1,1,338,0,0.996462," ","integrate((e*x+d)^2*(C*x^2+B*x+A)*(-e^2*x^2+d^2)^(1/2),x, algorithm=""maxima"")","-\frac{1}{6} \, {\left(-e^{2} x^{2} + d^{2}\right)}^{\frac{3}{2}} C x^{3} + \frac{C d^{6} \arcsin\left(\frac{e x}{d}\right)}{16 \, e^{3}} + \frac{A d^{4} \arcsin\left(\frac{e x}{d}\right)}{2 \, e} + \frac{1}{2} \, \sqrt{-e^{2} x^{2} + d^{2}} A d^{2} x + \frac{\sqrt{-e^{2} x^{2} + d^{2}} C d^{4} x}{16 \, e^{2}} - \frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{\frac{3}{2}} C d^{2} x}{8 \, e^{2}} + \frac{{\left(C d^{2} + 2 \, B d e + A e^{2}\right)} d^{4} \arcsin\left(\frac{e x}{d}\right)}{8 \, e^{3}} - \frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{\frac{3}{2}} B d^{2}}{3 \, e^{2}} - \frac{2 \, {\left(-e^{2} x^{2} + d^{2}\right)}^{\frac{3}{2}} A d}{3 \, e} + \frac{\sqrt{-e^{2} x^{2} + d^{2}} {\left(C d^{2} + 2 \, B d e + A e^{2}\right)} d^{2} x}{8 \, e^{2}} - \frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{\frac{3}{2}} {\left(2 \, C d e + B e^{2}\right)} x^{2}}{5 \, e^{2}} - \frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{\frac{3}{2}} {\left(C d^{2} + 2 \, B d e + A e^{2}\right)} x}{4 \, e^{2}} - \frac{2 \, {\left(-e^{2} x^{2} + d^{2}\right)}^{\frac{3}{2}} {\left(2 \, C d e + B e^{2}\right)} d^{2}}{15 \, e^{4}}"," ",0,"-1/6*(-e^2*x^2 + d^2)^(3/2)*C*x^3 + 1/16*C*d^6*arcsin(e*x/d)/e^3 + 1/2*A*d^4*arcsin(e*x/d)/e + 1/2*sqrt(-e^2*x^2 + d^2)*A*d^2*x + 1/16*sqrt(-e^2*x^2 + d^2)*C*d^4*x/e^2 - 1/8*(-e^2*x^2 + d^2)^(3/2)*C*d^2*x/e^2 + 1/8*(C*d^2 + 2*B*d*e + A*e^2)*d^4*arcsin(e*x/d)/e^3 - 1/3*(-e^2*x^2 + d^2)^(3/2)*B*d^2/e^2 - 2/3*(-e^2*x^2 + d^2)^(3/2)*A*d/e + 1/8*sqrt(-e^2*x^2 + d^2)*(C*d^2 + 2*B*d*e + A*e^2)*d^2*x/e^2 - 1/5*(-e^2*x^2 + d^2)^(3/2)*(2*C*d*e + B*e^2)*x^2/e^2 - 1/4*(-e^2*x^2 + d^2)^(3/2)*(C*d^2 + 2*B*d*e + A*e^2)*x/e^2 - 2/15*(-e^2*x^2 + d^2)^(3/2)*(2*C*d*e + B*e^2)*d^2/e^4","A",0
2,1,202,0,0.975878," ","integrate((e*x+d)*(C*x^2+B*x+A)*(-e^2*x^2+d^2)^(1/2),x, algorithm=""maxima"")","\frac{A d^{3} \arcsin\left(\frac{e x}{d}\right)}{2 \, e} + \frac{1}{2} \, \sqrt{-e^{2} x^{2} + d^{2}} A d x - \frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{\frac{3}{2}} C x^{2}}{5 \, e} + \frac{{\left(C d + B e\right)} d^{4} \arcsin\left(\frac{e x}{d}\right)}{8 \, e^{3}} + \frac{\sqrt{-e^{2} x^{2} + d^{2}} {\left(C d + B e\right)} d^{2} x}{8 \, e^{2}} - \frac{2 \, {\left(-e^{2} x^{2} + d^{2}\right)}^{\frac{3}{2}} C d^{2}}{15 \, e^{3}} - \frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{\frac{3}{2}} B d}{3 \, e^{2}} - \frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{\frac{3}{2}} A}{3 \, e} - \frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{\frac{3}{2}} {\left(C d + B e\right)} x}{4 \, e^{2}}"," ",0,"1/2*A*d^3*arcsin(e*x/d)/e + 1/2*sqrt(-e^2*x^2 + d^2)*A*d*x - 1/5*(-e^2*x^2 + d^2)^(3/2)*C*x^2/e + 1/8*(C*d + B*e)*d^4*arcsin(e*x/d)/e^3 + 1/8*sqrt(-e^2*x^2 + d^2)*(C*d + B*e)*d^2*x/e^2 - 2/15*(-e^2*x^2 + d^2)^(3/2)*C*d^2/e^3 - 1/3*(-e^2*x^2 + d^2)^(3/2)*B*d/e^2 - 1/3*(-e^2*x^2 + d^2)^(3/2)*A/e - 1/4*(-e^2*x^2 + d^2)^(3/2)*(C*d + B*e)*x/e^2","A",0
3,1,116,0,0.964055," ","integrate((C*x^2+B*x+A)*(-e^2*x^2+d^2)^(1/2),x, algorithm=""maxima"")","\frac{C d^{4} \arcsin\left(\frac{e x}{d}\right)}{8 \, e^{3}} + \frac{A d^{2} \arcsin\left(\frac{e x}{d}\right)}{2 \, e} + \frac{1}{2} \, \sqrt{-e^{2} x^{2} + d^{2}} A x + \frac{\sqrt{-e^{2} x^{2} + d^{2}} C d^{2} x}{8 \, e^{2}} - \frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{\frac{3}{2}} C x}{4 \, e^{2}} - \frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{\frac{3}{2}} B}{3 \, e^{2}}"," ",0,"1/8*C*d^4*arcsin(e*x/d)/e^3 + 1/2*A*d^2*arcsin(e*x/d)/e + 1/2*sqrt(-e^2*x^2 + d^2)*A*x + 1/8*sqrt(-e^2*x^2 + d^2)*C*d^2*x/e^2 - 1/4*(-e^2*x^2 + d^2)^(3/2)*C*x/e^2 - 1/3*(-e^2*x^2 + d^2)^(3/2)*B/e^2","A",0
4,1,171,0,1.086138," ","integrate((C*x^2+B*x+A)*(-e^2*x^2+d^2)^(1/2)/(e*x+d),x, algorithm=""maxima"")","\frac{C d^{3} \arcsin\left(\frac{e x}{d}\right)}{2 \, e^{3}} - \frac{B d^{2} \arcsin\left(\frac{e x}{d}\right)}{2 \, e^{2}} + \frac{A d \arcsin\left(\frac{e x}{d}\right)}{e} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} C d x}{2 \, e^{2}} + \frac{\sqrt{-e^{2} x^{2} + d^{2}} B x}{2 \, e} + \frac{\sqrt{-e^{2} x^{2} + d^{2}} C d^{2}}{e^{3}} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} B d}{e^{2}} + \frac{\sqrt{-e^{2} x^{2} + d^{2}} A}{e} - \frac{{\left(-e^{2} x^{2} + d^{2}\right)}^{\frac{3}{2}} C}{3 \, e^{3}}"," ",0,"1/2*C*d^3*arcsin(e*x/d)/e^3 - 1/2*B*d^2*arcsin(e*x/d)/e^2 + A*d*arcsin(e*x/d)/e - 1/2*sqrt(-e^2*x^2 + d^2)*C*d*x/e^2 + 1/2*sqrt(-e^2*x^2 + d^2)*B*x/e + sqrt(-e^2*x^2 + d^2)*C*d^2/e^3 - sqrt(-e^2*x^2 + d^2)*B*d/e^2 + sqrt(-e^2*x^2 + d^2)*A/e - 1/3*(-e^2*x^2 + d^2)^(3/2)*C/e^3","A",0
5,1,197,0,1.013529," ","integrate((C*x^2+B*x+A)*(-e^2*x^2+d^2)^(1/2)/(e*x+d)^2,x, algorithm=""maxima"")","-\frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} C d^{2}}{e^{4} x + d e^{3}} + \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} B d}{e^{3} x + d e^{2}} - \frac{5 \, C d^{2} \arcsin\left(\frac{e x}{d}\right)}{2 \, e^{3}} + \frac{2 \, B d \arcsin\left(\frac{e x}{d}\right)}{e^{2}} - \frac{A \arcsin\left(\frac{e x}{d}\right)}{e} - \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} A}{e^{2} x + d e} + \frac{\sqrt{-e^{2} x^{2} + d^{2}} C x}{2 \, e^{2}} - \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} C d}{e^{3}} + \frac{\sqrt{-e^{2} x^{2} + d^{2}} B}{e^{2}}"," ",0,"-2*sqrt(-e^2*x^2 + d^2)*C*d^2/(e^4*x + d*e^3) + 2*sqrt(-e^2*x^2 + d^2)*B*d/(e^3*x + d*e^2) - 5/2*C*d^2*arcsin(e*x/d)/e^3 + 2*B*d*arcsin(e*x/d)/e^2 - A*arcsin(e*x/d)/e - 2*sqrt(-e^2*x^2 + d^2)*A/(e^2*x + d*e) + 1/2*sqrt(-e^2*x^2 + d^2)*C*x/e^2 - 2*sqrt(-e^2*x^2 + d^2)*C*d/e^3 + sqrt(-e^2*x^2 + d^2)*B/e^2","A",0
6,-1,0,0,0.000000," ","integrate((C*x^2+B*x+A)*(-e^2*x^2+d^2)^(1/2)/(e*x+d)^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
7,0,0,0,0.000000," ","integrate((C*x^2+B*x+A)*(-e^2*x^2+d^2)^(1/2)/(e*x+d)^4,x, algorithm=""maxima"")","\int \frac{\sqrt{-e^{2} x^{2} + d^{2}} {\left(C x^{2} + B x + A\right)}}{{\left(e x + d\right)}^{4}}\,{d x}"," ",0,"integrate(sqrt(-e^2*x^2 + d^2)*(C*x^2 + B*x + A)/(e*x + d)^4, x)","F",0
8,1,945,0,0.542211," ","integrate((C*x^2+B*x+A)*(-e^2*x^2+d^2)^(1/2)/(e*x+d)^5,x, algorithm=""maxima"")","-\frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} C d^{2}}{7 \, {\left(e^{7} x^{4} + 4 \, d e^{6} x^{3} + 6 \, d^{2} e^{5} x^{2} + 4 \, d^{3} e^{4} x + d^{4} e^{3}\right)}} + \frac{\sqrt{-e^{2} x^{2} + d^{2}} C d^{2}}{35 \, {\left(d e^{6} x^{3} + 3 \, d^{2} e^{5} x^{2} + 3 \, d^{3} e^{4} x + d^{4} e^{3}\right)}} + \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} C d^{2}}{105 \, {\left(d^{2} e^{5} x^{2} + 2 \, d^{3} e^{4} x + d^{4} e^{3}\right)}} + \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} C d^{2}}{105 \, {\left(d^{3} e^{4} x + d^{4} e^{3}\right)}} + \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} B d}{7 \, {\left(e^{6} x^{4} + 4 \, d e^{5} x^{3} + 6 \, d^{2} e^{4} x^{2} + 4 \, d^{3} e^{3} x + d^{4} e^{2}\right)}} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} B d}{35 \, {\left(d e^{5} x^{3} + 3 \, d^{2} e^{4} x^{2} + 3 \, d^{3} e^{3} x + d^{4} e^{2}\right)}} - \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} B d}{105 \, {\left(d^{2} e^{4} x^{2} + 2 \, d^{3} e^{3} x + d^{4} e^{2}\right)}} - \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} B d}{105 \, {\left(d^{3} e^{3} x + d^{4} e^{2}\right)}} + \frac{4 \, \sqrt{-e^{2} x^{2} + d^{2}} C d}{5 \, {\left(e^{6} x^{3} + 3 \, d e^{5} x^{2} + 3 \, d^{2} e^{4} x + d^{3} e^{3}\right)}} - \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} C d}{15 \, {\left(d e^{5} x^{2} + 2 \, d^{2} e^{4} x + d^{3} e^{3}\right)}} - \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} C d}{15 \, {\left(d^{2} e^{4} x + d^{3} e^{3}\right)}} - \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} A}{7 \, {\left(e^{5} x^{4} + 4 \, d e^{4} x^{3} + 6 \, d^{2} e^{3} x^{2} + 4 \, d^{3} e^{2} x + d^{4} e\right)}} + \frac{\sqrt{-e^{2} x^{2} + d^{2}} A}{35 \, {\left(d e^{4} x^{3} + 3 \, d^{2} e^{3} x^{2} + 3 \, d^{3} e^{2} x + d^{4} e\right)}} + \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} A}{105 \, {\left(d^{2} e^{3} x^{2} + 2 \, d^{3} e^{2} x + d^{4} e\right)}} + \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} A}{105 \, {\left(d^{3} e^{2} x + d^{4} e\right)}} - \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} B}{5 \, {\left(e^{5} x^{3} + 3 \, d e^{4} x^{2} + 3 \, d^{2} e^{3} x + d^{3} e^{2}\right)}} + \frac{\sqrt{-e^{2} x^{2} + d^{2}} B}{15 \, {\left(d e^{4} x^{2} + 2 \, d^{2} e^{3} x + d^{3} e^{2}\right)}} + \frac{\sqrt{-e^{2} x^{2} + d^{2}} B}{15 \, {\left(d^{2} e^{3} x + d^{3} e^{2}\right)}} - \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} C}{3 \, {\left(e^{5} x^{2} + 2 \, d e^{4} x + d^{2} e^{3}\right)}} + \frac{\sqrt{-e^{2} x^{2} + d^{2}} C}{3 \, {\left(d e^{4} x + d^{2} e^{3}\right)}}"," ",0,"-2/7*sqrt(-e^2*x^2 + d^2)*C*d^2/(e^7*x^4 + 4*d*e^6*x^3 + 6*d^2*e^5*x^2 + 4*d^3*e^4*x + d^4*e^3) + 1/35*sqrt(-e^2*x^2 + d^2)*C*d^2/(d*e^6*x^3 + 3*d^2*e^5*x^2 + 3*d^3*e^4*x + d^4*e^3) + 2/105*sqrt(-e^2*x^2 + d^2)*C*d^2/(d^2*e^5*x^2 + 2*d^3*e^4*x + d^4*e^3) + 2/105*sqrt(-e^2*x^2 + d^2)*C*d^2/(d^3*e^4*x + d^4*e^3) + 2/7*sqrt(-e^2*x^2 + d^2)*B*d/(e^6*x^4 + 4*d*e^5*x^3 + 6*d^2*e^4*x^2 + 4*d^3*e^3*x + d^4*e^2) - 1/35*sqrt(-e^2*x^2 + d^2)*B*d/(d*e^5*x^3 + 3*d^2*e^4*x^2 + 3*d^3*e^3*x + d^4*e^2) - 2/105*sqrt(-e^2*x^2 + d^2)*B*d/(d^2*e^4*x^2 + 2*d^3*e^3*x + d^4*e^2) - 2/105*sqrt(-e^2*x^2 + d^2)*B*d/(d^3*e^3*x + d^4*e^2) + 4/5*sqrt(-e^2*x^2 + d^2)*C*d/(e^6*x^3 + 3*d*e^5*x^2 + 3*d^2*e^4*x + d^3*e^3) - 2/15*sqrt(-e^2*x^2 + d^2)*C*d/(d*e^5*x^2 + 2*d^2*e^4*x + d^3*e^3) - 2/15*sqrt(-e^2*x^2 + d^2)*C*d/(d^2*e^4*x + d^3*e^3) - 2/7*sqrt(-e^2*x^2 + d^2)*A/(e^5*x^4 + 4*d*e^4*x^3 + 6*d^2*e^3*x^2 + 4*d^3*e^2*x + d^4*e) + 1/35*sqrt(-e^2*x^2 + d^2)*A/(d*e^4*x^3 + 3*d^2*e^3*x^2 + 3*d^3*e^2*x + d^4*e) + 2/105*sqrt(-e^2*x^2 + d^2)*A/(d^2*e^3*x^2 + 2*d^3*e^2*x + d^4*e) + 2/105*sqrt(-e^2*x^2 + d^2)*A/(d^3*e^2*x + d^4*e) - 2/5*sqrt(-e^2*x^2 + d^2)*B/(e^5*x^3 + 3*d*e^4*x^2 + 3*d^2*e^3*x + d^3*e^2) + 1/15*sqrt(-e^2*x^2 + d^2)*B/(d*e^4*x^2 + 2*d^2*e^3*x + d^3*e^2) + 1/15*sqrt(-e^2*x^2 + d^2)*B/(d^2*e^3*x + d^3*e^2) - 2/3*sqrt(-e^2*x^2 + d^2)*C/(e^5*x^2 + 2*d*e^4*x + d^2*e^3) + 1/3*sqrt(-e^2*x^2 + d^2)*C/(d*e^4*x + d^2*e^3)","B",0
9,1,1378,0,0.575433," ","integrate((C*x^2+B*x+A)*(-e^2*x^2+d^2)^(1/2)/(e*x+d)^6,x, algorithm=""maxima"")","-\frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} C d^{2}}{9 \, {\left(e^{8} x^{5} + 5 \, d e^{7} x^{4} + 10 \, d^{2} e^{6} x^{3} + 10 \, d^{3} e^{5} x^{2} + 5 \, d^{4} e^{4} x + d^{5} e^{3}\right)}} + \frac{\sqrt{-e^{2} x^{2} + d^{2}} C d^{2}}{63 \, {\left(d e^{7} x^{4} + 4 \, d^{2} e^{6} x^{3} + 6 \, d^{3} e^{5} x^{2} + 4 \, d^{4} e^{4} x + d^{5} e^{3}\right)}} + \frac{\sqrt{-e^{2} x^{2} + d^{2}} C d^{2}}{105 \, {\left(d^{2} e^{6} x^{3} + 3 \, d^{3} e^{5} x^{2} + 3 \, d^{4} e^{4} x + d^{5} e^{3}\right)}} + \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} C d^{2}}{315 \, {\left(d^{3} e^{5} x^{2} + 2 \, d^{4} e^{4} x + d^{5} e^{3}\right)}} + \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} C d^{2}}{315 \, {\left(d^{4} e^{4} x + d^{5} e^{3}\right)}} + \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} B d}{9 \, {\left(e^{7} x^{5} + 5 \, d e^{6} x^{4} + 10 \, d^{2} e^{5} x^{3} + 10 \, d^{3} e^{4} x^{2} + 5 \, d^{4} e^{3} x + d^{5} e^{2}\right)}} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} B d}{63 \, {\left(d e^{6} x^{4} + 4 \, d^{2} e^{5} x^{3} + 6 \, d^{3} e^{4} x^{2} + 4 \, d^{4} e^{3} x + d^{5} e^{2}\right)}} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} B d}{105 \, {\left(d^{2} e^{5} x^{3} + 3 \, d^{3} e^{4} x^{2} + 3 \, d^{4} e^{3} x + d^{5} e^{2}\right)}} - \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} B d}{315 \, {\left(d^{3} e^{4} x^{2} + 2 \, d^{4} e^{3} x + d^{5} e^{2}\right)}} - \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} B d}{315 \, {\left(d^{4} e^{3} x + d^{5} e^{2}\right)}} + \frac{4 \, \sqrt{-e^{2} x^{2} + d^{2}} C d}{7 \, {\left(e^{7} x^{4} + 4 \, d e^{6} x^{3} + 6 \, d^{2} e^{5} x^{2} + 4 \, d^{3} e^{4} x + d^{4} e^{3}\right)}} - \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} C d}{35 \, {\left(d e^{6} x^{3} + 3 \, d^{2} e^{5} x^{2} + 3 \, d^{3} e^{4} x + d^{4} e^{3}\right)}} - \frac{4 \, \sqrt{-e^{2} x^{2} + d^{2}} C d}{105 \, {\left(d^{2} e^{5} x^{2} + 2 \, d^{3} e^{4} x + d^{4} e^{3}\right)}} - \frac{4 \, \sqrt{-e^{2} x^{2} + d^{2}} C d}{105 \, {\left(d^{3} e^{4} x + d^{4} e^{3}\right)}} - \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} A}{9 \, {\left(e^{6} x^{5} + 5 \, d e^{5} x^{4} + 10 \, d^{2} e^{4} x^{3} + 10 \, d^{3} e^{3} x^{2} + 5 \, d^{4} e^{2} x + d^{5} e\right)}} + \frac{\sqrt{-e^{2} x^{2} + d^{2}} A}{63 \, {\left(d e^{5} x^{4} + 4 \, d^{2} e^{4} x^{3} + 6 \, d^{3} e^{3} x^{2} + 4 \, d^{4} e^{2} x + d^{5} e\right)}} + \frac{\sqrt{-e^{2} x^{2} + d^{2}} A}{105 \, {\left(d^{2} e^{4} x^{3} + 3 \, d^{3} e^{3} x^{2} + 3 \, d^{4} e^{2} x + d^{5} e\right)}} + \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} A}{315 \, {\left(d^{3} e^{3} x^{2} + 2 \, d^{4} e^{2} x + d^{5} e\right)}} + \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} A}{315 \, {\left(d^{4} e^{2} x + d^{5} e\right)}} - \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} B}{7 \, {\left(e^{6} x^{4} + 4 \, d e^{5} x^{3} + 6 \, d^{2} e^{4} x^{2} + 4 \, d^{3} e^{3} x + d^{4} e^{2}\right)}} + \frac{\sqrt{-e^{2} x^{2} + d^{2}} B}{35 \, {\left(d e^{5} x^{3} + 3 \, d^{2} e^{4} x^{2} + 3 \, d^{3} e^{3} x + d^{4} e^{2}\right)}} + \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} B}{105 \, {\left(d^{2} e^{4} x^{2} + 2 \, d^{3} e^{3} x + d^{4} e^{2}\right)}} + \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} B}{105 \, {\left(d^{3} e^{3} x + d^{4} e^{2}\right)}} - \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} C}{5 \, {\left(e^{6} x^{3} + 3 \, d e^{5} x^{2} + 3 \, d^{2} e^{4} x + d^{3} e^{3}\right)}} + \frac{\sqrt{-e^{2} x^{2} + d^{2}} C}{15 \, {\left(d e^{5} x^{2} + 2 \, d^{2} e^{4} x + d^{3} e^{3}\right)}} + \frac{\sqrt{-e^{2} x^{2} + d^{2}} C}{15 \, {\left(d^{2} e^{4} x + d^{3} e^{3}\right)}}"," ",0,"-2/9*sqrt(-e^2*x^2 + d^2)*C*d^2/(e^8*x^5 + 5*d*e^7*x^4 + 10*d^2*e^6*x^3 + 10*d^3*e^5*x^2 + 5*d^4*e^4*x + d^5*e^3) + 1/63*sqrt(-e^2*x^2 + d^2)*C*d^2/(d*e^7*x^4 + 4*d^2*e^6*x^3 + 6*d^3*e^5*x^2 + 4*d^4*e^4*x + d^5*e^3) + 1/105*sqrt(-e^2*x^2 + d^2)*C*d^2/(d^2*e^6*x^3 + 3*d^3*e^5*x^2 + 3*d^4*e^4*x + d^5*e^3) + 2/315*sqrt(-e^2*x^2 + d^2)*C*d^2/(d^3*e^5*x^2 + 2*d^4*e^4*x + d^5*e^3) + 2/315*sqrt(-e^2*x^2 + d^2)*C*d^2/(d^4*e^4*x + d^5*e^3) + 2/9*sqrt(-e^2*x^2 + d^2)*B*d/(e^7*x^5 + 5*d*e^6*x^4 + 10*d^2*e^5*x^3 + 10*d^3*e^4*x^2 + 5*d^4*e^3*x + d^5*e^2) - 1/63*sqrt(-e^2*x^2 + d^2)*B*d/(d*e^6*x^4 + 4*d^2*e^5*x^3 + 6*d^3*e^4*x^2 + 4*d^4*e^3*x + d^5*e^2) - 1/105*sqrt(-e^2*x^2 + d^2)*B*d/(d^2*e^5*x^3 + 3*d^3*e^4*x^2 + 3*d^4*e^3*x + d^5*e^2) - 2/315*sqrt(-e^2*x^2 + d^2)*B*d/(d^3*e^4*x^2 + 2*d^4*e^3*x + d^5*e^2) - 2/315*sqrt(-e^2*x^2 + d^2)*B*d/(d^4*e^3*x + d^5*e^2) + 4/7*sqrt(-e^2*x^2 + d^2)*C*d/(e^7*x^4 + 4*d*e^6*x^3 + 6*d^2*e^5*x^2 + 4*d^3*e^4*x + d^4*e^3) - 2/35*sqrt(-e^2*x^2 + d^2)*C*d/(d*e^6*x^3 + 3*d^2*e^5*x^2 + 3*d^3*e^4*x + d^4*e^3) - 4/105*sqrt(-e^2*x^2 + d^2)*C*d/(d^2*e^5*x^2 + 2*d^3*e^4*x + d^4*e^3) - 4/105*sqrt(-e^2*x^2 + d^2)*C*d/(d^3*e^4*x + d^4*e^3) - 2/9*sqrt(-e^2*x^2 + d^2)*A/(e^6*x^5 + 5*d*e^5*x^4 + 10*d^2*e^4*x^3 + 10*d^3*e^3*x^2 + 5*d^4*e^2*x + d^5*e) + 1/63*sqrt(-e^2*x^2 + d^2)*A/(d*e^5*x^4 + 4*d^2*e^4*x^3 + 6*d^3*e^3*x^2 + 4*d^4*e^2*x + d^5*e) + 1/105*sqrt(-e^2*x^2 + d^2)*A/(d^2*e^4*x^3 + 3*d^3*e^3*x^2 + 3*d^4*e^2*x + d^5*e) + 2/315*sqrt(-e^2*x^2 + d^2)*A/(d^3*e^3*x^2 + 2*d^4*e^2*x + d^5*e) + 2/315*sqrt(-e^2*x^2 + d^2)*A/(d^4*e^2*x + d^5*e) - 2/7*sqrt(-e^2*x^2 + d^2)*B/(e^6*x^4 + 4*d*e^5*x^3 + 6*d^2*e^4*x^2 + 4*d^3*e^3*x + d^4*e^2) + 1/35*sqrt(-e^2*x^2 + d^2)*B/(d*e^5*x^3 + 3*d^2*e^4*x^2 + 3*d^3*e^3*x + d^4*e^2) + 2/105*sqrt(-e^2*x^2 + d^2)*B/(d^2*e^4*x^2 + 2*d^3*e^3*x + d^4*e^2) + 2/105*sqrt(-e^2*x^2 + d^2)*B/(d^3*e^3*x + d^4*e^2) - 2/5*sqrt(-e^2*x^2 + d^2)*C/(e^6*x^3 + 3*d*e^5*x^2 + 3*d^2*e^4*x + d^3*e^3) + 1/15*sqrt(-e^2*x^2 + d^2)*C/(d*e^5*x^2 + 2*d^2*e^4*x + d^3*e^3) + 1/15*sqrt(-e^2*x^2 + d^2)*C/(d^2*e^4*x + d^3*e^3)","B",0
10,1,390,0,0.979356," ","integrate((e*x+d)^3*(C*x^2+B*x+A)/(-e^2*x^2+d^2)^(1/2),x, algorithm=""maxima"")","-\frac{1}{5} \, \sqrt{-e^{2} x^{2} + d^{2}} C e x^{4} - \frac{4 \, \sqrt{-e^{2} x^{2} + d^{2}} C d^{2} x^{2}}{15 \, e} + \frac{A d^{3} \arcsin\left(\frac{e x}{d}\right)}{e} - \frac{8 \, \sqrt{-e^{2} x^{2} + d^{2}} C d^{4}}{15 \, e^{3}} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} B d^{3}}{e^{2}} - \frac{3 \, \sqrt{-e^{2} x^{2} + d^{2}} A d^{2}}{e} - \frac{{\left(3 \, C d e^{2} + B e^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}} x^{3}}{4 \, e^{2}} - \frac{{\left(3 \, C d^{2} e + 3 \, B d e^{2} + A e^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}} x^{2}}{3 \, e^{2}} + \frac{3 \, {\left(3 \, C d e^{2} + B e^{3}\right)} d^{4} \arcsin\left(\frac{e x}{d}\right)}{8 \, e^{5}} + \frac{{\left(C d^{3} + 3 \, B d^{2} e + 3 \, A d e^{2}\right)} d^{2} \arcsin\left(\frac{e x}{d}\right)}{2 \, e^{3}} - \frac{3 \, {\left(3 \, C d e^{2} + B e^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}} d^{2} x}{8 \, e^{4}} - \frac{{\left(C d^{3} + 3 \, B d^{2} e + 3 \, A d e^{2}\right)} \sqrt{-e^{2} x^{2} + d^{2}} x}{2 \, e^{2}} - \frac{2 \, {\left(3 \, C d^{2} e + 3 \, B d e^{2} + A e^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}} d^{2}}{3 \, e^{4}}"," ",0,"-1/5*sqrt(-e^2*x^2 + d^2)*C*e*x^4 - 4/15*sqrt(-e^2*x^2 + d^2)*C*d^2*x^2/e + A*d^3*arcsin(e*x/d)/e - 8/15*sqrt(-e^2*x^2 + d^2)*C*d^4/e^3 - sqrt(-e^2*x^2 + d^2)*B*d^3/e^2 - 3*sqrt(-e^2*x^2 + d^2)*A*d^2/e - 1/4*(3*C*d*e^2 + B*e^3)*sqrt(-e^2*x^2 + d^2)*x^3/e^2 - 1/3*(3*C*d^2*e + 3*B*d*e^2 + A*e^3)*sqrt(-e^2*x^2 + d^2)*x^2/e^2 + 3/8*(3*C*d*e^2 + B*e^3)*d^4*arcsin(e*x/d)/e^5 + 1/2*(C*d^3 + 3*B*d^2*e + 3*A*d*e^2)*d^2*arcsin(e*x/d)/e^3 - 3/8*(3*C*d*e^2 + B*e^3)*sqrt(-e^2*x^2 + d^2)*d^2*x/e^4 - 1/2*(C*d^3 + 3*B*d^2*e + 3*A*d*e^2)*sqrt(-e^2*x^2 + d^2)*x/e^2 - 2/3*(3*C*d^2*e + 3*B*d*e^2 + A*e^3)*sqrt(-e^2*x^2 + d^2)*d^2/e^4","A",0
11,1,253,0,0.982538," ","integrate((e*x+d)^2*(C*x^2+B*x+A)/(-e^2*x^2+d^2)^(1/2),x, algorithm=""maxima"")","-\frac{1}{4} \, \sqrt{-e^{2} x^{2} + d^{2}} C x^{3} + \frac{3 \, C d^{4} \arcsin\left(\frac{e x}{d}\right)}{8 \, e^{3}} + \frac{A d^{2} \arcsin\left(\frac{e x}{d}\right)}{e} - \frac{3 \, \sqrt{-e^{2} x^{2} + d^{2}} C d^{2} x}{8 \, e^{2}} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} B d^{2}}{e^{2}} - \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} A d}{e} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} {\left(2 \, C d e + B e^{2}\right)} x^{2}}{3 \, e^{2}} + \frac{{\left(C d^{2} + 2 \, B d e + A e^{2}\right)} d^{2} \arcsin\left(\frac{e x}{d}\right)}{2 \, e^{3}} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} {\left(C d^{2} + 2 \, B d e + A e^{2}\right)} x}{2 \, e^{2}} - \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} {\left(2 \, C d e + B e^{2}\right)} d^{2}}{3 \, e^{4}}"," ",0,"-1/4*sqrt(-e^2*x^2 + d^2)*C*x^3 + 3/8*C*d^4*arcsin(e*x/d)/e^3 + A*d^2*arcsin(e*x/d)/e - 3/8*sqrt(-e^2*x^2 + d^2)*C*d^2*x/e^2 - sqrt(-e^2*x^2 + d^2)*B*d^2/e^2 - 2*sqrt(-e^2*x^2 + d^2)*A*d/e - 1/3*sqrt(-e^2*x^2 + d^2)*(2*C*d*e + B*e^2)*x^2/e^2 + 1/2*(C*d^2 + 2*B*d*e + A*e^2)*d^2*arcsin(e*x/d)/e^3 - 1/2*sqrt(-e^2*x^2 + d^2)*(C*d^2 + 2*B*d*e + A*e^2)*x/e^2 - 2/3*sqrt(-e^2*x^2 + d^2)*(2*C*d*e + B*e^2)*d^2/e^4","A",0
12,1,150,0,0.978993," ","integrate((e*x+d)*(C*x^2+B*x+A)/(-e^2*x^2+d^2)^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{-e^{2} x^{2} + d^{2}} C x^{2}}{3 \, e} + \frac{A d \arcsin\left(\frac{e x}{d}\right)}{e} + \frac{{\left(C d + B e\right)} d^{2} \arcsin\left(\frac{e x}{d}\right)}{2 \, e^{3}} - \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} C d^{2}}{3 \, e^{3}} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} B d}{e^{2}} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} A}{e} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} {\left(C d + B e\right)} x}{2 \, e^{2}}"," ",0,"-1/3*sqrt(-e^2*x^2 + d^2)*C*x^2/e + A*d*arcsin(e*x/d)/e + 1/2*(C*d + B*e)*d^2*arcsin(e*x/d)/e^3 - 2/3*sqrt(-e^2*x^2 + d^2)*C*d^2/e^3 - sqrt(-e^2*x^2 + d^2)*B*d/e^2 - sqrt(-e^2*x^2 + d^2)*A/e - 1/2*sqrt(-e^2*x^2 + d^2)*(C*d + B*e)*x/e^2","A",0
13,1,70,0,0.988153," ","integrate((C*x^2+B*x+A)/(-e^2*x^2+d^2)^(1/2),x, algorithm=""maxima"")","\frac{C d^{2} \arcsin\left(\frac{e x}{d}\right)}{2 \, e^{3}} + \frac{A \arcsin\left(\frac{e x}{d}\right)}{e} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} C x}{2 \, e^{2}} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} B}{e^{2}}"," ",0,"1/2*C*d^2*arcsin(e*x/d)/e^3 + A*arcsin(e*x/d)/e - 1/2*sqrt(-e^2*x^2 + d^2)*C*x/e^2 - sqrt(-e^2*x^2 + d^2)*B/e^2","A",0
14,1,138,0,0.993996," ","integrate((C*x^2+B*x+A)/(e*x+d)/(-e^2*x^2+d^2)^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{-e^{2} x^{2} + d^{2}} C d}{e^{4} x + d e^{3}} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} A}{d e^{2} x + d^{2} e} + \frac{\sqrt{-e^{2} x^{2} + d^{2}} B}{e^{3} x + d e^{2}} - \frac{C d \arcsin\left(\frac{e x}{d}\right)}{e^{3}} + \frac{B \arcsin\left(\frac{e x}{d}\right)}{e^{2}} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} C}{e^{3}}"," ",0,"-sqrt(-e^2*x^2 + d^2)*C*d/(e^4*x + d*e^3) - sqrt(-e^2*x^2 + d^2)*A/(d*e^2*x + d^2*e) + sqrt(-e^2*x^2 + d^2)*B/(e^3*x + d*e^2) - C*d*arcsin(e*x/d)/e^3 + B*arcsin(e*x/d)/e^2 - sqrt(-e^2*x^2 + d^2)*C/e^3","A",0
15,1,317,0,0.995219," ","integrate((C*x^2+B*x+A)/(e*x+d)^2/(-e^2*x^2+d^2)^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{-e^{2} x^{2} + d^{2}} C d^{2}}{3 \, {\left(d e^{5} x^{2} + 2 \, d^{2} e^{4} x + d^{3} e^{3}\right)}} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} C d^{2}}{3 \, {\left(d^{2} e^{4} x + d^{3} e^{3}\right)}} + \frac{\sqrt{-e^{2} x^{2} + d^{2}} B d}{3 \, {\left(d e^{4} x^{2} + 2 \, d^{2} e^{3} x + d^{3} e^{2}\right)}} + \frac{\sqrt{-e^{2} x^{2} + d^{2}} B d}{3 \, {\left(d^{2} e^{3} x + d^{3} e^{2}\right)}} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} A}{3 \, {\left(d e^{3} x^{2} + 2 \, d^{2} e^{2} x + d^{3} e\right)}} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} A}{3 \, {\left(d^{2} e^{2} x + d^{3} e\right)}} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} B}{d e^{3} x + d^{2} e^{2}} + \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} C}{e^{4} x + d e^{3}} + \frac{C \arcsin\left(\frac{e x}{d}\right)}{e^{3}}"," ",0,"-1/3*sqrt(-e^2*x^2 + d^2)*C*d^2/(d*e^5*x^2 + 2*d^2*e^4*x + d^3*e^3) - 1/3*sqrt(-e^2*x^2 + d^2)*C*d^2/(d^2*e^4*x + d^3*e^3) + 1/3*sqrt(-e^2*x^2 + d^2)*B*d/(d*e^4*x^2 + 2*d^2*e^3*x + d^3*e^2) + 1/3*sqrt(-e^2*x^2 + d^2)*B*d/(d^2*e^3*x + d^3*e^2) - 1/3*sqrt(-e^2*x^2 + d^2)*A/(d*e^3*x^2 + 2*d^2*e^2*x + d^3*e) - 1/3*sqrt(-e^2*x^2 + d^2)*A/(d^2*e^2*x + d^3*e) - sqrt(-e^2*x^2 + d^2)*B/(d*e^3*x + d^2*e^2) + 2*sqrt(-e^2*x^2 + d^2)*C/(e^4*x + d*e^3) + C*arcsin(e*x/d)/e^3","B",0
16,1,608,0,1.015067," ","integrate((C*x^2+B*x+A)/(e*x+d)^3/(-e^2*x^2+d^2)^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{-e^{2} x^{2} + d^{2}} C d^{2}}{5 \, {\left(d e^{6} x^{3} + 3 \, d^{2} e^{5} x^{2} + 3 \, d^{3} e^{4} x + d^{4} e^{3}\right)}} - \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} C d^{2}}{15 \, {\left(d^{2} e^{5} x^{2} + 2 \, d^{3} e^{4} x + d^{4} e^{3}\right)}} - \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} C d^{2}}{15 \, {\left(d^{3} e^{4} x + d^{4} e^{3}\right)}} + \frac{\sqrt{-e^{2} x^{2} + d^{2}} B d}{5 \, {\left(d e^{5} x^{3} + 3 \, d^{2} e^{4} x^{2} + 3 \, d^{3} e^{3} x + d^{4} e^{2}\right)}} + \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} B d}{15 \, {\left(d^{2} e^{4} x^{2} + 2 \, d^{3} e^{3} x + d^{4} e^{2}\right)}} + \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} B d}{15 \, {\left(d^{3} e^{3} x + d^{4} e^{2}\right)}} + \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} C d}{3 \, {\left(d e^{5} x^{2} + 2 \, d^{2} e^{4} x + d^{3} e^{3}\right)}} + \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} C d}{3 \, {\left(d^{2} e^{4} x + d^{3} e^{3}\right)}} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} A}{5 \, {\left(d e^{4} x^{3} + 3 \, d^{2} e^{3} x^{2} + 3 \, d^{3} e^{2} x + d^{4} e\right)}} - \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} A}{15 \, {\left(d^{2} e^{3} x^{2} + 2 \, d^{3} e^{2} x + d^{4} e\right)}} - \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} A}{15 \, {\left(d^{3} e^{2} x + d^{4} e\right)}} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} B}{3 \, {\left(d e^{4} x^{2} + 2 \, d^{2} e^{3} x + d^{3} e^{2}\right)}} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} B}{3 \, {\left(d^{2} e^{3} x + d^{3} e^{2}\right)}} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} C}{d e^{4} x + d^{2} e^{3}}"," ",0,"-1/5*sqrt(-e^2*x^2 + d^2)*C*d^2/(d*e^6*x^3 + 3*d^2*e^5*x^2 + 3*d^3*e^4*x + d^4*e^3) - 2/15*sqrt(-e^2*x^2 + d^2)*C*d^2/(d^2*e^5*x^2 + 2*d^3*e^4*x + d^4*e^3) - 2/15*sqrt(-e^2*x^2 + d^2)*C*d^2/(d^3*e^4*x + d^4*e^3) + 1/5*sqrt(-e^2*x^2 + d^2)*B*d/(d*e^5*x^3 + 3*d^2*e^4*x^2 + 3*d^3*e^3*x + d^4*e^2) + 2/15*sqrt(-e^2*x^2 + d^2)*B*d/(d^2*e^4*x^2 + 2*d^3*e^3*x + d^4*e^2) + 2/15*sqrt(-e^2*x^2 + d^2)*B*d/(d^3*e^3*x + d^4*e^2) + 2/3*sqrt(-e^2*x^2 + d^2)*C*d/(d*e^5*x^2 + 2*d^2*e^4*x + d^3*e^3) + 2/3*sqrt(-e^2*x^2 + d^2)*C*d/(d^2*e^4*x + d^3*e^3) - 1/5*sqrt(-e^2*x^2 + d^2)*A/(d*e^4*x^3 + 3*d^2*e^3*x^2 + 3*d^3*e^2*x + d^4*e) - 2/15*sqrt(-e^2*x^2 + d^2)*A/(d^2*e^3*x^2 + 2*d^3*e^2*x + d^4*e) - 2/15*sqrt(-e^2*x^2 + d^2)*A/(d^3*e^2*x + d^4*e) - 1/3*sqrt(-e^2*x^2 + d^2)*B/(d*e^4*x^2 + 2*d^2*e^3*x + d^3*e^2) - 1/3*sqrt(-e^2*x^2 + d^2)*B/(d^2*e^3*x + d^3*e^2) - sqrt(-e^2*x^2 + d^2)*C/(d*e^4*x + d^2*e^3)","B",0
17,1,975,0,1.061019," ","integrate((C*x^2+B*x+A)/(e*x+d)^4/(-e^2*x^2+d^2)^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{-e^{2} x^{2} + d^{2}} C d^{2}}{7 \, {\left(d e^{7} x^{4} + 4 \, d^{2} e^{6} x^{3} + 6 \, d^{3} e^{5} x^{2} + 4 \, d^{4} e^{4} x + d^{5} e^{3}\right)}} - \frac{3 \, \sqrt{-e^{2} x^{2} + d^{2}} C d^{2}}{35 \, {\left(d^{2} e^{6} x^{3} + 3 \, d^{3} e^{5} x^{2} + 3 \, d^{4} e^{4} x + d^{5} e^{3}\right)}} - \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} C d^{2}}{35 \, {\left(d^{3} e^{5} x^{2} + 2 \, d^{4} e^{4} x + d^{5} e^{3}\right)}} - \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} C d^{2}}{35 \, {\left(d^{4} e^{4} x + d^{5} e^{3}\right)}} + \frac{\sqrt{-e^{2} x^{2} + d^{2}} B d}{7 \, {\left(d e^{6} x^{4} + 4 \, d^{2} e^{5} x^{3} + 6 \, d^{3} e^{4} x^{2} + 4 \, d^{4} e^{3} x + d^{5} e^{2}\right)}} + \frac{3 \, \sqrt{-e^{2} x^{2} + d^{2}} B d}{35 \, {\left(d^{2} e^{5} x^{3} + 3 \, d^{3} e^{4} x^{2} + 3 \, d^{4} e^{3} x + d^{5} e^{2}\right)}} + \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} B d}{35 \, {\left(d^{3} e^{4} x^{2} + 2 \, d^{4} e^{3} x + d^{5} e^{2}\right)}} + \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} B d}{35 \, {\left(d^{4} e^{3} x + d^{5} e^{2}\right)}} + \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} C d}{5 \, {\left(d e^{6} x^{3} + 3 \, d^{2} e^{5} x^{2} + 3 \, d^{3} e^{4} x + d^{4} e^{3}\right)}} + \frac{4 \, \sqrt{-e^{2} x^{2} + d^{2}} C d}{15 \, {\left(d^{2} e^{5} x^{2} + 2 \, d^{3} e^{4} x + d^{4} e^{3}\right)}} + \frac{4 \, \sqrt{-e^{2} x^{2} + d^{2}} C d}{15 \, {\left(d^{3} e^{4} x + d^{4} e^{3}\right)}} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} A}{7 \, {\left(d e^{5} x^{4} + 4 \, d^{2} e^{4} x^{3} + 6 \, d^{3} e^{3} x^{2} + 4 \, d^{4} e^{2} x + d^{5} e\right)}} - \frac{3 \, \sqrt{-e^{2} x^{2} + d^{2}} A}{35 \, {\left(d^{2} e^{4} x^{3} + 3 \, d^{3} e^{3} x^{2} + 3 \, d^{4} e^{2} x + d^{5} e\right)}} - \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} A}{35 \, {\left(d^{3} e^{3} x^{2} + 2 \, d^{4} e^{2} x + d^{5} e\right)}} - \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} A}{35 \, {\left(d^{4} e^{2} x + d^{5} e\right)}} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} B}{5 \, {\left(d e^{5} x^{3} + 3 \, d^{2} e^{4} x^{2} + 3 \, d^{3} e^{3} x + d^{4} e^{2}\right)}} - \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} B}{15 \, {\left(d^{2} e^{4} x^{2} + 2 \, d^{3} e^{3} x + d^{4} e^{2}\right)}} - \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} B}{15 \, {\left(d^{3} e^{3} x + d^{4} e^{2}\right)}} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} C}{3 \, {\left(d e^{5} x^{2} + 2 \, d^{2} e^{4} x + d^{3} e^{3}\right)}} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} C}{3 \, {\left(d^{2} e^{4} x + d^{3} e^{3}\right)}}"," ",0,"-1/7*sqrt(-e^2*x^2 + d^2)*C*d^2/(d*e^7*x^4 + 4*d^2*e^6*x^3 + 6*d^3*e^5*x^2 + 4*d^4*e^4*x + d^5*e^3) - 3/35*sqrt(-e^2*x^2 + d^2)*C*d^2/(d^2*e^6*x^3 + 3*d^3*e^5*x^2 + 3*d^4*e^4*x + d^5*e^3) - 2/35*sqrt(-e^2*x^2 + d^2)*C*d^2/(d^3*e^5*x^2 + 2*d^4*e^4*x + d^5*e^3) - 2/35*sqrt(-e^2*x^2 + d^2)*C*d^2/(d^4*e^4*x + d^5*e^3) + 1/7*sqrt(-e^2*x^2 + d^2)*B*d/(d*e^6*x^4 + 4*d^2*e^5*x^3 + 6*d^3*e^4*x^2 + 4*d^4*e^3*x + d^5*e^2) + 3/35*sqrt(-e^2*x^2 + d^2)*B*d/(d^2*e^5*x^3 + 3*d^3*e^4*x^2 + 3*d^4*e^3*x + d^5*e^2) + 2/35*sqrt(-e^2*x^2 + d^2)*B*d/(d^3*e^4*x^2 + 2*d^4*e^3*x + d^5*e^2) + 2/35*sqrt(-e^2*x^2 + d^2)*B*d/(d^4*e^3*x + d^5*e^2) + 2/5*sqrt(-e^2*x^2 + d^2)*C*d/(d*e^6*x^3 + 3*d^2*e^5*x^2 + 3*d^3*e^4*x + d^4*e^3) + 4/15*sqrt(-e^2*x^2 + d^2)*C*d/(d^2*e^5*x^2 + 2*d^3*e^4*x + d^4*e^3) + 4/15*sqrt(-e^2*x^2 + d^2)*C*d/(d^3*e^4*x + d^4*e^3) - 1/7*sqrt(-e^2*x^2 + d^2)*A/(d*e^5*x^4 + 4*d^2*e^4*x^3 + 6*d^3*e^3*x^2 + 4*d^4*e^2*x + d^5*e) - 3/35*sqrt(-e^2*x^2 + d^2)*A/(d^2*e^4*x^3 + 3*d^3*e^3*x^2 + 3*d^4*e^2*x + d^5*e) - 2/35*sqrt(-e^2*x^2 + d^2)*A/(d^3*e^3*x^2 + 2*d^4*e^2*x + d^5*e) - 2/35*sqrt(-e^2*x^2 + d^2)*A/(d^4*e^2*x + d^5*e) - 1/5*sqrt(-e^2*x^2 + d^2)*B/(d*e^5*x^3 + 3*d^2*e^4*x^2 + 3*d^3*e^3*x + d^4*e^2) - 2/15*sqrt(-e^2*x^2 + d^2)*B/(d^2*e^4*x^2 + 2*d^3*e^3*x + d^4*e^2) - 2/15*sqrt(-e^2*x^2 + d^2)*B/(d^3*e^3*x + d^4*e^2) - 1/3*sqrt(-e^2*x^2 + d^2)*C/(d*e^5*x^2 + 2*d^2*e^4*x + d^3*e^3) - 1/3*sqrt(-e^2*x^2 + d^2)*C/(d^2*e^4*x + d^3*e^3)","B",0
18,1,202,0,0.445509," ","integrate((e*x+d)^3*(c*x^2+a)*(C*x^2+B*x+A),x, algorithm=""maxima"")","\frac{1}{8} \, C c e^{3} x^{8} + \frac{1}{7} \, {\left(3 \, C c d e^{2} + B c e^{3}\right)} x^{7} + \frac{1}{6} \, {\left(3 \, C c d^{2} e + 3 \, B c d e^{2} + {\left(C a + A c\right)} e^{3}\right)} x^{6} + A a d^{3} x + \frac{1}{5} \, {\left(C c d^{3} + 3 \, B c d^{2} e + B a e^{3} + 3 \, {\left(C a + A c\right)} d e^{2}\right)} x^{5} + \frac{1}{4} \, {\left(B c d^{3} + 3 \, B a d e^{2} + A a e^{3} + 3 \, {\left(C a + A c\right)} d^{2} e\right)} x^{4} + \frac{1}{3} \, {\left(3 \, B a d^{2} e + 3 \, A a d e^{2} + {\left(C a + A c\right)} d^{3}\right)} x^{3} + \frac{1}{2} \, {\left(B a d^{3} + 3 \, A a d^{2} e\right)} x^{2}"," ",0,"1/8*C*c*e^3*x^8 + 1/7*(3*C*c*d*e^2 + B*c*e^3)*x^7 + 1/6*(3*C*c*d^2*e + 3*B*c*d*e^2 + (C*a + A*c)*e^3)*x^6 + A*a*d^3*x + 1/5*(C*c*d^3 + 3*B*c*d^2*e + B*a*e^3 + 3*(C*a + A*c)*d*e^2)*x^5 + 1/4*(B*c*d^3 + 3*B*a*d*e^2 + A*a*e^3 + 3*(C*a + A*c)*d^2*e)*x^4 + 1/3*(3*B*a*d^2*e + 3*A*a*d*e^2 + (C*a + A*c)*d^3)*x^3 + 1/2*(B*a*d^3 + 3*A*a*d^2*e)*x^2","A",0
19,1,141,0,0.447898," ","integrate((e*x+d)^2*(c*x^2+a)*(C*x^2+B*x+A),x, algorithm=""maxima"")","\frac{1}{7} \, C c e^{2} x^{7} + \frac{1}{6} \, {\left(2 \, C c d e + B c e^{2}\right)} x^{6} + \frac{1}{5} \, {\left(C c d^{2} + 2 \, B c d e + {\left(C a + A c\right)} e^{2}\right)} x^{5} + A a d^{2} x + \frac{1}{4} \, {\left(B c d^{2} + B a e^{2} + 2 \, {\left(C a + A c\right)} d e\right)} x^{4} + \frac{1}{3} \, {\left(2 \, B a d e + A a e^{2} + {\left(C a + A c\right)} d^{2}\right)} x^{3} + \frac{1}{2} \, {\left(B a d^{2} + 2 \, A a d e\right)} x^{2}"," ",0,"1/7*C*c*e^2*x^7 + 1/6*(2*C*c*d*e + B*c*e^2)*x^6 + 1/5*(C*c*d^2 + 2*B*c*d*e + (C*a + A*c)*e^2)*x^5 + A*a*d^2*x + 1/4*(B*c*d^2 + B*a*e^2 + 2*(C*a + A*c)*d*e)*x^4 + 1/3*(2*B*a*d*e + A*a*e^2 + (C*a + A*c)*d^2)*x^3 + 1/2*(B*a*d^2 + 2*A*a*d*e)*x^2","A",0
20,1,80,0,0.452354," ","integrate((e*x+d)*(c*x^2+a)*(C*x^2+B*x+A),x, algorithm=""maxima"")","\frac{1}{6} \, C c e x^{6} + \frac{1}{5} \, {\left(C c d + B c e\right)} x^{5} + \frac{1}{4} \, {\left(B c d + {\left(C a + A c\right)} e\right)} x^{4} + A a d x + \frac{1}{3} \, {\left(B a e + {\left(C a + A c\right)} d\right)} x^{3} + \frac{1}{2} \, {\left(B a d + A a e\right)} x^{2}"," ",0,"1/6*C*c*e*x^6 + 1/5*(C*c*d + B*c*e)*x^5 + 1/4*(B*c*d + (C*a + A*c)*e)*x^4 + A*a*d*x + 1/3*(B*a*e + (C*a + A*c)*d)*x^3 + 1/2*(B*a*d + A*a*e)*x^2","A",0
21,1,38,0,0.439542," ","integrate((c*x^2+a)*(C*x^2+B*x+A),x, algorithm=""maxima"")","\frac{1}{5} \, C c x^{5} + \frac{1}{4} \, B c x^{4} + \frac{1}{2} \, B a x^{2} + \frac{1}{3} \, {\left(C a + A c\right)} x^{3} + A a x"," ",0,"1/5*C*c*x^5 + 1/4*B*c*x^4 + 1/2*B*a*x^2 + 1/3*(C*a + A*c)*x^3 + A*a*x","A",0
22,1,159,0,0.447914," ","integrate((c*x^2+a)*(C*x^2+B*x+A)/(e*x+d),x, algorithm=""maxima"")","\frac{3 \, C c e^{3} x^{4} - 4 \, {\left(C c d e^{2} - B c e^{3}\right)} x^{3} + 6 \, {\left(C c d^{2} e - B c d e^{2} + {\left(C a + A c\right)} e^{3}\right)} x^{2} - 12 \, {\left(C c d^{3} - B c d^{2} e - B a e^{3} + {\left(C a + A c\right)} d e^{2}\right)} x}{12 \, e^{4}} + \frac{{\left(C c d^{4} - B c d^{3} e - B a d e^{3} + A a e^{4} + {\left(C a + A c\right)} d^{2} e^{2}\right)} \log\left(e x + d\right)}{e^{5}}"," ",0,"1/12*(3*C*c*e^3*x^4 - 4*(C*c*d*e^2 - B*c*e^3)*x^3 + 6*(C*c*d^2*e - B*c*d*e^2 + (C*a + A*c)*e^3)*x^2 - 12*(C*c*d^3 - B*c*d^2*e - B*a*e^3 + (C*a + A*c)*d*e^2)*x)/e^4 + (C*c*d^4 - B*c*d^3*e - B*a*d*e^3 + A*a*e^4 + (C*a + A*c)*d^2*e^2)*log(e*x + d)/e^5","A",0
23,1,169,0,0.450807," ","integrate((c*x^2+a)*(C*x^2+B*x+A)/(e*x+d)^2,x, algorithm=""maxima"")","-\frac{C c d^{4} - B c d^{3} e - B a d e^{3} + A a e^{4} + {\left(C a + A c\right)} d^{2} e^{2}}{e^{6} x + d e^{5}} + \frac{2 \, C c e^{2} x^{3} - 3 \, {\left(2 \, C c d e - B c e^{2}\right)} x^{2} + 6 \, {\left(3 \, C c d^{2} - 2 \, B c d e + {\left(C a + A c\right)} e^{2}\right)} x}{6 \, e^{4}} - \frac{{\left(4 \, C c d^{3} - 3 \, B c d^{2} e - B a e^{3} + 2 \, {\left(C a + A c\right)} d e^{2}\right)} \log\left(e x + d\right)}{e^{5}}"," ",0,"-(C*c*d^4 - B*c*d^3*e - B*a*d*e^3 + A*a*e^4 + (C*a + A*c)*d^2*e^2)/(e^6*x + d*e^5) + 1/6*(2*C*c*e^2*x^3 - 3*(2*C*c*d*e - B*c*e^2)*x^2 + 6*(3*C*c*d^2 - 2*B*c*d*e + (C*a + A*c)*e^2)*x)/e^4 - (4*C*c*d^3 - 3*B*c*d^2*e - B*a*e^3 + 2*(C*a + A*c)*d*e^2)*log(e*x + d)/e^5","A",0
24,1,177,0,0.470562," ","integrate((c*x^2+a)*(C*x^2+B*x+A)/(e*x+d)^3,x, algorithm=""maxima"")","\frac{7 \, C c d^{4} - 5 \, B c d^{3} e - B a d e^{3} - A a e^{4} + 3 \, {\left(C a + A c\right)} d^{2} e^{2} + 2 \, {\left(4 \, C c d^{3} e - 3 \, B c d^{2} e^{2} - B a e^{4} + 2 \, {\left(C a + A c\right)} d e^{3}\right)} x}{2 \, {\left(e^{7} x^{2} + 2 \, d e^{6} x + d^{2} e^{5}\right)}} + \frac{C c e x^{2} - 2 \, {\left(3 \, C c d - B c e\right)} x}{2 \, e^{4}} + \frac{{\left(6 \, C c d^{2} - 3 \, B c d e + {\left(C a + A c\right)} e^{2}\right)} \log\left(e x + d\right)}{e^{5}}"," ",0,"1/2*(7*C*c*d^4 - 5*B*c*d^3*e - B*a*d*e^3 - A*a*e^4 + 3*(C*a + A*c)*d^2*e^2 + 2*(4*C*c*d^3*e - 3*B*c*d^2*e^2 - B*a*e^4 + 2*(C*a + A*c)*d*e^3)*x)/(e^7*x^2 + 2*d*e^6*x + d^2*e^5) + 1/2*(C*c*e*x^2 - 2*(3*C*c*d - B*c*e)*x)/e^4 + (6*C*c*d^2 - 3*B*c*d*e + (C*a + A*c)*e^2)*log(e*x + d)/e^5","A",0
25,1,360,0,0.449576," ","integrate((e*x+d)^3*(c*x^2+a)^2*(C*x^2+B*x+A),x, algorithm=""maxima"")","\frac{1}{10} \, C c^{2} e^{3} x^{10} + \frac{1}{9} \, {\left(3 \, C c^{2} d e^{2} + B c^{2} e^{3}\right)} x^{9} + \frac{1}{8} \, {\left(3 \, C c^{2} d^{2} e + 3 \, B c^{2} d e^{2} + {\left(2 \, C a c + A c^{2}\right)} e^{3}\right)} x^{8} + \frac{1}{7} \, {\left(C c^{2} d^{3} + 3 \, B c^{2} d^{2} e + 2 \, B a c e^{3} + 3 \, {\left(2 \, C a c + A c^{2}\right)} d e^{2}\right)} x^{7} + A a^{2} d^{3} x + \frac{1}{6} \, {\left(B c^{2} d^{3} + 6 \, B a c d e^{2} + 3 \, {\left(2 \, C a c + A c^{2}\right)} d^{2} e + {\left(C a^{2} + 2 \, A a c\right)} e^{3}\right)} x^{6} + \frac{1}{5} \, {\left(6 \, B a c d^{2} e + B a^{2} e^{3} + {\left(2 \, C a c + A c^{2}\right)} d^{3} + 3 \, {\left(C a^{2} + 2 \, A a c\right)} d e^{2}\right)} x^{5} + \frac{1}{4} \, {\left(2 \, B a c d^{3} + 3 \, B a^{2} d e^{2} + A a^{2} e^{3} + 3 \, {\left(C a^{2} + 2 \, A a c\right)} d^{2} e\right)} x^{4} + \frac{1}{3} \, {\left(3 \, B a^{2} d^{2} e + 3 \, A a^{2} d e^{2} + {\left(C a^{2} + 2 \, A a c\right)} d^{3}\right)} x^{3} + \frac{1}{2} \, {\left(B a^{2} d^{3} + 3 \, A a^{2} d^{2} e\right)} x^{2}"," ",0,"1/10*C*c^2*e^3*x^10 + 1/9*(3*C*c^2*d*e^2 + B*c^2*e^3)*x^9 + 1/8*(3*C*c^2*d^2*e + 3*B*c^2*d*e^2 + (2*C*a*c + A*c^2)*e^3)*x^8 + 1/7*(C*c^2*d^3 + 3*B*c^2*d^2*e + 2*B*a*c*e^3 + 3*(2*C*a*c + A*c^2)*d*e^2)*x^7 + A*a^2*d^3*x + 1/6*(B*c^2*d^3 + 6*B*a*c*d*e^2 + 3*(2*C*a*c + A*c^2)*d^2*e + (C*a^2 + 2*A*a*c)*e^3)*x^6 + 1/5*(6*B*a*c*d^2*e + B*a^2*e^3 + (2*C*a*c + A*c^2)*d^3 + 3*(C*a^2 + 2*A*a*c)*d*e^2)*x^5 + 1/4*(2*B*a*c*d^3 + 3*B*a^2*d*e^2 + A*a^2*e^3 + 3*(C*a^2 + 2*A*a*c)*d^2*e)*x^4 + 1/3*(3*B*a^2*d^2*e + 3*A*a^2*d*e^2 + (C*a^2 + 2*A*a*c)*d^3)*x^3 + 1/2*(B*a^2*d^3 + 3*A*a^2*d^2*e)*x^2","A",0
26,1,257,0,0.440632," ","integrate((e*x+d)^2*(c*x^2+a)^2*(C*x^2+B*x+A),x, algorithm=""maxima"")","\frac{1}{9} \, C c^{2} e^{2} x^{9} + \frac{1}{8} \, {\left(2 \, C c^{2} d e + B c^{2} e^{2}\right)} x^{8} + \frac{1}{7} \, {\left(C c^{2} d^{2} + 2 \, B c^{2} d e + {\left(2 \, C a c + A c^{2}\right)} e^{2}\right)} x^{7} + \frac{1}{6} \, {\left(B c^{2} d^{2} + 2 \, B a c e^{2} + 2 \, {\left(2 \, C a c + A c^{2}\right)} d e\right)} x^{6} + A a^{2} d^{2} x + \frac{1}{5} \, {\left(4 \, B a c d e + {\left(2 \, C a c + A c^{2}\right)} d^{2} + {\left(C a^{2} + 2 \, A a c\right)} e^{2}\right)} x^{5} + \frac{1}{4} \, {\left(2 \, B a c d^{2} + B a^{2} e^{2} + 2 \, {\left(C a^{2} + 2 \, A a c\right)} d e\right)} x^{4} + \frac{1}{3} \, {\left(2 \, B a^{2} d e + A a^{2} e^{2} + {\left(C a^{2} + 2 \, A a c\right)} d^{2}\right)} x^{3} + \frac{1}{2} \, {\left(B a^{2} d^{2} + 2 \, A a^{2} d e\right)} x^{2}"," ",0,"1/9*C*c^2*e^2*x^9 + 1/8*(2*C*c^2*d*e + B*c^2*e^2)*x^8 + 1/7*(C*c^2*d^2 + 2*B*c^2*d*e + (2*C*a*c + A*c^2)*e^2)*x^7 + 1/6*(B*c^2*d^2 + 2*B*a*c*e^2 + 2*(2*C*a*c + A*c^2)*d*e)*x^6 + A*a^2*d^2*x + 1/5*(4*B*a*c*d*e + (2*C*a*c + A*c^2)*d^2 + (C*a^2 + 2*A*a*c)*e^2)*x^5 + 1/4*(2*B*a*c*d^2 + B*a^2*e^2 + 2*(C*a^2 + 2*A*a*c)*d*e)*x^4 + 1/3*(2*B*a^2*d*e + A*a^2*e^2 + (C*a^2 + 2*A*a*c)*d^2)*x^3 + 1/2*(B*a^2*d^2 + 2*A*a^2*d*e)*x^2","A",0
27,1,154,0,0.447168," ","integrate((e*x+d)*(c*x^2+a)^2*(C*x^2+B*x+A),x, algorithm=""maxima"")","\frac{1}{8} \, C c^{2} e x^{8} + \frac{1}{7} \, {\left(C c^{2} d + B c^{2} e\right)} x^{7} + \frac{1}{6} \, {\left(B c^{2} d + {\left(2 \, C a c + A c^{2}\right)} e\right)} x^{6} + \frac{1}{5} \, {\left(2 \, B a c e + {\left(2 \, C a c + A c^{2}\right)} d\right)} x^{5} + A a^{2} d x + \frac{1}{4} \, {\left(2 \, B a c d + {\left(C a^{2} + 2 \, A a c\right)} e\right)} x^{4} + \frac{1}{3} \, {\left(B a^{2} e + {\left(C a^{2} + 2 \, A a c\right)} d\right)} x^{3} + \frac{1}{2} \, {\left(B a^{2} d + A a^{2} e\right)} x^{2}"," ",0,"1/8*C*c^2*e*x^8 + 1/7*(C*c^2*d + B*c^2*e)*x^7 + 1/6*(B*c^2*d + (2*C*a*c + A*c^2)*e)*x^6 + 1/5*(2*B*a*c*e + (2*C*a*c + A*c^2)*d)*x^5 + A*a^2*d*x + 1/4*(2*B*a*c*d + (C*a^2 + 2*A*a*c)*e)*x^4 + 1/3*(B*a^2*e + (C*a^2 + 2*A*a*c)*d)*x^3 + 1/2*(B*a^2*d + A*a^2*e)*x^2","A",0
28,1,74,0,0.438169," ","integrate((c*x^2+a)^2*(C*x^2+B*x+A),x, algorithm=""maxima"")","\frac{1}{7} \, C c^{2} x^{7} + \frac{1}{6} \, B c^{2} x^{6} + \frac{1}{2} \, B a c x^{4} + \frac{1}{5} \, {\left(2 \, C a c + A c^{2}\right)} x^{5} + \frac{1}{2} \, B a^{2} x^{2} + A a^{2} x + \frac{1}{3} \, {\left(C a^{2} + 2 \, A a c\right)} x^{3}"," ",0,"1/7*C*c^2*x^7 + 1/6*B*c^2*x^6 + 1/2*B*a*c*x^4 + 1/5*(2*C*a*c + A*c^2)*x^5 + 1/2*B*a^2*x^2 + A*a^2*x + 1/3*(C*a^2 + 2*A*a*c)*x^3","A",0
29,1,377,0,0.484790," ","integrate((c*x^2+a)^2*(C*x^2+B*x+A)/(e*x+d),x, algorithm=""maxima"")","\frac{10 \, C c^{2} e^{5} x^{6} - 12 \, {\left(C c^{2} d e^{4} - B c^{2} e^{5}\right)} x^{5} + 15 \, {\left(C c^{2} d^{2} e^{3} - B c^{2} d e^{4} + {\left(2 \, C a c + A c^{2}\right)} e^{5}\right)} x^{4} - 20 \, {\left(C c^{2} d^{3} e^{2} - B c^{2} d^{2} e^{3} - 2 \, B a c e^{5} + {\left(2 \, C a c + A c^{2}\right)} d e^{4}\right)} x^{3} + 30 \, {\left(C c^{2} d^{4} e - B c^{2} d^{3} e^{2} - 2 \, B a c d e^{4} + {\left(2 \, C a c + A c^{2}\right)} d^{2} e^{3} + {\left(C a^{2} + 2 \, A a c\right)} e^{5}\right)} x^{2} - 60 \, {\left(C c^{2} d^{5} - B c^{2} d^{4} e - 2 \, B a c d^{2} e^{3} - B a^{2} e^{5} + {\left(2 \, C a c + A c^{2}\right)} d^{3} e^{2} + {\left(C a^{2} + 2 \, A a c\right)} d e^{4}\right)} x}{60 \, e^{6}} + \frac{{\left(C c^{2} d^{6} - B c^{2} d^{5} e - 2 \, B a c d^{3} e^{3} - B a^{2} d e^{5} + A a^{2} e^{6} + {\left(2 \, C a c + A c^{2}\right)} d^{4} e^{2} + {\left(C a^{2} + 2 \, A a c\right)} d^{2} e^{4}\right)} \log\left(e x + d\right)}{e^{7}}"," ",0,"1/60*(10*C*c^2*e^5*x^6 - 12*(C*c^2*d*e^4 - B*c^2*e^5)*x^5 + 15*(C*c^2*d^2*e^3 - B*c^2*d*e^4 + (2*C*a*c + A*c^2)*e^5)*x^4 - 20*(C*c^2*d^3*e^2 - B*c^2*d^2*e^3 - 2*B*a*c*e^5 + (2*C*a*c + A*c^2)*d*e^4)*x^3 + 30*(C*c^2*d^4*e - B*c^2*d^3*e^2 - 2*B*a*c*d*e^4 + (2*C*a*c + A*c^2)*d^2*e^3 + (C*a^2 + 2*A*a*c)*e^5)*x^2 - 60*(C*c^2*d^5 - B*c^2*d^4*e - 2*B*a*c*d^2*e^3 - B*a^2*e^5 + (2*C*a*c + A*c^2)*d^3*e^2 + (C*a^2 + 2*A*a*c)*d*e^4)*x)/e^6 + (C*c^2*d^6 - B*c^2*d^5*e - 2*B*a*c*d^3*e^3 - B*a^2*d*e^5 + A*a^2*e^6 + (2*C*a*c + A*c^2)*d^4*e^2 + (C*a^2 + 2*A*a*c)*d^2*e^4)*log(e*x + d)/e^7","A",0
30,1,392,0,0.477749," ","integrate((c*x^2+a)^2*(C*x^2+B*x+A)/(e*x+d)^2,x, algorithm=""maxima"")","-\frac{C c^{2} d^{6} - B c^{2} d^{5} e - 2 \, B a c d^{3} e^{3} - B a^{2} d e^{5} + A a^{2} e^{6} + {\left(2 \, C a c + A c^{2}\right)} d^{4} e^{2} + {\left(C a^{2} + 2 \, A a c\right)} d^{2} e^{4}}{e^{8} x + d e^{7}} + \frac{12 \, C c^{2} e^{4} x^{5} - 15 \, {\left(2 \, C c^{2} d e^{3} - B c^{2} e^{4}\right)} x^{4} + 20 \, {\left(3 \, C c^{2} d^{2} e^{2} - 2 \, B c^{2} d e^{3} + {\left(2 \, C a c + A c^{2}\right)} e^{4}\right)} x^{3} - 30 \, {\left(4 \, C c^{2} d^{3} e - 3 \, B c^{2} d^{2} e^{2} - 2 \, B a c e^{4} + 2 \, {\left(2 \, C a c + A c^{2}\right)} d e^{3}\right)} x^{2} + 60 \, {\left(5 \, C c^{2} d^{4} - 4 \, B c^{2} d^{3} e - 4 \, B a c d e^{3} + 3 \, {\left(2 \, C a c + A c^{2}\right)} d^{2} e^{2} + {\left(C a^{2} + 2 \, A a c\right)} e^{4}\right)} x}{60 \, e^{6}} - \frac{{\left(6 \, C c^{2} d^{5} - 5 \, B c^{2} d^{4} e - 6 \, B a c d^{2} e^{3} - B a^{2} e^{5} + 4 \, {\left(2 \, C a c + A c^{2}\right)} d^{3} e^{2} + 2 \, {\left(C a^{2} + 2 \, A a c\right)} d e^{4}\right)} \log\left(e x + d\right)}{e^{7}}"," ",0,"-(C*c^2*d^6 - B*c^2*d^5*e - 2*B*a*c*d^3*e^3 - B*a^2*d*e^5 + A*a^2*e^6 + (2*C*a*c + A*c^2)*d^4*e^2 + (C*a^2 + 2*A*a*c)*d^2*e^4)/(e^8*x + d*e^7) + 1/60*(12*C*c^2*e^4*x^5 - 15*(2*C*c^2*d*e^3 - B*c^2*e^4)*x^4 + 20*(3*C*c^2*d^2*e^2 - 2*B*c^2*d*e^3 + (2*C*a*c + A*c^2)*e^4)*x^3 - 30*(4*C*c^2*d^3*e - 3*B*c^2*d^2*e^2 - 2*B*a*c*e^4 + 2*(2*C*a*c + A*c^2)*d*e^3)*x^2 + 60*(5*C*c^2*d^4 - 4*B*c^2*d^3*e - 4*B*a*c*d*e^3 + 3*(2*C*a*c + A*c^2)*d^2*e^2 + (C*a^2 + 2*A*a*c)*e^4)*x)/e^6 - (6*C*c^2*d^5 - 5*B*c^2*d^4*e - 6*B*a*c*d^2*e^3 - B*a^2*e^5 + 4*(2*C*a*c + A*c^2)*d^3*e^2 + 2*(C*a^2 + 2*A*a*c)*d*e^4)*log(e*x + d)/e^7","A",0
31,1,402,0,0.494323," ","integrate((c*x^2+a)^2*(C*x^2+B*x+A)/(e*x+d)^3,x, algorithm=""maxima"")","\frac{11 \, C c^{2} d^{6} - 9 \, B c^{2} d^{5} e - 10 \, B a c d^{3} e^{3} - B a^{2} d e^{5} - A a^{2} e^{6} + 7 \, {\left(2 \, C a c + A c^{2}\right)} d^{4} e^{2} + 3 \, {\left(C a^{2} + 2 \, A a c\right)} d^{2} e^{4} + 2 \, {\left(6 \, C c^{2} d^{5} e - 5 \, B c^{2} d^{4} e^{2} - 6 \, B a c d^{2} e^{4} - B a^{2} e^{6} + 4 \, {\left(2 \, C a c + A c^{2}\right)} d^{3} e^{3} + 2 \, {\left(C a^{2} + 2 \, A a c\right)} d e^{5}\right)} x}{2 \, {\left(e^{9} x^{2} + 2 \, d e^{8} x + d^{2} e^{7}\right)}} + \frac{3 \, C c^{2} e^{3} x^{4} - 4 \, {\left(3 \, C c^{2} d e^{2} - B c^{2} e^{3}\right)} x^{3} + 6 \, {\left(6 \, C c^{2} d^{2} e - 3 \, B c^{2} d e^{2} + {\left(2 \, C a c + A c^{2}\right)} e^{3}\right)} x^{2} - 12 \, {\left(10 \, C c^{2} d^{3} - 6 \, B c^{2} d^{2} e - 2 \, B a c e^{3} + 3 \, {\left(2 \, C a c + A c^{2}\right)} d e^{2}\right)} x}{12 \, e^{6}} + \frac{{\left(15 \, C c^{2} d^{4} - 10 \, B c^{2} d^{3} e - 6 \, B a c d e^{3} + 6 \, {\left(2 \, C a c + A c^{2}\right)} d^{2} e^{2} + {\left(C a^{2} + 2 \, A a c\right)} e^{4}\right)} \log\left(e x + d\right)}{e^{7}}"," ",0,"1/2*(11*C*c^2*d^6 - 9*B*c^2*d^5*e - 10*B*a*c*d^3*e^3 - B*a^2*d*e^5 - A*a^2*e^6 + 7*(2*C*a*c + A*c^2)*d^4*e^2 + 3*(C*a^2 + 2*A*a*c)*d^2*e^4 + 2*(6*C*c^2*d^5*e - 5*B*c^2*d^4*e^2 - 6*B*a*c*d^2*e^4 - B*a^2*e^6 + 4*(2*C*a*c + A*c^2)*d^3*e^3 + 2*(C*a^2 + 2*A*a*c)*d*e^5)*x)/(e^9*x^2 + 2*d*e^8*x + d^2*e^7) + 1/12*(3*C*c^2*e^3*x^4 - 4*(3*C*c^2*d*e^2 - B*c^2*e^3)*x^3 + 6*(6*C*c^2*d^2*e - 3*B*c^2*d*e^2 + (2*C*a*c + A*c^2)*e^3)*x^2 - 12*(10*C*c^2*d^3 - 6*B*c^2*d^2*e - 2*B*a*c*e^3 + 3*(2*C*a*c + A*c^2)*d*e^2)*x)/e^6 + (15*C*c^2*d^4 - 10*B*c^2*d^3*e - 6*B*a*c*d*e^3 + 6*(2*C*a*c + A*c^2)*d^2*e^2 + (C*a^2 + 2*A*a*c)*e^4)*log(e*x + d)/e^7","A",0
32,1,512,0,0.469634," ","integrate((e*x+d)^3*(c*x^2+a)^3*(C*x^2+B*x+A),x, algorithm=""maxima"")","\frac{1}{12} \, C c^{3} e^{3} x^{12} + \frac{1}{11} \, {\left(3 \, C c^{3} d e^{2} + B c^{3} e^{3}\right)} x^{11} + \frac{1}{10} \, {\left(3 \, C c^{3} d^{2} e + 3 \, B c^{3} d e^{2} + {\left(3 \, C a c^{2} + A c^{3}\right)} e^{3}\right)} x^{10} + \frac{1}{9} \, {\left(C c^{3} d^{3} + 3 \, B c^{3} d^{2} e + 3 \, B a c^{2} e^{3} + 3 \, {\left(3 \, C a c^{2} + A c^{3}\right)} d e^{2}\right)} x^{9} + \frac{1}{8} \, {\left(B c^{3} d^{3} + 9 \, B a c^{2} d e^{2} + 3 \, {\left(3 \, C a c^{2} + A c^{3}\right)} d^{2} e + 3 \, {\left(C a^{2} c + A a c^{2}\right)} e^{3}\right)} x^{8} + A a^{3} d^{3} x + \frac{1}{7} \, {\left(9 \, B a c^{2} d^{2} e + 3 \, B a^{2} c e^{3} + {\left(3 \, C a c^{2} + A c^{3}\right)} d^{3} + 9 \, {\left(C a^{2} c + A a c^{2}\right)} d e^{2}\right)} x^{7} + \frac{1}{6} \, {\left(3 \, B a c^{2} d^{3} + 9 \, B a^{2} c d e^{2} + 9 \, {\left(C a^{2} c + A a c^{2}\right)} d^{2} e + {\left(C a^{3} + 3 \, A a^{2} c\right)} e^{3}\right)} x^{6} + \frac{1}{5} \, {\left(9 \, B a^{2} c d^{2} e + B a^{3} e^{3} + 3 \, {\left(C a^{2} c + A a c^{2}\right)} d^{3} + 3 \, {\left(C a^{3} + 3 \, A a^{2} c\right)} d e^{2}\right)} x^{5} + \frac{1}{4} \, {\left(3 \, B a^{2} c d^{3} + 3 \, B a^{3} d e^{2} + A a^{3} e^{3} + 3 \, {\left(C a^{3} + 3 \, A a^{2} c\right)} d^{2} e\right)} x^{4} + \frac{1}{3} \, {\left(3 \, B a^{3} d^{2} e + 3 \, A a^{3} d e^{2} + {\left(C a^{3} + 3 \, A a^{2} c\right)} d^{3}\right)} x^{3} + \frac{1}{2} \, {\left(B a^{3} d^{3} + 3 \, A a^{3} d^{2} e\right)} x^{2}"," ",0,"1/12*C*c^3*e^3*x^12 + 1/11*(3*C*c^3*d*e^2 + B*c^3*e^3)*x^11 + 1/10*(3*C*c^3*d^2*e + 3*B*c^3*d*e^2 + (3*C*a*c^2 + A*c^3)*e^3)*x^10 + 1/9*(C*c^3*d^3 + 3*B*c^3*d^2*e + 3*B*a*c^2*e^3 + 3*(3*C*a*c^2 + A*c^3)*d*e^2)*x^9 + 1/8*(B*c^3*d^3 + 9*B*a*c^2*d*e^2 + 3*(3*C*a*c^2 + A*c^3)*d^2*e + 3*(C*a^2*c + A*a*c^2)*e^3)*x^8 + A*a^3*d^3*x + 1/7*(9*B*a*c^2*d^2*e + 3*B*a^2*c*e^3 + (3*C*a*c^2 + A*c^3)*d^3 + 9*(C*a^2*c + A*a*c^2)*d*e^2)*x^7 + 1/6*(3*B*a*c^2*d^3 + 9*B*a^2*c*d*e^2 + 9*(C*a^2*c + A*a*c^2)*d^2*e + (C*a^3 + 3*A*a^2*c)*e^3)*x^6 + 1/5*(9*B*a^2*c*d^2*e + B*a^3*e^3 + 3*(C*a^2*c + A*a*c^2)*d^3 + 3*(C*a^3 + 3*A*a^2*c)*d*e^2)*x^5 + 1/4*(3*B*a^2*c*d^3 + 3*B*a^3*d*e^2 + A*a^3*e^3 + 3*(C*a^3 + 3*A*a^2*c)*d^2*e)*x^4 + 1/3*(3*B*a^3*d^2*e + 3*A*a^3*d*e^2 + (C*a^3 + 3*A*a^2*c)*d^3)*x^3 + 1/2*(B*a^3*d^3 + 3*A*a^3*d^2*e)*x^2","A",0
33,1,367,0,0.453567," ","integrate((e*x+d)^2*(c*x^2+a)^3*(C*x^2+B*x+A),x, algorithm=""maxima"")","\frac{1}{11} \, C c^{3} e^{2} x^{11} + \frac{1}{10} \, {\left(2 \, C c^{3} d e + B c^{3} e^{2}\right)} x^{10} + \frac{1}{9} \, {\left(C c^{3} d^{2} + 2 \, B c^{3} d e + {\left(3 \, C a c^{2} + A c^{3}\right)} e^{2}\right)} x^{9} + \frac{1}{8} \, {\left(B c^{3} d^{2} + 3 \, B a c^{2} e^{2} + 2 \, {\left(3 \, C a c^{2} + A c^{3}\right)} d e\right)} x^{8} + \frac{1}{7} \, {\left(6 \, B a c^{2} d e + {\left(3 \, C a c^{2} + A c^{3}\right)} d^{2} + 3 \, {\left(C a^{2} c + A a c^{2}\right)} e^{2}\right)} x^{7} + A a^{3} d^{2} x + \frac{1}{2} \, {\left(B a c^{2} d^{2} + B a^{2} c e^{2} + 2 \, {\left(C a^{2} c + A a c^{2}\right)} d e\right)} x^{6} + \frac{1}{5} \, {\left(6 \, B a^{2} c d e + 3 \, {\left(C a^{2} c + A a c^{2}\right)} d^{2} + {\left(C a^{3} + 3 \, A a^{2} c\right)} e^{2}\right)} x^{5} + \frac{1}{4} \, {\left(3 \, B a^{2} c d^{2} + B a^{3} e^{2} + 2 \, {\left(C a^{3} + 3 \, A a^{2} c\right)} d e\right)} x^{4} + \frac{1}{3} \, {\left(2 \, B a^{3} d e + A a^{3} e^{2} + {\left(C a^{3} + 3 \, A a^{2} c\right)} d^{2}\right)} x^{3} + \frac{1}{2} \, {\left(B a^{3} d^{2} + 2 \, A a^{3} d e\right)} x^{2}"," ",0,"1/11*C*c^3*e^2*x^11 + 1/10*(2*C*c^3*d*e + B*c^3*e^2)*x^10 + 1/9*(C*c^3*d^2 + 2*B*c^3*d*e + (3*C*a*c^2 + A*c^3)*e^2)*x^9 + 1/8*(B*c^3*d^2 + 3*B*a*c^2*e^2 + 2*(3*C*a*c^2 + A*c^3)*d*e)*x^8 + 1/7*(6*B*a*c^2*d*e + (3*C*a*c^2 + A*c^3)*d^2 + 3*(C*a^2*c + A*a*c^2)*e^2)*x^7 + A*a^3*d^2*x + 1/2*(B*a*c^2*d^2 + B*a^2*c*e^2 + 2*(C*a^2*c + A*a*c^2)*d*e)*x^6 + 1/5*(6*B*a^2*c*d*e + 3*(C*a^2*c + A*a*c^2)*d^2 + (C*a^3 + 3*A*a^2*c)*e^2)*x^5 + 1/4*(3*B*a^2*c*d^2 + B*a^3*e^2 + 2*(C*a^3 + 3*A*a^2*c)*d*e)*x^4 + 1/3*(2*B*a^3*d*e + A*a^3*e^2 + (C*a^3 + 3*A*a^2*c)*d^2)*x^3 + 1/2*(B*a^3*d^2 + 2*A*a^3*d*e)*x^2","A",0
34,1,222,0,0.439631," ","integrate((e*x+d)*(c*x^2+a)^3*(C*x^2+B*x+A),x, algorithm=""maxima"")","\frac{1}{10} \, C c^{3} e x^{10} + \frac{1}{9} \, {\left(C c^{3} d + B c^{3} e\right)} x^{9} + \frac{1}{8} \, {\left(B c^{3} d + {\left(3 \, C a c^{2} + A c^{3}\right)} e\right)} x^{8} + \frac{1}{7} \, {\left(3 \, B a c^{2} e + {\left(3 \, C a c^{2} + A c^{3}\right)} d\right)} x^{7} + \frac{1}{2} \, {\left(B a c^{2} d + {\left(C a^{2} c + A a c^{2}\right)} e\right)} x^{6} + A a^{3} d x + \frac{3}{5} \, {\left(B a^{2} c e + {\left(C a^{2} c + A a c^{2}\right)} d\right)} x^{5} + \frac{1}{4} \, {\left(3 \, B a^{2} c d + {\left(C a^{3} + 3 \, A a^{2} c\right)} e\right)} x^{4} + \frac{1}{3} \, {\left(B a^{3} e + {\left(C a^{3} + 3 \, A a^{2} c\right)} d\right)} x^{3} + \frac{1}{2} \, {\left(B a^{3} d + A a^{3} e\right)} x^{2}"," ",0,"1/10*C*c^3*e*x^10 + 1/9*(C*c^3*d + B*c^3*e)*x^9 + 1/8*(B*c^3*d + (3*C*a*c^2 + A*c^3)*e)*x^8 + 1/7*(3*B*a*c^2*e + (3*C*a*c^2 + A*c^3)*d)*x^7 + 1/2*(B*a*c^2*d + (C*a^2*c + A*a*c^2)*e)*x^6 + A*a^3*d*x + 3/5*(B*a^2*c*e + (C*a^2*c + A*a*c^2)*d)*x^5 + 1/4*(3*B*a^2*c*d + (C*a^3 + 3*A*a^2*c)*e)*x^4 + 1/3*(B*a^3*e + (C*a^3 + 3*A*a^2*c)*d)*x^3 + 1/2*(B*a^3*d + A*a^3*e)*x^2","A",0
35,1,108,0,0.431767," ","integrate((c*x^2+a)^3*(C*x^2+B*x+A),x, algorithm=""maxima"")","\frac{1}{9} \, C c^{3} x^{9} + \frac{1}{8} \, B c^{3} x^{8} + \frac{1}{2} \, B a c^{2} x^{6} + \frac{3}{4} \, B a^{2} c x^{4} + \frac{1}{7} \, {\left(3 \, C a c^{2} + A c^{3}\right)} x^{7} + \frac{1}{2} \, B a^{3} x^{2} + \frac{3}{5} \, {\left(C a^{2} c + A a c^{2}\right)} x^{5} + A a^{3} x + \frac{1}{3} \, {\left(C a^{3} + 3 \, A a^{2} c\right)} x^{3}"," ",0,"1/9*C*c^3*x^9 + 1/8*B*c^3*x^8 + 1/2*B*a*c^2*x^6 + 3/4*B*a^2*c*x^4 + 1/7*(3*C*a*c^2 + A*c^3)*x^7 + 1/2*B*a^3*x^2 + 3/5*(C*a^2*c + A*a*c^2)*x^5 + A*a^3*x + 1/3*(C*a^3 + 3*A*a^2*c)*x^3","A",0
36,1,672,0,0.486784," ","integrate((c*x^2+a)^3*(C*x^2+B*x+A)/(e*x+d),x, algorithm=""maxima"")","\frac{105 \, C c^{3} e^{7} x^{8} - 120 \, {\left(C c^{3} d e^{6} - B c^{3} e^{7}\right)} x^{7} + 140 \, {\left(C c^{3} d^{2} e^{5} - B c^{3} d e^{6} + {\left(3 \, C a c^{2} + A c^{3}\right)} e^{7}\right)} x^{6} - 168 \, {\left(C c^{3} d^{3} e^{4} - B c^{3} d^{2} e^{5} - 3 \, B a c^{2} e^{7} + {\left(3 \, C a c^{2} + A c^{3}\right)} d e^{6}\right)} x^{5} + 210 \, {\left(C c^{3} d^{4} e^{3} - B c^{3} d^{3} e^{4} - 3 \, B a c^{2} d e^{6} + {\left(3 \, C a c^{2} + A c^{3}\right)} d^{2} e^{5} + 3 \, {\left(C a^{2} c + A a c^{2}\right)} e^{7}\right)} x^{4} - 280 \, {\left(C c^{3} d^{5} e^{2} - B c^{3} d^{4} e^{3} - 3 \, B a c^{2} d^{2} e^{5} - 3 \, B a^{2} c e^{7} + {\left(3 \, C a c^{2} + A c^{3}\right)} d^{3} e^{4} + 3 \, {\left(C a^{2} c + A a c^{2}\right)} d e^{6}\right)} x^{3} + 420 \, {\left(C c^{3} d^{6} e - B c^{3} d^{5} e^{2} - 3 \, B a c^{2} d^{3} e^{4} - 3 \, B a^{2} c d e^{6} + {\left(3 \, C a c^{2} + A c^{3}\right)} d^{4} e^{3} + 3 \, {\left(C a^{2} c + A a c^{2}\right)} d^{2} e^{5} + {\left(C a^{3} + 3 \, A a^{2} c\right)} e^{7}\right)} x^{2} - 840 \, {\left(C c^{3} d^{7} - B c^{3} d^{6} e - 3 \, B a c^{2} d^{4} e^{3} - 3 \, B a^{2} c d^{2} e^{5} - B a^{3} e^{7} + {\left(3 \, C a c^{2} + A c^{3}\right)} d^{5} e^{2} + 3 \, {\left(C a^{2} c + A a c^{2}\right)} d^{3} e^{4} + {\left(C a^{3} + 3 \, A a^{2} c\right)} d e^{6}\right)} x}{840 \, e^{8}} + \frac{{\left(C c^{3} d^{8} - B c^{3} d^{7} e - 3 \, B a c^{2} d^{5} e^{3} - 3 \, B a^{2} c d^{3} e^{5} - B a^{3} d e^{7} + A a^{3} e^{8} + {\left(3 \, C a c^{2} + A c^{3}\right)} d^{6} e^{2} + 3 \, {\left(C a^{2} c + A a c^{2}\right)} d^{4} e^{4} + {\left(C a^{3} + 3 \, A a^{2} c\right)} d^{2} e^{6}\right)} \log\left(e x + d\right)}{e^{9}}"," ",0,"1/840*(105*C*c^3*e^7*x^8 - 120*(C*c^3*d*e^6 - B*c^3*e^7)*x^7 + 140*(C*c^3*d^2*e^5 - B*c^3*d*e^6 + (3*C*a*c^2 + A*c^3)*e^7)*x^6 - 168*(C*c^3*d^3*e^4 - B*c^3*d^2*e^5 - 3*B*a*c^2*e^7 + (3*C*a*c^2 + A*c^3)*d*e^6)*x^5 + 210*(C*c^3*d^4*e^3 - B*c^3*d^3*e^4 - 3*B*a*c^2*d*e^6 + (3*C*a*c^2 + A*c^3)*d^2*e^5 + 3*(C*a^2*c + A*a*c^2)*e^7)*x^4 - 280*(C*c^3*d^5*e^2 - B*c^3*d^4*e^3 - 3*B*a*c^2*d^2*e^5 - 3*B*a^2*c*e^7 + (3*C*a*c^2 + A*c^3)*d^3*e^4 + 3*(C*a^2*c + A*a*c^2)*d*e^6)*x^3 + 420*(C*c^3*d^6*e - B*c^3*d^5*e^2 - 3*B*a*c^2*d^3*e^4 - 3*B*a^2*c*d*e^6 + (3*C*a*c^2 + A*c^3)*d^4*e^3 + 3*(C*a^2*c + A*a*c^2)*d^2*e^5 + (C*a^3 + 3*A*a^2*c)*e^7)*x^2 - 840*(C*c^3*d^7 - B*c^3*d^6*e - 3*B*a*c^2*d^4*e^3 - 3*B*a^2*c*d^2*e^5 - B*a^3*e^7 + (3*C*a*c^2 + A*c^3)*d^5*e^2 + 3*(C*a^2*c + A*a*c^2)*d^3*e^4 + (C*a^3 + 3*A*a^2*c)*d*e^6)*x)/e^8 + (C*c^3*d^8 - B*c^3*d^7*e - 3*B*a*c^2*d^5*e^3 - 3*B*a^2*c*d^3*e^5 - B*a^3*d*e^7 + A*a^3*e^8 + (3*C*a*c^2 + A*c^3)*d^6*e^2 + 3*(C*a^2*c + A*a*c^2)*d^4*e^4 + (C*a^3 + 3*A*a^2*c)*d^2*e^6)*log(e*x + d)/e^9","A",0
37,1,691,0,0.487241," ","integrate((c*x^2+a)^3*(C*x^2+B*x+A)/(e*x+d)^2,x, algorithm=""maxima"")","-\frac{C c^{3} d^{8} - B c^{3} d^{7} e - 3 \, B a c^{2} d^{5} e^{3} - 3 \, B a^{2} c d^{3} e^{5} - B a^{3} d e^{7} + A a^{3} e^{8} + {\left(3 \, C a c^{2} + A c^{3}\right)} d^{6} e^{2} + 3 \, {\left(C a^{2} c + A a c^{2}\right)} d^{4} e^{4} + {\left(C a^{3} + 3 \, A a^{2} c\right)} d^{2} e^{6}}{e^{10} x + d e^{9}} + \frac{60 \, C c^{3} e^{6} x^{7} - 70 \, {\left(2 \, C c^{3} d e^{5} - B c^{3} e^{6}\right)} x^{6} + 84 \, {\left(3 \, C c^{3} d^{2} e^{4} - 2 \, B c^{3} d e^{5} + {\left(3 \, C a c^{2} + A c^{3}\right)} e^{6}\right)} x^{5} - 105 \, {\left(4 \, C c^{3} d^{3} e^{3} - 3 \, B c^{3} d^{2} e^{4} - 3 \, B a c^{2} e^{6} + 2 \, {\left(3 \, C a c^{2} + A c^{3}\right)} d e^{5}\right)} x^{4} + 140 \, {\left(5 \, C c^{3} d^{4} e^{2} - 4 \, B c^{3} d^{3} e^{3} - 6 \, B a c^{2} d e^{5} + 3 \, {\left(3 \, C a c^{2} + A c^{3}\right)} d^{2} e^{4} + 3 \, {\left(C a^{2} c + A a c^{2}\right)} e^{6}\right)} x^{3} - 210 \, {\left(6 \, C c^{3} d^{5} e - 5 \, B c^{3} d^{4} e^{2} - 9 \, B a c^{2} d^{2} e^{4} - 3 \, B a^{2} c e^{6} + 4 \, {\left(3 \, C a c^{2} + A c^{3}\right)} d^{3} e^{3} + 6 \, {\left(C a^{2} c + A a c^{2}\right)} d e^{5}\right)} x^{2} + 420 \, {\left(7 \, C c^{3} d^{6} - 6 \, B c^{3} d^{5} e - 12 \, B a c^{2} d^{3} e^{3} - 6 \, B a^{2} c d e^{5} + 5 \, {\left(3 \, C a c^{2} + A c^{3}\right)} d^{4} e^{2} + 9 \, {\left(C a^{2} c + A a c^{2}\right)} d^{2} e^{4} + {\left(C a^{3} + 3 \, A a^{2} c\right)} e^{6}\right)} x}{420 \, e^{8}} - \frac{{\left(8 \, C c^{3} d^{7} - 7 \, B c^{3} d^{6} e - 15 \, B a c^{2} d^{4} e^{3} - 9 \, B a^{2} c d^{2} e^{5} - B a^{3} e^{7} + 6 \, {\left(3 \, C a c^{2} + A c^{3}\right)} d^{5} e^{2} + 12 \, {\left(C a^{2} c + A a c^{2}\right)} d^{3} e^{4} + 2 \, {\left(C a^{3} + 3 \, A a^{2} c\right)} d e^{6}\right)} \log\left(e x + d\right)}{e^{9}}"," ",0,"-(C*c^3*d^8 - B*c^3*d^7*e - 3*B*a*c^2*d^5*e^3 - 3*B*a^2*c*d^3*e^5 - B*a^3*d*e^7 + A*a^3*e^8 + (3*C*a*c^2 + A*c^3)*d^6*e^2 + 3*(C*a^2*c + A*a*c^2)*d^4*e^4 + (C*a^3 + 3*A*a^2*c)*d^2*e^6)/(e^10*x + d*e^9) + 1/420*(60*C*c^3*e^6*x^7 - 70*(2*C*c^3*d*e^5 - B*c^3*e^6)*x^6 + 84*(3*C*c^3*d^2*e^4 - 2*B*c^3*d*e^5 + (3*C*a*c^2 + A*c^3)*e^6)*x^5 - 105*(4*C*c^3*d^3*e^3 - 3*B*c^3*d^2*e^4 - 3*B*a*c^2*e^6 + 2*(3*C*a*c^2 + A*c^3)*d*e^5)*x^4 + 140*(5*C*c^3*d^4*e^2 - 4*B*c^3*d^3*e^3 - 6*B*a*c^2*d*e^5 + 3*(3*C*a*c^2 + A*c^3)*d^2*e^4 + 3*(C*a^2*c + A*a*c^2)*e^6)*x^3 - 210*(6*C*c^3*d^5*e - 5*B*c^3*d^4*e^2 - 9*B*a*c^2*d^2*e^4 - 3*B*a^2*c*e^6 + 4*(3*C*a*c^2 + A*c^3)*d^3*e^3 + 6*(C*a^2*c + A*a*c^2)*d*e^5)*x^2 + 420*(7*C*c^3*d^6 - 6*B*c^3*d^5*e - 12*B*a*c^2*d^3*e^3 - 6*B*a^2*c*d*e^5 + 5*(3*C*a*c^2 + A*c^3)*d^4*e^2 + 9*(C*a^2*c + A*a*c^2)*d^2*e^4 + (C*a^3 + 3*A*a^2*c)*e^6)*x)/e^8 - (8*C*c^3*d^7 - 7*B*c^3*d^6*e - 15*B*a*c^2*d^4*e^3 - 9*B*a^2*c*d^2*e^5 - B*a^3*e^7 + 6*(3*C*a*c^2 + A*c^3)*d^5*e^2 + 12*(C*a^2*c + A*a*c^2)*d^3*e^4 + 2*(C*a^3 + 3*A*a^2*c)*d*e^6)*log(e*x + d)/e^9","A",0
38,1,701,0,0.530021," ","integrate((c*x^2+a)^3*(C*x^2+B*x+A)/(e*x+d)^3,x, algorithm=""maxima"")","\frac{15 \, C c^{3} d^{8} - 13 \, B c^{3} d^{7} e - 27 \, B a c^{2} d^{5} e^{3} - 15 \, B a^{2} c d^{3} e^{5} - B a^{3} d e^{7} - A a^{3} e^{8} + 11 \, {\left(3 \, C a c^{2} + A c^{3}\right)} d^{6} e^{2} + 21 \, {\left(C a^{2} c + A a c^{2}\right)} d^{4} e^{4} + 3 \, {\left(C a^{3} + 3 \, A a^{2} c\right)} d^{2} e^{6} + 2 \, {\left(8 \, C c^{3} d^{7} e - 7 \, B c^{3} d^{6} e^{2} - 15 \, B a c^{2} d^{4} e^{4} - 9 \, B a^{2} c d^{2} e^{6} - B a^{3} e^{8} + 6 \, {\left(3 \, C a c^{2} + A c^{3}\right)} d^{5} e^{3} + 12 \, {\left(C a^{2} c + A a c^{2}\right)} d^{3} e^{5} + 2 \, {\left(C a^{3} + 3 \, A a^{2} c\right)} d e^{7}\right)} x}{2 \, {\left(e^{11} x^{2} + 2 \, d e^{10} x + d^{2} e^{9}\right)}} + \frac{10 \, C c^{3} e^{5} x^{6} - 12 \, {\left(3 \, C c^{3} d e^{4} - B c^{3} e^{5}\right)} x^{5} + 15 \, {\left(6 \, C c^{3} d^{2} e^{3} - 3 \, B c^{3} d e^{4} + {\left(3 \, C a c^{2} + A c^{3}\right)} e^{5}\right)} x^{4} - 20 \, {\left(10 \, C c^{3} d^{3} e^{2} - 6 \, B c^{3} d^{2} e^{3} - 3 \, B a c^{2} e^{5} + 3 \, {\left(3 \, C a c^{2} + A c^{3}\right)} d e^{4}\right)} x^{3} + 30 \, {\left(15 \, C c^{3} d^{4} e - 10 \, B c^{3} d^{3} e^{2} - 9 \, B a c^{2} d e^{4} + 6 \, {\left(3 \, C a c^{2} + A c^{3}\right)} d^{2} e^{3} + 3 \, {\left(C a^{2} c + A a c^{2}\right)} e^{5}\right)} x^{2} - 60 \, {\left(21 \, C c^{3} d^{5} - 15 \, B c^{3} d^{4} e - 18 \, B a c^{2} d^{2} e^{3} - 3 \, B a^{2} c e^{5} + 10 \, {\left(3 \, C a c^{2} + A c^{3}\right)} d^{3} e^{2} + 9 \, {\left(C a^{2} c + A a c^{2}\right)} d e^{4}\right)} x}{60 \, e^{8}} + \frac{{\left(28 \, C c^{3} d^{6} - 21 \, B c^{3} d^{5} e - 30 \, B a c^{2} d^{3} e^{3} - 9 \, B a^{2} c d e^{5} + 15 \, {\left(3 \, C a c^{2} + A c^{3}\right)} d^{4} e^{2} + 18 \, {\left(C a^{2} c + A a c^{2}\right)} d^{2} e^{4} + {\left(C a^{3} + 3 \, A a^{2} c\right)} e^{6}\right)} \log\left(e x + d\right)}{e^{9}}"," ",0,"1/2*(15*C*c^3*d^8 - 13*B*c^3*d^7*e - 27*B*a*c^2*d^5*e^3 - 15*B*a^2*c*d^3*e^5 - B*a^3*d*e^7 - A*a^3*e^8 + 11*(3*C*a*c^2 + A*c^3)*d^6*e^2 + 21*(C*a^2*c + A*a*c^2)*d^4*e^4 + 3*(C*a^3 + 3*A*a^2*c)*d^2*e^6 + 2*(8*C*c^3*d^7*e - 7*B*c^3*d^6*e^2 - 15*B*a*c^2*d^4*e^4 - 9*B*a^2*c*d^2*e^6 - B*a^3*e^8 + 6*(3*C*a*c^2 + A*c^3)*d^5*e^3 + 12*(C*a^2*c + A*a*c^2)*d^3*e^5 + 2*(C*a^3 + 3*A*a^2*c)*d*e^7)*x)/(e^11*x^2 + 2*d*e^10*x + d^2*e^9) + 1/60*(10*C*c^3*e^5*x^6 - 12*(3*C*c^3*d*e^4 - B*c^3*e^5)*x^5 + 15*(6*C*c^3*d^2*e^3 - 3*B*c^3*d*e^4 + (3*C*a*c^2 + A*c^3)*e^5)*x^4 - 20*(10*C*c^3*d^3*e^2 - 6*B*c^3*d^2*e^3 - 3*B*a*c^2*e^5 + 3*(3*C*a*c^2 + A*c^3)*d*e^4)*x^3 + 30*(15*C*c^3*d^4*e - 10*B*c^3*d^3*e^2 - 9*B*a*c^2*d*e^4 + 6*(3*C*a*c^2 + A*c^3)*d^2*e^3 + 3*(C*a^2*c + A*a*c^2)*e^5)*x^2 - 60*(21*C*c^3*d^5 - 15*B*c^3*d^4*e - 18*B*a*c^2*d^2*e^3 - 3*B*a^2*c*e^5 + 10*(3*C*a*c^2 + A*c^3)*d^3*e^2 + 9*(C*a^2*c + A*a*c^2)*d*e^4)*x)/e^8 + (28*C*c^3*d^6 - 21*B*c^3*d^5*e - 30*B*a*c^2*d^3*e^3 - 9*B*a^2*c*d*e^5 + 15*(3*C*a*c^2 + A*c^3)*d^4*e^2 + 18*(C*a^2*c + A*a*c^2)*d^2*e^4 + (C*a^3 + 3*A*a^2*c)*e^6)*log(e*x + d)/e^9","A",0
39,1,82,0,0.458294," ","integrate((b*x^2+a)*(3*b*d*x^2+4*b*c*x-a*d)/(d*x+c)^2,x, algorithm=""maxima"")","\frac{b^{2} c^{4} + 2 \, a b c^{2} d^{2} + a^{2} d^{4}}{d^{5} x + c d^{4}} + \frac{b^{2} d^{2} x^{3} - b^{2} c d x^{2} + {\left(b^{2} c^{2} + 2 \, a b d^{2}\right)} x}{d^{3}}"," ",0,"(b^2*c^4 + 2*a*b*c^2*d^2 + a^2*d^4)/(d^5*x + c*d^4) + (b^2*d^2*x^3 - b^2*c*d*x^2 + (b^2*c^2 + 2*a*b*d^2)*x)/d^3","B",0
40,1,82,0,0.466435," ","integrate((b*x^2+a)*(-a*d+b*x*(3*d*x+4*c))/(d*x+c)^2,x, algorithm=""maxima"")","\frac{b^{2} c^{4} + 2 \, a b c^{2} d^{2} + a^{2} d^{4}}{d^{5} x + c d^{4}} + \frac{b^{2} d^{2} x^{3} - b^{2} c d x^{2} + {\left(b^{2} c^{2} + 2 \, a b d^{2}\right)} x}{d^{3}}"," ",0,"(b^2*c^4 + 2*a*b*c^2*d^2 + a^2*d^4)/(d^5*x + c*d^4) + (b^2*d^2*x^3 - b^2*c*d*x^2 + (b^2*c^2 + 2*a*b*d^2)*x)/d^3","B",0
41,1,160,0,0.451823," ","integrate((b*x^2+a)^2*(5*b*d*x^2+6*b*c*x-a*d)/(d*x+c)^2,x, algorithm=""maxima"")","\frac{b^{3} c^{6} + 3 \, a b^{2} c^{4} d^{2} + 3 \, a^{2} b c^{2} d^{4} + a^{3} d^{6}}{d^{7} x + c d^{6}} + \frac{b^{3} d^{4} x^{5} - b^{3} c d^{3} x^{4} + {\left(b^{3} c^{2} d^{2} + 3 \, a b^{2} d^{4}\right)} x^{3} - {\left(b^{3} c^{3} d + 3 \, a b^{2} c d^{3}\right)} x^{2} + {\left(b^{3} c^{4} + 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b d^{4}\right)} x}{d^{5}}"," ",0,"(b^3*c^6 + 3*a*b^2*c^4*d^2 + 3*a^2*b*c^2*d^4 + a^3*d^6)/(d^7*x + c*d^6) + (b^3*d^4*x^5 - b^3*c*d^3*x^4 + (b^3*c^2*d^2 + 3*a*b^2*d^4)*x^3 - (b^3*c^3*d + 3*a*b^2*c*d^3)*x^2 + (b^3*c^4 + 3*a*b^2*c^2*d^2 + 3*a^2*b*d^4)*x)/d^5","B",0
42,1,160,0,0.443890," ","integrate((b*x^2+a)^2*(-a*d+b*x*(5*d*x+6*c))/(d*x+c)^2,x, algorithm=""maxima"")","\frac{b^{3} c^{6} + 3 \, a b^{2} c^{4} d^{2} + 3 \, a^{2} b c^{2} d^{4} + a^{3} d^{6}}{d^{7} x + c d^{6}} + \frac{b^{3} d^{4} x^{5} - b^{3} c d^{3} x^{4} + {\left(b^{3} c^{2} d^{2} + 3 \, a b^{2} d^{4}\right)} x^{3} - {\left(b^{3} c^{3} d + 3 \, a b^{2} c d^{3}\right)} x^{2} + {\left(b^{3} c^{4} + 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b d^{4}\right)} x}{d^{5}}"," ",0,"(b^3*c^6 + 3*a*b^2*c^4*d^2 + 3*a^2*b*c^2*d^4 + a^3*d^6)/(d^7*x + c*d^6) + (b^3*d^4*x^5 - b^3*c*d^3*x^4 + (b^3*c^2*d^2 + 3*a*b^2*d^4)*x^3 - (b^3*c^3*d + 3*a*b^2*c*d^3)*x^2 + (b^3*c^4 + 3*a*b^2*c^2*d^2 + 3*a^2*b*d^4)*x)/d^5","B",0
43,1,244,0,0.981814," ","integrate((e*x+d)^3*(C*x^2+B*x+A)/(c*x^2+a),x, algorithm=""maxima"")","-\frac{{\left(3 \, B a c d^{2} e - B a^{2} e^{3} + {\left(C a c - A c^{2}\right)} d^{3} - 3 \, {\left(C a^{2} - A a c\right)} d e^{2}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{\sqrt{a c} c^{2}} + \frac{3 \, C c e^{3} x^{4} + 4 \, {\left(3 \, C c d e^{2} + B c e^{3}\right)} x^{3} + 6 \, {\left(3 \, C c d^{2} e + 3 \, B c d e^{2} - {\left(C a - A c\right)} e^{3}\right)} x^{2} + 12 \, {\left(C c d^{3} + 3 \, B c d^{2} e - B a e^{3} - 3 \, {\left(C a - A c\right)} d e^{2}\right)} x}{12 \, c^{2}} + \frac{{\left(B c^{2} d^{3} - 3 \, B a c d e^{2} - 3 \, {\left(C a c - A c^{2}\right)} d^{2} e + {\left(C a^{2} - A a c\right)} e^{3}\right)} \log\left(c x^{2} + a\right)}{2 \, c^{3}}"," ",0,"-(3*B*a*c*d^2*e - B*a^2*e^3 + (C*a*c - A*c^2)*d^3 - 3*(C*a^2 - A*a*c)*d*e^2)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*c^2) + 1/12*(3*C*c*e^3*x^4 + 4*(3*C*c*d*e^2 + B*c*e^3)*x^3 + 6*(3*C*c*d^2*e + 3*B*c*d*e^2 - (C*a - A*c)*e^3)*x^2 + 12*(C*c*d^3 + 3*B*c*d^2*e - B*a*e^3 - 3*(C*a - A*c)*d*e^2)*x)/c^2 + 1/2*(B*c^2*d^3 - 3*B*a*c*d*e^2 - 3*(C*a*c - A*c^2)*d^2*e + (C*a^2 - A*a*c)*e^3)*log(c*x^2 + a)/c^3","A",0
44,1,161,0,0.990016," ","integrate((e*x+d)^2*(C*x^2+B*x+A)/(c*x^2+a),x, algorithm=""maxima"")","\frac{{\left(B c d^{2} - B a e^{2} - 2 \, {\left(C a - A c\right)} d e\right)} \log\left(c x^{2} + a\right)}{2 \, c^{2}} - \frac{{\left(2 \, B a c d e + {\left(C a c - A c^{2}\right)} d^{2} - {\left(C a^{2} - A a c\right)} e^{2}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{\sqrt{a c} c^{2}} + \frac{2 \, C c e^{2} x^{3} + 3 \, {\left(2 \, C c d e + B c e^{2}\right)} x^{2} + 6 \, {\left(C c d^{2} + 2 \, B c d e - {\left(C a - A c\right)} e^{2}\right)} x}{6 \, c^{2}}"," ",0,"1/2*(B*c*d^2 - B*a*e^2 - 2*(C*a - A*c)*d*e)*log(c*x^2 + a)/c^2 - (2*B*a*c*d*e + (C*a*c - A*c^2)*d^2 - (C*a^2 - A*a*c)*e^2)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*c^2) + 1/6*(2*C*c*e^2*x^3 + 3*(2*C*c*d*e + B*c*e^2)*x^2 + 6*(C*c*d^2 + 2*B*c*d*e - (C*a - A*c)*e^2)*x)/c^2","A",0
45,1,86,0,0.971913," ","integrate((e*x+d)*(C*x^2+B*x+A)/(c*x^2+a),x, algorithm=""maxima"")","-\frac{{\left(B a e + {\left(C a - A c\right)} d\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{\sqrt{a c} c} + \frac{C e x^{2} + 2 \, {\left(C d + B e\right)} x}{2 \, c} + \frac{{\left(B c d - {\left(C a - A c\right)} e\right)} \log\left(c x^{2} + a\right)}{2 \, c^{2}}"," ",0,"-(B*a*e + (C*a - A*c)*d)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*c) + 1/2*(C*e*x^2 + 2*(C*d + B*e)*x)/c + 1/2*(B*c*d - (C*a - A*c)*e)*log(c*x^2 + a)/c^2","A",0
46,1,48,0,0.965835," ","integrate((C*x^2+B*x+A)/(c*x^2+a),x, algorithm=""maxima"")","\frac{C x}{c} + \frac{B \log\left(c x^{2} + a\right)}{2 \, c} - \frac{{\left(C a - A c\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{\sqrt{a c} c}"," ",0,"C*x/c + 1/2*B*log(c*x^2 + a)/c - (C*a - A*c)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*c)","A",0
47,1,123,0,0.969404," ","integrate((C*x^2+B*x+A)/(e*x+d)/(c*x^2+a),x, algorithm=""maxima"")","\frac{{\left(B c d + {\left(C a - A c\right)} e\right)} \log\left(c x^{2} + a\right)}{2 \, {\left(c^{2} d^{2} + a c e^{2}\right)}} + \frac{{\left(C d^{2} - B d e + A e^{2}\right)} \log\left(e x + d\right)}{c d^{2} e + a e^{3}} + \frac{{\left(B a e - {\left(C a - A c\right)} d\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{{\left(c d^{2} + a e^{2}\right)} \sqrt{a c}}"," ",0,"1/2*(B*c*d + (C*a - A*c)*e)*log(c*x^2 + a)/(c^2*d^2 + a*c*e^2) + (C*d^2 - B*d*e + A*e^2)*log(e*x + d)/(c*d^2*e + a*e^3) + (B*a*e - (C*a - A*c)*d)*arctan(c*x/sqrt(a*c))/((c*d^2 + a*e^2)*sqrt(a*c))","A",0
48,1,255,0,1.035365," ","integrate((C*x^2+B*x+A)/(e*x+d)^2/(c*x^2+a),x, algorithm=""maxima"")","\frac{{\left(B c d^{2} - B a e^{2} + 2 \, {\left(C a - A c\right)} d e\right)} \log\left(c x^{2} + a\right)}{2 \, {\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)}} - \frac{{\left(B c d^{2} - B a e^{2} + 2 \, {\left(C a - A c\right)} d e\right)} \log\left(e x + d\right)}{c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}} + \frac{{\left(2 \, B a c d e - {\left(C a c - A c^{2}\right)} d^{2} + {\left(C a^{2} - A a c\right)} e^{2}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{{\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \sqrt{a c}} - \frac{C d^{2} - B d e + A e^{2}}{c d^{3} e + a d e^{3} + {\left(c d^{2} e^{2} + a e^{4}\right)} x}"," ",0,"1/2*(B*c*d^2 - B*a*e^2 + 2*(C*a - A*c)*d*e)*log(c*x^2 + a)/(c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4) - (B*c*d^2 - B*a*e^2 + 2*(C*a - A*c)*d*e)*log(e*x + d)/(c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4) + (2*B*a*c*d*e - (C*a*c - A*c^2)*d^2 + (C*a^2 - A*a*c)*e^2)*arctan(c*x/sqrt(a*c))/((c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(a*c)) - (C*d^2 - B*d*e + A*e^2)/(c*d^3*e + a*d*e^3 + (c*d^2*e^2 + a*e^4)*x)","A",0
49,1,495,0,1.051949," ","integrate((C*x^2+B*x+A)/(e*x+d)^3/(c*x^2+a),x, algorithm=""maxima"")","\frac{{\left(B c^{2} d^{3} - 3 \, B a c d e^{2} + 3 \, {\left(C a c - A c^{2}\right)} d^{2} e - {\left(C a^{2} - A a c\right)} e^{3}\right)} \log\left(c x^{2} + a\right)}{2 \, {\left(c^{3} d^{6} + 3 \, a c^{2} d^{4} e^{2} + 3 \, a^{2} c d^{2} e^{4} + a^{3} e^{6}\right)}} - \frac{{\left(B c^{2} d^{3} - 3 \, B a c d e^{2} + 3 \, {\left(C a c - A c^{2}\right)} d^{2} e - {\left(C a^{2} - A a c\right)} e^{3}\right)} \log\left(e x + d\right)}{c^{3} d^{6} + 3 \, a c^{2} d^{4} e^{2} + 3 \, a^{2} c d^{2} e^{4} + a^{3} e^{6}} + \frac{{\left(3 \, B a c^{2} d^{2} e - B a^{2} c e^{3} - {\left(C a c^{2} - A c^{3}\right)} d^{3} + 3 \, {\left(C a^{2} c - A a c^{2}\right)} d e^{2}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{{\left(c^{3} d^{6} + 3 \, a c^{2} d^{4} e^{2} + 3 \, a^{2} c d^{2} e^{4} + a^{3} e^{6}\right)} \sqrt{a c}} - \frac{C c d^{4} - 3 \, B c d^{3} e + B a d e^{3} + A a e^{4} - {\left(3 \, C a - 5 \, A c\right)} d^{2} e^{2} - 2 \, {\left(B c d^{2} e^{2} - B a e^{4} + 2 \, {\left(C a - A c\right)} d e^{3}\right)} x}{2 \, {\left(c^{2} d^{6} e + 2 \, a c d^{4} e^{3} + a^{2} d^{2} e^{5} + {\left(c^{2} d^{4} e^{3} + 2 \, a c d^{2} e^{5} + a^{2} e^{7}\right)} x^{2} + 2 \, {\left(c^{2} d^{5} e^{2} + 2 \, a c d^{3} e^{4} + a^{2} d e^{6}\right)} x\right)}}"," ",0,"1/2*(B*c^2*d^3 - 3*B*a*c*d*e^2 + 3*(C*a*c - A*c^2)*d^2*e - (C*a^2 - A*a*c)*e^3)*log(c*x^2 + a)/(c^3*d^6 + 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 + a^3*e^6) - (B*c^2*d^3 - 3*B*a*c*d*e^2 + 3*(C*a*c - A*c^2)*d^2*e - (C*a^2 - A*a*c)*e^3)*log(e*x + d)/(c^3*d^6 + 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 + a^3*e^6) + (3*B*a*c^2*d^2*e - B*a^2*c*e^3 - (C*a*c^2 - A*c^3)*d^3 + 3*(C*a^2*c - A*a*c^2)*d*e^2)*arctan(c*x/sqrt(a*c))/((c^3*d^6 + 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 + a^3*e^6)*sqrt(a*c)) - 1/2*(C*c*d^4 - 3*B*c*d^3*e + B*a*d*e^3 + A*a*e^4 - (3*C*a - 5*A*c)*d^2*e^2 - 2*(B*c*d^2*e^2 - B*a*e^4 + 2*(C*a - A*c)*d*e^3)*x)/(c^2*d^6*e + 2*a*c*d^4*e^3 + a^2*d^2*e^5 + (c^2*d^4*e^3 + 2*a*c*d^2*e^5 + a^2*e^7)*x^2 + 2*(c^2*d^5*e^2 + 2*a*c*d^3*e^4 + a^2*d*e^6)*x)","A",0
50,1,287,0,0.984401," ","integrate((e*x+d)^3*(C*x^2+B*x+A)/(c*x^2+a)^2,x, algorithm=""maxima"")","-\frac{B a c^{2} d^{3} - 3 \, B a^{2} c d e^{2} - 3 \, {\left(C a^{2} c - A a c^{2}\right)} d^{2} e + {\left(C a^{3} - A a^{2} c\right)} e^{3} + {\left(3 \, B a c^{2} d^{2} e - B a^{2} c e^{3} + {\left(C a c^{2} - A c^{3}\right)} d^{3} - 3 \, {\left(C a^{2} c - A a c^{2}\right)} d e^{2}\right)} x}{2 \, {\left(a c^{4} x^{2} + a^{2} c^{3}\right)}} + \frac{C e^{3} x^{2} + 2 \, {\left(3 \, C d e^{2} + B e^{3}\right)} x}{2 \, c^{2}} + \frac{{\left(3 \, C c d^{2} e + 3 \, B c d e^{2} - {\left(2 \, C a - A c\right)} e^{3}\right)} \log\left(c x^{2} + a\right)}{2 \, c^{3}} + \frac{{\left(3 \, B a c d^{2} e - 3 \, B a^{2} e^{3} + {\left(C a c + A c^{2}\right)} d^{3} - 3 \, {\left(3 \, C a^{2} - A a c\right)} d e^{2}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{2 \, \sqrt{a c} a c^{2}}"," ",0,"-1/2*(B*a*c^2*d^3 - 3*B*a^2*c*d*e^2 - 3*(C*a^2*c - A*a*c^2)*d^2*e + (C*a^3 - A*a^2*c)*e^3 + (3*B*a*c^2*d^2*e - B*a^2*c*e^3 + (C*a*c^2 - A*c^3)*d^3 - 3*(C*a^2*c - A*a*c^2)*d*e^2)*x)/(a*c^4*x^2 + a^2*c^3) + 1/2*(C*e^3*x^2 + 2*(3*C*d*e^2 + B*e^3)*x)/c^2 + 1/2*(3*C*c*d^2*e + 3*B*c*d*e^2 - (2*C*a - A*c)*e^3)*log(c*x^2 + a)/c^3 + 1/2*(3*B*a*c*d^2*e - 3*B*a^2*e^3 + (C*a*c + A*c^2)*d^3 - 3*(3*C*a^2 - A*a*c)*d*e^2)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a*c^2)","A",0
