6*e^2*f + 21*B*b^6*e*f^2 - (C*a^2*b^4 - 7*A*b^6)*f^3)*x^4 - 336*(2*C*a^4*b^2 + 5*A*a^2*b^4)*e^2*f - 32*(4*C*a^6 + 7*A*a^4*b^2)*f^3 + 70*(6*C*b^6*e^3 + 18*B*b^6*e^2*f - B*a^2*b^4*f^3 - 3*(C*a^2*b^4 - 6*A*b^6)*e*f^2)*x^3 + 16*(35*B*b^6*e^3 - 21*B*a^2*b^4*e*f^2 - 21*(C*a^2*b^4 - 5*A*b^6)*e^2*f - (4*C*a^4*b^2 + 7*A*a^2*b^4)*f^3)*x^2 - 105*(6*B*a^2*b^4*e^2*f + B*a^4*b^2*f^3 + 2*(C*a^2*b^4 - 4*A*b^6)*e^3 + 3*(C*a^4*b^2 + 2*A*a^2*b^4)*e*f^2)*x)*sqrt(-b*c*x + a*c)*sqrt(b*x + a))/b^6, -1/1680*(105*(6*B*a^4*b^3*e^2*f + B*a^6*b*f^3 + 2*(C*a^4*b^3 + 4*A*a^2*b^5)*e^3 + 3*(C*a^6*b + 2*A*a^4*b^3)*e*f^2)*sqrt(c)*arctan(sqrt(-b*c*x + a*c)*sqrt(b*x + a)*b*sqrt(c)*x/(b^2*c*x^2 - a^2*c)) - (240*C*b^6*f^3*x^6 - 560*B*a^2*b^4*e^3 - 672*B*a^4*b^2*e*f^2 + 280*(3*C*b^6*e*f^2 + B*b^6*f^3)*x^5 + 48*(21*C*b^6*e^2*f + 21*B*b^6*e*f^2 - (C*a^2*b^4 - 7*A*b^6)*f^3)*x^4 - 336*(2*C*a^4*b^2 + 5*A*a^2*b^4)*e^2*f - 32*(4*C*a^6 + 7*A*a^4*b^2)*f^3 + 70*(6*C*b^6*e^3 + 18*B*b^6*e^2*f - B*a^2*b^4*f^3 - 3*(C*a^2*b^4 - 6*A*b^6)*e*f^2)*x^3 + 16*(35*B*b^6*e^3 - 21*B*a^2*b^4*e*f^2 - 21*(C*a^2*b^4 - 5*A*b^6)*e^2*f - (4*C*a^4*b^2 + 7*A*a^2*b^4)*f^3)*x^2 - 105*(6*B*a^2*b^4*e^2*f + B*a^4*b^2*f^3 + 2*(C*a^2*b^4 - 4*A*b^6)*e^3 + 3*(C*a^4*b^2 + 2*A*a^2*b^4)*e*f^2)*x)*sqrt(-b*c*x + a*c)*sqrt(b*x + a))/b^6]","A",0
21,1,703,0,0.983435," ","integrate((f*x+e)^2*(C*x^2+B*x+A)*(b*x+a)^(1/2)*(-b*c*x+a*c)^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(4 \, B a^{4} b^{2} e f + 2 \, {\left(C a^{4} b^{2} + 4 \, A a^{2} b^{4}\right)} e^{2} + {\left(C a^{6} + 2 \, A a^{4} b^{2}\right)} f^{2}\right)} \sqrt{-c} \log\left(2 \, b^{2} c x^{2} + 2 \, \sqrt{-b c x + a c} \sqrt{b x + a} b \sqrt{-c} x - a^{2} c\right) + 2 \, {\left(40 \, C b^{5} f^{2} x^{5} - 80 \, B a^{2} b^{3} e^{2} - 32 \, B a^{4} b f^{2} + 48 \, {\left(2 \, C b^{5} e f + B b^{5} f^{2}\right)} x^{4} + 10 \, {\left(6 \, C b^{5} e^{2} + 12 \, B b^{5} e f - {\left(C a^{2} b^{3} - 6 \, A b^{5}\right)} f^{2}\right)} x^{3} - 32 \, {\left(2 \, C a^{4} b + 5 \, A a^{2} b^{3}\right)} e f + 16 \, {\left(5 \, B b^{5} e^{2} - B a^{2} b^{3} f^{2} - 2 \, {\left(C a^{2} b^{3} - 5 \, A b^{5}\right)} e f\right)} x^{2} - 15 \, {\left(4 \, B a^{2} b^{3} e f + 2 \, {\left(C a^{2} b^{3} - 4 \, A b^{5}\right)} e^{2} + {\left(C a^{4} b + 2 \, A a^{2} b^{3}\right)} f^{2}\right)} x\right)} \sqrt{-b c x + a c} \sqrt{b x + a}}{480 \, b^{5}}, -\frac{15 \, {\left(4 \, B a^{4} b^{2} e f + 2 \, {\left(C a^{4} b^{2} + 4 \, A a^{2} b^{4}\right)} e^{2} + {\left(C a^{6} + 2 \, A a^{4} b^{2}\right)} f^{2}\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-b c x + a c} \sqrt{b x + a} b \sqrt{c} x}{b^{2} c x^{2} - a^{2} c}\right) - {\left(40 \, C b^{5} f^{2} x^{5} - 80 \, B a^{2} b^{3} e^{2} - 32 \, B a^{4} b f^{2} + 48 \, {\left(2 \, C b^{5} e f + B b^{5} f^{2}\right)} x^{4} + 10 \, {\left(6 \, C b^{5} e^{2} + 12 \, B b^{5} e f - {\left(C a^{2} b^{3} - 6 \, A b^{5}\right)} f^{2}\right)} x^{3} - 32 \, {\left(2 \, C a^{4} b + 5 \, A a^{2} b^{3}\right)} e f + 16 \, {\left(5 \, B b^{5} e^{2} - B a^{2} b^{3} f^{2} - 2 \, {\left(C a^{2} b^{3} - 5 \, A b^{5}\right)} e f\right)} x^{2} - 15 \, {\left(4 \, B a^{2} b^{3} e f + 2 \, {\left(C a^{2} b^{3} - 4 \, A b^{5}\right)} e^{2} + {\left(C a^{4} b + 2 \, A a^{2} b^{3}\right)} f^{2}\right)} x\right)} \sqrt{-b c x + a c} \sqrt{b x + a}}{240 \, b^{5}}\right]"," ",0,"[1/480*(15*(4*B*a^4*b^2*e*f + 2*(C*a^4*b^2 + 4*A*a^2*b^4)*e^2 + (C*a^6 + 2*A*a^4*b^2)*f^2)*sqrt(-c)*log(2*b^2*c*x^2 + 2*sqrt(-b*c*x + a*c)*sqrt(b*x + a)*b*sqrt(-c)*x - a^2*c) + 2*(40*C*b^5*f^2*x^5 - 80*B*a^2*b^3*e^2 - 32*B*a^4*b*f^2 + 48*(2*C*b^5*e*f + B*b^5*f^2)*x^4 + 10*(6*C*b^5*e^2 + 12*B*b^5*e*f - (C*a^2*b^3 - 6*A*b^5)*f^2)*x^3 - 32*(2*C*a^4*b + 5*A*a^2*b^3)*e*f + 16*(5*B*b^5*e^2 - B*a^2*b^3*f^2 - 2*(C*a^2*b^3 - 5*A*b^5)*e*f)*x^2 - 15*(4*B*a^2*b^3*e*f + 2*(C*a^2*b^3 - 4*A*b^5)*e^2 + (C*a^4*b + 2*A*a^2*b^3)*f^2)*x)*sqrt(-b*c*x + a*c)*sqrt(b*x + a))/b^5, -1/240*(15*(4*B*a^4*b^2*e*f + 2*(C*a^4*b^2 + 4*A*a^2*b^4)*e^2 + (C*a^6 + 2*A*a^4*b^2)*f^2)*sqrt(c)*arctan(sqrt(-b*c*x + a*c)*sqrt(b*x + a)*b*sqrt(c)*x/(b^2*c*x^2 - a^2*c)) - (40*C*b^5*f^2*x^5 - 80*B*a^2*b^3*e^2 - 32*B*a^4*b*f^2 + 48*(2*C*b^5*e*f + B*b^5*f^2)*x^4 + 10*(6*C*b^5*e^2 + 12*B*b^5*e*f - (C*a^2*b^3 - 6*A*b^5)*f^2)*x^3 - 32*(2*C*a^4*b + 5*A*a^2*b^3)*e*f + 16*(5*B*b^5*e^2 - B*a^2*b^3*f^2 - 2*(C*a^2*b^3 - 5*A*b^5)*e*f)*x^2 - 15*(4*B*a^2*b^3*e*f + 2*(C*a^2*b^3 - 4*A*b^5)*e^2 + (C*a^4*b + 2*A*a^2*b^3)*f^2)*x)*sqrt(-b*c*x + a*c)*sqrt(b*x + a))/b^5]","A",0
22,1,441,0,1.198768," ","integrate((f*x+e)*(C*x^2+B*x+A)*(b*x+a)^(1/2)*(-b*c*x+a*c)^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(B a^{4} b f + {\left(C a^{4} b + 4 \, A a^{2} b^{3}\right)} e\right)} \sqrt{-c} \log\left(2 \, b^{2} c x^{2} + 2 \, \sqrt{-b c x + a c} \sqrt{b x + a} b \sqrt{-c} x - a^{2} c\right) + 2 \, {\left(24 \, C b^{4} f x^{4} - 40 \, B a^{2} b^{2} e + 30 \, {\left(C b^{4} e + B b^{4} f\right)} x^{3} + 8 \, {\left(5 \, B b^{4} e - {\left(C a^{2} b^{2} - 5 \, A b^{4}\right)} f\right)} x^{2} - 8 \, {\left(2 \, C a^{4} + 5 \, A a^{2} b^{2}\right)} f - 15 \, {\left(B a^{2} b^{2} f + {\left(C a^{2} b^{2} - 4 \, A b^{4}\right)} e\right)} x\right)} \sqrt{-b c x + a c} \sqrt{b x + a}}{240 \, b^{4}}, -\frac{15 \, {\left(B a^{4} b f + {\left(C a^{4} b + 4 \, A a^{2} b^{3}\right)} e\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-b c x + a c} \sqrt{b x + a} b \sqrt{c} x}{b^{2} c x^{2} - a^{2} c}\right) - {\left(24 \, C b^{4} f x^{4} - 40 \, B a^{2} b^{2} e + 30 \, {\left(C b^{4} e + B b^{4} f\right)} x^{3} + 8 \, {\left(5 \, B b^{4} e - {\left(C a^{2} b^{2} - 5 \, A b^{4}\right)} f\right)} x^{2} - 8 \, {\left(2 \, C a^{4} + 5 \, A a^{2} b^{2}\right)} f - 15 \, {\left(B a^{2} b^{2} f + {\left(C a^{2} b^{2} - 4 \, A b^{4}\right)} e\right)} x\right)} \sqrt{-b c x + a c} \sqrt{b x + a}}{120 \, b^{4}}\right]"," ",0,"[1/240*(15*(B*a^4*b*f + (C*a^4*b + 4*A*a^2*b^3)*e)*sqrt(-c)*log(2*b^2*c*x^2 + 2*sqrt(-b*c*x + a*c)*sqrt(b*x + a)*b*sqrt(-c)*x - a^2*c) + 2*(24*C*b^4*f*x^4 - 40*B*a^2*b^2*e + 30*(C*b^4*e + B*b^4*f)*x^3 + 8*(5*B*b^4*e - (C*a^2*b^2 - 5*A*b^4)*f)*x^2 - 8*(2*C*a^4 + 5*A*a^2*b^2)*f - 15*(B*a^2*b^2*f + (C*a^2*b^2 - 4*A*b^4)*e)*x)*sqrt(-b*c*x + a*c)*sqrt(b*x + a))/b^4, -1/120*(15*(B*a^4*b*f + (C*a^4*b + 4*A*a^2*b^3)*e)*sqrt(c)*arctan(sqrt(-b*c*x + a*c)*sqrt(b*x + a)*b*sqrt(c)*x/(b^2*c*x^2 - a^2*c)) - (24*C*b^4*f*x^4 - 40*B*a^2*b^2*e + 30*(C*b^4*e + B*b^4*f)*x^3 + 8*(5*B*b^4*e - (C*a^2*b^2 - 5*A*b^4)*f)*x^2 - 8*(2*C*a^4 + 5*A*a^2*b^2)*f - 15*(B*a^2*b^2*f + (C*a^2*b^2 - 4*A*b^4)*e)*x)*sqrt(-b*c*x + a*c)*sqrt(b*x + a))/b^4]","A",0
23,1,265,0,0.845184," ","integrate((C*x^2+B*x+A)*(b*x+a)^(1/2)*(-b*c*x+a*c)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(C a^{4} + 4 \, A a^{2} b^{2}\right)} \sqrt{-c} \log\left(2 \, b^{2} c x^{2} + 2 \, \sqrt{-b c x + a c} \sqrt{b x + a} b \sqrt{-c} x - a^{2} c\right) + 2 \, {\left(6 \, C b^{3} x^{3} + 8 \, B b^{3} x^{2} - 8 \, B a^{2} b - 3 \, {\left(C a^{2} b - 4 \, A b^{3}\right)} x\right)} \sqrt{-b c x + a c} \sqrt{b x + a}}{48 \, b^{3}}, -\frac{3 \, {\left(C a^{4} + 4 \, A a^{2} b^{2}\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-b c x + a c} \sqrt{b x + a} b \sqrt{c} x}{b^{2} c x^{2} - a^{2} c}\right) - {\left(6 \, C b^{3} x^{3} + 8 \, B b^{3} x^{2} - 8 \, B a^{2} b - 3 \, {\left(C a^{2} b - 4 \, A b^{3}\right)} x\right)} \sqrt{-b c x + a c} \sqrt{b x + a}}{24 \, b^{3}}\right]"," ",0,"[1/48*(3*(C*a^4 + 4*A*a^2*b^2)*sqrt(-c)*log(2*b^2*c*x^2 + 2*sqrt(-b*c*x + a*c)*sqrt(b*x + a)*b*sqrt(-c)*x - a^2*c) + 2*(6*C*b^3*x^3 + 8*B*b^3*x^2 - 8*B*a^2*b - 3*(C*a^2*b - 4*A*b^3)*x)*sqrt(-b*c*x + a*c)*sqrt(b*x + a))/b^3, -1/24*(3*(C*a^4 + 4*A*a^2*b^2)*sqrt(c)*arctan(sqrt(-b*c*x + a*c)*sqrt(b*x + a)*b*sqrt(c)*x/(b^2*c*x^2 - a^2*c)) - (6*C*b^3*x^3 + 8*B*b^3*x^2 - 8*B*a^2*b - 3*(C*a^2*b - 4*A*b^3)*x)*sqrt(-b*c*x + a*c)*sqrt(b*x + a))/b^3]","A",0
24,-1,0,0,0.000000," ","integrate((C*x^2+B*x+A)/(f*x+e)/(b*x+a)^(1/2)/(-b*c*x+a*c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
25,-1,0,0,0.000000," ","integrate((C*x^2+B*x+A)/(f*x+e)^2/(b*x+a)^(1/2)/(-b*c*x+a*c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
26,1,1355,0,163.672208," ","integrate((C*x^2+B*x+A)/(f*x+e)^3/(b*x+a)^(1/2)/(-b*c*x+a*c)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(3 \, B a^{2} b^{2} e^{3} f - {\left(C a^{2} b^{2} + 2 \, A b^{4}\right)} e^{4} - {\left(2 \, C a^{4} + A a^{2} b^{2}\right)} e^{2} f^{2} + {\left(3 \, B a^{2} b^{2} e f^{3} - {\left(C a^{2} b^{2} + 2 \, A b^{4}\right)} e^{2} f^{2} - {\left(2 \, C a^{4} + A a^{2} b^{2}\right)} f^{4}\right)} x^{2} + 2 \, {\left(3 \, B a^{2} b^{2} e^{2} f^{2} - {\left(C a^{2} b^{2} + 2 \, A b^{4}\right)} e^{3} f - {\left(2 \, C a^{4} + A a^{2} b^{2}\right)} e f^{3}\right)} x\right)} \sqrt{-b^{2} c e^{2} + a^{2} c f^{2}} \log\left(\frac{2 \, a^{2} b^{2} c e f x - a^{2} b^{2} c e^{2} + 2 \, a^{4} c f^{2} + {\left(2 \, b^{4} c e^{2} - a^{2} b^{2} c f^{2}\right)} x^{2} - 2 \, \sqrt{-b^{2} c e^{2} + a^{2} c f^{2}} {\left(b^{2} e x + a^{2} f\right)} \sqrt{-b c x + a c} \sqrt{b x + a}}{f^{2} x^{2} + 2 \, e f x + e^{2}}\right) - 2 \, {\left(2 \, B b^{4} e^{5} - B a^{2} b^{2} e^{3} f^{2} - B a^{4} e f^{4} - A a^{4} f^{5} - {\left(3 \, C a^{2} b^{2} + 4 \, A b^{4}\right)} e^{4} f + {\left(3 \, C a^{4} + 5 \, A a^{2} b^{2}\right)} e^{2} f^{3} + {\left(C b^{4} e^{5} + B b^{4} e^{4} f + B a^{2} b^{2} e^{2} f^{3} - 2 \, B a^{4} f^{5} - {\left(5 \, C a^{2} b^{2} + 3 \, A b^{4}\right)} e^{3} f^{2} + {\left(4 \, C a^{4} + 3 \, A a^{2} b^{2}\right)} e f^{4}\right)} x\right)} \sqrt{-b c x + a c} \sqrt{b x + a}}{4 \, {\left(b^{6} c e^{8} - 3 \, a^{2} b^{4} c e^{6} f^{2} + 3 \, a^{4} b^{2} c e^{4} f^{4} - a^{6} c e^{2} f^{6} + {\left(b^{6} c e^{6} f^{2} - 3 \, a^{2} b^{4} c e^{4} f^{4} + 3 \, a^{4} b^{2} c e^{2} f^{6} - a^{6} c f^{8}\right)} x^{2} + 2 \, {\left(b^{6} c e^{7} f - 3 \, a^{2} b^{4} c e^{5} f^{3} + 3 \, a^{4} b^{2} c e^{3} f^{5} - a^{6} c e f^{7}\right)} x\right)}}, -\frac{{\left(3 \, B a^{2} b^{2} e^{3} f - {\left(C a^{2} b^{2} + 2 \, A b^{4}\right)} e^{4} - {\left(2 \, C a^{4} + A a^{2} b^{2}\right)} e^{2} f^{2} + {\left(3 \, B a^{2} b^{2} e f^{3} - {\left(C a^{2} b^{2} + 2 \, A b^{4}\right)} e^{2} f^{2} - {\left(2 \, C a^{4} + A a^{2} b^{2}\right)} f^{4}\right)} x^{2} + 2 \, {\left(3 \, B a^{2} b^{2} e^{2} f^{2} - {\left(C a^{2} b^{2} + 2 \, A b^{4}\right)} e^{3} f - {\left(2 \, C a^{4} + A a^{2} b^{2}\right)} e f^{3}\right)} x\right)} \sqrt{b^{2} c e^{2} - a^{2} c f^{2}} \arctan\left(\frac{\sqrt{b^{2} c e^{2} - a^{2} c f^{2}} {\left(b^{2} e x + a^{2} f\right)} \sqrt{-b c x + a c} \sqrt{b x + a}}{a^{2} b^{2} c e^{2} - a^{4} c f^{2} - {\left(b^{4} c e^{2} - a^{2} b^{2} c f^{2}\right)} x^{2}}\right) + {\left(2 \, B b^{4} e^{5} - B a^{2} b^{2} e^{3} f^{2} - B a^{4} e f^{4} - A a^{4} f^{5} - {\left(3 \, C a^{2} b^{2} + 4 \, A b^{4}\right)} e^{4} f + {\left(3 \, C a^{4} + 5 \, A a^{2} b^{2}\right)} e^{2} f^{3} + {\left(C b^{4} e^{5} + B b^{4} e^{4} f + B a^{2} b^{2} e^{2} f^{3} - 2 \, B a^{4} f^{5} - {\left(5 \, C a^{2} b^{2} + 3 \, A b^{4}\right)} e^{3} f^{2} + {\left(4 \, C a^{4} + 3 \, A a^{2} b^{2}\right)} e f^{4}\right)} x\right)} \sqrt{-b c x + a c} \sqrt{b x + a}}{2 \, {\left(b^{6} c e^{8} - 3 \, a^{2} b^{4} c e^{6} f^{2} + 3 \, a^{4} b^{2} c e^{4} f^{4} - a^{6} c e^{2} f^{6} + {\left(b^{6} c e^{6} f^{2} - 3 \, a^{2} b^{4} c e^{4} f^{4} + 3 \, a^{4} b^{2} c e^{2} f^{6} - a^{6} c f^{8}\right)} x^{2} + 2 \, {\left(b^{6} c e^{7} f - 3 \, a^{2} b^{4} c e^{5} f^{3} + 3 \, a^{4} b^{2} c e^{3} f^{5} - a^{6} c e f^{7}\right)} x\right)}}\right]"," ",0,"[1/4*((3*B*a^2*b^2*e^3*f - (C*a^2*b^2 + 2*A*b^4)*e^4 - (2*C*a^4 + A*a^2*b^2)*e^2*f^2 + (3*B*a^2*b^2*e*f^3 - (C*a^2*b^2 + 2*A*b^4)*e^2*f^2 - (2*C*a^4 + A*a^2*b^2)*f^4)*x^2 + 2*(3*B*a^2*b^2*e^2*f^2 - (C*a^2*b^2 + 2*A*b^4)*e^3*f - (2*C*a^4 + A*a^2*b^2)*e*f^3)*x)*sqrt(-b^2*c*e^2 + a^2*c*f^2)*log((2*a^2*b^2*c*e*f*x - a^2*b^2*c*e^2 + 2*a^4*c*f^2 + (2*b^4*c*e^2 - a^2*b^2*c*f^2)*x^2 - 2*sqrt(-b^2*c*e^2 + a^2*c*f^2)*(b^2*e*x + a^2*f)*sqrt(-b*c*x + a*c)*sqrt(b*x + a))/(f^2*x^2 + 2*e*f*x + e^2)) - 2*(2*B*b^4*e^5 - B*a^2*b^2*e^3*f^2 - B*a^4*e*f^4 - A*a^4*f^5 - (3*C*a^2*b^2 + 4*A*b^4)*e^4*f + (3*C*a^4 + 5*A*a^2*b^2)*e^2*f^3 + (C*b^4*e^5 + B*b^4*e^4*f + B*a^2*b^2*e^2*f^3 - 2*B*a^4*f^5 - (5*C*a^2*b^2 + 3*A*b^4)*e^3*f^2 + (4*C*a^4 + 3*A*a^2*b^2)*e*f^4)*x)*sqrt(-b*c*x + a*c)*sqrt(b*x + a))/(b^6*c*e^8 - 3*a^2*b^4*c*e^6*f^2 + 3*a^4*b^2*c*e^4*f^4 - a^6*c*e^2*f^6 + (b^6*c*e^6*f^2 - 3*a^2*b^4*c*e^4*f^4 + 3*a^4*b^2*c*e^2*f^6 - a^6*c*f^8)*x^2 + 2*(b^6*c*e^7*f - 3*a^2*b^4*c*e^5*f^3 + 3*a^4*b^2*c*e^3*f^5 - a^6*c*e*f^7)*x), -1/2*((3*B*a^2*b^2*e^3*f - (C*a^2*b^2 + 2*A*b^4)*e^4 - (2*C*a^4 + A*a^2*b^2)*e^2*f^2 + (3*B*a^2*b^2*e*f^3 - (C*a^2*b^2 + 2*A*b^4)*e^2*f^2 - (2*C*a^4 + A*a^2*b^2)*f^4)*x^2 + 2*(3*B*a^2*b^2*e^2*f^2 - (C*a^2*b^2 + 2*A*b^4)*e^3*f - (2*C*a^4 + A*a^2*b^2)*e*f^3)*x)*sqrt(b^2*c*e^2 - a^2*c*f^2)*arctan(sqrt(b^2*c*e^2 - a^2*c*f^2)*(b^2*e*x + a^2*f)*sqrt(-b*c*x + a*c)*sqrt(b*x + a)/(a^2*b^2*c*e^2 - a^4*c*f^2 - (b^4*c*e^2 - a^2*b^2*c*f^2)*x^2)) + (2*B*b^4*e^5 - B*a^2*b^2*e^3*f^2 - B*a^4*e*f^4 - A*a^4*f^5 - (3*C*a^2*b^2 + 4*A*b^4)*e^4*f + (3*C*a^4 + 5*A*a^2*b^2)*e^2*f^3 + (C*b^4*e^5 + B*b^4*e^4*f + B*a^2*b^2*e^2*f^3 - 2*B*a^4*f^5 - (5*C*a^2*b^2 + 3*A*b^4)*e^3*f^2 + (4*C*a^4 + 3*A*a^2*b^2)*e*f^4)*x)*sqrt(-b*c*x + a*c)*sqrt(b*x + a))/(b^6*c*e^8 - 3*a^2*b^4*c*e^6*f^2 + 3*a^4*b^2*c*e^4*f^4 - a^6*c*e^2*f^6 + (b^6*c*e^6*f^2 - 3*a^2*b^4*c*e^4*f^4 + 3*a^4*b^2*c*e^2*f^6 - a^6*c*f^8)*x^2 + 2*(b^6*c*e^7*f - 3*a^2*b^4*c*e^5*f^3 + 3*a^4*b^2*c*e^3*f^5 - a^6*c*e*f^7)*x)]","A",0
