1,1,197,0,0.224183," ","integrate((e*x+d)^2*(C*x^2+B*x+A)*(-e^2*x^2+d^2)^(1/2),x, algorithm=""giac"")","\frac{1}{16} \, {\left(3 \, C d^{6} + 4 \, B d^{5} e + 10 \, A d^{4} e^{2}\right)} \arcsin\left(\frac{x e}{d}\right) e^{\left(-3\right)} \mathrm{sgn}\left(d\right) + \frac{1}{240} \, \sqrt{-x^{2} e^{2} + d^{2}} {\left({\left(2 \, {\left({\left(4 \, {\left(5 \, C x e^{2} + 6 \, {\left(2 \, C d e^{9} + B e^{10}\right)} e^{\left(-8\right)}\right)} x + 5 \, {\left(5 \, C d^{2} e^{8} + 12 \, B d e^{9} + 6 \, A e^{10}\right)} e^{\left(-8\right)}\right)} x - 16 \, {\left(C d^{3} e^{7} - 2 \, B d^{2} e^{8} - 5 \, A d e^{9}\right)} e^{\left(-8\right)}\right)} x - 15 \, {\left(3 \, C d^{4} e^{6} + 4 \, B d^{3} e^{7} - 6 \, A d^{2} e^{8}\right)} e^{\left(-8\right)}\right)} x - 16 \, {\left(4 \, C d^{5} e^{5} + 7 \, B d^{4} e^{6} + 10 \, A d^{3} e^{7}\right)} e^{\left(-8\right)}\right)}"," ",0,"1/16*(3*C*d^6 + 4*B*d^5*e + 10*A*d^4*e^2)*arcsin(x*e/d)*e^(-3)*sgn(d) + 1/240*sqrt(-x^2*e^2 + d^2)*((2*((4*(5*C*x*e^2 + 6*(2*C*d*e^9 + B*e^10)*e^(-8))*x + 5*(5*C*d^2*e^8 + 12*B*d*e^9 + 6*A*e^10)*e^(-8))*x - 16*(C*d^3*e^7 - 2*B*d^2*e^8 - 5*A*d*e^9)*e^(-8))*x - 15*(3*C*d^4*e^6 + 4*B*d^3*e^7 - 6*A*d^2*e^8)*e^(-8))*x - 16*(4*C*d^5*e^5 + 7*B*d^4*e^6 + 10*A*d^3*e^7)*e^(-8))","A",0
2,1,160,0,0.212955," ","integrate((e*x+d)*(C*x^2+B*x+A)*(-e^2*x^2+d^2)^(1/2),x, algorithm=""giac"")","\frac{1}{8} \, {\left(C d^{5} + B d^{4} e + 4 \, A d^{3} e^{2}\right)} \arcsin\left(\frac{x e}{d}\right) e^{\left(-3\right)} \mathrm{sgn}\left(d\right) + \frac{1}{120} \, \sqrt{-x^{2} e^{2} + d^{2}} {\left({\left(2 \, {\left(3 \, {\left(4 \, C x e + 5 \, {\left(C d e^{6} + B e^{7}\right)} e^{\left(-6\right)}\right)} x - 4 \, {\left(C d^{2} e^{5} - 5 \, B d e^{6} - 5 \, A e^{7}\right)} e^{\left(-6\right)}\right)} x - 15 \, {\left(C d^{3} e^{4} + B d^{2} e^{5} - 4 \, A d e^{6}\right)} e^{\left(-6\right)}\right)} x - 8 \, {\left(2 \, C d^{4} e^{3} + 5 \, B d^{3} e^{4} + 5 \, A d^{2} e^{5}\right)} e^{\left(-6\right)}\right)}"," ",0,"1/8*(C*d^5 + B*d^4*e + 4*A*d^3*e^2)*arcsin(x*e/d)*e^(-3)*sgn(d) + 1/120*sqrt(-x^2*e^2 + d^2)*((2*(3*(4*C*x*e + 5*(C*d*e^6 + B*e^7)*e^(-6))*x - 4*(C*d^2*e^5 - 5*B*d*e^6 - 5*A*e^7)*e^(-6))*x - 15*(C*d^3*e^4 + B*d^2*e^5 - 4*A*d*e^6)*e^(-6))*x - 8*(2*C*d^4*e^3 + 5*B*d^3*e^4 + 5*A*d^2*e^5)*e^(-6))","A",0
3,1,85,0,0.201856," ","integrate((C*x^2+B*x+A)*(-e^2*x^2+d^2)^(1/2),x, algorithm=""giac"")","\frac{1}{8} \, {\left(C d^{4} + 4 \, A d^{2} e^{2}\right)} \arcsin\left(\frac{x e}{d}\right) e^{\left(-3\right)} \mathrm{sgn}\left(d\right) - \frac{1}{24} \, {\left(8 \, B d^{2} e^{\left(-2\right)} - {\left(2 \, {\left(3 \, C x + 4 \, B\right)} x - 3 \, {\left(C d^{2} e^{2} - 4 \, A e^{4}\right)} e^{\left(-4\right)}\right)} x\right)} \sqrt{-x^{2} e^{2} + d^{2}}"," ",0,"1/8*(C*d^4 + 4*A*d^2*e^2)*arcsin(x*e/d)*e^(-3)*sgn(d) - 1/24*(8*B*d^2*e^(-2) - (2*(3*C*x + 4*B)*x - 3*(C*d^2*e^2 - 4*A*e^4)*e^(-4))*x)*sqrt(-x^2*e^2 + d^2)","A",0
4,-2,0,0,0.000000," ","integrate((C*x^2+B*x+A)*(-e^2*x^2+d^2)^(1/2)/(e*x+d),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 1/2*(4*A*d*exp(2)^3-4*A*d*exp(1)^4*exp(2)+4*B*d^2*exp(1)^3*exp(2)-4*B*d^2*exp(1)*exp(2)^2)*atan((-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x+exp(2))/sqrt(-exp(1)^4+exp(2)^2))/sqrt(-exp(1)^4+exp(2)^2)/exp(1)^4/exp(1)-1/4*(-2*C*d^3-4*A*d*exp(2)+2*B*d^2*exp(1))*sign(d)*asin(x*exp(2)/d/exp(1))/exp(1)/exp(2)+2*((16*exp(1)^4*C*1/96/exp(1)^5*x-(-24*exp(1)^4*B+24*exp(1)^3*C*d)*1/96/exp(1)^5)*x-(-48*exp(1)^4*A+48*exp(1)^3*d*B-32*exp(1)^2*C*d^2)*1/96/exp(1)^5)*sqrt(d^2-x^2*exp(2))","F(-2)",0
5,0,0,0,0.000000," ","integrate((C*x^2+B*x+A)*(-e^2*x^2+d^2)^(1/2)/(e*x+d)^2,x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
6,-2,0,0,0.000000," ","integrate((C*x^2+B*x+A)*(-e^2*x^2+d^2)^(1/2)/(e*x+d)^3,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: (-8*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^8*exp(2)^2-2*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^10*exp(2)-2*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^8*exp(2)^2-4*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^6*exp(2)^3-A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^6*exp(2)^3+A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^4*exp(2)^4-4*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^4*exp(2)^4-A*exp(1)^6*exp(2)^3-B*d*exp(1)^5*exp(2)^3-4*A*exp(1)^4*exp(2)^4+4*B*d*exp(1)^3*exp(2)^4-8*C*d^2*exp(2)^5+2*B*d*exp(1)*exp(2)^5+2*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^6*exp(2)^2+8*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^7*exp(2)^2+4*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^5*exp(2)^3-8*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^6*exp(2)^2-4*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^4*exp(2)^3+3*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^5*exp(2)^3+B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^3*exp(2)^4-5*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^4*exp(2)^3-3*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(2)^5+4*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^3*exp(2)^4+3*C*d^2*exp(1)^4*exp(2)^3-8*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(2)^5+1/2*A*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^4*exp(2)^4/x/exp(2)+6*A*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^6*exp(2)^3/x/exp(2)+A*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^8*exp(2)^2/x/exp(2)-2*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^9*exp(2)+2*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)*exp(2)^5+6*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^8*exp(2)+13/2*C*d^2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(2)^5/x/exp(2)-7/2*B*d*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^3*exp(2)^4/x/exp(2)-6*B*d*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^5*exp(2)^3/x/exp(2)+2*B*d*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^7*exp(2)^2/x/exp(2)+6*C*d^2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^4*exp(2)^3/x/exp(2)-5*C*d^2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^6*exp(2)^2/x/exp(2))/((-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(2)-(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x+exp(2))^2/(-d*exp(1)^9+d*exp(1)^5*exp(2)^2-d*exp(1)^7*exp(2)+d*exp(1)*exp(2)^4)+1/2*(4*A*exp(1)^8*exp(2)^2-12*B*d*exp(1)^7*exp(2)^2+20*C*d^2*exp(1)^6*exp(2)^2+2*A*exp(1)^6*exp(2)^3-6*B*d*exp(1)^5*exp(2)^3+18*C*d^2*exp(1)^4*exp(2)^3+4*A*exp(1)^4*exp(2)^4+4*B*d*exp(1)^3*exp(2)^4-24*C*d^2*exp(2)^5+4*B*d*exp(1)*exp(2)^5-4*C*d^2*exp(1)^8*exp(2))*atan((-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x+exp(2))/sqrt(-exp(1)^4+exp(2)^2))/sqrt(-exp(1)^4+exp(2)^2)/(d*exp(1)^11-d*exp(1)^7*exp(2)^2-d*exp(1)^5*exp(2)^3+d*exp(1)^9*exp(2))-1/4*(4*B*exp(1)-12*C*d)*sign(d)*asin(x*exp(2)/d/exp(1))/exp(1)/exp(2)+4*exp(1)^2*C*1/4/exp(1)^5*sqrt(d^2-x^2*exp(2))","F(-2)",0
7,-2,0,0,0.000000," ","integrate((C*x^2+B*x+A)*(-e^2*x^2+d^2)^(1/2)/(e*x+d)^4,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: (8*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^16*exp(2)+12*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^14*exp(2)^2+6*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^12*exp(2)^3+3/2*A*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^4*exp(2)^7/x/exp(2)+42*A*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^6*exp(2)^6/x/exp(2)+9*A*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^8*exp(2)^5/x/exp(2)+3*A*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^10*exp(2)^4/x/exp(2)-3*A*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^12*exp(2)^3/x/exp(2)+6*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^13*exp(2)^2+12*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^12*exp(2)^3+6*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^10*exp(2)^4+48*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^13*exp(2)^2+36*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^11*exp(2)^3+6*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^9*exp(2)^4-96*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^12*exp(2)^2-84*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^10*exp(2)^3-18*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^8*exp(2)^4+12*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^14*exp(2)^2-8*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^12*exp(2)^3-24*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^10*exp(2)^4-12*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^8*exp(2)^5+6*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^13*exp(2)^2+14*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^11*exp(2)^3+3*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^9*exp(2)^4+3*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^7*exp(2)^5+24*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^12*exp(2)^2-32*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^10*exp(2)^3-24*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^8*exp(2)^4-6*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^6*exp(2)^5-12*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^12*exp(2)^3-72*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^10*exp(2)^4-84*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^8*exp(2)^5-24*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^6*exp(2)^6+108*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^11*exp(2)^3+96*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^9*exp(2)^4+48*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^7*exp(2)^5+12*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^5*exp(2)^6-204*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^10*exp(2)^3-120*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^8*exp(2)^4-12*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^6*exp(2)^5-30*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^10*exp(2)^4-30*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^8*exp(2)^5-3*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^6*exp(2)^6+3*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^4*exp(2)^7+24*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^9*exp(2)^4+12*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^7*exp(2)^5+6*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^5*exp(2)^6-102*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^8*exp(2)^4-42*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^6*exp(2)^5+3*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^4*exp(2)^6-132*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^8*exp(2)^5-108*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^6*exp(2)^6-18*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^4*exp(2)^7+3*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(2)^8+60*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^7*exp(2)^5+36*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^5*exp(2)^6+6*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^3*exp(2)^7+12*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^6*exp(2)^5+36*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^4*exp(2)^6+2*A*exp(1)^10*exp(2)^4-12*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^6*exp(2)^6+B*d*exp(1)^9*exp(2)^4+2*C*d^2*exp(1)^8*exp(2)^4+12*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(2)^8+36*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^4*exp(2)^6-36*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^4*exp(2)^7+12*B*d*exp(1)^7*exp(2)^5-24*C*d^2*exp(1)^6*exp(2)^5+36*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(2)^8+12*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^3*exp(2)^7-5*A*exp(1)^6*exp(2)^6+2*B*d*exp(1)^5*exp(2)^6-11*C*d^2*exp(1)^4*exp(2)^6+24*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(2)^8-18*A*exp(1)^4*exp(2)^7+6*B*d*exp(1)^3*exp(2)^7+12*C*d^2*exp(2)^8+4*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^15*exp(2)+8*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^14*exp(2)-33/2*C*d^2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(2)^8/x/exp(2)-12*B*d*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^5*exp(2)^6/x/exp(2)-9/2*B*d*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^7*exp(2)^5/x/exp(2)-33*B*d*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^9*exp(2)^4/x/exp(2)-3*B*d*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^11*exp(2)^3/x/exp(2)-18*C*d^2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^4*exp(2)^6/x/exp(2)+30*C*d^2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^6*exp(2)^5/x/exp(2)+63*C*d^2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^8*exp(2)^4/x/exp(2)-6*C*d^2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^10*exp(2)^3/x/exp(2))/((-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(2)-(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x+exp(2))^3/(3*d^2*exp(1)^13-6*d^2*exp(1)^9*exp(2)^2-6*d^2*exp(1)^7*exp(2)^3+3*d^2*exp(1)^5*exp(2)^4+3*d^2*exp(1)^11*exp(2)+3*d^2*exp(1)*exp(2)^6)+1/2*(-4*B*d*exp(1)^11*exp(2)^2+16*C*d^2*exp(1)^10*exp(2)^2-2*B*d*exp(1)^9*exp(2)^3+8*C*d^2*exp(1)^8*exp(2)^3+8*A*exp(1)^8*exp(2)^4-8*B*d*exp(1)^7*exp(2)^4-8*C*d^2*exp(1)^6*exp(2)^4+2*A*exp(1)^6*exp(2)^5-10*C*d^2*exp(1)^4*exp(2)^5+4*A*exp(1)^4*exp(2)^6+8*C*d^2*exp(2)^7)*atan((-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x+exp(2))/sqrt(-exp(1)^4+exp(2)^2))/sqrt(-exp(1)^4+exp(2)^2)/(-d^2*exp(1)^15+2*d^2*exp(1)^11*exp(2)^2+2*d^2*exp(1)^9*exp(2)^3-d^2*exp(1)^7*exp(2)^4-d^2*exp(1)^5*exp(2)^5-d^2*exp(1)^13*exp(2))-C*sign(d)*asin(x*exp(2)/d/exp(1))/exp(1)/exp(2)","F(-2)",0
8,-2,0,0,0.000000," ","integrate((C*x^2+B*x+A)*(-e^2*x^2+d^2)^(1/2)/(e*x+d)^5,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Warning, choosing root of [1,0,%%%{2,[2,0]%%%},0,%%%{1,[4,0]%%%}+%%%{-4,[2,1]%%%}+%%%{4,[0,2]%%%}] at parameters values [86,-97]Limit: Max order reached or unable to make series expansion Error: Bad Argument Value","F(-2)",0
9,-2,0,0,0.000000," ","integrate((C*x^2+B*x+A)*(-e^2*x^2+d^2)^(1/2)/(e*x+d)^6,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: (-960*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^24*exp(2)^2-320*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^24*exp(2)^2-384*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^26*exp(2)-960*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^22*exp(2)^3-480*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^20*exp(2)^4-120*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^18*exp(2)^5-800*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^22*exp(2)^3-800*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^20*exp(2)^4-480*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^18*exp(2)^5-120*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^16*exp(2)^6-960*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^24*exp(2)^2-352*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^22*exp(2)^3+2480*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^20*exp(2)^4+3440*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^18*exp(2)^5+1920*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^16*exp(2)^6+480*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^14*exp(2)^7-800*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^22*exp(2)^3-160*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^20*exp(2)^4+1680*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^18*exp(2)^5+2640*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^16*exp(2)^6+1920*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^14*exp(2)^7+480*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^12*exp(2)^8-960*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^22*exp(2)^3+2480*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^20*exp(2)^4+4736*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^18*exp(2)^5-320*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^16*exp(2)^6-4160*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^14*exp(2)^7-2880*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^12*exp(2)^8-720*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^10*exp(2)^9-800*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^20*exp(2)^4+3120*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^18*exp(2)^5+12680*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^16*exp(2)^6+15140*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^14*exp(2)^7+5900*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^12*exp(2)^8-450*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^10*exp(2)^9-450*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^8*exp(2)^10-480*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^20*exp(2)^4+3440*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^18*exp(2)^5-80*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^16*exp(2)^6-6100*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^14*exp(2)^7-2010*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^12*exp(2)^8+2850*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^10*exp(2)^9+2325*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^8*exp(2)^10+525*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^6*exp(2)^11-320*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^18*exp(2)^5+3760*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^16*exp(2)^6+25860*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^14*exp(2)^7+42700*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^12*exp(2)^8+36780*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^10*exp(2)^9+21780*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^8*exp(2)^10+7860*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^6*exp(2)^11+1140*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^4*exp(2)^12+1880*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^16*exp(2)^6-3840*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^14*exp(2)^7-490*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^12*exp(2)^8+9930*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^10*exp(2)^9+9030*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^8*exp(2)^10+2730*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^6*exp(2)^11+60*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^4*exp(2)^12-60*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(2)^14+1580*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^14*exp(2)^7+28100*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^12*exp(2)^8+57720*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^10*exp(2)^9+59400*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^8*exp(2)^10+33000*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^6*exp(2)^11+8280*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^4*exp(2)^12-24*A*exp(1)^16*exp(2)^6+600*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(2)^14-2590*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^12*exp(2)^8+5590*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^10*exp(2)^9+11080*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^8*exp(2)^10+5400*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^6*exp(2)^11+600*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^4*exp(2)^12-6*B*d*exp(1)^15*exp(2)^6-20*A*exp(1)^14*exp(2)^7-120*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(2)^14+16100*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^10*exp(2)^9+41420*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^8*exp(2)^10+42800*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^6*exp(2)^11+18000*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^4*exp(2)^12+98*A*exp(1)^12*exp(2)^8+2400*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(2)^14+4130*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^8*exp(2)^10+4470*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^6*exp(2)^11+1200*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^4*exp(2)^12+27*B*d*exp(1)^11*exp(2)^8+90*A*exp(1)^10*exp(2)^9+18040*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^6*exp(2)^11+15720*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^4*exp(2)^12-170*B*d*exp(1)^9*exp(2)^9-149*A*exp(1)^8*exp(2)^10+3600*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(2)^14+840*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^4*exp(2)^12-86*B*d*exp(1)^7*exp(2)^10+380*A*exp(1)^6*exp(2)^11+120*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(2)^14-30*A*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(2)^14/x/exp(2)-760*B*d*exp(1)^5*exp(2)^11+180*A*exp(1)^4*exp(2)^12+2400*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(2)^14-40*B*d*exp(1)^3*exp(2)^12+600*A*exp(2)^14-120*B*d*exp(1)*exp(2)^13-2430*A*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^4*exp(2)^12/x/exp(2)-1275/2*A*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^6*exp(2)^11/x/exp(2)-2125*A*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^8*exp(2)^10/x/exp(2)+385*A*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^10*exp(2)^9/x/exp(2)-210*A*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^12*exp(2)^8/x/exp(2)-250*A*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^14*exp(2)^7/x/exp(2)+40*A*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^16*exp(2)^6/x/exp(2)+60*A*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^18*exp(2)^5/x/exp(2)-480*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)*exp(2)^13-240*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^23*exp(2)^2-240*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^21*exp(2)^3-120*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^19*exp(2)^4-160*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^22*exp(2)^2-160*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^20*exp(2)^3-240*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^19*exp(2)^4-120*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^17*exp(2)^5+320*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^22*exp(2)^2-160*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^20*exp(2)^3-160*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^18*exp(2)^4-240*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^23*exp(2)^2-48*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^21*exp(2)^3+720*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^19*exp(2)^4+960*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^17*exp(2)^5+480*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^15*exp(2)^6-160*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^22*exp(2)^2+128*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^20*exp(2)^3+640*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^18*exp(2)^4+640*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^16*exp(2)^5-2720*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^19*exp(2)^4-3560*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^17*exp(2)^5-920*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^15*exp(2)^6-60*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^13*exp(2)^7-60*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^11*exp(2)^8+1760*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^20*exp(2)^3+11360*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^18*exp(2)^4+19120*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^16*exp(2)^5+11920*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^14*exp(2)^6+3240*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^12*exp(2)^7+360*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^10*exp(2)^8-240*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^21*exp(2)^3+720*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^19*exp(2)^4+604*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^17*exp(2)^5-1250*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^15*exp(2)^6-1910*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^13*exp(2)^7-855*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^11*exp(2)^8-15*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^9*exp(2)^9-160*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^20*exp(2)^3+1120*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^18*exp(2)^4+3416*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^16*exp(2)^5+3660*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^14*exp(2)^6+1860*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^12*exp(2)^7+810*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^10*exp(2)^8+90*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^8*exp(2)^9+240*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^19*exp(2)^4-10040*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^17*exp(2)^5-25760*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^15*exp(2)^6-32380*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^13*exp(2)^7-21460*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^11*exp(2)^8-6390*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^9*exp(2)^9-630*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^7*exp(2)^10+1760*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^18*exp(2)^4+32080*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^16*exp(2)^5+56120*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^14*exp(2)^6+43140*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^12*exp(2)^7+20460*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^10*exp(2)^8+5670*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^8*exp(2)^9+630*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^6*exp(2)^10-120*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^19*exp(2)^4+960*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^17*exp(2)^5-2450*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^15*exp(2)^6-720*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)*exp(2)^13-6710*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^13*exp(2)^7-96*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^25*exp(2)-5590*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^11*exp(2)^8-1930*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^9*exp(2)^9-330*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^7*exp(2)^10-90*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^5*exp(2)^11-160*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^18*exp(2)^4+1440*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^16*exp(2)^5+6140*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^14*exp(2)^6+7320*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^12*exp(2)^7+4350*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^10*exp(2)^8+1530*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^8*exp(2)^9+135*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^6*exp(2)^10+15*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^4*exp(2)^11+120*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^17*exp(2)^5-12680*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^15*exp(2)^6-48820*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^13*exp(2)^7-67820*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^11*exp(2)^8-41940*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^9*exp(2)^9-13260*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^7*exp(2)^10-2760*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^5*exp(2)^11-360*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^3*exp(2)^12+800*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^16*exp(2)^5+37680*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^14*exp(2)^6+63860*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^12*exp(2)^7+51900*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^10*exp(2)^8+24300*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^8*exp(2)^9+5460*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^6*exp(2)^10+540*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^4*exp(2)^11+60*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(2)^13+570*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^15*exp(2)^6-3890*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^13*exp(2)^7-7660*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^11*exp(2)^8-5780*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^9*exp(2)^9-2220*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^7*exp(2)^10-480*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)*exp(2)^13-660*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^5*exp(2)^11-120*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^3*exp(2)^12-6740*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^13*exp(2)^7-46140*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^11*exp(2)^8-60560*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^9*exp(2)^9-32400*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^7*exp(2)^10-9840*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^5*exp(2)^11-1920*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^3*exp(2)^12-4*C*d^2*exp(1)^14*exp(2)^6+120*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(2)^13-2450*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^11*exp(2)^8-4710*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^9*exp(2)^9-3440*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^7*exp(2)^10-1200*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^5*exp(2)^11-240*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^3*exp(2)^12+20*C*d^2*exp(1)^12*exp(2)^7-24860*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^9*exp(2)^9-26740*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^7*exp(2)^10-12160*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^5*exp(2)^11-3600*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^3*exp(2)^12+28*C*d^2*exp(1)^10*exp(2)^8-1700*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^7*exp(2)^10-940*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^5*exp(2)^11-160*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^3*exp(2)^12+610*C*d^2*exp(1)^8*exp(2)^9-5840*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^5*exp(2)^11-2880*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^3*exp(2)^12+81*C*d^2*exp(1)^6*exp(2)^10-120*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(2)^13-80*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^3*exp(2)^12+420*C*d^2*exp(1)^4*exp(2)^11-120*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)*exp(2)^13+1100*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^14*exp(2)^6+5740*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^12*exp(2)^7+5650*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^10*exp(2)^8+2430*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^8*exp(2)^9+330*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^6*exp(2)^10-90*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^4*exp(2)^11+21260*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^12*exp(2)^7+37540*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^10*exp(2)^8+32200*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^8*exp(2)^9+12600*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^6*exp(2)^10+1800*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^4*exp(2)^11+2570*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^10*exp(2)^8+1710*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^8*exp(2)^9+480*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^6*exp(2)^10+14180*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^8*exp(2)^9+11340*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^6*exp(2)^10+2400*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^4*exp(2)^11+270*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^6*exp(2)^10+90*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^4*exp(2)^11+1560*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^4*exp(2)^11-64*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^24*exp(2)+30*C*d^2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(2)^13/x/exp(2)+420*B*d*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^3*exp(2)^12/x/exp(2)+155*B*d*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^5*exp(2)^11/x/exp(2)+3485*B*d*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^7*exp(2)^10/x/exp(2)+845/2*B*d*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^9*exp(2)^9/x/exp(2)+820*B*d*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^11*exp(2)^8/x/exp(2)-135*B*d*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^13*exp(2)^7/x/exp(2)+30*B*d*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^17*exp(2)^5/x/exp(2)+15/2*C*d^2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^4*exp(2)^11/x/exp(2)-1785*C*d^2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^6*exp(2)^10/x/exp(2)-360*C*d^2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^8*exp(2)^9/x/exp(2)-2870*C*d^2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^10*exp(2)^8/x/exp(2)-140*C*d^2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^12*exp(2)^7/x/exp(2)-100*C*d^2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^14*exp(2)^6/x/exp(2)+20*C*d^2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^16*exp(2)^5/x/exp(2))/((-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(2)-(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x+exp(2))^5/(-60*d^4*exp(1)^19+240*d^4*exp(1)^15*exp(2)^2+240*d^4*exp(1)^13*exp(2)^3-360*d^4*exp(1)^11*exp(2)^4-360*d^4*exp(1)^9*exp(2)^5+240*d^4*exp(1)^7*exp(2)^6+240*d^4*exp(1)^5*exp(2)^7-60*d^4*exp(1)^17*exp(2)-120*d^4*exp(1)*exp(2)^9)+1/2*(-4*B*d*exp(1)^11*exp(2)^4+24*C*d^2*exp(1)^10*exp(2)^4-B*d*exp(1)^9*exp(2)^5+6*C*d^2*exp(1)^8*exp(2)^5+18*A*exp(1)^8*exp(2)^6-42*B*d*exp(1)^7*exp(2)^6+42*C*d^2*exp(1)^6*exp(2)^6+3*A*exp(1)^6*exp(2)^7-6*B*d*exp(1)^5*exp(2)^7+C*d^2*exp(1)^4*exp(2)^7+44*A*exp(1)^4*exp(2)^8-24*B*d*exp(1)^3*exp(2)^8+4*C*d^2*exp(2)^9+12*A*exp(2)^10)*atan((-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x+exp(2))/sqrt(-exp(1)^4+exp(2)^2))/sqrt(-exp(1)^4+exp(2)^2)/(-2*d^4*exp(1)^19+8*d^4*exp(1)^15*exp(2)^2+8*d^4*exp(1)^13*exp(2)^3-12*d^4*exp(1)^11*exp(2)^4-12*d^4*exp(1)^9*exp(2)^5+8*d^4*exp(1)^7*exp(2)^6+8*d^4*exp(1)^5*exp(2)^7-2*d^4*exp(1)^17*exp(2)-4*d^4*exp(1)*exp(2)^9)","F(-2)",0
10,1,166,0,0.368191," ","integrate((e*x+d)^3*(C*x^2+B*x+A)/(-e^2*x^2+d^2)^(1/2),x, algorithm=""giac"")","\frac{1}{8} \, {\left(13 \, C d^{5} + 15 \, B d^{4} e + 20 \, A d^{3} e^{2}\right)} \arcsin\left(\frac{x e}{d}\right) e^{\left(-3\right)} \mathrm{sgn}\left(d\right) - \frac{1}{120} \, \sqrt{-x^{2} e^{2} + d^{2}} {\left({\left(2 \, {\left(3 \, {\left(4 \, C x e + 5 \, {\left(3 \, C d e^{6} + B e^{7}\right)} e^{\left(-6\right)}\right)} x + 4 \, {\left(19 \, C d^{2} e^{5} + 15 \, B d e^{6} + 5 \, A e^{7}\right)} e^{\left(-6\right)}\right)} x + 15 \, {\left(13 \, C d^{3} e^{4} + 15 \, B d^{2} e^{5} + 12 \, A d e^{6}\right)} e^{\left(-6\right)}\right)} x + 8 \, {\left(38 \, C d^{4} e^{3} + 45 \, B d^{3} e^{4} + 55 \, A d^{2} e^{5}\right)} e^{\left(-6\right)}\right)}"," ",0,"1/8*(13*C*d^5 + 15*B*d^4*e + 20*A*d^3*e^2)*arcsin(x*e/d)*e^(-3)*sgn(d) - 1/120*sqrt(-x^2*e^2 + d^2)*((2*(3*(4*C*x*e + 5*(3*C*d*e^6 + B*e^7)*e^(-6))*x + 4*(19*C*d^2*e^5 + 15*B*d*e^6 + 5*A*e^7)*e^(-6))*x + 15*(13*C*d^3*e^4 + 15*B*d^2*e^5 + 12*A*d*e^6)*e^(-6))*x + 8*(38*C*d^4*e^3 + 45*B*d^3*e^4 + 55*A*d^2*e^5)*e^(-6))","A",0
11,1,131,0,0.315837," ","integrate((e*x+d)^2*(C*x^2+B*x+A)/(-e^2*x^2+d^2)^(1/2),x, algorithm=""giac"")","\frac{1}{8} \, {\left(7 \, C d^{4} + 8 \, B d^{3} e + 12 \, A d^{2} e^{2}\right)} \arcsin\left(\frac{x e}{d}\right) e^{\left(-3\right)} \mathrm{sgn}\left(d\right) - \frac{1}{24} \, \sqrt{-x^{2} e^{2} + d^{2}} {\left({\left(2 \, {\left(3 \, C x + 4 \, {\left(2 \, C d e^{4} + B e^{5}\right)} e^{\left(-5\right)}\right)} x + 3 \, {\left(7 \, C d^{2} e^{3} + 8 \, B d e^{4} + 4 \, A e^{5}\right)} e^{\left(-5\right)}\right)} x + 8 \, {\left(4 \, C d^{3} e^{2} + 5 \, B d^{2} e^{3} + 6 \, A d e^{4}\right)} e^{\left(-5\right)}\right)}"," ",0,"1/8*(7*C*d^4 + 8*B*d^3*e + 12*A*d^2*e^2)*arcsin(x*e/d)*e^(-3)*sgn(d) - 1/24*sqrt(-x^2*e^2 + d^2)*((2*(3*C*x + 4*(2*C*d*e^4 + B*e^5)*e^(-5))*x + 3*(7*C*d^2*e^3 + 8*B*d*e^4 + 4*A*e^5)*e^(-5))*x + 8*(4*C*d^3*e^2 + 5*B*d^2*e^3 + 6*A*d*e^4)*e^(-5))","A",0
12,1,97,0,0.291925," ","integrate((e*x+d)*(C*x^2+B*x+A)/(-e^2*x^2+d^2)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, {\left(C d^{3} + B d^{2} e + 2 \, A d e^{2}\right)} \arcsin\left(\frac{x e}{d}\right) e^{\left(-3\right)} \mathrm{sgn}\left(d\right) - \frac{1}{6} \, \sqrt{-x^{2} e^{2} + d^{2}} {\left({\left(2 \, C x e^{\left(-1\right)} + 3 \, {\left(C d e^{3} + B e^{4}\right)} e^{\left(-5\right)}\right)} x + 2 \, {\left(2 \, C d^{2} e^{2} + 3 \, B d e^{3} + 3 \, A e^{4}\right)} e^{\left(-5\right)}\right)}"," ",0,"1/2*(C*d^3 + B*d^2*e + 2*A*d*e^2)*arcsin(x*e/d)*e^(-3)*sgn(d) - 1/6*sqrt(-x^2*e^2 + d^2)*((2*C*x*e^(-1) + 3*(C*d*e^3 + B*e^4)*e^(-5))*x + 2*(2*C*d^2*e^2 + 3*B*d*e^3 + 3*A*e^4)*e^(-5))","A",0
13,1,52,0,0.344144," ","integrate((C*x^2+B*x+A)/(-e^2*x^2+d^2)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, {\left(C d^{2} + 2 \, A e^{2}\right)} \arcsin\left(\frac{x e}{d}\right) e^{\left(-3\right)} \mathrm{sgn}\left(d\right) - \frac{1}{2} \, \sqrt{-x^{2} e^{2} + d^{2}} {\left(C x e^{\left(-2\right)} + 2 \, B e^{\left(-2\right)}\right)}"," ",0,"1/2*(C*d^2 + 2*A*e^2)*arcsin(x*e/d)*e^(-3)*sgn(d) - 1/2*sqrt(-x^2*e^2 + d^2)*(C*x*e^(-2) + 2*B*e^(-2))","A",0
14,-2,0,0,0.000000," ","integrate((C*x^2+B*x+A)/(e*x+d)/(-e^2*x^2+d^2)^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 1/2*(-4*A*exp(2)^2-4*C*d^2*exp(2)+4*B*d*exp(1)*exp(2))*atan((-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x+exp(2))/sqrt(-exp(1)^4+exp(2)^2))/sqrt(-exp(1)^4+exp(2)^2)/d/exp(1)/exp(2)-1/4*(-4*B*exp(1)+4*C*d)*sign(d)*asin(x*exp(2)/d/exp(1))/exp(1)/exp(2)-4*exp(1)^2*C*1/4/exp(1)^5*sqrt(-exp(2)*x^2+d^2)","F(-2)",0
15,-2,0,0,0.000000," ","integrate((C*x^2+B*x+A)/(e*x+d)^2/(-e^2*x^2+d^2)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]index.cc index_m i_lex_is_greater Error: Bad Argument Value","F(-2)",0
16,-2,0,0,0.000000," ","integrate((C*x^2+B*x+A)/(e*x+d)^3/(-e^2*x^2+d^2)^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: (-2*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^8*exp(2)^2+7*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^6*exp(2)^3-2*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^10*exp(2)-2*B*d*exp(1)*exp(2)^5+2*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^6*exp(2)^2+5*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^4*exp(2)^4-11/2*A*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^4*exp(2)^4/x/exp(2)+A*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^8*exp(2)^2/x/exp(2)-5*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^5*exp(2)^3-2*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^9*exp(2)-2*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)*exp(2)^5-3*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^3*exp(2)^4+3*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^4*exp(2)^3+C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(2)^5-A*exp(1)^6*exp(2)^3-B*d*exp(1)^5*exp(2)^3+3*C*d^2*exp(1)^4*exp(2)^3+4*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(2)^6+4*A*exp(2)^6+6*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^8*exp(2)+1/2*C*d^2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(2)^5/x/exp(2)+5/2*B*d*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^3*exp(2)^4/x/exp(2)+2*B*d*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^7*exp(2)^2/x/exp(2)-5*C*d^2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^6*exp(2)^2/x/exp(2))/((-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(2)-(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x+exp(2))^2/(-d^3*exp(1)^9+2*d^3*exp(1)^5*exp(2)^2-d^3*exp(1)*exp(2)^4)+1/2*(-2*A*exp(1)^4*exp(2)^3+6*B*d*exp(1)^3*exp(2)^3-2*C*d^2*exp(2)^4-4*A*exp(2)^5-4*C*d^2*exp(1)^6*exp(2))*atan((-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x+exp(2))/sqrt(-exp(1)^4+exp(2)^2))/sqrt(-exp(1)^4+exp(2)^2)/(d^3*exp(1)^9-2*d^3*exp(1)^5*exp(2)^2+d^3*exp(1)*exp(2)^4)","F(-2)",0
17,-2,0,0,0.000000," ","integrate((C*x^2+B*x+A)/(e*x+d)^4/(-e^2*x^2+d^2)^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: (64*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^10*exp(2)^3-18*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^10*exp(2)^4+8*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^16*exp(2)+12*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^14*exp(2)^2+6*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^12*exp(2)^3+6*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^13*exp(2)^2+12*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^14*exp(2)^2-8*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^12*exp(2)^3-36*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^10*exp(2)^4-18*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^8*exp(2)^5+6*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^13*exp(2)^2-34*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^11*exp(2)^3-33*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^9*exp(2)^4-3*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^7*exp(2)^5+24*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^12*exp(2)^2+60*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^8*exp(2)^4+12*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^6*exp(2)^5+42*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^8*exp(2)^5+81*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^6*exp(2)^6+27*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^4*exp(2)^7-84*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^9*exp(2)^4-84*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^7*exp(2)^5-42*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^5*exp(2)^6-12*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^3*exp(2)^7+102*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^8*exp(2)^4+78*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^6*exp(2)^5+15*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^4*exp(2)^6+3*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(2)^8+2*A*exp(1)^10*exp(2)^4+120*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^6*exp(2)^6+108*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^4*exp(2)^7+B*d*exp(1)^9*exp(2)^4+2*C*d^2*exp(1)^8*exp(2)^4-60*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^5*exp(2)^6+18*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(2)^9-10*B*d*exp(1)^5*exp(2)^6-6*B*d*exp(1)*exp(2)^8-36*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^3*exp(2)^7+24*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^4*exp(2)^6-5*A*exp(1)^6*exp(2)^6+13*C*d^2*exp(1)^4*exp(2)^6+36*A*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(2)^9+18*A*exp(2)^9-81/2*A*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^4*exp(2)^7/x/exp(2)+6*A*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^8*exp(2)^5/x/exp(2)-3*A*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^12*exp(2)^3/x/exp(2)-12*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)*exp(2)^8+4*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^15*exp(2)-6*B*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)*exp(2)^8+8*C*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^14*exp(2)+3/2*C*d^2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(2)^8/x/exp(2)+12*B*d*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^3*exp(2)^7/x/exp(2)+57/2*B*d*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^7*exp(2)^5/x/exp(2)-3*B*d*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^11*exp(2)^3/x/exp(2)-33*C*d^2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^6*exp(2)^5/x/exp(2)-6*C*d^2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^10*exp(2)^3/x/exp(2))/((-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(2)-(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x+exp(2))^3/(3*d^4*exp(1)^13-9*d^4*exp(1)^9*exp(2)^2+9*d^4*exp(1)^5*exp(2)^4-3*d^4*exp(1)*exp(2)^6)+1/2*(2*B*d*exp(1)^7*exp(2)^3-8*C*d^2*exp(1)^6*exp(2)^3-6*A*exp(1)^4*exp(2)^5+8*B*d*exp(1)^3*exp(2)^5-2*C*d^2*exp(2)^6-4*A*exp(2)^7)*atan((-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x+exp(2))/sqrt(-exp(1)^4+exp(2)^2))/sqrt(-exp(1)^4+exp(2)^2)/(-d^4*exp(1)^13+3*d^4*exp(1)^9*exp(2)^2-3*d^4*exp(1)^5*exp(2)^4+d^4*exp(1)*exp(2)^6)","F(-2)",0
18,1,242,0,0.169791," ","integrate((e*x+d)^3*(c*x^2+a)*(C*x^2+B*x+A),x, algorithm=""giac"")","\frac{1}{8} \, C c x^{8} e^{3} + \frac{3}{7} \, C c d x^{7} e^{2} + \frac{1}{2} \, C c d^{2} x^{6} e + \frac{1}{5} \, C c d^{3} x^{5} + \frac{1}{7} \, B c x^{7} e^{3} + \frac{1}{2} \, B c d x^{6} e^{2} + \frac{3}{5} \, B c d^{2} x^{5} e + \frac{1}{4} \, B c d^{3} x^{4} + \frac{1}{6} \, C a x^{6} e^{3} + \frac{1}{6} \, A c x^{6} e^{3} + \frac{3}{5} \, C a d x^{5} e^{2} + \frac{3}{5} \, A c d x^{5} e^{2} + \frac{3}{4} \, C a d^{2} x^{4} e + \frac{3}{4} \, A c d^{2} x^{4} e + \frac{1}{3} \, C a d^{3} x^{3} + \frac{1}{3} \, A c d^{3} x^{3} + \frac{1}{5} \, B a x^{5} e^{3} + \frac{3}{4} \, B a d x^{4} e^{2} + B a d^{2} x^{3} e + \frac{1}{2} \, B a d^{3} x^{2} + \frac{1}{4} \, A a x^{4} e^{3} + A a d x^{3} e^{2} + \frac{3}{2} \, A a d^{2} x^{2} e + A a d^{3} x"," ",0,"1/8*C*c*x^8*e^3 + 3/7*C*c*d*x^7*e^2 + 1/2*C*c*d^2*x^6*e + 1/5*C*c*d^3*x^5 + 1/7*B*c*x^7*e^3 + 1/2*B*c*d*x^6*e^2 + 3/5*B*c*d^2*x^5*e + 1/4*B*c*d^3*x^4 + 1/6*C*a*x^6*e^3 + 1/6*A*c*x^6*e^3 + 3/5*C*a*d*x^5*e^2 + 3/5*A*c*d*x^5*e^2 + 3/4*C*a*d^2*x^4*e + 3/4*A*c*d^2*x^4*e + 1/3*C*a*d^3*x^3 + 1/3*A*c*d^3*x^3 + 1/5*B*a*x^5*e^3 + 3/4*B*a*d*x^4*e^2 + B*a*d^2*x^3*e + 1/2*B*a*d^3*x^2 + 1/4*A*a*x^4*e^3 + A*a*d*x^3*e^2 + 3/2*A*a*d^2*x^2*e + A*a*d^3*x","A",0
19,1,171,0,0.151560," ","integrate((e*x+d)^2*(c*x^2+a)*(C*x^2+B*x+A),x, algorithm=""giac"")","\frac{1}{7} \, C c x^{7} e^{2} + \frac{1}{3} \, C c d x^{6} e + \frac{1}{5} \, C c d^{2} x^{5} + \frac{1}{6} \, B c x^{6} e^{2} + \frac{2}{5} \, B c d x^{5} e + \frac{1}{4} \, B c d^{2} x^{4} + \frac{1}{5} \, C a x^{5} e^{2} + \frac{1}{5} \, A c x^{5} e^{2} + \frac{1}{2} \, C a d x^{4} e + \frac{1}{2} \, A c d x^{4} e + \frac{1}{3} \, C a d^{2} x^{3} + \frac{1}{3} \, A c d^{2} x^{3} + \frac{1}{4} \, B a x^{4} e^{2} + \frac{2}{3} \, B a d x^{3} e + \frac{1}{2} \, B a d^{2} x^{2} + \frac{1}{3} \, A a x^{3} e^{2} + A a d x^{2} e + A a d^{2} x"," ",0,"1/7*C*c*x^7*e^2 + 1/3*C*c*d*x^6*e + 1/5*C*c*d^2*x^5 + 1/6*B*c*x^6*e^2 + 2/5*B*c*d*x^5*e + 1/4*B*c*d^2*x^4 + 1/5*C*a*x^5*e^2 + 1/5*A*c*x^5*e^2 + 1/2*C*a*d*x^4*e + 1/2*A*c*d*x^4*e + 1/3*C*a*d^2*x^3 + 1/3*A*c*d^2*x^3 + 1/4*B*a*x^4*e^2 + 2/3*B*a*d*x^3*e + 1/2*B*a*d^2*x^2 + 1/3*A*a*x^3*e^2 + A*a*d*x^2*e + A*a*d^2*x","A",0
20,1,100,0,0.154410," ","integrate((e*x+d)*(c*x^2+a)*(C*x^2+B*x+A),x, algorithm=""giac"")","\frac{1}{6} \, C c x^{6} e + \frac{1}{5} \, C c d x^{5} + \frac{1}{5} \, B c x^{5} e + \frac{1}{4} \, B c d x^{4} + \frac{1}{4} \, C a x^{4} e + \frac{1}{4} \, A c x^{4} e + \frac{1}{3} \, C a d x^{3} + \frac{1}{3} \, A c d x^{3} + \frac{1}{3} \, B a x^{3} e + \frac{1}{2} \, B a d x^{2} + \frac{1}{2} \, A a x^{2} e + A a d x"," ",0,"1/6*C*c*x^6*e + 1/5*C*c*d*x^5 + 1/5*B*c*x^5*e + 1/4*B*c*d*x^4 + 1/4*C*a*x^4*e + 1/4*A*c*x^4*e + 1/3*C*a*d*x^3 + 1/3*A*c*d*x^3 + 1/3*B*a*x^3*e + 1/2*B*a*d*x^2 + 1/2*A*a*x^2*e + A*a*d*x","A",0
21,1,40,0,0.157437," ","integrate((c*x^2+a)*(C*x^2+B*x+A),x, algorithm=""giac"")","\frac{1}{5} \, C c x^{5} + \frac{1}{4} \, B c x^{4} + \frac{1}{3} \, C a x^{3} + \frac{1}{3} \, A c x^{3} + \frac{1}{2} \, B a x^{2} + A a x"," ",0,"1/5*C*c*x^5 + 1/4*B*c*x^4 + 1/3*C*a*x^3 + 1/3*A*c*x^3 + 1/2*B*a*x^2 + A*a*x","A",0
22,1,170,0,0.151041," ","integrate((c*x^2+a)*(C*x^2+B*x+A)/(e*x+d),x, algorithm=""giac"")","{\left(C c d^{4} - B c d^{3} e + C a d^{2} e^{2} + A c d^{2} e^{2} - B a d e^{3} + A a e^{4}\right)} e^{\left(-5\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{12} \, {\left(3 \, C c x^{4} e^{3} - 4 \, C c d x^{3} e^{2} + 6 \, C c d^{2} x^{2} e - 12 \, C c d^{3} x + 4 \, B c x^{3} e^{3} - 6 \, B c d x^{2} e^{2} + 12 \, B c d^{2} x e + 6 \, C a x^{2} e^{3} + 6 \, A c x^{2} e^{3} - 12 \, C a d x e^{2} - 12 \, A c d x e^{2} + 12 \, B a x e^{3}\right)} e^{\left(-4\right)}"," ",0,"(C*c*d^4 - B*c*d^3*e + C*a*d^2*e^2 + A*c*d^2*e^2 - B*a*d*e^3 + A*a*e^4)*e^(-5)*log(abs(x*e + d)) + 1/12*(3*C*c*x^4*e^3 - 4*C*c*d*x^3*e^2 + 6*C*c*d^2*x^2*e - 12*C*c*d^3*x + 4*B*c*x^3*e^3 - 6*B*c*d*x^2*e^2 + 12*B*c*d^2*x*e + 6*C*a*x^2*e^3 + 6*A*c*x^2*e^3 - 12*C*a*d*x*e^2 - 12*A*c*d*x*e^2 + 12*B*a*x*e^3)*e^(-4)","A",0
23,1,240,0,0.162595," ","integrate((c*x^2+a)*(C*x^2+B*x+A)/(e*x+d)^2,x, algorithm=""giac"")","\frac{1}{6} \, {\left(2 \, C c - \frac{3 \, {\left(4 \, C c d e - B c e^{2}\right)} e^{\left(-1\right)}}{x e + d} + \frac{6 \, {\left(6 \, C c d^{2} e^{2} - 3 \, B c d e^{3} + C a e^{4} + A c e^{4}\right)} e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}}\right)} {\left(x e + d\right)}^{3} e^{\left(-5\right)} + {\left(4 \, C c d^{3} - 3 \, B c d^{2} e + 2 \, C a d e^{2} + 2 \, A c d e^{2} - B a e^{3}\right)} e^{\left(-5\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) - {\left(\frac{C c d^{4} e^{3}}{x e + d} - \frac{B c d^{3} e^{4}}{x e + d} + \frac{C a d^{2} e^{5}}{x e + d} + \frac{A c d^{2} e^{5}}{x e + d} - \frac{B a d e^{6}}{x e + d} + \frac{A a e^{7}}{x e + d}\right)} e^{\left(-8\right)}"," ",0,"1/6*(2*C*c - 3*(4*C*c*d*e - B*c*e^2)*e^(-1)/(x*e + d) + 6*(6*C*c*d^2*e^2 - 3*B*c*d*e^3 + C*a*e^4 + A*c*e^4)*e^(-2)/(x*e + d)^2)*(x*e + d)^3*e^(-5) + (4*C*c*d^3 - 3*B*c*d^2*e + 2*C*a*d*e^2 + 2*A*c*d*e^2 - B*a*e^3)*e^(-5)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) - (C*c*d^4*e^3/(x*e + d) - B*c*d^3*e^4/(x*e + d) + C*a*d^2*e^5/(x*e + d) + A*c*d^2*e^5/(x*e + d) - B*a*d*e^6/(x*e + d) + A*a*e^7/(x*e + d))*e^(-8)","A",0
24,1,167,0,0.151791," ","integrate((c*x^2+a)*(C*x^2+B*x+A)/(e*x+d)^3,x, algorithm=""giac"")","{\left(6 \, C c d^{2} - 3 \, B c d e + C a e^{2} + A c e^{2}\right)} e^{\left(-5\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{2} \, {\left(C c x^{2} e^{3} - 6 \, C c d x e^{2} + 2 \, B c x e^{3}\right)} e^{\left(-6\right)} + \frac{{\left(7 \, C c d^{4} - 5 \, B c d^{3} e + 3 \, C a d^{2} e^{2} + 3 \, A c d^{2} e^{2} - B a d e^{3} - A a e^{4} + 2 \, {\left(4 \, C c d^{3} e - 3 \, B c d^{2} e^{2} + 2 \, C a d e^{3} + 2 \, A c d e^{3} - B a e^{4}\right)} x\right)} e^{\left(-5\right)}}{2 \, {\left(x e + d\right)}^{2}}"," ",0,"(6*C*c*d^2 - 3*B*c*d*e + C*a*e^2 + A*c*e^2)*e^(-5)*log(abs(x*e + d)) + 1/2*(C*c*x^2*e^3 - 6*C*c*d*x*e^2 + 2*B*c*x*e^3)*e^(-6) + 1/2*(7*C*c*d^4 - 5*B*c*d^3*e + 3*C*a*d^2*e^2 + 3*A*c*d^2*e^2 - B*a*d*e^3 - A*a*e^4 + 2*(4*C*c*d^3*e - 3*B*c*d^2*e^2 + 2*C*a*d*e^3 + 2*A*c*d*e^3 - B*a*e^4)*x)*e^(-5)/(x*e + d)^2","A",0
25,1,423,0,0.158853," ","integrate((e*x+d)^3*(c*x^2+a)^2*(C*x^2+B*x+A),x, algorithm=""giac"")","\frac{1}{10} \, C c^{2} x^{10} e^{3} + \frac{1}{3} \, C c^{2} d x^{9} e^{2} + \frac{3}{8} \, C c^{2} d^{2} x^{8} e + \frac{1}{7} \, C c^{2} d^{3} x^{7} + \frac{1}{9} \, B c^{2} x^{9} e^{3} + \frac{3}{8} \, B c^{2} d x^{8} e^{2} + \frac{3}{7} \, B c^{2} d^{2} x^{7} e + \frac{1}{6} \, B c^{2} d^{3} x^{6} + \frac{1}{4} \, C a c x^{8} e^{3} + \frac{1}{8} \, A c^{2} x^{8} e^{3} + \frac{6}{7} \, C a c d x^{7} e^{2} + \frac{3}{7} \, A c^{2} d x^{7} e^{2} + C a c d^{2} x^{6} e + \frac{1}{2} \, A c^{2} d^{2} x^{6} e + \frac{2}{5} \, C a c d^{3} x^{5} + \frac{1}{5} \, A c^{2} d^{3} x^{5} + \frac{2}{7} \, B a c x^{7} e^{3} + B a c d x^{6} e^{2} + \frac{6}{5} \, B a c d^{2} x^{5} e + \frac{1}{2} \, B a c d^{3} x^{4} + \frac{1}{6} \, C a^{2} x^{6} e^{3} + \frac{1}{3} \, A a c x^{6} e^{3} + \frac{3}{5} \, C a^{2} d x^{5} e^{2} + \frac{6}{5} \, A a c d x^{5} e^{2} + \frac{3}{4} \, C a^{2} d^{2} x^{4} e + \frac{3}{2} \, A a c d^{2} x^{4} e + \frac{1}{3} \, C a^{2} d^{3} x^{3} + \frac{2}{3} \, A a c d^{3} x^{3} + \frac{1}{5} \, B a^{2} x^{5} e^{3} + \frac{3}{4} \, B a^{2} d x^{4} e^{2} + B a^{2} d^{2} x^{3} e + \frac{1}{2} \, B a^{2} d^{3} x^{2} + \frac{1}{4} \, A a^{2} x^{4} e^{3} + A a^{2} d x^{3} e^{2} + \frac{3}{2} \, A a^{2} d^{2} x^{2} e + A a^{2} d^{3} x"," ",0,"1/10*C*c^2*x^10*e^3 + 1/3*C*c^2*d*x^9*e^2 + 3/8*C*c^2*d^2*x^8*e + 1/7*C*c^2*d^3*x^7 + 1/9*B*c^2*x^9*e^3 + 3/8*B*c^2*d*x^8*e^2 + 3/7*B*c^2*d^2*x^7*e + 1/6*B*c^2*d^3*x^6 + 1/4*C*a*c*x^8*e^3 + 1/8*A*c^2*x^8*e^3 + 6/7*C*a*c*d*x^7*e^2 + 3/7*A*c^2*d*x^7*e^2 + C*a*c*d^2*x^6*e + 1/2*A*c^2*d^2*x^6*e + 2/5*C*a*c*d^3*x^5 + 1/5*A*c^2*d^3*x^5 + 2/7*B*a*c*x^7*e^3 + B*a*c*d*x^6*e^2 + 6/5*B*a*c*d^2*x^5*e + 1/2*B*a*c*d^3*x^4 + 1/6*C*a^2*x^6*e^3 + 1/3*A*a*c*x^6*e^3 + 3/5*C*a^2*d*x^5*e^2 + 6/5*A*a*c*d*x^5*e^2 + 3/4*C*a^2*d^2*x^4*e + 3/2*A*a*c*d^2*x^4*e + 1/3*C*a^2*d^3*x^3 + 2/3*A*a*c*d^3*x^3 + 1/5*B*a^2*x^5*e^3 + 3/4*B*a^2*d*x^4*e^2 + B*a^2*d^2*x^3*e + 1/2*B*a^2*d^3*x^2 + 1/4*A*a^2*x^4*e^3 + A*a^2*d*x^3*e^2 + 3/2*A*a^2*d^2*x^2*e + A*a^2*d^3*x","A",0
26,1,302,0,0.168028," ","integrate((e*x+d)^2*(c*x^2+a)^2*(C*x^2+B*x+A),x, algorithm=""giac"")","\frac{1}{9} \, C c^{2} x^{9} e^{2} + \frac{1}{4} \, C c^{2} d x^{8} e + \frac{1}{7} \, C c^{2} d^{2} x^{7} + \frac{1}{8} \, B c^{2} x^{8} e^{2} + \frac{2}{7} \, B c^{2} d x^{7} e + \frac{1}{6} \, B c^{2} d^{2} x^{6} + \frac{2}{7} \, C a c x^{7} e^{2} + \frac{1}{7} \, A c^{2} x^{7} e^{2} + \frac{2}{3} \, C a c d x^{6} e + \frac{1}{3} \, A c^{2} d x^{6} e + \frac{2}{5} \, C a c d^{2} x^{5} + \frac{1}{5} \, A c^{2} d^{2} x^{5} + \frac{1}{3} \, B a c x^{6} e^{2} + \frac{4}{5} \, B a c d x^{5} e + \frac{1}{2} \, B a c d^{2} x^{4} + \frac{1}{5} \, C a^{2} x^{5} e^{2} + \frac{2}{5} \, A a c x^{5} e^{2} + \frac{1}{2} \, C a^{2} d x^{4} e + A a c d x^{4} e + \frac{1}{3} \, C a^{2} d^{2} x^{3} + \frac{2}{3} \, A a c d^{2} x^{3} + \frac{1}{4} \, B a^{2} x^{4} e^{2} + \frac{2}{3} \, B a^{2} d x^{3} e + \frac{1}{2} \, B a^{2} d^{2} x^{2} + \frac{1}{3} \, A a^{2} x^{3} e^{2} + A a^{2} d x^{2} e + A a^{2} d^{2} x"," ",0,"1/9*C*c^2*x^9*e^2 + 1/4*C*c^2*d*x^8*e + 1/7*C*c^2*d^2*x^7 + 1/8*B*c^2*x^8*e^2 + 2/7*B*c^2*d*x^7*e + 1/6*B*c^2*d^2*x^6 + 2/7*C*a*c*x^7*e^2 + 1/7*A*c^2*x^7*e^2 + 2/3*C*a*c*d*x^6*e + 1/3*A*c^2*d*x^6*e + 2/5*C*a*c*d^2*x^5 + 1/5*A*c^2*d^2*x^5 + 1/3*B*a*c*x^6*e^2 + 4/5*B*a*c*d*x^5*e + 1/2*B*a*c*d^2*x^4 + 1/5*C*a^2*x^5*e^2 + 2/5*A*a*c*x^5*e^2 + 1/2*C*a^2*d*x^4*e + A*a*c*d*x^4*e + 1/3*C*a^2*d^2*x^3 + 2/3*A*a*c*d^2*x^3 + 1/4*B*a^2*x^4*e^2 + 2/3*B*a^2*d*x^3*e + 1/2*B*a^2*d^2*x^2 + 1/3*A*a^2*x^3*e^2 + A*a^2*d*x^2*e + A*a^2*d^2*x","A",0
27,1,181,0,0.151716," ","integrate((e*x+d)*(c*x^2+a)^2*(C*x^2+B*x+A),x, algorithm=""giac"")","\frac{1}{8} \, C c^{2} x^{8} e + \frac{1}{7} \, C c^{2} d x^{7} + \frac{1}{7} \, B c^{2} x^{7} e + \frac{1}{6} \, B c^{2} d x^{6} + \frac{1}{3} \, C a c x^{6} e + \frac{1}{6} \, A c^{2} x^{6} e + \frac{2}{5} \, C a c d x^{5} + \frac{1}{5} \, A c^{2} d x^{5} + \frac{2}{5} \, B a c x^{5} e + \frac{1}{2} \, B a c d x^{4} + \frac{1}{4} \, C a^{2} x^{4} e + \frac{1}{2} \, A a c x^{4} e + \frac{1}{3} \, C a^{2} d x^{3} + \frac{2}{3} \, A a c d x^{3} + \frac{1}{3} \, B a^{2} x^{3} e + \frac{1}{2} \, B a^{2} d x^{2} + \frac{1}{2} \, A a^{2} x^{2} e + A a^{2} d x"," ",0,"1/8*C*c^2*x^8*e + 1/7*C*c^2*d*x^7 + 1/7*B*c^2*x^7*e + 1/6*B*c^2*d*x^6 + 1/3*C*a*c*x^6*e + 1/6*A*c^2*x^6*e + 2/5*C*a*c*d*x^5 + 1/5*A*c^2*d*x^5 + 2/5*B*a*c*x^5*e + 1/2*B*a*c*d*x^4 + 1/4*C*a^2*x^4*e + 1/2*A*a*c*x^4*e + 1/3*C*a^2*d*x^3 + 2/3*A*a*c*d*x^3 + 1/3*B*a^2*x^3*e + 1/2*B*a^2*d*x^2 + 1/2*A*a^2*x^2*e + A*a^2*d*x","A",0
28,1,76,0,0.151060," ","integrate((c*x^2+a)^2*(C*x^2+B*x+A),x, algorithm=""giac"")","\frac{1}{7} \, C c^{2} x^{7} + \frac{1}{6} \, B c^{2} x^{6} + \frac{2}{5} \, C a c x^{5} + \frac{1}{5} \, A c^{2} x^{5} + \frac{1}{2} \, B a c x^{4} + \frac{1}{3} \, C a^{2} x^{3} + \frac{2}{3} \, A a c x^{3} + \frac{1}{2} \, B a^{2} x^{2} + A a^{2} x"," ",0,"1/7*C*c^2*x^7 + 1/6*B*c^2*x^6 + 2/5*C*a*c*x^5 + 1/5*A*c^2*x^5 + 1/2*B*a*c*x^4 + 1/3*C*a^2*x^3 + 2/3*A*a*c*x^3 + 1/2*B*a^2*x^2 + A*a^2*x","A",0
29,1,416,0,0.157980," ","integrate((c*x^2+a)^2*(C*x^2+B*x+A)/(e*x+d),x, algorithm=""giac"")","{\left(C c^{2} d^{6} - B c^{2} d^{5} e + 2 \, C a c d^{4} e^{2} + A c^{2} d^{4} e^{2} - 2 \, B a c d^{3} e^{3} + C a^{2} d^{2} e^{4} + 2 \, A a c d^{2} e^{4} - B a^{2} d e^{5} + A a^{2} e^{6}\right)} e^{\left(-7\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{60} \, {\left(10 \, C c^{2} x^{6} e^{5} - 12 \, C c^{2} d x^{5} e^{4} + 15 \, C c^{2} d^{2} x^{4} e^{3} - 20 \, C c^{2} d^{3} x^{3} e^{2} + 30 \, C c^{2} d^{4} x^{2} e - 60 \, C c^{2} d^{5} x + 12 \, B c^{2} x^{5} e^{5} - 15 \, B c^{2} d x^{4} e^{4} + 20 \, B c^{2} d^{2} x^{3} e^{3} - 30 \, B c^{2} d^{3} x^{2} e^{2} + 60 \, B c^{2} d^{4} x e + 30 \, C a c x^{4} e^{5} + 15 \, A c^{2} x^{4} e^{5} - 40 \, C a c d x^{3} e^{4} - 20 \, A c^{2} d x^{3} e^{4} + 60 \, C a c d^{2} x^{2} e^{3} + 30 \, A c^{2} d^{2} x^{2} e^{3} - 120 \, C a c d^{3} x e^{2} - 60 \, A c^{2} d^{3} x e^{2} + 40 \, B a c x^{3} e^{5} - 60 \, B a c d x^{2} e^{4} + 120 \, B a c d^{2} x e^{3} + 30 \, C a^{2} x^{2} e^{5} + 60 \, A a c x^{2} e^{5} - 60 \, C a^{2} d x e^{4} - 120 \, A a c d x e^{4} + 60 \, B a^{2} x e^{5}\right)} e^{\left(-6\right)}"," ",0,"(C*c^2*d^6 - B*c^2*d^5*e + 2*C*a*c*d^4*e^2 + A*c^2*d^4*e^2 - 2*B*a*c*d^3*e^3 + C*a^2*d^2*e^4 + 2*A*a*c*d^2*e^4 - B*a^2*d*e^5 + A*a^2*e^6)*e^(-7)*log(abs(x*e + d)) + 1/60*(10*C*c^2*x^6*e^5 - 12*C*c^2*d*x^5*e^4 + 15*C*c^2*d^2*x^4*e^3 - 20*C*c^2*d^3*x^3*e^2 + 30*C*c^2*d^4*x^2*e - 60*C*c^2*d^5*x + 12*B*c^2*x^5*e^5 - 15*B*c^2*d*x^4*e^4 + 20*B*c^2*d^2*x^3*e^3 - 30*B*c^2*d^3*x^2*e^2 + 60*B*c^2*d^4*x*e + 30*C*a*c*x^4*e^5 + 15*A*c^2*x^4*e^5 - 40*C*a*c*d*x^3*e^4 - 20*A*c^2*d*x^3*e^4 + 60*C*a*c*d^2*x^2*e^3 + 30*A*c^2*d^2*x^2*e^3 - 120*C*a*c*d^3*x*e^2 - 60*A*c^2*d^3*x*e^2 + 40*B*a*c*x^3*e^5 - 60*B*a*c*d*x^2*e^4 + 120*B*a*c*d^2*x*e^3 + 30*C*a^2*x^2*e^5 + 60*A*a*c*x^2*e^5 - 60*C*a^2*d*x*e^4 - 120*A*a*c*d*x*e^4 + 60*B*a^2*x*e^5)*e^(-6)","A",0
30,1,497,0,0.184536," ","integrate((c*x^2+a)^2*(C*x^2+B*x+A)/(e*x+d)^2,x, algorithm=""giac"")","\frac{1}{60} \, {\left(12 \, C c^{2} - \frac{15 \, {\left(6 \, C c^{2} d e - B c^{2} e^{2}\right)} e^{\left(-1\right)}}{x e + d} + \frac{20 \, {\left(15 \, C c^{2} d^{2} e^{2} - 5 \, B c^{2} d e^{3} + 2 \, C a c e^{4} + A c^{2} e^{4}\right)} e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}} - \frac{60 \, {\left(10 \, C c^{2} d^{3} e^{3} - 5 \, B c^{2} d^{2} e^{4} + 4 \, C a c d e^{5} + 2 \, A c^{2} d e^{5} - B a c e^{6}\right)} e^{\left(-3\right)}}{{\left(x e + d\right)}^{3}} + \frac{60 \, {\left(15 \, C c^{2} d^{4} e^{4} - 10 \, B c^{2} d^{3} e^{5} + 12 \, C a c d^{2} e^{6} + 6 \, A c^{2} d^{2} e^{6} - 6 \, B a c d e^{7} + C a^{2} e^{8} + 2 \, A a c e^{8}\right)} e^{\left(-4\right)}}{{\left(x e + d\right)}^{4}}\right)} {\left(x e + d\right)}^{5} e^{\left(-7\right)} + {\left(6 \, C c^{2} d^{5} - 5 \, B c^{2} d^{4} e + 8 \, C a c d^{3} e^{2} + 4 \, A c^{2} d^{3} e^{2} - 6 \, B a c d^{2} e^{3} + 2 \, C a^{2} d e^{4} + 4 \, A a c d e^{4} - B a^{2} e^{5}\right)} e^{\left(-7\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) - {\left(\frac{C c^{2} d^{6} e^{5}}{x e + d} - \frac{B c^{2} d^{5} e^{6}}{x e + d} + \frac{2 \, C a c d^{4} e^{7}}{x e + d} + \frac{A c^{2} d^{4} e^{7}}{x e + d} - \frac{2 \, B a c d^{3} e^{8}}{x e + d} + \frac{C a^{2} d^{2} e^{9}}{x e + d} + \frac{2 \, A a c d^{2} e^{9}}{x e + d} - \frac{B a^{2} d e^{10}}{x e + d} + \frac{A a^{2} e^{11}}{x e + d}\right)} e^{\left(-12\right)}"," ",0,"1/60*(12*C*c^2 - 15*(6*C*c^2*d*e - B*c^2*e^2)*e^(-1)/(x*e + d) + 20*(15*C*c^2*d^2*e^2 - 5*B*c^2*d*e^3 + 2*C*a*c*e^4 + A*c^2*e^4)*e^(-2)/(x*e + d)^2 - 60*(10*C*c^2*d^3*e^3 - 5*B*c^2*d^2*e^4 + 4*C*a*c*d*e^5 + 2*A*c^2*d*e^5 - B*a*c*e^6)*e^(-3)/(x*e + d)^3 + 60*(15*C*c^2*d^4*e^4 - 10*B*c^2*d^3*e^5 + 12*C*a*c*d^2*e^6 + 6*A*c^2*d^2*e^6 - 6*B*a*c*d*e^7 + C*a^2*e^8 + 2*A*a*c*e^8)*e^(-4)/(x*e + d)^4)*(x*e + d)^5*e^(-7) + (6*C*c^2*d^5 - 5*B*c^2*d^4*e + 8*C*a*c*d^3*e^2 + 4*A*c^2*d^3*e^2 - 6*B*a*c*d^2*e^3 + 2*C*a^2*d*e^4 + 4*A*a*c*d*e^4 - B*a^2*e^5)*e^(-7)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) - (C*c^2*d^6*e^5/(x*e + d) - B*c^2*d^5*e^6/(x*e + d) + 2*C*a*c*d^4*e^7/(x*e + d) + A*c^2*d^4*e^7/(x*e + d) - 2*B*a*c*d^3*e^8/(x*e + d) + C*a^2*d^2*e^9/(x*e + d) + 2*A*a*c*d^2*e^9/(x*e + d) - B*a^2*d*e^10/(x*e + d) + A*a^2*e^11/(x*e + d))*e^(-12)","A",0
31,1,397,0,0.160187," ","integrate((c*x^2+a)^2*(C*x^2+B*x+A)/(e*x+d)^3,x, algorithm=""giac"")","{\left(15 \, C c^{2} d^{4} - 10 \, B c^{2} d^{3} e + 12 \, C a c d^{2} e^{2} + 6 \, A c^{2} d^{2} e^{2} - 6 \, B a c d e^{3} + C a^{2} e^{4} + 2 \, A a c e^{4}\right)} e^{\left(-7\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{12} \, {\left(3 \, C c^{2} x^{4} e^{9} - 12 \, C c^{2} d x^{3} e^{8} + 36 \, C c^{2} d^{2} x^{2} e^{7} - 120 \, C c^{2} d^{3} x e^{6} + 4 \, B c^{2} x^{3} e^{9} - 18 \, B c^{2} d x^{2} e^{8} + 72 \, B c^{2} d^{2} x e^{7} + 12 \, C a c x^{2} e^{9} + 6 \, A c^{2} x^{2} e^{9} - 72 \, C a c d x e^{8} - 36 \, A c^{2} d x e^{8} + 24 \, B a c x e^{9}\right)} e^{\left(-12\right)} + \frac{{\left(11 \, C c^{2} d^{6} - 9 \, B c^{2} d^{5} e + 14 \, C a c d^{4} e^{2} + 7 \, A c^{2} d^{4} e^{2} - 10 \, B a c d^{3} e^{3} + 3 \, C a^{2} d^{2} e^{4} + 6 \, A a c d^{2} e^{4} - B a^{2} d e^{5} - A a^{2} e^{6} + 2 \, {\left(6 \, C c^{2} d^{5} e - 5 \, B c^{2} d^{4} e^{2} + 8 \, C a c d^{3} e^{3} + 4 \, A c^{2} d^{3} e^{3} - 6 \, B a c d^{2} e^{4} + 2 \, C a^{2} d e^{5} + 4 \, A a c d e^{5} - B a^{2} e^{6}\right)} x\right)} e^{\left(-7\right)}}{2 \, {\left(x e + d\right)}^{2}}"," ",0,"(15*C*c^2*d^4 - 10*B*c^2*d^3*e + 12*C*a*c*d^2*e^2 + 6*A*c^2*d^2*e^2 - 6*B*a*c*d*e^3 + C*a^2*e^4 + 2*A*a*c*e^4)*e^(-7)*log(abs(x*e + d)) + 1/12*(3*C*c^2*x^4*e^9 - 12*C*c^2*d*x^3*e^8 + 36*C*c^2*d^2*x^2*e^7 - 120*C*c^2*d^3*x*e^6 + 4*B*c^2*x^3*e^9 - 18*B*c^2*d*x^2*e^8 + 72*B*c^2*d^2*x*e^7 + 12*C*a*c*x^2*e^9 + 6*A*c^2*x^2*e^9 - 72*C*a*c*d*x*e^8 - 36*A*c^2*d*x*e^8 + 24*B*a*c*x*e^9)*e^(-12) + 1/2*(11*C*c^2*d^6 - 9*B*c^2*d^5*e + 14*C*a*c*d^4*e^2 + 7*A*c^2*d^4*e^2 - 10*B*a*c*d^3*e^3 + 3*C*a^2*d^2*e^4 + 6*A*a*c*d^2*e^4 - B*a^2*d*e^5 - A*a^2*e^6 + 2*(6*C*c^2*d^5*e - 5*B*c^2*d^4*e^2 + 8*C*a*c*d^3*e^3 + 4*A*c^2*d^3*e^3 - 6*B*a*c*d^2*e^4 + 2*C*a^2*d*e^5 + 4*A*a*c*d*e^5 - B*a^2*e^6)*x)*e^(-7)/(x*e + d)^2","A",0
32,1,606,0,0.202418," ","integrate((e*x+d)^3*(c*x^2+a)^3*(C*x^2+B*x+A),x, algorithm=""giac"")","\frac{1}{12} \, C c^{3} x^{12} e^{3} + \frac{3}{11} \, C c^{3} d x^{11} e^{2} + \frac{3}{10} \, C c^{3} d^{2} x^{10} e + \frac{1}{9} \, C c^{3} d^{3} x^{9} + \frac{1}{11} \, B c^{3} x^{11} e^{3} + \frac{3}{10} \, B c^{3} d x^{10} e^{2} + \frac{1}{3} \, B c^{3} d^{2} x^{9} e + \frac{1}{8} \, B c^{3} d^{3} x^{8} + \frac{3}{10} \, C a c^{2} x^{10} e^{3} + \frac{1}{10} \, A c^{3} x^{10} e^{3} + C a c^{2} d x^{9} e^{2} + \frac{1}{3} \, A c^{3} d x^{9} e^{2} + \frac{9}{8} \, C a c^{2} d^{2} x^{8} e + \frac{3}{8} \, A c^{3} d^{2} x^{8} e + \frac{3}{7} \, C a c^{2} d^{3} x^{7} + \frac{1}{7} \, A c^{3} d^{3} x^{7} + \frac{1}{3} \, B a c^{2} x^{9} e^{3} + \frac{9}{8} \, B a c^{2} d x^{8} e^{2} + \frac{9}{7} \, B a c^{2} d^{2} x^{7} e + \frac{1}{2} \, B a c^{2} d^{3} x^{6} + \frac{3}{8} \, C a^{2} c x^{8} e^{3} + \frac{3}{8} \, A a c^{2} x^{8} e^{3} + \frac{9}{7} \, C a^{2} c d x^{7} e^{2} + \frac{9}{7} \, A a c^{2} d x^{7} e^{2} + \frac{3}{2} \, C a^{2} c d^{2} x^{6} e + \frac{3}{2} \, A a c^{2} d^{2} x^{6} e + \frac{3}{5} \, C a^{2} c d^{3} x^{5} + \frac{3}{5} \, A a c^{2} d^{3} x^{5} + \frac{3}{7} \, B a^{2} c x^{7} e^{3} + \frac{3}{2} \, B a^{2} c d x^{6} e^{2} + \frac{9}{5} \, B a^{2} c d^{2} x^{5} e + \frac{3}{4} \, B a^{2} c d^{3} x^{4} + \frac{1}{6} \, C a^{3} x^{6} e^{3} + \frac{1}{2} \, A a^{2} c x^{6} e^{3} + \frac{3}{5} \, C a^{3} d x^{5} e^{2} + \frac{9}{5} \, A a^{2} c d x^{5} e^{2} + \frac{3}{4} \, C a^{3} d^{2} x^{4} e + \frac{9}{4} \, A a^{2} c d^{2} x^{4} e + \frac{1}{3} \, C a^{3} d^{3} x^{3} + A a^{2} c d^{3} x^{3} + \frac{1}{5} \, B a^{3} x^{5} e^{3} + \frac{3}{4} \, B a^{3} d x^{4} e^{2} + B a^{3} d^{2} x^{3} e + \frac{1}{2} \, B a^{3} d^{3} x^{2} + \frac{1}{4} \, A a^{3} x^{4} e^{3} + A a^{3} d x^{3} e^{2} + \frac{3}{2} \, A a^{3} d^{2} x^{2} e + A a^{3} d^{3} x"," ",0,"1/12*C*c^3*x^12*e^3 + 3/11*C*c^3*d*x^11*e^2 + 3/10*C*c^3*d^2*x^10*e + 1/9*C*c^3*d^3*x^9 + 1/11*B*c^3*x^11*e^3 + 3/10*B*c^3*d*x^10*e^2 + 1/3*B*c^3*d^2*x^9*e + 1/8*B*c^3*d^3*x^8 + 3/10*C*a*c^2*x^10*e^3 + 1/10*A*c^3*x^10*e^3 + C*a*c^2*d*x^9*e^2 + 1/3*A*c^3*d*x^9*e^2 + 9/8*C*a*c^2*d^2*x^8*e + 3/8*A*c^3*d^2*x^8*e + 3/7*C*a*c^2*d^3*x^7 + 1/7*A*c^3*d^3*x^7 + 1/3*B*a*c^2*x^9*e^3 + 9/8*B*a*c^2*d*x^8*e^2 + 9/7*B*a*c^2*d^2*x^7*e + 1/2*B*a*c^2*d^3*x^6 + 3/8*C*a^2*c*x^8*e^3 + 3/8*A*a*c^2*x^8*e^3 + 9/7*C*a^2*c*d*x^7*e^2 + 9/7*A*a*c^2*d*x^7*e^2 + 3/2*C*a^2*c*d^2*x^6*e + 3/2*A*a*c^2*d^2*x^6*e + 3/5*C*a^2*c*d^3*x^5 + 3/5*A*a*c^2*d^3*x^5 + 3/7*B*a^2*c*x^7*e^3 + 3/2*B*a^2*c*d*x^6*e^2 + 9/5*B*a^2*c*d^2*x^5*e + 3/4*B*a^2*c*d^3*x^4 + 1/6*C*a^3*x^6*e^3 + 1/2*A*a^2*c*x^6*e^3 + 3/5*C*a^3*d*x^5*e^2 + 9/5*A*a^2*c*d*x^5*e^2 + 3/4*C*a^3*d^2*x^4*e + 9/4*A*a^2*c*d^2*x^4*e + 1/3*C*a^3*d^3*x^3 + A*a^2*c*d^3*x^3 + 1/5*B*a^3*x^5*e^3 + 3/4*B*a^3*d*x^4*e^2 + B*a^3*d^2*x^3*e + 1/2*B*a^3*d^3*x^2 + 1/4*A*a^3*x^4*e^3 + A*a^3*d*x^3*e^2 + 3/2*A*a^3*d^2*x^2*e + A*a^3*d^3*x","A",0
33,1,432,0,0.154549," ","integrate((e*x+d)^2*(c*x^2+a)^3*(C*x^2+B*x+A),x, algorithm=""giac"")","\frac{1}{11} \, C c^{3} x^{11} e^{2} + \frac{1}{5} \, C c^{3} d x^{10} e + \frac{1}{9} \, C c^{3} d^{2} x^{9} + \frac{1}{10} \, B c^{3} x^{10} e^{2} + \frac{2}{9} \, B c^{3} d x^{9} e + \frac{1}{8} \, B c^{3} d^{2} x^{8} + \frac{1}{3} \, C a c^{2} x^{9} e^{2} + \frac{1}{9} \, A c^{3} x^{9} e^{2} + \frac{3}{4} \, C a c^{2} d x^{8} e + \frac{1}{4} \, A c^{3} d x^{8} e + \frac{3}{7} \, C a c^{2} d^{2} x^{7} + \frac{1}{7} \, A c^{3} d^{2} x^{7} + \frac{3}{8} \, B a c^{2} x^{8} e^{2} + \frac{6}{7} \, B a c^{2} d x^{7} e + \frac{1}{2} \, B a c^{2} d^{2} x^{6} + \frac{3}{7} \, C a^{2} c x^{7} e^{2} + \frac{3}{7} \, A a c^{2} x^{7} e^{2} + C a^{2} c d x^{6} e + A a c^{2} d x^{6} e + \frac{3}{5} \, C a^{2} c d^{2} x^{5} + \frac{3}{5} \, A a c^{2} d^{2} x^{5} + \frac{1}{2} \, B a^{2} c x^{6} e^{2} + \frac{6}{5} \, B a^{2} c d x^{5} e + \frac{3}{4} \, B a^{2} c d^{2} x^{4} + \frac{1}{5} \, C a^{3} x^{5} e^{2} + \frac{3}{5} \, A a^{2} c x^{5} e^{2} + \frac{1}{2} \, C a^{3} d x^{4} e + \frac{3}{2} \, A a^{2} c d x^{4} e + \frac{1}{3} \, C a^{3} d^{2} x^{3} + A a^{2} c d^{2} x^{3} + \frac{1}{4} \, B a^{3} x^{4} e^{2} + \frac{2}{3} \, B a^{3} d x^{3} e + \frac{1}{2} \, B a^{3} d^{2} x^{2} + \frac{1}{3} \, A a^{3} x^{3} e^{2} + A a^{3} d x^{2} e + A a^{3} d^{2} x"," ",0,"1/11*C*c^3*x^11*e^2 + 1/5*C*c^3*d*x^10*e + 1/9*C*c^3*d^2*x^9 + 1/10*B*c^3*x^10*e^2 + 2/9*B*c^3*d*x^9*e + 1/8*B*c^3*d^2*x^8 + 1/3*C*a*c^2*x^9*e^2 + 1/9*A*c^3*x^9*e^2 + 3/4*C*a*c^2*d*x^8*e + 1/4*A*c^3*d*x^8*e + 3/7*C*a*c^2*d^2*x^7 + 1/7*A*c^3*d^2*x^7 + 3/8*B*a*c^2*x^8*e^2 + 6/7*B*a*c^2*d*x^7*e + 1/2*B*a*c^2*d^2*x^6 + 3/7*C*a^2*c*x^7*e^2 + 3/7*A*a*c^2*x^7*e^2 + C*a^2*c*d*x^6*e + A*a*c^2*d*x^6*e + 3/5*C*a^2*c*d^2*x^5 + 3/5*A*a*c^2*d^2*x^5 + 1/2*B*a^2*c*x^6*e^2 + 6/5*B*a^2*c*d*x^5*e + 3/4*B*a^2*c*d^2*x^4 + 1/5*C*a^3*x^5*e^2 + 3/5*A*a^2*c*x^5*e^2 + 1/2*C*a^3*d*x^4*e + 3/2*A*a^2*c*d*x^4*e + 1/3*C*a^3*d^2*x^3 + A*a^2*c*d^2*x^3 + 1/4*B*a^3*x^4*e^2 + 2/3*B*a^3*d*x^3*e + 1/2*B*a^3*d^2*x^2 + 1/3*A*a^3*x^3*e^2 + A*a^3*d*x^2*e + A*a^3*d^2*x","A",0
34,1,261,0,0.185394," ","integrate((e*x+d)*(c*x^2+a)^3*(C*x^2+B*x+A),x, algorithm=""giac"")","\frac{1}{10} \, C c^{3} x^{10} e + \frac{1}{9} \, C c^{3} d x^{9} + \frac{1}{9} \, B c^{3} x^{9} e + \frac{1}{8} \, B c^{3} d x^{8} + \frac{3}{8} \, C a c^{2} x^{8} e + \frac{1}{8} \, A c^{3} x^{8} e + \frac{3}{7} \, C a c^{2} d x^{7} + \frac{1}{7} \, A c^{3} d x^{7} + \frac{3}{7} \, B a c^{2} x^{7} e + \frac{1}{2} \, B a c^{2} d x^{6} + \frac{1}{2} \, C a^{2} c x^{6} e + \frac{1}{2} \, A a c^{2} x^{6} e + \frac{3}{5} \, C a^{2} c d x^{5} + \frac{3}{5} \, A a c^{2} d x^{5} + \frac{3}{5} \, B a^{2} c x^{5} e + \frac{3}{4} \, B a^{2} c d x^{4} + \frac{1}{4} \, C a^{3} x^{4} e + \frac{3}{4} \, A a^{2} c x^{4} e + \frac{1}{3} \, C a^{3} d x^{3} + A a^{2} c d x^{3} + \frac{1}{3} \, B a^{3} x^{3} e + \frac{1}{2} \, B a^{3} d x^{2} + \frac{1}{2} \, A a^{3} x^{2} e + A a^{3} d x"," ",0,"1/10*C*c^3*x^10*e + 1/9*C*c^3*d*x^9 + 1/9*B*c^3*x^9*e + 1/8*B*c^3*d*x^8 + 3/8*C*a*c^2*x^8*e + 1/8*A*c^3*x^8*e + 3/7*C*a*c^2*d*x^7 + 1/7*A*c^3*d*x^7 + 3/7*B*a*c^2*x^7*e + 1/2*B*a*c^2*d*x^6 + 1/2*C*a^2*c*x^6*e + 1/2*A*a*c^2*x^6*e + 3/5*C*a^2*c*d*x^5 + 3/5*A*a*c^2*d*x^5 + 3/5*B*a^2*c*x^5*e + 3/4*B*a^2*c*d*x^4 + 1/4*C*a^3*x^4*e + 3/4*A*a^2*c*x^4*e + 1/3*C*a^3*d*x^3 + A*a^2*c*d*x^3 + 1/3*B*a^3*x^3*e + 1/2*B*a^3*d*x^2 + 1/2*A*a^3*x^2*e + A*a^3*d*x","A",0
35,1,111,0,0.185912," ","integrate((c*x^2+a)^3*(C*x^2+B*x+A),x, algorithm=""giac"")","\frac{1}{9} \, C c^{3} x^{9} + \frac{1}{8} \, B c^{3} x^{8} + \frac{3}{7} \, C a c^{2} x^{7} + \frac{1}{7} \, A c^{3} x^{7} + \frac{1}{2} \, B a c^{2} x^{6} + \frac{3}{5} \, C a^{2} c x^{5} + \frac{3}{5} \, A a c^{2} x^{5} + \frac{3}{4} \, B a^{2} c x^{4} + \frac{1}{3} \, C a^{3} x^{3} + A a^{2} c x^{3} + \frac{1}{2} \, B a^{3} x^{2} + A a^{3} x"," ",0,"1/9*C*c^3*x^9 + 1/8*B*c^3*x^8 + 3/7*C*a*c^2*x^7 + 1/7*A*c^3*x^7 + 1/2*B*a*c^2*x^6 + 3/5*C*a^2*c*x^5 + 3/5*A*a*c^2*x^5 + 3/4*B*a^2*c*x^4 + 1/3*C*a^3*x^3 + A*a^2*c*x^3 + 1/2*B*a^3*x^2 + A*a^3*x","A",0
36,1,764,0,0.167340," ","integrate((c*x^2+a)^3*(C*x^2+B*x+A)/(e*x+d),x, algorithm=""giac"")","{\left(C c^{3} d^{8} - B c^{3} d^{7} e + 3 \, C a c^{2} d^{6} e^{2} + A c^{3} d^{6} e^{2} - 3 \, B a c^{2} d^{5} e^{3} + 3 \, C a^{2} c d^{4} e^{4} + 3 \, A a c^{2} d^{4} e^{4} - 3 \, B a^{2} c d^{3} e^{5} + C a^{3} d^{2} e^{6} + 3 \, A a^{2} c d^{2} e^{6} - B a^{3} d e^{7} + A a^{3} e^{8}\right)} e^{\left(-9\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{840} \, {\left(105 \, C c^{3} x^{8} e^{7} - 120 \, C c^{3} d x^{7} e^{6} + 140 \, C c^{3} d^{2} x^{6} e^{5} - 168 \, C c^{3} d^{3} x^{5} e^{4} + 210 \, C c^{3} d^{4} x^{4} e^{3} - 280 \, C c^{3} d^{5} x^{3} e^{2} + 420 \, C c^{3} d^{6} x^{2} e - 840 \, C c^{3} d^{7} x + 120 \, B c^{3} x^{7} e^{7} - 140 \, B c^{3} d x^{6} e^{6} + 168 \, B c^{3} d^{2} x^{5} e^{5} - 210 \, B c^{3} d^{3} x^{4} e^{4} + 280 \, B c^{3} d^{4} x^{3} e^{3} - 420 \, B c^{3} d^{5} x^{2} e^{2} + 840 \, B c^{3} d^{6} x e + 420 \, C a c^{2} x^{6} e^{7} + 140 \, A c^{3} x^{6} e^{7} - 504 \, C a c^{2} d x^{5} e^{6} - 168 \, A c^{3} d x^{5} e^{6} + 630 \, C a c^{2} d^{2} x^{4} e^{5} + 210 \, A c^{3} d^{2} x^{4} e^{5} - 840 \, C a c^{2} d^{3} x^{3} e^{4} - 280 \, A c^{3} d^{3} x^{3} e^{4} + 1260 \, C a c^{2} d^{4} x^{2} e^{3} + 420 \, A c^{3} d^{4} x^{2} e^{3} - 2520 \, C a c^{2} d^{5} x e^{2} - 840 \, A c^{3} d^{5} x e^{2} + 504 \, B a c^{2} x^{5} e^{7} - 630 \, B a c^{2} d x^{4} e^{6} + 840 \, B a c^{2} d^{2} x^{3} e^{5} - 1260 \, B a c^{2} d^{3} x^{2} e^{4} + 2520 \, B a c^{2} d^{4} x e^{3} + 630 \, C a^{2} c x^{4} e^{7} + 630 \, A a c^{2} x^{4} e^{7} - 840 \, C a^{2} c d x^{3} e^{6} - 840 \, A a c^{2} d x^{3} e^{6} + 1260 \, C a^{2} c d^{2} x^{2} e^{5} + 1260 \, A a c^{2} d^{2} x^{2} e^{5} - 2520 \, C a^{2} c d^{3} x e^{4} - 2520 \, A a c^{2} d^{3} x e^{4} + 840 \, B a^{2} c x^{3} e^{7} - 1260 \, B a^{2} c d x^{2} e^{6} + 2520 \, B a^{2} c d^{2} x e^{5} + 420 \, C a^{3} x^{2} e^{7} + 1260 \, A a^{2} c x^{2} e^{7} - 840 \, C a^{3} d x e^{6} - 2520 \, A a^{2} c d x e^{6} + 840 \, B a^{3} x e^{7}\right)} e^{\left(-8\right)}"," ",0,"(C*c^3*d^8 - B*c^3*d^7*e + 3*C*a*c^2*d^6*e^2 + A*c^3*d^6*e^2 - 3*B*a*c^2*d^5*e^3 + 3*C*a^2*c*d^4*e^4 + 3*A*a*c^2*d^4*e^4 - 3*B*a^2*c*d^3*e^5 + C*a^3*d^2*e^6 + 3*A*a^2*c*d^2*e^6 - B*a^3*d*e^7 + A*a^3*e^8)*e^(-9)*log(abs(x*e + d)) + 1/840*(105*C*c^3*x^8*e^7 - 120*C*c^3*d*x^7*e^6 + 140*C*c^3*d^2*x^6*e^5 - 168*C*c^3*d^3*x^5*e^4 + 210*C*c^3*d^4*x^4*e^3 - 280*C*c^3*d^5*x^3*e^2 + 420*C*c^3*d^6*x^2*e - 840*C*c^3*d^7*x + 120*B*c^3*x^7*e^7 - 140*B*c^3*d*x^6*e^6 + 168*B*c^3*d^2*x^5*e^5 - 210*B*c^3*d^3*x^4*e^4 + 280*B*c^3*d^4*x^3*e^3 - 420*B*c^3*d^5*x^2*e^2 + 840*B*c^3*d^6*x*e + 420*C*a*c^2*x^6*e^7 + 140*A*c^3*x^6*e^7 - 504*C*a*c^2*d*x^5*e^6 - 168*A*c^3*d*x^5*e^6 + 630*C*a*c^2*d^2*x^4*e^5 + 210*A*c^3*d^2*x^4*e^5 - 840*C*a*c^2*d^3*x^3*e^4 - 280*A*c^3*d^3*x^3*e^4 + 1260*C*a*c^2*d^4*x^2*e^3 + 420*A*c^3*d^4*x^2*e^3 - 2520*C*a*c^2*d^5*x*e^2 - 840*A*c^3*d^5*x*e^2 + 504*B*a*c^2*x^5*e^7 - 630*B*a*c^2*d*x^4*e^6 + 840*B*a*c^2*d^2*x^3*e^5 - 1260*B*a*c^2*d^3*x^2*e^4 + 2520*B*a*c^2*d^4*x*e^3 + 630*C*a^2*c*x^4*e^7 + 630*A*a*c^2*x^4*e^7 - 840*C*a^2*c*d*x^3*e^6 - 840*A*a*c^2*d*x^3*e^6 + 1260*C*a^2*c*d^2*x^2*e^5 + 1260*A*a*c^2*d^2*x^2*e^5 - 2520*C*a^2*c*d^3*x*e^4 - 2520*A*a*c^2*d^3*x*e^4 + 840*B*a^2*c*x^3*e^7 - 1260*B*a^2*c*d*x^2*e^6 + 2520*B*a^2*c*d^2*x*e^5 + 420*C*a^3*x^2*e^7 + 1260*A*a^2*c*x^2*e^7 - 840*C*a^3*d*x*e^6 - 2520*A*a^2*c*d*x*e^6 + 840*B*a^3*x*e^7)*e^(-8)","A",0
37,1,838,0,0.196297," ","integrate((c*x^2+a)^3*(C*x^2+B*x+A)/(e*x+d)^2,x, algorithm=""giac"")","\frac{1}{420} \, {\left(60 \, C c^{3} - \frac{70 \, {\left(8 \, C c^{3} d e - B c^{3} e^{2}\right)} e^{\left(-1\right)}}{x e + d} + \frac{84 \, {\left(28 \, C c^{3} d^{2} e^{2} - 7 \, B c^{3} d e^{3} + 3 \, C a c^{2} e^{4} + A c^{3} e^{4}\right)} e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}} - \frac{105 \, {\left(56 \, C c^{3} d^{3} e^{3} - 21 \, B c^{3} d^{2} e^{4} + 18 \, C a c^{2} d e^{5} + 6 \, A c^{3} d e^{5} - 3 \, B a c^{2} e^{6}\right)} e^{\left(-3\right)}}{{\left(x e + d\right)}^{3}} + \frac{140 \, {\left(70 \, C c^{3} d^{4} e^{4} - 35 \, B c^{3} d^{3} e^{5} + 45 \, C a c^{2} d^{2} e^{6} + 15 \, A c^{3} d^{2} e^{6} - 15 \, B a c^{2} d e^{7} + 3 \, C a^{2} c e^{8} + 3 \, A a c^{2} e^{8}\right)} e^{\left(-4\right)}}{{\left(x e + d\right)}^{4}} - \frac{210 \, {\left(56 \, C c^{3} d^{5} e^{5} - 35 \, B c^{3} d^{4} e^{6} + 60 \, C a c^{2} d^{3} e^{7} + 20 \, A c^{3} d^{3} e^{7} - 30 \, B a c^{2} d^{2} e^{8} + 12 \, C a^{2} c d e^{9} + 12 \, A a c^{2} d e^{9} - 3 \, B a^{2} c e^{10}\right)} e^{\left(-5\right)}}{{\left(x e + d\right)}^{5}} + \frac{420 \, {\left(28 \, C c^{3} d^{6} e^{6} - 21 \, B c^{3} d^{5} e^{7} + 45 \, C a c^{2} d^{4} e^{8} + 15 \, A c^{3} d^{4} e^{8} - 30 \, B a c^{2} d^{3} e^{9} + 18 \, C a^{2} c d^{2} e^{10} + 18 \, A a c^{2} d^{2} e^{10} - 9 \, B a^{2} c d e^{11} + C a^{3} e^{12} + 3 \, A a^{2} c e^{12}\right)} e^{\left(-6\right)}}{{\left(x e + d\right)}^{6}}\right)} {\left(x e + d\right)}^{7} e^{\left(-9\right)} + {\left(8 \, C c^{3} d^{7} - 7 \, B c^{3} d^{6} e + 18 \, C a c^{2} d^{5} e^{2} + 6 \, A c^{3} d^{5} e^{2} - 15 \, B a c^{2} d^{4} e^{3} + 12 \, C a^{2} c d^{3} e^{4} + 12 \, A a c^{2} d^{3} e^{4} - 9 \, B a^{2} c d^{2} e^{5} + 2 \, C a^{3} d e^{6} + 6 \, A a^{2} c d e^{6} - B a^{3} e^{7}\right)} e^{\left(-9\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) - {\left(\frac{C c^{3} d^{8} e^{7}}{x e + d} - \frac{B c^{3} d^{7} e^{8}}{x e + d} + \frac{3 \, C a c^{2} d^{6} e^{9}}{x e + d} + \frac{A c^{3} d^{6} e^{9}}{x e + d} - \frac{3 \, B a c^{2} d^{5} e^{10}}{x e + d} + \frac{3 \, C a^{2} c d^{4} e^{11}}{x e + d} + \frac{3 \, A a c^{2} d^{4} e^{11}}{x e + d} - \frac{3 \, B a^{2} c d^{3} e^{12}}{x e + d} + \frac{C a^{3} d^{2} e^{13}}{x e + d} + \frac{3 \, A a^{2} c d^{2} e^{13}}{x e + d} - \frac{B a^{3} d e^{14}}{x e + d} + \frac{A a^{3} e^{15}}{x e + d}\right)} e^{\left(-16\right)}"," ",0,"1/420*(60*C*c^3 - 70*(8*C*c^3*d*e - B*c^3*e^2)*e^(-1)/(x*e + d) + 84*(28*C*c^3*d^2*e^2 - 7*B*c^3*d*e^3 + 3*C*a*c^2*e^4 + A*c^3*e^4)*e^(-2)/(x*e + d)^2 - 105*(56*C*c^3*d^3*e^3 - 21*B*c^3*d^2*e^4 + 18*C*a*c^2*d*e^5 + 6*A*c^3*d*e^5 - 3*B*a*c^2*e^6)*e^(-3)/(x*e + d)^3 + 140*(70*C*c^3*d^4*e^4 - 35*B*c^3*d^3*e^5 + 45*C*a*c^2*d^2*e^6 + 15*A*c^3*d^2*e^6 - 15*B*a*c^2*d*e^7 + 3*C*a^2*c*e^8 + 3*A*a*c^2*e^8)*e^(-4)/(x*e + d)^4 - 210*(56*C*c^3*d^5*e^5 - 35*B*c^3*d^4*e^6 + 60*C*a*c^2*d^3*e^7 + 20*A*c^3*d^3*e^7 - 30*B*a*c^2*d^2*e^8 + 12*C*a^2*c*d*e^9 + 12*A*a*c^2*d*e^9 - 3*B*a^2*c*e^10)*e^(-5)/(x*e + d)^5 + 420*(28*C*c^3*d^6*e^6 - 21*B*c^3*d^5*e^7 + 45*C*a*c^2*d^4*e^8 + 15*A*c^3*d^4*e^8 - 30*B*a*c^2*d^3*e^9 + 18*C*a^2*c*d^2*e^10 + 18*A*a*c^2*d^2*e^10 - 9*B*a^2*c*d*e^11 + C*a^3*e^12 + 3*A*a^2*c*e^12)*e^(-6)/(x*e + d)^6)*(x*e + d)^7*e^(-9) + (8*C*c^3*d^7 - 7*B*c^3*d^6*e + 18*C*a*c^2*d^5*e^2 + 6*A*c^3*d^5*e^2 - 15*B*a*c^2*d^4*e^3 + 12*C*a^2*c*d^3*e^4 + 12*A*a*c^2*d^3*e^4 - 9*B*a^2*c*d^2*e^5 + 2*C*a^3*d*e^6 + 6*A*a^2*c*d*e^6 - B*a^3*e^7)*e^(-9)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) - (C*c^3*d^8*e^7/(x*e + d) - B*c^3*d^7*e^8/(x*e + d) + 3*C*a*c^2*d^6*e^9/(x*e + d) + A*c^3*d^6*e^9/(x*e + d) - 3*B*a*c^2*d^5*e^10/(x*e + d) + 3*C*a^2*c*d^4*e^11/(x*e + d) + 3*A*a*c^2*d^4*e^11/(x*e + d) - 3*B*a^2*c*d^3*e^12/(x*e + d) + C*a^3*d^2*e^13/(x*e + d) + 3*A*a^2*c*d^2*e^13/(x*e + d) - B*a^3*d*e^14/(x*e + d) + A*a^3*e^15/(x*e + d))*e^(-16)","A",0
38,1,727,0,0.173757," ","integrate((c*x^2+a)^3*(C*x^2+B*x+A)/(e*x+d)^3,x, algorithm=""giac"")","{\left(28 \, C c^{3} d^{6} - 21 \, B c^{3} d^{5} e + 45 \, C a c^{2} d^{4} e^{2} + 15 \, A c^{3} d^{4} e^{2} - 30 \, B a c^{2} d^{3} e^{3} + 18 \, C a^{2} c d^{2} e^{4} + 18 \, A a c^{2} d^{2} e^{4} - 9 \, B a^{2} c d e^{5} + C a^{3} e^{6} + 3 \, A a^{2} c e^{6}\right)} e^{\left(-9\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{60} \, {\left(10 \, C c^{3} x^{6} e^{15} - 36 \, C c^{3} d x^{5} e^{14} + 90 \, C c^{3} d^{2} x^{4} e^{13} - 200 \, C c^{3} d^{3} x^{3} e^{12} + 450 \, C c^{3} d^{4} x^{2} e^{11} - 1260 \, C c^{3} d^{5} x e^{10} + 12 \, B c^{3} x^{5} e^{15} - 45 \, B c^{3} d x^{4} e^{14} + 120 \, B c^{3} d^{2} x^{3} e^{13} - 300 \, B c^{3} d^{3} x^{2} e^{12} + 900 \, B c^{3} d^{4} x e^{11} + 45 \, C a c^{2} x^{4} e^{15} + 15 \, A c^{3} x^{4} e^{15} - 180 \, C a c^{2} d x^{3} e^{14} - 60 \, A c^{3} d x^{3} e^{14} + 540 \, C a c^{2} d^{2} x^{2} e^{13} + 180 \, A c^{3} d^{2} x^{2} e^{13} - 1800 \, C a c^{2} d^{3} x e^{12} - 600 \, A c^{3} d^{3} x e^{12} + 60 \, B a c^{2} x^{3} e^{15} - 270 \, B a c^{2} d x^{2} e^{14} + 1080 \, B a c^{2} d^{2} x e^{13} + 90 \, C a^{2} c x^{2} e^{15} + 90 \, A a c^{2} x^{2} e^{15} - 540 \, C a^{2} c d x e^{14} - 540 \, A a c^{2} d x e^{14} + 180 \, B a^{2} c x e^{15}\right)} e^{\left(-18\right)} + \frac{{\left(15 \, C c^{3} d^{8} - 13 \, B c^{3} d^{7} e + 33 \, C a c^{2} d^{6} e^{2} + 11 \, A c^{3} d^{6} e^{2} - 27 \, B a c^{2} d^{5} e^{3} + 21 \, C a^{2} c d^{4} e^{4} + 21 \, A a c^{2} d^{4} e^{4} - 15 \, B a^{2} c d^{3} e^{5} + 3 \, C a^{3} d^{2} e^{6} + 9 \, A a^{2} c d^{2} e^{6} - B a^{3} d e^{7} - A a^{3} e^{8} + 2 \, {\left(8 \, C c^{3} d^{7} e - 7 \, B c^{3} d^{6} e^{2} + 18 \, C a c^{2} d^{5} e^{3} + 6 \, A c^{3} d^{5} e^{3} - 15 \, B a c^{2} d^{4} e^{4} + 12 \, C a^{2} c d^{3} e^{5} + 12 \, A a c^{2} d^{3} e^{5} - 9 \, B a^{2} c d^{2} e^{6} + 2 \, C a^{3} d e^{7} + 6 \, A a^{2} c d e^{7} - B a^{3} e^{8}\right)} x\right)} e^{\left(-9\right)}}{2 \, {\left(x e + d\right)}^{2}}"," ",0,"(28*C*c^3*d^6 - 21*B*c^3*d^5*e + 45*C*a*c^2*d^4*e^2 + 15*A*c^3*d^4*e^2 - 30*B*a*c^2*d^3*e^3 + 18*C*a^2*c*d^2*e^4 + 18*A*a*c^2*d^2*e^4 - 9*B*a^2*c*d*e^5 + C*a^3*e^6 + 3*A*a^2*c*e^6)*e^(-9)*log(abs(x*e + d)) + 1/60*(10*C*c^3*x^6*e^15 - 36*C*c^3*d*x^5*e^14 + 90*C*c^3*d^2*x^4*e^13 - 200*C*c^3*d^3*x^3*e^12 + 450*C*c^3*d^4*x^2*e^11 - 1260*C*c^3*d^5*x*e^10 + 12*B*c^3*x^5*e^15 - 45*B*c^3*d*x^4*e^14 + 120*B*c^3*d^2*x^3*e^13 - 300*B*c^3*d^3*x^2*e^12 + 900*B*c^3*d^4*x*e^11 + 45*C*a*c^2*x^4*e^15 + 15*A*c^3*x^4*e^15 - 180*C*a*c^2*d*x^3*e^14 - 60*A*c^3*d*x^3*e^14 + 540*C*a*c^2*d^2*x^2*e^13 + 180*A*c^3*d^2*x^2*e^13 - 1800*C*a*c^2*d^3*x*e^12 - 600*A*c^3*d^3*x*e^12 + 60*B*a*c^2*x^3*e^15 - 270*B*a*c^2*d*x^2*e^14 + 1080*B*a*c^2*d^2*x*e^13 + 90*C*a^2*c*x^2*e^15 + 90*A*a*c^2*x^2*e^15 - 540*C*a^2*c*d*x*e^14 - 540*A*a*c^2*d*x*e^14 + 180*B*a^2*c*x*e^15)*e^(-18) + 1/2*(15*C*c^3*d^8 - 13*B*c^3*d^7*e + 33*C*a*c^2*d^6*e^2 + 11*A*c^3*d^6*e^2 - 27*B*a*c^2*d^5*e^3 + 21*C*a^2*c*d^4*e^4 + 21*A*a*c^2*d^4*e^4 - 15*B*a^2*c*d^3*e^5 + 3*C*a^3*d^2*e^6 + 9*A*a^2*c*d^2*e^6 - B*a^3*d*e^7 - A*a^3*e^8 + 2*(8*C*c^3*d^7*e - 7*B*c^3*d^6*e^2 + 18*C*a*c^2*d^5*e^3 + 6*A*c^3*d^5*e^3 - 15*B*a*c^2*d^4*e^4 + 12*C*a^2*c*d^3*e^5 + 12*A*a*c^2*d^3*e^5 - 9*B*a^2*c*d^2*e^6 + 2*C*a^3*d*e^7 + 6*A*a^2*c*d*e^7 - B*a^3*e^8)*x)*e^(-9)/(x*e + d)^2","A",0
39,1,111,0,0.174583," ","integrate((b*x^2+a)*(3*b*d*x^2+4*b*c*x-a*d)/(d*x+c)^2,x, algorithm=""giac"")","\frac{{\left(b^{2} - \frac{4 \, b^{2} c}{d x + c} + \frac{6 \, b^{2} c^{2}}{{\left(d x + c\right)}^{2}} + \frac{2 \, a b d^{2}}{{\left(d x + c\right)}^{2}}\right)} {\left(d x + c\right)}^{3}}{d^{4}} + \frac{\frac{b^{2} c^{4} d^{3}}{d x + c} + \frac{2 \, a b c^{2} d^{5}}{d x + c} + \frac{a^{2} d^{7}}{d x + c}}{d^{7}}"," ",0,"(b^2 - 4*b^2*c/(d*x + c) + 6*b^2*c^2/(d*x + c)^2 + 2*a*b*d^2/(d*x + c)^2)*(d*x + c)^3/d^4 + (b^2*c^4*d^3/(d*x + c) + 2*a*b*c^2*d^5/(d*x + c) + a^2*d^7/(d*x + c))/d^7","B",0
40,1,111,0,0.154890," ","integrate((b*x^2+a)*(-a*d+b*x*(3*d*x+4*c))/(d*x+c)^2,x, algorithm=""giac"")","\frac{{\left(b^{2} - \frac{4 \, b^{2} c}{d x + c} + \frac{6 \, b^{2} c^{2}}{{\left(d x + c\right)}^{2}} + \frac{2 \, a b d^{2}}{{\left(d x + c\right)}^{2}}\right)} {\left(d x + c\right)}^{3}}{d^{4}} + \frac{\frac{b^{2} c^{4} d^{3}}{d x + c} + \frac{2 \, a b c^{2} d^{5}}{d x + c} + \frac{a^{2} d^{7}}{d x + c}}{d^{7}}"," ",0,"(b^2 - 4*b^2*c/(d*x + c) + 6*b^2*c^2/(d*x + c)^2 + 2*a*b*d^2/(d*x + c)^2)*(d*x + c)^3/d^4 + (b^2*c^4*d^3/(d*x + c) + 2*a*b*c^2*d^5/(d*x + c) + a^2*d^7/(d*x + c))/d^7","B",0
41,1,216,0,0.182962," ","integrate((b*x^2+a)^2*(5*b*d*x^2+6*b*c*x-a*d)/(d*x+c)^2,x, algorithm=""giac"")","\frac{{\left(b^{3} - \frac{6 \, b^{3} c}{d x + c} + \frac{15 \, b^{3} c^{2}}{{\left(d x + c\right)}^{2}} - \frac{20 \, b^{3} c^{3}}{{\left(d x + c\right)}^{3}} + \frac{15 \, b^{3} c^{4}}{{\left(d x + c\right)}^{4}} + \frac{3 \, a b^{2} d^{2}}{{\left(d x + c\right)}^{2}} - \frac{12 \, a b^{2} c d^{2}}{{\left(d x + c\right)}^{3}} + \frac{18 \, a b^{2} c^{2} d^{2}}{{\left(d x + c\right)}^{4}} + \frac{3 \, a^{2} b d^{4}}{{\left(d x + c\right)}^{4}}\right)} {\left(d x + c\right)}^{5}}{d^{6}} + \frac{\frac{b^{3} c^{6} d^{5}}{d x + c} + \frac{3 \, a b^{2} c^{4} d^{7}}{d x + c} + \frac{3 \, a^{2} b c^{2} d^{9}}{d x + c} + \frac{a^{3} d^{11}}{d x + c}}{d^{11}}"," ",0,"(b^3 - 6*b^3*c/(d*x + c) + 15*b^3*c^2/(d*x + c)^2 - 20*b^3*c^3/(d*x + c)^3 + 15*b^3*c^4/(d*x + c)^4 + 3*a*b^2*d^2/(d*x + c)^2 - 12*a*b^2*c*d^2/(d*x + c)^3 + 18*a*b^2*c^2*d^2/(d*x + c)^4 + 3*a^2*b*d^4/(d*x + c)^4)*(d*x + c)^5/d^6 + (b^3*c^6*d^5/(d*x + c) + 3*a*b^2*c^4*d^7/(d*x + c) + 3*a^2*b*c^2*d^9/(d*x + c) + a^3*d^11/(d*x + c))/d^11","B",0
42,1,216,0,0.198775," ","integrate((b*x^2+a)^2*(-a*d+b*x*(5*d*x+6*c))/(d*x+c)^2,x, algorithm=""giac"")","\frac{{\left(b^{3} - \frac{6 \, b^{3} c}{d x + c} + \frac{15 \, b^{3} c^{2}}{{\left(d x + c\right)}^{2}} - \frac{20 \, b^{3} c^{3}}{{\left(d x + c\right)}^{3}} + \frac{15 \, b^{3} c^{4}}{{\left(d x + c\right)}^{4}} + \frac{3 \, a b^{2} d^{2}}{{\left(d x + c\right)}^{2}} - \frac{12 \, a b^{2} c d^{2}}{{\left(d x + c\right)}^{3}} + \frac{18 \, a b^{2} c^{2} d^{2}}{{\left(d x + c\right)}^{4}} + \frac{3 \, a^{2} b d^{4}}{{\left(d x + c\right)}^{4}}\right)} {\left(d x + c\right)}^{5}}{d^{6}} + \frac{\frac{b^{3} c^{6} d^{5}}{d x + c} + \frac{3 \, a b^{2} c^{4} d^{7}}{d x + c} + \frac{3 \, a^{2} b c^{2} d^{9}}{d x + c} + \frac{a^{3} d^{11}}{d x + c}}{d^{11}}"," ",0,"(b^3 - 6*b^3*c/(d*x + c) + 15*b^3*c^2/(d*x + c)^2 - 20*b^3*c^3/(d*x + c)^3 + 15*b^3*c^4/(d*x + c)^4 + 3*a*b^2*d^2/(d*x + c)^2 - 12*a*b^2*c*d^2/(d*x + c)^3 + 18*a*b^2*c^2*d^2/(d*x + c)^4 + 3*a^2*b*d^4/(d*x + c)^4)*(d*x + c)^5/d^6 + (b^3*c^6*d^5/(d*x + c) + 3*a*b^2*c^4*d^7/(d*x + c) + 3*a^2*b*c^2*d^9/(d*x + c) + a^3*d^11/(d*x + c))/d^11","B",0
43,1,279,0,0.170365," ","integrate((e*x+d)^3*(C*x^2+B*x+A)/(c*x^2+a),x, algorithm=""giac"")","-\frac{{\left(C a c d^{3} - A c^{2} d^{3} + 3 \, B a c d^{2} e - 3 \, C a^{2} d e^{2} + 3 \, A a c d e^{2} - B a^{2} e^{3}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{\sqrt{a c} c^{2}} + \frac{{\left(B c^{2} d^{3} - 3 \, C a c d^{2} e + 3 \, A c^{2} d^{2} e - 3 \, B a c d e^{2} + C a^{2} e^{3} - A a c e^{3}\right)} \log\left(c x^{2} + a\right)}{2 \, c^{3}} + \frac{3 \, C c^{3} x^{4} e^{3} + 12 \, C c^{3} d x^{3} e^{2} + 18 \, C c^{3} d^{2} x^{2} e + 12 \, C c^{3} d^{3} x + 4 \, B c^{3} x^{3} e^{3} + 18 \, B c^{3} d x^{2} e^{2} + 36 \, B c^{3} d^{2} x e - 6 \, C a c^{2} x^{2} e^{3} + 6 \, A c^{3} x^{2} e^{3} - 36 \, C a c^{2} d x e^{2} + 36 \, A c^{3} d x e^{2} - 12 \, B a c^{2} x e^{3}}{12 \, c^{4}}"," ",0,"-(C*a*c*d^3 - A*c^2*d^3 + 3*B*a*c*d^2*e - 3*C*a^2*d*e^2 + 3*A*a*c*d*e^2 - B*a^2*e^3)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*c^2) + 1/2*(B*c^2*d^3 - 3*C*a*c*d^2*e + 3*A*c^2*d^2*e - 3*B*a*c*d*e^2 + C*a^2*e^3 - A*a*c*e^3)*log(c*x^2 + a)/c^3 + 1/12*(3*C*c^3*x^4*e^3 + 12*C*c^3*d*x^3*e^2 + 18*C*c^3*d^2*x^2*e + 12*C*c^3*d^3*x + 4*B*c^3*x^3*e^3 + 18*B*c^3*d*x^2*e^2 + 36*B*c^3*d^2*x*e - 6*C*a*c^2*x^2*e^3 + 6*A*c^3*x^2*e^3 - 36*C*a*c^2*d*x*e^2 + 36*A*c^3*d*x*e^2 - 12*B*a*c^2*x*e^3)/c^4","A",0
44,1,176,0,0.156920," ","integrate((e*x+d)^2*(C*x^2+B*x+A)/(c*x^2+a),x, algorithm=""giac"")","\frac{{\left(B c d^{2} - 2 \, C a d e + 2 \, A c d e - B a e^{2}\right)} \log\left(c x^{2} + a\right)}{2 \, c^{2}} - \frac{{\left(C a c d^{2} - A c^{2} d^{2} + 2 \, B a c d e - C a^{2} e^{2} + A a c e^{2}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{\sqrt{a c} c^{2}} + \frac{2 \, C c^{2} x^{3} e^{2} + 6 \, C c^{2} d x^{2} e + 6 \, C c^{2} d^{2} x + 3 \, B c^{2} x^{2} e^{2} + 12 \, B c^{2} d x e - 6 \, C a c x e^{2} + 6 \, A c^{2} x e^{2}}{6 \, c^{3}}"," ",0,"1/2*(B*c*d^2 - 2*C*a*d*e + 2*A*c*d*e - B*a*e^2)*log(c*x^2 + a)/c^2 - (C*a*c*d^2 - A*c^2*d^2 + 2*B*a*c*d*e - C*a^2*e^2 + A*a*c*e^2)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*c^2) + 1/6*(2*C*c^2*x^3*e^2 + 6*C*c^2*d*x^2*e + 6*C*c^2*d^2*x + 3*B*c^2*x^2*e^2 + 12*B*c^2*d*x*e - 6*C*a*c*x*e^2 + 6*A*c^2*x*e^2)/c^3","A",0
45,1,91,0,0.158162," ","integrate((e*x+d)*(C*x^2+B*x+A)/(c*x^2+a),x, algorithm=""giac"")","-\frac{{\left(C a d - A c d + B a e\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{\sqrt{a c} c} + \frac{{\left(B c d - C a e + A c e\right)} \log\left(c x^{2} + a\right)}{2 \, c^{2}} + \frac{C c x^{2} e + 2 \, C c d x + 2 \, B c x e}{2 \, c^{2}}"," ",0,"-(C*a*d - A*c*d + B*a*e)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*c) + 1/2*(B*c*d - C*a*e + A*c*e)*log(c*x^2 + a)/c^2 + 1/2*(C*c*x^2*e + 2*C*c*d*x + 2*B*c*x*e)/c^2","A",0
46,1,48,0,0.158545," ","integrate((C*x^2+B*x+A)/(c*x^2+a),x, algorithm=""giac"")","\frac{C x}{c} + \frac{B \log\left(c x^{2} + a\right)}{2 \, c} - \frac{{\left(C a - A c\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{\sqrt{a c} c}"," ",0,"C*x/c + 1/2*B*log(c*x^2 + a)/c - (C*a - A*c)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*c)","A",0
47,1,125,0,0.158599," ","integrate((C*x^2+B*x+A)/(e*x+d)/(c*x^2+a),x, algorithm=""giac"")","\frac{{\left(B c d + C a e - A c e\right)} \log\left(c x^{2} + a\right)}{2 \, {\left(c^{2} d^{2} + a c e^{2}\right)}} + \frac{{\left(C d^{2} - B d e + A e^{2}\right)} \log\left({\left| x e + d \right|}\right)}{c d^{2} e + a e^{3}} - \frac{{\left(C a d - A c d - B a e\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{{\left(c d^{2} + a e^{2}\right)} \sqrt{a c}}"," ",0,"1/2*(B*c*d + C*a*e - A*c*e)*log(c*x^2 + a)/(c^2*d^2 + a*c*e^2) + (C*d^2 - B*d*e + A*e^2)*log(abs(x*e + d))/(c*d^2*e + a*e^3) - (C*a*d - A*c*d - B*a*e)*arctan(c*x/sqrt(a*c))/((c*d^2 + a*e^2)*sqrt(a*c))","A",0
48,1,270,0,0.170270," ","integrate((C*x^2+B*x+A)/(e*x+d)^2/(c*x^2+a),x, algorithm=""giac"")","-\frac{{\left(C a c d^{2} e^{2} - A c^{2} d^{2} e^{2} - 2 \, B a c d e^{3} - C a^{2} e^{4} + A a c e^{4}\right)} \arctan\left(\frac{{\left(c d - \frac{c d^{2}}{x e + d} - \frac{a e^{2}}{x e + d}\right)} e^{\left(-1\right)}}{\sqrt{a c}}\right) e^{\left(-2\right)}}{{\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \sqrt{a c}} + \frac{{\left(B c d^{2} + 2 \, C a d e - 2 \, A c d e - B a e^{2}\right)} \log\left(c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)}{2 \, {\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)}} - \frac{\frac{C d^{2} e}{x e + d} - \frac{B d e^{2}}{x e + d} + \frac{A e^{3}}{x e + d}}{c d^{2} e^{2} + a e^{4}}"," ",0,"-(C*a*c*d^2*e^2 - A*c^2*d^2*e^2 - 2*B*a*c*d*e^3 - C*a^2*e^4 + A*a*c*e^4)*arctan((c*d - c*d^2/(x*e + d) - a*e^2/(x*e + d))*e^(-1)/sqrt(a*c))*e^(-2)/((c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(a*c)) + 1/2*(B*c*d^2 + 2*C*a*d*e - 2*A*c*d*e - B*a*e^2)*log(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + a*e^2/(x*e + d)^2)/(c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4) - (C*d^2*e/(x*e + d) - B*d*e^2/(x*e + d) + A*e^3/(x*e + d))/(c*d^2*e^2 + a*e^4)","A",0
49,1,489,0,0.197416," ","integrate((C*x^2+B*x+A)/(e*x+d)^3/(c*x^2+a),x, algorithm=""giac"")","\frac{{\left(B c^{2} d^{3} + 3 \, C a c d^{2} e - 3 \, A c^{2} d^{2} e - 3 \, B a c d e^{2} - C a^{2} e^{3} + A a c e^{3}\right)} \log\left(c x^{2} + a\right)}{2 \, {\left(c^{3} d^{6} + 3 \, a c^{2} d^{4} e^{2} + 3 \, a^{2} c d^{2} e^{4} + a^{3} e^{6}\right)}} - \frac{{\left(B c^{2} d^{3} e + 3 \, C a c d^{2} e^{2} - 3 \, A c^{2} d^{2} e^{2} - 3 \, B a c d e^{3} - C a^{2} e^{4} + A a c e^{4}\right)} \log\left({\left| x e + d \right|}\right)}{c^{3} d^{6} e + 3 \, a c^{2} d^{4} e^{3} + 3 \, a^{2} c d^{2} e^{5} + a^{3} e^{7}} - \frac{{\left(C a c^{2} d^{3} - A c^{3} d^{3} - 3 \, B a c^{2} d^{2} e - 3 \, C a^{2} c d e^{2} + 3 \, A a c^{2} d e^{2} + B a^{2} c e^{3}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{{\left(c^{3} d^{6} + 3 \, a c^{2} d^{4} e^{2} + 3 \, a^{2} c d^{2} e^{4} + a^{3} e^{6}\right)} \sqrt{a c}} - \frac{{\left(C c^{2} d^{6} - 3 \, B c^{2} d^{5} e - 2 \, C a c d^{4} e^{2} + 5 \, A c^{2} d^{4} e^{2} - 2 \, B a c d^{3} e^{3} - 3 \, C a^{2} d^{2} e^{4} + 6 \, A a c d^{2} e^{4} + B a^{2} d e^{5} + A a^{2} e^{6} - 2 \, {\left(B c^{2} d^{4} e^{2} + 2 \, C a c d^{3} e^{3} - 2 \, A c^{2} d^{3} e^{3} + 2 \, C a^{2} d e^{5} - 2 \, A a c d e^{5} - B a^{2} e^{6}\right)} x\right)} e^{\left(-1\right)}}{2 \, {\left(c d^{2} + a e^{2}\right)}^{3} {\left(x e + d\right)}^{2}}"," ",0,"1/2*(B*c^2*d^3 + 3*C*a*c*d^2*e - 3*A*c^2*d^2*e - 3*B*a*c*d*e^2 - C*a^2*e^3 + A*a*c*e^3)*log(c*x^2 + a)/(c^3*d^6 + 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 + a^3*e^6) - (B*c^2*d^3*e + 3*C*a*c*d^2*e^2 - 3*A*c^2*d^2*e^2 - 3*B*a*c*d*e^3 - C*a^2*e^4 + A*a*c*e^4)*log(abs(x*e + d))/(c^3*d^6*e + 3*a*c^2*d^4*e^3 + 3*a^2*c*d^2*e^5 + a^3*e^7) - (C*a*c^2*d^3 - A*c^3*d^3 - 3*B*a*c^2*d^2*e - 3*C*a^2*c*d*e^2 + 3*A*a*c^2*d*e^2 + B*a^2*c*e^3)*arctan(c*x/sqrt(a*c))/((c^3*d^6 + 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 + a^3*e^6)*sqrt(a*c)) - 1/2*(C*c^2*d^6 - 3*B*c^2*d^5*e - 2*C*a*c*d^4*e^2 + 5*A*c^2*d^4*e^2 - 2*B*a*c*d^3*e^3 - 3*C*a^2*d^2*e^4 + 6*A*a*c*d^2*e^4 + B*a^2*d*e^5 + A*a^2*e^6 - 2*(B*c^2*d^4*e^2 + 2*C*a*c*d^3*e^3 - 2*A*c^2*d^3*e^3 + 2*C*a^2*d*e^5 - 2*A*a*c*d*e^5 - B*a^2*e^6)*x)*e^(-1)/((c*d^2 + a*e^2)^3*(x*e + d)^2)","A",0
50,1,289,0,0.174247," ","integrate((e*x+d)^3*(C*x^2+B*x+A)/(c*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left(3 \, C c d^{2} e + 3 \, B c d e^{2} - 2 \, C a e^{3} + A c e^{3}\right)} \log\left(c x^{2} + a\right)}{2 \, c^{3}} + \frac{{\left(C a c d^{3} + A c^{2} d^{3} + 3 \, B a c d^{2} e - 9 \, C a^{2} d e^{2} + 3 \, A a c d e^{2} - 3 \, B a^{2} e^{3}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{2 \, \sqrt{a c} a c^{2}} + \frac{C c^{2} x^{2} e^{3} + 6 \, C c^{2} d x e^{2} + 2 \, B c^{2} x e^{3}}{2 \, c^{4}} - \frac{B a c^{2} d^{3} - 3 \, C a^{2} c d^{2} e + 3 \, A a c^{2} d^{2} e - 3 \, B a^{2} c d e^{2} + C a^{3} e^{3} - A a^{2} c e^{3} + {\left(C a c^{2} d^{3} - A c^{3} d^{3} + 3 \, B a c^{2} d^{2} e - 3 \, C a^{2} c d e^{2} + 3 \, A a c^{2} d e^{2} - B a^{2} c e^{3}\right)} x}{2 \, {\left(c x^{2} + a\right)} a c^{3}}"," ",0,"1/2*(3*C*c*d^2*e + 3*B*c*d*e^2 - 2*C*a*e^3 + A*c*e^3)*log(c*x^2 + a)/c^3 + 1/2*(C*a*c*d^3 + A*c^2*d^3 + 3*B*a*c*d^2*e - 9*C*a^2*d*e^2 + 3*A*a*c*d*e^2 - 3*B*a^2*e^3)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a*c^2) + 1/2*(C*c^2*x^2*e^3 + 6*C*c^2*d*x*e^2 + 2*B*c^2*x*e^3)/c^4 - 1/2*(B*a*c^2*d^3 - 3*C*a^2*c*d^2*e + 3*A*a*c^2*d^2*e - 3*B*a^2*c*d*e^2 + C*a^3*e^3 - A*a^2*c*e^3 + (C*a*c^2*d^3 - A*c^3*d^3 + 3*B*a*c^2*d^2*e - 3*C*a^2*c*d*e^2 + 3*A*a*c^2*d*e^2 - B*a^2*c*e^3)*x)/((c*x^2 + a)*a*c^3)","A",0
51,1,184,0,0.170177," ","integrate((e*x+d)^2*(C*x^2+B*x+A)/(c*x^2+a)^2,x, algorithm=""giac"")","\frac{C x e^{2}}{c^{2}} + \frac{{\left(2 \, C d e + B e^{2}\right)} \log\left(c x^{2} + a\right)}{2 \, c^{2}} + \frac{{\left(C a c d^{2} + A c^{2} d^{2} + 2 \, B a c d e - 3 \, C a^{2} e^{2} + A a c e^{2}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{2 \, \sqrt{a c} a c^{2}} - \frac{B a c d^{2} - 2 \, C a^{2} d e + 2 \, A a c d e - B a^{2} e^{2} + {\left(C a c d^{2} - A c^{2} d^{2} + 2 \, B a c d e - C a^{2} e^{2} + A a c e^{2}\right)} x}{2 \, {\left(c x^{2} + a\right)} a c^{2}}"," ",0,"C*x*e^2/c^2 + 1/2*(2*C*d*e + B*e^2)*log(c*x^2 + a)/c^2 + 1/2*(C*a*c*d^2 + A*c^2*d^2 + 2*B*a*c*d*e - 3*C*a^2*e^2 + A*a*c*e^2)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a*c^2) - 1/2*(B*a*c*d^2 - 2*C*a^2*d*e + 2*A*a*c*d*e - B*a^2*e^2 + (C*a*c*d^2 - A*c^2*d^2 + 2*B*a*c*d*e - C*a^2*e^2 + A*a*c*e^2)*x)/((c*x^2 + a)*a*c^2)","A",0
52,1,112,0,0.218319," ","integrate((e*x+d)*(C*x^2+B*x+A)/(c*x^2+a)^2,x, algorithm=""giac"")","\frac{C e \log\left(c x^{2} + a\right)}{2 \, c^{2}} + \frac{{\left(C a d + A c d + B a e\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{2 \, \sqrt{a c} a c} - \frac{{\left(C a d - A c d + B a e\right)} x + \frac{B a c d - C a^{2} e + A a c e}{c}}{2 \, {\left(c x^{2} + a\right)} a c}"," ",0,"1/2*C*e*log(c*x^2 + a)/c^2 + 1/2*(C*a*d + A*c*d + B*a*e)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a*c) - 1/2*((C*a*d - A*c*d + B*a*e)*x + (B*a*c*d - C*a^2*e + A*a*c*e)/c)/((c*x^2 + a)*a*c)","A",0
53,1,60,0,0.182590," ","integrate((C*x^2+B*x+A)/(c*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left(C a + A c\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{2 \, \sqrt{a c} a c} - \frac{C a x - A c x + B a}{2 \, {\left(c x^{2} + a\right)} a c}"," ",0,"1/2*(C*a + A*c)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a*c) - 1/2*(C*a*x - A*c*x + B*a)/((c*x^2 + a)*a*c)","A",0
54,1,350,0,0.193367," ","integrate((C*x^2+B*x+A)/(e*x+d)/(c*x^2+a)^2,x, algorithm=""giac"")","-\frac{{\left(C d^{2} e - B d e^{2} + A e^{3}\right)} \log\left(c x^{2} + a\right)}{2 \, {\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)}} + \frac{{\left(C d^{2} e^{2} - B d e^{3} + A e^{4}\right)} \log\left({\left| x e + d \right|}\right)}{c^{2} d^{4} e + 2 \, a c d^{2} e^{3} + a^{2} e^{5}} + \frac{{\left(C a c d^{3} + A c^{2} d^{3} - B a c d^{2} e - C a^{2} d e^{2} + 3 \, A a c d e^{2} + B a^{2} e^{3}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{2 \, {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} \sqrt{a c}} - \frac{B a c^{2} d^{3} + C a^{2} c d^{2} e - A a c^{2} d^{2} e + B a^{2} c d e^{2} + C a^{3} e^{3} - A a^{2} c e^{3} + {\left(C a c^{2} d^{3} - A c^{3} d^{3} - B a c^{2} d^{2} e + C a^{2} c d e^{2} - A a c^{2} d e^{2} - B a^{2} c e^{3}\right)} x}{2 \, {\left(c d^{2} + a e^{2}\right)}^{2} {\left(c x^{2} + a\right)} a c}"," ",0,"-1/2*(C*d^2*e - B*d*e^2 + A*e^3)*log(c*x^2 + a)/(c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4) + (C*d^2*e^2 - B*d*e^3 + A*e^4)*log(abs(x*e + d))/(c^2*d^4*e + 2*a*c*d^2*e^3 + a^2*e^5) + 1/2*(C*a*c*d^3 + A*c^2*d^3 - B*a*c*d^2*e - C*a^2*d*e^2 + 3*A*a*c*d*e^2 + B*a^2*e^3)*arctan(c*x/sqrt(a*c))/((a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4)*sqrt(a*c)) - 1/2*(B*a*c^2*d^3 + C*a^2*c*d^2*e - A*a*c^2*d^2*e + B*a^2*c*d*e^2 + C*a^3*e^3 - A*a^2*c*e^3 + (C*a*c^2*d^3 - A*c^3*d^3 - B*a*c^2*d^2*e + C*a^2*c*d*e^2 - A*a*c^2*d*e^2 - B*a^2*c*e^3)*x)/((c*d^2 + a*e^2)^2*(c*x^2 + a)*a*c)","A",0
55,1,608,0,0.189607," ","integrate((C*x^2+B*x+A)/(e*x+d)^2/(c*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left(C a c^{2} d^{4} e^{2} + A c^{3} d^{4} e^{2} - 2 \, B a c^{2} d^{3} e^{3} - 6 \, C a^{2} c d^{2} e^{4} + 6 \, A a c^{2} d^{2} e^{4} + 6 \, B a^{2} c d e^{5} + C a^{3} e^{6} - 3 \, A a^{2} c e^{6}\right)} \arctan\left(\frac{{\left(c d - \frac{c d^{2}}{x e + d} - \frac{a e^{2}}{x e + d}\right)} e^{\left(-1\right)}}{\sqrt{a c}}\right) e^{\left(-2\right)}}{2 \, {\left(a c^{3} d^{6} + 3 \, a^{2} c^{2} d^{4} e^{2} + 3 \, a^{3} c d^{2} e^{4} + a^{4} e^{6}\right)} \sqrt{a c}} - \frac{{\left(2 \, C c d^{3} e - 3 \, B c d^{2} e^{2} - 2 \, C a d e^{3} + 4 \, A c d e^{3} + B a e^{4}\right)} \log\left(c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)}{2 \, {\left(c^{3} d^{6} + 3 \, a c^{2} d^{4} e^{2} + 3 \, a^{2} c d^{2} e^{4} + a^{3} e^{6}\right)}} - \frac{\frac{C d^{2} e^{5}}{x e + d} - \frac{B d e^{6}}{x e + d} + \frac{A e^{7}}{x e + d}}{c^{2} d^{4} e^{4} + 2 \, a c d^{2} e^{6} + a^{2} e^{8}} - \frac{\frac{C a c^{2} d^{3} e - A c^{3} d^{3} e - 3 \, B a c^{2} d^{2} e^{2} - 3 \, C a^{2} c d e^{3} + 3 \, A a c^{2} d e^{3} + B a^{2} c e^{4}}{c d^{2} + a e^{2}} - \frac{{\left(C a c^{2} d^{4} e^{2} - A c^{3} d^{4} e^{2} - 4 \, B a c^{2} d^{3} e^{3} - 6 \, C a^{2} c d^{2} e^{4} + 6 \, A a c^{2} d^{2} e^{4} + 4 \, B a^{2} c d e^{5} + C a^{3} e^{6} - A a^{2} c e^{6}\right)} e^{\left(-1\right)}}{{\left(c d^{2} + a e^{2}\right)} {\left(x e + d\right)}}}{2 \, {\left(c d^{2} + a e^{2}\right)}^{2} a {\left(c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)}}"," ",0,"1/2*(C*a*c^2*d^4*e^2 + A*c^3*d^4*e^2 - 2*B*a*c^2*d^3*e^3 - 6*C*a^2*c*d^2*e^4 + 6*A*a*c^2*d^2*e^4 + 6*B*a^2*c*d*e^5 + C*a^3*e^6 - 3*A*a^2*c*e^6)*arctan((c*d - c*d^2/(x*e + d) - a*e^2/(x*e + d))*e^(-1)/sqrt(a*c))*e^(-2)/((a*c^3*d^6 + 3*a^2*c^2*d^4*e^2 + 3*a^3*c*d^2*e^4 + a^4*e^6)*sqrt(a*c)) - 1/2*(2*C*c*d^3*e - 3*B*c*d^2*e^2 - 2*C*a*d*e^3 + 4*A*c*d*e^3 + B*a*e^4)*log(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + a*e^2/(x*e + d)^2)/(c^3*d^6 + 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 + a^3*e^6) - (C*d^2*e^5/(x*e + d) - B*d*e^6/(x*e + d) + A*e^7/(x*e + d))/(c^2*d^4*e^4 + 2*a*c*d^2*e^6 + a^2*e^8) - 1/2*((C*a*c^2*d^3*e - A*c^3*d^3*e - 3*B*a*c^2*d^2*e^2 - 3*C*a^2*c*d*e^3 + 3*A*a*c^2*d*e^3 + B*a^2*c*e^4)/(c*d^2 + a*e^2) - (C*a*c^2*d^4*e^2 - A*c^3*d^4*e^2 - 4*B*a*c^2*d^3*e^3 - 6*C*a^2*c*d^2*e^4 + 6*A*a*c^2*d^2*e^4 + 4*B*a^2*c*d*e^5 + C*a^3*e^6 - A*a^2*c*e^6)*e^(-1)/((c*d^2 + a*e^2)*(x*e + d)))/((c*d^2 + a*e^2)^2*a*(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + a*e^2/(x*e + d)^2))","A",0
56,1,957,0,0.185434," ","integrate((C*x^2+B*x+A)/(e*x+d)^3/(c*x^2+a)^2,x, algorithm=""giac"")","-\frac{{\left(3 \, C c^{2} d^{4} e - 6 \, B c^{2} d^{3} e^{2} - 8 \, C a c d^{2} e^{3} + 10 \, A c^{2} d^{2} e^{3} + 6 \, B a c d e^{4} + C a^{2} e^{5} - 2 \, A a c e^{5}\right)} \log\left(c x^{2} + a\right)}{2 \, {\left(c^{4} d^{8} + 4 \, a c^{3} d^{6} e^{2} + 6 \, a^{2} c^{2} d^{4} e^{4} + 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}\right)}} + \frac{{\left(3 \, C c^{2} d^{4} e^{2} - 6 \, B c^{2} d^{3} e^{3} - 8 \, C a c d^{2} e^{4} + 10 \, A c^{2} d^{2} e^{4} + 6 \, B a c d e^{5} + C a^{2} e^{6} - 2 \, A a c e^{6}\right)} \log\left({\left| x e + d \right|}\right)}{c^{4} d^{8} e + 4 \, a c^{3} d^{6} e^{3} + 6 \, a^{2} c^{2} d^{4} e^{5} + 4 \, a^{3} c d^{2} e^{7} + a^{4} e^{9}} + \frac{{\left(C a c^{3} d^{5} + A c^{4} d^{5} - 3 \, B a c^{3} d^{4} e - 14 \, C a^{2} c^{2} d^{3} e^{2} + 10 \, A a c^{3} d^{3} e^{2} + 18 \, B a^{2} c^{2} d^{2} e^{3} + 9 \, C a^{3} c d e^{4} - 15 \, A a^{2} c^{2} d e^{4} - 3 \, B a^{3} c e^{5}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{2 \, {\left(a c^{4} d^{8} + 4 \, a^{2} c^{3} d^{6} e^{2} + 6 \, a^{3} c^{2} d^{4} e^{4} + 4 \, a^{4} c d^{2} e^{6} + a^{5} e^{8}\right)} \sqrt{a c}} - \frac{B a c^{3} d^{7} + 8 \, C a^{2} c^{2} d^{6} e - 3 \, A a c^{3} d^{6} e - 9 \, B a^{2} c^{2} d^{5} e^{2} + 4 \, C a^{3} c d^{4} e^{3} + 7 \, A a^{2} c^{2} d^{4} e^{3} - 9 \, B a^{3} c d^{3} e^{4} - 4 \, C a^{4} d^{2} e^{5} + 11 \, A a^{3} c d^{2} e^{5} + B a^{4} d e^{6} + A a^{4} e^{7} + {\left(5 \, C a c^{3} d^{5} e^{2} - A c^{4} d^{5} e^{2} - 9 \, B a c^{3} d^{4} e^{3} - 2 \, C a^{2} c^{2} d^{3} e^{4} + 10 \, A a c^{3} d^{3} e^{4} - 6 \, B a^{2} c^{2} d^{2} e^{5} - 7 \, C a^{3} c d e^{6} + 11 \, A a^{2} c^{2} d e^{6} + 3 \, B a^{3} c e^{7}\right)} x^{3} + {\left(7 \, C a c^{3} d^{6} e - 2 \, A c^{4} d^{6} e - 12 \, B a c^{3} d^{5} e^{2} + C a^{2} c^{2} d^{4} e^{3} + 10 \, A a c^{3} d^{4} e^{3} - 12 \, B a^{2} c^{2} d^{3} e^{4} - 7 \, C a^{3} c d^{2} e^{5} + 14 \, A a^{2} c^{2} d^{2} e^{5} - C a^{4} e^{7} + 2 \, A a^{3} c e^{7}\right)} x^{2} + {\left(C a c^{3} d^{7} - A c^{4} d^{7} - B a c^{3} d^{6} e + 8 \, C a^{2} c^{2} d^{5} e^{2} - 4 \, A a c^{3} d^{5} e^{2} - 12 \, B a^{2} c^{2} d^{4} e^{3} + C a^{3} c d^{3} e^{4} + 7 \, A a^{2} c^{2} d^{3} e^{4} - 9 \, B a^{3} c d^{2} e^{5} - 6 \, C a^{4} d e^{6} + 10 \, A a^{3} c d e^{6} + 2 \, B a^{4} e^{7}\right)} x}{2 \, {\left(c d^{2} + a e^{2}\right)}^{4} {\left(c x^{2} + a\right)} {\left(x e + d\right)}^{2} a}"," ",0,"-1/2*(3*C*c^2*d^4*e - 6*B*c^2*d^3*e^2 - 8*C*a*c*d^2*e^3 + 10*A*c^2*d^2*e^3 + 6*B*a*c*d*e^4 + C*a^2*e^5 - 2*A*a*c*e^5)*log(c*x^2 + a)/(c^4*d^8 + 4*a*c^3*d^6*e^2 + 6*a^2*c^2*d^4*e^4 + 4*a^3*c*d^2*e^6 + a^4*e^8) + (3*C*c^2*d^4*e^2 - 6*B*c^2*d^3*e^3 - 8*C*a*c*d^2*e^4 + 10*A*c^2*d^2*e^4 + 6*B*a*c*d*e^5 + C*a^2*e^6 - 2*A*a*c*e^6)*log(abs(x*e + d))/(c^4*d^8*e + 4*a*c^3*d^6*e^3 + 6*a^2*c^2*d^4*e^5 + 4*a^3*c*d^2*e^7 + a^4*e^9) + 1/2*(C*a*c^3*d^5 + A*c^4*d^5 - 3*B*a*c^3*d^4*e - 14*C*a^2*c^2*d^3*e^2 + 10*A*a*c^3*d^3*e^2 + 18*B*a^2*c^2*d^2*e^3 + 9*C*a^3*c*d*e^4 - 15*A*a^2*c^2*d*e^4 - 3*B*a^3*c*e^5)*arctan(c*x/sqrt(a*c))/((a*c^4*d^8 + 4*a^2*c^3*d^6*e^2 + 6*a^3*c^2*d^4*e^4 + 4*a^4*c*d^2*e^6 + a^5*e^8)*sqrt(a*c)) - 1/2*(B*a*c^3*d^7 + 8*C*a^2*c^2*d^6*e - 3*A*a*c^3*d^6*e - 9*B*a^2*c^2*d^5*e^2 + 4*C*a^3*c*d^4*e^3 + 7*A*a^2*c^2*d^4*e^3 - 9*B*a^3*c*d^3*e^4 - 4*C*a^4*d^2*e^5 + 11*A*a^3*c*d^2*e^5 + B*a^4*d*e^6 + A*a^4*e^7 + (5*C*a*c^3*d^5*e^2 - A*c^4*d^5*e^2 - 9*B*a*c^3*d^4*e^3 - 2*C*a^2*c^2*d^3*e^4 + 10*A*a*c^3*d^3*e^4 - 6*B*a^2*c^2*d^2*e^5 - 7*C*a^3*c*d*e^6 + 11*A*a^2*c^2*d*e^6 + 3*B*a^3*c*e^7)*x^3 + (7*C*a*c^3*d^6*e - 2*A*c^4*d^6*e - 12*B*a*c^3*d^5*e^2 + C*a^2*c^2*d^4*e^3 + 10*A*a*c^3*d^4*e^3 - 12*B*a^2*c^2*d^3*e^4 - 7*C*a^3*c*d^2*e^5 + 14*A*a^2*c^2*d^2*e^5 - C*a^4*e^7 + 2*A*a^3*c*e^7)*x^2 + (C*a*c^3*d^7 - A*c^4*d^7 - B*a*c^3*d^6*e + 8*C*a^2*c^2*d^5*e^2 - 4*A*a*c^3*d^5*e^2 - 12*B*a^2*c^2*d^4*e^3 + C*a^3*c*d^3*e^4 + 7*A*a^2*c^2*d^3*e^4 - 9*B*a^3*c*d^2*e^5 - 6*C*a^4*d*e^6 + 10*A*a^3*c*d*e^6 + 2*B*a^4*e^7)*x)/((c*d^2 + a*e^2)^4*(c*x^2 + a)*(x*e + d)^2*a)","A",0
57,1,348,0,0.268941," ","integrate((e*x+d)^3*(C*x^2+B*x+A)/(c*x^2+a)^3,x, algorithm=""giac"")","\frac{C e^{3} \log\left(c x^{2} + a\right)}{2 \, c^{3}} + \frac{{\left(C a c d^{3} + 3 \, A c^{2} d^{3} + 3 \, B a c d^{2} e + 9 \, C a^{2} d e^{2} + 3 \, A a c d e^{2} + 3 \, B a^{2} e^{3}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{8 \, \sqrt{a c} a^{2} c^{2}} + \frac{{\left(C a c^{2} d^{3} + 3 \, A c^{3} d^{3} + 3 \, B a c^{2} d^{2} e - 15 \, C a^{2} c d e^{2} + 3 \, A a c^{2} d e^{2} - 5 \, B a^{2} c e^{3}\right)} x^{3} - 4 \, {\left(3 \, C a^{2} c d^{2} e + 3 \, B a^{2} c d e^{2} - 2 \, C a^{3} e^{3} + A a^{2} c e^{3}\right)} x^{2} - {\left(C a^{2} c d^{3} - 5 \, A a c^{2} d^{3} + 3 \, B a^{2} c d^{2} e + 9 \, C a^{3} d e^{2} + 3 \, A a^{2} c d e^{2} + 3 \, B a^{3} e^{3}\right)} x - \frac{2 \, {\left(B a^{2} c^{2} d^{3} + 3 \, C a^{3} c d^{2} e + 3 \, A a^{2} c^{2} d^{2} e + 3 \, B a^{3} c d e^{2} - 3 \, C a^{4} e^{3} + A a^{3} c e^{3}\right)}}{c}}{8 \, {\left(c x^{2} + a\right)}^{2} a^{2} c^{2}}"," ",0,"1/2*C*e^3*log(c*x^2 + a)/c^3 + 1/8*(C*a*c*d^3 + 3*A*c^2*d^3 + 3*B*a*c*d^2*e + 9*C*a^2*d*e^2 + 3*A*a*c*d*e^2 + 3*B*a^2*e^3)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a^2*c^2) + 1/8*((C*a*c^2*d^3 + 3*A*c^3*d^3 + 3*B*a*c^2*d^2*e - 15*C*a^2*c*d*e^2 + 3*A*a*c^2*d*e^2 - 5*B*a^2*c*e^3)*x^3 - 4*(3*C*a^2*c*d^2*e + 3*B*a^2*c*d*e^2 - 2*C*a^3*e^3 + A*a^2*c*e^3)*x^2 - (C*a^2*c*d^3 - 5*A*a*c^2*d^3 + 3*B*a^2*c*d^2*e + 9*C*a^3*d*e^2 + 3*A*a^2*c*d*e^2 + 3*B*a^3*e^3)*x - 2*(B*a^2*c^2*d^3 + 3*C*a^3*c*d^2*e + 3*A*a^2*c^2*d^2*e + 3*B*a^3*c*d*e^2 - 3*C*a^4*e^3 + A*a^3*c*e^3)/c)/((c*x^2 + a)^2*a^2*c^2)","A",0
