1,1,959,391,0.035000," ","int((f*x+e)^3*(C*x^2+B*x+A)*(-d*x+1)^(1/2)*(d*x+1)^(1/2),x)","\frac{\sqrt{-d x +1}\, \sqrt{d x +1}\, \left(240 \sqrt{-d^{2} x^{2}+1}\, C \,d^{6} f^{3} x^{6} \mathrm{csgn}\left(d \right)+280 \sqrt{-d^{2} x^{2}+1}\, B \,d^{6} f^{3} x^{5} \mathrm{csgn}\left(d \right)+840 \sqrt{-d^{2} x^{2}+1}\, C \,d^{6} e \,f^{2} x^{5} \mathrm{csgn}\left(d \right)+336 \sqrt{-d^{2} x^{2}+1}\, A \,d^{6} f^{3} x^{4} \mathrm{csgn}\left(d \right)+1008 \sqrt{-d^{2} x^{2}+1}\, B \,d^{6} e \,f^{2} x^{4} \mathrm{csgn}\left(d \right)+1008 \sqrt{-d^{2} x^{2}+1}\, C \,d^{6} e^{2} f \,x^{4} \mathrm{csgn}\left(d \right)+1260 \sqrt{-d^{2} x^{2}+1}\, A \,d^{6} e \,f^{2} x^{3} \mathrm{csgn}\left(d \right)+1260 \sqrt{-d^{2} x^{2}+1}\, B \,d^{6} e^{2} f \,x^{3} \mathrm{csgn}\left(d \right)+420 \sqrt{-d^{2} x^{2}+1}\, C \,d^{6} e^{3} x^{3} \mathrm{csgn}\left(d \right)+1680 \sqrt{-d^{2} x^{2}+1}\, A \,d^{6} e^{2} f \,x^{2} \mathrm{csgn}\left(d \right)+560 \sqrt{-d^{2} x^{2}+1}\, B \,d^{6} e^{3} x^{2} \mathrm{csgn}\left(d \right)-48 \sqrt{-d^{2} x^{2}+1}\, C \,d^{4} f^{3} x^{4} \mathrm{csgn}\left(d \right)+840 \sqrt{-d^{2} x^{2}+1}\, A \,d^{6} e^{3} x \,\mathrm{csgn}\left(d \right)-70 \sqrt{-d^{2} x^{2}+1}\, B \,d^{4} f^{3} x^{3} \mathrm{csgn}\left(d \right)-210 \sqrt{-d^{2} x^{2}+1}\, C \,d^{4} e \,f^{2} x^{3} \mathrm{csgn}\left(d \right)-112 \sqrt{-d^{2} x^{2}+1}\, A \,d^{4} f^{3} x^{2} \mathrm{csgn}\left(d \right)-336 \sqrt{-d^{2} x^{2}+1}\, B \,d^{4} e \,f^{2} x^{2} \mathrm{csgn}\left(d \right)-336 \sqrt{-d^{2} x^{2}+1}\, C \,d^{4} e^{2} f \,x^{2} \mathrm{csgn}\left(d \right)+840 A \,d^{5} e^{3} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)-630 \sqrt{-d^{2} x^{2}+1}\, A \,d^{4} e \,f^{2} x \,\mathrm{csgn}\left(d \right)-630 \sqrt{-d^{2} x^{2}+1}\, B \,d^{4} e^{2} f x \,\mathrm{csgn}\left(d \right)-210 \sqrt{-d^{2} x^{2}+1}\, C \,d^{4} e^{3} x \,\mathrm{csgn}\left(d \right)-1680 \sqrt{-d^{2} x^{2}+1}\, A \,d^{4} e^{2} f \,\mathrm{csgn}\left(d \right)-560 \sqrt{-d^{2} x^{2}+1}\, B \,d^{4} e^{3} \mathrm{csgn}\left(d \right)-64 \sqrt{-d^{2} x^{2}+1}\, C \,d^{2} f^{3} x^{2} \mathrm{csgn}\left(d \right)+630 A \,d^{3} e \,f^{2} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)+630 B \,d^{3} e^{2} f \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)-105 \sqrt{-d^{2} x^{2}+1}\, B \,d^{2} f^{3} x \,\mathrm{csgn}\left(d \right)+210 C \,d^{3} e^{3} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)-315 \sqrt{-d^{2} x^{2}+1}\, C \,d^{2} e \,f^{2} x \,\mathrm{csgn}\left(d \right)-224 \sqrt{-d^{2} x^{2}+1}\, A \,d^{2} f^{3} \mathrm{csgn}\left(d \right)-672 \sqrt{-d^{2} x^{2}+1}\, B \,d^{2} e \,f^{2} \mathrm{csgn}\left(d \right)-672 \sqrt{-d^{2} x^{2}+1}\, C \,d^{2} e^{2} f \,\mathrm{csgn}\left(d \right)+105 B d \,f^{3} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)+315 C d e \,f^{2} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)-128 \sqrt{-d^{2} x^{2}+1}\, C \,f^{3} \mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)}{1680 \sqrt{-d^{2} x^{2}+1}\, d^{6}}"," ",0,"1/1680*(-d*x+1)^(1/2)*(d*x+1)^(1/2)*(-128*C*csgn(d)*(-d^2*x^2+1)^(1/2)*f^3+840*A*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))*d^5*e^3+210*C*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))*d^3*e^3+105*B*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))*d*f^3-560*B*csgn(d)*(-d^2*x^2+1)^(1/2)*d^4*e^3-224*A*csgn(d)*(-d^2*x^2+1)^(1/2)*d^2*f^3+630*A*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))*d^3*e*f^2+630*B*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))*d^3*e^2*f+315*C*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))*d*e*f^2+336*A*csgn(d)*x^4*d^6*f^3*(-d^2*x^2+1)^(1/2)+420*C*csgn(d)*x^3*d^6*e^3*(-d^2*x^2+1)^(1/2)+560*B*csgn(d)*x^2*d^6*e^3*(-d^2*x^2+1)^(1/2)-48*C*csgn(d)*(-d^2*x^2+1)^(1/2)*x^4*d^4*f^3-70*B*csgn(d)*(-d^2*x^2+1)^(1/2)*x^3*d^4*f^3-112*A*csgn(d)*(-d^2*x^2+1)^(1/2)*x^2*d^4*f^3-1680*A*csgn(d)*(-d^2*x^2+1)^(1/2)*d^4*e^2*f-64*C*csgn(d)*(-d^2*x^2+1)^(1/2)*x^2*d^2*f^3+840*A*csgn(d)*(-d^2*x^2+1)^(1/2)*x*d^6*e^3-210*C*csgn(d)*(-d^2*x^2+1)^(1/2)*x*d^4*e^3-105*B*csgn(d)*(-d^2*x^2+1)^(1/2)*x*d^2*f^3-672*B*csgn(d)*(-d^2*x^2+1)^(1/2)*d^2*e*f^2-672*C*csgn(d)*(-d^2*x^2+1)^(1/2)*d^2*e^2*f+240*C*csgn(d)*x^6*d^6*f^3*(-d^2*x^2+1)^(1/2)+280*B*csgn(d)*x^5*d^6*f^3*(-d^2*x^2+1)^(1/2)-630*A*csgn(d)*(-d^2*x^2+1)^(1/2)*x*d^4*e*f^2-630*B*csgn(d)*(-d^2*x^2+1)^(1/2)*x*d^4*e^2*f-315*C*csgn(d)*(-d^2*x^2+1)^(1/2)*x*d^2*e*f^2+840*C*csgn(d)*x^5*d^6*e*f^2*(-d^2*x^2+1)^(1/2)+1008*B*csgn(d)*x^4*d^6*e*f^2*(-d^2*x^2+1)^(1/2)+1008*C*csgn(d)*x^4*d^6*e^2*f*(-d^2*x^2+1)^(1/2)+1260*A*csgn(d)*x^3*d^6*e*f^2*(-d^2*x^2+1)^(1/2)+1260*B*csgn(d)*x^3*d^6*e^2*f*(-d^2*x^2+1)^(1/2)+1680*A*csgn(d)*x^2*d^6*e^2*f*(-d^2*x^2+1)^(1/2)-210*C*csgn(d)*(-d^2*x^2+1)^(1/2)*x^3*d^4*e*f^2-336*B*csgn(d)*(-d^2*x^2+1)^(1/2)*x^2*d^4*e*f^2-336*C*csgn(d)*(-d^2*x^2+1)^(1/2)*x^2*d^4*e^2*f)*csgn(d)/d^6/(-d^2*x^2+1)^(1/2)","C"
2,1,652,266,0.018000," ","int((f*x+e)^2*(C*x^2+B*x+A)*(-d*x+1)^(1/2)*(d*x+1)^(1/2),x)","\frac{\sqrt{-d x +1}\, \sqrt{d x +1}\, \left(40 \sqrt{-d^{2} x^{2}+1}\, C \,d^{5} f^{2} x^{5} \mathrm{csgn}\left(d \right)+48 \sqrt{-d^{2} x^{2}+1}\, B \,d^{5} f^{2} x^{4} \mathrm{csgn}\left(d \right)+96 \sqrt{-d^{2} x^{2}+1}\, C \,d^{5} e f \,x^{4} \mathrm{csgn}\left(d \right)+60 \sqrt{-d^{2} x^{2}+1}\, A \,d^{5} f^{2} x^{3} \mathrm{csgn}\left(d \right)+120 \sqrt{-d^{2} x^{2}+1}\, B \,d^{5} e f \,x^{3} \mathrm{csgn}\left(d \right)+60 \sqrt{-d^{2} x^{2}+1}\, C \,d^{5} e^{2} x^{3} \mathrm{csgn}\left(d \right)+160 \sqrt{-d^{2} x^{2}+1}\, A \,d^{5} e f \,x^{2} \mathrm{csgn}\left(d \right)+80 \sqrt{-d^{2} x^{2}+1}\, B \,d^{5} e^{2} x^{2} \mathrm{csgn}\left(d \right)+120 \sqrt{-d^{2} x^{2}+1}\, A \,d^{5} e^{2} x \,\mathrm{csgn}\left(d \right)-10 \sqrt{-d^{2} x^{2}+1}\, C \,d^{3} f^{2} x^{3} \mathrm{csgn}\left(d \right)-16 \sqrt{-d^{2} x^{2}+1}\, B \,d^{3} f^{2} x^{2} \mathrm{csgn}\left(d \right)-32 \sqrt{-d^{2} x^{2}+1}\, C \,d^{3} e f \,x^{2} \mathrm{csgn}\left(d \right)+120 A \,d^{4} e^{2} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)-30 \sqrt{-d^{2} x^{2}+1}\, A \,d^{3} f^{2} x \,\mathrm{csgn}\left(d \right)-60 \sqrt{-d^{2} x^{2}+1}\, B \,d^{3} e f x \,\mathrm{csgn}\left(d \right)-30 \sqrt{-d^{2} x^{2}+1}\, C \,d^{3} e^{2} x \,\mathrm{csgn}\left(d \right)-160 \sqrt{-d^{2} x^{2}+1}\, A \,d^{3} e f \,\mathrm{csgn}\left(d \right)-80 \sqrt{-d^{2} x^{2}+1}\, B \,d^{3} e^{2} \mathrm{csgn}\left(d \right)+30 A \,d^{2} f^{2} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)+60 B \,d^{2} e f \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)+30 C \,d^{2} e^{2} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)-15 \sqrt{-d^{2} x^{2}+1}\, C d \,f^{2} x \,\mathrm{csgn}\left(d \right)-32 \sqrt{-d^{2} x^{2}+1}\, B d \,f^{2} \mathrm{csgn}\left(d \right)-64 \sqrt{-d^{2} x^{2}+1}\, C d e f \,\mathrm{csgn}\left(d \right)+15 C \,f^{2} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)\right) \mathrm{csgn}\left(d \right)}{240 \sqrt{-d^{2} x^{2}+1}\, d^{5}}"," ",0,"1/240*(-d*x+1)^(1/2)*(d*x+1)^(1/2)*(-160*A*csgn(d)*d^3*(-d^2*x^2+1)^(1/2)*e*f-64*C*csgn(d)*d*(-d^2*x^2+1)^(1/2)*e*f+40*C*csgn(d)*x^5*d^5*f^2*(-d^2*x^2+1)^(1/2)+48*B*csgn(d)*x^4*d^5*f^2*(-d^2*x^2+1)^(1/2)+60*A*csgn(d)*x^3*d^5*f^2*(-d^2*x^2+1)^(1/2)+60*C*csgn(d)*x^3*d^5*e^2*(-d^2*x^2+1)^(1/2)+30*A*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))*d^2*f^2+30*C*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))*d^2*e^2+120*A*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))*d^4*e^2+15*C*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))*f^2+60*B*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))*d^2*e*f+80*B*csgn(d)*x^2*d^5*e^2*(-d^2*x^2+1)^(1/2)-32*B*csgn(d)*d*(-d^2*x^2+1)^(1/2)*f^2-80*B*csgn(d)*d^3*(-d^2*x^2+1)^(1/2)*e^2-10*C*csgn(d)*d^3*(-d^2*x^2+1)^(1/2)*x^3*f^2-16*B*csgn(d)*d^3*(-d^2*x^2+1)^(1/2)*x^2*f^2-30*C*csgn(d)*d^3*(-d^2*x^2+1)^(1/2)*x*e^2-30*A*csgn(d)*d^3*(-d^2*x^2+1)^(1/2)*x*f^2+120*A*csgn(d)*d^5*(-d^2*x^2+1)^(1/2)*x*e^2-15*C*csgn(d)*d*(-d^2*x^2+1)^(1/2)*x*f^2+160*A*csgn(d)*x^2*d^5*e*f*(-d^2*x^2+1)^(1/2)-60*B*csgn(d)*d^3*(-d^2*x^2+1)^(1/2)*x*e*f-32*C*csgn(d)*d^3*(-d^2*x^2+1)^(1/2)*x^2*e*f+96*C*csgn(d)*x^4*d^5*e*f*(-d^2*x^2+1)^(1/2)+120*B*csgn(d)*x^3*d^5*e*f*(-d^2*x^2+1)^(1/2))*csgn(d)/(-d^2*x^2+1)^(1/2)/d^5","C"
3,1,377,151,0.013000," ","int((f*x+e)*(C*x^2+B*x+A)*(-d*x+1)^(1/2)*(d*x+1)^(1/2),x)","\frac{\sqrt{-d x +1}\, \sqrt{d x +1}\, \left(24 \sqrt{-d^{2} x^{2}+1}\, C \,d^{4} f \,x^{4} \mathrm{csgn}\left(d \right)+30 \sqrt{-d^{2} x^{2}+1}\, B \,d^{4} f \,x^{3} \mathrm{csgn}\left(d \right)+30 \sqrt{-d^{2} x^{2}+1}\, C \,d^{4} e \,x^{3} \mathrm{csgn}\left(d \right)+40 \sqrt{-d^{2} x^{2}+1}\, A \,d^{4} f \,x^{2} \mathrm{csgn}\left(d \right)+40 \sqrt{-d^{2} x^{2}+1}\, B \,d^{4} e \,x^{2} \mathrm{csgn}\left(d \right)+60 \sqrt{-d^{2} x^{2}+1}\, A \,d^{4} e x \,\mathrm{csgn}\left(d \right)-8 \sqrt{-d^{2} x^{2}+1}\, C \,d^{2} f \,x^{2} \mathrm{csgn}\left(d \right)+60 A \,d^{3} e \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)-15 \sqrt{-d^{2} x^{2}+1}\, B \,d^{2} f x \,\mathrm{csgn}\left(d \right)-15 \sqrt{-d^{2} x^{2}+1}\, C \,d^{2} e x \,\mathrm{csgn}\left(d \right)-40 \sqrt{-d^{2} x^{2}+1}\, A \,d^{2} f \,\mathrm{csgn}\left(d \right)-40 \sqrt{-d^{2} x^{2}+1}\, B \,d^{2} e \,\mathrm{csgn}\left(d \right)+15 B d f \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)+15 C d e \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)-16 \sqrt{-d^{2} x^{2}+1}\, C f \,\mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)}{120 \sqrt{-d^{2} x^{2}+1}\, d^{4}}"," ",0,"1/120*(-d*x+1)^(1/2)*(d*x+1)^(1/2)*(24*C*csgn(d)*x^4*d^4*f*(-d^2*x^2+1)^(1/2)+30*B*csgn(d)*x^3*d^4*f*(-d^2*x^2+1)^(1/2)+30*C*csgn(d)*x^3*d^4*e*(-d^2*x^2+1)^(1/2)+40*A*csgn(d)*x^2*d^4*f*(-d^2*x^2+1)^(1/2)+40*B*csgn(d)*x^2*d^4*e*(-d^2*x^2+1)^(1/2)+60*A*csgn(d)*(-d^2*x^2+1)^(1/2)*x*d^4*e-8*C*csgn(d)*(-d^2*x^2+1)^(1/2)*x^2*d^2*f-15*B*csgn(d)*(-d^2*x^2+1)^(1/2)*x*d^2*f-15*C*csgn(d)*(-d^2*x^2+1)^(1/2)*x*d^2*e-40*A*csgn(d)*(-d^2*x^2+1)^(1/2)*d^2*f+60*A*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))*d^3*e-40*B*csgn(d)*(-d^2*x^2+1)^(1/2)*d^2*e+15*B*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))*d*f-16*C*csgn(d)*(-d^2*x^2+1)^(1/2)*f+15*C*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))*d*e)*csgn(d)/d^4/(-d^2*x^2+1)^(1/2)","C"
4,1,185,81,0.012000," ","int((C*x^2+B*x+A)*(-d*x+1)^(1/2)*(d*x+1)^(1/2),x)","\frac{\sqrt{-d x +1}\, \sqrt{d x +1}\, \left(6 \sqrt{-d^{2} x^{2}+1}\, C \,d^{3} x^{3} \mathrm{csgn}\left(d \right)+8 \sqrt{-d^{2} x^{2}+1}\, B \,d^{3} x^{2} \mathrm{csgn}\left(d \right)+12 \sqrt{-d^{2} x^{2}+1}\, A \,d^{3} x \,\mathrm{csgn}\left(d \right)+12 A \,d^{2} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)-3 \sqrt{-d^{2} x^{2}+1}\, C d x \,\mathrm{csgn}\left(d \right)-8 \sqrt{-d^{2} x^{2}+1}\, B d \,\mathrm{csgn}\left(d \right)+3 C \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)\right) \mathrm{csgn}\left(d \right)}{24 \sqrt{-d^{2} x^{2}+1}\, d^{3}}"," ",0,"1/24*(-d*x+1)^(1/2)*(d*x+1)^(1/2)*(6*C*csgn(d)*x^3*d^3*(-d^2*x^2+1)^(1/2)+8*B*csgn(d)*x^2*d^3*(-d^2*x^2+1)^(1/2)+12*A*csgn(d)*d^3*(-d^2*x^2+1)^(1/2)*x-3*C*csgn(d)*d*(-d^2*x^2+1)^(1/2)*x+12*A*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))*d^2-8*B*(-d^2*x^2+1)^(1/2)*csgn(d)*d+3*C*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d)))*csgn(d)/(-d^2*x^2+1)^(1/2)/d^3","C"
5,1,373,114,0.049000," ","int((C*x^2+B*x+A)/(f*x+e)/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x)","\frac{\left(-A \,d^{2} f^{2} \mathrm{csgn}\left(d \right) \ln \left(\frac{2 d^{2} e x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f +2 f}{f x +e}\right)+B \,d^{2} e f \,\mathrm{csgn}\left(d \right) \ln \left(\frac{2 d^{2} e x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f +2 f}{f x +e}\right)-C \,d^{2} e^{2} \mathrm{csgn}\left(d \right) \ln \left(\frac{2 d^{2} e x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f +2 f}{f x +e}\right)+\sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, B d \,f^{2} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)-\sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, C d e f \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)-\sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, C \,f^{2} \mathrm{csgn}\left(d \right)\right) \sqrt{-d x +1}\, \sqrt{d x +1}\, \mathrm{csgn}\left(d \right)}{\sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, \sqrt{-d^{2} x^{2}+1}\, d^{2} f^{3}}"," ",0,"(-A*csgn(d)*ln(2*(d^2*e*x+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*f+f)/(f*x+e))*d^2*f^2+B*csgn(d)*ln(2*(d^2*e*x+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*f+f)/(f*x+e))*d^2*e*f-C*csgn(d)*ln(2*(d^2*e*x+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*f+f)/(f*x+e))*d^2*e^2+B*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))*d*f^2*(-(d^2*e^2-f^2)/f^2)^(1/2)-C*csgn(d)*f^2*(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)-C*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))*d*e*f*(-(d^2*e^2-f^2)/f^2)^(1/2))*(-d*x+1)^(1/2)*(d*x+1)^(1/2)*csgn(d)/(-(d^2*e^2-f^2)/f^2)^(1/2)/f^3/(-d^2*x^2+1)^(1/2)/d^2","C"
6,1,899,155,0.039000," ","int((C*x^2+B*x+A)/(f*x+e)^2/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x)","\frac{\left(-A \,d^{3} e \,f^{3} x \,\mathrm{csgn}\left(d \right) \ln \left(\frac{2 d^{2} e x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f +2 f}{f x +e}\right)+C \,d^{3} e^{3} f x \,\mathrm{csgn}\left(d \right) \ln \left(\frac{2 d^{2} e x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f +2 f}{f x +e}\right)-A \,d^{3} e^{2} f^{2} \mathrm{csgn}\left(d \right) \ln \left(\frac{2 d^{2} e x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f +2 f}{f x +e}\right)+C \,d^{3} e^{4} \mathrm{csgn}\left(d \right) \ln \left(\frac{2 d^{2} e x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f +2 f}{f x +e}\right)+B d \,f^{4} x \,\mathrm{csgn}\left(d \right) \ln \left(\frac{2 d^{2} e x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f +2 f}{f x +e}\right)+\sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, C \,d^{2} e^{2} f^{2} x \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)-2 C d e \,f^{3} x \,\mathrm{csgn}\left(d \right) \ln \left(\frac{2 d^{2} e x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f +2 f}{f x +e}\right)+B d e \,f^{3} \mathrm{csgn}\left(d \right) \ln \left(\frac{2 d^{2} e x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f +2 f}{f x +e}\right)+\sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, C \,d^{2} e^{3} f \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)-2 C d \,e^{2} f^{2} \mathrm{csgn}\left(d \right) \ln \left(\frac{2 d^{2} e x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f +2 f}{f x +e}\right)+\sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, A d \,f^{4} \mathrm{csgn}\left(d \right)-\sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, B d e \,f^{3} \mathrm{csgn}\left(d \right)+\sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, C d \,e^{2} f^{2} \mathrm{csgn}\left(d \right)-\sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, C \,f^{4} x \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)-\sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, C e \,f^{3} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)\right) \sqrt{d x +1}\, \sqrt{-d x +1}\, \mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}\, \left(d e +f \right) \left(d e -f \right) \left(f x +e \right) \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, d \,f^{3}}"," ",0,"(-A*csgn(d)*ln(2*(d^2*e*x+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*f+f)/(f*x+e))*x*d^3*e*f^3+C*csgn(d)*ln(2*(d^2*e*x+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*f+f)/(f*x+e))*x*d^3*e^3*f-A*csgn(d)*ln(2*(d^2*e*x+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*f+f)/(f*x+e))*d^3*e^2*f^2+C*csgn(d)*ln(2*(d^2*e*x+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*f+f)/(f*x+e))*d^3*e^4+C*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))*x*d^2*e^2*f^2*(-(d^2*e^2-f^2)/f^2)^(1/2)+A*csgn(d)*d*f^4*(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)+B*csgn(d)*ln(2*(d^2*e*x+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*f+f)/(f*x+e))*x*d*f^4-B*csgn(d)*d*e*f^3*(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)-2*C*csgn(d)*ln(2*(d^2*e*x+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*f+f)/(f*x+e))*x*d*e*f^3+C*csgn(d)*d*e^2*f^2*(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)+C*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))*d^2*e^3*f*(-(d^2*e^2-f^2)/f^2)^(1/2)+B*csgn(d)*ln(2*(d^2*e*x+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*f+f)/(f*x+e))*d*e*f^3-2*C*csgn(d)*ln(2*(d^2*e*x+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*f+f)/(f*x+e))*d*e^2*f^2-C*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))*x*f^4*(-(d^2*e^2-f^2)/f^2)^(1/2)-C*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))*e*f^3*(-(d^2*e^2-f^2)/f^2)^(1/2))*csgn(d)*(d*x+1)^(1/2)*(-d*x+1)^(1/2)/(-d^2*x^2+1)^(1/2)/(d*e+f)/d/(d*e-f)/(f*x+e)/(-(d^2*e^2-f^2)/f^2)^(1/2)/f^3","C"
7,1,1449,232,0.050000," ","int((C*x^2+B*x+A)/(f*x+e)^3/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x)","-\frac{\left(2 A \,d^{4} e^{4} \ln \left(\frac{2 d^{2} e x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f +2 f}{f x +e}\right)+C \,d^{2} e^{4} \ln \left(\frac{2 d^{2} e x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f +2 f}{f x +e}\right)+2 C \,f^{4} x^{2} \ln \left(\frac{2 d^{2} e x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f +2 f}{f x +e}\right)+2 C \,e^{2} f^{2} \ln \left(\frac{2 d^{2} e x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f +2 f}{f x +e}\right)+\sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, \sqrt{-d^{2} x^{2}+1}\, A \,f^{4}+2 C \,d^{2} e^{3} f x \ln \left(\frac{2 d^{2} e x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f +2 f}{f x +e}\right)-6 B \,d^{2} e^{2} f^{2} x \ln \left(\frac{2 d^{2} e x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f +2 f}{f x +e}\right)-4 \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, \sqrt{-d^{2} x^{2}+1}\, A \,d^{2} e^{2} f^{2}+2 \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, \sqrt{-d^{2} x^{2}+1}\, B \,d^{2} e^{3} f +2 A \,d^{4} e^{2} f^{2} x^{2} \ln \left(\frac{2 d^{2} e x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f +2 f}{f x +e}\right)+4 A \,d^{4} e^{3} f x \ln \left(\frac{2 d^{2} e x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f +2 f}{f x +e}\right)-3 B \,d^{2} e \,f^{3} x^{2} \ln \left(\frac{2 d^{2} e x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f +2 f}{f x +e}\right)+C \,d^{2} e^{2} f^{2} x^{2} \ln \left(\frac{2 d^{2} e x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f +2 f}{f x +e}\right)+2 A \,d^{2} e \,f^{3} x \ln \left(\frac{2 d^{2} e x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f +2 f}{f x +e}\right)-4 \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, \sqrt{-d^{2} x^{2}+1}\, C e \,f^{3} x +A \,d^{2} f^{4} x^{2} \ln \left(\frac{2 d^{2} e x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f +2 f}{f x +e}\right)+A \,d^{2} e^{2} f^{2} \ln \left(\frac{2 d^{2} e x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f +2 f}{f x +e}\right)-3 B \,d^{2} e^{3} f \ln \left(\frac{2 d^{2} e x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f +2 f}{f x +e}\right)+2 \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, \sqrt{-d^{2} x^{2}+1}\, B \,f^{4} x +\sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, \sqrt{-d^{2} x^{2}+1}\, B e \,f^{3}-3 \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, \sqrt{-d^{2} x^{2}+1}\, C \,e^{2} f^{2}+4 C e \,f^{3} x \ln \left(\frac{2 d^{2} e x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f +2 f}{f x +e}\right)-3 \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, \sqrt{-d^{2} x^{2}+1}\, A \,d^{2} e \,f^{3} x +\sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, \sqrt{-d^{2} x^{2}+1}\, B \,d^{2} e^{2} f^{2} x +\sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, \sqrt{-d^{2} x^{2}+1}\, C \,d^{2} e^{3} f x \right) \sqrt{d x +1}\, \sqrt{-d x +1}\, \mathrm{csgn}\left(d \right)^{2}}{2 \sqrt{-d^{2} x^{2}+1}\, \left(d e +f \right) \left(d e -f \right) \left(d^{2} e^{2}-f^{2}\right) \left(f x +e \right)^{2} \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f}"," ",0,"-1/2*(A*f^4*(-(d^2*e^2-f^2)/f^2)^(1/2)*(-d^2*x^2+1)^(1/2)+2*C*ln(2*(d^2*e*x+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*f+f)/(f*x+e))*e^2*f^2+C*ln(2*(d^2*e*x+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*f+f)/(f*x+e))*d^2*e^4+2*C*ln(2*(d^2*e*x+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*f+f)/(f*x+e))*x^2*f^4+2*A*ln(2*(d^2*e*x+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*f+f)/(f*x+e))*d^4*e^4-3*B*ln(2*(d^2*e*x+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*f+f)/(f*x+e))*d^2*e^3*f+2*C*ln(2*(d^2*e*x+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*f+f)/(f*x+e))*x*d^2*e^3*f-4*A*d^2*e^2*f^2*(-(d^2*e^2-f^2)/f^2)^(1/2)*(-d^2*x^2+1)^(1/2)+2*B*d^2*e^3*f*(-(d^2*e^2-f^2)/f^2)^(1/2)*(-d^2*x^2+1)^(1/2)+2*A*ln(2*(d^2*e*x+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*f+f)/(f*x+e))*x*d^2*e*f^3-6*B*ln(2*(d^2*e*x+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*f+f)/(f*x+e))*x*d^2*e^2*f^2+C*ln(2*(d^2*e*x+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*f+f)/(f*x+e))*x^2*d^2*e^2*f^2-3*B*ln(2*(d^2*e*x+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*f+f)/(f*x+e))*x^2*d^2*e*f^3+2*A*ln(2*(d^2*e*x+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*f+f)/(f*x+e))*x^2*d^4*e^2*f^2+4*A*ln(2*(d^2*e*x+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*f+f)/(f*x+e))*x*d^4*e^3*f-4*C*x*e*f^3*(-(d^2*e^2-f^2)/f^2)^(1/2)*(-d^2*x^2+1)^(1/2)+4*C*ln(2*(d^2*e*x+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*f+f)/(f*x+e))*x*e*f^3+2*B*x*f^4*(-(d^2*e^2-f^2)/f^2)^(1/2)*(-d^2*x^2+1)^(1/2)+B*e*f^3*(-(d^2*e^2-f^2)/f^2)^(1/2)*(-d^2*x^2+1)^(1/2)-3*C*e^2*f^2*(-(d^2*e^2-f^2)/f^2)^(1/2)*(-d^2*x^2+1)^(1/2)+A*ln(2*(d^2*e*x+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*f+f)/(f*x+e))*x^2*d^2*f^4+A*ln(2*(d^2*e*x+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*f+f)/(f*x+e))*d^2*e^2*f^2-3*A*x*d^2*e*f^3*(-(d^2*e^2-f^2)/f^2)^(1/2)*(-d^2*x^2+1)^(1/2)+B*x*d^2*e^2*f^2*(-(d^2*e^2-f^2)/f^2)^(1/2)*(-d^2*x^2+1)^(1/2)+C*x*d^2*e^3*f*(-(d^2*e^2-f^2)/f^2)^(1/2)*(-d^2*x^2+1)^(1/2))*csgn(d)^2*(d*x+1)^(1/2)*(-d*x+1)^(1/2)/(-d^2*x^2+1)^(1/2)/(d*e+f)/(d*e-f)/(d^2*e^2-f^2)/(f*x+e)^2/(-(d^2*e^2-f^2)/f^2)^(1/2)/f","C"
8,1,643,320,0.029000," ","int((f*x+e)^3*(C*x^2+B*x+A)/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x)","-\frac{\sqrt{-d x +1}\, \sqrt{d x +1}\, \left(24 \sqrt{-d^{2} x^{2}+1}\, C \,d^{4} f^{3} x^{4} \mathrm{csgn}\left(d \right)+30 \sqrt{-d^{2} x^{2}+1}\, B \,d^{4} f^{3} x^{3} \mathrm{csgn}\left(d \right)+90 \sqrt{-d^{2} x^{2}+1}\, C \,d^{4} e \,f^{2} x^{3} \mathrm{csgn}\left(d \right)+40 \sqrt{-d^{2} x^{2}+1}\, A \,d^{4} f^{3} x^{2} \mathrm{csgn}\left(d \right)+120 \sqrt{-d^{2} x^{2}+1}\, B \,d^{4} e \,f^{2} x^{2} \mathrm{csgn}\left(d \right)+120 \sqrt{-d^{2} x^{2}+1}\, C \,d^{4} e^{2} f \,x^{2} \mathrm{csgn}\left(d \right)-120 A \,d^{5} e^{3} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)+180 \sqrt{-d^{2} x^{2}+1}\, A \,d^{4} e \,f^{2} x \,\mathrm{csgn}\left(d \right)+180 \sqrt{-d^{2} x^{2}+1}\, B \,d^{4} e^{2} f x \,\mathrm{csgn}\left(d \right)+60 \sqrt{-d^{2} x^{2}+1}\, C \,d^{4} e^{3} x \,\mathrm{csgn}\left(d \right)+360 \sqrt{-d^{2} x^{2}+1}\, A \,d^{4} e^{2} f \,\mathrm{csgn}\left(d \right)+120 \sqrt{-d^{2} x^{2}+1}\, B \,d^{4} e^{3} \mathrm{csgn}\left(d \right)+32 \sqrt{-d^{2} x^{2}+1}\, C \,d^{2} f^{3} x^{2} \mathrm{csgn}\left(d \right)-180 A \,d^{3} e \,f^{2} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)-180 B \,d^{3} e^{2} f \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)+45 \sqrt{-d^{2} x^{2}+1}\, B \,d^{2} f^{3} x \,\mathrm{csgn}\left(d \right)-60 C \,d^{3} e^{3} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)+135 \sqrt{-d^{2} x^{2}+1}\, C \,d^{2} e \,f^{2} x \,\mathrm{csgn}\left(d \right)+80 \sqrt{-d^{2} x^{2}+1}\, A \,d^{2} f^{3} \mathrm{csgn}\left(d \right)+240 \sqrt{-d^{2} x^{2}+1}\, B \,d^{2} e \,f^{2} \mathrm{csgn}\left(d \right)+240 \sqrt{-d^{2} x^{2}+1}\, C \,d^{2} e^{2} f \,\mathrm{csgn}\left(d \right)-45 B d \,f^{3} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)-135 C d e \,f^{2} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)+64 \sqrt{-d^{2} x^{2}+1}\, C \,f^{3} \mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)}{120 \sqrt{-d^{2} x^{2}+1}\, d^{6}}"," ",0,"-1/120*(-d*x+1)^(1/2)*(d*x+1)^(1/2)*(24*(-d^2*x^2+1)^(1/2)*C*d^4*f^3*x^4*csgn(d)+30*(-d^2*x^2+1)^(1/2)*B*d^4*f^3*x^3*csgn(d)+90*(-d^2*x^2+1)^(1/2)*C*d^4*e*f^2*x^3*csgn(d)+40*(-d^2*x^2+1)^(1/2)*A*d^4*f^3*x^2*csgn(d)+120*(-d^2*x^2+1)^(1/2)*B*d^4*e*f^2*x^2*csgn(d)+120*(-d^2*x^2+1)^(1/2)*C*d^4*e^2*f*x^2*csgn(d)+180*(-d^2*x^2+1)^(1/2)*A*d^4*e*f^2*x*csgn(d)+180*(-d^2*x^2+1)^(1/2)*B*d^4*e^2*f*x*csgn(d)+60*(-d^2*x^2+1)^(1/2)*C*d^4*e^3*x*csgn(d)+360*(-d^2*x^2+1)^(1/2)*A*d^4*e^2*f*csgn(d)-120*A*d^5*e^3*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))+120*(-d^2*x^2+1)^(1/2)*B*d^4*e^3*csgn(d)+32*(-d^2*x^2+1)^(1/2)*C*d^2*f^3*x^2*csgn(d)+45*(-d^2*x^2+1)^(1/2)*B*d^2*f^3*x*csgn(d)+135*(-d^2*x^2+1)^(1/2)*C*d^2*e*f^2*x*csgn(d)+80*(-d^2*x^2+1)^(1/2)*A*d^2*f^3*csgn(d)-180*A*d^3*e*f^2*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))+240*(-d^2*x^2+1)^(1/2)*B*d^2*e*f^2*csgn(d)-180*B*d^3*e^2*f*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))+240*(-d^2*x^2+1)^(1/2)*C*d^2*e^2*f*csgn(d)-60*C*d^3*e^3*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))-45*B*d*f^3*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))+64*(-d^2*x^2+1)^(1/2)*C*f^3*csgn(d)-135*C*d*e*f^2*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d)))*csgn(d)/d^6/(-d^2*x^2+1)^(1/2)","C"