27,1,700,0,0.777442," ","integrate((f*x+e)^3*(C*x^2+B*x+A)/(b*x+a)^(1/2)/(-b*c*x+a*c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(12 \, B a^{2} b^{3} e^{2} f + 3 \, B a^{4} b f^{3} + 4 \, {\left(C a^{2} b^{3} + 2 \, A b^{5}\right)} e^{3} + 3 \, {\left(3 \, C a^{4} b + 4 \, A a^{2} b^{3}\right)} e f^{2}\right)} \sqrt{-c} \log\left(2 \, b^{2} c x^{2} - 2 \, \sqrt{-b c x + a c} \sqrt{b x + a} b \sqrt{-c} x - a^{2} c\right) + 2 \, {\left(24 \, C b^{4} f^{3} x^{4} + 120 \, B b^{4} e^{3} + 240 \, B a^{2} b^{2} e f^{2} + 120 \, {\left(2 \, C a^{2} b^{2} + 3 \, A b^{4}\right)} e^{2} f + 16 \, {\left(4 \, C a^{4} + 5 \, A a^{2} b^{2}\right)} f^{3} + 30 \, {\left(3 \, C b^{4} e f^{2} + B b^{4} f^{3}\right)} x^{3} + 8 \, {\left(15 \, C b^{4} e^{2} f + 15 \, B b^{4} e f^{2} + {\left(4 \, C a^{2} b^{2} + 5 \, A b^{4}\right)} f^{3}\right)} x^{2} + 15 \, {\left(4 \, C b^{4} e^{3} + 12 \, B b^{4} e^{2} f + 3 \, B a^{2} b^{2} f^{3} + 3 \, {\left(3 \, C a^{2} b^{2} + 4 \, A b^{4}\right)} e f^{2}\right)} x\right)} \sqrt{-b c x + a c} \sqrt{b x + a}}{240 \, b^{6} c}, -\frac{15 \, {\left(12 \, B a^{2} b^{3} e^{2} f + 3 \, B a^{4} b f^{3} + 4 \, {\left(C a^{2} b^{3} + 2 \, A b^{5}\right)} e^{3} + 3 \, {\left(3 \, C a^{4} b + 4 \, A a^{2} b^{3}\right)} e f^{2}\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-b c x + a c} \sqrt{b x + a} b \sqrt{c} x}{b^{2} c x^{2} - a^{2} c}\right) + {\left(24 \, C b^{4} f^{3} x^{4} + 120 \, B b^{4} e^{3} + 240 \, B a^{2} b^{2} e f^{2} + 120 \, {\left(2 \, C a^{2} b^{2} + 3 \, A b^{4}\right)} e^{2} f + 16 \, {\left(4 \, C a^{4} + 5 \, A a^{2} b^{2}\right)} f^{3} + 30 \, {\left(3 \, C b^{4} e f^{2} + B b^{4} f^{3}\right)} x^{3} + 8 \, {\left(15 \, C b^{4} e^{2} f + 15 \, B b^{4} e f^{2} + {\left(4 \, C a^{2} b^{2} + 5 \, A b^{4}\right)} f^{3}\right)} x^{2} + 15 \, {\left(4 \, C b^{4} e^{3} + 12 \, B b^{4} e^{2} f + 3 \, B a^{2} b^{2} f^{3} + 3 \, {\left(3 \, C a^{2} b^{2} + 4 \, A b^{4}\right)} e f^{2}\right)} x\right)} \sqrt{-b c x + a c} \sqrt{b x + a}}{120 \, b^{6} c}\right]"," ",0,"[-1/240*(15*(12*B*a^2*b^3*e^2*f + 3*B*a^4*b*f^3 + 4*(C*a^2*b^3 + 2*A*b^5)*e^3 + 3*(3*C*a^4*b + 4*A*a^2*b^3)*e*f^2)*sqrt(-c)*log(2*b^2*c*x^2 - 2*sqrt(-b*c*x + a*c)*sqrt(b*x + a)*b*sqrt(-c)*x - a^2*c) + 2*(24*C*b^4*f^3*x^4 + 120*B*b^4*e^3 + 240*B*a^2*b^2*e*f^2 + 120*(2*C*a^2*b^2 + 3*A*b^4)*e^2*f + 16*(4*C*a^4 + 5*A*a^2*b^2)*f^3 + 30*(3*C*b^4*e*f^2 + B*b^4*f^3)*x^3 + 8*(15*C*b^4*e^2*f + 15*B*b^4*e*f^2 + (4*C*a^2*b^2 + 5*A*b^4)*f^3)*x^2 + 15*(4*C*b^4*e^3 + 12*B*b^4*e^2*f + 3*B*a^2*b^2*f^3 + 3*(3*C*a^2*b^2 + 4*A*b^4)*e*f^2)*x)*sqrt(-b*c*x + a*c)*sqrt(b*x + a))/(b^6*c), -1/120*(15*(12*B*a^2*b^3*e^2*f + 3*B*a^4*b*f^3 + 4*(C*a^2*b^3 + 2*A*b^5)*e^3 + 3*(3*C*a^4*b + 4*A*a^2*b^3)*e*f^2)*sqrt(c)*arctan(sqrt(-b*c*x + a*c)*sqrt(b*x + a)*b*sqrt(c)*x/(b^2*c*x^2 - a^2*c)) + (24*C*b^4*f^3*x^4 + 120*B*b^4*e^3 + 240*B*a^2*b^2*e*f^2 + 120*(2*C*a^2*b^2 + 3*A*b^4)*e^2*f + 16*(4*C*a^4 + 5*A*a^2*b^2)*f^3 + 30*(3*C*b^4*e*f^2 + B*b^4*f^3)*x^3 + 8*(15*C*b^4*e^2*f + 15*B*b^4*e*f^2 + (4*C*a^2*b^2 + 5*A*b^4)*f^3)*x^2 + 15*(4*C*b^4*e^3 + 12*B*b^4*e^2*f + 3*B*a^2*b^2*f^3 + 3*(3*C*a^2*b^2 + 4*A*b^4)*e*f^2)*x)*sqrt(-b*c*x + a*c)*sqrt(b*x + a))/(b^6*c)]","A",0
28,1,482,0,1.220320," ","integrate((f*x+e)^2*(C*x^2+B*x+A)/(b*x+a)^(1/2)/(-b*c*x+a*c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(8 \, B a^{2} b^{2} e f + 4 \, {\left(C a^{2} b^{2} + 2 \, A b^{4}\right)} e^{2} + {\left(3 \, C a^{4} + 4 \, A a^{2} b^{2}\right)} f^{2}\right)} \sqrt{-c} \log\left(2 \, b^{2} c x^{2} - 2 \, \sqrt{-b c x + a c} \sqrt{b x + a} b \sqrt{-c} x - a^{2} c\right) + 2 \, {\left(6 \, C b^{3} f^{2} x^{3} + 24 \, B b^{3} e^{2} + 16 \, B a^{2} b f^{2} + 16 \, {\left(2 \, C a^{2} b + 3 \, A b^{3}\right)} e f + 8 \, {\left(2 \, C b^{3} e f + B b^{3} f^{2}\right)} x^{2} + 3 \, {\left(4 \, C b^{3} e^{2} + 8 \, B b^{3} e f + {\left(3 \, C a^{2} b + 4 \, A b^{3}\right)} f^{2}\right)} x\right)} \sqrt{-b c x + a c} \sqrt{b x + a}}{48 \, b^{5} c}, -\frac{3 \, {\left(8 \, B a^{2} b^{2} e f + 4 \, {\left(C a^{2} b^{2} + 2 \, A b^{4}\right)} e^{2} + {\left(3 \, C a^{4} + 4 \, A a^{2} b^{2}\right)} f^{2}\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-b c x + a c} \sqrt{b x + a} b \sqrt{c} x}{b^{2} c x^{2} - a^{2} c}\right) + {\left(6 \, C b^{3} f^{2} x^{3} + 24 \, B b^{3} e^{2} + 16 \, B a^{2} b f^{2} + 16 \, {\left(2 \, C a^{2} b + 3 \, A b^{3}\right)} e f + 8 \, {\left(2 \, C b^{3} e f + B b^{3} f^{2}\right)} x^{2} + 3 \, {\left(4 \, C b^{3} e^{2} + 8 \, B b^{3} e f + {\left(3 \, C a^{2} b + 4 \, A b^{3}\right)} f^{2}\right)} x\right)} \sqrt{-b c x + a c} \sqrt{b x + a}}{24 \, b^{5} c}\right]"," ",0,"[-1/48*(3*(8*B*a^2*b^2*e*f + 4*(C*a^2*b^2 + 2*A*b^4)*e^2 + (3*C*a^4 + 4*A*a^2*b^2)*f^2)*sqrt(-c)*log(2*b^2*c*x^2 - 2*sqrt(-b*c*x + a*c)*sqrt(b*x + a)*b*sqrt(-c)*x - a^2*c) + 2*(6*C*b^3*f^2*x^3 + 24*B*b^3*e^2 + 16*B*a^2*b*f^2 + 16*(2*C*a^2*b + 3*A*b^3)*e*f + 8*(2*C*b^3*e*f + B*b^3*f^2)*x^2 + 3*(4*C*b^3*e^2 + 8*B*b^3*e*f + (3*C*a^2*b + 4*A*b^3)*f^2)*x)*sqrt(-b*c*x + a*c)*sqrt(b*x + a))/(b^5*c), -1/24*(3*(8*B*a^2*b^2*e*f + 4*(C*a^2*b^2 + 2*A*b^4)*e^2 + (3*C*a^4 + 4*A*a^2*b^2)*f^2)*sqrt(c)*arctan(sqrt(-b*c*x + a*c)*sqrt(b*x + a)*b*sqrt(c)*x/(b^2*c*x^2 - a^2*c)) + (6*C*b^3*f^2*x^3 + 24*B*b^3*e^2 + 16*B*a^2*b*f^2 + 16*(2*C*a^2*b + 3*A*b^3)*e*f + 8*(2*C*b^3*e*f + B*b^3*f^2)*x^2 + 3*(4*C*b^3*e^2 + 8*B*b^3*e*f + (3*C*a^2*b + 4*A*b^3)*f^2)*x)*sqrt(-b*c*x + a*c)*sqrt(b*x + a))/(b^5*c)]","A",0
29,1,302,0,0.710924," ","integrate((f*x+e)*(C*x^2+B*x+A)/(b*x+a)^(1/2)/(-b*c*x+a*c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(B a^{2} b f + {\left(C a^{2} b + 2 \, A b^{3}\right)} e\right)} \sqrt{-c} \log\left(2 \, b^{2} c x^{2} - 2 \, \sqrt{-b c x + a c} \sqrt{b x + a} b \sqrt{-c} x - a^{2} c\right) + 2 \, {\left(2 \, C b^{2} f x^{2} + 6 \, B b^{2} e + 2 \, {\left(2 \, C a^{2} + 3 \, A b^{2}\right)} f + 3 \, {\left(C b^{2} e + B b^{2} f\right)} x\right)} \sqrt{-b c x + a c} \sqrt{b x + a}}{12 \, b^{4} c}, -\frac{3 \, {\left(B a^{2} b f + {\left(C a^{2} b + 2 \, A b^{3}\right)} e\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-b c x + a c} \sqrt{b x + a} b \sqrt{c} x}{b^{2} c x^{2} - a^{2} c}\right) + {\left(2 \, C b^{2} f x^{2} + 6 \, B b^{2} e + 2 \, {\left(2 \, C a^{2} + 3 \, A b^{2}\right)} f + 3 \, {\left(C b^{2} e + B b^{2} f\right)} x\right)} \sqrt{-b c x + a c} \sqrt{b x + a}}{6 \, b^{4} c}\right]"," ",0,"[-1/12*(3*(B*a^2*b*f + (C*a^2*b + 2*A*b^3)*e)*sqrt(-c)*log(2*b^2*c*x^2 - 2*sqrt(-b*c*x + a*c)*sqrt(b*x + a)*b*sqrt(-c)*x - a^2*c) + 2*(2*C*b^2*f*x^2 + 6*B*b^2*e + 2*(2*C*a^2 + 3*A*b^2)*f + 3*(C*b^2*e + B*b^2*f)*x)*sqrt(-b*c*x + a*c)*sqrt(b*x + a))/(b^4*c), -1/6*(3*(B*a^2*b*f + (C*a^2*b + 2*A*b^3)*e)*sqrt(c)*arctan(sqrt(-b*c*x + a*c)*sqrt(b*x + a)*b*sqrt(c)*x/(b^2*c*x^2 - a^2*c)) + (2*C*b^2*f*x^2 + 6*B*b^2*e + 2*(2*C*a^2 + 3*A*b^2)*f + 3*(C*b^2*e + B*b^2*f)*x)*sqrt(-b*c*x + a*c)*sqrt(b*x + a))/(b^4*c)]","A",0
30,1,196,0,0.771846," ","integrate((C*x^2+B*x+A)/(b*x+a)^(1/2)/(-b*c*x+a*c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(C a^{2} + 2 \, A b^{2}\right)} \sqrt{-c} \log\left(2 \, b^{2} c x^{2} - 2 \, \sqrt{-b c x + a c} \sqrt{b x + a} b \sqrt{-c} x - a^{2} c\right) + 2 \, {\left(C b x + 2 \, B b\right)} \sqrt{-b c x + a c} \sqrt{b x + a}}{4 \, b^{3} c}, -\frac{{\left(C a^{2} + 2 \, A b^{2}\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-b c x + a c} \sqrt{b x + a} b \sqrt{c} x}{b^{2} c x^{2} - a^{2} c}\right) + {\left(C b x + 2 \, B b\right)} \sqrt{-b c x + a c} \sqrt{b x + a}}{2 \, b^{3} c}\right]"," ",0,"[-1/4*((C*a^2 + 2*A*b^2)*sqrt(-c)*log(2*b^2*c*x^2 - 2*sqrt(-b*c*x + a*c)*sqrt(b*x + a)*b*sqrt(-c)*x - a^2*c) + 2*(C*b*x + 2*B*b)*sqrt(-b*c*x + a*c)*sqrt(b*x + a))/(b^3*c), -1/2*((C*a^2 + 2*A*b^2)*sqrt(c)*arctan(sqrt(-b*c*x + a*c)*sqrt(b*x + a)*b*sqrt(c)*x/(b^2*c*x^2 - a^2*c)) + (C*b*x + 2*B*b)*sqrt(-b*c*x + a*c)*sqrt(b*x + a))/(b^3*c)]","A",0
31,-1,0,0,0.000000," ","integrate((C*x^2+B*x+A)/(f*x+e)/(b*x+a)^(1/2)/(-b*c*x+a*c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
32,-1,0,0,0.000000," ","integrate((C*x^2+B*x+A)/(f*x+e)^2/(b*x+a)^(1/2)/(-b*c*x+a*c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
33,-1,0,0,0.000000," ","integrate((C*x^2+B*x+A)/(f*x+e)^3/(b*x+a)^(1/2)/(-b*c*x+a*c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
34,1,73,0,1.286350," ","integrate(x*(c*x^2+b*x+a)/(d*x-1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""fricas"")","-\frac{3 \, b d \log\left(-d x + \sqrt{d x + 1} \sqrt{d x - 1}\right) - {\left(2 \, c d^{2} x^{2} + 3 \, b d^{2} x + 6 \, a d^{2} + 4 \, c\right)} \sqrt{d x + 1} \sqrt{d x - 1}}{6 \, d^{4}}"," ",0,"-1/6*(3*b*d*log(-d*x + sqrt(d*x + 1)*sqrt(d*x - 1)) - (2*c*d^2*x^2 + 3*b*d^2*x + 6*a*d^2 + 4*c)*sqrt(d*x + 1)*sqrt(d*x - 1))/d^4","A",0
35,1,61,0,1.079818," ","integrate((c*x^2+b*x+a)/(d*x-1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""fricas"")","\frac{{\left(c d x + 2 \, b d\right)} \sqrt{d x + 1} \sqrt{d x - 1} - {\left(2 \, a d^{2} + c\right)} \log\left(-d x + \sqrt{d x + 1} \sqrt{d x - 1}\right)}{2 \, d^{3}}"," ",0,"1/2*((c*d*x + 2*b*d)*sqrt(d*x + 1)*sqrt(d*x - 1) - (2*a*d^2 + c)*log(-d*x + sqrt(d*x + 1)*sqrt(d*x - 1)))/d^3","A",0
36,1,73,0,0.626774," ","integrate((c*x^2+b*x+a)/x/(d*x-1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""fricas"")","\frac{2 \, a d^{2} \arctan\left(-d x + \sqrt{d x + 1} \sqrt{d x - 1}\right) - b d \log\left(-d x + \sqrt{d x + 1} \sqrt{d x - 1}\right) + \sqrt{d x + 1} \sqrt{d x - 1} c}{d^{2}}"," ",0,"(2*a*d^2*arctan(-d*x + sqrt(d*x + 1)*sqrt(d*x - 1)) - b*d*log(-d*x + sqrt(d*x + 1)*sqrt(d*x - 1)) + sqrt(d*x + 1)*sqrt(d*x - 1)*c)/d^2","A",0
37,1,82,0,1.027145," ","integrate((c*x^2+b*x+a)/x^2/(d*x-1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""fricas"")","\frac{a d^{2} x + 2 \, b d x \arctan\left(-d x + \sqrt{d x + 1} \sqrt{d x - 1}\right) + \sqrt{d x + 1} \sqrt{d x - 1} a d - c x \log\left(-d x + \sqrt{d x + 1} \sqrt{d x - 1}\right)}{d x}"," ",0,"(a*d^2*x + 2*b*d*x*arctan(-d*x + sqrt(d*x + 1)*sqrt(d*x - 1)) + sqrt(d*x + 1)*sqrt(d*x - 1)*a*d - c*x*log(-d*x + sqrt(d*x + 1)*sqrt(d*x - 1)))/(d*x)","A",0
38,1,69,0,1.113531," ","integrate((c*x^2+b*x+a)/x^3/(d*x-1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""fricas"")","\frac{2 \, b d x^{2} + 2 \, {\left(a d^{2} + 2 \, c\right)} x^{2} \arctan\left(-d x + \sqrt{d x + 1} \sqrt{d x - 1}\right) + {\left(2 \, b x + a\right)} \sqrt{d x + 1} \sqrt{d x - 1}}{2 \, x^{2}}"," ",0,"1/2*(2*b*d*x^2 + 2*(a*d^2 + 2*c)*x^2*arctan(-d*x + sqrt(d*x + 1)*sqrt(d*x - 1)) + (2*b*x + a)*sqrt(d*x + 1)*sqrt(d*x - 1))/x^2","A",0