58,1,254,0,0.160051," ","integrate((e*x+d)^2*(C*x^2+B*x+A)/(c*x^2+a)^3,x, algorithm=""giac"")","\frac{{\left(C a c d^{2} + 3 \, A c^{2} d^{2} + 2 \, B a c d e + 3 \, C a^{2} e^{2} + A a c e^{2}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{8 \, \sqrt{a c} a^{2} c^{2}} + \frac{C a c^{2} d^{2} x^{3} + 3 \, A c^{3} d^{2} x^{3} + 2 \, B a c^{2} d x^{3} e - 5 \, C a^{2} c x^{3} e^{2} + A a c^{2} x^{3} e^{2} - 8 \, C a^{2} c d x^{2} e - C a^{2} c d^{2} x + 5 \, A a c^{2} d^{2} x - 4 \, B a^{2} c x^{2} e^{2} - 2 \, B a^{2} c d x e - 2 \, B a^{2} c d^{2} - 3 \, C a^{3} x e^{2} - A a^{2} c x e^{2} - 4 \, C a^{3} d e - 4 \, A a^{2} c d e - 2 \, B a^{3} e^{2}}{8 \, {\left(c x^{2} + a\right)}^{2} a^{2} c^{2}}"," ",0,"1/8*(C*a*c*d^2 + 3*A*c^2*d^2 + 2*B*a*c*d*e + 3*C*a^2*e^2 + A*a*c*e^2)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a^2*c^2) + 1/8*(C*a*c^2*d^2*x^3 + 3*A*c^3*d^2*x^3 + 2*B*a*c^2*d*x^3*e - 5*C*a^2*c*x^3*e^2 + A*a*c^2*x^3*e^2 - 8*C*a^2*c*d*x^2*e - C*a^2*c*d^2*x + 5*A*a*c^2*d^2*x - 4*B*a^2*c*x^2*e^2 - 2*B*a^2*c*d*x*e - 2*B*a^2*c*d^2 - 3*C*a^3*x*e^2 - A*a^2*c*x*e^2 - 4*C*a^3*d*e - 4*A*a^2*c*d*e - 2*B*a^3*e^2)/((c*x^2 + a)^2*a^2*c^2)","A",0
59,1,152,0,0.185040," ","integrate((e*x+d)*(C*x^2+B*x+A)/(c*x^2+a)^3,x, algorithm=""giac"")","\frac{{\left(C a d + 3 \, A c d + B a e\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{8 \, \sqrt{a c} a^{2} c} + \frac{C a c^{2} d x^{3} + 3 \, A c^{3} d x^{3} + B a c^{2} x^{3} e - 4 \, C a^{2} c x^{2} e - C a^{2} c d x + 5 \, A a c^{2} d x - B a^{2} c x e - 2 \, B a^{2} c d - 2 \, C a^{3} e - 2 \, A a^{2} c e}{8 \, {\left(c x^{2} + a\right)}^{2} a^{2} c^{2}}"," ",0,"1/8*(C*a*d + 3*A*c*d + B*a*e)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a^2*c) + 1/8*(C*a*c^2*d*x^3 + 3*A*c^3*d*x^3 + B*a*c^2*x^3*e - 4*C*a^2*c*x^2*e - C*a^2*c*d*x + 5*A*a*c^2*d*x - B*a^2*c*x*e - 2*B*a^2*c*d - 2*C*a^3*e - 2*A*a^2*c*e)/((c*x^2 + a)^2*a^2*c^2)","A",0
60,1,84,0,0.162492," ","integrate((C*x^2+B*x+A)/(c*x^2+a)^3,x, algorithm=""giac"")","\frac{{\left(C a + 3 \, A c\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{8 \, \sqrt{a c} a^{2} c} + \frac{C a c x^{3} + 3 \, A c^{2} x^{3} - C a^{2} x + 5 \, A a c x - 2 \, B a^{2}}{8 \, {\left(c x^{2} + a\right)}^{2} a^{2} c}"," ",0,"1/8*(C*a + 3*A*c)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a^2*c) + 1/8*(C*a*c*x^3 + 3*A*c^2*x^3 - C*a^2*x + 5*A*a*c*x - 2*B*a^2)/((c*x^2 + a)^2*a^2*c)","A",0
61,1,715,0,0.177063," ","integrate((C*x^2+B*x+A)/(e*x+d)/(c*x^2+a)^3,x, algorithm=""giac"")","-\frac{{\left(C d^{2} e^{3} - B d e^{4} + A e^{5}\right)} \log\left(c x^{2} + a\right)}{2 \, {\left(c^{3} d^{6} + 3 \, a c^{2} d^{4} e^{2} + 3 \, a^{2} c d^{2} e^{4} + a^{3} e^{6}\right)}} + \frac{{\left(C d^{2} e^{4} - B d e^{5} + A e^{6}\right)} \log\left({\left| x e + d \right|}\right)}{c^{3} d^{6} e + 3 \, a c^{2} d^{4} e^{3} + 3 \, a^{2} c d^{2} e^{5} + a^{3} e^{7}} + \frac{{\left(C a c^{2} d^{5} + 3 \, A c^{3} d^{5} - B a c^{2} d^{4} e + 6 \, C a^{2} c d^{3} e^{2} + 10 \, A a c^{2} d^{3} e^{2} - 6 \, B a^{2} c d^{2} e^{3} - 3 \, C a^{3} d e^{4} + 15 \, A a^{2} c d e^{4} + 3 \, B a^{3} e^{5}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{8 \, {\left(a^{2} c^{3} d^{6} + 3 \, a^{3} c^{2} d^{4} e^{2} + 3 \, a^{4} c d^{2} e^{4} + a^{5} e^{6}\right)} \sqrt{a c}} - \frac{2 \, B a^{2} c^{3} d^{5} - 2 \, C a^{3} c^{2} d^{4} e - 2 \, A a^{2} c^{3} d^{4} e + 8 \, B a^{3} c^{2} d^{3} e^{2} - 8 \, A a^{3} c^{2} d^{2} e^{3} + 6 \, B a^{4} c d e^{4} + 2 \, C a^{5} e^{5} - 6 \, A a^{4} c e^{5} - {\left(C a c^{4} d^{5} + 3 \, A c^{5} d^{5} - B a c^{4} d^{4} e - 2 \, C a^{2} c^{3} d^{3} e^{2} + 10 \, A a c^{4} d^{3} e^{2} + 2 \, B a^{2} c^{3} d^{2} e^{3} - 3 \, C a^{3} c^{2} d e^{4} + 7 \, A a^{2} c^{3} d e^{4} + 3 \, B a^{3} c^{2} e^{5}\right)} x^{3} - 4 \, {\left(C a^{2} c^{3} d^{4} e - B a^{2} c^{3} d^{3} e^{2} + C a^{3} c^{2} d^{2} e^{3} + A a^{2} c^{3} d^{2} e^{3} - B a^{3} c^{2} d e^{4} + A a^{3} c^{2} e^{5}\right)} x^{2} + {\left(C a^{2} c^{3} d^{5} - 5 \, A a c^{4} d^{5} - B a^{2} c^{3} d^{4} e + 6 \, C a^{3} c^{2} d^{3} e^{2} - 14 \, A a^{2} c^{3} d^{3} e^{2} - 6 \, B a^{3} c^{2} d^{2} e^{3} + 5 \, C a^{4} c d e^{4} - 9 \, A a^{3} c^{2} d e^{4} - 5 \, B a^{4} c e^{5}\right)} x}{8 \, {\left(c d^{2} + a e^{2}\right)}^{3} {\left(c x^{2} + a\right)}^{2} a^{2} c}"," ",0,"-1/2*(C*d^2*e^3 - B*d*e^4 + A*e^5)*log(c*x^2 + a)/(c^3*d^6 + 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 + a^3*e^6) + (C*d^2*e^4 - B*d*e^5 + A*e^6)*log(abs(x*e + d))/(c^3*d^6*e + 3*a*c^2*d^4*e^3 + 3*a^2*c*d^2*e^5 + a^3*e^7) + 1/8*(C*a*c^2*d^5 + 3*A*c^3*d^5 - B*a*c^2*d^4*e + 6*C*a^2*c*d^3*e^2 + 10*A*a*c^2*d^3*e^2 - 6*B*a^2*c*d^2*e^3 - 3*C*a^3*d*e^4 + 15*A*a^2*c*d*e^4 + 3*B*a^3*e^5)*arctan(c*x/sqrt(a*c))/((a^2*c^3*d^6 + 3*a^3*c^2*d^4*e^2 + 3*a^4*c*d^2*e^4 + a^5*e^6)*sqrt(a*c)) - 1/8*(2*B*a^2*c^3*d^5 - 2*C*a^3*c^2*d^4*e - 2*A*a^2*c^3*d^4*e + 8*B*a^3*c^2*d^3*e^2 - 8*A*a^3*c^2*d^2*e^3 + 6*B*a^4*c*d*e^4 + 2*C*a^5*e^5 - 6*A*a^4*c*e^5 - (C*a*c^4*d^5 + 3*A*c^5*d^5 - B*a*c^4*d^4*e - 2*C*a^2*c^3*d^3*e^2 + 10*A*a*c^4*d^3*e^2 + 2*B*a^2*c^3*d^2*e^3 - 3*C*a^3*c^2*d*e^4 + 7*A*a^2*c^3*d*e^4 + 3*B*a^3*c^2*e^5)*x^3 - 4*(C*a^2*c^3*d^4*e - B*a^2*c^3*d^3*e^2 + C*a^3*c^2*d^2*e^3 + A*a^2*c^3*d^2*e^3 - B*a^3*c^2*d*e^4 + A*a^3*c^2*e^5)*x^2 + (C*a^2*c^3*d^5 - 5*A*a*c^4*d^5 - B*a^2*c^3*d^4*e + 6*C*a^3*c^2*d^3*e^2 - 14*A*a^2*c^3*d^3*e^2 - 6*B*a^3*c^2*d^2*e^3 + 5*C*a^4*c*d*e^4 - 9*A*a^3*c^2*d*e^4 - 5*B*a^4*c*e^5)*x)/((c*d^2 + a*e^2)^3*(c*x^2 + a)^2*a^2*c)","B",0
62,1,1107,0,0.235394," ","integrate((C*x^2+B*x+A)/(e*x+d)^2/(c*x^2+a)^3,x, algorithm=""giac"")","\frac{{\left(C a c^{3} d^{6} e^{2} + 3 \, A c^{4} d^{6} e^{2} - 2 \, B a c^{3} d^{5} e^{3} + 13 \, C a^{2} c^{2} d^{4} e^{4} + 15 \, A a c^{3} d^{4} e^{4} - 20 \, B a^{2} c^{2} d^{3} e^{5} - 33 \, C a^{3} c d^{2} e^{6} + 45 \, A a^{2} c^{2} d^{2} e^{6} + 30 \, B a^{3} c d e^{7} + 3 \, C a^{4} e^{8} - 15 \, A a^{3} c e^{8}\right)} \arctan\left(\frac{{\left(c d - \frac{c d^{2}}{x e + d} - \frac{a e^{2}}{x e + d}\right)} e^{\left(-1\right)}}{\sqrt{a c}}\right) e^{\left(-2\right)}}{8 \, {\left(a^{2} c^{4} d^{8} + 4 \, a^{3} c^{3} d^{6} e^{2} + 6 \, a^{4} c^{2} d^{4} e^{4} + 4 \, a^{5} c d^{2} e^{6} + a^{6} e^{8}\right)} \sqrt{a c}} - \frac{{\left(4 \, C c d^{3} e^{3} - 5 \, B c d^{2} e^{4} - 2 \, C a d e^{5} + 6 \, A c d e^{5} + B a e^{6}\right)} \log\left(c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)}{2 \, {\left(c^{4} d^{8} + 4 \, a c^{3} d^{6} e^{2} + 6 \, a^{2} c^{2} d^{4} e^{4} + 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}\right)}} - \frac{\frac{C d^{2} e^{9}}{x e + d} - \frac{B d e^{10}}{x e + d} + \frac{A e^{11}}{x e + d}}{c^{3} d^{6} e^{6} + 3 \, a c^{2} d^{4} e^{8} + 3 \, a^{2} c d^{2} e^{10} + a^{3} e^{12}} + \frac{C a c^{4} d^{5} e + 3 \, A c^{5} d^{5} e - 2 \, B a c^{4} d^{4} e^{2} - 22 \, C a^{2} c^{3} d^{3} e^{3} + 14 \, A a c^{4} d^{3} e^{3} + 32 \, B a^{2} c^{3} d^{2} e^{4} + 17 \, C a^{3} c^{2} d e^{5} - 29 \, A a^{2} c^{3} d e^{5} - 6 \, B a^{3} c^{2} e^{6} - \frac{{\left(3 \, C a c^{4} d^{6} e^{2} + 9 \, A c^{5} d^{6} e^{2} - 6 \, B a c^{4} d^{5} e^{3} - 77 \, C a^{2} c^{3} d^{4} e^{4} + 41 \, A a c^{4} d^{4} e^{4} + 116 \, B a^{2} c^{3} d^{3} e^{5} + 77 \, C a^{3} c^{2} d^{2} e^{6} - 121 \, A a^{2} c^{3} d^{2} e^{6} - 38 \, B a^{3} c^{2} d e^{7} - 3 \, C a^{4} c e^{8} + 7 \, A a^{3} c^{2} e^{8}\right)} e^{\left(-1\right)}}{x e + d} + \frac{{\left(3 \, C a c^{4} d^{7} e^{3} + 9 \, A c^{5} d^{7} e^{3} - 6 \, B a c^{4} d^{6} e^{4} - 89 \, C a^{2} c^{3} d^{5} e^{5} + 45 \, A a c^{4} d^{5} e^{5} + 140 \, B a^{2} c^{3} d^{4} e^{6} + 85 \, C a^{3} c^{2} d^{3} e^{7} - 145 \, A a^{2} c^{3} d^{3} e^{7} - 22 \, B a^{3} c^{2} d^{2} e^{8} + 17 \, C a^{4} c d e^{9} - 21 \, A a^{3} c^{2} d e^{9} - 8 \, B a^{4} c e^{10}\right)} e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}} - \frac{{\left(C a c^{4} d^{8} e^{4} + 3 \, A c^{5} d^{8} e^{4} - 2 \, B a c^{4} d^{7} e^{5} - 34 \, C a^{2} c^{3} d^{6} e^{6} + 18 \, A a c^{4} d^{6} e^{6} + 58 \, B a^{2} c^{3} d^{5} e^{7} + 20 \, C a^{3} c^{2} d^{4} e^{8} - 60 \, A a^{2} c^{3} d^{4} e^{8} + 26 \, B a^{3} c^{2} d^{3} e^{9} + 50 \, C a^{4} c d^{2} e^{10} - 66 \, A a^{3} c^{2} d^{2} e^{10} - 34 \, B a^{4} c d e^{11} - 5 \, C a^{5} e^{12} + 9 \, A a^{4} c e^{12}\right)} e^{\left(-3\right)}}{{\left(x e + d\right)}^{3}}}{8 \, {\left(c d^{2} + a e^{2}\right)}^{4} a^{2} {\left(c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)}^{2}}"," ",0,"1/8*(C*a*c^3*d^6*e^2 + 3*A*c^4*d^6*e^2 - 2*B*a*c^3*d^5*e^3 + 13*C*a^2*c^2*d^4*e^4 + 15*A*a*c^3*d^4*e^4 - 20*B*a^2*c^2*d^3*e^5 - 33*C*a^3*c*d^2*e^6 + 45*A*a^2*c^2*d^2*e^6 + 30*B*a^3*c*d*e^7 + 3*C*a^4*e^8 - 15*A*a^3*c*e^8)*arctan((c*d - c*d^2/(x*e + d) - a*e^2/(x*e + d))*e^(-1)/sqrt(a*c))*e^(-2)/((a^2*c^4*d^8 + 4*a^3*c^3*d^6*e^2 + 6*a^4*c^2*d^4*e^4 + 4*a^5*c*d^2*e^6 + a^6*e^8)*sqrt(a*c)) - 1/2*(4*C*c*d^3*e^3 - 5*B*c*d^2*e^4 - 2*C*a*d*e^5 + 6*A*c*d*e^5 + B*a*e^6)*log(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + a*e^2/(x*e + d)^2)/(c^4*d^8 + 4*a*c^3*d^6*e^2 + 6*a^2*c^2*d^4*e^4 + 4*a^3*c*d^2*e^6 + a^4*e^8) - (C*d^2*e^9/(x*e + d) - B*d*e^10/(x*e + d) + A*e^11/(x*e + d))/(c^3*d^6*e^6 + 3*a*c^2*d^4*e^8 + 3*a^2*c*d^2*e^10 + a^3*e^12) + 1/8*(C*a*c^4*d^5*e + 3*A*c^5*d^5*e - 2*B*a*c^4*d^4*e^2 - 22*C*a^2*c^3*d^3*e^3 + 14*A*a*c^4*d^3*e^3 + 32*B*a^2*c^3*d^2*e^4 + 17*C*a^3*c^2*d*e^5 - 29*A*a^2*c^3*d*e^5 - 6*B*a^3*c^2*e^6 - (3*C*a*c^4*d^6*e^2 + 9*A*c^5*d^6*e^2 - 6*B*a*c^4*d^5*e^3 - 77*C*a^2*c^3*d^4*e^4 + 41*A*a*c^4*d^4*e^4 + 116*B*a^2*c^3*d^3*e^5 + 77*C*a^3*c^2*d^2*e^6 - 121*A*a^2*c^3*d^2*e^6 - 38*B*a^3*c^2*d*e^7 - 3*C*a^4*c*e^8 + 7*A*a^3*c^2*e^8)*e^(-1)/(x*e + d) + (3*C*a*c^4*d^7*e^3 + 9*A*c^5*d^7*e^3 - 6*B*a*c^4*d^6*e^4 - 89*C*a^2*c^3*d^5*e^5 + 45*A*a*c^4*d^5*e^5 + 140*B*a^2*c^3*d^4*e^6 + 85*C*a^3*c^2*d^3*e^7 - 145*A*a^2*c^3*d^3*e^7 - 22*B*a^3*c^2*d^2*e^8 + 17*C*a^4*c*d*e^9 - 21*A*a^3*c^2*d*e^9 - 8*B*a^4*c*e^10)*e^(-2)/(x*e + d)^2 - (C*a*c^4*d^8*e^4 + 3*A*c^5*d^8*e^4 - 2*B*a*c^4*d^7*e^5 - 34*C*a^2*c^3*d^6*e^6 + 18*A*a*c^4*d^6*e^6 + 58*B*a^2*c^3*d^5*e^7 + 20*C*a^3*c^2*d^4*e^8 - 60*A*a^2*c^3*d^4*e^8 + 26*B*a^3*c^2*d^3*e^9 + 50*C*a^4*c*d^2*e^10 - 66*A*a^3*c^2*d^2*e^10 - 34*B*a^4*c*d*e^11 - 5*C*a^5*e^12 + 9*A*a^4*c*e^12)*e^(-3)/(x*e + d)^3)/((c*d^2 + a*e^2)^4*a^2*(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + a*e^2/(x*e + d)^2)^2)","A",0
63,1,1532,0,0.200837," ","integrate((C*x^2+B*x+A)/(e*x+d)^3/(c*x^2+a)^3,x, algorithm=""giac"")","-\frac{{\left(10 \, C c^{2} d^{4} e^{3} - 15 \, B c^{2} d^{3} e^{4} - 13 \, C a c d^{2} e^{5} + 21 \, A c^{2} d^{2} e^{5} + 9 \, B a c d e^{6} + C a^{2} e^{7} - 3 \, A a c e^{7}\right)} \log\left(c x^{2} + a\right)}{2 \, {\left(c^{5} d^{10} + 5 \, a c^{4} d^{8} e^{2} + 10 \, a^{2} c^{3} d^{6} e^{4} + 10 \, a^{3} c^{2} d^{4} e^{6} + 5 \, a^{4} c d^{2} e^{8} + a^{5} e^{10}\right)}} + \frac{{\left(10 \, C c^{2} d^{4} e^{4} - 15 \, B c^{2} d^{3} e^{5} - 13 \, C a c d^{2} e^{6} + 21 \, A c^{2} d^{2} e^{6} + 9 \, B a c d e^{7} + C a^{2} e^{8} - 3 \, A a c e^{8}\right)} \log\left({\left| x e + d \right|}\right)}{c^{5} d^{10} e + 5 \, a c^{4} d^{8} e^{3} + 10 \, a^{2} c^{3} d^{6} e^{5} + 10 \, a^{3} c^{2} d^{4} e^{7} + 5 \, a^{4} c d^{2} e^{9} + a^{5} e^{11}} + \frac{{\left(C a c^{4} d^{7} + 3 \, A c^{5} d^{7} - 3 \, B a c^{4} d^{6} e + 23 \, C a^{2} c^{3} d^{5} e^{2} + 21 \, A a c^{4} d^{5} e^{2} - 45 \, B a^{2} c^{3} d^{4} e^{3} - 125 \, C a^{3} c^{2} d^{3} e^{4} + 105 \, A a^{2} c^{3} d^{3} e^{4} + 135 \, B a^{3} c^{2} d^{2} e^{5} + 45 \, C a^{4} c d e^{6} - 105 \, A a^{3} c^{2} d e^{6} - 15 \, B a^{4} c e^{7}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{8 \, {\left(a^{2} c^{5} d^{10} + 5 \, a^{3} c^{4} d^{8} e^{2} + 10 \, a^{4} c^{3} d^{6} e^{4} + 10 \, a^{5} c^{2} d^{4} e^{6} + 5 \, a^{6} c d^{2} e^{8} + a^{7} e^{10}\right)} \sqrt{a c}} + \frac{C a c^{4} d^{5} x^{5} e^{2} + 3 \, A c^{5} d^{5} x^{5} e^{2} + 2 \, C a c^{4} d^{6} x^{4} e + 6 \, A c^{5} d^{6} x^{4} e + C a c^{4} d^{7} x^{3} + 3 \, A c^{5} d^{7} x^{3} - 3 \, B a c^{4} d^{4} x^{5} e^{3} - 6 \, B a c^{4} d^{5} x^{4} e^{2} - 3 \, B a c^{4} d^{6} x^{3} e - 58 \, C a^{2} c^{3} d^{3} x^{5} e^{4} + 18 \, A a c^{4} d^{3} x^{5} e^{4} - 76 \, C a^{2} c^{3} d^{4} x^{4} e^{3} + 36 \, A a c^{4} d^{4} x^{4} e^{3} - 3 \, C a^{2} c^{3} d^{5} x^{3} e^{2} + 23 \, A a c^{4} d^{5} x^{3} e^{2} + 10 \, C a^{2} c^{3} d^{6} x^{2} e + 10 \, A a c^{4} d^{6} x^{2} e - C a^{2} c^{3} d^{7} x + 5 \, A a c^{4} d^{7} x + 78 \, B a^{2} c^{3} d^{2} x^{5} e^{5} + 96 \, B a^{2} c^{3} d^{3} x^{4} e^{4} - 7 \, B a^{2} c^{3} d^{4} x^{3} e^{3} - 20 \, B a^{2} c^{3} d^{5} x^{2} e^{2} - B a^{2} c^{3} d^{6} x e - 2 \, B a^{2} c^{3} d^{7} + 37 \, C a^{3} c^{2} d x^{5} e^{6} - 81 \, A a^{2} c^{3} d x^{5} e^{6} + 22 \, C a^{3} c^{2} d^{2} x^{4} e^{5} - 78 \, A a^{2} c^{3} d^{2} x^{4} e^{5} - 129 \, C a^{3} c^{2} d^{3} x^{3} e^{4} + 61 \, A a^{2} c^{3} d^{3} x^{3} e^{4} - 142 \, C a^{3} c^{2} d^{4} x^{2} e^{3} + 74 \, A a^{2} c^{3} d^{4} x^{2} e^{3} - 10 \, C a^{3} c^{2} d^{5} x e^{2} + 26 \, A a^{2} c^{3} d^{5} x e^{2} + 6 \, C a^{3} c^{2} d^{6} e + 6 \, A a^{2} c^{3} d^{6} e - 15 \, B a^{3} c^{2} x^{5} e^{7} + 6 \, B a^{3} c^{2} d x^{4} e^{6} + 163 \, B a^{3} c^{2} d^{2} x^{3} e^{5} + 176 \, B a^{3} c^{2} d^{3} x^{2} e^{4} + 2 \, B a^{3} c^{2} d^{4} x e^{3} - 20 \, B a^{3} c^{2} d^{5} e^{2} + 4 \, C a^{4} c x^{4} e^{7} - 12 \, A a^{3} c^{2} x^{4} e^{7} + 67 \, C a^{4} c d x^{3} e^{6} - 151 \, A a^{3} c^{2} d x^{3} e^{6} + 46 \, C a^{4} c d^{2} x^{2} e^{5} - 146 \, A a^{3} c^{2} d^{2} x^{2} e^{5} - 77 \, C a^{4} c d^{3} x e^{4} + 49 \, A a^{3} c^{2} d^{3} x e^{4} - 72 \, C a^{4} c d^{4} e^{3} + 44 \, A a^{3} c^{2} d^{4} e^{3} - 25 \, B a^{4} c x^{3} e^{7} + 4 \, B a^{4} c d x^{2} e^{6} + 91 \, B a^{4} c d^{2} x e^{5} + 74 \, B a^{4} c d^{3} e^{4} + 6 \, C a^{5} x^{2} e^{7} - 18 \, A a^{4} c x^{2} e^{7} + 28 \, C a^{5} d x e^{6} - 68 \, A a^{4} c d x e^{6} + 18 \, C a^{5} d^{2} e^{5} - 62 \, A a^{4} c d^{2} e^{5} - 8 \, B a^{5} x e^{7} - 4 \, B a^{5} d e^{6} - 4 \, A a^{5} e^{7}}{8 \, {\left(a^{2} c^{4} d^{8} + 4 \, a^{3} c^{3} d^{6} e^{2} + 6 \, a^{4} c^{2} d^{4} e^{4} + 4 \, a^{5} c d^{2} e^{6} + a^{6} e^{8}\right)} {\left(c x^{3} e + c d x^{2} + a x e + a d\right)}^{2}}"," ",0,"-1/2*(10*C*c^2*d^4*e^3 - 15*B*c^2*d^3*e^4 - 13*C*a*c*d^2*e^5 + 21*A*c^2*d^2*e^5 + 9*B*a*c*d*e^6 + C*a^2*e^7 - 3*A*a*c*e^7)*log(c*x^2 + a)/(c^5*d^10 + 5*a*c^4*d^8*e^2 + 10*a^2*c^3*d^6*e^4 + 10*a^3*c^2*d^4*e^6 + 5*a^4*c*d^2*e^8 + a^5*e^10) + (10*C*c^2*d^4*e^4 - 15*B*c^2*d^3*e^5 - 13*C*a*c*d^2*e^6 + 21*A*c^2*d^2*e^6 + 9*B*a*c*d*e^7 + C*a^2*e^8 - 3*A*a*c*e^8)*log(abs(x*e + d))/(c^5*d^10*e + 5*a*c^4*d^8*e^3 + 10*a^2*c^3*d^6*e^5 + 10*a^3*c^2*d^4*e^7 + 5*a^4*c*d^2*e^9 + a^5*e^11) + 1/8*(C*a*c^4*d^7 + 3*A*c^5*d^7 - 3*B*a*c^4*d^6*e + 23*C*a^2*c^3*d^5*e^2 + 21*A*a*c^4*d^5*e^2 - 45*B*a^2*c^3*d^4*e^3 - 125*C*a^3*c^2*d^3*e^4 + 105*A*a^2*c^3*d^3*e^4 + 135*B*a^3*c^2*d^2*e^5 + 45*C*a^4*c*d*e^6 - 105*A*a^3*c^2*d*e^6 - 15*B*a^4*c*e^7)*arctan(c*x/sqrt(a*c))/((a^2*c^5*d^10 + 5*a^3*c^4*d^8*e^2 + 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6 + 5*a^6*c*d^2*e^8 + a^7*e^10)*sqrt(a*c)) + 1/8*(C*a*c^4*d^5*x^5*e^2 + 3*A*c^5*d^5*x^5*e^2 + 2*C*a*c^4*d^6*x^4*e + 6*A*c^5*d^6*x^4*e + C*a*c^4*d^7*x^3 + 3*A*c^5*d^7*x^3 - 3*B*a*c^4*d^4*x^5*e^3 - 6*B*a*c^4*d^5*x^4*e^2 - 3*B*a*c^4*d^6*x^3*e - 58*C*a^2*c^3*d^3*x^5*e^4 + 18*A*a*c^4*d^3*x^5*e^4 - 76*C*a^2*c^3*d^4*x^4*e^3 + 36*A*a*c^4*d^4*x^4*e^3 - 3*C*a^2*c^3*d^5*x^3*e^2 + 23*A*a*c^4*d^5*x^3*e^2 + 10*C*a^2*c^3*d^6*x^2*e + 10*A*a*c^4*d^6*x^2*e - C*a^2*c^3*d^7*x + 5*A*a*c^4*d^7*x + 78*B*a^2*c^3*d^2*x^5*e^5 + 96*B*a^2*c^3*d^3*x^4*e^4 - 7*B*a^2*c^3*d^4*x^3*e^3 - 20*B*a^2*c^3*d^5*x^2*e^2 - B*a^2*c^3*d^6*x*e - 2*B*a^2*c^3*d^7 + 37*C*a^3*c^2*d*x^5*e^6 - 81*A*a^2*c^3*d*x^5*e^6 + 22*C*a^3*c^2*d^2*x^4*e^5 - 78*A*a^2*c^3*d^2*x^4*e^5 - 129*C*a^3*c^2*d^3*x^3*e^4 + 61*A*a^2*c^3*d^3*x^3*e^4 - 142*C*a^3*c^2*d^4*x^2*e^3 + 74*A*a^2*c^3*d^4*x^2*e^3 - 10*C*a^3*c^2*d^5*x*e^2 + 26*A*a^2*c^3*d^5*x*e^2 + 6*C*a^3*c^2*d^6*e + 6*A*a^2*c^3*d^6*e - 15*B*a^3*c^2*x^5*e^7 + 6*B*a^3*c^2*d*x^4*e^6 + 163*B*a^3*c^2*d^2*x^3*e^5 + 176*B*a^3*c^2*d^3*x^2*e^4 + 2*B*a^3*c^2*d^4*x*e^3 - 20*B*a^3*c^2*d^5*e^2 + 4*C*a^4*c*x^4*e^7 - 12*A*a^3*c^2*x^4*e^7 + 67*C*a^4*c*d*x^3*e^6 - 151*A*a^3*c^2*d*x^3*e^6 + 46*C*a^4*c*d^2*x^2*e^5 - 146*A*a^3*c^2*d^2*x^2*e^5 - 77*C*a^4*c*d^3*x*e^4 + 49*A*a^3*c^2*d^3*x*e^4 - 72*C*a^4*c*d^4*e^3 + 44*A*a^3*c^2*d^4*e^3 - 25*B*a^4*c*x^3*e^7 + 4*B*a^4*c*d*x^2*e^6 + 91*B*a^4*c*d^2*x*e^5 + 74*B*a^4*c*d^3*e^4 + 6*C*a^5*x^2*e^7 - 18*A*a^4*c*x^2*e^7 + 28*C*a^5*d*x*e^6 - 68*A*a^4*c*d*x*e^6 + 18*C*a^5*d^2*e^5 - 62*A*a^4*c*d^2*e^5 - 8*B*a^5*x*e^7 - 4*B*a^5*d*e^6 - 4*A*a^5*e^7)/((a^2*c^4*d^8 + 4*a^3*c^3*d^6*e^2 + 6*a^4*c^2*d^4*e^4 + 4*a^5*c*d^2*e^6 + a^6*e^8)*(c*x^3*e + c*d*x^2 + a*x*e + a*d)^2)","B",0
64,1,636,0,0.178458," ","integrate((e*x+d)^4*(C*x^2+B*x+A)/(c*x^2+a)^4,x, algorithm=""giac"")","\frac{{\left(C a c^{2} d^{4} + 5 \, A c^{3} d^{4} + 4 \, B a c^{2} d^{3} e + 6 \, C a^{2} c d^{2} e^{2} + 6 \, A a c^{2} d^{2} e^{2} + 4 \, B a^{2} c d e^{3} + 5 \, C a^{3} e^{4} + A a^{2} c e^{4}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{16 \, \sqrt{a c} a^{3} c^{3}} + \frac{3 \, C a c^{4} d^{4} x^{5} + 15 \, A c^{5} d^{4} x^{5} + 12 \, B a c^{4} d^{3} x^{5} e + 18 \, C a^{2} c^{3} d^{2} x^{5} e^{2} + 18 \, A a c^{4} d^{2} x^{5} e^{2} + 8 \, C a^{2} c^{3} d^{4} x^{3} + 40 \, A a c^{4} d^{4} x^{3} + 12 \, B a^{2} c^{3} d x^{5} e^{3} + 32 \, B a^{2} c^{3} d^{3} x^{3} e - 33 \, C a^{3} c^{2} x^{5} e^{4} + 3 \, A a^{2} c^{3} x^{5} e^{4} - 96 \, C a^{3} c^{2} d x^{4} e^{3} - 48 \, C a^{3} c^{2} d^{2} x^{3} e^{2} + 48 \, A a^{2} c^{3} d^{2} x^{3} e^{2} - 48 \, C a^{3} c^{2} d^{3} x^{2} e - 3 \, C a^{3} c^{2} d^{4} x + 33 \, A a^{2} c^{3} d^{4} x - 24 \, B a^{3} c^{2} x^{4} e^{4} - 32 \, B a^{3} c^{2} d x^{3} e^{3} - 72 \, B a^{3} c^{2} d^{2} x^{2} e^{2} - 12 \, B a^{3} c^{2} d^{3} x e - 8 \, B a^{3} c^{2} d^{4} - 40 \, C a^{4} c x^{3} e^{4} - 8 \, A a^{3} c^{2} x^{3} e^{4} - 96 \, C a^{4} c d x^{2} e^{3} - 48 \, A a^{3} c^{2} d x^{2} e^{3} - 18 \, C a^{4} c d^{2} x e^{2} - 18 \, A a^{3} c^{2} d^{2} x e^{2} - 16 \, C a^{4} c d^{3} e - 32 \, A a^{3} c^{2} d^{3} e - 24 \, B a^{4} c x^{2} e^{4} - 12 \, B a^{4} c d x e^{3} - 24 \, B a^{4} c d^{2} e^{2} - 15 \, C a^{5} x e^{4} - 3 \, A a^{4} c x e^{4} - 32 \, C a^{5} d e^{3} - 16 \, A a^{4} c d e^{3} - 8 \, B a^{5} e^{4}}{48 \, {\left(c x^{2} + a\right)}^{3} a^{3} c^{3}}"," ",0,"1/16*(C*a*c^2*d^4 + 5*A*c^3*d^4 + 4*B*a*c^2*d^3*e + 6*C*a^2*c*d^2*e^2 + 6*A*a*c^2*d^2*e^2 + 4*B*a^2*c*d*e^3 + 5*C*a^3*e^4 + A*a^2*c*e^4)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a^3*c^3) + 1/48*(3*C*a*c^4*d^4*x^5 + 15*A*c^5*d^4*x^5 + 12*B*a*c^4*d^3*x^5*e + 18*C*a^2*c^3*d^2*x^5*e^2 + 18*A*a*c^4*d^2*x^5*e^2 + 8*C*a^2*c^3*d^4*x^3 + 40*A*a*c^4*d^4*x^3 + 12*B*a^2*c^3*d*x^5*e^3 + 32*B*a^2*c^3*d^3*x^3*e - 33*C*a^3*c^2*x^5*e^4 + 3*A*a^2*c^3*x^5*e^4 - 96*C*a^3*c^2*d*x^4*e^3 - 48*C*a^3*c^2*d^2*x^3*e^2 + 48*A*a^2*c^3*d^2*x^3*e^2 - 48*C*a^3*c^2*d^3*x^2*e - 3*C*a^3*c^2*d^4*x + 33*A*a^2*c^3*d^4*x - 24*B*a^3*c^2*x^4*e^4 - 32*B*a^3*c^2*d*x^3*e^3 - 72*B*a^3*c^2*d^2*x^2*e^2 - 12*B*a^3*c^2*d^3*x*e - 8*B*a^3*c^2*d^4 - 40*C*a^4*c*x^3*e^4 - 8*A*a^3*c^2*x^3*e^4 - 96*C*a^4*c*d*x^2*e^3 - 48*A*a^3*c^2*d*x^2*e^3 - 18*C*a^4*c*d^2*x*e^2 - 18*A*a^3*c^2*d^2*x*e^2 - 16*C*a^4*c*d^3*e - 32*A*a^3*c^2*d^3*e - 24*B*a^4*c*x^2*e^4 - 12*B*a^4*c*d*x*e^3 - 24*B*a^4*c*d^2*e^2 - 15*C*a^5*x*e^4 - 3*A*a^4*c*x*e^4 - 32*C*a^5*d*e^3 - 16*A*a^4*c*d*e^3 - 8*B*a^5*e^4)/((c*x^2 + a)^3*a^3*c^3)","B",0
65,1,475,0,0.165632," ","integrate((e*x+d)^3*(C*x^2+B*x+A)/(c*x^2+a)^4,x, algorithm=""giac"")","\frac{{\left(C a c d^{3} + 5 \, A c^{2} d^{3} + 3 \, B a c d^{2} e + 3 \, C a^{2} d e^{2} + 3 \, A a c d e^{2} + B a^{2} e^{3}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{16 \, \sqrt{a c} a^{3} c^{2}} + \frac{3 \, C a c^{4} d^{3} x^{5} + 15 \, A c^{5} d^{3} x^{5} + 9 \, B a c^{4} d^{2} x^{5} e + 9 \, C a^{2} c^{3} d x^{5} e^{2} + 9 \, A a c^{4} d x^{5} e^{2} + 8 \, C a^{2} c^{3} d^{3} x^{3} + 40 \, A a c^{4} d^{3} x^{3} + 3 \, B a^{2} c^{3} x^{5} e^{3} + 24 \, B a^{2} c^{3} d^{2} x^{3} e - 24 \, C a^{3} c^{2} x^{4} e^{3} - 24 \, C a^{3} c^{2} d x^{3} e^{2} + 24 \, A a^{2} c^{3} d x^{3} e^{2} - 36 \, C a^{3} c^{2} d^{2} x^{2} e - 3 \, C a^{3} c^{2} d^{3} x + 33 \, A a^{2} c^{3} d^{3} x - 8 \, B a^{3} c^{2} x^{3} e^{3} - 36 \, B a^{3} c^{2} d x^{2} e^{2} - 9 \, B a^{3} c^{2} d^{2} x e - 8 \, B a^{3} c^{2} d^{3} - 24 \, C a^{4} c x^{2} e^{3} - 12 \, A a^{3} c^{2} x^{2} e^{3} - 9 \, C a^{4} c d x e^{2} - 9 \, A a^{3} c^{2} d x e^{2} - 12 \, C a^{4} c d^{2} e - 24 \, A a^{3} c^{2} d^{2} e - 3 \, B a^{4} c x e^{3} - 12 \, B a^{4} c d e^{2} - 8 \, C a^{5} e^{3} - 4 \, A a^{4} c e^{3}}{48 \, {\left(c x^{2} + a\right)}^{3} a^{3} c^{3}}"," ",0,"1/16*(C*a*c*d^3 + 5*A*c^2*d^3 + 3*B*a*c*d^2*e + 3*C*a^2*d*e^2 + 3*A*a*c*d*e^2 + B*a^2*e^3)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a^3*c^2) + 1/48*(3*C*a*c^4*d^3*x^5 + 15*A*c^5*d^3*x^5 + 9*B*a*c^4*d^2*x^5*e + 9*C*a^2*c^3*d*x^5*e^2 + 9*A*a*c^4*d*x^5*e^2 + 8*C*a^2*c^3*d^3*x^3 + 40*A*a*c^4*d^3*x^3 + 3*B*a^2*c^3*x^5*e^3 + 24*B*a^2*c^3*d^2*x^3*e - 24*C*a^3*c^2*x^4*e^3 - 24*C*a^3*c^2*d*x^3*e^2 + 24*A*a^2*c^3*d*x^3*e^2 - 36*C*a^3*c^2*d^2*x^2*e - 3*C*a^3*c^2*d^3*x + 33*A*a^2*c^3*d^3*x - 8*B*a^3*c^2*x^3*e^3 - 36*B*a^3*c^2*d*x^2*e^2 - 9*B*a^3*c^2*d^2*x*e - 8*B*a^3*c^2*d^3 - 24*C*a^4*c*x^2*e^3 - 12*A*a^3*c^2*x^2*e^3 - 9*C*a^4*c*d*x*e^2 - 9*A*a^3*c^2*d*x*e^2 - 12*C*a^4*c*d^2*e - 24*A*a^3*c^2*d^2*e - 3*B*a^4*c*x*e^3 - 12*B*a^4*c*d*e^2 - 8*C*a^5*e^3 - 4*A*a^4*c*e^3)/((c*x^2 + a)^3*a^3*c^3)","B",0
66,1,328,0,0.166230," ","integrate((e*x+d)^2*(C*x^2+B*x+A)/(c*x^2+a)^4,x, algorithm=""giac"")","\frac{{\left(C a c d^{2} + 5 \, A c^{2} d^{2} + 2 \, B a c d e + C a^{2} e^{2} + A a c e^{2}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{16 \, \sqrt{a c} a^{3} c^{2}} + \frac{3 \, C a c^{3} d^{2} x^{5} + 15 \, A c^{4} d^{2} x^{5} + 6 \, B a c^{3} d x^{5} e + 3 \, C a^{2} c^{2} x^{5} e^{2} + 3 \, A a c^{3} x^{5} e^{2} + 8 \, C a^{2} c^{2} d^{2} x^{3} + 40 \, A a c^{3} d^{2} x^{3} + 16 \, B a^{2} c^{2} d x^{3} e - 8 \, C a^{3} c x^{3} e^{2} + 8 \, A a^{2} c^{2} x^{3} e^{2} - 24 \, C a^{3} c d x^{2} e - 3 \, C a^{3} c d^{2} x + 33 \, A a^{2} c^{2} d^{2} x - 12 \, B a^{3} c x^{2} e^{2} - 6 \, B a^{3} c d x e - 8 \, B a^{3} c d^{2} - 3 \, C a^{4} x e^{2} - 3 \, A a^{3} c x e^{2} - 8 \, C a^{4} d e - 16 \, A a^{3} c d e - 4 \, B a^{4} e^{2}}{48 \, {\left(c x^{2} + a\right)}^{3} a^{3} c^{2}}"," ",0,"1/16*(C*a*c*d^2 + 5*A*c^2*d^2 + 2*B*a*c*d*e + C*a^2*e^2 + A*a*c*e^2)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a^3*c^2) + 1/48*(3*C*a*c^3*d^2*x^5 + 15*A*c^4*d^2*x^5 + 6*B*a*c^3*d*x^5*e + 3*C*a^2*c^2*x^5*e^2 + 3*A*a*c^3*x^5*e^2 + 8*C*a^2*c^2*d^2*x^3 + 40*A*a*c^3*d^2*x^3 + 16*B*a^2*c^2*d*x^3*e - 8*C*a^3*c*x^3*e^2 + 8*A*a^2*c^2*x^3*e^2 - 24*C*a^3*c*d*x^2*e - 3*C*a^3*c*d^2*x + 33*A*a^2*c^2*d^2*x - 12*B*a^3*c*x^2*e^2 - 6*B*a^3*c*d*x*e - 8*B*a^3*c*d^2 - 3*C*a^4*x*e^2 - 3*A*a^3*c*x*e^2 - 8*C*a^4*d*e - 16*A*a^3*c*d*e - 4*B*a^4*e^2)/((c*x^2 + a)^3*a^3*c^2)","A",0
67,1,194,0,0.156714," ","integrate((e*x+d)*(C*x^2+B*x+A)/(c*x^2+a)^4,x, algorithm=""giac"")","\frac{{\left(C a d + 5 \, A c d + B a e\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{16 \, \sqrt{a c} a^{3} c} + \frac{3 \, C a c^{3} d x^{5} + 15 \, A c^{4} d x^{5} + 3 \, B a c^{3} x^{5} e + 8 \, C a^{2} c^{2} d x^{3} + 40 \, A a c^{3} d x^{3} + 8 \, B a^{2} c^{2} x^{3} e - 12 \, C a^{3} c x^{2} e - 3 \, C a^{3} c d x + 33 \, A a^{2} c^{2} d x - 3 \, B a^{3} c x e - 8 \, B a^{3} c d - 4 \, C a^{4} e - 8 \, A a^{3} c e}{48 \, {\left(c x^{2} + a\right)}^{3} a^{3} c^{2}}"," ",0,"1/16*(C*a*d + 5*A*c*d + B*a*e)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a^3*c) + 1/48*(3*C*a*c^3*d*x^5 + 15*A*c^4*d*x^5 + 3*B*a*c^3*x^5*e + 8*C*a^2*c^2*d*x^3 + 40*A*a*c^3*d*x^3 + 8*B*a^2*c^2*x^3*e - 12*C*a^3*c*x^2*e - 3*C*a^3*c*d*x + 33*A*a^2*c^2*d*x - 3*B*a^3*c*x*e - 8*B*a^3*c*d - 4*C*a^4*e - 8*A*a^3*c*e)/((c*x^2 + a)^3*a^3*c^2)","A",0
68,1,109,0,0.179858," ","integrate((C*x^2+B*x+A)/(c*x^2+a)^4,x, algorithm=""giac"")","\frac{{\left(C a + 5 \, A c\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{16 \, \sqrt{a c} a^{3} c} + \frac{3 \, C a c^{2} x^{5} + 15 \, A c^{3} x^{5} + 8 \, C a^{2} c x^{3} + 40 \, A a c^{2} x^{3} - 3 \, C a^{3} x + 33 \, A a^{2} c x - 8 \, B a^{3}}{48 \, {\left(c x^{2} + a\right)}^{3} a^{3} c}"," ",0,"1/16*(C*a + 5*A*c)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a^3*c) + 1/48*(3*C*a*c^2*x^5 + 15*A*c^3*x^5 + 8*C*a^2*c*x^3 + 40*A*a*c^2*x^3 - 3*C*a^3*x + 33*A*a^2*c*x - 8*B*a^3)/((c*x^2 + a)^3*a^3*c)","A",0
69,1,29,0,0.148392," ","integrate(x^3*(x^2+x+1)/(x^2+1)^2,x, algorithm=""giac"")","\frac{1}{2} \, x^{2} + x + \frac{x}{2 \, {\left(x^{2} + 1\right)}} - \frac{3}{2} \, \arctan\left(x\right) - \frac{1}{2} \, \log\left(x^{2} + 1\right)"," ",0,"1/2*x^2 + x + 1/2*x/(x^2 + 1) - 3/2*arctan(x) - 1/2*log(x^2 + 1)","A",0
70,1,23,0,0.210604," ","integrate(x^2*(x^2+x+1)/(x^2+1)^2,x, algorithm=""giac"")","x + \frac{1}{2 \, {\left(x^{2} + 1\right)}} - \arctan\left(x\right) + \frac{1}{2} \, \log\left(x^{2} + 1\right)"," ",0,"x + 1/2/(x^2 + 1) - arctan(x) + 1/2*log(x^2 + 1)","A",0
71,1,23,0,0.153422," ","integrate(x*(x^2+x+1)/(x^2+1)^2,x, algorithm=""giac"")","-\frac{x}{2 \, {\left(x^{2} + 1\right)}} + \frac{1}{2} \, \arctan\left(x\right) + \frac{1}{2} \, \log\left(x^{2} + 1\right)"," ",0,"-1/2*x/(x^2 + 1) + 1/2*arctan(x) + 1/2*log(x^2 + 1)","A",0
72,1,12,0,0.147778," ","integrate((x^2+x+1)/(x^2+1)^2,x, algorithm=""giac"")","-\frac{1}{2 \, {\left(x^{2} + 1\right)}} + \arctan\left(x\right)"," ",0,"-1/2/(x^2 + 1) + arctan(x)","A",0
73,1,26,0,0.154393," ","integrate((x^2+x+1)/x/(x^2+1)^2,x, algorithm=""giac"")","\frac{x}{2 \, {\left(x^{2} + 1\right)}} + \frac{1}{2} \, \arctan\left(x\right) - \frac{1}{2} \, \log\left(x^{2} + 1\right) + \log\left({\left| x \right|}\right)"," ",0,"1/2*x/(x^2 + 1) + 1/2*arctan(x) - 1/2*log(x^2 + 1) + log(abs(x))","A",0
74,1,35,0,0.184447," ","integrate((x^2+x+1)/x^2/(x^2+1)^2,x, algorithm=""giac"")","-\frac{2 \, x^{2} - x + 2}{2 \, {\left(x^{3} + x\right)}} - \arctan\left(x\right) - \frac{1}{2} \, \log\left(x^{2} + 1\right) + \log\left({\left| x \right|}\right)"," ",0,"-1/2*(2*x^2 - x + 2)/(x^3 + x) - arctan(x) - 1/2*log(x^2 + 1) + log(abs(x))","A",0
75,1,43,0,0.162347," ","integrate((x^2+x+1)/x^3/(x^2+1)^2,x, algorithm=""giac"")","-\frac{3 \, x^{3} + x^{2} + 2 \, x + 1}{2 \, {\left(x^{2} + 1\right)} x^{2}} - \frac{3}{2} \, \arctan\left(x\right) + \frac{1}{2} \, \log\left(x^{2} + 1\right) - \log\left({\left| x \right|}\right)"," ",0,"-1/2*(3*x^3 + x^2 + 2*x + 1)/((x^2 + 1)*x^2) - 3/2*arctan(x) + 1/2*log(x^2 + 1) - log(abs(x))","A",0
76,1,12,0,0.150342," ","integrate((x^2+2*x+1)/(x^2+1)^2,x, algorithm=""giac"")","-\frac{1}{x^{2} + 1} + \arctan\left(x\right)"," ",0,"-1/(x^2 + 1) + arctan(x)","A",0
77,1,21,0,0.183276," ","integrate((3*x^2+12*x+2)/(x^2+4)^2,x, algorithm=""giac"")","-\frac{5 \, x + 24}{4 \, {\left(x^{2} + 4\right)}} + \frac{7}{8} \, \arctan\left(\frac{1}{2} \, x\right)"," ",0,"-1/4*(5*x + 24)/(x^2 + 4) + 7/8*arctan(1/2*x)","A",0
78,1,475,0,0.227455," ","integrate((h*x+g)^3*(f*x^2+e*x+d)*(c*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{1}{1680} \, \sqrt{c x^{2} + a} {\left({\left(2 \, {\left({\left(4 \, {\left(5 \, {\left(6 \, f h^{3} x + \frac{7 \, {\left(3 \, c^{5} f g h^{2} + c^{5} h^{3} e\right)}}{c^{5}}\right)} x + \frac{6 \, {\left(21 \, c^{5} f g^{2} h + 7 \, c^{5} d h^{3} + a c^{4} f h^{3} + 21 \, c^{5} g h^{2} e\right)}}{c^{5}}\right)} x + \frac{35 \, {\left(6 \, c^{5} f g^{3} + 18 \, c^{5} d g h^{2} + 3 \, a c^{4} f g h^{2} + 18 \, c^{5} g^{2} h e + a c^{4} h^{3} e\right)}}{c^{5}}\right)} x + \frac{8 \, {\left(105 \, c^{5} d g^{2} h + 21 \, a c^{4} f g^{2} h + 7 \, a c^{4} d h^{3} - 4 \, a^{2} c^{3} f h^{3} + 35 \, c^{5} g^{3} e + 21 \, a c^{4} g h^{2} e\right)}}{c^{5}}\right)} x + \frac{105 \, {\left(8 \, c^{5} d g^{3} + 2 \, a c^{4} f g^{3} + 6 \, a c^{4} d g h^{2} - 3 \, a^{2} c^{3} f g h^{2} + 6 \, a c^{4} g^{2} h e - a^{2} c^{3} h^{3} e\right)}}{c^{5}}\right)} x + \frac{16 \, {\left(105 \, a c^{4} d g^{2} h - 42 \, a^{2} c^{3} f g^{2} h - 14 \, a^{2} c^{3} d h^{3} + 8 \, a^{3} c^{2} f h^{3} + 35 \, a c^{4} g^{3} e - 42 \, a^{2} c^{3} g h^{2} e\right)}}{c^{5}}\right)} - \frac{{\left(8 \, a c^{2} d g^{3} - 2 \, a^{2} c f g^{3} - 6 \, a^{2} c d g h^{2} + 3 \, a^{3} f g h^{2} - 6 \, a^{2} c g^{2} h e + a^{3} h^{3} e\right)} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{16 \, c^{\frac{5}{2}}}"," ",0,"1/1680*sqrt(c*x^2 + a)*((2*((4*(5*(6*f*h^3*x + 7*(3*c^5*f*g*h^2 + c^5*h^3*e)/c^5)*x + 6*(21*c^5*f*g^2*h + 7*c^5*d*h^3 + a*c^4*f*h^3 + 21*c^5*g*h^2*e)/c^5)*x + 35*(6*c^5*f*g^3 + 18*c^5*d*g*h^2 + 3*a*c^4*f*g*h^2 + 18*c^5*g^2*h*e + a*c^4*h^3*e)/c^5)*x + 8*(105*c^5*d*g^2*h + 21*a*c^4*f*g^2*h + 7*a*c^4*d*h^3 - 4*a^2*c^3*f*h^3 + 35*c^5*g^3*e + 21*a*c^4*g*h^2*e)/c^5)*x + 105*(8*c^5*d*g^3 + 2*a*c^4*f*g^3 + 6*a*c^4*d*g*h^2 - 3*a^2*c^3*f*g*h^2 + 6*a*c^4*g^2*h*e - a^2*c^3*h^3*e)/c^5)*x + 16*(105*a*c^4*d*g^2*h - 42*a^2*c^3*f*g^2*h - 14*a^2*c^3*d*h^3 + 8*a^3*c^2*f*h^3 + 35*a*c^4*g^3*e - 42*a^2*c^3*g*h^2*e)/c^5) - 1/16*(8*a*c^2*d*g^3 - 2*a^2*c*f*g^3 - 6*a^2*c*d*g*h^2 + 3*a^3*f*g*h^2 - 6*a^2*c*g^2*h*e + a^3*h^3*e)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(5/2)","A",0
79,1,321,0,0.206007," ","integrate((h*x+g)^2*(f*x^2+e*x+d)*(c*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{1}{240} \, \sqrt{c x^{2} + a} {\left({\left(2 \, {\left({\left(4 \, {\left(5 \, f h^{2} x + \frac{6 \, {\left(2 \, c^{4} f g h + c^{4} h^{2} e\right)}}{c^{4}}\right)} x + \frac{5 \, {\left(6 \, c^{4} f g^{2} + 6 \, c^{4} d h^{2} + a c^{3} f h^{2} + 12 \, c^{4} g h e\right)}}{c^{4}}\right)} x + \frac{8 \, {\left(10 \, c^{4} d g h + 2 \, a c^{3} f g h + 5 \, c^{4} g^{2} e + a c^{3} h^{2} e\right)}}{c^{4}}\right)} x + \frac{15 \, {\left(8 \, c^{4} d g^{2} + 2 \, a c^{3} f g^{2} + 2 \, a c^{3} d h^{2} - a^{2} c^{2} f h^{2} + 4 \, a c^{3} g h e\right)}}{c^{4}}\right)} x + \frac{16 \, {\left(10 \, a c^{3} d g h - 4 \, a^{2} c^{2} f g h + 5 \, a c^{3} g^{2} e - 2 \, a^{2} c^{2} h^{2} e\right)}}{c^{4}}\right)} - \frac{{\left(8 \, a c^{2} d g^{2} - 2 \, a^{2} c f g^{2} - 2 \, a^{2} c d h^{2} + a^{3} f h^{2} - 4 \, a^{2} c g h e\right)} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{16 \, c^{\frac{5}{2}}}"," ",0,"1/240*sqrt(c*x^2 + a)*((2*((4*(5*f*h^2*x + 6*(2*c^4*f*g*h + c^4*h^2*e)/c^4)*x + 5*(6*c^4*f*g^2 + 6*c^4*d*h^2 + a*c^3*f*h^2 + 12*c^4*g*h*e)/c^4)*x + 8*(10*c^4*d*g*h + 2*a*c^3*f*g*h + 5*c^4*g^2*e + a*c^3*h^2*e)/c^4)*x + 15*(8*c^4*d*g^2 + 2*a*c^3*f*g^2 + 2*a*c^3*d*h^2 - a^2*c^2*f*h^2 + 4*a*c^3*g*h*e)/c^4)*x + 16*(10*a*c^3*d*g*h - 4*a^2*c^2*f*g*h + 5*a*c^3*g^2*e - 2*a^2*c^2*h^2*e)/c^4) - 1/16*(8*a*c^2*d*g^2 - 2*a^2*c*f*g^2 - 2*a^2*c*d*h^2 + a^3*f*h^2 - 4*a^2*c*g*h*e)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(5/2)","A",0
80,1,180,0,0.207687," ","integrate((h*x+g)*(f*x^2+e*x+d)*(c*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{1}{120} \, \sqrt{c x^{2} + a} {\left({\left(2 \, {\left(3 \, {\left(4 \, f h x + \frac{5 \, {\left(c^{3} f g + c^{3} h e\right)}}{c^{3}}\right)} x + \frac{4 \, {\left(5 \, c^{3} d h + a c^{2} f h + 5 \, c^{3} g e\right)}}{c^{3}}\right)} x + \frac{15 \, {\left(4 \, c^{3} d g + a c^{2} f g + a c^{2} h e\right)}}{c^{3}}\right)} x + \frac{8 \, {\left(5 \, a c^{2} d h - 2 \, a^{2} c f h + 5 \, a c^{2} g e\right)}}{c^{3}}\right)} - \frac{{\left(4 \, a c d g - a^{2} f g - a^{2} h e\right)} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{8 \, c^{\frac{3}{2}}}"," ",0,"1/120*sqrt(c*x^2 + a)*((2*(3*(4*f*h*x + 5*(c^3*f*g + c^3*h*e)/c^3)*x + 4*(5*c^3*d*h + a*c^2*f*h + 5*c^3*g*e)/c^3)*x + 15*(4*c^3*d*g + a*c^2*f*g + a*c^2*h*e)/c^3)*x + 8*(5*a*c^2*d*h - 2*a^2*c*f*h + 5*a*c^2*g*e)/c^3) - 1/8*(4*a*c*d*g - a^2*f*g - a^2*h*e)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(3/2)","A",0
81,1,87,0,0.183747," ","integrate((f*x^2+e*x+d)*(c*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{1}{24} \, \sqrt{c x^{2} + a} {\left({\left(2 \, {\left(3 \, f x + 4 \, e\right)} x + \frac{3 \, {\left(4 \, c^{2} d + a c f\right)}}{c^{2}}\right)} x + \frac{8 \, a e}{c}\right)} - \frac{{\left(4 \, a c d - a^{2} f\right)} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{8 \, c^{\frac{3}{2}}}"," ",0,"1/24*sqrt(c*x^2 + a)*((2*(3*f*x + 4*e)*x + 3*(4*c^2*d + a*c*f)/c^2)*x + 8*a*e/c) - 1/8*(4*a*c*d - a^2*f)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(3/2)","A",0
82,1,278,0,0.224119," ","integrate((f*x^2+e*x+d)*(c*x^2+a)^(1/2)/(h*x+g),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{c x^{2} + a} {\left({\left(\frac{2 \, f x}{h} - \frac{3 \, {\left(c f g h^{8} - c h^{9} e\right)}}{c h^{10}}\right)} x + \frac{2 \, {\left(3 \, c f g^{2} h^{7} + 3 \, c d h^{9} + a f h^{9} - 3 \, c g h^{8} e\right)}}{c h^{10}}\right)} + \frac{2 \, {\left(c f g^{4} + c d g^{2} h^{2} + a f g^{2} h^{2} + a d h^{4} - c g^{3} h e - a g h^{3} e\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} h + \sqrt{c} g}{\sqrt{-c g^{2} - a h^{2}}}\right)}{\sqrt{-c g^{2} - a h^{2}} h^{4}} + \frac{{\left(2 \, c^{\frac{3}{2}} f g^{3} + 2 \, c^{\frac{3}{2}} d g h^{2} + a \sqrt{c} f g h^{2} - 2 \, c^{\frac{3}{2}} g^{2} h e - a \sqrt{c} h^{3} e\right)} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{2 \, c h^{4}}"," ",0,"1/6*sqrt(c*x^2 + a)*((2*f*x/h - 3*(c*f*g*h^8 - c*h^9*e)/(c*h^10))*x + 2*(3*c*f*g^2*h^7 + 3*c*d*h^9 + a*f*h^9 - 3*c*g*h^8*e)/(c*h^10)) + 2*(c*f*g^4 + c*d*g^2*h^2 + a*f*g^2*h^2 + a*d*h^4 - c*g^3*h*e - a*g*h^3*e)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + a))*h + sqrt(c)*g)/sqrt(-c*g^2 - a*h^2))/(sqrt(-c*g^2 - a*h^2)*h^4) + 1/2*(2*c^(3/2)*f*g^3 + 2*c^(3/2)*d*g*h^2 + a*sqrt(c)*f*g*h^2 - 2*c^(3/2)*g^2*h*e - a*sqrt(c)*h^3*e)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/(c*h^4)","A",0
83,-1,0,0,0.000000," ","integrate((f*x^2+e*x+d)*(c*x^2+a)^(1/2)/(h*x+g)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
84,1,923,0,0.352590," ","integrate((f*x^2+e*x+d)*(c*x^2+a)^(1/2)/(h*x+g)^3,x, algorithm=""giac"")","-\frac{{\left(6 \, c^{2} f g^{4} + 9 \, a c f g^{2} h^{2} + a c d h^{4} + 2 \, a^{2} f h^{4} - 2 \, c^{2} g^{3} h e - 3 \, a c g h^{3} e\right)} \arctan\left(\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} h + \sqrt{c} g}{\sqrt{-c g^{2} - a h^{2}}}\right)}{{\left(c g^{2} h^{4} + a h^{6}\right)} \sqrt{-c g^{2} - a h^{2}}} + \frac{\sqrt{c x^{2} + a} f}{h^{3}} + \frac{6 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} c^{2} f g^{4} h + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} c^{2} d g^{2} h^{3} + 5 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a c f g^{2} h^{3} + {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a c d h^{5} - 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} c^{2} g^{3} h^{2} e - 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a c g h^{4} e + 10 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} c^{\frac{5}{2}} f g^{5} + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} c^{\frac{5}{2}} d g^{3} h^{2} + 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a c^{\frac{3}{2}} f g^{3} h^{2} - {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a c^{\frac{3}{2}} d g h^{4} - 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{2} \sqrt{c} f g h^{4} - 6 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} c^{\frac{5}{2}} g^{4} h e - {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a c^{\frac{3}{2}} g^{2} h^{3} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{2} \sqrt{c} h^{5} e - 14 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a c^{2} f g^{4} h - 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a c^{2} d g^{2} h^{3} - 11 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{2} c f g^{2} h^{3} + {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{2} c d h^{5} + 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a c^{2} g^{3} h^{2} e + 5 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{2} c g h^{4} e + 5 \, a^{2} c^{\frac{3}{2}} f g^{3} h^{2} + a^{2} c^{\frac{3}{2}} d g h^{4} + 4 \, a^{3} \sqrt{c} f g h^{4} - 3 \, a^{2} c^{\frac{3}{2}} g^{2} h^{3} e - 2 \, a^{3} \sqrt{c} h^{5} e}{{\left(c g^{2} h^{4} + a h^{6}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} h + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} \sqrt{c} g - a h\right)}^{2}} + \frac{{\left(3 \, \sqrt{c} f g - \sqrt{c} h e\right)} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{h^{4}}"," ",0,"-(6*c^2*f*g^4 + 9*a*c*f*g^2*h^2 + a*c*d*h^4 + 2*a^2*f*h^4 - 2*c^2*g^3*h*e - 3*a*c*g*h^3*e)*arctan(((sqrt(c)*x - sqrt(c*x^2 + a))*h + sqrt(c)*g)/sqrt(-c*g^2 - a*h^2))/((c*g^2*h^4 + a*h^6)*sqrt(-c*g^2 - a*h^2)) + sqrt(c*x^2 + a)*f/h^3 + (6*(sqrt(c)*x - sqrt(c*x^2 + a))^3*c^2*f*g^4*h + 2*(sqrt(c)*x - sqrt(c*x^2 + a))^3*c^2*d*g^2*h^3 + 5*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a*c*f*g^2*h^3 + (sqrt(c)*x - sqrt(c*x^2 + a))^3*a*c*d*h^5 - 4*(sqrt(c)*x - sqrt(c*x^2 + a))^3*c^2*g^3*h^2*e - 3*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a*c*g*h^4*e + 10*(sqrt(c)*x - sqrt(c*x^2 + a))^2*c^(5/2)*f*g^5 + 2*(sqrt(c)*x - sqrt(c*x^2 + a))^2*c^(5/2)*d*g^3*h^2 + 3*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a*c^(3/2)*f*g^3*h^2 - (sqrt(c)*x - sqrt(c*x^2 + a))^2*a*c^(3/2)*d*g*h^4 - 4*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^2*sqrt(c)*f*g*h^4 - 6*(sqrt(c)*x - sqrt(c*x^2 + a))^2*c^(5/2)*g^4*h*e - (sqrt(c)*x - sqrt(c*x^2 + a))^2*a*c^(3/2)*g^2*h^3*e + 2*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^2*sqrt(c)*h^5*e - 14*(sqrt(c)*x - sqrt(c*x^2 + a))*a*c^2*f*g^4*h - 2*(sqrt(c)*x - sqrt(c*x^2 + a))*a*c^2*d*g^2*h^3 - 11*(sqrt(c)*x - sqrt(c*x^2 + a))*a^2*c*f*g^2*h^3 + (sqrt(c)*x - sqrt(c*x^2 + a))*a^2*c*d*h^5 + 8*(sqrt(c)*x - sqrt(c*x^2 + a))*a*c^2*g^3*h^2*e + 5*(sqrt(c)*x - sqrt(c*x^2 + a))*a^2*c*g*h^4*e + 5*a^2*c^(3/2)*f*g^3*h^2 + a^2*c^(3/2)*d*g*h^4 + 4*a^3*sqrt(c)*f*g*h^4 - 3*a^2*c^(3/2)*g^2*h^3*e - 2*a^3*sqrt(c)*h^5*e)/((c*g^2*h^4 + a*h^6)*((sqrt(c)*x - sqrt(c*x^2 + a))^2*h + 2*(sqrt(c)*x - sqrt(c*x^2 + a))*sqrt(c)*g - a*h)^2) + (3*sqrt(c)*f*g - sqrt(c)*h*e)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/h^4","B",0
85,1,1719,0,0.502866," ","integrate((f*x^2+e*x+d)*(c*x^2+a)^(1/2)/(h*x+g)^4,x, algorithm=""giac"")","-\frac{{\left(2 \, c^{3} f g^{5} + 5 \, a c^{2} f g^{3} h^{2} - a c^{2} d g h^{4} + 4 \, a^{2} c f g h^{4} - a^{2} c h^{5} e\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} h + \sqrt{c} g}{\sqrt{-c g^{2} - a h^{2}}}\right)}{{\left(c^{2} g^{4} h^{4} + 2 \, a c g^{2} h^{6} + a^{2} h^{8}\right)} \sqrt{-c g^{2} - a h^{2}}} - \frac{\sqrt{c} f \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{h^{4}} - \frac{18 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} c^{3} f g^{5} h^{2} + 33 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a c^{2} f g^{3} h^{4} + 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a c^{2} d g h^{6} + 12 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{2} c f g h^{6} - 6 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} c^{3} g^{4} h^{3} e - 12 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a c^{2} g^{2} h^{5} e - 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{2} c h^{7} e + 54 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} c^{\frac{7}{2}} f g^{6} h - 6 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} c^{\frac{7}{2}} d g^{4} h^{3} + 87 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a c^{\frac{5}{2}} f g^{4} h^{3} + 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a c^{\frac{5}{2}} d g^{2} h^{5} + 12 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{2} c^{\frac{3}{2}} f g^{2} h^{5} - 6 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{2} c^{\frac{3}{2}} d h^{7} - 6 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{3} \sqrt{c} f h^{7} - 12 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} c^{\frac{7}{2}} g^{5} h^{2} e - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a c^{\frac{5}{2}} g^{3} h^{4} e + 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{2} c^{\frac{3}{2}} g h^{6} e + 44 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} c^{4} f g^{7} - 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} c^{4} d g^{5} h^{2} + 14 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a c^{3} f g^{5} h^{2} + 14 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a c^{3} d g^{3} h^{4} - 96 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{2} c^{2} f g^{3} h^{4} - 12 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{2} c^{2} d g h^{6} - 36 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{3} c f g h^{6} - 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} c^{4} g^{6} h e - 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a c^{3} g^{4} h^{3} e + 30 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{2} c^{2} g^{2} h^{5} e - 78 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a c^{\frac{7}{2}} f g^{6} h + 6 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a c^{\frac{7}{2}} d g^{4} h^{3} - 120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{2} c^{\frac{5}{2}} f g^{4} h^{3} - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{2} c^{\frac{5}{2}} d g^{2} h^{5} + 12 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{4} \sqrt{c} f h^{7} + 12 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a c^{\frac{7}{2}} g^{5} h^{2} e + 30 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{2} c^{\frac{5}{2}} g^{3} h^{4} e - 12 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{3} c^{\frac{3}{2}} g h^{6} e + 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{2} c^{3} f g^{5} h^{2} - 6 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{2} c^{3} d g^{3} h^{4} + 87 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{3} c^{2} f g^{3} h^{4} + 9 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{3} c^{2} d g h^{6} + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{4} c f g h^{6} - 6 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{2} c^{3} g^{4} h^{3} e - 18 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{3} c^{2} g^{2} h^{5} e + 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{4} c h^{7} e - 11 \, a^{3} c^{\frac{5}{2}} f g^{4} h^{3} + a^{3} c^{\frac{5}{2}} d g^{2} h^{5} - 20 \, a^{4} c^{\frac{3}{2}} f g^{2} h^{5} - 2 \, a^{4} c^{\frac{3}{2}} d h^{7} - 6 \, a^{5} \sqrt{c} f h^{7} + 2 \, a^{3} c^{\frac{5}{2}} g^{3} h^{4} e + 5 \, a^{4} c^{\frac{3}{2}} g h^{6} e}{3 \, {\left(c^{2} g^{4} h^{4} + 2 \, a c g^{2} h^{6} + a^{2} h^{8}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} h + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} \sqrt{c} g - a h\right)}^{3}}"," ",0,"-(2*c^3*f*g^5 + 5*a*c^2*f*g^3*h^2 - a*c^2*d*g*h^4 + 4*a^2*c*f*g*h^4 - a^2*c*h^5*e)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + a))*h + sqrt(c)*g)/sqrt(-c*g^2 - a*h^2))/((c^2*g^4*h^4 + 2*a*c*g^2*h^6 + a^2*h^8)*sqrt(-c*g^2 - a*h^2)) - sqrt(c)*f*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/h^4 - 1/3*(18*(sqrt(c)*x - sqrt(c*x^2 + a))^5*c^3*f*g^5*h^2 + 33*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a*c^2*f*g^3*h^4 + 3*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a*c^2*d*g*h^6 + 12*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^2*c*f*g*h^6 - 6*(sqrt(c)*x - sqrt(c*x^2 + a))^5*c^3*g^4*h^3*e - 12*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a*c^2*g^2*h^5*e - 3*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^2*c*h^7*e + 54*(sqrt(c)*x - sqrt(c*x^2 + a))^4*c^(7/2)*f*g^6*h - 6*(sqrt(c)*x - sqrt(c*x^2 + a))^4*c^(7/2)*d*g^4*h^3 + 87*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a*c^(5/2)*f*g^4*h^3 + 3*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a*c^(5/2)*d*g^2*h^5 + 12*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^2*c^(3/2)*f*g^2*h^5 - 6*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^2*c^(3/2)*d*h^7 - 6*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^3*sqrt(c)*f*h^7 - 12*(sqrt(c)*x - sqrt(c*x^2 + a))^4*c^(7/2)*g^5*h^2*e - 24*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a*c^(5/2)*g^3*h^4*e + 3*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^2*c^(3/2)*g*h^6*e + 44*(sqrt(c)*x - sqrt(c*x^2 + a))^3*c^4*f*g^7 - 4*(sqrt(c)*x - sqrt(c*x^2 + a))^3*c^4*d*g^5*h^2 + 14*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a*c^3*f*g^5*h^2 + 14*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a*c^3*d*g^3*h^4 - 96*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^2*c^2*f*g^3*h^4 - 12*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^2*c^2*d*g*h^6 - 36*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^3*c*f*g*h^6 - 8*(sqrt(c)*x - sqrt(c*x^2 + a))^3*c^4*g^6*h*e - 8*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a*c^3*g^4*h^3*e + 30*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^2*c^2*g^2*h^5*e - 78*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a*c^(7/2)*f*g^6*h + 6*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a*c^(7/2)*d*g^4*h^3 - 120*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^2*c^(5/2)*f*g^4*h^3 - 24*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^2*c^(5/2)*d*g^2*h^5 + 12*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^4*sqrt(c)*f*h^7 + 12*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a*c^(7/2)*g^5*h^2*e + 30*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^2*c^(5/2)*g^3*h^4*e - 12*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^3*c^(3/2)*g*h^6*e + 48*(sqrt(c)*x - sqrt(c*x^2 + a))*a^2*c^3*f*g^5*h^2 - 6*(sqrt(c)*x - sqrt(c*x^2 + a))*a^2*c^3*d*g^3*h^4 + 87*(sqrt(c)*x - sqrt(c*x^2 + a))*a^3*c^2*f*g^3*h^4 + 9*(sqrt(c)*x - sqrt(c*x^2 + a))*a^3*c^2*d*g*h^6 + 24*(sqrt(c)*x - sqrt(c*x^2 + a))*a^4*c*f*g*h^6 - 6*(sqrt(c)*x - sqrt(c*x^2 + a))*a^2*c^3*g^4*h^3*e - 18*(sqrt(c)*x - sqrt(c*x^2 + a))*a^3*c^2*g^2*h^5*e + 3*(sqrt(c)*x - sqrt(c*x^2 + a))*a^4*c*h^7*e - 11*a^3*c^(5/2)*f*g^4*h^3 + a^3*c^(5/2)*d*g^2*h^5 - 20*a^4*c^(3/2)*f*g^2*h^5 - 2*a^4*c^(3/2)*d*h^7 - 6*a^5*sqrt(c)*f*h^7 + 2*a^3*c^(5/2)*g^3*h^4*e + 5*a^4*c^(3/2)*g*h^6*e)/((c^2*g^4*h^4 + 2*a*c*g^2*h^6 + a^2*h^8)*((sqrt(c)*x - sqrt(c*x^2 + a))^2*h + 2*(sqrt(c)*x - sqrt(c*x^2 + a))*sqrt(c)*g - a*h)^3)","B",0
86,-1,0,0,0.000000," ","integrate((f*x^2+e*x+d)*(c*x^2+a)^(1/2)/(h*x+g)^5,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
87,1,4212,0,0.655621," ","integrate((f*x^2+e*x+d)*(c*x^2+a)^(1/2)/(h*x+g)^6,x, algorithm=""giac"")","-\frac{{\left(4 \, a c^{4} d g^{3} - a^{2} c^{3} f g^{3} - 3 \, a^{2} c^{3} d g h^{2} + 6 \, a^{3} c^{2} f g h^{2} + 6 \, a^{2} c^{3} g^{2} h e - a^{3} c^{2} h^{3} e\right)} \arctan\left(\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} h + \sqrt{c} g}{\sqrt{-c g^{2} - a h^{2}}}\right)}{4 \, {\left(c^{4} g^{8} + 4 \, a c^{3} g^{6} h^{2} + 6 \, a^{2} c^{2} g^{4} h^{4} + 4 \, a^{3} c g^{2} h^{6} + a^{4} h^{8}\right)} \sqrt{-c g^{2} - a h^{2}}} - \frac{60 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a c^{4} d g^{3} h^{8} - 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a^{2} c^{3} f g^{3} h^{8} - 45 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a^{2} c^{3} d g h^{10} + 90 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a^{3} c^{2} f g h^{10} + 90 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a^{2} c^{3} g^{2} h^{9} e - 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a^{3} c^{2} h^{11} e - 120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} c^{\frac{11}{2}} f g^{8} h^{3} - 480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a c^{\frac{9}{2}} f g^{6} h^{5} + 540 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a c^{\frac{9}{2}} d g^{4} h^{7} - 855 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{2} c^{\frac{7}{2}} f g^{4} h^{7} - 405 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{2} c^{\frac{7}{2}} d g^{2} h^{9} + 330 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{3} c^{\frac{5}{2}} f g^{2} h^{9} - 120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{4} c^{\frac{3}{2}} f h^{11} + 810 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{2} c^{\frac{7}{2}} g^{3} h^{8} e - 135 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{3} c^{\frac{5}{2}} g h^{10} e - 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} c^{6} f g^{9} h^{2} - 960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a c^{5} f g^{7} h^{4} + 1880 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a c^{5} d g^{5} h^{6} - 1910 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{2} c^{4} f g^{5} h^{6} - 1690 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{2} c^{4} d g^{3} h^{8} + 1930 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{3} c^{3} f g^{3} h^{8} + 210 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{3} c^{3} d g h^{10} - 660 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{4} c^{2} f g h^{10} - 160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} c^{6} g^{8} h^{3} e - 640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a c^{5} g^{6} h^{5} e + 1860 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{2} c^{4} g^{4} h^{7} e - 1530 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{3} c^{3} g^{2} h^{9} e - 90 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{4} c^{2} h^{11} e - 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} c^{\frac{13}{2}} f g^{10} h - 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} c^{\frac{13}{2}} d g^{8} h^{3} - 720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a c^{\frac{11}{2}} f g^{8} h^{3} + 2120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a c^{\frac{11}{2}} d g^{6} h^{5} - 1250 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{2} c^{\frac{9}{2}} f g^{6} h^{5} - 5710 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{2} c^{\frac{9}{2}} d g^{4} h^{7} + 5590 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{3} c^{\frac{7}{2}} f g^{4} h^{7} + 510 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{3} c^{\frac{7}{2}} d g^{2} h^{9} - 2220 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{4} c^{\frac{5}{2}} f g^{2} h^{9} - 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{4} c^{\frac{5}{2}} d h^{11} + 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{5} c^{\frac{3}{2}} f h^{11} - 160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} c^{\frac{13}{2}} g^{9} h^{2} e - 640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a c^{\frac{11}{2}} g^{7} h^{4} e + 3660 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{2} c^{\frac{9}{2}} g^{5} h^{6} e - 4350 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{3} c^{\frac{7}{2}} g^{3} h^{8} e + 330 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{4} c^{\frac{5}{2}} g h^{10} e - 96 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} c^{7} f g^{11} - 96 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} c^{7} d g^{9} h^{2} + 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a c^{6} f g^{9} h^{2} + 1808 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a c^{6} d g^{7} h^{4} + 604 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{2} c^{5} f g^{7} h^{4} - 7076 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{2} c^{5} d g^{5} h^{6} + 6710 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{3} c^{4} f g^{5} h^{6} + 3770 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{3} c^{4} d g^{3} h^{8} - 5780 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{4} c^{3} f g^{3} h^{8} - 480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{4} c^{3} d g h^{10} + 1200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{5} c^{2} f g h^{10} - 64 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} c^{7} g^{10} h e - 128 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a c^{6} g^{8} h^{3} e + 3416 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{2} c^{5} g^{6} h^{5} e - 7320 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{3} c^{4} g^{4} h^{7} e + 2430 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{4} c^{3} g^{2} h^{9} e + 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a c^{\frac{13}{2}} f g^{10} h + 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a c^{\frac{13}{2}} d g^{8} h^{3} + 720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{2} c^{\frac{11}{2}} f g^{8} h^{3} - 5240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{2} c^{\frac{11}{2}} d g^{6} h^{5} + 2450 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{3} c^{\frac{9}{2}} f g^{6} h^{5} + 5590 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{3} c^{\frac{9}{2}} d g^{4} h^{7} - 7660 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{4} c^{\frac{7}{2}} f g^{4} h^{7} - 2240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{4} c^{\frac{7}{2}} d g^{2} h^{9} + 3440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{5} c^{\frac{5}{2}} f g^{2} h^{9} - 80 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{5} c^{\frac{5}{2}} d h^{11} - 160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{6} c^{\frac{3}{2}} f h^{11} + 160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a c^{\frac{13}{2}} g^{9} h^{2} e + 1120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{2} c^{\frac{11}{2}} g^{7} h^{4} e - 6140 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{3} c^{\frac{9}{2}} g^{5} h^{6} e + 5650 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{4} c^{\frac{7}{2}} g^{3} h^{8} e - 480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{5} c^{\frac{5}{2}} g h^{10} e - 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{2} c^{6} f g^{9} h^{2} - 480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{2} c^{6} d g^{7} h^{4} - 960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{3} c^{5} f g^{7} h^{4} + 5000 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{3} c^{5} d g^{5} h^{6} - 3890 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{4} c^{4} f g^{5} h^{6} - 2910 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{4} c^{4} d g^{3} h^{8} + 4710 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{5} c^{3} f g^{3} h^{8} + 430 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{5} c^{3} d g h^{10} - 940 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{6} c^{2} f g h^{10} - 160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{2} c^{6} g^{8} h^{3} e - 1440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{3} c^{5} g^{6} h^{5} e + 5740 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{4} c^{4} g^{4} h^{7} e - 1710 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{5} c^{3} g^{2} h^{9} e + 90 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{6} c^{2} h^{11} e + 120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{3} c^{\frac{11}{2}} f g^{8} h^{3} + 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{3} c^{\frac{11}{2}} d g^{6} h^{5} + 570 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{4} c^{\frac{9}{2}} f g^{6} h^{5} - 2810 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{4} c^{\frac{9}{2}} d g^{4} h^{7} + 2450 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{5} c^{\frac{7}{2}} f g^{4} h^{7} + 650 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{5} c^{\frac{7}{2}} d g^{2} h^{9} - 1700 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{6} c^{\frac{5}{2}} f g^{2} h^{9} - 80 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{6} c^{\frac{5}{2}} d h^{11} + 80 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{7} c^{\frac{3}{2}} f h^{11} + 160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{3} c^{\frac{11}{2}} g^{7} h^{4} e + 1100 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{4} c^{\frac{9}{2}} g^{5} h^{6} e - 2570 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{5} c^{\frac{7}{2}} g^{3} h^{8} e + 270 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{6} c^{\frac{5}{2}} g h^{10} e - 60 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{4} c^{5} f g^{7} h^{4} - 60 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{4} c^{5} d g^{5} h^{6} - 270 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{5} c^{4} f g^{5} h^{6} + 770 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{5} c^{4} d g^{3} h^{8} - 845 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{6} c^{3} f g^{3} h^{8} - 115 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{6} c^{3} d g h^{10} + 310 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{7} c^{2} f g h^{10} - 40 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{4} c^{5} g^{6} h^{5} e - 280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{5} c^{4} g^{4} h^{7} e + 720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{6} c^{3} g^{2} h^{9} e + 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{7} c^{2} h^{11} e + 6 \, a^{5} c^{\frac{9}{2}} f g^{6} h^{5} + 6 \, a^{5} c^{\frac{9}{2}} d g^{4} h^{7} + 27 \, a^{6} c^{\frac{7}{2}} f g^{4} h^{7} - 83 \, a^{6} c^{\frac{7}{2}} d g^{2} h^{9} + 86 \, a^{7} c^{\frac{5}{2}} f g^{2} h^{9} + 16 \, a^{7} c^{\frac{5}{2}} d h^{11} - 40 \, a^{8} c^{\frac{3}{2}} f h^{11} + 4 \, a^{5} c^{\frac{9}{2}} g^{5} h^{6} e + 28 \, a^{6} c^{\frac{7}{2}} g^{3} h^{8} e - 81 \, a^{7} c^{\frac{5}{2}} g h^{10} e}{60 \, {\left(c^{4} g^{8} h^{4} + 4 \, a c^{3} g^{6} h^{6} + 6 \, a^{2} c^{2} g^{4} h^{8} + 4 \, a^{3} c g^{2} h^{10} + a^{4} h^{12}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} h + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} \sqrt{c} g - a h\right)}^{5}}"," ",0,"-1/4*(4*a*c^4*d*g^3 - a^2*c^3*f*g^3 - 3*a^2*c^3*d*g*h^2 + 6*a^3*c^2*f*g*h^2 + 6*a^2*c^3*g^2*h*e - a^3*c^2*h^3*e)*arctan(((sqrt(c)*x - sqrt(c*x^2 + a))*h + sqrt(c)*g)/sqrt(-c*g^2 - a*h^2))/((c^4*g^8 + 4*a*c^3*g^6*h^2 + 6*a^2*c^2*g^4*h^4 + 4*a^3*c*g^2*h^6 + a^4*h^8)*sqrt(-c*g^2 - a*h^2)) - 1/60*(60*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a*c^4*d*g^3*h^8 - 15*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a^2*c^3*f*g^3*h^8 - 45*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a^2*c^3*d*g*h^10 + 90*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a^3*c^2*f*g*h^10 + 90*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a^2*c^3*g^2*h^9*e - 15*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a^3*c^2*h^11*e - 120*(sqrt(c)*x - sqrt(c*x^2 + a))^8*c^(11/2)*f*g^8*h^3 - 480*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a*c^(9/2)*f*g^6*h^5 + 540*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a*c^(9/2)*d*g^4*h^7 - 855*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^2*c^(7/2)*f*g^4*h^7 - 405*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^2*c^(7/2)*d*g^2*h^9 + 330*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^3*c^(5/2)*f*g^2*h^9 - 120*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^4*c^(3/2)*f*h^11 + 810*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^2*c^(7/2)*g^3*h^8*e - 135*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^3*c^(5/2)*g*h^10*e - 240*(sqrt(c)*x - sqrt(c*x^2 + a))^7*c^6*f*g^9*h^2 - 960*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a*c^5*f*g^7*h^4 + 1880*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a*c^5*d*g^5*h^6 - 1910*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^2*c^4*f*g^5*h^6 - 1690*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^2*c^4*d*g^3*h^8 + 1930*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^3*c^3*f*g^3*h^8 + 210*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^3*c^3*d*g*h^10 - 660*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^4*c^2*f*g*h^10 - 160*(sqrt(c)*x - sqrt(c*x^2 + a))^7*c^6*g^8*h^3*e - 640*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a*c^5*g^6*h^5*e + 1860*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^2*c^4*g^4*h^7*e - 1530*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^3*c^3*g^2*h^9*e - 90*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^4*c^2*h^11*e - 240*(sqrt(c)*x - sqrt(c*x^2 + a))^6*c^(13/2)*f*g^10*h - 240*(sqrt(c)*x - sqrt(c*x^2 + a))^6*c^(13/2)*d*g^8*h^3 - 720*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a*c^(11/2)*f*g^8*h^3 + 2120*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a*c^(11/2)*d*g^6*h^5 - 1250*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^2*c^(9/2)*f*g^6*h^5 - 5710*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^2*c^(9/2)*d*g^4*h^7 + 5590*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^3*c^(7/2)*f*g^4*h^7 + 510*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^3*c^(7/2)*d*g^2*h^9 - 2220*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^4*c^(5/2)*f*g^2*h^9 - 240*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^4*c^(5/2)*d*h^11 + 240*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^5*c^(3/2)*f*h^11 - 160*(sqrt(c)*x - sqrt(c*x^2 + a))^6*c^(13/2)*g^9*h^2*e - 640*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a*c^(11/2)*g^7*h^4*e + 3660*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^2*c^(9/2)*g^5*h^6*e - 4350*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^3*c^(7/2)*g^3*h^8*e + 330*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^4*c^(5/2)*g*h^10*e - 96*(sqrt(c)*x - sqrt(c*x^2 + a))^5*c^7*f*g^11 - 96*(sqrt(c)*x - sqrt(c*x^2 + a))^5*c^7*d*g^9*h^2 + 48*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a*c^6*f*g^9*h^2 + 1808*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a*c^6*d*g^7*h^4 + 604*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^2*c^5*f*g^7*h^4 - 7076*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^2*c^5*d*g^5*h^6 + 6710*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^3*c^4*f*g^5*h^6 + 3770*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^3*c^4*d*g^3*h^8 - 5780*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^4*c^3*f*g^3*h^8 - 480*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^4*c^3*d*g*h^10 + 1200*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^5*c^2*f*g*h^10 - 64*(sqrt(c)*x - sqrt(c*x^2 + a))^5*c^7*g^10*h*e - 128*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a*c^6*g^8*h^3*e + 3416*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^2*c^5*g^6*h^5*e - 7320*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^3*c^4*g^4*h^7*e + 2430*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^4*c^3*g^2*h^9*e + 240*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a*c^(13/2)*f*g^10*h + 240*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a*c^(13/2)*d*g^8*h^3 + 720*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^2*c^(11/2)*f*g^8*h^3 - 5240*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^2*c^(11/2)*d*g^6*h^5 + 2450*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^3*c^(9/2)*f*g^6*h^5 + 5590*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^3*c^(9/2)*d*g^4*h^7 - 7660*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^4*c^(7/2)*f*g^4*h^7 - 2240*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^4*c^(7/2)*d*g^2*h^9 + 3440*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^5*c^(5/2)*f*g^2*h^9 - 80*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^5*c^(5/2)*d*h^11 - 160*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^6*c^(3/2)*f*h^11 + 160*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a*c^(13/2)*g^9*h^2*e + 1120*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^2*c^(11/2)*g^7*h^4*e - 6140*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^3*c^(9/2)*g^5*h^6*e + 5650*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^4*c^(7/2)*g^3*h^8*e - 480*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^5*c^(5/2)*g*h^10*e - 240*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^2*c^6*f*g^9*h^2 - 480*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^2*c^6*d*g^7*h^4 - 960*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^3*c^5*f*g^7*h^4 + 5000*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^3*c^5*d*g^5*h^6 - 3890*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^4*c^4*f*g^5*h^6 - 2910*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^4*c^4*d*g^3*h^8 + 4710*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^5*c^3*f*g^3*h^8 + 430*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^5*c^3*d*g*h^10 - 940*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^6*c^2*f*g*h^10 - 160*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^2*c^6*g^8*h^3*e - 1440*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^3*c^5*g^6*h^5*e + 5740*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^4*c^4*g^4*h^7*e - 1710*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^5*c^3*g^2*h^9*e + 90*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^6*c^2*h^11*e + 120*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^3*c^(11/2)*f*g^8*h^3 + 240*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^3*c^(11/2)*d*g^6*h^5 + 570*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^4*c^(9/2)*f*g^6*h^5 - 2810*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^4*c^(9/2)*d*g^4*h^7 + 2450*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^5*c^(7/2)*f*g^4*h^7 + 650*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^5*c^(7/2)*d*g^2*h^9 - 1700*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^6*c^(5/2)*f*g^2*h^9 - 80*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^6*c^(5/2)*d*h^11 + 80*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^7*c^(3/2)*f*h^11 + 160*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^3*c^(11/2)*g^7*h^4*e + 1100*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^4*c^(9/2)*g^5*h^6*e - 2570*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^5*c^(7/2)*g^3*h^8*e + 270*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^6*c^(5/2)*g*h^10*e - 60*(sqrt(c)*x - sqrt(c*x^2 + a))*a^4*c^5*f*g^7*h^4 - 60*(sqrt(c)*x - sqrt(c*x^2 + a))*a^4*c^5*d*g^5*h^6 - 270*(sqrt(c)*x - sqrt(c*x^2 + a))*a^5*c^4*f*g^5*h^6 + 770*(sqrt(c)*x - sqrt(c*x^2 + a))*a^5*c^4*d*g^3*h^8 - 845*(sqrt(c)*x - sqrt(c*x^2 + a))*a^6*c^3*f*g^3*h^8 - 115*(sqrt(c)*x - sqrt(c*x^2 + a))*a^6*c^3*d*g*h^10 + 310*(sqrt(c)*x - sqrt(c*x^2 + a))*a^7*c^2*f*g*h^10 - 40*(sqrt(c)*x - sqrt(c*x^2 + a))*a^4*c^5*g^6*h^5*e - 280*(sqrt(c)*x - sqrt(c*x^2 + a))*a^5*c^4*g^4*h^7*e + 720*(sqrt(c)*x - sqrt(c*x^2 + a))*a^6*c^3*g^2*h^9*e + 15*(sqrt(c)*x - sqrt(c*x^2 + a))*a^7*c^2*h^11*e + 6*a^5*c^(9/2)*f*g^6*h^5 + 6*a^5*c^(9/2)*d*g^4*h^7 + 27*a^6*c^(7/2)*f*g^4*h^7 - 83*a^6*c^(7/2)*d*g^2*h^9 + 86*a^7*c^(5/2)*f*g^2*h^9 + 16*a^7*c^(5/2)*d*h^11 - 40*a^8*c^(3/2)*f*h^11 + 4*a^5*c^(9/2)*g^5*h^6*e + 28*a^6*c^(7/2)*g^3*h^8*e - 81*a^7*c^(5/2)*g*h^10*e)/((c^4*g^8*h^4 + 4*a*c^3*g^6*h^6 + 6*a^2*c^2*g^4*h^8 + 4*a^3*c*g^2*h^10 + a^4*h^12)*((sqrt(c)*x - sqrt(c*x^2 + a))^2*h + 2*(sqrt(c)*x - sqrt(c*x^2 + a))*sqrt(c)*g - a*h)^5)","B",0
88,1,652,0,0.274009," ","integrate((h*x+g)^3*(c*x^2+a)^(3/2)*(f*x^2+e*x+d),x, algorithm=""giac"")","\frac{1}{40320} \, \sqrt{c x^{2} + a} {\left({\left(2 \, {\left({\left(4 \, {\left(5 \, {\left(2 \, {\left(7 \, {\left(8 \, c f h^{3} x + \frac{9 \, {\left(3 \, c^{8} f g h^{2} + c^{8} h^{3} e\right)}}{c^{7}}\right)} x + \frac{8 \, {\left(27 \, c^{8} f g^{2} h + 9 \, c^{8} d h^{3} + 10 \, a c^{7} f h^{3} + 27 \, c^{8} g h^{2} e\right)}}{c^{7}}\right)} x + \frac{21 \, {\left(8 \, c^{8} f g^{3} + 24 \, c^{8} d g h^{2} + 27 \, a c^{7} f g h^{2} + 24 \, c^{8} g^{2} h e + 9 \, a c^{7} h^{3} e\right)}}{c^{7}}\right)} x + \frac{48 \, {\left(63 \, c^{8} d g^{2} h + 72 \, a c^{7} f g^{2} h + 24 \, a c^{7} d h^{3} + a^{2} c^{6} f h^{3} + 21 \, c^{8} g^{3} e + 72 \, a c^{7} g h^{2} e\right)}}{c^{7}}\right)} x + \frac{105 \, {\left(48 \, c^{8} d g^{3} + 56 \, a c^{7} f g^{3} + 168 \, a c^{7} d g h^{2} + 9 \, a^{2} c^{6} f g h^{2} + 168 \, a c^{7} g^{2} h e + 3 \, a^{2} c^{6} h^{3} e\right)}}{c^{7}}\right)} x + \frac{64 \, {\left(378 \, a c^{7} d g^{2} h + 27 \, a^{2} c^{6} f g^{2} h + 9 \, a^{2} c^{6} d h^{3} - 4 \, a^{3} c^{5} f h^{3} + 126 \, a c^{7} g^{3} e + 27 \, a^{2} c^{6} g h^{2} e\right)}}{c^{7}}\right)} x + \frac{315 \, {\left(80 \, a c^{7} d g^{3} + 8 \, a^{2} c^{6} f g^{3} + 24 \, a^{2} c^{6} d g h^{2} - 9 \, a^{3} c^{5} f g h^{2} + 24 \, a^{2} c^{6} g^{2} h e - 3 \, a^{3} c^{5} h^{3} e\right)}}{c^{7}}\right)} x + \frac{128 \, {\left(189 \, a^{2} c^{6} d g^{2} h - 54 \, a^{3} c^{5} f g^{2} h - 18 \, a^{3} c^{5} d h^{3} + 8 \, a^{4} c^{4} f h^{3} + 63 \, a^{2} c^{6} g^{3} e - 54 \, a^{3} c^{5} g h^{2} e\right)}}{c^{7}}\right)} - \frac{{\left(48 \, a^{2} c^{2} d g^{3} - 8 \, a^{3} c f g^{3} - 24 \, a^{3} c d g h^{2} + 9 \, a^{4} f g h^{2} - 24 \, a^{3} c g^{2} h e + 3 \, a^{4} h^{3} e\right)} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{128 \, c^{\frac{5}{2}}}"," ",0,"1/40320*sqrt(c*x^2 + a)*((2*((4*(5*(2*(7*(8*c*f*h^3*x + 9*(3*c^8*f*g*h^2 + c^8*h^3*e)/c^7)*x + 8*(27*c^8*f*g^2*h + 9*c^8*d*h^3 + 10*a*c^7*f*h^3 + 27*c^8*g*h^2*e)/c^7)*x + 21*(8*c^8*f*g^3 + 24*c^8*d*g*h^2 + 27*a*c^7*f*g*h^2 + 24*c^8*g^2*h*e + 9*a*c^7*h^3*e)/c^7)*x + 48*(63*c^8*d*g^2*h + 72*a*c^7*f*g^2*h + 24*a*c^7*d*h^3 + a^2*c^6*f*h^3 + 21*c^8*g^3*e + 72*a*c^7*g*h^2*e)/c^7)*x + 105*(48*c^8*d*g^3 + 56*a*c^7*f*g^3 + 168*a*c^7*d*g*h^2 + 9*a^2*c^6*f*g*h^2 + 168*a*c^7*g^2*h*e + 3*a^2*c^6*h^3*e)/c^7)*x + 64*(378*a*c^7*d*g^2*h + 27*a^2*c^6*f*g^2*h + 9*a^2*c^6*d*h^3 - 4*a^3*c^5*f*h^3 + 126*a*c^7*g^3*e + 27*a^2*c^6*g*h^2*e)/c^7)*x + 315*(80*a*c^7*d*g^3 + 8*a^2*c^6*f*g^3 + 24*a^2*c^6*d*g*h^2 - 9*a^3*c^5*f*g*h^2 + 24*a^2*c^6*g^2*h*e - 3*a^3*c^5*h^3*e)/c^7)*x + 128*(189*a^2*c^6*d*g^2*h - 54*a^3*c^5*f*g^2*h - 18*a^3*c^5*d*h^3 + 8*a^4*c^4*f*h^3 + 63*a^2*c^6*g^3*e - 54*a^3*c^5*g*h^2*e)/c^7) - 1/128*(48*a^2*c^2*d*g^3 - 8*a^3*c*f*g^3 - 24*a^3*c*d*g*h^2 + 9*a^4*f*g*h^2 - 24*a^3*c*g^2*h*e + 3*a^4*h^3*e)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(5/2)","A",0
89,1,452,0,0.264388," ","integrate((h*x+g)^2*(c*x^2+a)^(3/2)*(f*x^2+e*x+d),x, algorithm=""giac"")","\frac{1}{13440} \, \sqrt{c x^{2} + a} {\left({\left(2 \, {\left({\left(4 \, {\left(5 \, {\left(6 \, {\left(7 \, c f h^{2} x + \frac{8 \, {\left(2 \, c^{7} f g h + c^{7} h^{2} e\right)}}{c^{6}}\right)} x + \frac{7 \, {\left(8 \, c^{7} f g^{2} + 8 \, c^{7} d h^{2} + 9 \, a c^{6} f h^{2} + 16 \, c^{7} g h e\right)}}{c^{6}}\right)} x + \frac{48 \, {\left(14 \, c^{7} d g h + 16 \, a c^{6} f g h + 7 \, c^{7} g^{2} e + 8 \, a c^{6} h^{2} e\right)}}{c^{6}}\right)} x + \frac{35 \, {\left(48 \, c^{7} d g^{2} + 56 \, a c^{6} f g^{2} + 56 \, a c^{6} d h^{2} + 3 \, a^{2} c^{5} f h^{2} + 112 \, a c^{6} g h e\right)}}{c^{6}}\right)} x + \frac{192 \, {\left(28 \, a c^{6} d g h + 2 \, a^{2} c^{5} f g h + 14 \, a c^{6} g^{2} e + a^{2} c^{5} h^{2} e\right)}}{c^{6}}\right)} x + \frac{105 \, {\left(80 \, a c^{6} d g^{2} + 8 \, a^{2} c^{5} f g^{2} + 8 \, a^{2} c^{5} d h^{2} - 3 \, a^{3} c^{4} f h^{2} + 16 \, a^{2} c^{5} g h e\right)}}{c^{6}}\right)} x + \frac{384 \, {\left(14 \, a^{2} c^{5} d g h - 4 \, a^{3} c^{4} f g h + 7 \, a^{2} c^{5} g^{2} e - 2 \, a^{3} c^{4} h^{2} e\right)}}{c^{6}}\right)} - \frac{{\left(48 \, a^{2} c^{2} d g^{2} - 8 \, a^{3} c f g^{2} - 8 \, a^{3} c d h^{2} + 3 \, a^{4} f h^{2} - 16 \, a^{3} c g h e\right)} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{128 \, c^{\frac{5}{2}}}"," ",0,"1/13440*sqrt(c*x^2 + a)*((2*((4*(5*(6*(7*c*f*h^2*x + 8*(2*c^7*f*g*h + c^7*h^2*e)/c^6)*x + 7*(8*c^7*f*g^2 + 8*c^7*d*h^2 + 9*a*c^6*f*h^2 + 16*c^7*g*h*e)/c^6)*x + 48*(14*c^7*d*g*h + 16*a*c^6*f*g*h + 7*c^7*g^2*e + 8*a*c^6*h^2*e)/c^6)*x + 35*(48*c^7*d*g^2 + 56*a*c^6*f*g^2 + 56*a*c^6*d*h^2 + 3*a^2*c^5*f*h^2 + 112*a*c^6*g*h*e)/c^6)*x + 192*(28*a*c^6*d*g*h + 2*a^2*c^5*f*g*h + 14*a*c^6*g^2*e + a^2*c^5*h^2*e)/c^6)*x + 105*(80*a*c^6*d*g^2 + 8*a^2*c^5*f*g^2 + 8*a^2*c^5*d*h^2 - 3*a^3*c^4*f*h^2 + 16*a^2*c^5*g*h*e)/c^6)*x + 384*(14*a^2*c^5*d*g*h - 4*a^3*c^4*f*g*h + 7*a^2*c^5*g^2*e - 2*a^3*c^4*h^2*e)/c^6) - 1/128*(48*a^2*c^2*d*g^2 - 8*a^3*c*f*g^2 - 8*a^3*c*d*h^2 + 3*a^4*f*h^2 - 16*a^3*c*g*h*e)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(5/2)","A",0
90,1,264,0,0.253671," ","integrate((h*x+g)*(c*x^2+a)^(3/2)*(f*x^2+e*x+d),x, algorithm=""giac"")","\frac{1}{1680} \, \sqrt{c x^{2} + a} {\left({\left(2 \, {\left({\left(4 \, {\left(5 \, {\left(6 \, c f h x + \frac{7 \, {\left(c^{6} f g + c^{6} h e\right)}}{c^{5}}\right)} x + \frac{6 \, {\left(7 \, c^{6} d h + 8 \, a c^{5} f h + 7 \, c^{6} g e\right)}}{c^{5}}\right)} x + \frac{35 \, {\left(6 \, c^{6} d g + 7 \, a c^{5} f g + 7 \, a c^{5} h e\right)}}{c^{5}}\right)} x + \frac{24 \, {\left(14 \, a c^{5} d h + a^{2} c^{4} f h + 14 \, a c^{5} g e\right)}}{c^{5}}\right)} x + \frac{105 \, {\left(10 \, a c^{5} d g + a^{2} c^{4} f g + a^{2} c^{4} h e\right)}}{c^{5}}\right)} x + \frac{48 \, {\left(7 \, a^{2} c^{4} d h - 2 \, a^{3} c^{3} f h + 7 \, a^{2} c^{4} g e\right)}}{c^{5}}\right)} - \frac{{\left(6 \, a^{2} c d g - a^{3} f g - a^{3} h e\right)} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{16 \, c^{\frac{3}{2}}}"," ",0,"1/1680*sqrt(c*x^2 + a)*((2*((4*(5*(6*c*f*h*x + 7*(c^6*f*g + c^6*h*e)/c^5)*x + 6*(7*c^6*d*h + 8*a*c^5*f*h + 7*c^6*g*e)/c^5)*x + 35*(6*c^6*d*g + 7*a*c^5*f*g + 7*a*c^5*h*e)/c^5)*x + 24*(14*a*c^5*d*h + a^2*c^4*f*h + 14*a*c^5*g*e)/c^5)*x + 105*(10*a*c^5*d*g + a^2*c^4*f*g + a^2*c^4*h*e)/c^5)*x + 48*(7*a^2*c^4*d*h - 2*a^3*c^3*f*h + 7*a^2*c^4*g*e)/c^5) - 1/16*(6*a^2*c*d*g - a^3*f*g - a^3*h*e)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(3/2)","A",0
91,1,129,0,0.233829," ","integrate((c*x^2+a)^(3/2)*(f*x^2+e*x+d),x, algorithm=""giac"")","\frac{1}{240} \, \sqrt{c x^{2} + a} {\left({\left(2 \, {\left({\left(4 \, {\left(5 \, c f x + 6 \, c e\right)} x + \frac{5 \, {\left(6 \, c^{5} d + 7 \, a c^{4} f\right)}}{c^{4}}\right)} x + 48 \, a e\right)} x + \frac{15 \, {\left(10 \, a c^{4} d + a^{2} c^{3} f\right)}}{c^{4}}\right)} x + \frac{48 \, a^{2} e}{c}\right)} - \frac{{\left(6 \, a^{2} c d - a^{3} f\right)} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{16 \, c^{\frac{3}{2}}}"," ",0,"1/240*sqrt(c*x^2 + a)*((2*((4*(5*c*f*x + 6*c*e)*x + 5*(6*c^5*d + 7*a*c^4*f)/c^4)*x + 48*a*e)*x + 15*(10*a*c^4*d + a^2*c^3*f)/c^4)*x + 48*a^2*e/c) - 1/16*(6*a^2*c*d - a^3*f)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(3/2)","A",0
92,1,551,0,0.293308," ","integrate((c*x^2+a)^(3/2)*(f*x^2+e*x+d)/(h*x+g),x, algorithm=""giac"")","\frac{1}{120} \, \sqrt{c x^{2} + a} {\left({\left(2 \, {\left(3 \, {\left(\frac{4 \, c f x}{h} - \frac{5 \, {\left(c^{4} f g h^{19} - c^{4} h^{20} e\right)}}{c^{3} h^{21}}\right)} x + \frac{4 \, {\left(5 \, c^{4} f g^{2} h^{18} + 5 \, c^{4} d h^{20} + 6 \, a c^{3} f h^{20} - 5 \, c^{4} g h^{19} e\right)}}{c^{3} h^{21}}\right)} x - \frac{15 \, {\left(4 \, c^{4} f g^{3} h^{17} + 4 \, c^{4} d g h^{19} + 5 \, a c^{3} f g h^{19} - 4 \, c^{4} g^{2} h^{18} e - 5 \, a c^{3} h^{20} e\right)}}{c^{3} h^{21}}\right)} x + \frac{8 \, {\left(15 \, c^{4} f g^{4} h^{16} + 15 \, c^{4} d g^{2} h^{18} + 20 \, a c^{3} f g^{2} h^{18} + 20 \, a c^{3} d h^{20} + 3 \, a^{2} c^{2} f h^{20} - 15 \, c^{4} g^{3} h^{17} e - 20 \, a c^{3} g h^{19} e\right)}}{c^{3} h^{21}}\right)} + \frac{2 \, {\left(c^{2} f g^{6} + c^{2} d g^{4} h^{2} + 2 \, a c f g^{4} h^{2} + 2 \, a c d g^{2} h^{4} + a^{2} f g^{2} h^{4} + a^{2} d h^{6} - c^{2} g^{5} h e - 2 \, a c g^{3} h^{3} e - a^{2} g h^{5} e\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} h + \sqrt{c} g}{\sqrt{-c g^{2} - a h^{2}}}\right)}{\sqrt{-c g^{2} - a h^{2}} h^{6}} + \frac{{\left(8 \, c^{\frac{5}{2}} f g^{5} + 8 \, c^{\frac{5}{2}} d g^{3} h^{2} + 12 \, a c^{\frac{3}{2}} f g^{3} h^{2} + 12 \, a c^{\frac{3}{2}} d g h^{4} + 3 \, a^{2} \sqrt{c} f g h^{4} - 8 \, c^{\frac{5}{2}} g^{4} h e - 12 \, a c^{\frac{3}{2}} g^{2} h^{3} e - 3 \, a^{2} \sqrt{c} h^{5} e\right)} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{8 \, c h^{6}}"," ",0,"1/120*sqrt(c*x^2 + a)*((2*(3*(4*c*f*x/h - 5*(c^4*f*g*h^19 - c^4*h^20*e)/(c^3*h^21))*x + 4*(5*c^4*f*g^2*h^18 + 5*c^4*d*h^20 + 6*a*c^3*f*h^20 - 5*c^4*g*h^19*e)/(c^3*h^21))*x - 15*(4*c^4*f*g^3*h^17 + 4*c^4*d*g*h^19 + 5*a*c^3*f*g*h^19 - 4*c^4*g^2*h^18*e - 5*a*c^3*h^20*e)/(c^3*h^21))*x + 8*(15*c^4*f*g^4*h^16 + 15*c^4*d*g^2*h^18 + 20*a*c^3*f*g^2*h^18 + 20*a*c^3*d*h^20 + 3*a^2*c^2*f*h^20 - 15*c^4*g^3*h^17*e - 20*a*c^3*g*h^19*e)/(c^3*h^21)) + 2*(c^2*f*g^6 + c^2*d*g^4*h^2 + 2*a*c*f*g^4*h^2 + 2*a*c*d*g^2*h^4 + a^2*f*g^2*h^4 + a^2*d*h^6 - c^2*g^5*h*e - 2*a*c*g^3*h^3*e - a^2*g*h^5*e)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + a))*h + sqrt(c)*g)/sqrt(-c*g^2 - a*h^2))/(sqrt(-c*g^2 - a*h^2)*h^6) + 1/8*(8*c^(5/2)*f*g^5 + 8*c^(5/2)*d*g^3*h^2 + 12*a*c^(3/2)*f*g^3*h^2 + 12*a*c^(3/2)*d*g*h^4 + 3*a^2*sqrt(c)*f*g*h^4 - 8*c^(5/2)*g^4*h*e - 12*a*c^(3/2)*g^2*h^3*e - 3*a^2*sqrt(c)*h^5*e)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/(c*h^6)","A",0
93,-1,0,0,0.000000," ","integrate((c*x^2+a)^(3/2)*(f*x^2+e*x+d)/(h*x+g)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
94,1,1036,0,0.432758," ","integrate((c*x^2+a)^(3/2)*(f*x^2+e*x+d)/(h*x+g)^3,x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{c x^{2} + a} {\left(x {\left(\frac{2 \, c f x}{h^{3}} - \frac{3 \, {\left(3 \, c^{2} f g h^{14} - c^{2} h^{15} e\right)}}{c h^{18}}\right)} + \frac{2 \, {\left(18 \, c^{2} f g^{2} h^{13} + 3 \, c^{2} d h^{15} + 4 \, a c f h^{15} - 9 \, c^{2} g h^{14} e\right)}}{c h^{18}}\right)} + \frac{{\left(20 \, c^{\frac{3}{2}} f g^{3} + 6 \, c^{\frac{3}{2}} d g h^{2} + 9 \, a \sqrt{c} f g h^{2} - 12 \, c^{\frac{3}{2}} g^{2} h e - 3 \, a \sqrt{c} h^{3} e\right)} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{2 \, h^{6}} + \frac{{\left(20 \, c^{2} f g^{4} + 6 \, c^{2} d g^{2} h^{2} + 19 \, a c f g^{2} h^{2} + 3 \, a c d h^{4} + 2 \, a^{2} f h^{4} - 12 \, c^{2} g^{3} h e - 9 \, a c g h^{3} e\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} h + \sqrt{c} g}{\sqrt{-c g^{2} - a h^{2}}}\right)}{\sqrt{-c g^{2} - a h^{2}} h^{6}} + \frac{10 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} c^{2} f g^{4} h + 6 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} c^{2} d g^{2} h^{3} + 5 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a c f g^{2} h^{3} + {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a c d h^{5} - 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} c^{2} g^{3} h^{2} e - 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a c g h^{4} e + 18 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} c^{\frac{5}{2}} f g^{5} + 10 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} c^{\frac{5}{2}} d g^{3} h^{2} - {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a c^{\frac{3}{2}} f g^{3} h^{2} - 5 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a c^{\frac{3}{2}} d g h^{4} - 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{2} \sqrt{c} f g h^{4} - 14 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} c^{\frac{5}{2}} g^{4} h e + 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a c^{\frac{3}{2}} g^{2} h^{3} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{2} \sqrt{c} h^{5} e - 26 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a c^{2} f g^{4} h - 14 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a c^{2} d g^{2} h^{3} - 11 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{2} c f g^{2} h^{3} + {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{2} c d h^{5} + 20 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a c^{2} g^{3} h^{2} e + 5 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{2} c g h^{4} e + 9 \, a^{2} c^{\frac{3}{2}} f g^{3} h^{2} + 5 \, a^{2} c^{\frac{3}{2}} d g h^{4} + 4 \, a^{3} \sqrt{c} f g h^{4} - 7 \, a^{2} c^{\frac{3}{2}} g^{2} h^{3} e - 2 \, a^{3} \sqrt{c} h^{5} e}{{\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} h + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} \sqrt{c} g - a h\right)}^{2} h^{6}}"," ",0,"1/6*sqrt(c*x^2 + a)*(x*(2*c*f*x/h^3 - 3*(3*c^2*f*g*h^14 - c^2*h^15*e)/(c*h^18)) + 2*(18*c^2*f*g^2*h^13 + 3*c^2*d*h^15 + 4*a*c*f*h^15 - 9*c^2*g*h^14*e)/(c*h^18)) + 1/2*(20*c^(3/2)*f*g^3 + 6*c^(3/2)*d*g*h^2 + 9*a*sqrt(c)*f*g*h^2 - 12*c^(3/2)*g^2*h*e - 3*a*sqrt(c)*h^3*e)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/h^6 + (20*c^2*f*g^4 + 6*c^2*d*g^2*h^2 + 19*a*c*f*g^2*h^2 + 3*a*c*d*h^4 + 2*a^2*f*h^4 - 12*c^2*g^3*h*e - 9*a*c*g*h^3*e)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + a))*h + sqrt(c)*g)/sqrt(-c*g^2 - a*h^2))/(sqrt(-c*g^2 - a*h^2)*h^6) + (10*(sqrt(c)*x - sqrt(c*x^2 + a))^3*c^2*f*g^4*h + 6*(sqrt(c)*x - sqrt(c*x^2 + a))^3*c^2*d*g^2*h^3 + 5*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a*c*f*g^2*h^3 + (sqrt(c)*x - sqrt(c*x^2 + a))^3*a*c*d*h^5 - 8*(sqrt(c)*x - sqrt(c*x^2 + a))^3*c^2*g^3*h^2*e - 3*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a*c*g*h^4*e + 18*(sqrt(c)*x - sqrt(c*x^2 + a))^2*c^(5/2)*f*g^5 + 10*(sqrt(c)*x - sqrt(c*x^2 + a))^2*c^(5/2)*d*g^3*h^2 - (sqrt(c)*x - sqrt(c*x^2 + a))^2*a*c^(3/2)*f*g^3*h^2 - 5*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a*c^(3/2)*d*g*h^4 - 4*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^2*sqrt(c)*f*g*h^4 - 14*(sqrt(c)*x - sqrt(c*x^2 + a))^2*c^(5/2)*g^4*h*e + 3*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a*c^(3/2)*g^2*h^3*e + 2*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^2*sqrt(c)*h^5*e - 26*(sqrt(c)*x - sqrt(c*x^2 + a))*a*c^2*f*g^4*h - 14*(sqrt(c)*x - sqrt(c*x^2 + a))*a*c^2*d*g^2*h^3 - 11*(sqrt(c)*x - sqrt(c*x^2 + a))*a^2*c*f*g^2*h^3 + (sqrt(c)*x - sqrt(c*x^2 + a))*a^2*c*d*h^5 + 20*(sqrt(c)*x - sqrt(c*x^2 + a))*a*c^2*g^3*h^2*e + 5*(sqrt(c)*x - sqrt(c*x^2 + a))*a^2*c*g*h^4*e + 9*a^2*c^(3/2)*f*g^3*h^2 + 5*a^2*c^(3/2)*d*g*h^4 + 4*a^3*sqrt(c)*f*g*h^4 - 7*a^2*c^(3/2)*g^2*h^3*e - 2*a^3*sqrt(c)*h^5*e)/(((sqrt(c)*x - sqrt(c*x^2 + a))^2*h + 2*(sqrt(c)*x - sqrt(c*x^2 + a))*sqrt(c)*g - a*h)^2*h^6)","B",0
95,1,1900,0,0.611773," ","integrate((c*x^2+a)^(3/2)*(f*x^2+e*x+d)/(h*x+g)^4,x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{c x^{2} + a} {\left(\frac{c f x}{h^{4}} - \frac{2 \, {\left(4 \, c f g h^{10} - c h^{11} e\right)}}{h^{15}}\right)} - \frac{{\left(20 \, c^{3} f g^{5} + 2 \, c^{3} d g^{3} h^{2} + 33 \, a c^{2} f g^{3} h^{2} + 3 \, a c^{2} d g h^{4} + 12 \, a^{2} c f g h^{4} - 8 \, c^{3} g^{4} h e - 12 \, a c^{2} g^{2} h^{3} e - 3 \, a^{2} c h^{5} e\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} h + \sqrt{c} g}{\sqrt{-c g^{2} - a h^{2}}}\right)}{{\left(c g^{2} h^{6} + a h^{8}\right)} \sqrt{-c g^{2} - a h^{2}}} - \frac{60 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} c^{3} f g^{5} h^{2} + 18 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} c^{3} d g^{3} h^{4} + 69 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a c^{2} f g^{3} h^{4} + 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a c^{2} d g h^{6} + 12 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{2} c f g h^{6} - 36 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} c^{3} g^{4} h^{3} e - 36 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a c^{2} g^{2} h^{5} e - 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{2} c h^{7} e + 210 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} c^{\frac{7}{2}} f g^{6} h + 54 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} c^{\frac{7}{2}} d g^{4} h^{3} + 183 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a c^{\frac{5}{2}} f g^{4} h^{3} + 27 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a c^{\frac{5}{2}} d g^{2} h^{5} - 18 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{2} c^{\frac{3}{2}} f g^{2} h^{5} - 12 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{2} c^{\frac{3}{2}} d h^{7} - 6 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{3} \sqrt{c} f h^{7} - 120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} c^{\frac{7}{2}} g^{5} h^{2} e - 84 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a c^{\frac{5}{2}} g^{3} h^{4} e + 21 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{2} c^{\frac{3}{2}} g h^{6} e + 188 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} c^{4} f g^{7} + 44 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} c^{4} d g^{5} h^{2} - 82 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a c^{3} f g^{5} h^{2} - 34 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a c^{3} d g^{3} h^{4} - 276 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{2} c^{2} f g^{3} h^{4} - 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{2} c^{2} d g h^{6} - 36 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{3} c f g h^{6} - 104 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} c^{4} g^{6} h e + 64 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a c^{3} g^{4} h^{3} e + 138 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{2} c^{2} g^{2} h^{5} e - 354 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a c^{\frac{7}{2}} f g^{6} h - 78 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a c^{\frac{7}{2}} d g^{4} h^{3} - 276 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{2} c^{\frac{5}{2}} f g^{4} h^{3} - 36 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{2} c^{\frac{5}{2}} d g^{2} h^{5} + 60 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{3} c^{\frac{3}{2}} f g^{2} h^{5} + 12 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{3} c^{\frac{3}{2}} d h^{7} + 12 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{4} \sqrt{c} f h^{7} + 192 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a c^{\frac{7}{2}} g^{5} h^{2} e + 114 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{2} c^{\frac{5}{2}} g^{3} h^{4} e - 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{3} c^{\frac{3}{2}} g h^{6} e + 222 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{2} c^{3} f g^{5} h^{2} + 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{2} c^{3} d g^{3} h^{4} + 231 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{3} c^{2} f g^{3} h^{4} + 33 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{3} c^{2} d g h^{6} + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{4} c f g h^{6} - 120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{2} c^{3} g^{4} h^{3} e - 102 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{3} c^{2} g^{2} h^{5} e + 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{4} c h^{7} e - 47 \, a^{3} c^{\frac{5}{2}} f g^{4} h^{3} - 11 \, a^{3} c^{\frac{5}{2}} d g^{2} h^{5} - 50 \, a^{4} c^{\frac{3}{2}} f g^{2} h^{5} - 8 \, a^{4} c^{\frac{3}{2}} d h^{7} - 6 \, a^{5} \sqrt{c} f h^{7} + 26 \, a^{3} c^{\frac{5}{2}} g^{3} h^{4} e + 23 \, a^{4} c^{\frac{3}{2}} g h^{6} e}{3 \, {\left(c g^{2} h^{6} + a h^{8}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} h + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} \sqrt{c} g - a h\right)}^{3}} - \frac{{\left(20 \, c^{\frac{3}{2}} f g^{2} + 2 \, c^{\frac{3}{2}} d h^{2} + 3 \, a \sqrt{c} f h^{2} - 8 \, c^{\frac{3}{2}} g h e\right)} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{2 \, h^{6}}"," ",0,"1/2*sqrt(c*x^2 + a)*(c*f*x/h^4 - 2*(4*c*f*g*h^10 - c*h^11*e)/h^15) - (20*c^3*f*g^5 + 2*c^3*d*g^3*h^2 + 33*a*c^2*f*g^3*h^2 + 3*a*c^2*d*g*h^4 + 12*a^2*c*f*g*h^4 - 8*c^3*g^4*h*e - 12*a*c^2*g^2*h^3*e - 3*a^2*c*h^5*e)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + a))*h + sqrt(c)*g)/sqrt(-c*g^2 - a*h^2))/((c*g^2*h^6 + a*h^8)*sqrt(-c*g^2 - a*h^2)) - 1/3*(60*(sqrt(c)*x - sqrt(c*x^2 + a))^5*c^3*f*g^5*h^2 + 18*(sqrt(c)*x - sqrt(c*x^2 + a))^5*c^3*d*g^3*h^4 + 69*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a*c^2*f*g^3*h^4 + 15*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a*c^2*d*g*h^6 + 12*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^2*c*f*g*h^6 - 36*(sqrt(c)*x - sqrt(c*x^2 + a))^5*c^3*g^4*h^3*e - 36*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a*c^2*g^2*h^5*e - 3*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^2*c*h^7*e + 210*(sqrt(c)*x - sqrt(c*x^2 + a))^4*c^(7/2)*f*g^6*h + 54*(sqrt(c)*x - sqrt(c*x^2 + a))^4*c^(7/2)*d*g^4*h^3 + 183*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a*c^(5/2)*f*g^4*h^3 + 27*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a*c^(5/2)*d*g^2*h^5 - 18*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^2*c^(3/2)*f*g^2*h^5 - 12*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^2*c^(3/2)*d*h^7 - 6*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^3*sqrt(c)*f*h^7 - 120*(sqrt(c)*x - sqrt(c*x^2 + a))^4*c^(7/2)*g^5*h^2*e - 84*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a*c^(5/2)*g^3*h^4*e + 21*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^2*c^(3/2)*g*h^6*e + 188*(sqrt(c)*x - sqrt(c*x^2 + a))^3*c^4*f*g^7 + 44*(sqrt(c)*x - sqrt(c*x^2 + a))^3*c^4*d*g^5*h^2 - 82*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a*c^3*f*g^5*h^2 - 34*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a*c^3*d*g^3*h^4 - 276*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^2*c^2*f*g^3*h^4 - 48*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^2*c^2*d*g*h^6 - 36*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^3*c*f*g*h^6 - 104*(sqrt(c)*x - sqrt(c*x^2 + a))^3*c^4*g^6*h*e + 64*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a*c^3*g^4*h^3*e + 138*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^2*c^2*g^2*h^5*e - 354*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a*c^(7/2)*f*g^6*h - 78*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a*c^(7/2)*d*g^4*h^3 - 276*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^2*c^(5/2)*f*g^4*h^3 - 36*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^2*c^(5/2)*d*g^2*h^5 + 60*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^3*c^(3/2)*f*g^2*h^5 + 12*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^3*c^(3/2)*d*h^7 + 12*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^4*sqrt(c)*f*h^7 + 192*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a*c^(7/2)*g^5*h^2*e + 114*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^2*c^(5/2)*g^3*h^4*e - 48*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^3*c^(3/2)*g*h^6*e + 222*(sqrt(c)*x - sqrt(c*x^2 + a))*a^2*c^3*f*g^5*h^2 + 48*(sqrt(c)*x - sqrt(c*x^2 + a))*a^2*c^3*d*g^3*h^4 + 231*(sqrt(c)*x - sqrt(c*x^2 + a))*a^3*c^2*f*g^3*h^4 + 33*(sqrt(c)*x - sqrt(c*x^2 + a))*a^3*c^2*d*g*h^6 + 24*(sqrt(c)*x - sqrt(c*x^2 + a))*a^4*c*f*g*h^6 - 120*(sqrt(c)*x - sqrt(c*x^2 + a))*a^2*c^3*g^4*h^3*e - 102*(sqrt(c)*x - sqrt(c*x^2 + a))*a^3*c^2*g^2*h^5*e + 3*(sqrt(c)*x - sqrt(c*x^2 + a))*a^4*c*h^7*e - 47*a^3*c^(5/2)*f*g^4*h^3 - 11*a^3*c^(5/2)*d*g^2*h^5 - 50*a^4*c^(3/2)*f*g^2*h^5 - 8*a^4*c^(3/2)*d*h^7 - 6*a^5*sqrt(c)*f*h^7 + 26*a^3*c^(5/2)*g^3*h^4*e + 23*a^4*c^(3/2)*g*h^6*e)/((c*g^2*h^6 + a*h^8)*((sqrt(c)*x - sqrt(c*x^2 + a))^2*h + 2*(sqrt(c)*x - sqrt(c*x^2 + a))*sqrt(c)*g - a*h)^3) - 1/2*(20*c^(3/2)*f*g^2 + 2*c^(3/2)*d*h^2 + 3*a*sqrt(c)*f*h^2 - 8*c^(3/2)*g*h*e)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/h^6","B",0
96,-1,0,0,0.000000," ","integrate((c*x^2+a)^(3/2)*(f*x^2+e*x+d)/(h*x+g)^5,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
97,1,4408,0,1.327260," ","integrate((c*x^2+a)^(3/2)*(f*x^2+e*x+d)/(h*x+g)^6,x, algorithm=""giac"")","-\frac{{\left(8 \, c^{5} f g^{7} + 28 \, a c^{4} f g^{5} h^{2} + 35 \, a^{2} c^{3} f g^{3} h^{4} - 3 \, a^{2} c^{3} d g h^{6} + 18 \, a^{3} c^{2} f g h^{6} - 3 \, a^{3} c^{2} h^{7} e\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} h + \sqrt{c} g}{\sqrt{-c g^{2} - a h^{2}}}\right)}{4 \, {\left(c^{3} g^{6} h^{6} + 3 \, a c^{2} g^{4} h^{8} + 3 \, a^{2} c g^{2} h^{10} + a^{3} h^{12}\right)} \sqrt{-c g^{2} - a h^{2}}} - \frac{c^{\frac{3}{2}} f \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{h^{6}} - \frac{600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} c^{5} f g^{7} h^{4} + 1740 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a c^{4} f g^{5} h^{6} + 1635 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a^{2} c^{3} f g^{3} h^{8} + 45 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a^{2} c^{3} d g h^{10} + 450 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a^{3} c^{2} f g h^{10} - 120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} c^{5} g^{6} h^{5} e - 360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a c^{4} g^{4} h^{7} e - 360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a^{2} c^{3} g^{2} h^{9} e - 75 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a^{3} c^{2} h^{11} e + 3600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} c^{\frac{11}{2}} f g^{8} h^{3} - 120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} c^{\frac{11}{2}} d g^{6} h^{5} + 10020 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a c^{\frac{9}{2}} f g^{6} h^{5} - 360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a c^{\frac{9}{2}} d g^{4} h^{7} + 8595 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{2} c^{\frac{7}{2}} f g^{4} h^{7} + 45 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{2} c^{\frac{7}{2}} d g^{2} h^{9} + 1530 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{3} c^{\frac{5}{2}} f g^{2} h^{9} - 120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{3} c^{\frac{5}{2}} d h^{11} - 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{4} c^{\frac{3}{2}} f h^{11} - 480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} c^{\frac{11}{2}} g^{7} h^{4} e - 1440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a c^{\frac{9}{2}} g^{5} h^{6} e - 1440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{2} c^{\frac{7}{2}} g^{3} h^{8} e - 75 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{3} c^{\frac{5}{2}} g h^{10} e + 8800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} c^{6} f g^{9} h^{2} - 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} c^{6} d g^{7} h^{4} + 21240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a c^{5} f g^{7} h^{4} - 720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a c^{5} d g^{5} h^{6} + 11670 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{2} c^{4} f g^{5} h^{6} + 690 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{2} c^{4} d g^{3} h^{8} - 4970 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{3} c^{3} f g^{3} h^{8} - 450 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{3} c^{3} d g h^{10} - 2580 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{4} c^{2} f g h^{10} - 960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} c^{6} g^{8} h^{3} e - 2640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a c^{5} g^{6} h^{5} e - 2160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{2} c^{4} g^{4} h^{7} e + 1170 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{3} c^{3} g^{2} h^{9} e + 30 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{4} c^{2} h^{11} e + 10000 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} c^{\frac{13}{2}} f g^{10} h - 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} c^{\frac{13}{2}} d g^{8} h^{3} + 14040 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a c^{\frac{11}{2}} f g^{8} h^{3} - 720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a c^{\frac{11}{2}} d g^{6} h^{5} - 14430 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{2} c^{\frac{9}{2}} f g^{6} h^{5} + 1590 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{2} c^{\frac{9}{2}} d g^{4} h^{7} - 28790 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{3} c^{\frac{7}{2}} f g^{4} h^{7} - 1710 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{3} c^{\frac{7}{2}} d g^{2} h^{9} - 5820 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{4} c^{\frac{5}{2}} f g^{2} h^{9} + 720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{5} c^{\frac{3}{2}} f h^{11} - 960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} c^{\frac{13}{2}} g^{9} h^{2} e - 1680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a c^{\frac{11}{2}} g^{7} h^{4} e + 720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{2} c^{\frac{9}{2}} g^{5} h^{6} e + 4950 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{3} c^{\frac{7}{2}} g^{3} h^{8} e - 270 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{4} c^{\frac{5}{2}} g h^{10} e + 4384 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} c^{7} f g^{11} - 96 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} c^{7} d g^{9} h^{2} - 9392 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a c^{6} f g^{9} h^{2} + 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a c^{6} d g^{7} h^{4} - 42996 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{2} c^{5} f g^{7} h^{4} + 2364 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{2} c^{5} d g^{5} h^{6} - 31070 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{3} c^{4} f g^{5} h^{6} - 2730 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{3} c^{4} d g^{3} h^{8} + 8620 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{4} c^{3} f g^{3} h^{8} + 720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{4} c^{3} d g h^{10} + 4800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{5} c^{2} f g h^{10} - 384 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} c^{7} g^{10} h e + 672 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a c^{6} g^{8} h^{3} e + 3936 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{2} c^{5} g^{6} h^{5} e + 5580 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{3} c^{4} g^{4} h^{7} e - 2970 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{4} c^{3} g^{2} h^{9} e - 11920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a c^{\frac{13}{2}} f g^{10} h + 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a c^{\frac{13}{2}} d g^{8} h^{3} - 15720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{2} c^{\frac{11}{2}} f g^{8} h^{3} + 720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{2} c^{\frac{11}{2}} d g^{6} h^{5} + 19670 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{3} c^{\frac{9}{2}} f g^{6} h^{5} - 3510 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{3} c^{\frac{9}{2}} d g^{4} h^{7} + 36260 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{4} c^{\frac{7}{2}} f g^{4} h^{7} + 1440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{4} c^{\frac{7}{2}} d g^{2} h^{9} + 6240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{5} c^{\frac{5}{2}} f g^{2} h^{9} - 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{5} c^{\frac{5}{2}} d h^{11} - 880 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{6} c^{\frac{3}{2}} f h^{11} + 960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a c^{\frac{13}{2}} g^{9} h^{2} e + 1680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{2} c^{\frac{11}{2}} g^{7} h^{4} e - 480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{3} c^{\frac{9}{2}} g^{5} h^{6} e - 6150 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{4} c^{\frac{7}{2}} g^{3} h^{8} e + 720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{5} c^{\frac{5}{2}} g h^{10} e + 13120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{2} c^{6} f g^{9} h^{2} - 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{2} c^{6} d g^{7} h^{4} + 30440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{3} c^{5} f g^{7} h^{4} - 1200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{3} c^{5} d g^{5} h^{6} + 14130 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{4} c^{4} f g^{5} h^{6} + 2310 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{4} c^{4} d g^{3} h^{8} - 10790 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{5} c^{3} f g^{3} h^{8} - 510 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{5} c^{3} d g h^{10} - 3820 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{6} c^{2} f g h^{10} - 960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{2} c^{6} g^{8} h^{3} e - 2640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{3} c^{5} g^{6} h^{5} e - 2640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{4} c^{4} g^{4} h^{7} e + 2790 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{5} c^{3} g^{2} h^{9} e - 30 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{6} c^{2} h^{11} e - 7360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{3} c^{\frac{11}{2}} f g^{8} h^{3} + 120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{3} c^{\frac{11}{2}} d g^{6} h^{5} - 19930 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{4} c^{\frac{9}{2}} f g^{6} h^{5} + 690 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{4} c^{\frac{9}{2}} d g^{4} h^{7} - 16050 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{5} c^{\frac{7}{2}} f g^{4} h^{7} - 1050 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{5} c^{\frac{7}{2}} d g^{2} h^{9} - 1300 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{6} c^{\frac{5}{2}} f g^{2} h^{9} + 560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{7} c^{\frac{3}{2}} f h^{11} + 480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{3} c^{\frac{11}{2}} g^{7} h^{4} e + 1560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{4} c^{\frac{9}{2}} g^{5} h^{6} e + 2130 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{5} c^{\frac{7}{2}} g^{3} h^{8} e - 570 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{6} c^{\frac{5}{2}} g h^{10} e + 2140 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{4} c^{5} f g^{7} h^{4} - 60 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{4} c^{5} d g^{5} h^{6} + 6090 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{5} c^{4} f g^{5} h^{6} - 270 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{5} c^{4} d g^{3} h^{8} + 5505 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{6} c^{3} f g^{3} h^{8} + 195 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{6} c^{3} d g h^{10} + 1150 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{7} c^{2} f g h^{10} - 120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{4} c^{5} g^{6} h^{5} e - 420 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{5} c^{4} g^{4} h^{7} e - 630 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{6} c^{3} g^{2} h^{9} e + 75 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{7} c^{2} h^{11} e - 274 \, a^{5} c^{\frac{9}{2}} f g^{6} h^{5} + 6 \, a^{5} c^{\frac{9}{2}} d g^{4} h^{7} - 783 \, a^{6} c^{\frac{7}{2}} f g^{4} h^{7} + 27 \, a^{6} c^{\frac{7}{2}} d g^{2} h^{9} - 714 \, a^{7} c^{\frac{5}{2}} f g^{2} h^{9} - 24 \, a^{7} c^{\frac{5}{2}} d h^{11} - 160 \, a^{8} c^{\frac{3}{2}} f h^{11} + 24 \, a^{5} c^{\frac{9}{2}} g^{5} h^{6} e + 78 \, a^{6} c^{\frac{7}{2}} g^{3} h^{8} e + 99 \, a^{7} c^{\frac{5}{2}} g h^{10} e}{60 \, {\left(c^{3} g^{6} h^{6} + 3 \, a c^{2} g^{4} h^{8} + 3 \, a^{2} c g^{2} h^{10} + a^{3} h^{12}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} h + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} \sqrt{c} g - a h\right)}^{5}}"," ",0,"-1/4*(8*c^5*f*g^7 + 28*a*c^4*f*g^5*h^2 + 35*a^2*c^3*f*g^3*h^4 - 3*a^2*c^3*d*g*h^6 + 18*a^3*c^2*f*g*h^6 - 3*a^3*c^2*h^7*e)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + a))*h + sqrt(c)*g)/sqrt(-c*g^2 - a*h^2))/((c^3*g^6*h^6 + 3*a*c^2*g^4*h^8 + 3*a^2*c*g^2*h^10 + a^3*h^12)*sqrt(-c*g^2 - a*h^2)) - c^(3/2)*f*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/h^6 - 1/60*(600*(sqrt(c)*x - sqrt(c*x^2 + a))^9*c^5*f*g^7*h^4 + 1740*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a*c^4*f*g^5*h^6 + 1635*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a^2*c^3*f*g^3*h^8 + 45*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a^2*c^3*d*g*h^10 + 450*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a^3*c^2*f*g*h^10 - 120*(sqrt(c)*x - sqrt(c*x^2 + a))^9*c^5*g^6*h^5*e - 360*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a*c^4*g^4*h^7*e - 360*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a^2*c^3*g^2*h^9*e - 75*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a^3*c^2*h^11*e + 3600*(sqrt(c)*x - sqrt(c*x^2 + a))^8*c^(11/2)*f*g^8*h^3 - 120*(sqrt(c)*x - sqrt(c*x^2 + a))^8*c^(11/2)*d*g^6*h^5 + 10020*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a*c^(9/2)*f*g^6*h^5 - 360*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a*c^(9/2)*d*g^4*h^7 + 8595*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^2*c^(7/2)*f*g^4*h^7 + 45*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^2*c^(7/2)*d*g^2*h^9 + 1530*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^3*c^(5/2)*f*g^2*h^9 - 120*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^3*c^(5/2)*d*h^11 - 240*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^4*c^(3/2)*f*h^11 - 480*(sqrt(c)*x - sqrt(c*x^2 + a))^8*c^(11/2)*g^7*h^4*e - 1440*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a*c^(9/2)*g^5*h^6*e - 1440*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^2*c^(7/2)*g^3*h^8*e - 75*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^3*c^(5/2)*g*h^10*e + 8800*(sqrt(c)*x - sqrt(c*x^2 + a))^7*c^6*f*g^9*h^2 - 240*(sqrt(c)*x - sqrt(c*x^2 + a))^7*c^6*d*g^7*h^4 + 21240*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a*c^5*f*g^7*h^4 - 720*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a*c^5*d*g^5*h^6 + 11670*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^2*c^4*f*g^5*h^6 + 690*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^2*c^4*d*g^3*h^8 - 4970*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^3*c^3*f*g^3*h^8 - 450*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^3*c^3*d*g*h^10 - 2580*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^4*c^2*f*g*h^10 - 960*(sqrt(c)*x - sqrt(c*x^2 + a))^7*c^6*g^8*h^3*e - 2640*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a*c^5*g^6*h^5*e - 2160*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^2*c^4*g^4*h^7*e + 1170*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^3*c^3*g^2*h^9*e + 30*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^4*c^2*h^11*e + 10000*(sqrt(c)*x - sqrt(c*x^2 + a))^6*c^(13/2)*f*g^10*h - 240*(sqrt(c)*x - sqrt(c*x^2 + a))^6*c^(13/2)*d*g^8*h^3 + 14040*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a*c^(11/2)*f*g^8*h^3 - 720*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a*c^(11/2)*d*g^6*h^5 - 14430*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^2*c^(9/2)*f*g^6*h^5 + 1590*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^2*c^(9/2)*d*g^4*h^7 - 28790*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^3*c^(7/2)*f*g^4*h^7 - 1710*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^3*c^(7/2)*d*g^2*h^9 - 5820*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^4*c^(5/2)*f*g^2*h^9 + 720*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^5*c^(3/2)*f*h^11 - 960*(sqrt(c)*x - sqrt(c*x^2 + a))^6*c^(13/2)*g^9*h^2*e - 1680*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a*c^(11/2)*g^7*h^4*e + 720*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^2*c^(9/2)*g^5*h^6*e + 4950*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^3*c^(7/2)*g^3*h^8*e - 270*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^4*c^(5/2)*g*h^10*e + 4384*(sqrt(c)*x - sqrt(c*x^2 + a))^5*c^7*f*g^11 - 96*(sqrt(c)*x - sqrt(c*x^2 + a))^5*c^7*d*g^9*h^2 - 9392*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a*c^6*f*g^9*h^2 + 48*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a*c^6*d*g^7*h^4 - 42996*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^2*c^5*f*g^7*h^4 + 2364*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^2*c^5*d*g^5*h^6 - 31070*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^3*c^4*f*g^5*h^6 - 2730*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^3*c^4*d*g^3*h^8 + 8620*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^4*c^3*f*g^3*h^8 + 720*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^4*c^3*d*g*h^10 + 4800*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^5*c^2*f*g*h^10 - 384*(sqrt(c)*x - sqrt(c*x^2 + a))^5*c^7*g^10*h*e + 672*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a*c^6*g^8*h^3*e + 3936*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^2*c^5*g^6*h^5*e + 5580*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^3*c^4*g^4*h^7*e - 2970*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^4*c^3*g^2*h^9*e - 11920*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a*c^(13/2)*f*g^10*h + 240*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a*c^(13/2)*d*g^8*h^3 - 15720*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^2*c^(11/2)*f*g^8*h^3 + 720*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^2*c^(11/2)*d*g^6*h^5 + 19670*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^3*c^(9/2)*f*g^6*h^5 - 3510*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^3*c^(9/2)*d*g^4*h^7 + 36260*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^4*c^(7/2)*f*g^4*h^7 + 1440*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^4*c^(7/2)*d*g^2*h^9 + 6240*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^5*c^(5/2)*f*g^2*h^9 - 240*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^5*c^(5/2)*d*h^11 - 880*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^6*c^(3/2)*f*h^11 + 960*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a*c^(13/2)*g^9*h^2*e + 1680*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^2*c^(11/2)*g^7*h^4*e - 480*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^3*c^(9/2)*g^5*h^6*e - 6150*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^4*c^(7/2)*g^3*h^8*e + 720*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^5*c^(5/2)*g*h^10*e + 13120*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^2*c^6*f*g^9*h^2 - 240*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^2*c^6*d*g^7*h^4 + 30440*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^3*c^5*f*g^7*h^4 - 1200*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^3*c^5*d*g^5*h^6 + 14130*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^4*c^4*f*g^5*h^6 + 2310*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^4*c^4*d*g^3*h^8 - 10790*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^5*c^3*f*g^3*h^8 - 510*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^5*c^3*d*g*h^10 - 3820*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^6*c^2*f*g*h^10 - 960*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^2*c^6*g^8*h^3*e - 2640*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^3*c^5*g^6*h^5*e - 2640*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^4*c^4*g^4*h^7*e + 2790*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^5*c^3*g^2*h^9*e - 30*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^6*c^2*h^11*e - 7360*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^3*c^(11/2)*f*g^8*h^3 + 120*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^3*c^(11/2)*d*g^6*h^5 - 19930*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^4*c^(9/2)*f*g^6*h^5 + 690*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^4*c^(9/2)*d*g^4*h^7 - 16050*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^5*c^(7/2)*f*g^4*h^7 - 1050*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^5*c^(7/2)*d*g^2*h^9 - 1300*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^6*c^(5/2)*f*g^2*h^9 + 560*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^7*c^(3/2)*f*h^11 + 480*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^3*c^(11/2)*g^7*h^4*e + 1560*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^4*c^(9/2)*g^5*h^6*e + 2130*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^5*c^(7/2)*g^3*h^8*e - 570*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^6*c^(5/2)*g*h^10*e + 2140*(sqrt(c)*x - sqrt(c*x^2 + a))*a^4*c^5*f*g^7*h^4 - 60*(sqrt(c)*x - sqrt(c*x^2 + a))*a^4*c^5*d*g^5*h^6 + 6090*(sqrt(c)*x - sqrt(c*x^2 + a))*a^5*c^4*f*g^5*h^6 - 270*(sqrt(c)*x - sqrt(c*x^2 + a))*a^5*c^4*d*g^3*h^8 + 5505*(sqrt(c)*x - sqrt(c*x^2 + a))*a^6*c^3*f*g^3*h^8 + 195*(sqrt(c)*x - sqrt(c*x^2 + a))*a^6*c^3*d*g*h^10 + 1150*(sqrt(c)*x - sqrt(c*x^2 + a))*a^7*c^2*f*g*h^10 - 120*(sqrt(c)*x - sqrt(c*x^2 + a))*a^4*c^5*g^6*h^5*e - 420*(sqrt(c)*x - sqrt(c*x^2 + a))*a^5*c^4*g^4*h^7*e - 630*(sqrt(c)*x - sqrt(c*x^2 + a))*a^6*c^3*g^2*h^9*e + 75*(sqrt(c)*x - sqrt(c*x^2 + a))*a^7*c^2*h^11*e - 274*a^5*c^(9/2)*f*g^6*h^5 + 6*a^5*c^(9/2)*d*g^4*h^7 - 783*a^6*c^(7/2)*f*g^4*h^7 + 27*a^6*c^(7/2)*d*g^2*h^9 - 714*a^7*c^(5/2)*f*g^2*h^9 - 24*a^7*c^(5/2)*d*h^11 - 160*a^8*c^(3/2)*f*h^11 + 24*a^5*c^(9/2)*g^5*h^6*e + 78*a^6*c^(7/2)*g^3*h^8*e + 99*a^7*c^(5/2)*g*h^10*e)/((c^3*g^6*h^6 + 3*a*c^2*g^4*h^8 + 3*a^2*c*g^2*h^10 + a^3*h^12)*((sqrt(c)*x - sqrt(c*x^2 + a))^2*h + 2*(sqrt(c)*x - sqrt(c*x^2 + a))*sqrt(c)*g - a*h)^5)","B",0
