1,1,19,0,0.886054," ","integrate(x^2*(c*x^4+b*x^3+a*x^2),x, algorithm=""fricas"")","\frac{1}{7} x^{7} c + \frac{1}{6} x^{6} b + \frac{1}{5} x^{5} a"," ",0,"1/7*x^7*c + 1/6*x^6*b + 1/5*x^5*a","A",0
2,1,19,0,0.976800," ","integrate(x*(c*x^4+b*x^3+a*x^2),x, algorithm=""fricas"")","\frac{1}{6} x^{6} c + \frac{1}{5} x^{5} b + \frac{1}{4} x^{4} a"," ",0,"1/6*x^6*c + 1/5*x^5*b + 1/4*x^4*a","A",0
3,1,19,0,0.837299," ","integrate(c*x^4+b*x^3+a*x^2,x, algorithm=""fricas"")","\frac{1}{5} x^{5} c + \frac{1}{4} x^{4} b + \frac{1}{3} x^{3} a"," ",0,"1/5*x^5*c + 1/4*x^4*b + 1/3*x^3*a","A",0
4,1,19,0,0.531276," ","integrate((c*x^4+b*x^3+a*x^2)/x,x, algorithm=""fricas"")","\frac{1}{4} \, c x^{4} + \frac{1}{3} \, b x^{3} + \frac{1}{2} \, a x^{2}"," ",0,"1/4*c*x^4 + 1/3*b*x^3 + 1/2*a*x^2","A",0
5,1,16,0,0.727711," ","integrate((c*x^4+b*x^3+a*x^2)/x^2,x, algorithm=""fricas"")","\frac{1}{3} \, c x^{3} + \frac{1}{2} \, b x^{2} + a x"," ",0,"1/3*c*x^3 + 1/2*b*x^2 + a*x","A",0
6,1,46,0,0.901636," ","integrate(x^2*(c*x^4+b*x^3+a*x^2)^2,x, algorithm=""fricas"")","\frac{1}{11} x^{11} c^{2} + \frac{1}{5} x^{10} c b + \frac{1}{9} x^{9} b^{2} + \frac{2}{9} x^{9} c a + \frac{1}{4} x^{8} b a + \frac{1}{7} x^{7} a^{2}"," ",0,"1/11*x^11*c^2 + 1/5*x^10*c*b + 1/9*x^9*b^2 + 2/9*x^9*c*a + 1/4*x^8*b*a + 1/7*x^7*a^2","A",0
7,1,46,0,0.774340," ","integrate(x*(c*x^4+b*x^3+a*x^2)^2,x, algorithm=""fricas"")","\frac{1}{10} x^{10} c^{2} + \frac{2}{9} x^{9} c b + \frac{1}{8} x^{8} b^{2} + \frac{1}{4} x^{8} c a + \frac{2}{7} x^{7} b a + \frac{1}{6} x^{6} a^{2}"," ",0,"1/10*x^10*c^2 + 2/9*x^9*c*b + 1/8*x^8*b^2 + 1/4*x^8*c*a + 2/7*x^7*b*a + 1/6*x^6*a^2","A",0
8,1,46,0,0.877494," ","integrate((c*x^4+b*x^3+a*x^2)^2,x, algorithm=""fricas"")","\frac{1}{9} x^{9} c^{2} + \frac{1}{4} x^{8} c b + \frac{1}{7} x^{7} b^{2} + \frac{2}{7} x^{7} c a + \frac{1}{3} x^{6} b a + \frac{1}{5} x^{5} a^{2}"," ",0,"1/9*x^9*c^2 + 1/4*x^8*c*b + 1/7*x^7*b^2 + 2/7*x^7*c*a + 1/3*x^6*b*a + 1/5*x^5*a^2","A",0
9,1,44,0,0.757325," ","integrate((c*x^4+b*x^3+a*x^2)^2/x,x, algorithm=""fricas"")","\frac{1}{8} \, c^{2} x^{8} + \frac{2}{7} \, b c x^{7} + \frac{2}{5} \, a b x^{5} + \frac{1}{6} \, {\left(b^{2} + 2 \, a c\right)} x^{6} + \frac{1}{4} \, a^{2} x^{4}"," ",0,"1/8*c^2*x^8 + 2/7*b*c*x^7 + 2/5*a*b*x^5 + 1/6*(b^2 + 2*a*c)*x^6 + 1/4*a^2*x^4","A",0
10,1,44,0,0.956561," ","integrate((c*x^4+b*x^3+a*x^2)^2/x^2,x, algorithm=""fricas"")","\frac{1}{7} \, c^{2} x^{7} + \frac{1}{3} \, b c x^{6} + \frac{1}{2} \, a b x^{4} + \frac{1}{5} \, {\left(b^{2} + 2 \, a c\right)} x^{5} + \frac{1}{3} \, a^{2} x^{3}"," ",0,"1/7*c^2*x^7 + 1/3*b*c*x^6 + 1/2*a*b*x^4 + 1/5*(b^2 + 2*a*c)*x^5 + 1/3*a^2*x^3","A",0
11,1,297,0,0.862090," ","integrate(x^5/(c*x^4+b*x^3+a*x^2),x, algorithm=""fricas"")","\left[\frac{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{2} - {\left(b^{3} - 3 \, a b c\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} x + {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)}}, \frac{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{2} + 2 \, {\left(b^{3} - 3 \, a b c\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} x + {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)}}\right]"," ",0,"[1/2*((b^2*c^2 - 4*a*c^3)*x^2 - (b^3 - 3*a*b*c)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - 2*(b^3*c - 4*a*b*c^2)*x + (b^4 - 5*a*b^2*c + 4*a^2*c^2)*log(c*x^2 + b*x + a))/(b^2*c^3 - 4*a*c^4), 1/2*((b^2*c^2 - 4*a*c^3)*x^2 + 2*(b^3 - 3*a*b*c)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - 2*(b^3*c - 4*a*b*c^2)*x + (b^4 - 5*a*b^2*c + 4*a^2*c^2)*log(c*x^2 + b*x + a))/(b^2*c^3 - 4*a*c^4)]","A",0
12,1,235,0,0.804523," ","integrate(x^4/(c*x^4+b*x^3+a*x^2),x, algorithm=""fricas"")","\left[-\frac{{\left(b^{2} - 2 \, a c\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - 2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} x + {\left(b^{3} - 4 \, a b c\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}}, -\frac{2 \, {\left(b^{2} - 2 \, a c\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - 2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} x + {\left(b^{3} - 4 \, a b c\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}}\right]"," ",0,"[-1/2*((b^2 - 2*a*c)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - 2*(b^2*c - 4*a*c^2)*x + (b^3 - 4*a*b*c)*log(c*x^2 + b*x + a))/(b^2*c^2 - 4*a*c^3), -1/2*(2*(b^2 - 2*a*c)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - 2*(b^2*c - 4*a*c^2)*x + (b^3 - 4*a*b*c)*log(c*x^2 + b*x + a))/(b^2*c^2 - 4*a*c^3)]","A",0
13,1,185,0,0.763448," ","integrate(x^3/(c*x^4+b*x^3+a*x^2),x, algorithm=""fricas"")","\left[\frac{\sqrt{b^{2} - 4 \, a c} b \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + {\left(b^{2} - 4 \, a c\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)}}, \frac{2 \, \sqrt{-b^{2} + 4 \, a c} b \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + {\left(b^{2} - 4 \, a c\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)}}\right]"," ",0,"[1/2*(sqrt(b^2 - 4*a*c)*b*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + (b^2 - 4*a*c)*log(c*x^2 + b*x + a))/(b^2*c - 4*a*c^2), 1/2*(2*sqrt(-b^2 + 4*a*c)*b*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + (b^2 - 4*a*c)*log(c*x^2 + b*x + a))/(b^2*c - 4*a*c^2)]","A",0
14,1,120,0,0.956287," ","integrate(x^2/(c*x^4+b*x^3+a*x^2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right)}{\sqrt{b^{2} - 4 \, a c}}, -\frac{2 \, \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right)}{b^{2} - 4 \, a c}\right]"," ",0,"[log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a))/sqrt(b^2 - 4*a*c), -2*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c))/(b^2 - 4*a*c)]","A",0
15,1,211,0,0.915470," ","integrate(x/(c*x^4+b*x^3+a*x^2),x, algorithm=""fricas"")","\left[\frac{\sqrt{b^{2} - 4 \, a c} b \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - {\left(b^{2} - 4 \, a c\right)} \log\left(c x^{2} + b x + a\right) + 2 \, {\left(b^{2} - 4 \, a c\right)} \log\left(x\right)}{2 \, {\left(a b^{2} - 4 \, a^{2} c\right)}}, \frac{2 \, \sqrt{-b^{2} + 4 \, a c} b \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - {\left(b^{2} - 4 \, a c\right)} \log\left(c x^{2} + b x + a\right) + 2 \, {\left(b^{2} - 4 \, a c\right)} \log\left(x\right)}{2 \, {\left(a b^{2} - 4 \, a^{2} c\right)}}\right]"," ",0,"[1/2*(sqrt(b^2 - 4*a*c)*b*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - (b^2 - 4*a*c)*log(c*x^2 + b*x + a) + 2*(b^2 - 4*a*c)*log(x))/(a*b^2 - 4*a^2*c), 1/2*(2*sqrt(-b^2 + 4*a*c)*b*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - (b^2 - 4*a*c)*log(c*x^2 + b*x + a) + 2*(b^2 - 4*a*c)*log(x))/(a*b^2 - 4*a^2*c)]","A",0
16,1,269,0,1.038221," ","integrate(1/(c*x^4+b*x^3+a*x^2),x, algorithm=""fricas"")","\left[-\frac{{\left(b^{2} - 2 \, a c\right)} \sqrt{b^{2} - 4 \, a c} x \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 2 \, a b^{2} - 8 \, a^{2} c - {\left(b^{3} - 4 \, a b c\right)} x \log\left(c x^{2} + b x + a\right) + 2 \, {\left(b^{3} - 4 \, a b c\right)} x \log\left(x\right)}{2 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} x}, -\frac{2 \, {\left(b^{2} - 2 \, a c\right)} \sqrt{-b^{2} + 4 \, a c} x \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 2 \, a b^{2} - 8 \, a^{2} c - {\left(b^{3} - 4 \, a b c\right)} x \log\left(c x^{2} + b x + a\right) + 2 \, {\left(b^{3} - 4 \, a b c\right)} x \log\left(x\right)}{2 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} x}\right]"," ",0,"[-1/2*((b^2 - 2*a*c)*sqrt(b^2 - 4*a*c)*x*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 2*a*b^2 - 8*a^2*c - (b^3 - 4*a*b*c)*x*log(c*x^2 + b*x + a) + 2*(b^3 - 4*a*b*c)*x*log(x))/((a^2*b^2 - 4*a^3*c)*x), -1/2*(2*(b^2 - 2*a*c)*sqrt(-b^2 + 4*a*c)*x*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 2*a*b^2 - 8*a^2*c - (b^3 - 4*a*b*c)*x*log(c*x^2 + b*x + a) + 2*(b^3 - 4*a*b*c)*x*log(x))/((a^2*b^2 - 4*a^3*c)*x)]","A",0
17,1,358,0,0.908459," ","integrate(1/x/(c*x^4+b*x^3+a*x^2),x, algorithm=""fricas"")","\left[-\frac{{\left(b^{3} - 3 \, a b c\right)} \sqrt{b^{2} - 4 \, a c} x^{2} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + a^{2} b^{2} - 4 \, a^{3} c + {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} x^{2} \log\left(c x^{2} + b x + a\right) - 2 \, {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} x^{2} \log\left(x\right) - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} x}{2 \, {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} x^{2}}, \frac{2 \, {\left(b^{3} - 3 \, a b c\right)} \sqrt{-b^{2} + 4 \, a c} x^{2} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - a^{2} b^{2} + 4 \, a^{3} c - {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} x^{2} \log\left(c x^{2} + b x + a\right) + 2 \, {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} x^{2} \log\left(x\right) + 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} x}{2 \, {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} x^{2}}\right]"," ",0,"[-1/2*((b^3 - 3*a*b*c)*sqrt(b^2 - 4*a*c)*x^2*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + a^2*b^2 - 4*a^3*c + (b^4 - 5*a*b^2*c + 4*a^2*c^2)*x^2*log(c*x^2 + b*x + a) - 2*(b^4 - 5*a*b^2*c + 4*a^2*c^2)*x^2*log(x) - 2*(a*b^3 - 4*a^2*b*c)*x)/((a^3*b^2 - 4*a^4*c)*x^2), 1/2*(2*(b^3 - 3*a*b*c)*sqrt(-b^2 + 4*a*c)*x^2*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - a^2*b^2 + 4*a^3*c - (b^4 - 5*a*b^2*c + 4*a^2*c^2)*x^2*log(c*x^2 + b*x + a) + 2*(b^4 - 5*a*b^2*c + 4*a^2*c^2)*x^2*log(x) + 2*(a*b^3 - 4*a^2*b*c)*x)/((a^3*b^2 - 4*a^4*c)*x^2)]","A",0
18,1,445,0,1.119610," ","integrate(1/x^2/(c*x^4+b*x^3+a*x^2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} \sqrt{b^{2} - 4 \, a c} x^{3} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - 2 \, a^{3} b^{2} + 8 \, a^{4} c + 3 \, {\left(b^{5} - 6 \, a b^{3} c + 8 \, a^{2} b c^{2}\right)} x^{3} \log\left(c x^{2} + b x + a\right) - 6 \, {\left(b^{5} - 6 \, a b^{3} c + 8 \, a^{2} b c^{2}\right)} x^{3} \log\left(x\right) - 6 \, {\left(a b^{4} - 5 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} x^{2} + 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} x}{6 \, {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} x^{3}}, -\frac{6 \, {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} \sqrt{-b^{2} + 4 \, a c} x^{3} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 2 \, a^{3} b^{2} - 8 \, a^{4} c - 3 \, {\left(b^{5} - 6 \, a b^{3} c + 8 \, a^{2} b c^{2}\right)} x^{3} \log\left(c x^{2} + b x + a\right) + 6 \, {\left(b^{5} - 6 \, a b^{3} c + 8 \, a^{2} b c^{2}\right)} x^{3} \log\left(x\right) + 6 \, {\left(a b^{4} - 5 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} x^{2} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} x}{6 \, {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} x^{3}}\right]"," ",0,"[1/6*(3*(b^4 - 4*a*b^2*c + 2*a^2*c^2)*sqrt(b^2 - 4*a*c)*x^3*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - 2*a^3*b^2 + 8*a^4*c + 3*(b^5 - 6*a*b^3*c + 8*a^2*b*c^2)*x^3*log(c*x^2 + b*x + a) - 6*(b^5 - 6*a*b^3*c + 8*a^2*b*c^2)*x^3*log(x) - 6*(a*b^4 - 5*a^2*b^2*c + 4*a^3*c^2)*x^2 + 3*(a^2*b^3 - 4*a^3*b*c)*x)/((a^4*b^2 - 4*a^5*c)*x^3), -1/6*(6*(b^4 - 4*a*b^2*c + 2*a^2*c^2)*sqrt(-b^2 + 4*a*c)*x^3*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 2*a^3*b^2 - 8*a^4*c - 3*(b^5 - 6*a*b^3*c + 8*a^2*b*c^2)*x^3*log(c*x^2 + b*x + a) + 6*(b^5 - 6*a*b^3*c + 8*a^2*b*c^2)*x^3*log(x) + 6*(a*b^4 - 5*a^2*b^2*c + 4*a^3*c^2)*x^2 - 3*(a^2*b^3 - 4*a^3*b*c)*x)/((a^4*b^2 - 4*a^5*c)*x^3)]","A",0
19,1,837,0,0.894077," ","integrate(x^8/(c*x^4+b*x^3+a*x^2)^2,x, algorithm=""fricas"")","\left[-\frac{a b^{5} - 7 \, a^{2} b^{3} c + 12 \, a^{3} b c^{2} - {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{3} - {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{2} + {\left(a b^{4} - 6 \, a^{2} b^{2} c + 6 \, a^{3} c^{2} + {\left(b^{4} c - 6 \, a b^{2} c^{2} + 6 \, a^{2} c^{3}\right)} x^{2} + {\left(b^{5} - 6 \, a b^{3} c + 6 \, a^{2} b c^{2}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + {\left(b^{6} - 9 \, a b^{4} c + 26 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} x + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2} + {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{2} + {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} x\right)} \log\left(c x^{2} + b x + a\right)}{a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5} + {\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} x^{2} + {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} x}, -\frac{a b^{5} - 7 \, a^{2} b^{3} c + 12 \, a^{3} b c^{2} - {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{3} - {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{2} + 2 \, {\left(a b^{4} - 6 \, a^{2} b^{2} c + 6 \, a^{3} c^{2} + {\left(b^{4} c - 6 \, a b^{2} c^{2} + 6 \, a^{2} c^{3}\right)} x^{2} + {\left(b^{5} - 6 \, a b^{3} c + 6 \, a^{2} b c^{2}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + {\left(b^{6} - 9 \, a b^{4} c + 26 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} x + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2} + {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{2} + {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} x\right)} \log\left(c x^{2} + b x + a\right)}{a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5} + {\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} x^{2} + {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} x}\right]"," ",0,"[-(a*b^5 - 7*a^2*b^3*c + 12*a^3*b*c^2 - (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^3 - (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^2 + (a*b^4 - 6*a^2*b^2*c + 6*a^3*c^2 + (b^4*c - 6*a*b^2*c^2 + 6*a^2*c^3)*x^2 + (b^5 - 6*a*b^3*c + 6*a^2*b*c^2)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + (b^6 - 9*a*b^4*c + 26*a^2*b^2*c^2 - 24*a^3*c^3)*x + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2 + (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^2 + (b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*x)*log(c*x^2 + b*x + a))/(a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5 + (b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*x^2 + (b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*x), -(a*b^5 - 7*a^2*b^3*c + 12*a^3*b*c^2 - (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^3 - (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^2 + 2*(a*b^4 - 6*a^2*b^2*c + 6*a^3*c^2 + (b^4*c - 6*a*b^2*c^2 + 6*a^2*c^3)*x^2 + (b^5 - 6*a*b^3*c + 6*a^2*b*c^2)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + (b^6 - 9*a*b^4*c + 26*a^2*b^2*c^2 - 24*a^3*c^3)*x + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2 + (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^2 + (b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*x)*log(c*x^2 + b*x + a))/(a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5 + (b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*x^2 + (b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*x)]","B",0
20,1,635,0,0.865125," ","integrate(x^7/(c*x^4+b*x^3+a*x^2)^2,x, algorithm=""fricas"")","\left[\frac{2 \, a b^{4} - 12 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + {\left(a b^{3} - 6 \, a^{2} b c + {\left(b^{3} c - 6 \, a b c^{2}\right)} x^{2} + {\left(b^{4} - 6 \, a b^{2} c\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 2 \, {\left(b^{5} - 7 \, a b^{3} c + 12 \, a^{2} b c^{2}\right)} x + {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} x^{2} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4} + {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} x^{2} + {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} x\right)}}, \frac{2 \, a b^{4} - 12 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + 2 \, {\left(a b^{3} - 6 \, a^{2} b c + {\left(b^{3} c - 6 \, a b c^{2}\right)} x^{2} + {\left(b^{4} - 6 \, a b^{2} c\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 2 \, {\left(b^{5} - 7 \, a b^{3} c + 12 \, a^{2} b c^{2}\right)} x + {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} x^{2} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4} + {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} x^{2} + {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} x\right)}}\right]"," ",0,"[1/2*(2*a*b^4 - 12*a^2*b^2*c + 16*a^3*c^2 + (a*b^3 - 6*a^2*b*c + (b^3*c - 6*a*b*c^2)*x^2 + (b^4 - 6*a*b^2*c)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 2*(b^5 - 7*a*b^3*c + 12*a^2*b*c^2)*x + (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2 + (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*x^2 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*x)*log(c*x^2 + b*x + a))/(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4 + (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*x^2 + (b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*x), 1/2*(2*a*b^4 - 12*a^2*b^2*c + 16*a^3*c^2 + 2*(a*b^3 - 6*a^2*b*c + (b^3*c - 6*a*b*c^2)*x^2 + (b^4 - 6*a*b^2*c)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 2*(b^5 - 7*a*b^3*c + 12*a^2*b*c^2)*x + (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2 + (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*x^2 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*x)*log(c*x^2 + b*x + a))/(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4 + (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*x^2 + (b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*x)]","B",0
21,1,387,0,1.043281," ","integrate(x^6/(c*x^4+b*x^3+a*x^2)^2,x, algorithm=""fricas"")","\left[-\frac{a b^{3} - 4 \, a^{2} b c + 2 \, {\left(a c^{2} x^{2} + a b c x + a^{2} c\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} x}{a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3} + {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{2} + {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x}, -\frac{a b^{3} - 4 \, a^{2} b c - 4 \, {\left(a c^{2} x^{2} + a b c x + a^{2} c\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} x}{a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3} + {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{2} + {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x}\right]"," ",0,"[-(a*b^3 - 4*a^2*b*c + 2*(a*c^2*x^2 + a*b*c*x + a^2*c)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + (b^4 - 6*a*b^2*c + 8*a^2*c^2)*x)/(a*b^4*c - 8*a^2*b^2*c^2 + 16*a^3*c^3 + (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^2 + (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x), -(a*b^3 - 4*a^2*b*c - 4*(a*c^2*x^2 + a*b*c*x + a^2*c)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + (b^4 - 6*a*b^2*c + 8*a^2*c^2)*x)/(a*b^4*c - 8*a^2*b^2*c^2 + 16*a^3*c^3 + (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^2 + (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x)]","B",0
22,1,338,0,0.855820," ","integrate(x^5/(c*x^4+b*x^3+a*x^2)^2,x, algorithm=""fricas"")","\left[\frac{2 \, a b^{2} - 8 \, a^{2} c - {\left(b c x^{2} + b^{2} x + a b\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + {\left(b^{3} - 4 \, a b c\right)} x}{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} x^{2} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x}, \frac{2 \, a b^{2} - 8 \, a^{2} c - 2 \, {\left(b c x^{2} + b^{2} x + a b\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + {\left(b^{3} - 4 \, a b c\right)} x}{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} x^{2} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x}\right]"," ",0,"[(2*a*b^2 - 8*a^2*c - (b*c*x^2 + b^2*x + a*b)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + (b^3 - 4*a*b*c)*x)/(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2 + (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*x^2 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*x), (2*a*b^2 - 8*a^2*c - 2*(b*c*x^2 + b^2*x + a*b)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + (b^3 - 4*a*b*c)*x)/(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2 + (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*x^2 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*x)]","B",0
23,1,341,0,0.919556," ","integrate(x^4/(c*x^4+b*x^3+a*x^2)^2,x, algorithm=""fricas"")","\left[-\frac{b^{3} - 4 \, a b c + 2 \, {\left(c^{2} x^{2} + b c x + a c\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} x}{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} x^{2} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x}, -\frac{b^{3} - 4 \, a b c - 4 \, {\left(c^{2} x^{2} + b c x + a c\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} x}{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} x^{2} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x}\right]"," ",0,"[-(b^3 - 4*a*b*c + 2*(c^2*x^2 + b*c*x + a*c)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 2*(b^2*c - 4*a*c^2)*x)/(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2 + (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*x^2 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*x), -(b^3 - 4*a*b*c - 4*(c^2*x^2 + b*c*x + a*c)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 2*(b^2*c - 4*a*c^2)*x)/(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2 + (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*x^2 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*x)]","B",0
24,1,781,0,1.403827," ","integrate(x^3/(c*x^4+b*x^3+a*x^2)^2,x, algorithm=""fricas"")","\left[\frac{2 \, a b^{4} - 12 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + {\left(a b^{3} - 6 \, a^{2} b c + {\left(b^{3} c - 6 \, a b c^{2}\right)} x^{2} + {\left(b^{4} - 6 \, a b^{2} c\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} x - {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} x^{2} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x\right)} \log\left(c x^{2} + b x + a\right) + 2 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} x^{2} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x\right)} \log\left(x\right)}{2 \, {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2} + {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)} x^{2} + {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} x\right)}}, \frac{2 \, a b^{4} - 12 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + 2 \, {\left(a b^{3} - 6 \, a^{2} b c + {\left(b^{3} c - 6 \, a b c^{2}\right)} x^{2} + {\left(b^{4} - 6 \, a b^{2} c\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} x - {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} x^{2} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x\right)} \log\left(c x^{2} + b x + a\right) + 2 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} x^{2} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x\right)} \log\left(x\right)}{2 \, {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2} + {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)} x^{2} + {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} x\right)}}\right]"," ",0,"[1/2*(2*a*b^4 - 12*a^2*b^2*c + 16*a^3*c^2 + (a*b^3 - 6*a^2*b*c + (b^3*c - 6*a*b*c^2)*x^2 + (b^4 - 6*a*b^2*c)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 2*(a*b^3*c - 4*a^2*b*c^2)*x - (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2 + (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*x^2 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*x)*log(c*x^2 + b*x + a) + 2*(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2 + (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*x^2 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*x)*log(x))/(a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2 + (a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3)*x^2 + (a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*x), 1/2*(2*a*b^4 - 12*a^2*b^2*c + 16*a^3*c^2 + 2*(a*b^3 - 6*a^2*b*c + (b^3*c - 6*a*b*c^2)*x^2 + (b^4 - 6*a*b^2*c)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 2*(a*b^3*c - 4*a^2*b*c^2)*x - (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2 + (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*x^2 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*x)*log(c*x^2 + b*x + a) + 2*(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2 + (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*x^2 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*x)*log(x))/(a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2 + (a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3)*x^2 + (a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*x)]","B",0
25,1,975,0,1.357660," ","integrate(x^2/(c*x^4+b*x^3+a*x^2)^2,x, algorithm=""fricas"")","\left[-\frac{a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + 2 \, {\left(a b^{4} c - 7 \, a^{2} b^{2} c^{2} + 12 \, a^{3} c^{3}\right)} x^{2} + {\left({\left(b^{4} c - 6 \, a b^{2} c^{2} + 6 \, a^{2} c^{3}\right)} x^{3} + {\left(b^{5} - 6 \, a b^{3} c + 6 \, a^{2} b c^{2}\right)} x^{2} + {\left(a b^{4} - 6 \, a^{2} b^{2} c + 6 \, a^{3} c^{2}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + {\left(2 \, a b^{5} - 15 \, a^{2} b^{3} c + 28 \, a^{3} b c^{2}\right)} x - {\left({\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{3} + {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} x^{2} + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x\right)} \log\left(c x^{2} + b x + a\right) + 2 \, {\left({\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{3} + {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} x^{2} + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x\right)} \log\left(x\right)}{{\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} x^{3} + {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} x^{2} + {\left(a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2}\right)} x}, -\frac{a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + 2 \, {\left(a b^{4} c - 7 \, a^{2} b^{2} c^{2} + 12 \, a^{3} c^{3}\right)} x^{2} + 2 \, {\left({\left(b^{4} c - 6 \, a b^{2} c^{2} + 6 \, a^{2} c^{3}\right)} x^{3} + {\left(b^{5} - 6 \, a b^{3} c + 6 \, a^{2} b c^{2}\right)} x^{2} + {\left(a b^{4} - 6 \, a^{2} b^{2} c + 6 \, a^{3} c^{2}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + {\left(2 \, a b^{5} - 15 \, a^{2} b^{3} c + 28 \, a^{3} b c^{2}\right)} x - {\left({\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{3} + {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} x^{2} + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x\right)} \log\left(c x^{2} + b x + a\right) + 2 \, {\left({\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{3} + {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} x^{2} + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x\right)} \log\left(x\right)}{{\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} x^{3} + {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} x^{2} + {\left(a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2}\right)} x}\right]"," ",0,"[-(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + 2*(a*b^4*c - 7*a^2*b^2*c^2 + 12*a^3*c^3)*x^2 + ((b^4*c - 6*a*b^2*c^2 + 6*a^2*c^3)*x^3 + (b^5 - 6*a*b^3*c + 6*a^2*b*c^2)*x^2 + (a*b^4 - 6*a^2*b^2*c + 6*a^3*c^2)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + (2*a*b^5 - 15*a^2*b^3*c + 28*a^3*b*c^2)*x - ((b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^3 + (b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*x^2 + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x)*log(c*x^2 + b*x + a) + 2*((b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^3 + (b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*x^2 + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x)*log(x))/((a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*x^3 + (a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*x^2 + (a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2)*x), -(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + 2*(a*b^4*c - 7*a^2*b^2*c^2 + 12*a^3*c^3)*x^2 + 2*((b^4*c - 6*a*b^2*c^2 + 6*a^2*c^3)*x^3 + (b^5 - 6*a*b^3*c + 6*a^2*b*c^2)*x^2 + (a*b^4 - 6*a^2*b^2*c + 6*a^3*c^2)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + (2*a*b^5 - 15*a^2*b^3*c + 28*a^3*b*c^2)*x - ((b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^3 + (b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*x^2 + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x)*log(c*x^2 + b*x + a) + 2*((b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^3 + (b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*x^2 + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x)*log(x))/((a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*x^3 + (a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*x^2 + (a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2)*x)]","B",0
26,1,1226,0,1.686061," ","integrate(x/(c*x^4+b*x^3+a*x^2)^2,x, algorithm=""fricas"")","\left[-\frac{a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2} - 2 \, {\left(3 \, a b^{5} c - 23 \, a^{2} b^{3} c^{2} + 44 \, a^{3} b c^{3}\right)} x^{3} - {\left(6 \, a b^{6} - 49 \, a^{2} b^{4} c + 108 \, a^{3} b^{2} c^{2} - 32 \, a^{4} c^{3}\right)} x^{2} + {\left({\left(3 \, b^{5} c - 20 \, a b^{3} c^{2} + 30 \, a^{2} b c^{3}\right)} x^{4} + {\left(3 \, b^{6} - 20 \, a b^{4} c + 30 \, a^{2} b^{2} c^{2}\right)} x^{3} + {\left(3 \, a b^{5} - 20 \, a^{2} b^{3} c + 30 \, a^{3} b c^{2}\right)} x^{2}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - 3 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} x + {\left({\left(3 \, b^{6} c - 26 \, a b^{4} c^{2} + 64 \, a^{2} b^{2} c^{3} - 32 \, a^{3} c^{4}\right)} x^{4} + {\left(3 \, b^{7} - 26 \, a b^{5} c + 64 \, a^{2} b^{3} c^{2} - 32 \, a^{3} b c^{3}\right)} x^{3} + {\left(3 \, a b^{6} - 26 \, a^{2} b^{4} c + 64 \, a^{3} b^{2} c^{2} - 32 \, a^{4} c^{3}\right)} x^{2}\right)} \log\left(c x^{2} + b x + a\right) - 2 \, {\left({\left(3 \, b^{6} c - 26 \, a b^{4} c^{2} + 64 \, a^{2} b^{2} c^{3} - 32 \, a^{3} c^{4}\right)} x^{4} + {\left(3 \, b^{7} - 26 \, a b^{5} c + 64 \, a^{2} b^{3} c^{2} - 32 \, a^{3} b c^{3}\right)} x^{3} + {\left(3 \, a b^{6} - 26 \, a^{2} b^{4} c + 64 \, a^{3} b^{2} c^{2} - 32 \, a^{4} c^{3}\right)} x^{2}\right)} \log\left(x\right)}{2 \, {\left({\left(a^{4} b^{4} c - 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3}\right)} x^{4} + {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} x^{3} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} x^{2}\right)}}, -\frac{a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2} - 2 \, {\left(3 \, a b^{5} c - 23 \, a^{2} b^{3} c^{2} + 44 \, a^{3} b c^{3}\right)} x^{3} - {\left(6 \, a b^{6} - 49 \, a^{2} b^{4} c + 108 \, a^{3} b^{2} c^{2} - 32 \, a^{4} c^{3}\right)} x^{2} - 2 \, {\left({\left(3 \, b^{5} c - 20 \, a b^{3} c^{2} + 30 \, a^{2} b c^{3}\right)} x^{4} + {\left(3 \, b^{6} - 20 \, a b^{4} c + 30 \, a^{2} b^{2} c^{2}\right)} x^{3} + {\left(3 \, a b^{5} - 20 \, a^{2} b^{3} c + 30 \, a^{3} b c^{2}\right)} x^{2}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - 3 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} x + {\left({\left(3 \, b^{6} c - 26 \, a b^{4} c^{2} + 64 \, a^{2} b^{2} c^{3} - 32 \, a^{3} c^{4}\right)} x^{4} + {\left(3 \, b^{7} - 26 \, a b^{5} c + 64 \, a^{2} b^{3} c^{2} - 32 \, a^{3} b c^{3}\right)} x^{3} + {\left(3 \, a b^{6} - 26 \, a^{2} b^{4} c + 64 \, a^{3} b^{2} c^{2} - 32 \, a^{4} c^{3}\right)} x^{2}\right)} \log\left(c x^{2} + b x + a\right) - 2 \, {\left({\left(3 \, b^{6} c - 26 \, a b^{4} c^{2} + 64 \, a^{2} b^{2} c^{3} - 32 \, a^{3} c^{4}\right)} x^{4} + {\left(3 \, b^{7} - 26 \, a b^{5} c + 64 \, a^{2} b^{3} c^{2} - 32 \, a^{3} b c^{3}\right)} x^{3} + {\left(3 \, a b^{6} - 26 \, a^{2} b^{4} c + 64 \, a^{3} b^{2} c^{2} - 32 \, a^{4} c^{3}\right)} x^{2}\right)} \log\left(x\right)}{2 \, {\left({\left(a^{4} b^{4} c - 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3}\right)} x^{4} + {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} x^{3} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} x^{2}\right)}}\right]"," ",0,"[-1/2*(a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2 - 2*(3*a*b^5*c - 23*a^2*b^3*c^2 + 44*a^3*b*c^3)*x^3 - (6*a*b^6 - 49*a^2*b^4*c + 108*a^3*b^2*c^2 - 32*a^4*c^3)*x^2 + ((3*b^5*c - 20*a*b^3*c^2 + 30*a^2*b*c^3)*x^4 + (3*b^6 - 20*a*b^4*c + 30*a^2*b^2*c^2)*x^3 + (3*a*b^5 - 20*a^2*b^3*c + 30*a^3*b*c^2)*x^2)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - 3*(a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*x + ((3*b^6*c - 26*a*b^4*c^2 + 64*a^2*b^2*c^3 - 32*a^3*c^4)*x^4 + (3*b^7 - 26*a*b^5*c + 64*a^2*b^3*c^2 - 32*a^3*b*c^3)*x^3 + (3*a*b^6 - 26*a^2*b^4*c + 64*a^3*b^2*c^2 - 32*a^4*c^3)*x^2)*log(c*x^2 + b*x + a) - 2*((3*b^6*c - 26*a*b^4*c^2 + 64*a^2*b^2*c^3 - 32*a^3*c^4)*x^4 + (3*b^7 - 26*a*b^5*c + 64*a^2*b^3*c^2 - 32*a^3*b*c^3)*x^3 + (3*a*b^6 - 26*a^2*b^4*c + 64*a^3*b^2*c^2 - 32*a^4*c^3)*x^2)*log(x))/((a^4*b^4*c - 8*a^5*b^2*c^2 + 16*a^6*c^3)*x^4 + (a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*x^3 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*x^2), -1/2*(a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2 - 2*(3*a*b^5*c - 23*a^2*b^3*c^2 + 44*a^3*b*c^3)*x^3 - (6*a*b^6 - 49*a^2*b^4*c + 108*a^3*b^2*c^2 - 32*a^4*c^3)*x^2 - 2*((3*b^5*c - 20*a*b^3*c^2 + 30*a^2*b*c^3)*x^4 + (3*b^6 - 20*a*b^4*c + 30*a^2*b^2*c^2)*x^3 + (3*a*b^5 - 20*a^2*b^3*c + 30*a^3*b*c^2)*x^2)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - 3*(a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*x + ((3*b^6*c - 26*a*b^4*c^2 + 64*a^2*b^2*c^3 - 32*a^3*c^4)*x^4 + (3*b^7 - 26*a*b^5*c + 64*a^2*b^3*c^2 - 32*a^3*b*c^3)*x^3 + (3*a*b^6 - 26*a^2*b^4*c + 64*a^3*b^2*c^2 - 32*a^4*c^3)*x^2)*log(c*x^2 + b*x + a) - 2*((3*b^6*c - 26*a*b^4*c^2 + 64*a^2*b^2*c^3 - 32*a^3*c^4)*x^4 + (3*b^7 - 26*a*b^5*c + 64*a^2*b^3*c^2 - 32*a^3*b*c^3)*x^3 + (3*a*b^6 - 26*a^2*b^4*c + 64*a^3*b^2*c^2 - 32*a^4*c^3)*x^2)*log(x))/((a^4*b^4*c - 8*a^5*b^2*c^2 + 16*a^6*c^3)*x^4 + (a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*x^3 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*x^2)]","B",0