51,1,188,0,0.964741," ","integrate((e*x+d)^2*(C*x^2+B*x+A)/(c*x^2+a)^2,x, algorithm=""maxima"")","\frac{C e^{2} x}{c^{2}} - \frac{B a c d^{2} - B a^{2} e^{2} - 2 \, {\left(C a^{2} - A a c\right)} d e + {\left(2 \, B a c d e + {\left(C a c - A c^{2}\right)} d^{2} - {\left(C a^{2} - A a c\right)} e^{2}\right)} x}{2 \, {\left(a c^{3} x^{2} + a^{2} c^{2}\right)}} + \frac{{\left(2 \, C d e + B e^{2}\right)} \log\left(c x^{2} + a\right)}{2 \, c^{2}} + \frac{{\left(2 \, B a c d e + {\left(C a c + A c^{2}\right)} d^{2} - {\left(3 \, C a^{2} - A a c\right)} e^{2}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{2 \, \sqrt{a c} a c^{2}}"," ",0,"C*e^2*x/c^2 - 1/2*(B*a*c*d^2 - B*a^2*e^2 - 2*(C*a^2 - A*a*c)*d*e + (2*B*a*c*d*e + (C*a*c - A*c^2)*d^2 - (C*a^2 - A*a*c)*e^2)*x)/(a*c^3*x^2 + a^2*c^2) + 1/2*(2*C*d*e + B*e^2)*log(c*x^2 + a)/c^2 + 1/2*(2*B*a*c*d*e + (C*a*c + A*c^2)*d^2 - (3*C*a^2 - A*a*c)*e^2)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a*c^2)","A",0
52,1,113,0,0.971900," ","integrate((e*x+d)*(C*x^2+B*x+A)/(c*x^2+a)^2,x, algorithm=""maxima"")","\frac{C e \log\left(c x^{2} + a\right)}{2 \, c^{2}} - \frac{B a c d - {\left(C a^{2} - A a c\right)} e + {\left(B a c e + {\left(C a c - A c^{2}\right)} d\right)} x}{2 \, {\left(a c^{3} x^{2} + a^{2} c^{2}\right)}} + \frac{{\left(B a e + {\left(C a + A c\right)} d\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{2 \, \sqrt{a c} a c}"," ",0,"1/2*C*e*log(c*x^2 + a)/c^2 - 1/2*(B*a*c*d - (C*a^2 - A*a*c)*e + (B*a*c*e + (C*a*c - A*c^2)*d)*x)/(a*c^3*x^2 + a^2*c^2) + 1/2*(B*a*e + (C*a + A*c)*d)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a*c)","A",0
53,1,62,0,0.964904," ","integrate((C*x^2+B*x+A)/(c*x^2+a)^2,x, algorithm=""maxima"")","-\frac{B a + {\left(C a - A c\right)} x}{2 \, {\left(a c^{2} x^{2} + a^{2} c\right)}} + \frac{{\left(C a + A c\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{2 \, \sqrt{a c} a c}"," ",0,"-1/2*(B*a + (C*a - A*c)*x)/(a*c^2*x^2 + a^2*c) + 1/2*(C*a + A*c)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a*c)","A",0
54,1,293,0,1.001966," ","integrate((C*x^2+B*x+A)/(e*x+d)/(c*x^2+a)^2,x, algorithm=""maxima"")","-\frac{{\left(C d^{2} e - B d e^{2} + A e^{3}\right)} \log\left(c x^{2} + a\right)}{2 \, {\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)}} + \frac{{\left(C d^{2} e - B d e^{2} + A e^{3}\right)} \log\left(e x + d\right)}{c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}} - \frac{{\left(B a c d^{2} e - B a^{2} e^{3} - {\left(C a c + A c^{2}\right)} d^{3} + {\left(C a^{2} - 3 \, A a c\right)} d e^{2}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{2 \, {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} \sqrt{a c}} - \frac{B a c d + {\left(C a^{2} - A a c\right)} e - {\left(B a c e - {\left(C a c - A c^{2}\right)} d\right)} x}{2 \, {\left(a^{2} c^{2} d^{2} + a^{3} c e^{2} + {\left(a c^{3} d^{2} + a^{2} c^{2} e^{2}\right)} x^{2}\right)}}"," ",0,"-1/2*(C*d^2*e - B*d*e^2 + A*e^3)*log(c*x^2 + a)/(c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4) + (C*d^2*e - B*d*e^2 + A*e^3)*log(e*x + d)/(c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4) - 1/2*(B*a*c*d^2*e - B*a^2*e^3 - (C*a*c + A*c^2)*d^3 + (C*a^2 - 3*A*a*c)*d*e^2)*arctan(c*x/sqrt(a*c))/((a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4)*sqrt(a*c)) - 1/2*(B*a*c*d + (C*a^2 - A*a*c)*e - (B*a*c*e - (C*a*c - A*c^2)*d)*x)/(a^2*c^2*d^2 + a^3*c*e^2 + (a*c^3*d^2 + a^2*c^2*e^2)*x^2)","A",0
55,1,604,0,1.038654," ","integrate((C*x^2+B*x+A)/(e*x+d)^2/(c*x^2+a)^2,x, algorithm=""maxima"")","-\frac{{\left(2 \, C c d^{3} e - 3 \, B c d^{2} e^{2} + B a e^{4} - 2 \, {\left(C a - 2 \, A c\right)} d e^{3}\right)} \log\left(c x^{2} + a\right)}{2 \, {\left(c^{3} d^{6} + 3 \, a c^{2} d^{4} e^{2} + 3 \, a^{2} c d^{2} e^{4} + a^{3} e^{6}\right)}} + \frac{{\left(2 \, C c d^{3} e - 3 \, B c d^{2} e^{2} + B a e^{4} - 2 \, {\left(C a - 2 \, A c\right)} d e^{3}\right)} \log\left(e x + d\right)}{c^{3} d^{6} + 3 \, a c^{2} d^{4} e^{2} + 3 \, a^{2} c d^{2} e^{4} + a^{3} e^{6}} - \frac{{\left(2 \, B a c^{2} d^{3} e - 6 \, B a^{2} c d e^{3} - {\left(C a c^{2} + A c^{3}\right)} d^{4} + 6 \, {\left(C a^{2} c - A a c^{2}\right)} d^{2} e^{2} - {\left(C a^{3} - 3 \, A a^{2} c\right)} e^{4}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{2 \, {\left(a c^{3} d^{6} + 3 \, a^{2} c^{2} d^{4} e^{2} + 3 \, a^{3} c d^{2} e^{4} + a^{4} e^{6}\right)} \sqrt{a c}} - \frac{B a c d^{3} - 3 \, B a^{2} d e^{2} + 2 \, A a^{2} e^{3} + 2 \, {\left(2 \, C a^{2} - A a c\right)} d^{2} e - {\left(4 \, B a c d e^{2} - {\left(3 \, C a c - A c^{2}\right)} d^{2} e + {\left(C a^{2} - 3 \, A a c\right)} e^{3}\right)} x^{2} - {\left(B a c d^{2} e + B a^{2} e^{3} - {\left(C a c - A c^{2}\right)} d^{3} - {\left(C a^{2} - A a c\right)} d e^{2}\right)} x}{2 \, {\left(a^{2} c^{2} d^{5} + 2 \, a^{3} c d^{3} e^{2} + a^{4} d e^{4} + {\left(a c^{3} d^{4} e + 2 \, a^{2} c^{2} d^{2} e^{3} + a^{3} c e^{5}\right)} x^{3} + {\left(a c^{3} d^{5} + 2 \, a^{2} c^{2} d^{3} e^{2} + a^{3} c d e^{4}\right)} x^{2} + {\left(a^{2} c^{2} d^{4} e + 2 \, a^{3} c d^{2} e^{3} + a^{4} e^{5}\right)} x\right)}}"," ",0,"-1/2*(2*C*c*d^3*e - 3*B*c*d^2*e^2 + B*a*e^4 - 2*(C*a - 2*A*c)*d*e^3)*log(c*x^2 + a)/(c^3*d^6 + 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 + a^3*e^6) + (2*C*c*d^3*e - 3*B*c*d^2*e^2 + B*a*e^4 - 2*(C*a - 2*A*c)*d*e^3)*log(e*x + d)/(c^3*d^6 + 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 + a^3*e^6) - 1/2*(2*B*a*c^2*d^3*e - 6*B*a^2*c*d*e^3 - (C*a*c^2 + A*c^3)*d^4 + 6*(C*a^2*c - A*a*c^2)*d^2*e^2 - (C*a^3 - 3*A*a^2*c)*e^4)*arctan(c*x/sqrt(a*c))/((a*c^3*d^6 + 3*a^2*c^2*d^4*e^2 + 3*a^3*c*d^2*e^4 + a^4*e^6)*sqrt(a*c)) - 1/2*(B*a*c*d^3 - 3*B*a^2*d*e^2 + 2*A*a^2*e^3 + 2*(2*C*a^2 - A*a*c)*d^2*e - (4*B*a*c*d*e^2 - (3*C*a*c - A*c^2)*d^2*e + (C*a^2 - 3*A*a*c)*e^3)*x^2 - (B*a*c*d^2*e + B*a^2*e^3 - (C*a*c - A*c^2)*d^3 - (C*a^2 - A*a*c)*d*e^2)*x)/(a^2*c^2*d^5 + 2*a^3*c*d^3*e^2 + a^4*d*e^4 + (a*c^3*d^4*e + 2*a^2*c^2*d^2*e^3 + a^3*c*e^5)*x^3 + (a*c^3*d^5 + 2*a^2*c^2*d^3*e^2 + a^3*c*d*e^4)*x^2 + (a^2*c^2*d^4*e + 2*a^3*c*d^2*e^3 + a^4*e^5)*x)","A",0
56,1,1030,0,1.215002," ","integrate((C*x^2+B*x+A)/(e*x+d)^3/(c*x^2+a)^2,x, algorithm=""maxima"")","-\frac{{\left(3 \, C c^{2} d^{4} e - 6 \, B c^{2} d^{3} e^{2} + 6 \, B a c d e^{4} - 2 \, {\left(4 \, C a c - 5 \, A c^{2}\right)} d^{2} e^{3} + {\left(C a^{2} - 2 \, A a c\right)} e^{5}\right)} \log\left(c x^{2} + a\right)}{2 \, {\left(c^{4} d^{8} + 4 \, a c^{3} d^{6} e^{2} + 6 \, a^{2} c^{2} d^{4} e^{4} + 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}\right)}} + \frac{{\left(3 \, C c^{2} d^{4} e - 6 \, B c^{2} d^{3} e^{2} + 6 \, B a c d e^{4} - 2 \, {\left(4 \, C a c - 5 \, A c^{2}\right)} d^{2} e^{3} + {\left(C a^{2} - 2 \, A a c\right)} e^{5}\right)} \log\left(e x + d\right)}{c^{4} d^{8} + 4 \, a c^{3} d^{6} e^{2} + 6 \, a^{2} c^{2} d^{4} e^{4} + 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}} - \frac{{\left(3 \, B a c^{3} d^{4} e - 18 \, B a^{2} c^{2} d^{2} e^{3} + 3 \, B a^{3} c e^{5} - {\left(C a c^{3} + A c^{4}\right)} d^{5} + 2 \, {\left(7 \, C a^{2} c^{2} - 5 \, A a c^{3}\right)} d^{3} e^{2} - 3 \, {\left(3 \, C a^{3} c - 5 \, A a^{2} c^{2}\right)} d e^{4}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{2 \, {\left(a c^{4} d^{8} + 4 \, a^{2} c^{3} d^{6} e^{2} + 6 \, a^{3} c^{2} d^{4} e^{4} + 4 \, a^{4} c d^{2} e^{6} + a^{5} e^{8}\right)} \sqrt{a c}} - \frac{B a c^{2} d^{5} - 10 \, B a^{2} c d^{3} e^{2} + B a^{3} d e^{4} + A a^{3} e^{5} + {\left(8 \, C a^{2} c - 3 \, A a c^{2}\right)} d^{4} e - 2 \, {\left(2 \, C a^{3} - 5 \, A a^{2} c\right)} d^{2} e^{3} - {\left(9 \, B a c^{2} d^{2} e^{3} - 3 \, B a^{2} c e^{5} - {\left(5 \, C a c^{2} - A c^{3}\right)} d^{3} e^{2} + {\left(7 \, C a^{2} c - 11 \, A a c^{2}\right)} d e^{4}\right)} x^{3} - {\left(12 \, B a c^{2} d^{3} e^{2} - {\left(7 \, C a c^{2} - 2 \, A c^{3}\right)} d^{4} e + 6 \, {\left(C a^{2} c - 2 \, A a c^{2}\right)} d^{2} e^{3} + {\left(C a^{3} - 2 \, A a^{2} c\right)} e^{5}\right)} x^{2} - {\left(B a c^{2} d^{4} e + 11 \, B a^{2} c d^{2} e^{3} - 2 \, B a^{3} e^{5} - {\left(C a c^{2} - A c^{3}\right)} d^{5} - {\left(7 \, C a^{2} c - 3 \, A a c^{2}\right)} d^{3} e^{2} + 2 \, {\left(3 \, C a^{3} - 5 \, A a^{2} c\right)} d e^{4}\right)} x}{2 \, {\left(a^{2} c^{3} d^{8} + 3 \, a^{3} c^{2} d^{6} e^{2} + 3 \, a^{4} c d^{4} e^{4} + a^{5} d^{2} e^{6} + {\left(a c^{4} d^{6} e^{2} + 3 \, a^{2} c^{3} d^{4} e^{4} + 3 \, a^{3} c^{2} d^{2} e^{6} + a^{4} c e^{8}\right)} x^{4} + 2 \, {\left(a c^{4} d^{7} e + 3 \, a^{2} c^{3} d^{5} e^{3} + 3 \, a^{3} c^{2} d^{3} e^{5} + a^{4} c d e^{7}\right)} x^{3} + {\left(a c^{4} d^{8} + 4 \, a^{2} c^{3} d^{6} e^{2} + 6 \, a^{3} c^{2} d^{4} e^{4} + 4 \, a^{4} c d^{2} e^{6} + a^{5} e^{8}\right)} x^{2} + 2 \, {\left(a^{2} c^{3} d^{7} e + 3 \, a^{3} c^{2} d^{5} e^{3} + 3 \, a^{4} c d^{3} e^{5} + a^{5} d e^{7}\right)} x\right)}}"," ",0,"-1/2*(3*C*c^2*d^4*e - 6*B*c^2*d^3*e^2 + 6*B*a*c*d*e^4 - 2*(4*C*a*c - 5*A*c^2)*d^2*e^3 + (C*a^2 - 2*A*a*c)*e^5)*log(c*x^2 + a)/(c^4*d^8 + 4*a*c^3*d^6*e^2 + 6*a^2*c^2*d^4*e^4 + 4*a^3*c*d^2*e^6 + a^4*e^8) + (3*C*c^2*d^4*e - 6*B*c^2*d^3*e^2 + 6*B*a*c*d*e^4 - 2*(4*C*a*c - 5*A*c^2)*d^2*e^3 + (C*a^2 - 2*A*a*c)*e^5)*log(e*x + d)/(c^4*d^8 + 4*a*c^3*d^6*e^2 + 6*a^2*c^2*d^4*e^4 + 4*a^3*c*d^2*e^6 + a^4*e^8) - 1/2*(3*B*a*c^3*d^4*e - 18*B*a^2*c^2*d^2*e^3 + 3*B*a^3*c*e^5 - (C*a*c^3 + A*c^4)*d^5 + 2*(7*C*a^2*c^2 - 5*A*a*c^3)*d^3*e^2 - 3*(3*C*a^3*c - 5*A*a^2*c^2)*d*e^4)*arctan(c*x/sqrt(a*c))/((a*c^4*d^8 + 4*a^2*c^3*d^6*e^2 + 6*a^3*c^2*d^4*e^4 + 4*a^4*c*d^2*e^6 + a^5*e^8)*sqrt(a*c)) - 1/2*(B*a*c^2*d^5 - 10*B*a^2*c*d^3*e^2 + B*a^3*d*e^4 + A*a^3*e^5 + (8*C*a^2*c - 3*A*a*c^2)*d^4*e - 2*(2*C*a^3 - 5*A*a^2*c)*d^2*e^3 - (9*B*a*c^2*d^2*e^3 - 3*B*a^2*c*e^5 - (5*C*a*c^2 - A*c^3)*d^3*e^2 + (7*C*a^2*c - 11*A*a*c^2)*d*e^4)*x^3 - (12*B*a*c^2*d^3*e^2 - (7*C*a*c^2 - 2*A*c^3)*d^4*e + 6*(C*a^2*c - 2*A*a*c^2)*d^2*e^3 + (C*a^3 - 2*A*a^2*c)*e^5)*x^2 - (B*a*c^2*d^4*e + 11*B*a^2*c*d^2*e^3 - 2*B*a^3*e^5 - (C*a*c^2 - A*c^3)*d^5 - (7*C*a^2*c - 3*A*a*c^2)*d^3*e^2 + 2*(3*C*a^3 - 5*A*a^2*c)*d*e^4)*x)/(a^2*c^3*d^8 + 3*a^3*c^2*d^6*e^2 + 3*a^4*c*d^4*e^4 + a^5*d^2*e^6 + (a*c^4*d^6*e^2 + 3*a^2*c^3*d^4*e^4 + 3*a^3*c^2*d^2*e^6 + a^4*c*e^8)*x^4 + 2*(a*c^4*d^7*e + 3*a^2*c^3*d^5*e^3 + 3*a^3*c^2*d^3*e^5 + a^4*c*d*e^7)*x^3 + (a*c^4*d^8 + 4*a^2*c^3*d^6*e^2 + 6*a^3*c^2*d^4*e^4 + 4*a^4*c*d^2*e^6 + a^5*e^8)*x^2 + 2*(a^2*c^3*d^7*e + 3*a^3*c^2*d^5*e^3 + 3*a^4*c*d^3*e^5 + a^5*d*e^7)*x)","B",0
57,1,379,0,1.001172," ","integrate((e*x+d)^3*(C*x^2+B*x+A)/(c*x^2+a)^3,x, algorithm=""maxima"")","\frac{C e^{3} \log\left(c x^{2} + a\right)}{2 \, c^{3}} - \frac{2 \, B a^{2} c^{2} d^{3} + 6 \, B a^{3} c d e^{2} + 6 \, {\left(C a^{3} c + A a^{2} c^{2}\right)} d^{2} e - 2 \, {\left(3 \, C a^{4} - A a^{3} c\right)} e^{3} - {\left(3 \, B a c^{3} d^{2} e - 5 \, B a^{2} c^{2} e^{3} + {\left(C a c^{3} + 3 \, A c^{4}\right)} d^{3} - 3 \, {\left(5 \, C a^{2} c^{2} - A a c^{3}\right)} d e^{2}\right)} x^{3} + 4 \, {\left(3 \, C a^{2} c^{2} d^{2} e + 3 \, B a^{2} c^{2} d e^{2} - {\left(2 \, C a^{3} c - A a^{2} c^{2}\right)} e^{3}\right)} x^{2} + {\left(3 \, B a^{2} c^{2} d^{2} e + 3 \, B a^{3} c e^{3} + {\left(C a^{2} c^{2} - 5 \, A a c^{3}\right)} d^{3} + 3 \, {\left(3 \, C a^{3} c + A a^{2} c^{2}\right)} d e^{2}\right)} x}{8 \, {\left(a^{2} c^{5} x^{4} + 2 \, a^{3} c^{4} x^{2} + a^{4} c^{3}\right)}} + \frac{{\left(3 \, B a c d^{2} e + 3 \, B a^{2} e^{3} + {\left(C a c + 3 \, A c^{2}\right)} d^{3} + 3 \, {\left(3 \, C a^{2} + A a c\right)} d e^{2}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{8 \, \sqrt{a c} a^{2} c^{2}}"," ",0,"1/2*C*e^3*log(c*x^2 + a)/c^3 - 1/8*(2*B*a^2*c^2*d^3 + 6*B*a^3*c*d*e^2 + 6*(C*a^3*c + A*a^2*c^2)*d^2*e - 2*(3*C*a^4 - A*a^3*c)*e^3 - (3*B*a*c^3*d^2*e - 5*B*a^2*c^2*e^3 + (C*a*c^3 + 3*A*c^4)*d^3 - 3*(5*C*a^2*c^2 - A*a*c^3)*d*e^2)*x^3 + 4*(3*C*a^2*c^2*d^2*e + 3*B*a^2*c^2*d*e^2 - (2*C*a^3*c - A*a^2*c^2)*e^3)*x^2 + (3*B*a^2*c^2*d^2*e + 3*B*a^3*c*e^3 + (C*a^2*c^2 - 5*A*a*c^3)*d^3 + 3*(3*C*a^3*c + A*a^2*c^2)*d*e^2)*x)/(a^2*c^5*x^4 + 2*a^3*c^4*x^2 + a^4*c^3) + 1/8*(3*B*a*c*d^2*e + 3*B*a^2*e^3 + (C*a*c + 3*A*c^2)*d^3 + 3*(3*C*a^2 + A*a*c)*d*e^2)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a^2*c^2)","A",0
58,1,253,0,0.994688," ","integrate((e*x+d)^2*(C*x^2+B*x+A)/(c*x^2+a)^3,x, algorithm=""maxima"")","-\frac{2 \, B a^{2} c d^{2} + 2 \, B a^{3} e^{2} - {\left(2 \, B a c^{2} d e + {\left(C a c^{2} + 3 \, A c^{3}\right)} d^{2} - {\left(5 \, C a^{2} c - A a c^{2}\right)} e^{2}\right)} x^{3} + 4 \, {\left(C a^{3} + A a^{2} c\right)} d e + 4 \, {\left(2 \, C a^{2} c d e + B a^{2} c e^{2}\right)} x^{2} + {\left(2 \, B a^{2} c d e + {\left(C a^{2} c - 5 \, A a c^{2}\right)} d^{2} + {\left(3 \, C a^{3} + A a^{2} c\right)} e^{2}\right)} x}{8 \, {\left(a^{2} c^{4} x^{4} + 2 \, a^{3} c^{3} x^{2} + a^{4} c^{2}\right)}} + \frac{{\left(2 \, B a c d e + {\left(C a c + 3 \, A c^{2}\right)} d^{2} + {\left(3 \, C a^{2} + A a c\right)} e^{2}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{8 \, \sqrt{a c} a^{2} c^{2}}"," ",0,"-1/8*(2*B*a^2*c*d^2 + 2*B*a^3*e^2 - (2*B*a*c^2*d*e + (C*a*c^2 + 3*A*c^3)*d^2 - (5*C*a^2*c - A*a*c^2)*e^2)*x^3 + 4*(C*a^3 + A*a^2*c)*d*e + 4*(2*C*a^2*c*d*e + B*a^2*c*e^2)*x^2 + (2*B*a^2*c*d*e + (C*a^2*c - 5*A*a*c^2)*d^2 + (3*C*a^3 + A*a^2*c)*e^2)*x)/(a^2*c^4*x^4 + 2*a^3*c^3*x^2 + a^4*c^2) + 1/8*(2*B*a*c*d*e + (C*a*c + 3*A*c^2)*d^2 + (3*C*a^2 + A*a*c)*e^2)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a^2*c^2)","A",0
59,1,160,0,0.982549," ","integrate((e*x+d)*(C*x^2+B*x+A)/(c*x^2+a)^3,x, algorithm=""maxima"")","-\frac{4 \, C a^{2} c e x^{2} + 2 \, B a^{2} c d - {\left(B a c^{2} e + {\left(C a c^{2} + 3 \, A c^{3}\right)} d\right)} x^{3} + 2 \, {\left(C a^{3} + A a^{2} c\right)} e + {\left(B a^{2} c e + {\left(C a^{2} c - 5 \, A a c^{2}\right)} d\right)} x}{8 \, {\left(a^{2} c^{4} x^{4} + 2 \, a^{3} c^{3} x^{2} + a^{4} c^{2}\right)}} + \frac{{\left(B a e + {\left(C a + 3 \, A c\right)} d\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{8 \, \sqrt{a c} a^{2} c}"," ",0,"-1/8*(4*C*a^2*c*e*x^2 + 2*B*a^2*c*d - (B*a*c^2*e + (C*a*c^2 + 3*A*c^3)*d)*x^3 + 2*(C*a^3 + A*a^2*c)*e + (B*a^2*c*e + (C*a^2*c - 5*A*a*c^2)*d)*x)/(a^2*c^4*x^4 + 2*a^3*c^3*x^2 + a^4*c^2) + 1/8*(B*a*e + (C*a + 3*A*c)*d)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a^2*c)","A",0
60,1,98,0,0.971389," ","integrate((C*x^2+B*x+A)/(c*x^2+a)^3,x, algorithm=""maxima"")","\frac{{\left(C a c + 3 \, A c^{2}\right)} x^{3} - 2 \, B a^{2} - {\left(C a^{2} - 5 \, A a c\right)} x}{8 \, {\left(a^{2} c^{3} x^{4} + 2 \, a^{3} c^{2} x^{2} + a^{4} c\right)}} + \frac{{\left(C a + 3 \, A c\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{8 \, \sqrt{a c} a^{2} c}"," ",0,"1/8*((C*a*c + 3*A*c^2)*x^3 - 2*B*a^2 - (C*a^2 - 5*A*a*c)*x)/(a^2*c^3*x^4 + 2*a^3*c^2*x^2 + a^4*c) + 1/8*(C*a + 3*A*c)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a^2*c)","A",0
61,1,655,0,1.097017," ","integrate((C*x^2+B*x+A)/(e*x+d)/(c*x^2+a)^3,x, algorithm=""maxima"")","-\frac{{\left(C d^{2} e^{3} - B d e^{4} + A e^{5}\right)} \log\left(c x^{2} + a\right)}{2 \, {\left(c^{3} d^{6} + 3 \, a c^{2} d^{4} e^{2} + 3 \, a^{2} c d^{2} e^{4} + a^{3} e^{6}\right)}} + \frac{{\left(C d^{2} e^{3} - B d e^{4} + A e^{5}\right)} \log\left(e x + d\right)}{c^{3} d^{6} + 3 \, a c^{2} d^{4} e^{2} + 3 \, a^{2} c d^{2} e^{4} + a^{3} e^{6}} - \frac{{\left(B a c^{2} d^{4} e + 6 \, B a^{2} c d^{2} e^{3} - 3 \, B a^{3} e^{5} - {\left(C a c^{2} + 3 \, A c^{3}\right)} d^{5} - 2 \, {\left(3 \, C a^{2} c + 5 \, A a c^{2}\right)} d^{3} e^{2} + 3 \, {\left(C a^{3} - 5 \, A a^{2} c\right)} d e^{4}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{8 \, {\left(a^{2} c^{3} d^{6} + 3 \, a^{3} c^{2} d^{4} e^{2} + 3 \, a^{4} c d^{2} e^{4} + a^{5} e^{6}\right)} \sqrt{a c}} - \frac{2 \, B a^{2} c^{2} d^{3} + 6 \, B a^{3} c d e^{2} - 2 \, {\left(C a^{3} c + A a^{2} c^{2}\right)} d^{2} e + 2 \, {\left(C a^{4} - 3 \, A a^{3} c\right)} e^{3} + {\left(B a c^{3} d^{2} e - 3 \, B a^{2} c^{2} e^{3} - {\left(C a c^{3} + 3 \, A c^{4}\right)} d^{3} + {\left(3 \, C a^{2} c^{2} - 7 \, A a c^{3}\right)} d e^{2}\right)} x^{3} - 4 \, {\left(C a^{2} c^{2} d^{2} e - B a^{2} c^{2} d e^{2} + A a^{2} c^{2} e^{3}\right)} x^{2} - {\left(B a^{2} c^{2} d^{2} e + 5 \, B a^{3} c e^{3} - {\left(C a^{2} c^{2} - 5 \, A a c^{3}\right)} d^{3} - {\left(5 \, C a^{3} c - 9 \, A a^{2} c^{2}\right)} d e^{2}\right)} x}{8 \, {\left(a^{4} c^{3} d^{4} + 2 \, a^{5} c^{2} d^{2} e^{2} + a^{6} c e^{4} + {\left(a^{2} c^{5} d^{4} + 2 \, a^{3} c^{4} d^{2} e^{2} + a^{4} c^{3} e^{4}\right)} x^{4} + 2 \, {\left(a^{3} c^{4} d^{4} + 2 \, a^{4} c^{3} d^{2} e^{2} + a^{5} c^{2} e^{4}\right)} x^{2}\right)}}"," ",0,"-1/2*(C*d^2*e^3 - B*d*e^4 + A*e^5)*log(c*x^2 + a)/(c^3*d^6 + 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 + a^3*e^6) + (C*d^2*e^3 - B*d*e^4 + A*e^5)*log(e*x + d)/(c^3*d^6 + 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 + a^3*e^6) - 1/8*(B*a*c^2*d^4*e + 6*B*a^2*c*d^2*e^3 - 3*B*a^3*e^5 - (C*a*c^2 + 3*A*c^3)*d^5 - 2*(3*C*a^2*c + 5*A*a*c^2)*d^3*e^2 + 3*(C*a^3 - 5*A*a^2*c)*d*e^4)*arctan(c*x/sqrt(a*c))/((a^2*c^3*d^6 + 3*a^3*c^2*d^4*e^2 + 3*a^4*c*d^2*e^4 + a^5*e^6)*sqrt(a*c)) - 1/8*(2*B*a^2*c^2*d^3 + 6*B*a^3*c*d*e^2 - 2*(C*a^3*c + A*a^2*c^2)*d^2*e + 2*(C*a^4 - 3*A*a^3*c)*e^3 + (B*a*c^3*d^2*e - 3*B*a^2*c^2*e^3 - (C*a*c^3 + 3*A*c^4)*d^3 + (3*C*a^2*c^2 - 7*A*a*c^3)*d*e^2)*x^3 - 4*(C*a^2*c^2*d^2*e - B*a^2*c^2*d*e^2 + A*a^2*c^2*e^3)*x^2 - (B*a^2*c^2*d^2*e + 5*B*a^3*c*e^3 - (C*a^2*c^2 - 5*A*a*c^3)*d^3 - (5*C*a^3*c - 9*A*a^2*c^2)*d*e^2)*x)/(a^4*c^3*d^4 + 2*a^5*c^2*d^2*e^2 + a^6*c*e^4 + (a^2*c^5*d^4 + 2*a^3*c^4*d^2*e^2 + a^4*c^3*e^4)*x^4 + 2*(a^3*c^4*d^4 + 2*a^4*c^3*d^2*e^2 + a^5*c^2*e^4)*x^2)","A",0
62,1,1196,0,1.238819," ","integrate((C*x^2+B*x+A)/(e*x+d)^2/(c*x^2+a)^3,x, algorithm=""maxima"")","-\frac{{\left(4 \, C c d^{3} e^{3} - 5 \, B c d^{2} e^{4} + B a e^{6} - 2 \, {\left(C a - 3 \, A c\right)} d e^{5}\right)} \log\left(c x^{2} + a\right)}{2 \, {\left(c^{4} d^{8} + 4 \, a c^{3} d^{6} e^{2} + 6 \, a^{2} c^{2} d^{4} e^{4} + 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}\right)}} + \frac{{\left(4 \, C c d^{3} e^{3} - 5 \, B c d^{2} e^{4} + B a e^{6} - 2 \, {\left(C a - 3 \, A c\right)} d e^{5}\right)} \log\left(e x + d\right)}{c^{4} d^{8} + 4 \, a c^{3} d^{6} e^{2} + 6 \, a^{2} c^{2} d^{4} e^{4} + 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}} - \frac{{\left(2 \, B a c^{3} d^{5} e + 20 \, B a^{2} c^{2} d^{3} e^{3} - 30 \, B a^{3} c d e^{5} - {\left(C a c^{3} + 3 \, A c^{4}\right)} d^{6} - {\left(13 \, C a^{2} c^{2} + 15 \, A a c^{3}\right)} d^{4} e^{2} + 3 \, {\left(11 \, C a^{3} c - 15 \, A a^{2} c^{2}\right)} d^{2} e^{4} - 3 \, {\left(C a^{4} - 5 \, A a^{3} c\right)} e^{6}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{8 \, {\left(a^{2} c^{4} d^{8} + 4 \, a^{3} c^{3} d^{6} e^{2} + 6 \, a^{4} c^{2} d^{4} e^{4} + 4 \, a^{5} c d^{2} e^{6} + a^{6} e^{8}\right)} \sqrt{a c}} - \frac{2 \, B a^{2} c^{2} d^{5} + 12 \, B a^{3} c d^{3} e^{2} - 14 \, B a^{4} d e^{4} + 8 \, A a^{4} e^{5} - 4 \, {\left(C a^{3} c + A a^{2} c^{2}\right)} d^{4} e + 20 \, {\left(C a^{4} - A a^{3} c\right)} d^{2} e^{3} + {\left(2 \, B a c^{3} d^{3} e^{2} - 22 \, B a^{2} c^{2} d e^{4} - {\left(C a c^{3} + 3 \, A c^{4}\right)} d^{4} e + 4 \, {\left(5 \, C a^{2} c^{2} - 3 \, A a c^{3}\right)} d^{2} e^{3} - 3 \, {\left(C a^{3} c - 5 \, A a^{2} c^{2}\right)} e^{5}\right)} x^{4} + {\left(2 \, B a c^{3} d^{4} e - 2 \, B a^{2} c^{2} d^{2} e^{3} - 4 \, B a^{3} c e^{5} - {\left(C a c^{3} + 3 \, A c^{4}\right)} d^{5} + 4 \, {\left(C a^{2} c^{2} - 3 \, A a c^{3}\right)} d^{3} e^{2} + {\left(5 \, C a^{3} c - 9 \, A a^{2} c^{2}\right)} d e^{4}\right)} x^{3} + {\left(10 \, B a^{2} c^{2} d^{3} e^{2} - 38 \, B a^{3} c d e^{4} - {\left(7 \, C a^{2} c^{2} + 5 \, A a c^{3}\right)} d^{4} e + 4 \, {\left(9 \, C a^{3} c - 7 \, A a^{2} c^{2}\right)} d^{2} e^{3} - 5 \, {\left(C a^{4} - 5 \, A a^{3} c\right)} e^{5}\right)} x^{2} - {\left(6 \, B a^{3} c d^{2} e^{3} + 6 \, B a^{4} e^{5} - {\left(C a^{2} c^{2} - 5 \, A a c^{3}\right)} d^{5} - 8 \, {\left(C a^{3} c - 2 \, A a^{2} c^{2}\right)} d^{3} e^{2} - {\left(7 \, C a^{4} - 11 \, A a^{3} c\right)} d e^{4}\right)} x}{8 \, {\left(a^{4} c^{3} d^{7} + 3 \, a^{5} c^{2} d^{5} e^{2} + 3 \, a^{6} c d^{3} e^{4} + a^{7} d e^{6} + {\left(a^{2} c^{5} d^{6} e + 3 \, a^{3} c^{4} d^{4} e^{3} + 3 \, a^{4} c^{3} d^{2} e^{5} + a^{5} c^{2} e^{7}\right)} x^{5} + {\left(a^{2} c^{5} d^{7} + 3 \, a^{3} c^{4} d^{5} e^{2} + 3 \, a^{4} c^{3} d^{3} e^{4} + a^{5} c^{2} d e^{6}\right)} x^{4} + 2 \, {\left(a^{3} c^{4} d^{6} e + 3 \, a^{4} c^{3} d^{4} e^{3} + 3 \, a^{5} c^{2} d^{2} e^{5} + a^{6} c e^{7}\right)} x^{3} + 2 \, {\left(a^{3} c^{4} d^{7} + 3 \, a^{4} c^{3} d^{5} e^{2} + 3 \, a^{5} c^{2} d^{3} e^{4} + a^{6} c d e^{6}\right)} x^{2} + {\left(a^{4} c^{3} d^{6} e + 3 \, a^{5} c^{2} d^{4} e^{3} + 3 \, a^{6} c d^{2} e^{5} + a^{7} e^{7}\right)} x\right)}}"," ",0,"-1/2*(4*C*c*d^3*e^3 - 5*B*c*d^2*e^4 + B*a*e^6 - 2*(C*a - 3*A*c)*d*e^5)*log(c*x^2 + a)/(c^4*d^8 + 4*a*c^3*d^6*e^2 + 6*a^2*c^2*d^4*e^4 + 4*a^3*c*d^2*e^6 + a^4*e^8) + (4*C*c*d^3*e^3 - 5*B*c*d^2*e^4 + B*a*e^6 - 2*(C*a - 3*A*c)*d*e^5)*log(e*x + d)/(c^4*d^8 + 4*a*c^3*d^6*e^2 + 6*a^2*c^2*d^4*e^4 + 4*a^3*c*d^2*e^6 + a^4*e^8) - 1/8*(2*B*a*c^3*d^5*e + 20*B*a^2*c^2*d^3*e^3 - 30*B*a^3*c*d*e^5 - (C*a*c^3 + 3*A*c^4)*d^6 - (13*C*a^2*c^2 + 15*A*a*c^3)*d^4*e^2 + 3*(11*C*a^3*c - 15*A*a^2*c^2)*d^2*e^4 - 3*(C*a^4 - 5*A*a^3*c)*e^6)*arctan(c*x/sqrt(a*c))/((a^2*c^4*d^8 + 4*a^3*c^3*d^6*e^2 + 6*a^4*c^2*d^4*e^4 + 4*a^5*c*d^2*e^6 + a^6*e^8)*sqrt(a*c)) - 1/8*(2*B*a^2*c^2*d^5 + 12*B*a^3*c*d^3*e^2 - 14*B*a^4*d*e^4 + 8*A*a^4*e^5 - 4*(C*a^3*c + A*a^2*c^2)*d^4*e + 20*(C*a^4 - A*a^3*c)*d^2*e^3 + (2*B*a*c^3*d^3*e^2 - 22*B*a^2*c^2*d*e^4 - (C*a*c^3 + 3*A*c^4)*d^4*e + 4*(5*C*a^2*c^2 - 3*A*a*c^3)*d^2*e^3 - 3*(C*a^3*c - 5*A*a^2*c^2)*e^5)*x^4 + (2*B*a*c^3*d^4*e - 2*B*a^2*c^2*d^2*e^3 - 4*B*a^3*c*e^5 - (C*a*c^3 + 3*A*c^4)*d^5 + 4*(C*a^2*c^2 - 3*A*a*c^3)*d^3*e^2 + (5*C*a^3*c - 9*A*a^2*c^2)*d*e^4)*x^3 + (10*B*a^2*c^2*d^3*e^2 - 38*B*a^3*c*d*e^4 - (7*C*a^2*c^2 + 5*A*a*c^3)*d^4*e + 4*(9*C*a^3*c - 7*A*a^2*c^2)*d^2*e^3 - 5*(C*a^4 - 5*A*a^3*c)*e^5)*x^2 - (6*B*a^3*c*d^2*e^3 + 6*B*a^4*e^5 - (C*a^2*c^2 - 5*A*a*c^3)*d^5 - 8*(C*a^3*c - 2*A*a^2*c^2)*d^3*e^2 - (7*C*a^4 - 11*A*a^3*c)*d*e^4)*x)/(a^4*c^3*d^7 + 3*a^5*c^2*d^5*e^2 + 3*a^6*c*d^3*e^4 + a^7*d*e^6 + (a^2*c^5*d^6*e + 3*a^3*c^4*d^4*e^3 + 3*a^4*c^3*d^2*e^5 + a^5*c^2*e^7)*x^5 + (a^2*c^5*d^7 + 3*a^3*c^4*d^5*e^2 + 3*a^4*c^3*d^3*e^4 + a^5*c^2*d*e^6)*x^4 + 2*(a^3*c^4*d^6*e + 3*a^4*c^3*d^4*e^3 + 3*a^5*c^2*d^2*e^5 + a^6*c*e^7)*x^3 + 2*(a^3*c^4*d^7 + 3*a^4*c^3*d^5*e^2 + 3*a^5*c^2*d^3*e^4 + a^6*c*d*e^6)*x^2 + (a^4*c^3*d^6*e + 3*a^5*c^2*d^4*e^3 + 3*a^6*c*d^2*e^5 + a^7*e^7)*x)","B",0
63,1,1835,0,1.273524," ","integrate((C*x^2+B*x+A)/(e*x+d)^3/(c*x^2+a)^3,x, algorithm=""maxima"")","-\frac{{\left(10 \, C c^{2} d^{4} e^{3} - 15 \, B c^{2} d^{3} e^{4} + 9 \, B a c d e^{6} - {\left(13 \, C a c - 21 \, A c^{2}\right)} d^{2} e^{5} + {\left(C a^{2} - 3 \, A a c\right)} e^{7}\right)} \log\left(c x^{2} + a\right)}{2 \, {\left(c^{5} d^{10} + 5 \, a c^{4} d^{8} e^{2} + 10 \, a^{2} c^{3} d^{6} e^{4} + 10 \, a^{3} c^{2} d^{4} e^{6} + 5 \, a^{4} c d^{2} e^{8} + a^{5} e^{10}\right)}} + \frac{{\left(10 \, C c^{2} d^{4} e^{3} - 15 \, B c^{2} d^{3} e^{4} + 9 \, B a c d e^{6} - {\left(13 \, C a c - 21 \, A c^{2}\right)} d^{2} e^{5} + {\left(C a^{2} - 3 \, A a c\right)} e^{7}\right)} \log\left(e x + d\right)}{c^{5} d^{10} + 5 \, a c^{4} d^{8} e^{2} + 10 \, a^{2} c^{3} d^{6} e^{4} + 10 \, a^{3} c^{2} d^{4} e^{6} + 5 \, a^{4} c d^{2} e^{8} + a^{5} e^{10}} - \frac{{\left(3 \, B a c^{4} d^{6} e + 45 \, B a^{2} c^{3} d^{4} e^{3} - 135 \, B a^{3} c^{2} d^{2} e^{5} + 15 \, B a^{4} c e^{7} - {\left(C a c^{4} + 3 \, A c^{5}\right)} d^{7} - {\left(23 \, C a^{2} c^{3} + 21 \, A a c^{4}\right)} d^{5} e^{2} + 5 \, {\left(25 \, C a^{3} c^{2} - 21 \, A a^{2} c^{3}\right)} d^{3} e^{4} - 15 \, {\left(3 \, C a^{4} c - 7 \, A a^{3} c^{2}\right)} d e^{6}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{8 \, {\left(a^{2} c^{5} d^{10} + 5 \, a^{3} c^{4} d^{8} e^{2} + 10 \, a^{4} c^{3} d^{6} e^{4} + 10 \, a^{5} c^{2} d^{4} e^{6} + 5 \, a^{6} c d^{2} e^{8} + a^{7} e^{10}\right)} \sqrt{a c}} - \frac{2 \, B a^{2} c^{3} d^{7} + 20 \, B a^{3} c^{2} d^{5} e^{2} - 74 \, B a^{4} c d^{3} e^{4} + 4 \, B a^{5} d e^{6} + 4 \, A a^{5} e^{7} - 6 \, {\left(C a^{3} c^{2} + A a^{2} c^{3}\right)} d^{6} e + 4 \, {\left(18 \, C a^{4} c - 11 \, A a^{3} c^{2}\right)} d^{4} e^{3} - 2 \, {\left(9 \, C a^{5} - 31 \, A a^{4} c\right)} d^{2} e^{5} + {\left(3 \, B a c^{4} d^{4} e^{3} - 78 \, B a^{2} c^{3} d^{2} e^{5} + 15 \, B a^{3} c^{2} e^{7} - {\left(C a c^{4} + 3 \, A c^{5}\right)} d^{5} e^{2} + 2 \, {\left(29 \, C a^{2} c^{3} - 9 \, A a c^{4}\right)} d^{3} e^{4} - {\left(37 \, C a^{3} c^{2} - 81 \, A a^{2} c^{3}\right)} d e^{6}\right)} x^{5} + 2 \, {\left(3 \, B a c^{4} d^{5} e^{2} - 48 \, B a^{2} c^{3} d^{3} e^{4} - 3 \, B a^{3} c^{2} d e^{6} - {\left(C a c^{4} + 3 \, A c^{5}\right)} d^{6} e + 2 \, {\left(19 \, C a^{2} c^{3} - 9 \, A a c^{4}\right)} d^{4} e^{3} - {\left(11 \, C a^{3} c^{2} - 39 \, A a^{2} c^{3}\right)} d^{2} e^{5} - 2 \, {\left(C a^{4} c - 3 \, A a^{3} c^{2}\right)} e^{7}\right)} x^{4} + {\left(3 \, B a c^{4} d^{6} e + 7 \, B a^{2} c^{3} d^{4} e^{3} - 163 \, B a^{3} c^{2} d^{2} e^{5} + 25 \, B a^{4} c e^{7} - {\left(C a c^{4} + 3 \, A c^{5}\right)} d^{7} + {\left(3 \, C a^{2} c^{3} - 23 \, A a c^{4}\right)} d^{5} e^{2} + {\left(129 \, C a^{3} c^{2} - 61 \, A a^{2} c^{3}\right)} d^{3} e^{4} - {\left(67 \, C a^{4} c - 151 \, A a^{3} c^{2}\right)} d e^{6}\right)} x^{3} + 2 \, {\left(10 \, B a^{2} c^{3} d^{5} e^{2} - 88 \, B a^{3} c^{2} d^{3} e^{4} - 2 \, B a^{4} c d e^{6} - 5 \, {\left(C a^{2} c^{3} + A a c^{4}\right)} d^{6} e + {\left(71 \, C a^{3} c^{2} - 37 \, A a^{2} c^{3}\right)} d^{4} e^{3} - {\left(23 \, C a^{4} c - 73 \, A a^{3} c^{2}\right)} d^{2} e^{5} - 3 \, {\left(C a^{5} - 3 \, A a^{4} c\right)} e^{7}\right)} x^{2} + {\left(B a^{2} c^{3} d^{6} e - 2 \, B a^{3} c^{2} d^{4} e^{3} - 91 \, B a^{4} c d^{2} e^{5} + 8 \, B a^{5} e^{7} + {\left(C a^{2} c^{3} - 5 \, A a c^{4}\right)} d^{7} + 2 \, {\left(5 \, C a^{3} c^{2} - 13 \, A a^{2} c^{3}\right)} d^{5} e^{2} + 7 \, {\left(11 \, C a^{4} c - 7 \, A a^{3} c^{2}\right)} d^{3} e^{4} - 4 \, {\left(7 \, C a^{5} - 17 \, A a^{4} c\right)} d e^{6}\right)} x}{8 \, {\left(a^{4} c^{4} d^{10} + 4 \, a^{5} c^{3} d^{8} e^{2} + 6 \, a^{6} c^{2} d^{6} e^{4} + 4 \, a^{7} c d^{4} e^{6} + a^{8} d^{2} e^{8} + {\left(a^{2} c^{6} d^{8} e^{2} + 4 \, a^{3} c^{5} d^{6} e^{4} + 6 \, a^{4} c^{4} d^{4} e^{6} + 4 \, a^{5} c^{3} d^{2} e^{8} + a^{6} c^{2} e^{10}\right)} x^{6} + 2 \, {\left(a^{2} c^{6} d^{9} e + 4 \, a^{3} c^{5} d^{7} e^{3} + 6 \, a^{4} c^{4} d^{5} e^{5} + 4 \, a^{5} c^{3} d^{3} e^{7} + a^{6} c^{2} d e^{9}\right)} x^{5} + {\left(a^{2} c^{6} d^{10} + 6 \, a^{3} c^{5} d^{8} e^{2} + 14 \, a^{4} c^{4} d^{6} e^{4} + 16 \, a^{5} c^{3} d^{4} e^{6} + 9 \, a^{6} c^{2} d^{2} e^{8} + 2 \, a^{7} c e^{10}\right)} x^{4} + 4 \, {\left(a^{3} c^{5} d^{9} e + 4 \, a^{4} c^{4} d^{7} e^{3} + 6 \, a^{5} c^{3} d^{5} e^{5} + 4 \, a^{6} c^{2} d^{3} e^{7} + a^{7} c d e^{9}\right)} x^{3} + {\left(2 \, a^{3} c^{5} d^{10} + 9 \, a^{4} c^{4} d^{8} e^{2} + 16 \, a^{5} c^{3} d^{6} e^{4} + 14 \, a^{6} c^{2} d^{4} e^{6} + 6 \, a^{7} c d^{2} e^{8} + a^{8} e^{10}\right)} x^{2} + 2 \, {\left(a^{4} c^{4} d^{9} e + 4 \, a^{5} c^{3} d^{7} e^{3} + 6 \, a^{6} c^{2} d^{5} e^{5} + 4 \, a^{7} c d^{3} e^{7} + a^{8} d e^{9}\right)} x\right)}}"," ",0,"-1/2*(10*C*c^2*d^4*e^3 - 15*B*c^2*d^3*e^4 + 9*B*a*c*d*e^6 - (13*C*a*c - 21*A*c^2)*d^2*e^5 + (C*a^2 - 3*A*a*c)*e^7)*log(c*x^2 + a)/(c^5*d^10 + 5*a*c^4*d^8*e^2 + 10*a^2*c^3*d^6*e^4 + 10*a^3*c^2*d^4*e^6 + 5*a^4*c*d^2*e^8 + a^5*e^10) + (10*C*c^2*d^4*e^3 - 15*B*c^2*d^3*e^4 + 9*B*a*c*d*e^6 - (13*C*a*c - 21*A*c^2)*d^2*e^5 + (C*a^2 - 3*A*a*c)*e^7)*log(e*x + d)/(c^5*d^10 + 5*a*c^4*d^8*e^2 + 10*a^2*c^3*d^6*e^4 + 10*a^3*c^2*d^4*e^6 + 5*a^4*c*d^2*e^8 + a^5*e^10) - 1/8*(3*B*a*c^4*d^6*e + 45*B*a^2*c^3*d^4*e^3 - 135*B*a^3*c^2*d^2*e^5 + 15*B*a^4*c*e^7 - (C*a*c^4 + 3*A*c^5)*d^7 - (23*C*a^2*c^3 + 21*A*a*c^4)*d^5*e^2 + 5*(25*C*a^3*c^2 - 21*A*a^2*c^3)*d^3*e^4 - 15*(3*C*a^4*c - 7*A*a^3*c^2)*d*e^6)*arctan(c*x/sqrt(a*c))/((a^2*c^5*d^10 + 5*a^3*c^4*d^8*e^2 + 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6 + 5*a^6*c*d^2*e^8 + a^7*e^10)*sqrt(a*c)) - 1/8*(2*B*a^2*c^3*d^7 + 20*B*a^3*c^2*d^5*e^2 - 74*B*a^4*c*d^3*e^4 + 4*B*a^5*d*e^6 + 4*A*a^5*e^7 - 6*(C*a^3*c^2 + A*a^2*c^3)*d^6*e + 4*(18*C*a^4*c - 11*A*a^3*c^2)*d^4*e^3 - 2*(9*C*a^5 - 31*A*a^4*c)*d^2*e^5 + (3*B*a*c^4*d^4*e^3 - 78*B*a^2*c^3*d^2*e^5 + 15*B*a^3*c^2*e^7 - (C*a*c^4 + 3*A*c^5)*d^5*e^2 + 2*(29*C*a^2*c^3 - 9*A*a*c^4)*d^3*e^4 - (37*C*a^3*c^2 - 81*A*a^2*c^3)*d*e^6)*x^5 + 2*(3*B*a*c^4*d^5*e^2 - 48*B*a^2*c^3*d^3*e^4 - 3*B*a^3*c^2*d*e^6 - (C*a*c^4 + 3*A*c^5)*d^6*e + 2*(19*C*a^2*c^3 - 9*A*a*c^4)*d^4*e^3 - (11*C*a^3*c^2 - 39*A*a^2*c^3)*d^2*e^5 - 2*(C*a^4*c - 3*A*a^3*c^2)*e^7)*x^4 + (3*B*a*c^4*d^6*e + 7*B*a^2*c^3*d^4*e^3 - 163*B*a^3*c^2*d^2*e^5 + 25*B*a^4*c*e^7 - (C*a*c^4 + 3*A*c^5)*d^7 + (3*C*a^2*c^3 - 23*A*a*c^4)*d^5*e^2 + (129*C*a^3*c^2 - 61*A*a^2*c^3)*d^3*e^4 - (67*C*a^4*c - 151*A*a^3*c^2)*d*e^6)*x^3 + 2*(10*B*a^2*c^3*d^5*e^2 - 88*B*a^3*c^2*d^3*e^4 - 2*B*a^4*c*d*e^6 - 5*(C*a^2*c^3 + A*a*c^4)*d^6*e + (71*C*a^3*c^2 - 37*A*a^2*c^3)*d^4*e^3 - (23*C*a^4*c - 73*A*a^3*c^2)*d^2*e^5 - 3*(C*a^5 - 3*A*a^4*c)*e^7)*x^2 + (B*a^2*c^3*d^6*e - 2*B*a^3*c^2*d^4*e^3 - 91*B*a^4*c*d^2*e^5 + 8*B*a^5*e^7 + (C*a^2*c^3 - 5*A*a*c^4)*d^7 + 2*(5*C*a^3*c^2 - 13*A*a^2*c^3)*d^5*e^2 + 7*(11*C*a^4*c - 7*A*a^3*c^2)*d^3*e^4 - 4*(7*C*a^5 - 17*A*a^4*c)*d*e^6)*x)/(a^4*c^4*d^10 + 4*a^5*c^3*d^8*e^2 + 6*a^6*c^2*d^6*e^4 + 4*a^7*c*d^4*e^6 + a^8*d^2*e^8 + (a^2*c^6*d^8*e^2 + 4*a^3*c^5*d^6*e^4 + 6*a^4*c^4*d^4*e^6 + 4*a^5*c^3*d^2*e^8 + a^6*c^2*e^10)*x^6 + 2*(a^2*c^6*d^9*e + 4*a^3*c^5*d^7*e^3 + 6*a^4*c^4*d^5*e^5 + 4*a^5*c^3*d^3*e^7 + a^6*c^2*d*e^9)*x^5 + (a^2*c^6*d^10 + 6*a^3*c^5*d^8*e^2 + 14*a^4*c^4*d^6*e^4 + 16*a^5*c^3*d^4*e^6 + 9*a^6*c^2*d^2*e^8 + 2*a^7*c*e^10)*x^4 + 4*(a^3*c^5*d^9*e + 4*a^4*c^4*d^7*e^3 + 6*a^5*c^3*d^5*e^5 + 4*a^6*c^2*d^3*e^7 + a^7*c*d*e^9)*x^3 + (2*a^3*c^5*d^10 + 9*a^4*c^4*d^8*e^2 + 16*a^5*c^3*d^6*e^4 + 14*a^6*c^2*d^4*e^6 + 6*a^7*c*d^2*e^8 + a^8*e^10)*x^2 + 2*(a^4*c^4*d^9*e + 4*a^5*c^3*d^7*e^3 + 6*a^6*c^2*d^5*e^5 + 4*a^7*c*d^3*e^7 + a^8*d*e^9)*x)","B",0
64,1,599,0,1.041886," ","integrate((e*x+d)^4*(C*x^2+B*x+A)/(c*x^2+a)^4,x, algorithm=""maxima"")","-\frac{8 \, B a^{3} c^{2} d^{4} + 24 \, B a^{4} c d^{2} e^{2} + 8 \, B a^{5} e^{4} - 3 \, {\left(4 \, B a c^{4} d^{3} e + 4 \, B a^{2} c^{3} d e^{3} + {\left(C a c^{4} + 5 \, A c^{5}\right)} d^{4} + 6 \, {\left(C a^{2} c^{3} + A a c^{4}\right)} d^{2} e^{2} - {\left(11 \, C a^{3} c^{2} - A a^{2} c^{3}\right)} e^{4}\right)} x^{5} + 16 \, {\left(C a^{4} c + 2 \, A a^{3} c^{2}\right)} d^{3} e + 16 \, {\left(2 \, C a^{5} + A a^{4} c\right)} d e^{3} + 24 \, {\left(4 \, C a^{3} c^{2} d e^{3} + B a^{3} c^{2} e^{4}\right)} x^{4} - 8 \, {\left(4 \, B a^{2} c^{3} d^{3} e - 4 \, B a^{3} c^{2} d e^{3} + {\left(C a^{2} c^{3} + 5 \, A a c^{4}\right)} d^{4} - 6 \, {\left(C a^{3} c^{2} - A a^{2} c^{3}\right)} d^{2} e^{2} - {\left(5 \, C a^{4} c + A a^{3} c^{2}\right)} e^{4}\right)} x^{3} + 24 \, {\left(2 \, C a^{3} c^{2} d^{3} e + 3 \, B a^{3} c^{2} d^{2} e^{2} + B a^{4} c e^{4} + 2 \, {\left(2 \, C a^{4} c + A a^{3} c^{2}\right)} d e^{3}\right)} x^{2} + 3 \, {\left(4 \, B a^{3} c^{2} d^{3} e + 4 \, B a^{4} c d e^{3} + {\left(C a^{3} c^{2} - 11 \, A a^{2} c^{3}\right)} d^{4} + 6 \, {\left(C a^{4} c + A a^{3} c^{2}\right)} d^{2} e^{2} + {\left(5 \, C a^{5} + A a^{4} c\right)} e^{4}\right)} x}{48 \, {\left(a^{3} c^{6} x^{6} + 3 \, a^{4} c^{5} x^{4} + 3 \, a^{5} c^{4} x^{2} + a^{6} c^{3}\right)}} + \frac{{\left(4 \, B a c^{2} d^{3} e + 4 \, B a^{2} c d e^{3} + {\left(C a c^{2} + 5 \, A c^{3}\right)} d^{4} + 6 \, {\left(C a^{2} c + A a c^{2}\right)} d^{2} e^{2} + {\left(5 \, C a^{3} + A a^{2} c\right)} e^{4}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{16 \, \sqrt{a c} a^{3} c^{3}}"," ",0,"-1/48*(8*B*a^3*c^2*d^4 + 24*B*a^4*c*d^2*e^2 + 8*B*a^5*e^4 - 3*(4*B*a*c^4*d^3*e + 4*B*a^2*c^3*d*e^3 + (C*a*c^4 + 5*A*c^5)*d^4 + 6*(C*a^2*c^3 + A*a*c^4)*d^2*e^2 - (11*C*a^3*c^2 - A*a^2*c^3)*e^4)*x^5 + 16*(C*a^4*c + 2*A*a^3*c^2)*d^3*e + 16*(2*C*a^5 + A*a^4*c)*d*e^3 + 24*(4*C*a^3*c^2*d*e^3 + B*a^3*c^2*e^4)*x^4 - 8*(4*B*a^2*c^3*d^3*e - 4*B*a^3*c^2*d*e^3 + (C*a^2*c^3 + 5*A*a*c^4)*d^4 - 6*(C*a^3*c^2 - A*a^2*c^3)*d^2*e^2 - (5*C*a^4*c + A*a^3*c^2)*e^4)*x^3 + 24*(2*C*a^3*c^2*d^3*e + 3*B*a^3*c^2*d^2*e^2 + B*a^4*c*e^4 + 2*(2*C*a^4*c + A*a^3*c^2)*d*e^3)*x^2 + 3*(4*B*a^3*c^2*d^3*e + 4*B*a^4*c*d*e^3 + (C*a^3*c^2 - 11*A*a^2*c^3)*d^4 + 6*(C*a^4*c + A*a^3*c^2)*d^2*e^2 + (5*C*a^5 + A*a^4*c)*e^4)*x)/(a^3*c^6*x^6 + 3*a^4*c^5*x^4 + 3*a^5*c^4*x^2 + a^6*c^3) + 1/16*(4*B*a*c^2*d^3*e + 4*B*a^2*c*d*e^3 + (C*a*c^2 + 5*A*c^3)*d^4 + 6*(C*a^2*c + A*a*c^2)*d^2*e^2 + (5*C*a^3 + A*a^2*c)*e^4)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a^3*c^3)","B",0
65,1,457,0,1.018049," ","integrate((e*x+d)^3*(C*x^2+B*x+A)/(c*x^2+a)^4,x, algorithm=""maxima"")","-\frac{24 \, C a^{3} c^{2} e^{3} x^{4} + 8 \, B a^{3} c^{2} d^{3} + 12 \, B a^{4} c d e^{2} - 3 \, {\left(3 \, B a c^{4} d^{2} e + B a^{2} c^{3} e^{3} + {\left(C a c^{4} + 5 \, A c^{5}\right)} d^{3} + 3 \, {\left(C a^{2} c^{3} + A a c^{4}\right)} d e^{2}\right)} x^{5} + 12 \, {\left(C a^{4} c + 2 \, A a^{3} c^{2}\right)} d^{2} e + 4 \, {\left(2 \, C a^{5} + A a^{4} c\right)} e^{3} - 8 \, {\left(3 \, B a^{2} c^{3} d^{2} e - B a^{3} c^{2} e^{3} + {\left(C a^{2} c^{3} + 5 \, A a c^{4}\right)} d^{3} - 3 \, {\left(C a^{3} c^{2} - A a^{2} c^{3}\right)} d e^{2}\right)} x^{3} + 12 \, {\left(3 \, C a^{3} c^{2} d^{2} e + 3 \, B a^{3} c^{2} d e^{2} + {\left(2 \, C a^{4} c + A a^{3} c^{2}\right)} e^{3}\right)} x^{2} + 3 \, {\left(3 \, B a^{3} c^{2} d^{2} e + B a^{4} c e^{3} + {\left(C a^{3} c^{2} - 11 \, A a^{2} c^{3}\right)} d^{3} + 3 \, {\left(C a^{4} c + A a^{3} c^{2}\right)} d e^{2}\right)} x}{48 \, {\left(a^{3} c^{6} x^{6} + 3 \, a^{4} c^{5} x^{4} + 3 \, a^{5} c^{4} x^{2} + a^{6} c^{3}\right)}} + \frac{{\left(3 \, B a c d^{2} e + B a^{2} e^{3} + {\left(C a c + 5 \, A c^{2}\right)} d^{3} + 3 \, {\left(C a^{2} + A a c\right)} d e^{2}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{16 \, \sqrt{a c} a^{3} c^{2}}"," ",0,"-1/48*(24*C*a^3*c^2*e^3*x^4 + 8*B*a^3*c^2*d^3 + 12*B*a^4*c*d*e^2 - 3*(3*B*a*c^4*d^2*e + B*a^2*c^3*e^3 + (C*a*c^4 + 5*A*c^5)*d^3 + 3*(C*a^2*c^3 + A*a*c^4)*d*e^2)*x^5 + 12*(C*a^4*c + 2*A*a^3*c^2)*d^2*e + 4*(2*C*a^5 + A*a^4*c)*e^3 - 8*(3*B*a^2*c^3*d^2*e - B*a^3*c^2*e^3 + (C*a^2*c^3 + 5*A*a*c^4)*d^3 - 3*(C*a^3*c^2 - A*a^2*c^3)*d*e^2)*x^3 + 12*(3*C*a^3*c^2*d^2*e + 3*B*a^3*c^2*d*e^2 + (2*C*a^4*c + A*a^3*c^2)*e^3)*x^2 + 3*(3*B*a^3*c^2*d^2*e + B*a^4*c*e^3 + (C*a^3*c^2 - 11*A*a^2*c^3)*d^3 + 3*(C*a^4*c + A*a^3*c^2)*d*e^2)*x)/(a^3*c^6*x^6 + 3*a^4*c^5*x^4 + 3*a^5*c^4*x^2 + a^6*c^3) + 1/16*(3*B*a*c*d^2*e + B*a^2*e^3 + (C*a*c + 5*A*c^2)*d^3 + 3*(C*a^2 + A*a*c)*d*e^2)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a^3*c^2)","A",0
66,1,323,0,1.005461," ","integrate((e*x+d)^2*(C*x^2+B*x+A)/(c*x^2+a)^4,x, algorithm=""maxima"")","-\frac{8 \, B a^{3} c d^{2} + 4 \, B a^{4} e^{2} - 3 \, {\left(2 \, B a c^{3} d e + {\left(C a c^{3} + 5 \, A c^{4}\right)} d^{2} + {\left(C a^{2} c^{2} + A a c^{3}\right)} e^{2}\right)} x^{5} - 8 \, {\left(2 \, B a^{2} c^{2} d e + {\left(C a^{2} c^{2} + 5 \, A a c^{3}\right)} d^{2} - {\left(C a^{3} c - A a^{2} c^{2}\right)} e^{2}\right)} x^{3} + 8 \, {\left(C a^{4} + 2 \, A a^{3} c\right)} d e + 12 \, {\left(2 \, C a^{3} c d e + B a^{3} c e^{2}\right)} x^{2} + 3 \, {\left(2 \, B a^{3} c d e + {\left(C a^{3} c - 11 \, A a^{2} c^{2}\right)} d^{2} + {\left(C a^{4} + A a^{3} c\right)} e^{2}\right)} x}{48 \, {\left(a^{3} c^{5} x^{6} + 3 \, a^{4} c^{4} x^{4} + 3 \, a^{5} c^{3} x^{2} + a^{6} c^{2}\right)}} + \frac{{\left(2 \, B a c d e + {\left(C a c + 5 \, A c^{2}\right)} d^{2} + {\left(C a^{2} + A a c\right)} e^{2}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{16 \, \sqrt{a c} a^{3} c^{2}}"," ",0,"-1/48*(8*B*a^3*c*d^2 + 4*B*a^4*e^2 - 3*(2*B*a*c^3*d*e + (C*a*c^3 + 5*A*c^4)*d^2 + (C*a^2*c^2 + A*a*c^3)*e^2)*x^5 - 8*(2*B*a^2*c^2*d*e + (C*a^2*c^2 + 5*A*a*c^3)*d^2 - (C*a^3*c - A*a^2*c^2)*e^2)*x^3 + 8*(C*a^4 + 2*A*a^3*c)*d*e + 12*(2*C*a^3*c*d*e + B*a^3*c*e^2)*x^2 + 3*(2*B*a^3*c*d*e + (C*a^3*c - 11*A*a^2*c^2)*d^2 + (C*a^4 + A*a^3*c)*e^2)*x)/(a^3*c^5*x^6 + 3*a^4*c^4*x^4 + 3*a^5*c^3*x^2 + a^6*c^2) + 1/16*(2*B*a*c*d*e + (C*a*c + 5*A*c^2)*d^2 + (C*a^2 + A*a*c)*e^2)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a^3*c^2)","A",0
67,1,208,0,0.981329," ","integrate((e*x+d)*(C*x^2+B*x+A)/(c*x^2+a)^4,x, algorithm=""maxima"")","-\frac{12 \, C a^{3} c e x^{2} + 8 \, B a^{3} c d - 3 \, {\left(B a c^{3} e + {\left(C a c^{3} + 5 \, A c^{4}\right)} d\right)} x^{5} - 8 \, {\left(B a^{2} c^{2} e + {\left(C a^{2} c^{2} + 5 \, A a c^{3}\right)} d\right)} x^{3} + 4 \, {\left(C a^{4} + 2 \, A a^{3} c\right)} e + 3 \, {\left(B a^{3} c e + {\left(C a^{3} c - 11 \, A a^{2} c^{2}\right)} d\right)} x}{48 \, {\left(a^{3} c^{5} x^{6} + 3 \, a^{4} c^{4} x^{4} + 3 \, a^{5} c^{3} x^{2} + a^{6} c^{2}\right)}} + \frac{{\left(B a e + {\left(C a + 5 \, A c\right)} d\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{16 \, \sqrt{a c} a^{3} c}"," ",0,"-1/48*(12*C*a^3*c*e*x^2 + 8*B*a^3*c*d - 3*(B*a*c^3*e + (C*a*c^3 + 5*A*c^4)*d)*x^5 - 8*(B*a^2*c^2*e + (C*a^2*c^2 + 5*A*a*c^3)*d)*x^3 + 4*(C*a^4 + 2*A*a^3*c)*e + 3*(B*a^3*c*e + (C*a^3*c - 11*A*a^2*c^2)*d)*x)/(a^3*c^5*x^6 + 3*a^4*c^4*x^4 + 3*a^5*c^3*x^2 + a^6*c^2) + 1/16*(B*a*e + (C*a + 5*A*c)*d)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a^3*c)","A",0
68,1,133,0,0.976397," ","integrate((C*x^2+B*x+A)/(c*x^2+a)^4,x, algorithm=""maxima"")","\frac{3 \, {\left(C a c^{2} + 5 \, A c^{3}\right)} x^{5} - 8 \, B a^{3} + 8 \, {\left(C a^{2} c + 5 \, A a c^{2}\right)} x^{3} - 3 \, {\left(C a^{3} - 11 \, A a^{2} c\right)} x}{48 \, {\left(a^{3} c^{4} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{5} c^{2} x^{2} + a^{6} c\right)}} + \frac{{\left(C a + 5 \, A c\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{16 \, \sqrt{a c} a^{3} c}"," ",0,"1/48*(3*(C*a*c^2 + 5*A*c^3)*x^5 - 8*B*a^3 + 8*(C*a^2*c + 5*A*a*c^2)*x^3 - 3*(C*a^3 - 11*A*a^2*c)*x)/(a^3*c^4*x^6 + 3*a^4*c^3*x^4 + 3*a^5*c^2*x^2 + a^6*c) + 1/16*(C*a + 5*A*c)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a^3*c)","A",0
69,1,29,0,0.952905," ","integrate(x^3*(x^2+x+1)/(x^2+1)^2,x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} + x + \frac{x}{2 \, {\left(x^{2} + 1\right)}} - \frac{3}{2} \, \arctan\left(x\right) - \frac{1}{2} \, \log\left(x^{2} + 1\right)"," ",0,"1/2*x^2 + x + 1/2*x/(x^2 + 1) - 3/2*arctan(x) - 1/2*log(x^2 + 1)","A",0
70,1,23,0,0.959499," ","integrate(x^2*(x^2+x+1)/(x^2+1)^2,x, algorithm=""maxima"")","x + \frac{1}{2 \, {\left(x^{2} + 1\right)}} - \arctan\left(x\right) + \frac{1}{2} \, \log\left(x^{2} + 1\right)"," ",0,"x + 1/2/(x^2 + 1) - arctan(x) + 1/2*log(x^2 + 1)","A",0
71,1,23,0,0.963478," ","integrate(x*(x^2+x+1)/(x^2+1)^2,x, algorithm=""maxima"")","-\frac{x}{2 \, {\left(x^{2} + 1\right)}} + \frac{1}{2} \, \arctan\left(x\right) + \frac{1}{2} \, \log\left(x^{2} + 1\right)"," ",0,"-1/2*x/(x^2 + 1) + 1/2*arctan(x) + 1/2*log(x^2 + 1)","A",0
72,1,12,0,0.955039," ","integrate((x^2+x+1)/(x^2+1)^2,x, algorithm=""maxima"")","-\frac{1}{2 \, {\left(x^{2} + 1\right)}} + \arctan\left(x\right)"," ",0,"-1/2/(x^2 + 1) + arctan(x)","A",0
73,1,25,0,0.956330," ","integrate((x^2+x+1)/x/(x^2+1)^2,x, algorithm=""maxima"")","\frac{x}{2 \, {\left(x^{2} + 1\right)}} + \frac{1}{2} \, \arctan\left(x\right) - \frac{1}{2} \, \log\left(x^{2} + 1\right) + \log\left(x\right)"," ",0,"1/2*x/(x^2 + 1) + 1/2*arctan(x) - 1/2*log(x^2 + 1) + log(x)","A",0
74,1,34,0,0.952492," ","integrate((x^2+x+1)/x^2/(x^2+1)^2,x, algorithm=""maxima"")","-\frac{2 \, x^{2} - x + 2}{2 \, {\left(x^{3} + x\right)}} - \arctan\left(x\right) - \frac{1}{2} \, \log\left(x^{2} + 1\right) + \log\left(x\right)"," ",0,"-1/2*(2*x^2 - x + 2)/(x^3 + x) - arctan(x) - 1/2*log(x^2 + 1) + log(x)","A",0
75,1,41,0,0.971424," ","integrate((x^2+x+1)/x^3/(x^2+1)^2,x, algorithm=""maxima"")","-\frac{3 \, x^{3} + x^{2} + 2 \, x + 1}{2 \, {\left(x^{4} + x^{2}\right)}} - \frac{3}{2} \, \arctan\left(x\right) + \frac{1}{2} \, \log\left(x^{2} + 1\right) - \log\left(x\right)"," ",0,"-1/2*(3*x^3 + x^2 + 2*x + 1)/(x^4 + x^2) - 3/2*arctan(x) + 1/2*log(x^2 + 1) - log(x)","A",0
76,1,12,0,0.950551," ","integrate((x^2+2*x+1)/(x^2+1)^2,x, algorithm=""maxima"")","-\frac{1}{x^{2} + 1} + \arctan\left(x\right)"," ",0,"-1/(x^2 + 1) + arctan(x)","A",0
77,1,21,0,0.965003," ","integrate((3*x^2+12*x+2)/(x^2+4)^2,x, algorithm=""maxima"")","-\frac{5 \, x + 24}{4 \, {\left(x^{2} + 4\right)}} + \frac{7}{8} \, \arctan\left(\frac{1}{2} \, x\right)"," ",0,"-1/4*(5*x + 24)/(x^2 + 4) + 7/8*arctan(1/2*x)","A",0
78,1,436,0,0.465558," ","integrate((h*x+g)^3*(f*x^2+e*x+d)*(c*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} f h^{3} x^{4}}{7 \, c} - \frac{4 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} a f h^{3} x^{2}}{35 \, c^{2}} + \frac{1}{2} \, \sqrt{c x^{2} + a} d g^{3} x + \frac{a d g^{3} \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{2 \, \sqrt{c}} + \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} e g^{3}}{3 \, c} + \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} d g^{2} h}{c} + \frac{8 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} a^{2} f h^{3}}{105 \, c^{3}} + \frac{{\left(3 \, f g h^{2} + e h^{3}\right)} {\left(c x^{2} + a\right)}^{\frac{3}{2}} x^{3}}{6 \, c} + \frac{{\left(3 \, f g^{2} h + 3 \, e g h^{2} + d h^{3}\right)} {\left(c x^{2} + a\right)}^{\frac{3}{2}} x^{2}}{5 \, c} - \frac{{\left(3 \, f g h^{2} + e h^{3}\right)} {\left(c x^{2} + a\right)}^{\frac{3}{2}} a x}{8 \, c^{2}} + \frac{{\left(3 \, f g h^{2} + e h^{3}\right)} \sqrt{c x^{2} + a} a^{2} x}{16 \, c^{2}} + \frac{{\left(f g^{3} + 3 \, e g^{2} h + 3 \, d g h^{2}\right)} {\left(c x^{2} + a\right)}^{\frac{3}{2}} x}{4 \, c} - \frac{{\left(f g^{3} + 3 \, e g^{2} h + 3 \, d g h^{2}\right)} \sqrt{c x^{2} + a} a x}{8 \, c} + \frac{{\left(3 \, f g h^{2} + e h^{3}\right)} a^{3} \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{16 \, c^{\frac{5}{2}}} - \frac{{\left(f g^{3} + 3 \, e g^{2} h + 3 \, d g h^{2}\right)} a^{2} \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{8 \, c^{\frac{3}{2}}} - \frac{2 \, {\left(3 \, f g^{2} h + 3 \, e g h^{2} + d h^{3}\right)} {\left(c x^{2} + a\right)}^{\frac{3}{2}} a}{15 \, c^{2}}"," ",0,"1/7*(c*x^2 + a)^(3/2)*f*h^3*x^4/c - 4/35*(c*x^2 + a)^(3/2)*a*f*h^3*x^2/c^2 + 1/2*sqrt(c*x^2 + a)*d*g^3*x + 1/2*a*d*g^3*arcsinh(c*x/sqrt(a*c))/sqrt(c) + 1/3*(c*x^2 + a)^(3/2)*e*g^3/c + (c*x^2 + a)^(3/2)*d*g^2*h/c + 8/105*(c*x^2 + a)^(3/2)*a^2*f*h^3/c^3 + 1/6*(3*f*g*h^2 + e*h^3)*(c*x^2 + a)^(3/2)*x^3/c + 1/5*(3*f*g^2*h + 3*e*g*h^2 + d*h^3)*(c*x^2 + a)^(3/2)*x^2/c - 1/8*(3*f*g*h^2 + e*h^3)*(c*x^2 + a)^(3/2)*a*x/c^2 + 1/16*(3*f*g*h^2 + e*h^3)*sqrt(c*x^2 + a)*a^2*x/c^2 + 1/4*(f*g^3 + 3*e*g^2*h + 3*d*g*h^2)*(c*x^2 + a)^(3/2)*x/c - 1/8*(f*g^3 + 3*e*g^2*h + 3*d*g*h^2)*sqrt(c*x^2 + a)*a*x/c + 1/16*(3*f*g*h^2 + e*h^3)*a^3*arcsinh(c*x/sqrt(a*c))/c^(5/2) - 1/8*(f*g^3 + 3*e*g^2*h + 3*d*g*h^2)*a^2*arcsinh(c*x/sqrt(a*c))/c^(3/2) - 2/15*(3*f*g^2*h + 3*e*g*h^2 + d*h^3)*(c*x^2 + a)^(3/2)*a/c^2","A",0
79,1,305,0,0.463448," ","integrate((h*x+g)^2*(f*x^2+e*x+d)*(c*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} f h^{2} x^{3}}{6 \, c} + \frac{1}{2} \, \sqrt{c x^{2} + a} d g^{2} x - \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} a f h^{2} x}{8 \, c^{2}} + \frac{\sqrt{c x^{2} + a} a^{2} f h^{2} x}{16 \, c^{2}} + \frac{a d g^{2} \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{2 \, \sqrt{c}} + \frac{a^{3} f h^{2} \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{16 \, c^{\frac{5}{2}}} + \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} e g^{2}}{3 \, c} + \frac{2 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} d g h}{3 \, c} + \frac{{\left(2 \, f g h + e h^{2}\right)} {\left(c x^{2} + a\right)}^{\frac{3}{2}} x^{2}}{5 \, c} + \frac{{\left(f g^{2} + 2 \, e g h + d h^{2}\right)} {\left(c x^{2} + a\right)}^{\frac{3}{2}} x}{4 \, c} - \frac{{\left(f g^{2} + 2 \, e g h + d h^{2}\right)} \sqrt{c x^{2} + a} a x}{8 \, c} - \frac{{\left(f g^{2} + 2 \, e g h + d h^{2}\right)} a^{2} \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{8 \, c^{\frac{3}{2}}} - \frac{2 \, {\left(2 \, f g h + e h^{2}\right)} {\left(c x^{2} + a\right)}^{\frac{3}{2}} a}{15 \, c^{2}}"," ",0,"1/6*(c*x^2 + a)^(3/2)*f*h^2*x^3/c + 1/2*sqrt(c*x^2 + a)*d*g^2*x - 1/8*(c*x^2 + a)^(3/2)*a*f*h^2*x/c^2 + 1/16*sqrt(c*x^2 + a)*a^2*f*h^2*x/c^2 + 1/2*a*d*g^2*arcsinh(c*x/sqrt(a*c))/sqrt(c) + 1/16*a^3*f*h^2*arcsinh(c*x/sqrt(a*c))/c^(5/2) + 1/3*(c*x^2 + a)^(3/2)*e*g^2/c + 2/3*(c*x^2 + a)^(3/2)*d*g*h/c + 1/5*(2*f*g*h + e*h^2)*(c*x^2 + a)^(3/2)*x^2/c + 1/4*(f*g^2 + 2*e*g*h + d*h^2)*(c*x^2 + a)^(3/2)*x/c - 1/8*(f*g^2 + 2*e*g*h + d*h^2)*sqrt(c*x^2 + a)*a*x/c - 1/8*(f*g^2 + 2*e*g*h + d*h^2)*a^2*arcsinh(c*x/sqrt(a*c))/c^(3/2) - 2/15*(2*f*g*h + e*h^2)*(c*x^2 + a)^(3/2)*a/c^2","A",0
80,1,169,0,0.448939," ","integrate((h*x+g)*(f*x^2+e*x+d)*(c*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} f h x^{2}}{5 \, c} + \frac{1}{2} \, \sqrt{c x^{2} + a} d g x + \frac{a d g \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{2 \, \sqrt{c}} + \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} e g}{3 \, c} + \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} d h}{3 \, c} - \frac{2 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} a f h}{15 \, c^{2}} + \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} {\left(f g + e h\right)} x}{4 \, c} - \frac{\sqrt{c x^{2} + a} {\left(f g + e h\right)} a x}{8 \, c} - \frac{{\left(f g + e h\right)} a^{2} \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{8 \, c^{\frac{3}{2}}}"," ",0,"1/5*(c*x^2 + a)^(3/2)*f*h*x^2/c + 1/2*sqrt(c*x^2 + a)*d*g*x + 1/2*a*d*g*arcsinh(c*x/sqrt(a*c))/sqrt(c) + 1/3*(c*x^2 + a)^(3/2)*e*g/c + 1/3*(c*x^2 + a)^(3/2)*d*h/c - 2/15*(c*x^2 + a)^(3/2)*a*f*h/c^2 + 1/4*(c*x^2 + a)^(3/2)*(f*g + e*h)*x/c - 1/8*sqrt(c*x^2 + a)*(f*g + e*h)*a*x/c - 1/8*(f*g + e*h)*a^2*arcsinh(c*x/sqrt(a*c))/c^(3/2)","A",0
81,1,96,0,0.450928," ","integrate((f*x^2+e*x+d)*(c*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{1}{2} \, \sqrt{c x^{2} + a} d x + \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} f x}{4 \, c} - \frac{\sqrt{c x^{2} + a} a f x}{8 \, c} + \frac{a d \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{2 \, \sqrt{c}} - \frac{a^{2} f \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{8 \, c^{\frac{3}{2}}} + \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} e}{3 \, c}"," ",0,"1/2*sqrt(c*x^2 + a)*d*x + 1/4*(c*x^2 + a)^(3/2)*f*x/c - 1/8*sqrt(c*x^2 + a)*a*f*x/c + 1/2*a*d*arcsinh(c*x/sqrt(a*c))/sqrt(c) - 1/8*a^2*f*arcsinh(c*x/sqrt(a*c))/c^(3/2) + 1/3*(c*x^2 + a)^(3/2)*e/c","A",0
82,1,362,0,0.606008," ","integrate((f*x^2+e*x+d)*(c*x^2+a)^(1/2)/(h*x+g),x, algorithm=""maxima"")","-\frac{\sqrt{c x^{2} + a} f g x}{2 \, h^{2}} + \frac{\sqrt{c x^{2} + a} e x}{2 \, h} - \frac{\sqrt{c} f g^{3} \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{h^{4}} + \frac{\sqrt{c} e g^{2} \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{h^{3}} - \frac{\sqrt{c} d g \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{h^{2}} - \frac{a f g \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{2 \, \sqrt{c} h^{2}} + \frac{a e \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{2 \, \sqrt{c} h} + \frac{\sqrt{a + \frac{c g^{2}}{h^{2}}} f g^{2} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{h^{3}} - \frac{\sqrt{a + \frac{c g^{2}}{h^{2}}} e g \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{h^{2}} + \frac{\sqrt{a + \frac{c g^{2}}{h^{2}}} d \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{h} + \frac{\sqrt{c x^{2} + a} f g^{2}}{h^{3}} - \frac{\sqrt{c x^{2} + a} e g}{h^{2}} + \frac{\sqrt{c x^{2} + a} d}{h} + \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} f}{3 \, c h}"," ",0,"-1/2*sqrt(c*x^2 + a)*f*g*x/h^2 + 1/2*sqrt(c*x^2 + a)*e*x/h - sqrt(c)*f*g^3*arcsinh(c*x/sqrt(a*c))/h^4 + sqrt(c)*e*g^2*arcsinh(c*x/sqrt(a*c))/h^3 - sqrt(c)*d*g*arcsinh(c*x/sqrt(a*c))/h^2 - 1/2*a*f*g*arcsinh(c*x/sqrt(a*c))/(sqrt(c)*h^2) + 1/2*a*e*arcsinh(c*x/sqrt(a*c))/(sqrt(c)*h) + sqrt(a + c*g^2/h^2)*f*g^2*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/h^3 - sqrt(a + c*g^2/h^2)*e*g*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/h^2 + sqrt(a + c*g^2/h^2)*d*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/h + sqrt(c*x^2 + a)*f*g^2/h^3 - sqrt(c*x^2 + a)*e*g/h^2 + sqrt(c*x^2 + a)*d/h + 1/3*(c*x^2 + a)^(3/2)*f/(c*h)","A",0
83,1,478,0,0.646898," ","integrate((f*x^2+e*x+d)*(c*x^2+a)^(1/2)/(h*x+g)^2,x, algorithm=""maxima"")","-\frac{\sqrt{c x^{2} + a} f g^{2}}{h^{4} x + g h^{3}} + \frac{\sqrt{c x^{2} + a} e g}{h^{3} x + g h^{2}} - \frac{\sqrt{c x^{2} + a} d}{h^{2} x + g h} + \frac{\sqrt{c x^{2} + a} f x}{2 \, h^{2}} + \frac{3 \, \sqrt{c} f g^{2} \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{h^{4}} - \frac{2 \, \sqrt{c} e g \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{h^{3}} + \frac{\sqrt{c} d \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{h^{2}} + \frac{a f \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{2 \, \sqrt{c} h^{2}} - \frac{c f g^{3} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{\sqrt{a + \frac{c g^{2}}{h^{2}}} h^{5}} + \frac{c e g^{2} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{\sqrt{a + \frac{c g^{2}}{h^{2}}} h^{4}} - \frac{c d g \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{\sqrt{a + \frac{c g^{2}}{h^{2}}} h^{3}} - \frac{2 \, \sqrt{a + \frac{c g^{2}}{h^{2}}} f g \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{h^{3}} + \frac{\sqrt{a + \frac{c g^{2}}{h^{2}}} e \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{h^{2}} - \frac{2 \, \sqrt{c x^{2} + a} f g}{h^{3}} + \frac{\sqrt{c x^{2} + a} e}{h^{2}}"," ",0,"-sqrt(c*x^2 + a)*f*g^2/(h^4*x + g*h^3) + sqrt(c*x^2 + a)*e*g/(h^3*x + g*h^2) - sqrt(c*x^2 + a)*d/(h^2*x + g*h) + 1/2*sqrt(c*x^2 + a)*f*x/h^2 + 3*sqrt(c)*f*g^2*arcsinh(c*x/sqrt(a*c))/h^4 - 2*sqrt(c)*e*g*arcsinh(c*x/sqrt(a*c))/h^3 + sqrt(c)*d*arcsinh(c*x/sqrt(a*c))/h^2 + 1/2*a*f*arcsinh(c*x/sqrt(a*c))/(sqrt(c)*h^2) - c*f*g^3*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/(sqrt(a + c*g^2/h^2)*h^5) + c*e*g^2*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/(sqrt(a + c*g^2/h^2)*h^4) - c*d*g*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/(sqrt(a + c*g^2/h^2)*h^3) - 2*sqrt(a + c*g^2/h^2)*f*g*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/h^3 + sqrt(a + c*g^2/h^2)*e*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/h^2 - 2*sqrt(c*x^2 + a)*f*g/h^3 + sqrt(c*x^2 + a)*e/h^2","A",0
84,1,927,0,0.703303," ","integrate((f*x^2+e*x+d)*(c*x^2+a)^(1/2)/(h*x+g)^3,x, algorithm=""maxima"")","-\frac{\sqrt{c x^{2} + a} c f g^{3}}{2 \, {\left(c g^{2} h^{4} x + a h^{6} x + c g^{3} h^{3} + a g h^{5}\right)}} + \frac{\sqrt{c x^{2} + a} c e g^{2}}{2 \, {\left(c g^{2} h^{3} x + a h^{5} x + c g^{3} h^{2} + a g h^{4}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} f g^{2}}{2 \, {\left(c g^{2} h^{3} x^{2} + a h^{5} x^{2} + 2 \, c g^{3} h^{2} x + 2 \, a g h^{4} x + c g^{4} h + a g^{2} h^{3}\right)}} + \frac{\sqrt{c x^{2} + a} c f g^{2}}{2 \, {\left(c g^{2} h^{3} + a h^{5}\right)}} - \frac{\sqrt{c x^{2} + a} c d g}{2 \, {\left(c g^{2} h^{2} x + a h^{4} x + c g^{3} h + a g h^{3}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} e g}{2 \, {\left(c g^{2} h^{2} x^{2} + a h^{4} x^{2} + 2 \, c g^{3} h x + 2 \, a g h^{3} x + c g^{4} + a g^{2} h^{2}\right)}} - \frac{\sqrt{c x^{2} + a} c e g}{2 \, {\left(c g^{2} h^{2} + a h^{4}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} d}{2 \, {\left(c g^{2} h x^{2} + a h^{3} x^{2} + 2 \, c g^{3} x + 2 \, a g h^{2} x + \frac{c g^{4}}{h} + a g^{2} h\right)}} + \frac{\sqrt{c x^{2} + a} c d}{2 \, {\left(c g^{2} h + a h^{3}\right)}} + \frac{2 \, \sqrt{c x^{2} + a} f g}{h^{4} x + g h^{3}} - \frac{\sqrt{c x^{2} + a} e}{h^{3} x + g h^{2}} - \frac{3 \, \sqrt{c} f g \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{h^{4}} + \frac{\sqrt{c} e \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{h^{3}} - \frac{c^{2} f g^{4} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{2 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{3}{2}} h^{7}} + \frac{c^{2} e g^{3} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{2 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{3}{2}} h^{6}} - \frac{c^{2} d g^{2} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{2 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{3}{2}} h^{5}} + \frac{5 \, c f g^{2} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{2 \, \sqrt{a + \frac{c g^{2}}{h^{2}}} h^{5}} - \frac{3 \, c e g \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{2 \, \sqrt{a + \frac{c g^{2}}{h^{2}}} h^{4}} + \frac{c d \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{2 \, \sqrt{a + \frac{c g^{2}}{h^{2}}} h^{3}} + \frac{\sqrt{a + \frac{c g^{2}}{h^{2}}} f \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{h^{3}} + \frac{\sqrt{c x^{2} + a} f}{h^{3}}"," ",0,"-1/2*sqrt(c*x^2 + a)*c*f*g^3/(c*g^2*h^4*x + a*h^6*x + c*g^3*h^3 + a*g*h^5) + 1/2*sqrt(c*x^2 + a)*c*e*g^2/(c*g^2*h^3*x + a*h^5*x + c*g^3*h^2 + a*g*h^4) - 1/2*(c*x^2 + a)^(3/2)*f*g^2/(c*g^2*h^3*x^2 + a*h^5*x^2 + 2*c*g^3*h^2*x + 2*a*g*h^4*x + c*g^4*h + a*g^2*h^3) + 1/2*sqrt(c*x^2 + a)*c*f*g^2/(c*g^2*h^3 + a*h^5) - 1/2*sqrt(c*x^2 + a)*c*d*g/(c*g^2*h^2*x + a*h^4*x + c*g^3*h + a*g*h^3) + 1/2*(c*x^2 + a)^(3/2)*e*g/(c*g^2*h^2*x^2 + a*h^4*x^2 + 2*c*g^3*h*x + 2*a*g*h^3*x + c*g^4 + a*g^2*h^2) - 1/2*sqrt(c*x^2 + a)*c*e*g/(c*g^2*h^2 + a*h^4) - 1/2*(c*x^2 + a)^(3/2)*d/(c*g^2*h*x^2 + a*h^3*x^2 + 2*c*g^3*x + 2*a*g*h^2*x + c*g^4/h + a*g^2*h) + 1/2*sqrt(c*x^2 + a)*c*d/(c*g^2*h + a*h^3) + 2*sqrt(c*x^2 + a)*f*g/(h^4*x + g*h^3) - sqrt(c*x^2 + a)*e/(h^3*x + g*h^2) - 3*sqrt(c)*f*g*arcsinh(c*x/sqrt(a*c))/h^4 + sqrt(c)*e*arcsinh(c*x/sqrt(a*c))/h^3 - 1/2*c^2*f*g^4*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(3/2)*h^7) + 1/2*c^2*e*g^3*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(3/2)*h^6) - 1/2*c^2*d*g^2*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(3/2)*h^5) + 5/2*c*f*g^2*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/(sqrt(a + c*g^2/h^2)*h^5) - 3/2*c*e*g*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/(sqrt(a + c*g^2/h^2)*h^4) + 1/2*c*d*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/(sqrt(a + c*g^2/h^2)*h^3) + sqrt(a + c*g^2/h^2)*f*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/h^3 + sqrt(c*x^2 + a)*f/h^3","B",0
85,1,1772,0,0.841232," ","integrate((f*x^2+e*x+d)*(c*x^2+a)^(1/2)/(h*x+g)^4,x, algorithm=""maxima"")","-\frac{\sqrt{c x^{2} + a} c^{2} f g^{4}}{2 \, {\left(c^{2} g^{4} h^{4} x + 2 \, a c g^{2} h^{6} x + a^{2} h^{8} x + c^{2} g^{5} h^{3} + 2 \, a c g^{3} h^{5} + a^{2} g h^{7}\right)}} + \frac{\sqrt{c x^{2} + a} c^{2} e g^{3}}{2 \, {\left(c^{2} g^{4} h^{3} x + 2 \, a c g^{2} h^{5} x + a^{2} h^{7} x + c^{2} g^{5} h^{2} + 2 \, a c g^{3} h^{4} + a^{2} g h^{6}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} c f g^{3}}{2 \, {\left(c^{2} g^{4} h^{3} x^{2} + 2 \, a c g^{2} h^{5} x^{2} + a^{2} h^{7} x^{2} + 2 \, c^{2} g^{5} h^{2} x + 4 \, a c g^{3} h^{4} x + 2 \, a^{2} g h^{6} x + c^{2} g^{6} h + 2 \, a c g^{4} h^{3} + a^{2} g^{2} h^{5}\right)}} + \frac{\sqrt{c x^{2} + a} c^{2} f g^{3}}{2 \, {\left(c^{2} g^{4} h^{3} + 2 \, a c g^{2} h^{5} + a^{2} h^{7}\right)}} - \frac{\sqrt{c x^{2} + a} c^{2} d g^{2}}{2 \, {\left(c^{2} g^{4} h^{2} x + 2 \, a c g^{2} h^{4} x + a^{2} h^{6} x + c^{2} g^{5} h + 2 \, a c g^{3} h^{3} + a^{2} g h^{5}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} c e g^{2}}{2 \, {\left(c^{2} g^{4} h^{2} x^{2} + 2 \, a c g^{2} h^{4} x^{2} + a^{2} h^{6} x^{2} + 2 \, c^{2} g^{5} h x + 4 \, a c g^{3} h^{3} x + 2 \, a^{2} g h^{5} x + c^{2} g^{6} + 2 \, a c g^{4} h^{2} + a^{2} g^{2} h^{4}\right)}} - \frac{\sqrt{c x^{2} + a} c^{2} e g^{2}}{2 \, {\left(c^{2} g^{4} h^{2} + 2 \, a c g^{2} h^{4} + a^{2} h^{6}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} c d g}{2 \, {\left(c^{2} g^{4} h x^{2} + 2 \, a c g^{2} h^{3} x^{2} + a^{2} h^{5} x^{2} + 2 \, c^{2} g^{5} x + 4 \, a c g^{3} h^{2} x + 2 \, a^{2} g h^{4} x + \frac{c^{2} g^{6}}{h} + 2 \, a c g^{4} h + a^{2} g^{2} h^{3}\right)}} + \frac{\sqrt{c x^{2} + a} c^{2} d g}{2 \, {\left(c^{2} g^{4} h + 2 \, a c g^{2} h^{3} + a^{2} h^{5}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} f g^{2}}{3 \, {\left(c g^{2} h^{4} x^{3} + a h^{6} x^{3} + 3 \, c g^{3} h^{3} x^{2} + 3 \, a g h^{5} x^{2} + 3 \, c g^{4} h^{2} x + 3 \, a g^{2} h^{4} x + c g^{5} h + a g^{3} h^{3}\right)}} + \frac{\sqrt{c x^{2} + a} c f g^{2}}{c g^{2} h^{4} x + a h^{6} x + c g^{3} h^{3} + a g h^{5}} + \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} e g}{3 \, {\left(c g^{2} h^{3} x^{3} + a h^{5} x^{3} + 3 \, c g^{3} h^{2} x^{2} + 3 \, a g h^{4} x^{2} + 3 \, c g^{4} h x + 3 \, a g^{2} h^{3} x + c g^{5} + a g^{3} h^{2}\right)}} - \frac{\sqrt{c x^{2} + a} c e g}{2 \, {\left(c g^{2} h^{3} x + a h^{5} x + c g^{3} h^{2} + a g h^{4}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} f g}{c g^{2} h^{3} x^{2} + a h^{5} x^{2} + 2 \, c g^{3} h^{2} x + 2 \, a g h^{4} x + c g^{4} h + a g^{2} h^{3}} - \frac{\sqrt{c x^{2} + a} c f g}{c g^{2} h^{3} + a h^{5}} - \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} d}{3 \, {\left(c g^{2} h^{2} x^{3} + a h^{4} x^{3} + 3 \, c g^{3} h x^{2} + 3 \, a g h^{3} x^{2} + 3 \, c g^{4} x + 3 \, a g^{2} h^{2} x + \frac{c g^{5}}{h} + a g^{3} h\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} e}{2 \, {\left(c g^{2} h^{2} x^{2} + a h^{4} x^{2} + 2 \, c g^{3} h x + 2 \, a g h^{3} x + c g^{4} + a g^{2} h^{2}\right)}} + \frac{\sqrt{c x^{2} + a} c e}{2 \, {\left(c g^{2} h^{2} + a h^{4}\right)}} - \frac{\sqrt{c x^{2} + a} f}{h^{4} x + g h^{3}} + \frac{\sqrt{c} f \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{h^{4}} - \frac{c^{3} f g^{5} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{2 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{5}{2}} h^{9}} + \frac{c^{3} e g^{4} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{2 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{5}{2}} h^{8}} - \frac{c^{3} d g^{3} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{2 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{5}{2}} h^{7}} + \frac{3 \, c^{2} f g^{3} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{2 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{3}{2}} h^{7}} - \frac{c^{2} e g^{2} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{{\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{3}{2}} h^{6}} + \frac{c^{2} d g \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{2 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{3}{2}} h^{5}} - \frac{2 \, c f g \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{\sqrt{a + \frac{c g^{2}}{h^{2}}} h^{5}} + \frac{c e \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{2 \, \sqrt{a + \frac{c g^{2}}{h^{2}}} h^{4}}"," ",0,"-1/2*sqrt(c*x^2 + a)*c^2*f*g^4/(c^2*g^4*h^4*x + 2*a*c*g^2*h^6*x + a^2*h^8*x + c^2*g^5*h^3 + 2*a*c*g^3*h^5 + a^2*g*h^7) + 1/2*sqrt(c*x^2 + a)*c^2*e*g^3/(c^2*g^4*h^3*x + 2*a*c*g^2*h^5*x + a^2*h^7*x + c^2*g^5*h^2 + 2*a*c*g^3*h^4 + a^2*g*h^6) - 1/2*(c*x^2 + a)^(3/2)*c*f*g^3/(c^2*g^4*h^3*x^2 + 2*a*c*g^2*h^5*x^2 + a^2*h^7*x^2 + 2*c^2*g^5*h^2*x + 4*a*c*g^3*h^4*x + 2*a^2*g*h^6*x + c^2*g^6*h + 2*a*c*g^4*h^3 + a^2*g^2*h^5) + 1/2*sqrt(c*x^2 + a)*c^2*f*g^3/(c^2*g^4*h^3 + 2*a*c*g^2*h^5 + a^2*h^7) - 1/2*sqrt(c*x^2 + a)*c^2*d*g^2/(c^2*g^4*h^2*x + 2*a*c*g^2*h^4*x + a^2*h^6*x + c^2*g^5*h + 2*a*c*g^3*h^3 + a^2*g*h^5) + 1/2*(c*x^2 + a)^(3/2)*c*e*g^2/(c^2*g^4*h^2*x^2 + 2*a*c*g^2*h^4*x^2 + a^2*h^6*x^2 + 2*c^2*g^5*h*x + 4*a*c*g^3*h^3*x + 2*a^2*g*h^5*x + c^2*g^6 + 2*a*c*g^4*h^2 + a^2*g^2*h^4) - 1/2*sqrt(c*x^2 + a)*c^2*e*g^2/(c^2*g^4*h^2 + 2*a*c*g^2*h^4 + a^2*h^6) - 1/2*(c*x^2 + a)^(3/2)*c*d*g/(c^2*g^4*h*x^2 + 2*a*c*g^2*h^3*x^2 + a^2*h^5*x^2 + 2*c^2*g^5*x + 4*a*c*g^3*h^2*x + 2*a^2*g*h^4*x + c^2*g^6/h + 2*a*c*g^4*h + a^2*g^2*h^3) + 1/2*sqrt(c*x^2 + a)*c^2*d*g/(c^2*g^4*h + 2*a*c*g^2*h^3 + a^2*h^5) - 1/3*(c*x^2 + a)^(3/2)*f*g^2/(c*g^2*h^4*x^3 + a*h^6*x^3 + 3*c*g^3*h^3*x^2 + 3*a*g*h^5*x^2 + 3*c*g^4*h^2*x + 3*a*g^2*h^4*x + c*g^5*h + a*g^3*h^3) + sqrt(c*x^2 + a)*c*f*g^2/(c*g^2*h^4*x + a*h^6*x + c*g^3*h^3 + a*g*h^5) + 1/3*(c*x^2 + a)^(3/2)*e*g/(c*g^2*h^3*x^3 + a*h^5*x^3 + 3*c*g^3*h^2*x^2 + 3*a*g*h^4*x^2 + 3*c*g^4*h*x + 3*a*g^2*h^3*x + c*g^5 + a*g^3*h^2) - 1/2*sqrt(c*x^2 + a)*c*e*g/(c*g^2*h^3*x + a*h^5*x + c*g^3*h^2 + a*g*h^4) + (c*x^2 + a)^(3/2)*f*g/(c*g^2*h^3*x^2 + a*h^5*x^2 + 2*c*g^3*h^2*x + 2*a*g*h^4*x + c*g^4*h + a*g^2*h^3) - sqrt(c*x^2 + a)*c*f*g/(c*g^2*h^3 + a*h^5) - 1/3*(c*x^2 + a)^(3/2)*d/(c*g^2*h^2*x^3 + a*h^4*x^3 + 3*c*g^3*h*x^2 + 3*a*g*h^3*x^2 + 3*c*g^4*x + 3*a*g^2*h^2*x + c*g^5/h + a*g^3*h) - 1/2*(c*x^2 + a)^(3/2)*e/(c*g^2*h^2*x^2 + a*h^4*x^2 + 2*c*g^3*h*x + 2*a*g*h^3*x + c*g^4 + a*g^2*h^2) + 1/2*sqrt(c*x^2 + a)*c*e/(c*g^2*h^2 + a*h^4) - sqrt(c*x^2 + a)*f/(h^4*x + g*h^3) + sqrt(c)*f*arcsinh(c*x/sqrt(a*c))/h^4 - 1/2*c^3*f*g^5*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(5/2)*h^9) + 1/2*c^3*e*g^4*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(5/2)*h^8) - 1/2*c^3*d*g^3*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(5/2)*h^7) + 3/2*c^2*f*g^3*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(3/2)*h^7) - c^2*e*g^2*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(3/2)*h^6) + 1/2*c^2*d*g*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(3/2)*h^5) - 2*c*f*g*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/(sqrt(a + c*g^2/h^2)*h^5) + 1/2*c*e*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/(sqrt(a + c*g^2/h^2)*h^4)","B",0
86,1,3404,0,1.139514," ","integrate((f*x^2+e*x+d)*(c*x^2+a)^(1/2)/(h*x+g)^5,x, algorithm=""maxima"")","-\frac{5 \, \sqrt{c x^{2} + a} c^{3} f g^{5}}{8 \, {\left(c^{3} g^{6} h^{4} x + 3 \, a c^{2} g^{4} h^{6} x + 3 \, a^{2} c g^{2} h^{8} x + a^{3} h^{10} x + c^{3} g^{7} h^{3} + 3 \, a c^{2} g^{5} h^{5} + 3 \, a^{2} c g^{3} h^{7} + a^{3} g h^{9}\right)}} + \frac{5 \, \sqrt{c x^{2} + a} c^{3} e g^{4}}{8 \, {\left(c^{3} g^{6} h^{3} x + 3 \, a c^{2} g^{4} h^{5} x + 3 \, a^{2} c g^{2} h^{7} x + a^{3} h^{9} x + c^{3} g^{7} h^{2} + 3 \, a c^{2} g^{5} h^{4} + 3 \, a^{2} c g^{3} h^{6} + a^{3} g h^{8}\right)}} - \frac{5 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{2} f g^{4}}{8 \, {\left(c^{3} g^{6} h^{3} x^{2} + 3 \, a c^{2} g^{4} h^{5} x^{2} + 3 \, a^{2} c g^{2} h^{7} x^{2} + a^{3} h^{9} x^{2} + 2 \, c^{3} g^{7} h^{2} x + 6 \, a c^{2} g^{5} h^{4} x + 6 \, a^{2} c g^{3} h^{6} x + 2 \, a^{3} g h^{8} x + c^{3} g^{8} h + 3 \, a c^{2} g^{6} h^{3} + 3 \, a^{2} c g^{4} h^{5} + a^{3} g^{2} h^{7}\right)}} + \frac{5 \, \sqrt{c x^{2} + a} c^{3} f g^{4}}{8 \, {\left(c^{3} g^{6} h^{3} + 3 \, a c^{2} g^{4} h^{5} + 3 \, a^{2} c g^{2} h^{7} + a^{3} h^{9}\right)}} - \frac{5 \, \sqrt{c x^{2} + a} c^{3} d g^{3}}{8 \, {\left(c^{3} g^{6} h^{2} x + 3 \, a c^{2} g^{4} h^{4} x + 3 \, a^{2} c g^{2} h^{6} x + a^{3} h^{8} x + c^{3} g^{7} h + 3 \, a c^{2} g^{5} h^{3} + 3 \, a^{2} c g^{3} h^{5} + a^{3} g h^{7}\right)}} + \frac{5 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{2} e g^{3}}{8 \, {\left(c^{3} g^{6} h^{2} x^{2} + 3 \, a c^{2} g^{4} h^{4} x^{2} + 3 \, a^{2} c g^{2} h^{6} x^{2} + a^{3} h^{8} x^{2} + 2 \, c^{3} g^{7} h x + 6 \, a c^{2} g^{5} h^{3} x + 6 \, a^{2} c g^{3} h^{5} x + 2 \, a^{3} g h^{7} x + c^{3} g^{8} + 3 \, a c^{2} g^{6} h^{2} + 3 \, a^{2} c g^{4} h^{4} + a^{3} g^{2} h^{6}\right)}} - \frac{5 \, \sqrt{c x^{2} + a} c^{3} e g^{3}}{8 \, {\left(c^{3} g^{6} h^{2} + 3 \, a c^{2} g^{4} h^{4} + 3 \, a^{2} c g^{2} h^{6} + a^{3} h^{8}\right)}} - \frac{5 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{2} d g^{2}}{8 \, {\left(c^{3} g^{6} h x^{2} + 3 \, a c^{2} g^{4} h^{3} x^{2} + 3 \, a^{2} c g^{2} h^{5} x^{2} + a^{3} h^{7} x^{2} + 2 \, c^{3} g^{7} x + 6 \, a c^{2} g^{5} h^{2} x + 6 \, a^{2} c g^{3} h^{4} x + 2 \, a^{3} g h^{6} x + \frac{c^{3} g^{8}}{h} + 3 \, a c^{2} g^{6} h + 3 \, a^{2} c g^{4} h^{3} + a^{3} g^{2} h^{5}\right)}} + \frac{5 \, \sqrt{c x^{2} + a} c^{3} d g^{2}}{8 \, {\left(c^{3} g^{6} h + 3 \, a c^{2} g^{4} h^{3} + 3 \, a^{2} c g^{2} h^{5} + a^{3} h^{7}\right)}} - \frac{5 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c f g^{3}}{12 \, {\left(c^{2} g^{4} h^{4} x^{3} + 2 \, a c g^{2} h^{6} x^{3} + a^{2} h^{8} x^{3} + 3 \, c^{2} g^{5} h^{3} x^{2} + 6 \, a c g^{3} h^{5} x^{2} + 3 \, a^{2} g h^{7} x^{2} + 3 \, c^{2} g^{6} h^{2} x + 6 \, a c g^{4} h^{4} x + 3 \, a^{2} g^{2} h^{6} x + c^{2} g^{7} h + 2 \, a c g^{5} h^{3} + a^{2} g^{3} h^{5}\right)}} + \frac{9 \, \sqrt{c x^{2} + a} c^{2} f g^{3}}{8 \, {\left(c^{2} g^{4} h^{4} x + 2 \, a c g^{2} h^{6} x + a^{2} h^{8} x + c^{2} g^{5} h^{3} + 2 \, a c g^{3} h^{5} + a^{2} g h^{7}\right)}} + \frac{5 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c e g^{2}}{12 \, {\left(c^{2} g^{4} h^{3} x^{3} + 2 \, a c g^{2} h^{5} x^{3} + a^{2} h^{7} x^{3} + 3 \, c^{2} g^{5} h^{2} x^{2} + 6 \, a c g^{3} h^{4} x^{2} + 3 \, a^{2} g h^{6} x^{2} + 3 \, c^{2} g^{6} h x + 6 \, a c g^{4} h^{3} x + 3 \, a^{2} g^{2} h^{5} x + c^{2} g^{7} + 2 \, a c g^{5} h^{2} + a^{2} g^{3} h^{4}\right)}} - \frac{5 \, \sqrt{c x^{2} + a} c^{2} e g^{2}}{8 \, {\left(c^{2} g^{4} h^{3} x + 2 \, a c g^{2} h^{5} x + a^{2} h^{7} x + c^{2} g^{5} h^{2} + 2 \, a c g^{3} h^{4} + a^{2} g h^{6}\right)}} + \frac{9 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c f g^{2}}{8 \, {\left(c^{2} g^{4} h^{3} x^{2} + 2 \, a c g^{2} h^{5} x^{2} + a^{2} h^{7} x^{2} + 2 \, c^{2} g^{5} h^{2} x + 4 \, a c g^{3} h^{4} x + 2 \, a^{2} g h^{6} x + c^{2} g^{6} h + 2 \, a c g^{4} h^{3} + a^{2} g^{2} h^{5}\right)}} - \frac{9 \, \sqrt{c x^{2} + a} c^{2} f g^{2}}{8 \, {\left(c^{2} g^{4} h^{3} + 2 \, a c g^{2} h^{5} + a^{2} h^{7}\right)}} - \frac{5 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c d g}{12 \, {\left(c^{2} g^{4} h^{2} x^{3} + 2 \, a c g^{2} h^{4} x^{3} + a^{2} h^{6} x^{3} + 3 \, c^{2} g^{5} h x^{2} + 6 \, a c g^{3} h^{3} x^{2} + 3 \, a^{2} g h^{5} x^{2} + 3 \, c^{2} g^{6} x + 6 \, a c g^{4} h^{2} x + 3 \, a^{2} g^{2} h^{4} x + \frac{c^{2} g^{7}}{h} + 2 \, a c g^{5} h + a^{2} g^{3} h^{3}\right)}} + \frac{\sqrt{c x^{2} + a} c^{2} d g}{8 \, {\left(c^{2} g^{4} h^{2} x + 2 \, a c g^{2} h^{4} x + a^{2} h^{6} x + c^{2} g^{5} h + 2 \, a c g^{3} h^{3} + a^{2} g h^{5}\right)}} - \frac{5 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c e g}{8 \, {\left(c^{2} g^{4} h^{2} x^{2} + 2 \, a c g^{2} h^{4} x^{2} + a^{2} h^{6} x^{2} + 2 \, c^{2} g^{5} h x + 4 \, a c g^{3} h^{3} x + 2 \, a^{2} g h^{5} x + c^{2} g^{6} + 2 \, a c g^{4} h^{2} + a^{2} g^{2} h^{4}\right)}} + \frac{5 \, \sqrt{c x^{2} + a} c^{2} e g}{8 \, {\left(c^{2} g^{4} h^{2} + 2 \, a c g^{2} h^{4} + a^{2} h^{6}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} f g^{2}}{4 \, {\left(c g^{2} h^{5} x^{4} + a h^{7} x^{4} + 4 \, c g^{3} h^{4} x^{3} + 4 \, a g h^{6} x^{3} + 6 \, c g^{4} h^{3} x^{2} + 6 \, a g^{2} h^{5} x^{2} + 4 \, c g^{5} h^{2} x + 4 \, a g^{3} h^{4} x + c g^{6} h + a g^{4} h^{3}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} c d}{8 \, {\left(c^{2} g^{4} h x^{2} + 2 \, a c g^{2} h^{3} x^{2} + a^{2} h^{5} x^{2} + 2 \, c^{2} g^{5} x + 4 \, a c g^{3} h^{2} x + 2 \, a^{2} g h^{4} x + \frac{c^{2} g^{6}}{h} + 2 \, a c g^{4} h + a^{2} g^{2} h^{3}\right)}} - \frac{\sqrt{c x^{2} + a} c^{2} d}{8 \, {\left(c^{2} g^{4} h + 2 \, a c g^{2} h^{3} + a^{2} h^{5}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} e g}{4 \, {\left(c g^{2} h^{4} x^{4} + a h^{6} x^{4} + 4 \, c g^{3} h^{3} x^{3} + 4 \, a g h^{5} x^{3} + 6 \, c g^{4} h^{2} x^{2} + 6 \, a g^{2} h^{4} x^{2} + 4 \, c g^{5} h x + 4 \, a g^{3} h^{3} x + c g^{6} + a g^{4} h^{2}\right)}} + \frac{2 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} f g}{3 \, {\left(c g^{2} h^{4} x^{3} + a h^{6} x^{3} + 3 \, c g^{3} h^{3} x^{2} + 3 \, a g h^{5} x^{2} + 3 \, c g^{4} h^{2} x + 3 \, a g^{2} h^{4} x + c g^{5} h + a g^{3} h^{3}\right)}} - \frac{\sqrt{c x^{2} + a} c f g}{2 \, {\left(c g^{2} h^{4} x + a h^{6} x + c g^{3} h^{3} + a g h^{5}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} d}{4 \, {\left(c g^{2} h^{3} x^{4} + a h^{5} x^{4} + 4 \, c g^{3} h^{2} x^{3} + 4 \, a g h^{4} x^{3} + 6 \, c g^{4} h x^{2} + 6 \, a g^{2} h^{3} x^{2} + 4 \, c g^{5} x + 4 \, a g^{3} h^{2} x + \frac{c g^{6}}{h} + a g^{4} h\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} e}{3 \, {\left(c g^{2} h^{3} x^{3} + a h^{5} x^{3} + 3 \, c g^{3} h^{2} x^{2} + 3 \, a g h^{4} x^{2} + 3 \, c g^{4} h x + 3 \, a g^{2} h^{3} x + c g^{5} + a g^{3} h^{2}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} f}{2 \, {\left(c g^{2} h^{3} x^{2} + a h^{5} x^{2} + 2 \, c g^{3} h^{2} x + 2 \, a g h^{4} x + c g^{4} h + a g^{2} h^{3}\right)}} + \frac{\sqrt{c x^{2} + a} c f}{2 \, {\left(c g^{2} h^{3} + a h^{5}\right)}} - \frac{5 \, c^{4} f g^{6} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{8 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{7}{2}} h^{11}} + \frac{5 \, c^{4} e g^{5} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{8 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{7}{2}} h^{10}} - \frac{5 \, c^{4} d g^{4} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{8 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{7}{2}} h^{9}} + \frac{7 \, c^{3} f g^{4} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{4 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{5}{2}} h^{9}} - \frac{5 \, c^{3} e g^{3} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{4 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{5}{2}} h^{8}} + \frac{3 \, c^{3} d g^{2} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{4 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{5}{2}} h^{7}} - \frac{13 \, c^{2} f g^{2} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{8 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{3}{2}} h^{7}} + \frac{5 \, c^{2} e g \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{8 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{3}{2}} h^{6}} - \frac{c^{2} d \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{8 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{3}{2}} h^{5}} + \frac{c f \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{2 \, \sqrt{a + \frac{c g^{2}}{h^{2}}} h^{5}}"," ",0,"-5/8*sqrt(c*x^2 + a)*c^3*f*g^5/(c^3*g^6*h^4*x + 3*a*c^2*g^4*h^6*x + 3*a^2*c*g^2*h^8*x + a^3*h^10*x + c^3*g^7*h^3 + 3*a*c^2*g^5*h^5 + 3*a^2*c*g^3*h^7 + a^3*g*h^9) + 5/8*sqrt(c*x^2 + a)*c^3*e*g^4/(c^3*g^6*h^3*x + 3*a*c^2*g^4*h^5*x + 3*a^2*c*g^2*h^7*x + a^3*h^9*x + c^3*g^7*h^2 + 3*a*c^2*g^5*h^4 + 3*a^2*c*g^3*h^6 + a^3*g*h^8) - 5/8*(c*x^2 + a)^(3/2)*c^2*f*g^4/(c^3*g^6*h^3*x^2 + 3*a*c^2*g^4*h^5*x^2 + 3*a^2*c*g^2*h^7*x^2 + a^3*h^9*x^2 + 2*c^3*g^7*h^2*x + 6*a*c^2*g^5*h^4*x + 6*a^2*c*g^3*h^6*x + 2*a^3*g*h^8*x + c^3*g^8*h + 3*a*c^2*g^6*h^3 + 3*a^2*c*g^4*h^5 + a^3*g^2*h^7) + 5/8*sqrt(c*x^2 + a)*c^3*f*g^4/(c^3*g^6*h^3 + 3*a*c^2*g^4*h^5 + 3*a^2*c*g^2*h^7 + a^3*h^9) - 5/8*sqrt(c*x^2 + a)*c^3*d*g^3/(c^3*g^6*h^2*x + 3*a*c^2*g^4*h^4*x + 3*a^2*c*g^2*h^6*x + a^3*h^8*x + c^3*g^7*h + 3*a*c^2*g^5*h^3 + 3*a^2*c*g^3*h^5 + a^3*g*h^7) + 5/8*(c*x^2 + a)^(3/2)*c^2*e*g^3/(c^3*g^6*h^2*x^2 + 3*a*c^2*g^4*h^4*x^2 + 3*a^2*c*g^2*h^6*x^2 + a^3*h^8*x^2 + 2*c^3*g^7*h*x + 6*a*c^2*g^5*h^3*x + 6*a^2*c*g^3*h^5*x + 2*a^3*g*h^7*x + c^3*g^8 + 3*a*c^2*g^6*h^2 + 3*a^2*c*g^4*h^4 + a^3*g^2*h^6) - 5/8*sqrt(c*x^2 + a)*c^3*e*g^3/(c^3*g^6*h^2 + 3*a*c^2*g^4*h^4 + 3*a^2*c*g^2*h^6 + a^3*h^8) - 5/8*(c*x^2 + a)^(3/2)*c^2*d*g^2/(c^3*g^6*h*x^2 + 3*a*c^2*g^4*h^3*x^2 + 3*a^2*c*g^2*h^5*x^2 + a^3*h^7*x^2 + 2*c^3*g^7*x + 6*a*c^2*g^5*h^2*x + 6*a^2*c*g^3*h^4*x + 2*a^3*g*h^6*x + c^3*g^8/h + 3*a*c^2*g^6*h + 3*a^2*c*g^4*h^3 + a^3*g^2*h^5) + 5/8*sqrt(c*x^2 + a)*c^3*d*g^2/(c^3*g^6*h + 3*a*c^2*g^4*h^3 + 3*a^2*c*g^2*h^5 + a^3*h^7) - 5/12*(c*x^2 + a)^(3/2)*c*f*g^3/(c^2*g^4*h^4*x^3 + 2*a*c*g^2*h^6*x^3 + a^2*h^8*x^3 + 3*c^2*g^5*h^3*x^2 + 6*a*c*g^3*h^5*x^2 + 3*a^2*g*h^7*x^2 + 3*c^2*g^6*h^2*x + 6*a*c*g^4*h^4*x + 3*a^2*g^2*h^6*x + c^2*g^7*h + 2*a*c*g^5*h^3 + a^2*g^3*h^5) + 9/8*sqrt(c*x^2 + a)*c^2*f*g^3/(c^2*g^4*h^4*x + 2*a*c*g^2*h^6*x + a^2*h^8*x + c^2*g^5*h^3 + 2*a*c*g^3*h^5 + a^2*g*h^7) + 5/12*(c*x^2 + a)^(3/2)*c*e*g^2/(c^2*g^4*h^3*x^3 + 2*a*c*g^2*h^5*x^3 + a^2*h^7*x^3 + 3*c^2*g^5*h^2*x^2 + 6*a*c*g^3*h^4*x^2 + 3*a^2*g*h^6*x^2 + 3*c^2*g^6*h*x + 6*a*c*g^4*h^3*x + 3*a^2*g^2*h^5*x + c^2*g^7 + 2*a*c*g^5*h^2 + a^2*g^3*h^4) - 5/8*sqrt(c*x^2 + a)*c^2*e*g^2/(c^2*g^4*h^3*x + 2*a*c*g^2*h^5*x + a^2*h^7*x + c^2*g^5*h^2 + 2*a*c*g^3*h^4 + a^2*g*h^6) + 9/8*(c*x^2 + a)^(3/2)*c*f*g^2/(c^2*g^4*h^3*x^2 + 2*a*c*g^2*h^5*x^2 + a^2*h^7*x^2 + 2*c^2*g^5*h^2*x + 4*a*c*g^3*h^4*x + 2*a^2*g*h^6*x + c^2*g^6*h + 2*a*c*g^4*h^3 + a^2*g^2*h^5) - 9/8*sqrt(c*x^2 + a)*c^2*f*g^2/(c^2*g^4*h^3 + 2*a*c*g^2*h^5 + a^2*h^7) - 5/12*(c*x^2 + a)^(3/2)*c*d*g/(c^2*g^4*h^2*x^3 + 2*a*c*g^2*h^4*x^3 + a^2*h^6*x^3 + 3*c^2*g^5*h*x^2 + 6*a*c*g^3*h^3*x^2 + 3*a^2*g*h^5*x^2 + 3*c^2*g^6*x + 6*a*c*g^4*h^2*x + 3*a^2*g^2*h^4*x + c^2*g^7/h + 2*a*c*g^5*h + a^2*g^3*h^3) + 1/8*sqrt(c*x^2 + a)*c^2*d*g/(c^2*g^4*h^2*x + 2*a*c*g^2*h^4*x + a^2*h^6*x + c^2*g^5*h + 2*a*c*g^3*h^3 + a^2*g*h^5) - 5/8*(c*x^2 + a)^(3/2)*c*e*g/(c^2*g^4*h^2*x^2 + 2*a*c*g^2*h^4*x^2 + a^2*h^6*x^2 + 2*c^2*g^5*h*x + 4*a*c*g^3*h^3*x + 2*a^2*g*h^5*x + c^2*g^6 + 2*a*c*g^4*h^2 + a^2*g^2*h^4) + 5/8*sqrt(c*x^2 + a)*c^2*e*g/(c^2*g^4*h^2 + 2*a*c*g^2*h^4 + a^2*h^6) - 1/4*(c*x^2 + a)^(3/2)*f*g^2/(c*g^2*h^5*x^4 + a*h^7*x^4 + 4*c*g^3*h^4*x^3 + 4*a*g*h^6*x^3 + 6*c*g^4*h^3*x^2 + 6*a*g^2*h^5*x^2 + 4*c*g^5*h^2*x + 4*a*g^3*h^4*x + c*g^6*h + a*g^4*h^3) + 1/8*(c*x^2 + a)^(3/2)*c*d/(c^2*g^4*h*x^2 + 2*a*c*g^2*h^3*x^2 + a^2*h^5*x^2 + 2*c^2*g^5*x + 4*a*c*g^3*h^2*x + 2*a^2*g*h^4*x + c^2*g^6/h + 2*a*c*g^4*h + a^2*g^2*h^3) - 1/8*sqrt(c*x^2 + a)*c^2*d/(c^2*g^4*h + 2*a*c*g^2*h^3 + a^2*h^5) + 1/4*(c*x^2 + a)^(3/2)*e*g/(c*g^2*h^4*x^4 + a*h^6*x^4 + 4*c*g^3*h^3*x^3 + 4*a*g*h^5*x^3 + 6*c*g^4*h^2*x^2 + 6*a*g^2*h^4*x^2 + 4*c*g^5*h*x + 4*a*g^3*h^3*x + c*g^6 + a*g^4*h^2) + 2/3*(c*x^2 + a)^(3/2)*f*g/(c*g^2*h^4*x^3 + a*h^6*x^3 + 3*c*g^3*h^3*x^2 + 3*a*g*h^5*x^2 + 3*c*g^4*h^2*x + 3*a*g^2*h^4*x + c*g^5*h + a*g^3*h^3) - 1/2*sqrt(c*x^2 + a)*c*f*g/(c*g^2*h^4*x + a*h^6*x + c*g^3*h^3 + a*g*h^5) - 1/4*(c*x^2 + a)^(3/2)*d/(c*g^2*h^3*x^4 + a*h^5*x^4 + 4*c*g^3*h^2*x^3 + 4*a*g*h^4*x^3 + 6*c*g^4*h*x^2 + 6*a*g^2*h^3*x^2 + 4*c*g^5*x + 4*a*g^3*h^2*x + c*g^6/h + a*g^4*h) - 1/3*(c*x^2 + a)^(3/2)*e/(c*g^2*h^3*x^3 + a*h^5*x^3 + 3*c*g^3*h^2*x^2 + 3*a*g*h^4*x^2 + 3*c*g^4*h*x + 3*a*g^2*h^3*x + c*g^5 + a*g^3*h^2) - 1/2*(c*x^2 + a)^(3/2)*f/(c*g^2*h^3*x^2 + a*h^5*x^2 + 2*c*g^3*h^2*x + 2*a*g*h^4*x + c*g^4*h + a*g^2*h^3) + 1/2*sqrt(c*x^2 + a)*c*f/(c*g^2*h^3 + a*h^5) - 5/8*c^4*f*g^6*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(7/2)*h^11) + 5/8*c^4*e*g^5*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(7/2)*h^10) - 5/8*c^4*d*g^4*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(7/2)*h^9) + 7/4*c^3*f*g^4*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(5/2)*h^9) - 5/4*c^3*e*g^3*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(5/2)*h^8) + 3/4*c^3*d*g^2*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(5/2)*h^7) - 13/8*c^2*f*g^2*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(3/2)*h^7) + 5/8*c^2*e*g*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(3/2)*h^6) - 1/8*c^2*d*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(3/2)*h^5) + 1/2*c*f*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/(sqrt(a + c*g^2/h^2)*h^5)","B",0