9,1,423,212,0.028000," ","int((f*x+e)^2*(C*x^2+B*x+A)/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x)","-\frac{\sqrt{-d x +1}\, \sqrt{d x +1}\, \left(6 \sqrt{-d^{2} x^{2}+1}\, C \,d^{3} f^{2} x^{3} \mathrm{csgn}\left(d \right)+8 \sqrt{-d^{2} x^{2}+1}\, B \,d^{3} f^{2} x^{2} \mathrm{csgn}\left(d \right)+16 \sqrt{-d^{2} x^{2}+1}\, C \,d^{3} e f \,x^{2} \mathrm{csgn}\left(d \right)-24 A \,d^{4} e^{2} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)+12 \sqrt{-d^{2} x^{2}+1}\, A \,d^{3} f^{2} x \,\mathrm{csgn}\left(d \right)+24 \sqrt{-d^{2} x^{2}+1}\, B \,d^{3} e f x \,\mathrm{csgn}\left(d \right)+12 \sqrt{-d^{2} x^{2}+1}\, C \,d^{3} e^{2} x \,\mathrm{csgn}\left(d \right)+48 \sqrt{-d^{2} x^{2}+1}\, A \,d^{3} e f \,\mathrm{csgn}\left(d \right)+24 \sqrt{-d^{2} x^{2}+1}\, B \,d^{3} e^{2} \mathrm{csgn}\left(d \right)-12 A \,d^{2} f^{2} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)-24 B \,d^{2} e f \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)-12 C \,d^{2} e^{2} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)+9 \sqrt{-d^{2} x^{2}+1}\, C d \,f^{2} x \,\mathrm{csgn}\left(d \right)+16 \sqrt{-d^{2} x^{2}+1}\, B d \,f^{2} \mathrm{csgn}\left(d \right)+32 \sqrt{-d^{2} x^{2}+1}\, C d e f \,\mathrm{csgn}\left(d \right)-9 C \,f^{2} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)\right) \mathrm{csgn}\left(d \right)}{24 \sqrt{-d^{2} x^{2}+1}\, d^{5}}"," ",0,"-1/24*(-d*x+1)^(1/2)*(d*x+1)^(1/2)*(6*(-d^2*x^2+1)^(1/2)*C*d^3*f^2*x^3*csgn(d)+8*(-d^2*x^2+1)^(1/2)*B*d^3*f^2*x^2*csgn(d)+16*(-d^2*x^2+1)^(1/2)*C*d^3*e*f*x^2*csgn(d)+12*(-d^2*x^2+1)^(1/2)*A*d^3*f^2*x*csgn(d)+24*(-d^2*x^2+1)^(1/2)*B*d^3*e*f*x*csgn(d)+12*(-d^2*x^2+1)^(1/2)*C*d^3*e^2*x*csgn(d)+48*(-d^2*x^2+1)^(1/2)*A*d^3*e*f*csgn(d)-24*A*d^4*e^2*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))+24*(-d^2*x^2+1)^(1/2)*B*d^3*e^2*csgn(d)+9*(-d^2*x^2+1)^(1/2)*C*d*f^2*x*csgn(d)-12*A*d^2*f^2*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))+16*(-d^2*x^2+1)^(1/2)*B*d*f^2*csgn(d)-24*B*d^2*e*f*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))+32*(-d^2*x^2+1)^(1/2)*C*d*e*f*csgn(d)-12*C*d^2*e^2*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))-9*C*f^2*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d)))*csgn(d)/d^5/(-d^2*x^2+1)^(1/2)","C"
10,1,235,117,0.023000," ","int((f*x+e)*(C*x^2+B*x+A)/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x)","-\frac{\sqrt{-d x +1}\, \sqrt{d x +1}\, \left(2 \sqrt{-d^{2} x^{2}+1}\, C \,d^{2} f \,x^{2} \mathrm{csgn}\left(d \right)-6 A \,d^{3} e \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)+3 \sqrt{-d^{2} x^{2}+1}\, B \,d^{2} f x \,\mathrm{csgn}\left(d \right)+3 \sqrt{-d^{2} x^{2}+1}\, C \,d^{2} e x \,\mathrm{csgn}\left(d \right)+6 \sqrt{-d^{2} x^{2}+1}\, A \,d^{2} f \,\mathrm{csgn}\left(d \right)+6 \sqrt{-d^{2} x^{2}+1}\, B \,d^{2} e \,\mathrm{csgn}\left(d \right)-3 B d f \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)-3 C d e \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)+4 \sqrt{-d^{2} x^{2}+1}\, C f \,\mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)}{6 \sqrt{-d^{2} x^{2}+1}\, d^{4}}"," ",0,"-1/6*(-d*x+1)^(1/2)*(d*x+1)^(1/2)*(2*(-d^2*x^2+1)^(1/2)*C*d^2*f*x^2*csgn(d)+3*(-d^2*x^2+1)^(1/2)*B*d^2*f*x*csgn(d)+3*(-d^2*x^2+1)^(1/2)*C*d^2*e*x*csgn(d)+6*(-d^2*x^2+1)^(1/2)*A*d^2*f*csgn(d)-6*A*d^3*e*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))+6*(-d^2*x^2+1)^(1/2)*B*d^2*e*csgn(d)-3*B*d*f*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))+4*(-d^2*x^2+1)^(1/2)*C*f*csgn(d)-3*C*d*e*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d)))*csgn(d)/d^4/(-d^2*x^2+1)^(1/2)","C"
11,1,117,55,0.017000," ","int((C*x^2+B*x+A)/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x)","\frac{\sqrt{-d x +1}\, \sqrt{d x +1}\, \left(2 A \,d^{2} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)-\sqrt{-d^{2} x^{2}+1}\, C d x \,\mathrm{csgn}\left(d \right)-2 \sqrt{-d^{2} x^{2}+1}\, B d \,\mathrm{csgn}\left(d \right)+C \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)\right) \mathrm{csgn}\left(d \right)}{2 \sqrt{-d^{2} x^{2}+1}\, d^{3}}"," ",0,"1/2*(-d*x+1)^(1/2)*(d*x+1)^(1/2)/d^3*(2*A*d^2*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))-(-d^2*x^2+1)^(1/2)*C*d*x*csgn(d)-2*(-d^2*x^2+1)^(1/2)*B*d*csgn(d)+C*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d)))/(-d^2*x^2+1)^(1/2)*csgn(d)","C"
12,1,373,114,0.000000," ","int((C*x^2+B*x+A)/(f*x+e)/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x)","\frac{\left(-A \,d^{2} f^{2} \mathrm{csgn}\left(d \right) \ln \left(\frac{2 d^{2} e x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f +2 f}{f x +e}\right)+B \,d^{2} e f \,\mathrm{csgn}\left(d \right) \ln \left(\frac{2 d^{2} e x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f +2 f}{f x +e}\right)-C \,d^{2} e^{2} \mathrm{csgn}\left(d \right) \ln \left(\frac{2 d^{2} e x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f +2 f}{f x +e}\right)+\sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, B d \,f^{2} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)-\sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, C d e f \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)-\sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, C \,f^{2} \mathrm{csgn}\left(d \right)\right) \sqrt{-d x +1}\, \sqrt{d x +1}\, \mathrm{csgn}\left(d \right)}{\sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, \sqrt{-d^{2} x^{2}+1}\, d^{2} f^{3}}"," ",0,"(-A*d^2*f^2*csgn(d)*ln(2*(d^2*e*x+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*f+f)/(f*x+e))+B*d^2*e*f*csgn(d)*ln(2*(d^2*e*x+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*f+f)/(f*x+e))-C*d^2*e^2*csgn(d)*ln(2*(d^2*e*x+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*f+f)/(f*x+e))+(-(d^2*e^2-f^2)/f^2)^(1/2)*B*d*f^2*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))-(-(d^2*e^2-f^2)/f^2)^(1/2)*C*d*e*f*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))-(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*C*f^2*csgn(d))*(-d*x+1)^(1/2)*(d*x+1)^(1/2)/(-(d^2*e^2-f^2)/f^2)^(1/2)/(-d^2*x^2+1)^(1/2)/d^2/f^3*csgn(d)","C"
13,1,899,155,0.000000," ","int((C*x^2+B*x+A)/(f*x+e)^2/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x)","\frac{\left(-A \,d^{3} e \,f^{3} x \,\mathrm{csgn}\left(d \right) \ln \left(\frac{2 d^{2} e x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f +2 f}{f x +e}\right)+C \,d^{3} e^{3} f x \,\mathrm{csgn}\left(d \right) \ln \left(\frac{2 d^{2} e x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f +2 f}{f x +e}\right)-A \,d^{3} e^{2} f^{2} \mathrm{csgn}\left(d \right) \ln \left(\frac{2 d^{2} e x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f +2 f}{f x +e}\right)+C \,d^{3} e^{4} \mathrm{csgn}\left(d \right) \ln \left(\frac{2 d^{2} e x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f +2 f}{f x +e}\right)+B d \,f^{4} x \,\mathrm{csgn}\left(d \right) \ln \left(\frac{2 d^{2} e x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f +2 f}{f x +e}\right)+\sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, C \,d^{2} e^{2} f^{2} x \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)-2 C d e \,f^{3} x \,\mathrm{csgn}\left(d \right) \ln \left(\frac{2 d^{2} e x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f +2 f}{f x +e}\right)+B d e \,f^{3} \mathrm{csgn}\left(d \right) \ln \left(\frac{2 d^{2} e x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f +2 f}{f x +e}\right)+\sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, C \,d^{2} e^{3} f \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)-2 C d \,e^{2} f^{2} \mathrm{csgn}\left(d \right) \ln \left(\frac{2 d^{2} e x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f +2 f}{f x +e}\right)+\sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, A d \,f^{4} \mathrm{csgn}\left(d \right)-\sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, B d e \,f^{3} \mathrm{csgn}\left(d \right)+\sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, C d \,e^{2} f^{2} \mathrm{csgn}\left(d \right)-\sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, C \,f^{4} x \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)-\sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, C e \,f^{3} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)\right) \sqrt{d x +1}\, \sqrt{-d x +1}\, \mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}\, \left(d e +f \right) \left(d e -f \right) \left(f x +e \right) \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, d \,f^{3}}"," ",0,"(-A*d^3*e*f^3*x*csgn(d)*ln(2*(d^2*e*x+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*f+f)/(f*x+e))+C*d^3*e^3*f*x*csgn(d)*ln(2*(d^2*e*x+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*f+f)/(f*x+e))-A*d^3*e^2*f^2*csgn(d)*ln(2*(d^2*e*x+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*f+f)/(f*x+e))+C*d^3*e^4*csgn(d)*ln(2*(d^2*e*x+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*f+f)/(f*x+e))+B*d*f^4*x*csgn(d)*ln(2*(d^2*e*x+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*f+f)/(f*x+e))+(-(d^2*e^2-f^2)/f^2)^(1/2)*C*d^2*e^2*f^2*x*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))-2*C*d*e*f^3*x*csgn(d)*ln(2*(d^2*e*x+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*f+f)/(f*x+e))+B*d*e*f^3*csgn(d)*ln(2*(d^2*e*x+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*f+f)/(f*x+e))+(-(d^2*e^2-f^2)/f^2)^(1/2)*C*d^2*e^3*f*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))-2*C*d*e^2*f^2*csgn(d)*ln(2*(d^2*e*x+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*f+f)/(f*x+e))+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*A*d*f^4*csgn(d)-(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*B*d*e*f^3*csgn(d)+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*C*d*e^2*f^2*csgn(d)-(-(d^2*e^2-f^2)/f^2)^(1/2)*C*f^4*x*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))-(-(d^2*e^2-f^2)/f^2)^(1/2)*C*e*f^3*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d)))*(d*x+1)^(1/2)*(-d*x+1)^(1/2)/(-d^2*x^2+1)^(1/2)/(d*e+f)/(d*e-f)/(f*x+e)/(-(d^2*e^2-f^2)/f^2)^(1/2)/d/f^3*csgn(d)","C"
14,1,1449,232,0.000000," ","int((C*x^2+B*x+A)/(f*x+e)^3/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x)","-\frac{\left(2 A \,d^{4} e^{4} \ln \left(\frac{2 d^{2} e x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f +2 f}{f x +e}\right)+C \,d^{2} e^{4} \ln \left(\frac{2 d^{2} e x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f +2 f}{f x +e}\right)+2 C \,f^{4} x^{2} \ln \left(\frac{2 d^{2} e x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f +2 f}{f x +e}\right)+2 C \,e^{2} f^{2} \ln \left(\frac{2 d^{2} e x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f +2 f}{f x +e}\right)+\sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, \sqrt{-d^{2} x^{2}+1}\, A \,f^{4}+2 C \,d^{2} e^{3} f x \ln \left(\frac{2 d^{2} e x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f +2 f}{f x +e}\right)-6 B \,d^{2} e^{2} f^{2} x \ln \left(\frac{2 d^{2} e x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f +2 f}{f x +e}\right)-4 \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, \sqrt{-d^{2} x^{2}+1}\, A \,d^{2} e^{2} f^{2}+2 \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, \sqrt{-d^{2} x^{2}+1}\, B \,d^{2} e^{3} f +2 A \,d^{4} e^{2} f^{2} x^{2} \ln \left(\frac{2 d^{2} e x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f +2 f}{f x +e}\right)+4 A \,d^{4} e^{3} f x \ln \left(\frac{2 d^{2} e x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f +2 f}{f x +e}\right)-3 B \,d^{2} e \,f^{3} x^{2} \ln \left(\frac{2 d^{2} e x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f +2 f}{f x +e}\right)+C \,d^{2} e^{2} f^{2} x^{2} \ln \left(\frac{2 d^{2} e x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f +2 f}{f x +e}\right)+2 A \,d^{2} e \,f^{3} x \ln \left(\frac{2 d^{2} e x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f +2 f}{f x +e}\right)-4 \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, \sqrt{-d^{2} x^{2}+1}\, C e \,f^{3} x +A \,d^{2} f^{4} x^{2} \ln \left(\frac{2 d^{2} e x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f +2 f}{f x +e}\right)+A \,d^{2} e^{2} f^{2} \ln \left(\frac{2 d^{2} e x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f +2 f}{f x +e}\right)-3 B \,d^{2} e^{3} f \ln \left(\frac{2 d^{2} e x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f +2 f}{f x +e}\right)+2 \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, \sqrt{-d^{2} x^{2}+1}\, B \,f^{4} x +\sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, \sqrt{-d^{2} x^{2}+1}\, B e \,f^{3}-3 \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, \sqrt{-d^{2} x^{2}+1}\, C \,e^{2} f^{2}+4 C e \,f^{3} x \ln \left(\frac{2 d^{2} e x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f +2 f}{f x +e}\right)-3 \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, \sqrt{-d^{2} x^{2}+1}\, A \,d^{2} e \,f^{3} x +\sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, \sqrt{-d^{2} x^{2}+1}\, B \,d^{2} e^{2} f^{2} x +\sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, \sqrt{-d^{2} x^{2}+1}\, C \,d^{2} e^{3} f x \right) \sqrt{d x +1}\, \sqrt{-d x +1}\, \mathrm{csgn}\left(d \right)^{2}}{2 \sqrt{-d^{2} x^{2}+1}\, \left(d e +f \right) \left(d e -f \right) \left(d^{2} e^{2}-f^{2}\right) \left(f x +e \right)^{2} \sqrt{-\frac{d^{2} e^{2}-f^{2}}{f^{2}}}\, f}"," ",0,"-1/2*(2*A*d^4*e^2*f^2*x^2*ln(2*(d^2*e*x+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*f+f)/(f*x+e))+4*A*d^4*e^3*f*x*ln(2*(d^2*e*x+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*f+f)/(f*x+e))+2*A*d^4*e^4*ln(2*(d^2*e*x+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*f+f)/(f*x+e))+A*d^2*f^4*x^2*ln(2*(d^2*e*x+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*f+f)/(f*x+e))-3*B*d^2*e*f^3*x^2*ln(2*(d^2*e*x+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*f+f)/(f*x+e))+C*d^2*e^2*f^2*x^2*ln(2*(d^2*e*x+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*f+f)/(f*x+e))+2*A*d^2*e*f^3*x*ln(2*(d^2*e*x+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*f+f)/(f*x+e))-6*B*d^2*e^2*f^2*x*ln(2*(d^2*e*x+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*f+f)/(f*x+e))+2*C*d^2*e^3*f*x*ln(2*(d^2*e*x+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*f+f)/(f*x+e))+A*d^2*e^2*f^2*ln(2*(d^2*e*x+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*f+f)/(f*x+e))-3*(-(d^2*e^2-f^2)/f^2)^(1/2)*(-d^2*x^2+1)^(1/2)*A*d^2*e*f^3*x-3*B*d^2*e^3*f*ln(2*(d^2*e*x+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*f+f)/(f*x+e))+(-(d^2*e^2-f^2)/f^2)^(1/2)*(-d^2*x^2+1)^(1/2)*B*d^2*e^2*f^2*x+C*d^2*e^4*ln(2*(d^2*e*x+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*f+f)/(f*x+e))+(-(d^2*e^2-f^2)/f^2)^(1/2)*(-d^2*x^2+1)^(1/2)*C*d^2*e^3*f*x+2*C*f^4*x^2*ln(2*(d^2*e*x+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*f+f)/(f*x+e))-4*(-(d^2*e^2-f^2)/f^2)^(1/2)*(-d^2*x^2+1)^(1/2)*A*d^2*e^2*f^2+2*(-(d^2*e^2-f^2)/f^2)^(1/2)*(-d^2*x^2+1)^(1/2)*B*d^2*e^3*f+4*C*e*f^3*x*ln(2*(d^2*e*x+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*f+f)/(f*x+e))+2*(-(d^2*e^2-f^2)/f^2)^(1/2)*(-d^2*x^2+1)^(1/2)*B*f^4*x+2*C*e^2*f^2*ln(2*(d^2*e*x+(-d^2*x^2+1)^(1/2)*(-(d^2*e^2-f^2)/f^2)^(1/2)*f+f)/(f*x+e))-4*(-(d^2*e^2-f^2)/f^2)^(1/2)*(-d^2*x^2+1)^(1/2)*C*e*f^3*x+(-(d^2*e^2-f^2)/f^2)^(1/2)*(-d^2*x^2+1)^(1/2)*A*f^4+(-(d^2*e^2-f^2)/f^2)^(1/2)*(-d^2*x^2+1)^(1/2)*B*e*f^3-3*(-(d^2*e^2-f^2)/f^2)^(1/2)*(-d^2*x^2+1)^(1/2)*C*e^2*f^2)*(d*x+1)^(1/2)*(-d*x+1)^(1/2)/(-d^2*x^2+1)^(1/2)/(d*e+f)/(d*e-f)/(d^2*e^2-f^2)/(f*x+e)^2/(-(d^2*e^2-f^2)/f^2)^(1/2)/f*csgn(d)^2","C"
15,1,139,66,0.000000," ","int(x*(c*x^2+b*x+a)/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x)","-\frac{\sqrt{-d x +1}\, \sqrt{d x +1}\, \left(2 \sqrt{-d^{2} x^{2}+1}\, c \,d^{2} x^{2} \mathrm{csgn}\left(d \right)+3 \sqrt{-d^{2} x^{2}+1}\, b \,d^{2} x \,\mathrm{csgn}\left(d \right)+6 \sqrt{-d^{2} x^{2}+1}\, a \,d^{2} \mathrm{csgn}\left(d \right)-3 b d \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)+4 \sqrt{-d^{2} x^{2}+1}\, c \,\mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)}{6 \sqrt{-d^{2} x^{2}+1}\, d^{4}}"," ",0,"-1/6*(-d*x+1)^(1/2)*(d*x+1)^(1/2)*(2*(-d^2*x^2+1)^(1/2)*c*d^2*x^2*csgn(d)+3*(-d^2*x^2+1)^(1/2)*b*d^2*x*csgn(d)+6*(-d^2*x^2+1)^(1/2)*a*d^2*csgn(d)-3*b*d*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))+4*(-d^2*x^2+1)^(1/2)*c*csgn(d))/(-d^2*x^2+1)^(1/2)/d^4*csgn(d)","C"
16,1,117,55,0.000000," ","int((c*x^2+b*x+a)/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x)","-\frac{\sqrt{-d x +1}\, \sqrt{d x +1}\, \left(-2 a \,d^{2} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)+\sqrt{-d^{2} x^{2}+1}\, c d x \,\mathrm{csgn}\left(d \right)+2 \sqrt{-d^{2} x^{2}+1}\, b d \,\mathrm{csgn}\left(d \right)-c \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)\right) \mathrm{csgn}\left(d \right)}{2 \sqrt{-d^{2} x^{2}+1}\, d^{3}}"," ",0,"-1/2*(-d*x+1)^(1/2)*(d*x+1)^(1/2)*(-2*a*d^2*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))+(-d^2*x^2+1)^(1/2)*c*d*x*csgn(d)+2*(-d^2*x^2+1)^(1/2)*b*d*csgn(d)-c*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d)))/(-d^2*x^2+1)^(1/2)/d^3*csgn(d)","C"
17,1,96,44,0.001000," ","int((c*x^2+b*x+a)/x/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x)","\frac{\left(-a \,d^{2} \arctanh \left(\frac{1}{\sqrt{-d^{2} x^{2}+1}}\right) \mathrm{csgn}\left(d \right)+b d \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-\left(d x +1\right) \left(d x -1\right)}}\right)-\sqrt{-d^{2} x^{2}+1}\, c \,\mathrm{csgn}\left(d \right)\right) \sqrt{-d x +1}\, \sqrt{d x +1}\, \mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}\, d^{2}}"," ",0,"(-csgn(d)*arctanh(1/(-d^2*x^2+1)^(1/2))*a*d^2-(-d^2*x^2+1)^(1/2)*c*csgn(d)+b*d*arctan(1/(-(d*x+1)*(d*x-1))^(1/2)*d*x*csgn(d)))*(-d*x+1)^(1/2)*(d*x+1)^(1/2)/d^2*csgn(d)/(-d^2*x^2+1)^(1/2)","C"
18,1,97,44,0.000000," ","int((c*x^2+b*x+a)/x^2/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x)","\frac{\left(-b d x \arctanh \left(\frac{1}{\sqrt{-d^{2} x^{2}+1}}\right) \mathrm{csgn}\left(d \right)-\sqrt{-d^{2} x^{2}+1}\, a d \,\mathrm{csgn}\left(d \right)+c x \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)\right) \sqrt{-d x +1}\, \sqrt{d x +1}\, \mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}\, d x}"," ",0,"(-csgn(d)*d*arctanh(1/(-d^2*x^2+1)^(1/2))*x*b-(-d^2*x^2+1)^(1/2)*a*d*csgn(d)+c*x*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d)))*(-d*x+1)^(1/2)*(d*x+1)^(1/2)*csgn(d)/(-d^2*x^2+1)^(1/2)/x/d","C"
19,1,108,61,0.000000," ","int((c*x^2+b*x+a)/x^3/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x)","-\frac{\sqrt{-d x +1}\, \sqrt{d x +1}\, \left(a \,d^{2} x^{2} \arctanh \left(\frac{1}{\sqrt{-d^{2} x^{2}+1}}\right)+2 c \,x^{2} \arctanh \left(\frac{1}{\sqrt{-d^{2} x^{2}+1}}\right)+2 \sqrt{-d^{2} x^{2}+1}\, b x +\sqrt{-d^{2} x^{2}+1}\, a \right) \mathrm{csgn}\left(d \right)^{2}}{2 \sqrt{-d^{2} x^{2}+1}\, x^{2}}"," ",0,"-1/2*(-d*x+1)^(1/2)*(d*x+1)^(1/2)*csgn(d)^2*(arctanh(1/(-d^2*x^2+1)^(1/2))*x^2*a*d^2+2*arctanh(1/(-d^2*x^2+1)^(1/2))*x^2*c+2*(-d^2*x^2+1)^(1/2)*b*x+(-d^2*x^2+1)^(1/2)*a)/(-d^2*x^2+1)^(1/2)/x^2","C"
20,1,1446,544,0.043000," ","int((f*x+e)^3*(C*x^2+B*x+A)*(b*x+a)^(1/2)*(-b*c*x+a*c)^(1/2),x)","\frac{\sqrt{b x +a}\, \sqrt{-\left(b x -a \right) c}\, \left(240 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, C \,b^{6} f^{3} x^{6}+280 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, B \,b^{6} f^{3} x^{5}+840 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, C \,b^{6} e \,f^{2} x^{5}+630 A \,a^{4} b^{4} c e \,f^{2} \arctan \left(\frac{\sqrt{b^{2} c}\, x}{\sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}}\right)+840 A \,a^{2} b^{6} c \,e^{3} \arctan \left(\frac{\sqrt{b^{2} c}\, x}{\sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}}\right)+336 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, A \,b^{6} f^{3} x^{4}+105 B \,a^{6} b^{2} c \,f^{3} \arctan \left(\frac{\sqrt{b^{2} c}\, x}{\sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}}\right)+630 B \,a^{4} b^{4} c \,e^{2} f \arctan \left(\frac{\sqrt{b^{2} c}\, x}{\sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}}\right)+1008 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, B \,b^{6} e \,f^{2} x^{4}+315 C \,a^{6} b^{2} c e \,f^{2} \arctan \left(\frac{\sqrt{b^{2} c}\, x}{\sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}}\right)+210 C \,a^{4} b^{4} c \,e^{3} \arctan \left(\frac{\sqrt{b^{2} c}\, x}{\sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}}\right)-48 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, C \,a^{2} b^{4} f^{3} x^{4}+1008 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, C \,b^{6} e^{2} f \,x^{4}+1260 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, A \,b^{6} e \,f^{2} x^{3}-70 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, B \,a^{2} b^{4} f^{3} x^{3}+1260 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, B \,b^{6} e^{2} f \,x^{3}-210 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, C \,a^{2} b^{4} e \,f^{2} x^{3}+420 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, C \,b^{6} e^{3} x^{3}-112 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, A \,a^{2} b^{4} f^{3} x^{2}+1680 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, A \,b^{6} e^{2} f \,x^{2}-336 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, B \,a^{2} b^{4} e \,f^{2} x^{2}+560 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, B \,b^{6} e^{3} x^{2}-64 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, C \,a^{4} b^{2} f^{3} x^{2}-336 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, C \,a^{2} b^{4} e^{2} f \,x^{2}-630 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, A \,a^{2} b^{4} e \,f^{2} x +840 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, A \,b^{6} e^{3} x -105 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, B \,a^{4} b^{2} f^{3} x -630 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, B \,a^{2} b^{4} e^{2} f x -315 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, C \,a^{4} b^{2} e \,f^{2} x -210 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, C \,a^{2} b^{4} e^{3} x -224 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, A \,a^{4} b^{2} f^{3}-1680 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, A \,a^{2} b^{4} e^{2} f -672 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, B \,a^{4} b^{2} e \,f^{2}-560 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, B \,a^{2} b^{4} e^{3}-128 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, C \,a^{6} f^{3}-672 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, C \,a^{4} b^{2} e^{2} f \right)}{1680 \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, \sqrt{b^{2} c}\, b^{6}}"," ",0,"1/1680*(b*x+a)^(1/2)*(-c*(b*x-a))^(1/2)*(-630*B*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*x*a^2*b^4*e^2*f+105*B*arctan((b^2*c)^(1/2)*x/(-(b^2*x^2-a^2)*c)^(1/2))*a^6*b^2*c*f^3+240*C*x^6*b^6*f^3*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)+280*B*x^5*b^6*f^3*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)+336*A*x^4*b^6*f^3*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)+420*C*x^3*b^6*e^3*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)+560*B*x^2*b^6*e^3*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)-224*A*a^4*b^2*f^3*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)-560*B*a^2*b^4*e^3*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)+210*C*arctan((b^2*c)^(1/2)*x/(-(b^2*x^2-a^2)*c)^(1/2))*a^4*b^4*c*e^3+840*A*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*x*b^6*e^3+840*A*arctan((b^2*c)^(1/2)*x/(-(b^2*x^2-a^2)*c)^(1/2))*a^2*b^6*c*e^3-128*C*a^6*f^3*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)-112*A*x^2*a^2*b^4*f^3*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)+1680*A*x^2*b^6*e^2*f*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)-64*C*x^2*a^4*b^2*f^3*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)-1680*A*a^2*b^4*e^2*f*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)-672*B*a^4*b^2*e*f^2*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)-672*C*a^4*b^2*e^2*f*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)+630*A*arctan((b^2*c)^(1/2)*x/(-(b^2*x^2-a^2)*c)^(1/2))*a^4*b^4*c*e*f^2+630*B*arctan((b^2*c)^(1/2)*x/(-(b^2*x^2-a^2)*c)^(1/2))*a^4*b^4*c*e^2*f-105*B*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*x*a^4*b^2*f^3-210*C*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*x*a^2*b^4*e^3+1008*C*x^4*b^6*e^2*f*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)+1260*A*x^3*b^6*e*f^2*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)-70*B*x^3*a^2*b^4*f^3*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)+1260*B*x^3*b^6*e^2*f*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)-315*C*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*x*a^4*b^2*e*f^2-630*A*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*x*a^2*b^4*e*f^2-210*C*x^3*a^2*b^4*e*f^2*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)-336*B*x^2*a^2*b^4*e*f^2*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)-336*C*x^2*a^2*b^4*e^2*f*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)+315*C*arctan((b^2*c)^(1/2)*x/(-(b^2*x^2-a^2)*c)^(1/2))*a^6*b^2*c*e*f^2+840*C*x^5*b^6*e*f^2*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)+1008*B*x^4*b^6*e*f^2*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)-48*C*x^4*a^2*b^4*f^3*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2))/(-(b^2*x^2-a^2)*c)^(1/2)/b^6/(b^2*c)^(1/2)","B"