39,1,90,0,1.072920," ","integrate((c*x^2+b*x+a)/x^4/(d*x-1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""fricas"")","\frac{6 \, b d^{2} x^{3} \arctan\left(-d x + \sqrt{d x + 1} \sqrt{d x - 1}\right) + 2 \, {\left(2 \, a d^{3} + 3 \, c d\right)} x^{3} + {\left(2 \, {\left(2 \, a d^{2} + 3 \, c\right)} x^{2} + 3 \, b x + 2 \, a\right)} \sqrt{d x + 1} \sqrt{d x - 1}}{6 \, x^{3}}"," ",0,"1/6*(6*b*d^2*x^3*arctan(-d*x + sqrt(d*x + 1)*sqrt(d*x - 1)) + 2*(2*a*d^3 + 3*c*d)*x^3 + (2*(2*a*d^2 + 3*c)*x^2 + 3*b*x + 2*a)*sqrt(d*x + 1)*sqrt(d*x - 1))/x^3","A",0
40,1,1186,0,0.998879," ","integrate((c*x^2+b*x+a)/(e*x+d)^3/(-1+x)^(1/2)/(1+x)^(1/2),x, algorithm=""fricas"")","\left[\frac{c d^{7} + b d^{6} e - {\left(3 \, a + 5 \, c\right)} d^{5} e^{2} + b d^{4} e^{3} + {\left(3 \, a + 4 \, c\right)} d^{3} e^{4} - 2 \, b d^{2} e^{5} + {\left(c d^{5} e^{2} + b d^{4} e^{3} - {\left(3 \, a + 5 \, c\right)} d^{3} e^{4} + b d^{2} e^{5} + {\left(3 \, a + 4 \, c\right)} d e^{6} - 2 \, b e^{7}\right)} x^{2} + {\left({\left(2 \, a + c\right)} d^{4} e^{2} - 3 \, b d^{3} e^{3} + {\left(a + 2 \, c\right)} d^{2} e^{4} + {\left({\left(2 \, a + c\right)} d^{2} e^{4} - 3 \, b d e^{5} + {\left(a + 2 \, c\right)} e^{6}\right)} x^{2} + 2 \, {\left({\left(2 \, a + c\right)} d^{3} e^{3} - 3 \, b d^{2} e^{4} + {\left(a + 2 \, c\right)} d e^{5}\right)} x\right)} \sqrt{d^{2} - e^{2}} \log\left(\frac{d^{2} x + d e + {\left(d^{2} - e^{2} + \sqrt{d^{2} - e^{2}} d\right)} \sqrt{x + 1} \sqrt{x - 1} + \sqrt{d^{2} - e^{2}} {\left(d x + e\right)}}{e x + d}\right) + {\left(2 \, b d^{5} e^{2} - {\left(4 \, a + 3 \, c\right)} d^{4} e^{3} - b d^{3} e^{4} + {\left(5 \, a + 3 \, c\right)} d^{2} e^{5} - b d e^{6} - a e^{7} + {\left(c d^{5} e^{2} + b d^{4} e^{3} - {\left(3 \, a + 5 \, c\right)} d^{3} e^{4} + b d^{2} e^{5} + {\left(3 \, a + 4 \, c\right)} d e^{6} - 2 \, b e^{7}\right)} x\right)} \sqrt{x + 1} \sqrt{x - 1} + 2 \, {\left(c d^{6} e + b d^{5} e^{2} - {\left(3 \, a + 5 \, c\right)} d^{4} e^{3} + b d^{3} e^{4} + {\left(3 \, a + 4 \, c\right)} d^{2} e^{5} - 2 \, b d e^{6}\right)} x}{2 \, {\left(d^{8} e^{2} - 3 \, d^{6} e^{4} + 3 \, d^{4} e^{6} - d^{2} e^{8} + {\left(d^{6} e^{4} - 3 \, d^{4} e^{6} + 3 \, d^{2} e^{8} - e^{10}\right)} x^{2} + 2 \, {\left(d^{7} e^{3} - 3 \, d^{5} e^{5} + 3 \, d^{3} e^{7} - d e^{9}\right)} x\right)}}, \frac{c d^{7} + b d^{6} e - {\left(3 \, a + 5 \, c\right)} d^{5} e^{2} + b d^{4} e^{3} + {\left(3 \, a + 4 \, c\right)} d^{3} e^{4} - 2 \, b d^{2} e^{5} + {\left(c d^{5} e^{2} + b d^{4} e^{3} - {\left(3 \, a + 5 \, c\right)} d^{3} e^{4} + b d^{2} e^{5} + {\left(3 \, a + 4 \, c\right)} d e^{6} - 2 \, b e^{7}\right)} x^{2} - 2 \, {\left({\left(2 \, a + c\right)} d^{4} e^{2} - 3 \, b d^{3} e^{3} + {\left(a + 2 \, c\right)} d^{2} e^{4} + {\left({\left(2 \, a + c\right)} d^{2} e^{4} - 3 \, b d e^{5} + {\left(a + 2 \, c\right)} e^{6}\right)} x^{2} + 2 \, {\left({\left(2 \, a + c\right)} d^{3} e^{3} - 3 \, b d^{2} e^{4} + {\left(a + 2 \, c\right)} d e^{5}\right)} x\right)} \sqrt{-d^{2} + e^{2}} \arctan\left(-\frac{\sqrt{-d^{2} + e^{2}} e \sqrt{x + 1} \sqrt{x - 1} - \sqrt{-d^{2} + e^{2}} {\left(e x + d\right)}}{d^{2} - e^{2}}\right) + {\left(2 \, b d^{5} e^{2} - {\left(4 \, a + 3 \, c\right)} d^{4} e^{3} - b d^{3} e^{4} + {\left(5 \, a + 3 \, c\right)} d^{2} e^{5} - b d e^{6} - a e^{7} + {\left(c d^{5} e^{2} + b d^{4} e^{3} - {\left(3 \, a + 5 \, c\right)} d^{3} e^{4} + b d^{2} e^{5} + {\left(3 \, a + 4 \, c\right)} d e^{6} - 2 \, b e^{7}\right)} x\right)} \sqrt{x + 1} \sqrt{x - 1} + 2 \, {\left(c d^{6} e + b d^{5} e^{2} - {\left(3 \, a + 5 \, c\right)} d^{4} e^{3} + b d^{3} e^{4} + {\left(3 \, a + 4 \, c\right)} d^{2} e^{5} - 2 \, b d e^{6}\right)} x}{2 \, {\left(d^{8} e^{2} - 3 \, d^{6} e^{4} + 3 \, d^{4} e^{6} - d^{2} e^{8} + {\left(d^{6} e^{4} - 3 \, d^{4} e^{6} + 3 \, d^{2} e^{8} - e^{10}\right)} x^{2} + 2 \, {\left(d^{7} e^{3} - 3 \, d^{5} e^{5} + 3 \, d^{3} e^{7} - d e^{9}\right)} x\right)}}\right]"," ",0,"[1/2*(c*d^7 + b*d^6*e - (3*a + 5*c)*d^5*e^2 + b*d^4*e^3 + (3*a + 4*c)*d^3*e^4 - 2*b*d^2*e^5 + (c*d^5*e^2 + b*d^4*e^3 - (3*a + 5*c)*d^3*e^4 + b*d^2*e^5 + (3*a + 4*c)*d*e^6 - 2*b*e^7)*x^2 + ((2*a + c)*d^4*e^2 - 3*b*d^3*e^3 + (a + 2*c)*d^2*e^4 + ((2*a + c)*d^2*e^4 - 3*b*d*e^5 + (a + 2*c)*e^6)*x^2 + 2*((2*a + c)*d^3*e^3 - 3*b*d^2*e^4 + (a + 2*c)*d*e^5)*x)*sqrt(d^2 - e^2)*log((d^2*x + d*e + (d^2 - e^2 + sqrt(d^2 - e^2)*d)*sqrt(x + 1)*sqrt(x - 1) + sqrt(d^2 - e^2)*(d*x + e))/(e*x + d)) + (2*b*d^5*e^2 - (4*a + 3*c)*d^4*e^3 - b*d^3*e^4 + (5*a + 3*c)*d^2*e^5 - b*d*e^6 - a*e^7 + (c*d^5*e^2 + b*d^4*e^3 - (3*a + 5*c)*d^3*e^4 + b*d^2*e^5 + (3*a + 4*c)*d*e^6 - 2*b*e^7)*x)*sqrt(x + 1)*sqrt(x - 1) + 2*(c*d^6*e + b*d^5*e^2 - (3*a + 5*c)*d^4*e^3 + b*d^3*e^4 + (3*a + 4*c)*d^2*e^5 - 2*b*d*e^6)*x)/(d^8*e^2 - 3*d^6*e^4 + 3*d^4*e^6 - d^2*e^8 + (d^6*e^4 - 3*d^4*e^6 + 3*d^2*e^8 - e^10)*x^2 + 2*(d^7*e^3 - 3*d^5*e^5 + 3*d^3*e^7 - d*e^9)*x), 1/2*(c*d^7 + b*d^6*e - (3*a + 5*c)*d^5*e^2 + b*d^4*e^3 + (3*a + 4*c)*d^3*e^4 - 2*b*d^2*e^5 + (c*d^5*e^2 + b*d^4*e^3 - (3*a + 5*c)*d^3*e^4 + b*d^2*e^5 + (3*a + 4*c)*d*e^6 - 2*b*e^7)*x^2 - 2*((2*a + c)*d^4*e^2 - 3*b*d^3*e^3 + (a + 2*c)*d^2*e^4 + ((2*a + c)*d^2*e^4 - 3*b*d*e^5 + (a + 2*c)*e^6)*x^2 + 2*((2*a + c)*d^3*e^3 - 3*b*d^2*e^4 + (a + 2*c)*d*e^5)*x)*sqrt(-d^2 + e^2)*arctan(-(sqrt(-d^2 + e^2)*e*sqrt(x + 1)*sqrt(x - 1) - sqrt(-d^2 + e^2)*(e*x + d))/(d^2 - e^2)) + (2*b*d^5*e^2 - (4*a + 3*c)*d^4*e^3 - b*d^3*e^4 + (5*a + 3*c)*d^2*e^5 - b*d*e^6 - a*e^7 + (c*d^5*e^2 + b*d^4*e^3 - (3*a + 5*c)*d^3*e^4 + b*d^2*e^5 + (3*a + 4*c)*d*e^6 - 2*b*e^7)*x)*sqrt(x + 1)*sqrt(x - 1) + 2*(c*d^6*e + b*d^5*e^2 - (3*a + 5*c)*d^4*e^3 + b*d^3*e^4 + (3*a + 4*c)*d^2*e^5 - 2*b*d*e^6)*x)/(d^8*e^2 - 3*d^6*e^4 + 3*d^4*e^6 - d^2*e^8 + (d^6*e^4 - 3*d^4*e^6 + 3*d^2*e^8 - e^10)*x^2 + 2*(d^7*e^3 - 3*d^5*e^5 + 3*d^3*e^7 - d*e^9)*x)]","B",0
41,1,3096,0,8.081037," ","integrate((b*x+a)^2*(C*x^2+B*x+A)*(d*x+c)^(1/2)*(f*x+e)^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(21 \, C b^{2} d^{6} e^{6} - 14 \, {\left(C b^{2} c d^{5} + 2 \, {\left(2 \, C a b + B b^{2}\right)} d^{6}\right)} e^{5} f - 5 \, {\left(C b^{2} c^{2} d^{4} - 4 \, {\left(2 \, C a b + B b^{2}\right)} c d^{5} - 8 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} d^{6}\right)} e^{4} f^{2} - 4 \, {\left(C b^{2} c^{3} d^{3} - 2 \, {\left(2 \, C a b + B b^{2}\right)} c^{2} d^{4} + 8 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c d^{5} + 16 \, {\left(B a^{2} + 2 \, A a b\right)} d^{6}\right)} e^{3} f^{3} - {\left(5 \, C b^{2} c^{4} d^{2} - 128 \, A a^{2} d^{6} - 8 \, {\left(2 \, C a b + B b^{2}\right)} c^{3} d^{3} + 16 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c^{2} d^{4} - 64 \, {\left(B a^{2} + 2 \, A a b\right)} c d^{5}\right)} e^{2} f^{4} - 2 \, {\left(7 \, C b^{2} c^{5} d + 128 \, A a^{2} c d^{5} - 10 \, {\left(2 \, C a b + B b^{2}\right)} c^{4} d^{2} + 16 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c^{3} d^{3} - 32 \, {\left(B a^{2} + 2 \, A a b\right)} c^{2} d^{4}\right)} e f^{5} + {\left(21 \, C b^{2} c^{6} + 128 \, A a^{2} c^{2} d^{4} - 28 \, {\left(2 \, C a b + B b^{2}\right)} c^{5} d + 40 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c^{4} d^{2} - 64 \, {\left(B a^{2} + 2 \, A a b\right)} c^{3} d^{3}\right)} f^{6}\right)} \sqrt{d f} \log\left(8 \, d^{2} f^{2} x^{2} + d^{2} e^{2} + 6 \, c d e f + c^{2} f^{2} - 4 \, {\left(2 \, d f x + d e + c f\right)} \sqrt{d f} \sqrt{d x + c} \sqrt{f x + e} + 8 \, {\left(d^{2} e f + c d f^{2}\right)} x\right) + 4 \, {\left(1280 \, C b^{2} d^{6} f^{6} x^{5} + 315 \, C b^{2} d^{6} e^{5} f - 105 \, {\left(C b^{2} c d^{5} + 4 \, {\left(2 \, C a b + B b^{2}\right)} d^{6}\right)} e^{4} f^{2} - 2 \, {\left(41 \, C b^{2} c^{2} d^{4} - 80 \, {\left(2 \, C a b + B b^{2}\right)} c d^{5} - 300 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} d^{6}\right)} e^{3} f^{3} - 2 \, {\left(41 \, C b^{2} c^{3} d^{3} - 68 \, {\left(2 \, C a b + B b^{2}\right)} c^{2} d^{4} + 140 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c d^{5} + 480 \, {\left(B a^{2} + 2 \, A a b\right)} d^{6}\right)} e^{2} f^{4} - 5 \, {\left(21 \, C b^{2} c^{4} d^{2} - 384 \, A a^{2} d^{6} - 32 \, {\left(2 \, C a b + B b^{2}\right)} c^{3} d^{3} + 56 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c^{2} d^{4} - 128 \, {\left(B a^{2} + 2 \, A a b\right)} c d^{5}\right)} e f^{5} + 15 \, {\left(21 \, C b^{2} c^{5} d + 128 \, A a^{2} c d^{5} - 28 \, {\left(2 \, C a b + B b^{2}\right)} c^{4} d^{2} + 40 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c^{3} d^{3} - 64 \, {\left(B a^{2} + 2 \, A a b\right)} c^{2} d^{4}\right)} f^{6} + 128 \, {\left(C b^{2} d^{6} e f^{5} + {\left(C b^{2} c d^{5} + 12 \, {\left(2 \, C a b + B b^{2}\right)} d^{6}\right)} f^{6}\right)} x^{4} - 16 \, {\left(9 \, C b^{2} d^{6} e^{2} f^{4} - 2 \, {\left(C b^{2} c d^{5} + 6 \, {\left(2 \, C a b + B b^{2}\right)} d^{6}\right)} e f^{5} + 3 \, {\left(3 \, C b^{2} c^{2} d^{4} - 4 \, {\left(2 \, C a b + B b^{2}\right)} c d^{5} - 40 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} d^{6}\right)} f^{6}\right)} x^{3} + 8 \, {\left(21 \, C b^{2} d^{6} e^{3} f^{3} - {\left(5 \, C b^{2} c d^{5} + 28 \, {\left(2 \, C a b + B b^{2}\right)} d^{6}\right)} e^{2} f^{4} - {\left(5 \, C b^{2} c^{2} d^{4} - 8 \, {\left(2 \, C a b + B b^{2}\right)} c d^{5} - 40 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} d^{6}\right)} e f^{5} + {\left(21 \, C b^{2} c^{3} d^{3} - 28 \, {\left(2 \, C a b + B b^{2}\right)} c^{2} d^{4} + 40 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c d^{5} + 320 \, {\left(B a^{2} + 2 \, A a b\right)} d^{6}\right)} f^{6}\right)} x^{2} - 2 \, {\left(105 \, C b^{2} d^{6} e^{4} f^{2} - 28 \, {\left(C b^{2} c d^{5} + 5 \, {\left(2 \, C a b + B b^{2}\right)} d^{6}\right)} e^{3} f^{3} - 2 \, {\left(13 \, C b^{2} c^{2} d^{4} - 22 \, {\left(2 \, C a b + B b^{2}\right)} c d^{5} - 100 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} d^{6}\right)} e^{2} f^{4} - 4 \, {\left(7 \, C b^{2} c^{3} d^{3} - 11 \, {\left(2 \, C a b + B b^{2}\right)} c^{2} d^{4} + 20 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c d^{5} + 80 \, {\left(B a^{2} + 2 \, A a b\right)} d^{6}\right)} e f^{5} + 5 \, {\left(21 \, C b^{2} c^{4} d^{2} - 384 \, A a^{2} d^{6} - 28 \, {\left(2 \, C a b + B b^{2}\right)} c^{3} d^{3} + 40 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c^{2} d^{4} - 64 \, {\left(B a^{2} + 2 \, A a b\right)} c d^{5}\right)} f^{6}\right)} x\right)} \sqrt{d x + c} \sqrt{f x + e}}{30720 \, d^{6} f^{6}}, \frac{15 \, {\left(21 \, C b^{2} d^{6} e^{6} - 14 \, {\left(C b^{2} c d^{5} + 2 \, {\left(2 \, C a b + B b^{2}\right)} d^{6}\right)} e^{5} f - 5 \, {\left(C b^{2} c^{2} d^{4} - 4 \, {\left(2 \, C a b + B b^{2}\right)} c d^{5} - 8 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} d^{6}\right)} e^{4} f^{2} - 4 \, {\left(C b^{2} c^{3} d^{3} - 2 \, {\left(2 \, C a b + B b^{2}\right)} c^{2} d^{4} + 8 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c d^{5} + 16 \, {\left(B a^{2} + 2 \, A a b\right)} d^{6}\right)} e^{3} f^{3} - {\left(5 \, C b^{2} c^{4} d^{2} - 128 \, A a^{2} d^{6} - 8 \, {\left(2 \, C a b + B b^{2}\right)} c^{3} d^{3} + 16 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c^{2} d^{4} - 64 \, {\left(B a^{2} + 2 \, A a b\right)} c d^{5}\right)} e^{2} f^{4} - 2 \, {\left(7 \, C b^{2} c^{5} d + 128 \, A a^{2} c d^{5} - 10 \, {\left(2 \, C a b + B b^{2}\right)} c^{4} d^{2} + 16 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c^{3} d^{3} - 32 \, {\left(B a^{2} + 2 \, A a b\right)} c^{2} d^{4}\right)} e f^{5} + {\left(21 \, C b^{2} c^{6} + 128 \, A a^{2} c^{2} d^{4} - 28 \, {\left(2 \, C a b + B b^{2}\right)} c^{5} d + 40 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c^{4} d^{2} - 64 \, {\left(B a^{2} + 2 \, A a b\right)} c^{3} d^{3}\right)} f^{6}\right)} \sqrt{-d f} \arctan\left(\frac{{\left(2 \, d f x + d e + c f\right)} \sqrt{-d f} \sqrt{d x + c} \sqrt{f x + e}}{2 \, {\left(d^{2} f^{2} x^{2} + c d e f + {\left(d^{2} e f + c d f^{2}\right)} x\right)}}\right) + 2 \, {\left(1280 \, C b^{2} d^{6} f^{6} x^{5} + 315 \, C b^{2} d^{6} e^{5} f - 105 \, {\left(C b^{2} c d^{5} + 4 \, {\left(2 \, C a b + B b^{2}\right)} d^{6}\right)} e^{4} f^{2} - 2 \, {\left(41 \, C b^{2} c^{2} d^{4} - 80 \, {\left(2 \, C a b + B b^{2}\right)} c