87,1,5793,0,1.525467," ","integrate((f*x^2+e*x+d)*(c*x^2+a)^(1/2)/(h*x+g)^6,x, algorithm=""maxima"")","-\frac{7 \, \sqrt{c x^{2} + a} c^{4} f g^{6}}{8 \, {\left(c^{4} g^{8} h^{4} x + 4 \, a c^{3} g^{6} h^{6} x + 6 \, a^{2} c^{2} g^{4} h^{8} x + 4 \, a^{3} c g^{2} h^{10} x + a^{4} h^{12} x + c^{4} g^{9} h^{3} + 4 \, a c^{3} g^{7} h^{5} + 6 \, a^{2} c^{2} g^{5} h^{7} + 4 \, a^{3} c g^{3} h^{9} + a^{4} g h^{11}\right)}} + \frac{7 \, \sqrt{c x^{2} + a} c^{4} e g^{5}}{8 \, {\left(c^{4} g^{8} h^{3} x + 4 \, a c^{3} g^{6} h^{5} x + 6 \, a^{2} c^{2} g^{4} h^{7} x + 4 \, a^{3} c g^{2} h^{9} x + a^{4} h^{11} x + c^{4} g^{9} h^{2} + 4 \, a c^{3} g^{7} h^{4} + 6 \, a^{2} c^{2} g^{5} h^{6} + 4 \, a^{3} c g^{3} h^{8} + a^{4} g h^{10}\right)}} - \frac{7 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{3} f g^{5}}{8 \, {\left(c^{4} g^{8} h^{3} x^{2} + 4 \, a c^{3} g^{6} h^{5} x^{2} + 6 \, a^{2} c^{2} g^{4} h^{7} x^{2} + 4 \, a^{3} c g^{2} h^{9} x^{2} + a^{4} h^{11} x^{2} + 2 \, c^{4} g^{9} h^{2} x + 8 \, a c^{3} g^{7} h^{4} x + 12 \, a^{2} c^{2} g^{5} h^{6} x + 8 \, a^{3} c g^{3} h^{8} x + 2 \, a^{4} g h^{10} x + c^{4} g^{10} h + 4 \, a c^{3} g^{8} h^{3} + 6 \, a^{2} c^{2} g^{6} h^{5} + 4 \, a^{3} c g^{4} h^{7} + a^{4} g^{2} h^{9}\right)}} + \frac{7 \, \sqrt{c x^{2} + a} c^{4} f g^{5}}{8 \, {\left(c^{4} g^{8} h^{3} + 4 \, a c^{3} g^{6} h^{5} + 6 \, a^{2} c^{2} g^{4} h^{7} + 4 \, a^{3} c g^{2} h^{9} + a^{4} h^{11}\right)}} - \frac{7 \, \sqrt{c x^{2} + a} c^{4} d g^{4}}{8 \, {\left(c^{4} g^{8} h^{2} x + 4 \, a c^{3} g^{6} h^{4} x + 6 \, a^{2} c^{2} g^{4} h^{6} x + 4 \, a^{3} c g^{2} h^{8} x + a^{4} h^{10} x + c^{4} g^{9} h + 4 \, a c^{3} g^{7} h^{3} + 6 \, a^{2} c^{2} g^{5} h^{5} + 4 \, a^{3} c g^{3} h^{7} + a^{4} g h^{9}\right)}} + \frac{7 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{3} e g^{4}}{8 \, {\left(c^{4} g^{8} h^{2} x^{2} + 4 \, a c^{3} g^{6} h^{4} x^{2} + 6 \, a^{2} c^{2} g^{4} h^{6} x^{2} + 4 \, a^{3} c g^{2} h^{8} x^{2} + a^{4} h^{10} x^{2} + 2 \, c^{4} g^{9} h x + 8 \, a c^{3} g^{7} h^{3} x + 12 \, a^{2} c^{2} g^{5} h^{5} x + 8 \, a^{3} c g^{3} h^{7} x + 2 \, a^{4} g h^{9} x + c^{4} g^{10} + 4 \, a c^{3} g^{8} h^{2} + 6 \, a^{2} c^{2} g^{6} h^{4} + 4 \, a^{3} c g^{4} h^{6} + a^{4} g^{2} h^{8}\right)}} - \frac{7 \, \sqrt{c x^{2} + a} c^{4} e g^{4}}{8 \, {\left(c^{4} g^{8} h^{2} + 4 \, a c^{3} g^{6} h^{4} + 6 \, a^{2} c^{2} g^{4} h^{6} + 4 \, a^{3} c g^{2} h^{8} + a^{4} h^{10}\right)}} - \frac{7 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{3} d g^{3}}{8 \, {\left(c^{4} g^{8} h x^{2} + 4 \, a c^{3} g^{6} h^{3} x^{2} + 6 \, a^{2} c^{2} g^{4} h^{5} x^{2} + 4 \, a^{3} c g^{2} h^{7} x^{2} + a^{4} h^{9} x^{2} + 2 \, c^{4} g^{9} x + 8 \, a c^{3} g^{7} h^{2} x + 12 \, a^{2} c^{2} g^{5} h^{4} x + 8 \, a^{3} c g^{3} h^{6} x + 2 \, a^{4} g h^{8} x + \frac{c^{4} g^{10}}{h} + 4 \, a c^{3} g^{8} h + 6 \, a^{2} c^{2} g^{6} h^{3} + 4 \, a^{3} c g^{4} h^{5} + a^{4} g^{2} h^{7}\right)}} + \frac{7 \, \sqrt{c x^{2} + a} c^{4} d g^{3}}{8 \, {\left(c^{4} g^{8} h + 4 \, a c^{3} g^{6} h^{3} + 6 \, a^{2} c^{2} g^{4} h^{5} + 4 \, a^{3} c g^{2} h^{7} + a^{4} h^{9}\right)}} - \frac{7 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{2} f g^{4}}{12 \, {\left(c^{3} g^{6} h^{4} x^{3} + 3 \, a c^{2} g^{4} h^{6} x^{3} + 3 \, a^{2} c g^{2} h^{8} x^{3} + a^{3} h^{10} x^{3} + 3 \, c^{3} g^{7} h^{3} x^{2} + 9 \, a c^{2} g^{5} h^{5} x^{2} + 9 \, a^{2} c g^{3} h^{7} x^{2} + 3 \, a^{3} g h^{9} x^{2} + 3 \, c^{3} g^{8} h^{2} x + 9 \, a c^{2} g^{6} h^{4} x + 9 \, a^{2} c g^{4} h^{6} x + 3 \, a^{3} g^{2} h^{8} x + c^{3} g^{9} h + 3 \, a c^{2} g^{7} h^{3} + 3 \, a^{2} c g^{5} h^{5} + a^{3} g^{3} h^{7}\right)}} + \frac{13 \, \sqrt{c x^{2} + a} c^{3} f g^{4}}{8 \, {\left(c^{3} g^{6} h^{4} x + 3 \, a c^{2} g^{4} h^{6} x + 3 \, a^{2} c g^{2} h^{8} x + a^{3} h^{10} x + c^{3} g^{7} h^{3} + 3 \, a c^{2} g^{5} h^{5} + 3 \, a^{2} c g^{3} h^{7} + a^{3} g h^{9}\right)}} + \frac{7 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{2} e g^{3}}{12 \, {\left(c^{3} g^{6} h^{3} x^{3} + 3 \, a c^{2} g^{4} h^{5} x^{3} + 3 \, a^{2} c g^{2} h^{7} x^{3} + a^{3} h^{9} x^{3} + 3 \, c^{3} g^{7} h^{2} x^{2} + 9 \, a c^{2} g^{5} h^{4} x^{2} + 9 \, a^{2} c g^{3} h^{6} x^{2} + 3 \, a^{3} g h^{8} x^{2} + 3 \, c^{3} g^{8} h x + 9 \, a c^{2} g^{6} h^{3} x + 9 \, a^{2} c g^{4} h^{5} x + 3 \, a^{3} g^{2} h^{7} x + c^{3} g^{9} + 3 \, a c^{2} g^{7} h^{2} + 3 \, a^{2} c g^{5} h^{4} + a^{3} g^{3} h^{6}\right)}} - \frac{\sqrt{c x^{2} + a} c^{3} e g^{3}}{c^{3} g^{6} h^{3} x + 3 \, a c^{2} g^{4} h^{5} x + 3 \, a^{2} c g^{2} h^{7} x + a^{3} h^{9} x + c^{3} g^{7} h^{2} + 3 \, a c^{2} g^{5} h^{4} + 3 \, a^{2} c g^{3} h^{6} + a^{3} g h^{8}} + \frac{13 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{2} f g^{3}}{8 \, {\left(c^{3} g^{6} h^{3} x^{2} + 3 \, a c^{2} g^{4} h^{5} x^{2} + 3 \, a^{2} c g^{2} h^{7} x^{2} + a^{3} h^{9} x^{2} + 2 \, c^{3} g^{7} h^{2} x + 6 \, a c^{2} g^{5} h^{4} x + 6 \, a^{2} c g^{3} h^{6} x + 2 \, a^{3} g h^{8} x + c^{3} g^{8} h + 3 \, a c^{2} g^{6} h^{3} + 3 \, a^{2} c g^{4} h^{5} + a^{3} g^{2} h^{7}\right)}} - \frac{13 \, \sqrt{c x^{2} + a} c^{3} f g^{3}}{8 \, {\left(c^{3} g^{6} h^{3} + 3 \, a c^{2} g^{4} h^{5} + 3 \, a^{2} c g^{2} h^{7} + a^{3} h^{9}\right)}} - \frac{7 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{2} d g^{2}}{12 \, {\left(c^{3} g^{6} h^{2} x^{3} + 3 \, a c^{2} g^{4} h^{4} x^{3} + 3 \, a^{2} c g^{2} h^{6} x^{3} + a^{3} h^{8} x^{3} + 3 \, c^{3} g^{7} h x^{2} + 9 \, a c^{2} g^{5} h^{3} x^{2} + 9 \, a^{2} c g^{3} h^{5} x^{2} + 3 \, a^{3} g h^{7} x^{2} + 3 \, c^{3} g^{8} x + 9 \, a c^{2} g^{6} h^{2} x + 9 \, a^{2} c g^{4} h^{4} x + 3 \, a^{3} g^{2} h^{6} x + \frac{c^{3} g^{9}}{h} + 3 \, a c^{2} g^{7} h + 3 \, a^{2} c g^{5} h^{3} + a^{3} g^{3} h^{5}\right)}} + \frac{3 \, \sqrt{c x^{2} + a} c^{3} d g^{2}}{8 \, {\left(c^{3} g^{6} h^{2} x + 3 \, a c^{2} g^{4} h^{4} x + 3 \, a^{2} c g^{2} h^{6} x + a^{3} h^{8} x + c^{3} g^{7} h + 3 \, a c^{2} g^{5} h^{3} + 3 \, a^{2} c g^{3} h^{5} + a^{3} g h^{7}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{2} e g^{2}}{c^{3} g^{6} h^{2} x^{2} + 3 \, a c^{2} g^{4} h^{4} x^{2} + 3 \, a^{2} c g^{2} h^{6} x^{2} + a^{3} h^{8} x^{2} + 2 \, c^{3} g^{7} h x + 6 \, a c^{2} g^{5} h^{3} x + 6 \, a^{2} c g^{3} h^{5} x + 2 \, a^{3} g h^{7} x + c^{3} g^{8} + 3 \, a c^{2} g^{6} h^{2} + 3 \, a^{2} c g^{4} h^{4} + a^{3} g^{2} h^{6}} + \frac{\sqrt{c x^{2} + a} c^{3} e g^{2}}{c^{3} g^{6} h^{2} + 3 \, a c^{2} g^{4} h^{4} + 3 \, a^{2} c g^{2} h^{6} + a^{3} h^{8}} - \frac{7 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c f g^{3}}{20 \, {\left(c^{2} g^{4} h^{5} x^{4} + 2 \, a c g^{2} h^{7} x^{4} + a^{2} h^{9} x^{4} + 4 \, c^{2} g^{5} h^{4} x^{3} + 8 \, a c g^{3} h^{6} x^{3} + 4 \, a^{2} g h^{8} x^{3} + 6 \, c^{2} g^{6} h^{3} x^{2} + 12 \, a c g^{4} h^{5} x^{2} + 6 \, a^{2} g^{2} h^{7} x^{2} + 4 \, c^{2} g^{7} h^{2} x + 8 \, a c g^{5} h^{4} x + 4 \, a^{2} g^{3} h^{6} x + c^{2} g^{8} h + 2 \, a c g^{6} h^{3} + a^{2} g^{4} h^{5}\right)}} + \frac{3 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{2} d g}{8 \, {\left(c^{3} g^{6} h x^{2} + 3 \, a c^{2} g^{4} h^{3} x^{2} + 3 \, a^{2} c g^{2} h^{5} x^{2} + a^{3} h^{7} x^{2} + 2 \, c^{3} g^{7} x + 6 \, a c^{2} g^{5} h^{2} x + 6 \, a^{2} c g^{3} h^{4} x + 2 \, a^{3} g h^{6} x + \frac{c^{3} g^{8}}{h} + 3 \, a c^{2} g^{6} h + 3 \, a^{2} c g^{4} h^{3} + a^{3} g^{2} h^{5}\right)}} - \frac{3 \, \sqrt{c x^{2} + a} c^{3} d g}{8 \, {\left(c^{3} g^{6} h + 3 \, a c^{2} g^{4} h^{3} + 3 \, a^{2} c g^{2} h^{5} + a^{3} h^{7}\right)}} + \frac{7 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c e g^{2}}{20 \, {\left(c^{2} g^{4} h^{4} x^{4} + 2 \, a c g^{2} h^{6} x^{4} + a^{2} h^{8} x^{4} + 4 \, c^{2} g^{5} h^{3} x^{3} + 8 \, a c g^{3} h^{5} x^{3} + 4 \, a^{2} g h^{7} x^{3} + 6 \, c^{2} g^{6} h^{2} x^{2} + 12 \, a c g^{4} h^{4} x^{2} + 6 \, a^{2} g^{2} h^{6} x^{2} + 4 \, c^{2} g^{7} h x + 8 \, a c g^{5} h^{3} x + 4 \, a^{2} g^{3} h^{5} x + c^{2} g^{8} + 2 \, a c g^{6} h^{2} + a^{2} g^{4} h^{4}\right)}} + \frac{29 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c f g^{2}}{30 \, {\left(c^{2} g^{4} h^{4} x^{3} + 2 \, a c g^{2} h^{6} x^{3} + a^{2} h^{8} x^{3} + 3 \, c^{2} g^{5} h^{3} x^{2} + 6 \, a c g^{3} h^{5} x^{2} + 3 \, a^{2} g h^{7} x^{2} + 3 \, c^{2} g^{6} h^{2} x + 6 \, a c g^{4} h^{4} x + 3 \, a^{2} g^{2} h^{6} x + c^{2} g^{7} h + 2 \, a c g^{5} h^{3} + a^{2} g^{3} h^{5}\right)}} - \frac{3 \, \sqrt{c x^{2} + a} c^{2} f g^{2}}{4 \, {\left(c^{2} g^{4} h^{4} x + 2 \, a c g^{2} h^{6} x + a^{2} h^{8} x + c^{2} g^{5} h^{3} + 2 \, a c g^{3} h^{5} + a^{2} g h^{7}\right)}} - \frac{7 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c d g}{20 \, {\left(c^{2} g^{4} h^{3} x^{4} + 2 \, a c g^{2} h^{5} x^{4} + a^{2} h^{7} x^{4} + 4 \, c^{2} g^{5} h^{2} x^{3} + 8 \, a c g^{3} h^{4} x^{3} + 4 \, a^{2} g h^{6} x^{3} + 6 \, c^{2} g^{6} h x^{2} + 12 \, a c g^{4} h^{3} x^{2} + 6 \, a^{2} g^{2} h^{5} x^{2} + 4 \, c^{2} g^{7} x + 8 \, a c g^{5} h^{2} x + 4 \, a^{2} g^{3} h^{4} x + \frac{c^{2} g^{8}}{h} + 2 \, a c g^{6} h + a^{2} g^{4} h^{3}\right)}} - \frac{11 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c e g}{20 \, {\left(c^{2} g^{4} h^{3} x^{3} + 2 \, a c g^{2} h^{5} x^{3} + a^{2} h^{7} x^{3} + 3 \, c^{2} g^{5} h^{2} x^{2} + 6 \, a c g^{3} h^{4} x^{2} + 3 \, a^{2} g h^{6} x^{2} + 3 \, c^{2} g^{6} h x + 6 \, a c g^{4} h^{3} x + 3 \, a^{2} g^{2} h^{5} x + c^{2} g^{7} + 2 \, a c g^{5} h^{2} + a^{2} g^{3} h^{4}\right)}} + \frac{\sqrt{c x^{2} + a} c^{2} e g}{8 \, {\left(c^{2} g^{4} h^{3} x + 2 \, a c g^{2} h^{5} x + a^{2} h^{7} x + c^{2} g^{5} h^{2} + 2 \, a c g^{3} h^{4} + a^{2} g h^{6}\right)}} - \frac{3 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c f g}{4 \, {\left(c^{2} g^{4} h^{3} x^{2} + 2 \, a c g^{2} h^{5} x^{2} + a^{2} h^{7} x^{2} + 2 \, c^{2} g^{5} h^{2} x + 4 \, a c g^{3} h^{4} x + 2 \, a^{2} g h^{6} x + c^{2} g^{6} h + 2 \, a c g^{4} h^{3} + a^{2} g^{2} h^{5}\right)}} + \frac{3 \, \sqrt{c x^{2} + a} c^{2} f g}{4 \, {\left(c^{2} g^{4} h^{3} + 2 \, a c g^{2} h^{5} + a^{2} h^{7}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} f g^{2}}{5 \, {\left(c g^{2} h^{6} x^{5} + a h^{8} x^{5} + 5 \, c g^{3} h^{5} x^{4} + 5 \, a g h^{7} x^{4} + 10 \, c g^{4} h^{4} x^{3} + 10 \, a g^{2} h^{6} x^{3} + 10 \, c g^{5} h^{3} x^{2} + 10 \, a g^{3} h^{5} x^{2} + 5 \, c g^{6} h^{2} x + 5 \, a g^{4} h^{4} x + c g^{7} h + a g^{5} h^{3}\right)}} + \frac{2 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c d}{15 \, {\left(c^{2} g^{4} h^{2} x^{3} + 2 \, a c g^{2} h^{4} x^{3} + a^{2} h^{6} x^{3} + 3 \, c^{2} g^{5} h x^{2} + 6 \, a c g^{3} h^{3} x^{2} + 3 \, a^{2} g h^{5} x^{2} + 3 \, c^{2} g^{6} x + 6 \, a c g^{4} h^{2} x + 3 \, a^{2} g^{2} h^{4} x + \frac{c^{2} g^{7}}{h} + 2 \, a c g^{5} h + a^{2} g^{3} h^{3}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} c e}{8 \, {\left(c^{2} g^{4} h^{2} x^{2} + 2 \, a c g^{2} h^{4} x^{2} + a^{2} h^{6} x^{2} + 2 \, c^{2} g^{5} h x + 4 \, a c g^{3} h^{3} x + 2 \, a^{2} g h^{5} x + c^{2} g^{6} + 2 \, a c g^{4} h^{2} + a^{2} g^{2} h^{4}\right)}} - \frac{\sqrt{c x^{2} + a} c^{2} e}{8 \, {\left(c^{2} g^{4} h^{2} + 2 \, a c g^{2} h^{4} + a^{2} h^{6}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} e g}{5 \, {\left(c g^{2} h^{5} x^{5} + a h^{7} x^{5} + 5 \, c g^{3} h^{4} x^{4} + 5 \, a g h^{6} x^{4} + 10 \, c g^{4} h^{3} x^{3} + 10 \, a g^{2} h^{5} x^{3} + 10 \, c g^{5} h^{2} x^{2} + 10 \, a g^{3} h^{4} x^{2} + 5 \, c g^{6} h x + 5 \, a g^{4} h^{3} x + c g^{7} + a g^{5} h^{2}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} f g}{2 \, {\left(c g^{2} h^{5} x^{4} + a h^{7} x^{4} + 4 \, c g^{3} h^{4} x^{3} + 4 \, a g h^{6} x^{3} + 6 \, c g^{4} h^{3} x^{2} + 6 \, a g^{2} h^{5} x^{2} + 4 \, c g^{5} h^{2} x + 4 \, a g^{3} h^{4} x + c g^{6} h + a g^{4} h^{3}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} d}{5 \, {\left(c g^{2} h^{4} x^{5} + a h^{6} x^{5} + 5 \, c g^{3} h^{3} x^{4} + 5 \, a g h^{5} x^{4} + 10 \, c g^{4} h^{2} x^{3} + 10 \, a g^{2} h^{4} x^{3} + 10 \, c g^{5} h x^{2} + 10 \, a g^{3} h^{3} x^{2} + 5 \, c g^{6} x + 5 \, a g^{4} h^{2} x + \frac{c g^{7}}{h} + a g^{5} h\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} e}{4 \, {\left(c g^{2} h^{4} x^{4} + a h^{6} x^{4} + 4 \, c g^{3} h^{3} x^{3} + 4 \, a g h^{5} x^{3} + 6 \, c g^{4} h^{2} x^{2} + 6 \, a g^{2} h^{4} x^{2} + 4 \, c g^{5} h x + 4 \, a g^{3} h^{3} x + c g^{6} + a g^{4} h^{2}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} f}{3 \, {\left(c g^{2} h^{4} x^{3} + a h^{6} x^{3} + 3 \, c g^{3} h^{3} x^{2} + 3 \, a g h^{5} x^{2} + 3 \, c g^{4} h^{2} x + 3 \, a g^{2} h^{4} x + c g^{5} h + a g^{3} h^{3}\right)}} - \frac{7 \, c^{5} f g^{7} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{8 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{9}{2}} h^{13}} + \frac{7 \, c^{5} e g^{6} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{8 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{9}{2}} h^{12}} - \frac{7 \, c^{5} d g^{5} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{8 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{9}{2}} h^{11}} + \frac{5 \, c^{4} f g^{5} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{2 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{7}{2}} h^{11}} - \frac{15 \, c^{4} e g^{4} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{8 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{7}{2}} h^{10}} + \frac{5 \, c^{4} d g^{3} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{4 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{7}{2}} h^{9}} - \frac{19 \, c^{3} f g^{3} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{8 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{5}{2}} h^{9}} + \frac{9 \, c^{3} e g^{2} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{8 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{5}{2}} h^{8}} - \frac{3 \, c^{3} d g \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{8 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{5}{2}} h^{7}} + \frac{3 \, c^{2} f g \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{4 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{3}{2}} h^{7}} - \frac{c^{2} e \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{8 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{3}{2}} h^{6}}"," ",0,"-7/8*sqrt(c*x^2 + a)*c^4*f*g^6/(c^4*g^8*h^4*x + 4*a*c^3*g^6*h^6*x + 6*a^2*c^2*g^4*h^8*x + 4*a^3*c*g^2*h^10*x + a^4*h^12*x + c^4*g^9*h^3 + 4*a*c^3*g^7*h^5 + 6*a^2*c^2*g^5*h^7 + 4*a^3*c*g^3*h^9 + a^4*g*h^11) + 7/8*sqrt(c*x^2 + a)*c^4*e*g^5/(c^4*g^8*h^3*x + 4*a*c^3*g^6*h^5*x + 6*a^2*c^2*g^4*h^7*x + 4*a^3*c*g^2*h^9*x + a^4*h^11*x + c^4*g^9*h^2 + 4*a*c^3*g^7*h^4 + 6*a^2*c^2*g^5*h^6 + 4*a^3*c*g^3*h^8 + a^4*g*h^10) - 7/8*(c*x^2 + a)^(3/2)*c^3*f*g^5/(c^4*g^8*h^3*x^2 + 4*a*c^3*g^6*h^5*x^2 + 6*a^2*c^2*g^4*h^7*x^2 + 4*a^3*c*g^2*h^9*x^2 + a^4*h^11*x^2 + 2*c^4*g^9*h^2*x + 8*a*c^3*g^7*h^4*x + 12*a^2*c^2*g^5*h^6*x + 8*a^3*c*g^3*h^8*x + 2*a^4*g*h^10*x + c^4*g^10*h + 4*a*c^3*g^8*h^3 + 6*a^2*c^2*g^6*h^5 + 4*a^3*c*g^4*h^7 + a^4*g^2*h^9) + 7/8*sqrt(c*x^2 + a)*c^4*f*g^5/(c^4*g^8*h^3 + 4*a*c^3*g^6*h^5 + 6*a^2*c^2*g^4*h^7 + 4*a^3*c*g^2*h^9 + a^4*h^11) - 7/8*sqrt(c*x^2 + a)*c^4*d*g^4/(c^4*g^8*h^2*x + 4*a*c^3*g^6*h^4*x + 6*a^2*c^2*g^4*h^6*x + 4*a^3*c*g^2*h^8*x + a^4*h^10*x + c^4*g^9*h + 4*a*c^3*g^7*h^3 + 6*a^2*c^2*g^5*h^5 + 4*a^3*c*g^3*h^7 + a^4*g*h^9) + 7/8*(c*x^2 + a)^(3/2)*c^3*e*g^4/(c^4*g^8*h^2*x^2 + 4*a*c^3*g^6*h^4*x^2 + 6*a^2*c^2*g^4*h^6*x^2 + 4*a^3*c*g^2*h^8*x^2 + a^4*h^10*x^2 + 2*c^4*g^9*h*x + 8*a*c^3*g^7*h^3*x + 12*a^2*c^2*g^5*h^5*x + 8*a^3*c*g^3*h^7*x + 2*a^4*g*h^9*x + c^4*g^10 + 4*a*c^3*g^8*h^2 + 6*a^2*c^2*g^6*h^4 + 4*a^3*c*g^4*h^6 + a^4*g^2*h^8) - 7/8*sqrt(c*x^2 + a)*c^4*e*g^4/(c^4*g^8*h^2 + 4*a*c^3*g^6*h^4 + 6*a^2*c^2*g^4*h^6 + 4*a^3*c*g^2*h^8 + a^4*h^10) - 7/8*(c*x^2 + a)^(3/2)*c^3*d*g^3/(c^4*g^8*h*x^2 + 4*a*c^3*g^6*h^3*x^2 + 6*a^2*c^2*g^4*h^5*x^2 + 4*a^3*c*g^2*h^7*x^2 + a^4*h^9*x^2 + 2*c^4*g^9*x + 8*a*c^3*g^7*h^2*x + 12*a^2*c^2*g^5*h^4*x + 8*a^3*c*g^3*h^6*x + 2*a^4*g*h^8*x + c^4*g^10/h + 4*a*c^3*g^8*h + 6*a^2*c^2*g^6*h^3 + 4*a^3*c*g^4*h^5 + a^4*g^2*h^7) + 7/8*sqrt(c*x^2 + a)*c^4*d*g^3/(c^4*g^8*h + 4*a*c^3*g^6*h^3 + 6*a^2*c^2*g^4*h^5 + 4*a^3*c*g^2*h^7 + a^4*h^9) - 7/12*(c*x^2 + a)^(3/2)*c^2*f*g^4/(c^3*g^6*h^4*x^3 + 3*a*c^2*g^4*h^6*x^3 + 3*a^2*c*g^2*h^8*x^3 + a^3*h^10*x^3 + 3*c^3*g^7*h^3*x^2 + 9*a*c^2*g^5*h^5*x^2 + 9*a^2*c*g^3*h^7*x^2 + 3*a^3*g*h^9*x^2 + 3*c^3*g^8*h^2*x + 9*a*c^2*g^6*h^4*x + 9*a^2*c*g^4*h^6*x + 3*a^3*g^2*h^8*x + c^3*g^9*h + 3*a*c^2*g^7*h^3 + 3*a^2*c*g^5*h^5 + a^3*g^3*h^7) + 13/8*sqrt(c*x^2 + a)*c^3*f*g^4/(c^3*g^6*h^4*x + 3*a*c^2*g^4*h^6*x + 3*a^2*c*g^2*h^8*x + a^3*h^10*x + c^3*g^7*h^3 + 3*a*c^2*g^5*h^5 + 3*a^2*c*g^3*h^7 + a^3*g*h^9) + 7/12*(c*x^2 + a)^(3/2)*c^2*e*g^3/(c^3*g^6*h^3*x^3 + 3*a*c^2*g^4*h^5*x^3 + 3*a^2*c*g^2*h^7*x^3 + a^3*h^9*x^3 + 3*c^3*g^7*h^2*x^2 + 9*a*c^2*g^5*h^4*x^2 + 9*a^2*c*g^3*h^6*x^2 + 3*a^3*g*h^8*x^2 + 3*c^3*g^8*h*x + 9*a*c^2*g^6*h^3*x + 9*a^2*c*g^4*h^5*x + 3*a^3*g^2*h^7*x + c^3*g^9 + 3*a*c^2*g^7*h^2 + 3*a^2*c*g^5*h^4 + a^3*g^3*h^6) - sqrt(c*x^2 + a)*c^3*e*g^3/(c^3*g^6*h^3*x + 3*a*c^2*g^4*h^5*x + 3*a^2*c*g^2*h^7*x + a^3*h^9*x + c^3*g^7*h^2 + 3*a*c^2*g^5*h^4 + 3*a^2*c*g^3*h^6 + a^3*g*h^8) + 13/8*(c*x^2 + a)^(3/2)*c^2*f*g^3/(c^3*g^6*h^3*x^2 + 3*a*c^2*g^4*h^5*x^2 + 3*a^2*c*g^2*h^7*x^2 + a^3*h^9*x^2 + 2*c^3*g^7*h^2*x + 6*a*c^2*g^5*h^4*x + 6*a^2*c*g^3*h^6*x + 2*a^3*g*h^8*x + c^3*g^8*h + 3*a*c^2*g^6*h^3 + 3*a^2*c*g^4*h^5 + a^3*g^2*h^7) - 13/8*sqrt(c*x^2 + a)*c^3*f*g^3/(c^3*g^6*h^3 + 3*a*c^2*g^4*h^5 + 3*a^2*c*g^2*h^7 + a^3*h^9) - 7/12*(c*x^2 + a)^(3/2)*c^2*d*g^2/(c^3*g^6*h^2*x^3 + 3*a*c^2*g^4*h^4*x^3 + 3*a^2*c*g^2*h^6*x^3 + a^3*h^8*x^3 + 3*c^3*g^7*h*x^2 + 9*a*c^2*g^5*h^3*x^2 + 9*a^2*c*g^3*h^5*x^2 + 3*a^3*g*h^7*x^2 + 3*c^3*g^8*x + 9*a*c^2*g^6*h^2*x + 9*a^2*c*g^4*h^4*x + 3*a^3*g^2*h^6*x + c^3*g^9/h + 3*a*c^2*g^7*h + 3*a^2*c*g^5*h^3 + a^3*g^3*h^5) + 3/8*sqrt(c*x^2 + a)*c^3*d*g^2/(c^3*g^6*h^2*x + 3*a*c^2*g^4*h^4*x + 3*a^2*c*g^2*h^6*x + a^3*h^8*x + c^3*g^7*h + 3*a*c^2*g^5*h^3 + 3*a^2*c*g^3*h^5 + a^3*g*h^7) - (c*x^2 + a)^(3/2)*c^2*e*g^2/(c^3*g^6*h^2*x^2 + 3*a*c^2*g^4*h^4*x^2 + 3*a^2*c*g^2*h^6*x^2 + a^3*h^8*x^2 + 2*c^3*g^7*h*x + 6*a*c^2*g^5*h^3*x + 6*a^2*c*g^3*h^5*x + 2*a^3*g*h^7*x + c^3*g^8 + 3*a*c^2*g^6*h^2 + 3*a^2*c*g^4*h^4 + a^3*g^2*h^6) + sqrt(c*x^2 + a)*c^3*e*g^2/(c^3*g^6*h^2 + 3*a*c^2*g^4*h^4 + 3*a^2*c*g^2*h^6 + a^3*h^8) - 7/20*(c*x^2 + a)^(3/2)*c*f*g^3/(c^2*g^4*h^5*x^4 + 2*a*c*g^2*h^7*x^4 + a^2*h^9*x^4 + 4*c^2*g^5*h^4*x^3 + 8*a*c*g^3*h^6*x^3 + 4*a^2*g*h^8*x^3 + 6*c^2*g^6*h^3*x^2 + 12*a*c*g^4*h^5*x^2 + 6*a^2*g^2*h^7*x^2 + 4*c^2*g^7*h^2*x + 8*a*c*g^5*h^4*x + 4*a^2*g^3*h^6*x + c^2*g^8*h + 2*a*c*g^6*h^3 + a^2*g^4*h^5) + 3/8*(c*x^2 + a)^(3/2)*c^2*d*g/(c^3*g^6*h*x^2 + 3*a*c^2*g^4*h^3*x^2 + 3*a^2*c*g^2*h^5*x^2 + a^3*h^7*x^2 + 2*c^3*g^7*x + 6*a*c^2*g^5*h^2*x + 6*a^2*c*g^3*h^4*x + 2*a^3*g*h^6*x + c^3*g^8/h + 3*a*c^2*g^6*h + 3*a^2*c*g^4*h^3 + a^3*g^2*h^5) - 3/8*sqrt(c*x^2 + a)*c^3*d*g/(c^3*g^6*h + 3*a*c^2*g^4*h^3 + 3*a^2*c*g^2*h^5 + a^3*h^7) + 7/20*(c*x^2 + a)^(3/2)*c*e*g^2/(c^2*g^4*h^4*x^4 + 2*a*c*g^2*h^6*x^4 + a^2*h^8*x^4 + 4*c^2*g^5*h^3*x^3 + 8*a*c*g^3*h^5*x^3 + 4*a^2*g*h^7*x^3 + 6*c^2*g^6*h^2*x^2 + 12*a*c*g^4*h^4*x^2 + 6*a^2*g^2*h^6*x^2 + 4*c^2*g^7*h*x + 8*a*c*g^5*h^3*x + 4*a^2*g^3*h^5*x + c^2*g^8 + 2*a*c*g^6*h^2 + a^2*g^4*h^4) + 29/30*(c*x^2 + a)^(3/2)*c*f*g^2/(c^2*g^4*h^4*x^3 + 2*a*c*g^2*h^6*x^3 + a^2*h^8*x^3 + 3*c^2*g^5*h^3*x^2 + 6*a*c*g^3*h^5*x^2 + 3*a^2*g*h^7*x^2 + 3*c^2*g^6*h^2*x + 6*a*c*g^4*h^4*x + 3*a^2*g^2*h^6*x + c^2*g^7*h + 2*a*c*g^5*h^3 + a^2*g^3*h^5) - 3/4*sqrt(c*x^2 + a)*c^2*f*g^2/(c^2*g^4*h^4*x + 2*a*c*g^2*h^6*x + a^2*h^8*x + c^2*g^5*h^3 + 2*a*c*g^3*h^5 + a^2*g*h^7) - 7/20*(c*x^2 + a)^(3/2)*c*d*g/(c^2*g^4*h^3*x^4 + 2*a*c*g^2*h^5*x^4 + a^2*h^7*x^4 + 4*c^2*g^5*h^2*x^3 + 8*a*c*g^3*h^4*x^3 + 4*a^2*g*h^6*x^3 + 6*c^2*g^6*h*x^2 + 12*a*c*g^4*h^3*x^2 + 6*a^2*g^2*h^5*x^2 + 4*c^2*g^7*x + 8*a*c*g^5*h^2*x + 4*a^2*g^3*h^4*x + c^2*g^8/h + 2*a*c*g^6*h + a^2*g^4*h^3) - 11/20*(c*x^2 + a)^(3/2)*c*e*g/(c^2*g^4*h^3*x^3 + 2*a*c*g^2*h^5*x^3 + a^2*h^7*x^3 + 3*c^2*g^5*h^2*x^2 + 6*a*c*g^3*h^4*x^2 + 3*a^2*g*h^6*x^2 + 3*c^2*g^6*h*x + 6*a*c*g^4*h^3*x + 3*a^2*g^2*h^5*x + c^2*g^7 + 2*a*c*g^5*h^2 + a^2*g^3*h^4) + 1/8*sqrt(c*x^2 + a)*c^2*e*g/(c^2*g^4*h^3*x + 2*a*c*g^2*h^5*x + a^2*h^7*x + c^2*g^5*h^2 + 2*a*c*g^3*h^4 + a^2*g*h^6) - 3/4*(c*x^2 + a)^(3/2)*c*f*g/(c^2*g^4*h^3*x^2 + 2*a*c*g^2*h^5*x^2 + a^2*h^7*x^2 + 2*c^2*g^5*h^2*x + 4*a*c*g^3*h^4*x + 2*a^2*g*h^6*x + c^2*g^6*h + 2*a*c*g^4*h^3 + a^2*g^2*h^5) + 3/4*sqrt(c*x^2 + a)*c^2*f*g/(c^2*g^4*h^3 + 2*a*c*g^2*h^5 + a^2*h^7) - 1/5*(c*x^2 + a)^(3/2)*f*g^2/(c*g^2*h^6*x^5 + a*h^8*x^5 + 5*c*g^3*h^5*x^4 + 5*a*g*h^7*x^4 + 10*c*g^4*h^4*x^3 + 10*a*g^2*h^6*x^3 + 10*c*g^5*h^3*x^2 + 10*a*g^3*h^5*x^2 + 5*c*g^6*h^2*x + 5*a*g^4*h^4*x + c*g^7*h + a*g^5*h^3) + 2/15*(c*x^2 + a)^(3/2)*c*d/(c^2*g^4*h^2*x^3 + 2*a*c*g^2*h^4*x^3 + a^2*h^6*x^3 + 3*c^2*g^5*h*x^2 + 6*a*c*g^3*h^3*x^2 + 3*a^2*g*h^5*x^2 + 3*c^2*g^6*x + 6*a*c*g^4*h^2*x + 3*a^2*g^2*h^4*x + c^2*g^7/h + 2*a*c*g^5*h + a^2*g^3*h^3) + 1/8*(c*x^2 + a)^(3/2)*c*e/(c^2*g^4*h^2*x^2 + 2*a*c*g^2*h^4*x^2 + a^2*h^6*x^2 + 2*c^2*g^5*h*x + 4*a*c*g^3*h^3*x + 2*a^2*g*h^5*x + c^2*g^6 + 2*a*c*g^4*h^2 + a^2*g^2*h^4) - 1/8*sqrt(c*x^2 + a)*c^2*e/(c^2*g^4*h^2 + 2*a*c*g^2*h^4 + a^2*h^6) + 1/5*(c*x^2 + a)^(3/2)*e*g/(c*g^2*h^5*x^5 + a*h^7*x^5 + 5*c*g^3*h^4*x^4 + 5*a*g*h^6*x^4 + 10*c*g^4*h^3*x^3 + 10*a*g^2*h^5*x^3 + 10*c*g^5*h^2*x^2 + 10*a*g^3*h^4*x^2 + 5*c*g^6*h*x + 5*a*g^4*h^3*x + c*g^7 + a*g^5*h^2) + 1/2*(c*x^2 + a)^(3/2)*f*g/(c*g^2*h^5*x^4 + a*h^7*x^4 + 4*c*g^3*h^4*x^3 + 4*a*g*h^6*x^3 + 6*c*g^4*h^3*x^2 + 6*a*g^2*h^5*x^2 + 4*c*g^5*h^2*x + 4*a*g^3*h^4*x + c*g^6*h + a*g^4*h^3) - 1/5*(c*x^2 + a)^(3/2)*d/(c*g^2*h^4*x^5 + a*h^6*x^5 + 5*c*g^3*h^3*x^4 + 5*a*g*h^5*x^4 + 10*c*g^4*h^2*x^3 + 10*a*g^2*h^4*x^3 + 10*c*g^5*h*x^2 + 10*a*g^3*h^3*x^2 + 5*c*g^6*x + 5*a*g^4*h^2*x + c*g^7/h + a*g^5*h) - 1/4*(c*x^2 + a)^(3/2)*e/(c*g^2*h^4*x^4 + a*h^6*x^4 + 4*c*g^3*h^3*x^3 + 4*a*g*h^5*x^3 + 6*c*g^4*h^2*x^2 + 6*a*g^2*h^4*x^2 + 4*c*g^5*h*x + 4*a*g^3*h^3*x + c*g^6 + a*g^4*h^2) - 1/3*(c*x^2 + a)^(3/2)*f/(c*g^2*h^4*x^3 + a*h^6*x^3 + 3*c*g^3*h^3*x^2 + 3*a*g*h^5*x^2 + 3*c*g^4*h^2*x + 3*a*g^2*h^4*x + c*g^5*h + a*g^3*h^3) - 7/8*c^5*f*g^7*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(9/2)*h^13) + 7/8*c^5*e*g^6*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(9/2)*h^12) - 7/8*c^5*d*g^5*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(9/2)*h^11) + 5/2*c^4*f*g^5*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(7/2)*h^11) - 15/8*c^4*e*g^4*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(7/2)*h^10) + 5/4*c^4*d*g^3*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(7/2)*h^9) - 19/8*c^3*f*g^3*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(5/2)*h^9) + 9/8*c^3*e*g^2*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(5/2)*h^8) - 3/8*c^3*d*g*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(5/2)*h^7) + 3/4*c^2*f*g*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(3/2)*h^7) - 1/8*c^2*e*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(3/2)*h^6)","B",0
88,1,525,0,0.456136," ","integrate((h*x+g)^3*(c*x^2+a)^(3/2)*(f*x^2+e*x+d),x, algorithm=""maxima"")","\frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} f h^{3} x^{4}}{9 \, c} - \frac{4 \, {\left(c x^{2} + a\right)}^{\frac{5}{2}} a f h^{3} x^{2}}{63 \, c^{2}} + \frac{1}{4} \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} d g^{3} x + \frac{3}{8} \, \sqrt{c x^{2} + a} a d g^{3} x + \frac{3 \, a^{2} d g^{3} \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{8 \, \sqrt{c}} + \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} e g^{3}}{5 \, c} + \frac{3 \, {\left(c x^{2} + a\right)}^{\frac{5}{2}} d g^{2} h}{5 \, c} + \frac{8 \, {\left(c x^{2} + a\right)}^{\frac{5}{2}} a^{2} f h^{3}}{315 \, c^{3}} + \frac{{\left(3 \, f g h^{2} + e h^{3}\right)} {\left(c x^{2} + a\right)}^{\frac{5}{2}} x^{3}}{8 \, c} + \frac{{\left(3 \, f g^{2} h + 3 \, e g h^{2} + d h^{3}\right)} {\left(c x^{2} + a\right)}^{\frac{5}{2}} x^{2}}{7 \, c} - \frac{{\left(3 \, f g h^{2} + e h^{3}\right)} {\left(c x^{2} + a\right)}^{\frac{5}{2}} a x}{16 \, c^{2}} + \frac{{\left(3 \, f g h^{2} + e h^{3}\right)} {\left(c x^{2} + a\right)}^{\frac{3}{2}} a^{2} x}{64 \, c^{2}} + \frac{3 \, {\left(3 \, f g h^{2} + e h^{3}\right)} \sqrt{c x^{2} + a} a^{3} x}{128 \, c^{2}} + \frac{{\left(f g^{3} + 3 \, e g^{2} h + 3 \, d g h^{2}\right)} {\left(c x^{2} + a\right)}^{\frac{5}{2}} x}{6 \, c} - \frac{{\left(f g^{3} + 3 \, e g^{2} h + 3 \, d g h^{2}\right)} {\left(c x^{2} + a\right)}^{\frac{3}{2}} a x}{24 \, c} - \frac{{\left(f g^{3} + 3 \, e g^{2} h + 3 \, d g h^{2}\right)} \sqrt{c x^{2} + a} a^{2} x}{16 \, c} + \frac{3 \, {\left(3 \, f g h^{2} + e h^{3}\right)} a^{4} \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{128 \, c^{\frac{5}{2}}} - \frac{{\left(f g^{3} + 3 \, e g^{2} h + 3 \, d g h^{2}\right)} a^{3} \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{16 \, c^{\frac{3}{2}}} - \frac{2 \, {\left(3 \, f g^{2} h + 3 \, e g h^{2} + d h^{3}\right)} {\left(c x^{2} + a\right)}^{\frac{5}{2}} a}{35 \, c^{2}}"," ",0,"1/9*(c*x^2 + a)^(5/2)*f*h^3*x^4/c - 4/63*(c*x^2 + a)^(5/2)*a*f*h^3*x^2/c^2 + 1/4*(c*x^2 + a)^(3/2)*d*g^3*x + 3/8*sqrt(c*x^2 + a)*a*d*g^3*x + 3/8*a^2*d*g^3*arcsinh(c*x/sqrt(a*c))/sqrt(c) + 1/5*(c*x^2 + a)^(5/2)*e*g^3/c + 3/5*(c*x^2 + a)^(5/2)*d*g^2*h/c + 8/315*(c*x^2 + a)^(5/2)*a^2*f*h^3/c^3 + 1/8*(3*f*g*h^2 + e*h^3)*(c*x^2 + a)^(5/2)*x^3/c + 1/7*(3*f*g^2*h + 3*e*g*h^2 + d*h^3)*(c*x^2 + a)^(5/2)*x^2/c - 1/16*(3*f*g*h^2 + e*h^3)*(c*x^2 + a)^(5/2)*a*x/c^2 + 1/64*(3*f*g*h^2 + e*h^3)*(c*x^2 + a)^(3/2)*a^2*x/c^2 + 3/128*(3*f*g*h^2 + e*h^3)*sqrt(c*x^2 + a)*a^3*x/c^2 + 1/6*(f*g^3 + 3*e*g^2*h + 3*d*g*h^2)*(c*x^2 + a)^(5/2)*x/c - 1/24*(f*g^3 + 3*e*g^2*h + 3*d*g*h^2)*(c*x^2 + a)^(3/2)*a*x/c - 1/16*(f*g^3 + 3*e*g^2*h + 3*d*g*h^2)*sqrt(c*x^2 + a)*a^2*x/c + 3/128*(3*f*g*h^2 + e*h^3)*a^4*arcsinh(c*x/sqrt(a*c))/c^(5/2) - 1/16*(f*g^3 + 3*e*g^2*h + 3*d*g*h^2)*a^3*arcsinh(c*x/sqrt(a*c))/c^(3/2) - 2/35*(3*f*g^2*h + 3*e*g*h^2 + d*h^3)*(c*x^2 + a)^(5/2)*a/c^2","A",0
89,1,380,0,0.452087," ","integrate((h*x+g)^2*(c*x^2+a)^(3/2)*(f*x^2+e*x+d),x, algorithm=""maxima"")","\frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} f h^{2} x^{3}}{8 \, c} + \frac{1}{4} \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} d g^{2} x + \frac{3}{8} \, \sqrt{c x^{2} + a} a d g^{2} x - \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} a f h^{2} x}{16 \, c^{2}} + \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} a^{2} f h^{2} x}{64 \, c^{2}} + \frac{3 \, \sqrt{c x^{2} + a} a^{3} f h^{2} x}{128 \, c^{2}} + \frac{3 \, a^{2} d g^{2} \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{8 \, \sqrt{c}} + \frac{3 \, a^{4} f h^{2} \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{128 \, c^{\frac{5}{2}}} + \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} e g^{2}}{5 \, c} + \frac{2 \, {\left(c x^{2} + a\right)}^{\frac{5}{2}} d g h}{5 \, c} + \frac{{\left(2 \, f g h + e h^{2}\right)} {\left(c x^{2} + a\right)}^{\frac{5}{2}} x^{2}}{7 \, c} + \frac{{\left(f g^{2} + 2 \, e g h + d h^{2}\right)} {\left(c x^{2} + a\right)}^{\frac{5}{2}} x}{6 \, c} - \frac{{\left(f g^{2} + 2 \, e g h + d h^{2}\right)} {\left(c x^{2} + a\right)}^{\frac{3}{2}} a x}{24 \, c} - \frac{{\left(f g^{2} + 2 \, e g h + d h^{2}\right)} \sqrt{c x^{2} + a} a^{2} x}{16 \, c} - \frac{{\left(f g^{2} + 2 \, e g h + d h^{2}\right)} a^{3} \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{16 \, c^{\frac{3}{2}}} - \frac{2 \, {\left(2 \, f g h + e h^{2}\right)} {\left(c x^{2} + a\right)}^{\frac{5}{2}} a}{35 \, c^{2}}"," ",0,"1/8*(c*x^2 + a)^(5/2)*f*h^2*x^3/c + 1/4*(c*x^2 + a)^(3/2)*d*g^2*x + 3/8*sqrt(c*x^2 + a)*a*d*g^2*x - 1/16*(c*x^2 + a)^(5/2)*a*f*h^2*x/c^2 + 1/64*(c*x^2 + a)^(3/2)*a^2*f*h^2*x/c^2 + 3/128*sqrt(c*x^2 + a)*a^3*f*h^2*x/c^2 + 3/8*a^2*d*g^2*arcsinh(c*x/sqrt(a*c))/sqrt(c) + 3/128*a^4*f*h^2*arcsinh(c*x/sqrt(a*c))/c^(5/2) + 1/5*(c*x^2 + a)^(5/2)*e*g^2/c + 2/5*(c*x^2 + a)^(5/2)*d*g*h/c + 1/7*(2*f*g*h + e*h^2)*(c*x^2 + a)^(5/2)*x^2/c + 1/6*(f*g^2 + 2*e*g*h + d*h^2)*(c*x^2 + a)^(5/2)*x/c - 1/24*(f*g^2 + 2*e*g*h + d*h^2)*(c*x^2 + a)^(3/2)*a*x/c - 1/16*(f*g^2 + 2*e*g*h + d*h^2)*sqrt(c*x^2 + a)*a^2*x/c - 1/16*(f*g^2 + 2*e*g*h + d*h^2)*a^3*arcsinh(c*x/sqrt(a*c))/c^(3/2) - 2/35*(2*f*g*h + e*h^2)*(c*x^2 + a)^(5/2)*a/c^2","A",0
90,1,211,0,0.446962," ","integrate((h*x+g)*(c*x^2+a)^(3/2)*(f*x^2+e*x+d),x, algorithm=""maxima"")","\frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} f h x^{2}}{7 \, c} + \frac{1}{4} \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} d g x + \frac{3}{8} \, \sqrt{c x^{2} + a} a d g x + \frac{3 \, a^{2} d g \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{8 \, \sqrt{c}} + \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} e g}{5 \, c} + \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} d h}{5 \, c} - \frac{2 \, {\left(c x^{2} + a\right)}^{\frac{5}{2}} a f h}{35 \, c^{2}} + \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} {\left(f g + e h\right)} x}{6 \, c} - \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} {\left(f g + e h\right)} a x}{24 \, c} - \frac{\sqrt{c x^{2} + a} {\left(f g + e h\right)} a^{2} x}{16 \, c} - \frac{{\left(f g + e h\right)} a^{3} \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{16 \, c^{\frac{3}{2}}}"," ",0,"1/7*(c*x^2 + a)^(5/2)*f*h*x^2/c + 1/4*(c*x^2 + a)^(3/2)*d*g*x + 3/8*sqrt(c*x^2 + a)*a*d*g*x + 3/8*a^2*d*g*arcsinh(c*x/sqrt(a*c))/sqrt(c) + 1/5*(c*x^2 + a)^(5/2)*e*g/c + 1/5*(c*x^2 + a)^(5/2)*d*h/c - 2/35*(c*x^2 + a)^(5/2)*a*f*h/c^2 + 1/6*(c*x^2 + a)^(5/2)*(f*g + e*h)*x/c - 1/24*(c*x^2 + a)^(3/2)*(f*g + e*h)*a*x/c - 1/16*sqrt(c*x^2 + a)*(f*g + e*h)*a^2*x/c - 1/16*(f*g + e*h)*a^3*arcsinh(c*x/sqrt(a*c))/c^(3/2)","A",0
91,1,131,0,0.448257," ","integrate((c*x^2+a)^(3/2)*(f*x^2+e*x+d),x, algorithm=""maxima"")","\frac{1}{4} \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} d x + \frac{3}{8} \, \sqrt{c x^{2} + a} a d x + \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} f x}{6 \, c} - \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} a f x}{24 \, c} - \frac{\sqrt{c x^{2} + a} a^{2} f x}{16 \, c} + \frac{3 \, a^{2} d \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{8 \, \sqrt{c}} - \frac{a^{3} f \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{16 \, c^{\frac{3}{2}}} + \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} e}{5 \, c}"," ",0,"1/4*(c*x^2 + a)^(3/2)*d*x + 3/8*sqrt(c*x^2 + a)*a*d*x + 1/6*(c*x^2 + a)^(5/2)*f*x/c - 1/24*(c*x^2 + a)^(3/2)*a*f*x/c - 1/16*sqrt(c*x^2 + a)*a^2*f*x/c + 3/8*a^2*d*arcsinh(c*x/sqrt(a*c))/sqrt(c) - 1/16*a^3*f*arcsinh(c*x/sqrt(a*c))/c^(3/2) + 1/5*(c*x^2 + a)^(5/2)*e/c","A",0
92,1,632,0,0.789401," ","integrate((c*x^2+a)^(3/2)*(f*x^2+e*x+d)/(h*x+g),x, algorithm=""maxima"")","-\frac{\sqrt{c x^{2} + a} c f g^{3} x}{2 \, h^{4}} + \frac{\sqrt{c x^{2} + a} c e g^{2} x}{2 \, h^{3}} - \frac{\sqrt{c x^{2} + a} c d g x}{2 \, h^{2}} - \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} f g x}{4 \, h^{2}} - \frac{3 \, \sqrt{c x^{2} + a} a f g x}{8 \, h^{2}} + \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} e x}{4 \, h} + \frac{3 \, \sqrt{c x^{2} + a} a e x}{8 \, h} - \frac{c^{\frac{3}{2}} f g^{5} \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{h^{6}} + \frac{c^{\frac{3}{2}} e g^{4} \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{h^{5}} - \frac{c^{\frac{3}{2}} d g^{3} \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{h^{4}} - \frac{3 \, a \sqrt{c} f g^{3} \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{2 \, h^{4}} + \frac{3 \, a \sqrt{c} e g^{2} \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{2 \, h^{3}} - \frac{3 \, a \sqrt{c} d g \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{2 \, h^{2}} - \frac{3 \, a^{2} f g \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{8 \, \sqrt{c} h^{2}} + \frac{3 \, a^{2} e \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{8 \, \sqrt{c} h} + \frac{{\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{3}{2}} f g^{2} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{h^{3}} - \frac{{\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{3}{2}} e g \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{h^{2}} + \frac{{\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{3}{2}} d \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{h} + \frac{\sqrt{c x^{2} + a} c f g^{4}}{h^{5}} - \frac{\sqrt{c x^{2} + a} c e g^{3}}{h^{4}} + \frac{\sqrt{c x^{2} + a} c d g^{2}}{h^{3}} + \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} f g^{2}}{3 \, h^{3}} + \frac{\sqrt{c x^{2} + a} a f g^{2}}{h^{3}} - \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} e g}{3 \, h^{2}} - \frac{\sqrt{c x^{2} + a} a e g}{h^{2}} + \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} d}{3 \, h} + \frac{\sqrt{c x^{2} + a} a d}{h} + \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} f}{5 \, c h}"," ",0,"-1/2*sqrt(c*x^2 + a)*c*f*g^3*x/h^4 + 1/2*sqrt(c*x^2 + a)*c*e*g^2*x/h^3 - 1/2*sqrt(c*x^2 + a)*c*d*g*x/h^2 - 1/4*(c*x^2 + a)^(3/2)*f*g*x/h^2 - 3/8*sqrt(c*x^2 + a)*a*f*g*x/h^2 + 1/4*(c*x^2 + a)^(3/2)*e*x/h + 3/8*sqrt(c*x^2 + a)*a*e*x/h - c^(3/2)*f*g^5*arcsinh(c*x/sqrt(a*c))/h^6 + c^(3/2)*e*g^4*arcsinh(c*x/sqrt(a*c))/h^5 - c^(3/2)*d*g^3*arcsinh(c*x/sqrt(a*c))/h^4 - 3/2*a*sqrt(c)*f*g^3*arcsinh(c*x/sqrt(a*c))/h^4 + 3/2*a*sqrt(c)*e*g^2*arcsinh(c*x/sqrt(a*c))/h^3 - 3/2*a*sqrt(c)*d*g*arcsinh(c*x/sqrt(a*c))/h^2 - 3/8*a^2*f*g*arcsinh(c*x/sqrt(a*c))/(sqrt(c)*h^2) + 3/8*a^2*e*arcsinh(c*x/sqrt(a*c))/(sqrt(c)*h) + (a + c*g^2/h^2)^(3/2)*f*g^2*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/h^3 - (a + c*g^2/h^2)^(3/2)*e*g*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/h^2 + (a + c*g^2/h^2)^(3/2)*d*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/h + sqrt(c*x^2 + a)*c*f*g^4/h^5 - sqrt(c*x^2 + a)*c*e*g^3/h^4 + sqrt(c*x^2 + a)*c*d*g^2/h^3 + 1/3*(c*x^2 + a)^(3/2)*f*g^2/h^3 + sqrt(c*x^2 + a)*a*f*g^2/h^3 - 1/3*(c*x^2 + a)^(3/2)*e*g/h^2 - sqrt(c*x^2 + a)*a*e*g/h^2 + 1/3*(c*x^2 + a)^(3/2)*d/h + sqrt(c*x^2 + a)*a*d/h + 1/5*(c*x^2 + a)^(5/2)*f/(c*h)","B",0
93,1,708,0,0.783377," ","integrate((c*x^2+a)^(3/2)*(f*x^2+e*x+d)/(h*x+g)^2,x, algorithm=""maxima"")","-\frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} f g^{2}}{h^{4} x + g h^{3}} + \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} e g}{h^{3} x + g h^{2}} - \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} d}{h^{2} x + g h} + \frac{5 \, \sqrt{c x^{2} + a} c f g^{2} x}{2 \, h^{4}} - \frac{2 \, \sqrt{c x^{2} + a} c e g x}{h^{3}} + \frac{3 \, \sqrt{c x^{2} + a} c d x}{2 \, h^{2}} + \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} f x}{4 \, h^{2}} + \frac{3 \, \sqrt{c x^{2} + a} a f x}{8 \, h^{2}} + \frac{5 \, c^{\frac{3}{2}} f g^{4} \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{h^{6}} - \frac{4 \, c^{\frac{3}{2}} e g^{3} \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{h^{5}} + \frac{3 \, c^{\frac{3}{2}} d g^{2} \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{h^{4}} + \frac{9 \, a \sqrt{c} f g^{2} \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{2 \, h^{4}} - \frac{3 \, a \sqrt{c} e g \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{h^{3}} + \frac{3 \, a \sqrt{c} d \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{2 \, h^{2}} + \frac{3 \, a^{2} f \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{8 \, \sqrt{c} h^{2}} - \frac{3 \, \sqrt{a + \frac{c g^{2}}{h^{2}}} c f g^{3} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{h^{5}} + \frac{3 \, \sqrt{a + \frac{c g^{2}}{h^{2}}} c e g^{2} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{h^{4}} - \frac{3 \, \sqrt{a + \frac{c g^{2}}{h^{2}}} c d g \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{h^{3}} - \frac{2 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{3}{2}} f g \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{h^{3}} + \frac{{\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{3}{2}} e \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{h^{2}} - \frac{5 \, \sqrt{c x^{2} + a} c f g^{3}}{h^{5}} + \frac{4 \, \sqrt{c x^{2} + a} c e g^{2}}{h^{4}} - \frac{3 \, \sqrt{c x^{2} + a} c d g}{h^{3}} - \frac{2 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} f g}{3 \, h^{3}} - \frac{2 \, \sqrt{c x^{2} + a} a f g}{h^{3}} + \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} e}{3 \, h^{2}} + \frac{\sqrt{c x^{2} + a} a e}{h^{2}}"," ",0,"-(c*x^2 + a)^(3/2)*f*g^2/(h^4*x + g*h^3) + (c*x^2 + a)^(3/2)*e*g/(h^3*x + g*h^2) - (c*x^2 + a)^(3/2)*d/(h^2*x + g*h) + 5/2*sqrt(c*x^2 + a)*c*f*g^2*x/h^4 - 2*sqrt(c*x^2 + a)*c*e*g*x/h^3 + 3/2*sqrt(c*x^2 + a)*c*d*x/h^2 + 1/4*(c*x^2 + a)^(3/2)*f*x/h^2 + 3/8*sqrt(c*x^2 + a)*a*f*x/h^2 + 5*c^(3/2)*f*g^4*arcsinh(c*x/sqrt(a*c))/h^6 - 4*c^(3/2)*e*g^3*arcsinh(c*x/sqrt(a*c))/h^5 + 3*c^(3/2)*d*g^2*arcsinh(c*x/sqrt(a*c))/h^4 + 9/2*a*sqrt(c)*f*g^2*arcsinh(c*x/sqrt(a*c))/h^4 - 3*a*sqrt(c)*e*g*arcsinh(c*x/sqrt(a*c))/h^3 + 3/2*a*sqrt(c)*d*arcsinh(c*x/sqrt(a*c))/h^2 + 3/8*a^2*f*arcsinh(c*x/sqrt(a*c))/(sqrt(c)*h^2) - 3*sqrt(a + c*g^2/h^2)*c*f*g^3*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/h^5 + 3*sqrt(a + c*g^2/h^2)*c*e*g^2*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/h^4 - 3*sqrt(a + c*g^2/h^2)*c*d*g*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/h^3 - 2*(a + c*g^2/h^2)^(3/2)*f*g*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/h^3 + (a + c*g^2/h^2)^(3/2)*e*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/h^2 - 5*sqrt(c*x^2 + a)*c*f*g^3/h^5 + 4*sqrt(c*x^2 + a)*c*e*g^2/h^4 - 3*sqrt(c*x^2 + a)*c*d*g/h^3 - 2/3*(c*x^2 + a)^(3/2)*f*g/h^3 - 2*sqrt(c*x^2 + a)*a*f*g/h^3 + 1/3*(c*x^2 + a)^(3/2)*e/h^2 + sqrt(c*x^2 + a)*a*e/h^2","A",0
94,1,1299,0,0.877645," ","integrate((c*x^2+a)^(3/2)*(f*x^2+e*x+d)/(h*x+g)^3,x, algorithm=""maxima"")","\frac{3 \, \sqrt{c x^{2} + a} c^{2} f g^{4}}{2 \, {\left(c g^{2} h^{5} + a h^{7}\right)}} - \frac{3 \, \sqrt{c x^{2} + a} c^{2} f g^{3} x}{2 \, {\left(c g^{2} h^{4} + a h^{6}\right)}} - \frac{3 \, \sqrt{c x^{2} + a} c^{2} e g^{3}}{2 \, {\left(c g^{2} h^{4} + a h^{6}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} c f g^{3}}{2 \, {\left(c g^{2} h^{4} x + a h^{6} x + c g^{3} h^{3} + a g h^{5}\right)}} + \frac{3 \, \sqrt{c x^{2} + a} c^{2} e g^{2} x}{2 \, {\left(c g^{2} h^{3} + a h^{5}\right)}} + \frac{3 \, \sqrt{c x^{2} + a} c^{2} d g^{2}}{2 \, {\left(c g^{2} h^{3} + a h^{5}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} c e g^{2}}{2 \, {\left(c g^{2} h^{3} x + a h^{5} x + c g^{3} h^{2} + a g h^{4}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} f g^{2}}{2 \, {\left(c g^{2} h^{3} x^{2} + a h^{5} x^{2} + 2 \, c g^{3} h^{2} x + 2 \, a g h^{4} x + c g^{4} h + a g^{2} h^{3}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} c f g^{2}}{2 \, {\left(c g^{2} h^{3} + a h^{5}\right)}} - \frac{3 \, \sqrt{c x^{2} + a} c^{2} d g x}{2 \, {\left(c g^{2} h^{2} + a h^{4}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} c d g}{2 \, {\left(c g^{2} h^{2} x + a h^{4} x + c g^{3} h + a g h^{3}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} e g}{2 \, {\left(c g^{2} h^{2} x^{2} + a h^{4} x^{2} + 2 \, c g^{3} h x + 2 \, a g h^{3} x + c g^{4} + a g^{2} h^{2}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} c e g}{2 \, {\left(c g^{2} h^{2} + a h^{4}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} d}{2 \, {\left(c g^{2} h x^{2} + a h^{3} x^{2} + 2 \, c g^{3} x + 2 \, a g h^{2} x + \frac{c g^{4}}{h} + a g^{2} h\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} c d}{2 \, {\left(c g^{2} h + a h^{3}\right)}} + \frac{2 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} f g}{h^{4} x + g h^{3}} - \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} e}{h^{3} x + g h^{2}} - \frac{7 \, \sqrt{c x^{2} + a} c f g x}{2 \, h^{4}} + \frac{3 \, \sqrt{c x^{2} + a} c e x}{2 \, h^{3}} - \frac{10 \, c^{\frac{3}{2}} f g^{3} \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{h^{6}} + \frac{6 \, c^{\frac{3}{2}} e g^{2} \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{h^{5}} - \frac{3 \, c^{\frac{3}{2}} d g \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{h^{4}} - \frac{9 \, a \sqrt{c} f g \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{2 \, h^{4}} + \frac{3 \, a \sqrt{c} e \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{2 \, h^{3}} + \frac{3 \, c^{2} f g^{4} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{2 \, \sqrt{a + \frac{c g^{2}}{h^{2}}} h^{7}} - \frac{3 \, c^{2} e g^{3} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{2 \, \sqrt{a + \frac{c g^{2}}{h^{2}}} h^{6}} + \frac{3 \, c^{2} d g^{2} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{2 \, \sqrt{a + \frac{c g^{2}}{h^{2}}} h^{5}} + \frac{15 \, \sqrt{a + \frac{c g^{2}}{h^{2}}} c f g^{2} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{2 \, h^{5}} - \frac{9 \, \sqrt{a + \frac{c g^{2}}{h^{2}}} c e g \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{2 \, h^{4}} + \frac{3 \, \sqrt{a + \frac{c g^{2}}{h^{2}}} c d \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{2 \, h^{3}} + \frac{{\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{3}{2}} f \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{h^{3}} + \frac{17 \, \sqrt{c x^{2} + a} c f g^{2}}{2 \, h^{5}} - \frac{9 \, \sqrt{c x^{2} + a} c e g}{2 \, h^{4}} + \frac{3 \, \sqrt{c x^{2} + a} c d}{2 \, h^{3}} + \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} f}{3 \, h^{3}} + \frac{\sqrt{c x^{2} + a} a f}{h^{3}}"," ",0,"3/2*sqrt(c*x^2 + a)*c^2*f*g^4/(c*g^2*h^5 + a*h^7) - 3/2*sqrt(c*x^2 + a)*c^2*f*g^3*x/(c*g^2*h^4 + a*h^6) - 3/2*sqrt(c*x^2 + a)*c^2*e*g^3/(c*g^2*h^4 + a*h^6) + 1/2*(c*x^2 + a)^(3/2)*c*f*g^3/(c*g^2*h^4*x + a*h^6*x + c*g^3*h^3 + a*g*h^5) + 3/2*sqrt(c*x^2 + a)*c^2*e*g^2*x/(c*g^2*h^3 + a*h^5) + 3/2*sqrt(c*x^2 + a)*c^2*d*g^2/(c*g^2*h^3 + a*h^5) - 1/2*(c*x^2 + a)^(3/2)*c*e*g^2/(c*g^2*h^3*x + a*h^5*x + c*g^3*h^2 + a*g*h^4) - 1/2*(c*x^2 + a)^(5/2)*f*g^2/(c*g^2*h^3*x^2 + a*h^5*x^2 + 2*c*g^3*h^2*x + 2*a*g*h^4*x + c*g^4*h + a*g^2*h^3) + 1/2*(c*x^2 + a)^(3/2)*c*f*g^2/(c*g^2*h^3 + a*h^5) - 3/2*sqrt(c*x^2 + a)*c^2*d*g*x/(c*g^2*h^2 + a*h^4) + 1/2*(c*x^2 + a)^(3/2)*c*d*g/(c*g^2*h^2*x + a*h^4*x + c*g^3*h + a*g*h^3) + 1/2*(c*x^2 + a)^(5/2)*e*g/(c*g^2*h^2*x^2 + a*h^4*x^2 + 2*c*g^3*h*x + 2*a*g*h^3*x + c*g^4 + a*g^2*h^2) - 1/2*(c*x^2 + a)^(3/2)*c*e*g/(c*g^2*h^2 + a*h^4) - 1/2*(c*x^2 + a)^(5/2)*d/(c*g^2*h*x^2 + a*h^3*x^2 + 2*c*g^3*x + 2*a*g*h^2*x + c*g^4/h + a*g^2*h) + 1/2*(c*x^2 + a)^(3/2)*c*d/(c*g^2*h + a*h^3) + 2*(c*x^2 + a)^(3/2)*f*g/(h^4*x + g*h^3) - (c*x^2 + a)^(3/2)*e/(h^3*x + g*h^2) - 7/2*sqrt(c*x^2 + a)*c*f*g*x/h^4 + 3/2*sqrt(c*x^2 + a)*c*e*x/h^3 - 10*c^(3/2)*f*g^3*arcsinh(c*x/sqrt(a*c))/h^6 + 6*c^(3/2)*e*g^2*arcsinh(c*x/sqrt(a*c))/h^5 - 3*c^(3/2)*d*g*arcsinh(c*x/sqrt(a*c))/h^4 - 9/2*a*sqrt(c)*f*g*arcsinh(c*x/sqrt(a*c))/h^4 + 3/2*a*sqrt(c)*e*arcsinh(c*x/sqrt(a*c))/h^3 + 3/2*c^2*f*g^4*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/(sqrt(a + c*g^2/h^2)*h^7) - 3/2*c^2*e*g^3*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/(sqrt(a + c*g^2/h^2)*h^6) + 3/2*c^2*d*g^2*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/(sqrt(a + c*g^2/h^2)*h^5) + 15/2*sqrt(a + c*g^2/h^2)*c*f*g^2*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/h^5 - 9/2*sqrt(a + c*g^2/h^2)*c*e*g*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/h^4 + 3/2*sqrt(a + c*g^2/h^2)*c*d*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/h^3 + (a + c*g^2/h^2)^(3/2)*f*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/h^3 + 17/2*sqrt(c*x^2 + a)*c*f*g^2/h^5 - 9/2*sqrt(c*x^2 + a)*c*e*g/h^4 + 3/2*sqrt(c*x^2 + a)*c*d/h^3 + 1/3*(c*x^2 + a)^(3/2)*f/h^3 + sqrt(c*x^2 + a)*a*f/h^3","B",0
95,1,2415,0,1.095431," ","integrate((c*x^2+a)^(3/2)*(f*x^2+e*x+d)/(h*x+g)^4,x, algorithm=""maxima"")","\frac{\sqrt{c x^{2} + a} c^{3} f g^{5}}{2 \, {\left(c^{2} g^{4} h^{5} + 2 \, a c g^{2} h^{7} + a^{2} h^{9}\right)}} - \frac{\sqrt{c x^{2} + a} c^{3} f g^{4} x}{2 \, {\left(c^{2} g^{4} h^{4} + 2 \, a c g^{2} h^{6} + a^{2} h^{8}\right)}} - \frac{\sqrt{c x^{2} + a} c^{3} e g^{4}}{2 \, {\left(c^{2} g^{4} h^{4} + 2 \, a c g^{2} h^{6} + a^{2} h^{8}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{2} f g^{4}}{6 \, {\left(c^{2} g^{4} h^{4} x + 2 \, a c g^{2} h^{6} x + a^{2} h^{8} x + c^{2} g^{5} h^{3} + 2 \, a c g^{3} h^{5} + a^{2} g h^{7}\right)}} + \frac{\sqrt{c x^{2} + a} c^{3} e g^{3} x}{2 \, {\left(c^{2} g^{4} h^{3} + 2 \, a c g^{2} h^{5} + a^{2} h^{7}\right)}} + \frac{\sqrt{c x^{2} + a} c^{3} d g^{3}}{2 \, {\left(c^{2} g^{4} h^{3} + 2 \, a c g^{2} h^{5} + a^{2} h^{7}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{2} e g^{3}}{6 \, {\left(c^{2} g^{4} h^{3} x + 2 \, a c g^{2} h^{5} x + a^{2} h^{7} x + c^{2} g^{5} h^{2} + 2 \, a c g^{3} h^{4} + a^{2} g h^{6}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} c f g^{3}}{6 \, {\left(c^{2} g^{4} h^{3} x^{2} + 2 \, a c g^{2} h^{5} x^{2} + a^{2} h^{7} x^{2} + 2 \, c^{2} g^{5} h^{2} x + 4 \, a c g^{3} h^{4} x + 2 \, a^{2} g h^{6} x + c^{2} g^{6} h + 2 \, a c g^{4} h^{3} + a^{2} g^{2} h^{5}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{2} f g^{3}}{6 \, {\left(c^{2} g^{4} h^{3} + 2 \, a c g^{2} h^{5} + a^{2} h^{7}\right)}} - \frac{\sqrt{c x^{2} + a} c^{3} d g^{2} x}{2 \, {\left(c^{2} g^{4} h^{2} + 2 \, a c g^{2} h^{4} + a^{2} h^{6}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{2} d g^{2}}{6 \, {\left(c^{2} g^{4} h^{2} x + 2 \, a c g^{2} h^{4} x + a^{2} h^{6} x + c^{2} g^{5} h + 2 \, a c g^{3} h^{3} + a^{2} g h^{5}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} c e g^{2}}{6 \, {\left(c^{2} g^{4} h^{2} x^{2} + 2 \, a c g^{2} h^{4} x^{2} + a^{2} h^{6} x^{2} + 2 \, c^{2} g^{5} h x + 4 \, a c g^{3} h^{3} x + 2 \, a^{2} g h^{5} x + c^{2} g^{6} + 2 \, a c g^{4} h^{2} + a^{2} g^{2} h^{4}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{2} e g^{2}}{6 \, {\left(c^{2} g^{4} h^{2} + 2 \, a c g^{2} h^{4} + a^{2} h^{6}\right)}} - \frac{9 \, \sqrt{c x^{2} + a} c^{2} f g^{3}}{2 \, {\left(c g^{2} h^{5} + a h^{7}\right)}} + \frac{4 \, \sqrt{c x^{2} + a} c^{2} f g^{2} x}{c g^{2} h^{4} + a h^{6}} - \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} c d g}{6 \, {\left(c^{2} g^{4} h x^{2} + 2 \, a c g^{2} h^{3} x^{2} + a^{2} h^{5} x^{2} + 2 \, c^{2} g^{5} x + 4 \, a c g^{3} h^{2} x + 2 \, a^{2} g h^{4} x + \frac{c^{2} g^{6}}{h} + 2 \, a c g^{4} h + a^{2} g^{2} h^{3}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{2} d g}{6 \, {\left(c^{2} g^{4} h + 2 \, a c g^{2} h^{3} + a^{2} h^{5}\right)}} + \frac{3 \, \sqrt{c x^{2} + a} c^{2} e g^{2}}{c g^{2} h^{4} + a h^{6}} - \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} f g^{2}}{3 \, {\left(c g^{2} h^{4} x^{3} + a h^{6} x^{3} + 3 \, c g^{3} h^{3} x^{2} + 3 \, a g h^{5} x^{2} + 3 \, c g^{4} h^{2} x + 3 \, a g^{2} h^{4} x + c g^{5} h + a g^{3} h^{3}\right)}} - \frac{5 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c f g^{2}}{3 \, {\left(c g^{2} h^{4} x + a h^{6} x + c g^{3} h^{3} + a g h^{5}\right)}} - \frac{5 \, \sqrt{c x^{2} + a} c^{2} e g x}{2 \, {\left(c g^{2} h^{3} + a h^{5}\right)}} - \frac{3 \, \sqrt{c x^{2} + a} c^{2} d g}{2 \, {\left(c g^{2} h^{3} + a h^{5}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} e g}{3 \, {\left(c g^{2} h^{3} x^{3} + a h^{5} x^{3} + 3 \, c g^{3} h^{2} x^{2} + 3 \, a g h^{4} x^{2} + 3 \, c g^{4} h x + 3 \, a g^{2} h^{3} x + c g^{5} + a g^{3} h^{2}\right)}} + \frac{7 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c e g}{6 \, {\left(c g^{2} h^{3} x + a h^{5} x + c g^{3} h^{2} + a g h^{4}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} f g}{c g^{2} h^{3} x^{2} + a h^{5} x^{2} + 2 \, c g^{3} h^{2} x + 2 \, a g h^{4} x + c g^{4} h + a g^{2} h^{3}} - \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} c f g}{c g^{2} h^{3} + a h^{5}} + \frac{\sqrt{c x^{2} + a} c^{2} d x}{c g^{2} h^{2} + a h^{4}} - \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} d}{3 \, {\left(c g^{2} h^{2} x^{3} + a h^{4} x^{3} + 3 \, c g^{3} h x^{2} + 3 \, a g h^{3} x^{2} + 3 \, c g^{4} x + 3 \, a g^{2} h^{2} x + \frac{c g^{5}}{h} + a g^{3} h\right)}} - \frac{2 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c d}{3 \, {\left(c g^{2} h^{2} x + a h^{4} x + c g^{3} h + a g h^{3}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} e}{2 \, {\left(c g^{2} h^{2} x^{2} + a h^{4} x^{2} + 2 \, c g^{3} h x + 2 \, a g h^{3} x + c g^{4} + a g^{2} h^{2}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} c e}{2 \, {\left(c g^{2} h^{2} + a h^{4}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} f}{h^{4} x + g h^{3}} + \frac{3 \, \sqrt{c x^{2} + a} c f x}{2 \, h^{4}} + \frac{10 \, c^{\frac{3}{2}} f g^{2} \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{h^{6}} - \frac{4 \, c^{\frac{3}{2}} e g \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{h^{5}} + \frac{c^{\frac{3}{2}} d \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{h^{4}} + \frac{3 \, a \sqrt{c} f \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{2 \, h^{4}} + \frac{c^{3} f g^{5} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{2 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{3}{2}} h^{9}} - \frac{c^{3} e g^{4} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{2 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{3}{2}} h^{8}} + \frac{c^{3} d g^{3} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{2 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{3}{2}} h^{7}} - \frac{9 \, c^{2} f g^{3} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{2 \, \sqrt{a + \frac{c g^{2}}{h^{2}}} h^{7}} + \frac{3 \, c^{2} e g^{2} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{\sqrt{a + \frac{c g^{2}}{h^{2}}} h^{6}} - \frac{3 \, c^{2} d g \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{2 \, \sqrt{a + \frac{c g^{2}}{h^{2}}} h^{5}} - \frac{6 \, \sqrt{a + \frac{c g^{2}}{h^{2}}} c f g \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{h^{5}} + \frac{3 \, \sqrt{a + \frac{c g^{2}}{h^{2}}} c e \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{2 \, h^{4}} - \frac{6 \, \sqrt{c x^{2} + a} c f g}{h^{5}} + \frac{3 \, \sqrt{c x^{2} + a} c e}{2 \, h^{4}}"," ",0,"1/2*sqrt(c*x^2 + a)*c^3*f*g^5/(c^2*g^4*h^5 + 2*a*c*g^2*h^7 + a^2*h^9) - 1/2*sqrt(c*x^2 + a)*c^3*f*g^4*x/(c^2*g^4*h^4 + 2*a*c*g^2*h^6 + a^2*h^8) - 1/2*sqrt(c*x^2 + a)*c^3*e*g^4/(c^2*g^4*h^4 + 2*a*c*g^2*h^6 + a^2*h^8) + 1/6*(c*x^2 + a)^(3/2)*c^2*f*g^4/(c^2*g^4*h^4*x + 2*a*c*g^2*h^6*x + a^2*h^8*x + c^2*g^5*h^3 + 2*a*c*g^3*h^5 + a^2*g*h^7) + 1/2*sqrt(c*x^2 + a)*c^3*e*g^3*x/(c^2*g^4*h^3 + 2*a*c*g^2*h^5 + a^2*h^7) + 1/2*sqrt(c*x^2 + a)*c^3*d*g^3/(c^2*g^4*h^3 + 2*a*c*g^2*h^5 + a^2*h^7) - 1/6*(c*x^2 + a)^(3/2)*c^2*e*g^3/(c^2*g^4*h^3*x + 2*a*c*g^2*h^5*x + a^2*h^7*x + c^2*g^5*h^2 + 2*a*c*g^3*h^4 + a^2*g*h^6) - 1/6*(c*x^2 + a)^(5/2)*c*f*g^3/(c^2*g^4*h^3*x^2 + 2*a*c*g^2*h^5*x^2 + a^2*h^7*x^2 + 2*c^2*g^5*h^2*x + 4*a*c*g^3*h^4*x + 2*a^2*g*h^6*x + c^2*g^6*h + 2*a*c*g^4*h^3 + a^2*g^2*h^5) + 1/6*(c*x^2 + a)^(3/2)*c^2*f*g^3/(c^2*g^4*h^3 + 2*a*c*g^2*h^5 + a^2*h^7) - 1/2*sqrt(c*x^2 + a)*c^3*d*g^2*x/(c^2*g^4*h^2 + 2*a*c*g^2*h^4 + a^2*h^6) + 1/6*(c*x^2 + a)^(3/2)*c^2*d*g^2/(c^2*g^4*h^2*x + 2*a*c*g^2*h^4*x + a^2*h^6*x + c^2*g^5*h + 2*a*c*g^3*h^3 + a^2*g*h^5) + 1/6*(c*x^2 + a)^(5/2)*c*e*g^2/(c^2*g^4*h^2*x^2 + 2*a*c*g^2*h^4*x^2 + a^2*h^6*x^2 + 2*c^2*g^5*h*x + 4*a*c*g^3*h^3*x + 2*a^2*g*h^5*x + c^2*g^6 + 2*a*c*g^4*h^2 + a^2*g^2*h^4) - 1/6*(c*x^2 + a)^(3/2)*c^2*e*g^2/(c^2*g^4*h^2 + 2*a*c*g^2*h^4 + a^2*h^6) - 9/2*sqrt(c*x^2 + a)*c^2*f*g^3/(c*g^2*h^5 + a*h^7) + 4*sqrt(c*x^2 + a)*c^2*f*g^2*x/(c*g^2*h^4 + a*h^6) - 1/6*(c*x^2 + a)^(5/2)*c*d*g/(c^2*g^4*h*x^2 + 2*a*c*g^2*h^3*x^2 + a^2*h^5*x^2 + 2*c^2*g^5*x + 4*a*c*g^3*h^2*x + 2*a^2*g*h^4*x + c^2*g^6/h + 2*a*c*g^4*h + a^2*g^2*h^3) + 1/6*(c*x^2 + a)^(3/2)*c^2*d*g/(c^2*g^4*h + 2*a*c*g^2*h^3 + a^2*h^5) + 3*sqrt(c*x^2 + a)*c^2*e*g^2/(c*g^2*h^4 + a*h^6) - 1/3*(c*x^2 + a)^(5/2)*f*g^2/(c*g^2*h^4*x^3 + a*h^6*x^3 + 3*c*g^3*h^3*x^2 + 3*a*g*h^5*x^2 + 3*c*g^4*h^2*x + 3*a*g^2*h^4*x + c*g^5*h + a*g^3*h^3) - 5/3*(c*x^2 + a)^(3/2)*c*f*g^2/(c*g^2*h^4*x + a*h^6*x + c*g^3*h^3 + a*g*h^5) - 5/2*sqrt(c*x^2 + a)*c^2*e*g*x/(c*g^2*h^3 + a*h^5) - 3/2*sqrt(c*x^2 + a)*c^2*d*g/(c*g^2*h^3 + a*h^5) + 1/3*(c*x^2 + a)^(5/2)*e*g/(c*g^2*h^3*x^3 + a*h^5*x^3 + 3*c*g^3*h^2*x^2 + 3*a*g*h^4*x^2 + 3*c*g^4*h*x + 3*a*g^2*h^3*x + c*g^5 + a*g^3*h^2) + 7/6*(c*x^2 + a)^(3/2)*c*e*g/(c*g^2*h^3*x + a*h^5*x + c*g^3*h^2 + a*g*h^4) + (c*x^2 + a)^(5/2)*f*g/(c*g^2*h^3*x^2 + a*h^5*x^2 + 2*c*g^3*h^2*x + 2*a*g*h^4*x + c*g^4*h + a*g^2*h^3) - (c*x^2 + a)^(3/2)*c*f*g/(c*g^2*h^3 + a*h^5) + sqrt(c*x^2 + a)*c^2*d*x/(c*g^2*h^2 + a*h^4) - 1/3*(c*x^2 + a)^(5/2)*d/(c*g^2*h^2*x^3 + a*h^4*x^3 + 3*c*g^3*h*x^2 + 3*a*g*h^3*x^2 + 3*c*g^4*x + 3*a*g^2*h^2*x + c*g^5/h + a*g^3*h) - 2/3*(c*x^2 + a)^(3/2)*c*d/(c*g^2*h^2*x + a*h^4*x + c*g^3*h + a*g*h^3) - 1/2*(c*x^2 + a)^(5/2)*e/(c*g^2*h^2*x^2 + a*h^4*x^2 + 2*c*g^3*h*x + 2*a*g*h^3*x + c*g^4 + a*g^2*h^2) + 1/2*(c*x^2 + a)^(3/2)*c*e/(c*g^2*h^2 + a*h^4) - (c*x^2 + a)^(3/2)*f/(h^4*x + g*h^3) + 3/2*sqrt(c*x^2 + a)*c*f*x/h^4 + 10*c^(3/2)*f*g^2*arcsinh(c*x/sqrt(a*c))/h^6 - 4*c^(3/2)*e*g*arcsinh(c*x/sqrt(a*c))/h^5 + c^(3/2)*d*arcsinh(c*x/sqrt(a*c))/h^4 + 3/2*a*sqrt(c)*f*arcsinh(c*x/sqrt(a*c))/h^4 + 1/2*c^3*f*g^5*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(3/2)*h^9) - 1/2*c^3*e*g^4*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(3/2)*h^8) + 1/2*c^3*d*g^3*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(3/2)*h^7) - 9/2*c^2*f*g^3*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/(sqrt(a + c*g^2/h^2)*h^7) + 3*c^2*e*g^2*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/(sqrt(a + c*g^2/h^2)*h^6) - 3/2*c^2*d*g*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/(sqrt(a + c*g^2/h^2)*h^5) - 6*sqrt(a + c*g^2/h^2)*c*f*g*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/h^5 + 3/2*sqrt(a + c*g^2/h^2)*c*e*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/h^4 - 6*sqrt(c*x^2 + a)*c*f*g/h^5 + 3/2*sqrt(c*x^2 + a)*c*e/h^4","B",0
96,1,4326,0,1.503248," ","integrate((c*x^2+a)^(3/2)*(f*x^2+e*x+d)/(h*x+g)^5,x, algorithm=""maxima"")","\frac{3 \, \sqrt{c x^{2} + a} c^{4} f g^{6}}{8 \, {\left(c^{3} g^{6} h^{5} + 3 \, a c^{2} g^{4} h^{7} + 3 \, a^{2} c g^{2} h^{9} + a^{3} h^{11}\right)}} - \frac{3 \, \sqrt{c x^{2} + a} c^{4} f g^{5} x}{8 \, {\left(c^{3} g^{6} h^{4} + 3 \, a c^{2} g^{4} h^{6} + 3 \, a^{2} c g^{2} h^{8} + a^{3} h^{10}\right)}} - \frac{3 \, \sqrt{c x^{2} + a} c^{4} e g^{5}}{8 \, {\left(c^{3} g^{6} h^{4} + 3 \, a c^{2} g^{4} h^{6} + 3 \, a^{2} c g^{2} h^{8} + a^{3} h^{10}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{3} f g^{5}}{8 \, {\left(c^{3} g^{6} h^{4} x + 3 \, a c^{2} g^{4} h^{6} x + 3 \, a^{2} c g^{2} h^{8} x + a^{3} h^{10} x + c^{3} g^{7} h^{3} + 3 \, a c^{2} g^{5} h^{5} + 3 \, a^{2} c g^{3} h^{7} + a^{3} g h^{9}\right)}} + \frac{3 \, \sqrt{c x^{2} + a} c^{4} e g^{4} x}{8 \, {\left(c^{3} g^{6} h^{3} + 3 \, a c^{2} g^{4} h^{5} + 3 \, a^{2} c g^{2} h^{7} + a^{3} h^{9}\right)}} + \frac{3 \, \sqrt{c x^{2} + a} c^{4} d g^{4}}{8 \, {\left(c^{3} g^{6} h^{3} + 3 \, a c^{2} g^{4} h^{5} + 3 \, a^{2} c g^{2} h^{7} + a^{3} h^{9}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{3} e g^{4}}{8 \, {\left(c^{3} g^{6} h^{3} x + 3 \, a c^{2} g^{4} h^{5} x + 3 \, a^{2} c g^{2} h^{7} x + a^{3} h^{9} x + c^{3} g^{7} h^{2} + 3 \, a c^{2} g^{5} h^{4} + 3 \, a^{2} c g^{3} h^{6} + a^{3} g h^{8}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} c^{2} f g^{4}}{8 \, {\left(c^{3} g^{6} h^{3} x^{2} + 3 \, a c^{2} g^{4} h^{5} x^{2} + 3 \, a^{2} c g^{2} h^{7} x^{2} + a^{3} h^{9} x^{2} + 2 \, c^{3} g^{7} h^{2} x + 6 \, a c^{2} g^{5} h^{4} x + 6 \, a^{2} c g^{3} h^{6} x + 2 \, a^{3} g h^{8} x + c^{3} g^{8} h + 3 \, a c^{2} g^{6} h^{3} + 3 \, a^{2} c g^{4} h^{5} + a^{3} g^{2} h^{7}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{3} f g^{4}}{8 \, {\left(c^{3} g^{6} h^{3} + 3 \, a c^{2} g^{4} h^{5} + 3 \, a^{2} c g^{2} h^{7} + a^{3} h^{9}\right)}} - \frac{3 \, \sqrt{c x^{2} + a} c^{4} d g^{3} x}{8 \, {\left(c^{3} g^{6} h^{2} + 3 \, a c^{2} g^{4} h^{4} + 3 \, a^{2} c g^{2} h^{6} + a^{3} h^{8}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{3} d g^{3}}{8 \, {\left(c^{3} g^{6} h^{2} x + 3 \, a c^{2} g^{4} h^{4} x + 3 \, a^{2} c g^{2} h^{6} x + a^{3} h^{8} x + c^{3} g^{7} h + 3 \, a c^{2} g^{5} h^{3} + 3 \, a^{2} c g^{3} h^{5} + a^{3} g h^{7}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} c^{2} e g^{3}}{8 \, {\left(c^{3} g^{6} h^{2} x^{2} + 3 \, a c^{2} g^{4} h^{4} x^{2} + 3 \, a^{2} c g^{2} h^{6} x^{2} + a^{3} h^{8} x^{2} + 2 \, c^{3} g^{7} h x + 6 \, a c^{2} g^{5} h^{3} x + 6 \, a^{2} c g^{3} h^{5} x + 2 \, a^{3} g h^{7} x + c^{3} g^{8} + 3 \, a c^{2} g^{6} h^{2} + 3 \, a^{2} c g^{4} h^{4} + a^{3} g^{2} h^{6}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{3} e g^{3}}{8 \, {\left(c^{3} g^{6} h^{2} + 3 \, a c^{2} g^{4} h^{4} + 3 \, a^{2} c g^{2} h^{6} + a^{3} h^{8}\right)}} - \frac{7 \, \sqrt{c x^{2} + a} c^{3} f g^{4}}{4 \, {\left(c^{2} g^{4} h^{5} + 2 \, a c g^{2} h^{7} + a^{2} h^{9}\right)}} + \frac{11 \, \sqrt{c x^{2} + a} c^{3} f g^{3} x}{8 \, {\left(c^{2} g^{4} h^{4} + 2 \, a c g^{2} h^{6} + a^{2} h^{8}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} c^{2} d g^{2}}{8 \, {\left(c^{3} g^{6} h x^{2} + 3 \, a c^{2} g^{4} h^{3} x^{2} + 3 \, a^{2} c g^{2} h^{5} x^{2} + a^{3} h^{7} x^{2} + 2 \, c^{3} g^{7} x + 6 \, a c^{2} g^{5} h^{2} x + 6 \, a^{2} c g^{3} h^{4} x + 2 \, a^{3} g h^{6} x + \frac{c^{3} g^{8}}{h} + 3 \, a c^{2} g^{6} h + 3 \, a^{2} c g^{4} h^{3} + a^{3} g^{2} h^{5}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{3} d g^{2}}{8 \, {\left(c^{3} g^{6} h + 3 \, a c^{2} g^{4} h^{3} + 3 \, a^{2} c g^{2} h^{5} + a^{3} h^{7}\right)}} + \frac{5 \, \sqrt{c x^{2} + a} c^{3} e g^{3}}{4 \, {\left(c^{2} g^{4} h^{4} + 2 \, a c g^{2} h^{6} + a^{2} h^{8}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} c f g^{3}}{4 \, {\left(c^{2} g^{4} h^{4} x^{3} + 2 \, a c g^{2} h^{6} x^{3} + a^{2} h^{8} x^{3} + 3 \, c^{2} g^{5} h^{3} x^{2} + 6 \, a c g^{3} h^{5} x^{2} + 3 \, a^{2} g h^{7} x^{2} + 3 \, c^{2} g^{6} h^{2} x + 6 \, a c g^{4} h^{4} x + 3 \, a^{2} g^{2} h^{6} x + c^{2} g^{7} h + 2 \, a c g^{5} h^{3} + a^{2} g^{3} h^{5}\right)}} - \frac{17 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{2} f g^{3}}{24 \, {\left(c^{2} g^{4} h^{4} x + 2 \, a c g^{2} h^{6} x + a^{2} h^{8} x + c^{2} g^{5} h^{3} + 2 \, a c g^{3} h^{5} + a^{2} g h^{7}\right)}} - \frac{7 \, \sqrt{c x^{2} + a} c^{3} e g^{2} x}{8 \, {\left(c^{2} g^{4} h^{3} + 2 \, a c g^{2} h^{5} + a^{2} h^{7}\right)}} - \frac{3 \, \sqrt{c x^{2} + a} c^{3} d g^{2}}{4 \, {\left(c^{2} g^{4} h^{3} + 2 \, a c g^{2} h^{5} + a^{2} h^{7}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} c e g^{2}}{4 \, {\left(c^{2} g^{4} h^{3} x^{3} + 2 \, a c g^{2} h^{5} x^{3} + a^{2} h^{7} x^{3} + 3 \, c^{2} g^{5} h^{2} x^{2} + 6 \, a c g^{3} h^{4} x^{2} + 3 \, a^{2} g h^{6} x^{2} + 3 \, c^{2} g^{6} h x + 6 \, a c g^{4} h^{3} x + 3 \, a^{2} g^{2} h^{5} x + c^{2} g^{7} + 2 \, a c g^{5} h^{2} + a^{2} g^{3} h^{4}\right)}} + \frac{13 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{2} e g^{2}}{24 \, {\left(c^{2} g^{4} h^{3} x + 2 \, a c g^{2} h^{5} x + a^{2} h^{7} x + c^{2} g^{5} h^{2} + 2 \, a c g^{3} h^{4} + a^{2} g h^{6}\right)}} + \frac{5 \, {\left(c x^{2} + a\right)}^{\frac{5}{2}} c f g^{2}}{24 \, {\left(c^{2} g^{4} h^{3} x^{2} + 2 \, a c g^{2} h^{5} x^{2} + a^{2} h^{7} x^{2} + 2 \, c^{2} g^{5} h^{2} x + 4 \, a c g^{3} h^{4} x + 2 \, a^{2} g h^{6} x + c^{2} g^{6} h + 2 \, a c g^{4} h^{3} + a^{2} g^{2} h^{5}\right)}} - \frac{5 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{2} f g^{2}}{24 \, {\left(c^{2} g^{4} h^{3} + 2 \, a c g^{2} h^{5} + a^{2} h^{7}\right)}} + \frac{3 \, \sqrt{c x^{2} + a} c^{3} d g x}{8 \, {\left(c^{2} g^{4} h^{2} + 2 \, a c g^{2} h^{4} + a^{2} h^{6}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} c d g}{4 \, {\left(c^{2} g^{4} h^{2} x^{3} + 2 \, a c g^{2} h^{4} x^{3} + a^{2} h^{6} x^{3} + 3 \, c^{2} g^{5} h x^{2} + 6 \, a c g^{3} h^{3} x^{2} + 3 \, a^{2} g h^{5} x^{2} + 3 \, c^{2} g^{6} x + 6 \, a c g^{4} h^{2} x + 3 \, a^{2} g^{2} h^{4} x + \frac{c^{2} g^{7}}{h} + 2 \, a c g^{5} h + a^{2} g^{3} h^{3}\right)}} - \frac{3 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{2} d g}{8 \, {\left(c^{2} g^{4} h^{2} x + 2 \, a c g^{2} h^{4} x + a^{2} h^{6} x + c^{2} g^{5} h + 2 \, a c g^{3} h^{3} + a^{2} g h^{5}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} c e g}{24 \, {\left(c^{2} g^{4} h^{2} x^{2} + 2 \, a c g^{2} h^{4} x^{2} + a^{2} h^{6} x^{2} + 2 \, c^{2} g^{5} h x + 4 \, a c g^{3} h^{3} x + 2 \, a^{2} g h^{5} x + c^{2} g^{6} + 2 \, a c g^{4} h^{2} + a^{2} g^{2} h^{4}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{2} e g}{24 \, {\left(c^{2} g^{4} h^{2} + 2 \, a c g^{2} h^{4} + a^{2} h^{6}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} f g^{2}}{4 \, {\left(c g^{2} h^{5} x^{4} + a h^{7} x^{4} + 4 \, c g^{3} h^{4} x^{3} + 4 \, a g h^{6} x^{3} + 6 \, c g^{4} h^{3} x^{2} + 6 \, a g^{2} h^{5} x^{2} + 4 \, c g^{5} h^{2} x + 4 \, a g^{3} h^{4} x + c g^{6} h + a g^{4} h^{3}\right)}} + \frac{39 \, \sqrt{c x^{2} + a} c^{2} f g^{2}}{8 \, {\left(c g^{2} h^{5} + a h^{7}\right)}} - \frac{7 \, \sqrt{c x^{2} + a} c^{2} f g x}{2 \, {\left(c g^{2} h^{4} + a h^{6}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} c d}{8 \, {\left(c^{2} g^{4} h x^{2} + 2 \, a c g^{2} h^{3} x^{2} + a^{2} h^{5} x^{2} + 2 \, c^{2} g^{5} x + 4 \, a c g^{3} h^{2} x + 2 \, a^{2} g h^{4} x + \frac{c^{2} g^{6}}{h} + 2 \, a c g^{4} h + a^{2} g^{2} h^{3}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{2} d}{8 \, {\left(c^{2} g^{4} h + 2 \, a c g^{2} h^{3} + a^{2} h^{5}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} e g}{4 \, {\left(c g^{2} h^{4} x^{4} + a h^{6} x^{4} + 4 \, c g^{3} h^{3} x^{3} + 4 \, a g h^{5} x^{3} + 6 \, c g^{4} h^{2} x^{2} + 6 \, a g^{2} h^{4} x^{2} + 4 \, c g^{5} h x + 4 \, a g^{3} h^{3} x + c g^{6} + a g^{4} h^{2}\right)}} - \frac{15 \, \sqrt{c x^{2} + a} c^{2} e g}{8 \, {\left(c g^{2} h^{4} + a h^{6}\right)}} + \frac{2 \, {\left(c x^{2} + a\right)}^{\frac{5}{2}} f g}{3 \, {\left(c g^{2} h^{4} x^{3} + a h^{6} x^{3} + 3 \, c g^{3} h^{3} x^{2} + 3 \, a g h^{5} x^{2} + 3 \, c g^{4} h^{2} x + 3 \, a g^{2} h^{4} x + c g^{5} h + a g^{3} h^{3}\right)}} + \frac{11 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c f g}{6 \, {\left(c g^{2} h^{4} x + a h^{6} x + c g^{3} h^{3} + a g h^{5}\right)}} + \frac{\sqrt{c x^{2} + a} c^{2} e x}{c g^{2} h^{3} + a h^{5}} - \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} d}{4 \, {\left(c g^{2} h^{3} x^{4} + a h^{5} x^{4} + 4 \, c g^{3} h^{2} x^{3} + 4 \, a g h^{4} x^{3} + 6 \, c g^{4} h x^{2} + 6 \, a g^{2} h^{3} x^{2} + 4 \, c g^{5} x + 4 \, a g^{3} h^{2} x + \frac{c g^{6}}{h} + a g^{4} h\right)}} + \frac{3 \, \sqrt{c x^{2} + a} c^{2} d}{8 \, {\left(c g^{2} h^{3} + a h^{5}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} e}{3 \, {\left(c g^{2} h^{3} x^{3} + a h^{5} x^{3} + 3 \, c g^{3} h^{2} x^{2} + 3 \, a g h^{4} x^{2} + 3 \, c g^{4} h x + 3 \, a g^{2} h^{3} x + c g^{5} + a g^{3} h^{2}\right)}} - \frac{2 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c e}{3 \, {\left(c g^{2} h^{3} x + a h^{5} x + c g^{3} h^{2} + a g h^{4}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} f}{2 \, {\left(c g^{2} h^{3} x^{2} + a h^{5} x^{2} + 2 \, c g^{3} h^{2} x + 2 \, a g h^{4} x + c g^{4} h + a g^{2} h^{3}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} c f}{2 \, {\left(c g^{2} h^{3} + a h^{5}\right)}} - \frac{5 \, c^{\frac{3}{2}} f g \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{h^{6}} + \frac{c^{\frac{3}{2}} e \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{h^{5}} + \frac{3 \, c^{4} f g^{6} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{8 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{5}{2}} h^{11}} - \frac{3 \, c^{4} e g^{5} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{8 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{5}{2}} h^{10}} + \frac{3 \, c^{4} d g^{4} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{8 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{5}{2}} h^{9}} - \frac{7 \, c^{3} f g^{4} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{4 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{3}{2}} h^{9}} + \frac{5 \, c^{3} e g^{3} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{4 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{3}{2}} h^{8}} - \frac{3 \, c^{3} d g^{2} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{4 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{3}{2}} h^{7}} + \frac{39 \, c^{2} f g^{2} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{8 \, \sqrt{a + \frac{c g^{2}}{h^{2}}} h^{7}} - \frac{15 \, c^{2} e g \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{8 \, \sqrt{a + \frac{c g^{2}}{h^{2}}} h^{6}} + \frac{3 \, c^{2} d \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{8 \, \sqrt{a + \frac{c g^{2}}{h^{2}}} h^{5}} + \frac{3 \, \sqrt{a + \frac{c g^{2}}{h^{2}}} c f \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{2 \, h^{5}} + \frac{3 \, \sqrt{c x^{2} + a} c f}{2 \, h^{5}}"," ",0,"3/8*sqrt(c*x^2 + a)*c^4*f*g^6/(c^3*g^6*h^5 + 3*a*c^2*g^4*h^7 + 3*a^2*c*g^2*h^9 + a^3*h^11) - 3/8*sqrt(c*x^2 + a)*c^4*f*g^5*x/(c^3*g^6*h^4 + 3*a*c^2*g^4*h^6 + 3*a^2*c*g^2*h^8 + a^3*h^10) - 3/8*sqrt(c*x^2 + a)*c^4*e*g^5/(c^3*g^6*h^4 + 3*a*c^2*g^4*h^6 + 3*a^2*c*g^2*h^8 + a^3*h^10) + 1/8*(c*x^2 + a)^(3/2)*c^3*f*g^5/(c^3*g^6*h^4*x + 3*a*c^2*g^4*h^6*x + 3*a^2*c*g^2*h^8*x + a^3*h^10*x + c^3*g^7*h^3 + 3*a*c^2*g^5*h^5 + 3*a^2*c*g^3*h^7 + a^3*g*h^9) + 3/8*sqrt(c*x^2 + a)*c^4*e*g^4*x/(c^3*g^6*h^3 + 3*a*c^2*g^4*h^5 + 3*a^2*c*g^2*h^7 + a^3*h^9) + 3/8*sqrt(c*x^2 + a)*c^4*d*g^4/(c^3*g^6*h^3 + 3*a*c^2*g^4*h^5 + 3*a^2*c*g^2*h^7 + a^3*h^9) - 1/8*(c*x^2 + a)^(3/2)*c^3*e*g^4/(c^3*g^6*h^3*x + 3*a*c^2*g^4*h^5*x + 3*a^2*c*g^2*h^7*x + a^3*h^9*x + c^3*g^7*h^2 + 3*a*c^2*g^5*h^4 + 3*a^2*c*g^3*h^6 + a^3*g*h^8) - 1/8*(c*x^2 + a)^(5/2)*c^2*f*g^4/(c^3*g^6*h^3*x^2 + 3*a*c^2*g^4*h^5*x^2 + 3*a^2*c*g^2*h^7*x^2 + a^3*h^9*x^2 + 2*c^3*g^7*h^2*x + 6*a*c^2*g^5*h^4*x + 6*a^2*c*g^3*h^6*x + 2*a^3*g*h^8*x + c^3*g^8*h + 3*a*c^2*g^6*h^3 + 3*a^2*c*g^4*h^5 + a^3*g^2*h^7) + 1/8*(c*x^2 + a)^(3/2)*c^3*f*g^4/(c^3*g^6*h^3 + 3*a*c^2*g^4*h^5 + 3*a^2*c*g^2*h^7 + a^3*h^9) - 3/8*sqrt(c*x^2 + a)*c^4*d*g^3*x/(c^3*g^6*h^2 + 3*a*c^2*g^4*h^4 + 3*a^2*c*g^2*h^6 + a^3*h^8) + 1/8*(c*x^2 + a)^(3/2)*c^3*d*g^3/(c^3*g^6*h^2*x + 3*a*c^2*g^4*h^4*x + 3*a^2*c*g^2*h^6*x + a^3*h^8*x + c^3*g^7*h + 3*a*c^2*g^5*h^3 + 3*a^2*c*g^3*h^5 + a^3*g*h^7) + 1/8*(c*x^2 + a)^(5/2)*c^2*e*g^3/(c^3*g^6*h^2*x^2 + 3*a*c^2*g^4*h^4*x^2 + 3*a^2*c*g^2*h^6*x^2 + a^3*h^8*x^2 + 2*c^3*g^7*h*x + 6*a*c^2*g^5*h^3*x + 6*a^2*c*g^3*h^5*x + 2*a^3*g*h^7*x + c^3*g^8 + 3*a*c^2*g^6*h^2 + 3*a^2*c*g^4*h^4 + a^3*g^2*h^6) - 1/8*(c*x^2 + a)^(3/2)*c^3*e*g^3/(c^3*g^6*h^2 + 3*a*c^2*g^4*h^4 + 3*a^2*c*g^2*h^6 + a^3*h^8) - 7/4*sqrt(c*x^2 + a)*c^3*f*g^4/(c^2*g^4*h^5 + 2*a*c*g^2*h^7 + a^2*h^9) + 11/8*sqrt(c*x^2 + a)*c^3*f*g^3*x/(c^2*g^4*h^4 + 2*a*c*g^2*h^6 + a^2*h^8) - 1/8*(c*x^2 + a)^(5/2)*c^2*d*g^2/(c^3*g^6*h*x^2 + 3*a*c^2*g^4*h^3*x^2 + 3*a^2*c*g^2*h^5*x^2 + a^3*h^7*x^2 + 2*c^3*g^7*x + 6*a*c^2*g^5*h^2*x + 6*a^2*c*g^3*h^4*x + 2*a^3*g*h^6*x + c^3*g^8/h + 3*a*c^2*g^6*h + 3*a^2*c*g^4*h^3 + a^3*g^2*h^5) + 1/8*(c*x^2 + a)^(3/2)*c^3*d*g^2/(c^3*g^6*h + 3*a*c^2*g^4*h^3 + 3*a^2*c*g^2*h^5 + a^3*h^7) + 5/4*sqrt(c*x^2 + a)*c^3*e*g^3/(c^2*g^4*h^4 + 2*a*c*g^2*h^6 + a^2*h^8) - 1/4*(c*x^2 + a)^(5/2)*c*f*g^3/(c^2*g^4*h^4*x^3 + 2*a*c*g^2*h^6*x^3 + a^2*h^8*x^3 + 3*c^2*g^5*h^3*x^2 + 6*a*c*g^3*h^5*x^2 + 3*a^2*g*h^7*x^2 + 3*c^2*g^6*h^2*x + 6*a*c*g^4*h^4*x + 3*a^2*g^2*h^6*x + c^2*g^7*h + 2*a*c*g^5*h^3 + a^2*g^3*h^5) - 17/24*(c*x^2 + a)^(3/2)*c^2*f*g^3/(c^2*g^4*h^4*x + 2*a*c*g^2*h^6*x + a^2*h^8*x + c^2*g^5*h^3 + 2*a*c*g^3*h^5 + a^2*g*h^7) - 7/8*sqrt(c*x^2 + a)*c^3*e*g^2*x/(c^2*g^4*h^3 + 2*a*c*g^2*h^5 + a^2*h^7) - 3/4*sqrt(c*x^2 + a)*c^3*d*g^2/(c^2*g^4*h^3 + 2*a*c*g^2*h^5 + a^2*h^7) + 1/4*(c*x^2 + a)^(5/2)*c*e*g^2/(c^2*g^4*h^3*x^3 + 2*a*c*g^2*h^5*x^3 + a^2*h^7*x^3 + 3*c^2*g^5*h^2*x^2 + 6*a*c*g^3*h^4*x^2 + 3*a^2*g*h^6*x^2 + 3*c^2*g^6*h*x + 6*a*c*g^4*h^3*x + 3*a^2*g^2*h^5*x + c^2*g^7 + 2*a*c*g^5*h^2 + a^2*g^3*h^4) + 13/24*(c*x^2 + a)^(3/2)*c^2*e*g^2/(c^2*g^4*h^3*x + 2*a*c*g^2*h^5*x + a^2*h^7*x + c^2*g^5*h^2 + 2*a*c*g^3*h^4 + a^2*g*h^6) + 5/24*(c*x^2 + a)^(5/2)*c*f*g^2/(c^2*g^4*h^3*x^2 + 2*a*c*g^2*h^5*x^2 + a^2*h^7*x^2 + 2*c^2*g^5*h^2*x + 4*a*c*g^3*h^4*x + 2*a^2*g*h^6*x + c^2*g^6*h + 2*a*c*g^4*h^3 + a^2*g^2*h^5) - 5/24*(c*x^2 + a)^(3/2)*c^2*f*g^2/(c^2*g^4*h^3 + 2*a*c*g^2*h^5 + a^2*h^7) + 3/8*sqrt(c*x^2 + a)*c^3*d*g*x/(c^2*g^4*h^2 + 2*a*c*g^2*h^4 + a^2*h^6) - 1/4*(c*x^2 + a)^(5/2)*c*d*g/(c^2*g^4*h^2*x^3 + 2*a*c*g^2*h^4*x^3 + a^2*h^6*x^3 + 3*c^2*g^5*h*x^2 + 6*a*c*g^3*h^3*x^2 + 3*a^2*g*h^5*x^2 + 3*c^2*g^6*x + 6*a*c*g^4*h^2*x + 3*a^2*g^2*h^4*x + c^2*g^7/h + 2*a*c*g^5*h + a^2*g^3*h^3) - 3/8*(c*x^2 + a)^(3/2)*c^2*d*g/(c^2*g^4*h^2*x + 2*a*c*g^2*h^4*x + a^2*h^6*x + c^2*g^5*h + 2*a*c*g^3*h^3 + a^2*g*h^5) - 1/24*(c*x^2 + a)^(5/2)*c*e*g/(c^2*g^4*h^2*x^2 + 2*a*c*g^2*h^4*x^2 + a^2*h^6*x^2 + 2*c^2*g^5*h*x + 4*a*c*g^3*h^3*x + 2*a^2*g*h^5*x + c^2*g^6 + 2*a*c*g^4*h^2 + a^2*g^2*h^4) + 1/24*(c*x^2 + a)^(3/2)*c^2*e*g/(c^2*g^4*h^2 + 2*a*c*g^2*h^4 + a^2*h^6) - 1/4*(c*x^2 + a)^(5/2)*f*g^2/(c*g^2*h^5*x^4 + a*h^7*x^4 + 4*c*g^3*h^4*x^3 + 4*a*g*h^6*x^3 + 6*c*g^4*h^3*x^2 + 6*a*g^2*h^5*x^2 + 4*c*g^5*h^2*x + 4*a*g^3*h^4*x + c*g^6*h + a*g^4*h^3) + 39/8*sqrt(c*x^2 + a)*c^2*f*g^2/(c*g^2*h^5 + a*h^7) - 7/2*sqrt(c*x^2 + a)*c^2*f*g*x/(c*g^2*h^4 + a*h^6) - 1/8*(c*x^2 + a)^(5/2)*c*d/(c^2*g^4*h*x^2 + 2*a*c*g^2*h^3*x^2 + a^2*h^5*x^2 + 2*c^2*g^5*x + 4*a*c*g^3*h^2*x + 2*a^2*g*h^4*x + c^2*g^6/h + 2*a*c*g^4*h + a^2*g^2*h^3) + 1/8*(c*x^2 + a)^(3/2)*c^2*d/(c^2*g^4*h + 2*a*c*g^2*h^3 + a^2*h^5) + 1/4*(c*x^2 + a)^(5/2)*e*g/(c*g^2*h^4*x^4 + a*h^6*x^4 + 4*c*g^3*h^3*x^3 + 4*a*g*h^5*x^3 + 6*c*g^4*h^2*x^2 + 6*a*g^2*h^4*x^2 + 4*c*g^5*h*x + 4*a*g^3*h^3*x + c*g^6 + a*g^4*h^2) - 15/8*sqrt(c*x^2 + a)*c^2*e*g/(c*g^2*h^4 + a*h^6) + 2/3*(c*x^2 + a)^(5/2)*f*g/(c*g^2*h^4*x^3 + a*h^6*x^3 + 3*c*g^3*h^3*x^2 + 3*a*g*h^5*x^2 + 3*c*g^4*h^2*x + 3*a*g^2*h^4*x + c*g^5*h + a*g^3*h^3) + 11/6*(c*x^2 + a)^(3/2)*c*f*g/(c*g^2*h^4*x + a*h^6*x + c*g^3*h^3 + a*g*h^5) + sqrt(c*x^2 + a)*c^2*e*x/(c*g^2*h^3 + a*h^5) - 1/4*(c*x^2 + a)^(5/2)*d/(c*g^2*h^3*x^4 + a*h^5*x^4 + 4*c*g^3*h^2*x^3 + 4*a*g*h^4*x^3 + 6*c*g^4*h*x^2 + 6*a*g^2*h^3*x^2 + 4*c*g^5*x + 4*a*g^3*h^2*x + c*g^6/h + a*g^4*h) + 3/8*sqrt(c*x^2 + a)*c^2*d/(c*g^2*h^3 + a*h^5) - 1/3*(c*x^2 + a)^(5/2)*e/(c*g^2*h^3*x^3 + a*h^5*x^3 + 3*c*g^3*h^2*x^2 + 3*a*g*h^4*x^2 + 3*c*g^4*h*x + 3*a*g^2*h^3*x + c*g^5 + a*g^3*h^2) - 2/3*(c*x^2 + a)^(3/2)*c*e/(c*g^2*h^3*x + a*h^5*x + c*g^3*h^2 + a*g*h^4) - 1/2*(c*x^2 + a)^(5/2)*f/(c*g^2*h^3*x^2 + a*h^5*x^2 + 2*c*g^3*h^2*x + 2*a*g*h^4*x + c*g^4*h + a*g^2*h^3) + 1/2*(c*x^2 + a)^(3/2)*c*f/(c*g^2*h^3 + a*h^5) - 5*c^(3/2)*f*g*arcsinh(c*x/sqrt(a*c))/h^6 + c^(3/2)*e*arcsinh(c*x/sqrt(a*c))/h^5 + 3/8*c^4*f*g^6*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(5/2)*h^11) - 3/8*c^4*e*g^5*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(5/2)*h^10) + 3/8*c^4*d*g^4*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(5/2)*h^9) - 7/4*c^3*f*g^4*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(3/2)*h^9) + 5/4*c^3*e*g^3*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(3/2)*h^8) - 3/4*c^3*d*g^2*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(3/2)*h^7) + 39/8*c^2*f*g^2*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/(sqrt(a + c*g^2/h^2)*h^7) - 15/8*c^2*e*g*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/(sqrt(a + c*g^2/h^2)*h^6) + 3/8*c^2*d*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/(sqrt(a + c*g^2/h^2)*h^5) + 3/2*sqrt(a + c*g^2/h^2)*c*f*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/h^5 + 3/2*sqrt(c*x^2 + a)*c*f/h^5","B",0