98,1,6122,0,1.122905," ","integrate((c*x^2+a)^(3/2)*(f*x^2+e*x+d)/(h*x+g)^7,x, algorithm=""giac"")","\frac{{\left(6 \, a^{2} c^{4} d g^{2} - a^{3} c^{3} f g^{2} - a^{3} c^{3} d h^{2} + 6 \, a^{4} c^{2} f h^{2} + 7 \, a^{3} c^{3} g h e\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} h + \sqrt{c} g}{\sqrt{-c g^{2} - a h^{2}}}\right)}{8 \, {\left(c^{4} g^{8} + 4 \, a c^{3} g^{6} h^{2} + 6 \, a^{2} c^{2} g^{4} h^{4} + 4 \, a^{3} c g^{2} h^{6} + a^{4} h^{8}\right)} \sqrt{-c g^{2} - a h^{2}}} + \frac{240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{11} c^{6} f g^{8} h^{5} + 960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{11} a c^{5} f g^{6} h^{7} + 1440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{11} a^{2} c^{4} f g^{4} h^{9} - 90 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{11} a^{2} c^{4} d g^{2} h^{11} + 975 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{11} a^{3} c^{3} f g^{2} h^{11} + 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{11} a^{3} c^{3} d h^{13} + 150 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{11} a^{4} c^{2} f h^{13} - 105 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{11} a^{3} c^{3} g h^{12} e + 1200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} c^{\frac{13}{2}} f g^{9} h^{4} + 4800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} a c^{\frac{11}{2}} f g^{7} h^{6} + 7200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} a^{2} c^{\frac{9}{2}} f g^{5} h^{8} - 990 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} a^{2} c^{\frac{9}{2}} d g^{3} h^{10} + 4965 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} a^{3} c^{\frac{7}{2}} f g^{3} h^{10} + 165 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} a^{3} c^{\frac{7}{2}} d g h^{12} + 210 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} a^{4} c^{\frac{5}{2}} f g h^{12} + 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} c^{\frac{13}{2}} g^{8} h^{5} e + 960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} a c^{\frac{11}{2}} g^{6} h^{7} e + 1440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} a^{2} c^{\frac{9}{2}} g^{4} h^{9} e - 195 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} a^{3} c^{\frac{7}{2}} g^{2} h^{11} e + 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} a^{4} c^{\frac{5}{2}} h^{13} e + 3200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} c^{7} f g^{10} h^{3} + 320 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} c^{7} d g^{8} h^{5} + 12080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a c^{6} f g^{8} h^{5} + 1280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a c^{6} d g^{6} h^{7} + 16320 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a^{2} c^{5} f g^{6} h^{7} - 2520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a^{2} c^{5} d g^{4} h^{9} + 9220 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a^{3} c^{4} f g^{4} h^{9} + 2530 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a^{3} c^{4} d g^{2} h^{11} - 4205 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a^{4} c^{3} f g^{2} h^{11} + 235 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a^{4} c^{3} d h^{13} - 210 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a^{5} c^{2} f h^{13} + 640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} c^{7} g^{9} h^{4} e + 2560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a c^{6} g^{7} h^{6} e + 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a^{2} c^{5} g^{5} h^{8} e - 2620 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a^{3} c^{4} g^{3} h^{10} e + 1235 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a^{4} c^{3} g h^{12} e + 4800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} c^{\frac{15}{2}} f g^{11} h^{2} + 480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} c^{\frac{15}{2}} d g^{9} h^{4} + 15120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a c^{\frac{13}{2}} f g^{9} h^{4} + 1920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a c^{\frac{13}{2}} d g^{7} h^{6} + 12480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{2} c^{\frac{11}{2}} f g^{7} h^{6} - 7380 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{2} c^{\frac{11}{2}} d g^{5} h^{8} - 3570 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{3} c^{\frac{9}{2}} f g^{5} h^{8} + 8220 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{3} c^{\frac{9}{2}} d g^{3} h^{10} - 22545 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{4} c^{\frac{7}{2}} f g^{3} h^{10} - 285 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{4} c^{\frac{7}{2}} d g h^{12} + 510 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{5} c^{\frac{5}{2}} f g h^{12} + 960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} c^{\frac{15}{2}} g^{10} h^{3} e + 3600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a c^{\frac{13}{2}} g^{8} h^{5} e + 4800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{2} c^{\frac{11}{2}} g^{6} h^{7} e - 9570 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{3} c^{\frac{9}{2}} g^{4} h^{9} e + 5355 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{4} c^{\frac{7}{2}} g^{2} h^{11} e - 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{5} c^{\frac{5}{2}} h^{13} e + 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} c^{8} f g^{12} h + 384 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} c^{8} d g^{10} h^{3} + 6336 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a c^{7} f g^{10} h^{3} + 1728 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a c^{7} d g^{8} h^{5} - 11808 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{2} c^{6} f g^{8} h^{5} - 9456 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{2} c^{6} d g^{6} h^{7} - 31704 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{3} c^{5} f g^{6} h^{7} + 20760 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{3} c^{5} d g^{4} h^{9} - 39960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{4} c^{4} f g^{4} h^{9} - 2700 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{4} c^{4} d g^{2} h^{11} + 12150 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{5} c^{3} f g^{2} h^{11} + 390 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{5} c^{3} d h^{13} + 60 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{6} c^{2} f h^{13} + 768 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} c^{8} g^{11} h^{2} e + 1728 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a c^{7} g^{9} h^{4} e - 768 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{2} c^{6} g^{7} h^{6} e - 19608 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{3} c^{5} g^{5} h^{8} e + 14040 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{4} c^{4} g^{3} h^{10} e - 2730 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{5} c^{3} g h^{12} e + 1280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} c^{\frac{17}{2}} f g^{13} + 128 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} c^{\frac{17}{2}} d g^{11} h^{2} - 4288 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a c^{\frac{15}{2}} f g^{11} h^{2} - 64 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a c^{\frac{15}{2}} d g^{9} h^{4} - 24096 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{2} c^{\frac{13}{2}} f g^{9} h^{4} - 8592 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{2} c^{\frac{13}{2}} d g^{7} h^{6} - 26728 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{3} c^{\frac{11}{2}} f g^{7} h^{6} + 24440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{3} c^{\frac{11}{2}} d g^{5} h^{8} - 12640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{4} c^{\frac{9}{2}} f g^{5} h^{8} - 14860 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{4} c^{\frac{9}{2}} d g^{3} h^{10} + 41610 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{5} c^{\frac{7}{2}} f g^{3} h^{10} + 810 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{5} c^{\frac{7}{2}} d g h^{12} - 2460 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{6} c^{\frac{5}{2}} f g h^{12} + 256 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} c^{\frac{17}{2}} g^{12} h e - 704 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a c^{\frac{15}{2}} g^{10} h^{3} e - 4896 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{2} c^{\frac{13}{2}} g^{8} h^{5} e - 15656 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{3} c^{\frac{11}{2}} g^{6} h^{7} e + 26800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{4} c^{\frac{9}{2}} g^{4} h^{9} e - 9510 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{5} c^{\frac{7}{2}} g^{2} h^{11} e + 480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{6} c^{\frac{5}{2}} h^{13} e - 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a c^{8} f g^{12} h - 384 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a c^{8} d g^{10} h^{3} - 6336 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{2} c^{7} f g^{10} h^{3} - 1728 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{2} c^{7} d g^{8} h^{5} + 11808 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{3} c^{6} f g^{8} h^{5} + 19056 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{3} c^{6} d g^{6} h^{7} + 29304 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{4} c^{5} f g^{6} h^{7} - 21480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{4} c^{5} d g^{4} h^{9} + 46080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{5} c^{4} f g^{4} h^{9} + 7020 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{5} c^{4} d g^{2} h^{11} - 17370 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{6} c^{3} f g^{2} h^{11} + 390 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{6} c^{3} d h^{13} + 60 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{7} c^{2} f h^{13} - 768 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a c^{8} g^{11} h^{2} e - 1728 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{2} c^{7} g^{9} h^{4} e - 192 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{3} c^{6} g^{7} h^{6} e + 26808 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{4} c^{5} g^{5} h^{8} e - 19440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{5} c^{4} g^{3} h^{10} e + 3030 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{6} c^{3} g h^{12} e + 4800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{2} c^{\frac{15}{2}} f g^{11} h^{2} + 480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{2} c^{\frac{15}{2}} d g^{9} h^{4} + 15120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{3} c^{\frac{13}{2}} f g^{9} h^{4} + 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{3} c^{\frac{13}{2}} d g^{7} h^{6} + 12360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{4} c^{\frac{11}{2}} f g^{7} h^{6} - 18720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{4} c^{\frac{11}{2}} d g^{5} h^{8} + 1020 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{5} c^{\frac{9}{2}} f g^{5} h^{8} + 11640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{5} c^{\frac{9}{2}} d g^{3} h^{10} - 32490 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{6} c^{\frac{7}{2}} f g^{3} h^{10} - 930 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{6} c^{\frac{7}{2}} d g h^{12} + 3180 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{7} c^{\frac{5}{2}} f g h^{12} + 960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{2} c^{\frac{15}{2}} g^{10} h^{3} e + 3600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{3} c^{\frac{13}{2}} g^{8} h^{5} e + 7080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{4} c^{\frac{11}{2}} g^{6} h^{7} e - 22260 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{5} c^{\frac{9}{2}} g^{4} h^{9} e + 7470 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{6} c^{\frac{7}{2}} g^{2} h^{11} e - 480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{7} c^{\frac{5}{2}} h^{13} e - 3200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{3} c^{7} f g^{10} h^{3} - 320 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{3} c^{7} d g^{8} h^{5} - 12080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{4} c^{6} f g^{8} h^{5} - 2960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{4} c^{6} d g^{6} h^{7} - 16440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{5} c^{5} f g^{6} h^{7} + 12120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{5} c^{5} d g^{4} h^{9} - 14120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{6} c^{4} f g^{4} h^{9} - 2330 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{6} c^{4} d g^{2} h^{11} + 10555 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{7} c^{3} f g^{2} h^{11} + 235 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{7} c^{3} d h^{13} - 210 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{8} c^{2} f h^{13} - 640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{3} c^{7} g^{9} h^{4} e - 3040 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{4} c^{6} g^{7} h^{6} e - 7800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{5} c^{5} g^{5} h^{8} e + 10280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{6} c^{4} g^{3} h^{10} e - 1645 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{7} c^{3} g h^{12} e + 1200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{4} c^{\frac{13}{2}} f g^{9} h^{4} + 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{4} c^{\frac{13}{2}} d g^{7} h^{6} + 4920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{5} c^{\frac{11}{2}} f g^{7} h^{6} + 1656 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{5} c^{\frac{11}{2}} d g^{5} h^{8} + 7824 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{6} c^{\frac{9}{2}} f g^{5} h^{8} - 4038 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{6} c^{\frac{9}{2}} d g^{3} h^{10} + 8193 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{7} c^{\frac{7}{2}} f g^{3} h^{10} + 321 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{7} c^{\frac{7}{2}} d g h^{12} - 1686 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{8} c^{\frac{5}{2}} f g h^{12} + 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{4} c^{\frac{13}{2}} g^{8} h^{5} e + 1272 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{5} c^{\frac{11}{2}} g^{6} h^{7} e + 3552 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{6} c^{\frac{9}{2}} g^{4} h^{9} e - 3207 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{7} c^{\frac{7}{2}} g^{2} h^{11} e + 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{8} c^{\frac{5}{2}} h^{13} e - 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{5} c^{6} f g^{8} h^{5} - 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{5} c^{6} d g^{6} h^{7} - 1032 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{6} c^{5} f g^{6} h^{7} - 336 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{6} c^{5} d g^{4} h^{9} - 1764 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{7} c^{4} f g^{4} h^{9} + 882 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{7} c^{4} d g^{2} h^{11} - 1977 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{8} c^{3} f g^{2} h^{11} + 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{8} c^{3} d h^{13} + 150 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{9} c^{2} f h^{13} - 96 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{5} c^{6} g^{7} h^{6} e - 456 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{6} c^{5} g^{5} h^{8} e - 1044 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{7} c^{4} g^{3} h^{10} e + 471 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{8} c^{3} g h^{12} e + 40 \, a^{6} c^{\frac{11}{2}} f g^{7} h^{6} + 4 \, a^{6} c^{\frac{11}{2}} d g^{5} h^{8} + 166 \, a^{7} c^{\frac{9}{2}} f g^{5} h^{8} + 28 \, a^{7} c^{\frac{9}{2}} d g^{3} h^{10} + 267 \, a^{8} c^{\frac{7}{2}} f g^{3} h^{10} - 81 \, a^{8} c^{\frac{7}{2}} d g h^{12} + 246 \, a^{9} c^{\frac{5}{2}} f g h^{12} + 8 \, a^{6} c^{\frac{11}{2}} g^{6} h^{7} e + 38 \, a^{7} c^{\frac{9}{2}} g^{4} h^{9} e + 87 \, a^{8} c^{\frac{7}{2}} g^{2} h^{11} e - 48 \, a^{9} c^{\frac{5}{2}} h^{13} e}{120 \, {\left(c^{4} g^{8} h^{6} + 4 \, a c^{3} g^{6} h^{8} + 6 \, a^{2} c^{2} g^{4} h^{10} + 4 \, a^{3} c g^{2} h^{12} + a^{4} h^{14}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} h + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} \sqrt{c} g - a h\right)}^{6}}"," ",0,"1/8*(6*a^2*c^4*d*g^2 - a^3*c^3*f*g^2 - a^3*c^3*d*h^2 + 6*a^4*c^2*f*h^2 + 7*a^3*c^3*g*h*e)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + a))*h + sqrt(c)*g)/sqrt(-c*g^2 - a*h^2))/((c^4*g^8 + 4*a*c^3*g^6*h^2 + 6*a^2*c^2*g^4*h^4 + 4*a^3*c*g^2*h^6 + a^4*h^8)*sqrt(-c*g^2 - a*h^2)) + 1/120*(240*(sqrt(c)*x - sqrt(c*x^2 + a))^11*c^6*f*g^8*h^5 + 960*(sqrt(c)*x - sqrt(c*x^2 + a))^11*a*c^5*f*g^6*h^7 + 1440*(sqrt(c)*x - sqrt(c*x^2 + a))^11*a^2*c^4*f*g^4*h^9 - 90*(sqrt(c)*x - sqrt(c*x^2 + a))^11*a^2*c^4*d*g^2*h^11 + 975*(sqrt(c)*x - sqrt(c*x^2 + a))^11*a^3*c^3*f*g^2*h^11 + 15*(sqrt(c)*x - sqrt(c*x^2 + a))^11*a^3*c^3*d*h^13 + 150*(sqrt(c)*x - sqrt(c*x^2 + a))^11*a^4*c^2*f*h^13 - 105*(sqrt(c)*x - sqrt(c*x^2 + a))^11*a^3*c^3*g*h^12*e + 1200*(sqrt(c)*x - sqrt(c*x^2 + a))^10*c^(13/2)*f*g^9*h^4 + 4800*(sqrt(c)*x - sqrt(c*x^2 + a))^10*a*c^(11/2)*f*g^7*h^6 + 7200*(sqrt(c)*x - sqrt(c*x^2 + a))^10*a^2*c^(9/2)*f*g^5*h^8 - 990*(sqrt(c)*x - sqrt(c*x^2 + a))^10*a^2*c^(9/2)*d*g^3*h^10 + 4965*(sqrt(c)*x - sqrt(c*x^2 + a))^10*a^3*c^(7/2)*f*g^3*h^10 + 165*(sqrt(c)*x - sqrt(c*x^2 + a))^10*a^3*c^(7/2)*d*g*h^12 + 210*(sqrt(c)*x - sqrt(c*x^2 + a))^10*a^4*c^(5/2)*f*g*h^12 + 240*(sqrt(c)*x - sqrt(c*x^2 + a))^10*c^(13/2)*g^8*h^5*e + 960*(sqrt(c)*x - sqrt(c*x^2 + a))^10*a*c^(11/2)*g^6*h^7*e + 1440*(sqrt(c)*x - sqrt(c*x^2 + a))^10*a^2*c^(9/2)*g^4*h^9*e - 195*(sqrt(c)*x - sqrt(c*x^2 + a))^10*a^3*c^(7/2)*g^2*h^11*e + 240*(sqrt(c)*x - sqrt(c*x^2 + a))^10*a^4*c^(5/2)*h^13*e + 3200*(sqrt(c)*x - sqrt(c*x^2 + a))^9*c^7*f*g^10*h^3 + 320*(sqrt(c)*x - sqrt(c*x^2 + a))^9*c^7*d*g^8*h^5 + 12080*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a*c^6*f*g^8*h^5 + 1280*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a*c^6*d*g^6*h^7 + 16320*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a^2*c^5*f*g^6*h^7 - 2520*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a^2*c^5*d*g^4*h^9 + 9220*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a^3*c^4*f*g^4*h^9 + 2530*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a^3*c^4*d*g^2*h^11 - 4205*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a^4*c^3*f*g^2*h^11 + 235*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a^4*c^3*d*h^13 - 210*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a^5*c^2*f*h^13 + 640*(sqrt(c)*x - sqrt(c*x^2 + a))^9*c^7*g^9*h^4*e + 2560*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a*c^6*g^7*h^6*e + 3840*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a^2*c^5*g^5*h^8*e - 2620*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a^3*c^4*g^3*h^10*e + 1235*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a^4*c^3*g*h^12*e + 4800*(sqrt(c)*x - sqrt(c*x^2 + a))^8*c^(15/2)*f*g^11*h^2 + 480*(sqrt(c)*x - sqrt(c*x^2 + a))^8*c^(15/2)*d*g^9*h^4 + 15120*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a*c^(13/2)*f*g^9*h^4 + 1920*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a*c^(13/2)*d*g^7*h^6 + 12480*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^2*c^(11/2)*f*g^7*h^6 - 7380*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^2*c^(11/2)*d*g^5*h^8 - 3570*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^3*c^(9/2)*f*g^5*h^8 + 8220*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^3*c^(9/2)*d*g^3*h^10 - 22545*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^4*c^(7/2)*f*g^3*h^10 - 285*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^4*c^(7/2)*d*g*h^12 + 510*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^5*c^(5/2)*f*g*h^12 + 960*(sqrt(c)*x - sqrt(c*x^2 + a))^8*c^(15/2)*g^10*h^3*e + 3600*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a*c^(13/2)*g^8*h^5*e + 4800*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^2*c^(11/2)*g^6*h^7*e - 9570*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^3*c^(9/2)*g^4*h^9*e + 5355*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^4*c^(7/2)*g^2*h^11*e - 240*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^5*c^(5/2)*h^13*e + 3840*(sqrt(c)*x - sqrt(c*x^2 + a))^7*c^8*f*g^12*h + 384*(sqrt(c)*x - sqrt(c*x^2 + a))^7*c^8*d*g^10*h^3 + 6336*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a*c^7*f*g^10*h^3 + 1728*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a*c^7*d*g^8*h^5 - 11808*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^2*c^6*f*g^8*h^5 - 9456*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^2*c^6*d*g^6*h^7 - 31704*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^3*c^5*f*g^6*h^7 + 20760*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^3*c^5*d*g^4*h^9 - 39960*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^4*c^4*f*g^4*h^9 - 2700*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^4*c^4*d*g^2*h^11 + 12150*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^5*c^3*f*g^2*h^11 + 390*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^5*c^3*d*h^13 + 60*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^6*c^2*f*h^13 + 768*(sqrt(c)*x - sqrt(c*x^2 + a))^7*c^8*g^11*h^2*e + 1728*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a*c^7*g^9*h^4*e - 768*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^2*c^6*g^7*h^6*e - 19608*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^3*c^5*g^5*h^8*e + 14040*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^4*c^4*g^3*h^10*e - 2730*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^5*c^3*g*h^12*e + 1280*(sqrt(c)*x - sqrt(c*x^2 + a))^6*c^(17/2)*f*g^13 + 128*(sqrt(c)*x - sqrt(c*x^2 + a))^6*c^(17/2)*d*g^11*h^2 - 4288*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a*c^(15/2)*f*g^11*h^2 - 64*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a*c^(15/2)*d*g^9*h^4 - 24096*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^2*c^(13/2)*f*g^9*h^4 - 8592*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^2*c^(13/2)*d*g^7*h^6 - 26728*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^3*c^(11/2)*f*g^7*h^6 + 24440*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^3*c^(11/2)*d*g^5*h^8 - 12640*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^4*c^(9/2)*f*g^5*h^8 - 14860*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^4*c^(9/2)*d*g^3*h^10 + 41610*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^5*c^(7/2)*f*g^3*h^10 + 810*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^5*c^(7/2)*d*g*h^12 - 2460*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^6*c^(5/2)*f*g*h^12 + 256*(sqrt(c)*x - sqrt(c*x^2 + a))^6*c^(17/2)*g^12*h*e - 704*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a*c^(15/2)*g^10*h^3*e - 4896*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^2*c^(13/2)*g^8*h^5*e - 15656*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^3*c^(11/2)*g^6*h^7*e + 26800*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^4*c^(9/2)*g^4*h^9*e - 9510*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^5*c^(7/2)*g^2*h^11*e + 480*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^6*c^(5/2)*h^13*e - 3840*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a*c^8*f*g^12*h - 384*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a*c^8*d*g^10*h^3 - 6336*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^2*c^7*f*g^10*h^3 - 1728*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^2*c^7*d*g^8*h^5 + 11808*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^3*c^6*f*g^8*h^5 + 19056*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^3*c^6*d*g^6*h^7 + 29304*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^4*c^5*f*g^6*h^7 - 21480*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^4*c^5*d*g^4*h^9 + 46080*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^5*c^4*f*g^4*h^9 + 7020*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^5*c^4*d*g^2*h^11 - 17370*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^6*c^3*f*g^2*h^11 + 390*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^6*c^3*d*h^13 + 60*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^7*c^2*f*h^13 - 768*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a*c^8*g^11*h^2*e - 1728*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^2*c^7*g^9*h^4*e - 192*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^3*c^6*g^7*h^6*e + 26808*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^4*c^5*g^5*h^8*e - 19440*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^5*c^4*g^3*h^10*e + 3030*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^6*c^3*g*h^12*e + 4800*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^2*c^(15/2)*f*g^11*h^2 + 480*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^2*c^(15/2)*d*g^9*h^4 + 15120*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^3*c^(13/2)*f*g^9*h^4 + 3840*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^3*c^(13/2)*d*g^7*h^6 + 12360*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^4*c^(11/2)*f*g^7*h^6 - 18720*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^4*c^(11/2)*d*g^5*h^8 + 1020*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^5*c^(9/2)*f*g^5*h^8 + 11640*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^5*c^(9/2)*d*g^3*h^10 - 32490*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^6*c^(7/2)*f*g^3*h^10 - 930*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^6*c^(7/2)*d*g*h^12 + 3180*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^7*c^(5/2)*f*g*h^12 + 960*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^2*c^(15/2)*g^10*h^3*e + 3600*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^3*c^(13/2)*g^8*h^5*e + 7080*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^4*c^(11/2)*g^6*h^7*e - 22260*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^5*c^(9/2)*g^4*h^9*e + 7470*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^6*c^(7/2)*g^2*h^11*e - 480*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^7*c^(5/2)*h^13*e - 3200*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^3*c^7*f*g^10*h^3 - 320*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^3*c^7*d*g^8*h^5 - 12080*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^4*c^6*f*g^8*h^5 - 2960*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^4*c^6*d*g^6*h^7 - 16440*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^5*c^5*f*g^6*h^7 + 12120*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^5*c^5*d*g^4*h^9 - 14120*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^6*c^4*f*g^4*h^9 - 2330*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^6*c^4*d*g^2*h^11 + 10555*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^7*c^3*f*g^2*h^11 + 235*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^7*c^3*d*h^13 - 210*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^8*c^2*f*h^13 - 640*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^3*c^7*g^9*h^4*e - 3040*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^4*c^6*g^7*h^6*e - 7800*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^5*c^5*g^5*h^8*e + 10280*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^6*c^4*g^3*h^10*e - 1645*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^7*c^3*g*h^12*e + 1200*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^4*c^(13/2)*f*g^9*h^4 + 240*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^4*c^(13/2)*d*g^7*h^6 + 4920*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^5*c^(11/2)*f*g^7*h^6 + 1656*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^5*c^(11/2)*d*g^5*h^8 + 7824*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^6*c^(9/2)*f*g^5*h^8 - 4038*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^6*c^(9/2)*d*g^3*h^10 + 8193*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^7*c^(7/2)*f*g^3*h^10 + 321*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^7*c^(7/2)*d*g*h^12 - 1686*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^8*c^(5/2)*f*g*h^12 + 240*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^4*c^(13/2)*g^8*h^5*e + 1272*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^5*c^(11/2)*g^6*h^7*e + 3552*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^6*c^(9/2)*g^4*h^9*e - 3207*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^7*c^(7/2)*g^2*h^11*e + 48*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^8*c^(5/2)*h^13*e - 240*(sqrt(c)*x - sqrt(c*x^2 + a))*a^5*c^6*f*g^8*h^5 - 48*(sqrt(c)*x - sqrt(c*x^2 + a))*a^5*c^6*d*g^6*h^7 - 1032*(sqrt(c)*x - sqrt(c*x^2 + a))*a^6*c^5*f*g^6*h^7 - 336*(sqrt(c)*x - sqrt(c*x^2 + a))*a^6*c^5*d*g^4*h^9 - 1764*(sqrt(c)*x - sqrt(c*x^2 + a))*a^7*c^4*f*g^4*h^9 + 882*(sqrt(c)*x - sqrt(c*x^2 + a))*a^7*c^4*d*g^2*h^11 - 1977*(sqrt(c)*x - sqrt(c*x^2 + a))*a^8*c^3*f*g^2*h^11 + 15*(sqrt(c)*x - sqrt(c*x^2 + a))*a^8*c^3*d*h^13 + 150*(sqrt(c)*x - sqrt(c*x^2 + a))*a^9*c^2*f*h^13 - 96*(sqrt(c)*x - sqrt(c*x^2 + a))*a^5*c^6*g^7*h^6*e - 456*(sqrt(c)*x - sqrt(c*x^2 + a))*a^6*c^5*g^5*h^8*e - 1044*(sqrt(c)*x - sqrt(c*x^2 + a))*a^7*c^4*g^3*h^10*e + 471*(sqrt(c)*x - sqrt(c*x^2 + a))*a^8*c^3*g*h^12*e + 40*a^6*c^(11/2)*f*g^7*h^6 + 4*a^6*c^(11/2)*d*g^5*h^8 + 166*a^7*c^(9/2)*f*g^5*h^8 + 28*a^7*c^(9/2)*d*g^3*h^10 + 267*a^8*c^(7/2)*f*g^3*h^10 - 81*a^8*c^(7/2)*d*g*h^12 + 246*a^9*c^(5/2)*f*g*h^12 + 8*a^6*c^(11/2)*g^6*h^7*e + 38*a^7*c^(9/2)*g^4*h^9*e + 87*a^8*c^(7/2)*g^2*h^11*e - 48*a^9*c^(5/2)*h^13*e)/((c^4*g^8*h^6 + 4*a*c^3*g^6*h^8 + 6*a^2*c^2*g^4*h^10 + 4*a^3*c*g^2*h^12 + a^4*h^14)*((sqrt(c)*x - sqrt(c*x^2 + a))^2*h + 2*(sqrt(c)*x - sqrt(c*x^2 + a))*sqrt(c)*g - a*h)^6)","B",0
99,1,7936,0,1.117629," ","integrate((c*x^2+a)^(3/2)*(f*x^2+e*x+d)/(h*x+g)^8,x, algorithm=""giac"")","-\frac{{\left(6 \, a^{2} c^{5} d g^{3} - a^{3} c^{4} f g^{3} - 3 \, a^{3} c^{4} d g h^{2} + 8 \, a^{4} c^{3} f g h^{2} + 8 \, a^{3} c^{4} g^{2} h e - a^{4} c^{3} h^{3} e\right)} \arctan\left(\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} h + \sqrt{c} g}{\sqrt{-c g^{2} - a h^{2}}}\right)}{8 \, {\left(c^{5} g^{10} + 5 \, a c^{4} g^{8} h^{2} + 10 \, a^{2} c^{3} g^{6} h^{4} + 10 \, a^{3} c^{2} g^{4} h^{6} + 5 \, a^{4} c g^{2} h^{8} + a^{5} h^{10}\right)} \sqrt{-c g^{2} - a h^{2}}} - \frac{630 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{13} a^{2} c^{5} d g^{3} h^{12} - 105 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{13} a^{3} c^{4} f g^{3} h^{12} - 315 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{13} a^{3} c^{4} d g h^{14} + 840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{13} a^{4} c^{3} f g h^{14} + 840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{13} a^{3} c^{4} g^{2} h^{13} e - 105 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{13} a^{4} c^{3} h^{15} e - 1680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{12} c^{\frac{15}{2}} f g^{10} h^{5} - 8400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{12} a c^{\frac{13}{2}} f g^{8} h^{7} - 16800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{12} a^{2} c^{\frac{11}{2}} f g^{6} h^{9} + 8190 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{12} a^{2} c^{\frac{11}{2}} d g^{4} h^{11} - 18165 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{12} a^{3} c^{\frac{9}{2}} f g^{4} h^{11} - 4095 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{12} a^{3} c^{\frac{9}{2}} d g^{2} h^{13} + 2520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{12} a^{4} c^{\frac{7}{2}} f g^{2} h^{13} - 1680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{12} a^{5} c^{\frac{5}{2}} f h^{15} + 10920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{12} a^{3} c^{\frac{9}{2}} g^{3} h^{12} e - 1365 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{12} a^{4} c^{\frac{7}{2}} g h^{14} e - 5600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{11} c^{8} f g^{11} h^{4} - 28000 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{11} a c^{7} f g^{9} h^{6} - 56000 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{11} a^{2} c^{6} f g^{7} h^{8} + 44940 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{11} a^{2} c^{6} d g^{5} h^{10} - 63490 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{11} a^{3} c^{5} f g^{5} h^{10} - 26670 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{11} a^{3} c^{5} d g^{3} h^{12} + 32620 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{11} a^{4} c^{4} f g^{3} h^{12} + 2100 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{11} a^{4} c^{4} d g h^{14} - 11200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{11} a^{5} c^{3} f g h^{14} - 2240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{11} c^{8} g^{10} h^{5} e - 11200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{11} a c^{7} g^{8} h^{7} e - 22400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{11} a^{2} c^{6} g^{6} h^{9} e + 37520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{11} a^{3} c^{5} g^{4} h^{11} e - 24290 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{11} a^{4} c^{4} g^{2} h^{13} e - 1540 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{11} a^{5} c^{3} h^{15} e - 11200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} c^{\frac{17}{2}} f g^{12} h^{3} - 3360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} c^{\frac{17}{2}} d g^{10} h^{5} - 52640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} a c^{\frac{15}{2}} f g^{10} h^{5} - 16800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} a c^{\frac{15}{2}} d g^{8} h^{7} - 95200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} a^{2} c^{\frac{13}{2}} f g^{8} h^{7} + 100380 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} a^{2} c^{\frac{13}{2}} d g^{6} h^{9} - 100730 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} a^{3} c^{\frac{11}{2}} f g^{6} h^{9} - 146790 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} a^{3} c^{\frac{11}{2}} d g^{4} h^{11} + 163940 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} a^{4} c^{\frac{9}{2}} f g^{4} h^{11} + 6300 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} a^{4} c^{\frac{9}{2}} d g^{2} h^{13} - 56000 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} a^{5} c^{\frac{7}{2}} f g^{2} h^{13} - 3360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} a^{5} c^{\frac{7}{2}} d h^{15} + 3360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} a^{6} c^{\frac{5}{2}} f h^{15} - 4480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} c^{\frac{17}{2}} g^{11} h^{4} e - 22400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} a c^{\frac{15}{2}} g^{9} h^{6} e - 44800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} a^{2} c^{\frac{13}{2}} g^{7} h^{8} e + 133840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} a^{3} c^{\frac{11}{2}} g^{5} h^{10} e - 106330 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} a^{4} c^{\frac{9}{2}} g^{3} h^{12} e + 3220 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} a^{5} c^{\frac{7}{2}} g h^{14} e - 13440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} c^{9} f g^{13} h^{2} - 4032 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} c^{9} d g^{11} h^{4} - 50848 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a c^{8} f g^{11} h^{4} - 20160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a c^{8} d g^{9} h^{6} - 52640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a^{2} c^{7} f g^{9} h^{6} + 191016 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a^{2} c^{7} d g^{7} h^{8} - 9436 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a^{3} c^{6} f g^{7} h^{8} - 363216 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a^{3} c^{6} d g^{5} h^{10} + 439306 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a^{4} c^{5} f g^{5} h^{10} + 95340 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a^{4} c^{5} d g^{3} h^{12} - 209965 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a^{5} c^{4} f g^{3} h^{12} - 9975 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a^{5} c^{4} d g h^{14} + 32200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a^{6} c^{3} f g h^{14} - 5376 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} c^{9} g^{12} h^{3} e - 25984 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a c^{8} g^{10} h^{5} e - 49280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a^{2} c^{7} g^{8} h^{7} e + 263648 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a^{3} c^{6} g^{6} h^{9} e - 332780 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a^{4} c^{5} g^{4} h^{11} e + 49490 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a^{5} c^{4} g^{2} h^{13} e - 1085 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a^{6} c^{3} h^{15} e - 8960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} c^{\frac{19}{2}} f g^{14} h - 2688 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} c^{\frac{19}{2}} d g^{12} h^{3} - 15232 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a c^{\frac{17}{2}} f g^{12} h^{3} - 16800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a c^{\frac{17}{2}} d g^{10} h^{5} + 53200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{2} c^{\frac{15}{2}} f g^{10} h^{5} + 181104 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{2} c^{\frac{15}{2}} d g^{8} h^{7} + 143416 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{3} c^{\frac{13}{2}} f g^{8} h^{7} - 651924 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{3} c^{\frac{13}{2}} d g^{6} h^{9} + 580034 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{4} c^{\frac{11}{2}} f g^{6} h^{9} + 299460 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{4} c^{\frac{11}{2}} d g^{4} h^{11} - 568085 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{5} c^{\frac{9}{2}} f g^{4} h^{11} - 72975 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{5} c^{\frac{9}{2}} d g^{2} h^{13} + 147000 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{6} c^{\frac{7}{2}} f g^{2} h^{13} - 3360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{6} c^{\frac{7}{2}} d h^{15} - 5040 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{7} c^{\frac{5}{2}} f h^{15} - 3584 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} c^{\frac{19}{2}} g^{13} h^{2} e - 9856 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a c^{\frac{17}{2}} g^{11} h^{4} e + 4480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{2} c^{\frac{15}{2}} g^{9} h^{6} e + 344512 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{3} c^{\frac{13}{2}} g^{7} h^{8} e - 613480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{4} c^{\frac{11}{2}} g^{5} h^{10} e + 259210 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{5} c^{\frac{9}{2}} g^{3} h^{12} e - 9765 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{6} c^{\frac{7}{2}} g h^{14} e - 2560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} c^{10} f g^{15} - 768 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} c^{10} d g^{13} h^{2} + 12928 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a c^{9} f g^{13} h^{2} + 384 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a c^{9} d g^{11} h^{4} + 80576 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{2} c^{8} f g^{11} h^{4} + 117984 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{2} c^{8} d g^{9} h^{6} + 101936 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{3} c^{7} f g^{9} h^{6} - 603216 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{3} c^{7} d g^{7} h^{8} + 256816 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{4} c^{6} f g^{7} h^{8} + 703752 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{4} c^{6} d g^{5} h^{10} - 941332 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{5} c^{5} f g^{5} h^{10} - 184380 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{5} c^{5} d g^{3} h^{12} + 413280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{6} c^{4} f g^{3} h^{12} + 13440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{6} c^{4} d g h^{14} - 47040 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{7} c^{3} f g h^{14} - 1024 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} c^{10} g^{14} h e + 4096 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a c^{9} g^{12} h^{3} e + 32768 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{2} c^{8} g^{10} h^{5} e + 205952 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{3} c^{7} g^{8} h^{7} e - 741776 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{4} c^{6} g^{6} h^{9} e + 608720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{5} c^{5} g^{4} h^{11} e - 92820 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{6} c^{4} g^{2} h^{13} e + 8960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a c^{\frac{19}{2}} f g^{14} h + 2688 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a c^{\frac{19}{2}} d g^{12} h^{3} + 15232 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{2} c^{\frac{17}{2}} f g^{12} h^{3} + 16800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{2} c^{\frac{17}{2}} d g^{10} h^{5} - 53200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{3} c^{\frac{15}{2}} f g^{10} h^{5} - 342384 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{3} c^{\frac{15}{2}} d g^{8} h^{7} - 103936 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{4} c^{\frac{13}{2}} f g^{8} h^{7} + 736344 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{4} c^{\frac{13}{2}} d g^{6} h^{9} - 726404 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{5} c^{\frac{11}{2}} f g^{6} h^{9} - 488460 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{5} c^{\frac{11}{2}} d g^{4} h^{11} + 764960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{6} c^{\frac{9}{2}} f g^{4} h^{11} + 33600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{6} c^{\frac{9}{2}} d g^{2} h^{13} - 168000 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{7} c^{\frac{7}{2}} f g^{2} h^{13} - 6720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{7} c^{\frac{7}{2}} d h^{15} + 6720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{8} c^{\frac{5}{2}} f h^{15} + 3584 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a c^{\frac{19}{2}} g^{13} h^{2} e + 9856 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{2} c^{\frac{17}{2}} g^{11} h^{4} e + 8960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{3} c^{\frac{15}{2}} g^{9} h^{6} e - 487312 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{4} c^{\frac{13}{2}} g^{7} h^{8} e + 807520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{5} c^{\frac{11}{2}} g^{5} h^{10} e - 310660 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{6} c^{\frac{9}{2}} g^{3} h^{12} e + 13440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{7} c^{\frac{7}{2}} g h^{14} e - 13440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{2} c^{9} f g^{13} h^{2} - 4032 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{2} c^{9} d g^{11} h^{4} - 50848 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{3} c^{8} f g^{11} h^{4} - 47040 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{3} c^{8} d g^{9} h^{6} - 50960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{4} c^{7} f g^{9} h^{6} + 438816 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{4} c^{7} d g^{7} h^{8} - 99736 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{5} c^{6} f g^{7} h^{8} - 556416 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{5} c^{6} d g^{5} h^{10} + 728756 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{6} c^{5} f g^{5} h^{10} + 167790 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{6} c^{5} d g^{3} h^{12} - 362915 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{7} c^{4} f g^{3} h^{12} - 10185 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{7} c^{4} d g h^{14} + 38360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{8} c^{3} f g h^{14} - 5376 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{2} c^{9} g^{12} h^{3} e - 25984 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{3} c^{8} g^{10} h^{5} e - 86240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{4} c^{7} g^{8} h^{7} e + 574448 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{5} c^{6} g^{6} h^{9} e - 487480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{6} c^{5} g^{4} h^{11} e + 89740 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{7} c^{4} g^{2} h^{13} e + 1085 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{8} c^{3} h^{15} e + 11200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{3} c^{\frac{17}{2}} f g^{12} h^{3} + 3360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{3} c^{\frac{17}{2}} d g^{10} h^{5} + 52640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{4} c^{\frac{15}{2}} f g^{10} h^{5} + 45360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{4} c^{\frac{15}{2}} d g^{8} h^{7} + 96880 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{5} c^{\frac{13}{2}} f g^{8} h^{7} - 364728 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{5} c^{\frac{13}{2}} d g^{6} h^{9} + 215908 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{6} c^{\frac{11}{2}} f g^{6} h^{9} + 220710 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{6} c^{\frac{11}{2}} d g^{4} h^{11} - 406735 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{7} c^{\frac{9}{2}} f g^{4} h^{11} - 49581 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{7} c^{\frac{9}{2}} d g^{2} h^{13} + 104776 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{8} c^{\frac{7}{2}} f g^{2} h^{13} - 1344 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{8} c^{\frac{7}{2}} d h^{15} - 3696 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{9} c^{\frac{5}{2}} f h^{15} + 4480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{3} c^{\frac{17}{2}} g^{11} h^{4} e + 29120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{4} c^{\frac{15}{2}} g^{9} h^{6} e + 119056 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{5} c^{\frac{13}{2}} g^{7} h^{8} e - 390656 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{6} c^{\frac{11}{2}} g^{5} h^{10} e + 179900 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{7} c^{\frac{9}{2}} g^{3} h^{12} e - 10703 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{8} c^{\frac{7}{2}} g h^{14} e - 5600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{4} c^{8} f g^{11} h^{4} - 3360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{4} c^{8} d g^{9} h^{6} - 29680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{5} c^{7} f g^{9} h^{6} - 32592 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{5} c^{7} d g^{7} h^{8} - 67088 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{6} c^{6} f g^{7} h^{8} + 172620 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{6} c^{6} d g^{5} h^{10} - 156170 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{7} c^{5} f g^{5} h^{10} - 62454 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{7} c^{5} d g^{3} h^{12} + 140084 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{8} c^{4} f g^{3} h^{12} + 5964 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{8} c^{4} d g h^{14} - 17024 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{9} c^{3} f g h^{14} - 2240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{4} c^{8} g^{10} h^{5} e - 16576 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{5} c^{7} g^{8} h^{7} e - 72464 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{6} c^{6} g^{6} h^{9} e + 179200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{7} c^{5} g^{4} h^{11} e - 31402 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{8} c^{4} g^{2} h^{13} e + 1540 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{9} c^{3} h^{15} e + 1680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{5} c^{\frac{15}{2}} f g^{10} h^{5} + 1008 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{5} c^{\frac{15}{2}} d g^{8} h^{7} + 9632 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{6} c^{\frac{13}{2}} f g^{8} h^{7} + 9996 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{6} c^{\frac{13}{2}} d g^{6} h^{9} + 24094 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{7} c^{\frac{11}{2}} f g^{6} h^{9} - 54894 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{7} c^{\frac{11}{2}} d g^{4} h^{11} + 56924 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{8} c^{\frac{9}{2}} f g^{4} h^{11} + 9156 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{8} c^{\frac{9}{2}} d g^{2} h^{13} - 32256 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{9} c^{\frac{7}{2}} f g^{2} h^{13} - 672 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{9} c^{\frac{7}{2}} d h^{15} + 672 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{10} c^{\frac{5}{2}} f h^{15} + 1344 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{5} c^{\frac{15}{2}} g^{9} h^{6} e + 8624 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{6} c^{\frac{13}{2}} g^{7} h^{8} e + 30352 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{7} c^{\frac{11}{2}} g^{5} h^{10} e - 47362 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{8} c^{\frac{9}{2}} g^{3} h^{12} e + 3276 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{9} c^{\frac{7}{2}} g h^{14} e - 560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{6} c^{7} f g^{9} h^{6} - 168 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{6} c^{7} d g^{7} h^{8} - 3052 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{7} c^{6} f g^{7} h^{8} - 1680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{7} c^{6} d g^{5} h^{10} - 7070 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{8} c^{5} f g^{5} h^{10} + 9744 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{8} c^{5} d g^{3} h^{12} - 12999 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{9} c^{4} f g^{3} h^{12} - 1029 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{9} c^{4} d g h^{14} + 3864 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{10} c^{3} f g h^{14} - 224 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{6} c^{7} g^{8} h^{7} e - 1456 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{7} c^{6} g^{6} h^{9} e - 5180 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{8} c^{5} g^{4} h^{11} e + 8442 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{9} c^{4} g^{2} h^{13} e + 105 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{10} c^{3} h^{15} e + 40 \, a^{7} c^{\frac{13}{2}} f g^{8} h^{7} + 12 \, a^{7} c^{\frac{13}{2}} d g^{6} h^{9} + 218 \, a^{8} c^{\frac{11}{2}} f g^{6} h^{9} + 120 \, a^{8} c^{\frac{11}{2}} d g^{4} h^{11} + 505 \, a^{9} c^{\frac{9}{2}} f g^{4} h^{11} - 741 \, a^{9} c^{\frac{9}{2}} d g^{2} h^{13} + 936 \, a^{10} c^{\frac{7}{2}} f g^{2} h^{13} + 96 \, a^{10} c^{\frac{7}{2}} d h^{15} - 336 \, a^{11} c^{\frac{5}{2}} f h^{15} + 16 \, a^{7} c^{\frac{13}{2}} g^{7} h^{8} e + 104 \, a^{8} c^{\frac{11}{2}} g^{5} h^{10} e + 370 \, a^{9} c^{\frac{9}{2}} g^{3} h^{12} e - 663 \, a^{10} c^{\frac{7}{2}} g h^{14} e}{840 \, {\left(c^{5} g^{10} h^{6} + 5 \, a c^{4} g^{8} h^{8} + 10 \, a^{2} c^{3} g^{6} h^{10} + 10 \, a^{3} c^{2} g^{4} h^{12} + 5 \, a^{4} c g^{2} h^{14} + a^{5} h^{16}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} h + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} \sqrt{c} g - a h\right)}^{7}}"," ",0,"-1/8*(6*a^2*c^5*d*g^3 - a^3*c^4*f*g^3 - 3*a^3*c^4*d*g*h^2 + 8*a^4*c^3*f*g*h^2 + 8*a^3*c^4*g^2*h*e - a^4*c^3*h^3*e)*arctan(((sqrt(c)*x - sqrt(c*x^2 + a))*h + sqrt(c)*g)/sqrt(-c*g^2 - a*h^2))/((c^5*g^10 + 5*a*c^4*g^8*h^2 + 10*a^2*c^3*g^6*h^4 + 10*a^3*c^2*g^4*h^6 + 5*a^4*c*g^2*h^8 + a^5*h^10)*sqrt(-c*g^2 - a*h^2)) - 1/840*(630*(sqrt(c)*x - sqrt(c*x^2 + a))^13*a^2*c^5*d*g^3*h^12 - 105*(sqrt(c)*x - sqrt(c*x^2 + a))^13*a^3*c^4*f*g^3*h^12 - 315*(sqrt(c)*x - sqrt(c*x^2 + a))^13*a^3*c^4*d*g*h^14 + 840*(sqrt(c)*x - sqrt(c*x^2 + a))^13*a^4*c^3*f*g*h^14 + 840*(sqrt(c)*x - sqrt(c*x^2 + a))^13*a^3*c^4*g^2*h^13*e - 105*(sqrt(c)*x - sqrt(c*x^2 + a))^13*a^4*c^3*h^15*e - 1680*(sqrt(c)*x - sqrt(c*x^2 + a))^12*c^(15/2)*f*g^10*h^5 - 8400*(sqrt(c)*x - sqrt(c*x^2 + a))^12*a*c^(13/2)*f*g^8*h^7 - 16800*(sqrt(c)*x - sqrt(c*x^2 + a))^12*a^2*c^(11/2)*f*g^6*h^9 + 8190*(sqrt(c)*x - sqrt(c*x^2 + a))^12*a^2*c^(11/2)*d*g^4*h^11 - 18165*(sqrt(c)*x - sqrt(c*x^2 + a))^12*a^3*c^(9/2)*f*g^4*h^11 - 4095*(sqrt(c)*x - sqrt(c*x^2 + a))^12*a^3*c^(9/2)*d*g^2*h^13 + 2520*(sqrt(c)*x - sqrt(c*x^2 + a))^12*a^4*c^(7/2)*f*g^2*h^13 - 1680*(sqrt(c)*x - sqrt(c*x^2 + a))^12*a^5*c^(5/2)*f*h^15 + 10920*(sqrt(c)*x - sqrt(c*x^2 + a))^12*a^3*c^(9/2)*g^3*h^12*e - 1365*(sqrt(c)*x - sqrt(c*x^2 + a))^12*a^4*c^(7/2)*g*h^14*e - 5600*(sqrt(c)*x - sqrt(c*x^2 + a))^11*c^8*f*g^11*h^4 - 28000*(sqrt(c)*x - sqrt(c*x^2 + a))^11*a*c^7*f*g^9*h^6 - 56000*(sqrt(c)*x - sqrt(c*x^2 + a))^11*a^2*c^6*f*g^7*h^8 + 44940*(sqrt(c)*x - sqrt(c*x^2 + a))^11*a^2*c^6*d*g^5*h^10 - 63490*(sqrt(c)*x - sqrt(c*x^2 + a))^11*a^3*c^5*f*g^5*h^10 - 26670*(sqrt(c)*x - sqrt(c*x^2 + a))^11*a^3*c^5*d*g^3*h^12 + 32620*(sqrt(c)*x - sqrt(c*x^2 + a))^11*a^4*c^4*f*g^3*h^12 + 2100*(sqrt(c)*x - sqrt(c*x^2 + a))^11*a^4*c^4*d*g*h^14 - 11200*(sqrt(c)*x - sqrt(c*x^2 + a))^11*a^5*c^3*f*g*h^14 - 2240*(sqrt(c)*x - sqrt(c*x^2 + a))^11*c^8*g^10*h^5*e - 11200*(sqrt(c)*x - sqrt(c*x^2 + a))^11*a*c^7*g^8*h^7*e - 22400*(sqrt(c)*x - sqrt(c*x^2 + a))^11*a^2*c^6*g^6*h^9*e + 37520*(sqrt(c)*x - sqrt(c*x^2 + a))^11*a^3*c^5*g^4*h^11*e - 24290*(sqrt(c)*x - sqrt(c*x^2 + a))^11*a^4*c^4*g^2*h^13*e - 1540*(sqrt(c)*x - sqrt(c*x^2 + a))^11*a^5*c^3*h^15*e - 11200*(sqrt(c)*x - sqrt(c*x^2 + a))^10*c^(17/2)*f*g^12*h^3 - 3360*(sqrt(c)*x - sqrt(c*x^2 + a))^10*c^(17/2)*d*g^10*h^5 - 52640*(sqrt(c)*x - sqrt(c*x^2 + a))^10*a*c^(15/2)*f*g^10*h^5 - 16800*(sqrt(c)*x - sqrt(c*x^2 + a))^10*a*c^(15/2)*d*g^8*h^7 - 95200*(sqrt(c)*x - sqrt(c*x^2 + a))^10*a^2*c^(13/2)*f*g^8*h^7 + 100380*(sqrt(c)*x - sqrt(c*x^2 + a))^10*a^2*c^(13/2)*d*g^6*h^9 - 100730*(sqrt(c)*x - sqrt(c*x^2 + a))^10*a^3*c^(11/2)*f*g^6*h^9 - 146790*(sqrt(c)*x - sqrt(c*x^2 + a))^10*a^3*c^(11/2)*d*g^4*h^11 + 163940*(sqrt(c)*x - sqrt(c*x^2 + a))^10*a^4*c^(9/2)*f*g^4*h^11 + 6300*(sqrt(c)*x - sqrt(c*x^2 + a))^10*a^4*c^(9/2)*d*g^2*h^13 - 56000*(sqrt(c)*x - sqrt(c*x^2 + a))^10*a^5*c^(7/2)*f*g^2*h^13 - 3360*(sqrt(c)*x - sqrt(c*x^2 + a))^10*a^5*c^(7/2)*d*h^15 + 3360*(sqrt(c)*x - sqrt(c*x^2 + a))^10*a^6*c^(5/2)*f*h^15 - 4480*(sqrt(c)*x - sqrt(c*x^2 + a))^10*c^(17/2)*g^11*h^4*e - 22400*(sqrt(c)*x - sqrt(c*x^2 + a))^10*a*c^(15/2)*g^9*h^6*e - 44800*(sqrt(c)*x - sqrt(c*x^2 + a))^10*a^2*c^(13/2)*g^7*h^8*e + 133840*(sqrt(c)*x - sqrt(c*x^2 + a))^10*a^3*c^(11/2)*g^5*h^10*e - 106330*(sqrt(c)*x - sqrt(c*x^2 + a))^10*a^4*c^(9/2)*g^3*h^12*e + 3220*(sqrt(c)*x - sqrt(c*x^2 + a))^10*a^5*c^(7/2)*g*h^14*e - 13440*(sqrt(c)*x - sqrt(c*x^2 + a))^9*c^9*f*g^13*h^2 - 4032*(sqrt(c)*x - sqrt(c*x^2 + a))^9*c^9*d*g^11*h^4 - 50848*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a*c^8*f*g^11*h^4 - 20160*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a*c^8*d*g^9*h^6 - 52640*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a^2*c^7*f*g^9*h^6 + 191016*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a^2*c^7*d*g^7*h^8 - 9436*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a^3*c^6*f*g^7*h^8 - 363216*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a^3*c^6*d*g^5*h^10 + 439306*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a^4*c^5*f*g^5*h^10 + 95340*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a^4*c^5*d*g^3*h^12 - 209965*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a^5*c^4*f*g^3*h^12 - 9975*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a^5*c^4*d*g*h^14 + 32200*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a^6*c^3*f*g*h^14 - 5376*(sqrt(c)*x - sqrt(c*x^2 + a))^9*c^9*g^12*h^3*e - 25984*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a*c^8*g^10*h^5*e - 49280*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a^2*c^7*g^8*h^7*e + 263648*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a^3*c^6*g^6*h^9*e - 332780*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a^4*c^5*g^4*h^11*e + 49490*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a^5*c^4*g^2*h^13*e - 1085*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a^6*c^3*h^15*e - 8960*(sqrt(c)*x - sqrt(c*x^2 + a))^8*c^(19/2)*f*g^14*h - 2688*(sqrt(c)*x - sqrt(c*x^2 + a))^8*c^(19/2)*d*g^12*h^3 - 15232*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a*c^(17/2)*f*g^12*h^3 - 16800*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a*c^(17/2)*d*g^10*h^5 + 53200*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^2*c^(15/2)*f*g^10*h^5 + 181104*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^2*c^(15/2)*d*g^8*h^7 + 143416*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^3*c^(13/2)*f*g^8*h^7 - 651924*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^3*c^(13/2)*d*g^6*h^9 + 580034*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^4*c^(11/2)*f*g^6*h^9 + 299460*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^4*c^(11/2)*d*g^4*h^11 - 568085*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^5*c^(9/2)*f*g^4*h^11 - 72975*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^5*c^(9/2)*d*g^2*h^13 + 147000*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^6*c^(7/2)*f*g^2*h^13 - 3360*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^6*c^(7/2)*d*h^15 - 5040*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^7*c^(5/2)*f*h^15 - 3584*(sqrt(c)*x - sqrt(c*x^2 + a))^8*c^(19/2)*g^13*h^2*e - 9856*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a*c^(17/2)*g^11*h^4*e + 4480*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^2*c^(15/2)*g^9*h^6*e + 344512*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^3*c^(13/2)*g^7*h^8*e - 613480*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^4*c^(11/2)*g^5*h^10*e + 259210*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^5*c^(9/2)*g^3*h^12*e - 9765*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^6*c^(7/2)*g*h^14*e - 2560*(sqrt(c)*x - sqrt(c*x^2 + a))^7*c^10*f*g^15 - 768*(sqrt(c)*x - sqrt(c*x^2 + a))^7*c^10*d*g^13*h^2 + 12928*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a*c^9*f*g^13*h^2 + 384*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a*c^9*d*g^11*h^4 + 80576*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^2*c^8*f*g^11*h^4 + 117984*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^2*c^8*d*g^9*h^6 + 101936*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^3*c^7*f*g^9*h^6 - 603216*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^3*c^7*d*g^7*h^8 + 256816*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^4*c^6*f*g^7*h^8 + 703752*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^4*c^6*d*g^5*h^10 - 941332*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^5*c^5*f*g^5*h^10 - 184380*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^5*c^5*d*g^3*h^12 + 413280*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^6*c^4*f*g^3*h^12 + 13440*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^6*c^4*d*g*h^14 - 47040*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^7*c^3*f*g*h^14 - 1024*(sqrt(c)*x - sqrt(c*x^2 + a))^7*c^10*g^14*h*e + 4096*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a*c^9*g^12*h^3*e + 32768*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^2*c^8*g^10*h^5*e + 205952*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^3*c^7*g^8*h^7*e - 741776*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^4*c^6*g^6*h^9*e + 608720*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^5*c^5*g^4*h^11*e - 92820*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^6*c^4*g^2*h^13*e + 8960*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a*c^(19/2)*f*g^14*h + 2688*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a*c^(19/2)*d*g^12*h^3 + 15232*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^2*c^(17/2)*f*g^12*h^3 + 16800*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^2*c^(17/2)*d*g^10*h^5 - 53200*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^3*c^(15/2)*f*g^10*h^5 - 342384*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^3*c^(15/2)*d*g^8*h^7 - 103936*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^4*c^(13/2)*f*g^8*h^7 + 736344*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^4*c^(13/2)*d*g^6*h^9 - 726404*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^5*c^(11/2)*f*g^6*h^9 - 488460*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^5*c^(11/2)*d*g^4*h^11 + 764960*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^6*c^(9/2)*f*g^4*h^11 + 33600*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^6*c^(9/2)*d*g^2*h^13 - 168000*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^7*c^(7/2)*f*g^2*h^13 - 6720*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^7*c^(7/2)*d*h^15 + 6720*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^8*c^(5/2)*f*h^15 + 3584*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a*c^(19/2)*g^13*h^2*e + 9856*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^2*c^(17/2)*g^11*h^4*e + 8960*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^3*c^(15/2)*g^9*h^6*e - 487312*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^4*c^(13/2)*g^7*h^8*e + 807520*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^5*c^(11/2)*g^5*h^10*e - 310660*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^6*c^(9/2)*g^3*h^12*e + 13440*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^7*c^(7/2)*g*h^14*e - 13440*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^2*c^9*f*g^13*h^2 - 4032*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^2*c^9*d*g^11*h^4 - 50848*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^3*c^8*f*g^11*h^4 - 47040*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^3*c^8*d*g^9*h^6 - 50960*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^4*c^7*f*g^9*h^6 + 438816*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^4*c^7*d*g^7*h^8 - 99736*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^5*c^6*f*g^7*h^8 - 556416*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^5*c^6*d*g^5*h^10 + 728756*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^6*c^5*f*g^5*h^10 + 167790*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^6*c^5*d*g^3*h^12 - 362915*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^7*c^4*f*g^3*h^12 - 10185*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^7*c^4*d*g*h^14 + 38360*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^8*c^3*f*g*h^14 - 5376*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^2*c^9*g^12*h^3*e - 25984*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^3*c^8*g^10*h^5*e - 86240*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^4*c^7*g^8*h^7*e + 574448*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^5*c^6*g^6*h^9*e - 487480*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^6*c^5*g^4*h^11*e + 89740*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^7*c^4*g^2*h^13*e + 1085*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^8*c^3*h^15*e + 11200*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^3*c^(17/2)*f*g^12*h^3 + 3360*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^3*c^(17/2)*d*g^10*h^5 + 52640*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^4*c^(15/2)*f*g^10*h^5 + 45360*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^4*c^(15/2)*d*g^8*h^7 + 96880*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^5*c^(13/2)*f*g^8*h^7 - 364728*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^5*c^(13/2)*d*g^6*h^9 + 215908*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^6*c^(11/2)*f*g^6*h^9 + 220710*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^6*c^(11/2)*d*g^4*h^11 - 406735*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^7*c^(9/2)*f*g^4*h^11 - 49581*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^7*c^(9/2)*d*g^2*h^13 + 104776*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^8*c^(7/2)*f*g^2*h^13 - 1344*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^8*c^(7/2)*d*h^15 - 3696*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^9*c^(5/2)*f*h^15 + 4480*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^3*c^(17/2)*g^11*h^4*e + 29120*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^4*c^(15/2)*g^9*h^6*e + 119056*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^5*c^(13/2)*g^7*h^8*e - 390656*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^6*c^(11/2)*g^5*h^10*e + 179900*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^7*c^(9/2)*g^3*h^12*e - 10703*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^8*c^(7/2)*g*h^14*e - 5600*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^4*c^8*f*g^11*h^4 - 3360*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^4*c^8*d*g^9*h^6 - 29680*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^5*c^7*f*g^9*h^6 - 32592*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^5*c^7*d*g^7*h^8 - 67088*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^6*c^6*f*g^7*h^8 + 172620*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^6*c^6*d*g^5*h^10 - 156170*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^7*c^5*f*g^5*h^10 - 62454*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^7*c^5*d*g^3*h^12 + 140084*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^8*c^4*f*g^3*h^12 + 5964*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^8*c^4*d*g*h^14 - 17024*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^9*c^3*f*g*h^14 - 2240*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^4*c^8*g^10*h^5*e - 16576*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^5*c^7*g^8*h^7*e - 72464*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^6*c^6*g^6*h^9*e + 179200*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^7*c^5*g^4*h^11*e - 31402*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^8*c^4*g^2*h^13*e + 1540*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^9*c^3*h^15*e + 1680*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^5*c^(15/2)*f*g^10*h^5 + 1008*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^5*c^(15/2)*d*g^8*h^7 + 9632*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^6*c^(13/2)*f*g^8*h^7 + 9996*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^6*c^(13/2)*d*g^6*h^9 + 24094*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^7*c^(11/2)*f*g^6*h^9 - 54894*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^7*c^(11/2)*d*g^4*h^11 + 56924*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^8*c^(9/2)*f*g^4*h^11 + 9156*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^8*c^(9/2)*d*g^2*h^13 - 32256*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^9*c^(7/2)*f*g^2*h^13 - 672*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^9*c^(7/2)*d*h^15 + 672*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^10*c^(5/2)*f*h^15 + 1344*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^5*c^(15/2)*g^9*h^6*e + 8624*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^6*c^(13/2)*g^7*h^8*e + 30352*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^7*c^(11/2)*g^5*h^10*e - 47362*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^8*c^(9/2)*g^3*h^12*e + 3276*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^9*c^(7/2)*g*h^14*e - 560*(sqrt(c)*x - sqrt(c*x^2 + a))*a^6*c^7*f*g^9*h^6 - 168*(sqrt(c)*x - sqrt(c*x^2 + a))*a^6*c^7*d*g^7*h^8 - 3052*(sqrt(c)*x - sqrt(c*x^2 + a))*a^7*c^6*f*g^7*h^8 - 1680*(sqrt(c)*x - sqrt(c*x^2 + a))*a^7*c^6*d*g^5*h^10 - 7070*(sqrt(c)*x - sqrt(c*x^2 + a))*a^8*c^5*f*g^5*h^10 + 9744*(sqrt(c)*x - sqrt(c*x^2 + a))*a^8*c^5*d*g^3*h^12 - 12999*(sqrt(c)*x - sqrt(c*x^2 + a))*a^9*c^4*f*g^3*h^12 - 1029*(sqrt(c)*x - sqrt(c*x^2 + a))*a^9*c^4*d*g*h^14 + 3864*(sqrt(c)*x - sqrt(c*x^2 + a))*a^10*c^3*f*g*h^14 - 224*(sqrt(c)*x - sqrt(c*x^2 + a))*a^6*c^7*g^8*h^7*e - 1456*(sqrt(c)*x - sqrt(c*x^2 + a))*a^7*c^6*g^6*h^9*e - 5180*(sqrt(c)*x - sqrt(c*x^2 + a))*a^8*c^5*g^4*h^11*e + 8442*(sqrt(c)*x - sqrt(c*x^2 + a))*a^9*c^4*g^2*h^13*e + 105*(sqrt(c)*x - sqrt(c*x^2 + a))*a^10*c^3*h^15*e + 40*a^7*c^(13/2)*f*g^8*h^7 + 12*a^7*c^(13/2)*d*g^6*h^9 + 218*a^8*c^(11/2)*f*g^6*h^9 + 120*a^8*c^(11/2)*d*g^4*h^11 + 505*a^9*c^(9/2)*f*g^4*h^11 - 741*a^9*c^(9/2)*d*g^2*h^13 + 936*a^10*c^(7/2)*f*g^2*h^13 + 96*a^10*c^(7/2)*d*h^15 - 336*a^11*c^(5/2)*f*h^15 + 16*a^7*c^(13/2)*g^7*h^8*e + 104*a^8*c^(11/2)*g^5*h^10*e + 370*a^9*c^(9/2)*g^3*h^12*e - 663*a^10*c^(7/2)*g*h^14*e)/((c^5*g^10*h^6 + 5*a*c^4*g^8*h^8 + 10*a^2*c^3*g^6*h^10 + 10*a^3*c^2*g^4*h^12 + 5*a^4*c*g^2*h^14 + a^5*h^16)*((sqrt(c)*x - sqrt(c*x^2 + a))^2*h + 2*(sqrt(c)*x - sqrt(c*x^2 + a))*sqrt(c)*g - a*h)^7)","B",0
100,1,168,0,0.212885," ","integrate((c*x^2+a)^(5/2)*(C*x^2+B*x+A),x, algorithm=""giac"")","\frac{1}{2688} \, {\left(\frac{384 \, B a^{3}}{c} + {\left(2 \, {\left(576 \, B a^{2} + {\left(4 \, {\left(144 \, B a c + {\left(6 \, {\left(7 \, C c^{2} x + 8 \, B c^{2}\right)} x + \frac{7 \, {\left(17 \, C a c^{7} + 8 \, A c^{8}\right)}}{c^{6}}\right)} x\right)} x + \frac{7 \, {\left(59 \, C a^{2} c^{6} + 104 \, A a c^{7}\right)}}{c^{6}}\right)} x\right)} x + \frac{21 \, {\left(5 \, C a^{3} c^{5} + 88 \, A a^{2} c^{6}\right)}}{c^{6}}\right)} x\right)} \sqrt{c x^{2} + a} + \frac{5 \, {\left(C a^{4} - 8 \, A a^{3} c\right)} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{128 \, c^{\frac{3}{2}}}"," ",0,"1/2688*(384*B*a^3/c + (2*(576*B*a^2 + (4*(144*B*a*c + (6*(7*C*c^2*x + 8*B*c^2)*x + 7*(17*C*a*c^7 + 8*A*c^8)/c^6)*x)*x + 7*(59*C*a^2*c^6 + 104*A*a*c^7)/c^6)*x)*x + 21*(5*C*a^3*c^5 + 88*A*a^2*c^6)/c^6)*x)*sqrt(c*x^2 + a) + 5/128*(C*a^4 - 8*A*a^3*c)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(3/2)","A",0
101,1,314,0,0.255341," ","integrate((h*x+g)^3*(f*x^2+e*x+d)/(c*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{1}{120} \, \sqrt{c x^{2} + a} {\left({\left(2 \, {\left(3 \, {\left(\frac{4 \, f h^{3} x}{c} + \frac{5 \, {\left(3 \, c^{4} f g h^{2} + c^{4} h^{3} e\right)}}{c^{5}}\right)} x + \frac{4 \, {\left(15 \, c^{4} f g^{2} h + 5 \, c^{4} d h^{3} - 4 \, a c^{3} f h^{3} + 15 \, c^{4} g h^{2} e\right)}}{c^{5}}\right)} x + \frac{15 \, {\left(4 \, c^{4} f g^{3} + 12 \, c^{4} d g h^{2} - 9 \, a c^{3} f g h^{2} + 12 \, c^{4} g^{2} h e - 3 \, a c^{3} h^{3} e\right)}}{c^{5}}\right)} x + \frac{8 \, {\left(45 \, c^{4} d g^{2} h - 30 \, a c^{3} f g^{2} h - 10 \, a c^{3} d h^{3} + 8 \, a^{2} c^{2} f h^{3} + 15 \, c^{4} g^{3} e - 30 \, a c^{3} g h^{2} e\right)}}{c^{5}}\right)} - \frac{{\left(8 \, c^{2} d g^{3} - 4 \, a c f g^{3} - 12 \, a c d g h^{2} + 9 \, a^{2} f g h^{2} - 12 \, a c g^{2} h e + 3 \, a^{2} h^{3} e\right)} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{8 \, c^{\frac{5}{2}}}"," ",0,"1/120*sqrt(c*x^2 + a)*((2*(3*(4*f*h^3*x/c + 5*(3*c^4*f*g*h^2 + c^4*h^3*e)/c^5)*x + 4*(15*c^4*f*g^2*h + 5*c^4*d*h^3 - 4*a*c^3*f*h^3 + 15*c^4*g*h^2*e)/c^5)*x + 15*(4*c^4*f*g^3 + 12*c^4*d*g*h^2 - 9*a*c^3*f*g*h^2 + 12*c^4*g^2*h*e - 3*a*c^3*h^3*e)/c^5)*x + 8*(45*c^4*d*g^2*h - 30*a*c^3*f*g^2*h - 10*a*c^3*d*h^3 + 8*a^2*c^2*f*h^3 + 15*c^4*g^3*e - 30*a*c^3*g*h^2*e)/c^5) - 1/8*(8*c^2*d*g^3 - 4*a*c*f*g^3 - 12*a*c*d*g*h^2 + 9*a^2*f*g*h^2 - 12*a*c*g^2*h*e + 3*a^2*h^3*e)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(5/2)","A",0
102,1,206,0,0.229732," ","integrate((h*x+g)^2*(f*x^2+e*x+d)/(c*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{1}{24} \, \sqrt{c x^{2} + a} {\left({\left(2 \, {\left(\frac{3 \, f h^{2} x}{c} + \frac{4 \, {\left(2 \, c^{3} f g h + c^{3} h^{2} e\right)}}{c^{4}}\right)} x + \frac{3 \, {\left(4 \, c^{3} f g^{2} + 4 \, c^{3} d h^{2} - 3 \, a c^{2} f h^{2} + 8 \, c^{3} g h e\right)}}{c^{4}}\right)} x + \frac{8 \, {\left(6 \, c^{3} d g h - 4 \, a c^{2} f g h + 3 \, c^{3} g^{2} e - 2 \, a c^{2} h^{2} e\right)}}{c^{4}}\right)} - \frac{{\left(8 \, c^{2} d g^{2} - 4 \, a c f g^{2} - 4 \, a c d h^{2} + 3 \, a^{2} f h^{2} - 8 \, a c g h e\right)} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{8 \, c^{\frac{5}{2}}}"," ",0,"1/24*sqrt(c*x^2 + a)*((2*(3*f*h^2*x/c + 4*(2*c^3*f*g*h + c^3*h^2*e)/c^4)*x + 3*(4*c^3*f*g^2 + 4*c^3*d*h^2 - 3*a*c^2*f*h^2 + 8*c^3*g*h*e)/c^4)*x + 8*(6*c^3*d*g*h - 4*a*c^2*f*g*h + 3*c^3*g^2*e - 2*a*c^2*h^2*e)/c^4) - 1/8*(8*c^2*d*g^2 - 4*a*c*f*g^2 - 4*a*c*d*h^2 + 3*a^2*f*h^2 - 8*a*c*g*h*e)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(5/2)","A",0
103,1,110,0,0.210661," ","integrate((h*x+g)*(f*x^2+e*x+d)/(c*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{c x^{2} + a} {\left({\left(\frac{2 \, f h x}{c} + \frac{3 \, {\left(c^{2} f g + c^{2} h e\right)}}{c^{3}}\right)} x + \frac{2 \, {\left(3 \, c^{2} d h - 2 \, a c f h + 3 \, c^{2} g e\right)}}{c^{3}}\right)} - \frac{{\left(2 \, c d g - a f g - a h e\right)} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{2 \, c^{\frac{3}{2}}}"," ",0,"1/6*sqrt(c*x^2 + a)*((2*f*h*x/c + 3*(c^2*f*g + c^2*h*e)/c^3)*x + 2*(3*c^2*d*h - 2*a*c*f*h + 3*c^2*g*e)/c^3) - 1/2*(2*c*d*g - a*f*g - a*h*e)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(3/2)","A",0
104,1,58,0,0.197253," ","integrate((f*x^2+e*x+d)/(c*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{c x^{2} + a} {\left(\frac{f x}{c} + \frac{2 \, e}{c}\right)} - \frac{{\left(2 \, c d - a f\right)} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{2 \, c^{\frac{3}{2}}}"," ",0,"1/2*sqrt(c*x^2 + a)*(f*x/c + 2*e/c) - 1/2*(2*c*d - a*f)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(3/2)","A",0
105,1,138,0,0.223282," ","integrate((f*x^2+e*x+d)/(h*x+g)/(c*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{c x^{2} + a} f}{c h} + \frac{2 \, {\left(f g^{2} + d h^{2} - g h e\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} h + \sqrt{c} g}{\sqrt{-c g^{2} - a h^{2}}}\right)}{\sqrt{-c g^{2} - a h^{2}} h^{2}} + \frac{{\left(\sqrt{c} f g - \sqrt{c} h e\right)} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{c h^{2}}"," ",0,"sqrt(c*x^2 + a)*f/(c*h) + 2*(f*g^2 + d*h^2 - g*h*e)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + a))*h + sqrt(c)*g)/sqrt(-c*g^2 - a*h^2))/(sqrt(-c*g^2 - a*h^2)*h^2) + (sqrt(c)*f*g - sqrt(c)*h*e)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/(c*h^2)","A",0
106,-2,0,0,0.000000," ","integrate((f*x^2+e*x+d)/(h*x+g)^2/(c*x^2+a)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Error: Bad Argument Type","F(-2)",0
107,1,848,0,0.263499," ","integrate((f*x^2+e*x+d)/(h*x+g)^3/(c*x^2+a)^(1/2),x, algorithm=""giac"")","-\frac{{\left(2 \, c^{2} d g^{2} - a c f g^{2} - a c d h^{2} + 2 \, a^{2} f h^{2} + 3 \, a c g h e\right)} \arctan\left(\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} h + \sqrt{c} g}{\sqrt{-c g^{2} - a h^{2}}}\right)}{{\left(c^{2} g^{4} + 2 \, a c g^{2} h^{2} + a^{2} h^{4}\right)} \sqrt{-c g^{2} - a h^{2}}} + \frac{2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} c^{2} f g^{4} h - 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} c^{2} d g^{2} h^{3} + 5 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a c f g^{2} h^{3} + {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a c d h^{5} - 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a c g h^{4} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} c^{\frac{5}{2}} f g^{5} - 6 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} c^{\frac{5}{2}} d g^{3} h^{2} + 7 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a c^{\frac{3}{2}} f g^{3} h^{2} + 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a c^{\frac{3}{2}} d g h^{4} - 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{2} \sqrt{c} f g h^{4} + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} c^{\frac{5}{2}} g^{4} h e - 5 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a c^{\frac{3}{2}} g^{2} h^{3} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{2} \sqrt{c} h^{5} e - 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a c^{2} f g^{4} h + 10 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a c^{2} d g^{2} h^{3} - 11 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{2} c f g^{2} h^{3} + {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{2} c d h^{5} - 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a c^{2} g^{3} h^{2} e + 5 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{2} c g h^{4} e + a^{2} c^{\frac{3}{2}} f g^{3} h^{2} - 3 \, a^{2} c^{\frac{3}{2}} d g h^{4} + 4 \, a^{3} \sqrt{c} f g h^{4} + a^{2} c^{\frac{3}{2}} g^{2} h^{3} e - 2 \, a^{3} \sqrt{c} h^{5} e}{{\left(c^{2} g^{4} h^{2} + 2 \, a c g^{2} h^{4} + a^{2} h^{6}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} h + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} \sqrt{c} g - a h\right)}^{2}}"," ",0,"-(2*c^2*d*g^2 - a*c*f*g^2 - a*c*d*h^2 + 2*a^2*f*h^2 + 3*a*c*g*h*e)*arctan(((sqrt(c)*x - sqrt(c*x^2 + a))*h + sqrt(c)*g)/sqrt(-c*g^2 - a*h^2))/((c^2*g^4 + 2*a*c*g^2*h^2 + a^2*h^4)*sqrt(-c*g^2 - a*h^2)) + (2*(sqrt(c)*x - sqrt(c*x^2 + a))^3*c^2*f*g^4*h - 2*(sqrt(c)*x - sqrt(c*x^2 + a))^3*c^2*d*g^2*h^3 + 5*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a*c*f*g^2*h^3 + (sqrt(c)*x - sqrt(c*x^2 + a))^3*a*c*d*h^5 - 3*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a*c*g*h^4*e + 2*(sqrt(c)*x - sqrt(c*x^2 + a))^2*c^(5/2)*f*g^5 - 6*(sqrt(c)*x - sqrt(c*x^2 + a))^2*c^(5/2)*d*g^3*h^2 + 7*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a*c^(3/2)*f*g^3*h^2 + 3*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a*c^(3/2)*d*g*h^4 - 4*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^2*sqrt(c)*f*g*h^4 + 2*(sqrt(c)*x - sqrt(c*x^2 + a))^2*c^(5/2)*g^4*h*e - 5*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a*c^(3/2)*g^2*h^3*e + 2*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^2*sqrt(c)*h^5*e - 2*(sqrt(c)*x - sqrt(c*x^2 + a))*a*c^2*f*g^4*h + 10*(sqrt(c)*x - sqrt(c*x^2 + a))*a*c^2*d*g^2*h^3 - 11*(sqrt(c)*x - sqrt(c*x^2 + a))*a^2*c*f*g^2*h^3 + (sqrt(c)*x - sqrt(c*x^2 + a))*a^2*c*d*h^5 - 4*(sqrt(c)*x - sqrt(c*x^2 + a))*a*c^2*g^3*h^2*e + 5*(sqrt(c)*x - sqrt(c*x^2 + a))*a^2*c*g*h^4*e + a^2*c^(3/2)*f*g^3*h^2 - 3*a^2*c^(3/2)*d*g*h^4 + 4*a^3*sqrt(c)*f*g*h^4 + a^2*c^(3/2)*g^2*h^3*e - 2*a^3*sqrt(c)*h^5*e)/((c^2*g^4*h^2 + 2*a*c*g^2*h^4 + a^2*h^6)*((sqrt(c)*x - sqrt(c*x^2 + a))^2*h + 2*(sqrt(c)*x - sqrt(c*x^2 + a))*sqrt(c)*g - a*h)^2)","B",0
108,1,339,0,0.253103," ","integrate((h*x+g)^3*(f*x^2+e*x+d)/(c*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{{\left({\left({\left(\frac{2 \, f h^{3} x}{c} + \frac{3 \, {\left(3 \, a c^{4} f g h^{2} + a c^{4} h^{3} e\right)}}{a c^{5}}\right)} x + \frac{2 \, {\left(9 \, a c^{4} f g^{2} h + 3 \, a c^{4} d h^{3} - 4 \, a^{2} c^{3} f h^{3} + 9 \, a c^{4} g h^{2} e\right)}}{a c^{5}}\right)} x + \frac{3 \, {\left(2 \, c^{5} d g^{3} - 2 \, a c^{4} f g^{3} - 6 \, a c^{4} d g h^{2} + 9 \, a^{2} c^{3} f g h^{2} - 6 \, a c^{4} g^{2} h e + 3 \, a^{2} c^{3} h^{3} e\right)}}{a c^{5}}\right)} x - \frac{2 \, {\left(9 \, a c^{4} d g^{2} h - 18 \, a^{2} c^{3} f g^{2} h - 6 \, a^{2} c^{3} d h^{3} + 8 \, a^{3} c^{2} f h^{3} + 3 \, a c^{4} g^{3} e - 18 \, a^{2} c^{3} g h^{2} e\right)}}{a c^{5}}}{6 \, \sqrt{c x^{2} + a}} - \frac{{\left(2 \, c f g^{3} + 6 \, c d g h^{2} - 9 \, a f g h^{2} + 6 \, c g^{2} h e - 3 \, a h^{3} e\right)} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{2 \, c^{\frac{5}{2}}}"," ",0,"1/6*((((2*f*h^3*x/c + 3*(3*a*c^4*f*g*h^2 + a*c^4*h^3*e)/(a*c^5))*x + 2*(9*a*c^4*f*g^2*h + 3*a*c^4*d*h^3 - 4*a^2*c^3*f*h^3 + 9*a*c^4*g*h^2*e)/(a*c^5))*x + 3*(2*c^5*d*g^3 - 2*a*c^4*f*g^3 - 6*a*c^4*d*g*h^2 + 9*a^2*c^3*f*g*h^2 - 6*a*c^4*g^2*h*e + 3*a^2*c^3*h^3*e)/(a*c^5))*x - 2*(9*a*c^4*d*g^2*h - 18*a^2*c^3*f*g^2*h - 6*a^2*c^3*d*h^3 + 8*a^3*c^2*f*h^3 + 3*a*c^4*g^3*e - 18*a^2*c^3*g*h^2*e)/(a*c^5))/sqrt(c*x^2 + a) - 1/2*(2*c*f*g^3 + 6*c*d*g*h^2 - 9*a*f*g*h^2 + 6*c*g^2*h*e - 3*a*h^3*e)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(5/2)","A",0
109,1,219,0,0.247093," ","integrate((h*x+g)^2*(f*x^2+e*x+d)/(c*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{{\left({\left(\frac{f h^{2} x}{c} + \frac{2 \, {\left(2 \, a c^{3} f g h + a c^{3} h^{2} e\right)}}{a c^{4}}\right)} x + \frac{2 \, c^{4} d g^{2} - 2 \, a c^{3} f g^{2} - 2 \, a c^{3} d h^{2} + 3 \, a^{2} c^{2} f h^{2} - 4 \, a c^{3} g h e}{a c^{4}}\right)} x - \frac{2 \, {\left(2 \, a c^{3} d g h - 4 \, a^{2} c^{2} f g h + a c^{3} g^{2} e - 2 \, a^{2} c^{2} h^{2} e\right)}}{a c^{4}}}{2 \, \sqrt{c x^{2} + a}} - \frac{{\left(2 \, c f g^{2} + 2 \, c d h^{2} - 3 \, a f h^{2} + 4 \, c g h e\right)} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{2 \, c^{\frac{5}{2}}}"," ",0,"1/2*(((f*h^2*x/c + 2*(2*a*c^3*f*g*h + a*c^3*h^2*e)/(a*c^4))*x + (2*c^4*d*g^2 - 2*a*c^3*f*g^2 - 2*a*c^3*d*h^2 + 3*a^2*c^2*f*h^2 - 4*a*c^3*g*h*e)/(a*c^4))*x - 2*(2*a*c^3*d*g*h - 4*a^2*c^2*f*g*h + a*c^3*g^2*e - 2*a^2*c^2*h^2*e)/(a*c^4))/sqrt(c*x^2 + a) - 1/2*(2*c*f*g^2 + 2*c*d*h^2 - 3*a*f*h^2 + 4*c*g*h*e)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(5/2)","A",0
110,1,116,0,0.249846," ","integrate((h*x+g)*(f*x^2+e*x+d)/(c*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{{\left(\frac{f h x}{c} + \frac{c^{3} d g - a c^{2} f g - a c^{2} h e}{a c^{3}}\right)} x - \frac{a c^{2} d h - 2 \, a^{2} c f h + a c^{2} g e}{a c^{3}}}{\sqrt{c x^{2} + a}} - \frac{{\left(f g + h e\right)} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{c^{\frac{3}{2}}}"," ",0,"((f*h*x/c + (c^3*d*g - a*c^2*f*g - a*c^2*h*e)/(a*c^3))*x - (a*c^2*d*h - 2*a^2*c*f*h + a*c^2*g*e)/(a*c^3))/sqrt(c*x^2 + a) - (f*g + h*e)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(3/2)","A",0
111,1,63,0,0.200756," ","integrate((f*x^2+e*x+d)/(c*x^2+a)^(3/2),x, algorithm=""giac"")","-\frac{\frac{e}{c} - \frac{{\left(c^{2} d - a c f\right)} x}{a c^{2}}}{\sqrt{c x^{2} + a}} - \frac{f \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{c^{\frac{3}{2}}}"," ",0,"-(e/c - (c^2*d - a*c*f)*x/(a*c^2))/sqrt(c*x^2 + a) - f*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(3/2)","A",0
112,1,294,0,0.294312," ","integrate((f*x^2+e*x+d)/(h*x+g)/(c*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{\frac{{\left(c^{3} d g^{3} - a c^{2} f g^{3} + a c^{2} d g h^{2} - a^{2} c f g h^{2} + a c^{2} g^{2} h e + a^{2} c h^{3} e\right)} x}{a c^{3} g^{4} + 2 \, a^{2} c^{2} g^{2} h^{2} + a^{3} c h^{4}} + \frac{a c^{2} d g^{2} h - a^{2} c f g^{2} h + a^{2} c d h^{3} - a^{3} f h^{3} - a c^{2} g^{3} e - a^{2} c g h^{2} e}{a c^{3} g^{4} + 2 \, a^{2} c^{2} g^{2} h^{2} + a^{3} c h^{4}}}{\sqrt{c x^{2} + a}} - \frac{2 \, {\left(f g^{2} + d h^{2} - g h e\right)} \arctan\left(\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} h + \sqrt{c} g}{\sqrt{-c g^{2} - a h^{2}}}\right)}{{\left(c g^{2} + a h^{2}\right)} \sqrt{-c g^{2} - a h^{2}}}"," ",0,"((c^3*d*g^3 - a*c^2*f*g^3 + a*c^2*d*g*h^2 - a^2*c*f*g*h^2 + a*c^2*g^2*h*e + a^2*c*h^3*e)*x/(a*c^3*g^4 + 2*a^2*c^2*g^2*h^2 + a^3*c*h^4) + (a*c^2*d*g^2*h - a^2*c*f*g^2*h + a^2*c*d*h^3 - a^3*f*h^3 - a*c^2*g^3*e - a^2*c*g*h^2*e)/(a*c^3*g^4 + 2*a^2*c^2*g^2*h^2 + a^3*c*h^4))/sqrt(c*x^2 + a) - 2*(f*g^2 + d*h^2 - g*h*e)*arctan(((sqrt(c)*x - sqrt(c*x^2 + a))*h + sqrt(c)*g)/sqrt(-c*g^2 - a*h^2))/((c*g^2 + a*h^2)*sqrt(-c*g^2 - a*h^2))","B",0
113,-1,0,0,0.000000," ","integrate((f*x^2+e*x+d)/(h*x+g)^2/(c*x^2+a)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
114,1,1440,0,0.393980," ","integrate((f*x^2+e*x+d)/(h*x+g)^3/(c*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{\frac{{\left(c^{6} d g^{9} - a c^{5} f g^{9} - 6 \, a^{2} c^{4} d g^{5} h^{4} + 6 \, a^{3} c^{3} f g^{5} h^{4} - 8 \, a^{3} c^{3} d g^{3} h^{6} + 8 \, a^{4} c^{2} f g^{3} h^{6} - 3 \, a^{4} c^{2} d g h^{8} + 3 \, a^{5} c f g h^{8} + 3 \, a c^{5} g^{8} h e + 8 \, a^{2} c^{4} g^{6} h^{3} e + 6 \, a^{3} c^{3} g^{4} h^{5} e - a^{5} c h^{9} e\right)} x}{a c^{6} g^{12} + 6 \, a^{2} c^{5} g^{10} h^{2} + 15 \, a^{3} c^{4} g^{8} h^{4} + 20 \, a^{4} c^{3} g^{6} h^{6} + 15 \, a^{5} c^{2} g^{4} h^{8} + 6 \, a^{6} c g^{2} h^{10} + a^{7} h^{12}} + \frac{3 \, a c^{5} d g^{8} h - 3 \, a^{2} c^{4} f g^{8} h + 8 \, a^{2} c^{4} d g^{6} h^{3} - 8 \, a^{3} c^{3} f g^{6} h^{3} + 6 \, a^{3} c^{3} d g^{4} h^{5} - 6 \, a^{4} c^{2} f g^{4} h^{5} - a^{5} c d h^{9} + a^{6} f h^{9} - a c^{5} g^{9} e + 6 \, a^{3} c^{3} g^{5} h^{4} e + 8 \, a^{4} c^{2} g^{3} h^{6} e + 3 \, a^{5} c g h^{8} e}{a c^{6} g^{12} + 6 \, a^{2} c^{5} g^{10} h^{2} + 15 \, a^{3} c^{4} g^{8} h^{4} + 20 \, a^{4} c^{3} g^{6} h^{6} + 15 \, a^{5} c^{2} g^{4} h^{8} + 6 \, a^{6} c g^{2} h^{10} + a^{7} h^{12}}}{\sqrt{c x^{2} + a}} - \frac{{\left(2 \, c^{2} f g^{4} + 12 \, c^{2} d g^{2} h^{2} - 11 \, a c f g^{2} h^{2} - 3 \, a c d h^{4} + 2 \, a^{2} f h^{4} - 6 \, c^{2} g^{3} h e + 9 \, a c g h^{3} e\right)} \arctan\left(\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} h + \sqrt{c} g}{\sqrt{-c g^{2} - a h^{2}}}\right)}{{\left(c^{3} g^{6} + 3 \, a c^{2} g^{4} h^{2} + 3 \, a^{2} c g^{2} h^{4} + a^{3} h^{6}\right)} \sqrt{-c g^{2} - a h^{2}}} - \frac{2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} c^{2} f g^{4} h + 6 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} c^{2} d g^{2} h^{3} - 5 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a c f g^{2} h^{3} - {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a c d h^{5} - 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} c^{2} g^{3} h^{2} e + 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a c g h^{4} e + 6 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} c^{\frac{5}{2}} f g^{5} + 14 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} c^{\frac{5}{2}} d g^{3} h^{2} - 11 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a c^{\frac{3}{2}} f g^{3} h^{2} - 7 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a c^{\frac{3}{2}} d g h^{4} + 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{2} \sqrt{c} f g h^{4} - 10 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} c^{\frac{5}{2}} g^{4} h e + 9 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a c^{\frac{3}{2}} g^{2} h^{3} e - 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{2} \sqrt{c} h^{5} e - 10 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a c^{2} f g^{4} h - 22 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a c^{2} d g^{2} h^{3} + 11 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{2} c f g^{2} h^{3} - {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{2} c d h^{5} + 16 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a c^{2} g^{3} h^{2} e - 5 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{2} c g h^{4} e + 3 \, a^{2} c^{\frac{3}{2}} f g^{3} h^{2} + 7 \, a^{2} c^{\frac{3}{2}} d g h^{4} - 4 \, a^{3} \sqrt{c} f g h^{4} - 5 \, a^{2} c^{\frac{3}{2}} g^{2} h^{3} e + 2 \, a^{3} \sqrt{c} h^{5} e}{{\left(c^{3} g^{6} + 3 \, a c^{2} g^{4} h^{2} + 3 \, a^{2} c g^{2} h^{4} + a^{3} h^{6}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} h + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} \sqrt{c} g - a h\right)}^{2}}"," ",0,"((c^6*d*g^9 - a*c^5*f*g^9 - 6*a^2*c^4*d*g^5*h^4 + 6*a^3*c^3*f*g^5*h^4 - 8*a^3*c^3*d*g^3*h^6 + 8*a^4*c^2*f*g^3*h^6 - 3*a^4*c^2*d*g*h^8 + 3*a^5*c*f*g*h^8 + 3*a*c^5*g^8*h*e + 8*a^2*c^4*g^6*h^3*e + 6*a^3*c^3*g^4*h^5*e - a^5*c*h^9*e)*x/(a*c^6*g^12 + 6*a^2*c^5*g^10*h^2 + 15*a^3*c^4*g^8*h^4 + 20*a^4*c^3*g^6*h^6 + 15*a^5*c^2*g^4*h^8 + 6*a^6*c*g^2*h^10 + a^7*h^12) + (3*a*c^5*d*g^8*h - 3*a^2*c^4*f*g^8*h + 8*a^2*c^4*d*g^6*h^3 - 8*a^3*c^3*f*g^6*h^3 + 6*a^3*c^3*d*g^4*h^5 - 6*a^4*c^2*f*g^4*h^5 - a^5*c*d*h^9 + a^6*f*h^9 - a*c^5*g^9*e + 6*a^3*c^3*g^5*h^4*e + 8*a^4*c^2*g^3*h^6*e + 3*a^5*c*g*h^8*e)/(a*c^6*g^12 + 6*a^2*c^5*g^10*h^2 + 15*a^3*c^4*g^8*h^4 + 20*a^4*c^3*g^6*h^6 + 15*a^5*c^2*g^4*h^8 + 6*a^6*c*g^2*h^10 + a^7*h^12))/sqrt(c*x^2 + a) - (2*c^2*f*g^4 + 12*c^2*d*g^2*h^2 - 11*a*c*f*g^2*h^2 - 3*a*c*d*h^4 + 2*a^2*f*h^4 - 6*c^2*g^3*h*e + 9*a*c*g*h^3*e)*arctan(((sqrt(c)*x - sqrt(c*x^2 + a))*h + sqrt(c)*g)/sqrt(-c*g^2 - a*h^2))/((c^3*g^6 + 3*a*c^2*g^4*h^2 + 3*a^2*c*g^2*h^4 + a^3*h^6)*sqrt(-c*g^2 - a*h^2)) - (2*(sqrt(c)*x - sqrt(c*x^2 + a))^3*c^2*f*g^4*h + 6*(sqrt(c)*x - sqrt(c*x^2 + a))^3*c^2*d*g^2*h^3 - 5*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a*c*f*g^2*h^3 - (sqrt(c)*x - sqrt(c*x^2 + a))^3*a*c*d*h^5 - 4*(sqrt(c)*x - sqrt(c*x^2 + a))^3*c^2*g^3*h^2*e + 3*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a*c*g*h^4*e + 6*(sqrt(c)*x - sqrt(c*x^2 + a))^2*c^(5/2)*f*g^5 + 14*(sqrt(c)*x - sqrt(c*x^2 + a))^2*c^(5/2)*d*g^3*h^2 - 11*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a*c^(3/2)*f*g^3*h^2 - 7*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a*c^(3/2)*d*g*h^4 + 4*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^2*sqrt(c)*f*g*h^4 - 10*(sqrt(c)*x - sqrt(c*x^2 + a))^2*c^(5/2)*g^4*h*e + 9*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a*c^(3/2)*g^2*h^3*e - 2*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^2*sqrt(c)*h^5*e - 10*(sqrt(c)*x - sqrt(c*x^2 + a))*a*c^2*f*g^4*h - 22*(sqrt(c)*x - sqrt(c*x^2 + a))*a*c^2*d*g^2*h^3 + 11*(sqrt(c)*x - sqrt(c*x^2 + a))*a^2*c*f*g^2*h^3 - (sqrt(c)*x - sqrt(c*x^2 + a))*a^2*c*d*h^5 + 16*(sqrt(c)*x - sqrt(c*x^2 + a))*a*c^2*g^3*h^2*e - 5*(sqrt(c)*x - sqrt(c*x^2 + a))*a^2*c*g*h^4*e + 3*a^2*c^(3/2)*f*g^3*h^2 + 7*a^2*c^(3/2)*d*g*h^4 - 4*a^3*sqrt(c)*f*g*h^4 - 5*a^2*c^(3/2)*g^2*h^3*e + 2*a^3*sqrt(c)*h^5*e)/((c^3*g^6 + 3*a*c^2*g^4*h^2 + 3*a^2*c*g^2*h^4 + a^3*h^6)*((sqrt(c)*x - sqrt(c*x^2 + a))^2*h + 2*(sqrt(c)*x - sqrt(c*x^2 + a))*sqrt(c)*g - a*h)^2)","B",0
115,1,48,0,0.210955," ","integrate((C*x^2+B*x+A)/(c*x^2+a)^(5/2),x, algorithm=""giac"")","\frac{x {\left(\frac{3 \, A}{a} + \frac{{\left(C a c + 2 \, A c^{2}\right)} x^{2}}{a^{2} c}\right)} - \frac{B}{c}}{3 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}}}"," ",0,"1/3*(x*(3*A/a + (C*a*c + 2*A*c^2)*x^2/(a^2*c)) - B/c)/(c*x^2 + a)^(3/2)","A",0
116,1,80,0,0.264030," ","integrate((C*x^2+B*x+A)/(c*x^2+a)^(7/2),x, algorithm=""giac"")","\frac{{\left(x^{2} {\left(\frac{2 \, {\left(C a c^{3} + 4 \, A c^{4}\right)} x^{2}}{a^{3} c^{2}} + \frac{5 \, {\left(C a^{2} c^{2} + 4 \, A a c^{3}\right)}}{a^{3} c^{2}}\right)} + \frac{15 \, A}{a}\right)} x - \frac{3 \, B}{c}}{15 \, {\left(c x^{2} + a\right)}^{\frac{5}{2}}}"," ",0,"1/15*((x^2*(2*(C*a*c^3 + 4*A*c^4)*x^2/(a^3*c^2) + 5*(C*a^2*c^2 + 4*A*a*c^3)/(a^3*c^2)) + 15*A/a)*x - 3*B/c)/(c*x^2 + a)^(5/2)","A",0
117,1,112,0,0.266170," ","integrate((C*x^2+B*x+A)/(c*x^2+a)^(9/2),x, algorithm=""giac"")","\frac{{\left({\left(4 \, x^{2} {\left(\frac{2 \, {\left(C a c^{5} + 6 \, A c^{6}\right)} x^{2}}{a^{4} c^{3}} + \frac{7 \, {\left(C a^{2} c^{4} + 6 \, A a c^{5}\right)}}{a^{4} c^{3}}\right)} + \frac{35 \, {\left(C a^{3} c^{3} + 6 \, A a^{2} c^{4}\right)}}{a^{4} c^{3}}\right)} x^{2} + \frac{105 \, A}{a}\right)} x - \frac{15 \, B}{c}}{105 \, {\left(c x^{2} + a\right)}^{\frac{7}{2}}}"," ",0,"1/105*(((4*x^2*(2*(C*a*c^5 + 6*A*c^6)*x^2/(a^4*c^3) + 7*(C*a^2*c^4 + 6*A*a*c^5)/(a^4*c^3)) + 35*(C*a^3*c^3 + 6*A*a^2*c^4)/(a^4*c^3))*x^2 + 105*A/a)*x - 15*B/c)/(c*x^2 + a)^(7/2)","A",0
118,1,54,0,0.225761," ","integrate((1+2*x)^3*(4*x^2+3*x+1)/(3*x^2+2)^(1/2),x, algorithm=""giac"")","\frac{1}{405} \, {\left(3 \, {\left(2 \, {\left(9 \, {\left(16 \, x + 45\right)} x + 382\right)} x - 45\right)} x - 1841\right)} \sqrt{3 \, x^{2} + 2} - \frac{5}{9} \, \sqrt{3} \log\left(-\sqrt{3} x + \sqrt{3 \, x^{2} + 2}\right)"," ",0,"1/405*(3*(2*(9*(16*x + 45)*x + 382)*x - 45)*x - 1841)*sqrt(3*x^2 + 2) - 5/9*sqrt(3)*log(-sqrt(3)*x + sqrt(3*x^2 + 2))","A",0
119,1,48,0,0.201725," ","integrate((1+2*x)^2*(4*x^2+3*x+1)/(3*x^2+2)^(1/2),x, algorithm=""giac"")","\frac{1}{27} \, {\left(6 \, {\left(2 \, {\left(3 \, x + 7\right)} x + 9\right)} x - 49\right)} \sqrt{3 \, x^{2} + 2} + \sqrt{3} \log\left(-\sqrt{3} x + \sqrt{3 \, x^{2} + 2}\right)"," ",0,"1/27*(6*(2*(3*x + 7)*x + 9)*x - 49)*sqrt(3*x^2 + 2) + sqrt(3)*log(-sqrt(3)*x + sqrt(3*x^2 + 2))","A",0
120,1,44,0,0.194417," ","integrate((1+2*x)*(4*x^2+3*x+1)/(3*x^2+2)^(1/2),x, algorithm=""giac"")","\frac{1}{27} \, {\left(3 \, {\left(8 \, x + 15\right)} x + 13\right)} \sqrt{3 \, x^{2} + 2} + \frac{7}{9} \, \sqrt{3} \log\left(-\sqrt{3} x + \sqrt{3 \, x^{2} + 2}\right)"," ",0,"1/27*(3*(8*x + 15)*x + 13)*sqrt(3*x^2 + 2) + 7/9*sqrt(3)*log(-sqrt(3)*x + sqrt(3*x^2 + 2))","A",0
121,1,99,0,0.234726," ","integrate((4*x^2+3*x+1)/(1+2*x)/(3*x^2+2)^(1/2),x, algorithm=""giac"")","-\frac{1}{6} \, \sqrt{3} \log\left(-\sqrt{3} x + \sqrt{3 \, x^{2} + 2}\right) + \frac{1}{22} \, \sqrt{11} \log\left(-\frac{{\left| -2 \, \sqrt{3} x - \sqrt{11} - \sqrt{3} + 2 \, \sqrt{3 \, x^{2} + 2} \right|}}{2 \, \sqrt{3} x - \sqrt{11} + \sqrt{3} - 2 \, \sqrt{3 \, x^{2} + 2}}\right) + \frac{2}{3} \, \sqrt{3 \, x^{2} + 2}"," ",0,"-1/6*sqrt(3)*log(-sqrt(3)*x + sqrt(3*x^2 + 2)) + 1/22*sqrt(11)*log(-abs(-2*sqrt(3)*x - sqrt(11) - sqrt(3) + 2*sqrt(3*x^2 + 2))/(2*sqrt(3)*x - sqrt(11) + sqrt(3) - 2*sqrt(3*x^2 + 2))) + 2/3*sqrt(3*x^2 + 2)","B",0
122,1,48,0,0.319727," ","integrate((4*x^2+3*x+1)/(1+2*x)^2/(3*x^2+2)^(1/2),x, algorithm=""giac"")","\frac{1}{22} \, \sqrt{3} \mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right) - \frac{\sqrt{-\frac{6}{2 \, x + 1} + \frac{11}{{\left(2 \, x + 1\right)}^{2}} + 3}}{22 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right)}"," ",0,"1/22*sqrt(3)*sgn(1/(2*x + 1)) - 1/22*sqrt(-6/(2*x + 1) + 11/(2*x + 1)^2 + 3)/sgn(1/(2*x + 1))","A",0
123,1,180,0,0.257304," ","integrate((4*x^2+3*x+1)/(1+2*x)^3/(3*x^2+2)^(1/2),x, algorithm=""giac"")","\frac{103}{1331} \, \sqrt{11} \log\left(-\frac{{\left| -2 \, \sqrt{3} x - \sqrt{11} - \sqrt{3} + 2 \, \sqrt{3 \, x^{2} + 2} \right|}}{2 \, \sqrt{3} x - \sqrt{11} + \sqrt{3} - 2 \, \sqrt{3 \, x^{2} + 2}}\right) + \frac{72 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{3} - 13 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} - 168 \, \sqrt{3} x + 104 \, \sqrt{3} + 168 \, \sqrt{3 \, x^{2} + 2}}{484 \, {\left({\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} + \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)} - 2\right)}^{2}}"," ",0,"103/1331*sqrt(11)*log(-abs(-2*sqrt(3)*x - sqrt(11) - sqrt(3) + 2*sqrt(3*x^2 + 2))/(2*sqrt(3)*x - sqrt(11) + sqrt(3) - 2*sqrt(3*x^2 + 2))) + 1/484*(72*(sqrt(3)*x - sqrt(3*x^2 + 2))^3 - 13*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^2 - 168*sqrt(3)*x + 104*sqrt(3) + 168*sqrt(3*x^2 + 2))/((sqrt(3)*x - sqrt(3*x^2 + 2))^2 + sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2)) - 2)^2","B",0
124,1,54,0,0.214047," ","integrate((1+2*x)^3*(4*x^2+3*x+1)/(3*x^2+2)^(3/2),x, algorithm=""giac"")","\frac{38}{9} \, \sqrt{3} \log\left(-\sqrt{3} x + \sqrt{3 \, x^{2} + 2}\right) + \frac{3 \, {\left(8 \, {\left(3 \, {\left(8 \, x + 27\right)} x + 89\right)} x + 711\right)} x + 2362}{162 \, \sqrt{3 \, x^{2} + 2}}"," ",0,"38/9*sqrt(3)*log(-sqrt(3)*x + sqrt(3*x^2 + 2)) + 1/162*(3*(8*(3*(8*x + 27)*x + 89)*x + 711)*x + 2362)/sqrt(3*x^2 + 2)","A",0
125,1,49,0,0.196183," ","integrate((1+2*x)^2*(4*x^2+3*x+1)/(3*x^2+2)^(3/2),x, algorithm=""giac"")","-\frac{4}{9} \, \sqrt{3} \log\left(-\sqrt{3} x + \sqrt{3 \, x^{2} + 2}\right) + \frac{3 \, {\left(8 \, {\left(2 \, x + 7\right)} x - 5\right)} x + 182}{18 \, \sqrt{3 \, x^{2} + 2}}"," ",0,"-4/9*sqrt(3)*log(-sqrt(3)*x + sqrt(3*x^2 + 2)) + 1/18*(3*(8*(2*x + 7)*x - 5)*x + 182)/sqrt(3*x^2 + 2)","A",0
126,1,44,0,0.234739," ","integrate((1+2*x)*(4*x^2+3*x+1)/(3*x^2+2)^(3/2),x, algorithm=""giac"")","-\frac{10}{9} \, \sqrt{3} \log\left(-\sqrt{3} x + \sqrt{3 \, x^{2} + 2}\right) + \frac{3 \, {\left(16 \, x - 17\right)} x + 34}{18 \, \sqrt{3 \, x^{2} + 2}}"," ",0,"-10/9*sqrt(3)*log(-sqrt(3)*x + sqrt(3*x^2 + 2)) + 1/18*(3*(16*x - 17)*x + 34)/sqrt(3*x^2 + 2)","A",0