d^{5} - 300 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} d^{6}\right)} e^{3} f^{3} - 2 \, {\left(41 \, C b^{2} c^{3} d^{3} - 68 \, {\left(2 \, C a b + B b^{2}\right)} c^{2} d^{4} + 140 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c d^{5} + 480 \, {\left(B a^{2} + 2 \, A a b\right)} d^{6}\right)} e^{2} f^{4} - 5 \, {\left(21 \, C b^{2} c^{4} d^{2} - 384 \, A a^{2} d^{6} - 32 \, {\left(2 \, C a b + B b^{2}\right)} c^{3} d^{3} + 56 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c^{2} d^{4} - 128 \, {\left(B a^{2} + 2 \, A a b\right)} c d^{5}\right)} e f^{5} + 15 \, {\left(21 \, C b^{2} c^{5} d + 128 \, A a^{2} c d^{5} - 28 \, {\left(2 \, C a b + B b^{2}\right)} c^{4} d^{2} + 40 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c^{3} d^{3} - 64 \, {\left(B a^{2} + 2 \, A a b\right)} c^{2} d^{4}\right)} f^{6} + 128 \, {\left(C b^{2} d^{6} e f^{5} + {\left(C b^{2} c d^{5} + 12 \, {\left(2 \, C a b + B b^{2}\right)} d^{6}\right)} f^{6}\right)} x^{4} - 16 \, {\left(9 \, C b^{2} d^{6} e^{2} f^{4} - 2 \, {\left(C b^{2} c d^{5} + 6 \, {\left(2 \, C a b + B b^{2}\right)} d^{6}\right)} e f^{5} + 3 \, {\left(3 \, C b^{2} c^{2} d^{4} - 4 \, {\left(2 \, C a b + B b^{2}\right)} c d^{5} - 40 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} d^{6}\right)} f^{6}\right)} x^{3} + 8 \, {\left(21 \, C b^{2} d^{6} e^{3} f^{3} - {\left(5 \, C b^{2} c d^{5} + 28 \, {\left(2 \, C a b + B b^{2}\right)} d^{6}\right)} e^{2} f^{4} - {\left(5 \, C b^{2} c^{2} d^{4} - 8 \, {\left(2 \, C a b + B b^{2}\right)} c d^{5} - 40 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} d^{6}\right)} e f^{5} + {\left(21 \, C b^{2} c^{3} d^{3} - 28 \, {\left(2 \, C a b + B b^{2}\right)} c^{2} d^{4} + 40 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c d^{5} + 320 \, {\left(B a^{2} + 2 \, A a b\right)} d^{6}\right)} f^{6}\right)} x^{2} - 2 \, {\left(105 \, C b^{2} d^{6} e^{4} f^{2} - 28 \, {\left(C b^{2} c d^{5} + 5 \, {\left(2 \, C a b + B b^{2}\right)} d^{6}\right)} e^{3} f^{3} - 2 \, {\left(13 \, C b^{2} c^{2} d^{4} - 22 \, {\left(2 \, C a b + B b^{2}\right)} c d^{5} - 100 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} d^{6}\right)} e^{2} f^{4} - 4 \, {\left(7 \, C b^{2} c^{3} d^{3} - 11 \, {\left(2 \, C a b + B b^{2}\right)} c^{2} d^{4} + 20 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c d^{5} + 80 \, {\left(B a^{2} + 2 \, A a b\right)} d^{6}\right)} e f^{5} + 5 \, {\left(21 \, C b^{2} c^{4} d^{2} - 384 \, A a^{2} d^{6} - 28 \, {\left(2 \, C a b + B b^{2}\right)} c^{3} d^{3} + 40 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c^{2} d^{4} - 64 \, {\left(B a^{2} + 2 \, A a b\right)} c d^{5}\right)} f^{6}\right)} x\right)} \sqrt{d x + c} \sqrt{f x + e}}{15360 \, d^{6} f^{6}}\right]"," ",0,"[1/30720*(15*(21*C*b^2*d^6*e^6 - 14*(C*b^2*c*d^5 + 2*(2*C*a*b + B*b^2)*d^6)*e^5*f - 5*(C*b^2*c^2*d^4 - 4*(2*C*a*b + B*b^2)*c*d^5 - 8*(C*a^2 + 2*B*a*b + A*b^2)*d^6)*e^4*f^2 - 4*(C*b^2*c^3*d^3 - 2*(2*C*a*b + B*b^2)*c^2*d^4 + 8*(C*a^2 + 2*B*a*b + A*b^2)*c*d^5 + 16*(B*a^2 + 2*A*a*b)*d^6)*e^3*f^3 - (5*C*b^2*c^4*d^2 - 128*A*a^2*d^6 - 8*(2*C*a*b + B*b^2)*c^3*d^3 + 16*(C*a^2 + 2*B*a*b + A*b^2)*c^2*d^4 - 64*(B*a^2 + 2*A*a*b)*c*d^5)*e^2*f^4 - 2*(7*C*b^2*c^5*d + 128*A*a^2*c*d^5 - 10*(2*C*a*b + B*b^2)*c^4*d^2 + 16*(C*a^2 + 2*B*a*b + A*b^2)*c^3*d^3 - 32*(B*a^2 + 2*A*a*b)*c^2*d^4)*e*f^5 + (21*C*b^2*c^6 + 128*A*a^2*c^2*d^4 - 28*(2*C*a*b + B*b^2)*c^5*d + 40*(C*a^2 + 2*B*a*b + A*b^2)*c^4*d^2 - 64*(B*a^2 + 2*A*a*b)*c^3*d^3)*f^6)*sqrt(d*f)*log(8*d^2*f^2*x^2 + d^2*e^2 + 6*c*d*e*f + c^2*f^2 - 4*(2*d*f*x + d*e + c*f)*sqrt(d*f)*sqrt(d*x + c)*sqrt(f*x + e) + 8*(d^2*e*f + c*d*f^2)*x) + 4*(1280*C*b^2*d^6*f^6*x^5 + 315*C*b^2*d^6*e^5*f - 105*(C*b^2*c*d^5 + 4*(2*C*a*b + B*b^2)*d^6)*e^4*f^2 - 2*(41*C*b^2*c^2*d^4 - 80*(2*C*a*b + B*b^2)*c*d^5 - 300*(C*a^2 + 2*B*a*b + A*b^2)*d^6)*e^3*f^3 - 2*(41*C*b^2*c^3*d^3 - 68*(2*C*a*b + B*b^2)*c^2*d^4 + 140*(C*a^2 + 2*B*a*b + A*b^2)*c*d^5 + 480*(B*a^2 + 2*A*a*b)*d^6)*e^2*f^4 - 5*(21*C*b^2*c^4*d^2 - 384*A*a^2*d^6 - 32*(2*C*a*b + B*b^2)*c^3*d^3 + 56*(C*a^2 + 2*B*a*b + A*b^2)*c^2*d^4 - 128*(B*a^2 + 2*A*a*b)*c*d^5)*e*f^5 + 15*(21*C*b^2*c^5*d + 128*A*a^2*c*d^5 - 28*(2*C*a*b + B*b^2)*c^4*d^2 + 40*(C*a^2 + 2*B*a*b + A*b^2)*c^3*d^3 - 64*(B*a^2 + 2*A*a*b)*c^2*d^4)*f^6 + 128*(C*b^2*d^6*e*f^5 + (C*b^2*c*d^5 + 12*(2*C*a*b + B*b^2)*d^6)*f^6)*x^4 - 16*(9*C*b^2*d^6*e^2*f^4 - 2*(C*b^2*c*d^5 + 6*(2*C*a*b + B*b^2)*d^6)*e*f^5 + 3*(3*C*b^2*c^2*d^4 - 4*(2*C*a*b + B*b^2)*c*d^5 - 40*(C*a^2 + 2*B*a*b + A*b^2)*d^6)*f^6)*x^3 + 8*(21*C*b^2*d^6*e^3*f^3 - (5*C*b^2*c*d^5 + 28*(2*C*a*b + B*b^2)*d^6)*e^2*f^4 - (5*C*b^2*c^2*d^4 - 8*(2*C*a*b + B*b^2)*c*d^5 - 40*(C*a^2 + 2*B*a*b + A*b^2)*d^6)*e*f^5 + (21*C*b^2*c^3*d^3 - 28*(2*C*a*b + B*b^2)*c^2*d^4 + 40*(C*a^2 + 2*B*a*b + A*b^2)*c*d^5 + 320*(B*a^2 + 2*A*a*b)*d^6)*f^6)*x^2 - 2*(105*C*b^2*d^6*e^4*f^2 - 28*(C*b^2*c*d^5 + 5*(2*C*a*b + B*b^2)*d^6)*e^3*f^3 - 2*(13*C*b^2*c^2*d^4 - 22*(2*C*a*b + B*b^2)*c*d^5 - 100*(C*a^2 + 2*B*a*b + A*b^2)*d^6)*e^2*f^4 - 4*(7*C*b^2*c^3*d^3 - 11*(2*C*a*b + B*b^2)*c^2*d^4 + 20*(C*a^2 + 2*B*a*b + A*b^2)*c*d^5 + 80*(B*a^2 + 2*A*a*b)*d^6)*e*f^5 + 5*(21*C*b^2*c^4*d^2 - 384*A*a^2*d^6 - 28*(2*C*a*b + B*b^2)*c^3*d^3 + 40*(C*a^2 + 2*B*a*b + A*b^2)*c^2*d^4 - 64*(B*a^2 + 2*A*a*b)*c*d^5)*f^6)*x)*sqrt(d*x + c)*sqrt(f*x + e))/(d^6*f^6), 1/15360*(15*(21*C*b^2*d^6*e^6 - 14*(C*b^2*c*d^5 + 2*(2*C*a*b + B*b^2)*d^6)*e^5*f - 5*(C*b^2*c^2*d^4 - 4*(2*C*a*b + B*b^2)*c*d^5 - 8*(C*a^2 + 2*B*a*b + A*b^2)*d^6)*e^4*f^2 - 4*(C*b^2*c^3*d^3 - 2*(2*C*a*b + B*b^2)*c^2*d^4 + 8*(C*a^2 + 2*B*a*b + A*b^2)*c*d^5 + 16*(B*a^2 + 2*A*a*b)*d^6)*e^3*f^3 - (5*C*b^2*c^4*d^2 - 128*A*a^2*d^6 - 8*(2*C*a*b + B*b^2)*c^3*d^3 + 16*(C*a^2 + 2*B*a*b + A*b^2)*c^2*d^4 - 64*(B*a^2 + 2*A*a*b)*c*d^5)*e^2*f^4 - 2*(7*C*b^2*c^5*d + 128*A*a^2*c*d^5 - 10*(2*C*a*b + B*b^2)*c^4*d^2 + 16*(C*a^2 + 2*B*a*b + A*b^2)*c^3*d^3 - 32*(B*a^2 + 2*A*a*b)*c^2*d^4)*e*f^5 + (21*C*b^2*c^6 + 128*A*a^2*c^2*d^4 - 28*(2*C*a*b + B*b^2)*c^5*d + 40*(C*a^2 + 2*B*a*b + A*b^2)*c^4*d^2 - 64*(B*a^2 + 2*A*a*b)*c^3*d^3)*f^6)*sqrt(-d*f)*arctan(1/2*(2*d*f*x + d*e + c*f)*sqrt(-d*f)*sqrt(d*x + c)*sqrt(f*x + e)/(d^2*f^2*x^2 + c*d*e*f + (d^2*e*f + c*d*f^2)*x)) + 2*(1280*C*b^2*d^6*f^6*x^5 + 315*C*b^2*d^6*e^5*f - 105*(C*b^2*c*d^5 + 4*(2*C*a*b + B*b^2)*d^6)*e^4*f^2 - 2*(41*C*b^2*c^2*d^4 - 80*(2*C*a*b + B*b^2)*c*d^5 - 300*(C*a^2 + 2*B*a*b + A*b^2)*d^6)*e^3*f^3 - 2*(41*C*b^2*c^3*d^3 - 68*(2*C*a*b + B*b^2)*c^2*d^4 + 140*(C*a^2 + 2*B*a*b + A*b^2)*c*d^5 + 480*(B*a^2 + 2*A*a*b)*d^6)*e^2*f^4 - 5*(21*C*b^2*c^4*d^2 - 384*A*a^2*d^6 - 32*(2*C*a*b + B*b^2)*c^3*d^3 + 56*(C*a^2 + 2*B*a*b + A*b^2)*c^2*d^4 - 128*(B*a^2 + 2*A*a*b)*c*d^5)*e*f^5 + 15*(21*C*b^2*c^5*d + 128*A*a^2*c*d^5 - 28*(2*C*a*b + B*b^2)*c^4*d^2 + 40*(C*a^2 + 2*B*a*b + A*b^2)*c^3*d^3 - 64*(B*a^2 + 2*A*a*b)*c^2*d^4)*f^6 + 128*(C*b^2*d^6*e*f^5 + (C*b^2*c*d^5 + 12*(2*C*a*b + B*b^2)*d^6)*f^6)*x^4 - 16*(9*C*b^2*d^6*e^2*f^4 - 2*(C*b^2*c*d^5 + 6*(2*C*a*b + B*b^2)*d^6)*e*f^5 + 3*(3*C*b^2*c^2*d^4 - 4*(2*C*a*b + B*b^2)*c*d^5 - 40*(C*a^2 + 2*B*a*b + A*b^2)*d^6)*f^6)*x^3 + 8*(21*C*b^2*d^6*e^3*f^3 - (5*C*b^2*c*d^5 + 28*(2*C*a*b + B*b^2)*d^6)*e^2*f^4 - (5*C*b^2*c^2*d^4 - 8*(2*C*a*b + B*b^2)*c*d^5 - 40*(C*a^2 + 2*B*a*b + A*b^2)*d^6)*e*f^5 + (21*C*b^2*c^3*d^3 - 28*(2*C*a*b + B*b^2)*c^2*d^4 + 40*(C*a^2 + 2*B*a*b + A*b^2)*c*d^5 + 320*(B*a^2 + 2*A*a*b)*d^6)*f^6)*x^2 - 2*(105*C*b^2*d^6*e^4*f^2 - 28*(C*b^2*c*d^5 + 5*(2*C*a*b + B*b^2)*d^6)*e^3*f^3 - 2*(13*C*b^2*c^2*d^4 - 22*(2*C*a*b + B*b^2)*c*d^5 - 100*(C*a^2 + 2*B*a*b + A*b^2)*d^6)*e^2*f^4 - 4*(7*C*b^2*c^3*d^3 - 11*(2*C*a*b + B*b^2)*c^2*d^4 + 20*(C*a^2 + 2*B*a*b + A*b^2)*c*d^5 + 80*(B*a^2 + 2*A*a*b)*d^6)*e*f^5 + 5*(21*C*b^2*c^4*d^2 - 384*A*a^2*d^6 - 28*(2*C*a*b + B*b^2)*c^3*d^3 + 40*(C*a^2 + 2*B*a*b + A*b^2)*c^2*d^4 - 64*(B*a^2 + 2*A*a*b)*c*d^5)*f^6)*x)*sqrt(d*x + c)*sqrt(f*x + e))/(d^6*f^6)]","A",0
42,1,1620,0,2.958276," ","integrate((b*x+a)*(C*x^2+B*x+A)*(d*x+c)^(1/2)*(f*x+e)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(7 \, C b d^{5} e^{5} - 5 \, {\left(C b c d^{4} + 2 \, {\left(C a + B b\right)} d^{5}\right)} e^{4} f - 2 \, {\left(C b c^{2} d^{3} - 4 \, {\left(C a + B b\right)} c d^{4} - 8 \, {\left(B a + A b\right)} d^{5}\right)} e^{3} f^{2} - 2 \, {\left(C b c^{3} d^{2} + 16 \, A a d^{5} - 2 \, {\left(C a + B b\right)} c^{2} d^{3} + 8 \, {\left(B a + A b\right)} c d^{4}\right)} e^{2} f^{3} - {\left(5 \, C b c^{4} d - 64 \, A a c d^{4} - 8 \, {\left(C a + B b\right)} c^{3} d^{2} + 16 \, {\left(B a + A b\right)} c^{2} d^{3}\right)} e f^{4} + {\left(7 \, C b c^{5} - 32 \, A a c^{2} d^{3} - 10 \, {\left(C a + B b\right)} c^{4} d + 16 \, {\left(B a + A b\right)} c^{3} d^{2}\right)} f^{5}\right)} \sqrt{d f} \log\left(8 \, d^{2} f^{2} x^{2} + d^{2} e^{2} + 6 \, c d e f + c^{2} f^{2} - 4 \, {\left(2 \, d f x + d e + c f\right)} \sqrt{d f} \sqrt{d x + c} \sqrt{f x + e} + 8 \, {\left(d^{2} e f + c d f^{2}\right)} x\right) - 4 \, {\left(384 \, C b d^{5} f^{5} x^{4} - 105 \, C b d^{5} e^{4} f + 10 \, {\left(4 \, C b c d^{4} + 15 \, {\left(C a + B b\right)} d^{5}\right)} e^{3} f^{2} + 2 \, {\left(17 \, C b c^{2} d^{3} - 35 \, {\left(C a + B b\right)} c d^{4} - 120 \, {\left(B a + A b\right)} d^{5}\right)} e^{2} f^{3} + 10 \, {\left(4 \, C b c^{3} d^{2} + 48 \, A a d^{5} - 7 \, {\left(C a + B b\right)} c^{2} d^{3} + 16 \, {\left(B a + A b\right)} c d^{4}\right)} e f^{4} - 15 \, {\left(7 \, C b c^{4} d - 32 \, A a c d^{4} - 10 \, {\left(C a + B b\right)} c^{3} d^{2} + 16 \, {\left(B a + A b\right)} c^{2} d^{3}\right)} f^{5} + 48 \, {\left(C b d^{5} e f^{4} + {\left(C b c d^{4} + 10 \, {\left(C a + B b\right)} d^{5}\right)} f^{5}\right)} x^{3} - 8 \, {\left(7 \, C b d^{5} e^{2} f^{3} - 2 \, {\left(C b c d^{4} + 5 \, {\left(C a + B b\right)} d^{5}\right)} e f^{4} + {\left(7 \, C b c^{2} d^{3} - 10 \, {\left(C a + B b\right)} c d^{4} - 80 \, {\left(B a + A b\right)} d^{5}\right)} f^{5}\right)} x^{2} + 2 \, {\left(35 \, C b d^{5} e^{3} f^{2} - {\left(11 \, C b c d^{4} + 50 \, {\left(C a + B b\right)} d^{5}\right)} e^{2} f^{3} - {\left(11 \, C b c^{2} d^{3} - 20 \, {\left(C a + B b\right)} c d^{4} - 80 \, {\left(B a + A b\right)} d^{5}\right)} e f^{4} + 5 \, {\left(7 \, C b c^{3} d^{2} + 96 \, A a d^{5} - 10 \, {\left(C a + B b\right)} c^{2} d^{3} + 16 \, {\left(B a + A b\right)} c d^{4}\right)} f^{5}\right)} x\right)} \sqrt{d x + c} \sqrt{f x + e}}{7680 \, d^{5} f^{5}}, -\frac{15 \, {\left(7 \, C b d^{5} e^{5} - 5 \, {\left(C b c d^{4} + 2 \, {\left(C a + B b\right)} d^{5}\right)} e^{4} f - 2 \, {\left(C b c^{2} d^{3} - 4 \, {\left(C a + B b\right)} c d^{4} - 8 \, {\left(B a + A b\right)} d^{5}\right)} e^{3} f^{2} - 2 \, {\left(C b c^{3} d^{2} + 16 \, A a d^{5} - 2 \, {\left(C a + B b\right)} c^{2} d^{3} + 8 \, {\left(B a + A b\right)} c d^{4}\right)} e^{2} f^{3} - {\left(5 \, C b c^{4} d - 64 \, A a c d^{4} - 8 \, {\left(C a + B b\right)} c^{3} d^{2} + 16 \, {\left(B a + A b\right)} c^{2} d^{3}\right)} e f^{4} + {\left(7 \, C b c^{5} - 32 \, A a c^{2} d^{3} - 10 \, {\left(C a + B b\right)} c^{4} d + 16 \, {\left(B a + A b\right)} c^{3} d^{2}\right)} f^{5}\right)} \sqrt{-d f} \arctan\left(\frac{{\left(2 \, d f x + d e + c f\right)} \sqrt{-d f} \sqrt{d x + c} \sqrt{f x + e}}{2 \, {\left(d^{2} f^{2} x^{2} + c d e f + {\left(d^{2} e f + c d f^{2}\right)} x\right)}}\right) - 2 \, {\left(384 \, C b d^{5} f^{5} x^{4} - 105 \, C b d^{5} e^{4} f + 10 \, {\left(4 \, C b c d^{4} + 15 \, {\left(C a + B b\right)} d^{5}\right)} e^{3} f^{2} + 2 \, {\left(17 \, C b c^{2} d^{3} - 35 \, {\left(C a + B b\right)} c d^{4} - 120 \, {\left(B a + A b\right)} d^{5}\right)} e^{2} f^{3} + 10 \, {\left(4 \, C b c^{3} d^{2} + 48 \, A a d^{5} - 7 \, {\left(C a + B b\right)} c^{2} d^{3} + 16 \, {\left(B a + A b\right)} c d^{4}\right)} e f^{4} - 15 \, {\left(7 \, C b c^{4} d - 32 \, A a c d^{4} - 10 \, {\left(C a + B b\right)} c^{3} d^{2} + 16 \, {\left(B a + A b\right)} c^{2} d^{3}\right)} f^{5} + 48 \, {\left(C b d^{5} e f^{4} + {\left(C b c d^{4} + 10 \, {\left(C a + B b\right)} d^{5}\right)} f^{5}\right)} x^{3} - 8 \, {\left(7 \, C b d^{5} e^{2} f^{3} - 2 \, {\left(C b c d^{4} + 5 \, {\left(C a + B b\right)} d^{5}\right)} e f^{4} + {\left(7 \, C b