27,1,1407,0,2.465013," ","integrate(1/(c*x^4+b*x^3+a*x^2)^2,x, algorithm=""fricas"")","\left[-\frac{a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2} + 6 \, {\left(2 \, a b^{6} c - 17 \, a^{2} b^{4} c^{2} + 41 \, a^{3} b^{2} c^{3} - 20 \, a^{4} c^{4}\right)} x^{4} + 3 \, {\left(4 \, a b^{7} - 36 \, a^{2} b^{5} c + 97 \, a^{3} b^{3} c^{2} - 68 \, a^{4} b c^{3}\right)} x^{3} + {\left(6 \, a^{2} b^{6} - 53 \, a^{3} b^{4} c + 136 \, a^{4} b^{2} c^{2} - 80 \, a^{5} c^{3}\right)} x^{2} - 3 \, {\left({\left(2 \, b^{6} c - 15 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3} - 10 \, a^{3} c^{4}\right)} x^{5} + {\left(2 \, b^{7} - 15 \, a b^{5} c + 30 \, a^{2} b^{3} c^{2} - 10 \, a^{3} b c^{3}\right)} x^{4} + {\left(2 \, a b^{6} - 15 \, a^{2} b^{4} c + 30 \, a^{3} b^{2} c^{2} - 10 \, a^{4} c^{3}\right)} x^{3}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - 2 \, {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} x - 3 \, {\left({\left(2 \, b^{7} c - 19 \, a b^{5} c^{2} + 56 \, a^{2} b^{3} c^{3} - 48 \, a^{3} b c^{4}\right)} x^{5} + {\left(2 \, b^{8} - 19 \, a b^{6} c + 56 \, a^{2} b^{4} c^{2} - 48 \, a^{3} b^{2} c^{3}\right)} x^{4} + {\left(2 \, a b^{7} - 19 \, a^{2} b^{5} c + 56 \, a^{3} b^{3} c^{2} - 48 \, a^{4} b c^{3}\right)} x^{3}\right)} \log\left(c x^{2} + b x + a\right) + 6 \, {\left({\left(2 \, b^{7} c - 19 \, a b^{5} c^{2} + 56 \, a^{2} b^{3} c^{3} - 48 \, a^{3} b c^{4}\right)} x^{5} + {\left(2 \, b^{8} - 19 \, a b^{6} c + 56 \, a^{2} b^{4} c^{2} - 48 \, a^{3} b^{2} c^{3}\right)} x^{4} + {\left(2 \, a b^{7} - 19 \, a^{2} b^{5} c + 56 \, a^{3} b^{3} c^{2} - 48 \, a^{4} b c^{3}\right)} x^{3}\right)} \log\left(x\right)}{3 \, {\left({\left(a^{5} b^{4} c - 8 \, a^{6} b^{2} c^{2} + 16 \, a^{7} c^{3}\right)} x^{5} + {\left(a^{5} b^{5} - 8 \, a^{6} b^{3} c + 16 \, a^{7} b c^{2}\right)} x^{4} + {\left(a^{6} b^{4} - 8 \, a^{7} b^{2} c + 16 \, a^{8} c^{2}\right)} x^{3}\right)}}, -\frac{a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2} + 6 \, {\left(2 \, a b^{6} c - 17 \, a^{2} b^{4} c^{2} + 41 \, a^{3} b^{2} c^{3} - 20 \, a^{4} c^{4}\right)} x^{4} + 3 \, {\left(4 \, a b^{7} - 36 \, a^{2} b^{5} c + 97 \, a^{3} b^{3} c^{2} - 68 \, a^{4} b c^{3}\right)} x^{3} + {\left(6 \, a^{2} b^{6} - 53 \, a^{3} b^{4} c + 136 \, a^{4} b^{2} c^{2} - 80 \, a^{5} c^{3}\right)} x^{2} + 6 \, {\left({\left(2 \, b^{6} c - 15 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3} - 10 \, a^{3} c^{4}\right)} x^{5} + {\left(2 \, b^{7} - 15 \, a b^{5} c + 30 \, a^{2} b^{3} c^{2} - 10 \, a^{3} b c^{3}\right)} x^{4} + {\left(2 \, a b^{6} - 15 \, a^{2} b^{4} c + 30 \, a^{3} b^{2} c^{2} - 10 \, a^{4} c^{3}\right)} x^{3}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - 2 \, {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} x - 3 \, {\left({\left(2 \, b^{7} c - 19 \, a b^{5} c^{2} + 56 \, a^{2} b^{3} c^{3} - 48 \, a^{3} b c^{4}\right)} x^{5} + {\left(2 \, b^{8} - 19 \, a b^{6} c + 56 \, a^{2} b^{4} c^{2} - 48 \, a^{3} b^{2} c^{3}\right)} x^{4} + {\left(2 \, a b^{7} - 19 \, a^{2} b^{5} c + 56 \, a^{3} b^{3} c^{2} - 48 \, a^{4} b c^{3}\right)} x^{3}\right)} \log\left(c x^{2} + b x + a\right) + 6 \, {\left({\left(2 \, b^{7} c - 19 \, a b^{5} c^{2} + 56 \, a^{2} b^{3} c^{3} - 48 \, a^{3} b c^{4}\right)} x^{5} + {\left(2 \, b^{8} - 19 \, a b^{6} c + 56 \, a^{2} b^{4} c^{2} - 48 \, a^{3} b^{2} c^{3}\right)} x^{4} + {\left(2 \, a b^{7} - 19 \, a^{2} b^{5} c + 56 \, a^{3} b^{3} c^{2} - 48 \, a^{4} b c^{3}\right)} x^{3}\right)} \log\left(x\right)}{3 \, {\left({\left(a^{5} b^{4} c - 8 \, a^{6} b^{2} c^{2} + 16 \, a^{7} c^{3}\right)} x^{5} + {\left(a^{5} b^{5} - 8 \, a^{6} b^{3} c + 16 \, a^{7} b c^{2}\right)} x^{4} + {\left(a^{6} b^{4} - 8 \, a^{7} b^{2} c + 16 \, a^{8} c^{2}\right)} x^{3}\right)}}\right]"," ",0,"[-1/3*(a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2 + 6*(2*a*b^6*c - 17*a^2*b^4*c^2 + 41*a^3*b^2*c^3 - 20*a^4*c^4)*x^4 + 3*(4*a*b^7 - 36*a^2*b^5*c + 97*a^3*b^3*c^2 - 68*a^4*b*c^3)*x^3 + (6*a^2*b^6 - 53*a^3*b^4*c + 136*a^4*b^2*c^2 - 80*a^5*c^3)*x^2 - 3*((2*b^6*c - 15*a*b^4*c^2 + 30*a^2*b^2*c^3 - 10*a^3*c^4)*x^5 + (2*b^7 - 15*a*b^5*c + 30*a^2*b^3*c^2 - 10*a^3*b*c^3)*x^4 + (2*a*b^6 - 15*a^2*b^4*c + 30*a^3*b^2*c^2 - 10*a^4*c^3)*x^3)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - 2*(a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*x - 3*((2*b^7*c - 19*a*b^5*c^2 + 56*a^2*b^3*c^3 - 48*a^3*b*c^4)*x^5 + (2*b^8 - 19*a*b^6*c + 56*a^2*b^4*c^2 - 48*a^3*b^2*c^3)*x^4 + (2*a*b^7 - 19*a^2*b^5*c + 56*a^3*b^3*c^2 - 48*a^4*b*c^3)*x^3)*log(c*x^2 + b*x + a) + 6*((2*b^7*c - 19*a*b^5*c^2 + 56*a^2*b^3*c^3 - 48*a^3*b*c^4)*x^5 + (2*b^8 - 19*a*b^6*c + 56*a^2*b^4*c^2 - 48*a^3*b^2*c^3)*x^4 + (2*a*b^7 - 19*a^2*b^5*c + 56*a^3*b^3*c^2 - 48*a^4*b*c^3)*x^3)*log(x))/((a^5*b^4*c - 8*a^6*b^2*c^2 + 16*a^7*c^3)*x^5 + (a^5*b^5 - 8*a^6*b^3*c + 16*a^7*b*c^2)*x^4 + (a^6*b^4 - 8*a^7*b^2*c + 16*a^8*c^2)*x^3), -1/3*(a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2 + 6*(2*a*b^6*c - 17*a^2*b^4*c^2 + 41*a^3*b^2*c^3 - 20*a^4*c^4)*x^4 + 3*(4*a*b^7 - 36*a^2*b^5*c + 97*a^3*b^3*c^2 - 68*a^4*b*c^3)*x^3 + (6*a^2*b^6 - 53*a^3*b^4*c + 136*a^4*b^2*c^2 - 80*a^5*c^3)*x^2 + 6*((2*b^6*c - 15*a*b^4*c^2 + 30*a^2*b^2*c^3 - 10*a^3*c^4)*x^5 + (2*b^7 - 15*a*b^5*c + 30*a^2*b^3*c^2 - 10*a^3*b*c^3)*x^4 + (2*a*b^6 - 15*a^2*b^4*c + 30*a^3*b^2*c^2 - 10*a^4*c^3)*x^3)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - 2*(a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*x - 3*((2*b^7*c - 19*a*b^5*c^2 + 56*a^2*b^3*c^3 - 48*a^3*b*c^4)*x^5 + (2*b^8 - 19*a*b^6*c + 56*a^2*b^4*c^2 - 48*a^3*b^2*c^3)*x^4 + (2*a*b^7 - 19*a^2*b^5*c + 56*a^3*b^3*c^2 - 48*a^4*b*c^3)*x^3)*log(c*x^2 + b*x + a) + 6*((2*b^7*c - 19*a*b^5*c^2 + 56*a^2*b^3*c^3 - 48*a^3*b*c^4)*x^5 + (2*b^8 - 19*a*b^6*c + 56*a^2*b^4*c^2 - 48*a^3*b^2*c^3)*x^4 + (2*a*b^7 - 19*a^2*b^5*c + 56*a^3*b^3*c^2 - 48*a^4*b*c^3)*x^3)*log(x))/((a^5*b^4*c - 8*a^6*b^2*c^2 + 16*a^7*c^3)*x^5 + (a^5*b^5 - 8*a^6*b^3*c + 16*a^7*b*c^2)*x^4 + (a^6*b^4 - 8*a^7*b^2*c + 16*a^8*c^2)*x^3)]","B",0
28,1,1640,0,3.175141," ","integrate(1/x/(c*x^4+b*x^3+a*x^2)^2,x, algorithm=""fricas"")","\left[-\frac{3 \, a^{5} b^{4} - 24 \, a^{6} b^{2} c + 48 \, a^{7} c^{2} - 12 \, {\left(5 \, a b^{7} c - 47 \, a^{2} b^{5} c^{2} + 137 \, a^{3} b^{3} c^{3} - 116 \, a^{4} b c^{4}\right)} x^{5} - 6 \, {\left(10 \, a b^{8} - 99 \, a^{2} b^{6} c + 316 \, a^{3} b^{4} c^{2} - 332 \, a^{4} b^{2} c^{3} + 48 \, a^{5} c^{4}\right)} x^{4} - 2 \, {\left(15 \, a^{2} b^{7} - 146 \, a^{3} b^{5} c + 448 \, a^{4} b^{3} c^{2} - 416 \, a^{5} b c^{3}\right)} x^{3} + {\left(10 \, a^{3} b^{6} - 89 \, a^{4} b^{4} c + 232 \, a^{5} b^{2} c^{2} - 144 \, a^{6} c^{3}\right)} x^{2} - 6 \, {\left({\left(5 \, b^{7} c - 42 \, a b^{5} c^{2} + 105 \, a^{2} b^{3} c^{3} - 70 \, a^{3} b c^{4}\right)} x^{6} + {\left(5 \, b^{8} - 42 \, a b^{6} c + 105 \, a^{2} b^{4} c^{2} - 70 \, a^{3} b^{2} c^{3}\right)} x^{5} + {\left(5 \, a b^{7} - 42 \, a^{2} b^{5} c + 105 \, a^{3} b^{3} c^{2} - 70 \, a^{4} b c^{3}\right)} x^{4}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - 5 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} x + 6 \, {\left({\left(5 \, b^{8} c - 52 \, a b^{6} c^{2} + 179 \, a^{2} b^{4} c^{3} - 216 \, a^{3} b^{2} c^{4} + 48 \, a^{4} c^{5}\right)} x^{6} + {\left(5 \, b^{9} - 52 \, a b^{7} c + 179 \, a^{2} b^{5} c^{2} - 216 \, a^{3} b^{3} c^{3} + 48 \, a^{4} b c^{4}\right)} x^{5} + {\left(5 \, a b^{8} - 52 \, a^{2} b^{6} c + 179 \, a^{3} b^{4} c^{2} - 216 \, a^{4} b^{2} c^{3} + 48 \, a^{5} c^{4}\right)} x^{4}\right)} \log\left(c x^{2} + b x + a\right) - 12 \, {\left({\left(5 \, b^{8} c - 52 \, a b^{6} c^{2} + 179 \, a^{2} b^{4} c^{3} - 216 \, a^{3} b^{2} c^{4} + 48 \, a^{4} c^{5}\right)} x^{6} + {\left(5 \, b^{9} - 52 \, a b^{7} c + 179 \, a^{2} b^{5} c^{2} - 216 \, a^{3} b^{3} c^{3} + 48 \, a^{4} b c^{4}\right)} x^{5} + {\left(5 \, a b^{8} - 52 \, a^{2} b^{6} c + 179 \, a^{3} b^{4} c^{2} - 216 \, a^{4} b^{2} c^{3} + 48 \, a^{5} c^{4}\right)} x^{4}\right)} \log\left(x\right)}{12 \, {\left({\left(a^{6} b^{4} c - 8 \, a^{7} b^{2} c^{2} + 16 \, a^{8} c^{3}\right)} x^{6} + {\left(a^{6} b^{5} - 8 \, a^{7} b^{3} c + 16 \, a^{8} b c^{2}\right)} x^{5} + {\left(a^{7} b^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}\right)} x^{4}\right)}}, -\frac{3 \, a^{5} b^{4} - 24 \, a^{6} b^{2} c + 48 \, a^{7} c^{2} - 12 \, {\left(5 \, a b^{7} c - 47 \, a^{2} b^{5} c^{2} + 137 \, a^{3} b^{3} c^{3} - 116 \, a^{4} b c^{4}\right)} x^{5} - 6 \, {\left(10 \, a b^{8} - 99 \, a^{2} b^{6} c + 316 \, a^{3} b^{4} c^{2} - 332 \, a^{4} b^{2} c^{3} + 48 \, a^{5} c^{4}\right)} x^{4} - 2 \, {\left(15 \, a^{2} b^{7} - 146 \, a^{3} b^{5} c + 448 \, a^{4} b^{3} c^{2} - 416 \, a^{5} b c^{3}\right)} x^{3} + {\left(10 \, a^{3} b^{6} - 89 \, a^{4} b^{4} c + 232 \, a^{5} b^{2} c^{2} - 144 \, a^{6} c^{3}\right)} x^{2} - 12 \, {\left({\left(5 \, b^{7} c - 42 \, a b^{5} c^{2} + 105 \, a^{2} b^{3} c^{3} - 70 \, a^{3} b c^{4}\right)} x^{6} + {\left(5 \, b^{8} - 42 \, a b^{6} c + 105 \, a^{2} b^{4} c^{2} - 70 \, a^{3} b^{2} c^{3}\right)} x^{5} + {\left(5 \, a b^{7} - 42 \, a^{2} b^{5} c + 105 \, a^{3} b^{3} c^{2} - 70 \, a^{4} b c^{3}\right)} x^{4}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - 5 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} x + 6 \, {\left({\left(5 \, b^{8} c - 52 \, a b^{6} c^{2} + 179 \, a^{2} b^{4} c^{3} - 216 \, a^{3} b^{2} c^{4} + 48 \, a^{4} c^{5}\right)} x^{6} + {\left(5 \, b^{9} - 52 \, a b^{7} c + 179 \, a^{2} b^{5} c^{2} - 216 \, a^{3} b^{3} c^{3} + 48 \, a^{4} b c^{4}\right)} x^{5} + {\left(5 \, a b^{8} - 52 \, a^{2} b^{6} c + 179 \, a^{3} b^{4} c^{2} - 216 \, a^{4} b^{2} c^{3} + 48 \, a^{5} c^{4}\right)} x^{4}\right)} \log\left(c x^{2} + b x + a\right) - 12 \, {\left({\left(5 \, b^{8} c - 52 \, a b^{6} c^{2} + 179 \, a^{2} b^{4} c^{3} - 216 \, a^{3} b^{2} c^{4} + 48 \, a^{4} c^{5}\right)} x^{6} + {\left(5 \, b^{9} - 52 \, a b^{7} c + 179 \, a^{2} b^{5} c^{2} - 216 \, a^{3} b^{3} c^{3} + 48 \, a^{4} b c^{4}\right)} x^{5} + {\left(5 \, a b^{8} - 52 \, a^{2} b^{6} c + 179 \, a^{3} b^{4} c^{2} - 216 \, a^{4} b^{2} c^{3} + 48 \, a^{5} c^{4}\right)} x^{4}\right)} \log\left(x\right)}{12 \, {\left({\left(a^{6} b^{4} c - 8 \, a^{7} b^{2} c^{2} + 16 \, a^{8} c^{3}\right)} x^{6} + {\left(a^{6} b^{5} - 8 \, a^{7} b^{3} c + 16 \, a^{8} b c^{2}\right)} x^{5} + {\left(a^{7} b^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}\right)} x^{4}\right)}}\right]"," ",0,"[-1/12*(3*a^5*b^4 - 24*a^6*b^2*c + 48*a^7*c^2 - 12*(5*a*b^7*c - 47*a^2*b^5*c^2 + 137*a^3*b^3*c^3 - 116*a^4*b*c^4)*x^5 - 6*(10*a*b^8 - 99*a^2*b^6*c + 316*a^3*b^4*c^2 - 332*a^4*b^2*c^3 + 48*a^5*c^4)*x^4 - 2*(15*a^2*b^7 - 146*a^3*b^5*c + 448*a^4*b^3*c^2 - 416*a^5*b*c^3)*x^3 + (10*a^3*b^6 - 89*a^4*b^4*c + 232*a^5*b^2*c^2 - 144*a^6*c^3)*x^2 - 6*((5*b^7*c - 42*a*b^5*c^2 + 105*a^2*b^3*c^3 - 70*a^3*b*c^4)*x^6 + (5*b^8 - 42*a*b^6*c + 105*a^2*b^4*c^2 - 70*a^3*b^2*c^3)*x^5 + (5*a*b^7 - 42*a^2*b^5*c + 105*a^3*b^3*c^2 - 70*a^4*b*c^3)*x^4)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - 5*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*x + 6*((5*b^8*c - 52*a*b^6*c^2 + 179*a^2*b^4*c^3 - 216*a^3*b^2*c^4 + 48*a^4*c^5)*x^6 + (5*b^9 - 52*a*b^7*c + 179*a^2*b^5*c^2 - 216*a^3*b^3*c^3 + 48*a^4*b*c^4)*x^5 + (5*a*b^8 - 52*a^2*b^6*c + 179*a^3*b^4*c^2 - 216*a^4*b^2*c^3 + 48*a^5*c^4)*x^4)*log(c*x^2 + b*x + a) - 12*((5*b^8*c - 52*a*b^6*c^2 + 179*a^2*b^4*c^3 - 216*a^3*b^2*c^4 + 48*a^4*c^5)*x^6 + (5*b^9 - 52*a*b^7*c + 179*a^2*b^5*c^2 - 216*a^3*b^3*c^3 + 48*a^4*b*c^4)*x^5 + (5*a*b^8 - 52*a^2*b^6*c + 179*a^3*b^4*c^2 - 216*a^4*b^2*c^3 + 48*a^5*c^4)*x^4)*log(x))/((a^6*b^4*c - 8*a^7*b^2*c^2 + 16*a^8*c^3)*x^6 + (a^6*b^5 - 8*a^7*b^3*c + 16*a^8*b*c^2)*x^5 + (a^7*b^4 - 8*a^8*b^2*c + 16*a^9*c^2)*x^4), -1/12*(3*a^5*b^4 - 24*a^6*b^2*c + 48*a^7*c^2 - 12*(5*a*b^7*c - 47*a^2*b^5*c^2 + 137*a^3*b^3*c^3 - 116*a^4*b*c^4)*x^5 - 6*(10*a*b^8 - 99*a^2*b^6*c + 316*a^3*b^4*c^2 - 332*a^4*b^2*c^3 + 48*a^5*c^4)*x^4 - 2*(15*a^2*b^7 - 146*a^3*b^5*c + 448*a^4*b^3*c^2 - 416*a^5*b*c^3)*x^3 + (10*a^3*b^6 - 89*a^4*b^4*c + 232*a^5*b^2*c^2 - 144*a^6*c^3)*x^2 - 12*((5*b^7*c - 42*a*b^5*c^2 + 105*a^2*b^3*c^3 - 70*a^3*b*c^4)*x^6 + (5*b^8 - 42*a*b^6*c + 105*a^2*b^4*c^2 - 70*a^3*b^2*c^3)*x^5 + (5*a*b^7 - 42*a^2*b^5*c + 105*a^3*b^3*c^2 - 70*a^4*b*c^3)*x^4)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - 5*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*x + 6*((5*b^8*c - 52*a*b^6*c^2 + 179*a^2*b^4*c^3 - 216*a^3*b^2*c^4 + 48*a^4*c^5)*x^6 + (5*b^9 - 52*a*b^7*c + 179*a^2*b^5*c^2 - 216*a^3*b^3*c^3 + 48*a^4*b*c^4)*x^5 + (5*a*b^8 - 52*a^2*b^6*c + 179*a^3*b^4*c^2 - 216*a^4*b^2*c^3 + 48*a^5*c^4)*x^4)*log(c*x^2 + b*x + a) - 12*((5*b^8*c - 52*a*b^6*c^2 + 179*a^2*b^4*c^3 - 216*a^3*b^2*c^4 + 48*a^4*c^5)*x^6 + (5*b^9 - 52*a*b^7*c + 179*a^2*b^5*c^2 - 216*a^3*b^3*c^3 + 48*a^4*b*c^4)*x^5 + (5*a*b^8 - 52*a^2*b^6*c + 179*a^3*b^4*c^2 - 216*a^4*b^2*c^3 + 48*a^5*c^4)*x^4)*log(x))/((a^6*b^4*c - 8*a^7*b^2*c^2 + 16*a^8*c^3)*x^6 + (a^6*b^5 - 8*a^7*b^3*c + 16*a^8*b*c^2)*x^5 + (a^7*b^4 - 8*a^8*b^2*c + 16*a^9*c^2)*x^4)]","B",0
29,1,390,0,1.232373," ","integrate(x^2*(c*x^4+b*x^3+a*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(7 \, b^{5} - 40 \, a b^{3} c + 48 \, a^{2} b c^{2}\right)} \sqrt{c} x \log\left(-\frac{8 \, c^{2} x^{3} + 8 \, b c x^{2} + 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{c} + {\left(b^{2} + 4 \, a c\right)} x}{x}\right) + 4 \, {\left(384 \, c^{5} x^{4} + 48 \, b c^{4} x^{3} - 105 \, b^{4} c + 460 \, a b^{2} c^{2} - 256 \, a^{2} c^{3} - 8 \, {\left(7 \, b^{2} c^{3} - 16 \, a c^{4}\right)} x^{2} + 2 \, {\left(35 \, b^{3} c^{2} - 116 \, a b c^{3}\right)} x\right)} \sqrt{c x^{4} + b x^{3} + a x^{2}}}{7680 \, c^{5} x}, -\frac{15 \, {\left(7 \, b^{5} - 40 \, a b^{3} c + 48 \, a^{2} b c^{2}\right)} \sqrt{-c} x \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{3} + b c x^{2} + a c x\right)}}\right) - 2 \, {\left(384 \, c^{5} x^{4} + 48 \, b c^{4} x^{3} - 105 \, b^{4} c + 460 \, a b^{2} c^{2} - 256 \, a^{2} c^{3} - 8 \, {\left(7 \, b^{2} c^{3} - 16 \, a c^{4}\right)} x^{2} + 2 \, {\left(35 \, b^{3} c^{2} - 116 \, a b c^{3}\right)} x\right)} \sqrt{c x^{4} + b x^{3} + a x^{2}}}{3840 \, c^{5} x}\right]"," ",0,"[1/7680*(15*(7*b^5 - 40*a*b^3*c + 48*a^2*b*c^2)*sqrt(c)*x*log(-(8*c^2*x^3 + 8*b*c*x^2 + 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(c) + (b^2 + 4*a*c)*x)/x) + 4*(384*c^5*x^4 + 48*b*c^4*x^3 - 105*b^4*c + 460*a*b^2*c^2 - 256*a^2*c^3 - 8*(7*b^2*c^3 - 16*a*c^4)*x^2 + 2*(35*b^3*c^2 - 116*a*b*c^3)*x)*sqrt(c*x^4 + b*x^3 + a*x^2))/(c^5*x), -1/3840*(15*(7*b^5 - 40*a*b^3*c + 48*a^2*b*c^2)*sqrt(-c)*x*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(-c)/(c^2*x^3 + b*c*x^2 + a*c*x)) - 2*(384*c^5*x^4 + 48*b*c^4*x^3 - 105*b^4*c + 460*a*b^2*c^2 - 256*a^2*c^3 - 8*(7*b^2*c^3 - 16*a*c^4)*x^2 + 2*(35*b^3*c^2 - 116*a*b*c^3)*x)*sqrt(c*x^4 + b*x^3 + a*x^2))/(c^5*x)]","A",0
30,1,326,0,0.675796," ","integrate(x*(c*x^4+b*x^3+a*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(5 \, b^{4} - 24 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{c} x \log\left(-\frac{8 \, c^{2} x^{3} + 8 \, b c x^{2} - 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{c} + {\left(b^{2} + 4 \, a c\right)} x}{x}\right) + 4 \, {\left(48 \, c^{4} x^{3} + 8 \, b c^{3} x^{2} + 15 \, b^{3} c - 52 \, a b c^{2} - 2 \, {\left(5 \, b^{2} c^{2} - 12 \, a c^{3}\right)} x\right)} \sqrt{c x^{4} + b x^{3} + a x^{2}}}{768 \, c^{4} x}, \frac{3 \, {\left(5 \, b^{4} - 24 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{-c} x \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{3} + b c x^{2} + a c x\right)}}\right) + 2 \, {\left(48 \, c^{4} x^{3} + 8 \, b c^{3} x^{2} + 15 \, b^{3} c - 52 \, a b c^{2} - 2 \, {\left(5 \, b^{2} c^{2} - 12 \, a c^{3}\right)} x\right)} \sqrt{c x^{4} + b x^{3} + a x^{2}}}{384 \, c^{4} x}\right]"," ",0,"[1/768*(3*(5*b^4 - 24*a*b^2*c + 16*a^2*c^2)*sqrt(c)*x*log(-(8*c^2*x^3 + 8*b*c*x^2 - 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(c) + (b^2 + 4*a*c)*x)/x) + 4*(48*c^4*x^3 + 8*b*c^3*x^2 + 15*b^3*c - 52*a*b*c^2 - 2*(5*b^2*c^2 - 12*a*c^3)*x)*sqrt(c*x^4 + b*x^3 + a*x^2))/(c^4*x), 1/384*(3*(5*b^4 - 24*a*b^2*c + 16*a^2*c^2)*sqrt(-c)*x*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(-c)/(c^2*x^3 + b*c*x^2 + a*c*x)) + 2*(48*c^4*x^3 + 8*b*c^3*x^2 + 15*b^3*c - 52*a*b*c^2 - 2*(5*b^2*c^2 - 12*a*c^3)*x)*sqrt(c*x^4 + b*x^3 + a*x^2))/(c^4*x)]","A",0
31,1,260,0,1.245612," ","integrate((c*x^4+b*x^3+a*x^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(b^{3} - 4 \, a b c\right)} \sqrt{c} x \log\left(-\frac{8 \, c^{2} x^{3} + 8 \, b c x^{2} - 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{c} + {\left(b^{2} + 4 \, a c\right)} x}{x}\right) - 4 \, {\left(8 \, c^{3} x^{2} + 2 \, b c^{2} x - 3 \, b^{2} c + 8 \, a c^{2}\right)} \sqrt{c x^{4} + b x^{3} + a x^{2}}}{96 \, c^{3} x}, -\frac{3 \, {\left(b^{3} - 4 \, a b c\right)} \sqrt{-c} x \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{3} + b c x^{2} + a c x\right)}}\right) - 2 \, {\left(8 \, c^{3} x^{2} + 2 \, b c^{2} x - 3 \, b^{2} c + 8 \, a c^{2}\right)} \sqrt{c x^{4} + b x^{3} + a x^{2}}}{48 \, c^{3} x}\right]"," ",0,"[-1/96*(3*(b^3 - 4*a*b*c)*sqrt(c)*x*log(-(8*c^2*x^3 + 8*b*c*x^2 - 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(c) + (b^2 + 4*a*c)*x)/x) - 4*(8*c^3*x^2 + 2*b*c^2*x - 3*b^2*c + 8*a*c^2)*sqrt(c*x^4 + b*x^3 + a*x^2))/(c^3*x), -1/48*(3*(b^3 - 4*a*b*c)*sqrt(-c)*x*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(-c)/(c^2*x^3 + b*c*x^2 + a*c*x)) - 2*(8*c^3*x^2 + 2*b*c^2*x - 3*b^2*c + 8*a*c^2)*sqrt(c*x^4 + b*x^3 + a*x^2))/(c^3*x)]","A",0
32,1,220,0,1.106452," ","integrate((c*x^4+b*x^3+a*x^2)^(1/2)/x,x, algorithm=""fricas"")","\left[-\frac{{\left(b^{2} - 4 \, a c\right)} \sqrt{c} x \log\left(-\frac{8 \, c^{2} x^{3} + 8 \, b c x^{2} + 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{c} + {\left(b^{2} + 4 \, a c\right)} x}{x}\right) - 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c^{2} x + b c\right)}}{16 \, c^{2} x}, \frac{{\left(b^{2} - 4 \, a c\right)} \sqrt{-c} x \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{3} + b c x^{2} + a c x\right)}}\right) + 2 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c^{2} x + b c\right)}}{8 \, c^{2} x}\right]"," ",0,"[-1/16*((b^2 - 4*a*c)*sqrt(c)*x*log(-(8*c^2*x^3 + 8*b*c*x^2 + 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(c) + (b^2 + 4*a*c)*x)/x) - 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c^2*x + b*c))/(c^2*x), 1/8*((b^2 - 4*a*c)*sqrt(-c)*x*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(-c)/(c^2*x^3 + b*c*x^2 + a*c*x)) + 2*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c^2*x + b*c))/(c^2*x)]","A",0
33,1,638,0,1.409382," ","integrate((c*x^4+b*x^3+a*x^2)^(1/2)/x^2,x, algorithm=""fricas"")","\left[\frac{b \sqrt{c} x \log\left(-\frac{8 \, c^{2} x^{3} + 8 \, b c x^{2} + 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{c} + {\left(b^{2} + 4 \, a c\right)} x}{x}\right) + 2 \, \sqrt{a} c x \log\left(-\frac{8 \, a b x^{2} + {\left(b^{2} + 4 \, a c\right)} x^{3} + 8 \, a^{2} x - 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)} \sqrt{a}}{x^{3}}\right) + 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} c}{4 \, c x}, -\frac{b \sqrt{-c} x \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{3} + b c x^{2} + a c x\right)}}\right) - \sqrt{a} c x \log\left(-\frac{8 \, a b x^{2} + {\left(b^{2} + 4 \, a c\right)} x^{3} + 8 \, a^{2} x - 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)} \sqrt{a}}{x^{3}}\right) - 2 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} c}{2 \, c x}, \frac{4 \, \sqrt{-a} c x \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{3} + a b x^{2} + a^{2} x\right)}}\right) + b \sqrt{c} x \log\left(-\frac{8 \, c^{2} x^{3} + 8 \, b c x^{2} + 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{c} + {\left(b^{2} + 4 \, a c\right)} x}{x}\right) + 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} c}{4 \, c x}, \frac{2 \, \sqrt{-a} c x \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{3} + a b x^{2} + a^{2} x\right)}}\right) - b \sqrt{-c} x \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{3} + b c x^{2} + a c x\right)}}\right) + 2 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} c}{2 \, c x}\right]"," ",0,"[1/4*(b*sqrt(c)*x*log(-(8*c^2*x^3 + 8*b*c*x^2 + 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(c) + (b^2 + 4*a*c)*x)/x) + 2*sqrt(a)*c*x*log(-(8*a*b*x^2 + (b^2 + 4*a*c)*x^3 + 8*a^2*x - 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)*sqrt(a))/x^3) + 4*sqrt(c*x^4 + b*x^3 + a*x^2)*c)/(c*x), -1/2*(b*sqrt(-c)*x*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(-c)/(c^2*x^3 + b*c*x^2 + a*c*x)) - sqrt(a)*c*x*log(-(8*a*b*x^2 + (b^2 + 4*a*c)*x^3 + 8*a^2*x - 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)*sqrt(a))/x^3) - 2*sqrt(c*x^4 + b*x^3 + a*x^2)*c)/(c*x), 1/4*(4*sqrt(-a)*c*x*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)*sqrt(-a)/(a*c*x^3 + a*b*x^2 + a^2*x)) + b*sqrt(c)*x*log(-(8*c^2*x^3 + 8*b*c*x^2 + 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(c) + (b^2 + 4*a*c)*x)/x) + 4*sqrt(c*x^4 + b*x^3 + a*x^2)*c)/(c*x), 1/2*(2*sqrt(-a)*c*x*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)*sqrt(-a)/(a*c*x^3 + a*b*x^2 + a^2*x)) - b*sqrt(-c)*x*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(-c)/(c^2*x^3 + b*c*x^2 + a*c*x)) + 2*sqrt(c*x^4 + b*x^3 + a*x^2)*c)/(c*x)]","A",0
34,1,653,0,1.430707," ","integrate((c*x^4+b*x^3+a*x^2)^(1/2)/x^3,x, algorithm=""fricas"")","\left[\frac{2 \, a \sqrt{c} x^{2} \log\left(-\frac{8 \, c^{2} x^{3} + 8 \, b c x^{2} + 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{c} + {\left(b^{2} + 4 \, a c\right)} x}{x}\right) + \sqrt{a} b x^{2} \log\left(-\frac{8 \, a b x^{2} + {\left(b^{2} + 4 \, a c\right)} x^{3} + 8 \, a^{2} x - 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)} \sqrt{a}}{x^{3}}\right) - 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} a}{4 \, a x^{2}}, -\frac{4 \, a \sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{3} + b c x^{2} + a c x\right)}}\right) - \sqrt{a} b x^{2} \log\left(-\frac{8 \, a b x^{2} + {\left(b^{2} + 4 \, a c\right)} x^{3} + 8 \, a^{2} x - 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)} \sqrt{a}}{x^{3}}\right) + 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} a}{4 \, a x^{2}}, \frac{\sqrt{-a} b x^{2} \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{3} + a b x^{2} + a^{2} x\right)}}\right) + a \sqrt{c} x^{2} \log\left(-\frac{8 \, c^{2} x^{3} + 8 \, b c x^{2} + 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{c} + {\left(b^{2} + 4 \, a c\right)} x}{x}\right) - 2 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} a}{2 \, a x^{2}}, \frac{\sqrt{-a} b x^{2} \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{3} + a b x^{2} + a^{2} x\right)}}\right) - 2 \, a \sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{3} + b c x^{2} + a c x\right)}}\right) - 2 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} a}{2 \, a x^{2}}\right]"," ",0,"[1/4*(2*a*sqrt(c)*x^2*log(-(8*c^2*x^3 + 8*b*c*x^2 + 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(c) + (b^2 + 4*a*c)*x)/x) + sqrt(a)*b*x^2*log(-(8*a*b*x^2 + (b^2 + 4*a*c)*x^3 + 8*a^2*x - 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)*sqrt(a))/x^3) - 4*sqrt(c*x^4 + b*x^3 + a*x^2)*a)/(a*x^2), -1/4*(4*a*sqrt(-c)*x^2*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(-c)/(c^2*x^3 + b*c*x^2 + a*c*x)) - sqrt(a)*b*x^2*log(-(8*a*b*x^2 + (b^2 + 4*a*c)*x^3 + 8*a^2*x - 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)*sqrt(a))/x^3) + 4*sqrt(c*x^4 + b*x^3 + a*x^2)*a)/(a*x^2), 1/2*(sqrt(-a)*b*x^2*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)*sqrt(-a)/(a*c*x^3 + a*b*x^2 + a^2*x)) + a*sqrt(c)*x^2*log(-(8*c^2*x^3 + 8*b*c*x^2 + 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(c) + (b^2 + 4*a*c)*x)/x) - 2*sqrt(c*x^4 + b*x^3 + a*x^2)*a)/(a*x^2), 1/2*(sqrt(-a)*b*x^2*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)*sqrt(-a)/(a*c*x^3 + a*b*x^2 + a^2*x)) - 2*a*sqrt(-c)*x^2*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(-c)/(c^2*x^3 + b*c*x^2 + a*c*x)) - 2*sqrt(c*x^4 + b*x^3 + a*x^2)*a)/(a*x^2)]","A",0
35,1,226,0,1.269122," ","integrate((c*x^4+b*x^3+a*x^2)^(1/2)/x^4,x, algorithm=""fricas"")","\left[-\frac{{\left(b^{2} - 4 \, a c\right)} \sqrt{a} x^{3} \log\left(-\frac{8 \, a b x^{2} + {\left(b^{2} + 4 \, a c\right)} x^{3} + 8 \, a^{2} x - 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)} \sqrt{a}}{x^{3}}\right) + 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(a b x + 2 \, a^{2}\right)}}{16 \, a^{2} x^{3}}, -\frac{{\left(b^{2} - 4 \, a c\right)} \sqrt{-a} x^{3} \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{3} + a b x^{2} + a^{2} x\right)}}\right) + 2 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(a b x + 2 \, a^{2}\right)}}{8 \, a^{2} x^{3}}\right]"," ",0,"[-1/16*((b^2 - 4*a*c)*sqrt(a)*x^3*log(-(8*a*b*x^2 + (b^2 + 4*a*c)*x^3 + 8*a^2*x - 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)*sqrt(a))/x^3) + 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(a*b*x + 2*a^2))/(a^2*x^3), -1/8*((b^2 - 4*a*c)*sqrt(-a)*x^3*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)*sqrt(-a)/(a*c*x^3 + a*b*x^2 + a^2*x)) + 2*sqrt(c*x^4 + b*x^3 + a*x^2)*(a*b*x + 2*a^2))/(a^2*x^3)]","A",0
36,1,272,0,1.333496," ","integrate((c*x^4+b*x^3+a*x^2)^(1/2)/x^5,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(b^{3} - 4 \, a b c\right)} \sqrt{a} x^{4} \log\left(-\frac{8 \, a b x^{2} + {\left(b^{2} + 4 \, a c\right)} x^{3} + 8 \, a^{2} x + 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)} \sqrt{a}}{x^{3}}\right) + 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, a^{2} b x + 8 \, a^{3} - {\left(3 \, a b^{2} - 8 \, a^{2} c\right)} x^{2}\right)}}{96 \, a^{3} x^{4}}, \frac{3 \, {\left(b^{3} - 4 \, a b c\right)} \sqrt{-a} x^{4} \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{3} + a b x^{2} + a^{2} x\right)}}\right) - 2 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, a^{2} b x + 8 \, a^{3} - {\left(3 \, a b^{2} - 8 \, a^{2} c\right)} x^{2}\right)}}{48 \, a^{3} x^{4}}\right]"," ",0,"[-1/96*(3*(b^3 - 4*a*b*c)*sqrt(a)*x^4*log(-(8*a*b*x^2 + (b^2 + 4*a*c)*x^3 + 8*a^2*x + 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)*sqrt(a))/x^3) + 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*a^2*b*x + 8*a^3 - (3*a*b^2 - 8*a^2*c)*x^2))/(a^3*x^4), 1/48*(3*(b^3 - 4*a*b*c)*sqrt(-a)*x^4*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)*sqrt(-a)/(a*c*x^3 + a*b*x^2 + a^2*x)) - 2*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*a^2*b*x + 8*a^3 - (3*a*b^2 - 8*a^2*c)*x^2))/(a^3*x^4)]","A",0
37,1,336,0,1.349101," ","integrate((c*x^4+b*x^3+a*x^2)^(1/2)/x^6,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(5 \, b^{4} - 24 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{a} x^{5} \log\left(-\frac{8 \, a b x^{2} + {\left(b^{2} + 4 \, a c\right)} x^{3} + 8 \, a^{2} x + 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)} \sqrt{a}}{x^{3}}\right) - 4 \, {\left(8 \, a^{3} b x + 48 \, a^{4} + {\left(15 \, a b^{3} - 52 \, a^{2} b c\right)} x^{3} - 2 \, {\left(5 \, a^{2} b^{2} - 12 \, a^{3} c\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{3} + a x^{2}}}{768 \, a^{4} x^{5}}, -\frac{3 \, {\left(5 \, b^{4} - 24 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{-a} x^{5} \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{3} + a b x^{2} + a^{2} x\right)}}\right) + 2 \, {\left(8 \, a^{3} b x + 48 \, a^{4} + {\left(15 \, a b^{3} - 52 \, a^{2} b c\right)} x^{3} - 2 \, {\left(5 \, a^{2} b^{2} - 12 \, a^{3} c\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{3} + a x^{2}}}{384 \, a^{4} x^{5}}\right]"," ",0,"[1/768*(3*(5*b^4 - 24*a*b^2*c + 16*a^2*c^2)*sqrt(a)*x^5*log(-(8*a*b*x^2 + (b^2 + 4*a*c)*x^3 + 8*a^2*x + 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)*sqrt(a))/x^3) - 4*(8*a^3*b*x + 48*a^4 + (15*a*b^3 - 52*a^2*b*c)*x^3 - 2*(5*a^2*b^2 - 12*a^3*c)*x^2)*sqrt(c*x^4 + b*x^3 + a*x^2))/(a^4*x^5), -1/384*(3*(5*b^4 - 24*a*b^2*c + 16*a^2*c^2)*sqrt(-a)*x^5*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)*sqrt(-a)/(a*c*x^3 + a*b*x^2 + a^2*x)) + 2*(8*a^3*b*x + 48*a^4 + (15*a*b^3 - 52*a^2*b*c)*x^3 - 2*(5*a^2*b^2 - 12*a^3*c)*x^2)*sqrt(c*x^4 + b*x^3 + a*x^2))/(a^4*x^5)]","A",0
38,1,664,0,1.383445," ","integrate(x*(c*x^4+b*x^3+a*x^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(33 \, b^{8} - 336 \, a b^{6} c + 1120 \, a^{2} b^{4} c^{2} - 1280 \, a^{3} b^{2} c^{3} + 256 \, a^{4} c^{4}\right)} \sqrt{c} x \log\left(-\frac{8 \, c^{2} x^{3} + 8 \, b c x^{2} + 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{c} + {\left(b^{2} + 4 \, a c\right)} x}{x}\right) + 4 \, {\left(71680 \, c^{8} x^{7} + 87040 \, b c^{7} x^{6} - 3465 \, b^{7} c + 30660 \, a b^{5} c^{2} - 81648 \, a^{2} b^{3} c^{3} + 58816 \, a^{3} b c^{4} + 1280 \, {\left(b^{2} c^{6} + 84 \, a c^{7}\right)} x^{5} - 128 \, {\left(11 \, b^{3} c^{5} - 52 \, a b c^{6}\right)} x^{4} + 16 \, {\left(99 \, b^{4} c^{4} - 568 \, a b^{2} c^{5} + 560 \, a^{2} c^{6}\right)} x^{3} - 8 \, {\left(231 \, b^{5} c^{3} - 1560 \, a b^{3} c^{4} + 2416 \, a^{2} b c^{5}\right)} x^{2} + 2 \, {\left(1155 \, b^{6} c^{2} - 8988 \, a b^{4} c^{3} + 18896 \, a^{2} b^{2} c^{4} - 6720 \, a^{3} c^{5}\right)} x\right)} \sqrt{c x^{4} + b x^{3} + a x^{2}}}{2293760 \, c^{7} x}, -\frac{105 \, {\left(33 \, b^{8} - 336 \, a b^{6} c + 1120 \, a^{2} b^{4} c^{2} - 1280 \, a^{3} b^{2} c^{3} + 256 \, a^{4} c^{4}\right)} \sqrt{-c} x \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{3} + b c x^{2} + a c x\right)}}\right) - 2 \, {\left(71680 \, c^{8} x^{7} + 87040 \, b c^{7} x^{6} - 3465 \, b^{7} c + 30660 \, a b^{5} c^{2} - 81648 \, a^{2} b^{3} c^{3} + 58816 \, a^{3} b c^{4} + 1280 \, {\left(b^{2} c^{6} + 84 \, a c^{7}\right)} x^{5} - 128 \, {\left(11 \, b^{3} c^{5} - 52 \, a b c^{6}\right)} x^{4} + 16 \, {\left(99 \, b^{4} c^{4} - 568 \, a b^{2} c^{5} + 560 \, a^{2} c^{6}\right)} x^{3} - 8 \, {\left(231 \, b^{5} c^{3} - 1560 \, a b^{3} c^{4} + 2416 \, a^{2} b c^{5}\right)} x^{2} + 2 \, {\left(1155 \, b^{6} c^{2} - 8988 \, a b^{4} c^{3} + 18896 \, a^{2} b^{2} c^{4} - 6720 \, a^{3} c^{5}\right)} x\right)} \sqrt{c x^{4} + b x^{3} + a x^{2}}}{1146880 \, c^{7} x}\right]"," ",0,"[1/2293760*(105*(33*b^8 - 336*a*b^6*c + 1120*a^2*b^4*c^2 - 1280*a^3*b^2*c^3 + 256*a^4*c^4)*sqrt(c)*x*log(-(8*c^2*x^3 + 8*b*c*x^2 + 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(c) + (b^2 + 4*a*c)*x)/x) + 4*(71680*c^8*x^7 + 87040*b*c^7*x^6 - 3465*b^7*c + 30660*a*b^5*c^2 - 81648*a^2*b^3*c^3 + 58816*a^3*b*c^4 + 1280*(b^2*c^6 + 84*a*c^7)*x^5 - 128*(11*b^3*c^5 - 52*a*b*c^6)*x^4 + 16*(99*b^4*c^4 - 568*a*b^2*c^5 + 560*a^2*c^6)*x^3 - 8*(231*b^5*c^3 - 1560*a*b^3*c^4 + 2416*a^2*b*c^5)*x^2 + 2*(1155*b^6*c^2 - 8988*a*b^4*c^3 + 18896*a^2*b^2*c^4 - 6720*a^3*c^5)*x)*sqrt(c*x^4 + b*x^3 + a*x^2))/(c^7*x), -1/1146880*(105*(33*b^8 - 336*a*b^6*c + 1120*a^2*b^4*c^2 - 1280*a^3*b^2*c^3 + 256*a^4*c^4)*sqrt(-c)*x*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(-c)/(c^2*x^3 + b*c*x^2 + a*c*x)) - 2*(71680*c^8*x^7 + 87040*b*c^7*x^6 - 3465*b^7*c + 30660*a*b^5*c^2 - 81648*a^2*b^3*c^3 + 58816*a^3*b*c^4 + 1280*(b^2*c^6 + 84*a*c^7)*x^5 - 128*(11*b^3*c^5 - 52*a*b*c^6)*x^4 + 16*(99*b^4*c^4 - 568*a*b^2*c^5 + 560*a^2*c^6)*x^3 - 8*(231*b^5*c^3 - 1560*a*b^3*c^4 + 2416*a^2*b*c^5)*x^2 + 2*(1155*b^6*c^2 - 8988*a*b^4*c^3 + 18896*a^2*b^2*c^4 - 6720*a^3*c^5)*x)*sqrt(c*x^4 + b*x^3 + a*x^2))/(c^7*x)]","A",0