127,1,82,0,0.207694," ","integrate((4*x^2+3*x+1)/(1+2*x)/(3*x^2+2)^(3/2),x, algorithm=""giac"")","\frac{2}{121} \, \sqrt{11} \log\left(-\frac{{\left| -2 \, \sqrt{3} x - \sqrt{11} - \sqrt{3} + 2 \, \sqrt{3 \, x^{2} + 2} \right|}}{2 \, \sqrt{3} x - \sqrt{11} + \sqrt{3} - 2 \, \sqrt{3 \, x^{2} + 2}}\right) + \frac{21 \, x - 38}{66 \, \sqrt{3 \, x^{2} + 2}}"," ",0,"2/121*sqrt(11)*log(-abs(-2*sqrt(3)*x - sqrt(11) - sqrt(3) + 2*sqrt(3*x^2 + 2))/(2*sqrt(3)*x - sqrt(11) + sqrt(3) - 2*sqrt(3*x^2 + 2))) + 1/66*(21*x - 38)/sqrt(3*x^2 + 2)","A",0
128,1,168,0,0.274412," ","integrate((4*x^2+3*x+1)/(1+2*x)^2/(3*x^2+2)^(3/2),x, algorithm=""giac"")","-\frac{1}{7986} \, \sqrt{11} {\left(85 \, \sqrt{11} \sqrt{3} + 24 \, \log\left(\sqrt{11} \sqrt{3} - 3\right)\right)} \mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right) - \frac{\frac{\frac{93}{\mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right)} + \frac{44}{{\left(2 \, x + 1\right)} \mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right)}}{2 \, x + 1} - \frac{85}{\mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right)}}{242 \, \sqrt{-\frac{6}{2 \, x + 1} + \frac{11}{{\left(2 \, x + 1\right)}^{2}} + 3}} + \frac{4 \, \sqrt{11} \log\left(\sqrt{11} {\left(\sqrt{-\frac{6}{2 \, x + 1} + \frac{11}{{\left(2 \, x + 1\right)}^{2}} + 3} + \frac{\sqrt{11}}{2 \, x + 1}\right)} - 3\right)}{1331 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right)}"," ",0,"-1/7986*sqrt(11)*(85*sqrt(11)*sqrt(3) + 24*log(sqrt(11)*sqrt(3) - 3))*sgn(1/(2*x + 1)) - 1/242*((93/sgn(1/(2*x + 1)) + 44/((2*x + 1)*sgn(1/(2*x + 1))))/(2*x + 1) - 85/sgn(1/(2*x + 1)))/sqrt(-6/(2*x + 1) + 11/(2*x + 1)^2 + 3) + 4/1331*sqrt(11)*log(sqrt(11)*(sqrt(-6/(2*x + 1) + 11/(2*x + 1)^2 + 3) + sqrt(11)/(2*x + 1)) - 3)/sgn(1/(2*x + 1))","B",0
129,1,196,0,0.244773," ","integrate((4*x^2+3*x+1)/(1+2*x)^3/(3*x^2+2)^(3/2),x, algorithm=""giac"")","\frac{322}{14641} \, \sqrt{11} \log\left(-\frac{{\left| -2 \, \sqrt{3} x - \sqrt{11} - \sqrt{3} + 2 \, \sqrt{3 \, x^{2} + 2} \right|}}{2 \, \sqrt{3} x - \sqrt{11} + \sqrt{3} - 2 \, \sqrt{3 \, x^{2} + 2}}\right) + \frac{351 \, x + 358}{2662 \, \sqrt{3 \, x^{2} + 2}} + \frac{36 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{3} - \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} + 48 \, \sqrt{3} x + 8 \, \sqrt{3} - 48 \, \sqrt{3 \, x^{2} + 2}}{1331 \, {\left({\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} + \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)} - 2\right)}^{2}}"," ",0,"322/14641*sqrt(11)*log(-abs(-2*sqrt(3)*x - sqrt(11) - sqrt(3) + 2*sqrt(3*x^2 + 2))/(2*sqrt(3)*x - sqrt(11) + sqrt(3) - 2*sqrt(3*x^2 + 2))) + 1/2662*(351*x + 358)/sqrt(3*x^2 + 2) + 1/1331*(36*(sqrt(3)*x - sqrt(3*x^2 + 2))^3 - sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^2 + 48*sqrt(3)*x + 8*sqrt(3) - 48*sqrt(3*x^2 + 2))/((sqrt(3)*x - sqrt(3*x^2 + 2))^2 + sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2)) - 2)^2","B",0
130,1,53,0,0.183765," ","integrate((1+2*x)^3*(4*x^2+3*x+1)/(3*x^2+2)^(5/2),x, algorithm=""giac"")","-\frac{8}{3} \, \sqrt{3} \log\left(-\sqrt{3} x + \sqrt{3 \, x^{2} + 2}\right) + \frac{9 \, {\left({\left(3 \, {\left(64 \, x - 155\right)} x + 104\right)} x - 279\right)} x + 254}{162 \, {\left(3 \, x^{2} + 2\right)}^{\frac{3}{2}}}"," ",0,"-8/3*sqrt(3)*log(-sqrt(3)*x + sqrt(3*x^2 + 2)) + 1/162*(9*((3*(64*x - 155)*x + 104)*x - 279)*x + 254)/(3*x^2 + 2)^(3/2)","A",0
131,1,48,0,0.193868," ","integrate((1+2*x)^2*(4*x^2+3*x+1)/(3*x^2+2)^(5/2),x, algorithm=""giac"")","-\frac{16}{27} \, \sqrt{3} \log\left(-\sqrt{3} x + \sqrt{3 \, x^{2} + 2}\right) - \frac{3 \, {\left({\left(59 \, x + 168\right)} x + 55\right)} x + 266}{54 \, {\left(3 \, x^{2} + 2\right)}^{\frac{3}{2}}}"," ",0,"-16/27*sqrt(3)*log(-sqrt(3)*x + sqrt(3*x^2 + 2)) - 1/54*(3*((59*x + 168)*x + 55)*x + 266)/(3*x^2 + 2)^(3/2)","A",0
132,1,25,0,0.336300," ","integrate((1+2*x)*(4*x^2+3*x+1)/(3*x^2+2)^(5/2),x, algorithm=""giac"")","\frac{9 \, {\left({\left(13 \, x - 16\right)} x + 3\right)} x - 94}{54 \, {\left(3 \, x^{2} + 2\right)}^{\frac{3}{2}}}"," ",0,"1/54*(9*((13*x - 16)*x + 3)*x - 94)/(3*x^2 + 2)^(3/2)","A",0
133,1,91,0,0.214085," ","integrate((4*x^2+3*x+1)/(1+2*x)/(3*x^2+2)^(5/2),x, algorithm=""giac"")","\frac{8}{1331} \, \sqrt{11} \log\left(-\frac{{\left| -2 \, \sqrt{3} x - \sqrt{11} - \sqrt{3} + 2 \, \sqrt{3 \, x^{2} + 2} \right|}}{2 \, \sqrt{3} x - \sqrt{11} + \sqrt{3} - 2 \, \sqrt{3 \, x^{2} + 2}}\right) + \frac{9 \, {\left({\left(95 \, x + 24\right)} x + 89\right)} x - 274}{2178 \, {\left(3 \, x^{2} + 2\right)}^{\frac{3}{2}}}"," ",0,"8/1331*sqrt(11)*log(-abs(-2*sqrt(3)*x - sqrt(11) - sqrt(3) + 2*sqrt(3*x^2 + 2))/(2*sqrt(3)*x - sqrt(11) + sqrt(3) - 2*sqrt(3*x^2 + 2))) + 1/2178*(9*((95*x + 24)*x + 89)*x - 274)/(3*x^2 + 2)^(3/2)","A",0
134,1,233,0,0.516803," ","integrate((4*x^2+3*x+1)/(1+2*x)^2/(3*x^2+2)^(5/2),x, algorithm=""giac"")","-\frac{1}{263538} \, \sqrt{11} {\left(743 \, \sqrt{11} \sqrt{3} - 576 \, \log\left(\sqrt{11} \sqrt{3} - 3\right)\right)} \mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right) - \frac{32 \, \sqrt{11} \log\left(\sqrt{11} {\left(\sqrt{-\frac{6}{2 \, x + 1} + \frac{11}{{\left(2 \, x + 1\right)}^{2}} + 3} + \frac{\sqrt{11}}{2 \, x + 1}\right)} - 3\right)}{14641 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right)} + \frac{\frac{\frac{\frac{11 \, {\left(\frac{731}{\mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right)} + \frac{528}{{\left(2 \, x + 1\right)} \mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right)}\right)}}{2 \, x + 1} - \frac{14163}{\mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right)}}{2 \, x + 1} + \frac{6111}{\mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right)}}{2 \, x + 1} - \frac{2229}{\mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right)}}{7986 \, {\left(\frac{6}{2 \, x + 1} - \frac{11}{{\left(2 \, x + 1\right)}^{2}} - 3\right)} \sqrt{-\frac{6}{2 \, x + 1} + \frac{11}{{\left(2 \, x + 1\right)}^{2}} + 3}}"," ",0,"-1/263538*sqrt(11)*(743*sqrt(11)*sqrt(3) - 576*log(sqrt(11)*sqrt(3) - 3))*sgn(1/(2*x + 1)) - 32/14641*sqrt(11)*log(sqrt(11)*(sqrt(-6/(2*x + 1) + 11/(2*x + 1)^2 + 3) + sqrt(11)/(2*x + 1)) - 3)/sgn(1/(2*x + 1)) + 1/7986*(((11*(731/sgn(1/(2*x + 1)) + 528/((2*x + 1)*sgn(1/(2*x + 1))))/(2*x + 1) - 14163/sgn(1/(2*x + 1)))/(2*x + 1) + 6111/sgn(1/(2*x + 1)))/(2*x + 1) - 2229/sgn(1/(2*x + 1)))/((6/(2*x + 1) - 11/(2*x + 1)^2 - 3)*sqrt(-6/(2*x + 1) + 11/(2*x + 1)^2 + 3))","B",0
135,1,183,0,0.294769," ","integrate((4*x^2+3*x+1)/(1+2*x)^3/(3*x^2+2)^(5/2),x, algorithm=""giac"")","\frac{1216}{161051} \, \sqrt{11} \log\left(-\frac{{\left| -2 \, \sqrt{3} x - \sqrt{11} - \sqrt{3} + 2 \, \sqrt{3 \, x^{2} + 2} \right|}}{2 \, \sqrt{3} x - \sqrt{11} + \sqrt{3} - 2 \, \sqrt{3 \, x^{2} + 2}}\right) + \frac{9 \, {\left({\left(2133 \, x + 1216\right)} x + 1851\right)} x + 11234}{87846 \, {\left(3 \, x^{2} + 2\right)}^{\frac{3}{2}}} + \frac{4 \, {\left(\sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} + 24 \, \sqrt{3} x - 8 \, \sqrt{3} - 24 \, \sqrt{3 \, x^{2} + 2}\right)}}{1331 \, {\left({\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)}^{2} + \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right)} - 2\right)}^{2}}"," ",0,"1216/161051*sqrt(11)*log(-abs(-2*sqrt(3)*x - sqrt(11) - sqrt(3) + 2*sqrt(3*x^2 + 2))/(2*sqrt(3)*x - sqrt(11) + sqrt(3) - 2*sqrt(3*x^2 + 2))) + 1/87846*(9*((2133*x + 1216)*x + 1851)*x + 11234)/(3*x^2 + 2)^(3/2) + 4/1331*(sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^2 + 24*sqrt(3)*x - 8*sqrt(3) - 24*sqrt(3*x^2 + 2))/((sqrt(3)*x - sqrt(3*x^2 + 2))^2 + sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2)) - 2)^2","A",0
136,0,0,0,0.000000," ","integrate((h*x+g)^m*(c*x^2+a)^p*(f*x^2+e*x+d),x, algorithm=""giac"")","\int {\left(f x^{2} + e x + d\right)} {\left(c x^{2} + a\right)}^{p} {\left(h x + g\right)}^{m}\,{d x}"," ",0,"integrate((f*x^2 + e*x + d)*(c*x^2 + a)^p*(h*x + g)^m, x)","F",0
137,0,0,0,0.000000," ","integrate((h*x+g)^m*(f*x^2+e*x+d)*(c*x^2+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{2} + a} {\left(f x^{2} + e x + d\right)} {\left(h x + g\right)}^{m}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + a)*(f*x^2 + e*x + d)*(h*x + g)^m, x)","F",0
138,0,0,0,0.000000," ","integrate((h*x+g)^(-3-2*p)*(c*x^2+a)^p*(f*x^2+e*x+d),x, algorithm=""giac"")","\int {\left(f x^{2} + e x + d\right)} {\left(c x^{2} + a\right)}^{p} {\left(h x + g\right)}^{-2 \, p - 3}\,{d x}"," ",0,"integrate((f*x^2 + e*x + d)*(c*x^2 + a)^p*(h*x + g)^(-2*p - 3), x)","F",0
139,0,0,0,0.000000," ","integrate((e*x+d)^m*(c*e^2*x^2+b*e^2*x+b*d*e-c*d^2)^p*(-(-b*e+c*d)*f+(b*e*g-c*d*g+c*e*f)*x+c*e*g*x^2),x, algorithm=""giac"")","\int {\left(c e g x^{2} - {\left(c d - b e\right)} f + {\left(c e f - c d g + b e g\right)} x\right)} {\left(c e^{2} x^{2} + b e^{2} x - c d^{2} + b d e\right)}^{p} {\left(e x + d\right)}^{m}\,{d x}"," ",0,"integrate((c*e*g*x^2 - (c*d - b*e)*f + (c*e*f - c*d*g + b*e*g)*x)*(c*e^2*x^2 + b*e^2*x - c*d^2 + b*d*e)^p*(e*x + d)^m, x)","F",0
140,1,308,0,0.154746," ","integrate((c*x^2+b*x+a)^4*(C*x^2+A),x, algorithm=""giac"")","\frac{1}{11} \, C c^{4} x^{11} + \frac{2}{5} \, C b c^{3} x^{10} + \frac{2}{3} \, C b^{2} c^{2} x^{9} + \frac{4}{9} \, C a c^{3} x^{9} + \frac{1}{9} \, A c^{4} x^{9} + \frac{1}{2} \, C b^{3} c x^{8} + \frac{3}{2} \, C a b c^{2} x^{8} + \frac{1}{2} \, A b c^{3} x^{8} + \frac{1}{7} \, C b^{4} x^{7} + \frac{12}{7} \, C a b^{2} c x^{7} + \frac{6}{7} \, C a^{2} c^{2} x^{7} + \frac{6}{7} \, A b^{2} c^{2} x^{7} + \frac{4}{7} \, A a c^{3} x^{7} + \frac{2}{3} \, C a b^{3} x^{6} + 2 \, C a^{2} b c x^{6} + \frac{2}{3} \, A b^{3} c x^{6} + 2 \, A a b c^{2} x^{6} + \frac{6}{5} \, C a^{2} b^{2} x^{5} + \frac{1}{5} \, A b^{4} x^{5} + \frac{4}{5} \, C a^{3} c x^{5} + \frac{12}{5} \, A a b^{2} c x^{5} + \frac{6}{5} \, A a^{2} c^{2} x^{5} + C a^{3} b x^{4} + A a b^{3} x^{4} + 3 \, A a^{2} b c x^{4} + \frac{1}{3} \, C a^{4} x^{3} + 2 \, A a^{2} b^{2} x^{3} + \frac{4}{3} \, A a^{3} c x^{3} + 2 \, A a^{3} b x^{2} + A a^{4} x"," ",0,"1/11*C*c^4*x^11 + 2/5*C*b*c^3*x^10 + 2/3*C*b^2*c^2*x^9 + 4/9*C*a*c^3*x^9 + 1/9*A*c^4*x^9 + 1/2*C*b^3*c*x^8 + 3/2*C*a*b*c^2*x^8 + 1/2*A*b*c^3*x^8 + 1/7*C*b^4*x^7 + 12/7*C*a*b^2*c*x^7 + 6/7*C*a^2*c^2*x^7 + 6/7*A*b^2*c^2*x^7 + 4/7*A*a*c^3*x^7 + 2/3*C*a*b^3*x^6 + 2*C*a^2*b*c*x^6 + 2/3*A*b^3*c*x^6 + 2*A*a*b*c^2*x^6 + 6/5*C*a^2*b^2*x^5 + 1/5*A*b^4*x^5 + 4/5*C*a^3*c*x^5 + 12/5*A*a*b^2*c*x^5 + 6/5*A*a^2*c^2*x^5 + C*a^3*b*x^4 + A*a*b^3*x^4 + 3*A*a^2*b*c*x^4 + 1/3*C*a^4*x^3 + 2*A*a^2*b^2*x^3 + 4/3*A*a^3*c*x^3 + 2*A*a^3*b*x^2 + A*a^4*x","A",0
141,1,187,0,0.168577," ","integrate((c*x^2+b*x+a)^3*(C*x^2+A),x, algorithm=""giac"")","\frac{1}{9} \, C c^{3} x^{9} + \frac{3}{8} \, C b c^{2} x^{8} + \frac{3}{7} \, C b^{2} c x^{7} + \frac{3}{7} \, C a c^{2} x^{7} + \frac{1}{7} \, A c^{3} x^{7} + \frac{1}{6} \, C b^{3} x^{6} + C a b c x^{6} + \frac{1}{2} \, A b c^{2} x^{6} + \frac{3}{5} \, C a b^{2} x^{5} + \frac{3}{5} \, C a^{2} c x^{5} + \frac{3}{5} \, A b^{2} c x^{5} + \frac{3}{5} \, A a c^{2} x^{5} + \frac{3}{4} \, C a^{2} b x^{4} + \frac{1}{4} \, A b^{3} x^{4} + \frac{3}{2} \, A a b c x^{4} + \frac{1}{3} \, C a^{3} x^{3} + A a b^{2} x^{3} + A a^{2} c x^{3} + \frac{3}{2} \, A a^{2} b x^{2} + A a^{3} x"," ",0,"1/9*C*c^3*x^9 + 3/8*C*b*c^2*x^8 + 3/7*C*b^2*c*x^7 + 3/7*C*a*c^2*x^7 + 1/7*A*c^3*x^7 + 1/6*C*b^3*x^6 + C*a*b*c*x^6 + 1/2*A*b*c^2*x^6 + 3/5*C*a*b^2*x^5 + 3/5*C*a^2*c*x^5 + 3/5*A*b^2*c*x^5 + 3/5*A*a*c^2*x^5 + 3/4*C*a^2*b*x^4 + 1/4*A*b^3*x^4 + 3/2*A*a*b*c*x^4 + 1/3*C*a^3*x^3 + A*a*b^2*x^3 + A*a^2*c*x^3 + 3/2*A*a^2*b*x^2 + A*a^3*x","A",0
142,1,99,0,0.154530," ","integrate((c*x^2+b*x+a)^2*(C*x^2+A),x, algorithm=""giac"")","\frac{1}{7} \, C c^{2} x^{7} + \frac{1}{3} \, C b c x^{6} + \frac{1}{5} \, C b^{2} x^{5} + \frac{2}{5} \, C a c x^{5} + \frac{1}{5} \, A c^{2} x^{5} + \frac{1}{2} \, C a b x^{4} + \frac{1}{2} \, A b c x^{4} + \frac{1}{3} \, C a^{2} x^{3} + \frac{1}{3} \, A b^{2} x^{3} + \frac{2}{3} \, A a c x^{3} + A a b x^{2} + A a^{2} x"," ",0,"1/7*C*c^2*x^7 + 1/3*C*b*c*x^6 + 1/5*C*b^2*x^5 + 2/5*C*a*c*x^5 + 1/5*A*c^2*x^5 + 1/2*C*a*b*x^4 + 1/2*A*b*c*x^4 + 1/3*C*a^2*x^3 + 1/3*A*b^2*x^3 + 2/3*A*a*c*x^3 + A*a*b*x^2 + A*a^2*x","A",0
143,1,40,0,0.179982," ","integrate((c*x^2+b*x+a)*(C*x^2+A),x, algorithm=""giac"")","\frac{1}{5} \, C c x^{5} + \frac{1}{4} \, C b x^{4} + \frac{1}{3} \, C a x^{3} + \frac{1}{3} \, A c x^{3} + \frac{1}{2} \, A b x^{2} + A a x"," ",0,"1/5*C*c*x^5 + 1/4*C*b*x^4 + 1/3*C*a*x^3 + 1/3*A*c*x^3 + 1/2*A*b*x^2 + A*a*x","A",0
144,1,78,0,0.154416," ","integrate((C*x^2+A)/(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{C x}{c} - \frac{C b \log\left(c x^{2} + b x + a\right)}{2 \, c^{2}} + \frac{{\left(C b^{2} - 2 \, C a c + 2 \, A c^{2}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c} c^{2}}"," ",0,"C*x/c - 1/2*C*b*log(c*x^2 + b*x + a)/c^2 + (C*b^2 - 2*C*a*c + 2*A*c^2)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c^2)","A",0
145,1,108,0,0.158800," ","integrate((C*x^2+A)/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","-\frac{4 \, {\left(C a + A c\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{2} - 4 \, a c\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{C b^{2} x - 2 \, C a c x + 2 \, A c^{2} x + C a b + A b c}{{\left(b^{2} c - 4 \, a c^{2}\right)} {\left(c x^{2} + b x + a\right)}}"," ",0,"-4*(C*a + A*c)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^2 - 4*a*c)*sqrt(-b^2 + 4*a*c)) - (C*b^2*x - 2*C*a*c*x + 2*A*c^2*x + C*a*b + A*b*c)/((b^2*c - 4*a*c^2)*(c*x^2 + b*x + a))","A",0
146,1,217,0,0.180935," ","integrate((C*x^2+A)/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{2 \, {\left(C b^{2} + 2 \, C a c + 6 \, A c^{2}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{2 \, C b^{2} c x^{3} + 4 \, C a c^{2} x^{3} + 12 \, A c^{3} x^{3} + 3 \, C b^{3} x^{2} + 6 \, C a b c x^{2} + 18 \, A b c^{2} x^{2} + 10 \, C a b^{2} x - 4 \, C a^{2} c x + 4 \, A b^{2} c x + 20 \, A a c^{2} x + 6 \, C a^{2} b - A b^{3} + 10 \, A a b c}{2 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} {\left(c x^{2} + b x + a\right)}^{2}}"," ",0,"2*(C*b^2 + 2*C*a*c + 6*A*c^2)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(-b^2 + 4*a*c)) + 1/2*(2*C*b^2*c*x^3 + 4*C*a*c^2*x^3 + 12*A*c^3*x^3 + 3*C*b^3*x^2 + 6*C*a*b*c*x^2 + 18*A*b*c^2*x^2 + 10*C*a*b^2*x - 4*C*a^2*c*x + 4*A*b^2*c*x + 20*A*a*c^2*x + 6*C*a^2*b - A*b^3 + 10*A*a*b*c)/((b^4 - 8*a*b^2*c + 16*a^2*c^2)*(c*x^2 + b*x + a)^2)","A",0
147,1,407,0,0.171693," ","integrate((C*x^2+A)/(c*x^2+b*x+a)^4,x, algorithm=""giac"")","-\frac{8 \, {\left(C b^{2} c + C a c^{2} + 5 \, A c^{3}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{12 \, C b^{2} c^{3} x^{5} + 12 \, C a c^{4} x^{5} + 60 \, A c^{5} x^{5} + 30 \, C b^{3} c^{2} x^{4} + 30 \, C a b c^{3} x^{4} + 150 \, A b c^{4} x^{4} + 22 \, C b^{4} c x^{3} + 54 \, C a b^{2} c^{2} x^{3} + 32 \, C a^{2} c^{3} x^{3} + 110 \, A b^{2} c^{3} x^{3} + 160 \, A a c^{4} x^{3} + 3 \, C b^{5} x^{2} + 51 \, C a b^{3} c x^{2} + 48 \, C a^{2} b c^{2} x^{2} + 15 \, A b^{3} c^{2} x^{2} + 240 \, A a b c^{3} x^{2} + 3 \, C a b^{4} x + 66 \, C a^{2} b^{2} c x - 3 \, A b^{4} c x - 12 \, C a^{3} c^{2} x + 54 \, A a b^{2} c^{2} x + 132 \, A a^{2} c^{3} x + C a^{2} b^{3} + A b^{5} + 26 \, C a^{3} b c - 13 \, A a b^{3} c + 66 \, A a^{2} b c^{2}}{3 \, {\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} {\left(c x^{2} + b x + a\right)}^{3}}"," ",0,"-8*(C*b^2*c + C*a*c^2 + 5*A*c^3)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*sqrt(-b^2 + 4*a*c)) - 1/3*(12*C*b^2*c^3*x^5 + 12*C*a*c^4*x^5 + 60*A*c^5*x^5 + 30*C*b^3*c^2*x^4 + 30*C*a*b*c^3*x^4 + 150*A*b*c^4*x^4 + 22*C*b^4*c*x^3 + 54*C*a*b^2*c^2*x^3 + 32*C*a^2*c^3*x^3 + 110*A*b^2*c^3*x^3 + 160*A*a*c^4*x^3 + 3*C*b^5*x^2 + 51*C*a*b^3*c*x^2 + 48*C*a^2*b*c^2*x^2 + 15*A*b^3*c^2*x^2 + 240*A*a*b*c^3*x^2 + 3*C*a*b^4*x + 66*C*a^2*b^2*c*x - 3*A*b^4*c*x - 12*C*a^3*c^2*x + 54*A*a*b^2*c^2*x + 132*A*a^2*c^3*x + C*a^2*b^3 + A*b^5 + 26*C*a^3*b*c - 13*A*a*b^3*c + 66*A*a^2*b*c^2)/((b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*(c*x^2 + b*x + a)^3)","B",0
148,1,771,0,0.170736," ","integrate((e*x+d)^3*(h*x^2+g*x+f)/(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{3 \, c^{3} h x^{4} e^{3} + 12 \, c^{3} d h x^{3} e^{2} + 18 \, c^{3} d^{2} h x^{2} e + 12 \, c^{3} d^{3} h x + 4 \, c^{3} g x^{3} e^{3} - 4 \, b c^{2} h x^{3} e^{3} + 18 \, c^{3} d g x^{2} e^{2} - 18 \, b c^{2} d h x^{2} e^{2} + 36 \, c^{3} d^{2} g x e - 36 \, b c^{2} d^{2} h x e + 6 \, c^{3} f x^{2} e^{3} - 6 \, b c^{2} g x^{2} e^{3} + 6 \, b^{2} c h x^{2} e^{3} - 6 \, a c^{2} h x^{2} e^{3} + 36 \, c^{3} d f x e^{2} - 36 \, b c^{2} d g x e^{2} + 36 \, b^{2} c d h x e^{2} - 36 \, a c^{2} d h x e^{2} - 12 \, b c^{2} f x e^{3} + 12 \, b^{2} c g x e^{3} - 12 \, a c^{2} g x e^{3} - 12 \, b^{3} h x e^{3} + 24 \, a b c h x e^{3}}{12 \, c^{4}} + \frac{{\left(c^{4} d^{3} g - b c^{3} d^{3} h + 3 \, c^{4} d^{2} f e - 3 \, b c^{3} d^{2} g e + 3 \, b^{2} c^{2} d^{2} h e - 3 \, a c^{3} d^{2} h e - 3 \, b c^{3} d f e^{2} + 3 \, b^{2} c^{2} d g e^{2} - 3 \, a c^{3} d g e^{2} - 3 \, b^{3} c d h e^{2} + 6 \, a b c^{2} d h e^{2} + b^{2} c^{2} f e^{3} - a c^{3} f e^{3} - b^{3} c g e^{3} + 2 \, a b c^{2} g e^{3} + b^{4} h e^{3} - 3 \, a b^{2} c h e^{3} + a^{2} c^{2} h e^{3}\right)} \log\left(c x^{2} + b x + a\right)}{2 \, c^{5}} + \frac{{\left(2 \, c^{5} d^{3} f - b c^{4} d^{3} g + b^{2} c^{3} d^{3} h - 2 \, a c^{4} d^{3} h - 3 \, b c^{4} d^{2} f e + 3 \, b^{2} c^{3} d^{2} g e - 6 \, a c^{4} d^{2} g e - 3 \, b^{3} c^{2} d^{2} h e + 9 \, a b c^{3} d^{2} h e + 3 \, b^{2} c^{3} d f e^{2} - 6 \, a c^{4} d f e^{2} - 3 \, b^{3} c^{2} d g e^{2} + 9 \, a b c^{3} d g e^{2} + 3 \, b^{4} c d h e^{2} - 12 \, a b^{2} c^{2} d h e^{2} + 6 \, a^{2} c^{3} d h e^{2} - b^{3} c^{2} f e^{3} + 3 \, a b c^{3} f e^{3} + b^{4} c g e^{3} - 4 \, a b^{2} c^{2} g e^{3} + 2 \, a^{2} c^{3} g e^{3} - b^{5} h e^{3} + 5 \, a b^{3} c h e^{3} - 5 \, a^{2} b c^{2} h e^{3}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c} c^{5}}"," ",0,"1/12*(3*c^3*h*x^4*e^3 + 12*c^3*d*h*x^3*e^2 + 18*c^3*d^2*h*x^2*e + 12*c^3*d^3*h*x + 4*c^3*g*x^3*e^3 - 4*b*c^2*h*x^3*e^3 + 18*c^3*d*g*x^2*e^2 - 18*b*c^2*d*h*x^2*e^2 + 36*c^3*d^2*g*x*e - 36*b*c^2*d^2*h*x*e + 6*c^3*f*x^2*e^3 - 6*b*c^2*g*x^2*e^3 + 6*b^2*c*h*x^2*e^3 - 6*a*c^2*h*x^2*e^3 + 36*c^3*d*f*x*e^2 - 36*b*c^2*d*g*x*e^2 + 36*b^2*c*d*h*x*e^2 - 36*a*c^2*d*h*x*e^2 - 12*b*c^2*f*x*e^3 + 12*b^2*c*g*x*e^3 - 12*a*c^2*g*x*e^3 - 12*b^3*h*x*e^3 + 24*a*b*c*h*x*e^3)/c^4 + 1/2*(c^4*d^3*g - b*c^3*d^3*h + 3*c^4*d^2*f*e - 3*b*c^3*d^2*g*e + 3*b^2*c^2*d^2*h*e - 3*a*c^3*d^2*h*e - 3*b*c^3*d*f*e^2 + 3*b^2*c^2*d*g*e^2 - 3*a*c^3*d*g*e^2 - 3*b^3*c*d*h*e^2 + 6*a*b*c^2*d*h*e^2 + b^2*c^2*f*e^3 - a*c^3*f*e^3 - b^3*c*g*e^3 + 2*a*b*c^2*g*e^3 + b^4*h*e^3 - 3*a*b^2*c*h*e^3 + a^2*c^2*h*e^3)*log(c*x^2 + b*x + a)/c^5 + (2*c^5*d^3*f - b*c^4*d^3*g + b^2*c^3*d^3*h - 2*a*c^4*d^3*h - 3*b*c^4*d^2*f*e + 3*b^2*c^3*d^2*g*e - 6*a*c^4*d^2*g*e - 3*b^3*c^2*d^2*h*e + 9*a*b*c^3*d^2*h*e + 3*b^2*c^3*d*f*e^2 - 6*a*c^4*d*f*e^2 - 3*b^3*c^2*d*g*e^2 + 9*a*b*c^3*d*g*e^2 + 3*b^4*c*d*h*e^2 - 12*a*b^2*c^2*d*h*e^2 + 6*a^2*c^3*d*h*e^2 - b^3*c^2*f*e^3 + 3*a*b*c^3*f*e^3 + b^4*c*g*e^3 - 4*a*b^2*c^2*g*e^3 + 2*a^2*c^3*g*e^3 - b^5*h*e^3 + 5*a*b^3*c*h*e^3 - 5*a^2*b*c^2*h*e^3)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c^5)","A",0
149,1,426,0,0.160988," ","integrate((e*x+d)^2*(h*x^2+g*x+f)/(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{2 \, c^{2} h x^{3} e^{2} + 6 \, c^{2} d h x^{2} e + 6 \, c^{2} d^{2} h x + 3 \, c^{2} g x^{2} e^{2} - 3 \, b c h x^{2} e^{2} + 12 \, c^{2} d g x e - 12 \, b c d h x e + 6 \, c^{2} f x e^{2} - 6 \, b c g x e^{2} + 6 \, b^{2} h x e^{2} - 6 \, a c h x e^{2}}{6 \, c^{3}} + \frac{{\left(c^{3} d^{2} g - b c^{2} d^{2} h + 2 \, c^{3} d f e - 2 \, b c^{2} d g e + 2 \, b^{2} c d h e - 2 \, a c^{2} d h e - b c^{2} f e^{2} + b^{2} c g e^{2} - a c^{2} g e^{2} - b^{3} h e^{2} + 2 \, a b c h e^{2}\right)} \log\left(c x^{2} + b x + a\right)}{2 \, c^{4}} + \frac{{\left(2 \, c^{4} d^{2} f - b c^{3} d^{2} g + b^{2} c^{2} d^{2} h - 2 \, a c^{3} d^{2} h - 2 \, b c^{3} d f e + 2 \, b^{2} c^{2} d g e - 4 \, a c^{3} d g e - 2 \, b^{3} c d h e + 6 \, a b c^{2} d h e + b^{2} c^{2} f e^{2} - 2 \, a c^{3} f e^{2} - b^{3} c g e^{2} + 3 \, a b c^{2} g e^{2} + b^{4} h e^{2} - 4 \, a b^{2} c h e^{2} + 2 \, a^{2} c^{2} h e^{2}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c} c^{4}}"," ",0,"1/6*(2*c^2*h*x^3*e^2 + 6*c^2*d*h*x^2*e + 6*c^2*d^2*h*x + 3*c^2*g*x^2*e^2 - 3*b*c*h*x^2*e^2 + 12*c^2*d*g*x*e - 12*b*c*d*h*x*e + 6*c^2*f*x*e^2 - 6*b*c*g*x*e^2 + 6*b^2*h*x*e^2 - 6*a*c*h*x*e^2)/c^3 + 1/2*(c^3*d^2*g - b*c^2*d^2*h + 2*c^3*d*f*e - 2*b*c^2*d*g*e + 2*b^2*c*d*h*e - 2*a*c^2*d*h*e - b*c^2*f*e^2 + b^2*c*g*e^2 - a*c^2*g*e^2 - b^3*h*e^2 + 2*a*b*c*h*e^2)*log(c*x^2 + b*x + a)/c^4 + (2*c^4*d^2*f - b*c^3*d^2*g + b^2*c^2*d^2*h - 2*a*c^3*d^2*h - 2*b*c^3*d*f*e + 2*b^2*c^2*d*g*e - 4*a*c^3*d*g*e - 2*b^3*c*d*h*e + 6*a*b*c^2*d*h*e + b^2*c^2*f*e^2 - 2*a*c^3*f*e^2 - b^3*c*g*e^2 + 3*a*b*c^2*g*e^2 + b^4*h*e^2 - 4*a*b^2*c*h*e^2 + 2*a^2*c^2*h*e^2)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c^4)","A",0
150,1,201,0,0.193627," ","integrate((e*x+d)*(h*x^2+g*x+f)/(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{c h x^{2} e + 2 \, c d h x + 2 \, c g x e - 2 \, b h x e}{2 \, c^{2}} + \frac{{\left(c^{2} d g - b c d h + c^{2} f e - b c g e + b^{2} h e - a c h e\right)} \log\left(c x^{2} + b x + a\right)}{2 \, c^{3}} + \frac{{\left(2 \, c^{3} d f - b c^{2} d g + b^{2} c d h - 2 \, a c^{2} d h - b c^{2} f e + b^{2} c g e - 2 \, a c^{2} g e - b^{3} h e + 3 \, a b c h e\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c} c^{3}}"," ",0,"1/2*(c*h*x^2*e + 2*c*d*h*x + 2*c*g*x*e - 2*b*h*x*e)/c^2 + 1/2*(c^2*d*g - b*c*d*h + c^2*f*e - b*c*g*e + b^2*h*e - a*c*h*e)*log(c*x^2 + b*x + a)/c^3 + (2*c^3*d*f - b*c^2*d*g + b^2*c*d*h - 2*a*c^2*d*h - b*c^2*f*e + b^2*c*g*e - 2*a*c^2*g*e - b^3*h*e + 3*a*b*c*h*e)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c^3)","A",0
151,1,89,0,0.156039," ","integrate((h*x^2+g*x+f)/(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{h x}{c} + \frac{{\left(c g - b h\right)} \log\left(c x^{2} + b x + a\right)}{2 \, c^{2}} + \frac{{\left(2 \, c^{2} f - b c g + b^{2} h - 2 \, a c h\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c} c^{2}}"," ",0,"h*x/c + 1/2*(c*g - b*h)*log(c*x^2 + b*x + a)/c^2 + (2*c^2*f - b*c*g + b^2*h - 2*a*c*h)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c^2)","A",0
152,1,204,0,0.162620," ","integrate((h*x^2+g*x+f)/(e*x+d)/(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{{\left(c d g - b d h - c f e + a h e\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)}} + \frac{{\left(d^{2} h - d g e + f e^{2}\right)} \log\left({\left| x e + d \right|}\right)}{c d^{2} e - b d e^{2} + a e^{3}} + \frac{{\left(2 \, c^{2} d f - b c d g + b^{2} d h - 2 \, a c d h - b c f e + 2 \, a c g e - a b h e\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} \sqrt{-b^{2} + 4 \, a c}}"," ",0,"1/2*(c*d*g - b*d*h - c*f*e + a*h*e)*log(c*x^2 + b*x + a)/(c^2*d^2 - b*c*d*e + a*c*e^2) + (d^2*h - d*g*e + f*e^2)*log(abs(x*e + d))/(c*d^2*e - b*d*e^2 + a*e^3) + (2*c^2*d*f - b*c*d*g + b^2*d*h - 2*a*c*d*h - b*c*f*e + 2*a*c*g*e - a*b*h*e)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((c^2*d^2 - b*c*d*e + a*c*e^2)*sqrt(-b^2 + 4*a*c))","A",0
153,1,449,0,0.195938," ","integrate((h*x^2+g*x+f)/(e*x+d)^2/(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{{\left(2 \, c^{2} d^{2} f e^{2} - b c d^{2} g e^{2} + b^{2} d^{2} h e^{2} - 2 \, a c d^{2} h e^{2} - 2 \, b c d f e^{3} + 4 \, a c d g e^{3} - 2 \, a b d h e^{3} + b^{2} f e^{4} - 2 \, a c f e^{4} - a b g e^{4} + 2 \, a^{2} h e^{4}\right)} \arctan\left(\frac{{\left(2 \, c d - \frac{2 \, c d^{2}}{x e + d} - b e + \frac{2 \, b d e}{x e + d} - \frac{2 \, a e^{2}}{x e + d}\right)} e^{\left(-1\right)}}{\sqrt{-b^{2} + 4 \, a c}}\right) e^{\left(-2\right)}}{{\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2} + 2 \, a c d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{{\left(c d^{2} g - b d^{2} h - 2 \, c d f e + 2 \, a d h e + b f e^{2} - a g e^{2}\right)} \log\left(c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{b e}{x e + d} - \frac{b d e}{{\left(x e + d\right)}^{2}} + \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)}{2 \, {\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2} + 2 \, a c d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4}\right)}} - \frac{\frac{d^{2} h e}{x e + d} - \frac{d g e^{2}}{x e + d} + \frac{f e^{3}}{x e + d}}{c d^{2} e^{2} - b d e^{3} + a e^{4}}"," ",0,"(2*c^2*d^2*f*e^2 - b*c*d^2*g*e^2 + b^2*d^2*h*e^2 - 2*a*c*d^2*h*e^2 - 2*b*c*d*f*e^3 + 4*a*c*d*g*e^3 - 2*a*b*d*h*e^3 + b^2*f*e^4 - 2*a*c*f*e^4 - a*b*g*e^4 + 2*a^2*h*e^4)*arctan((2*c*d - 2*c*d^2/(x*e + d) - b*e + 2*b*d*e/(x*e + d) - 2*a*e^2/(x*e + d))*e^(-1)/sqrt(-b^2 + 4*a*c))*e^(-2)/((c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2 + 2*a*c*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4)*sqrt(-b^2 + 4*a*c)) + 1/2*(c*d^2*g - b*d^2*h - 2*c*d*f*e + 2*a*d*h*e + b*f*e^2 - a*g*e^2)*log(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + b*e/(x*e + d) - b*d*e/(x*e + d)^2 + a*e^2/(x*e + d)^2)/(c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2 + 2*a*c*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4) - (d^2*h*e/(x*e + d) - d*g*e^2/(x*e + d) + f*e^3/(x*e + d))/(c*d^2*e^2 - b*d*e^3 + a*e^4)","A",0
154,1,1002,0,0.206131," ","integrate((h*x^2+g*x+f)/(e*x+d)^3/(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{{\left(c^{2} d^{3} g - b c d^{3} h - 3 \, c^{2} d^{2} f e + 3 \, a c d^{2} h e + 3 \, b c d f e^{2} - 3 \, a c d g e^{2} - b^{2} f e^{3} + a c f e^{3} + a b g e^{3} - a^{2} h e^{3}\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(c^{3} d^{6} - 3 \, b c^{2} d^{5} e + 3 \, b^{2} c d^{4} e^{2} + 3 \, a c^{2} d^{4} e^{2} - b^{3} d^{3} e^{3} - 6 \, a b c d^{3} e^{3} + 3 \, a b^{2} d^{2} e^{4} + 3 \, a^{2} c d^{2} e^{4} - 3 \, a^{2} b d e^{5} + a^{3} e^{6}\right)}} - \frac{{\left(c^{2} d^{3} g e - b c d^{3} h e - 3 \, c^{2} d^{2} f e^{2} + 3 \, a c d^{2} h e^{2} + 3 \, b c d f e^{3} - 3 \, a c d g e^{3} - b^{2} f e^{4} + a c f e^{4} + a b g e^{4} - a^{2} h e^{4}\right)} \log\left({\left| x e + d \right|}\right)}{c^{3} d^{6} e - 3 \, b c^{2} d^{5} e^{2} + 3 \, b^{2} c d^{4} e^{3} + 3 \, a c^{2} d^{4} e^{3} - b^{3} d^{3} e^{4} - 6 \, a b c d^{3} e^{4} + 3 \, a b^{2} d^{2} e^{5} + 3 \, a^{2} c d^{2} e^{5} - 3 \, a^{2} b d e^{6} + a^{3} e^{7}} + \frac{{\left(2 \, c^{3} d^{3} f - b c^{2} d^{3} g + b^{2} c d^{3} h - 2 \, a c^{2} d^{3} h - 3 \, b c^{2} d^{2} f e + 6 \, a c^{2} d^{2} g e - 3 \, a b c d^{2} h e + 3 \, b^{2} c d f e^{2} - 6 \, a c^{2} d f e^{2} - 3 \, a b c d g e^{2} + 6 \, a^{2} c d h e^{2} - b^{3} f e^{3} + 3 \, a b c f e^{3} + a b^{2} g e^{3} - 2 \, a^{2} c g e^{3} - a^{2} b h e^{3}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(c^{3} d^{6} - 3 \, b c^{2} d^{5} e + 3 \, b^{2} c d^{4} e^{2} + 3 \, a c^{2} d^{4} e^{2} - b^{3} d^{3} e^{3} - 6 \, a b c d^{3} e^{3} + 3 \, a b^{2} d^{2} e^{4} + 3 \, a^{2} c d^{2} e^{4} - 3 \, a^{2} b d e^{5} + a^{3} e^{6}\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{{\left(c^{2} d^{6} h - 3 \, c^{2} d^{5} g e + 5 \, c^{2} d^{4} f e^{2} + 4 \, b c d^{4} g e^{2} - b^{2} d^{4} h e^{2} - 2 \, a c d^{4} h e^{2} - 8 \, b c d^{3} f e^{3} - b^{2} d^{3} g e^{3} - 2 \, a c d^{3} g e^{3} + 4 \, a b d^{3} h e^{3} + 3 \, b^{2} d^{2} f e^{4} + 6 \, a c d^{2} f e^{4} - 3 \, a^{2} d^{2} h e^{4} - 4 \, a b d f e^{5} + a^{2} d g e^{5} + a^{2} f e^{6} - 2 \, {\left(c^{2} d^{4} g e^{2} - b c d^{4} h e^{2} - 2 \, c^{2} d^{3} f e^{3} - b c d^{3} g e^{3} + b^{2} d^{3} h e^{3} + 2 \, a c d^{3} h e^{3} + 3 \, b c d^{2} f e^{4} - 3 \, a b d^{2} h e^{4} - b^{2} d f e^{5} - 2 \, a c d f e^{5} + a b d g e^{5} + 2 \, a^{2} d h e^{5} + a b f e^{6} - a^{2} g e^{6}\right)} x\right)} e^{\left(-1\right)}}{2 \, {\left(c d^{2} - b d e + a e^{2}\right)}^{3} {\left(x e + d\right)}^{2}}"," ",0,"1/2*(c^2*d^3*g - b*c*d^3*h - 3*c^2*d^2*f*e + 3*a*c*d^2*h*e + 3*b*c*d*f*e^2 - 3*a*c*d*g*e^2 - b^2*f*e^3 + a*c*f*e^3 + a*b*g*e^3 - a^2*h*e^3)*log(c*x^2 + b*x + a)/(c^3*d^6 - 3*b*c^2*d^5*e + 3*b^2*c*d^4*e^2 + 3*a*c^2*d^4*e^2 - b^3*d^3*e^3 - 6*a*b*c*d^3*e^3 + 3*a*b^2*d^2*e^4 + 3*a^2*c*d^2*e^4 - 3*a^2*b*d*e^5 + a^3*e^6) - (c^2*d^3*g*e - b*c*d^3*h*e - 3*c^2*d^2*f*e^2 + 3*a*c*d^2*h*e^2 + 3*b*c*d*f*e^3 - 3*a*c*d*g*e^3 - b^2*f*e^4 + a*c*f*e^4 + a*b*g*e^4 - a^2*h*e^4)*log(abs(x*e + d))/(c^3*d^6*e - 3*b*c^2*d^5*e^2 + 3*b^2*c*d^4*e^3 + 3*a*c^2*d^4*e^3 - b^3*d^3*e^4 - 6*a*b*c*d^3*e^4 + 3*a*b^2*d^2*e^5 + 3*a^2*c*d^2*e^5 - 3*a^2*b*d*e^6 + a^3*e^7) + (2*c^3*d^3*f - b*c^2*d^3*g + b^2*c*d^3*h - 2*a*c^2*d^3*h - 3*b*c^2*d^2*f*e + 6*a*c^2*d^2*g*e - 3*a*b*c*d^2*h*e + 3*b^2*c*d*f*e^2 - 6*a*c^2*d*f*e^2 - 3*a*b*c*d*g*e^2 + 6*a^2*c*d*h*e^2 - b^3*f*e^3 + 3*a*b*c*f*e^3 + a*b^2*g*e^3 - 2*a^2*c*g*e^3 - a^2*b*h*e^3)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((c^3*d^6 - 3*b*c^2*d^5*e + 3*b^2*c*d^4*e^2 + 3*a*c^2*d^4*e^2 - b^3*d^3*e^3 - 6*a*b*c*d^3*e^3 + 3*a*b^2*d^2*e^4 + 3*a^2*c*d^2*e^4 - 3*a^2*b*d*e^5 + a^3*e^6)*sqrt(-b^2 + 4*a*c)) - 1/2*(c^2*d^6*h - 3*c^2*d^5*g*e + 5*c^2*d^4*f*e^2 + 4*b*c*d^4*g*e^2 - b^2*d^4*h*e^2 - 2*a*c*d^4*h*e^2 - 8*b*c*d^3*f*e^3 - b^2*d^3*g*e^3 - 2*a*c*d^3*g*e^3 + 4*a*b*d^3*h*e^3 + 3*b^2*d^2*f*e^4 + 6*a*c*d^2*f*e^4 - 3*a^2*d^2*h*e^4 - 4*a*b*d*f*e^5 + a^2*d*g*e^5 + a^2*f*e^6 - 2*(c^2*d^4*g*e^2 - b*c*d^4*h*e^2 - 2*c^2*d^3*f*e^3 - b*c*d^3*g*e^3 + b^2*d^3*h*e^3 + 2*a*c*d^3*h*e^3 + 3*b*c*d^2*f*e^4 - 3*a*b*d^2*h*e^4 - b^2*d*f*e^5 - 2*a*c*d*f*e^5 + a*b*d*g*e^5 + 2*a^2*d*h*e^5 + a*b*f*e^6 - a^2*g*e^6)*x)*e^(-1)/((c*d^2 - b*d*e + a*e^2)^3*(x*e + d)^2)","A",0
155,1,540,0,0.184298," ","integrate((e*x+d)^2*(h*x^2+g*x+f)/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{h x e^{2}}{c^{2}} - \frac{{\left(4 \, c^{4} d^{2} f - 2 \, b c^{3} d^{2} g + 4 \, a c^{3} d^{2} h - 4 \, b c^{3} d f e + 8 \, a c^{3} d g e + 2 \, b^{3} c d h e - 12 \, a b c^{2} d h e + 4 \, a c^{3} f e^{2} + b^{3} c g e^{2} - 6 \, a b c^{2} g e^{2} - 2 \, b^{4} h e^{2} + 12 \, a b^{2} c h e^{2} - 12 \, a^{2} c^{2} h e^{2}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{{\left(2 \, c d h e + c g e^{2} - 2 \, b h e^{2}\right)} \log\left(c x^{2} + b x + a\right)}{2 \, c^{3}} - \frac{\frac{{\left(2 \, c^{4} d^{2} f - b c^{3} d^{2} g + b^{2} c^{2} d^{2} h - 2 \, a c^{3} d^{2} h - 2 \, b c^{3} d f e + 2 \, b^{2} c^{2} d g e - 4 \, a c^{3} d g e - 2 \, b^{3} c d h e + 6 \, a b c^{2} d h e + b^{2} c^{2} f e^{2} - 2 \, a c^{3} f e^{2} - b^{3} c g e^{2} + 3 \, a b c^{2} g e^{2} + b^{4} h e^{2} - 4 \, a b^{2} c h e^{2} + 2 \, a^{2} c^{2} h e^{2}\right)} x}{c} + \frac{b c^{3} d^{2} f - 2 \, a c^{3} d^{2} g + a b c^{2} d^{2} h - 4 \, a c^{3} d f e + 2 \, a b c^{2} d g e - 2 \, a b^{2} c d h e + 4 \, a^{2} c^{2} d h e + a b c^{2} f e^{2} - a b^{2} c g e^{2} + 2 \, a^{2} c^{2} g e^{2} + a b^{3} h e^{2} - 3 \, a^{2} b c h e^{2}}{c}}{{\left(c x^{2} + b x + a\right)} {\left(b^{2} - 4 \, a c\right)} c^{2}}"," ",0,"h*x*e^2/c^2 - (4*c^4*d^2*f - 2*b*c^3*d^2*g + 4*a*c^3*d^2*h - 4*b*c^3*d*f*e + 8*a*c^3*d*g*e + 2*b^3*c*d*h*e - 12*a*b*c^2*d*h*e + 4*a*c^3*f*e^2 + b^3*c*g*e^2 - 6*a*b*c^2*g*e^2 - 2*b^4*h*e^2 + 12*a*b^2*c*h*e^2 - 12*a^2*c^2*h*e^2)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^2*c^3 - 4*a*c^4)*sqrt(-b^2 + 4*a*c)) + 1/2*(2*c*d*h*e + c*g*e^2 - 2*b*h*e^2)*log(c*x^2 + b*x + a)/c^3 - ((2*c^4*d^2*f - b*c^3*d^2*g + b^2*c^2*d^2*h - 2*a*c^3*d^2*h - 2*b*c^3*d*f*e + 2*b^2*c^2*d*g*e - 4*a*c^3*d*g*e - 2*b^3*c*d*h*e + 6*a*b*c^2*d*h*e + b^2*c^2*f*e^2 - 2*a*c^3*f*e^2 - b^3*c*g*e^2 + 3*a*b*c^2*g*e^2 + b^4*h*e^2 - 4*a*b^2*c*h*e^2 + 2*a^2*c^2*h*e^2)*x/c + (b*c^3*d^2*f - 2*a*c^3*d^2*g + a*b*c^2*d^2*h - 4*a*c^3*d*f*e + 2*a*b*c^2*d*g*e - 2*a*b^2*c*d*h*e + 4*a^2*c^2*d*h*e + a*b*c^2*f*e^2 - a*b^2*c*g*e^2 + 2*a^2*c^2*g*e^2 + a*b^3*h*e^2 - 3*a^2*b*c*h*e^2)/c)/((c*x^2 + b*x + a)*(b^2 - 4*a*c)*c^2)","A",0
156,1,285,0,0.166599," ","integrate((e*x+d)*(h*x^2+g*x+f)/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{h e \log\left(c x^{2} + b x + a\right)}{2 \, c^{2}} - \frac{{\left(4 \, c^{3} d f - 2 \, b c^{2} d g + 4 \, a c^{2} d h - 2 \, b c^{2} f e + 4 \, a c^{2} g e + b^{3} h e - 6 \, a b c h e\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{b c^{2} d f - 2 \, a c^{2} d g + a b c d h - 2 \, a c^{2} f e + a b c g e - a b^{2} h e + 2 \, a^{2} c h e + {\left(2 \, c^{3} d f - b c^{2} d g + b^{2} c d h - 2 \, a c^{2} d h - b c^{2} f e + b^{2} c g e - 2 \, a c^{2} g e - b^{3} h e + 3 \, a b c h e\right)} x}{{\left(c x^{2} + b x + a\right)} {\left(b^{2} - 4 \, a c\right)} c^{2}}"," ",0,"1/2*h*e*log(c*x^2 + b*x + a)/c^2 - (4*c^3*d*f - 2*b*c^2*d*g + 4*a*c^2*d*h - 2*b*c^2*f*e + 4*a*c^2*g*e + b^3*h*e - 6*a*b*c*h*e)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^2*c^2 - 4*a*c^3)*sqrt(-b^2 + 4*a*c)) - (b*c^2*d*f - 2*a*c^2*d*g + a*b*c*d*h - 2*a*c^2*f*e + a*b*c*g*e - a*b^2*h*e + 2*a^2*c*h*e + (2*c^3*d*f - b*c^2*d*g + b^2*c*d*h - 2*a*c^2*d*h - b*c^2*f*e + b^2*c*g*e - 2*a*c^2*g*e - b^3*h*e + 3*a*b*c*h*e)*x)/((c*x^2 + b*x + a)*(b^2 - 4*a*c)*c^2)","A",0
157,1,125,0,0.160447," ","integrate((h*x^2+g*x+f)/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","-\frac{2 \, {\left(2 \, c f - b g + 2 \, a h\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{2} - 4 \, a c\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{2 \, c^{2} f x - b c g x + b^{2} h x - 2 \, a c h x + b c f - 2 \, a c g + a b h}{{\left(b^{2} c - 4 \, a c^{2}\right)} {\left(c x^{2} + b x + a\right)}}"," ",0,"-2*(2*c*f - b*g + 2*a*h)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^2 - 4*a*c)*sqrt(-b^2 + 4*a*c)) - (2*c^2*f*x - b*c*g*x + b^2*h*x - 2*a*c*h*x + b*c*f - 2*a*c*g + a*b*h)/((b^2*c - 4*a*c^2)*(c*x^2 + b*x + a))","A",0
158,1,860,0,0.192886," ","integrate((h*x^2+g*x+f)/(e*x+d)/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","-\frac{{\left(d^{2} h e - d g e^{2} + f e^{3}\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2} + 2 \, a c d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4}\right)}} + \frac{{\left(d^{2} h e^{2} - d g e^{3} + f e^{4}\right)} \log\left({\left| x e + d \right|}\right)}{c^{2} d^{4} e - 2 \, b c d^{3} e^{2} + b^{2} d^{2} e^{3} + 2 \, a c d^{2} e^{3} - 2 \, a b d e^{4} + a^{2} e^{5}} - \frac{{\left(4 \, c^{3} d^{3} f - 2 \, b c^{2} d^{3} g + 4 \, a c^{2} d^{3} h - 6 \, b c^{2} d^{2} f e + 4 \, b^{2} c d^{2} g e - 4 \, a c^{2} d^{2} g e - b^{3} d^{2} h e - 2 \, a b c d^{2} h e + 12 \, a c^{2} d f e^{2} - b^{3} d g e^{2} - 2 \, a b c d g e^{2} + 4 \, a b^{2} d h e^{2} - 4 \, a^{2} c d h e^{2} + b^{3} f e^{3} - 6 \, a b c f e^{3} + 4 \, a^{2} c g e^{3} - 2 \, a^{2} b h e^{3}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{2} c^{2} d^{4} - 4 \, a c^{3} d^{4} - 2 \, b^{3} c d^{3} e + 8 \, a b c^{2} d^{3} e + b^{4} d^{2} e^{2} - 2 \, a b^{2} c d^{2} e^{2} - 8 \, a^{2} c^{2} d^{2} e^{2} - 2 \, a b^{3} d e^{3} + 8 \, a^{2} b c d e^{3} + a^{2} b^{2} e^{4} - 4 \, a^{3} c e^{4}\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{b c^{2} d^{3} f - 2 \, a c^{2} d^{3} g + a b c d^{3} h - 2 \, b^{2} c d^{2} f e + 2 \, a c^{2} d^{2} f e + 3 \, a b c d^{2} g e - a b^{2} d^{2} h e - 2 \, a^{2} c d^{2} h e + b^{3} d f e^{2} - a b c d f e^{2} - a b^{2} d g e^{2} - 2 \, a^{2} c d g e^{2} + 3 \, a^{2} b d h e^{2} - a b^{2} f e^{3} + 2 \, a^{2} c f e^{3} + a^{2} b g e^{3} - 2 \, a^{3} h e^{3} + {\left(2 \, c^{3} d^{3} f - b c^{2} d^{3} g + b^{2} c d^{3} h - 2 \, a c^{2} d^{3} h - 3 \, b c^{2} d^{2} f e + b^{2} c d^{2} g e + 2 \, a c^{2} d^{2} g e - b^{3} d^{2} h e + a b c d^{2} h e + b^{2} c d f e^{2} + 2 \, a c^{2} d f e^{2} - 3 \, a b c d g e^{2} + 2 \, a b^{2} d h e^{2} - 2 \, a^{2} c d h e^{2} - a b c f e^{3} + 2 \, a^{2} c g e^{3} - a^{2} b h e^{3}\right)} x}{{\left(c d^{2} - b d e + a e^{2}\right)}^{2} {\left(c x^{2} + b x + a\right)} {\left(b^{2} - 4 \, a c\right)}}"," ",0,"-1/2*(d^2*h*e - d*g*e^2 + f*e^3)*log(c*x^2 + b*x + a)/(c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2 + 2*a*c*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4) + (d^2*h*e^2 - d*g*e^3 + f*e^4)*log(abs(x*e + d))/(c^2*d^4*e - 2*b*c*d^3*e^2 + b^2*d^2*e^3 + 2*a*c*d^2*e^3 - 2*a*b*d*e^4 + a^2*e^5) - (4*c^3*d^3*f - 2*b*c^2*d^3*g + 4*a*c^2*d^3*h - 6*b*c^2*d^2*f*e + 4*b^2*c*d^2*g*e - 4*a*c^2*d^2*g*e - b^3*d^2*h*e - 2*a*b*c*d^2*h*e + 12*a*c^2*d*f*e^2 - b^3*d*g*e^2 - 2*a*b*c*d*g*e^2 + 4*a*b^2*d*h*e^2 - 4*a^2*c*d*h*e^2 + b^3*f*e^3 - 6*a*b*c*f*e^3 + 4*a^2*c*g*e^3 - 2*a^2*b*h*e^3)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^2*c^2*d^4 - 4*a*c^3*d^4 - 2*b^3*c*d^3*e + 8*a*b*c^2*d^3*e + b^4*d^2*e^2 - 2*a*b^2*c*d^2*e^2 - 8*a^2*c^2*d^2*e^2 - 2*a*b^3*d*e^3 + 8*a^2*b*c*d*e^3 + a^2*b^2*e^4 - 4*a^3*c*e^4)*sqrt(-b^2 + 4*a*c)) - (b*c^2*d^3*f - 2*a*c^2*d^3*g + a*b*c*d^3*h - 2*b^2*c*d^2*f*e + 2*a*c^2*d^2*f*e + 3*a*b*c*d^2*g*e - a*b^2*d^2*h*e - 2*a^2*c*d^2*h*e + b^3*d*f*e^2 - a*b*c*d*f*e^2 - a*b^2*d*g*e^2 - 2*a^2*c*d*g*e^2 + 3*a^2*b*d*h*e^2 - a*b^2*f*e^3 + 2*a^2*c*f*e^3 + a^2*b*g*e^3 - 2*a^3*h*e^3 + (2*c^3*d^3*f - b*c^2*d^3*g + b^2*c*d^3*h - 2*a*c^2*d^3*h - 3*b*c^2*d^2*f*e + b^2*c*d^2*g*e + 2*a*c^2*d^2*g*e - b^3*d^2*h*e + a*b*c*d^2*h*e + b^2*c*d*f*e^2 + 2*a*c^2*d*f*e^2 - 3*a*b*c*d*g*e^2 + 2*a*b^2*d*h*e^2 - 2*a^2*c*d*h*e^2 - a*b*c*f*e^3 + 2*a^2*c*g*e^3 - a^2*b*h*e^3)*x)/((c*d^2 - b*d*e + a*e^2)^2*(c*x^2 + b*x + a)*(b^2 - 4*a*c))","B",0
159,1,1437,0,0.327446," ","integrate((h*x^2+g*x+f)/(e*x+d)^2/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","-\frac{{\left(4 \, c^{4} d^{4} f e^{2} - 2 \, b c^{3} d^{4} g e^{2} + 4 \, a c^{3} d^{4} h e^{2} - 8 \, b c^{3} d^{3} f e^{3} + 6 \, b^{2} c^{2} d^{3} g e^{3} - 8 \, a c^{3} d^{3} g e^{3} - 2 \, b^{3} c d^{3} h e^{3} + 24 \, a c^{3} d^{2} f e^{4} - 3 \, b^{3} c d^{2} g e^{4} + 12 \, a b^{2} c d^{2} h e^{4} - 24 \, a^{2} c^{2} d^{2} h e^{4} + 4 \, b^{3} c d f e^{5} - 24 \, a b c^{2} d f e^{5} + b^{4} d g e^{5} - 6 \, a b^{2} c d g e^{5} + 24 \, a^{2} c^{2} d g e^{5} - 2 \, a b^{3} d h e^{5} - 2 \, b^{4} f e^{6} + 12 \, a b^{2} c f e^{6} - 12 \, a^{2} c^{2} f e^{6} + a b^{3} g e^{6} - 6 \, a^{2} b c g e^{6} + 4 \, a^{3} c h e^{6}\right)} \arctan\left(\frac{{\left(2 \, c d - \frac{2 \, c d^{2}}{x e + d} - b e + \frac{2 \, b d e}{x e + d} - \frac{2 \, a e^{2}}{x e + d}\right)} e^{\left(-1\right)}}{\sqrt{-b^{2} + 4 \, a c}}\right) e^{\left(-2\right)}}{{\left(b^{2} c^{3} d^{6} - 4 \, a c^{4} d^{6} - 3 \, b^{3} c^{2} d^{5} e + 12 \, a b c^{3} d^{5} e + 3 \, b^{4} c d^{4} e^{2} - 9 \, a b^{2} c^{2} d^{4} e^{2} - 12 \, a^{2} c^{3} d^{4} e^{2} - b^{5} d^{3} e^{3} - 2 \, a b^{3} c d^{3} e^{3} + 24 \, a^{2} b c^{2} d^{3} e^{3} + 3 \, a b^{4} d^{2} e^{4} - 9 \, a^{2} b^{2} c d^{2} e^{4} - 12 \, a^{3} c^{2} d^{2} e^{4} - 3 \, a^{2} b^{3} d e^{5} + 12 \, a^{3} b c d e^{5} + a^{3} b^{2} e^{6} - 4 \, a^{4} c e^{6}\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{{\left(2 \, c d^{3} h e - 3 \, c d^{2} g e^{2} + 4 \, c d f e^{3} + b d g e^{3} - 2 \, a d h e^{3} - 2 \, b f e^{4} + a g e^{4}\right)} \log\left(c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{b e}{x e + d} - \frac{b d e}{{\left(x e + d\right)}^{2}} + \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)}{2 \, {\left(c^{3} d^{6} - 3 \, b c^{2} d^{5} e + 3 \, b^{2} c d^{4} e^{2} + 3 \, a c^{2} d^{4} e^{2} - b^{3} d^{3} e^{3} - 6 \, a b c d^{3} e^{3} + 3 \, a b^{2} d^{2} e^{4} + 3 \, a^{2} c d^{2} e^{4} - 3 \, a^{2} b d e^{5} + a^{3} e^{6}\right)}} - \frac{\frac{d^{2} h e^{5}}{x e + d} - \frac{d g e^{6}}{x e + d} + \frac{f e^{7}}{x e + d}}{c^{2} d^{4} e^{4} - 2 \, b c d^{3} e^{5} + b^{2} d^{2} e^{6} + 2 \, a c d^{2} e^{6} - 2 \, a b d e^{7} + a^{2} e^{8}} - \frac{\frac{2 \, c^{4} d^{3} f e - b c^{3} d^{3} g e + b^{2} c^{2} d^{3} h e - 2 \, a c^{3} d^{3} h e - 3 \, b c^{3} d^{2} f e^{2} + 6 \, a c^{3} d^{2} g e^{2} - 3 \, a b c^{2} d^{2} h e^{2} + 3 \, b^{2} c^{2} d f e^{3} - 6 \, a c^{3} d f e^{3} - 3 \, a b c^{2} d g e^{3} + 6 \, a^{2} c^{2} d h e^{3} - b^{3} c f e^{4} + 3 \, a b c^{2} f e^{4} + a b^{2} c g e^{4} - 2 \, a^{2} c^{2} g e^{4} - a^{2} b c h e^{4}}{c d^{2} - b d e + a e^{2}} - \frac{{\left(2 \, c^{4} d^{4} f e^{2} - b c^{3} d^{4} g e^{2} + b^{2} c^{2} d^{4} h e^{2} - 2 \, a c^{3} d^{4} h e^{2} - 4 \, b c^{3} d^{3} f e^{3} + 8 \, a c^{3} d^{3} g e^{3} - 4 \, a b c^{2} d^{3} h e^{3} + 6 \, b^{2} c^{2} d^{2} f e^{4} - 12 \, a c^{3} d^{2} f e^{4} - 6 \, a b c^{2} d^{2} g e^{4} + 12 \, a^{2} c^{2} d^{2} h e^{4} - 4 \, b^{3} c d f e^{5} + 12 \, a b c^{2} d f e^{5} + 4 \, a b^{2} c d g e^{5} - 8 \, a^{2} c^{2} d g e^{5} - 4 \, a^{2} b c d h e^{5} + b^{4} f e^{6} - 4 \, a b^{2} c f e^{6} + 2 \, a^{2} c^{2} f e^{6} - a b^{3} g e^{6} + 3 \, a^{2} b c g e^{6} + a^{2} b^{2} h e^{6} - 2 \, a^{3} c h e^{6}\right)} e^{\left(-1\right)}}{{\left(c d^{2} - b d e + a e^{2}\right)} {\left(x e + d\right)}}}{{\left(c d^{2} - b d e + a e^{2}\right)}^{2} {\left(b^{2} - 4 \, a c\right)} {\left(c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{b e}{x e + d} - \frac{b d e}{{\left(x e + d\right)}^{2}} + \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)}}"," ",0,"-(4*c^4*d^4*f*e^2 - 2*b*c^3*d^4*g*e^2 + 4*a*c^3*d^4*h*e^2 - 8*b*c^3*d^3*f*e^3 + 6*b^2*c^2*d^3*g*e^3 - 8*a*c^3*d^3*g*e^3 - 2*b^3*c*d^3*h*e^3 + 24*a*c^3*d^2*f*e^4 - 3*b^3*c*d^2*g*e^4 + 12*a*b^2*c*d^2*h*e^4 - 24*a^2*c^2*d^2*h*e^4 + 4*b^3*c*d*f*e^5 - 24*a*b*c^2*d*f*e^5 + b^4*d*g*e^5 - 6*a*b^2*c*d*g*e^5 + 24*a^2*c^2*d*g*e^5 - 2*a*b^3*d*h*e^5 - 2*b^4*f*e^6 + 12*a*b^2*c*f*e^6 - 12*a^2*c^2*f*e^6 + a*b^3*g*e^6 - 6*a^2*b*c*g*e^6 + 4*a^3*c*h*e^6)*arctan((2*c*d - 2*c*d^2/(x*e + d) - b*e + 2*b*d*e/(x*e + d) - 2*a*e^2/(x*e + d))*e^(-1)/sqrt(-b^2 + 4*a*c))*e^(-2)/((b^2*c^3*d^6 - 4*a*c^4*d^6 - 3*b^3*c^2*d^5*e + 12*a*b*c^3*d^5*e + 3*b^4*c*d^4*e^2 - 9*a*b^2*c^2*d^4*e^2 - 12*a^2*c^3*d^4*e^2 - b^5*d^3*e^3 - 2*a*b^3*c*d^3*e^3 + 24*a^2*b*c^2*d^3*e^3 + 3*a*b^4*d^2*e^4 - 9*a^2*b^2*c*d^2*e^4 - 12*a^3*c^2*d^2*e^4 - 3*a^2*b^3*d*e^5 + 12*a^3*b*c*d*e^5 + a^3*b^2*e^6 - 4*a^4*c*e^6)*sqrt(-b^2 + 4*a*c)) - 1/2*(2*c*d^3*h*e - 3*c*d^2*g*e^2 + 4*c*d*f*e^3 + b*d*g*e^3 - 2*a*d*h*e^3 - 2*b*f*e^4 + a*g*e^4)*log(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + b*e/(x*e + d) - b*d*e/(x*e + d)^2 + a*e^2/(x*e + d)^2)/(c^3*d^6 - 3*b*c^2*d^5*e + 3*b^2*c*d^4*e^2 + 3*a*c^2*d^4*e^2 - b^3*d^3*e^3 - 6*a*b*c*d^3*e^3 + 3*a*b^2*d^2*e^4 + 3*a^2*c*d^2*e^4 - 3*a^2*b*d*e^5 + a^3*e^6) - (d^2*h*e^5/(x*e + d) - d*g*e^6/(x*e + d) + f*e^7/(x*e + d))/(c^2*d^4*e^4 - 2*b*c*d^3*e^5 + b^2*d^2*e^6 + 2*a*c*d^2*e^6 - 2*a*b*d*e^7 + a^2*e^8) - ((2*c^4*d^3*f*e - b*c^3*d^3*g*e + b^2*c^2*d^3*h*e - 2*a*c^3*d^3*h*e - 3*b*c^3*d^2*f*e^2 + 6*a*c^3*d^2*g*e^2 - 3*a*b*c^2*d^2*h*e^2 + 3*b^2*c^2*d*f*e^3 - 6*a*c^3*d*f*e^3 - 3*a*b*c^2*d*g*e^3 + 6*a^2*c^2*d*h*e^3 - b^3*c*f*e^4 + 3*a*b*c^2*f*e^4 + a*b^2*c*g*e^4 - 2*a^2*c^2*g*e^4 - a^2*b*c*h*e^4)/(c*d^2 - b*d*e + a*e^2) - (2*c^4*d^4*f*e^2 - b*c^3*d^4*g*e^2 + b^2*c^2*d^4*h*e^2 - 2*a*c^3*d^4*h*e^2 - 4*b*c^3*d^3*f*e^3 + 8*a*c^3*d^3*g*e^3 - 4*a*b*c^2*d^3*h*e^3 + 6*b^2*c^2*d^2*f*e^4 - 12*a*c^3*d^2*f*e^4 - 6*a*b*c^2*d^2*g*e^4 + 12*a^2*c^2*d^2*h*e^4 - 4*b^3*c*d*f*e^5 + 12*a*b*c^2*d*f*e^5 + 4*a*b^2*c*d*g*e^5 - 8*a^2*c^2*d*g*e^5 - 4*a^2*b*c*d*h*e^5 + b^4*f*e^6 - 4*a*b^2*c*f*e^6 + 2*a^2*c^2*f*e^6 - a*b^3*g*e^6 + 3*a^2*b*c*g*e^6 + a^2*b^2*h*e^6 - 2*a^3*c*h*e^6)*e^(-1)/((c*d^2 - b*d*e + a*e^2)*(x*e + d)))/((c*d^2 - b*d*e + a*e^2)^2*(b^2 - 4*a*c)*(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + b*e/(x*e + d) - b*d*e/(x*e + d)^2 + a*e^2/(x*e + d)^2))","B",0
160,1,51,0,0.158153," ","integrate(x^3*(x^2+x+1)/(x^2-x+1)^2,x, algorithm=""giac"")","\frac{1}{2} \, x^{2} - \frac{10}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + 3 \, x - \frac{2 \, {\left(x - 2\right)}}{3 \, {\left(x^{2} - x + 1\right)}} + 2 \, \log\left(x^{2} - x + 1\right)"," ",0,"1/2*x^2 - 10/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) + 3*x - 2/3*(x - 2)/(x^2 - x + 1) + 2*log(x^2 - x + 1)","A",0
161,1,46,0,0.159247," ","integrate(x^2*(x^2+x+1)/(x^2-x+1)^2,x, algorithm=""giac"")","\frac{7}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + x - \frac{2 \, {\left(2 \, x - 1\right)}}{3 \, {\left(x^{2} - x + 1\right)}} + \frac{3}{2} \, \log\left(x^{2} - x + 1\right)"," ",0,"7/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) + x - 2/3*(2*x - 1)/(x^2 - x + 1) + 3/2*log(x^2 - x + 1)","A",0
162,1,43,0,0.150847," ","integrate(x*(x^2+x+1)/(x^2-x+1)^2,x, algorithm=""giac"")","\frac{11}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) - \frac{2 \, {\left(x + 1\right)}}{3 \, {\left(x^{2} - x + 1\right)}} + \frac{1}{2} \, \log\left(x^{2} - x + 1\right)"," ",0,"11/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) - 2/3*(x + 1)/(x^2 - x + 1) + 1/2*log(x^2 - x + 1)","A",0
163,1,32,0,0.156595," ","integrate((x^2+x+1)/(x^2-x+1)^2,x, algorithm=""giac"")","\frac{10}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + \frac{2 \, {\left(x - 2\right)}}{3 \, {\left(x^{2} - x + 1\right)}}"," ",0,"10/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) + 2/3*(x - 2)/(x^2 - x + 1)","A",0
164,1,48,0,0.151163," ","integrate((x^2+x+1)/x/(x^2-x+1)^2,x, algorithm=""giac"")","\frac{11}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + \frac{2 \, {\left(2 \, x - 1\right)}}{3 \, {\left(x^{2} - x + 1\right)}} - \frac{1}{2} \, \log\left(x^{2} - x + 1\right) + \log\left({\left| x \right|}\right)"," ",0,"11/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) + 2/3*(2*x - 1)/(x^2 - x + 1) - 1/2*log(x^2 - x + 1) + log(abs(x))","A",0
165,1,55,0,0.150188," ","integrate((x^2+x+1)/x^2/(x^2-x+1)^2,x, algorithm=""giac"")","\frac{7}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) - \frac{x^{2} - 5 \, x + 3}{3 \, {\left(x^{3} - x^{2} + x\right)}} - \frac{3}{2} \, \log\left(x^{2} - x + 1\right) + 3 \, \log\left({\left| x \right|}\right)"," ",0,"7/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) - 1/3*(x^2 - 5*x + 3)/(x^3 - x^2 + x) - 3/2*log(x^2 - x + 1) + 3*log(abs(x))","A",0
166,1,63,0,0.158194," ","integrate((x^2+x+1)/x^3/(x^2-x+1)^2,x, algorithm=""giac"")","-\frac{10}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) - \frac{22 \, x^{3} - 23 \, x^{2} + 15 \, x + 3}{6 \, {\left(x^{2} - x + 1\right)} x^{2}} - 2 \, \log\left(x^{2} - x + 1\right) + 4 \, \log\left({\left| x \right|}\right)"," ",0,"-10/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) - 1/6*(22*x^3 - 23*x^2 + 15*x + 3)/((x^2 - x + 1)*x^2) - 2*log(x^2 - x + 1) + 4*log(abs(x))","A",0
167,1,8,0,0.148663," ","integrate((-x^2+1)/(x^2+x+1)^2,x, algorithm=""giac"")","\frac{1}{x + \frac{1}{x} + 1}"," ",0,"1/(x + 1/x + 1)","A",0
168,1,27,0,0.172548," ","integrate((x^2+1)/(x^2+x+1),x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + x - \frac{1}{2} \, \log\left(x^{2} + x + 1\right)"," ",0,"1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) + x - 1/2*log(x^2 + x + 1)","A",0
169,1,21,0,0.150505," ","integrate((x^2-1)/(x^2-6*x+25),x, algorithm=""giac"")","x - 2 \, \arctan\left(\frac{1}{4} \, x - \frac{3}{4}\right) + 3 \, \log\left(x^{2} - 6 \, x + 25\right)"," ",0,"x - 2*arctan(1/4*x - 3/4) + 3*log(x^2 - 6*x + 25)","A",0
170,1,18,0,0.165970," ","integrate((3*x^2-10)/(x^2-4*x+4),x, algorithm=""giac"")","3 \, x - \frac{2}{x - 2} + 12 \, \log\left({\left| x - 2 \right|}\right)"," ",0,"3*x - 2/(x - 2) + 12*log(abs(x - 2))","A",0
171,1,16,0,0.149021," ","integrate((x^2+8)/(x^2-5*x+6),x, algorithm=""giac"")","x - 12 \, \log\left({\left| x - 2 \right|}\right) + 17 \, \log\left({\left| x - 3 \right|}\right)"," ",0,"x - 12*log(abs(x - 2)) + 17*log(abs(x - 3))","A",0
172,1,14,0,0.155561," ","integrate((x^2+3*x-4)/(x^2-2*x-8),x, algorithm=""giac"")","x + \log\left({\left| x + 2 \right|}\right) + 4 \, \log\left({\left| x - 4 \right|}\right)"," ",0,"x + log(abs(x + 2)) + 4*log(abs(x - 4))","A",0
173,1,21,0,0.150949," ","integrate((4*x^2+5*x+7)/(4*x^2+4*x+5),x, algorithm=""giac"")","x + \frac{3}{8} \, \arctan\left(x + \frac{1}{2}\right) + \frac{1}{8} \, \log\left(4 \, x^{2} + 4 \, x + 5\right)"," ",0,"x + 3/8*arctan(x + 1/2) + 1/8*log(4*x^2 + 4*x + 5)","A",0
174,1,45,0,0.189832," ","integrate((x^2-x+2)/(x^2+2*x-5),x, algorithm=""giac"")","\frac{5}{6} \, \sqrt{6} \log\left(\frac{{\left| 2 \, x - 2 \, \sqrt{6} + 2 \right|}}{{\left| 2 \, x + 2 \, \sqrt{6} + 2 \right|}}\right) + x - \frac{3}{2} \, \log\left({\left| x^{2} + 2 \, x - 5 \right|}\right)"," ",0,"5/6*sqrt(6)*log(abs(2*x - 2*sqrt(6) + 2)/abs(2*x + 2*sqrt(6) + 2)) + x - 3/2*log(abs(x^2 + 2*x - 5))","A",0
175,1,19,0,0.156844," ","integrate((3*x^2+4*x+1)/(2*x^2+7*x+4)^2,x, algorithm=""giac"")","-\frac{3 \, x + 2}{2 \, {\left(2 \, x^{2} + 7 \, x + 4\right)}}"," ",0,"-1/2*(3*x + 2)/(2*x^2 + 7*x + 4)","A",0
176,1,30,0,0.164641," ","integrate((x^2+x+1)/(x^2+2*x+3)^2,x, algorithm=""giac"")","\frac{3}{8} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(x + 1\right)}\right) - \frac{x - 1}{4 \, {\left(x^{2} + 2 \, x + 3\right)}}"," ",0,"3/8*sqrt(2)*arctan(1/2*sqrt(2)*(x + 1)) - 1/4*(x - 1)/(x^2 + 2*x + 3)","A",0
177,1,11,0,0.150707," ","integrate((5*x^2+2*x-1)/(x^2+x+1)^4,x, algorithm=""giac"")","-\frac{x}{{\left(x^{2} + x + 1\right)}^{3}}"," ",0,"-x/(x^2 + x + 1)^3","A",0
178,1,482,0,0.274973," ","integrate((c*x^2+b*x+a)^(5/2)*(C*x^2+A),x, algorithm=""giac"")","\frac{1}{344064} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(2 \, {\left(12 \, {\left(14 \, C c^{2} x + 33 \, C b c\right)} x + \frac{243 \, C b^{2} c^{7} + 476 \, C a c^{8} + 224 \, A c^{9}}{c^{7}}\right)} x + \frac{3 \, C b^{3} c^{6} + 1228 \, C a b c^{7} + 1120 \, A b c^{8}}{c^{7}}\right)} x - \frac{27 \, C b^{4} c^{5} - 216 \, C a b^{2} c^{6} - 6608 \, C a^{2} c^{7} - 6048 \, A b^{2} c^{7} - 11648 \, A a c^{8}}{c^{7}}\right)} x + \frac{63 \, C b^{5} c^{4} - 568 \, C a b^{3} c^{5} + 1392 \, C a^{2} b c^{6} + 224 \, A b^{3} c^{6} + 34944 \, A a b c^{7}}{c^{7}}\right)} x - \frac{315 \, C b^{6} c^{3} - 3164 \, C a b^{4} c^{4} + 9552 \, C a^{2} b^{2} c^{5} + 1120 \, A b^{4} c^{5} - 6720 \, C a^{3} c^{6} - 10752 \, A a b^{2} c^{6} - 118272 \, A a^{2} c^{7}}{c^{7}}\right)} x + \frac{945 \, C b^{7} c^{2} - 10500 \, C a b^{5} c^{3} + 37744 \, C a^{2} b^{3} c^{4} + 3360 \, A b^{5} c^{4} - 42432 \, C a^{3} b c^{5} - 35840 \, A a b^{3} c^{5} + 118272 \, A a^{2} b c^{6}}{c^{7}}\right)} + \frac{5 \, {\left(9 \, C b^{8} - 112 \, C a b^{6} c + 480 \, C a^{2} b^{4} c^{2} + 32 \, A b^{6} c^{2} - 768 \, C a^{3} b^{2} c^{3} - 384 \, A a b^{4} c^{3} + 256 \, C a^{4} c^{4} + 1536 \, A a^{2} b^{2} c^{4} - 2048 \, A a^{3} c^{5}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{32768 \, c^{\frac{11}{2}}}"," ",0,"1/344064*sqrt(c*x^2 + b*x + a)*(2*(4*(2*(8*(2*(12*(14*C*c^2*x + 33*C*b*c)*x + (243*C*b^2*c^7 + 476*C*a*c^8 + 224*A*c^9)/c^7)*x + (3*C*b^3*c^6 + 1228*C*a*b*c^7 + 1120*A*b*c^8)/c^7)*x - (27*C*b^4*c^5 - 216*C*a*b^2*c^6 - 6608*C*a^2*c^7 - 6048*A*b^2*c^7 - 11648*A*a*c^8)/c^7)*x + (63*C*b^5*c^4 - 568*C*a*b^3*c^5 + 1392*C*a^2*b*c^6 + 224*A*b^3*c^6 + 34944*A*a*b*c^7)/c^7)*x - (315*C*b^6*c^3 - 3164*C*a*b^4*c^4 + 9552*C*a^2*b^2*c^5 + 1120*A*b^4*c^5 - 6720*C*a^3*c^6 - 10752*A*a*b^2*c^6 - 118272*A*a^2*c^7)/c^7)*x + (945*C*b^7*c^2 - 10500*C*a*b^5*c^3 + 37744*C*a^2*b^3*c^4 + 3360*A*b^5*c^4 - 42432*C*a^3*b*c^5 - 35840*A*a*b^3*c^5 + 118272*A*a^2*b*c^6)/c^7) + 5/32768*(9*C*b^8 - 112*C*a*b^6*c + 480*C*a^2*b^4*c^2 + 32*A*b^6*c^2 - 768*C*a^3*b^2*c^3 - 384*A*a*b^4*c^3 + 256*C*a^4*c^4 + 1536*A*a^2*b^2*c^4 - 2048*A*a^3*c^5)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(11/2)","B",0
179,1,297,0,0.282086," ","integrate((c*x^2+b*x+a)^(3/2)*(C*x^2+A),x, algorithm=""giac"")","\frac{1}{7680} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(10 \, C c x + 13 \, C b\right)} x + \frac{3 \, C b^{2} c^{4} + 140 \, C a c^{5} + 120 \, A c^{6}}{c^{5}}\right)} x - \frac{7 \, C b^{3} c^{3} - 36 \, C a b c^{4} - 360 \, A b c^{5}}{c^{5}}\right)} x + \frac{35 \, C b^{4} c^{2} - 216 \, C a b^{2} c^{3} + 240 \, C a^{2} c^{4} + 120 \, A b^{2} c^{4} + 2400 \, A a c^{5}}{c^{5}}\right)} x - \frac{105 \, C b^{5} c - 760 \, C a b^{3} c^{2} + 1296 \, C a^{2} b c^{3} + 360 \, A b^{3} c^{3} - 2400 \, A a b c^{4}}{c^{5}}\right)} - \frac{{\left(7 \, C b^{6} - 60 \, C a b^{4} c + 144 \, C a^{2} b^{2} c^{2} + 24 \, A b^{4} c^{2} - 64 \, C a^{3} c^{3} - 192 \, A a b^{2} c^{3} + 384 \, A a^{2} c^{4}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{1024 \, c^{\frac{9}{2}}}"," ",0,"1/7680*sqrt(c*x^2 + b*x + a)*(2*(4*(2*(8*(10*C*c*x + 13*C*b)*x + (3*C*b^2*c^4 + 140*C*a*c^5 + 120*A*c^6)/c^5)*x - (7*C*b^3*c^3 - 36*C*a*b*c^4 - 360*A*b*c^5)/c^5)*x + (35*C*b^4*c^2 - 216*C*a*b^2*c^3 + 240*C*a^2*c^4 + 120*A*b^2*c^4 + 2400*A*a*c^5)/c^5)*x - (105*C*b^5*c - 760*C*a*b^3*c^2 + 1296*C*a^2*b*c^3 + 360*A*b^3*c^3 - 2400*A*a*b*c^4)/c^5) - 1/1024*(7*C*b^6 - 60*C*a*b^4*c + 144*C*a^2*b^2*c^2 + 24*A*b^4*c^2 - 64*C*a^3*c^3 - 192*A*a*b^2*c^3 + 384*A*a^2*c^4)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(9/2)","A",0
180,1,160,0,0.217065," ","integrate((c*x^2+b*x+a)^(1/2)*(C*x^2+A),x, algorithm=""giac"")","\frac{1}{192} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(6 \, C x + \frac{C b}{c}\right)} x - \frac{5 \, C b^{2} c - 12 \, C a c^{2} - 48 \, A c^{3}}{c^{3}}\right)} x + \frac{15 \, C b^{3} - 52 \, C a b c + 48 \, A b c^{2}}{c^{3}}\right)} + \frac{{\left(5 \, C b^{4} - 24 \, C a b^{2} c + 16 \, C a^{2} c^{2} + 16 \, A b^{2} c^{2} - 64 \, A a c^{3}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{128 \, c^{\frac{7}{2}}}"," ",0,"1/192*sqrt(c*x^2 + b*x + a)*(2*(4*(6*C*x + C*b/c)*x - (5*C*b^2*c - 12*C*a*c^2 - 48*A*c^3)/c^3)*x + (15*C*b^3 - 52*C*a*b*c + 48*A*b*c^2)/c^3) + 1/128*(5*C*b^4 - 24*C*a*b^2*c + 16*C*a^2*c^2 + 16*A*b^2*c^2 - 64*A*a*c^3)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(7/2)","A",0
181,1,84,0,0.247071," ","integrate((C*x^2+A)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{c x^{2} + b x + a} {\left(\frac{2 \, C x}{c} - \frac{3 \, C b}{c^{2}}\right)} - \frac{{\left(3 \, C b^{2} - 4 \, C a c + 8 \, A c^{2}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{8 \, c^{\frac{5}{2}}}"," ",0,"1/4*sqrt(c*x^2 + b*x + a)*(2*C*x/c - 3*C*b/c^2) - 1/8*(3*C*b^2 - 4*C*a*c + 8*A*c^2)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(5/2)","A",0
182,1,110,0,0.270361," ","integrate((C*x^2+A)/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{{\left(C b^{2} - 2 \, C a c + 2 \, A c^{2}\right)} x}{b^{2} c - 4 \, a c^{2}} + \frac{C a b + A b c}{b^{2} c - 4 \, a c^{2}}\right)}}{\sqrt{c x^{2} + b x + a}} - \frac{C \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{c^{\frac{3}{2}}}"," ",0,"-2*((C*b^2 - 2*C*a*c + 2*A*c^2)*x/(b^2*c - 4*a*c^2) + (C*a*b + A*b*c)/(b^2*c - 4*a*c^2))/sqrt(c*x^2 + b*x + a) - C*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(3/2)","A",0
183,1,193,0,0.257548," ","integrate((C*x^2+A)/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\frac{2 \, {\left({\left({\left(\frac{2 \, {\left(C b^{2} c + 4 \, C a c^{2} + 8 \, A c^{3}\right)} x}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}} + \frac{3 \, {\left(C b^{3} + 4 \, C a b c + 8 \, A b c^{2}\right)}}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}}\right)} x + \frac{6 \, {\left(2 \, C a b^{2} + A b^{2} c + 4 \, A a c^{2}\right)}}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}}\right)} x + \frac{8 \, C a^{2} b - A b^{3} + 12 \, A a b c}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}}\right)}}{3 \, {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}"," ",0,"2/3*(((2*(C*b^2*c + 4*C*a*c^2 + 8*A*c^3)*x/(b^4 - 8*a*b^2*c + 16*a^2*c^2) + 3*(C*b^3 + 4*C*a*b*c + 8*A*b*c^2)/(b^4 - 8*a*b^2*c + 16*a^2*c^2))*x + 6*(2*C*a*b^2 + A*b^2*c + 4*A*a*c^2)/(b^4 - 8*a*b^2*c + 16*a^2*c^2))*x + (8*C*a^2*b - A*b^3 + 12*A*a*b*c)/(b^4 - 8*a*b^2*c + 16*a^2*c^2))/(c*x^2 + b*x + a)^(3/2)","A",0
184,1,452,0,0.284155," ","integrate((C*x^2+A)/(c*x^2+b*x+a)^(7/2),x, algorithm=""giac"")","-\frac{2 \, {\left({\left({\left(2 \, {\left(4 \, {\left(\frac{2 \, {\left(3 \, C b^{2} c^{3} + 4 \, C a c^{4} + 16 \, A c^{5}\right)} x}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}} + \frac{5 \, {\left(3 \, C b^{3} c^{2} + 4 \, C a b c^{3} + 16 \, A b c^{4}\right)}}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}\right)} x + \frac{5 \, {\left(9 \, C b^{4} c + 24 \, C a b^{2} c^{2} + 16 \, C a^{2} c^{3} + 48 \, A b^{2} c^{3} + 64 \, A a c^{4}\right)}}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}\right)} x + \frac{5 \, {\left(3 \, C b^{5} + 40 \, C a b^{3} c + 48 \, C a^{2} b c^{2} + 16 \, A b^{3} c^{2} + 192 \, A a b c^{3}\right)}}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}\right)} x + \frac{10 \, {\left(2 \, C a b^{4} + 24 \, C a^{2} b^{2} c - A b^{4} c + 24 \, A a b^{2} c^{2} + 48 \, A a^{2} c^{3}\right)}}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}\right)} x + \frac{8 \, C a^{2} b^{3} + 3 \, A b^{5} + 96 \, C a^{3} b c - 40 \, A a b^{3} c + 240 \, A a^{2} b c^{2}}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}\right)}}{15 \, {\left(c x^{2} + b x + a\right)}^{\frac{5}{2}}}"," ",0,"-2/15*(((2*(4*(2*(3*C*b^2*c^3 + 4*C*a*c^4 + 16*A*c^5)*x/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3) + 5*(3*C*b^3*c^2 + 4*C*a*b*c^3 + 16*A*b*c^4)/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3))*x + 5*(9*C*b^4*c + 24*C*a*b^2*c^2 + 16*C*a^2*c^3 + 48*A*b^2*c^3 + 64*A*a*c^4)/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3))*x + 5*(3*C*b^5 + 40*C*a*b^3*c + 48*C*a^2*b*c^2 + 16*A*b^3*c^2 + 192*A*a*b*c^3)/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3))*x + 10*(2*C*a*b^4 + 24*C*a^2*b^2*c - A*b^4*c + 24*A*a*b^2*c^2 + 48*A*a^2*c^3)/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3))*x + (8*C*a^2*b^3 + 3*A*b^5 + 96*C*a^3*b*c - 40*A*a*b^3*c + 240*A*a^2*b*c^2)/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3))/(c*x^2 + b*x + a)^(5/2)","B",0
185,1,805,0,0.313055," ","integrate((C*x^2+A)/(c*x^2+b*x+a)^(9/2),x, algorithm=""giac"")","\frac{2 \, {\left({\left({\left(2 \, {\left(8 \, {\left(2 \, {\left(4 \, {\left(\frac{2 \, {\left(5 \, C b^{2} c^{5} + 4 \, C a c^{6} + 24 \, A c^{7}\right)} x}{b^{8} - 16 \, a b^{6} c + 96 \, a^{2} b^{4} c^{2} - 256 \, a^{3} b^{2} c^{3} + 256 \, a^{4} c^{4}} + \frac{7 \, {\left(5 \, C b^{3} c^{4} + 4 \, C a b c^{5} + 24 \, A b c^{6}\right)}}{b^{8} - 16 \, a b^{6} c + 96 \, a^{2} b^{4} c^{2} - 256 \, a^{3} b^{2} c^{3} + 256 \, a^{4} c^{4}}\right)} x + \frac{7 \, {\left(25 \, C b^{4} c^{3} + 40 \, C a b^{2} c^{4} + 16 \, C a^{2} c^{5} + 120 \, A b^{2} c^{5} + 96 \, A a c^{6}\right)}}{b^{8} - 16 \, a b^{6} c + 96 \, a^{2} b^{4} c^{2} - 256 \, a^{3} b^{2} c^{3} + 256 \, a^{4} c^{4}}\right)} x + \frac{35 \, {\left(5 \, C b^{5} c^{2} + 24 \, C a b^{3} c^{3} + 16 \, C a^{2} b c^{4} + 24 \, A b^{3} c^{4} + 96 \, A a b c^{5}\right)}}{b^{8} - 16 \, a b^{6} c + 96 \, a^{2} b^{4} c^{2} - 256 \, a^{3} b^{2} c^{3} + 256 \, a^{4} c^{4}}\right)} x + \frac{35 \, {\left(5 \, C b^{6} c + 124 \, C a b^{4} c^{2} + 176 \, C a^{2} b^{2} c^{3} + 24 \, A b^{4} c^{3} + 64 \, C a^{3} c^{4} + 576 \, A a b^{2} c^{4} + 384 \, A a^{2} c^{5}\right)}}{b^{8} - 16 \, a b^{6} c + 96 \, a^{2} b^{4} c^{2} - 256 \, a^{3} b^{2} c^{3} + 256 \, a^{4} c^{4}}\right)} x - \frac{7 \, {\left(5 \, C b^{7} - 196 \, C a b^{5} c - 1360 \, C a^{2} b^{3} c^{2} + 24 \, A b^{5} c^{2} - 960 \, C a^{3} b c^{3} - 960 \, A a b^{3} c^{3} - 5760 \, A a^{2} b c^{4}\right)}}{b^{8} - 16 \, a b^{6} c + 96 \, a^{2} b^{4} c^{2} - 256 \, a^{3} b^{2} c^{3} + 256 \, a^{4} c^{4}}\right)} x - \frac{14 \, {\left(2 \, C a b^{6} - 80 \, C a^{2} b^{4} c - 3 \, A b^{6} c - 480 \, C a^{3} b^{2} c^{2} + 60 \, A a b^{4} c^{2} - 720 \, A a^{2} b^{2} c^{3} - 960 \, A a^{3} c^{4}\right)}}{b^{8} - 16 \, a b^{6} c + 96 \, a^{2} b^{4} c^{2} - 256 \, a^{3} b^{2} c^{3} + 256 \, a^{4} c^{4}}\right)} x - \frac{8 \, C a^{2} b^{5} + 15 \, A b^{7} - 320 \, C a^{3} b^{3} c - 252 \, A a b^{5} c - 1920 \, C a^{4} b c^{2} + 1680 \, A a^{2} b^{3} c^{2} - 6720 \, A a^{3} b c^{3}}{b^{8} - 16 \, a b^{6} c + 96 \, a^{2} b^{4} c^{2} - 256 \, a^{3} b^{2} c^{3} + 256 \, a^{4} c^{4}}\right)}}{105 \, {\left(c x^{2} + b x + a\right)}^{\frac{7}{2}}}"," ",0,"2/105*(((2*(8*(2*(4*(2*(5*C*b^2*c^5 + 4*C*a*c^6 + 24*A*c^7)*x/(b^8 - 16*a*b^6*c + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 + 256*a^4*c^4) + 7*(5*C*b^3*c^4 + 4*C*a*b*c^5 + 24*A*b*c^6)/(b^8 - 16*a*b^6*c + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 + 256*a^4*c^4))*x + 7*(25*C*b^4*c^3 + 40*C*a*b^2*c^4 + 16*C*a^2*c^5 + 120*A*b^2*c^5 + 96*A*a*c^6)/(b^8 - 16*a*b^6*c + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 + 256*a^4*c^4))*x + 35*(5*C*b^5*c^2 + 24*C*a*b^3*c^3 + 16*C*a^2*b*c^4 + 24*A*b^3*c^4 + 96*A*a*b*c^5)/(b^8 - 16*a*b^6*c + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 + 256*a^4*c^4))*x + 35*(5*C*b^6*c + 124*C*a*b^4*c^2 + 176*C*a^2*b^2*c^3 + 24*A*b^4*c^3 + 64*C*a^3*c^4 + 576*A*a*b^2*c^4 + 384*A*a^2*c^5)/(b^8 - 16*a*b^6*c + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 + 256*a^4*c^4))*x - 7*(5*C*b^7 - 196*C*a*b^5*c - 1360*C*a^2*b^3*c^2 + 24*A*b^5*c^2 - 960*C*a^3*b*c^3 - 960*A*a*b^3*c^3 - 5760*A*a^2*b*c^4)/(b^8 - 16*a*b^6*c + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 + 256*a^4*c^4))*x - 14*(2*C*a*b^6 - 80*C*a^2*b^4*c - 3*A*b^6*c - 480*C*a^3*b^2*c^2 + 60*A*a*b^4*c^2 - 720*A*a^2*b^2*c^3 - 960*A*a^3*c^4)/(b^8 - 16*a*b^6*c + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 + 256*a^4*c^4))*x - (8*C*a^2*b^5 + 15*A*b^7 - 320*C*a^3*b^3*c - 252*A*a*b^5*c - 1920*C*a^4*b*c^2 + 1680*A*a^2*b^3*c^2 - 6720*A*a^3*b*c^3)/(b^8 - 16*a*b^6*c + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 + 256*a^4*c^4))/(c*x^2 + b*x + a)^(7/2)","B",0
186,1,1702,0,0.305559," ","integrate((h*x+g)^3*(f*x^2+e*x+d)*(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{1}{107520} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(10 \, {\left(12 \, f h^{3} x + \frac{42 \, c^{6} f g h^{2} + b c^{5} f h^{3} + 14 \, c^{6} h^{3} e}{c^{6}}\right)} x + \frac{504 \, c^{6} f g^{2} h + 42 \, b c^{5} f g h^{2} + 168 \, c^{6} d h^{3} - 11 \, b^{2} c^{4} f h^{3} + 24 \, a c^{5} f h^{3} + 504 \, c^{6} g h^{2} e + 14 \, b c^{5} h^{3} e}{c^{6}}\right)} x + \frac{1680 \, c^{6} f g^{3} + 504 \, b c^{5} f g^{2} h + 5040 \, c^{6} d g h^{2} - 378 \, b^{2} c^{4} f g h^{2} + 840 \, a c^{5} f g h^{2} + 168 \, b c^{5} d h^{3} + 99 \, b^{3} c^{3} f h^{3} - 316 \, a b c^{4} f h^{3} + 5040 \, c^{6} g^{2} h e + 504 \, b c^{5} g h^{2} e - 126 \, b^{2} c^{4} h^{3} e + 280 \, a c^{5} h^{3} e}{c^{6}}\right)} x + \frac{560 \, b c^{5} f g^{3} + 13440 \, c^{6} d g^{2} h - 1176 \, b^{2} c^{4} f g^{2} h + 2688 \, a c^{5} f g^{2} h + 1680 \, b c^{5} d g h^{2} + 882 \, b^{3} c^{3} f g h^{2} - 2856 \, a b c^{4} f g h^{2} - 392 \, b^{2} c^{4} d h^{3} + 896 \, a c^{5} d h^{3} - 231 \, b^{4} c^{2} f h^{3} + 972 \, a b^{2} c^{3} f h^{3} - 512 \, a^{2} c^{4} f h^{3} + 4480 \, c^{6} g^{3} e + 1680 \, b c^{5} g^{2} h e - 1176 \, b^{2} c^{4} g h^{2} e + 2688 \, a c^{5} g h^{2} e + 294 \, b^{3} c^{3} h^{3} e - 952 \, a b c^{4} h^{3} e}{c^{6}}\right)} x + \frac{26880 \, c^{6} d g^{3} - 2800 \, b^{2} c^{4} f g^{3} + 6720 \, a c^{5} f g^{3} + 13440 \, b c^{5} d g^{2} h + 5880 \, b^{3} c^{3} f g^{2} h - 19488 \, a b c^{4} f g^{2} h - 8400 \, b^{2} c^{4} d g h^{2} + 20160 \, a c^{5} d g h^{2} - 4410 \, b^{4} c^{2} f g h^{2} + 18816 \, a b^{2} c^{3} f g h^{2} - 10080 \, a^{2} c^{4} f g h^{2} + 1960 \, b^{3} c^{3} d h^{3} - 6496 \, a b c^{4} d h^{3} + 1155 \, b^{5} c f h^{3} - 6048 \, a b^{3} c^{2} f h^{3} + 6352 \, a^{2} b c^{3} f h^{3} + 4480 \, b c^{5} g^{3} e - 8400 \, b^{2} c^{4} g^{2} h e + 20160 \, a c^{5} g^{2} h e + 5880 \, b^{3} c^{3} g h^{2} e - 19488 \, a b c^{4} g h^{2} e - 1470 \, b^{4} c^{2} h^{3} e + 6272 \, a b^{2} c^{3} h^{3} e - 3360 \, a^{2} c^{4} h^{3} e}{c^{6}}\right)} x + \frac{26880 \, b c^{5} d g^{3} + 8400 \, b^{3} c^{3} f g^{3} - 29120 \, a b c^{4} f g^{3} - 40320 \, b^{2} c^{4} d g^{2} h + 107520 \, a c^{5} d g^{2} h - 17640 \, b^{4} c^{2} f g^{2} h + 77280 \, a b^{2} c^{3} f g^{2} h - 43008 \, a^{2} c^{4} f g^{2} h + 25200 \, b^{3} c^{3} d g h^{2} - 87360 \, a b c^{4} d g h^{2} + 13230 \, b^{5} c f g h^{2} - 70560 \, a b^{3} c^{2} f g h^{2} + 75936 \, a^{2} b c^{3} f g h^{2} - 5880 \, b^{4} c^{2} d h^{3} + 25760 \, a b^{2} c^{3} d h^{3} - 14336 \, a^{2} c^{4} d h^{3} - 3465 \, b^{6} f h^{3} + 21840 \, a b^{4} c f h^{3} - 34608 \, a^{2} b^{2} c^{2} f h^{3} + 8192 \, a^{3} c^{3} f h^{3} - 13440 \, b^{2} c^{4} g^{3} e + 35840 \, a c^{5} g^{3} e + 25200 \, b^{3} c^{3} g^{2} h e - 87360 \, a b c^{4} g^{2} h e - 17640 \, b^{4} c^{2} g h^{2} e + 77280 \, a b^{2} c^{3} g h^{2} e - 43008 \, a^{2} c^{4} g h^{2} e + 4410 \, b^{5} c h^{3} e - 23520 \, a b^{3} c^{2} h^{3} e + 25312 \, a^{2} b c^{3} h^{3} e}{c^{6}}\right)} + \frac{{\left(256 \, b^{2} c^{5} d g^{3} - 1024 \, a c^{6} d g^{3} + 80 \, b^{4} c^{3} f g^{3} - 384 \, a b^{2} c^{4} f g^{3} + 256 \, a^{2} c^{5} f g^{3} - 384 \, b^{3} c^{4} d g^{2} h + 1536 \, a b c^{5} d g^{2} h - 168 \, b^{5} c^{2} f g^{2} h + 960 \, a b^{3} c^{3} f g^{2} h - 1152 \, a^{2} b c^{4} f g^{2} h + 240 \, b^{4} c^{3} d g h^{2} - 1152 \, a b^{2} c^{4} d g h^{2} + 768 \, a^{2} c^{5} d g h^{2} + 126 \, b^{6} c f g h^{2} - 840 \, a b^{4} c^{2} f g h^{2} + 1440 \, a^{2} b^{2} c^{3} f g h^{2} - 384 \, a^{3} c^{4} f g h^{2} - 56 \, b^{5} c^{2} d h^{3} + 320 \, a b^{3} c^{3} d h^{3} - 384 \, a^{2} b c^{4} d h^{3} - 33 \, b^{7} f h^{3} + 252 \, a b^{5} c f h^{3} - 560 \, a^{2} b^{3} c^{2} f h^{3} + 320 \, a^{3} b c^{3} f h^{3} - 128 \, b^{3} c^{4} g^{3} e + 512 \, a b c^{5} g^{3} e + 240 \, b^{4} c^{3} g^{2} h e - 1152 \, a b^{2} c^{4} g^{2} h e + 768 \, a^{2} c^{5} g^{2} h e - 168 \, b^{5} c^{2} g h^{2} e + 960 \, a b^{3} c^{3} g h^{2} e - 1152 \, a^{2} b c^{4} g h^{2} e + 42 \, b^{6} c h^{3} e - 280 \, a b^{4} c^{2} h^{3} e + 480 \, a^{2} b^{2} c^{3} h^{3} e - 128 \, a^{3} c^{4} h^{3} e\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{2048 \, c^{\frac{13}{2}}}"," ",0,"1/107520*sqrt(c*x^2 + b*x + a)*(2*(4*(2*(8*(10*(12*f*h^3*x + (42*c^6*f*g*h^2 + b*c^5*f*h^3 + 14*c^6*h^3*e)/c^6)*x + (504*c^6*f*g^2*h + 42*b*c^5*f*g*h^2 + 168*c^6*d*h^3 - 11*b^2*c^4*f*h^3 + 24*a*c^5*f*h^3 + 504*c^6*g*h^2*e + 14*b*c^5*h^3*e)/c^6)*x + (1680*c^6*f*g^3 + 504*b*c^5*f*g^2*h + 5040*c^6*d*g*h^2 - 378*b^2*c^4*f*g*h^2 + 840*a*c^5*f*g*h^2 + 168*b*c^5*d*h^3 + 99*b^3*c^3*f*h^3 - 316*a*b*c^4*f*h^3 + 5040*c^6*g^2*h*e + 504*b*c^5*g*h^2*e - 126*b^2*c^4*h^3*e + 280*a*c^5*h^3*e)/c^6)*x + (560*b*c^5*f*g^3 + 13440*c^6*d*g^2*h - 1176*b^2*c^4*f*g^2*h + 2688*a*c^5*f*g^2*h + 1680*b*c^5*d*g*h^2 + 882*b^3*c^3*f*g*h^2 - 2856*a*b*c^4*f*g*h^2 - 392*b^2*c^4*d*h^3 + 896*a*c^5*d*h^3 - 231*b^4*c^2*f*h^3 + 972*a*b^2*c^3*f*h^3 - 512*a^2*c^4*f*h^3 + 4480*c^6*g^3*e + 1680*b*c^5*g^2*h*e - 1176*b^2*c^4*g*h^2*e + 2688*a*c^5*g*h^2*e + 294*b^3*c^3*h^3*e - 952*a*b*c^4*h^3*e)/c^6)*x + (26880*c^6*d*g^3 - 2800*b^2*c^4*f*g^3 + 6720*a*c^5*f*g^3 + 13440*b*c^5*d*g^2*h + 5880*b^3*c^3*f*g^2*h - 19488*a*b*c^4*f*g^2*h - 8400*b^2*c^4*d*g*h^2 + 20160*a*c^5*d*g*h^2 - 4410*b^4*c^2*f*g*h^2 + 18816*a*b^2*c^3*f*g*h^2 - 10080*a^2*c^4*f*g*h^2 + 1960*b^3*c^3*d*h^3 - 6496*a*b*c^4*d*h^3 + 1155*b^5*c*f*h^3 - 6048*a*b^3*c^2*f*h^3 + 6352*a^2*b*c^3*f*h^3 + 4480*b*c^5*g^3*e - 8400*b^2*c^4*g^2*h*e + 20160*a*c^5*g^2*h*e + 5880*b^3*c^3*g*h^2*e - 19488*a*b*c^4*g*h^2*e - 1470*b^4*c^2*h^3*e + 6272*a*b^2*c^3*h^3*e - 3360*a^2*c^4*h^3*e)/c^6)*x + (26880*b*c^5*d*g^3 + 8400*b^3*c^3*f*g^3 - 29120*a*b*c^4*f*g^3 - 40320*b^2*c^4*d*g^2*h + 107520*a*c^5*d*g^2*h - 17640*b^4*c^2*f*g^2*h + 77280*a*b^2*c^3*f*g^2*h - 43008*a^2*c^4*f*g^2*h + 25200*b^3*c^3*d*g*h^2 - 87360*a*b*c^4*d*g*h^2 + 13230*b^5*c*f*g*h^2 - 70560*a*b^3*c^2*f*g*h^2 + 75936*a^2*b*c^3*f*g*h^2 - 5880*b^4*c^2*d*h^3 + 25760*a*b^2*c^3*d*h^3 - 14336*a^2*c^4*d*h^3 - 3465*b^6*f*h^3 + 21840*a*b^4*c*f*h^3 - 34608*a^2*b^2*c^2*f*h^3 + 8192*a^3*c^3*f*h^3 - 13440*b^2*c^4*g^3*e + 35840*a*c^5*g^3*e + 25200*b^3*c^3*g^2*h*e - 87360*a*b*c^4*g^2*h*e - 17640*b^4*c^2*g*h^2*e + 77280*a*b^2*c^3*g*h^2*e - 43008*a^2*c^4*g*h^2*e + 4410*b^5*c*h^3*e - 23520*a*b^3*c^2*h^3*e + 25312*a^2*b*c^3*h^3*e)/c^6) + 1/2048*(256*b^2*c^5*d*g^3 - 1024*a*c^6*d*g^3 + 80*b^4*c^3*f*g^3 - 384*a*b^2*c^4*f*g^3 + 256*a^2*c^5*f*g^3 - 384*b^3*c^4*d*g^2*h + 1536*a*b*c^5*d*g^2*h - 168*b^5*c^2*f*g^2*h + 960*a*b^3*c^3*f*g^2*h - 1152*a^2*b*c^4*f*g^2*h + 240*b^4*c^3*d*g*h^2 - 1152*a*b^2*c^4*d*g*h^2 + 768*a^2*c^5*d*g*h^2 + 126*b^6*c*f*g*h^2 - 840*a*b^4*c^2*f*g*h^2 + 1440*a^2*b^2*c^3*f*g*h^2 - 384*a^3*c^4*f*g*h^2 - 56*b^5*c^2*d*h^3 + 320*a*b^3*c^3*d*h^3 - 384*a^2*b*c^4*d*h^3 - 33*b^7*f*h^3 + 252*a*b^5*c*f*h^3 - 560*a^2*b^3*c^2*f*h^3 + 320*a^3*b*c^3*f*h^3 - 128*b^3*c^4*g^3*e + 512*a*b*c^5*g^3*e + 240*b^4*c^3*g^2*h*e - 1152*a*b^2*c^4*g^2*h*e + 768*a^2*c^5*g^2*h*e - 168*b^5*c^2*g*h^2*e + 960*a*b^3*c^3*g*h^2*e - 1152*a^2*b*c^4*g*h^2*e + 42*b^6*c*h^3*e - 280*a*b^4*c^2*h^3*e + 480*a^2*b^2*c^3*h^3*e - 128*a^3*c^4*h^3*e)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(13/2)","A",0
187,1,1012,0,0.312473," ","integrate((h*x+g)^2*(f*x^2+e*x+d)*(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{1}{7680} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(10 \, f h^{2} x + \frac{24 \, c^{5} f g h + b c^{4} f h^{2} + 12 \, c^{5} h^{2} e}{c^{5}}\right)} x + \frac{120 \, c^{5} f g^{2} + 24 \, b c^{4} f g h + 120 \, c^{5} d h^{2} - 9 \, b^{2} c^{3} f h^{2} + 20 \, a c^{4} f h^{2} + 240 \, c^{5} g h e + 12 \, b c^{4} h^{2} e}{c^{5}}\right)} x + \frac{40 \, b c^{4} f g^{2} + 640 \, c^{5} d g h - 56 \, b^{2} c^{3} f g h + 128 \, a c^{4} f g h + 40 \, b c^{4} d h^{2} + 21 \, b^{3} c^{2} f h^{2} - 68 \, a b c^{3} f h^{2} + 320 \, c^{5} g^{2} e + 80 \, b c^{4} g h e - 28 \, b^{2} c^{3} h^{2} e + 64 \, a c^{4} h^{2} e}{c^{5}}\right)} x + \frac{1920 \, c^{5} d g^{2} - 200 \, b^{2} c^{3} f g^{2} + 480 \, a c^{4} f g^{2} + 640 \, b c^{4} d g h + 280 \, b^{3} c^{2} f g h - 928 \, a b c^{3} f g h - 200 \, b^{2} c^{3} d h^{2} + 480 \, a c^{4} d h^{2} - 105 \, b^{4} c f h^{2} + 448 \, a b^{2} c^{2} f h^{2} - 240 \, a^{2} c^{3} f h^{2} + 320 \, b c^{4} g^{2} e - 400 \, b^{2} c^{3} g h e + 960 \, a c^{4} g h e + 140 \, b^{3} c^{2} h^{2} e - 464 \, a b c^{3} h^{2} e}{c^{5}}\right)} x + \frac{1920 \, b c^{4} d g^{2} + 600 \, b^{3} c^{2} f g^{2} - 2080 \, a b c^{3} f g^{2} - 1920 \, b^{2} c^{3} d g h + 5120 \, a c^{4} d g h - 840 \, b^{4} c f g h + 3680 \, a b^{2} c^{2} f g h - 2048 \, a^{2} c^{3} f g h + 600 \, b^{3} c^{2} d h^{2} - 2080 \, a b c^{3} d h^{2} + 315 \, b^{5} f h^{2} - 1680 \, a b^{3} c f h^{2} + 1808 \, a^{2} b c^{2} f h^{2} - 960 \, b^{2} c^{3} g^{2} e + 2560 \, a c^{4} g^{2} e + 1200 \, b^{3} c^{2} g h e - 4160 \, a b c^{3} g h e - 420 \, b^{4} c h^{2} e + 1840 \, a b^{2} c^{2} h^{2} e - 1024 \, a^{2} c^{3} h^{2} e}{c^{5}}\right)} + \frac{{\left(128 \, b^{2} c^{4} d g^{2} - 512 \, a c^{5} d g^{2} + 40 \, b^{4} c^{2} f g^{2} - 192 \, a b^{2} c^{3} f g^{2} + 128 \, a^{2} c^{4} f g^{2} - 128 \, b^{3} c^{3} d g h + 512 \, a b c^{4} d g h - 56 \, b^{5} c f g h + 320 \, a b^{3} c^{2} f g h - 384 \, a^{2} b c^{3} f g h + 40 \, b^{4} c^{2} d h^{2} - 192 \, a b^{2} c^{3} d h^{2} + 128 \, a^{2} c^{4} d h^{2} + 21 \, b^{6} f h^{2} - 140 \, a b^{4} c f h^{2} + 240 \, a^{2} b^{2} c^{2} f h^{2} - 64 \, a^{3} c^{3} f h^{2} - 64 \, b^{3} c^{3} g^{2} e + 256 \, a b c^{4} g^{2} e + 80 \, b^{4} c^{2} g h e - 384 \, a b^{2} c^{3} g h e + 256 \, a^{2} c^{4} g h e - 28 \, b^{5} c h^{2} e + 160 \, a b^{3} c^{2} h^{2} e - 192 \, a^{2} b c^{3} h^{2} e\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{1024 \, c^{\frac{11}{2}}}"," ",0,"1/7680*sqrt(c*x^2 + b*x + a)*(2*(4*(2*(8*(10*f*h^2*x + (24*c^5*f*g*h + b*c^4*f*h^2 + 12*c^5*h^2*e)/c^5)*x + (120*c^5*f*g^2 + 24*b*c^4*f*g*h + 120*c^5*d*h^2 - 9*b^2*c^3*f*h^2 + 20*a*c^4*f*h^2 + 240*c^5*g*h*e + 12*b*c^4*h^2*e)/c^5)*x + (40*b*c^4*f*g^2 + 640*c^5*d*g*h - 56*b^2*c^3*f*g*h + 128*a*c^4*f*g*h + 40*b*c^4*d*h^2 + 21*b^3*c^2*f*h^2 - 68*a*b*c^3*f*h^2 + 320*c^5*g^2*e + 80*b*c^4*g*h*e - 28*b^2*c^3*h^2*e + 64*a*c^4*h^2*e)/c^5)*x + (1920*c^5*d*g^2 - 200*b^2*c^3*f*g^2 + 480*a*c^4*f*g^2 + 640*b*c^4*d*g*h + 280*b^3*c^2*f*g*h - 928*a*b*c^3*f*g*h - 200*b^2*c^3*d*h^2 + 480*a*c^4*d*h^2 - 105*b^4*c*f*h^2 + 448*a*b^2*c^2*f*h^2 - 240*a^2*c^3*f*h^2 + 320*b*c^4*g^2*e - 400*b^2*c^3*g*h*e + 960*a*c^4*g*h*e + 140*b^3*c^2*h^2*e - 464*a*b*c^3*h^2*e)/c^5)*x + (1920*b*c^4*d*g^2 + 600*b^3*c^2*f*g^2 - 2080*a*b*c^3*f*g^2 - 1920*b^2*c^3*d*g*h + 5120*a*c^4*d*g*h - 840*b^4*c*f*g*h + 3680*a*b^2*c^2*f*g*h - 2048*a^2*c^3*f*g*h + 600*b^3*c^2*d*h^2 - 2080*a*b*c^3*d*h^2 + 315*b^5*f*h^2 - 1680*a*b^3*c*f*h^2 + 1808*a^2*b*c^2*f*h^2 - 960*b^2*c^3*g^2*e + 2560*a*c^4*g^2*e + 1200*b^3*c^2*g*h*e - 4160*a*b*c^3*g*h*e - 420*b^4*c*h^2*e + 1840*a*b^2*c^2*h^2*e - 1024*a^2*c^3*h^2*e)/c^5) + 1/1024*(128*b^2*c^4*d*g^2 - 512*a*c^5*d*g^2 + 40*b^4*c^2*f*g^2 - 192*a*b^2*c^3*f*g^2 + 128*a^2*c^4*f*g^2 - 128*b^3*c^3*d*g*h + 512*a*b*c^4*d*g*h - 56*b^5*c*f*g*h + 320*a*b^3*c^2*f*g*h - 384*a^2*b*c^3*f*g*h + 40*b^4*c^2*d*h^2 - 192*a*b^2*c^3*d*h^2 + 128*a^2*c^4*d*h^2 + 21*b^6*f*h^2 - 140*a*b^4*c*f*h^2 + 240*a^2*b^2*c^2*f*h^2 - 64*a^3*c^3*f*h^2 - 64*b^3*c^3*g^2*e + 256*a*b*c^4*g^2*e + 80*b^4*c^2*g*h*e - 384*a*b^2*c^3*g*h*e + 256*a^2*c^4*g*h*e - 28*b^5*c*h^2*e + 160*a*b^3*c^2*h^2*e - 192*a^2*b*c^3*h^2*e)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(11/2)","A",0
188,1,495,0,0.237101," ","integrate((h*x+g)*(f*x^2+e*x+d)*(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{1}{1920} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(6 \, {\left(8 \, f h x + \frac{10 \, c^{4} f g + b c^{3} f h + 10 \, c^{4} h e}{c^{4}}\right)} x + \frac{10 \, b c^{3} f g + 80 \, c^{4} d h - 7 \, b^{2} c^{2} f h + 16 \, a c^{3} f h + 80 \, c^{4} g e + 10 \, b c^{3} h e}{c^{4}}\right)} x + \frac{480 \, c^{4} d g - 50 \, b^{2} c^{2} f g + 120 \, a c^{3} f g + 80 \, b c^{3} d h + 35 \, b^{3} c f h - 116 \, a b c^{2} f h + 80 \, b c^{3} g e - 50 \, b^{2} c^{2} h e + 120 \, a c^{3} h e}{c^{4}}\right)} x + \frac{480 \, b c^{3} d g + 150 \, b^{3} c f g - 520 \, a b c^{2} f g - 240 \, b^{2} c^{2} d h + 640 \, a c^{3} d h - 105 \, b^{4} f h + 460 \, a b^{2} c f h - 256 \, a^{2} c^{2} f h - 240 \, b^{2} c^{2} g e + 640 \, a c^{3} g e + 150 \, b^{3} c h e - 520 \, a b c^{2} h e}{c^{4}}\right)} + \frac{{\left(32 \, b^{2} c^{3} d g - 128 \, a c^{4} d g + 10 \, b^{4} c f g - 48 \, a b^{2} c^{2} f g + 32 \, a^{2} c^{3} f g - 16 \, b^{3} c^{2} d h + 64 \, a b c^{3} d h - 7 \, b^{5} f h + 40 \, a b^{3} c f h - 48 \, a^{2} b c^{2} f h - 16 \, b^{3} c^{2} g e + 64 \, a b c^{3} g e + 10 \, b^{4} c h e - 48 \, a b^{2} c^{2} h e + 32 \, a^{2} c^{3} h e\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{256 \, c^{\frac{9}{2}}}"," ",0,"1/1920*sqrt(c*x^2 + b*x + a)*(2*(4*(6*(8*f*h*x + (10*c^4*f*g + b*c^3*f*h + 10*c^4*h*e)/c^4)*x + (10*b*c^3*f*g + 80*c^4*d*h - 7*b^2*c^2*f*h + 16*a*c^3*f*h + 80*c^4*g*e + 10*b*c^3*h*e)/c^4)*x + (480*c^4*d*g - 50*b^2*c^2*f*g + 120*a*c^3*f*g + 80*b*c^3*d*h + 35*b^3*c*f*h - 116*a*b*c^2*f*h + 80*b*c^3*g*e - 50*b^2*c^2*h*e + 120*a*c^3*h*e)/c^4)*x + (480*b*c^3*d*g + 150*b^3*c*f*g - 520*a*b*c^2*f*g - 240*b^2*c^2*d*h + 640*a*c^3*d*h - 105*b^4*f*h + 460*a*b^2*c*f*h - 256*a^2*c^2*f*h - 240*b^2*c^2*g*e + 640*a*c^3*g*e + 150*b^3*c*h*e - 520*a*b*c^2*h*e)/c^4) + 1/256*(32*b^2*c^3*d*g - 128*a*c^4*d*g + 10*b^4*c*f*g - 48*a*b^2*c^2*f*g + 32*a^2*c^3*f*g - 16*b^3*c^2*d*h + 64*a*b*c^3*d*h - 7*b^5*f*h + 40*a*b^3*c*f*h - 48*a^2*b*c^2*f*h - 16*b^3*c^2*g*e + 64*a*b*c^3*g*e + 10*b^4*c*h*e - 48*a*b^2*c^2*h*e + 32*a^2*c^3*h*e)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(9/2)","A",0
189,1,212,0,0.235753," ","integrate((c*x^2+b*x+a)^(1/2)*(f*x^2+e*x+d),x, algorithm=""giac"")","\frac{1}{192} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(6 \, f x + \frac{b c^{2} f + 8 \, c^{3} e}{c^{3}}\right)} x + \frac{48 \, c^{3} d - 5 \, b^{2} c f + 12 \, a c^{2} f + 8 \, b c^{2} e}{c^{3}}\right)} x + \frac{48 \, b c^{2} d + 15 \, b^{3} f - 52 \, a b c f - 24 \, b^{2} c e + 64 \, a c^{2} e}{c^{3}}\right)} + \frac{{\left(16 \, b^{2} c^{2} d - 64 \, a c^{3} d + 5 \, b^{4} f - 24 \, a b^{2} c f + 16 \, a^{2} c^{2} f - 8 \, b^{3} c e + 32 \, a b c^{2} e\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{128 \, c^{\frac{7}{2}}}"," ",0,"1/192*sqrt(c*x^2 + b*x + a)*(2*(4*(6*f*x + (b*c^2*f + 8*c^3*e)/c^3)*x + (48*c^3*d - 5*b^2*c*f + 12*a*c^2*f + 8*b*c^2*e)/c^3)*x + (48*b*c^2*d + 15*b^3*f - 52*a*b*c*f - 24*b^2*c*e + 64*a*c^2*e)/c^3) + 1/128*(16*b^2*c^2*d - 64*a*c^3*d + 5*b^4*f - 24*a*b^2*c*f + 16*a^2*c^2*f - 8*b^3*c*e + 32*a*b*c^2*e)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(7/2)","A",0
190,-2,0,0,0.000000," ","integrate((f*x^2+e*x+d)*(c*x^2+b*x+a)^(1/2)/(h*x+g),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
191,-1,0,0,0.000000," ","integrate((f*x^2+e*x+d)*(c*x^2+b*x+a)^(1/2)/(h*x+g)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
192,-2,0,0,0.000000," ","integrate((f*x^2+e*x+d)*(c*x^2+b*x+a)^(1/2)/(h*x+g)^3,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 0.81Unable to divide, perhaps due to rounding error%%%{1,[6,0,0,7,0,0,0,0]%%%}+%%%{%%{[-6,0]:[1,0,%%%{-1,[1]%%%}]%%},[5,0,0,6,1,0,0,0]%%%}+%%%{3,[4,1,0,6,1,0,0,0]%%%}+%%%{-3,[4,0,0,7,0,0,1,0]%%%}+%%%{%%%{12,[1]%%%},[4,0,0,5,2,0,0,0]%%%}+%%%{%%{[-12,0]:[1,0,%%%{-1,[1]%%%}]%%},[3,1,0,5,2,0,0,0]%%%}+%%%{%%{[12,0]:[1,0,%%%{-1,[1]%%%}]%%},[3,0,0,6,1,0,1,0]%%%}+%%%{%%{[%%%{-8,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,0,0,4,3,0,0,0]%%%}+%%%{3,[2,2,0,5,2,0,0,0]%%%}+%%%{-6,[2,1,0,6,1,0,1,0]%%%}+%%%{%%%{12,[1]%%%},[2,1,0,4,3,0,0,0]%%%}+%%%{3,[2,0,0,7,0,0,2,0]%%%}+%%%{%%%{-12,[1]%%%},[2,0,0,5,2,0,1,0]%%%}+%%%{%%{[-6,0]:[1,0,%%%{-1,[1]%%%}]%%},[1,2,0,4,3,0,0,0]%%%}+%%%{%%{[12,0]:[1,0,%%%{-1,[1]%%%}]%%},[1,1,0,5,2,0,1,0]%%%}+%%%{%%{[-6,0]:[1,0,%%%{-1,[1]%%%}]%%},[1,0,0,6,1,0,2,0]%%%}+%%%{1,[0,3,0,4,3,0,0,0]%%%}+%%%{-3,[0,2,0,5,2,0,1,0]%%%}+%%%{3,[0,1,0,6,1,0,2,0]%%%}+%%%{-1,[0,0,0,7,0,0,3,0]%%%} / %%%{%%{poly1[%%%{1,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,0,3,0,0,0,0]%%%}+%%%{%%%{-6,[2]%%%},[5,0,0,2,1,0,0,0]%%%}+%%%{%%{[%%%{3,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,1,0,2,1,0,0,0]%%%}+%%%{%%{poly1[%%%{-3,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,0,3,0,0,1,0]%%%}+%%%{%%{poly1[%%%{12,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,0,1,2,0,0,0]%%%}+%%%{%%%{-12,[2]%%%},[3,1,0,1,2,0,0,0]%%%}+%%%{%%%{12,[2]%%%},[3,0,0,2,1,0,1,0]%%%}+%%%{%%%{-8,[3]%%%},[3,0,0,0,3,0,0,0]%%%}+%%%{%%{[%%%{3,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,2,0,1,2,0,0,0]%%%}+%%%{%%{[%%%{-6,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,1,0,2,1,0,1,0]%%%}+%%%{%%{[%%%{12,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,1,0,0,3,0,0,0]%%%}+%%%{%%{poly1[%%%{3,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,0,3,0,0,2,0]%%%}+%%%{%%{poly1[%%%{-12,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,0,1,2,0,1,0]%%%}+%%%{%%%{-6,[2]%%%},[1,2,0,0,3,0,0,0]%%%}+%%%{%%%{12,[2]%%%},[1,1,0,1,2,0,1,0]%%%}+%%%{%%%{-6,[2]%%%},[1,0,0,2,1,0,2,0]%%%}+%%%{%%{[%%%{1,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,3,0,0,3,0,0,0]%%%}+%%%{%%{[%%%{-3,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,2,0,1,2,0,1,0]%%%}+%%%{%%{[%%%{3,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,1,0,2,1,0,2,0]%%%}+%%%{%%{poly1[%%%{-1,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,0,3,0,0,3,0]%%%} Error: Bad Argument Value","F(-2)",0
193,-2,0,0,0.000000," ","integrate((f*x^2+e*x+d)*(c*x^2+b*x+a)^(1/2)/(h*x+g)^4,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 42.01Unable to divide, perhaps due to rounding error%%%{%%{[-1,0]:[1,0,%%%{-1,[1]%%%}]%%},[8,0,0,0,0,0,8,0]%%%}+%%%{%%%{8,[1]%%%},[7,0,0,0,0,0,7,1]%%%}+%%%{%%{[-4,0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,1,0,0,0,7,1]%%%}+%%%{%%{[4,0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,0,0,1,0,8,0]%%%}+%%%{%%{[%%%{-24,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,0,0,0,0,6,2]%%%}+%%%{%%%{24,[1]%%%},[5,0,1,0,0,0,6,2]%%%}+%%%{%%%{-24,[1]%%%},[5,0,0,0,1,0,7,1]%%%}+%%%{%%%{32,[2]%%%},[5,0,0,0,0,0,5,3]%%%}+%%%{%%{[-6,0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,2,0,0,0,6,2]%%%}+%%%{%%{[12,0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,1,0,1,0,7,1]%%%}+%%%{%%{[%%%{-48,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,1,0,0,0,5,3]%%%}+%%%{%%{[-6,0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,0,0,2,0,8,0]%%%}+%%%{%%{[%%%{48,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,0,0,1,0,6,2]%%%}+%%%{%%{[%%%{-16,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,0,0,0,0,4,4]%%%}+%%%{%%%{24,[1]%%%},[3,0,2,0,0,0,5,3]%%%}+%%%{%%%{-48,[1]%%%},[3,0,1,0,1,0,6,2]%%%}+%%%{%%%{32,[2]%%%},[3,0,1,0,0,0,4,4]%%%}+%%%{%%%{24,[1]%%%},[3,0,0,0,2,0,7,1]%%%}+%%%{%%%{-32,[2]%%%},[3,0,0,0,1,0,5,3]%%%}+%%%{%%{[-4,0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,3,0,0,0,5,3]%%%}+%%%{%%{[12,0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,2,0,1,0,6,2]%%%}+%%%{%%{[%%%{-24,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,2,0,0,0,4,4]%%%}+%%%{%%{[-12,0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,1,0,2,0,7,1]%%%}+%%%{%%{[%%%{48,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,1,0,1,0,5,3]%%%}+%%%{%%{[4,0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,0,0,3,0,8,0]%%%}+%%%{%%{[%%%{-24,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,0,0,2,0,6,2]%%%}+%%%{%%%{8,[1]%%%},[1,0,3,0,0,0,4,4]%%%}+%%%{%%%{-24,[1]%%%},[1,0,2,0,1,0,5,3]%%%}+%%%{%%%{24,[1]%%%},[1,0,1,0,2,0,6,2]%%%}+%%%{%%%{-8,[1]%%%},[1,0,0,0,3,0,7,1]%%%}+%%%{%%{[-1,0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,4,0,0,0,4,4]%%%}+%%%{%%{[4,0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,3,0,1,0,5,3]%%%}+%%%{%%{[-6,0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,2,0,2,0,6,2]%%%}+%%%{%%{[4,0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,1,0,3,0,7,1]%%%}+%%%{%%{[-1,0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,0,0,4,0,8,0]%%%} / %%%{%%%{1,[2]%%%},[8,0,0,0,0,0,4,0]%%%}+%%%{%%{poly1[%%%{-8,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,0,0,0,0,0,3,1]%%%}+%%%{%%%{4,[2]%%%},[6,0,1,0,0,0,3,1]%%%}+%%%{%%%{-4,[2]%%%},[6,0,0,0,1,0,4,0]%%%}+%%%{%%%{24,[3]%%%},[6,0,0,0,0,0,2,2]%%%}+%%%{%%{[%%%{-24,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,0,1,0,0,0,2,2]%%%}+%%%{%%{poly1[%%%{24,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,0,0,0,1,0,3,1]%%%}+%%%{%%{poly1[%%%{-32,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,0,0,0,0,0,1,3]%%%}+%%%{%%%{6,[2]%%%},[4,0,2,0,0,0,2,2]%%%}+%%%{%%%{-12,[2]%%%},[4,0,1,0,1,0,3,1]%%%}+%%%{%%%{48,[3]%%%},[4,0,1,0,0,0,1,3]%%%}+%%%{%%%{6,[2]%%%},[4,0,0,0,2,0,4,0]%%%}+%%%{%%%{-48,[3]%%%},[4,0,0,0,1,0,2,2]%%%}+%%%{%%%{16,[4]%%%},[4,0,0,0,0,0,0,4]%%%}+%%%{%%{poly1[%%%{-24,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,0,2,0,0,0,1,3]%%%}+%%%{%%{[%%%{48,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,0,1,0,1,0,2,2]%%%}+%%%{%%{[%%%{-32,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,0,1,0,0,0,0,4]%%%}+%%%{%%{poly1[%%%{-24,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,0,0,0,2,0,3,1]%%%}+%%%{%%{poly1[%%%{32,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,0,0,0,1,0,1,3]%%%}+%%%{%%%{4,[2]%%%},[2,0,3,0,0,0,1,3]%%%}+%%%{%%%{-12,[2]%%%},[2,0,2,0,1,0,2,2]%%%}+%%%{%%%{24,[3]%%%},[2,0,2,0,0,0,0,4]%%%}+%%%{%%%{12,[2]%%%},[2,0,1,0,2,0,3,1]%%%}+%%%{%%%{-48,[3]%%%},[2,0,1,0,1,0,1,3]%%%}+%%%{%%%{-4,[2]%%%},[2,0,0,0,3,0,4,0]%%%}+%%%{%%%{24,[3]%%%},[2,0,0,0,2,0,2,2]%%%}+%%%{%%{[%%%{-8,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,0,3,0,0,0,0,4]%%%}+%%%{%%{poly1[%%%{24,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,0,2,0,1,0,1,3]%%%}+%%%{%%{[%%%{-24,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,0,1,0,2,0,2,2]%%%}+%%%{%%{poly1[%%%{8,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,0,0,0,3,0,3,1]%%%}+%%%{%%%{1,[2]%%%},[0,0,4,0,0,0,0,4]%%%}+%%%{%%%{-4,[2]%%%},[0,0,3,0,1,0,1,3]%%%}+%%%{%%%{6,[2]%%%},[0,0,2,0,2,0,2,2]%%%}+%%%{%%%{-4,[2]%%%},[0,0,1,0,3,0,3,1]%%%}+%%%{%%%{1,[2]%%%},[0,0,0,0,4,0,4,0]%%%} Error: Bad Argument Value","F(-2)",0
194,-1,0,0,0.000000," ","integrate((f*x^2+e*x+d)*(c*x^2+b*x+a)^(1/2)/(h*x+g)^5,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
195,-1,0,0,0.000000," ","integrate((f*x^2+e*x+d)*(c*x^2+b*x+a)^(1/2)/(h*x+g)^6,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
196,1,2977,0,0.438455," ","integrate((h*x+g)^3*(c*x^2+b*x+a)^(3/2)*(f*x^2+e*x+d),x, algorithm=""giac"")","\frac{1}{10321920} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(10 \, {\left(4 \, {\left(14 \, {\left(16 \, c f h^{3} x + \frac{54 \, c^{9} f g h^{2} + 19 \, b c^{8} f h^{3} + 18 \, c^{9} h^{3} e}{c^{8}}\right)} x + \frac{864 \, c^{9} f g^{2} h + 918 \, b c^{8} f g h^{2} + 288 \, c^{9} d h^{3} + 3 \, b^{2} c^{7} f h^{3} + 320 \, a c^{8} f h^{3} + 864 \, c^{9} g h^{2} e + 306 \, b c^{8} h^{3} e}{c^{8}}\right)} x + \frac{1344 \, c^{9} f g^{3} + 4320 \, b c^{8} f g^{2} h + 4032 \, c^{9} d g h^{2} + 54 \, b^{2} c^{7} f g h^{2} + 4536 \, a c^{8} f g h^{2} + 1440 \, b c^{8} d h^{3} - 13 \, b^{3} c^{6} f h^{3} + 60 \, a b c^{7} f h^{3} + 4032 \, c^{9} g^{2} h e + 4320 \, b c^{8} g h^{2} e + 18 \, b^{2} c^{7} h^{3} e + 1512 \, a c^{8} h^{3} e}{c^{8}}\right)} x + \frac{17472 \, b c^{8} f g^{3} + 48384 \, c^{9} d g^{2} h + 864 \, b^{2} c^{7} f g^{2} h + 55296 \, a c^{8} f g^{2} h + 52416 \, b c^{8} d g h^{2} - 594 \, b^{3} c^{6} f g h^{2} + 2808 \, a b c^{7} f g h^{2} + 288 \, b^{2} c^{7} d h^{3} + 18432 \, a c^{8} d h^{3} + 143 \, b^{4} c^{5} f h^{3} - 804 \, a b^{2} c^{6} f h^{3} + 768 \, a^{2} c^{7} f h^{3} + 16128 \, c^{9} g^{3} e + 52416 \, b c^{8} g^{2} h e + 864 \, b^{2} c^{7} g h^{2} e + 55296 \, a c^{8} g h^{2} e - 198 \, b^{3} c^{6} h^{3} e + 936 \, a b c^{7} h^{3} e}{c^{8}}\right)} x + \frac{161280 \, c^{9} d g^{3} + 4032 \, b^{2} c^{7} f g^{3} + 188160 \, a c^{8} f g^{3} + 532224 \, b c^{8} d g^{2} h - 7776 \, b^{3} c^{6} f g^{2} h + 38016 \, a b c^{7} f g^{2} h + 12096 \, b^{2} c^{7} d g h^{2} + 564480 \, a c^{8} d g h^{2} + 5346 \, b^{4} c^{5} f g h^{2} - 30672 \, a b^{2} c^{6} f g h^{2} + 30240 \, a^{2} c^{7} f g h^{2} - 2592 \, b^{3} c^{6} d h^{3} + 12672 \, a b c^{7} d h^{3} - 1287 \, b^{5} c^{4} f h^{3} + 8536 \, a b^{3} c^{5} f h^{3} - 12912 \, a^{2} b c^{6} f h^{3} + 177408 \, b c^{8} g^{3} e + 12096 \, b^{2} c^{7} g^{2} h e + 564480 \, a c^{8} g^{2} h e - 7776 \, b^{3} c^{6} g h^{2} e + 38016 \, a b c^{7} g h^{2} e + 1782 \, b^{4} c^{5} h^{3} e - 10224 \, a b^{2} c^{6} h^{3} e + 10080 \, a^{2} c^{7} h^{3} e}{c^{8}}\right)} x + \frac{483840 \, b c^{8} d g^{3} - 9408 \, b^{3} c^{6} f g^{3} + 48384 \, a b c^{7} f g^{3} + 48384 \, b^{2} c^{7} d g^{2} h + 1548288 \, a c^{8} d g^{2} h + 18144 \, b^{4} c^{5} f g^{2} h - 107136 \, a b^{2} c^{6} f g^{2} h + 110592 \, a^{2} c^{7} f g^{2} h - 28224 \, b^{3} c^{6} d g h^{2} + 145152 \, a b c^{7} d g h^{2} - 12474 \, b^{5} c^{4} f g h^{2} + 84240 \, a b^{3} c^{5} f g h^{2} - 130464 \, a^{2} b c^{6} f g h^{2} + 6048 \, b^{4} c^{5} d h^{3} - 35712 \, a b^{2} c^{6} d h^{3} + 36864 \, a^{2} c^{7} d h^{3} + 3003 \, b^{6} c^{3} f h^{3} - 22968 \, a b^{4} c^{4} f h^{3} + 47280 \, a^{2} b^{2} c^{5} f h^{3} - 16384 \, a^{3} c^{6} f h^{3} + 16128 \, b^{2} c^{7} g^{3} e + 516096 \, a c^{8} g^{3} e - 28224 \, b^{3} c^{6} g^{2} h e + 145152 \, a b c^{7} g^{2} h e + 18144 \, b^{4} c^{5} g h^{2} e - 107136 \, a b^{2} c^{6} g h^{2} e + 110592 \, a^{2} c^{7} g h^{2} e - 4158 \, b^{5} c^{4} h^{3} e + 28080 \, a b^{3} c^{5} h^{3} e - 43488 \, a^{2} b c^{6} h^{3} e}{c^{8}}\right)} x + \frac{161280 \, b^{2} c^{7} d g^{3} + 3225600 \, a c^{8} d g^{3} + 47040 \, b^{4} c^{5} f g^{3} - 290304 \, a b^{2} c^{6} f g^{3} + 322560 \, a^{2} c^{7} f g^{3} - 241920 \, b^{3} c^{6} d g^{2} h + 1354752 \, a b c^{7} d g^{2} h - 90720 \, b^{5} c^{4} f g^{2} h + 628992 \, a b^{3} c^{5} f g^{2} h - 1009152 \, a^{2} b c^{6} f g^{2} h + 141120 \, b^{4} c^{5} d g h^{2} - 870912 \, a b^{2} c^{6} d g h^{2} + 967680 \, a^{2} c^{7} d g h^{2} + 62370 \, b^{6} c^{3} f g h^{2} - 485352 \, a b^{4} c^{4} f g h^{2} + 1020384 \, a^{2} b^{2} c^{5} f g h^{2} - 362880 \, a^{3} c^{6} f g h^{2} - 30240 \, b^{5} c^{4} d h^{3} + 209664 \, a b^{3} c^{5} d h^{3} - 336384 \, a^{2} b c^{6} d h^{3} - 15015 \, b^{7} c^{2} f h^{3} + 130284 \, a b^{5} c^{3} f h^{3} - 338832 \, a^{2} b^{3} c^{4} f h^{3} + 236864 \, a^{3} b c^{5} f h^{3} - 80640 \, b^{3} c^{6} g^{3} e + 451584 \, a b c^{7} g^{3} e + 141120 \, b^{4} c^{5} g^{2} h e - 870912 \, a b^{2} c^{6} g^{2} h e + 967680 \, a^{2} c^{7} g^{2} h e - 90720 \, b^{5} c^{4} g h^{2} e + 628992 \, a b^{3} c^{5} g h^{2} e - 1009152 \, a^{2} b c^{6} g h^{2} e + 20790 \, b^{6} c^{3} h^{3} e - 161784 \, a b^{4} c^{4} h^{3} e + 340128 \, a^{2} b^{2} c^{5} h^{3} e - 120960 \, a^{3} c^{6} h^{3} e}{c^{8}}\right)} x - \frac{483840 \, b^{3} c^{6} d g^{3} - 3225600 \, a b c^{7} d g^{3} + 141120 \, b^{5} c^{4} f g^{3} - 1021440 \, a b^{3} c^{5} f g^{3} + 1741824 \, a^{2} b c^{6} f g^{3} - 725760 \, b^{4} c^{5} d g^{2} h + 4838400 \, a b^{2} c^{6} d g^{2} h - 6193152 \, a^{2} c^{7} d g^{2} h - 272160 \, b^{6} c^{3} f g^{2} h + 2177280 \, a b^{4} c^{4} f g^{2} h - 4741632 \, a^{2} b^{2} c^{5} f g^{2} h + 1769472 \, a^{3} c^{6} f g^{2} h + 423360 \, b^{5} c^{4} d g h^{2} - 3064320 \, a b^{3} c^{5} d g h^{2} + 5225472 \, a^{2} b c^{6} d g h^{2} + 187110 \, b^{7} c^{2} f g h^{2} - 1655640 \, a b^{5} c^{3} f g h^{2} + 4408992 \, a^{2} b^{3} c^{4} f g h^{2} - 3176064 \, a^{3} b c^{5} f g h^{2} - 90720 \, b^{6} c^{3} d h^{3} + 725760 \, a b^{4} c^{4} d h^{3} - 1580544 \, a^{2} b^{2} c^{5} d h^{3} + 589824 \, a^{3} c^{6} d h^{3} - 45045 \, b^{8} c f h^{3} + 438900 \, a b^{6} c^{2} f h^{3} - 1383984 \, a^{2} b^{4} c^{3} f h^{3} + 1467072 \, a^{3} b^{2} c^{4} f h^{3} - 262144 \, a^{4} c^{5} f h^{3} - 241920 \, b^{4} c^{5} g^{3} e + 1612800 \, a b^{2} c^{6} g^{3} e - 2064384 \, a^{2} c^{7} g^{3} e + 423360 \, b^{5} c^{4} g^{2} h e - 3064320 \, a b^{3} c^{5} g^{2} h e + 5225472 \, a^{2} b c^{6} g^{2} h e - 272160 \, b^{6} c^{3} g h^{2} e + 2177280 \, a b^{4} c^{4} g h^{2} e - 4741632 \, a^{2} b^{2} c^{5} g h^{2} e + 1769472 \, a^{3} c^{6} g h^{2} e + 62370 \, b^{7} c^{2} h^{3} e - 551880 \, a b^{5} c^{3} h^{3} e + 1469664 \, a^{2} b^{3} c^{4} h^{3} e - 1058688 \, a^{3} b c^{5} h^{3} e}{c^{8}}\right)} - \frac{{\left(1536 \, b^{4} c^{5} d g^{3} - 12288 \, a b^{2} c^{6} d g^{3} + 24576 \, a^{2} c^{7} d g^{3} + 448 \, b^{6} c^{3} f g^{3} - 3840 \, a b^{4} c^{4} f g^{3} + 9216 \, a^{2} b^{2} c^{5} f g^{3} - 4096 \, a^{3} c^{6} f g^{3} - 2304 \, b^{5} c^{4} d g^{2} h + 18432 \, a b^{3} c^{5} d g^{2} h - 36864 \, a^{2} b c^{6} d g^{2} h - 864 \, b^{7} c^{2} f g^{2} h + 8064 \, a b^{5} c^{3} f g^{2} h - 23040 \, a^{2} b^{3} c^{4} f g^{2} h + 18432 \, a^{3} b c^{5} f g^{2} h + 1344 \, b^{6} c^{3} d g h^{2} - 11520 \, a b^{4} c^{4} d g h^{2} + 27648 \, a^{2} b^{2} c^{5} d g h^{2} - 12288 \, a^{3} c^{6} d g h^{2} + 594 \, b^{8} c f g h^{2} - 6048 \, a b^{6} c^{2} f g h^{2} + 20160 \, a^{2} b^{4} c^{3} f g h^{2} - 23040 \, a^{3} b^{2} c^{4} f g h^{2} + 4608 \, a^{4} c^{5} f g h^{2} - 288 \, b^{7} c^{2} d h^{3} + 2688 \, a b^{5} c^{3} d h^{3} - 7680 \, a^{2} b^{3} c^{4} d h^{3} + 6144 \, a^{3} b c^{5} d h^{3} - 143 \, b^{9} f h^{3} + 1584 \, a b^{7} c f h^{3} - 6048 \, a^{2} b^{5} c^{2} f h^{3} + 8960 \, a^{3} b^{3} c^{3} f h^{3} - 3840 \, a^{4} b c^{4} f h^{3} - 768 \, b^{5} c^{4} g^{3} e + 6144 \, a b^{3} c^{5} g^{3} e - 12288 \, a^{2} b c^{6} g^{3} e + 1344 \, b^{6} c^{3} g^{2} h e - 11520 \, a b^{4} c^{4} g^{2} h e + 27648 \, a^{2} b^{2} c^{5} g^{2} h e - 12288 \, a^{3} c^{6} g^{2} h e - 864 \, b^{7} c^{2} g h^{2} e + 8064 \, a b^{5} c^{3} g h^{2} e - 23040 \, a^{2} b^{3} c^{4} g h^{2} e + 18432 \, a^{3} b c^{5} g h^{2} e + 198 \, b^{8} c h^{3} e - 2016 \, a b^{6} c^{2} h^{3} e + 6720 \, a^{2} b^{4} c^{3} h^{3} e - 7680 \, a^{3} b^{2} c^{4} h^{3} e + 1536 \, a^{4} c^{5} h^{3} e\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{65536 \, c^{\frac{15}{2}}}"," ",0,"1/10321920*sqrt(c*x^2 + b*x + a)*(2*(4*(2*(8*(10*(4*(14*(16*c*f*h^3*x + (54*c^9*f*g*h^2 + 19*b*c^8*f*h^3 + 18*c^9*h^3*e)/c^8)*x + (864*c^9*f*g^2*h + 918*b*c^8*f*g*h^2 + 288*c^9*d*h^3 + 3*b^2*c^7*f*h^3 + 320*a*c^8*f*h^3 + 864*c^9*g*h^2*e + 306*b*c^8*h^3*e)/c^8)*x + (1344*c^9*f*g^3 + 4320*b*c^8*f*g^2*h + 4032*c^9*d*g*h^2 + 54*b^2*c^7*f*g*h^2 + 4536*a*c^8*f*g*h^2 + 1440*b*c^8*d*h^3 - 13*b^3*c^6*f*h^3 + 60*a*b*c^7*f*h^3 + 4032*c^9*g^2*h*e + 4320*b*c^8*g*h^2*e + 18*b^2*c^7*h^3*e + 1512*a*c^8*h^3*e)/c^8)*x + (17472*b*c^8*f*g^3 + 48384*c^9*d*g^2*h + 864*b^2*c^7*f*g^2*h + 55296*a*c^8*f*g^2*h + 52416*b*c^8*d*g*h^2 - 594*b^3*c^6*f*g*h^2 + 2808*a*b*c^7*f*g*h^2 + 288*b^2*c^7*d*h^3 + 18432*a*c^8*d*h^3 + 143*b^4*c^5*f*h^3 - 804*a*b^2*c^6*f*h^3 + 768*a^2*c^7*f*h^3 + 16128*c^9*g^3*e + 52416*b*c^8*g^2*h*e + 864*b^2*c^7*g*h^2*e + 55296*a*c^8*g*h^2*e - 198*b^3*c^6*h^3*e + 936*a*b*c^7*h^3*e)/c^8)*x + (161280*c^9*d*g^3 + 4032*b^2*c^7*f*g^3 + 188160*a*c^8*f*g^3 + 532224*b*c^8*d*g^2*h - 7776*b^3*c^6*f*g^2*h + 38016*a*b*c^7*f*g^2*h + 12096*b^2*c^7*d*g*h^2 + 564480*a*c^8*d*g*h^2 + 5346*b^4*c^5*f*g*h^2 - 30672*a*b^2*c^6*f*g*h^2 + 30240*a^2*c^7*f*g*h^2 - 2592*b^3*c^6*d*h^3 + 12672*a*b*c^7*d*h^3 - 1287*b^5*c^4*f*h^3 + 8536*a*b^3*c^5*f*h^3 - 12912*a^2*b*c^6*f*h^3 + 177408*b*c^8*g^3*e + 12096*b^2*c^7*g^2*h*e + 564480*a*c^8*g^2*h*e - 7776*b^3*c^6*g*h^2*e + 38016*a*b*c^7*g*h^2*e + 1782*b^4*c^5*h^3*e - 10224*a*b^2*c^6*h^3*e + 10080*a^2*c^7*h^3*e)/c^8)*x + (483840*b*c^8*d*g^3 - 9408*b^3*c^6*f*g^3 + 48384*a*b*c^7*f*g^3 + 48384*b^2*c^7*d*g^2*h + 1548288*a*c^8*d*g^2*h + 18144*b^4*c^5*f*g^2*h - 107136*a*b^2*c^6*f*g^2*h + 110592*a^2*c^7*f*g^2*h - 28224*b^3*c^6*d*g*h^2 + 145152*a*b*c^7*d*g*h^2 - 12474*b^5*c^4*f*g*h^2 + 84240*a*b^3*c^5*f*g*h^2 - 130464*a^2*b*c^6*f*g*h^2 + 6048*b^4*c^5*d*h^3 - 35712*a*b^2*c^6*d*h^3 + 36864*a^2*c^7*d*h^3 + 3003*b^6*c^3*f*h^3 - 22968*a*b^4*c^4*f*h^3 + 47280*a^2*b^2*c^5*f*h^3 - 16384*a^3*c^6*f*h^3 + 16128*b^2*c^7*g^3*e + 516096*a*c^8*g^3*e - 28224*b^3*c^6*g^2*h*e + 145152*a*b*c^7*g^2*h*e + 18144*b^4*c^5*g*h^2*e - 107136*a*b^2*c^6*g*h^2*e + 110592*a^2*c^7*g*h^2*e - 4158*b^5*c^4*h^3*e + 28080*a*b^3*c^5*h^3*e - 43488*a^2*b*c^6*h^3*e)/c^8)*x + (161280*b^2*c^7*d*g^3 + 3225600*a*c^8*d*g^3 + 47040*b^4*c^5*f*g^3 - 290304*a*b^2*c^6*f*g^3 + 322560*a^2*c^7*f*g^3 - 241920*b^3*c^6*d*g^2*h + 1354752*a*b*c^7*d*g^2*h - 90720*b^5*c^4*f*g^2*h + 628992*a*b^3*c^5*f*g^2*h - 1009152*a^2*b*c^6*f*g^2*h + 141120*b^4*c^5*d*g*h^2 - 870912*a*b^2*c^6*d*g*h^2 + 967680*a^2*c^7*d*g*h^2 + 62370*b^6*c^3*f*g*h^2 - 485352*a*b^4*c^4*f*g*h^2 + 1020384*a^2*b^2*c^5*f*g*h^2 - 362880*a^3*c^6*f*g*h^2 - 30240*b^5*c^4*d*h^3 + 209664*a*b^3*c^5*d*h^3 - 336384*a^2*b*c^6*d*h^3 - 15015*b^7*c^2*f*h^3 + 130284*a*b^5*c^3*f*h^3 - 338832*a^2*b^3*c^4*f*h^3 + 236864*a^3*b*c^5*f*h^3 - 80640*b^3*c^6*g^3*e + 451584*a*b*c^7*g^3*e + 141120*b^4*c^5*g^2*h*e - 870912*a*b^2*c^6*g^2*h*e + 967680*a^2*c^7*g^2*h*e - 90720*b^5*c^4*g*h^2*e + 628992*a*b^3*c^5*g*h^2*e - 1009152*a^2*b*c^6*g*h^2*e + 20790*b^6*c^3*h^3*e - 161784*a*b^4*c^4*h^3*e + 340128*a^2*b^2*c^5*h^3*e - 120960*a^3*c^6*h^3*e)/c^8)*x - (483840*b^3*c^6*d*g^3 - 3225600*a*b*c^7*d*g^3 + 141120*b^5*c^4*f*g^3 - 1021440*a*b^3*c^5*f*g^3 + 1741824*a^2*b*c^6*f*g^3 - 725760*b^4*c^5*d*g^2*h + 4838400*a*b^2*c^6*d*g^2*h - 6193152*a^2*c^7*d*g^2*h - 272160*b^6*c^3*f*g^2*h + 2177280*a*b^4*c^4*f*g^2*h - 4741632*a^2*b^2*c^5*f*g^2*h + 1769472*a^3*c^6*f*g^2*h + 423360*b^5*c^4*d*g*h^2 - 3064320*a*b^3*c^5*d*g*h^2 + 5225472*a^2*b*c^6*d*g*h^2 + 187110*b^7*c^2*f*g*h^2 - 1655640*a*b^5*c^3*f*g*h^2 + 4408992*a^2*b^3*c^4*f*g*h^2 - 3176064*a^3*b*c^5*f*g*h^2 - 90720*b^6*c^3*d*h^3 + 725760*a*b^4*c^4*d*h^3 - 1580544*a^2*b^2*c^5*d*h^3 + 589824*a^3*c^6*d*h^3 - 45045*b^8*c*f*h^3 + 438900*a*b^6*c^2*f*h^3 - 1383984*a^2*b^4*c^3*f*h^3 + 1467072*a^3*b^2*c^4*f*h^3 - 262144*a^4*c^5*f*h^3 - 241920*b^4*c^5*g^3*e + 1612800*a*b^2*c^6*g^3*e - 2064384*a^2*c^7*g^3*e + 423360*b^5*c^4*g^2*h*e - 3064320*a*b^3*c^5*g^2*h*e + 5225472*a^2*b*c^6*g^2*h*e - 272160*b^6*c^3*g*h^2*e + 2177280*a*b^4*c^4*g*h^2*e - 4741632*a^2*b^2*c^5*g*h^2*e + 1769472*a^3*c^6*g*h^2*e + 62370*b^7*c^2*h^3*e - 551880*a*b^5*c^3*h^3*e + 1469664*a^2*b^3*c^4*h^3*e - 1058688*a^3*b*c^5*h^3*e)/c^8) - 1/65536*(1536*b^4*c^5*d*g^3 - 12288*a*b^2*c^6*d*g^3 + 24576*a^2*c^7*d*g^3 + 448*b^6*c^3*f*g^3 - 3840*a*b^4*c^4*f*g^3 + 9216*a^2*b^2*c^5*f*g^3 - 4096*a^3*c^6*f*g^3 - 2304*b^5*c^4*d*g^2*h + 18432*a*b^3*c^5*d*g^2*h - 36864*a^2*b*c^6*d*g^2*h - 864*b^7*c^2*f*g^2*h + 8064*a*b^5*c^3*f*g^2*h - 23040*a^2*b^3*c^4*f*g^2*h + 18432*a^3*b*c^5*f*g^2*h + 1344*b^6*c^3*d*g*h^2 - 11520*a*b^4*c^4*d*g*h^2 + 27648*a^2*b^2*c^5*d*g*h^2 - 12288*a^3*c^6*d*g*h^2 + 594*b^8*c*f*g*h^2 - 6048*a*b^6*c^2*f*g*h^2 + 20160*a^2*b^4*c^3*f*g*h^2 - 23040*a^3*b^2*c^4*f*g*h^2 + 4608*a^4*c^5*f*g*h^2 - 288*b^7*c^2*d*h^3 + 2688*a*b^5*c^3*d*h^3 - 7680*a^2*b^3*c^4*d*h^3 + 6144*a^3*b*c^5*d*h^3 - 143*b^9*f*h^3 + 1584*a*b^7*c*f*h^3 - 6048*a^2*b^5*c^2*f*h^3 + 8960*a^3*b^3*c^3*f*h^3 - 3840*a^4*b*c^4*f*h^3 - 768*b^5*c^4*g^3*e + 6144*a*b^3*c^5*g^3*e - 12288*a^2*b*c^6*g^3*e + 1344*b^6*c^3*g^2*h*e - 11520*a*b^4*c^4*g^2*h*e + 27648*a^2*b^2*c^5*g^2*h*e - 12288*a^3*c^6*g^2*h*e - 864*b^7*c^2*g*h^2*e + 8064*a*b^5*c^3*g*h^2*e - 23040*a^2*b^3*c^4*g*h^2*e + 18432*a^3*b*c^5*g*h^2*e + 198*b^8*c*h^3*e - 2016*a*b^6*c^2*h^3*e + 6720*a^2*b^4*c^3*h^3*e - 7680*a^3*b^2*c^4*h^3*e + 1536*a^4*c^5*h^3*e)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(15/2)","B",0
197,1,1852,0,0.366685," ","integrate((h*x+g)^2*(c*x^2+b*x+a)^(3/2)*(f*x^2+e*x+d),x, algorithm=""giac"")","\frac{1}{1720320} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(10 \, {\left(12 \, {\left(14 \, c f h^{2} x + \frac{32 \, c^{8} f g h + 17 \, b c^{7} f h^{2} + 16 \, c^{8} h^{2} e}{c^{7}}\right)} x + \frac{224 \, c^{8} f g^{2} + 480 \, b c^{7} f g h + 224 \, c^{8} d h^{2} + 3 \, b^{2} c^{6} f h^{2} + 252 \, a c^{7} f h^{2} + 448 \, c^{8} g h e + 240 \, b c^{7} h^{2} e}{c^{7}}\right)} x + \frac{2912 \, b c^{7} f g^{2} + 5376 \, c^{8} d g h + 96 \, b^{2} c^{6} f g h + 6144 \, a c^{7} f g h + 2912 \, b c^{7} d h^{2} - 33 \, b^{3} c^{5} f h^{2} + 156 \, a b c^{6} f h^{2} + 2688 \, c^{8} g^{2} e + 5824 \, b c^{7} g h e + 48 \, b^{2} c^{6} h^{2} e + 3072 \, a c^{7} h^{2} e}{c^{7}}\right)} x + \frac{26880 \, c^{8} d g^{2} + 672 \, b^{2} c^{6} f g^{2} + 31360 \, a c^{7} f g^{2} + 59136 \, b c^{7} d g h - 864 \, b^{3} c^{5} f g h + 4224 \, a b c^{6} f g h + 672 \, b^{2} c^{6} d h^{2} + 31360 \, a c^{7} d h^{2} + 297 \, b^{4} c^{4} f h^{2} - 1704 \, a b^{2} c^{5} f h^{2} + 1680 \, a^{2} c^{6} f h^{2} + 29568 \, b c^{7} g^{2} e + 1344 \, b^{2} c^{6} g h e + 62720 \, a c^{7} g h e - 432 \, b^{3} c^{5} h^{2} e + 2112 \, a b c^{6} h^{2} e}{c^{7}}\right)} x + \frac{80640 \, b c^{7} d g^{2} - 1568 \, b^{3} c^{5} f g^{2} + 8064 \, a b c^{6} f g^{2} + 5376 \, b^{2} c^{6} d g h + 172032 \, a c^{7} d g h + 2016 \, b^{4} c^{4} f g h - 11904 \, a b^{2} c^{5} f g h + 12288 \, a^{2} c^{6} f g h - 1568 \, b^{3} c^{5} d h^{2} + 8064 \, a b c^{6} d h^{2} - 693 \, b^{5} c^{3} f h^{2} + 4680 \, a b^{3} c^{4} f h^{2} - 7248 \, a^{2} b c^{5} f h^{2} + 2688 \, b^{2} c^{6} g^{2} e + 86016 \, a c^{7} g^{2} e - 3136 \, b^{3} c^{5} g h e + 16128 \, a b c^{6} g h e + 1008 \, b^{4} c^{4} h^{2} e - 5952 \, a b^{2} c^{5} h^{2} e + 6144 \, a^{2} c^{6} h^{2} e}{c^{7}}\right)} x + \frac{26880 \, b^{2} c^{6} d g^{2} + 537600 \, a c^{7} d g^{2} + 7840 \, b^{4} c^{4} f g^{2} - 48384 \, a b^{2} c^{5} f g^{2} + 53760 \, a^{2} c^{6} f g^{2} - 26880 \, b^{3} c^{5} d g h + 150528 \, a b c^{6} d g h - 10080 \, b^{5} c^{3} f g h + 69888 \, a b^{3} c^{4} f g h - 112128 \, a^{2} b c^{5} f g h + 7840 \, b^{4} c^{4} d h^{2} - 48384 \, a b^{2} c^{5} d h^{2} + 53760 \, a^{2} c^{6} d h^{2} + 3465 \, b^{6} c^{2} f h^{2} - 26964 \, a b^{4} c^{3} f h^{2} + 56688 \, a^{2} b^{2} c^{4} f h^{2} - 20160 \, a^{3} c^{5} f h^{2} - 13440 \, b^{3} c^{5} g^{2} e + 75264 \, a b c^{6} g^{2} e + 15680 \, b^{4} c^{4} g h e - 96768 \, a b^{2} c^{5} g h e + 107520 \, a^{2} c^{6} g h e - 5040 \, b^{5} c^{3} h^{2} e + 34944 \, a b^{3} c^{4} h^{2} e - 56064 \, a^{2} b c^{5} h^{2} e}{c^{7}}\right)} x - \frac{80640 \, b^{3} c^{5} d g^{2} - 537600 \, a b c^{6} d g^{2} + 23520 \, b^{5} c^{3} f g^{2} - 170240 \, a b^{3} c^{4} f g^{2} + 290304 \, a^{2} b c^{5} f g^{2} - 80640 \, b^{4} c^{4} d g h + 537600 \, a b^{2} c^{5} d g h - 688128 \, a^{2} c^{6} d g h - 30240 \, b^{6} c^{2} f g h + 241920 \, a b^{4} c^{3} f g h - 526848 \, a^{2} b^{2} c^{4} f g h + 196608 \, a^{3} c^{5} f g h + 23520 \, b^{5} c^{3} d h^{2} - 170240 \, a b^{3} c^{4} d h^{2} + 290304 \, a^{2} b c^{5} d h^{2} + 10395 \, b^{7} c f h^{2} - 91980 \, a b^{5} c^{2} f h^{2} + 244944 \, a^{2} b^{3} c^{3} f h^{2} - 176448 \, a^{3} b c^{4} f h^{2} - 40320 \, b^{4} c^{4} g^{2} e + 268800 \, a b^{2} c^{5} g^{2} e - 344064 \, a^{2} c^{6} g^{2} e + 47040 \, b^{5} c^{3} g h e - 340480 \, a b^{3} c^{4} g h e + 580608 \, a^{2} b c^{5} g h e - 15120 \, b^{6} c^{2} h^{2} e + 120960 \, a b^{4} c^{3} h^{2} e - 263424 \, a^{2} b^{2} c^{4} h^{2} e + 98304 \, a^{3} c^{5} h^{2} e}{c^{7}}\right)} - \frac{{\left(768 \, b^{4} c^{4} d g^{2} - 6144 \, a b^{2} c^{5} d g^{2} + 12288 \, a^{2} c^{6} d g^{2} + 224 \, b^{6} c^{2} f g^{2} - 1920 \, a b^{4} c^{3} f g^{2} + 4608 \, a^{2} b^{2} c^{4} f g^{2} - 2048 \, a^{3} c^{5} f g^{2} - 768 \, b^{5} c^{3} d g h + 6144 \, a b^{3} c^{4} d g h - 12288 \, a^{2} b c^{5} d g h - 288 \, b^{7} c f g h + 2688 \, a b^{5} c^{2} f g h - 7680 \, a^{2} b^{3} c^{3} f g h + 6144 \, a^{3} b c^{4} f g h + 224 \, b^{6} c^{2} d h^{2} - 1920 \, a b^{4} c^{3} d h^{2} + 4608 \, a^{2} b^{2} c^{4} d h^{2} - 2048 \, a^{3} c^{5} d h^{2} + 99 \, b^{8} f h^{2} - 1008 \, a b^{6} c f h^{2} + 3360 \, a^{2} b^{4} c^{2} f h^{2} - 3840 \, a^{3} b^{2} c^{3} f h^{2} + 768 \, a^{4} c^{4} f h^{2} - 384 \, b^{5} c^{3} g^{2} e + 3072 \, a b^{3} c^{4} g^{2} e - 6144 \, a^{2} b c^{5} g^{2} e + 448 \, b^{6} c^{2} g h e - 3840 \, a b^{4} c^{3} g h e + 9216 \, a^{2} b^{2} c^{4} g h e - 4096 \, a^{3} c^{5} g h e - 144 \, b^{7} c h^{2} e + 1344 \, a b^{5} c^{2} h^{2} e - 3840 \, a^{2} b^{3} c^{3} h^{2} e + 3072 \, a^{3} b c^{4} h^{2} e\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{32768 \, c^{\frac{13}{2}}}"," ",0,"1/1720320*sqrt(c*x^2 + b*x + a)*(2*(4*(2*(8*(10*(12*(14*c*f*h^2*x + (32*c^8*f*g*h + 17*b*c^7*f*h^2 + 16*c^8*h^2*e)/c^7)*x + (224*c^8*f*g^2 + 480*b*c^7*f*g*h + 224*c^8*d*h^2 + 3*b^2*c^6*f*h^2 + 252*a*c^7*f*h^2 + 448*c^8*g*h*e + 240*b*c^7*h^2*e)/c^7)*x + (2912*b*c^7*f*g^2 + 5376*c^8*d*g*h + 96*b^2*c^6*f*g*h + 6144*a*c^7*f*g*h + 2912*b*c^7*d*h^2 - 33*b^3*c^5*f*h^2 + 156*a*b*c^6*f*h^2 + 2688*c^8*g^2*e + 5824*b*c^7*g*h*e + 48*b^2*c^6*h^2*e + 3072*a*c^7*h^2*e)/c^7)*x + (26880*c^8*d*g^2 + 672*b^2*c^6*f*g^2 + 31360*a*c^7*f*g^2 + 59136*b*c^7*d*g*h - 864*b^3*c^5*f*g*h + 4224*a*b*c^6*f*g*h + 672*b^2*c^6*d*h^2 + 31360*a*c^7*d*h^2 + 297*b^4*c^4*f*h^2 - 1704*a*b^2*c^5*f*h^2 + 1680*a^2*c^6*f*h^2 + 29568*b*c^7*g^2*e + 1344*b^2*c^6*g*h*e + 62720*a*c^7*g*h*e - 432*b^3*c^5*h^2*e + 2112*a*b*c^6*h^2*e)/c^7)*x + (80640*b*c^7*d*g^2 - 1568*b^3*c^5*f*g^2 + 8064*a*b*c^6*f*g^2 + 5376*b^2*c^6*d*g*h + 172032*a*c^7*d*g*h + 2016*b^4*c^4*f*g*h - 11904*a*b^2*c^5*f*g*h + 12288*a^2*c^6*f*g*h - 1568*b^3*c^5*d*h^2 + 8064*a*b*c^6*d*h^2 - 693*b^5*c^3*f*h^2 + 4680*a*b^3*c^4*f*h^2 - 7248*a^2*b*c^5*f*h^2 + 2688*b^2*c^6*g^2*e + 86016*a*c^7*g^2*e - 3136*b^3*c^5*g*h*e + 16128*a*b*c^6*g*h*e + 1008*b^4*c^4*h^2*e - 5952*a*b^2*c^5*h^2*e + 6144*a^2*c^6*h^2*e)/c^7)*x + (26880*b^2*c^6*d*g^2 + 537600*a*c^7*d*g^2 + 7840*b^4*c^4*f*g^2 - 48384*a*b^2*c^5*f*g^2 + 53760*a^2*c^6*f*g^2 - 26880*b^3*c^5*d*g*h + 150528*a*b*c^6*d*g*h - 10080*b^5*c^3*f*g*h + 69888*a*b^3*c^4*f*g*h - 112128*a^2*b*c^5*f*g*h + 7840*b^4*c^4*d*h^2 - 48384*a*b^2*c^5*d*h^2 + 53760*a^2*c^6*d*h^2 + 3465*b^6*c^2*f*h^2 - 26964*a*b^4*c^3*f*h^2 + 56688*a^2*b^2*c^4*f*h^2 - 20160*a^3*c^5*f*h^2 - 13440*b^3*c^5*g^2*e + 75264*a*b*c^6*g^2*e + 15680*b^4*c^4*g*h*e - 96768*a*b^2*c^5*g*h*e + 107520*a^2*c^6*g*h*e - 5040*b^5*c^3*h^2*e + 34944*a*b^3*c^4*h^2*e - 56064*a^2*b*c^5*h^2*e)/c^7)*x - (80640*b^3*c^5*d*g^2 - 537600*a*b*c^6*d*g^2 + 23520*b^5*c^3*f*g^2 - 170240*a*b^3*c^4*f*g^2 + 290304*a^2*b*c^5*f*g^2 - 80640*b^4*c^4*d*g*h + 537600*a*b^2*c^5*d*g*h - 688128*a^2*c^6*d*g*h - 30240*b^6*c^2*f*g*h + 241920*a*b^4*c^3*f*g*h - 526848*a^2*b^2*c^4*f*g*h + 196608*a^3*c^5*f*g*h + 23520*b^5*c^3*d*h^2 - 170240*a*b^3*c^4*d*h^2 + 290304*a^2*b*c^5*d*h^2 + 10395*b^7*c*f*h^2 - 91980*a*b^5*c^2*f*h^2 + 244944*a^2*b^3*c^3*f*h^2 - 176448*a^3*b*c^4*f*h^2 - 40320*b^4*c^4*g^2*e + 268800*a*b^2*c^5*g^2*e - 344064*a^2*c^6*g^2*e + 47040*b^5*c^3*g*h*e - 340480*a*b^3*c^4*g*h*e + 580608*a^2*b*c^5*g*h*e - 15120*b^6*c^2*h^2*e + 120960*a*b^4*c^3*h^2*e - 263424*a^2*b^2*c^4*h^2*e + 98304*a^3*c^5*h^2*e)/c^7) - 1/32768*(768*b^4*c^4*d*g^2 - 6144*a*b^2*c^5*d*g^2 + 12288*a^2*c^6*d*g^2 + 224*b^6*c^2*f*g^2 - 1920*a*b^4*c^3*f*g^2 + 4608*a^2*b^2*c^4*f*g^2 - 2048*a^3*c^5*f*g^2 - 768*b^5*c^3*d*g*h + 6144*a*b^3*c^4*d*g*h - 12288*a^2*b*c^5*d*g*h - 288*b^7*c*f*g*h + 2688*a*b^5*c^2*f*g*h - 7680*a^2*b^3*c^3*f*g*h + 6144*a^3*b*c^4*f*g*h + 224*b^6*c^2*d*h^2 - 1920*a*b^4*c^3*d*h^2 + 4608*a^2*b^2*c^4*d*h^2 - 2048*a^3*c^5*d*h^2 + 99*b^8*f*h^2 - 1008*a*b^6*c*f*h^2 + 3360*a^2*b^4*c^2*f*h^2 - 3840*a^3*b^2*c^3*f*h^2 + 768*a^4*c^4*f*h^2 - 384*b^5*c^3*g^2*e + 3072*a*b^3*c^4*g^2*e - 6144*a^2*b*c^5*g^2*e + 448*b^6*c^2*g*h*e - 3840*a*b^4*c^3*g*h*e + 9216*a^2*b^2*c^4*g*h*e - 4096*a^3*c^5*g*h*e - 144*b^7*c*h^2*e + 1344*a*b^5*c^2*h^2*e - 3840*a^2*b^3*c^3*h^2*e + 3072*a^3*b*c^4*h^2*e)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(13/2)","B",0