97,1,6650,0,1.893056," ","integrate((c*x^2+a)^(3/2)*(f*x^2+e*x+d)/(h*x+g)^6,x, algorithm=""maxima"")","\frac{3 \, \sqrt{c x^{2} + a} c^{5} f g^{7}}{8 \, {\left(c^{4} g^{8} h^{5} + 4 \, a c^{3} g^{6} h^{7} + 6 \, a^{2} c^{2} g^{4} h^{9} + 4 \, a^{3} c g^{2} h^{11} + a^{4} h^{13}\right)}} - \frac{3 \, \sqrt{c x^{2} + a} c^{5} f g^{6} x}{8 \, {\left(c^{4} g^{8} h^{4} + 4 \, a c^{3} g^{6} h^{6} + 6 \, a^{2} c^{2} g^{4} h^{8} + 4 \, a^{3} c g^{2} h^{10} + a^{4} h^{12}\right)}} - \frac{3 \, \sqrt{c x^{2} + a} c^{5} e g^{6}}{8 \, {\left(c^{4} g^{8} h^{4} + 4 \, a c^{3} g^{6} h^{6} + 6 \, a^{2} c^{2} g^{4} h^{8} + 4 \, a^{3} c g^{2} h^{10} + a^{4} h^{12}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{4} f g^{6}}{8 \, {\left(c^{4} g^{8} h^{4} x + 4 \, a c^{3} g^{6} h^{6} x + 6 \, a^{2} c^{2} g^{4} h^{8} x + 4 \, a^{3} c g^{2} h^{10} x + a^{4} h^{12} x + c^{4} g^{9} h^{3} + 4 \, a c^{3} g^{7} h^{5} + 6 \, a^{2} c^{2} g^{5} h^{7} + 4 \, a^{3} c g^{3} h^{9} + a^{4} g h^{11}\right)}} + \frac{3 \, \sqrt{c x^{2} + a} c^{5} e g^{5} x}{8 \, {\left(c^{4} g^{8} h^{3} + 4 \, a c^{3} g^{6} h^{5} + 6 \, a^{2} c^{2} g^{4} h^{7} + 4 \, a^{3} c g^{2} h^{9} + a^{4} h^{11}\right)}} + \frac{3 \, \sqrt{c x^{2} + a} c^{5} d g^{5}}{8 \, {\left(c^{4} g^{8} h^{3} + 4 \, a c^{3} g^{6} h^{5} + 6 \, a^{2} c^{2} g^{4} h^{7} + 4 \, a^{3} c g^{2} h^{9} + a^{4} h^{11}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{4} e g^{5}}{8 \, {\left(c^{4} g^{8} h^{3} x + 4 \, a c^{3} g^{6} h^{5} x + 6 \, a^{2} c^{2} g^{4} h^{7} x + 4 \, a^{3} c g^{2} h^{9} x + a^{4} h^{11} x + c^{4} g^{9} h^{2} + 4 \, a c^{3} g^{7} h^{4} + 6 \, a^{2} c^{2} g^{5} h^{6} + 4 \, a^{3} c g^{3} h^{8} + a^{4} g h^{10}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} c^{3} f g^{5}}{8 \, {\left(c^{4} g^{8} h^{3} x^{2} + 4 \, a c^{3} g^{6} h^{5} x^{2} + 6 \, a^{2} c^{2} g^{4} h^{7} x^{2} + 4 \, a^{3} c g^{2} h^{9} x^{2} + a^{4} h^{11} x^{2} + 2 \, c^{4} g^{9} h^{2} x + 8 \, a c^{3} g^{7} h^{4} x + 12 \, a^{2} c^{2} g^{5} h^{6} x + 8 \, a^{3} c g^{3} h^{8} x + 2 \, a^{4} g h^{10} x + c^{4} g^{10} h + 4 \, a c^{3} g^{8} h^{3} + 6 \, a^{2} c^{2} g^{6} h^{5} + 4 \, a^{3} c g^{4} h^{7} + a^{4} g^{2} h^{9}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{4} f g^{5}}{8 \, {\left(c^{4} g^{8} h^{3} + 4 \, a c^{3} g^{6} h^{5} + 6 \, a^{2} c^{2} g^{4} h^{7} + 4 \, a^{3} c g^{2} h^{9} + a^{4} h^{11}\right)}} - \frac{3 \, \sqrt{c x^{2} + a} c^{5} d g^{4} x}{8 \, {\left(c^{4} g^{8} h^{2} + 4 \, a c^{3} g^{6} h^{4} + 6 \, a^{2} c^{2} g^{4} h^{6} + 4 \, a^{3} c g^{2} h^{8} + a^{4} h^{10}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{4} d g^{4}}{8 \, {\left(c^{4} g^{8} h^{2} x + 4 \, a c^{3} g^{6} h^{4} x + 6 \, a^{2} c^{2} g^{4} h^{6} x + 4 \, a^{3} c g^{2} h^{8} x + a^{4} h^{10} x + c^{4} g^{9} h + 4 \, a c^{3} g^{7} h^{3} + 6 \, a^{2} c^{2} g^{5} h^{5} + 4 \, a^{3} c g^{3} h^{7} + a^{4} g h^{9}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} c^{3} e g^{4}}{8 \, {\left(c^{4} g^{8} h^{2} x^{2} + 4 \, a c^{3} g^{6} h^{4} x^{2} + 6 \, a^{2} c^{2} g^{4} h^{6} x^{2} + 4 \, a^{3} c g^{2} h^{8} x^{2} + a^{4} h^{10} x^{2} + 2 \, c^{4} g^{9} h x + 8 \, a c^{3} g^{7} h^{3} x + 12 \, a^{2} c^{2} g^{5} h^{5} x + 8 \, a^{3} c g^{3} h^{7} x + 2 \, a^{4} g h^{9} x + c^{4} g^{10} + 4 \, a c^{3} g^{8} h^{2} + 6 \, a^{2} c^{2} g^{6} h^{4} + 4 \, a^{3} c g^{4} h^{6} + a^{4} g^{2} h^{8}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{4} e g^{4}}{8 \, {\left(c^{4} g^{8} h^{2} + 4 \, a c^{3} g^{6} h^{4} + 6 \, a^{2} c^{2} g^{4} h^{6} + 4 \, a^{3} c g^{2} h^{8} + a^{4} h^{10}\right)}} - \frac{3 \, \sqrt{c x^{2} + a} c^{4} f g^{5}}{2 \, {\left(c^{3} g^{6} h^{5} + 3 \, a c^{2} g^{4} h^{7} + 3 \, a^{2} c g^{2} h^{9} + a^{3} h^{11}\right)}} + \frac{9 \, \sqrt{c x^{2} + a} c^{4} f g^{4} x}{8 \, {\left(c^{3} g^{6} h^{4} + 3 \, a c^{2} g^{4} h^{6} + 3 \, a^{2} c g^{2} h^{8} + a^{3} h^{10}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} c^{3} d g^{3}}{8 \, {\left(c^{4} g^{8} h x^{2} + 4 \, a c^{3} g^{6} h^{3} x^{2} + 6 \, a^{2} c^{2} g^{4} h^{5} x^{2} + 4 \, a^{3} c g^{2} h^{7} x^{2} + a^{4} h^{9} x^{2} + 2 \, c^{4} g^{9} x + 8 \, a c^{3} g^{7} h^{2} x + 12 \, a^{2} c^{2} g^{5} h^{4} x + 8 \, a^{3} c g^{3} h^{6} x + 2 \, a^{4} g h^{8} x + \frac{c^{4} g^{10}}{h} + 4 \, a c^{3} g^{8} h + 6 \, a^{2} c^{2} g^{6} h^{3} + 4 \, a^{3} c g^{4} h^{5} + a^{4} g^{2} h^{7}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{4} d g^{3}}{8 \, {\left(c^{4} g^{8} h + 4 \, a c^{3} g^{6} h^{3} + 6 \, a^{2} c^{2} g^{4} h^{5} + 4 \, a^{3} c g^{2} h^{7} + a^{4} h^{9}\right)}} + \frac{9 \, \sqrt{c x^{2} + a} c^{4} e g^{4}}{8 \, {\left(c^{3} g^{6} h^{4} + 3 \, a c^{2} g^{4} h^{6} + 3 \, a^{2} c g^{2} h^{8} + a^{3} h^{10}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} c^{2} f g^{4}}{4 \, {\left(c^{3} g^{6} h^{4} x^{3} + 3 \, a c^{2} g^{4} h^{6} x^{3} + 3 \, a^{2} c g^{2} h^{8} x^{3} + a^{3} h^{10} x^{3} + 3 \, c^{3} g^{7} h^{3} x^{2} + 9 \, a c^{2} g^{5} h^{5} x^{2} + 9 \, a^{2} c g^{3} h^{7} x^{2} + 3 \, a^{3} g h^{9} x^{2} + 3 \, c^{3} g^{8} h^{2} x + 9 \, a c^{2} g^{6} h^{4} x + 9 \, a^{2} c g^{4} h^{6} x + 3 \, a^{3} g^{2} h^{8} x + c^{3} g^{9} h + 3 \, a c^{2} g^{7} h^{3} + 3 \, a^{2} c g^{5} h^{5} + a^{3} g^{3} h^{7}\right)}} - \frac{5 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{3} f g^{4}}{8 \, {\left(c^{3} g^{6} h^{4} x + 3 \, a c^{2} g^{4} h^{6} x + 3 \, a^{2} c g^{2} h^{8} x + a^{3} h^{10} x + c^{3} g^{7} h^{3} + 3 \, a c^{2} g^{5} h^{5} + 3 \, a^{2} c g^{3} h^{7} + a^{3} g h^{9}\right)}} - \frac{3 \, \sqrt{c x^{2} + a} c^{4} e g^{3} x}{4 \, {\left(c^{3} g^{6} h^{3} + 3 \, a c^{2} g^{4} h^{5} + 3 \, a^{2} c g^{2} h^{7} + a^{3} h^{9}\right)}} - \frac{3 \, \sqrt{c x^{2} + a} c^{4} d g^{3}}{4 \, {\left(c^{3} g^{6} h^{3} + 3 \, a c^{2} g^{4} h^{5} + 3 \, a^{2} c g^{2} h^{7} + a^{3} h^{9}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} c^{2} e g^{3}}{4 \, {\left(c^{3} g^{6} h^{3} x^{3} + 3 \, a c^{2} g^{4} h^{5} x^{3} + 3 \, a^{2} c g^{2} h^{7} x^{3} + a^{3} h^{9} x^{3} + 3 \, c^{3} g^{7} h^{2} x^{2} + 9 \, a c^{2} g^{5} h^{4} x^{2} + 9 \, a^{2} c g^{3} h^{6} x^{2} + 3 \, a^{3} g h^{8} x^{2} + 3 \, c^{3} g^{8} h x + 9 \, a c^{2} g^{6} h^{3} x + 9 \, a^{2} c g^{4} h^{5} x + 3 \, a^{3} g^{2} h^{7} x + c^{3} g^{9} + 3 \, a c^{2} g^{7} h^{2} + 3 \, a^{2} c g^{5} h^{4} + a^{3} g^{3} h^{6}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{3} e g^{3}}{2 \, {\left(c^{3} g^{6} h^{3} x + 3 \, a c^{2} g^{4} h^{5} x + 3 \, a^{2} c g^{2} h^{7} x + a^{3} h^{9} x + c^{3} g^{7} h^{2} + 3 \, a c^{2} g^{5} h^{4} + 3 \, a^{2} c g^{3} h^{6} + a^{3} g h^{8}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} c^{2} f g^{3}}{8 \, {\left(c^{3} g^{6} h^{3} x^{2} + 3 \, a c^{2} g^{4} h^{5} x^{2} + 3 \, a^{2} c g^{2} h^{7} x^{2} + a^{3} h^{9} x^{2} + 2 \, c^{3} g^{7} h^{2} x + 6 \, a c^{2} g^{5} h^{4} x + 6 \, a^{2} c g^{3} h^{6} x + 2 \, a^{3} g h^{8} x + c^{3} g^{8} h + 3 \, a c^{2} g^{6} h^{3} + 3 \, a^{2} c g^{4} h^{5} + a^{3} g^{2} h^{7}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{3} f g^{3}}{8 \, {\left(c^{3} g^{6} h^{3} + 3 \, a c^{2} g^{4} h^{5} + 3 \, a^{2} c g^{2} h^{7} + a^{3} h^{9}\right)}} + \frac{3 \, \sqrt{c x^{2} + a} c^{4} d g^{2} x}{8 \, {\left(c^{3} g^{6} h^{2} + 3 \, a c^{2} g^{4} h^{4} + 3 \, a^{2} c g^{2} h^{6} + a^{3} h^{8}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} c^{2} d g^{2}}{4 \, {\left(c^{3} g^{6} h^{2} x^{3} + 3 \, a c^{2} g^{4} h^{4} x^{3} + 3 \, a^{2} c g^{2} h^{6} x^{3} + a^{3} h^{8} x^{3} + 3 \, c^{3} g^{7} h x^{2} + 9 \, a c^{2} g^{5} h^{3} x^{2} + 9 \, a^{2} c g^{3} h^{5} x^{2} + 3 \, a^{3} g h^{7} x^{2} + 3 \, c^{3} g^{8} x + 9 \, a c^{2} g^{6} h^{2} x + 9 \, a^{2} c g^{4} h^{4} x + 3 \, a^{3} g^{2} h^{6} x + \frac{c^{3} g^{9}}{h} + 3 \, a c^{2} g^{7} h + 3 \, a^{2} c g^{5} h^{3} + a^{3} g^{3} h^{5}\right)}} - \frac{3 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{3} d g^{2}}{8 \, {\left(c^{3} g^{6} h^{2} x + 3 \, a c^{2} g^{4} h^{4} x + 3 \, a^{2} c g^{2} h^{6} x + a^{3} h^{8} x + c^{3} g^{7} h + 3 \, a c^{2} g^{5} h^{3} + 3 \, a^{2} c g^{3} h^{5} + a^{3} g h^{7}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} c f g^{3}}{4 \, {\left(c^{2} g^{4} h^{5} x^{4} + 2 \, a c g^{2} h^{7} x^{4} + a^{2} h^{9} x^{4} + 4 \, c^{2} g^{5} h^{4} x^{3} + 8 \, a c g^{3} h^{6} x^{3} + 4 \, a^{2} g h^{8} x^{3} + 6 \, c^{2} g^{6} h^{3} x^{2} + 12 \, a c g^{4} h^{5} x^{2} + 6 \, a^{2} g^{2} h^{7} x^{2} + 4 \, c^{2} g^{7} h^{2} x + 8 \, a c g^{5} h^{4} x + 4 \, a^{2} g^{3} h^{6} x + c^{2} g^{8} h + 2 \, a c g^{6} h^{3} + a^{2} g^{4} h^{5}\right)}} + \frac{19 \, \sqrt{c x^{2} + a} c^{3} f g^{3}}{8 \, {\left(c^{2} g^{4} h^{5} + 2 \, a c g^{2} h^{7} + a^{2} h^{9}\right)}} - \frac{5 \, \sqrt{c x^{2} + a} c^{3} f g^{2} x}{4 \, {\left(c^{2} g^{4} h^{4} + 2 \, a c g^{2} h^{6} + a^{2} h^{8}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} c^{2} d g}{8 \, {\left(c^{3} g^{6} h x^{2} + 3 \, a c^{2} g^{4} h^{3} x^{2} + 3 \, a^{2} c g^{2} h^{5} x^{2} + a^{3} h^{7} x^{2} + 2 \, c^{3} g^{7} x + 6 \, a c^{2} g^{5} h^{2} x + 6 \, a^{2} c g^{3} h^{4} x + 2 \, a^{3} g h^{6} x + \frac{c^{3} g^{8}}{h} + 3 \, a c^{2} g^{6} h + 3 \, a^{2} c g^{4} h^{3} + a^{3} g^{2} h^{5}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{3} d g}{8 \, {\left(c^{3} g^{6} h + 3 \, a c^{2} g^{4} h^{3} + 3 \, a^{2} c g^{2} h^{5} + a^{3} h^{7}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} c e g^{2}}{4 \, {\left(c^{2} g^{4} h^{4} x^{4} + 2 \, a c g^{2} h^{6} x^{4} + a^{2} h^{8} x^{4} + 4 \, c^{2} g^{5} h^{3} x^{3} + 8 \, a c g^{3} h^{5} x^{3} + 4 \, a^{2} g h^{7} x^{3} + 6 \, c^{2} g^{6} h^{2} x^{2} + 12 \, a c g^{4} h^{4} x^{2} + 6 \, a^{2} g^{2} h^{6} x^{2} + 4 \, c^{2} g^{7} h x + 8 \, a c g^{5} h^{3} x + 4 \, a^{2} g^{3} h^{5} x + c^{2} g^{8} + 2 \, a c g^{6} h^{2} + a^{2} g^{4} h^{4}\right)}} - \frac{9 \, \sqrt{c x^{2} + a} c^{3} e g^{2}}{8 \, {\left(c^{2} g^{4} h^{4} + 2 \, a c g^{2} h^{6} + a^{2} h^{8}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} c f g^{2}}{2 \, {\left(c^{2} g^{4} h^{4} x^{3} + 2 \, a c g^{2} h^{6} x^{3} + a^{2} h^{8} x^{3} + 3 \, c^{2} g^{5} h^{3} x^{2} + 6 \, a c g^{3} h^{5} x^{2} + 3 \, a^{2} g h^{7} x^{2} + 3 \, c^{2} g^{6} h^{2} x + 6 \, a c g^{4} h^{4} x + 3 \, a^{2} g^{2} h^{6} x + c^{2} g^{7} h + 2 \, a c g^{5} h^{3} + a^{2} g^{3} h^{5}\right)}} + \frac{11 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{2} f g^{2}}{12 \, {\left(c^{2} g^{4} h^{4} x + 2 \, a c g^{2} h^{6} x + a^{2} h^{8} x + c^{2} g^{5} h^{3} + 2 \, a c g^{3} h^{5} + a^{2} g h^{7}\right)}} + \frac{3 \, \sqrt{c x^{2} + a} c^{3} e g x}{8 \, {\left(c^{2} g^{4} h^{3} + 2 \, a c g^{2} h^{5} + a^{2} h^{7}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} c d g}{4 \, {\left(c^{2} g^{4} h^{3} x^{4} + 2 \, a c g^{2} h^{5} x^{4} + a^{2} h^{7} x^{4} + 4 \, c^{2} g^{5} h^{2} x^{3} + 8 \, a c g^{3} h^{4} x^{3} + 4 \, a^{2} g h^{6} x^{3} + 6 \, c^{2} g^{6} h x^{2} + 12 \, a c g^{4} h^{3} x^{2} + 6 \, a^{2} g^{2} h^{5} x^{2} + 4 \, c^{2} g^{7} x + 8 \, a c g^{5} h^{2} x + 4 \, a^{2} g^{3} h^{4} x + \frac{c^{2} g^{8}}{h} + 2 \, a c g^{6} h + a^{2} g^{4} h^{3}\right)}} + \frac{3 \, \sqrt{c x^{2} + a} c^{3} d g}{8 \, {\left(c^{2} g^{4} h^{3} + 2 \, a c g^{2} h^{5} + a^{2} h^{7}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} c e g}{4 \, {\left(c^{2} g^{4} h^{3} x^{3} + 2 \, a c g^{2} h^{5} x^{3} + a^{2} h^{7} x^{3} + 3 \, c^{2} g^{5} h^{2} x^{2} + 6 \, a c g^{3} h^{4} x^{2} + 3 \, a^{2} g h^{6} x^{2} + 3 \, c^{2} g^{6} h x + 6 \, a c g^{4} h^{3} x + 3 \, a^{2} g^{2} h^{5} x + c^{2} g^{7} + 2 \, a c g^{5} h^{2} + a^{2} g^{3} h^{4}\right)}} - \frac{3 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{2} e g}{8 \, {\left(c^{2} g^{4} h^{3} x + 2 \, a c g^{2} h^{5} x + a^{2} h^{7} x + c^{2} g^{5} h^{2} + 2 \, a c g^{3} h^{4} + a^{2} g h^{6}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} c f g}{12 \, {\left(c^{2} g^{4} h^{3} x^{2} + 2 \, a c g^{2} h^{5} x^{2} + a^{2} h^{7} x^{2} + 2 \, c^{2} g^{5} h^{2} x + 4 \, a c g^{3} h^{4} x + 2 \, a^{2} g h^{6} x + c^{2} g^{6} h + 2 \, a c g^{4} h^{3} + a^{2} g^{2} h^{5}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{2} f g}{12 \, {\left(c^{2} g^{4} h^{3} + 2 \, a c g^{2} h^{5} + a^{2} h^{7}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} f g^{2}}{5 \, {\left(c g^{2} h^{6} x^{5} + a h^{8} x^{5} + 5 \, c g^{3} h^{5} x^{4} + 5 \, a g h^{7} x^{4} + 10 \, c g^{4} h^{4} x^{3} + 10 \, a g^{2} h^{6} x^{3} + 10 \, c g^{5} h^{3} x^{2} + 10 \, a g^{3} h^{5} x^{2} + 5 \, c g^{6} h^{2} x + 5 \, a g^{4} h^{4} x + c g^{7} h + a g^{5} h^{3}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} c e}{8 \, {\left(c^{2} g^{4} h^{2} x^{2} + 2 \, a c g^{2} h^{4} x^{2} + a^{2} h^{6} x^{2} + 2 \, c^{2} g^{5} h x + 4 \, a c g^{3} h^{3} x + 2 \, a^{2} g h^{5} x + c^{2} g^{6} + 2 \, a c g^{4} h^{2} + a^{2} g^{2} h^{4}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{2} e}{8 \, {\left(c^{2} g^{4} h^{2} + 2 \, a c g^{2} h^{4} + a^{2} h^{6}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} e g}{5 \, {\left(c g^{2} h^{5} x^{5} + a h^{7} x^{5} + 5 \, c g^{3} h^{4} x^{4} + 5 \, a g h^{6} x^{4} + 10 \, c g^{4} h^{3} x^{3} + 10 \, a g^{2} h^{5} x^{3} + 10 \, c g^{5} h^{2} x^{2} + 10 \, a g^{3} h^{4} x^{2} + 5 \, c g^{6} h x + 5 \, a g^{4} h^{3} x + c g^{7} + a g^{5} h^{2}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} f g}{2 \, {\left(c g^{2} h^{5} x^{4} + a h^{7} x^{4} + 4 \, c g^{3} h^{4} x^{3} + 4 \, a g h^{6} x^{3} + 6 \, c g^{4} h^{3} x^{2} + 6 \, a g^{2} h^{5} x^{2} + 4 \, c g^{5} h^{2} x + 4 \, a g^{3} h^{4} x + c g^{6} h + a g^{4} h^{3}\right)}} - \frac{9 \, \sqrt{c x^{2} + a} c^{2} f g}{4 \, {\left(c g^{2} h^{5} + a h^{7}\right)}} + \frac{\sqrt{c x^{2} + a} c^{2} f x}{c g^{2} h^{4} + a h^{6}} - \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} d}{5 \, {\left(c g^{2} h^{4} x^{5} + a h^{6} x^{5} + 5 \, c g^{3} h^{3} x^{4} + 5 \, a g h^{5} x^{4} + 10 \, c g^{4} h^{2} x^{3} + 10 \, a g^{2} h^{4} x^{3} + 10 \, c g^{5} h x^{2} + 10 \, a g^{3} h^{3} x^{2} + 5 \, c g^{6} x + 5 \, a g^{4} h^{2} x + \frac{c g^{7}}{h} + a g^{5} h\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} e}{4 \, {\left(c g^{2} h^{4} x^{4} + a h^{6} x^{4} + 4 \, c g^{3} h^{3} x^{3} + 4 \, a g h^{5} x^{3} + 6 \, c g^{4} h^{2} x^{2} + 6 \, a g^{2} h^{4} x^{2} + 4 \, c g^{5} h x + 4 \, a g^{3} h^{3} x + c g^{6} + a g^{4} h^{2}\right)}} + \frac{3 \, \sqrt{c x^{2} + a} c^{2} e}{8 \, {\left(c g^{2} h^{4} + a h^{6}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} f}{3 \, {\left(c g^{2} h^{4} x^{3} + a h^{6} x^{3} + 3 \, c g^{3} h^{3} x^{2} + 3 \, a g h^{5} x^{2} + 3 \, c g^{4} h^{2} x + 3 \, a g^{2} h^{4} x + c g^{5} h + a g^{3} h^{3}\right)}} - \frac{2 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c f}{3 \, {\left(c g^{2} h^{4} x + a h^{6} x + c g^{3} h^{3} + a g h^{5}\right)}} + \frac{c^{\frac{3}{2}} f \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{h^{6}} + \frac{3 \, c^{5} f g^{7} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{8 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{7}{2}} h^{13}} - \frac{3 \, c^{5} e g^{6} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{8 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{7}{2}} h^{12}} + \frac{3 \, c^{5} d g^{5} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{8 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{7}{2}} h^{11}} - \frac{3 \, c^{4} f g^{5} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{2 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{5}{2}} h^{11}} + \frac{9 \, c^{4} e g^{4} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{8 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{5}{2}} h^{10}} - \frac{3 \, c^{4} d g^{3} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{4 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{5}{2}} h^{9}} + \frac{19 \, c^{3} f g^{3} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{8 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{3}{2}} h^{9}} - \frac{9 \, c^{3} e g^{2} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{8 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{3}{2}} h^{8}} + \frac{3 \, c^{3} d g \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{8 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{3}{2}} h^{7}} - \frac{9 \, c^{2} f g \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{4 \, \sqrt{a + \frac{c g^{2}}{h^{2}}} h^{7}} + \frac{3 \, c^{2} e \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{8 \, \sqrt{a + \frac{c g^{2}}{h^{2}}} h^{6}}"," ",0,"3/8*sqrt(c*x^2 + a)*c^5*f*g^7/(c^4*g^8*h^5 + 4*a*c^3*g^6*h^7 + 6*a^2*c^2*g^4*h^9 + 4*a^3*c*g^2*h^11 + a^4*h^13) - 3/8*sqrt(c*x^2 + a)*c^5*f*g^6*x/(c^4*g^8*h^4 + 4*a*c^3*g^6*h^6 + 6*a^2*c^2*g^4*h^8 + 4*a^3*c*g^2*h^10 + a^4*h^12) - 3/8*sqrt(c*x^2 + a)*c^5*e*g^6/(c^4*g^8*h^4 + 4*a*c^3*g^6*h^6 + 6*a^2*c^2*g^4*h^8 + 4*a^3*c*g^2*h^10 + a^4*h^12) + 1/8*(c*x^2 + a)^(3/2)*c^4*f*g^6/(c^4*g^8*h^4*x + 4*a*c^3*g^6*h^6*x + 6*a^2*c^2*g^4*h^8*x + 4*a^3*c*g^2*h^10*x + a^4*h^12*x + c^4*g^9*h^3 + 4*a*c^3*g^7*h^5 + 6*a^2*c^2*g^5*h^7 + 4*a^3*c*g^3*h^9 + a^4*g*h^11) + 3/8*sqrt(c*x^2 + a)*c^5*e*g^5*x/(c^4*g^8*h^3 + 4*a*c^3*g^6*h^5 + 6*a^2*c^2*g^4*h^7 + 4*a^3*c*g^2*h^9 + a^4*h^11) + 3/8*sqrt(c*x^2 + a)*c^5*d*g^5/(c^4*g^8*h^3 + 4*a*c^3*g^6*h^5 + 6*a^2*c^2*g^4*h^7 + 4*a^3*c*g^2*h^9 + a^4*h^11) - 1/8*(c*x^2 + a)^(3/2)*c^4*e*g^5/(c^4*g^8*h^3*x + 4*a*c^3*g^6*h^5*x + 6*a^2*c^2*g^4*h^7*x + 4*a^3*c*g^2*h^9*x + a^4*h^11*x + c^4*g^9*h^2 + 4*a*c^3*g^7*h^4 + 6*a^2*c^2*g^5*h^6 + 4*a^3*c*g^3*h^8 + a^4*g*h^10) - 1/8*(c*x^2 + a)^(5/2)*c^3*f*g^5/(c^4*g^8*h^3*x^2 + 4*a*c^3*g^6*h^5*x^2 + 6*a^2*c^2*g^4*h^7*x^2 + 4*a^3*c*g^2*h^9*x^2 + a^4*h^11*x^2 + 2*c^4*g^9*h^2*x + 8*a*c^3*g^7*h^4*x + 12*a^2*c^2*g^5*h^6*x + 8*a^3*c*g^3*h^8*x + 2*a^4*g*h^10*x + c^4*g^10*h + 4*a*c^3*g^8*h^3 + 6*a^2*c^2*g^6*h^5 + 4*a^3*c*g^4*h^7 + a^4*g^2*h^9) + 1/8*(c*x^2 + a)^(3/2)*c^4*f*g^5/(c^4*g^8*h^3 + 4*a*c^3*g^6*h^5 + 6*a^2*c^2*g^4*h^7 + 4*a^3*c*g^2*h^9 + a^4*h^11) - 3/8*sqrt(c*x^2 + a)*c^5*d*g^4*x/(c^4*g^8*h^2 + 4*a*c^3*g^6*h^4 + 6*a^2*c^2*g^4*h^6 + 4*a^3*c*g^2*h^8 + a^4*h^10) + 1/8*(c*x^2 + a)^(3/2)*c^4*d*g^4/(c^4*g^8*h^2*x + 4*a*c^3*g^6*h^4*x + 6*a^2*c^2*g^4*h^6*x + 4*a^3*c*g^2*h^8*x + a^4*h^10*x + c^4*g^9*h + 4*a*c^3*g^7*h^3 + 6*a^2*c^2*g^5*h^5 + 4*a^3*c*g^3*h^7 + a^4*g*h^9) + 1/8*(c*x^2 + a)^(5/2)*c^3*e*g^4/(c^4*g^8*h^2*x^2 + 4*a*c^3*g^6*h^4*x^2 + 6*a^2*c^2*g^4*h^6*x^2 + 4*a^3*c*g^2*h^8*x^2 + a^4*h^10*x^2 + 2*c^4*g^9*h*x + 8*a*c^3*g^7*h^3*x + 12*a^2*c^2*g^5*h^5*x + 8*a^3*c*g^3*h^7*x + 2*a^4*g*h^9*x + c^4*g^10 + 4*a*c^3*g^8*h^2 + 6*a^2*c^2*g^6*h^4 + 4*a^3*c*g^4*h^6 + a^4*g^2*h^8) - 1/8*(c*x^2 + a)^(3/2)*c^4*e*g^4/(c^4*g^8*h^2 + 4*a*c^3*g^6*h^4 + 6*a^2*c^2*g^4*h^6 + 4*a^3*c*g^2*h^8 + a^4*h^10) - 3/2*sqrt(c*x^2 + a)*c^4*f*g^5/(c^3*g^6*h^5 + 3*a*c^2*g^4*h^7 + 3*a^2*c*g^2*h^9 + a^3*h^11) + 9/8*sqrt(c*x^2 + a)*c^4*f*g^4*x/(c^3*g^6*h^4 + 3*a*c^2*g^4*h^6 + 3*a^2*c*g^2*h^8 + a^3*h^10) - 1/8*(c*x^2 + a)^(5/2)*c^3*d*g^3/(c^4*g^8*h*x^2 + 4*a*c^3*g^6*h^3*x^2 + 6*a^2*c^2*g^4*h^5*x^2 + 4*a^3*c*g^2*h^7*x^2 + a^4*h^9*x^2 + 2*c^4*g^9*x + 8*a*c^3*g^7*h^2*x + 12*a^2*c^2*g^5*h^4*x + 8*a^3*c*g^3*h^6*x + 2*a^4*g*h^8*x + c^4*g^10/h + 4*a*c^3*g^8*h + 6*a^2*c^2*g^6*h^3 + 4*a^3*c*g^4*h^5 + a^4*g^2*h^7) + 1/8*(c*x^2 + a)^(3/2)*c^4*d*g^3/(c^4*g^8*h + 4*a*c^3*g^6*h^3 + 6*a^2*c^2*g^4*h^5 + 4*a^3*c*g^2*h^7 + a^4*h^9) + 9/8*sqrt(c*x^2 + a)*c^4*e*g^4/(c^3*g^6*h^4 + 3*a*c^2*g^4*h^6 + 3*a^2*c*g^2*h^8 + a^3*h^10) - 1/4*(c*x^2 + a)^(5/2)*c^2*f*g^4/(c^3*g^6*h^4*x^3 + 3*a*c^2*g^4*h^6*x^3 + 3*a^2*c*g^2*h^8*x^3 + a^3*h^10*x^3 + 3*c^3*g^7*h^3*x^2 + 9*a*c^2*g^5*h^5*x^2 + 9*a^2*c*g^3*h^7*x^2 + 3*a^3*g*h^9*x^2 + 3*c^3*g^8*h^2*x + 9*a*c^2*g^6*h^4*x + 9*a^2*c*g^4*h^6*x + 3*a^3*g^2*h^8*x + c^3*g^9*h + 3*a*c^2*g^7*h^3 + 3*a^2*c*g^5*h^5 + a^3*g^3*h^7) - 5/8*(c*x^2 + a)^(3/2)*c^3*f*g^4/(c^3*g^6*h^4*x + 3*a*c^2*g^4*h^6*x + 3*a^2*c*g^2*h^8*x + a^3*h^10*x + c^3*g^7*h^3 + 3*a*c^2*g^5*h^5 + 3*a^2*c*g^3*h^7 + a^3*g*h^9) - 3/4*sqrt(c*x^2 + a)*c^4*e*g^3*x/(c^3*g^6*h^3 + 3*a*c^2*g^4*h^5 + 3*a^2*c*g^2*h^7 + a^3*h^9) - 3/4*sqrt(c*x^2 + a)*c^4*d*g^3/(c^3*g^6*h^3 + 3*a*c^2*g^4*h^5 + 3*a^2*c*g^2*h^7 + a^3*h^9) + 1/4*(c*x^2 + a)^(5/2)*c^2*e*g^3/(c^3*g^6*h^3*x^3 + 3*a*c^2*g^4*h^5*x^3 + 3*a^2*c*g^2*h^7*x^3 + a^3*h^9*x^3 + 3*c^3*g^7*h^2*x^2 + 9*a*c^2*g^5*h^4*x^2 + 9*a^2*c*g^3*h^6*x^2 + 3*a^3*g*h^8*x^2 + 3*c^3*g^8*h*x + 9*a*c^2*g^6*h^3*x + 9*a^2*c*g^4*h^5*x + 3*a^3*g^2*h^7*x + c^3*g^9 + 3*a*c^2*g^7*h^2 + 3*a^2*c*g^5*h^4 + a^3*g^3*h^6) + 1/2*(c*x^2 + a)^(3/2)*c^3*e*g^3/(c^3*g^6*h^3*x + 3*a*c^2*g^4*h^5*x + 3*a^2*c*g^2*h^7*x + a^3*h^9*x + c^3*g^7*h^2 + 3*a*c^2*g^5*h^4 + 3*a^2*c*g^3*h^6 + a^3*g*h^8) + 1/8*(c*x^2 + a)^(5/2)*c^2*f*g^3/(c^3*g^6*h^3*x^2 + 3*a*c^2*g^4*h^5*x^2 + 3*a^2*c*g^2*h^7*x^2 + a^3*h^9*x^2 + 2*c^3*g^7*h^2*x + 6*a*c^2*g^5*h^4*x + 6*a^2*c*g^3*h^6*x + 2*a^3*g*h^8*x + c^3*g^8*h + 3*a*c^2*g^6*h^3 + 3*a^2*c*g^4*h^5 + a^3*g^2*h^7) - 1/8*(c*x^2 + a)^(3/2)*c^3*f*g^3/(c^3*g^6*h^3 + 3*a*c^2*g^4*h^5 + 3*a^2*c*g^2*h^7 + a^3*h^9) + 3/8*sqrt(c*x^2 + a)*c^4*d*g^2*x/(c^3*g^6*h^2 + 3*a*c^2*g^4*h^4 + 3*a^2*c*g^2*h^6 + a^3*h^8) - 1/4*(c*x^2 + a)^(5/2)*c^2*d*g^2/(c^3*g^6*h^2*x^3 + 3*a*c^2*g^4*h^4*x^3 + 3*a^2*c*g^2*h^6*x^3 + a^3*h^8*x^3 + 3*c^3*g^7*h*x^2 + 9*a*c^2*g^5*h^3*x^2 + 9*a^2*c*g^3*h^5*x^2 + 3*a^3*g*h^7*x^2 + 3*c^3*g^8*x + 9*a*c^2*g^6*h^2*x + 9*a^2*c*g^4*h^4*x + 3*a^3*g^2*h^6*x + c^3*g^9/h + 3*a*c^2*g^7*h + 3*a^2*c*g^5*h^3 + a^3*g^3*h^5) - 3/8*(c*x^2 + a)^(3/2)*c^3*d*g^2/(c^3*g^6*h^2*x + 3*a*c^2*g^4*h^4*x + 3*a^2*c*g^2*h^6*x + a^3*h^8*x + c^3*g^7*h + 3*a*c^2*g^5*h^3 + 3*a^2*c*g^3*h^5 + a^3*g*h^7) - 1/4*(c*x^2 + a)^(5/2)*c*f*g^3/(c^2*g^4*h^5*x^4 + 2*a*c*g^2*h^7*x^4 + a^2*h^9*x^4 + 4*c^2*g^5*h^4*x^3 + 8*a*c*g^3*h^6*x^3 + 4*a^2*g*h^8*x^3 + 6*c^2*g^6*h^3*x^2 + 12*a*c*g^4*h^5*x^2 + 6*a^2*g^2*h^7*x^2 + 4*c^2*g^7*h^2*x + 8*a*c*g^5*h^4*x + 4*a^2*g^3*h^6*x + c^2*g^8*h + 2*a*c*g^6*h^3 + a^2*g^4*h^5) + 19/8*sqrt(c*x^2 + a)*c^3*f*g^3/(c^2*g^4*h^5 + 2*a*c*g^2*h^7 + a^2*h^9) - 5/4*sqrt(c*x^2 + a)*c^3*f*g^2*x/(c^2*g^4*h^4 + 2*a*c*g^2*h^6 + a^2*h^8) - 1/8*(c*x^2 + a)^(5/2)*c^2*d*g/(c^3*g^6*h*x^2 + 3*a*c^2*g^4*h^3*x^2 + 3*a^2*c*g^2*h^5*x^2 + a^3*h^7*x^2 + 2*c^3*g^7*x + 6*a*c^2*g^5*h^2*x + 6*a^2*c*g^3*h^4*x + 2*a^3*g*h^6*x + c^3*g^8/h + 3*a*c^2*g^6*h + 3*a^2*c*g^4*h^3 + a^3*g^2*h^5) + 1/8*(c*x^2 + a)^(3/2)*c^3*d*g/(c^3*g^6*h + 3*a*c^2*g^4*h^3 + 3*a^2*c*g^2*h^5 + a^3*h^7) + 1/4*(c*x^2 + a)^(5/2)*c*e*g^2/(c^2*g^4*h^4*x^4 + 2*a*c*g^2*h^6*x^4 + a^2*h^8*x^4 + 4*c^2*g^5*h^3*x^3 + 8*a*c*g^3*h^5*x^3 + 4*a^2*g*h^7*x^3 + 6*c^2*g^6*h^2*x^2 + 12*a*c*g^4*h^4*x^2 + 6*a^2*g^2*h^6*x^2 + 4*c^2*g^7*h*x + 8*a*c*g^5*h^3*x + 4*a^2*g^3*h^5*x + c^2*g^8 + 2*a*c*g^6*h^2 + a^2*g^4*h^4) - 9/8*sqrt(c*x^2 + a)*c^3*e*g^2/(c^2*g^4*h^4 + 2*a*c*g^2*h^6 + a^2*h^8) + 1/2*(c*x^2 + a)^(5/2)*c*f*g^2/(c^2*g^4*h^4*x^3 + 2*a*c*g^2*h^6*x^3 + a^2*h^8*x^3 + 3*c^2*g^5*h^3*x^2 + 6*a*c*g^3*h^5*x^2 + 3*a^2*g*h^7*x^2 + 3*c^2*g^6*h^2*x + 6*a*c*g^4*h^4*x + 3*a^2*g^2*h^6*x + c^2*g^7*h + 2*a*c*g^5*h^3 + a^2*g^3*h^5) + 11/12*(c*x^2 + a)^(3/2)*c^2*f*g^2/(c^2*g^4*h^4*x + 2*a*c*g^2*h^6*x + a^2*h^8*x + c^2*g^5*h^3 + 2*a*c*g^3*h^5 + a^2*g*h^7) + 3/8*sqrt(c*x^2 + a)*c^3*e*g*x/(c^2*g^4*h^3 + 2*a*c*g^2*h^5 + a^2*h^7) - 1/4*(c*x^2 + a)^(5/2)*c*d*g/(c^2*g^4*h^3*x^4 + 2*a*c*g^2*h^5*x^4 + a^2*h^7*x^4 + 4*c^2*g^5*h^2*x^3 + 8*a*c*g^3*h^4*x^3 + 4*a^2*g*h^6*x^3 + 6*c^2*g^6*h*x^2 + 12*a*c*g^4*h^3*x^2 + 6*a^2*g^2*h^5*x^2 + 4*c^2*g^7*x + 8*a*c*g^5*h^2*x + 4*a^2*g^3*h^4*x + c^2*g^8/h + 2*a*c*g^6*h + a^2*g^4*h^3) + 3/8*sqrt(c*x^2 + a)*c^3*d*g/(c^2*g^4*h^3 + 2*a*c*g^2*h^5 + a^2*h^7) - 1/4*(c*x^2 + a)^(5/2)*c*e*g/(c^2*g^4*h^3*x^3 + 2*a*c*g^2*h^5*x^3 + a^2*h^7*x^3 + 3*c^2*g^5*h^2*x^2 + 6*a*c*g^3*h^4*x^2 + 3*a^2*g*h^6*x^2 + 3*c^2*g^6*h*x + 6*a*c*g^4*h^3*x + 3*a^2*g^2*h^5*x + c^2*g^7 + 2*a*c*g^5*h^2 + a^2*g^3*h^4) - 3/8*(c*x^2 + a)^(3/2)*c^2*e*g/(c^2*g^4*h^3*x + 2*a*c*g^2*h^5*x + a^2*h^7*x + c^2*g^5*h^2 + 2*a*c*g^3*h^4 + a^2*g*h^6) + 1/12*(c*x^2 + a)^(5/2)*c*f*g/(c^2*g^4*h^3*x^2 + 2*a*c*g^2*h^5*x^2 + a^2*h^7*x^2 + 2*c^2*g^5*h^2*x + 4*a*c*g^3*h^4*x + 2*a^2*g*h^6*x + c^2*g^6*h + 2*a*c*g^4*h^3 + a^2*g^2*h^5) - 1/12*(c*x^2 + a)^(3/2)*c^2*f*g/(c^2*g^4*h^3 + 2*a*c*g^2*h^5 + a^2*h^7) - 1/5*(c*x^2 + a)^(5/2)*f*g^2/(c*g^2*h^6*x^5 + a*h^8*x^5 + 5*c*g^3*h^5*x^4 + 5*a*g*h^7*x^4 + 10*c*g^4*h^4*x^3 + 10*a*g^2*h^6*x^3 + 10*c*g^5*h^3*x^2 + 10*a*g^3*h^5*x^2 + 5*c*g^6*h^2*x + 5*a*g^4*h^4*x + c*g^7*h + a*g^5*h^3) - 1/8*(c*x^2 + a)^(5/2)*c*e/(c^2*g^4*h^2*x^2 + 2*a*c*g^2*h^4*x^2 + a^2*h^6*x^2 + 2*c^2*g^5*h*x + 4*a*c*g^3*h^3*x + 2*a^2*g*h^5*x + c^2*g^6 + 2*a*c*g^4*h^2 + a^2*g^2*h^4) + 1/8*(c*x^2 + a)^(3/2)*c^2*e/(c^2*g^4*h^2 + 2*a*c*g^2*h^4 + a^2*h^6) + 1/5*(c*x^2 + a)^(5/2)*e*g/(c*g^2*h^5*x^5 + a*h^7*x^5 + 5*c*g^3*h^4*x^4 + 5*a*g*h^6*x^4 + 10*c*g^4*h^3*x^3 + 10*a*g^2*h^5*x^3 + 10*c*g^5*h^2*x^2 + 10*a*g^3*h^4*x^2 + 5*c*g^6*h*x + 5*a*g^4*h^3*x + c*g^7 + a*g^5*h^2) + 1/2*(c*x^2 + a)^(5/2)*f*g/(c*g^2*h^5*x^4 + a*h^7*x^4 + 4*c*g^3*h^4*x^3 + 4*a*g*h^6*x^3 + 6*c*g^4*h^3*x^2 + 6*a*g^2*h^5*x^2 + 4*c*g^5*h^2*x + 4*a*g^3*h^4*x + c*g^6*h + a*g^4*h^3) - 9/4*sqrt(c*x^2 + a)*c^2*f*g/(c*g^2*h^5 + a*h^7) + sqrt(c*x^2 + a)*c^2*f*x/(c*g^2*h^4 + a*h^6) - 1/5*(c*x^2 + a)^(5/2)*d/(c*g^2*h^4*x^5 + a*h^6*x^5 + 5*c*g^3*h^3*x^4 + 5*a*g*h^5*x^4 + 10*c*g^4*h^2*x^3 + 10*a*g^2*h^4*x^3 + 10*c*g^5*h*x^2 + 10*a*g^3*h^3*x^2 + 5*c*g^6*x + 5*a*g^4*h^2*x + c*g^7/h + a*g^5*h) - 1/4*(c*x^2 + a)^(5/2)*e/(c*g^2*h^4*x^4 + a*h^6*x^4 + 4*c*g^3*h^3*x^3 + 4*a*g*h^5*x^3 + 6*c*g^4*h^2*x^2 + 6*a*g^2*h^4*x^2 + 4*c*g^5*h*x + 4*a*g^3*h^3*x + c*g^6 + a*g^4*h^2) + 3/8*sqrt(c*x^2 + a)*c^2*e/(c*g^2*h^4 + a*h^6) - 1/3*(c*x^2 + a)^(5/2)*f/(c*g^2*h^4*x^3 + a*h^6*x^3 + 3*c*g^3*h^3*x^2 + 3*a*g*h^5*x^2 + 3*c*g^4*h^2*x + 3*a*g^2*h^4*x + c*g^5*h + a*g^3*h^3) - 2/3*(c*x^2 + a)^(3/2)*c*f/(c*g^2*h^4*x + a*h^6*x + c*g^3*h^3 + a*g*h^5) + c^(3/2)*f*arcsinh(c*x/sqrt(a*c))/h^6 + 3/8*c^5*f*g^7*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(7/2)*h^13) - 3/8*c^5*e*g^6*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(7/2)*h^12) + 3/8*c^5*d*g^5*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(7/2)*h^11) - 3/2*c^4*f*g^5*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(5/2)*h^11) + 9/8*c^4*e*g^4*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(5/2)*h^10) - 3/4*c^4*d*g^3*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(5/2)*h^9) + 19/8*c^3*f*g^3*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(3/2)*h^9) - 9/8*c^3*e*g^2*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(3/2)*h^8) + 3/8*c^3*d*g*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(3/2)*h^7) - 9/4*c^2*f*g*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/(sqrt(a + c*g^2/h^2)*h^7) + 3/8*c^2*e*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/(sqrt(a + c*g^2/h^2)*h^6)","B",0
98,1,10724,0,2.729011," ","integrate((c*x^2+a)^(3/2)*(f*x^2+e*x+d)/(h*x+g)^7,x, algorithm=""maxima"")","\frac{7 \, \sqrt{c x^{2} + a} c^{6} f g^{8}}{16 \, {\left(c^{5} g^{10} h^{5} + 5 \, a c^{4} g^{8} h^{7} + 10 \, a^{2} c^{3} g^{6} h^{9} + 10 \, a^{3} c^{2} g^{4} h^{11} + 5 \, a^{4} c g^{2} h^{13} + a^{5} h^{15}\right)}} - \frac{7 \, \sqrt{c x^{2} + a} c^{6} f g^{7} x}{16 \, {\left(c^{5} g^{10} h^{4} + 5 \, a c^{4} g^{8} h^{6} + 10 \, a^{2} c^{3} g^{6} h^{8} + 10 \, a^{3} c^{2} g^{4} h^{10} + 5 \, a^{4} c g^{2} h^{12} + a^{5} h^{14}\right)}} - \frac{7 \, \sqrt{c x^{2} + a} c^{6} e g^{7}}{16 \, {\left(c^{5} g^{10} h^{4} + 5 \, a c^{4} g^{8} h^{6} + 10 \, a^{2} c^{3} g^{6} h^{8} + 10 \, a^{3} c^{2} g^{4} h^{10} + 5 \, a^{4} c g^{2} h^{12} + a^{5} h^{14}\right)}} + \frac{7 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{5} f g^{7}}{48 \, {\left(c^{5} g^{10} h^{4} x + 5 \, a c^{4} g^{8} h^{6} x + 10 \, a^{2} c^{3} g^{6} h^{8} x + 10 \, a^{3} c^{2} g^{4} h^{10} x + 5 \, a^{4} c g^{2} h^{12} x + a^{5} h^{14} x + c^{5} g^{11} h^{3} + 5 \, a c^{4} g^{9} h^{5} + 10 \, a^{2} c^{3} g^{7} h^{7} + 10 \, a^{3} c^{2} g^{5} h^{9} + 5 \, a^{4} c g^{3} h^{11} + a^{5} g h^{13}\right)}} + \frac{7 \, \sqrt{c x^{2} + a} c^{6} e g^{6} x}{16 \, {\left(c^{5} g^{10} h^{3} + 5 \, a c^{4} g^{8} h^{5} + 10 \, a^{2} c^{3} g^{6} h^{7} + 10 \, a^{3} c^{2} g^{4} h^{9} + 5 \, a^{4} c g^{2} h^{11} + a^{5} h^{13}\right)}} + \frac{7 \, \sqrt{c x^{2} + a} c^{6} d g^{6}}{16 \, {\left(c^{5} g^{10} h^{3} + 5 \, a c^{4} g^{8} h^{5} + 10 \, a^{2} c^{3} g^{6} h^{7} + 10 \, a^{3} c^{2} g^{4} h^{9} + 5 \, a^{4} c g^{2} h^{11} + a^{5} h^{13}\right)}} - \frac{7 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{5} e g^{6}}{48 \, {\left(c^{5} g^{10} h^{3} x + 5 \, a c^{4} g^{8} h^{5} x + 10 \, a^{2} c^{3} g^{6} h^{7} x + 10 \, a^{3} c^{2} g^{4} h^{9} x + 5 \, a^{4} c g^{2} h^{11} x + a^{5} h^{13} x + c^{5} g^{11} h^{2} + 5 \, a c^{4} g^{9} h^{4} + 10 \, a^{2} c^{3} g^{7} h^{6} + 10 \, a^{3} c^{2} g^{5} h^{8} + 5 \, a^{4} c g^{3} h^{10} + a^{5} g h^{12}\right)}} - \frac{7 \, {\left(c x^{2} + a\right)}^{\frac{5}{2}} c^{4} f g^{6}}{48 \, {\left(c^{5} g^{10} h^{3} x^{2} + 5 \, a c^{4} g^{8} h^{5} x^{2} + 10 \, a^{2} c^{3} g^{6} h^{7} x^{2} + 10 \, a^{3} c^{2} g^{4} h^{9} x^{2} + 5 \, a^{4} c g^{2} h^{11} x^{2} + a^{5} h^{13} x^{2} + 2 \, c^{5} g^{11} h^{2} x + 10 \, a c^{4} g^{9} h^{4} x + 20 \, a^{2} c^{3} g^{7} h^{6} x + 20 \, a^{3} c^{2} g^{5} h^{8} x + 10 \, a^{4} c g^{3} h^{10} x + 2 \, a^{5} g h^{12} x + c^{5} g^{12} h + 5 \, a c^{4} g^{10} h^{3} + 10 \, a^{2} c^{3} g^{8} h^{5} + 10 \, a^{3} c^{2} g^{6} h^{7} + 5 \, a^{4} c g^{4} h^{9} + a^{5} g^{2} h^{11}\right)}} + \frac{7 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{5} f g^{6}}{48 \, {\left(c^{5} g^{10} h^{3} + 5 \, a c^{4} g^{8} h^{5} + 10 \, a^{2} c^{3} g^{6} h^{7} + 10 \, a^{3} c^{2} g^{4} h^{9} + 5 \, a^{4} c g^{2} h^{11} + a^{5} h^{13}\right)}} - \frac{7 \, \sqrt{c x^{2} + a} c^{6} d g^{5} x}{16 \, {\left(c^{5} g^{10} h^{2} + 5 \, a c^{4} g^{8} h^{4} + 10 \, a^{2} c^{3} g^{6} h^{6} + 10 \, a^{3} c^{2} g^{4} h^{8} + 5 \, a^{4} c g^{2} h^{10} + a^{5} h^{12}\right)}} + \frac{7 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{5} d g^{5}}{48 \, {\left(c^{5} g^{10} h^{2} x + 5 \, a c^{4} g^{8} h^{4} x + 10 \, a^{2} c^{3} g^{6} h^{6} x + 10 \, a^{3} c^{2} g^{4} h^{8} x + 5 \, a^{4} c g^{2} h^{10} x + a^{5} h^{12} x + c^{5} g^{11} h + 5 \, a c^{4} g^{9} h^{3} + 10 \, a^{2} c^{3} g^{7} h^{5} + 10 \, a^{3} c^{2} g^{5} h^{7} + 5 \, a^{4} c g^{3} h^{9} + a^{5} g h^{11}\right)}} + \frac{7 \, {\left(c x^{2} + a\right)}^{\frac{5}{2}} c^{4} e g^{5}}{48 \, {\left(c^{5} g^{10} h^{2} x^{2} + 5 \, a c^{4} g^{8} h^{4} x^{2} + 10 \, a^{2} c^{3} g^{6} h^{6} x^{2} + 10 \, a^{3} c^{2} g^{4} h^{8} x^{2} + 5 \, a^{4} c g^{2} h^{10} x^{2} + a^{5} h^{12} x^{2} + 2 \, c^{5} g^{11} h x + 10 \, a c^{4} g^{9} h^{3} x + 20 \, a^{2} c^{3} g^{7} h^{5} x + 20 \, a^{3} c^{2} g^{5} h^{7} x + 10 \, a^{4} c g^{3} h^{9} x + 2 \, a^{5} g h^{11} x + c^{5} g^{12} + 5 \, a c^{4} g^{10} h^{2} + 10 \, a^{2} c^{3} g^{8} h^{4} + 10 \, a^{3} c^{2} g^{6} h^{6} + 5 \, a^{4} c g^{4} h^{8} + a^{5} g^{2} h^{10}\right)}} - \frac{7 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{5} e g^{5}}{48 \, {\left(c^{5} g^{10} h^{2} + 5 \, a c^{4} g^{8} h^{4} + 10 \, a^{2} c^{3} g^{6} h^{6} + 10 \, a^{3} c^{2} g^{4} h^{8} + 5 \, a^{4} c g^{2} h^{10} + a^{5} h^{12}\right)}} - \frac{27 \, \sqrt{c x^{2} + a} c^{5} f g^{6}}{16 \, {\left(c^{4} g^{8} h^{5} + 4 \, a c^{3} g^{6} h^{7} + 6 \, a^{2} c^{2} g^{4} h^{9} + 4 \, a^{3} c g^{2} h^{11} + a^{4} h^{13}\right)}} + \frac{5 \, \sqrt{c x^{2} + a} c^{5} f g^{5} x}{4 \, {\left(c^{4} g^{8} h^{4} + 4 \, a c^{3} g^{6} h^{6} + 6 \, a^{2} c^{2} g^{4} h^{8} + 4 \, a^{3} c g^{2} h^{10} + a^{4} h^{12}\right)}} - \frac{7 \, {\left(c x^{2} + a\right)}^{\frac{5}{2}} c^{4} d g^{4}}{48 \, {\left(c^{5} g^{10} h x^{2} + 5 \, a c^{4} g^{8} h^{3} x^{2} + 10 \, a^{2} c^{3} g^{6} h^{5} x^{2} + 10 \, a^{3} c^{2} g^{4} h^{7} x^{2} + 5 \, a^{4} c g^{2} h^{9} x^{2} + a^{5} h^{11} x^{2} + 2 \, c^{5} g^{11} x + 10 \, a c^{4} g^{9} h^{2} x + 20 \, a^{2} c^{3} g^{7} h^{4} x + 20 \, a^{3} c^{2} g^{5} h^{6} x + 10 \, a^{4} c g^{3} h^{8} x + 2 \, a^{5} g h^{10} x + \frac{c^{5} g^{12}}{h} + 5 \, a c^{4} g^{10} h + 10 \, a^{2} c^{3} g^{8} h^{3} + 10 \, a^{3} c^{2} g^{6} h^{5} + 5 \, a^{4} c g^{4} h^{7} + a^{5} g^{2} h^{9}\right)}} + \frac{7 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{5} d g^{4}}{48 \, {\left(c^{5} g^{10} h + 5 \, a c^{4} g^{8} h^{3} + 10 \, a^{2} c^{3} g^{6} h^{5} + 10 \, a^{3} c^{2} g^{4} h^{7} + 5 \, a^{4} c g^{2} h^{9} + a^{5} h^{11}\right)}} + \frac{21 \, \sqrt{c x^{2} + a} c^{5} e g^{5}}{16 \, {\left(c^{4} g^{8} h^{4} + 4 \, a c^{3} g^{6} h^{6} + 6 \, a^{2} c^{2} g^{4} h^{8} + 4 \, a^{3} c g^{2} h^{10} + a^{4} h^{12}\right)}} - \frac{7 \, {\left(c x^{2} + a\right)}^{\frac{5}{2}} c^{3} f g^{5}}{24 \, {\left(c^{4} g^{8} h^{4} x^{3} + 4 \, a c^{3} g^{6} h^{6} x^{3} + 6 \, a^{2} c^{2} g^{4} h^{8} x^{3} + 4 \, a^{3} c g^{2} h^{10} x^{3} + a^{4} h^{12} x^{3} + 3 \, c^{4} g^{9} h^{3} x^{2} + 12 \, a c^{3} g^{7} h^{5} x^{2} + 18 \, a^{2} c^{2} g^{5} h^{7} x^{2} + 12 \, a^{3} c g^{3} h^{9} x^{2} + 3 \, a^{4} g h^{11} x^{2} + 3 \, c^{4} g^{10} h^{2} x + 12 \, a c^{3} g^{8} h^{4} x + 18 \, a^{2} c^{2} g^{6} h^{6} x + 12 \, a^{3} c g^{4} h^{8} x + 3 \, a^{4} g^{2} h^{10} x + c^{4} g^{11} h + 4 \, a c^{3} g^{9} h^{3} + 6 \, a^{2} c^{2} g^{7} h^{5} + 4 \, a^{3} c g^{5} h^{7} + a^{4} g^{3} h^{9}\right)}} - \frac{17 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{4} f g^{5}}{24 \, {\left(c^{4} g^{8} h^{4} x + 4 \, a c^{3} g^{6} h^{6} x + 6 \, a^{2} c^{2} g^{4} h^{8} x + 4 \, a^{3} c g^{2} h^{10} x + a^{4} h^{12} x + c^{4} g^{9} h^{3} + 4 \, a c^{3} g^{7} h^{5} + 6 \, a^{2} c^{2} g^{5} h^{7} + 4 \, a^{3} c g^{3} h^{9} + a^{4} g h^{11}\right)}} - \frac{7 \, \sqrt{c x^{2} + a} c^{5} e g^{4} x}{8 \, {\left(c^{4} g^{8} h^{3} + 4 \, a c^{3} g^{6} h^{5} + 6 \, a^{2} c^{2} g^{4} h^{7} + 4 \, a^{3} c g^{2} h^{9} + a^{4} h^{11}\right)}} - \frac{15 \, \sqrt{c x^{2} + a} c^{5} d g^{4}}{16 \, {\left(c^{4} g^{8} h^{3} + 4 \, a c^{3} g^{6} h^{5} + 6 \, a^{2} c^{2} g^{4} h^{7} + 4 \, a^{3} c g^{2} h^{9} + a^{4} h^{11}\right)}} + \frac{7 \, {\left(c x^{2} + a\right)}^{\frac{5}{2}} c^{3} e g^{4}}{24 \, {\left(c^{4} g^{8} h^{3} x^{3} + 4 \, a c^{3} g^{6} h^{5} x^{3} + 6 \, a^{2} c^{2} g^{4} h^{7} x^{3} + 4 \, a^{3} c g^{2} h^{9} x^{3} + a^{4} h^{11} x^{3} + 3 \, c^{4} g^{9} h^{2} x^{2} + 12 \, a c^{3} g^{7} h^{4} x^{2} + 18 \, a^{2} c^{2} g^{5} h^{6} x^{2} + 12 \, a^{3} c g^{3} h^{8} x^{2} + 3 \, a^{4} g h^{10} x^{2} + 3 \, c^{4} g^{10} h x + 12 \, a c^{3} g^{8} h^{3} x + 18 \, a^{2} c^{2} g^{6} h^{5} x + 12 \, a^{3} c g^{4} h^{7} x + 3 \, a^{4} g^{2} h^{9} x + c^{4} g^{11} + 4 \, a c^{3} g^{9} h^{2} + 6 \, a^{2} c^{2} g^{7} h^{4} + 4 \, a^{3} c g^{5} h^{6} + a^{4} g^{3} h^{8}\right)}} + \frac{7 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{4} e g^{4}}{12 \, {\left(c^{4} g^{8} h^{3} x + 4 \, a c^{3} g^{6} h^{5} x + 6 \, a^{2} c^{2} g^{4} h^{7} x + 4 \, a^{3} c g^{2} h^{9} x + a^{4} h^{11} x + c^{4} g^{9} h^{2} + 4 \, a c^{3} g^{7} h^{4} + 6 \, a^{2} c^{2} g^{5} h^{6} + 4 \, a^{3} c g^{3} h^{8} + a^{4} g h^{10}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} c^{3} f g^{4}}{8 \, {\left(c^{4} g^{8} h^{3} x^{2} + 4 \, a c^{3} g^{6} h^{5} x^{2} + 6 \, a^{2} c^{2} g^{4} h^{7} x^{2} + 4 \, a^{3} c g^{2} h^{9} x^{2} + a^{4} h^{11} x^{2} + 2 \, c^{4} g^{9} h^{2} x + 8 \, a c^{3} g^{7} h^{4} x + 12 \, a^{2} c^{2} g^{5} h^{6} x + 8 \, a^{3} c g^{3} h^{8} x + 2 \, a^{4} g h^{10} x + c^{4} g^{10} h + 4 \, a c^{3} g^{8} h^{3} + 6 \, a^{2} c^{2} g^{6} h^{5} + 4 \, a^{3} c g^{4} h^{7} + a^{4} g^{2} h^{9}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{4} f g^{4}}{8 \, {\left(c^{4} g^{8} h^{3} + 4 \, a c^{3} g^{6} h^{5} + 6 \, a^{2} c^{2} g^{4} h^{7} + 4 \, a^{3} c g^{2} h^{9} + a^{4} h^{11}\right)}} + \frac{\sqrt{c x^{2} + a} c^{5} d g^{3} x}{2 \, {\left(c^{4} g^{8} h^{2} + 4 \, a c^{3} g^{6} h^{4} + 6 \, a^{2} c^{2} g^{4} h^{6} + 4 \, a^{3} c g^{2} h^{8} + a^{4} h^{10}\right)}} - \frac{7 \, {\left(c x^{2} + a\right)}^{\frac{5}{2}} c^{3} d g^{3}}{24 \, {\left(c^{4} g^{8} h^{2} x^{3} + 4 \, a c^{3} g^{6} h^{4} x^{3} + 6 \, a^{2} c^{2} g^{4} h^{6} x^{3} + 4 \, a^{3} c g^{2} h^{8} x^{3} + a^{4} h^{10} x^{3} + 3 \, c^{4} g^{9} h x^{2} + 12 \, a c^{3} g^{7} h^{3} x^{2} + 18 \, a^{2} c^{2} g^{5} h^{5} x^{2} + 12 \, a^{3} c g^{3} h^{7} x^{2} + 3 \, a^{4} g h^{9} x^{2} + 3 \, c^{4} g^{10} x + 12 \, a c^{3} g^{8} h^{2} x + 18 \, a^{2} c^{2} g^{6} h^{4} x + 12 \, a^{3} c g^{4} h^{6} x + 3 \, a^{4} g^{2} h^{8} x + \frac{c^{4} g^{11}}{h} + 4 \, a c^{3} g^{9} h + 6 \, a^{2} c^{2} g^{7} h^{3} + 4 \, a^{3} c g^{5} h^{5} + a^{4} g^{3} h^{7}\right)}} - \frac{11 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{4} d g^{3}}{24 \, {\left(c^{4} g^{8} h^{2} x + 4 \, a c^{3} g^{6} h^{4} x + 6 \, a^{2} c^{2} g^{4} h^{6} x + 4 \, a^{3} c g^{2} h^{8} x + a^{4} h^{10} x + c^{4} g^{9} h + 4 \, a c^{3} g^{7} h^{3} + 6 \, a^{2} c^{2} g^{5} h^{5} + 4 \, a^{3} c g^{3} h^{7} + a^{4} g h^{9}\right)}} - \frac{7 \, {\left(c x^{2} + a\right)}^{\frac{5}{2}} c^{2} f g^{4}}{24 \, {\left(c^{3} g^{6} h^{5} x^{4} + 3 \, a c^{2} g^{4} h^{7} x^{4} + 3 \, a^{2} c g^{2} h^{9} x^{4} + a^{3} h^{11} x^{4} + 4 \, c^{3} g^{7} h^{4} x^{3} + 12 \, a c^{2} g^{5} h^{6} x^{3} + 12 \, a^{2} c g^{3} h^{8} x^{3} + 4 \, a^{3} g h^{10} x^{3} + 6 \, c^{3} g^{8} h^{3} x^{2} + 18 \, a c^{2} g^{6} h^{5} x^{2} + 18 \, a^{2} c g^{4} h^{7} x^{2} + 6 \, a^{3} g^{2} h^{9} x^{2} + 4 \, c^{3} g^{9} h^{2} x + 12 \, a c^{2} g^{7} h^{4} x + 12 \, a^{2} c g^{5} h^{6} x + 4 \, a^{3} g^{3} h^{8} x + c^{3} g^{10} h + 3 \, a c^{2} g^{8} h^{3} + 3 \, a^{2} c g^{6} h^{5} + a^{3} g^{4} h^{7}\right)}} + \frac{39 \, \sqrt{c x^{2} + a} c^{4} f g^{4}}{16 \, {\left(c^{3} g^{6} h^{5} + 3 \, a c^{2} g^{4} h^{7} + 3 \, a^{2} c g^{2} h^{9} + a^{3} h^{11}\right)}} - \frac{19 \, \sqrt{c x^{2} + a} c^{4} f g^{3} x}{16 \, {\left(c^{3} g^{6} h^{4} + 3 \, a c^{2} g^{4} h^{6} + 3 \, a^{2} c g^{2} h^{8} + a^{3} h^{10}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} c^{3} d g^{2}}{8 \, {\left(c^{4} g^{8} h x^{2} + 4 \, a c^{3} g^{6} h^{3} x^{2} + 6 \, a^{2} c^{2} g^{4} h^{5} x^{2} + 4 \, a^{3} c g^{2} h^{7} x^{2} + a^{4} h^{9} x^{2} + 2 \, c^{4} g^{9} x + 8 \, a c^{3} g^{7} h^{2} x + 12 \, a^{2} c^{2} g^{5} h^{4} x + 8 \, a^{3} c g^{3} h^{6} x + 2 \, a^{4} g h^{8} x + \frac{c^{4} g^{10}}{h} + 4 \, a c^{3} g^{8} h + 6 \, a^{2} c^{2} g^{6} h^{3} + 4 \, a^{3} c g^{4} h^{5} + a^{4} g^{2} h^{7}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{4} d g^{2}}{8 \, {\left(c^{4} g^{8} h + 4 \, a c^{3} g^{6} h^{3} + 6 \, a^{2} c^{2} g^{4} h^{5} + 4 \, a^{3} c g^{2} h^{7} + a^{4} h^{9}\right)}} + \frac{7 \, {\left(c x^{2} + a\right)}^{\frac{5}{2}} c^{2} e g^{3}}{24 \, {\left(c^{3} g^{6} h^{4} x^{4} + 3 \, a c^{2} g^{4} h^{6} x^{4} + 3 \, a^{2} c g^{2} h^{8} x^{4} + a^{3} h^{10} x^{4} + 4 \, c^{3} g^{7} h^{3} x^{3} + 12 \, a c^{2} g^{5} h^{5} x^{3} + 12 \, a^{2} c g^{3} h^{7} x^{3} + 4 \, a^{3} g h^{9} x^{3} + 6 \, c^{3} g^{8} h^{2} x^{2} + 18 \, a c^{2} g^{6} h^{4} x^{2} + 18 \, a^{2} c g^{4} h^{6} x^{2} + 6 \, a^{3} g^{2} h^{8} x^{2} + 4 \, c^{3} g^{9} h x + 12 \, a c^{2} g^{7} h^{3} x + 12 \, a^{2} c g^{5} h^{5} x + 4 \, a^{3} g^{3} h^{7} x + c^{3} g^{10} + 3 \, a c^{2} g^{8} h^{2} + 3 \, a^{2} c g^{6} h^{4} + a^{3} g^{4} h^{6}\right)}} - \frac{21 \, \sqrt{c x^{2} + a} c^{4} e g^{3}}{16 \, {\left(c^{3} g^{6} h^{4} + 3 \, a c^{2} g^{4} h^{6} + 3 \, a^{2} c g^{2} h^{8} + a^{3} h^{10}\right)}} + \frac{13 \, {\left(c x^{2} + a\right)}^{\frac{5}{2}} c^{2} f g^{3}}{24 \, {\left(c^{3} g^{6} h^{4} x^{3} + 3 \, a c^{2} g^{4} h^{6} x^{3} + 3 \, a^{2} c g^{2} h^{8} x^{3} + a^{3} h^{10} x^{3} + 3 \, c^{3} g^{7} h^{3} x^{2} + 9 \, a c^{2} g^{5} h^{5} x^{2} + 9 \, a^{2} c g^{3} h^{7} x^{2} + 3 \, a^{3} g h^{9} x^{2} + 3 \, c^{3} g^{8} h^{2} x + 9 \, a c^{2} g^{6} h^{4} x + 9 \, a^{2} c g^{4} h^{6} x + 3 \, a^{3} g^{2} h^{8} x + c^{3} g^{9} h + 3 \, a c^{2} g^{7} h^{3} + 3 \, a^{2} c g^{5} h^{5} + a^{3} g^{3} h^{7}\right)}} + \frac{15 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{3} f g^{3}}{16 \, {\left(c^{3} g^{6} h^{4} x + 3 \, a c^{2} g^{4} h^{6} x + 3 \, a^{2} c g^{2} h^{8} x + a^{3} h^{10} x + c^{3} g^{7} h^{3} + 3 \, a c^{2} g^{5} h^{5} + 3 \, a^{2} c g^{3} h^{7} + a^{3} g h^{9}\right)}} + \frac{7 \, \sqrt{c x^{2} + a} c^{4} e g^{2} x}{16 \, {\left(c^{3} g^{6} h^{3} + 3 \, a c^{2} g^{4} h^{5} + 3 \, a^{2} c g^{2} h^{7} + a^{3} h^{9}\right)}} - \frac{7 \, {\left(c x^{2} + a\right)}^{\frac{5}{2}} c^{2} d g^{2}}{24 \, {\left(c^{3} g^{6} h^{3} x^{4} + 3 \, a c^{2} g^{4} h^{5} x^{4} + 3 \, a^{2} c g^{2} h^{7} x^{4} + a^{3} h^{9} x^{4} + 4 \, c^{3} g^{7} h^{2} x^{3} + 12 \, a c^{2} g^{5} h^{4} x^{3} + 12 \, a^{2} c g^{3} h^{6} x^{3} + 4 \, a^{3} g h^{8} x^{3} + 6 \, c^{3} g^{8} h x^{2} + 18 \, a c^{2} g^{6} h^{3} x^{2} + 18 \, a^{2} c g^{4} h^{5} x^{2} + 6 \, a^{3} g^{2} h^{7} x^{2} + 4 \, c^{3} g^{9} x + 12 \, a c^{2} g^{7} h^{2} x + 12 \, a^{2} c g^{5} h^{4} x + 4 \, a^{3} g^{3} h^{6} x + \frac{c^{3} g^{10}}{h} + 3 \, a c^{2} g^{8} h + 3 \, a^{2} c g^{6} h^{3} + a^{3} g^{4} h^{5}\right)}} + \frac{9 \, \sqrt{c x^{2} + a} c^{4} d g^{2}}{16 \, {\left(c^{3} g^{6} h^{3} + 3 \, a c^{2} g^{4} h^{5} + 3 \, a^{2} c g^{2} h^{7} + a^{3} h^{9}\right)}} - \frac{7 \, {\left(c x^{2} + a\right)}^{\frac{5}{2}} c^{2} e g^{2}}{24 \, {\left(c^{3} g^{6} h^{3} x^{3} + 3 \, a c^{2} g^{4} h^{5} x^{3} + 3 \, a^{2} c g^{2} h^{7} x^{3} + a^{3} h^{9} x^{3} + 3 \, c^{3} g^{7} h^{2} x^{2} + 9 \, a c^{2} g^{5} h^{4} x^{2} + 9 \, a^{2} c g^{3} h^{6} x^{2} + 3 \, a^{3} g h^{8} x^{2} + 3 \, c^{3} g^{8} h x + 9 \, a c^{2} g^{6} h^{3} x + 9 \, a^{2} c g^{4} h^{5} x + 3 \, a^{3} g^{2} h^{7} x + c^{3} g^{9} + 3 \, a c^{2} g^{7} h^{2} + 3 \, a^{2} c g^{5} h^{4} + a^{3} g^{3} h^{6}\right)}} - \frac{7 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{3} e g^{2}}{16 \, {\left(c^{3} g^{6} h^{3} x + 3 \, a c^{2} g^{4} h^{5} x + 3 \, a^{2} c g^{2} h^{7} x + a^{3} h^{9} x + c^{3} g^{7} h^{2} + 3 \, a c^{2} g^{5} h^{4} + 3 \, a^{2} c g^{3} h^{6} + a^{3} g h^{8}\right)}} + \frac{7 \, {\left(c x^{2} + a\right)}^{\frac{5}{2}} c^{2} f g^{2}}{48 \, {\left(c^{3} g^{6} h^{3} x^{2} + 3 \, a c^{2} g^{4} h^{5} x^{2} + 3 \, a^{2} c g^{2} h^{7} x^{2} + a^{3} h^{9} x^{2} + 2 \, c^{3} g^{7} h^{2} x + 6 \, a c^{2} g^{5} h^{4} x + 6 \, a^{2} c g^{3} h^{6} x + 2 \, a^{3} g h^{8} x + c^{3} g^{8} h + 3 \, a c^{2} g^{6} h^{3} + 3 \, a^{2} c g^{4} h^{5} + a^{3} g^{2} h^{7}\right)}} - \frac{7 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{3} f g^{2}}{48 \, {\left(c^{3} g^{6} h^{3} + 3 \, a c^{2} g^{4} h^{5} + 3 \, a^{2} c g^{2} h^{7} + a^{3} h^{9}\right)}} - \frac{7 \, {\left(c x^{2} + a\right)}^{\frac{5}{2}} c f g^{3}}{30 \, {\left(c^{2} g^{4} h^{6} x^{5} + 2 \, a c g^{2} h^{8} x^{5} + a^{2} h^{10} x^{5} + 5 \, c^{2} g^{5} h^{5} x^{4} + 10 \, a c g^{3} h^{7} x^{4} + 5 \, a^{2} g h^{9} x^{4} + 10 \, c^{2} g^{6} h^{4} x^{3} + 20 \, a c g^{4} h^{6} x^{3} + 10 \, a^{2} g^{2} h^{8} x^{3} + 10 \, c^{2} g^{7} h^{3} x^{2} + 20 \, a c g^{5} h^{5} x^{2} + 10 \, a^{2} g^{3} h^{7} x^{2} + 5 \, c^{2} g^{8} h^{2} x + 10 \, a c g^{6} h^{4} x + 5 \, a^{2} g^{4} h^{6} x + c^{2} g^{9} h + 2 \, a c g^{7} h^{3} + a^{2} g^{5} h^{5}\right)}} - \frac{\sqrt{c x^{2} + a} c^{4} d g x}{16 \, {\left(c^{3} g^{6} h^{2} + 3 \, a c^{2} g^{4} h^{4} + 3 \, a^{2} c g^{2} h^{6} + a^{3} h^{8}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} c^{2} d g}{24 \, {\left(c^{3} g^{6} h^{2} x^{3} + 3 \, a c^{2} g^{4} h^{4} x^{3} + 3 \, a^{2} c g^{2} h^{6} x^{3} + a^{3} h^{8} x^{3} + 3 \, c^{3} g^{7} h x^{2} + 9 \, a c^{2} g^{5} h^{3} x^{2} + 9 \, a^{2} c g^{3} h^{5} x^{2} + 3 \, a^{3} g h^{7} x^{2} + 3 \, c^{3} g^{8} x + 9 \, a c^{2} g^{6} h^{2} x + 9 \, a^{2} c g^{4} h^{4} x + 3 \, a^{3} g^{2} h^{6} x + \frac{c^{3} g^{9}}{h} + 3 \, a c^{2} g^{7} h + 3 \, a^{2} c g^{5} h^{3} + a^{3} g^{3} h^{5}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{3} d g}{16 \, {\left(c^{3} g^{6} h^{2} x + 3 \, a c^{2} g^{4} h^{4} x + 3 \, a^{2} c g^{2} h^{6} x + a^{3} h^{8} x + c^{3} g^{7} h + 3 \, a c^{2} g^{5} h^{3} + 3 \, a^{2} c g^{3} h^{5} + a^{3} g h^{7}\right)}} - \frac{7 \, {\left(c x^{2} + a\right)}^{\frac{5}{2}} c^{2} e g}{48 \, {\left(c^{3} g^{6} h^{2} x^{2} + 3 \, a c^{2} g^{4} h^{4} x^{2} + 3 \, a^{2} c g^{2} h^{6} x^{2} + a^{3} h^{8} x^{2} + 2 \, c^{3} g^{7} h x + 6 \, a c^{2} g^{5} h^{3} x + 6 \, a^{2} c g^{3} h^{5} x + 2 \, a^{3} g h^{7} x + c^{3} g^{8} + 3 \, a c^{2} g^{6} h^{2} + 3 \, a^{2} c g^{4} h^{4} + a^{3} g^{2} h^{6}\right)}} + \frac{7 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{3} e g}{48 \, {\left(c^{3} g^{6} h^{2} + 3 \, a c^{2} g^{4} h^{4} + 3 \, a^{2} c g^{2} h^{6} + a^{3} h^{8}\right)}} + \frac{7 \, {\left(c x^{2} + a\right)}^{\frac{5}{2}} c e g^{2}}{30 \, {\left(c^{2} g^{4} h^{5} x^{5} + 2 \, a c g^{2} h^{7} x^{5} + a^{2} h^{9} x^{5} + 5 \, c^{2} g^{5} h^{4} x^{4} + 10 \, a c g^{3} h^{6} x^{4} + 5 \, a^{2} g h^{8} x^{4} + 10 \, c^{2} g^{6} h^{3} x^{3} + 20 \, a c g^{4} h^{5} x^{3} + 10 \, a^{2} g^{2} h^{7} x^{3} + 10 \, c^{2} g^{7} h^{2} x^{2} + 20 \, a c g^{5} h^{4} x^{2} + 10 \, a^{2} g^{3} h^{6} x^{2} + 5 \, c^{2} g^{8} h x + 10 \, a c g^{6} h^{3} x + 5 \, a^{2} g^{4} h^{5} x + c^{2} g^{9} + 2 \, a c g^{7} h^{2} + a^{2} g^{5} h^{4}\right)}} + \frac{13 \, {\left(c x^{2} + a\right)}^{\frac{5}{2}} c f g^{2}}{24 \, {\left(c^{2} g^{4} h^{5} x^{4} + 2 \, a c g^{2} h^{7} x^{4} + a^{2} h^{9} x^{4} + 4 \, c^{2} g^{5} h^{4} x^{3} + 8 \, a c g^{3} h^{6} x^{3} + 4 \, a^{2} g h^{8} x^{3} + 6 \, c^{2} g^{6} h^{3} x^{2} + 12 \, a c g^{4} h^{5} x^{2} + 6 \, a^{2} g^{2} h^{7} x^{2} + 4 \, c^{2} g^{7} h^{2} x + 8 \, a c g^{5} h^{4} x + 4 \, a^{2} g^{3} h^{6} x + c^{2} g^{8} h + 2 \, a c g^{6} h^{3} + a^{2} g^{4} h^{5}\right)}} - \frac{25 \, \sqrt{c x^{2} + a} c^{3} f g^{2}}{16 \, {\left(c^{2} g^{4} h^{5} + 2 \, a c g^{2} h^{7} + a^{2} h^{9}\right)}} + \frac{3 \, \sqrt{c x^{2} + a} c^{3} f g x}{8 \, {\left(c^{2} g^{4} h^{4} + 2 \, a c g^{2} h^{6} + a^{2} h^{8}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} c^{2} d}{48 \, {\left(c^{3} g^{6} h x^{2} + 3 \, a c^{2} g^{4} h^{3} x^{2} + 3 \, a^{2} c g^{2} h^{5} x^{2} + a^{3} h^{7} x^{2} + 2 \, c^{3} g^{7} x + 6 \, a c^{2} g^{5} h^{2} x + 6 \, a^{2} c g^{3} h^{4} x + 2 \, a^{3} g h^{6} x + \frac{c^{3} g^{8}}{h} + 3 \, a c^{2} g^{6} h + 3 \, a^{2} c g^{4} h^{3} + a^{3} g^{2} h^{5}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{3} d}{48 \, {\left(c^{3} g^{6} h + 3 \, a c^{2} g^{4} h^{3} + 3 \, a^{2} c g^{2} h^{5} + a^{3} h^{7}\right)}} - \frac{7 \, {\left(c x^{2} + a\right)}^{\frac{5}{2}} c d g}{30 \, {\left(c^{2} g^{4} h^{4} x^{5} + 2 \, a c g^{2} h^{6} x^{5} + a^{2} h^{8} x^{5} + 5 \, c^{2} g^{5} h^{3} x^{4} + 10 \, a c g^{3} h^{5} x^{4} + 5 \, a^{2} g h^{7} x^{4} + 10 \, c^{2} g^{6} h^{2} x^{3} + 20 \, a c g^{4} h^{4} x^{3} + 10 \, a^{2} g^{2} h^{6} x^{3} + 10 \, c^{2} g^{7} h x^{2} + 20 \, a c g^{5} h^{3} x^{2} + 10 \, a^{2} g^{3} h^{5} x^{2} + 5 \, c^{2} g^{8} x + 10 \, a c g^{6} h^{2} x + 5 \, a^{2} g^{4} h^{4} x + \frac{c^{2} g^{9}}{h} + 2 \, a c g^{7} h + a^{2} g^{5} h^{3}\right)}} - \frac{7 \, {\left(c x^{2} + a\right)}^{\frac{5}{2}} c e g}{24 \, {\left(c^{2} g^{4} h^{4} x^{4} + 2 \, a c g^{2} h^{6} x^{4} + a^{2} h^{8} x^{4} + 4 \, c^{2} g^{5} h^{3} x^{3} + 8 \, a c g^{3} h^{5} x^{3} + 4 \, a^{2} g h^{7} x^{3} + 6 \, c^{2} g^{6} h^{2} x^{2} + 12 \, a c g^{4} h^{4} x^{2} + 6 \, a^{2} g^{2} h^{6} x^{2} + 4 \, c^{2} g^{7} h x + 8 \, a c g^{5} h^{3} x + 4 \, a^{2} g^{3} h^{5} x + c^{2} g^{8} + 2 \, a c g^{6} h^{2} + a^{2} g^{4} h^{4}\right)}} + \frac{7 \, \sqrt{c x^{2} + a} c^{3} e g}{16 \, {\left(c^{2} g^{4} h^{4} + 2 \, a c g^{2} h^{6} + a^{2} h^{8}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} c f g}{4 \, {\left(c^{2} g^{4} h^{4} x^{3} + 2 \, a c g^{2} h^{6} x^{3} + a^{2} h^{8} x^{3} + 3 \, c^{2} g^{5} h^{3} x^{2} + 6 \, a c g^{3} h^{5} x^{2} + 3 \, a^{2} g h^{7} x^{2} + 3 \, c^{2} g^{6} h^{2} x + 6 \, a c g^{4} h^{4} x + 3 \, a^{2} g^{2} h^{6} x + c^{2} g^{7} h + 2 \, a c g^{5} h^{3} + a^{2} g^{3} h^{5}\right)}} - \frac{3 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{2} f g}{8 \, {\left(c^{2} g^{4} h^{4} x + 2 \, a c g^{2} h^{6} x + a^{2} h^{8} x + c^{2} g^{5} h^{3} + 2 \, a c g^{3} h^{5} + a^{2} g h^{7}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} f g^{2}}{6 \, {\left(c g^{2} h^{7} x^{6} + a h^{9} x^{6} + 6 \, c g^{3} h^{6} x^{5} + 6 \, a g h^{8} x^{5} + 15 \, c g^{4} h^{5} x^{4} + 15 \, a g^{2} h^{7} x^{4} + 20 \, c g^{5} h^{4} x^{3} + 20 \, a g^{3} h^{6} x^{3} + 15 \, c g^{6} h^{3} x^{2} + 15 \, a g^{4} h^{5} x^{2} + 6 \, c g^{7} h^{2} x + 6 \, a g^{5} h^{4} x + c g^{8} h + a g^{6} h^{3}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} c d}{24 \, {\left(c^{2} g^{4} h^{3} x^{4} + 2 \, a c g^{2} h^{5} x^{4} + a^{2} h^{7} x^{4} + 4 \, c^{2} g^{5} h^{2} x^{3} + 8 \, a c g^{3} h^{4} x^{3} + 4 \, a^{2} g h^{6} x^{3} + 6 \, c^{2} g^{6} h x^{2} + 12 \, a c g^{4} h^{3} x^{2} + 6 \, a^{2} g^{2} h^{5} x^{2} + 4 \, c^{2} g^{7} x + 8 \, a c g^{5} h^{2} x + 4 \, a^{2} g^{3} h^{4} x + \frac{c^{2} g^{8}}{h} + 2 \, a c g^{6} h + a^{2} g^{4} h^{3}\right)}} - \frac{\sqrt{c x^{2} + a} c^{3} d}{16 \, {\left(c^{2} g^{4} h^{3} + 2 \, a c g^{2} h^{5} + a^{2} h^{7}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} c f}{8 \, {\left(c^{2} g^{4} h^{3} x^{2} + 2 \, a c g^{2} h^{5} x^{2} + a^{2} h^{7} x^{2} + 2 \, c^{2} g^{5} h^{2} x + 4 \, a c g^{3} h^{4} x + 2 \, a^{2} g h^{6} x + c^{2} g^{6} h + 2 \, a c g^{4} h^{3} + a^{2} g^{2} h^{5}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} c^{2} f}{8 \, {\left(c^{2} g^{4} h^{3} + 2 \, a c g^{2} h^{5} + a^{2} h^{7}\right)}} + \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} e g}{6 \, {\left(c g^{2} h^{6} x^{6} + a h^{8} x^{6} + 6 \, c g^{3} h^{5} x^{5} + 6 \, a g h^{7} x^{5} + 15 \, c g^{4} h^{4} x^{4} + 15 \, a g^{2} h^{6} x^{4} + 20 \, c g^{5} h^{3} x^{3} + 20 \, a g^{3} h^{5} x^{3} + 15 \, c g^{6} h^{2} x^{2} + 15 \, a g^{4} h^{4} x^{2} + 6 \, c g^{7} h x + 6 \, a g^{5} h^{3} x + c g^{8} + a g^{6} h^{2}\right)}} + \frac{2 \, {\left(c x^{2} + a\right)}^{\frac{5}{2}} f g}{5 \, {\left(c g^{2} h^{6} x^{5} + a h^{8} x^{5} + 5 \, c g^{3} h^{5} x^{4} + 5 \, a g h^{7} x^{4} + 10 \, c g^{4} h^{4} x^{3} + 10 \, a g^{2} h^{6} x^{3} + 10 \, c g^{5} h^{3} x^{2} + 10 \, a g^{3} h^{5} x^{2} + 5 \, c g^{6} h^{2} x + 5 \, a g^{4} h^{4} x + c g^{7} h + a g^{5} h^{3}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} d}{6 \, {\left(c g^{2} h^{5} x^{6} + a h^{7} x^{6} + 6 \, c g^{3} h^{4} x^{5} + 6 \, a g h^{6} x^{5} + 15 \, c g^{4} h^{3} x^{4} + 15 \, a g^{2} h^{5} x^{4} + 20 \, c g^{5} h^{2} x^{3} + 20 \, a g^{3} h^{4} x^{3} + 15 \, c g^{6} h x^{2} + 15 \, a g^{4} h^{3} x^{2} + 6 \, c g^{7} x + 6 \, a g^{5} h^{2} x + \frac{c g^{8}}{h} + a g^{6} h\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} e}{5 \, {\left(c g^{2} h^{5} x^{5} + a h^{7} x^{5} + 5 \, c g^{3} h^{4} x^{4} + 5 \, a g h^{6} x^{4} + 10 \, c g^{4} h^{3} x^{3} + 10 \, a g^{2} h^{5} x^{3} + 10 \, c g^{5} h^{2} x^{2} + 10 \, a g^{3} h^{4} x^{2} + 5 \, c g^{6} h x + 5 \, a g^{4} h^{3} x + c g^{7} + a g^{5} h^{2}\right)}} - \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} f}{4 \, {\left(c g^{2} h^{5} x^{4} + a h^{7} x^{4} + 4 \, c g^{3} h^{4} x^{3} + 4 \, a g h^{6} x^{3} + 6 \, c g^{4} h^{3} x^{2} + 6 \, a g^{2} h^{5} x^{2} + 4 \, c g^{5} h^{2} x + 4 \, a g^{3} h^{4} x + c g^{6} h + a g^{4} h^{3}\right)}} + \frac{3 \, \sqrt{c x^{2} + a} c^{2} f}{8 \, {\left(c g^{2} h^{5} + a h^{7}\right)}} + \frac{7 \, c^{6} f g^{8} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{16 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{9}{2}} h^{15}} - \frac{7 \, c^{6} e g^{7} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{16 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{9}{2}} h^{14}} + \frac{7 \, c^{6} d g^{6} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{16 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{9}{2}} h^{13}} - \frac{27 \, c^{5} f g^{6} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{16 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{7}{2}} h^{13}} + \frac{21 \, c^{5} e g^{5} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{16 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{7}{2}} h^{12}} - \frac{15 \, c^{5} d g^{4} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{16 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{7}{2}} h^{11}} + \frac{39 \, c^{4} f g^{4} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{16 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{5}{2}} h^{11}} - \frac{21 \, c^{4} e g^{3} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{16 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{5}{2}} h^{10}} + \frac{9 \, c^{4} d g^{2} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{16 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{5}{2}} h^{9}} - \frac{25 \, c^{3} f g^{2} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{16 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{3}{2}} h^{9}} + \frac{7 \, c^{3} e g \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{16 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{3}{2}} h^{8}} - \frac{c^{3} d \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{16 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{3}{2}} h^{7}} + \frac{3 \, c^{2} f \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{8 \, \sqrt{a + \frac{c g^{2}}{h^{2}}} h^{7}}"," ",0,"7/16*sqrt(c*x^2 + a)*c^6*f*g^8/(c^5*g^10*h^5 + 5*a*c^4*g^8*h^7 + 10*a^2*c^3*g^6*h^9 + 10*a^3*c^2*g^4*h^11 + 5*a^4*c*g^2*h^13 + a^5*h^15) - 7/16*sqrt(c*x^2 + a)*c^6*f*g^7*x/(c^5*g^10*h^4 + 5*a*c^4*g^8*h^6 + 10*a^2*c^3*g^6*h^8 + 10*a^3*c^2*g^4*h^10 + 5*a^4*c*g^2*h^12 + a^5*h^14) - 7/16*sqrt(c*x^2 + a)*c^6*e*g^7/(c^5*g^10*h^4 + 5*a*c^4*g^8*h^6 + 10*a^2*c^3*g^6*h^8 + 10*a^3*c^2*g^4*h^10 + 5*a^4*c*g^2*h^12 + a^5*h^14) + 7/48*(c*x^2 + a)^(3/2)*c^5*f*g^7/(c^5*g^10*h^4*x + 5*a*c^4*g^8*h^6*x + 10*a^2*c^3*g^6*h^8*x + 10*a^3*c^2*g^4*h^10*x + 5*a^4*c*g^2*h^12*x + a^5*h^14*x + c^5*g^11*h^3 + 5*a*c^4*g^9*h^5 + 10*a^2*c^3*g^7*h^7 + 10*a^3*c^2*g^5*h^9 + 5*a^4*c*g^3*h^11 + a^5*g*h^13) + 7/16*sqrt(c*x^2 + a)*c^6*e*g^6*x/(c^5*g^10*h^3 + 5*a*c^4*g^8*h^5 + 10*a^2*c^3*g^6*h^7 + 10*a^3*c^2*g^4*h^9 + 5*a^4*c*g^2*h^11 + a^5*h^13) + 7/16*sqrt(c*x^2 + a)*c^6*d*g^6/(c^5*g^10*h^3 + 5*a*c^4*g^8*h^5 + 10*a^2*c^3*g^6*h^7 + 10*a^3*c^2*g^4*h^9 + 5*a^4*c*g^2*h^11 + a^5*h^13) - 7/48*(c*x^2 + a)^(3/2)*c^5*e*g^6/(c^5*g^10*h^3*x + 5*a*c^4*g^8*h^5*x + 10*a^2*c^3*g^6*h^7*x + 10*a^3*c^2*g^4*h^9*x + 5*a^4*c*g^2*h^11*x + a^5*h^13*x + c^5*g^11*h^2 + 5*a*c^4*g^9*h^4 + 10*a^2*c^3*g^7*h^6 + 10*a^3*c^2*g^5*h^8 + 5*a^4*c*g^3*h^10 + a^5*g*h^12) - 7/48*(c*x^2 + a)^(5/2)*c^4*f*g^6/(c^5*g^10*h^3*x^2 + 5*a*c^4*g^8*h^5*x^2 + 10*a^2*c^3*g^6*h^7*x^2 + 10*a^3*c^2*g^4*h^9*x^2 + 5*a^4*c*g^2*h^11*x^2 + a^5*h^13*x^2 + 2*c^5*g^11*h^2*x + 10*a*c^4*g^9*h^4*x + 20*a^2*c^3*g^7*h^6*x + 20*a^3*c^2*g^5*h^8*x + 10*a^4*c*g^3*h^10*x + 2*a^5*g*h^12*x + c^5*g^12*h + 5*a*c^4*g^10*h^3 + 10*a^2*c^3*g^8*h^5 + 10*a^3*c^2*g^6*h^7 + 5*a^4*c*g^4*h^9 + a^5*g^2*h^11) + 7/48*(c*x^2 + a)^(3/2)*c^5*f*g^6/(c^5*g^10*h^3 + 5*a*c^4*g^8*h^5 + 10*a^2*c^3*g^6*h^7 + 10*a^3*c^2*g^4*h^9 + 5*a^4*c*g^2*h^11 + a^5*h^13) - 7/16*sqrt(c*x^2 + a)*c^6*d*g^5*x/(c^5*g^10*h^2 + 5*a*c^4*g^8*h^4 + 10*a^2*c^3*g^6*h^6 + 10*a^3*c^2*g^4*h^8 + 5*a^4*c*g^2*h^10 + a^5*h^12) + 7/48*(c*x^2 + a)^(3/2)*c^5*d*g^5/(c^5*g^10*h^2*x + 5*a*c^4*g^8*h^4*x + 10*a^2*c^3*g^6*h^6*x + 10*a^3*c^2*g^4*h^8*x + 5*a^4*c*g^2*h^10*x + a^5*h^12*x + c^5*g^11*h + 5*a*c^4*g^9*h^3 + 10*a^2*c^3*g^7*h^5 + 10*a^3*c^2*g^5*h^7 + 5*a^4*c*g^3*h^9 + a^5*g*h^11) + 7/48*(c*x^2 + a)^(5/2)*c^4*e*g^5/(c^5*g^10*h^2*x^2 + 5*a*c^4*g^8*h^4*x^2 + 10*a^2*c^3*g^6*h^6*x^2 + 10*a^3*c^2*g^4*h^8*x^2 + 5*a^4*c*g^2*h^10*x^2 + a^5*h^12*x^2 + 2*c^5*g^11*h*x + 10*a*c^4*g^9*h^3*x + 20*a^2*c^3*g^7*h^5*x + 20*a^3*c^2*g^5*h^7*x + 10*a^4*c*g^3*h^9*x + 2*a^5*g*h^11*x + c^5*g^12 + 5*a*c^4*g^10*h^2 + 10*a^2*c^3*g^8*h^4 + 10*a^3*c^2*g^6*h^6 + 5*a^4*c*g^4*h^8 + a^5*g^2*h^10) - 7/48*(c*x^2 + a)^(3/2)*c^5*e*g^5/(c^5*g^10*h^2 + 5*a*c^4*g^8*h^4 + 10*a^2*c^3*g^6*h^6 + 10*a^3*c^2*g^4*h^8 + 5*a^4*c*g^2*h^10 + a^5*h^12) - 27/16*sqrt(c*x^2 + a)*c^5*f*g^6/(c^4*g^8*h^5 + 4*a*c^3*g^6*h^7 + 6*a^2*c^2*g^4*h^9 + 4*a^3*c*g^2*h^11 + a^4*h^13) + 5/4*sqrt(c*x^2 + a)*c^5*f*g^5*x/(c^4*g^8*h^4 + 4*a*c^3*g^6*h^6 + 6*a^2*c^2*g^4*h^8 + 4*a^3*c*g^2*h^10 + a^4*h^12) - 7/48*(c*x^2 + a)^(5/2)*c^4*d*g^4/(c^5*g^10*h*x^2 + 5*a*c^4*g^8*h^3*x^2 + 10*a^2*c^3*g^6*h^5*x^2 + 10*a^3*c^2*g^4*h^7*x^2 + 5*a^4*c*g^2*h^9*x^2 + a^5*h^11*x^2 + 2*c^5*g^11*x + 10*a*c^4*g^9*h^2*x + 20*a^2*c^3*g^7*h^4*x + 20*a^3*c^2*g^5*h^6*x + 10*a^4*c*g^3*h^8*x + 2*a^5*g*h^10*x + c^5*g^12/h + 5*a*c^4*g^10*h + 10*a^2*c^3*g^8*h^3 + 10*a^3*c^2*g^6*h^5 + 5*a^4*c*g^4*h^7 + a^5*g^2*h^9) + 7/48*(c*x^2 + a)^(3/2)*c^5*d*g^4/(c^5*g^10*h + 5*a*c^4*g^8*h^3 + 10*a^2*c^3*g^6*h^5 + 10*a^3*c^2*g^4*h^7 + 5*a^4*c*g^2*h^9 + a^5*h^11) + 21/16*sqrt(c*x^2 + a)*c^5*e*g^5/(c^4*g^8*h^4 + 4*a*c^3*g^6*h^6 + 6*a^2*c^2*g^4*h^8 + 4*a^3*c*g^2*h^10 + a^4*h^12) - 7/24*(c*x^2 + a)^(5/2)*c^3*f*g^5/(c^4*g^8*h^4*x^3 + 4*a*c^3*g^6*h^6*x^3 + 6*a^2*c^2*g^4*h^8*x^3 + 4*a^3*c*g^2*h^10*x^3 + a^4*h^12*x^3 + 3*c^4*g^9*h^3*x^2 + 12*a*c^3*g^7*h^5*x^2 + 18*a^2*c^2*g^5*h^7*x^2 + 12*a^3*c*g^3*h^9*x^2 + 3*a^4*g*h^11*x^2 + 3*c^4*g^10*h^2*x + 12*a*c^3*g^8*h^4*x + 18*a^2*c^2*g^6*h^6*x + 12*a^3*c*g^4*h^8*x + 3*a^4*g^2*h^10*x + c^4*g^11*h + 4*a*c^3*g^9*h^3 + 6*a^2*c^2*g^7*h^5 + 4*a^3*c*g^5*h^7 + a^4*g^3*h^9) - 17/24*(c*x^2 + a)^(3/2)*c^4*f*g^5/(c^4*g^8*h^4*x + 4*a*c^3*g^6*h^6*x + 6*a^2*c^2*g^4*h^8*x + 4*a^3*c*g^2*h^10*x + a^4*h^12*x + c^4*g^9*h^3 + 4*a*c^3*g^7*h^5 + 6*a^2*c^2*g^5*h^7 + 4*a^3*c*g^3*h^9 + a^4*g*h^11) - 7/8*sqrt(c*x^2 + a)*c^5*e*g^4*x/(c^4*g^8*h^3 + 4*a*c^3*g^6*h^5 + 6*a^2*c^2*g^4*h^7 + 4*a^3*c*g^2*h^9 + a^4*h^11) - 15/16*sqrt(c*x^2 + a)*c^5*d*g^4/(c^4*g^8*h^3 + 4*a*c^3*g^6*h^5 + 6*a^2*c^2*g^4*h^7 + 4*a^3*c*g^2*h^9 + a^4*h^11) + 7/24*(c*x^2 + a)^(5/2)*c^3*e*g^4/(c^4*g^8*h^3*x^3 + 4*a*c^3*g^6*h^5*x^3 + 6*a^2*c^2*g^4*h^7*x^3 + 4*a^3*c*g^2*h^9*x^3 + a^4*h^11*x^3 + 3*c^4*g^9*h^2*x^2 + 12*a*c^3*g^7*h^4*x^2 + 18*a^2*c^2*g^5*h^6*x^2 + 12*a^3*c*g^3*h^8*x^2 + 3*a^4*g*h^10*x^2 + 3*c^4*g^10*h*x + 12*a*c^3*g^8*h^3*x + 18*a^2*c^2*g^6*h^5*x + 12*a^3*c*g^4*h^7*x + 3*a^4*g^2*h^9*x + c^4*g^11 + 4*a*c^3*g^9*h^2 + 6*a^2*c^2*g^7*h^4 + 4*a^3*c*g^5*h^6 + a^4*g^3*h^8) + 7/12*(c*x^2 + a)^(3/2)*c^4*e*g^4/(c^4*g^8*h^3*x + 4*a*c^3*g^6*h^5*x + 6*a^2*c^2*g^4*h^7*x + 4*a^3*c*g^2*h^9*x + a^4*h^11*x + c^4*g^9*h^2 + 4*a*c^3*g^7*h^4 + 6*a^2*c^2*g^5*h^6 + 4*a^3*c*g^3*h^8 + a^4*g*h^10) + 1/8*(c*x^2 + a)^(5/2)*c^3*f*g^4/(c^4*g^8*h^3*x^2 + 4*a*c^3*g^6*h^5*x^2 + 6*a^2*c^2*g^4*h^7*x^2 + 4*a^3*c*g^2*h^9*x^2 + a^4*h^11*x^2 + 2*c^4*g^9*h^2*x + 8*a*c^3*g^7*h^4*x + 12*a^2*c^2*g^5*h^6*x + 8*a^3*c*g^3*h^8*x + 2*a^4*g*h^10*x + c^4*g^10*h + 4*a*c^3*g^8*h^3 + 6*a^2*c^2*g^6*h^5 + 4*a^3*c*g^4*h^7 + a^4*g^2*h^9) - 1/8*(c*x^2 + a)^(3/2)*c^4*f*g^4/(c^4*g^8*h^3 + 4*a*c^3*g^6*h^5 + 6*a^2*c^2*g^4*h^7 + 4*a^3*c*g^2*h^9 + a^4*h^11) + 1/2*sqrt(c*x^2 + a)*c^5*d*g^3*x/(c^4*g^8*h^2 + 4*a*c^3*g^6*h^4 + 6*a^2*c^2*g^4*h^6 + 4*a^3*c*g^2*h^8 + a^4*h^10) - 7/24*(c*x^2 + a)^(5/2)*c^3*d*g^3/(c^4*g^8*h^2*x^3 + 4*a*c^3*g^6*h^4*x^3 + 6*a^2*c^2*g^4*h^6*x^3 + 4*a^3*c*g^2*h^8*x^3 + a^4*h^10*x^3 + 3*c^4*g^9*h*x^2 + 12*a*c^3*g^7*h^3*x^2 + 18*a^2*c^2*g^5*h^5*x^2 + 12*a^3*c*g^3*h^7*x^2 + 3*a^4*g*h^9*x^2 + 3*c^4*g^10*x + 12*a*c^3*g^8*h^2*x + 18*a^2*c^2*g^6*h^4*x + 12*a^3*c*g^4*h^6*x + 3*a^4*g^2*h^8*x + c^4*g^11/h + 4*a*c^3*g^9*h + 6*a^2*c^2*g^7*h^3 + 4*a^3*c*g^5*h^5 + a^4*g^3*h^7) - 11/24*(c*x^2 + a)^(3/2)*c^4*d*g^3/(c^4*g^8*h^2*x + 4*a*c^3*g^6*h^4*x + 6*a^2*c^2*g^4*h^6*x + 4*a^3*c*g^2*h^8*x + a^4*h^10*x + c^4*g^9*h + 4*a*c^3*g^7*h^3 + 6*a^2*c^2*g^5*h^5 + 4*a^3*c*g^3*h^7 + a^4*g*h^9) - 7/24*(c*x^2 + a)^(5/2)*c^2*f*g^4/(c^3*g^6*h^5*x^4 + 3*a*c^2*g^4*h^7*x^4 + 3*a^2*c*g^2*h^9*x^4 + a^3*h^11*x^4 + 4*c^3*g^7*h^4*x^3 + 12*a*c^2*g^5*h^6*x^3 + 12*a^2*c*g^3*h^8*x^3 + 4*a^3*g*h^10*x^3 + 6*c^3*g^8*h^3*x^2 + 18*a*c^2*g^6*h^5*x^2 + 18*a^2*c*g^4*h^7*x^2 + 6*a^3*g^2*h^9*x^2 + 4*c^3*g^9*h^2*x + 12*a*c^2*g^7*h^4*x + 12*a^2*c*g^5*h^6*x + 4*a^3*g^3*h^8*x + c^3*g^10*h + 3*a*c^2*g^8*h^3 + 3*a^2*c*g^6*h^5 + a^3*g^4*h^7) + 39/16*sqrt(c*x^2 + a)*c^4*f*g^4/(c^3*g^6*h^5 + 3*a*c^2*g^4*h^7 + 3*a^2*c*g^2*h^9 + a^3*h^11) - 19/16*sqrt(c*x^2 + a)*c^4*f*g^3*x/(c^3*g^6*h^4 + 3*a*c^2*g^4*h^6 + 3*a^2*c*g^2*h^8 + a^3*h^10) - 1/8*(c*x^2 + a)^(5/2)*c^3*d*g^2/(c^4*g^8*h*x^2 + 4*a*c^3*g^6*h^3*x^2 + 6*a^2*c^2*g^4*h^5*x^2 + 4*a^3*c*g^2*h^7*x^2 + a^4*h^9*x^2 + 2*c^4*g^9*x + 8*a*c^3*g^7*h^2*x + 12*a^2*c^2*g^5*h^4*x + 8*a^3*c*g^3*h^6*x + 2*a^4*g*h^8*x + c^4*g^10/h + 4*a*c^3*g^8*h + 6*a^2*c^2*g^6*h^3 + 4*a^3*c*g^4*h^5 + a^4*g^2*h^7) + 1/8*(c*x^2 + a)^(3/2)*c^4*d*g^2/(c^4*g^8*h + 4*a*c^3*g^6*h^3 + 6*a^2*c^2*g^4*h^5 + 4*a^3*c*g^2*h^7 + a^4*h^9) + 7/24*(c*x^2 + a)^(5/2)*c^2*e*g^3/(c^3*g^6*h^4*x^4 + 3*a*c^2*g^4*h^6*x^4 + 3*a^2*c*g^2*h^8*x^4 + a^3*h^10*x^4 + 4*c^3*g^7*h^3*x^3 + 12*a*c^2*g^5*h^5*x^3 + 12*a^2*c*g^3*h^7*x^3 + 4*a^3*g*h^9*x^3 + 6*c^3*g^8*h^2*x^2 + 18*a*c^2*g^6*h^4*x^2 + 18*a^2*c*g^4*h^6*x^2 + 6*a^3*g^2*h^8*x^2 + 4*c^3*g^9*h*x + 12*a*c^2*g^7*h^3*x + 12*a^2*c*g^5*h^5*x + 4*a^3*g^3*h^7*x + c^3*g^10 + 3*a*c^2*g^8*h^2 + 3*a^2*c*g^6*h^4 + a^3*g^4*h^6) - 21/16*sqrt(c*x^2 + a)*c^4*e*g^3/(c^3*g^6*h^4 + 3*a*c^2*g^4*h^6 + 3*a^2*c*g^2*h^8 + a^3*h^10) + 13/24*(c*x^2 + a)^(5/2)*c^2*f*g^3/(c^3*g^6*h^4*x^3 + 3*a*c^2*g^4*h^6*x^3 + 3*a^2*c*g^2*h^8*x^3 + a^3*h^10*x^3 + 3*c^3*g^7*h^3*x^2 + 9*a*c^2*g^5*h^5*x^2 + 9*a^2*c*g^3*h^7*x^2 + 3*a^3*g*h^9*x^2 + 3*c^3*g^8*h^2*x + 9*a*c^2*g^6*h^4*x + 9*a^2*c*g^4*h^6*x + 3*a^3*g^2*h^8*x + c^3*g^9*h + 3*a*c^2*g^7*h^3 + 3*a^2*c*g^5*h^5 + a^3*g^3*h^7) + 15/16*(c*x^2 + a)^(3/2)*c^3*f*g^3/(c^3*g^6*h^4*x + 3*a*c^2*g^4*h^6*x + 3*a^2*c*g^2*h^8*x + a^3*h^10*x + c^3*g^7*h^3 + 3*a*c^2*g^5*h^5 + 3*a^2*c*g^3*h^7 + a^3*g*h^9) + 7/16*sqrt(c*x^2 + a)*c^4*e*g^2*x/(c^3*g^6*h^3 + 3*a*c^2*g^4*h^5 + 3*a^2*c*g^2*h^7 + a^3*h^9) - 7/24*(c*x^2 + a)^(5/2)*c^2*d*g^2/(c^3*g^6*h^3*x^4 + 3*a*c^2*g^4*h^5*x^4 + 3*a^2*c*g^2*h^7*x^4 + a^3*h^9*x^4 + 4*c^3*g^7*h^2*x^3 + 12*a*c^2*g^5*h^4*x^3 + 12*a^2*c*g^3*h^6*x^3 + 4*a^3*g*h^8*x^3 + 6*c^3*g^8*h*x^2 + 18*a*c^2*g^6*h^3*x^2 + 18*a^2*c*g^4*h^5*x^2 + 6*a^3*g^2*h^7*x^2 + 4*c^3*g^9*x + 12*a*c^2*g^7*h^2*x + 12*a^2*c*g^5*h^4*x + 4*a^3*g^3*h^6*x + c^3*g^10/h + 3*a*c^2*g^8*h + 3*a^2*c*g^6*h^3 + a^3*g^4*h^5) + 9/16*sqrt(c*x^2 + a)*c^4*d*g^2/(c^3*g^6*h^3 + 3*a*c^2*g^4*h^5 + 3*a^2*c*g^2*h^7 + a^3*h^9) - 7/24*(c*x^2 + a)^(5/2)*c^2*e*g^2/(c^3*g^6*h^3*x^3 + 3*a*c^2*g^4*h^5*x^3 + 3*a^2*c*g^2*h^7*x^3 + a^3*h^9*x^3 + 3*c^3*g^7*h^2*x^2 + 9*a*c^2*g^5*h^4*x^2 + 9*a^2*c*g^3*h^6*x^2 + 3*a^3*g*h^8*x^2 + 3*c^3*g^8*h*x + 9*a*c^2*g^6*h^3*x + 9*a^2*c*g^4*h^5*x + 3*a^3*g^2*h^7*x + c^3*g^9 + 3*a*c^2*g^7*h^2 + 3*a^2*c*g^5*h^4 + a^3*g^3*h^6) - 7/16*(c*x^2 + a)^(3/2)*c^3*e*g^2/(c^3*g^6*h^3*x + 3*a*c^2*g^4*h^5*x + 3*a^2*c*g^2*h^7*x + a^3*h^9*x + c^3*g^7*h^2 + 3*a*c^2*g^5*h^4 + 3*a^2*c*g^3*h^6 + a^3*g*h^8) + 7/48*(c*x^2 + a)^(5/2)*c^2*f*g^2/(c^3*g^6*h^3*x^2 + 3*a*c^2*g^4*h^5*x^2 + 3*a^2*c*g^2*h^7*x^2 + a^3*h^9*x^2 + 2*c^3*g^7*h^2*x + 6*a*c^2*g^5*h^4*x + 6*a^2*c*g^3*h^6*x + 2*a^3*g*h^8*x + c^3*g^8*h + 3*a*c^2*g^6*h^3 + 3*a^2*c*g^4*h^5 + a^3*g^2*h^7) - 7/48*(c*x^2 + a)^(3/2)*c^3*f*g^2/(c^3*g^6*h^3 + 3*a*c^2*g^4*h^5 + 3*a^2*c*g^2*h^7 + a^3*h^9) - 7/30*(c*x^2 + a)^(5/2)*c*f*g^3/(c^2*g^4*h^6*x^5 + 2*a*c*g^2*h^8*x^5 + a^2*h^10*x^5 + 5*c^2*g^5*h^5*x^4 + 10*a*c*g^3*h^7*x^4 + 5*a^2*g*h^9*x^4 + 10*c^2*g^6*h^4*x^3 + 20*a*c*g^4*h^6*x^3 + 10*a^2*g^2*h^8*x^3 + 10*c^2*g^7*h^3*x^2 + 20*a*c*g^5*h^5*x^2 + 10*a^2*g^3*h^7*x^2 + 5*c^2*g^8*h^2*x + 10*a*c*g^6*h^4*x + 5*a^2*g^4*h^6*x + c^2*g^9*h + 2*a*c*g^7*h^3 + a^2*g^5*h^5) - 1/16*sqrt(c*x^2 + a)*c^4*d*g*x/(c^3*g^6*h^2 + 3*a*c^2*g^4*h^4 + 3*a^2*c*g^2*h^6 + a^3*h^8) + 1/24*(c*x^2 + a)^(5/2)*c^2*d*g/(c^3*g^6*h^2*x^3 + 3*a*c^2*g^4*h^4*x^3 + 3*a^2*c*g^2*h^6*x^3 + a^3*h^8*x^3 + 3*c^3*g^7*h*x^2 + 9*a*c^2*g^5*h^3*x^2 + 9*a^2*c*g^3*h^5*x^2 + 3*a^3*g*h^7*x^2 + 3*c^3*g^8*x + 9*a*c^2*g^6*h^2*x + 9*a^2*c*g^4*h^4*x + 3*a^3*g^2*h^6*x + c^3*g^9/h + 3*a*c^2*g^7*h + 3*a^2*c*g^5*h^3 + a^3*g^3*h^5) + 1/16*(c*x^2 + a)^(3/2)*c^3*d*g/(c^3*g^6*h^2*x + 3*a*c^2*g^4*h^4*x + 3*a^2*c*g^2*h^6*x + a^3*h^8*x + c^3*g^7*h + 3*a*c^2*g^5*h^3 + 3*a^2*c*g^3*h^5 + a^3*g*h^7) - 7/48*(c*x^2 + a)^(5/2)*c^2*e*g/(c^3*g^6*h^2*x^2 + 3*a*c^2*g^4*h^4*x^2 + 3*a^2*c*g^2*h^6*x^2 + a^3*h^8*x^2 + 2*c^3*g^7*h*x + 6*a*c^2*g^5*h^3*x + 6*a^2*c*g^3*h^5*x + 2*a^3*g*h^7*x + c^3*g^8 + 3*a*c^2*g^6*h^2 + 3*a^2*c*g^4*h^4 + a^3*g^2*h^6) + 7/48*(c*x^2 + a)^(3/2)*c^3*e*g/(c^3*g^6*h^2 + 3*a*c^2*g^4*h^4 + 3*a^2*c*g^2*h^6 + a^3*h^8) + 7/30*(c*x^2 + a)^(5/2)*c*e*g^2/(c^2*g^4*h^5*x^5 + 2*a*c*g^2*h^7*x^5 + a^2*h^9*x^5 + 5*c^2*g^5*h^4*x^4 + 10*a*c*g^3*h^6*x^4 + 5*a^2*g*h^8*x^4 + 10*c^2*g^6*h^3*x^3 + 20*a*c*g^4*h^5*x^3 + 10*a^2*g^2*h^7*x^3 + 10*c^2*g^7*h^2*x^2 + 20*a*c*g^5*h^4*x^2 + 10*a^2*g^3*h^6*x^2 + 5*c^2*g^8*h*x + 10*a*c*g^6*h^3*x + 5*a^2*g^4*h^5*x + c^2*g^9 + 2*a*c*g^7*h^2 + a^2*g^5*h^4) + 13/24*(c*x^2 + a)^(5/2)*c*f*g^2/(c^2*g^4*h^5*x^4 + 2*a*c*g^2*h^7*x^4 + a^2*h^9*x^4 + 4*c^2*g^5*h^4*x^3 + 8*a*c*g^3*h^6*x^3 + 4*a^2*g*h^8*x^3 + 6*c^2*g^6*h^3*x^2 + 12*a*c*g^4*h^5*x^2 + 6*a^2*g^2*h^7*x^2 + 4*c^2*g^7*h^2*x + 8*a*c*g^5*h^4*x + 4*a^2*g^3*h^6*x + c^2*g^8*h + 2*a*c*g^6*h^3 + a^2*g^4*h^5) - 25/16*sqrt(c*x^2 + a)*c^3*f*g^2/(c^2*g^4*h^5 + 2*a*c*g^2*h^7 + a^2*h^9) + 3/8*sqrt(c*x^2 + a)*c^3*f*g*x/(c^2*g^4*h^4 + 2*a*c*g^2*h^6 + a^2*h^8) + 1/48*(c*x^2 + a)^(5/2)*c^2*d/(c^3*g^6*h*x^2 + 3*a*c^2*g^4*h^3*x^2 + 3*a^2*c*g^2*h^5*x^2 + a^3*h^7*x^2 + 2*c^3*g^7*x + 6*a*c^2*g^5*h^2*x + 6*a^2*c*g^3*h^4*x + 2*a^3*g*h^6*x + c^3*g^8/h + 3*a*c^2*g^6*h + 3*a^2*c*g^4*h^3 + a^3*g^2*h^5) - 1/48*(c*x^2 + a)^(3/2)*c^3*d/(c^3*g^6*h + 3*a*c^2*g^4*h^3 + 3*a^2*c*g^2*h^5 + a^3*h^7) - 7/30*(c*x^2 + a)^(5/2)*c*d*g/(c^2*g^4*h^4*x^5 + 2*a*c*g^2*h^6*x^5 + a^2*h^8*x^5 + 5*c^2*g^5*h^3*x^4 + 10*a*c*g^3*h^5*x^4 + 5*a^2*g*h^7*x^4 + 10*c^2*g^6*h^2*x^3 + 20*a*c*g^4*h^4*x^3 + 10*a^2*g^2*h^6*x^3 + 10*c^2*g^7*h*x^2 + 20*a*c*g^5*h^3*x^2 + 10*a^2*g^3*h^5*x^2 + 5*c^2*g^8*x + 10*a*c*g^6*h^2*x + 5*a^2*g^4*h^4*x + c^2*g^9/h + 2*a*c*g^7*h + a^2*g^5*h^3) - 7/24*(c*x^2 + a)^(5/2)*c*e*g/(c^2*g^4*h^4*x^4 + 2*a*c*g^2*h^6*x^4 + a^2*h^8*x^4 + 4*c^2*g^5*h^3*x^3 + 8*a*c*g^3*h^5*x^3 + 4*a^2*g*h^7*x^3 + 6*c^2*g^6*h^2*x^2 + 12*a*c*g^4*h^4*x^2 + 6*a^2*g^2*h^6*x^2 + 4*c^2*g^7*h*x + 8*a*c*g^5*h^3*x + 4*a^2*g^3*h^5*x + c^2*g^8 + 2*a*c*g^6*h^2 + a^2*g^4*h^4) + 7/16*sqrt(c*x^2 + a)*c^3*e*g/(c^2*g^4*h^4 + 2*a*c*g^2*h^6 + a^2*h^8) - 1/4*(c*x^2 + a)^(5/2)*c*f*g/(c^2*g^4*h^4*x^3 + 2*a*c*g^2*h^6*x^3 + a^2*h^8*x^3 + 3*c^2*g^5*h^3*x^2 + 6*a*c*g^3*h^5*x^2 + 3*a^2*g*h^7*x^2 + 3*c^2*g^6*h^2*x + 6*a*c*g^4*h^4*x + 3*a^2*g^2*h^6*x + c^2*g^7*h + 2*a*c*g^5*h^3 + a^2*g^3*h^5) - 3/8*(c*x^2 + a)^(3/2)*c^2*f*g/(c^2*g^4*h^4*x + 2*a*c*g^2*h^6*x + a^2*h^8*x + c^2*g^5*h^3 + 2*a*c*g^3*h^5 + a^2*g*h^7) - 1/6*(c*x^2 + a)^(5/2)*f*g^2/(c*g^2*h^7*x^6 + a*h^9*x^6 + 6*c*g^3*h^6*x^5 + 6*a*g*h^8*x^5 + 15*c*g^4*h^5*x^4 + 15*a*g^2*h^7*x^4 + 20*c*g^5*h^4*x^3 + 20*a*g^3*h^6*x^3 + 15*c*g^6*h^3*x^2 + 15*a*g^4*h^5*x^2 + 6*c*g^7*h^2*x + 6*a*g^5*h^4*x + c*g^8*h + a*g^6*h^3) + 1/24*(c*x^2 + a)^(5/2)*c*d/(c^2*g^4*h^3*x^4 + 2*a*c*g^2*h^5*x^4 + a^2*h^7*x^4 + 4*c^2*g^5*h^2*x^3 + 8*a*c*g^3*h^4*x^3 + 4*a^2*g*h^6*x^3 + 6*c^2*g^6*h*x^2 + 12*a*c*g^4*h^3*x^2 + 6*a^2*g^2*h^5*x^2 + 4*c^2*g^7*x + 8*a*c*g^5*h^2*x + 4*a^2*g^3*h^4*x + c^2*g^8/h + 2*a*c*g^6*h + a^2*g^4*h^3) - 1/16*sqrt(c*x^2 + a)*c^3*d/(c^2*g^4*h^3 + 2*a*c*g^2*h^5 + a^2*h^7) - 1/8*(c*x^2 + a)^(5/2)*c*f/(c^2*g^4*h^3*x^2 + 2*a*c*g^2*h^5*x^2 + a^2*h^7*x^2 + 2*c^2*g^5*h^2*x + 4*a*c*g^3*h^4*x + 2*a^2*g*h^6*x + c^2*g^6*h + 2*a*c*g^4*h^3 + a^2*g^2*h^5) + 1/8*(c*x^2 + a)^(3/2)*c^2*f/(c^2*g^4*h^3 + 2*a*c*g^2*h^5 + a^2*h^7) + 1/6*(c*x^2 + a)^(5/2)*e*g/(c*g^2*h^6*x^6 + a*h^8*x^6 + 6*c*g^3*h^5*x^5 + 6*a*g*h^7*x^5 + 15*c*g^4*h^4*x^4 + 15*a*g^2*h^6*x^4 + 20*c*g^5*h^3*x^3 + 20*a*g^3*h^5*x^3 + 15*c*g^6*h^2*x^2 + 15*a*g^4*h^4*x^2 + 6*c*g^7*h*x + 6*a*g^5*h^3*x + c*g^8 + a*g^6*h^2) + 2/5*(c*x^2 + a)^(5/2)*f*g/(c*g^2*h^6*x^5 + a*h^8*x^5 + 5*c*g^3*h^5*x^4 + 5*a*g*h^7*x^4 + 10*c*g^4*h^4*x^3 + 10*a*g^2*h^6*x^3 + 10*c*g^5*h^3*x^2 + 10*a*g^3*h^5*x^2 + 5*c*g^6*h^2*x + 5*a*g^4*h^4*x + c*g^7*h + a*g^5*h^3) - 1/6*(c*x^2 + a)^(5/2)*d/(c*g^2*h^5*x^6 + a*h^7*x^6 + 6*c*g^3*h^4*x^5 + 6*a*g*h^6*x^5 + 15*c*g^4*h^3*x^4 + 15*a*g^2*h^5*x^4 + 20*c*g^5*h^2*x^3 + 20*a*g^3*h^4*x^3 + 15*c*g^6*h*x^2 + 15*a*g^4*h^3*x^2 + 6*c*g^7*x + 6*a*g^5*h^2*x + c*g^8/h + a*g^6*h) - 1/5*(c*x^2 + a)^(5/2)*e/(c*g^2*h^5*x^5 + a*h^7*x^5 + 5*c*g^3*h^4*x^4 + 5*a*g*h^6*x^4 + 10*c*g^4*h^3*x^3 + 10*a*g^2*h^5*x^3 + 10*c*g^5*h^2*x^2 + 10*a*g^3*h^4*x^2 + 5*c*g^6*h*x + 5*a*g^4*h^3*x + c*g^7 + a*g^5*h^2) - 1/4*(c*x^2 + a)^(5/2)*f/(c*g^2*h^5*x^4 + a*h^7*x^4 + 4*c*g^3*h^4*x^3 + 4*a*g*h^6*x^3 + 6*c*g^4*h^3*x^2 + 6*a*g^2*h^5*x^2 + 4*c*g^5*h^2*x + 4*a*g^3*h^4*x + c*g^6*h + a*g^4*h^3) + 3/8*sqrt(c*x^2 + a)*c^2*f/(c*g^2*h^5 + a*h^7) + 7/16*c^6*f*g^8*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(9/2)*h^15) - 7/16*c^6*e*g^7*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(9/2)*h^14) + 7/16*c^6*d*g^6*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(9/2)*h^13) - 27/16*c^5*f*g^6*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(7/2)*h^13) + 21/16*c^5*e*g^5*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(7/2)*h^12) - 15/16*c^5*d*g^4*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(7/2)*h^11) + 39/16*c^4*f*g^4*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(5/2)*h^11) - 21/16*c^4*e*g^3*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(5/2)*h^10) + 9/16*c^4*d*g^2*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(5/2)*h^9) - 25/16*c^3*f*g^2*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(3/2)*h^9) + 7/16*c^3*e*g*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(3/2)*h^8) - 1/16*c^3*d*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(3/2)*h^7) + 3/8*c^2*f*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/(sqrt(a + c*g^2/h^2)*h^7)","B",0