39,1,558,0,1.330787," ","integrate((c*x^4+b*x^3+a*x^2)^(3/2),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(3 \, b^{7} - 28 \, a b^{5} c + 80 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} \sqrt{c} x \log\left(-\frac{8 \, c^{2} x^{3} + 8 \, b c x^{2} + 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{c} + {\left(b^{2} + 4 \, a c\right)} x}{x}\right) - 4 \, {\left(5120 \, c^{7} x^{6} + 6400 \, b c^{6} x^{5} + 315 \, b^{6} c - 2520 \, a b^{4} c^{2} + 5488 \, a^{2} b^{2} c^{3} - 2048 \, a^{3} c^{4} + 128 \, {\left(b^{2} c^{5} + 64 \, a c^{6}\right)} x^{4} - 16 \, {\left(9 \, b^{3} c^{4} - 44 \, a b c^{5}\right)} x^{3} + 8 \, {\left(21 \, b^{4} c^{3} - 124 \, a b^{2} c^{4} + 128 \, a^{2} c^{5}\right)} x^{2} - 2 \, {\left(105 \, b^{5} c^{2} - 728 \, a b^{3} c^{3} + 1168 \, a^{2} b c^{4}\right)} x\right)} \sqrt{c x^{4} + b x^{3} + a x^{2}}}{143360 \, c^{6} x}, \frac{105 \, {\left(3 \, b^{7} - 28 \, a b^{5} c + 80 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} \sqrt{-c} x \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{3} + b c x^{2} + a c x\right)}}\right) + 2 \, {\left(5120 \, c^{7} x^{6} + 6400 \, b c^{6} x^{5} + 315 \, b^{6} c - 2520 \, a b^{4} c^{2} + 5488 \, a^{2} b^{2} c^{3} - 2048 \, a^{3} c^{4} + 128 \, {\left(b^{2} c^{5} + 64 \, a c^{6}\right)} x^{4} - 16 \, {\left(9 \, b^{3} c^{4} - 44 \, a b c^{5}\right)} x^{3} + 8 \, {\left(21 \, b^{4} c^{3} - 124 \, a b^{2} c^{4} + 128 \, a^{2} c^{5}\right)} x^{2} - 2 \, {\left(105 \, b^{5} c^{2} - 728 \, a b^{3} c^{3} + 1168 \, a^{2} b c^{4}\right)} x\right)} \sqrt{c x^{4} + b x^{3} + a x^{2}}}{71680 \, c^{6} x}\right]"," ",0,"[-1/143360*(105*(3*b^7 - 28*a*b^5*c + 80*a^2*b^3*c^2 - 64*a^3*b*c^3)*sqrt(c)*x*log(-(8*c^2*x^3 + 8*b*c*x^2 + 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(c) + (b^2 + 4*a*c)*x)/x) - 4*(5120*c^7*x^6 + 6400*b*c^6*x^5 + 315*b^6*c - 2520*a*b^4*c^2 + 5488*a^2*b^2*c^3 - 2048*a^3*c^4 + 128*(b^2*c^5 + 64*a*c^6)*x^4 - 16*(9*b^3*c^4 - 44*a*b*c^5)*x^3 + 8*(21*b^4*c^3 - 124*a*b^2*c^4 + 128*a^2*c^5)*x^2 - 2*(105*b^5*c^2 - 728*a*b^3*c^3 + 1168*a^2*b*c^4)*x)*sqrt(c*x^4 + b*x^3 + a*x^2))/(c^6*x), 1/71680*(105*(3*b^7 - 28*a*b^5*c + 80*a^2*b^3*c^2 - 64*a^3*b*c^3)*sqrt(-c)*x*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(-c)/(c^2*x^3 + b*c*x^2 + a*c*x)) + 2*(5120*c^7*x^6 + 6400*b*c^6*x^5 + 315*b^6*c - 2520*a*b^4*c^2 + 5488*a^2*b^2*c^3 - 2048*a^3*c^4 + 128*(b^2*c^5 + 64*a*c^6)*x^4 - 16*(9*b^3*c^4 - 44*a*b*c^5)*x^3 + 8*(21*b^4*c^3 - 124*a*b^2*c^4 + 128*a^2*c^5)*x^2 - 2*(105*b^5*c^2 - 728*a*b^3*c^3 + 1168*a^2*b*c^4)*x)*sqrt(c*x^4 + b*x^3 + a*x^2))/(c^6*x)]","A",0
40,1,474,0,1.174291," ","integrate((c*x^4+b*x^3+a*x^2)^(3/2)/x,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(7 \, b^{6} - 60 \, a b^{4} c + 144 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} \sqrt{c} x \log\left(-\frac{8 \, c^{2} x^{3} + 8 \, b c x^{2} - 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{c} + {\left(b^{2} + 4 \, a c\right)} x}{x}\right) - 4 \, {\left(1280 \, c^{6} x^{5} + 1664 \, b c^{5} x^{4} - 105 \, b^{5} c + 760 \, a b^{3} c^{2} - 1296 \, a^{2} b c^{3} + 16 \, {\left(3 \, b^{2} c^{4} + 140 \, a c^{5}\right)} x^{3} - 8 \, {\left(7 \, b^{3} c^{3} - 36 \, a b c^{4}\right)} x^{2} + 2 \, {\left(35 \, b^{4} c^{2} - 216 \, a b^{2} c^{3} + 240 \, a^{2} c^{4}\right)} x\right)} \sqrt{c x^{4} + b x^{3} + a x^{2}}}{30720 \, c^{5} x}, -\frac{15 \, {\left(7 \, b^{6} - 60 \, a b^{4} c + 144 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} \sqrt{-c} x \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{3} + b c x^{2} + a c x\right)}}\right) - 2 \, {\left(1280 \, c^{6} x^{5} + 1664 \, b c^{5} x^{4} - 105 \, b^{5} c + 760 \, a b^{3} c^{2} - 1296 \, a^{2} b c^{3} + 16 \, {\left(3 \, b^{2} c^{4} + 140 \, a c^{5}\right)} x^{3} - 8 \, {\left(7 \, b^{3} c^{3} - 36 \, a b c^{4}\right)} x^{2} + 2 \, {\left(35 \, b^{4} c^{2} - 216 \, a b^{2} c^{3} + 240 \, a^{2} c^{4}\right)} x\right)} \sqrt{c x^{4} + b x^{3} + a x^{2}}}{15360 \, c^{5} x}\right]"," ",0,"[-1/30720*(15*(7*b^6 - 60*a*b^4*c + 144*a^2*b^2*c^2 - 64*a^3*c^3)*sqrt(c)*x*log(-(8*c^2*x^3 + 8*b*c*x^2 - 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(c) + (b^2 + 4*a*c)*x)/x) - 4*(1280*c^6*x^5 + 1664*b*c^5*x^4 - 105*b^5*c + 760*a*b^3*c^2 - 1296*a^2*b*c^3 + 16*(3*b^2*c^4 + 140*a*c^5)*x^3 - 8*(7*b^3*c^3 - 36*a*b*c^4)*x^2 + 2*(35*b^4*c^2 - 216*a*b^2*c^3 + 240*a^2*c^4)*x)*sqrt(c*x^4 + b*x^3 + a*x^2))/(c^5*x), -1/15360*(15*(7*b^6 - 60*a*b^4*c + 144*a^2*b^2*c^2 - 64*a^3*c^3)*sqrt(-c)*x*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(-c)/(c^2*x^3 + b*c*x^2 + a*c*x)) - 2*(1280*c^6*x^5 + 1664*b*c^5*x^4 - 105*b^5*c + 760*a*b^3*c^2 - 1296*a^2*b*c^3 + 16*(3*b^2*c^4 + 140*a*c^5)*x^3 - 8*(7*b^3*c^3 - 36*a*b*c^4)*x^2 + 2*(35*b^4*c^2 - 216*a*b^2*c^3 + 240*a^2*c^4)*x)*sqrt(c*x^4 + b*x^3 + a*x^2))/(c^5*x)]","A",0
41,1,384,0,1.205499," ","integrate((c*x^4+b*x^3+a*x^2)^(3/2)/x^2,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} \sqrt{c} x \log\left(-\frac{8 \, c^{2} x^{3} + 8 \, b c x^{2} - 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{c} + {\left(b^{2} + 4 \, a c\right)} x}{x}\right) + 4 \, {\left(128 \, c^{5} x^{4} + 176 \, b c^{4} x^{3} + 15 \, b^{4} c - 100 \, a b^{2} c^{2} + 128 \, a^{2} c^{3} + 8 \, {\left(b^{2} c^{3} + 32 \, a c^{4}\right)} x^{2} - 2 \, {\left(5 \, b^{3} c^{2} - 28 \, a b c^{3}\right)} x\right)} \sqrt{c x^{4} + b x^{3} + a x^{2}}}{2560 \, c^{4} x}, \frac{15 \, {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} \sqrt{-c} x \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{3} + b c x^{2} + a c x\right)}}\right) + 2 \, {\left(128 \, c^{5} x^{4} + 176 \, b c^{4} x^{3} + 15 \, b^{4} c - 100 \, a b^{2} c^{2} + 128 \, a^{2} c^{3} + 8 \, {\left(b^{2} c^{3} + 32 \, a c^{4}\right)} x^{2} - 2 \, {\left(5 \, b^{3} c^{2} - 28 \, a b c^{3}\right)} x\right)} \sqrt{c x^{4} + b x^{3} + a x^{2}}}{1280 \, c^{4} x}\right]"," ",0,"[1/2560*(15*(b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*sqrt(c)*x*log(-(8*c^2*x^3 + 8*b*c*x^2 - 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(c) + (b^2 + 4*a*c)*x)/x) + 4*(128*c^5*x^4 + 176*b*c^4*x^3 + 15*b^4*c - 100*a*b^2*c^2 + 128*a^2*c^3 + 8*(b^2*c^3 + 32*a*c^4)*x^2 - 2*(5*b^3*c^2 - 28*a*b*c^3)*x)*sqrt(c*x^4 + b*x^3 + a*x^2))/(c^4*x), 1/1280*(15*(b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*sqrt(-c)*x*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(-c)/(c^2*x^3 + b*c*x^2 + a*c*x)) + 2*(128*c^5*x^4 + 176*b*c^4*x^3 + 15*b^4*c - 100*a*b^2*c^2 + 128*a^2*c^3 + 8*(b^2*c^3 + 32*a*c^4)*x^2 - 2*(5*b^3*c^2 - 28*a*b*c^3)*x)*sqrt(c*x^4 + b*x^3 + a*x^2))/(c^4*x)]","A",0
42,1,320,0,1.311630," ","integrate((c*x^4+b*x^3+a*x^2)^(3/2)/x^3,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{c} x \log\left(-\frac{8 \, c^{2} x^{3} + 8 \, b c x^{2} + 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{c} + {\left(b^{2} + 4 \, a c\right)} x}{x}\right) + 4 \, {\left(16 \, c^{4} x^{3} + 24 \, b c^{3} x^{2} - 3 \, b^{3} c + 20 \, a b c^{2} + 2 \, {\left(b^{2} c^{2} + 20 \, a c^{3}\right)} x\right)} \sqrt{c x^{4} + b x^{3} + a x^{2}}}{256 \, c^{3} x}, -\frac{3 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{-c} x \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{3} + b c x^{2} + a c x\right)}}\right) - 2 \, {\left(16 \, c^{4} x^{3} + 24 \, b c^{3} x^{2} - 3 \, b^{3} c + 20 \, a b c^{2} + 2 \, {\left(b^{2} c^{2} + 20 \, a c^{3}\right)} x\right)} \sqrt{c x^{4} + b x^{3} + a x^{2}}}{128 \, c^{3} x}\right]"," ",0,"[1/256*(3*(b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(c)*x*log(-(8*c^2*x^3 + 8*b*c*x^2 + 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(c) + (b^2 + 4*a*c)*x)/x) + 4*(16*c^4*x^3 + 24*b*c^3*x^2 - 3*b^3*c + 20*a*b*c^2 + 2*(b^2*c^2 + 20*a*c^3)*x)*sqrt(c*x^4 + b*x^3 + a*x^2))/(c^3*x), -1/128*(3*(b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(-c)*x*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(-c)/(c^2*x^3 + b*c*x^2 + a*c*x)) - 2*(16*c^4*x^3 + 24*b*c^3*x^2 - 3*b^3*c + 20*a*b*c^2 + 2*(b^2*c^2 + 20*a*c^3)*x)*sqrt(c*x^4 + b*x^3 + a*x^2))/(c^3*x)]","A",0
43,1,791,0,1.421295," ","integrate((c*x^4+b*x^3+a*x^2)^(3/2)/x^4,x, algorithm=""fricas"")","\left[\frac{48 \, a^{\frac{3}{2}} c^{2} x \log\left(-\frac{8 \, a b x^{2} + {\left(b^{2} + 4 \, a c\right)} x^{3} + 8 \, a^{2} x - 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)} \sqrt{a}}{x^{3}}\right) - 3 \, {\left(b^{3} - 12 \, a b c\right)} \sqrt{c} x \log\left(-\frac{8 \, c^{2} x^{3} + 8 \, b c x^{2} + 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{c} + {\left(b^{2} + 4 \, a c\right)} x}{x}\right) + 4 \, {\left(8 \, c^{3} x^{2} + 14 \, b c^{2} x + 3 \, b^{2} c + 32 \, a c^{2}\right)} \sqrt{c x^{4} + b x^{3} + a x^{2}}}{96 \, c^{2} x}, \frac{24 \, a^{\frac{3}{2}} c^{2} x \log\left(-\frac{8 \, a b x^{2} + {\left(b^{2} + 4 \, a c\right)} x^{3} + 8 \, a^{2} x - 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)} \sqrt{a}}{x^{3}}\right) + 3 \, {\left(b^{3} - 12 \, a b c\right)} \sqrt{-c} x \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{3} + b c x^{2} + a c x\right)}}\right) + 2 \, {\left(8 \, c^{3} x^{2} + 14 \, b c^{2} x + 3 \, b^{2} c + 32 \, a c^{2}\right)} \sqrt{c x^{4} + b x^{3} + a x^{2}}}{48 \, c^{2} x}, \frac{96 \, \sqrt{-a} a c^{2} x \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{3} + a b x^{2} + a^{2} x\right)}}\right) - 3 \, {\left(b^{3} - 12 \, a b c\right)} \sqrt{c} x \log\left(-\frac{8 \, c^{2} x^{3} + 8 \, b c x^{2} + 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{c} + {\left(b^{2} + 4 \, a c\right)} x}{x}\right) + 4 \, {\left(8 \, c^{3} x^{2} + 14 \, b c^{2} x + 3 \, b^{2} c + 32 \, a c^{2}\right)} \sqrt{c x^{4} + b x^{3} + a x^{2}}}{96 \, c^{2} x}, \frac{48 \, \sqrt{-a} a c^{2} x \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{3} + a b x^{2} + a^{2} x\right)}}\right) + 3 \, {\left(b^{3} - 12 \, a b c\right)} \sqrt{-c} x \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{3} + b c x^{2} + a c x\right)}}\right) + 2 \, {\left(8 \, c^{3} x^{2} + 14 \, b c^{2} x + 3 \, b^{2} c + 32 \, a c^{2}\right)} \sqrt{c x^{4} + b x^{3} + a x^{2}}}{48 \, c^{2} x}\right]"," ",0,"[1/96*(48*a^(3/2)*c^2*x*log(-(8*a*b*x^2 + (b^2 + 4*a*c)*x^3 + 8*a^2*x - 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)*sqrt(a))/x^3) - 3*(b^3 - 12*a*b*c)*sqrt(c)*x*log(-(8*c^2*x^3 + 8*b*c*x^2 + 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(c) + (b^2 + 4*a*c)*x)/x) + 4*(8*c^3*x^2 + 14*b*c^2*x + 3*b^2*c + 32*a*c^2)*sqrt(c*x^4 + b*x^3 + a*x^2))/(c^2*x), 1/48*(24*a^(3/2)*c^2*x*log(-(8*a*b*x^2 + (b^2 + 4*a*c)*x^3 + 8*a^2*x - 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)*sqrt(a))/x^3) + 3*(b^3 - 12*a*b*c)*sqrt(-c)*x*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(-c)/(c^2*x^3 + b*c*x^2 + a*c*x)) + 2*(8*c^3*x^2 + 14*b*c^2*x + 3*b^2*c + 32*a*c^2)*sqrt(c*x^4 + b*x^3 + a*x^2))/(c^2*x), 1/96*(96*sqrt(-a)*a*c^2*x*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)*sqrt(-a)/(a*c*x^3 + a*b*x^2 + a^2*x)) - 3*(b^3 - 12*a*b*c)*sqrt(c)*x*log(-(8*c^2*x^3 + 8*b*c*x^2 + 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(c) + (b^2 + 4*a*c)*x)/x) + 4*(8*c^3*x^2 + 14*b*c^2*x + 3*b^2*c + 32*a*c^2)*sqrt(c*x^4 + b*x^3 + a*x^2))/(c^2*x), 1/48*(48*sqrt(-a)*a*c^2*x*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)*sqrt(-a)/(a*c*x^3 + a*b*x^2 + a^2*x)) + 3*(b^3 - 12*a*b*c)*sqrt(-c)*x*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(-c)/(c^2*x^3 + b*c*x^2 + a*c*x)) + 2*(8*c^3*x^2 + 14*b*c^2*x + 3*b^2*c + 32*a*c^2)*sqrt(c*x^4 + b*x^3 + a*x^2))/(c^2*x)]","A",0
44,1,757,0,1.318843," ","integrate((c*x^4+b*x^3+a*x^2)^(3/2)/x^5,x, algorithm=""fricas"")","\left[\frac{12 \, \sqrt{a} b c x^{2} \log\left(-\frac{8 \, a b x^{2} + {\left(b^{2} + 4 \, a c\right)} x^{3} + 8 \, a^{2} x - 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)} \sqrt{a}}{x^{3}}\right) + 3 \, {\left(b^{2} + 4 \, a c\right)} \sqrt{c} x^{2} \log\left(-\frac{8 \, c^{2} x^{3} + 8 \, b c x^{2} + 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{c} + {\left(b^{2} + 4 \, a c\right)} x}{x}\right) + 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c^{2} x^{2} + 5 \, b c x - 4 \, a c\right)}}{16 \, c x^{2}}, \frac{6 \, \sqrt{a} b c x^{2} \log\left(-\frac{8 \, a b x^{2} + {\left(b^{2} + 4 \, a c\right)} x^{3} + 8 \, a^{2} x - 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)} \sqrt{a}}{x^{3}}\right) - 3 \, {\left(b^{2} + 4 \, a c\right)} \sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{3} + b c x^{2} + a c x\right)}}\right) + 2 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c^{2} x^{2} + 5 \, b c x - 4 \, a c\right)}}{8 \, c x^{2}}, \frac{24 \, \sqrt{-a} b c x^{2} \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{3} + a b x^{2} + a^{2} x\right)}}\right) + 3 \, {\left(b^{2} + 4 \, a c\right)} \sqrt{c} x^{2} \log\left(-\frac{8 \, c^{2} x^{3} + 8 \, b c x^{2} + 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{c} + {\left(b^{2} + 4 \, a c\right)} x}{x}\right) + 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c^{2} x^{2} + 5 \, b c x - 4 \, a c\right)}}{16 \, c x^{2}}, \frac{12 \, \sqrt{-a} b c x^{2} \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{3} + a b x^{2} + a^{2} x\right)}}\right) - 3 \, {\left(b^{2} + 4 \, a c\right)} \sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{3} + b c x^{2} + a c x\right)}}\right) + 2 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c^{2} x^{2} + 5 \, b c x - 4 \, a c\right)}}{8 \, c x^{2}}\right]"," ",0,"[1/16*(12*sqrt(a)*b*c*x^2*log(-(8*a*b*x^2 + (b^2 + 4*a*c)*x^3 + 8*a^2*x - 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)*sqrt(a))/x^3) + 3*(b^2 + 4*a*c)*sqrt(c)*x^2*log(-(8*c^2*x^3 + 8*b*c*x^2 + 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(c) + (b^2 + 4*a*c)*x)/x) + 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c^2*x^2 + 5*b*c*x - 4*a*c))/(c*x^2), 1/8*(6*sqrt(a)*b*c*x^2*log(-(8*a*b*x^2 + (b^2 + 4*a*c)*x^3 + 8*a^2*x - 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)*sqrt(a))/x^3) - 3*(b^2 + 4*a*c)*sqrt(-c)*x^2*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(-c)/(c^2*x^3 + b*c*x^2 + a*c*x)) + 2*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c^2*x^2 + 5*b*c*x - 4*a*c))/(c*x^2), 1/16*(24*sqrt(-a)*b*c*x^2*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)*sqrt(-a)/(a*c*x^3 + a*b*x^2 + a^2*x)) + 3*(b^2 + 4*a*c)*sqrt(c)*x^2*log(-(8*c^2*x^3 + 8*b*c*x^2 + 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(c) + (b^2 + 4*a*c)*x)/x) + 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c^2*x^2 + 5*b*c*x - 4*a*c))/(c*x^2), 1/8*(12*sqrt(-a)*b*c*x^2*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)*sqrt(-a)/(a*c*x^3 + a*b*x^2 + a^2*x)) - 3*(b^2 + 4*a*c)*sqrt(-c)*x^2*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(-c)/(c^2*x^3 + b*c*x^2 + a*c*x)) + 2*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c^2*x^2 + 5*b*c*x - 4*a*c))/(c*x^2)]","A",0
45,1,757,0,1.587014," ","integrate((c*x^4+b*x^3+a*x^2)^(3/2)/x^6,x, algorithm=""fricas"")","\left[\frac{12 \, a b \sqrt{c} x^{3} \log\left(-\frac{8 \, c^{2} x^{3} + 8 \, b c x^{2} + 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{c} + {\left(b^{2} + 4 \, a c\right)} x}{x}\right) + 3 \, {\left(b^{2} + 4 \, a c\right)} \sqrt{a} x^{3} \log\left(-\frac{8 \, a b x^{2} + {\left(b^{2} + 4 \, a c\right)} x^{3} + 8 \, a^{2} x - 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)} \sqrt{a}}{x^{3}}\right) + 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(4 \, a c x^{2} - 5 \, a b x - 2 \, a^{2}\right)}}{16 \, a x^{3}}, -\frac{24 \, a b \sqrt{-c} x^{3} \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{3} + b c x^{2} + a c x\right)}}\right) - 3 \, {\left(b^{2} + 4 \, a c\right)} \sqrt{a} x^{3} \log\left(-\frac{8 \, a b x^{2} + {\left(b^{2} + 4 \, a c\right)} x^{3} + 8 \, a^{2} x - 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)} \sqrt{a}}{x^{3}}\right) - 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(4 \, a c x^{2} - 5 \, a b x - 2 \, a^{2}\right)}}{16 \, a x^{3}}, \frac{6 \, a b \sqrt{c} x^{3} \log\left(-\frac{8 \, c^{2} x^{3} + 8 \, b c x^{2} + 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{c} + {\left(b^{2} + 4 \, a c\right)} x}{x}\right) + 3 \, {\left(b^{2} + 4 \, a c\right)} \sqrt{-a} x^{3} \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{3} + a b x^{2} + a^{2} x\right)}}\right) + 2 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(4 \, a c x^{2} - 5 \, a b x - 2 \, a^{2}\right)}}{8 \, a x^{3}}, -\frac{12 \, a b \sqrt{-c} x^{3} \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{3} + b c x^{2} + a c x\right)}}\right) - 3 \, {\left(b^{2} + 4 \, a c\right)} \sqrt{-a} x^{3} \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{3} + a b x^{2} + a^{2} x\right)}}\right) - 2 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(4 \, a c x^{2} - 5 \, a b x - 2 \, a^{2}\right)}}{8 \, a x^{3}}\right]"," ",0,"[1/16*(12*a*b*sqrt(c)*x^3*log(-(8*c^2*x^3 + 8*b*c*x^2 + 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(c) + (b^2 + 4*a*c)*x)/x) + 3*(b^2 + 4*a*c)*sqrt(a)*x^3*log(-(8*a*b*x^2 + (b^2 + 4*a*c)*x^3 + 8*a^2*x - 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)*sqrt(a))/x^3) + 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(4*a*c*x^2 - 5*a*b*x - 2*a^2))/(a*x^3), -1/16*(24*a*b*sqrt(-c)*x^3*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(-c)/(c^2*x^3 + b*c*x^2 + a*c*x)) - 3*(b^2 + 4*a*c)*sqrt(a)*x^3*log(-(8*a*b*x^2 + (b^2 + 4*a*c)*x^3 + 8*a^2*x - 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)*sqrt(a))/x^3) - 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(4*a*c*x^2 - 5*a*b*x - 2*a^2))/(a*x^3), 1/8*(6*a*b*sqrt(c)*x^3*log(-(8*c^2*x^3 + 8*b*c*x^2 + 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(c) + (b^2 + 4*a*c)*x)/x) + 3*(b^2 + 4*a*c)*sqrt(-a)*x^3*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)*sqrt(-a)/(a*c*x^3 + a*b*x^2 + a^2*x)) + 2*sqrt(c*x^4 + b*x^3 + a*x^2)*(4*a*c*x^2 - 5*a*b*x - 2*a^2))/(a*x^3), -1/8*(12*a*b*sqrt(-c)*x^3*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(-c)/(c^2*x^3 + b*c*x^2 + a*c*x)) - 3*(b^2 + 4*a*c)*sqrt(-a)*x^3*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)*sqrt(-a)/(a*c*x^3 + a*b*x^2 + a^2*x)) - 2*sqrt(c*x^4 + b*x^3 + a*x^2)*(4*a*c*x^2 - 5*a*b*x - 2*a^2))/(a*x^3)]","A",0
46,1,815,0,1.545843," ","integrate((c*x^4+b*x^3+a*x^2)^(3/2)/x^7,x, algorithm=""fricas"")","\left[\frac{48 \, a^{2} c^{\frac{3}{2}} x^{4} \log\left(-\frac{8 \, c^{2} x^{3} + 8 \, b c x^{2} + 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{c} + {\left(b^{2} + 4 \, a c\right)} x}{x}\right) - 3 \, {\left(b^{3} - 12 \, a b c\right)} \sqrt{a} x^{4} \log\left(-\frac{8 \, a b x^{2} + {\left(b^{2} + 4 \, a c\right)} x^{3} + 8 \, a^{2} x - 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)} \sqrt{a}}{x^{3}}\right) - 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(14 \, a^{2} b x + 8 \, a^{3} + {\left(3 \, a b^{2} + 32 \, a^{2} c\right)} x^{2}\right)}}{96 \, a^{2} x^{4}}, -\frac{96 \, a^{2} \sqrt{-c} c x^{4} \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{3} + b c x^{2} + a c x\right)}}\right) + 3 \, {\left(b^{3} - 12 \, a b c\right)} \sqrt{a} x^{4} \log\left(-\frac{8 \, a b x^{2} + {\left(b^{2} + 4 \, a c\right)} x^{3} + 8 \, a^{2} x - 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)} \sqrt{a}}{x^{3}}\right) + 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(14 \, a^{2} b x + 8 \, a^{3} + {\left(3 \, a b^{2} + 32 \, a^{2} c\right)} x^{2}\right)}}{96 \, a^{2} x^{4}}, \frac{24 \, a^{2} c^{\frac{3}{2}} x^{4} \log\left(-\frac{8 \, c^{2} x^{3} + 8 \, b c x^{2} + 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{c} + {\left(b^{2} + 4 \, a c\right)} x}{x}\right) - 3 \, {\left(b^{3} - 12 \, a b c\right)} \sqrt{-a} x^{4} \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{3} + a b x^{2} + a^{2} x\right)}}\right) - 2 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(14 \, a^{2} b x + 8 \, a^{3} + {\left(3 \, a b^{2} + 32 \, a^{2} c\right)} x^{2}\right)}}{48 \, a^{2} x^{4}}, -\frac{48 \, a^{2} \sqrt{-c} c x^{4} \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{3} + b c x^{2} + a c x\right)}}\right) + 3 \, {\left(b^{3} - 12 \, a b c\right)} \sqrt{-a} x^{4} \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{3} + a b x^{2} + a^{2} x\right)}}\right) + 2 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(14 \, a^{2} b x + 8 \, a^{3} + {\left(3 \, a b^{2} + 32 \, a^{2} c\right)} x^{2}\right)}}{48 \, a^{2} x^{4}}\right]"," ",0,"[1/96*(48*a^2*c^(3/2)*x^4*log(-(8*c^2*x^3 + 8*b*c*x^2 + 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(c) + (b^2 + 4*a*c)*x)/x) - 3*(b^3 - 12*a*b*c)*sqrt(a)*x^4*log(-(8*a*b*x^2 + (b^2 + 4*a*c)*x^3 + 8*a^2*x - 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)*sqrt(a))/x^3) - 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(14*a^2*b*x + 8*a^3 + (3*a*b^2 + 32*a^2*c)*x^2))/(a^2*x^4), -1/96*(96*a^2*sqrt(-c)*c*x^4*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(-c)/(c^2*x^3 + b*c*x^2 + a*c*x)) + 3*(b^3 - 12*a*b*c)*sqrt(a)*x^4*log(-(8*a*b*x^2 + (b^2 + 4*a*c)*x^3 + 8*a^2*x - 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)*sqrt(a))/x^3) + 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(14*a^2*b*x + 8*a^3 + (3*a*b^2 + 32*a^2*c)*x^2))/(a^2*x^4), 1/48*(24*a^2*c^(3/2)*x^4*log(-(8*c^2*x^3 + 8*b*c*x^2 + 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(c) + (b^2 + 4*a*c)*x)/x) - 3*(b^3 - 12*a*b*c)*sqrt(-a)*x^4*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)*sqrt(-a)/(a*c*x^3 + a*b*x^2 + a^2*x)) - 2*sqrt(c*x^4 + b*x^3 + a*x^2)*(14*a^2*b*x + 8*a^3 + (3*a*b^2 + 32*a^2*c)*x^2))/(a^2*x^4), -1/48*(48*a^2*sqrt(-c)*c*x^4*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(-c)/(c^2*x^3 + b*c*x^2 + a*c*x)) + 3*(b^3 - 12*a*b*c)*sqrt(-a)*x^4*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)*sqrt(-a)/(a*c*x^3 + a*b*x^2 + a^2*x)) + 2*sqrt(c*x^4 + b*x^3 + a*x^2)*(14*a^2*b*x + 8*a^3 + (3*a*b^2 + 32*a^2*c)*x^2))/(a^2*x^4)]","A",0
47,1,332,0,1.633279," ","integrate((c*x^4+b*x^3+a*x^2)^(3/2)/x^8,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{a} x^{5} \log\left(-\frac{8 \, a b x^{2} + {\left(b^{2} + 4 \, a c\right)} x^{3} + 8 \, a^{2} x - 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)} \sqrt{a}}{x^{3}}\right) - 4 \, {\left(24 \, a^{3} b x + 16 \, a^{4} - {\left(3 \, a b^{3} - 20 \, a^{2} b c\right)} x^{3} + 2 \, {\left(a^{2} b^{2} + 20 \, a^{3} c\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{3} + a x^{2}}}{256 \, a^{3} x^{5}}, \frac{3 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{-a} x^{5} \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{3} + a b x^{2} + a^{2} x\right)}}\right) - 2 \, {\left(24 \, a^{3} b x + 16 \, a^{4} - {\left(3 \, a b^{3} - 20 \, a^{2} b c\right)} x^{3} + 2 \, {\left(a^{2} b^{2} + 20 \, a^{3} c\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{3} + a x^{2}}}{128 \, a^{3} x^{5}}\right]"," ",0,"[1/256*(3*(b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(a)*x^5*log(-(8*a*b*x^2 + (b^2 + 4*a*c)*x^3 + 8*a^2*x - 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)*sqrt(a))/x^3) - 4*(24*a^3*b*x + 16*a^4 - (3*a*b^3 - 20*a^2*b*c)*x^3 + 2*(a^2*b^2 + 20*a^3*c)*x^2)*sqrt(c*x^4 + b*x^3 + a*x^2))/(a^3*x^5), 1/128*(3*(b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(-a)*x^5*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)*sqrt(-a)/(a*c*x^3 + a*b*x^2 + a^2*x)) - 2*(24*a^3*b*x + 16*a^4 - (3*a*b^3 - 20*a^2*b*c)*x^3 + 2*(a^2*b^2 + 20*a^3*c)*x^2)*sqrt(c*x^4 + b*x^3 + a*x^2))/(a^3*x^5)]","A",0
48,1,394,0,1.766471," ","integrate((c*x^4+b*x^3+a*x^2)^(3/2)/x^9,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} \sqrt{a} x^{6} \log\left(-\frac{8 \, a b x^{2} + {\left(b^{2} + 4 \, a c\right)} x^{3} + 8 \, a^{2} x + 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)} \sqrt{a}}{x^{3}}\right) - 4 \, {\left(176 \, a^{4} b x + 128 \, a^{5} + {\left(15 \, a b^{4} - 100 \, a^{2} b^{2} c + 128 \, a^{3} c^{2}\right)} x^{4} - 2 \, {\left(5 \, a^{2} b^{3} - 28 \, a^{3} b c\right)} x^{3} + 8 \, {\left(a^{3} b^{2} + 32 \, a^{4} c\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{3} + a x^{2}}}{2560 \, a^{4} x^{6}}, -\frac{15 \, {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} \sqrt{-a} x^{6} \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{3} + a b x^{2} + a^{2} x\right)}}\right) + 2 \, {\left(176 \, a^{4} b x + 128 \, a^{5} + {\left(15 \, a b^{4} - 100 \, a^{2} b^{2} c + 128 \, a^{3} c^{2}\right)} x^{4} - 2 \, {\left(5 \, a^{2} b^{3} - 28 \, a^{3} b c\right)} x^{3} + 8 \, {\left(a^{3} b^{2} + 32 \, a^{4} c\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{3} + a x^{2}}}{1280 \, a^{4} x^{6}}\right]"," ",0,"[1/2560*(15*(b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*sqrt(a)*x^6*log(-(8*a*b*x^2 + (b^2 + 4*a*c)*x^3 + 8*a^2*x + 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)*sqrt(a))/x^3) - 4*(176*a^4*b*x + 128*a^5 + (15*a*b^4 - 100*a^2*b^2*c + 128*a^3*c^2)*x^4 - 2*(5*a^2*b^3 - 28*a^3*b*c)*x^3 + 8*(a^3*b^2 + 32*a^4*c)*x^2)*sqrt(c*x^4 + b*x^3 + a*x^2))/(a^4*x^6), -1/1280*(15*(b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*sqrt(-a)*x^6*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)*sqrt(-a)/(a*c*x^3 + a*b*x^2 + a^2*x)) + 2*(176*a^4*b*x + 128*a^5 + (15*a*b^4 - 100*a^2*b^2*c + 128*a^3*c^2)*x^4 - 2*(5*a^2*b^3 - 28*a^3*b*c)*x^3 + 8*(a^3*b^2 + 32*a^4*c)*x^2)*sqrt(c*x^4 + b*x^3 + a*x^2))/(a^4*x^6)]","A",0
49,1,226,0,1.015404," ","integrate(x^3/(c*x^4+b*x^3+a*x^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(3 \, b^{2} - 4 \, a c\right)} \sqrt{c} x \log\left(-\frac{8 \, c^{2} x^{3} + 8 \, b c x^{2} - 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{c} + {\left(b^{2} + 4 \, a c\right)} x}{x}\right) - 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c^{2} x - 3 \, b c\right)}}{16 \, c^{3} x}, -\frac{{\left(3 \, b^{2} - 4 \, a c\right)} \sqrt{-c} x \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{3} + b c x^{2} + a c x\right)}}\right) - 2 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c^{2} x - 3 \, b c\right)}}{8 \, c^{3} x}\right]"," ",0,"[-1/16*((3*b^2 - 4*a*c)*sqrt(c)*x*log(-(8*c^2*x^3 + 8*b*c*x^2 - 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(c) + (b^2 + 4*a*c)*x)/x) - 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c^2*x - 3*b*c))/(c^3*x), -1/8*((3*b^2 - 4*a*c)*sqrt(-c)*x*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(-c)/(c^2*x^3 + b*c*x^2 + a*c*x)) - 2*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c^2*x - 3*b*c))/(c^3*x)]","A",0
50,1,188,0,1.132980," ","integrate(x^2/(c*x^4+b*x^3+a*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{b \sqrt{c} x \log\left(-\frac{8 \, c^{2} x^{3} + 8 \, b c x^{2} - 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{c} + {\left(b^{2} + 4 \, a c\right)} x}{x}\right) + 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} c}{4 \, c^{2} x}, \frac{b \sqrt{-c} x \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{3} + b c x^{2} + a c x\right)}}\right) + 2 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} c}{2 \, c^{2} x}\right]"," ",0,"[1/4*(b*sqrt(c)*x*log(-(8*c^2*x^3 + 8*b*c*x^2 - 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(c) + (b^2 + 4*a*c)*x)/x) + 4*sqrt(c*x^4 + b*x^3 + a*x^2)*c)/(c^2*x), 1/2*(b*sqrt(-c)*x*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(-c)/(c^2*x^3 + b*c*x^2 + a*c*x)) + 2*sqrt(c*x^4 + b*x^3 + a*x^2)*c)/(c^2*x)]","A",0
51,1,129,0,1.058130," ","integrate(x/(c*x^4+b*x^3+a*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(-\frac{8 \, c^{2} x^{3} + 8 \, b c x^{2} + 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{c} + {\left(b^{2} + 4 \, a c\right)} x}{x}\right)}{2 \, \sqrt{c}}, -\frac{\sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{3} + b c x^{2} + a c x\right)}}\right)}{c}\right]"," ",0,"[1/2*log(-(8*c^2*x^3 + 8*b*c*x^2 + 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(c) + (b^2 + 4*a*c)*x)/x)/sqrt(c), -sqrt(-c)*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(-c)/(c^2*x^3 + b*c*x^2 + a*c*x))/c]","A",0
52,1,130,0,1.274651," ","integrate(1/(c*x^4+b*x^3+a*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(-\frac{8 \, a b x^{2} + {\left(b^{2} + 4 \, a c\right)} x^{3} + 8 \, a^{2} x - 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)} \sqrt{a}}{x^{3}}\right)}{2 \, \sqrt{a}}, \frac{\sqrt{-a} \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{3} + a b x^{2} + a^{2} x\right)}}\right)}{a}\right]"," ",0,"[1/2*log(-(8*a*b*x^2 + (b^2 + 4*a*c)*x^3 + 8*a^2*x - 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)*sqrt(a))/x^3)/sqrt(a), sqrt(-a)*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)*sqrt(-a)/(a*c*x^3 + a*b*x^2 + a^2*x))/a]","A",0
53,1,194,0,1.275140," ","integrate(1/x/(c*x^4+b*x^3+a*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a} b x^{2} \log\left(-\frac{8 \, a b x^{2} + {\left(b^{2} + 4 \, a c\right)} x^{3} + 8 \, a^{2} x + 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)} \sqrt{a}}{x^{3}}\right) - 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} a}{4 \, a^{2} x^{2}}, -\frac{\sqrt{-a} b x^{2} \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{3} + a b x^{2} + a^{2} x\right)}}\right) + 2 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} a}{2 \, a^{2} x^{2}}\right]"," ",0,"[1/4*(sqrt(a)*b*x^2*log(-(8*a*b*x^2 + (b^2 + 4*a*c)*x^3 + 8*a^2*x + 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)*sqrt(a))/x^3) - 4*sqrt(c*x^4 + b*x^3 + a*x^2)*a)/(a^2*x^2), -1/2*(sqrt(-a)*b*x^2*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)*sqrt(-a)/(a*c*x^3 + a*b*x^2 + a^2*x)) + 2*sqrt(c*x^4 + b*x^3 + a*x^2)*a)/(a^2*x^2)]","A",0
54,1,232,0,1.292564," ","integrate(1/x^2/(c*x^4+b*x^3+a*x^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(3 \, b^{2} - 4 \, a c\right)} \sqrt{a} x^{3} \log\left(-\frac{8 \, a b x^{2} + {\left(b^{2} + 4 \, a c\right)} x^{3} + 8 \, a^{2} x + 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)} \sqrt{a}}{x^{3}}\right) - 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(3 \, a b x - 2 \, a^{2}\right)}}{16 \, a^{3} x^{3}}, \frac{{\left(3 \, b^{2} - 4 \, a c\right)} \sqrt{-a} x^{3} \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{3} + a b x^{2} + a^{2} x\right)}}\right) + 2 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(3 \, a b x - 2 \, a^{2}\right)}}{8 \, a^{3} x^{3}}\right]"," ",0,"[-1/16*((3*b^2 - 4*a*c)*sqrt(a)*x^3*log(-(8*a*b*x^2 + (b^2 + 4*a*c)*x^3 + 8*a^2*x + 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)*sqrt(a))/x^3) - 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(3*a*b*x - 2*a^2))/(a^3*x^3), 1/8*((3*b^2 - 4*a*c)*sqrt(-a)*x^3*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)*sqrt(-a)/(a*c*x^3 + a*b*x^2 + a^2*x)) + 2*sqrt(c*x^4 + b*x^3 + a*x^2)*(3*a*b*x - 2*a^2))/(a^3*x^3)]","A",0