c^{2} d^{3} - 10 \, {\left(C a + B b\right)} c d^{4} - 80 \, {\left(B a + A b\right)} d^{5}\right)} f^{5}\right)} x^{2} + 2 \, {\left(35 \, C b d^{5} e^{3} f^{2} - {\left(11 \, C b c d^{4} + 50 \, {\left(C a + B b\right)} d^{5}\right)} e^{2} f^{3} - {\left(11 \, C b c^{2} d^{3} - 20 \, {\left(C a + B b\right)} c d^{4} - 80 \, {\left(B a + A b\right)} d^{5}\right)} e f^{4} + 5 \, {\left(7 \, C b c^{3} d^{2} + 96 \, A a d^{5} - 10 \, {\left(C a + B b\right)} c^{2} d^{3} + 16 \, {\left(B a + A b\right)} c d^{4}\right)} f^{5}\right)} x\right)} \sqrt{d x + c} \sqrt{f x + e}}{3840 \, d^{5} f^{5}}\right]"," ",0,"[-1/7680*(15*(7*C*b*d^5*e^5 - 5*(C*b*c*d^4 + 2*(C*a + B*b)*d^5)*e^4*f - 2*(C*b*c^2*d^3 - 4*(C*a + B*b)*c*d^4 - 8*(B*a + A*b)*d^5)*e^3*f^2 - 2*(C*b*c^3*d^2 + 16*A*a*d^5 - 2*(C*a + B*b)*c^2*d^3 + 8*(B*a + A*b)*c*d^4)*e^2*f^3 - (5*C*b*c^4*d - 64*A*a*c*d^4 - 8*(C*a + B*b)*c^3*d^2 + 16*(B*a + A*b)*c^2*d^3)*e*f^4 + (7*C*b*c^5 - 32*A*a*c^2*d^3 - 10*(C*a + B*b)*c^4*d + 16*(B*a + A*b)*c^3*d^2)*f^5)*sqrt(d*f)*log(8*d^2*f^2*x^2 + d^2*e^2 + 6*c*d*e*f + c^2*f^2 - 4*(2*d*f*x + d*e + c*f)*sqrt(d*f)*sqrt(d*x + c)*sqrt(f*x + e) + 8*(d^2*e*f + c*d*f^2)*x) - 4*(384*C*b*d^5*f^5*x^4 - 105*C*b*d^5*e^4*f + 10*(4*C*b*c*d^4 + 15*(C*a + B*b)*d^5)*e^3*f^2 + 2*(17*C*b*c^2*d^3 - 35*(C*a + B*b)*c*d^4 - 120*(B*a + A*b)*d^5)*e^2*f^3 + 10*(4*C*b*c^3*d^2 + 48*A*a*d^5 - 7*(C*a + B*b)*c^2*d^3 + 16*(B*a + A*b)*c*d^4)*e*f^4 - 15*(7*C*b*c^4*d - 32*A*a*c*d^4 - 10*(C*a + B*b)*c^3*d^2 + 16*(B*a + A*b)*c^2*d^3)*f^5 + 48*(C*b*d^5*e*f^4 + (C*b*c*d^4 + 10*(C*a + B*b)*d^5)*f^5)*x^3 - 8*(7*C*b*d^5*e^2*f^3 - 2*(C*b*c*d^4 + 5*(C*a + B*b)*d^5)*e*f^4 + (7*C*b*c^2*d^3 - 10*(C*a + B*b)*c*d^4 - 80*(B*a + A*b)*d^5)*f^5)*x^2 + 2*(35*C*b*d^5*e^3*f^2 - (11*C*b*c*d^4 + 50*(C*a + B*b)*d^5)*e^2*f^3 - (11*C*b*c^2*d^3 - 20*(C*a + B*b)*c*d^4 - 80*(B*a + A*b)*d^5)*e*f^4 + 5*(7*C*b*c^3*d^2 + 96*A*a*d^5 - 10*(C*a + B*b)*c^2*d^3 + 16*(B*a + A*b)*c*d^4)*f^5)*x)*sqrt(d*x + c)*sqrt(f*x + e))/(d^5*f^5), -1/3840*(15*(7*C*b*d^5*e^5 - 5*(C*b*c*d^4 + 2*(C*a + B*b)*d^5)*e^4*f - 2*(C*b*c^2*d^3 - 4*(C*a + B*b)*c*d^4 - 8*(B*a + A*b)*d^5)*e^3*f^2 - 2*(C*b*c^3*d^2 + 16*A*a*d^5 - 2*(C*a + B*b)*c^2*d^3 + 8*(B*a + A*b)*c*d^4)*e^2*f^3 - (5*C*b*c^4*d - 64*A*a*c*d^4 - 8*(C*a + B*b)*c^3*d^2 + 16*(B*a + A*b)*c^2*d^3)*e*f^4 + (7*C*b*c^5 - 32*A*a*c^2*d^3 - 10*(C*a + B*b)*c^4*d + 16*(B*a + A*b)*c^3*d^2)*f^5)*sqrt(-d*f)*arctan(1/2*(2*d*f*x + d*e + c*f)*sqrt(-d*f)*sqrt(d*x + c)*sqrt(f*x + e)/(d^2*f^2*x^2 + c*d*e*f + (d^2*e*f + c*d*f^2)*x)) - 2*(384*C*b*d^5*f^5*x^4 - 105*C*b*d^5*e^4*f + 10*(4*C*b*c*d^4 + 15*(C*a + B*b)*d^5)*e^3*f^2 + 2*(17*C*b*c^2*d^3 - 35*(C*a + B*b)*c*d^4 - 120*(B*a + A*b)*d^5)*e^2*f^3 + 10*(4*C*b*c^3*d^2 + 48*A*a*d^5 - 7*(C*a + B*b)*c^2*d^3 + 16*(B*a + A*b)*c*d^4)*e*f^4 - 15*(7*C*b*c^4*d - 32*A*a*c*d^4 - 10*(C*a + B*b)*c^3*d^2 + 16*(B*a + A*b)*c^2*d^3)*f^5 + 48*(C*b*d^5*e*f^4 + (C*b*c*d^4 + 10*(C*a + B*b)*d^5)*f^5)*x^3 - 8*(7*C*b*d^5*e^2*f^3 - 2*(C*b*c*d^4 + 5*(C*a + B*b)*d^5)*e*f^4 + (7*C*b*c^2*d^3 - 10*(C*a + B*b)*c*d^4 - 80*(B*a + A*b)*d^5)*f^5)*x^2 + 2*(35*C*b*d^5*e^3*f^2 - (11*C*b*c*d^4 + 50*(C*a + B*b)*d^5)*e^2*f^3 - (11*C*b*c^2*d^3 - 20*(C*a + B*b)*c*d^4 - 80*(B*a + A*b)*d^5)*e*f^4 + 5*(7*C*b*c^3*d^2 + 96*A*a*d^5 - 10*(C*a + B*b)*c^2*d^3 + 16*(B*a + A*b)*c*d^4)*f^5)*x)*sqrt(d*x + c)*sqrt(f*x + e))/(d^5*f^5)]","A",0
43,1,840,0,0.974373," ","integrate((C*x^2+B*x+A)*(d*x+c)^(1/2)*(f*x+e)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(5 \, C d^{4} e^{4} - 4 \, {\left(C c d^{3} + 2 \, B d^{4}\right)} e^{3} f - 2 \, {\left(C c^{2} d^{2} - 4 \, B c d^{3} - 8 \, A d^{4}\right)} e^{2} f^{2} - 4 \, {\left(C c^{3} d - 2 \, B c^{2} d^{2} + 8 \, A c d^{3}\right)} e f^{3} + {\left(5 \, C c^{4} - 8 \, B c^{3} d + 16 \, A c^{2} d^{2}\right)} f^{4}\right)} \sqrt{d f} \log\left(8 \, d^{2} f^{2} x^{2} + d^{2} e^{2} + 6 \, c d e f + c^{2} f^{2} - 4 \, {\left(2 \, d f x + d e + c f\right)} \sqrt{d f} \sqrt{d x + c} \sqrt{f x + e} + 8 \, {\left(d^{2} e f + c d f^{2}\right)} x\right) + 4 \, {\left(48 \, C d^{4} f^{4} x^{3} + 15 \, C d^{4} e^{3} f - {\left(7 \, C c d^{3} + 24 \, B d^{4}\right)} e^{2} f^{2} - {\left(7 \, C c^{2} d^{2} - 16 \, B c d^{3} - 48 \, A d^{4}\right)} e f^{3} + 3 \, {\left(5 \, C c^{3} d - 8 \, B c^{2} d^{2} + 16 \, A c d^{3}\right)} f^{4} + 8 \, {\left(C d^{4} e f^{3} + {\left(C c d^{3} + 8 \, B d^{4}\right)} f^{4}\right)} x^{2} - 2 \, {\left(5 \, C d^{4} e^{2} f^{2} - 2 \, {\left(C c d^{3} + 4 \, B d^{4}\right)} e f^{3} + {\left(5 \, C c^{2} d^{2} - 8 \, B c d^{3} - 48 \, A d^{4}\right)} f^{4}\right)} x\right)} \sqrt{d x + c} \sqrt{f x + e}}{768 \, d^{4} f^{4}}, \frac{3 \, {\left(5 \, C d^{4} e^{4} - 4 \, {\left(C c d^{3} + 2 \, B d^{4}\right)} e^{3} f - 2 \, {\left(C c^{2} d^{2} - 4 \, B c d^{3} - 8 \, A d^{4}\right)} e^{2} f^{2} - 4 \, {\left(C c^{3} d - 2 \, B c^{2} d^{2} + 8 \, A c d^{3}\right)} e f^{3} + {\left(5 \, C c^{4} - 8 \, B c^{3} d + 16 \, A c^{2} d^{2}\right)} f^{4}\right)} \sqrt{-d f} \arctan\left(\frac{{\left(2 \, d f x + d e + c f\right)} \sqrt{-d f} \sqrt{d x + c} \sqrt{f x + e}}{2 \, {\left(d^{2} f^{2} x^{2} + c d e f + {\left(d^{2} e f + c d f^{2}\right)} x\right)}}\right) + 2 \, {\left(48 \, C d^{4} f^{4} x^{3} + 15 \, C d^{4} e^{3} f - {\left(7 \, C c d^{3} + 24 \, B d^{4}\right)} e^{2} f^{2} - {\left(7 \, C c^{2} d^{2} - 16 \, B c d^{3} - 48 \, A d^{4}\right)} e f^{3} + 3 \, {\left(5 \, C c^{3} d - 8 \, B c^{2} d^{2} + 16 \, A c d^{3}\right)} f^{4} + 8 \, {\left(C d^{4} e f^{3} + {\left(C c d^{3} + 8 \, B d^{4}\right)} f^{4}\right)} x^{2} - 2 \, {\left(5 \, C d^{4} e^{2} f^{2} - 2 \, {\left(C c d^{3} + 4 \, B d^{4}\right)} e f^{3} + {\left(5 \, C c^{2} d^{2} - 8 \, B c d^{3} - 48 \, A d^{4}\right)} f^{4}\right)} x\right)} \sqrt{d x + c} \sqrt{f x + e}}{384 \, d^{4} f^{4}}\right]"," ",0,"[1/768*(3*(5*C*d^4*e^4 - 4*(C*c*d^3 + 2*B*d^4)*e^3*f - 2*(C*c^2*d^2 - 4*B*c*d^3 - 8*A*d^4)*e^2*f^2 - 4*(C*c^3*d - 2*B*c^2*d^2 + 8*A*c*d^3)*e*f^3 + (5*C*c^4 - 8*B*c^3*d + 16*A*c^2*d^2)*f^4)*sqrt(d*f)*log(8*d^2*f^2*x^2 + d^2*e^2 + 6*c*d*e*f + c^2*f^2 - 4*(2*d*f*x + d*e + c*f)*sqrt(d*f)*sqrt(d*x + c)*sqrt(f*x + e) + 8*(d^2*e*f + c*d*f^2)*x) + 4*(48*C*d^4*f^4*x^3 + 15*C*d^4*e^3*f - (7*C*c*d^3 + 24*B*d^4)*e^2*f^2 - (7*C*c^2*d^2 - 16*B*c*d^3 - 48*A*d^4)*e*f^3 + 3*(5*C*c^3*d - 8*B*c^2*d^2 + 16*A*c*d^3)*f^4 + 8*(C*d^4*e*f^3 + (C*c*d^3 + 8*B*d^4)*f^4)*x^2 - 2*(5*C*d^4*e^2*f^2 - 2*(C*c*d^3 + 4*B*d^4)*e*f^3 + (5*C*c^2*d^2 - 8*B*c*d^3 - 48*A*d^4)*f^4)*x)*sqrt(d*x + c)*sqrt(f*x + e))/(d^4*f^4), 1/384*(3*(5*C*d^4*e^4 - 4*(C*c*d^3 + 2*B*d^4)*e^3*f - 2*(C*c^2*d^2 - 4*B*c*d^3 - 8*A*d^4)*e^2*f^2 - 4*(C*c^3*d - 2*B*c^2*d^2 + 8*A*c*d^3)*e*f^3 + (5*C*c^4 - 8*B*c^3*d + 16*A*c^2*d^2)*f^4)*sqrt(-d*f)*arctan(1/2*(2*d*f*x + d*e + c*f)*sqrt(-d*f)*sqrt(d*x + c)*sqrt(f*x + e)/(d^2*f^2*x^2 + c*d*e*f + (d^2*e*f + c*d*f^2)*x)) + 2*(48*C*d^4*f^4*x^3 + 15*C*d^4*e^3*f - (7*C*c*d^3 + 24*B*d^4)*e^2*f^2 - (7*C*c^2*d^2 - 16*B*c*d^3 - 48*A*d^4)*e*f^3 + 3*(5*C*c^3*d - 8*B*c^2*d^2 + 16*A*c*d^3)*f^4 + 8*(C*d^4*e*f^3 + (C*c*d^3 + 8*B*d^4)*f^4)*x^2 - 2*(5*C*d^4*e^2*f^2 - 2*(C*c*d^3 + 4*B*d^4)*e*f^3 + (5*C*c^2*d^2 - 8*B*c*d^3 - 48*A*d^4)*f^4)*x)*sqrt(d*x + c)*sqrt(f*x + e))/(d^4*f^4)]","A",0
44,-1,0,0,0.000000," ","integrate((C*x^2+B*x+A)*(d*x+c)^(1/2)*(f*x+e)^(1/2)/(b*x+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
45,-1,0,0,0.000000," ","integrate((C*x^2+B*x+A)*(d*x+c)^(1/2)*(f*x+e)^(1/2)/(b*x+a)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
46,-1,0,0,0.000000," ","integrate((C*x^2+B*x+A)*(d*x+c)^(1/2)*(f*x+e)^(1/2)/(b*x+a)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
47,1,2176,0,13.800671," ","integrate((b*x+a)^2*(C*x^2+B*x+A)*(d*x+c)^(1/2)/(f*x+e)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(63 \, C b^{2} d^{5} e^{5} - 35 \, {\left(C b^{2} c d^{4} + 2 \, {\left(2 \, C a b + B b^{2}\right)} d^{5}\right)} e^{4} f - 10 \, {\left(C b^{2} c^{2} d^{3} - 4 \, {\left(2 \, C a b + B b^{2}\right)} c d^{4} - 8 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} d^{5}\right)} e^{3} f^{2} - 6 \, {\left(C b^{2} c^{3} d^{2} - 2 \, {\left(2 \, C a b + B b^{2}\right)} c^{2} d^{3} + 8 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c d^{4} + 16 \, {\left(B a^{2} + 2 \, A a b\right)} d^{5}\right)} e^{2} f^{3} - {\left(5 \, C b^{2} c^{4} d - 128 \, A a^{2} d^{5} - 8 \, {\left(2 \, C a b + B b^{2}\right)} c^{3} d^{2} + 16 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c^{2} d^{3} - 64 \, {\left(B a^{2} + 2 \, A a b\right)} c d^{4}\right)} e f^{4} - {\left(7 \, C b^{2} c^{5} + 128 \, A a^{2} c d^{4} - 10 \, {\left(2 \, C a b + B b^{2}\right)} c^{4} d + 16 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c^{3} d^{2} - 32 \, {\left(B a^{2} + 2 \, A a b\right)} c^{2} d^{3}\right)} f^{5}\right)} \sqrt{d f} \log\left(8 \, d^{2} f^{2} x^{2} + d^{2} e^{2} + 6 \, c d e f + c^{2} f^{2} + 4 \, {\left(2 \, d f x + d e + c f\right)} \sqrt{d f} \sqrt{d x + c} \sqrt{f x + e} + 8 \, {\left(d^{2} e f + c d f^{2}\right)} x\right) - 4 \, {\left(384 \, C b^{2} d^{5} f^{5} x^{4} + 945 \, C b^{2} d^{5} e^{4} f - 210 \, {\left(C b^{2} c d^{4} + 5 \, {\left(2 \, C a b + B b^{2}\right)} d^{5}\right)} e^{3} f^{2} - 2 \, {\left(68 \, C b^{2} c^{2} d^{3} - 125 \, {\left(2 \, C a b + B b^{2}\right)} c d^{4} - 600 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} d^{5}\right)} e^{2} f^{3} - 10 \, {\left(11 \, C b^{2} c^{3} d^{2} - 17 \, {\left(2 \, C a b + B b^{2}\right)} c^{2} d^{3} + 32 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c d^{4} + 144 \, {\left(B a^{2} + 2 \, A a b\right)} d^{5}\right)} e f^{4} - 15 \, {\left(7 \, C b^{2} c^{4} d - 128 \, A a^{2} d^{5} - 10 \, {\left(2 \, C a b + B b^{2}\right)} c^{3} d^{2} + 16 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c^{2} d^{3} - 32 \, {\left(B a^{2} + 2 \, A a b\right)} c d^{4}\right)} f^{5} - 48 \, {\left(9 \, C b^{2} d^{5} e f^{4} - {\left(C b^{2} c d^{4} + 10 \, {\left(2 \, C a b + B b^{2}\right)} d^{5}\right)} f^{5}\right)} x^{3} + 8 \, {\left(63 \, C b^{2} d^{5} e^{2} f^{3} - 2 \, {\left(4 \, C b^{2} c d^{4} + 35 \, {\left(2 \, C a b + B b^{2}\right)} d^{5}\right)} e f^{4} - {\left(7 \, C b^{2} c^{2} d^{3} - 10 \, {\left(2 \, C a b + B b^{2}\right)} c d^{4} - 80 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} d^{5}\right)} f^{5}\right)} x^{2} - 2 \, {\left(315 \, C b^{2} d^{5} e^{3} f^{2} - 7 \, {\left(7 \, C b^{2} c d^{4} + 50 \, {\left(2 \, C a b + B b^{2}\right)} d^{5}\right)} e^{2} f^{3} - {\left(39 \, C b^{2} c^{2} d^{3} - 60 \, {\left(2 \, C a b + B b^{2}\right)} c d^{4} - 400 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} d^{5}\right)} e f^{4} - 5 \, {\left(7 \, C b^{2} c^{3} d^{2} - 10 \, {\left(2 \, C a b + B b^{2}\right)} c^{2} d^{3} + 16 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c d^{4} + 96 \, {\left(B a^{2} + 2 \, A a b\right)} d^{5}\right)} f^{5}\right)} x\right)} \sqrt{d x + c} \sqrt{f x + e}}{7680 \, d^{5} f^{6}}, \frac{15 \, {\left(63 \, C b^{2} d^{5} e^{5} - 35 \, {\left(C b^{2} c d^{4} + 2 \, {\left(2 \, C a b + B b^{2}\right)} d^{5}\right)} e^{4} f - 10 \, {\left(C b^{2} c^{2} d^{3} - 4 \, {\left(2 \, C a b + B b^{2}\right)} c d^{4} - 8 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} d^{5}\right)} e^{3} f^{2} - 6 \, {\left(C b^{2} c^{3} d^{2} - 2 \, {\left(2 \, C a b + B b^{2}\right)} c^{2} d^{3} + 8 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c d^{4} + 16 \, {\left(B a^{2} + 2 \, A a b\right)} d^{5}\right)} e^{2} f^{3} - {\left(5 \, C b^{2} c^{4} d - 128 \, A a^{2} d^{5} - 8 \, {\left(2 \, C a b + B b^{2}\right)} c^{3} d^{2} + 16 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c^{2} d^{3} - 64 \, {\left(B a^{2} + 2 \, A a b\right)} c d^{4}\right)} e f^{4} - {\left(7 \, C b^{2} c^{5} + 128 \, A a^{2} c d^{4} - 10 \, {\left(2 \, C a b + B b^{2}\right)} c^{4} d + 16 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c^{3} d^{2} - 32 \, {\left(B a^{2} + 2 \, A a b\right)} c^{2} d^{3}\right)} f^{5}\right)} \sqrt{-d f} \arctan\left(\frac{{\left(2 \, d f x + d e + c f\right)} \sqrt{-d f} \sqrt{d x + c} \sqrt{f x + e}}{2 \, {\left(d^{2} f^{2} x^{2} + c d e f + {\left(d^{2} e f + c d f^{2}\right)} x\right)}}\right) + 