99,-1,0,0,0.000000," ","integrate((c*x^2+a)^(3/2)*(f*x^2+e*x+d)/(h*x+g)^8,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
100,1,166,0,0.452728," ","integrate((c*x^2+a)^(5/2)*(C*x^2+B*x+A),x, algorithm=""maxima"")","\frac{1}{6} \, {\left(c x^{2} + a\right)}^{\frac{5}{2}} A x + \frac{5}{24} \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} A a x + \frac{5}{16} \, \sqrt{c x^{2} + a} A a^{2} x + \frac{{\left(c x^{2} + a\right)}^{\frac{7}{2}} C x}{8 \, c} - \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}} C a x}{48 \, c} - \frac{5 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} C a^{2} x}{192 \, c} - \frac{5 \, \sqrt{c x^{2} + a} C a^{3} x}{128 \, c} - \frac{5 \, C a^{4} \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{128 \, c^{\frac{3}{2}}} + \frac{5 \, A a^{3} \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{16 \, \sqrt{c}} + \frac{{\left(c x^{2} + a\right)}^{\frac{7}{2}} B}{7 \, c}"," ",0,"1/6*(c*x^2 + a)^(5/2)*A*x + 5/24*(c*x^2 + a)^(3/2)*A*a*x + 5/16*sqrt(c*x^2 + a)*A*a^2*x + 1/8*(c*x^2 + a)^(7/2)*C*x/c - 1/48*(c*x^2 + a)^(5/2)*C*a*x/c - 5/192*(c*x^2 + a)^(3/2)*C*a^2*x/c - 5/128*sqrt(c*x^2 + a)*C*a^3*x/c - 5/128*C*a^4*arcsinh(c*x/sqrt(a*c))/c^(3/2) + 5/16*A*a^3*arcsinh(c*x/sqrt(a*c))/sqrt(c) + 1/7*(c*x^2 + a)^(7/2)*B/c","A",0
101,1,349,0,0.451953," ","integrate((h*x+g)^3*(f*x^2+e*x+d)/(c*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{c x^{2} + a} f h^{3} x^{4}}{5 \, c} - \frac{4 \, \sqrt{c x^{2} + a} a f h^{3} x^{2}}{15 \, c^{2}} + \frac{d g^{3} \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{\sqrt{c}} + \frac{\sqrt{c x^{2} + a} e g^{3}}{c} + \frac{3 \, \sqrt{c x^{2} + a} d g^{2} h}{c} + \frac{8 \, \sqrt{c x^{2} + a} a^{2} f h^{3}}{15 \, c^{3}} + \frac{{\left(3 \, f g h^{2} + e h^{3}\right)} \sqrt{c x^{2} + a} x^{3}}{4 \, c} + \frac{{\left(3 \, f g^{2} h + 3 \, e g h^{2} + d h^{3}\right)} \sqrt{c x^{2} + a} x^{2}}{3 \, c} - \frac{3 \, {\left(3 \, f g h^{2} + e h^{3}\right)} \sqrt{c x^{2} + a} a x}{8 \, c^{2}} + \frac{{\left(f g^{3} + 3 \, e g^{2} h + 3 \, d g h^{2}\right)} \sqrt{c x^{2} + a} x}{2 \, c} + \frac{3 \, {\left(3 \, f g h^{2} + e h^{3}\right)} a^{2} \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{8 \, c^{\frac{5}{2}}} - \frac{{\left(f g^{3} + 3 \, e g^{2} h + 3 \, d g h^{2}\right)} a \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{2 \, c^{\frac{3}{2}}} - \frac{2 \, {\left(3 \, f g^{2} h + 3 \, e g h^{2} + d h^{3}\right)} \sqrt{c x^{2} + a} a}{3 \, c^{2}}"," ",0,"1/5*sqrt(c*x^2 + a)*f*h^3*x^4/c - 4/15*sqrt(c*x^2 + a)*a*f*h^3*x^2/c^2 + d*g^3*arcsinh(c*x/sqrt(a*c))/sqrt(c) + sqrt(c*x^2 + a)*e*g^3/c + 3*sqrt(c*x^2 + a)*d*g^2*h/c + 8/15*sqrt(c*x^2 + a)*a^2*f*h^3/c^3 + 1/4*(3*f*g*h^2 + e*h^3)*sqrt(c*x^2 + a)*x^3/c + 1/3*(3*f*g^2*h + 3*e*g*h^2 + d*h^3)*sqrt(c*x^2 + a)*x^2/c - 3/8*(3*f*g*h^2 + e*h^3)*sqrt(c*x^2 + a)*a*x/c^2 + 1/2*(f*g^3 + 3*e*g^2*h + 3*d*g*h^2)*sqrt(c*x^2 + a)*x/c + 3/8*(3*f*g*h^2 + e*h^3)*a^2*arcsinh(c*x/sqrt(a*c))/c^(5/2) - 1/2*(f*g^3 + 3*e*g^2*h + 3*d*g*h^2)*a*arcsinh(c*x/sqrt(a*c))/c^(3/2) - 2/3*(3*f*g^2*h + 3*e*g*h^2 + d*h^3)*sqrt(c*x^2 + a)*a/c^2","A",0
102,1,230,0,0.452730," ","integrate((h*x+g)^2*(f*x^2+e*x+d)/(c*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{c x^{2} + a} f h^{2} x^{3}}{4 \, c} - \frac{3 \, \sqrt{c x^{2} + a} a f h^{2} x}{8 \, c^{2}} + \frac{d g^{2} \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{\sqrt{c}} + \frac{3 \, a^{2} f h^{2} \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{8 \, c^{\frac{5}{2}}} + \frac{\sqrt{c x^{2} + a} e g^{2}}{c} + \frac{2 \, \sqrt{c x^{2} + a} d g h}{c} + \frac{{\left(2 \, f g h + e h^{2}\right)} \sqrt{c x^{2} + a} x^{2}}{3 \, c} + \frac{{\left(f g^{2} + 2 \, e g h + d h^{2}\right)} \sqrt{c x^{2} + a} x}{2 \, c} - \frac{{\left(f g^{2} + 2 \, e g h + d h^{2}\right)} a \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{2 \, c^{\frac{3}{2}}} - \frac{2 \, {\left(2 \, f g h + e h^{2}\right)} \sqrt{c x^{2} + a} a}{3 \, c^{2}}"," ",0,"1/4*sqrt(c*x^2 + a)*f*h^2*x^3/c - 3/8*sqrt(c*x^2 + a)*a*f*h^2*x/c^2 + d*g^2*arcsinh(c*x/sqrt(a*c))/sqrt(c) + 3/8*a^2*f*h^2*arcsinh(c*x/sqrt(a*c))/c^(5/2) + sqrt(c*x^2 + a)*e*g^2/c + 2*sqrt(c*x^2 + a)*d*g*h/c + 1/3*(2*f*g*h + e*h^2)*sqrt(c*x^2 + a)*x^2/c + 1/2*(f*g^2 + 2*e*g*h + d*h^2)*sqrt(c*x^2 + a)*x/c - 1/2*(f*g^2 + 2*e*g*h + d*h^2)*a*arcsinh(c*x/sqrt(a*c))/c^(3/2) - 2/3*(2*f*g*h + e*h^2)*sqrt(c*x^2 + a)*a/c^2","A",0
103,1,126,0,0.436206," ","integrate((h*x+g)*(f*x^2+e*x+d)/(c*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{c x^{2} + a} f h x^{2}}{3 \, c} + \frac{d g \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{\sqrt{c}} + \frac{\sqrt{c x^{2} + a} e g}{c} + \frac{\sqrt{c x^{2} + a} d h}{c} - \frac{2 \, \sqrt{c x^{2} + a} a f h}{3 \, c^{2}} + \frac{\sqrt{c x^{2} + a} {\left(f g + e h\right)} x}{2 \, c} - \frac{{\left(f g + e h\right)} a \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{2 \, c^{\frac{3}{2}}}"," ",0,"1/3*sqrt(c*x^2 + a)*f*h*x^2/c + d*g*arcsinh(c*x/sqrt(a*c))/sqrt(c) + sqrt(c*x^2 + a)*e*g/c + sqrt(c*x^2 + a)*d*h/c - 2/3*sqrt(c*x^2 + a)*a*f*h/c^2 + 1/2*sqrt(c*x^2 + a)*(f*g + e*h)*x/c - 1/2*(f*g + e*h)*a*arcsinh(c*x/sqrt(a*c))/c^(3/2)","A",0
104,1,61,0,0.434975," ","integrate((f*x^2+e*x+d)/(c*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{c x^{2} + a} f x}{2 \, c} + \frac{d \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{\sqrt{c}} - \frac{a f \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{2 \, c^{\frac{3}{2}}} + \frac{\sqrt{c x^{2} + a} e}{c}"," ",0,"1/2*sqrt(c*x^2 + a)*f*x/c + d*arcsinh(c*x/sqrt(a*c))/sqrt(c) - 1/2*a*f*arcsinh(c*x/sqrt(a*c))/c^(3/2) + sqrt(c*x^2 + a)*e/c","A",0
105,1,218,0,0.563709," ","integrate((f*x^2+e*x+d)/(h*x+g)/(c*x^2+a)^(1/2),x, algorithm=""maxima"")","-\frac{f g \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{\sqrt{c} h^{2}} + \frac{e \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{\sqrt{c} h} + \frac{f g^{2} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{\sqrt{a + \frac{c g^{2}}{h^{2}}} h^{3}} - \frac{e g \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{\sqrt{a + \frac{c g^{2}}{h^{2}}} h^{2}} + \frac{d \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{\sqrt{a + \frac{c g^{2}}{h^{2}}} h} + \frac{\sqrt{c x^{2} + a} f}{c h}"," ",0,"-f*g*arcsinh(c*x/sqrt(a*c))/(sqrt(c)*h^2) + e*arcsinh(c*x/sqrt(a*c))/(sqrt(c)*h) + f*g^2*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/(sqrt(a + c*g^2/h^2)*h^3) - e*g*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/(sqrt(a + c*g^2/h^2)*h^2) + d*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/(sqrt(a + c*g^2/h^2)*h) + sqrt(c*x^2 + a)*f/(c*h)","A",0
106,1,419,0,0.578192," ","integrate((f*x^2+e*x+d)/(h*x+g)^2/(c*x^2+a)^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{c x^{2} + a} f g^{2}}{c g^{2} h^{2} x + a h^{4} x + c g^{3} h + a g h^{3}} + \frac{\sqrt{c x^{2} + a} e g}{c g^{2} h x + a h^{3} x + c g^{3} + a g h^{2}} - \frac{\sqrt{c x^{2} + a} d}{c g^{2} x + a h^{2} x + \frac{c g^{3}}{h} + a g h} + \frac{f \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{\sqrt{c} h^{2}} + \frac{c f g^{3} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{{\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{3}{2}} h^{5}} - \frac{c e g^{2} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{{\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{3}{2}} h^{4}} + \frac{c d g \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{{\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{3}{2}} h^{3}} - \frac{2 \, f g \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{\sqrt{a + \frac{c g^{2}}{h^{2}}} h^{3}} + \frac{e \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{\sqrt{a + \frac{c g^{2}}{h^{2}}} h^{2}}"," ",0,"-sqrt(c*x^2 + a)*f*g^2/(c*g^2*h^2*x + a*h^4*x + c*g^3*h + a*g*h^3) + sqrt(c*x^2 + a)*e*g/(c*g^2*h*x + a*h^3*x + c*g^3 + a*g*h^2) - sqrt(c*x^2 + a)*d/(c*g^2*x + a*h^2*x + c*g^3/h + a*g*h) + f*arcsinh(c*x/sqrt(a*c))/(sqrt(c)*h^2) + c*f*g^3*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(3/2)*h^5) - c*e*g^2*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(3/2)*h^4) + c*d*g*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(3/2)*h^3) - 2*f*g*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/(sqrt(a + c*g^2/h^2)*h^3) + e*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/(sqrt(a + c*g^2/h^2)*h^2)","B",0
107,1,896,0,0.671950," ","integrate((f*x^2+e*x+d)/(h*x+g)^3/(c*x^2+a)^(1/2),x, algorithm=""maxima"")","-\frac{3 \, \sqrt{c x^{2} + a} c f g^{3}}{2 \, {\left(c^{2} g^{4} h^{2} x + 2 \, a c g^{2} h^{4} x + a^{2} h^{6} x + c^{2} g^{5} h + 2 \, a c g^{3} h^{3} + a^{2} g h^{5}\right)}} + \frac{3 \, \sqrt{c x^{2} + a} c e g^{2}}{2 \, {\left(c^{2} g^{4} h x + 2 \, a c g^{2} h^{3} x + a^{2} h^{5} x + c^{2} g^{5} + 2 \, a c g^{3} h^{2} + a^{2} g h^{4}\right)}} - \frac{3 \, \sqrt{c x^{2} + a} c d g}{2 \, {\left(c^{2} g^{4} x + 2 \, a c g^{2} h^{2} x + a^{2} h^{4} x + \frac{c^{2} g^{5}}{h} + 2 \, a c g^{3} h + a^{2} g h^{3}\right)}} - \frac{\sqrt{c x^{2} + a} f g^{2}}{2 \, {\left(c g^{2} h^{3} x^{2} + a h^{5} x^{2} + 2 \, c g^{3} h^{2} x + 2 \, a g h^{4} x + c g^{4} h + a g^{2} h^{3}\right)}} + \frac{\sqrt{c x^{2} + a} e g}{2 \, {\left(c g^{2} h^{2} x^{2} + a h^{4} x^{2} + 2 \, c g^{3} h x + 2 \, a g h^{3} x + c g^{4} + a g^{2} h^{2}\right)}} + \frac{2 \, \sqrt{c x^{2} + a} f g}{c g^{2} h^{2} x + a h^{4} x + c g^{3} h + a g h^{3}} - \frac{\sqrt{c x^{2} + a} d}{2 \, {\left(c g^{2} h x^{2} + a h^{3} x^{2} + 2 \, c g^{3} x + 2 \, a g h^{2} x + \frac{c g^{4}}{h} + a g^{2} h\right)}} - \frac{\sqrt{c x^{2} + a} e}{c g^{2} h x + a h^{3} x + c g^{3} + a g h^{2}} + \frac{3 \, c^{2} f g^{4} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{2 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{5}{2}} h^{7}} - \frac{3 \, c^{2} e g^{3} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{2 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{5}{2}} h^{6}} + \frac{3 \, c^{2} d g^{2} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{2 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{5}{2}} h^{5}} - \frac{5 \, c f g^{2} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{2 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{3}{2}} h^{5}} + \frac{3 \, c e g \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{2 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{3}{2}} h^{4}} - \frac{c d \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{2 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{3}{2}} h^{3}} + \frac{f \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{\sqrt{a + \frac{c g^{2}}{h^{2}}} h^{3}}"," ",0,"-3/2*sqrt(c*x^2 + a)*c*f*g^3/(c^2*g^4*h^2*x + 2*a*c*g^2*h^4*x + a^2*h^6*x + c^2*g^5*h + 2*a*c*g^3*h^3 + a^2*g*h^5) + 3/2*sqrt(c*x^2 + a)*c*e*g^2/(c^2*g^4*h*x + 2*a*c*g^2*h^3*x + a^2*h^5*x + c^2*g^5 + 2*a*c*g^3*h^2 + a^2*g*h^4) - 3/2*sqrt(c*x^2 + a)*c*d*g/(c^2*g^4*x + 2*a*c*g^2*h^2*x + a^2*h^4*x + c^2*g^5/h + 2*a*c*g^3*h + a^2*g*h^3) - 1/2*sqrt(c*x^2 + a)*f*g^2/(c*g^2*h^3*x^2 + a*h^5*x^2 + 2*c*g^3*h^2*x + 2*a*g*h^4*x + c*g^4*h + a*g^2*h^3) + 1/2*sqrt(c*x^2 + a)*e*g/(c*g^2*h^2*x^2 + a*h^4*x^2 + 2*c*g^3*h*x + 2*a*g*h^3*x + c*g^4 + a*g^2*h^2) + 2*sqrt(c*x^2 + a)*f*g/(c*g^2*h^2*x + a*h^4*x + c*g^3*h + a*g*h^3) - 1/2*sqrt(c*x^2 + a)*d/(c*g^2*h*x^2 + a*h^3*x^2 + 2*c*g^3*x + 2*a*g*h^2*x + c*g^4/h + a*g^2*h) - sqrt(c*x^2 + a)*e/(c*g^2*h*x + a*h^3*x + c*g^3 + a*g*h^2) + 3/2*c^2*f*g^4*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(5/2)*h^7) - 3/2*c^2*e*g^3*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(5/2)*h^6) + 3/2*c^2*d*g^2*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(5/2)*h^5) - 5/2*c*f*g^2*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(3/2)*h^5) + 3/2*c*e*g*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(3/2)*h^4) - 1/2*c*d*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(3/2)*h^3) + f*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/(sqrt(a + c*g^2/h^2)*h^3)","B",0
108,1,346,0,0.456582," ","integrate((h*x+g)^3*(f*x^2+e*x+d)/(c*x^2+a)^(3/2),x, algorithm=""maxima"")","\frac{f h^{3} x^{4}}{3 \, \sqrt{c x^{2} + a} c} - \frac{4 \, a f h^{3} x^{2}}{3 \, \sqrt{c x^{2} + a} c^{2}} + \frac{d g^{3} x}{\sqrt{c x^{2} + a} a} - \frac{e g^{3}}{\sqrt{c x^{2} + a} c} - \frac{3 \, d g^{2} h}{\sqrt{c x^{2} + a} c} - \frac{8 \, a^{2} f h^{3}}{3 \, \sqrt{c x^{2} + a} c^{3}} + \frac{{\left(3 \, f g h^{2} + e h^{3}\right)} x^{3}}{2 \, \sqrt{c x^{2} + a} c} + \frac{{\left(3 \, f g^{2} h + 3 \, e g h^{2} + d h^{3}\right)} x^{2}}{\sqrt{c x^{2} + a} c} + \frac{3 \, {\left(3 \, f g h^{2} + e h^{3}\right)} a x}{2 \, \sqrt{c x^{2} + a} c^{2}} - \frac{{\left(f g^{3} + 3 \, e g^{2} h + 3 \, d g h^{2}\right)} x}{\sqrt{c x^{2} + a} c} - \frac{3 \, {\left(3 \, f g h^{2} + e h^{3}\right)} a \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{2 \, c^{\frac{5}{2}}} + \frac{{\left(f g^{3} + 3 \, e g^{2} h + 3 \, d g h^{2}\right)} \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{c^{\frac{3}{2}}} + \frac{2 \, {\left(3 \, f g^{2} h + 3 \, e g h^{2} + d h^{3}\right)} a}{\sqrt{c x^{2} + a} c^{2}}"," ",0,"1/3*f*h^3*x^4/(sqrt(c*x^2 + a)*c) - 4/3*a*f*h^3*x^2/(sqrt(c*x^2 + a)*c^2) + d*g^3*x/(sqrt(c*x^2 + a)*a) - e*g^3/(sqrt(c*x^2 + a)*c) - 3*d*g^2*h/(sqrt(c*x^2 + a)*c) - 8/3*a^2*f*h^3/(sqrt(c*x^2 + a)*c^3) + 1/2*(3*f*g*h^2 + e*h^3)*x^3/(sqrt(c*x^2 + a)*c) + (3*f*g^2*h + 3*e*g*h^2 + d*h^3)*x^2/(sqrt(c*x^2 + a)*c) + 3/2*(3*f*g*h^2 + e*h^3)*a*x/(sqrt(c*x^2 + a)*c^2) - (f*g^3 + 3*e*g^2*h + 3*d*g*h^2)*x/(sqrt(c*x^2 + a)*c) - 3/2*(3*f*g*h^2 + e*h^3)*a*arcsinh(c*x/sqrt(a*c))/c^(5/2) + (f*g^3 + 3*e*g^2*h + 3*d*g*h^2)*arcsinh(c*x/sqrt(a*c))/c^(3/2) + 2*(3*f*g^2*h + 3*e*g*h^2 + d*h^3)*a/(sqrt(c*x^2 + a)*c^2)","A",0
109,1,227,0,0.447650," ","integrate((h*x+g)^2*(f*x^2+e*x+d)/(c*x^2+a)^(3/2),x, algorithm=""maxima"")","\frac{f h^{2} x^{3}}{2 \, \sqrt{c x^{2} + a} c} + \frac{d g^{2} x}{\sqrt{c x^{2} + a} a} + \frac{3 \, a f h^{2} x}{2 \, \sqrt{c x^{2} + a} c^{2}} - \frac{3 \, a f h^{2} \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{2 \, c^{\frac{5}{2}}} - \frac{e g^{2}}{\sqrt{c x^{2} + a} c} - \frac{2 \, d g h}{\sqrt{c x^{2} + a} c} + \frac{{\left(2 \, f g h + e h^{2}\right)} x^{2}}{\sqrt{c x^{2} + a} c} - \frac{{\left(f g^{2} + 2 \, e g h + d h^{2}\right)} x}{\sqrt{c x^{2} + a} c} + \frac{{\left(f g^{2} + 2 \, e g h + d h^{2}\right)} \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{c^{\frac{3}{2}}} + \frac{2 \, {\left(2 \, f g h + e h^{2}\right)} a}{\sqrt{c x^{2} + a} c^{2}}"," ",0,"1/2*f*h^2*x^3/(sqrt(c*x^2 + a)*c) + d*g^2*x/(sqrt(c*x^2 + a)*a) + 3/2*a*f*h^2*x/(sqrt(c*x^2 + a)*c^2) - 3/2*a*f*h^2*arcsinh(c*x/sqrt(a*c))/c^(5/2) - e*g^2/(sqrt(c*x^2 + a)*c) - 2*d*g*h/(sqrt(c*x^2 + a)*c) + (2*f*g*h + e*h^2)*x^2/(sqrt(c*x^2 + a)*c) - (f*g^2 + 2*e*g*h + d*h^2)*x/(sqrt(c*x^2 + a)*c) + (f*g^2 + 2*e*g*h + d*h^2)*arcsinh(c*x/sqrt(a*c))/c^(3/2) + 2*(2*f*g*h + e*h^2)*a/(sqrt(c*x^2 + a)*c^2)","A",0
110,1,126,0,0.436933," ","integrate((h*x+g)*(f*x^2+e*x+d)/(c*x^2+a)^(3/2),x, algorithm=""maxima"")","\frac{f h x^{2}}{\sqrt{c x^{2} + a} c} + \frac{d g x}{\sqrt{c x^{2} + a} a} - \frac{e g}{\sqrt{c x^{2} + a} c} - \frac{d h}{\sqrt{c x^{2} + a} c} + \frac{2 \, a f h}{\sqrt{c x^{2} + a} c^{2}} - \frac{{\left(f g + e h\right)} x}{\sqrt{c x^{2} + a} c} + \frac{{\left(f g + e h\right)} \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{c^{\frac{3}{2}}}"," ",0,"f*h*x^2/(sqrt(c*x^2 + a)*c) + d*g*x/(sqrt(c*x^2 + a)*a) - e*g/(sqrt(c*x^2 + a)*c) - d*h/(sqrt(c*x^2 + a)*c) + 2*a*f*h/(sqrt(c*x^2 + a)*c^2) - (f*g + e*h)*x/(sqrt(c*x^2 + a)*c) + (f*g + e*h)*arcsinh(c*x/sqrt(a*c))/c^(3/2)","A",0
111,1,61,0,0.430453," ","integrate((f*x^2+e*x+d)/(c*x^2+a)^(3/2),x, algorithm=""maxima"")","\frac{d x}{\sqrt{c x^{2} + a} a} - \frac{f x}{\sqrt{c x^{2} + a} c} + \frac{f \operatorname{arsinh}\left(\frac{c x}{\sqrt{a c}}\right)}{c^{\frac{3}{2}}} - \frac{e}{\sqrt{c x^{2} + a} c}"," ",0,"d*x/(sqrt(c*x^2 + a)*a) - f*x/(sqrt(c*x^2 + a)*c) + f*arcsinh(c*x/sqrt(a*c))/c^(3/2) - e/(sqrt(c*x^2 + a)*c)","A",0
112,1,453,0,0.621621," ","integrate((f*x^2+e*x+d)/(h*x+g)/(c*x^2+a)^(3/2),x, algorithm=""maxima"")","\frac{c f g^{3} x}{\sqrt{c x^{2} + a} a c g^{2} h^{2} + \sqrt{c x^{2} + a} a^{2} h^{4}} - \frac{c e g^{2} x}{\sqrt{c x^{2} + a} a c g^{2} h + \sqrt{c x^{2} + a} a^{2} h^{3}} + \frac{c d g x}{\sqrt{c x^{2} + a} a c g^{2} + \sqrt{c x^{2} + a} a^{2} h^{2}} + \frac{f g^{2}}{\sqrt{c x^{2} + a} c g^{2} h + \sqrt{c x^{2} + a} a h^{3}} - \frac{e g}{\sqrt{c x^{2} + a} c g^{2} + \sqrt{c x^{2} + a} a h^{2}} + \frac{d}{\frac{\sqrt{c x^{2} + a} c g^{2}}{h} + \sqrt{c x^{2} + a} a h} - \frac{f g x}{\sqrt{c x^{2} + a} a h^{2}} + \frac{e x}{\sqrt{c x^{2} + a} a h} + \frac{f g^{2} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{{\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{3}{2}} h^{3}} - \frac{e g \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{{\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{3}{2}} h^{2}} + \frac{d \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{{\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{3}{2}} h} - \frac{f}{\sqrt{c x^{2} + a} c h}"," ",0,"c*f*g^3*x/(sqrt(c*x^2 + a)*a*c*g^2*h^2 + sqrt(c*x^2 + a)*a^2*h^4) - c*e*g^2*x/(sqrt(c*x^2 + a)*a*c*g^2*h + sqrt(c*x^2 + a)*a^2*h^3) + c*d*g*x/(sqrt(c*x^2 + a)*a*c*g^2 + sqrt(c*x^2 + a)*a^2*h^2) + f*g^2/(sqrt(c*x^2 + a)*c*g^2*h + sqrt(c*x^2 + a)*a*h^3) - e*g/(sqrt(c*x^2 + a)*c*g^2 + sqrt(c*x^2 + a)*a*h^2) + d/(sqrt(c*x^2 + a)*c*g^2/h + sqrt(c*x^2 + a)*a*h) - f*g*x/(sqrt(c*x^2 + a)*a*h^2) + e*x/(sqrt(c*x^2 + a)*a*h) + f*g^2*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(3/2)*h^3) - e*g*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(3/2)*h^2) + d*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(3/2)*h) - f/(sqrt(c*x^2 + a)*c*h)","B",0
113,1,1085,0,0.767346," ","integrate((f*x^2+e*x+d)/(h*x+g)^2/(c*x^2+a)^(3/2),x, algorithm=""maxima"")","\frac{3 \, c^{2} f g^{4} x}{\sqrt{c x^{2} + a} a c^{2} g^{4} h^{2} + 2 \, \sqrt{c x^{2} + a} a^{2} c g^{2} h^{4} + \sqrt{c x^{2} + a} a^{3} h^{6}} - \frac{3 \, c^{2} e g^{3} x}{\sqrt{c x^{2} + a} a c^{2} g^{4} h + 2 \, \sqrt{c x^{2} + a} a^{2} c g^{2} h^{3} + \sqrt{c x^{2} + a} a^{3} h^{5}} + \frac{3 \, c^{2} d g^{2} x}{\sqrt{c x^{2} + a} a c^{2} g^{4} + 2 \, \sqrt{c x^{2} + a} a^{2} c g^{2} h^{2} + \sqrt{c x^{2} + a} a^{3} h^{4}} + \frac{3 \, c f g^{3}}{\sqrt{c x^{2} + a} c^{2} g^{4} h + 2 \, \sqrt{c x^{2} + a} a c g^{2} h^{3} + \sqrt{c x^{2} + a} a^{2} h^{5}} - \frac{4 \, c f g^{2} x}{\sqrt{c x^{2} + a} a c g^{2} h^{2} + \sqrt{c x^{2} + a} a^{2} h^{4}} - \frac{3 \, c e g^{2}}{\sqrt{c x^{2} + a} c^{2} g^{4} + 2 \, \sqrt{c x^{2} + a} a c g^{2} h^{2} + \sqrt{c x^{2} + a} a^{2} h^{4}} + \frac{3 \, c e g x}{\sqrt{c x^{2} + a} a c g^{2} h + \sqrt{c x^{2} + a} a^{2} h^{3}} + \frac{3 \, c d g}{\frac{\sqrt{c x^{2} + a} c^{2} g^{4}}{h} + 2 \, \sqrt{c x^{2} + a} a c g^{2} h + \sqrt{c x^{2} + a} a^{2} h^{3}} - \frac{f g^{2}}{\sqrt{c x^{2} + a} c g^{2} h^{2} x + \sqrt{c x^{2} + a} a h^{4} x + \sqrt{c x^{2} + a} c g^{3} h + \sqrt{c x^{2} + a} a g h^{3}} - \frac{2 \, c d x}{\sqrt{c x^{2} + a} a c g^{2} + \sqrt{c x^{2} + a} a^{2} h^{2}} + \frac{e g}{\sqrt{c x^{2} + a} c g^{2} h x + \sqrt{c x^{2} + a} a h^{3} x + \sqrt{c x^{2} + a} c g^{3} + \sqrt{c x^{2} + a} a g h^{2}} - \frac{2 \, f g}{\sqrt{c x^{2} + a} c g^{2} h + \sqrt{c x^{2} + a} a h^{3}} - \frac{d}{\sqrt{c x^{2} + a} c g^{2} x + \sqrt{c x^{2} + a} a h^{2} x + \frac{\sqrt{c x^{2} + a} c g^{3}}{h} + \sqrt{c x^{2} + a} a g h} + \frac{e}{\sqrt{c x^{2} + a} c g^{2} + \sqrt{c x^{2} + a} a h^{2}} + \frac{f x}{\sqrt{c x^{2} + a} a h^{2}} + \frac{3 \, c f g^{3} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{{\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{5}{2}} h^{5}} - \frac{3 \, c e g^{2} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{{\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{5}{2}} h^{4}} + \frac{3 \, c d g \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{{\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{5}{2}} h^{3}} - \frac{2 \, f g \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{{\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{3}{2}} h^{3}} + \frac{e \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{{\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{3}{2}} h^{2}}"," ",0,"3*c^2*f*g^4*x/(sqrt(c*x^2 + a)*a*c^2*g^4*h^2 + 2*sqrt(c*x^2 + a)*a^2*c*g^2*h^4 + sqrt(c*x^2 + a)*a^3*h^6) - 3*c^2*e*g^3*x/(sqrt(c*x^2 + a)*a*c^2*g^4*h + 2*sqrt(c*x^2 + a)*a^2*c*g^2*h^3 + sqrt(c*x^2 + a)*a^3*h^5) + 3*c^2*d*g^2*x/(sqrt(c*x^2 + a)*a*c^2*g^4 + 2*sqrt(c*x^2 + a)*a^2*c*g^2*h^2 + sqrt(c*x^2 + a)*a^3*h^4) + 3*c*f*g^3/(sqrt(c*x^2 + a)*c^2*g^4*h + 2*sqrt(c*x^2 + a)*a*c*g^2*h^3 + sqrt(c*x^2 + a)*a^2*h^5) - 4*c*f*g^2*x/(sqrt(c*x^2 + a)*a*c*g^2*h^2 + sqrt(c*x^2 + a)*a^2*h^4) - 3*c*e*g^2/(sqrt(c*x^2 + a)*c^2*g^4 + 2*sqrt(c*x^2 + a)*a*c*g^2*h^2 + sqrt(c*x^2 + a)*a^2*h^4) + 3*c*e*g*x/(sqrt(c*x^2 + a)*a*c*g^2*h + sqrt(c*x^2 + a)*a^2*h^3) + 3*c*d*g/(sqrt(c*x^2 + a)*c^2*g^4/h + 2*sqrt(c*x^2 + a)*a*c*g^2*h + sqrt(c*x^2 + a)*a^2*h^3) - f*g^2/(sqrt(c*x^2 + a)*c*g^2*h^2*x + sqrt(c*x^2 + a)*a*h^4*x + sqrt(c*x^2 + a)*c*g^3*h + sqrt(c*x^2 + a)*a*g*h^3) - 2*c*d*x/(sqrt(c*x^2 + a)*a*c*g^2 + sqrt(c*x^2 + a)*a^2*h^2) + e*g/(sqrt(c*x^2 + a)*c*g^2*h*x + sqrt(c*x^2 + a)*a*h^3*x + sqrt(c*x^2 + a)*c*g^3 + sqrt(c*x^2 + a)*a*g*h^2) - 2*f*g/(sqrt(c*x^2 + a)*c*g^2*h + sqrt(c*x^2 + a)*a*h^3) - d/(sqrt(c*x^2 + a)*c*g^2*x + sqrt(c*x^2 + a)*a*h^2*x + sqrt(c*x^2 + a)*c*g^3/h + sqrt(c*x^2 + a)*a*g*h) + e/(sqrt(c*x^2 + a)*c*g^2 + sqrt(c*x^2 + a)*a*h^2) + f*x/(sqrt(c*x^2 + a)*a*h^2) + 3*c*f*g^3*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(5/2)*h^5) - 3*c*e*g^2*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(5/2)*h^4) + 3*c*d*g*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(5/2)*h^3) - 2*f*g*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(3/2)*h^3) + e*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(3/2)*h^2)","B",0
114,1,2254,0,1.016687," ","integrate((f*x^2+e*x+d)/(h*x+g)^3/(c*x^2+a)^(3/2),x, algorithm=""maxima"")","\frac{15 \, c^{3} f g^{5} x}{2 \, {\left(\sqrt{c x^{2} + a} a c^{3} g^{6} h^{2} + 3 \, \sqrt{c x^{2} + a} a^{2} c^{2} g^{4} h^{4} + 3 \, \sqrt{c x^{2} + a} a^{3} c g^{2} h^{6} + \sqrt{c x^{2} + a} a^{4} h^{8}\right)}} - \frac{15 \, c^{3} e g^{4} x}{2 \, {\left(\sqrt{c x^{2} + a} a c^{3} g^{6} h + 3 \, \sqrt{c x^{2} + a} a^{2} c^{2} g^{4} h^{3} + 3 \, \sqrt{c x^{2} + a} a^{3} c g^{2} h^{5} + \sqrt{c x^{2} + a} a^{4} h^{7}\right)}} + \frac{15 \, c^{3} d g^{3} x}{2 \, {\left(\sqrt{c x^{2} + a} a c^{3} g^{6} + 3 \, \sqrt{c x^{2} + a} a^{2} c^{2} g^{4} h^{2} + 3 \, \sqrt{c x^{2} + a} a^{3} c g^{2} h^{4} + \sqrt{c x^{2} + a} a^{4} h^{6}\right)}} + \frac{15 \, c^{2} f g^{4}}{2 \, {\left(\sqrt{c x^{2} + a} c^{3} g^{6} h + 3 \, \sqrt{c x^{2} + a} a c^{2} g^{4} h^{3} + 3 \, \sqrt{c x^{2} + a} a^{2} c g^{2} h^{5} + \sqrt{c x^{2} + a} a^{3} h^{7}\right)}} - \frac{25 \, c^{2} f g^{3} x}{2 \, {\left(\sqrt{c x^{2} + a} a c^{2} g^{4} h^{2} + 2 \, \sqrt{c x^{2} + a} a^{2} c g^{2} h^{4} + \sqrt{c x^{2} + a} a^{3} h^{6}\right)}} - \frac{15 \, c^{2} e g^{3}}{2 \, {\left(\sqrt{c x^{2} + a} c^{3} g^{6} + 3 \, \sqrt{c x^{2} + a} a c^{2} g^{4} h^{2} + 3 \, \sqrt{c x^{2} + a} a^{2} c g^{2} h^{4} + \sqrt{c x^{2} + a} a^{3} h^{6}\right)}} + \frac{19 \, c^{2} e g^{2} x}{2 \, {\left(\sqrt{c x^{2} + a} a c^{2} g^{4} h + 2 \, \sqrt{c x^{2} + a} a^{2} c g^{2} h^{3} + \sqrt{c x^{2} + a} a^{3} h^{5}\right)}} + \frac{15 \, c^{2} d g^{2}}{2 \, {\left(\frac{\sqrt{c x^{2} + a} c^{3} g^{6}}{h} + 3 \, \sqrt{c x^{2} + a} a c^{2} g^{4} h + 3 \, \sqrt{c x^{2} + a} a^{2} c g^{2} h^{3} + \sqrt{c x^{2} + a} a^{3} h^{5}\right)}} - \frac{5 \, c f g^{3}}{2 \, {\left(\sqrt{c x^{2} + a} c^{2} g^{4} h^{2} x + 2 \, \sqrt{c x^{2} + a} a c g^{2} h^{4} x + \sqrt{c x^{2} + a} a^{2} h^{6} x + \sqrt{c x^{2} + a} c^{2} g^{5} h + 2 \, \sqrt{c x^{2} + a} a c g^{3} h^{3} + \sqrt{c x^{2} + a} a^{2} g h^{5}\right)}} - \frac{13 \, c^{2} d g x}{2 \, {\left(\sqrt{c x^{2} + a} a c^{2} g^{4} + 2 \, \sqrt{c x^{2} + a} a^{2} c g^{2} h^{2} + \sqrt{c x^{2} + a} a^{3} h^{4}\right)}} + \frac{5 \, c e g^{2}}{2 \, {\left(\sqrt{c x^{2} + a} c^{2} g^{4} h x + 2 \, \sqrt{c x^{2} + a} a c g^{2} h^{3} x + \sqrt{c x^{2} + a} a^{2} h^{5} x + \sqrt{c x^{2} + a} c^{2} g^{5} + 2 \, \sqrt{c x^{2} + a} a c g^{3} h^{2} + \sqrt{c x^{2} + a} a^{2} g h^{4}\right)}} - \frac{15 \, c f g^{2}}{2 \, {\left(\sqrt{c x^{2} + a} c^{2} g^{4} h + 2 \, \sqrt{c x^{2} + a} a c g^{2} h^{3} + \sqrt{c x^{2} + a} a^{2} h^{5}\right)}} + \frac{5 \, c f g x}{\sqrt{c x^{2} + a} a c g^{2} h^{2} + \sqrt{c x^{2} + a} a^{2} h^{4}} - \frac{5 \, c d g}{2 \, {\left(\sqrt{c x^{2} + a} c^{2} g^{4} x + 2 \, \sqrt{c x^{2} + a} a c g^{2} h^{2} x + \sqrt{c x^{2} + a} a^{2} h^{4} x + \frac{\sqrt{c x^{2} + a} c^{2} g^{5}}{h} + 2 \, \sqrt{c x^{2} + a} a c g^{3} h + \sqrt{c x^{2} + a} a^{2} g h^{3}\right)}} + \frac{9 \, c e g}{2 \, {\left(\sqrt{c x^{2} + a} c^{2} g^{4} + 2 \, \sqrt{c x^{2} + a} a c g^{2} h^{2} + \sqrt{c x^{2} + a} a^{2} h^{4}\right)}} - \frac{f g^{2}}{2 \, {\left(\sqrt{c x^{2} + a} c g^{2} h^{3} x^{2} + \sqrt{c x^{2} + a} a h^{5} x^{2} + 2 \, \sqrt{c x^{2} + a} c g^{3} h^{2} x + 2 \, \sqrt{c x^{2} + a} a g h^{4} x + \sqrt{c x^{2} + a} c g^{4} h + \sqrt{c x^{2} + a} a g^{2} h^{3}\right)}} - \frac{2 \, c e x}{\sqrt{c x^{2} + a} a c g^{2} h + \sqrt{c x^{2} + a} a^{2} h^{3}} - \frac{3 \, c d}{2 \, {\left(\frac{\sqrt{c x^{2} + a} c^{2} g^{4}}{h} + 2 \, \sqrt{c x^{2} + a} a c g^{2} h + \sqrt{c x^{2} + a} a^{2} h^{3}\right)}} + \frac{e g}{2 \, {\left(\sqrt{c x^{2} + a} c g^{2} h^{2} x^{2} + \sqrt{c x^{2} + a} a h^{4} x^{2} + 2 \, \sqrt{c x^{2} + a} c g^{3} h x + 2 \, \sqrt{c x^{2} + a} a g h^{3} x + \sqrt{c x^{2} + a} c g^{4} + \sqrt{c x^{2} + a} a g^{2} h^{2}\right)}} + \frac{2 \, f g}{\sqrt{c x^{2} + a} c g^{2} h^{2} x + \sqrt{c x^{2} + a} a h^{4} x + \sqrt{c x^{2} + a} c g^{3} h + \sqrt{c x^{2} + a} a g h^{3}} - \frac{d}{2 \, {\left(\sqrt{c x^{2} + a} c g^{2} h x^{2} + \sqrt{c x^{2} + a} a h^{3} x^{2} + 2 \, \sqrt{c x^{2} + a} c g^{3} x + 2 \, \sqrt{c x^{2} + a} a g h^{2} x + \frac{\sqrt{c x^{2} + a} c g^{4}}{h} + \sqrt{c x^{2} + a} a g^{2} h\right)}} - \frac{e}{\sqrt{c x^{2} + a} c g^{2} h x + \sqrt{c x^{2} + a} a h^{3} x + \sqrt{c x^{2} + a} c g^{3} + \sqrt{c x^{2} + a} a g h^{2}} + \frac{f}{\sqrt{c x^{2} + a} c g^{2} h + \sqrt{c x^{2} + a} a h^{3}} + \frac{15 \, c^{2} f g^{4} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{2 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{7}{2}} h^{7}} - \frac{15 \, c^{2} e g^{3} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{2 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{7}{2}} h^{6}} + \frac{15 \, c^{2} d g^{2} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{2 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{7}{2}} h^{5}} - \frac{15 \, c f g^{2} \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{2 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{5}{2}} h^{5}} + \frac{9 \, c e g \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{2 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{5}{2}} h^{4}} - \frac{3 \, c d \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{2 \, {\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{5}{2}} h^{3}} + \frac{f \operatorname{arsinh}\left(\frac{c g x}{\sqrt{a c} {\left| h x + g \right|}} - \frac{a h}{\sqrt{a c} {\left| h x + g \right|}}\right)}{{\left(a + \frac{c g^{2}}{h^{2}}\right)}^{\frac{3}{2}} h^{3}}"," ",0,"15/2*c^3*f*g^5*x/(sqrt(c*x^2 + a)*a*c^3*g^6*h^2 + 3*sqrt(c*x^2 + a)*a^2*c^2*g^4*h^4 + 3*sqrt(c*x^2 + a)*a^3*c*g^2*h^6 + sqrt(c*x^2 + a)*a^4*h^8) - 15/2*c^3*e*g^4*x/(sqrt(c*x^2 + a)*a*c^3*g^6*h + 3*sqrt(c*x^2 + a)*a^2*c^2*g^4*h^3 + 3*sqrt(c*x^2 + a)*a^3*c*g^2*h^5 + sqrt(c*x^2 + a)*a^4*h^7) + 15/2*c^3*d*g^3*x/(sqrt(c*x^2 + a)*a*c^3*g^6 + 3*sqrt(c*x^2 + a)*a^2*c^2*g^4*h^2 + 3*sqrt(c*x^2 + a)*a^3*c*g^2*h^4 + sqrt(c*x^2 + a)*a^4*h^6) + 15/2*c^2*f*g^4/(sqrt(c*x^2 + a)*c^3*g^6*h + 3*sqrt(c*x^2 + a)*a*c^2*g^4*h^3 + 3*sqrt(c*x^2 + a)*a^2*c*g^2*h^5 + sqrt(c*x^2 + a)*a^3*h^7) - 25/2*c^2*f*g^3*x/(sqrt(c*x^2 + a)*a*c^2*g^4*h^2 + 2*sqrt(c*x^2 + a)*a^2*c*g^2*h^4 + sqrt(c*x^2 + a)*a^3*h^6) - 15/2*c^2*e*g^3/(sqrt(c*x^2 + a)*c^3*g^6 + 3*sqrt(c*x^2 + a)*a*c^2*g^4*h^2 + 3*sqrt(c*x^2 + a)*a^2*c*g^2*h^4 + sqrt(c*x^2 + a)*a^3*h^6) + 19/2*c^2*e*g^2*x/(sqrt(c*x^2 + a)*a*c^2*g^4*h + 2*sqrt(c*x^2 + a)*a^2*c*g^2*h^3 + sqrt(c*x^2 + a)*a^3*h^5) + 15/2*c^2*d*g^2/(sqrt(c*x^2 + a)*c^3*g^6/h + 3*sqrt(c*x^2 + a)*a*c^2*g^4*h + 3*sqrt(c*x^2 + a)*a^2*c*g^2*h^3 + sqrt(c*x^2 + a)*a^3*h^5) - 5/2*c*f*g^3/(sqrt(c*x^2 + a)*c^2*g^4*h^2*x + 2*sqrt(c*x^2 + a)*a*c*g^2*h^4*x + sqrt(c*x^2 + a)*a^2*h^6*x + sqrt(c*x^2 + a)*c^2*g^5*h + 2*sqrt(c*x^2 + a)*a*c*g^3*h^3 + sqrt(c*x^2 + a)*a^2*g*h^5) - 13/2*c^2*d*g*x/(sqrt(c*x^2 + a)*a*c^2*g^4 + 2*sqrt(c*x^2 + a)*a^2*c*g^2*h^2 + sqrt(c*x^2 + a)*a^3*h^4) + 5/2*c*e*g^2/(sqrt(c*x^2 + a)*c^2*g^4*h*x + 2*sqrt(c*x^2 + a)*a*c*g^2*h^3*x + sqrt(c*x^2 + a)*a^2*h^5*x + sqrt(c*x^2 + a)*c^2*g^5 + 2*sqrt(c*x^2 + a)*a*c*g^3*h^2 + sqrt(c*x^2 + a)*a^2*g*h^4) - 15/2*c*f*g^2/(sqrt(c*x^2 + a)*c^2*g^4*h + 2*sqrt(c*x^2 + a)*a*c*g^2*h^3 + sqrt(c*x^2 + a)*a^2*h^5) + 5*c*f*g*x/(sqrt(c*x^2 + a)*a*c*g^2*h^2 + sqrt(c*x^2 + a)*a^2*h^4) - 5/2*c*d*g/(sqrt(c*x^2 + a)*c^2*g^4*x + 2*sqrt(c*x^2 + a)*a*c*g^2*h^2*x + sqrt(c*x^2 + a)*a^2*h^4*x + sqrt(c*x^2 + a)*c^2*g^5/h + 2*sqrt(c*x^2 + a)*a*c*g^3*h + sqrt(c*x^2 + a)*a^2*g*h^3) + 9/2*c*e*g/(sqrt(c*x^2 + a)*c^2*g^4 + 2*sqrt(c*x^2 + a)*a*c*g^2*h^2 + sqrt(c*x^2 + a)*a^2*h^4) - 1/2*f*g^2/(sqrt(c*x^2 + a)*c*g^2*h^3*x^2 + sqrt(c*x^2 + a)*a*h^5*x^2 + 2*sqrt(c*x^2 + a)*c*g^3*h^2*x + 2*sqrt(c*x^2 + a)*a*g*h^4*x + sqrt(c*x^2 + a)*c*g^4*h + sqrt(c*x^2 + a)*a*g^2*h^3) - 2*c*e*x/(sqrt(c*x^2 + a)*a*c*g^2*h + sqrt(c*x^2 + a)*a^2*h^3) - 3/2*c*d/(sqrt(c*x^2 + a)*c^2*g^4/h + 2*sqrt(c*x^2 + a)*a*c*g^2*h + sqrt(c*x^2 + a)*a^2*h^3) + 1/2*e*g/(sqrt(c*x^2 + a)*c*g^2*h^2*x^2 + sqrt(c*x^2 + a)*a*h^4*x^2 + 2*sqrt(c*x^2 + a)*c*g^3*h*x + 2*sqrt(c*x^2 + a)*a*g*h^3*x + sqrt(c*x^2 + a)*c*g^4 + sqrt(c*x^2 + a)*a*g^2*h^2) + 2*f*g/(sqrt(c*x^2 + a)*c*g^2*h^2*x + sqrt(c*x^2 + a)*a*h^4*x + sqrt(c*x^2 + a)*c*g^3*h + sqrt(c*x^2 + a)*a*g*h^3) - 1/2*d/(sqrt(c*x^2 + a)*c*g^2*h*x^2 + sqrt(c*x^2 + a)*a*h^3*x^2 + 2*sqrt(c*x^2 + a)*c*g^3*x + 2*sqrt(c*x^2 + a)*a*g*h^2*x + sqrt(c*x^2 + a)*c*g^4/h + sqrt(c*x^2 + a)*a*g^2*h) - e/(sqrt(c*x^2 + a)*c*g^2*h*x + sqrt(c*x^2 + a)*a*h^3*x + sqrt(c*x^2 + a)*c*g^3 + sqrt(c*x^2 + a)*a*g*h^2) + f/(sqrt(c*x^2 + a)*c*g^2*h + sqrt(c*x^2 + a)*a*h^3) + 15/2*c^2*f*g^4*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(7/2)*h^7) - 15/2*c^2*e*g^3*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(7/2)*h^6) + 15/2*c^2*d*g^2*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(7/2)*h^5) - 15/2*c*f*g^2*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(5/2)*h^5) + 9/2*c*e*g*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(5/2)*h^4) - 3/2*c*d*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(5/2)*h^3) + f*arcsinh(c*g*x/(sqrt(a*c)*abs(h*x + g)) - a*h/(sqrt(a*c)*abs(h*x + g)))/((a + c*g^2/h^2)^(3/2)*h^3)","B",0
115,1,83,0,0.434612," ","integrate((C*x^2+B*x+A)/(c*x^2+a)^(5/2),x, algorithm=""maxima"")","\frac{2 \, A x}{3 \, \sqrt{c x^{2} + a} a^{2}} + \frac{A x}{3 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} a} - \frac{C x}{3 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c} + \frac{C x}{3 \, \sqrt{c x^{2} + a} a c} - \frac{B}{3 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} c}"," ",0,"2/3*A*x/(sqrt(c*x^2 + a)*a^2) + 1/3*A*x/((c*x^2 + a)^(3/2)*a) - 1/3*C*x/((c*x^2 + a)^(3/2)*c) + 1/3*C*x/(sqrt(c*x^2 + a)*a*c) - 1/3*B/((c*x^2 + a)^(3/2)*c)","A",0
116,1,118,0,0.441027," ","integrate((C*x^2+B*x+A)/(c*x^2+a)^(7/2),x, algorithm=""maxima"")","\frac{8 \, A x}{15 \, \sqrt{c x^{2} + a} a^{3}} + \frac{4 \, A x}{15 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} a^{2}} + \frac{A x}{5 \, {\left(c x^{2} + a\right)}^{\frac{5}{2}} a} - \frac{C x}{5 \, {\left(c x^{2} + a\right)}^{\frac{5}{2}} c} + \frac{2 \, C x}{15 \, \sqrt{c x^{2} + a} a^{2} c} + \frac{C x}{15 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} a c} - \frac{B}{5 \, {\left(c x^{2} + a\right)}^{\frac{5}{2}} c}"," ",0,"8/15*A*x/(sqrt(c*x^2 + a)*a^3) + 4/15*A*x/((c*x^2 + a)^(3/2)*a^2) + 1/5*A*x/((c*x^2 + a)^(5/2)*a) - 1/5*C*x/((c*x^2 + a)^(5/2)*c) + 2/15*C*x/(sqrt(c*x^2 + a)*a^2*c) + 1/15*C*x/((c*x^2 + a)^(3/2)*a*c) - 1/5*B/((c*x^2 + a)^(5/2)*c)","A",0
117,1,153,0,0.450686," ","integrate((C*x^2+B*x+A)/(c*x^2+a)^(9/2),x, algorithm=""maxima"")","\frac{16 \, A x}{35 \, \sqrt{c x^{2} + a} a^{4}} + \frac{8 \, A x}{35 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} a^{3}} + \frac{6 \, A x}{35 \, {\left(c x^{2} + a\right)}^{\frac{5}{2}} a^{2}} + \frac{A x}{7 \, {\left(c x^{2} + a\right)}^{\frac{7}{2}} a} - \frac{C x}{7 \, {\left(c x^{2} + a\right)}^{\frac{7}{2}} c} + \frac{8 \, C x}{105 \, \sqrt{c x^{2} + a} a^{3} c} + \frac{4 \, C x}{105 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}} a^{2} c} + \frac{C x}{35 \, {\left(c x^{2} + a\right)}^{\frac{5}{2}} a c} - \frac{B}{7 \, {\left(c x^{2} + a\right)}^{\frac{7}{2}} c}"," ",0,"16/35*A*x/(sqrt(c*x^2 + a)*a^4) + 8/35*A*x/((c*x^2 + a)^(3/2)*a^3) + 6/35*A*x/((c*x^2 + a)^(5/2)*a^2) + 1/7*A*x/((c*x^2 + a)^(7/2)*a) - 1/7*C*x/((c*x^2 + a)^(7/2)*c) + 8/105*C*x/(sqrt(c*x^2 + a)*a^3*c) + 4/105*C*x/((c*x^2 + a)^(3/2)*a^2*c) + 1/35*C*x/((c*x^2 + a)^(5/2)*a*c) - 1/7*B/((c*x^2 + a)^(7/2)*c)","A",0
118,1,78,0,0.948158," ","integrate((1+2*x)^3*(4*x^2+3*x+1)/(3*x^2+2)^(1/2),x, algorithm=""maxima"")","\frac{32}{15} \, \sqrt{3 \, x^{2} + 2} x^{4} + 6 \, \sqrt{3 \, x^{2} + 2} x^{3} + \frac{764}{135} \, \sqrt{3 \, x^{2} + 2} x^{2} - \frac{1}{3} \, \sqrt{3 \, x^{2} + 2} x + \frac{5}{9} \, \sqrt{3} \operatorname{arsinh}\left(\frac{1}{2} \, \sqrt{6} x\right) - \frac{1841}{405} \, \sqrt{3 \, x^{2} + 2}"," ",0,"32/15*sqrt(3*x^2 + 2)*x^4 + 6*sqrt(3*x^2 + 2)*x^3 + 764/135*sqrt(3*x^2 + 2)*x^2 - 1/3*sqrt(3*x^2 + 2)*x + 5/9*sqrt(3)*arcsinh(1/2*sqrt(6)*x) - 1841/405*sqrt(3*x^2 + 2)","A",0
119,1,64,0,0.959450," ","integrate((1+2*x)^2*(4*x^2+3*x+1)/(3*x^2+2)^(1/2),x, algorithm=""maxima"")","\frac{4}{3} \, \sqrt{3 \, x^{2} + 2} x^{3} + \frac{28}{9} \, \sqrt{3 \, x^{2} + 2} x^{2} + 2 \, \sqrt{3 \, x^{2} + 2} x - \sqrt{3} \operatorname{arsinh}\left(\frac{1}{2} \, \sqrt{6} x\right) - \frac{49}{27} \, \sqrt{3 \, x^{2} + 2}"," ",0,"4/3*sqrt(3*x^2 + 2)*x^3 + 28/9*sqrt(3*x^2 + 2)*x^2 + 2*sqrt(3*x^2 + 2)*x - sqrt(3)*arcsinh(1/2*sqrt(6)*x) - 49/27*sqrt(3*x^2 + 2)","A",0
120,1,50,0,0.962363," ","integrate((1+2*x)*(4*x^2+3*x+1)/(3*x^2+2)^(1/2),x, algorithm=""maxima"")","\frac{8}{9} \, \sqrt{3 \, x^{2} + 2} x^{2} + \frac{5}{3} \, \sqrt{3 \, x^{2} + 2} x - \frac{7}{9} \, \sqrt{3} \operatorname{arsinh}\left(\frac{1}{2} \, \sqrt{6} x\right) + \frac{13}{27} \, \sqrt{3 \, x^{2} + 2}"," ",0,"8/9*sqrt(3*x^2 + 2)*x^2 + 5/3*sqrt(3*x^2 + 2)*x - 7/9*sqrt(3)*arcsinh(1/2*sqrt(6)*x) + 13/27*sqrt(3*x^2 + 2)","A",0
121,1,58,0,0.961980," ","integrate((4*x^2+3*x+1)/(1+2*x)/(3*x^2+2)^(1/2),x, algorithm=""maxima"")","\frac{1}{6} \, \sqrt{3} \operatorname{arsinh}\left(\frac{1}{2} \, \sqrt{6} x\right) + \frac{1}{22} \, \sqrt{11} \operatorname{arsinh}\left(\frac{\sqrt{6} x}{2 \, {\left| 2 \, x + 1 \right|}} - \frac{2 \, \sqrt{6}}{3 \, {\left| 2 \, x + 1 \right|}}\right) + \frac{2}{3} \, \sqrt{3 \, x^{2} + 2}"," ",0,"1/6*sqrt(3)*arcsinh(1/2*sqrt(6)*x) + 1/22*sqrt(11)*arcsinh(1/2*sqrt(6)*x/abs(2*x + 1) - 2/3*sqrt(6)/abs(2*x + 1)) + 2/3*sqrt(3*x^2 + 2)","A",0
122,1,65,0,0.969273," ","integrate((4*x^2+3*x+1)/(1+2*x)^2/(3*x^2+2)^(1/2),x, algorithm=""maxima"")","\frac{1}{3} \, \sqrt{3} \operatorname{arsinh}\left(\frac{1}{2} \, \sqrt{6} x\right) - \frac{4}{121} \, \sqrt{11} \operatorname{arsinh}\left(\frac{\sqrt{6} x}{2 \, {\left| 2 \, x + 1 \right|}} - \frac{2 \, \sqrt{6}}{3 \, {\left| 2 \, x + 1 \right|}}\right) - \frac{\sqrt{3 \, x^{2} + 2}}{11 \, {\left(2 \, x + 1\right)}}"," ",0,"1/3*sqrt(3)*arcsinh(1/2*sqrt(6)*x) - 4/121*sqrt(11)*arcsinh(1/2*sqrt(6)*x/abs(2*x + 1) - 2/3*sqrt(6)/abs(2*x + 1)) - 1/11*sqrt(3*x^2 + 2)/(2*x + 1)","A",0
123,1,76,0,0.970625," ","integrate((4*x^2+3*x+1)/(1+2*x)^3/(3*x^2+2)^(1/2),x, algorithm=""maxima"")","\frac{103}{1331} \, \sqrt{11} \operatorname{arsinh}\left(\frac{\sqrt{6} x}{2 \, {\left| 2 \, x + 1 \right|}} - \frac{2 \, \sqrt{6}}{3 \, {\left| 2 \, x + 1 \right|}}\right) - \frac{\sqrt{3 \, x^{2} + 2}}{22 \, {\left(4 \, x^{2} + 4 \, x + 1\right)}} + \frac{13 \, \sqrt{3 \, x^{2} + 2}}{242 \, {\left(2 \, x + 1\right)}}"," ",0,"103/1331*sqrt(11)*arcsinh(1/2*sqrt(6)*x/abs(2*x + 1) - 2/3*sqrt(6)/abs(2*x + 1)) - 1/22*sqrt(3*x^2 + 2)/(4*x^2 + 4*x + 1) + 13/242*sqrt(3*x^2 + 2)/(2*x + 1)","A",0
124,1,78,0,0.959452," ","integrate((1+2*x)^3*(4*x^2+3*x+1)/(3*x^2+2)^(3/2),x, algorithm=""maxima"")","\frac{32 \, x^{4}}{9 \, \sqrt{3 \, x^{2} + 2}} + \frac{12 \, x^{3}}{\sqrt{3 \, x^{2} + 2}} + \frac{356 \, x^{2}}{27 \, \sqrt{3 \, x^{2} + 2}} - \frac{38}{9} \, \sqrt{3} \operatorname{arsinh}\left(\frac{1}{2} \, \sqrt{6} x\right) + \frac{79 \, x}{6 \, \sqrt{3 \, x^{2} + 2}} + \frac{1181}{81 \, \sqrt{3 \, x^{2} + 2}}"," ",0,"32/9*x^4/sqrt(3*x^2 + 2) + 12*x^3/sqrt(3*x^2 + 2) + 356/27*x^2/sqrt(3*x^2 + 2) - 38/9*sqrt(3)*arcsinh(1/2*sqrt(6)*x) + 79/6*x/sqrt(3*x^2 + 2) + 1181/81/sqrt(3*x^2 + 2)","A",0
125,1,64,0,0.962501," ","integrate((1+2*x)^2*(4*x^2+3*x+1)/(3*x^2+2)^(3/2),x, algorithm=""maxima"")","\frac{8 \, x^{3}}{3 \, \sqrt{3 \, x^{2} + 2}} + \frac{28 \, x^{2}}{3 \, \sqrt{3 \, x^{2} + 2}} + \frac{4}{9} \, \sqrt{3} \operatorname{arsinh}\left(\frac{1}{2} \, \sqrt{6} x\right) - \frac{5 \, x}{6 \, \sqrt{3 \, x^{2} + 2}} + \frac{91}{9 \, \sqrt{3 \, x^{2} + 2}}"," ",0,"8/3*x^3/sqrt(3*x^2 + 2) + 28/3*x^2/sqrt(3*x^2 + 2) + 4/9*sqrt(3)*arcsinh(1/2*sqrt(6)*x) - 5/6*x/sqrt(3*x^2 + 2) + 91/9/sqrt(3*x^2 + 2)","A",0
126,1,50,0,0.959361," ","integrate((1+2*x)*(4*x^2+3*x+1)/(3*x^2+2)^(3/2),x, algorithm=""maxima"")","\frac{8 \, x^{2}}{3 \, \sqrt{3 \, x^{2} + 2}} + \frac{10}{9} \, \sqrt{3} \operatorname{arsinh}\left(\frac{1}{2} \, \sqrt{6} x\right) - \frac{17 \, x}{6 \, \sqrt{3 \, x^{2} + 2}} + \frac{17}{9 \, \sqrt{3 \, x^{2} + 2}}"," ",0,"8/3*x^2/sqrt(3*x^2 + 2) + 10/9*sqrt(3)*arcsinh(1/2*sqrt(6)*x) - 17/6*x/sqrt(3*x^2 + 2) + 17/9/sqrt(3*x^2 + 2)","A",0
127,1,58,0,0.962792," ","integrate((4*x^2+3*x+1)/(1+2*x)/(3*x^2+2)^(3/2),x, algorithm=""maxima"")","\frac{2}{121} \, \sqrt{11} \operatorname{arsinh}\left(\frac{\sqrt{6} x}{2 \, {\left| 2 \, x + 1 \right|}} - \frac{2 \, \sqrt{6}}{3 \, {\left| 2 \, x + 1 \right|}}\right) + \frac{7 \, x}{22 \, \sqrt{3 \, x^{2} + 2}} - \frac{19}{33 \, \sqrt{3 \, x^{2} + 2}}"," ",0,"2/121*sqrt(11)*arcsinh(1/2*sqrt(6)*x/abs(2*x + 1) - 2/3*sqrt(6)/abs(2*x + 1)) + 7/22*x/sqrt(3*x^2 + 2) - 19/33/sqrt(3*x^2 + 2)","A",0
128,1,84,0,0.965066," ","integrate((4*x^2+3*x+1)/(1+2*x)^2/(3*x^2+2)^(3/2),x, algorithm=""maxima"")","-\frac{4}{1331} \, \sqrt{11} \operatorname{arsinh}\left(\frac{\sqrt{6} x}{2 \, {\left| 2 \, x + 1 \right|}} - \frac{2 \, \sqrt{6}}{3 \, {\left| 2 \, x + 1 \right|}}\right) + \frac{85 \, x}{242 \, \sqrt{3 \, x^{2} + 2}} - \frac{2}{121 \, \sqrt{3 \, x^{2} + 2}} - \frac{1}{11 \, {\left(2 \, \sqrt{3 \, x^{2} + 2} x + \sqrt{3 \, x^{2} + 2}\right)}}"," ",0,"-4/1331*sqrt(11)*arcsinh(1/2*sqrt(6)*x/abs(2*x + 1) - 2/3*sqrt(6)/abs(2*x + 1)) + 85/242*x/sqrt(3*x^2 + 2) - 2/121/sqrt(3*x^2 + 2) - 1/11/(2*sqrt(3*x^2 + 2)*x + sqrt(3*x^2 + 2))","A",0
129,1,124,0,0.980731," ","integrate((4*x^2+3*x+1)/(1+2*x)^3/(3*x^2+2)^(3/2),x, algorithm=""maxima"")","\frac{322}{14641} \, \sqrt{11} \operatorname{arsinh}\left(\frac{\sqrt{6} x}{2 \, {\left| 2 \, x + 1 \right|}} - \frac{2 \, \sqrt{6}}{3 \, {\left| 2 \, x + 1 \right|}}\right) + \frac{357 \, x}{2662 \, \sqrt{3 \, x^{2} + 2}} + \frac{161}{1331 \, \sqrt{3 \, x^{2} + 2}} - \frac{1}{22 \, {\left(4 \, \sqrt{3 \, x^{2} + 2} x^{2} + 4 \, \sqrt{3 \, x^{2} + 2} x + \sqrt{3 \, x^{2} + 2}\right)}} + \frac{7}{242 \, {\left(2 \, \sqrt{3 \, x^{2} + 2} x + \sqrt{3 \, x^{2} + 2}\right)}}"," ",0,"322/14641*sqrt(11)*arcsinh(1/2*sqrt(6)*x/abs(2*x + 1) - 2/3*sqrt(6)/abs(2*x + 1)) + 357/2662*x/sqrt(3*x^2 + 2) + 161/1331/sqrt(3*x^2 + 2) - 1/22/(4*sqrt(3*x^2 + 2)*x^2 + 4*sqrt(3*x^2 + 2)*x + sqrt(3*x^2 + 2)) + 7/242/(2*sqrt(3*x^2 + 2)*x + sqrt(3*x^2 + 2))","A",0
130,1,105,0,0.951132," ","integrate((1+2*x)^3*(4*x^2+3*x+1)/(3*x^2+2)^(5/2),x, algorithm=""maxima"")","\frac{32 \, x^{4}}{3 \, {\left(3 \, x^{2} + 2\right)}^{\frac{3}{2}}} - \frac{8}{3} \, x {\left(\frac{9 \, x^{2}}{{\left(3 \, x^{2} + 2\right)}^{\frac{3}{2}}} + \frac{4}{{\left(3 \, x^{2} + 2\right)}^{\frac{3}{2}}}\right)} + \frac{8}{3} \, \sqrt{3} \operatorname{arsinh}\left(\frac{1}{2} \, \sqrt{6} x\right) - \frac{11 \, x}{18 \, \sqrt{3 \, x^{2} + 2}} + \frac{52 \, x^{2}}{9 \, {\left(3 \, x^{2} + 2\right)}^{\frac{3}{2}}} - \frac{65 \, x}{18 \, {\left(3 \, x^{2} + 2\right)}^{\frac{3}{2}}} + \frac{127}{81 \, {\left(3 \, x^{2} + 2\right)}^{\frac{3}{2}}}"," ",0,"32/3*x^4/(3*x^2 + 2)^(3/2) - 8/3*x*(9*x^2/(3*x^2 + 2)^(3/2) + 4/(3*x^2 + 2)^(3/2)) + 8/3*sqrt(3)*arcsinh(1/2*sqrt(6)*x) - 11/18*x/sqrt(3*x^2 + 2) + 52/9*x^2/(3*x^2 + 2)^(3/2) - 65/18*x/(3*x^2 + 2)^(3/2) + 127/81/(3*x^2 + 2)^(3/2)","A",0
131,1,91,0,0.961689," ","integrate((1+2*x)^2*(4*x^2+3*x+1)/(3*x^2+2)^(5/2),x, algorithm=""maxima"")","-\frac{16}{27} \, x {\left(\frac{9 \, x^{2}}{{\left(3 \, x^{2} + 2\right)}^{\frac{3}{2}}} + \frac{4}{{\left(3 \, x^{2} + 2\right)}^{\frac{3}{2}}}\right)} + \frac{16}{27} \, \sqrt{3} \operatorname{arsinh}\left(\frac{1}{2} \, \sqrt{6} x\right) + \frac{37 \, x}{54 \, \sqrt{3 \, x^{2} + 2}} - \frac{28 \, x^{2}}{3 \, {\left(3 \, x^{2} + 2\right)}^{\frac{3}{2}}} - \frac{37 \, x}{18 \, {\left(3 \, x^{2} + 2\right)}^{\frac{3}{2}}} - \frac{133}{27 \, {\left(3 \, x^{2} + 2\right)}^{\frac{3}{2}}}"," ",0,"-16/27*x*(9*x^2/(3*x^2 + 2)^(3/2) + 4/(3*x^2 + 2)^(3/2)) + 16/27*sqrt(3)*arcsinh(1/2*sqrt(6)*x) + 37/54*x/sqrt(3*x^2 + 2) - 28/3*x^2/(3*x^2 + 2)^(3/2) - 37/18*x/(3*x^2 + 2)^(3/2) - 133/27/(3*x^2 + 2)^(3/2)","B",0
132,1,50,0,0.424568," ","integrate((1+2*x)*(4*x^2+3*x+1)/(3*x^2+2)^(5/2),x, algorithm=""maxima"")","\frac{13 \, x}{18 \, \sqrt{3 \, x^{2} + 2}} - \frac{8 \, x^{2}}{3 \, {\left(3 \, x^{2} + 2\right)}^{\frac{3}{2}}} - \frac{17 \, x}{18 \, {\left(3 \, x^{2} + 2\right)}^{\frac{3}{2}}} - \frac{47}{27 \, {\left(3 \, x^{2} + 2\right)}^{\frac{3}{2}}}"," ",0,"13/18*x/sqrt(3*x^2 + 2) - 8/3*x^2/(3*x^2 + 2)^(3/2) - 17/18*x/(3*x^2 + 2)^(3/2) - 47/27/(3*x^2 + 2)^(3/2)","A",0
133,1,81,0,0.971504," ","integrate((4*x^2+3*x+1)/(1+2*x)/(3*x^2+2)^(5/2),x, algorithm=""maxima"")","\frac{8}{1331} \, \sqrt{11} \operatorname{arsinh}\left(\frac{\sqrt{6} x}{2 \, {\left| 2 \, x + 1 \right|}} - \frac{2 \, \sqrt{6}}{3 \, {\left| 2 \, x + 1 \right|}}\right) + \frac{95 \, x}{726 \, \sqrt{3 \, x^{2} + 2}} + \frac{4}{121 \, \sqrt{3 \, x^{2} + 2}} + \frac{7 \, x}{66 \, {\left(3 \, x^{2} + 2\right)}^{\frac{3}{2}}} - \frac{19}{99 \, {\left(3 \, x^{2} + 2\right)}^{\frac{3}{2}}}"," ",0,"8/1331*sqrt(11)*arcsinh(1/2*sqrt(6)*x/abs(2*x + 1) - 2/3*sqrt(6)/abs(2*x + 1)) + 95/726*x/sqrt(3*x^2 + 2) + 4/121/sqrt(3*x^2 + 2) + 7/66*x/(3*x^2 + 2)^(3/2) - 19/99/(3*x^2 + 2)^(3/2)","A",0
134,1,107,0,0.977449," ","integrate((4*x^2+3*x+1)/(1+2*x)^2/(3*x^2+2)^(5/2),x, algorithm=""maxima"")","\frac{32}{14641} \, \sqrt{11} \operatorname{arsinh}\left(\frac{\sqrt{6} x}{2 \, {\left| 2 \, x + 1 \right|}} - \frac{2 \, \sqrt{6}}{3 \, {\left| 2 \, x + 1 \right|}}\right) + \frac{743 \, x}{7986 \, \sqrt{3 \, x^{2} + 2}} + \frac{16}{1331 \, \sqrt{3 \, x^{2} + 2}} + \frac{61 \, x}{726 \, {\left(3 \, x^{2} + 2\right)}^{\frac{3}{2}}} - \frac{1}{11 \, {\left(2 \, {\left(3 \, x^{2} + 2\right)}^{\frac{3}{2}} x + {\left(3 \, x^{2} + 2\right)}^{\frac{3}{2}}\right)}} + \frac{4}{363 \, {\left(3 \, x^{2} + 2\right)}^{\frac{3}{2}}}"," ",0,"32/14641*sqrt(11)*arcsinh(1/2*sqrt(6)*x/abs(2*x + 1) - 2/3*sqrt(6)/abs(2*x + 1)) + 743/7986*x/sqrt(3*x^2 + 2) + 16/1331/sqrt(3*x^2 + 2) + 61/726*x/(3*x^2 + 2)^(3/2) - 1/11/(2*(3*x^2 + 2)^(3/2)*x + (3*x^2 + 2)^(3/2)) + 4/363/(3*x^2 + 2)^(3/2)","A",0
135,1,147,0,0.987312," ","integrate((4*x^2+3*x+1)/(1+2*x)^3/(3*x^2+2)^(5/2),x, algorithm=""maxima"")","\frac{1216}{161051} \, \sqrt{11} \operatorname{arsinh}\left(\frac{\sqrt{6} x}{2 \, {\left| 2 \, x + 1 \right|}} - \frac{2 \, \sqrt{6}}{3 \, {\left| 2 \, x + 1 \right|}}\right) + \frac{1869 \, x}{29282 \, \sqrt{3 \, x^{2} + 2}} + \frac{608}{14641 \, \sqrt{3 \, x^{2} + 2}} + \frac{87 \, x}{2662 \, {\left(3 \, x^{2} + 2\right)}^{\frac{3}{2}}} - \frac{1}{22 \, {\left(4 \, {\left(3 \, x^{2} + 2\right)}^{\frac{3}{2}} x^{2} + 4 \, {\left(3 \, x^{2} + 2\right)}^{\frac{3}{2}} x + {\left(3 \, x^{2} + 2\right)}^{\frac{3}{2}}\right)}} + \frac{1}{242 \, {\left(2 \, {\left(3 \, x^{2} + 2\right)}^{\frac{3}{2}} x + {\left(3 \, x^{2} + 2\right)}^{\frac{3}{2}}\right)}} + \frac{152}{3993 \, {\left(3 \, x^{2} + 2\right)}^{\frac{3}{2}}}"," ",0,"1216/161051*sqrt(11)*arcsinh(1/2*sqrt(6)*x/abs(2*x + 1) - 2/3*sqrt(6)/abs(2*x + 1)) + 1869/29282*x/sqrt(3*x^2 + 2) + 608/14641/sqrt(3*x^2 + 2) + 87/2662*x/(3*x^2 + 2)^(3/2) - 1/22/(4*(3*x^2 + 2)^(3/2)*x^2 + 4*(3*x^2 + 2)^(3/2)*x + (3*x^2 + 2)^(3/2)) + 1/242/(2*(3*x^2 + 2)^(3/2)*x + (3*x^2 + 2)^(3/2)) + 152/3993/(3*x^2 + 2)^(3/2)","A",0
136,0,0,0,0.000000," ","integrate((h*x+g)^m*(c*x^2+a)^p*(f*x^2+e*x+d),x, algorithm=""maxima"")","\int {\left(f x^{2} + e x + d\right)} {\left(c x^{2} + a\right)}^{p} {\left(h x + g\right)}^{m}\,{d x}"," ",0,"integrate((f*x^2 + e*x + d)*(c*x^2 + a)^p*(h*x + g)^m, x)","F",0
137,0,0,0,0.000000," ","integrate((h*x+g)^m*(f*x^2+e*x+d)*(c*x^2+a)^(1/2),x, algorithm=""maxima"")","\int \sqrt{c x^{2} + a} {\left(f x^{2} + e x + d\right)} {\left(h x + g\right)}^{m}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + a)*(f*x^2 + e*x + d)*(h*x + g)^m, x)","F",0
138,0,0,0,0.000000," ","integrate((h*x+g)^(-3-2*p)*(c*x^2+a)^p*(f*x^2+e*x+d),x, algorithm=""maxima"")","\int {\left(f x^{2} + e x + d\right)} {\left(c x^{2} + a\right)}^{p} {\left(h x + g\right)}^{-2 \, p - 3}\,{d x}"," ",0,"integrate((f*x^2 + e*x + d)*(c*x^2 + a)^p*(h*x + g)^(-2*p - 3), x)","F",0
139,0,0,0,0.000000," ","integrate((e*x+d)^m*(c*e^2*x^2+b*e^2*x+b*d*e-c*d^2)^p*(-(-b*e+c*d)*f+(b*e*g-c*d*g+c*e*f)*x+c*e*g*x^2),x, algorithm=""maxima"")","\int {\left(c e g x^{2} - {\left(c d - b e\right)} f + {\left(c e f - c d g + b e g\right)} x\right)} {\left(c e^{2} x^{2} + b e^{2} x - c d^{2} + b d e\right)}^{p} {\left(e x + d\right)}^{m}\,{d x}"," ",0,"integrate((c*e*g*x^2 - (c*d - b*e)*f + (c*e*f - c*d*g + b*e*g)*x)*(c*e^2*x^2 + b*e^2*x - c*d^2 + b*d*e)^p*(e*x + d)^m, x)","F",0
140,1,263,0,0.435809," ","integrate((c*x^2+b*x+a)^4*(C*x^2+A),x, algorithm=""maxima"")","\frac{1}{11} \, C c^{4} x^{11} + \frac{2}{5} \, C b c^{3} x^{10} + \frac{1}{9} \, {\left(6 \, C b^{2} c^{2} + 4 \, C a c^{3} + A c^{4}\right)} x^{9} + \frac{1}{2} \, {\left(C b^{3} c + 3 \, C a b c^{2} + A b c^{3}\right)} x^{8} + \frac{1}{7} \, {\left(C b^{4} + 12 \, C a b^{2} c + 4 \, A a c^{3} + 6 \, {\left(C a^{2} + A b^{2}\right)} c^{2}\right)} x^{7} + 2 \, A a^{3} b x^{2} + \frac{2}{3} \, {\left(C a b^{3} + 3 \, A a b c^{2} + {\left(3 \, C a^{2} b + A b^{3}\right)} c\right)} x^{6} + A a^{4} x + \frac{1}{5} \, {\left(6 \, C a^{2} b^{2} + A b^{4} + 6 \, A a^{2} c^{2} + 4 \, {\left(C a^{3} + 3 \, A a b^{2}\right)} c\right)} x^{5} + {\left(C a^{3} b + A a b^{3} + 3 \, A a^{2} b c\right)} x^{4} + \frac{1}{3} \, {\left(C a^{4} + 6 \, A a^{2} b^{2} + 4 \, A a^{3} c\right)} x^{3}"," ",0,"1/11*C*c^4*x^11 + 2/5*C*b*c^3*x^10 + 1/9*(6*C*b^2*c^2 + 4*C*a*c^3 + A*c^4)*x^9 + 1/2*(C*b^3*c + 3*C*a*b*c^2 + A*b*c^3)*x^8 + 1/7*(C*b^4 + 12*C*a*b^2*c + 4*A*a*c^3 + 6*(C*a^2 + A*b^2)*c^2)*x^7 + 2*A*a^3*b*x^2 + 2/3*(C*a*b^3 + 3*A*a*b*c^2 + (3*C*a^2*b + A*b^3)*c)*x^6 + A*a^4*x + 1/5*(6*C*a^2*b^2 + A*b^4 + 6*A*a^2*c^2 + 4*(C*a^3 + 3*A*a*b^2)*c)*x^5 + (C*a^3*b + A*a*b^3 + 3*A*a^2*b*c)*x^4 + 1/3*(C*a^4 + 6*A*a^2*b^2 + 4*A*a^3*c)*x^3","A",0
141,1,165,0,0.428511," ","integrate((c*x^2+b*x+a)^3*(C*x^2+A),x, algorithm=""maxima"")","\frac{1}{9} \, C c^{3} x^{9} + \frac{3}{8} \, C b c^{2} x^{8} + \frac{1}{7} \, {\left(3 \, C b^{2} c + 3 \, C a c^{2} + A c^{3}\right)} x^{7} + \frac{1}{6} \, {\left(C b^{3} + 6 \, C a b c + 3 \, A b c^{2}\right)} x^{6} + \frac{3}{2} \, A a^{2} b x^{2} + \frac{3}{5} \, {\left(C a b^{2} + A a c^{2} + {\left(C a^{2} + A b^{2}\right)} c\right)} x^{5} + A a^{3} x + \frac{1}{4} \, {\left(3 \, C a^{2} b + A b^{3} + 6 \, A a b c\right)} x^{4} + \frac{1}{3} \, {\left(C a^{3} + 3 \, A a b^{2} + 3 \, A a^{2} c\right)} x^{3}"," ",0,"1/9*C*c^3*x^9 + 3/8*C*b*c^2*x^8 + 1/7*(3*C*b^2*c + 3*C*a*c^2 + A*c^3)*x^7 + 1/6*(C*b^3 + 6*C*a*b*c + 3*A*b*c^2)*x^6 + 3/2*A*a^2*b*x^2 + 3/5*(C*a*b^2 + A*a*c^2 + (C*a^2 + A*b^2)*c)*x^5 + A*a^3*x + 1/4*(3*C*a^2*b + A*b^3 + 6*A*a*b*c)*x^4 + 1/3*(C*a^3 + 3*A*a*b^2 + 3*A*a^2*c)*x^3","A",0
142,1,87,0,0.430406," ","integrate((c*x^2+b*x+a)^2*(C*x^2+A),x, algorithm=""maxima"")","\frac{1}{7} \, C c^{2} x^{7} + \frac{1}{3} \, C b c x^{6} + \frac{1}{5} \, {\left(C b^{2} + 2 \, C a c + A c^{2}\right)} x^{5} + A a b x^{2} + \frac{1}{2} \, {\left(C a b + A b c\right)} x^{4} + A a^{2} x + \frac{1}{3} \, {\left(C a^{2} + A b^{2} + 2 \, A a c\right)} x^{3}"," ",0,"1/7*C*c^2*x^7 + 1/3*C*b*c*x^6 + 1/5*(C*b^2 + 2*C*a*c + A*c^2)*x^5 + A*a*b*x^2 + 1/2*(C*a*b + A*b*c)*x^4 + A*a^2*x + 1/3*(C*a^2 + A*b^2 + 2*A*a*c)*x^3","A",0
143,1,38,0,0.429733," ","integrate((c*x^2+b*x+a)*(C*x^2+A),x, algorithm=""maxima"")","\frac{1}{5} \, C c x^{5} + \frac{1}{4} \, C b x^{4} + \frac{1}{2} \, A b x^{2} + \frac{1}{3} \, {\left(C a + A c\right)} x^{3} + A a x"," ",0,"1/5*C*c*x^5 + 1/4*C*b*x^4 + 1/2*A*b*x^2 + 1/3*(C*a + A*c)*x^3 + A*a*x","A",0
144,-2,0,0,0.000000," ","integrate((C*x^2+A)/(c*x^2+b*x+a),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
145,-2,0,0,0.000000," ","integrate((C*x^2+A)/(c*x^2+b*x+a)^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
146,-2,0,0,0.000000," ","integrate((C*x^2+A)/(c*x^2+b*x+a)^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
147,-2,0,0,0.000000," ","integrate((C*x^2+A)/(c*x^2+b*x+a)^4,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
148,-2,0,0,0.000000," ","integrate((e*x+d)^3*(h*x^2+g*x+f)/(c*x^2+b*x+a),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
149,-2,0,0,0.000000," ","integrate((e*x+d)^2*(h*x^2+g*x+f)/(c*x^2+b*x+a),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
150,-2,0,0,0.000000," ","integrate((e*x+d)*(h*x^2+g*x+f)/(c*x^2+b*x+a),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
151,-2,0,0,0.000000," ","integrate((h*x^2+g*x+f)/(c*x^2+b*x+a),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
152,-2,0,0,0.000000," ","integrate((h*x^2+g*x+f)/(e*x+d)/(c*x^2+b*x+a),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
153,-2,0,0,0.000000," ","integrate((h*x^2+g*x+f)/(e*x+d)^2/(c*x^2+b*x+a),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
154,-2,0,0,0.000000," ","integrate((h*x^2+g*x+f)/(e*x+d)^3/(c*x^2+b*x+a),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
155,-2,0,0,0.000000," ","integrate((e*x+d)^2*(h*x^2+g*x+f)/(c*x^2+b*x+a)^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
156,-2,0,0,0.000000," ","integrate((e*x+d)*(h*x^2+g*x+f)/(c*x^2+b*x+a)^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
157,-2,0,0,0.000000," ","integrate((h*x^2+g*x+f)/(c*x^2+b*x+a)^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
158,-2,0,0,0.000000," ","integrate((h*x^2+g*x+f)/(e*x+d)/(c*x^2+b*x+a)^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
159,-2,0,0,0.000000," ","integrate((h*x^2+g*x+f)/(e*x+d)^2/(c*x^2+b*x+a)^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
160,1,51,0,0.955269," ","integrate(x^3*(x^2+x+1)/(x^2-x+1)^2,x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} - \frac{10}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + 3 \, x - \frac{2 \, {\left(x - 2\right)}}{3 \, {\left(x^{2} - x + 1\right)}} + 2 \, \log\left(x^{2} - x + 1\right)"," ",0,"1/2*x^2 - 10/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) + 3*x - 2/3*(x - 2)/(x^2 - x + 1) + 2*log(x^2 - x + 1)","A",0
161,1,46,0,0.950068," ","integrate(x^2*(x^2+x+1)/(x^2-x+1)^2,x, algorithm=""maxima"")","\frac{7}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + x - \frac{2 \, {\left(2 \, x - 1\right)}}{3 \, {\left(x^{2} - x + 1\right)}} + \frac{3}{2} \, \log\left(x^{2} - x + 1\right)"," ",0,"7/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) + x - 2/3*(2*x - 1)/(x^2 - x + 1) + 3/2*log(x^2 - x + 1)","A",0
162,1,43,0,0.955504," ","integrate(x*(x^2+x+1)/(x^2-x+1)^2,x, algorithm=""maxima"")","\frac{11}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) - \frac{2 \, {\left(x + 1\right)}}{3 \, {\left(x^{2} - x + 1\right)}} + \frac{1}{2} \, \log\left(x^{2} - x + 1\right)"," ",0,"11/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) - 2/3*(x + 1)/(x^2 - x + 1) + 1/2*log(x^2 - x + 1)","A",0
163,1,32,0,0.945269," ","integrate((x^2+x+1)/(x^2-x+1)^2,x, algorithm=""maxima"")","\frac{10}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + \frac{2 \, {\left(x - 2\right)}}{3 \, {\left(x^{2} - x + 1\right)}}"," ",0,"10/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) + 2/3*(x - 2)/(x^2 - x + 1)","A",0
164,1,47,0,0.952799," ","integrate((x^2+x+1)/x/(x^2-x+1)^2,x, algorithm=""maxima"")","\frac{11}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + \frac{2 \, {\left(2 \, x - 1\right)}}{3 \, {\left(x^{2} - x + 1\right)}} - \frac{1}{2} \, \log\left(x^{2} - x + 1\right) + \log\left(x\right)"," ",0,"11/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) + 2/3*(2*x - 1)/(x^2 - x + 1) - 1/2*log(x^2 - x + 1) + log(x)","A",0
165,1,54,0,0.957730," ","integrate((x^2+x+1)/x^2/(x^2-x+1)^2,x, algorithm=""maxima"")","\frac{7}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) - \frac{x^{2} - 5 \, x + 3}{3 \, {\left(x^{3} - x^{2} + x\right)}} - \frac{3}{2} \, \log\left(x^{2} - x + 1\right) + 3 \, \log\left(x\right)"," ",0,"7/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) - 1/3*(x^2 - 5*x + 3)/(x^3 - x^2 + x) - 3/2*log(x^2 - x + 1) + 3*log(x)","A",0
166,1,63,0,0.954202," ","integrate((x^2+x+1)/x^3/(x^2-x+1)^2,x, algorithm=""maxima"")","-\frac{10}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) - \frac{22 \, x^{3} - 23 \, x^{2} + 15 \, x + 3}{6 \, {\left(x^{4} - x^{3} + x^{2}\right)}} - 2 \, \log\left(x^{2} - x + 1\right) + 4 \, \log\left(x\right)"," ",0,"-10/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) - 1/6*(22*x^3 - 23*x^2 + 15*x + 3)/(x^4 - x^3 + x^2) - 2*log(x^2 - x + 1) + 4*log(x)","A",0
167,1,10,0,0.430378," ","integrate((-x^2+1)/(x^2+x+1)^2,x, algorithm=""maxima"")","\frac{x}{x^{2} + x + 1}"," ",0,"x/(x^2 + x + 1)","A",0
168,1,27,0,0.953498," ","integrate((x^2+1)/(x^2+x+1),x, algorithm=""maxima"")","\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + x - \frac{1}{2} \, \log\left(x^{2} + x + 1\right)"," ",0,"1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) + x - 1/2*log(x^2 + x + 1)","A",0
169,1,21,0,0.953051," ","integrate((x^2-1)/(x^2-6*x+25),x, algorithm=""maxima"")","x - 2 \, \arctan\left(\frac{1}{4} \, x - \frac{3}{4}\right) + 3 \, \log\left(x^{2} - 6 \, x + 25\right)"," ",0,"x - 2*arctan(1/4*x - 3/4) + 3*log(x^2 - 6*x + 25)","A",0
170,1,17,0,0.419625," ","integrate((3*x^2-10)/(x^2-4*x+4),x, algorithm=""maxima"")","3 \, x - \frac{2}{x - 2} + 12 \, \log\left(x - 2\right)"," ",0,"3*x - 2/(x - 2) + 12*log(x - 2)","A",0
171,1,14,0,0.426678," ","integrate((x^2+8)/(x^2-5*x+6),x, algorithm=""maxima"")","x - 12 \, \log\left(x - 2\right) + 17 \, \log\left(x - 3\right)"," ",0,"x - 12*log(x - 2) + 17*log(x - 3)","A",0
172,1,12,0,0.426007," ","integrate((x^2+3*x-4)/(x^2-2*x-8),x, algorithm=""maxima"")","x + \log\left(x + 2\right) + 4 \, \log\left(x - 4\right)"," ",0,"x + log(x + 2) + 4*log(x - 4)","A",0
173,1,21,0,0.943334," ","integrate((4*x^2+5*x+7)/(4*x^2+4*x+5),x, algorithm=""maxima"")","x + \frac{3}{8} \, \arctan\left(x + \frac{1}{2}\right) + \frac{1}{8} \, \log\left(4 \, x^{2} + 4 \, x + 5\right)"," ",0,"x + 3/8*arctan(x + 1/2) + 1/8*log(4*x^2 + 4*x + 5)","A",0
174,1,36,0,0.956069," ","integrate((x^2-x+2)/(x^2+2*x-5),x, algorithm=""maxima"")","\frac{5}{6} \, \sqrt{6} \log\left(\frac{x - \sqrt{6} + 1}{x + \sqrt{6} + 1}\right) + x - \frac{3}{2} \, \log\left(x^{2} + 2 \, x - 5\right)"," ",0,"5/6*sqrt(6)*log((x - sqrt(6) + 1)/(x + sqrt(6) + 1)) + x - 3/2*log(x^2 + 2*x - 5)","A",0
175,1,19,0,0.425015," ","integrate((3*x^2+4*x+1)/(2*x^2+7*x+4)^2,x, algorithm=""maxima"")","-\frac{3 \, x + 2}{2 \, {\left(2 \, x^{2} + 7 \, x + 4\right)}}"," ",0,"-1/2*(3*x + 2)/(2*x^2 + 7*x + 4)","A",0
176,1,30,0,0.958390," ","integrate((x^2+x+1)/(x^2+2*x+3)^2,x, algorithm=""maxima"")","\frac{3}{8} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(x + 1\right)}\right) - \frac{x - 1}{4 \, {\left(x^{2} + 2 \, x + 3\right)}}"," ",0,"3/8*sqrt(2)*arctan(1/2*sqrt(2)*(x + 1)) - 1/4*(x - 1)/(x^2 + 2*x + 3)","A",0
177,1,33,0,0.436055," ","integrate((5*x^2+2*x-1)/(x^2+x+1)^4,x, algorithm=""maxima"")","-\frac{x}{x^{6} + 3 \, x^{5} + 6 \, x^{4} + 7 \, x^{3} + 6 \, x^{2} + 3 \, x + 1}"," ",0,"-x/(x^6 + 3*x^5 + 6*x^4 + 7*x^3 + 6*x^2 + 3*x + 1)","B",0
178,-2,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(5/2)*(C*x^2+A),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive, negative or zero?","F(-2)",0
179,-2,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)*(C*x^2+A),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive, negative or zero?","F(-2)",0
180,-2,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(1/2)*(C*x^2+A),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive, negative or zero?","F(-2)",0
181,-2,0,0,0.000000," ","integrate((C*x^2+A)/(c*x^2+b*x+a)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 zero or nonzero?","F(-2)",0
182,-2,0,0,0.000000," ","integrate((C*x^2+A)/(c*x^2+b*x+a)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 zero or nonzero?","F(-2)",0
183,-2,0,0,0.000000," ","integrate((C*x^2+A)/(c*x^2+b*x+a)^(5/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 zero or nonzero?","F(-2)",0
184,-2,0,0,0.000000," ","integrate((C*x^2+A)/(c*x^2+b*x+a)^(7/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 zero or nonzero?","F(-2)",0
185,-2,0,0,0.000000," ","integrate((C*x^2+A)/(c*x^2+b*x+a)^(9/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 zero or nonzero?","F(-2)",0
186,-2,0,0,0.000000," ","integrate((h*x+g)^3*(f*x^2+e*x+d)*(c*x^2+b*x+a)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive, negative or zero?","F(-2)",0
187,-2,0,0,0.000000," ","integrate((h*x+g)^2*(f*x^2+e*x+d)*(c*x^2+b*x+a)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive, negative or zero?","F(-2)",0
188,-2,0,0,0.000000," ","integrate((h*x+g)*(f*x^2+e*x+d)*(c*x^2+b*x+a)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive, negative or zero?","F(-2)",0
189,-2,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(1/2)*(f*x^2+e*x+d),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive, negative or zero?","F(-2)",0
190,-2,0,0,0.000000," ","integrate((f*x^2+e*x+d)*(c*x^2+b*x+a)^(1/2)/(h*x+g),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b*h-2*c*g>0)', see `assume?` for more details)Is b*h-2*c*g zero or nonzero?","F(-2)",0
191,-2,0,0,0.000000," ","integrate((f*x^2+e*x+d)*(c*x^2+b*x+a)^(1/2)/(h*x+g)^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b*h-2*c*g>0)', see `assume?` for more details)Is b*h-2*c*g zero or nonzero?","F(-2)",0
192,-2,0,0,0.000000," ","integrate((f*x^2+e*x+d)*(c*x^2+b*x+a)^(1/2)/(h*x+g)^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*h^2-b*g*h>0)', see `assume?` for more details)Is a*h^2-b*g*h                            +c*g^2 zero or nonzero?","F(-2)",0
193,-2,0,0,0.000000," ","integrate((f*x^2+e*x+d)*(c*x^2+b*x+a)^(1/2)/(h*x+g)^4,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*h^2-b*g*h>0)', see `assume?` for more details)Is a*h^2-b*g*h                            +c*g^2 zero or nonzero?","F(-2)",0
194,-2,0,0,0.000000," ","integrate((f*x^2+e*x+d)*(c*x^2+b*x+a)^(1/2)/(h*x+g)^5,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*h^2-b*g*h>0)', see `assume?` for more details)Is a*h^2-b*g*h                            +c*g^2 zero or nonzero?","F(-2)",0
195,-2,0,0,0.000000," ","integrate((f*x^2+e*x+d)*(c*x^2+b*x+a)^(1/2)/(h*x+g)^6,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*h^2-b*g*h>0)', see `assume?` for more details)Is a*h^2-b*g*h                            +c*g^2 zero or nonzero?","F(-2)",0
196,-2,0,0,0.000000," ","integrate((h*x+g)^3*(c*x^2+b*x+a)^(3/2)*(f*x^2+e*x+d),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive, negative or zero?","F(-2)",0
197,-2,0,0,0.000000," ","integrate((h*x+g)^2*(c*x^2+b*x+a)^(3/2)*(f*x^2+e*x+d),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive, negative or zero?","F(-2)",0
198,-2,0,0,0.000000," ","integrate((h*x+g)*(c*x^2+b*x+a)^(3/2)*(f*x^2+e*x+d),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive, negative or zero?","F(-2)",0
199,-2,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)*(f*x^2+e*x+d),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive, negative or zero?","F(-2)",0
200,-2,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)*(f*x^2+e*x+d)/(h*x+g),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b*h-2*c*g>0)', see `assume?` for more details)Is b*h-2*c*g zero or nonzero?","F(-2)",0
201,-2,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)*(f*x^2+e*x+d)/(h*x+g)^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b*h-2*c*g>0)', see `assume?` for more details)Is b*h-2*c*g zero or nonzero?","F(-2)",0
202,-2,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)*(f*x^2+e*x+d)/(h*x+g)^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*h^2-b*g*h>0)', see `assume?` for more details)Is a*h^2-b*g*h                            +c*g^2 zero or nonzero?","F(-2)",0
203,-2,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)*(f*x^2+e*x+d)/(h*x+g)^4,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*h^2-b*g*h>0)', see `assume?` for more details)Is a*h^2-b*g*h                            +c*g^2 zero or nonzero?","F(-2)",0
204,-2,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)*(f*x^2+e*x+d)/(h*x+g)^5,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*h^2-b*g*h>0)', see `assume?` for more details)Is a*h^2-b*g*h                            +c*g^2 zero or nonzero?","F(-2)",0
205,-2,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)*(f*x^2+e*x+d)/(h*x+g)^6,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*h^2-b*g*h>0)', see `assume?` for more details)Is a*h^2-b*g*h                            +c*g^2 zero or nonzero?","F(-2)",0
206,-2,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)*(f*x^2+e*x+d)/(h*x+g)^7,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*h^2-b*g*h>0)', see `assume?` for more details)Is a*h^2-b*g*h                            +c*g^2 zero or nonzero?","F(-2)",0
207,-2,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)*(f*x^2+e*x+d)/(h*x+g)^8,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*h^2-b*g*h>0)', see `assume?` for more details)Is a*h^2-b*g*h                            +c*g^2 zero or nonzero?","F(-2)",0
208,1,126,0,0.950908," ","integrate((1+2*x)^3*(4*x^2+3*x+1)*(3*x^2-x+2)^(1/2),x, algorithm=""maxima"")","\frac{32}{21} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}} x^{4} + \frac{844}{189} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}} x^{3} + \frac{1594}{315} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}} x^{2} + \frac{7849}{3780} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}} x - \frac{45739}{68040} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}} - \frac{5393}{2592} \, \sqrt{3 \, x^{2} - x + 2} x - \frac{124039}{93312} \, \sqrt{3} \operatorname{arsinh}\left(\frac{1}{23} \, \sqrt{23} {\left(6 \, x - 1\right)}\right) + \frac{5393}{15552} \, \sqrt{3 \, x^{2} - x + 2}"," ",0,"32/21*(3*x^2 - x + 2)^(3/2)*x^4 + 844/189*(3*x^2 - x + 2)^(3/2)*x^3 + 1594/315*(3*x^2 - x + 2)^(3/2)*x^2 + 7849/3780*(3*x^2 - x + 2)^(3/2)*x - 45739/68040*(3*x^2 - x + 2)^(3/2) - 5393/2592*sqrt(3*x^2 - x + 2)*x - 124039/93312*sqrt(3)*arcsinh(1/23*sqrt(23)*(6*x - 1)) + 5393/15552*sqrt(3*x^2 - x + 2)","A",0
209,1,109,0,0.956627," ","integrate((1+2*x)^2*(4*x^2+3*x+1)*(3*x^2-x+2)^(1/2),x, algorithm=""maxima"")","\frac{8}{9} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}} x^{3} + \frac{32}{15} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}} x^{2} + \frac{83}{45} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}} x + \frac{277}{810} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}} - \frac{235}{216} \, \sqrt{3 \, x^{2} - x + 2} x - \frac{5405}{7776} \, \sqrt{3} \operatorname{arsinh}\left(\frac{1}{23} \, \sqrt{23} {\left(6 \, x - 1\right)}\right) + \frac{235}{1296} \, \sqrt{3 \, x^{2} - x + 2}"," ",0,"8/9*(3*x^2 - x + 2)^(3/2)*x^3 + 32/15*(3*x^2 - x + 2)^(3/2)*x^2 + 83/45*(3*x^2 - x + 2)^(3/2)*x + 277/810*(3*x^2 - x + 2)^(3/2) - 235/216*sqrt(3*x^2 - x + 2)*x - 5405/7776*sqrt(3)*arcsinh(1/23*sqrt(23)*(6*x - 1)) + 235/1296*sqrt(3*x^2 - x + 2)","A",0
210,1,92,0,0.956986," ","integrate((1+2*x)*(4*x^2+3*x+1)*(3*x^2-x+2)^(1/2),x, algorithm=""maxima"")","\frac{8}{15} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}} x^{2} + \frac{89}{90} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}} x + \frac{961}{1620} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}} - \frac{19}{432} \, \sqrt{3 \, x^{2} - x + 2} x - \frac{437}{15552} \, \sqrt{3} \operatorname{arsinh}\left(\frac{1}{23} \, \sqrt{23} {\left(6 \, x - 1\right)}\right) + \frac{19}{2592} \, \sqrt{3 \, x^{2} - x + 2}"," ",0,"8/15*(3*x^2 - x + 2)^(3/2)*x^2 + 89/90*(3*x^2 - x + 2)^(3/2)*x + 961/1620*(3*x^2 - x + 2)^(3/2) - 19/432*sqrt(3*x^2 - x + 2)*x - 437/15552*sqrt(3)*arcsinh(1/23*sqrt(23)*(6*x - 1)) + 19/2592*sqrt(3*x^2 - x + 2)","A",0
211,1,96,0,0.962944," ","integrate((4*x^2+3*x+1)*(3*x^2-x+2)^(1/2)/(1+2*x),x, algorithm=""maxima"")","\frac{2}{9} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}} + \frac{5}{12} \, \sqrt{3 \, x^{2} - x + 2} x + \frac{43}{432} \, \sqrt{3} \operatorname{arsinh}\left(\frac{6}{23} \, \sqrt{23} x - \frac{1}{23} \, \sqrt{23}\right) + \frac{1}{8} \, \sqrt{13} \operatorname{arsinh}\left(\frac{8 \, \sqrt{23} x}{23 \, {\left| 2 \, x + 1 \right|}} - \frac{9 \, \sqrt{23}}{23 \, {\left| 2 \, x + 1 \right|}}\right) + \frac{13}{72} \, \sqrt{3 \, x^{2} - x + 2}"," ",0,"2/9*(3*x^2 - x + 2)^(3/2) + 5/12*sqrt(3*x^2 - x + 2)*x + 43/432*sqrt(3)*arcsinh(6/23*sqrt(23)*x - 1/23*sqrt(23)) + 1/8*sqrt(13)*arcsinh(8/23*sqrt(23)*x/abs(2*x + 1) - 9/23*sqrt(23)/abs(2*x + 1)) + 13/72*sqrt(3*x^2 - x + 2)","A",0
212,1,103,0,0.973856," ","integrate((4*x^2+3*x+1)*(3*x^2-x+2)^(1/2)/(1+2*x)^2,x, algorithm=""maxima"")","\frac{1}{2} \, \sqrt{3 \, x^{2} - x + 2} x + \frac{11}{18} \, \sqrt{3} \operatorname{arsinh}\left(\frac{6}{23} \, \sqrt{23} x - \frac{1}{23} \, \sqrt{23}\right) - \frac{17}{104} \, \sqrt{13} \operatorname{arsinh}\left(\frac{8 \, \sqrt{23} x}{23 \, {\left| 2 \, x + 1 \right|}} - \frac{9 \, \sqrt{23}}{23 \, {\left| 2 \, x + 1 \right|}}\right) - \frac{1}{3} \, \sqrt{3 \, x^{2} - x + 2} - \frac{\sqrt{3 \, x^{2} - x + 2}}{4 \, {\left(2 \, x + 1\right)}}"," ",0,"1/2*sqrt(3*x^2 - x + 2)*x + 11/18*sqrt(3)*arcsinh(6/23*sqrt(23)*x - 1/23*sqrt(23)) - 17/104*sqrt(13)*arcsinh(8/23*sqrt(23)*x/abs(2*x + 1) - 9/23*sqrt(23)/abs(2*x + 1)) - 1/3*sqrt(3*x^2 - x + 2) - 1/4*sqrt(3*x^2 - x + 2)/(2*x + 1)","A",0
213,1,114,0,0.986011," ","integrate((4*x^2+3*x+1)*(3*x^2-x+2)^(1/2)/(1+2*x)^3,x, algorithm=""maxima"")","-\frac{11}{24} \, \sqrt{3} \operatorname{arsinh}\left(\frac{6}{23} \, \sqrt{23} x - \frac{1}{23} \, \sqrt{23}\right) + \frac{803}{2704} \, \sqrt{13} \operatorname{arsinh}\left(\frac{8 \, \sqrt{23} x}{23 \, {\left| 2 \, x + 1 \right|}} - \frac{9 \, \sqrt{23}}{23 \, {\left| 2 \, x + 1 \right|}}\right) + \frac{55}{104} \, \sqrt{3 \, x^{2} - x + 2} - \frac{{\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}}}{26 \, {\left(4 \, x^{2} + 4 \, x + 1\right)}} + \frac{11 \, \sqrt{3 \, x^{2} - x + 2}}{52 \, {\left(2 \, x + 1\right)}}"," ",0,"-11/24*sqrt(3)*arcsinh(6/23*sqrt(23)*x - 1/23*sqrt(23)) + 803/2704*sqrt(13)*arcsinh(8/23*sqrt(23)*x/abs(2*x + 1) - 9/23*sqrt(23)/abs(2*x + 1)) + 55/104*sqrt(3*x^2 - x + 2) - 1/26*(3*x^2 - x + 2)^(3/2)/(4*x^2 + 4*x + 1) + 11/52*sqrt(3*x^2 - x + 2)/(2*x + 1)","A",0