55,1,616,0,1.551397," ","integrate(x^7/(c*x^4+b*x^3+a*x^2)^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(5 \, b^{4} c - 24 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} x^{3} + {\left(5 \, b^{5} - 24 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x^{2} + {\left(5 \, a b^{4} - 24 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} x\right)} \sqrt{c} \log\left(-\frac{8 \, c^{2} x^{3} + 8 \, b c x^{2} - 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{c} + {\left(b^{2} + 4 \, a c\right)} x}{x}\right) + 4 \, {\left(15 \, a b^{3} c - 52 \, a^{2} b c^{2} - 2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{3} + 5 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x^{2} + {\left(15 \, b^{4} c - 62 \, a b^{2} c^{2} + 24 \, a^{2} c^{3}\right)} x\right)} \sqrt{c x^{4} + b x^{3} + a x^{2}}}{16 \, {\left({\left(b^{2} c^{5} - 4 \, a c^{6}\right)} x^{3} + {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} x^{2} + {\left(a b^{2} c^{4} - 4 \, a^{2} c^{5}\right)} x\right)}}, -\frac{3 \, {\left({\left(5 \, b^{4} c - 24 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} x^{3} + {\left(5 \, b^{5} - 24 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x^{2} + {\left(5 \, a b^{4} - 24 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{3} + b c x^{2} + a c x\right)}}\right) + 2 \, {\left(15 \, a b^{3} c - 52 \, a^{2} b c^{2} - 2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{3} + 5 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x^{2} + {\left(15 \, b^{4} c - 62 \, a b^{2} c^{2} + 24 \, a^{2} c^{3}\right)} x\right)} \sqrt{c x^{4} + b x^{3} + a x^{2}}}{8 \, {\left({\left(b^{2} c^{5} - 4 \, a c^{6}\right)} x^{3} + {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} x^{2} + {\left(a b^{2} c^{4} - 4 \, a^{2} c^{5}\right)} x\right)}}\right]"," ",0,"[-1/16*(3*((5*b^4*c - 24*a*b^2*c^2 + 16*a^2*c^3)*x^3 + (5*b^5 - 24*a*b^3*c + 16*a^2*b*c^2)*x^2 + (5*a*b^4 - 24*a^2*b^2*c + 16*a^3*c^2)*x)*sqrt(c)*log(-(8*c^2*x^3 + 8*b*c*x^2 - 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(c) + (b^2 + 4*a*c)*x)/x) + 4*(15*a*b^3*c - 52*a^2*b*c^2 - 2*(b^2*c^3 - 4*a*c^4)*x^3 + 5*(b^3*c^2 - 4*a*b*c^3)*x^2 + (15*b^4*c - 62*a*b^2*c^2 + 24*a^2*c^3)*x)*sqrt(c*x^4 + b*x^3 + a*x^2))/((b^2*c^5 - 4*a*c^6)*x^3 + (b^3*c^4 - 4*a*b*c^5)*x^2 + (a*b^2*c^4 - 4*a^2*c^5)*x), -1/8*(3*((5*b^4*c - 24*a*b^2*c^2 + 16*a^2*c^3)*x^3 + (5*b^5 - 24*a*b^3*c + 16*a^2*b*c^2)*x^2 + (5*a*b^4 - 24*a^2*b^2*c + 16*a^3*c^2)*x)*sqrt(-c)*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(-c)/(c^2*x^3 + b*c*x^2 + a*c*x)) + 2*(15*a*b^3*c - 52*a^2*b*c^2 - 2*(b^2*c^3 - 4*a*c^4)*x^3 + 5*(b^3*c^2 - 4*a*b*c^3)*x^2 + (15*b^4*c - 62*a*b^2*c^2 + 24*a^2*c^3)*x)*sqrt(c*x^4 + b*x^3 + a*x^2))/((b^2*c^5 - 4*a*c^6)*x^3 + (b^3*c^4 - 4*a*b*c^5)*x^2 + (a*b^2*c^4 - 4*a^2*c^5)*x)]","A",0
56,1,486,0,1.362023," ","integrate(x^6/(c*x^4+b*x^3+a*x^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(b^{3} c - 4 \, a b c^{2}\right)} x^{3} + {\left(b^{4} - 4 \, a b^{2} c\right)} x^{2} + {\left(a b^{3} - 4 \, a^{2} b c\right)} x\right)} \sqrt{c} \log\left(-\frac{8 \, c^{2} x^{3} + 8 \, b c x^{2} - 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{c} + {\left(b^{2} + 4 \, a c\right)} x}{x}\right) + 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(3 \, a b^{2} c - 8 \, a^{2} c^{2} + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{2} + {\left(3 \, b^{3} c - 10 \, a b c^{2}\right)} x\right)}}{4 \, {\left({\left(b^{2} c^{4} - 4 \, a c^{5}\right)} x^{3} + {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} x^{2} + {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} x\right)}}, \frac{3 \, {\left({\left(b^{3} c - 4 \, a b c^{2}\right)} x^{3} + {\left(b^{4} - 4 \, a b^{2} c\right)} x^{2} + {\left(a b^{3} - 4 \, a^{2} b c\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{3} + b c x^{2} + a c x\right)}}\right) + 2 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(3 \, a b^{2} c - 8 \, a^{2} c^{2} + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{2} + {\left(3 \, b^{3} c - 10 \, a b c^{2}\right)} x\right)}}{2 \, {\left({\left(b^{2} c^{4} - 4 \, a c^{5}\right)} x^{3} + {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} x^{2} + {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} x\right)}}\right]"," ",0,"[1/4*(3*((b^3*c - 4*a*b*c^2)*x^3 + (b^4 - 4*a*b^2*c)*x^2 + (a*b^3 - 4*a^2*b*c)*x)*sqrt(c)*log(-(8*c^2*x^3 + 8*b*c*x^2 - 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(c) + (b^2 + 4*a*c)*x)/x) + 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(3*a*b^2*c - 8*a^2*c^2 + (b^2*c^2 - 4*a*c^3)*x^2 + (3*b^3*c - 10*a*b*c^2)*x))/((b^2*c^4 - 4*a*c^5)*x^3 + (b^3*c^3 - 4*a*b*c^4)*x^2 + (a*b^2*c^3 - 4*a^2*c^4)*x), 1/2*(3*((b^3*c - 4*a*b*c^2)*x^3 + (b^4 - 4*a*b^2*c)*x^2 + (a*b^3 - 4*a^2*b*c)*x)*sqrt(-c)*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(-c)/(c^2*x^3 + b*c*x^2 + a*c*x)) + 2*sqrt(c*x^4 + b*x^3 + a*x^2)*(3*a*b^2*c - 8*a^2*c^2 + (b^2*c^2 - 4*a*c^3)*x^2 + (3*b^3*c - 10*a*b*c^2)*x))/((b^2*c^4 - 4*a*c^5)*x^3 + (b^3*c^3 - 4*a*b*c^4)*x^2 + (a*b^2*c^3 - 4*a^2*c^4)*x)]","A",0
57,1,414,0,1.179461," ","integrate(x^5/(c*x^4+b*x^3+a*x^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(b^{2} c - 4 \, a c^{2}\right)} x^{3} + {\left(b^{3} - 4 \, a b c\right)} x^{2} + {\left(a b^{2} - 4 \, a^{2} c\right)} x\right)} \sqrt{c} \log\left(-\frac{8 \, c^{2} x^{3} + 8 \, b c x^{2} + 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{c} + {\left(b^{2} + 4 \, a c\right)} x}{x}\right) - 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(a b c + {\left(b^{2} c - 2 \, a c^{2}\right)} x\right)}}{2 \, {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{3} + {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x^{2} + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} x\right)}}, -\frac{{\left({\left(b^{2} c - 4 \, a c^{2}\right)} x^{3} + {\left(b^{3} - 4 \, a b c\right)} x^{2} + {\left(a b^{2} - 4 \, a^{2} c\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{3} + b c x^{2} + a c x\right)}}\right) + 2 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(a b c + {\left(b^{2} c - 2 \, a c^{2}\right)} x\right)}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{3} + {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x^{2} + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} x}\right]"," ",0,"[1/2*(((b^2*c - 4*a*c^2)*x^3 + (b^3 - 4*a*b*c)*x^2 + (a*b^2 - 4*a^2*c)*x)*sqrt(c)*log(-(8*c^2*x^3 + 8*b*c*x^2 + 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(c) + (b^2 + 4*a*c)*x)/x) - 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(a*b*c + (b^2*c - 2*a*c^2)*x))/((b^2*c^3 - 4*a*c^4)*x^3 + (b^3*c^2 - 4*a*b*c^3)*x^2 + (a*b^2*c^2 - 4*a^2*c^3)*x), -(((b^2*c - 4*a*c^2)*x^3 + (b^3 - 4*a*b*c)*x^2 + (a*b^2 - 4*a^2*c)*x)*sqrt(-c)*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)*sqrt(-c)/(c^2*x^3 + b*c*x^2 + a*c*x)) + 2*sqrt(c*x^4 + b*x^3 + a*x^2)*(a*b*c + (b^2*c - 2*a*c^2)*x))/((b^2*c^3 - 4*a*c^4)*x^3 + (b^3*c^2 - 4*a*b*c^3)*x^2 + (a*b^2*c^2 - 4*a^2*c^3)*x)]","A",0
58,1,73,0,1.350553," ","integrate(x^4/(c*x^4+b*x^3+a*x^2)^(3/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)}}{{\left(b^{2} c - 4 \, a c^{2}\right)} x^{3} + {\left(b^{3} - 4 \, a b c\right)} x^{2} + {\left(a b^{2} - 4 \, a^{2} c\right)} x}"," ",0,"2*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)/((b^2*c - 4*a*c^2)*x^3 + (b^3 - 4*a*b*c)*x^2 + (a*b^2 - 4*a^2*c)*x)","A",0
59,1,72,0,1.351456," ","integrate(x^3/(c*x^4+b*x^3+a*x^2)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(2 \, c x + b\right)}}{{\left(b^{2} c - 4 \, a c^{2}\right)} x^{3} + {\left(b^{3} - 4 \, a b c\right)} x^{2} + {\left(a b^{2} - 4 \, a^{2} c\right)} x}"," ",0,"-2*sqrt(c*x^4 + b*x^3 + a*x^2)*(2*c*x + b)/((b^2*c - 4*a*c^2)*x^3 + (b^3 - 4*a*b*c)*x^2 + (a*b^2 - 4*a^2*c)*x)","A",0
60,1,411,0,1.405198," ","integrate(x^2/(c*x^4+b*x^3+a*x^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(b^{2} c - 4 \, a c^{2}\right)} x^{3} + {\left(b^{3} - 4 \, a b c\right)} x^{2} + {\left(a b^{2} - 4 \, a^{2} c\right)} x\right)} \sqrt{a} \log\left(-\frac{8 \, a b x^{2} + {\left(b^{2} + 4 \, a c\right)} x^{3} + 8 \, a^{2} x - 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)} \sqrt{a}}{x^{3}}\right) + 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(a b c x + a b^{2} - 2 \, a^{2} c\right)}}{2 \, {\left({\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} x^{3} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} x^{2} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} x\right)}}, \frac{{\left({\left(b^{2} c - 4 \, a c^{2}\right)} x^{3} + {\left(b^{3} - 4 \, a b c\right)} x^{2} + {\left(a b^{2} - 4 \, a^{2} c\right)} x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{3} + a b x^{2} + a^{2} x\right)}}\right) + 2 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(a b c x + a b^{2} - 2 \, a^{2} c\right)}}{{\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} x^{3} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} x^{2} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} x}\right]"," ",0,"[1/2*(((b^2*c - 4*a*c^2)*x^3 + (b^3 - 4*a*b*c)*x^2 + (a*b^2 - 4*a^2*c)*x)*sqrt(a)*log(-(8*a*b*x^2 + (b^2 + 4*a*c)*x^3 + 8*a^2*x - 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)*sqrt(a))/x^3) + 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(a*b*c*x + a*b^2 - 2*a^2*c))/((a^2*b^2*c - 4*a^3*c^2)*x^3 + (a^2*b^3 - 4*a^3*b*c)*x^2 + (a^3*b^2 - 4*a^4*c)*x), (((b^2*c - 4*a*c^2)*x^3 + (b^3 - 4*a*b*c)*x^2 + (a*b^2 - 4*a^2*c)*x)*sqrt(-a)*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)*sqrt(-a)/(a*c*x^3 + a*b*x^2 + a^2*x)) + 2*sqrt(c*x^4 + b*x^3 + a*x^2)*(a*b*c*x + a*b^2 - 2*a^2*c))/((a^2*b^2*c - 4*a^3*c^2)*x^3 + (a^2*b^3 - 4*a^3*b*c)*x^2 + (a^3*b^2 - 4*a^4*c)*x)]","B",0
61,1,496,0,1.020065," ","integrate(x/(c*x^4+b*x^3+a*x^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(b^{3} c - 4 \, a b c^{2}\right)} x^{4} + {\left(b^{4} - 4 \, a b^{2} c\right)} x^{3} + {\left(a b^{3} - 4 \, a^{2} b c\right)} x^{2}\right)} \sqrt{a} \log\left(-\frac{8 \, a b x^{2} + {\left(b^{2} + 4 \, a c\right)} x^{3} + 8 \, a^{2} x + 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)} \sqrt{a}}{x^{3}}\right) - 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(a^{2} b^{2} - 4 \, a^{3} c + {\left(3 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} x^{2} + {\left(3 \, a b^{3} - 10 \, a^{2} b c\right)} x\right)}}{4 \, {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} x^{4} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} x^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} x^{2}\right)}}, -\frac{3 \, {\left({\left(b^{3} c - 4 \, a b c^{2}\right)} x^{4} + {\left(b^{4} - 4 \, a b^{2} c\right)} x^{3} + {\left(a b^{3} - 4 \, a^{2} b c\right)} x^{2}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{3} + a b x^{2} + a^{2} x\right)}}\right) + 2 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(a^{2} b^{2} - 4 \, a^{3} c + {\left(3 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} x^{2} + {\left(3 \, a b^{3} - 10 \, a^{2} b c\right)} x\right)}}{2 \, {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} x^{4} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} x^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} x^{2}\right)}}\right]"," ",0,"[1/4*(3*((b^3*c - 4*a*b*c^2)*x^4 + (b^4 - 4*a*b^2*c)*x^3 + (a*b^3 - 4*a^2*b*c)*x^2)*sqrt(a)*log(-(8*a*b*x^2 + (b^2 + 4*a*c)*x^3 + 8*a^2*x + 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)*sqrt(a))/x^3) - 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(a^2*b^2 - 4*a^3*c + (3*a*b^2*c - 8*a^2*c^2)*x^2 + (3*a*b^3 - 10*a^2*b*c)*x))/((a^3*b^2*c - 4*a^4*c^2)*x^4 + (a^3*b^3 - 4*a^4*b*c)*x^3 + (a^4*b^2 - 4*a^5*c)*x^2), -1/2*(3*((b^3*c - 4*a*b*c^2)*x^4 + (b^4 - 4*a*b^2*c)*x^3 + (a*b^3 - 4*a^2*b*c)*x^2)*sqrt(-a)*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)*sqrt(-a)/(a*c*x^3 + a*b*x^2 + a^2*x)) + 2*sqrt(c*x^4 + b*x^3 + a*x^2)*(a^2*b^2 - 4*a^3*c + (3*a*b^2*c - 8*a^2*c^2)*x^2 + (3*a*b^3 - 10*a^2*b*c)*x))/((a^3*b^2*c - 4*a^4*c^2)*x^4 + (a^3*b^3 - 4*a^4*b*c)*x^3 + (a^4*b^2 - 4*a^5*c)*x^2)]","A",0
62,1,630,0,1.557417," ","integrate(1/(c*x^4+b*x^3+a*x^2)^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(5 \, b^{4} c - 24 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} x^{5} + {\left(5 \, b^{5} - 24 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x^{4} + {\left(5 \, a b^{4} - 24 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} x^{3}\right)} \sqrt{a} \log\left(-\frac{8 \, a b x^{2} + {\left(b^{2} + 4 \, a c\right)} x^{3} + 8 \, a^{2} x + 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)} \sqrt{a}}{x^{3}}\right) + 4 \, {\left(2 \, a^{3} b^{2} - 8 \, a^{4} c - {\left(15 \, a b^{3} c - 52 \, a^{2} b c^{2}\right)} x^{3} - {\left(15 \, a b^{4} - 62 \, a^{2} b^{2} c + 24 \, a^{3} c^{2}\right)} x^{2} - 5 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} x\right)} \sqrt{c x^{4} + b x^{3} + a x^{2}}}{16 \, {\left({\left(a^{4} b^{2} c - 4 \, a^{5} c^{2}\right)} x^{5} + {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} x^{4} + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} x^{3}\right)}}, \frac{3 \, {\left({\left(5 \, b^{4} c - 24 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} x^{5} + {\left(5 \, b^{5} - 24 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x^{4} + {\left(5 \, a b^{4} - 24 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} x^{3}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{3} + a b x^{2} + a^{2} x\right)}}\right) - 2 \, {\left(2 \, a^{3} b^{2} - 8 \, a^{4} c - {\left(15 \, a b^{3} c - 52 \, a^{2} b c^{2}\right)} x^{3} - {\left(15 \, a b^{4} - 62 \, a^{2} b^{2} c + 24 \, a^{3} c^{2}\right)} x^{2} - 5 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} x\right)} \sqrt{c x^{4} + b x^{3} + a x^{2}}}{8 \, {\left({\left(a^{4} b^{2} c - 4 \, a^{5} c^{2}\right)} x^{5} + {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} x^{4} + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} x^{3}\right)}}\right]"," ",0,"[-1/16*(3*((5*b^4*c - 24*a*b^2*c^2 + 16*a^2*c^3)*x^5 + (5*b^5 - 24*a*b^3*c + 16*a^2*b*c^2)*x^4 + (5*a*b^4 - 24*a^2*b^2*c + 16*a^3*c^2)*x^3)*sqrt(a)*log(-(8*a*b*x^2 + (b^2 + 4*a*c)*x^3 + 8*a^2*x + 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)*sqrt(a))/x^3) + 4*(2*a^3*b^2 - 8*a^4*c - (15*a*b^3*c - 52*a^2*b*c^2)*x^3 - (15*a*b^4 - 62*a^2*b^2*c + 24*a^3*c^2)*x^2 - 5*(a^2*b^3 - 4*a^3*b*c)*x)*sqrt(c*x^4 + b*x^3 + a*x^2))/((a^4*b^2*c - 4*a^5*c^2)*x^5 + (a^4*b^3 - 4*a^5*b*c)*x^4 + (a^5*b^2 - 4*a^6*c)*x^3), 1/8*(3*((5*b^4*c - 24*a*b^2*c^2 + 16*a^2*c^3)*x^5 + (5*b^5 - 24*a*b^3*c + 16*a^2*b*c^2)*x^4 + (5*a*b^4 - 24*a^2*b^2*c + 16*a^3*c^2)*x^3)*sqrt(-a)*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)*sqrt(-a)/(a*c*x^3 + a*b*x^2 + a^2*x)) - 2*(2*a^3*b^2 - 8*a^4*c - (15*a*b^3*c - 52*a^2*b*c^2)*x^3 - (15*a*b^4 - 62*a^2*b^2*c + 24*a^3*c^2)*x^2 - 5*(a^2*b^3 - 4*a^3*b*c)*x)*sqrt(c*x^4 + b*x^3 + a*x^2))/((a^4*b^2*c - 4*a^5*c^2)*x^5 + (a^4*b^3 - 4*a^5*b*c)*x^4 + (a^5*b^2 - 4*a^6*c)*x^3)]","A",0
63,1,716,0,2.084003," ","integrate(1/x/(c*x^4+b*x^3+a*x^2)^(3/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left({\left(7 \, b^{5} c - 40 \, a b^{3} c^{2} + 48 \, a^{2} b c^{3}\right)} x^{6} + {\left(7 \, b^{6} - 40 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2}\right)} x^{5} + {\left(7 \, a b^{5} - 40 \, a^{2} b^{3} c + 48 \, a^{3} b c^{2}\right)} x^{4}\right)} \sqrt{a} \log\left(-\frac{8 \, a b x^{2} + {\left(b^{2} + 4 \, a c\right)} x^{3} + 8 \, a^{2} x - 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)} \sqrt{a}}{x^{3}}\right) + 4 \, {\left(8 \, a^{4} b^{2} - 32 \, a^{5} c + {\left(105 \, a b^{4} c - 460 \, a^{2} b^{2} c^{2} + 256 \, a^{3} c^{3}\right)} x^{4} + {\left(105 \, a b^{5} - 530 \, a^{2} b^{3} c + 488 \, a^{3} b c^{2}\right)} x^{3} + {\left(35 \, a^{2} b^{4} - 172 \, a^{3} b^{2} c + 128 \, a^{4} c^{2}\right)} x^{2} - 14 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} x\right)} \sqrt{c x^{4} + b x^{3} + a x^{2}}}{96 \, {\left({\left(a^{5} b^{2} c - 4 \, a^{6} c^{2}\right)} x^{6} + {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} x^{5} + {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} x^{4}\right)}}, -\frac{15 \, {\left({\left(7 \, b^{5} c - 40 \, a b^{3} c^{2} + 48 \, a^{2} b c^{3}\right)} x^{6} + {\left(7 \, b^{6} - 40 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2}\right)} x^{5} + {\left(7 \, a b^{5} - 40 \, a^{2} b^{3} c + 48 \, a^{3} b c^{2}\right)} x^{4}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{3} + a b x^{2} + a^{2} x\right)}}\right) + 2 \, {\left(8 \, a^{4} b^{2} - 32 \, a^{5} c + {\left(105 \, a b^{4} c - 460 \, a^{2} b^{2} c^{2} + 256 \, a^{3} c^{3}\right)} x^{4} + {\left(105 \, a b^{5} - 530 \, a^{2} b^{3} c + 488 \, a^{3} b c^{2}\right)} x^{3} + {\left(35 \, a^{2} b^{4} - 172 \, a^{3} b^{2} c + 128 \, a^{4} c^{2}\right)} x^{2} - 14 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} x\right)} \sqrt{c x^{4} + b x^{3} + a x^{2}}}{48 \, {\left({\left(a^{5} b^{2} c - 4 \, a^{6} c^{2}\right)} x^{6} + {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} x^{5} + {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} x^{4}\right)}}\right]"," ",0,"[-1/96*(15*((7*b^5*c - 40*a*b^3*c^2 + 48*a^2*b*c^3)*x^6 + (7*b^6 - 40*a*b^4*c + 48*a^2*b^2*c^2)*x^5 + (7*a*b^5 - 40*a^2*b^3*c + 48*a^3*b*c^2)*x^4)*sqrt(a)*log(-(8*a*b*x^2 + (b^2 + 4*a*c)*x^3 + 8*a^2*x - 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)*sqrt(a))/x^3) + 4*(8*a^4*b^2 - 32*a^5*c + (105*a*b^4*c - 460*a^2*b^2*c^2 + 256*a^3*c^3)*x^4 + (105*a*b^5 - 530*a^2*b^3*c + 488*a^3*b*c^2)*x^3 + (35*a^2*b^4 - 172*a^3*b^2*c + 128*a^4*c^2)*x^2 - 14*(a^3*b^3 - 4*a^4*b*c)*x)*sqrt(c*x^4 + b*x^3 + a*x^2))/((a^5*b^2*c - 4*a^6*c^2)*x^6 + (a^5*b^3 - 4*a^6*b*c)*x^5 + (a^6*b^2 - 4*a^7*c)*x^4), -1/48*(15*((7*b^5*c - 40*a*b^3*c^2 + 48*a^2*b*c^3)*x^6 + (7*b^6 - 40*a*b^4*c + 48*a^2*b^2*c^2)*x^5 + (7*a*b^5 - 40*a^2*b^3*c + 48*a^3*b*c^2)*x^4)*sqrt(-a)*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)*sqrt(-a)/(a*c*x^3 + a*b*x^2 + a^2*x)) + 2*(8*a^4*b^2 - 32*a^5*c + (105*a*b^4*c - 460*a^2*b^2*c^2 + 256*a^3*c^3)*x^4 + (105*a*b^5 - 530*a^2*b^3*c + 488*a^3*b*c^2)*x^3 + (35*a^2*b^4 - 172*a^3*b^2*c + 128*a^4*c^2)*x^2 - 14*(a^3*b^3 - 4*a^4*b*c)*x)*sqrt(c*x^4 + b*x^3 + a*x^2))/((a^5*b^2*c - 4*a^6*c^2)*x^6 + (a^5*b^3 - 4*a^6*b*c)*x^5 + (a^6*b^2 - 4*a^7*c)*x^4)]","A",0
64,1,866,0,2.350174," ","integrate(1/x^2/(c*x^4+b*x^3+a*x^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left({\left(21 \, b^{6} c - 140 \, a b^{4} c^{2} + 240 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} x^{7} + {\left(21 \, b^{7} - 140 \, a b^{5} c + 240 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} x^{6} + {\left(21 \, a b^{6} - 140 \, a^{2} b^{4} c + 240 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} x^{5}\right)} \sqrt{a} \log\left(-\frac{8 \, a b x^{2} + {\left(b^{2} + 4 \, a c\right)} x^{3} + 8 \, a^{2} x - 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)} \sqrt{a}}{x^{3}}\right) - 4 \, {\left(16 \, a^{5} b^{2} - 64 \, a^{6} c - {\left(315 \, a b^{5} c - 1680 \, a^{2} b^{3} c^{2} + 1808 \, a^{3} b c^{3}\right)} x^{5} - {\left(315 \, a b^{6} - 1890 \, a^{2} b^{4} c + 2704 \, a^{3} b^{2} c^{2} - 480 \, a^{4} c^{3}\right)} x^{4} - 7 \, {\left(15 \, a^{2} b^{5} - 88 \, a^{3} b^{3} c + 112 \, a^{4} b c^{2}\right)} x^{3} + 2 \, {\left(21 \, a^{3} b^{4} - 104 \, a^{4} b^{2} c + 80 \, a^{5} c^{2}\right)} x^{2} - 24 \, {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} x\right)} \sqrt{c x^{4} + b x^{3} + a x^{2}}}{256 \, {\left({\left(a^{6} b^{2} c - 4 \, a^{7} c^{2}\right)} x^{7} + {\left(a^{6} b^{3} - 4 \, a^{7} b c\right)} x^{6} + {\left(a^{7} b^{2} - 4 \, a^{8} c\right)} x^{5}\right)}}, \frac{15 \, {\left({\left(21 \, b^{6} c - 140 \, a b^{4} c^{2} + 240 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} x^{7} + {\left(21 \, b^{7} - 140 \, a b^{5} c + 240 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} x^{6} + {\left(21 \, a b^{6} - 140 \, a^{2} b^{4} c + 240 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} x^{5}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{3} + a b x^{2} + a^{2} x\right)}}\right) - 2 \, {\left(16 \, a^{5} b^{2} - 64 \, a^{6} c - {\left(315 \, a b^{5} c - 1680 \, a^{2} b^{3} c^{2} + 1808 \, a^{3} b c^{3}\right)} x^{5} - {\left(315 \, a b^{6} - 1890 \, a^{2} b^{4} c + 2704 \, a^{3} b^{2} c^{2} - 480 \, a^{4} c^{3}\right)} x^{4} - 7 \, {\left(15 \, a^{2} b^{5} - 88 \, a^{3} b^{3} c + 112 \, a^{4} b c^{2}\right)} x^{3} + 2 \, {\left(21 \, a^{3} b^{4} - 104 \, a^{4} b^{2} c + 80 \, a^{5} c^{2}\right)} x^{2} - 24 \, {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} x\right)} \sqrt{c x^{4} + b x^{3} + a x^{2}}}{128 \, {\left({\left(a^{6} b^{2} c - 4 \, a^{7} c^{2}\right)} x^{7} + {\left(a^{6} b^{3} - 4 \, a^{7} b c\right)} x^{6} + {\left(a^{7} b^{2} - 4 \, a^{8} c\right)} x^{5}\right)}}\right]"," ",0,"[1/256*(15*((21*b^6*c - 140*a*b^4*c^2 + 240*a^2*b^2*c^3 - 64*a^3*c^4)*x^7 + (21*b^7 - 140*a*b^5*c + 240*a^2*b^3*c^2 - 64*a^3*b*c^3)*x^6 + (21*a*b^6 - 140*a^2*b^4*c + 240*a^3*b^2*c^2 - 64*a^4*c^3)*x^5)*sqrt(a)*log(-(8*a*b*x^2 + (b^2 + 4*a*c)*x^3 + 8*a^2*x - 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)*sqrt(a))/x^3) - 4*(16*a^5*b^2 - 64*a^6*c - (315*a*b^5*c - 1680*a^2*b^3*c^2 + 1808*a^3*b*c^3)*x^5 - (315*a*b^6 - 1890*a^2*b^4*c + 2704*a^3*b^2*c^2 - 480*a^4*c^3)*x^4 - 7*(15*a^2*b^5 - 88*a^3*b^3*c + 112*a^4*b*c^2)*x^3 + 2*(21*a^3*b^4 - 104*a^4*b^2*c + 80*a^5*c^2)*x^2 - 24*(a^4*b^3 - 4*a^5*b*c)*x)*sqrt(c*x^4 + b*x^3 + a*x^2))/((a^6*b^2*c - 4*a^7*c^2)*x^7 + (a^6*b^3 - 4*a^7*b*c)*x^6 + (a^7*b^2 - 4*a^8*c)*x^5), 1/128*(15*((21*b^6*c - 140*a*b^4*c^2 + 240*a^2*b^2*c^3 - 64*a^3*c^4)*x^7 + (21*b^7 - 140*a*b^5*c + 240*a^2*b^3*c^2 - 64*a^3*b*c^3)*x^6 + (21*a*b^6 - 140*a^2*b^4*c + 240*a^3*b^2*c^2 - 64*a^4*c^3)*x^5)*sqrt(-a)*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)*sqrt(-a)/(a*c*x^3 + a*b*x^2 + a^2*x)) - 2*(16*a^5*b^2 - 64*a^6*c - (315*a*b^5*c - 1680*a^2*b^3*c^2 + 1808*a^3*b*c^3)*x^5 - (315*a*b^6 - 1890*a^2*b^4*c + 2704*a^3*b^2*c^2 - 480*a^4*c^3)*x^4 - 7*(15*a^2*b^5 - 88*a^3*b^3*c + 112*a^4*b*c^2)*x^3 + 2*(21*a^3*b^4 - 104*a^4*b^2*c + 80*a^5*c^2)*x^2 - 24*(a^4*b^3 - 4*a^5*b*c)*x)*sqrt(c*x^4 + b*x^3 + a*x^2))/((a^6*b^2*c - 4*a^7*c^2)*x^7 + (a^6*b^3 - 4*a^7*b*c)*x^6 + (a^7*b^2 - 4*a^8*c)*x^5)]","A",0
65,1,71,0,1.264502," ","integrate(x^m*(c*x^5+b*x^3+a*x),x, algorithm=""fricas"")","\frac{{\left({\left(c m^{2} + 6 \, c m + 8 \, c\right)} x^{6} + {\left(b m^{2} + 8 \, b m + 12 \, b\right)} x^{4} + {\left(a m^{2} + 10 \, a m + 24 \, a\right)} x^{2}\right)} x^{m}}{m^{3} + 12 \, m^{2} + 44 \, m + 48}"," ",0,"((c*m^2 + 6*c*m + 8*c)*x^6 + (b*m^2 + 8*b*m + 12*b)*x^4 + (a*m^2 + 10*a*m + 24*a)*x^2)*x^m/(m^3 + 12*m^2 + 44*m + 48)","A",0
66,1,19,0,0.993916," ","integrate(x^2*(c*x^5+b*x^3+a*x),x, algorithm=""fricas"")","\frac{1}{8} x^{8} c + \frac{1}{6} x^{6} b + \frac{1}{4} x^{4} a"," ",0,"1/8*x^8*c + 1/6*x^6*b + 1/4*x^4*a","A",0
67,1,19,0,1.231465," ","integrate(x*(c*x^5+b*x^3+a*x),x, algorithm=""fricas"")","\frac{1}{7} x^{7} c + \frac{1}{5} x^{5} b + \frac{1}{3} x^{3} a"," ",0,"1/7*x^7*c + 1/5*x^5*b + 1/3*x^3*a","A",0
68,1,19,0,1.022349," ","integrate(c*x^5+b*x^3+a*x,x, algorithm=""fricas"")","\frac{1}{6} x^{6} c + \frac{1}{4} x^{4} b + \frac{1}{2} x^{2} a"," ",0,"1/6*x^6*c + 1/4*x^4*b + 1/2*x^2*a","A",0
69,1,16,0,1.353390," ","integrate((c*x^5+b*x^3+a*x)/x,x, algorithm=""fricas"")","\frac{1}{5} \, c x^{5} + \frac{1}{3} \, b x^{3} + a x"," ",0,"1/5*c*x^5 + 1/3*b*x^3 + a*x","A",0
70,1,17,0,1.242748," ","integrate((c*x^5+b*x^3+a*x)/x^2,x, algorithm=""fricas"")","\frac{1}{4} \, c x^{4} + \frac{1}{2} \, b x^{2} + a \log\left(x\right)"," ",0,"1/4*c*x^4 + 1/2*b*x^2 + a*log(x)","A",0
71,1,20,0,1.018178," ","integrate((c*x^5+b*x^3+a*x)/x^3,x, algorithm=""fricas"")","\frac{c x^{4} + 3 \, b x^{2} - 3 \, a}{3 \, x}"," ",0,"1/3*(c*x^4 + 3*b*x^2 - 3*a)/x","A",0
72,1,241,0,1.445246," ","integrate(x^m*(c*x^5+b*x^3+a*x)^2,x, algorithm=""fricas"")","\frac{{\left({\left(c^{2} m^{4} + 24 \, c^{2} m^{3} + 206 \, c^{2} m^{2} + 744 \, c^{2} m + 945 \, c^{2}\right)} x^{11} + 2 \, {\left(b c m^{4} + 26 \, b c m^{3} + 236 \, b c m^{2} + 886 \, b c m + 1155 \, b c\right)} x^{9} + {\left({\left(b^{2} + 2 \, a c\right)} m^{4} + 28 \, {\left(b^{2} + 2 \, a c\right)} m^{3} + 274 \, {\left(b^{2} + 2 \, a c\right)} m^{2} + 1485 \, b^{2} + 2970 \, a c + 1092 \, {\left(b^{2} + 2 \, a c\right)} m\right)} x^{7} + 2 \, {\left(a b m^{4} + 30 \, a b m^{3} + 320 \, a b m^{2} + 1410 \, a b m + 2079 \, a b\right)} x^{5} + {\left(a^{2} m^{4} + 32 \, a^{2} m^{3} + 374 \, a^{2} m^{2} + 1888 \, a^{2} m + 3465 \, a^{2}\right)} x^{3}\right)} x^{m}}{m^{5} + 35 \, m^{4} + 470 \, m^{3} + 3010 \, m^{2} + 9129 \, m + 10395}"," ",0,"((c^2*m^4 + 24*c^2*m^3 + 206*c^2*m^2 + 744*c^2*m + 945*c^2)*x^11 + 2*(b*c*m^4 + 26*b*c*m^3 + 236*b*c*m^2 + 886*b*c*m + 1155*b*c)*x^9 + ((b^2 + 2*a*c)*m^4 + 28*(b^2 + 2*a*c)*m^3 + 274*(b^2 + 2*a*c)*m^2 + 1485*b^2 + 2970*a*c + 1092*(b^2 + 2*a*c)*m)*x^7 + 2*(a*b*m^4 + 30*a*b*m^3 + 320*a*b*m^2 + 1410*a*b*m + 2079*a*b)*x^5 + (a^2*m^4 + 32*a^2*m^3 + 374*a^2*m^2 + 1888*a^2*m + 3465*a^2)*x^3)*x^m/(m^5 + 35*m^4 + 470*m^3 + 3010*m^2 + 9129*m + 10395)","B",0
73,1,46,0,1.056971," ","integrate(x^2*(c*x^5+b*x^3+a*x)^2,x, algorithm=""fricas"")","\frac{1}{13} x^{13} c^{2} + \frac{2}{11} x^{11} c b + \frac{1}{9} x^{9} b^{2} + \frac{2}{9} x^{9} c a + \frac{2}{7} x^{7} b a + \frac{1}{5} x^{5} a^{2}"," ",0,"1/13*x^13*c^2 + 2/11*x^11*c*b + 1/9*x^9*b^2 + 2/9*x^9*c*a + 2/7*x^7*b*a + 1/5*x^5*a^2","A",0
74,1,46,0,0.780156," ","integrate(x*(c*x^5+b*x^3+a*x)^2,x, algorithm=""fricas"")","\frac{1}{12} x^{12} c^{2} + \frac{1}{5} x^{10} c b + \frac{1}{8} x^{8} b^{2} + \frac{1}{4} x^{8} c a + \frac{1}{3} x^{6} b a + \frac{1}{4} x^{4} a^{2}"," ",0,"1/12*x^12*c^2 + 1/5*x^10*c*b + 1/8*x^8*b^2 + 1/4*x^8*c*a + 1/3*x^6*b*a + 1/4*x^4*a^2","A",0
75,1,46,0,1.030605," ","integrate((c*x^5+b*x^3+a*x)^2,x, algorithm=""fricas"")","\frac{1}{11} x^{11} c^{2} + \frac{2}{9} x^{9} c b + \frac{1}{7} x^{7} b^{2} + \frac{2}{7} x^{7} c a + \frac{2}{5} x^{5} b a + \frac{1}{3} x^{3} a^{2}"," ",0,"1/11*x^11*c^2 + 2/9*x^9*c*b + 1/7*x^7*b^2 + 2/7*x^7*c*a + 2/5*x^5*b*a + 1/3*x^3*a^2","A",0
76,1,44,0,0.947146," ","integrate((c*x^5+b*x^3+a*x)^2/x,x, algorithm=""fricas"")","\frac{1}{10} \, c^{2} x^{10} + \frac{1}{4} \, b c x^{8} + \frac{1}{6} \, {\left(b^{2} + 2 \, a c\right)} x^{6} + \frac{1}{2} \, a b x^{4} + \frac{1}{2} \, a^{2} x^{2}"," ",0,"1/10*c^2*x^10 + 1/4*b*c*x^8 + 1/6*(b^2 + 2*a*c)*x^6 + 1/2*a*b*x^4 + 1/2*a^2*x^2","A",0
77,1,41,0,1.283134," ","integrate((c*x^5+b*x^3+a*x)^2/x^2,x, algorithm=""fricas"")","\frac{1}{9} \, c^{2} x^{9} + \frac{2}{7} \, b c x^{7} + \frac{1}{5} \, {\left(b^{2} + 2 \, a c\right)} x^{5} + \frac{2}{3} \, a b x^{3} + a^{2} x"," ",0,"1/9*c^2*x^9 + 2/7*b*c*x^7 + 1/5*(b^2 + 2*a*c)*x^5 + 2/3*a*b*x^3 + a^2*x","A",0
78,1,313,0,1.151164," ","integrate(x^8/(c*x^5+b*x^3+a*x),x, algorithm=""fricas"")","\left[\frac{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} x^{2} - {\left(b^{3} - 3 \, a b c\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{4} + 2 \, b c x^{2} + b^{2} - 2 \, a c - {\left(2 \, c x^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{4} + b x^{2} + a}\right) + {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)}}, \frac{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} x^{2} + 2 \, {\left(b^{3} - 3 \, a b c\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c x^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) + {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)}}\right]"," ",0,"[1/4*((b^2*c^2 - 4*a*c^3)*x^4 - 2*(b^3*c - 4*a*b*c^2)*x^2 - (b^3 - 3*a*b*c)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^4 + 2*b*c*x^2 + b^2 - 2*a*c - (2*c*x^2 + b)*sqrt(b^2 - 4*a*c))/(c*x^4 + b*x^2 + a)) + (b^4 - 5*a*b^2*c + 4*a^2*c^2)*log(c*x^4 + b*x^2 + a))/(b^2*c^3 - 4*a*c^4), 1/4*((b^2*c^2 - 4*a*c^3)*x^4 - 2*(b^3*c - 4*a*b*c^2)*x^2 + 2*(b^3 - 3*a*b*c)*sqrt(-b^2 + 4*a*c)*arctan(-(2*c*x^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) + (b^4 - 5*a*b^2*c + 4*a^2*c^2)*log(c*x^4 + b*x^2 + a))/(b^2*c^3 - 4*a*c^4)]","A",0
79,1,1564,0,1.597183," ","integrate(x^7/(c*x^5+b*x^3+a*x),x, algorithm=""fricas"")","\frac{2 \, c x^{3} - 3 \, \sqrt{\frac{1}{2}} c^{2} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}} \log\left(2 \, {\left(a^{2} b^{4} - 3 \, a^{3} b^{2} c + a^{4} c^{2}\right)} x + \sqrt{\frac{1}{2}} {\left(b^{7} - 7 \, a b^{5} c + 13 \, a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3} - {\left(b^{4} c^{5} - 6 \, a b^{2} c^{6} + 8 \, a^{2} c^{7}\right)} \sqrt{\frac{b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}}{b^{2} c^{10} - 4 \, a c^{11}}}\right)} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}}\right) + 3 \, \sqrt{\frac{1}{2}} c^{2} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}} \log\left(2 \, {\left(a^{2} b^{4} - 3 \, a^{3} b^{2} c + a^{4} c^{2}\right)} x - \sqrt{\frac{1}{2}} {\left(b^{7} - 7 \, a b^{5} c + 13 \, a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3} - {\left(b^{4} c^{5} - 6 \, a b^{2} c^{6} + 8 \, a^{2} c^{7}\right)} \sqrt{\frac{b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}}{b^{2} c^{10} - 4 \, a c^{11}}}\right)} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}}\right) - 3 \, \sqrt{\frac{1}{2}} c^{2} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}} \log\left(2 \, {\left(a^{2} b^{4} - 3 \, a^{3} b^{2} c + a^{4} c^{2}\right)} x + \sqrt{\frac{1}{2}} {\left(b^{7} - 7 \, a b^{5} c + 13 \, a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3} + {\left(b^{4} c^{5} - 6 \, a b^{2} c^{6} + 8 \, a^{2} c^{7}\right)} \sqrt{\frac{b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}}{b^{2} c^{10} - 4 \, a c^{11}}}\right)} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}}\right) + 3 \, \sqrt{\frac{1}{2}} c^{2} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}} \log\left(2 \, {\left(a^{2} b^{4} - 3 \, a^{3} b^{2} c + a^{4} c^{2}\right)} x - \sqrt{\frac{1}{2}} {\left(b^{7} - 7 \, a b^{5} c + 13 \, a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3} + {\left(b^{4} c^{5} - 6 \, a b^{2} c^{6} + 8 \, a^{2} c^{7}\right)} \sqrt{\frac{b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}}{b^{2} c^{10} - 4 \, a c^{11}}}\right)} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}}\right) - 6 \, b x}{6 \, c^{2}}"," ",0,"1/6*(2*c*x^3 - 3*sqrt(1/2)*c^2*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (b^2*c^5 - 4*a*c^6)*sqrt((b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6))*log(2*(a^2*b^4 - 3*a^3*b^2*c + a^4*c^2)*x + sqrt(1/2)*(b^7 - 7*a*b^5*c + 13*a^2*b^3*c^2 - 4*a^3*b*c^3 - (b^4*c^5 - 6*a*b^2*c^6 + 8*a^2*c^7)*sqrt((b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)/(b^2*c^10 - 4*a*c^11)))*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (b^2*c^5 - 4*a*c^6)*sqrt((b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6))) + 3*sqrt(1/2)*c^2*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (b^2*c^5 - 4*a*c^6)*sqrt((b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6))*log(2*(a^2*b^4 - 3*a^3*b^2*c + a^4*c^2)*x - sqrt(1/2)*(b^7 - 7*a*b^5*c + 13*a^2*b^3*c^2 - 4*a^3*b*c^3 - (b^4*c^5 - 6*a*b^2*c^6 + 8*a^2*c^7)*sqrt((b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)/(b^2*c^10 - 4*a*c^11)))*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (b^2*c^5 - 4*a*c^6)*sqrt((b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6))) - 3*sqrt(1/2)*c^2*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (b^2*c^5 - 4*a*c^6)*sqrt((b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6))*log(2*(a^2*b^4 - 3*a^3*b^2*c + a^4*c^2)*x + sqrt(1/2)*(b^7 - 7*a*b^5*c + 13*a^2*b^3*c^2 - 4*a^3*b*c^3 + (b^4*c^5 - 6*a*b^2*c^6 + 8*a^2*c^7)*sqrt((b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)/(b^2*c^10 - 4*a*c^11)))*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (b^2*c^5 - 4*a*c^6)*sqrt((b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6))) + 3*sqrt(1/2)*c^2*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (b^2*c^5 - 4*a*c^6)*sqrt((b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6))*log(2*(a^2*b^4 - 3*a^3*b^2*c + a^4*c^2)*x - sqrt(1/2)*(b^7 - 7*a*b^5*c + 13*a^2*b^3*c^2 - 4*a^3*b*c^3 + (b^4*c^5 - 6*a*b^2*c^6 + 8*a^2*c^7)*sqrt((b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)/(b^2*c^10 - 4*a*c^11)))*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (b^2*c^5 - 4*a*c^6)*sqrt((b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6))) - 6*b*x)/c^2","B",0