2 \, {\left(384 \, C b^{2} d^{5} f^{5} x^{4} + 945 \, C b^{2} d^{5} e^{4} f - 210 \, {\left(C b^{2} c d^{4} + 5 \, {\left(2 \, C a b + B b^{2}\right)} d^{5}\right)} e^{3} f^{2} - 2 \, {\left(68 \, C b^{2} c^{2} d^{3} - 125 \, {\left(2 \, C a b + B b^{2}\right)} c d^{4} - 600 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} d^{5}\right)} e^{2} f^{3} - 10 \, {\left(11 \, C b^{2} c^{3} d^{2} - 17 \, {\left(2 \, C a b + B b^{2}\right)} c^{2} d^{3} + 32 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c d^{4} + 144 \, {\left(B a^{2} + 2 \, A a b\right)} d^{5}\right)} e f^{4} - 15 \, {\left(7 \, C b^{2} c^{4} d - 128 \, A a^{2} d^{5} - 10 \, {\left(2 \, C a b + B b^{2}\right)} c^{3} d^{2} + 16 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c^{2} d^{3} - 32 \, {\left(B a^{2} + 2 \, A a b\right)} c d^{4}\right)} f^{5} - 48 \, {\left(9 \, C b^{2} d^{5} e f^{4} - {\left(C b^{2} c d^{4} + 10 \, {\left(2 \, C a b + B b^{2}\right)} d^{5}\right)} f^{5}\right)} x^{3} + 8 \, {\left(63 \, C b^{2} d^{5} e^{2} f^{3} - 2 \, {\left(4 \, C b^{2} c d^{4} + 35 \, {\left(2 \, C a b + B b^{2}\right)} d^{5}\right)} e f^{4} - {\left(7 \, C b^{2} c^{2} d^{3} - 10 \, {\left(2 \, C a b + B b^{2}\right)} c d^{4} - 80 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} d^{5}\right)} f^{5}\right)} x^{2} - 2 \, {\left(315 \, C b^{2} d^{5} e^{3} f^{2} - 7 \, {\left(7 \, C b^{2} c d^{4} + 50 \, {\left(2 \, C a b + B b^{2}\right)} d^{5}\right)} e^{2} f^{3} - {\left(39 \, C b^{2} c^{2} d^{3} - 60 \, {\left(2 \, C a b + B b^{2}\right)} c d^{4} - 400 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} d^{5}\right)} e f^{4} - 5 \, {\left(7 \, C b^{2} c^{3} d^{2} - 10 \, {\left(2 \, C a b + B b^{2}\right)} c^{2} d^{3} + 16 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c d^{4} + 96 \, {\left(B a^{2} + 2 \, A a b\right)} d^{5}\right)} f^{5}\right)} x\right)} \sqrt{d x + c} \sqrt{f x + e}}{3840 \, d^{5} f^{6}}\right]"," ",0,"[-1/7680*(15*(63*C*b^2*d^5*e^5 - 35*(C*b^2*c*d^4 + 2*(2*C*a*b + B*b^2)*d^5)*e^4*f - 10*(C*b^2*c^2*d^3 - 4*(2*C*a*b + B*b^2)*c*d^4 - 8*(C*a^2 + 2*B*a*b + A*b^2)*d^5)*e^3*f^2 - 6*(C*b^2*c^3*d^2 - 2*(2*C*a*b + B*b^2)*c^2*d^3 + 8*(C*a^2 + 2*B*a*b + A*b^2)*c*d^4 + 16*(B*a^2 + 2*A*a*b)*d^5)*e^2*f^3 - (5*C*b^2*c^4*d - 128*A*a^2*d^5 - 8*(2*C*a*b + B*b^2)*c^3*d^2 + 16*(C*a^2 + 2*B*a*b + A*b^2)*c^2*d^3 - 64*(B*a^2 + 2*A*a*b)*c*d^4)*e*f^4 - (7*C*b^2*c^5 + 128*A*a^2*c*d^4 - 10*(2*C*a*b + B*b^2)*c^4*d + 16*(C*a^2 + 2*B*a*b + A*b^2)*c^3*d^2 - 32*(B*a^2 + 2*A*a*b)*c^2*d^3)*f^5)*sqrt(d*f)*log(8*d^2*f^2*x^2 + d^2*e^2 + 6*c*d*e*f + c^2*f^2 + 4*(2*d*f*x + d*e + c*f)*sqrt(d*f)*sqrt(d*x + c)*sqrt(f*x + e) + 8*(d^2*e*f + c*d*f^2)*x) - 4*(384*C*b^2*d^5*f^5*x^4 + 945*C*b^2*d^5*e^4*f - 210*(C*b^2*c*d^4 + 5*(2*C*a*b + B*b^2)*d^5)*e^3*f^2 - 2*(68*C*b^2*c^2*d^3 - 125*(2*C*a*b + B*b^2)*c*d^4 - 600*(C*a^2 + 2*B*a*b + A*b^2)*d^5)*e^2*f^3 - 10*(11*C*b^2*c^3*d^2 - 17*(2*C*a*b + B*b^2)*c^2*d^3 + 32*(C*a^2 + 2*B*a*b + A*b^2)*c*d^4 + 144*(B*a^2 + 2*A*a*b)*d^5)*e*f^4 - 15*(7*C*b^2*c^4*d - 128*A*a^2*d^5 - 10*(2*C*a*b + B*b^2)*c^3*d^2 + 16*(C*a^2 + 2*B*a*b + A*b^2)*c^2*d^3 - 32*(B*a^2 + 2*A*a*b)*c*d^4)*f^5 - 48*(9*C*b^2*d^5*e*f^4 - (C*b^2*c*d^4 + 10*(2*C*a*b + B*b^2)*d^5)*f^5)*x^3 + 8*(63*C*b^2*d^5*e^2*f^3 - 2*(4*C*b^2*c*d^4 + 35*(2*C*a*b + B*b^2)*d^5)*e*f^4 - (7*C*b^2*c^2*d^3 - 10*(2*C*a*b + B*b^2)*c*d^4 - 80*(C*a^2 + 2*B*a*b + A*b^2)*d^5)*f^5)*x^2 - 2*(315*C*b^2*d^5*e^3*f^2 - 7*(7*C*b^2*c*d^4 + 50*(2*C*a*b + B*b^2)*d^5)*e^2*f^3 - (39*C*b^2*c^2*d^3 - 60*(2*C*a*b + B*b^2)*c*d^4 - 400*(C*a^2 + 2*B*a*b + A*b^2)*d^5)*e*f^4 - 5*(7*C*b^2*c^3*d^2 - 10*(2*C*a*b + B*b^2)*c^2*d^3 + 16*(C*a^2 + 2*B*a*b + A*b^2)*c*d^4 + 96*(B*a^2 + 2*A*a*b)*d^5)*f^5)*x)*sqrt(d*x + c)*sqrt(f*x + e))/(d^5*f^6), 1/3840*(15*(63*C*b^2*d^5*e^5 - 35*(C*b^2*c*d^4 + 2*(2*C*a*b + B*b^2)*d^5)*e^4*f - 10*(C*b^2*c^2*d^3 - 4*(2*C*a*b + B*b^2)*c*d^4 - 8*(C*a^2 + 2*B*a*b + A*b^2)*d^5)*e^3*f^2 - 6*(C*b^2*c^3*d^2 - 2*(2*C*a*b + B*b^2)*c^2*d^3 + 8*(C*a^2 + 2*B*a*b + A*b^2)*c*d^4 + 16*(B*a^2 + 2*A*a*b)*d^5)*e^2*f^3 - (5*C*b^2*c^4*d - 128*A*a^2*d^5 - 8*(2*C*a*b + B*b^2)*c^3*d^2 + 16*(C*a^2 + 2*B*a*b + A*b^2)*c^2*d^3 - 64*(B*a^2 + 2*A*a*b)*c*d^4)*e*f^4 - (7*C*b^2*c^5 + 128*A*a^2*c*d^4 - 10*(2*C*a*b + B*b^2)*c^4*d + 16*(C*a^2 + 2*B*a*b + A*b^2)*c^3*d^2 - 32*(B*a^2 + 2*A*a*b)*c^2*d^3)*f^5)*sqrt(-d*f)*arctan(1/2*(2*d*f*x + d*e + c*f)*sqrt(-d*f)*sqrt(d*x + c)*sqrt(f*x + e)/(d^2*f^2*x^2 + c*d*e*f + (d^2*e*f + c*d*f^2)*x)) + 2*(384*C*b^2*d^5*f^5*x^4 + 945*C*b^2*d^5*e^4*f - 210*(C*b^2*c*d^4 + 5*(2*C*a*b + B*b^2)*d^5)*e^3*f^2 - 2*(68*C*b^2*c^2*d^3 - 125*(2*C*a*b + B*b^2)*c*d^4 - 600*(C*a^2 + 2*B*a*b + A*b^2)*d^5)*e^2*f^3 - 10*(11*C*b^2*c^3*d^2 - 17*(2*C*a*b + B*b^2)*c^2*d^3 + 32*(C*a^2 + 2*B*a*b + A*b^2)*c*d^4 + 144*(B*a^2 + 2*A*a*b)*d^5)*e*f^4 - 15*(7*C*b^2*c^4*d - 128*A*a^2*d^5 - 10*(2*C*a*b + B*b^2)*c^3*d^2 + 16*(C*a^2 + 2*B*a*b + A*b^2)*c^2*d^3 - 32*(B*a^2 + 2*A*a*b)*c*d^4)*f^5 - 48*(9*C*b^2*d^5*e*f^4 - (C*b^2*c*d^4 + 10*(2*C*a*b + B*b^2)*d^5)*f^5)*x^3 + 8*(63*C*b^2*d^5*e^2*f^3 - 2*(4*C*b^2*c*d^4 + 35*(2*C*a*b + B*b^2)*d^5)*e*f^4 - (7*C*b^2*c^2*d^3 - 10*(2*C*a*b + B*b^2)*c*d^4 - 80*(C*a^2 + 2*B*a*b + A*b^2)*d^5)*f^5)*x^2 - 2*(315*C*b^2*d^5*e^3*f^2 - 7*(7*C*b^2*c*d^4 + 50*(2*C*a*b + B*b^2)*d^5)*e^2*f^3 - (39*C*b^2*c^2*d^3 - 60*(2*C*a*b + B*b^2)*c*d^4 - 400*(C*a^2 + 2*B*a*b + A*b^2)*d^5)*e*f^4 - 5*(7*C*b^2*c^3*d^2 - 10*(2*C*a*b + B*b^2)*c^2*d^3 + 16*(C*a^2 + 2*B*a*b + A*b^2)*c*d^4 + 96*(B*a^2 + 2*A*a*b)*d^5)*f^5)*x)*sqrt(d*x + c)*sqrt(f*x + e))/(d^5*f^6)]","A",0
48,1,1114,0,3.758178," ","integrate((b*x+a)*(C*x^2+B*x+A)*(d*x+c)^(1/2)/(f*x+e)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(35 \, C b d^{4} e^{4} - 20 \, {\left(C b c d^{3} + 2 \, {\left(C a + B b\right)} d^{4}\right)} e^{3} f - 6 \, {\left(C b c^{2} d^{2} - 4 \, {\left(C a + B b\right)} c d^{3} - 8 \, {\left(B a + A b\right)} d^{4}\right)} e^{2} f^{2} - 4 \, {\left(C b c^{3} d + 16 \, A a d^{4} - 2 \, {\left(C a + B b\right)} c^{2} d^{2} + 8 \, {\left(B a + A b\right)} c d^{3}\right)} e f^{3} - {\left(5 \, C b c^{4} - 64 \, A a c d^{3} - 8 \, {\left(C a + B b\right)} c^{3} d + 16 \, {\left(B a + A b\right)} c^{2} d^{2}\right)} f^{4}\right)} \sqrt{d f} \log\left(8 \, d^{2} f^{2} x^{2} + d^{2} e^{2} + 6 \, c d e f + c^{2} f^{2} + 4 \, {\left(2 \, d f x + d e + c f\right)} \sqrt{d f} \sqrt{d x + c} \sqrt{f x + e} + 8 \, {\left(d^{2} e f + c d f^{2}\right)} x\right) + 4 \, {\left(48 \, C b d^{4} f^{4} x^{3} - 105 \, C b d^{4} e^{3} f + 5 \, {\left(5 \, C b c d^{3} + 24 \, {\left(C a + B b\right)} d^{4}\right)} e^{2} f^{2} + {\left(17 \, C b c^{2} d^{2} - 32 \, {\left(C a + B b\right)} c d^{3} - 144 \, {\left(B a + A b\right)} d^{4}\right)} e f^{3} + 3 \, {\left(5 \, C b c^{3} d + 64 \, A a d^{4} - 8 \, {\left(C a + B b\right)} c^{2} d^{2} + 16 \, {\left(B a + A b\right)} c d^{3}\right)} f^{4} - 8 \, {\left(7 \, C b d^{4} e f^{3} - {\left(C b c d^{3} + 8 \, {\left(C a + B b\right)} d^{4}\right)} f^{4}\right)} x^{2} + 2 \, {\left(35 \, C b d^{4} e^{2} f^{2} - 2 \, {\left(3 \, C b c d^{3} + 20 \, {\left(C a + B b\right)} d^{4}\right)} e f^{3} - {\left(5 \, C b c^{2} d^{2} - 8 \, {\left(C a + B b\right)} c d^{3} - 48 \, {\left(B a + A b\right)} d^{4}\right)} f^{4}\right)} x\right)} \sqrt{d x + c} \sqrt{f x + e}}{768 \, d^{4} f^{5}}, -\frac{3 \, {\left(35 \, C b d^{4} e^{4} - 20 \, {\left(C b c d^{3} + 2 \, {\left(C a + B b\right)} d^{4}\right)} e^{3} f - 6 \, {\left(C b c^{2} d^{2} - 4 \, {\left(C a + B b\right)} c d^{3} - 8 \, {\left(B a + A b\right)} d^{4}\right)} e^{2} f^{2} - 4 \, {\left(C b c^{3} d + 16 \, A a d^{4} - 2 \, {\left(C a + B b\right)} c^{2} d^{2} + 8 \, {\left(B a + A b\right)} c d^{3}\right)} e f^{3} - {\left(5 \, C b c^{4} - 64 \, A a c d^{3} - 8 \, {\left(C a + B b\right)} c^{3} d + 16 \, {\left(B a + A b\right)} c^{2} d^{2}\right)} f^{4}\right)} \sqrt{-d f} \arctan\left(\frac{{\left(2 \, d f x + d e + c f\right)} \sqrt{-d f} \sqrt{d x + c} \sqrt{f x + e}}{2 \, {\left(d^{2} f^{2} x^{2} + c d e f + {\left(d^{2} e f + c d f^{2}\right)} x\right)}}\right) - 2 \, {\left(48 \, C b d^{4} f^{4} x^{3} - 105 \, C b d^{4} e^{3} f + 5 \, {\left(5 \, C b c d^{3} + 24 \, {\left(C a + B b\right)} d^{4}\right)} e^{2} f^{2} + {\left(17 \, C b c^{2} d^{2} - 32 \, {\left(C a + B b\right)} c d^{3} - 144 \, {\left(B a + A b\right)} d^{4}\right)} e f^{3} + 3 \, {\left(5 \, C b c^{3} d + 64 \, A a d^{4} - 8 \, {\left(C a + B b\right)} c^{2} d^{2} + 16 \, {\left(B a + A b\right)} c d^{3}\right)} f^{4} - 8 \, {\left(7 \, C b d^{4} e f^{3} - {\left(C b c d^{3} + 8 \, {\left(C a + B b\right)} d^{4}\right)} f^{4}\right)} x^{2} + 2 \, {\left(35 \, C b d^{4} e^{2} f^{2} - 2 \, {\left(3 \, C b c d^{3} + 20 \, {\left(C a + B b\right)} d^{4}\right)} e f^{3} - {\left(5 \, C b c^{2} d^{2} - 8 \, {\left(C a + B b\right)} c d^{3} - 48 \, {\left(B a + A b\right)} d^{4}\right)} f^{4}\right)} x\right)} \sqrt{d x + c} \sqrt{f x + e}}{384 \, d^{4} f^{5}}\right]"," ",0,"[1/768*(3*(35*C*b*d^4*e^4 - 20*(C*b*c*d^3 + 2*(C*a + B*b)*d^4)*e^3*f - 6*(C*b*c^2*d^2 - 4*(C*a + B*b)*c*d^3 - 8*(B*a + A*b)*d^4)*e^2*f^2 - 4*(C*b*c^3*d + 16*A*a*d^4 - 2*(C*a + B*b)*c^2*d^2 + 8*(B*a + A*b)*c*d^3)*e*f^3 - (5*C*b*c^4 - 64*A*a*c*d^3 - 8*(C*a + B*b)*c^3*d + 16*(B*a + A*b)*c^2*d^2)*f^4)*sqrt(d*f)*log(8*d^2*f^2*x^2 + d^2*e^2 + 6*c*d*e*f + c^2*f^2 + 4*(2*d*f*x + d*e + c*f)*sqrt(d*f)*sqrt(d*x + c)*sqrt(f*x + e) + 8*(d^2*e*f + c*d*f^2)*x) + 4*(48*C*b*d^4*f^4*x^3 - 105*C*b*d^4*e^3*f + 5*(5*C*b*c*d^3 + 24*(C*a + B*b)*d^4)*e^2*f^2 + (17*C*b*c^2*d^2 - 32*(C*a + B*b)*c*d^3 - 144*(B*a + A*b)*d^4)*e*f^3 + 3*(5*C*b*c^3*d + 64*A*a*d^4 - 8*(C*a + B*b)*c^2*d^2 + 16*(B*a + A*b)*c*d^3)*f^4 - 8*(7*C*b*d^4*e*f^3 - (C*b*c*d^3 + 8*(C*a + B*b)*d^4)*f^4)*x^2 + 2*(35*C*b*d^4*e^2*f^2 - 2*(3*C*b*c*d^3 + 20*(C*a + B*b)*d^4)*e*f^3 - (5*C*b*c^2*d^2 - 8*(C*a + B*b)*c*d^3 - 48*(B*a + A*b)*d^4)*f^4)*x)*sqrt(d*x + c)*sqrt(f*x + e))/(d^4*f^5), -1/384*(3*(35*C*b*d^4*e^4 - 20*(C*b*c*d^3 + 2*(C*a + B*b)*d^4)*e^3*f - 6*(C*b*c^2*d^2 - 4*(C*a + B*b)*c*d^3 - 8*(B*a + A*b)*d^4)*e^2*f^2 - 4*(C*b*c^3*d + 16*A*a*d^4 - 2*(C*a + B*b)*c^2*d^2 + 8*(B*a + A*b)*c*d^3)*e*f^3 - (5*C*b*c^4 - 64*A*a*c*d^3 - 8*(C*a + B*b)*c^3*d + 16*(B*a + A*b)*c^2*d^2)*f^4)*sqrt(-d*f)*arctan(1/2*(2*d*f*x + d*e + c*f)*sqrt(-d*f)*sqrt(d*x + c)*sqrt(f*x + e)/(d^2*f^2*x^2 + c*d*e*f + (d^2*e*f + c*d*f^2)*x)) - 2*(48*C*b*d^4*f^4*x^3 - 105*C*b*d^4*e^3*f + 5*(5*C*b*c*d^3 + 24*(C*a + B*b)*d^4)*e^2*f^2 + (17*C*b*c^2*d^2 - 32*(C*a + B*b)*c*d^3 - 144*(B*a + A*b)*d^4)*e*f^3 + 3*(5*C*b*c^3*d + 64*A*a*d^4 - 8*(C*a + B*b)*c^2*d^2 + 16*(B*a + A*b)*c*d^3)*f^4 - 8*(7*C*b*d^4*e*f^3 - (C*b*c*d^3 + 8*(C*a + B*b)*d^4)*f^4)*x^2 + 2*(35*C*b*d^4*e^2*f^2 - 2*(3*C*b*c*d^3 + 20*(C*a + B*b)*d^4)*e*f^3 - (5*C*b*c^2*d^2 - 8*(C*a + B*b)*c*d^3 - 48*(B*a + A*b)*d^4)*f^4)*x)*sqrt(d*x + c)*sqrt(f*x + e))/(d^4*f^5)]","A",0
49,1,576,0,1.485336," ","integrate((C*x^2+B*x+A)*(d*x+c)^(1/2)/(f*x+e)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, C d^{3} e^{3} - 3 \, {\left(C c d^{2} + 2 \, B d^{3}\right)} e^{2} f - {\left(C c^{2} d - 4 \, B c d^{2} - 8 \, A d^{3}\right)} e f^{2} - {\left(C c^{3} - 2 \, B c^{2} d + 8 \, A c d^{2}\right)} f^{3}\right)} \sqrt{d f} \log\left(8 \, d^{2} f^{2} x^{2} + d^{2} e^{2} + 6 \, c d e f + c^{2} f^{2} + 4 \, {\left(2 \, d f x + d e + c f\right)} \sqrt{d f} \sqrt{d x + c} \sqrt{f x + e} + 8 \, {\left(d^{2} e f + c d f^{2}\right)} x\right) - 4 \, {\left(8 \, C d^{3} f^{3} x^{2} + 15 \, C d^{3} e^{2} f - 2 \, {\left(2 \, C c d^{2} + 9 \, B d^{3}\right)} e f^{2} - 3 \, {\left(C c^{2} d - 2 \, B c d^{2} - 8 \, A d^{3}\right)} f^{3} - 2 \, {\left(5 \, C d^{3} e f^{2} - {\left(C c d^{2} + 6 \, B d^{3}\right)} f^{3}\right)} x\right)} \sqrt{d x + c} \sqrt{f x + e}}{96 \, d^{3} f^{4}}, \frac{3 \, {\left(5 \, C d^{3} e^{3} - 3 \, {\left(C c d^{2} + 2 \, B d^{3}\right)} e^{2} f - {\left(C c^{2} d - 4 \, B c d^{2} - 8 \, A d^{3}\right)} e f^{2} - {\left(C c^{3} - 2 \, B c^{2} d + 8 \, A c d^{2}\right)} f^{3}\right)} \sqrt{-d f} \arctan\left(\frac{{\left(2 \, d f x + d e + c f\right)} \sqrt{-d f} \sqrt{d x + c} \sqrt{f x + e}}{2 \, {\left(d^{2} f^{2} x^{2} + c d e f + {\left(d^{2} e f + c d f^{2}\right)} x\right)}}\right) + 2 \, {\left(8 \, C d^{3} f^{3} x^{2} + 15 \, C d^{3} e^{2} f - 2 \, {\left(2 \, C c d^{2} + 9 \, B d^{3}\right)} e f^{2} - 3 \, {\left(C c^{2} d - 2 \, B c d^{2} - 8 \, A d^{3}\right)} f^{3} - 2 \, {\left(5 \, C d^{3} e f^{2} - {\left(C c d^{2} + 6 \, B d^{3}\right)} f^{3}\right)} x\right)} \sqrt{d x + c} \sqrt{f x + e}}{48 \, d^{3} f^{4}}\right]"," ",0,"[-1/96*(3*(5*C*d^3*e^3 - 3*(C*c*d^2 + 2*B*d^3)*e^2*f - (C*c^2*d - 4*B*c*d^2 - 8*A*d^3)*e*f^2 - (C*c^3 - 2*B*c^2*d + 8*A*c*d^2)*f^3)*sqrt(d*f)*log(8*d^2*f^2*x^2 + d^2*e^2 + 6*c*d*e*f + c^2*f^2 + 4*(2*d*f*x + d*e + c*f)*sqrt(d*f)*sqrt(d*x + c)*sqrt(f*x + e) + 8*(d^2*e*f + c*d*f^2)*x) - 4*(8*C*d^3*f^3*x^2 + 15*C*d^3*e^2*f - 2*(2*C*c*d^2 + 9*B*d^3)*e*f^2 - 3*(C*c^2*d - 2*B*c*d^2 - 8*A*d^3)*f^3 - 2*(5*C*d^3*e*f^2 - (C*c*d^2 + 6*B*d^3)*f^3)*x)*sqrt(d*x + c)*sqrt(f*x + e))/(d^3*f^4), 1/48*(3*(5*C*d^3*e^3 - 3*(C*c*d^2 + 2*B*d^3)*e^2*f - (C*c^2*d - 4*B*c*d^2 - 8*A*d^3)*e*f^2 - (C*c^3 - 2*B*c^2*d + 8*A*c*d^2)*f^3)*sqrt(-d*f)*arctan(1/2*(2*d*f*x + d*e + c*f)*sqrt(-d*f)*sqrt(d*x + c)*sqrt(f*x + e)/(d^2*f^2*x^2 + c*d*e*f + (d^2*e*f + c*d*f^2)*x)) + 2*(8*C*d^3*f^3*x^2 + 15*C*d^3*e^2*f - 2*(2*C*c*d^2 + 9*B*d^3)*e*f^2 - 3*(C*c^2*d - 2*B*c*d^2 - 8*A*d^3)*f^3 - 2*(5*C*d^3*e*f^2 - (C*c*d^2 + 6*B*d^3)*f^3)*x)*sqrt(d*x + c)*sqrt(f*x + e))/(d^3*f^4)]","A",0