214,1,155,0,0.977956," ","integrate((1+2*x)^3*(3*x^2-x+2)^(3/2)*(4*x^2+3*x+1),x, algorithm=""maxima"")","\frac{32}{27} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{5}{2}} x^{4} + \frac{269}{81} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{5}{2}} x^{3} + \frac{1777}{486} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{5}{2}} x^{2} + \frac{1099}{648} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{5}{2}} x + \frac{1207}{58320} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{5}{2}} - \frac{54593}{93312} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}} x + \frac{54593}{559872} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}} - \frac{1255639}{746496} \, \sqrt{3 \, x^{2} - x + 2} x - \frac{28879697}{26873856} \, \sqrt{3} \operatorname{arsinh}\left(\frac{1}{23} \, \sqrt{23} {\left(6 \, x - 1\right)}\right) + \frac{1255639}{4478976} \, \sqrt{3 \, x^{2} - x + 2}"," ",0,"32/27*(3*x^2 - x + 2)^(5/2)*x^4 + 269/81*(3*x^2 - x + 2)^(5/2)*x^3 + 1777/486*(3*x^2 - x + 2)^(5/2)*x^2 + 1099/648*(3*x^2 - x + 2)^(5/2)*x + 1207/58320*(3*x^2 - x + 2)^(5/2) - 54593/93312*(3*x^2 - x + 2)^(3/2)*x + 54593/559872*(3*x^2 - x + 2)^(3/2) - 1255639/746496*sqrt(3*x^2 - x + 2)*x - 28879697/26873856*sqrt(3)*arcsinh(1/23*sqrt(23)*(6*x - 1)) + 1255639/4478976*sqrt(3*x^2 - x + 2)","A",0
215,1,138,0,0.927272," ","integrate((1+2*x)^2*(3*x^2-x+2)^(3/2)*(4*x^2+3*x+1),x, algorithm=""maxima"")","\frac{2}{3} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{5}{2}} x^{3} + \frac{95}{63} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{5}{2}} x^{2} + \frac{319}{252} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{5}{2}} x + \frac{907}{2520} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{5}{2}} - \frac{91}{576} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}} x + \frac{91}{3456} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}} - \frac{2093}{4608} \, \sqrt{3 \, x^{2} - x + 2} x - \frac{48139}{165888} \, \sqrt{3} \operatorname{arsinh}\left(\frac{1}{23} \, \sqrt{23} {\left(6 \, x - 1\right)}\right) + \frac{2093}{27648} \, \sqrt{3 \, x^{2} - x + 2}"," ",0,"2/3*(3*x^2 - x + 2)^(5/2)*x^3 + 95/63*(3*x^2 - x + 2)^(5/2)*x^2 + 319/252*(3*x^2 - x + 2)^(5/2)*x + 907/2520*(3*x^2 - x + 2)^(5/2) - 91/576*(3*x^2 - x + 2)^(3/2)*x + 91/3456*(3*x^2 - x + 2)^(3/2) - 2093/4608*sqrt(3*x^2 - x + 2)*x - 48139/165888*sqrt(3)*arcsinh(1/23*sqrt(23)*(6*x - 1)) + 2093/27648*sqrt(3*x^2 - x + 2)","A",0
216,1,121,0,0.966455," ","integrate((1+2*x)*(3*x^2-x+2)^(3/2)*(4*x^2+3*x+1),x, algorithm=""maxima"")","\frac{8}{21} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{5}{2}} x^{2} + \frac{41}{63} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{5}{2}} x + \frac{145}{378} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{5}{2}} + \frac{71}{432} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}} x - \frac{71}{2592} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}} + \frac{1633}{3456} \, \sqrt{3 \, x^{2} - x + 2} x + \frac{37559}{124416} \, \sqrt{3} \operatorname{arsinh}\left(\frac{1}{23} \, \sqrt{23} {\left(6 \, x - 1\right)}\right) - \frac{1633}{20736} \, \sqrt{3 \, x^{2} - x + 2}"," ",0,"8/21*(3*x^2 - x + 2)^(5/2)*x^2 + 41/63*(3*x^2 - x + 2)^(5/2)*x + 145/378*(3*x^2 - x + 2)^(5/2) + 71/432*(3*x^2 - x + 2)^(3/2)*x - 71/2592*(3*x^2 - x + 2)^(3/2) + 1633/3456*sqrt(3*x^2 - x + 2)*x + 37559/124416*sqrt(3)*arcsinh(1/23*sqrt(23)*(6*x - 1)) - 1633/20736*sqrt(3*x^2 - x + 2)","A",0
217,1,125,0,0.987639," ","integrate((3*x^2-x+2)^(3/2)*(4*x^2+3*x+1)/(1+2*x),x, algorithm=""maxima"")","\frac{2}{15} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{5}{2}} + \frac{5}{24} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}} x + \frac{7}{144} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}} + \frac{67}{192} \, \sqrt{3 \, x^{2} - x + 2} x - \frac{2203}{6912} \, \sqrt{3} \operatorname{arsinh}\left(\frac{6}{23} \, \sqrt{23} x - \frac{1}{23} \, \sqrt{23}\right) + \frac{13}{32} \, \sqrt{13} \operatorname{arsinh}\left(\frac{8 \, \sqrt{23} x}{23 \, {\left| 2 \, x + 1 \right|}} - \frac{9 \, \sqrt{23}}{23 \, {\left| 2 \, x + 1 \right|}}\right) + \frac{869}{1152} \, \sqrt{3 \, x^{2} - x + 2}"," ",0,"2/15*(3*x^2 - x + 2)^(5/2) + 5/24*(3*x^2 - x + 2)^(3/2)*x + 7/144*(3*x^2 - x + 2)^(3/2) + 67/192*sqrt(3*x^2 - x + 2)*x - 2203/6912*sqrt(3)*arcsinh(6/23*sqrt(23)*x - 1/23*sqrt(23)) + 13/32*sqrt(13)*arcsinh(8/23*sqrt(23)*x/abs(2*x + 1) - 9/23*sqrt(23)/abs(2*x + 1)) + 869/1152*sqrt(3*x^2 - x + 2)","A",0
218,1,132,0,0.977752," ","integrate((3*x^2-x+2)^(3/2)*(4*x^2+3*x+1)/(1+2*x)^2,x, algorithm=""maxima"")","\frac{1}{4} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}} x - \frac{1}{8} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}} + \frac{49}{32} \, \sqrt{3 \, x^{2} - x + 2} x + \frac{2327}{1152} \, \sqrt{3} \operatorname{arsinh}\left(\frac{6}{23} \, \sqrt{23} x - \frac{1}{23} \, \sqrt{23}\right) - \frac{25}{32} \, \sqrt{13} \operatorname{arsinh}\left(\frac{8 \, \sqrt{23} x}{23 \, {\left| 2 \, x + 1 \right|}} - \frac{9 \, \sqrt{23}}{23 \, {\left| 2 \, x + 1 \right|}}\right) - \frac{349}{192} \, \sqrt{3 \, x^{2} - x + 2} - \frac{{\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}}}{4 \, {\left(2 \, x + 1\right)}}"," ",0,"1/4*(3*x^2 - x + 2)^(3/2)*x - 1/8*(3*x^2 - x + 2)^(3/2) + 49/32*sqrt(3*x^2 - x + 2)*x + 2327/1152*sqrt(3)*arcsinh(6/23*sqrt(23)*x - 1/23*sqrt(23)) - 25/32*sqrt(13)*arcsinh(8/23*sqrt(23)*x/abs(2*x + 1) - 9/23*sqrt(23)/abs(2*x + 1)) - 349/192*sqrt(3*x^2 - x + 2) - 1/4*(3*x^2 - x + 2)^(3/2)/(2*x + 1)","A",0
219,1,143,0,0.984432," ","integrate((3*x^2-x+2)^(3/2)*(4*x^2+3*x+1)/(1+2*x)^3,x, algorithm=""maxima"")","\frac{61}{312} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}} - \frac{{\left(3 \, x^{2} - x + 2\right)}^{\frac{5}{2}}}{26 \, {\left(4 \, x^{2} + 4 \, x + 1\right)}} - \frac{257}{208} \, \sqrt{3 \, x^{2} - x + 2} x - \frac{1519}{576} \, \sqrt{3} \operatorname{arsinh}\left(\frac{6}{23} \, \sqrt{23} x - \frac{1}{23} \, \sqrt{23}\right) + \frac{1153}{832} \, \sqrt{13} \operatorname{arsinh}\left(\frac{8 \, \sqrt{23} x}{23 \, {\left| 2 \, x + 1 \right|}} - \frac{9 \, \sqrt{23}}{23 \, {\left| 2 \, x + 1 \right|}}\right) + \frac{929}{312} \, \sqrt{3 \, x^{2} - x + 2} + \frac{15 \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}}}{52 \, {\left(2 \, x + 1\right)}}"," ",0,"61/312*(3*x^2 - x + 2)^(3/2) - 1/26*(3*x^2 - x + 2)^(5/2)/(4*x^2 + 4*x + 1) - 257/208*sqrt(3*x^2 - x + 2)*x - 1519/576*sqrt(3)*arcsinh(6/23*sqrt(23)*x - 1/23*sqrt(23)) + 1153/832*sqrt(13)*arcsinh(8/23*sqrt(23)*x/abs(2*x + 1) - 9/23*sqrt(23)/abs(2*x + 1)) + 929/312*sqrt(3*x^2 - x + 2) + 15/52*(3*x^2 - x + 2)^(3/2)/(2*x + 1)","A",0
220,1,184,0,0.977635," ","integrate((1+2*x)^3*(3*x^2-x+2)^(5/2)*(4*x^2+3*x+1),x, algorithm=""maxima"")","\frac{32}{33} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{7}{2}} x^{4} + \frac{436}{165} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{7}{2}} x^{3} + \frac{4258}{1485} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{7}{2}} x^{2} + \frac{10073}{7128} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{7}{2}} x + \frac{92423}{498960} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{7}{2}} - \frac{5089}{25920} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{5}{2}} x + \frac{5089}{155520} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{5}{2}} - \frac{117047}{248832} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}} x + \frac{117047}{1492992} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}} - \frac{2692081}{1990656} \, \sqrt{3 \, x^{2} - x + 2} x - \frac{61917863}{71663616} \, \sqrt{3} \operatorname{arsinh}\left(\frac{1}{23} \, \sqrt{23} {\left(6 \, x - 1\right)}\right) + \frac{2692081}{11943936} \, \sqrt{3 \, x^{2} - x + 2}"," ",0,"32/33*(3*x^2 - x + 2)^(7/2)*x^4 + 436/165*(3*x^2 - x + 2)^(7/2)*x^3 + 4258/1485*(3*x^2 - x + 2)^(7/2)*x^2 + 10073/7128*(3*x^2 - x + 2)^(7/2)*x + 92423/498960*(3*x^2 - x + 2)^(7/2) - 5089/25920*(3*x^2 - x + 2)^(5/2)*x + 5089/155520*(3*x^2 - x + 2)^(5/2) - 117047/248832*(3*x^2 - x + 2)^(3/2)*x + 117047/1492992*(3*x^2 - x + 2)^(3/2) - 2692081/1990656*sqrt(3*x^2 - x + 2)*x - 61917863/71663616*sqrt(3)*arcsinh(1/23*sqrt(23)*(6*x - 1)) + 2692081/11943936*sqrt(3*x^2 - x + 2)","A",0
221,1,167,0,0.971119," ","integrate((1+2*x)^2*(3*x^2-x+2)^(5/2)*(4*x^2+3*x+1),x, algorithm=""maxima"")","\frac{8}{15} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{7}{2}} x^{3} + \frac{472}{405} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{7}{2}} x^{2} + \frac{235}{243} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{7}{2}} x + \frac{5419}{17010} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{7}{2}} + \frac{293}{9720} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{5}{2}} x - \frac{293}{58320} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{5}{2}} + \frac{6739}{93312} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}} x - \frac{6739}{559872} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}} + \frac{154997}{746496} \, \sqrt{3 \, x^{2} - x + 2} x + \frac{3564931}{26873856} \, \sqrt{3} \operatorname{arsinh}\left(\frac{1}{23} \, \sqrt{23} {\left(6 \, x - 1\right)}\right) - \frac{154997}{4478976} \, \sqrt{3 \, x^{2} - x + 2}"," ",0,"8/15*(3*x^2 - x + 2)^(7/2)*x^3 + 472/405*(3*x^2 - x + 2)^(7/2)*x^2 + 235/243*(3*x^2 - x + 2)^(7/2)*x + 5419/17010*(3*x^2 - x + 2)^(7/2) + 293/9720*(3*x^2 - x + 2)^(5/2)*x - 293/58320*(3*x^2 - x + 2)^(5/2) + 6739/93312*(3*x^2 - x + 2)^(3/2)*x - 6739/559872*(3*x^2 - x + 2)^(3/2) + 154997/746496*sqrt(3*x^2 - x + 2)*x + 3564931/26873856*sqrt(3)*arcsinh(1/23*sqrt(23)*(6*x - 1)) - 154997/4478976*sqrt(3*x^2 - x + 2)","A",0
222,1,150,0,0.967259," ","integrate((1+2*x)*(3*x^2-x+2)^(5/2)*(4*x^2+3*x+1),x, algorithm=""maxima"")","\frac{8}{27} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{7}{2}} x^{2} + \frac{157}{324} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{7}{2}} x + \frac{185}{648} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{7}{2}} + \frac{445}{2592} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{5}{2}} x - \frac{445}{15552} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{5}{2}} + \frac{51175}{124416} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}} x - \frac{51175}{746496} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}} + \frac{1177025}{995328} \, \sqrt{3 \, x^{2} - x + 2} x + \frac{27071575}{35831808} \, \sqrt{3} \operatorname{arsinh}\left(\frac{1}{23} \, \sqrt{23} {\left(6 \, x - 1\right)}\right) - \frac{1177025}{5971968} \, \sqrt{3 \, x^{2} - x + 2}"," ",0,"8/27*(3*x^2 - x + 2)^(7/2)*x^2 + 157/324*(3*x^2 - x + 2)^(7/2)*x + 185/648*(3*x^2 - x + 2)^(7/2) + 445/2592*(3*x^2 - x + 2)^(5/2)*x - 445/15552*(3*x^2 - x + 2)^(5/2) + 51175/124416*(3*x^2 - x + 2)^(3/2)*x - 51175/746496*(3*x^2 - x + 2)^(3/2) + 1177025/995328*sqrt(3*x^2 - x + 2)*x + 27071575/35831808*sqrt(3)*arcsinh(1/23*sqrt(23)*(6*x - 1)) - 1177025/5971968*sqrt(3*x^2 - x + 2)","A",0
223,1,154,0,0.972434," ","integrate((3*x^2-x+2)^(5/2)*(4*x^2+3*x+1)/(1+2*x),x, algorithm=""maxima"")","\frac{2}{21} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{7}{2}} + \frac{5}{36} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{5}{2}} x + \frac{29}{1080} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{5}{2}} + \frac{359}{1728} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}} x + \frac{2449}{10368} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}} - \frac{2975}{13824} \, \sqrt{3 \, x^{2} - x + 2} x - \frac{944521}{497664} \, \sqrt{3} \operatorname{arsinh}\left(\frac{6}{23} \, \sqrt{23} x - \frac{1}{23} \, \sqrt{23}\right) + \frac{169}{128} \, \sqrt{13} \operatorname{arsinh}\left(\frac{8 \, \sqrt{23} x}{23 \, {\left| 2 \, x + 1 \right|}} - \frac{9 \, \sqrt{23}}{23 \, {\left| 2 \, x + 1 \right|}}\right) + \frac{221999}{82944} \, \sqrt{3 \, x^{2} - x + 2}"," ",0,"2/21*(3*x^2 - x + 2)^(7/2) + 5/36*(3*x^2 - x + 2)^(5/2)*x + 29/1080*(3*x^2 - x + 2)^(5/2) + 359/1728*(3*x^2 - x + 2)^(3/2)*x + 2449/10368*(3*x^2 - x + 2)^(3/2) - 2975/13824*sqrt(3*x^2 - x + 2)*x - 944521/497664*sqrt(3)*arcsinh(6/23*sqrt(23)*x - 1/23*sqrt(23)) + 169/128*sqrt(13)*arcsinh(8/23*sqrt(23)*x/abs(2*x + 1) - 9/23*sqrt(23)/abs(2*x + 1)) + 221999/82944*sqrt(3*x^2 - x + 2)","A",0
224,1,161,0,0.998516," ","integrate((3*x^2-x+2)^(5/2)*(4*x^2+3*x+1)/(1+2*x)^2,x, algorithm=""maxima"")","\frac{1}{6} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{5}{2}} x - \frac{7}{90} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{5}{2}} + \frac{143}{144} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}} x - \frac{737}{864} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}} - \frac{{\left(3 \, x^{2} - x + 2\right)}^{\frac{5}{2}}}{4 \, {\left(2 \, x + 1\right)}} + \frac{5665}{1152} \, \sqrt{3 \, x^{2} - x + 2} x + \frac{315623}{41472} \, \sqrt{3} \operatorname{arsinh}\left(\frac{6}{23} \, \sqrt{23} x - \frac{1}{23} \, \sqrt{23}\right) - \frac{429}{128} \, \sqrt{13} \operatorname{arsinh}\left(\frac{8 \, \sqrt{23} x}{23 \, {\left| 2 \, x + 1 \right|}} - \frac{9 \, \sqrt{23}}{23 \, {\left| 2 \, x + 1 \right|}}\right) - \frac{51997}{6912} \, \sqrt{3 \, x^{2} - x + 2}"," ",0,"1/6*(3*x^2 - x + 2)^(5/2)*x - 7/90*(3*x^2 - x + 2)^(5/2) + 143/144*(3*x^2 - x + 2)^(3/2)*x - 737/864*(3*x^2 - x + 2)^(3/2) - 1/4*(3*x^2 - x + 2)^(5/2)/(2*x + 1) + 5665/1152*sqrt(3*x^2 - x + 2)*x + 315623/41472*sqrt(3)*arcsinh(6/23*sqrt(23)*x - 1/23*sqrt(23)) - 429/128*sqrt(13)*arcsinh(8/23*sqrt(23)*x/abs(2*x + 1) - 9/23*sqrt(23)/abs(2*x + 1)) - 51997/6912*sqrt(3*x^2 - x + 2)","A",0
225,1,172,0,0.994455," ","integrate((3*x^2-x+2)^(5/2)*(4*x^2+3*x+1)/(1+2*x)^3,x, algorithm=""maxima"")","\frac{67}{520} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{5}{2}} - \frac{{\left(3 \, x^{2} - x + 2\right)}^{\frac{7}{2}}}{26 \, {\left(4 \, x^{2} + 4 \, x + 1\right)}} - \frac{419}{416} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}} x + \frac{1227}{832} \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}} + \frac{19 \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{5}{2}}}{52 \, {\left(2 \, x + 1\right)}} - \frac{1745}{256} \, \sqrt{3 \, x^{2} - x + 2} x - \frac{118423}{9216} \, \sqrt{3} \operatorname{arsinh}\left(\frac{6}{23} \, \sqrt{23} x - \frac{1}{23} \, \sqrt{23}\right) + \frac{1631}{256} \, \sqrt{13} \operatorname{arsinh}\left(\frac{8 \, \sqrt{23} x}{23 \, {\left| 2 \, x + 1 \right|}} - \frac{9 \, \sqrt{23}}{23 \, {\left| 2 \, x + 1 \right|}}\right) + \frac{21317}{1536} \, \sqrt{3 \, x^{2} - x + 2}"," ",0,"67/520*(3*x^2 - x + 2)^(5/2) - 1/26*(3*x^2 - x + 2)^(7/2)/(4*x^2 + 4*x + 1) - 419/416*(3*x^2 - x + 2)^(3/2)*x + 1227/832*(3*x^2 - x + 2)^(3/2) + 19/52*(3*x^2 - x + 2)^(5/2)/(2*x + 1) - 1745/256*sqrt(3*x^2 - x + 2)*x - 118423/9216*sqrt(3)*arcsinh(6/23*sqrt(23)*x - 1/23*sqrt(23)) + 1631/256*sqrt(13)*arcsinh(8/23*sqrt(23)*x/abs(2*x + 1) - 9/23*sqrt(23)/abs(2*x + 1)) + 21317/1536*sqrt(3*x^2 - x + 2)","A",0
226,-2,0,0,0.000000," ","integrate((h*x+g)^3*(f*x^2+e*x+d)/(c*x^2+b*x+a)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 zero or nonzero?","F(-2)",0
227,-2,0,0,0.000000," ","integrate((h*x+g)^2*(f*x^2+e*x+d)/(c*x^2+b*x+a)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 zero or nonzero?","F(-2)",0
228,-2,0,0,0.000000," ","integrate((h*x+g)*(f*x^2+e*x+d)/(c*x^2+b*x+a)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 zero or nonzero?","F(-2)",0
229,-2,0,0,0.000000," ","integrate((f*x^2+e*x+d)/(c*x^2+b*x+a)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 zero or nonzero?","F(-2)",0
230,-2,0,0,0.000000," ","integrate((f*x^2+e*x+d)/(h*x+g)/(c*x^2+b*x+a)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume((b/h-(2*c*g)/h^2)^2>0)', see `assume?` for more details)Is (b/h-(2*c*g)/h^2)^2    -(4*c       *((-(b*g)/h)        +(c*g^2)/h^2+a))     /h^2 zero or nonzero?","F(-2)",0
231,-2,0,0,0.000000," ","integrate((f*x^2+e*x+d)/(h*x+g)^2/(c*x^2+b*x+a)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume((b/h-(2*c*g)/h^2)^2>0)', see `assume?` for more details)Is (b/h-(2*c*g)/h^2)^2    -(4*c       *((-(b*g)/h)        +(c*g^2)/h^2+a))     /h^2 zero or nonzero?","F(-2)",0
232,-2,0,0,0.000000," ","integrate((f*x^2+e*x+d)/(h*x+g)^3/(c*x^2+b*x+a)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*h^2-b*g*h>0)', see `assume?` for more details)Is a*h^2-b*g*h                            +c*g^2    positive, negative or zero?","F(-2)",0
233,-2,0,0,0.000000," ","integrate((h*x+g)^3*(f*x^2+e*x+d)/(c*x^2+b*x+a)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 zero or nonzero?","F(-2)",0
234,-2,0,0,0.000000," ","integrate((h*x+g)^2*(f*x^2+e*x+d)/(c*x^2+b*x+a)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 zero or nonzero?","F(-2)",0
235,-2,0,0,0.000000," ","integrate((h*x+g)*(f*x^2+e*x+d)/(c*x^2+b*x+a)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 zero or nonzero?","F(-2)",0
236,-2,0,0,0.000000," ","integrate((f*x^2+e*x+d)/(c*x^2+b*x+a)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 zero or nonzero?","F(-2)",0
237,-2,0,0,0.000000," ","integrate((f*x^2+e*x+d)/(h*x+g)/(c*x^2+b*x+a)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume((b/h-(2*c*g)/h^2)^2>0)', see `assume?` for more details)Is (b/h-(2*c*g)/h^2)^2    -(4*c       *((-(b*g)/h)        +(c*g^2)/h^2+a))     /h^2 zero or nonzero?","F(-2)",0
238,-2,0,0,0.000000," ","integrate((f*x^2+e*x+d)/(h*x+g)^2/(c*x^2+b*x+a)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume((b/h-(2*c*g)/h^2)^2>0)', see `assume?` for more details)Is (b/h-(2*c*g)/h^2)^2    -(4*c       *((-(b*g)/h)        +(c*g^2)/h^2+a))     /h^2 zero or nonzero?","F(-2)",0
239,-2,0,0,0.000000," ","integrate((f*x^2+e*x+d)/(h*x+g)^3/(c*x^2+b*x+a)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*h^2-b*g*h>0)', see `assume?` for more details)Is a*h^2-b*g*h                            +c*g^2    positive, negative or zero?","F(-2)",0
240,1,97,0,0.954108," ","integrate((1+2*x)^3*(4*x^2+3*x+1)/(3*x^2-x+2)^(1/2),x, algorithm=""maxima"")","\frac{32}{15} \, \sqrt{3 \, x^{2} - x + 2} x^{4} + \frac{34}{5} \, \sqrt{3 \, x^{2} - x + 2} x^{3} + \frac{1121}{135} \, \sqrt{3 \, x^{2} - x + 2} x^{2} + \frac{3769}{1620} \, \sqrt{3 \, x^{2} - x + 2} x - \frac{9211}{3888} \, \sqrt{3} \operatorname{arsinh}\left(\frac{1}{23} \, \sqrt{23} {\left(6 \, x - 1\right)}\right) - \frac{829}{120} \, \sqrt{3 \, x^{2} - x + 2}"," ",0,"32/15*sqrt(3*x^2 - x + 2)*x^4 + 34/5*sqrt(3*x^2 - x + 2)*x^3 + 1121/135*sqrt(3*x^2 - x + 2)*x^2 + 3769/1620*sqrt(3*x^2 - x + 2)*x - 9211/3888*sqrt(3)*arcsinh(1/23*sqrt(23)*(6*x - 1)) - 829/120*sqrt(3*x^2 - x + 2)","A",0
241,1,80,0,0.971627," ","integrate((1+2*x)^2*(4*x^2+3*x+1)/(3*x^2-x+2)^(1/2),x, algorithm=""maxima"")","\frac{4}{3} \, \sqrt{3 \, x^{2} - x + 2} x^{3} + \frac{98}{27} \, \sqrt{3 \, x^{2} - x + 2} x^{2} + \frac{569}{162} \, \sqrt{3 \, x^{2} - x + 2} x - \frac{4147}{1944} \, \sqrt{3} \operatorname{arsinh}\left(\frac{1}{23} \, \sqrt{23} {\left(6 \, x - 1\right)}\right) - \frac{3}{4} \, \sqrt{3 \, x^{2} - x + 2}"," ",0,"4/3*sqrt(3*x^2 - x + 2)*x^3 + 98/27*sqrt(3*x^2 - x + 2)*x^2 + 569/162*sqrt(3*x^2 - x + 2)*x - 4147/1944*sqrt(3)*arcsinh(1/23*sqrt(23)*(6*x - 1)) - 3/4*sqrt(3*x^2 - x + 2)","A",0
242,1,63,0,0.959508," ","integrate((1+2*x)*(4*x^2+3*x+1)/(3*x^2-x+2)^(1/2),x, algorithm=""maxima"")","\frac{8}{9} \, \sqrt{3 \, x^{2} - x + 2} x^{2} + \frac{55}{27} \, \sqrt{3 \, x^{2} - x + 2} x - \frac{251}{324} \, \sqrt{3} \operatorname{arsinh}\left(\frac{1}{23} \, \sqrt{23} {\left(6 \, x - 1\right)}\right) + \frac{3}{2} \, \sqrt{3 \, x^{2} - x + 2}"," ",0,"8/9*sqrt(3*x^2 - x + 2)*x^2 + 55/27*sqrt(3*x^2 - x + 2)*x - 251/324*sqrt(3)*arcsinh(1/23*sqrt(23)*(6*x - 1)) + 3/2*sqrt(3*x^2 - x + 2)","A",0
243,1,67,0,0.972762," ","integrate((4*x^2+3*x+1)/(1+2*x)/(3*x^2-x+2)^(1/2),x, algorithm=""maxima"")","\frac{5}{18} \, \sqrt{3} \operatorname{arsinh}\left(\frac{6}{23} \, \sqrt{23} x - \frac{1}{23} \, \sqrt{23}\right) + \frac{1}{26} \, \sqrt{13} \operatorname{arsinh}\left(\frac{8 \, \sqrt{23} x}{23 \, {\left| 2 \, x + 1 \right|}} - \frac{9 \, \sqrt{23}}{23 \, {\left| 2 \, x + 1 \right|}}\right) + \frac{2}{3} \, \sqrt{3 \, x^{2} - x + 2}"," ",0,"5/18*sqrt(3)*arcsinh(6/23*sqrt(23)*x - 1/23*sqrt(23)) + 1/26*sqrt(13)*arcsinh(8/23*sqrt(23)*x/abs(2*x + 1) - 9/23*sqrt(23)/abs(2*x + 1)) + 2/3*sqrt(3*x^2 - x + 2)","A",0
244,1,74,0,0.978693," ","integrate((4*x^2+3*x+1)/(1+2*x)^2/(3*x^2-x+2)^(1/2),x, algorithm=""maxima"")","\frac{1}{3} \, \sqrt{3} \operatorname{arsinh}\left(\frac{6}{23} \, \sqrt{23} x - \frac{1}{23} \, \sqrt{23}\right) - \frac{9}{338} \, \sqrt{13} \operatorname{arsinh}\left(\frac{8 \, \sqrt{23} x}{23 \, {\left| 2 \, x + 1 \right|}} - \frac{9 \, \sqrt{23}}{23 \, {\left| 2 \, x + 1 \right|}}\right) - \frac{\sqrt{3 \, x^{2} - x + 2}}{13 \, {\left(2 \, x + 1\right)}}"," ",0,"1/3*sqrt(3)*arcsinh(6/23*sqrt(23)*x - 1/23*sqrt(23)) - 9/338*sqrt(13)*arcsinh(8/23*sqrt(23)*x/abs(2*x + 1) - 9/23*sqrt(23)/abs(2*x + 1)) - 1/13*sqrt(3*x^2 - x + 2)/(2*x + 1)","A",0
245,1,82,0,0.976936," ","integrate((4*x^2+3*x+1)/(1+2*x)^3/(3*x^2-x+2)^(1/2),x, algorithm=""maxima"")","\frac{581}{8788} \, \sqrt{13} \operatorname{arsinh}\left(\frac{8 \, \sqrt{23} x}{23 \, {\left| 2 \, x + 1 \right|}} - \frac{9 \, \sqrt{23}}{23 \, {\left| 2 \, x + 1 \right|}}\right) - \frac{\sqrt{3 \, x^{2} - x + 2}}{26 \, {\left(4 \, x^{2} + 4 \, x + 1\right)}} + \frac{7 \, \sqrt{3 \, x^{2} - x + 2}}{169 \, {\left(2 \, x + 1\right)}}"," ",0,"581/8788*sqrt(13)*arcsinh(8/23*sqrt(23)*x/abs(2*x + 1) - 9/23*sqrt(23)/abs(2*x + 1)) - 1/26*sqrt(3*x^2 - x + 2)/(4*x^2 + 4*x + 1) + 7/169*sqrt(3*x^2 - x + 2)/(2*x + 1)","A",0
246,1,97,0,0.964803," ","integrate((1+2*x)^3*(4*x^2+3*x+1)/(3*x^2-x+2)^(3/2),x, algorithm=""maxima"")","\frac{32 \, x^{4}}{9 \, \sqrt{3 \, x^{2} - x + 2}} + \frac{380 \, x^{3}}{27 \, \sqrt{3 \, x^{2} - x + 2}} + \frac{2018 \, x^{2}}{81 \, \sqrt{3 \, x^{2} - x + 2}} - \frac{353}{243} \, \sqrt{3} \operatorname{arsinh}\left(\frac{1}{23} \, \sqrt{23} {\left(6 \, x - 1\right)}\right) - \frac{5948 \, x}{1863 \, \sqrt{3 \, x^{2} - x + 2}} + \frac{2222}{69 \, \sqrt{3 \, x^{2} - x + 2}}"," ",0,"32/9*x^4/sqrt(3*x^2 - x + 2) + 380/27*x^3/sqrt(3*x^2 - x + 2) + 2018/81*x^2/sqrt(3*x^2 - x + 2) - 353/243*sqrt(3)*arcsinh(1/23*sqrt(23)*(6*x - 1)) - 5948/1863*x/sqrt(3*x^2 - x + 2) + 2222/69/sqrt(3*x^2 - x + 2)","A",0
247,1,80,0,0.968745," ","integrate((1+2*x)^2*(4*x^2+3*x+1)/(3*x^2-x+2)^(3/2),x, algorithm=""maxima"")","\frac{8 \, x^{3}}{3 \, \sqrt{3 \, x^{2} - x + 2}} + \frac{104 \, x^{2}}{9 \, \sqrt{3 \, x^{2} - x + 2}} + \frac{64}{27} \, \sqrt{3} \operatorname{arsinh}\left(\frac{1}{23} \, \sqrt{23} {\left(6 \, x - 1\right)}\right) - \frac{2006 \, x}{207 \, \sqrt{3 \, x^{2} - x + 2}} + \frac{850}{69 \, \sqrt{3 \, x^{2} - x + 2}}"," ",0,"8/3*x^3/sqrt(3*x^2 - x + 2) + 104/9*x^2/sqrt(3*x^2 - x + 2) + 64/27*sqrt(3)*arcsinh(1/23*sqrt(23)*(6*x - 1)) - 2006/207*x/sqrt(3*x^2 - x + 2) + 850/69/sqrt(3*x^2 - x + 2)","A",0
248,1,63,0,0.943181," ","integrate((1+2*x)*(4*x^2+3*x+1)/(3*x^2-x+2)^(3/2),x, algorithm=""maxima"")","\frac{8 \, x^{2}}{3 \, \sqrt{3 \, x^{2} - x + 2}} + \frac{14}{9} \, \sqrt{3} \operatorname{arsinh}\left(\frac{1}{23} \, \sqrt{23} {\left(6 \, x - 1\right)}\right) - \frac{102 \, x}{23 \, \sqrt{3 \, x^{2} - x + 2}} + \frac{74}{69 \, \sqrt{3 \, x^{2} - x + 2}}"," ",0,"8/3*x^2/sqrt(3*x^2 - x + 2) + 14/9*sqrt(3)*arcsinh(1/23*sqrt(23)*(6*x - 1)) - 102/23*x/sqrt(3*x^2 - x + 2) + 74/69/sqrt(3*x^2 - x + 2)","A",0
249,1,64,0,0.965262," ","integrate((4*x^2+3*x+1)/(1+2*x)/(3*x^2-x+2)^(3/2),x, algorithm=""maxima"")","\frac{2}{169} \, \sqrt{13} \operatorname{arsinh}\left(\frac{8 \, \sqrt{23} x}{23 \, {\left| 2 \, x + 1 \right|}} - \frac{9 \, \sqrt{23}}{23 \, {\left| 2 \, x + 1 \right|}}\right) + \frac{154 \, x}{299 \, \sqrt{3 \, x^{2} - x + 2}} - \frac{202}{299 \, \sqrt{3 \, x^{2} - x + 2}}"," ",0,"2/169*sqrt(13)*arcsinh(8/23*sqrt(23)*x/abs(2*x + 1) - 9/23*sqrt(23)/abs(2*x + 1)) + 154/299*x/sqrt(3*x^2 - x + 2) - 202/299/sqrt(3*x^2 - x + 2)","A",0
250,1,96,0,0.955296," ","integrate((4*x^2+3*x+1)/(1+2*x)^2/(3*x^2-x+2)^(3/2),x, algorithm=""maxima"")","-\frac{2}{2197} \, \sqrt{13} \operatorname{arsinh}\left(\frac{8 \, \sqrt{23} x}{23 \, {\left| 2 \, x + 1 \right|}} - \frac{9 \, \sqrt{23}}{23 \, {\left| 2 \, x + 1 \right|}}\right) + \frac{1536 \, x}{3887 \, \sqrt{3 \, x^{2} - x + 2}} - \frac{279}{3887 \, \sqrt{3 \, x^{2} - x + 2}} - \frac{1}{13 \, {\left(2 \, \sqrt{3 \, x^{2} - x + 2} x + \sqrt{3 \, x^{2} - x + 2}\right)}}"," ",0,"-2/2197*sqrt(13)*arcsinh(8/23*sqrt(23)*x/abs(2*x + 1) - 9/23*sqrt(23)/abs(2*x + 1)) + 1536/3887*x/sqrt(3*x^2 - x + 2) - 279/3887/sqrt(3*x^2 - x + 2) - 1/13/(2*sqrt(3*x^2 - x + 2)*x + sqrt(3*x^2 - x + 2))","A",0
251,1,145,0,0.967295," ","integrate((4*x^2+3*x+1)/(1+2*x)^3/(3*x^2-x+2)^(3/2),x, algorithm=""maxima"")","\frac{487}{28561} \, \sqrt{13} \operatorname{arsinh}\left(\frac{8 \, \sqrt{23} x}{23 \, {\left| 2 \, x + 1 \right|}} - \frac{9 \, \sqrt{23}}{23 \, {\left| 2 \, x + 1 \right|}}\right) + \frac{7248 \, x}{50531 \, \sqrt{3 \, x^{2} - x + 2}} + \frac{8785}{101062 \, \sqrt{3 \, x^{2} - x + 2}} - \frac{1}{26 \, {\left(4 \, \sqrt{3 \, x^{2} - x + 2} x^{2} + 4 \, \sqrt{3 \, x^{2} - x + 2} x + \sqrt{3 \, x^{2} - x + 2}\right)}} + \frac{3}{169 \, {\left(2 \, \sqrt{3 \, x^{2} - x + 2} x + \sqrt{3 \, x^{2} - x + 2}\right)}}"," ",0,"487/28561*sqrt(13)*arcsinh(8/23*sqrt(23)*x/abs(2*x + 1) - 9/23*sqrt(23)/abs(2*x + 1)) + 7248/50531*x/sqrt(3*x^2 - x + 2) + 8785/101062/sqrt(3*x^2 - x + 2) - 1/26/(4*sqrt(3*x^2 - x + 2)*x^2 + 4*sqrt(3*x^2 - x + 2)*x + sqrt(3*x^2 - x + 2)) + 3/169/(2*sqrt(3*x^2 - x + 2)*x + sqrt(3*x^2 - x + 2))","A",0
252,1,202,0,0.962633," ","integrate((1+2*x)^3*(4*x^2+3*x+1)/(3*x^2-x+2)^(5/2),x, algorithm=""maxima"")","\frac{32 \, x^{4}}{3 \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}}} + \frac{296}{42849} \, x {\left(\frac{426 \, x}{\sqrt{3 \, x^{2} - x + 2}} - \frac{4761 \, x^{2}}{{\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}}} - \frac{71}{\sqrt{3 \, x^{2} - x + 2}} + \frac{805 \, x}{{\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}}} - \frac{2162}{{\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}}}\right)} + \frac{296}{81} \, \sqrt{3} \operatorname{arsinh}\left(\frac{1}{23} \, \sqrt{23} {\left(6 \, x - 1\right)}\right) - \frac{42032}{42849} \, \sqrt{3 \, x^{2} - x + 2} - \frac{47072 \, x}{42849 \, \sqrt{3 \, x^{2} - x + 2}} + \frac{52 \, x^{2}}{9 \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}}} - \frac{23104}{14283 \, \sqrt{3 \, x^{2} - x + 2}} - \frac{7742 \, x}{1863 \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}}} + \frac{1666}{1863 \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}}}"," ",0,"32/3*x^4/(3*x^2 - x + 2)^(3/2) + 296/42849*x*(426*x/sqrt(3*x^2 - x + 2) - 4761*x^2/(3*x^2 - x + 2)^(3/2) - 71/sqrt(3*x^2 - x + 2) + 805*x/(3*x^2 - x + 2)^(3/2) - 2162/(3*x^2 - x + 2)^(3/2)) + 296/81*sqrt(3)*arcsinh(1/23*sqrt(23)*(6*x - 1)) - 42032/42849*sqrt(3*x^2 - x + 2) - 47072/42849*x/sqrt(3*x^2 - x + 2) + 52/9*x^2/(3*x^2 - x + 2)^(3/2) - 23104/14283/sqrt(3*x^2 - x + 2) - 7742/1863*x/(3*x^2 - x + 2)^(3/2) + 1666/1863/(3*x^2 - x + 2)^(3/2)","B",0
253,1,185,0,0.966956," ","integrate((1+2*x)^2*(4*x^2+3*x+1)/(3*x^2-x+2)^(5/2),x, algorithm=""maxima"")","\frac{16}{14283} \, x {\left(\frac{426 \, x}{\sqrt{3 \, x^{2} - x + 2}} - \frac{4761 \, x^{2}}{{\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}}} - \frac{71}{\sqrt{3 \, x^{2} - x + 2}} + \frac{805 \, x}{{\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}}} - \frac{2162}{{\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}}}\right)} + \frac{16}{27} \, \sqrt{3} \operatorname{arsinh}\left(\frac{1}{23} \, \sqrt{23} {\left(6 \, x - 1\right)}\right) - \frac{2272}{14283} \, \sqrt{3 \, x^{2} - x + 2} + \frac{28184 \, x}{14283 \, \sqrt{3 \, x^{2} - x + 2}} - \frac{28 \, x^{2}}{3 \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}}} - \frac{2956}{4761 \, \sqrt{3 \, x^{2} - x + 2}} - \frac{106 \, x}{621 \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}}} - \frac{3394}{621 \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}}}"," ",0,"16/14283*x*(426*x/sqrt(3*x^2 - x + 2) - 4761*x^2/(3*x^2 - x + 2)^(3/2) - 71/sqrt(3*x^2 - x + 2) + 805*x/(3*x^2 - x + 2)^(3/2) - 2162/(3*x^2 - x + 2)^(3/2)) + 16/27*sqrt(3)*arcsinh(1/23*sqrt(23)*(6*x - 1)) - 2272/14283*sqrt(3*x^2 - x + 2) + 28184/14283*x/sqrt(3*x^2 - x + 2) - 28/3*x^2/(3*x^2 - x + 2)^(3/2) - 2956/4761/sqrt(3*x^2 - x + 2) - 106/621*x/(3*x^2 - x + 2)^(3/2) - 3394/621/(3*x^2 - x + 2)^(3/2)","B",0
254,1,76,0,0.437360," ","integrate((1+2*x)*(4*x^2+3*x+1)/(3*x^2-x+2)^(5/2),x, algorithm=""maxima"")","\frac{5720 \, x}{4761 \, \sqrt{3 \, x^{2} - x + 2}} - \frac{8 \, x^{2}}{3 \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}}} - \frac{2860}{14283 \, \sqrt{3 \, x^{2} - x + 2}} - \frac{182 \, x}{621 \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}}} - \frac{1250}{621 \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}}}"," ",0,"5720/4761*x/sqrt(3*x^2 - x + 2) - 8/3*x^2/(3*x^2 - x + 2)^(3/2) - 2860/14283/sqrt(3*x^2 - x + 2) - 182/621*x/(3*x^2 - x + 2)^(3/2) - 1250/621/(3*x^2 - x + 2)^(3/2)","A",0
255,1,93,0,0.962133," ","integrate((4*x^2+3*x+1)/(1+2*x)/(3*x^2-x+2)^(5/2),x, algorithm=""maxima"")","\frac{8}{2197} \, \sqrt{13} \operatorname{arsinh}\left(\frac{8 \, \sqrt{23} x}{23 \, {\left| 2 \, x + 1 \right|}} - \frac{9 \, \sqrt{23}}{23 \, {\left| 2 \, x + 1 \right|}}\right) + \frac{18224 \, x}{89401 \, \sqrt{3 \, x^{2} - x + 2}} - \frac{2764}{268203 \, \sqrt{3 \, x^{2} - x + 2}} + \frac{154 \, x}{897 \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}}} - \frac{202}{897 \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}}}"," ",0,"8/2197*sqrt(13)*arcsinh(8/23*sqrt(23)*x/abs(2*x + 1) - 9/23*sqrt(23)/abs(2*x + 1)) + 18224/89401*x/sqrt(3*x^2 - x + 2) - 2764/268203/sqrt(3*x^2 - x + 2) + 154/897*x/(3*x^2 - x + 2)^(3/2) - 202/897/(3*x^2 - x + 2)^(3/2)","A",0
256,1,125,0,0.973856," ","integrate((4*x^2+3*x+1)/(1+2*x)^2/(3*x^2-x+2)^(5/2),x, algorithm=""maxima"")","\frac{56}{28561} \, \sqrt{13} \operatorname{arsinh}\left(\frac{8 \, \sqrt{23} x}{23 \, {\left| 2 \, x + 1 \right|}} - \frac{9 \, \sqrt{23}}{23 \, {\left| 2 \, x + 1 \right|}}\right) + \frac{146496 \, x}{1162213 \, \sqrt{3 \, x^{2} - x + 2}} - \frac{9604}{1162213 \, \sqrt{3 \, x^{2} - x + 2}} + \frac{420 \, x}{3887 \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}}} - \frac{1}{13 \, {\left(2 \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}} x + {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}}\right)}} - \frac{49}{11661 \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}}}"," ",0,"56/28561*sqrt(13)*arcsinh(8/23*sqrt(23)*x/abs(2*x + 1) - 9/23*sqrt(23)/abs(2*x + 1)) + 146496/1162213*x/sqrt(3*x^2 - x + 2) - 9604/1162213/sqrt(3*x^2 - x + 2) + 420/3887*x/(3*x^2 - x + 2)^(3/2) - 1/13/(2*(3*x^2 - x + 2)^(3/2)*x + (3*x^2 - x + 2)^(3/2)) - 49/11661/(3*x^2 - x + 2)^(3/2)","A",0
257,1,174,0,0.990673," ","integrate((4*x^2+3*x+1)/(1+2*x)^3/(3*x^2-x+2)^(5/2),x, algorithm=""maxima"")","\frac{2084}{371293} \, \sqrt{13} \operatorname{arsinh}\left(\frac{8 \, \sqrt{23} x}{23 \, {\left| 2 \, x + 1 \right|}} - \frac{9 \, \sqrt{23}}{23 \, {\left| 2 \, x + 1 \right|}}\right) + \frac{1128048 \, x}{15108769 \, \sqrt{3 \, x^{2} - x + 2}} + \frac{363210}{15108769 \, \sqrt{3 \, x^{2} - x + 2}} + \frac{1772 \, x}{50531 \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}}} - \frac{1}{26 \, {\left(4 \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}} x^{2} + 4 \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}} x + {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}}\right)}} - \frac{1}{169 \, {\left(2 \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}} x + {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}}\right)}} + \frac{10211}{303186 \, {\left(3 \, x^{2} - x + 2\right)}^{\frac{3}{2}}}"," ",0,"2084/371293*sqrt(13)*arcsinh(8/23*sqrt(23)*x/abs(2*x + 1) - 9/23*sqrt(23)/abs(2*x + 1)) + 1128048/15108769*x/sqrt(3*x^2 - x + 2) + 363210/15108769/sqrt(3*x^2 - x + 2) + 1772/50531*x/(3*x^2 - x + 2)^(3/2) - 1/26/(4*(3*x^2 - x + 2)^(3/2)*x^2 + 4*(3*x^2 - x + 2)^(3/2)*x + (3*x^2 - x + 2)^(3/2)) - 1/169/(2*(3*x^2 - x + 2)^(3/2)*x + (3*x^2 - x + 2)^(3/2)) + 10211/303186/(3*x^2 - x + 2)^(3/2)","A",0
258,-2,0,0,0.000000," ","integrate((f*x^2+e*x+d)/(h*x+g)/(c*h^2*x^2+b*h^2*x+b*g*h-c*g^2)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b*h-2*c*g>0)', see `assume?` for more details)Is b*h-2*c*g zero or nonzero?","F(-2)",0
259,0,0,0,0.000000," ","integrate((e*x+d)^(1/2)*(C*x^2+B*x+A)*(c*x^2+b*x+a)^(1/2),x, algorithm=""maxima"")","\int {\left(C x^{2} + B x + A\right)} \sqrt{c x^{2} + b x + a} \sqrt{e x + d}\,{d x}"," ",0,"integrate((C*x^2 + B*x + A)*sqrt(c*x^2 + b*x + a)*sqrt(e*x + d), x)","F",0
260,0,0,0,0.000000," ","integrate((C*x^2+B*x+A)*(c*x^2+b*x+a)^(1/2)/(e*x+d)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C x^{2} + B x + A\right)} \sqrt{c x^{2} + b x + a}}{\sqrt{e x + d}}\,{d x}"," ",0,"integrate((C*x^2 + B*x + A)*sqrt(c*x^2 + b*x + a)/sqrt(e*x + d), x)","F",0
261,0,0,0,0.000000," ","integrate((C*x^2+B*x+A)*(c*x^2+b*x+a)^(1/2)/(e*x+d)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C x^{2} + B x + A\right)} \sqrt{c x^{2} + b x + a}}{{\left(e x + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*x^2 + B*x + A)*sqrt(c*x^2 + b*x + a)/(e*x + d)^(3/2), x)","F",0
262,0,0,0,0.000000," ","integrate((C*x^2+B*x+A)*(c*x^2+b*x+a)^(1/2)/(e*x+d)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C x^{2} + B x + A\right)} \sqrt{c x^{2} + b x + a}}{{\left(e x + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*x^2 + B*x + A)*sqrt(c*x^2 + b*x + a)/(e*x + d)^(5/2), x)","F",0
263,0,0,0,0.000000," ","integrate((C*x^2+B*x+A)*(c*x^2+b*x+a)^(1/2)/(e*x+d)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(C x^{2} + B x + A\right)} \sqrt{c x^{2} + b x + a}}{{\left(e x + d\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*x^2 + B*x + A)*sqrt(c*x^2 + b*x + a)/(e*x + d)^(7/2), x)","F",0
264,0,0,0,0.000000," ","integrate((C*x^2+B*x+A)*(c*x^2+b*x+a)^(1/2)/(e*x+d)^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(C x^{2} + B x + A\right)} \sqrt{c x^{2} + b x + a}}{{\left(e x + d\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*x^2 + B*x + A)*sqrt(c*x^2 + b*x + a)/(e*x + d)^(9/2), x)","F",0
265,0,0,0,0.000000," ","integrate((C*x^2+B*x+A)*(c*x^2+b*x+a)^(1/2)/(e*x+d)^(11/2),x, algorithm=""maxima"")","\int \frac{{\left(C x^{2} + B x + A\right)} \sqrt{c x^{2} + b x + a}}{{\left(e x + d\right)}^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((C*x^2 + B*x + A)*sqrt(c*x^2 + b*x + a)/(e*x + d)^(11/2), x)","F",0
266,0,0,0,0.000000," ","integrate((e*x+d)^(3/2)*(C*x^2+B*x+A)/(c*x^2+b*x+a)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C x^{2} + B x + A\right)} {\left(e x + d\right)}^{\frac{3}{2}}}{\sqrt{c x^{2} + b x + a}}\,{d x}"," ",0,"integrate((C*x^2 + B*x + A)*(e*x + d)^(3/2)/sqrt(c*x^2 + b*x + a), x)","F",0
267,0,0,0,0.000000," ","integrate((e*x+d)^(1/2)*(C*x^2+B*x+A)/(c*x^2+b*x+a)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C x^{2} + B x + A\right)} \sqrt{e x + d}}{\sqrt{c x^{2} + b x + a}}\,{d x}"," ",0,"integrate((C*x^2 + B*x + A)*sqrt(e*x + d)/sqrt(c*x^2 + b*x + a), x)","F",0
268,0,0,0,0.000000," ","integrate((C*x^2+B*x+A)/(e*x+d)^(1/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""maxima"")","\int \frac{C x^{2} + B x + A}{\sqrt{c x^{2} + b x + a} \sqrt{e x + d}}\,{d x}"," ",0,"integrate((C*x^2 + B*x + A)/(sqrt(c*x^2 + b*x + a)*sqrt(e*x + d)), x)","F",0
269,0,0,0,0.000000," ","integrate((C*x^2+B*x+A)/(e*x+d)^(3/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""maxima"")","\int \frac{C x^{2} + B x + A}{\sqrt{c x^{2} + b x + a} {\left(e x + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*x^2 + B*x + A)/(sqrt(c*x^2 + b*x + a)*(e*x + d)^(3/2)), x)","F",0
270,0,0,0,0.000000," ","integrate((C*x^2+B*x+A)/(e*x+d)^(5/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""maxima"")","\int \frac{C x^{2} + B x + A}{\sqrt{c x^{2} + b x + a} {\left(e x + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*x^2 + B*x + A)/(sqrt(c*x^2 + b*x + a)*(e*x + d)^(5/2)), x)","F",0
271,0,0,0,0.000000," ","integrate((C*x^2+B*x+A)/(e*x+d)^(7/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""maxima"")","\int \frac{C x^{2} + B x + A}{\sqrt{c x^{2} + b x + a} {\left(e x + d\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*x^2 + B*x + A)/(sqrt(c*x^2 + b*x + a)*(e*x + d)^(7/2)), x)","F",0
272,0,0,0,0.000000," ","integrate((h*x+g)^m*(c*x^2+b*x+a)^p*(f*x^2+e*x+d),x, algorithm=""maxima"")","\int {\left(f x^{2} + e x + d\right)} {\left(c x^{2} + b x + a\right)}^{p} {\left(h x + g\right)}^{m}\,{d x}"," ",0,"integrate((f*x^2 + e*x + d)*(c*x^2 + b*x + a)^p*(h*x + g)^m, x)","F",0
273,0,0,0,0.000000," ","integrate((h*x+g)^m*(f*x^2+e*x+d)*(c*x^2+b*x+a)^(1/2),x, algorithm=""maxima"")","\int \sqrt{c x^{2} + b x + a} {\left(f x^{2} + e x + d\right)} {\left(h x + g\right)}^{m}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + b*x + a)*(f*x^2 + e*x + d)*(h*x + g)^m, x)","F",0
274,0,0,0,0.000000," ","integrate((h*x+g)^(-3-2*p)*(c*x^2+b*x+a)^p*(f*x^2+e*x+d),x, algorithm=""maxima"")","\int {\left(f x^{2} + e x + d\right)} {\left(c x^{2} + b x + a\right)}^{p} {\left(h x + g\right)}^{-2 \, p - 3}\,{d x}"," ",0,"integrate((f*x^2 + e*x + d)*(c*x^2 + b*x + a)^p*(h*x + g)^(-2*p - 3), x)","F",0
275,1,59,0,0.576297," ","integrate((f*x^2+d)^p*(2*c*d*f+2*b*f^2*(3+2*p)*x+2*c*f^2*(3+2*p)*x^2),x, algorithm=""maxima"")","\frac{{\left(2 \, c f^{2} {\left(p + 1\right)} x^{3} + b f^{2} {\left(2 \, p + 3\right)} x^{2} + 2 \, c d f {\left(p + 1\right)} x + b d f {\left(2 \, p + 3\right)}\right)} {\left(f x^{2} + d\right)}^{p}}{p + 1}"," ",0,"(2*c*f^2*(p + 1)*x^3 + b*f^2*(2*p + 3)*x^2 + 2*c*d*f*(p + 1)*x + b*d*f*(2*p + 3))*(f*x^2 + d)^p/(p + 1)","A",0
276,1,66,0,0.575509," ","integrate((f*x^2+e*x+d)^p*(-2*c*e^2+2*c*d*f-c*e^2*p+2*c*f^2*(3+2*p)*x^2),x, algorithm=""maxima"")","\frac{{\left(2 \, c f^{2} {\left(p + 1\right)} x^{3} + c e f p x^{2} - c d e {\left(p + 2\right)} - {\left(e^{2} {\left(p + 2\right)} - 2 \, d f {\left(p + 1\right)}\right)} c x\right)} {\left(f x^{2} + e x + d\right)}^{p}}{p + 1}"," ",0,"(2*c*f^2*(p + 1)*x^3 + c*e*f*p*x^2 - c*d*e*(p + 2) - (e^2*(p + 2) - 2*d*f*(p + 1))*c*x)*(f*x^2 + e*x + d)^p/(p + 1)","A",0
277,1,98,0,0.598354," ","integrate((f*x^2+e*x+d)^p*(-2*c*e^2+2*c*d*f+3*b*e*f-c*e^2*p+2*b*e*f*p+2*b*f^2*(3+2*p)*x+2*c*f^2*(3+2*p)*x^2),x, algorithm=""maxima"")","\frac{{\left(2 \, c f^{2} {\left(p + 1\right)} x^{3} + b d f {\left(2 \, p + 3\right)} - c d e {\left(p + 2\right)} + {\left(b f^{2} {\left(2 \, p + 3\right)} + c e f p\right)} x^{2} + {\left(b e f {\left(2 \, p + 3\right)} - {\left(e^{2} {\left(p + 2\right)} - 2 \, d f {\left(p + 1\right)}\right)} c\right)} x\right)} {\left(f x^{2} + e x + d\right)}^{p}}{p + 1}"," ",0,"(2*c*f^2*(p + 1)*x^3 + b*d*f*(2*p + 3) - c*d*e*(p + 2) + (b*f^2*(2*p + 3) + c*e*f*p)*x^2 + (b*e*f*(2*p + 3) - (e^2*(p + 2) - 2*d*f*(p + 1))*c)*x)*(f*x^2 + e*x + d)^p/(p + 1)","A",0
278,1,1779,0,0.500271," ","integrate((e*x+d)^3*(c*x^2+b*x+a)^5*(d*(5*a*e+6*b*d)+(5*a*e^2+17*b*d*e+12*c*d^2)*x+e*(11*b*e+29*c*d)*x^2+17*c*e^2*x^3),x, algorithm=""maxima"")","c^{6} e^{5} x^{17} + {\left(5 \, c^{6} d e^{4} + 6 \, b c^{5} e^{5}\right)} x^{16} + {\left(10 \, c^{6} d^{2} e^{3} + 30 \, b c^{5} d e^{4} + 3 \, {\left(5 \, b^{2} c^{4} + 2 \, a c^{5}\right)} e^{5}\right)} x^{15} + 5 \, {\left(2 \, c^{6} d^{3} e^{2} + 12 \, b c^{5} d^{2} e^{3} + 3 \, {\left(5 \, b^{2} c^{4} + 2 \, a c^{5}\right)} d e^{4} + 2 \, {\left(2 \, b^{3} c^{3} + 3 \, a b c^{4}\right)} e^{5}\right)} x^{14} + 5 \, {\left(c^{6} d^{4} e + 12 \, b c^{5} d^{3} e^{2} + 6 \, {\left(5 \, b^{2} c^{4} + 2 \, a c^{5}\right)} d^{2} e^{3} + 10 \, {\left(2 \, b^{3} c^{3} + 3 \, a b c^{4}\right)} d e^{4} + 3 \, {\left(b^{4} c^{2} + 4 \, a b^{2} c^{3} + a^{2} c^{4}\right)} e^{5}\right)} x^{13} + {\left(c^{6} d^{5} + 30 \, b c^{5} d^{4} e + 30 \, {\left(5 \, b^{2} c^{4} + 2 \, a c^{5}\right)} d^{3} e^{2} + 100 \, {\left(2 \, b^{3} c^{3} + 3 \, a b c^{4}\right)} d^{2} e^{3} + 75 \, {\left(b^{4} c^{2} + 4 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d e^{4} + 6 \, {\left(b^{5} c + 10 \, a b^{3} c^{2} + 10 \, a^{2} b c^{3}\right)} e^{5}\right)} x^{12} + {\left(6 \, b c^{5} d^{5} + 15 \, {\left(5 \, b^{2} c^{4} + 2 \, a c^{5}\right)} d^{4} e + 100 \, {\left(2 \, b^{3} c^{3} + 3 \, a b c^{4}\right)} d^{3} e^{2} + 150 \, {\left(b^{4} c^{2} + 4 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{2} e^{3} + 30 \, {\left(b^{5} c + 10 \, a b^{3} c^{2} + 10 \, a^{2} b c^{3}\right)} d e^{4} + {\left(b^{6} + 30 \, a b^{4} c + 90 \, a^{2} b^{2} c^{2} + 20 \, a^{3} c^{3}\right)} e^{5}\right)} x^{11} + {\left(3 \, {\left(5 \, b^{2} c^{4} + 2 \, a c^{5}\right)} d^{5} + 50 \, {\left(2 \, b^{3} c^{3} + 3 \, a b c^{4}\right)} d^{4} e + 150 \, {\left(b^{4} c^{2} + 4 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{3} e^{2} + 60 \, {\left(b^{5} c + 10 \, a b^{3} c^{2} + 10 \, a^{2} b c^{3}\right)} d^{2} e^{3} + 5 \, {\left(b^{6} + 30 \, a b^{4} c + 90 \, a^{2} b^{2} c^{2} + 20 \, a^{3} c^{3}\right)} d e^{4} + 6 \, {\left(a b^{5} + 10 \, a^{2} b^{3} c + 10 \, a^{3} b c^{2}\right)} e^{5}\right)} x^{10} + 5 \, {\left(2 \, {\left(2 \, b^{3} c^{3} + 3 \, a b c^{4}\right)} d^{5} + 15 \, {\left(b^{4} c^{2} + 4 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{4} e + 12 \, {\left(b^{5} c + 10 \, a b^{3} c^{2} + 10 \, a^{2} b c^{3}\right)} d^{3} e^{2} + 2 \, {\left(b^{6} + 30 \, a b^{4} c + 90 \, a^{2} b^{2} c^{2} + 20 \, a^{3} c^{3}\right)} d^{2} e^{3} + 6 \, {\left(a b^{5} + 10 \, a^{2} b^{3} c + 10 \, a^{3} b c^{2}\right)} d e^{4} + 3 \, {\left(a^{2} b^{4} + 4 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{5}\right)} x^{9} + 5 \, {\left(3 \, {\left(b^{4} c^{2} + 4 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{5} + 6 \, {\left(b^{5} c + 10 \, a b^{3} c^{2} + 10 \, a^{2} b c^{3}\right)} d^{4} e + 2 \, {\left(b^{6} + 30 \, a b^{4} c + 90 \, a^{2} b^{2} c^{2} + 20 \, a^{3} c^{3}\right)} d^{3} e^{2} + 12 \, {\left(a b^{5} + 10 \, a^{2} b^{3} c + 10 \, a^{3} b c^{2}\right)} d^{2} e^{3} + 15 \, {\left(a^{2} b^{4} + 4 \, a^{3} b^{2} c + a^{4} c^{2}\right)} d e^{4} + 2 \, {\left(2 \, a^{3} b^{3} + 3 \, a^{4} b c\right)} e^{5}\right)} x^{8} + {\left(6 \, {\left(b^{5} c + 10 \, a b^{3} c^{2} + 10 \, a^{2} b c^{3}\right)} d^{5} + 5 \, {\left(b^{6} + 30 \, a b^{4} c + 90 \, a^{2} b^{2} c^{2} + 20 \, a^{3} c^{3}\right)} d^{4} e + 60 \, {\left(a b^{5} + 10 \, a^{2} b^{3} c + 10 \, a^{3} b c^{2}\right)} d^{3} e^{2} + 150 \, {\left(a^{2} b^{4} + 4 \, a^{3} b^{2} c + a^{4} c^{2}\right)} d^{2} e^{3} + 50 \, {\left(2 \, a^{3} b^{3} + 3 \, a^{4} b c\right)} d e^{4} + 3 \, {\left(5 \, a^{4} b^{2} + 2 \, a^{5} c\right)} e^{5}\right)} x^{7} + {\left(6 \, a^{5} b e^{5} + {\left(b^{6} + 30 \, a b^{4} c + 90 \, a^{2} b^{2} c^{2} + 20 \, a^{3} c^{3}\right)} d^{5} + 30 \, {\left(a b^{5} + 10 \, a^{2} b^{3} c + 10 \, a^{3} b c^{2}\right)} d^{4} e + 150 \, {\left(a^{2} b^{4} + 4 \, a^{3} b^{2} c + a^{4} c^{2}\right)} d^{3} e^{2} + 100 \, {\left(2 \, a^{3} b^{3} + 3 \, a^{4} b c\right)} d^{2} e^{3} + 15 \, {\left(5 \, a^{4} b^{2} + 2 \, a^{5} c\right)} d e^{4}\right)} x^{6} + {\left(30 \, a^{5} b d e^{4} + a^{6} e^{5} + 6 \, {\left(a b^{5} + 10 \, a^{2} b^{3} c + 10 \, a^{3} b c^{2}\right)} d^{5} + 75 \, {\left(a^{2} b^{4} + 4 \, a^{3} b^{2} c + a^{4} c^{2}\right)} d^{4} e + 100 \, {\left(2 \, a^{3} b^{3} + 3 \, a^{4} b c\right)} d^{3} e^{2} + 30 \, {\left(5 \, a^{4} b^{2} + 2 \, a^{5} c\right)} d^{2} e^{3}\right)} x^{5} + 5 \, {\left(12 \, a^{5} b d^{2} e^{3} + a^{6} d e^{4} + 3 \, {\left(a^{2} b^{4} + 4 \, a^{3} b^{2} c + a^{4} c^{2}\right)} d^{5} + 10 \, {\left(2 \, a^{3} b^{3} + 3 \, a^{4} b c\right)} d^{4} e + 6 \, {\left(5 \, a^{4} b^{2} + 2 \, a^{5} c\right)} d^{3} e^{2}\right)} x^{4} + 5 \, {\left(12 \, a^{5} b d^{3} e^{2} + 2 \, a^{6} d^{2} e^{3} + 2 \, {\left(2 \, a^{3} b^{3} + 3 \, a^{4} b c\right)} d^{5} + 3 \, {\left(5 \, a^{4} b^{2} + 2 \, a^{5} c\right)} d^{4} e\right)} x^{3} + {\left(30 \, a^{5} b d^{4} e + 10 \, a^{6} d^{3} e^{2} + 3 \, {\left(5 \, a^{4} b^{2} + 2 \, a^{5} c\right)} d^{5}\right)} x^{2} + {\left(6 \, a^{5} b d^{5} + 5 \, a^{6} d^{4} e\right)} x"," ",0,"c^6*e^5*x^17 + (5*c^6*d*e^4 + 6*b*c^5*e^5)*x^16 + (10*c^6*d^2*e^3 + 30*b*c^5*d*e^4 + 3*(5*b^2*c^4 + 2*a*c^5)*e^5)*x^15 + 5*(2*c^6*d^3*e^2 + 12*b*c^5*d^2*e^3 + 3*(5*b^2*c^4 + 2*a*c^5)*d*e^4 + 2*(2*b^3*c^3 + 3*a*b*c^4)*e^5)*x^14 + 5*(c^6*d^4*e + 12*b*c^5*d^3*e^2 + 6*(5*b^2*c^4 + 2*a*c^5)*d^2*e^3 + 10*(2*b^3*c^3 + 3*a*b*c^4)*d*e^4 + 3*(b^4*c^2 + 4*a*b^2*c^3 + a^2*c^4)*e^5)*x^13 + (c^6*d^5 + 30*b*c^5*d^4*e + 30*(5*b^2*c^4 + 2*a*c^5)*d^3*e^2 + 100*(2*b^3*c^3 + 3*a*b*c^4)*d^2*e^3 + 75*(b^4*c^2 + 4*a*b^2*c^3 + a^2*c^4)*d*e^4 + 6*(b^5*c + 10*a*b^3*c^2 + 10*a^2*b*c^3)*e^5)*x^12 + (6*b*c^5*d^5 + 15*(5*b^2*c^4 + 2*a*c^5)*d^4*e + 100*(2*b^3*c^3 + 3*a*b*c^4)*d^3*e^2 + 150*(b^4*c^2 + 4*a*b^2*c^3 + a^2*c^4)*d^2*e^3 + 30*(b^5*c + 10*a*b^3*c^2 + 10*a^2*b*c^3)*d*e^4 + (b^6 + 30*a*b^4*c + 90*a^2*b^2*c^2 + 20*a^3*c^3)*e^5)*x^11 + (3*(5*b^2*c^4 + 2*a*c^5)*d^5 + 50*(2*b^3*c^3 + 3*a*b*c^4)*d^4*e + 150*(b^4*c^2 + 4*a*b^2*c^3 + a^2*c^4)*d^3*e^2 + 60*(b^5*c + 10*a*b^3*c^2 + 10*a^2*b*c^3)*d^2*e^3 + 5*(b^6 + 30*a*b^4*c + 90*a^2*b^2*c^2 + 20*a^3*c^3)*d*e^4 + 6*(a*b^5 + 10*a^2*b^3*c + 10*a^3*b*c^2)*e^5)*x^10 + 5*(2*(2*b^3*c^3 + 3*a*b*c^4)*d^5 + 15*(b^4*c^2 + 4*a*b^2*c^3 + a^2*c^4)*d^4*e + 12*(b^5*c + 10*a*b^3*c^2 + 10*a^2*b*c^3)*d^3*e^2 + 2*(b^6 + 30*a*b^4*c + 90*a^2*b^2*c^2 + 20*a^3*c^3)*d^2*e^3 + 6*(a*b^5 + 10*a^2*b^3*c + 10*a^3*b*c^2)*d*e^4 + 3*(a^2*b^4 + 4*a^3*b^2*c + a^4*c^2)*e^5)*x^9 + 5*(3*(b^4*c^2 + 4*a*b^2*c^3 + a^2*c^4)*d^5 + 6*(b^5*c + 10*a*b^3*c^2 + 10*a^2*b*c^3)*d^4*e + 2*(b^6 + 30*a*b^4*c + 90*a^2*b^2*c^2 + 20*a^3*c^3)*d^3*e^2 + 12*(a*b^5 + 10*a^2*b^3*c + 10*a^3*b*c^2)*d^2*e^3 + 15*(a^2*b^4 + 4*a^3*b^2*c + a^4*c^2)*d*e^4 + 2*(2*a^3*b^3 + 3*a^4*b*c)*e^5)*x^8 + (6*(b^5*c + 10*a*b^3*c^2 + 10*a^2*b*c^3)*d^5 + 5*(b^6 + 30*a*b^4*c + 90*a^2*b^2*c^2 + 20*a^3*c^3)*d^4*e + 60*(a*b^5 + 10*a^2*b^3*c + 10*a^3*b*c^2)*d^3*e^2 + 150*(a^2*b^4 + 4*a^3*b^2*c + a^4*c^2)*d^2*e^3 + 50*(2*a^3*b^3 + 3*a^4*b*c)*d*e^4 + 3*(5*a^4*b^2 + 2*a^5*c)*e^5)*x^7 + (6*a^5*b*e^5 + (b^6 + 30*a*b^4*c + 90*a^2*b^2*c^2 + 20*a^3*c^3)*d^5 + 30*(a*b^5 + 10*a^2*b^3*c + 10*a^3*b*c^2)*d^4*e + 150*(a^2*b^4 + 4*a^3*b^2*c + a^4*c^2)*d^3*e^2 + 100*(2*a^3*b^3 + 3*a^4*b*c)*d^2*e^3 + 15*(5*a^4*b^2 + 2*a^5*c)*d*e^4)*x^6 + (30*a^5*b*d*e^4 + a^6*e^5 + 6*(a*b^5 + 10*a^2*b^3*c + 10*a^3*b*c^2)*d^5 + 75*(a^2*b^4 + 4*a^3*b^2*c + a^4*c^2)*d^4*e + 100*(2*a^3*b^3 + 3*a^4*b*c)*d^3*e^2 + 30*(5*a^4*b^2 + 2*a^5*c)*d^2*e^3)*x^5 + 5*(12*a^5*b*d^2*e^3 + a^6*d*e^4 + 3*(a^2*b^4 + 4*a^3*b^2*c + a^4*c^2)*d^5 + 10*(2*a^3*b^3 + 3*a^4*b*c)*d^4*e + 6*(5*a^4*b^2 + 2*a^5*c)*d^3*e^2)*x^4 + 5*(12*a^5*b*d^3*e^2 + 2*a^6*d^2*e^3 + 2*(2*a^3*b^3 + 3*a^4*b*c)*d^5 + 3*(5*a^4*b^2 + 2*a^5*c)*d^4*e)*x^3 + (30*a^5*b*d^4*e + 10*a^6*d^3*e^2 + 3*(5*a^4*b^2 + 2*a^5*c)*d^5)*x^2 + (6*a^5*b*d^5 + 5*a^6*d^4*e)*x","B",0
279,1,18,0,0.426085," ","integrate((x^3+x^2)/(x^2+x-2),x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} + \frac{4}{3} \, \log\left(x + 2\right) + \frac{2}{3} \, \log\left(x - 1\right)"," ",0,"1/2*x^2 + 4/3*log(x + 2) + 2/3*log(x - 1)","A",0
280,-2,0,0,0.000000," ","integrate(x^2*(g*x^3+f*x^2+e*x+d)/(c*x^2+b*x+a)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 zero or nonzero?","F(-2)",0
281,-2,0,0,0.000000," ","integrate(x*(g*x^3+f*x^2+e*x+d)/(c*x^2+b*x+a)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 zero or nonzero?","F(-2)",0
282,-2,0,0,0.000000," ","integrate((g*x^3+f*x^2+e*x+d)/(c*x^2+b*x+a)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 zero or nonzero?","F(-2)",0
283,-2,0,0,0.000000," ","integrate((g*x^3+f*x^2+e*x+d)/x/(c*x^2+b*x+a)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 zero or nonzero?","F(-2)",0
284,-2,0,0,0.000000," ","integrate((g*x^3+f*x^2+e*x+d)/x^2/(c*x^2+b*x+a)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 zero or nonzero?","F(-2)",0
285,-2,0,0,0.000000," ","integrate((g*x^3+f*x^2+e*x+d)/x^3/(c*x^2+b*x+a)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 zero or nonzero?","F(-2)",0
286,-2,0,0,0.000000," ","integrate((g*x^3+f*x^2+e*x+d)/x^4/(c*x^2+b*x+a)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive, negative or zero?","F(-2)",0
287,-2,0,0,0.000000," ","integrate((g*x^3+f*x^2+e*x+d)/x^5/(c*x^2+b*x+a)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive, negative or zero?","F(-2)",0
288,-2,0,0,0.000000," ","integrate((g*x^3+f*x^2+e*x+d)/x^6/(c*x^2+b*x+a)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive, negative or zero?","F(-2)",0
289,1,206,0,0.433798," ","integrate((e*x+d)^3*(5*x^2+2*x+3)*(4*x^4-5*x^3+3*x^2+x+2),x, algorithm=""maxima"")","2 \, e^{3} x^{10} + \frac{1}{9} \, {\left(60 \, d e^{2} - 17 \, e^{3}\right)} x^{9} + \frac{1}{8} \, {\left(60 \, d^{2} e - 51 \, d e^{2} + 17 \, e^{3}\right)} x^{8} + \frac{1}{7} \, {\left(20 \, d^{3} - 51 \, d^{2} e + 51 \, d e^{2} - 4 \, e^{3}\right)} x^{7} - \frac{1}{6} \, {\left(17 \, d^{3} - 51 \, d^{2} e + 12 \, d e^{2} - 21 \, e^{3}\right)} x^{6} + \frac{1}{5} \, {\left(17 \, d^{3} - 12 \, d^{2} e + 63 \, d e^{2} + 7 \, e^{3}\right)} x^{5} - \frac{1}{4} \, {\left(4 \, d^{3} - 63 \, d^{2} e - 21 \, d e^{2} - 6 \, e^{3}\right)} x^{4} + 6 \, d^{3} x + {\left(7 \, d^{3} + 7 \, d^{2} e + 6 \, d e^{2}\right)} x^{3} + \frac{1}{2} \, {\left(7 \, d^{3} + 18 \, d^{2} e\right)} x^{2}"," ",0,"2*e^3*x^10 + 1/9*(60*d*e^2 - 17*e^3)*x^9 + 1/8*(60*d^2*e - 51*d*e^2 + 17*e^3)*x^8 + 1/7*(20*d^3 - 51*d^2*e + 51*d*e^2 - 4*e^3)*x^7 - 1/6*(17*d^3 - 51*d^2*e + 12*d*e^2 - 21*e^3)*x^6 + 1/5*(17*d^3 - 12*d^2*e + 63*d*e^2 + 7*e^3)*x^5 - 1/4*(4*d^3 - 63*d^2*e - 21*d*e^2 - 6*e^3)*x^4 + 6*d^3*x + (7*d^3 + 7*d^2*e + 6*d*e^2)*x^3 + 1/2*(7*d^3 + 18*d^2*e)*x^2","A",0
290,1,145,0,0.432184," ","integrate((e*x+d)^2*(5*x^2+2*x+3)*(4*x^4-5*x^3+3*x^2+x+2),x, algorithm=""maxima"")","\frac{20}{9} \, e^{2} x^{9} + \frac{1}{8} \, {\left(40 \, d e - 17 \, e^{2}\right)} x^{8} + \frac{1}{7} \, {\left(20 \, d^{2} - 34 \, d e + 17 \, e^{2}\right)} x^{7} - \frac{1}{6} \, {\left(17 \, d^{2} - 34 \, d e + 4 \, e^{2}\right)} x^{6} + \frac{1}{5} \, {\left(17 \, d^{2} - 8 \, d e + 21 \, e^{2}\right)} x^{5} - \frac{1}{4} \, {\left(4 \, d^{2} - 42 \, d e - 7 \, e^{2}\right)} x^{4} + \frac{1}{3} \, {\left(21 \, d^{2} + 14 \, d e + 6 \, e^{2}\right)} x^{3} + 6 \, d^{2} x + \frac{1}{2} \, {\left(7 \, d^{2} + 12 \, d e\right)} x^{2}"," ",0,"20/9*e^2*x^9 + 1/8*(40*d*e - 17*e^2)*x^8 + 1/7*(20*d^2 - 34*d*e + 17*e^2)*x^7 - 1/6*(17*d^2 - 34*d*e + 4*e^2)*x^6 + 1/5*(17*d^2 - 8*d*e + 21*e^2)*x^5 - 1/4*(4*d^2 - 42*d*e - 7*e^2)*x^4 + 1/3*(21*d^2 + 14*d*e + 6*e^2)*x^3 + 6*d^2*x + 1/2*(7*d^2 + 12*d*e)*x^2","A",0
291,1,79,0,0.428179," ","integrate((e*x+d)*(5*x^2+2*x+3)*(4*x^4-5*x^3+3*x^2+x+2),x, algorithm=""maxima"")","\frac{5}{2} \, e x^{8} + \frac{1}{7} \, {\left(20 \, d - 17 \, e\right)} x^{7} - \frac{17}{6} \, {\left(d - e\right)} x^{6} + \frac{1}{5} \, {\left(17 \, d - 4 \, e\right)} x^{5} - \frac{1}{4} \, {\left(4 \, d - 21 \, e\right)} x^{4} + \frac{7}{3} \, {\left(3 \, d + e\right)} x^{3} + \frac{1}{2} \, {\left(7 \, d + 6 \, e\right)} x^{2} + 6 \, d x"," ",0,"5/2*e*x^8 + 1/7*(20*d - 17*e)*x^7 - 17/6*(d - e)*x^6 + 1/5*(17*d - 4*e)*x^5 - 1/4*(4*d - 21*e)*x^4 + 7/3*(3*d + e)*x^3 + 1/2*(7*d + 6*e)*x^2 + 6*d*x","A",0
292,1,34,0,0.423257," ","integrate((5*x^2+2*x+3)*(4*x^4-5*x^3+3*x^2+x+2),x, algorithm=""maxima"")","\frac{20}{7} \, x^{7} - \frac{17}{6} \, x^{6} + \frac{17}{5} \, x^{5} - x^{4} + 7 \, x^{3} + \frac{7}{2} \, x^{2} + 6 \, x"," ",0,"20/7*x^7 - 17/6*x^6 + 17/5*x^5 - x^4 + 7*x^3 + 7/2*x^2 + 6*x","A",0
293,1,228,0,0.433294," ","integrate((5*x^2+2*x+3)*(4*x^4-5*x^3+3*x^2+x+2)/(e*x+d),x, algorithm=""maxima"")","\frac{200 \, e^{5} x^{6} - 12 \, {\left(20 \, d e^{4} + 17 \, e^{5}\right)} x^{5} + 15 \, {\left(20 \, d^{2} e^{3} + 17 \, d e^{4} + 17 \, e^{5}\right)} x^{4} - 20 \, {\left(20 \, d^{3} e^{2} + 17 \, d^{2} e^{3} + 17 \, d e^{4} + 4 \, e^{5}\right)} x^{3} + 30 \, {\left(20 \, d^{4} e + 17 \, d^{3} e^{2} + 17 \, d^{2} e^{3} + 4 \, d e^{4} + 21 \, e^{5}\right)} x^{2} - 60 \, {\left(20 \, d^{5} + 17 \, d^{4} e + 17 \, d^{3} e^{2} + 4 \, d^{2} e^{3} + 21 \, d e^{4} - 7 \, e^{5}\right)} x}{60 \, e^{6}} + \frac{{\left(20 \, d^{6} + 17 \, d^{5} e + 17 \, d^{4} e^{2} + 4 \, d^{3} e^{3} + 21 \, d^{2} e^{4} - 7 \, d e^{5} + 6 \, e^{6}\right)} \log\left(e x + d\right)}{e^{7}}"," ",0,"1/60*(200*e^5*x^6 - 12*(20*d*e^4 + 17*e^5)*x^5 + 15*(20*d^2*e^3 + 17*d*e^4 + 17*e^5)*x^4 - 20*(20*d^3*e^2 + 17*d^2*e^3 + 17*d*e^4 + 4*e^5)*x^3 + 30*(20*d^4*e + 17*d^3*e^2 + 17*d^2*e^3 + 4*d*e^4 + 21*e^5)*x^2 - 60*(20*d^5 + 17*d^4*e + 17*d^3*e^2 + 4*d^2*e^3 + 21*d*e^4 - 7*e^5)*x)/e^6 + (20*d^6 + 17*d^5*e + 17*d^4*e^2 + 4*d^3*e^3 + 21*d^2*e^4 - 7*d*e^5 + 6*e^6)*log(e*x + d)/e^7","A",0
294,1,234,0,0.434612," ","integrate((5*x^2+2*x+3)*(4*x^4-5*x^3+3*x^2+x+2)/(e*x+d)^2,x, algorithm=""maxima"")","-\frac{20 \, d^{6} + 17 \, d^{5} e + 17 \, d^{4} e^{2} + 4 \, d^{3} e^{3} + 21 \, d^{2} e^{4} - 7 \, d e^{5} + 6 \, e^{6}}{e^{8} x + d e^{7}} + \frac{48 \, e^{4} x^{5} - 3 \, {\left(40 \, d e^{3} + 17 \, e^{4}\right)} x^{4} + 4 \, {\left(60 \, d^{2} e^{2} + 34 \, d e^{3} + 17 \, e^{4}\right)} x^{3} - 6 \, {\left(80 \, d^{3} e + 51 \, d^{2} e^{2} + 34 \, d e^{3} + 4 \, e^{4}\right)} x^{2} + 12 \, {\left(100 \, d^{4} + 68 \, d^{3} e + 51 \, d^{2} e^{2} + 8 \, d e^{3} + 21 \, e^{4}\right)} x}{12 \, e^{6}} - \frac{{\left(120 \, d^{5} + 85 \, d^{4} e + 68 \, d^{3} e^{2} + 12 \, d^{2} e^{3} + 42 \, d e^{4} - 7 \, e^{5}\right)} \log\left(e x + d\right)}{e^{7}}"," ",0,"-(20*d^6 + 17*d^5*e + 17*d^4*e^2 + 4*d^3*e^3 + 21*d^2*e^4 - 7*d*e^5 + 6*e^6)/(e^8*x + d*e^7) + 1/12*(48*e^4*x^5 - 3*(40*d*e^3 + 17*e^4)*x^4 + 4*(60*d^2*e^2 + 34*d*e^3 + 17*e^4)*x^3 - 6*(80*d^3*e + 51*d^2*e^2 + 34*d*e^3 + 4*e^4)*x^2 + 12*(100*d^4 + 68*d^3*e + 51*d^2*e^2 + 8*d*e^3 + 21*e^4)*x)/e^6 - (120*d^5 + 85*d^4*e + 68*d^3*e^2 + 12*d^2*e^3 + 42*d*e^4 - 7*e^5)*log(e*x + d)/e^7","A",0
295,1,240,0,0.443781," ","integrate((5*x^2+2*x+3)*(4*x^4-5*x^3+3*x^2+x+2)/(e*x+d)^3,x, algorithm=""maxima"")","\frac{220 \, d^{6} + 153 \, d^{5} e + 119 \, d^{4} e^{2} + 20 \, d^{3} e^{3} + 63 \, d^{2} e^{4} - 7 \, d e^{5} - 6 \, e^{6} + 2 \, {\left(120 \, d^{5} e + 85 \, d^{4} e^{2} + 68 \, d^{3} e^{3} + 12 \, d^{2} e^{4} + 42 \, d e^{5} - 7 \, e^{6}\right)} x}{2 \, {\left(e^{9} x^{2} + 2 \, d e^{8} x + d^{2} e^{7}\right)}} + \frac{30 \, e^{3} x^{4} - 2 \, {\left(60 \, d e^{2} + 17 \, e^{3}\right)} x^{3} + 3 \, {\left(120 \, d^{2} e + 51 \, d e^{2} + 17 \, e^{3}\right)} x^{2} - 6 \, {\left(200 \, d^{3} + 102 \, d^{2} e + 51 \, d e^{2} + 4 \, e^{3}\right)} x}{6 \, e^{6}} + \frac{{\left(300 \, d^{4} + 170 \, d^{3} e + 102 \, d^{2} e^{2} + 12 \, d e^{3} + 21 \, e^{4}\right)} \log\left(e x + d\right)}{e^{7}}"," ",0,"1/2*(220*d^6 + 153*d^5*e + 119*d^4*e^2 + 20*d^3*e^3 + 63*d^2*e^4 - 7*d*e^5 - 6*e^6 + 2*(120*d^5*e + 85*d^4*e^2 + 68*d^3*e^3 + 12*d^2*e^4 + 42*d*e^5 - 7*e^6)*x)/(e^9*x^2 + 2*d*e^8*x + d^2*e^7) + 1/6*(30*e^3*x^4 - 2*(60*d*e^2 + 17*e^3)*x^3 + 3*(120*d^2*e + 51*d*e^2 + 17*e^3)*x^2 - 6*(200*d^3 + 102*d^2*e + 51*d*e^2 + 4*e^3)*x)/e^6 + (300*d^4 + 170*d^3*e + 102*d^2*e^2 + 12*d*e^3 + 21*e^4)*log(e*x + d)/e^7","A",0
296,1,263,0,0.434993," ","integrate((e*x+d)^3*(5*x^2+2*x+3)^2*(4*x^4-5*x^3+3*x^2+x+2),x, algorithm=""maxima"")","\frac{25}{3} \, e^{3} x^{12} + \frac{15}{11} \, {\left(20 \, d e^{2} - 3 \, e^{3}\right)} x^{11} + \frac{3}{10} \, {\left(100 \, d^{2} e - 45 \, d e^{2} + 37 \, e^{3}\right)} x^{10} + \frac{1}{9} \, {\left(100 \, d^{3} - 135 \, d^{2} e + 333 \, d e^{2} - 37 \, e^{3}\right)} x^{9} - \frac{1}{8} \, {\left(45 \, d^{3} - 333 \, d^{2} e + 111 \, d e^{2} - 148 \, e^{3}\right)} x^{8} + \frac{1}{7} \, {\left(111 \, d^{3} - 111 \, d^{2} e + 444 \, d e^{2} + 65 \, e^{3}\right)} x^{7} - \frac{1}{6} \, {\left(37 \, d^{3} - 444 \, d^{2} e - 195 \, d e^{2} - 107 \, e^{3}\right)} x^{6} + \frac{1}{5} \, {\left(148 \, d^{3} + 195 \, d^{2} e + 321 \, d e^{2} + 33 \, e^{3}\right)} x^{5} + \frac{1}{4} \, {\left(65 \, d^{3} + 321 \, d^{2} e + 99 \, d e^{2} + 18 \, e^{3}\right)} x^{4} + 18 \, d^{3} x + \frac{1}{3} \, {\left(107 \, d^{3} + 99 \, d^{2} e + 54 \, d e^{2}\right)} x^{3} + \frac{3}{2} \, {\left(11 \, d^{3} + 18 \, d^{2} e\right)} x^{2}"," ",0,"25/3*e^3*x^12 + 15/11*(20*d*e^2 - 3*e^3)*x^11 + 3/10*(100*d^2*e - 45*d*e^2 + 37*e^3)*x^10 + 1/9*(100*d^3 - 135*d^2*e + 333*d*e^2 - 37*e^3)*x^9 - 1/8*(45*d^3 - 333*d^2*e + 111*d*e^2 - 148*e^3)*x^8 + 1/7*(111*d^3 - 111*d^2*e + 444*d*e^2 + 65*e^3)*x^7 - 1/6*(37*d^3 - 444*d^2*e - 195*d*e^2 - 107*e^3)*x^6 + 1/5*(148*d^3 + 195*d^2*e + 321*d*e^2 + 33*e^3)*x^5 + 1/4*(65*d^3 + 321*d^2*e + 99*d*e^2 + 18*e^3)*x^4 + 18*d^3*x + 1/3*(107*d^3 + 99*d^2*e + 54*d*e^2)*x^3 + 3/2*(11*d^3 + 18*d^2*e)*x^2","A",0
297,1,185,0,0.429041," ","integrate((e*x+d)^2*(5*x^2+2*x+3)^2*(4*x^4-5*x^3+3*x^2+x+2),x, algorithm=""maxima"")","\frac{100}{11} \, e^{2} x^{11} + \frac{1}{2} \, {\left(40 \, d e - 9 \, e^{2}\right)} x^{10} + \frac{1}{9} \, {\left(100 \, d^{2} - 90 \, d e + 111 \, e^{2}\right)} x^{9} - \frac{1}{8} \, {\left(45 \, d^{2} - 222 \, d e + 37 \, e^{2}\right)} x^{8} + \frac{37}{7} \, {\left(3 \, d^{2} - 2 \, d e + 4 \, e^{2}\right)} x^{7} - \frac{1}{6} \, {\left(37 \, d^{2} - 296 \, d e - 65 \, e^{2}\right)} x^{6} + \frac{1}{5} \, {\left(148 \, d^{2} + 130 \, d e + 107 \, e^{2}\right)} x^{5} + \frac{1}{4} \, {\left(65 \, d^{2} + 214 \, d e + 33 \, e^{2}\right)} x^{4} + \frac{1}{3} \, {\left(107 \, d^{2} + 66 \, d e + 18 \, e^{2}\right)} x^{3} + 18 \, d^{2} x + \frac{3}{2} \, {\left(11 \, d^{2} + 12 \, d e\right)} x^{2}"," ",0,"100/11*e^2*x^11 + 1/2*(40*d*e - 9*e^2)*x^10 + 1/9*(100*d^2 - 90*d*e + 111*e^2)*x^9 - 1/8*(45*d^2 - 222*d*e + 37*e^2)*x^8 + 37/7*(3*d^2 - 2*d*e + 4*e^2)*x^7 - 1/6*(37*d^2 - 296*d*e - 65*e^2)*x^6 + 1/5*(148*d^2 + 130*d*e + 107*e^2)*x^5 + 1/4*(65*d^2 + 214*d*e + 33*e^2)*x^4 + 1/3*(107*d^2 + 66*d*e + 18*e^2)*x^3 + 18*d^2*x + 3/2*(11*d^2 + 12*d*e)*x^2","A",0
298,1,105,0,0.431431," ","integrate((e*x+d)*(5*x^2+2*x+3)^2*(4*x^4-5*x^3+3*x^2+x+2),x, algorithm=""maxima"")","10 \, e x^{10} + \frac{5}{9} \, {\left(20 \, d - 9 \, e\right)} x^{9} - \frac{3}{8} \, {\left(15 \, d - 37 \, e\right)} x^{8} + \frac{37}{7} \, {\left(3 \, d - e\right)} x^{7} - \frac{37}{6} \, {\left(d - 4 \, e\right)} x^{6} + \frac{1}{5} \, {\left(148 \, d + 65 \, e\right)} x^{5} + \frac{1}{4} \, {\left(65 \, d + 107 \, e\right)} x^{4} + \frac{1}{3} \, {\left(107 \, d + 33 \, e\right)} x^{3} + \frac{3}{2} \, {\left(11 \, d + 6 \, e\right)} x^{2} + 18 \, d x"," ",0,"10*e*x^10 + 5/9*(20*d - 9*e)*x^9 - 3/8*(15*d - 37*e)*x^8 + 37/7*(3*d - e)*x^7 - 37/6*(d - 4*e)*x^6 + 1/5*(148*d + 65*e)*x^5 + 1/4*(65*d + 107*e)*x^4 + 1/3*(107*d + 33*e)*x^3 + 3/2*(11*d + 6*e)*x^2 + 18*d*x","A",0
299,1,44,0,0.423347," ","integrate((5*x^2+2*x+3)^2*(4*x^4-5*x^3+3*x^2+x+2),x, algorithm=""maxima"")","\frac{100}{9} \, x^{9} - \frac{45}{8} \, x^{8} + \frac{111}{7} \, x^{7} - \frac{37}{6} \, x^{6} + \frac{148}{5} \, x^{5} + \frac{65}{4} \, x^{4} + \frac{107}{3} \, x^{3} + \frac{33}{2} \, x^{2} + 18 \, x"," ",0,"100/9*x^9 - 45/8*x^8 + 111/7*x^7 - 37/6*x^6 + 148/5*x^5 + 65/4*x^4 + 107/3*x^3 + 33/2*x^2 + 18*x","A",0
300,1,366,0,0.435535," ","integrate((5*x^2+2*x+3)^2*(4*x^4-5*x^3+3*x^2+x+2)/(e*x+d),x, algorithm=""maxima"")","\frac{5250 \, e^{7} x^{8} - 300 \, {\left(20 \, d e^{6} + 9 \, e^{7}\right)} x^{7} + 70 \, {\left(100 \, d^{2} e^{5} + 45 \, d e^{6} + 111 \, e^{7}\right)} x^{6} - 84 \, {\left(100 \, d^{3} e^{4} + 45 \, d^{2} e^{5} + 111 \, d e^{6} + 37 \, e^{7}\right)} x^{5} + 105 \, {\left(100 \, d^{4} e^{3} + 45 \, d^{3} e^{4} + 111 \, d^{2} e^{5} + 37 \, d e^{6} + 148 \, e^{7}\right)} x^{4} - 140 \, {\left(100 \, d^{5} e^{2} + 45 \, d^{4} e^{3} + 111 \, d^{3} e^{4} + 37 \, d^{2} e^{5} + 148 \, d e^{6} - 65 \, e^{7}\right)} x^{3} + 210 \, {\left(100 \, d^{6} e + 45 \, d^{5} e^{2} + 111 \, d^{4} e^{3} + 37 \, d^{3} e^{4} + 148 \, d^{2} e^{5} - 65 \, d e^{6} + 107 \, e^{7}\right)} x^{2} - 420 \, {\left(100 \, d^{7} + 45 \, d^{6} e + 111 \, d^{5} e^{2} + 37 \, d^{4} e^{3} + 148 \, d^{3} e^{4} - 65 \, d^{2} e^{5} + 107 \, d e^{6} - 33 \, e^{7}\right)} x}{420 \, e^{8}} + \frac{{\left(100 \, d^{8} + 45 \, d^{7} e + 111 \, d^{6} e^{2} + 37 \, d^{5} e^{3} + 148 \, d^{4} e^{4} - 65 \, d^{3} e^{5} + 107 \, d^{2} e^{6} - 33 \, d e^{7} + 18 \, e^{8}\right)} \log\left(e x + d\right)}{e^{9}}"," ",0,"1/420*(5250*e^7*x^8 - 300*(20*d*e^6 + 9*e^7)*x^7 + 70*(100*d^2*e^5 + 45*d*e^6 + 111*e^7)*x^6 - 84*(100*d^3*e^4 + 45*d^2*e^5 + 111*d*e^6 + 37*e^7)*x^5 + 105*(100*d^4*e^3 + 45*d^3*e^4 + 111*d^2*e^5 + 37*d*e^6 + 148*e^7)*x^4 - 140*(100*d^5*e^2 + 45*d^4*e^3 + 111*d^3*e^4 + 37*d^2*e^5 + 148*d*e^6 - 65*e^7)*x^3 + 210*(100*d^6*e + 45*d^5*e^2 + 111*d^4*e^3 + 37*d^3*e^4 + 148*d^2*e^5 - 65*d*e^6 + 107*e^7)*x^2 - 420*(100*d^7 + 45*d^6*e + 111*d^5*e^2 + 37*d^4*e^3 + 148*d^3*e^4 - 65*d^2*e^5 + 107*d*e^6 - 33*e^7)*x)/e^8 + (100*d^8 + 45*d^7*e + 111*d^6*e^2 + 37*d^5*e^3 + 148*d^4*e^4 - 65*d^3*e^5 + 107*d^2*e^6 - 33*d*e^7 + 18*e^8)*log(e*x + d)/e^9","A",0
301,1,372,0,0.437980," ","integrate((5*x^2+2*x+3)^2*(4*x^4-5*x^3+3*x^2+x+2)/(e*x+d)^2,x, algorithm=""maxima"")","-\frac{100 \, d^{8} + 45 \, d^{7} e + 111 \, d^{6} e^{2} + 37 \, d^{5} e^{3} + 148 \, d^{4} e^{4} - 65 \, d^{3} e^{5} + 107 \, d^{2} e^{6} - 33 \, d e^{7} + 18 \, e^{8}}{e^{10} x + d e^{9}} + \frac{6000 \, e^{6} x^{7} - 350 \, {\left(40 \, d e^{5} + 9 \, e^{6}\right)} x^{6} + 252 \, {\left(100 \, d^{2} e^{4} + 30 \, d e^{5} + 37 \, e^{6}\right)} x^{5} - 105 \, {\left(400 \, d^{3} e^{3} + 135 \, d^{2} e^{4} + 222 \, d e^{5} + 37 \, e^{6}\right)} x^{4} + 140 \, {\left(500 \, d^{4} e^{2} + 180 \, d^{3} e^{3} + 333 \, d^{2} e^{4} + 74 \, d e^{5} + 148 \, e^{6}\right)} x^{3} - 210 \, {\left(600 \, d^{5} e + 225 \, d^{4} e^{2} + 444 \, d^{3} e^{3} + 111 \, d^{2} e^{4} + 296 \, d e^{5} - 65 \, e^{6}\right)} x^{2} + 420 \, {\left(700 \, d^{6} + 270 \, d^{5} e + 555 \, d^{4} e^{2} + 148 \, d^{3} e^{3} + 444 \, d^{2} e^{4} - 130 \, d e^{5} + 107 \, e^{6}\right)} x}{420 \, e^{8}} - \frac{{\left(800 \, d^{7} + 315 \, d^{6} e + 666 \, d^{5} e^{2} + 185 \, d^{4} e^{3} + 592 \, d^{3} e^{4} - 195 \, d^{2} e^{5} + 214 \, d e^{6} - 33 \, e^{7}\right)} \log\left(e x + d\right)}{e^{9}}"," ",0,"-(100*d^8 + 45*d^7*e + 111*d^6*e^2 + 37*d^5*e^3 + 148*d^4*e^4 - 65*d^3*e^5 + 107*d^2*e^6 - 33*d*e^7 + 18*e^8)/(e^10*x + d*e^9) + 1/420*(6000*e^6*x^7 - 350*(40*d*e^5 + 9*e^6)*x^6 + 252*(100*d^2*e^4 + 30*d*e^5 + 37*e^6)*x^5 - 105*(400*d^3*e^3 + 135*d^2*e^4 + 222*d*e^5 + 37*e^6)*x^4 + 140*(500*d^4*e^2 + 180*d^3*e^3 + 333*d^2*e^4 + 74*d*e^5 + 148*e^6)*x^3 - 210*(600*d^5*e + 225*d^4*e^2 + 444*d^3*e^3 + 111*d^2*e^4 + 296*d*e^5 - 65*e^6)*x^2 + 420*(700*d^6 + 270*d^5*e + 555*d^4*e^2 + 148*d^3*e^3 + 444*d^2*e^4 - 130*d*e^5 + 107*e^6)*x)/e^8 - (800*d^7 + 315*d^6*e + 666*d^5*e^2 + 185*d^4*e^3 + 592*d^3*e^4 - 195*d^2*e^5 + 214*d*e^6 - 33*e^7)*log(e*x + d)/e^9","A",0
302,1,378,0,0.449475," ","integrate((5*x^2+2*x+3)^2*(4*x^4-5*x^3+3*x^2+x+2)/(e*x+d)^3,x, algorithm=""maxima"")","\frac{1500 \, d^{8} + 585 \, d^{7} e + 1221 \, d^{6} e^{2} + 333 \, d^{5} e^{3} + 1036 \, d^{4} e^{4} - 325 \, d^{3} e^{5} + 321 \, d^{2} e^{6} - 33 \, d e^{7} - 18 \, e^{8} + 2 \, {\left(800 \, d^{7} e + 315 \, d^{6} e^{2} + 666 \, d^{5} e^{3} + 185 \, d^{4} e^{4} + 592 \, d^{3} e^{5} - 195 \, d^{2} e^{6} + 214 \, d e^{7} - 33 \, e^{8}\right)} x}{2 \, {\left(e^{11} x^{2} + 2 \, d e^{10} x + d^{2} e^{9}\right)}} + \frac{200 \, e^{5} x^{6} - 36 \, {\left(20 \, d e^{4} + 3 \, e^{5}\right)} x^{5} + 9 \, {\left(200 \, d^{2} e^{3} + 45 \, d e^{4} + 37 \, e^{5}\right)} x^{4} - 4 \, {\left(1000 \, d^{3} e^{2} + 270 \, d^{2} e^{3} + 333 \, d e^{4} + 37 \, e^{5}\right)} x^{3} + 6 \, {\left(1500 \, d^{4} e + 450 \, d^{3} e^{2} + 666 \, d^{2} e^{3} + 111 \, d e^{4} + 148 \, e^{5}\right)} x^{2} - 12 \, {\left(2100 \, d^{5} + 675 \, d^{4} e + 1110 \, d^{3} e^{2} + 222 \, d^{2} e^{3} + 444 \, d e^{4} - 65 \, e^{5}\right)} x}{12 \, e^{8}} + \frac{{\left(2800 \, d^{6} + 945 \, d^{5} e + 1665 \, d^{4} e^{2} + 370 \, d^{3} e^{3} + 888 \, d^{2} e^{4} - 195 \, d e^{5} + 107 \, e^{6}\right)} \log\left(e x + d\right)}{e^{9}}"," ",0,"1/2*(1500*d^8 + 585*d^7*e + 1221*d^6*e^2 + 333*d^5*e^3 + 1036*d^4*e^4 - 325*d^3*e^5 + 321*d^2*e^6 - 33*d*e^7 - 18*e^8 + 2*(800*d^7*e + 315*d^6*e^2 + 666*d^5*e^3 + 185*d^4*e^4 + 592*d^3*e^5 - 195*d^2*e^6 + 214*d*e^7 - 33*e^8)*x)/(e^11*x^2 + 2*d*e^10*x + d^2*e^9) + 1/12*(200*e^5*x^6 - 36*(20*d*e^4 + 3*e^5)*x^5 + 9*(200*d^2*e^3 + 45*d*e^4 + 37*e^5)*x^4 - 4*(1000*d^3*e^2 + 270*d^2*e^3 + 333*d*e^4 + 37*e^5)*x^3 + 6*(1500*d^4*e + 450*d^3*e^2 + 666*d^2*e^3 + 111*d*e^4 + 148*e^5)*x^2 - 12*(2100*d^5 + 675*d^4*e + 1110*d^3*e^2 + 222*d^2*e^3 + 444*d*e^4 - 65*e^5)*x)/e^8 + (2800*d^6 + 945*d^5*e + 1665*d^4*e^2 + 370*d^3*e^3 + 888*d^2*e^4 - 195*d*e^5 + 107*e^6)*log(e*x + d)/e^9","A",0
303,1,390,0,0.462170," ","integrate((5*x^2+2*x+3)^2*(4*x^4-5*x^3+3*x^2+x+2)/(e*x+d)^4,x, algorithm=""maxima"")","-\frac{14600 \, d^{8} + 4815 \, d^{7} e + 8214 \, d^{6} e^{2} + 1739 \, d^{5} e^{3} + 3848 \, d^{4} e^{4} - 715 \, d^{3} e^{5} + 214 \, d^{2} e^{6} + 33 \, d e^{7} + 36 \, e^{8} + 6 \, {\left(2800 \, d^{6} e^{2} + 945 \, d^{5} e^{3} + 1665 \, d^{4} e^{4} + 370 \, d^{3} e^{5} + 888 \, d^{2} e^{6} - 195 \, d e^{7} + 107 \, e^{8}\right)} x^{2} + 3 \, {\left(10400 \, d^{7} e + 3465 \, d^{6} e^{2} + 5994 \, d^{5} e^{3} + 1295 \, d^{4} e^{4} + 2960 \, d^{3} e^{5} - 585 \, d^{2} e^{6} + 214 \, d e^{7} + 33 \, e^{8}\right)} x}{6 \, {\left(e^{12} x^{3} + 3 \, d e^{11} x^{2} + 3 \, d^{2} e^{10} x + d^{3} e^{9}\right)}} + \frac{240 \, e^{4} x^{5} - 15 \, {\left(80 \, d e^{3} + 9 \, e^{4}\right)} x^{4} + 4 \, {\left(1000 \, d^{2} e^{2} + 180 \, d e^{3} + 111 \, e^{4}\right)} x^{3} - 6 \, {\left(2000 \, d^{3} e + 450 \, d^{2} e^{2} + 444 \, d e^{3} + 37 \, e^{4}\right)} x^{2} + 24 \, {\left(1750 \, d^{4} + 450 \, d^{3} e + 555 \, d^{2} e^{2} + 74 \, d e^{3} + 74 \, e^{4}\right)} x}{12 \, e^{8}} - \frac{{\left(5600 \, d^{5} + 1575 \, d^{4} e + 2220 \, d^{3} e^{2} + 370 \, d^{2} e^{3} + 592 \, d e^{4} - 65 \, e^{5}\right)} \log\left(e x + d\right)}{e^{9}}"," ",0,"-1/6*(14600*d^8 + 4815*d^7*e + 8214*d^6*e^2 + 1739*d^5*e^3 + 3848*d^4*e^4 - 715*d^3*e^5 + 214*d^2*e^6 + 33*d*e^7 + 36*e^8 + 6*(2800*d^6*e^2 + 945*d^5*e^3 + 1665*d^4*e^4 + 370*d^3*e^5 + 888*d^2*e^6 - 195*d*e^7 + 107*e^8)*x^2 + 3*(10400*d^7*e + 3465*d^6*e^2 + 5994*d^5*e^3 + 1295*d^4*e^4 + 2960*d^3*e^5 - 585*d^2*e^6 + 214*d*e^7 + 33*e^8)*x)/(e^12*x^3 + 3*d*e^11*x^2 + 3*d^2*e^10*x + d^3*e^9) + 1/12*(240*e^4*x^5 - 15*(80*d*e^3 + 9*e^4)*x^4 + 4*(1000*d^2*e^2 + 180*d*e^3 + 111*e^4)*x^3 - 6*(2000*d^3*e + 450*d^2*e^2 + 444*d*e^3 + 37*e^4)*x^2 + 24*(1750*d^4 + 450*d^3*e + 555*d^2*e^2 + 74*d*e^3 + 74*e^4)*x)/e^8 - (5600*d^5 + 1575*d^4*e + 2220*d^3*e^2 + 370*d^2*e^3 + 592*d*e^4 - 65*e^5)*log(e*x + d)/e^9","A",0
304,1,206,0,0.963729," ","integrate((e*x+d)^3*(4*x^4-5*x^3+3*x^2+x+2)/(5*x^2+2*x+3),x, algorithm=""maxima"")","\frac{2}{15} \, e^{3} x^{6} + \frac{3}{125} \, {\left(20 \, d e^{2} - 11 \, e^{3}\right)} x^{5} + \frac{3}{500} \, {\left(100 \, d^{2} e - 165 \, d e^{2} + 27 \, e^{3}\right)} x^{4} + \frac{1}{1875} \, {\left(500 \, d^{3} - 2475 \, d^{2} e + 1215 \, d e^{2} + 458 \, e^{3}\right)} x^{3} - \frac{1}{6250} \, {\left(4125 \, d^{3} - 6075 \, d^{2} e - 6870 \, d e^{2} + 881 \, e^{3}\right)} x^{2} - \frac{1}{1093750} \, \sqrt{14} {\left(52875 \, d^{3} + 449175 \, d^{2} e - 274845 \, d e^{2} - 53189 \, e^{3}\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) + \frac{1}{15625} \, {\left(10125 \, d^{3} + 34350 \, d^{2} e - 13215 \, d e^{2} - 5108 \, e^{3}\right)} x + \frac{1}{156250} \, {\left(57250 \, d^{3} - 66075 \, d^{2} e - 76620 \, d e^{2} + 23431 \, e^{3}\right)} \log\left(5 \, x^{2} + 2 \, x + 3\right)"," ",0,"2/15*e^3*x^6 + 3/125*(20*d*e^2 - 11*e^3)*x^5 + 3/500*(100*d^2*e - 165*d*e^2 + 27*e^3)*x^4 + 1/1875*(500*d^3 - 2475*d^2*e + 1215*d*e^2 + 458*e^3)*x^3 - 1/6250*(4125*d^3 - 6075*d^2*e - 6870*d*e^2 + 881*e^3)*x^2 - 1/1093750*sqrt(14)*(52875*d^3 + 449175*d^2*e - 274845*d*e^2 - 53189*e^3)*arctan(1/14*sqrt(14)*(5*x + 1)) + 1/15625*(10125*d^3 + 34350*d^2*e - 13215*d*e^2 - 5108*e^3)*x + 1/156250*(57250*d^3 - 66075*d^2*e - 76620*d*e^2 + 23431*e^3)*log(5*x^2 + 2*x + 3)","A",0
305,1,141,0,0.961277," ","integrate((e*x+d)^2*(4*x^4-5*x^3+3*x^2+x+2)/(5*x^2+2*x+3),x, algorithm=""maxima"")","\frac{4}{25} \, e^{2} x^{5} + \frac{1}{100} \, {\left(40 \, d e - 33 \, e^{2}\right)} x^{4} + \frac{1}{375} \, {\left(100 \, d^{2} - 330 \, d e + 81 \, e^{2}\right)} x^{3} - \frac{1}{1250} \, {\left(825 \, d^{2} - 810 \, d e - 458 \, e^{2}\right)} x^{2} - \frac{1}{218750} \, \sqrt{14} {\left(10575 \, d^{2} + 59890 \, d e - 18323 \, e^{2}\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) + \frac{1}{3125} \, {\left(2025 \, d^{2} + 4580 \, d e - 881 \, e^{2}\right)} x + \frac{1}{15625} \, {\left(5725 \, d^{2} - 4405 \, d e - 2554 \, e^{2}\right)} \log\left(5 \, x^{2} + 2 \, x + 3\right)"," ",0,"4/25*e^2*x^5 + 1/100*(40*d*e - 33*e^2)*x^4 + 1/375*(100*d^2 - 330*d*e + 81*e^2)*x^3 - 1/1250*(825*d^2 - 810*d*e - 458*e^2)*x^2 - 1/218750*sqrt(14)*(10575*d^2 + 59890*d*e - 18323*e^2)*arctan(1/14*sqrt(14)*(5*x + 1)) + 1/3125*(2025*d^2 + 4580*d*e - 881*e^2)*x + 1/15625*(5725*d^2 - 4405*d*e - 2554*e^2)*log(5*x^2 + 2*x + 3)","A",0
306,1,84,0,0.956235," ","integrate((e*x+d)*(4*x^4-5*x^3+3*x^2+x+2)/(5*x^2+2*x+3),x, algorithm=""maxima"")","\frac{1}{5} \, e x^{4} + \frac{1}{75} \, {\left(20 \, d - 33 \, e\right)} x^{3} - \frac{3}{250} \, {\left(55 \, d - 27 \, e\right)} x^{2} - \frac{1}{43750} \, \sqrt{14} {\left(2115 \, d + 5989 \, e\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) + \frac{1}{625} \, {\left(405 \, d + 458 \, e\right)} x + \frac{1}{6250} \, {\left(2290 \, d - 881 \, e\right)} \log\left(5 \, x^{2} + 2 \, x + 3\right)"," ",0,"1/5*e*x^4 + 1/75*(20*d - 33*e)*x^3 - 3/250*(55*d - 27*e)*x^2 - 1/43750*sqrt(14)*(2115*d + 5989*e)*arctan(1/14*sqrt(14)*(5*x + 1)) + 1/625*(405*d + 458*e)*x + 1/6250*(2290*d - 881*e)*log(5*x^2 + 2*x + 3)","A",0
307,1,43,0,0.967263," ","integrate((4*x^4-5*x^3+3*x^2+x+2)/(5*x^2+2*x+3),x, algorithm=""maxima"")","\frac{4}{15} \, x^{3} - \frac{33}{50} \, x^{2} - \frac{423}{8750} \, \sqrt{14} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) + \frac{81}{125} \, x + \frac{229}{625} \, \log\left(5 \, x^{2} + 2 \, x + 3\right)"," ",0,"4/15*x^3 - 33/50*x^2 - 423/8750*sqrt(14)*arctan(1/14*sqrt(14)*(5*x + 1)) + 81/125*x + 229/625*log(5*x^2 + 2*x + 3)","A",0
308,1,160,0,0.963552," ","integrate((4*x^4-5*x^3+3*x^2+x+2)/(e*x+d)/(5*x^2+2*x+3),x, algorithm=""maxima"")","-\frac{\sqrt{14} {\left(423 \, d - 1367 \, e\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right)}{1750 \, {\left(5 \, d^{2} - 2 \, d e + 3 \, e^{2}\right)}} + \frac{{\left(4 \, d^{4} + 5 \, d^{3} e + 3 \, d^{2} e^{2} - d e^{3} + 2 \, e^{4}\right)} \log\left(e x + d\right)}{5 \, d^{2} e^{3} - 2 \, d e^{4} + 3 \, e^{5}} + \frac{{\left(458 \, d - 7 \, e\right)} \log\left(5 \, x^{2} + 2 \, x + 3\right)}{250 \, {\left(5 \, d^{2} - 2 \, d e + 3 \, e^{2}\right)}} + \frac{10 \, e x^{2} - {\left(20 \, d + 33 \, e\right)} x}{25 \, e^{2}}"," ",0,"-1/1750*sqrt(14)*(423*d - 1367*e)*arctan(1/14*sqrt(14)*(5*x + 1))/(5*d^2 - 2*d*e + 3*e^2) + (4*d^4 + 5*d^3*e + 3*d^2*e^2 - d*e^3 + 2*e^4)*log(e*x + d)/(5*d^2*e^3 - 2*d*e^4 + 3*e^5) + 1/250*(458*d - 7*e)*log(5*x^2 + 2*x + 3)/(5*d^2 - 2*d*e + 3*e^2) + 1/25*(10*e*x^2 - (20*d + 33*e)*x)/e^2","A",0