21,1,987,410,0.018000," ","int((f*x+e)^2*(C*x^2+B*x+A)*(b*x+a)^(1/2)*(-b*c*x+a*c)^(1/2),x)","\frac{\sqrt{b x +a}\, \sqrt{-\left(b x -a \right) c}\, \left(40 \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, \sqrt{b^{2} c}\, C \,b^{4} f^{2} x^{5}+30 A \,a^{4} b^{2} c \,f^{2} \arctan \left(\frac{\sqrt{b^{2} c}\, x}{\sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}}\right)+120 A \,a^{2} b^{4} c \,e^{2} \arctan \left(\frac{\sqrt{b^{2} c}\, x}{\sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}}\right)+60 B \,a^{4} b^{2} c e f \arctan \left(\frac{\sqrt{b^{2} c}\, x}{\sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}}\right)+48 \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, \sqrt{b^{2} c}\, B \,b^{4} f^{2} x^{4}+15 C \,a^{6} c \,f^{2} \arctan \left(\frac{\sqrt{b^{2} c}\, x}{\sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}}\right)+30 C \,a^{4} b^{2} c \,e^{2} \arctan \left(\frac{\sqrt{b^{2} c}\, x}{\sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}}\right)+96 \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, \sqrt{b^{2} c}\, C \,b^{4} e f \,x^{4}+60 \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, \sqrt{b^{2} c}\, A \,b^{4} f^{2} x^{3}+120 \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, \sqrt{b^{2} c}\, B \,b^{4} e f \,x^{3}-10 \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, \sqrt{b^{2} c}\, C \,a^{2} b^{2} f^{2} x^{3}+60 \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, \sqrt{b^{2} c}\, C \,b^{4} e^{2} x^{3}+160 \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, \sqrt{b^{2} c}\, A \,b^{4} e f \,x^{2}-16 \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, \sqrt{b^{2} c}\, B \,a^{2} b^{2} f^{2} x^{2}+80 \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, \sqrt{b^{2} c}\, B \,b^{4} e^{2} x^{2}-32 \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, \sqrt{b^{2} c}\, C \,a^{2} b^{2} e f \,x^{2}-30 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, A \,a^{2} b^{2} f^{2} x +120 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, A \,b^{4} e^{2} x -60 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, B \,a^{2} b^{2} e f x -15 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, C \,a^{4} f^{2} x -30 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, C \,a^{2} b^{2} e^{2} x -160 \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, \sqrt{b^{2} c}\, A \,a^{2} b^{2} e f -32 \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, \sqrt{b^{2} c}\, B \,a^{4} f^{2}-80 \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, \sqrt{b^{2} c}\, B \,a^{2} b^{2} e^{2}-64 \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, \sqrt{b^{2} c}\, C \,a^{4} e f \right)}{240 \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, \sqrt{b^{2} c}\, b^{4}}"," ",0,"1/240*(b*x+a)^(1/2)*(-(b*x-a)*c)^(1/2)*(40*C*x^5*b^4*f^2*(-(b^2*x^2-a^2)*c)^(1/2)*(b^2*c)^(1/2)+48*B*x^4*b^4*f^2*(-(b^2*x^2-a^2)*c)^(1/2)*(b^2*c)^(1/2)+60*A*x^3*b^4*f^2*(-(b^2*x^2-a^2)*c)^(1/2)*(b^2*c)^(1/2)+60*C*x^3*b^4*e^2*(-(b^2*x^2-a^2)*c)^(1/2)*(b^2*c)^(1/2)+80*B*x^2*b^4*e^2*(-(b^2*x^2-a^2)*c)^(1/2)*(b^2*c)^(1/2)-80*B*a^2*b^2*e^2*(-(b^2*x^2-a^2)*c)^(1/2)*(b^2*c)^(1/2)-60*B*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*x*a^2*b^2*e*f+15*C*arctan((b^2*c)^(1/2)/(-(b^2*x^2-a^2)*c)^(1/2)*x)*a^6*c*f^2-32*B*a^4*f^2*(-(b^2*x^2-a^2)*c)^(1/2)*(b^2*c)^(1/2)-64*C*a^4*e*f*(-(b^2*x^2-a^2)*c)^(1/2)*(b^2*c)^(1/2)+30*A*arctan((b^2*c)^(1/2)/(-(b^2*x^2-a^2)*c)^(1/2)*x)*a^4*b^2*c*f^2+120*A*arctan((b^2*c)^(1/2)/(-(b^2*x^2-a^2)*c)^(1/2)*x)*a^2*b^4*c*e^2+30*C*arctan((b^2*c)^(1/2)/(-(b^2*x^2-a^2)*c)^(1/2)*x)*a^4*b^2*c*e^2+120*A*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*x*b^4*e^2-15*C*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*x*a^4*f^2-32*C*x^2*a^2*b^2*e*f*(-(b^2*x^2-a^2)*c)^(1/2)*(b^2*c)^(1/2)-30*A*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*x*a^2*b^2*f^2-30*C*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*x*a^2*b^2*e^2-10*C*x^3*a^2*b^2*f^2*(-(b^2*x^2-a^2)*c)^(1/2)*(b^2*c)^(1/2)+160*A*x^2*b^4*e*f*(-(b^2*x^2-a^2)*c)^(1/2)*(b^2*c)^(1/2)-16*B*x^2*a^2*b^2*f^2*(-(b^2*x^2-a^2)*c)^(1/2)*(b^2*c)^(1/2)-160*A*a^2*b^2*e*f*(-(b^2*x^2-a^2)*c)^(1/2)*(b^2*c)^(1/2)+60*B*arctan((b^2*c)^(1/2)/(-(b^2*x^2-a^2)*c)^(1/2)*x)*a^4*b^2*c*e*f+96*C*x^4*b^4*e*f*(-(b^2*x^2-a^2)*c)^(1/2)*(b^2*c)^(1/2)+120*B*x^3*b^4*e*f*(-(b^2*x^2-a^2)*c)^(1/2)*(b^2*c)^(1/2))/(-(b^2*x^2-a^2)*c)^(1/2)/b^4/(b^2*c)^(1/2)","B"
22,1,588,265,0.014000," ","int((f*x+e)*(C*x^2+B*x+A)*(b*x+a)^(1/2)*(-b*c*x+a*c)^(1/2),x)","\frac{\sqrt{b x +a}\, \sqrt{-\left(b x -a \right) c}\, \left(60 A \,a^{2} b^{4} c e \arctan \left(\frac{\sqrt{b^{2} c}\, x}{\sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}}\right)+15 B \,a^{4} b^{2} c f \arctan \left(\frac{\sqrt{b^{2} c}\, x}{\sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}}\right)+15 C \,a^{4} b^{2} c e \arctan \left(\frac{\sqrt{b^{2} c}\, x}{\sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}}\right)+24 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, C \,b^{4} f \,x^{4}+30 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, B \,b^{4} f \,x^{3}+30 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, C \,b^{4} e \,x^{3}+40 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, A \,b^{4} f \,x^{2}+40 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, B \,b^{4} e \,x^{2}-8 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, C \,a^{2} b^{2} f \,x^{2}+60 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, A \,b^{4} e x -15 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, B \,a^{2} b^{2} f x -15 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, C \,a^{2} b^{2} e x -40 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, A \,a^{2} b^{2} f -40 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, B \,a^{2} b^{2} e -16 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, C \,a^{4} f \right)}{120 \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, \sqrt{b^{2} c}\, b^{4}}"," ",0,"1/120*(b*x+a)^(1/2)*(-(b*x-a)*c)^(1/2)*(24*C*x^4*b^4*f*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)+30*B*x^3*b^4*f*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)+30*C*x^3*b^4*e*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)+60*A*arctan((b^2*c)^(1/2)/(-(b^2*x^2-a^2)*c)^(1/2)*x)*a^2*b^4*c*e+40*A*x^2*b^4*f*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)+15*B*arctan((b^2*c)^(1/2)/(-(b^2*x^2-a^2)*c)^(1/2)*x)*a^4*b^2*c*f+40*B*x^2*b^4*e*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)+15*C*arctan((b^2*c)^(1/2)/(-(b^2*x^2-a^2)*c)^(1/2)*x)*a^4*b^2*c*e-8*C*x^2*a^2*b^2*f*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)+60*A*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*x*b^4*e-15*B*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*x*a^2*b^2*f-15*C*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*x*a^2*b^2*e-40*A*a^2*b^2*f*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)-40*B*a^2*b^2*e*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)-16*C*a^4*f*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2))/(-(b^2*x^2-a^2)*c)^(1/2)/b^4/(b^2*c)^(1/2)","B"
23,1,287,189,0.013000," ","int((C*x^2+B*x+A)*(b*x+a)^(1/2)*(-b*c*x+a*c)^(1/2),x)","\frac{\sqrt{b x +a}\, \sqrt{-\left(b x -a \right) c}\, \left(12 A \,a^{2} b^{2} c \arctan \left(\frac{\sqrt{b^{2} c}\, x}{\sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}}\right)+3 C \,a^{4} c \arctan \left(\frac{\sqrt{b^{2} c}\, x}{\sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}}\right)+6 \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, \sqrt{b^{2} c}\, C \,b^{2} x^{3}+8 \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, \sqrt{b^{2} c}\, B \,b^{2} x^{2}+12 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, A \,b^{2} x -3 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, C \,a^{2} x -8 \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, \sqrt{b^{2} c}\, B \,a^{2}\right)}{24 \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, \sqrt{b^{2} c}\, b^{2}}"," ",0,"1/24*(b*x+a)^(1/2)*(-(b*x-a)*c)^(1/2)*(6*C*x^3*b^2*(-(b^2*x^2-a^2)*c)^(1/2)*(b^2*c)^(1/2)+12*A*arctan((b^2*c)^(1/2)/(-(b^2*x^2-a^2)*c)^(1/2)*x)*a^2*b^2*c+8*B*x^2*b^2*(-(b^2*x^2-a^2)*c)^(1/2)*(b^2*c)^(1/2)+3*C*arctan((b^2*c)^(1/2)/(-(b^2*x^2-a^2)*c)^(1/2)*x)*a^4*c+12*A*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*x*b^2-3*C*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*x*a^2-8*B*a^2*(-(b^2*x^2-a^2)*c)^(1/2)*(b^2*c)^(1/2))/(-(b^2*x^2-a^2)*c)^(1/2)/b^2/(b^2*c)^(1/2)","A"
24,1,503,246,0.069000," ","int((C*x^2+B*x+A)/(f*x+e)/(b*x+a)^(1/2)/(-b*c*x+a*c)^(1/2),x)","\frac{\left(-\sqrt{b^{2} c}\, A \,b^{2} c \,f^{2} \ln \left(\frac{2 b^{2} c e x +2 a^{2} c f +2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, f}{f x +e}\right)+\sqrt{b^{2} c}\, B \,b^{2} c e f \ln \left(\frac{2 b^{2} c e x +2 a^{2} c f +2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, f}{f x +e}\right)+\sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, B \,b^{2} c \,f^{2} \arctan \left(\frac{\sqrt{b^{2} c}\, x}{\sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}}\right)-\sqrt{b^{2} c}\, C \,b^{2} c \,e^{2} \ln \left(\frac{2 b^{2} c e x +2 a^{2} c f +2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, f}{f x +e}\right)-\sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, C \,b^{2} c e f \arctan \left(\frac{\sqrt{b^{2} c}\, x}{\sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}}\right)-\sqrt{b^{2} c}\, \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, C \,f^{2}\right) \sqrt{b x +a}\, \sqrt{-\left(b x -a \right) c}}{\sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, b^{2} c \,f^{3}}"," ",0,"(-A*ln(2*(b^2*c*e*x+a^2*c*f+(c*(a^2*f^2-b^2*e^2)/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*f)/(f*x+e))*b^2*c*f^2*(b^2*c)^(1/2)+B*ln(2*(b^2*c*e*x+a^2*c*f+(c*(a^2*f^2-b^2*e^2)/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*f)/(f*x+e))*b^2*c*e*f*(b^2*c)^(1/2)+B*arctan((b^2*c)^(1/2)/(-(b^2*x^2-a^2)*c)^(1/2)*x)*b^2*c*f^2*(c*(a^2*f^2-b^2*e^2)/f^2)^(1/2)-C*ln(2*(b^2*c*e*x+a^2*c*f+(c*(a^2*f^2-b^2*e^2)/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*f)/(f*x+e))*b^2*c*e^2*(b^2*c)^(1/2)-C*arctan((b^2*c)^(1/2)/(-(b^2*x^2-a^2)*c)^(1/2)*x)*b^2*c*e*f*(c*(a^2*f^2-b^2*e^2)/f^2)^(1/2)-C*f^2*(b^2*c)^(1/2)*(c*(a^2*f^2-b^2*e^2)/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2))*(b*x+a)^(1/2)*(-(b*x-a)*c)^(1/2)/(c*(a^2*f^2-b^2*e^2)/f^2)^(1/2)/f^3/(b^2*c)^(1/2)/b^2/c/(-(b^2*x^2-a^2)*c)^(1/2)","B"
25,1,1200,290,0.044000," ","int((C*x^2+B*x+A)/(f*x+e)^2/(b*x+a)^(1/2)/(-b*c*x+a*c)^(1/2),x)","\frac{\left(\sqrt{b^{2} c}\, A \,b^{2} c e \,f^{3} x \ln \left(\frac{2 b^{2} c e x +2 a^{2} c f +2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, f}{f x +e}\right)-\sqrt{b^{2} c}\, B \,a^{2} c \,f^{4} x \ln \left(\frac{2 b^{2} c e x +2 a^{2} c f +2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, f}{f x +e}\right)+2 \sqrt{b^{2} c}\, C \,a^{2} c e \,f^{3} x \ln \left(\frac{2 b^{2} c e x +2 a^{2} c f +2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, f}{f x +e}\right)+\sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, C \,a^{2} c \,f^{4} x \arctan \left(\frac{\sqrt{b^{2} c}\, x}{\sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}}\right)-\sqrt{b^{2} c}\, C \,b^{2} c \,e^{3} f x \ln \left(\frac{2 b^{2} c e x +2 a^{2} c f +2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, f}{f x +e}\right)-\sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, C \,b^{2} c \,e^{2} f^{2} x \arctan \left(\frac{\sqrt{b^{2} c}\, x}{\sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}}\right)+\sqrt{b^{2} c}\, A \,b^{2} c \,e^{2} f^{2} \ln \left(\frac{2 b^{2} c e x +2 a^{2} c f +2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, f}{f x +e}\right)-\sqrt{b^{2} c}\, B \,a^{2} c e \,f^{3} \ln \left(\frac{2 b^{2} c e x +2 a^{2} c f +2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, f}{f x +e}\right)+2 \sqrt{b^{2} c}\, C \,a^{2} c \,e^{2} f^{2} \ln \left(\frac{2 b^{2} c e x +2 a^{2} c f +2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, f}{f x +e}\right)+\sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, C \,a^{2} c e \,f^{3} \arctan \left(\frac{\sqrt{b^{2} c}\, x}{\sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}}\right)-\sqrt{b^{2} c}\, C \,b^{2} c \,e^{4} \ln \left(\frac{2 b^{2} c e x +2 a^{2} c f +2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, f}{f x +e}\right)-\sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, C \,b^{2} c \,e^{3} f \arctan \left(\frac{\sqrt{b^{2} c}\, x}{\sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}}\right)-\sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, A \,f^{4}+\sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, B e \,f^{3}-\sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, C \,e^{2} f^{2}\right) \sqrt{-\left(b x -a \right) c}\, \sqrt{b x +a}}{\sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, \left(a f -b e \right) \sqrt{b^{2} c}\, \left(a f +b e \right) \left(f x +e \right) \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, c \,f^{3}}"," ",0,"(A*ln(2*(b^2*c*e*x+a^2*c*f+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*f)/(f*x+e))*x*b^2*c*e*f^3*(b^2*c)^(1/2)-B*ln(2*(b^2*c*e*x+a^2*c*f+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*f)/(f*x+e))*x*a^2*c*f^4*(b^2*c)^(1/2)+2*C*ln(2*(b^2*c*e*x+a^2*c*f+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*f)/(f*x+e))*x*a^2*c*e*f^3*(b^2*c)^(1/2)-C*ln(2*(b^2*c*e*x+a^2*c*f+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*f)/(f*x+e))*x*b^2*c*e^3*f*(b^2*c)^(1/2)+C*arctan((b^2*c)^(1/2)/(-(b^2*x^2-a^2)*c)^(1/2)*x)*x*a^2*c*f^4*((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)-C*arctan((b^2*c)^(1/2)/(-(b^2*x^2-a^2)*c)^(1/2)*x)*x*b^2*c*e^2*f^2*((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)+A*ln(2*(b^2*c*e*x+a^2*c*f+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*f)/(f*x+e))*b^2*c*e^2*f^2*(b^2*c)^(1/2)-B*ln(2*(b^2*c*e*x+a^2*c*f+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*f)/(f*x+e))*a^2*c*e*f^3*(b^2*c)^(1/2)+2*C*ln(2*(b^2*c*e*x+a^2*c*f+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*f)/(f*x+e))*a^2*c*e^2*f^2*(b^2*c)^(1/2)-C*ln(2*(b^2*c*e*x+a^2*c*f+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*f)/(f*x+e))*b^2*c*e^4*(b^2*c)^(1/2)+C*arctan((b^2*c)^(1/2)/(-(b^2*x^2-a^2)*c)^(1/2)*x)*a^2*c*e*f^3*((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)-C*arctan((b^2*c)^(1/2)/(-(b^2*x^2-a^2)*c)^(1/2)*x)*b^2*c*e^3*f*((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)-A*f^4*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)+B*e*f^3*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)-C*e^2*f^2*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*((a^2*f^2-b^2*e^2)*c/f^2)^(1/2))/c*(-(b*x-a)*c)^(1/2)*(b*x+a)^(1/2)/(-(b^2*x^2-a^2)*c)^(1/2)/(a*f-b*e)/(b^2*c)^(1/2)/(a*f+b*e)/(f*x+e)/((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)/f^3","B"
26,1,1848,333,0.057000," ","int((C*x^2+B*x+A)/(f*x+e)^3/(b*x+a)^(1/2)/(-b*c*x+a*c)^(1/2),x)","-\frac{\left(2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, B \,a^{2} f^{4} x -4 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, A \,b^{2} e^{2} f^{2}+\sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, B \,a^{2} e \,f^{3}+2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, B \,b^{2} e^{3} f -3 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, C \,a^{2} e^{2} f^{2}+2 C \,a^{4} c \,f^{4} x^{2} \ln \left(\frac{2 b^{2} c e x +2 a^{2} c f +2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, f}{f x +e}\right)+2 C \,a^{4} c \,e^{2} f^{2} \ln \left(\frac{2 b^{2} c e x +2 a^{2} c f +2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, f}{f x +e}\right)+C \,a^{2} b^{2} c \,e^{4} \ln \left(\frac{2 b^{2} c e x +2 a^{2} c f +2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, f}{f x +e}\right)+2 A \,b^{4} c \,e^{4} \ln \left(\frac{2 b^{2} c e x +2 a^{2} c f +2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, f}{f x +e}\right)+\sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, A \,a^{2} f^{4}-3 B \,a^{2} b^{2} c e \,f^{3} x^{2} \ln \left(\frac{2 b^{2} c e x +2 a^{2} c f +2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, f}{f x +e}\right)+C \,a^{2} b^{2} c \,e^{2} f^{2} x^{2} \ln \left(\frac{2 b^{2} c e x +2 a^{2} c f +2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, f}{f x +e}\right)+2 A \,a^{2} b^{2} c e \,f^{3} x \ln \left(\frac{2 b^{2} c e x +2 a^{2} c f +2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, f}{f x +e}\right)-6 B \,a^{2} b^{2} c \,e^{2} f^{2} x \ln \left(\frac{2 b^{2} c e x +2 a^{2} c f +2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, f}{f x +e}\right)+2 C \,a^{2} b^{2} c \,e^{3} f x \ln \left(\frac{2 b^{2} c e x +2 a^{2} c f +2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, f}{f x +e}\right)-4 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, C \,a^{2} e \,f^{3} x +\sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, C \,b^{2} e^{3} f x -3 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, A \,b^{2} e \,f^{3} x +\sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, B \,b^{2} e^{2} f^{2} x +A \,a^{2} b^{2} c \,f^{4} x^{2} \ln \left(\frac{2 b^{2} c e x +2 a^{2} c f +2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, f}{f x +e}\right)+2 A \,b^{4} c \,e^{2} f^{2} x^{2} \ln \left(\frac{2 b^{2} c e x +2 a^{2} c f +2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, f}{f x +e}\right)+4 A \,b^{4} c \,e^{3} f x \ln \left(\frac{2 b^{2} c e x +2 a^{2} c f +2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, f}{f x +e}\right)+4 C \,a^{4} c e \,f^{3} x \ln \left(\frac{2 b^{2} c e x +2 a^{2} c f +2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, f}{f x +e}\right)+A \,a^{2} b^{2} c \,e^{2} f^{2} \ln \left(\frac{2 b^{2} c e x +2 a^{2} c f +2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, f}{f x +e}\right)-3 B \,a^{2} b^{2} c \,e^{3} f \ln \left(\frac{2 b^{2} c e x +2 a^{2} c f +2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, f}{f x +e}\right)\right) \sqrt{-\left(b x -a \right) c}\, \sqrt{b x +a}}{2 \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, \left(a f -b e \right) \left(a f +b e \right) \left(a^{2} f^{2}-b^{2} e^{2}\right) \left(f x +e \right)^{2} \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, c f}"," ",0,"-1/2*(C*ln(2*(b^2*c*e*x+a^2*c*f+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*f)/(f*x+e))*x^2*a^2*b^2*c*e^2*f^2+2*A*ln(2*(b^2*c*e*x+a^2*c*f+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*f)/(f*x+e))*x*a^2*b^2*c*e*f^3+2*A*ln(2*(b^2*c*e*x+a^2*c*f+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*f)/(f*x+e))*b^4*c*e^4+2*C*ln(2*(b^2*c*e*x+a^2*c*f+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*f)/(f*x+e))*x^2*a^4*c*f^4+2*C*ln(2*(b^2*c*e*x+a^2*c*f+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*f)/(f*x+e))*a^4*c*e^2*f^2+C*ln(2*(b^2*c*e*x+a^2*c*f+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*f)/(f*x+e))*a^2*b^2*c*e^4+2*B*x*a^2*f^4*((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)-4*A*b^2*e^2*f^2*((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)+B*a^2*e*f^3*((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)+2*B*b^2*e^3*f*((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)-3*C*a^2*e^2*f^2*((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)-3*B*ln(2*(b^2*c*e*x+a^2*c*f+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*f)/(f*x+e))*x^2*a^2*b^2*c*e*f^3+A*a^2*f^4*((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)-6*B*ln(2*(b^2*c*e*x+a^2*c*f+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*f)/(f*x+e))*x*a^2*b^2*c*e^2*f^2+2*C*ln(2*(b^2*c*e*x+a^2*c*f+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*f)/(f*x+e))*x*a^2*b^2*c*e^3*f-4*C*x*a^2*e*f^3*((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)+A*ln(2*(b^2*c*e*x+a^2*c*f+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*f)/(f*x+e))*x^2*a^2*b^2*c*f^4+2*A*ln(2*(b^2*c*e*x+a^2*c*f+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*f)/(f*x+e))*x^2*b^4*c*e^2*f^2+4*A*ln(2*(b^2*c*e*x+a^2*c*f+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*f)/(f*x+e))*x*b^4*c*e^3*f+4*C*ln(2*(b^2*c*e*x+a^2*c*f+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*f)/(f*x+e))*x*a^4*c*e*f^3+A*ln(2*(b^2*c*e*x+a^2*c*f+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*f)/(f*x+e))*a^2*b^2*c*e^2*f^2-3*B*ln(2*(b^2*c*e*x+a^2*c*f+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*f)/(f*x+e))*a^2*b^2*c*e^3*f+C*x*b^2*e^3*f*((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)-3*A*x*b^2*e*f^3*((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)+B*x*b^2*e^2*f^2*((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2))/c*(-(b*x-a)*c)^(1/2)*(b*x+a)^(1/2)/(-(b^2*x^2-a^2)*c)^(1/2)/(a*f-b*e)/(a*f+b*e)/(a^2*f^2-b^2*e^2)/(f*x+e)^2/((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)/f","B"
27,1,965,460,0.031000," ","int((f*x+e)^3*(C*x^2+B*x+A)/(b*x+a)^(1/2)/(-b*c*x+a*c)^(1/2),x)","\frac{\sqrt{b x +a}\, \sqrt{-\left(b x -a \right) c}\, \left(180 A \,a^{2} b^{4} c e \,f^{2} \arctan \left(\frac{\sqrt{b^{2} c}\, x}{\sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}}\right)+120 A \,b^{6} c \,e^{3} \arctan \left(\frac{\sqrt{b^{2} c}\, x}{\sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}}\right)+45 B \,a^{4} b^{2} c \,f^{3} \arctan \left(\frac{\sqrt{b^{2} c}\, x}{\sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}}\right)+180 B \,a^{2} b^{4} c \,e^{2} f \arctan \left(\frac{\sqrt{b^{2} c}\, x}{\sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}}\right)+135 C \,a^{4} b^{2} c e \,f^{2} \arctan \left(\frac{\sqrt{b^{2} c}\, x}{\sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}}\right)+60 C \,a^{2} b^{4} c \,e^{3} \arctan \left(\frac{\sqrt{b^{2} c}\, x}{\sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}}\right)-24 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, C \,b^{4} f^{3} x^{4}-30 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, B \,b^{4} f^{3} x^{3}-90 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, C \,b^{4} e \,f^{2} x^{3}-40 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, A \,b^{4} f^{3} x^{2}-120 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, B \,b^{4} e \,f^{2} x^{2}-32 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, C \,a^{2} b^{2} f^{3} x^{2}-120 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, C \,b^{4} e^{2} f \,x^{2}-180 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, A \,b^{4} e \,f^{2} x -45 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, B \,a^{2} b^{2} f^{3} x -180 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, B \,b^{4} e^{2} f x -135 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, C \,a^{2} b^{2} e \,f^{2} x -60 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, C \,b^{4} e^{3} x -80 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, A \,a^{2} b^{2} f^{3}-360 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, A \,b^{4} e^{2} f -240 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, B \,a^{2} b^{2} e \,f^{2}-120 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, B \,b^{4} e^{3}-64 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, C \,a^{4} f^{3}-240 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, C \,a^{2} b^{2} e^{2} f \right)}{120 \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, \sqrt{b^{2} c}\, b^{6} c}"," ",0,"1/120*(b*x+a)^(1/2)*(-(b*x-a)*c)^(1/2)/c*(-24*C*x^4*b^4*f^3*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)-30*B*x^3*b^4*f^3*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)-90*C*x^3*b^4*e*f^2*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)+180*A*arctan((b^2*c)^(1/2)/(-(b^2*x^2-a^2)*c)^(1/2)*x)*a^2*b^4*c*e*f^2+120*A*arctan((b^2*c)^(1/2)/(-(b^2*x^2-a^2)*c)^(1/2)*x)*b^6*c*e^3-40*A*x^2*b^4*f^3*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)+45*B*arctan((b^2*c)^(1/2)/(-(b^2*x^2-a^2)*c)^(1/2)*x)*a^4*b^2*c*f^3+180*B*arctan((b^2*c)^(1/2)/(-(b^2*x^2-a^2)*c)^(1/2)*x)*a^2*b^4*c*e^2*f-120*B*x^2*b^4*e*f^2*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)+135*C*arctan((b^2*c)^(1/2)/(-(b^2*x^2-a^2)*c)^(1/2)*x)*a^4*b^2*c*e*f^2+60*C*arctan((b^2*c)^(1/2)/(-(b^2*x^2-a^2)*c)^(1/2)*x)*a^2*b^4*c*e^3-32*C*x^2*a^2*b^2*f^3*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)-120*C*x^2*b^4*e^2*f*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)-180*A*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*x*b^4*e*f^2-45*B*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*x*a^2*b^2*f^3-180*B*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*x*b^4*e^2*f-135*C*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*x*a^2*b^2*e*f^2-60*C*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*x*b^4*e^3-80*A*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*a^2*b^2*f^3-360*A*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*b^4*e^2*f-240*B*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*a^2*b^2*e*f^2-120*B*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*b^4*e^3-64*C*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*a^4*f^3-240*C*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*a^2*b^2*e^2*f)/b^6/(-(b^2*x^2-a^2)*c)^(1/2)/(b^2*c)^(1/2)","B"