50,-1,0,0,0.000000," ","integrate((C*x^2+B*x+A)*(d*x+c)^(1/2)/(b*x+a)/(f*x+e)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
51,-1,0,0,0.000000," ","integrate((C*x^2+B*x+A)*(d*x+c)^(1/2)/(b*x+a)^2/(f*x+e)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
52,-1,0,0,0.000000," ","integrate((C*x^2+B*x+A)*(d*x+c)^(1/2)/(b*x+a)^3/(f*x+e)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
53,-1,0,0,0.000000," ","integrate((C*x^2+B*x+A)*(d*x+c)^(1/2)/(b*x+a)^4/(f*x+e)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
54,1,1436,0,5.323431," ","integrate((b*x+a)^2*(C*x^2+B*x+A)/(d*x+c)^(1/2)/(f*x+e)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(35 \, C b^{2} d^{4} e^{4} + 20 \, {\left(C b^{2} c d^{3} - 2 \, {\left(2 \, C a b + B b^{2}\right)} d^{4}\right)} e^{3} f + 6 \, {\left(3 \, C b^{2} c^{2} d^{2} - 4 \, {\left(2 \, C a b + B b^{2}\right)} c d^{3} + 8 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} d^{4}\right)} e^{2} f^{2} + 4 \, {\left(5 \, C b^{2} c^{3} d - 6 \, {\left(2 \, C a b + B b^{2}\right)} c^{2} d^{2} + 8 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c d^{3} - 16 \, {\left(B a^{2} + 2 \, A a b\right)} d^{4}\right)} e f^{3} + {\left(35 \, C b^{2} c^{4} + 128 \, A a^{2} d^{4} - 40 \, {\left(2 \, C a b + B b^{2}\right)} c^{3} d + 48 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c^{2} d^{2} - 64 \, {\left(B a^{2} + 2 \, A a b\right)} c d^{3}\right)} f^{4}\right)} \sqrt{d f} \log\left(8 \, d^{2} f^{2} x^{2} + d^{2} e^{2} + 6 \, c d e f + c^{2} f^{2} + 4 \, {\left(2 \, d f x + d e + c f\right)} \sqrt{d f} \sqrt{d x + c} \sqrt{f x + e} + 8 \, {\left(d^{2} e f + c d f^{2}\right)} x\right) + 4 \, {\left(48 \, C b^{2} d^{4} f^{4} x^{3} - 105 \, C b^{2} d^{4} e^{3} f - 5 \, {\left(19 \, C b^{2} c d^{3} - 24 \, {\left(2 \, C a b + B b^{2}\right)} d^{4}\right)} e^{2} f^{2} - {\left(95 \, C b^{2} c^{2} d^{2} - 112 \, {\left(2 \, C a b + B b^{2}\right)} c d^{3} + 144 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} d^{4}\right)} e f^{3} - 3 \, {\left(35 \, C b^{2} c^{3} d - 40 \, {\left(2 \, C a b + B b^{2}\right)} c^{2} d^{2} + 48 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c d^{3} - 64 \, {\left(B a^{2} + 2 \, A a b\right)} d^{4}\right)} f^{4} - 8 \, {\left(7 \, C b^{2} d^{4} e f^{3} + {\left(7 \, C b^{2} c d^{3} - 8 \, {\left(2 \, C a b + B b^{2}\right)} d^{4}\right)} f^{4}\right)} x^{2} + 2 \, {\left(35 \, C b^{2} d^{4} e^{2} f^{2} + 2 \, {\left(17 \, C b^{2} c d^{3} - 20 \, {\left(2 \, C a b + B b^{2}\right)} d^{4}\right)} e f^{3} + {\left(35 \, C b^{2} c^{2} d^{2} - 40 \, {\left(2 \, C a b + B b^{2}\right)} c d^{3} + 48 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} d^{4}\right)} f^{4}\right)} x\right)} \sqrt{d x + c} \sqrt{f x + e}}{768 \, d^{5} f^{5}}, -\frac{3 \, {\left(35 \, C b^{2} d^{4} e^{4} + 20 \, {\left(C b^{2} c d^{3} - 2 \, {\left(2 \, C a b + B b^{2}\right)} d^{4}\right)} e^{3} f + 6 \, {\left(3 \, C b^{2} c^{2} d^{2} - 4 \, {\left(2 \, C a b + B b^{2}\right)} c d^{3} + 8 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} d^{4}\right)} e^{2} f^{2} + 4 \, {\left(5 \, C b^{2} c^{3} d - 6 \, {\left(2 \, C a b + B b^{2}\right)} c^{2} d^{2} + 8 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c d^{3} - 16 \, {\left(B a^{2} + 2 \, A a b\right)} d^{4}\right)} e f^{3} + {\left(35 \, C b^{2} c^{4} + 128 \, A a^{2} d^{4} - 40 \, {\left(2 \, C a b + B b^{2}\right)} c^{3} d + 48 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c^{2} d^{2} - 64 \, {\left(B a^{2} + 2 \, A a b\right)} c d^{3}\right)} f^{4}\right)} \sqrt{-d f} \arctan\left(\frac{{\left(2 \, d f x + d e + c f\right)} \sqrt{-d f} \sqrt{d x + c} \sqrt{f x + e}}{2 \, {\left(d^{2} f^{2} x^{2} + c d e f + {\left(d^{2} e f + c d f^{2}\right)} x\right)}}\right) - 2 \, {\left(48 \, C b^{2} d^{4} f^{4} x^{3} - 105 \, C b^{2} d^{4} e^{3} f - 5 \, {\left(19 \, C b^{2} c d^{3} - 24 \, {\left(2 \, C a b + B b^{2}\right)} d^{4}\right)} e^{2} f^{2} - {\left(95 \, C b^{2} c^{2} d^{2} - 112 \, {\left(2 \, C a b + B b^{2}\right)} c d^{3} + 144 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} d^{4}\right)} e f^{3} - 3 \, {\left(35 \, C b^{2} c^{3} d - 40 \, {\left(2 \, C a b + B b^{2}\right)} c^{2} d^{2} + 48 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c d^{3} - 64 \, {\left(B a^{2} + 2 \, A a b\right)} d^{4}\right)} f^{4} - 8 \, {\left(7 \, C b^{2} d^{4} e f^{3} + {\left(7 \, C b^{2} c d^{3} - 8 \, {\left(2 \, C a b + B b^{2}\right)} d^{4}\right)} f^{4}\right)} x^{2} + 2 \, {\left(35 \, C b^{2} d^{4} e^{2} f^{2} + 2 \, {\left(17 \, C b^{2} c d^{3} - 20 \, {\left(2 \, C a b + B b^{2}\right)} d^{4}\right)} e f^{3} + {\left(35 \, C b^{2} c^{2} d^{2} - 40 \, {\left(2 \, C a b + B b^{2}\right)} c d^{3} + 48 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} d^{4}\right)} f^{4}\right)} x\right)} \sqrt{d x + c} \sqrt{f x + e}}{384 \, d^{5} f^{5}}\right]"," ",0,"[1/768*(3*(35*C*b^2*d^4*e^4 + 20*(C*b^2*c*d^3 - 2*(2*C*a*b + B*b^2)*d^4)*e^3*f + 6*(3*C*b^2*c^2*d^2 - 4*(2*C*a*b + B*b^2)*c*d^3 + 8*(C*a^2 + 2*B*a*b + A*b^2)*d^4)*e^2*f^2 + 4*(5*C*b^2*c^3*d - 6*(2*C*a*b + B*b^2)*c^2*d^2 + 8*(C*a^2 + 2*B*a*b + A*b^2)*c*d^3 - 16*(B*a^2 + 2*A*a*b)*d^4)*e*f^3 + (35*C*b^2*c^4 + 128*A*a^2*d^4 - 40*(2*C*a*b + B*b^2)*c^3*d + 48*(C*a^2 + 2*B*a*b + A*b^2)*c^2*d^2 - 64*(B*a^2 + 2*A*a*b)*c*d^3)*f^4)*sqrt(d*f)*log(8*d^2*f^2*x^2 + d^2*e^2 + 6*c*d*e*f + c^2*f^2 + 4*(2*d*f*x + d*e + c*f)*sqrt(d*f)*sqrt(d*x + c)*sqrt(f*x + e) + 8*(d^2*e*f + c*d*f^2)*x) + 4*(48*C*b^2*d^4*f^4*x^3 - 105*C*b^2*d^4*e^3*f - 5*(19*C*b^2*c*d^3 - 24*(2*C*a*b + B*b^2)*d^4)*e^2*f^2 - (95*C*b^2*c^2*d^2 - 112*(2*C*a*b + B*b^2)*c*d^3 + 144*(C*a^2 + 2*B*a*b + A*b^2)*d^4)*e*f^3 - 3*(35*C*b^2*c^3*d - 40*(2*C*a*b + B*b^2)*c^2*d^2 + 48*(C*a^2 + 2*B*a*b + A*b^2)*c*d^3 - 64*(B*a^2 + 2*A*a*b)*d^4)*f^4 - 8*(7*C*b^2*d^4*e*f^3 + (7*C*b^2*c*d^3 - 8*(2*C*a*b + B*b^2)*d^4)*f^4)*x^2 + 2*(35*C*b^2*d^4*e^2*f^2 + 2*(17*C*b^2*c*d^3 - 20*(2*C*a*b + B*b^2)*d^4)*e*f^3 + (35*C*b^2*c^2*d^2 - 40*(2*C*a*b + B*b^2)*c*d^3 + 48*(C*a^2 + 2*B*a*b + A*b^2)*d^4)*f^4)*x)*sqrt(d*x + c)*sqrt(f*x + e))/(d^5*f^5), -1/384*(3*(35*C*b^2*d^4*e^4 + 20*(C*b^2*c*d^3 - 2*(2*C*a*b + B*b^2)*d^4)*e^3*f + 6*(3*C*b^2*c^2*d^2 - 4*(2*C*a*b + B*b^2)*c*d^3 + 8*(C*a^2 + 2*B*a*b + A*b^2)*d^4)*e^2*f^2 + 4*(5*C*b^2*c^3*d - 6*(2*C*a*b + B*b^2)*c^2*d^2 + 8*(C*a^2 + 2*B*a*b + A*b^2)*c*d^3 - 16*(B*a^2 + 2*A*a*b)*d^4)*e*f^3 + (35*C*b^2*c^4 + 128*A*a^2*d^4 - 40*(2*C*a*b + B*b^2)*c^3*d + 48*(C*a^2 + 2*B*a*b + A*b^2)*c^2*d^2 - 64*(B*a^2 + 2*A*a*b)*c*d^3)*f^4)*sqrt(-d*f)*arctan(1/2*(2*d*f*x + d*e + c*f)*sqrt(-d*f)*sqrt(d*x + c)*sqrt(f*x + e)/(d^2*f^2*x^2 + c*d*e*f + (d^2*e*f + c*d*f^2)*x)) - 2*(48*C*b^2*d^4*f^4*x^3 - 105*C*b^2*d^4*e^3*f - 5*(19*C*b^2*c*d^3 - 24*(2*C*a*b + B*b^2)*d^4)*e^2*f^2 - (95*C*b^2*c^2*d^2 - 112*(2*C*a*b + B*b^2)*c*d^3 + 144*(C*a^2 + 2*B*a*b + A*b^2)*d^4)*e*f^3 - 3*(35*C*b^2*c^3*d - 40*(2*C*a*b + B*b^2)*c^2*d^2 + 48*(C*a^2 + 2*B*a*b + A*b^2)*c*d^3 - 64*(B*a^2 + 2*A*a*b)*d^4)*f^4 - 8*(7*C*b^2*d^4*e*f^3 + (7*C*b^2*c*d^3 - 8*(2*C*a*b + B*b^2)*d^4)*f^4)*x^2 + 2*(35*C*b^2*d^4*e^2*f^2 + 2*(17*C*b^2*c*d^3 - 20*(2*C*a*b + B*b^2)*d^4)*e*f^3 + (35*C*b^2*c^2*d^2 - 40*(2*C*a*b + B*b^2)*c*d^3 + 48*(C*a^2 + 2*B*a*b + A*b^2)*d^4)*f^4)*x)*sqrt(d*x + c)*sqrt(f*x + e))/(d^5*f^5)]","A",0
55,1,720,0,2.265502," ","integrate((b*x+a)*(C*x^2+B*x+A)/(d*x+c)^(1/2)/(f*x+e)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, C b d^{3} e^{3} + 3 \, {\left(C b c d^{2} - 2 \, {\left(C a + B b\right)} d^{3}\right)} e^{2} f + {\left(3 \, C b c^{2} d - 4 \, {\left(C a + B b\right)} c d^{2} + 8 \, {\left(B a + A b\right)} d^{3}\right)} e f^{2} + {\left(5 \, C b c^{3} - 16 \, A a d^{3} - 6 \, {\left(C a + B b\right)} c^{2} d + 8 \, {\left(B a + A b\right)} c d^{2}\right)} f^{3}\right)} \sqrt{d f} \log\left(8 \, d^{2} f^{2} x^{2} + d^{2} e^{2} + 6 \, c d e f + c^{2} f^{2} + 4 \, {\left(2 \, d f x + d e + c f\right)} \sqrt{d f} \sqrt{d x + c} \sqrt{f x + e} + 8 \, {\left(d^{2} e f + c d f^{2}\right)} x\right) - 4 \, {\left(8 \, C b d^{3} f^{3} x^{2} + 15 \, C b d^{3} e^{2} f + 2 \, {\left(7 \, C b c d^{2} - 9 \, {\left(C a + B b\right)} d^{3}\right)} e f^{2} + 3 \, {\left(5 \, C b c^{2} d - 6 \, {\left(C a + B b\right)} c d^{2} + 8 \, {\left(B a + A b\right)} d^{3}\right)} f^{3} - 2 \, {\left(5 \, C b d^{3} e f^{2} + {\left(5 \, C b c d^{2} - 6 \, {\left(C a + B b\right)} d^{3}\right)} f^{3}\right)} x\right)} \sqrt{d x + c} \sqrt{f x + e}}{96 \, d^{4} f^{4}}, \frac{3 \, {\left(5 \, C b d^{3} e^{3} + 3 \, {\left(C b c d^{2} - 2 \, {\left(C a + B b\right)} d^{3}\right)} e^{2} f + {\left(3 \, C b c^{2} d - 4 \, {\left(C a + B b\right)} c d^{2} + 8 \, {\left(B a + A b\right)} d^{3}\right)} e f^{2} + {\left(5 \, C b c^{3} - 16 \, A a d^{3} - 6 \, {\left(C a + B b\right)} c^{2} d + 8 \, {\left(B a + A b\right)} c d^{2}\right)} f^{3}\right)} \sqrt{-d f} \arctan\left(\frac{{\left(2 \, d f x + d e + c f\right)} \sqrt{-d f} \sqrt{d x + c} \sqrt{f x + e}}{2 \, {\left(d^{2} f^{2} x^{2} + c d e f + {\left(d^{2} e f + c d f^{2}\right)} x\right)}}\right) + 2 \, {\left(8 \, C b d^{3} f^{3} x^{2} + 15 \, C b d^{3} e^{2} f + 2 \, {\left(7 \, C b c d^{2} - 9 \, {\left(C a + B b\right)} d^{3}\right)} e f^{2} + 3 \, {\left(5 \, C b c^{2} d - 6 \, {\left(C a + B b\right)} c d^{2} + 8 \, {\left(B a + A b\right)} d^{3}\right)} f^{3} - 2 \, {\left(5 \, C b d^{3} e f^{2} + {\left(5 \, C b c d^{2} - 6 \, {\left(C a + B b\right)} d^{3}\right)} f^{3}\right)} x\right)} \sqrt{d x + c} \sqrt{f x + e}}{48 \, d^{4} f^{4}}\right]"," ",0,"[-1/96*(3*(5*C*b*d^3*e^3 + 3*(C*b*c*d^2 - 2*(C*a + B*b)*d^3)*e^2*f + (3*C*b*c^2*d - 4*(C*a + B*b)*c*d^2 + 8*(B*a + A*b)*d^3)*e*f^2 + (5*C*b*c^3 - 16*A*a*d^3 - 6*(C*a + B*b)*c^2*d + 8*(B*a + A*b)*c*d^2)*f^3)*sqrt(d*f)*log(8*d^2*f^2*x^2 + d^2*e^2 + 6*c*d*e*f + c^2*f^2 + 4*(2*d*f*x + d*e + c*f)*sqrt(d*f)*sqrt(d*x + c)*sqrt(f*x + e) + 8*(d^2*e*f + c*d*f^2)*x) - 4*(8*C*b*d^3*f^3*x^2 + 15*C*b*d^3*e^2*f + 2*(7*C*b*c*d^2 - 9*(C*a + B*b)*d^3)*e*f^2 + 3*(5*C*b*c^2*d - 6*(C*a + B*b)*c*d^2 + 8*(B*a + A*b)*d^3)*f^3 - 2*(5*C*b*d^3*e*f^2 + (5*C*b*c*d^2 - 6*(C*a + B*b)*d^3)*f^3)*x)*sqrt(d*x + c)*sqrt(f*x + e))/(d^4*f^4), 1/48*(3*(5*C*b*d^3*e^3 + 3*(C*b*c*d^2 - 2*(C*a + B*b)*d^3)*e^2*f + (3*C*b*c^2*d - 4*(C*a + B*b)*c*d^2 + 8*(B*a + A*b)*d^3)*e*f^2 + (5*C*b*c^3 - 16*A*a*d^3 - 6*(C*a + B*b)*c^2*d + 8*(B*a + A*b)*c*d^2)*f^3)*sqrt(-d*f)*arctan(1/2*(2*d*f*x + d*e + c*f)*sqrt(-d*f)*sqrt(d*x + c)*sqrt(f*x + e)/(d^2*f^2*x^2 + c*d*e*f + (d^2*e*f + c*d*f^2)*x)) + 2*(8*C*b*d^3*f^3*x^2 + 15*C*b*d^3*e^2*f + 2*(7*C*b*c*d^2 - 9*(C*a + B*b)*d^3)*e*f^2 + 3*(5*C*b*c^2*d - 6*(C*a + B*b)*c*d^2 + 8*(B*a + A*b)*d^3)*f^3 - 2*(5*C*b*d^3*e*f^2 + (5*C*b*c*d^2 - 6*(C*a + B*b)*d^3)*f^3)*x)*sqrt(d*x + c)*sqrt(f*x + e))/(d^4*f^4)]","A",0