309,1,294,0,0.982686," ","integrate((4*x^4-5*x^3+3*x^2+x+2)/(e*x+d)^2/(5*x^2+2*x+3),x, algorithm=""maxima"")","-\frac{\sqrt{14} {\left(423 \, d^{2} - 2734 \, d e + 293 \, e^{2}\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right)}{350 \, {\left(25 \, d^{4} - 20 \, d^{3} e + 34 \, d^{2} e^{2} - 12 \, d e^{3} + 9 \, e^{4}\right)}} - \frac{{\left(40 \, d^{5} + d^{4} e + 28 \, d^{3} e^{2} + 44 \, d^{2} e^{3} - 2 \, d e^{4} + e^{5}\right)} \log\left(e x + d\right)}{25 \, d^{4} e^{3} - 20 \, d^{3} e^{4} + 34 \, d^{2} e^{5} - 12 \, d e^{6} + 9 \, e^{7}} + \frac{{\left(229 \, d^{2} - 7 \, d e - 136 \, e^{2}\right)} \log\left(5 \, x^{2} + 2 \, x + 3\right)}{25 \, {\left(25 \, d^{4} - 20 \, d^{3} e + 34 \, d^{2} e^{2} - 12 \, d e^{3} + 9 \, e^{4}\right)}} - \frac{4 \, d^{4} + 5 \, d^{3} e + 3 \, d^{2} e^{2} - d e^{3} + 2 \, e^{4}}{5 \, d^{3} e^{3} - 2 \, d^{2} e^{4} + 3 \, d e^{5} + {\left(5 \, d^{2} e^{4} - 2 \, d e^{5} + 3 \, e^{6}\right)} x} + \frac{4 \, x}{5 \, e^{2}}"," ",0,"-1/350*sqrt(14)*(423*d^2 - 2734*d*e + 293*e^2)*arctan(1/14*sqrt(14)*(5*x + 1))/(25*d^4 - 20*d^3*e + 34*d^2*e^2 - 12*d*e^3 + 9*e^4) - (40*d^5 + d^4*e + 28*d^3*e^2 + 44*d^2*e^3 - 2*d*e^4 + e^5)*log(e*x + d)/(25*d^4*e^3 - 20*d^3*e^4 + 34*d^2*e^5 - 12*d*e^6 + 9*e^7) + 1/25*(229*d^2 - 7*d*e - 136*e^2)*log(5*x^2 + 2*x + 3)/(25*d^4 - 20*d^3*e + 34*d^2*e^2 - 12*d*e^3 + 9*e^4) - (4*d^4 + 5*d^3*e + 3*d^2*e^2 - d*e^3 + 2*e^4)/(5*d^3*e^3 - 2*d^2*e^4 + 3*d*e^5 + (5*d^2*e^4 - 2*d*e^5 + 3*e^6)*x) + 4/5*x/e^2","A",0
310,1,498,0,0.997568," ","integrate((4*x^4-5*x^3+3*x^2+x+2)/(e*x+d)^3/(5*x^2+2*x+3),x, algorithm=""maxima"")","-\frac{\sqrt{14} {\left(423 \, d^{3} - 4101 \, d^{2} e + 879 \, d e^{2} + 703 \, e^{3}\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right)}{70 \, {\left(125 \, d^{6} - 150 \, d^{5} e + 285 \, d^{4} e^{2} - 188 \, d^{3} e^{3} + 171 \, d^{2} e^{4} - 54 \, d e^{5} + 27 \, e^{6}\right)}} + \frac{{\left(100 \, d^{6} - 120 \, d^{5} e + 228 \, d^{4} e^{2} - 242 \, d^{3} e^{3} + 141 \, d^{2} e^{4} + 120 \, d e^{5} - e^{6}\right)} \log\left(e x + d\right)}{125 \, d^{6} e^{3} - 150 \, d^{5} e^{4} + 285 \, d^{4} e^{5} - 188 \, d^{3} e^{6} + 171 \, d^{2} e^{7} - 54 \, d e^{8} + 27 \, e^{9}} + \frac{{\left(458 \, d^{3} - 21 \, d^{2} e - 816 \, d e^{2} + 113 \, e^{3}\right)} \log\left(5 \, x^{2} + 2 \, x + 3\right)}{10 \, {\left(125 \, d^{6} - 150 \, d^{5} e + 285 \, d^{4} e^{2} - 188 \, d^{3} e^{3} + 171 \, d^{2} e^{4} - 54 \, d e^{5} + 27 \, e^{6}\right)}} + \frac{60 \, d^{6} - 15 \, d^{5} e + 39 \, d^{4} e^{2} + 84 \, d^{3} e^{3} - 25 \, d^{2} e^{4} + 9 \, d e^{5} - 6 \, e^{6} + 2 \, {\left(40 \, d^{5} e + d^{4} e^{2} + 28 \, d^{3} e^{3} + 44 \, d^{2} e^{4} - 2 \, d e^{5} + e^{6}\right)} x}{2 \, {\left(25 \, d^{6} e^{3} - 20 \, d^{5} e^{4} + 34 \, d^{4} e^{5} - 12 \, d^{3} e^{6} + 9 \, d^{2} e^{7} + {\left(25 \, d^{4} e^{5} - 20 \, d^{3} e^{6} + 34 \, d^{2} e^{7} - 12 \, d e^{8} + 9 \, e^{9}\right)} x^{2} + 2 \, {\left(25 \, d^{5} e^{4} - 20 \, d^{4} e^{5} + 34 \, d^{3} e^{6} - 12 \, d^{2} e^{7} + 9 \, d e^{8}\right)} x\right)}}"," ",0,"-1/70*sqrt(14)*(423*d^3 - 4101*d^2*e + 879*d*e^2 + 703*e^3)*arctan(1/14*sqrt(14)*(5*x + 1))/(125*d^6 - 150*d^5*e + 285*d^4*e^2 - 188*d^3*e^3 + 171*d^2*e^4 - 54*d*e^5 + 27*e^6) + (100*d^6 - 120*d^5*e + 228*d^4*e^2 - 242*d^3*e^3 + 141*d^2*e^4 + 120*d*e^5 - e^6)*log(e*x + d)/(125*d^6*e^3 - 150*d^5*e^4 + 285*d^4*e^5 - 188*d^3*e^6 + 171*d^2*e^7 - 54*d*e^8 + 27*e^9) + 1/10*(458*d^3 - 21*d^2*e - 816*d*e^2 + 113*e^3)*log(5*x^2 + 2*x + 3)/(125*d^6 - 150*d^5*e + 285*d^4*e^2 - 188*d^3*e^3 + 171*d^2*e^4 - 54*d*e^5 + 27*e^6) + 1/2*(60*d^6 - 15*d^5*e + 39*d^4*e^2 + 84*d^3*e^3 - 25*d^2*e^4 + 9*d*e^5 - 6*e^6 + 2*(40*d^5*e + d^4*e^2 + 28*d^3*e^3 + 44*d^2*e^4 - 2*d*e^5 + e^6)*x)/(25*d^6*e^3 - 20*d^5*e^4 + 34*d^4*e^5 - 12*d^3*e^6 + 9*d^2*e^7 + (25*d^4*e^5 - 20*d^3*e^6 + 34*d^2*e^7 - 12*d*e^8 + 9*e^9)*x^2 + 2*(25*d^5*e^4 - 20*d^4*e^5 + 34*d^3*e^6 - 12*d^2*e^7 + 9*d*e^8)*x)","A",0
311,1,212,0,0.958134," ","integrate((e*x+d)^3*(4*x^4-5*x^3+3*x^2+x+2)/(5*x^2+2*x+3)^2,x, algorithm=""maxima"")","\frac{1}{25} \, e^{3} x^{4} + \frac{1}{375} \, {\left(60 \, d e^{2} - 41 \, e^{3}\right)} x^{3} + \frac{1}{1250} \, {\left(300 \, d^{2} e - 615 \, d e^{2} + 103 \, e^{3}\right)} x^{2} + \frac{1}{1225000} \, \sqrt{14} {\left(32825 \, d^{3} + 317565 \, d^{2} e - 221643 \, d e^{2} - 67499 \, e^{3}\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) + \frac{1}{3125} \, {\left(500 \, d^{3} - 3075 \, d^{2} e + 1545 \, d e^{2} + 867 \, e^{3}\right)} x - \frac{1}{6250} \, {\left(1025 \, d^{3} - 1545 \, d^{2} e - 2601 \, d e^{2} + 832 \, e^{3}\right)} \log\left(5 \, x^{2} + 2 \, x + 3\right) - \frac{170875 \, d^{3} - 95175 \, d^{2} e - 269505 \, d e^{2} + 54969 \, e^{3} + {\left(52875 \, d^{3} + 449175 \, d^{2} e - 274845 \, d e^{2} - 53189 \, e^{3}\right)} x}{437500 \, {\left(5 \, x^{2} + 2 \, x + 3\right)}}"," ",0,"1/25*e^3*x^4 + 1/375*(60*d*e^2 - 41*e^3)*x^3 + 1/1250*(300*d^2*e - 615*d*e^2 + 103*e^3)*x^2 + 1/1225000*sqrt(14)*(32825*d^3 + 317565*d^2*e - 221643*d*e^2 - 67499*e^3)*arctan(1/14*sqrt(14)*(5*x + 1)) + 1/3125*(500*d^3 - 3075*d^2*e + 1545*d*e^2 + 867*e^3)*x - 1/6250*(1025*d^3 - 1545*d^2*e - 2601*d*e^2 + 832*e^3)*log(5*x^2 + 2*x + 3) - 1/437500*(170875*d^3 - 95175*d^2*e - 269505*d*e^2 + 54969*e^3 + (52875*d^3 + 449175*d^2*e - 274845*d*e^2 - 53189*e^3)*x)/(5*x^2 + 2*x + 3)","A",0
312,1,147,0,0.959619," ","integrate((e*x+d)^2*(4*x^4-5*x^3+3*x^2+x+2)/(5*x^2+2*x+3)^2,x, algorithm=""maxima"")","\frac{4}{75} \, e^{2} x^{3} + \frac{1}{250} \, {\left(40 \, d e - 41 \, e^{2}\right)} x^{2} + \frac{1}{1225000} \, \sqrt{14} {\left(32825 \, d^{2} + 211710 \, d e - 73881 \, e^{2}\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) + \frac{1}{625} \, {\left(100 \, d^{2} - 410 \, d e + 103 \, e^{2}\right)} x - \frac{1}{6250} \, {\left(1025 \, d^{2} - 1030 \, d e - 867 \, e^{2}\right)} \log\left(5 \, x^{2} + 2 \, x + 3\right) - \frac{34175 \, d^{2} - 12690 \, d e - 17967 \, e^{2} + {\left(10575 \, d^{2} + 59890 \, d e - 18323 \, e^{2}\right)} x}{87500 \, {\left(5 \, x^{2} + 2 \, x + 3\right)}}"," ",0,"4/75*e^2*x^3 + 1/250*(40*d*e - 41*e^2)*x^2 + 1/1225000*sqrt(14)*(32825*d^2 + 211710*d*e - 73881*e^2)*arctan(1/14*sqrt(14)*(5*x + 1)) + 1/625*(100*d^2 - 410*d*e + 103*e^2)*x - 1/6250*(1025*d^2 - 1030*d*e - 867*e^2)*log(5*x^2 + 2*x + 3) - 1/87500*(34175*d^2 - 12690*d*e - 17967*e^2 + (10575*d^2 + 59890*d*e - 18323*e^2)*x)/(5*x^2 + 2*x + 3)","A",0
313,1,90,0,0.960680," ","integrate((e*x+d)*(4*x^4-5*x^3+3*x^2+x+2)/(5*x^2+2*x+3)^2,x, algorithm=""maxima"")","\frac{2}{25} \, e x^{2} + \frac{1}{245000} \, \sqrt{14} {\left(6565 \, d + 21171 \, e\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) + \frac{1}{125} \, {\left(20 \, d - 41 \, e\right)} x - \frac{1}{1250} \, {\left(205 \, d - 103 \, e\right)} \log\left(5 \, x^{2} + 2 \, x + 3\right) - \frac{{\left(2115 \, d + 5989 \, e\right)} x + 6835 \, d - 1269 \, e}{17500 \, {\left(5 \, x^{2} + 2 \, x + 3\right)}}"," ",0,"2/25*e*x^2 + 1/245000*sqrt(14)*(6565*d + 21171*e)*arctan(1/14*sqrt(14)*(5*x + 1)) + 1/125*(20*d - 41*e)*x - 1/1250*(205*d - 103*e)*log(5*x^2 + 2*x + 3) - 1/17500*((2115*d + 5989*e)*x + 6835*d - 1269*e)/(5*x^2 + 2*x + 3)","A",0
314,1,52,0,0.952052," ","integrate((4*x^4-5*x^3+3*x^2+x+2)/(5*x^2+2*x+3)^2,x, algorithm=""maxima"")","\frac{1313}{49000} \, \sqrt{14} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) + \frac{4}{25} \, x - \frac{423 \, x + 1367}{3500 \, {\left(5 \, x^{2} + 2 \, x + 3\right)}} - \frac{41}{250} \, \log\left(5 \, x^{2} + 2 \, x + 3\right)"," ",0,"1313/49000*sqrt(14)*arctan(1/14*sqrt(14)*(5*x + 1)) + 4/25*x - 1/3500*(423*x + 1367)/(5*x^2 + 2*x + 3) - 41/250*log(5*x^2 + 2*x + 3)","A",0
315,1,289,0,0.982420," ","integrate((4*x^4-5*x^3+3*x^2+x+2)/(e*x+d)/(5*x^2+2*x+3)^2,x, algorithm=""maxima"")","\frac{\sqrt{14} {\left(6565 \, d^{3} - 26423 \, d^{2} e + 11089 \, d e^{2} - 6623 \, e^{3}\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right)}{9800 \, {\left(25 \, d^{4} - 20 \, d^{3} e + 34 \, d^{2} e^{2} - 12 \, d e^{3} + 9 \, e^{4}\right)}} + \frac{{\left(4 \, d^{4} + 5 \, d^{3} e + 3 \, d^{2} e^{2} - d e^{3} + 2 \, e^{4}\right)} \log\left(e x + d\right)}{25 \, d^{4} e - 20 \, d^{3} e^{2} + 34 \, d^{2} e^{3} - 12 \, d e^{4} + 9 \, e^{5}} - \frac{{\left(205 \, d^{3} - 61 \, d^{2} e + 23 \, d e^{2} + 14 \, e^{3}\right)} \log\left(5 \, x^{2} + 2 \, x + 3\right)}{50 \, {\left(25 \, d^{4} - 20 \, d^{3} e + 34 \, d^{2} e^{2} - 12 \, d e^{3} + 9 \, e^{4}\right)}} - \frac{{\left(423 \, d - 1367 \, e\right)} x + 1367 \, d - 293 \, e}{700 \, {\left(5 \, {\left(5 \, d^{2} - 2 \, d e + 3 \, e^{2}\right)} x^{2} + 15 \, d^{2} - 6 \, d e + 9 \, e^{2} + 2 \, {\left(5 \, d^{2} - 2 \, d e + 3 \, e^{2}\right)} x\right)}}"," ",0,"1/9800*sqrt(14)*(6565*d^3 - 26423*d^2*e + 11089*d*e^2 - 6623*e^3)*arctan(1/14*sqrt(14)*(5*x + 1))/(25*d^4 - 20*d^3*e + 34*d^2*e^2 - 12*d*e^3 + 9*e^4) + (4*d^4 + 5*d^3*e + 3*d^2*e^2 - d*e^3 + 2*e^4)*log(e*x + d)/(25*d^4*e - 20*d^3*e^2 + 34*d^2*e^3 - 12*d*e^4 + 9*e^5) - 1/50*(205*d^3 - 61*d^2*e + 23*d*e^2 + 14*e^3)*log(5*x^2 + 2*x + 3)/(25*d^4 - 20*d^3*e + 34*d^2*e^2 - 12*d*e^3 + 9*e^4) - 1/700*((423*d - 1367*e)*x + 1367*d - 293*e)/(5*(5*d^2 - 2*d*e + 3*e^2)*x^2 + 15*d^2 - 6*d*e + 9*e^2 + 2*(5*d^2 - 2*d*e + 3*e^2)*x)","A",0
316,1,548,0,1.015460," ","integrate((4*x^4-5*x^3+3*x^2+x+2)/(e*x+d)^2/(5*x^2+2*x+3)^2,x, algorithm=""maxima"")","\frac{\sqrt{14} {\left(1313 \, d^{4} - 10044 \, d^{3} e + 4290 \, d^{2} e^{2} + 156 \, d e^{3} - 271 \, e^{4}\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right)}{392 \, {\left(125 \, d^{6} - 150 \, d^{5} e + 285 \, d^{4} e^{2} - 188 \, d^{3} e^{3} + 171 \, d^{2} e^{4} - 54 \, d e^{5} + 27 \, e^{6}\right)}} + \frac{{\left(41 \, d^{4} - 8 \, d^{3} e - 60 \, d^{2} e^{2} + 24 \, d e^{3} - 5 \, e^{4}\right)} \log\left(e x + d\right)}{125 \, d^{6} - 150 \, d^{5} e + 285 \, d^{4} e^{2} - 188 \, d^{3} e^{3} + 171 \, d^{2} e^{4} - 54 \, d e^{5} + 27 \, e^{6}} - \frac{{\left(41 \, d^{4} - 8 \, d^{3} e - 60 \, d^{2} e^{2} + 24 \, d e^{3} - 5 \, e^{4}\right)} \log\left(5 \, x^{2} + 2 \, x + 3\right)}{2 \, {\left(125 \, d^{6} - 150 \, d^{5} e + 285 \, d^{4} e^{2} - 188 \, d^{3} e^{3} + 171 \, d^{2} e^{4} - 54 \, d e^{5} + 27 \, e^{6}\right)}} - \frac{1680 \, d^{4} + 3467 \, d^{3} e + 674 \, d^{2} e^{2} - 1123 \, d e^{3} + 840 \, e^{4} + {\left(2800 \, d^{4} + 3500 \, d^{3} e + 2523 \, d^{2} e^{2} - 3434 \, d e^{3} + 1693 \, e^{4}\right)} x^{2} + {\left(1120 \, d^{4} + 1823 \, d^{3} e - 527 \, d^{2} e^{2} - 573 \, d e^{3} - 143 \, e^{4}\right)} x}{140 \, {\left(75 \, d^{5} e - 60 \, d^{4} e^{2} + 102 \, d^{3} e^{3} - 36 \, d^{2} e^{4} + 27 \, d e^{5} + 5 \, {\left(25 \, d^{4} e^{2} - 20 \, d^{3} e^{3} + 34 \, d^{2} e^{4} - 12 \, d e^{5} + 9 \, e^{6}\right)} x^{3} + {\left(125 \, d^{5} e - 50 \, d^{4} e^{2} + 130 \, d^{3} e^{3} + 8 \, d^{2} e^{4} + 21 \, d e^{5} + 18 \, e^{6}\right)} x^{2} + {\left(50 \, d^{5} e + 35 \, d^{4} e^{2} + 8 \, d^{3} e^{3} + 78 \, d^{2} e^{4} - 18 \, d e^{5} + 27 \, e^{6}\right)} x\right)}}"," ",0,"1/392*sqrt(14)*(1313*d^4 - 10044*d^3*e + 4290*d^2*e^2 + 156*d*e^3 - 271*e^4)*arctan(1/14*sqrt(14)*(5*x + 1))/(125*d^6 - 150*d^5*e + 285*d^4*e^2 - 188*d^3*e^3 + 171*d^2*e^4 - 54*d*e^5 + 27*e^6) + (41*d^4 - 8*d^3*e - 60*d^2*e^2 + 24*d*e^3 - 5*e^4)*log(e*x + d)/(125*d^6 - 150*d^5*e + 285*d^4*e^2 - 188*d^3*e^3 + 171*d^2*e^4 - 54*d*e^5 + 27*e^6) - 1/2*(41*d^4 - 8*d^3*e - 60*d^2*e^2 + 24*d*e^3 - 5*e^4)*log(5*x^2 + 2*x + 3)/(125*d^6 - 150*d^5*e + 285*d^4*e^2 - 188*d^3*e^3 + 171*d^2*e^4 - 54*d*e^5 + 27*e^6) - 1/140*(1680*d^4 + 3467*d^3*e + 674*d^2*e^2 - 1123*d*e^3 + 840*e^4 + (2800*d^4 + 3500*d^3*e + 2523*d^2*e^2 - 3434*d*e^3 + 1693*e^4)*x^2 + (1120*d^4 + 1823*d^3*e - 527*d^2*e^2 - 573*d*e^3 - 143*e^4)*x)/(75*d^5*e - 60*d^4*e^2 + 102*d^3*e^3 - 36*d^2*e^4 + 27*d*e^5 + 5*(25*d^4*e^2 - 20*d^3*e^3 + 34*d^2*e^4 - 12*d*e^5 + 9*e^6)*x^3 + (125*d^5*e - 50*d^4*e^2 + 130*d^3*e^3 + 8*d^2*e^4 + 21*d*e^5 + 18*e^6)*x^2 + (50*d^5*e + 35*d^4*e^2 + 8*d^3*e^3 + 78*d^2*e^4 - 18*d*e^5 + 27*e^6)*x)","A",0
317,1,851,0,1.089668," ","integrate((4*x^4-5*x^3+3*x^2+x+2)/(e*x+d)^3/(5*x^2+2*x+3)^2,x, algorithm=""maxima"")","\frac{\sqrt{14} {\left(6565 \, d^{5} - 74017 \, d^{4} e + 35022 \, d^{3} e^{2} + 42858 \, d^{2} e^{3} - 17247 \, d e^{4} + 579 \, e^{5}\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right)}{392 \, {\left(625 \, d^{8} - 1000 \, d^{7} e + 2100 \, d^{6} e^{2} - 1960 \, d^{5} e^{3} + 2086 \, d^{4} e^{4} - 1176 \, d^{3} e^{5} + 756 \, d^{2} e^{6} - 216 \, d e^{7} + 81 \, e^{8}\right)}} + \frac{{\left(205 \, d^{5} - 19 \, d^{4} e - 846 \, d^{3} e^{2} + 396 \, d^{2} e^{3} + 57 \, d e^{4} - 21 \, e^{5}\right)} \log\left(e x + d\right)}{625 \, d^{8} - 1000 \, d^{7} e + 2100 \, d^{6} e^{2} - 1960 \, d^{5} e^{3} + 2086 \, d^{4} e^{4} - 1176 \, d^{3} e^{5} + 756 \, d^{2} e^{6} - 216 \, d e^{7} + 81 \, e^{8}} - \frac{{\left(205 \, d^{5} - 19 \, d^{4} e - 846 \, d^{3} e^{2} + 396 \, d^{2} e^{3} + 57 \, d e^{4} - 21 \, e^{5}\right)} \log\left(5 \, x^{2} + 2 \, x + 3\right)}{2 \, {\left(625 \, d^{8} - 1000 \, d^{7} e + 2100 \, d^{6} e^{2} - 1960 \, d^{5} e^{3} + 2086 \, d^{4} e^{4} - 1176 \, d^{3} e^{5} + 756 \, d^{2} e^{6} - 216 \, d e^{7} + 81 \, e^{8}\right)}} - \frac{840 \, d^{6} + 5525 \, d^{5} e - 837 \, d^{4} e^{2} - 6981 \, d^{3} e^{3} + 3355 \, d^{2} e^{4} - 714 \, d e^{5} + 252 \, e^{6} + {\left(5740 \, d^{4} e^{2} - 697 \, d^{3} e^{3} - 12501 \, d^{2} e^{4} + 4239 \, d e^{5} + 3 \, e^{6}\right)} x^{3} + {\left(1400 \, d^{6} + 6930 \, d^{5} e + 3212 \, d^{4} e^{2} - 15403 \, d^{3} e^{3} + 2349 \, d^{2} e^{4} - 549 \, d e^{5} + 597 \, e^{6}\right)} x^{2} + {\left(560 \, d^{6} + 3195 \, d^{5} e + 2105 \, d^{4} e^{2} - 4799 \, d^{3} e^{3} - 6623 \, d^{2} e^{4} + 2454 \, d e^{5} - 252 \, e^{6}\right)} x}{28 \, {\left(375 \, d^{8} e - 450 \, d^{7} e^{2} + 855 \, d^{6} e^{3} - 564 \, d^{5} e^{4} + 513 \, d^{4} e^{5} - 162 \, d^{3} e^{6} + 81 \, d^{2} e^{7} + 5 \, {\left(125 \, d^{6} e^{3} - 150 \, d^{5} e^{4} + 285 \, d^{4} e^{5} - 188 \, d^{3} e^{6} + 171 \, d^{2} e^{7} - 54 \, d e^{8} + 27 \, e^{9}\right)} x^{4} + 2 \, {\left(625 \, d^{7} e^{2} - 625 \, d^{6} e^{3} + 1275 \, d^{5} e^{4} - 655 \, d^{4} e^{5} + 667 \, d^{3} e^{6} - 99 \, d^{2} e^{7} + 81 \, d e^{8} + 27 \, e^{9}\right)} x^{3} + {\left(625 \, d^{8} e - 250 \, d^{7} e^{2} + 1200 \, d^{6} e^{3} - 250 \, d^{5} e^{4} + 958 \, d^{4} e^{5} - 150 \, d^{3} e^{6} + 432 \, d^{2} e^{7} - 54 \, d e^{8} + 81 \, e^{9}\right)} x^{2} + 2 \, {\left(125 \, d^{8} e + 225 \, d^{7} e^{2} - 165 \, d^{6} e^{3} + 667 \, d^{5} e^{4} - 393 \, d^{4} e^{5} + 459 \, d^{3} e^{6} - 135 \, d^{2} e^{7} + 81 \, d e^{8}\right)} x\right)}}"," ",0,"1/392*sqrt(14)*(6565*d^5 - 74017*d^4*e + 35022*d^3*e^2 + 42858*d^2*e^3 - 17247*d*e^4 + 579*e^5)*arctan(1/14*sqrt(14)*(5*x + 1))/(625*d^8 - 1000*d^7*e + 2100*d^6*e^2 - 1960*d^5*e^3 + 2086*d^4*e^4 - 1176*d^3*e^5 + 756*d^2*e^6 - 216*d*e^7 + 81*e^8) + (205*d^5 - 19*d^4*e - 846*d^3*e^2 + 396*d^2*e^3 + 57*d*e^4 - 21*e^5)*log(e*x + d)/(625*d^8 - 1000*d^7*e + 2100*d^6*e^2 - 1960*d^5*e^3 + 2086*d^4*e^4 - 1176*d^3*e^5 + 756*d^2*e^6 - 216*d*e^7 + 81*e^8) - 1/2*(205*d^5 - 19*d^4*e - 846*d^3*e^2 + 396*d^2*e^3 + 57*d*e^4 - 21*e^5)*log(5*x^2 + 2*x + 3)/(625*d^8 - 1000*d^7*e + 2100*d^6*e^2 - 1960*d^5*e^3 + 2086*d^4*e^4 - 1176*d^3*e^5 + 756*d^2*e^6 - 216*d*e^7 + 81*e^8) - 1/28*(840*d^6 + 5525*d^5*e - 837*d^4*e^2 - 6981*d^3*e^3 + 3355*d^2*e^4 - 714*d*e^5 + 252*e^6 + (5740*d^4*e^2 - 697*d^3*e^3 - 12501*d^2*e^4 + 4239*d*e^5 + 3*e^6)*x^3 + (1400*d^6 + 6930*d^5*e + 3212*d^4*e^2 - 15403*d^3*e^3 + 2349*d^2*e^4 - 549*d*e^5 + 597*e^6)*x^2 + (560*d^6 + 3195*d^5*e + 2105*d^4*e^2 - 4799*d^3*e^3 - 6623*d^2*e^4 + 2454*d*e^5 - 252*e^6)*x)/(375*d^8*e - 450*d^7*e^2 + 855*d^6*e^3 - 564*d^5*e^4 + 513*d^4*e^5 - 162*d^3*e^6 + 81*d^2*e^7 + 5*(125*d^6*e^3 - 150*d^5*e^4 + 285*d^4*e^5 - 188*d^3*e^6 + 171*d^2*e^7 - 54*d*e^8 + 27*e^9)*x^4 + 2*(625*d^7*e^2 - 625*d^6*e^3 + 1275*d^5*e^4 - 655*d^4*e^5 + 667*d^3*e^6 - 99*d^2*e^7 + 81*d*e^8 + 27*e^9)*x^3 + (625*d^8*e - 250*d^7*e^2 + 1200*d^6*e^3 - 250*d^5*e^4 + 958*d^4*e^5 - 150*d^3*e^6 + 432*d^2*e^7 - 54*d*e^8 + 81*e^9)*x^2 + 2*(125*d^8*e + 225*d^7*e^2 - 165*d^6*e^3 + 667*d^5*e^4 - 393*d^4*e^5 + 459*d^3*e^6 - 135*d^2*e^7 + 81*d*e^8)*x)","B",0
318,1,222,0,0.968158," ","integrate((e*x+d)^3*(4*x^4-5*x^3+3*x^2+x+2)/(5*x^2+2*x+3)^3,x, algorithm=""maxima"")","\frac{2}{125} \, e^{3} x^{2} + \frac{3}{68600000} \, \sqrt{14} {\left(353125 \, d^{3} - 855175 \, d^{2} e + 74085 \, d e^{2} + 556349 \, e^{3}\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) + \frac{1}{625} \, {\left(60 \, d e^{2} - 49 \, e^{3}\right)} x + \frac{3}{6250} \, {\left(100 \, d^{2} e - 245 \, d e^{2} + 47 \, e^{3}\right)} \log\left(5 \, x^{2} + 2 \, x + 3\right) + \frac{5 \, {\left(275375 \, d^{3} + 2726475 \, d^{2} e - 1941585 \, d e^{2} - 621801 \, e^{3}\right)} x^{3} + 1619125 \, d^{3} - 1464975 \, d^{2} e - 5773275 \, d e^{2} + 1275957 \, e^{3} + {\left(4844125 \, d^{3} + 2123025 \, d^{2} e - 16020675 \, d e^{2} + 1396037 \, e^{3}\right)} x^{2} + 3 \, {\left(749125 \, d^{3} + 1444025 \, d^{2} e - 3046875 \, d e^{2} - 170563 \, e^{3}\right)} x}{4900000 \, {\left(25 \, x^{4} + 20 \, x^{3} + 34 \, x^{2} + 12 \, x + 9\right)}}"," ",0,"2/125*e^3*x^2 + 3/68600000*sqrt(14)*(353125*d^3 - 855175*d^2*e + 74085*d*e^2 + 556349*e^3)*arctan(1/14*sqrt(14)*(5*x + 1)) + 1/625*(60*d*e^2 - 49*e^3)*x + 3/6250*(100*d^2*e - 245*d*e^2 + 47*e^3)*log(5*x^2 + 2*x + 3) + 1/4900000*(5*(275375*d^3 + 2726475*d^2*e - 1941585*d*e^2 - 621801*e^3)*x^3 + 1619125*d^3 - 1464975*d^2*e - 5773275*d*e^2 + 1275957*e^3 + (4844125*d^3 + 2123025*d^2*e - 16020675*d*e^2 + 1396037*e^3)*x^2 + 3*(749125*d^3 + 1444025*d^2*e - 3046875*d*e^2 - 170563*e^3)*x)/(25*x^4 + 20*x^3 + 34*x^2 + 12*x + 9)","A",0
319,1,155,0,0.960792," ","integrate((e*x+d)^2*(4*x^4-5*x^3+3*x^2+x+2)/(5*x^2+2*x+3)^3,x, algorithm=""maxima"")","\frac{4}{125} \, e^{2} x + \frac{1}{13720000} \, \sqrt{14} {\left(211875 \, d^{2} - 342070 \, d e + 14817 \, e^{2}\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) + \frac{1}{1250} \, {\left(40 \, d e - 49 \, e^{2}\right)} \log\left(5 \, x^{2} + 2 \, x + 3\right) + \frac{{\left(55075 \, d^{2} + 363530 \, d e - 129439 \, e^{2}\right)} x^{3} + {\left(193765 \, d^{2} + 56614 \, d e - 213609 \, e^{2}\right)} x^{2} + 64765 \, d^{2} - 39066 \, d e - 76977 \, e^{2} + {\left(89895 \, d^{2} + 115522 \, d e - 121875 \, e^{2}\right)} x}{196000 \, {\left(25 \, x^{4} + 20 \, x^{3} + 34 \, x^{2} + 12 \, x + 9\right)}}"," ",0,"4/125*e^2*x + 1/13720000*sqrt(14)*(211875*d^2 - 342070*d*e + 14817*e^2)*arctan(1/14*sqrt(14)*(5*x + 1)) + 1/1250*(40*d*e - 49*e^2)*log(5*x^2 + 2*x + 3) + 1/196000*((55075*d^2 + 363530*d*e - 129439*e^2)*x^3 + (193765*d^2 + 56614*d*e - 213609*e^2)*x^2 + 64765*d^2 - 39066*d*e - 76977*e^2 + (89895*d^2 + 115522*d*e - 121875*e^2)*x)/(25*x^4 + 20*x^3 + 34*x^2 + 12*x + 9)","A",0
320,1,101,0,0.955676," ","integrate((e*x+d)*(4*x^4-5*x^3+3*x^2+x+2)/(5*x^2+2*x+3)^3,x, algorithm=""maxima"")","\frac{1}{2744000} \, \sqrt{14} {\left(42375 \, d - 34207 \, e\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) + \frac{2}{125} \, e \log\left(5 \, x^{2} + 2 \, x + 3\right) + \frac{5 \, {\left(11015 \, d + 36353 \, e\right)} x^{3} + {\left(193765 \, d + 28307 \, e\right)} x^{2} + {\left(89895 \, d + 57761 \, e\right)} x + 64765 \, d - 19533 \, e}{196000 \, {\left(25 \, x^{4} + 20 \, x^{3} + 34 \, x^{2} + 12 \, x + 9\right)}}"," ",0,"1/2744000*sqrt(14)*(42375*d - 34207*e)*arctan(1/14*sqrt(14)*(5*x + 1)) + 2/125*e*log(5*x^2 + 2*x + 3) + 1/196000*(5*(11015*d + 36353*e)*x^3 + (193765*d + 28307*e)*x^2 + (89895*d + 57761*e)*x + 64765*d - 19533*e)/(25*x^4 + 20*x^3 + 34*x^2 + 12*x + 9)","A",0
321,1,56,0,0.958405," ","integrate((4*x^4-5*x^3+3*x^2+x+2)/(5*x^2+2*x+3)^3,x, algorithm=""maxima"")","\frac{339}{21952} \, \sqrt{14} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) + \frac{11015 \, x^{3} + 38753 \, x^{2} + 17979 \, x + 12953}{39200 \, {\left(25 \, x^{4} + 20 \, x^{3} + 34 \, x^{2} + 12 \, x + 9\right)}}"," ",0,"339/21952*sqrt(14)*arctan(1/14*sqrt(14)*(5*x + 1)) + 1/39200*(11015*x^3 + 38753*x^2 + 17979*x + 12953)/(25*x^4 + 20*x^3 + 34*x^2 + 12*x + 9)","A",0
322,1,571,0,1.030241," ","integrate((4*x^4-5*x^3+3*x^2+x+2)/(e*x+d)/(5*x^2+2*x+3)^3,x, algorithm=""maxima"")","\frac{\sqrt{14} {\left(42375 \, d^{5} - 16643 \, d^{4} e + 58530 \, d^{3} e^{2} - 56058 \, d^{2} e^{3} + 31811 \, d e^{4} - 8623 \, e^{5}\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right)}{21952 \, {\left(125 \, d^{6} - 150 \, d^{5} e + 285 \, d^{4} e^{2} - 188 \, d^{3} e^{3} + 171 \, d^{2} e^{4} - 54 \, d e^{5} + 27 \, e^{6}\right)}} + \frac{{\left(4 \, d^{4} e + 5 \, d^{3} e^{2} + 3 \, d^{2} e^{3} - d e^{4} + 2 \, e^{5}\right)} \log\left(e x + d\right)}{125 \, d^{6} - 150 \, d^{5} e + 285 \, d^{4} e^{2} - 188 \, d^{3} e^{3} + 171 \, d^{2} e^{4} - 54 \, d e^{5} + 27 \, e^{6}} - \frac{{\left(4 \, d^{4} e + 5 \, d^{3} e^{2} + 3 \, d^{2} e^{3} - d e^{4} + 2 \, e^{5}\right)} \log\left(5 \, x^{2} + 2 \, x + 3\right)}{2 \, {\left(125 \, d^{6} - 150 \, d^{5} e + 285 \, d^{4} e^{2} - 188 \, d^{3} e^{3} + 171 \, d^{2} e^{4} - 54 \, d e^{5} + 27 \, e^{6}\right)}} + \frac{25 \, {\left(2203 \, d^{3} - 9033 \, d^{2} e + 3635 \, d e^{2} - 1829 \, e^{3}\right)} x^{3} + 64765 \, d^{3} - 32279 \, d^{2} e - 4523 \, d e^{2} + 6021 \, e^{3} + {\left(193765 \, d^{3} - 183319 \, d^{2} e + 72557 \, d e^{2} - 16459 \, e^{3}\right)} x^{2} + {\left(89895 \, d^{3} - 129677 \, d^{2} e + 46591 \, d e^{2} - 3737 \, e^{3}\right)} x}{7840 \, {\left(25 \, {\left(25 \, d^{4} - 20 \, d^{3} e + 34 \, d^{2} e^{2} - 12 \, d e^{3} + 9 \, e^{4}\right)} x^{4} + 225 \, d^{4} - 180 \, d^{3} e + 306 \, d^{2} e^{2} - 108 \, d e^{3} + 81 \, e^{4} + 20 \, {\left(25 \, d^{4} - 20 \, d^{3} e + 34 \, d^{2} e^{2} - 12 \, d e^{3} + 9 \, e^{4}\right)} x^{3} + 34 \, {\left(25 \, d^{4} - 20 \, d^{3} e + 34 \, d^{2} e^{2} - 12 \, d e^{3} + 9 \, e^{4}\right)} x^{2} + 12 \, {\left(25 \, d^{4} - 20 \, d^{3} e + 34 \, d^{2} e^{2} - 12 \, d e^{3} + 9 \, e^{4}\right)} x\right)}}"," ",0,"1/21952*sqrt(14)*(42375*d^5 - 16643*d^4*e + 58530*d^3*e^2 - 56058*d^2*e^3 + 31811*d*e^4 - 8623*e^5)*arctan(1/14*sqrt(14)*(5*x + 1))/(125*d^6 - 150*d^5*e + 285*d^4*e^2 - 188*d^3*e^3 + 171*d^2*e^4 - 54*d*e^5 + 27*e^6) + (4*d^4*e + 5*d^3*e^2 + 3*d^2*e^3 - d*e^4 + 2*e^5)*log(e*x + d)/(125*d^6 - 150*d^5*e + 285*d^4*e^2 - 188*d^3*e^3 + 171*d^2*e^4 - 54*d*e^5 + 27*e^6) - 1/2*(4*d^4*e + 5*d^3*e^2 + 3*d^2*e^3 - d*e^4 + 2*e^5)*log(5*x^2 + 2*x + 3)/(125*d^6 - 150*d^5*e + 285*d^4*e^2 - 188*d^3*e^3 + 171*d^2*e^4 - 54*d*e^5 + 27*e^6) + 1/7840*(25*(2203*d^3 - 9033*d^2*e + 3635*d*e^2 - 1829*e^3)*x^3 + 64765*d^3 - 32279*d^2*e - 4523*d*e^2 + 6021*e^3 + (193765*d^3 - 183319*d^2*e + 72557*d*e^2 - 16459*e^3)*x^2 + (89895*d^3 - 129677*d^2*e + 46591*d*e^2 - 3737*e^3)*x)/(25*(25*d^4 - 20*d^3*e + 34*d^2*e^2 - 12*d*e^3 + 9*e^4)*x^4 + 225*d^4 - 180*d^3*e + 306*d^2*e^2 - 108*d*e^3 + 81*e^4 + 20*(25*d^4 - 20*d^3*e + 34*d^2*e^2 - 12*d*e^3 + 9*e^4)*x^3 + 34*(25*d^4 - 20*d^3*e + 34*d^2*e^2 - 12*d*e^3 + 9*e^4)*x^2 + 12*(25*d^4 - 20*d^3*e + 34*d^2*e^2 - 12*d*e^3 + 9*e^4)*x)","A",0
323,1,916,0,1.133956," ","integrate((4*x^4-5*x^3+3*x^2+x+2)/(e*x+d)^2/(5*x^2+2*x+3)^3,x, algorithm=""maxima"")","\frac{\sqrt{14} {\left(211875 \, d^{6} + 3070 \, d^{5} e + 209039 \, d^{4} e^{2} - 921444 \, d^{3} e^{3} + 380621 \, d^{2} e^{4} - 49586 \, d e^{5} - 43695 \, e^{6}\right)} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right)}{21952 \, {\left(625 \, d^{8} - 1000 \, d^{7} e + 2100 \, d^{6} e^{2} - 1960 \, d^{5} e^{3} + 2086 \, d^{4} e^{4} - 1176 \, d^{3} e^{5} + 756 \, d^{2} e^{6} - 216 \, d e^{7} + 81 \, e^{8}\right)}} + \frac{{\left(40 \, d^{5} e + 83 \, d^{4} e^{2} + 12 \, d^{3} e^{3} - 76 \, d^{2} e^{4} + 46 \, d e^{5} - 9 \, e^{6}\right)} \log\left(e x + d\right)}{625 \, d^{8} - 1000 \, d^{7} e + 2100 \, d^{6} e^{2} - 1960 \, d^{5} e^{3} + 2086 \, d^{4} e^{4} - 1176 \, d^{3} e^{5} + 756 \, d^{2} e^{6} - 216 \, d e^{7} + 81 \, e^{8}} - \frac{{\left(40 \, d^{5} e + 83 \, d^{4} e^{2} + 12 \, d^{3} e^{3} - 76 \, d^{2} e^{4} + 46 \, d e^{5} - 9 \, e^{6}\right)} \log\left(5 \, x^{2} + 2 \, x + 3\right)}{2 \, {\left(625 \, d^{8} - 1000 \, d^{7} e + 2100 \, d^{6} e^{2} - 1960 \, d^{5} e^{3} + 2086 \, d^{4} e^{4} - 1176 \, d^{3} e^{5} + 756 \, d^{2} e^{6} - 216 \, d e^{7} + 81 \, e^{8}\right)}} + \frac{64765 \, d^{5} - 95100 \, d^{4} e - 200706 \, d^{3} e^{2} + 22292 \, d^{2} e^{3} + 12009 \, d e^{4} - 28224 \, e^{5} - 5 \, {\left(20345 \, d^{4} e + 125124 \, d^{3} e^{2} - 11178 \, d^{2} e^{3} - 18188 \, d e^{4} + 19269 \, e^{5}\right)} x^{4} + {\left(55075 \, d^{5} - 361295 \, d^{4} e - 272442 \, d^{3} e^{2} - 173446 \, d^{2} e^{3} + 138539 \, d e^{4} - 93087 \, e^{5}\right)} x^{3} + {\left(193765 \, d^{5} - 412485 \, d^{4} e - 621062 \, d^{3} e^{2} - 56850 \, d^{2} e^{3} + 144973 \, d e^{4} - 131589 \, e^{5}\right)} x^{2} + 3 \, {\left(29965 \, d^{5} - 77965 \, d^{4} e - 51590 \, d^{3} e^{2} - 21522 \, d^{2} e^{3} + 19493 \, d e^{4} - 13245 \, e^{5}\right)} x}{1568 \, {\left(1125 \, d^{7} - 1350 \, d^{6} e + 2565 \, d^{5} e^{2} - 1692 \, d^{4} e^{3} + 1539 \, d^{3} e^{4} - 486 \, d^{2} e^{5} + 243 \, d e^{6} + 25 \, {\left(125 \, d^{6} e - 150 \, d^{5} e^{2} + 285 \, d^{4} e^{3} - 188 \, d^{3} e^{4} + 171 \, d^{2} e^{5} - 54 \, d e^{6} + 27 \, e^{7}\right)} x^{5} + 5 \, {\left(625 \, d^{7} - 250 \, d^{6} e + 825 \, d^{5} e^{2} + 200 \, d^{4} e^{3} + 103 \, d^{3} e^{4} + 414 \, d^{2} e^{5} - 81 \, d e^{6} + 108 \, e^{7}\right)} x^{4} + 2 \, {\left(1250 \, d^{7} + 625 \, d^{6} e + 300 \, d^{5} e^{2} + 2965 \, d^{4} e^{3} - 1486 \, d^{3} e^{4} + 2367 \, d^{2} e^{5} - 648 \, d e^{6} + 459 \, e^{7}\right)} x^{3} + 2 \, {\left(2125 \, d^{7} - 1800 \, d^{6} e + 3945 \, d^{5} e^{2} - 1486 \, d^{4} e^{3} + 1779 \, d^{3} e^{4} + 108 \, d^{2} e^{5} + 135 \, d e^{6} + 162 \, e^{7}\right)} x^{2} + 3 \, {\left(500 \, d^{7} - 225 \, d^{6} e + 690 \, d^{5} e^{2} + 103 \, d^{4} e^{3} + 120 \, d^{3} e^{4} + 297 \, d^{2} e^{5} - 54 \, d e^{6} + 81 \, e^{7}\right)} x\right)}}"," ",0,"1/21952*sqrt(14)*(211875*d^6 + 3070*d^5*e + 209039*d^4*e^2 - 921444*d^3*e^3 + 380621*d^2*e^4 - 49586*d*e^5 - 43695*e^6)*arctan(1/14*sqrt(14)*(5*x + 1))/(625*d^8 - 1000*d^7*e + 2100*d^6*e^2 - 1960*d^5*e^3 + 2086*d^4*e^4 - 1176*d^3*e^5 + 756*d^2*e^6 - 216*d*e^7 + 81*e^8) + (40*d^5*e + 83*d^4*e^2 + 12*d^3*e^3 - 76*d^2*e^4 + 46*d*e^5 - 9*e^6)*log(e*x + d)/(625*d^8 - 1000*d^7*e + 2100*d^6*e^2 - 1960*d^5*e^3 + 2086*d^4*e^4 - 1176*d^3*e^5 + 756*d^2*e^6 - 216*d*e^7 + 81*e^8) - 1/2*(40*d^5*e + 83*d^4*e^2 + 12*d^3*e^3 - 76*d^2*e^4 + 46*d*e^5 - 9*e^6)*log(5*x^2 + 2*x + 3)/(625*d^8 - 1000*d^7*e + 2100*d^6*e^2 - 1960*d^5*e^3 + 2086*d^4*e^4 - 1176*d^3*e^5 + 756*d^2*e^6 - 216*d*e^7 + 81*e^8) + 1/1568*(64765*d^5 - 95100*d^4*e - 200706*d^3*e^2 + 22292*d^2*e^3 + 12009*d*e^4 - 28224*e^5 - 5*(20345*d^4*e + 125124*d^3*e^2 - 11178*d^2*e^3 - 18188*d*e^4 + 19269*e^5)*x^4 + (55075*d^5 - 361295*d^4*e - 272442*d^3*e^2 - 173446*d^2*e^3 + 138539*d*e^4 - 93087*e^5)*x^3 + (193765*d^5 - 412485*d^4*e - 621062*d^3*e^2 - 56850*d^2*e^3 + 144973*d*e^4 - 131589*e^5)*x^2 + 3*(29965*d^5 - 77965*d^4*e - 51590*d^3*e^2 - 21522*d^2*e^3 + 19493*d*e^4 - 13245*e^5)*x)/(1125*d^7 - 1350*d^6*e + 2565*d^5*e^2 - 1692*d^4*e^3 + 1539*d^3*e^4 - 486*d^2*e^5 + 243*d*e^6 + 25*(125*d^6*e - 150*d^5*e^2 + 285*d^4*e^3 - 188*d^3*e^4 + 171*d^2*e^5 - 54*d*e^6 + 27*e^7)*x^5 + 5*(625*d^7 - 250*d^6*e + 825*d^5*e^2 + 200*d^4*e^3 + 103*d^3*e^4 + 414*d^2*e^5 - 81*d*e^6 + 108*e^7)*x^4 + 2*(1250*d^7 + 625*d^6*e + 300*d^5*e^2 + 2965*d^4*e^3 - 1486*d^3*e^4 + 2367*d^2*e^5 - 648*d*e^6 + 459*e^7)*x^3 + 2*(2125*d^7 - 1800*d^6*e + 3945*d^5*e^2 - 1486*d^4*e^3 + 1779*d^3*e^4 + 108*d^2*e^5 + 135*d*e^6 + 162*e^7)*x^2 + 3*(500*d^7 - 225*d^6*e + 690*d^5*e^2 + 103*d^4*e^3 + 120*d^3*e^4 + 297*d^2*e^5 - 54*d*e^6 + 81*e^7)*x)","B",0
324,1,126,0,0.965493," ","integrate((5+2*x)*(5*x^4-x^3+3*x^2+x+2)*(2*x^2-x+3)^(1/2),x, algorithm=""maxima"")","\frac{5}{7} \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}} x^{4} + \frac{377}{168} \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}} x^{3} + \frac{283}{1120} \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}} x^{2} - \frac{5179}{17920} \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}} x + \frac{242329}{215040} \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}} + \frac{51435}{8192} \, \sqrt{2 \, x^{2} - x + 3} x + \frac{1183005}{131072} \, \sqrt{2} \operatorname{arsinh}\left(\frac{1}{23} \, \sqrt{23} {\left(4 \, x - 1\right)}\right) - \frac{51435}{32768} \, \sqrt{2 \, x^{2} - x + 3}"," ",0,"5/7*(2*x^2 - x + 3)^(3/2)*x^4 + 377/168*(2*x^2 - x + 3)^(3/2)*x^3 + 283/1120*(2*x^2 - x + 3)^(3/2)*x^2 - 5179/17920*(2*x^2 - x + 3)^(3/2)*x + 242329/215040*(2*x^2 - x + 3)^(3/2) + 51435/8192*sqrt(2*x^2 - x + 3)*x + 1183005/131072*sqrt(2)*arcsinh(1/23*sqrt(23)*(4*x - 1)) - 51435/32768*sqrt(2*x^2 - x + 3)","A",0
325,1,109,0,0.954221," ","integrate((5*x^4-x^3+3*x^2+x+2)*(2*x^2-x+3)^(1/2),x, algorithm=""maxima"")","\frac{5}{12} \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}} x^{3} + \frac{7}{80} \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}} x^{2} - \frac{71}{1280} \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}} x + \frac{287}{5120} \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}} + \frac{4609}{4096} \, \sqrt{2 \, x^{2} - x + 3} x + \frac{106007}{65536} \, \sqrt{2} \operatorname{arsinh}\left(\frac{1}{23} \, \sqrt{23} {\left(4 \, x - 1\right)}\right) - \frac{4609}{16384} \, \sqrt{2 \, x^{2} - x + 3}"," ",0,"5/12*(2*x^2 - x + 3)^(3/2)*x^3 + 7/80*(2*x^2 - x + 3)^(3/2)*x^2 - 71/1280*(2*x^2 - x + 3)^(3/2)*x + 287/5120*(2*x^2 - x + 3)^(3/2) + 4609/4096*sqrt(2*x^2 - x + 3)*x + 106007/65536*sqrt(2)*arcsinh(1/23*sqrt(23)*(4*x - 1)) - 4609/16384*sqrt(2*x^2 - x + 3)","A",0
326,1,128,0,1.005872," ","integrate((5*x^4-x^3+3*x^2+x+2)*(2*x^2-x+3)^(1/2)/(5+2*x),x, algorithm=""maxima"")","\frac{1}{4} \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}} x^{2} - \frac{47}{64} \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}} x + \frac{1925}{768} \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}} - \frac{20211}{1024} \, \sqrt{2 \, x^{2} - x + 3} x - \frac{5627989}{16384} \, \sqrt{2} \operatorname{arsinh}\left(\frac{4}{23} \, \sqrt{23} x - \frac{1}{23} \, \sqrt{23}\right) + \frac{11001}{32} \, \sqrt{2} \operatorname{arsinh}\left(\frac{22 \, \sqrt{23} x}{23 \, {\left| 2 \, x + 5 \right|}} - \frac{17 \, \sqrt{23}}{23 \, {\left| 2 \, x + 5 \right|}}\right) + \frac{489587}{4096} \, \sqrt{2 \, x^{2} - x + 3}"," ",0,"1/4*(2*x^2 - x + 3)^(3/2)*x^2 - 47/64*(2*x^2 - x + 3)^(3/2)*x + 1925/768*(2*x^2 - x + 3)^(3/2) - 20211/1024*sqrt(2*x^2 - x + 3)*x - 5627989/16384*sqrt(2)*arcsinh(4/23*sqrt(23)*x - 1/23*sqrt(23)) + 11001/32*sqrt(2)*arcsinh(22/23*sqrt(23)*x/abs(2*x + 5) - 17/23*sqrt(23)/abs(2*x + 5)) + 489587/4096*sqrt(2*x^2 - x + 3)","A",0
327,1,132,0,1.002515," ","integrate((5*x^4-x^3+3*x^2+x+2)*(2*x^2-x+3)^(1/2)/(5+2*x)^2,x, algorithm=""maxima"")","\frac{5}{32} \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}} x - \frac{391}{384} \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}} + \frac{6001}{512} \, \sqrt{2 \, x^{2} - x + 3} x + \frac{2551847}{8192} \, \sqrt{2} \operatorname{arsinh}\left(\frac{4}{23} \, \sqrt{23} x - \frac{1}{23} \, \sqrt{23}\right) - \frac{239201}{768} \, \sqrt{2} \operatorname{arsinh}\left(\frac{22 \, \sqrt{23} x}{23 \, {\left| 2 \, x + 5 \right|}} - \frac{17 \, \sqrt{23}}{23 \, {\left| 2 \, x + 5 \right|}}\right) - \frac{182769}{2048} \, \sqrt{2 \, x^{2} - x + 3} - \frac{3667 \, \sqrt{2 \, x^{2} - x + 3}}{32 \, {\left(2 \, x + 5\right)}}"," ",0,"5/32*(2*x^2 - x + 3)^(3/2)*x - 391/384*(2*x^2 - x + 3)^(3/2) + 6001/512*sqrt(2*x^2 - x + 3)*x + 2551847/8192*sqrt(2)*arcsinh(4/23*sqrt(23)*x - 1/23*sqrt(23)) - 239201/768*sqrt(2)*arcsinh(22/23*sqrt(23)*x/abs(2*x + 5) - 17/23*sqrt(23)/abs(2*x + 5)) - 182769/2048*sqrt(2*x^2 - x + 3) - 3667/32*sqrt(2*x^2 - x + 3)/(2*x + 5)","A",0
328,1,143,0,1.001983," ","integrate((5*x^4-x^3+3*x^2+x+2)*(2*x^2-x+3)^(1/2)/(5+2*x)^3,x, algorithm=""maxima"")","\frac{5}{48} \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}} - \frac{149}{64} \, \sqrt{2 \, x^{2} - x + 3} x - \frac{117315}{1024} \, \sqrt{2} \operatorname{arsinh}\left(\frac{4}{23} \, \sqrt{23} x - \frac{1}{23} \, \sqrt{23}\right) + \frac{12670805}{110592} \, \sqrt{2} \operatorname{arsinh}\left(\frac{22 \, \sqrt{23} x}{23 \, {\left| 2 \, x + 5 \right|}} - \frac{17 \, \sqrt{23}}{23 \, {\left| 2 \, x + 5 \right|}}\right) + \frac{3877}{144} \, \sqrt{2 \, x^{2} - x + 3} - \frac{3667 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}}{1152 \, {\left(4 \, x^{2} + 20 \, x + 25\right)}} + \frac{357391 \, \sqrt{2 \, x^{2} - x + 3}}{4608 \, {\left(2 \, x + 5\right)}}"," ",0,"5/48*(2*x^2 - x + 3)^(3/2) - 149/64*sqrt(2*x^2 - x + 3)*x - 117315/1024*sqrt(2)*arcsinh(4/23*sqrt(23)*x - 1/23*sqrt(23)) + 12670805/110592*sqrt(2)*arcsinh(22/23*sqrt(23)*x/abs(2*x + 5) - 17/23*sqrt(23)/abs(2*x + 5)) + 3877/144*sqrt(2*x^2 - x + 3) - 3667/1152*(2*x^2 - x + 3)^(3/2)/(4*x^2 + 20*x + 25) + 357391/4608*sqrt(2*x^2 - x + 3)/(2*x + 5)","A",0
329,1,160,0,0.980408," ","integrate((5*x^4-x^3+3*x^2+x+2)*(2*x^2-x+3)^(1/2)/(5+2*x)^4,x, algorithm=""maxima"")","\frac{5}{32} \, \sqrt{2 \, x^{2} - x + 3} x + \frac{10939}{512} \, \sqrt{2} \operatorname{arsinh}\left(\frac{4}{23} \, \sqrt{23} x - \frac{1}{23} \, \sqrt{23}\right) - \frac{170114729}{7962624} \, \sqrt{2} \operatorname{arsinh}\left(\frac{22 \, \sqrt{23} x}{23 \, {\left| 2 \, x + 5 \right|}} - \frac{17 \, \sqrt{23}}{23 \, {\left| 2 \, x + 5 \right|}}\right) - \frac{693775}{165888} \, \sqrt{2 \, x^{2} - x + 3} - \frac{3667 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}}{1728 \, {\left(8 \, x^{3} + 60 \, x^{2} + 150 \, x + 125\right)}} + \frac{158527 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}}{82944 \, {\left(4 \, x^{2} + 20 \, x + 25\right)}} - \frac{6467659 \, \sqrt{2 \, x^{2} - x + 3}}{331776 \, {\left(2 \, x + 5\right)}}"," ",0,"5/32*sqrt(2*x^2 - x + 3)*x + 10939/512*sqrt(2)*arcsinh(4/23*sqrt(23)*x - 1/23*sqrt(23)) - 170114729/7962624*sqrt(2)*arcsinh(22/23*sqrt(23)*x/abs(2*x + 5) - 17/23*sqrt(23)/abs(2*x + 5)) - 693775/165888*sqrt(2*x^2 - x + 3) - 3667/1728*(2*x^2 - x + 3)^(3/2)/(8*x^3 + 60*x^2 + 150*x + 125) + 158527/82944*(2*x^2 - x + 3)^(3/2)/(4*x^2 + 20*x + 25) - 6467659/331776*sqrt(2*x^2 - x + 3)/(2*x + 5)","A",0
330,1,181,0,1.022089," ","integrate((5*x^4-x^3+3*x^2+x+2)*(2*x^2-x+3)^(1/2)/(5+2*x)^5,x, algorithm=""maxima"")","-\frac{259}{128} \, \sqrt{2} \operatorname{arsinh}\left(\frac{4}{23} \, \sqrt{23} x - \frac{1}{23} \, \sqrt{23}\right) + \frac{4640586097}{2293235712} \, \sqrt{2} \operatorname{arsinh}\left(\frac{22 \, \sqrt{23} x}{23 \, {\left| 2 \, x + 5 \right|}} - \frac{17 \, \sqrt{23}}{23 \, {\left| 2 \, x + 5 \right|}}\right) + \frac{16828343}{47775744} \, \sqrt{2 \, x^{2} - x + 3} - \frac{3667 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}}{2304 \, {\left(16 \, x^{4} + 160 \, x^{3} + 600 \, x^{2} + 1000 \, x + 625\right)}} + \frac{593771 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}}{497664 \, {\left(8 \, x^{3} + 60 \, x^{2} + 150 \, x + 125\right)}} - \frac{9363383 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}}{23887872 \, {\left(4 \, x^{2} + 20 \, x + 25\right)}} + \frac{201573155 \, \sqrt{2 \, x^{2} - x + 3}}{95551488 \, {\left(2 \, x + 5\right)}}"," ",0,"-259/128*sqrt(2)*arcsinh(4/23*sqrt(23)*x - 1/23*sqrt(23)) + 4640586097/2293235712*sqrt(2)*arcsinh(22/23*sqrt(23)*x/abs(2*x + 5) - 17/23*sqrt(23)/abs(2*x + 5)) + 16828343/47775744*sqrt(2*x^2 - x + 3) - 3667/2304*(2*x^2 - x + 3)^(3/2)/(16*x^4 + 160*x^3 + 600*x^2 + 1000*x + 625) + 593771/497664*(2*x^2 - x + 3)^(3/2)/(8*x^3 + 60*x^2 + 150*x + 125) - 9363383/23887872*(2*x^2 - x + 3)^(3/2)/(4*x^2 + 20*x + 25) + 201573155/95551488*sqrt(2*x^2 - x + 3)/(2*x + 5)","A",0
331,1,222,0,1.043539," ","integrate((5*x^4-x^3+3*x^2+x+2)*(2*x^2-x+3)^(1/2)/(5+2*x)^6,x, algorithm=""maxima"")","\frac{5}{64} \, \sqrt{2} \operatorname{arsinh}\left(\frac{4}{23} \, \sqrt{23} x - \frac{1}{23} \, \sqrt{23}\right) - \frac{12895597463}{165112971264} \, \sqrt{2} \operatorname{arsinh}\left(\frac{22 \, \sqrt{23} x}{23 \, {\left| 2 \, x + 5 \right|}} - \frac{17 \, \sqrt{23}}{23 \, {\left| 2 \, x + 5 \right|}}\right) - \frac{46569601}{3439853568} \, \sqrt{2 \, x^{2} - x + 3} - \frac{3667 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}}{2880 \, {\left(32 \, x^{5} + 400 \, x^{4} + 2000 \, x^{3} + 5000 \, x^{2} + 6250 \, x + 3125\right)}} + \frac{711961 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}}{829440 \, {\left(16 \, x^{4} + 160 \, x^{3} + 600 \, x^{2} + 1000 \, x + 625\right)}} - \frac{38732321 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}}{179159040 \, {\left(8 \, x^{3} + 60 \, x^{2} + 150 \, x + 125\right)}} + \frac{46569601 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}}{1719926784 \, {\left(4 \, x^{2} + 20 \, x + 25\right)}} - \frac{562688629 \, \sqrt{2 \, x^{2} - x + 3}}{6879707136 \, {\left(2 \, x + 5\right)}}"," ",0,"5/64*sqrt(2)*arcsinh(4/23*sqrt(23)*x - 1/23*sqrt(23)) - 12895597463/165112971264*sqrt(2)*arcsinh(22/23*sqrt(23)*x/abs(2*x + 5) - 17/23*sqrt(23)/abs(2*x + 5)) - 46569601/3439853568*sqrt(2*x^2 - x + 3) - 3667/2880*(2*x^2 - x + 3)^(3/2)/(32*x^5 + 400*x^4 + 2000*x^3 + 5000*x^2 + 6250*x + 3125) + 711961/829440*(2*x^2 - x + 3)^(3/2)/(16*x^4 + 160*x^3 + 600*x^2 + 1000*x + 625) - 38732321/179159040*(2*x^2 - x + 3)^(3/2)/(8*x^3 + 60*x^2 + 150*x + 125) + 46569601/1719926784*(2*x^2 - x + 3)^(3/2)/(4*x^2 + 20*x + 25) - 562688629/6879707136*sqrt(2*x^2 - x + 3)/(2*x + 5)","A",0
332,1,250,0,1.049741," ","integrate((5*x^4-x^3+3*x^2+x+2)*(2*x^2-x+3)^(1/2)/(5+2*x)^7,x, algorithm=""maxima"")","\frac{26972675}{7925422620672} \, \sqrt{2} \operatorname{arsinh}\left(\frac{22 \, \sqrt{23} x}{23 \, {\left| 2 \, x + 5 \right|}} - \frac{17 \, \sqrt{23}}{23 \, {\left| 2 \, x + 5 \right|}}\right) + \frac{1172725}{165112971264} \, \sqrt{2 \, x^{2} - x + 3} - \frac{3667 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}}{3456 \, {\left(64 \, x^{6} + 960 \, x^{5} + 6000 \, x^{4} + 20000 \, x^{3} + 37500 \, x^{2} + 37500 \, x + 15625\right)}} + \frac{92239 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}}{138240 \, {\left(32 \, x^{5} + 400 \, x^{4} + 2000 \, x^{3} + 5000 \, x^{2} + 6250 \, x + 3125\right)}} - \frac{5703277 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}}{39813120 \, {\left(16 \, x^{4} + 160 \, x^{3} + 600 \, x^{2} + 1000 \, x + 625\right)}} + \frac{87677717 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}}{8599633920 \, {\left(8 \, x^{3} + 60 \, x^{2} + 150 \, x + 125\right)}} - \frac{1172725 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}}{82556485632 \, {\left(4 \, x^{2} + 20 \, x + 25\right)}} - \frac{12899975 \, \sqrt{2 \, x^{2} - x + 3}}{330225942528 \, {\left(2 \, x + 5\right)}}"," ",0,"26972675/7925422620672*sqrt(2)*arcsinh(22/23*sqrt(23)*x/abs(2*x + 5) - 17/23*sqrt(23)/abs(2*x + 5)) + 1172725/165112971264*sqrt(2*x^2 - x + 3) - 3667/3456*(2*x^2 - x + 3)^(3/2)/(64*x^6 + 960*x^5 + 6000*x^4 + 20000*x^3 + 37500*x^2 + 37500*x + 15625) + 92239/138240*(2*x^2 - x + 3)^(3/2)/(32*x^5 + 400*x^4 + 2000*x^3 + 5000*x^2 + 6250*x + 3125) - 5703277/39813120*(2*x^2 - x + 3)^(3/2)/(16*x^4 + 160*x^3 + 600*x^2 + 1000*x + 625) + 87677717/8599633920*(2*x^2 - x + 3)^(3/2)/(8*x^3 + 60*x^2 + 150*x + 125) - 1172725/82556485632*(2*x^2 - x + 3)^(3/2)/(4*x^2 + 20*x + 25) - 12899975/330225942528*sqrt(2*x^2 - x + 3)/(2*x + 5)","A",0
333,1,301,0,1.038562," ","integrate((5*x^4-x^3+3*x^2+x+2)*(2*x^2-x+3)^(1/2)/(5+2*x)^8,x, algorithm=""maxima"")","\frac{289071245}{570630428688384} \, \sqrt{2} \operatorname{arsinh}\left(\frac{22 \, \sqrt{23} x}{23 \, {\left| 2 \, x + 5 \right|}} - \frac{17 \, \sqrt{23}}{23 \, {\left| 2 \, x + 5 \right|}}\right) + \frac{12568315}{11888133931008} \, \sqrt{2 \, x^{2} - x + 3} - \frac{3667 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}}{4032 \, {\left(128 \, x^{7} + 2240 \, x^{6} + 16800 \, x^{5} + 70000 \, x^{4} + 175000 \, x^{3} + 262500 \, x^{2} + 218750 \, x + 78125\right)}} + \frac{948341 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}}{1741824 \, {\left(64 \, x^{6} + 960 \, x^{5} + 6000 \, x^{4} + 20000 \, x^{3} + 37500 \, x^{2} + 37500 \, x + 15625\right)}} - \frac{1464037 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}}{13934592 \, {\left(32 \, x^{5} + 400 \, x^{4} + 2000 \, x^{3} + 5000 \, x^{2} + 6250 \, x + 3125\right)}} + \frac{19414831 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}}{4013162496 \, {\left(16 \, x^{4} + 160 \, x^{3} + 600 \, x^{2} + 1000 \, x + 625\right)}} + \frac{246159769 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}}{866843099136 \, {\left(8 \, x^{3} + 60 \, x^{2} + 150 \, x + 125\right)}} - \frac{12568315 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}}{5944066965504 \, {\left(4 \, x^{2} + 20 \, x + 25\right)}} - \frac{138251465 \, \sqrt{2 \, x^{2} - x + 3}}{23776267862016 \, {\left(2 \, x + 5\right)}}"," ",0,"289071245/570630428688384*sqrt(2)*arcsinh(22/23*sqrt(23)*x/abs(2*x + 5) - 17/23*sqrt(23)/abs(2*x + 5)) + 12568315/11888133931008*sqrt(2*x^2 - x + 3) - 3667/4032*(2*x^2 - x + 3)^(3/2)/(128*x^7 + 2240*x^6 + 16800*x^5 + 70000*x^4 + 175000*x^3 + 262500*x^2 + 218750*x + 78125) + 948341/1741824*(2*x^2 - x + 3)^(3/2)/(64*x^6 + 960*x^5 + 6000*x^4 + 20000*x^3 + 37500*x^2 + 37500*x + 15625) - 1464037/13934592*(2*x^2 - x + 3)^(3/2)/(32*x^5 + 400*x^4 + 2000*x^3 + 5000*x^2 + 6250*x + 3125) + 19414831/4013162496*(2*x^2 - x + 3)^(3/2)/(16*x^4 + 160*x^3 + 600*x^2 + 1000*x + 625) + 246159769/866843099136*(2*x^2 - x + 3)^(3/2)/(8*x^3 + 60*x^2 + 150*x + 125) - 12568315/5944066965504*(2*x^2 - x + 3)^(3/2)/(4*x^2 + 20*x + 25) - 138251465/23776267862016*sqrt(2*x^2 - x + 3)/(2*x + 5)","A",0
334,1,155,0,0.976757," ","integrate((5+2*x)*(2*x^2-x+3)^(3/2)*(5*x^4-x^3+3*x^2+x+2),x, algorithm=""maxima"")","\frac{5}{9} \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{5}{2}} x^{4} + \frac{479}{288} \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{5}{2}} x^{3} + \frac{2005}{8064} \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{5}{2}} x^{2} + \frac{5645}{21504} \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{5}{2}} x + \frac{120809}{143360} \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{5}{2}} + \frac{92727}{32768} \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}} x - \frac{92727}{131072} \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}} + \frac{6398163}{524288} \, \sqrt{2 \, x^{2} - x + 3} x + \frac{147157749}{8388608} \, \sqrt{2} \operatorname{arsinh}\left(\frac{1}{23} \, \sqrt{23} {\left(4 \, x - 1\right)}\right) - \frac{6398163}{2097152} \, \sqrt{2 \, x^{2} - x + 3}"," ",0,"5/9*(2*x^2 - x + 3)^(5/2)*x^4 + 479/288*(2*x^2 - x + 3)^(5/2)*x^3 + 2005/8064*(2*x^2 - x + 3)^(5/2)*x^2 + 5645/21504*(2*x^2 - x + 3)^(5/2)*x + 120809/143360*(2*x^2 - x + 3)^(5/2) + 92727/32768*(2*x^2 - x + 3)^(3/2)*x - 92727/131072*(2*x^2 - x + 3)^(3/2) + 6398163/524288*sqrt(2*x^2 - x + 3)*x + 147157749/8388608*sqrt(2)*arcsinh(1/23*sqrt(23)*(4*x - 1)) - 6398163/2097152*sqrt(2*x^2 - x + 3)","A",0
335,1,138,0,1.003008," ","integrate((2*x^2-x+3)^(3/2)*(5*x^4-x^3+3*x^2+x+2),x, algorithm=""maxima"")","\frac{5}{16} \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{5}{2}} x^{3} + \frac{23}{448} \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{5}{2}} x^{2} + \frac{125}{3584} \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{5}{2}} x + \frac{1167}{14336} \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{5}{2}} + \frac{8597}{16384} \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}} x - \frac{8597}{65536} \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}} + \frac{593193}{262144} \, \sqrt{2 \, x^{2} - x + 3} x + \frac{13643439}{4194304} \, \sqrt{2} \operatorname{arsinh}\left(\frac{1}{23} \, \sqrt{23} {\left(4 \, x - 1\right)}\right) - \frac{593193}{1048576} \, \sqrt{2 \, x^{2} - x + 3}"," ",0,"5/16*(2*x^2 - x + 3)^(5/2)*x^3 + 23/448*(2*x^2 - x + 3)^(5/2)*x^2 + 125/3584*(2*x^2 - x + 3)^(5/2)*x + 1167/14336*(2*x^2 - x + 3)^(5/2) + 8597/16384*(2*x^2 - x + 3)^(3/2)*x - 8597/65536*(2*x^2 - x + 3)^(3/2) + 593193/262144*sqrt(2*x^2 - x + 3)*x + 13643439/4194304*sqrt(2)*arcsinh(1/23*sqrt(23)*(4*x - 1)) - 593193/1048576*sqrt(2*x^2 - x + 3)","A",0
336,1,157,0,1.002059," ","integrate((2*x^2-x+3)^(3/2)*(5*x^4-x^3+3*x^2+x+2)/(5+2*x),x, algorithm=""maxima"")","\frac{5}{28} \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{5}{2}} x^{2} - \frac{111}{224} \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{5}{2}} x + \frac{1395}{896} \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{5}{2}} - \frac{10255}{1024} \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}} x + \frac{500141}{12288} \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}} - \frac{5870731}{16384} \, \sqrt{2 \, x^{2} - x + 3} x - \frac{1622009981}{262144} \, \sqrt{2} \operatorname{arsinh}\left(\frac{4}{23} \, \sqrt{23} x - \frac{1}{23} \, \sqrt{23}\right) + \frac{99009}{16} \, \sqrt{2} \operatorname{arsinh}\left(\frac{22 \, \sqrt{23} x}{23 \, {\left| 2 \, x + 5 \right|}} - \frac{17 \, \sqrt{23}}{23 \, {\left| 2 \, x + 5 \right|}}\right) + \frac{141051019}{65536} \, \sqrt{2 \, x^{2} - x + 3}"," ",0,"5/28*(2*x^2 - x + 3)^(5/2)*x^2 - 111/224*(2*x^2 - x + 3)^(5/2)*x + 1395/896*(2*x^2 - x + 3)^(5/2) - 10255/1024*(2*x^2 - x + 3)^(3/2)*x + 500141/12288*(2*x^2 - x + 3)^(3/2) - 5870731/16384*sqrt(2*x^2 - x + 3)*x - 1622009981/262144*sqrt(2)*arcsinh(4/23*sqrt(23)*x - 1/23*sqrt(23)) + 99009/16*sqrt(2)*arcsinh(22/23*sqrt(23)*x/abs(2*x + 5) - 17/23*sqrt(23)/abs(2*x + 5)) + 141051019/65536*sqrt(2*x^2 - x + 3)","A",0
337,1,161,0,1.012715," ","integrate((2*x^2-x+3)^(3/2)*(5*x^4-x^3+3*x^2+x+2)/(5+2*x)^2,x, algorithm=""maxima"")","\frac{5}{48} \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{5}{2}} x - \frac{589}{960} \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{5}{2}} + \frac{9059}{1536} \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}} x - \frac{185827}{6144} \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}} + \frac{3560933}{8192} \, \sqrt{2 \, x^{2} - x + 3} x + \frac{982669459}{131072} \, \sqrt{2} \operatorname{arsinh}\left(\frac{4}{23} \, \sqrt{23} x - \frac{1}{23} \, \sqrt{23}\right) - \frac{959625}{128} \, \sqrt{2} \operatorname{arsinh}\left(\frac{22 \, \sqrt{23} x}{23 \, {\left| 2 \, x + 5 \right|}} - \frac{17 \, \sqrt{23}}{23 \, {\left| 2 \, x + 5 \right|}}\right) - \frac{85448933}{32768} \, \sqrt{2 \, x^{2} - x + 3} - \frac{3667 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}}{32 \, {\left(2 \, x + 5\right)}}"," ",0,"5/48*(2*x^2 - x + 3)^(5/2)*x - 589/960*(2*x^2 - x + 3)^(5/2) + 9059/1536*(2*x^2 - x + 3)^(3/2)*x - 185827/6144*(2*x^2 - x + 3)^(3/2) + 3560933/8192*sqrt(2*x^2 - x + 3)*x + 982669459/131072*sqrt(2)*arcsinh(4/23*sqrt(23)*x - 1/23*sqrt(23)) - 959625/128*sqrt(2)*arcsinh(22/23*sqrt(23)*x/abs(2*x + 5) - 17/23*sqrt(23)/abs(2*x + 5)) - 85448933/32768*sqrt(2*x^2 - x + 3) - 3667/32*(2*x^2 - x + 3)^(3/2)/(2*x + 5)","A",0
338,1,172,0,1.001045," ","integrate((2*x^2-x+3)^(3/2)*(5*x^4-x^3+3*x^2+x+2)/(5+2*x)^3,x, algorithm=""maxima"")","\frac{1}{16} \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{5}{2}} - \frac{149}{128} \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}} x + \frac{46691}{4608} \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}} - \frac{3667 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{5}{2}}}{1152 \, {\left(4 \, x^{2} + 20 \, x + 25\right)}} - \frac{1405823}{6144} \, \sqrt{2 \, x^{2} - x + 3} x - \frac{129342063}{32768} \, \sqrt{2} \operatorname{arsinh}\left(\frac{4}{23} \, \sqrt{23} x - \frac{1}{23} \, \sqrt{23}\right) + \frac{8083915}{2048} \, \sqrt{2} \operatorname{arsinh}\left(\frac{22 \, \sqrt{23} x}{23 \, {\left| 2 \, x + 5 \right|}} - \frac{17 \, \sqrt{23}}{23 \, {\left| 2 \, x + 5 \right|}}\right) + \frac{11247161}{8192} \, \sqrt{2 \, x^{2} - x + 3} + \frac{438065 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}}{4608 \, {\left(2 \, x + 5\right)}}"," ",0,"1/16*(2*x^2 - x + 3)^(5/2) - 149/128*(2*x^2 - x + 3)^(3/2)*x + 46691/4608*(2*x^2 - x + 3)^(3/2) - 3667/1152*(2*x^2 - x + 3)^(5/2)/(4*x^2 + 20*x + 25) - 1405823/6144*sqrt(2*x^2 - x + 3)*x - 129342063/32768*sqrt(2)*arcsinh(4/23*sqrt(23)*x - 1/23*sqrt(23)) + 8083915/2048*sqrt(2)*arcsinh(22/23*sqrt(23)*x/abs(2*x + 5) - 17/23*sqrt(23)/abs(2*x + 5)) + 11247161/8192*sqrt(2*x^2 - x + 3) + 438065/4608*(2*x^2 - x + 3)^(3/2)/(2*x + 5)","A",0
339,1,189,0,1.036306," ","integrate((2*x^2-x+3)^(3/2)*(5*x^4-x^3+3*x^2+x+2)/(5+2*x)^4,x, algorithm=""maxima"")","\frac{5}{64} \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}} x - \frac{1094743}{497664} \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}} - \frac{3667 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{5}{2}}}{1728 \, {\left(8 \, x^{3} + 60 \, x^{2} + 150 \, x + 125\right)}} + \frac{556255 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{5}{2}}}{248832 \, {\left(4 \, x^{2} + 20 \, x + 25\right)}} + \frac{22512089}{331776} \, \sqrt{2 \, x^{2} - x + 3} x + \frac{19176431}{16384} \, \sqrt{2} \operatorname{arsinh}\left(\frac{4}{23} \, \sqrt{23} x - \frac{1}{23} \, \sqrt{23}\right) - \frac{517762327}{442368} \, \sqrt{2} \operatorname{arsinh}\left(\frac{22 \, \sqrt{23} x}{23 \, {\left| 2 \, x + 5 \right|}} - \frac{17 \, \sqrt{23}}{23 \, {\left| 2 \, x + 5 \right|}}\right) - \frac{11255717}{27648} \, \sqrt{2 \, x^{2} - x + 3} - \frac{32865365 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}}{995328 \, {\left(2 \, x + 5\right)}}"," ",0,"5/64*(2*x^2 - x + 3)^(3/2)*x - 1094743/497664*(2*x^2 - x + 3)^(3/2) - 3667/1728*(2*x^2 - x + 3)^(5/2)/(8*x^3 + 60*x^2 + 150*x + 125) + 556255/248832*(2*x^2 - x + 3)^(5/2)/(4*x^2 + 20*x + 25) + 22512089/331776*sqrt(2*x^2 - x + 3)*x + 19176431/16384*sqrt(2)*arcsinh(4/23*sqrt(23)*x - 1/23*sqrt(23)) - 517762327/442368*sqrt(2)*arcsinh(22/23*sqrt(23)*x/abs(2*x + 5) - 17/23*sqrt(23)/abs(2*x + 5)) - 11255717/27648*sqrt(2*x^2 - x + 3) - 32865365/995328*(2*x^2 - x + 3)^(3/2)/(2*x + 5)","A",0
340,1,210,0,1.042386," ","integrate((2*x^2-x+3)^(3/2)*(5*x^4-x^3+3*x^2+x+2)/(5+2*x)^5,x, algorithm=""maxima"")","\frac{16966315}{47775744} \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}} - \frac{3667 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{5}{2}}}{2304 \, {\left(16 \, x^{4} + 160 \, x^{3} + 600 \, x^{2} + 1000 \, x + 625\right)}} + \frac{224815 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{5}{2}}}{165888 \, {\left(8 \, x^{3} + 60 \, x^{2} + 150 \, x + 125\right)}} - \frac{14477995 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{5}{2}}}{23887872 \, {\left(4 \, x^{2} + 20 \, x + 25\right)}} - \frac{389975609}{31850496} \, \sqrt{2 \, x^{2} - x + 3} x - \frac{432565}{2048} \, \sqrt{2} \operatorname{arsinh}\left(\frac{4}{23} \, \sqrt{23} x - \frac{1}{23} \, \sqrt{23}\right) + \frac{8969688643}{42467328} \, \sqrt{2} \operatorname{arsinh}\left(\frac{22 \, \sqrt{23} x}{23 \, {\left| 2 \, x + 5 \right|}} - \frac{17 \, \sqrt{23}}{23 \, {\left| 2 \, x + 5 \right|}}\right) + \frac{779972021}{10616832} \, \sqrt{2 \, x^{2} - x + 3} + \frac{593321753 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}}{95551488 \, {\left(2 \, x + 5\right)}}"," ",0,"16966315/47775744*(2*x^2 - x + 3)^(3/2) - 3667/2304*(2*x^2 - x + 3)^(5/2)/(16*x^4 + 160*x^3 + 600*x^2 + 1000*x + 625) + 224815/165888*(2*x^2 - x + 3)^(5/2)/(8*x^3 + 60*x^2 + 150*x + 125) - 14477995/23887872*(2*x^2 - x + 3)^(5/2)/(4*x^2 + 20*x + 25) - 389975609/31850496*sqrt(2*x^2 - x + 3)*x - 432565/2048*sqrt(2)*arcsinh(4/23*sqrt(23)*x - 1/23*sqrt(23)) + 8969688643/42467328*sqrt(2)*arcsinh(22/23*sqrt(23)*x/abs(2*x + 5) - 17/23*sqrt(23)/abs(2*x + 5)) + 779972021/10616832*sqrt(2*x^2 - x + 3) + 593321753/95551488*(2*x^2 - x + 3)^(3/2)/(2*x + 5)","A",0
341,1,251,0,1.059594," ","integrate((2*x^2-x+3)^(3/2)*(5*x^4-x^3+3*x^2+x+2)/(5+2*x)^6,x, algorithm=""maxima"")","-\frac{134077495}{3439853568} \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}} - \frac{3667 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{5}{2}}}{2880 \, {\left(32 \, x^{5} + 400 \, x^{4} + 2000 \, x^{3} + 5000 \, x^{2} + 6250 \, x + 3125\right)}} + \frac{158527 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{5}{2}}}{165888 \, {\left(16 \, x^{4} + 160 \, x^{3} + 600 \, x^{2} + 1000 \, x + 625\right)}} - \frac{3730507 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{5}{2}}}{11943936 \, {\left(8 \, x^{3} + 60 \, x^{2} + 150 \, x + 125\right)}} + \frac{134077495 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{5}{2}}}{1719926784 \, {\left(4 \, x^{2} + 20 \, x + 25\right)}} + \frac{3086715581}{2293235712} \, \sqrt{2 \, x^{2} - x + 3} x + \frac{23775}{1024} \, \sqrt{2} \operatorname{arsinh}\left(\frac{4}{23} \, \sqrt{23} x - \frac{1}{23} \, \sqrt{23}\right) - \frac{70991525167}{3057647616} \, \sqrt{2} \operatorname{arsinh}\left(\frac{22 \, \sqrt{23} x}{23 \, {\left| 2 \, x + 5 \right|}} - \frac{17 \, \sqrt{23}}{23 \, {\left| 2 \, x + 5 \right|}}\right) - \frac{6173186729}{764411904} \, \sqrt{2 \, x^{2} - x + 3} - \frac{4698578717 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}}{6879707136 \, {\left(2 \, x + 5\right)}}"," ",0,"-134077495/3439853568*(2*x^2 - x + 3)^(3/2) - 3667/2880*(2*x^2 - x + 3)^(5/2)/(32*x^5 + 400*x^4 + 2000*x^3 + 5000*x^2 + 6250*x + 3125) + 158527/165888*(2*x^2 - x + 3)^(5/2)/(16*x^4 + 160*x^3 + 600*x^2 + 1000*x + 625) - 3730507/11943936*(2*x^2 - x + 3)^(5/2)/(8*x^3 + 60*x^2 + 150*x + 125) + 134077495/1719926784*(2*x^2 - x + 3)^(5/2)/(4*x^2 + 20*x + 25) + 3086715581/2293235712*sqrt(2*x^2 - x + 3)*x + 23775/1024*sqrt(2)*arcsinh(4/23*sqrt(23)*x - 1/23*sqrt(23)) - 70991525167/3057647616*sqrt(2)*arcsinh(22/23*sqrt(23)*x/abs(2*x + 5) - 17/23*sqrt(23)/abs(2*x + 5)) - 6173186729/764411904*sqrt(2*x^2 - x + 3) - 4698578717/6879707136*(2*x^2 - x + 3)^(3/2)/(2*x + 5)","A",0
342,1,297,0,1.072047," ","integrate((2*x^2-x+3)^(3/2)*(5*x^4-x^3+3*x^2+x+2)/(5+2*x)^7,x, algorithm=""maxima"")","\frac{3607708597}{1486016741376} \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}} - \frac{3667 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{5}{2}}}{3456 \, {\left(64 \, x^{6} + 960 \, x^{5} + 6000 \, x^{4} + 20000 \, x^{3} + 37500 \, x^{2} + 37500 \, x + 15625\right)}} + \frac{182165 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{5}{2}}}{248832 \, {\left(32 \, x^{5} + 400 \, x^{4} + 2000 \, x^{3} + 5000 \, x^{2} + 6250 \, x + 3125\right)}} - \frac{14087245 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{5}{2}}}{71663616 \, {\left(16 \, x^{4} + 160 \, x^{3} + 600 \, x^{2} + 1000 \, x + 625\right)}} + \frac{149610673 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{5}{2}}}{5159780352 \, {\left(8 \, x^{3} + 60 \, x^{2} + 150 \, x + 125\right)}} - \frac{3607708597 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{5}{2}}}{743008370688 \, {\left(4 \, x^{2} + 20 \, x + 25\right)}} - \frac{82772668391}{990677827584} \, \sqrt{2 \, x^{2} - x + 3} x - \frac{369}{256} \, \sqrt{2} \operatorname{arsinh}\left(\frac{4}{23} \, \sqrt{23} x - \frac{1}{23} \, \sqrt{23}\right) + \frac{1903976002333}{1320903770112} \, \sqrt{2} \operatorname{arsinh}\left(\frac{22 \, \sqrt{23} x}{23 \, {\left| 2 \, x + 5 \right|}} - \frac{17 \, \sqrt{23}}{23 \, {\left| 2 \, x + 5 \right|}}\right) + \frac{165562389227}{330225942528} \, \sqrt{2 \, x^{2} - x + 3} + \frac{125860542215 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}}{2972033482752 \, {\left(2 \, x + 5\right)}}"," ",0,"3607708597/1486016741376*(2*x^2 - x + 3)^(3/2) - 3667/3456*(2*x^2 - x + 3)^(5/2)/(64*x^6 + 960*x^5 + 6000*x^4 + 20000*x^3 + 37500*x^2 + 37500*x + 15625) + 182165/248832*(2*x^2 - x + 3)^(5/2)/(32*x^5 + 400*x^4 + 2000*x^3 + 5000*x^2 + 6250*x + 3125) - 14087245/71663616*(2*x^2 - x + 3)^(5/2)/(16*x^4 + 160*x^3 + 600*x^2 + 1000*x + 625) + 149610673/5159780352*(2*x^2 - x + 3)^(5/2)/(8*x^3 + 60*x^2 + 150*x + 125) - 3607708597/743008370688*(2*x^2 - x + 3)^(5/2)/(4*x^2 + 20*x + 25) - 82772668391/990677827584*sqrt(2*x^2 - x + 3)*x - 369/256*sqrt(2)*arcsinh(4/23*sqrt(23)*x - 1/23*sqrt(23)) + 1903976002333/1320903770112*sqrt(2)*arcsinh(22/23*sqrt(23)*x/abs(2*x + 5) - 17/23*sqrt(23)/abs(2*x + 5)) + 165562389227/330225942528*sqrt(2*x^2 - x + 3) + 125860542215/2972033482752*(2*x^2 - x + 3)^(3/2)/(2*x + 5)","A",0
343,1,348,0,1.074258," ","integrate((2*x^2-x+3)^(3/2)*(5*x^4-x^3+3*x^2+x+2)/(5+2*x)^8,x, algorithm=""maxima"")","-\frac{769352975}{11888133931008} \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}} - \frac{3667 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{5}{2}}}{4032 \, {\left(128 \, x^{7} + 2240 \, x^{6} + 16800 \, x^{5} + 70000 \, x^{4} + 175000 \, x^{3} + 262500 \, x^{2} + 218750 \, x + 78125\right)}} + \frac{114335 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{5}{2}}}{193536 \, {\left(64 \, x^{6} + 960 \, x^{5} + 6000 \, x^{4} + 20000 \, x^{3} + 37500 \, x^{2} + 37500 \, x + 15625\right)}} - \frac{1930441 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{5}{2}}}{13934592 \, {\left(32 \, x^{5} + 400 \, x^{4} + 2000 \, x^{3} + 5000 \, x^{2} + 6250 \, x + 3125\right)}} + \frac{7861079 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{5}{2}}}{573308928 \, {\left(16 \, x^{4} + 160 \, x^{3} + 600 \, x^{2} + 1000 \, x + 625\right)}} - \frac{32967491 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{5}{2}}}{41278242816 \, {\left(8 \, x^{3} + 60 \, x^{2} + 150 \, x + 125\right)}} + \frac{769352975 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{5}{2}}}{5944066965504 \, {\left(4 \, x^{2} + 20 \, x + 25\right)}} + \frac{17957520133}{7925422620672} \, \sqrt{2 \, x^{2} - x + 3} x + \frac{5}{128} \, \sqrt{2} \operatorname{arsinh}\left(\frac{4}{23} \, \sqrt{23} x - \frac{1}{23} \, \sqrt{23}\right) - \frac{412760561351}{10567230160896} \, \sqrt{2} \operatorname{arsinh}\left(\frac{22 \, \sqrt{23} x}{23 \, {\left| 2 \, x + 5 \right|}} - \frac{17 \, \sqrt{23}}{23 \, {\left| 2 \, x + 5 \right|}}\right) - \frac{35893173457}{2641807540224} \, \sqrt{2 \, x^{2} - x + 3} - \frac{27452157541 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}}{23776267862016 \, {\left(2 \, x + 5\right)}}"," ",0,"-769352975/11888133931008*(2*x^2 - x + 3)^(3/2) - 3667/4032*(2*x^2 - x + 3)^(5/2)/(128*x^7 + 2240*x^6 + 16800*x^5 + 70000*x^4 + 175000*x^3 + 262500*x^2 + 218750*x + 78125) + 114335/193536*(2*x^2 - x + 3)^(5/2)/(64*x^6 + 960*x^5 + 6000*x^4 + 20000*x^3 + 37500*x^2 + 37500*x + 15625) - 1930441/13934592*(2*x^2 - x + 3)^(5/2)/(32*x^5 + 400*x^4 + 2000*x^3 + 5000*x^2 + 6250*x + 3125) + 7861079/573308928*(2*x^2 - x + 3)^(5/2)/(16*x^4 + 160*x^3 + 600*x^2 + 1000*x + 625) - 32967491/41278242816*(2*x^2 - x + 3)^(5/2)/(8*x^3 + 60*x^2 + 150*x + 125) + 769352975/5944066965504*(2*x^2 - x + 3)^(5/2)/(4*x^2 + 20*x + 25) + 17957520133/7925422620672*sqrt(2*x^2 - x + 3)*x + 5/128*sqrt(2)*arcsinh(4/23*sqrt(23)*x - 1/23*sqrt(23)) - 412760561351/10567230160896*sqrt(2)*arcsinh(22/23*sqrt(23)*x/abs(2*x + 5) - 17/23*sqrt(23)/abs(2*x + 5)) - 35893173457/2641807540224*sqrt(2*x^2 - x + 3) - 27452157541/23776267862016*(2*x^2 - x + 3)^(3/2)/(2*x + 5)","B",0
344,1,96,0,0.974254," ","integrate((5+2*x)*(5*x^4-x^3+3*x^2+x+2)/(2*x^2-x+3)^(1/2),x, algorithm=""maxima"")","\sqrt{2 \, x^{2} - x + 3} x^{4} + \frac{55}{16} \, \sqrt{2 \, x^{2} - x + 3} x^{3} + \frac{11}{64} \, \sqrt{2 \, x^{2} - x + 3} x^{2} - \frac{1729}{512} \, \sqrt{2 \, x^{2} - x + 3} x + \frac{85429}{8192} \, \sqrt{2} \operatorname{arsinh}\left(\frac{1}{23} \, \sqrt{23} {\left(4 \, x - 1\right)}\right) + \frac{2973}{2048} \, \sqrt{2 \, x^{2} - x + 3}"," ",0,"sqrt(2*x^2 - x + 3)*x^4 + 55/16*sqrt(2*x^2 - x + 3)*x^3 + 11/64*sqrt(2*x^2 - x + 3)*x^2 - 1729/512*sqrt(2*x^2 - x + 3)*x + 85429/8192*sqrt(2)*arcsinh(1/23*sqrt(23)*(4*x - 1)) + 2973/2048*sqrt(2*x^2 - x + 3)","A",0
345,1,80,0,0.963139," ","integrate((5*x^4-x^3+3*x^2+x+2)/(2*x^2-x+3)^(1/2),x, algorithm=""maxima"")","\frac{5}{8} \, \sqrt{2 \, x^{2} - x + 3} x^{3} + \frac{19}{96} \, \sqrt{2 \, x^{2} - x + 3} x^{2} - \frac{409}{768} \, \sqrt{2 \, x^{2} - x + 3} x + \frac{6863}{4096} \, \sqrt{2} \operatorname{arsinh}\left(\frac{1}{23} \, \sqrt{23} {\left(4 \, x - 1\right)}\right) - \frac{505}{1024} \, \sqrt{2 \, x^{2} - x + 3}"," ",0,"5/8*sqrt(2*x^2 - x + 3)*x^3 + 19/96*sqrt(2*x^2 - x + 3)*x^2 - 409/768*sqrt(2*x^2 - x + 3)*x + 6863/4096*sqrt(2)*arcsinh(1/23*sqrt(23)*(4*x - 1)) - 505/1024*sqrt(2*x^2 - x + 3)","A",0
346,1,99,0,0.980590," ","integrate((5*x^4-x^3+3*x^2+x+2)/(5+2*x)/(2*x^2-x+3)^(1/2),x, algorithm=""maxima"")","\frac{5}{12} \, \sqrt{2 \, x^{2} - x + 3} x^{2} - \frac{137}{96} \, \sqrt{2 \, x^{2} - x + 3} x - \frac{9657}{512} \, \sqrt{2} \operatorname{arsinh}\left(\frac{4}{23} \, \sqrt{23} x - \frac{1}{23} \, \sqrt{23}\right) + \frac{3667}{192} \, \sqrt{2} \operatorname{arsinh}\left(\frac{22 \, \sqrt{23} x}{23 \, {\left| 2 \, x + 5 \right|}} - \frac{17 \, \sqrt{23}}{23 \, {\left| 2 \, x + 5 \right|}}\right) + \frac{879}{128} \, \sqrt{2 \, x^{2} - x + 3}"," ",0,"5/12*sqrt(2*x^2 - x + 3)*x^2 - 137/96*sqrt(2*x^2 - x + 3)*x - 9657/512*sqrt(2)*arcsinh(4/23*sqrt(23)*x - 1/23*sqrt(23)) + 3667/192*sqrt(2)*arcsinh(22/23*sqrt(23)*x/abs(2*x + 5) - 17/23*sqrt(23)/abs(2*x + 5)) + 879/128*sqrt(2*x^2 - x + 3)","A",0
347,1,103,0,0.979947," ","integrate((5*x^4-x^3+3*x^2+x+2)/(5+2*x)^2/(2*x^2-x+3)^(1/2),x, algorithm=""maxima"")","\frac{5}{16} \, \sqrt{2 \, x^{2} - x + 3} x + \frac{2943}{256} \, \sqrt{2} \operatorname{arsinh}\left(\frac{4}{23} \, \sqrt{23} x - \frac{1}{23} \, \sqrt{23}\right) - \frac{158527}{13824} \, \sqrt{2} \operatorname{arsinh}\left(\frac{22 \, \sqrt{23} x}{23 \, {\left| 2 \, x + 5 \right|}} - \frac{17 \, \sqrt{23}}{23 \, {\left| 2 \, x + 5 \right|}}\right) - \frac{193}{64} \, \sqrt{2 \, x^{2} - x + 3} - \frac{3667 \, \sqrt{2 \, x^{2} - x + 3}}{576 \, {\left(2 \, x + 5\right)}}"," ",0,"5/16*sqrt(2*x^2 - x + 3)*x + 2943/256*sqrt(2)*arcsinh(4/23*sqrt(23)*x - 1/23*sqrt(23)) - 158527/13824*sqrt(2)*arcsinh(22/23*sqrt(23)*x/abs(2*x + 5) - 17/23*sqrt(23)/abs(2*x + 5)) - 193/64*sqrt(2*x^2 - x + 3) - 3667/576*sqrt(2*x^2 - x + 3)/(2*x + 5)","A",0
348,1,114,0,0.984154," ","integrate((5*x^4-x^3+3*x^2+x+2)/(5+2*x)^3/(2*x^2-x+3)^(1/2),x, algorithm=""maxima"")","-\frac{149}{64} \, \sqrt{2} \operatorname{arsinh}\left(\frac{4}{23} \, \sqrt{23} x - \frac{1}{23} \, \sqrt{23}\right) + \frac{1546507}{663552} \, \sqrt{2} \operatorname{arsinh}\left(\frac{22 \, \sqrt{23} x}{23 \, {\left| 2 \, x + 5 \right|}} - \frac{17 \, \sqrt{23}}{23 \, {\left| 2 \, x + 5 \right|}}\right) + \frac{5}{16} \, \sqrt{2 \, x^{2} - x + 3} - \frac{3667 \, \sqrt{2 \, x^{2} - x + 3}}{1152 \, {\left(4 \, x^{2} + 20 \, x + 25\right)}} + \frac{92239 \, \sqrt{2 \, x^{2} - x + 3}}{27648 \, {\left(2 \, x + 5\right)}}"," ",0,"-149/64*sqrt(2)*arcsinh(4/23*sqrt(23)*x - 1/23*sqrt(23)) + 1546507/663552*sqrt(2)*arcsinh(22/23*sqrt(23)*x/abs(2*x + 5) - 17/23*sqrt(23)/abs(2*x + 5)) + 5/16*sqrt(2*x^2 - x + 3) - 3667/1152*sqrt(2*x^2 - x + 3)/(4*x^2 + 20*x + 25) + 92239/27648*sqrt(2*x^2 - x + 3)/(2*x + 5)","A",0
349,1,131,0,1.002669," ","integrate((5*x^4-x^3+3*x^2+x+2)/(5+2*x)^4/(2*x^2-x+3)^(1/2),x, algorithm=""maxima"")","\frac{5}{32} \, \sqrt{2} \operatorname{arsinh}\left(\frac{4}{23} \, \sqrt{23} x - \frac{1}{23} \, \sqrt{23}\right) - \frac{22389491}{143327232} \, \sqrt{2} \operatorname{arsinh}\left(\frac{22 \, \sqrt{23} x}{23 \, {\left| 2 \, x + 5 \right|}} - \frac{17 \, \sqrt{23}}{23 \, {\left| 2 \, x + 5 \right|}}\right) - \frac{3667 \, \sqrt{2 \, x^{2} - x + 3}}{1728 \, {\left(8 \, x^{3} + 60 \, x^{2} + 150 \, x + 125\right)}} + \frac{394907 \, \sqrt{2 \, x^{2} - x + 3}}{248832 \, {\left(4 \, x^{2} + 20 \, x + 25\right)}} - \frac{3163415 \, \sqrt{2 \, x^{2} - x + 3}}{5971968 \, {\left(2 \, x + 5\right)}}"," ",0,"5/32*sqrt(2)*arcsinh(4/23*sqrt(23)*x - 1/23*sqrt(23)) - 22389491/143327232*sqrt(2)*arcsinh(22/23*sqrt(23)*x/abs(2*x + 5) - 17/23*sqrt(23)/abs(2*x + 5)) - 3667/1728*sqrt(2*x^2 - x + 3)/(8*x^3 + 60*x^2 + 150*x + 125) + 394907/248832*sqrt(2*x^2 - x + 3)/(4*x^2 + 20*x + 25) - 3163415/5971968*sqrt(2*x^2 - x + 3)/(2*x + 5)","A",0
350,1,149,0,1.024447," ","integrate((5*x^4-x^3+3*x^2+x+2)/(5+2*x)^5/(2*x^2-x+3)^(1/2),x, algorithm=""maxima"")","-\frac{2053207}{41278242816} \, \sqrt{2} \operatorname{arsinh}\left(\frac{22 \, \sqrt{23} x}{23 \, {\left| 2 \, x + 5 \right|}} - \frac{17 \, \sqrt{23}}{23 \, {\left| 2 \, x + 5 \right|}}\right) - \frac{3667 \, \sqrt{2 \, x^{2} - x + 3}}{2304 \, {\left(16 \, x^{4} + 160 \, x^{3} + 600 \, x^{2} + 1000 \, x + 625\right)}} + \frac{513097 \, \sqrt{2 \, x^{2} - x + 3}}{497664 \, {\left(8 \, x^{3} + 60 \, x^{2} + 150 \, x + 125\right)}} - \frac{16295969 \, \sqrt{2 \, x^{2} - x + 3}}{71663616 \, {\left(4 \, x^{2} + 20 \, x + 25\right)}} + \frac{26800085 \, \sqrt{2 \, x^{2} - x + 3}}{1719926784 \, {\left(2 \, x + 5\right)}}"," ",0,"-2053207/41278242816*sqrt(2)*arcsinh(22/23*sqrt(23)*x/abs(2*x + 5) - 17/23*sqrt(23)/abs(2*x + 5)) - 3667/2304*sqrt(2*x^2 - x + 3)/(16*x^4 + 160*x^3 + 600*x^2 + 1000*x + 625) + 513097/497664*sqrt(2*x^2 - x + 3)/(8*x^3 + 60*x^2 + 150*x + 125) - 16295969/71663616*sqrt(2*x^2 - x + 3)/(4*x^2 + 20*x + 25) + 26800085/1719926784*sqrt(2*x^2 - x + 3)/(2*x + 5)","A",0
351,1,114,0,0.971671," ","integrate((5+2*x)^2*(5*x^4-x^3+3*x^2+x+2)/(2*x^2-x+3)^(3/2),x, algorithm=""maxima"")","\frac{5 \, x^{5}}{2 \, \sqrt{2 \, x^{2} - x + 3}} + \frac{143 \, x^{4}}{8 \, \sqrt{2 \, x^{2} - x + 3}} + \frac{2273 \, x^{3}}{64 \, \sqrt{2 \, x^{2} - x + 3}} - \frac{11099 \, x^{2}}{256 \, \sqrt{2 \, x^{2} - x + 3}} - \frac{144217}{2048} \, \sqrt{2} \operatorname{arsinh}\left(\frac{1}{23} \, \sqrt{23} {\left(4 \, x - 1\right)}\right) + \frac{2124123 \, x}{11776 \, \sqrt{2 \, x^{2} - x + 3}} - \frac{1616165}{11776 \, \sqrt{2 \, x^{2} - x + 3}}"," ",0,"5/2*x^5/sqrt(2*x^2 - x + 3) + 143/8*x^4/sqrt(2*x^2 - x + 3) + 2273/64*x^3/sqrt(2*x^2 - x + 3) - 11099/256*x^2/sqrt(2*x^2 - x + 3) - 144217/2048*sqrt(2)*arcsinh(1/23*sqrt(23)*(4*x - 1)) + 2124123/11776*x/sqrt(2*x^2 - x + 3) - 1616165/11776/sqrt(2*x^2 - x + 3)","A",0
352,1,97,0,0.969930," ","integrate((5+2*x)*(5*x^4-x^3+3*x^2+x+2)/(2*x^2-x+3)^(3/2),x, algorithm=""maxima"")","\frac{5 \, x^{4}}{3 \, \sqrt{2 \, x^{2} - x + 3}} + \frac{173 \, x^{3}}{24 \, \sqrt{2 \, x^{2} - x + 3}} - \frac{47 \, x^{2}}{96 \, \sqrt{2 \, x^{2} - x + 3}} - \frac{3111}{256} \, \sqrt{2} \operatorname{arsinh}\left(\frac{1}{23} \, \sqrt{23} {\left(4 \, x - 1\right)}\right) + \frac{40869 \, x}{1472 \, \sqrt{2 \, x^{2} - x + 3}} - \frac{1115}{1472 \, \sqrt{2 \, x^{2} - x + 3}}"," ",0,"5/3*x^4/sqrt(2*x^2 - x + 3) + 173/24*x^3/sqrt(2*x^2 - x + 3) - 47/96*x^2/sqrt(2*x^2 - x + 3) - 3111/256*sqrt(2)*arcsinh(1/23*sqrt(23)*(4*x - 1)) + 40869/1472*x/sqrt(2*x^2 - x + 3) - 1115/1472/sqrt(2*x^2 - x + 3)","A",0
353,1,80,0,0.951738," ","integrate((5*x^4-x^3+3*x^2+x+2)/(2*x^2-x+3)^(3/2),x, algorithm=""maxima"")","\frac{5 \, x^{3}}{4 \, \sqrt{2 \, x^{2} - x + 3}} + \frac{17 \, x^{2}}{16 \, \sqrt{2 \, x^{2} - x + 3}} - \frac{213}{128} \, \sqrt{2} \operatorname{arsinh}\left(\frac{1}{23} \, \sqrt{23} {\left(4 \, x - 1\right)}\right) + \frac{2511 \, x}{736 \, \sqrt{2 \, x^{2} - x + 3}} + \frac{2575}{736 \, \sqrt{2 \, x^{2} - x + 3}}"," ",0,"5/4*x^3/sqrt(2*x^2 - x + 3) + 17/16*x^2/sqrt(2*x^2 - x + 3) - 213/128*sqrt(2)*arcsinh(1/23*sqrt(23)*(4*x - 1)) + 2511/736*x/sqrt(2*x^2 - x + 3) + 2575/736/sqrt(2*x^2 - x + 3)","A",0
354,1,99,0,0.977393," ","integrate((5*x^4-x^3+3*x^2+x+2)/(5+2*x)/(2*x^2-x+3)^(3/2),x, algorithm=""maxima"")","\frac{5 \, x^{2}}{4 \, \sqrt{2 \, x^{2} - x + 3}} - \frac{39}{32} \, \sqrt{2} \operatorname{arsinh}\left(\frac{4}{23} \, \sqrt{23} x - \frac{1}{23} \, \sqrt{23}\right) + \frac{3667}{3456} \, \sqrt{2} \operatorname{arsinh}\left(\frac{22 \, \sqrt{23} x}{23 \, {\left| 2 \, x + 5 \right|}} - \frac{17 \, \sqrt{23}}{23 \, {\left| 2 \, x + 5 \right|}}\right) - \frac{1153 \, x}{3312 \, \sqrt{2 \, x^{2} - x + 3}} + \frac{2467}{1104 \, \sqrt{2 \, x^{2} - x + 3}}"," ",0,"5/4*x^2/sqrt(2*x^2 - x + 3) - 39/32*sqrt(2)*arcsinh(4/23*sqrt(23)*x - 1/23*sqrt(23)) + 3667/3456*sqrt(2)*arcsinh(22/23*sqrt(23)*x/abs(2*x + 5) - 17/23*sqrt(23)/abs(2*x + 5)) - 1153/3312*x/sqrt(2*x^2 - x + 3) + 2467/1104/sqrt(2*x^2 - x + 3)","A",0
355,1,116,0,1.007222," ","integrate((5*x^4-x^3+3*x^2+x+2)/(5+2*x)^2/(2*x^2-x+3)^(3/2),x, algorithm=""maxima"")","\frac{5}{16} \, \sqrt{2} \operatorname{arsinh}\left(\frac{4}{23} \, \sqrt{23} x - \frac{1}{23} \, \sqrt{23}\right) - \frac{25951}{82944} \, \sqrt{2} \operatorname{arsinh}\left(\frac{22 \, \sqrt{23} x}{23 \, {\left| 2 \, x + 5 \right|}} - \frac{17 \, \sqrt{23}}{23 \, {\left| 2 \, x + 5 \right|}}\right) - \frac{26645 \, x}{79488 \, \sqrt{2 \, x^{2} - x + 3}} + \frac{30313}{26496 \, \sqrt{2 \, x^{2} - x + 3}} - \frac{3667}{576 \, {\left(2 \, \sqrt{2 \, x^{2} - x + 3} x + 5 \, \sqrt{2 \, x^{2} - x + 3}\right)}}"," ",0,"5/16*sqrt(2)*arcsinh(4/23*sqrt(23)*x - 1/23*sqrt(23)) - 25951/82944*sqrt(2)*arcsinh(22/23*sqrt(23)*x/abs(2*x + 5) - 17/23*sqrt(23)/abs(2*x + 5)) - 26645/79488*x/sqrt(2*x^2 - x + 3) + 30313/26496/sqrt(2*x^2 - x + 3) - 3667/576/(2*sqrt(2*x^2 - x + 3)*x + 5*sqrt(2*x^2 - x + 3))","A",0
356,1,149,0,0.984777," ","integrate((5*x^4-x^3+3*x^2+x+2)/(5+2*x)^3/(2*x^2-x+3)^(3/2),x, algorithm=""maxima"")","\frac{52631}{11943936} \, \sqrt{2} \operatorname{arsinh}\left(\frac{22 \, \sqrt{23} x}{23 \, {\left| 2 \, x + 5 \right|}} - \frac{17 \, \sqrt{23}}{23 \, {\left| 2 \, x + 5 \right|}}\right) + \frac{861085 \, x}{11446272 \, \sqrt{2 \, x^{2} - x + 3}} - \frac{1163201}{3815424 \, \sqrt{2 \, x^{2} - x + 3}} - \frac{3667}{1152 \, {\left(4 \, \sqrt{2 \, x^{2} - x + 3} x^{2} + 20 \, \sqrt{2 \, x^{2} - x + 3} x + 25 \, \sqrt{2 \, x^{2} - x + 3}\right)}} + \frac{196043}{82944 \, {\left(2 \, \sqrt{2 \, x^{2} - x + 3} x + 5 \, \sqrt{2 \, x^{2} - x + 3}\right)}}"," ",0,"52631/11943936*sqrt(2)*arcsinh(22/23*sqrt(23)*x/abs(2*x + 5) - 17/23*sqrt(23)/abs(2*x + 5)) + 861085/11446272*x/sqrt(2*x^2 - x + 3) - 1163201/3815424/sqrt(2*x^2 - x + 3) - 3667/1152/(4*sqrt(2*x^2 - x + 3)*x^2 + 20*sqrt(2*x^2 - x + 3)*x + 25*sqrt(2*x^2 - x + 3)) + 196043/82944/(2*sqrt(2*x^2 - x + 3)*x + 5*sqrt(2*x^2 - x + 3))","A",0
357,1,217,0,1.006654," ","integrate((5*x^4-x^3+3*x^2+x+2)/(5+2*x)^4/(2*x^2-x+3)^(3/2),x, algorithm=""maxima"")","\frac{3505819}{2579890176} \, \sqrt{2} \operatorname{arsinh}\left(\frac{22 \, \sqrt{23} x}{23 \, {\left| 2 \, x + 5 \right|}} - \frac{17 \, \sqrt{23}}{23 \, {\left| 2 \, x + 5 \right|}}\right) + \frac{7094345 \, x}{2472394752 \, \sqrt{2 \, x^{2} - x + 3}} + \frac{6128291}{824131584 \, \sqrt{2 \, x^{2} - x + 3}} - \frac{3667}{1728 \, {\left(8 \, \sqrt{2 \, x^{2} - x + 3} x^{3} + 60 \, \sqrt{2 \, x^{2} - x + 3} x^{2} + 150 \, \sqrt{2 \, x^{2} - x + 3} x + 125 \, \sqrt{2 \, x^{2} - x + 3}\right)}} + \frac{314233}{248832 \, {\left(4 \, \sqrt{2 \, x^{2} - x + 3} x^{2} + 20 \, \sqrt{2 \, x^{2} - x + 3} x + 25 \, \sqrt{2 \, x^{2} - x + 3}\right)}} - \frac{3127169}{17915904 \, {\left(2 \, \sqrt{2 \, x^{2} - x + 3} x + 5 \, \sqrt{2 \, x^{2} - x + 3}\right)}}"," ",0,"3505819/2579890176*sqrt(2)*arcsinh(22/23*sqrt(23)*x/abs(2*x + 5) - 17/23*sqrt(23)/abs(2*x + 5)) + 7094345/2472394752*x/sqrt(2*x^2 - x + 3) + 6128291/824131584/sqrt(2*x^2 - x + 3) - 3667/1728/(8*sqrt(2*x^2 - x + 3)*x^3 + 60*sqrt(2*x^2 - x + 3)*x^2 + 150*sqrt(2*x^2 - x + 3)*x + 125*sqrt(2*x^2 - x + 3)) + 314233/248832/(4*sqrt(2*x^2 - x + 3)*x^2 + 20*sqrt(2*x^2 - x + 3)*x + 25*sqrt(2*x^2 - x + 3)) - 3127169/17915904/(2*sqrt(2*x^2 - x + 3)*x + 5*sqrt(2*x^2 - x + 3))","A",0