28,1,635,333,0.029000," ","int((f*x+e)^2*(C*x^2+B*x+A)/(b*x+a)^(1/2)/(-b*c*x+a*c)^(1/2),x)","\frac{\sqrt{b x +a}\, \sqrt{-\left(b x -a \right) c}\, \left(12 A \,a^{2} b^{2} c \,f^{2} \arctan \left(\frac{\sqrt{b^{2} c}\, x}{\sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}}\right)+24 A \,b^{4} c \,e^{2} \arctan \left(\frac{\sqrt{b^{2} c}\, x}{\sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}}\right)+24 B \,a^{2} b^{2} c e f \arctan \left(\frac{\sqrt{b^{2} c}\, x}{\sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}}\right)+9 C \,a^{4} c \,f^{2} \arctan \left(\frac{\sqrt{b^{2} c}\, x}{\sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}}\right)+12 C \,a^{2} b^{2} c \,e^{2} \arctan \left(\frac{\sqrt{b^{2} c}\, x}{\sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}}\right)-6 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, C \,b^{2} f^{2} x^{3}-8 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, B \,b^{2} f^{2} x^{2}-16 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, C \,b^{2} e f \,x^{2}-12 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, A \,b^{2} f^{2} x -24 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, B \,b^{2} e f x -9 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, C \,a^{2} f^{2} x -12 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, C \,b^{2} e^{2} x -48 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, A \,b^{2} e f -16 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, B \,a^{2} f^{2}-24 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, B \,b^{2} e^{2}-32 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, C \,a^{2} e f \right)}{24 \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, \sqrt{b^{2} c}\, b^{4} c}"," ",0,"1/24*(b*x+a)^(1/2)*(-(b*x-a)*c)^(1/2)/c*(-6*C*x^3*b^2*f^2*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)+12*A*arctan((b^2*c)^(1/2)/(-(b^2*x^2-a^2)*c)^(1/2)*x)*a^2*b^2*c*f^2+24*A*arctan((b^2*c)^(1/2)/(-(b^2*x^2-a^2)*c)^(1/2)*x)*b^4*c*e^2+24*B*arctan((b^2*c)^(1/2)/(-(b^2*x^2-a^2)*c)^(1/2)*x)*a^2*b^2*c*e*f-8*B*x^2*b^2*f^2*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)+9*C*arctan((b^2*c)^(1/2)/(-(b^2*x^2-a^2)*c)^(1/2)*x)*a^4*c*f^2+12*C*arctan((b^2*c)^(1/2)/(-(b^2*x^2-a^2)*c)^(1/2)*x)*a^2*b^2*c*e^2-16*C*x^2*b^2*e*f*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)-12*A*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*x*b^2*f^2-24*B*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*x*b^2*e*f-9*C*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*x*a^2*f^2-12*C*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*x*b^2*e^2-48*A*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*b^2*e*f-16*B*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*a^2*f^2-24*B*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*b^2*e^2-32*C*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*a^2*e*f)/b^4/(-(b^2*x^2-a^2)*c)^(1/2)/(b^2*c)^(1/2)","A"
29,1,365,217,0.026000," ","int((f*x+e)*(C*x^2+B*x+A)/(b*x+a)^(1/2)/(-b*c*x+a*c)^(1/2),x)","\frac{\sqrt{b x +a}\, \sqrt{-\left(b x -a \right) c}\, \left(6 A \,b^{4} c e \arctan \left(\frac{\sqrt{b^{2} c}\, x}{\sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}}\right)+3 B \,a^{2} b^{2} c f \arctan \left(\frac{\sqrt{b^{2} c}\, x}{\sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}}\right)+3 C \,a^{2} b^{2} c e \arctan \left(\frac{\sqrt{b^{2} c}\, x}{\sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}}\right)-2 \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, \sqrt{b^{2} c}\, C \,b^{2} f \,x^{2}-3 \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, \sqrt{b^{2} c}\, B \,b^{2} f x -3 \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, \sqrt{b^{2} c}\, C \,b^{2} e x -6 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, A \,b^{2} f -6 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, B \,b^{2} e -4 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, C \,a^{2} f \right)}{6 \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, \sqrt{b^{2} c}\, b^{4} c}"," ",0,"1/6*(b*x+a)^(1/2)*(-(b*x-a)*c)^(1/2)/c*(6*A*arctan((b^2*c)^(1/2)/(-(b^2*x^2-a^2)*c)^(1/2)*x)*b^4*c*e+3*B*arctan((b^2*c)^(1/2)/(-(b^2*x^2-a^2)*c)^(1/2)*x)*a^2*b^2*c*f+3*C*arctan((b^2*c)^(1/2)/(-(b^2*x^2-a^2)*c)^(1/2)*x)*a^2*b^2*c*e-2*C*x^2*b^2*f*(-(b^2*x^2-a^2)*c)^(1/2)*(b^2*c)^(1/2)-3*B*(-(b^2*x^2-a^2)*c)^(1/2)*(b^2*c)^(1/2)*x*b^2*f-3*C*(-(b^2*x^2-a^2)*c)^(1/2)*(b^2*c)^(1/2)*x*b^2*e-6*A*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*b^2*f-6*B*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*b^2*e-4*C*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*a^2*f)/(-(b^2*x^2-a^2)*c)^(1/2)/b^4/(b^2*c)^(1/2)","A"
30,1,180,153,0.020000," ","int((C*x^2+B*x+A)/(b*x+a)^(1/2)/(-b*c*x+a*c)^(1/2),x)","\frac{\sqrt{b x +a}\, \sqrt{-\left(b x -a \right) c}\, \left(2 A \,b^{2} c \arctan \left(\frac{\sqrt{b^{2} c}\, x}{\sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}}\right)+C \,a^{2} c \arctan \left(\frac{\sqrt{b^{2} c}\, x}{\sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}}\right)-\sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, C x -2 \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, B \right)}{2 \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, \sqrt{b^{2} c}\, b^{2} c}"," ",0,"1/2*(b*x+a)^(1/2)*(-(b*x-a)*c)^(1/2)/b^2*(2*A*arctan((b^2*c)^(1/2)/(-(b^2*x^2-a^2)*c)^(1/2)*x)*b^2*c+C*arctan((b^2*c)^(1/2)/(-(b^2*x^2-a^2)*c)^(1/2)*x)*a^2*c-C*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*x-2*B*(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2))/(-(b^2*x^2-a^2)*c)^(1/2)/c/(b^2*c)^(1/2)","A"
31,1,503,246,0.000000," ","int((C*x^2+B*x+A)/(f*x+e)/(b*x+a)^(1/2)/(-b*c*x+a*c)^(1/2),x)","\frac{\left(-\sqrt{b^{2} c}\, A \,b^{2} c \,f^{2} \ln \left(\frac{2 b^{2} c e x +2 a^{2} c f +2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, f}{f x +e}\right)+\sqrt{b^{2} c}\, B \,b^{2} c e f \ln \left(\frac{2 b^{2} c e x +2 a^{2} c f +2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, f}{f x +e}\right)+\sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, B \,b^{2} c \,f^{2} \arctan \left(\frac{\sqrt{b^{2} c}\, x}{\sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}}\right)-\sqrt{b^{2} c}\, C \,b^{2} c \,e^{2} \ln \left(\frac{2 b^{2} c e x +2 a^{2} c f +2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, f}{f x +e}\right)-\sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, C \,b^{2} c e f \arctan \left(\frac{\sqrt{b^{2} c}\, x}{\sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}}\right)-\sqrt{b^{2} c}\, \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, C \,f^{2}\right) \sqrt{b x +a}\, \sqrt{-\left(b x -a \right) c}}{\sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, b^{2} c \,f^{3}}"," ",0,"(-(b^2*c)^(1/2)*A*b^2*c*f^2*ln(2*(b^2*c*e*x+a^2*c*f+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*f)/(f*x+e))+(b^2*c)^(1/2)*B*b^2*c*e*f*ln(2*(b^2*c*e*x+a^2*c*f+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*f)/(f*x+e))+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*B*b^2*c*f^2*arctan((b^2*c)^(1/2)/(-(b^2*x^2-a^2)*c)^(1/2)*x)-(b^2*c)^(1/2)*C*b^2*c*e^2*ln(2*(b^2*c*e*x+a^2*c*f+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*f)/(f*x+e))-((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*C*b^2*c*e*f*arctan((b^2*c)^(1/2)/(-(b^2*x^2-a^2)*c)^(1/2)*x)-(b^2*c)^(1/2)*((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*C*f^2)*(b*x+a)^(1/2)*(-(b*x-a)*c)^(1/2)/((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)/(b^2*c)^(1/2)/(-(b^2*x^2-a^2)*c)^(1/2)/b^2/c/f^3","B"
32,1,1200,290,0.000000," ","int((C*x^2+B*x+A)/(f*x+e)^2/(b*x+a)^(1/2)/(-b*c*x+a*c)^(1/2),x)","\frac{\left(\sqrt{b^{2} c}\, A \,b^{2} c e \,f^{3} x \ln \left(\frac{2 b^{2} c e x +2 a^{2} c f +2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, f}{f x +e}\right)-\sqrt{b^{2} c}\, B \,a^{2} c \,f^{4} x \ln \left(\frac{2 b^{2} c e x +2 a^{2} c f +2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, f}{f x +e}\right)+2 \sqrt{b^{2} c}\, C \,a^{2} c e \,f^{3} x \ln \left(\frac{2 b^{2} c e x +2 a^{2} c f +2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, f}{f x +e}\right)+\sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, C \,a^{2} c \,f^{4} x \arctan \left(\frac{\sqrt{b^{2} c}\, x}{\sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}}\right)-\sqrt{b^{2} c}\, C \,b^{2} c \,e^{3} f x \ln \left(\frac{2 b^{2} c e x +2 a^{2} c f +2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, f}{f x +e}\right)-\sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, C \,b^{2} c \,e^{2} f^{2} x \arctan \left(\frac{\sqrt{b^{2} c}\, x}{\sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}}\right)+\sqrt{b^{2} c}\, A \,b^{2} c \,e^{2} f^{2} \ln \left(\frac{2 b^{2} c e x +2 a^{2} c f +2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, f}{f x +e}\right)-\sqrt{b^{2} c}\, B \,a^{2} c e \,f^{3} \ln \left(\frac{2 b^{2} c e x +2 a^{2} c f +2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, f}{f x +e}\right)+2 \sqrt{b^{2} c}\, C \,a^{2} c \,e^{2} f^{2} \ln \left(\frac{2 b^{2} c e x +2 a^{2} c f +2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, f}{f x +e}\right)+\sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, C \,a^{2} c e \,f^{3} \arctan \left(\frac{\sqrt{b^{2} c}\, x}{\sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}}\right)-\sqrt{b^{2} c}\, C \,b^{2} c \,e^{4} \ln \left(\frac{2 b^{2} c e x +2 a^{2} c f +2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, f}{f x +e}\right)-\sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, C \,b^{2} c \,e^{3} f \arctan \left(\frac{\sqrt{b^{2} c}\, x}{\sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}}\right)-\sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, A \,f^{4}+\sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, B e \,f^{3}-\sqrt{b^{2} c}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, C \,e^{2} f^{2}\right) \sqrt{-\left(b x -a \right) c}\, \sqrt{b x +a}}{\sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, \left(a f -b e \right) \sqrt{b^{2} c}\, \left(a f +b e \right) \left(f x +e \right) \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, c \,f^{3}}"," ",0,"((b^2*c)^(1/2)*A*b^2*c*e*f^3*x*ln(2*(b^2*c*e*x+a^2*c*f+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*f)/(f*x+e))-(b^2*c)^(1/2)*B*a^2*c*f^4*x*ln(2*(b^2*c*e*x+a^2*c*f+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*f)/(f*x+e))+2*(b^2*c)^(1/2)*C*a^2*c*e*f^3*x*ln(2*(b^2*c*e*x+a^2*c*f+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*f)/(f*x+e))+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*C*a^2*c*f^4*x*arctan((b^2*c)^(1/2)/(-(b^2*x^2-a^2)*c)^(1/2)*x)-(b^2*c)^(1/2)*C*b^2*c*e^3*f*x*ln(2*(b^2*c*e*x+a^2*c*f+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*f)/(f*x+e))-((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*C*b^2*c*e^2*f^2*x*arctan((b^2*c)^(1/2)/(-(b^2*x^2-a^2)*c)^(1/2)*x)+(b^2*c)^(1/2)*A*b^2*c*e^2*f^2*ln(2*(b^2*c*e*x+a^2*c*f+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*f)/(f*x+e))-(b^2*c)^(1/2)*B*a^2*c*e*f^3*ln(2*(b^2*c*e*x+a^2*c*f+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*f)/(f*x+e))+2*(b^2*c)^(1/2)*C*a^2*c*e^2*f^2*ln(2*(b^2*c*e*x+a^2*c*f+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*f)/(f*x+e))+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*C*a^2*c*e*f^3*arctan((b^2*c)^(1/2)/(-(b^2*x^2-a^2)*c)^(1/2)*x)-(b^2*c)^(1/2)*C*b^2*c*e^4*ln(2*(b^2*c*e*x+a^2*c*f+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*f)/(f*x+e))-((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*C*b^2*c*e^3*f*arctan((b^2*c)^(1/2)/(-(b^2*x^2-a^2)*c)^(1/2)*x)-(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*A*f^4+(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*B*e*f^3-(b^2*c)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*C*e^2*f^2)*(-(b*x-a)*c)^(1/2)*(b*x+a)^(1/2)/(-(b^2*x^2-a^2)*c)^(1/2)/(a*f-b*e)/(b^2*c)^(1/2)/(a*f+b*e)/(f*x+e)/((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)/c/f^3","B"
33,1,1848,333,0.000000," ","int((C*x^2+B*x+A)/(f*x+e)^3/(b*x+a)^(1/2)/(-b*c*x+a*c)^(1/2),x)","-\frac{\left(2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, B \,a^{2} f^{4} x -4 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, A \,b^{2} e^{2} f^{2}+\sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, B \,a^{2} e \,f^{3}+2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, B \,b^{2} e^{3} f -3 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, C \,a^{2} e^{2} f^{2}+2 C \,a^{4} c \,f^{4} x^{2} \ln \left(\frac{2 b^{2} c e x +2 a^{2} c f +2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, f}{f x +e}\right)+2 C \,a^{4} c \,e^{2} f^{2} \ln \left(\frac{2 b^{2} c e x +2 a^{2} c f +2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, f}{f x +e}\right)+C \,a^{2} b^{2} c \,e^{4} \ln \left(\frac{2 b^{2} c e x +2 a^{2} c f +2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, f}{f x +e}\right)+2 A \,b^{4} c \,e^{4} \ln \left(\frac{2 b^{2} c e x +2 a^{2} c f +2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, f}{f x +e}\right)+\sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, A \,a^{2} f^{4}-3 B \,a^{2} b^{2} c e \,f^{3} x^{2} \ln \left(\frac{2 b^{2} c e x +2 a^{2} c f +2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, f}{f x +e}\right)+C \,a^{2} b^{2} c \,e^{2} f^{2} x^{2} \ln \left(\frac{2 b^{2} c e x +2 a^{2} c f +2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, f}{f x +e}\right)+2 A \,a^{2} b^{2} c e \,f^{3} x \ln \left(\frac{2 b^{2} c e x +2 a^{2} c f +2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, f}{f x +e}\right)-6 B \,a^{2} b^{2} c \,e^{2} f^{2} x \ln \left(\frac{2 b^{2} c e x +2 a^{2} c f +2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, f}{f x +e}\right)+2 C \,a^{2} b^{2} c \,e^{3} f x \ln \left(\frac{2 b^{2} c e x +2 a^{2} c f +2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, f}{f x +e}\right)-4 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, C \,a^{2} e \,f^{3} x +\sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, C \,b^{2} e^{3} f x -3 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, A \,b^{2} e \,f^{3} x +\sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, B \,b^{2} e^{2} f^{2} x +A \,a^{2} b^{2} c \,f^{4} x^{2} \ln \left(\frac{2 b^{2} c e x +2 a^{2} c f +2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, f}{f x +e}\right)+2 A \,b^{4} c \,e^{2} f^{2} x^{2} \ln \left(\frac{2 b^{2} c e x +2 a^{2} c f +2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, f}{f x +e}\right)+4 A \,b^{4} c \,e^{3} f x \ln \left(\frac{2 b^{2} c e x +2 a^{2} c f +2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, f}{f x +e}\right)+4 C \,a^{4} c e \,f^{3} x \ln \left(\frac{2 b^{2} c e x +2 a^{2} c f +2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, f}{f x +e}\right)+A \,a^{2} b^{2} c \,e^{2} f^{2} \ln \left(\frac{2 b^{2} c e x +2 a^{2} c f +2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, f}{f x +e}\right)-3 B \,a^{2} b^{2} c \,e^{3} f \ln \left(\frac{2 b^{2} c e x +2 a^{2} c f +2 \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, f}{f x +e}\right)\right) \sqrt{-\left(b x -a \right) c}\, \sqrt{b x +a}}{2 \sqrt{-\left(b^{2} x^{2}-a^{2}\right) c}\, \left(a f -b e \right) \left(a f +b e \right) \left(a^{2} f^{2}-b^{2} e^{2}\right) \left(f x +e \right)^{2} \sqrt{\frac{\left(a^{2} f^{2}-b^{2} e^{2}\right) c}{f^{2}}}\, c f}"," ",0,"-1/2*(A*a^2*b^2*c*f^4*x^2*ln(2*(b^2*c*e*x+a^2*c*f+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*f)/(f*x+e))+2*A*b^4*c*e^2*f^2*x^2*ln(2*(b^2*c*e*x+a^2*c*f+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*f)/(f*x+e))-3*B*a^2*b^2*c*e*f^3*x^2*ln(2*(b^2*c*e*x+a^2*c*f+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*f)/(f*x+e))+2*C*a^4*c*f^4*x^2*ln(2*(b^2*c*e*x+a^2*c*f+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*f)/(f*x+e))+C*a^2*b^2*c*e^2*f^2*x^2*ln(2*(b^2*c*e*x+a^2*c*f+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*f)/(f*x+e))+2*A*a^2*b^2*c*e*f^3*x*ln(2*(b^2*c*e*x+a^2*c*f+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*f)/(f*x+e))+4*A*b^4*c*e^3*f*x*ln(2*(b^2*c*e*x+a^2*c*f+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*f)/(f*x+e))-6*B*a^2*b^2*c*e^2*f^2*x*ln(2*(b^2*c*e*x+a^2*c*f+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*f)/(f*x+e))+4*C*a^4*c*e*f^3*x*ln(2*(b^2*c*e*x+a^2*c*f+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*f)/(f*x+e))+2*C*a^2*b^2*c*e^3*f*x*ln(2*(b^2*c*e*x+a^2*c*f+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*f)/(f*x+e))+A*a^2*b^2*c*e^2*f^2*ln(2*(b^2*c*e*x+a^2*c*f+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*f)/(f*x+e))+2*A*b^4*c*e^4*ln(2*(b^2*c*e*x+a^2*c*f+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*f)/(f*x+e))-3*B*a^2*b^2*c*e^3*f*ln(2*(b^2*c*e*x+a^2*c*f+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*f)/(f*x+e))+2*C*a^4*c*e^2*f^2*ln(2*(b^2*c*e*x+a^2*c*f+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*f)/(f*x+e))+C*a^2*b^2*c*e^4*ln(2*(b^2*c*e*x+a^2*c*f+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*f)/(f*x+e))-3*((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*A*b^2*e*f^3*x+2*((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*B*a^2*f^4*x+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*B*b^2*e^2*f^2*x-4*((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*C*a^2*e*f^3*x+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*C*b^2*e^3*f*x+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*A*a^2*f^4-4*((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*A*b^2*e^2*f^2+((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*B*a^2*e*f^3+2*((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*B*b^2*e^3*f-3*((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)*(-(b^2*x^2-a^2)*c)^(1/2)*C*a^2*e^2*f^2)*(-(b*x-a)*c)^(1/2)*(b*x+a)^(1/2)/(-(b^2*x^2-a^2)*c)^(1/2)/(a*f-b*e)/(a*f+b*e)/(a^2*f^2-b^2*e^2)/(f*x+e)^2/((a^2*f^2-b^2*e^2)*c/f^2)^(1/2)/c/f","B"
34,1,137,70,0.000000," ","int(x*(c*x^2+b*x+a)/(d*x-1)^(1/2)/(d*x+1)^(1/2),x)","\frac{\sqrt{d x -1}\, \sqrt{d x +1}\, \left(2 \sqrt{d^{2} x^{2}-1}\, c \,d^{2} x^{2} \mathrm{csgn}\left(d \right)+3 \sqrt{d^{2} x^{2}-1}\, b \,d^{2} x \,\mathrm{csgn}\left(d \right)+6 \sqrt{d^{2} x^{2}-1}\, a \,d^{2} \mathrm{csgn}\left(d \right)+3 b d \ln \left(\left(d x +\sqrt{d^{2} x^{2}-1}\, \mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)\right)+4 \sqrt{d^{2} x^{2}-1}\, c \,\mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)}{6 \sqrt{d^{2} x^{2}-1}\, d^{4}}"," ",0,"1/6*(d*x-1)^(1/2)*(d*x+1)^(1/2)*(2*(d^2*x^2-1)^(1/2)*c*d^2*x^2*csgn(d)+3*(d^2*x^2-1)^(1/2)*b*d^2*x*csgn(d)+6*(d^2*x^2-1)^(1/2)*a*d^2*csgn(d)+3*b*d*ln((d*x+(d^2*x^2-1)^(1/2)*csgn(d))*csgn(d))+4*(d^2*x^2-1)^(1/2)*c*csgn(d))/(d^2*x^2-1)^(1/2)/d^4*csgn(d)","C"
35,1,120,44,0.000000," ","int((c*x^2+b*x+a)/(d*x-1)^(1/2)/(d*x+1)^(1/2),x)","\frac{\sqrt{d x -1}\, \sqrt{d x +1}\, \left(2 a \,d^{2} \ln \left(\left(d x +\sqrt{d^{2} x^{2}-1}\, \mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)\right)+\sqrt{d^{2} x^{2}-1}\, c d x \,\mathrm{csgn}\left(d \right)+2 \sqrt{d^{2} x^{2}-1}\, b d \,\mathrm{csgn}\left(d \right)+c \ln \left(\left(d x +\sqrt{d^{2} x^{2}-1}\, \mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)\right)\right) \mathrm{csgn}\left(d \right)}{2 \sqrt{d^{2} x^{2}-1}\, d^{3}}"," ",0,"1/2*(d*x-1)^(1/2)*(d*x+1)^(1/2)*(2*a*d^2*ln((d*x+(d^2*x^2-1)^(1/2)*csgn(d))*csgn(d))+(d^2*x^2-1)^(1/2)*c*d*x*csgn(d)+2*(d^2*x^2-1)^(1/2)*b*d*csgn(d)+c*ln((d*x+(d^2*x^2-1)^(1/2)*csgn(d))*csgn(d)))/(d^2*x^2-1)^(1/2)/d^3*csgn(d)","C"
36,1,95,47,0.000000," ","int((c*x^2+b*x+a)/x/(d*x-1)^(1/2)/(d*x+1)^(1/2),x)","\frac{\left(-a \,d^{2} \arctan \left(\frac{1}{\sqrt{d^{2} x^{2}-1}}\right) \mathrm{csgn}\left(d \right)+b d \ln \left(\left(d x +\sqrt{\left(d x +1\right) \left(d x -1\right)}\, \mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)\right)+\sqrt{d^{2} x^{2}-1}\, c \,\mathrm{csgn}\left(d \right)\right) \sqrt{d x -1}\, \sqrt{d x +1}\, \mathrm{csgn}\left(d \right)}{\sqrt{d^{2} x^{2}-1}\, d^{2}}"," ",0,"(-a*d^2*arctan(1/(d^2*x^2-1)^(1/2))*csgn(d)+b*d*ln((d*x+((d*x+1)*(d*x-1))^(1/2)*csgn(d))*csgn(d))+(d^2*x^2-1)^(1/2)*c*csgn(d))*(d*x-1)^(1/2)*(d*x+1)^(1/2)/(d^2*x^2-1)^(1/2)/d^2*csgn(d)","C"
37,1,96,47,0.001000," ","int((c*x^2+b*x+a)/x^2/(d*x-1)^(1/2)/(d*x+1)^(1/2),x)","\frac{\left(-b d x \arctan \left(\frac{1}{\sqrt{d^{2} x^{2}-1}}\right) \mathrm{csgn}\left(d \right)+\sqrt{d^{2} x^{2}-1}\, a d \,\mathrm{csgn}\left(d \right)+c x \ln \left(\left(d x +\sqrt{d^{2} x^{2}-1}\, \mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)\right)\right) \sqrt{d x -1}\, \sqrt{d x +1}\, \mathrm{csgn}\left(d \right)}{\sqrt{d^{2} x^{2}-1}\, d x}"," ",0,"(-b*d*x*arctan(1/(d^2*x^2-1)^(1/2))*csgn(d)+(d^2*x^2-1)^(1/2)*a*d*csgn(d)+c*x*ln((d*x+(d^2*x^2-1)^(1/2)*csgn(d))*csgn(d)))*(d*x-1)^(1/2)*(d*x+1)^(1/2)/(d^2*x^2-1)^(1/2)/d/x*csgn(d)","C"
38,1,103,67,0.000000," ","int((c*x^2+b*x+a)/x^3/(d*x-1)^(1/2)/(d*x+1)^(1/2),x)","-\frac{\sqrt{d x -1}\, \sqrt{d x +1}\, \left(a \,d^{2} x^{2} \arctan \left(\frac{1}{\sqrt{d^{2} x^{2}-1}}\right)+2 c \,x^{2} \arctan \left(\frac{1}{\sqrt{d^{2} x^{2}-1}}\right)-2 \sqrt{d^{2} x^{2}-1}\, b x -\sqrt{d^{2} x^{2}-1}\, a \right) \mathrm{csgn}\left(d \right)^{2}}{2 \sqrt{d^{2} x^{2}-1}\, x^{2}}"," ",0,"-1/2*(d*x-1)^(1/2)*(d*x+1)^(1/2)*(a*d^2*x^2*arctan(1/(d^2*x^2-1)^(1/2))+2*c*x^2*arctan(1/(d^2*x^2-1)^(1/2))-2*(d^2*x^2-1)^(1/2)*b*x-(d^2*x^2-1)^(1/2)*a)/(d^2*x^2-1)^(1/2)/x^2*csgn(d)^2","C"
39,1,123,92,0.000000," ","int((c*x^2+b*x+a)/x^4/(d*x-1)^(1/2)/(d*x+1)^(1/2),x)","-\frac{\sqrt{d x -1}\, \sqrt{d x +1}\, \left(3 b \,d^{2} x^{3} \arctan \left(\frac{1}{\sqrt{d^{2} x^{2}-1}}\right)-4 \sqrt{d^{2} x^{2}-1}\, a \,d^{2} x^{2}-6 \sqrt{d^{2} x^{2}-1}\, c \,x^{2}-3 \sqrt{d^{2} x^{2}-1}\, b x -2 \sqrt{d^{2} x^{2}-1}\, a \right) \mathrm{csgn}\left(d \right)^{2}}{6 \sqrt{d^{2} x^{2}-1}\, x^{3}}"," ",0,"-1/6*(d*x-1)^(1/2)*(d*x+1)^(1/2)*(3*b*d^2*x^3*arctan(1/(d^2*x^2-1)^(1/2))-4*(d^2*x^2-1)^(1/2)*a*d^2*x^2-6*(d^2*x^2-1)^(1/2)*c*x^2-3*(d^2*x^2-1)^(1/2)*b*x-2*(d^2*x^2-1)^(1/2)*a)/(d^2*x^2-1)^(1/2)/x^3*csgn(d)^2","C"