80,1,254,0,1.456559," ","integrate(x^6/(c*x^5+b*x^3+a*x),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} x^{2} - {\left(b^{2} - 2 \, a c\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{4} + 2 \, b c x^{2} + b^{2} - 2 \, a c + {\left(2 \, c x^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{4} + b x^{2} + a}\right) - {\left(b^{3} - 4 \, a b c\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}}, \frac{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} x^{2} - 2 \, {\left(b^{2} - 2 \, a c\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c x^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) - {\left(b^{3} - 4 \, a b c\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}}\right]"," ",0,"[1/4*(2*(b^2*c - 4*a*c^2)*x^2 - (b^2 - 2*a*c)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^4 + 2*b*c*x^2 + b^2 - 2*a*c + (2*c*x^2 + b)*sqrt(b^2 - 4*a*c))/(c*x^4 + b*x^2 + a)) - (b^3 - 4*a*b*c)*log(c*x^4 + b*x^2 + a))/(b^2*c^2 - 4*a*c^3), 1/4*(2*(b^2*c - 4*a*c^2)*x^2 - 2*(b^2 - 2*a*c)*sqrt(-b^2 + 4*a*c)*arctan(-(2*c*x^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) - (b^3 - 4*a*b*c)*log(c*x^4 + b*x^2 + a))/(b^2*c^2 - 4*a*c^3)]","A",0
81,1,1059,0,1.269927," ","integrate(x^5/(c*x^5+b*x^3+a*x),x, algorithm=""fricas"")","-\frac{\sqrt{\frac{1}{2}} c \sqrt{-\frac{b^{3} - 3 \, a b c + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} \log\left(-2 \, {\left(a b^{2} - a^{2} c\right)} x + \sqrt{\frac{1}{2}} {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2} - {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}\right)} \sqrt{-\frac{b^{3} - 3 \, a b c + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}}\right) - \sqrt{\frac{1}{2}} c \sqrt{-\frac{b^{3} - 3 \, a b c + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} \log\left(-2 \, {\left(a b^{2} - a^{2} c\right)} x - \sqrt{\frac{1}{2}} {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2} - {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}\right)} \sqrt{-\frac{b^{3} - 3 \, a b c + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}}\right) + \sqrt{\frac{1}{2}} c \sqrt{-\frac{b^{3} - 3 \, a b c - {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} \log\left(-2 \, {\left(a b^{2} - a^{2} c\right)} x + \sqrt{\frac{1}{2}} {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2} + {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}\right)} \sqrt{-\frac{b^{3} - 3 \, a b c - {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}}\right) - \sqrt{\frac{1}{2}} c \sqrt{-\frac{b^{3} - 3 \, a b c - {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} \log\left(-2 \, {\left(a b^{2} - a^{2} c\right)} x - \sqrt{\frac{1}{2}} {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2} + {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}\right)} \sqrt{-\frac{b^{3} - 3 \, a b c - {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}}\right) - 2 \, x}{2 \, c}"," ",0,"-1/2*(sqrt(1/2)*c*sqrt(-(b^3 - 3*a*b*c + (b^2*c^3 - 4*a*c^4)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))*log(-2*(a*b^2 - a^2*c)*x + sqrt(1/2)*(b^4 - 5*a*b^2*c + 4*a^2*c^2 - (b^3*c^3 - 4*a*b*c^4)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^2*c^6 - 4*a*c^7)))*sqrt(-(b^3 - 3*a*b*c + (b^2*c^3 - 4*a*c^4)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))) - sqrt(1/2)*c*sqrt(-(b^3 - 3*a*b*c + (b^2*c^3 - 4*a*c^4)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))*log(-2*(a*b^2 - a^2*c)*x - sqrt(1/2)*(b^4 - 5*a*b^2*c + 4*a^2*c^2 - (b^3*c^3 - 4*a*b*c^4)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^2*c^6 - 4*a*c^7)))*sqrt(-(b^3 - 3*a*b*c + (b^2*c^3 - 4*a*c^4)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))) + sqrt(1/2)*c*sqrt(-(b^3 - 3*a*b*c - (b^2*c^3 - 4*a*c^4)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))*log(-2*(a*b^2 - a^2*c)*x + sqrt(1/2)*(b^4 - 5*a*b^2*c + 4*a^2*c^2 + (b^3*c^3 - 4*a*b*c^4)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^2*c^6 - 4*a*c^7)))*sqrt(-(b^3 - 3*a*b*c - (b^2*c^3 - 4*a*c^4)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))) - sqrt(1/2)*c*sqrt(-(b^3 - 3*a*b*c - (b^2*c^3 - 4*a*c^4)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))*log(-2*(a*b^2 - a^2*c)*x - sqrt(1/2)*(b^4 - 5*a*b^2*c + 4*a^2*c^2 + (b^3*c^3 - 4*a*b*c^4)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^2*c^6 - 4*a*c^7)))*sqrt(-(b^3 - 3*a*b*c - (b^2*c^3 - 4*a*c^4)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))) - 2*x)/c","B",0
82,1,197,0,1.419677," ","integrate(x^4/(c*x^5+b*x^3+a*x),x, algorithm=""fricas"")","\left[\frac{\sqrt{b^{2} - 4 \, a c} b \log\left(\frac{2 \, c^{2} x^{4} + 2 \, b c x^{2} + b^{2} - 2 \, a c + {\left(2 \, c x^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{4} + b x^{2} + a}\right) + {\left(b^{2} - 4 \, a c\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, {\left(b^{2} c - 4 \, a c^{2}\right)}}, \frac{2 \, \sqrt{-b^{2} + 4 \, a c} b \arctan\left(-\frac{{\left(2 \, c x^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) + {\left(b^{2} - 4 \, a c\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, {\left(b^{2} c - 4 \, a c^{2}\right)}}\right]"," ",0,"[1/4*(sqrt(b^2 - 4*a*c)*b*log((2*c^2*x^4 + 2*b*c*x^2 + b^2 - 2*a*c + (2*c*x^2 + b)*sqrt(b^2 - 4*a*c))/(c*x^4 + b*x^2 + a)) + (b^2 - 4*a*c)*log(c*x^4 + b*x^2 + a))/(b^2*c - 4*a*c^2), 1/4*(2*sqrt(-b^2 + 4*a*c)*b*arctan(-(2*c*x^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) + (b^2 - 4*a*c)*log(c*x^4 + b*x^2 + a))/(b^2*c - 4*a*c^2)]","A",0
83,1,559,0,1.393667," ","integrate(x^3/(c*x^5+b*x^3+a*x),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{b + \frac{b^{2} c - 4 \, a c^{2}}{\sqrt{b^{2} c^{2} - 4 \, a c^{3}}}}{b^{2} c - 4 \, a c^{2}}} \log\left(\frac{\sqrt{\frac{1}{2}} {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{-\frac{b + \frac{b^{2} c - 4 \, a c^{2}}{\sqrt{b^{2} c^{2} - 4 \, a c^{3}}}}{b^{2} c - 4 \, a c^{2}}}}{\sqrt{b^{2} c^{2} - 4 \, a c^{3}}} + x\right) - \frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{b + \frac{b^{2} c - 4 \, a c^{2}}{\sqrt{b^{2} c^{2} - 4 \, a c^{3}}}}{b^{2} c - 4 \, a c^{2}}} \log\left(-\frac{\sqrt{\frac{1}{2}} {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{-\frac{b + \frac{b^{2} c - 4 \, a c^{2}}{\sqrt{b^{2} c^{2} - 4 \, a c^{3}}}}{b^{2} c - 4 \, a c^{2}}}}{\sqrt{b^{2} c^{2} - 4 \, a c^{3}}} + x\right) - \frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{b - \frac{b^{2} c - 4 \, a c^{2}}{\sqrt{b^{2} c^{2} - 4 \, a c^{3}}}}{b^{2} c - 4 \, a c^{2}}} \log\left(\frac{\sqrt{\frac{1}{2}} {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{-\frac{b - \frac{b^{2} c - 4 \, a c^{2}}{\sqrt{b^{2} c^{2} - 4 \, a c^{3}}}}{b^{2} c - 4 \, a c^{2}}}}{\sqrt{b^{2} c^{2} - 4 \, a c^{3}}} + x\right) + \frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{b - \frac{b^{2} c - 4 \, a c^{2}}{\sqrt{b^{2} c^{2} - 4 \, a c^{3}}}}{b^{2} c - 4 \, a c^{2}}} \log\left(-\frac{\sqrt{\frac{1}{2}} {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{-\frac{b - \frac{b^{2} c - 4 \, a c^{2}}{\sqrt{b^{2} c^{2} - 4 \, a c^{3}}}}{b^{2} c - 4 \, a c^{2}}}}{\sqrt{b^{2} c^{2} - 4 \, a c^{3}}} + x\right)"," ",0,"1/2*sqrt(1/2)*sqrt(-(b + (b^2*c - 4*a*c^2)/sqrt(b^2*c^2 - 4*a*c^3))/(b^2*c - 4*a*c^2))*log(sqrt(1/2)*(b^2*c - 4*a*c^2)*sqrt(-(b + (b^2*c - 4*a*c^2)/sqrt(b^2*c^2 - 4*a*c^3))/(b^2*c - 4*a*c^2))/sqrt(b^2*c^2 - 4*a*c^3) + x) - 1/2*sqrt(1/2)*sqrt(-(b + (b^2*c - 4*a*c^2)/sqrt(b^2*c^2 - 4*a*c^3))/(b^2*c - 4*a*c^2))*log(-sqrt(1/2)*(b^2*c - 4*a*c^2)*sqrt(-(b + (b^2*c - 4*a*c^2)/sqrt(b^2*c^2 - 4*a*c^3))/(b^2*c - 4*a*c^2))/sqrt(b^2*c^2 - 4*a*c^3) + x) - 1/2*sqrt(1/2)*sqrt(-(b - (b^2*c - 4*a*c^2)/sqrt(b^2*c^2 - 4*a*c^3))/(b^2*c - 4*a*c^2))*log(sqrt(1/2)*(b^2*c - 4*a*c^2)*sqrt(-(b - (b^2*c - 4*a*c^2)/sqrt(b^2*c^2 - 4*a*c^3))/(b^2*c - 4*a*c^2))/sqrt(b^2*c^2 - 4*a*c^3) + x) + 1/2*sqrt(1/2)*sqrt(-(b - (b^2*c - 4*a*c^2)/sqrt(b^2*c^2 - 4*a*c^3))/(b^2*c - 4*a*c^2))*log(-sqrt(1/2)*(b^2*c - 4*a*c^2)*sqrt(-(b - (b^2*c - 4*a*c^2)/sqrt(b^2*c^2 - 4*a*c^3))/(b^2*c - 4*a*c^2))/sqrt(b^2*c^2 - 4*a*c^3) + x)","B",0
84,1,129,0,1.232993," ","integrate(x^2/(c*x^5+b*x^3+a*x),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{2 \, c^{2} x^{4} + 2 \, b c x^{2} + b^{2} - 2 \, a c - {\left(2 \, c x^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{4} + b x^{2} + a}\right)}{2 \, \sqrt{b^{2} - 4 \, a c}}, -\frac{\sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c x^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right)}{b^{2} - 4 \, a c}\right]"," ",0,"[1/2*log((2*c^2*x^4 + 2*b*c*x^2 + b^2 - 2*a*c - (2*c*x^2 + b)*sqrt(b^2 - 4*a*c))/(c*x^4 + b*x^2 + a))/sqrt(b^2 - 4*a*c), -sqrt(-b^2 + 4*a*c)*arctan(-(2*c*x^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c))/(b^2 - 4*a*c)]","A",0
85,1,613,0,1.313966," ","integrate(x/(c*x^5+b*x^3+a*x),x, algorithm=""fricas"")","-\frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{b + \frac{a b^{2} - 4 \, a^{2} c}{\sqrt{a^{2} b^{2} - 4 \, a^{3} c}}}{a b^{2} - 4 \, a^{2} c}} \log\left(2 \, c x + \sqrt{\frac{1}{2}} {\left(b^{2} - 4 \, a c - \frac{a b^{3} - 4 \, a^{2} b c}{\sqrt{a^{2} b^{2} - 4 \, a^{3} c}}\right)} \sqrt{-\frac{b + \frac{a b^{2} - 4 \, a^{2} c}{\sqrt{a^{2} b^{2} - 4 \, a^{3} c}}}{a b^{2} - 4 \, a^{2} c}}\right) + \frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{b + \frac{a b^{2} - 4 \, a^{2} c}{\sqrt{a^{2} b^{2} - 4 \, a^{3} c}}}{a b^{2} - 4 \, a^{2} c}} \log\left(2 \, c x - \sqrt{\frac{1}{2}} {\left(b^{2} - 4 \, a c - \frac{a b^{3} - 4 \, a^{2} b c}{\sqrt{a^{2} b^{2} - 4 \, a^{3} c}}\right)} \sqrt{-\frac{b + \frac{a b^{2} - 4 \, a^{2} c}{\sqrt{a^{2} b^{2} - 4 \, a^{3} c}}}{a b^{2} - 4 \, a^{2} c}}\right) - \frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{b - \frac{a b^{2} - 4 \, a^{2} c}{\sqrt{a^{2} b^{2} - 4 \, a^{3} c}}}{a b^{2} - 4 \, a^{2} c}} \log\left(2 \, c x + \sqrt{\frac{1}{2}} {\left(b^{2} - 4 \, a c + \frac{a b^{3} - 4 \, a^{2} b c}{\sqrt{a^{2} b^{2} - 4 \, a^{3} c}}\right)} \sqrt{-\frac{b - \frac{a b^{2} - 4 \, a^{2} c}{\sqrt{a^{2} b^{2} - 4 \, a^{3} c}}}{a b^{2} - 4 \, a^{2} c}}\right) + \frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{b - \frac{a b^{2} - 4 \, a^{2} c}{\sqrt{a^{2} b^{2} - 4 \, a^{3} c}}}{a b^{2} - 4 \, a^{2} c}} \log\left(2 \, c x - \sqrt{\frac{1}{2}} {\left(b^{2} - 4 \, a c + \frac{a b^{3} - 4 \, a^{2} b c}{\sqrt{a^{2} b^{2} - 4 \, a^{3} c}}\right)} \sqrt{-\frac{b - \frac{a b^{2} - 4 \, a^{2} c}{\sqrt{a^{2} b^{2} - 4 \, a^{3} c}}}{a b^{2} - 4 \, a^{2} c}}\right)"," ",0,"-1/2*sqrt(1/2)*sqrt(-(b + (a*b^2 - 4*a^2*c)/sqrt(a^2*b^2 - 4*a^3*c))/(a*b^2 - 4*a^2*c))*log(2*c*x + sqrt(1/2)*(b^2 - 4*a*c - (a*b^3 - 4*a^2*b*c)/sqrt(a^2*b^2 - 4*a^3*c))*sqrt(-(b + (a*b^2 - 4*a^2*c)/sqrt(a^2*b^2 - 4*a^3*c))/(a*b^2 - 4*a^2*c))) + 1/2*sqrt(1/2)*sqrt(-(b + (a*b^2 - 4*a^2*c)/sqrt(a^2*b^2 - 4*a^3*c))/(a*b^2 - 4*a^2*c))*log(2*c*x - sqrt(1/2)*(b^2 - 4*a*c - (a*b^3 - 4*a^2*b*c)/sqrt(a^2*b^2 - 4*a^3*c))*sqrt(-(b + (a*b^2 - 4*a^2*c)/sqrt(a^2*b^2 - 4*a^3*c))/(a*b^2 - 4*a^2*c))) - 1/2*sqrt(1/2)*sqrt(-(b - (a*b^2 - 4*a^2*c)/sqrt(a^2*b^2 - 4*a^3*c))/(a*b^2 - 4*a^2*c))*log(2*c*x + sqrt(1/2)*(b^2 - 4*a*c + (a*b^3 - 4*a^2*b*c)/sqrt(a^2*b^2 - 4*a^3*c))*sqrt(-(b - (a*b^2 - 4*a^2*c)/sqrt(a^2*b^2 - 4*a^3*c))/(a*b^2 - 4*a^2*c))) + 1/2*sqrt(1/2)*sqrt(-(b - (a*b^2 - 4*a^2*c)/sqrt(a^2*b^2 - 4*a^3*c))/(a*b^2 - 4*a^2*c))*log(2*c*x - sqrt(1/2)*(b^2 - 4*a*c + (a*b^3 - 4*a^2*b*c)/sqrt(a^2*b^2 - 4*a^3*c))*sqrt(-(b - (a*b^2 - 4*a^2*c)/sqrt(a^2*b^2 - 4*a^3*c))/(a*b^2 - 4*a^2*c)))","B",0
86,1,223,0,1.345650," ","integrate(1/(c*x^5+b*x^3+a*x),x, algorithm=""fricas"")","\left[\frac{\sqrt{b^{2} - 4 \, a c} b \log\left(\frac{2 \, c^{2} x^{4} + 2 \, b c x^{2} + b^{2} - 2 \, a c + {\left(2 \, c x^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{4} + b x^{2} + a}\right) - {\left(b^{2} - 4 \, a c\right)} \log\left(c x^{4} + b x^{2} + a\right) + 4 \, {\left(b^{2} - 4 \, a c\right)} \log\left(x\right)}{4 \, {\left(a b^{2} - 4 \, a^{2} c\right)}}, \frac{2 \, \sqrt{-b^{2} + 4 \, a c} b \arctan\left(-\frac{{\left(2 \, c x^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) - {\left(b^{2} - 4 \, a c\right)} \log\left(c x^{4} + b x^{2} + a\right) + 4 \, {\left(b^{2} - 4 \, a c\right)} \log\left(x\right)}{4 \, {\left(a b^{2} - 4 \, a^{2} c\right)}}\right]"," ",0,"[1/4*(sqrt(b^2 - 4*a*c)*b*log((2*c^2*x^4 + 2*b*c*x^2 + b^2 - 2*a*c + (2*c*x^2 + b)*sqrt(b^2 - 4*a*c))/(c*x^4 + b*x^2 + a)) - (b^2 - 4*a*c)*log(c*x^4 + b*x^2 + a) + 4*(b^2 - 4*a*c)*log(x))/(a*b^2 - 4*a^2*c), 1/4*(2*sqrt(-b^2 + 4*a*c)*b*arctan(-(2*c*x^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) - (b^2 - 4*a*c)*log(c*x^4 + b*x^2 + a) + 4*(b^2 - 4*a*c)*log(x))/(a*b^2 - 4*a^2*c)]","A",0
87,1,1116,0,1.389867," ","integrate(1/x/(c*x^5+b*x^3+a*x),x, algorithm=""fricas"")","-\frac{\sqrt{\frac{1}{2}} a x \sqrt{-\frac{b^{3} - 3 \, a b c + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}} \log\left(-2 \, {\left(b^{2} c^{2} - a c^{3}\right)} x + \sqrt{\frac{1}{2}} {\left(b^{5} - 5 \, a b^{3} c + 4 \, a^{2} b c^{2} - {\left(a^{3} b^{4} - 6 \, a^{4} b^{2} c + 8 \, a^{5} c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{a^{6} b^{2} - 4 \, a^{7} c}}\right)} \sqrt{-\frac{b^{3} - 3 \, a b c + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}}\right) - \sqrt{\frac{1}{2}} a x \sqrt{-\frac{b^{3} - 3 \, a b c + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}} \log\left(-2 \, {\left(b^{2} c^{2} - a c^{3}\right)} x - \sqrt{\frac{1}{2}} {\left(b^{5} - 5 \, a b^{3} c + 4 \, a^{2} b c^{2} - {\left(a^{3} b^{4} - 6 \, a^{4} b^{2} c + 8 \, a^{5} c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{a^{6} b^{2} - 4 \, a^{7} c}}\right)} \sqrt{-\frac{b^{3} - 3 \, a b c + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}}\right) + \sqrt{\frac{1}{2}} a x \sqrt{-\frac{b^{3} - 3 \, a b c - {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}} \log\left(-2 \, {\left(b^{2} c^{2} - a c^{3}\right)} x + \sqrt{\frac{1}{2}} {\left(b^{5} - 5 \, a b^{3} c + 4 \, a^{2} b c^{2} + {\left(a^{3} b^{4} - 6 \, a^{4} b^{2} c + 8 \, a^{5} c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{a^{6} b^{2} - 4 \, a^{7} c}}\right)} \sqrt{-\frac{b^{3} - 3 \, a b c - {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}}\right) - \sqrt{\frac{1}{2}} a x \sqrt{-\frac{b^{3} - 3 \, a b c - {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}} \log\left(-2 \, {\left(b^{2} c^{2} - a c^{3}\right)} x - \sqrt{\frac{1}{2}} {\left(b^{5} - 5 \, a b^{3} c + 4 \, a^{2} b c^{2} + {\left(a^{3} b^{4} - 6 \, a^{4} b^{2} c + 8 \, a^{5} c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{a^{6} b^{2} - 4 \, a^{7} c}}\right)} \sqrt{-\frac{b^{3} - 3 \, a b c - {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}}\right) + 2}{2 \, a x}"," ",0,"-1/2*(sqrt(1/2)*a*x*sqrt(-(b^3 - 3*a*b*c + (a^3*b^2 - 4*a^4*c)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c))*log(-2*(b^2*c^2 - a*c^3)*x + sqrt(1/2)*(b^5 - 5*a*b^3*c + 4*a^2*b*c^2 - (a^3*b^4 - 6*a^4*b^2*c + 8*a^5*c^2)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(a^6*b^2 - 4*a^7*c)))*sqrt(-(b^3 - 3*a*b*c + (a^3*b^2 - 4*a^4*c)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c))) - sqrt(1/2)*a*x*sqrt(-(b^3 - 3*a*b*c + (a^3*b^2 - 4*a^4*c)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c))*log(-2*(b^2*c^2 - a*c^3)*x - sqrt(1/2)*(b^5 - 5*a*b^3*c + 4*a^2*b*c^2 - (a^3*b^4 - 6*a^4*b^2*c + 8*a^5*c^2)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(a^6*b^2 - 4*a^7*c)))*sqrt(-(b^3 - 3*a*b*c + (a^3*b^2 - 4*a^4*c)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c))) + sqrt(1/2)*a*x*sqrt(-(b^3 - 3*a*b*c - (a^3*b^2 - 4*a^4*c)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c))*log(-2*(b^2*c^2 - a*c^3)*x + sqrt(1/2)*(b^5 - 5*a*b^3*c + 4*a^2*b*c^2 + (a^3*b^4 - 6*a^4*b^2*c + 8*a^5*c^2)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(a^6*b^2 - 4*a^7*c)))*sqrt(-(b^3 - 3*a*b*c - (a^3*b^2 - 4*a^4*c)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c))) - sqrt(1/2)*a*x*sqrt(-(b^3 - 3*a*b*c - (a^3*b^2 - 4*a^4*c)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c))*log(-2*(b^2*c^2 - a*c^3)*x - sqrt(1/2)*(b^5 - 5*a*b^3*c + 4*a^2*b*c^2 + (a^3*b^4 - 6*a^4*b^2*c + 8*a^5*c^2)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(a^6*b^2 - 4*a^7*c)))*sqrt(-(b^3 - 3*a*b*c - (a^3*b^2 - 4*a^4*c)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c))) + 2)/(a*x)","B",0
88,1,293,0,1.374164," ","integrate(1/x^2/(c*x^5+b*x^3+a*x),x, algorithm=""fricas"")","\left[-\frac{{\left(b^{2} - 2 \, a c\right)} \sqrt{b^{2} - 4 \, a c} x^{2} \log\left(\frac{2 \, c^{2} x^{4} + 2 \, b c x^{2} + b^{2} - 2 \, a c + {\left(2 \, c x^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{4} + b x^{2} + a}\right) - {\left(b^{3} - 4 \, a b c\right)} x^{2} \log\left(c x^{4} + b x^{2} + a\right) + 4 \, {\left(b^{3} - 4 \, a b c\right)} x^{2} \log\left(x\right) + 2 \, a b^{2} - 8 \, a^{2} c}{4 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} x^{2}}, -\frac{2 \, {\left(b^{2} - 2 \, a c\right)} \sqrt{-b^{2} + 4 \, a c} x^{2} \arctan\left(-\frac{{\left(2 \, c x^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) - {\left(b^{3} - 4 \, a b c\right)} x^{2} \log\left(c x^{4} + b x^{2} + a\right) + 4 \, {\left(b^{3} - 4 \, a b c\right)} x^{2} \log\left(x\right) + 2 \, a b^{2} - 8 \, a^{2} c}{4 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} x^{2}}\right]"," ",0,"[-1/4*((b^2 - 2*a*c)*sqrt(b^2 - 4*a*c)*x^2*log((2*c^2*x^4 + 2*b*c*x^2 + b^2 - 2*a*c + (2*c*x^2 + b)*sqrt(b^2 - 4*a*c))/(c*x^4 + b*x^2 + a)) - (b^3 - 4*a*b*c)*x^2*log(c*x^4 + b*x^2 + a) + 4*(b^3 - 4*a*b*c)*x^2*log(x) + 2*a*b^2 - 8*a^2*c)/((a^2*b^2 - 4*a^3*c)*x^2), -1/4*(2*(b^2 - 2*a*c)*sqrt(-b^2 + 4*a*c)*x^2*arctan(-(2*c*x^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) - (b^3 - 4*a*b*c)*x^2*log(c*x^4 + b*x^2 + a) + 4*(b^3 - 4*a*b*c)*x^2*log(x) + 2*a*b^2 - 8*a^2*c)/((a^2*b^2 - 4*a^3*c)*x^2)]","A",0
89,1,868,0,1.388282," ","integrate(x^11/(c*x^5+b*x^3+a*x)^2,x, algorithm=""fricas"")","\left[\frac{{\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{6} - a b^{5} + 7 \, a^{2} b^{3} c - 12 \, a^{3} b c^{2} + {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{4} - {\left(b^{6} - 9 \, a b^{4} c + 26 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} x^{2} - {\left(a b^{4} - 6 \, a^{2} b^{2} c + 6 \, a^{3} c^{2} + {\left(b^{4} c - 6 \, a b^{2} c^{2} + 6 \, a^{2} c^{3}\right)} x^{4} + {\left(b^{5} - 6 \, a b^{3} c + 6 \, a^{2} b c^{2}\right)} x^{2}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{4} + 2 \, b c x^{2} + b^{2} - 2 \, a c + {\left(2 \, c x^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{4} + b x^{2} + a}\right) - {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2} + {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{4} + {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} x^{2}\right)} \log\left(c x^{4} + b x^{2} + a\right)}{2 \, {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5} + {\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} x^{4} + {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} x^{2}\right)}}, \frac{{\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{6} - a b^{5} + 7 \, a^{2} b^{3} c - 12 \, a^{3} b c^{2} + {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{4} - {\left(b^{6} - 9 \, a b^{4} c + 26 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} x^{2} - 2 \, {\left(a b^{4} - 6 \, a^{2} b^{2} c + 6 \, a^{3} c^{2} + {\left(b^{4} c - 6 \, a b^{2} c^{2} + 6 \, a^{2} c^{3}\right)} x^{4} + {\left(b^{5} - 6 \, a b^{3} c + 6 \, a^{2} b c^{2}\right)} x^{2}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c x^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) - {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2} + {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{4} + {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} x^{2}\right)} \log\left(c x^{4} + b x^{2} + a\right)}{2 \, {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5} + {\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} x^{4} + {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} x^{2}\right)}}\right]"," ",0,"[1/2*((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^6 - a*b^5 + 7*a^2*b^3*c - 12*a^3*b*c^2 + (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^4 - (b^6 - 9*a*b^4*c + 26*a^2*b^2*c^2 - 24*a^3*c^3)*x^2 - (a*b^4 - 6*a^2*b^2*c + 6*a^3*c^2 + (b^4*c - 6*a*b^2*c^2 + 6*a^2*c^3)*x^4 + (b^5 - 6*a*b^3*c + 6*a^2*b*c^2)*x^2)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^4 + 2*b*c*x^2 + b^2 - 2*a*c + (2*c*x^2 + b)*sqrt(b^2 - 4*a*c))/(c*x^4 + b*x^2 + a)) - (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2 + (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^4 + (b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*x^2)*log(c*x^4 + b*x^2 + a))/(a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5 + (b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*x^4 + (b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*x^2), 1/2*((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^6 - a*b^5 + 7*a^2*b^3*c - 12*a^3*b*c^2 + (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^4 - (b^6 - 9*a*b^4*c + 26*a^2*b^2*c^2 - 24*a^3*c^3)*x^2 - 2*(a*b^4 - 6*a^2*b^2*c + 6*a^3*c^2 + (b^4*c - 6*a*b^2*c^2 + 6*a^2*c^3)*x^4 + (b^5 - 6*a*b^3*c + 6*a^2*b*c^2)*x^2)*sqrt(-b^2 + 4*a*c)*arctan(-(2*c*x^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) - (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2 + (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^4 + (b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*x^2)*log(c*x^4 + b*x^2 + a))/(a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5 + (b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*x^4 + (b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*x^2)]","B",0
90,1,2856,0,1.721940," ","integrate(x^10/(c*x^5+b*x^3+a*x)^2,x, algorithm=""fricas"")","\frac{4 \, {\left(b^{2} c - 4 \, a c^{2}\right)} x^{5} + 2 \, {\left(3 \, b^{3} - 11 \, a b c\right)} x^{3} + \sqrt{\frac{1}{2}} {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{4} + {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x^{2}\right)} \sqrt{-\frac{9 \, b^{7} - 105 \, a b^{5} c + 385 \, a^{2} b^{3} c^{2} - 420 \, a^{3} b c^{3} + {\left(b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}\right)} \sqrt{\frac{81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}}} \log\left(-{\left(189 \, a^{2} b^{6} - 1971 \, a^{3} b^{4} c + 5625 \, a^{4} b^{2} c^{2} - 2500 \, a^{5} c^{3}\right)} x + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(27 \, b^{10} - 459 \, a b^{8} c + 2961 \, a^{2} b^{6} c^{2} - 8818 \, a^{3} b^{4} c^{3} + 11360 \, a^{4} b^{2} c^{4} - 4000 \, a^{5} c^{5} - {\left(3 \, b^{9} c^{5} - 52 \, a b^{7} c^{6} + 336 \, a^{2} b^{5} c^{7} - 960 \, a^{3} b^{3} c^{8} + 1024 \, a^{4} b c^{9}\right)} \sqrt{\frac{81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}\right)} \sqrt{-\frac{9 \, b^{7} - 105 \, a b^{5} c + 385 \, a^{2} b^{3} c^{2} - 420 \, a^{3} b c^{3} + {\left(b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}\right)} \sqrt{\frac{81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}}}\right) - \sqrt{\frac{1}{2}} {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{4} + {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x^{2}\right)} \sqrt{-\frac{9 \, b^{7} - 105 \, a b^{5} c + 385 \, a^{2} b^{3} c^{2} - 420 \, a^{3} b c^{3} + {\left(b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}\right)} \sqrt{\frac{81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}}} \log\left(-{\left(189 \, a^{2} b^{6} - 1971 \, a^{3} b^{4} c + 5625 \, a^{4} b^{2} c^{2} - 2500 \, a^{5} c^{3}\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(27 \, b^{10} - 459 \, a b^{8} c + 2961 \, a^{2} b^{6} c^{2} - 8818 \, a^{3} b^{4} c^{3} + 11360 \, a^{4} b^{2} c^{4} - 4000 \, a^{5} c^{5} - {\left(3 \, b^{9} c^{5} - 52 \, a b^{7} c^{6} + 336 \, a^{2} b^{5} c^{7} - 960 \, a^{3} b^{3} c^{8} + 1024 \, a^{4} b c^{9}\right)} \sqrt{\frac{81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}\right)} \sqrt{-\frac{9 \, b^{7} - 105 \, a b^{5} c + 385 \, a^{2} b^{3} c^{2} - 420 \, a^{3} b c^{3} + {\left(b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}\right)} \sqrt{\frac{81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}}}\right) + \sqrt{\frac{1}{2}} {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{4} + {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x^{2}\right)} \sqrt{-\frac{9 \, b^{7} - 105 \, a b^{5} c + 385 \, a^{2} b^{3} c^{2} - 420 \, a^{3} b c^{3} - {\left(b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}\right)} \sqrt{\frac{81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}}} \log\left(-{\left(189 \, a^{2} b^{6} - 1971 \, a^{3} b^{4} c + 5625 \, a^{4} b^{2} c^{2} - 2500 \, a^{5} c^{3}\right)} x + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(27 \, b^{10} - 459 \, a b^{8} c + 2961 \, a^{2} b^{6} c^{2} - 8818 \, a^{3} b^{4} c^{3} + 11360 \, a^{4} b^{2} c^{4} - 4000 \, a^{5} c^{5} + {\left(3 \, b^{9} c^{5} - 52 \, a b^{7} c^{6} + 336 \, a^{2} b^{5} c^{7} - 960 \, a^{3} b^{3} c^{8} + 1024 \, a^{4} b c^{9}\right)} \sqrt{\frac{81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}\right)} \sqrt{-\frac{9 \, b^{7} - 105 \, a b^{5} c + 385 \, a^{2} b^{3} c^{2} - 420 \, a^{3} b c^{3} - {\left(b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}\right)} \sqrt{\frac{81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}}}\right) - \sqrt{\frac{1}{2}} {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{4} + {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x^{2}\right)} \sqrt{-\frac{9 \, b^{7} - 105 \, a b^{5} c + 385 \, a^{2} b^{3} c^{2} - 420 \, a^{3} b c^{3} - {\left(b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}\right)} \sqrt{\frac{81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}}} \log\left(-{\left(189 \, a^{2} b^{6} - 1971 \, a^{3} b^{4} c + 5625 \, a^{4} b^{2} c^{2} - 2500 \, a^{5} c^{3}\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(27 \, b^{10} - 459 \, a b^{8} c + 2961 \, a^{2} b^{6} c^{2} - 8818 \, a^{3} b^{4} c^{3} + 11360 \, a^{4} b^{2} c^{4} - 4000 \, a^{5} c^{5} + {\left(3 \, b^{9} c^{5} - 52 \, a b^{7} c^{6} + 336 \, a^{2} b^{5} c^{7} - 960 \, a^{3} b^{3} c^{8} + 1024 \, a^{4} b c^{9}\right)} \sqrt{\frac{81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}\right)} \sqrt{-\frac{9 \, b^{7} - 105 \, a b^{5} c + 385 \, a^{2} b^{3} c^{2} - 420 \, a^{3} b c^{3} - {\left(b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}\right)} \sqrt{\frac{81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}}}\right) + 2 \, {\left(3 \, a b^{2} - 10 \, a^{2} c\right)} x}{4 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{4} + {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x^{2}\right)}}"," ",0,"1/4*(4*(b^2*c - 4*a*c^2)*x^5 + 2*(3*b^3 - 11*a*b*c)*x^3 + sqrt(1/2)*(a*b^2*c^2 - 4*a^2*c^3 + (b^2*c^3 - 4*a*c^4)*x^4 + (b^3*c^2 - 4*a*b*c^3)*x^2)*sqrt(-(9*b^7 - 105*a*b^5*c + 385*a^2*b^3*c^2 - 420*a^3*b*c^3 + (b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)*sqrt((81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8))*log(-(189*a^2*b^6 - 1971*a^3*b^4*c + 5625*a^4*b^2*c^2 - 2500*a^5*c^3)*x + 1/2*sqrt(1/2)*(27*b^10 - 459*a*b^8*c + 2961*a^2*b^6*c^2 - 8818*a^3*b^4*c^3 + 11360*a^4*b^2*c^4 - 4000*a^5*c^5 - (3*b^9*c^5 - 52*a*b^7*c^6 + 336*a^2*b^5*c^7 - 960*a^3*b^3*c^8 + 1024*a^4*b*c^9)*sqrt((81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))*sqrt(-(9*b^7 - 105*a*b^5*c + 385*a^2*b^3*c^2 - 420*a^3*b*c^3 + (b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)*sqrt((81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8))) - sqrt(1/2)*(a*b^2*c^2 - 4*a^2*c^3 + (b^2*c^3 - 4*a*c^4)*x^4 + (b^3*c^2 - 4*a*b*c^3)*x^2)*sqrt(-(9*b^7 - 105*a*b^5*c + 385*a^2*b^3*c^2 - 420*a^3*b*c^3 + (b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)*sqrt((81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8))*log(-(189*a^2*b^6 - 1971*a^3*b^4*c + 5625*a^4*b^2*c^2 - 2500*a^5*c^3)*x - 1/2*sqrt(1/2)*(27*b^10 - 459*a*b^8*c + 2961*a^2*b^6*c^2 - 8818*a^3*b^4*c^3 + 11360*a^4*b^2*c^4 - 4000*a^5*c^5 - (3*b^9*c^5 - 52*a*b^7*c^6 + 336*a^2*b^5*c^7 - 960*a^3*b^3*c^8 + 1024*a^4*b*c^9)*sqrt((81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))*sqrt(-(9*b^7 - 105*a*b^5*c + 385*a^2*b^3*c^2 - 420*a^3*b*c^3 + (b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)*sqrt((81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8))) + sqrt(1/2)*(a*b^2*c^2 - 4*a^2*c^3 + (b^2*c^3 - 4*a*c^4)*x^4 + (b^3*c^2 - 4*a*b*c^3)*x^2)*sqrt(-(9*b^7 - 105*a*b^5*c + 385*a^2*b^3*c^2 - 420*a^3*b*c^3 - (b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)*sqrt((81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8))*log(-(189*a^2*b^6 - 1971*a^3*b^4*c + 5625*a^4*b^2*c^2 - 2500*a^5*c^3)*x + 1/2*sqrt(1/2)*(27*b^10 - 459*a*b^8*c + 2961*a^2*b^6*c^2 - 8818*a^3*b^4*c^3 + 11360*a^4*b^2*c^4 - 4000*a^5*c^5 + (3*b^9*c^5 - 52*a*b^7*c^6 + 336*a^2*b^5*c^7 - 960*a^3*b^3*c^8 + 1024*a^4*b*c^9)*sqrt((81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))*sqrt(-(9*b^7 - 105*a*b^5*c + 385*a^2*b^3*c^2 - 420*a^3*b*c^3 - (b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)*sqrt((81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8))) - sqrt(1/2)*(a*b^2*c^2 - 4*a^2*c^3 + (b^2*c^3 - 4*a*c^4)*x^4 + (b^3*c^2 - 4*a*b*c^3)*x^2)*sqrt(-(9*b^7 - 105*a*b^5*c + 385*a^2*b^3*c^2 - 420*a^3*b*c^3 - (b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)*sqrt((81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8))*log(-(189*a^2*b^6 - 1971*a^3*b^4*c + 5625*a^4*b^2*c^2 - 2500*a^5*c^3)*x - 1/2*sqrt(1/2)*(27*b^10 - 459*a*b^8*c + 2961*a^2*b^6*c^2 - 8818*a^3*b^4*c^3 + 11360*a^4*b^2*c^4 - 4000*a^5*c^5 + (3*b^9*c^5 - 52*a*b^7*c^6 + 336*a^2*b^5*c^7 - 960*a^3*b^3*c^8 + 1024*a^4*b*c^9)*sqrt((81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))*sqrt(-(9*b^7 - 105*a*b^5*c + 385*a^2*b^3*c^2 - 420*a^3*b*c^3 - (b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)*sqrt((81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8))) + 2*(3*a*b^2 - 10*a^2*c)*x)/(a*b^2*c^2 - 4*a^2*c^3 + (b^2*c^3 - 4*a*c^4)*x^4 + (b^3*c^2 - 4*a*b*c^3)*x^2)","B",0
91,1,663,0,1.287951," ","integrate(x^9/(c*x^5+b*x^3+a*x)^2,x, algorithm=""fricas"")","\left[\frac{2 \, a b^{4} - 12 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + 2 \, {\left(b^{5} - 7 \, a b^{3} c + 12 \, a^{2} b c^{2}\right)} x^{2} + {\left({\left(b^{3} c - 6 \, a b c^{2}\right)} x^{4} + a b^{3} - 6 \, a^{2} b c + {\left(b^{4} - 6 \, a b^{2} c\right)} x^{2}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{4} + 2 \, b c x^{2} + b^{2} - 2 \, a c + {\left(2 \, c x^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{4} + b x^{2} + a}\right) + {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} x^{4} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x^{2}\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4} + {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} x^{4} + {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} x^{2}\right)}}, \frac{2 \, a b^{4} - 12 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + 2 \, {\left(b^{5} - 7 \, a b^{3} c + 12 \, a^{2} b c^{2}\right)} x^{2} + 2 \, {\left({\left(b^{3} c - 6 \, a b c^{2}\right)} x^{4} + a b^{3} - 6 \, a^{2} b c + {\left(b^{4} - 6 \, a b^{2} c\right)} x^{2}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c x^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) + {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} x^{4} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x^{2}\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4} + {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} x^{4} + {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} x^{2}\right)}}\right]"," ",0,"[1/4*(2*a*b^4 - 12*a^2*b^2*c + 16*a^3*c^2 + 2*(b^5 - 7*a*b^3*c + 12*a^2*b*c^2)*x^2 + ((b^3*c - 6*a*b*c^2)*x^4 + a*b^3 - 6*a^2*b*c + (b^4 - 6*a*b^2*c)*x^2)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^4 + 2*b*c*x^2 + b^2 - 2*a*c + (2*c*x^2 + b)*sqrt(b^2 - 4*a*c))/(c*x^4 + b*x^2 + a)) + (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2 + (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*x^4 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*x^2)*log(c*x^4 + b*x^2 + a))/(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4 + (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*x^4 + (b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*x^2), 1/4*(2*a*b^4 - 12*a^2*b^2*c + 16*a^3*c^2 + 2*(b^5 - 7*a*b^3*c + 12*a^2*b*c^2)*x^2 + 2*((b^3*c - 6*a*b*c^2)*x^4 + a*b^3 - 6*a^2*b*c + (b^4 - 6*a*b^2*c)*x^2)*sqrt(-b^2 + 4*a*c)*arctan(-(2*c*x^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) + (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2 + (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*x^4 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*x^2)*log(c*x^4 + b*x^2 + a))/(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4 + (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*x^4 + (b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*x^2)]","B",0