358,1,219,0,0.983063," ","integrate((5+2*x)^2*(5*x^4-x^3+3*x^2+x+2)/(2*x^2-x+3)^(5/2),x, algorithm=""maxima"")","\frac{5 \, x^{5}}{{\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}} + \frac{227 \, x^{4}}{4 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}} + \frac{1471}{50784} \, x {\left(\frac{284 \, x}{\sqrt{2 \, x^{2} - x + 3}} - \frac{3174 \, x^{2}}{{\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}} - \frac{71}{\sqrt{2 \, x^{2} - x + 3}} + \frac{805 \, x}{{\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}} - \frac{3243}{{\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}}\right)} + \frac{1471}{64} \, \sqrt{2} \operatorname{arsinh}\left(\frac{1}{23} \, \sqrt{23} {\left(4 \, x - 1\right)}\right) - \frac{104441}{25392} \, \sqrt{2 \, x^{2} - x + 3} - \frac{383581 \, x}{12696 \, \sqrt{2 \, x^{2} - x + 3}} + \frac{321 \, x^{2}}{{\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}} - \frac{15965}{4232 \, \sqrt{2 \, x^{2} - x + 3}} - \frac{4147 \, x}{46 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}} + \frac{42883}{138 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}}"," ",0,"5*x^5/(2*x^2 - x + 3)^(3/2) + 227/4*x^4/(2*x^2 - x + 3)^(3/2) + 1471/50784*x*(284*x/sqrt(2*x^2 - x + 3) - 3174*x^2/(2*x^2 - x + 3)^(3/2) - 71/sqrt(2*x^2 - x + 3) + 805*x/(2*x^2 - x + 3)^(3/2) - 3243/(2*x^2 - x + 3)^(3/2)) + 1471/64*sqrt(2)*arcsinh(1/23*sqrt(23)*(4*x - 1)) - 104441/25392*sqrt(2*x^2 - x + 3) - 383581/12696*x/sqrt(2*x^2 - x + 3) + 321*x^2/(2*x^2 - x + 3)^(3/2) - 15965/4232/sqrt(2*x^2 - x + 3) - 4147/46*x/(2*x^2 - x + 3)^(3/2) + 42883/138/(2*x^2 - x + 3)^(3/2)","B",0
359,1,202,0,0.966561," ","integrate((5+2*x)*(5*x^4-x^3+3*x^2+x+2)/(2*x^2-x+3)^(5/2),x, algorithm=""maxima"")","\frac{5 \, x^{4}}{{\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}} + \frac{71}{12696} \, x {\left(\frac{284 \, x}{\sqrt{2 \, x^{2} - x + 3}} - \frac{3174 \, x^{2}}{{\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}} - \frac{71}{\sqrt{2 \, x^{2} - x + 3}} + \frac{805 \, x}{{\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}} - \frac{3243}{{\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}}\right)} + \frac{71}{16} \, \sqrt{2} \operatorname{arsinh}\left(\frac{1}{23} \, \sqrt{23} {\left(4 \, x - 1\right)}\right) - \frac{5041}{6348} \, \sqrt{2 \, x^{2} - x + 3} - \frac{10007 \, x}{3174 \, \sqrt{2 \, x^{2} - x + 3}} + \frac{59 \, x^{2}}{2 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}} - \frac{2959}{2116 \, \sqrt{2 \, x^{2} - x + 3}} - \frac{807 \, x}{92 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}} + \frac{7603}{276 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}}"," ",0,"5*x^4/(2*x^2 - x + 3)^(3/2) + 71/12696*x*(284*x/sqrt(2*x^2 - x + 3) - 3174*x^2/(2*x^2 - x + 3)^(3/2) - 71/sqrt(2*x^2 - x + 3) + 805*x/(2*x^2 - x + 3)^(3/2) - 3243/(2*x^2 - x + 3)^(3/2)) + 71/16*sqrt(2)*arcsinh(1/23*sqrt(23)*(4*x - 1)) - 5041/6348*sqrt(2*x^2 - x + 3) - 10007/3174*x/sqrt(2*x^2 - x + 3) + 59/2*x^2/(2*x^2 - x + 3)^(3/2) - 2959/2116/sqrt(2*x^2 - x + 3) - 807/92*x/(2*x^2 - x + 3)^(3/2) + 7603/276/(2*x^2 - x + 3)^(3/2)","B",0
360,1,185,0,0.982521," ","integrate((5*x^4-x^3+3*x^2+x+2)/(2*x^2-x+3)^(5/2),x, algorithm=""maxima"")","\frac{5}{6348} \, x {\left(\frac{284 \, x}{\sqrt{2 \, x^{2} - x + 3}} - \frac{3174 \, x^{2}}{{\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}} - \frac{71}{\sqrt{2 \, x^{2} - x + 3}} + \frac{805 \, x}{{\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}} - \frac{3243}{{\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}}\right)} + \frac{5}{8} \, \sqrt{2} \operatorname{arsinh}\left(\frac{1}{23} \, \sqrt{23} {\left(4 \, x - 1\right)}\right) - \frac{355}{3174} \, \sqrt{2 \, x^{2} - x + 3} - \frac{58 \, x}{1587 \, \sqrt{2 \, x^{2} - x + 3}} + \frac{x^{2}}{2 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}} - \frac{1897}{6348 \, \sqrt{2 \, x^{2} - x + 3}} - \frac{95 \, x}{276 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}} + \frac{41}{276 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}}"," ",0,"5/6348*x*(284*x/sqrt(2*x^2 - x + 3) - 3174*x^2/(2*x^2 - x + 3)^(3/2) - 71/sqrt(2*x^2 - x + 3) + 805*x/(2*x^2 - x + 3)^(3/2) - 3243/(2*x^2 - x + 3)^(3/2)) + 5/8*sqrt(2)*arcsinh(1/23*sqrt(23)*(4*x - 1)) - 355/3174*sqrt(2*x^2 - x + 3) - 58/1587*x/sqrt(2*x^2 - x + 3) + 1/2*x^2/(2*x^2 - x + 3)^(3/2) - 1897/6348/sqrt(2*x^2 - x + 3) - 95/276*x/(2*x^2 - x + 3)^(3/2) + 41/276/(2*x^2 - x + 3)^(3/2)","B",0
361,1,110,0,0.968357," ","integrate((5*x^4-x^3+3*x^2+x+2)/(5+2*x)/(2*x^2-x+3)^(5/2),x, algorithm=""maxima"")","\frac{3667}{62208} \, \sqrt{2} \operatorname{arsinh}\left(\frac{22 \, \sqrt{23} x}{23 \, {\left| 2 \, x + 5 \right|}} - \frac{17 \, \sqrt{23}}{23 \, {\left| 2 \, x + 5 \right|}}\right) - \frac{146729 \, x}{1371168 \, \sqrt{2 \, x^{2} - x + 3}} - \frac{5 \, x^{2}}{4 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}} + \frac{173881}{457056 \, \sqrt{2 \, x^{2} - x + 3}} + \frac{7127 \, x}{9936 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}} - \frac{5813}{3312 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}}"," ",0,"3667/62208*sqrt(2)*arcsinh(22/23*sqrt(23)*x/abs(2*x + 5) - 17/23*sqrt(23)/abs(2*x + 5)) - 146729/1371168*x/sqrt(2*x^2 - x + 3) - 5/4*x^2/(2*x^2 - x + 3)^(3/2) + 173881/457056/sqrt(2*x^2 - x + 3) + 7127/9936*x/(2*x^2 - x + 3)^(3/2) - 5813/3312/(2*x^2 - x + 3)^(3/2)","A",0
362,1,127,0,1.005783," ","integrate((5*x^4-x^3+3*x^2+x+2)/(5+2*x)^2/(2*x^2-x+3)^(5/2),x, algorithm=""maxima"")","\frac{2821}{4478976} \, \sqrt{2} \operatorname{arsinh}\left(\frac{22 \, \sqrt{23} x}{23 \, {\left| 2 \, x + 5 \right|}} - \frac{17 \, \sqrt{23}}{23 \, {\left| 2 \, x + 5 \right|}}\right) - \frac{1691759 \, x}{98724096 \, \sqrt{2 \, x^{2} - x + 3}} + \frac{265339}{32908032 \, \sqrt{2 \, x^{2} - x + 3}} - \frac{248617 \, x}{715392 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}} - \frac{3667}{576 \, {\left(2 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}} x + 5 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}\right)}} + \frac{259621}{238464 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}}"," ",0,"2821/4478976*sqrt(2)*arcsinh(22/23*sqrt(23)*x/abs(2*x + 5) - 17/23*sqrt(23)/abs(2*x + 5)) - 1691759/98724096*x/sqrt(2*x^2 - x + 3) + 265339/32908032/sqrt(2*x^2 - x + 3) - 248617/715392*x/(2*x^2 - x + 3)^(3/2) - 3667/576/(2*(2*x^2 - x + 3)^(3/2)*x + 5*(2*x^2 - x + 3)^(3/2)) + 259621/238464/(2*x^2 - x + 3)^(3/2)","A",0
363,1,178,0,0.997662," ","integrate((5*x^4-x^3+3*x^2+x+2)/(5+2*x)^3/(2*x^2-x+3)^(5/2),x, algorithm=""maxima"")","-\frac{774079}{644972544} \, \sqrt{2} \operatorname{arsinh}\left(\frac{22 \, \sqrt{23} x}{23 \, {\left| 2 \, x + 5 \right|}} - \frac{17 \, \sqrt{23}}{23 \, {\left| 2 \, x + 5 \right|}}\right) + \frac{27235421 \, x}{14216269824 \, \sqrt{2 \, x^{2} - x + 3}} - \frac{36393601}{4738756608 \, \sqrt{2 \, x^{2} - x + 3}} + \frac{2323723 \, x}{103016448 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}} - \frac{3667}{1152 \, {\left(4 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}} x^{2} + 20 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}} x + 25 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}\right)}} + \frac{115369}{82944 \, {\left(2 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}} x + 5 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}\right)}} - \frac{5254255}{34338816 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}}"," ",0,"-774079/644972544*sqrt(2)*arcsinh(22/23*sqrt(23)*x/abs(2*x + 5) - 17/23*sqrt(23)/abs(2*x + 5)) + 27235421/14216269824*x/sqrt(2*x^2 - x + 3) - 36393601/4738756608/sqrt(2*x^2 - x + 3) + 2323723/103016448*x/(2*x^2 - x + 3)^(3/2) - 3667/1152/(4*(2*x^2 - x + 3)^(3/2)*x^2 + 20*(2*x^2 - x + 3)^(3/2)*x + 25*(2*x^2 - x + 3)^(3/2)) + 115369/82944/(2*(2*x^2 - x + 3)^(3/2)*x + 5*(2*x^2 - x + 3)^(3/2)) - 5254255/34338816/(2*x^2 - x + 3)^(3/2)","A",0
364,1,246,0,1.013233," ","integrate((5*x^4-x^3+3*x^2+x+2)/(5+2*x)^4/(2*x^2-x+3)^(5/2),x, algorithm=""maxima"")","-\frac{4778789}{15479341056} \, \sqrt{2} \operatorname{arsinh}\left(\frac{22 \, \sqrt{23} x}{23 \, {\left| 2 \, x + 5 \right|}} - \frac{17 \, \sqrt{23}}{23 \, {\left| 2 \, x + 5 \right|}}\right) + \frac{416525263 \, x}{341190475776 \, \sqrt{2 \, x^{2} - x + 3}} - \frac{245375387}{113730158592 \, \sqrt{2 \, x^{2} - x + 3}} + \frac{16932905 \, x}{2472394752 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}} - \frac{3667}{1728 \, {\left(8 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}} x^{3} + 60 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}} x^{2} + 150 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}} x + 125 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}\right)}} + \frac{25951}{27648 \, {\left(4 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}} x^{2} + 20 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}} x + 25 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}\right)}} - \frac{34861}{1990656 \, {\left(2 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}} x + 5 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}\right)}} - \frac{10570421}{824131584 \, {\left(2 \, x^{2} - x + 3\right)}^{\frac{3}{2}}}"," ",0,"-4778789/15479341056*sqrt(2)*arcsinh(22/23*sqrt(23)*x/abs(2*x + 5) - 17/23*sqrt(23)/abs(2*x + 5)) + 416525263/341190475776*x/sqrt(2*x^2 - x + 3) - 245375387/113730158592/sqrt(2*x^2 - x + 3) + 16932905/2472394752*x/(2*x^2 - x + 3)^(3/2) - 3667/1728/(8*(2*x^2 - x + 3)^(3/2)*x^3 + 60*(2*x^2 - x + 3)^(3/2)*x^2 + 150*(2*x^2 - x + 3)^(3/2)*x + 125*(2*x^2 - x + 3)^(3/2)) + 25951/27648/(4*(2*x^2 - x + 3)^(3/2)*x^2 + 20*(2*x^2 - x + 3)^(3/2)*x + 25*(2*x^2 - x + 3)^(3/2)) - 34861/1990656/(2*(2*x^2 - x + 3)^(3/2)*x + 5*(2*x^2 - x + 3)^(3/2)) - 10570421/824131584/(2*x^2 - x + 3)^(3/2)","A",0
365,-2,0,0,0.000000," ","integrate((j*x^4+i*x^3+h*x^2+g*x+f)/(c*x^2+b*x+a)^(5/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 zero or nonzero?","F(-2)",0
366,0,0,0,0.000000," ","integrate((j*x^4+i*x^3+h*x^2+g*x+f)/(-c*x^2+b*x+a)^(5/2),x, algorithm=""maxima"")","-\frac{1}{3} \, i {\left(\frac{32 \, a b x}{\sqrt{-c x^{2} + b x + a} {\left(b^{2} + 4 \, a c\right)}^{2}} - \frac{16 \, a b^{2}}{\sqrt{-c x^{2} + b x + a} {\left(b^{2} + 4 \, a c\right)}^{2} c} + \frac{b^{3} x}{{\left(-c x^{2} + b x + a\right)}^{\frac{3}{2}} {\left(b^{2} + 4 \, a c\right)} c^{2}} + \frac{2 \, {\left(b^{2} - 4 \, a c\right)} b x}{\sqrt{-c x^{2} + b x + a} {\left(b^{2} + 4 \, a c\right)}^{2} c} + \frac{6 \, a b x}{{\left(-c x^{2} + b x + a\right)}^{\frac{3}{2}} {\left(b^{2} + 4 \, a c\right)} c} - \frac{3 \, x^{2}}{{\left(-c x^{2} + b x + a\right)}^{\frac{3}{2}} c} - \frac{{\left(b^{2} - 4 \, a c\right)} b^{2}}{\sqrt{-c x^{2} + b x + a} {\left(b^{2} + 4 \, a c\right)}^{2} c^{2}} - \frac{a b^{2}}{{\left(-c x^{2} + b x + a\right)}^{\frac{3}{2}} {\left(b^{2} + 4 \, a c\right)} c^{2}} + \frac{2 \, a}{{\left(-c x^{2} + b x + a\right)}^{\frac{3}{2}} c^{2}}\right)} + \frac{1}{3} \, g {\left(\frac{16 \, b c x}{\sqrt{-c x^{2} + b x + a} {\left(b^{2} + 4 \, a c\right)}^{2}} - \frac{8 \, b^{2}}{\sqrt{-c x^{2} + b x + a} {\left(b^{2} + 4 \, a c\right)}^{2}} + \frac{2 \, b x}{{\left(-c x^{2} + b x + a\right)}^{\frac{3}{2}} {\left(b^{2} + 4 \, a c\right)}} - \frac{b^{2}}{{\left(-c x^{2} + b x + a\right)}^{\frac{3}{2}} {\left(b^{2} + 4 \, a c\right)} c} + \frac{1}{{\left(-c x^{2} + b x + a\right)}^{\frac{3}{2}} c}\right)} + \frac{2}{3} \, f {\left(\frac{16 \, c^{2} x}{\sqrt{-c x^{2} + b x + a} {\left(b^{2} + 4 \, a c\right)}^{2}} - \frac{8 \, b c}{\sqrt{-c x^{2} + b x + a} {\left(b^{2} + 4 \, a c\right)}^{2}} + \frac{2 \, c x}{{\left(-c x^{2} + b x + a\right)}^{\frac{3}{2}} {\left(b^{2} + 4 \, a c\right)}} - \frac{b}{{\left(-c x^{2} + b x + a\right)}^{\frac{3}{2}} {\left(b^{2} + 4 \, a c\right)}}\right)} + \frac{2}{3} \, h {\left(\frac{2 \, {\left(b^{2} - 4 \, a c\right)} x}{\sqrt{-c x^{2} + b x + a} {\left(b^{2} + 4 \, a c\right)}^{2}} + \frac{2 \, a x}{{\left(-c x^{2} + b x + a\right)}^{\frac{3}{2}} {\left(b^{2} + 4 \, a c\right)}} + \frac{b^{2} x}{{\left(-c x^{2} + b x + a\right)}^{\frac{3}{2}} {\left(b^{2} + 4 \, a c\right)} c} - \frac{{\left(b^{2} - 4 \, a c\right)} b}{\sqrt{-c x^{2} + b x + a} {\left(b^{2} + 4 \, a c\right)}^{2} c} + \frac{a b}{{\left(-c x^{2} + b x + a\right)}^{\frac{3}{2}} {\left(b^{2} + 4 \, a c\right)} c}\right)} + j \int \frac{x^{4}}{{\left(c^{2} x^{4} - 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} - 2 \, a c\right)} x^{2} + a^{2}\right)} \sqrt{-c x^{2} + b x + a}}\,{d x}"," ",0,"-1/3*i*(32*a*b*x/(sqrt(-c*x^2 + b*x + a)*(b^2 + 4*a*c)^2) - 16*a*b^2/(sqrt(-c*x^2 + b*x + a)*(b^2 + 4*a*c)^2*c) + b^3*x/((-c*x^2 + b*x + a)^(3/2)*(b^2 + 4*a*c)*c^2) + 2*(b^2 - 4*a*c)*b*x/(sqrt(-c*x^2 + b*x + a)*(b^2 + 4*a*c)^2*c) + 6*a*b*x/((-c*x^2 + b*x + a)^(3/2)*(b^2 + 4*a*c)*c) - 3*x^2/((-c*x^2 + b*x + a)^(3/2)*c) - (b^2 - 4*a*c)*b^2/(sqrt(-c*x^2 + b*x + a)*(b^2 + 4*a*c)^2*c^2) - a*b^2/((-c*x^2 + b*x + a)^(3/2)*(b^2 + 4*a*c)*c^2) + 2*a/((-c*x^2 + b*x + a)^(3/2)*c^2)) + 1/3*g*(16*b*c*x/(sqrt(-c*x^2 + b*x + a)*(b^2 + 4*a*c)^2) - 8*b^2/(sqrt(-c*x^2 + b*x + a)*(b^2 + 4*a*c)^2) + 2*b*x/((-c*x^2 + b*x + a)^(3/2)*(b^2 + 4*a*c)) - b^2/((-c*x^2 + b*x + a)^(3/2)*(b^2 + 4*a*c)*c) + 1/((-c*x^2 + b*x + a)^(3/2)*c)) + 2/3*f*(16*c^2*x/(sqrt(-c*x^2 + b*x + a)*(b^2 + 4*a*c)^2) - 8*b*c/(sqrt(-c*x^2 + b*x + a)*(b^2 + 4*a*c)^2) + 2*c*x/((-c*x^2 + b*x + a)^(3/2)*(b^2 + 4*a*c)) - b/((-c*x^2 + b*x + a)^(3/2)*(b^2 + 4*a*c))) + 2/3*h*(2*(b^2 - 4*a*c)*x/(sqrt(-c*x^2 + b*x + a)*(b^2 + 4*a*c)^2) + 2*a*x/((-c*x^2 + b*x + a)^(3/2)*(b^2 + 4*a*c)) + b^2*x/((-c*x^2 + b*x + a)^(3/2)*(b^2 + 4*a*c)*c) - (b^2 - 4*a*c)*b/(sqrt(-c*x^2 + b*x + a)*(b^2 + 4*a*c)^2*c) + a*b/((-c*x^2 + b*x + a)^(3/2)*(b^2 + 4*a*c)*c)) + j*integrate(x^4/((c^2*x^4 - 2*b*c*x^3 + 2*a*b*x + (b^2 - 2*a*c)*x^2 + a^2)*sqrt(-c*x^2 + b*x + a)), x)","F",0
367,1,2292,0,0.744588," ","integrate((e*x+d)^m*(5*x^2+2*x+3)^3*(4*x^4-5*x^3+3*x^2+x+2),x, algorithm=""maxima"")","\frac{135 \, {\left(e^{2} {\left(m + 1\right)} x^{2} + d e m x - d^{2}\right)} {\left(e x + d\right)}^{m}}{{\left(m^{2} + 3 \, m + 2\right)} e^{2}} + \frac{54 \, {\left(e x + d\right)}^{m + 1}}{e {\left(m + 1\right)}} + \frac{477 \, {\left({\left(m^{2} + 3 \, m + 2\right)} e^{3} x^{3} + {\left(m^{2} + m\right)} d e^{2} x^{2} - 2 \, d^{2} e m x + 2 \, d^{3}\right)} {\left(e x + d\right)}^{m}}{{\left(m^{3} + 6 \, m^{2} + 11 \, m + 6\right)} e^{3}} + \frac{574 \, {\left({\left(m^{3} + 6 \, m^{2} + 11 \, m + 6\right)} e^{4} x^{4} + {\left(m^{3} + 3 \, m^{2} + 2 \, m\right)} d e^{3} x^{3} - 3 \, {\left(m^{2} + m\right)} d^{2} e^{2} x^{2} + 6 \, d^{3} e m x - 6 \, d^{4}\right)} {\left(e x + d\right)}^{m}}{{\left(m^{4} + 10 \, m^{3} + 35 \, m^{2} + 50 \, m + 24\right)} e^{4}} + \frac{1109 \, {\left({\left(m^{4} + 10 \, m^{3} + 35 \, m^{2} + 50 \, m + 24\right)} e^{5} x^{5} + {\left(m^{4} + 6 \, m^{3} + 11 \, m^{2} + 6 \, m\right)} d e^{4} x^{4} - 4 \, {\left(m^{3} + 3 \, m^{2} + 2 \, m\right)} d^{2} e^{3} x^{3} + 12 \, {\left(m^{2} + m\right)} d^{3} e^{2} x^{2} - 24 \, d^{4} e m x + 24 \, d^{5}\right)} {\left(e x + d\right)}^{m}}{{\left(m^{5} + 15 \, m^{4} + 85 \, m^{3} + 225 \, m^{2} + 274 \, m + 120\right)} e^{5}} + \frac{510 \, {\left({\left(m^{5} + 15 \, m^{4} + 85 \, m^{3} + 225 \, m^{2} + 274 \, m + 120\right)} e^{6} x^{6} + {\left(m^{5} + 10 \, m^{4} + 35 \, m^{3} + 50 \, m^{2} + 24 \, m\right)} d e^{5} x^{5} - 5 \, {\left(m^{4} + 6 \, m^{3} + 11 \, m^{2} + 6 \, m\right)} d^{2} e^{4} x^{4} + 20 \, {\left(m^{3} + 3 \, m^{2} + 2 \, m\right)} d^{3} e^{3} x^{3} - 60 \, {\left(m^{2} + m\right)} d^{4} e^{2} x^{2} + 120 \, d^{5} e m x - 120 \, d^{6}\right)} {\left(e x + d\right)}^{m}}{{\left(m^{6} + 21 \, m^{5} + 175 \, m^{4} + 735 \, m^{3} + 1624 \, m^{2} + 1764 \, m + 720\right)} e^{6}} + \frac{999 \, {\left({\left(m^{6} + 21 \, m^{5} + 175 \, m^{4} + 735 \, m^{3} + 1624 \, m^{2} + 1764 \, m + 720\right)} e^{7} x^{7} + {\left(m^{6} + 15 \, m^{5} + 85 \, m^{4} + 225 \, m^{3} + 274 \, m^{2} + 120 \, m\right)} d e^{6} x^{6} - 6 \, {\left(m^{5} + 10 \, m^{4} + 35 \, m^{3} + 50 \, m^{2} + 24 \, m\right)} d^{2} e^{5} x^{5} + 30 \, {\left(m^{4} + 6 \, m^{3} + 11 \, m^{2} + 6 \, m\right)} d^{3} e^{4} x^{4} - 120 \, {\left(m^{3} + 3 \, m^{2} + 2 \, m\right)} d^{4} e^{3} x^{3} + 360 \, {\left(m^{2} + m\right)} d^{5} e^{2} x^{2} - 720 \, d^{6} e m x + 720 \, d^{7}\right)} {\left(e x + d\right)}^{m}}{{\left(m^{7} + 28 \, m^{6} + 322 \, m^{5} + 1960 \, m^{4} + 6769 \, m^{3} + 13132 \, m^{2} + 13068 \, m + 5040\right)} e^{7}} - \frac{98 \, {\left({\left(m^{7} + 28 \, m^{6} + 322 \, m^{5} + 1960 \, m^{4} + 6769 \, m^{3} + 13132 \, m^{2} + 13068 \, m + 5040\right)} e^{8} x^{8} + {\left(m^{7} + 21 \, m^{6} + 175 \, m^{5} + 735 \, m^{4} + 1624 \, m^{3} + 1764 \, m^{2} + 720 \, m\right)} d e^{7} x^{7} - 7 \, {\left(m^{6} + 15 \, m^{5} + 85 \, m^{4} + 225 \, m^{3} + 274 \, m^{2} + 120 \, m\right)} d^{2} e^{6} x^{6} + 42 \, {\left(m^{5} + 10 \, m^{4} + 35 \, m^{3} + 50 \, m^{2} + 24 \, m\right)} d^{3} e^{5} x^{5} - 210 \, {\left(m^{4} + 6 \, m^{3} + 11 \, m^{2} + 6 \, m\right)} d^{4} e^{4} x^{4} + 840 \, {\left(m^{3} + 3 \, m^{2} + 2 \, m\right)} d^{5} e^{3} x^{3} - 2520 \, {\left(m^{2} + m\right)} d^{6} e^{2} x^{2} + 5040 \, d^{7} e m x - 5040 \, d^{8}\right)} {\left(e x + d\right)}^{m}}{{\left(m^{8} + 36 \, m^{7} + 546 \, m^{6} + 4536 \, m^{5} + 22449 \, m^{4} + 67284 \, m^{3} + 118124 \, m^{2} + 109584 \, m + 40320\right)} e^{8}} + \frac{765 \, {\left({\left(m^{8} + 36 \, m^{7} + 546 \, m^{6} + 4536 \, m^{5} + 22449 \, m^{4} + 67284 \, m^{3} + 118124 \, m^{2} + 109584 \, m + 40320\right)} e^{9} x^{9} + {\left(m^{8} + 28 \, m^{7} + 322 \, m^{6} + 1960 \, m^{5} + 6769 \, m^{4} + 13132 \, m^{3} + 13068 \, m^{2} + 5040 \, m\right)} d e^{8} x^{8} - 8 \, {\left(m^{7} + 21 \, m^{6} + 175 \, m^{5} + 735 \, m^{4} + 1624 \, m^{3} + 1764 \, m^{2} + 720 \, m\right)} d^{2} e^{7} x^{7} + 56 \, {\left(m^{6} + 15 \, m^{5} + 85 \, m^{4} + 225 \, m^{3} + 274 \, m^{2} + 120 \, m\right)} d^{3} e^{6} x^{6} - 336 \, {\left(m^{5} + 10 \, m^{4} + 35 \, m^{3} + 50 \, m^{2} + 24 \, m\right)} d^{4} e^{5} x^{5} + 1680 \, {\left(m^{4} + 6 \, m^{3} + 11 \, m^{2} + 6 \, m\right)} d^{5} e^{4} x^{4} - 6720 \, {\left(m^{3} + 3 \, m^{2} + 2 \, m\right)} d^{6} e^{3} x^{3} + 20160 \, {\left(m^{2} + m\right)} d^{7} e^{2} x^{2} - 40320 \, d^{8} e m x + 40320 \, d^{9}\right)} {\left(e x + d\right)}^{m}}{{\left(m^{9} + 45 \, m^{8} + 870 \, m^{7} + 9450 \, m^{6} + 63273 \, m^{5} + 269325 \, m^{4} + 723680 \, m^{3} + 1172700 \, m^{2} + 1026576 \, m + 362880\right)} e^{9}} - \frac{25 \, {\left({\left(m^{9} + 45 \, m^{8} + 870 \, m^{7} + 9450 \, m^{6} + 63273 \, m^{5} + 269325 \, m^{4} + 723680 \, m^{3} + 1172700 \, m^{2} + 1026576 \, m + 362880\right)} e^{10} x^{10} + {\left(m^{9} + 36 \, m^{8} + 546 \, m^{7} + 4536 \, m^{6} + 22449 \, m^{5} + 67284 \, m^{4} + 118124 \, m^{3} + 109584 \, m^{2} + 40320 \, m\right)} d e^{9} x^{9} - 9 \, {\left(m^{8} + 28 \, m^{7} + 322 \, m^{6} + 1960 \, m^{5} + 6769 \, m^{4} + 13132 \, m^{3} + 13068 \, m^{2} + 5040 \, m\right)} d^{2} e^{8} x^{8} + 72 \, {\left(m^{7} + 21 \, m^{6} + 175 \, m^{5} + 735 \, m^{4} + 1624 \, m^{3} + 1764 \, m^{2} + 720 \, m\right)} d^{3} e^{7} x^{7} - 504 \, {\left(m^{6} + 15 \, m^{5} + 85 \, m^{4} + 225 \, m^{3} + 274 \, m^{2} + 120 \, m\right)} d^{4} e^{6} x^{6} + 3024 \, {\left(m^{5} + 10 \, m^{4} + 35 \, m^{3} + 50 \, m^{2} + 24 \, m\right)} d^{5} e^{5} x^{5} - 15120 \, {\left(m^{4} + 6 \, m^{3} + 11 \, m^{2} + 6 \, m\right)} d^{6} e^{4} x^{4} + 60480 \, {\left(m^{3} + 3 \, m^{2} + 2 \, m\right)} d^{7} e^{3} x^{3} - 181440 \, {\left(m^{2} + m\right)} d^{8} e^{2} x^{2} + 362880 \, d^{9} e m x - 362880 \, d^{10}\right)} {\left(e x + d\right)}^{m}}{{\left(m^{10} + 55 \, m^{9} + 1320 \, m^{8} + 18150 \, m^{7} + 157773 \, m^{6} + 902055 \, m^{5} + 3416930 \, m^{4} + 8409500 \, m^{3} + 12753576 \, m^{2} + 10628640 \, m + 3628800\right)} e^{10}} + \frac{500 \, {\left({\left(m^{10} + 55 \, m^{9} + 1320 \, m^{8} + 18150 \, m^{7} + 157773 \, m^{6} + 902055 \, m^{5} + 3416930 \, m^{4} + 8409500 \, m^{3} + 12753576 \, m^{2} + 10628640 \, m + 3628800\right)} e^{11} x^{11} + {\left(m^{10} + 45 \, m^{9} + 870 \, m^{8} + 9450 \, m^{7} + 63273 \, m^{6} + 269325 \, m^{5} + 723680 \, m^{4} + 1172700 \, m^{3} + 1026576 \, m^{2} + 362880 \, m\right)} d e^{10} x^{10} - 10 \, {\left(m^{9} + 36 \, m^{8} + 546 \, m^{7} + 4536 \, m^{6} + 22449 \, m^{5} + 67284 \, m^{4} + 118124 \, m^{3} + 109584 \, m^{2} + 40320 \, m\right)} d^{2} e^{9} x^{9} + 90 \, {\left(m^{8} + 28 \, m^{7} + 322 \, m^{6} + 1960 \, m^{5} + 6769 \, m^{4} + 13132 \, m^{3} + 13068 \, m^{2} + 5040 \, m\right)} d^{3} e^{8} x^{8} - 720 \, {\left(m^{7} + 21 \, m^{6} + 175 \, m^{5} + 735 \, m^{4} + 1624 \, m^{3} + 1764 \, m^{2} + 720 \, m\right)} d^{4} e^{7} x^{7} + 5040 \, {\left(m^{6} + 15 \, m^{5} + 85 \, m^{4} + 225 \, m^{3} + 274 \, m^{2} + 120 \, m\right)} d^{5} e^{6} x^{6} - 30240 \, {\left(m^{5} + 10 \, m^{4} + 35 \, m^{3} + 50 \, m^{2} + 24 \, m\right)} d^{6} e^{5} x^{5} + 151200 \, {\left(m^{4} + 6 \, m^{3} + 11 \, m^{2} + 6 \, m\right)} d^{7} e^{4} x^{4} - 604800 \, {\left(m^{3} + 3 \, m^{2} + 2 \, m\right)} d^{8} e^{3} x^{3} + 1814400 \, {\left(m^{2} + m\right)} d^{9} e^{2} x^{2} - 3628800 \, d^{10} e m x + 3628800 \, d^{11}\right)} {\left(e x + d\right)}^{m}}{{\left(m^{11} + 66 \, m^{10} + 1925 \, m^{9} + 32670 \, m^{8} + 357423 \, m^{7} + 2637558 \, m^{6} + 13339535 \, m^{5} + 45995730 \, m^{4} + 105258076 \, m^{3} + 150917976 \, m^{2} + 120543840 \, m + 39916800\right)} e^{11}}"," ",0,"135*(e^2*(m + 1)*x^2 + d*e*m*x - d^2)*(e*x + d)^m/((m^2 + 3*m + 2)*e^2) + 54*(e*x + d)^(m + 1)/(e*(m + 1)) + 477*((m^2 + 3*m + 2)*e^3*x^3 + (m^2 + m)*d*e^2*x^2 - 2*d^2*e*m*x + 2*d^3)*(e*x + d)^m/((m^3 + 6*m^2 + 11*m + 6)*e^3) + 574*((m^3 + 6*m^2 + 11*m + 6)*e^4*x^4 + (m^3 + 3*m^2 + 2*m)*d*e^3*x^3 - 3*(m^2 + m)*d^2*e^2*x^2 + 6*d^3*e*m*x - 6*d^4)*(e*x + d)^m/((m^4 + 10*m^3 + 35*m^2 + 50*m + 24)*e^4) + 1109*((m^4 + 10*m^3 + 35*m^2 + 50*m + 24)*e^5*x^5 + (m^4 + 6*m^3 + 11*m^2 + 6*m)*d*e^4*x^4 - 4*(m^3 + 3*m^2 + 2*m)*d^2*e^3*x^3 + 12*(m^2 + m)*d^3*e^2*x^2 - 24*d^4*e*m*x + 24*d^5)*(e*x + d)^m/((m^5 + 15*m^4 + 85*m^3 + 225*m^2 + 274*m + 120)*e^5) + 510*((m^5 + 15*m^4 + 85*m^3 + 225*m^2 + 274*m + 120)*e^6*x^6 + (m^5 + 10*m^4 + 35*m^3 + 50*m^2 + 24*m)*d*e^5*x^5 - 5*(m^4 + 6*m^3 + 11*m^2 + 6*m)*d^2*e^4*x^4 + 20*(m^3 + 3*m^2 + 2*m)*d^3*e^3*x^3 - 60*(m^2 + m)*d^4*e^2*x^2 + 120*d^5*e*m*x - 120*d^6)*(e*x + d)^m/((m^6 + 21*m^5 + 175*m^4 + 735*m^3 + 1624*m^2 + 1764*m + 720)*e^6) + 999*((m^6 + 21*m^5 + 175*m^4 + 735*m^3 + 1624*m^2 + 1764*m + 720)*e^7*x^7 + (m^6 + 15*m^5 + 85*m^4 + 225*m^3 + 274*m^2 + 120*m)*d*e^6*x^6 - 6*(m^5 + 10*m^4 + 35*m^3 + 50*m^2 + 24*m)*d^2*e^5*x^5 + 30*(m^4 + 6*m^3 + 11*m^2 + 6*m)*d^3*e^4*x^4 - 120*(m^3 + 3*m^2 + 2*m)*d^4*e^3*x^3 + 360*(m^2 + m)*d^5*e^2*x^2 - 720*d^6*e*m*x + 720*d^7)*(e*x + d)^m/((m^7 + 28*m^6 + 322*m^5 + 1960*m^4 + 6769*m^3 + 13132*m^2 + 13068*m + 5040)*e^7) - 98*((m^7 + 28*m^6 + 322*m^5 + 1960*m^4 + 6769*m^3 + 13132*m^2 + 13068*m + 5040)*e^8*x^8 + (m^7 + 21*m^6 + 175*m^5 + 735*m^4 + 1624*m^3 + 1764*m^2 + 720*m)*d*e^7*x^7 - 7*(m^6 + 15*m^5 + 85*m^4 + 225*m^3 + 274*m^2 + 120*m)*d^2*e^6*x^6 + 42*(m^5 + 10*m^4 + 35*m^3 + 50*m^2 + 24*m)*d^3*e^5*x^5 - 210*(m^4 + 6*m^3 + 11*m^2 + 6*m)*d^4*e^4*x^4 + 840*(m^3 + 3*m^2 + 2*m)*d^5*e^3*x^3 - 2520*(m^2 + m)*d^6*e^2*x^2 + 5040*d^7*e*m*x - 5040*d^8)*(e*x + d)^m/((m^8 + 36*m^7 + 546*m^6 + 4536*m^5 + 22449*m^4 + 67284*m^3 + 118124*m^2 + 109584*m + 40320)*e^8) + 765*((m^8 + 36*m^7 + 546*m^6 + 4536*m^5 + 22449*m^4 + 67284*m^3 + 118124*m^2 + 109584*m + 40320)*e^9*x^9 + (m^8 + 28*m^7 + 322*m^6 + 1960*m^5 + 6769*m^4 + 13132*m^3 + 13068*m^2 + 5040*m)*d*e^8*x^8 - 8*(m^7 + 21*m^6 + 175*m^5 + 735*m^4 + 1624*m^3 + 1764*m^2 + 720*m)*d^2*e^7*x^7 + 56*(m^6 + 15*m^5 + 85*m^4 + 225*m^3 + 274*m^2 + 120*m)*d^3*e^6*x^6 - 336*(m^5 + 10*m^4 + 35*m^3 + 50*m^2 + 24*m)*d^4*e^5*x^5 + 1680*(m^4 + 6*m^3 + 11*m^2 + 6*m)*d^5*e^4*x^4 - 6720*(m^3 + 3*m^2 + 2*m)*d^6*e^3*x^3 + 20160*(m^2 + m)*d^7*e^2*x^2 - 40320*d^8*e*m*x + 40320*d^9)*(e*x + d)^m/((m^9 + 45*m^8 + 870*m^7 + 9450*m^6 + 63273*m^5 + 269325*m^4 + 723680*m^3 + 1172700*m^2 + 1026576*m + 362880)*e^9) - 25*((m^9 + 45*m^8 + 870*m^7 + 9450*m^6 + 63273*m^5 + 269325*m^4 + 723680*m^3 + 1172700*m^2 + 1026576*m + 362880)*e^10*x^10 + (m^9 + 36*m^8 + 546*m^7 + 4536*m^6 + 22449*m^5 + 67284*m^4 + 118124*m^3 + 109584*m^2 + 40320*m)*d*e^9*x^9 - 9*(m^8 + 28*m^7 + 322*m^6 + 1960*m^5 + 6769*m^4 + 13132*m^3 + 13068*m^2 + 5040*m)*d^2*e^8*x^8 + 72*(m^7 + 21*m^6 + 175*m^5 + 735*m^4 + 1624*m^3 + 1764*m^2 + 720*m)*d^3*e^7*x^7 - 504*(m^6 + 15*m^5 + 85*m^4 + 225*m^3 + 274*m^2 + 120*m)*d^4*e^6*x^6 + 3024*(m^5 + 10*m^4 + 35*m^3 + 50*m^2 + 24*m)*d^5*e^5*x^5 - 15120*(m^4 + 6*m^3 + 11*m^2 + 6*m)*d^6*e^4*x^4 + 60480*(m^3 + 3*m^2 + 2*m)*d^7*e^3*x^3 - 181440*(m^2 + m)*d^8*e^2*x^2 + 362880*d^9*e*m*x - 362880*d^10)*(e*x + d)^m/((m^10 + 55*m^9 + 1320*m^8 + 18150*m^7 + 157773*m^6 + 902055*m^5 + 3416930*m^4 + 8409500*m^3 + 12753576*m^2 + 10628640*m + 3628800)*e^10) + 500*((m^10 + 55*m^9 + 1320*m^8 + 18150*m^7 + 157773*m^6 + 902055*m^5 + 3416930*m^4 + 8409500*m^3 + 12753576*m^2 + 10628640*m + 3628800)*e^11*x^11 + (m^10 + 45*m^9 + 870*m^8 + 9450*m^7 + 63273*m^6 + 269325*m^5 + 723680*m^4 + 1172700*m^3 + 1026576*m^2 + 362880*m)*d*e^10*x^10 - 10*(m^9 + 36*m^8 + 546*m^7 + 4536*m^6 + 22449*m^5 + 67284*m^4 + 118124*m^3 + 109584*m^2 + 40320*m)*d^2*e^9*x^9 + 90*(m^8 + 28*m^7 + 322*m^6 + 1960*m^5 + 6769*m^4 + 13132*m^3 + 13068*m^2 + 5040*m)*d^3*e^8*x^8 - 720*(m^7 + 21*m^6 + 175*m^5 + 735*m^4 + 1624*m^3 + 1764*m^2 + 720*m)*d^4*e^7*x^7 + 5040*(m^6 + 15*m^5 + 85*m^4 + 225*m^3 + 274*m^2 + 120*m)*d^5*e^6*x^6 - 30240*(m^5 + 10*m^4 + 35*m^3 + 50*m^2 + 24*m)*d^6*e^5*x^5 + 151200*(m^4 + 6*m^3 + 11*m^2 + 6*m)*d^7*e^4*x^4 - 604800*(m^3 + 3*m^2 + 2*m)*d^8*e^3*x^3 + 1814400*(m^2 + m)*d^9*e^2*x^2 - 3628800*d^10*e*m*x + 3628800*d^11)*(e*x + d)^m/((m^11 + 66*m^10 + 1925*m^9 + 32670*m^8 + 357423*m^7 + 2637558*m^6 + 13339535*m^5 + 45995730*m^4 + 105258076*m^3 + 150917976*m^2 + 120543840*m + 39916800)*e^11)","B",0
368,1,1414,0,0.640918," ","integrate((e*x+d)^m*(5*x^2+2*x+3)^2*(4*x^4-5*x^3+3*x^2+x+2),x, algorithm=""maxima"")","\frac{33 \, {\left(e^{2} {\left(m + 1\right)} x^{2} + d e m x - d^{2}\right)} {\left(e x + d\right)}^{m}}{{\left(m^{2} + 3 \, m + 2\right)} e^{2}} + \frac{18 \, {\left(e x + d\right)}^{m + 1}}{e {\left(m + 1\right)}} + \frac{107 \, {\left({\left(m^{2} + 3 \, m + 2\right)} e^{3} x^{3} + {\left(m^{2} + m\right)} d e^{2} x^{2} - 2 \, d^{2} e m x + 2 \, d^{3}\right)} {\left(e x + d\right)}^{m}}{{\left(m^{3} + 6 \, m^{2} + 11 \, m + 6\right)} e^{3}} + \frac{65 \, {\left({\left(m^{3} + 6 \, m^{2} + 11 \, m + 6\right)} e^{4} x^{4} + {\left(m^{3} + 3 \, m^{2} + 2 \, m\right)} d e^{3} x^{3} - 3 \, {\left(m^{2} + m\right)} d^{2} e^{2} x^{2} + 6 \, d^{3} e m x - 6 \, d^{4}\right)} {\left(e x + d\right)}^{m}}{{\left(m^{4} + 10 \, m^{3} + 35 \, m^{2} + 50 \, m + 24\right)} e^{4}} + \frac{148 \, {\left({\left(m^{4} + 10 \, m^{3} + 35 \, m^{2} + 50 \, m + 24\right)} e^{5} x^{5} + {\left(m^{4} + 6 \, m^{3} + 11 \, m^{2} + 6 \, m\right)} d e^{4} x^{4} - 4 \, {\left(m^{3} + 3 \, m^{2} + 2 \, m\right)} d^{2} e^{3} x^{3} + 12 \, {\left(m^{2} + m\right)} d^{3} e^{2} x^{2} - 24 \, d^{4} e m x + 24 \, d^{5}\right)} {\left(e x + d\right)}^{m}}{{\left(m^{5} + 15 \, m^{4} + 85 \, m^{3} + 225 \, m^{2} + 274 \, m + 120\right)} e^{5}} - \frac{37 \, {\left({\left(m^{5} + 15 \, m^{4} + 85 \, m^{3} + 225 \, m^{2} + 274 \, m + 120\right)} e^{6} x^{6} + {\left(m^{5} + 10 \, m^{4} + 35 \, m^{3} + 50 \, m^{2} + 24 \, m\right)} d e^{5} x^{5} - 5 \, {\left(m^{4} + 6 \, m^{3} + 11 \, m^{2} + 6 \, m\right)} d^{2} e^{4} x^{4} + 20 \, {\left(m^{3} + 3 \, m^{2} + 2 \, m\right)} d^{3} e^{3} x^{3} - 60 \, {\left(m^{2} + m\right)} d^{4} e^{2} x^{2} + 120 \, d^{5} e m x - 120 \, d^{6}\right)} {\left(e x + d\right)}^{m}}{{\left(m^{6} + 21 \, m^{5} + 175 \, m^{4} + 735 \, m^{3} + 1624 \, m^{2} + 1764 \, m + 720\right)} e^{6}} + \frac{111 \, {\left({\left(m^{6} + 21 \, m^{5} + 175 \, m^{4} + 735 \, m^{3} + 1624 \, m^{2} + 1764 \, m + 720\right)} e^{7} x^{7} + {\left(m^{6} + 15 \, m^{5} + 85 \, m^{4} + 225 \, m^{3} + 274 \, m^{2} + 120 \, m\right)} d e^{6} x^{6} - 6 \, {\left(m^{5} + 10 \, m^{4} + 35 \, m^{3} + 50 \, m^{2} + 24 \, m\right)} d^{2} e^{5} x^{5} + 30 \, {\left(m^{4} + 6 \, m^{3} + 11 \, m^{2} + 6 \, m\right)} d^{3} e^{4} x^{4} - 120 \, {\left(m^{3} + 3 \, m^{2} + 2 \, m\right)} d^{4} e^{3} x^{3} + 360 \, {\left(m^{2} + m\right)} d^{5} e^{2} x^{2} - 720 \, d^{6} e m x + 720 \, d^{7}\right)} {\left(e x + d\right)}^{m}}{{\left(m^{7} + 28 \, m^{6} + 322 \, m^{5} + 1960 \, m^{4} + 6769 \, m^{3} + 13132 \, m^{2} + 13068 \, m + 5040\right)} e^{7}} - \frac{45 \, {\left({\left(m^{7} + 28 \, m^{6} + 322 \, m^{5} + 1960 \, m^{4} + 6769 \, m^{3} + 13132 \, m^{2} + 13068 \, m + 5040\right)} e^{8} x^{8} + {\left(m^{7} + 21 \, m^{6} + 175 \, m^{5} + 735 \, m^{4} + 1624 \, m^{3} + 1764 \, m^{2} + 720 \, m\right)} d e^{7} x^{7} - 7 \, {\left(m^{6} + 15 \, m^{5} + 85 \, m^{4} + 225 \, m^{3} + 274 \, m^{2} + 120 \, m\right)} d^{2} e^{6} x^{6} + 42 \, {\left(m^{5} + 10 \, m^{4} + 35 \, m^{3} + 50 \, m^{2} + 24 \, m\right)} d^{3} e^{5} x^{5} - 210 \, {\left(m^{4} + 6 \, m^{3} + 11 \, m^{2} + 6 \, m\right)} d^{4} e^{4} x^{4} + 840 \, {\left(m^{3} + 3 \, m^{2} + 2 \, m\right)} d^{5} e^{3} x^{3} - 2520 \, {\left(m^{2} + m\right)} d^{6} e^{2} x^{2} + 5040 \, d^{7} e m x - 5040 \, d^{8}\right)} {\left(e x + d\right)}^{m}}{{\left(m^{8} + 36 \, m^{7} + 546 \, m^{6} + 4536 \, m^{5} + 22449 \, m^{4} + 67284 \, m^{3} + 118124 \, m^{2} + 109584 \, m + 40320\right)} e^{8}} + \frac{100 \, {\left({\left(m^{8} + 36 \, m^{7} + 546 \, m^{6} + 4536 \, m^{5} + 22449 \, m^{4} + 67284 \, m^{3} + 118124 \, m^{2} + 109584 \, m + 40320\right)} e^{9} x^{9} + {\left(m^{8} + 28 \, m^{7} + 322 \, m^{6} + 1960 \, m^{5} + 6769 \, m^{4} + 13132 \, m^{3} + 13068 \, m^{2} + 5040 \, m\right)} d e^{8} x^{8} - 8 \, {\left(m^{7} + 21 \, m^{6} + 175 \, m^{5} + 735 \, m^{4} + 1624 \, m^{3} + 1764 \, m^{2} + 720 \, m\right)} d^{2} e^{7} x^{7} + 56 \, {\left(m^{6} + 15 \, m^{5} + 85 \, m^{4} + 225 \, m^{3} + 274 \, m^{2} + 120 \, m\right)} d^{3} e^{6} x^{6} - 336 \, {\left(m^{5} + 10 \, m^{4} + 35 \, m^{3} + 50 \, m^{2} + 24 \, m\right)} d^{4} e^{5} x^{5} + 1680 \, {\left(m^{4} + 6 \, m^{3} + 11 \, m^{2} + 6 \, m\right)} d^{5} e^{4} x^{4} - 6720 \, {\left(m^{3} + 3 \, m^{2} + 2 \, m\right)} d^{6} e^{3} x^{3} + 20160 \, {\left(m^{2} + m\right)} d^{7} e^{2} x^{2} - 40320 \, d^{8} e m x + 40320 \, d^{9}\right)} {\left(e x + d\right)}^{m}}{{\left(m^{9} + 45 \, m^{8} + 870 \, m^{7} + 9450 \, m^{6} + 63273 \, m^{5} + 269325 \, m^{4} + 723680 \, m^{3} + 1172700 \, m^{2} + 1026576 \, m + 362880\right)} e^{9}}"," ",0,"33*(e^2*(m + 1)*x^2 + d*e*m*x - d^2)*(e*x + d)^m/((m^2 + 3*m + 2)*e^2) + 18*(e*x + d)^(m + 1)/(e*(m + 1)) + 107*((m^2 + 3*m + 2)*e^3*x^3 + (m^2 + m)*d*e^2*x^2 - 2*d^2*e*m*x + 2*d^3)*(e*x + d)^m/((m^3 + 6*m^2 + 11*m + 6)*e^3) + 65*((m^3 + 6*m^2 + 11*m + 6)*e^4*x^4 + (m^3 + 3*m^2 + 2*m)*d*e^3*x^3 - 3*(m^2 + m)*d^2*e^2*x^2 + 6*d^3*e*m*x - 6*d^4)*(e*x + d)^m/((m^4 + 10*m^3 + 35*m^2 + 50*m + 24)*e^4) + 148*((m^4 + 10*m^3 + 35*m^2 + 50*m + 24)*e^5*x^5 + (m^4 + 6*m^3 + 11*m^2 + 6*m)*d*e^4*x^4 - 4*(m^3 + 3*m^2 + 2*m)*d^2*e^3*x^3 + 12*(m^2 + m)*d^3*e^2*x^2 - 24*d^4*e*m*x + 24*d^5)*(e*x + d)^m/((m^5 + 15*m^4 + 85*m^3 + 225*m^2 + 274*m + 120)*e^5) - 37*((m^5 + 15*m^4 + 85*m^3 + 225*m^2 + 274*m + 120)*e^6*x^6 + (m^5 + 10*m^4 + 35*m^3 + 50*m^2 + 24*m)*d*e^5*x^5 - 5*(m^4 + 6*m^3 + 11*m^2 + 6*m)*d^2*e^4*x^4 + 20*(m^3 + 3*m^2 + 2*m)*d^3*e^3*x^3 - 60*(m^2 + m)*d^4*e^2*x^2 + 120*d^5*e*m*x - 120*d^6)*(e*x + d)^m/((m^6 + 21*m^5 + 175*m^4 + 735*m^3 + 1624*m^2 + 1764*m + 720)*e^6) + 111*((m^6 + 21*m^5 + 175*m^4 + 735*m^3 + 1624*m^2 + 1764*m + 720)*e^7*x^7 + (m^6 + 15*m^5 + 85*m^4 + 225*m^3 + 274*m^2 + 120*m)*d*e^6*x^6 - 6*(m^5 + 10*m^4 + 35*m^3 + 50*m^2 + 24*m)*d^2*e^5*x^5 + 30*(m^4 + 6*m^3 + 11*m^2 + 6*m)*d^3*e^4*x^4 - 120*(m^3 + 3*m^2 + 2*m)*d^4*e^3*x^3 + 360*(m^2 + m)*d^5*e^2*x^2 - 720*d^6*e*m*x + 720*d^7)*(e*x + d)^m/((m^7 + 28*m^6 + 322*m^5 + 1960*m^4 + 6769*m^3 + 13132*m^2 + 13068*m + 5040)*e^7) - 45*((m^7 + 28*m^6 + 322*m^5 + 1960*m^4 + 6769*m^3 + 13132*m^2 + 13068*m + 5040)*e^8*x^8 + (m^7 + 21*m^6 + 175*m^5 + 735*m^4 + 1624*m^3 + 1764*m^2 + 720*m)*d*e^7*x^7 - 7*(m^6 + 15*m^5 + 85*m^4 + 225*m^3 + 274*m^2 + 120*m)*d^2*e^6*x^6 + 42*(m^5 + 10*m^4 + 35*m^3 + 50*m^2 + 24*m)*d^3*e^5*x^5 - 210*(m^4 + 6*m^3 + 11*m^2 + 6*m)*d^4*e^4*x^4 + 840*(m^3 + 3*m^2 + 2*m)*d^5*e^3*x^3 - 2520*(m^2 + m)*d^6*e^2*x^2 + 5040*d^7*e*m*x - 5040*d^8)*(e*x + d)^m/((m^8 + 36*m^7 + 546*m^6 + 4536*m^5 + 22449*m^4 + 67284*m^3 + 118124*m^2 + 109584*m + 40320)*e^8) + 100*((m^8 + 36*m^7 + 546*m^6 + 4536*m^5 + 22449*m^4 + 67284*m^3 + 118124*m^2 + 109584*m + 40320)*e^9*x^9 + (m^8 + 28*m^7 + 322*m^6 + 1960*m^5 + 6769*m^4 + 13132*m^3 + 13068*m^2 + 5040*m)*d*e^8*x^8 - 8*(m^7 + 21*m^6 + 175*m^5 + 735*m^4 + 1624*m^3 + 1764*m^2 + 720*m)*d^2*e^7*x^7 + 56*(m^6 + 15*m^5 + 85*m^4 + 225*m^3 + 274*m^2 + 120*m)*d^3*e^6*x^6 - 336*(m^5 + 10*m^4 + 35*m^3 + 50*m^2 + 24*m)*d^4*e^5*x^5 + 1680*(m^4 + 6*m^3 + 11*m^2 + 6*m)*d^5*e^4*x^4 - 6720*(m^3 + 3*m^2 + 2*m)*d^6*e^3*x^3 + 20160*(m^2 + m)*d^7*e^2*x^2 - 40320*d^8*e*m*x + 40320*d^9)*(e*x + d)^m/((m^9 + 45*m^8 + 870*m^7 + 9450*m^6 + 63273*m^5 + 269325*m^4 + 723680*m^3 + 1172700*m^2 + 1026576*m + 362880)*e^9)","B",0
369,1,788,0,0.548241," ","integrate((e*x+d)^m*(5*x^2+2*x+3)*(4*x^4-5*x^3+3*x^2+x+2),x, algorithm=""maxima"")","\frac{7 \, {\left(e^{2} {\left(m + 1\right)} x^{2} + d e m x - d^{2}\right)} {\left(e x + d\right)}^{m}}{{\left(m^{2} + 3 \, m + 2\right)} e^{2}} + \frac{6 \, {\left(e x + d\right)}^{m + 1}}{e {\left(m + 1\right)}} + \frac{21 \, {\left({\left(m^{2} + 3 \, m + 2\right)} e^{3} x^{3} + {\left(m^{2} + m\right)} d e^{2} x^{2} - 2 \, d^{2} e m x + 2 \, d^{3}\right)} {\left(e x + d\right)}^{m}}{{\left(m^{3} + 6 \, m^{2} + 11 \, m + 6\right)} e^{3}} - \frac{4 \, {\left({\left(m^{3} + 6 \, m^{2} + 11 \, m + 6\right)} e^{4} x^{4} + {\left(m^{3} + 3 \, m^{2} + 2 \, m\right)} d e^{3} x^{3} - 3 \, {\left(m^{2} + m\right)} d^{2} e^{2} x^{2} + 6 \, d^{3} e m x - 6 \, d^{4}\right)} {\left(e x + d\right)}^{m}}{{\left(m^{4} + 10 \, m^{3} + 35 \, m^{2} + 50 \, m + 24\right)} e^{4}} + \frac{17 \, {\left({\left(m^{4} + 10 \, m^{3} + 35 \, m^{2} + 50 \, m + 24\right)} e^{5} x^{5} + {\left(m^{4} + 6 \, m^{3} + 11 \, m^{2} + 6 \, m\right)} d e^{4} x^{4} - 4 \, {\left(m^{3} + 3 \, m^{2} + 2 \, m\right)} d^{2} e^{3} x^{3} + 12 \, {\left(m^{2} + m\right)} d^{3} e^{2} x^{2} - 24 \, d^{4} e m x + 24 \, d^{5}\right)} {\left(e x + d\right)}^{m}}{{\left(m^{5} + 15 \, m^{4} + 85 \, m^{3} + 225 \, m^{2} + 274 \, m + 120\right)} e^{5}} - \frac{17 \, {\left({\left(m^{5} + 15 \, m^{4} + 85 \, m^{3} + 225 \, m^{2} + 274 \, m + 120\right)} e^{6} x^{6} + {\left(m^{5} + 10 \, m^{4} + 35 \, m^{3} + 50 \, m^{2} + 24 \, m\right)} d e^{5} x^{5} - 5 \, {\left(m^{4} + 6 \, m^{3} + 11 \, m^{2} + 6 \, m\right)} d^{2} e^{4} x^{4} + 20 \, {\left(m^{3} + 3 \, m^{2} + 2 \, m\right)} d^{3} e^{3} x^{3} - 60 \, {\left(m^{2} + m\right)} d^{4} e^{2} x^{2} + 120 \, d^{5} e m x - 120 \, d^{6}\right)} {\left(e x + d\right)}^{m}}{{\left(m^{6} + 21 \, m^{5} + 175 \, m^{4} + 735 \, m^{3} + 1624 \, m^{2} + 1764 \, m + 720\right)} e^{6}} + \frac{20 \, {\left({\left(m^{6} + 21 \, m^{5} + 175 \, m^{4} + 735 \, m^{3} + 1624 \, m^{2} + 1764 \, m + 720\right)} e^{7} x^{7} + {\left(m^{6} + 15 \, m^{5} + 85 \, m^{4} + 225 \, m^{3} + 274 \, m^{2} + 120 \, m\right)} d e^{6} x^{6} - 6 \, {\left(m^{5} + 10 \, m^{4} + 35 \, m^{3} + 50 \, m^{2} + 24 \, m\right)} d^{2} e^{5} x^{5} + 30 \, {\left(m^{4} + 6 \, m^{3} + 11 \, m^{2} + 6 \, m\right)} d^{3} e^{4} x^{4} - 120 \, {\left(m^{3} + 3 \, m^{2} + 2 \, m\right)} d^{4} e^{3} x^{3} + 360 \, {\left(m^{2} + m\right)} d^{5} e^{2} x^{2} - 720 \, d^{6} e m x + 720 \, d^{7}\right)} {\left(e x + d\right)}^{m}}{{\left(m^{7} + 28 \, m^{6} + 322 \, m^{5} + 1960 \, m^{4} + 6769 \, m^{3} + 13132 \, m^{2} + 13068 \, m + 5040\right)} e^{7}}"," ",0,"7*(e^2*(m + 1)*x^2 + d*e*m*x - d^2)*(e*x + d)^m/((m^2 + 3*m + 2)*e^2) + 6*(e*x + d)^(m + 1)/(e*(m + 1)) + 21*((m^2 + 3*m + 2)*e^3*x^3 + (m^2 + m)*d*e^2*x^2 - 2*d^2*e*m*x + 2*d^3)*(e*x + d)^m/((m^3 + 6*m^2 + 11*m + 6)*e^3) - 4*((m^3 + 6*m^2 + 11*m + 6)*e^4*x^4 + (m^3 + 3*m^2 + 2*m)*d*e^3*x^3 - 3*(m^2 + m)*d^2*e^2*x^2 + 6*d^3*e*m*x - 6*d^4)*(e*x + d)^m/((m^4 + 10*m^3 + 35*m^2 + 50*m + 24)*e^4) + 17*((m^4 + 10*m^3 + 35*m^2 + 50*m + 24)*e^5*x^5 + (m^4 + 6*m^3 + 11*m^2 + 6*m)*d*e^4*x^4 - 4*(m^3 + 3*m^2 + 2*m)*d^2*e^3*x^3 + 12*(m^2 + m)*d^3*e^2*x^2 - 24*d^4*e*m*x + 24*d^5)*(e*x + d)^m/((m^5 + 15*m^4 + 85*m^3 + 225*m^2 + 274*m + 120)*e^5) - 17*((m^5 + 15*m^4 + 85*m^3 + 225*m^2 + 274*m + 120)*e^6*x^6 + (m^5 + 10*m^4 + 35*m^3 + 50*m^2 + 24*m)*d*e^5*x^5 - 5*(m^4 + 6*m^3 + 11*m^2 + 6*m)*d^2*e^4*x^4 + 20*(m^3 + 3*m^2 + 2*m)*d^3*e^3*x^3 - 60*(m^2 + m)*d^4*e^2*x^2 + 120*d^5*e*m*x - 120*d^6)*(e*x + d)^m/((m^6 + 21*m^5 + 175*m^4 + 735*m^3 + 1624*m^2 + 1764*m + 720)*e^6) + 20*((m^6 + 21*m^5 + 175*m^4 + 735*m^3 + 1624*m^2 + 1764*m + 720)*e^7*x^7 + (m^6 + 15*m^5 + 85*m^4 + 225*m^3 + 274*m^2 + 120*m)*d*e^6*x^6 - 6*(m^5 + 10*m^4 + 35*m^3 + 50*m^2 + 24*m)*d^2*e^5*x^5 + 30*(m^4 + 6*m^3 + 11*m^2 + 6*m)*d^3*e^4*x^4 - 120*(m^3 + 3*m^2 + 2*m)*d^4*e^3*x^3 + 360*(m^2 + m)*d^5*e^2*x^2 - 720*d^6*e*m*x + 720*d^7)*(e*x + d)^m/((m^7 + 28*m^6 + 322*m^5 + 1960*m^4 + 6769*m^3 + 13132*m^2 + 13068*m + 5040)*e^7)","B",0
370,0,0,0,0.000000," ","integrate((e*x+d)^m*(4*x^4-5*x^3+3*x^2+x+2)/(5*x^2+2*x+3),x, algorithm=""maxima"")","\int \frac{{\left(4 \, x^{4} - 5 \, x^{3} + 3 \, x^{2} + x + 2\right)} {\left(e x + d\right)}^{m}}{5 \, x^{2} + 2 \, x + 3}\,{d x}"," ",0,"integrate((4*x^4 - 5*x^3 + 3*x^2 + x + 2)*(e*x + d)^m/(5*x^2 + 2*x + 3), x)","F",0
371,0,0,0,0.000000," ","integrate((e*x+d)^m*(4*x^4-5*x^3+3*x^2+x+2)/(5*x^2+2*x+3)^2,x, algorithm=""maxima"")","\int \frac{{\left(4 \, x^{4} - 5 \, x^{3} + 3 \, x^{2} + x + 2\right)} {\left(e x + d\right)}^{m}}{{\left(5 \, x^{2} + 2 \, x + 3\right)}^{2}}\,{d x}"," ",0,"integrate((4*x^4 - 5*x^3 + 3*x^2 + x + 2)*(e*x + d)^m/(5*x^2 + 2*x + 3)^2, x)","F",0
372,-2,0,0,0.000000," ","integrate((i*x^5+h*x^4+g*x^3+f*x^2+e*x+d)/(c*x^2+b*x+a)^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
373,-2,0,0,0.000000," ","integrate((m*x^8+l*x^7+k*x^6+j*x^5+h*x^4+g*x^3+f*x^2+e*x+d)/(c*x^2+b*x+a),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
374,1,177,0,0.990009," ","integrate((-7*x^2+4*x+1)^3*(x^2+5*x+2)*(5*x^2+2*x+3)^(1/2),x, algorithm=""maxima"")","-\frac{343}{50} \, {\left(5 \, x^{2} + 2 \, x + 3\right)}^{\frac{3}{2}} x^{7} - \frac{50519}{2250} \, {\left(5 \, x^{2} + 2 \, x + 3\right)}^{\frac{3}{2}} x^{6} + \frac{190939}{3000} \, {\left(5 \, x^{2} + 2 \, x + 3\right)}^{\frac{3}{2}} x^{5} - \frac{888751}{105000} \, {\left(5 \, x^{2} + 2 \, x + 3\right)}^{\frac{3}{2}} x^{4} - \frac{90960857}{1575000} \, {\left(5 \, x^{2} + 2 \, x + 3\right)}^{\frac{3}{2}} x^{3} + \frac{98060877}{4375000} \, {\left(5 \, x^{2} + 2 \, x + 3\right)}^{\frac{3}{2}} x^{2} + \frac{1045360143}{43750000} \, {\left(5 \, x^{2} + 2 \, x + 3\right)}^{\frac{3}{2}} x - \frac{1968340667}{131250000} \, {\left(5 \, x^{2} + 2 \, x + 3\right)}^{\frac{3}{2}} - \frac{77159983}{6250000} \, \sqrt{5 \, x^{2} + 2 \, x + 3} x - \frac{540119881}{78125000} \, \sqrt{5} \operatorname{arsinh}\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) - \frac{77159983}{31250000} \, \sqrt{5 \, x^{2} + 2 \, x + 3}"," ",0,"-343/50*(5*x^2 + 2*x + 3)^(3/2)*x^7 - 50519/2250*(5*x^2 + 2*x + 3)^(3/2)*x^6 + 190939/3000*(5*x^2 + 2*x + 3)^(3/2)*x^5 - 888751/105000*(5*x^2 + 2*x + 3)^(3/2)*x^4 - 90960857/1575000*(5*x^2 + 2*x + 3)^(3/2)*x^3 + 98060877/4375000*(5*x^2 + 2*x + 3)^(3/2)*x^2 + 1045360143/43750000*(5*x^2 + 2*x + 3)^(3/2)*x - 1968340667/131250000*(5*x^2 + 2*x + 3)^(3/2) - 77159983/6250000*sqrt(5*x^2 + 2*x + 3)*x - 540119881/78125000*sqrt(5)*arcsinh(1/14*sqrt(14)*(5*x + 1)) - 77159983/31250000*sqrt(5*x^2 + 2*x + 3)","A",0
375,1,143,0,0.972553," ","integrate((-7*x^2+4*x+1)^2*(x^2+5*x+2)*(5*x^2+2*x+3)^(1/2),x, algorithm=""maxima"")","\frac{49}{40} \, {\left(5 \, x^{2} + 2 \, x + 3\right)}^{\frac{3}{2}} x^{5} + \frac{989}{200} \, {\left(5 \, x^{2} + 2 \, x + 3\right)}^{\frac{3}{2}} x^{4} - \frac{25277}{3000} \, {\left(5 \, x^{2} + 2 \, x + 3\right)}^{\frac{3}{2}} x^{3} - \frac{77509}{25000} \, {\left(5 \, x^{2} + 2 \, x + 3\right)}^{\frac{3}{2}} x^{2} + \frac{1781669}{250000} \, {\left(5 \, x^{2} + 2 \, x + 3\right)}^{\frac{3}{2}} x + \frac{198439}{750000} \, {\left(5 \, x^{2} + 2 \, x + 3\right)}^{\frac{3}{2}} - \frac{2521723}{250000} \, \sqrt{5 \, x^{2} + 2 \, x + 3} x - \frac{17652061}{3125000} \, \sqrt{5} \operatorname{arsinh}\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) - \frac{2521723}{1250000} \, \sqrt{5 \, x^{2} + 2 \, x + 3}"," ",0,"49/40*(5*x^2 + 2*x + 3)^(3/2)*x^5 + 989/200*(5*x^2 + 2*x + 3)^(3/2)*x^4 - 25277/3000*(5*x^2 + 2*x + 3)^(3/2)*x^3 - 77509/25000*(5*x^2 + 2*x + 3)^(3/2)*x^2 + 1781669/250000*(5*x^2 + 2*x + 3)^(3/2)*x + 198439/750000*(5*x^2 + 2*x + 3)^(3/2) - 2521723/250000*sqrt(5*x^2 + 2*x + 3)*x - 17652061/3125000*sqrt(5)*arcsinh(1/14*sqrt(14)*(5*x + 1)) - 2521723/1250000*sqrt(5*x^2 + 2*x + 3)","A",0
376,1,109,0,0.958581," ","integrate((-7*x^2+4*x+1)*(x^2+5*x+2)*(5*x^2+2*x+3)^(1/2),x, algorithm=""maxima"")","-\frac{7}{30} \, {\left(5 \, x^{2} + 2 \, x + 3\right)}^{\frac{3}{2}} x^{3} - \frac{289}{250} \, {\left(5 \, x^{2} + 2 \, x + 3\right)}^{\frac{3}{2}} x^{2} + \frac{2149}{2500} \, {\left(5 \, x^{2} + 2 \, x + 3\right)}^{\frac{3}{2}} x + \frac{7819}{7500} \, {\left(5 \, x^{2} + 2 \, x + 3\right)}^{\frac{3}{2}} - \frac{4633}{2500} \, \sqrt{5 \, x^{2} + 2 \, x + 3} x - \frac{32431}{31250} \, \sqrt{5} \operatorname{arsinh}\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) - \frac{4633}{12500} \, \sqrt{5 \, x^{2} + 2 \, x + 3}"," ",0,"-7/30*(5*x^2 + 2*x + 3)^(3/2)*x^3 - 289/250*(5*x^2 + 2*x + 3)^(3/2)*x^2 + 2149/2500*(5*x^2 + 2*x + 3)^(3/2)*x + 7819/7500*(5*x^2 + 2*x + 3)^(3/2) - 4633/2500*sqrt(5*x^2 + 2*x + 3)*x - 32431/31250*sqrt(5)*arcsinh(1/14*sqrt(14)*(5*x + 1)) - 4633/12500*sqrt(5*x^2 + 2*x + 3)","A",0
377,1,500,0,1.173466," ","integrate((x^2+5*x+2)*(5*x^2+2*x+3)^(1/2)/(-7*x^2+4*x+1),x, algorithm=""maxima"")","\frac{1}{188650} \, \sqrt{11} {\left(975 \, \sqrt{11} \sqrt{2} \sqrt{17 \, \sqrt{11} + 125} \operatorname{arsinh}\left(\frac{5 \, \sqrt{11} \sqrt{7} \sqrt{2} x}{7 \, {\left| 14 \, x - 2 \, \sqrt{11} - 4 \right|}} + \frac{17 \, \sqrt{7} \sqrt{2} x}{7 \, {\left| 14 \, x - 2 \, \sqrt{11} - 4 \right|}} + \frac{\sqrt{11} \sqrt{7} \sqrt{2}}{7 \, {\left| 14 \, x - 2 \, \sqrt{11} - 4 \right|}} + \frac{23 \, \sqrt{7} \sqrt{2}}{7 \, {\left| 14 \, x - 2 \, \sqrt{11} - 4 \right|}}\right) - 1225 \, \sqrt{11} \sqrt{5 \, x^{2} + 2 \, x + 3} x - 16466 \, \sqrt{11} \sqrt{5} \operatorname{arsinh}\left(\frac{5}{14} \, \sqrt{7} \sqrt{2} x + \frac{1}{14} \, \sqrt{7} \sqrt{2}\right) - 6825 \, \sqrt{11} \sqrt{-\frac{34}{49} \, \sqrt{11} + \frac{250}{49}} \operatorname{arsinh}\left(\frac{5 \, \sqrt{11} \sqrt{7} \sqrt{2} x}{7 \, {\left| 14 \, x + 2 \, \sqrt{11} - 4 \right|}} - \frac{17 \, \sqrt{7} \sqrt{2} x}{7 \, {\left| 14 \, x + 2 \, \sqrt{11} - 4 \right|}} + \frac{\sqrt{11} \sqrt{7} \sqrt{2}}{7 \, {\left| 14 \, x + 2 \, \sqrt{11} - 4 \right|}} - \frac{23 \, \sqrt{7} \sqrt{2}}{7 \, {\left| 14 \, x + 2 \, \sqrt{11} - 4 \right|}}\right) + 4575 \, \sqrt{2} \sqrt{17 \, \sqrt{11} + 125} \operatorname{arsinh}\left(\frac{5 \, \sqrt{11} \sqrt{7} \sqrt{2} x}{7 \, {\left| 14 \, x - 2 \, \sqrt{11} - 4 \right|}} + \frac{17 \, \sqrt{7} \sqrt{2} x}{7 \, {\left| 14 \, x - 2 \, \sqrt{11} - 4 \right|}} + \frac{\sqrt{11} \sqrt{7} \sqrt{2}}{7 \, {\left| 14 \, x - 2 \, \sqrt{11} - 4 \right|}} + \frac{23 \, \sqrt{7} \sqrt{2}}{7 \, {\left| 14 \, x - 2 \, \sqrt{11} - 4 \right|}}\right) + 32025 \, \sqrt{-\frac{34}{49} \, \sqrt{11} + \frac{250}{49}} \operatorname{arsinh}\left(\frac{5 \, \sqrt{11} \sqrt{7} \sqrt{2} x}{7 \, {\left| 14 \, x + 2 \, \sqrt{11} - 4 \right|}} - \frac{17 \, \sqrt{7} \sqrt{2} x}{7 \, {\left| 14 \, x + 2 \, \sqrt{11} - 4 \right|}} + \frac{\sqrt{11} \sqrt{7} \sqrt{2}}{7 \, {\left| 14 \, x + 2 \, \sqrt{11} - 4 \right|}} - \frac{23 \, \sqrt{7} \sqrt{2}}{7 \, {\left| 14 \, x + 2 \, \sqrt{11} - 4 \right|}}\right) - 13895 \, \sqrt{11} \sqrt{5 \, x^{2} + 2 \, x + 3}\right)}"," ",0,"1/188650*sqrt(11)*(975*sqrt(11)*sqrt(2)*sqrt(17*sqrt(11) + 125)*arcsinh(5/7*sqrt(11)*sqrt(7)*sqrt(2)*x/abs(14*x - 2*sqrt(11) - 4) + 17/7*sqrt(7)*sqrt(2)*x/abs(14*x - 2*sqrt(11) - 4) + 1/7*sqrt(11)*sqrt(7)*sqrt(2)/abs(14*x - 2*sqrt(11) - 4) + 23/7*sqrt(7)*sqrt(2)/abs(14*x - 2*sqrt(11) - 4)) - 1225*sqrt(11)*sqrt(5*x^2 + 2*x + 3)*x - 16466*sqrt(11)*sqrt(5)*arcsinh(5/14*sqrt(7)*sqrt(2)*x + 1/14*sqrt(7)*sqrt(2)) - 6825*sqrt(11)*sqrt(-34/49*sqrt(11) + 250/49)*arcsinh(5/7*sqrt(11)*sqrt(7)*sqrt(2)*x/abs(14*x + 2*sqrt(11) - 4) - 17/7*sqrt(7)*sqrt(2)*x/abs(14*x + 2*sqrt(11) - 4) + 1/7*sqrt(11)*sqrt(7)*sqrt(2)/abs(14*x + 2*sqrt(11) - 4) - 23/7*sqrt(7)*sqrt(2)/abs(14*x + 2*sqrt(11) - 4)) + 4575*sqrt(2)*sqrt(17*sqrt(11) + 125)*arcsinh(5/7*sqrt(11)*sqrt(7)*sqrt(2)*x/abs(14*x - 2*sqrt(11) - 4) + 17/7*sqrt(7)*sqrt(2)*x/abs(14*x - 2*sqrt(11) - 4) + 1/7*sqrt(11)*sqrt(7)*sqrt(2)/abs(14*x - 2*sqrt(11) - 4) + 23/7*sqrt(7)*sqrt(2)/abs(14*x - 2*sqrt(11) - 4)) + 32025*sqrt(-34/49*sqrt(11) + 250/49)*arcsinh(5/7*sqrt(11)*sqrt(7)*sqrt(2)*x/abs(14*x + 2*sqrt(11) - 4) - 17/7*sqrt(7)*sqrt(2)*x/abs(14*x + 2*sqrt(11) - 4) + 1/7*sqrt(11)*sqrt(7)*sqrt(2)/abs(14*x + 2*sqrt(11) - 4) - 23/7*sqrt(7)*sqrt(2)/abs(14*x + 2*sqrt(11) - 4)) - 13895*sqrt(11)*sqrt(5*x^2 + 2*x + 3))","B",0
378,0,0,0,0.000000," ","integrate((x^2+5*x+2)*(5*x^2+2*x+3)^(1/2)/(-7*x^2+4*x+1)^2,x, algorithm=""maxima"")","\int \frac{\sqrt{5 \, x^{2} + 2 \, x + 3} {\left(x^{2} + 5 \, x + 2\right)}}{{\left(7 \, x^{2} - 4 \, x - 1\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(5*x^2 + 2*x + 3)*(x^2 + 5*x + 2)/(7*x^2 - 4*x - 1)^2, x)","F",0
379,0,0,0,0.000000," ","integrate((x^2+5*x+2)*(5*x^2+2*x+3)^(1/2)/(-7*x^2+4*x+1)^3,x, algorithm=""maxima"")","-\int \frac{\sqrt{5 \, x^{2} + 2 \, x + 3} {\left(x^{2} + 5 \, x + 2\right)}}{{\left(7 \, x^{2} - 4 \, x - 1\right)}^{3}}\,{d x}"," ",0,"-integrate(sqrt(5*x^2 + 2*x + 3)*(x^2 + 5*x + 2)/(7*x^2 - 4*x - 1)^3, x)","F",0
380,1,206,0,1.005035," ","integrate((-7*x^2+4*x+1)^3*(x^2+5*x+2)*(5*x^2+2*x+3)^(3/2),x, algorithm=""maxima"")","-\frac{343}{60} \, {\left(5 \, x^{2} + 2 \, x + 3\right)}^{\frac{5}{2}} x^{7} - \frac{61103}{3300} \, {\left(5 \, x^{2} + 2 \, x + 3\right)}^{\frac{5}{2}} x^{6} + \frac{1031177}{20625} \, {\left(5 \, x^{2} + 2 \, x + 3\right)}^{\frac{5}{2}} x^{5} - \frac{796559}{123750} \, {\left(5 \, x^{2} + 2 \, x + 3\right)}^{\frac{5}{2}} x^{4} - \frac{190236913}{4950000} \, {\left(5 \, x^{2} + 2 \, x + 3\right)}^{\frac{5}{2}} x^{3} + \frac{2173004363}{173250000} \, {\left(5 \, x^{2} + 2 \, x + 3\right)}^{\frac{5}{2}} x^{2} + \frac{837379699}{72187500} \, {\left(5 \, x^{2} + 2 \, x + 3\right)}^{\frac{5}{2}} x - \frac{6133820867}{1203125000} \, {\left(5 \, x^{2} + 2 \, x + 3\right)}^{\frac{5}{2}} - \frac{22840599}{12500000} \, {\left(5 \, x^{2} + 2 \, x + 3\right)}^{\frac{3}{2}} x - \frac{22840599}{62500000} \, {\left(5 \, x^{2} + 2 \, x + 3\right)}^{\frac{3}{2}} - \frac{479652579}{62500000} \, \sqrt{5 \, x^{2} + 2 \, x + 3} x - \frac{3357568053}{781250000} \, \sqrt{5} \operatorname{arsinh}\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) - \frac{479652579}{312500000} \, \sqrt{5 \, x^{2} + 2 \, x + 3}"," ",0,"-343/60*(5*x^2 + 2*x + 3)^(5/2)*x^7 - 61103/3300*(5*x^2 + 2*x + 3)^(5/2)*x^6 + 1031177/20625*(5*x^2 + 2*x + 3)^(5/2)*x^5 - 796559/123750*(5*x^2 + 2*x + 3)^(5/2)*x^4 - 190236913/4950000*(5*x^2 + 2*x + 3)^(5/2)*x^3 + 2173004363/173250000*(5*x^2 + 2*x + 3)^(5/2)*x^2 + 837379699/72187500*(5*x^2 + 2*x + 3)^(5/2)*x - 6133820867/1203125000*(5*x^2 + 2*x + 3)^(5/2) - 22840599/12500000*(5*x^2 + 2*x + 3)^(3/2)*x - 22840599/62500000*(5*x^2 + 2*x + 3)^(3/2) - 479652579/62500000*sqrt(5*x^2 + 2*x + 3)*x - 3357568053/781250000*sqrt(5)*arcsinh(1/14*sqrt(14)*(5*x + 1)) - 479652579/312500000*sqrt(5*x^2 + 2*x + 3)","A",0
381,1,172,0,0.983707," ","integrate((-7*x^2+4*x+1)^2*(x^2+5*x+2)*(5*x^2+2*x+3)^(3/2),x, algorithm=""maxima"")","\frac{49}{50} \, {\left(5 \, x^{2} + 2 \, x + 3\right)}^{\frac{5}{2}} x^{5} + \frac{581}{150} \, {\left(5 \, x^{2} + 2 \, x + 3\right)}^{\frac{5}{2}} x^{4} - \frac{18379}{3000} \, {\left(5 \, x^{2} + 2 \, x + 3\right)}^{\frac{5}{2}} x^{3} - \frac{219271}{105000} \, {\left(5 \, x^{2} + 2 \, x + 3\right)}^{\frac{5}{2}} x^{2} + \frac{86721}{21875} \, {\left(5 \, x^{2} + 2 \, x + 3\right)}^{\frac{5}{2}} x + \frac{505667}{2187500} \, {\left(5 \, x^{2} + 2 \, x + 3\right)}^{\frac{5}{2}} - \frac{690561}{250000} \, {\left(5 \, x^{2} + 2 \, x + 3\right)}^{\frac{3}{2}} x - \frac{690561}{1250000} \, {\left(5 \, x^{2} + 2 \, x + 3\right)}^{\frac{3}{2}} - \frac{14501781}{1250000} \, \sqrt{5 \, x^{2} + 2 \, x + 3} x - \frac{101512467}{15625000} \, \sqrt{5} \operatorname{arsinh}\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) - \frac{14501781}{6250000} \, \sqrt{5 \, x^{2} + 2 \, x + 3}"," ",0,"49/50*(5*x^2 + 2*x + 3)^(5/2)*x^5 + 581/150*(5*x^2 + 2*x + 3)^(5/2)*x^4 - 18379/3000*(5*x^2 + 2*x + 3)^(5/2)*x^3 - 219271/105000*(5*x^2 + 2*x + 3)^(5/2)*x^2 + 86721/21875*(5*x^2 + 2*x + 3)^(5/2)*x + 505667/2187500*(5*x^2 + 2*x + 3)^(5/2) - 690561/250000*(5*x^2 + 2*x + 3)^(3/2)*x - 690561/1250000*(5*x^2 + 2*x + 3)^(3/2) - 14501781/1250000*sqrt(5*x^2 + 2*x + 3)*x - 101512467/15625000*sqrt(5)*arcsinh(1/14*sqrt(14)*(5*x + 1)) - 14501781/6250000*sqrt(5*x^2 + 2*x + 3)","A",0
382,1,138,0,0.957164," ","integrate((-7*x^2+4*x+1)*(x^2+5*x+2)*(5*x^2+2*x+3)^(3/2),x, algorithm=""maxima"")","-\frac{7}{40} \, {\left(5 \, x^{2} + 2 \, x + 3\right)}^{\frac{5}{2}} x^{3} - \frac{1163}{1400} \, {\left(5 \, x^{2} + 2 \, x + 3\right)}^{\frac{5}{2}} x^{2} + \frac{2809}{5250} \, {\left(5 \, x^{2} + 2 \, x + 3\right)}^{\frac{5}{2}} x + \frac{149509}{262500} \, {\left(5 \, x^{2} + 2 \, x + 3\right)}^{\frac{5}{2}} - \frac{18397}{30000} \, {\left(5 \, x^{2} + 2 \, x + 3\right)}^{\frac{3}{2}} x - \frac{18397}{150000} \, {\left(5 \, x^{2} + 2 \, x + 3\right)}^{\frac{3}{2}} - \frac{128779}{50000} \, \sqrt{5 \, x^{2} + 2 \, x + 3} x - \frac{901453}{625000} \, \sqrt{5} \operatorname{arsinh}\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) - \frac{128779}{250000} \, \sqrt{5 \, x^{2} + 2 \, x + 3}"," ",0,"-7/40*(5*x^2 + 2*x + 3)^(5/2)*x^3 - 1163/1400*(5*x^2 + 2*x + 3)^(5/2)*x^2 + 2809/5250*(5*x^2 + 2*x + 3)^(5/2)*x + 149509/262500*(5*x^2 + 2*x + 3)^(5/2) - 18397/30000*(5*x^2 + 2*x + 3)^(3/2)*x - 18397/150000*(5*x^2 + 2*x + 3)^(3/2) - 128779/50000*sqrt(5*x^2 + 2*x + 3)*x - 901453/625000*sqrt(5)*arcsinh(1/14*sqrt(14)*(5*x + 1)) - 128779/250000*sqrt(5*x^2 + 2*x + 3)","A",0
383,1,535,0,1.310126," ","integrate((x^2+5*x+2)*(5*x^2+2*x+3)^(3/2)/(-7*x^2+4*x+1),x, algorithm=""maxima"")","\frac{1}{92438500} \, \sqrt{11} {\left(19500 \, \sqrt{11} \sqrt{2} {\left(17 \, \sqrt{11} + 125\right)}^{\frac{3}{2}} \operatorname{arsinh}\left(\frac{5 \, \sqrt{11} \sqrt{7} \sqrt{2} x}{7 \, {\left| 14 \, x - 2 \, \sqrt{11} - 4 \right|}} + \frac{17 \, \sqrt{7} \sqrt{2} x}{7 \, {\left| 14 \, x - 2 \, \sqrt{11} - 4 \right|}} + \frac{\sqrt{11} \sqrt{7} \sqrt{2}}{7 \, {\left| 14 \, x - 2 \, \sqrt{11} - 4 \right|}} + \frac{23 \, \sqrt{7} \sqrt{2}}{7 \, {\left| 14 \, x - 2 \, \sqrt{11} - 4 \right|}}\right) - 300125 \, \sqrt{11} {\left(5 \, x^{2} + 2 \, x + 3\right)}^{\frac{3}{2}} x - 3344250 \, \sqrt{11} {\left(-\frac{34}{49} \, \sqrt{11} + \frac{250}{49}\right)}^{\frac{3}{2}} \operatorname{arsinh}\left(\frac{5 \, \sqrt{11} \sqrt{7} \sqrt{2} x}{7 \, {\left| 14 \, x + 2 \, \sqrt{11} - 4 \right|}} - \frac{17 \, \sqrt{7} \sqrt{2} x}{7 \, {\left| 14 \, x + 2 \, \sqrt{11} - 4 \right|}} + \frac{\sqrt{11} \sqrt{7} \sqrt{2}}{7 \, {\left| 14 \, x + 2 \, \sqrt{11} - 4 \right|}} - \frac{23 \, \sqrt{7} \sqrt{2}}{7 \, {\left| 14 \, x + 2 \, \sqrt{11} - 4 \right|}}\right) + 91500 \, \sqrt{2} {\left(17 \, \sqrt{11} + 125\right)}^{\frac{3}{2}} \operatorname{arsinh}\left(\frac{5 \, \sqrt{11} \sqrt{7} \sqrt{2} x}{7 \, {\left| 14 \, x - 2 \, \sqrt{11} - 4 \right|}} + \frac{17 \, \sqrt{7} \sqrt{2} x}{7 \, {\left| 14 \, x - 2 \, \sqrt{11} - 4 \right|}} + \frac{\sqrt{11} \sqrt{7} \sqrt{2}}{7 \, {\left| 14 \, x - 2 \, \sqrt{11} - 4 \right|}} + \frac{23 \, \sqrt{7} \sqrt{2}}{7 \, {\left| 14 \, x - 2 \, \sqrt{11} - 4 \right|}}\right) + 15692250 \, {\left(-\frac{34}{49} \, \sqrt{11} + \frac{250}{49}\right)}^{\frac{3}{2}} \operatorname{arsinh}\left(\frac{5 \, \sqrt{11} \sqrt{7} \sqrt{2} x}{7 \, {\left| 14 \, x + 2 \, \sqrt{11} - 4 \right|}} - \frac{17 \, \sqrt{7} \sqrt{2} x}{7 \, {\left| 14 \, x + 2 \, \sqrt{11} - 4 \right|}} + \frac{\sqrt{11} \sqrt{7} \sqrt{2}}{7 \, {\left| 14 \, x + 2 \, \sqrt{11} - 4 \right|}} - \frac{23 \, \sqrt{7} \sqrt{2}}{7 \, {\left| 14 \, x + 2 \, \sqrt{11} - 4 \right|}}\right) - 2289525 \, \sqrt{11} {\left(5 \, x^{2} + 2 \, x + 3\right)}^{\frac{3}{2}} - 20591025 \, \sqrt{11} \sqrt{5 \, x^{2} + 2 \, x + 3} x - 68851374 \, \sqrt{11} \sqrt{5} \operatorname{arsinh}\left(\frac{5}{14} \, \sqrt{7} \sqrt{2} x + \frac{1}{14} \, \sqrt{7} \sqrt{2}\right) - 60020205 \, \sqrt{11} \sqrt{5 \, x^{2} + 2 \, x + 3}\right)}"," ",0,"1/92438500*sqrt(11)*(19500*sqrt(11)*sqrt(2)*(17*sqrt(11) + 125)^(3/2)*arcsinh(5/7*sqrt(11)*sqrt(7)*sqrt(2)*x/abs(14*x - 2*sqrt(11) - 4) + 17/7*sqrt(7)*sqrt(2)*x/abs(14*x - 2*sqrt(11) - 4) + 1/7*sqrt(11)*sqrt(7)*sqrt(2)/abs(14*x - 2*sqrt(11) - 4) + 23/7*sqrt(7)*sqrt(2)/abs(14*x - 2*sqrt(11) - 4)) - 300125*sqrt(11)*(5*x^2 + 2*x + 3)^(3/2)*x - 3344250*sqrt(11)*(-34/49*sqrt(11) + 250/49)^(3/2)*arcsinh(5/7*sqrt(11)*sqrt(7)*sqrt(2)*x/abs(14*x + 2*sqrt(11) - 4) - 17/7*sqrt(7)*sqrt(2)*x/abs(14*x + 2*sqrt(11) - 4) + 1/7*sqrt(11)*sqrt(7)*sqrt(2)/abs(14*x + 2*sqrt(11) - 4) - 23/7*sqrt(7)*sqrt(2)/abs(14*x + 2*sqrt(11) - 4)) + 91500*sqrt(2)*(17*sqrt(11) + 125)^(3/2)*arcsinh(5/7*sqrt(11)*sqrt(7)*sqrt(2)*x/abs(14*x - 2*sqrt(11) - 4) + 17/7*sqrt(7)*sqrt(2)*x/abs(14*x - 2*sqrt(11) - 4) + 1/7*sqrt(11)*sqrt(7)*sqrt(2)/abs(14*x - 2*sqrt(11) - 4) + 23/7*sqrt(7)*sqrt(2)/abs(14*x - 2*sqrt(11) - 4)) + 15692250*(-34/49*sqrt(11) + 250/49)^(3/2)*arcsinh(5/7*sqrt(11)*sqrt(7)*sqrt(2)*x/abs(14*x + 2*sqrt(11) - 4) - 17/7*sqrt(7)*sqrt(2)*x/abs(14*x + 2*sqrt(11) - 4) + 1/7*sqrt(11)*sqrt(7)*sqrt(2)/abs(14*x + 2*sqrt(11) - 4) - 23/7*sqrt(7)*sqrt(2)/abs(14*x + 2*sqrt(11) - 4)) - 2289525*sqrt(11)*(5*x^2 + 2*x + 3)^(3/2) - 20591025*sqrt(11)*sqrt(5*x^2 + 2*x + 3)*x - 68851374*sqrt(11)*sqrt(5)*arcsinh(5/14*sqrt(7)*sqrt(2)*x + 1/14*sqrt(7)*sqrt(2)) - 60020205*sqrt(11)*sqrt(5*x^2 + 2*x + 3))","B",0
384,0,0,0,0.000000," ","integrate((x^2+5*x+2)*(5*x^2+2*x+3)^(3/2)/(-7*x^2+4*x+1)^2,x, algorithm=""maxima"")","\int \frac{{\left(5 \, x^{2} + 2 \, x + 3\right)}^{\frac{3}{2}} {\left(x^{2} + 5 \, x + 2\right)}}{{\left(7 \, x^{2} - 4 \, x - 1\right)}^{2}}\,{d x}"," ",0,"integrate((5*x^2 + 2*x + 3)^(3/2)*(x^2 + 5*x + 2)/(7*x^2 - 4*x - 1)^2, x)","F",0
385,0,0,0,0.000000," ","integrate((x^2+5*x+2)*(5*x^2+2*x+3)^(3/2)/(-7*x^2+4*x+1)^3,x, algorithm=""maxima"")","-\int \frac{{\left(5 \, x^{2} + 2 \, x + 3\right)}^{\frac{3}{2}} {\left(x^{2} + 5 \, x + 2\right)}}{{\left(7 \, x^{2} - 4 \, x - 1\right)}^{3}}\,{d x}"," ",0,"-integrate((5*x^2 + 2*x + 3)^(3/2)*(x^2 + 5*x + 2)/(7*x^2 - 4*x - 1)^3, x)","F",0
386,1,148,0,0.994329," ","integrate((-7*x^2+4*x+1)^3*(x^2+5*x+2)/(5*x^2+2*x+3)^(1/2),x, algorithm=""maxima"")","-\frac{343}{40} \, \sqrt{5 \, x^{2} + 2 \, x + 3} x^{7} - \frac{1141}{40} \, \sqrt{5 \, x^{2} + 2 \, x + 3} x^{6} + \frac{26159}{300} \, \sqrt{5 \, x^{2} + 2 \, x + 3} x^{5} - \frac{47807}{3750} \, \sqrt{5 \, x^{2} + 2 \, x + 3} x^{4} - \frac{5160533}{50000} \, \sqrt{5 \, x^{2} + 2 \, x + 3} x^{3} + \frac{40722851}{750000} \, \sqrt{5 \, x^{2} + 2 \, x + 3} x^{2} + \frac{5793077}{75000} \, \sqrt{5 \, x^{2} + 2 \, x + 3} x - \frac{77513689}{3125000} \, \sqrt{5} \operatorname{arsinh}\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) - \frac{16515809}{156250} \, \sqrt{5 \, x^{2} + 2 \, x + 3}"," ",0,"-343/40*sqrt(5*x^2 + 2*x + 3)*x^7 - 1141/40*sqrt(5*x^2 + 2*x + 3)*x^6 + 26159/300*sqrt(5*x^2 + 2*x + 3)*x^5 - 47807/3750*sqrt(5*x^2 + 2*x + 3)*x^4 - 5160533/50000*sqrt(5*x^2 + 2*x + 3)*x^3 + 40722851/750000*sqrt(5*x^2 + 2*x + 3)*x^2 + 5793077/75000*sqrt(5*x^2 + 2*x + 3)*x - 77513689/3125000*sqrt(5)*arcsinh(1/14*sqrt(14)*(5*x + 1)) - 16515809/156250*sqrt(5*x^2 + 2*x + 3)","A",0
387,1,114,0,0.973628," ","integrate((-7*x^2+4*x+1)^2*(x^2+5*x+2)/(5*x^2+2*x+3)^(1/2),x, algorithm=""maxima"")","\frac{49}{30} \, \sqrt{5 \, x^{2} + 2 \, x + 3} x^{5} + \frac{5131}{750} \, \sqrt{5 \, x^{2} + 2 \, x + 3} x^{4} - \frac{33259}{2500} \, \sqrt{5 \, x^{2} + 2 \, x + 3} x^{3} - \frac{207427}{37500} \, \sqrt{5 \, x^{2} + 2 \, x + 3} x^{2} + \frac{36073}{1875} \, \sqrt{5 \, x^{2} + 2 \, x + 3} x - \frac{1719097}{156250} \, \sqrt{5} \operatorname{arsinh}\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) - \frac{22053}{31250} \, \sqrt{5 \, x^{2} + 2 \, x + 3}"," ",0,"49/30*sqrt(5*x^2 + 2*x + 3)*x^5 + 5131/750*sqrt(5*x^2 + 2*x + 3)*x^4 - 33259/2500*sqrt(5*x^2 + 2*x + 3)*x^3 - 207427/37500*sqrt(5*x^2 + 2*x + 3)*x^2 + 36073/1875*sqrt(5*x^2 + 2*x + 3)*x - 1719097/156250*sqrt(5)*arcsinh(1/14*sqrt(14)*(5*x + 1)) - 22053/31250*sqrt(5*x^2 + 2*x + 3)","A",0
388,1,80,0,0.963992," ","integrate((-7*x^2+4*x+1)*(x^2+5*x+2)/(5*x^2+2*x+3)^(1/2),x, algorithm=""maxima"")","-\frac{7}{20} \, \sqrt{5 \, x^{2} + 2 \, x + 3} x^{3} - \frac{571}{300} \, \sqrt{5 \, x^{2} + 2 \, x + 3} x^{2} + \frac{59}{30} \, \sqrt{5 \, x^{2} + 2 \, x + 3} x - \frac{1901}{1250} \, \sqrt{5} \operatorname{arsinh}\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) + \frac{463}{125} \, \sqrt{5 \, x^{2} + 2 \, x + 3}"," ",0,"-7/20*sqrt(5*x^2 + 2*x + 3)*x^3 - 571/300*sqrt(5*x^2 + 2*x + 3)*x^2 + 59/30*sqrt(5*x^2 + 2*x + 3)*x - 1901/1250*sqrt(5)*arcsinh(1/14*sqrt(14)*(5*x + 1)) + 463/125*sqrt(5*x^2 + 2*x + 3)","A",0
389,1,465,0,1.138223," ","integrate((x^2+5*x+2)/(-7*x^2+4*x+1)/(5*x^2+2*x+3)^(1/2),x, algorithm=""maxima"")","-\frac{1}{10780} \, \sqrt{11} {\left(28 \, \sqrt{11} \sqrt{5} \operatorname{arsinh}\left(\frac{5}{14} \, \sqrt{7} \sqrt{2} x + \frac{1}{14} \, \sqrt{7} \sqrt{2}\right) - \frac{1365 \, \sqrt{11} \sqrt{2} \operatorname{arsinh}\left(\frac{5 \, \sqrt{11} \sqrt{7} \sqrt{2} x}{7 \, {\left| 14 \, x - 2 \, \sqrt{11} - 4 \right|}} + \frac{17 \, \sqrt{7} \sqrt{2} x}{7 \, {\left| 14 \, x - 2 \, \sqrt{11} - 4 \right|}} + \frac{\sqrt{11} \sqrt{7} \sqrt{2}}{7 \, {\left| 14 \, x - 2 \, \sqrt{11} - 4 \right|}} + \frac{23 \, \sqrt{7} \sqrt{2}}{7 \, {\left| 14 \, x - 2 \, \sqrt{11} - 4 \right|}}\right)}{\sqrt{17 \, \sqrt{11} + 125}} + \frac{390 \, \sqrt{11} \operatorname{arsinh}\left(\frac{5 \, \sqrt{11} \sqrt{7} \sqrt{2} x}{7 \, {\left| 14 \, x + 2 \, \sqrt{11} - 4 \right|}} - \frac{17 \, \sqrt{7} \sqrt{2} x}{7 \, {\left| 14 \, x + 2 \, \sqrt{11} - 4 \right|}} + \frac{\sqrt{11} \sqrt{7} \sqrt{2}}{7 \, {\left| 14 \, x + 2 \, \sqrt{11} - 4 \right|}} - \frac{23 \, \sqrt{7} \sqrt{2}}{7 \, {\left| 14 \, x + 2 \, \sqrt{11} - 4 \right|}}\right)}{\sqrt{-\frac{34}{49} \, \sqrt{11} + \frac{250}{49}}} - \frac{6405 \, \sqrt{2} \operatorname{arsinh}\left(\frac{5 \, \sqrt{11} \sqrt{7} \sqrt{2} x}{7 \, {\left| 14 \, x - 2 \, \sqrt{11} - 4 \right|}} + \frac{17 \, \sqrt{7} \sqrt{2} x}{7 \, {\left| 14 \, x - 2 \, \sqrt{11} - 4 \right|}} + \frac{\sqrt{11} \sqrt{7} \sqrt{2}}{7 \, {\left| 14 \, x - 2 \, \sqrt{11} - 4 \right|}} + \frac{23 \, \sqrt{7} \sqrt{2}}{7 \, {\left| 14 \, x - 2 \, \sqrt{11} - 4 \right|}}\right)}{\sqrt{17 \, \sqrt{11} + 125}} - \frac{1830 \, \operatorname{arsinh}\left(\frac{5 \, \sqrt{11} \sqrt{7} \sqrt{2} x}{7 \, {\left| 14 \, x + 2 \, \sqrt{11} - 4 \right|}} - \frac{17 \, \sqrt{7} \sqrt{2} x}{7 \, {\left| 14 \, x + 2 \, \sqrt{11} - 4 \right|}} + \frac{\sqrt{11} \sqrt{7} \sqrt{2}}{7 \, {\left| 14 \, x + 2 \, \sqrt{11} - 4 \right|}} - \frac{23 \, \sqrt{7} \sqrt{2}}{7 \, {\left| 14 \, x + 2 \, \sqrt{11} - 4 \right|}}\right)}{\sqrt{-\frac{34}{49} \, \sqrt{11} + \frac{250}{49}}}\right)}"," ",0,"-1/10780*sqrt(11)*(28*sqrt(11)*sqrt(5)*arcsinh(5/14*sqrt(7)*sqrt(2)*x + 1/14*sqrt(7)*sqrt(2)) - 1365*sqrt(11)*sqrt(2)*arcsinh(5/7*sqrt(11)*sqrt(7)*sqrt(2)*x/abs(14*x - 2*sqrt(11) - 4) + 17/7*sqrt(7)*sqrt(2)*x/abs(14*x - 2*sqrt(11) - 4) + 1/7*sqrt(11)*sqrt(7)*sqrt(2)/abs(14*x - 2*sqrt(11) - 4) + 23/7*sqrt(7)*sqrt(2)/abs(14*x - 2*sqrt(11) - 4))/sqrt(17*sqrt(11) + 125) + 390*sqrt(11)*arcsinh(5/7*sqrt(11)*sqrt(7)*sqrt(2)*x/abs(14*x + 2*sqrt(11) - 4) - 17/7*sqrt(7)*sqrt(2)*x/abs(14*x + 2*sqrt(11) - 4) + 1/7*sqrt(11)*sqrt(7)*sqrt(2)/abs(14*x + 2*sqrt(11) - 4) - 23/7*sqrt(7)*sqrt(2)/abs(14*x + 2*sqrt(11) - 4))/sqrt(-34/49*sqrt(11) + 250/49) - 6405*sqrt(2)*arcsinh(5/7*sqrt(11)*sqrt(7)*sqrt(2)*x/abs(14*x - 2*sqrt(11) - 4) + 17/7*sqrt(7)*sqrt(2)*x/abs(14*x - 2*sqrt(11) - 4) + 1/7*sqrt(11)*sqrt(7)*sqrt(2)/abs(14*x - 2*sqrt(11) - 4) + 23/7*sqrt(7)*sqrt(2)/abs(14*x - 2*sqrt(11) - 4))/sqrt(17*sqrt(11) + 125) - 1830*arcsinh(5/7*sqrt(11)*sqrt(7)*sqrt(2)*x/abs(14*x + 2*sqrt(11) - 4) - 17/7*sqrt(7)*sqrt(2)*x/abs(14*x + 2*sqrt(11) - 4) + 1/7*sqrt(11)*sqrt(7)*sqrt(2)/abs(14*x + 2*sqrt(11) - 4) - 23/7*sqrt(7)*sqrt(2)/abs(14*x + 2*sqrt(11) - 4))/sqrt(-34/49*sqrt(11) + 250/49))","B",0
390,0,0,0,0.000000," ","integrate((x^2+5*x+2)/(-7*x^2+4*x+1)^2/(5*x^2+2*x+3)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{2} + 5 \, x + 2}{{\left(7 \, x^{2} - 4 \, x - 1\right)}^{2} \sqrt{5 \, x^{2} + 2 \, x + 3}}\,{d x}"," ",0,"integrate((x^2 + 5*x + 2)/((7*x^2 - 4*x - 1)^2*sqrt(5*x^2 + 2*x + 3)), x)","F",0
391,0,0,0,0.000000," ","integrate((x^2+5*x+2)/(-7*x^2+4*x+1)^3/(5*x^2+2*x+3)^(1/2),x, algorithm=""maxima"")","-\int \frac{x^{2} + 5 \, x + 2}{{\left(7 \, x^{2} - 4 \, x - 1\right)}^{3} \sqrt{5 \, x^{2} + 2 \, x + 3}}\,{d x}"," ",0,"-integrate((x^2 + 5*x + 2)/((7*x^2 - 4*x - 1)^3*sqrt(5*x^2 + 2*x + 3)), x)","F",0
392,1,148,0,0.988517," ","integrate((-7*x^2+4*x+1)^3*(x^2+5*x+2)/(5*x^2+2*x+3)^(3/2),x, algorithm=""maxima"")","-\frac{343 \, x^{7}}{30 \, \sqrt{5 \, x^{2} + 2 \, x + 3}} - \frac{29351 \, x^{6}}{750 \, \sqrt{5 \, x^{2} + 2 \, x + 3}} + \frac{1025843 \, x^{5}}{7500 \, \sqrt{5 \, x^{2} + 2 \, x + 3}} - \frac{998969 \, x^{4}}{37500 \, \sqrt{5 \, x^{2} + 2 \, x + 3}} - \frac{51303971 \, x^{3}}{187500 \, \sqrt{5 \, x^{2} + 2 \, x + 3}} + \frac{61004099 \, x^{2}}{187500 \, \sqrt{5 \, x^{2} + 2 \, x + 3}} + \frac{50047657}{781250} \, \sqrt{5} \operatorname{arsinh}\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) - \frac{87141949 \, x}{546875 \, \sqrt{5 \, x^{2} + 2 \, x + 3}} + \frac{525961603}{1093750 \, \sqrt{5 \, x^{2} + 2 \, x + 3}}"," ",0,"-343/30*x^7/sqrt(5*x^2 + 2*x + 3) - 29351/750*x^6/sqrt(5*x^2 + 2*x + 3) + 1025843/7500*x^5/sqrt(5*x^2 + 2*x + 3) - 998969/37500*x^4/sqrt(5*x^2 + 2*x + 3) - 51303971/187500*x^3/sqrt(5*x^2 + 2*x + 3) + 61004099/187500*x^2/sqrt(5*x^2 + 2*x + 3) + 50047657/781250*sqrt(5)*arcsinh(1/14*sqrt(14)*(5*x + 1)) - 87141949/546875*x/sqrt(5*x^2 + 2*x + 3) + 525961603/1093750/sqrt(5*x^2 + 2*x + 3)","A",0
393,1,114,0,0.967983," ","integrate((-7*x^2+4*x+1)^2*(x^2+5*x+2)/(5*x^2+2*x+3)^(3/2),x, algorithm=""maxima"")","\frac{49 \, x^{5}}{20 \, \sqrt{5 \, x^{2} + 2 \, x + 3}} + \frac{1113 \, x^{4}}{100 \, \sqrt{5 \, x^{2} + 2 \, x + 3}} - \frac{14733 \, x^{3}}{500 \, \sqrt{5 \, x^{2} + 2 \, x + 3}} - \frac{8023 \, x^{2}}{500 \, \sqrt{5 \, x^{2} + 2 \, x + 3}} + \frac{89583}{6250} \, \sqrt{5} \operatorname{arsinh}\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) - \frac{649337 \, x}{8750 \, \sqrt{5 \, x^{2} + 2 \, x + 3}} - \frac{42134}{4375 \, \sqrt{5 \, x^{2} + 2 \, x + 3}}"," ",0,"49/20*x^5/sqrt(5*x^2 + 2*x + 3) + 1113/100*x^4/sqrt(5*x^2 + 2*x + 3) - 14733/500*x^3/sqrt(5*x^2 + 2*x + 3) - 8023/500*x^2/sqrt(5*x^2 + 2*x + 3) + 89583/6250*sqrt(5)*arcsinh(1/14*sqrt(14)*(5*x + 1)) - 649337/8750*x/sqrt(5*x^2 + 2*x + 3) - 42134/4375/sqrt(5*x^2 + 2*x + 3)","A",0
394,1,80,0,0.957515," ","integrate((-7*x^2+4*x+1)*(x^2+5*x+2)/(5*x^2+2*x+3)^(3/2),x, algorithm=""maxima"")","-\frac{7 \, x^{3}}{10 \, \sqrt{5 \, x^{2} + 2 \, x + 3}} - \frac{11 \, x^{2}}{2 \, \sqrt{5 \, x^{2} + 2 \, x + 3}} + \frac{149}{125} \, \sqrt{5} \operatorname{arsinh}\left(\frac{1}{14} \, \sqrt{14} {\left(5 \, x + 1\right)}\right) - \frac{2837 \, x}{350 \, \sqrt{5 \, x^{2} + 2 \, x + 3}} - \frac{2953}{350 \, \sqrt{5 \, x^{2} + 2 \, x + 3}}"," ",0,"-7/10*x^3/sqrt(5*x^2 + 2*x + 3) - 11/2*x^2/sqrt(5*x^2 + 2*x + 3) + 149/125*sqrt(5)*arcsinh(1/14*sqrt(14)*(5*x + 1)) - 2837/350*x/sqrt(5*x^2 + 2*x + 3) - 2953/350/sqrt(5*x^2 + 2*x + 3)","A",0
395,1,777,0,1.155347," ","integrate((x^2+5*x+2)/(-7*x^2+4*x+1)/(5*x^2+2*x+3)^(3/2),x, algorithm=""maxima"")","-\frac{1}{4312} \, \sqrt{11} {\left(\frac{20 \, \sqrt{11} x}{\sqrt{5 \, x^{2} + 2 \, x + 3}} - \frac{7890 \, \sqrt{11} x}{17 \, \sqrt{11} \sqrt{5 \, x^{2} + 2 \, x + 3} + 125 \, \sqrt{5 \, x^{2} + 2 \, x + 3}} + \frac{7890 \, \sqrt{11} x}{17 \, \sqrt{11} \sqrt{5 \, x^{2} + 2 \, x + 3} - 125 \, \sqrt{5 \, x^{2} + 2 \, x + 3}} - \frac{13377 \, \sqrt{11} \sqrt{2} \operatorname{arsinh}\left(\frac{5 \, \sqrt{11} \sqrt{7} \sqrt{2} x}{7 \, {\left| 14 \, x - 2 \, \sqrt{11} - 4 \right|}} + \frac{17 \, \sqrt{7} \sqrt{2} x}{7 \, {\left| 14 \, x - 2 \, \sqrt{11} - 4 \right|}} + \frac{\sqrt{11} \sqrt{7} \sqrt{2}}{7 \, {\left| 14 \, x - 2 \, \sqrt{11} - 4 \right|}} + \frac{23 \, \sqrt{7} \sqrt{2}}{7 \, {\left| 14 \, x - 2 \, \sqrt{11} - 4 \right|}}\right)}{{\left(17 \, \sqrt{11} + 125\right)}^{\frac{3}{2}}} + \frac{4 \, \sqrt{11}}{\sqrt{5 \, x^{2} + 2 \, x + 3}} - \frac{26280 \, x}{17 \, \sqrt{11} \sqrt{5 \, x^{2} + 2 \, x + 3} + 125 \, \sqrt{5 \, x^{2} + 2 \, x + 3}} - \frac{26280 \, x}{17 \, \sqrt{11} \sqrt{5 \, x^{2} + 2 \, x + 3} - 125 \, \sqrt{5 \, x^{2} + 2 \, x + 3}} + \frac{156 \, \sqrt{11} \operatorname{arsinh}\left(\frac{5 \, \sqrt{11} \sqrt{7} \sqrt{2} x}{7 \, {\left| 14 \, x + 2 \, \sqrt{11} - 4 \right|}} - \frac{17 \, \sqrt{7} \sqrt{2} x}{7 \, {\left| 14 \, x + 2 \, \sqrt{11} - 4 \right|}} + \frac{\sqrt{11} \sqrt{7} \sqrt{2}}{7 \, {\left| 14 \, x + 2 \, \sqrt{11} - 4 \right|}} - \frac{23 \, \sqrt{7} \sqrt{2}}{7 \, {\left| 14 \, x + 2 \, \sqrt{11} - 4 \right|}}\right)}{{\left(-\frac{34}{49} \, \sqrt{11} + \frac{250}{49}\right)}^{\frac{3}{2}}} - \frac{62769 \, \sqrt{2} \operatorname{arsinh}\left(\frac{5 \, \sqrt{11} \sqrt{7} \sqrt{2} x}{7 \, {\left| 14 \, x - 2 \, \sqrt{11} - 4 \right|}} + \frac{17 \, \sqrt{7} \sqrt{2} x}{7 \, {\left| 14 \, x - 2 \, \sqrt{11} - 4 \right|}} + \frac{\sqrt{11} \sqrt{7} \sqrt{2}}{7 \, {\left| 14 \, x - 2 \, \sqrt{11} - 4 \right|}} + \frac{23 \, \sqrt{7} \sqrt{2}}{7 \, {\left| 14 \, x - 2 \, \sqrt{11} - 4 \right|}}\right)}{{\left(17 \, \sqrt{11} + 125\right)}^{\frac{3}{2}}} + \frac{2244 \, \sqrt{11}}{17 \, \sqrt{11} \sqrt{5 \, x^{2} + 2 \, x + 3} + 125 \, \sqrt{5 \, x^{2} + 2 \, x + 3}} - \frac{2244 \, \sqrt{11}}{17 \, \sqrt{11} \sqrt{5 \, x^{2} + 2 \, x + 3} - 125 \, \sqrt{5 \, x^{2} + 2 \, x + 3}} - \frac{732 \, \operatorname{arsinh}\left(\frac{5 \, \sqrt{11} \sqrt{7} \sqrt{2} x}{7 \, {\left| 14 \, x + 2 \, \sqrt{11} - 4 \right|}} - \frac{17 \, \sqrt{7} \sqrt{2} x}{7 \, {\left| 14 \, x + 2 \, \sqrt{11} - 4 \right|}} + \frac{\sqrt{11} \sqrt{7} \sqrt{2}}{7 \, {\left| 14 \, x + 2 \, \sqrt{11} - 4 \right|}} - \frac{23 \, \sqrt{7} \sqrt{2}}{7 \, {\left| 14 \, x + 2 \, \sqrt{11} - 4 \right|}}\right)}{{\left(-\frac{34}{49} \, \sqrt{11} + \frac{250}{49}\right)}^{\frac{3}{2}}} + \frac{12678}{17 \, \sqrt{11} \sqrt{5 \, x^{2} + 2 \, x + 3} + 125 \, \sqrt{5 \, x^{2} + 2 \, x + 3}} + \frac{12678}{17 \, \sqrt{11} \sqrt{5 \, x^{2} + 2 \, x + 3} - 125 \, \sqrt{5 \, x^{2} + 2 \, x + 3}}\right)}"," ",0,"-1/4312*sqrt(11)*(20*sqrt(11)*x/sqrt(5*x^2 + 2*x + 3) - 7890*sqrt(11)*x/(17*sqrt(11)*sqrt(5*x^2 + 2*x + 3) + 125*sqrt(5*x^2 + 2*x + 3)) + 7890*sqrt(11)*x/(17*sqrt(11)*sqrt(5*x^2 + 2*x + 3) - 125*sqrt(5*x^2 + 2*x + 3)) - 13377*sqrt(11)*sqrt(2)*arcsinh(5/7*sqrt(11)*sqrt(7)*sqrt(2)*x/abs(14*x - 2*sqrt(11) - 4) + 17/7*sqrt(7)*sqrt(2)*x/abs(14*x - 2*sqrt(11) - 4) + 1/7*sqrt(11)*sqrt(7)*sqrt(2)/abs(14*x - 2*sqrt(11) - 4) + 23/7*sqrt(7)*sqrt(2)/abs(14*x - 2*sqrt(11) - 4))/(17*sqrt(11) + 125)^(3/2) + 4*sqrt(11)/sqrt(5*x^2 + 2*x + 3) - 26280*x/(17*sqrt(11)*sqrt(5*x^2 + 2*x + 3) + 125*sqrt(5*x^2 + 2*x + 3)) - 26280*x/(17*sqrt(11)*sqrt(5*x^2 + 2*x + 3) - 125*sqrt(5*x^2 + 2*x + 3)) + 156*sqrt(11)*arcsinh(5/7*sqrt(11)*sqrt(7)*sqrt(2)*x/abs(14*x + 2*sqrt(11) - 4) - 17/7*sqrt(7)*sqrt(2)*x/abs(14*x + 2*sqrt(11) - 4) + 1/7*sqrt(11)*sqrt(7)*sqrt(2)/abs(14*x + 2*sqrt(11) - 4) - 23/7*sqrt(7)*sqrt(2)/abs(14*x + 2*sqrt(11) - 4))/(-34/49*sqrt(11) + 250/49)^(3/2) - 62769*sqrt(2)*arcsinh(5/7*sqrt(11)*sqrt(7)*sqrt(2)*x/abs(14*x - 2*sqrt(11) - 4) + 17/7*sqrt(7)*sqrt(2)*x/abs(14*x - 2*sqrt(11) - 4) + 1/7*sqrt(11)*sqrt(7)*sqrt(2)/abs(14*x - 2*sqrt(11) - 4) + 23/7*sqrt(7)*sqrt(2)/abs(14*x - 2*sqrt(11) - 4))/(17*sqrt(11) + 125)^(3/2) + 2244*sqrt(11)/(17*sqrt(11)*sqrt(5*x^2 + 2*x + 3) + 125*sqrt(5*x^2 + 2*x + 3)) - 2244*sqrt(11)/(17*sqrt(11)*sqrt(5*x^2 + 2*x + 3) - 125*sqrt(5*x^2 + 2*x + 3)) - 732*arcsinh(5/7*sqrt(11)*sqrt(7)*sqrt(2)*x/abs(14*x + 2*sqrt(11) - 4) - 17/7*sqrt(7)*sqrt(2)*x/abs(14*x + 2*sqrt(11) - 4) + 1/7*sqrt(11)*sqrt(7)*sqrt(2)/abs(14*x + 2*sqrt(11) - 4) - 23/7*sqrt(7)*sqrt(2)/abs(14*x + 2*sqrt(11) - 4))/(-34/49*sqrt(11) + 250/49)^(3/2) + 12678/(17*sqrt(11)*sqrt(5*x^2 + 2*x + 3) + 125*sqrt(5*x^2 + 2*x + 3)) + 12678/(17*sqrt(11)*sqrt(5*x^2 + 2*x + 3) - 125*sqrt(5*x^2 + 2*x + 3)))","B",0
396,0,0,0,0.000000," ","integrate((x^2+5*x+2)/(-7*x^2+4*x+1)^2/(5*x^2+2*x+3)^(3/2),x, algorithm=""maxima"")","\int \frac{x^{2} + 5 \, x + 2}{{\left(7 \, x^{2} - 4 \, x - 1\right)}^{2} {\left(5 \, x^{2} + 2 \, x + 3\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((x^2 + 5*x + 2)/((7*x^2 - 4*x - 1)^2*(5*x^2 + 2*x + 3)^(3/2)), x)","F",0
397,0,0,0,0.000000," ","integrate((x^2+5*x+2)/(-7*x^2+4*x+1)^3/(5*x^2+2*x+3)^(3/2),x, algorithm=""maxima"")","-\int \frac{x^{2} + 5 \, x + 2}{{\left(7 \, x^{2} - 4 \, x - 1\right)}^{3} {\left(5 \, x^{2} + 2 \, x + 3\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"-integrate((x^2 + 5*x + 2)/((7*x^2 - 4*x - 1)^3*(5*x^2 + 2*x + 3)^(3/2)), x)","F",0
398,0,0,0,0.000000," ","integrate((c*x^2+a)^p*(C*x^2+A)*(f*x^2+d)^q,x, algorithm=""maxima"")","\int {\left(C x^{2} + A\right)} {\left(c x^{2} + a\right)}^{p} {\left(f x^{2} + d\right)}^{q}\,{d x}"," ",0,"integrate((C*x^2 + A)*(c*x^2 + a)^p*(f*x^2 + d)^q, x)","F",0
399,0,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+a)^p*(f*x^2+d)^q,x, algorithm=""maxima"")","\int {\left(B x + A\right)} {\left(c x^{2} + a\right)}^{p} {\left(f x^{2} + d\right)}^{q}\,{d x}"," ",0,"integrate((B*x + A)*(c*x^2 + a)^p*(f*x^2 + d)^q, x)","F",0
400,0,0,0,0.000000," ","integrate((c*x^2+a)^p*(C*x^2+B*x+A)*(f*x^2+d)^q,x, algorithm=""maxima"")","\int {\left(C x^{2} + B x + A\right)} {\left(c x^{2} + a\right)}^{p} {\left(f x^{2} + d\right)}^{q}\,{d x}"," ",0,"integrate((C*x^2 + B*x + A)*(c*x^2 + a)^p*(f*x^2 + d)^q, x)","F",0