40,1,1095,175,0.053000," ","int((c*x^2+b*x+a)/(e*x+d)^3/(x-1)^(1/2)/(x+1)^(1/2),x)","-\frac{\left(2 a \,d^{2} e^{2} x^{2} \ln \left(-\frac{2 \left(d x -\sqrt{\frac{d^{2}-e^{2}}{e^{2}}}\, \sqrt{x^{2}-1}\, e +e \right)}{e x +d}\right)+a \,e^{4} x^{2} \ln \left(-\frac{2 \left(d x -\sqrt{\frac{d^{2}-e^{2}}{e^{2}}}\, \sqrt{x^{2}-1}\, e +e \right)}{e x +d}\right)-3 b d \,e^{3} x^{2} \ln \left(-\frac{2 \left(d x -\sqrt{\frac{d^{2}-e^{2}}{e^{2}}}\, \sqrt{x^{2}-1}\, e +e \right)}{e x +d}\right)+c \,d^{2} e^{2} x^{2} \ln \left(-\frac{2 \left(d x -\sqrt{\frac{d^{2}-e^{2}}{e^{2}}}\, \sqrt{x^{2}-1}\, e +e \right)}{e x +d}\right)+2 c \,e^{4} x^{2} \ln \left(-\frac{2 \left(d x -\sqrt{\frac{d^{2}-e^{2}}{e^{2}}}\, \sqrt{x^{2}-1}\, e +e \right)}{e x +d}\right)+4 a \,d^{3} e x \ln \left(-\frac{2 \left(d x -\sqrt{\frac{d^{2}-e^{2}}{e^{2}}}\, \sqrt{x^{2}-1}\, e +e \right)}{e x +d}\right)+2 a d \,e^{3} x \ln \left(-\frac{2 \left(d x -\sqrt{\frac{d^{2}-e^{2}}{e^{2}}}\, \sqrt{x^{2}-1}\, e +e \right)}{e x +d}\right)-6 b \,d^{2} e^{2} x \ln \left(-\frac{2 \left(d x -\sqrt{\frac{d^{2}-e^{2}}{e^{2}}}\, \sqrt{x^{2}-1}\, e +e \right)}{e x +d}\right)+2 c \,d^{3} e x \ln \left(-\frac{2 \left(d x -\sqrt{\frac{d^{2}-e^{2}}{e^{2}}}\, \sqrt{x^{2}-1}\, e +e \right)}{e x +d}\right)+4 c d \,e^{3} x \ln \left(-\frac{2 \left(d x -\sqrt{\frac{d^{2}-e^{2}}{e^{2}}}\, \sqrt{x^{2}-1}\, e +e \right)}{e x +d}\right)+2 a \,d^{4} \ln \left(-\frac{2 \left(d x -\sqrt{\frac{d^{2}-e^{2}}{e^{2}}}\, \sqrt{x^{2}-1}\, e +e \right)}{e x +d}\right)+a \,d^{2} e^{2} \ln \left(-\frac{2 \left(d x -\sqrt{\frac{d^{2}-e^{2}}{e^{2}}}\, \sqrt{x^{2}-1}\, e +e \right)}{e x +d}\right)+3 \sqrt{\frac{d^{2}-e^{2}}{e^{2}}}\, \sqrt{x^{2}-1}\, a d \,e^{3} x -3 b \,d^{3} e \ln \left(-\frac{2 \left(d x -\sqrt{\frac{d^{2}-e^{2}}{e^{2}}}\, \sqrt{x^{2}-1}\, e +e \right)}{e x +d}\right)-\sqrt{\frac{d^{2}-e^{2}}{e^{2}}}\, \sqrt{x^{2}-1}\, b \,d^{2} e^{2} x -2 \sqrt{\frac{d^{2}-e^{2}}{e^{2}}}\, \sqrt{x^{2}-1}\, b \,e^{4} x +c \,d^{4} \ln \left(-\frac{2 \left(d x -\sqrt{\frac{d^{2}-e^{2}}{e^{2}}}\, \sqrt{x^{2}-1}\, e +e \right)}{e x +d}\right)-\sqrt{\frac{d^{2}-e^{2}}{e^{2}}}\, \sqrt{x^{2}-1}\, c \,d^{3} e x +2 c \,d^{2} e^{2} \ln \left(-\frac{2 \left(d x -\sqrt{\frac{d^{2}-e^{2}}{e^{2}}}\, \sqrt{x^{2}-1}\, e +e \right)}{e x +d}\right)+4 \sqrt{\frac{d^{2}-e^{2}}{e^{2}}}\, \sqrt{x^{2}-1}\, c d \,e^{3} x +4 \sqrt{\frac{d^{2}-e^{2}}{e^{2}}}\, \sqrt{x^{2}-1}\, a \,d^{2} e^{2}-\sqrt{\frac{d^{2}-e^{2}}{e^{2}}}\, \sqrt{x^{2}-1}\, a \,e^{4}-2 \sqrt{\frac{d^{2}-e^{2}}{e^{2}}}\, \sqrt{x^{2}-1}\, b \,d^{3} e -\sqrt{\frac{d^{2}-e^{2}}{e^{2}}}\, \sqrt{x^{2}-1}\, b d \,e^{3}+3 \sqrt{\frac{d^{2}-e^{2}}{e^{2}}}\, \sqrt{x^{2}-1}\, c \,d^{2} e^{2}\right) \sqrt{x +1}\, \sqrt{x -1}}{2 \sqrt{x^{2}-1}\, \left(d -e \right) \left(d +e \right) \sqrt{\frac{d^{2}-e^{2}}{e^{2}}}\, \left(d^{2}-e^{2}\right) \left(e x +d \right)^{2} e}"," ",0,"-1/2*(3*x*a*d*e^3*((d^2-e^2)/e^2)^(1/2)*(x^2-1)^(1/2)-2*x*b*e^4*((d^2-e^2)/e^2)^(1/2)*(x^2-1)^(1/2)+2*ln(-2*(-((d^2-e^2)/e^2)^(1/2)*(x^2-1)^(1/2)*e+d*x+e)/(e*x+d))*c*d^2*e^2-a*e^4*((d^2-e^2)/e^2)^(1/2)*(x^2-1)^(1/2)+ln(-2*(-((d^2-e^2)/e^2)^(1/2)*(x^2-1)^(1/2)*e+d*x+e)/(e*x+d))*x^2*a*e^4+2*ln(-2*(-((d^2-e^2)/e^2)^(1/2)*(x^2-1)^(1/2)*e+d*x+e)/(e*x+d))*x^2*c*e^4+ln(-2*(-((d^2-e^2)/e^2)^(1/2)*(x^2-1)^(1/2)*e+d*x+e)/(e*x+d))*a*d^2*e^2-3*ln(-2*(-((d^2-e^2)/e^2)^(1/2)*(x^2-1)^(1/2)*e+d*x+e)/(e*x+d))*b*d^3*e+2*ln(-2*(-((d^2-e^2)/e^2)^(1/2)*(x^2-1)^(1/2)*e+d*x+e)/(e*x+d))*a*d^4+ln(-2*(-((d^2-e^2)/e^2)^(1/2)*(x^2-1)^(1/2)*e+d*x+e)/(e*x+d))*c*d^4-x*b*d^2*e^2*((d^2-e^2)/e^2)^(1/2)*(x^2-1)^(1/2)-x*c*d^3*e*((d^2-e^2)/e^2)^(1/2)*(x^2-1)^(1/2)+4*x*c*d*e^3*((d^2-e^2)/e^2)^(1/2)*(x^2-1)^(1/2)+4*a*d^2*e^2*((d^2-e^2)/e^2)^(1/2)*(x^2-1)^(1/2)-2*b*d^3*e*((d^2-e^2)/e^2)^(1/2)*(x^2-1)^(1/2)-b*d*e^3*((d^2-e^2)/e^2)^(1/2)*(x^2-1)^(1/2)+3*c*d^2*e^2*((d^2-e^2)/e^2)^(1/2)*(x^2-1)^(1/2)+2*ln(-2*(-((d^2-e^2)/e^2)^(1/2)*(x^2-1)^(1/2)*e+d*x+e)/(e*x+d))*x^2*a*d^2*e^2-3*ln(-2*(-((d^2-e^2)/e^2)^(1/2)*(x^2-1)^(1/2)*e+d*x+e)/(e*x+d))*x^2*b*d*e^3+ln(-2*(-((d^2-e^2)/e^2)^(1/2)*(x^2-1)^(1/2)*e+d*x+e)/(e*x+d))*x^2*c*d^2*e^2+4*ln(-2*(-((d^2-e^2)/e^2)^(1/2)*(x^2-1)^(1/2)*e+d*x+e)/(e*x+d))*x*a*d^3*e+2*ln(-2*(-((d^2-e^2)/e^2)^(1/2)*(x^2-1)^(1/2)*e+d*x+e)/(e*x+d))*x*a*d*e^3-6*ln(-2*(-((d^2-e^2)/e^2)^(1/2)*(x^2-1)^(1/2)*e+d*x+e)/(e*x+d))*x*b*d^2*e^2+2*ln(-2*(-((d^2-e^2)/e^2)^(1/2)*(x^2-1)^(1/2)*e+d*x+e)/(e*x+d))*x*c*d^3*e+4*ln(-2*(-((d^2-e^2)/e^2)^(1/2)*(x^2-1)^(1/2)*e+d*x+e)/(e*x+d))*x*c*d*e^3)*(x+1)^(1/2)*(x-1)^(1/2)/(x^2-1)^(1/2)/(d-e)/(d+e)/((d^2-e^2)/e^2)^(1/2)/(d^2-e^2)/(e*x+d)^2/e","B"
41,1,6728,1304,0.053000," ","int((b*x+a)^2*(C*x^2+B*x+A)*(d*x+c)^(1/2)*(f*x+e)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
42,1,3571,683,0.024000," ","int((b*x+a)*(C*x^2+B*x+A)*(d*x+c)^(1/2)*(f*x+e)^(1/2),x)","\text{output too large to display}"," ",0,"-1/3840*(d*x+c)^(1/2)*(f*x+e)^(1/2)*(150*B*ln(1/2*(2*d*f*x+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*b*d^5*e^4*f+480*A*ln(1/2*(2*d*f*x+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*a*c^2*d^3*f^5+150*C*ln(1/2*(2*d*f*x+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*a*c^4*d*f^5+150*C*ln(1/2*(2*d*f*x+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*a*d^5*e^4*f+210*C*(d*f)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*b*c^4*f^4+210*C*(d*f)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*b*d^4*e^4-240*A*ln(1/2*(2*d*f*x+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*b*d^5*e^3*f^2-240*B*ln(1/2*(2*d*f*x+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*a*c^3*d^2*f^5-240*B*ln(1/2*(2*d*f*x+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*a*d^5*e^3*f^2+150*B*ln(1/2*(2*d*f*x+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*b*c^4*d*f^5+480*A*ln(1/2*(2*d*f*x+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*a*d^5*e^2*f^3-240*A*ln(1/2*(2*d*f*x+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*b*c^3*d^2*f^5-105*C*ln(1/2*(2*d*f*x+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*b*c^5*f^5-105*C*ln(1/2*(2*d*f*x+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*b*d^5*e^5-96*C*x^3*b*c*d^3*f^4*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)-96*C*x^3*b*d^4*e*f^3*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)-160*B*x^2*b*c*d^3*f^4*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)-1920*A*(d*f)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*x*a*d^4*f^4+240*B*ln(1/2*(2*d*f*x+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*a*c^2*d^3*e*f^4+240*B*ln(1/2*(2*d*f*x+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*a*c*d^4*e^2*f^3-120*B*ln(1/2*(2*d*f*x+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*b*c^3*d^2*e*f^4-60*B*ln(1/2*(2*d*f*x+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*b*c^2*d^3*e^2*f^3-960*A*ln(1/2*(2*d*f*x+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*a*c*d^4*e*f^4+240*A*ln(1/2*(2*d*f*x+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*b*c^2*d^3*e*f^4+240*A*ln(1/2*(2*d*f*x+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*b*c*d^4*e^2*f^3-120*C*ln(1/2*(2*d*f*x+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*a*c^3*d^2*e*f^4-60*C*ln(1/2*(2*d*f*x+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*a*c^2*d^3*e^2*f^3-120*C*ln(1/2*(2*d*f*x+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*a*c*d^4*e^3*f^2+75*C*ln(1/2*(2*d*f*x+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*b*c^4*d*e*f^4+30*C*ln(1/2*(2*d*f*x+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*b*c^3*d^2*e^2*f^3+44*C*(d*f)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*x*b*c*d^3*e^2*f^2-80*B*(d*f)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*x*b*c*d^3*e*f^3-80*C*(d*f)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*x*a*c*d^3*e*f^3+44*C*(d*f)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*x*b*c^2*d^2*e*f^3-32*C*x^2*b*c*d^3*e*f^3*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)+200*C*(d*f)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*x*a*c^2*d^2*f^4+200*C*(d*f)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*x*a*d^4*e^2*f^2-140*C*(d*f)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*x*b*c^3*d*f^4-140*C*(d*f)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*x*b*d^4*e^3*f-320*A*(d*f)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*b*c*d^3*e*f^3-320*B*(d*f)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*a*c*d^3*e*f^3+140*C*(d*f)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*a*c^2*d^2*e*f^3-320*A*(d*f)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*x*b*c*d^3*f^4-320*A*(d*f)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*x*b*d^4*e*f^3-320*B*(d*f)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*x*a*c*d^3*f^4-320*B*(d*f)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*x*a*d^4*e*f^3-80*C*(d*f)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*b*c*d^3*e^3*f+200*B*(d*f)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*x*b*c^2*d^2*f^4+200*B*(d*f)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*x*b*d^4*e^2*f^2+140*B*(d*f)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*b*c^2*d^2*e*f^3+140*C*(d*f)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*a*c*d^3*e^2*f^2-80*C*(d*f)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*b*c^3*d*e*f^3-68*C*(d*f)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*b*c^2*d^2*e^2*f^2+140*B*(d*f)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*b*c*d^3*e^2*f^2-160*B*x^2*b*d^4*e*f^3*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)-160*C*x^2*a*c*d^3*f^4*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)-160*C*x^2*a*d^4*e*f^3*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)+112*C*x^2*b*c^2*d^2*f^4*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)+112*C*x^2*b*d^4*e^2*f^2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)-768*C*x^4*b*d^4*f^4*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)-960*B*x^3*b*d^4*f^4*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)-960*C*x^3*a*d^4*f^4*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)-1280*A*x^2*b*d^4*f^4*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)-1280*B*x^2*a*d^4*f^4*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)-120*B*ln(1/2*(2*d*f*x+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*b*c*d^4*e^3*f^2+30*C*ln(1/2*(2*d*f*x+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*b*c^2*d^3*e^3*f^2+75*C*ln(1/2*(2*d*f*x+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*b*c*d^4*e^4*f-960*A*(d*f)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*a*c*d^3*f^4-960*A*(d*f)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*a*d^4*e*f^3+480*A*(d*f)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*b*c^2*d^2*f^4+480*A*(d*f)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*b*d^4*e^2*f^2+480*B*(d*f)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*a*c^2*d^2*f^4+480*B*(d*f)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*a*d^4*e^2*f^2-300*B*(d*f)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*b*c^3*d*f^4-300*B*(d*f)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*b*d^4*e^3*f-300*C*(d*f)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*a*c^3*d*f^4-300*C*(d*f)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*a*d^4*e^3*f)/(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)/d^4/f^4/(d*f)^(1/2)","B"
43,1,1431,292,0.020000," ","int((C*x^2+B*x+A)*(d*x+c)^(1/2)*(f*x+e)^(1/2),x)","-\frac{\sqrt{d x +c}\, \sqrt{f x +e}\, \left(48 A \,c^{2} d^{2} f^{4} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{d f \,x^{2}+c f x +d e x +c e}\, \sqrt{d f}}{2 \sqrt{d f}}\right)-96 A c \,d^{3} e \,f^{3} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{d f \,x^{2}+c f x +d e x +c e}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+48 A \,d^{4} e^{2} f^{2} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{d f \,x^{2}+c f x +d e x +c e}\, \sqrt{d f}}{2 \sqrt{d f}}\right)-24 B \,c^{3} d \,f^{4} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{d f \,x^{2}+c f x +d e x +c e}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+24 B \,c^{2} d^{2} e \,f^{3} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{d f \,x^{2}+c f x +d e x +c e}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+24 B c \,d^{3} e^{2} f^{2} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{d f \,x^{2}+c f x +d e x +c e}\, \sqrt{d f}}{2 \sqrt{d f}}\right)-24 B \,d^{4} e^{3} f \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{d f \,x^{2}+c f x +d e x +c e}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+15 C \,c^{4} f^{4} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{d f \,x^{2}+c f x +d e x +c e}\, \sqrt{d f}}{2 \sqrt{d f}}\right)-12 C \,c^{3} d e \,f^{3} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{d f \,x^{2}+c f x +d e x +c e}\, \sqrt{d f}}{2 \sqrt{d f}}\right)-6 C \,c^{2} d^{2} e^{2} f^{2} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{d f \,x^{2}+c f x +d e x +c e}\, \sqrt{d f}}{2 \sqrt{d f}}\right)-12 C c \,d^{3} e^{3} f \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{d f \,x^{2}+c f x +d e x +c e}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+15 C \,d^{4} e^{4} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{d f \,x^{2}+c f x +d e x +c e}\, \sqrt{d f}}{2 \sqrt{d f}}\right)-96 \sqrt{d f \,x^{2}+c f x +d e x +c e}\, \sqrt{d f}\, C \,d^{3} f^{3} x^{3}-128 \sqrt{d f \,x^{2}+c f x +d e x +c e}\, \sqrt{d f}\, B \,d^{3} f^{3} x^{2}-16 \sqrt{d f \,x^{2}+c f x +d e x +c e}\, \sqrt{d f}\, C c \,d^{2} f^{3} x^{2}-16 \sqrt{d f \,x^{2}+c f x +d e x +c e}\, \sqrt{d f}\, C \,d^{3} e \,f^{2} x^{2}-192 \sqrt{d f}\, \sqrt{d f \,x^{2}+c f x +d e x +c e}\, A \,d^{3} f^{3} x -32 \sqrt{d f}\, \sqrt{d f \,x^{2}+c f x +d e x +c e}\, B c \,d^{2} f^{3} x -32 \sqrt{d f}\, \sqrt{d f \,x^{2}+c f x +d e x +c e}\, B \,d^{3} e \,f^{2} x +20 \sqrt{d f}\, \sqrt{d f \,x^{2}+c f x +d e x +c e}\, C \,c^{2} d \,f^{3} x -8 \sqrt{d f}\, \sqrt{d f \,x^{2}+c f x +d e x +c e}\, C c \,d^{2} e \,f^{2} x +20 \sqrt{d f}\, \sqrt{d f \,x^{2}+c f x +d e x +c e}\, C \,d^{3} e^{2} f x -96 \sqrt{d f}\, \sqrt{d f \,x^{2}+c f x +d e x +c e}\, A c \,d^{2} f^{3}-96 \sqrt{d f}\, \sqrt{d f \,x^{2}+c f x +d e x +c e}\, A \,d^{3} e \,f^{2}+48 \sqrt{d f}\, \sqrt{d f \,x^{2}+c f x +d e x +c e}\, B \,c^{2} d \,f^{3}-32 \sqrt{d f}\, \sqrt{d f \,x^{2}+c f x +d e x +c e}\, B c \,d^{2} e \,f^{2}+48 \sqrt{d f}\, \sqrt{d f \,x^{2}+c f x +d e x +c e}\, B \,d^{3} e^{2} f -30 \sqrt{d f}\, \sqrt{d f \,x^{2}+c f x +d e x +c e}\, C \,c^{3} f^{3}+14 \sqrt{d f}\, \sqrt{d f \,x^{2}+c f x +d e x +c e}\, C \,c^{2} d e \,f^{2}+14 \sqrt{d f}\, \sqrt{d f \,x^{2}+c f x +d e x +c e}\, C c \,d^{2} e^{2} f -30 \sqrt{d f}\, \sqrt{d f \,x^{2}+c f x +d e x +c e}\, C \,d^{3} e^{3}\right)}{384 \sqrt{d f \,x^{2}+c f x +d e x +c e}\, \sqrt{d f}\, d^{3} f^{3}}"," ",0,"-1/384*(d*x+c)^(1/2)*(f*x+e)^(1/2)*(48*B*(d*f)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*d^3*e^2*f+48*A*ln(1/2*(2*d*f*x+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*d^4*e^2*f^2+15*C*ln(1/2*(2*d*f*x+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*c^4*f^4+15*C*ln(1/2*(2*d*f*x+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*d^4*e^4+48*B*(d*f)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*c^2*d*f^3-12*C*ln(1/2*(2*d*f*x+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*c^3*d*e*f^3-6*C*ln(1/2*(2*d*f*x+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*c^2*d^2*e^2*f^2-12*C*ln(1/2*(2*d*f*x+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*c*d^3*e^3*f-96*A*(d*f)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*c*d^2*f^3-96*A*(d*f)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*d^3*e*f^2-96*A*ln(1/2*(2*d*f*x+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*c*d^3*e*f^3-192*A*(d*f)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*x*d^3*f^3+24*B*ln(1/2*(2*d*f*x+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*c^2*d^2*e*f^3+24*B*ln(1/2*(2*d*f*x+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*c*d^3*e^2*f^2-96*C*x^3*d^3*f^3*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)-24*B*ln(1/2*(2*d*f*x+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*c^3*d*f^4-24*B*ln(1/2*(2*d*f*x+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*d^4*e^3*f-30*C*(d*f)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*c^3*f^3-30*C*(d*f)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*d^3*e^3+48*A*ln(1/2*(2*d*f*x+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*c^2*d^2*f^4-128*B*x^2*d^3*f^3*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)-8*C*(d*f)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*x*c*d^2*e*f^2-32*B*(d*f)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*x*c*d^2*f^3-32*B*(d*f)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*x*d^3*e*f^2+20*C*(d*f)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*x*c^2*d*f^3+20*C*(d*f)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*x*d^3*e^2*f-32*B*(d*f)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*c*d^2*e*f^2+14*C*(d*f)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*c^2*d*e*f^2+14*C*(d*f)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*c*d^2*e^2*f-16*C*x^2*c*d^2*f^3*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2)-16*C*x^2*d^3*e*f^2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2))/(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)/d^3/f^3/(d*f)^(1/2)","B"
44,1,4227,406,0.051000," ","int((C*x^2+B*x+A)*(d*x+c)^(1/2)*(f*x+e)^(1/2)/(b*x+a),x)","\text{output too large to display}"," ",0,"-1/48*(d*x+c)^(1/2)*(f*x+e)^(1/2)*(48*C*(d*f)^(1/2)*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*b-a*c*f-a*d*e+2*b*c*e)/(b*x+a))*a^4*d^3*f^3-3*C*ln(1/2*(2*d*f*x+c*f+d*e+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*b^4*c^3*f^3-3*C*ln(1/2*(2*d*f*x+c*f+d*e+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*b^4*d^3*e^3+48*B*(d*f)^(1/2)*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*b-a*c*f-a*d*e+2*b*c*e)/(b*x+a))*a^2*b^2*c*d^2*f^3-48*A*(d*f)^(1/2)*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*b-a*c*f-a*d*e+2*b*c*e)/(b*x+a))*a*b^3*c*d^2*f^3-48*A*(d*f)^(1/2)*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*b-a*c*f-a*d*e+2*b*c*e)/(b*x+a))*a*b^3*d^3*e*f^2+48*B*(d*f)^(1/2)*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*b-a*c*f-a*d*e+2*b*c*e)/(b*x+a))*a^2*b^2*d^3*e*f^2-24*B*(d*f)^(1/2)*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*x*b^4*d^2*f^2+24*B*ln(1/2*(2*d*f*x+c*f+d*e+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*a*b^3*c*d^2*f^3+24*B*ln(1/2*(2*d*f*x+c*f+d*e+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*a*b^3*d^3*e*f^2-16*C*x^2*b^4*d^2*f^2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*(d*f)^(1/2)-24*C*ln(1/2*(2*d*f*x+c*f+d*e+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*a^2*b^2*d^3*e*f^2-6*C*ln(1/2*(2*d*f*x+c*f+d*e+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*a*b^3*c^2*d*f^3+48*B*(d*f)^(1/2)*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*a*b^3*d^2*f^2-12*B*(d*f)^(1/2)*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*b^4*c*d*f^2-12*B*(d*f)^(1/2)*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*b^4*d^2*e*f-48*C*(d*f)^(1/2)*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*a^2*b^2*d^2*f^2-6*C*ln(1/2*(2*d*f*x+c*f+d*e+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*a*b^3*d^3*e^2*f+3*C*ln(1/2*(2*d*f*x+c*f+d*e+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*b^4*c^2*d*e*f^2+3*C*ln(1/2*(2*d*f*x+c*f+d*e+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*b^4*c*d^2*e^2*f-12*B*ln(1/2*(2*d*f*x+c*f+d*e+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*b^4*c*d^2*e*f^2-48*C*(d*f)^(1/2)*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*b-a*c*f-a*d*e+2*b*c*e)/(b*x+a))*a^3*b*c*d^2*f^3-48*C*(d*f)^(1/2)*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*b-a*c*f-a*d*e+2*b*c*e)/(b*x+a))*a^3*b*d^3*e*f^2-24*C*ln(1/2*(2*d*f*x+c*f+d*e+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*a^2*b^2*c*d^2*f^3+48*A*(d*f)^(1/2)*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*b-a*c*f-a*d*e+2*b*c*e)/(b*x+a))*a^2*b^2*d^3*f^3+48*A*ln(1/2*(2*d*f*x+c*f+d*e+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*a*b^3*d^3*f^3-24*A*ln(1/2*(2*d*f*x+c*f+d*e+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*b^4*c*d^2*f^3-24*A*ln(1/2*(2*d*f*x+c*f+d*e+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*b^4*d^3*e*f^2-48*B*(d*f)^(1/2)*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*b-a*c*f-a*d*e+2*b*c*e)/(b*x+a))*a^3*b*d^3*f^3-48*B*ln(1/2*(2*d*f*x+c*f+d*e+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*a^2*b^2*d^3*f^3+6*B*ln(1/2*(2*d*f*x+c*f+d*e+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*b^4*c^2*d*f^3+6*B*ln(1/2*(2*d*f*x+c*f+d*e+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*b^4*d^3*e^2*f+48*A*(d*f)^(1/2)*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*b-a*c*f-a*d*e+2*b*c*e)/(b*x+a))*b^4*c*d^2*e*f^2+48*C*ln(1/2*(2*d*f*x+c*f+d*e+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*a^3*b*d^3*f^3-48*A*(d*f)^(1/2)*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*b^4*d^2*f^2+6*C*(d*f)^(1/2)*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*b^4*c^2*f^2+6*C*(d*f)^(1/2)*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*b^4*d^2*e^2-4*C*(d*f)^(1/2)*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*b^4*c*d*e*f-4*C*(d*f)^(1/2)*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*x*b^4*c*d*f^2-4*C*(d*f)^(1/2)*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*x*b^4*d^2*e*f+12*C*ln(1/2*(2*d*f*x+c*f+d*e+2*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*a*b^3*c*d^2*e*f^2+12*C*(d*f)^(1/2)*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*a*b^3*c*d*f^2+12*C*(d*f)^(1/2)*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*a*b^3*d^2*e*f+48*C*(d*f)^(1/2)*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*b-a*c*f-a*d*e+2*b*c*e)/(b*x+a))*a^2*b^2*c*d^2*e*f^2+24*C*(d*f)^(1/2)*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*x*a*b^3*d^2*f^2-48*B*(d*f)^(1/2)*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)*b-a*c*f-a*d*e+2*b*c*e)/(b*x+a))*a*b^3*c*d^2*e*f^2)/(d*f*x^2+c*f*x+d*e*x+c*e)^(1/2)/b^5/d^2/f^2/(d*f)^(1/2)/((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)","B"
45,1,5051,479,0.048000," ","int((C*x^2+B*x+A)*(d*x+c)^(1/2)*(f*x+e)^(1/2)/(b*x+a)^2,x)","\text{output too large to display}"," ",0,"result too large to display","B"
46,1,12065,614,0.072000," ","int((C*x^2+B*x+A)*(d*x+c)^(1/2)*(f*x+e)^(1/2)/(b*x+a)^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