92,1,2257,0,1.502336," ","integrate(x^8/(c*x^5+b*x^3+a*x)^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(b^{2} - 2 \, a c\right)} x^{3} + 2 \, a b x - \sqrt{\frac{1}{2}} {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{4} + a b^{2} c - 4 \, a^{2} c^{2} + {\left(b^{3} c - 4 \, a b c^{2}\right)} x^{2}\right)} \sqrt{-\frac{b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2} + {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} \sqrt{\frac{b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}}} \log\left({\left(5 \, a b^{4} - 81 \, a^{2} b^{2} c + 324 \, a^{3} c^{2}\right)} x + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{7} - 17 \, a b^{5} c + 88 \, a^{2} b^{3} c^{2} - 144 \, a^{3} b c^{3} - {\left(b^{8} c^{3} - 24 \, a b^{6} c^{4} + 192 \, a^{2} b^{4} c^{5} - 640 \, a^{3} b^{2} c^{6} + 768 \, a^{4} c^{7}\right)} \sqrt{\frac{b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}\right)} \sqrt{-\frac{b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2} + {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} \sqrt{\frac{b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}}}\right) + \sqrt{\frac{1}{2}} {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{4} + a b^{2} c - 4 \, a^{2} c^{2} + {\left(b^{3} c - 4 \, a b c^{2}\right)} x^{2}\right)} \sqrt{-\frac{b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2} + {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} \sqrt{\frac{b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}}} \log\left({\left(5 \, a b^{4} - 81 \, a^{2} b^{2} c + 324 \, a^{3} c^{2}\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{7} - 17 \, a b^{5} c + 88 \, a^{2} b^{3} c^{2} - 144 \, a^{3} b c^{3} - {\left(b^{8} c^{3} - 24 \, a b^{6} c^{4} + 192 \, a^{2} b^{4} c^{5} - 640 \, a^{3} b^{2} c^{6} + 768 \, a^{4} c^{7}\right)} \sqrt{\frac{b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}\right)} \sqrt{-\frac{b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2} + {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} \sqrt{\frac{b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}}}\right) - \sqrt{\frac{1}{2}} {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{4} + a b^{2} c - 4 \, a^{2} c^{2} + {\left(b^{3} c - 4 \, a b c^{2}\right)} x^{2}\right)} \sqrt{-\frac{b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2} - {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} \sqrt{\frac{b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}}} \log\left({\left(5 \, a b^{4} - 81 \, a^{2} b^{2} c + 324 \, a^{3} c^{2}\right)} x + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{7} - 17 \, a b^{5} c + 88 \, a^{2} b^{3} c^{2} - 144 \, a^{3} b c^{3} + {\left(b^{8} c^{3} - 24 \, a b^{6} c^{4} + 192 \, a^{2} b^{4} c^{5} - 640 \, a^{3} b^{2} c^{6} + 768 \, a^{4} c^{7}\right)} \sqrt{\frac{b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}\right)} \sqrt{-\frac{b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2} - {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} \sqrt{\frac{b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}}}\right) + \sqrt{\frac{1}{2}} {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{4} + a b^{2} c - 4 \, a^{2} c^{2} + {\left(b^{3} c - 4 \, a b c^{2}\right)} x^{2}\right)} \sqrt{-\frac{b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2} - {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} \sqrt{\frac{b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}}} \log\left({\left(5 \, a b^{4} - 81 \, a^{2} b^{2} c + 324 \, a^{3} c^{2}\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{7} - 17 \, a b^{5} c + 88 \, a^{2} b^{3} c^{2} - 144 \, a^{3} b c^{3} + {\left(b^{8} c^{3} - 24 \, a b^{6} c^{4} + 192 \, a^{2} b^{4} c^{5} - 640 \, a^{3} b^{2} c^{6} + 768 \, a^{4} c^{7}\right)} \sqrt{\frac{b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}\right)} \sqrt{-\frac{b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2} - {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} \sqrt{\frac{b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}}}\right)}{4 \, {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{4} + a b^{2} c - 4 \, a^{2} c^{2} + {\left(b^{3} c - 4 \, a b c^{2}\right)} x^{2}\right)}}"," ",0,"-1/4*(2*(b^2 - 2*a*c)*x^3 + 2*a*b*x - sqrt(1/2)*((b^2*c^2 - 4*a*c^3)*x^4 + a*b^2*c - 4*a^2*c^2 + (b^3*c - 4*a*b*c^2)*x^2)*sqrt(-(b^5 - 15*a*b^3*c + 60*a^2*b*c^2 + (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*sqrt((b^4 - 18*a*b^2*c + 81*a^2*c^2)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6))*log((5*a*b^4 - 81*a^2*b^2*c + 324*a^3*c^2)*x + 1/2*sqrt(1/2)*(b^7 - 17*a*b^5*c + 88*a^2*b^3*c^2 - 144*a^3*b*c^3 - (b^8*c^3 - 24*a*b^6*c^4 + 192*a^2*b^4*c^5 - 640*a^3*b^2*c^6 + 768*a^4*c^7)*sqrt((b^4 - 18*a*b^2*c + 81*a^2*c^2)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))*sqrt(-(b^5 - 15*a*b^3*c + 60*a^2*b*c^2 + (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*sqrt((b^4 - 18*a*b^2*c + 81*a^2*c^2)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6))) + sqrt(1/2)*((b^2*c^2 - 4*a*c^3)*x^4 + a*b^2*c - 4*a^2*c^2 + (b^3*c - 4*a*b*c^2)*x^2)*sqrt(-(b^5 - 15*a*b^3*c + 60*a^2*b*c^2 + (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*sqrt((b^4 - 18*a*b^2*c + 81*a^2*c^2)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6))*log((5*a*b^4 - 81*a^2*b^2*c + 324*a^3*c^2)*x - 1/2*sqrt(1/2)*(b^7 - 17*a*b^5*c + 88*a^2*b^3*c^2 - 144*a^3*b*c^3 - (b^8*c^3 - 24*a*b^6*c^4 + 192*a^2*b^4*c^5 - 640*a^3*b^2*c^6 + 768*a^4*c^7)*sqrt((b^4 - 18*a*b^2*c + 81*a^2*c^2)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))*sqrt(-(b^5 - 15*a*b^3*c + 60*a^2*b*c^2 + (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*sqrt((b^4 - 18*a*b^2*c + 81*a^2*c^2)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6))) - sqrt(1/2)*((b^2*c^2 - 4*a*c^3)*x^4 + a*b^2*c - 4*a^2*c^2 + (b^3*c - 4*a*b*c^2)*x^2)*sqrt(-(b^5 - 15*a*b^3*c + 60*a^2*b*c^2 - (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*sqrt((b^4 - 18*a*b^2*c + 81*a^2*c^2)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6))*log((5*a*b^4 - 81*a^2*b^2*c + 324*a^3*c^2)*x + 1/2*sqrt(1/2)*(b^7 - 17*a*b^5*c + 88*a^2*b^3*c^2 - 144*a^3*b*c^3 + (b^8*c^3 - 24*a*b^6*c^4 + 192*a^2*b^4*c^5 - 640*a^3*b^2*c^6 + 768*a^4*c^7)*sqrt((b^4 - 18*a*b^2*c + 81*a^2*c^2)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))*sqrt(-(b^5 - 15*a*b^3*c + 60*a^2*b*c^2 - (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*sqrt((b^4 - 18*a*b^2*c + 81*a^2*c^2)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6))) + sqrt(1/2)*((b^2*c^2 - 4*a*c^3)*x^4 + a*b^2*c - 4*a^2*c^2 + (b^3*c - 4*a*b*c^2)*x^2)*sqrt(-(b^5 - 15*a*b^3*c + 60*a^2*b*c^2 - (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*sqrt((b^4 - 18*a*b^2*c + 81*a^2*c^2)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6))*log((5*a*b^4 - 81*a^2*b^2*c + 324*a^3*c^2)*x - 1/2*sqrt(1/2)*(b^7 - 17*a*b^5*c + 88*a^2*b^3*c^2 - 144*a^3*b*c^3 + (b^8*c^3 - 24*a*b^6*c^4 + 192*a^2*b^4*c^5 - 640*a^3*b^2*c^6 + 768*a^4*c^7)*sqrt((b^4 - 18*a*b^2*c + 81*a^2*c^2)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))*sqrt(-(b^5 - 15*a*b^3*c + 60*a^2*b*c^2 - (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*sqrt((b^4 - 18*a*b^2*c + 81*a^2*c^2)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6))))/((b^2*c^2 - 4*a*c^3)*x^4 + a*b^2*c - 4*a^2*c^2 + (b^3*c - 4*a*b*c^2)*x^2)","B",0
93,1,407,0,1.384941," ","integrate(x^7/(c*x^5+b*x^3+a*x)^2,x, algorithm=""fricas"")","\left[-\frac{a b^{3} - 4 \, a^{2} b c + {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} x^{2} + 2 \, {\left(a c^{2} x^{4} + a b c x^{2} + a^{2} c\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{4} + 2 \, b c x^{2} + b^{2} - 2 \, a c - {\left(2 \, c x^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{4} + b x^{2} + a}\right)}{2 \, {\left(a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3} + {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{4} + {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{2}\right)}}, -\frac{a b^{3} - 4 \, a^{2} b c + {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} x^{2} - 4 \, {\left(a c^{2} x^{4} + a b c x^{2} + a^{2} c\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c x^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right)}{2 \, {\left(a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3} + {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{4} + {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{2}\right)}}\right]"," ",0,"[-1/2*(a*b^3 - 4*a^2*b*c + (b^4 - 6*a*b^2*c + 8*a^2*c^2)*x^2 + 2*(a*c^2*x^4 + a*b*c*x^2 + a^2*c)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^4 + 2*b*c*x^2 + b^2 - 2*a*c - (2*c*x^2 + b)*sqrt(b^2 - 4*a*c))/(c*x^4 + b*x^2 + a)))/(a*b^4*c - 8*a^2*b^2*c^2 + 16*a^3*c^3 + (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^4 + (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^2), -1/2*(a*b^3 - 4*a^2*b*c + (b^4 - 6*a*b^2*c + 8*a^2*c^2)*x^2 - 4*(a*c^2*x^4 + a*b*c*x^2 + a^2*c)*sqrt(-b^2 + 4*a*c)*arctan(-(2*c*x^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)))/(a*b^4*c - 8*a^2*b^2*c^2 + 16*a^3*c^3 + (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^4 + (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^2)]","B",0
94,1,1668,0,0.886151," ","integrate(x^6/(c*x^5+b*x^3+a*x)^2,x, algorithm=""fricas"")","\frac{2 \, b x^{3} + \sqrt{\frac{1}{2}} {\left({\left(b^{2} c - 4 \, a c^{2}\right)} x^{4} + a b^{2} - 4 \, a^{2} c + {\left(b^{3} - 4 \, a b c\right)} x^{2}\right)} \sqrt{-\frac{b^{3} + 12 \, a b c + \frac{b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}}{b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}}} \log\left({\left(3 \, b^{2} + 4 \, a c\right)} x + \sqrt{\frac{1}{2}} {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2} + \frac{2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}\right)} \sqrt{-\frac{b^{3} + 12 \, a b c + \frac{b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}}{b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}}}\right) - \sqrt{\frac{1}{2}} {\left({\left(b^{2} c - 4 \, a c^{2}\right)} x^{4} + a b^{2} - 4 \, a^{2} c + {\left(b^{3} - 4 \, a b c\right)} x^{2}\right)} \sqrt{-\frac{b^{3} + 12 \, a b c + \frac{b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}}{b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}}} \log\left({\left(3 \, b^{2} + 4 \, a c\right)} x - \sqrt{\frac{1}{2}} {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2} + \frac{2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}\right)} \sqrt{-\frac{b^{3} + 12 \, a b c + \frac{b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}}{b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}}}\right) + \sqrt{\frac{1}{2}} {\left({\left(b^{2} c - 4 \, a c^{2}\right)} x^{4} + a b^{2} - 4 \, a^{2} c + {\left(b^{3} - 4 \, a b c\right)} x^{2}\right)} \sqrt{-\frac{b^{3} + 12 \, a b c - \frac{b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}}{b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}}} \log\left({\left(3 \, b^{2} + 4 \, a c\right)} x + \sqrt{\frac{1}{2}} {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2} - \frac{2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}\right)} \sqrt{-\frac{b^{3} + 12 \, a b c - \frac{b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}}{b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}}}\right) - \sqrt{\frac{1}{2}} {\left({\left(b^{2} c - 4 \, a c^{2}\right)} x^{4} + a b^{2} - 4 \, a^{2} c + {\left(b^{3} - 4 \, a b c\right)} x^{2}\right)} \sqrt{-\frac{b^{3} + 12 \, a b c - \frac{b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}}{b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}}} \log\left({\left(3 \, b^{2} + 4 \, a c\right)} x - \sqrt{\frac{1}{2}} {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2} - \frac{2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}\right)} \sqrt{-\frac{b^{3} + 12 \, a b c - \frac{b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}}{b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}}}\right) + 4 \, a x}{4 \, {\left({\left(b^{2} c - 4 \, a c^{2}\right)} x^{4} + a b^{2} - 4 \, a^{2} c + {\left(b^{3} - 4 \, a b c\right)} x^{2}\right)}}"," ",0,"1/4*(2*b*x^3 + sqrt(1/2)*((b^2*c - 4*a*c^2)*x^4 + a*b^2 - 4*a^2*c + (b^3 - 4*a*b*c)*x^2)*sqrt(-(b^3 + 12*a*b*c + (b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))/(b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4))*log((3*b^2 + 4*a*c)*x + sqrt(1/2)*(b^4 - 8*a*b^2*c + 16*a^2*c^2 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))*sqrt(-(b^3 + 12*a*b*c + (b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))/(b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4))) - sqrt(1/2)*((b^2*c - 4*a*c^2)*x^4 + a*b^2 - 4*a^2*c + (b^3 - 4*a*b*c)*x^2)*sqrt(-(b^3 + 12*a*b*c + (b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))/(b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4))*log((3*b^2 + 4*a*c)*x - sqrt(1/2)*(b^4 - 8*a*b^2*c + 16*a^2*c^2 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))*sqrt(-(b^3 + 12*a*b*c + (b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))/(b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4))) + sqrt(1/2)*((b^2*c - 4*a*c^2)*x^4 + a*b^2 - 4*a^2*c + (b^3 - 4*a*b*c)*x^2)*sqrt(-(b^3 + 12*a*b*c - (b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))/(b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4))*log((3*b^2 + 4*a*c)*x + sqrt(1/2)*(b^4 - 8*a*b^2*c + 16*a^2*c^2 - 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))*sqrt(-(b^3 + 12*a*b*c - (b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))/(b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4))) - sqrt(1/2)*((b^2*c - 4*a*c^2)*x^4 + a*b^2 - 4*a^2*c + (b^3 - 4*a*b*c)*x^2)*sqrt(-(b^3 + 12*a*b*c - (b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))/(b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4))*log((3*b^2 + 4*a*c)*x - sqrt(1/2)*(b^4 - 8*a*b^2*c + 16*a^2*c^2 - 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))*sqrt(-(b^3 + 12*a*b*c - (b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))/(b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4))) + 4*a*x)/((b^2*c - 4*a*c^2)*x^4 + a*b^2 - 4*a^2*c + (b^3 - 4*a*b*c)*x^2)","B",0
95,1,360,0,1.469911," ","integrate(x^5/(c*x^5+b*x^3+a*x)^2,x, algorithm=""fricas"")","\left[\frac{2 \, a b^{2} - 8 \, a^{2} c + {\left(b^{3} - 4 \, a b c\right)} x^{2} - {\left(b c x^{4} + b^{2} x^{2} + a b\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{4} + 2 \, b c x^{2} + b^{2} - 2 \, a c + {\left(2 \, c x^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{4} + b x^{2} + a}\right)}{2 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} x^{4} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x^{2}\right)}}, \frac{2 \, a b^{2} - 8 \, a^{2} c + {\left(b^{3} - 4 \, a b c\right)} x^{2} - 2 \, {\left(b c x^{4} + b^{2} x^{2} + a b\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c x^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right)}{2 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} x^{4} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x^{2}\right)}}\right]"," ",0,"[1/2*(2*a*b^2 - 8*a^2*c + (b^3 - 4*a*b*c)*x^2 - (b*c*x^4 + b^2*x^2 + a*b)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^4 + 2*b*c*x^2 + b^2 - 2*a*c + (2*c*x^2 + b)*sqrt(b^2 - 4*a*c))/(c*x^4 + b*x^2 + a)))/(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2 + (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*x^4 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*x^2), 1/2*(2*a*b^2 - 8*a^2*c + (b^3 - 4*a*b*c)*x^2 - 2*(b*c*x^4 + b^2*x^2 + a*b)*sqrt(-b^2 + 4*a*c)*arctan(-(2*c*x^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)))/(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2 + (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*x^4 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*x^2)]","B",0
96,1,1680,0,1.742210," ","integrate(x^4/(c*x^5+b*x^3+a*x)^2,x, algorithm=""fricas"")","-\frac{4 \, c x^{3} + \sqrt{\frac{1}{2}} {\left({\left(b^{2} c - 4 \, a c^{2}\right)} x^{4} + a b^{2} - 4 \, a^{2} c + {\left(b^{3} - 4 \, a b c\right)} x^{2}\right)} \sqrt{-\frac{b^{3} + 12 \, a b c + \frac{a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}}{\sqrt{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}}}{a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}}} \log\left({\left(3 \, b^{2} c + 4 \, a c^{2}\right)} x + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2} - \frac{a b^{8} - 8 \, a^{2} b^{6} c + 128 \, a^{4} b^{2} c^{3} - 256 \, a^{5} c^{4}}{\sqrt{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}}\right)} \sqrt{-\frac{b^{3} + 12 \, a b c + \frac{a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}}{\sqrt{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}}}{a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}}}\right) - \sqrt{\frac{1}{2}} {\left({\left(b^{2} c - 4 \, a c^{2}\right)} x^{4} + a b^{2} - 4 \, a^{2} c + {\left(b^{3} - 4 \, a b c\right)} x^{2}\right)} \sqrt{-\frac{b^{3} + 12 \, a b c + \frac{a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}}{\sqrt{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}}}{a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}}} \log\left({\left(3 \, b^{2} c + 4 \, a c^{2}\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2} - \frac{a b^{8} - 8 \, a^{2} b^{6} c + 128 \, a^{4} b^{2} c^{3} - 256 \, a^{5} c^{4}}{\sqrt{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}}\right)} \sqrt{-\frac{b^{3} + 12 \, a b c + \frac{a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}}{\sqrt{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}}}{a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}}}\right) + \sqrt{\frac{1}{2}} {\left({\left(b^{2} c - 4 \, a c^{2}\right)} x^{4} + a b^{2} - 4 \, a^{2} c + {\left(b^{3} - 4 \, a b c\right)} x^{2}\right)} \sqrt{-\frac{b^{3} + 12 \, a b c - \frac{a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}}{\sqrt{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}}}{a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}}} \log\left({\left(3 \, b^{2} c + 4 \, a c^{2}\right)} x + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2} + \frac{a b^{8} - 8 \, a^{2} b^{6} c + 128 \, a^{4} b^{2} c^{3} - 256 \, a^{5} c^{4}}{\sqrt{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}}\right)} \sqrt{-\frac{b^{3} + 12 \, a b c - \frac{a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}}{\sqrt{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}}}{a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}}}\right) - \sqrt{\frac{1}{2}} {\left({\left(b^{2} c - 4 \, a c^{2}\right)} x^{4} + a b^{2} - 4 \, a^{2} c + {\left(b^{3} - 4 \, a b c\right)} x^{2}\right)} \sqrt{-\frac{b^{3} + 12 \, a b c - \frac{a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}}{\sqrt{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}}}{a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}}} \log\left({\left(3 \, b^{2} c + 4 \, a c^{2}\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2} + \frac{a b^{8} - 8 \, a^{2} b^{6} c + 128 \, a^{4} b^{2} c^{3} - 256 \, a^{5} c^{4}}{\sqrt{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}}\right)} \sqrt{-\frac{b^{3} + 12 \, a b c - \frac{a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}}{\sqrt{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}}}{a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}}}\right) + 2 \, b x}{4 \, {\left({\left(b^{2} c - 4 \, a c^{2}\right)} x^{4} + a b^{2} - 4 \, a^{2} c + {\left(b^{3} - 4 \, a b c\right)} x^{2}\right)}}"," ",0,"-1/4*(4*c*x^3 + sqrt(1/2)*((b^2*c - 4*a*c^2)*x^4 + a*b^2 - 4*a^2*c + (b^3 - 4*a*b*c)*x^2)*sqrt(-(b^3 + 12*a*b*c + (a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)/sqrt(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3))/(a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3))*log((3*b^2*c + 4*a*c^2)*x + 1/2*sqrt(1/2)*(b^5 - 8*a*b^3*c + 16*a^2*b*c^2 - (a*b^8 - 8*a^2*b^6*c + 128*a^4*b^2*c^3 - 256*a^5*c^4)/sqrt(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3))*sqrt(-(b^3 + 12*a*b*c + (a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)/sqrt(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3))/(a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3))) - sqrt(1/2)*((b^2*c - 4*a*c^2)*x^4 + a*b^2 - 4*a^2*c + (b^3 - 4*a*b*c)*x^2)*sqrt(-(b^3 + 12*a*b*c + (a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)/sqrt(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3))/(a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3))*log((3*b^2*c + 4*a*c^2)*x - 1/2*sqrt(1/2)*(b^5 - 8*a*b^3*c + 16*a^2*b*c^2 - (a*b^8 - 8*a^2*b^6*c + 128*a^4*b^2*c^3 - 256*a^5*c^4)/sqrt(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3))*sqrt(-(b^3 + 12*a*b*c + (a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)/sqrt(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3))/(a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3))) + sqrt(1/2)*((b^2*c - 4*a*c^2)*x^4 + a*b^2 - 4*a^2*c + (b^3 - 4*a*b*c)*x^2)*sqrt(-(b^3 + 12*a*b*c - (a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)/sqrt(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3))/(a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3))*log((3*b^2*c + 4*a*c^2)*x + 1/2*sqrt(1/2)*(b^5 - 8*a*b^3*c + 16*a^2*b*c^2 + (a*b^8 - 8*a^2*b^6*c + 128*a^4*b^2*c^3 - 256*a^5*c^4)/sqrt(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3))*sqrt(-(b^3 + 12*a*b*c - (a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)/sqrt(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3))/(a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3))) - sqrt(1/2)*((b^2*c - 4*a*c^2)*x^4 + a*b^2 - 4*a^2*c + (b^3 - 4*a*b*c)*x^2)*sqrt(-(b^3 + 12*a*b*c - (a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)/sqrt(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3))/(a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3))*log((3*b^2*c + 4*a*c^2)*x - 1/2*sqrt(1/2)*(b^5 - 8*a*b^3*c + 16*a^2*b*c^2 + (a*b^8 - 8*a^2*b^6*c + 128*a^4*b^2*c^3 - 256*a^5*c^4)/sqrt(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3))*sqrt(-(b^3 + 12*a*b*c - (a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)/sqrt(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3))/(a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3))) + 2*b*x)/((b^2*c - 4*a*c^2)*x^4 + a*b^2 - 4*a^2*c + (b^3 - 4*a*b*c)*x^2)","B",0
97,1,361,0,1.258595," ","integrate(x^3/(c*x^5+b*x^3+a*x)^2,x, algorithm=""fricas"")","\left[-\frac{b^{3} - 4 \, a b c + 2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} x^{2} + 2 \, {\left(c^{2} x^{4} + b c x^{2} + a c\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{4} + 2 \, b c x^{2} + b^{2} - 2 \, a c - {\left(2 \, c x^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{4} + b x^{2} + a}\right)}{2 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} x^{4} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x^{2}\right)}}, -\frac{b^{3} - 4 \, a b c + 2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} x^{2} - 4 \, {\left(c^{2} x^{4} + b c x^{2} + a c\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c x^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right)}{2 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} x^{4} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x^{2}\right)}}\right]"," ",0,"[-1/2*(b^3 - 4*a*b*c + 2*(b^2*c - 4*a*c^2)*x^2 + 2*(c^2*x^4 + b*c*x^2 + a*c)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^4 + 2*b*c*x^2 + b^2 - 2*a*c - (2*c*x^2 + b)*sqrt(b^2 - 4*a*c))/(c*x^4 + b*x^2 + a)))/(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2 + (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*x^4 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*x^2), -1/2*(b^3 - 4*a*b*c + 2*(b^2*c - 4*a*c^2)*x^2 - 4*(c^2*x^4 + b*c*x^2 + a*c)*sqrt(-b^2 + 4*a*c)*arctan(-(2*c*x^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)))/(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2 + (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*x^4 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*x^2)]","B",0
98,1,2309,0,1.165349," ","integrate(x^2/(c*x^5+b*x^3+a*x)^2,x, algorithm=""fricas"")","\frac{2 \, b c x^{3} + \sqrt{\frac{1}{2}} {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + {\left(a b^{3} - 4 \, a^{2} b c\right)} x^{2}\right)} \sqrt{-\frac{b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2} + {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} \sqrt{\frac{b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}}{a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}}} \log\left({\left(5 \, b^{4} c^{2} - 81 \, a b^{2} c^{3} + 324 \, a^{2} c^{4}\right)} x + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{8} - 23 \, a b^{6} c + 190 \, a^{2} b^{4} c^{2} - 672 \, a^{3} b^{2} c^{3} + 864 \, a^{4} c^{4} - {\left(a^{3} b^{9} - 20 \, a^{4} b^{7} c + 144 \, a^{5} b^{5} c^{2} - 448 \, a^{6} b^{3} c^{3} + 512 \, a^{7} b c^{4}\right)} \sqrt{\frac{b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}\right)} \sqrt{-\frac{b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2} + {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} \sqrt{\frac{b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}}{a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}}}\right) - \sqrt{\frac{1}{2}} {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + {\left(a b^{3} - 4 \, a^{2} b c\right)} x^{2}\right)} \sqrt{-\frac{b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2} + {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} \sqrt{\frac{b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}}{a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}}} \log\left({\left(5 \, b^{4} c^{2} - 81 \, a b^{2} c^{3} + 324 \, a^{2} c^{4}\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{8} - 23 \, a b^{6} c + 190 \, a^{2} b^{4} c^{2} - 672 \, a^{3} b^{2} c^{3} + 864 \, a^{4} c^{4} - {\left(a^{3} b^{9} - 20 \, a^{4} b^{7} c + 144 \, a^{5} b^{5} c^{2} - 448 \, a^{6} b^{3} c^{3} + 512 \, a^{7} b c^{4}\right)} \sqrt{\frac{b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}\right)} \sqrt{-\frac{b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2} + {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} \sqrt{\frac{b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}}{a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}}}\right) + \sqrt{\frac{1}{2}} {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + {\left(a b^{3} - 4 \, a^{2} b c\right)} x^{2}\right)} \sqrt{-\frac{b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2} - {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} \sqrt{\frac{b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}}{a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}}} \log\left({\left(5 \, b^{4} c^{2} - 81 \, a b^{2} c^{3} + 324 \, a^{2} c^{4}\right)} x + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{8} - 23 \, a b^{6} c + 190 \, a^{2} b^{4} c^{2} - 672 \, a^{3} b^{2} c^{3} + 864 \, a^{4} c^{4} + {\left(a^{3} b^{9} - 20 \, a^{4} b^{7} c + 144 \, a^{5} b^{5} c^{2} - 448 \, a^{6} b^{3} c^{3} + 512 \, a^{7} b c^{4}\right)} \sqrt{\frac{b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}\right)} \sqrt{-\frac{b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2} - {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} \sqrt{\frac{b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}}{a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}}}\right) - \sqrt{\frac{1}{2}} {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + {\left(a b^{3} - 4 \, a^{2} b c\right)} x^{2}\right)} \sqrt{-\frac{b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2} - {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} \sqrt{\frac{b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}}{a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}}} \log\left({\left(5 \, b^{4} c^{2} - 81 \, a b^{2} c^{3} + 324 \, a^{2} c^{4}\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{8} - 23 \, a b^{6} c + 190 \, a^{2} b^{4} c^{2} - 672 \, a^{3} b^{2} c^{3} + 864 \, a^{4} c^{4} + {\left(a^{3} b^{9} - 20 \, a^{4} b^{7} c + 144 \, a^{5} b^{5} c^{2} - 448 \, a^{6} b^{3} c^{3} + 512 \, a^{7} b c^{4}\right)} \sqrt{\frac{b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}\right)} \sqrt{-\frac{b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2} - {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} \sqrt{\frac{b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}}{a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}}}\right) + 2 \, {\left(b^{2} - 2 \, a c\right)} x}{4 \, {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + {\left(a b^{3} - 4 \, a^{2} b c\right)} x^{2}\right)}}"," ",0,"1/4*(2*b*c*x^3 + sqrt(1/2)*((a*b^2*c - 4*a^2*c^2)*x^4 + a^2*b^2 - 4*a^3*c + (a*b^3 - 4*a^2*b*c)*x^2)*sqrt(-(b^5 - 15*a*b^3*c + 60*a^2*b*c^2 + (a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*sqrt((b^4 - 18*a*b^2*c + 81*a^2*c^2)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))/(a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3))*log((5*b^4*c^2 - 81*a*b^2*c^3 + 324*a^2*c^4)*x + 1/2*sqrt(1/2)*(b^8 - 23*a*b^6*c + 190*a^2*b^4*c^2 - 672*a^3*b^2*c^3 + 864*a^4*c^4 - (a^3*b^9 - 20*a^4*b^7*c + 144*a^5*b^5*c^2 - 448*a^6*b^3*c^3 + 512*a^7*b*c^4)*sqrt((b^4 - 18*a*b^2*c + 81*a^2*c^2)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))*sqrt(-(b^5 - 15*a*b^3*c + 60*a^2*b*c^2 + (a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*sqrt((b^4 - 18*a*b^2*c + 81*a^2*c^2)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))/(a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3))) - sqrt(1/2)*((a*b^2*c - 4*a^2*c^2)*x^4 + a^2*b^2 - 4*a^3*c + (a*b^3 - 4*a^2*b*c)*x^2)*sqrt(-(b^5 - 15*a*b^3*c + 60*a^2*b*c^2 + (a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*sqrt((b^4 - 18*a*b^2*c + 81*a^2*c^2)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))/(a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3))*log((5*b^4*c^2 - 81*a*b^2*c^3 + 324*a^2*c^4)*x - 1/2*sqrt(1/2)*(b^8 - 23*a*b^6*c + 190*a^2*b^4*c^2 - 672*a^3*b^2*c^3 + 864*a^4*c^4 - (a^3*b^9 - 20*a^4*b^7*c + 144*a^5*b^5*c^2 - 448*a^6*b^3*c^3 + 512*a^7*b*c^4)*sqrt((b^4 - 18*a*b^2*c + 81*a^2*c^2)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))*sqrt(-(b^5 - 15*a*b^3*c + 60*a^2*b*c^2 + (a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*sqrt((b^4 - 18*a*b^2*c + 81*a^2*c^2)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))/(a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3))) + sqrt(1/2)*((a*b^2*c - 4*a^2*c^2)*x^4 + a^2*b^2 - 4*a^3*c + (a*b^3 - 4*a^2*b*c)*x^2)*sqrt(-(b^5 - 15*a*b^3*c + 60*a^2*b*c^2 - (a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*sqrt((b^4 - 18*a*b^2*c + 81*a^2*c^2)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))/(a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3))*log((5*b^4*c^2 - 81*a*b^2*c^3 + 324*a^2*c^4)*x + 1/2*sqrt(1/2)*(b^8 - 23*a*b^6*c + 190*a^2*b^4*c^2 - 672*a^3*b^2*c^3 + 864*a^4*c^4 + (a^3*b^9 - 20*a^4*b^7*c + 144*a^5*b^5*c^2 - 448*a^6*b^3*c^3 + 512*a^7*b*c^4)*sqrt((b^4 - 18*a*b^2*c + 81*a^2*c^2)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))*sqrt(-(b^5 - 15*a*b^3*c + 60*a^2*b*c^2 - (a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*sqrt((b^4 - 18*a*b^2*c + 81*a^2*c^2)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))/(a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3))) - sqrt(1/2)*((a*b^2*c - 4*a^2*c^2)*x^4 + a^2*b^2 - 4*a^3*c + (a*b^3 - 4*a^2*b*c)*x^2)*sqrt(-(b^5 - 15*a*b^3*c + 60*a^2*b*c^2 - (a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*sqrt((b^4 - 18*a*b^2*c + 81*a^2*c^2)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))/(a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3))*log((5*b^4*c^2 - 81*a*b^2*c^3 + 324*a^2*c^4)*x - 1/2*sqrt(1/2)*(b^8 - 23*a*b^6*c + 190*a^2*b^4*c^2 - 672*a^3*b^2*c^3 + 864*a^4*c^4 + (a^3*b^9 - 20*a^4*b^7*c + 144*a^5*b^5*c^2 - 448*a^6*b^3*c^3 + 512*a^7*b*c^4)*sqrt((b^4 - 18*a*b^2*c + 81*a^2*c^2)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))*sqrt(-(b^5 - 15*a*b^3*c + 60*a^2*b*c^2 - (a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*sqrt((b^4 - 18*a*b^2*c + 81*a^2*c^2)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))/(a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3))) + 2*(b^2 - 2*a*c)*x)/((a*b^2*c - 4*a^2*c^2)*x^4 + a^2*b^2 - 4*a^3*c + (a*b^3 - 4*a^2*b*c)*x^2)","B",0