56,1,380,0,1.569455," ","integrate((C*x^2+B*x+A)/(d*x+c)^(1/2)/(f*x+e)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(3 \, C d^{2} e^{2} + 2 \, {\left(C c d - 2 \, B d^{2}\right)} e f + {\left(3 \, C c^{2} - 4 \, B c d + 8 \, A d^{2}\right)} f^{2}\right)} \sqrt{d f} \log\left(8 \, d^{2} f^{2} x^{2} + d^{2} e^{2} + 6 \, c d e f + c^{2} f^{2} + 4 \, {\left(2 \, d f x + d e + c f\right)} \sqrt{d f} \sqrt{d x + c} \sqrt{f x + e} + 8 \, {\left(d^{2} e f + c d f^{2}\right)} x\right) + 4 \, {\left(2 \, C d^{2} f^{2} x - 3 \, C d^{2} e f - {\left(3 \, C c d - 4 \, B d^{2}\right)} f^{2}\right)} \sqrt{d x + c} \sqrt{f x + e}}{16 \, d^{3} f^{3}}, -\frac{{\left(3 \, C d^{2} e^{2} + 2 \, {\left(C c d - 2 \, B d^{2}\right)} e f + {\left(3 \, C c^{2} - 4 \, B c d + 8 \, A d^{2}\right)} f^{2}\right)} \sqrt{-d f} \arctan\left(\frac{{\left(2 \, d f x + d e + c f\right)} \sqrt{-d f} \sqrt{d x + c} \sqrt{f x + e}}{2 \, {\left(d^{2} f^{2} x^{2} + c d e f + {\left(d^{2} e f + c d f^{2}\right)} x\right)}}\right) - 2 \, {\left(2 \, C d^{2} f^{2} x - 3 \, C d^{2} e f - {\left(3 \, C c d - 4 \, B d^{2}\right)} f^{2}\right)} \sqrt{d x + c} \sqrt{f x + e}}{8 \, d^{3} f^{3}}\right]"," ",0,"[1/16*((3*C*d^2*e^2 + 2*(C*c*d - 2*B*d^2)*e*f + (3*C*c^2 - 4*B*c*d + 8*A*d^2)*f^2)*sqrt(d*f)*log(8*d^2*f^2*x^2 + d^2*e^2 + 6*c*d*e*f + c^2*f^2 + 4*(2*d*f*x + d*e + c*f)*sqrt(d*f)*sqrt(d*x + c)*sqrt(f*x + e) + 8*(d^2*e*f + c*d*f^2)*x) + 4*(2*C*d^2*f^2*x - 3*C*d^2*e*f - (3*C*c*d - 4*B*d^2)*f^2)*sqrt(d*x + c)*sqrt(f*x + e))/(d^3*f^3), -1/8*((3*C*d^2*e^2 + 2*(C*c*d - 2*B*d^2)*e*f + (3*C*c^2 - 4*B*c*d + 8*A*d^2)*f^2)*sqrt(-d*f)*arctan(1/2*(2*d*f*x + d*e + c*f)*sqrt(-d*f)*sqrt(d*x + c)*sqrt(f*x + e)/(d^2*f^2*x^2 + c*d*e*f + (d^2*e*f + c*d*f^2)*x)) - 2*(2*C*d^2*f^2*x - 3*C*d^2*e*f - (3*C*c*d - 4*B*d^2)*f^2)*sqrt(d*x + c)*sqrt(f*x + e))/(d^3*f^3)]","A",0
57,-1,0,0,0.000000," ","integrate((C*x^2+B*x+A)/(b*x+a)/(d*x+c)^(1/2)/(f*x+e)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
58,-1,0,0,0.000000," ","integrate((C*x^2+B*x+A)/(b*x+a)^2/(d*x+c)^(1/2)/(f*x+e)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
59,-1,0,0,0.000000," ","integrate((C*x^2+B*x+A)/(b*x+a)^3/(d*x+c)^(1/2)/(f*x+e)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
60,-1,0,0,0.000000," ","integrate((C*x^2+B*x+A)/(b*x+a)^4/(d*x+c)^(1/2)/(f*x+e)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
61,0,0,0,1.781971," ","integrate((b*x+a)^(1/2)*(C*x^2+B*x+A)*(d*x+c)^(1/2)*(f*x+e)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C x^{2} + B x + A\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{f x + e}, x\right)"," ",0,"integral((C*x^2 + B*x + A)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(f*x + e), x)","F",0
62,0,0,0,1.465190," ","integrate((C*x^2+B*x+A)*(d*x+c)^(1/2)*(f*x+e)^(1/2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C x^{2} + B x + A\right)} \sqrt{d x + c} \sqrt{f x + e}}{\sqrt{b x + a}}, x\right)"," ",0,"integral((C*x^2 + B*x + A)*sqrt(d*x + c)*sqrt(f*x + e)/sqrt(b*x + a), x)","F",0
63,0,0,0,1.464675," ","integrate((C*x^2+B*x+A)*(d*x+c)^(1/2)*(f*x+e)^(1/2)/(b*x+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C x^{2} + B x + A\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{f x + e}}{b^{2} x^{2} + 2 \, a b x + a^{2}}, x\right)"," ",0,"integral((C*x^2 + B*x + A)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(f*x + e)/(b^2*x^2 + 2*a*b*x + a^2), x)","F",0
64,0,0,0,1.287370," ","integrate((C*x^2+B*x+A)*(d*x+c)^(1/2)*(f*x+e)^(1/2)/(b*x+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C x^{2} + B x + A\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{f x + e}}{b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3}}, x\right)"," ",0,"integral((C*x^2 + B*x + A)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(f*x + e)/(b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x + a^3), x)","F",0
65,0,0,0,1.687430," ","integrate((C*x^2+B*x+A)*(d*x+c)^(1/2)*(f*x+e)^(1/2)/(b*x+a)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C x^{2} + B x + A\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{f x + e}}{b^{4} x^{4} + 4 \, a b^{3} x^{3} + 6 \, a^{2} b^{2} x^{2} + 4 \, a^{3} b x + a^{4}}, x\right)"," ",0,"integral((C*x^2 + B*x + A)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(f*x + e)/(b^4*x^4 + 4*a*b^3*x^3 + 6*a^2*b^2*x^2 + 4*a^3*b*x + a^4), x)","F",0
66,0,0,0,1.812303," ","integrate((C*x^2+B*x+A)*(d*x+c)^(1/2)*(f*x+e)^(1/2)/(b*x+a)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C x^{2} + B x + A\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{f x + e}}{b^{5} x^{5} + 5 \, a b^{4} x^{4} + 10 \, a^{2} b^{3} x^{3} + 10 \, a^{3} b^{2} x^{2} + 5 \, a^{4} b x + a^{5}}, x\right)"," ",0,"integral((C*x^2 + B*x + A)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(f*x + e)/(b^5*x^5 + 5*a*b^4*x^4 + 10*a^2*b^3*x^3 + 10*a^3*b^2*x^2 + 5*a^4*b*x + a^5), x)","F",0
67,0,0,0,1.221172," ","integrate((b*x+a)^(3/2)*(C*x^2+B*x+A)*(d*x+c)^(1/2)/(f*x+e)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b x^{3} + {\left(C a + B b\right)} x^{2} + A a + {\left(B a + A b\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{\sqrt{f x + e}}, x\right)"," ",0,"integral((C*b*x^3 + (C*a + B*b)*x^2 + A*a + (B*a + A*b)*x)*sqrt(b*x + a)*sqrt(d*x + c)/sqrt(f*x + e), x)","F",0
68,0,0,0,1.702697," ","integrate((b*x+a)^(1/2)*(C*x^2+B*x+A)*(d*x+c)^(1/2)/(f*x+e)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C x^{2} + B x + A\right)} \sqrt{b x + a} \sqrt{d x + c}}{\sqrt{f x + e}}, x\right)"," ",0,"integral((C*x^2 + B*x + A)*sqrt(b*x + a)*sqrt(d*x + c)/sqrt(f*x + e), x)","F",0
69,0,0,0,1.202089," ","integrate((C*x^2+B*x+A)*(d*x+c)^(1/2)/(b*x+a)^(1/2)/(f*x+e)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C x^{2} + B x + A\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{f x + e}}{b f x^{2} + a e + {\left(b e + a f\right)} x}, x\right)"," ",0,"integral((C*x^2 + B*x + A)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(f*x + e)/(b*f*x^2 + a*e + (b*e + a*f)*x), x)","F",0
70,0,0,0,1.240127," ","integrate((C*x^2+B*x+A)*(d*x+c)^(1/2)/(b*x+a)^(3/2)/(f*x+e)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C x^{2} + B x + A\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{f x + e}}{b^{2} f x^{3} + a^{2} e + {\left(b^{2} e + 2 \, a b f\right)} x^{2} + {\left(2 \, a b e + a^{2} f\right)} x}, x\right)"," ",0,"integral((C*x^2 + B*x + A)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(f*x + e)/(b^2*f*x^3 + a^2*e + (b^2*e + 2*a*b*f)*x^2 + (2*a*b*e + a^2*f)*x), x)","F",0
71,0,0,0,1.256633," ","integrate((C*x^2+B*x+A)*(d*x+c)^(1/2)/(b*x+a)^(5/2)/(f*x+e)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C x^{2} + B x + A\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{f x + e}}{b^{3} f x^{4} + a^{3} e + {\left(b^{3} e + 3 \, a b^{2} f\right)} x^{3} + 3 \, {\left(a b^{2} e + a^{2} b f\right)} x^{2} + {\left(3 \, a^{2} b e + a^{3} f\right)} x}, x\right)"," ",0,"integral((C*x^2 + B*x + A)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(f*x + e)/(b^3*f*x^4 + a^3*e + (b^3*e + 3*a*b^2*f)*x^3 + 3*(a*b^2*e + a^2*b*f)*x^2 + (3*a^2*b*e + a^3*f)*x), x)","F",0
72,0,0,0,1.073958," ","integrate((C*x^2+B*x+A)*(d*x+c)^(1/2)/(b*x+a)^(7/2)/(f*x+e)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C x^{2} + B x + A\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{f x + e}}{b^{4} f x^{5} + a^{4} e + {\left(b^{4} e + 4 \, a b^{3} f\right)} x^{4} + 2 \, {\left(2 \, a b^{3} e + 3 \, a^{2} b^{2} f\right)} x^{3} + 2 \, {\left(3 \, a^{2} b^{2} e + 2 \, a^{3} b f\right)} x^{2} + {\left(4 \, a^{3} b e + a^{4} f\right)} x}, x\right)"," ",0,"integral((C*x^2 + B*x + A)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(f*x + e)/(b^4*f*x^5 + a^4*e + (b^4*e + 4*a*b^3*f)*x^4 + 2*(2*a*b^3*e + 3*a^2*b^2*f)*x^3 + 2*(3*a^2*b^2*e + 2*a^3*b*f)*x^2 + (4*a^3*b*e + a^4*f)*x), x)","F",0
73,0,0,0,1.142087," ","integrate((b*x+a)^(3/2)*(C*x^2+B*x+A)/(d*x+c)^(1/2)/(f*x+e)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b x^{3} + {\left(C a + B b\right)} x^{2} + A a + {\left(B a + A b\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{f x + e}}{d f x^{2} + c e + {\left(d e + c f\right)} x}, x\right)"," ",0,"integral((C*b*x^3 + (C*a + B*b)*x^2 + A*a + (B*a + A*b)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(f*x + e)/(d*f*x^2 + c*e + (d*e + c*f)*x), x)","F",0
74,0,0,0,0.855590," ","integrate((b*x+a)^(1/2)*(C*x^2+B*x+A)/(d*x+c)^(1/2)/(f*x+e)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C x^{2} + B x + A\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{f x + e}}{d f x^{2} + c e + {\left(d e + c f\right)} x}, x\right)"," ",0,"integral((C*x^2 + B*x + A)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(f*x + e)/(d*f*x^2 + c*e + (d*e + c*f)*x), x)","F",0
75,0,0,0,0.893869," ","integrate((C*x^2+B*x+A)/(b*x+a)^(1/2)/(d*x+c)^(1/2)/(f*x+e)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C x^{2} + B x + A\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{f x + e}}{b d f x^{3} + a c e + {\left(b d e + {\left(b c + a d\right)} f\right)} x^{2} + {\left(a c f + {\left(b c + a d\right)} e\right)} x}, x\right)"," ",0,"integral((C*x^2 + B*x + A)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(f*x + e)/(b*d*f*x^3 + a*c*e + (b*d*e + (b*c + a*d)*f)*x^2 + (a*c*f + (b*c + a*d)*e)*x), x)","F",0
76,0,0,0,1.127408," ","integrate((C*x^2+B*x+A)/(b*x+a)^(3/2)/(d*x+c)^(1/2)/(f*x+e)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C x^{2} + B x + A\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{f x + e}}{b^{2} d f x^{4} + a^{2} c e + {\left(b^{2} d e + {\left(b^{2} c + 2 \, a b d\right)} f\right)} x^{3} + {\left({\left(b^{2} c + 2 \, a b d\right)} e + {\left(2 \, a b c + a^{2} d\right)} f\right)} x^{2} + {\left(a^{2} c f + {\left(2 \, a b c + a^{2} d\right)} e\right)} x}, x\right)"," ",0,"integral((C*x^2 + B*x + A)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(f*x + e)/(b^2*d*f*x^4 + a^2*c*e + (b^2*d*e + (b^2*c + 2*a*b*d)*f)*x^3 + ((b^2*c + 2*a*b*d)*e + (2*a*b*c + a^2*d)*f)*x^2 + (a^2*c*f + (2*a*b*c + a^2*d)*e)*x), x)","F",0
77,0,0,0,1.414744," ","integrate((C*x^2+B*x+A)/(b*x+a)^(5/2)/(d*x+c)^(1/2)/(f*x+e)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C x^{2} + B x + A\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{f x + e}}{b^{3} d f x^{5} + a^{3} c e + {\left(b^{3} d e + {\left(b^{3} c + 3 \, a b^{2} d\right)} f\right)} x^{4} + {\left({\left(b^{3} c + 3 \, a b^{2} d\right)} e + 3 \, {\left(a b^{2} c + a^{2} b d\right)} f\right)} x^{3} + {\left(3 \, {\left(a b^{2} c + a^{2} b d\right)} e + {\left(3 \, a^{2} b c + a^{3} d\right)} f\right)} x^{2} + {\left(a^{3} c f + {\left(3 \, a^{2} b c + a^{3} d\right)} e\right)} x}, x\right)"," ",0,"integral((C*x^2 + B*x + A)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(f*x + e)/(b^3*d*f*x^5 + a^3*c*e + (b^3*d*e + (b^3*c + 3*a*b^2*d)*f)*x^4 + ((b^3*c + 3*a*b^2*d)*e + 3*(a*b^2*c + a^2*b*d)*f)*x^3 + (3*(a*b^2*c + a^2*b*d)*e + (3*a^2*b*c + a^3*d)*f)*x^2 + (a^3*c*f + (3*a^2*b*c + a^3*d)*e)*x), x)","F",0
78,0,0,0,1.123128," ","integrate((C*x^2+B*x+A)/(b*x+a)^(7/2)/(d*x+c)^(1/2)/(f*x+e)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C x^{2} + B x + A\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{f x + e}}{b^{4} d f x^{6} + a^{4} c e + {\left(b^{4} d e + {\left(b^{4} c + 4 \, a b^{3} d\right)} f\right)} x^{5} + {\left({\left(b^{4} c + 4 \, a b^{3} d\right)} e + 2 \, {\left(2 \, a b^{3} c + 3 \, a^{2} b^{2} d\right)} f\right)} x^{4} + 2 \, {\left({\left(2 \, a b^{3} c + 3 \, a^{2} b^{2} d\right)} e + {\left(3 \, a^{2} b^{2} c + 2 \, a^{3} b d\right)} f\right)} x^{3} + {\left(2 \, {\left(3 \, a^{2} b^{2} c + 2 \, a^{3} b d\right)} e + {\left(4 \, a^{3} b c + a^{4} d\right)} f\right)} x^{2} + {\left(a^{4} c f + {\left(4 \, a^{3} b c + a^{4} d\right)} e\right)} x}, x\right)"," ",0,"integral((C*x^2 + B*x + A)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(f*x + e)/(b^4*d*f*x^6 + a^4*c*e + (b^4*d*e + (b^4*c + 4*a*b^3*d)*f)*x^5 + ((b^4*c + 4*a*b^3*d)*e + 2*(2*a*b^3*c + 3*a^2*b^2*d)*f)*x^4 + 2*((2*a*b^3*c + 3*a^2*b^2*d)*e + (3*a^2*b^2*c + 2*a^3*b*d)*f)*x^3 + (2*(3*a^2*b^2*c + 2*a^3*b*d)*e + (4*a^3*b*c + a^4*d)*f)*x^2 + (a^4*c*f + (4*a^3*b*c + a^4*d)*e)*x), x)","F",0