198,1,955,0,0.294143," ","integrate((h*x+g)*(c*x^2+b*x+a)^(3/2)*(f*x^2+e*x+d),x, algorithm=""giac"")","\frac{1}{107520} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(10 \, {\left(12 \, c f h x + \frac{14 \, c^{7} f g + 15 \, b c^{6} f h + 14 \, c^{7} h e}{c^{6}}\right)} x + \frac{182 \, b c^{6} f g + 168 \, c^{7} d h + 3 \, b^{2} c^{5} f h + 192 \, a c^{6} f h + 168 \, c^{7} g e + 182 \, b c^{6} h e}{c^{6}}\right)} x + \frac{1680 \, c^{7} d g + 42 \, b^{2} c^{5} f g + 1960 \, a c^{6} f g + 1848 \, b c^{6} d h - 27 \, b^{3} c^{4} f h + 132 \, a b c^{5} f h + 1848 \, b c^{6} g e + 42 \, b^{2} c^{5} h e + 1960 \, a c^{6} h e}{c^{6}}\right)} x + \frac{5040 \, b c^{6} d g - 98 \, b^{3} c^{4} f g + 504 \, a b c^{5} f g + 168 \, b^{2} c^{5} d h + 5376 \, a c^{6} d h + 63 \, b^{4} c^{3} f h - 372 \, a b^{2} c^{4} f h + 384 \, a^{2} c^{5} f h + 168 \, b^{2} c^{5} g e + 5376 \, a c^{6} g e - 98 \, b^{3} c^{4} h e + 504 \, a b c^{5} h e}{c^{6}}\right)} x + \frac{1680 \, b^{2} c^{5} d g + 33600 \, a c^{6} d g + 490 \, b^{4} c^{3} f g - 3024 \, a b^{2} c^{4} f g + 3360 \, a^{2} c^{5} f g - 840 \, b^{3} c^{4} d h + 4704 \, a b c^{5} d h - 315 \, b^{5} c^{2} f h + 2184 \, a b^{3} c^{3} f h - 3504 \, a^{2} b c^{4} f h - 840 \, b^{3} c^{4} g e + 4704 \, a b c^{5} g e + 490 \, b^{4} c^{3} h e - 3024 \, a b^{2} c^{4} h e + 3360 \, a^{2} c^{5} h e}{c^{6}}\right)} x - \frac{5040 \, b^{3} c^{4} d g - 33600 \, a b c^{5} d g + 1470 \, b^{5} c^{2} f g - 10640 \, a b^{3} c^{3} f g + 18144 \, a^{2} b c^{4} f g - 2520 \, b^{4} c^{3} d h + 16800 \, a b^{2} c^{4} d h - 21504 \, a^{2} c^{5} d h - 945 \, b^{6} c f h + 7560 \, a b^{4} c^{2} f h - 16464 \, a^{2} b^{2} c^{3} f h + 6144 \, a^{3} c^{4} f h - 2520 \, b^{4} c^{3} g e + 16800 \, a b^{2} c^{4} g e - 21504 \, a^{2} c^{5} g e + 1470 \, b^{5} c^{2} h e - 10640 \, a b^{3} c^{3} h e + 18144 \, a^{2} b c^{4} h e}{c^{6}}\right)} - \frac{{\left(48 \, b^{4} c^{3} d g - 384 \, a b^{2} c^{4} d g + 768 \, a^{2} c^{5} d g + 14 \, b^{6} c f g - 120 \, a b^{4} c^{2} f g + 288 \, a^{2} b^{2} c^{3} f g - 128 \, a^{3} c^{4} f g - 24 \, b^{5} c^{2} d h + 192 \, a b^{3} c^{3} d h - 384 \, a^{2} b c^{4} d h - 9 \, b^{7} f h + 84 \, a b^{5} c f h - 240 \, a^{2} b^{3} c^{2} f h + 192 \, a^{3} b c^{3} f h - 24 \, b^{5} c^{2} g e + 192 \, a b^{3} c^{3} g e - 384 \, a^{2} b c^{4} g e + 14 \, b^{6} c h e - 120 \, a b^{4} c^{2} h e + 288 \, a^{2} b^{2} c^{3} h e - 128 \, a^{3} c^{4} h e\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{2048 \, c^{\frac{11}{2}}}"," ",0,"1/107520*sqrt(c*x^2 + b*x + a)*(2*(4*(2*(8*(10*(12*c*f*h*x + (14*c^7*f*g + 15*b*c^6*f*h + 14*c^7*h*e)/c^6)*x + (182*b*c^6*f*g + 168*c^7*d*h + 3*b^2*c^5*f*h + 192*a*c^6*f*h + 168*c^7*g*e + 182*b*c^6*h*e)/c^6)*x + (1680*c^7*d*g + 42*b^2*c^5*f*g + 1960*a*c^6*f*g + 1848*b*c^6*d*h - 27*b^3*c^4*f*h + 132*a*b*c^5*f*h + 1848*b*c^6*g*e + 42*b^2*c^5*h*e + 1960*a*c^6*h*e)/c^6)*x + (5040*b*c^6*d*g - 98*b^3*c^4*f*g + 504*a*b*c^5*f*g + 168*b^2*c^5*d*h + 5376*a*c^6*d*h + 63*b^4*c^3*f*h - 372*a*b^2*c^4*f*h + 384*a^2*c^5*f*h + 168*b^2*c^5*g*e + 5376*a*c^6*g*e - 98*b^3*c^4*h*e + 504*a*b*c^5*h*e)/c^6)*x + (1680*b^2*c^5*d*g + 33600*a*c^6*d*g + 490*b^4*c^3*f*g - 3024*a*b^2*c^4*f*g + 3360*a^2*c^5*f*g - 840*b^3*c^4*d*h + 4704*a*b*c^5*d*h - 315*b^5*c^2*f*h + 2184*a*b^3*c^3*f*h - 3504*a^2*b*c^4*f*h - 840*b^3*c^4*g*e + 4704*a*b*c^5*g*e + 490*b^4*c^3*h*e - 3024*a*b^2*c^4*h*e + 3360*a^2*c^5*h*e)/c^6)*x - (5040*b^3*c^4*d*g - 33600*a*b*c^5*d*g + 1470*b^5*c^2*f*g - 10640*a*b^3*c^3*f*g + 18144*a^2*b*c^4*f*g - 2520*b^4*c^3*d*h + 16800*a*b^2*c^4*d*h - 21504*a^2*c^5*d*h - 945*b^6*c*f*h + 7560*a*b^4*c^2*f*h - 16464*a^2*b^2*c^3*f*h + 6144*a^3*c^4*f*h - 2520*b^4*c^3*g*e + 16800*a*b^2*c^4*g*e - 21504*a^2*c^5*g*e + 1470*b^5*c^2*h*e - 10640*a*b^3*c^3*h*e + 18144*a^2*b*c^4*h*e)/c^6) - 1/2048*(48*b^4*c^3*d*g - 384*a*b^2*c^4*d*g + 768*a^2*c^5*d*g + 14*b^6*c*f*g - 120*a*b^4*c^2*f*g + 288*a^2*b^2*c^3*f*g - 128*a^3*c^4*f*g - 24*b^5*c^2*d*h + 192*a*b^3*c^3*d*h - 384*a^2*b*c^4*d*h - 9*b^7*f*h + 84*a*b^5*c*f*h - 240*a^2*b^3*c^2*f*h + 192*a^3*b*c^3*f*h - 24*b^5*c^2*g*e + 192*a*b^3*c^3*g*e - 384*a^2*b*c^4*g*e + 14*b^6*c*h*e - 120*a*b^4*c^2*h*e + 288*a^2*b^2*c^3*h*e - 128*a^3*c^4*h*e)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(11/2)","B",0
199,1,417,0,0.264325," ","integrate((c*x^2+b*x+a)^(3/2)*(f*x^2+e*x+d),x, algorithm=""giac"")","\frac{1}{7680} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(10 \, c f x + \frac{13 \, b c^{5} f + 12 \, c^{6} e}{c^{5}}\right)} x + \frac{120 \, c^{6} d + 3 \, b^{2} c^{4} f + 140 \, a c^{5} f + 132 \, b c^{5} e}{c^{5}}\right)} x + \frac{360 \, b c^{5} d - 7 \, b^{3} c^{3} f + 36 \, a b c^{4} f + 12 \, b^{2} c^{4} e + 384 \, a c^{5} e}{c^{5}}\right)} x + \frac{120 \, b^{2} c^{4} d + 2400 \, a c^{5} d + 35 \, b^{4} c^{2} f - 216 \, a b^{2} c^{3} f + 240 \, a^{2} c^{4} f - 60 \, b^{3} c^{3} e + 336 \, a b c^{4} e}{c^{5}}\right)} x - \frac{360 \, b^{3} c^{3} d - 2400 \, a b c^{4} d + 105 \, b^{5} c f - 760 \, a b^{3} c^{2} f + 1296 \, a^{2} b c^{3} f - 180 \, b^{4} c^{2} e + 1200 \, a b^{2} c^{3} e - 1536 \, a^{2} c^{4} e}{c^{5}}\right)} - \frac{{\left(24 \, b^{4} c^{2} d - 192 \, a b^{2} c^{3} d + 384 \, a^{2} c^{4} d + 7 \, b^{6} f - 60 \, a b^{4} c f + 144 \, a^{2} b^{2} c^{2} f - 64 \, a^{3} c^{3} f - 12 \, b^{5} c e + 96 \, a b^{3} c^{2} e - 192 \, a^{2} b c^{3} e\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{1024 \, c^{\frac{9}{2}}}"," ",0,"1/7680*sqrt(c*x^2 + b*x + a)*(2*(4*(2*(8*(10*c*f*x + (13*b*c^5*f + 12*c^6*e)/c^5)*x + (120*c^6*d + 3*b^2*c^4*f + 140*a*c^5*f + 132*b*c^5*e)/c^5)*x + (360*b*c^5*d - 7*b^3*c^3*f + 36*a*b*c^4*f + 12*b^2*c^4*e + 384*a*c^5*e)/c^5)*x + (120*b^2*c^4*d + 2400*a*c^5*d + 35*b^4*c^2*f - 216*a*b^2*c^3*f + 240*a^2*c^4*f - 60*b^3*c^3*e + 336*a*b*c^4*e)/c^5)*x - (360*b^3*c^3*d - 2400*a*b*c^4*d + 105*b^5*c*f - 760*a*b^3*c^2*f + 1296*a^2*b*c^3*f - 180*b^4*c^2*e + 1200*a*b^2*c^3*e - 1536*a^2*c^4*e)/c^5) - 1/1024*(24*b^4*c^2*d - 192*a*b^2*c^3*d + 384*a^2*c^4*d + 7*b^6*f - 60*a*b^4*c*f + 144*a^2*b^2*c^2*f - 64*a^3*c^3*f - 12*b^5*c*e + 96*a*b^3*c^2*e - 192*a^2*b*c^3*e)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(9/2)","A",0
200,-2,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)*(f*x^2+e*x+d)/(h*x+g),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
201,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)*(f*x^2+e*x+d)/(h*x+g)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
202,-2,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)*(f*x^2+e*x+d)/(h*x+g)^3,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 1.47Unable to divide, perhaps due to rounding error%%%{1,[6,0,0,0,9,0,0,0]%%%}+%%%{%%{[-6,0]:[1,0,%%%{-1,[1]%%%}]%%},[5,0,0,0,8,1,0,0]%%%}+%%%{-3,[4,1,0,0,9,0,0,0]%%%}+%%%{3,[4,0,1,0,8,1,0,0]%%%}+%%%{%%%{12,[1]%%%},[4,0,0,0,7,2,0,0]%%%}+%%%{%%{[12,0]:[1,0,%%%{-1,[1]%%%}]%%},[3,1,0,0,8,1,0,0]%%%}+%%%{%%{[-12,0]:[1,0,%%%{-1,[1]%%%}]%%},[3,0,1,0,7,2,0,0]%%%}+%%%{%%{[%%%{-8,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,0,0,0,6,3,0,0]%%%}+%%%{3,[2,2,0,0,9,0,0,0]%%%}+%%%{-6,[2,1,1,0,8,1,0,0]%%%}+%%%{%%%{-12,[1]%%%},[2,1,0,0,7,2,0,0]%%%}+%%%{3,[2,0,2,0,7,2,0,0]%%%}+%%%{%%%{12,[1]%%%},[2,0,1,0,6,3,0,0]%%%}+%%%{%%{[-6,0]:[1,0,%%%{-1,[1]%%%}]%%},[1,2,0,0,8,1,0,0]%%%}+%%%{%%{[12,0]:[1,0,%%%{-1,[1]%%%}]%%},[1,1,1,0,7,2,0,0]%%%}+%%%{%%{[-6,0]:[1,0,%%%{-1,[1]%%%}]%%},[1,0,2,0,6,3,0,0]%%%}+%%%{-1,[0,3,0,0,9,0,0,0]%%%}+%%%{3,[0,2,1,0,8,1,0,0]%%%}+%%%{-3,[0,1,2,0,7,2,0,0]%%%}+%%%{1,[0,0,3,0,6,3,0,0]%%%} / %%%{%%{poly1[%%%{1,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,0,0,3,0,0,0]%%%}+%%%{%%%{-6,[2]%%%},[5,0,0,0,2,1,0,0]%%%}+%%%{%%{[%%%{-3,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,1,0,0,3,0,0,0]%%%}+%%%{%%{poly1[%%%{3,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,1,0,2,1,0,0]%%%}+%%%{%%{poly1[%%%{12,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,0,0,1,2,0,0]%%%}+%%%{%%%{12,[2]%%%},[3,1,0,0,2,1,0,0]%%%}+%%%{%%%{-12,[2]%%%},[3,0,1,0,1,2,0,0]%%%}+%%%{%%%{-8,[3]%%%},[3,0,0,0,0,3,0,0]%%%}+%%%{%%{[%%%{3,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,2,0,0,3,0,0,0]%%%}+%%%{%%{[%%%{-6,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,1,1,0,2,1,0,0]%%%}+%%%{%%{[%%%{-12,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,1,0,0,1,2,0,0]%%%}+%%%{%%{poly1[%%%{3,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,2,0,1,2,0,0]%%%}+%%%{%%{poly1[%%%{12,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,1,0,0,3,0,0]%%%}+%%%{%%%{-6,[2]%%%},[1,2,0,0,2,1,0,0]%%%}+%%%{%%%{12,[2]%%%},[1,1,1,0,1,2,0,0]%%%}+%%%{%%%{-6,[2]%%%},[1,0,2,0,0,3,0,0]%%%}+%%%{%%{[%%%{-1,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,3,0,0,3,0,0,0]%%%}+%%%{%%{[%%%{3,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,2,1,0,2,1,0,0]%%%}+%%%{%%{[%%%{-3,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,1,2,0,1,2,0,0]%%%}+%%%{%%{poly1[%%%{1,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,3,0,0,3,0,0]%%%} Error: Bad Argument Value","F(-2)",0
203,1,7319,0,26.172029," ","integrate((c*x^2+b*x+a)^(3/2)*(f*x^2+e*x+d)/(h*x+g)^4,x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{c x^{2} + b x + a} {\left(\frac{2 \, c f x}{h^{4}} - \frac{16 \, c^{2} f g h^{10} - 5 \, b c f h^{11} - 4 \, c^{2} h^{11} e}{c h^{15}}\right)} - \frac{{\left(160 \, c^{3} f g^{5} - 336 \, b c^{2} f g^{4} h + 16 \, c^{3} d g^{3} h^{2} + 210 \, b^{2} c f g^{3} h^{2} + 264 \, a c^{2} f g^{3} h^{2} - 24 \, b c^{2} d g^{2} h^{3} - 35 \, b^{3} f g^{2} h^{3} - 300 \, a b c f g^{2} h^{3} + 6 \, b^{2} c d g h^{4} + 24 \, a c^{2} d g h^{4} + 60 \, a b^{2} f g h^{4} + 96 \, a^{2} c f g h^{4} + b^{3} d h^{5} - 12 \, a b c d h^{5} - 24 \, a^{2} b f h^{5} - 64 \, c^{3} g^{4} h e + 120 \, b c^{2} g^{3} h^{2} e - 60 \, b^{2} c g^{2} h^{3} e - 96 \, a c^{2} g^{2} h^{3} e + 5 \, b^{3} g h^{4} e + 84 \, a b c g h^{4} e - 6 \, a b^{2} h^{5} e - 24 \, a^{2} c h^{5} e\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} h + \sqrt{c} g}{\sqrt{-c g^{2} + b g h - a h^{2}}}\right)}{8 \, {\left(c g^{2} h^{6} - b g h^{7} + a h^{8}\right)} \sqrt{-c g^{2} + b g h - a h^{2}}} - \frac{480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} c^{\frac{7}{2}} f g^{5} h^{2} - 912 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b c^{\frac{5}{2}} f g^{4} h^{3} + 144 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} c^{\frac{7}{2}} d g^{3} h^{4} + 522 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b^{2} c^{\frac{3}{2}} f g^{3} h^{4} + 552 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a c^{\frac{5}{2}} f g^{3} h^{4} - 216 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b c^{\frac{5}{2}} d g^{2} h^{5} - 87 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b^{3} \sqrt{c} f g^{2} h^{5} - 540 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a b c^{\frac{3}{2}} f g^{2} h^{5} + 78 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b^{2} c^{\frac{3}{2}} d g h^{6} + 120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a c^{\frac{5}{2}} d g h^{6} + 108 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a b^{2} \sqrt{c} f g h^{6} + 96 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{2} c^{\frac{3}{2}} f g h^{6} - 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b^{3} \sqrt{c} d h^{7} - 60 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a b c^{\frac{3}{2}} d h^{7} - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{2} b \sqrt{c} f h^{7} - 288 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} c^{\frac{7}{2}} g^{4} h^{3} e + 504 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b c^{\frac{5}{2}} g^{3} h^{4} e - 252 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b^{2} c^{\frac{3}{2}} g^{2} h^{5} e - 288 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a c^{\frac{5}{2}} g^{2} h^{5} e + 33 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b^{3} \sqrt{c} g h^{6} e + 228 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a b c^{\frac{3}{2}} g h^{6} e - 30 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a b^{2} \sqrt{c} h^{7} e - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{2} c^{\frac{3}{2}} h^{7} e + 1680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} c^{4} f g^{6} h - 2880 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b c^{3} f g^{5} h^{2} + 432 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} c^{4} d g^{4} h^{3} + 1362 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b^{2} c^{2} f g^{4} h^{3} + 1464 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a c^{3} f g^{4} h^{3} - 504 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b c^{3} d g^{3} h^{4} - 147 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b^{3} c f g^{3} h^{4} - 876 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a b c^{2} f g^{3} h^{4} + 54 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b^{2} c^{2} d g^{2} h^{5} + 216 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a c^{3} d g^{2} h^{5} - 36 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a b^{2} c f g^{2} h^{5} - 144 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{2} c^{2} f g^{2} h^{5} + 33 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b^{3} c d g h^{6} + 84 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a b c^{2} d g h^{6} + 216 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{2} b c f g h^{6} - 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a b^{2} c d h^{7} - 96 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{2} c^{2} d h^{7} - 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{3} c f h^{7} - 960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} c^{4} g^{5} h^{2} e + 1464 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b c^{3} g^{4} h^{3} e - 540 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b^{2} c^{2} g^{3} h^{4} e - 672 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a c^{3} g^{3} h^{4} e + 21 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b^{3} c g^{2} h^{5} e + 180 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a b c^{2} g^{2} h^{5} e + 90 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a b^{2} c g h^{6} e + 168 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{2} c^{2} g h^{6} e - 96 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{2} b c h^{7} e + 1504 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} c^{\frac{9}{2}} f g^{7} - 1072 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b c^{\frac{7}{2}} f g^{6} h + 352 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} c^{\frac{9}{2}} d g^{5} h^{2} - 1308 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{2} c^{\frac{5}{2}} f g^{5} h^{2} - 656 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a c^{\frac{7}{2}} f g^{5} h^{2} - 16 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b c^{\frac{7}{2}} d g^{4} h^{3} + 1042 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{3} c^{\frac{3}{2}} f g^{4} h^{3} + 4056 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b c^{\frac{5}{2}} f g^{4} h^{3} - 420 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{2} c^{\frac{5}{2}} d g^{3} h^{4} - 272 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a c^{\frac{7}{2}} d g^{3} h^{4} - 136 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{4} \sqrt{c} f g^{3} h^{4} - 2712 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b^{2} c^{\frac{3}{2}} f g^{3} h^{4} - 2208 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{2} c^{\frac{5}{2}} f g^{3} h^{4} + 106 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{3} c^{\frac{3}{2}} d g^{2} h^{5} + 840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b c^{\frac{5}{2}} d g^{2} h^{5} + 328 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b^{3} \sqrt{c} f g^{2} h^{5} + 1920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{2} b c^{\frac{3}{2}} f g^{2} h^{5} + 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{4} \sqrt{c} d g h^{6} - 144 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b^{2} c^{\frac{3}{2}} d g h^{6} - 384 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{2} c^{\frac{5}{2}} d g h^{6} - 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{2} b^{2} \sqrt{c} f g h^{6} - 288 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{3} c^{\frac{3}{2}} f g h^{6} - 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b^{3} \sqrt{c} d h^{7} + 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{3} b \sqrt{c} f h^{7} - 832 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} c^{\frac{9}{2}} g^{6} h e + 400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b c^{\frac{7}{2}} g^{5} h^{2} e + 840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{2} c^{\frac{5}{2}} g^{4} h^{3} e + 512 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a c^{\frac{7}{2}} g^{4} h^{3} e - 478 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{3} c^{\frac{3}{2}} g^{3} h^{4} e - 2232 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b c^{\frac{5}{2}} g^{3} h^{4} e + 40 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{4} \sqrt{c} g^{2} h^{5} e + 1092 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b^{2} c^{\frac{3}{2}} g^{2} h^{5} e + 1104 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{2} c^{\frac{5}{2}} g^{2} h^{5} e - 88 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b^{3} \sqrt{c} g h^{6} e - 576 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{2} b c^{\frac{3}{2}} g h^{6} e + 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{2} b^{2} \sqrt{c} h^{7} e + 2256 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b c^{4} f g^{7} - 3420 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{2} c^{3} f g^{6} h - 2832 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a c^{4} f g^{6} h + 528 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b c^{4} d g^{5} h^{2} + 1218 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{3} c^{2} f g^{5} h^{2} + 5976 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b c^{3} f g^{5} h^{2} - 516 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{2} c^{3} d g^{4} h^{3} - 624 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a c^{4} d g^{4} h^{3} - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{4} c f g^{4} h^{3} - 1944 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b^{2} c^{2} f g^{4} h^{3} - 2208 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{2} c^{3} f g^{4} h^{3} - 6 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{3} c^{2} d g^{3} h^{4} + 840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b c^{3} d g^{3} h^{4} - 264 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b^{3} c f g^{3} h^{4} + 192 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{2} b c^{2} f g^{3} h^{4} + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{4} c d g^{2} h^{5} + 144 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b^{2} c^{2} d g^{2} h^{5} - 288 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{2} c^{3} d g^{2} h^{5} + 720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{2} b^{2} c f g^{2} h^{5} + 480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{3} c^{2} f g^{2} h^{5} - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b^{3} c d g h^{6} - 288 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{2} b c^{2} d g h^{6} - 528 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{3} b c f g h^{6} + 96 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{3} c^{2} d h^{7} + 96 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{4} c f h^{7} - 1248 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b c^{4} g^{6} h e + 1656 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{2} c^{3} g^{5} h^{2} e + 1536 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a c^{4} g^{5} h^{2} e - 414 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{3} c^{2} g^{4} h^{3} e - 2760 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b c^{3} g^{4} h^{3} e - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{4} c g^{3} h^{4} e + 420 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b^{2} c^{2} g^{3} h^{4} e + 912 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{2} c^{3} g^{3} h^{4} e + 168 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b^{3} c g^{2} h^{5} e + 432 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{2} b c^{2} g^{2} h^{5} e - 288 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{2} b^{2} c g h^{6} e - 384 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{3} c^{2} g h^{6} e + 144 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{3} b c h^{7} e + 1128 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{2} c^{\frac{7}{2}} f g^{7} - 1776 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{3} c^{\frac{5}{2}} f g^{6} h - 2832 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b c^{\frac{7}{2}} f g^{6} h + 264 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{2} c^{\frac{7}{2}} d g^{5} h^{2} + 720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{4} c^{\frac{3}{2}} f g^{5} h^{2} + 5580 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{2} c^{\frac{5}{2}} f g^{5} h^{2} + 1776 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} c^{\frac{7}{2}} f g^{5} h^{2} - 288 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{3} c^{\frac{5}{2}} d g^{4} h^{3} - 624 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b c^{\frac{7}{2}} d g^{4} h^{3} - 57 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{5} \sqrt{c} f g^{4} h^{3} - 2514 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{3} c^{\frac{3}{2}} f g^{4} h^{3} - 5688 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b c^{\frac{5}{2}} f g^{4} h^{3} + 36 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{4} c^{\frac{3}{2}} d g^{3} h^{4} + 852 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{2} c^{\frac{5}{2}} d g^{3} h^{4} + 384 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} c^{\frac{7}{2}} d g^{3} h^{4} + 198 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{4} \sqrt{c} f g^{3} h^{4} + 3078 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b^{2} c^{\frac{3}{2}} f g^{3} h^{4} + 1848 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{3} c^{\frac{5}{2}} f g^{3} h^{4} + 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{5} \sqrt{c} d g^{2} h^{5} - 90 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{3} c^{\frac{3}{2}} d g^{2} h^{5} - 864 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b c^{\frac{5}{2}} d g^{2} h^{5} - 249 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b^{3} \sqrt{c} f g^{2} h^{5} - 1476 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{3} b c^{\frac{3}{2}} f g^{2} h^{5} - 6 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{4} \sqrt{c} d g h^{6} + 90 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b^{2} c^{\frac{3}{2}} d g h^{6} + 264 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{3} c^{\frac{5}{2}} d g h^{6} + 132 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{3} b^{2} \sqrt{c} f g h^{6} + 192 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{4} c^{\frac{3}{2}} f g h^{6} + 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b^{3} \sqrt{c} d h^{7} - 36 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{3} b c^{\frac{3}{2}} d h^{7} - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{4} b \sqrt{c} f h^{7} - 624 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{2} c^{\frac{7}{2}} g^{6} h e + 876 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{3} c^{\frac{5}{2}} g^{5} h^{2} e + 1536 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b c^{\frac{7}{2}} g^{5} h^{2} e - 282 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{4} c^{\frac{3}{2}} g^{4} h^{3} e - 2664 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{2} c^{\frac{5}{2}} g^{4} h^{3} e - 960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} c^{\frac{7}{2}} g^{4} h^{3} e + 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{5} \sqrt{c} g^{3} h^{4} e + 894 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{3} c^{\frac{3}{2}} g^{3} h^{4} e + 2640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b c^{\frac{5}{2}} g^{3} h^{4} e - 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{4} \sqrt{c} g^{2} h^{5} e - 936 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b^{2} c^{\frac{3}{2}} g^{2} h^{5} e - 816 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{3} c^{\frac{5}{2}} g^{2} h^{5} e + 51 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b^{3} \sqrt{c} g h^{6} e + 300 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{3} b c^{\frac{3}{2}} g h^{6} e - 18 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{3} b^{2} \sqrt{c} h^{7} e + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{4} c^{\frac{3}{2}} h^{7} e + 188 \, b^{3} c^{3} f g^{7} - 272 \, b^{4} c^{2} f g^{6} h - 708 \, a b^{2} c^{3} f g^{6} h + 44 \, b^{3} c^{3} d g^{5} h^{2} + 87 \, b^{5} c f g^{5} h^{2} + 1214 \, a b^{3} c^{2} f g^{5} h^{2} + 888 \, a^{2} b c^{3} f g^{5} h^{2} - 44 \, b^{4} c^{2} d g^{4} h^{3} - 156 \, a b^{2} c^{3} d g^{4} h^{3} - 426 \, a b^{4} c f g^{4} h^{3} - 2010 \, a^{2} b^{2} c^{2} f g^{4} h^{3} - 376 \, a^{3} c^{3} f g^{4} h^{3} + 3 \, b^{5} c d g^{3} h^{4} + 182 \, a b^{3} c^{2} d g^{3} h^{4} + 192 \, a^{2} b c^{3} d g^{3} h^{4} + 807 \, a^{2} b^{3} c f g^{3} h^{4} + 1468 \, a^{3} b c^{2} f g^{3} h^{4} - 6 \, a b^{4} c d g^{2} h^{5} - 294 \, a^{2} b^{2} c^{2} d g^{2} h^{5} - 88 \, a^{3} c^{3} d g^{2} h^{5} - 732 \, a^{3} b^{2} c f g^{2} h^{5} - 400 \, a^{4} c^{2} f g^{2} h^{5} + 3 \, a^{2} b^{3} c d g h^{6} + 220 \, a^{3} b c^{2} d g h^{6} + 312 \, a^{4} b c f g h^{6} - 64 \, a^{4} c^{2} d h^{7} - 48 \, a^{5} c f h^{7} - 104 \, b^{3} c^{3} g^{6} h e + 134 \, b^{4} c^{2} g^{5} h^{2} e + 384 \, a b^{2} c^{3} g^{5} h^{2} e - 33 \, b^{5} c g^{4} h^{3} e - 578 \, a b^{3} c^{2} g^{4} h^{3} e - 480 \, a^{2} b c^{3} g^{4} h^{3} e + 144 \, a b^{4} c g^{3} h^{4} e + 936 \, a^{2} b^{2} c^{2} g^{3} h^{4} e + 208 \, a^{3} c^{3} g^{3} h^{4} e - 237 \, a^{2} b^{3} c g^{2} h^{5} e - 676 \, a^{3} b c^{2} g^{2} h^{5} e + 174 \, a^{3} b^{2} c g h^{6} e + 184 \, a^{4} c^{2} g h^{6} e - 48 \, a^{4} b c h^{7} e}{24 \, {\left(c^{\frac{3}{2}} g^{2} h^{6} - b \sqrt{c} g h^{7} + a \sqrt{c} h^{8}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} h + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} g + b g - a h\right)}^{3}} - \frac{{\left(80 \, c^{2} f g^{2} - 48 \, b c f g h + 8 \, c^{2} d h^{2} + 3 \, b^{2} f h^{2} + 12 \, a c f h^{2} - 32 \, c^{2} g h e + 12 \, b c h^{2} e\right)} \log\left({\left| 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} + b \right|}\right)}{8 \, \sqrt{c} h^{6}}"," ",0,"1/4*sqrt(c*x^2 + b*x + a)*(2*c*f*x/h^4 - (16*c^2*f*g*h^10 - 5*b*c*f*h^11 - 4*c^2*h^11*e)/(c*h^15)) - 1/8*(160*c^3*f*g^5 - 336*b*c^2*f*g^4*h + 16*c^3*d*g^3*h^2 + 210*b^2*c*f*g^3*h^2 + 264*a*c^2*f*g^3*h^2 - 24*b*c^2*d*g^2*h^3 - 35*b^3*f*g^2*h^3 - 300*a*b*c*f*g^2*h^3 + 6*b^2*c*d*g*h^4 + 24*a*c^2*d*g*h^4 + 60*a*b^2*f*g*h^4 + 96*a^2*c*f*g*h^4 + b^3*d*h^5 - 12*a*b*c*d*h^5 - 24*a^2*b*f*h^5 - 64*c^3*g^4*h*e + 120*b*c^2*g^3*h^2*e - 60*b^2*c*g^2*h^3*e - 96*a*c^2*g^2*h^3*e + 5*b^3*g*h^4*e + 84*a*b*c*g*h^4*e - 6*a*b^2*h^5*e - 24*a^2*c*h^5*e)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + b*x + a))*h + sqrt(c)*g)/sqrt(-c*g^2 + b*g*h - a*h^2))/((c*g^2*h^6 - b*g*h^7 + a*h^8)*sqrt(-c*g^2 + b*g*h - a*h^2)) - 1/24*(480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*c^(7/2)*f*g^5*h^2 - 912*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b*c^(5/2)*f*g^4*h^3 + 144*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*c^(7/2)*d*g^3*h^4 + 522*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^2*c^(3/2)*f*g^3*h^4 + 552*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*c^(5/2)*f*g^3*h^4 - 216*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b*c^(5/2)*d*g^2*h^5 - 87*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^3*sqrt(c)*f*g^2*h^5 - 540*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b*c^(3/2)*f*g^2*h^5 + 78*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^2*c^(3/2)*d*g*h^6 + 120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*c^(5/2)*d*g*h^6 + 108*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b^2*sqrt(c)*f*g*h^6 + 96*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^2*c^(3/2)*f*g*h^6 - 3*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^3*sqrt(c)*d*h^7 - 60*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b*c^(3/2)*d*h^7 - 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^2*b*sqrt(c)*f*h^7 - 288*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*c^(7/2)*g^4*h^3*e + 504*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b*c^(5/2)*g^3*h^4*e - 252*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^2*c^(3/2)*g^2*h^5*e - 288*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*c^(5/2)*g^2*h^5*e + 33*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^3*sqrt(c)*g*h^6*e + 228*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b*c^(3/2)*g*h^6*e - 30*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b^2*sqrt(c)*h^7*e - 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^2*c^(3/2)*h^7*e + 1680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*c^4*f*g^6*h - 2880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b*c^3*f*g^5*h^2 + 432*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*c^4*d*g^4*h^3 + 1362*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^2*c^2*f*g^4*h^3 + 1464*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*c^3*f*g^4*h^3 - 504*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b*c^3*d*g^3*h^4 - 147*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^3*c*f*g^3*h^4 - 876*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b*c^2*f*g^3*h^4 + 54*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^2*c^2*d*g^2*h^5 + 216*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*c^3*d*g^2*h^5 - 36*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b^2*c*f*g^2*h^5 - 144*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^2*c^2*f*g^2*h^5 + 33*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^3*c*d*g*h^6 + 84*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b*c^2*d*g*h^6 + 216*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^2*b*c*f*g*h^6 - 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b^2*c*d*h^7 - 96*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^2*c^2*d*h^7 - 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^3*c*f*h^7 - 960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*c^4*g^5*h^2*e + 1464*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b*c^3*g^4*h^3*e - 540*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^2*c^2*g^3*h^4*e - 672*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*c^3*g^3*h^4*e + 21*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^3*c*g^2*h^5*e + 180*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b*c^2*g^2*h^5*e + 90*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b^2*c*g*h^6*e + 168*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^2*c^2*g*h^6*e - 96*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^2*b*c*h^7*e + 1504*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*c^(9/2)*f*g^7 - 1072*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b*c^(7/2)*f*g^6*h + 352*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*c^(9/2)*d*g^5*h^2 - 1308*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^2*c^(5/2)*f*g^5*h^2 - 656*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*c^(7/2)*f*g^5*h^2 - 16*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b*c^(7/2)*d*g^4*h^3 + 1042*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^3*c^(3/2)*f*g^4*h^3 + 4056*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b*c^(5/2)*f*g^4*h^3 - 420*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^2*c^(5/2)*d*g^3*h^4 - 272*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*c^(7/2)*d*g^3*h^4 - 136*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^4*sqrt(c)*f*g^3*h^4 - 2712*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^2*c^(3/2)*f*g^3*h^4 - 2208*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*c^(5/2)*f*g^3*h^4 + 106*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^3*c^(3/2)*d*g^2*h^5 + 840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b*c^(5/2)*d*g^2*h^5 + 328*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^3*sqrt(c)*f*g^2*h^5 + 1920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b*c^(3/2)*f*g^2*h^5 + 8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^4*sqrt(c)*d*g*h^6 - 144*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^2*c^(3/2)*d*g*h^6 - 384*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*c^(5/2)*d*g*h^6 - 240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b^2*sqrt(c)*f*g*h^6 - 288*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^3*c^(3/2)*f*g*h^6 - 8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^3*sqrt(c)*d*h^7 + 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^3*b*sqrt(c)*f*h^7 - 832*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*c^(9/2)*g^6*h*e + 400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b*c^(7/2)*g^5*h^2*e + 840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^2*c^(5/2)*g^4*h^3*e + 512*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*c^(7/2)*g^4*h^3*e - 478*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^3*c^(3/2)*g^3*h^4*e - 2232*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b*c^(5/2)*g^3*h^4*e + 40*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^4*sqrt(c)*g^2*h^5*e + 1092*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^2*c^(3/2)*g^2*h^5*e + 1104*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*c^(5/2)*g^2*h^5*e - 88*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^3*sqrt(c)*g*h^6*e - 576*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b*c^(3/2)*g*h^6*e + 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b^2*sqrt(c)*h^7*e + 2256*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b*c^4*f*g^7 - 3420*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^2*c^3*f*g^6*h - 2832*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*c^4*f*g^6*h + 528*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b*c^4*d*g^5*h^2 + 1218*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^3*c^2*f*g^5*h^2 + 5976*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b*c^3*f*g^5*h^2 - 516*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^2*c^3*d*g^4*h^3 - 624*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*c^4*d*g^4*h^3 - 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^4*c*f*g^4*h^3 - 1944*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^2*c^2*f*g^4*h^3 - 2208*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*c^3*f*g^4*h^3 - 6*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^3*c^2*d*g^3*h^4 + 840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b*c^3*d*g^3*h^4 - 264*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^3*c*f*g^3*h^4 + 192*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b*c^2*f*g^3*h^4 + 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^4*c*d*g^2*h^5 + 144*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^2*c^2*d*g^2*h^5 - 288*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*c^3*d*g^2*h^5 + 720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b^2*c*f*g^2*h^5 + 480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^3*c^2*f*g^2*h^5 - 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^3*c*d*g*h^6 - 288*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b*c^2*d*g*h^6 - 528*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^3*b*c*f*g*h^6 + 96*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^3*c^2*d*h^7 + 96*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^4*c*f*h^7 - 1248*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b*c^4*g^6*h*e + 1656*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^2*c^3*g^5*h^2*e + 1536*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*c^4*g^5*h^2*e - 414*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^3*c^2*g^4*h^3*e - 2760*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b*c^3*g^4*h^3*e - 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^4*c*g^3*h^4*e + 420*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^2*c^2*g^3*h^4*e + 912*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*c^3*g^3*h^4*e + 168*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^3*c*g^2*h^5*e + 432*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b*c^2*g^2*h^5*e - 288*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b^2*c*g*h^6*e - 384*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^3*c^2*g*h^6*e + 144*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^3*b*c*h^7*e + 1128*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^2*c^(7/2)*f*g^7 - 1776*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^3*c^(5/2)*f*g^6*h - 2832*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b*c^(7/2)*f*g^6*h + 264*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^2*c^(7/2)*d*g^5*h^2 + 720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^4*c^(3/2)*f*g^5*h^2 + 5580*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^2*c^(5/2)*f*g^5*h^2 + 1776*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*c^(7/2)*f*g^5*h^2 - 288*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^3*c^(5/2)*d*g^4*h^3 - 624*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b*c^(7/2)*d*g^4*h^3 - 57*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^5*sqrt(c)*f*g^4*h^3 - 2514*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^3*c^(3/2)*f*g^4*h^3 - 5688*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b*c^(5/2)*f*g^4*h^3 + 36*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^4*c^(3/2)*d*g^3*h^4 + 852*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^2*c^(5/2)*d*g^3*h^4 + 384*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*c^(7/2)*d*g^3*h^4 + 198*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^4*sqrt(c)*f*g^3*h^4 + 3078*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^2*c^(3/2)*f*g^3*h^4 + 1848*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*c^(5/2)*f*g^3*h^4 + 3*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^5*sqrt(c)*d*g^2*h^5 - 90*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^3*c^(3/2)*d*g^2*h^5 - 864*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b*c^(5/2)*d*g^2*h^5 - 249*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^3*sqrt(c)*f*g^2*h^5 - 1476*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*b*c^(3/2)*f*g^2*h^5 - 6*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^4*sqrt(c)*d*g*h^6 + 90*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^2*c^(3/2)*d*g*h^6 + 264*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*c^(5/2)*d*g*h^6 + 132*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*b^2*sqrt(c)*f*g*h^6 + 192*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^4*c^(3/2)*f*g*h^6 + 3*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^3*sqrt(c)*d*h^7 - 36*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*b*c^(3/2)*d*h^7 - 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^4*b*sqrt(c)*f*h^7 - 624*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^2*c^(7/2)*g^6*h*e + 876*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^3*c^(5/2)*g^5*h^2*e + 1536*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b*c^(7/2)*g^5*h^2*e - 282*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^4*c^(3/2)*g^4*h^3*e - 2664*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^2*c^(5/2)*g^4*h^3*e - 960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*c^(7/2)*g^4*h^3*e + 15*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^5*sqrt(c)*g^3*h^4*e + 894*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^3*c^(3/2)*g^3*h^4*e + 2640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b*c^(5/2)*g^3*h^4*e - 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^4*sqrt(c)*g^2*h^5*e - 936*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^2*c^(3/2)*g^2*h^5*e - 816*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*c^(5/2)*g^2*h^5*e + 51*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^3*sqrt(c)*g*h^6*e + 300*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*b*c^(3/2)*g*h^6*e - 18*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*b^2*sqrt(c)*h^7*e + 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^4*c^(3/2)*h^7*e + 188*b^3*c^3*f*g^7 - 272*b^4*c^2*f*g^6*h - 708*a*b^2*c^3*f*g^6*h + 44*b^3*c^3*d*g^5*h^2 + 87*b^5*c*f*g^5*h^2 + 1214*a*b^3*c^2*f*g^5*h^2 + 888*a^2*b*c^3*f*g^5*h^2 - 44*b^4*c^2*d*g^4*h^3 - 156*a*b^2*c^3*d*g^4*h^3 - 426*a*b^4*c*f*g^4*h^3 - 2010*a^2*b^2*c^2*f*g^4*h^3 - 376*a^3*c^3*f*g^4*h^3 + 3*b^5*c*d*g^3*h^4 + 182*a*b^3*c^2*d*g^3*h^4 + 192*a^2*b*c^3*d*g^3*h^4 + 807*a^2*b^3*c*f*g^3*h^4 + 1468*a^3*b*c^2*f*g^3*h^4 - 6*a*b^4*c*d*g^2*h^5 - 294*a^2*b^2*c^2*d*g^2*h^5 - 88*a^3*c^3*d*g^2*h^5 - 732*a^3*b^2*c*f*g^2*h^5 - 400*a^4*c^2*f*g^2*h^5 + 3*a^2*b^3*c*d*g*h^6 + 220*a^3*b*c^2*d*g*h^6 + 312*a^4*b*c*f*g*h^6 - 64*a^4*c^2*d*h^7 - 48*a^5*c*f*h^7 - 104*b^3*c^3*g^6*h*e + 134*b^4*c^2*g^5*h^2*e + 384*a*b^2*c^3*g^5*h^2*e - 33*b^5*c*g^4*h^3*e - 578*a*b^3*c^2*g^4*h^3*e - 480*a^2*b*c^3*g^4*h^3*e + 144*a*b^4*c*g^3*h^4*e + 936*a^2*b^2*c^2*g^3*h^4*e + 208*a^3*c^3*g^3*h^4*e - 237*a^2*b^3*c*g^2*h^5*e - 676*a^3*b*c^2*g^2*h^5*e + 174*a^3*b^2*c*g*h^6*e + 184*a^4*c^2*g*h^6*e - 48*a^4*b*c*h^7*e)/((c^(3/2)*g^2*h^6 - b*sqrt(c)*g*h^7 + a*sqrt(c)*h^8)*((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*h + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c)*g + b*g - a*h)^3) - 1/8*(80*c^2*f*g^2 - 48*b*c*f*g*h + 8*c^2*d*h^2 + 3*b^2*f*h^2 + 12*a*c*f*h^2 - 32*c^2*g*h*e + 12*b*c*h^2*e)*log(abs(2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) + b))/(sqrt(c)*h^6)","B",0
204,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)*(f*x^2+e*x+d)/(h*x+g)^5,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
205,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)*(f*x^2+e*x+d)/(h*x+g)^6,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
206,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)*(f*x^2+e*x+d)/(h*x+g)^7,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
207,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)*(f*x^2+e*x+d)/(h*x+g)^8,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
208,1,78,0,0.262707," ","integrate((1+2*x)^3*(4*x^2+3*x+1)*(3*x^2-x+2)^(1/2),x, algorithm=""giac"")","\frac{1}{544320} \, {\left(2 \, {\left(12 \, {\left(6 \, {\left(8 \, {\left(30 \, {\left(72 \, x + 187\right)} x + 6503\right)} x + 38179\right)} x + 136703\right)} x + 746947\right)} x - 543069\right)} \sqrt{3 \, x^{2} - x + 2} + \frac{124039}{93312} \, \sqrt{3} \log\left(-2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} - x + 2}\right)} + 1\right)"," ",0,"1/544320*(2*(12*(6*(8*(30*(72*x + 187)*x + 6503)*x + 38179)*x + 136703)*x + 746947)*x - 543069)*sqrt(3*x^2 - x + 2) + 124039/93312*sqrt(3)*log(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 - x + 2)) + 1)","A",0
209,1,73,0,0.303401," ","integrate((1+2*x)^2*(4*x^2+3*x+1)*(3*x^2-x+2)^(1/2),x, algorithm=""giac"")","\frac{1}{6480} \, {\left(2 \, {\left(12 \, {\left(6 \, {\left(8 \, {\left(15 \, x + 31\right)} x + 233\right)} x + 931\right)} x + 7319\right)} x + 5607\right)} \sqrt{3 \, x^{2} - x + 2} + \frac{5405}{7776} \, \sqrt{3} \log\left(-2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} - x + 2}\right)} + 1\right)"," ",0,"1/6480*(2*(12*(6*(8*(15*x + 31)*x + 233)*x + 931)*x + 7319)*x + 5607)*sqrt(3*x^2 - x + 2) + 5405/7776*sqrt(3)*log(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 - x + 2)) + 1)","A",0
210,1,68,0,0.262866," ","integrate((1+2*x)*(4*x^2+3*x+1)*(3*x^2-x+2)^(1/2),x, algorithm=""giac"")","\frac{1}{12960} \, {\left(2 \, {\left(12 \, {\left(18 \, {\left(48 \, x + 73\right)} x + 1003\right)} x + 8687\right)} x + 15471\right)} \sqrt{3 \, x^{2} - x + 2} + \frac{437}{15552} \, \sqrt{3} \log\left(-2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} - x + 2}\right)} + 1\right)"," ",0,"1/12960*(2*(12*(18*(48*x + 73)*x + 1003)*x + 8687)*x + 15471)*sqrt(3*x^2 - x + 2) + 437/15552*sqrt(3)*log(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 - x + 2)) + 1)","A",0
211,1,126,0,0.394351," ","integrate((4*x^2+3*x+1)*(3*x^2-x+2)^(1/2)/(1+2*x),x, algorithm=""giac"")","\frac{1}{72} \, {\left(2 \, {\left(24 \, x + 7\right)} x + 45\right)} \sqrt{3 \, x^{2} - x + 2} - \frac{43}{432} \, \sqrt{3} \log\left(-6 \, \sqrt{3} x + \sqrt{3} + 6 \, \sqrt{3 \, x^{2} - x + 2}\right) + \frac{1}{8} \, \sqrt{13} \log\left(-\frac{{\left| -4 \, \sqrt{3} x - 2 \, \sqrt{13} - 2 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} - x + 2} \right|}}{2 \, {\left(2 \, \sqrt{3} x - \sqrt{13} + \sqrt{3} - 2 \, \sqrt{3 \, x^{2} - x + 2}\right)}}\right)"," ",0,"1/72*(2*(24*x + 7)*x + 45)*sqrt(3*x^2 - x + 2) - 43/432*sqrt(3)*log(-6*sqrt(3)*x + sqrt(3) + 6*sqrt(3*x^2 - x + 2)) + 1/8*sqrt(13)*log(-1/2*abs(-4*sqrt(3)*x - 2*sqrt(13) - 2*sqrt(3) + 4*sqrt(3*x^2 - x + 2))/(2*sqrt(3)*x - sqrt(13) + sqrt(3) - 2*sqrt(3*x^2 - x + 2)))","A",0
212,1,380,0,0.718620," ","integrate((4*x^2+3*x+1)*(3*x^2-x+2)^(1/2)/(1+2*x)^2,x, algorithm=""giac"")","\frac{17}{104} \, \sqrt{13} \log\left(\sqrt{13} {\left(\sqrt{-\frac{8}{2 \, x + 1} + \frac{13}{{\left(2 \, x + 1\right)}^{2}} + 3} + \frac{\sqrt{13}}{2 \, x + 1}\right)} - 4\right) \mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right) - \frac{11}{18} \, \sqrt{3} \log\left(\frac{{\left| -2 \, \sqrt{3} + 2 \, \sqrt{-\frac{8}{2 \, x + 1} + \frac{13}{{\left(2 \, x + 1\right)}^{2}} + 3} + \frac{2 \, \sqrt{13}}{2 \, x + 1} \right|}}{2 \, {\left(\sqrt{3} + \sqrt{-\frac{8}{2 \, x + 1} + \frac{13}{{\left(2 \, x + 1\right)}^{2}} + 3} + \frac{\sqrt{13}}{2 \, x + 1}\right)}}\right) \mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right) - \frac{1}{8} \, \sqrt{-\frac{8}{2 \, x + 1} + \frac{13}{{\left(2 \, x + 1\right)}^{2}} + 3} \mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right) + \frac{67 \, {\left(\sqrt{-\frac{8}{2 \, x + 1} + \frac{13}{{\left(2 \, x + 1\right)}^{2}} + 3} + \frac{\sqrt{13}}{2 \, x + 1}\right)}^{3} \mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right) - 57 \, \sqrt{13} {\left(\sqrt{-\frac{8}{2 \, x + 1} + \frac{13}{{\left(2 \, x + 1\right)}^{2}} + 3} + \frac{\sqrt{13}}{2 \, x + 1}\right)}^{2} \mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right) + 129 \, {\left(\sqrt{-\frac{8}{2 \, x + 1} + \frac{13}{{\left(2 \, x + 1\right)}^{2}} + 3} + \frac{\sqrt{13}}{2 \, x + 1}\right)} \mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right) + 27 \, \sqrt{13} \mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right)}{12 \, {\left({\left(\sqrt{-\frac{8}{2 \, x + 1} + \frac{13}{{\left(2 \, x + 1\right)}^{2}} + 3} + \frac{\sqrt{13}}{2 \, x + 1}\right)}^{2} - 3\right)}^{2}}"," ",0,"17/104*sqrt(13)*log(sqrt(13)*(sqrt(-8/(2*x + 1) + 13/(2*x + 1)^2 + 3) + sqrt(13)/(2*x + 1)) - 4)*sgn(1/(2*x + 1)) - 11/18*sqrt(3)*log(1/2*abs(-2*sqrt(3) + 2*sqrt(-8/(2*x + 1) + 13/(2*x + 1)^2 + 3) + 2*sqrt(13)/(2*x + 1))/(sqrt(3) + sqrt(-8/(2*x + 1) + 13/(2*x + 1)^2 + 3) + sqrt(13)/(2*x + 1)))*sgn(1/(2*x + 1)) - 1/8*sqrt(-8/(2*x + 1) + 13/(2*x + 1)^2 + 3)*sgn(1/(2*x + 1)) + 1/12*(67*(sqrt(-8/(2*x + 1) + 13/(2*x + 1)^2 + 3) + sqrt(13)/(2*x + 1))^3*sgn(1/(2*x + 1)) - 57*sqrt(13)*(sqrt(-8/(2*x + 1) + 13/(2*x + 1)^2 + 3) + sqrt(13)/(2*x + 1))^2*sgn(1/(2*x + 1)) + 129*(sqrt(-8/(2*x + 1) + 13/(2*x + 1)^2 + 3) + sqrt(13)/(2*x + 1))*sgn(1/(2*x + 1)) + 27*sqrt(13)*sgn(1/(2*x + 1)))/((sqrt(-8/(2*x + 1) + 13/(2*x + 1)^2 + 3) + sqrt(13)/(2*x + 1))^2 - 3)^2","B",0
213,-2,0,0,0.000000," ","integrate((4*x^2+3*x+1)*(3*x^2-x+2)^(1/2)/(1+2*x)^3,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{-389344,[6]%%%}+%%%{%%{[1168032,0]:[1,0,-3]%%},[5]%%%}+%%%{-584016,[4]%%%}+%%%{%%{[-4672128,0]:[1,0,-3]%%},[3]%%%}+%%%{1460040,[2]%%%}+%%%{%%{[7300200,0]:[1,0,-3]%%},[1]%%%}+%%%{6083500,[0]%%%} / %%%{%%{[24,0]:[1,0,-3]%%},[6]%%%}+%%%{-216,[5]%%%}+%%%{%%{[36,0]:[1,0,-3]%%},[4]%%%}+%%%{864,[3]%%%}+%%%{%%{[-90,0]:[1,0,-3]%%},[2]%%%}+%%%{-1350,[1]%%%}+%%%{%%{[-375,0]:[1,0,-3]%%},[0]%%%} Error: Bad Argument Value","F(-2)",0
214,1,88,0,0.259356," ","integrate((1+2*x)^3*(3*x^2-x+2)^(3/2)*(4*x^2+3*x+1),x, algorithm=""giac"")","\frac{1}{22394880} \, {\left(2 \, {\left(12 \, {\left(6 \, {\left(8 \, {\left(30 \, {\left(36 \, {\left(2 \, {\left(96 \, x + 205\right)} x + 511\right)} x + 20579\right)} x + 563761\right)} x + 2927963\right)} x + 8387071\right)} x + 42007139\right)} x + 12499587\right)} \sqrt{3 \, x^{2} - x + 2} + \frac{28879697}{26873856} \, \sqrt{3} \log\left(-2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} - x + 2}\right)} + 1\right)"," ",0,"1/22394880*(2*(12*(6*(8*(30*(36*(2*(96*x + 205)*x + 511)*x + 20579)*x + 563761)*x + 2927963)*x + 8387071)*x + 42007139)*x + 12499587)*sqrt(3*x^2 - x + 2) + 28879697/26873856*sqrt(3)*log(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 - x + 2)) + 1)","A",0
215,1,83,0,0.269804," ","integrate((1+2*x)^2*(3*x^2-x+2)^(3/2)*(4*x^2+3*x+1),x, algorithm=""giac"")","\frac{1}{967680} \, {\left(2 \, {\left(12 \, {\left(2 \, {\left(8 \, {\left(30 \, {\left(12 \, {\left(42 \, x + 67\right)} x + 925\right)} x + 31703\right)} x + 210829\right)} x + 237251\right)} x + 1367959\right)} x + 1517367\right)} \sqrt{3 \, x^{2} - x + 2} + \frac{48139}{165888} \, \sqrt{3} \log\left(-2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} - x + 2}\right)} + 1\right)"," ",0,"1/967680*(2*(12*(2*(8*(30*(12*(42*x + 67)*x + 925)*x + 31703)*x + 210829)*x + 237251)*x + 1367959)*x + 1517367)*sqrt(3*x^2 - x + 2) + 48139/165888*sqrt(3)*log(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 - x + 2)) + 1)","A",0
216,1,78,0,0.210856," ","integrate((1+2*x)*(3*x^2-x+2)^(3/2)*(4*x^2+3*x+1),x, algorithm=""giac"")","\frac{1}{145152} \, {\left(2 \, {\left(12 \, {\left(18 \, {\left(24 \, {\left(2 \, {\left(24 \, x + 25\right)} x + 63\right)} x + 1723\right)} x + 22141\right)} x + 137705\right)} x + 203337\right)} \sqrt{3 \, x^{2} - x + 2} - \frac{37559}{124416} \, \sqrt{3} \log\left(-2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} - x + 2}\right)} + 1\right)"," ",0,"1/145152*(2*(12*(18*(24*(2*(24*x + 25)*x + 63)*x + 1723)*x + 22141)*x + 137705)*x + 203337)*sqrt(3*x^2 - x + 2) - 37559/124416*sqrt(3)*log(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 - x + 2)) + 1)","A",0
217,1,136,0,0.283043," ","integrate((3*x^2-x+2)^(3/2)*(4*x^2+3*x+1)/(1+2*x),x, algorithm=""giac"")","\frac{1}{5760} \, {\left(2 \, {\left(12 \, {\left(6 \, {\left(48 \, x - 7\right)} x + 401\right)} x + 529\right)} x + 7977\right)} \sqrt{3 \, x^{2} - x + 2} + \frac{2203}{6912} \, \sqrt{3} \log\left(-6 \, \sqrt{3} x + \sqrt{3} + 6 \, \sqrt{3 \, x^{2} - x + 2}\right) + \frac{13}{32} \, \sqrt{13} \log\left(-\frac{{\left| -4 \, \sqrt{3} x - 2 \, \sqrt{13} - 2 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} - x + 2} \right|}}{2 \, {\left(2 \, \sqrt{3} x - \sqrt{13} + \sqrt{3} - 2 \, \sqrt{3 \, x^{2} - x + 2}\right)}}\right)"," ",0,"1/5760*(2*(12*(6*(48*x - 7)*x + 401)*x + 529)*x + 7977)*sqrt(3*x^2 - x + 2) + 2203/6912*sqrt(3)*log(-6*sqrt(3)*x + sqrt(3) + 6*sqrt(3*x^2 - x + 2)) + 13/32*sqrt(13)*log(-1/2*abs(-4*sqrt(3)*x - 2*sqrt(13) - 2*sqrt(3) + 4*sqrt(3*x^2 - x + 2))/(2*sqrt(3)*x - sqrt(13) + sqrt(3) - 2*sqrt(3*x^2 - x + 2)))","A",0
218,1,570,0,0.841154," ","integrate((3*x^2-x+2)^(3/2)*(4*x^2+3*x+1)/(1+2*x)^2,x, algorithm=""giac"")","\frac{25}{32} \, \sqrt{13} \log\left(\sqrt{13} {\left(\sqrt{-\frac{8}{2 \, x + 1} + \frac{13}{{\left(2 \, x + 1\right)}^{2}} + 3} + \frac{\sqrt{13}}{2 \, x + 1}\right)} - 4\right) \mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right) - \frac{2327}{1152} \, \sqrt{3} \log\left(\frac{{\left| -2 \, \sqrt{3} + 2 \, \sqrt{-\frac{8}{2 \, x + 1} + \frac{13}{{\left(2 \, x + 1\right)}^{2}} + 3} + \frac{2 \, \sqrt{13}}{2 \, x + 1} \right|}}{2 \, {\left(\sqrt{3} + \sqrt{-\frac{8}{2 \, x + 1} + \frac{13}{{\left(2 \, x + 1\right)}^{2}} + 3} + \frac{\sqrt{13}}{2 \, x + 1}\right)}}\right) \mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right) - \frac{13}{32} \, \sqrt{-\frac{8}{2 \, x + 1} + \frac{13}{{\left(2 \, x + 1\right)}^{2}} + 3} \mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right) + \frac{5929 \, {\left(\sqrt{-\frac{8}{2 \, x + 1} + \frac{13}{{\left(2 \, x + 1\right)}^{2}} + 3} + \frac{\sqrt{13}}{2 \, x + 1}\right)}^{7} \mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right) - 7272 \, \sqrt{13} {\left(\sqrt{-\frac{8}{2 \, x + 1} + \frac{13}{{\left(2 \, x + 1\right)}^{2}} + 3} + \frac{\sqrt{13}}{2 \, x + 1}\right)}^{6} \mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right) + 25101 \, {\left(\sqrt{-\frac{8}{2 \, x + 1} + \frac{13}{{\left(2 \, x + 1\right)}^{2}} + 3} + \frac{\sqrt{13}}{2 \, x + 1}\right)}^{5} \mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right) - 48 \, \sqrt{13} {\left(\sqrt{-\frac{8}{2 \, x + 1} + \frac{13}{{\left(2 \, x + 1\right)}^{2}} + 3} + \frac{\sqrt{13}}{2 \, x + 1}\right)}^{4} \mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right) + 112359 \, {\left(\sqrt{-\frac{8}{2 \, x + 1} + \frac{13}{{\left(2 \, x + 1\right)}^{2}} + 3} + \frac{\sqrt{13}}{2 \, x + 1}\right)}^{3} \mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right) - 69336 \, \sqrt{13} {\left(\sqrt{-\frac{8}{2 \, x + 1} + \frac{13}{{\left(2 \, x + 1\right)}^{2}} + 3} + \frac{\sqrt{13}}{2 \, x + 1}\right)}^{2} \mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right) + 71955 \, {\left(\sqrt{-\frac{8}{2 \, x + 1} + \frac{13}{{\left(2 \, x + 1\right)}^{2}} + 3} + \frac{\sqrt{13}}{2 \, x + 1}\right)} \mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right) + 24624 \, \sqrt{13} \mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right)}{192 \, {\left({\left(\sqrt{-\frac{8}{2 \, x + 1} + \frac{13}{{\left(2 \, x + 1\right)}^{2}} + 3} + \frac{\sqrt{13}}{2 \, x + 1}\right)}^{2} - 3\right)}^{4}}"," ",0,"25/32*sqrt(13)*log(sqrt(13)*(sqrt(-8/(2*x + 1) + 13/(2*x + 1)^2 + 3) + sqrt(13)/(2*x + 1)) - 4)*sgn(1/(2*x + 1)) - 2327/1152*sqrt(3)*log(1/2*abs(-2*sqrt(3) + 2*sqrt(-8/(2*x + 1) + 13/(2*x + 1)^2 + 3) + 2*sqrt(13)/(2*x + 1))/(sqrt(3) + sqrt(-8/(2*x + 1) + 13/(2*x + 1)^2 + 3) + sqrt(13)/(2*x + 1)))*sgn(1/(2*x + 1)) - 13/32*sqrt(-8/(2*x + 1) + 13/(2*x + 1)^2 + 3)*sgn(1/(2*x + 1)) + 1/192*(5929*(sqrt(-8/(2*x + 1) + 13/(2*x + 1)^2 + 3) + sqrt(13)/(2*x + 1))^7*sgn(1/(2*x + 1)) - 7272*sqrt(13)*(sqrt(-8/(2*x + 1) + 13/(2*x + 1)^2 + 3) + sqrt(13)/(2*x + 1))^6*sgn(1/(2*x + 1)) + 25101*(sqrt(-8/(2*x + 1) + 13/(2*x + 1)^2 + 3) + sqrt(13)/(2*x + 1))^5*sgn(1/(2*x + 1)) - 48*sqrt(13)*(sqrt(-8/(2*x + 1) + 13/(2*x + 1)^2 + 3) + sqrt(13)/(2*x + 1))^4*sgn(1/(2*x + 1)) + 112359*(sqrt(-8/(2*x + 1) + 13/(2*x + 1)^2 + 3) + sqrt(13)/(2*x + 1))^3*sgn(1/(2*x + 1)) - 69336*sqrt(13)*(sqrt(-8/(2*x + 1) + 13/(2*x + 1)^2 + 3) + sqrt(13)/(2*x + 1))^2*sgn(1/(2*x + 1)) + 71955*(sqrt(-8/(2*x + 1) + 13/(2*x + 1)^2 + 3) + sqrt(13)/(2*x + 1))*sgn(1/(2*x + 1)) + 24624*sqrt(13)*sgn(1/(2*x + 1)))/((sqrt(-8/(2*x + 1) + 13/(2*x + 1)^2 + 3) + sqrt(13)/(2*x + 1))^2 - 3)^4","B",0
219,-2,0,0,0.000000," ","integrate((3*x^2-x+2)^(3/2)*(4*x^2+3*x+1)/(1+2*x)^3,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{-18688512,[6]%%%}+%%%{%%{[56065536,0]:[1,0,-3]%%},[5]%%%}+%%%{-28032768,[4]%%%}+%%%{%%{[-224262144,0]:[1,0,-3]%%},[3]%%%}+%%%{70081920,[2]%%%}+%%%{%%{[350409600,0]:[1,0,-3]%%},[1]%%%}+%%%{292008000,[0]%%%} / %%%{%%{[24,0]:[1,0,-3]%%},[6]%%%}+%%%{-216,[5]%%%}+%%%{%%{[36,0]:[1,0,-3]%%},[4]%%%}+%%%{864,[3]%%%}+%%%{%%{[-90,0]:[1,0,-3]%%},[2]%%%}+%%%{-1350,[1]%%%}+%%%{%%{[-375,0]:[1,0,-3]%%},[0]%%%} Error: Bad Argument Value","F(-2)",0
220,1,98,0,0.201488," ","integrate((1+2*x)^3*(3*x^2-x+2)^(5/2)*(4*x^2+3*x+1),x, algorithm=""giac"")","\frac{1}{4598415360} \, {\left(2 \, {\left(12 \, {\left(6 \, {\left(8 \, {\left(6 \, {\left(36 \, {\left(14 \, {\left(48 \, {\left(18 \, {\left(40 \, x + 69\right)} x + 1847\right)} x + 120557\right)} x + 1671441\right)} x + 50238389\right)} x + 228850811\right)} x + 1119925033\right)} x + 3003691061\right)} x + 13323316609\right)} x + 9173509857\right)} \sqrt{3 \, x^{2} - x + 2} + \frac{61917863}{71663616} \, \sqrt{3} \log\left(-2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} - x + 2}\right)} + 1\right)"," ",0,"1/4598415360*(2*(12*(6*(8*(6*(36*(14*(48*(18*(40*x + 69)*x + 1847)*x + 120557)*x + 1671441)*x + 50238389)*x + 228850811)*x + 1119925033)*x + 3003691061)*x + 13323316609)*x + 9173509857)*sqrt(3*x^2 - x + 2) + 61917863/71663616*sqrt(3)*log(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 - x + 2)) + 1)","A",0
221,1,93,0,0.212165," ","integrate((1+2*x)^2*(3*x^2-x+2)^(5/2)*(4*x^2+3*x+1),x, algorithm=""giac"")","\frac{1}{156764160} \, {\left(2 \, {\left(12 \, {\left(6 \, {\left(8 \, {\left(6 \, {\left(36 \, {\left(14 \, {\left(24 \, {\left(27 \, x + 32\right)} x + 1271\right)} x + 22793\right)} x + 722917\right)} x + 3621163\right)} x + 21500729\right)} x + 70573573\right)} x + 346329617\right)} x + 387182961\right)} \sqrt{3 \, x^{2} - x + 2} - \frac{3564931}{26873856} \, \sqrt{3} \log\left(-2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} - x + 2}\right)} + 1\right)"," ",0,"1/156764160*(2*(12*(6*(8*(6*(36*(14*(24*(27*x + 32)*x + 1271)*x + 22793)*x + 722917)*x + 3621163)*x + 21500729)*x + 70573573)*x + 346329617)*x + 387182961)*sqrt(3*x^2 - x + 2) - 3564931/26873856*sqrt(3)*log(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 - x + 2)) + 1)","A",0
222,1,88,0,0.186947," ","integrate((1+2*x)*(3*x^2-x+2)^(5/2)*(4*x^2+3*x+1),x, algorithm=""giac"")","\frac{1}{5971968} \, {\left(2 \, {\left(12 \, {\left(6 \, {\left(8 \, {\left(6 \, {\left(36 \, {\left(2 \, {\left(96 \, x + 61\right)} x + 319\right)} x + 11579\right)} x + 58133\right)} x + 409351\right)} x + 1709627\right)} x + 9930031\right)} x + 10960335\right)} \sqrt{3 \, x^{2} - x + 2} - \frac{27071575}{35831808} \, \sqrt{3} \log\left(-2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} - x + 2}\right)} + 1\right)"," ",0,"1/5971968*(2*(12*(6*(8*(6*(36*(2*(96*x + 61)*x + 319)*x + 11579)*x + 58133)*x + 409351)*x + 1709627)*x + 9930031)*x + 10960335)*sqrt(3*x^2 - x + 2) - 27071575/35831808*sqrt(3)*log(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 - x + 2)) + 1)","A",0
223,1,146,0,0.307458," ","integrate((3*x^2-x+2)^(5/2)*(4*x^2+3*x+1)/(1+2*x),x, algorithm=""giac"")","\frac{1}{2903040} \, {\left(2 \, {\left(12 \, {\left(18 \, {\left(8 \, {\left(30 \, {\left(72 \, x - 37\right)} x + 4543\right)} x - 8441\right)} x + 519449\right)} x - 1060499\right)} x + 11665053\right)} \sqrt{3 \, x^{2} - x + 2} + \frac{944521}{497664} \, \sqrt{3} \log\left(-6 \, \sqrt{3} x + \sqrt{3} + 6 \, \sqrt{3 \, x^{2} - x + 2}\right) + \frac{169}{128} \, \sqrt{13} \log\left(-\frac{{\left| -4 \, \sqrt{3} x - 2 \, \sqrt{13} - 2 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} - x + 2} \right|}}{2 \, {\left(2 \, \sqrt{3} x - \sqrt{13} + \sqrt{3} - 2 \, \sqrt{3 \, x^{2} - x + 2}\right)}}\right)"," ",0,"1/2903040*(2*(12*(18*(8*(30*(72*x - 37)*x + 4543)*x - 8441)*x + 519449)*x - 1060499)*x + 11665053)*sqrt(3*x^2 - x + 2) + 944521/497664*sqrt(3)*log(-6*sqrt(3)*x + sqrt(3) + 6*sqrt(3*x^2 - x + 2)) + 169/128*sqrt(13)*log(-1/2*abs(-4*sqrt(3)*x - 2*sqrt(13) - 2*sqrt(3) + 4*sqrt(3*x^2 - x + 2))/(2*sqrt(3)*x - sqrt(13) + sqrt(3) - 2*sqrt(3*x^2 - x + 2)))","A",0
224,1,760,0,1.097341," ","integrate((3*x^2-x+2)^(5/2)*(4*x^2+3*x+1)/(1+2*x)^2,x, algorithm=""giac"")","\frac{429}{128} \, \sqrt{13} \log\left(\sqrt{13} {\left(\sqrt{-\frac{8}{2 \, x + 1} + \frac{13}{{\left(2 \, x + 1\right)}^{2}} + 3} + \frac{\sqrt{13}}{2 \, x + 1}\right)} - 4\right) \mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right) - \frac{315623}{41472} \, \sqrt{3} \log\left(\frac{{\left| -2 \, \sqrt{3} + 2 \, \sqrt{-\frac{8}{2 \, x + 1} + \frac{13}{{\left(2 \, x + 1\right)}^{2}} + 3} + \frac{2 \, \sqrt{13}}{2 \, x + 1} \right|}}{2 \, {\left(\sqrt{3} + \sqrt{-\frac{8}{2 \, x + 1} + \frac{13}{{\left(2 \, x + 1\right)}^{2}} + 3} + \frac{\sqrt{13}}{2 \, x + 1}\right)}}\right) \mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right) - \frac{169}{128} \, \sqrt{-\frac{8}{2 \, x + 1} + \frac{13}{{\left(2 \, x + 1\right)}^{2}} + 3} \mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right) + \frac{5154065 \, {\left(\sqrt{-\frac{8}{2 \, x + 1} + \frac{13}{{\left(2 \, x + 1\right)}^{2}} + 3} + \frac{\sqrt{13}}{2 \, x + 1}\right)}^{11} \mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right) - 7837020 \, \sqrt{13} {\left(\sqrt{-\frac{8}{2 \, x + 1} + \frac{13}{{\left(2 \, x + 1\right)}^{2}} + 3} + \frac{\sqrt{13}}{2 \, x + 1}\right)}^{10} \mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right) + 39468815 \, {\left(\sqrt{-\frac{8}{2 \, x + 1} + \frac{13}{{\left(2 \, x + 1\right)}^{2}} + 3} + \frac{\sqrt{13}}{2 \, x + 1}\right)}^{9} \mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right) - 14445540 \, \sqrt{13} {\left(\sqrt{-\frac{8}{2 \, x + 1} + \frac{13}{{\left(2 \, x + 1\right)}^{2}} + 3} + \frac{\sqrt{13}}{2 \, x + 1}\right)}^{8} \mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right) + 460893402 \, {\left(\sqrt{-\frac{8}{2 \, x + 1} + \frac{13}{{\left(2 \, x + 1\right)}^{2}} + 3} + \frac{\sqrt{13}}{2 \, x + 1}\right)}^{7} \mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right) - 343084680 \, \sqrt{13} {\left(\sqrt{-\frac{8}{2 \, x + 1} + \frac{13}{{\left(2 \, x + 1\right)}^{2}} + 3} + \frac{\sqrt{13}}{2 \, x + 1}\right)}^{6} \mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right) + 944150094 \, {\left(\sqrt{-\frac{8}{2 \, x + 1} + \frac{13}{{\left(2 \, x + 1\right)}^{2}} + 3} + \frac{\sqrt{13}}{2 \, x + 1}\right)}^{5} \mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right) - 22871160 \, \sqrt{13} {\left(\sqrt{-\frac{8}{2 \, x + 1} + \frac{13}{{\left(2 \, x + 1\right)}^{2}} + 3} + \frac{\sqrt{13}}{2 \, x + 1}\right)}^{4} \mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right) + 1397032245 \, {\left(\sqrt{-\frac{8}{2 \, x + 1} + \frac{13}{{\left(2 \, x + 1\right)}^{2}} + 3} + \frac{\sqrt{13}}{2 \, x + 1}\right)}^{3} \mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right) - 683367516 \, \sqrt{13} {\left(\sqrt{-\frac{8}{2 \, x + 1} + \frac{13}{{\left(2 \, x + 1\right)}^{2}} + 3} + \frac{\sqrt{13}}{2 \, x + 1}\right)}^{2} \mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right) + 392684355 \, {\left(\sqrt{-\frac{8}{2 \, x + 1} + \frac{13}{{\left(2 \, x + 1\right)}^{2}} + 3} + \frac{\sqrt{13}}{2 \, x + 1}\right)} \mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right) + 197538588 \, \sqrt{13} \mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right)}{34560 \, {\left({\left(\sqrt{-\frac{8}{2 \, x + 1} + \frac{13}{{\left(2 \, x + 1\right)}^{2}} + 3} + \frac{\sqrt{13}}{2 \, x + 1}\right)}^{2} - 3\right)}^{6}}"," ",0,"429/128*sqrt(13)*log(sqrt(13)*(sqrt(-8/(2*x + 1) + 13/(2*x + 1)^2 + 3) + sqrt(13)/(2*x + 1)) - 4)*sgn(1/(2*x + 1)) - 315623/41472*sqrt(3)*log(1/2*abs(-2*sqrt(3) + 2*sqrt(-8/(2*x + 1) + 13/(2*x + 1)^2 + 3) + 2*sqrt(13)/(2*x + 1))/(sqrt(3) + sqrt(-8/(2*x + 1) + 13/(2*x + 1)^2 + 3) + sqrt(13)/(2*x + 1)))*sgn(1/(2*x + 1)) - 169/128*sqrt(-8/(2*x + 1) + 13/(2*x + 1)^2 + 3)*sgn(1/(2*x + 1)) + 1/34560*(5154065*(sqrt(-8/(2*x + 1) + 13/(2*x + 1)^2 + 3) + sqrt(13)/(2*x + 1))^11*sgn(1/(2*x + 1)) - 7837020*sqrt(13)*(sqrt(-8/(2*x + 1) + 13/(2*x + 1)^2 + 3) + sqrt(13)/(2*x + 1))^10*sgn(1/(2*x + 1)) + 39468815*(sqrt(-8/(2*x + 1) + 13/(2*x + 1)^2 + 3) + sqrt(13)/(2*x + 1))^9*sgn(1/(2*x + 1)) - 14445540*sqrt(13)*(sqrt(-8/(2*x + 1) + 13/(2*x + 1)^2 + 3) + sqrt(13)/(2*x + 1))^8*sgn(1/(2*x + 1)) + 460893402*(sqrt(-8/(2*x + 1) + 13/(2*x + 1)^2 + 3) + sqrt(13)/(2*x + 1))^7*sgn(1/(2*x + 1)) - 343084680*sqrt(13)*(sqrt(-8/(2*x + 1) + 13/(2*x + 1)^2 + 3) + sqrt(13)/(2*x + 1))^6*sgn(1/(2*x + 1)) + 944150094*(sqrt(-8/(2*x + 1) + 13/(2*x + 1)^2 + 3) + sqrt(13)/(2*x + 1))^5*sgn(1/(2*x + 1)) - 22871160*sqrt(13)*(sqrt(-8/(2*x + 1) + 13/(2*x + 1)^2 + 3) + sqrt(13)/(2*x + 1))^4*sgn(1/(2*x + 1)) + 1397032245*(sqrt(-8/(2*x + 1) + 13/(2*x + 1)^2 + 3) + sqrt(13)/(2*x + 1))^3*sgn(1/(2*x + 1)) - 683367516*sqrt(13)*(sqrt(-8/(2*x + 1) + 13/(2*x + 1)^2 + 3) + sqrt(13)/(2*x + 1))^2*sgn(1/(2*x + 1)) + 392684355*(sqrt(-8/(2*x + 1) + 13/(2*x + 1)^2 + 3) + sqrt(13)/(2*x + 1))*sgn(1/(2*x + 1)) + 197538588*sqrt(13)*sgn(1/(2*x + 1)))/((sqrt(-8/(2*x + 1) + 13/(2*x + 1)^2 + 3) + sqrt(13)/(2*x + 1))^2 - 3)^6","B",0
225,-2,0,0,0.000000," ","integrate((3*x^2-x+2)^(5/2)*(4*x^2+3*x+1)/(1+2*x)^3,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{-299016192,[6]%%%}+%%%{%%{[897048576,0]:[1,0,-3]%%},[5]%%%}+%%%{-448524288,[4]%%%}+%%%{%%{[-3588194304,0]:[1,0,-3]%%},[3]%%%}+%%%{1121310720,[2]%%%}+%%%{%%{[5606553600,0]:[1,0,-3]%%},[1]%%%}+%%%{4672128000,[0]%%%} / %%%{%%{[24,0]:[1,0,-3]%%},[6]%%%}+%%%{-216,[5]%%%}+%%%{%%{[36,0]:[1,0,-3]%%},[4]%%%}+%%%{864,[3]%%%}+%%%{%%{[-90,0]:[1,0,-3]%%},[2]%%%}+%%%{-1350,[1]%%%}+%%%{%%{[-375,0]:[1,0,-3]%%},[0]%%%} Error: Bad Argument Value","F(-2)",0
226,1,822,0,0.322861," ","integrate((h*x+g)^3*(f*x^2+e*x+d)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{1}{1920} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(6 \, {\left(\frac{8 \, f h^{3} x}{c} + \frac{30 \, c^{4} f g h^{2} - 9 \, b c^{3} f h^{3} + 10 \, c^{4} h^{3} e}{c^{5}}\right)} x + \frac{240 \, c^{4} f g^{2} h - 210 \, b c^{3} f g h^{2} + 80 \, c^{4} d h^{3} + 63 \, b^{2} c^{2} f h^{3} - 64 \, a c^{3} f h^{3} + 240 \, c^{4} g h^{2} e - 70 \, b c^{3} h^{3} e}{c^{5}}\right)} x + \frac{480 \, c^{4} f g^{3} - 1200 \, b c^{3} f g^{2} h + 1440 \, c^{4} d g h^{2} + 1050 \, b^{2} c^{2} f g h^{2} - 1080 \, a c^{3} f g h^{2} - 400 \, b c^{3} d h^{3} - 315 \, b^{3} c f h^{3} + 644 \, a b c^{2} f h^{3} + 1440 \, c^{4} g^{2} h e - 1200 \, b c^{3} g h^{2} e + 350 \, b^{2} c^{2} h^{3} e - 360 \, a c^{3} h^{3} e}{c^{5}}\right)} x - \frac{1440 \, b c^{3} f g^{3} - 5760 \, c^{4} d g^{2} h - 3600 \, b^{2} c^{2} f g^{2} h + 3840 \, a c^{3} f g^{2} h + 4320 \, b c^{3} d g h^{2} + 3150 \, b^{3} c f g h^{2} - 6600 \, a b c^{2} f g h^{2} - 1200 \, b^{2} c^{2} d h^{3} + 1280 \, a c^{3} d h^{3} - 945 \, b^{4} f h^{3} + 2940 \, a b^{2} c f h^{3} - 1024 \, a^{2} c^{2} f h^{3} - 1920 \, c^{4} g^{3} e + 4320 \, b c^{3} g^{2} h e - 3600 \, b^{2} c^{2} g h^{2} e + 3840 \, a c^{3} g h^{2} e + 1050 \, b^{3} c h^{3} e - 2200 \, a b c^{2} h^{3} e}{c^{5}}\right)} - \frac{{\left(256 \, c^{5} d g^{3} + 96 \, b^{2} c^{3} f g^{3} - 128 \, a c^{4} f g^{3} - 384 \, b c^{4} d g^{2} h - 240 \, b^{3} c^{2} f g^{2} h + 576 \, a b c^{3} f g^{2} h + 288 \, b^{2} c^{3} d g h^{2} - 384 \, a c^{4} d g h^{2} + 210 \, b^{4} c f g h^{2} - 720 \, a b^{2} c^{2} f g h^{2} + 288 \, a^{2} c^{3} f g h^{2} - 80 \, b^{3} c^{2} d h^{3} + 192 \, a b c^{3} d h^{3} - 63 \, b^{5} f h^{3} + 280 \, a b^{3} c f h^{3} - 240 \, a^{2} b c^{2} f h^{3} - 128 \, b c^{4} g^{3} e + 288 \, b^{2} c^{3} g^{2} h e - 384 \, a c^{4} g^{2} h e - 240 \, b^{3} c^{2} g h^{2} e + 576 \, a b c^{3} g h^{2} e + 70 \, b^{4} c h^{3} e - 240 \, a b^{2} c^{2} h^{3} e + 96 \, a^{2} c^{3} h^{3} e\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{256 \, c^{\frac{11}{2}}}"," ",0,"1/1920*sqrt(c*x^2 + b*x + a)*(2*(4*(6*(8*f*h^3*x/c + (30*c^4*f*g*h^2 - 9*b*c^3*f*h^3 + 10*c^4*h^3*e)/c^5)*x + (240*c^4*f*g^2*h - 210*b*c^3*f*g*h^2 + 80*c^4*d*h^3 + 63*b^2*c^2*f*h^3 - 64*a*c^3*f*h^3 + 240*c^4*g*h^2*e - 70*b*c^3*h^3*e)/c^5)*x + (480*c^4*f*g^3 - 1200*b*c^3*f*g^2*h + 1440*c^4*d*g*h^2 + 1050*b^2*c^2*f*g*h^2 - 1080*a*c^3*f*g*h^2 - 400*b*c^3*d*h^3 - 315*b^3*c*f*h^3 + 644*a*b*c^2*f*h^3 + 1440*c^4*g^2*h*e - 1200*b*c^3*g*h^2*e + 350*b^2*c^2*h^3*e - 360*a*c^3*h^3*e)/c^5)*x - (1440*b*c^3*f*g^3 - 5760*c^4*d*g^2*h - 3600*b^2*c^2*f*g^2*h + 3840*a*c^3*f*g^2*h + 4320*b*c^3*d*g*h^2 + 3150*b^3*c*f*g*h^2 - 6600*a*b*c^2*f*g*h^2 - 1200*b^2*c^2*d*h^3 + 1280*a*c^3*d*h^3 - 945*b^4*f*h^3 + 2940*a*b^2*c*f*h^3 - 1024*a^2*c^2*f*h^3 - 1920*c^4*g^3*e + 4320*b*c^3*g^2*h*e - 3600*b^2*c^2*g*h^2*e + 3840*a*c^3*g*h^2*e + 1050*b^3*c*h^3*e - 2200*a*b*c^2*h^3*e)/c^5) - 1/256*(256*c^5*d*g^3 + 96*b^2*c^3*f*g^3 - 128*a*c^4*f*g^3 - 384*b*c^4*d*g^2*h - 240*b^3*c^2*f*g^2*h + 576*a*b*c^3*f*g^2*h + 288*b^2*c^3*d*g*h^2 - 384*a*c^4*d*g*h^2 + 210*b^4*c*f*g*h^2 - 720*a*b^2*c^2*f*g*h^2 + 288*a^2*c^3*f*g*h^2 - 80*b^3*c^2*d*h^3 + 192*a*b*c^3*d*h^3 - 63*b^5*f*h^3 + 280*a*b^3*c*f*h^3 - 240*a^2*b*c^2*f*h^3 - 128*b*c^4*g^3*e + 288*b^2*c^3*g^2*h*e - 384*a*c^4*g^2*h*e - 240*b^3*c^2*g*h^2*e + 576*a*b*c^3*g*h^2*e + 70*b^4*c*h^3*e - 240*a*b^2*c^2*h^3*e + 96*a^2*c^3*h^3*e)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(11/2)","A",0
227,1,457,0,0.295800," ","integrate((h*x+g)^2*(f*x^2+e*x+d)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{1}{192} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(\frac{6 \, f h^{2} x}{c} + \frac{16 \, c^{3} f g h - 7 \, b c^{2} f h^{2} + 8 \, c^{3} h^{2} e}{c^{4}}\right)} x + \frac{48 \, c^{3} f g^{2} - 80 \, b c^{2} f g h + 48 \, c^{3} d h^{2} + 35 \, b^{2} c f h^{2} - 36 \, a c^{2} f h^{2} + 96 \, c^{3} g h e - 40 \, b c^{2} h^{2} e}{c^{4}}\right)} x - \frac{144 \, b c^{2} f g^{2} - 384 \, c^{3} d g h - 240 \, b^{2} c f g h + 256 \, a c^{2} f g h + 144 \, b c^{2} d h^{2} + 105 \, b^{3} f h^{2} - 220 \, a b c f h^{2} - 192 \, c^{3} g^{2} e + 288 \, b c^{2} g h e - 120 \, b^{2} c h^{2} e + 128 \, a c^{2} h^{2} e}{c^{4}}\right)} - \frac{{\left(128 \, c^{4} d g^{2} + 48 \, b^{2} c^{2} f g^{2} - 64 \, a c^{3} f g^{2} - 128 \, b c^{3} d g h - 80 \, b^{3} c f g h + 192 \, a b c^{2} f g h + 48 \, b^{2} c^{2} d h^{2} - 64 \, a c^{3} d h^{2} + 35 \, b^{4} f h^{2} - 120 \, a b^{2} c f h^{2} + 48 \, a^{2} c^{2} f h^{2} - 64 \, b c^{3} g^{2} e + 96 \, b^{2} c^{2} g h e - 128 \, a c^{3} g h e - 40 \, b^{3} c h^{2} e + 96 \, a b c^{2} h^{2} e\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{128 \, c^{\frac{9}{2}}}"," ",0,"1/192*sqrt(c*x^2 + b*x + a)*(2*(4*(6*f*h^2*x/c + (16*c^3*f*g*h - 7*b*c^2*f*h^2 + 8*c^3*h^2*e)/c^4)*x + (48*c^3*f*g^2 - 80*b*c^2*f*g*h + 48*c^3*d*h^2 + 35*b^2*c*f*h^2 - 36*a*c^2*f*h^2 + 96*c^3*g*h*e - 40*b*c^2*h^2*e)/c^4)*x - (144*b*c^2*f*g^2 - 384*c^3*d*g*h - 240*b^2*c*f*g*h + 256*a*c^2*f*g*h + 144*b*c^2*d*h^2 + 105*b^3*f*h^2 - 220*a*b*c*f*h^2 - 192*c^3*g^2*e + 288*b*c^2*g*h*e - 120*b^2*c*h^2*e + 128*a*c^2*h^2*e)/c^4) - 1/128*(128*c^4*d*g^2 + 48*b^2*c^2*f*g^2 - 64*a*c^3*f*g^2 - 128*b*c^3*d*g*h - 80*b^3*c*f*g*h + 192*a*b*c^2*f*g*h + 48*b^2*c^2*d*h^2 - 64*a*c^3*d*h^2 + 35*b^4*f*h^2 - 120*a*b^2*c*f*h^2 + 48*a^2*c^2*f*h^2 - 64*b*c^3*g^2*e + 96*b^2*c^2*g*h*e - 128*a*c^3*g*h*e - 40*b^3*c*h^2*e + 96*a*b*c^2*h^2*e)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(9/2)","A",0
228,1,210,0,0.269053," ","integrate((h*x+g)*(f*x^2+e*x+d)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{1}{24} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(\frac{4 \, f h x}{c} + \frac{6 \, c^{2} f g - 5 \, b c f h + 6 \, c^{2} h e}{c^{3}}\right)} x - \frac{18 \, b c f g - 24 \, c^{2} d h - 15 \, b^{2} f h + 16 \, a c f h - 24 \, c^{2} g e + 18 \, b c h e}{c^{3}}\right)} - \frac{{\left(16 \, c^{3} d g + 6 \, b^{2} c f g - 8 \, a c^{2} f g - 8 \, b c^{2} d h - 5 \, b^{3} f h + 12 \, a b c f h - 8 \, b c^{2} g e + 6 \, b^{2} c h e - 8 \, a c^{2} h e\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{16 \, c^{\frac{7}{2}}}"," ",0,"1/24*sqrt(c*x^2 + b*x + a)*(2*(4*f*h*x/c + (6*c^2*f*g - 5*b*c*f*h + 6*c^2*h*e)/c^3)*x - (18*b*c*f*g - 24*c^2*d*h - 15*b^2*f*h + 16*a*c*f*h - 24*c^2*g*e + 18*b*c*h*e)/c^3) - 1/16*(16*c^3*d*g + 6*b^2*c*f*g - 8*a*c^2*f*g - 8*b*c^2*d*h - 5*b^3*f*h + 12*a*b*c*f*h - 8*b*c^2*g*e + 6*b^2*c*h*e - 8*a*c^2*h*e)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(7/2)","A",0
229,1,98,0,0.248608," ","integrate((f*x^2+e*x+d)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{c x^{2} + b x + a} {\left(\frac{2 \, f x}{c} - \frac{3 \, b f - 4 \, c e}{c^{2}}\right)} - \frac{{\left(8 \, c^{2} d + 3 \, b^{2} f - 4 \, a c f - 4 \, b c e\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{8 \, c^{\frac{5}{2}}}"," ",0,"1/4*sqrt(c*x^2 + b*x + a)*(2*f*x/c - (3*b*f - 4*c*e)/c^2) - 1/8*(8*c^2*d + 3*b^2*f - 4*a*c*f - 4*b*c*e)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(5/2)","A",0
230,-2,0,0,0.000000," ","integrate((f*x^2+e*x+d)/(h*x+g)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
231,-2,0,0,0.000000," ","integrate((f*x^2+e*x+d)/(h*x+g)^2/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Evaluation time: 0.71Error: Bad Argument Type","F(-2)",0
232,1,2307,0,0.544938," ","integrate((f*x^2+e*x+d)/(h*x+g)^3/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{{\left(8 \, c^{2} d g^{2} + 3 \, b^{2} f g^{2} - 4 \, a c f g^{2} - 8 \, b c d g h - 8 \, a b f g h + 3 \, b^{2} d h^{2} - 4 \, a c d h^{2} + 8 \, a^{2} f h^{2} - 4 \, b c g^{2} e + b^{2} g h e + 12 \, a c g h e - 4 \, a b h^{2} e\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} h + \sqrt{c} g}{\sqrt{-c g^{2} + b g h - a h^{2}}}\right)}{4 \, {\left(c^{2} g^{4} - 2 \, b c g^{3} h + b^{2} g^{2} h^{2} + 2 \, a c g^{2} h^{2} - 2 \, a b g h^{3} + a^{2} h^{4}\right)} \sqrt{-c g^{2} + b g h - a h^{2}}} + \frac{8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} c^{2} f g^{4} h - 16 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b c f g^{3} h^{2} - 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} c^{2} d g^{2} h^{3} + 5 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{2} f g^{2} h^{3} + 20 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a c f g^{2} h^{3} + 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b c d g h^{4} - 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b f g h^{4} - 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{2} d h^{5} + 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a c d h^{5} + 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b c g^{2} h^{3} e - {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{2} g h^{4} e - 12 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a c g h^{4} e + 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b h^{5} e + 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} c^{\frac{5}{2}} f g^{5} - 16 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b c^{\frac{3}{2}} f g^{4} h - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} c^{\frac{5}{2}} d g^{3} h^{2} - {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{2} \sqrt{c} f g^{3} h^{2} + 28 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a c^{\frac{3}{2}} f g^{3} h^{2} + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b c^{\frac{3}{2}} d g^{2} h^{3} + 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b \sqrt{c} f g^{2} h^{3} - 9 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{2} \sqrt{c} d g h^{4} + 12 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a c^{\frac{3}{2}} d g h^{4} - 16 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{2} \sqrt{c} f g h^{4} + 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} c^{\frac{5}{2}} g^{4} h e - 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b c^{\frac{3}{2}} g^{3} h^{2} e + 5 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{2} \sqrt{c} g^{2} h^{3} e - 20 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a c^{\frac{3}{2}} g^{2} h^{3} e - 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b \sqrt{c} g h^{4} e + 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{2} \sqrt{c} h^{5} e + 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b c^{2} f g^{5} - 20 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{2} c f g^{4} h - 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a c^{2} f g^{4} h - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b c^{2} d g^{3} h^{2} + 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{3} f g^{3} h^{2} + 60 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b c f g^{3} h^{2} + 20 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{2} c d g^{2} h^{3} + 40 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a c^{2} d g^{2} h^{3} - 11 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{2} f g^{2} h^{3} - 44 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} c f g^{2} h^{3} - 5 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{3} d g h^{4} - 28 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b c d g h^{4} + 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b f g h^{4} + 5 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{2} d h^{5} + 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} c d h^{5} + 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b c^{2} g^{4} h e - 16 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a c^{2} g^{3} h^{2} e + {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{3} g^{2} h^{3} e - 16 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b c g^{2} h^{3} e + 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{2} g h^{4} e + 20 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} c g h^{4} e - 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b h^{5} e + 2 \, b^{2} c^{\frac{3}{2}} f g^{5} - 5 \, b^{3} \sqrt{c} f g^{4} h - 4 \, a b c^{\frac{3}{2}} f g^{4} h - 6 \, b^{2} c^{\frac{3}{2}} d g^{3} h^{2} + 21 \, a b^{2} \sqrt{c} f g^{3} h^{2} + 4 \, a^{2} c^{\frac{3}{2}} f g^{3} h^{2} + 3 \, b^{3} \sqrt{c} d g^{2} h^{3} + 20 \, a b c^{\frac{3}{2}} d g^{2} h^{3} - 32 \, a^{2} b \sqrt{c} f g^{2} h^{3} - 11 \, a b^{2} \sqrt{c} d g h^{4} - 12 \, a^{2} c^{\frac{3}{2}} d g h^{4} + 16 \, a^{3} \sqrt{c} f g h^{4} + 8 \, a^{2} b \sqrt{c} d h^{5} + 2 \, b^{2} c^{\frac{3}{2}} g^{4} h e + b^{3} \sqrt{c} g^{3} h^{2} e - 8 \, a b c^{\frac{3}{2}} g^{3} h^{2} e - 5 \, a b^{2} \sqrt{c} g^{2} h^{3} e + 4 \, a^{2} c^{\frac{3}{2}} g^{2} h^{3} e + 12 \, a^{2} b \sqrt{c} g h^{4} e - 8 \, a^{3} \sqrt{c} h^{5} e}{4 \, {\left(c^{2} g^{4} h^{2} - 2 \, b c g^{3} h^{3} + b^{2} g^{2} h^{4} + 2 \, a c g^{2} h^{4} - 2 \, a b g h^{5} + a^{2} h^{6}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} h + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} g + b g - a h\right)}^{2}}"," ",0,"1/4*(8*c^2*d*g^2 + 3*b^2*f*g^2 - 4*a*c*f*g^2 - 8*b*c*d*g*h - 8*a*b*f*g*h + 3*b^2*d*h^2 - 4*a*c*d*h^2 + 8*a^2*f*h^2 - 4*b*c*g^2*e + b^2*g*h*e + 12*a*c*g*h*e - 4*a*b*h^2*e)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + b*x + a))*h + sqrt(c)*g)/sqrt(-c*g^2 + b*g*h - a*h^2))/((c^2*g^4 - 2*b*c*g^3*h + b^2*g^2*h^2 + 2*a*c*g^2*h^2 - 2*a*b*g*h^3 + a^2*h^4)*sqrt(-c*g^2 + b*g*h - a*h^2)) + 1/4*(8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*c^2*f*g^4*h - 16*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b*c*f*g^3*h^2 - 8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*c^2*d*g^2*h^3 + 5*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^2*f*g^2*h^3 + 20*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*c*f*g^2*h^3 + 8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b*c*d*g*h^4 - 8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b*f*g*h^4 - 3*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^2*d*h^5 + 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*c*d*h^5 + 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b*c*g^2*h^3*e - (sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^2*g*h^4*e - 12*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*c*g*h^4*e + 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b*h^5*e + 8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*c^(5/2)*f*g^5 - 16*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b*c^(3/2)*f*g^4*h - 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*c^(5/2)*d*g^3*h^2 - (sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^2*sqrt(c)*f*g^3*h^2 + 28*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*c^(3/2)*f*g^3*h^2 + 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b*c^(3/2)*d*g^2*h^3 + 8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b*sqrt(c)*f*g^2*h^3 - 9*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^2*sqrt(c)*d*g*h^4 + 12*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*c^(3/2)*d*g*h^4 - 16*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*sqrt(c)*f*g*h^4 + 8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*c^(5/2)*g^4*h*e - 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b*c^(3/2)*g^3*h^2*e + 5*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^2*sqrt(c)*g^2*h^3*e - 20*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*c^(3/2)*g^2*h^3*e - 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b*sqrt(c)*g*h^4*e + 8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*sqrt(c)*h^5*e + 8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b*c^2*f*g^5 - 20*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^2*c*f*g^4*h - 8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*c^2*f*g^4*h - 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b*c^2*d*g^3*h^2 + 3*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^3*f*g^3*h^2 + 60*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b*c*f*g^3*h^2 + 20*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^2*c*d*g^2*h^3 + 40*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*c^2*d*g^2*h^3 - 11*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^2*f*g^2*h^3 - 44*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*c*f*g^2*h^3 - 5*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^3*d*g*h^4 - 28*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b*c*d*g*h^4 + 8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b*f*g*h^4 + 5*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^2*d*h^5 + 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*c*d*h^5 + 8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b*c^2*g^4*h*e - 16*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*c^2*g^3*h^2*e + (sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^3*g^2*h^3*e - 16*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b*c*g^2*h^3*e + 3*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^2*g*h^4*e + 20*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*c*g*h^4*e - 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b*h^5*e + 2*b^2*c^(3/2)*f*g^5 - 5*b^3*sqrt(c)*f*g^4*h - 4*a*b*c^(3/2)*f*g^4*h - 6*b^2*c^(3/2)*d*g^3*h^2 + 21*a*b^2*sqrt(c)*f*g^3*h^2 + 4*a^2*c^(3/2)*f*g^3*h^2 + 3*b^3*sqrt(c)*d*g^2*h^3 + 20*a*b*c^(3/2)*d*g^2*h^3 - 32*a^2*b*sqrt(c)*f*g^2*h^3 - 11*a*b^2*sqrt(c)*d*g*h^4 - 12*a^2*c^(3/2)*d*g*h^4 + 16*a^3*sqrt(c)*f*g*h^4 + 8*a^2*b*sqrt(c)*d*h^5 + 2*b^2*c^(3/2)*g^4*h*e + b^3*sqrt(c)*g^3*h^2*e - 8*a*b*c^(3/2)*g^3*h^2*e - 5*a*b^2*sqrt(c)*g^2*h^3*e + 4*a^2*c^(3/2)*g^2*h^3*e + 12*a^2*b*sqrt(c)*g*h^4*e - 8*a^3*sqrt(c)*h^5*e)/((c^2*g^4*h^2 - 2*b*c*g^3*h^3 + b^2*g^2*h^4 + 2*a*c*g^2*h^4 - 2*a*b*g*h^5 + a^2*h^6)*((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*h + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c)*g + b*g - a*h)^2)","B",0
233,1,1054,0,0.349544," ","integrate((h*x+g)^3*(f*x^2+e*x+d)/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\frac{{\left({\left(2 \, {\left(\frac{4 \, {\left(b^{2} c^{3} f h^{3} - 4 \, a c^{4} f h^{3}\right)} x}{b^{2} c^{4} - 4 \, a c^{5}} + \frac{18 \, b^{2} c^{3} f g h^{2} - 72 \, a c^{4} f g h^{2} - 7 \, b^{3} c^{2} f h^{3} + 28 \, a b c^{3} f h^{3} + 6 \, b^{2} c^{3} h^{3} e - 24 \, a c^{4} h^{3} e}{b^{2} c^{4} - 4 \, a c^{5}}\right)} x + \frac{72 \, b^{2} c^{3} f g^{2} h - 288 \, a c^{4} f g^{2} h - 90 \, b^{3} c^{2} f g h^{2} + 360 \, a b c^{3} f g h^{2} + 24 \, b^{2} c^{3} d h^{3} - 96 \, a c^{4} d h^{3} + 35 \, b^{4} c f h^{3} - 172 \, a b^{2} c^{2} f h^{3} + 128 \, a^{2} c^{3} f h^{3} + 72 \, b^{2} c^{3} g h^{2} e - 288 \, a c^{4} g h^{2} e - 30 \, b^{3} c^{2} h^{3} e + 120 \, a b c^{3} h^{3} e}{b^{2} c^{4} - 4 \, a c^{5}}\right)} x - \frac{96 \, c^{5} d g^{3} + 48 \, b^{2} c^{3} f g^{3} - 96 \, a c^{4} f g^{3} - 144 \, b c^{4} d g^{2} h - 216 \, b^{3} c^{2} f g^{2} h + 720 \, a b c^{3} f g^{2} h + 144 \, b^{2} c^{3} d g h^{2} - 288 \, a c^{4} d g h^{2} + 270 \, b^{4} c f g h^{2} - 1116 \, a b^{2} c^{2} f g h^{2} + 432 \, a^{2} c^{3} f g h^{2} - 72 \, b^{3} c^{2} d h^{3} + 240 \, a b c^{3} d h^{3} - 105 \, b^{5} f h^{3} + 530 \, a b^{3} c f h^{3} - 488 \, a^{2} b c^{2} f h^{3} - 48 \, b c^{4} g^{3} e + 144 \, b^{2} c^{3} g^{2} h e - 288 \, a c^{4} g^{2} h e - 216 \, b^{3} c^{2} g h^{2} e + 720 \, a b c^{3} g h^{2} e + 90 \, b^{4} c h^{3} e - 372 \, a b^{2} c^{2} h^{3} e + 144 \, a^{2} c^{3} h^{3} e}{b^{2} c^{4} - 4 \, a c^{5}}\right)} x - \frac{48 \, b c^{4} d g^{3} + 48 \, a b c^{3} f g^{3} - 288 \, a c^{4} d g^{2} h - 216 \, a b^{2} c^{2} f g^{2} h + 576 \, a^{2} c^{3} f g^{2} h + 144 \, a b c^{3} d g h^{2} + 270 \, a b^{3} c f g h^{2} - 936 \, a^{2} b c^{2} f g h^{2} - 72 \, a b^{2} c^{2} d h^{3} + 192 \, a^{2} c^{3} d h^{3} - 105 \, a b^{4} f h^{3} + 460 \, a^{2} b^{2} c f h^{3} - 256 \, a^{3} c^{2} f h^{3} - 96 \, a c^{4} g^{3} e + 144 \, a b c^{3} g^{2} h e - 216 \, a b^{2} c^{2} g h^{2} e + 576 \, a^{2} c^{3} g h^{2} e + 90 \, a b^{3} c h^{3} e - 312 \, a^{2} b c^{2} h^{3} e}{b^{2} c^{4} - 4 \, a c^{5}}}{24 \, \sqrt{c x^{2} + b x + a}} - \frac{{\left(16 \, c^{3} f g^{3} - 72 \, b c^{2} f g^{2} h + 48 \, c^{3} d g h^{2} + 90 \, b^{2} c f g h^{2} - 72 \, a c^{2} f g h^{2} - 24 \, b c^{2} d h^{3} - 35 \, b^{3} f h^{3} + 60 \, a b c f h^{3} + 48 \, c^{3} g^{2} h e - 72 \, b c^{2} g h^{2} e + 30 \, b^{2} c h^{3} e - 24 \, a c^{2} h^{3} e\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{16 \, c^{\frac{9}{2}}}"," ",0,"1/24*(((2*(4*(b^2*c^3*f*h^3 - 4*a*c^4*f*h^3)*x/(b^2*c^4 - 4*a*c^5) + (18*b^2*c^3*f*g*h^2 - 72*a*c^4*f*g*h^2 - 7*b^3*c^2*f*h^3 + 28*a*b*c^3*f*h^3 + 6*b^2*c^3*h^3*e - 24*a*c^4*h^3*e)/(b^2*c^4 - 4*a*c^5))*x + (72*b^2*c^3*f*g^2*h - 288*a*c^4*f*g^2*h - 90*b^3*c^2*f*g*h^2 + 360*a*b*c^3*f*g*h^2 + 24*b^2*c^3*d*h^3 - 96*a*c^4*d*h^3 + 35*b^4*c*f*h^3 - 172*a*b^2*c^2*f*h^3 + 128*a^2*c^3*f*h^3 + 72*b^2*c^3*g*h^2*e - 288*a*c^4*g*h^2*e - 30*b^3*c^2*h^3*e + 120*a*b*c^3*h^3*e)/(b^2*c^4 - 4*a*c^5))*x - (96*c^5*d*g^3 + 48*b^2*c^3*f*g^3 - 96*a*c^4*f*g^3 - 144*b*c^4*d*g^2*h - 216*b^3*c^2*f*g^2*h + 720*a*b*c^3*f*g^2*h + 144*b^2*c^3*d*g*h^2 - 288*a*c^4*d*g*h^2 + 270*b^4*c*f*g*h^2 - 1116*a*b^2*c^2*f*g*h^2 + 432*a^2*c^3*f*g*h^2 - 72*b^3*c^2*d*h^3 + 240*a*b*c^3*d*h^3 - 105*b^5*f*h^3 + 530*a*b^3*c*f*h^3 - 488*a^2*b*c^2*f*h^3 - 48*b*c^4*g^3*e + 144*b^2*c^3*g^2*h*e - 288*a*c^4*g^2*h*e - 216*b^3*c^2*g*h^2*e + 720*a*b*c^3*g*h^2*e + 90*b^4*c*h^3*e - 372*a*b^2*c^2*h^3*e + 144*a^2*c^3*h^3*e)/(b^2*c^4 - 4*a*c^5))*x - (48*b*c^4*d*g^3 + 48*a*b*c^3*f*g^3 - 288*a*c^4*d*g^2*h - 216*a*b^2*c^2*f*g^2*h + 576*a^2*c^3*f*g^2*h + 144*a*b*c^3*d*g*h^2 + 270*a*b^3*c*f*g*h^2 - 936*a^2*b*c^2*f*g*h^2 - 72*a*b^2*c^2*d*h^3 + 192*a^2*c^3*d*h^3 - 105*a*b^4*f*h^3 + 460*a^2*b^2*c*f*h^3 - 256*a^3*c^2*f*h^3 - 96*a*c^4*g^3*e + 144*a*b*c^3*g^2*h*e - 216*a*b^2*c^2*g*h^2*e + 576*a^2*c^3*g*h^2*e + 90*a*b^3*c*h^3*e - 312*a^2*b*c^2*h^3*e)/(b^2*c^4 - 4*a*c^5))/sqrt(c*x^2 + b*x + a) - 1/16*(16*c^3*f*g^3 - 72*b*c^2*f*g^2*h + 48*c^3*d*g*h^2 + 90*b^2*c*f*g*h^2 - 72*a*c^2*f*g*h^2 - 24*b*c^2*d*h^3 - 35*b^3*f*h^3 + 60*a*b*c*f*h^3 + 48*c^3*g^2*h*e - 72*b*c^2*g*h^2*e + 30*b^2*c*h^3*e - 24*a*c^2*h^3*e)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(9/2)","B",0
234,1,580,0,0.321815," ","integrate((h*x+g)^2*(f*x^2+e*x+d)/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\frac{{\left({\left(\frac{2 \, {\left(b^{2} c^{2} f h^{2} - 4 \, a c^{3} f h^{2}\right)} x}{b^{2} c^{3} - 4 \, a c^{4}} + \frac{8 \, b^{2} c^{2} f g h - 32 \, a c^{3} f g h - 5 \, b^{3} c f h^{2} + 20 \, a b c^{2} f h^{2} + 4 \, b^{2} c^{2} h^{2} e - 16 \, a c^{3} h^{2} e}{b^{2} c^{3} - 4 \, a c^{4}}\right)} x - \frac{16 \, c^{4} d g^{2} + 8 \, b^{2} c^{2} f g^{2} - 16 \, a c^{3} f g^{2} - 16 \, b c^{3} d g h - 24 \, b^{3} c f g h + 80 \, a b c^{2} f g h + 8 \, b^{2} c^{2} d h^{2} - 16 \, a c^{3} d h^{2} + 15 \, b^{4} f h^{2} - 62 \, a b^{2} c f h^{2} + 24 \, a^{2} c^{2} f h^{2} - 8 \, b c^{3} g^{2} e + 16 \, b^{2} c^{2} g h e - 32 \, a c^{3} g h e - 12 \, b^{3} c h^{2} e + 40 \, a b c^{2} h^{2} e}{b^{2} c^{3} - 4 \, a c^{4}}\right)} x - \frac{8 \, b c^{3} d g^{2} + 8 \, a b c^{2} f g^{2} - 32 \, a c^{3} d g h - 24 \, a b^{2} c f g h + 64 \, a^{2} c^{2} f g h + 8 \, a b c^{2} d h^{2} + 15 \, a b^{3} f h^{2} - 52 \, a^{2} b c f h^{2} - 16 \, a c^{3} g^{2} e + 16 \, a b c^{2} g h e - 12 \, a b^{2} c h^{2} e + 32 \, a^{2} c^{2} h^{2} e}{b^{2} c^{3} - 4 \, a c^{4}}}{4 \, \sqrt{c x^{2} + b x + a}} - \frac{{\left(8 \, c^{2} f g^{2} - 24 \, b c f g h + 8 \, c^{2} d h^{2} + 15 \, b^{2} f h^{2} - 12 \, a c f h^{2} + 16 \, c^{2} g h e - 12 \, b c h^{2} e\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{8 \, c^{\frac{7}{2}}}"," ",0,"1/4*(((2*(b^2*c^2*f*h^2 - 4*a*c^3*f*h^2)*x/(b^2*c^3 - 4*a*c^4) + (8*b^2*c^2*f*g*h - 32*a*c^3*f*g*h - 5*b^3*c*f*h^2 + 20*a*b*c^2*f*h^2 + 4*b^2*c^2*h^2*e - 16*a*c^3*h^2*e)/(b^2*c^3 - 4*a*c^4))*x - (16*c^4*d*g^2 + 8*b^2*c^2*f*g^2 - 16*a*c^3*f*g^2 - 16*b*c^3*d*g*h - 24*b^3*c*f*g*h + 80*a*b*c^2*f*g*h + 8*b^2*c^2*d*h^2 - 16*a*c^3*d*h^2 + 15*b^4*f*h^2 - 62*a*b^2*c*f*h^2 + 24*a^2*c^2*f*h^2 - 8*b*c^3*g^2*e + 16*b^2*c^2*g*h*e - 32*a*c^3*g*h*e - 12*b^3*c*h^2*e + 40*a*b*c^2*h^2*e)/(b^2*c^3 - 4*a*c^4))*x - (8*b*c^3*d*g^2 + 8*a*b*c^2*f*g^2 - 32*a*c^3*d*g*h - 24*a*b^2*c*f*g*h + 64*a^2*c^2*f*g*h + 8*a*b*c^2*d*h^2 + 15*a*b^3*f*h^2 - 52*a^2*b*c*f*h^2 - 16*a*c^3*g^2*e + 16*a*b*c^2*g*h*e - 12*a*b^2*c*h^2*e + 32*a^2*c^2*h^2*e)/(b^2*c^3 - 4*a*c^4))/sqrt(c*x^2 + b*x + a) - 1/8*(8*c^2*f*g^2 - 24*b*c*f*g*h + 8*c^2*d*h^2 + 15*b^2*f*h^2 - 12*a*c*f*h^2 + 16*c^2*g*h*e - 12*b*c*h^2*e)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(7/2)","B",0
235,1,271,0,0.284443," ","integrate((h*x+g)*(f*x^2+e*x+d)/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\frac{{\left(\frac{{\left(b^{2} c f h - 4 \, a c^{2} f h\right)} x}{b^{2} c^{2} - 4 \, a c^{3}} - \frac{4 \, c^{3} d g + 2 \, b^{2} c f g - 4 \, a c^{2} f g - 2 \, b c^{2} d h - 3 \, b^{3} f h + 10 \, a b c f h - 2 \, b c^{2} g e + 2 \, b^{2} c h e - 4 \, a c^{2} h e}{b^{2} c^{2} - 4 \, a c^{3}}\right)} x - \frac{2 \, b c^{2} d g + 2 \, a b c f g - 4 \, a c^{2} d h - 3 \, a b^{2} f h + 8 \, a^{2} c f h - 4 \, a c^{2} g e + 2 \, a b c h e}{b^{2} c^{2} - 4 \, a c^{3}}}{\sqrt{c x^{2} + b x + a}} - \frac{{\left(2 \, c f g - 3 \, b f h + 2 \, c h e\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{2 \, c^{\frac{5}{2}}}"," ",0,"(((b^2*c*f*h - 4*a*c^2*f*h)*x/(b^2*c^2 - 4*a*c^3) - (4*c^3*d*g + 2*b^2*c*f*g - 4*a*c^2*f*g - 2*b*c^2*d*h - 3*b^3*f*h + 10*a*b*c*f*h - 2*b*c^2*g*e + 2*b^2*c*h*e - 4*a*c^2*h*e)/(b^2*c^2 - 4*a*c^3))*x - (2*b*c^2*d*g + 2*a*b*c*f*g - 4*a*c^2*d*h - 3*a*b^2*f*h + 8*a^2*c*f*h - 4*a*c^2*g*e + 2*a*b*c*h*e)/(b^2*c^2 - 4*a*c^3))/sqrt(c*x^2 + b*x + a) - 1/2*(2*c*f*g - 3*b*f*h + 2*c*h*e)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(5/2)","A",0
236,1,122,0,0.267382," ","integrate((f*x^2+e*x+d)/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{{\left(2 \, c^{2} d + b^{2} f - 2 \, a c f - b c e\right)} x}{b^{2} c - 4 \, a c^{2}} + \frac{b c d + a b f - 2 \, a c e}{b^{2} c - 4 \, a c^{2}}\right)}}{\sqrt{c x^{2} + b x + a}} - \frac{f \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{c^{\frac{3}{2}}}"," ",0,"-2*((2*c^2*d + b^2*f - 2*a*c*f - b*c*e)*x/(b^2*c - 4*a*c^2) + (b*c*d + a*b*f - 2*a*c*e)/(b^2*c - 4*a*c^2))/sqrt(c*x^2 + b*x + a) - f*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(3/2)","A",0
237,1,719,0,0.286248," ","integrate((f*x^2+e*x+d)/(h*x+g)/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{{\left(2 \, c^{3} d g^{3} + b^{2} c f g^{3} - 2 \, a c^{2} f g^{3} - 3 \, b c^{2} d g^{2} h - b^{3} f g^{2} h + a b c f g^{2} h + b^{2} c d g h^{2} + 2 \, a c^{2} d g h^{2} + 2 \, a b^{2} f g h^{2} - 2 \, a^{2} c f g h^{2} - a b c d h^{3} - a^{2} b f h^{3} - b c^{2} g^{3} e + b^{2} c g^{2} h e + 2 \, a c^{2} g^{2} h e - 3 \, a b c g h^{2} e + 2 \, a^{2} c h^{3} e\right)} x}{b^{2} c^{2} g^{4} - 4 \, a c^{3} g^{4} - 2 \, b^{3} c g^{3} h + 8 \, a b c^{2} g^{3} h + b^{4} g^{2} h^{2} - 2 \, a b^{2} c g^{2} h^{2} - 8 \, a^{2} c^{2} g^{2} h^{2} - 2 \, a b^{3} g h^{3} + 8 \, a^{2} b c g h^{3} + a^{2} b^{2} h^{4} - 4 \, a^{3} c h^{4}} + \frac{b c^{2} d g^{3} + a b c f g^{3} - 2 \, b^{2} c d g^{2} h + 2 \, a c^{2} d g^{2} h - a b^{2} f g^{2} h - 2 \, a^{2} c f g^{2} h + b^{3} d g h^{2} - a b c d g h^{2} + 3 \, a^{2} b f g h^{2} - a b^{2} d h^{3} + 2 \, a^{2} c d h^{3} - 2 \, a^{3} f h^{3} - 2 \, a c^{2} g^{3} e + 3 \, a b c g^{2} h e - a b^{2} g h^{2} e - 2 \, a^{2} c g h^{2} e + a^{2} b h^{3} e}{b^{2} c^{2} g^{4} - 4 \, a c^{3} g^{4} - 2 \, b^{3} c g^{3} h + 8 \, a b c^{2} g^{3} h + b^{4} g^{2} h^{2} - 2 \, a b^{2} c g^{2} h^{2} - 8 \, a^{2} c^{2} g^{2} h^{2} - 2 \, a b^{3} g h^{3} + 8 \, a^{2} b c g h^{3} + a^{2} b^{2} h^{4} - 4 \, a^{3} c h^{4}}\right)}}{\sqrt{c x^{2} + b x + a}} + \frac{2 \, {\left(f g^{2} + d h^{2} - g h e\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} h + \sqrt{c} g}{\sqrt{-c g^{2} + b g h - a h^{2}}}\right)}{{\left(c g^{2} - b g h + a h^{2}\right)} \sqrt{-c g^{2} + b g h - a h^{2}}}"," ",0,"-2*((2*c^3*d*g^3 + b^2*c*f*g^3 - 2*a*c^2*f*g^3 - 3*b*c^2*d*g^2*h - b^3*f*g^2*h + a*b*c*f*g^2*h + b^2*c*d*g*h^2 + 2*a*c^2*d*g*h^2 + 2*a*b^2*f*g*h^2 - 2*a^2*c*f*g*h^2 - a*b*c*d*h^3 - a^2*b*f*h^3 - b*c^2*g^3*e + b^2*c*g^2*h*e + 2*a*c^2*g^2*h*e - 3*a*b*c*g*h^2*e + 2*a^2*c*h^3*e)*x/(b^2*c^2*g^4 - 4*a*c^3*g^4 - 2*b^3*c*g^3*h + 8*a*b*c^2*g^3*h + b^4*g^2*h^2 - 2*a*b^2*c*g^2*h^2 - 8*a^2*c^2*g^2*h^2 - 2*a*b^3*g*h^3 + 8*a^2*b*c*g*h^3 + a^2*b^2*h^4 - 4*a^3*c*h^4) + (b*c^2*d*g^3 + a*b*c*f*g^3 - 2*b^2*c*d*g^2*h + 2*a*c^2*d*g^2*h - a*b^2*f*g^2*h - 2*a^2*c*f*g^2*h + b^3*d*g*h^2 - a*b*c*d*g*h^2 + 3*a^2*b*f*g*h^2 - a*b^2*d*h^3 + 2*a^2*c*d*h^3 - 2*a^3*f*h^3 - 2*a*c^2*g^3*e + 3*a*b*c*g^2*h*e - a*b^2*g*h^2*e - 2*a^2*c*g*h^2*e + a^2*b*h^3*e)/(b^2*c^2*g^4 - 4*a*c^3*g^4 - 2*b^3*c*g^3*h + 8*a*b*c^2*g^3*h + b^4*g^2*h^2 - 2*a*b^2*c*g^2*h^2 - 8*a^2*c^2*g^2*h^2 - 2*a*b^3*g*h^3 + 8*a^2*b*c*g*h^3 + a^2*b^2*h^4 - 4*a^3*c*h^4))/sqrt(c*x^2 + b*x + a) + 2*(f*g^2 + d*h^2 - g*h*e)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + b*x + a))*h + sqrt(c)*g)/sqrt(-c*g^2 + b*g*h - a*h^2))/((c*g^2 - b*g*h + a*h^2)*sqrt(-c*g^2 + b*g*h - a*h^2))","B",0
238,-1,0,0,0.000000," ","integrate((f*x^2+e*x+d)/(h*x+g)^2/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