99,1,813,0,2.063765," ","integrate(x/(c*x^5+b*x^3+a*x)^2,x, algorithm=""fricas"")","\left[\frac{2 \, a b^{4} - 12 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} x^{2} + {\left({\left(b^{3} c - 6 \, a b c^{2}\right)} x^{4} + a b^{3} - 6 \, a^{2} b c + {\left(b^{4} - 6 \, a b^{2} c\right)} x^{2}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{4} + 2 \, b c x^{2} + b^{2} - 2 \, a c + {\left(2 \, c x^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{4} + b x^{2} + a}\right) - {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} x^{4} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x^{2}\right)} \log\left(c x^{4} + b x^{2} + a\right) + 4 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} x^{4} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x^{2}\right)} \log\left(x\right)}{4 \, {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2} + {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)} x^{4} + {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} x^{2}\right)}}, \frac{2 \, a b^{4} - 12 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} x^{2} + 2 \, {\left({\left(b^{3} c - 6 \, a b c^{2}\right)} x^{4} + a b^{3} - 6 \, a^{2} b c + {\left(b^{4} - 6 \, a b^{2} c\right)} x^{2}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c x^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) - {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} x^{4} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x^{2}\right)} \log\left(c x^{4} + b x^{2} + a\right) + 4 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} x^{4} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x^{2}\right)} \log\left(x\right)}{4 \, {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2} + {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)} x^{4} + {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} x^{2}\right)}}\right]"," ",0,"[1/4*(2*a*b^4 - 12*a^2*b^2*c + 16*a^3*c^2 + 2*(a*b^3*c - 4*a^2*b*c^2)*x^2 + ((b^3*c - 6*a*b*c^2)*x^4 + a*b^3 - 6*a^2*b*c + (b^4 - 6*a*b^2*c)*x^2)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^4 + 2*b*c*x^2 + b^2 - 2*a*c + (2*c*x^2 + b)*sqrt(b^2 - 4*a*c))/(c*x^4 + b*x^2 + a)) - (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2 + (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*x^4 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*x^2)*log(c*x^4 + b*x^2 + a) + 4*(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2 + (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*x^4 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*x^2)*log(x))/(a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2 + (a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3)*x^4 + (a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*x^2), 1/4*(2*a*b^4 - 12*a^2*b^2*c + 16*a^3*c^2 + 2*(a*b^3*c - 4*a^2*b*c^2)*x^2 + 2*((b^3*c - 6*a*b*c^2)*x^4 + a*b^3 - 6*a^2*b*c + (b^4 - 6*a*b^2*c)*x^2)*sqrt(-b^2 + 4*a*c)*arctan(-(2*c*x^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) - (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2 + (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*x^4 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*x^2)*log(c*x^4 + b*x^2 + a) + 4*(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2 + (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*x^4 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*x^2)*log(x))/(a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2 + (a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3)*x^4 + (a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*x^2)]","B",0
100,1,2912,0,1.645314," ","integrate(1/(c*x^5+b*x^3+a*x)^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, b^{2} c - 10 \, a c^{2}\right)} x^{4} + 4 \, a b^{2} - 16 \, a^{2} c + 2 \, {\left(3 \, b^{3} - 11 \, a b c\right)} x^{2} - \sqrt{\frac{1}{2}} {\left({\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} x^{5} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} x^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} x\right)} \sqrt{-\frac{9 \, b^{7} - 105 \, a b^{5} c + 385 \, a^{2} b^{3} c^{2} - 420 \, a^{3} b c^{3} + {\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} \sqrt{\frac{81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}}{a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}}} \log\left(-{\left(189 \, b^{6} c^{3} - 1971 \, a b^{4} c^{4} + 5625 \, a^{2} b^{2} c^{5} - 2500 \, a^{3} c^{6}\right)} x + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(27 \, b^{11} - 486 \, a b^{9} c + 3330 \, a^{2} b^{7} c^{2} - 10549 \, a^{3} b^{5} c^{3} + 14408 \, a^{4} b^{3} c^{4} - 5200 \, a^{5} b c^{5} - {\left(3 \, a^{5} b^{10} - 55 \, a^{6} b^{8} c + 392 \, a^{7} b^{6} c^{2} - 1344 \, a^{8} b^{4} c^{3} + 2176 \, a^{9} b^{2} c^{4} - 1280 \, a^{10} c^{5}\right)} \sqrt{\frac{81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}\right)} \sqrt{-\frac{9 \, b^{7} - 105 \, a b^{5} c + 385 \, a^{2} b^{3} c^{2} - 420 \, a^{3} b c^{3} + {\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} \sqrt{\frac{81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}}{a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}}}\right) + \sqrt{\frac{1}{2}} {\left({\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} x^{5} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} x^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} x\right)} \sqrt{-\frac{9 \, b^{7} - 105 \, a b^{5} c + 385 \, a^{2} b^{3} c^{2} - 420 \, a^{3} b c^{3} + {\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} \sqrt{\frac{81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}}{a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}}} \log\left(-{\left(189 \, b^{6} c^{3} - 1971 \, a b^{4} c^{4} + 5625 \, a^{2} b^{2} c^{5} - 2500 \, a^{3} c^{6}\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(27 \, b^{11} - 486 \, a b^{9} c + 3330 \, a^{2} b^{7} c^{2} - 10549 \, a^{3} b^{5} c^{3} + 14408 \, a^{4} b^{3} c^{4} - 5200 \, a^{5} b c^{5} - {\left(3 \, a^{5} b^{10} - 55 \, a^{6} b^{8} c + 392 \, a^{7} b^{6} c^{2} - 1344 \, a^{8} b^{4} c^{3} + 2176 \, a^{9} b^{2} c^{4} - 1280 \, a^{10} c^{5}\right)} \sqrt{\frac{81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}\right)} \sqrt{-\frac{9 \, b^{7} - 105 \, a b^{5} c + 385 \, a^{2} b^{3} c^{2} - 420 \, a^{3} b c^{3} + {\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} \sqrt{\frac{81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}}{a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}}}\right) - \sqrt{\frac{1}{2}} {\left({\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} x^{5} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} x^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} x\right)} \sqrt{-\frac{9 \, b^{7} - 105 \, a b^{5} c + 385 \, a^{2} b^{3} c^{2} - 420 \, a^{3} b c^{3} - {\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} \sqrt{\frac{81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}}{a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}}} \log\left(-{\left(189 \, b^{6} c^{3} - 1971 \, a b^{4} c^{4} + 5625 \, a^{2} b^{2} c^{5} - 2500 \, a^{3} c^{6}\right)} x + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(27 \, b^{11} - 486 \, a b^{9} c + 3330 \, a^{2} b^{7} c^{2} - 10549 \, a^{3} b^{5} c^{3} + 14408 \, a^{4} b^{3} c^{4} - 5200 \, a^{5} b c^{5} + {\left(3 \, a^{5} b^{10} - 55 \, a^{6} b^{8} c + 392 \, a^{7} b^{6} c^{2} - 1344 \, a^{8} b^{4} c^{3} + 2176 \, a^{9} b^{2} c^{4} - 1280 \, a^{10} c^{5}\right)} \sqrt{\frac{81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}\right)} \sqrt{-\frac{9 \, b^{7} - 105 \, a b^{5} c + 385 \, a^{2} b^{3} c^{2} - 420 \, a^{3} b c^{3} - {\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} \sqrt{\frac{81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}}{a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}}}\right) + \sqrt{\frac{1}{2}} {\left({\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} x^{5} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} x^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} x\right)} \sqrt{-\frac{9 \, b^{7} - 105 \, a b^{5} c + 385 \, a^{2} b^{3} c^{2} - 420 \, a^{3} b c^{3} - {\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} \sqrt{\frac{81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}}{a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}}} \log\left(-{\left(189 \, b^{6} c^{3} - 1971 \, a b^{4} c^{4} + 5625 \, a^{2} b^{2} c^{5} - 2500 \, a^{3} c^{6}\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(27 \, b^{11} - 486 \, a b^{9} c + 3330 \, a^{2} b^{7} c^{2} - 10549 \, a^{3} b^{5} c^{3} + 14408 \, a^{4} b^{3} c^{4} - 5200 \, a^{5} b c^{5} + {\left(3 \, a^{5} b^{10} - 55 \, a^{6} b^{8} c + 392 \, a^{7} b^{6} c^{2} - 1344 \, a^{8} b^{4} c^{3} + 2176 \, a^{9} b^{2} c^{4} - 1280 \, a^{10} c^{5}\right)} \sqrt{\frac{81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}\right)} \sqrt{-\frac{9 \, b^{7} - 105 \, a b^{5} c + 385 \, a^{2} b^{3} c^{2} - 420 \, a^{3} b c^{3} - {\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} \sqrt{\frac{81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}}{a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}}}\right)}{4 \, {\left({\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} x^{5} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} x^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} x\right)}}"," ",0,"-1/4*(2*(3*b^2*c - 10*a*c^2)*x^4 + 4*a*b^2 - 16*a^2*c + 2*(3*b^3 - 11*a*b*c)*x^2 - sqrt(1/2)*((a^2*b^2*c - 4*a^3*c^2)*x^5 + (a^2*b^3 - 4*a^3*b*c)*x^3 + (a^3*b^2 - 4*a^4*c)*x)*sqrt(-(9*b^7 - 105*a*b^5*c + 385*a^2*b^3*c^2 - 420*a^3*b*c^3 + (a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*sqrt((81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))/(a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3))*log(-(189*b^6*c^3 - 1971*a*b^4*c^4 + 5625*a^2*b^2*c^5 - 2500*a^3*c^6)*x + 1/2*sqrt(1/2)*(27*b^11 - 486*a*b^9*c + 3330*a^2*b^7*c^2 - 10549*a^3*b^5*c^3 + 14408*a^4*b^3*c^4 - 5200*a^5*b*c^5 - (3*a^5*b^10 - 55*a^6*b^8*c + 392*a^7*b^6*c^2 - 1344*a^8*b^4*c^3 + 2176*a^9*b^2*c^4 - 1280*a^10*c^5)*sqrt((81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))*sqrt(-(9*b^7 - 105*a*b^5*c + 385*a^2*b^3*c^2 - 420*a^3*b*c^3 + (a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*sqrt((81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))/(a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3))) + sqrt(1/2)*((a^2*b^2*c - 4*a^3*c^2)*x^5 + (a^2*b^3 - 4*a^3*b*c)*x^3 + (a^3*b^2 - 4*a^4*c)*x)*sqrt(-(9*b^7 - 105*a*b^5*c + 385*a^2*b^3*c^2 - 420*a^3*b*c^3 + (a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*sqrt((81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))/(a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3))*log(-(189*b^6*c^3 - 1971*a*b^4*c^4 + 5625*a^2*b^2*c^5 - 2500*a^3*c^6)*x - 1/2*sqrt(1/2)*(27*b^11 - 486*a*b^9*c + 3330*a^2*b^7*c^2 - 10549*a^3*b^5*c^3 + 14408*a^4*b^3*c^4 - 5200*a^5*b*c^5 - (3*a^5*b^10 - 55*a^6*b^8*c + 392*a^7*b^6*c^2 - 1344*a^8*b^4*c^3 + 2176*a^9*b^2*c^4 - 1280*a^10*c^5)*sqrt((81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))*sqrt(-(9*b^7 - 105*a*b^5*c + 385*a^2*b^3*c^2 - 420*a^3*b*c^3 + (a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*sqrt((81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))/(a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3))) - sqrt(1/2)*((a^2*b^2*c - 4*a^3*c^2)*x^5 + (a^2*b^3 - 4*a^3*b*c)*x^3 + (a^3*b^2 - 4*a^4*c)*x)*sqrt(-(9*b^7 - 105*a*b^5*c + 385*a^2*b^3*c^2 - 420*a^3*b*c^3 - (a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*sqrt((81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))/(a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3))*log(-(189*b^6*c^3 - 1971*a*b^4*c^4 + 5625*a^2*b^2*c^5 - 2500*a^3*c^6)*x + 1/2*sqrt(1/2)*(27*b^11 - 486*a*b^9*c + 3330*a^2*b^7*c^2 - 10549*a^3*b^5*c^3 + 14408*a^4*b^3*c^4 - 5200*a^5*b*c^5 + (3*a^5*b^10 - 55*a^6*b^8*c + 392*a^7*b^6*c^2 - 1344*a^8*b^4*c^3 + 2176*a^9*b^2*c^4 - 1280*a^10*c^5)*sqrt((81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))*sqrt(-(9*b^7 - 105*a*b^5*c + 385*a^2*b^3*c^2 - 420*a^3*b*c^3 - (a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*sqrt((81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))/(a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3))) + sqrt(1/2)*((a^2*b^2*c - 4*a^3*c^2)*x^5 + (a^2*b^3 - 4*a^3*b*c)*x^3 + (a^3*b^2 - 4*a^4*c)*x)*sqrt(-(9*b^7 - 105*a*b^5*c + 385*a^2*b^3*c^2 - 420*a^3*b*c^3 - (a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*sqrt((81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))/(a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3))*log(-(189*b^6*c^3 - 1971*a*b^4*c^4 + 5625*a^2*b^2*c^5 - 2500*a^3*c^6)*x - 1/2*sqrt(1/2)*(27*b^11 - 486*a*b^9*c + 3330*a^2*b^7*c^2 - 10549*a^3*b^5*c^3 + 14408*a^4*b^3*c^4 - 5200*a^5*b*c^5 + (3*a^5*b^10 - 55*a^6*b^8*c + 392*a^7*b^6*c^2 - 1344*a^8*b^4*c^3 + 2176*a^9*b^2*c^4 - 1280*a^10*c^5)*sqrt((81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))*sqrt(-(9*b^7 - 105*a*b^5*c + 385*a^2*b^3*c^2 - 420*a^3*b*c^3 - (a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*sqrt((81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))/(a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3))))/((a^2*b^2*c - 4*a^3*c^2)*x^5 + (a^2*b^3 - 4*a^3*b*c)*x^3 + (a^3*b^2 - 4*a^4*c)*x)","B",0
101,1,1007,0,1.643734," ","integrate(1/x/(c*x^5+b*x^3+a*x)^2,x, algorithm=""fricas"")","\left[-\frac{a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + 2 \, {\left(a b^{4} c - 7 \, a^{2} b^{2} c^{2} + 12 \, a^{3} c^{3}\right)} x^{4} + {\left(2 \, a b^{5} - 15 \, a^{2} b^{3} c + 28 \, a^{3} b c^{2}\right)} x^{2} + {\left({\left(b^{4} c - 6 \, a b^{2} c^{2} + 6 \, a^{2} c^{3}\right)} x^{6} + {\left(b^{5} - 6 \, a b^{3} c + 6 \, a^{2} b c^{2}\right)} x^{4} + {\left(a b^{4} - 6 \, a^{2} b^{2} c + 6 \, a^{3} c^{2}\right)} x^{2}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{4} + 2 \, b c x^{2} + b^{2} - 2 \, a c + {\left(2 \, c x^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{4} + b x^{2} + a}\right) - {\left({\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{6} + {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} x^{4} + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x^{2}\right)} \log\left(c x^{4} + b x^{2} + a\right) + 4 \, {\left({\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{6} + {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} x^{4} + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x^{2}\right)} \log\left(x\right)}{2 \, {\left({\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} x^{6} + {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} x^{4} + {\left(a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2}\right)} x^{2}\right)}}, -\frac{a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + 2 \, {\left(a b^{4} c - 7 \, a^{2} b^{2} c^{2} + 12 \, a^{3} c^{3}\right)} x^{4} + {\left(2 \, a b^{5} - 15 \, a^{2} b^{3} c + 28 \, a^{3} b c^{2}\right)} x^{2} + 2 \, {\left({\left(b^{4} c - 6 \, a b^{2} c^{2} + 6 \, a^{2} c^{3}\right)} x^{6} + {\left(b^{5} - 6 \, a b^{3} c + 6 \, a^{2} b c^{2}\right)} x^{4} + {\left(a b^{4} - 6 \, a^{2} b^{2} c + 6 \, a^{3} c^{2}\right)} x^{2}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c x^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) - {\left({\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{6} + {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} x^{4} + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x^{2}\right)} \log\left(c x^{4} + b x^{2} + a\right) + 4 \, {\left({\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{6} + {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} x^{4} + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x^{2}\right)} \log\left(x\right)}{2 \, {\left({\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} x^{6} + {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} x^{4} + {\left(a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2}\right)} x^{2}\right)}}\right]"," ",0,"[-1/2*(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + 2*(a*b^4*c - 7*a^2*b^2*c^2 + 12*a^3*c^3)*x^4 + (2*a*b^5 - 15*a^2*b^3*c + 28*a^3*b*c^2)*x^2 + ((b^4*c - 6*a*b^2*c^2 + 6*a^2*c^3)*x^6 + (b^5 - 6*a*b^3*c + 6*a^2*b*c^2)*x^4 + (a*b^4 - 6*a^2*b^2*c + 6*a^3*c^2)*x^2)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^4 + 2*b*c*x^2 + b^2 - 2*a*c + (2*c*x^2 + b)*sqrt(b^2 - 4*a*c))/(c*x^4 + b*x^2 + a)) - ((b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^6 + (b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*x^4 + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x^2)*log(c*x^4 + b*x^2 + a) + 4*((b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^6 + (b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*x^4 + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x^2)*log(x))/((a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*x^6 + (a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*x^4 + (a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2)*x^2), -1/2*(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + 2*(a*b^4*c - 7*a^2*b^2*c^2 + 12*a^3*c^3)*x^4 + (2*a*b^5 - 15*a^2*b^3*c + 28*a^3*b*c^2)*x^2 + 2*((b^4*c - 6*a*b^2*c^2 + 6*a^2*c^3)*x^6 + (b^5 - 6*a*b^3*c + 6*a^2*b*c^2)*x^4 + (a*b^4 - 6*a^2*b^2*c + 6*a^3*c^2)*x^2)*sqrt(-b^2 + 4*a*c)*arctan(-(2*c*x^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) - ((b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^6 + (b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*x^4 + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x^2)*log(c*x^4 + b*x^2 + a) + 4*((b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^6 + (b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*x^4 + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x^2)*log(x))/((a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*x^6 + (a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*x^4 + (a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2)*x^2)]","B",0
102,1,3435,0,2.117459," ","integrate(1/x^2/(c*x^5+b*x^3+a*x)^2,x, algorithm=""fricas"")","\frac{6 \, {\left(5 \, b^{3} c - 19 \, a b c^{2}\right)} x^{6} + 2 \, {\left(15 \, b^{4} - 62 \, a b^{2} c + 14 \, a^{2} c^{2}\right)} x^{4} - 4 \, a^{2} b^{2} + 16 \, a^{3} c + 20 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} x^{2} + 3 \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} x^{7} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} x^{5} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} x^{3}\right)} \sqrt{-\frac{25 \, b^{9} - 315 \, a b^{7} c + 1386 \, a^{2} b^{5} c^{2} - 2415 \, a^{3} b^{3} c^{3} + 1260 \, a^{4} b c^{4} + {\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} \sqrt{\frac{625 \, b^{12} - 8250 \, a b^{10} c + 39525 \, a^{2} b^{8} c^{2} - 83630 \, a^{3} b^{6} c^{3} + 76686 \, a^{4} b^{4} c^{4} - 24108 \, a^{5} b^{2} c^{5} + 2401 \, a^{6} c^{6}}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}}{a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}}} \log\left({\left(1125 \, b^{8} c^{4} - 12325 \, a b^{6} c^{5} + 43410 \, a^{2} b^{4} c^{6} - 50421 \, a^{3} b^{2} c^{7} + 9604 \, a^{4} c^{8}\right)} x + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(125 \, b^{14} - 2425 \, a b^{12} c + 18940 \, a^{2} b^{10} c^{2} - 75579 \, a^{3} b^{8} c^{3} + 160932 \, a^{4} b^{6} c^{4} - 172990 \, a^{5} b^{4} c^{5} + 79408 \, a^{6} b^{2} c^{6} - 10976 \, a^{7} c^{7} - {\left(5 \, a^{7} b^{11} - 94 \, a^{8} b^{9} c + 700 \, a^{9} b^{7} c^{2} - 2576 \, a^{10} b^{5} c^{3} + 4672 \, a^{11} b^{3} c^{4} - 3328 \, a^{12} b c^{5}\right)} \sqrt{\frac{625 \, b^{12} - 8250 \, a b^{10} c + 39525 \, a^{2} b^{8} c^{2} - 83630 \, a^{3} b^{6} c^{3} + 76686 \, a^{4} b^{4} c^{4} - 24108 \, a^{5} b^{2} c^{5} + 2401 \, a^{6} c^{6}}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}\right)} \sqrt{-\frac{25 \, b^{9} - 315 \, a b^{7} c + 1386 \, a^{2} b^{5} c^{2} - 2415 \, a^{3} b^{3} c^{3} + 1260 \, a^{4} b c^{4} + {\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} \sqrt{\frac{625 \, b^{12} - 8250 \, a b^{10} c + 39525 \, a^{2} b^{8} c^{2} - 83630 \, a^{3} b^{6} c^{3} + 76686 \, a^{4} b^{4} c^{4} - 24108 \, a^{5} b^{2} c^{5} + 2401 \, a^{6} c^{6}}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}}{a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}}}\right) - 3 \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} x^{7} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} x^{5} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} x^{3}\right)} \sqrt{-\frac{25 \, b^{9} - 315 \, a b^{7} c + 1386 \, a^{2} b^{5} c^{2} - 2415 \, a^{3} b^{3} c^{3} + 1260 \, a^{4} b c^{4} + {\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} \sqrt{\frac{625 \, b^{12} - 8250 \, a b^{10} c + 39525 \, a^{2} b^{8} c^{2} - 83630 \, a^{3} b^{6} c^{3} + 76686 \, a^{4} b^{4} c^{4} - 24108 \, a^{5} b^{2} c^{5} + 2401 \, a^{6} c^{6}}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}}{a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}}} \log\left({\left(1125 \, b^{8} c^{4} - 12325 \, a b^{6} c^{5} + 43410 \, a^{2} b^{4} c^{6} - 50421 \, a^{3} b^{2} c^{7} + 9604 \, a^{4} c^{8}\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(125 \, b^{14} - 2425 \, a b^{12} c + 18940 \, a^{2} b^{10} c^{2} - 75579 \, a^{3} b^{8} c^{3} + 160932 \, a^{4} b^{6} c^{4} - 172990 \, a^{5} b^{4} c^{5} + 79408 \, a^{6} b^{2} c^{6} - 10976 \, a^{7} c^{7} - {\left(5 \, a^{7} b^{11} - 94 \, a^{8} b^{9} c + 700 \, a^{9} b^{7} c^{2} - 2576 \, a^{10} b^{5} c^{3} + 4672 \, a^{11} b^{3} c^{4} - 3328 \, a^{12} b c^{5}\right)} \sqrt{\frac{625 \, b^{12} - 8250 \, a b^{10} c + 39525 \, a^{2} b^{8} c^{2} - 83630 \, a^{3} b^{6} c^{3} + 76686 \, a^{4} b^{4} c^{4} - 24108 \, a^{5} b^{2} c^{5} + 2401 \, a^{6} c^{6}}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}\right)} \sqrt{-\frac{25 \, b^{9} - 315 \, a b^{7} c + 1386 \, a^{2} b^{5} c^{2} - 2415 \, a^{3} b^{3} c^{3} + 1260 \, a^{4} b c^{4} + {\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} \sqrt{\frac{625 \, b^{12} - 8250 \, a b^{10} c + 39525 \, a^{2} b^{8} c^{2} - 83630 \, a^{3} b^{6} c^{3} + 76686 \, a^{4} b^{4} c^{4} - 24108 \, a^{5} b^{2} c^{5} + 2401 \, a^{6} c^{6}}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}}{a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}}}\right) + 3 \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} x^{7} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} x^{5} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} x^{3}\right)} \sqrt{-\frac{25 \, b^{9} - 315 \, a b^{7} c + 1386 \, a^{2} b^{5} c^{2} - 2415 \, a^{3} b^{3} c^{3} + 1260 \, a^{4} b c^{4} - {\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} \sqrt{\frac{625 \, b^{12} - 8250 \, a b^{10} c + 39525 \, a^{2} b^{8} c^{2} - 83630 \, a^{3} b^{6} c^{3} + 76686 \, a^{4} b^{4} c^{4} - 24108 \, a^{5} b^{2} c^{5} + 2401 \, a^{6} c^{6}}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}}{a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}}} \log\left({\left(1125 \, b^{8} c^{4} - 12325 \, a b^{6} c^{5} + 43410 \, a^{2} b^{4} c^{6} - 50421 \, a^{3} b^{2} c^{7} + 9604 \, a^{4} c^{8}\right)} x + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(125 \, b^{14} - 2425 \, a b^{12} c + 18940 \, a^{2} b^{10} c^{2} - 75579 \, a^{3} b^{8} c^{3} + 160932 \, a^{4} b^{6} c^{4} - 172990 \, a^{5} b^{4} c^{5} + 79408 \, a^{6} b^{2} c^{6} - 10976 \, a^{7} c^{7} + {\left(5 \, a^{7} b^{11} - 94 \, a^{8} b^{9} c + 700 \, a^{9} b^{7} c^{2} - 2576 \, a^{10} b^{5} c^{3} + 4672 \, a^{11} b^{3} c^{4} - 3328 \, a^{12} b c^{5}\right)} \sqrt{\frac{625 \, b^{12} - 8250 \, a b^{10} c + 39525 \, a^{2} b^{8} c^{2} - 83630 \, a^{3} b^{6} c^{3} + 76686 \, a^{4} b^{4} c^{4} - 24108 \, a^{5} b^{2} c^{5} + 2401 \, a^{6} c^{6}}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}\right)} \sqrt{-\frac{25 \, b^{9} - 315 \, a b^{7} c + 1386 \, a^{2} b^{5} c^{2} - 2415 \, a^{3} b^{3} c^{3} + 1260 \, a^{4} b c^{4} - {\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} \sqrt{\frac{625 \, b^{12} - 8250 \, a b^{10} c + 39525 \, a^{2} b^{8} c^{2} - 83630 \, a^{3} b^{6} c^{3} + 76686 \, a^{4} b^{4} c^{4} - 24108 \, a^{5} b^{2} c^{5} + 2401 \, a^{6} c^{6}}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}}{a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}}}\right) - 3 \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} x^{7} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} x^{5} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} x^{3}\right)} \sqrt{-\frac{25 \, b^{9} - 315 \, a b^{7} c + 1386 \, a^{2} b^{5} c^{2} - 2415 \, a^{3} b^{3} c^{3} + 1260 \, a^{4} b c^{4} - {\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} \sqrt{\frac{625 \, b^{12} - 8250 \, a b^{10} c + 39525 \, a^{2} b^{8} c^{2} - 83630 \, a^{3} b^{6} c^{3} + 76686 \, a^{4} b^{4} c^{4} - 24108 \, a^{5} b^{2} c^{5} + 2401 \, a^{6} c^{6}}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}}{a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}}} \log\left({\left(1125 \, b^{8} c^{4} - 12325 \, a b^{6} c^{5} + 43410 \, a^{2} b^{4} c^{6} - 50421 \, a^{3} b^{2} c^{7} + 9604 \, a^{4} c^{8}\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(125 \, b^{14} - 2425 \, a b^{12} c + 18940 \, a^{2} b^{10} c^{2} - 75579 \, a^{3} b^{8} c^{3} + 160932 \, a^{4} b^{6} c^{4} - 172990 \, a^{5} b^{4} c^{5} + 79408 \, a^{6} b^{2} c^{6} - 10976 \, a^{7} c^{7} + {\left(5 \, a^{7} b^{11} - 94 \, a^{8} b^{9} c + 700 \, a^{9} b^{7} c^{2} - 2576 \, a^{10} b^{5} c^{3} + 4672 \, a^{11} b^{3} c^{4} - 3328 \, a^{12} b c^{5}\right)} \sqrt{\frac{625 \, b^{12} - 8250 \, a b^{10} c + 39525 \, a^{2} b^{8} c^{2} - 83630 \, a^{3} b^{6} c^{3} + 76686 \, a^{4} b^{4} c^{4} - 24108 \, a^{5} b^{2} c^{5} + 2401 \, a^{6} c^{6}}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}\right)} \sqrt{-\frac{25 \, b^{9} - 315 \, a b^{7} c + 1386 \, a^{2} b^{5} c^{2} - 2415 \, a^{3} b^{3} c^{3} + 1260 \, a^{4} b c^{4} - {\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} \sqrt{\frac{625 \, b^{12} - 8250 \, a b^{10} c + 39525 \, a^{2} b^{8} c^{2} - 83630 \, a^{3} b^{6} c^{3} + 76686 \, a^{4} b^{4} c^{4} - 24108 \, a^{5} b^{2} c^{5} + 2401 \, a^{6} c^{6}}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}}{a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}}}\right)}{12 \, {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} x^{7} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} x^{5} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} x^{3}\right)}}"," ",0,"1/12*(6*(5*b^3*c - 19*a*b*c^2)*x^6 + 2*(15*b^4 - 62*a*b^2*c + 14*a^2*c^2)*x^4 - 4*a^2*b^2 + 16*a^3*c + 20*(a*b^3 - 4*a^2*b*c)*x^2 + 3*sqrt(1/2)*((a^3*b^2*c - 4*a^4*c^2)*x^7 + (a^3*b^3 - 4*a^4*b*c)*x^5 + (a^4*b^2 - 4*a^5*c)*x^3)*sqrt(-(25*b^9 - 315*a*b^7*c + 1386*a^2*b^5*c^2 - 2415*a^3*b^3*c^3 + 1260*a^4*b*c^4 + (a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*sqrt((625*b^12 - 8250*a*b^10*c + 39525*a^2*b^8*c^2 - 83630*a^3*b^6*c^3 + 76686*a^4*b^4*c^4 - 24108*a^5*b^2*c^5 + 2401*a^6*c^6)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))/(a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3))*log((1125*b^8*c^4 - 12325*a*b^6*c^5 + 43410*a^2*b^4*c^6 - 50421*a^3*b^2*c^7 + 9604*a^4*c^8)*x + 1/2*sqrt(1/2)*(125*b^14 - 2425*a*b^12*c + 18940*a^2*b^10*c^2 - 75579*a^3*b^8*c^3 + 160932*a^4*b^6*c^4 - 172990*a^5*b^4*c^5 + 79408*a^6*b^2*c^6 - 10976*a^7*c^7 - (5*a^7*b^11 - 94*a^8*b^9*c + 700*a^9*b^7*c^2 - 2576*a^10*b^5*c^3 + 4672*a^11*b^3*c^4 - 3328*a^12*b*c^5)*sqrt((625*b^12 - 8250*a*b^10*c + 39525*a^2*b^8*c^2 - 83630*a^3*b^6*c^3 + 76686*a^4*b^4*c^4 - 24108*a^5*b^2*c^5 + 2401*a^6*c^6)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))*sqrt(-(25*b^9 - 315*a*b^7*c + 1386*a^2*b^5*c^2 - 2415*a^3*b^3*c^3 + 1260*a^4*b*c^4 + (a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*sqrt((625*b^12 - 8250*a*b^10*c + 39525*a^2*b^8*c^2 - 83630*a^3*b^6*c^3 + 76686*a^4*b^4*c^4 - 24108*a^5*b^2*c^5 + 2401*a^6*c^6)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))/(a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3))) - 3*sqrt(1/2)*((a^3*b^2*c - 4*a^4*c^2)*x^7 + (a^3*b^3 - 4*a^4*b*c)*x^5 + (a^4*b^2 - 4*a^5*c)*x^3)*sqrt(-(25*b^9 - 315*a*b^7*c + 1386*a^2*b^5*c^2 - 2415*a^3*b^3*c^3 + 1260*a^4*b*c^4 + (a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*sqrt((625*b^12 - 8250*a*b^10*c + 39525*a^2*b^8*c^2 - 83630*a^3*b^6*c^3 + 76686*a^4*b^4*c^4 - 24108*a^5*b^2*c^5 + 2401*a^6*c^6)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))/(a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3))*log((1125*b^8*c^4 - 12325*a*b^6*c^5 + 43410*a^2*b^4*c^6 - 50421*a^3*b^2*c^7 + 9604*a^4*c^8)*x - 1/2*sqrt(1/2)*(125*b^14 - 2425*a*b^12*c + 18940*a^2*b^10*c^2 - 75579*a^3*b^8*c^3 + 160932*a^4*b^6*c^4 - 172990*a^5*b^4*c^5 + 79408*a^6*b^2*c^6 - 10976*a^7*c^7 - (5*a^7*b^11 - 94*a^8*b^9*c + 700*a^9*b^7*c^2 - 2576*a^10*b^5*c^3 + 4672*a^11*b^3*c^4 - 3328*a^12*b*c^5)*sqrt((625*b^12 - 8250*a*b^10*c + 39525*a^2*b^8*c^2 - 83630*a^3*b^6*c^3 + 76686*a^4*b^4*c^4 - 24108*a^5*b^2*c^5 + 2401*a^6*c^6)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))*sqrt(-(25*b^9 - 315*a*b^7*c + 1386*a^2*b^5*c^2 - 2415*a^3*b^3*c^3 + 1260*a^4*b*c^4 + (a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*sqrt((625*b^12 - 8250*a*b^10*c + 39525*a^2*b^8*c^2 - 83630*a^3*b^6*c^3 + 76686*a^4*b^4*c^4 - 24108*a^5*b^2*c^5 + 2401*a^6*c^6)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))/(a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3))) + 3*sqrt(1/2)*((a^3*b^2*c - 4*a^4*c^2)*x^7 + (a^3*b^3 - 4*a^4*b*c)*x^5 + (a^4*b^2 - 4*a^5*c)*x^3)*sqrt(-(25*b^9 - 315*a*b^7*c + 1386*a^2*b^5*c^2 - 2415*a^3*b^3*c^3 + 1260*a^4*b*c^4 - (a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*sqrt((625*b^12 - 8250*a*b^10*c + 39525*a^2*b^8*c^2 - 83630*a^3*b^6*c^3 + 76686*a^4*b^4*c^4 - 24108*a^5*b^2*c^5 + 2401*a^6*c^6)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))/(a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3))*log((1125*b^8*c^4 - 12325*a*b^6*c^5 + 43410*a^2*b^4*c^6 - 50421*a^3*b^2*c^7 + 9604*a^4*c^8)*x + 1/2*sqrt(1/2)*(125*b^14 - 2425*a*b^12*c + 18940*a^2*b^10*c^2 - 75579*a^3*b^8*c^3 + 160932*a^4*b^6*c^4 - 172990*a^5*b^4*c^5 + 79408*a^6*b^2*c^6 - 10976*a^7*c^7 + (5*a^7*b^11 - 94*a^8*b^9*c + 700*a^9*b^7*c^2 - 2576*a^10*b^5*c^3 + 4672*a^11*b^3*c^4 - 3328*a^12*b*c^5)*sqrt((625*b^12 - 8250*a*b^10*c + 39525*a^2*b^8*c^2 - 83630*a^3*b^6*c^3 + 76686*a^4*b^4*c^4 - 24108*a^5*b^2*c^5 + 2401*a^6*c^6)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))*sqrt(-(25*b^9 - 315*a*b^7*c + 1386*a^2*b^5*c^2 - 2415*a^3*b^3*c^3 + 1260*a^4*b*c^4 - (a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*sqrt((625*b^12 - 8250*a*b^10*c + 39525*a^2*b^8*c^2 - 83630*a^3*b^6*c^3 + 76686*a^4*b^4*c^4 - 24108*a^5*b^2*c^5 + 2401*a^6*c^6)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))/(a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3))) - 3*sqrt(1/2)*((a^3*b^2*c - 4*a^4*c^2)*x^7 + (a^3*b^3 - 4*a^4*b*c)*x^5 + (a^4*b^2 - 4*a^5*c)*x^3)*sqrt(-(25*b^9 - 315*a*b^7*c + 1386*a^2*b^5*c^2 - 2415*a^3*b^3*c^3 + 1260*a^4*b*c^4 - (a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*sqrt((625*b^12 - 8250*a*b^10*c + 39525*a^2*b^8*c^2 - 83630*a^3*b^6*c^3 + 76686*a^4*b^4*c^4 - 24108*a^5*b^2*c^5 + 2401*a^6*c^6)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))/(a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3))*log((1125*b^8*c^4 - 12325*a*b^6*c^5 + 43410*a^2*b^4*c^6 - 50421*a^3*b^2*c^7 + 9604*a^4*c^8)*x - 1/2*sqrt(1/2)*(125*b^14 - 2425*a*b^12*c + 18940*a^2*b^10*c^2 - 75579*a^3*b^8*c^3 + 160932*a^4*b^6*c^4 - 172990*a^5*b^4*c^5 + 79408*a^6*b^2*c^6 - 10976*a^7*c^7 + (5*a^7*b^11 - 94*a^8*b^9*c + 700*a^9*b^7*c^2 - 2576*a^10*b^5*c^3 + 4672*a^11*b^3*c^4 - 3328*a^12*b*c^5)*sqrt((625*b^12 - 8250*a*b^10*c + 39525*a^2*b^8*c^2 - 83630*a^3*b^6*c^3 + 76686*a^4*b^4*c^4 - 24108*a^5*b^2*c^5 + 2401*a^6*c^6)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))*sqrt(-(25*b^9 - 315*a*b^7*c + 1386*a^2*b^5*c^2 - 2415*a^3*b^3*c^3 + 1260*a^4*b*c^4 - (a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*sqrt((625*b^12 - 8250*a*b^10*c + 39525*a^2*b^8*c^2 - 83630*a^3*b^6*c^3 + 76686*a^4*b^4*c^4 - 24108*a^5*b^2*c^5 + 2401*a^6*c^6)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))/(a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3))))/((a^3*b^2*c - 4*a^4*c^2)*x^7 + (a^3*b^3 - 4*a^4*b*c)*x^5 + (a^4*b^2 - 4*a^5*c)*x^3)","B",0