47,1,3958,994,0.046000," ","int((b*x+a)^2*(C*x^2+B*x+A)*(d*x+c)^(1/2)/(f*x+e)^(1/2),x)","\text{output too large to display}"," ",0,"1/3840*(d*x+c)^(1/2)*(f*x+e)^(1/2)*(1440*B*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*a^2*d^5*e^2*f^3+1280*C*x^2*a^2*d^4*f^4*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)-2880*B*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*a^2*d^4*e*f^3-2100*B*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b^2*d^4*e^3*f+2400*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*a^2*d^4*e^2*f^2+2880*A*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*a*b*d^5*e^2*f^3+720*A*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*b^2*c*d^4*e^2*f^3-960*B*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*a^2*c*d^4*e*f^4-2400*B*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*a*b*d^5*e^3*f^2-600*B*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*b^2*c*d^4*e^3*f^2+720*C*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*a^2*c*d^4*e^2*f^3+2100*C*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*a*b*d^5*e^4*f+525*C*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*b^2*c*d^4*e^4*f+2400*A*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b^2*d^4*e^2*f^2-960*A*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*a*b*c^2*d^3*f^5+105*C*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*b^2*c^5*f^5-420*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b^2*c*d^3*e^3*f-5760*A*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*a*b*d^4*e*f^3+4800*B*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*a*b*d^4*e^2*f^2-4200*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*a*b*d^4*e^3*f-1200*C*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*a*b*c*d^4*e^3*f^2-360*C*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*a*b*c^2*d^3*e^2*f^3+1440*B*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*a*b*c*d^4*e^2*f^3-1920*A*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*a*b*c*d^4*e*f^4-1200*C*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*a^2*d^5*e^3*f^2-150*B*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*b^2*c^4*d*f^5+240*C*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*a^2*c^3*d^2*f^5+240*A*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*b^2*c^3*d^2*f^5-480*B*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*a^2*c^2*d^3*f^5+3840*A*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*a^2*d^4*f^4+1920*A*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*a^2*c*d^4*f^5-1920*A*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*a^2*d^5*e*f^4-1200*A*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*b^2*d^5*e^3*f^2-210*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b^2*c^4*f^4+1890*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b^2*d^4*e^4-945*C*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*b^2*d^5*e^5+1050*B*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*b^2*d^5*e^4*f+768*C*x^4*b^2*d^4*f^4*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+960*B*x^3*b^2*d^4*f^4*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+1280*A*x^2*b^2*d^4*f^4*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+960*B*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*a^2*c*d^3*f^4+300*B*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b^2*c^3*d*f^4-480*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*a^2*c^2*d^2*f^4+1920*B*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*x*a^2*d^4*f^4+480*B*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*a*b*c^3*d^2*f^5-120*B*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*b^2*c^3*d^2*e*f^4-180*B*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*b^2*c^2*d^3*e^2*f^3+240*C*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*a^2*c^2*d^3*e*f^4-300*C*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*a*b*c^4*d*f^5+75*C*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*b^2*c^4*d*e*f^4+90*C*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*b^2*c^3*d^2*e^2*f^3+150*C*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*b^2*c^2*d^3*e^3*f^2-480*A*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b^2*c^2*d^2*f^4+240*A*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*b^2*c^2*d^3*e*f^4+680*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*a*b*c^2*d^2*e*f^3+640*B*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*x*a*b*c*d^3*f^4-3200*B*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*x*a*b*d^4*e*f^3+1000*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*a*b*c*d^3*e^2*f^2+320*C*x^2*a*b*c*d^3*f^4*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)-2240*C*x^2*a*b*d^4*e*f^3*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)-128*C*x^2*b^2*c*d^3*e*f^3*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)-240*B*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*x*b^2*c*d^3*e*f^3-400*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*x*a*b*c^2*d^2*f^4+2800*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*x*a*b*d^4*e^2*f^2+156*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*x*b^2*c^2*d^2*e*f^3+196*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*x*b^2*c*d^3*e^2*f^2-1280*B*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*a*b*c*d^3*e*f^3-200*B*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*x*b^2*c^2*d^2*f^4+1400*B*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*x*b^2*d^4*e^2*f^2+3840*A*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*x*a*b*d^4*f^4+320*A*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*x*b^2*c*d^3*f^4-1600*A*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*x*b^2*d^4*e*f^3+1920*C*x^3*a*b*d^4*f^4*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+96*C*x^3*b^2*c*d^3*f^4*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)-240*C*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*a*b*c^3*d^2*e*f^4+480*B*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*a*b*c^2*d^3*e*f^4-864*C*x^3*b^2*d^4*e*f^3*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+2560*B*x^2*a*b*d^4*f^4*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+160*B*x^2*b^2*c*d^3*f^4*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)-1120*B*x^2*b^2*d^4*e*f^3*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)-112*C*x^2*b^2*c^2*d^2*f^4*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+1008*C*x^2*b^2*d^4*e^2*f^2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+320*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*x*a^2*c*d^3*f^4-1600*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*x*a^2*d^4*e*f^3+140*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*x*b^2*c^3*d*f^4-1260*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*x*b^2*d^4*e^3*f+1920*A*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*a*b*c*d^3*f^4-640*A*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b^2*c*d^3*e*f^3-960*B*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*a*b*c^2*d^2*f^4+340*B*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b^2*c^2*d^2*e*f^3+500*B*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b^2*c*d^3*e^2*f^2-640*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*a^2*c*d^3*e*f^3+600*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*a*b*c^3*d*f^4-220*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b^2*c^3*d*e*f^3-272*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b^2*c^2*d^2*e^2*f^2-480*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*x*a*b*c*d^3*e*f^3)/((d*x+c)*(f*x+e))^(1/2)/f^5/d^4/(d*f)^(1/2)","B"
48,1,2002,508,0.030000," ","int((b*x+a)*(C*x^2+B*x+A)*(d*x+c)^(1/2)/(f*x+e)^(1/2),x)","\frac{\sqrt{d x +c}\, \sqrt{f x +e}\, \left(192 A a c \,d^{3} f^{4} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)-192 A a \,d^{4} e \,f^{3} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)-48 A b \,c^{2} d^{2} f^{4} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)-96 A b c \,d^{3} e \,f^{3} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+144 A b \,d^{4} e^{2} f^{2} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)-48 B a \,c^{2} d^{2} f^{4} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)-96 B a c \,d^{3} e \,f^{3} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+144 B a \,d^{4} e^{2} f^{2} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+24 B b \,c^{3} d \,f^{4} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+24 B b \,c^{2} d^{2} e \,f^{3} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+72 B b c \,d^{3} e^{2} f^{2} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)-120 B b \,d^{4} e^{3} f \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+24 C a \,c^{3} d \,f^{4} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+24 C a \,c^{2} d^{2} e \,f^{3} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+72 C a c \,d^{3} e^{2} f^{2} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)-120 C a \,d^{4} e^{3} f \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)-15 C b \,c^{4} f^{4} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)-12 C b \,c^{3} d e \,f^{3} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)-18 C b \,c^{2} d^{2} e^{2} f^{2} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)-60 C b c \,d^{3} e^{3} f \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+105 C b \,d^{4} e^{4} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+96 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, C b \,d^{3} f^{3} x^{3}+128 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, B b \,d^{3} f^{3} x^{2}+128 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, C a \,d^{3} f^{3} x^{2}+16 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, C b c \,d^{2} f^{3} x^{2}-112 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, C b \,d^{3} e \,f^{2} x^{2}+192 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, A b \,d^{3} f^{3} x +192 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, B a \,d^{3} f^{3} x +32 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, B b c \,d^{2} f^{3} x -160 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, B b \,d^{3} e \,f^{2} x +32 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, C a c \,d^{2} f^{3} x -160 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, C a \,d^{3} e \,f^{2} x -20 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, C b \,c^{2} d \,f^{3} x -24 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, C b c \,d^{2} e \,f^{2} x +140 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, C b \,d^{3} e^{2} f x +384 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, A a \,d^{3} f^{3}+96 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, A b c \,d^{2} f^{3}-288 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, A b \,d^{3} e \,f^{2}+96 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, B a c \,d^{2} f^{3}-288 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, B a \,d^{3} e \,f^{2}-48 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, B b \,c^{2} d \,f^{3}-64 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, B b c \,d^{2} e \,f^{2}+240 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, B b \,d^{3} e^{2} f -48 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, C a \,c^{2} d \,f^{3}-64 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, C a c \,d^{2} e \,f^{2}+240 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, C a \,d^{3} e^{2} f +30 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, C b \,c^{3} f^{3}+34 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, C b \,c^{2} d e \,f^{2}+50 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, C b c \,d^{2} e^{2} f -210 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, C b \,d^{3} e^{3}\right)}{384 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}\, d^{3} f^{4}}"," ",0,"1/384*(d*x+c)^(1/2)*(f*x+e)^(1/2)*(192*A*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*a*c*d^3*f^4+105*C*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*b*d^4*e^4-24*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*x*b*c*d^2*e*f^2-15*C*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*b*c^4*f^4-96*B*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*a*c*d^3*e*f^3+72*B*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*b*c*d^3*e^2*f^2+72*C*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*a*c*d^3*e^2*f^2-60*C*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*b*c*d^3*e^3*f-288*A*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b*d^3*e*f^2-96*A*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*b*c*d^3*e*f^3+24*B*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*b*c^2*d^2*e*f^3+24*C*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*a*c^2*d^2*e*f^3-12*C*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*b*c^3*d*e*f^3-192*A*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*a*d^4*e*f^3+144*B*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*a*d^4*e^2*f^2-120*B*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*b*d^4*e^3*f-120*C*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*a*d^4*e^3*f+384*A*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*a*d^3*f^3-210*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b*d^3*e^3-48*A*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*b*c^2*d^2*f^4+24*C*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*a*c^3*d*f^4+24*B*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*b*c^3*d*f^4-48*B*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*a*c^2*d^2*f^4+144*A*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*b*d^4*e^2*f^2+30*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b*c^3*f^3+192*B*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*x*a*d^3*f^3+96*A*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b*c*d^2*f^3+192*A*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*x*b*d^3*f^3+240*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*a*d^3*e^2*f+96*C*x^3*b*d^3*f^3*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)+128*B*x^2*b*d^3*f^3*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)+128*C*x^2*a*d^3*f^3*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)-18*C*ln(1/2*(2*d*f*x+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+c*f+d*e)/(d*f)^(1/2))*b*c^2*d^2*e^2*f^2-288*B*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*a*d^3*e*f^2+240*B*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b*d^3*e^2*f-48*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*a*c^2*d*f^3+96*B*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*a*c*d^2*f^3-48*B*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b*c^2*d*f^3-64*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*a*c*d^2*e*f^2+34*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b*c^2*d*e*f^2+50*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b*c*d^2*e^2*f+32*B*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*x*b*c*d^2*f^3-160*B*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*x*b*d^3*e*f^2+32*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*x*a*c*d^2*f^3-160*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*x*a*d^3*e*f^2-20*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*x*b*c^2*d*f^3+140*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*x*b*d^3*e^2*f-64*B*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b*c*d^2*e*f^2+16*C*x^2*b*c*d^2*f^3*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)-112*C*x^2*b*d^3*e*f^2*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2))/f^4/((d*x+c)*(f*x+e))^(1/2)/d^3/(d*f)^(1/2)","B"
49,1,763,214,0.024000," ","int((C*x^2+B*x+A)*(d*x+c)^(1/2)/(f*x+e)^(1/2),x)","\frac{\sqrt{d x +c}\, \sqrt{f x +e}\, \left(24 A c \,d^{2} f^{3} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)-24 A \,d^{3} e \,f^{2} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)-6 B \,c^{2} d \,f^{3} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)-12 B c \,d^{2} e \,f^{2} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+18 B \,d^{3} e^{2} f \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+3 C \,c^{3} f^{3} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+3 C \,c^{2} d e \,f^{2} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+9 C c \,d^{2} e^{2} f \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)-15 C \,d^{3} e^{3} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+16 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}\, C \,d^{2} f^{2} x^{2}+24 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, B \,d^{2} f^{2} x +4 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, C c d \,f^{2} x -20 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, C \,d^{2} e f x +48 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, A \,d^{2} f^{2}+12 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, B c d \,f^{2}-36 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, B \,d^{2} e f -6 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, C \,c^{2} f^{2}-8 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, C c d e f +30 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, C \,d^{2} e^{2}\right)}{48 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}\, d^{2} f^{3}}"," ",0,"1/48*(d*x+c)^(1/2)*(f*x+e)^(1/2)*(16*C*x^2*d^2*f^2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+24*A*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*c*d^2*f^3-24*A*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*d^3*e*f^2-6*B*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*c^2*d*f^3-12*B*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*c*d^2*e*f^2+18*B*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*d^3*e^2*f+24*B*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*x*d^2*f^2+3*C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*c^3*f^3+3*C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*c^2*d*e*f^2+9*C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*c*d^2*e^2*f-15*C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*d^3*e^3+4*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*x*c*d*f^2-20*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*x*d^2*e*f+48*A*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*d^2*f^2+12*B*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*c*d*f^2-36*B*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*d^2*e*f-6*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*c^2*f^2-8*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*c*d*e*f+30*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*d^2*e^2)/f^3/((d*x+c)*(f*x+e))^(1/2)/d^2/(d*f)^(1/2)","B"
50,1,1822,252,0.039000," ","int((C*x^2+B*x+A)*(d*x+c)^(1/2)/(b*x+a)/(f*x+e)^(1/2),x)","\frac{\left(8 \sqrt{d f}\, A a \,b^{2} d^{2} f^{2} \ln \left(\frac{-2 a d f x +b c f x +b d e x -a c f -a d e +2 b c e +2 \sqrt{\frac{a^{2} d f -a b c f -a b d e +b^{2} c e}{b^{2}}}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, b}{b x +a}\right)-8 \sqrt{d f}\, A \,b^{3} c d \,f^{2} \ln \left(\frac{-2 a d f x +b c f x +b d e x -a c f -a d e +2 b c e +2 \sqrt{\frac{a^{2} d f -a b c f -a b d e +b^{2} c e}{b^{2}}}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, b}{b x +a}\right)+8 \sqrt{\frac{a^{2} d f -a b c f -a b d e +b^{2} c e}{b^{2}}}\, A \,b^{3} d^{2} f^{2} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)-8 \sqrt{d f}\, B \,a^{2} b \,d^{2} f^{2} \ln \left(\frac{-2 a d f x +b c f x +b d e x -a c f -a d e +2 b c e +2 \sqrt{\frac{a^{2} d f -a b c f -a b d e +b^{2} c e}{b^{2}}}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, b}{b x +a}\right)+8 \sqrt{d f}\, B a \,b^{2} c d \,f^{2} \ln \left(\frac{-2 a d f x +b c f x +b d e x -a c f -a d e +2 b c e +2 \sqrt{\frac{a^{2} d f -a b c f -a b d e +b^{2} c e}{b^{2}}}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, b}{b x +a}\right)-8 \sqrt{\frac{a^{2} d f -a b c f -a b d e +b^{2} c e}{b^{2}}}\, B a \,b^{2} d^{2} f^{2} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+4 \sqrt{\frac{a^{2} d f -a b c f -a b d e +b^{2} c e}{b^{2}}}\, B \,b^{3} c d \,f^{2} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)-4 \sqrt{\frac{a^{2} d f -a b c f -a b d e +b^{2} c e}{b^{2}}}\, B \,b^{3} d^{2} e f \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+8 \sqrt{d f}\, C \,a^{3} d^{2} f^{2} \ln \left(\frac{-2 a d f x +b c f x +b d e x -a c f -a d e +2 b c e +2 \sqrt{\frac{a^{2} d f -a b c f -a b d e +b^{2} c e}{b^{2}}}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, b}{b x +a}\right)-8 \sqrt{d f}\, C \,a^{2} b c d \,f^{2} \ln \left(\frac{-2 a d f x +b c f x +b d e x -a c f -a d e +2 b c e +2 \sqrt{\frac{a^{2} d f -a b c f -a b d e +b^{2} c e}{b^{2}}}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, b}{b x +a}\right)+8 \sqrt{\frac{a^{2} d f -a b c f -a b d e +b^{2} c e}{b^{2}}}\, C \,a^{2} b \,d^{2} f^{2} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)-4 \sqrt{\frac{a^{2} d f -a b c f -a b d e +b^{2} c e}{b^{2}}}\, C a \,b^{2} c d \,f^{2} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+4 \sqrt{\frac{a^{2} d f -a b c f -a b d e +b^{2} c e}{b^{2}}}\, C a \,b^{2} d^{2} e f \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)-\sqrt{\frac{a^{2} d f -a b c f -a b d e +b^{2} c e}{b^{2}}}\, C \,b^{3} c^{2} f^{2} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)-2 \sqrt{\frac{a^{2} d f -a b c f -a b d e +b^{2} c e}{b^{2}}}\, C \,b^{3} c d e f \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+3 \sqrt{\frac{a^{2} d f -a b c f -a b d e +b^{2} c e}{b^{2}}}\, C \,b^{3} d^{2} e^{2} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+4 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}\, \sqrt{\frac{a^{2} d f -a b c f -a b d e +b^{2} c e}{b^{2}}}\, C \,b^{3} d f x +8 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}\, \sqrt{\frac{a^{2} d f -a b c f -a b d e +b^{2} c e}{b^{2}}}\, B \,b^{3} d f -8 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}\, \sqrt{\frac{a^{2} d f -a b c f -a b d e +b^{2} c e}{b^{2}}}\, C a \,b^{2} d f +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}\, \sqrt{\frac{a^{2} d f -a b c f -a b d e +b^{2} c e}{b^{2}}}\, C \,b^{3} c f -6 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}\, \sqrt{\frac{a^{2} d f -a b c f -a b d e +b^{2} c e}{b^{2}}}\, C \,b^{3} d e \right) \sqrt{f x +e}\, \sqrt{d x +c}}{8 \sqrt{\frac{a^{2} d f -a b c f -a b d e +b^{2} c e}{b^{2}}}\, \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, b^{4} d \,f^{2}}"," ",0,"1/8*(8*A*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*b^3*d^2*f^2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)+8*A*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b-a*c*f-a*d*e+2*b*c*e)/(b*x+a))*a*b^2*d^2*f^2*(d*f)^(1/2)-8*A*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b-a*c*f-a*d*e+2*b*c*e)/(b*x+a))*b^3*c*d*f^2*(d*f)^(1/2)-8*B*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*a*b^2*d^2*f^2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)+4*B*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*b^3*c*d*f^2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)-4*B*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*b^3*d^2*e*f*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)-8*B*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b-a*c*f-a*d*e+2*b*c*e)/(b*x+a))*a^2*b*d^2*f^2*(d*f)^(1/2)+8*B*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b-a*c*f-a*d*e+2*b*c*e)/(b*x+a))*a*b^2*c*d*f^2*(d*f)^(1/2)+8*C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*a^2*b*d^2*f^2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)-4*C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*a*b^2*c*d*f^2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)+4*C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*a*b^2*d^2*e*f*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)-C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*b^3*c^2*f^2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)-2*C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*b^3*c*d*e*f*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)+3*C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*b^3*d^2*e^2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)+8*C*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b-a*c*f-a*d*e+2*b*c*e)/(b*x+a))*a^3*d^2*f^2*(d*f)^(1/2)-8*C*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b-a*c*f-a*d*e+2*b*c*e)/(b*x+a))*a^2*b*c*d*f^2*(d*f)^(1/2)+4*C*x*b^3*d*f*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)+8*B*b^3*d*f*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)-8*C*a*b^2*d*f*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)+2*C*b^3*c*f*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)-6*C*b^3*d*e*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2))*(f*x+e)^(1/2)*(d*x+c)^(1/2)/((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)/(d*f)^(1/2)/d/f^2/b^4/((d*x+c)*(f*x+e))^(1/2)","B"
51,1,3670,332,0.049000," ","int((C*x^2+B*x+A)*(d*x+c)^(1/2)/(b*x+a)^2/(f*x+e)^(1/2),x)","\text{output too large to display}"," ",0,"-1/2*(d*x+c)^(1/2)*(f*x+e)^(1/2)*(-2*A*b^4*f*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+4*C*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x-a*c*f-a*d*e+2*b*c*e+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b)/(b*x+a))*a^4*d*f^2*(d*f)^(1/2)+B*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x-a*c*f-a*d*e+2*b*c*e+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b)/(b*x+a))*a^2*b^2*c*f^2*(d*f)^(1/2)-2*B*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*a^2*b^2*d*f^2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)-3*C*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x-a*c*f-a*d*e+2*b*c*e+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b)/(b*x+a))*a^3*b*c*f^2*(d*f)^(1/2)+4*C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*a^3*b*d*f^2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)-C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*a^2*b^2*c*f^2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)-C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*a*b^3*d*e^2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)+2*B*a*b^3*f*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+2*C*x*b^4*e*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)-4*C*a^2*b^2*f*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+2*C*a*b^3*e*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+A*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x-a*c*f-a*d*e+2*b*c*e+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b)/(b*x+a))*x*b^4*c*f^2*(d*f)^(1/2)-C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*x*b^4*d*e^2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)+A*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x-a*c*f-a*d*e+2*b*c*e+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b)/(b*x+a))*a*b^3*c*f^2*(d*f)^(1/2)-2*B*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x-a*c*f-a*d*e+2*b*c*e+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b)/(b*x+a))*a^3*b*d*f^2*(d*f)^(1/2)-2*B*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x-a*c*f-a*d*e+2*b*c*e+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b)/(b*x+a))*x*b^4*c*e*f*(d*f)^(1/2)+4*C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*x*a^2*b^2*d*f^2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)-C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*x*a*b^3*c*f^2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)+C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*x*b^4*c*e*f*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)-A*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x-a*c*f-a*d*e+2*b*c*e+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b)/(b*x+a))*a*b^3*d*e*f*(d*f)^(1/2)+3*B*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x-a*c*f-a*d*e+2*b*c*e+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b)/(b*x+a))*a^2*b^2*d*e*f*(d*f)^(1/2)-2*B*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x-a*c*f-a*d*e+2*b*c*e+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b)/(b*x+a))*a*b^3*c*e*f*(d*f)^(1/2)+2*B*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*a*b^3*d*e*f*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)-5*C*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x-a*c*f-a*d*e+2*b*c*e+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b)/(b*x+a))*a^3*b*d*e*f*(d*f)^(1/2)+4*C*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x-a*c*f-a*d*e+2*b*c*e+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b)/(b*x+a))*a^2*b^2*c*e*f*(d*f)^(1/2)-3*C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*a^2*b^2*d*e*f*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)+C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*a*b^3*c*e*f*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)-2*C*x*a*b^3*f*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)-A*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x-a*c*f-a*d*e+2*b*c*e+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b)/(b*x+a))*x*b^4*d*e*f*(d*f)^(1/2)-2*B*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x-a*c*f-a*d*e+2*b*c*e+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b)/(b*x+a))*x*a^2*b^2*d*f^2*(d*f)^(1/2)+B*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x-a*c*f-a*d*e+2*b*c*e+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b)/(b*x+a))*x*a*b^3*c*f^2*(d*f)^(1/2)-2*B*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*x*a*b^3*d*f^2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)+2*B*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*x*b^4*d*e*f*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)+4*C*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x-a*c*f-a*d*e+2*b*c*e+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b)/(b*x+a))*x*a^3*b*d*f^2*(d*f)^(1/2)-3*C*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x-a*c*f-a*d*e+2*b*c*e+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b)/(b*x+a))*x*a^2*b^2*c*f^2*(d*f)^(1/2)+3*B*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x-a*c*f-a*d*e+2*b*c*e+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b)/(b*x+a))*x*a*b^3*d*e*f*(d*f)^(1/2)-5*C*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x-a*c*f-a*d*e+2*b*c*e+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b)/(b*x+a))*x*a^2*b^2*d*e*f*(d*f)^(1/2)+4*C*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x-a*c*f-a*d*e+2*b*c*e+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b)/(b*x+a))*x*a*b^3*c*e*f*(d*f)^(1/2)-3*C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*x*a*b^3*d*e*f*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2))/((d*x+c)*(f*x+e))^(1/2)/(a*f-b*e)/(b*x+a)/(d*f)^(1/2)/((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)/f/b^4","B"