239,1,5637,0,0.881963," ","integrate((f*x^2+e*x+d)/(h*x+g)^3/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{{\left(2 \, c^{7} d g^{9} + b^{2} c^{5} f g^{9} - 2 \, a c^{6} f g^{9} - 9 \, b c^{6} d g^{8} h - 3 \, b^{3} c^{4} f g^{8} h + 3 \, a b c^{5} f g^{8} h + 18 \, b^{2} c^{5} d g^{7} h^{2} + 3 \, b^{4} c^{3} f g^{7} h^{2} + 6 \, a b^{2} c^{4} f g^{7} h^{2} - 21 \, b^{3} c^{4} d g^{6} h^{3} - b^{5} c^{2} f g^{6} h^{3} - 13 \, a b^{3} c^{3} f g^{6} h^{3} - 16 \, a^{2} b c^{4} f g^{6} h^{3} + 15 \, b^{4} c^{3} d g^{5} h^{4} + 6 \, a b^{2} c^{4} d g^{5} h^{4} - 12 \, a^{2} c^{5} d g^{5} h^{4} + 6 \, a b^{4} c^{2} f g^{5} h^{4} + 36 \, a^{2} b^{2} c^{3} f g^{5} h^{4} + 12 \, a^{3} c^{4} f g^{5} h^{4} - 6 \, b^{5} c^{2} d g^{4} h^{5} - 15 \, a b^{3} c^{3} d g^{4} h^{5} + 30 \, a^{2} b c^{4} d g^{4} h^{5} - 21 \, a^{2} b^{3} c^{2} f g^{4} h^{5} - 42 \, a^{3} b c^{3} f g^{4} h^{5} + b^{6} c d g^{3} h^{6} + 12 \, a b^{4} c^{2} d g^{3} h^{6} - 18 \, a^{2} b^{2} c^{3} d g^{3} h^{6} - 16 \, a^{3} c^{4} d g^{3} h^{6} + a^{2} b^{4} c f g^{3} h^{6} + 34 \, a^{3} b^{2} c^{2} f g^{3} h^{6} + 16 \, a^{4} c^{3} f g^{3} h^{6} - 3 \, a b^{5} c d g^{2} h^{7} - 3 \, a^{2} b^{3} c^{2} d g^{2} h^{7} + 24 \, a^{3} b c^{3} d g^{2} h^{7} - 3 \, a^{3} b^{3} c f g^{2} h^{7} - 24 \, a^{4} b c^{2} f g^{2} h^{7} + 3 \, a^{2} b^{4} c d g h^{8} - 6 \, a^{3} b^{2} c^{2} d g h^{8} - 6 \, a^{4} c^{3} d g h^{8} + 3 \, a^{4} b^{2} c f g h^{8} + 6 \, a^{5} c^{2} f g h^{8} - a^{3} b^{3} c d h^{9} + 3 \, a^{4} b c^{2} d h^{9} - a^{5} b c f h^{9} - b c^{6} g^{9} e + 3 \, b^{2} c^{5} g^{8} h e + 6 \, a c^{6} g^{8} h e - 3 \, b^{3} c^{4} g^{7} h^{2} e - 24 \, a b c^{5} g^{7} h^{2} e + b^{4} c^{3} g^{6} h^{3} e + 34 \, a b^{2} c^{4} g^{6} h^{3} e + 16 \, a^{2} c^{5} g^{6} h^{3} e - 21 \, a b^{3} c^{3} g^{5} h^{4} e - 42 \, a^{2} b c^{4} g^{5} h^{4} e + 6 \, a b^{4} c^{2} g^{4} h^{5} e + 36 \, a^{2} b^{2} c^{3} g^{4} h^{5} e + 12 \, a^{3} c^{4} g^{4} h^{5} e - a b^{5} c g^{3} h^{6} e - 13 \, a^{2} b^{3} c^{2} g^{3} h^{6} e - 16 \, a^{3} b c^{3} g^{3} h^{6} e + 3 \, a^{2} b^{4} c g^{2} h^{7} e + 6 \, a^{3} b^{2} c^{2} g^{2} h^{7} e - 3 \, a^{3} b^{3} c g h^{8} e + 3 \, a^{4} b c^{2} g h^{8} e + a^{4} b^{2} c h^{9} e - 2 \, a^{5} c^{2} h^{9} e\right)} x}{b^{2} c^{6} g^{12} - 4 \, a c^{7} g^{12} - 6 \, b^{3} c^{5} g^{11} h + 24 \, a b c^{6} g^{11} h + 15 \, b^{4} c^{4} g^{10} h^{2} - 54 \, a b^{2} c^{5} g^{10} h^{2} - 24 \, a^{2} c^{6} g^{10} h^{2} - 20 \, b^{5} c^{3} g^{9} h^{3} + 50 \, a b^{3} c^{4} g^{9} h^{3} + 120 \, a^{2} b c^{5} g^{9} h^{3} + 15 \, b^{6} c^{2} g^{8} h^{4} - 225 \, a^{2} b^{2} c^{4} g^{8} h^{4} - 60 \, a^{3} c^{5} g^{8} h^{4} - 6 \, b^{7} c g^{7} h^{5} - 36 \, a b^{5} c^{2} g^{7} h^{5} + 180 \, a^{2} b^{3} c^{3} g^{7} h^{5} + 240 \, a^{3} b c^{4} g^{7} h^{5} + b^{8} g^{6} h^{6} + 26 \, a b^{6} c g^{6} h^{6} - 30 \, a^{2} b^{4} c^{2} g^{6} h^{6} - 340 \, a^{3} b^{2} c^{3} g^{6} h^{6} - 80 \, a^{4} c^{4} g^{6} h^{6} - 6 \, a b^{7} g^{5} h^{7} - 36 \, a^{2} b^{5} c g^{5} h^{7} + 180 \, a^{3} b^{3} c^{2} g^{5} h^{7} + 240 \, a^{4} b c^{3} g^{5} h^{7} + 15 \, a^{2} b^{6} g^{4} h^{8} - 225 \, a^{4} b^{2} c^{2} g^{4} h^{8} - 60 \, a^{5} c^{3} g^{4} h^{8} - 20 \, a^{3} b^{5} g^{3} h^{9} + 50 \, a^{4} b^{3} c g^{3} h^{9} + 120 \, a^{5} b c^{2} g^{3} h^{9} + 15 \, a^{4} b^{4} g^{2} h^{10} - 54 \, a^{5} b^{2} c g^{2} h^{10} - 24 \, a^{6} c^{2} g^{2} h^{10} - 6 \, a^{5} b^{3} g h^{11} + 24 \, a^{6} b c g h^{11} + a^{6} b^{2} h^{12} - 4 \, a^{7} c h^{12}} + \frac{b c^{6} d g^{9} + a b c^{5} f g^{9} - 6 \, b^{2} c^{5} d g^{8} h + 6 \, a c^{6} d g^{8} h - 3 \, a b^{2} c^{4} f g^{8} h - 6 \, a^{2} c^{5} f g^{8} h + 15 \, b^{3} c^{4} d g^{7} h^{2} - 24 \, a b c^{5} d g^{7} h^{2} + 3 \, a b^{3} c^{3} f g^{7} h^{2} + 24 \, a^{2} b c^{4} f g^{7} h^{2} - 20 \, b^{4} c^{3} d g^{6} h^{3} + 34 \, a b^{2} c^{4} d g^{6} h^{3} + 16 \, a^{2} c^{5} d g^{6} h^{3} - a b^{4} c^{2} f g^{6} h^{3} - 34 \, a^{2} b^{2} c^{3} f g^{6} h^{3} - 16 \, a^{3} c^{4} f g^{6} h^{3} + 15 \, b^{5} c^{2} d g^{5} h^{4} - 15 \, a b^{3} c^{3} d g^{5} h^{4} - 54 \, a^{2} b c^{4} d g^{5} h^{4} + 21 \, a^{2} b^{3} c^{2} f g^{5} h^{4} + 42 \, a^{3} b c^{3} f g^{5} h^{4} - 6 \, b^{6} c d g^{4} h^{5} - 9 \, a b^{4} c^{2} d g^{4} h^{5} + 66 \, a^{2} b^{2} c^{3} d g^{4} h^{5} + 12 \, a^{3} c^{4} d g^{4} h^{5} - 6 \, a^{2} b^{4} c f g^{4} h^{5} - 36 \, a^{3} b^{2} c^{2} f g^{4} h^{5} - 12 \, a^{4} c^{3} f g^{4} h^{5} + b^{7} d g^{3} h^{6} + 11 \, a b^{5} c d g^{3} h^{6} - 31 \, a^{2} b^{3} c^{2} d g^{3} h^{6} - 32 \, a^{3} b c^{3} d g^{3} h^{6} + a^{2} b^{5} f g^{3} h^{6} + 13 \, a^{3} b^{3} c f g^{3} h^{6} + 16 \, a^{4} b c^{2} f g^{3} h^{6} - 3 \, a b^{6} d g^{2} h^{7} + 30 \, a^{3} b^{2} c^{2} d g^{2} h^{7} - 3 \, a^{3} b^{4} f g^{2} h^{7} - 6 \, a^{4} b^{2} c f g^{2} h^{7} + 3 \, a^{2} b^{5} d g h^{8} - 9 \, a^{3} b^{3} c d g h^{8} - 3 \, a^{4} b c^{2} d g h^{8} + 3 \, a^{4} b^{3} f g h^{8} - 3 \, a^{5} b c f g h^{8} - a^{3} b^{4} d h^{9} + 4 \, a^{4} b^{2} c d h^{9} - 2 \, a^{5} c^{2} d h^{9} - a^{5} b^{2} f h^{9} + 2 \, a^{6} c f h^{9} - 2 \, a c^{6} g^{9} e + 9 \, a b c^{5} g^{8} h e - 18 \, a b^{2} c^{4} g^{7} h^{2} e + 21 \, a b^{3} c^{3} g^{6} h^{3} e - 15 \, a b^{4} c^{2} g^{5} h^{4} e - 6 \, a^{2} b^{2} c^{3} g^{5} h^{4} e + 12 \, a^{3} c^{4} g^{5} h^{4} e + 6 \, a b^{5} c g^{4} h^{5} e + 15 \, a^{2} b^{3} c^{2} g^{4} h^{5} e - 30 \, a^{3} b c^{3} g^{4} h^{5} e - a b^{6} g^{3} h^{6} e - 12 \, a^{2} b^{4} c g^{3} h^{6} e + 18 \, a^{3} b^{2} c^{2} g^{3} h^{6} e + 16 \, a^{4} c^{3} g^{3} h^{6} e + 3 \, a^{2} b^{5} g^{2} h^{7} e + 3 \, a^{3} b^{3} c g^{2} h^{7} e - 24 \, a^{4} b c^{2} g^{2} h^{7} e - 3 \, a^{3} b^{4} g h^{8} e + 6 \, a^{4} b^{2} c g h^{8} e + 6 \, a^{5} c^{2} g h^{8} e + a^{4} b^{3} h^{9} e - 3 \, a^{5} b c h^{9} e}{b^{2} c^{6} g^{12} - 4 \, a c^{7} g^{12} - 6 \, b^{3} c^{5} g^{11} h + 24 \, a b c^{6} g^{11} h + 15 \, b^{4} c^{4} g^{10} h^{2} - 54 \, a b^{2} c^{5} g^{10} h^{2} - 24 \, a^{2} c^{6} g^{10} h^{2} - 20 \, b^{5} c^{3} g^{9} h^{3} + 50 \, a b^{3} c^{4} g^{9} h^{3} + 120 \, a^{2} b c^{5} g^{9} h^{3} + 15 \, b^{6} c^{2} g^{8} h^{4} - 225 \, a^{2} b^{2} c^{4} g^{8} h^{4} - 60 \, a^{3} c^{5} g^{8} h^{4} - 6 \, b^{7} c g^{7} h^{5} - 36 \, a b^{5} c^{2} g^{7} h^{5} + 180 \, a^{2} b^{3} c^{3} g^{7} h^{5} + 240 \, a^{3} b c^{4} g^{7} h^{5} + b^{8} g^{6} h^{6} + 26 \, a b^{6} c g^{6} h^{6} - 30 \, a^{2} b^{4} c^{2} g^{6} h^{6} - 340 \, a^{3} b^{2} c^{3} g^{6} h^{6} - 80 \, a^{4} c^{4} g^{6} h^{6} - 6 \, a b^{7} g^{5} h^{7} - 36 \, a^{2} b^{5} c g^{5} h^{7} + 180 \, a^{3} b^{3} c^{2} g^{5} h^{7} + 240 \, a^{4} b c^{3} g^{5} h^{7} + 15 \, a^{2} b^{6} g^{4} h^{8} - 225 \, a^{4} b^{2} c^{2} g^{4} h^{8} - 60 \, a^{5} c^{3} g^{4} h^{8} - 20 \, a^{3} b^{5} g^{3} h^{9} + 50 \, a^{4} b^{3} c g^{3} h^{9} + 120 \, a^{5} b c^{2} g^{3} h^{9} + 15 \, a^{4} b^{4} g^{2} h^{10} - 54 \, a^{5} b^{2} c g^{2} h^{10} - 24 \, a^{6} c^{2} g^{2} h^{10} - 6 \, a^{5} b^{3} g h^{11} + 24 \, a^{6} b c g h^{11} + a^{6} b^{2} h^{12} - 4 \, a^{7} c h^{12}}\right)}}{\sqrt{c x^{2} + b x + a}} + \frac{{\left(8 \, c^{2} f g^{4} + 8 \, b c f g^{3} h + 48 \, c^{2} d g^{2} h^{2} - b^{2} f g^{2} h^{2} - 44 \, a c f g^{2} h^{2} - 48 \, b c d g h^{3} + 8 \, a b f g h^{3} + 15 \, b^{2} d h^{4} - 12 \, a c d h^{4} + 8 \, a^{2} f h^{4} - 24 \, c^{2} g^{3} h e + 12 \, b c g^{2} h^{2} e - 3 \, b^{2} g h^{3} e + 36 \, a c g h^{3} e - 12 \, a b h^{4} e\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} h + \sqrt{c} g}{\sqrt{-c g^{2} + b g h - a h^{2}}}\right)}{4 \, {\left(c^{3} g^{6} - 3 \, b c^{2} g^{5} h + 3 \, b^{2} c g^{4} h^{2} + 3 \, a c^{2} g^{4} h^{2} - b^{3} g^{3} h^{3} - 6 \, a b c g^{3} h^{3} + 3 \, a b^{2} g^{2} h^{4} + 3 \, a^{2} c g^{2} h^{4} - 3 \, a^{2} b g h^{5} + a^{3} h^{6}\right)} \sqrt{-c g^{2} + b g h - a h^{2}}} - \frac{8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} c^{2} f g^{4} h + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} c^{2} d g^{2} h^{3} - {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{2} f g^{2} h^{3} - 20 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a c f g^{2} h^{3} - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b c d g h^{4} + 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b f g h^{4} + 7 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{2} d h^{5} - 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a c d h^{5} - 16 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} c^{2} g^{3} h^{2} e + 12 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b c g^{2} h^{3} e - 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{2} g h^{4} e + 12 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a c g h^{4} e - 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b h^{5} e + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} c^{\frac{5}{2}} f g^{5} - 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b c^{\frac{3}{2}} f g^{4} h + 56 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} c^{\frac{5}{2}} d g^{3} h^{2} + 5 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{2} \sqrt{c} f g^{3} h^{2} - 44 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a c^{\frac{3}{2}} f g^{3} h^{2} - 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b c^{\frac{3}{2}} d g^{2} h^{3} + 13 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{2} \sqrt{c} d g h^{4} - 28 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a c^{\frac{3}{2}} d g h^{4} + 16 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{2} \sqrt{c} f g h^{4} + 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b \sqrt{c} d h^{5} - 40 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} c^{\frac{5}{2}} g^{4} h e + 28 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b c^{\frac{3}{2}} g^{3} h^{2} e - 9 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{2} \sqrt{c} g^{2} h^{3} e + 36 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a c^{\frac{3}{2}} g^{2} h^{3} e - 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b \sqrt{c} g h^{4} e - 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{2} \sqrt{c} h^{5} e + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b c^{2} f g^{5} - 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{2} c f g^{4} h - 40 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a c^{2} f g^{4} h + 56 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b c^{2} d g^{3} h^{2} + {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{3} f g^{3} h^{2} - 28 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b c f g^{3} h^{2} - 44 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{2} c d g^{2} h^{3} - 88 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a c^{2} d g^{2} h^{3} + 7 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{2} f g^{2} h^{3} + 44 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} c f g^{2} h^{3} + 9 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{3} d g h^{4} + 60 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b c d g h^{4} - 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b f g h^{4} - 9 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{2} d h^{5} - 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} c d h^{5} - 40 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b c^{2} g^{4} h e + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{2} c g^{3} h^{2} e + 64 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a c^{2} g^{3} h^{2} e - 5 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{3} g^{2} h^{3} e - 16 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b c g^{2} h^{3} e + {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{2} g h^{4} e - 20 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} c g h^{4} e + 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b h^{5} e + 6 \, b^{2} c^{\frac{3}{2}} f g^{5} + b^{3} \sqrt{c} f g^{4} h - 20 \, a b c^{\frac{3}{2}} f g^{4} h + 14 \, b^{2} c^{\frac{3}{2}} d g^{3} h^{2} - 9 \, a b^{2} \sqrt{c} f g^{3} h^{2} + 12 \, a^{2} c^{\frac{3}{2}} f g^{3} h^{2} - 7 \, b^{3} \sqrt{c} d g^{2} h^{3} - 44 \, a b c^{\frac{3}{2}} d g^{2} h^{3} + 24 \, a^{2} b \sqrt{c} f g^{2} h^{3} + 23 \, a b^{2} \sqrt{c} d g h^{4} + 28 \, a^{2} c^{\frac{3}{2}} d g h^{4} - 16 \, a^{3} \sqrt{c} f g h^{4} - 16 \, a^{2} b \sqrt{c} d h^{5} - 10 \, b^{2} c^{\frac{3}{2}} g^{4} h e + 3 \, b^{3} \sqrt{c} g^{3} h^{2} e + 32 \, a b c^{\frac{3}{2}} g^{3} h^{2} e - 7 \, a b^{2} \sqrt{c} g^{2} h^{3} e - 20 \, a^{2} c^{\frac{3}{2}} g^{2} h^{3} e - 4 \, a^{2} b \sqrt{c} g h^{4} e + 8 \, a^{3} \sqrt{c} h^{5} e}{4 \, {\left(c^{3} g^{6} - 3 \, b c^{2} g^{5} h + 3 \, b^{2} c g^{4} h^{2} + 3 \, a c^{2} g^{4} h^{2} - b^{3} g^{3} h^{3} - 6 \, a b c g^{3} h^{3} + 3 \, a b^{2} g^{2} h^{4} + 3 \, a^{2} c g^{2} h^{4} - 3 \, a^{2} b g h^{5} + a^{3} h^{6}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} h + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} g + b g - a h\right)}^{2}}"," ",0,"-2*((2*c^7*d*g^9 + b^2*c^5*f*g^9 - 2*a*c^6*f*g^9 - 9*b*c^6*d*g^8*h - 3*b^3*c^4*f*g^8*h + 3*a*b*c^5*f*g^8*h + 18*b^2*c^5*d*g^7*h^2 + 3*b^4*c^3*f*g^7*h^2 + 6*a*b^2*c^4*f*g^7*h^2 - 21*b^3*c^4*d*g^6*h^3 - b^5*c^2*f*g^6*h^3 - 13*a*b^3*c^3*f*g^6*h^3 - 16*a^2*b*c^4*f*g^6*h^3 + 15*b^4*c^3*d*g^5*h^4 + 6*a*b^2*c^4*d*g^5*h^4 - 12*a^2*c^5*d*g^5*h^4 + 6*a*b^4*c^2*f*g^5*h^4 + 36*a^2*b^2*c^3*f*g^5*h^4 + 12*a^3*c^4*f*g^5*h^4 - 6*b^5*c^2*d*g^4*h^5 - 15*a*b^3*c^3*d*g^4*h^5 + 30*a^2*b*c^4*d*g^4*h^5 - 21*a^2*b^3*c^2*f*g^4*h^5 - 42*a^3*b*c^3*f*g^4*h^5 + b^6*c*d*g^3*h^6 + 12*a*b^4*c^2*d*g^3*h^6 - 18*a^2*b^2*c^3*d*g^3*h^6 - 16*a^3*c^4*d*g^3*h^6 + a^2*b^4*c*f*g^3*h^6 + 34*a^3*b^2*c^2*f*g^3*h^6 + 16*a^4*c^3*f*g^3*h^6 - 3*a*b^5*c*d*g^2*h^7 - 3*a^2*b^3*c^2*d*g^2*h^7 + 24*a^3*b*c^3*d*g^2*h^7 - 3*a^3*b^3*c*f*g^2*h^7 - 24*a^4*b*c^2*f*g^2*h^7 + 3*a^2*b^4*c*d*g*h^8 - 6*a^3*b^2*c^2*d*g*h^8 - 6*a^4*c^3*d*g*h^8 + 3*a^4*b^2*c*f*g*h^8 + 6*a^5*c^2*f*g*h^8 - a^3*b^3*c*d*h^9 + 3*a^4*b*c^2*d*h^9 - a^5*b*c*f*h^9 - b*c^6*g^9*e + 3*b^2*c^5*g^8*h*e + 6*a*c^6*g^8*h*e - 3*b^3*c^4*g^7*h^2*e - 24*a*b*c^5*g^7*h^2*e + b^4*c^3*g^6*h^3*e + 34*a*b^2*c^4*g^6*h^3*e + 16*a^2*c^5*g^6*h^3*e - 21*a*b^3*c^3*g^5*h^4*e - 42*a^2*b*c^4*g^5*h^4*e + 6*a*b^4*c^2*g^4*h^5*e + 36*a^2*b^2*c^3*g^4*h^5*e + 12*a^3*c^4*g^4*h^5*e - a*b^5*c*g^3*h^6*e - 13*a^2*b^3*c^2*g^3*h^6*e - 16*a^3*b*c^3*g^3*h^6*e + 3*a^2*b^4*c*g^2*h^7*e + 6*a^3*b^2*c^2*g^2*h^7*e - 3*a^3*b^3*c*g*h^8*e + 3*a^4*b*c^2*g*h^8*e + a^4*b^2*c*h^9*e - 2*a^5*c^2*h^9*e)*x/(b^2*c^6*g^12 - 4*a*c^7*g^12 - 6*b^3*c^5*g^11*h + 24*a*b*c^6*g^11*h + 15*b^4*c^4*g^10*h^2 - 54*a*b^2*c^5*g^10*h^2 - 24*a^2*c^6*g^10*h^2 - 20*b^5*c^3*g^9*h^3 + 50*a*b^3*c^4*g^9*h^3 + 120*a^2*b*c^5*g^9*h^3 + 15*b^6*c^2*g^8*h^4 - 225*a^2*b^2*c^4*g^8*h^4 - 60*a^3*c^5*g^8*h^4 - 6*b^7*c*g^7*h^5 - 36*a*b^5*c^2*g^7*h^5 + 180*a^2*b^3*c^3*g^7*h^5 + 240*a^3*b*c^4*g^7*h^5 + b^8*g^6*h^6 + 26*a*b^6*c*g^6*h^6 - 30*a^2*b^4*c^2*g^6*h^6 - 340*a^3*b^2*c^3*g^6*h^6 - 80*a^4*c^4*g^6*h^6 - 6*a*b^7*g^5*h^7 - 36*a^2*b^5*c*g^5*h^7 + 180*a^3*b^3*c^2*g^5*h^7 + 240*a^4*b*c^3*g^5*h^7 + 15*a^2*b^6*g^4*h^8 - 225*a^4*b^2*c^2*g^4*h^8 - 60*a^5*c^3*g^4*h^8 - 20*a^3*b^5*g^3*h^9 + 50*a^4*b^3*c*g^3*h^9 + 120*a^5*b*c^2*g^3*h^9 + 15*a^4*b^4*g^2*h^10 - 54*a^5*b^2*c*g^2*h^10 - 24*a^6*c^2*g^2*h^10 - 6*a^5*b^3*g*h^11 + 24*a^6*b*c*g*h^11 + a^6*b^2*h^12 - 4*a^7*c*h^12) + (b*c^6*d*g^9 + a*b*c^5*f*g^9 - 6*b^2*c^5*d*g^8*h + 6*a*c^6*d*g^8*h - 3*a*b^2*c^4*f*g^8*h - 6*a^2*c^5*f*g^8*h + 15*b^3*c^4*d*g^7*h^2 - 24*a*b*c^5*d*g^7*h^2 + 3*a*b^3*c^3*f*g^7*h^2 + 24*a^2*b*c^4*f*g^7*h^2 - 20*b^4*c^3*d*g^6*h^3 + 34*a*b^2*c^4*d*g^6*h^3 + 16*a^2*c^5*d*g^6*h^3 - a*b^4*c^2*f*g^6*h^3 - 34*a^2*b^2*c^3*f*g^6*h^3 - 16*a^3*c^4*f*g^6*h^3 + 15*b^5*c^2*d*g^5*h^4 - 15*a*b^3*c^3*d*g^5*h^4 - 54*a^2*b*c^4*d*g^5*h^4 + 21*a^2*b^3*c^2*f*g^5*h^4 + 42*a^3*b*c^3*f*g^5*h^4 - 6*b^6*c*d*g^4*h^5 - 9*a*b^4*c^2*d*g^4*h^5 + 66*a^2*b^2*c^3*d*g^4*h^5 + 12*a^3*c^4*d*g^4*h^5 - 6*a^2*b^4*c*f*g^4*h^5 - 36*a^3*b^2*c^2*f*g^4*h^5 - 12*a^4*c^3*f*g^4*h^5 + b^7*d*g^3*h^6 + 11*a*b^5*c*d*g^3*h^6 - 31*a^2*b^3*c^2*d*g^3*h^6 - 32*a^3*b*c^3*d*g^3*h^6 + a^2*b^5*f*g^3*h^6 + 13*a^3*b^3*c*f*g^3*h^6 + 16*a^4*b*c^2*f*g^3*h^6 - 3*a*b^6*d*g^2*h^7 + 30*a^3*b^2*c^2*d*g^2*h^7 - 3*a^3*b^4*f*g^2*h^7 - 6*a^4*b^2*c*f*g^2*h^7 + 3*a^2*b^5*d*g*h^8 - 9*a^3*b^3*c*d*g*h^8 - 3*a^4*b*c^2*d*g*h^8 + 3*a^4*b^3*f*g*h^8 - 3*a^5*b*c*f*g*h^8 - a^3*b^4*d*h^9 + 4*a^4*b^2*c*d*h^9 - 2*a^5*c^2*d*h^9 - a^5*b^2*f*h^9 + 2*a^6*c*f*h^9 - 2*a*c^6*g^9*e + 9*a*b*c^5*g^8*h*e - 18*a*b^2*c^4*g^7*h^2*e + 21*a*b^3*c^3*g^6*h^3*e - 15*a*b^4*c^2*g^5*h^4*e - 6*a^2*b^2*c^3*g^5*h^4*e + 12*a^3*c^4*g^5*h^4*e + 6*a*b^5*c*g^4*h^5*e + 15*a^2*b^3*c^2*g^4*h^5*e - 30*a^3*b*c^3*g^4*h^5*e - a*b^6*g^3*h^6*e - 12*a^2*b^4*c*g^3*h^6*e + 18*a^3*b^2*c^2*g^3*h^6*e + 16*a^4*c^3*g^3*h^6*e + 3*a^2*b^5*g^2*h^7*e + 3*a^3*b^3*c*g^2*h^7*e - 24*a^4*b*c^2*g^2*h^7*e - 3*a^3*b^4*g*h^8*e + 6*a^4*b^2*c*g*h^8*e + 6*a^5*c^2*g*h^8*e + a^4*b^3*h^9*e - 3*a^5*b*c*h^9*e)/(b^2*c^6*g^12 - 4*a*c^7*g^12 - 6*b^3*c^5*g^11*h + 24*a*b*c^6*g^11*h + 15*b^4*c^4*g^10*h^2 - 54*a*b^2*c^5*g^10*h^2 - 24*a^2*c^6*g^10*h^2 - 20*b^5*c^3*g^9*h^3 + 50*a*b^3*c^4*g^9*h^3 + 120*a^2*b*c^5*g^9*h^3 + 15*b^6*c^2*g^8*h^4 - 225*a^2*b^2*c^4*g^8*h^4 - 60*a^3*c^5*g^8*h^4 - 6*b^7*c*g^7*h^5 - 36*a*b^5*c^2*g^7*h^5 + 180*a^2*b^3*c^3*g^7*h^5 + 240*a^3*b*c^4*g^7*h^5 + b^8*g^6*h^6 + 26*a*b^6*c*g^6*h^6 - 30*a^2*b^4*c^2*g^6*h^6 - 340*a^3*b^2*c^3*g^6*h^6 - 80*a^4*c^4*g^6*h^6 - 6*a*b^7*g^5*h^7 - 36*a^2*b^5*c*g^5*h^7 + 180*a^3*b^3*c^2*g^5*h^7 + 240*a^4*b*c^3*g^5*h^7 + 15*a^2*b^6*g^4*h^8 - 225*a^4*b^2*c^2*g^4*h^8 - 60*a^5*c^3*g^4*h^8 - 20*a^3*b^5*g^3*h^9 + 50*a^4*b^3*c*g^3*h^9 + 120*a^5*b*c^2*g^3*h^9 + 15*a^4*b^4*g^2*h^10 - 54*a^5*b^2*c*g^2*h^10 - 24*a^6*c^2*g^2*h^10 - 6*a^5*b^3*g*h^11 + 24*a^6*b*c*g*h^11 + a^6*b^2*h^12 - 4*a^7*c*h^12))/sqrt(c*x^2 + b*x + a) + 1/4*(8*c^2*f*g^4 + 8*b*c*f*g^3*h + 48*c^2*d*g^2*h^2 - b^2*f*g^2*h^2 - 44*a*c*f*g^2*h^2 - 48*b*c*d*g*h^3 + 8*a*b*f*g*h^3 + 15*b^2*d*h^4 - 12*a*c*d*h^4 + 8*a^2*f*h^4 - 24*c^2*g^3*h*e + 12*b*c*g^2*h^2*e - 3*b^2*g*h^3*e + 36*a*c*g*h^3*e - 12*a*b*h^4*e)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + b*x + a))*h + sqrt(c)*g)/sqrt(-c*g^2 + b*g*h - a*h^2))/((c^3*g^6 - 3*b*c^2*g^5*h + 3*b^2*c*g^4*h^2 + 3*a*c^2*g^4*h^2 - b^3*g^3*h^3 - 6*a*b*c*g^3*h^3 + 3*a*b^2*g^2*h^4 + 3*a^2*c*g^2*h^4 - 3*a^2*b*g*h^5 + a^3*h^6)*sqrt(-c*g^2 + b*g*h - a*h^2)) - 1/4*(8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*c^2*f*g^4*h + 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*c^2*d*g^2*h^3 - (sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^2*f*g^2*h^3 - 20*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*c*f*g^2*h^3 - 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b*c*d*g*h^4 + 8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b*f*g*h^4 + 7*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^2*d*h^5 - 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*c*d*h^5 - 16*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*c^2*g^3*h^2*e + 12*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b*c*g^2*h^3*e - 3*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^2*g*h^4*e + 12*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*c*g*h^4*e - 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b*h^5*e + 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*c^(5/2)*f*g^5 - 8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b*c^(3/2)*f*g^4*h + 56*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*c^(5/2)*d*g^3*h^2 + 5*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^2*sqrt(c)*f*g^3*h^2 - 44*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*c^(3/2)*f*g^3*h^2 - 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b*c^(3/2)*d*g^2*h^3 + 13*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^2*sqrt(c)*d*g*h^4 - 28*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*c^(3/2)*d*g*h^4 + 16*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*sqrt(c)*f*g*h^4 + 8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b*sqrt(c)*d*h^5 - 40*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*c^(5/2)*g^4*h*e + 28*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b*c^(3/2)*g^3*h^2*e - 9*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^2*sqrt(c)*g^2*h^3*e + 36*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*c^(3/2)*g^2*h^3*e - 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b*sqrt(c)*g*h^4*e - 8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*sqrt(c)*h^5*e + 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b*c^2*f*g^5 - 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^2*c*f*g^4*h - 40*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*c^2*f*g^4*h + 56*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b*c^2*d*g^3*h^2 + (sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^3*f*g^3*h^2 - 28*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b*c*f*g^3*h^2 - 44*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^2*c*d*g^2*h^3 - 88*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*c^2*d*g^2*h^3 + 7*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^2*f*g^2*h^3 + 44*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*c*f*g^2*h^3 + 9*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^3*d*g*h^4 + 60*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b*c*d*g*h^4 - 8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b*f*g*h^4 - 9*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^2*d*h^5 - 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*c*d*h^5 - 40*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b*c^2*g^4*h*e + 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^2*c*g^3*h^2*e + 64*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*c^2*g^3*h^2*e - 5*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^3*g^2*h^3*e - 16*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b*c*g^2*h^3*e + (sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^2*g*h^4*e - 20*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*c*g*h^4*e + 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b*h^5*e + 6*b^2*c^(3/2)*f*g^5 + b^3*sqrt(c)*f*g^4*h - 20*a*b*c^(3/2)*f*g^4*h + 14*b^2*c^(3/2)*d*g^3*h^2 - 9*a*b^2*sqrt(c)*f*g^3*h^2 + 12*a^2*c^(3/2)*f*g^3*h^2 - 7*b^3*sqrt(c)*d*g^2*h^3 - 44*a*b*c^(3/2)*d*g^2*h^3 + 24*a^2*b*sqrt(c)*f*g^2*h^3 + 23*a*b^2*sqrt(c)*d*g*h^4 + 28*a^2*c^(3/2)*d*g*h^4 - 16*a^3*sqrt(c)*f*g*h^4 - 16*a^2*b*sqrt(c)*d*h^5 - 10*b^2*c^(3/2)*g^4*h*e + 3*b^3*sqrt(c)*g^3*h^2*e + 32*a*b*c^(3/2)*g^3*h^2*e - 7*a*b^2*sqrt(c)*g^2*h^3*e - 20*a^2*c^(3/2)*g^2*h^3*e - 4*a^2*b*sqrt(c)*g*h^4*e + 8*a^3*sqrt(c)*h^5*e)/((c^3*g^6 - 3*b*c^2*g^5*h + 3*b^2*c*g^4*h^2 + 3*a*c^2*g^4*h^2 - b^3*g^3*h^3 - 6*a*b*c*g^3*h^3 + 3*a*b^2*g^2*h^4 + 3*a^2*c*g^2*h^4 - 3*a^2*b*g*h^5 + a^3*h^6)*((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*h + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c)*g + b*g - a*h)^2)","B",0
240,1,68,0,0.244488," ","integrate((1+2*x)^3*(4*x^2+3*x+1)/(3*x^2-x+2)^(1/2),x, algorithm=""giac"")","\frac{1}{3240} \, {\left(2 \, {\left(12 \, {\left(18 \, {\left(16 \, x + 51\right)} x + 1121\right)} x + 3769\right)} x - 22383\right)} \sqrt{3 \, x^{2} - x + 2} + \frac{9211}{3888} \, \sqrt{3} \log\left(-2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} - x + 2}\right)} + 1\right)"," ",0,"1/3240*(2*(12*(18*(16*x + 51)*x + 1121)*x + 3769)*x - 22383)*sqrt(3*x^2 - x + 2) + 9211/3888*sqrt(3)*log(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 - x + 2)) + 1)","A",0
241,1,63,0,0.220757," ","integrate((1+2*x)^2*(4*x^2+3*x+1)/(3*x^2-x+2)^(1/2),x, algorithm=""giac"")","\frac{1}{324} \, {\left(2 \, {\left(12 \, {\left(18 \, x + 49\right)} x + 569\right)} x - 243\right)} \sqrt{3 \, x^{2} - x + 2} + \frac{4147}{1944} \, \sqrt{3} \log\left(-2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} - x + 2}\right)} + 1\right)"," ",0,"1/324*(2*(12*(18*x + 49)*x + 569)*x - 243)*sqrt(3*x^2 - x + 2) + 4147/1944*sqrt(3)*log(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 - x + 2)) + 1)","A",0
242,1,58,0,0.263986," ","integrate((1+2*x)*(4*x^2+3*x+1)/(3*x^2-x+2)^(1/2),x, algorithm=""giac"")","\frac{1}{54} \, {\left(2 \, {\left(24 \, x + 55\right)} x + 81\right)} \sqrt{3 \, x^{2} - x + 2} + \frac{251}{324} \, \sqrt{3} \log\left(-2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} - x + 2}\right)} + 1\right)"," ",0,"1/54*(2*(24*x + 55)*x + 81)*sqrt(3*x^2 - x + 2) + 251/324*sqrt(3)*log(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 - x + 2)) + 1)","A",0
243,1,116,0,0.571591," ","integrate((4*x^2+3*x+1)/(1+2*x)/(3*x^2-x+2)^(1/2),x, algorithm=""giac"")","-\frac{5}{18} \, \sqrt{3} \log\left(-6 \, \sqrt{3} x + \sqrt{3} + 6 \, \sqrt{3 \, x^{2} - x + 2}\right) + \frac{1}{26} \, \sqrt{13} \log\left(-\frac{{\left| -4 \, \sqrt{3} x - 2 \, \sqrt{13} - 2 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} - x + 2} \right|}}{2 \, {\left(2 \, \sqrt{3} x - \sqrt{13} + \sqrt{3} - 2 \, \sqrt{3 \, x^{2} - x + 2}\right)}}\right) + \frac{2}{3} \, \sqrt{3 \, x^{2} - x + 2}"," ",0,"-5/18*sqrt(3)*log(-6*sqrt(3)*x + sqrt(3) + 6*sqrt(3*x^2 - x + 2)) + 1/26*sqrt(13)*log(-1/2*abs(-4*sqrt(3)*x - 2*sqrt(13) - 2*sqrt(3) + 4*sqrt(3*x^2 - x + 2))/(2*sqrt(3)*x - sqrt(13) + sqrt(3) - 2*sqrt(3*x^2 - x + 2))) + 2/3*sqrt(3*x^2 - x + 2)","A",0
244,1,48,0,0.277044," ","integrate((4*x^2+3*x+1)/(1+2*x)^2/(3*x^2-x+2)^(1/2),x, algorithm=""giac"")","\frac{1}{26} \, \sqrt{3} \mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right) - \frac{\sqrt{-\frac{8}{2 \, x + 1} + \frac{13}{{\left(2 \, x + 1\right)}^{2}} + 3}}{26 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right)}"," ",0,"1/26*sqrt(3)*sgn(1/(2*x + 1)) - 1/26*sqrt(-8/(2*x + 1) + 13/(2*x + 1)^2 + 3)/sgn(1/(2*x + 1))","A",0
245,1,204,0,0.328006," ","integrate((4*x^2+3*x+1)/(1+2*x)^3/(3*x^2-x+2)^(1/2),x, algorithm=""giac"")","\frac{581}{8788} \, \sqrt{13} \log\left(-\frac{{\left| -4 \, \sqrt{3} x - 2 \, \sqrt{13} - 2 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} - x + 2} \right|}}{2 \, {\left(2 \, \sqrt{3} x - \sqrt{13} + \sqrt{3} - 2 \, \sqrt{3 \, x^{2} - x + 2}\right)}}\right) + \frac{190 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} - x + 2}\right)}^{3} - 53 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} - x + 2}\right)}^{2} - 489 \, \sqrt{3} x + 289 \, \sqrt{3} + 489 \, \sqrt{3 \, x^{2} - x + 2}}{338 \, {\left(2 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} - x + 2}\right)}^{2} + 2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} - x + 2}\right)} - 5\right)}^{2}}"," ",0,"581/8788*sqrt(13)*log(-1/2*abs(-4*sqrt(3)*x - 2*sqrt(13) - 2*sqrt(3) + 4*sqrt(3*x^2 - x + 2))/(2*sqrt(3)*x - sqrt(13) + sqrt(3) - 2*sqrt(3*x^2 - x + 2))) + 1/338*(190*(sqrt(3)*x - sqrt(3*x^2 - x + 2))^3 - 53*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 - x + 2))^2 - 489*sqrt(3)*x + 289*sqrt(3) + 489*sqrt(3*x^2 - x + 2))/(2*(sqrt(3)*x - sqrt(3*x^2 - x + 2))^2 + 2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 - x + 2)) - 5)^2","B",0
246,1,67,0,0.209882," ","integrate((1+2*x)^3*(4*x^2+3*x+1)/(3*x^2-x+2)^(3/2),x, algorithm=""giac"")","\frac{353}{243} \, \sqrt{3} \log\left(-2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} - x + 2}\right)} + 1\right) + \frac{2 \, {\left({\left(23 \, {\left(6 \, {\left(24 \, x + 95\right)} x + 1009\right)} x - 2974\right)} x + 29997\right)}}{1863 \, \sqrt{3 \, x^{2} - x + 2}}"," ",0,"353/243*sqrt(3)*log(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 - x + 2)) + 1) + 2/1863*((23*(6*(24*x + 95)*x + 1009)*x - 2974)*x + 29997)/sqrt(3*x^2 - x + 2)","A",0
247,1,62,0,0.270815," ","integrate((1+2*x)^2*(4*x^2+3*x+1)/(3*x^2-x+2)^(3/2),x, algorithm=""giac"")","-\frac{64}{27} \, \sqrt{3} \log\left(-2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} - x + 2}\right)} + 1\right) + \frac{2 \, {\left({\left(92 \, {\left(3 \, x + 13\right)} x - 1003\right)} x + 1275\right)}}{207 \, \sqrt{3 \, x^{2} - x + 2}}"," ",0,"-64/27*sqrt(3)*log(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 - x + 2)) + 1) + 2/207*((92*(3*x + 13)*x - 1003)*x + 1275)/sqrt(3*x^2 - x + 2)","A",0
248,1,57,0,0.271713," ","integrate((1+2*x)*(4*x^2+3*x+1)/(3*x^2-x+2)^(3/2),x, algorithm=""giac"")","-\frac{14}{9} \, \sqrt{3} \log\left(-2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} - x + 2}\right)} + 1\right) + \frac{2 \, {\left({\left(92 \, x - 153\right)} x + 37\right)}}{69 \, \sqrt{3 \, x^{2} - x + 2}}"," ",0,"-14/9*sqrt(3)*log(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 - x + 2)) + 1) + 2/69*((92*x - 153)*x + 37)/sqrt(3*x^2 - x + 2)","A",0
249,1,91,0,0.580681," ","integrate((4*x^2+3*x+1)/(1+2*x)/(3*x^2-x+2)^(3/2),x, algorithm=""giac"")","\frac{2}{169} \, \sqrt{13} \log\left(-\frac{{\left| -4 \, \sqrt{3} x - 2 \, \sqrt{13} - 2 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} - x + 2} \right|}}{2 \, {\left(2 \, \sqrt{3} x - \sqrt{13} + \sqrt{3} - 2 \, \sqrt{3 \, x^{2} - x + 2}\right)}}\right) + \frac{2 \, {\left(77 \, x - 101\right)}}{299 \, \sqrt{3 \, x^{2} - x + 2}}"," ",0,"2/169*sqrt(13)*log(-1/2*abs(-4*sqrt(3)*x - 2*sqrt(13) - 2*sqrt(3) + 4*sqrt(3*x^2 - x + 2))/(2*sqrt(3)*x - sqrt(13) + sqrt(3) - 2*sqrt(3*x^2 - x + 2))) + 2/299*(77*x - 101)/sqrt(3*x^2 - x + 2)","A",0
250,1,168,0,0.297397," ","integrate((4*x^2+3*x+1)/(1+2*x)^2/(3*x^2-x+2)^(3/2),x, algorithm=""giac"")","-\frac{2}{50531} \, \sqrt{13} {\left(256 \, \sqrt{13} \sqrt{3} + 23 \, \log\left(\sqrt{13} \sqrt{3} - 4\right)\right)} \mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right) - \frac{2 \, {\left(\frac{\frac{1047}{\mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right)} + \frac{299}{{\left(2 \, x + 1\right)} \mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right)}}{2 \, x + 1} - \frac{768}{\mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right)}\right)}}{3887 \, \sqrt{-\frac{8}{2 \, x + 1} + \frac{13}{{\left(2 \, x + 1\right)}^{2}} + 3}} + \frac{2 \, \sqrt{13} \log\left(\sqrt{13} {\left(\sqrt{-\frac{8}{2 \, x + 1} + \frac{13}{{\left(2 \, x + 1\right)}^{2}} + 3} + \frac{\sqrt{13}}{2 \, x + 1}\right)} - 4\right)}{2197 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right)}"," ",0,"-2/50531*sqrt(13)*(256*sqrt(13)*sqrt(3) + 23*log(sqrt(13)*sqrt(3) - 4))*sgn(1/(2*x + 1)) - 2/3887*((1047/sgn(1/(2*x + 1)) + 299/((2*x + 1)*sgn(1/(2*x + 1))))/(2*x + 1) - 768/sgn(1/(2*x + 1)))/sqrt(-8/(2*x + 1) + 13/(2*x + 1)^2 + 3) + 2/2197*sqrt(13)*log(sqrt(13)*(sqrt(-8/(2*x + 1) + 13/(2*x + 1)^2 + 3) + sqrt(13)/(2*x + 1)) - 4)/sgn(1/(2*x + 1))","B",0
251,1,223,0,0.313259," ","integrate((4*x^2+3*x+1)/(1+2*x)^3/(3*x^2-x+2)^(3/2),x, algorithm=""giac"")","\frac{487}{28561} \, \sqrt{13} \log\left(-\frac{{\left| -4 \, \sqrt{3} x - 2 \, \sqrt{13} - 2 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} - x + 2} \right|}}{2 \, {\left(2 \, \sqrt{3} x - \sqrt{13} + \sqrt{3} - 2 \, \sqrt{3 \, x^{2} - x + 2}\right)}}\right) + \frac{2 \, {\left(3693 \, x + 2363\right)}}{50531 \, \sqrt{3 \, x^{2} - x + 2}} + \frac{2 \, {\left(62 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} - x + 2}\right)}^{3} - 37 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} - x + 2}\right)}^{2} + 263 \, \sqrt{3} x - 71 \, \sqrt{3} - 263 \, \sqrt{3 \, x^{2} - x + 2}\right)}}{2197 \, {\left(2 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} - x + 2}\right)}^{2} + 2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} - x + 2}\right)} - 5\right)}^{2}}"," ",0,"487/28561*sqrt(13)*log(-1/2*abs(-4*sqrt(3)*x - 2*sqrt(13) - 2*sqrt(3) + 4*sqrt(3*x^2 - x + 2))/(2*sqrt(3)*x - sqrt(13) + sqrt(3) - 2*sqrt(3*x^2 - x + 2))) + 2/50531*(3693*x + 2363)/sqrt(3*x^2 - x + 2) + 2/2197*(62*(sqrt(3)*x - sqrt(3*x^2 - x + 2))^3 - 37*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 - x + 2))^2 + 263*sqrt(3)*x - 71*sqrt(3) - 263*sqrt(3*x^2 - x + 2))/(2*(sqrt(3)*x - sqrt(3*x^2 - x + 2))^2 + 2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 - x + 2)) - 5)^2","B",0
252,1,67,0,0.207711," ","integrate((1+2*x)^3*(4*x^2+3*x+1)/(3*x^2-x+2)^(5/2),x, algorithm=""giac"")","-\frac{296}{81} \, \sqrt{3} \log\left(-2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} - x + 2}\right)} + 1\right) + \frac{2 \, {\left({\left(2 \, {\left(8 \, {\left(4761 \, x - 15494\right)} x + 4315\right)} x - 119459\right)} x - 44739\right)}}{14283 \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}}}"," ",0,"-296/81*sqrt(3)*log(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 - x + 2)) + 1) + 2/14283*((2*(8*(4761*x - 15494)*x + 4315)*x - 119459)*x - 44739)/(3*x^2 - x + 2)^(3/2)","A",0
253,1,62,0,0.237078," ","integrate((1+2*x)^2*(4*x^2+3*x+1)/(3*x^2-x+2)^(5/2),x, algorithm=""giac"")","-\frac{16}{27} \, \sqrt{3} \log\left(-2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} - x + 2}\right)} + 1\right) + \frac{2 \, {\left({\left(4 \, {\left(491 \, x - 7916\right)} x + 5837\right)} x - 17481\right)}}{4761 \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}}}"," ",0,"-16/27*sqrt(3)*log(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 - x + 2)) + 1) + 2/4761*((4*(491*x - 7916)*x + 5837)*x - 17481)/(3*x^2 - x + 2)^(3/2)","A",0
254,1,28,0,0.196224," ","integrate((1+2*x)*(4*x^2+3*x+1)/(3*x^2-x+2)^(5/2),x, algorithm=""giac"")","\frac{2 \, {\left({\left(2 \, {\left(1430 \, x - 1773\right)} x + 1833\right)} x - 1915\right)}}{1587 \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}}}"," ",0,"2/1587*((2*(1430*x - 1773)*x + 1833)*x - 1915)/(3*x^2 - x + 2)^(3/2)","A",0
255,1,101,0,0.433583," ","integrate((4*x^2+3*x+1)/(1+2*x)/(3*x^2-x+2)^(5/2),x, algorithm=""giac"")","\frac{8}{2197} \, \sqrt{13} \log\left(-\frac{{\left| -4 \, \sqrt{3} x - 2 \, \sqrt{13} - 2 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} - x + 2} \right|}}{2 \, {\left(2 \, \sqrt{3} x - \sqrt{13} + \sqrt{3} - 2 \, \sqrt{3 \, x^{2} - x + 2}\right)}}\right) + \frac{2 \, {\left(3 \, {\left(6 \, {\left(4556 \, x - 1749\right)} x + 26359\right)} x - 32963\right)}}{268203 \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}}}"," ",0,"8/2197*sqrt(13)*log(-1/2*abs(-4*sqrt(3)*x - 2*sqrt(13) - 2*sqrt(3) + 4*sqrt(3*x^2 - x + 2))/(2*sqrt(3)*x - sqrt(13) + sqrt(3) - 2*sqrt(3*x^2 - x + 2))) + 2/268203*(3*(6*(4556*x - 1749)*x + 26359)*x - 32963)/(3*x^2 - x + 2)^(3/2)","A",0
256,1,233,0,0.363095," ","integrate((4*x^2+3*x+1)/(1+2*x)^2/(3*x^2-x+2)^(5/2),x, algorithm=""giac"")","-\frac{56}{15108769} \, \sqrt{13} {\left(872 \, \sqrt{13} \sqrt{3} - 529 \, \log\left(\sqrt{13} \sqrt{3} - 4\right)\right)} \mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right) - \frac{56 \, \sqrt{13} \log\left(\sqrt{13} {\left(\sqrt{-\frac{8}{2 \, x + 1} + \frac{13}{{\left(2 \, x + 1\right)}^{2}} + 3} + \frac{\sqrt{13}}{2 \, x + 1}\right)} - 4\right)}{28561 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right)} + \frac{8 \, {\left(\frac{\frac{\frac{13 \, {\left(\frac{77756}{\mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right)} + \frac{20631}{{\left(2 \, x + 1\right)} \mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right)}\right)}}{2 \, x + 1} - \frac{1399650}{\mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right)}}{2 \, x + 1} + \frac{625905}{\mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right)}}{2 \, x + 1} - \frac{164808}{\mathrm{sgn}\left(\frac{1}{2 \, x + 1}\right)}\right)}}{3486639 \, {\left(\frac{8}{2 \, x + 1} - \frac{13}{{\left(2 \, x + 1\right)}^{2}} - 3\right)} \sqrt{-\frac{8}{2 \, x + 1} + \frac{13}{{\left(2 \, x + 1\right)}^{2}} + 3}}"," ",0,"-56/15108769*sqrt(13)*(872*sqrt(13)*sqrt(3) - 529*log(sqrt(13)*sqrt(3) - 4))*sgn(1/(2*x + 1)) - 56/28561*sqrt(13)*log(sqrt(13)*(sqrt(-8/(2*x + 1) + 13/(2*x + 1)^2 + 3) + sqrt(13)/(2*x + 1)) - 4)/sgn(1/(2*x + 1)) + 8/3486639*(((13*(77756/sgn(1/(2*x + 1)) + 20631/((2*x + 1)*sgn(1/(2*x + 1))))/(2*x + 1) - 1399650/sgn(1/(2*x + 1)))/(2*x + 1) + 625905/sgn(1/(2*x + 1)))/(2*x + 1) - 164808/sgn(1/(2*x + 1)))/((8/(2*x + 1) - 13/(2*x + 1)^2 - 3)*sqrt(-8/(2*x + 1) + 13/(2*x + 1)^2 + 3))","B",0
257,1,233,0,0.348770," ","integrate((4*x^2+3*x+1)/(1+2*x)^3/(3*x^2-x+2)^(5/2),x, algorithm=""giac"")","\frac{2084}{371293} \, \sqrt{13} \log\left(-\frac{{\left| -4 \, \sqrt{3} x - 2 \, \sqrt{13} - 2 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} - x + 2} \right|}}{2 \, {\left(2 \, \sqrt{3} x - \sqrt{13} + \sqrt{3} - 2 \, \sqrt{3 \, x^{2} - x + 2}\right)}}\right) + \frac{2 \, {\left(3 \, {\left(6 \, {\left(310578 \, x - 26213\right)} x + 1455755\right)} x + 1634293\right)}}{45326307 \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}}} - \frac{8 \, {\left(66 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} - x + 2}\right)}^{3} + 21 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} - x + 2}\right)}^{2} - 1015 \, \sqrt{3} x + 431 \, \sqrt{3} + 1015 \, \sqrt{3 \, x^{2} - x + 2}\right)}}{28561 \, {\left(2 \, {\left(\sqrt{3} x - \sqrt{3 \, x^{2} - x + 2}\right)}^{2} + 2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} - x + 2}\right)} - 5\right)}^{2}}"," ",0,"2084/371293*sqrt(13)*log(-1/2*abs(-4*sqrt(3)*x - 2*sqrt(13) - 2*sqrt(3) + 4*sqrt(3*x^2 - x + 2))/(2*sqrt(3)*x - sqrt(13) + sqrt(3) - 2*sqrt(3*x^2 - x + 2))) + 2/45326307*(3*(6*(310578*x - 26213)*x + 1455755)*x + 1634293)/(3*x^2 - x + 2)^(3/2) - 8/28561*(66*(sqrt(3)*x - sqrt(3*x^2 - x + 2))^3 + 21*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 - x + 2))^2 - 1015*sqrt(3)*x + 431*sqrt(3) + 1015*sqrt(3*x^2 - x + 2))/(2*(sqrt(3)*x - sqrt(3*x^2 - x + 2))^2 + 2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 - x + 2)) - 5)^2","B",0
258,0,0,0,0.000000," ","integrate((f*x^2+e*x+d)/(h*x+g)/(c*h^2*x^2+b*h^2*x+b*g*h-c*g^2)^(3/2),x, algorithm=""giac"")","\int \frac{f x^{2} + e x + d}{{\left(c h^{2} x^{2} + b h^{2} x - c g^{2} + b g h\right)}^{\frac{3}{2}} {\left(h x + g\right)}}\,{d x}"," ",0,"integrate((f*x^2 + e*x + d)/((c*h^2*x^2 + b*h^2*x - c*g^2 + b*g*h)^(3/2)*(h*x + g)), x)","F",0
259,0,0,0,0.000000," ","integrate((e*x+d)^(1/2)*(C*x^2+B*x+A)*(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int {\left(C x^{2} + B x + A\right)} \sqrt{c x^{2} + b x + a} \sqrt{e x + d}\,{d x}"," ",0,"integrate((C*x^2 + B*x + A)*sqrt(c*x^2 + b*x + a)*sqrt(e*x + d), x)","F",0
260,0,0,0,0.000000," ","integrate((C*x^2+B*x+A)*(c*x^2+b*x+a)^(1/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C x^{2} + B x + A\right)} \sqrt{c x^{2} + b x + a}}{\sqrt{e x + d}}\,{d x}"," ",0,"integrate((C*x^2 + B*x + A)*sqrt(c*x^2 + b*x + a)/sqrt(e*x + d), x)","F",0
261,0,0,0,0.000000," ","integrate((C*x^2+B*x+A)*(c*x^2+b*x+a)^(1/2)/(e*x+d)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C x^{2} + B x + A\right)} \sqrt{c x^{2} + b x + a}}{{\left(e x + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*x^2 + B*x + A)*sqrt(c*x^2 + b*x + a)/(e*x + d)^(3/2), x)","F",0
262,0,0,0,0.000000," ","integrate((C*x^2+B*x+A)*(c*x^2+b*x+a)^(1/2)/(e*x+d)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C x^{2} + B x + A\right)} \sqrt{c x^{2} + b x + a}}{{\left(e x + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*x^2 + B*x + A)*sqrt(c*x^2 + b*x + a)/(e*x + d)^(5/2), x)","F",0
263,-2,0,0,0.000000," ","integrate((C*x^2+B*x+A)*(c*x^2+b*x+a)^(1/2)/(e*x+d)^(7/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(d*exp(1)+x*exp(1)^2)]integrate()  Bad Argument Typeintegrate()  Bad Argument TypeEvaluation time: 23.8Unable to transpose Error: Bad Argument Value","F(-2)",0
264,0,0,0,0.000000," ","integrate((C*x^2+B*x+A)*(c*x^2+b*x+a)^(1/2)/(e*x+d)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(C x^{2} + B x + A\right)} \sqrt{c x^{2} + b x + a}}{{\left(e x + d\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*x^2 + B*x + A)*sqrt(c*x^2 + b*x + a)/(e*x + d)^(9/2), x)","F",0
265,0,0,0,0.000000," ","integrate((C*x^2+B*x+A)*(c*x^2+b*x+a)^(1/2)/(e*x+d)^(11/2),x, algorithm=""giac"")","\int \frac{{\left(C x^{2} + B x + A\right)} \sqrt{c x^{2} + b x + a}}{{\left(e x + d\right)}^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((C*x^2 + B*x + A)*sqrt(c*x^2 + b*x + a)/(e*x + d)^(11/2), x)","F",0
266,0,0,0,0.000000," ","integrate((e*x+d)^(3/2)*(C*x^2+B*x+A)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C x^{2} + B x + A\right)} {\left(e x + d\right)}^{\frac{3}{2}}}{\sqrt{c x^{2} + b x + a}}\,{d x}"," ",0,"integrate((C*x^2 + B*x + A)*(e*x + d)^(3/2)/sqrt(c*x^2 + b*x + a), x)","F",0
267,0,0,0,0.000000," ","integrate((e*x+d)^(1/2)*(C*x^2+B*x+A)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C x^{2} + B x + A\right)} \sqrt{e x + d}}{\sqrt{c x^{2} + b x + a}}\,{d x}"," ",0,"integrate((C*x^2 + B*x + A)*sqrt(e*x + d)/sqrt(c*x^2 + b*x + a), x)","F",0
268,0,0,0,0.000000," ","integrate((C*x^2+B*x+A)/(e*x+d)^(1/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \frac{C x^{2} + B x + A}{\sqrt{c x^{2} + b x + a} \sqrt{e x + d}}\,{d x}"," ",0,"integrate((C*x^2 + B*x + A)/(sqrt(c*x^2 + b*x + a)*sqrt(e*x + d)), x)","F",0
269,0,0,0,0.000000," ","integrate((C*x^2+B*x+A)/(e*x+d)^(3/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \frac{C x^{2} + B x + A}{\sqrt{c x^{2} + b x + a} {\left(e x + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*x^2 + B*x + A)/(sqrt(c*x^2 + b*x + a)*(e*x + d)^(3/2)), x)","F",0
270,0,0,0,0.000000," ","integrate((C*x^2+B*x+A)/(e*x+d)^(5/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \frac{C x^{2} + B x + A}{\sqrt{c x^{2} + b x + a} {\left(e x + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*x^2 + B*x + A)/(sqrt(c*x^2 + b*x + a)*(e*x + d)^(5/2)), x)","F",0
271,0,0,0,0.000000," ","integrate((C*x^2+B*x+A)/(e*x+d)^(7/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \frac{C x^{2} + B x + A}{\sqrt{c x^{2} + b x + a} {\left(e x + d\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*x^2 + B*x + A)/(sqrt(c*x^2 + b*x + a)*(e*x + d)^(7/2)), x)","F",0
272,0,0,0,0.000000," ","integrate((h*x+g)^m*(c*x^2+b*x+a)^p*(f*x^2+e*x+d),x, algorithm=""giac"")","\int {\left(f x^{2} + e x + d\right)} {\left(c x^{2} + b x + a\right)}^{p} {\left(h x + g\right)}^{m}\,{d x}"," ",0,"integrate((f*x^2 + e*x + d)*(c*x^2 + b*x + a)^p*(h*x + g)^m, x)","F",0
273,0,0,0,0.000000," ","integrate((h*x+g)^m*(f*x^2+e*x+d)*(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{2} + b x + a} {\left(f x^{2} + e x + d\right)} {\left(h x + g\right)}^{m}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + b*x + a)*(f*x^2 + e*x + d)*(h*x + g)^m, x)","F",0
274,0,0,0,0.000000," ","integrate((h*x+g)^(-3-2*p)*(c*x^2+b*x+a)^p*(f*x^2+e*x+d),x, algorithm=""giac"")","\int {\left(f x^{2} + e x + d\right)} {\left(c x^{2} + b x + a\right)}^{p} {\left(h x + g\right)}^{-2 \, p - 3}\,{d x}"," ",0,"integrate((f*x^2 + e*x + d)*(c*x^2 + b*x + a)^p*(h*x + g)^(-2*p - 3), x)","F",0
275,1,141,0,0.181300," ","integrate((f*x^2+d)^p*(2*c*d*f+2*b*f^2*(3+2*p)*x+2*c*f^2*(3+2*p)*x^2),x, algorithm=""giac"")","\frac{2 \, {\left(f x^{2} + d\right)}^{p} c f^{2} p x^{3} + 2 \, {\left(f x^{2} + d\right)}^{p} b f^{2} p x^{2} + 2 \, {\left(f x^{2} + d\right)}^{p} c f^{2} x^{3} + 2 \, {\left(f x^{2} + d\right)}^{p} c d f p x + 3 \, {\left(f x^{2} + d\right)}^{p} b f^{2} x^{2} + 2 \, {\left(f x^{2} + d\right)}^{p} b d f p + 2 \, {\left(f x^{2} + d\right)}^{p} c d f x + 3 \, {\left(f x^{2} + d\right)}^{p} b d f}{p + 1}"," ",0,"(2*(f*x^2 + d)^p*c*f^2*p*x^3 + 2*(f*x^2 + d)^p*b*f^2*p*x^2 + 2*(f*x^2 + d)^p*c*f^2*x^3 + 2*(f*x^2 + d)^p*c*d*f*p*x + 3*(f*x^2 + d)^p*b*f^2*x^2 + 2*(f*x^2 + d)^p*b*d*f*p + 2*(f*x^2 + d)^p*c*d*f*x + 3*(f*x^2 + d)^p*b*d*f)/(p + 1)","B",0
276,1,191,0,0.243775," ","integrate((f*x^2+e*x+d)^p*(-2*c*e^2+2*c*d*f-c*e^2*p+2*c*f^2*(3+2*p)*x^2),x, algorithm=""giac"")","\frac{2 \, {\left(f x^{2} + x e + d\right)}^{p} c f^{2} p x^{3} + 2 \, {\left(f x^{2} + x e + d\right)}^{p} c f^{2} x^{3} + {\left(f x^{2} + x e + d\right)}^{p} c f p x^{2} e + 2 \, {\left(f x^{2} + x e + d\right)}^{p} c d f p x + 2 \, {\left(f x^{2} + x e + d\right)}^{p} c d f x - {\left(f x^{2} + x e + d\right)}^{p} c p x e^{2} - {\left(f x^{2} + x e + d\right)}^{p} c d p e - 2 \, {\left(f x^{2} + x e + d\right)}^{p} c x e^{2} - 2 \, {\left(f x^{2} + x e + d\right)}^{p} c d e}{p + 1}"," ",0,"(2*(f*x^2 + x*e + d)^p*c*f^2*p*x^3 + 2*(f*x^2 + x*e + d)^p*c*f^2*x^3 + (f*x^2 + x*e + d)^p*c*f*p*x^2*e + 2*(f*x^2 + x*e + d)^p*c*d*f*p*x + 2*(f*x^2 + x*e + d)^p*c*d*f*x - (f*x^2 + x*e + d)^p*c*p*x*e^2 - (f*x^2 + x*e + d)^p*c*d*p*e - 2*(f*x^2 + x*e + d)^p*c*x*e^2 - 2*(f*x^2 + x*e + d)^p*c*d*e)/(p + 1)","B",0
277,1,314,0,0.305554," ","integrate((f*x^2+e*x+d)^p*(-2*c*e^2+2*c*d*f+3*b*e*f-c*e^2*p+2*b*e*f*p+2*b*f^2*(3+2*p)*x+2*c*f^2*(3+2*p)*x^2),x, algorithm=""giac"")","\frac{2 \, {\left(f x^{2} + x e + d\right)}^{p} c f^{2} p x^{3} + 2 \, {\left(f x^{2} + x e + d\right)}^{p} b f^{2} p x^{2} + 2 \, {\left(f x^{2} + x e + d\right)}^{p} c f^{2} x^{3} + {\left(f x^{2} + x e + d\right)}^{p} c f p x^{2} e + 2 \, {\left(f x^{2} + x e + d\right)}^{p} c d f p x + 3 \, {\left(f x^{2} + x e + d\right)}^{p} b f^{2} x^{2} + 2 \, {\left(f x^{2} + x e + d\right)}^{p} b f p x e + 2 \, {\left(f x^{2} + x e + d\right)}^{p} b d f p + 2 \, {\left(f x^{2} + x e + d\right)}^{p} c d f x - {\left(f x^{2} + x e + d\right)}^{p} c p x e^{2} - {\left(f x^{2} + x e + d\right)}^{p} c d p e + 3 \, {\left(f x^{2} + x e + d\right)}^{p} b f x e + 3 \, {\left(f x^{2} + x e + d\right)}^{p} b d f - 2 \, {\left(f x^{2} + x e + d\right)}^{p} c x e^{2} - 2 \, {\left(f x^{2} + x e + d\right)}^{p} c d e}{p + 1}"," ",0,"(2*(f*x^2 + x*e + d)^p*c*f^2*p*x^3 + 2*(f*x^2 + x*e + d)^p*b*f^2*p*x^2 + 2*(f*x^2 + x*e + d)^p*c*f^2*x^3 + (f*x^2 + x*e + d)^p*c*f*p*x^2*e + 2*(f*x^2 + x*e + d)^p*c*d*f*p*x + 3*(f*x^2 + x*e + d)^p*b*f^2*x^2 + 2*(f*x^2 + x*e + d)^p*b*f*p*x*e + 2*(f*x^2 + x*e + d)^p*b*d*f*p + 2*(f*x^2 + x*e + d)^p*c*d*f*x - (f*x^2 + x*e + d)^p*c*p*x*e^2 - (f*x^2 + x*e + d)^p*c*d*p*e + 3*(f*x^2 + x*e + d)^p*b*f*x*e + 3*(f*x^2 + x*e + d)^p*b*d*f - 2*(f*x^2 + x*e + d)^p*c*x*e^2 - 2*(f*x^2 + x*e + d)^p*c*d*e)/(p + 1)","B",0
278,1,2383,0,0.230432," ","integrate((e*x+d)^3*(c*x^2+b*x+a)^5*(d*(5*a*e+6*b*d)+(5*a*e^2+17*b*d*e+12*c*d^2)*x+e*(11*b*e+29*c*d)*x^2+17*c*e^2*x^3),x, algorithm=""giac"")","c^{6} x^{17} e^{5} + 5 \, c^{6} d x^{16} e^{4} + 10 \, c^{6} d^{2} x^{15} e^{3} + 10 \, c^{6} d^{3} x^{14} e^{2} + 5 \, c^{6} d^{4} x^{13} e + c^{6} d^{5} x^{12} + 6 \, b c^{5} x^{16} e^{5} + 30 \, b c^{5} d x^{15} e^{4} + 60 \, b c^{5} d^{2} x^{14} e^{3} + 60 \, b c^{5} d^{3} x^{13} e^{2} + 30 \, b c^{5} d^{4} x^{12} e + 6 \, b c^{5} d^{5} x^{11} + 15 \, b^{2} c^{4} x^{15} e^{5} + 6 \, a c^{5} x^{15} e^{5} + 75 \, b^{2} c^{4} d x^{14} e^{4} + 30 \, a c^{5} d x^{14} e^{4} + 150 \, b^{2} c^{4} d^{2} x^{13} e^{3} + 60 \, a c^{5} d^{2} x^{13} e^{3} + 150 \, b^{2} c^{4} d^{3} x^{12} e^{2} + 60 \, a c^{5} d^{3} x^{12} e^{2} + 75 \, b^{2} c^{4} d^{4} x^{11} e + 30 \, a c^{5} d^{4} x^{11} e + 15 \, b^{2} c^{4} d^{5} x^{10} + 6 \, a c^{5} d^{5} x^{10} + 20 \, b^{3} c^{3} x^{14} e^{5} + 30 \, a b c^{4} x^{14} e^{5} + 100 \, b^{3} c^{3} d x^{13} e^{4} + 150 \, a b c^{4} d x^{13} e^{4} + 200 \, b^{3} c^{3} d^{2} x^{12} e^{3} + 300 \, a b c^{4} d^{2} x^{12} e^{3} + 200 \, b^{3} c^{3} d^{3} x^{11} e^{2} + 300 \, a b c^{4} d^{3} x^{11} e^{2} + 100 \, b^{3} c^{3} d^{4} x^{10} e + 150 \, a b c^{4} d^{4} x^{10} e + 20 \, b^{3} c^{3} d^{5} x^{9} + 30 \, a b c^{4} d^{5} x^{9} + 15 \, b^{4} c^{2} x^{13} e^{5} + 60 \, a b^{2} c^{3} x^{13} e^{5} + 15 \, a^{2} c^{4} x^{13} e^{5} + 75 \, b^{4} c^{2} d x^{12} e^{4} + 300 \, a b^{2} c^{3} d x^{12} e^{4} + 75 \, a^{2} c^{4} d x^{12} e^{4} + 150 \, b^{4} c^{2} d^{2} x^{11} e^{3} + 600 \, a b^{2} c^{3} d^{2} x^{11} e^{3} + 150 \, a^{2} c^{4} d^{2} x^{11} e^{3} + 150 \, b^{4} c^{2} d^{3} x^{10} e^{2} + 600 \, a b^{2} c^{3} d^{3} x^{10} e^{2} + 150 \, a^{2} c^{4} d^{3} x^{10} e^{2} + 75 \, b^{4} c^{2} d^{4} x^{9} e + 300 \, a b^{2} c^{3} d^{4} x^{9} e + 75 \, a^{2} c^{4} d^{4} x^{9} e + 15 \, b^{4} c^{2} d^{5} x^{8} + 60 \, a b^{2} c^{3} d^{5} x^{8} + 15 \, a^{2} c^{4} d^{5} x^{8} + 6 \, b^{5} c x^{12} e^{5} + 60 \, a b^{3} c^{2} x^{12} e^{5} + 60 \, a^{2} b c^{3} x^{12} e^{5} + 30 \, b^{5} c d x^{11} e^{4} + 300 \, a b^{3} c^{2} d x^{11} e^{4} + 300 \, a^{2} b c^{3} d x^{11} e^{4} + 60 \, b^{5} c d^{2} x^{10} e^{3} + 600 \, a b^{3} c^{2} d^{2} x^{10} e^{3} + 600 \, a^{2} b c^{3} d^{2} x^{10} e^{3} + 60 \, b^{5} c d^{3} x^{9} e^{2} + 600 \, a b^{3} c^{2} d^{3} x^{9} e^{2} + 600 \, a^{2} b c^{3} d^{3} x^{9} e^{2} + 30 \, b^{5} c d^{4} x^{8} e + 300 \, a b^{3} c^{2} d^{4} x^{8} e + 300 \, a^{2} b c^{3} d^{4} x^{8} e + 6 \, b^{5} c d^{5} x^{7} + 60 \, a b^{3} c^{2} d^{5} x^{7} + 60 \, a^{2} b c^{3} d^{5} x^{7} + b^{6} x^{11} e^{5} + 30 \, a b^{4} c x^{11} e^{5} + 90 \, a^{2} b^{2} c^{2} x^{11} e^{5} + 20 \, a^{3} c^{3} x^{11} e^{5} + 5 \, b^{6} d x^{10} e^{4} + 150 \, a b^{4} c d x^{10} e^{4} + 450 \, a^{2} b^{2} c^{2} d x^{10} e^{4} + 100 \, a^{3} c^{3} d x^{10} e^{4} + 10 \, b^{6} d^{2} x^{9} e^{3} + 300 \, a b^{4} c d^{2} x^{9} e^{3} + 900 \, a^{2} b^{2} c^{2} d^{2} x^{9} e^{3} + 200 \, a^{3} c^{3} d^{2} x^{9} e^{3} + 10 \, b^{6} d^{3} x^{8} e^{2} + 300 \, a b^{4} c d^{3} x^{8} e^{2} + 900 \, a^{2} b^{2} c^{2} d^{3} x^{8} e^{2} + 200 \, a^{3} c^{3} d^{3} x^{8} e^{2} + 5 \, b^{6} d^{4} x^{7} e + 150 \, a b^{4} c d^{4} x^{7} e + 450 \, a^{2} b^{2} c^{2} d^{4} x^{7} e + 100 \, a^{3} c^{3} d^{4} x^{7} e + b^{6} d^{5} x^{6} + 30 \, a b^{4} c d^{5} x^{6} + 90 \, a^{2} b^{2} c^{2} d^{5} x^{6} + 20 \, a^{3} c^{3} d^{5} x^{6} + 6 \, a b^{5} x^{10} e^{5} + 60 \, a^{2} b^{3} c x^{10} e^{5} + 60 \, a^{3} b c^{2} x^{10} e^{5} + 30 \, a b^{5} d x^{9} e^{4} + 300 \, a^{2} b^{3} c d x^{9} e^{4} + 300 \, a^{3} b c^{2} d x^{9} e^{4} + 60 \, a b^{5} d^{2} x^{8} e^{3} + 600 \, a^{2} b^{3} c d^{2} x^{8} e^{3} + 600 \, a^{3} b c^{2} d^{2} x^{8} e^{3} + 60 \, a b^{5} d^{3} x^{7} e^{2} + 600 \, a^{2} b^{3} c d^{3} x^{7} e^{2} + 600 \, a^{3} b c^{2} d^{3} x^{7} e^{2} + 30 \, a b^{5} d^{4} x^{6} e + 300 \, a^{2} b^{3} c d^{4} x^{6} e + 300 \, a^{3} b c^{2} d^{4} x^{6} e + 6 \, a b^{5} d^{5} x^{5} + 60 \, a^{2} b^{3} c d^{5} x^{5} + 60 \, a^{3} b c^{2} d^{5} x^{5} + 15 \, a^{2} b^{4} x^{9} e^{5} + 60 \, a^{3} b^{2} c x^{9} e^{5} + 15 \, a^{4} c^{2} x^{9} e^{5} + 75 \, a^{2} b^{4} d x^{8} e^{4} + 300 \, a^{3} b^{2} c d x^{8} e^{4} + 75 \, a^{4} c^{2} d x^{8} e^{4} + 150 \, a^{2} b^{4} d^{2} x^{7} e^{3} + 600 \, a^{3} b^{2} c d^{2} x^{7} e^{3} + 150 \, a^{4} c^{2} d^{2} x^{7} e^{3} + 150 \, a^{2} b^{4} d^{3} x^{6} e^{2} + 600 \, a^{3} b^{2} c d^{3} x^{6} e^{2} + 150 \, a^{4} c^{2} d^{3} x^{6} e^{2} + 75 \, a^{2} b^{4} d^{4} x^{5} e + 300 \, a^{3} b^{2} c d^{4} x^{5} e + 75 \, a^{4} c^{2} d^{4} x^{5} e + 15 \, a^{2} b^{4} d^{5} x^{4} + 60 \, a^{3} b^{2} c d^{5} x^{4} + 15 \, a^{4} c^{2} d^{5} x^{4} + 20 \, a^{3} b^{3} x^{8} e^{5} + 30 \, a^{4} b c x^{8} e^{5} + 100 \, a^{3} b^{3} d x^{7} e^{4} + 150 \, a^{4} b c d x^{7} e^{4} + 200 \, a^{3} b^{3} d^{2} x^{6} e^{3} + 300 \, a^{4} b c d^{2} x^{6} e^{3} + 200 \, a^{3} b^{3} d^{3} x^{5} e^{2} + 300 \, a^{4} b c d^{3} x^{5} e^{2} + 100 \, a^{3} b^{3} d^{4} x^{4} e + 150 \, a^{4} b c d^{4} x^{4} e + 20 \, a^{3} b^{3} d^{5} x^{3} + 30 \, a^{4} b c d^{5} x^{3} + 15 \, a^{4} b^{2} x^{7} e^{5} + 6 \, a^{5} c x^{7} e^{5} + 75 \, a^{4} b^{2} d x^{6} e^{4} + 30 \, a^{5} c d x^{6} e^{4} + 150 \, a^{4} b^{2} d^{2} x^{5} e^{3} + 60 \, a^{5} c d^{2} x^{5} e^{3} + 150 \, a^{4} b^{2} d^{3} x^{4} e^{2} + 60 \, a^{5} c d^{3} x^{4} e^{2} + 75 \, a^{4} b^{2} d^{4} x^{3} e + 30 \, a^{5} c d^{4} x^{3} e + 15 \, a^{4} b^{2} d^{5} x^{2} + 6 \, a^{5} c d^{5} x^{2} + 6 \, a^{5} b x^{6} e^{5} + 30 \, a^{5} b d x^{5} e^{4} + 60 \, a^{5} b d^{2} x^{4} e^{3} + 60 \, a^{5} b d^{3} x^{3} e^{2} + 30 \, a^{5} b d^{4} x^{2} e + 6 \, a^{5} b d^{5} x + a^{6} x^{5} e^{5} + 5 \, a^{6} d x^{4} e^{4} + 10 \, a^{6} d^{2} x^{3} e^{3} + 10 \, a^{6} d^{3} x^{2} e^{2} + 5 \, a^{6} d^{4} x e"," ",0,"c^6*x^17*e^5 + 5*c^6*d*x^16*e^4 + 10*c^6*d^2*x^15*e^3 + 10*c^6*d^3*x^14*e^2 + 5*c^6*d^4*x^13*e + c^6*d^5*x^12 + 6*b*c^5*x^16*e^5 + 30*b*c^5*d*x^15*e^4 + 60*b*c^5*d^2*x^14*e^3 + 60*b*c^5*d^3*x^13*e^2 + 30*b*c^5*d^4*x^12*e + 6*b*c^5*d^5*x^11 + 15*b^2*c^4*x^15*e^5 + 6*a*c^5*x^15*e^5 + 75*b^2*c^4*d*x^14*e^4 + 30*a*c^5*d*x^14*e^4 + 150*b^2*c^4*d^2*x^13*e^3 + 60*a*c^5*d^2*x^13*e^3 + 150*b^2*c^4*d^3*x^12*e^2 + 60*a*c^5*d^3*x^12*e^2 + 75*b^2*c^4*d^4*x^11*e + 30*a*c^5*d^4*x^11*e + 15*b^2*c^4*d^5*x^10 + 6*a*c^5*d^5*x^10 + 20*b^3*c^3*x^14*e^5 + 30*a*b*c^4*x^14*e^5 + 100*b^3*c^3*d*x^13*e^4 + 150*a*b*c^4*d*x^13*e^4 + 200*b^3*c^3*d^2*x^12*e^3 + 300*a*b*c^4*d^2*x^12*e^3 + 200*b^3*c^3*d^3*x^11*e^2 + 300*a*b*c^4*d^3*x^11*e^2 + 100*b^3*c^3*d^4*x^10*e + 150*a*b*c^4*d^4*x^10*e + 20*b^3*c^3*d^5*x^9 + 30*a*b*c^4*d^5*x^9 + 15*b^4*c^2*x^13*e^5 + 60*a*b^2*c^3*x^13*e^5 + 15*a^2*c^4*x^13*e^5 + 75*b^4*c^2*d*x^12*e^4 + 300*a*b^2*c^3*d*x^12*e^4 + 75*a^2*c^4*d*x^12*e^4 + 150*b^4*c^2*d^2*x^11*e^3 + 600*a*b^2*c^3*d^2*x^11*e^3 + 150*a^2*c^4*d^2*x^11*e^3 + 150*b^4*c^2*d^3*x^10*e^2 + 600*a*b^2*c^3*d^3*x^10*e^2 + 150*a^2*c^4*d^3*x^10*e^2 + 75*b^4*c^2*d^4*x^9*e + 300*a*b^2*c^3*d^4*x^9*e + 75*a^2*c^4*d^4*x^9*e + 15*b^4*c^2*d^5*x^8 + 60*a*b^2*c^3*d^5*x^8 + 15*a^2*c^4*d^5*x^8 + 6*b^5*c*x^12*e^5 + 60*a*b^3*c^2*x^12*e^5 + 60*a^2*b*c^3*x^12*e^5 + 30*b^5*c*d*x^11*e^4 + 300*a*b^3*c^2*d*x^11*e^4 + 300*a^2*b*c^3*d*x^11*e^4 + 60*b^5*c*d^2*x^10*e^3 + 600*a*b^3*c^2*d^2*x^10*e^3 + 600*a^2*b*c^3*d^2*x^10*e^3 + 60*b^5*c*d^3*x^9*e^2 + 600*a*b^3*c^2*d^3*x^9*e^2 + 600*a^2*b*c^3*d^3*x^9*e^2 + 30*b^5*c*d^4*x^8*e + 300*a*b^3*c^2*d^4*x^8*e + 300*a^2*b*c^3*d^4*x^8*e + 6*b^5*c*d^5*x^7 + 60*a*b^3*c^2*d^5*x^7 + 60*a^2*b*c^3*d^5*x^7 + b^6*x^11*e^5 + 30*a*b^4*c*x^11*e^5 + 90*a^2*b^2*c^2*x^11*e^5 + 20*a^3*c^3*x^11*e^5 + 5*b^6*d*x^10*e^4 + 150*a*b^4*c*d*x^10*e^4 + 450*a^2*b^2*c^2*d*x^10*e^4 + 100*a^3*c^3*d*x^10*e^4 + 10*b^6*d^2*x^9*e^3 + 300*a*b^4*c*d^2*x^9*e^3 + 900*a^2*b^2*c^2*d^2*x^9*e^3 + 200*a^3*c^3*d^2*x^9*e^3 + 10*b^6*d^3*x^8*e^2 + 300*a*b^4*c*d^3*x^8*e^2 + 900*a^2*b^2*c^2*d^3*x^8*e^2 + 200*a^3*c^3*d^3*x^8*e^2 + 5*b^6*d^4*x^7*e + 150*a*b^4*c*d^4*x^7*e + 450*a^2*b^2*c^2*d^4*x^7*e + 100*a^3*c^3*d^4*x^7*e + b^6*d^5*x^6 + 30*a*b^4*c*d^5*x^6 + 90*a^2*b^2*c^2*d^5*x^6 + 20*a^3*c^3*d^5*x^6 + 6*a*b^5*x^10*e^5 + 60*a^2*b^3*c*x^10*e^5 + 60*a^3*b*c^2*x^10*e^5 + 30*a*b^5*d*x^9*e^4 + 300*a^2*b^3*c*d*x^9*e^4 + 300*a^3*b*c^2*d*x^9*e^4 + 60*a*b^5*d^2*x^8*e^3 + 600*a^2*b^3*c*d^2*x^8*e^3 + 600*a^3*b*c^2*d^2*x^8*e^3 + 60*a*b^5*d^3*x^7*e^2 + 600*a^2*b^3*c*d^3*x^7*e^2 + 600*a^3*b*c^2*d^3*x^7*e^2 + 30*a*b^5*d^4*x^6*e + 300*a^2*b^3*c*d^4*x^6*e + 300*a^3*b*c^2*d^4*x^6*e + 6*a*b^5*d^5*x^5 + 60*a^2*b^3*c*d^5*x^5 + 60*a^3*b*c^2*d^5*x^5 + 15*a^2*b^4*x^9*e^5 + 60*a^3*b^2*c*x^9*e^5 + 15*a^4*c^2*x^9*e^5 + 75*a^2*b^4*d*x^8*e^4 + 300*a^3*b^2*c*d*x^8*e^4 + 75*a^4*c^2*d*x^8*e^4 + 150*a^2*b^4*d^2*x^7*e^3 + 600*a^3*b^2*c*d^2*x^7*e^3 + 150*a^4*c^2*d^2*x^7*e^3 + 150*a^2*b^4*d^3*x^6*e^2 + 600*a^3*b^2*c*d^3*x^6*e^2 + 150*a^4*c^2*d^3*x^6*e^2 + 75*a^2*b^4*d^4*x^5*e + 300*a^3*b^2*c*d^4*x^5*e + 75*a^4*c^2*d^4*x^5*e + 15*a^2*b^4*d^5*x^4 + 60*a^3*b^2*c*d^5*x^4 + 15*a^4*c^2*d^5*x^4 + 20*a^3*b^3*x^8*e^5 + 30*a^4*b*c*x^8*e^5 + 100*a^3*b^3*d*x^7*e^4 + 150*a^4*b*c*d*x^7*e^4 + 200*a^3*b^3*d^2*x^6*e^3 + 300*a^4*b*c*d^2*x^6*e^3 + 200*a^3*b^3*d^3*x^5*e^2 + 300*a^4*b*c*d^3*x^5*e^2 + 100*a^3*b^3*d^4*x^4*e + 150*a^4*b*c*d^4*x^4*e + 20*a^3*b^3*d^5*x^3 + 30*a^4*b*c*d^5*x^3 + 15*a^4*b^2*x^7*e^5 + 6*a^5*c*x^7*e^5 + 75*a^4*b^2*d*x^6*e^4 + 30*a^5*c*d*x^6*e^4 + 150*a^4*b^2*d^2*x^5*e^3 + 60*a^5*c*d^2*x^5*e^3 + 150*a^4*b^2*d^3*x^4*e^2 + 60*a^5*c*d^3*x^4*e^2 + 75*a^4*b^2*d^4*x^3*e + 30*a^5*c*d^4*x^3*e + 15*a^4*b^2*d^5*x^2 + 6*a^5*c*d^5*x^2 + 6*a^5*b*x^6*e^5 + 30*a^5*b*d*x^5*e^4 + 60*a^5*b*d^2*x^4*e^3 + 60*a^5*b*d^3*x^3*e^2 + 30*a^5*b*d^4*x^2*e + 6*a^5*b*d^5*x + a^6*x^5*e^5 + 5*a^6*d*x^4*e^4 + 10*a^6*d^2*x^3*e^3 + 10*a^6*d^3*x^2*e^2 + 5*a^6*d^4*x*e","B",0
279,1,20,0,0.164649," ","integrate((x^3+x^2)/(x^2+x-2),x, algorithm=""giac"")","\frac{1}{2} \, x^{2} + \frac{4}{3} \, \log\left({\left| x + 2 \right|}\right) + \frac{2}{3} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"1/2*x^2 + 4/3*log(abs(x + 2)) + 2/3*log(abs(x - 1))","A",0
280,1,330,0,0.313801," ","integrate(x^2*(g*x^3+f*x^2+e*x+d)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{1}{1920} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(6 \, {\left(\frac{8 \, g x}{c} + \frac{10 \, c^{4} f - 9 \, b c^{3} g}{c^{5}}\right)} x - \frac{70 \, b c^{3} f - 63 \, b^{2} c^{2} g + 64 \, a c^{3} g - 80 \, c^{4} e}{c^{5}}\right)} x + \frac{480 \, c^{4} d + 350 \, b^{2} c^{2} f - 360 \, a c^{3} f - 315 \, b^{3} c g + 644 \, a b c^{2} g - 400 \, b c^{3} e}{c^{5}}\right)} x - \frac{1440 \, b c^{3} d + 1050 \, b^{3} c f - 2200 \, a b c^{2} f - 945 \, b^{4} g + 2940 \, a b^{2} c g - 1024 \, a^{2} c^{2} g - 1200 \, b^{2} c^{2} e + 1280 \, a c^{3} e}{c^{5}}\right)} - \frac{{\left(96 \, b^{2} c^{3} d - 128 \, a c^{4} d + 70 \, b^{4} c f - 240 \, a b^{2} c^{2} f + 96 \, a^{2} c^{3} f - 63 \, b^{5} g + 280 \, a b^{3} c g - 240 \, a^{2} b c^{2} g - 80 \, b^{3} c^{2} e + 192 \, a b c^{3} e\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{256 \, c^{\frac{11}{2}}}"," ",0,"1/1920*sqrt(c*x^2 + b*x + a)*(2*(4*(6*(8*g*x/c + (10*c^4*f - 9*b*c^3*g)/c^5)*x - (70*b*c^3*f - 63*b^2*c^2*g + 64*a*c^3*g - 80*c^4*e)/c^5)*x + (480*c^4*d + 350*b^2*c^2*f - 360*a*c^3*f - 315*b^3*c*g + 644*a*b*c^2*g - 400*b*c^3*e)/c^5)*x - (1440*b*c^3*d + 1050*b^3*c*f - 2200*a*b*c^2*f - 945*b^4*g + 2940*a*b^2*c*g - 1024*a^2*c^2*g - 1200*b^2*c^2*e + 1280*a*c^3*e)/c^5) - 1/256*(96*b^2*c^3*d - 128*a*c^4*d + 70*b^4*c*f - 240*a*b^2*c^2*f + 96*a^2*c^3*f - 63*b^5*g + 280*a*b^3*c*g - 240*a^2*b*c^2*g - 80*b^3*c^2*e + 192*a*b*c^3*e)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(11/2)","A",0
281,1,228,0,0.386008," ","integrate(x*(g*x^3+f*x^2+e*x+d)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{1}{192} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(\frac{6 \, g x}{c} + \frac{8 \, c^{3} f - 7 \, b c^{2} g}{c^{4}}\right)} x - \frac{40 \, b c^{2} f - 35 \, b^{2} c g + 36 \, a c^{2} g - 48 \, c^{3} e}{c^{4}}\right)} x + \frac{192 \, c^{3} d + 120 \, b^{2} c f - 128 \, a c^{2} f - 105 \, b^{3} g + 220 \, a b c g - 144 \, b c^{2} e}{c^{4}}\right)} + \frac{{\left(64 \, b c^{3} d + 40 \, b^{3} c f - 96 \, a b c^{2} f - 35 \, b^{4} g + 120 \, a b^{2} c g - 48 \, a^{2} c^{2} g - 48 \, b^{2} c^{2} e + 64 \, a c^{3} e\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{128 \, c^{\frac{9}{2}}}"," ",0,"1/192*sqrt(c*x^2 + b*x + a)*(2*(4*(6*g*x/c + (8*c^3*f - 7*b*c^2*g)/c^4)*x - (40*b*c^2*f - 35*b^2*c*g + 36*a*c^2*g - 48*c^3*e)/c^4)*x + (192*c^3*d + 120*b^2*c*f - 128*a*c^2*f - 105*b^3*g + 220*a*b*c*g - 144*b*c^2*e)/c^4) + 1/128*(64*b*c^3*d + 40*b^3*c*f - 96*a*b*c^2*f - 35*b^4*g + 120*a*b^2*c*g - 48*a^2*c^2*g - 48*b^2*c^2*e + 64*a*c^3*e)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(9/2)","A",0
282,1,149,0,0.267615," ","integrate((g*x^3+f*x^2+e*x+d)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{1}{24} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(\frac{4 \, g x}{c} + \frac{6 \, c^{2} f - 5 \, b c g}{c^{3}}\right)} x - \frac{18 \, b c f - 15 \, b^{2} g + 16 \, a c g - 24 \, c^{2} e}{c^{3}}\right)} - \frac{{\left(16 \, c^{3} d + 6 \, b^{2} c f - 8 \, a c^{2} f - 5 \, b^{3} g + 12 \, a b c g - 8 \, b c^{2} e\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{16 \, c^{\frac{7}{2}}}"," ",0,"1/24*sqrt(c*x^2 + b*x + a)*(2*(4*g*x/c + (6*c^2*f - 5*b*c*g)/c^3)*x - (18*b*c*f - 15*b^2*g + 16*a*c*g - 24*c^2*e)/c^3) - 1/16*(16*c^3*d + 6*b^2*c*f - 8*a*c^2*f - 5*b^3*g + 12*a*b*c*g - 8*b*c^2*e)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(7/2)","A",0
283,-2,0,0,0.000000," ","integrate((g*x^3+f*x^2+e*x+d)/x/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.index.cc index_m operator + Error: Bad Argument Value","F(-2)",0
284,1,171,0,0.372113," ","integrate((g*x^3+f*x^2+e*x+d)/x^2/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{c x^{2} + b x + a} g}{c} - \frac{{\left(b d - 2 \, a e\right)} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + b x + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a} - \frac{{\left(2 \, c f - b g\right)} \log\left({\left| 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} + b \right|}\right)}{2 \, c^{\frac{3}{2}}} + \frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b d + 2 \, a \sqrt{c} d}{{\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} - a\right)} a}"," ",0,"sqrt(c*x^2 + b*x + a)*g/c - (b*d - 2*a*e)*arctan(-(sqrt(c)*x - sqrt(c*x^2 + b*x + a))/sqrt(-a))/(sqrt(-a)*a) - 1/2*(2*c*f - b*g)*log(abs(2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) + b))/c^(3/2) + ((sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b*d + 2*a*sqrt(c)*d)/(((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2 - a)*a)","A",0
285,1,352,0,0.360767," ","integrate((g*x^3+f*x^2+e*x+d)/x^3/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","-\frac{g \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} c - b \sqrt{c} \right|}\right)}{\sqrt{c}} + \frac{{\left(3 \, b^{2} d - 4 \, a c d + 8 \, a^{2} f - 4 \, a b e\right)} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + b x + a}}{\sqrt{-a}}\right)}{4 \, \sqrt{-a} a^{2}} - \frac{3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{2} d - 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a c d - 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b e - 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{2} \sqrt{c} e - 5 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{2} d - 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} c d + 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b e - 8 \, a^{2} b \sqrt{c} d + 8 \, a^{3} \sqrt{c} e}{4 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} - a\right)}^{2} a^{2}}"," ",0,"-g*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*c - b*sqrt(c)))/sqrt(c) + 1/4*(3*b^2*d - 4*a*c*d + 8*a^2*f - 4*a*b*e)*arctan(-(sqrt(c)*x - sqrt(c*x^2 + b*x + a))/sqrt(-a))/(sqrt(-a)*a^2) - 1/4*(3*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^2*d - 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*c*d - 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b*e - 8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*sqrt(c)*e - 5*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^2*d - 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*c*d + 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b*e - 8*a^2*b*sqrt(c)*d + 8*a^3*sqrt(c)*e)/(((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2 - a)^2*a^2)","B",0
286,1,689,0,0.291688," ","integrate((g*x^3+f*x^2+e*x+d)/x^4/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","-\frac{{\left(5 \, b^{3} d - 12 \, a b c d + 8 \, a^{2} b f - 16 \, a^{3} g - 6 \, a b^{2} e + 8 \, a^{2} c e\right)} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + b x + a}}{\sqrt{-a}}\right)}{8 \, \sqrt{-a} a^{3}} + \frac{15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b^{3} d - 36 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a b c d + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{2} b f - 18 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a b^{2} e + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{2} c e + 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{3} \sqrt{c} f - 40 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b^{3} d + 96 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{2} b c d - 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{3} b f + 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{2} b^{2} e + 96 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{3} c^{\frac{3}{2}} d - 96 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{4} \sqrt{c} f + 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{3} b \sqrt{c} e + 33 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b^{3} d + 36 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{3} b c d + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{4} b f - 30 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{3} b^{2} e - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{4} c e + 48 \, a^{3} b^{2} \sqrt{c} d - 32 \, a^{4} c^{\frac{3}{2}} d + 48 \, a^{5} \sqrt{c} f - 48 \, a^{4} b \sqrt{c} e}{24 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} - a\right)}^{3} a^{3}}"," ",0,"-1/8*(5*b^3*d - 12*a*b*c*d + 8*a^2*b*f - 16*a^3*g - 6*a*b^2*e + 8*a^2*c*e)*arctan(-(sqrt(c)*x - sqrt(c*x^2 + b*x + a))/sqrt(-a))/(sqrt(-a)*a^3) + 1/24*(15*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^3*d - 36*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b*c*d + 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^2*b*f - 18*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b^2*e + 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^2*c*e + 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^3*sqrt(c)*f - 40*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^3*d + 96*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b*c*d - 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^3*b*f + 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b^2*e + 96*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^3*c^(3/2)*d - 96*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^4*sqrt(c)*f + 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^3*b*sqrt(c)*e + 33*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^3*d + 36*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*b*c*d + 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^4*b*f - 30*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*b^2*e - 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^4*c*e + 48*a^3*b^2*sqrt(c)*d - 32*a^4*c^(3/2)*d + 48*a^5*sqrt(c)*f - 48*a^4*b*sqrt(c)*e)/(((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2 - a)^3*a^3)","B",0
287,1,1448,0,0.300287," ","integrate((g*x^3+f*x^2+e*x+d)/x^5/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{{\left(35 \, b^{4} d - 120 \, a b^{2} c d + 48 \, a^{2} c^{2} d + 48 \, a^{2} b^{2} f - 64 \, a^{3} c f - 64 \, a^{3} b g - 40 \, a b^{3} e + 96 \, a^{2} b c e\right)} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + b x + a}}{\sqrt{-a}}\right)}{64 \, \sqrt{-a} a^{4}} - \frac{105 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} b^{4} d - 360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a b^{2} c d + 144 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a^{2} c^{2} d + 144 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a^{2} b^{2} f - 192 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a^{3} c f - 192 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a^{3} b g - 120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a b^{3} e + 288 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a^{2} b c e - 384 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} a^{4} \sqrt{c} g - 385 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a b^{4} d + 1320 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{2} b^{2} c d - 528 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{3} c^{2} d - 528 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{3} b^{2} f + 192 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{4} c f + 576 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{4} b g + 440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{2} b^{3} e - 1056 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{3} b c e - 384 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{4} b \sqrt{c} f + 1152 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{5} \sqrt{c} g - 768 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{4} c^{\frac{3}{2}} e + 511 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{2} b^{4} d - 1752 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{3} b^{2} c d - 528 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{4} c^{2} d + 624 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{4} b^{2} f + 192 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{5} c f - 576 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{5} b g - 584 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{3} b^{3} e + 480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{4} b c e - 2048 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{4} b c^{\frac{3}{2}} d + 768 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{5} b \sqrt{c} f - 1152 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{6} \sqrt{c} g - 384 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{4} b^{2} \sqrt{c} e + 1024 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{5} c^{\frac{3}{2}} e - 279 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{3} b^{4} d - 360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{4} b^{2} c d + 144 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{5} c^{2} d - 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{5} b^{2} f - 192 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{6} c f + 192 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{6} b g + 264 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{4} b^{3} e + 288 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{5} b c e - 384 \, a^{4} b^{3} \sqrt{c} d + 512 \, a^{5} b c^{\frac{3}{2}} d - 384 \, a^{6} b \sqrt{c} f + 384 \, a^{7} \sqrt{c} g + 384 \, a^{5} b^{2} \sqrt{c} e - 256 \, a^{6} c^{\frac{3}{2}} e}{192 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} - a\right)}^{4} a^{4}}"," ",0,"1/64*(35*b^4*d - 120*a*b^2*c*d + 48*a^2*c^2*d + 48*a^2*b^2*f - 64*a^3*c*f - 64*a^3*b*g - 40*a*b^3*e + 96*a^2*b*c*e)*arctan(-(sqrt(c)*x - sqrt(c*x^2 + b*x + a))/sqrt(-a))/(sqrt(-a)*a^4) - 1/192*(105*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*b^4*d - 360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a*b^2*c*d + 144*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^2*c^2*d + 144*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^2*b^2*f - 192*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^3*c*f - 192*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^3*b*g - 120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a*b^3*e + 288*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^2*b*c*e - 384*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^4*sqrt(c)*g - 385*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b^4*d + 1320*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^2*b^2*c*d - 528*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^3*c^2*d - 528*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^3*b^2*f + 192*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^4*c*f + 576*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^4*b*g + 440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^2*b^3*e - 1056*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^3*b*c*e - 384*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^4*b*sqrt(c)*f + 1152*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^5*sqrt(c)*g - 768*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^4*c^(3/2)*e + 511*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b^4*d - 1752*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^3*b^2*c*d - 528*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^4*c^2*d + 624*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^4*b^2*f + 192*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^5*c*f - 576*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^5*b*g - 584*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^3*b^3*e + 480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^4*b*c*e - 2048*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^4*b*c^(3/2)*d + 768*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^5*b*sqrt(c)*f - 1152*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^6*sqrt(c)*g - 384*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^4*b^2*sqrt(c)*e + 1024*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^5*c^(3/2)*e - 279*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*b^4*d - 360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^4*b^2*c*d + 144*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^5*c^2*d - 240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^5*b^2*f - 192*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^6*c*f + 192*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^6*b*g + 264*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^4*b^3*e + 288*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^5*b*c*e - 384*a^4*b^3*sqrt(c)*d + 512*a^5*b*c^(3/2)*d - 384*a^6*b*sqrt(c)*f + 384*a^7*sqrt(c)*g + 384*a^5*b^2*sqrt(c)*e - 256*a^6*c^(3/2)*e)/(((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2 - a)^4*a^4)","B",0
288,1,2177,0,0.508205," ","integrate((g*x^3+f*x^2+e*x+d)/x^6/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","-\frac{{\left(63 \, b^{5} d - 280 \, a b^{3} c d + 240 \, a^{2} b c^{2} d + 80 \, a^{2} b^{3} f - 192 \, a^{3} b c f - 96 \, a^{3} b^{2} g + 128 \, a^{4} c g - 70 \, a b^{4} e + 240 \, a^{2} b^{2} c e - 96 \, a^{3} c^{2} e\right)} \arctan\left(-\frac{\sqrt{c} x - \sqrt{c x^{2} + b x + a}}{\sqrt{-a}}\right)}{128 \, \sqrt{-a} a^{5}} + \frac{945 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} b^{5} d - 4200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} a b^{3} c d + 3600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} a^{2} b c^{2} d + 1200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} a^{2} b^{3} f - 2880 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} a^{3} b c f - 1440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} a^{3} b^{2} g + 1920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} a^{4} c g - 1050 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} a b^{4} e + 3600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} a^{2} b^{2} c e - 1440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} a^{3} c^{2} e - 4410 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a b^{5} d + 19600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a^{2} b^{3} c d - 16800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a^{3} b c^{2} d - 5600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a^{3} b^{3} f + 13440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a^{4} b c f + 6720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a^{4} b^{2} g - 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a^{5} c g + 4900 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a^{2} b^{4} e - 16800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a^{3} b^{2} c e + 6720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a^{4} c^{2} e + 7680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} a^{5} c^{\frac{3}{2}} f + 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} a^{5} b \sqrt{c} g + 8064 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{2} b^{5} d - 35840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{3} b^{3} c d + 30720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{4} b c^{2} d + 10240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{4} b^{3} f - 15360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{5} b c f - 11520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{5} b^{2} g - 8960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{3} b^{4} e + 30720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{4} b^{2} c e + 20480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{5} c^{\frac{5}{2}} d + 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{5} b^{2} \sqrt{c} f - 17920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{6} c^{\frac{3}{2}} f - 11520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{6} b \sqrt{c} g + 20480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{5} b c^{\frac{3}{2}} e - 7110 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{3} b^{5} d + 31600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{4} b^{3} c d + 16800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{5} b c^{2} d - 8480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{5} b^{3} f + 1920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{6} b c f + 8640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{6} b^{2} g + 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{7} c g + 7900 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{4} b^{4} e - 13920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{5} b^{2} c e - 6720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{6} c^{2} e + 38400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{5} b^{2} c^{\frac{3}{2}} d - 10240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{6} c^{\frac{5}{2}} d - 7680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{6} b^{2} \sqrt{c} f + 12800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{7} c^{\frac{3}{2}} f + 11520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{7} b \sqrt{c} g + 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{5} b^{3} \sqrt{c} e - 25600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{6} b c^{\frac{3}{2}} e + 2895 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{4} b^{5} d + 4200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{5} b^{3} c d - 3600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{6} b c^{2} d + 2640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{6} b^{3} f + 2880 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{7} b c f - 2400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{7} b^{2} g - 1920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{8} c g - 2790 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{5} b^{4} e - 3600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{6} b^{2} c e + 1440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{7} c^{2} e + 3840 \, a^{5} b^{4} \sqrt{c} d - 7680 \, a^{6} b^{2} c^{\frac{3}{2}} d + 2048 \, a^{7} c^{\frac{5}{2}} d + 3840 \, a^{7} b^{2} \sqrt{c} f - 2560 \, a^{8} c^{\frac{3}{2}} f - 3840 \, a^{8} b \sqrt{c} g - 3840 \, a^{6} b^{3} \sqrt{c} e + 5120 \, a^{7} b c^{\frac{3}{2}} e}{1920 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} - a\right)}^{5} a^{5}}"," ",0,"-1/128*(63*b^5*d - 280*a*b^3*c*d + 240*a^2*b*c^2*d + 80*a^2*b^3*f - 192*a^3*b*c*f - 96*a^3*b^2*g + 128*a^4*c*g - 70*a*b^4*e + 240*a^2*b^2*c*e - 96*a^3*c^2*e)*arctan(-(sqrt(c)*x - sqrt(c*x^2 + b*x + a))/sqrt(-a))/(sqrt(-a)*a^5) + 1/1920*(945*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*b^5*d - 4200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a*b^3*c*d + 3600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a^2*b*c^2*d + 1200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a^2*b^3*f - 2880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a^3*b*c*f - 1440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a^3*b^2*g + 1920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a^4*c*g - 1050*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a*b^4*e + 3600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a^2*b^2*c*e - 1440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a^3*c^2*e - 4410*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a*b^5*d + 19600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^2*b^3*c*d - 16800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^3*b*c^2*d - 5600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^3*b^3*f + 13440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^4*b*c*f + 6720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^4*b^2*g - 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^5*c*g + 4900*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^2*b^4*e - 16800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^3*b^2*c*e + 6720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^4*c^2*e + 7680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^5*c^(3/2)*f + 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^5*b*sqrt(c)*g + 8064*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^2*b^5*d - 35840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^3*b^3*c*d + 30720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^4*b*c^2*d + 10240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^4*b^3*f - 15360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^5*b*c*f - 11520*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^5*b^2*g - 8960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^3*b^4*e + 30720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^4*b^2*c*e + 20480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^5*c^(5/2)*d + 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^5*b^2*sqrt(c)*f - 17920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^6*c^(3/2)*f - 11520*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^6*b*sqrt(c)*g + 20480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^5*b*c^(3/2)*e - 7110*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^3*b^5*d + 31600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^4*b^3*c*d + 16800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^5*b*c^2*d - 8480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^5*b^3*f + 1920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^6*b*c*f + 8640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^6*b^2*g + 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^7*c*g + 7900*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^4*b^4*e - 13920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^5*b^2*c*e - 6720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^6*c^2*e + 38400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^5*b^2*c^(3/2)*d - 10240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^6*c^(5/2)*d - 7680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^6*b^2*sqrt(c)*f + 12800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^7*c^(3/2)*f + 11520*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^7*b*sqrt(c)*g + 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^5*b^3*sqrt(c)*e - 25600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^6*b*c^(3/2)*e + 2895*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^4*b^5*d + 4200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^5*b^3*c*d - 3600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^6*b*c^2*d + 2640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^6*b^3*f + 2880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^7*b*c*f - 2400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^7*b^2*g - 1920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^8*c*g - 2790*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^5*b^4*e - 3600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^6*b^2*c*e + 1440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^7*c^2*e + 3840*a^5*b^4*sqrt(c)*d - 7680*a^6*b^2*c^(3/2)*d + 2048*a^7*c^(5/2)*d + 3840*a^7*b^2*sqrt(c)*f - 2560*a^8*c^(3/2)*f - 3840*a^8*b*sqrt(c)*g - 3840*a^6*b^3*sqrt(c)*e + 5120*a^7*b*c^(3/2)*e)/(((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2 - a)^5*a^5)","B",0
289,1,230,0,0.168041," ","integrate((e*x+d)^3*(5*x^2+2*x+3)*(4*x^4-5*x^3+3*x^2+x+2),x, algorithm=""giac"")","2 \, x^{10} e^{3} + \frac{20}{3} \, d x^{9} e^{2} + \frac{15}{2} \, d^{2} x^{8} e + \frac{20}{7} \, d^{3} x^{7} - \frac{17}{9} \, x^{9} e^{3} - \frac{51}{8} \, d x^{8} e^{2} - \frac{51}{7} \, d^{2} x^{7} e - \frac{17}{6} \, d^{3} x^{6} + \frac{17}{8} \, x^{8} e^{3} + \frac{51}{7} \, d x^{7} e^{2} + \frac{17}{2} \, d^{2} x^{6} e + \frac{17}{5} \, d^{3} x^{5} - \frac{4}{7} \, x^{7} e^{3} - 2 \, d x^{6} e^{2} - \frac{12}{5} \, d^{2} x^{5} e - d^{3} x^{4} + \frac{7}{2} \, x^{6} e^{3} + \frac{63}{5} \, d x^{5} e^{2} + \frac{63}{4} \, d^{2} x^{4} e + 7 \, d^{3} x^{3} + \frac{7}{5} \, x^{5} e^{3} + \frac{21}{4} \, d x^{4} e^{2} + 7 \, d^{2} x^{3} e + \frac{7}{2} \, d^{3} x^{2} + \frac{3}{2} \, x^{4} e^{3} + 6 \, d x^{3} e^{2} + 9 \, d^{2} x^{2} e + 6 \, d^{3} x"," ",0,"2*x^10*e^3 + 20/3*d*x^9*e^2 + 15/2*d^2*x^8*e + 20/7*d^3*x^7 - 17/9*x^9*e^3 - 51/8*d*x^8*e^2 - 51/7*d^2*x^7*e - 17/6*d^3*x^6 + 17/8*x^8*e^3 + 51/7*d*x^7*e^2 + 17/2*d^2*x^6*e + 17/5*d^3*x^5 - 4/7*x^7*e^3 - 2*d*x^6*e^2 - 12/5*d^2*x^5*e - d^3*x^4 + 7/2*x^6*e^3 + 63/5*d*x^5*e^2 + 63/4*d^2*x^4*e + 7*d^3*x^3 + 7/5*x^5*e^3 + 21/4*d*x^4*e^2 + 7*d^2*x^3*e + 7/2*d^3*x^2 + 3/2*x^4*e^3 + 6*d*x^3*e^2 + 9*d^2*x^2*e + 6*d^3*x","A",0
290,1,160,0,0.156834," ","integrate((e*x+d)^2*(5*x^2+2*x+3)*(4*x^4-5*x^3+3*x^2+x+2),x, algorithm=""giac"")","\frac{20}{9} \, x^{9} e^{2} + 5 \, d x^{8} e + \frac{20}{7} \, d^{2} x^{7} - \frac{17}{8} \, x^{8} e^{2} - \frac{34}{7} \, d x^{7} e - \frac{17}{6} \, d^{2} x^{6} + \frac{17}{7} \, x^{7} e^{2} + \frac{17}{3} \, d x^{6} e + \frac{17}{5} \, d^{2} x^{5} - \frac{2}{3} \, x^{6} e^{2} - \frac{8}{5} \, d x^{5} e - d^{2} x^{4} + \frac{21}{5} \, x^{5} e^{2} + \frac{21}{2} \, d x^{4} e + 7 \, d^{2} x^{3} + \frac{7}{4} \, x^{4} e^{2} + \frac{14}{3} \, d x^{3} e + \frac{7}{2} \, d^{2} x^{2} + 2 \, x^{3} e^{2} + 6 \, d x^{2} e + 6 \, d^{2} x"," ",0,"20/9*x^9*e^2 + 5*d*x^8*e + 20/7*d^2*x^7 - 17/8*x^8*e^2 - 34/7*d*x^7*e - 17/6*d^2*x^6 + 17/7*x^7*e^2 + 17/3*d*x^6*e + 17/5*d^2*x^5 - 2/3*x^6*e^2 - 8/5*d*x^5*e - d^2*x^4 + 21/5*x^5*e^2 + 21/2*d*x^4*e + 7*d^2*x^3 + 7/4*x^4*e^2 + 14/3*d*x^3*e + 7/2*d^2*x^2 + 2*x^3*e^2 + 6*d*x^2*e + 6*d^2*x","A",0
291,1,90,0,0.150527," ","integrate((e*x+d)*(5*x^2+2*x+3)*(4*x^4-5*x^3+3*x^2+x+2),x, algorithm=""giac"")","\frac{5}{2} \, x^{8} e + \frac{20}{7} \, d x^{7} - \frac{17}{7} \, x^{7} e - \frac{17}{6} \, d x^{6} + \frac{17}{6} \, x^{6} e + \frac{17}{5} \, d x^{5} - \frac{4}{5} \, x^{5} e - d x^{4} + \frac{21}{4} \, x^{4} e + 7 \, d x^{3} + \frac{7}{3} \, x^{3} e + \frac{7}{2} \, d x^{2} + 3 \, x^{2} e + 6 \, d x"," ",0,"5/2*x^8*e + 20/7*d*x^7 - 17/7*x^7*e - 17/6*d*x^6 + 17/6*x^6*e + 17/5*d*x^5 - 4/5*x^5*e - d*x^4 + 21/4*x^4*e + 7*d*x^3 + 7/3*x^3*e + 7/2*d*x^2 + 3*x^2*e + 6*d*x","A",0
292,1,34,0,0.147819," ","integrate((5*x^2+2*x+3)*(4*x^4-5*x^3+3*x^2+x+2),x, algorithm=""giac"")","\frac{20}{7} \, x^{7} - \frac{17}{6} \, x^{6} + \frac{17}{5} \, x^{5} - x^{4} + 7 \, x^{3} + \frac{7}{2} \, x^{2} + 6 \, x"," ",0,"20/7*x^7 - 17/6*x^6 + 17/5*x^5 - x^4 + 7*x^3 + 7/2*x^2 + 6*x","A",0
293,1,228,0,0.155455," ","integrate((5*x^2+2*x+3)*(4*x^4-5*x^3+3*x^2+x+2)/(e*x+d),x, algorithm=""giac"")","{\left(20 \, d^{6} + 17 \, d^{5} e + 17 \, d^{4} e^{2} + 4 \, d^{3} e^{3} + 21 \, d^{2} e^{4} - 7 \, d e^{5} + 6 \, e^{6}\right)} e^{\left(-7\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{60} \, {\left(200 \, x^{6} e^{5} - 240 \, d x^{5} e^{4} + 300 \, d^{2} x^{4} e^{3} - 400 \, d^{3} x^{3} e^{2} + 600 \, d^{4} x^{2} e - 1200 \, d^{5} x - 204 \, x^{5} e^{5} + 255 \, d x^{4} e^{4} - 340 \, d^{2} x^{3} e^{3} + 510 \, d^{3} x^{2} e^{2} - 1020 \, d^{4} x e + 255 \, x^{4} e^{5} - 340 \, d x^{3} e^{4} + 510 \, d^{2} x^{2} e^{3} - 1020 \, d^{3} x e^{2} - 80 \, x^{3} e^{5} + 120 \, d x^{2} e^{4} - 240 \, d^{2} x e^{3} + 630 \, x^{2} e^{5} - 1260 \, d x e^{4} + 420 \, x e^{5}\right)} e^{\left(-6\right)}"," ",0,"(20*d^6 + 17*d^5*e + 17*d^4*e^2 + 4*d^3*e^3 + 21*d^2*e^4 - 7*d*e^5 + 6*e^6)*e^(-7)*log(abs(x*e + d)) + 1/60*(200*x^6*e^5 - 240*d*x^5*e^4 + 300*d^2*x^4*e^3 - 400*d^3*x^3*e^2 + 600*d^4*x^2*e - 1200*d^5*x - 204*x^5*e^5 + 255*d*x^4*e^4 - 340*d^2*x^3*e^3 + 510*d^3*x^2*e^2 - 1020*d^4*x*e + 255*x^4*e^5 - 340*d*x^3*e^4 + 510*d^2*x^2*e^3 - 1020*d^3*x*e^2 - 80*x^3*e^5 + 120*d*x^2*e^4 - 240*d^2*x*e^3 + 630*x^2*e^5 - 1260*d*x*e^4 + 420*x*e^5)*e^(-6)","A",0
294,1,308,0,0.172742," ","integrate((5*x^2+2*x+3)*(4*x^4-5*x^3+3*x^2+x+2)/(e*x+d)^2,x, algorithm=""giac"")","-\frac{1}{12} \, {\left(x e + d\right)}^{5} {\left(\frac{3 \, {\left(120 \, d e + 17 \, e^{2}\right)} e^{\left(-1\right)}}{x e + d} - \frac{4 \, {\left(300 \, d^{2} e^{2} + 85 \, d e^{3} + 17 \, e^{4}\right)} e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}} + \frac{12 \, {\left(200 \, d^{3} e^{3} + 85 \, d^{2} e^{4} + 34 \, d e^{5} + 2 \, e^{6}\right)} e^{\left(-3\right)}}{{\left(x e + d\right)}^{3}} - \frac{12 \, {\left(300 \, d^{4} e^{4} + 170 \, d^{3} e^{5} + 102 \, d^{2} e^{6} + 12 \, d e^{7} + 21 \, e^{8}\right)} e^{\left(-4\right)}}{{\left(x e + d\right)}^{4}} - 48\right)} e^{\left(-7\right)} + {\left(120 \, d^{5} + 85 \, d^{4} e + 68 \, d^{3} e^{2} + 12 \, d^{2} e^{3} + 42 \, d e^{4} - 7 \, e^{5}\right)} e^{\left(-7\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) - {\left(\frac{20 \, d^{6} e^{5}}{x e + d} + \frac{17 \, d^{5} e^{6}}{x e + d} + \frac{17 \, d^{4} e^{7}}{x e + d} + \frac{4 \, d^{3} e^{8}}{x e + d} + \frac{21 \, d^{2} e^{9}}{x e + d} - \frac{7 \, d e^{10}}{x e + d} + \frac{6 \, e^{11}}{x e + d}\right)} e^{\left(-12\right)}"," ",0,"-1/12*(x*e + d)^5*(3*(120*d*e + 17*e^2)*e^(-1)/(x*e + d) - 4*(300*d^2*e^2 + 85*d*e^3 + 17*e^4)*e^(-2)/(x*e + d)^2 + 12*(200*d^3*e^3 + 85*d^2*e^4 + 34*d*e^5 + 2*e^6)*e^(-3)/(x*e + d)^3 - 12*(300*d^4*e^4 + 170*d^3*e^5 + 102*d^2*e^6 + 12*d*e^7 + 21*e^8)*e^(-4)/(x*e + d)^4 - 48)*e^(-7) + (120*d^5 + 85*d^4*e + 68*d^3*e^2 + 12*d^2*e^3 + 42*d*e^4 - 7*e^5)*e^(-7)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) - (20*d^6*e^5/(x*e + d) + 17*d^5*e^6/(x*e + d) + 17*d^4*e^7/(x*e + d) + 4*d^3*e^8/(x*e + d) + 21*d^2*e^9/(x*e + d) - 7*d*e^10/(x*e + d) + 6*e^11/(x*e + d))*e^(-12)","A",0
295,1,216,0,0.179550," ","integrate((5*x^2+2*x+3)*(4*x^4-5*x^3+3*x^2+x+2)/(e*x+d)^3,x, algorithm=""giac"")","{\left(300 \, d^{4} + 170 \, d^{3} e + 102 \, d^{2} e^{2} + 12 \, d e^{3} + 21 \, e^{4}\right)} e^{\left(-7\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{6} \, {\left(30 \, x^{4} e^{9} - 120 \, d x^{3} e^{8} + 360 \, d^{2} x^{2} e^{7} - 1200 \, d^{3} x e^{6} - 34 \, x^{3} e^{9} + 153 \, d x^{2} e^{8} - 612 \, d^{2} x e^{7} + 51 \, x^{2} e^{9} - 306 \, d x e^{8} - 24 \, x e^{9}\right)} e^{\left(-12\right)} + \frac{{\left(220 \, d^{6} + 153 \, d^{5} e + 119 \, d^{4} e^{2} + 20 \, d^{3} e^{3} + 63 \, d^{2} e^{4} + 2 \, {\left(120 \, d^{5} e + 85 \, d^{4} e^{2} + 68 \, d^{3} e^{3} + 12 \, d^{2} e^{4} + 42 \, d e^{5} - 7 \, e^{6}\right)} x - 7 \, d e^{5} - 6 \, e^{6}\right)} e^{\left(-7\right)}}{2 \, {\left(x e + d\right)}^{2}}"," ",0,"(300*d^4 + 170*d^3*e + 102*d^2*e^2 + 12*d*e^3 + 21*e^4)*e^(-7)*log(abs(x*e + d)) + 1/6*(30*x^4*e^9 - 120*d*x^3*e^8 + 360*d^2*x^2*e^7 - 1200*d^3*x*e^6 - 34*x^3*e^9 + 153*d*x^2*e^8 - 612*d^2*x*e^7 + 51*x^2*e^9 - 306*d*x*e^8 - 24*x*e^9)*e^(-12) + 1/2*(220*d^6 + 153*d^5*e + 119*d^4*e^2 + 20*d^3*e^3 + 63*d^2*e^4 + 2*(120*d^5*e + 85*d^4*e^2 + 68*d^3*e^3 + 12*d^2*e^4 + 42*d*e^5 - 7*e^6)*x - 7*d*e^5 - 6*e^6)*e^(-7)/(x*e + d)^2","A",0
296,1,296,0,0.156539," ","integrate((e*x+d)^3*(5*x^2+2*x+3)^2*(4*x^4-5*x^3+3*x^2+x+2),x, algorithm=""giac"")","\frac{25}{3} \, x^{12} e^{3} + \frac{300}{11} \, d x^{11} e^{2} + 30 \, d^{2} x^{10} e + \frac{100}{9} \, d^{3} x^{9} - \frac{45}{11} \, x^{11} e^{3} - \frac{27}{2} \, d x^{10} e^{2} - 15 \, d^{2} x^{9} e - \frac{45}{8} \, d^{3} x^{8} + \frac{111}{10} \, x^{10} e^{3} + 37 \, d x^{9} e^{2} + \frac{333}{8} \, d^{2} x^{8} e + \frac{111}{7} \, d^{3} x^{7} - \frac{37}{9} \, x^{9} e^{3} - \frac{111}{8} \, d x^{8} e^{2} - \frac{111}{7} \, d^{2} x^{7} e - \frac{37}{6} \, d^{3} x^{6} + \frac{37}{2} \, x^{8} e^{3} + \frac{444}{7} \, d x^{7} e^{2} + 74 \, d^{2} x^{6} e + \frac{148}{5} \, d^{3} x^{5} + \frac{65}{7} \, x^{7} e^{3} + \frac{65}{2} \, d x^{6} e^{2} + 39 \, d^{2} x^{5} e + \frac{65}{4} \, d^{3} x^{4} + \frac{107}{6} \, x^{6} e^{3} + \frac{321}{5} \, d x^{5} e^{2} + \frac{321}{4} \, d^{2} x^{4} e + \frac{107}{3} \, d^{3} x^{3} + \frac{33}{5} \, x^{5} e^{3} + \frac{99}{4} \, d x^{4} e^{2} + 33 \, d^{2} x^{3} e + \frac{33}{2} \, d^{3} x^{2} + \frac{9}{2} \, x^{4} e^{3} + 18 \, d x^{3} e^{2} + 27 \, d^{2} x^{2} e + 18 \, d^{3} x"," ",0,"25/3*x^12*e^3 + 300/11*d*x^11*e^2 + 30*d^2*x^10*e + 100/9*d^3*x^9 - 45/11*x^11*e^3 - 27/2*d*x^10*e^2 - 15*d^2*x^9*e - 45/8*d^3*x^8 + 111/10*x^10*e^3 + 37*d*x^9*e^2 + 333/8*d^2*x^8*e + 111/7*d^3*x^7 - 37/9*x^9*e^3 - 111/8*d*x^8*e^2 - 111/7*d^2*x^7*e - 37/6*d^3*x^6 + 37/2*x^8*e^3 + 444/7*d*x^7*e^2 + 74*d^2*x^6*e + 148/5*d^3*x^5 + 65/7*x^7*e^3 + 65/2*d*x^6*e^2 + 39*d^2*x^5*e + 65/4*d^3*x^4 + 107/6*x^6*e^3 + 321/5*d*x^5*e^2 + 321/4*d^2*x^4*e + 107/3*d^3*x^3 + 33/5*x^5*e^3 + 99/4*d*x^4*e^2 + 33*d^2*x^3*e + 33/2*d^3*x^2 + 9/2*x^4*e^3 + 18*d*x^3*e^2 + 27*d^2*x^2*e + 18*d^3*x","A",0
297,1,206,0,0.160816," ","integrate((e*x+d)^2*(5*x^2+2*x+3)^2*(4*x^4-5*x^3+3*x^2+x+2),x, algorithm=""giac"")","\frac{100}{11} \, x^{11} e^{2} + 20 \, d x^{10} e + \frac{100}{9} \, d^{2} x^{9} - \frac{9}{2} \, x^{10} e^{2} - 10 \, d x^{9} e - \frac{45}{8} \, d^{2} x^{8} + \frac{37}{3} \, x^{9} e^{2} + \frac{111}{4} \, d x^{8} e + \frac{111}{7} \, d^{2} x^{7} - \frac{37}{8} \, x^{8} e^{2} - \frac{74}{7} \, d x^{7} e - \frac{37}{6} \, d^{2} x^{6} + \frac{148}{7} \, x^{7} e^{2} + \frac{148}{3} \, d x^{6} e + \frac{148}{5} \, d^{2} x^{5} + \frac{65}{6} \, x^{6} e^{2} + 26 \, d x^{5} e + \frac{65}{4} \, d^{2} x^{4} + \frac{107}{5} \, x^{5} e^{2} + \frac{107}{2} \, d x^{4} e + \frac{107}{3} \, d^{2} x^{3} + \frac{33}{4} \, x^{4} e^{2} + 22 \, d x^{3} e + \frac{33}{2} \, d^{2} x^{2} + 6 \, x^{3} e^{2} + 18 \, d x^{2} e + 18 \, d^{2} x"," ",0,"100/11*x^11*e^2 + 20*d*x^10*e + 100/9*d^2*x^9 - 9/2*x^10*e^2 - 10*d*x^9*e - 45/8*d^2*x^8 + 37/3*x^9*e^2 + 111/4*d*x^8*e + 111/7*d^2*x^7 - 37/8*x^8*e^2 - 74/7*d*x^7*e - 37/6*d^2*x^6 + 148/7*x^7*e^2 + 148/3*d*x^6*e + 148/5*d^2*x^5 + 65/6*x^6*e^2 + 26*d*x^5*e + 65/4*d^2*x^4 + 107/5*x^5*e^2 + 107/2*d*x^4*e + 107/3*d^2*x^3 + 33/4*x^4*e^2 + 22*d*x^3*e + 33/2*d^2*x^2 + 6*x^3*e^2 + 18*d*x^2*e + 18*d^2*x","A",0
298,1,116,0,0.155615," ","integrate((e*x+d)*(5*x^2+2*x+3)^2*(4*x^4-5*x^3+3*x^2+x+2),x, algorithm=""giac"")","10 \, x^{10} e + \frac{100}{9} \, d x^{9} - 5 \, x^{9} e - \frac{45}{8} \, d x^{8} + \frac{111}{8} \, x^{8} e + \frac{111}{7} \, d x^{7} - \frac{37}{7} \, x^{7} e - \frac{37}{6} \, d x^{6} + \frac{74}{3} \, x^{6} e + \frac{148}{5} \, d x^{5} + 13 \, x^{5} e + \frac{65}{4} \, d x^{4} + \frac{107}{4} \, x^{4} e + \frac{107}{3} \, d x^{3} + 11 \, x^{3} e + \frac{33}{2} \, d x^{2} + 9 \, x^{2} e + 18 \, d x"," ",0,"10*x^10*e + 100/9*d*x^9 - 5*x^9*e - 45/8*d*x^8 + 111/8*x^8*e + 111/7*d*x^7 - 37/7*x^7*e - 37/6*d*x^6 + 74/3*x^6*e + 148/5*d*x^5 + 13*x^5*e + 65/4*d*x^4 + 107/4*x^4*e + 107/3*d*x^3 + 11*x^3*e + 33/2*d*x^2 + 9*x^2*e + 18*d*x","A",0
299,1,44,0,0.149045," ","integrate((5*x^2+2*x+3)^2*(4*x^4-5*x^3+3*x^2+x+2),x, algorithm=""giac"")","\frac{100}{9} \, x^{9} - \frac{45}{8} \, x^{8} + \frac{111}{7} \, x^{7} - \frac{37}{6} \, x^{6} + \frac{148}{5} \, x^{5} + \frac{65}{4} \, x^{4} + \frac{107}{3} \, x^{3} + \frac{33}{2} \, x^{2} + 18 \, x"," ",0,"100/9*x^9 - 45/8*x^8 + 111/7*x^7 - 37/6*x^6 + 148/5*x^5 + 65/4*x^4 + 107/3*x^3 + 33/2*x^2 + 18*x","A",0
300,1,378,0,0.170073," ","integrate((5*x^2+2*x+3)^2*(4*x^4-5*x^3+3*x^2+x+2)/(e*x+d),x, algorithm=""giac"")","{\left(100 \, d^{8} + 45 \, d^{7} e + 111 \, d^{6} e^{2} + 37 \, d^{5} e^{3} + 148 \, d^{4} e^{4} - 65 \, d^{3} e^{5} + 107 \, d^{2} e^{6} - 33 \, d e^{7} + 18 \, e^{8}\right)} e^{\left(-9\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{420} \, {\left(5250 \, x^{8} e^{7} - 6000 \, d x^{7} e^{6} + 7000 \, d^{2} x^{6} e^{5} - 8400 \, d^{3} x^{5} e^{4} + 10500 \, d^{4} x^{4} e^{3} - 14000 \, d^{5} x^{3} e^{2} + 21000 \, d^{6} x^{2} e - 42000 \, d^{7} x - 2700 \, x^{7} e^{7} + 3150 \, d x^{6} e^{6} - 3780 \, d^{2} x^{5} e^{5} + 4725 \, d^{3} x^{4} e^{4} - 6300 \, d^{4} x^{3} e^{3} + 9450 \, d^{5} x^{2} e^{2} - 18900 \, d^{6} x e + 7770 \, x^{6} e^{7} - 9324 \, d x^{5} e^{6} + 11655 \, d^{2} x^{4} e^{5} - 15540 \, d^{3} x^{3} e^{4} + 23310 \, d^{4} x^{2} e^{3} - 46620 \, d^{5} x e^{2} - 3108 \, x^{5} e^{7} + 3885 \, d x^{4} e^{6} - 5180 \, d^{2} x^{3} e^{5} + 7770 \, d^{3} x^{2} e^{4} - 15540 \, d^{4} x e^{3} + 15540 \, x^{4} e^{7} - 20720 \, d x^{3} e^{6} + 31080 \, d^{2} x^{2} e^{5} - 62160 \, d^{3} x e^{4} + 9100 \, x^{3} e^{7} - 13650 \, d x^{2} e^{6} + 27300 \, d^{2} x e^{5} + 22470 \, x^{2} e^{7} - 44940 \, d x e^{6} + 13860 \, x e^{7}\right)} e^{\left(-8\right)}"," ",0,"(100*d^8 + 45*d^7*e + 111*d^6*e^2 + 37*d^5*e^3 + 148*d^4*e^4 - 65*d^3*e^5 + 107*d^2*e^6 - 33*d*e^7 + 18*e^8)*e^(-9)*log(abs(x*e + d)) + 1/420*(5250*x^8*e^7 - 6000*d*x^7*e^6 + 7000*d^2*x^6*e^5 - 8400*d^3*x^5*e^4 + 10500*d^4*x^4*e^3 - 14000*d^5*x^3*e^2 + 21000*d^6*x^2*e - 42000*d^7*x - 2700*x^7*e^7 + 3150*d*x^6*e^6 - 3780*d^2*x^5*e^5 + 4725*d^3*x^4*e^4 - 6300*d^4*x^3*e^3 + 9450*d^5*x^2*e^2 - 18900*d^6*x*e + 7770*x^6*e^7 - 9324*d*x^5*e^6 + 11655*d^2*x^4*e^5 - 15540*d^3*x^3*e^4 + 23310*d^4*x^2*e^3 - 46620*d^5*x*e^2 - 3108*x^5*e^7 + 3885*d*x^4*e^6 - 5180*d^2*x^3*e^5 + 7770*d^3*x^2*e^4 - 15540*d^4*x*e^3 + 15540*x^4*e^7 - 20720*d*x^3*e^6 + 31080*d^2*x^2*e^5 - 62160*d^3*x*e^4 + 9100*x^3*e^7 - 13650*d*x^2*e^6 + 27300*d^2*x*e^5 + 22470*x^2*e^7 - 44940*d*x*e^6 + 13860*x*e^7)*e^(-8)","A",0
301,1,459,0,0.180294," ","integrate((5*x^2+2*x+3)^2*(4*x^4-5*x^3+3*x^2+x+2)/(e*x+d)^2,x, algorithm=""giac"")","-\frac{1}{420} \, {\left(x e + d\right)}^{7} {\left(\frac{350 \, {\left(160 \, d e + 9 \, e^{2}\right)} e^{\left(-1\right)}}{x e + d} - \frac{84 \, {\left(2800 \, d^{2} e^{2} + 315 \, d e^{3} + 111 \, e^{4}\right)} e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}} + \frac{105 \, {\left(5600 \, d^{3} e^{3} + 945 \, d^{2} e^{4} + 666 \, d e^{5} + 37 \, e^{6}\right)} e^{\left(-3\right)}}{{\left(x e + d\right)}^{3}} - \frac{140 \, {\left(7000 \, d^{4} e^{4} + 1575 \, d^{3} e^{5} + 1665 \, d^{2} e^{6} + 185 \, d e^{7} + 148 \, e^{8}\right)} e^{\left(-4\right)}}{{\left(x e + d\right)}^{4}} + \frac{210 \, {\left(5600 \, d^{5} e^{5} + 1575 \, d^{4} e^{6} + 2220 \, d^{3} e^{7} + 370 \, d^{2} e^{8} + 592 \, d e^{9} - 65 \, e^{10}\right)} e^{\left(-5\right)}}{{\left(x e + d\right)}^{5}} - \frac{420 \, {\left(2800 \, d^{6} e^{6} + 945 \, d^{5} e^{7} + 1665 \, d^{4} e^{8} + 370 \, d^{3} e^{9} + 888 \, d^{2} e^{10} - 195 \, d e^{11} + 107 \, e^{12}\right)} e^{\left(-6\right)}}{{\left(x e + d\right)}^{6}} - 6000\right)} e^{\left(-9\right)} + {\left(800 \, d^{7} + 315 \, d^{6} e + 666 \, d^{5} e^{2} + 185 \, d^{4} e^{3} + 592 \, d^{3} e^{4} - 195 \, d^{2} e^{5} + 214 \, d e^{6} - 33 \, e^{7}\right)} e^{\left(-9\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) - {\left(\frac{100 \, d^{8} e^{7}}{x e + d} + \frac{45 \, d^{7} e^{8}}{x e + d} + \frac{111 \, d^{6} e^{9}}{x e + d} + \frac{37 \, d^{5} e^{10}}{x e + d} + \frac{148 \, d^{4} e^{11}}{x e + d} - \frac{65 \, d^{3} e^{12}}{x e + d} + \frac{107 \, d^{2} e^{13}}{x e + d} - \frac{33 \, d e^{14}}{x e + d} + \frac{18 \, e^{15}}{x e + d}\right)} e^{\left(-16\right)}"," ",0,"-1/420*(x*e + d)^7*(350*(160*d*e + 9*e^2)*e^(-1)/(x*e + d) - 84*(2800*d^2*e^2 + 315*d*e^3 + 111*e^4)*e^(-2)/(x*e + d)^2 + 105*(5600*d^3*e^3 + 945*d^2*e^4 + 666*d*e^5 + 37*e^6)*e^(-3)/(x*e + d)^3 - 140*(7000*d^4*e^4 + 1575*d^3*e^5 + 1665*d^2*e^6 + 185*d*e^7 + 148*e^8)*e^(-4)/(x*e + d)^4 + 210*(5600*d^5*e^5 + 1575*d^4*e^6 + 2220*d^3*e^7 + 370*d^2*e^8 + 592*d*e^9 - 65*e^10)*e^(-5)/(x*e + d)^5 - 420*(2800*d^6*e^6 + 945*d^5*e^7 + 1665*d^4*e^8 + 370*d^3*e^9 + 888*d^2*e^10 - 195*d*e^11 + 107*e^12)*e^(-6)/(x*e + d)^6 - 6000)*e^(-9) + (800*d^7 + 315*d^6*e + 666*d^5*e^2 + 185*d^4*e^3 + 592*d^3*e^4 - 195*d^2*e^5 + 214*d*e^6 - 33*e^7)*e^(-9)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) - (100*d^8*e^7/(x*e + d) + 45*d^7*e^8/(x*e + d) + 111*d^6*e^9/(x*e + d) + 37*d^5*e^10/(x*e + d) + 148*d^4*e^11/(x*e + d) - 65*d^3*e^12/(x*e + d) + 107*d^2*e^13/(x*e + d) - 33*d*e^14/(x*e + d) + 18*e^15/(x*e + d))*e^(-16)","A",0
302,1,354,0,0.161106," ","integrate((5*x^2+2*x+3)^2*(4*x^4-5*x^3+3*x^2+x+2)/(e*x+d)^3,x, algorithm=""giac"")","{\left(2800 \, d^{6} + 945 \, d^{5} e + 1665 \, d^{4} e^{2} + 370 \, d^{3} e^{3} + 888 \, d^{2} e^{4} - 195 \, d e^{5} + 107 \, e^{6}\right)} e^{\left(-9\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{12} \, {\left(200 \, x^{6} e^{15} - 720 \, d x^{5} e^{14} + 1800 \, d^{2} x^{4} e^{13} - 4000 \, d^{3} x^{3} e^{12} + 9000 \, d^{4} x^{2} e^{11} - 25200 \, d^{5} x e^{10} - 108 \, x^{5} e^{15} + 405 \, d x^{4} e^{14} - 1080 \, d^{2} x^{3} e^{13} + 2700 \, d^{3} x^{2} e^{12} - 8100 \, d^{4} x e^{11} + 333 \, x^{4} e^{15} - 1332 \, d x^{3} e^{14} + 3996 \, d^{2} x^{2} e^{13} - 13320 \, d^{3} x e^{12} - 148 \, x^{3} e^{15} + 666 \, d x^{2} e^{14} - 2664 \, d^{2} x e^{13} + 888 \, x^{2} e^{15} - 5328 \, d x e^{14} + 780 \, x e^{15}\right)} e^{\left(-18\right)} + \frac{{\left(1500 \, d^{8} + 585 \, d^{7} e + 1221 \, d^{6} e^{2} + 333 \, d^{5} e^{3} + 1036 \, d^{4} e^{4} - 325 \, d^{3} e^{5} + 321 \, d^{2} e^{6} + 2 \, {\left(800 \, d^{7} e + 315 \, d^{6} e^{2} + 666 \, d^{5} e^{3} + 185 \, d^{4} e^{4} + 592 \, d^{3} e^{5} - 195 \, d^{2} e^{6} + 214 \, d e^{7} - 33 \, e^{8}\right)} x - 33 \, d e^{7} - 18 \, e^{8}\right)} e^{\left(-9\right)}}{2 \, {\left(x e + d\right)}^{2}}"," ",0,"(2800*d^6 + 945*d^5*e + 1665*d^4*e^2 + 370*d^3*e^3 + 888*d^2*e^4 - 195*d*e^5 + 107*e^6)*e^(-9)*log(abs(x*e + d)) + 1/12*(200*x^6*e^15 - 720*d*x^5*e^14 + 1800*d^2*x^4*e^13 - 4000*d^3*x^3*e^12 + 9000*d^4*x^2*e^11 - 25200*d^5*x*e^10 - 108*x^5*e^15 + 405*d*x^4*e^14 - 1080*d^2*x^3*e^13 + 2700*d^3*x^2*e^12 - 8100*d^4*x*e^11 + 333*x^4*e^15 - 1332*d*x^3*e^14 + 3996*d^2*x^2*e^13 - 13320*d^3*x*e^12 - 148*x^3*e^15 + 666*d*x^2*e^14 - 2664*d^2*x*e^13 + 888*x^2*e^15 - 5328*d*x*e^14 + 780*x*e^15)*e^(-18) + 1/2*(1500*d^8 + 585*d^7*e + 1221*d^6*e^2 + 333*d^5*e^3 + 1036*d^4*e^4 - 325*d^3*e^5 + 321*d^2*e^6 + 2*(800*d^7*e + 315*d^6*e^2 + 666*d^5*e^3 + 185*d^4*e^4 + 592*d^3*e^5 - 195*d^2*e^6 + 214*d*e^7 - 33*e^8)*x - 33*d*e^7 - 18*e^8)*e^(-9)/(x*e + d)^2","A",0
303,1,345,0,0.158872," ","integrate((5*x^2+2*x+3)^2*(4*x^4-5*x^3+3*x^2+x+2)/(e*x+d)^4,x, algorithm=""giac"")","-{\left(5600 \, d^{5} + 1575 \, d^{4} e + 2220 \, d^{3} e^{2} + 370 \, d^{2} e^{3} + 592 \, d e^{4} - 65 \, e^{5}\right)} e^{\left(-9\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{12} \, {\left(240 \, x^{5} e^{16} - 1200 \, d x^{4} e^{15} + 4000 \, d^{2} x^{3} e^{14} - 12000 \, d^{3} x^{2} e^{13} + 42000 \, d^{4} x e^{12} - 135 \, x^{4} e^{16} + 720 \, d x^{3} e^{15} - 2700 \, d^{2} x^{2} e^{14} + 10800 \, d^{3} x e^{13} + 444 \, x^{3} e^{16} - 2664 \, d x^{2} e^{15} + 13320 \, d^{2} x e^{14} - 222 \, x^{2} e^{16} + 1776 \, d x e^{15} + 1776 \, x e^{16}\right)} e^{\left(-20\right)} - \frac{{\left(14600 \, d^{8} + 4815 \, d^{7} e + 8214 \, d^{6} e^{2} + 1739 \, d^{5} e^{3} + 3848 \, d^{4} e^{4} - 715 \, d^{3} e^{5} + 6 \, {\left(2800 \, d^{6} e^{2} + 945 \, d^{5} e^{3} + 1665 \, d^{4} e^{4} + 370 \, d^{3} e^{5} + 888 \, d^{2} e^{6} - 195 \, d e^{7} + 107 \, e^{8}\right)} x^{2} + 214 \, d^{2} e^{6} + 3 \, {\left(10400 \, d^{7} e + 3465 \, d^{6} e^{2} + 5994 \, d^{5} e^{3} + 1295 \, d^{4} e^{4} + 2960 \, d^{3} e^{5} - 585 \, d^{2} e^{6} + 214 \, d e^{7} + 33 \, e^{8}\right)} x + 33 \, d e^{7} + 36 \, e^{8}\right)} e^{\left(-9\right)}}{6 \, {\left(x e + d\right)}^{3}}"," ",0,"-(5600*d^5 + 1575*d^4*e + 2220*d^3*e^2 + 370*d^2*e^3 + 592*d*e^4 - 65*e^5)*e^(-9)*log(abs(x*e + d)) + 1/12*(240*x^5*e^16 - 1200*d*x^4*e^15 + 4000*d^2*x^3*e^14 - 12000*d^3*x^2*e^13 + 42000*d^4*x*e^12 - 135*x^4*e^16 + 720*d*x^3*e^15 - 2700*d^2*x^2*e^14 + 10800*d^3*x*e^13 + 444*x^3*e^16 - 2664*d*x^2*e^15 + 13320*d^2*x*e^14 - 222*x^2*e^16 + 1776*d*x*e^15 + 1776*x*e^16)*e^(-20) - 1/6*(14600*d^8 + 4815*d^7*e + 8214*d^6*e^2 + 1739*d^5*e^3 + 3848*d^4*e^4 - 715*d^3*e^5 + 6*(2800*d^6*e^2 + 945*d^5*e^3 + 1665*d^4*e^4 + 370*d^3*e^5 + 888*d^2*e^6 - 195*d*e^7 + 107*e^8)*x^2 + 214*d^2*e^6 + 3*(10400*d^7*e + 3465*d^6*e^2 + 5994*d^5*e^3 + 1295*d^4*e^4 + 2960*d^3*e^5 - 585*d^2*e^6 + 214*d*e^7 + 33*e^8)*x + 33*d*e^7 + 36*e^8)*e^(-9)/(x*e + d)^3","A",0
304,1,212,0,0.167039," ","integrate((e*x+d)^3*(4*x^4-5*x^3+3*x^2+x+2)/(5*x^2+2*x+3),x, algorithm=""giac"")","\frac{2}{15} \, x^{6} e^{3} + \frac{12}{25} \, d x^{5} e^{2} + \frac{3}{5} \, d^{2} x^{4} e + \frac{4}{15} \, d^{3} x^{3} - \frac{33}{125} \, x^{5} e^{3} - \frac{99}{100} \, d x^{4} e^{2} - \frac{33}{25} \, d^{2} x^{3} e - \frac{33}{50} \, d^{3} x^{2} + \frac{81}{500} \, x^{4} e^{3} + \frac{81}{125} \, d x^{3} e^{2} + \frac{243}{250} \, d^{2} x^{2} e + \frac{81}{125} \, d^{3} x + \frac{458}{1875} \, x^{3} e^{3} + \frac{687}{625} \, d x^{2} e^{2} + \frac{1374}{625} \, d^{2} x e - \frac{881}{6250} \, x^{2} e^{3} - \frac{2643}{3125} \, d x e^{2} - \frac{1}{1093750} \, \sqrt{14} {\left(52875 \, d^{3} + 449175 \, d^{2} e - 274845 \, d e^{2} - 53189 \, e^{3}\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) - \frac{5108}{15625} \, x e^{3} + \frac{1}{156250} \, {\left(57250 \, d^{3} - 66075 \, d^{2} e - 76620 \, d e^{2} + 23431 \, e^{3}\right)} \log\left(5 \, x^{2} + 2 \, x + 3\right)"," ",0,"2/15*x^6*e^3 + 12/25*d*x^5*e^2 + 3/5*d^2*x^4*e + 4/15*d^3*x^3 - 33/125*x^5*e^3 - 99/100*d*x^4*e^2 - 33/25*d^2*x^3*e - 33/50*d^3*x^2 + 81/500*x^4*e^3 + 81/125*d*x^3*e^2 + 243/250*d^2*x^2*e + 81/125*d^3*x + 458/1875*x^3*e^3 + 687/625*d*x^2*e^2 + 1374/625*d^2*x*e - 881/6250*x^2*e^3 - 2643/3125*d*x*e^2 - 1/1093750*sqrt(14)*(52875*d^3 + 449175*d^2*e - 274845*d*e^2 - 53189*e^3)*arctan(1/14*sqrt(14)*(5*x + 1)) - 5108/15625*x*e^3 + 1/156250*(57250*d^3 - 66075*d^2*e - 76620*d*e^2 + 23431*e^3)*log(5*x^2 + 2*x + 3)","A",0
305,1,145,0,0.158870," ","integrate((e*x+d)^2*(4*x^4-5*x^3+3*x^2+x+2)/(5*x^2+2*x+3),x, algorithm=""giac"")","\frac{4}{25} \, x^{5} e^{2} + \frac{2}{5} \, d x^{4} e + \frac{4}{15} \, d^{2} x^{3} - \frac{33}{100} \, x^{4} e^{2} - \frac{22}{25} \, d x^{3} e - \frac{33}{50} \, d^{2} x^{2} + \frac{27}{125} \, x^{3} e^{2} + \frac{81}{125} \, d x^{2} e + \frac{81}{125} \, d^{2} x + \frac{229}{625} \, x^{2} e^{2} + \frac{916}{625} \, d x e - \frac{1}{218750} \, \sqrt{14} {\left(10575 \, d^{2} + 59890 \, d e - 18323 \, e^{2}\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) - \frac{881}{3125} \, x e^{2} + \frac{1}{15625} \, {\left(5725 \, d^{2} - 4405 \, d e - 2554 \, e^{2}\right)} \log\left(5 \, x^{2} + 2 \, x + 3\right)"," ",0,"4/25*x^5*e^2 + 2/5*d*x^4*e + 4/15*d^2*x^3 - 33/100*x^4*e^2 - 22/25*d*x^3*e - 33/50*d^2*x^2 + 27/125*x^3*e^2 + 81/125*d*x^2*e + 81/125*d^2*x + 229/625*x^2*e^2 + 916/625*d*x*e - 1/218750*sqrt(14)*(10575*d^2 + 59890*d*e - 18323*e^2)*arctan(1/14*sqrt(14)*(5*x + 1)) - 881/3125*x*e^2 + 1/15625*(5725*d^2 - 4405*d*e - 2554*e^2)*log(5*x^2 + 2*x + 3)","A",0
306,1,88,0,0.155152," ","integrate((e*x+d)*(4*x^4-5*x^3+3*x^2+x+2)/(5*x^2+2*x+3),x, algorithm=""giac"")","\frac{1}{5} \, x^{4} e + \frac{4}{15} \, d x^{3} - \frac{11}{25} \, x^{3} e - \frac{33}{50} \, d x^{2} + \frac{81}{250} \, x^{2} e - \frac{1}{43750} \, \sqrt{14} {\left(2115 \, d + 5989 \, e\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) + \frac{81}{125} \, d x + \frac{458}{625} \, x e + \frac{1}{6250} \, {\left(2290 \, d - 881 \, e\right)} \log\left(5 \, x^{2} + 2 \, x + 3\right)"," ",0,"1/5*x^4*e + 4/15*d*x^3 - 11/25*x^3*e - 33/50*d*x^2 + 81/250*x^2*e - 1/43750*sqrt(14)*(2115*d + 5989*e)*arctan(1/14*sqrt(14)*(5*x + 1)) + 81/125*d*x + 458/625*x*e + 1/6250*(2290*d - 881*e)*log(5*x^2 + 2*x + 3)","A",0
307,1,43,0,0.162090," ","integrate((4*x^4-5*x^3+3*x^2+x+2)/(5*x^2+2*x+3),x, algorithm=""giac"")","\frac{4}{15} \, x^{3} - \frac{33}{50} \, x^{2} - \frac{423}{8750} \, \sqrt{14} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) + \frac{81}{125} \, x + \frac{229}{625} \, \log\left(5 \, x^{2} + 2 \, x + 3\right)"," ",0,"4/15*x^3 - 33/50*x^2 - 423/8750*sqrt(14)*arctan(1/14*sqrt(14)*(5*x + 1)) + 81/125*x + 229/625*log(5*x^2 + 2*x + 3)","A",0
308,1,158,0,0.216292," ","integrate((4*x^4-5*x^3+3*x^2+x+2)/(e*x+d)/(5*x^2+2*x+3),x, algorithm=""giac"")","\frac{1}{25} \, {\left(10 \, x^{2} e - 20 \, d x - 33 \, x e\right)} e^{\left(-2\right)} - \frac{\sqrt{14} {\left(423 \, d - 1367 \, e\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right)}{1750 \, {\left(5 \, d^{2} - 2 \, d e + 3 \, e^{2}\right)}} + \frac{{\left(458 \, d - 7 \, e\right)} \log\left(5 \, x^{2} + 2 \, x + 3\right)}{250 \, {\left(5 \, d^{2} - 2 \, d e + 3 \, e^{2}\right)}} + \frac{{\left(4 \, d^{4} + 5 \, d^{3} e + 3 \, d^{2} e^{2} - d e^{3} + 2 \, e^{4}\right)} \log\left({\left| x e + d \right|}\right)}{5 \, d^{2} e^{3} - 2 \, d e^{4} + 3 \, e^{5}}"," ",0,"1/25*(10*x^2*e - 20*d*x - 33*x*e)*e^(-2) - 1/1750*sqrt(14)*(423*d - 1367*e)*arctan(1/14*sqrt(14)*(5*x + 1))/(5*d^2 - 2*d*e + 3*e^2) + 1/250*(458*d - 7*e)*log(5*x^2 + 2*x + 3)/(5*d^2 - 2*d*e + 3*e^2) + (4*d^4 + 5*d^3*e + 3*d^2*e^2 - d*e^3 + 2*e^4)*log(abs(x*e + d))/(5*d^2*e^3 - 2*d*e^4 + 3*e^5)","A",0
309,1,355,0,0.176917," ","integrate((4*x^4-5*x^3+3*x^2+x+2)/(e*x+d)^2/(5*x^2+2*x+3),x, algorithm=""giac"")","\frac{1}{25} \, {\left(40 \, d + 33 \, e\right)} e^{\left(-3\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) - \frac{\sqrt{14} {\left(423 \, d^{2} e^{2} - 2734 \, d e^{3} + 293 \, e^{4}\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, d - \frac{5 \, d^{2}}{x e + d} + \frac{2 \, d e}{x e + d} - \frac{3 \, e^{2}}{x e + d} - e\right)} e^{\left(-1\right)}\right) e^{\left(-2\right)}}{350 \, {\left(25 \, d^{4} - 20 \, d^{3} e + 34 \, d^{2} e^{2} - 12 \, d e^{3} + 9 \, e^{4}\right)}} + \frac{4}{5} \, {\left(x e + d\right)} e^{\left(-3\right)} + \frac{{\left(229 \, d^{2} - 7 \, d e - 136 \, e^{2}\right)} \log\left(-\frac{10 \, d}{x e + d} + \frac{5 \, d^{2}}{{\left(x e + d\right)}^{2}} + \frac{2 \, e}{x e + d} - \frac{2 \, d e}{{\left(x e + d\right)}^{2}} + \frac{3 \, e^{2}}{{\left(x e + d\right)}^{2}} + 5\right)}{25 \, {\left(25 \, d^{4} - 20 \, d^{3} e + 34 \, d^{2} e^{2} - 12 \, d e^{3} + 9 \, e^{4}\right)}} - \frac{\frac{4 \, d^{4} e^{3}}{x e + d} + \frac{5 \, d^{3} e^{4}}{x e + d} + \frac{3 \, d^{2} e^{5}}{x e + d} - \frac{d e^{6}}{x e + d} + \frac{2 \, e^{7}}{x e + d}}{5 \, d^{2} e^{6} - 2 \, d e^{7} + 3 \, e^{8}}"," ",0,"1/25*(40*d + 33*e)*e^(-3)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) - 1/350*sqrt(14)*(423*d^2*e^2 - 2734*d*e^3 + 293*e^4)*arctan(1/14*sqrt(14)*(5*d - 5*d^2/(x*e + d) + 2*d*e/(x*e + d) - 3*e^2/(x*e + d) - e)*e^(-1))*e^(-2)/(25*d^4 - 20*d^3*e + 34*d^2*e^2 - 12*d*e^3 + 9*e^4) + 4/5*(x*e + d)*e^(-3) + 1/25*(229*d^2 - 7*d*e - 136*e^2)*log(-10*d/(x*e + d) + 5*d^2/(x*e + d)^2 + 2*e/(x*e + d) - 2*d*e/(x*e + d)^2 + 3*e^2/(x*e + d)^2 + 5)/(25*d^4 - 20*d^3*e + 34*d^2*e^2 - 12*d*e^3 + 9*e^4) - (4*d^4*e^3/(x*e + d) + 5*d^3*e^4/(x*e + d) + 3*d^2*e^5/(x*e + d) - d*e^6/(x*e + d) + 2*e^7/(x*e + d))/(5*d^2*e^6 - 2*d*e^7 + 3*e^8)","A",0
310,1,406,0,0.179095," ","integrate((4*x^4-5*x^3+3*x^2+x+2)/(e*x+d)^3/(5*x^2+2*x+3),x, algorithm=""giac"")","-\frac{\sqrt{14} {\left(423 \, d^{3} - 4101 \, d^{2} e + 879 \, d e^{2} + 703 \, e^{3}\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right)}{70 \, {\left(125 \, d^{6} - 150 \, d^{5} e + 285 \, d^{4} e^{2} - 188 \, d^{3} e^{3} + 171 \, d^{2} e^{4} - 54 \, d e^{5} + 27 \, e^{6}\right)}} + \frac{{\left(458 \, d^{3} - 21 \, d^{2} e - 816 \, d e^{2} + 113 \, e^{3}\right)} \log\left(5 \, x^{2} + 2 \, x + 3\right)}{10 \, {\left(125 \, d^{6} - 150 \, d^{5} e + 285 \, d^{4} e^{2} - 188 \, d^{3} e^{3} + 171 \, d^{2} e^{4} - 54 \, d e^{5} + 27 \, e^{6}\right)}} + \frac{{\left(100 \, d^{6} - 120 \, d^{5} e + 228 \, d^{4} e^{2} - 242 \, d^{3} e^{3} + 141 \, d^{2} e^{4} + 120 \, d e^{5} - e^{6}\right)} \log\left({\left| x e + d \right|}\right)}{125 \, d^{6} e^{3} - 150 \, d^{5} e^{4} + 285 \, d^{4} e^{5} - 188 \, d^{3} e^{6} + 171 \, d^{2} e^{7} - 54 \, d e^{8} + 27 \, e^{9}} + \frac{{\left(2 \, {\left(200 \, d^{7} - 75 \, d^{6} e + 258 \, d^{5} e^{2} + 167 \, d^{4} e^{3} - 14 \, d^{3} e^{4} + 141 \, d^{2} e^{5} - 8 \, d e^{6} + 3 \, e^{7}\right)} x + {\left(300 \, d^{8} - 195 \, d^{7} e + 405 \, d^{6} e^{2} + 297 \, d^{5} e^{3} - 176 \, d^{4} e^{4} + 347 \, d^{3} e^{5} - 123 \, d^{2} e^{6} + 39 \, d e^{7} - 18 \, e^{8}\right)} e^{\left(-1\right)}\right)} e^{\left(-2\right)}}{2 \, {\left(5 \, d^{2} - 2 \, d e + 3 \, e^{2}\right)}^{3} {\left(x e + d\right)}^{2}}"," ",0,"-1/70*sqrt(14)*(423*d^3 - 4101*d^2*e + 879*d*e^2 + 703*e^3)*arctan(1/14*sqrt(14)*(5*x + 1))/(125*d^6 - 150*d^5*e + 285*d^4*e^2 - 188*d^3*e^3 + 171*d^2*e^4 - 54*d*e^5 + 27*e^6) + 1/10*(458*d^3 - 21*d^2*e - 816*d*e^2 + 113*e^3)*log(5*x^2 + 2*x + 3)/(125*d^6 - 150*d^5*e + 285*d^4*e^2 - 188*d^3*e^3 + 171*d^2*e^4 - 54*d*e^5 + 27*e^6) + (100*d^6 - 120*d^5*e + 228*d^4*e^2 - 242*d^3*e^3 + 141*d^2*e^4 + 120*d*e^5 - e^6)*log(abs(x*e + d))/(125*d^6*e^3 - 150*d^5*e^4 + 285*d^4*e^5 - 188*d^3*e^6 + 171*d^2*e^7 - 54*d*e^8 + 27*e^9) + 1/2*(2*(200*d^7 - 75*d^6*e + 258*d^5*e^2 + 167*d^4*e^3 - 14*d^3*e^4 + 141*d^2*e^5 - 8*d*e^6 + 3*e^7)*x + (300*d^8 - 195*d^7*e + 405*d^6*e^2 + 297*d^5*e^3 - 176*d^4*e^4 + 347*d^3*e^5 - 123*d^2*e^6 + 39*d*e^7 - 18*e^8)*e^(-1))*e^(-2)/((5*d^2 - 2*d*e + 3*e^2)^3*(x*e + d)^2)","A",0