52,1,9100,446,0.095000," ","int((C*x^2+B*x+A)*(d*x+c)^(1/2)/(b*x+a)^3/(f*x+e)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
53,1,15990,653,0.159000," ","int((C*x^2+B*x+A)*(d*x+c)^(1/2)/(b*x+a)^4/(f*x+e)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
54,1,2528,686,0.046000," ","int((b*x+a)^2*(C*x^2+B*x+A)/(d*x+c)^(1/2)/(f*x+e)^(1/2),x)","\frac{\left(384 A \,a^{2} d^{4} f^{4} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)-384 A a b c \,d^{3} f^{4} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)-384 A a b \,d^{4} e \,f^{3} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+144 A \,b^{2} c^{2} d^{2} f^{4} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+96 A \,b^{2} c \,d^{3} e \,f^{3} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+144 A \,b^{2} d^{4} e^{2} f^{2} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)-192 B \,a^{2} c \,d^{3} f^{4} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)-192 B \,a^{2} d^{4} e \,f^{3} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+288 B a b \,c^{2} d^{2} f^{4} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+192 B a b c \,d^{3} e \,f^{3} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+288 B a b \,d^{4} e^{2} f^{2} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)-120 B \,b^{2} c^{3} d \,f^{4} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)-72 B \,b^{2} c^{2} d^{2} e \,f^{3} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)-72 B \,b^{2} c \,d^{3} e^{2} f^{2} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)-120 B \,b^{2} d^{4} e^{3} f \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+144 C \,a^{2} c^{2} d^{2} f^{4} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+96 C \,a^{2} c \,d^{3} e \,f^{3} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+144 C \,a^{2} d^{4} e^{2} f^{2} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)-240 C a b \,c^{3} d \,f^{4} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)-144 C a b \,c^{2} d^{2} e \,f^{3} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)-144 C a b c \,d^{3} e^{2} f^{2} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)-240 C a b \,d^{4} e^{3} f \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+105 C \,b^{2} c^{4} f^{4} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+60 C \,b^{2} c^{3} d e \,f^{3} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+54 C \,b^{2} c^{2} d^{2} e^{2} f^{2} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+60 C \,b^{2} c \,d^{3} e^{3} f \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+105 C \,b^{2} d^{4} e^{4} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+96 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, C \,b^{2} d^{3} f^{3} x^{3}+128 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, B \,b^{2} d^{3} f^{3} x^{2}+256 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, C a b \,d^{3} f^{3} x^{2}-112 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, C \,b^{2} c \,d^{2} f^{3} x^{2}-112 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, C \,b^{2} d^{3} e \,f^{2} x^{2}+192 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, A \,b^{2} d^{3} f^{3} x +384 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, B a b \,d^{3} f^{3} x -160 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, B \,b^{2} c \,d^{2} f^{3} x -160 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, B \,b^{2} d^{3} e \,f^{2} x +192 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, C \,a^{2} d^{3} f^{3} x -320 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, C a b c \,d^{2} f^{3} x -320 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, C a b \,d^{3} e \,f^{2} x +140 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, C \,b^{2} c^{2} d \,f^{3} x +136 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, C \,b^{2} c \,d^{2} e \,f^{2} x +140 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, C \,b^{2} d^{3} e^{2} f x +768 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, A a b \,d^{3} f^{3}-288 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, A \,b^{2} c \,d^{2} f^{3}-288 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, A \,b^{2} d^{3} e \,f^{2}+384 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, B \,a^{2} d^{3} f^{3}-576 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, B a b c \,d^{2} f^{3}-576 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, B a b \,d^{3} e \,f^{2}+240 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, B \,b^{2} c^{2} d \,f^{3}+224 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, B \,b^{2} c \,d^{2} e \,f^{2}+240 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, B \,b^{2} d^{3} e^{2} f -288 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, C \,a^{2} c \,d^{2} f^{3}-288 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, C \,a^{2} d^{3} e \,f^{2}+480 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, C a b \,c^{2} d \,f^{3}+448 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, C a b c \,d^{2} e \,f^{2}+480 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, C a b \,d^{3} e^{2} f -210 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, C \,b^{2} c^{3} f^{3}-190 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, C \,b^{2} c^{2} d e \,f^{2}-190 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, C \,b^{2} c \,d^{2} e^{2} f -210 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, C \,b^{2} d^{3} e^{3}\right) \sqrt{d x +c}\, \sqrt{f x +e}}{384 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, d^{4} f^{4}}"," ",0,"1/384*(144*A*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*b^2*d^4*e^2*f^2+192*A*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*x*b^2*d^3*f^3-384*A*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*a*b*c*d^3*f^4-384*A*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*a*b*d^4*e*f^3+96*C*x^3*b^2*d^3*f^3*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)+128*B*x^2*b^2*d^3*f^3*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)+96*A*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*b^2*c*d^3*e*f^3+60*C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*b^2*c*d^3*e^3*f-72*B*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*b^2*c^2*d^2*e*f^3-72*B*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*b^2*c*d^3*e^2*f^2+96*C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*a^2*c*d^3*e*f^3+60*C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*b^2*c^3*d*e*f^3+54*C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*b^2*c^2*d^2*e^2*f^2+192*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*x*a^2*d^3*f^3-240*C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*a*b*c^3*d*f^4-240*C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*a*b*d^4*e^3*f+768*A*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*a*b*d^3*f^3-288*A*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b^2*c*d^2*f^3-288*A*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b^2*d^3*e*f^2+288*B*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*a*b*c^2*d^2*f^4+288*B*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*a*b*d^4*e^2*f^2+240*B*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b^2*c^2*d*f^3+240*B*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b^2*d^3*e^2*f+105*C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*b^2*c^4*f^4+105*C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*b^2*d^4*e^4-192*B*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*a^2*c*d^3*f^4-192*B*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*a^2*d^4*e*f^3+144*A*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*b^2*c^2*d^2*f^4-120*B*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*b^2*c^3*d*f^4-120*B*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*b^2*d^4*e^3*f+144*C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*a^2*c^2*d^2*f^4+144*C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*a^2*d^4*e^2*f^2+384*B*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*a^2*d^3*f^3-210*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b^2*c^3*f^3-210*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b^2*d^3*e^3+384*A*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*a^2*d^4*f^4-288*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*a^2*c*d^2*f^3-288*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*a^2*d^3*e*f^2-190*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b^2*c^2*d*e*f^2-190*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b^2*c*d^2*e^2*f-160*B*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*x*b^2*d^3*e*f^2+140*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*x*b^2*c^2*d*f^3-144*C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*a*b*c*d^3*e^2*f^2+192*B*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*a*b*c*d^3*e*f^3-144*C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*a*b*c^2*d^2*e*f^3-576*B*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*a*b*c*d^2*f^3-576*B*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*a*b*d^3*e*f^2+224*B*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b^2*c*d^2*e*f^2+480*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*a*b*c^2*d*f^3+140*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*x*b^2*d^3*e^2*f+256*C*x^2*a*b*d^3*f^3*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)-112*C*x^2*b^2*c*d^2*f^3*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)-112*C*x^2*b^2*d^3*e*f^2*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)+384*B*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*x*a*b*d^3*f^3-160*B*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*x*b^2*c*d^2*f^3+480*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*a*b*d^3*e^2*f+448*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*a*b*c*d^2*e*f^2-320*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*x*a*b*c*d^2*f^3-320*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*x*a*b*d^3*e*f^2+136*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*x*b^2*c*d^2*e*f^2)*(d*x+c)^(1/2)*(f*x+e)^(1/2)/(d*f)^(1/2)/f^4/d^4/((d*x+c)*(f*x+e))^(1/2)","B"
55,1,1199,345,0.033000," ","int((b*x+a)*(C*x^2+B*x+A)/(d*x+c)^(1/2)/(f*x+e)^(1/2),x)","\frac{\left(48 A a \,d^{3} f^{3} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)-24 A b c \,d^{2} f^{3} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)-24 A b \,d^{3} e \,f^{2} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)-24 B a c \,d^{2} f^{3} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)-24 B a \,d^{3} e \,f^{2} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+18 B b \,c^{2} d \,f^{3} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+12 B b c \,d^{2} e \,f^{2} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+18 B b \,d^{3} e^{2} f \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+18 C a \,c^{2} d \,f^{3} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+12 C a c \,d^{2} e \,f^{2} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+18 C a \,d^{3} e^{2} f \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)-15 C b \,c^{3} f^{3} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)-9 C b \,c^{2} d e \,f^{2} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)-9 C b c \,d^{2} e^{2} f \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)-15 C b \,d^{3} e^{3} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+16 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}\, C b \,d^{2} f^{2} x^{2}+24 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, B b \,d^{2} f^{2} x +24 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, C a \,d^{2} f^{2} x -20 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, C b c d \,f^{2} x -20 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, C b \,d^{2} e f x +48 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, A b \,d^{2} f^{2}+48 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, B a \,d^{2} f^{2}-36 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, B b c d \,f^{2}-36 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, B b \,d^{2} e f -36 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, C a c d \,f^{2}-36 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, C a \,d^{2} e f +30 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, C b \,c^{2} f^{2}+28 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, C b c d e f +30 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, C b \,d^{2} e^{2}\right) \sqrt{d x +c}\, \sqrt{f x +e}}{48 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, d^{3} f^{3}}"," ",0,"1/48*(18*C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*a*d^3*e^2*f+48*A*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b*d^2*f^2+48*B*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*a*d^2*f^2+30*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b*c^2*f^2+30*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b*d^2*e^2-24*A*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*b*c*d^2*f^3-24*A*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*b*d^3*e*f^2-24*B*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*a*c*d^2*f^3-24*B*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*a*d^3*e*f^2+18*B*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*b*c^2*d*f^3+18*B*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*b*d^3*e^2*f+18*C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*a*c^2*d*f^3+48*A*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*a*d^3*f^3+16*C*x^2*b*d^2*f^2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)+12*B*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*b*c*d^2*e*f^2+12*C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*a*c*d^2*e*f^2-9*C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*b*c^2*d*e*f^2-9*C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*b*c*d^2*e^2*f+24*B*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*x*b*d^2*f^2+24*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*x*a*d^2*f^2-36*B*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b*c*d*f^2-36*B*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b*d^2*e*f-36*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*a*c*d*f^2-36*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*a*d^2*e*f-15*C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*b*c^3*f^3-15*C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*b*d^3*e^3+28*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b*c*d*e*f-20*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*x*b*d^2*e*f-20*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*x*b*c*d*f^2)*(d*x+c)^(1/2)*(f*x+e)^(1/2)/f^3/d^3/(d*f)^(1/2)/((d*x+c)*(f*x+e))^(1/2)","B"
56,1,425,138,0.023000," ","int((C*x^2+B*x+A)/(d*x+c)^(1/2)/(f*x+e)^(1/2),x)","\frac{\left(8 A \,d^{2} f^{2} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)-4 B c d \,f^{2} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)-4 B \,d^{2} e f \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+3 C \,c^{2} f^{2} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+2 C c d e f \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+3 C \,d^{2} e^{2} \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+4 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, C d f x +8 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, B d f -6 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, C c f -6 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, C d e \right) \sqrt{d x +c}\, \sqrt{f x +e}}{8 \sqrt{d f}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, d^{2} f^{2}}"," ",0,"1/8*(8*A*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*d^2*f^2-4*B*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*c*d*f^2-4*B*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*d^2*e*f+3*C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*c^2*f^2+2*C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*c*d*e*f+3*C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*d^2*e^2+4*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*x*d*f+8*B*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*d*f-6*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*c*f-6*C*(d*f)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*d*e)*(d*x+c)^(1/2)*(f*x+e)^(1/2)/(d*f)^(1/2)/f^2/d^2/((d*x+c)*(f*x+e))^(1/2)","B"
57,1,746,160,0.034000," ","int((C*x^2+B*x+A)/(b*x+a)/(d*x+c)^(1/2)/(f*x+e)^(1/2),x)","-\frac{\left(2 \sqrt{d f}\, A \,b^{2} d f \ln \left(\frac{-2 a d f x +b c f x +b d e x -a c f -a d e +2 b c e +2 \sqrt{\frac{a^{2} d f -a b c f -a b d e +b^{2} c e}{b^{2}}}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, b}{b x +a}\right)-2 \sqrt{d f}\, B a b d f \ln \left(\frac{-2 a d f x +b c f x +b d e x -a c f -a d e +2 b c e +2 \sqrt{\frac{a^{2} d f -a b c f -a b d e +b^{2} c e}{b^{2}}}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, b}{b x +a}\right)-2 \sqrt{\frac{a^{2} d f -a b c f -a b d e +b^{2} c e}{b^{2}}}\, B \,b^{2} d f \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+2 \sqrt{d f}\, C \,a^{2} d f \ln \left(\frac{-2 a d f x +b c f x +b d e x -a c f -a d e +2 b c e +2 \sqrt{\frac{a^{2} d f -a b c f -a b d e +b^{2} c e}{b^{2}}}\, \sqrt{\left(d x +c \right) \left(f x +e \right)}\, b}{b x +a}\right)+2 \sqrt{\frac{a^{2} d f -a b c f -a b d e +b^{2} c e}{b^{2}}}\, C a b d f \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+\sqrt{\frac{a^{2} d f -a b c f -a b d e +b^{2} c e}{b^{2}}}\, C \,b^{2} c f \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)+\sqrt{\frac{a^{2} d f -a b c f -a b d e +b^{2} c e}{b^{2}}}\, C \,b^{2} d e \ln \left(\frac{2 d f x +c f +d e +2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}}{2 \sqrt{d f}}\right)-2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}\, \sqrt{\frac{a^{2} d f -a b c f -a b d e +b^{2} c e}{b^{2}}}\, C \,b^{2}\right) \sqrt{f x +e}\, \sqrt{d x +c}}{2 \sqrt{\left(d x +c \right) \left(f x +e \right)}\, \sqrt{d f}\, \sqrt{\frac{a^{2} d f -a b c f -a b d e +b^{2} c e}{b^{2}}}\, b^{3} d f}"," ",0,"-1/2*(2*A*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x-a*c*f-a*d*e+2*b*c*e+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b)/(b*x+a))*b^2*d*f*(d*f)^(1/2)-2*B*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*b^2*d*f*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)-2*B*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x-a*c*f-a*d*e+2*b*c*e+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b)/(b*x+a))*a*b*d*f*(d*f)^(1/2)+2*C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*a*b*d*f*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)+C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*b^2*c*f*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)+C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*b^2*d*e*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)+2*C*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x-a*c*f-a*d*e+2*b*c*e+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b)/(b*x+a))*a^2*d*f*(d*f)^(1/2)-2*C*b^2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2)*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2))*(f*x+e)^(1/2)*(d*x+c)^(1/2)/((d*x+c)*(f*x+e))^(1/2)/d/(d*f)^(1/2)/b^3/((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)/f","B"
58,1,2973,226,0.059000," ","int((C*x^2+B*x+A)/(b*x+a)^2/(d*x+c)^(1/2)/(f*x+e)^(1/2),x)","\text{output too large to display}"," ",0,"-1/2*(d*x+c)^(1/2)*(f*x+e)^(1/2)*(-2*B*a*b^3*(d*f)^(1/2)*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)+2*A*b^4*(d*f)^(1/2)*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)-B*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x-a*c*f-a*d*e+2*b*c*e+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b)/(b*x+a))*x*a*b^3*d*e*(d*f)^(1/2)-2*C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*x*a^2*b^2*d*f*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)+2*C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*x*a*b^3*c*f*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)+2*C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*x*a*b^3*d*e*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)-2*C*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x-a*c*f-a*d*e+2*b*c*e+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b)/(b*x+a))*x*a^3*b*d*f*(d*f)^(1/2)+3*C*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x-a*c*f-a*d*e+2*b*c*e+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b)/(b*x+a))*x*a^2*b^2*c*f*(d*f)^(1/2)+3*C*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x-a*c*f-a*d*e+2*b*c*e+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b)/(b*x+a))*x*a^2*b^2*d*e*(d*f)^(1/2)-4*C*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x-a*c*f-a*d*e+2*b*c*e+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b)/(b*x+a))*x*a*b^3*c*e*(d*f)^(1/2)+2*A*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x-a*c*f-a*d*e+2*b*c*e+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b)/(b*x+a))*x*a*b^3*d*f*(d*f)^(1/2)-B*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x-a*c*f-a*d*e+2*b*c*e+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b)/(b*x+a))*x*a*b^3*c*f*(d*f)^(1/2)+2*C*a^2*b^2*(d*f)^(1/2)*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)-2*C*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x-a*c*f-a*d*e+2*b*c*e+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b)/(b*x+a))*a^4*d*f*(d*f)^(1/2)-A*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x-a*c*f-a*d*e+2*b*c*e+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b)/(b*x+a))*x*b^4*c*f*(d*f)^(1/2)-A*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x-a*c*f-a*d*e+2*b*c*e+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b)/(b*x+a))*x*b^4*d*e*(d*f)^(1/2)+2*B*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x-a*c*f-a*d*e+2*b*c*e+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b)/(b*x+a))*x*b^4*c*e*(d*f)^(1/2)-2*C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*x*b^4*c*e*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)+2*A*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x-a*c*f-a*d*e+2*b*c*e+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b)/(b*x+a))*a^2*b^2*d*f*(d*f)^(1/2)-A*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x-a*c*f-a*d*e+2*b*c*e+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b)/(b*x+a))*a*b^3*c*f*(d*f)^(1/2)-A*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x-a*c*f-a*d*e+2*b*c*e+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b)/(b*x+a))*a*b^3*d*e*(d*f)^(1/2)-B*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x-a*c*f-a*d*e+2*b*c*e+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b)/(b*x+a))*a^2*b^2*c*f*(d*f)^(1/2)-B*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x-a*c*f-a*d*e+2*b*c*e+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b)/(b*x+a))*a^2*b^2*d*e*(d*f)^(1/2)+2*B*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x-a*c*f-a*d*e+2*b*c*e+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b)/(b*x+a))*a*b^3*c*e*(d*f)^(1/2)-2*C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*a^3*b*d*f*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)+2*C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*a^2*b^2*c*f*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)+2*C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*a^2*b^2*d*e*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)-2*C*ln(1/2*(2*d*f*x+c*f+d*e+2*((d*x+c)*(f*x+e))^(1/2)*(d*f)^(1/2))/(d*f)^(1/2))*a*b^3*c*e*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)+3*C*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x-a*c*f-a*d*e+2*b*c*e+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b)/(b*x+a))*a^3*b*c*f*(d*f)^(1/2)+3*C*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x-a*c*f-a*d*e+2*b*c*e+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b)/(b*x+a))*a^3*b*d*e*(d*f)^(1/2)-4*C*ln((-2*a*d*f*x+b*c*f*x+b*d*e*x-a*c*f-a*d*e+2*b*c*e+2*((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)*((d*x+c)*(f*x+e))^(1/2)*b)/(b*x+a))*a^2*b^2*c*e*(d*f)^(1/2))/((d*x+c)*(f*x+e))^(1/2)/(a*d-b*c)/(a*f-b*e)/(b*x+a)/(d*f)^(1/2)/((a^2*d*f-a*b*c*f-a*b*d*e+b^2*c*e)/b^2)^(1/2)/b^3","B"