311,1,206,0,0.162239," ","integrate((e*x+d)^3*(4*x^4-5*x^3+3*x^2+x+2)/(5*x^2+2*x+3)^2,x, algorithm=""giac"")","\frac{1}{25} \, x^{4} e^{3} + \frac{4}{25} \, d x^{3} e^{2} + \frac{6}{25} \, d^{2} x^{2} e + \frac{4}{25} \, d^{3} x - \frac{41}{375} \, x^{3} e^{3} - \frac{123}{250} \, d x^{2} e^{2} - \frac{123}{125} \, d^{2} x e + \frac{103}{1250} \, x^{2} e^{3} + \frac{309}{625} \, d x e^{2} + \frac{1}{1225000} \, \sqrt{14} {\left(32825 \, d^{3} + 317565 \, d^{2} e - 221643 \, d e^{2} - 67499 \, e^{3}\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) + \frac{867}{3125} \, x e^{3} - \frac{1}{6250} \, {\left(1025 \, d^{3} - 1545 \, d^{2} e - 2601 \, d e^{2} + 832 \, e^{3}\right)} \log\left(5 \, x^{2} + 2 \, x + 3\right) - \frac{170875 \, d^{3} - 95175 \, d^{2} e + {\left(52875 \, d^{3} + 449175 \, d^{2} e - 274845 \, d e^{2} - 53189 \, e^{3}\right)} x - 269505 \, d e^{2} + 54969 \, e^{3}}{437500 \, {\left(5 \, x^{2} + 2 \, x + 3\right)}}"," ",0,"1/25*x^4*e^3 + 4/25*d*x^3*e^2 + 6/25*d^2*x^2*e + 4/25*d^3*x - 41/375*x^3*e^3 - 123/250*d*x^2*e^2 - 123/125*d^2*x*e + 103/1250*x^2*e^3 + 309/625*d*x*e^2 + 1/1225000*sqrt(14)*(32825*d^3 + 317565*d^2*e - 221643*d*e^2 - 67499*e^3)*arctan(1/14*sqrt(14)*(5*x + 1)) + 867/3125*x*e^3 - 1/6250*(1025*d^3 - 1545*d^2*e - 2601*d*e^2 + 832*e^3)*log(5*x^2 + 2*x + 3) - 1/437500*(170875*d^3 - 95175*d^2*e + (52875*d^3 + 449175*d^2*e - 274845*d*e^2 - 53189*e^3)*x - 269505*d*e^2 + 54969*e^3)/(5*x^2 + 2*x + 3)","A",0
312,1,145,0,0.156068," ","integrate((e*x+d)^2*(4*x^4-5*x^3+3*x^2+x+2)/(5*x^2+2*x+3)^2,x, algorithm=""giac"")","\frac{4}{75} \, x^{3} e^{2} + \frac{4}{25} \, d x^{2} e + \frac{4}{25} \, d^{2} x - \frac{41}{250} \, x^{2} e^{2} - \frac{82}{125} \, d x e + \frac{1}{1225000} \, \sqrt{14} {\left(32825 \, d^{2} + 211710 \, d e - 73881 \, e^{2}\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) + \frac{103}{625} \, x e^{2} - \frac{1}{6250} \, {\left(1025 \, d^{2} - 1030 \, d e - 867 \, e^{2}\right)} \log\left(5 \, x^{2} + 2 \, x + 3\right) - \frac{34175 \, d^{2} + {\left(10575 \, d^{2} + 59890 \, d e - 18323 \, e^{2}\right)} x - 12690 \, d e - 17967 \, e^{2}}{87500 \, {\left(5 \, x^{2} + 2 \, x + 3\right)}}"," ",0,"4/75*x^3*e^2 + 4/25*d*x^2*e + 4/25*d^2*x - 41/250*x^2*e^2 - 82/125*d*x*e + 1/1225000*sqrt(14)*(32825*d^2 + 211710*d*e - 73881*e^2)*arctan(1/14*sqrt(14)*(5*x + 1)) + 103/625*x*e^2 - 1/6250*(1025*d^2 - 1030*d*e - 867*e^2)*log(5*x^2 + 2*x + 3) - 1/87500*(34175*d^2 + (10575*d^2 + 59890*d*e - 18323*e^2)*x - 12690*d*e - 17967*e^2)/(5*x^2 + 2*x + 3)","A",0
313,1,94,0,0.156038," ","integrate((e*x+d)*(4*x^4-5*x^3+3*x^2+x+2)/(5*x^2+2*x+3)^2,x, algorithm=""giac"")","\frac{2}{25} \, x^{2} e + \frac{1}{245000} \, \sqrt{14} {\left(6565 \, d + 21171 \, e\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) + \frac{4}{25} \, d x - \frac{41}{125} \, x e - \frac{1}{1250} \, {\left(205 \, d - 103 \, e\right)} \log\left(5 \, x^{2} + 2 \, x + 3\right) - \frac{{\left(2115 \, d + 5989 \, e\right)} x + 6835 \, d - 1269 \, e}{17500 \, {\left(5 \, x^{2} + 2 \, x + 3\right)}}"," ",0,"2/25*x^2*e + 1/245000*sqrt(14)*(6565*d + 21171*e)*arctan(1/14*sqrt(14)*(5*x + 1)) + 4/25*d*x - 41/125*x*e - 1/1250*(205*d - 103*e)*log(5*x^2 + 2*x + 3) - 1/17500*((2115*d + 5989*e)*x + 6835*d - 1269*e)/(5*x^2 + 2*x + 3)","A",0
314,1,52,0,0.153291," ","integrate((4*x^4-5*x^3+3*x^2+x+2)/(5*x^2+2*x+3)^2,x, algorithm=""giac"")","\frac{1313}{49000} \, \sqrt{14} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) + \frac{4}{25} \, x - \frac{423 \, x + 1367}{3500 \, {\left(5 \, x^{2} + 2 \, x + 3\right)}} - \frac{41}{250} \, \log\left(5 \, x^{2} + 2 \, x + 3\right)"," ",0,"1313/49000*sqrt(14)*arctan(1/14*sqrt(14)*(5*x + 1)) + 4/25*x - 1/3500*(423*x + 1367)/(5*x^2 + 2*x + 3) - 41/250*log(5*x^2 + 2*x + 3)","A",0
315,1,284,0,0.170291," ","integrate((4*x^4-5*x^3+3*x^2+x+2)/(e*x+d)/(5*x^2+2*x+3)^2,x, algorithm=""giac"")","\frac{\sqrt{14} {\left(6565 \, d^{3} - 26423 \, d^{2} e + 11089 \, d e^{2} - 6623 \, e^{3}\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right)}{9800 \, {\left(25 \, d^{4} - 20 \, d^{3} e + 34 \, d^{2} e^{2} - 12 \, d e^{3} + 9 \, e^{4}\right)}} - \frac{{\left(205 \, d^{3} - 61 \, d^{2} e + 23 \, d e^{2} + 14 \, e^{3}\right)} \log\left(5 \, x^{2} + 2 \, x + 3\right)}{50 \, {\left(25 \, d^{4} - 20 \, d^{3} e + 34 \, d^{2} e^{2} - 12 \, d e^{3} + 9 \, e^{4}\right)}} + \frac{{\left(4 \, d^{4} + 5 \, d^{3} e + 3 \, d^{2} e^{2} - d e^{3} + 2 \, e^{4}\right)} \log\left({\left| x e + d \right|}\right)}{25 \, d^{4} e - 20 \, d^{3} e^{2} + 34 \, d^{2} e^{3} - 12 \, d e^{4} + 9 \, e^{5}} - \frac{6835 \, d^{3} - 4199 \, d^{2} e + {\left(2115 \, d^{3} - 7681 \, d^{2} e + 4003 \, d e^{2} - 4101 \, e^{3}\right)} x + 4687 \, d e^{2} - 879 \, e^{3}}{700 \, {\left(5 \, d^{2} - 2 \, d e + 3 \, e^{2}\right)}^{2} {\left(5 \, x^{2} + 2 \, x + 3\right)}}"," ",0,"1/9800*sqrt(14)*(6565*d^3 - 26423*d^2*e + 11089*d*e^2 - 6623*e^3)*arctan(1/14*sqrt(14)*(5*x + 1))/(25*d^4 - 20*d^3*e + 34*d^2*e^2 - 12*d*e^3 + 9*e^4) - 1/50*(205*d^3 - 61*d^2*e + 23*d*e^2 + 14*e^3)*log(5*x^2 + 2*x + 3)/(25*d^4 - 20*d^3*e + 34*d^2*e^2 - 12*d*e^3 + 9*e^4) + (4*d^4 + 5*d^3*e + 3*d^2*e^2 - d*e^3 + 2*e^4)*log(abs(x*e + d))/(25*d^4*e - 20*d^3*e^2 + 34*d^2*e^3 - 12*d*e^4 + 9*e^5) - 1/700*(6835*d^3 - 4199*d^2*e + (2115*d^3 - 7681*d^2*e + 4003*d*e^2 - 4101*e^3)*x + 4687*d*e^2 - 879*e^3)/((5*d^2 - 2*d*e + 3*e^2)^2*(5*x^2 + 2*x + 3))","A",0
316,1,571,0,0.203757," ","integrate((4*x^4-5*x^3+3*x^2+x+2)/(e*x+d)^2/(5*x^2+2*x+3)^2,x, algorithm=""giac"")","\frac{\sqrt{14} {\left(1313 \, d^{4} e^{2} - 10044 \, d^{3} e^{3} + 4290 \, d^{2} e^{4} + 156 \, d e^{5} - 271 \, e^{6}\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, d - \frac{5 \, d^{2}}{x e + d} + \frac{2 \, d e}{x e + d} - \frac{3 \, e^{2}}{x e + d} - e\right)} e^{\left(-1\right)}\right) e^{\left(-2\right)}}{392 \, {\left(125 \, d^{6} - 150 \, d^{5} e + 285 \, d^{4} e^{2} - 188 \, d^{3} e^{3} + 171 \, d^{2} e^{4} - 54 \, d e^{5} + 27 \, e^{6}\right)}} - \frac{{\left(41 \, d^{4} - 8 \, d^{3} e - 60 \, d^{2} e^{2} + 24 \, d e^{3} - 5 \, e^{4}\right)} \log\left(-\frac{10 \, d}{x e + d} + \frac{5 \, d^{2}}{{\left(x e + d\right)}^{2}} + \frac{2 \, e}{x e + d} - \frac{2 \, d e}{{\left(x e + d\right)}^{2}} + \frac{3 \, e^{2}}{{\left(x e + d\right)}^{2}} + 5\right)}{2 \, {\left(125 \, d^{6} - 150 \, d^{5} e + 285 \, d^{4} e^{2} - 188 \, d^{3} e^{3} + 171 \, d^{2} e^{4} - 54 \, d e^{5} + 27 \, e^{6}\right)}} - \frac{\frac{4 \, d^{4} e^{3}}{x e + d} + \frac{5 \, d^{3} e^{4}}{x e + d} + \frac{3 \, d^{2} e^{5}}{x e + d} - \frac{d e^{6}}{x e + d} + \frac{2 \, e^{7}}{x e + d}}{25 \, d^{4} e^{4} - 20 \, d^{3} e^{5} + 34 \, d^{2} e^{6} - 12 \, d e^{7} + 9 \, e^{8}} + \frac{\frac{423 \, d^{3} e - 4101 \, d^{2} e^{2} + 879 \, d e^{3} + 703 \, e^{4}}{5 \, d^{2} - 2 \, d e + 3 \, e^{2}} - \frac{{\left(423 \, d^{4} e^{2} - 5468 \, d^{3} e^{3} + 1758 \, d^{2} e^{4} + 2812 \, d e^{5} - 457 \, e^{6}\right)} e^{\left(-1\right)}}{{\left(5 \, d^{2} - 2 \, d e + 3 \, e^{2}\right)} {\left(x e + d\right)}}}{28 \, {\left(5 \, d^{2} - 2 \, d e + 3 \, e^{2}\right)}^{2} {\left(\frac{10 \, d}{x e + d} - \frac{5 \, d^{2}}{{\left(x e + d\right)}^{2}} - \frac{2 \, e}{x e + d} + \frac{2 \, d e}{{\left(x e + d\right)}^{2}} - \frac{3 \, e^{2}}{{\left(x e + d\right)}^{2}} - 5\right)}}"," ",0,"1/392*sqrt(14)*(1313*d^4*e^2 - 10044*d^3*e^3 + 4290*d^2*e^4 + 156*d*e^5 - 271*e^6)*arctan(1/14*sqrt(14)*(5*d - 5*d^2/(x*e + d) + 2*d*e/(x*e + d) - 3*e^2/(x*e + d) - e)*e^(-1))*e^(-2)/(125*d^6 - 150*d^5*e + 285*d^4*e^2 - 188*d^3*e^3 + 171*d^2*e^4 - 54*d*e^5 + 27*e^6) - 1/2*(41*d^4 - 8*d^3*e - 60*d^2*e^2 + 24*d*e^3 - 5*e^4)*log(-10*d/(x*e + d) + 5*d^2/(x*e + d)^2 + 2*e/(x*e + d) - 2*d*e/(x*e + d)^2 + 3*e^2/(x*e + d)^2 + 5)/(125*d^6 - 150*d^5*e + 285*d^4*e^2 - 188*d^3*e^3 + 171*d^2*e^4 - 54*d*e^5 + 27*e^6) - (4*d^4*e^3/(x*e + d) + 5*d^3*e^4/(x*e + d) + 3*d^2*e^5/(x*e + d) - d*e^6/(x*e + d) + 2*e^7/(x*e + d))/(25*d^4*e^4 - 20*d^3*e^5 + 34*d^2*e^6 - 12*d*e^7 + 9*e^8) + 1/28*((423*d^3*e - 4101*d^2*e^2 + 879*d*e^3 + 703*e^4)/(5*d^2 - 2*d*e + 3*e^2) - (423*d^4*e^2 - 5468*d^3*e^3 + 1758*d^2*e^4 + 2812*d*e^5 - 457*e^6)*e^(-1)/((5*d^2 - 2*d*e + 3*e^2)*(x*e + d)))/((5*d^2 - 2*d*e + 3*e^2)^2*(10*d/(x*e + d) - 5*d^2/(x*e + d)^2 - 2*e/(x*e + d) + 2*d*e/(x*e + d)^2 - 3*e^2/(x*e + d)^2 - 5))","A",0
317,1,595,0,0.204451," ","integrate((4*x^4-5*x^3+3*x^2+x+2)/(e*x+d)^3/(5*x^2+2*x+3)^2,x, algorithm=""giac"")","\frac{\sqrt{14} {\left(6565 \, d^{5} - 74017 \, d^{4} e + 35022 \, d^{3} e^{2} + 42858 \, d^{2} e^{3} - 17247 \, d e^{4} + 579 \, e^{5}\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right)}{392 \, {\left(625 \, d^{8} - 1000 \, d^{7} e + 2100 \, d^{6} e^{2} - 1960 \, d^{5} e^{3} + 2086 \, d^{4} e^{4} - 1176 \, d^{3} e^{5} + 756 \, d^{2} e^{6} - 216 \, d e^{7} + 81 \, e^{8}\right)}} - \frac{{\left(205 \, d^{5} - 19 \, d^{4} e - 846 \, d^{3} e^{2} + 396 \, d^{2} e^{3} + 57 \, d e^{4} - 21 \, e^{5}\right)} \log\left(5 \, x^{2} + 2 \, x + 3\right)}{2 \, {\left(625 \, d^{8} - 1000 \, d^{7} e + 2100 \, d^{6} e^{2} - 1960 \, d^{5} e^{3} + 2086 \, d^{4} e^{4} - 1176 \, d^{3} e^{5} + 756 \, d^{2} e^{6} - 216 \, d e^{7} + 81 \, e^{8}\right)}} + \frac{{\left(205 \, d^{5} e - 19 \, d^{4} e^{2} - 846 \, d^{3} e^{3} + 396 \, d^{2} e^{4} + 57 \, d e^{5} - 21 \, e^{6}\right)} \log\left({\left| x e + d \right|}\right)}{625 \, d^{8} e - 1000 \, d^{7} e^{2} + 2100 \, d^{6} e^{3} - 1960 \, d^{5} e^{4} + 2086 \, d^{4} e^{5} - 1176 \, d^{3} e^{6} + 756 \, d^{2} e^{7} - 216 \, d e^{8} + 81 \, e^{9}} - \frac{{\left(4200 \, d^{8} + 25945 \, d^{7} e - 12715 \, d^{6} e^{2} - 16656 \, d^{5} e^{3} + 28226 \, d^{4} e^{4} + {\left(28700 \, d^{6} e^{2} - 14965 \, d^{5} e^{3} - 43891 \, d^{4} e^{4} + 44106 \, d^{3} e^{5} - 45966 \, d^{2} e^{6} + 12711 \, d e^{7} + 9 \, e^{8}\right)} x^{3} - 31223 \, d^{3} e^{5} + {\left(7000 \, d^{8} + 31850 \, d^{7} e + 6400 \, d^{6} e^{2} - 62649 \, d^{5} e^{3} + 52187 \, d^{4} e^{4} - 53652 \, d^{3} e^{5} + 11130 \, d^{2} e^{6} - 2841 \, d e^{7} + 1791 \, e^{8}\right)} x^{2} + 12753 \, d^{2} e^{6} + {\left(2800 \, d^{8} + 14855 \, d^{7} e + 5815 \, d^{6} e^{2} - 18620 \, d^{5} e^{3} - 17202 \, d^{4} e^{4} + 11119 \, d^{3} e^{5} - 26037 \, d^{2} e^{6} + 7866 \, d e^{7} - 756 \, e^{8}\right)} x - 2646 \, d e^{7} + 756 \, e^{8}\right)} e^{\left(-1\right)}}{28 \, {\left(5 \, d^{2} - 2 \, d e + 3 \, e^{2}\right)}^{4} {\left(5 \, x^{2} + 2 \, x + 3\right)} {\left(x e + d\right)}^{2}}"," ",0,"1/392*sqrt(14)*(6565*d^5 - 74017*d^4*e + 35022*d^3*e^2 + 42858*d^2*e^3 - 17247*d*e^4 + 579*e^5)*arctan(1/14*sqrt(14)*(5*x + 1))/(625*d^8 - 1000*d^7*e + 2100*d^6*e^2 - 1960*d^5*e^3 + 2086*d^4*e^4 - 1176*d^3*e^5 + 756*d^2*e^6 - 216*d*e^7 + 81*e^8) - 1/2*(205*d^5 - 19*d^4*e - 846*d^3*e^2 + 396*d^2*e^3 + 57*d*e^4 - 21*e^5)*log(5*x^2 + 2*x + 3)/(625*d^8 - 1000*d^7*e + 2100*d^6*e^2 - 1960*d^5*e^3 + 2086*d^4*e^4 - 1176*d^3*e^5 + 756*d^2*e^6 - 216*d*e^7 + 81*e^8) + (205*d^5*e - 19*d^4*e^2 - 846*d^3*e^3 + 396*d^2*e^4 + 57*d*e^5 - 21*e^6)*log(abs(x*e + d))/(625*d^8*e - 1000*d^7*e^2 + 2100*d^6*e^3 - 1960*d^5*e^4 + 2086*d^4*e^5 - 1176*d^3*e^6 + 756*d^2*e^7 - 216*d*e^8 + 81*e^9) - 1/28*(4200*d^8 + 25945*d^7*e - 12715*d^6*e^2 - 16656*d^5*e^3 + 28226*d^4*e^4 + (28700*d^6*e^2 - 14965*d^5*e^3 - 43891*d^4*e^4 + 44106*d^3*e^5 - 45966*d^2*e^6 + 12711*d*e^7 + 9*e^8)*x^3 - 31223*d^3*e^5 + (7000*d^8 + 31850*d^7*e + 6400*d^6*e^2 - 62649*d^5*e^3 + 52187*d^4*e^4 - 53652*d^3*e^5 + 11130*d^2*e^6 - 2841*d*e^7 + 1791*e^8)*x^2 + 12753*d^2*e^6 + (2800*d^8 + 14855*d^7*e + 5815*d^6*e^2 - 18620*d^5*e^3 - 17202*d^4*e^4 + 11119*d^3*e^5 - 26037*d^2*e^6 + 7866*d*e^7 - 756*e^8)*x - 2646*d*e^7 + 756*e^8)*e^(-1)/((5*d^2 - 2*d*e + 3*e^2)^4*(5*x^2 + 2*x + 3)*(x*e + d)^2)","A",0
318,1,201,0,0.207969," ","integrate((e*x+d)^3*(4*x^4-5*x^3+3*x^2+x+2)/(5*x^2+2*x+3)^3,x, algorithm=""giac"")","\frac{2}{125} \, x^{2} e^{3} + \frac{12}{125} \, d x e^{2} + \frac{3}{68600000} \, \sqrt{14} {\left(353125 \, d^{3} - 855175 \, d^{2} e + 74085 \, d e^{2} + 556349 \, e^{3}\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) - \frac{49}{625} \, x e^{3} + \frac{3}{6250} \, {\left(100 \, d^{2} e - 245 \, d e^{2} + 47 \, e^{3}\right)} \log\left(5 \, x^{2} + 2 \, x + 3\right) + \frac{5 \, {\left(275375 \, d^{3} + 2726475 \, d^{2} e - 1941585 \, d e^{2} - 621801 \, e^{3}\right)} x^{3} + 1619125 \, d^{3} + {\left(4844125 \, d^{3} + 2123025 \, d^{2} e - 16020675 \, d e^{2} + 1396037 \, e^{3}\right)} x^{2} - 1464975 \, d^{2} e + 3 \, {\left(749125 \, d^{3} + 1444025 \, d^{2} e - 3046875 \, d e^{2} - 170563 \, e^{3}\right)} x - 5773275 \, d e^{2} + 1275957 \, e^{3}}{4900000 \, {\left(5 \, x^{2} + 2 \, x + 3\right)}^{2}}"," ",0,"2/125*x^2*e^3 + 12/125*d*x*e^2 + 3/68600000*sqrt(14)*(353125*d^3 - 855175*d^2*e + 74085*d*e^2 + 556349*e^3)*arctan(1/14*sqrt(14)*(5*x + 1)) - 49/625*x*e^3 + 3/6250*(100*d^2*e - 245*d*e^2 + 47*e^3)*log(5*x^2 + 2*x + 3) + 1/4900000*(5*(275375*d^3 + 2726475*d^2*e - 1941585*d*e^2 - 621801*e^3)*x^3 + 1619125*d^3 + (4844125*d^3 + 2123025*d^2*e - 16020675*d*e^2 + 1396037*e^3)*x^2 - 1464975*d^2*e + 3*(749125*d^3 + 1444025*d^2*e - 3046875*d*e^2 - 170563*e^3)*x - 5773275*d*e^2 + 1275957*e^3)/(5*x^2 + 2*x + 3)^2","A",0
319,1,144,0,0.164987," ","integrate((e*x+d)^2*(4*x^4-5*x^3+3*x^2+x+2)/(5*x^2+2*x+3)^3,x, algorithm=""giac"")","\frac{1}{13720000} \, \sqrt{14} {\left(211875 \, d^{2} - 342070 \, d e + 14817 \, e^{2}\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) + \frac{4}{125} \, x e^{2} + \frac{1}{1250} \, {\left(40 \, d e - 49 \, e^{2}\right)} \log\left(5 \, x^{2} + 2 \, x + 3\right) + \frac{{\left(55075 \, d^{2} + 363530 \, d e - 129439 \, e^{2}\right)} x^{3} + {\left(193765 \, d^{2} + 56614 \, d e - 213609 \, e^{2}\right)} x^{2} + 64765 \, d^{2} + {\left(89895 \, d^{2} + 115522 \, d e - 121875 \, e^{2}\right)} x - 39066 \, d e - 76977 \, e^{2}}{196000 \, {\left(5 \, x^{2} + 2 \, x + 3\right)}^{2}}"," ",0,"1/13720000*sqrt(14)*(211875*d^2 - 342070*d*e + 14817*e^2)*arctan(1/14*sqrt(14)*(5*x + 1)) + 4/125*x*e^2 + 1/1250*(40*d*e - 49*e^2)*log(5*x^2 + 2*x + 3) + 1/196000*((55075*d^2 + 363530*d*e - 129439*e^2)*x^3 + (193765*d^2 + 56614*d*e - 213609*e^2)*x^2 + 64765*d^2 + (89895*d^2 + 115522*d*e - 121875*e^2)*x - 39066*d*e - 76977*e^2)/(5*x^2 + 2*x + 3)^2","A",0
320,1,97,0,0.185340," ","integrate((e*x+d)*(4*x^4-5*x^3+3*x^2+x+2)/(5*x^2+2*x+3)^3,x, algorithm=""giac"")","\frac{1}{2744000} \, \sqrt{14} {\left(42375 \, d - 34207 \, e\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) + \frac{2}{125} \, e \log\left(5 \, x^{2} + 2 \, x + 3\right) + \frac{5 \, {\left(11015 \, d + 36353 \, e\right)} x^{3} + {\left(193765 \, d + 28307 \, e\right)} x^{2} + {\left(89895 \, d + 57761 \, e\right)} x + 64765 \, d - 19533 \, e}{196000 \, {\left(5 \, x^{2} + 2 \, x + 3\right)}^{2}}"," ",0,"1/2744000*sqrt(14)*(42375*d - 34207*e)*arctan(1/14*sqrt(14)*(5*x + 1)) + 2/125*e*log(5*x^2 + 2*x + 3) + 1/196000*(5*(11015*d + 36353*e)*x^3 + (193765*d + 28307*e)*x^2 + (89895*d + 57761*e)*x + 64765*d - 19533*e)/(5*x^2 + 2*x + 3)^2","A",0
321,1,46,0,0.155450," ","integrate((4*x^4-5*x^3+3*x^2+x+2)/(5*x^2+2*x+3)^3,x, algorithm=""giac"")","\frac{339}{21952} \, \sqrt{14} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) + \frac{11015 \, x^{3} + 38753 \, x^{2} + 17979 \, x + 12953}{39200 \, {\left(5 \, x^{2} + 2 \, x + 3\right)}^{2}}"," ",0,"339/21952*sqrt(14)*arctan(1/14*sqrt(14)*(5*x + 1)) + 1/39200*(11015*x^3 + 38753*x^2 + 17979*x + 12953)/(5*x^2 + 2*x + 3)^2","A",0
322,1,460,0,0.246517," ","integrate((4*x^4-5*x^3+3*x^2+x+2)/(e*x+d)/(5*x^2+2*x+3)^3,x, algorithm=""giac"")","\frac{\sqrt{14} {\left(42375 \, d^{5} - 16643 \, d^{4} e + 58530 \, d^{3} e^{2} - 56058 \, d^{2} e^{3} + 31811 \, d e^{4} - 8623 \, e^{5}\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right)}{21952 \, {\left(125 \, d^{6} - 150 \, d^{5} e + 285 \, d^{4} e^{2} - 188 \, d^{3} e^{3} + 171 \, d^{2} e^{4} - 54 \, d e^{5} + 27 \, e^{6}\right)}} - \frac{{\left(4 \, d^{4} e + 5 \, d^{3} e^{2} + 3 \, d^{2} e^{3} - d e^{4} + 2 \, e^{5}\right)} \log\left(5 \, x^{2} + 2 \, x + 3\right)}{2 \, {\left(125 \, d^{6} - 150 \, d^{5} e + 285 \, d^{4} e^{2} - 188 \, d^{3} e^{3} + 171 \, d^{2} e^{4} - 54 \, d e^{5} + 27 \, e^{6}\right)}} + \frac{{\left(4 \, d^{4} e^{2} + 5 \, d^{3} e^{3} + 3 \, d^{2} e^{4} - d e^{5} + 2 \, e^{6}\right)} \log\left({\left| x e + d \right|}\right)}{125 \, d^{6} e - 150 \, d^{5} e^{2} + 285 \, d^{4} e^{3} - 188 \, d^{3} e^{4} + 171 \, d^{2} e^{5} - 54 \, d e^{6} + 27 \, e^{7}} + \frac{323825 \, d^{5} - 290925 \, d^{4} e + 25 \, {\left(11015 \, d^{5} - 49571 \, d^{4} e + 42850 \, d^{3} e^{2} - 43514 \, d^{2} e^{3} + 14563 \, d e^{4} - 5487 \, e^{5}\right)} x^{3} + 236238 \, d^{3} e^{2} + {\left(968825 \, d^{5} - 1304125 \, d^{4} e + 1310718 \, d^{3} e^{2} - 777366 \, d^{2} e^{3} + 250589 \, d e^{4} - 49377 \, e^{5}\right)} x^{2} - 57686 \, d^{2} e^{3} + {\left(449475 \, d^{5} - 828175 \, d^{4} e + 761994 \, d^{3} e^{2} - 500898 \, d^{2} e^{3} + 147247 \, d e^{4} - 11211 \, e^{5}\right)} x - 25611 \, d e^{4} + 18063 \, e^{5}}{7840 \, {\left(5 \, d^{2} - 2 \, d e + 3 \, e^{2}\right)}^{3} {\left(5 \, x^{2} + 2 \, x + 3\right)}^{2}}"," ",0,"1/21952*sqrt(14)*(42375*d^5 - 16643*d^4*e + 58530*d^3*e^2 - 56058*d^2*e^3 + 31811*d*e^4 - 8623*e^5)*arctan(1/14*sqrt(14)*(5*x + 1))/(125*d^6 - 150*d^5*e + 285*d^4*e^2 - 188*d^3*e^3 + 171*d^2*e^4 - 54*d*e^5 + 27*e^6) - 1/2*(4*d^4*e + 5*d^3*e^2 + 3*d^2*e^3 - d*e^4 + 2*e^5)*log(5*x^2 + 2*x + 3)/(125*d^6 - 150*d^5*e + 285*d^4*e^2 - 188*d^3*e^3 + 171*d^2*e^4 - 54*d*e^5 + 27*e^6) + (4*d^4*e^2 + 5*d^3*e^3 + 3*d^2*e^4 - d*e^5 + 2*e^6)*log(abs(x*e + d))/(125*d^6*e - 150*d^5*e^2 + 285*d^4*e^3 - 188*d^3*e^4 + 171*d^2*e^5 - 54*d*e^6 + 27*e^7) + 1/7840*(323825*d^5 - 290925*d^4*e + 25*(11015*d^5 - 49571*d^4*e + 42850*d^3*e^2 - 43514*d^2*e^3 + 14563*d*e^4 - 5487*e^5)*x^3 + 236238*d^3*e^2 + (968825*d^5 - 1304125*d^4*e + 1310718*d^3*e^2 - 777366*d^2*e^3 + 250589*d*e^4 - 49377*e^5)*x^2 - 57686*d^2*e^3 + (449475*d^5 - 828175*d^4*e + 761994*d^3*e^2 - 500898*d^2*e^3 + 147247*d*e^4 - 11211*e^5)*x - 25611*d*e^4 + 18063*e^5)/((5*d^2 - 2*d*e + 3*e^2)^3*(5*x^2 + 2*x + 3)^2)","A",0
323,1,762,0,0.255853," ","integrate((4*x^4-5*x^3+3*x^2+x+2)/(e*x+d)^2/(5*x^2+2*x+3)^3,x, algorithm=""giac"")","\frac{\sqrt{14} {\left(211875 \, d^{6} e^{2} + 3070 \, d^{5} e^{3} + 209039 \, d^{4} e^{4} - 921444 \, d^{3} e^{5} + 380621 \, d^{2} e^{6} - 49586 \, d e^{7} - 43695 \, e^{8}\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, d - \frac{5 \, d^{2}}{x e + d} + \frac{2 \, d e}{x e + d} - \frac{3 \, e^{2}}{x e + d} - e\right)} e^{\left(-1\right)}\right) e^{\left(-2\right)}}{21952 \, {\left(625 \, d^{8} - 1000 \, d^{7} e + 2100 \, d^{6} e^{2} - 1960 \, d^{5} e^{3} + 2086 \, d^{4} e^{4} - 1176 \, d^{3} e^{5} + 756 \, d^{2} e^{6} - 216 \, d e^{7} + 81 \, e^{8}\right)}} - \frac{{\left(40 \, d^{5} e + 83 \, d^{4} e^{2} + 12 \, d^{3} e^{3} - 76 \, d^{2} e^{4} + 46 \, d e^{5} - 9 \, e^{6}\right)} \log\left(-\frac{10 \, d}{x e + d} + \frac{5 \, d^{2}}{{\left(x e + d\right)}^{2}} + \frac{2 \, e}{x e + d} - \frac{2 \, d e}{{\left(x e + d\right)}^{2}} + \frac{3 \, e^{2}}{{\left(x e + d\right)}^{2}} + 5\right)}{2 \, {\left(625 \, d^{8} - 1000 \, d^{7} e + 2100 \, d^{6} e^{2} - 1960 \, d^{5} e^{3} + 2086 \, d^{4} e^{4} - 1176 \, d^{3} e^{5} + 756 \, d^{2} e^{6} - 216 \, d e^{7} + 81 \, e^{8}\right)}} - \frac{\frac{4 \, d^{4} e^{7}}{x e + d} + \frac{5 \, d^{3} e^{8}}{x e + d} + \frac{3 \, d^{2} e^{9}}{x e + d} - \frac{d e^{10}}{x e + d} + \frac{2 \, e^{11}}{x e + d}}{125 \, d^{6} e^{6} - 150 \, d^{5} e^{7} + 285 \, d^{4} e^{8} - 188 \, d^{3} e^{9} + 171 \, d^{2} e^{10} - 54 \, d e^{11} + 27 \, e^{12}} + \frac{275375 \, d^{5} e - 3006775 \, d^{4} e^{2} + 1394650 \, d^{3} e^{3} + 1835350 \, d^{2} e^{4} - 734925 \, d e^{5} - \frac{5 \, {\left(165225 \, d^{6} e^{2} - 1997830 \, d^{5} e^{3} + 1218421 \, d^{4} e^{4} + 1520564 \, d^{3} e^{5} - 947049 \, d^{2} e^{6} + 93386 \, d e^{7} + 7963 \, e^{8}\right)} e^{\left(-1\right)}}{x e + d} + \frac{{\left(826125 \, d^{7} e^{3} - 10957975 \, d^{6} e^{4} + 8449735 \, d^{5} e^{5} + 8211175 \, d^{4} e^{6} - 7879025 \, d^{3} e^{7} + 2996315 \, d^{2} e^{8} - 443947 \, d e^{9} - 67267 \, e^{10}\right)} e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}} - \frac{{\left(275375 \, d^{8} e^{4} - 3975600 \, d^{7} e^{5} + 3752280 \, d^{6} e^{6} + 2119880 \, d^{5} e^{7} - 3655050 \, d^{4} e^{8} + 4008480 \, d^{3} e^{9} - 1453312 \, d^{2} e^{10} - 197784 \, d e^{11} + 66483 \, e^{12}\right)} e^{\left(-3\right)}}{{\left(x e + d\right)}^{3}} + 17525 \, e^{6}}{1568 \, {\left(5 \, d^{2} - 2 \, d e + 3 \, e^{2}\right)}^{4} {\left(\frac{10 \, d}{x e + d} - \frac{5 \, d^{2}}{{\left(x e + d\right)}^{2}} - \frac{2 \, e}{x e + d} + \frac{2 \, d e}{{\left(x e + d\right)}^{2}} - \frac{3 \, e^{2}}{{\left(x e + d\right)}^{2}} - 5\right)}^{2}}"," ",0,"1/21952*sqrt(14)*(211875*d^6*e^2 + 3070*d^5*e^3 + 209039*d^4*e^4 - 921444*d^3*e^5 + 380621*d^2*e^6 - 49586*d*e^7 - 43695*e^8)*arctan(1/14*sqrt(14)*(5*d - 5*d^2/(x*e + d) + 2*d*e/(x*e + d) - 3*e^2/(x*e + d) - e)*e^(-1))*e^(-2)/(625*d^8 - 1000*d^7*e + 2100*d^6*e^2 - 1960*d^5*e^3 + 2086*d^4*e^4 - 1176*d^3*e^5 + 756*d^2*e^6 - 216*d*e^7 + 81*e^8) - 1/2*(40*d^5*e + 83*d^4*e^2 + 12*d^3*e^3 - 76*d^2*e^4 + 46*d*e^5 - 9*e^6)*log(-10*d/(x*e + d) + 5*d^2/(x*e + d)^2 + 2*e/(x*e + d) - 2*d*e/(x*e + d)^2 + 3*e^2/(x*e + d)^2 + 5)/(625*d^8 - 1000*d^7*e + 2100*d^6*e^2 - 1960*d^5*e^3 + 2086*d^4*e^4 - 1176*d^3*e^5 + 756*d^2*e^6 - 216*d*e^7 + 81*e^8) - (4*d^4*e^7/(x*e + d) + 5*d^3*e^8/(x*e + d) + 3*d^2*e^9/(x*e + d) - d*e^10/(x*e + d) + 2*e^11/(x*e + d))/(125*d^6*e^6 - 150*d^5*e^7 + 285*d^4*e^8 - 188*d^3*e^9 + 171*d^2*e^10 - 54*d*e^11 + 27*e^12) + 1/1568*(275375*d^5*e - 3006775*d^4*e^2 + 1394650*d^3*e^3 + 1835350*d^2*e^4 - 734925*d*e^5 - 5*(165225*d^6*e^2 - 1997830*d^5*e^3 + 1218421*d^4*e^4 + 1520564*d^3*e^5 - 947049*d^2*e^6 + 93386*d*e^7 + 7963*e^8)*e^(-1)/(x*e + d) + (826125*d^7*e^3 - 10957975*d^6*e^4 + 8449735*d^5*e^5 + 8211175*d^4*e^6 - 7879025*d^3*e^7 + 2996315*d^2*e^8 - 443947*d*e^9 - 67267*e^10)*e^(-2)/(x*e + d)^2 - (275375*d^8*e^4 - 3975600*d^7*e^5 + 3752280*d^6*e^6 + 2119880*d^5*e^7 - 3655050*d^4*e^8 + 4008480*d^3*e^9 - 1453312*d^2*e^10 - 197784*d*e^11 + 66483*e^12)*e^(-3)/(x*e + d)^3 + 17525*e^6)/((5*d^2 - 2*d*e + 3*e^2)^4*(10*d/(x*e + d) - 5*d^2/(x*e + d)^2 - 2*e/(x*e + d) + 2*d*e/(x*e + d)^2 - 3*e^2/(x*e + d)^2 - 5)^2)","A",0
324,1,78,0,0.203686," ","integrate((5+2*x)*(5*x^4-x^3+3*x^2+x+2)*(2*x^2-x+3)^(1/2),x, algorithm=""giac"")","\frac{1}{3440640} \, {\left(4 \, {\left(8 \, {\left(4 \, {\left(16 \, {\left(20 \, {\left(120 \, x + 317\right)} x + 679\right)} x + 158631\right)} x + 354907\right)} x + 3685583\right)} x + 6231117\right)} \sqrt{2 \, x^{2} - x + 3} - \frac{1183005}{131072} \, \sqrt{2} \log\left(-2 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} + 1\right)"," ",0,"1/3440640*(4*(8*(4*(16*(20*(120*x + 317)*x + 679)*x + 158631)*x + 354907)*x + 3685583)*x + 6231117)*sqrt(2*x^2 - x + 3) - 1183005/131072*sqrt(2)*log(-2*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) + 1)","A",0
325,1,73,0,0.199472," ","integrate((5*x^4-x^3+3*x^2+x+2)*(2*x^2-x+3)^(1/2),x, algorithm=""giac"")","\frac{1}{245760} \, {\left(4 \, {\left(8 \, {\left(4 \, {\left(16 \, {\left(100 \, x - 29\right)} x + 2019\right)} x + 3303\right)} x + 55467\right)} x - 27807\right)} \sqrt{2 \, x^{2} - x + 3} - \frac{106007}{65536} \, \sqrt{2} \log\left(-2 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} + 1\right)"," ",0,"1/245760*(4*(8*(4*(16*(100*x - 29)*x + 2019)*x + 3303)*x + 55467)*x - 27807)*sqrt(2*x^2 - x + 3) - 106007/65536*sqrt(2)*log(-2*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) + 1)","A",0
326,1,129,0,0.224243," ","integrate((5*x^4-x^3+3*x^2+x+2)*(2*x^2-x+3)^(1/2)/(5+2*x),x, algorithm=""giac"")","\frac{1}{12288} \, {\left(4 \, {\left(8 \, {\left(12 \, {\left(16 \, x - 55\right)} x + 2495\right)} x - 75101\right)} x + 1561161\right)} \sqrt{2 \, x^{2} - x + 3} + \frac{5627989}{16384} \, \sqrt{2} \log\left(-4 \, \sqrt{2} x + \sqrt{2} + 4 \, \sqrt{2 \, x^{2} - x + 3}\right) - \frac{11001}{32} \, \sqrt{2} \log\left({\left| -2 \, \sqrt{2} x + \sqrt{2} + 2 \, \sqrt{2 \, x^{2} - x + 3} \right|}\right) + \frac{11001}{32} \, \sqrt{2} \log\left({\left| -2 \, \sqrt{2} x - 11 \, \sqrt{2} + 2 \, \sqrt{2 \, x^{2} - x + 3} \right|}\right)"," ",0,"1/12288*(4*(8*(12*(16*x - 55)*x + 2495)*x - 75101)*x + 1561161)*sqrt(2*x^2 - x + 3) + 5627989/16384*sqrt(2)*log(-4*sqrt(2)*x + sqrt(2) + 4*sqrt(2*x^2 - x + 3)) - 11001/32*sqrt(2)*log(abs(-2*sqrt(2)*x + sqrt(2) + 2*sqrt(2*x^2 - x + 3))) + 11001/32*sqrt(2)*log(abs(-2*sqrt(2)*x - 11*sqrt(2) + 2*sqrt(2*x^2 - x + 3)))","A",0
327,1,531,0,0.531460," ","integrate((5*x^4-x^3+3*x^2+x+2)*(2*x^2-x+3)^(1/2)/(5+2*x)^2,x, algorithm=""giac"")","\frac{1}{24576} \, \sqrt{2} {\left(7654432 \, \log\left(12 \, \sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{72}{2 \, x + 5} - 11\right) \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right) + 7655541 \, \log\left({\left| \sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{6}{2 \, x + 5} + 1 \right|}\right) \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right) - 7655541 \, \log\left({\left| \sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{6}{2 \, x + 5} - 1 \right|}\right) \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right) - 1408128 \, \sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right) + \frac{2 \, {\left(16367883 \, {\left(\sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{6}{2 \, x + 5}\right)}^{7} \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right) - 34896384 \, {\left(\sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{6}{2 \, x + 5}\right)}^{6} \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right) - 93395 \, {\left(\sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{6}{2 \, x + 5}\right)}^{5} \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right) + 25574400 \, {\left(\sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{6}{2 \, x + 5}\right)}^{4} \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right) + 19752365 \, {\left(\sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{6}{2 \, x + 5}\right)}^{3} \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right) - 31921920 \, {\left(\sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{6}{2 \, x + 5}\right)}^{2} \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right) - 2445813 \, {\left(\sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{6}{2 \, x + 5}\right)} \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right) + 7663104 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right)\right)}}{{\left({\left(\sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{6}{2 \, x + 5}\right)}^{2} - 1\right)}^{4}}\right)}"," ",0,"1/24576*sqrt(2)*(7654432*log(12*sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 72/(2*x + 5) - 11)*sgn(1/(2*x + 5)) + 7655541*log(abs(sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 6/(2*x + 5) + 1))*sgn(1/(2*x + 5)) - 7655541*log(abs(sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 6/(2*x + 5) - 1))*sgn(1/(2*x + 5)) - 1408128*sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1)*sgn(1/(2*x + 5)) + 2*(16367883*(sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 6/(2*x + 5))^7*sgn(1/(2*x + 5)) - 34896384*(sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 6/(2*x + 5))^6*sgn(1/(2*x + 5)) - 93395*(sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 6/(2*x + 5))^5*sgn(1/(2*x + 5)) + 25574400*(sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 6/(2*x + 5))^4*sgn(1/(2*x + 5)) + 19752365*(sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 6/(2*x + 5))^3*sgn(1/(2*x + 5)) - 31921920*(sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 6/(2*x + 5))^2*sgn(1/(2*x + 5)) - 2445813*(sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 6/(2*x + 5))*sgn(1/(2*x + 5)) + 7663104*sgn(1/(2*x + 5)))/((sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 6/(2*x + 5))^2 - 1)^4)","B",0
328,1,258,0,0.244097," ","integrate((5*x^4-x^3+3*x^2+x+2)*(2*x^2-x+3)^(1/2)/(5+2*x)^3,x, algorithm=""giac"")","\frac{1}{768} \, {\left(4 \, {\left(40 \, x - 467\right)} x + 19695\right)} \sqrt{2 \, x^{2} - x + 3} + \frac{117315}{1024} \, \sqrt{2} \log\left(-2 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} + 1\right) - \frac{12670805}{110592} \, \sqrt{2} \log\left({\left| -2 \, \sqrt{2} x + \sqrt{2} + 2 \, \sqrt{2 \, x^{2} - x + 3} \right|}\right) + \frac{12670805}{110592} \, \sqrt{2} \log\left({\left| -2 \, \sqrt{2} x - 11 \, \sqrt{2} + 2 \, \sqrt{2 \, x^{2} - x + 3} \right|}\right) + \frac{\sqrt{2} {\left(10693526 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{3} + 79895946 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{2} - 124044603 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} + 80334011\right)}}{9216 \, {\left(2 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{2} + 10 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} - 11\right)}^{2}}"," ",0,"1/768*(4*(40*x - 467)*x + 19695)*sqrt(2*x^2 - x + 3) + 117315/1024*sqrt(2)*log(-2*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) + 1) - 12670805/110592*sqrt(2)*log(abs(-2*sqrt(2)*x + sqrt(2) + 2*sqrt(2*x^2 - x + 3))) + 12670805/110592*sqrt(2)*log(abs(-2*sqrt(2)*x - 11*sqrt(2) + 2*sqrt(2*x^2 - x + 3))) + 1/9216*sqrt(2)*(10693526*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^3 + 79895946*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^2 - 124044603*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) + 80334011)/(2*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^2 + 10*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) - 11)^2","B",0
329,1,304,0,0.257550," ","integrate((5*x^4-x^3+3*x^2+x+2)*(2*x^2-x+3)^(1/2)/(5+2*x)^4,x, algorithm=""giac"")","\frac{1}{128} \, \sqrt{2 \, x^{2} - x + 3} {\left(20 \, x - 413\right)} - \frac{10939}{512} \, \sqrt{2} \log\left(-2 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} + 1\right) + \frac{170114729}{7962624} \, \sqrt{2} \log\left({\left| -2 \, \sqrt{2} x + \sqrt{2} + 2 \, \sqrt{2 \, x^{2} - x + 3} \right|}\right) - \frac{170114729}{7962624} \, \sqrt{2} \log\left({\left| -2 \, \sqrt{2} x - 11 \, \sqrt{2} + 2 \, \sqrt{2 \, x^{2} - x + 3} \right|}\right) - \frac{\sqrt{2} {\left(575810908 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{5} + 9206213116 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{4} + 9688786604 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{3} - 73157325092 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{2} + 49481952947 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} - 20269228621\right)}}{663552 \, {\left(2 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{2} + 10 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} - 11\right)}^{3}}"," ",0,"1/128*sqrt(2*x^2 - x + 3)*(20*x - 413) - 10939/512*sqrt(2)*log(-2*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) + 1) + 170114729/7962624*sqrt(2)*log(abs(-2*sqrt(2)*x + sqrt(2) + 2*sqrt(2*x^2 - x + 3))) - 170114729/7962624*sqrt(2)*log(abs(-2*sqrt(2)*x - 11*sqrt(2) + 2*sqrt(2*x^2 - x + 3))) - 1/663552*sqrt(2)*(575810908*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^5 + 9206213116*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^4 + 9688786604*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^3 - 73157325092*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^2 + 49481952947*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) - 20269228621)/(2*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^2 + 10*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) - 11)^3","B",0
330,1,327,0,0.372817," ","integrate((5*x^4-x^3+3*x^2+x+2)*(2*x^2-x+3)^(1/2)/(5+2*x)^5,x, algorithm=""giac"")","-\frac{1}{2293235712} \, \sqrt{2} {\left(4640586097 \, \log\left(12 \, \sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{72}{2 \, x + 5} - 11\right) \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right) + 4640219136 \, \log\left({\left| \sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{6}{2 \, x + 5} + 1 \right|}\right) \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right) - 4640219136 \, \log\left({\left| \sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{6}{2 \, x + 5} - 1 \right|}\right) \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right) + 12 \, {\left(\frac{24 \, {\left(\frac{144 \, {\left(\frac{792072 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right)}{2 \, x + 5} - 835793 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right)\right)}}{2 \, x + 5} + 57384361 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right)\right)}}{2 \, x + 5} - 464569597 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right)\right)} \sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{179159040 \, {\left(11 \, {\left(\sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{6}{2 \, x + 5}\right)} \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right) - 12 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right)\right)}}{{\left(\sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{6}{2 \, x + 5}\right)}^{2} - 1}\right)}"," ",0,"-1/2293235712*sqrt(2)*(4640586097*log(12*sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 72/(2*x + 5) - 11)*sgn(1/(2*x + 5)) + 4640219136*log(abs(sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 6/(2*x + 5) + 1))*sgn(1/(2*x + 5)) - 4640219136*log(abs(sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 6/(2*x + 5) - 1))*sgn(1/(2*x + 5)) + 12*(24*(144*(792072*sgn(1/(2*x + 5))/(2*x + 5) - 835793*sgn(1/(2*x + 5)))/(2*x + 5) + 57384361*sgn(1/(2*x + 5)))/(2*x + 5) - 464569597*sgn(1/(2*x + 5)))*sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 179159040*(11*(sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 6/(2*x + 5))*sgn(1/(2*x + 5)) - 12*sgn(1/(2*x + 5)))/((sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 6/(2*x + 5))^2 - 1))","B",0
331,1,387,0,0.277730," ","integrate((5*x^4-x^3+3*x^2+x+2)*(2*x^2-x+3)^(1/2)/(5+2*x)^6,x, algorithm=""giac"")","-\frac{5}{64} \, \sqrt{2} \log\left(-2 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} + 1\right) + \frac{12895597463}{165112971264} \, \sqrt{2} \log\left({\left| -2 \, \sqrt{2} x + \sqrt{2} + 2 \, \sqrt{2 \, x^{2} - x + 3} \right|}\right) - \frac{12895597463}{165112971264} \, \sqrt{2} \log\left({\left| -2 \, \sqrt{2} x - 11 \, \sqrt{2} + 2 \, \sqrt{2 \, x^{2} - x + 3} \right|}\right) - \frac{\sqrt{2} {\left(4368922304720 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{9} + 124570969998480 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{8} + 637804348664160 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{7} + 1828845222532320 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{6} - 3763189300187016 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{5} - 10794416351958120 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{4} + 25049834283305880 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{3} - 34708488692384520 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{2} + 10654664764755165 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} - 2507056315485767\right)}}{68797071360 \, {\left(2 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{2} + 10 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} - 11\right)}^{5}}"," ",0,"-5/64*sqrt(2)*log(-2*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) + 1) + 12895597463/165112971264*sqrt(2)*log(abs(-2*sqrt(2)*x + sqrt(2) + 2*sqrt(2*x^2 - x + 3))) - 12895597463/165112971264*sqrt(2)*log(abs(-2*sqrt(2)*x - 11*sqrt(2) + 2*sqrt(2*x^2 - x + 3))) - 1/68797071360*sqrt(2)*(4368922304720*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^9 + 124570969998480*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^8 + 637804348664160*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^7 + 1828845222532320*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^6 - 3763189300187016*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^5 - 10794416351958120*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^4 + 25049834283305880*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^3 - 34708488692384520*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^2 + 10654664764755165*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) - 2507056315485767)/(2*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^2 + 10*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) - 11)^5","B",0
332,1,405,0,0.264221," ","integrate((5*x^4-x^3+3*x^2+x+2)*(2*x^2-x+3)^(1/2)/(5+2*x)^7,x, algorithm=""giac"")","-\frac{26972675}{7925422620672} \, \sqrt{2} \log\left({\left| -2 \, \sqrt{2} x + \sqrt{2} + 2 \, \sqrt{2 \, x^{2} - x + 3} \right|}\right) + \frac{26972675}{7925422620672} \, \sqrt{2} \log\left({\left| -2 \, \sqrt{2} x - 11 \, \sqrt{2} + 2 \, \sqrt{2 \, x^{2} - x + 3} \right|}\right) + \frac{\sqrt{2} {\left(16506981498400 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{11} + 389429252643040 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{10} + 2263923918689840 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{9} + 11663651054548560 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{8} + 902212326134736 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{7} - 84192729519861840 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{6} - 4317200555009448 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{5} + 351543414066518760 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{4} - 376787166452923830 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{3} + 356306707647610982 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{2} - 82348353128195465 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} + 15499394004553969\right)}}{3302259425280 \, {\left(2 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{2} + 10 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} - 11\right)}^{6}}"," ",0,"-26972675/7925422620672*sqrt(2)*log(abs(-2*sqrt(2)*x + sqrt(2) + 2*sqrt(2*x^2 - x + 3))) + 26972675/7925422620672*sqrt(2)*log(abs(-2*sqrt(2)*x - 11*sqrt(2) + 2*sqrt(2*x^2 - x + 3))) + 1/3302259425280*sqrt(2)*(16506981498400*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^11 + 389429252643040*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^10 + 2263923918689840*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^9 + 11663651054548560*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^8 + 902212326134736*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^7 - 84192729519861840*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^6 - 4317200555009448*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^5 + 351543414066518760*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^4 - 376787166452923830*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^3 + 356306707647610982*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^2 - 82348353128195465*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) + 15499394004553969)/(2*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^2 + 10*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) - 11)^6","B",0
333,1,456,0,0.293293," ","integrate((5*x^4-x^3+3*x^2+x+2)*(2*x^2-x+3)^(1/2)/(5+2*x)^8,x, algorithm=""giac"")","-\frac{289071245}{570630428688384} \, \sqrt{2} \log\left({\left| -2 \, \sqrt{2} x + \sqrt{2} + 2 \, \sqrt{2 \, x^{2} - x + 3} \right|}\right) + \frac{289071245}{570630428688384} \, \sqrt{2} \log\left({\left| -2 \, \sqrt{2} x - 11 \, \sqrt{2} + 2 \, \sqrt{2 \, x^{2} - x + 3} \right|}\right) - \frac{\sqrt{2} {\left(129503917760 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{13} - 3320259746027840 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{12} - 23966708071916736 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{11} - 186055342532355520 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{10} - 274256644494948976 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{9} + 796135370176031760 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{8} + 2531523139171005408 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{7} - 4610393811900786336 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{6} - 7997126854300052364 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{5} + 30842713619423538868 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{4} - 21873571601855032556 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{3} + 16204706960604668100 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{2} - 3196254593191113265 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} + 536799032216117911\right)}}{332867750068224 \, {\left(2 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{2} + 10 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} - 11\right)}^{7}}"," ",0,"-289071245/570630428688384*sqrt(2)*log(abs(-2*sqrt(2)*x + sqrt(2) + 2*sqrt(2*x^2 - x + 3))) + 289071245/570630428688384*sqrt(2)*log(abs(-2*sqrt(2)*x - 11*sqrt(2) + 2*sqrt(2*x^2 - x + 3))) - 1/332867750068224*sqrt(2)*(129503917760*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^13 - 3320259746027840*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^12 - 23966708071916736*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^11 - 186055342532355520*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^10 - 274256644494948976*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^9 + 796135370176031760*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^8 + 2531523139171005408*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^7 - 4610393811900786336*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^6 - 7997126854300052364*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^5 + 30842713619423538868*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^4 - 21873571601855032556*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^3 + 16204706960604668100*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^2 - 3196254593191113265*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) + 536799032216117911)/(2*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^2 + 10*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) - 11)^7","B",0
334,1,88,0,0.190643," ","integrate((5+2*x)*(2*x^2-x+3)^(3/2)*(5*x^4-x^3+3*x^2+x+2),x, algorithm=""giac"")","\frac{1}{660602880} \, {\left(4 \, {\left(8 \, {\left(4 \, {\left(16 \, {\left(20 \, {\left(8 \, {\left(28 \, {\left(160 \, x + 319\right)} x + 3153\right)} x + 295847\right)} x + 185101\right)} x + 98978829\right)} x + 152207433\right)} x + 3089440197\right)} x + 1592737263\right)} \sqrt{2 \, x^{2} - x + 3} - \frac{147157749}{8388608} \, \sqrt{2} \log\left(-2 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} + 1\right)"," ",0,"1/660602880*(4*(8*(4*(16*(20*(8*(28*(160*x + 319)*x + 3153)*x + 295847)*x + 185101)*x + 98978829)*x + 152207433)*x + 3089440197)*x + 1592737263)*sqrt(2*x^2 - x + 3) - 147157749/8388608*sqrt(2)*log(-2*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) + 1)","A",0
335,1,83,0,0.333827," ","integrate((2*x^2-x+3)^(3/2)*(5*x^4-x^3+3*x^2+x+2),x, algorithm=""giac"")","\frac{1}{7340032} \, {\left(4 \, {\left(8 \, {\left(4 \, {\left(16 \, {\left(4 \, {\left(8 \, {\left(140 \, x - 117\right)} x + 3581\right)} x - 3661\right)} x + 211123\right)} x + 120183\right)} x + 6961403\right)} x - 1663407\right)} \sqrt{2 \, x^{2} - x + 3} - \frac{13643439}{4194304} \, \sqrt{2} \log\left(-2 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} + 1\right)"," ",0,"1/7340032*(4*(8*(4*(16*(4*(8*(140*x - 117)*x + 3581)*x - 3661)*x + 211123)*x + 120183)*x + 6961403)*x - 1663407)*sqrt(2*x^2 - x + 3) - 13643439/4194304*sqrt(2)*log(-2*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) + 1)","A",0
336,1,139,0,0.231019," ","integrate((2*x^2-x+3)^(3/2)*(5*x^4-x^3+3*x^2+x+2)/(5+2*x),x, algorithm=""giac"")","\frac{1}{1376256} \, {\left(4 \, {\left(8 \, {\left(12 \, {\left(16 \, {\left(4 \, {\left(40 \, x - 151\right)} x + 2359\right)} x - 121033\right)} x + 4999169\right)} x - 152374883\right)} x + 3149403255\right)} \sqrt{2 \, x^{2} - x + 3} + \frac{1622009981}{262144} \, \sqrt{2} \log\left(-4 \, \sqrt{2} x + \sqrt{2} + 4 \, \sqrt{2 \, x^{2} - x + 3}\right) - \frac{99009}{16} \, \sqrt{2} \log\left({\left| -2 \, \sqrt{2} x + \sqrt{2} + 2 \, \sqrt{2 \, x^{2} - x + 3} \right|}\right) + \frac{99009}{16} \, \sqrt{2} \log\left({\left| -2 \, \sqrt{2} x - 11 \, \sqrt{2} + 2 \, \sqrt{2 \, x^{2} - x + 3} \right|}\right)"," ",0,"1/1376256*(4*(8*(12*(16*(4*(40*x - 151)*x + 2359)*x - 121033)*x + 4999169)*x - 152374883)*x + 3149403255)*sqrt(2*x^2 - x + 3) + 1622009981/262144*sqrt(2)*log(-4*sqrt(2)*x + sqrt(2) + 4*sqrt(2*x^2 - x + 3)) - 99009/16*sqrt(2)*log(abs(-2*sqrt(2)*x + sqrt(2) + 2*sqrt(2*x^2 - x + 3))) + 99009/16*sqrt(2)*log(abs(-2*sqrt(2)*x - 11*sqrt(2) + 2*sqrt(2*x^2 - x + 3)))","A",0
337,1,707,0,0.451029," ","integrate((2*x^2-x+3)^(3/2)*(5*x^4-x^3+3*x^2+x+2)/(5+2*x)^2,x, algorithm=""giac"")","\frac{1}{1966080} \, \sqrt{2} {\left(14739840000 \, \log\left(12 \, \sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{72}{2 \, x + 5} - 11\right) \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right) + 14740041885 \, \log\left({\left| \sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{6}{2 \, x + 5} + 1 \right|}\right) \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right) - 14740041885 \, \log\left({\left| \sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{6}{2 \, x + 5} - 1 \right|}\right) \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right) - 2027704320 \, \sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right) + \frac{2 \, {\left(45496763235 \, {\left(\sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{6}{2 \, x + 5}\right)}^{11} \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right) - 126553743360 \, {\left(\sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{6}{2 \, x + 5}\right)}^{10} \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right) + 44062768335 \, {\left(\sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{6}{2 \, x + 5}\right)}^{9} \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right) + 33178982400 \, {\left(\sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{6}{2 \, x + 5}\right)}^{8} \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right) + 294206421582 \, {\left(\sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{6}{2 \, x + 5}\right)}^{7} \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right) - 463672074240 \, {\left(\sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{6}{2 \, x + 5}\right)}^{6} \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right) + 35099942478 \, {\left(\sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{6}{2 \, x + 5}\right)}^{5} \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right) + 171324610560 \, {\left(\sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{6}{2 \, x + 5}\right)}^{4} \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right) + 60059281615 \, {\left(\sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{6}{2 \, x + 5}\right)}^{3} \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right) - 105051009024 \, {\left(\sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{6}{2 \, x + 5}\right)}^{2} \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right) - 5210329245 \, {\left(\sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{6}{2 \, x + 5}\right)} \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right) + 17058392064 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right)\right)}}{{\left({\left(\sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{6}{2 \, x + 5}\right)}^{2} - 1\right)}^{6}}\right)}"," ",0,"1/1966080*sqrt(2)*(14739840000*log(12*sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 72/(2*x + 5) - 11)*sgn(1/(2*x + 5)) + 14740041885*log(abs(sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 6/(2*x + 5) + 1))*sgn(1/(2*x + 5)) - 14740041885*log(abs(sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 6/(2*x + 5) - 1))*sgn(1/(2*x + 5)) - 2027704320*sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1)*sgn(1/(2*x + 5)) + 2*(45496763235*(sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 6/(2*x + 5))^11*sgn(1/(2*x + 5)) - 126553743360*(sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 6/(2*x + 5))^10*sgn(1/(2*x + 5)) + 44062768335*(sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 6/(2*x + 5))^9*sgn(1/(2*x + 5)) + 33178982400*(sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 6/(2*x + 5))^8*sgn(1/(2*x + 5)) + 294206421582*(sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 6/(2*x + 5))^7*sgn(1/(2*x + 5)) - 463672074240*(sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 6/(2*x + 5))^6*sgn(1/(2*x + 5)) + 35099942478*(sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 6/(2*x + 5))^5*sgn(1/(2*x + 5)) + 171324610560*(sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 6/(2*x + 5))^4*sgn(1/(2*x + 5)) + 60059281615*(sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 6/(2*x + 5))^3*sgn(1/(2*x + 5)) - 105051009024*(sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 6/(2*x + 5))^2*sgn(1/(2*x + 5)) - 5210329245*(sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 6/(2*x + 5))*sgn(1/(2*x + 5)) + 17058392064*sgn(1/(2*x + 5)))/((sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 6/(2*x + 5))^2 - 1)^6)","B",0
338,1,268,0,0.302815," ","integrate((2*x^2-x+3)^(3/2)*(5*x^4-x^3+3*x^2+x+2)/(5+2*x)^3,x, algorithm=""giac"")","\frac{1}{8192} \, {\left(4 \, {\left(8 \, {\left(4 \, {\left(16 \, x - 165\right)} x + 4879\right)} x - 263469\right)} x + 8460377\right)} \sqrt{2 \, x^{2} - x + 3} + \frac{129342063}{32768} \, \sqrt{2} \log\left(-2 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} + 1\right) - \frac{8083915}{2048} \, \sqrt{2} \log\left({\left| -2 \, \sqrt{2} x + \sqrt{2} + 2 \, \sqrt{2 \, x^{2} - x + 3} \right|}\right) + \frac{8083915}{2048} \, \sqrt{2} \log\left({\left| -2 \, \sqrt{2} x - 11 \, \sqrt{2} + 2 \, \sqrt{2 \, x^{2} - x + 3} \right|}\right) + \frac{\sqrt{2} {\left(14243182 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{3} + 109906674 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{2} - 170996871 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} + 110506087\right)}}{512 \, {\left(2 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{2} + 10 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} - 11\right)}^{2}}"," ",0,"1/8192*(4*(8*(4*(16*x - 165)*x + 4879)*x - 263469)*x + 8460377)*sqrt(2*x^2 - x + 3) + 129342063/32768*sqrt(2)*log(-2*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) + 1) - 8083915/2048*sqrt(2)*log(abs(-2*sqrt(2)*x + sqrt(2) + 2*sqrt(2*x^2 - x + 3))) + 8083915/2048*sqrt(2)*log(abs(-2*sqrt(2)*x - 11*sqrt(2) + 2*sqrt(2*x^2 - x + 3))) + 1/512*sqrt(2)*(14243182*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^3 + 109906674*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^2 - 170996871*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) + 110506087)/(2*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^2 + 10*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) - 11)^2","A",0
339,1,314,0,0.268650," ","integrate((2*x^2-x+3)^(3/2)*(5*x^4-x^3+3*x^2+x+2)/(5+2*x)^4,x, algorithm=""giac"")","\frac{1}{4096} \, {\left(4 \, {\left(8 \, {\left(20 \, x - 287\right)} x + 23341\right)} x - 1004633\right)} \sqrt{2 \, x^{2} - x + 3} - \frac{19176431}{16384} \, \sqrt{2} \log\left(-2 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} + 1\right) + \frac{517762327}{442368} \, \sqrt{2} \log\left({\left| -2 \, \sqrt{2} x + \sqrt{2} + 2 \, \sqrt{2 \, x^{2} - x + 3} \right|}\right) - \frac{517762327}{442368} \, \sqrt{2} \log\left({\left| -2 \, \sqrt{2} x - 11 \, \sqrt{2} + 2 \, \sqrt{2 \, x^{2} - x + 3} \right|}\right) - \frac{\sqrt{2} {\left(1092794276 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{5} + 18284336132 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{4} + 20314214356 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{3} - 151449344092 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{2} + 102529692109 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} - 41882448755\right)}}{36864 \, {\left(2 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{2} + 10 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} - 11\right)}^{3}}"," ",0,"1/4096*(4*(8*(20*x - 287)*x + 23341)*x - 1004633)*sqrt(2*x^2 - x + 3) - 19176431/16384*sqrt(2)*log(-2*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) + 1) + 517762327/442368*sqrt(2)*log(abs(-2*sqrt(2)*x + sqrt(2) + 2*sqrt(2*x^2 - x + 3))) - 517762327/442368*sqrt(2)*log(abs(-2*sqrt(2)*x - 11*sqrt(2) + 2*sqrt(2*x^2 - x + 3))) - 1/36864*sqrt(2)*(1092794276*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^5 + 18284336132*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^4 + 20314214356*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^3 - 151449344092*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^2 + 102529692109*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) - 41882448755)/(2*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^2 + 10*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) - 11)^3","B",0
340,1,503,0,0.420730," ","integrate((2*x^2-x+3)^(3/2)*(5*x^4-x^3+3*x^2+x+2)/(5+2*x)^5,x, algorithm=""giac"")","-\frac{1}{42467328} \, \sqrt{2} {\left(8969688643 \, \log\left(12 \, \sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{72}{2 \, x + 5} - 11\right) \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right) + 8969667840 \, \log\left({\left| \sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{6}{2 \, x + 5} + 1 \right|}\right) \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right) - 8969667840 \, \log\left({\left| \sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{6}{2 \, x + 5} - 1 \right|}\right) \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right) + 12 \, {\left(\frac{24 \, {\left(\frac{1296 \, {\left(\frac{29336 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right)}{2 \, x + 5} - 42907 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right)\right)}}{2 \, x + 5} + 39923563 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right)\right)}}{2 \, x + 5} - 541312039 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right)\right)} \sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{13824 \, {\left(806241 \, {\left(\sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{6}{2 \, x + 5}\right)}^{5} \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right) - 1152288 \, {\left(\sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{6}{2 \, x + 5}\right)}^{4} \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right) - 957352 \, {\left(\sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{6}{2 \, x + 5}\right)}^{3} \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right) + 1529280 \, {\left(\sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{6}{2 \, x + 5}\right)}^{2} \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right) + 394431 \, {\left(\sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{6}{2 \, x + 5}\right)} \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right) - 620352 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right)\right)}}{{\left({\left(\sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{6}{2 \, x + 5}\right)}^{2} - 1\right)}^{3}}\right)}"," ",0,"-1/42467328*sqrt(2)*(8969688643*log(12*sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 72/(2*x + 5) - 11)*sgn(1/(2*x + 5)) + 8969667840*log(abs(sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 6/(2*x + 5) + 1))*sgn(1/(2*x + 5)) - 8969667840*log(abs(sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 6/(2*x + 5) - 1))*sgn(1/(2*x + 5)) + 12*(24*(1296*(29336*sgn(1/(2*x + 5))/(2*x + 5) - 42907*sgn(1/(2*x + 5)))/(2*x + 5) + 39923563*sgn(1/(2*x + 5)))/(2*x + 5) - 541312039*sgn(1/(2*x + 5)))*sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 13824*(806241*(sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 6/(2*x + 5))^5*sgn(1/(2*x + 5)) - 1152288*(sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 6/(2*x + 5))^4*sgn(1/(2*x + 5)) - 957352*(sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 6/(2*x + 5))^3*sgn(1/(2*x + 5)) + 1529280*(sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 6/(2*x + 5))^2*sgn(1/(2*x + 5)) + 394431*(sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 6/(2*x + 5))*sgn(1/(2*x + 5)) - 620352*sgn(1/(2*x + 5)))/((sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 6/(2*x + 5))^2 - 1)^3)","B",0
341,1,406,0,0.324403," ","integrate((2*x^2-x+3)^(3/2)*(5*x^4-x^3+3*x^2+x+2)/(5+2*x)^6,x, algorithm=""giac"")","\frac{1}{256} \, \sqrt{2 \, x^{2} - x + 3} {\left(20 \, x - 633\right)} - \frac{23775}{1024} \, \sqrt{2} \log\left(-2 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} + 1\right) + \frac{70991525167}{3057647616} \, \sqrt{2} \log\left({\left| -2 \, \sqrt{2} x + \sqrt{2} + 2 \, \sqrt{2 \, x^{2} - x + 3} \right|}\right) - \frac{70991525167}{3057647616} \, \sqrt{2} \log\left({\left| -2 \, \sqrt{2} x - 11 \, \sqrt{2} + 2 \, \sqrt{2 \, x^{2} - x + 3} \right|}\right) - \frac{\sqrt{2} {\left(8281387393360 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{9} + 275661428628240 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{8} + 1560382703345760 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{7} + 4938646760855520 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{6} - 9673562837036232 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{5} - 30647310393849000 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{4} + 70060241036847960 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{3} - 97730658088823880 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{2} + 30180638363071845 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} - 7096913381268319\right)}}{1274019840 \, {\left(2 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{2} + 10 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} - 11\right)}^{5}}"," ",0,"1/256*sqrt(2*x^2 - x + 3)*(20*x - 633) - 23775/1024*sqrt(2)*log(-2*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) + 1) + 70991525167/3057647616*sqrt(2)*log(abs(-2*sqrt(2)*x + sqrt(2) + 2*sqrt(2*x^2 - x + 3))) - 70991525167/3057647616*sqrt(2)*log(abs(-2*sqrt(2)*x - 11*sqrt(2) + 2*sqrt(2*x^2 - x + 3))) - 1/1274019840*sqrt(2)*(8281387393360*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^9 + 275661428628240*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^8 + 1560382703345760*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^7 + 4938646760855520*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^6 - 9673562837036232*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^5 - 30647310393849000*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^4 + 70060241036847960*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^3 - 97730658088823880*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^2 + 30180638363071845*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) - 7096913381268319)/(2*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^2 + 10*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) - 11)^5","B",0
342,1,452,0,0.344623," ","integrate((2*x^2-x+3)^(3/2)*(5*x^4-x^3+3*x^2+x+2)/(5+2*x)^7,x, algorithm=""giac"")","\frac{369}{256} \, \sqrt{2} \log\left(-2 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} + 1\right) - \frac{1903976002333}{1320903770112} \, \sqrt{2} \log\left({\left| -2 \, \sqrt{2} x + \sqrt{2} + 2 \, \sqrt{2 \, x^{2} - x + 3} \right|}\right) + \frac{1903976002333}{1320903770112} \, \sqrt{2} \log\left({\left| -2 \, \sqrt{2} x - 11 \, \sqrt{2} + 2 \, \sqrt{2 \, x^{2} - x + 3} \right|}\right) + \frac{5}{64} \, \sqrt{2 \, x^{2} - x + 3} + \frac{\sqrt{2} {\left(159278433934432 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{11} + 6347903280912544 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{10} + 48544526840833424 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{9} + 305716670132783088 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{8} + 88313821135911024 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{7} - 2423668581998843376 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{6} - 397211131697032056 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{5} + 11708897232532299576 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{4} - 12803484860728491138 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{3} + 12593033197867577234 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{2} - 3042533760672408875 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} + 589526263249780195\right)}}{110075314176 \, {\left(2 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{2} + 10 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} - 11\right)}^{6}}"," ",0,"369/256*sqrt(2)*log(-2*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) + 1) - 1903976002333/1320903770112*sqrt(2)*log(abs(-2*sqrt(2)*x + sqrt(2) + 2*sqrt(2*x^2 - x + 3))) + 1903976002333/1320903770112*sqrt(2)*log(abs(-2*sqrt(2)*x - 11*sqrt(2) + 2*sqrt(2*x^2 - x + 3))) + 5/64*sqrt(2*x^2 - x + 3) + 1/110075314176*sqrt(2)*(159278433934432*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^11 + 6347903280912544*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^10 + 48544526840833424*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^9 + 305716670132783088*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^8 + 88313821135911024*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^7 - 2423668581998843376*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^6 - 397211131697032056*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^5 + 11708897232532299576*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^4 - 12803484860728491138*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^3 + 12593033197867577234*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^2 - 3042533760672408875*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) + 589526263249780195)/(2*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^2 + 10*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) - 11)^6","B",0
343,1,489,0,0.332401," ","integrate((2*x^2-x+3)^(3/2)*(5*x^4-x^3+3*x^2+x+2)/(5+2*x)^8,x, algorithm=""giac"")","-\frac{5}{128} \, \sqrt{2} \log\left(-2 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} + 1\right) + \frac{412760561351}{10567230160896} \, \sqrt{2} \log\left({\left| -2 \, \sqrt{2} x + \sqrt{2} + 2 \, \sqrt{2 \, x^{2} - x + 3} \right|}\right) - \frac{412760561351}{10567230160896} \, \sqrt{2} \log\left({\left| -2 \, \sqrt{2} x - 11 \, \sqrt{2} + 2 \, \sqrt{2 \, x^{2} - x + 3} \right|}\right) - \frac{\sqrt{2} {\left(1121897398412224 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{13} + 48260296303776704 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{12} + 444673458321712704 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{11} + 3996455936659982656 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{10} + 6725227967167489360 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{9} - 17132661028483948080 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{8} - 63713012094737246112 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{7} + 106515880136064432096 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{6} + 226947197958946260516 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{5} - 856601202771483308188 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{4} + 617998258357377713732 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{3} - 467121785339763351756 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{2} + 92292080735560562227 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} - 15161716093827501349\right)}}{6164217593856 \, {\left(2 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{2} + 10 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} - 11\right)}^{7}}"," ",0,"-5/128*sqrt(2)*log(-2*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) + 1) + 412760561351/10567230160896*sqrt(2)*log(abs(-2*sqrt(2)*x + sqrt(2) + 2*sqrt(2*x^2 - x + 3))) - 412760561351/10567230160896*sqrt(2)*log(abs(-2*sqrt(2)*x - 11*sqrt(2) + 2*sqrt(2*x^2 - x + 3))) - 1/6164217593856*sqrt(2)*(1121897398412224*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^13 + 48260296303776704*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^12 + 444673458321712704*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^11 + 3996455936659982656*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^10 + 6725227967167489360*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^9 - 17132661028483948080*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^8 - 63713012094737246112*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^7 + 106515880136064432096*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^6 + 226947197958946260516*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^5 - 856601202771483308188*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^4 + 617998258357377713732*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^3 - 467121785339763351756*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^2 + 92292080735560562227*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) - 15161716093827501349)/(2*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^2 + 10*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) - 11)^7","B",0
344,1,68,0,0.194066," ","integrate((5+2*x)*(5*x^4-x^3+3*x^2+x+2)/(2*x^2-x+3)^(1/2),x, algorithm=""giac"")","\frac{1}{2048} \, {\left(4 \, {\left(8 \, {\left(4 \, {\left(16 \, x + 55\right)} x + 11\right)} x - 1729\right)} x + 2973\right)} \sqrt{2 \, x^{2} - x + 3} - \frac{85429}{8192} \, \sqrt{2} \log\left(-2 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} + 1\right)"," ",0,"1/2048*(4*(8*(4*(16*x + 55)*x + 11)*x - 1729)*x + 2973)*sqrt(2*x^2 - x + 3) - 85429/8192*sqrt(2)*log(-2*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) + 1)","A",0
345,1,63,0,0.195750," ","integrate((5*x^4-x^3+3*x^2+x+2)/(2*x^2-x+3)^(1/2),x, algorithm=""giac"")","\frac{1}{3072} \, {\left(4 \, {\left(8 \, {\left(60 \, x + 19\right)} x - 409\right)} x - 1515\right)} \sqrt{2 \, x^{2} - x + 3} - \frac{6863}{4096} \, \sqrt{2} \log\left(-2 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} + 1\right)"," ",0,"1/3072*(4*(8*(60*x + 19)*x - 409)*x - 1515)*sqrt(2*x^2 - x + 3) - 6863/4096*sqrt(2)*log(-2*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) + 1)","A",0
346,1,119,0,0.232080," ","integrate((5*x^4-x^3+3*x^2+x+2)/(5+2*x)/(2*x^2-x+3)^(1/2),x, algorithm=""giac"")","\frac{1}{384} \, {\left(4 \, {\left(40 \, x - 137\right)} x + 2637\right)} \sqrt{2 \, x^{2} - x + 3} + \frac{9657}{512} \, \sqrt{2} \log\left(-4 \, \sqrt{2} x + \sqrt{2} + 4 \, \sqrt{2 \, x^{2} - x + 3}\right) - \frac{3667}{192} \, \sqrt{2} \log\left({\left| -2 \, \sqrt{2} x + \sqrt{2} + 2 \, \sqrt{2 \, x^{2} - x + 3} \right|}\right) + \frac{3667}{192} \, \sqrt{2} \log\left({\left| -2 \, \sqrt{2} x - 11 \, \sqrt{2} + 2 \, \sqrt{2 \, x^{2} - x + 3} \right|}\right)"," ",0,"1/384*(4*(40*x - 137)*x + 2637)*sqrt(2*x^2 - x + 3) + 9657/512*sqrt(2)*log(-4*sqrt(2)*x + sqrt(2) + 4*sqrt(2*x^2 - x + 3)) - 3667/192*sqrt(2)*log(abs(-2*sqrt(2)*x + sqrt(2) + 2*sqrt(2*x^2 - x + 3))) + 3667/192*sqrt(2)*log(abs(-2*sqrt(2)*x - 11*sqrt(2) + 2*sqrt(2*x^2 - x + 3)))","A",0
347,1,339,0,0.401684," ","integrate((5*x^4-x^3+3*x^2+x+2)/(5+2*x)^2/(2*x^2-x+3)^(1/2),x, algorithm=""giac"")","\frac{1}{13824} \, \sqrt{2} {\left(\frac{158527 \, \log\left(12 \, \sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{72}{2 \, x + 5} - 11\right)}{\mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right)} + \frac{158922 \, \log\left({\left| \sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{6}{2 \, x + 5} + 1 \right|}\right)}{\mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right)} - \frac{158922 \, \log\left({\left| \sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{6}{2 \, x + 5} - 1 \right|}\right)}{\mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right)} - \frac{44004 \, \sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1}}{\mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right)} + \frac{108 \, {\left(3393 \, {\left(\sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{6}{2 \, x + 5}\right)}^{3} - 4896 \, {\left(\sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{6}{2 \, x + 5}\right)}^{2} - 743 \, \sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} - \frac{4458}{2 \, x + 5} + 2256\right)}}{{\left({\left(\sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{6}{2 \, x + 5}\right)}^{2} - 1\right)}^{2} \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right)}\right)}"," ",0,"1/13824*sqrt(2)*(158527*log(12*sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 72/(2*x + 5) - 11)/sgn(1/(2*x + 5)) + 158922*log(abs(sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 6/(2*x + 5) + 1))/sgn(1/(2*x + 5)) - 158922*log(abs(sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 6/(2*x + 5) - 1))/sgn(1/(2*x + 5)) - 44004*sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1)/sgn(1/(2*x + 5)) + 108*(3393*(sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 6/(2*x + 5))^3 - 4896*(sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 6/(2*x + 5))^2 - 743*sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) - 4458/(2*x + 5) + 2256)/(((sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 6/(2*x + 5))^2 - 1)^2*sgn(1/(2*x + 5))))","B",0
348,1,248,0,0.255115," ","integrate((5*x^4-x^3+3*x^2+x+2)/(5+2*x)^3/(2*x^2-x+3)^(1/2),x, algorithm=""giac"")","\frac{149}{64} \, \sqrt{2} \log\left(-2 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} + 1\right) - \frac{1546507}{663552} \, \sqrt{2} \log\left({\left| -2 \, \sqrt{2} x + \sqrt{2} + 2 \, \sqrt{2 \, x^{2} - x + 3} \right|}\right) + \frac{1546507}{663552} \, \sqrt{2} \log\left({\left| -2 \, \sqrt{2} x - 11 \, \sqrt{2} + 2 \, \sqrt{2 \, x^{2} - x + 3} \right|}\right) + \frac{5}{16} \, \sqrt{2 \, x^{2} - x + 3} + \frac{\sqrt{2} {\left(2381290 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{3} + 16628406 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{2} - 25697445 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} + 16720645\right)}}{55296 \, {\left(2 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{2} + 10 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} - 11\right)}^{2}}"," ",0,"149/64*sqrt(2)*log(-2*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) + 1) - 1546507/663552*sqrt(2)*log(abs(-2*sqrt(2)*x + sqrt(2) + 2*sqrt(2*x^2 - x + 3))) + 1546507/663552*sqrt(2)*log(abs(-2*sqrt(2)*x - 11*sqrt(2) + 2*sqrt(2*x^2 - x + 3))) + 5/16*sqrt(2*x^2 - x + 3) + 1/55296*sqrt(2)*(2381290*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^3 + 16628406*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^2 - 25697445*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) + 16720645)/(2*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^2 + 10*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) - 11)^2","B",0
349,1,285,0,0.257262," ","integrate((5*x^4-x^3+3*x^2+x+2)/(5+2*x)^4/(2*x^2-x+3)^(1/2),x, algorithm=""giac"")","-\frac{5}{32} \, \sqrt{2} \log\left(-2 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} + 1\right) + \frac{22389491}{143327232} \, \sqrt{2} \log\left({\left| -2 \, \sqrt{2} x + \sqrt{2} + 2 \, \sqrt{2 \, x^{2} - x + 3} \right|}\right) - \frac{22389491}{143327232} \, \sqrt{2} \log\left({\left| -2 \, \sqrt{2} x - 11 \, \sqrt{2} + 2 \, \sqrt{2 \, x^{2} - x + 3} \right|}\right) - \frac{\sqrt{2} {\left(215012404 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{5} + 3010410772 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{4} + 2740802468 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{3} - 21459328844 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{2} + 14434519361 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} - 5957650879\right)}}{11943936 \, {\left(2 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{2} + 10 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} - 11\right)}^{3}}"," ",0,"-5/32*sqrt(2)*log(-2*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) + 1) + 22389491/143327232*sqrt(2)*log(abs(-2*sqrt(2)*x + sqrt(2) + 2*sqrt(2*x^2 - x + 3))) - 22389491/143327232*sqrt(2)*log(abs(-2*sqrt(2)*x - 11*sqrt(2) + 2*sqrt(2*x^2 - x + 3))) - 1/11943936*sqrt(2)*(215012404*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^5 + 3010410772*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^4 + 2740802468*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^3 - 21459328844*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^2 + 14434519361*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) - 5957650879)/(2*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^2 + 10*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) - 11)^3","B",0
350,1,164,0,0.283011," ","integrate((5*x^4-x^3+3*x^2+x+2)/(5+2*x)^5/(2*x^2-x+3)^(1/2),x, algorithm=""giac"")","\frac{1}{41278242816} \, \sqrt{2} {\left(12 \, {\left(\frac{24 \, {\left(\frac{144 \, {\left(\frac{513097}{\mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right)} - \frac{792072}{{\left(2 \, x + 5\right)} \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right)}\right)}}{2 \, x + 5} - \frac{16295969}{\mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right)}\right)}}{2 \, x + 5} + \frac{26800085}{\mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right)}\right)} \sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{2053207 \, \log\left(12 \, \sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{72}{2 \, x + 5} - 11\right)}{\mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right)} - 321601020 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right)\right)}"," ",0,"1/41278242816*sqrt(2)*(12*(24*(144*(513097/sgn(1/(2*x + 5)) - 792072/((2*x + 5)*sgn(1/(2*x + 5))))/(2*x + 5) - 16295969/sgn(1/(2*x + 5)))/(2*x + 5) + 26800085/sgn(1/(2*x + 5)))*sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 2053207*log(12*sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 72/(2*x + 5) - 11)/sgn(1/(2*x + 5)) - 321601020*sgn(1/(2*x + 5)))","A",0
351,1,72,0,0.224618," ","integrate((5+2*x)^2*(5*x^4-x^3+3*x^2+x+2)/(2*x^2-x+3)^(3/2),x, algorithm=""giac"")","\frac{144217}{2048} \, \sqrt{2} \log\left(-2 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} + 1\right) + \frac{{\left(46 \, {\left(4 \, {\left(8 \, {\left(20 \, x + 143\right)} x + 2273\right)} x - 11099\right)} x + 2124123\right)} x - 1616165}{11776 \, \sqrt{2 \, x^{2} - x + 3}}"," ",0,"144217/2048*sqrt(2)*log(-2*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) + 1) + 1/11776*((46*(4*(8*(20*x + 143)*x + 2273)*x - 11099)*x + 2124123)*x - 1616165)/sqrt(2*x^2 - x + 3)","A",0
352,1,67,0,0.215518," ","integrate((5+2*x)*(5*x^4-x^3+3*x^2+x+2)/(2*x^2-x+3)^(3/2),x, algorithm=""giac"")","\frac{3111}{256} \, \sqrt{2} \log\left(-2 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} + 1\right) + \frac{{\left(46 \, {\left(4 \, {\left(40 \, x + 173\right)} x - 47\right)} x + 122607\right)} x - 3345}{4416 \, \sqrt{2 \, x^{2} - x + 3}}"," ",0,"3111/256*sqrt(2)*log(-2*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) + 1) + 1/4416*((46*(4*(40*x + 173)*x - 47)*x + 122607)*x - 3345)/sqrt(2*x^2 - x + 3)","A",0
353,1,62,0,0.219059," ","integrate((5*x^4-x^3+3*x^2+x+2)/(2*x^2-x+3)^(3/2),x, algorithm=""giac"")","\frac{213}{128} \, \sqrt{2} \log\left(-2 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} + 1\right) + \frac{{\left(46 \, {\left(20 \, x + 17\right)} x + 2511\right)} x + 2575}{736 \, \sqrt{2 \, x^{2} - x + 3}}"," ",0,"213/128*sqrt(2)*log(-2*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) + 1) + 1/736*((46*(20*x + 17)*x + 2511)*x + 2575)/sqrt(2*x^2 - x + 3)","A",0
354,1,118,0,0.396048," ","integrate((5*x^4-x^3+3*x^2+x+2)/(5+2*x)/(2*x^2-x+3)^(3/2),x, algorithm=""giac"")","\frac{39}{32} \, \sqrt{2} \log\left(-4 \, \sqrt{2} x + \sqrt{2} + 4 \, \sqrt{2 \, x^{2} - x + 3}\right) - \frac{3667}{3456} \, \sqrt{2} \log\left({\left| -2 \, \sqrt{2} x + \sqrt{2} + 2 \, \sqrt{2 \, x^{2} - x + 3} \right|}\right) + \frac{3667}{3456} \, \sqrt{2} \log\left({\left| -2 \, \sqrt{2} x - 11 \, \sqrt{2} + 2 \, \sqrt{2 \, x^{2} - x + 3} \right|}\right) + \frac{{\left(4140 \, x - 1153\right)} x + 7401}{3312 \, \sqrt{2 \, x^{2} - x + 3}}"," ",0,"39/32*sqrt(2)*log(-4*sqrt(2)*x + sqrt(2) + 4*sqrt(2*x^2 - x + 3)) - 3667/3456*sqrt(2)*log(abs(-2*sqrt(2)*x + sqrt(2) + 2*sqrt(2*x^2 - x + 3))) + 3667/3456*sqrt(2)*log(abs(-2*sqrt(2)*x - 11*sqrt(2) + 2*sqrt(2*x^2 - x + 3))) + 1/3312*((4140*x - 1153)*x + 7401)/sqrt(2*x^2 - x + 3)","A",0
355,1,225,0,0.423442," ","integrate((5*x^4-x^3+3*x^2+x+2)/(5+2*x)^2/(2*x^2-x+3)^(3/2),x, algorithm=""giac"")","\frac{1}{1907712} \, \sqrt{2} {\left(\frac{12 \, {\left(\frac{\frac{315103}{\mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right)} - \frac{1012092}{{\left(2 \, x + 5\right)} \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right)}}{2 \, x + 5} - \frac{26645}{\mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right)}\right)}}{\sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1}} + \frac{596873 \, \log\left(12 \, \sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{72}{2 \, x + 5} - 11\right)}{\mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right)} + \frac{596160 \, \log\left({\left| \sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{6}{2 \, x + 5} + 1 \right|}\right)}{\mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right)} - \frac{596160 \, \log\left({\left| \sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{6}{2 \, x + 5} - 1 \right|}\right)}{\mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right)}\right)}"," ",0,"1/1907712*sqrt(2)*(12*((315103/sgn(1/(2*x + 5)) - 1012092/((2*x + 5)*sgn(1/(2*x + 5))))/(2*x + 5) - 26645/sgn(1/(2*x + 5)))/sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 596873*log(12*sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 72/(2*x + 5) - 11)/sgn(1/(2*x + 5)) + 596160*log(abs(sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 6/(2*x + 5) + 1))/sgn(1/(2*x + 5)) - 596160*log(abs(sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 6/(2*x + 5) - 1))/sgn(1/(2*x + 5)))","B",0
356,1,220,0,0.246903," ","integrate((5*x^4-x^3+3*x^2+x+2)/(5+2*x)^3/(2*x^2-x+3)^(3/2),x, algorithm=""giac"")","-\frac{52631}{11943936} \, \sqrt{2} \log\left({\left| -2 \, \sqrt{2} x + \sqrt{2} + 2 \, \sqrt{2 \, x^{2} - x + 3} \right|}\right) + \frac{52631}{11943936} \, \sqrt{2} \log\left({\left| -2 \, \sqrt{2} x - 11 \, \sqrt{2} + 2 \, \sqrt{2 \, x^{2} - x + 3} \right|}\right) - \frac{8779 \, x - 65991}{4292352 \, \sqrt{2 \, x^{2} - x + 3}} + \frac{\sqrt{2} {\left(3594214 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{3} + 19874490 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{2} - 30140067 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} + 19989859\right)}}{2985984 \, {\left(2 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{2} + 10 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} - 11\right)}^{2}}"," ",0,"-52631/11943936*sqrt(2)*log(abs(-2*sqrt(2)*x + sqrt(2) + 2*sqrt(2*x^2 - x + 3))) + 52631/11943936*sqrt(2)*log(abs(-2*sqrt(2)*x - 11*sqrt(2) + 2*sqrt(2*x^2 - x + 3))) - 1/4292352*(8779*x - 65991)/sqrt(2*x^2 - x + 3) + 1/2985984*sqrt(2)*(3594214*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^3 + 19874490*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^2 - 30140067*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) + 19989859)/(2*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^2 + 10*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) - 11)^2","B",0
357,1,271,0,0.291981," ","integrate((5*x^4-x^3+3*x^2+x+2)/(5+2*x)^4/(2*x^2-x+3)^(3/2),x, algorithm=""giac"")","-\frac{3505819}{2579890176} \, \sqrt{2} \log\left({\left| -2 \, \sqrt{2} x + \sqrt{2} + 2 \, \sqrt{2 \, x^{2} - x + 3} \right|}\right) + \frac{3505819}{2579890176} \, \sqrt{2} \log\left({\left| -2 \, \sqrt{2} x - 11 \, \sqrt{2} + 2 \, \sqrt{2 \, x^{2} - x + 3} \right|}\right) - \frac{175877 \, x - 369609}{154524672 \, \sqrt{2 \, x^{2} - x + 3}} - \frac{\sqrt{2} {\left(10398764 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{5} - 303070900 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{4} - 529738052 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{3} + 3644644652 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{2} - 2612608649 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} + 1052284471\right)}}{214990848 \, {\left(2 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{2} + 10 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} - 11\right)}^{3}}"," ",0,"-3505819/2579890176*sqrt(2)*log(abs(-2*sqrt(2)*x + sqrt(2) + 2*sqrt(2*x^2 - x + 3))) + 3505819/2579890176*sqrt(2)*log(abs(-2*sqrt(2)*x - 11*sqrt(2) + 2*sqrt(2*x^2 - x + 3))) - 1/154524672*(175877*x - 369609)/sqrt(2*x^2 - x + 3) - 1/214990848*sqrt(2)*(10398764*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^5 - 303070900*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^4 - 529738052*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^3 + 3644644652*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^2 - 2612608649*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) + 1052284471)/(2*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^2 + 10*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) - 11)^3","B",0
358,1,71,0,0.215822," ","integrate((5+2*x)^2*(5*x^4-x^3+3*x^2+x+2)/(2*x^2-x+3)^(5/2),x, algorithm=""giac"")","-\frac{1471}{64} \, \sqrt{2} \log\left(-2 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} + 1\right) + \frac{{\left({\left(4 \, {\left(1587 \, {\left(20 \, x + 227\right)} x - 941090\right)} x + 8639625\right)} x - 6410082\right)} x + 6663133}{25392 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}}"," ",0,"-1471/64*sqrt(2)*log(-2*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) + 1) + 1/25392*(((4*(1587*(20*x + 227)*x - 941090)*x + 8639625)*x - 6410082)*x + 6663133)/(2*x^2 - x + 3)^(3/2)","A",0
359,1,66,0,0.205881," ","integrate((5+2*x)*(5*x^4-x^3+3*x^2+x+2)/(2*x^2-x+3)^(5/2),x, algorithm=""giac"")","-\frac{71}{16} \, \sqrt{2} \log\left(-2 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} + 1\right) + \frac{{\left({\left(4 \, {\left(7935 \, x - 36916\right)} x + 185337\right)} x - 199290\right)} x + 102869}{6348 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}}"," ",0,"-71/16*sqrt(2)*log(-2*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) + 1) + 1/6348*(((4*(7935*x - 36916)*x + 185337)*x - 199290)*x + 102869)/(2*x^2 - x + 3)^(3/2)","A",0
360,1,62,0,0.303758," ","integrate((5*x^4-x^3+3*x^2+x+2)/(2*x^2-x+3)^(5/2),x, algorithm=""giac"")","-\frac{5}{8} \, \sqrt{2} \log\left(-2 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} + 1\right) - \frac{3 \, {\left({\left(2604 \, x + 163\right)} x + 2334\right)} x + 5569}{3174 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}}"," ",0,"-5/8*sqrt(2)*log(-2*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) + 1) - 1/3174*(3*((2604*x + 163)*x + 2334)*x + 5569)/(2*x^2 - x + 3)^(3/2)","A",0
361,1,92,0,0.229201," ","integrate((5*x^4-x^3+3*x^2+x+2)/(5+2*x)/(2*x^2-x+3)^(5/2),x, algorithm=""giac"")","-\frac{3667}{62208} \, \sqrt{2} \log\left({\left| -2 \, \sqrt{2} x + \sqrt{2} + 2 \, \sqrt{2 \, x^{2} - x + 3} \right|}\right) + \frac{3667}{62208} \, \sqrt{2} \log\left({\left| -2 \, \sqrt{2} x - 11 \, \sqrt{2} + 2 \, \sqrt{2 \, x^{2} - x + 3} \right|}\right) - \frac{{\left({\left(293458 \, x + 523945\right)} x - 21696\right)} x + 841653}{1371168 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}}"," ",0,"-3667/62208*sqrt(2)*log(abs(-2*sqrt(2)*x + sqrt(2) + 2*sqrt(2*x^2 - x + 3))) + 3667/62208*sqrt(2)*log(abs(-2*sqrt(2)*x - 11*sqrt(2) + 2*sqrt(2*x^2 - x + 3))) - 1/1371168*(((293458*x + 523945)*x - 21696)*x + 841653)/(2*x^2 - x + 3)^(3/2)","A",0
362,1,206,0,0.399042," ","integrate((5*x^4-x^3+3*x^2+x+2)/(5+2*x)^2/(2*x^2-x+3)^(5/2),x, algorithm=""giac"")","-\frac{1}{2369378304} \, \sqrt{2} {\left(\frac{1492309 \, \log\left(12 \, \sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1} + \frac{72}{2 \, x + 5} - 11\right)}{\mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right)} + \frac{12 \, {\left(\frac{\frac{\frac{48 \, {\left(\frac{23642785}{\mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right)} - \frac{52375761}{{\left(2 \, x + 5\right)} \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right)}\right)}}{2 \, x + 5} - \frac{240080735}{\mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right)}}{2 \, x + 5} + \frac{28660178}{\mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right)}}{2 \, x + 5} - \frac{1691759}{\mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right)}\right)}}{{\left(\frac{11}{2 \, x + 5} - \frac{36}{{\left(2 \, x + 5\right)}^{2}} - 1\right)} \sqrt{-\frac{11}{2 \, x + 5} + \frac{36}{{\left(2 \, x + 5\right)}^{2}} + 1}} - 20301108 \, \mathrm{sgn}\left(\frac{1}{2 \, x + 5}\right)\right)}"," ",0,"-1/2369378304*sqrt(2)*(1492309*log(12*sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1) + 72/(2*x + 5) - 11)/sgn(1/(2*x + 5)) + 12*(((48*(23642785/sgn(1/(2*x + 5)) - 52375761/((2*x + 5)*sgn(1/(2*x + 5))))/(2*x + 5) - 240080735/sgn(1/(2*x + 5)))/(2*x + 5) + 28660178/sgn(1/(2*x + 5)))/(2*x + 5) - 1691759/sgn(1/(2*x + 5)))/((11/(2*x + 5) - 36/(2*x + 5)^2 - 1)*sqrt(-11/(2*x + 5) + 36/(2*x + 5)^2 + 1)) - 20301108*sgn(1/(2*x + 5)))","B",0
363,1,228,0,0.265341," ","integrate((5*x^4-x^3+3*x^2+x+2)/(5+2*x)^3/(2*x^2-x+3)^(5/2),x, algorithm=""giac"")","\frac{774079}{644972544} \, \sqrt{2} \log\left({\left| -2 \, \sqrt{2} x + \sqrt{2} + 2 \, \sqrt{2 \, x^{2} - x + 3} \right|}\right) - \frac{774079}{644972544} \, \sqrt{2} \log\left({\left| -2 \, \sqrt{2} x - 11 \, \sqrt{2} + 2 \, \sqrt{2 \, x^{2} - x + 3} \right|}\right) + \frac{\sqrt{2} {\left(44558 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{3} - 10136238 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{2} + 16812201 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} - 10182217\right)}}{53747712 \, {\left(2 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{2} + 10 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} - 11\right)}^{2}} + \frac{{\left({\left(4296526 \, x - 11507857\right)} x + 10720752\right)} x - 11003805}{592344576 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}}"," ",0,"774079/644972544*sqrt(2)*log(abs(-2*sqrt(2)*x + sqrt(2) + 2*sqrt(2*x^2 - x + 3))) - 774079/644972544*sqrt(2)*log(abs(-2*sqrt(2)*x - 11*sqrt(2) + 2*sqrt(2*x^2 - x + 3))) + 1/53747712*sqrt(2)*(44558*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^3 - 10136238*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^2 + 16812201*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) - 10182217)/(2*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^2 + 10*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) - 11)^2 + 1/592344576*(((4296526*x - 11507857)*x + 10720752)*x - 11003805)/(2*x^2 - x + 3)^(3/2)","B",0
364,1,279,0,0.279751," ","integrate((5*x^4-x^3+3*x^2+x+2)/(5+2*x)^4/(2*x^2-x+3)^(5/2),x, algorithm=""giac"")","\frac{4778789}{15479341056} \, \sqrt{2} \log\left({\left| -2 \, \sqrt{2} x + \sqrt{2} + 2 \, \sqrt{2 \, x^{2} - x + 3} \right|}\right) - \frac{4778789}{15479341056} \, \sqrt{2} \log\left({\left| -2 \, \sqrt{2} x - 11 \, \sqrt{2} + 2 \, \sqrt{2 \, x^{2} - x + 3} \right|}\right) + \frac{{\left({\left(15595499 \, x - 21675019\right)} x + 27298005\right)} x - 14440149}{7996651776 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}} + \frac{\sqrt{2} {\left(38030012 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{5} + 734231900 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{4} + 122834956 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{3} - 2154595396 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{2} + 1659431083 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} - 760577429\right)}}{3869835264 \, {\left(2 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)}^{2} + 10 \, \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} - x + 3}\right)} - 11\right)}^{3}}"," ",0,"4778789/15479341056*sqrt(2)*log(abs(-2*sqrt(2)*x + sqrt(2) + 2*sqrt(2*x^2 - x + 3))) - 4778789/15479341056*sqrt(2)*log(abs(-2*sqrt(2)*x - 11*sqrt(2) + 2*sqrt(2*x^2 - x + 3))) + 1/7996651776*(((15595499*x - 21675019)*x + 27298005)*x - 14440149)/(2*x^2 - x + 3)^(3/2) + 1/3869835264*sqrt(2)*(38030012*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^5 + 734231900*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^4 + 122834956*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^3 - 2154595396*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^2 + 1659431083*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) - 760577429)/(2*(sqrt(2)*x - sqrt(2*x^2 - x + 3))^2 + 10*sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 - x + 3)) - 11)^3","B",0
365,1,465,0,0.306427," ","integrate((j*x^4+i*x^3+h*x^2+g*x+f)/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\frac{2 \, {\left({\left({\left(\frac{{\left(16 \, c^{5} f - 8 \, b c^{4} g + 2 \, b^{2} c^{3} h + 8 \, a c^{4} h + b^{3} c^{2} i - 12 \, a b c^{3} i - 4 \, b^{4} c j + 28 \, a b^{2} c^{2} j - 32 \, a^{2} c^{3} j\right)} x}{b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}} + \frac{3 \, {\left(8 \, b c^{4} f - 4 \, b^{2} c^{3} g + b^{3} c^{2} h + 4 \, a b c^{3} h - 2 \, a b^{2} c^{2} i - 8 \, a^{2} c^{3} i - b^{5} j + 6 \, a b^{3} c j\right)}}{b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}}\right)} x + \frac{3 \, {\left(2 \, b^{2} c^{3} f + 8 \, a c^{4} f - b^{3} c^{2} g - 4 \, a b c^{3} g + 4 \, a b^{2} c^{2} h - 8 \, a^{2} b c^{2} i - 2 \, a b^{4} j + 14 \, a^{2} b^{2} c j - 8 \, a^{3} c^{2} j\right)}}{b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}}\right)} x - \frac{b^{3} c^{2} f - 12 \, a b c^{3} f + 2 \, a b^{2} c^{2} g + 8 \, a^{2} c^{3} g - 8 \, a^{2} b c^{2} h + 16 \, a^{3} c^{2} i + 3 \, a^{2} b^{3} j - 20 \, a^{3} b c j}{b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}}\right)}}{3 \, {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}} - \frac{j \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{c^{\frac{5}{2}}}"," ",0,"2/3*((((16*c^5*f - 8*b*c^4*g + 2*b^2*c^3*h + 8*a*c^4*h + b^3*c^2*i - 12*a*b*c^3*i - 4*b^4*c*j + 28*a*b^2*c^2*j - 32*a^2*c^3*j)*x/(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4) + 3*(8*b*c^4*f - 4*b^2*c^3*g + b^3*c^2*h + 4*a*b*c^3*h - 2*a*b^2*c^2*i - 8*a^2*c^3*i - b^5*j + 6*a*b^3*c*j)/(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4))*x + 3*(2*b^2*c^3*f + 8*a*c^4*f - b^3*c^2*g - 4*a*b*c^3*g + 4*a*b^2*c^2*h - 8*a^2*b*c^2*i - 2*a*b^4*j + 14*a^2*b^2*c*j - 8*a^3*c^2*j)/(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4))*x - (b^3*c^2*f - 12*a*b*c^3*f + 2*a*b^2*c^2*g + 8*a^2*c^3*g - 8*a^2*b*c^2*h + 16*a^3*c^2*i + 3*a^2*b^3*j - 20*a^3*b*c*j)/(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4))/(c*x^2 + b*x + a)^(3/2) - j*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(5/2)","A",0
366,1,488,0,0.448484," ","integrate((j*x^4+i*x^3+h*x^2+g*x+f)/(-c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","-\frac{2 \, \sqrt{-c x^{2} + b x + a} {\left({\left({\left(\frac{{\left(16 \, c^{5} f + 8 \, b c^{4} g + 2 \, b^{2} c^{3} h - 8 \, a c^{4} h - b^{3} c^{2} i - 12 \, a b c^{3} i - 4 \, b^{4} c j - 28 \, a b^{2} c^{2} j - 32 \, a^{2} c^{3} j\right)} x}{b^{4} c^{2} + 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}} - \frac{3 \, {\left(8 \, b c^{4} f + 4 \, b^{2} c^{3} g + b^{3} c^{2} h - 4 \, a b c^{3} h - 2 \, a b^{2} c^{2} i + 8 \, a^{2} c^{3} i - b^{5} j - 6 \, a b^{3} c j\right)}}{b^{4} c^{2} + 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}}\right)} x + \frac{3 \, {\left(2 \, b^{2} c^{3} f - 8 \, a c^{4} f + b^{3} c^{2} g - 4 \, a b c^{3} g - 4 \, a b^{2} c^{2} h + 8 \, a^{2} b c^{2} i + 2 \, a b^{4} j + 14 \, a^{2} b^{2} c j + 8 \, a^{3} c^{2} j\right)}}{b^{4} c^{2} + 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}}\right)} x + \frac{b^{3} c^{2} f + 12 \, a b c^{3} f + 2 \, a b^{2} c^{2} g - 8 \, a^{2} c^{3} g - 8 \, a^{2} b c^{2} h + 16 \, a^{3} c^{2} i + 3 \, a^{2} b^{3} j + 20 \, a^{3} b c j}{b^{4} c^{2} + 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}}\right)}}{3 \, {\left(c x^{2} - b x - a\right)}^{2}} - \frac{j \log\left({\left| 2 \, {\left(\sqrt{-c} x - \sqrt{-c x^{2} + b x + a}\right)} \sqrt{-c} + b \right|}\right)}{\sqrt{-c} c^{2}}"," ",0,"-2/3*sqrt(-c*x^2 + b*x + a)*((((16*c^5*f + 8*b*c^4*g + 2*b^2*c^3*h - 8*a*c^4*h - b^3*c^2*i - 12*a*b*c^3*i - 4*b^4*c*j - 28*a*b^2*c^2*j - 32*a^2*c^3*j)*x/(b^4*c^2 + 8*a*b^2*c^3 + 16*a^2*c^4) - 3*(8*b*c^4*f + 4*b^2*c^3*g + b^3*c^2*h - 4*a*b*c^3*h - 2*a*b^2*c^2*i + 8*a^2*c^3*i - b^5*j - 6*a*b^3*c*j)/(b^4*c^2 + 8*a*b^2*c^3 + 16*a^2*c^4))*x + 3*(2*b^2*c^3*f - 8*a*c^4*f + b^3*c^2*g - 4*a*b*c^3*g - 4*a*b^2*c^2*h + 8*a^2*b*c^2*i + 2*a*b^4*j + 14*a^2*b^2*c*j + 8*a^3*c^2*j)/(b^4*c^2 + 8*a*b^2*c^3 + 16*a^2*c^4))*x + (b^3*c^2*f + 12*a*b*c^3*f + 2*a*b^2*c^2*g - 8*a^2*c^3*g - 8*a^2*b*c^2*h + 16*a^3*c^2*i + 3*a^2*b^3*j + 20*a^3*b*c*j)/(b^4*c^2 + 8*a*b^2*c^3 + 16*a^2*c^4))/(c*x^2 - b*x - a)^2 - j*log(abs(2*(sqrt(-c)*x - sqrt(-c*x^2 + b*x + a))*sqrt(-c) + b))/(sqrt(-c)*c^2)","A",0
367,1,10960,0,0.621409," ","integrate((e*x+d)^m*(5*x^2+2*x+3)^3*(4*x^4-5*x^3+3*x^2+x+2),x, algorithm=""giac"")","\frac{500 \, {\left(x e + d\right)}^{m} m^{10} x^{11} e^{11} + 500 \, {\left(x e + d\right)}^{m} d m^{10} x^{10} e^{10} - 25 \, {\left(x e + d\right)}^{m} m^{10} x^{10} e^{11} + 27500 \, {\left(x e + d\right)}^{m} m^{9} x^{11} e^{11} - 25 \, {\left(x e + d\right)}^{m} d m^{10} x^{9} e^{10} + 22500 \, {\left(x e + d\right)}^{m} d m^{9} x^{10} e^{10} - 5000 \, {\left(x e + d\right)}^{m} d^{2} m^{9} x^{9} e^{9} + 765 \, {\left(x e + d\right)}^{m} m^{10} x^{9} e^{11} - 1400 \, {\left(x e + d\right)}^{m} m^{9} x^{10} e^{11} + 660000 \, {\left(x e + d\right)}^{m} m^{8} x^{11} e^{11} + 765 \, {\left(x e + d\right)}^{m} d m^{10} x^{8} e^{10} - 1175 \, {\left(x e + d\right)}^{m} d m^{9} x^{9} e^{10} + 435000 \, {\left(x e + d\right)}^{m} d m^{8} x^{10} e^{10} + 225 \, {\left(x e + d\right)}^{m} d^{2} m^{9} x^{8} e^{9} - 180000 \, {\left(x e + d\right)}^{m} d^{2} m^{8} x^{9} e^{9} + 45000 \, {\left(x e + d\right)}^{m} d^{3} m^{8} x^{8} e^{8} - 98 \, {\left(x e + d\right)}^{m} m^{10} x^{8} e^{11} + 43605 \, {\left(x e + d\right)}^{m} m^{9} x^{9} e^{11} - 34125 \, {\left(x e + d\right)}^{m} m^{8} x^{10} e^{11} + 9075000 \, {\left(x e + d\right)}^{m} m^{7} x^{11} e^{11} - 98 \, {\left(x e + d\right)}^{m} d m^{10} x^{7} e^{10} + 37485 \, {\left(x e + d\right)}^{m} d m^{9} x^{8} e^{10} - 23550 \, {\left(x e + d\right)}^{m} d m^{8} x^{9} e^{10} + 4725000 \, {\left(x e + d\right)}^{m} d m^{7} x^{10} e^{10} - 6120 \, {\left(x e + d\right)}^{m} d^{2} m^{9} x^{7} e^{9} + 8775 \, {\left(x e + d\right)}^{m} d^{2} m^{8} x^{8} e^{9} - 2730000 \, {\left(x e + d\right)}^{m} d^{2} m^{7} x^{9} e^{9} - 1800 \, {\left(x e + d\right)}^{m} d^{3} m^{8} x^{7} e^{8} + 1260000 \, {\left(x e + d\right)}^{m} d^{3} m^{7} x^{8} e^{8} - 360000 \, {\left(x e + d\right)}^{m} d^{4} m^{7} x^{7} e^{7} + 999 \, {\left(x e + d\right)}^{m} m^{10} x^{7} e^{11} - 5684 \, {\left(x e + d\right)}^{m} m^{9} x^{8} e^{11} + 1080180 \, {\left(x e + d\right)}^{m} m^{8} x^{9} e^{11} - 475500 \, {\left(x e + d\right)}^{m} m^{7} x^{10} e^{11} + 78886500 \, {\left(x e + d\right)}^{m} m^{6} x^{11} e^{11} + 999 \, {\left(x e + d\right)}^{m} d m^{10} x^{6} e^{10} - 4998 \, {\left(x e + d\right)}^{m} d m^{9} x^{7} e^{10} + 780300 \, {\left(x e + d\right)}^{m} d m^{8} x^{8} e^{10} - 263550 \, {\left(x e + d\right)}^{m} d m^{7} x^{9} e^{10} + 31636500 \, {\left(x e + d\right)}^{m} d m^{6} x^{10} e^{10} + 686 \, {\left(x e + d\right)}^{m} d^{2} m^{9} x^{6} e^{9} - 257040 \, {\left(x e + d\right)}^{m} d^{2} m^{8} x^{7} e^{9} + 141750 \, {\left(x e + d\right)}^{m} d^{2} m^{7} x^{8} e^{9} - 22680000 \, {\left(x e + d\right)}^{m} d^{2} m^{6} x^{9} e^{9} + 42840 \, {\left(x e + d\right)}^{m} d^{3} m^{8} x^{6} e^{8} - 57600 \, {\left(x e + d\right)}^{m} d^{3} m^{7} x^{7} e^{8} + 14490000 \, {\left(x e + d\right)}^{m} d^{3} m^{6} x^{8} e^{8} + 12600 \, {\left(x e + d\right)}^{m} d^{4} m^{7} x^{6} e^{7} - 7560000 \, {\left(x e + d\right)}^{m} d^{4} m^{6} x^{7} e^{7} + 2520000 \, {\left(x e + d\right)}^{m} d^{5} m^{6} x^{6} e^{6} + 510 \, {\left(x e + d\right)}^{m} m^{10} x^{6} e^{11} + 58941 \, {\left(x e + d\right)}^{m} m^{9} x^{7} e^{11} - 143178 \, {\left(x e + d\right)}^{m} m^{8} x^{8} e^{11} + 15270930 \, {\left(x e + d\right)}^{m} m^{7} x^{9} e^{11} - 4180575 \, {\left(x e + d\right)}^{m} m^{6} x^{10} e^{11} + 451027500 \, {\left(x e + d\right)}^{m} m^{5} x^{11} e^{11} + 510 \, {\left(x e + d\right)}^{m} d m^{10} x^{5} e^{10} + 52947 \, {\left(x e + d\right)}^{m} d m^{9} x^{6} e^{10} - 108192 \, {\left(x e + d\right)}^{m} d m^{8} x^{7} e^{10} + 9028530 \, {\left(x e + d\right)}^{m} d m^{7} x^{8} e^{10} - 1808625 \, {\left(x e + d\right)}^{m} d m^{6} x^{9} e^{10} + 134662500 \, {\left(x e + d\right)}^{m} d m^{5} x^{10} e^{10} - 5994 \, {\left(x e + d\right)}^{m} d^{2} m^{9} x^{5} e^{9} + 30870 \, {\left(x e + d\right)}^{m} d^{2} m^{8} x^{6} e^{9} - 4443120 \, {\left(x e + d\right)}^{m} d^{2} m^{7} x^{7} e^{9} + 1237950 \, {\left(x e + d\right)}^{m} d^{2} m^{6} x^{8} e^{9} - 112245000 \, {\left(x e + d\right)}^{m} d^{2} m^{5} x^{9} e^{9} - 4116 \, {\left(x e + d\right)}^{m} d^{3} m^{8} x^{5} e^{8} + 1542240 \, {\left(x e + d\right)}^{m} d^{3} m^{7} x^{6} e^{8} - 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36710415 \, {\left(x e + d\right)}^{m} d^{2} m^{5} e^{9} - 1102270680 \, {\left(x e + d\right)}^{m} d^{2} m^{4} x e^{9} - 3745839048 \, {\left(x e + d\right)}^{m} d^{2} m^{3} x^{2} e^{9} - 6600448608 \, {\left(x e + d\right)}^{m} d^{2} m^{2} x^{3} e^{9} - 848232000 \, {\left(x e + d\right)}^{m} d^{2} m x^{4} e^{9} + 194510106 \, {\left(x e + d\right)}^{m} d^{3} m^{4} e^{8} + 2127097056 \, {\left(x e + d\right)}^{m} d^{3} m^{3} x e^{8} + 7687286352 \, {\left(x e + d\right)}^{m} d^{3} m^{2} x^{2} e^{8} + 1130976000 \, {\left(x e + d\right)}^{m} d^{3} m x^{3} e^{8} - 463042356 \, {\left(x e + d\right)}^{m} d^{4} m^{3} e^{7} - 6521026464 \, {\left(x e + d\right)}^{m} d^{4} m^{2} x e^{7} - 1696464000 \, {\left(x e + d\right)}^{m} d^{4} m x^{2} e^{7} + 1983530784 \, {\left(x e + d\right)}^{m} d^{5} m^{2} e^{6} + 3392928000 \, {\left(x e + d\right)}^{m} d^{5} m x e^{6} - 1933552800 \, {\left(x e + d\right)}^{m} d^{6} m e^{5} + 5696697600 \, {\left(x e + d\right)}^{m} d^{7} e^{4} + 124791030 \, {\left(x e + d\right)}^{m} m^{5} x e^{11} + 1250302905 \, {\left(x e + d\right)}^{m} m^{4} x^{2} e^{11} + 10631923596 \, {\left(x e + d\right)}^{m} m^{3} x^{3} e^{11} + 17690223096 \, {\left(x e + d\right)}^{m} m^{2} x^{4} e^{11} + 24965914464 \, {\left(x e + d\right)}^{m} m x^{5} e^{11} + 3392928000 \, {\left(x e + d\right)}^{m} x^{6} e^{11} + 124791030 \, {\left(x e + d\right)}^{m} d m^{5} e^{10} + 1011746160 \, {\left(x e + d\right)}^{m} d m^{4} x e^{10} + 5686792092 \, {\left(x e + d\right)}^{m} d m^{3} x^{2} e^{10} + 4652224080 \, {\left(x e + d\right)}^{m} d m^{2} x^{3} e^{10} + 2213386560 \, {\left(x e + d\right)}^{m} d m x^{4} e^{10} - 238556745 \, {\left(x e + d\right)}^{m} d^{2} m^{4} e^{9} - 3842860824 \, {\left(x e + d\right)}^{m} d^{2} m^{3} x e^{9} - 5546320920 \, {\left(x e + d\right)}^{m} d^{2} m^{2} x^{2} e^{9} - 2951182080 \, {\left(x e + d\right)}^{m} d^{2} m x^{3} e^{9} + 1102270680 \, {\left(x e + d\right)}^{m} d^{3} m^{3} e^{8} + 5364581040 \, {\left(x e + d\right)}^{m} d^{3} m^{2} x e^{8} + 4426773120 \, {\left(x e + d\right)}^{m} d^{3} m x^{2} e^{8} - 2127097056 \, {\left(x e + d\right)}^{m} d^{4} m^{2} e^{7} - 8853546240 \, {\left(x e + d\right)}^{m} d^{4} m x e^{7} + 6521026464 \, {\left(x e + d\right)}^{m} d^{5} m e^{6} - 3392928000 \, {\left(x e + d\right)}^{m} d^{6} e^{5} + 595543860 \, {\left(x e + d\right)}^{m} m^{4} x e^{11} + 3708817740 \, {\left(x e + d\right)}^{m} m^{3} x^{2} e^{11} + 18312331464 \, {\left(x e + d\right)}^{m} m^{2} x^{3} e^{11} + 15866025840 \, {\left(x e + d\right)}^{m} m x^{4} e^{11} + 8853546240 \, {\left(x e + d\right)}^{m} x^{5} e^{11} + 595543860 \, {\left(x e + d\right)}^{m} d m^{4} e^{10} + 2697071580 \, {\left(x e + d\right)}^{m} d m^{3} x e^{10} + 6938747280 \, {\left(x e + d\right)}^{m} d m^{2} x^{2} e^{10} + 1909353600 \, {\left(x e + d\right)}^{m} d m x^{3} e^{10} - 1011746160 \, {\left(x e + d\right)}^{m} d^{2} m^{3} e^{9} - 7530723360 \, {\left(x e + d\right)}^{m} d^{2} m^{2} x e^{9} - 2864030400 \, {\left(x e + d\right)}^{m} d^{2} m x^{2} e^{9} + 3842860824 \, {\left(x e + d\right)}^{m} d^{3} m^{2} e^{8} + 5728060800 \, {\left(x e + d\right)}^{m} d^{3} m x e^{8} - 5364581040 \, {\left(x e + d\right)}^{m} d^{4} m e^{7} + 8853546240 \, {\left(x e + d\right)}^{m} d^{5} e^{6} + 1888225560 \, {\left(x e + d\right)}^{m} m^{3} x e^{11} + 6792204780 \, {\left(x e + d\right)}^{m} m^{2} x^{2} e^{11} + 17050880160 \, {\left(x e + d\right)}^{m} m x^{3} e^{11} + 5728060800 \, {\left(x e + d\right)}^{m} x^{4} e^{11} + 1888225560 \, {\left(x e + d\right)}^{m} d m^{3} e^{10} + 4095133200 \, {\left(x e + d\right)}^{m} d m^{2} x e^{10} + 3173385600 \, {\left(x e + d\right)}^{m} d m x^{2} e^{10} - 2697071580 \, {\left(x e + d\right)}^{m} d^{2} m^{2} e^{9} - 6346771200 \, {\left(x e + d\right)}^{m} d^{2} m x e^{9} + 7530723360 \, {\left(x e + d\right)}^{m} d^{3} m e^{8} - 5728060800 \, {\left(x e + d\right)}^{m} d^{4} e^{7} + 3795710544 \, {\left(x e + d\right)}^{m} m^{2} x e^{11} + 6789517200 \, {\left(x e + d\right)}^{m} m x^{2} e^{11} + 6346771200 \, {\left(x e + d\right)}^{m} x^{3} e^{11} + 3795710544 \, {\left(x e + d\right)}^{m} d m^{2} e^{10} + 2694384000 \, {\left(x e + d\right)}^{m} d m x e^{10} - 4095133200 \, {\left(x e + d\right)}^{m} d^{2} m e^{9} + 6346771200 \, {\left(x e + d\right)}^{m} d^{3} e^{8} + 4353860160 \, {\left(x e + d\right)}^{m} m x e^{11} + 2694384000 \, {\left(x e + d\right)}^{m} x^{2} e^{11} + 4353860160 \, {\left(x e + d\right)}^{m} d m e^{10} - 2694384000 \, {\left(x e + d\right)}^{m} d^{2} e^{9} + 2155507200 \, {\left(x e + d\right)}^{m} x e^{11} + 2155507200 \, {\left(x e + d\right)}^{m} d e^{10}}{m^{11} e^{11} + 66 \, m^{10} e^{11} + 1925 \, m^{9} e^{11} + 32670 \, m^{8} e^{11} + 357423 \, m^{7} e^{11} + 2637558 \, m^{6} e^{11} + 13339535 \, m^{5} e^{11} + 45995730 \, m^{4} e^{11} + 105258076 \, m^{3} e^{11} + 150917976 \, m^{2} e^{11} + 120543840 \, m e^{11} + 39916800 \, e^{11}}"," ",0,"(500*(x*e + d)^m*m^10*x^11*e^11 + 500*(x*e + d)^m*d*m^10*x^10*e^10 - 25*(x*e + d)^m*m^10*x^10*e^11 + 27500*(x*e + d)^m*m^9*x^11*e^11 - 25*(x*e + d)^m*d*m^10*x^9*e^10 + 22500*(x*e + d)^m*d*m^9*x^10*e^10 - 5000*(x*e + d)^m*d^2*m^9*x^9*e^9 + 765*(x*e + d)^m*m^10*x^9*e^11 - 1400*(x*e + d)^m*m^9*x^10*e^11 + 660000*(x*e + d)^m*m^8*x^11*e^11 + 765*(x*e + d)^m*d*m^10*x^8*e^10 - 1175*(x*e + d)^m*d*m^9*x^9*e^10 + 435000*(x*e + d)^m*d*m^8*x^10*e^10 + 225*(x*e + d)^m*d^2*m^9*x^8*e^9 - 180000*(x*e + d)^m*d^2*m^8*x^9*e^9 + 45000*(x*e + d)^m*d^3*m^8*x^8*e^8 - 98*(x*e + d)^m*m^10*x^8*e^11 + 43605*(x*e + d)^m*m^9*x^9*e^11 - 34125*(x*e + d)^m*m^8*x^10*e^11 + 9075000*(x*e + d)^m*m^7*x^11*e^11 - 98*(x*e + d)^m*d*m^10*x^7*e^10 + 37485*(x*e + d)^m*d*m^9*x^8*e^10 - 23550*(x*e + d)^m*d*m^8*x^9*e^10 + 4725000*(x*e + d)^m*d*m^7*x^10*e^10 - 6120*(x*e + d)^m*d^2*m^9*x^7*e^9 + 8775*(x*e + d)^m*d^2*m^8*x^8*e^9 - 2730000*(x*e + d)^m*d^2*m^7*x^9*e^9 - 1800*(x*e + d)^m*d^3*m^8*x^7*e^8 + 1260000*(x*e + d)^m*d^3*m^7*x^8*e^8 - 360000*(x*e + d)^m*d^4*m^7*x^7*e^7 + 999*(x*e + d)^m*m^10*x^7*e^11 - 5684*(x*e + d)^m*m^9*x^8*e^11 + 1080180*(x*e + d)^m*m^8*x^9*e^11 - 475500*(x*e + d)^m*m^7*x^10*e^11 + 78886500*(x*e + d)^m*m^6*x^11*e^11 + 999*(x*e + d)^m*d*m^10*x^6*e^10 - 4998*(x*e + d)^m*d*m^9*x^7*e^10 + 780300*(x*e + d)^m*d*m^8*x^8*e^10 - 263550*(x*e + d)^m*d*m^7*x^9*e^10 + 31636500*(x*e + d)^m*d*m^6*x^10*e^10 + 686*(x*e + d)^m*d^2*m^9*x^6*e^9 - 257040*(x*e + d)^m*d^2*m^8*x^7*e^9 + 141750*(x*e + d)^m*d^2*m^7*x^8*e^9 - 22680000*(x*e + d)^m*d^2*m^6*x^9*e^9 + 42840*(x*e + d)^m*d^3*m^8*x^6*e^8 - 57600*(x*e + d)^m*d^3*m^7*x^7*e^8 + 14490000*(x*e + d)^m*d^3*m^6*x^8*e^8 + 12600*(x*e + d)^m*d^4*m^7*x^6*e^7 - 7560000*(x*e + d)^m*d^4*m^6*x^7*e^7 + 2520000*(x*e + d)^m*d^5*m^6*x^6*e^6 + 510*(x*e + d)^m*m^10*x^6*e^11 + 58941*(x*e + d)^m*m^9*x^7*e^11 - 143178*(x*e + d)^m*m^8*x^8*e^11 + 15270930*(x*e + d)^m*m^7*x^9*e^11 - 4180575*(x*e + d)^m*m^6*x^10*e^11 + 451027500*(x*e + d)^m*m^5*x^11*e^11 + 510*(x*e + d)^m*d*m^10*x^5*e^10 + 52947*(x*e + d)^m*d*m^9*x^6*e^10 - 108192*(x*e + d)^m*d*m^8*x^7*e^10 + 9028530*(x*e + d)^m*d*m^7*x^8*e^10 - 1808625*(x*e + d)^m*d*m^6*x^9*e^10 + 134662500*(x*e + d)^m*d*m^5*x^10*e^10 - 5994*(x*e + d)^m*d^2*m^9*x^5*e^9 + 30870*(x*e + d)^m*d^2*m^8*x^6*e^9 - 4443120*(x*e + d)^m*d^2*m^7*x^7*e^9 + 1237950*(x*e + d)^m*d^2*m^6*x^8*e^9 - 112245000*(x*e + d)^m*d^2*m^5*x^9*e^9 - 4116*(x*e + d)^m*d^3*m^8*x^5*e^8 + 1542240*(x*e + d)^m*d^3*m^7*x^6*e^8 - 730800*(x*e + d)^m*d^3*m^6*x^7*e^8 + 88200000*(x*e + d)^m*d^3*m^5*x^8*e^8 - 257040*(x*e + d)^m*d^4*m^7*x^5*e^7 + 327600*(x*e + d)^m*d^4*m^6*x^6*e^7 - 63000000*(x*e + d)^m*d^4*m^5*x^7*e^7 - 75600*(x*e + d)^m*d^5*m^6*x^5*e^6 + 37800000*(x*e + d)^m*d^5*m^5*x^6*e^6 - 15120000*(x*e + d)^m*d^6*m^5*x^5*e^5 + 1109*(x*e + d)^m*m^10*x^5*e^11 + 30600*(x*e + d)^m*m^9*x^6*e^11 + 1510488*(x*e + d)^m*m^8*x^7*e^11 - 2056236*(x*e + d)^m*m^7*x^8*e^11 + 135990225*(x*e + d)^m*m^6*x^9*e^11 - 24133200*(x*e + d)^m*m^5*x^10*e^11 + 1708465000*(x*e + d)^m*m^4*x^11*e^11 + 1109*(x*e + d)^m*d*m^10*x^4*e^10 + 28050*(x*e + d)^m*d*m^9*x^5*e^10 + 1192806*(x*e + d)^m*d*m^8*x^6*e^10 - 1298892*(x*e + d)^m*d*m^7*x^7*e^10 + 63761985*(x*e + d)^m*d*m^6*x^8*e^10 - 7855575*(x*e + d)^m*d*m^5*x^9*e^10 + 361840000*(x*e + d)^m*d*m^4*x^10*e^10 - 2550*(x*e + d)^m*d^2*m^9*x^4*e^9 - 287712*(x*e + d)^m*d^2*m^8*x^5*e^9 + 572124*(x*e + d)^m*d^2*m^7*x^6*e^9 - 41126400*(x*e + d)^m*d^2*m^6*x^7*e^9 + 6374025*(x*e + d)^m*d^2*m^5*x^8*e^9 - 336420000*(x*e + d)^m*d^2*m^4*x^9*e^9 + 29970*(x*e + d)^m*d^3*m^8*x^4*e^8 - 164640*(x*e + d)^m*d^3*m^7*x^5*e^8 + 21848400*(x*e + d)^m*d^3*m^6*x^6*e^8 - 4788000*(x*e + d)^m*d^3*m^5*x^7*e^8 + 304605000*(x*e + d)^m*d^3*m^4*x^8*e^8 + 20580*(x*e + d)^m*d^4*m^7*x^4*e^7 - 7968240*(x*e + d)^m*d^4*m^6*x^5*e^7 + 3150000*(x*e + d)^m*d^4*m^5*x^6*e^7 - 264600000*(x*e + d)^m*d^4*m^4*x^7*e^7 + 1285200*(x*e + d)^m*d^5*m^6*x^4*e^6 - 1587600*(x*e + d)^m*d^5*m^5*x^5*e^6 + 214200000*(x*e + d)^m*d^5*m^4*x^6*e^6 + 378000*(x*e + d)^m*d^6*m^5*x^4*e^5 - 151200000*(x*e + d)^m*d^6*m^4*x^5*e^5 + 75600000*(x*e + d)^m*d^7*m^4*x^4*e^4 + 574*(x*e + d)^m*m^10*x^4*e^11 + 67649*(x*e + d)^m*m^9*x^5*e^11 + 798150*(x*e + d)^m*m^8*x^6*e^11 + 22063914*(x*e + d)^m*m^7*x^7*e^11 - 18577566*(x*e + d)^m*m^6*x^8*e^11 + 793819845*(x*e + d)^m*m^5*x^9*e^11 - 92156375*(x*e + d)^m*m^4*x^10*e^11 + 4204750000*(x*e + d)^m*m^3*x^11*e^11 + 574*(x*e + d)^m*d*m^10*x^3*e^10 + 63213*(x*e + d)^m*d*m^9*x^4*e^10 + 657900*(x*e + d)^m*d*m^8*x^5*e^10 + 14907078*(x*e + d)^m*d*m^7*x^6*e^10 - 9485322*(x*e + d)^m*d*m^6*x^7*e^10 + 283723965*(x*e + d)^m*d*m^5*x^8*e^10 - 21456200*(x*e + d)^m*d*m^4*x^9*e^10 + 586350000*(x*e + d)^m*d*m^3*x^10*e^10 - 4436*(x*e + d)^m*d^2*m^9*x^3*e^9 - 130050*(x*e + d)^m*d^2*m^8*x^4*e^9 - 5718276*(x*e + d)^m*d^2*m^7*x^5*e^9 + 5659500*(x*e + d)^m*d^2*m^6*x^6*e^9 - 222211080*(x*e + d)^m*d^2*m^5*x^7*e^9 + 19707975*(x*e + d)^m*d^2*m^4*x^8*e^9 - 590620000*(x*e + d)^m*d^2*m^3*x^9*e^9 + 10200*(x*e + d)^m*d^3*m^8*x^3*e^8 + 1318680*(x*e + d)^m*d^3*m^7*x^4*e^8 - 2609544*(x*e + d)^m*d^3*m^6*x^5*e^8 + 156794400*(x*e + d)^m*d^3*m^5*x^6*e^8 - 17476200*(x*e + d)^m*d^3*m^4*x^7*e^8 + 590940000*(x*e + d)^m*d^3*m^3*x^8*e^8 - 119880*(x*e + d)^m*d^4*m^7*x^3*e^7 + 740880*(x*e + d)^m*d^4*m^6*x^4*e^7 - 91249200*(x*e + d)^m*d^4*m^5*x^5*e^7 + 14616000*(x*e + d)^m*d^4*m^4*x^6*e^7 - 584640000*(x*e + d)^m*d^4*m^3*x^7*e^7 - 82320*(x*e + d)^m*d^5*m^6*x^3*e^6 + 34700400*(x*e + d)^m*d^5*m^5*x^4*e^6 - 10962000*(x*e + d)^m*d^5*m^4*x^5*e^6 + 567000000*(x*e + d)^m*d^5*m^3*x^6*e^6 - 5140800*(x*e + d)^m*d^6*m^5*x^3*e^5 + 6426000*(x*e + d)^m*d^6*m^4*x^4*e^5 - 529200000*(x*e + d)^m*d^6*m^3*x^5*e^5 - 1512000*(x*e + d)^m*d^7*m^4*x^3*e^4 + 453600000*(x*e + d)^m*d^7*m^3*x^4*e^4 - 302400000*(x*e + d)^m*d^8*m^3*x^3*e^3 + 477*(x*e + d)^m*m^10*x^3*e^11 + 35588*(x*e + d)^m*m^9*x^4*e^11 + 1796580*(x*e + d)^m*m^8*x^5*e^11 + 11872800*(x*e + d)^m*m^7*x^6*e^11 + 202618179*(x*e + d)^m*m^6*x^7*e^11 - 109860156*(x*e + d)^m*m^5*x^8*e^11 + 3060365670*(x*e + d)^m*m^4*x^9*e^11 - 228329500*(x*e + d)^m*m^3*x^10*e^11 + 6376788000*(x*e + d)^m*m^2*x^11*e^11 + 477*(x*e + d)^m*d*m^10*x^2*e^10 + 33866*(x*e + d)^m*d*m^9*x^3*e^10 + 1543728*(x*e + d)^m*d*m^8*x^4*e^10 + 8583300*(x*e + d)^m*d*m^7*x^5*e^10 + 113175711*(x*e + d)^m*d*m^6*x^6*e^10 - 43462902*(x*e + d)^m*d*m^5*x^7*e^10 + 790573950*(x*e + d)^m*d*m^4*x^8*e^10 - 35223700*(x*e + d)^m*d*m^3*x^9*e^10 + 513288000*(x*e + d)^m*d*m^2*x^10*e^10 - 1722*(x*e + d)^m*d^2*m^9*x^2*e^9 - 239544*(x*e + d)^m*d^2*m^8*x^3*e^9 - 2769300*(x*e + d)^m*d^2*m^7*x^4*e^9 - 60851088*(x*e + d)^m*d^2*m^6*x^5*e^9 + 32440254*(x*e + d)^m*d^2*m^5*x^6*e^9 - 714314160*(x*e + d)^m*d^2*m^4*x^7*e^9 + 35442000*(x*e + d)^m*d^2*m^3*x^8*e^9 - 547920000*(x*e + d)^m*d^2*m^2*x^9*e^9 + 13308*(x*e + d)^m*d^3*m^8*x^2*e^8 + 489600*(x*e + d)^m*d^3*m^7*x^3*e^8 + 23316660*(x*e + d)^m*d^3*m^6*x^4*e^8 - 20909280*(x*e + d)^m*d^3*m^5*x^5*e^8 + 614711160*(x*e + d)^m*d^3*m^4*x^6*e^8 - 35330400*(x*e + d)^m*d^3*m^3*x^7*e^8 + 588060000*(x*e + d)^m*d^3*m^2*x^8*e^8 - 30600*(x*e + d)^m*d^4*m^7*x^2*e^7 - 4915080*(x*e + d)^m*d^4*m^6*x^3*e^7 + 10084200*(x*e + d)^m*d^4*m^5*x^4*e^7 - 484520400*(x*e + d)^m*d^4*m^4*x^5*e^7 + 34637400*(x*e + d)^m*d^4*m^3*x^6*e^7 - 635040000*(x*e + d)^m*d^4*m^2*x^7*e^7 + 359640*(x*e + d)^m*d^5*m^6*x^2*e^6 - 2716560*(x*e + d)^m*d^5*m^5*x^3*e^6 + 317444400*(x*e + d)^m*d^5*m^4*x^4*e^6 - 32886000*(x*e + d)^m*d^5*m^3*x^5*e^6 + 690480000*(x*e + d)^m*d^5*m^2*x^6*e^6 + 246960*(x*e + d)^m*d^6*m^5*x^2*e^5 - 123379200*(x*e + d)^m*d^6*m^4*x^3*e^5 + 29106000*(x*e + d)^m*d^6*m^3*x^4*e^5 - 756000000*(x*e + d)^m*d^6*m^2*x^5*e^5 + 15422400*(x*e + d)^m*d^7*m^4*x^2*e^4 - 21168000*(x*e + d)^m*d^7*m^3*x^3*e^4 + 831600000*(x*e + d)^m*d^7*m^2*x^4*e^4 + 4536000*(x*e + d)^m*d^8*m^3*x^2*e^3 - 907200000*(x*e + d)^m*d^8*m^2*x^3*e^3 + 907200000*(x*e + d)^m*d^9*m^2*x^2*e^2 + 135*(x*e + d)^m*m^10*x^2*e^11 + 30051*(x*e + d)^m*m^9*x^3*e^11 + 962598*(x*e + d)^m*m^8*x^4*e^11 + 27248130*(x*e + d)^m*m^7*x^5*e^11 + 111048930*(x*e + d)^m*m^6*x^6*e^11 + 1216593189*(x*e + d)^m*m^5*x^7*e^11 - 428393182*(x*e + d)^m*m^4*x^8*e^11 + 7643442420*(x*e + d)^m*m^3*x^9*e^11 - 348156900*(x*e + d)^m*m^2*x^10*e^11 + 5314320000*(x*e + d)^m*m*x^11*e^11 + 135*(x*e + d)^m*d*m^10*x*e^10 + 29097*(x*e + d)^m*d*m^9*x^2*e^10 + 861000*(x*e + d)^m*d*m^8*x^3*e^10 + 21073218*(x*e + d)^m*d*m^7*x^4*e^10 + 68132430*(x*e + d)^m*d*m^6*x^5*e^10 + 537538923*(x*e + d)^m*d*m^5*x^6*e^10 - 124152868*(x*e + d)^m*d*m^4*x^7*e^10 + 1318850820*(x*e + d)^m*d*m^3*x^8*e^10 - 31143600*(x*e + d)^m*d*m^2*x^9*e^10 + 181440000*(x*e + d)^m*d*m*x^10*e^10 - 954*(x*e + d)^m*d^2*m^9*x*e^9 - 98154*(x*e + d)^m*d^2*m^8*x^2*e^9 - 5456280*(x*e + d)^m*d^2*m^7*x^3*e^9 - 31839300*(x*e + d)^m*d^2*m^6*x^4*e^9 - 374798826*(x*e + d)^m*d^2*m^5*x^5*e^9 + 109598790*(x*e + d)^m*d^2*m^4*x^6*e^9 - 1324392480*(x*e + d)^m*d^2*m^3*x^7*e^9 + 33477300*(x*e + d)^m*d^2*m^2*x^8*e^9 - 201600000*(x*e + d)^m*d^2*m*x^9*e^9 + 3444*(x*e + d)^m*d^3*m^8*x*e^8 + 692016*(x*e + d)^m*d^3*m^7*x^2*e^8 + 9608400*(x*e + d)^m*d^3*m^6*x^3*e^8 + 210988800*(x*e + d)^m*d^3*m^5*x^4*e^8 - 90095124*(x*e + d)^m*d^3*m^4*x^5*e^8 + 1311932160*(x*e + d)^m*d^3*m^3*x^6*e^8 - 36223200*(x*e + d)^m*d^3*m^2*x^7*e^8 + 226800000*(x*e + d)^m*d^3*m*x^8*e^8 - 26616*(x*e + d)^m*d^4*m^7*x*e^7 - 1407600*(x*e + d)^m*d^4*m^6*x^2*e^7 - 78521400*(x*e + d)^m*d^4*m^5*x^3*e^7 + 64209600*(x*e + d)^m*d^4*m^4*x^4*e^7 - 1265664960*(x*e + d)^m*d^4*m^3*x^5*e^7 + 39488400*(x*e + d)^m*d^4*m^2*x^6*e^7 - 259200000*(x*e + d)^m*d^4*m*x^7*e^7 + 61200*(x*e + d)^m*d^5*m^6*x*e^6 + 14025960*(x*e + d)^m*d^5*m^5*x^2*e^6 - 32187120*(x*e + d)^m*d^5*m^4*x^3*e^6 + 1152824400*(x*e + d)^m*d^5*m^3*x^4*e^6 - 43394400*(x*e + d)^m*d^5*m^2*x^5*e^6 + 302400000*(x*e + d)^m*d^5*m*x^6*e^6 - 719280*(x*e + d)^m*d^6*m^5*x*e^5 + 7655760*(x*e + d)^m*d^6*m^4*x^2*e^5 - 899640000*(x*e + d)^m*d^6*m^3*x^3*e^5 + 48006000*(x*e + d)^m*d^6*m^2*x^4*e^5 - 362880000*(x*e + d)^m*d^6*m*x^5*e^5 - 493920*(x*e + d)^m*d^7*m^4*x*e^4 + 339292800*(x*e + d)^m*d^7*m^3*x^2*e^4 - 52920000*(x*e + d)^m*d^7*m^2*x^3*e^4 + 453600000*(x*e + d)^m*d^7*m*x^4*e^4 - 30844800*(x*e + d)^m*d^8*m^3*x*e^3 + 54432000*(x*e + d)^m*d^8*m^2*x^2*e^3 - 604800000*(x*e + d)^m*d^8*m*x^3*e^3 - 9072000*(x*e + d)^m*d^9*m^2*x*e^2 + 907200000*(x*e + d)^m*d^9*m*x^2*e^2 - 1814400000*(x*e + d)^m*d^10*m*x*e + 54*(x*e + d)^m*m^10*x*e^11 + 8640*(x*e + d)^m*m^9*x^2*e^11 + 828072*(x*e + d)^m*m^8*x^3*e^11 + 14902188*(x*e + d)^m*m^7*x^4*e^11 + 260141457*(x*e + d)^m*m^6*x^5*e^11 + 678861000*(x*e + d)^m*m^5*x^6*e^11 + 4810043142*(x*e + d)^m*m^4*x^7*e^11 - 1080436084*(x*e + d)^m*m^3*x^8*e^11 + 11731446360*(x*e + d)^m*m^2*x^9*e^11 - 291380400*(x*e + d)^m*m*x^10*e^11 + 1814400000*(x*e + d)^m*x^11*e^11 + 54*(x*e + d)^m*d*m^10*e^10 + 8505*(x*e + d)^m*d*m^9*x*e^10 + 769878*(x*e + d)^m*d*m^8*x^2*e^10 + 12319188*(x*e + d)^m*d*m^7*x^3*e^10 + 175848585*(x*e + d)^m*d*m^6*x^4*e^10 + 338198850*(x*e + d)^m*d*m^5*x^5*e^10 + 1584809604*(x*e + d)^m*d*m^4*x^6*e^10 - 211366008*(x*e + d)^m*d*m^3*x^7*e^10 + 1180639800*(x*e + d)^m*d*m^2*x^8*e^10 - 11088000*(x*e + d)^m*d*m*x^9*e^10 - 135*(x*e + d)^m*d^2*m^9*e^9 - 57240*(x*e + d)^m*d^2*m^8*x*e^9 - 2386692*(x*e + d)^m*d^2*m^7*x^2*e^9 - 67924032*(x*e + d)^m*d^2*m^6*x^3*e^9 - 213304950*(x*e + d)^m*d^2*m^5*x^4*e^9 - 1351239408*(x*e + d)^m*d^2*m^4*x^5*e^9 + 211477336*(x*e + d)^m*d^2*m^3*x^6*e^9 - 1280059200*(x*e + d)^m*d^2*m^2*x^7*e^9 + 12474000*(x*e + d)^m*d^2*m*x^8*e^9 + 954*(x*e + d)^m*d^3*m^8*e^8 + 192864*(x*e + d)^m*d^3*m^7*x*e^8 + 14984808*(x*e + d)^m*d^3*m^6*x^2*e^8 + 98532000*(x*e + d)^m*d^3*m^5*x^3*e^8 + 1030038930*(x*e + d)^m*d^3*m^4*x^4*e^8 - 207117120*(x*e + d)^m*d^3*m^3*x^5*e^8 + 1399154400*(x*e + d)^m*d^3*m^2*x^6*e^8 - 14256000*(x*e + d)^m*d^3*m*x^7*e^8 - 3444*(x*e + d)^m*d^4*m^7*e^7 - 1357416*(x*e + d)^m*d^4*m^6*x*e^7 - 26010000*(x*e + d)^m*d^4*m^5*x^2*e^7 - 608391000*(x*e + d)^m*d^4*m^4*x^3*e^7 + 193637220*(x*e + d)^m*d^4*m^3*x^4*e^7 - 1543268160*(x*e + d)^m*d^4*m^2*x^5*e^7 + 16632000*(x*e + d)^m*d^4*m*x^6*e^7 + 26616*(x*e + d)^m*d^5*m^6*e^6 + 2754000*(x*e + d)^m*d^5*m^5*x*e^6 + 207512280*(x*e + d)^m*d^5*m^4*x^2*e^6 - 160277040*(x*e + d)^m*d^5*m^3*x^3*e^6 + 1717027200*(x*e + d)^m*d^5*m^2*x^4*e^6 - 19958400*(x*e + d)^m*d^5*m*x^5*e^6 - 61200*(x*e + d)^m*d^6*m^5*e^5 - 27332640*(x*e + d)^m*d^6*m^4*x*e^5 + 81249840*(x*e + d)^m*d^6*m^3*x^2*e^5 - 1912377600*(x*e + d)^m*d^6*m^2*x^3*e^5 + 24948000*(x*e + d)^m*d^6*m*x^4*e^5 + 719280*(x*e + d)^m*d^7*m^4*e^4 - 14817600*(x*e + d)^m*d^7*m^3*x*e^4 + 2020334400*(x*e + d)^m*d^7*m^2*x^2*e^4 - 33264000*(x*e + d)^m*d^7*m*x^3*e^4 + 493920*(x*e + d)^m*d^8*m^3*e^3 - 647740800*(x*e + d)^m*d^8*m^2*x*e^3 + 49896000*(x*e + d)^m*d^8*m*x^2*e^3 + 30844800*(x*e + d)^m*d^9*m^2*e^2 - 99792000*(x*e + d)^m*d^9*m*x*e^2 + 9072000*(x*e + d)^m*d^10*m*e + 1814400000*(x*e + d)^m*d^11 + 3510*(x*e + d)^m*m^9*x*e^11 + 242595*(x*e + d)^m*m^8*x^2*e^11 + 13099374*(x*e + d)^m*m^7*x^3*e^11 + 145552050*(x*e + d)^m*m^6*x^4*e^11 + 1624344537*(x*e + d)^m*m^5*x^5*e^11 + 2729996850*(x*e + d)^m*m^4*x^6*e^11 + 12279432276*(x*e + d)^m*m^3*x^7*e^11 - 1671802776*(x*e + d)^m*m^2*x^8*e^11 + 9869234400*(x*e + d)^m*m*x^9*e^11 - 99792000*(x*e + d)^m*x^10*e^11 + 3510*(x*e + d)^m*d*m^9*e^10 + 234090*(x*e + d)^m*d*m^8*x*e^10 + 11559618*(x*e + d)^m*d*m^7*x^2*e^10 + 108594486*(x*e + d)^m*d*m^6*x^3*e^10 + 920950197*(x*e + d)^m*d*m^5*x^4*e^10 + 1039002600*(x*e + d)^m*d*m^4*x^5*e^10 + 2770574652*(x*e + d)^m*d*m^3*x^6*e^10 - 192240720*(x*e + d)^m*d*m^2*x^7*e^10 + 424116000*(x*e + d)^m*d*m*x^8*e^10 - 8505*(x*e + d)^m*d^2*m^8*e^9 - 1482516*(x*e + d)^m*d^2*m^7*x*e^9 - 32184180*(x*e + d)^m*d^2*m^6*x^2*e^9 - 499622244*(x*e + d)^m*d^2*m^5*x^3*e^9 - 837774450*(x*e + d)^m*d^2*m^4*x^4*e^9 - 2752660584*(x*e + d)^m*d^2*m^3*x^5*e^9 + 210698040*(x*e + d)^m*d^2*m^2*x^6*e^9 - 484704000*(x*e + d)^m*d^2*m*x^7*e^9 + 57240*(x*e + d)^m*d^3*m^7*e^8 + 4580520*(x*e + d)^m*d^3*m^6*x*e^8 + 173802480*(x*e + d)^m*d^3*m^5*x^2*e^8 + 557623800*(x*e + d)^m*d^3*m^4*x^3*e^8 + 2636041320*(x*e + d)^m*d^3*m^3*x^4*e^8 - 233278416*(x*e + d)^m*d^3*m^2*x^5*e^8 + 565488000*(x*e + d)^m*d^3*m*x^6*e^8 - 192864*(x*e + d)^m*d^4*m^6*e^7 - 28612200*(x*e + d)^m*d^4*m^5*x*e^7 - 243576000*(x*e + d)^m*d^4*m^4*x^2*e^7 - 2294982720*(x*e + d)^m*d^4*m^3*x^3*e^7 + 261036720*(x*e + d)^m*d^4*m^2*x^4*e^7 - 678585600*(x*e + d)^m*d^4*m*x^5*e^7 + 1357416*(x*e + d)^m*d^5*m^5*e^6 + 49266000*(x*e + d)^m*d^5*m^4*x*e^6 + 1410148440*(x*e + d)^m*d^5*m^3*x^2*e^6 - 293717760*(x*e + d)^m*d^5*m^2*x^3*e^6 + 848232000*(x*e + d)^m*d^5*m*x^4*e^6 - 2754000*(x*e + d)^m*d^6*m^4*e^5 - 387691920*(x*e + d)^m*d^6*m^3*x*e^5 + 318331440*(x*e + d)^m*d^6*m^2*x^2*e^5 - 1130976000*(x*e + d)^m*d^6*m*x^3*e^5 + 27332640*(x*e + d)^m*d^7*m^3*e^4 - 147682080*(x*e + d)^m*d^7*m^2*x*e^4 + 1696464000*(x*e + d)^m*d^7*m*x^2*e^4 + 14817600*(x*e + d)^m*d^8*m^2*e^3 - 3392928000*(x*e + d)^m*d^8*m*x*e^3 + 647740800*(x*e + d)^m*d^9*m*e^2 + 99792000*(x*e + d)^m*d^10*e + 100440*(x*e + d)^m*m^8*x*e^11 + 3925260*(x*e + d)^m*m^7*x^2*e^11 + 131192649*(x*e + d)^m*m^6*x^3*e^11 + 931750092*(x*e + d)^m*m^5*x^4*e^11 + 6671821630*(x*e + d)^m*m^4*x^5*e^11 + 7077841200*(x*e + d)^m*m^3*x^6*e^11 + 19196791992*(x*e + d)^m*m^2*x^7*e^11 - 1415539440*(x*e + d)^m*m*x^8*e^11 + 3392928000*(x*e + d)^m*x^9*e^11 + 100440*(x*e + d)^m*d*m^8*e^10 + 3691170*(x*e + d)^m*d*m^7*x*e^10 + 108073413*(x*e + d)^m*d*m^6*x^2*e^10 + 605966634*(x*e + d)^m*d*m^5*x^3*e^10 + 2988020842*(x*e + d)^m*d*m^4*x^4*e^10 + 1882828200*(x*e + d)^m*d*m^3*x^5*e^10 + 2573344080*(x*e + d)^m*d*m^2*x^6*e^10 - 69854400*(x*e + d)^m*d*m*x^7*e^10 - 234090*(x*e + d)^m*d^2*m^7*e^9 - 21636720*(x*e + d)^m*d^2*m^6*x*e^9 - 261415098*(x*e + d)^m*d^2*m^5*x^2*e^9 - 2184934056*(x*e + d)^m*d^2*m^4*x^3*e^9 - 1843915200*(x*e + d)^m*d^2*m^3*x^4*e^9 - 2860144992*(x*e + d)^m*d^2*m^2*x^5*e^9 + 81496800*(x*e + d)^m*d^2*m*x^6*e^9 + 1482516*(x*e + d)^m*d^3*m^6*e^8 + 59787840*(x*e + d)^m*d^3*m^5*x*e^8 + 1151261772*(x*e + d)^m*d^3*m^4*x^2*e^8 + 1678226400*(x*e + d)^m*d^3*m^3*x^3*e^8 + 3219137640*(x*e + d)^m*d^3*m^2*x^4*e^8 - 97796160*(x*e + d)^m*d^3*m*x^5*e^8 - 4580520*(x*e + d)^m*d^4*m^5*e^7 - 318992760*(x*e + d)^m*d^4*m^4*x*e^7 - 1185719400*(x*e + d)^m*d^4*m^3*x^2*e^7 - 3659217120*(x*e + d)^m*d^4*m^2*x^3*e^7 + 122245200*(x*e + d)^m*d^4*m*x^4*e^7 + 28612200*(x*e + d)^m*d^5*m^4*e^6 + 437886000*(x*e + d)^m*d^5*m^3*x*e^6 + 4064651280*(x*e + d)^m*d^5*m^2*x^2*e^6 - 162993600*(x*e + d)^m*d^5*m*x^3*e^6 - 49266000*(x*e + d)^m*d^6*m^3*e^5 - 2432604960*(x*e + d)^m*d^6*m^2*x*e^5 + 244490400*(x*e + d)^m*d^6*m*x^2*e^5 + 387691920*(x*e + d)^m*d^7*m^2*e^4 - 488980800*(x*e + d)^m*d^7*m*x*e^4 + 147682080*(x*e + d)^m*d^8*m*e^3 + 3392928000*(x*e + d)^m*d^9*e^2 + 1663740*(x*e + d)^m*m^7*x*e^11 + 40401585*(x*e + d)^m*m^6*x^2*e^11 + 864537219*(x*e + d)^m*m^5*x^3*e^11 + 3929892722*(x*e + d)^m*m^4*x^4*e^11 + 17650156420*(x*e + d)^m*m^3*x^5*e^11 + 11214571560*(x*e + d)^m*m^2*x^6*e^11 + 16389514080*(x*e + d)^m*m*x^7*e^11 - 488980800*(x*e + d)^m*x^8*e^11 + 1663740*(x*e + d)^m*d*m^7*e^10 + 36710415*(x*e + d)^m*d*m^6*x*e^10 + 648390393*(x*e + d)^m*d*m^5*x^2*e^10 + 2111992820*(x*e + d)^m*d*m^4*x^3*e^10 + 5698073052*(x*e + d)^m*d*m^3*x^4*e^10 + 1800430560*(x*e + d)^m*d*m^2*x^5*e^10 + 949449600*(x*e + d)^m*d*m*x^6*e^10 - 3691170*(x*e + d)^m*d^2*m^6*e^9 - 194510106*(x*e + d)^m*d^2*m^5*x*e^9 - 1295069706*(x*e + d)^m*d^2*m^4*x^2*e^9 - 5397281200*(x*e + d)^m*d^2*m^3*x^3*e^9 - 2038480200*(x*e + d)^m*d^2*m^2*x^4*e^9 - 1139339520*(x*e + d)^m*d^2*m*x^5*e^9 + 21636720*(x*e + d)^m*d^3*m^5*e^8 + 463042356*(x*e + d)^m*d^3*m^4*x*e^8 + 4252278624*(x*e + d)^m*d^3*m^3*x^2*e^8 + 2340981600*(x*e + d)^m*d^3*m^2*x^3*e^8 + 1424174400*(x*e + d)^m*d^3*m*x^4*e^8 - 59787840*(x*e + d)^m*d^4*m^4*e^7 - 1983530784*(x*e + d)^m*d^4*m^3*x*e^7 - 2663240400*(x*e + d)^m*d^4*m^2*x^2*e^7 - 1898899200*(x*e + d)^m*d^4*m*x^3*e^7 + 318992760*(x*e + d)^m*d^5*m^3*e^6 + 1933552800*(x*e + d)^m*d^5*m^2*x*e^6 + 2848348800*(x*e + d)^m*d^5*m*x^2*e^6 - 437886000*(x*e + d)^m*d^6*m^2*e^5 - 5696697600*(x*e + d)^m*d^6*m*x*e^5 + 2432604960*(x*e + d)^m*d^7*m*e^4 + 488980800*(x*e + d)^m*d^8*e^3 + 17637102*(x*e + d)^m*m^6*x*e^11 + 275267160*(x*e + d)^m*m^5*x^2*e^11 + 3769346538*(x*e + d)^m*m^4*x^3*e^11 + 10681978132*(x*e + d)^m*m^3*x^4*e^11 + 28480424184*(x*e + d)^m*m^2*x^5*e^11 + 9680738400*(x*e + d)^m*m*x^6*e^11 + 5696697600*(x*e + d)^m*x^7*e^11 + 17637102*(x*e + d)^m*d*m^6*e^10 + 238556745*(x*e + d)^m*d*m^5*x*e^10 + 2472565752*(x*e + d)^m*d*m^4*x^2*e^10 + 4345999672*(x*e + d)^m*d*m^3*x^3*e^10 + 5688131976*(x*e + d)^m*d*m^2*x^4*e^10 + 678585600*(x*e + d)^m*d*m*x^5*e^10 - 36710415*(x*e + d)^m*d^2*m^5*e^9 - 1102270680*(x*e + d)^m*d^2*m^4*x*e^9 - 3745839048*(x*e + d)^m*d^2*m^3*x^2*e^9 - 6600448608*(x*e + d)^m*d^2*m^2*x^3*e^9 - 848232000*(x*e + d)^m*d^2*m*x^4*e^9 + 194510106*(x*e + d)^m*d^3*m^4*e^8 + 2127097056*(x*e + d)^m*d^3*m^3*x*e^8 + 7687286352*(x*e + d)^m*d^3*m^2*x^2*e^8 + 1130976000*(x*e + d)^m*d^3*m*x^3*e^8 - 463042356*(x*e + d)^m*d^4*m^3*e^7 - 6521026464*(x*e + d)^m*d^4*m^2*x*e^7 - 1696464000*(x*e + d)^m*d^4*m*x^2*e^7 + 1983530784*(x*e + d)^m*d^5*m^2*e^6 + 3392928000*(x*e + d)^m*d^5*m*x*e^6 - 1933552800*(x*e + d)^m*d^6*m*e^5 + 5696697600*(x*e + d)^m*d^7*e^4 + 124791030*(x*e + d)^m*m^5*x*e^11 + 1250302905*(x*e + d)^m*m^4*x^2*e^11 + 10631923596*(x*e + d)^m*m^3*x^3*e^11 + 17690223096*(x*e + d)^m*m^2*x^4*e^11 + 24965914464*(x*e + d)^m*m*x^5*e^11 + 3392928000*(x*e + d)^m*x^6*e^11 + 124791030*(x*e + d)^m*d*m^5*e^10 + 1011746160*(x*e + d)^m*d*m^4*x*e^10 + 5686792092*(x*e + d)^m*d*m^3*x^2*e^10 + 4652224080*(x*e + d)^m*d*m^2*x^3*e^10 + 2213386560*(x*e + d)^m*d*m*x^4*e^10 - 238556745*(x*e + d)^m*d^2*m^4*e^9 - 3842860824*(x*e + d)^m*d^2*m^3*x*e^9 - 5546320920*(x*e + d)^m*d^2*m^2*x^2*e^9 - 2951182080*(x*e + d)^m*d^2*m*x^3*e^9 + 1102270680*(x*e + d)^m*d^3*m^3*e^8 + 5364581040*(x*e + d)^m*d^3*m^2*x*e^8 + 4426773120*(x*e + d)^m*d^3*m*x^2*e^8 - 2127097056*(x*e + d)^m*d^4*m^2*e^7 - 8853546240*(x*e + d)^m*d^4*m*x*e^7 + 6521026464*(x*e + d)^m*d^5*m*e^6 - 3392928000*(x*e + d)^m*d^6*e^5 + 595543860*(x*e + d)^m*m^4*x*e^11 + 3708817740*(x*e + d)^m*m^3*x^2*e^11 + 18312331464*(x*e + d)^m*m^2*x^3*e^11 + 15866025840*(x*e + d)^m*m*x^4*e^11 + 8853546240*(x*e + d)^m*x^5*e^11 + 595543860*(x*e + d)^m*d*m^4*e^10 + 2697071580*(x*e + d)^m*d*m^3*x*e^10 + 6938747280*(x*e + d)^m*d*m^2*x^2*e^10 + 1909353600*(x*e + d)^m*d*m*x^3*e^10 - 1011746160*(x*e + d)^m*d^2*m^3*e^9 - 7530723360*(x*e + d)^m*d^2*m^2*x*e^9 - 2864030400*(x*e + d)^m*d^2*m*x^2*e^9 + 3842860824*(x*e + d)^m*d^3*m^2*e^8 + 5728060800*(x*e + d)^m*d^3*m*x*e^8 - 5364581040*(x*e + d)^m*d^4*m*e^7 + 8853546240*(x*e + d)^m*d^5*e^6 + 1888225560*(x*e + d)^m*m^3*x*e^11 + 6792204780*(x*e + d)^m*m^2*x^2*e^11 + 17050880160*(x*e + d)^m*m*x^3*e^11 + 5728060800*(x*e + d)^m*x^4*e^11 + 1888225560*(x*e + d)^m*d*m^3*e^10 + 4095133200*(x*e + d)^m*d*m^2*x*e^10 + 3173385600*(x*e + d)^m*d*m*x^2*e^10 - 2697071580*(x*e + d)^m*d^2*m^2*e^9 - 6346771200*(x*e + d)^m*d^2*m*x*e^9 + 7530723360*(x*e + d)^m*d^3*m*e^8 - 5728060800*(x*e + d)^m*d^4*e^7 + 3795710544*(x*e + d)^m*m^2*x*e^11 + 6789517200*(x*e + d)^m*m*x^2*e^11 + 6346771200*(x*e + d)^m*x^3*e^11 + 3795710544*(x*e + d)^m*d*m^2*e^10 + 2694384000*(x*e + d)^m*d*m*x*e^10 - 4095133200*(x*e + d)^m*d^2*m*e^9 + 6346771200*(x*e + d)^m*d^3*e^8 + 4353860160*(x*e + d)^m*m*x*e^11 + 2694384000*(x*e + d)^m*x^2*e^11 + 4353860160*(x*e + d)^m*d*m*e^10 - 2694384000*(x*e + d)^m*d^2*e^9 + 2155507200*(x*e + d)^m*x*e^11 + 2155507200*(x*e + d)^m*d*e^10)/(m^11*e^11 + 66*m^10*e^11 + 1925*m^9*e^11 + 32670*m^8*e^11 + 357423*m^7*e^11 + 2637558*m^6*e^11 + 13339535*m^5*e^11 + 45995730*m^4*e^11 + 105258076*m^3*e^11 + 150917976*m^2*e^11 + 120543840*m*e^11 + 39916800*e^11)","B",0
368,1,6223,0,0.392365," ","integrate((e*x+d)^m*(5*x^2+2*x+3)^2*(4*x^4-5*x^3+3*x^2+x+2),x, algorithm=""giac"")","\frac{100 \, {\left(x e + d\right)}^{m} m^{8} x^{9} e^{9} + 100 \, {\left(x e + d\right)}^{m} d m^{8} x^{8} e^{8} - 45 \, {\left(x e + d\right)}^{m} m^{8} x^{8} e^{9} + 3600 \, {\left(x e + d\right)}^{m} m^{7} x^{9} e^{9} - 45 \, {\left(x e + d\right)}^{m} d m^{8} x^{7} e^{8} + 2800 \, {\left(x e + d\right)}^{m} d m^{7} x^{8} e^{8} - 800 \, {\left(x e + d\right)}^{m} d^{2} m^{7} x^{7} e^{7} + 111 \, {\left(x e + d\right)}^{m} m^{8} x^{7} e^{9} - 1665 \, {\left(x e + d\right)}^{m} m^{7} x^{8} e^{9} + 54600 \, {\left(x e + d\right)}^{m} m^{6} x^{9} e^{9} + 111 \, {\left(x e + d\right)}^{m} d m^{8} x^{6} e^{8} - 1350 \, {\left(x e + d\right)}^{m} d m^{7} x^{7} e^{8} + 32200 \, {\left(x e + d\right)}^{m} d m^{6} x^{8} e^{8} + 315 \, {\left(x e + d\right)}^{m} d^{2} m^{7} x^{6} e^{7} - 16800 \, {\left(x e + d\right)}^{m} d^{2} m^{6} x^{7} e^{7} + 5600 \, {\left(x e + d\right)}^{m} d^{3} m^{6} x^{6} e^{6} - 37 \, {\left(x e + d\right)}^{m} m^{8} x^{6} e^{9} + 4218 \, {\left(x e + d\right)}^{m} m^{7} x^{7} e^{9} - 25830 \, {\left(x e + d\right)}^{m} m^{6} x^{8} e^{9} + 453600 \, {\left(x e + d\right)}^{m} m^{5} x^{9} e^{9} - 37 \, {\left(x e + d\right)}^{m} d m^{8} x^{5} e^{8} + 3552 \, {\left(x e + d\right)}^{m} d m^{7} x^{6} e^{8} - 16380 \, {\left(x e + d\right)}^{m} d m^{6} x^{7} e^{8} + 196000 \, {\left(x e + d\right)}^{m} d m^{5} x^{8} e^{8} - 666 \, {\left(x e + d\right)}^{m} d^{2} m^{7} x^{5} e^{7} + 7560 \, {\left(x e + d\right)}^{m} d^{2} m^{6} x^{6} e^{7} - 140000 \, {\left(x e + d\right)}^{m} d^{2} m^{5} x^{7} e^{7} - 1890 \, {\left(x e + d\right)}^{m} d^{3} m^{6} x^{5} e^{6} + 84000 \, {\left(x e + d\right)}^{m} d^{3} m^{5} x^{6} e^{6} - 33600 \, {\left(x e + d\right)}^{m} d^{4} m^{5} x^{5} e^{5} + 148 \, {\left(x e + d\right)}^{m} m^{8} x^{5} e^{9} - 1443 \, {\left(x e + d\right)}^{m} m^{7} x^{6} e^{9} + 67044 \, {\left(x e + d\right)}^{m} m^{6} x^{7} e^{9} - 218610 \, {\left(x e + d\right)}^{m} m^{5} x^{8} e^{9} + 2244900 \, {\left(x e + d\right)}^{m} m^{4} x^{9} e^{9} + 148 \, {\left(x e + d\right)}^{m} d m^{8} x^{4} e^{8} - 1258 \, {\left(x e + d\right)}^{m} d m^{7} x^{5} e^{8} + 45732 \, {\left(x e + d\right)}^{m} d m^{6} x^{6} e^{8} - 103950 \, {\left(x e + d\right)}^{m} d m^{5} x^{7} e^{8} + 676900 \, {\left(x e + d\right)}^{m} d m^{4} x^{8} e^{8} + 185 \, {\left(x e + d\right)}^{m} d^{2} m^{7} x^{4} e^{7} - 17982 \, {\left(x e + d\right)}^{m} d^{2} m^{6} x^{5} e^{7} + 69300 \, {\left(x e + d\right)}^{m} d^{2} m^{5} x^{6} e^{7} - 588000 \, {\left(x e + d\right)}^{m} d^{2} m^{4} x^{7} e^{7} + 3330 \, {\left(x e + d\right)}^{m} d^{3} m^{6} x^{4} e^{6} - 35910 \, {\left(x e + d\right)}^{m} d^{3} m^{5} x^{5} e^{6} + 476000 \, {\left(x e + d\right)}^{m} d^{3} m^{4} x^{6} e^{6} + 9450 \, {\left(x e + d\right)}^{m} d^{4} m^{5} x^{4} e^{5} - 336000 \, {\left(x e + d\right)}^{m} d^{4} m^{4} x^{5} e^{5} + 168000 \, {\left(x e + d\right)}^{m} d^{5} m^{4} x^{4} e^{4} + 65 \, {\left(x e + d\right)}^{m} m^{8} x^{4} e^{9} + 5920 \, {\left(x e + d\right)}^{m} m^{7} x^{5} e^{9} - 23532 \, {\left(x e + d\right)}^{m} m^{6} x^{6} e^{9} + 579642 \, {\left(x e + d\right)}^{m} m^{5} x^{7} e^{9} - 1098405 \, {\left(x e + d\right)}^{m} m^{4} x^{8} e^{9} + 6728400 \, {\left(x e + d\right)}^{m} m^{3} x^{9} e^{9} + 65 \, {\left(x e + d\right)}^{m} d m^{8} x^{3} e^{8} + 5328 \, {\left(x e + d\right)}^{m} d m^{7} x^{4} e^{8} - 17242 \, {\left(x e + d\right)}^{m} d m^{6} x^{5} e^{8} + 305250 \, {\left(x e + d\right)}^{m} d m^{5} x^{6} e^{8} - 370755 \, {\left(x e + d\right)}^{m} d m^{4} x^{7} e^{8} + 1313200 \, {\left(x e + d\right)}^{m} d m^{3} x^{8} e^{8} - 592 \, {\left(x e + d\right)}^{m} d^{2} m^{7} x^{3} e^{7} + 5550 \, {\left(x e + d\right)}^{m} d^{2} m^{6} x^{4} e^{7} - 184482 \, {\left(x e + d\right)}^{m} d^{2} m^{5} x^{5} e^{7} + 311850 \, {\left(x e + d\right)}^{m} d^{2} m^{4} x^{6} e^{7} - 1299200 \, {\left(x e + d\right)}^{m} d^{2} m^{3} x^{7} e^{7} - 740 \, {\left(x e + d\right)}^{m} d^{3} m^{6} x^{3} e^{6} + 76590 \, {\left(x e + d\right)}^{m} d^{3} m^{5} x^{4} e^{6} - 236250 \, {\left(x e + d\right)}^{m} d^{3} m^{4} x^{5} e^{6} + 1260000 \, {\left(x e + d\right)}^{m} d^{3} m^{3} x^{6} e^{6} - 13320 \, {\left(x e + d\right)}^{m} d^{4} m^{5} x^{3} e^{5} + 141750 \, {\left(x e + d\right)}^{m} d^{4} m^{4} x^{4} e^{5} - 1176000 \, {\left(x e + d\right)}^{m} d^{4} m^{3} x^{5} e^{5} - 37800 \, {\left(x e + d\right)}^{m} d^{5} m^{4} x^{3} e^{4} + 1008000 \, {\left(x e + d\right)}^{m} d^{5} m^{3} x^{4} e^{4} - 672000 \, {\left(x e + d\right)}^{m} d^{6} m^{3} x^{3} e^{3} + 107 \, {\left(x e + d\right)}^{m} m^{8} x^{3} e^{9} + 2665 \, {\left(x e + d\right)}^{m} m^{7} x^{4} e^{9} + 99160 \, {\left(x e + d\right)}^{m} m^{6} x^{5} e^{9} - 208458 \, {\left(x e + d\right)}^{m} m^{5} x^{6} e^{9} + 2965809 \, {\left(x e + d\right)}^{m} m^{4} x^{7} e^{9} - 3332385 \, {\left(x e + d\right)}^{m} m^{3} x^{8} e^{9} + 11812400 \, {\left(x e + d\right)}^{m} m^{2} x^{9} e^{9} + 107 \, {\left(x e + d\right)}^{m} d m^{8} x^{2} e^{8} + 2470 \, {\left(x e + d\right)}^{m} d m^{7} x^{3} e^{8} + 77848 \, {\left(x e + d\right)}^{m} d m^{6} x^{4} e^{8} - 122248 \, {\left(x e + d\right)}^{m} d m^{5} x^{5} e^{8} + 1134309 \, {\left(x e + d\right)}^{m} d m^{4} x^{6} e^{8} - 737100 \, {\left(x e + d\right)}^{m} d m^{3} x^{7} e^{8} + 1306800 \, {\left(x e + d\right)}^{m} d m^{2} x^{8} e^{8} - 195 \, {\left(x e + d\right)}^{m} d^{2} m^{7} x^{2} e^{7} - 19536 \, {\left(x e + d\right)}^{m} d^{2} m^{6} x^{3} e^{7} + 64010 \, {\left(x e + d\right)}^{m} d^{2} m^{5} x^{4} e^{7} - 909090 \, {\left(x e + d\right)}^{m} d^{2} m^{4} x^{5} e^{7} + 724185 \, {\left(x e + d\right)}^{m} d^{2} m^{3} x^{6} e^{7} - 1411200 \, {\left(x e + d\right)}^{m} d^{2} m^{2} x^{7} e^{7} + 1776 \, {\left(x e + d\right)}^{m} d^{3} m^{6} x^{2} e^{6} - 19980 \, {\left(x e + d\right)}^{m} d^{3} m^{5} x^{3} e^{6} + 616050 \, {\left(x e + d\right)}^{m} d^{3} m^{4} x^{4} e^{6} - 689850 \, {\left(x e + d\right)}^{m} d^{3} m^{3} x^{5} e^{6} + 1534400 \, {\left(x e + d\right)}^{m} d^{3} m^{2} x^{6} e^{6} + 2220 \, {\left(x e + d\right)}^{m} d^{4} m^{5} x^{2} e^{5} - 266400 \, {\left(x e + d\right)}^{m} d^{4} m^{4} x^{3} e^{5} + 614250 \, {\left(x e + d\right)}^{m} d^{4} m^{3} x^{4} e^{5} - 1680000 \, {\left(x e + d\right)}^{m} d^{4} m^{2} x^{5} e^{5} + 39960 \, {\left(x e + d\right)}^{m} d^{5} m^{4} x^{2} e^{4} - 453600 \, {\left(x e + d\right)}^{m} d^{5} m^{3} x^{3} e^{4} + 1848000 \, {\left(x e + d\right)}^{m} d^{5} m^{2} x^{4} e^{4} + 113400 \, {\left(x e + d\right)}^{m} d^{6} m^{3} x^{2} e^{3} - 2016000 \, {\left(x e + d\right)}^{m} d^{6} m^{2} x^{3} e^{3} + 2016000 \, {\left(x e + d\right)}^{m} d^{7} m^{2} x^{2} e^{2} + 33 \, {\left(x e + d\right)}^{m} m^{8} x^{2} e^{9} + 4494 \, {\left(x e + d\right)}^{m} m^{7} x^{3} e^{9} + 45890 \, {\left(x e + d\right)}^{m} m^{6} x^{4} e^{9} + 902800 \, {\left(x e + d\right)}^{m} m^{5} x^{5} e^{9} - 1090353 \, {\left(x e + d\right)}^{m} m^{4} x^{6} e^{9} + 9134412 \, {\left(x e + d\right)}^{m} m^{3} x^{7} e^{9} - 5906520 \, {\left(x e + d\right)}^{m} m^{2} x^{8} e^{9} + 10958400 \, {\left(x e + d\right)}^{m} m x^{9} e^{9} + 33 \, {\left(x e + d\right)}^{m} d m^{8} x e^{8} + 4280 \, {\left(x e + d\right)}^{m} d m^{7} x^{2} e^{8} + 38480 \, {\left(x e + d\right)}^{m} d m^{6} x^{3} e^{8} + 591408 \, {\left(x e + d\right)}^{m} d m^{5} x^{4} e^{8} - 479113 \, {\left(x e + d\right)}^{m} d m^{4} x^{5} e^{8} + 2328558 \, {\left(x e + d\right)}^{m} d m^{3} x^{6} e^{8} - 746820 \, {\left(x e + d\right)}^{m} d m^{2} x^{7} e^{8} + 504000 \, {\left(x e + d\right)}^{m} d m x^{8} e^{8} - 214 \, {\left(x e + d\right)}^{m} d^{2} m^{7} x e^{7} - 7020 \, {\left(x e + d\right)}^{m} d^{2} m^{6} x^{2} e^{7} - 252784 \, {\left(x e + d\right)}^{m} d^{2} m^{5} x^{3} e^{7} + 355200 \, {\left(x e + d\right)}^{m} d^{2} m^{4} x^{4} e^{7} - 2260404 \, {\left(x e + d\right)}^{m} d^{2} m^{3} x^{5} e^{7} + 814590 \, {\left(x e + d\right)}^{m} d^{2} m^{2} x^{6} e^{7} - 576000 \, {\left(x e + d\right)}^{m} d^{2} m x^{7} e^{7} + 390 \, {\left(x e + d\right)}^{m} d^{3} m^{6} x e^{6} + 55056 \, {\left(x e + d\right)}^{m} d^{3} m^{5} x^{2} e^{6} - 196100 \, {\left(x e + d\right)}^{m} d^{3} m^{4} x^{3} e^{6} + 2081250 \, {\left(x e + d\right)}^{m} d^{3} m^{3} x^{4} e^{6} - 895860 \, {\left(x e + d\right)}^{m} d^{3} m^{2} x^{5} e^{6} + 672000 \, {\left(x e + d\right)}^{m} d^{3} m x^{6} e^{6} - 3552 \, {\left(x e + d\right)}^{m} d^{4} m^{5} x e^{5} + 55500 \, {\left(x e + d\right)}^{m} d^{4} m^{4} x^{2} e^{5} - 1665000 \, {\left(x e + d\right)}^{m} d^{4} m^{3} x^{3} e^{5} + 992250 \, {\left(x e + d\right)}^{m} d^{4} m^{2} x^{4} e^{5} - 806400 \, {\left(x e + d\right)}^{m} d^{4} m x^{5} e^{5} - 4440 \, {\left(x e + d\right)}^{m} d^{5} m^{4} x e^{4} + 719280 \, {\left(x e + d\right)}^{m} d^{5} m^{3} x^{2} e^{4} - 1096200 \, {\left(x e + d\right)}^{m} d^{5} m^{2} x^{3} e^{4} + 1008000 \, {\left(x e + d\right)}^{m} d^{5} m x^{4} e^{4} - 79920 \, {\left(x e + d\right)}^{m} d^{6} m^{3} x e^{3} + 1134000 \, {\left(x e + d\right)}^{m} d^{6} m^{2} x^{2} e^{3} - 1344000 \, {\left(x e + d\right)}^{m} d^{6} m x^{3} e^{3} - 226800 \, {\left(x e + d\right)}^{m} d^{7} m^{2} x e^{2} + 2016000 \, {\left(x e + d\right)}^{m} d^{7} m x^{2} e^{2} - 4032000 \, {\left(x e + d\right)}^{m} d^{8} m x e + 18 \, {\left(x e + d\right)}^{m} m^{8} x e^{9} + 1419 \, {\left(x e + d\right)}^{m} m^{7} x^{2} e^{9} + 79608 \, {\left(x e + d\right)}^{m} m^{6} x^{3} e^{9} + 430690 \, {\left(x e + d\right)}^{m} m^{5} x^{4} e^{9} + 4850404 \, {\left(x e + d\right)}^{m} m^{4} x^{5} e^{9} - 3422907 \, {\left(x e + d\right)}^{m} m^{3} x^{6} e^{9} + 16387596 \, {\left(x e + d\right)}^{m} m^{2} x^{7} e^{9} - 5519340 \, {\left(x e + d\right)}^{m} m x^{8} e^{9} + 4032000 \, {\left(x e + d\right)}^{m} x^{9} e^{9} + 18 \, {\left(x e + d\right)}^{m} d m^{8} e^{8} + 1386 \, {\left(x e + d\right)}^{m} d m^{7} x e^{8} + 71048 \, {\left(x e + d\right)}^{m} d m^{6} x^{2} e^{8} + 315250 \, {\left(x e + d\right)}^{m} d m^{5} x^{3} e^{8} + 2484772 \, {\left(x e + d\right)}^{m} d m^{4} x^{4} e^{8} - 1027342 \, {\left(x e + d\right)}^{m} d m^{3} x^{5} e^{8} + 2416248 \, {\left(x e + d\right)}^{m} d m^{2} x^{6} e^{8} - 291600 \, {\left(x e + d\right)}^{m} d m x^{7} e^{8} - 33 \, {\left(x e + d\right)}^{m} d^{2} m^{7} e^{7} - 8346 \, {\left(x e + d\right)}^{m} d^{2} m^{6} x e^{7} - 101400 \, {\left(x e + d\right)}^{m} d^{2} m^{5} x^{2} e^{7} - 1607280 \, {\left(x e + d\right)}^{m} d^{2} m^{4} x^{3} e^{7} + 974765 \, {\left(x e + d\right)}^{m} d^{2} m^{3} x^{4} e^{7} - 2669328 \, {\left(x e + d\right)}^{m} d^{2} m^{2} x^{5} e^{7} + 340200 \, {\left(x e + d\right)}^{m} d^{2} m x^{6} e^{7} + 214 \, {\left(x e + d\right)}^{m} d^{3} m^{6} e^{6} + 13650 \, {\left(x e + d\right)}^{m} d^{3} m^{5} x e^{6} + 648240 \, {\left(x e + d\right)}^{m} d^{3} m^{4} x^{2} e^{6} - 832500 \, {\left(x e + d\right)}^{m} d^{3} m^{3} x^{3} e^{6} + 2977020 \, {\left(x e + d\right)}^{m} d^{3} m^{2} x^{4} e^{6} - 408240 \, {\left(x e + d\right)}^{m} d^{3} m x^{5} e^{6} - 390 \, {\left(x e + d\right)}^{m} d^{4} m^{5} e^{5} - 106560 \, {\left(x e + d\right)}^{m} d^{4} m^{4} x e^{5} + 477300 \, {\left(x e + d\right)}^{m} d^{4} m^{3} x^{2} e^{5} - 3330000 \, {\left(x e + d\right)}^{m} d^{4} m^{2} x^{3} e^{5} + 510300 \, {\left(x e + d\right)}^{m} d^{4} m x^{4} e^{5} + 3552 \, {\left(x e + d\right)}^{m} d^{5} m^{4} e^{4} - 106560 \, {\left(x e + d\right)}^{m} d^{5} m^{3} x e^{4} + 3556440 \, {\left(x e + d\right)}^{m} d^{5} m^{2} x^{2} e^{4} - 680400 \, {\left(x e + d\right)}^{m} d^{5} m x^{3} e^{4} + 4440 \, {\left(x e + d\right)}^{m} d^{6} m^{3} e^{3} - 1358640 \, {\left(x e + d\right)}^{m} d^{6} m^{2} x e^{3} + 1020600 \, {\left(x e + d\right)}^{m} d^{6} m x^{2} e^{3} + 79920 \, {\left(x e + d\right)}^{m} d^{7} m^{2} e^{2} - 2041200 \, {\left(x e + d\right)}^{m} d^{7} m x e^{2} + 226800 \, {\left(x e + d\right)}^{m} d^{8} m e + 4032000 \, {\left(x e + d\right)}^{m} d^{9} + 792 \, {\left(x e + d\right)}^{m} m^{7} x e^{9} + 25872 \, {\left(x e + d\right)}^{m} m^{6} x^{2} e^{9} + 772326 \, {\left(x e + d\right)}^{m} m^{5} x^{3} e^{9} + 2389985 \, {\left(x e + d\right)}^{m} m^{4} x^{4} e^{9} + 15608080 \, {\left(x e + d\right)}^{m} m^{3} x^{5} e^{9} - 6238718 \, {\left(x e + d\right)}^{m} m^{2} x^{6} e^{9} + 15456528 \, {\left(x e + d\right)}^{m} m x^{7} e^{9} - 2041200 \, {\left(x e + d\right)}^{m} x^{8} e^{9} + 792 \, {\left(x e + d\right)}^{m} d m^{7} e^{8} + 24486 \, {\left(x e + d\right)}^{m} d m^{6} x e^{8} + 630230 \, {\left(x e + d\right)}^{m} d m^{5} x^{2} e^{8} + 1444235 \, {\left(x e + d\right)}^{m} d m^{4} x^{3} e^{8} + 5668992 \, {\left(x e + d\right)}^{m} d m^{3} x^{4} e^{8} - 1102008 \, {\left(x e + d\right)}^{m} d m^{2} x^{5} e^{8} + 959040 \, {\left(x e + d\right)}^{m} d m x^{6} e^{8} - 1386 \, {\left(x e + d\right)}^{m} d^{2} m^{6} e^{7} - 133750 \, {\left(x e + d\right)}^{m} d^{2} m^{5} x e^{7} - 742950 \, {\left(x e + d\right)}^{m} d^{2} m^{4} x^{2} e^{7} - 5117248 \, {\left(x e + d\right)}^{m} d^{2} m^{3} x^{3} e^{7} + 1237650 \, {\left(x e + d\right)}^{m} d^{2} m^{2} x^{4} e^{7} - 1150848 \, {\left(x e + d\right)}^{m} d^{2} m x^{5} e^{7} + 8346 \, {\left(x e + d\right)}^{m} d^{3} m^{5} e^{6} + 189150 \, {\left(x e + d\right)}^{m} d^{3} m^{4} x e^{6} + 3525360 \, {\left(x e + d\right)}^{m} d^{3} m^{3} x^{2} e^{6} - 1401560 \, {\left(x e + d\right)}^{m} d^{3} m^{2} x^{3} e^{6} + 1438560 \, {\left(x e + d\right)}^{m} d^{3} m x^{4} e^{6} - 13650 \, {\left(x e + d\right)}^{m} d^{4} m^{4} e^{5} - 1189920 \, {\left(x e + d\right)}^{m} d^{4} m^{3} x e^{5} + 1542900 \, {\left(x e + d\right)}^{m} d^{4} m^{2} x^{2} e^{5} - 1918080 \, {\left(x e + d\right)}^{m} d^{4} m x^{3} e^{5} + 106560 \, {\left(x e + d\right)}^{m} d^{5} m^{3} e^{4} - 848040 \, {\left(x e + d\right)}^{m} d^{5} m^{2} x e^{4} + 2877120 \, {\left(x e + d\right)}^{m} d^{5} m x^{2} e^{4} + 106560 \, {\left(x e + d\right)}^{m} d^{6} m^{2} e^{3} - 5754240 \, {\left(x e + d\right)}^{m} d^{6} m x e^{3} + 1358640 \, {\left(x e + d\right)}^{m} d^{7} m e^{2} + 2041200 \, {\left(x e + d\right)}^{m} d^{8} e + 14868 \, {\left(x e + d\right)}^{m} m^{6} x e^{9} + 260106 \, {\left(x e + d\right)}^{m} m^{5} x^{2} e^{9} + 4453233 \, {\left(x e + d\right)}^{m} m^{4} x^{3} e^{9} + 7946185 \, {\left(x e + d\right)}^{m} m^{3} x^{4} e^{9} + 29064240 \, {\left(x e + d\right)}^{m} m^{2} x^{5} e^{9} - 5957592 \, {\left(x e + d\right)}^{m} m x^{6} e^{9} + 5754240 \, {\left(x e + d\right)}^{m} x^{7} e^{9} + 14868 \, {\left(x e + d\right)}^{m} d m^{6} e^{8} + 235620 \, {\left(x e + d\right)}^{m} d m^{5} x e^{8} + 3192773 \, {\left(x e + d\right)}^{m} d m^{4} x^{2} e^{8} + 3613480 \, {\left(x e + d\right)}^{m} d m^{3} x^{3} e^{8} + 6388272 \, {\left(x e + d\right)}^{m} d m^{2} x^{4} e^{8} - 447552 \, {\left(x e + d\right)}^{m} d m x^{5} e^{8} - 24486 \, {\left(x e + d\right)}^{m} d^{2} m^{5} e^{7} - 1126710 \, {\left(x e + d\right)}^{m} d^{2} m^{4} x e^{7} - 2846805 \, {\left(x e + d\right)}^{m} d^{2} m^{3} x^{2} e^{7} - 7324224 \, {\left(x e + d\right)}^{m} d^{2} m^{2} x^{3} e^{7} + 559440 \, {\left(x e + d\right)}^{m} d^{2} m x^{4} e^{7} + 133750 \, {\left(x e + d\right)}^{m} d^{3} m^{4} e^{6} + 1296750 \, {\left(x e + d\right)}^{m} d^{3} m^{3} x e^{6} + 8301024 \, {\left(x e + d\right)}^{m} d^{3} m^{2} x^{2} e^{6} - 745920 \, {\left(x e + d\right)}^{m} d^{3} m x^{3} e^{6} - 189150 \, {\left(x e + d\right)}^{m} d^{4} m^{3} e^{5} - 5860800 \, {\left(x e + d\right)}^{m} d^{4} m^{2} x e^{5} + 1118880 \, {\left(x e + d\right)}^{m} d^{4} m x^{2} e^{5} + 1189920 \, {\left(x e + d\right)}^{m} d^{5} m^{2} e^{4} - 2237760 \, {\left(x e + d\right)}^{m} d^{5} m x e^{4} + 848040 \, {\left(x e + d\right)}^{m} d^{6} m e^{3} + 5754240 \, {\left(x e + d\right)}^{m} d^{7} e^{2} + 155232 \, {\left(x e + d\right)}^{m} m^{5} x e^{9} + 1567797 \, {\left(x e + d\right)}^{m} m^{4} x^{2} e^{9} + 15458076 \, {\left(x e + d\right)}^{m} m^{3} x^{3} e^{9} + 15254460 \, {\left(x e + d\right)}^{m} m^{2} x^{4} e^{9} + 28238400 \, {\left(x e + d\right)}^{m} m x^{5} e^{9} - 2237760 \, {\left(x e + d\right)}^{m} x^{6} e^{9} + 155232 \, {\left(x e + d\right)}^{m} d m^{5} e^{8} + 1332177 \, {\left(x e + d\right)}^{m} d m^{4} x e^{8} + 9072530 \, {\left(x e + d\right)}^{m} d m^{3} x^{2} e^{8} + 4414020 \, {\left(x e + d\right)}^{m} d m^{2} x^{3} e^{8} + 2685312 \, {\left(x e + d\right)}^{m} d m x^{4} e^{8} - 235620 \, {\left(x e + d\right)}^{m} d^{2} m^{4} e^{7} - 5258836 \, {\left(x e + d\right)}^{m} d^{2} m^{3} x e^{7} - 5146830 \, {\left(x e + d\right)}^{m} d^{2} m^{2} x^{2} e^{7} - 3580416 \, {\left(x e + d\right)}^{m} d^{2} m x^{3} e^{7} + 1126710 \, {\left(x e + d\right)}^{m} d^{3} m^{3} e^{6} + 4396860 \, {\left(x e + d\right)}^{m} d^{3} m^{2} x e^{6} + 5370624 \, {\left(x e + d\right)}^{m} d^{3} m x^{2} e^{6} - 1296750 \, {\left(x e + d\right)}^{m} d^{4} m^{2} e^{5} - 10741248 \, {\left(x e + d\right)}^{m} d^{4} m x e^{5} + 5860800 \, {\left(x e + d\right)}^{m} d^{5} m e^{4} + 2237760 \, {\left(x e + d\right)}^{m} d^{6} e^{3} + 983682 \, {\left(x e + d\right)}^{m} m^{4} x e^{9} + 5752131 \, {\left(x e + d\right)}^{m} m^{3} x^{2} e^{9} + 31059532 \, {\left(x e + d\right)}^{m} m^{2} x^{3} e^{9} + 15207660 \, {\left(x e + d\right)}^{m} m x^{4} e^{9} + 10741248 \, {\left(x e + d\right)}^{m} x^{5} e^{9} + 983682 \, {\left(x e + d\right)}^{m} d m^{4} e^{8} + 4419954 \, {\left(x e + d\right)}^{m} d m^{3} x e^{8} + 12914472 \, {\left(x e + d\right)}^{m} d m^{2} x^{2} e^{8} + 1965600 \, {\left(x e + d\right)}^{m} d m x^{3} e^{8} - 1332177 \, {\left(x e + d\right)}^{m} d^{2} m^{3} e^{7} - 12886224 \, {\left(x e + d\right)}^{m} d^{2} m^{2} x e^{7} - 2948400 \, {\left(x e + d\right)}^{m} d^{2} m x^{2} e^{7} + 5258836 \, {\left(x e + d\right)}^{m} d^{3} m^{2} e^{6} + 5896800 \, {\left(x e + d\right)}^{m} d^{3} m x e^{6} - 4396860 \, {\left(x e + d\right)}^{m} d^{4} m e^{5} + 10741248 \, {\left(x e + d\right)}^{m} d^{5} e^{4} + 3864168 \, {\left(x e + d\right)}^{m} m^{3} x e^{9} + 12377178 \, {\left(x e + d\right)}^{m} m^{2} x^{2} e^{9} + 32300304 \, {\left(x e + d\right)}^{m} m x^{3} e^{9} + 5896800 \, {\left(x e + d\right)}^{m} x^{4} e^{9} + 3864168 \, {\left(x e + d\right)}^{m} d m^{3} e^{8} + 7957224 \, {\left(x e + d\right)}^{m} d m^{2} x e^{8} + 6471360 \, {\left(x e + d\right)}^{m} d m x^{2} e^{8} - 4419954 \, {\left(x e + d\right)}^{m} d^{2} m^{2} e^{7} - 12942720 \, {\left(x e + d\right)}^{m} d^{2} m x e^{7} + 12886224 \, {\left(x e + d\right)}^{m} d^{3} m e^{6} - 5896800 \, {\left(x e + d\right)}^{m} d^{4} e^{5} + 9162072 \, {\left(x e + d\right)}^{m} m^{2} x e^{9} + 13944744 \, {\left(x e + d\right)}^{m} m x^{2} e^{9} + 12942720 \, {\left(x e + d\right)}^{m} x^{3} e^{9} + 9162072 \, {\left(x e + d\right)}^{m} d m^{2} e^{8} + 5987520 \, {\left(x e + d\right)}^{m} d m x e^{8} - 7957224 \, {\left(x e + d\right)}^{m} d^{2} m e^{7} + 12942720 \, {\left(x e + d\right)}^{m} d^{3} e^{6} + 11946528 \, {\left(x e + d\right)}^{m} m x e^{9} + 5987520 \, {\left(x e + d\right)}^{m} x^{2} e^{9} + 11946528 \, {\left(x e + d\right)}^{m} d m e^{8} - 5987520 \, {\left(x e + d\right)}^{m} d^{2} e^{7} + 6531840 \, {\left(x e + d\right)}^{m} x e^{9} + 6531840 \, {\left(x e + d\right)}^{m} d e^{8}}{m^{9} e^{9} + 45 \, m^{8} e^{9} + 870 \, m^{7} e^{9} + 9450 \, m^{6} e^{9} + 63273 \, m^{5} e^{9} + 269325 \, m^{4} e^{9} + 723680 \, m^{3} e^{9} + 1172700 \, m^{2} e^{9} + 1026576 \, m e^{9} + 362880 \, e^{9}}"," ",0,"(100*(x*e + d)^m*m^8*x^9*e^9 + 100*(x*e + d)^m*d*m^8*x^8*e^8 - 45*(x*e + d)^m*m^8*x^8*e^9 + 3600*(x*e + d)^m*m^7*x^9*e^9 - 45*(x*e + d)^m*d*m^8*x^7*e^8 + 2800*(x*e + d)^m*d*m^7*x^8*e^8 - 800*(x*e + d)^m*d^2*m^7*x^7*e^7 + 111*(x*e + d)^m*m^8*x^7*e^9 - 1665*(x*e + d)^m*m^7*x^8*e^9 + 54600*(x*e + d)^m*m^6*x^9*e^9 + 111*(x*e + d)^m*d*m^8*x^6*e^8 - 1350*(x*e + d)^m*d*m^7*x^7*e^8 + 32200*(x*e + d)^m*d*m^6*x^8*e^8 + 315*(x*e + d)^m*d^2*m^7*x^6*e^7 - 16800*(x*e + d)^m*d^2*m^6*x^7*e^7 + 5600*(x*e + d)^m*d^3*m^6*x^6*e^6 - 37*(x*e + d)^m*m^8*x^6*e^9 + 4218*(x*e + d)^m*m^7*x^7*e^9 - 25830*(x*e + d)^m*m^6*x^8*e^9 + 453600*(x*e + d)^m*m^5*x^9*e^9 - 37*(x*e + d)^m*d*m^8*x^5*e^8 + 3552*(x*e + d)^m*d*m^7*x^6*e^8 - 16380*(x*e + d)^m*d*m^6*x^7*e^8 + 196000*(x*e + d)^m*d*m^5*x^8*e^8 - 666*(x*e + d)^m*d^2*m^7*x^5*e^7 + 7560*(x*e + d)^m*d^2*m^6*x^6*e^7 - 140000*(x*e + d)^m*d^2*m^5*x^7*e^7 - 1890*(x*e + d)^m*d^3*m^6*x^5*e^6 + 84000*(x*e + d)^m*d^3*m^5*x^6*e^6 - 33600*(x*e + d)^m*d^4*m^5*x^5*e^5 + 148*(x*e + d)^m*m^8*x^5*e^9 - 1443*(x*e + d)^m*m^7*x^6*e^9 + 67044*(x*e + d)^m*m^6*x^7*e^9 - 218610*(x*e + d)^m*m^5*x^8*e^9 + 2244900*(x*e + d)^m*m^4*x^9*e^9 + 148*(x*e + d)^m*d*m^8*x^4*e^8 - 1258*(x*e + d)^m*d*m^7*x^5*e^8 + 45732*(x*e + d)^m*d*m^6*x^6*e^8 - 103950*(x*e + d)^m*d*m^5*x^7*e^8 + 676900*(x*e + d)^m*d*m^4*x^8*e^8 + 185*(x*e + d)^m*d^2*m^7*x^4*e^7 - 17982*(x*e + d)^m*d^2*m^6*x^5*e^7 + 69300*(x*e + d)^m*d^2*m^5*x^6*e^7 - 588000*(x*e + d)^m*d^2*m^4*x^7*e^7 + 3330*(x*e + d)^m*d^3*m^6*x^4*e^6 - 35910*(x*e + d)^m*d^3*m^5*x^5*e^6 + 476000*(x*e + d)^m*d^3*m^4*x^6*e^6 + 9450*(x*e + d)^m*d^4*m^5*x^4*e^5 - 336000*(x*e + d)^m*d^4*m^4*x^5*e^5 + 168000*(x*e + d)^m*d^5*m^4*x^4*e^4 + 65*(x*e + d)^m*m^8*x^4*e^9 + 5920*(x*e + d)^m*m^7*x^5*e^9 - 23532*(x*e + d)^m*m^6*x^6*e^9 + 579642*(x*e + d)^m*m^5*x^7*e^9 - 1098405*(x*e + d)^m*m^4*x^8*e^9 + 6728400*(x*e + d)^m*m^3*x^9*e^9 + 65*(x*e + d)^m*d*m^8*x^3*e^8 + 5328*(x*e + d)^m*d*m^7*x^4*e^8 - 17242*(x*e + d)^m*d*m^6*x^5*e^8 + 305250*(x*e + d)^m*d*m^5*x^6*e^8 - 370755*(x*e + d)^m*d*m^4*x^7*e^8 + 1313200*(x*e + d)^m*d*m^3*x^8*e^8 - 592*(x*e + d)^m*d^2*m^7*x^3*e^7 + 5550*(x*e + d)^m*d^2*m^6*x^4*e^7 - 184482*(x*e + d)^m*d^2*m^5*x^5*e^7 + 311850*(x*e + d)^m*d^2*m^4*x^6*e^7 - 1299200*(x*e + d)^m*d^2*m^3*x^7*e^7 - 740*(x*e + d)^m*d^3*m^6*x^3*e^6 + 76590*(x*e + d)^m*d^3*m^5*x^4*e^6 - 236250*(x*e + d)^m*d^3*m^4*x^5*e^6 + 1260000*(x*e + d)^m*d^3*m^3*x^6*e^6 - 13320*(x*e + d)^m*d^4*m^5*x^3*e^5 + 141750*(x*e + d)^m*d^4*m^4*x^4*e^5 - 1176000*(x*e + d)^m*d^4*m^3*x^5*e^5 - 37800*(x*e + d)^m*d^5*m^4*x^3*e^4 + 1008000*(x*e + d)^m*d^5*m^3*x^4*e^4 - 672000*(x*e + d)^m*d^6*m^3*x^3*e^3 + 107*(x*e + d)^m*m^8*x^3*e^9 + 2665*(x*e + d)^m*m^7*x^4*e^9 + 99160*(x*e + d)^m*m^6*x^5*e^9 - 208458*(x*e + d)^m*m^5*x^6*e^9 + 2965809*(x*e + d)^m*m^4*x^7*e^9 - 3332385*(x*e + d)^m*m^3*x^8*e^9 + 11812400*(x*e + d)^m*m^2*x^9*e^9 + 107*(x*e + d)^m*d*m^8*x^2*e^8 + 2470*(x*e + d)^m*d*m^7*x^3*e^8 + 77848*(x*e + d)^m*d*m^6*x^4*e^8 - 122248*(x*e + d)^m*d*m^5*x^5*e^8 + 1134309*(x*e + d)^m*d*m^4*x^6*e^8 - 737100*(x*e + d)^m*d*m^3*x^7*e^8 + 1306800*(x*e + d)^m*d*m^2*x^8*e^8 - 195*(x*e + d)^m*d^2*m^7*x^2*e^7 - 19536*(x*e + d)^m*d^2*m^6*x^3*e^7 + 64010*(x*e + d)^m*d^2*m^5*x^4*e^7 - 909090*(x*e + d)^m*d^2*m^4*x^5*e^7 + 724185*(x*e + d)^m*d^2*m^3*x^6*e^7 - 1411200*(x*e + d)^m*d^2*m^2*x^7*e^7 + 1776*(x*e + d)^m*d^3*m^6*x^2*e^6 - 19980*(x*e + d)^m*d^3*m^5*x^3*e^6 + 616050*(x*e + d)^m*d^3*m^4*x^4*e^6 - 689850*(x*e + d)^m*d^3*m^3*x^5*e^6 + 1534400*(x*e + d)^m*d^3*m^2*x^6*e^6 + 2220*(x*e + d)^m*d^4*m^5*x^2*e^5 - 266400*(x*e + d)^m*d^4*m^4*x^3*e^5 + 614250*(x*e + d)^m*d^4*m^3*x^4*e^5 - 1680000*(x*e + d)^m*d^4*m^2*x^5*e^5 + 39960*(x*e + d)^m*d^5*m^4*x^2*e^4 - 453600*(x*e + d)^m*d^5*m^3*x^3*e^4 + 1848000*(x*e + d)^m*d^5*m^2*x^4*e^4 + 113400*(x*e + d)^m*d^6*m^3*x^2*e^3 - 2016000*(x*e + d)^m*d^6*m^2*x^3*e^3 + 2016000*(x*e + d)^m*d^7*m^2*x^2*e^2 + 33*(x*e + d)^m*m^8*x^2*e^9 + 4494*(x*e + d)^m*m^7*x^3*e^9 + 45890*(x*e + d)^m*m^6*x^4*e^9 + 902800*(x*e + d)^m*m^5*x^5*e^9 - 1090353*(x*e + d)^m*m^4*x^6*e^9 + 9134412*(x*e + d)^m*m^3*x^7*e^9 - 5906520*(x*e + d)^m*m^2*x^8*e^9 + 10958400*(x*e + d)^m*m*x^9*e^9 + 33*(x*e + d)^m*d*m^8*x*e^8 + 4280*(x*e + d)^m*d*m^7*x^2*e^8 + 38480*(x*e + d)^m*d*m^6*x^3*e^8 + 591408*(x*e + d)^m*d*m^5*x^4*e^8 - 479113*(x*e + d)^m*d*m^4*x^5*e^8 + 2328558*(x*e + d)^m*d*m^3*x^6*e^8 - 746820*(x*e + d)^m*d*m^2*x^7*e^8 + 504000*(x*e + d)^m*d*m*x^8*e^8 - 214*(x*e + d)^m*d^2*m^7*x*e^7 - 7020*(x*e + d)^m*d^2*m^6*x^2*e^7 - 252784*(x*e + d)^m*d^2*m^5*x^3*e^7 + 355200*(x*e + d)^m*d^2*m^4*x^4*e^7 - 2260404*(x*e + d)^m*d^2*m^3*x^5*e^7 + 814590*(x*e + d)^m*d^2*m^2*x^6*e^7 - 576000*(x*e + d)^m*d^2*m*x^7*e^7 + 390*(x*e + d)^m*d^3*m^6*x*e^6 + 55056*(x*e + d)^m*d^3*m^5*x^2*e^6 - 196100*(x*e + d)^m*d^3*m^4*x^3*e^6 + 2081250*(x*e + d)^m*d^3*m^3*x^4*e^6 - 895860*(x*e + d)^m*d^3*m^2*x^5*e^6 + 672000*(x*e + d)^m*d^3*m*x^6*e^6 - 3552*(x*e + d)^m*d^4*m^5*x*e^5 + 55500*(x*e + d)^m*d^4*m^4*x^2*e^5 - 1665000*(x*e + d)^m*d^4*m^3*x^3*e^5 + 992250*(x*e + d)^m*d^4*m^2*x^4*e^5 - 806400*(x*e + d)^m*d^4*m*x^5*e^5 - 4440*(x*e + d)^m*d^5*m^4*x*e^4 + 719280*(x*e + d)^m*d^5*m^3*x^2*e^4 - 1096200*(x*e + d)^m*d^5*m^2*x^3*e^4 + 1008000*(x*e + d)^m*d^5*m*x^4*e^4 - 79920*(x*e + d)^m*d^6*m^3*x*e^3 + 1134000*(x*e + d)^m*d^6*m^2*x^2*e^3 - 1344000*(x*e + d)^m*d^6*m*x^3*e^3 - 226800*(x*e + d)^m*d^7*m^2*x*e^2 + 2016000*(x*e + d)^m*d^7*m*x^2*e^2 - 4032000*(x*e + d)^m*d^8*m*x*e + 18*(x*e + d)^m*m^8*x*e^9 + 1419*(x*e + d)^m*m^7*x^2*e^9 + 79608*(x*e + d)^m*m^6*x^3*e^9 + 430690*(x*e + d)^m*m^5*x^4*e^9 + 4850404*(x*e + d)^m*m^4*x^5*e^9 - 3422907*(x*e + d)^m*m^3*x^6*e^9 + 16387596*(x*e + d)^m*m^2*x^7*e^9 - 5519340*(x*e + d)^m*m*x^8*e^9 + 4032000*(x*e + d)^m*x^9*e^9 + 18*(x*e + d)^m*d*m^8*e^8 + 1386*(x*e + d)^m*d*m^7*x*e^8 + 71048*(x*e + d)^m*d*m^6*x^2*e^8 + 315250*(x*e + d)^m*d*m^5*x^3*e^8 + 2484772*(x*e + d)^m*d*m^4*x^4*e^8 - 1027342*(x*e + d)^m*d*m^3*x^5*e^8 + 2416248*(x*e + d)^m*d*m^2*x^6*e^8 - 291600*(x*e + d)^m*d*m*x^7*e^8 - 33*(x*e + d)^m*d^2*m^7*e^7 - 8346*(x*e + d)^m*d^2*m^6*x*e^7 - 101400*(x*e + d)^m*d^2*m^5*x^2*e^7 - 1607280*(x*e + d)^m*d^2*m^4*x^3*e^7 + 974765*(x*e + d)^m*d^2*m^3*x^4*e^7 - 2669328*(x*e + d)^m*d^2*m^2*x^5*e^7 + 340200*(x*e + d)^m*d^2*m*x^6*e^7 + 214*(x*e + d)^m*d^3*m^6*e^6 + 13650*(x*e + d)^m*d^3*m^5*x*e^6 + 648240*(x*e + d)^m*d^3*m^4*x^2*e^6 - 832500*(x*e + d)^m*d^3*m^3*x^3*e^6 + 2977020*(x*e + d)^m*d^3*m^2*x^4*e^6 - 408240*(x*e + d)^m*d^3*m*x^5*e^6 - 390*(x*e + d)^m*d^4*m^5*e^5 - 106560*(x*e + d)^m*d^4*m^4*x*e^5 + 477300*(x*e + d)^m*d^4*m^3*x^2*e^5 - 3330000*(x*e + d)^m*d^4*m^2*x^3*e^5 + 510300*(x*e + d)^m*d^4*m*x^4*e^5 + 3552*(x*e + d)^m*d^5*m^4*e^4 - 106560*(x*e + d)^m*d^5*m^3*x*e^4 + 3556440*(x*e + d)^m*d^5*m^2*x^2*e^4 - 680400*(x*e + d)^m*d^5*m*x^3*e^4 + 4440*(x*e + d)^m*d^6*m^3*e^3 - 1358640*(x*e + d)^m*d^6*m^2*x*e^3 + 1020600*(x*e + d)^m*d^6*m*x^2*e^3 + 79920*(x*e + d)^m*d^7*m^2*e^2 - 2041200*(x*e + d)^m*d^7*m*x*e^2 + 226800*(x*e + d)^m*d^8*m*e + 4032000*(x*e + d)^m*d^9 + 792*(x*e + d)^m*m^7*x*e^9 + 25872*(x*e + d)^m*m^6*x^2*e^9 + 772326*(x*e + d)^m*m^5*x^3*e^9 + 2389985*(x*e + d)^m*m^4*x^4*e^9 + 15608080*(x*e + d)^m*m^3*x^5*e^9 - 6238718*(x*e + d)^m*m^2*x^6*e^9 + 15456528*(x*e + d)^m*m*x^7*e^9 - 2041200*(x*e + d)^m*x^8*e^9 + 792*(x*e + d)^m*d*m^7*e^8 + 24486*(x*e + d)^m*d*m^6*x*e^8 + 630230*(x*e + d)^m*d*m^5*x^2*e^8 + 1444235*(x*e + d)^m*d*m^4*x^3*e^8 + 5668992*(x*e + d)^m*d*m^3*x^4*e^8 - 1102008*(x*e + d)^m*d*m^2*x^5*e^8 + 959040*(x*e + d)^m*d*m*x^6*e^8 - 1386*(x*e + d)^m*d^2*m^6*e^7 - 133750*(x*e + d)^m*d^2*m^5*x*e^7 - 742950*(x*e + d)^m*d^2*m^4*x^2*e^7 - 5117248*(x*e + d)^m*d^2*m^3*x^3*e^7 + 1237650*(x*e + d)^m*d^2*m^2*x^4*e^7 - 1150848*(x*e + d)^m*d^2*m*x^5*e^7 + 8346*(x*e + d)^m*d^3*m^5*e^6 + 189150*(x*e + d)^m*d^3*m^4*x*e^6 + 3525360*(x*e + d)^m*d^3*m^3*x^2*e^6 - 1401560*(x*e + d)^m*d^3*m^2*x^3*e^6 + 1438560*(x*e + d)^m*d^3*m*x^4*e^6 - 13650*(x*e + d)^m*d^4*m^4*e^5 - 1189920*(x*e + d)^m*d^4*m^3*x*e^5 + 1542900*(x*e + d)^m*d^4*m^2*x^2*e^5 - 1918080*(x*e + d)^m*d^4*m*x^3*e^5 + 106560*(x*e + d)^m*d^5*m^3*e^4 - 848040*(x*e + d)^m*d^5*m^2*x*e^4 + 2877120*(x*e + d)^m*d^5*m*x^2*e^4 + 106560*(x*e + d)^m*d^6*m^2*e^3 - 5754240*(x*e + d)^m*d^6*m*x*e^3 + 1358640*(x*e + d)^m*d^7*m*e^2 + 2041200*(x*e + d)^m*d^8*e + 14868*(x*e + d)^m*m^6*x*e^9 + 260106*(x*e + d)^m*m^5*x^2*e^9 + 4453233*(x*e + d)^m*m^4*x^3*e^9 + 7946185*(x*e + d)^m*m^3*x^4*e^9 + 29064240*(x*e + d)^m*m^2*x^5*e^9 - 5957592*(x*e + d)^m*m*x^6*e^9 + 5754240*(x*e + d)^m*x^7*e^9 + 14868*(x*e + d)^m*d*m^6*e^8 + 235620*(x*e + d)^m*d*m^5*x*e^8 + 3192773*(x*e + d)^m*d*m^4*x^2*e^8 + 3613480*(x*e + d)^m*d*m^3*x^3*e^8 + 6388272*(x*e + d)^m*d*m^2*x^4*e^8 - 447552*(x*e + d)^m*d*m*x^5*e^8 - 24486*(x*e + d)^m*d^2*m^5*e^7 - 1126710*(x*e + d)^m*d^2*m^4*x*e^7 - 2846805*(x*e + d)^m*d^2*m^3*x^2*e^7 - 7324224*(x*e + d)^m*d^2*m^2*x^3*e^7 + 559440*(x*e + d)^m*d^2*m*x^4*e^7 + 133750*(x*e + d)^m*d^3*m^4*e^6 + 1296750*(x*e + d)^m*d^3*m^3*x*e^6 + 8301024*(x*e + d)^m*d^3*m^2*x^2*e^6 - 745920*(x*e + d)^m*d^3*m*x^3*e^6 - 189150*(x*e + d)^m*d^4*m^3*e^5 - 5860800*(x*e + d)^m*d^4*m^2*x*e^5 + 1118880*(x*e + d)^m*d^4*m*x^2*e^5 + 1189920*(x*e + d)^m*d^5*m^2*e^4 - 2237760*(x*e + d)^m*d^5*m*x*e^4 + 848040*(x*e + d)^m*d^6*m*e^3 + 5754240*(x*e + d)^m*d^7*e^2 + 155232*(x*e + d)^m*m^5*x*e^9 + 1567797*(x*e + d)^m*m^4*x^2*e^9 + 15458076*(x*e + d)^m*m^3*x^3*e^9 + 15254460*(x*e + d)^m*m^2*x^4*e^9 + 28238400*(x*e + d)^m*m*x^5*e^9 - 2237760*(x*e + d)^m*x^6*e^9 + 155232*(x*e + d)^m*d*m^5*e^8 + 1332177*(x*e + d)^m*d*m^4*x*e^8 + 9072530*(x*e + d)^m*d*m^3*x^2*e^8 + 4414020*(x*e + d)^m*d*m^2*x^3*e^8 + 2685312*(x*e + d)^m*d*m*x^4*e^8 - 235620*(x*e + d)^m*d^2*m^4*e^7 - 5258836*(x*e + d)^m*d^2*m^3*x*e^7 - 5146830*(x*e + d)^m*d^2*m^2*x^2*e^7 - 3580416*(x*e + d)^m*d^2*m*x^3*e^7 + 1126710*(x*e + d)^m*d^3*m^3*e^6 + 4396860*(x*e + d)^m*d^3*m^2*x*e^6 + 5370624*(x*e + d)^m*d^3*m*x^2*e^6 - 1296750*(x*e + d)^m*d^4*m^2*e^5 - 10741248*(x*e + d)^m*d^4*m*x*e^5 + 5860800*(x*e + d)^m*d^5*m*e^4 + 2237760*(x*e + d)^m*d^6*e^3 + 983682*(x*e + d)^m*m^4*x*e^9 + 5752131*(x*e + d)^m*m^3*x^2*e^9 + 31059532*(x*e + d)^m*m^2*x^3*e^9 + 15207660*(x*e + d)^m*m*x^4*e^9 + 10741248*(x*e + d)^m*x^5*e^9 + 983682*(x*e + d)^m*d*m^4*e^8 + 4419954*(x*e + d)^m*d*m^3*x*e^8 + 12914472*(x*e + d)^m*d*m^2*x^2*e^8 + 1965600*(x*e + d)^m*d*m*x^3*e^8 - 1332177*(x*e + d)^m*d^2*m^3*e^7 - 12886224*(x*e + d)^m*d^2*m^2*x*e^7 - 2948400*(x*e + d)^m*d^2*m*x^2*e^7 + 5258836*(x*e + d)^m*d^3*m^2*e^6 + 5896800*(x*e + d)^m*d^3*m*x*e^6 - 4396860*(x*e + d)^m*d^4*m*e^5 + 10741248*(x*e + d)^m*d^5*e^4 + 3864168*(x*e + d)^m*m^3*x*e^9 + 12377178*(x*e + d)^m*m^2*x^2*e^9 + 32300304*(x*e + d)^m*m*x^3*e^9 + 5896800*(x*e + d)^m*x^4*e^9 + 3864168*(x*e + d)^m*d*m^3*e^8 + 7957224*(x*e + d)^m*d*m^2*x*e^8 + 6471360*(x*e + d)^m*d*m*x^2*e^8 - 4419954*(x*e + d)^m*d^2*m^2*e^7 - 12942720*(x*e + d)^m*d^2*m*x*e^7 + 12886224*(x*e + d)^m*d^3*m*e^6 - 5896800*(x*e + d)^m*d^4*e^5 + 9162072*(x*e + d)^m*m^2*x*e^9 + 13944744*(x*e + d)^m*m*x^2*e^9 + 12942720*(x*e + d)^m*x^3*e^9 + 9162072*(x*e + d)^m*d*m^2*e^8 + 5987520*(x*e + d)^m*d*m*x*e^8 - 7957224*(x*e + d)^m*d^2*m*e^7 + 12942720*(x*e + d)^m*d^3*e^6 + 11946528*(x*e + d)^m*m*x*e^9 + 5987520*(x*e + d)^m*x^2*e^9 + 11946528*(x*e + d)^m*d*m*e^8 - 5987520*(x*e + d)^m*d^2*e^7 + 6531840*(x*e + d)^m*x*e^9 + 6531840*(x*e + d)^m*d*e^8)/(m^9*e^9 + 45*m^8*e^9 + 870*m^7*e^9 + 9450*m^6*e^9 + 63273*m^5*e^9 + 269325*m^4*e^9 + 723680*m^3*e^9 + 1172700*m^2*e^9 + 1026576*m*e^9 + 362880*e^9)","B",0
369,1,3098,0,0.265566," ","integrate((e*x+d)^m*(5*x^2+2*x+3)*(4*x^4-5*x^3+3*x^2+x+2),x, algorithm=""giac"")","\frac{20 \, {\left(x e + d\right)}^{m} m^{6} x^{7} e^{7} + 20 \, {\left(x e + d\right)}^{m} d m^{6} x^{6} e^{6} - 17 \, {\left(x e + d\right)}^{m} m^{6} x^{6} e^{7} + 420 \, {\left(x e + d\right)}^{m} m^{5} x^{7} e^{7} - 17 \, {\left(x e + d\right)}^{m} d m^{6} x^{5} e^{6} + 300 \, {\left(x e + d\right)}^{m} d m^{5} x^{6} e^{6} - 120 \, {\left(x e + d\right)}^{m} d^{2} m^{5} x^{5} e^{5} + 17 \, {\left(x e + d\right)}^{m} m^{6} x^{5} e^{7} - 374 \, {\left(x e + d\right)}^{m} m^{5} x^{6} e^{7} + 3500 \, {\left(x e + d\right)}^{m} m^{4} x^{7} e^{7} + 17 \, {\left(x e + d\right)}^{m} d m^{6} x^{4} e^{6} - 289 \, {\left(x e + d\right)}^{m} d m^{5} x^{5} e^{6} + 1700 \, {\left(x e + d\right)}^{m} d m^{4} x^{6} e^{6} + 85 \, {\left(x e + d\right)}^{m} d^{2} m^{5} x^{4} e^{5} - 1200 \, {\left(x e + d\right)}^{m} d^{2} m^{4} x^{5} e^{5} + 600 \, {\left(x e + d\right)}^{m} d^{3} m^{4} x^{4} e^{4} - 4 \, {\left(x e + d\right)}^{m} m^{6} x^{4} e^{7} + 391 \, {\left(x e + d\right)}^{m} m^{5} x^{5} e^{7} - 3230 \, {\left(x e + d\right)}^{m} m^{4} x^{6} e^{7} + 14700 \, {\left(x e + d\right)}^{m} m^{3} x^{7} e^{7} - 4 \, {\left(x e + d\right)}^{m} d m^{6} x^{3} e^{6} + 323 \, {\left(x e + d\right)}^{m} d m^{5} x^{4} e^{6} - 1785 \, {\left(x e + d\right)}^{m} d m^{4} x^{5} e^{6} + 4500 \, {\left(x e + d\right)}^{m} d m^{3} x^{6} e^{6} - 68 \, {\left(x e + d\right)}^{m} d^{2} m^{5} x^{3} e^{5} + 1105 \, {\left(x e + d\right)}^{m} d^{2} m^{4} x^{4} e^{5} - 4200 \, {\left(x e + d\right)}^{m} d^{2} m^{3} x^{5} e^{5} - 340 \, {\left(x e + d\right)}^{m} d^{3} m^{4} x^{3} e^{4} + 3600 \, {\left(x e + d\right)}^{m} d^{3} m^{3} x^{4} e^{4} - 2400 \, {\left(x e + d\right)}^{m} d^{4} m^{3} x^{3} e^{3} + 21 \, {\left(x e + d\right)}^{m} m^{6} x^{3} e^{7} - 96 \, {\left(x e + d\right)}^{m} m^{5} x^{4} e^{7} + 3519 \, {\left(x e + d\right)}^{m} m^{4} x^{5} e^{7} - 13940 \, {\left(x e + d\right)}^{m} m^{3} x^{6} e^{7} + 32480 \, {\left(x e + d\right)}^{m} m^{2} x^{7} e^{7} + 21 \, {\left(x e + d\right)}^{m} d m^{6} x^{2} e^{6} - 84 \, {\left(x e + d\right)}^{m} d m^{5} x^{3} e^{6} + 2227 \, {\left(x e + d\right)}^{m} d m^{4} x^{4} e^{6} - 5015 \, {\left(x e + d\right)}^{m} d m^{3} x^{5} e^{6} + 5480 \, {\left(x e + d\right)}^{m} d m^{2} x^{6} e^{6} + 12 \, {\left(x e + d\right)}^{m} d^{2} m^{5} x^{2} e^{5} - 1088 \, {\left(x e + d\right)}^{m} d^{2} m^{4} x^{3} e^{5} + 4505 \, {\left(x e + d\right)}^{m} d^{2} m^{3} x^{4} e^{5} - 6000 \, {\left(x e + d\right)}^{m} d^{2} m^{2} x^{5} e^{5} + 204 \, {\left(x e + d\right)}^{m} d^{3} m^{4} x^{2} e^{4} - 3400 \, {\left(x e + d\right)}^{m} d^{3} m^{3} x^{3} e^{4} + 6600 \, {\left(x e + d\right)}^{m} d^{3} m^{2} x^{4} e^{4} + 1020 \, {\left(x e + d\right)}^{m} d^{4} m^{3} x^{2} e^{3} - 7200 \, {\left(x e + d\right)}^{m} d^{4} m^{2} x^{3} e^{3} + 7200 \, {\left(x e + d\right)}^{m} d^{5} m^{2} x^{2} e^{2} + 7 \, {\left(x e + d\right)}^{m} m^{6} x^{2} e^{7} + 525 \, {\left(x e + d\right)}^{m} m^{5} x^{3} e^{7} - 904 \, {\left(x e + d\right)}^{m} m^{4} x^{4} e^{7} + 15725 \, {\left(x e + d\right)}^{m} m^{3} x^{5} e^{7} - 31433 \, {\left(x e + d\right)}^{m} m^{2} x^{6} e^{7} + 35280 \, {\left(x e + d\right)}^{m} m x^{7} e^{7} + 7 \, {\left(x e + d\right)}^{m} d m^{6} x e^{6} + 483 \, {\left(x e + d\right)}^{m} d m^{5} x^{2} e^{6} - 652 \, {\left(x e + d\right)}^{m} d m^{4} x^{3} e^{6} + 6817 \, {\left(x e + d\right)}^{m} d m^{3} x^{4} e^{6} - 6358 \, {\left(x e + d\right)}^{m} d m^{2} x^{5} e^{6} + 2400 \, {\left(x e + d\right)}^{m} d m x^{6} e^{6} - 42 \, {\left(x e + d\right)}^{m} d^{2} m^{5} x e^{5} + 228 \, {\left(x e + d\right)}^{m} d^{2} m^{4} x^{2} e^{5} - 5644 \, {\left(x e + d\right)}^{m} d^{2} m^{3} x^{3} e^{5} + 7055 \, {\left(x e + d\right)}^{m} d^{2} m^{2} x^{4} e^{5} - 2880 \, {\left(x e + d\right)}^{m} d^{2} m x^{5} e^{5} - 24 \, {\left(x e + d\right)}^{m} d^{3} m^{4} x e^{4} + 2856 \, {\left(x e + d\right)}^{m} d^{3} m^{3} x^{2} e^{4} - 7820 \, {\left(x e + d\right)}^{m} d^{3} m^{2} x^{3} e^{4} + 3600 \, {\left(x e + d\right)}^{m} d^{3} m x^{4} e^{4} - 408 \, {\left(x e + d\right)}^{m} d^{4} m^{3} x e^{3} + 8160 \, {\left(x e + d\right)}^{m} d^{4} m^{2} x^{2} e^{3} - 4800 \, {\left(x e + d\right)}^{m} d^{4} m x^{3} e^{3} - 2040 \, {\left(x e + d\right)}^{m} d^{5} m^{2} x e^{2} + 7200 \, {\left(x e + d\right)}^{m} d^{5} m x^{2} e^{2} - 14400 \, {\left(x e + d\right)}^{m} d^{6} m x e + 6 \, {\left(x e + d\right)}^{m} m^{6} x e^{7} + 182 \, {\left(x e + d\right)}^{m} m^{5} x^{2} e^{7} + 5187 \, {\left(x e + d\right)}^{m} m^{4} x^{3} e^{7} - 4224 \, {\left(x e + d\right)}^{m} m^{3} x^{4} e^{7} + 36448 \, {\left(x e + d\right)}^{m} m^{2} x^{5} e^{7} - 34646 \, {\left(x e + d\right)}^{m} m x^{6} e^{7} + 14400 \, {\left(x e + d\right)}^{m} x^{7} e^{7} + 6 \, {\left(x e + d\right)}^{m} d m^{6} e^{6} + 175 \, {\left(x e + d\right)}^{m} d m^{5} x e^{6} + 4221 \, {\left(x e + d\right)}^{m} d m^{4} x^{2} e^{6} - 2268 \, {\left(x e + d\right)}^{m} d m^{3} x^{3} e^{6} + 9180 \, {\left(x e + d\right)}^{m} d m^{2} x^{4} e^{6} - 2856 \, {\left(x e + d\right)}^{m} d m x^{5} e^{6} - 7 \, {\left(x e + d\right)}^{m} d^{2} m^{5} e^{5} - 924 \, {\left(x e + d\right)}^{m} d^{2} m^{4} x e^{5} + 1500 \, {\left(x e + d\right)}^{m} d^{2} m^{3} x^{2} e^{5} - 10336 \, {\left(x e + d\right)}^{m} d^{2} m^{2} x^{3} e^{5} + 3570 \, {\left(x e + d\right)}^{m} d^{2} m x^{4} e^{5} + 42 \, {\left(x e + d\right)}^{m} d^{3} m^{4} e^{4} - 432 \, {\left(x e + d\right)}^{m} d^{3} m^{3} x e^{4} + 11220 \, {\left(x e + d\right)}^{m} d^{3} m^{2} x^{2} e^{4} - 4760 \, {\left(x e + d\right)}^{m} d^{3} m x^{3} e^{4} + 24 \, {\left(x e + d\right)}^{m} d^{4} m^{3} e^{3} - 5304 \, {\left(x e + d\right)}^{m} d^{4} m^{2} x e^{3} + 7140 \, {\left(x e + d\right)}^{m} d^{4} m x^{2} e^{3} + 408 \, {\left(x e + d\right)}^{m} d^{5} m^{2} e^{2} - 14280 \, {\left(x e + d\right)}^{m} d^{5} m x e^{2} + 2040 \, {\left(x e + d\right)}^{m} d^{6} m e + 14400 \, {\left(x e + d\right)}^{m} d^{7} + 162 \, {\left(x e + d\right)}^{m} m^{5} x e^{7} + 1890 \, {\left(x e + d\right)}^{m} m^{4} x^{2} e^{7} + 25599 \, {\left(x e + d\right)}^{m} m^{3} x^{3} e^{7} - 10180 \, {\left(x e + d\right)}^{m} m^{2} x^{4} e^{7} + 41004 \, {\left(x e + d\right)}^{m} m x^{5} e^{7} - 14280 \, {\left(x e + d\right)}^{m} x^{6} e^{7} + 162 \, {\left(x e + d\right)}^{m} d m^{5} e^{6} + 1715 \, {\left(x e + d\right)}^{m} d m^{4} x e^{6} + 17157 \, {\left(x e + d\right)}^{m} d m^{3} x^{2} e^{6} - 3376 \, {\left(x e + d\right)}^{m} d m^{2} x^{3} e^{6} + 4284 \, {\left(x e + d\right)}^{m} d m x^{4} e^{6} - 175 \, {\left(x e + d\right)}^{m} d^{2} m^{4} e^{5} - 7518 \, {\left(x e + d\right)}^{m} d^{2} m^{3} x e^{5} + 3804 \, {\left(x e + d\right)}^{m} d^{2} m^{2} x^{2} e^{5} - 5712 \, {\left(x e + d\right)}^{m} d^{2} m x^{3} e^{5} + 924 \, {\left(x e + d\right)}^{m} d^{3} m^{3} e^{4} - 2568 \, {\left(x e + d\right)}^{m} d^{3} m^{2} x e^{4} + 8568 \, {\left(x e + d\right)}^{m} d^{3} m x^{2} e^{4} + 432 \, {\left(x e + d\right)}^{m} d^{4} m^{2} e^{3} - 17136 \, {\left(x e + d\right)}^{m} d^{4} m x e^{3} + 5304 \, {\left(x e + d\right)}^{m} d^{5} m e^{2} + 14280 \, {\left(x e + d\right)}^{m} d^{6} e + 1770 \, {\left(x e + d\right)}^{m} m^{4} x e^{7} + 9940 \, {\left(x e + d\right)}^{m} m^{3} x^{2} e^{7} + 65352 \, {\left(x e + d\right)}^{m} m^{2} x^{3} e^{7} - 11808 \, {\left(x e + d\right)}^{m} m x^{4} e^{7} + 17136 \, {\left(x e + d\right)}^{m} x^{5} e^{7} + 1770 \, {\left(x e + d\right)}^{m} d m^{4} e^{6} + 8225 \, {\left(x e + d\right)}^{m} d m^{3} x e^{6} + 31038 \, {\left(x e + d\right)}^{m} d m^{2} x^{2} e^{6} - 1680 \, {\left(x e + d\right)}^{m} d m x^{3} e^{6} - 1715 \, {\left(x e + d\right)}^{m} d^{2} m^{3} e^{5} - 26796 \, {\left(x e + d\right)}^{m} d^{2} m^{2} x e^{5} + 2520 \, {\left(x e + d\right)}^{m} d^{2} m x^{2} e^{5} + 7518 \, {\left(x e + d\right)}^{m} d^{3} m^{2} e^{4} - 5040 \, {\left(x e + d\right)}^{m} d^{3} m x e^{4} + 2568 \, {\left(x e + d\right)}^{m} d^{4} m e^{3} + 17136 \, {\left(x e + d\right)}^{m} d^{5} e^{2} + 9990 \, {\left(x e + d\right)}^{m} m^{3} x e^{7} + 27503 \, {\left(x e + d\right)}^{m} m^{2} x^{2} e^{7} + 79716 \, {\left(x e + d\right)}^{m} m x^{3} e^{7} - 5040 \, {\left(x e + d\right)}^{m} x^{4} e^{7} + 9990 \, {\left(x e + d\right)}^{m} d m^{3} e^{6} + 19278 \, {\left(x e + d\right)}^{m} d m^{2} x e^{6} + 17640 \, {\left(x e + d\right)}^{m} d m x^{2} e^{6} - 8225 \, {\left(x e + d\right)}^{m} d^{2} m^{2} e^{5} - 35280 \, {\left(x e + d\right)}^{m} d^{2} m x e^{5} + 26796 \, {\left(x e + d\right)}^{m} d^{3} m e^{4} + 5040 \, {\left(x e + d\right)}^{m} d^{4} e^{3} + 30624 \, {\left(x e + d\right)}^{m} m^{2} x e^{7} + 36918 \, {\left(x e + d\right)}^{m} m x^{2} e^{7} + 35280 \, {\left(x e + d\right)}^{m} x^{3} e^{7} + 30624 \, {\left(x e + d\right)}^{m} d m^{2} e^{6} + 17640 \, {\left(x e + d\right)}^{m} d m x e^{6} - 19278 \, {\left(x e + d\right)}^{m} d^{2} m e^{5} + 35280 \, {\left(x e + d\right)}^{m} d^{3} e^{4} + 48168 \, {\left(x e + d\right)}^{m} m x e^{7} + 17640 \, {\left(x e + d\right)}^{m} x^{2} e^{7} + 48168 \, {\left(x e + d\right)}^{m} d m e^{6} - 17640 \, {\left(x e + d\right)}^{m} d^{2} e^{5} + 30240 \, {\left(x e + d\right)}^{m} x e^{7} + 30240 \, {\left(x e + d\right)}^{m} d e^{6}}{m^{7} e^{7} + 28 \, m^{6} e^{7} + 322 \, m^{5} e^{7} + 1960 \, m^{4} e^{7} + 6769 \, m^{3} e^{7} + 13132 \, m^{2} e^{7} + 13068 \, m e^{7} + 5040 \, e^{7}}"," ",0,"(20*(x*e + d)^m*m^6*x^7*e^7 + 20*(x*e + d)^m*d*m^6*x^6*e^6 - 17*(x*e + d)^m*m^6*x^6*e^7 + 420*(x*e + d)^m*m^5*x^7*e^7 - 17*(x*e + d)^m*d*m^6*x^5*e^6 + 300*(x*e + d)^m*d*m^5*x^6*e^6 - 120*(x*e + d)^m*d^2*m^5*x^5*e^5 + 17*(x*e + d)^m*m^6*x^5*e^7 - 374*(x*e + d)^m*m^5*x^6*e^7 + 3500*(x*e + d)^m*m^4*x^7*e^7 + 17*(x*e + d)^m*d*m^6*x^4*e^6 - 289*(x*e + d)^m*d*m^5*x^5*e^6 + 1700*(x*e + d)^m*d*m^4*x^6*e^6 + 85*(x*e + d)^m*d^2*m^5*x^4*e^5 - 1200*(x*e + d)^m*d^2*m^4*x^5*e^5 + 600*(x*e + d)^m*d^3*m^4*x^4*e^4 - 4*(x*e + d)^m*m^6*x^4*e^7 + 391*(x*e + d)^m*m^5*x^5*e^7 - 3230*(x*e + d)^m*m^4*x^6*e^7 + 14700*(x*e + d)^m*m^3*x^7*e^7 - 4*(x*e + d)^m*d*m^6*x^3*e^6 + 323*(x*e + d)^m*d*m^5*x^4*e^6 - 1785*(x*e + d)^m*d*m^4*x^5*e^6 + 4500*(x*e + d)^m*d*m^3*x^6*e^6 - 68*(x*e + d)^m*d^2*m^5*x^3*e^5 + 1105*(x*e + d)^m*d^2*m^4*x^4*e^5 - 4200*(x*e + d)^m*d^2*m^3*x^5*e^5 - 340*(x*e + d)^m*d^3*m^4*x^3*e^4 + 3600*(x*e + d)^m*d^3*m^3*x^4*e^4 - 2400*(x*e + d)^m*d^4*m^3*x^3*e^3 + 21*(x*e + d)^m*m^6*x^3*e^7 - 96*(x*e + d)^m*m^5*x^4*e^7 + 3519*(x*e + d)^m*m^4*x^5*e^7 - 13940*(x*e + d)^m*m^3*x^6*e^7 + 32480*(x*e + d)^m*m^2*x^7*e^7 + 21*(x*e + d)^m*d*m^6*x^2*e^6 - 84*(x*e + d)^m*d*m^5*x^3*e^6 + 2227*(x*e + d)^m*d*m^4*x^4*e^6 - 5015*(x*e + d)^m*d*m^3*x^5*e^6 + 5480*(x*e + d)^m*d*m^2*x^6*e^6 + 12*(x*e + d)^m*d^2*m^5*x^2*e^5 - 1088*(x*e + d)^m*d^2*m^4*x^3*e^5 + 4505*(x*e + d)^m*d^2*m^3*x^4*e^5 - 6000*(x*e + d)^m*d^2*m^2*x^5*e^5 + 204*(x*e + d)^m*d^3*m^4*x^2*e^4 - 3400*(x*e + d)^m*d^3*m^3*x^3*e^4 + 6600*(x*e + d)^m*d^3*m^2*x^4*e^4 + 1020*(x*e + d)^m*d^4*m^3*x^2*e^3 - 7200*(x*e + d)^m*d^4*m^2*x^3*e^3 + 7200*(x*e + d)^m*d^5*m^2*x^2*e^2 + 7*(x*e + d)^m*m^6*x^2*e^7 + 525*(x*e + d)^m*m^5*x^3*e^7 - 904*(x*e + d)^m*m^4*x^4*e^7 + 15725*(x*e + d)^m*m^3*x^5*e^7 - 31433*(x*e + d)^m*m^2*x^6*e^7 + 35280*(x*e + d)^m*m*x^7*e^7 + 7*(x*e + d)^m*d*m^6*x*e^6 + 483*(x*e + d)^m*d*m^5*x^2*e^6 - 652*(x*e + d)^m*d*m^4*x^3*e^6 + 6817*(x*e + d)^m*d*m^3*x^4*e^6 - 6358*(x*e + d)^m*d*m^2*x^5*e^6 + 2400*(x*e + d)^m*d*m*x^6*e^6 - 42*(x*e + d)^m*d^2*m^5*x*e^5 + 228*(x*e + d)^m*d^2*m^4*x^2*e^5 - 5644*(x*e + d)^m*d^2*m^3*x^3*e^5 + 7055*(x*e + d)^m*d^2*m^2*x^4*e^5 - 2880*(x*e + d)^m*d^2*m*x^5*e^5 - 24*(x*e + d)^m*d^3*m^4*x*e^4 + 2856*(x*e + d)^m*d^3*m^3*x^2*e^4 - 7820*(x*e + d)^m*d^3*m^2*x^3*e^4 + 3600*(x*e + d)^m*d^3*m*x^4*e^4 - 408*(x*e + d)^m*d^4*m^3*x*e^3 + 8160*(x*e + d)^m*d^4*m^2*x^2*e^3 - 4800*(x*e + d)^m*d^4*m*x^3*e^3 - 2040*(x*e + d)^m*d^5*m^2*x*e^2 + 7200*(x*e + d)^m*d^5*m*x^2*e^2 - 14400*(x*e + d)^m*d^6*m*x*e + 6*(x*e + d)^m*m^6*x*e^7 + 182*(x*e + d)^m*m^5*x^2*e^7 + 5187*(x*e + d)^m*m^4*x^3*e^7 - 4224*(x*e + d)^m*m^3*x^4*e^7 + 36448*(x*e + d)^m*m^2*x^5*e^7 - 34646*(x*e + d)^m*m*x^6*e^7 + 14400*(x*e + d)^m*x^7*e^7 + 6*(x*e + d)^m*d*m^6*e^6 + 175*(x*e + d)^m*d*m^5*x*e^6 + 4221*(x*e + d)^m*d*m^4*x^2*e^6 - 2268*(x*e + d)^m*d*m^3*x^3*e^6 + 9180*(x*e + d)^m*d*m^2*x^4*e^6 - 2856*(x*e + d)^m*d*m*x^5*e^6 - 7*(x*e + d)^m*d^2*m^5*e^5 - 924*(x*e + d)^m*d^2*m^4*x*e^5 + 1500*(x*e + d)^m*d^2*m^3*x^2*e^5 - 10336*(x*e + d)^m*d^2*m^2*x^3*e^5 + 3570*(x*e + d)^m*d^2*m*x^4*e^5 + 42*(x*e + d)^m*d^3*m^4*e^4 - 432*(x*e + d)^m*d^3*m^3*x*e^4 + 11220*(x*e + d)^m*d^3*m^2*x^2*e^4 - 4760*(x*e + d)^m*d^3*m*x^3*e^4 + 24*(x*e + d)^m*d^4*m^3*e^3 - 5304*(x*e + d)^m*d^4*m^2*x*e^3 + 7140*(x*e + d)^m*d^4*m*x^2*e^3 + 408*(x*e + d)^m*d^5*m^2*e^2 - 14280*(x*e + d)^m*d^5*m*x*e^2 + 2040*(x*e + d)^m*d^6*m*e + 14400*(x*e + d)^m*d^7 + 162*(x*e + d)^m*m^5*x*e^7 + 1890*(x*e + d)^m*m^4*x^2*e^7 + 25599*(x*e + d)^m*m^3*x^3*e^7 - 10180*(x*e + d)^m*m^2*x^4*e^7 + 41004*(x*e + d)^m*m*x^5*e^7 - 14280*(x*e + d)^m*x^6*e^7 + 162*(x*e + d)^m*d*m^5*e^6 + 1715*(x*e + d)^m*d*m^4*x*e^6 + 17157*(x*e + d)^m*d*m^3*x^2*e^6 - 3376*(x*e + d)^m*d*m^2*x^3*e^6 + 4284*(x*e + d)^m*d*m*x^4*e^6 - 175*(x*e + d)^m*d^2*m^4*e^5 - 7518*(x*e + d)^m*d^2*m^3*x*e^5 + 3804*(x*e + d)^m*d^2*m^2*x^2*e^5 - 5712*(x*e + d)^m*d^2*m*x^3*e^5 + 924*(x*e + d)^m*d^3*m^3*e^4 - 2568*(x*e + d)^m*d^3*m^2*x*e^4 + 8568*(x*e + d)^m*d^3*m*x^2*e^4 + 432*(x*e + d)^m*d^4*m^2*e^3 - 17136*(x*e + d)^m*d^4*m*x*e^3 + 5304*(x*e + d)^m*d^5*m*e^2 + 14280*(x*e + d)^m*d^6*e + 1770*(x*e + d)^m*m^4*x*e^7 + 9940*(x*e + d)^m*m^3*x^2*e^7 + 65352*(x*e + d)^m*m^2*x^3*e^7 - 11808*(x*e + d)^m*m*x^4*e^7 + 17136*(x*e + d)^m*x^5*e^7 + 1770*(x*e + d)^m*d*m^4*e^6 + 8225*(x*e + d)^m*d*m^3*x*e^6 + 31038*(x*e + d)^m*d*m^2*x^2*e^6 - 1680*(x*e + d)^m*d*m*x^3*e^6 - 1715*(x*e + d)^m*d^2*m^3*e^5 - 26796*(x*e + d)^m*d^2*m^2*x*e^5 + 2520*(x*e + d)^m*d^2*m*x^2*e^5 + 7518*(x*e + d)^m*d^3*m^2*e^4 - 5040*(x*e + d)^m*d^3*m*x*e^4 + 2568*(x*e + d)^m*d^4*m*e^3 + 17136*(x*e + d)^m*d^5*e^2 + 9990*(x*e + d)^m*m^3*x*e^7 + 27503*(x*e + d)^m*m^2*x^2*e^7 + 79716*(x*e + d)^m*m*x^3*e^7 - 5040*(x*e + d)^m*x^4*e^7 + 9990*(x*e + d)^m*d*m^3*e^6 + 19278*(x*e + d)^m*d*m^2*x*e^6 + 17640*(x*e + d)^m*d*m*x^2*e^6 - 8225*(x*e + d)^m*d^2*m^2*e^5 - 35280*(x*e + d)^m*d^2*m*x*e^5 + 26796*(x*e + d)^m*d^3*m*e^4 + 5040*(x*e + d)^m*d^4*e^3 + 30624*(x*e + d)^m*m^2*x*e^7 + 36918*(x*e + d)^m*m*x^2*e^7 + 35280*(x*e + d)^m*x^3*e^7 + 30624*(x*e + d)^m*d*m^2*e^6 + 17640*(x*e + d)^m*d*m*x*e^6 - 19278*(x*e + d)^m*d^2*m*e^5 + 35280*(x*e + d)^m*d^3*e^4 + 48168*(x*e + d)^m*m*x*e^7 + 17640*(x*e + d)^m*x^2*e^7 + 48168*(x*e + d)^m*d*m*e^6 - 17640*(x*e + d)^m*d^2*e^5 + 30240*(x*e + d)^m*x*e^7 + 30240*(x*e + d)^m*d*e^6)/(m^7*e^7 + 28*m^6*e^7 + 322*m^5*e^7 + 1960*m^4*e^7 + 6769*m^3*e^7 + 13132*m^2*e^7 + 13068*m*e^7 + 5040*e^7)","B",0
370,0,0,0,0.000000," ","integrate((e*x+d)^m*(4*x^4-5*x^3+3*x^2+x+2)/(5*x^2+2*x+3),x, algorithm=""giac"")","\int \frac{{\left(4 \, x^{4} - 5 \, x^{3} + 3 \, x^{2} + x + 2\right)} {\left(e x + d\right)}^{m}}{5 \, x^{2} + 2 \, x + 3}\,{d x}"," ",0,"integrate((4*x^4 - 5*x^3 + 3*x^2 + x + 2)*(e*x + d)^m/(5*x^2 + 2*x + 3), x)","F",0
371,0,0,0,0.000000," ","integrate((e*x+d)^m*(4*x^4-5*x^3+3*x^2+x+2)/(5*x^2+2*x+3)^2,x, algorithm=""giac"")","\int \frac{{\left(4 \, x^{4} - 5 \, x^{3} + 3 \, x^{2} + x + 2\right)} {\left(e x + d\right)}^{m}}{{\left(5 \, x^{2} + 2 \, x + 3\right)}^{2}}\,{d x}"," ",0,"integrate((4*x^4 - 5*x^3 + 3*x^2 + x + 2)*(e*x + d)^m/(5*x^2 + 2*x + 3)^2, x)","F",0
372,1,657,0,0.220284," ","integrate((i*x^5+h*x^4+g*x^3+f*x^2+e*x+d)/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{{\left(12 \, c^{5} d i + 2 \, b^{2} c^{3} f i + 4 \, a c^{4} f i - 6 \, a b c^{3} g i + 12 \, a^{2} c^{3} h i - 6 \, b c^{4} i e + b^{5} - 10 \, a b^{3} c + 30 \, a^{2} b c^{2}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{4} c^{3} i - 8 \, a b^{2} c^{4} i + 16 \, a^{2} c^{5} i\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{i \log\left(c x^{2} + b x + a\right)}{2 \, c^{3}} - \frac{b^{3} c^{3} d - 10 \, a b c^{4} d - 6 \, a^{2} b c^{3} f + a^{2} b^{2} c^{2} g + 8 \, a^{3} c^{3} g + a^{2} b^{3} c h - 10 \, a^{3} b c^{2} h - 3 \, a^{2} b^{4} i + 21 \, a^{3} b^{2} c i - 24 \, a^{4} c^{2} i + a b^{2} c^{3} e + 8 \, a^{2} c^{4} e - 2 \, {\left(6 \, c^{6} d + b^{2} c^{4} f + 2 \, a c^{5} f - 3 \, a b c^{4} g - b^{4} c^{2} h + 8 \, a b^{2} c^{3} h - 10 \, a^{2} c^{4} h + 2 \, b^{5} c i - 15 \, a b^{3} c^{2} i + 25 \, a^{2} b c^{3} i - 3 \, b c^{5} e\right)} x^{3} - {\left(18 \, b c^{5} d + 3 \, b^{3} c^{3} f + 6 \, a b c^{4} f - b^{4} c^{2} g - a b^{2} c^{3} g - 16 \, a^{2} c^{4} g - b^{5} c h + 8 \, a b^{3} c^{2} h + 2 \, a^{2} b c^{3} h + 3 \, b^{6} i - 19 \, a b^{4} c i + 11 \, a^{2} b^{2} c^{2} i + 32 \, a^{3} c^{3} i - 9 \, b^{2} c^{4} e\right)} x^{2} - 2 \, {\left(2 \, b^{2} c^{4} d + 10 \, a c^{5} d + 5 \, a b^{2} c^{3} f - 2 \, a^{2} c^{4} f - a b^{3} c^{2} g - 5 \, a^{2} b c^{3} g - a b^{4} c h + 10 \, a^{2} b^{2} c^{2} h - 6 \, a^{3} c^{3} h + 3 \, a b^{5} i - 22 \, a^{2} b^{3} c i + 31 \, a^{3} b c^{2} i - b^{3} c^{3} e - 5 \, a b c^{4} e\right)} x}{2 \, {\left(c x^{2} + b x + a\right)}^{2} {\left(b^{2} - 4 \, a c\right)}^{2} c^{3}}"," ",0,"(12*c^5*d*i + 2*b^2*c^3*f*i + 4*a*c^4*f*i - 6*a*b*c^3*g*i + 12*a^2*c^3*h*i - 6*b*c^4*i*e + b^5 - 10*a*b^3*c + 30*a^2*b*c^2)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^4*c^3*i - 8*a*b^2*c^4*i + 16*a^2*c^5*i)*sqrt(-b^2 + 4*a*c)) + 1/2*i*log(c*x^2 + b*x + a)/c^3 - 1/2*(b^3*c^3*d - 10*a*b*c^4*d - 6*a^2*b*c^3*f + a^2*b^2*c^2*g + 8*a^3*c^3*g + a^2*b^3*c*h - 10*a^3*b*c^2*h - 3*a^2*b^4*i + 21*a^3*b^2*c*i - 24*a^4*c^2*i + a*b^2*c^3*e + 8*a^2*c^4*e - 2*(6*c^6*d + b^2*c^4*f + 2*a*c^5*f - 3*a*b*c^4*g - b^4*c^2*h + 8*a*b^2*c^3*h - 10*a^2*c^4*h + 2*b^5*c*i - 15*a*b^3*c^2*i + 25*a^2*b*c^3*i - 3*b*c^5*e)*x^3 - (18*b*c^5*d + 3*b^3*c^3*f + 6*a*b*c^4*f - b^4*c^2*g - a*b^2*c^3*g - 16*a^2*c^4*g - b^5*c*h + 8*a*b^3*c^2*h + 2*a^2*b*c^3*h + 3*b^6*i - 19*a*b^4*c*i + 11*a^2*b^2*c^2*i + 32*a^3*c^3*i - 9*b^2*c^4*e)*x^2 - 2*(2*b^2*c^4*d + 10*a*c^5*d + 5*a*b^2*c^3*f - 2*a^2*c^4*f - a*b^3*c^2*g - 5*a^2*b*c^3*g - a*b^4*c*h + 10*a^2*b^2*c^2*h - 6*a^3*c^3*h + 3*a*b^5*i - 22*a^2*b^3*c*i + 31*a^3*b*c^2*i - b^3*c^3*e - 5*a*b*c^4*e)*x)/((c*x^2 + b*x + a)^2*(b^2 - 4*a*c)^2*c^3)","A",0
373,1,982,0,0.177015," ","integrate((m*x^8+l*x^7+k*x^6+j*x^5+h*x^4+g*x^3+f*x^2+e*x+d)/(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{60 \, c^{6} m x^{7} + 70 \, c^{6} l x^{6} - 70 \, b c^{5} m x^{6} + 84 \, c^{6} k x^{5} - 84 \, b c^{5} l x^{5} + 84 \, b^{2} c^{4} m x^{5} - 84 \, a c^{5} m x^{5} + 105 \, c^{6} j x^{4} - 105 \, b c^{5} k x^{4} + 105 \, b^{2} c^{4} l x^{4} - 105 \, a c^{5} l x^{4} - 105 \, b^{3} c^{3} m x^{4} + 210 \, a b c^{4} m x^{4} + 140 \, c^{6} h x^{3} - 140 \, b c^{5} j x^{3} + 140 \, b^{2} c^{4} k x^{3} - 140 \, a c^{5} k x^{3} - 140 \, b^{3} c^{3} l x^{3} + 280 \, a b c^{4} l x^{3} + 140 \, b^{4} c^{2} m x^{3} - 420 \, a b^{2} c^{3} m x^{3} + 140 \, a^{2} c^{4} m x^{3} + 210 \, c^{6} g x^{2} - 210 \, b c^{5} h x^{2} + 210 \, b^{2} c^{4} j x^{2} - 210 \, a c^{5} j x^{2} - 210 \, b^{3} c^{3} k x^{2} + 420 \, a b c^{4} k x^{2} + 210 \, b^{4} c^{2} l x^{2} - 630 \, a b^{2} c^{3} l x^{2} + 210 \, a^{2} c^{4} l x^{2} - 210 \, b^{5} c m x^{2} + 840 \, a b^{3} c^{2} m x^{2} - 630 \, a^{2} b c^{3} m x^{2} + 420 \, c^{6} f x - 420 \, b c^{5} g x + 420 \, b^{2} c^{4} h x - 420 \, a c^{5} h x - 420 \, b^{3} c^{3} j x + 840 \, a b c^{4} j x + 420 \, b^{4} c^{2} k x - 1260 \, a b^{2} c^{3} k x + 420 \, a^{2} c^{4} k x - 420 \, b^{5} c l x + 1680 \, a b^{3} c^{2} l x - 1260 \, a^{2} b c^{3} l x + 420 \, b^{6} m x - 2100 \, a b^{4} c m x + 2520 \, a^{2} b^{2} c^{2} m x - 420 \, a^{3} c^{3} m x}{420 \, c^{7}} - \frac{{\left(b c^{6} f - b^{2} c^{5} g + a c^{6} g + b^{3} c^{4} h - 2 \, a b c^{5} h - b^{4} c^{3} j + 3 \, a b^{2} c^{4} j - a^{2} c^{5} j + b^{5} c^{2} k - 4 \, a b^{3} c^{3} k + 3 \, a^{2} b c^{4} k - b^{6} c l + 5 \, a b^{4} c^{2} l - 6 \, a^{2} b^{2} c^{3} l + a^{3} c^{4} l + b^{7} m - 6 \, a b^{5} c m + 10 \, a^{2} b^{3} c^{2} m - 4 \, a^{3} b c^{3} m - c^{7} e\right)} \log\left(c x^{2} + b x + a\right)}{2 \, c^{8}} + \frac{{\left(2 \, c^{8} d + b^{2} c^{6} f - 2 \, a c^{7} f - b^{3} c^{5} g + 3 \, a b c^{6} g + b^{4} c^{4} h - 4 \, a b^{2} c^{5} h + 2 \, a^{2} c^{6} h - b^{5} c^{3} j + 5 \, a b^{3} c^{4} j - 5 \, a^{2} b c^{5} j + b^{6} c^{2} k - 6 \, a b^{4} c^{3} k + 9 \, a^{2} b^{2} c^{4} k - 2 \, a^{3} c^{5} k - b^{7} c l + 7 \, a b^{5} c^{2} l - 14 \, a^{2} b^{3} c^{3} l + 7 \, a^{3} b c^{4} l + b^{8} m - 8 \, a b^{6} c m + 20 \, a^{2} b^{4} c^{2} m - 16 \, a^{3} b^{2} c^{3} m + 2 \, a^{4} c^{4} m - b c^{7} e\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c} c^{8}}"," ",0,"1/420*(60*c^6*m*x^7 + 70*c^6*l*x^6 - 70*b*c^5*m*x^6 + 84*c^6*k*x^5 - 84*b*c^5*l*x^5 + 84*b^2*c^4*m*x^5 - 84*a*c^5*m*x^5 + 105*c^6*j*x^4 - 105*b*c^5*k*x^4 + 105*b^2*c^4*l*x^4 - 105*a*c^5*l*x^4 - 105*b^3*c^3*m*x^4 + 210*a*b*c^4*m*x^4 + 140*c^6*h*x^3 - 140*b*c^5*j*x^3 + 140*b^2*c^4*k*x^3 - 140*a*c^5*k*x^3 - 140*b^3*c^3*l*x^3 + 280*a*b*c^4*l*x^3 + 140*b^4*c^2*m*x^3 - 420*a*b^2*c^3*m*x^3 + 140*a^2*c^4*m*x^3 + 210*c^6*g*x^2 - 210*b*c^5*h*x^2 + 210*b^2*c^4*j*x^2 - 210*a*c^5*j*x^2 - 210*b^3*c^3*k*x^2 + 420*a*b*c^4*k*x^2 + 210*b^4*c^2*l*x^2 - 630*a*b^2*c^3*l*x^2 + 210*a^2*c^4*l*x^2 - 210*b^5*c*m*x^2 + 840*a*b^3*c^2*m*x^2 - 630*a^2*b*c^3*m*x^2 + 420*c^6*f*x - 420*b*c^5*g*x + 420*b^2*c^4*h*x - 420*a*c^5*h*x - 420*b^3*c^3*j*x + 840*a*b*c^4*j*x + 420*b^4*c^2*k*x - 1260*a*b^2*c^3*k*x + 420*a^2*c^4*k*x - 420*b^5*c*l*x + 1680*a*b^3*c^2*l*x - 1260*a^2*b*c^3*l*x + 420*b^6*m*x - 2100*a*b^4*c*m*x + 2520*a^2*b^2*c^2*m*x - 420*a^3*c^3*m*x)/c^7 - 1/2*(b*c^6*f - b^2*c^5*g + a*c^6*g + b^3*c^4*h - 2*a*b*c^5*h - b^4*c^3*j + 3*a*b^2*c^4*j - a^2*c^5*j + b^5*c^2*k - 4*a*b^3*c^3*k + 3*a^2*b*c^4*k - b^6*c*l + 5*a*b^4*c^2*l - 6*a^2*b^2*c^3*l + a^3*c^4*l + b^7*m - 6*a*b^5*c*m + 10*a^2*b^3*c^2*m - 4*a^3*b*c^3*m - c^7*e)*log(c*x^2 + b*x + a)/c^8 + (2*c^8*d + b^2*c^6*f - 2*a*c^7*f - b^3*c^5*g + 3*a*b*c^6*g + b^4*c^4*h - 4*a*b^2*c^5*h + 2*a^2*c^6*h - b^5*c^3*j + 5*a*b^3*c^4*j - 5*a^2*b*c^5*j + b^6*c^2*k - 6*a*b^4*c^3*k + 9*a^2*b^2*c^4*k - 2*a^3*c^5*k - b^7*c*l + 7*a*b^5*c^2*l - 14*a^2*b^3*c^3*l + 7*a^3*b*c^4*l + b^8*m - 8*a*b^6*c*m + 20*a^2*b^4*c^2*m - 16*a^3*b^2*c^3*m + 2*a^4*c^4*m - b*c^7*e)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c^8)","A",0
374,1,92,0,0.210090," ","integrate((-7*x^2+4*x+1)^3*(x^2+5*x+2)*(5*x^2+2*x+3)^(1/2),x, algorithm=""giac"")","-\frac{1}{1968750000} \, {\left(5 \, {\left({\left(5 \, {\left(10 \, {\left(25 \, {\left(5 \, {\left(49 \, {\left(140 \, {\left(315 \, x + 1157\right)} x - 324959\right)} x - 1109589\right)} x + 36147578\right)} x + 227029652\right)} x + 705695691\right)} x - 15767809359\right)} x - 11553600930\right)} x + 93436408944\right)} \sqrt{5 \, x^{2} + 2 \, x + 3} + \frac{540119881}{78125000} \, \sqrt{5} \log\left(-\sqrt{5} {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)} - 1\right)"," ",0,"-1/1968750000*(5*((5*(10*(25*(5*(49*(140*(315*x + 1157)*x - 324959)*x - 1109589)*x + 36147578)*x + 227029652)*x + 705695691)*x - 15767809359)*x - 11553600930)*x + 93436408944)*sqrt(5*x^2 + 2*x + 3) + 540119881/78125000*sqrt(5)*log(-sqrt(5)*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3)) - 1)","A",0
375,1,82,0,0.203140," ","integrate((-7*x^2+4*x+1)^2*(x^2+5*x+2)*(5*x^2+2*x+3)^(1/2),x, algorithm=""giac"")","\frac{1}{3750000} \, {\left(5 \, {\left({\left(5 \, {\left(10 \, {\left(25 \, {\left(15 \, {\left(245 \, x + 1087\right)} x - 17138\right)} x - 262772\right)} x + 623349\right)} x + 4706399\right)} x + 8866730\right)} x - 4588584\right)} \sqrt{5 \, x^{2} + 2 \, x + 3} + \frac{17652061}{3125000} \, \sqrt{5} \log\left(-\sqrt{5} {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)} - 1\right)"," ",0,"1/3750000*(5*((5*(10*(25*(15*(245*x + 1087)*x - 17138)*x - 262772)*x + 623349)*x + 4706399)*x + 8866730)*x - 4588584)*sqrt(5*x^2 + 2*x + 3) + 17652061/3125000*sqrt(5)*log(-sqrt(5)*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3)) - 1)","A",0
376,1,72,0,0.189174," ","integrate((-7*x^2+4*x+1)*(x^2+5*x+2)*(5*x^2+2*x+3)^(1/2),x, algorithm=""giac"")","-\frac{1}{37500} \, {\left(5 \, {\left({\left(5 \, {\left(10 \, {\left(175 \, x + 937\right)} x - 1929\right)} x - 25979\right)} x - 21080\right)} x - 103386\right)} \sqrt{5 \, x^{2} + 2 \, x + 3} + \frac{32431}{31250} \, \sqrt{5} \log\left(-\sqrt{5} {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)} - 1\right)"," ",0,"-1/37500*(5*((5*(10*(175*x + 937)*x - 1929)*x - 25979)*x - 21080)*x - 103386)*sqrt(5*x^2 + 2*x + 3) + 32431/31250*sqrt(5)*log(-sqrt(5)*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3)) - 1)","A",0
377,1,144,0,0.265052," ","integrate((x^2+5*x+2)*(5*x^2+2*x+3)^(1/2)/(-7*x^2+4*x+1),x, algorithm=""giac"")","-\frac{1}{490} \, \sqrt{5 \, x^{2} + 2 \, x + 3} {\left(35 \, x + 397\right)} + \frac{8233}{8575} \, \sqrt{5} \log\left(-5 \, \sqrt{5} x - \sqrt{5} + 5 \, \sqrt{5 \, x^{2} + 2 \, x + 3}\right) + 2.61475869687464 \, \log\left(-\sqrt{5} x + \sqrt{5 \, x^{2} + 2 \, x + 3} + 4.41924736459000\right) - 0.276245077121866 \, \log\left(-\sqrt{5} x + \sqrt{5 \, x^{2} + 2 \, x + 3} + 1.25295163054000\right) - 2.61475869687464 \, \log\left(-\sqrt{5} x + \sqrt{5 \, x^{2} + 2 \, x + 3} - 1.02258038113000\right) + 0.276245077121866 \, \log\left(-\sqrt{5} x + \sqrt{5 \, x^{2} + 2 \, x + 3} - 2.09411235400000\right)"," ",0,"-1/490*sqrt(5*x^2 + 2*x + 3)*(35*x + 397) + 8233/8575*sqrt(5)*log(-5*sqrt(5)*x - sqrt(5) + 5*sqrt(5*x^2 + 2*x + 3)) + 2.61475869687464*log(-sqrt(5)*x + sqrt(5*x^2 + 2*x + 3) + 4.41924736459000) - 0.276245077121866*log(-sqrt(5)*x + sqrt(5*x^2 + 2*x + 3) + 1.25295163054000) - 2.61475869687464*log(-sqrt(5)*x + sqrt(5*x^2 + 2*x + 3) - 1.02258038113000) + 0.276245077121866*log(-sqrt(5)*x + sqrt(5*x^2 + 2*x + 3) - 2.09411235400000)","A",0
378,-2,0,0,0.000000," ","integrate((x^2+5*x+2)*(5*x^2+2*x+3)^(1/2)/(-7*x^2+4*x+1)^2,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{184473632,[8]%%%}+%%%{%%{[421654016,0]:[1,0,-5]%%},[7]%%%}+%%%{-2484746880,[6]%%%}+%%%{%%{[-5059848192,0]:[1,0,-5]%%},[5]%%%}+%%%{18003120576,[4]%%%}+%%%{%%{[13432692224,0]:[1,0,-5]%%},[3]%%%}+%%%{-38927701120,[2]%%%}+%%%{%%{[-9999223808,0]:[1,0,-5]%%},[1]%%%}+%%%{25935486752,[0]%%%} / %%%{245,[8]%%%}+%%%{%%{poly1[560,0]:[1,0,-5]%%},[7]%%%}+%%%{-3300,[6]%%%}+%%%{%%{poly1[-6720,0]:[1,0,-5]%%},[5]%%%}+%%%{23910,[4]%%%}+%%%{%%{poly1[17840,0]:[1,0,-5]%%},[3]%%%}+%%%{-51700,[2]%%%}+%%%{%%{poly1[-13280,0]:[1,0,-5]%%},[1]%%%}+%%%{34445,[0]%%%} Error: Bad Argument Value","F(-2)",0
379,1,378,0,0.262116," ","integrate((x^2+5*x+2)*(5*x^2+2*x+3)^(1/2)/(-7*x^2+4*x+1)^3,x, algorithm=""giac"")","\frac{6200558 \, {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)}^{7} - 835775 \, \sqrt{5} {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)}^{6} - 190947036 \, {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)}^{5} - 92732607 \, \sqrt{5} {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)}^{4} + 816321374 \, {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)}^{3} + 419437335 \, \sqrt{5} {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)}^{2} - 765111048 \, \sqrt{5} x - 376983161 \, \sqrt{5} + 765111048 \, \sqrt{5 \, x^{2} + 2 \, x + 3}}{430276 \, {\left(7 \, {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)}^{4} - 8 \, \sqrt{5} {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)}^{3} - 70 \, {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)}^{2} + 16 \, \sqrt{5} {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)} + 83\right)}^{2}} + 0.139051039089329 \, \log\left(-\sqrt{5} x + \sqrt{5 \, x^{2} + 2 \, x + 3} + 4.41924736459000\right) - 0.138209741946100 \, \log\left(-\sqrt{5} x + \sqrt{5 \, x^{2} + 2 \, x + 3} + 1.25295163054000\right) - 0.139051039089329 \, \log\left(-\sqrt{5} x + \sqrt{5 \, x^{2} + 2 \, x + 3} - 1.02258038113000\right) + 0.138209741946100 \, \log\left(-\sqrt{5} x + \sqrt{5 \, x^{2} + 2 \, x + 3} - 2.09411235400000\right)"," ",0,"1/430276*(6200558*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3))^7 - 835775*sqrt(5)*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3))^6 - 190947036*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3))^5 - 92732607*sqrt(5)*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3))^4 + 816321374*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3))^3 + 419437335*sqrt(5)*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3))^2 - 765111048*sqrt(5)*x - 376983161*sqrt(5) + 765111048*sqrt(5*x^2 + 2*x + 3))/(7*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3))^4 - 8*sqrt(5)*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3))^3 - 70*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3))^2 + 16*sqrt(5)*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3)) + 83)^2 + 0.139051039089329*log(-sqrt(5)*x + sqrt(5*x^2 + 2*x + 3) + 4.41924736459000) - 0.138209741946100*log(-sqrt(5)*x + sqrt(5*x^2 + 2*x + 3) + 1.25295163054000) - 0.139051039089329*log(-sqrt(5)*x + sqrt(5*x^2 + 2*x + 3) - 1.02258038113000) + 0.138209741946100*log(-sqrt(5)*x + sqrt(5*x^2 + 2*x + 3) - 2.09411235400000)","B",0
380,1,102,0,0.234902," ","integrate((-7*x^2+4*x+1)^3*(x^2+5*x+2)*(5*x^2+2*x+3)^(3/2),x, algorithm=""giac"")","-\frac{1}{216562500000} \, {\left(5 \, {\left({\left(5 \, {\left(10 \, {\left(25 \, {\left(5 \, {\left(7 \, {\left(20 \, {\left(105 \, {\left(875 \, {\left(77 \, x + 311\right)} x - 323034\right)} x - 6972676\right)} x - 333340559\right)} x + 1667418573\right)} x + 13620853454\right)} x - 10292359564\right)} x - 761667529587\right)} x - 3173168881737\right)} x - 1270555425990\right)} x + 10506617068392\right)} \sqrt{5 \, x^{2} + 2 \, x + 3} + \frac{3357568053}{781250000} \, \sqrt{5} \log\left(-\sqrt{5} {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)} - 1\right)"," ",0,"-1/216562500000*(5*((5*(10*(25*(5*(7*(20*(105*(875*(77*x + 311)*x - 323034)*x - 6972676)*x - 333340559)*x + 1667418573)*x + 13620853454)*x - 10292359564)*x - 761667529587)*x - 3173168881737)*x - 1270555425990)*x + 10506617068392)*sqrt(5*x^2 + 2*x + 3) + 3357568053/781250000*sqrt(5)*log(-sqrt(5)*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3)) - 1)","A",0
381,1,92,0,0.215705," ","integrate((-7*x^2+4*x+1)^2*(x^2+5*x+2)*(5*x^2+2*x+3)^(3/2),x, algorithm=""giac"")","\frac{1}{131250000} \, {\left(5 \, {\left({\left(5 \, {\left(10 \, {\left(25 \, {\left(5 \, {\left(7 \, {\left(140 \, {\left(105 \, x + 499\right)} x - 25423\right)} x - 131379\right)} x - 2008682\right)} x - 12910388\right)} x + 238374621\right)} x + 744208071\right)} x + 458335170\right)} x - 249003936\right)} \sqrt{5 \, x^{2} + 2 \, x + 3} + \frac{101512467}{15625000} \, \sqrt{5} \log\left(-\sqrt{5} {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)} - 1\right)"," ",0,"1/131250000*(5*((5*(10*(25*(5*(7*(140*(105*x + 499)*x - 25423)*x - 131379)*x - 2008682)*x - 12910388)*x + 238374621)*x + 744208071)*x + 458335170)*x - 249003936)*sqrt(5*x^2 + 2*x + 3) + 101512467/15625000*sqrt(5)*log(-sqrt(5)*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3)) - 1)","A",0
382,1,82,0,0.203584," ","integrate((-7*x^2+4*x+1)*(x^2+5*x+2)*(5*x^2+2*x+3)^(3/2),x, algorithm=""giac"")","-\frac{1}{5250000} \, {\left(5 \, {\left({\left(5 \, {\left(10 \, {\left(25 \, {\left(15 \, {\left(245 \, x + 1359\right)} x + 7718\right)} x + 113492\right)} x - 3144339\right)} x - 17292889\right)} x - 7339030\right)} x - 22275576\right)} \sqrt{5 \, x^{2} + 2 \, x + 3} + \frac{901453}{625000} \, \sqrt{5} \log\left(-\sqrt{5} {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)} - 1\right)"," ",0,"-1/5250000*(5*((5*(10*(25*(15*(245*x + 1359)*x + 7718)*x + 113492)*x - 3144339)*x - 17292889)*x - 7339030)*x - 22275576)*sqrt(5*x^2 + 2*x + 3) + 901453/625000*sqrt(5)*log(-sqrt(5)*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3)) - 1)","A",0
383,1,154,0,0.281679," ","integrate((x^2+5*x+2)*(5*x^2+2*x+3)^(3/2)/(-7*x^2+4*x+1),x, algorithm=""giac"")","-\frac{1}{240100} \, {\left(35 \, {\left(35 \, {\left(35 \, x + 281\right)} x + 21282\right)} x + 1911108\right)} \sqrt{5 \, x^{2} + 2 \, x + 3} + \frac{34425687}{4201750} \, \sqrt{5} \log\left(-5 \, \sqrt{5} x - \sqrt{5} + 5 \, \sqrt{5 \, x^{2} + 2 \, x + 3}\right) + 19.3580321168561 \, \log\left(-\sqrt{5} x + \sqrt{5 \, x^{2} + 2 \, x + 3} + 4.41924736459000\right) - 0.773682164624264 \, \log\left(-\sqrt{5} x + \sqrt{5 \, x^{2} + 2 \, x + 3} + 1.25295163054000\right) - 19.3580321168561 \, \log\left(-\sqrt{5} x + \sqrt{5 \, x^{2} + 2 \, x + 3} - 1.02258038113000\right) + 0.773682164625454 \, \log\left(-\sqrt{5} x + \sqrt{5 \, x^{2} + 2 \, x + 3} - 2.09411235400000\right)"," ",0,"-1/240100*(35*(35*(35*x + 281)*x + 21282)*x + 1911108)*sqrt(5*x^2 + 2*x + 3) + 34425687/4201750*sqrt(5)*log(-5*sqrt(5)*x - sqrt(5) + 5*sqrt(5*x^2 + 2*x + 3)) + 19.3580321168561*log(-sqrt(5)*x + sqrt(5*x^2 + 2*x + 3) + 4.41924736459000) - 0.773682164624264*log(-sqrt(5)*x + sqrt(5*x^2 + 2*x + 3) + 1.25295163054000) - 19.3580321168561*log(-sqrt(5)*x + sqrt(5*x^2 + 2*x + 3) - 1.02258038113000) + 0.773682164625454*log(-sqrt(5)*x + sqrt(5*x^2 + 2*x + 3) - 2.09411235400000)","A",0
384,-2,0,0,0.000000," ","integrate((x^2+5*x+2)*(5*x^2+2*x+3)^(3/2)/(-7*x^2+4*x+1)^2,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{63274455776,[8]%%%}+%%%{%%{[144627327488,0]:[1,0,-5]%%},[7]%%%}+%%%{-852268179840,[6]%%%}+%%%{%%{[-1735527929856,0]:[1,0,-5]%%},[5]%%%}+%%%{6175070357568,[4]%%%}+%%%{%%{[4607413432832,0]:[1,0,-5]%%},[3]%%%}+%%%{-13352201484160,[2]%%%}+%%%{%%{[-3429733766144,0]:[1,0,-5]%%},[1]%%%}+%%%{8895871955936,[0]%%%} / %%%{245,[8]%%%}+%%%{%%{poly1[560,0]:[1,0,-5]%%},[7]%%%}+%%%{-3300,[6]%%%}+%%%{%%{poly1[-6720,0]:[1,0,-5]%%},[5]%%%}+%%%{23910,[4]%%%}+%%%{%%{poly1[17840,0]:[1,0,-5]%%},[3]%%%}+%%%{-51700,[2]%%%}+%%%{%%{poly1[-13280,0]:[1,0,-5]%%},[1]%%%}+%%%{34445,[0]%%%} Error: Bad Argument Value","F(-2)",0
385,-2,0,0,0.000000," ","integrate((x^2+5*x+2)*(5*x^2+2*x+3)^(3/2)/(-7*x^2+4*x+1)^3,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{-1771684761728,[12]%%%}+%%%{%%{[-6074347754496,0]:[1,0,-5]%%},[11]%%%}+%%%{18439984254720,[10]%%%}+%%%{%%{[120412580657152,0]:[1,0,-5]%%},[9]%%%}+%%%{-108578966111616,[8]%%%}+%%%{%%{[-915119084156928,0]:[1,0,-5]%%},[7]%%%}+%%%{1093279290575360,[6]%%%}+%%%{%%{[2784778529734656,0]:[1,0,-5]%%},[5]%%%}+%%%{-4014694487954304,[4]%%%}+%%%{%%{[-3629195511796736,0]:[1,0,-5]%%},[3]%%%}+%%%{5826260235237120,[2]%%%}+%%%{%%{[1708007415539712,0]:[1,0,-5]%%},[1]%%%}+%%%{-2953429489370752,[0]%%%} / %%%{%%{[1715,0]:[1,0,-5]%%},[12]%%%}+%%%{29400,[11]%%%}+%%%{%%{[-17850,0]:[1,0,-5]%%},[10]%%%}+%%%{-582800,[9]%%%}+%%%{%%{[105105,0]:[1,0,-5]%%},[8]%%%}+%%%{4429200,[7]%%%}+%%%{%%{[-1058300,0]:[1,0,-5]%%},[6]%%%}+%%%{-13478400,[5]%%%}+%%%{%%{[3886245,0]:[1,0,-5]%%},[4]%%%}+%%%{17565400,[3]%%%}+%%%{%%{[-5639850,0]:[1,0,-5]%%},[2]%%%}+%%%{-8266800,[1]%%%}+%%%{%%{[2858935,0]:[1,0,-5]%%},[0]%%%} Error: Bad Argument Value","F(-2)",0
386,1,82,0,0.245281," ","integrate((-7*x^2+4*x+1)^3*(x^2+5*x+2)/(5*x^2+2*x+3)^(1/2),x, algorithm=""giac"")","-\frac{1}{3750000} \, {\left(5 \, {\left({\left(5 \, {\left(10 \, {\left(175 \, {\left(15 \, {\left(49 \, x + 163\right)} x - 7474\right)} x + 191228\right)} x + 15481599\right)} x - 40722851\right)} x - 57930770\right)} x + 396379416\right)} \sqrt{5 \, x^{2} + 2 \, x + 3} + \frac{77513689}{3125000} \, \sqrt{5} \log\left(-\sqrt{5} {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)} - 1\right)"," ",0,"-1/3750000*(5*((5*(10*(175*(15*(49*x + 163)*x - 7474)*x + 191228)*x + 15481599)*x - 40722851)*x - 57930770)*x + 396379416)*sqrt(5*x^2 + 2*x + 3) + 77513689/3125000*sqrt(5)*log(-sqrt(5)*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3)) - 1)","A",0
387,1,72,0,0.391819," ","integrate((-7*x^2+4*x+1)^2*(x^2+5*x+2)/(5*x^2+2*x+3)^(1/2),x, algorithm=""giac"")","\frac{1}{187500} \, {\left(5 \, {\left({\left(5 \, {\left(70 \, {\left(175 \, x + 733\right)} x - 99777\right)} x - 207427\right)} x + 721460\right)} x - 132318\right)} \sqrt{5 \, x^{2} + 2 \, x + 3} + \frac{1719097}{156250} \, \sqrt{5} \log\left(-\sqrt{5} {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)} - 1\right)"," ",0,"1/187500*(5*((5*(70*(175*x + 733)*x - 99777)*x - 207427)*x + 721460)*x - 132318)*sqrt(5*x^2 + 2*x + 3) + 1719097/156250*sqrt(5)*log(-sqrt(5)*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3)) - 1)","A",0
388,1,62,0,0.219711," ","integrate((-7*x^2+4*x+1)*(x^2+5*x+2)/(5*x^2+2*x+3)^(1/2),x, algorithm=""giac"")","-\frac{1}{1500} \, {\left(5 \, {\left({\left(105 \, x + 571\right)} x - 590\right)} x - 5556\right)} \sqrt{5 \, x^{2} + 2 \, x + 3} + \frac{1901}{1250} \, \sqrt{5} \log\left(-\sqrt{5} {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)} - 1\right)"," ",0,"-1/1500*(5*((105*x + 571)*x - 590)*x - 5556)*sqrt(5*x^2 + 2*x + 3) + 1901/1250*sqrt(5)*log(-sqrt(5)*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3)) - 1)","A",0
389,1,125,0,0.274760," ","integrate((x^2+5*x+2)/(-7*x^2+4*x+1)/(5*x^2+2*x+3)^(1/2),x, algorithm=""giac"")","\frac{1}{35} \, \sqrt{5} \log\left(-5 \, \sqrt{5} x - \sqrt{5} + 5 \, \sqrt{5 \, x^{2} + 2 \, x + 3}\right) + 0.353184817631429 \, \log\left(-\sqrt{5} x + \sqrt{5 \, x^{2} + 2 \, x + 3} + 4.41924736459000\right) - 0.0986339689905714 \, \log\left(-\sqrt{5} x + \sqrt{5 \, x^{2} + 2 \, x + 3} + 1.25295163054000\right) - 0.353184817631429 \, \log\left(-\sqrt{5} x + \sqrt{5 \, x^{2} + 2 \, x + 3} - 1.02258038113000\right) + 0.0986339689905714 \, \log\left(-\sqrt{5} x + \sqrt{5 \, x^{2} + 2 \, x + 3} - 2.09411235400000\right)"," ",0,"1/35*sqrt(5)*log(-5*sqrt(5)*x - sqrt(5) + 5*sqrt(5*x^2 + 2*x + 3)) + 0.353184817631429*log(-sqrt(5)*x + sqrt(5*x^2 + 2*x + 3) + 4.41924736459000) - 0.0986339689905714*log(-sqrt(5)*x + sqrt(5*x^2 + 2*x + 3) + 1.25295163054000) - 0.353184817631429*log(-sqrt(5)*x + sqrt(5*x^2 + 2*x + 3) - 1.02258038113000) + 0.0986339689905714*log(-sqrt(5)*x + sqrt(5*x^2 + 2*x + 3) - 2.09411235400000)","A",0
390,1,276,0,0.278651," ","integrate((x^2+5*x+2)/(-7*x^2+4*x+1)^2/(5*x^2+2*x+3)^(1/2),x, algorithm=""giac"")","\frac{3 \, {\left(1231 \, {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)}^{3} + 1735 \, \sqrt{5} {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)}^{2} - 3913 \, \sqrt{5} x - 3989 \, \sqrt{5} + 3913 \, \sqrt{5 \, x^{2} + 2 \, x + 3}\right)}}{2794 \, {\left(7 \, {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)}^{4} - 8 \, \sqrt{5} {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)}^{3} - 70 \, {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)}^{2} + 16 \, \sqrt{5} {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)} + 83\right)}} + 0.0924287071106453 \, \log\left(-\sqrt{5} x + \sqrt{5 \, x^{2} + 2 \, x + 3} + 4.41924736459000\right) - 0.0938608034604765 \, \log\left(-\sqrt{5} x + \sqrt{5 \, x^{2} + 2 \, x + 3} + 1.25295163054000\right) - 0.0924287071106453 \, \log\left(-\sqrt{5} x + \sqrt{5 \, x^{2} + 2 \, x + 3} - 1.02258038113000\right) + 0.0938608034604765 \, \log\left(-\sqrt{5} x + \sqrt{5 \, x^{2} + 2 \, x + 3} - 2.09411235400000\right)"," ",0,"3/2794*(1231*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3))^3 + 1735*sqrt(5)*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3))^2 - 3913*sqrt(5)*x - 3989*sqrt(5) + 3913*sqrt(5*x^2 + 2*x + 3))/(7*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3))^4 - 8*sqrt(5)*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3))^3 - 70*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3))^2 + 16*sqrt(5)*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3)) + 83) + 0.0924287071106453*log(-sqrt(5)*x + sqrt(5*x^2 + 2*x + 3) + 4.41924736459000) - 0.0938608034604765*log(-sqrt(5)*x + sqrt(5*x^2 + 2*x + 3) + 1.25295163054000) - 0.0924287071106453*log(-sqrt(5)*x + sqrt(5*x^2 + 2*x + 3) - 1.02258038113000) + 0.0938608034604765*log(-sqrt(5)*x + sqrt(5*x^2 + 2*x + 3) - 2.09411235400000)","B",0
391,1,378,0,0.321858," ","integrate((x^2+5*x+2)/(-7*x^2+4*x+1)^3/(5*x^2+2*x+3)^(1/2),x, algorithm=""giac"")","\frac{124397525 \, {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)}^{7} + 26796567 \, \sqrt{5} {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)}^{6} - 3595807617 \, {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)}^{5} - 1719888775 \, \sqrt{5} {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)}^{4} + 17096132999 \, {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)}^{3} + 8328401413 \, \sqrt{5} {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)}^{2} - 16383202915 \, \sqrt{5} x - 7800623485 \, \sqrt{5} + 16383202915 \, \sqrt{5 \, x^{2} + 2 \, x + 3}}{31225744 \, {\left(7 \, {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)}^{4} - 8 \, \sqrt{5} {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)}^{3} - 70 \, {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)}^{2} + 16 \, \sqrt{5} {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)} + 83\right)}^{2}} + 0.0423989586659649 \, \log\left(-\sqrt{5} x + \sqrt{5 \, x^{2} + 2 \, x + 3} + 4.41924736459000\right) - 0.0446437606656958 \, \log\left(-\sqrt{5} x + \sqrt{5 \, x^{2} + 2 \, x + 3} + 1.25295163054000\right) - 0.0423989586659649 \, \log\left(-\sqrt{5} x + \sqrt{5 \, x^{2} + 2 \, x + 3} - 1.02258038113000\right) + 0.0446437606656958 \, \log\left(-\sqrt{5} x + \sqrt{5 \, x^{2} + 2 \, x + 3} - 2.09411235400000\right)"," ",0,"1/31225744*(124397525*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3))^7 + 26796567*sqrt(5)*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3))^6 - 3595807617*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3))^5 - 1719888775*sqrt(5)*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3))^4 + 17096132999*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3))^3 + 8328401413*sqrt(5)*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3))^2 - 16383202915*sqrt(5)*x - 7800623485*sqrt(5) + 16383202915*sqrt(5*x^2 + 2*x + 3))/(7*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3))^4 - 8*sqrt(5)*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3))^3 - 70*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3))^2 + 16*sqrt(5)*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3)) + 83)^2 + 0.0423989586659649*log(-sqrt(5)*x + sqrt(5*x^2 + 2*x + 3) + 4.41924736459000) - 0.0446437606656958*log(-sqrt(5)*x + sqrt(5*x^2 + 2*x + 3) + 1.25295163054000) - 0.0423989586659649*log(-sqrt(5)*x + sqrt(5*x^2 + 2*x + 3) - 1.02258038113000) + 0.0446437606656958*log(-sqrt(5)*x + sqrt(5*x^2 + 2*x + 3) - 2.09411235400000)","B",0
392,1,81,0,0.260870," ","integrate((-7*x^2+4*x+1)^3*(x^2+5*x+2)/(5*x^2+2*x+3)^(3/2),x, algorithm=""giac"")","-\frac{50047657}{781250} \, \sqrt{5} \log\left(-\sqrt{5} {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)} - 1\right) - \frac{{\left(35 \, {\left({\left(5 \, {\left(35 \, {\left(70 \, {\left(175 \, x + 599\right)} x - 146549\right)} x + 998969\right)} x + 51303971\right)} x - 61004099\right)} x + 1045703388\right)} x - 3155769618}{6562500 \, \sqrt{5 \, x^{2} + 2 \, x + 3}}"," ",0,"-50047657/781250*sqrt(5)*log(-sqrt(5)*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3)) - 1) - 1/6562500*((35*((5*(35*(70*(175*x + 599)*x - 146549)*x + 998969)*x + 51303971)*x - 61004099)*x + 1045703388)*x - 3155769618)/sqrt(5*x^2 + 2*x + 3)","A",0
393,1,71,0,0.247806," ","integrate((-7*x^2+4*x+1)^2*(x^2+5*x+2)/(5*x^2+2*x+3)^(3/2),x, algorithm=""giac"")","-\frac{89583}{6250} \, \sqrt{5} \log\left(-\sqrt{5} {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)} - 1\right) + \frac{{\left(35 \, {\left({\left(35 \, {\left(35 \, x + 159\right)} x - 14733\right)} x - 8023\right)} x - 1298674\right)} x - 168536}{17500 \, \sqrt{5 \, x^{2} + 2 \, x + 3}}"," ",0,"-89583/6250*sqrt(5)*log(-sqrt(5)*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3)) - 1) + 1/17500*((35*((35*(35*x + 159)*x - 14733)*x - 8023)*x - 1298674)*x - 168536)/sqrt(5*x^2 + 2*x + 3)","A",0
394,1,62,0,0.215060," ","integrate((-7*x^2+4*x+1)*(x^2+5*x+2)/(5*x^2+2*x+3)^(3/2),x, algorithm=""giac"")","-\frac{149}{125} \, \sqrt{5} \log\left(-\sqrt{5} {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)} - 1\right) - \frac{{\left(35 \, {\left(7 \, x + 55\right)} x + 2837\right)} x + 2953}{350 \, \sqrt{5 \, x^{2} + 2 \, x + 3}}"," ",0,"-149/125*sqrt(5)*log(-sqrt(5)*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3)) - 1) - 1/350*((35*(7*x + 55)*x + 2837)*x + 2953)/sqrt(5*x^2 + 2*x + 3)","A",0
395,1,112,0,0.247997," ","integrate((x^2+5*x+2)/(-7*x^2+4*x+1)/(5*x^2+2*x+3)^(3/2),x, algorithm=""giac"")","\frac{605 \, x - 131}{3556 \, \sqrt{5 \, x^{2} + 2 \, x + 3}} + 0.0477059376663667 \, \log\left(-\sqrt{5} x + \sqrt{5 \, x^{2} + 2 \, x + 3} + 4.41924736459000\right) - 0.0352174957838020 \, \log\left(-\sqrt{5} x + \sqrt{5 \, x^{2} + 2 \, x + 3} + 1.25295163054000\right) - 0.0477059376663667 \, \log\left(-\sqrt{5} x + \sqrt{5 \, x^{2} + 2 \, x + 3} - 1.02258038113000\right) + 0.0352174957838020 \, \log\left(-\sqrt{5} x + \sqrt{5 \, x^{2} + 2 \, x + 3} - 2.09411235400000\right)"," ",0,"1/3556*(605*x - 131)/sqrt(5*x^2 + 2*x + 3) + 0.0477059376663667*log(-sqrt(5)*x + sqrt(5*x^2 + 2*x + 3) + 4.41924736459000) - 0.0352174957838020*log(-sqrt(5)*x + sqrt(5*x^2 + 2*x + 3) + 1.25295163054000) - 0.0477059376663667*log(-sqrt(5)*x + sqrt(5*x^2 + 2*x + 3) - 1.02258038113000) + 0.0352174957838020*log(-sqrt(5)*x + sqrt(5*x^2 + 2*x + 3) - 2.09411235400000)","A",0
396,1,295,0,0.274781," ","integrate((x^2+5*x+2)/(-7*x^2+4*x+1)^2/(5*x^2+2*x+3)^(3/2),x, algorithm=""giac"")","\frac{25230 \, x + 13397}{903224 \, \sqrt{5 \, x^{2} + 2 \, x + 3}} + \frac{3 \, {\left(42623 \, {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)}^{3} + 77302 \, \sqrt{5} {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)}^{2} - 275511 \, \sqrt{5} x - 219860 \, \sqrt{5} + 275511 \, \sqrt{5 \, x^{2} + 2 \, x + 3}\right)}}{709676 \, {\left(7 \, {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)}^{4} - 8 \, \sqrt{5} {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)}^{3} - 70 \, {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)}^{2} + 16 \, \sqrt{5} {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)} + 83\right)}} + 0.0218058276254033 \, \log\left(-\sqrt{5} x + \sqrt{5 \, x^{2} + 2 \, x + 3} + 4.41924736459000\right) - 0.0332874364433911 \, \log\left(-\sqrt{5} x + \sqrt{5 \, x^{2} + 2 \, x + 3} + 1.25295163054000\right) - 0.0218058276254033 \, \log\left(-\sqrt{5} x + \sqrt{5 \, x^{2} + 2 \, x + 3} - 1.02258038113000\right) + 0.0332874364433911 \, \log\left(-\sqrt{5} x + \sqrt{5 \, x^{2} + 2 \, x + 3} - 2.09411235400000\right)"," ",0,"1/903224*(25230*x + 13397)/sqrt(5*x^2 + 2*x + 3) + 3/709676*(42623*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3))^3 + 77302*sqrt(5)*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3))^2 - 275511*sqrt(5)*x - 219860*sqrt(5) + 275511*sqrt(5*x^2 + 2*x + 3))/(7*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3))^4 - 8*sqrt(5)*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3))^3 - 70*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3))^2 + 16*sqrt(5)*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3)) + 83) + 0.0218058276254033*log(-sqrt(5)*x + sqrt(5*x^2 + 2*x + 3) + 4.41924736459000) - 0.0332874364433911*log(-sqrt(5)*x + sqrt(5*x^2 + 2*x + 3) + 1.25295163054000) - 0.0218058276254033*log(-sqrt(5)*x + sqrt(5*x^2 + 2*x + 3) - 1.02258038113000) + 0.0332874364433911*log(-sqrt(5)*x + sqrt(5*x^2 + 2*x + 3) - 2.09411235400000)","A",0
397,1,397,0,0.323050," ","integrate((x^2+5*x+2)/(-7*x^2+4*x+1)^3/(5*x^2+2*x+3)^(3/2),x, algorithm=""giac"")","\frac{501205 \, x + 1702037}{458837792 \, \sqrt{5 \, x^{2} + 2 \, x + 3}} + \frac{6871871279 \, {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)}^{7} + 4012856750 \, \sqrt{5} {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)}^{6} - 223088535693 \, {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)}^{5} - 100577598176 \, \sqrt{5} {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)}^{4} + 1255097956673 \, {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)}^{3} + 566810398070 \, \sqrt{5} {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)}^{2} - 1246245909011 \, \sqrt{5} x - 561299654796 \, \sqrt{5} + 1246245909011 \, \sqrt{5 \, x^{2} + 2 \, x + 3}}{7931338976 \, {\left(7 \, {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)}^{4} - 8 \, \sqrt{5} {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)}^{3} - 70 \, {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)}^{2} + 16 \, \sqrt{5} {\left(\sqrt{5} x - \sqrt{5 \, x^{2} + 2 \, x + 3}\right)} + 83\right)}^{2}} + 0.0107382277384513 \, \log\left(-\sqrt{5} x + \sqrt{5 \, x^{2} + 2 \, x + 3} + 4.41924736459000\right) - 0.0142619066316905 \, \log\left(-\sqrt{5} x + \sqrt{5 \, x^{2} + 2 \, x + 3} + 1.25295163054000\right) - 0.0107382277384513 \, \log\left(-\sqrt{5} x + \sqrt{5 \, x^{2} + 2 \, x + 3} - 1.02258038113000\right) + 0.0142619066316905 \, \log\left(-\sqrt{5} x + \sqrt{5 \, x^{2} + 2 \, x + 3} - 2.09411235400000\right)"," ",0,"1/458837792*(501205*x + 1702037)/sqrt(5*x^2 + 2*x + 3) + 1/7931338976*(6871871279*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3))^7 + 4012856750*sqrt(5)*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3))^6 - 223088535693*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3))^5 - 100577598176*sqrt(5)*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3))^4 + 1255097956673*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3))^3 + 566810398070*sqrt(5)*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3))^2 - 1246245909011*sqrt(5)*x - 561299654796*sqrt(5) + 1246245909011*sqrt(5*x^2 + 2*x + 3))/(7*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3))^4 - 8*sqrt(5)*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3))^3 - 70*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3))^2 + 16*sqrt(5)*(sqrt(5)*x - sqrt(5*x^2 + 2*x + 3)) + 83)^2 + 0.0107382277384513*log(-sqrt(5)*x + sqrt(5*x^2 + 2*x + 3) + 4.41924736459000) - 0.0142619066316905*log(-sqrt(5)*x + sqrt(5*x^2 + 2*x + 3) + 1.25295163054000) - 0.0107382277384513*log(-sqrt(5)*x + sqrt(5*x^2 + 2*x + 3) - 1.02258038113000) + 0.0142619066316905*log(-sqrt(5)*x + sqrt(5*x^2 + 2*x + 3) - 2.09411235400000)","B",0
398,0,0,0,0.000000," ","integrate((c*x^2+a)^p*(C*x^2+A)*(f*x^2+d)^q,x, algorithm=""giac"")","\int {\left(C x^{2} + A\right)} {\left(c x^{2} + a\right)}^{p} {\left(f x^{2} + d\right)}^{q}\,{d x}"," ",0,"integrate((C*x^2 + A)*(c*x^2 + a)^p*(f*x^2 + d)^q, x)","F",0
399,0,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+a)^p*(f*x^2+d)^q,x, algorithm=""giac"")","\int {\left(B x + A\right)} {\left(c x^{2} + a\right)}^{p} {\left(f x^{2} + d\right)}^{q}\,{d x}"," ",0,"integrate((B*x + A)*(c*x^2 + a)^p*(f*x^2 + d)^q, x)","F",0
400,0,0,0,0.000000," ","integrate((c*x^2+a)^p*(C*x^2+B*x+A)*(f*x^2+d)^q,x, algorithm=""giac"")","\int {\left(C x^{2} + B x + A\right)} {\left(c x^{2} + a\right)}^{p} {\left(f x^{2} + d\right)}^{q}\,{d x}"," ",0,"integrate((C*x^2 + B*x + A)*(c*x^2 + a)^p*(f*x^2 + d)^q, x)","F",0