59,1,7119,398,0.130000," ","int((C*x^2+B*x+A)/(b*x+a)^3/(d*x+c)^(1/2)/(f*x+e)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
60,1,18802,794,0.312000," ","int((C*x^2+B*x+A)/(b*x+a)^4/(d*x+c)^(1/2)/(f*x+e)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
61,1,14778,1112,0.094000," ","int((b*x+a)^(1/2)*(C*x^2+B*x+A)*(d*x+c)^(1/2)*(f*x+e)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
62,1,10268,710,0.050000," ","int((C*x^2+B*x+A)*(d*x+c)^(1/2)*(f*x+e)^(1/2)/(b*x+a)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
63,1,6265,646,0.060000," ","int((C*x^2+B*x+A)*(d*x+c)^(1/2)*(f*x+e)^(1/2)/(b*x+a)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
64,1,16172,627,0.111000," ","int((C*x^2+B*x+A)*(d*x+c)^(1/2)*(f*x+e)^(1/2)/(b*x+a)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
65,1,34389,902,0.235000," ","int((C*x^2+B*x+A)*(d*x+c)^(1/2)*(f*x+e)^(1/2)/(b*x+a)^(7/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
66,1,68345,1646,0.398000," ","int((C*x^2+B*x+A)*(d*x+c)^(1/2)*(f*x+e)^(1/2)/(b*x+a)^(9/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
67,1,15855,1163,0.069000," ","int((b*x+a)^(3/2)*(C*x^2+B*x+A)*(d*x+c)^(1/2)/(f*x+e)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
68,1,9543,702,0.045000," ","int((b*x+a)^(1/2)*(C*x^2+B*x+A)*(d*x+c)^(1/2)/(f*x+e)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
69,1,6049,473,0.038000," ","int((C*x^2+B*x+A)*(d*x+c)^(1/2)/(b*x+a)^(1/2)/(f*x+e)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
70,1,4732,488,0.049000," ","int((C*x^2+B*x+A)*(d*x+c)^(1/2)/(b*x+a)^(3/2)/(f*x+e)^(1/2),x)","\text{output too large to display}"," ",0,"2/3*(C*x^3*a*b^3*d^2*f^3+13*C*EllipticE(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a^2*b^2*c*d*e*f^2*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)-2*C*EllipticE(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a*b^3*c*d*e^2*f*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)+4*C*x^2*a^2*b^2*d^2*f^3-3*A*EllipticE(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a*b^3*d^2*e*f^2*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)+3*A*EllipticE(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*b^4*c*d*e*f^2*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)+6*B*EllipticE(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a^2*b^2*c*d*f^3*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)-2*C*EllipticF(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a^2*b^2*d^2*e^2*f*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)-2*C*EllipticF(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a*b^3*c^2*e*f^2*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)-3*B*EllipticF(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a^2*b^2*d^2*e*f^2*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)+3*B*EllipticF(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a*b^3*d^2*e^2*f*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)-3*B*EllipticF(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*b^4*c*d*e^2*f*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)+3*A*x^2*b^4*d^2*f^3-3*A*EllipticE(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a*b^3*c*d*f^3*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)-9*C*EllipticE(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a^3*b*c*d*f^3*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)-11*C*EllipticE(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a^3*b*d^2*e*f^2*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)+C*EllipticE(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a^2*b^2*d^2*e^2*f*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)+9*B*EllipticE(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a^2*b^2*d^2*e*f^2*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)+C*x^2*a*b^3*c*d*f^3-C*x^2*b^4*c*d*e*f^2-3*B*x*a*b^3*c*d*f^3-3*B*x*a*b^3*d^2*e*f^2+4*C*x*a^2*b^2*c*d*f^3+4*C*x*a^2*b^2*d^2*e*f^2-C*x*a*b^3*d^2*e^2*f-C*x*b^4*c*d*e^2*f-3*B*EllipticE(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a*b^3*d^2*e^2*f*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)+3*B*EllipticE(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*b^4*c*d*e^2*f*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)+3*B*EllipticF(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a^2*b^2*c*d*f^3*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)-2*C*EllipticE(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a*b^3*c^2*e*f^2*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)-4*C*EllipticF(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a^3*b*c*d*f^3*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)+4*C*EllipticF(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a^3*b*d^2*e*f^2*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)+3*A*b^4*c*d*e*f^2+3*B*EllipticF(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*b^4*c^2*e*f^2*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)+C*EllipticE(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a^2*b^2*c^2*f^3*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)+2*C*EllipticE(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a*b^3*d^2*e^3*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)+C*EllipticE(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*b^4*c^2*e^2*f*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)-2*C*EllipticE(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*b^4*c*d*e^3*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)+4*C*EllipticF(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a^2*b^2*c^2*f^3*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)-2*C*EllipticF(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a*b^3*d^2*e^3*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)-2*C*EllipticF(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*b^4*c^2*e^2*f*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)+2*C*EllipticF(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*b^4*c*d*e^3*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)-2*C*EllipticF(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a^2*b^2*c*d*e*f^2*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)+4*C*EllipticF(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a*b^3*c*d*e^2*f*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)-C*x^2*b^4*d^2*e^2*f+3*A*x*b^4*c*d*f^3+3*A*x*b^4*d^2*e*f^2-C*x^3*b^4*d^2*e*f^2-3*B*x^2*a*b^3*d^2*f^3+3*A*EllipticE(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a^2*b^2*d^2*f^3*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)-6*B*EllipticE(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a^3*b*d^2*f^3*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)-3*B*EllipticF(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a*b^3*c^2*f^3*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)+8*C*EllipticE(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a^4*d^2*f^3*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)-3*B*a*b^3*c*d*e*f^2+4*C*a^2*b^2*c*d*e*f^2-C*a*b^3*c*d*e^2*f-9*B*EllipticE(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a*b^3*c*d*e*f^2*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2))*(f*x+e)^(1/2)*(b*x+a)^(1/2)*(d*x+c)^(1/2)/f^2/d/(a*f-b*e)/b^4/(b*d*f*x^3+a*d*f*x^2+b*c*f*x^2+b*d*e*x^2+a*c*f*x+a*d*e*x+b*c*e*x+a*c*e)","B"
71,1,13614,543,0.108000," ","int((C*x^2+B*x+A)*(d*x+c)^(1/2)/(b*x+a)^(5/2)/(f*x+e)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
72,1,33007,972,0.315000," ","int((C*x^2+B*x+A)*(d*x+c)^(1/2)/(b*x+a)^(7/2)/(f*x+e)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
73,1,10546,774,0.068000," ","int((b*x+a)^(3/2)*(C*x^2+B*x+A)/(d*x+c)^(1/2)/(f*x+e)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
74,1,6174,474,0.039000," ","int((b*x+a)^(1/2)*(C*x^2+B*x+A)/(d*x+c)^(1/2)/(f*x+e)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
75,1,2497,341,0.035000," ","int((C*x^2+B*x+A)/(b*x+a)^(1/2)/(d*x+c)^(1/2)/(f*x+e)^(1/2),x)","\frac{2 \left(C \,b^{3} d^{2} f^{2} x^{3}+C a \,b^{2} d^{2} f^{2} x^{2}+C \,b^{3} c d \,f^{2} x^{2}+C \,b^{3} d^{2} e f \,x^{2}+3 \sqrt{\frac{\left(b x +a \right) d}{a d -b c}}\, \sqrt{-\frac{\left(f x +e \right) b}{a f -b e}}\, \sqrt{-\frac{\left(d x +c \right) b}{a d -b c}}\, A a \,b^{2} d^{2} f^{2} \EllipticF \left(\sqrt{\frac{\left(b x +a \right) d}{a d -b c}}, \sqrt{\frac{\left(a d -b c \right) f}{\left(a f -b e \right) d}}\right)-3 \sqrt{\frac{\left(b x +a \right) d}{a d -b c}}\, \sqrt{-\frac{\left(f x +e \right) b}{a f -b e}}\, \sqrt{-\frac{\left(d x +c \right) b}{a d -b c}}\, A \,b^{3} c d \,f^{2} \EllipticF \left(\sqrt{\frac{\left(b x +a \right) d}{a d -b c}}, \sqrt{\frac{\left(a d -b c \right) f}{\left(a f -b e \right) d}}\right)-3 \sqrt{\frac{\left(b x +a \right) d}{a d -b c}}\, \sqrt{-\frac{\left(f x +e \right) b}{a f -b e}}\, \sqrt{-\frac{\left(d x +c \right) b}{a d -b c}}\, B \,a^{2} b \,d^{2} f^{2} \EllipticE \left(\sqrt{\frac{\left(b x +a \right) d}{a d -b c}}, \sqrt{\frac{\left(a d -b c \right) f}{\left(a f -b e \right) d}}\right)+3 \sqrt{\frac{\left(b x +a \right) d}{a d -b c}}\, \sqrt{-\frac{\left(f x +e \right) b}{a f -b e}}\, \sqrt{-\frac{\left(d x +c \right) b}{a d -b c}}\, B a \,b^{2} c d \,f^{2} \EllipticE \left(\sqrt{\frac{\left(b x +a \right) d}{a d -b c}}, \sqrt{\frac{\left(a d -b c \right) f}{\left(a f -b e \right) d}}\right)+3 \sqrt{\frac{\left(b x +a \right) d}{a d -b c}}\, \sqrt{-\frac{\left(f x +e \right) b}{a f -b e}}\, \sqrt{-\frac{\left(d x +c \right) b}{a d -b c}}\, B a \,b^{2} d^{2} e f \EllipticE \left(\sqrt{\frac{\left(b x +a \right) d}{a d -b c}}, \sqrt{\frac{\left(a d -b c \right) f}{\left(a f -b e \right) d}}\right)-3 \sqrt{\frac{\left(b x +a \right) d}{a d -b c}}\, \sqrt{-\frac{\left(f x +e \right) b}{a f -b e}}\, \sqrt{-\frac{\left(d x +c \right) b}{a d -b c}}\, B a \,b^{2} d^{2} e f \EllipticF \left(\sqrt{\frac{\left(b x +a \right) d}{a d -b c}}, \sqrt{\frac{\left(a d -b c \right) f}{\left(a f -b e \right) d}}\right)-3 \sqrt{\frac{\left(b x +a \right) d}{a d -b c}}\, \sqrt{-\frac{\left(f x +e \right) b}{a f -b e}}\, \sqrt{-\frac{\left(d x +c \right) b}{a d -b c}}\, B \,b^{3} c d e f \EllipticE \left(\sqrt{\frac{\left(b x +a \right) d}{a d -b c}}, \sqrt{\frac{\left(a d -b c \right) f}{\left(a f -b e \right) d}}\right)+3 \sqrt{\frac{\left(b x +a \right) d}{a d -b c}}\, \sqrt{-\frac{\left(f x +e \right) b}{a f -b e}}\, \sqrt{-\frac{\left(d x +c \right) b}{a d -b c}}\, B \,b^{3} c d e f \EllipticF \left(\sqrt{\frac{\left(b x +a \right) d}{a d -b c}}, \sqrt{\frac{\left(a d -b c \right) f}{\left(a f -b e \right) d}}\right)+2 \sqrt{\frac{\left(b x +a \right) d}{a d -b c}}\, \sqrt{-\frac{\left(f x +e \right) b}{a f -b e}}\, \sqrt{-\frac{\left(d x +c \right) b}{a d -b c}}\, C \,a^{3} d^{2} f^{2} \EllipticE \left(\sqrt{\frac{\left(b x +a \right) d}{a d -b c}}, \sqrt{\frac{\left(a d -b c \right) f}{\left(a f -b e \right) d}}\right)-\sqrt{\frac{\left(b x +a \right) d}{a d -b c}}\, \sqrt{-\frac{\left(f x +e \right) b}{a f -b e}}\, \sqrt{-\frac{\left(d x +c \right) b}{a d -b c}}\, C \,a^{2} b c d \,f^{2} \EllipticF \left(\sqrt{\frac{\left(b x +a \right) d}{a d -b c}}, \sqrt{\frac{\left(a d -b c \right) f}{\left(a f -b e \right) d}}\right)+\sqrt{\frac{\left(b x +a \right) d}{a d -b c}}\, \sqrt{-\frac{\left(f x +e \right) b}{a f -b e}}\, \sqrt{-\frac{\left(d x +c \right) b}{a d -b c}}\, C \,a^{2} b \,d^{2} e f \EllipticF \left(\sqrt{\frac{\left(b x +a \right) d}{a d -b c}}, \sqrt{\frac{\left(a d -b c \right) f}{\left(a f -b e \right) d}}\right)-2 \sqrt{\frac{\left(b x +a \right) d}{a d -b c}}\, \sqrt{-\frac{\left(f x +e \right) b}{a f -b e}}\, \sqrt{-\frac{\left(d x +c \right) b}{a d -b c}}\, C a \,b^{2} c^{2} f^{2} \EllipticE \left(\sqrt{\frac{\left(b x +a \right) d}{a d -b c}}, \sqrt{\frac{\left(a d -b c \right) f}{\left(a f -b e \right) d}}\right)+\sqrt{\frac{\left(b x +a \right) d}{a d -b c}}\, \sqrt{-\frac{\left(f x +e \right) b}{a f -b e}}\, \sqrt{-\frac{\left(d x +c \right) b}{a d -b c}}\, C a \,b^{2} c^{2} f^{2} \EllipticF \left(\sqrt{\frac{\left(b x +a \right) d}{a d -b c}}, \sqrt{\frac{\left(a d -b c \right) f}{\left(a f -b e \right) d}}\right)-2 \sqrt{\frac{\left(b x +a \right) d}{a d -b c}}\, \sqrt{-\frac{\left(f x +e \right) b}{a f -b e}}\, \sqrt{-\frac{\left(d x +c \right) b}{a d -b c}}\, C a \,b^{2} c d e f \EllipticE \left(\sqrt{\frac{\left(b x +a \right) d}{a d -b c}}, \sqrt{\frac{\left(a d -b c \right) f}{\left(a f -b e \right) d}}\right)+C a \,b^{2} c d \,f^{2} x -2 \sqrt{\frac{\left(b x +a \right) d}{a d -b c}}\, \sqrt{-\frac{\left(f x +e \right) b}{a f -b e}}\, \sqrt{-\frac{\left(d x +c \right) b}{a d -b c}}\, C a \,b^{2} d^{2} e^{2} \EllipticE \left(\sqrt{\frac{\left(b x +a \right) d}{a d -b c}}, \sqrt{\frac{\left(a d -b c \right) f}{\left(a f -b e \right) d}}\right)+2 \sqrt{\frac{\left(b x +a \right) d}{a d -b c}}\, \sqrt{-\frac{\left(f x +e \right) b}{a f -b e}}\, \sqrt{-\frac{\left(d x +c \right) b}{a d -b c}}\, C a \,b^{2} d^{2} e^{2} \EllipticF \left(\sqrt{\frac{\left(b x +a \right) d}{a d -b c}}, \sqrt{\frac{\left(a d -b c \right) f}{\left(a f -b e \right) d}}\right)+C a \,b^{2} d^{2} e f x +2 \sqrt{\frac{\left(b x +a \right) d}{a d -b c}}\, \sqrt{-\frac{\left(f x +e \right) b}{a f -b e}}\, \sqrt{-\frac{\left(d x +c \right) b}{a d -b c}}\, C \,b^{3} c^{2} e f \EllipticE \left(\sqrt{\frac{\left(b x +a \right) d}{a d -b c}}, \sqrt{\frac{\left(a d -b c \right) f}{\left(a f -b e \right) d}}\right)-\sqrt{\frac{\left(b x +a \right) d}{a d -b c}}\, \sqrt{-\frac{\left(f x +e \right) b}{a f -b e}}\, \sqrt{-\frac{\left(d x +c \right) b}{a d -b c}}\, C \,b^{3} c^{2} e f \EllipticF \left(\sqrt{\frac{\left(b x +a \right) d}{a d -b c}}, \sqrt{\frac{\left(a d -b c \right) f}{\left(a f -b e \right) d}}\right)+2 \sqrt{\frac{\left(b x +a \right) d}{a d -b c}}\, \sqrt{-\frac{\left(f x +e \right) b}{a f -b e}}\, \sqrt{-\frac{\left(d x +c \right) b}{a d -b c}}\, C \,b^{3} c d \,e^{2} \EllipticE \left(\sqrt{\frac{\left(b x +a \right) d}{a d -b c}}, \sqrt{\frac{\left(a d -b c \right) f}{\left(a f -b e \right) d}}\right)-2 \sqrt{\frac{\left(b x +a \right) d}{a d -b c}}\, \sqrt{-\frac{\left(f x +e \right) b}{a f -b e}}\, \sqrt{-\frac{\left(d x +c \right) b}{a d -b c}}\, C \,b^{3} c d \,e^{2} \EllipticF \left(\sqrt{\frac{\left(b x +a \right) d}{a d -b c}}, \sqrt{\frac{\left(a d -b c \right) f}{\left(a f -b e \right) d}}\right)+C \,b^{3} c d e f x +C a \,b^{2} c d e f \right) \sqrt{b x +a}\, \sqrt{d x +c}\, \sqrt{f x +e}}{3 \left(b d f \,x^{3}+a d f \,x^{2}+b c f \,x^{2}+b d e \,x^{2}+a c f x +a d e x +b c e x +a c e \right) b^{3} d^{2} f^{2}}"," ",0,"2/3*(-3*B*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)*EllipticE(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a^2*b*d^2*f^2+C*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)*EllipticF(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a*b^2*c^2*f^2+2*C*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)*EllipticF(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a*b^2*d^2*e^2-C*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)*EllipticF(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*b^3*c^2*e*f-2*C*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)*EllipticF(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*b^3*c*d*e^2-2*C*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)*EllipticE(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a*b^2*c^2*f^2-2*C*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)*EllipticE(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a*b^2*d^2*e^2+2*C*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)*EllipticE(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*b^3*c^2*e*f+2*C*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)*EllipticE(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*b^3*c*d*e^2+C*a*b^2*c*d*e*f+C*x^2*a*b^2*d^2*f^2+3*A*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)*EllipticF(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a*b^2*d^2*f^2-3*A*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)*EllipticF(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*b^3*c*d*f^2-3*B*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)*EllipticF(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a*b^2*d^2*e*f+3*B*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)*EllipticF(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*b^3*c*d*e*f+3*B*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)*EllipticE(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a*b^2*c*d*f^2+3*B*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)*EllipticE(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a*b^2*d^2*e*f-3*B*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)*EllipticE(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*b^3*c*d*e*f-C*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)*EllipticF(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a^2*b*c*d*f^2+C*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)*EllipticF(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a^2*b*d^2*e*f+C*x^3*b^3*d^2*f^2+C*x^2*b^3*c*d*f^2+C*x^2*b^3*d^2*e*f-2*C*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)*EllipticE(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a*b^2*c*d*e*f+2*C*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)*EllipticE(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a^3*d^2*f^2+C*x*a*b^2*d^2*e*f+C*x*b^3*c*d*e*f+C*x*a*b^2*c*d*f^2)*(b*x+a)^(1/2)*(d*x+c)^(1/2)*(f*x+e)^(1/2)/f^2/b^3/d^2/(b*d*f*x^3+a*d*f*x^2+b*c*f*x^2+b*d*e*x^2+a*c*f*x+a*d*e*x+b*c*e*x+a*c*e)","B"
76,1,3984,382,0.052000," ","int((C*x^2+B*x+A)/(b*x+a)^(3/2)/(d*x+c)^(1/2)/(f*x+e)^(1/2),x)","\text{output too large to display}"," ",0,"2*(B*x^2*a*b^3*d^2*f^2+B*x*a*b^3*c*d*f^2+B*x*a*b^3*d^2*e*f-C*x*a^2*b^2*c*d*f^2-C*x*a^2*b^2*d^2*e*f-2*C*EllipticE(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a^4*d^2*f^2*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)-C*EllipticE(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*b^4*c^2*e^2*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)+B*EllipticF(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a*b^3*c*d*e*f*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)+B*EllipticE(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a*b^3*c*d*e*f*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)+C*EllipticF(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a^2*b^2*c*d*e*f*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)-5*C*EllipticE(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a^2*b^2*c*d*e*f*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)+A*EllipticF(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a^2*b^2*d^2*f^2*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)-A*EllipticE(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a^2*b^2*d^2*f^2*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)+B*EllipticF(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a*b^3*c^2*f^2*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)-B*EllipticF(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*b^4*c^2*e*f*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)+B*EllipticE(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a^3*b*d^2*f^2*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)-C*EllipticF(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a^2*b^2*c^2*f^2*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)+C*EllipticF(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a^2*b^2*d^2*e^2*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)-C*EllipticE(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a^2*b^2*c^2*f^2*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)-C*EllipticE(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a^2*b^2*d^2*e^2*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)-A*x^2*b^4*d^2*f^2-C*a^2*b^2*c*d*e*f+B*a*b^3*c*d*e*f+3*C*EllipticE(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a^3*b*d^2*e*f*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)+2*C*EllipticE(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a*b^3*c^2*e*f*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)+2*C*EllipticE(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a*b^3*c*d*e^2*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)+A*EllipticE(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a*b^3*c*d*f^2*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)+A*EllipticE(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a*b^3*d^2*e*f*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)-A*EllipticE(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*b^4*c*d*e*f*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)-B*EllipticF(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a^2*b^2*c*d*f^2*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)-B*EllipticE(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a^2*b^2*c*d*f^2*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)-B*EllipticE(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a^2*b^2*d^2*e*f*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)+C*EllipticF(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a^3*b*c*d*f^2*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)-A*b^4*c*d*e*f-C*x^2*a^2*b^2*d^2*f^2-A*x*b^4*c*d*f^2-A*x*b^4*d^2*e*f-C*EllipticF(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a^3*b*d^2*e*f*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)-2*C*EllipticF(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a*b^3*c*d*e^2*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)+3*C*EllipticE(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a^3*b*c*d*f^2*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)-A*EllipticF(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a*b^3*c*d*f^2*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)-A*EllipticF(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*a*b^3*d^2*e*f*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)+A*EllipticF(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*b^4*c*d*e*f*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2)+C*EllipticF(((b*x+a)/(a*d-b*c)*d)^(1/2),((a*d-b*c)/(a*f-b*e)/d*f)^(1/2))*b^4*c^2*e^2*((b*x+a)/(a*d-b*c)*d)^(1/2)*(-(f*x+e)/(a*f-b*e)*b)^(1/2)*(-(d*x+c)/(a*d-b*c)*b)^(1/2))*(f*x+e)^(1/2)*(d*x+c)^(1/2)*(b*x+a)^(1/2)/f/d/b^3/(a*f-b*e)/(a*d-b*c)/(b*d*f*x^3+a*d*f*x^2+b*c*f*x^2+b*d*e*x^2+a*c*f*x+a*d*e*x+b*c*e*x+a*c*e)","B"
77,1,12988,588,0.140000," ","int((C*x^2+B*x+A)/(b*x+a)^(5/2)/(d*x+c)^(1/2)/(f*x+e)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
78,1,34102,1054,0.354000," ","int((C*x^2+B*x+A)/(b*x+a)^(7/2)/(d*x+c)^(1/2)/(f*x+e)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"