103,1,1242,0,2.284587," ","integrate(1/x^3/(c*x^5+b*x^3+a*x)^2,x, algorithm=""fricas"")","\left[-\frac{a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2} - 2 \, {\left(3 \, a b^{5} c - 23 \, a^{2} b^{3} c^{2} + 44 \, a^{3} b c^{3}\right)} x^{6} - {\left(6 \, a b^{6} - 49 \, a^{2} b^{4} c + 108 \, a^{3} b^{2} c^{2} - 32 \, a^{4} c^{3}\right)} x^{4} - 3 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} x^{2} + {\left({\left(3 \, b^{5} c - 20 \, a b^{3} c^{2} + 30 \, a^{2} b c^{3}\right)} x^{8} + {\left(3 \, b^{6} - 20 \, a b^{4} c + 30 \, a^{2} b^{2} c^{2}\right)} x^{6} + {\left(3 \, a b^{5} - 20 \, a^{2} b^{3} c + 30 \, a^{3} b c^{2}\right)} x^{4}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{4} + 2 \, b c x^{2} + b^{2} - 2 \, a c - {\left(2 \, c x^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{4} + b x^{2} + a}\right) + {\left({\left(3 \, b^{6} c - 26 \, a b^{4} c^{2} + 64 \, a^{2} b^{2} c^{3} - 32 \, a^{3} c^{4}\right)} x^{8} + {\left(3 \, b^{7} - 26 \, a b^{5} c + 64 \, a^{2} b^{3} c^{2} - 32 \, a^{3} b c^{3}\right)} x^{6} + {\left(3 \, a b^{6} - 26 \, a^{2} b^{4} c + 64 \, a^{3} b^{2} c^{2} - 32 \, a^{4} c^{3}\right)} x^{4}\right)} \log\left(c x^{4} + b x^{2} + a\right) - 4 \, {\left({\left(3 \, b^{6} c - 26 \, a b^{4} c^{2} + 64 \, a^{2} b^{2} c^{3} - 32 \, a^{3} c^{4}\right)} x^{8} + {\left(3 \, b^{7} - 26 \, a b^{5} c + 64 \, a^{2} b^{3} c^{2} - 32 \, a^{3} b c^{3}\right)} x^{6} + {\left(3 \, a b^{6} - 26 \, a^{2} b^{4} c + 64 \, a^{3} b^{2} c^{2} - 32 \, a^{4} c^{3}\right)} x^{4}\right)} \log\left(x\right)}{4 \, {\left({\left(a^{4} b^{4} c - 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3}\right)} x^{8} + {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} x^{6} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} x^{4}\right)}}, -\frac{a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2} - 2 \, {\left(3 \, a b^{5} c - 23 \, a^{2} b^{3} c^{2} + 44 \, a^{3} b c^{3}\right)} x^{6} - {\left(6 \, a b^{6} - 49 \, a^{2} b^{4} c + 108 \, a^{3} b^{2} c^{2} - 32 \, a^{4} c^{3}\right)} x^{4} - 3 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} x^{2} - 2 \, {\left({\left(3 \, b^{5} c - 20 \, a b^{3} c^{2} + 30 \, a^{2} b c^{3}\right)} x^{8} + {\left(3 \, b^{6} - 20 \, a b^{4} c + 30 \, a^{2} b^{2} c^{2}\right)} x^{6} + {\left(3 \, a b^{5} - 20 \, a^{2} b^{3} c + 30 \, a^{3} b c^{2}\right)} x^{4}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c x^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) + {\left({\left(3 \, b^{6} c - 26 \, a b^{4} c^{2} + 64 \, a^{2} b^{2} c^{3} - 32 \, a^{3} c^{4}\right)} x^{8} + {\left(3 \, b^{7} - 26 \, a b^{5} c + 64 \, a^{2} b^{3} c^{2} - 32 \, a^{3} b c^{3}\right)} x^{6} + {\left(3 \, a b^{6} - 26 \, a^{2} b^{4} c + 64 \, a^{3} b^{2} c^{2} - 32 \, a^{4} c^{3}\right)} x^{4}\right)} \log\left(c x^{4} + b x^{2} + a\right) - 4 \, {\left({\left(3 \, b^{6} c - 26 \, a b^{4} c^{2} + 64 \, a^{2} b^{2} c^{3} - 32 \, a^{3} c^{4}\right)} x^{8} + {\left(3 \, b^{7} - 26 \, a b^{5} c + 64 \, a^{2} b^{3} c^{2} - 32 \, a^{3} b c^{3}\right)} x^{6} + {\left(3 \, a b^{6} - 26 \, a^{2} b^{4} c + 64 \, a^{3} b^{2} c^{2} - 32 \, a^{4} c^{3}\right)} x^{4}\right)} \log\left(x\right)}{4 \, {\left({\left(a^{4} b^{4} c - 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3}\right)} x^{8} + {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} x^{6} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} x^{4}\right)}}\right]"," ",0,"[-1/4*(a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2 - 2*(3*a*b^5*c - 23*a^2*b^3*c^2 + 44*a^3*b*c^3)*x^6 - (6*a*b^6 - 49*a^2*b^4*c + 108*a^3*b^2*c^2 - 32*a^4*c^3)*x^4 - 3*(a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*x^2 + ((3*b^5*c - 20*a*b^3*c^2 + 30*a^2*b*c^3)*x^8 + (3*b^6 - 20*a*b^4*c + 30*a^2*b^2*c^2)*x^6 + (3*a*b^5 - 20*a^2*b^3*c + 30*a^3*b*c^2)*x^4)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^4 + 2*b*c*x^2 + b^2 - 2*a*c - (2*c*x^2 + b)*sqrt(b^2 - 4*a*c))/(c*x^4 + b*x^2 + a)) + ((3*b^6*c - 26*a*b^4*c^2 + 64*a^2*b^2*c^3 - 32*a^3*c^4)*x^8 + (3*b^7 - 26*a*b^5*c + 64*a^2*b^3*c^2 - 32*a^3*b*c^3)*x^6 + (3*a*b^6 - 26*a^2*b^4*c + 64*a^3*b^2*c^2 - 32*a^4*c^3)*x^4)*log(c*x^4 + b*x^2 + a) - 4*((3*b^6*c - 26*a*b^4*c^2 + 64*a^2*b^2*c^3 - 32*a^3*c^4)*x^8 + (3*b^7 - 26*a*b^5*c + 64*a^2*b^3*c^2 - 32*a^3*b*c^3)*x^6 + (3*a*b^6 - 26*a^2*b^4*c + 64*a^3*b^2*c^2 - 32*a^4*c^3)*x^4)*log(x))/((a^4*b^4*c - 8*a^5*b^2*c^2 + 16*a^6*c^3)*x^8 + (a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*x^6 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*x^4), -1/4*(a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2 - 2*(3*a*b^5*c - 23*a^2*b^3*c^2 + 44*a^3*b*c^3)*x^6 - (6*a*b^6 - 49*a^2*b^4*c + 108*a^3*b^2*c^2 - 32*a^4*c^3)*x^4 - 3*(a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*x^2 - 2*((3*b^5*c - 20*a*b^3*c^2 + 30*a^2*b*c^3)*x^8 + (3*b^6 - 20*a*b^4*c + 30*a^2*b^2*c^2)*x^6 + (3*a*b^5 - 20*a^2*b^3*c + 30*a^3*b*c^2)*x^4)*sqrt(-b^2 + 4*a*c)*arctan(-(2*c*x^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) + ((3*b^6*c - 26*a*b^4*c^2 + 64*a^2*b^2*c^3 - 32*a^3*c^4)*x^8 + (3*b^7 - 26*a*b^5*c + 64*a^2*b^3*c^2 - 32*a^3*b*c^3)*x^6 + (3*a*b^6 - 26*a^2*b^4*c + 64*a^3*b^2*c^2 - 32*a^4*c^3)*x^4)*log(c*x^4 + b*x^2 + a) - 4*((3*b^6*c - 26*a*b^4*c^2 + 64*a^2*b^2*c^3 - 32*a^3*c^4)*x^8 + (3*b^7 - 26*a*b^5*c + 64*a^2*b^3*c^2 - 32*a^3*b*c^3)*x^6 + (3*a*b^6 - 26*a^2*b^4*c + 64*a^3*b^2*c^2 - 32*a^4*c^3)*x^4)*log(x))/((a^4*b^4*c - 8*a^5*b^2*c^2 + 16*a^6*c^3)*x^8 + (a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*x^6 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*x^4)]","B",0
104,0,0,0,1.221845," ","integrate(x/(c*x^5+b*x^3+a*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{5} + b x^{3} + a x}}{c x^{4} + b x^{2} + a}, x\right)"," ",0,"integral(sqrt(c*x^5 + b*x^3 + a*x)/(c*x^4 + b*x^2 + a), x)","F",0
105,0,0,0,0.852762," ","integrate(x^(3/2)*(c*x^5+b*x^3+a*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{5} + b x^{3} + a x} x^{\frac{3}{2}}, x\right)"," ",0,"integral(sqrt(c*x^5 + b*x^3 + a*x)*x^(3/2), x)","F",0
106,1,232,0,1.043128," ","integrate(x^(1/2)*(c*x^5+b*x^3+a*x)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(b^{2} - 4 \, a c\right)} \sqrt{c} x \log\left(-\frac{8 \, c^{2} x^{5} + 8 \, b c x^{3} + 4 \, \sqrt{c x^{5} + b x^{3} + a x} {\left(2 \, c x^{2} + b\right)} \sqrt{c} \sqrt{x} + {\left(b^{2} + 4 \, a c\right)} x}{x}\right) - 4 \, \sqrt{c x^{5} + b x^{3} + a x} {\left(2 \, c^{2} x^{2} + b c\right)} \sqrt{x}}{32 \, c^{2} x}, \frac{{\left(b^{2} - 4 \, a c\right)} \sqrt{-c} x \arctan\left(\frac{\sqrt{c x^{5} + b x^{3} + a x} {\left(2 \, c x^{2} + b\right)} \sqrt{-c} \sqrt{x}}{2 \, {\left(c^{2} x^{5} + b c x^{3} + a c x\right)}}\right) + 2 \, \sqrt{c x^{5} + b x^{3} + a x} {\left(2 \, c^{2} x^{2} + b c\right)} \sqrt{x}}{16 \, c^{2} x}\right]"," ",0,"[-1/32*((b^2 - 4*a*c)*sqrt(c)*x*log(-(8*c^2*x^5 + 8*b*c*x^3 + 4*sqrt(c*x^5 + b*x^3 + a*x)*(2*c*x^2 + b)*sqrt(c)*sqrt(x) + (b^2 + 4*a*c)*x)/x) - 4*sqrt(c*x^5 + b*x^3 + a*x)*(2*c^2*x^2 + b*c)*sqrt(x))/(c^2*x), 1/16*((b^2 - 4*a*c)*sqrt(-c)*x*arctan(1/2*sqrt(c*x^5 + b*x^3 + a*x)*(2*c*x^2 + b)*sqrt(-c)*sqrt(x)/(c^2*x^5 + b*c*x^3 + a*c*x)) + 2*sqrt(c*x^5 + b*x^3 + a*x)*(2*c^2*x^2 + b*c)*sqrt(x))/(c^2*x)]","A",0
107,0,0,0,1.122497," ","integrate((c*x^5+b*x^3+a*x)^(1/2)/x^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{5} + b x^{3} + a x}}{\sqrt{x}}, x\right)"," ",0,"integral(sqrt(c*x^5 + b*x^3 + a*x)/sqrt(x), x)","F",0
108,1,666,0,1.395018," ","integrate((c*x^5+b*x^3+a*x)^(1/2)/x^(3/2),x, algorithm=""fricas"")","\left[\frac{b \sqrt{c} x \log\left(-\frac{8 \, c^{2} x^{5} + 8 \, b c x^{3} + 4 \, \sqrt{c x^{5} + b x^{3} + a x} {\left(2 \, c x^{2} + b\right)} \sqrt{c} \sqrt{x} + {\left(b^{2} + 4 \, a c\right)} x}{x}\right) + 2 \, \sqrt{a} c x \log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{5} + 8 \, a b x^{3} + 8 \, a^{2} x - 4 \, \sqrt{c x^{5} + b x^{3} + a x} {\left(b x^{2} + 2 \, a\right)} \sqrt{a} \sqrt{x}}{x^{5}}\right) + 4 \, \sqrt{c x^{5} + b x^{3} + a x} c \sqrt{x}}{8 \, c x}, -\frac{b \sqrt{-c} x \arctan\left(\frac{\sqrt{c x^{5} + b x^{3} + a x} {\left(2 \, c x^{2} + b\right)} \sqrt{-c} \sqrt{x}}{2 \, {\left(c^{2} x^{5} + b c x^{3} + a c x\right)}}\right) - \sqrt{a} c x \log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{5} + 8 \, a b x^{3} + 8 \, a^{2} x - 4 \, \sqrt{c x^{5} + b x^{3} + a x} {\left(b x^{2} + 2 \, a\right)} \sqrt{a} \sqrt{x}}{x^{5}}\right) - 2 \, \sqrt{c x^{5} + b x^{3} + a x} c \sqrt{x}}{4 \, c x}, \frac{4 \, \sqrt{-a} c x \arctan\left(\frac{\sqrt{c x^{5} + b x^{3} + a x} {\left(b x^{2} + 2 \, a\right)} \sqrt{-a} \sqrt{x}}{2 \, {\left(a c x^{5} + a b x^{3} + a^{2} x\right)}}\right) + b \sqrt{c} x \log\left(-\frac{8 \, c^{2} x^{5} + 8 \, b c x^{3} + 4 \, \sqrt{c x^{5} + b x^{3} + a x} {\left(2 \, c x^{2} + b\right)} \sqrt{c} \sqrt{x} + {\left(b^{2} + 4 \, a c\right)} x}{x}\right) + 4 \, \sqrt{c x^{5} + b x^{3} + a x} c \sqrt{x}}{8 \, c x}, \frac{2 \, \sqrt{-a} c x \arctan\left(\frac{\sqrt{c x^{5} + b x^{3} + a x} {\left(b x^{2} + 2 \, a\right)} \sqrt{-a} \sqrt{x}}{2 \, {\left(a c x^{5} + a b x^{3} + a^{2} x\right)}}\right) - b \sqrt{-c} x \arctan\left(\frac{\sqrt{c x^{5} + b x^{3} + a x} {\left(2 \, c x^{2} + b\right)} \sqrt{-c} \sqrt{x}}{2 \, {\left(c^{2} x^{5} + b c x^{3} + a c x\right)}}\right) + 2 \, \sqrt{c x^{5} + b x^{3} + a x} c \sqrt{x}}{4 \, c x}\right]"," ",0,"[1/8*(b*sqrt(c)*x*log(-(8*c^2*x^5 + 8*b*c*x^3 + 4*sqrt(c*x^5 + b*x^3 + a*x)*(2*c*x^2 + b)*sqrt(c)*sqrt(x) + (b^2 + 4*a*c)*x)/x) + 2*sqrt(a)*c*x*log(-((b^2 + 4*a*c)*x^5 + 8*a*b*x^3 + 8*a^2*x - 4*sqrt(c*x^5 + b*x^3 + a*x)*(b*x^2 + 2*a)*sqrt(a)*sqrt(x))/x^5) + 4*sqrt(c*x^5 + b*x^3 + a*x)*c*sqrt(x))/(c*x), -1/4*(b*sqrt(-c)*x*arctan(1/2*sqrt(c*x^5 + b*x^3 + a*x)*(2*c*x^2 + b)*sqrt(-c)*sqrt(x)/(c^2*x^5 + b*c*x^3 + a*c*x)) - sqrt(a)*c*x*log(-((b^2 + 4*a*c)*x^5 + 8*a*b*x^3 + 8*a^2*x - 4*sqrt(c*x^5 + b*x^3 + a*x)*(b*x^2 + 2*a)*sqrt(a)*sqrt(x))/x^5) - 2*sqrt(c*x^5 + b*x^3 + a*x)*c*sqrt(x))/(c*x), 1/8*(4*sqrt(-a)*c*x*arctan(1/2*sqrt(c*x^5 + b*x^3 + a*x)*(b*x^2 + 2*a)*sqrt(-a)*sqrt(x)/(a*c*x^5 + a*b*x^3 + a^2*x)) + b*sqrt(c)*x*log(-(8*c^2*x^5 + 8*b*c*x^3 + 4*sqrt(c*x^5 + b*x^3 + a*x)*(2*c*x^2 + b)*sqrt(c)*sqrt(x) + (b^2 + 4*a*c)*x)/x) + 4*sqrt(c*x^5 + b*x^3 + a*x)*c*sqrt(x))/(c*x), 1/4*(2*sqrt(-a)*c*x*arctan(1/2*sqrt(c*x^5 + b*x^3 + a*x)*(b*x^2 + 2*a)*sqrt(-a)*sqrt(x)/(a*c*x^5 + a*b*x^3 + a^2*x)) - b*sqrt(-c)*x*arctan(1/2*sqrt(c*x^5 + b*x^3 + a*x)*(2*c*x^2 + b)*sqrt(-c)*sqrt(x)/(c^2*x^5 + b*c*x^3 + a*c*x)) + 2*sqrt(c*x^5 + b*x^3 + a*x)*c*sqrt(x))/(c*x)]","A",0
109,1,396,0,1.281829," ","integrate(x^(3/2)*(c*x^5+b*x^3+a*x)^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} \sqrt{c} x \log\left(-\frac{8 \, c^{2} x^{5} + 8 \, b c x^{3} - 4 \, \sqrt{c x^{5} + b x^{3} + a x} {\left(2 \, c x^{2} + b\right)} \sqrt{c} \sqrt{x} + {\left(b^{2} + 4 \, a c\right)} x}{x}\right) + 4 \, {\left(128 \, c^{5} x^{8} + 176 \, b c^{4} x^{6} + 15 \, b^{4} c - 100 \, a b^{2} c^{2} + 128 \, a^{2} c^{3} + 8 \, {\left(b^{2} c^{3} + 32 \, a c^{4}\right)} x^{4} - 2 \, {\left(5 \, b^{3} c^{2} - 28 \, a b c^{3}\right)} x^{2}\right)} \sqrt{c x^{5} + b x^{3} + a x} \sqrt{x}}{5120 \, c^{4} x}, \frac{15 \, {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} \sqrt{-c} x \arctan\left(\frac{\sqrt{c x^{5} + b x^{3} + a x} {\left(2 \, c x^{2} + b\right)} \sqrt{-c} \sqrt{x}}{2 \, {\left(c^{2} x^{5} + b c x^{3} + a c x\right)}}\right) + 2 \, {\left(128 \, c^{5} x^{8} + 176 \, b c^{4} x^{6} + 15 \, b^{4} c - 100 \, a b^{2} c^{2} + 128 \, a^{2} c^{3} + 8 \, {\left(b^{2} c^{3} + 32 \, a c^{4}\right)} x^{4} - 2 \, {\left(5 \, b^{3} c^{2} - 28 \, a b c^{3}\right)} x^{2}\right)} \sqrt{c x^{5} + b x^{3} + a x} \sqrt{x}}{2560 \, c^{4} x}\right]"," ",0,"[1/5120*(15*(b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*sqrt(c)*x*log(-(8*c^2*x^5 + 8*b*c*x^3 - 4*sqrt(c*x^5 + b*x^3 + a*x)*(2*c*x^2 + b)*sqrt(c)*sqrt(x) + (b^2 + 4*a*c)*x)/x) + 4*(128*c^5*x^8 + 176*b*c^4*x^6 + 15*b^4*c - 100*a*b^2*c^2 + 128*a^2*c^3 + 8*(b^2*c^3 + 32*a*c^4)*x^4 - 2*(5*b^3*c^2 - 28*a*b*c^3)*x^2)*sqrt(c*x^5 + b*x^3 + a*x)*sqrt(x))/(c^4*x), 1/2560*(15*(b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*sqrt(-c)*x*arctan(1/2*sqrt(c*x^5 + b*x^3 + a*x)*(2*c*x^2 + b)*sqrt(-c)*sqrt(x)/(c^2*x^5 + b*c*x^3 + a*c*x)) + 2*(128*c^5*x^8 + 176*b*c^4*x^6 + 15*b^4*c - 100*a*b^2*c^2 + 128*a^2*c^3 + 8*(b^2*c^3 + 32*a*c^4)*x^4 - 2*(5*b^3*c^2 - 28*a*b*c^3)*x^2)*sqrt(c*x^5 + b*x^3 + a*x)*sqrt(x))/(c^4*x)]","A",0
110,0,0,0,0.952917," ","integrate((c*x^5+b*x^3+a*x)^(3/2)*x^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{5} + b x^{3} + a x\right)}^{\frac{3}{2}} \sqrt{x}, x\right)"," ",0,"integral((c*x^5 + b*x^3 + a*x)^(3/2)*sqrt(x), x)","F",0
111,1,332,0,1.019084," ","integrate((c*x^5+b*x^3+a*x)^(3/2)/x^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{c} x \log\left(-\frac{8 \, c^{2} x^{5} + 8 \, b c x^{3} + 4 \, \sqrt{c x^{5} + b x^{3} + a x} {\left(2 \, c x^{2} + b\right)} \sqrt{c} \sqrt{x} + {\left(b^{2} + 4 \, a c\right)} x}{x}\right) + 4 \, {\left(16 \, c^{4} x^{6} + 24 \, b c^{3} x^{4} - 3 \, b^{3} c + 20 \, a b c^{2} + 2 \, {\left(b^{2} c^{2} + 20 \, a c^{3}\right)} x^{2}\right)} \sqrt{c x^{5} + b x^{3} + a x} \sqrt{x}}{512 \, c^{3} x}, -\frac{3 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{-c} x \arctan\left(\frac{\sqrt{c x^{5} + b x^{3} + a x} {\left(2 \, c x^{2} + b\right)} \sqrt{-c} \sqrt{x}}{2 \, {\left(c^{2} x^{5} + b c x^{3} + a c x\right)}}\right) - 2 \, {\left(16 \, c^{4} x^{6} + 24 \, b c^{3} x^{4} - 3 \, b^{3} c + 20 \, a b c^{2} + 2 \, {\left(b^{2} c^{2} + 20 \, a c^{3}\right)} x^{2}\right)} \sqrt{c x^{5} + b x^{3} + a x} \sqrt{x}}{256 \, c^{3} x}\right]"," ",0,"[1/512*(3*(b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(c)*x*log(-(8*c^2*x^5 + 8*b*c*x^3 + 4*sqrt(c*x^5 + b*x^3 + a*x)*(2*c*x^2 + b)*sqrt(c)*sqrt(x) + (b^2 + 4*a*c)*x)/x) + 4*(16*c^4*x^6 + 24*b*c^3*x^4 - 3*b^3*c + 20*a*b*c^2 + 2*(b^2*c^2 + 20*a*c^3)*x^2)*sqrt(c*x^5 + b*x^3 + a*x)*sqrt(x))/(c^3*x), -1/256*(3*(b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(-c)*x*arctan(1/2*sqrt(c*x^5 + b*x^3 + a*x)*(2*c*x^2 + b)*sqrt(-c)*sqrt(x)/(c^2*x^5 + b*c*x^3 + a*c*x)) - 2*(16*c^4*x^6 + 24*b*c^3*x^4 - 3*b^3*c + 20*a*b*c^2 + 2*(b^2*c^2 + 20*a*c^3)*x^2)*sqrt(c*x^5 + b*x^3 + a*x)*sqrt(x))/(c^3*x)]","A",0
112,0,0,0,0.934002," ","integrate((c*x^5+b*x^3+a*x)^(3/2)/x^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{5} + b x^{3} + a x} {\left(c x^{4} + b x^{2} + a\right)}}{\sqrt{x}}, x\right)"," ",0,"integral(sqrt(c*x^5 + b*x^3 + a*x)*(c*x^4 + b*x^2 + a)/sqrt(x), x)","F",0
113,1,135,0,1.054543," ","integrate(x^(3/2)/(c*x^5+b*x^3+a*x)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(-\frac{8 \, c^{2} x^{5} + 8 \, b c x^{3} + 4 \, \sqrt{c x^{5} + b x^{3} + a x} {\left(2 \, c x^{2} + b\right)} \sqrt{c} \sqrt{x} + {\left(b^{2} + 4 \, a c\right)} x}{x}\right)}{4 \, \sqrt{c}}, -\frac{\sqrt{-c} \arctan\left(\frac{\sqrt{c x^{5} + b x^{3} + a x} {\left(2 \, c x^{2} + b\right)} \sqrt{-c} \sqrt{x}}{2 \, {\left(c^{2} x^{5} + b c x^{3} + a c x\right)}}\right)}{2 \, c}\right]"," ",0,"[1/4*log(-(8*c^2*x^5 + 8*b*c*x^3 + 4*sqrt(c*x^5 + b*x^3 + a*x)*(2*c*x^2 + b)*sqrt(c)*sqrt(x) + (b^2 + 4*a*c)*x)/x)/sqrt(c), -1/2*sqrt(-c)*arctan(1/2*sqrt(c*x^5 + b*x^3 + a*x)*(2*c*x^2 + b)*sqrt(-c)*sqrt(x)/(c^2*x^5 + b*c*x^3 + a*c*x))/c]","A",0
114,0,0,0,1.209898," ","integrate(x^(1/2)/(c*x^5+b*x^3+a*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x}}{\sqrt{c x^{5} + b x^{3} + a x}}, x\right)"," ",0,"integral(sqrt(x)/sqrt(c*x^5 + b*x^3 + a*x), x)","F",0
115,1,137,0,1.171102," ","integrate(1/x^(1/2)/(c*x^5+b*x^3+a*x)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{5} + 8 \, a b x^{3} + 8 \, a^{2} x - 4 \, \sqrt{c x^{5} + b x^{3} + a x} {\left(b x^{2} + 2 \, a\right)} \sqrt{a} \sqrt{x}}{x^{5}}\right)}{4 \, \sqrt{a}}, \frac{\sqrt{-a} \arctan\left(\frac{\sqrt{c x^{5} + b x^{3} + a x} {\left(b x^{2} + 2 \, a\right)} \sqrt{-a} \sqrt{x}}{2 \, {\left(a c x^{5} + a b x^{3} + a^{2} x\right)}}\right)}{2 \, a}\right]"," ",0,"[1/4*log(-((b^2 + 4*a*c)*x^5 + 8*a*b*x^3 + 8*a^2*x - 4*sqrt(c*x^5 + b*x^3 + a*x)*(b*x^2 + 2*a)*sqrt(a)*sqrt(x))/x^5)/sqrt(a), 1/2*sqrt(-a)*arctan(1/2*sqrt(c*x^5 + b*x^3 + a*x)*(b*x^2 + 2*a)*sqrt(-a)*sqrt(x)/(a*c*x^5 + a*b*x^3 + a^2*x))/a]","A",0
116,0,0,0,0.967393," ","integrate(1/x^(3/2)/(c*x^5+b*x^3+a*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{5} + b x^{3} + a x} \sqrt{x}}{c x^{7} + b x^{5} + a x^{3}}, x\right)"," ",0,"integral(sqrt(c*x^5 + b*x^3 + a*x)*sqrt(x)/(c*x^7 + b*x^5 + a*x^3), x)","F",0
117,0,0,0,1.170285," ","integrate(x^(3/2)/(c*x^5+b*x^3+a*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{5} + b x^{3} + a x} \sqrt{x}}{c^{2} x^{9} + 2 \, b c x^{7} + {\left(b^{2} + 2 \, a c\right)} x^{5} + 2 \, a b x^{3} + a^{2} x}, x\right)"," ",0,"integral(sqrt(c*x^5 + b*x^3 + a*x)*sqrt(x)/(c^2*x^9 + 2*b*c*x^7 + (b^2 + 2*a*c)*x^5 + 2*a*b*x^3 + a^2*x), x)","F",0
118,1,424,0,1.557427," ","integrate(x^(1/2)/(c*x^5+b*x^3+a*x)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(b^{2} c - 4 \, a c^{2}\right)} x^{5} + {\left(b^{3} - 4 \, a b c\right)} x^{3} + {\left(a b^{2} - 4 \, a^{2} c\right)} x\right)} \sqrt{a} \log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{5} + 8 \, a b x^{3} + 8 \, a^{2} x - 4 \, \sqrt{c x^{5} + b x^{3} + a x} {\left(b x^{2} + 2 \, a\right)} \sqrt{a} \sqrt{x}}{x^{5}}\right) + 4 \, \sqrt{c x^{5} + b x^{3} + a x} {\left(a b c x^{2} + a b^{2} - 2 \, a^{2} c\right)} \sqrt{x}}{4 \, {\left({\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} x^{5} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} x^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} x\right)}}, \frac{{\left({\left(b^{2} c - 4 \, a c^{2}\right)} x^{5} + {\left(b^{3} - 4 \, a b c\right)} x^{3} + {\left(a b^{2} - 4 \, a^{2} c\right)} x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{c x^{5} + b x^{3} + a x} {\left(b x^{2} + 2 \, a\right)} \sqrt{-a} \sqrt{x}}{2 \, {\left(a c x^{5} + a b x^{3} + a^{2} x\right)}}\right) + 2 \, \sqrt{c x^{5} + b x^{3} + a x} {\left(a b c x^{2} + a b^{2} - 2 \, a^{2} c\right)} \sqrt{x}}{2 \, {\left({\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} x^{5} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} x^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} x\right)}}\right]"," ",0,"[1/4*(((b^2*c - 4*a*c^2)*x^5 + (b^3 - 4*a*b*c)*x^3 + (a*b^2 - 4*a^2*c)*x)*sqrt(a)*log(-((b^2 + 4*a*c)*x^5 + 8*a*b*x^3 + 8*a^2*x - 4*sqrt(c*x^5 + b*x^3 + a*x)*(b*x^2 + 2*a)*sqrt(a)*sqrt(x))/x^5) + 4*sqrt(c*x^5 + b*x^3 + a*x)*(a*b*c*x^2 + a*b^2 - 2*a^2*c)*sqrt(x))/((a^2*b^2*c - 4*a^3*c^2)*x^5 + (a^2*b^3 - 4*a^3*b*c)*x^3 + (a^3*b^2 - 4*a^4*c)*x), 1/2*(((b^2*c - 4*a*c^2)*x^5 + (b^3 - 4*a*b*c)*x^3 + (a*b^2 - 4*a^2*c)*x)*sqrt(-a)*arctan(1/2*sqrt(c*x^5 + b*x^3 + a*x)*(b*x^2 + 2*a)*sqrt(-a)*sqrt(x)/(a*c*x^5 + a*b*x^3 + a^2*x)) + 2*sqrt(c*x^5 + b*x^3 + a*x)*(a*b*c*x^2 + a*b^2 - 2*a^2*c)*sqrt(x))/((a^2*b^2*c - 4*a^3*c^2)*x^5 + (a^2*b^3 - 4*a^3*b*c)*x^3 + (a^3*b^2 - 4*a^4*c)*x)]","B",0
119,0,0,0,1.292731," ","integrate(1/(c*x^5+b*x^3+a*x)^(3/2)/x^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{5} + b x^{3} + a x} \sqrt{x}}{c^{2} x^{11} + 2 \, b c x^{9} + {\left(b^{2} + 2 \, a c\right)} x^{7} + 2 \, a b x^{5} + a^{2} x^{3}}, x\right)"," ",0,"integral(sqrt(c*x^5 + b*x^3 + a*x)*sqrt(x)/(c^2*x^11 + 2*b*c*x^9 + (b^2 + 2*a*c)*x^7 + 2*a*b*x^5 + a^2*x^3), x)","F",0
120,1,508,0,1.340088," ","integrate(1/x^(3/2)/(c*x^5+b*x^3+a*x)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(b^{3} c - 4 \, a b c^{2}\right)} x^{7} + {\left(b^{4} - 4 \, a b^{2} c\right)} x^{5} + {\left(a b^{3} - 4 \, a^{2} b c\right)} x^{3}\right)} \sqrt{a} \log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{5} + 8 \, a b x^{3} + 8 \, a^{2} x + 4 \, \sqrt{c x^{5} + b x^{3} + a x} {\left(b x^{2} + 2 \, a\right)} \sqrt{a} \sqrt{x}}{x^{5}}\right) - 4 \, \sqrt{c x^{5} + b x^{3} + a x} {\left({\left(3 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + {\left(3 \, a b^{3} - 10 \, a^{2} b c\right)} x^{2}\right)} \sqrt{x}}{8 \, {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} x^{7} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} x^{5} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} x^{3}\right)}}, -\frac{3 \, {\left({\left(b^{3} c - 4 \, a b c^{2}\right)} x^{7} + {\left(b^{4} - 4 \, a b^{2} c\right)} x^{5} + {\left(a b^{3} - 4 \, a^{2} b c\right)} x^{3}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{c x^{5} + b x^{3} + a x} {\left(b x^{2} + 2 \, a\right)} \sqrt{-a} \sqrt{x}}{2 \, {\left(a c x^{5} + a b x^{3} + a^{2} x\right)}}\right) + 2 \, \sqrt{c x^{5} + b x^{3} + a x} {\left({\left(3 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + {\left(3 \, a b^{3} - 10 \, a^{2} b c\right)} x^{2}\right)} \sqrt{x}}{4 \, {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} x^{7} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} x^{5} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} x^{3}\right)}}\right]"," ",0,"[1/8*(3*((b^3*c - 4*a*b*c^2)*x^7 + (b^4 - 4*a*b^2*c)*x^5 + (a*b^3 - 4*a^2*b*c)*x^3)*sqrt(a)*log(-((b^2 + 4*a*c)*x^5 + 8*a*b*x^3 + 8*a^2*x + 4*sqrt(c*x^5 + b*x^3 + a*x)*(b*x^2 + 2*a)*sqrt(a)*sqrt(x))/x^5) - 4*sqrt(c*x^5 + b*x^3 + a*x)*((3*a*b^2*c - 8*a^2*c^2)*x^4 + a^2*b^2 - 4*a^3*c + (3*a*b^3 - 10*a^2*b*c)*x^2)*sqrt(x))/((a^3*b^2*c - 4*a^4*c^2)*x^7 + (a^3*b^3 - 4*a^4*b*c)*x^5 + (a^4*b^2 - 4*a^5*c)*x^3), -1/4*(3*((b^3*c - 4*a*b*c^2)*x^7 + (b^4 - 4*a*b^2*c)*x^5 + (a*b^3 - 4*a^2*b*c)*x^3)*sqrt(-a)*arctan(1/2*sqrt(c*x^5 + b*x^3 + a*x)*(b*x^2 + 2*a)*sqrt(-a)*sqrt(x)/(a*c*x^5 + a*b*x^3 + a^2*x)) + 2*sqrt(c*x^5 + b*x^3 + a*x)*((3*a*b^2*c - 8*a^2*c^2)*x^4 + a^2*b^2 - 4*a^3*c + (3*a*b^3 - 10*a^2*b*c)*x^2)*sqrt(x))/((a^3*b^2*c - 4*a^4*c^2)*x^7 + (a^3*b^3 - 4*a^4*b*c)*x^5 + (a^4*b^2 - 4*a^5*c)*x^3)]","A",0
121,1,83,0,1.077656," ","integrate(x^(-3/2+3/2*n)/(a*x^(-1+n)+b*x^n+c*x^(1+n))^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(2 \, c x^{2} + b x\right)} \sqrt{\frac{{\left(c x^{2} + b x + a\right)} x^{n + 1}}{x^{2}}}}{{\left(a b^{2} - 4 \, a^{2} c + {\left(b^{2} c - 4 \, a c^{2}\right)} x^{2} + {\left(b^{3} - 4 \, a b c\right)} x\right)} x^{\frac{1}{2} \, n + \frac{1}{2}}}"," ",0,"-2*(2*c*x^2 + b*x)*sqrt((c*x^2 + b*x + a)*x^(n + 1)/x^2)/((a*b^2 - 4*a^2*c + (b^2*c - 4*a*c^2)*x^2 + (b^3 - 4*a*b*c)*x)*x^(1/2*n + 1/2))","A",0
122,0,0,0,1.011790," ","integrate(x*(e*x^2+d)/(c*x^5+b*x^3+a*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{5} + b x^{3} + a x} {\left(e x^{2} + d\right)}}{c x^{4} + b x^{2} + a}, x\right)"," ",0,"integral(sqrt(c*x^5 + b*x^3 + a*x)*(e*x^2 + d)/(c*x^4 + b*x^2 + a), x)","F",0
123,1,55,0,1.015455," ","integrate(1/(x^6-3*x^4+3*x^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{6} \, \sqrt{3} \log\left(-\frac{3 \, x^{3} + 2 \, \sqrt{3} {\left(x^{3} - 2 \, x\right)} + 2 \, \sqrt{x^{6} - 3 \, x^{4} + 3 \, x^{2}} {\left(\sqrt{3} + 2\right)} - 6 \, x}{x^{3}}\right)"," ",0,"1/6*sqrt(3)*log(-(3*x^3 + 2*sqrt(3)*(x^3 - 2*x) + 2*sqrt(x^6 - 3*x^4 + 3*x^2)*(sqrt(3) + 2) - 6*x)/x^3)","A",0
124,1,55,0,1.226780," ","integrate(1/(x^2*(x^4-3*x^2+3))^(1/2),x, algorithm=""fricas"")","\frac{1}{6} \, \sqrt{3} \log\left(-\frac{3 \, x^{3} + 2 \, \sqrt{3} {\left(x^{3} - 2 \, x\right)} + 2 \, \sqrt{x^{6} - 3 \, x^{4} + 3 \, x^{2}} {\left(\sqrt{3} + 2\right)} - 6 \, x}{x^{3}}\right)"," ",0,"1/6*sqrt(3)*log(-(3*x^3 + 2*sqrt(3)*(x^3 - 2*x) + 2*sqrt(x^6 - 3*x^4 + 3*x^2)*(sqrt(3) + 2) - 6*x)/x^3)","A",0
125,1,55,0,0.883669," ","integrate(1/(1-(-x^2+1)^3)^(1/2),x, algorithm=""fricas"")","\frac{1}{6} \, \sqrt{3} \log\left(-\frac{3 \, x^{3} + 2 \, \sqrt{3} {\left(x^{3} - 2 \, x\right)} + 2 \, \sqrt{x^{6} - 3 \, x^{4} + 3 \, x^{2}} {\left(\sqrt{3} + 2\right)} - 6 \, x}{x^{3}}\right)"," ",0,"1/6*sqrt(3)*log(-(3*x^3 + 2*sqrt(3)*(x^3 - 2*x) + 2*sqrt(x^6 - 3*x^4 + 3*x^2)*(sqrt(3) + 2) - 6*x)/x^3)","A",0
126,1,70,0,1.090275," ","integrate((x^6-3*x^4+3*x^2)^(1/2),x, algorithm=""fricas"")","-\frac{12 \, x \log\left(-\frac{2 \, x^{3} - 3 \, x - 2 \, \sqrt{x^{6} - 3 \, x^{4} + 3 \, x^{2}}}{x}\right) - 8 \, \sqrt{x^{6} - 3 \, x^{4} + 3 \, x^{2}} {\left(2 \, x^{2} - 3\right)} - 9 \, x}{64 \, x}"," ",0,"-1/64*(12*x*log(-(2*x^3 - 3*x - 2*sqrt(x^6 - 3*x^4 + 3*x^2))/x) - 8*sqrt(x^6 - 3*x^4 + 3*x^2)*(2*x^2 - 3) - 9*x)/x","A",0
127,1,70,0,1.005833," ","integrate((x^2*(x^4-3*x^2+3))^(1/2),x, algorithm=""fricas"")","-\frac{12 \, x \log\left(-\frac{2 \, x^{3} - 3 \, x - 2 \, \sqrt{x^{6} - 3 \, x^{4} + 3 \, x^{2}}}{x}\right) - 8 \, \sqrt{x^{6} - 3 \, x^{4} + 3 \, x^{2}} {\left(2 \, x^{2} - 3\right)} - 9 \, x}{64 \, x}"," ",0,"-1/64*(12*x*log(-(2*x^3 - 3*x - 2*sqrt(x^6 - 3*x^4 + 3*x^2))/x) - 8*sqrt(x^6 - 3*x^4 + 3*x^2)*(2*x^2 - 3) - 9*x)/x","A",0
128,1,70,0,0.971395," ","integrate((1-(-x^2+1)^3)^(1/2),x, algorithm=""fricas"")","-\frac{12 \, x \log\left(-\frac{2 \, x^{3} - 3 \, x - 2 \, \sqrt{x^{6} - 3 \, x^{4} + 3 \, x^{2}}}{x}\right) - 8 \, \sqrt{x^{6} - 3 \, x^{4} + 3 \, x^{2}} {\left(2 \, x^{2} - 3\right)} - 9 \, x}{64 \, x}"," ",0,"-1/64*(12*x*log(-(2*x^3 - 3*x - 2*sqrt(x^6 - 3*x^4 + 3*x^2))/x) - 8*sqrt(x^6 - 3*x^4 + 3*x^2)*(2*x^2 - 3) - 9*x)/x","A",0
129,1,111,0,0.877830," ","integrate(1/x/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right)}{2 \, \sqrt{a}}, \frac{\sqrt{-a} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right)}{a}\right]"," ",0,"[1/2*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2)/sqrt(a), sqrt(-a)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2))/a]","A",0
130,1,130,0,0.957815," ","integrate(1/(x^2*(c*x^2+b*x+a))^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(-\frac{8 \, a b x^{2} + {\left(b^{2} + 4 \, a c\right)} x^{3} + 8 \, a^{2} x - 4 \, \sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)} \sqrt{a}}{x^{3}}\right)}{2 \, \sqrt{a}}, \frac{\sqrt{-a} \arctan\left(\frac{\sqrt{c x^{4} + b x^{3} + a x^{2}} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{3} + a b x^{2} + a^{2} x\right)}}\right)}{a}\right]"," ",0,"[1/2*log(-(8*a*b*x^2 + (b^2 + 4*a*c)*x^3 + 8*a^2*x - 4*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)*sqrt(a))/x^3)/sqrt(a), sqrt(-a)*arctan(1/2*sqrt(c*x^4 + b*x^3 + a*x^2)*(b*x + 2*a)*sqrt(-a)/(a*c*x^3 + a*b*x^2 + a^2*x))/a]","A",0
131,1,131,0,1.336372," ","integrate(1/x^(1/2)/(x*(c*x^2+b*x+a))^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{8 \, a b x^{2} + {\left(b^{2} + 4 \, a c\right)} x^{3} + 8 \, a^{2} x - 4 \, \sqrt{c x^{3} + b x^{2} + a x} {\left(b x + 2 \, a\right)} \sqrt{a} \sqrt{x}}{x^{3}}\right)}{2 \, \sqrt{a}}, \frac{\sqrt{-a} \arctan\left(\frac{\sqrt{c x^{3} + b x^{2} + a x} {\left(b x + 2 \, a\right)} \sqrt{-a} \sqrt{x}}{2 \, {\left(a c x^{3} + a b x^{2} + a^{2} x\right)}}\right)}{a}\right]"," ",0,"[1/2*log((8*a*b*x^2 + (b^2 + 4*a*c)*x^3 + 8*a^2*x - 4*sqrt(c*x^3 + b*x^2 + a*x)*(b*x + 2*a)*sqrt(a)*sqrt(x))/x^3)/sqrt(a), sqrt(-a)*arctan(1/2*sqrt(c*x^3 + b*x^2 + a*x)*(b*x + 2*a)*sqrt(-a)*sqrt(x)/(a*c*x^3 + a*b*x^2 + a^2*x))/a]","A",0
132,1,139,0,1.147537," ","integrate(x^(1/2)/(x^3*(c*x^2+b*x+a))^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{8 \, a b x^{3} + {\left(b^{2} + 4 \, a c\right)} x^{4} + 8 \, a^{2} x^{2} - 4 \, \sqrt{c x^{5} + b x^{4} + a x^{3}} {\left(b x + 2 \, a\right)} \sqrt{a} \sqrt{x}}{x^{4}}\right)}{2 \, \sqrt{a}}, \frac{\sqrt{-a} \arctan\left(\frac{\sqrt{c x^{5} + b x^{4} + a x^{3}} {\left(b x + 2 \, a\right)} \sqrt{-a} \sqrt{x}}{2 \, {\left(a c x^{4} + a b x^{3} + a^{2} x^{2}\right)}}\right)}{a}\right]"," ",0,"[1/2*log((8*a*b*x^3 + (b^2 + 4*a*c)*x^4 + 8*a^2*x^2 - 4*sqrt(c*x^5 + b*x^4 + a*x^3)*(b*x + 2*a)*sqrt(a)*sqrt(x))/x^4)/sqrt(a), sqrt(-a)*arctan(1/2*sqrt(c*x^5 + b*x^4 + a*x^3)*(b*x + 2*a)*sqrt(-a)*sqrt(x)/(a*c*x^4 + a*b*x^3 + a^2*x^2))/a]","A",0
133,1,124,0,1.367761," ","integrate(1/x/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{4} + 8 \, a b x^{2} - 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(b x^{2} + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{4}}\right)}{4 \, \sqrt{a}}, \frac{\sqrt{-a} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(b x^{2} + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{4} + a b x^{2} + a^{2}\right)}}\right)}{2 \, a}\right]"," ",0,"[1/4*log(-((b^2 + 4*a*c)*x^4 + 8*a*b*x^2 - 4*sqrt(c*x^4 + b*x^2 + a)*(b*x^2 + 2*a)*sqrt(a) + 8*a^2)/x^4)/sqrt(a), 1/2*sqrt(-a)*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(b*x^2 + 2*a)*sqrt(-a)/(a*c*x^4 + a*b*x^2 + a^2))/a]","A",0
134,1,135,0,1.315213," ","integrate(1/(x^2*(c*x^4+b*x^2+a))^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{5} + 8 \, a b x^{3} + 8 \, a^{2} x - 4 \, \sqrt{c x^{6} + b x^{4} + a x^{2}} {\left(b x^{2} + 2 \, a\right)} \sqrt{a}}{x^{5}}\right)}{4 \, \sqrt{a}}, \frac{\sqrt{-a} \arctan\left(\frac{\sqrt{c x^{6} + b x^{4} + a x^{2}} {\left(b x^{2} + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{5} + a b x^{3} + a^{2} x\right)}}\right)}{2 \, a}\right]"," ",0,"[1/4*log(-((b^2 + 4*a*c)*x^5 + 8*a*b*x^3 + 8*a^2*x - 4*sqrt(c*x^6 + b*x^4 + a*x^2)*(b*x^2 + 2*a)*sqrt(a))/x^5)/sqrt(a), 1/2*sqrt(-a)*arctan(1/2*sqrt(c*x^6 + b*x^4 + a*x^2)*(b*x^2 + 2*a)*sqrt(-a)/(a*c*x^5 + a*b*x^3 + a^2*x))/a]","A",0
135,1,137,0,1.363228," ","integrate(1/x^(1/2)/(x*(c*x^4+b*x^2+a))^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{5} + 8 \, a b x^{3} + 8 \, a^{2} x - 4 \, \sqrt{c x^{5} + b x^{3} + a x} {\left(b x^{2} + 2 \, a\right)} \sqrt{a} \sqrt{x}}{x^{5}}\right)}{4 \, \sqrt{a}}, \frac{\sqrt{-a} \arctan\left(\frac{\sqrt{c x^{5} + b x^{3} + a x} {\left(b x^{2} + 2 \, a\right)} \sqrt{-a} \sqrt{x}}{2 \, {\left(a c x^{5} + a b x^{3} + a^{2} x\right)}}\right)}{2 \, a}\right]"," ",0,"[1/4*log(-((b^2 + 4*a*c)*x^5 + 8*a*b*x^3 + 8*a^2*x - 4*sqrt(c*x^5 + b*x^3 + a*x)*(b*x^2 + 2*a)*sqrt(a)*sqrt(x))/x^5)/sqrt(a), 1/2*sqrt(-a)*arctan(1/2*sqrt(c*x^5 + b*x^3 + a*x)*(b*x^2 + 2*a)*sqrt(-a)*sqrt(x)/(a*c*x^5 + a*b*x^3 + a^2*x))/a]","A",0
136,1,145,0,1.193619," ","integrate(x^(1/2)/(x^3*(c*x^4+b*x^2+a))^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{6} + 8 \, a b x^{4} + 8 \, a^{2} x^{2} - 4 \, \sqrt{c x^{7} + b x^{5} + a x^{3}} {\left(b x^{2} + 2 \, a\right)} \sqrt{a} \sqrt{x}}{x^{6}}\right)}{4 \, \sqrt{a}}, \frac{\sqrt{-a} \arctan\left(\frac{\sqrt{c x^{7} + b x^{5} + a x^{3}} {\left(b x^{2} + 2 \, a\right)} \sqrt{-a} \sqrt{x}}{2 \, {\left(a c x^{6} + a b x^{4} + a^{2} x^{2}\right)}}\right)}{2 \, a}\right]"," ",0,"[1/4*log(-((b^2 + 4*a*c)*x^6 + 8*a*b*x^4 + 8*a^2*x^2 - 4*sqrt(c*x^7 + b*x^5 + a*x^3)*(b*x^2 + 2*a)*sqrt(a)*sqrt(x))/x^6)/sqrt(a), 1/2*sqrt(-a)*arctan(1/2*sqrt(c*x^7 + b*x^5 + a*x^3)*(b*x^2 + 2*a)*sqrt(-a)*sqrt(x)/(a*c*x^6 + a*b*x^4 + a^2*x^2))/a]","A",0
137,1,47,0,1.152174," ","integrate(1/x/(x^4-3*x^2+3)^(1/2),x, algorithm=""fricas"")","\frac{1}{6} \, \sqrt{3} \log\left(-\frac{3 \, x^{2} + 2 \, \sqrt{3} {\left(x^{2} - 2\right)} + 2 \, \sqrt{x^{4} - 3 \, x^{2} + 3} {\left(\sqrt{3} + 2\right)} - 6}{x^{2}}\right)"," ",0,"1/6*sqrt(3)*log(-(3*x^2 + 2*sqrt(3)*(x^2 - 2) + 2*sqrt(x^4 - 3*x^2 + 3)*(sqrt(3) + 2) - 6)/x^2)","A",0
138,1,55,0,1.051805," ","integrate(1/(x^2*(x^4-3*x^2+3))^(1/2),x, algorithm=""fricas"")","\frac{1}{6} \, \sqrt{3} \log\left(-\frac{3 \, x^{3} + 2 \, \sqrt{3} {\left(x^{3} - 2 \, x\right)} + 2 \, \sqrt{x^{6} - 3 \, x^{4} + 3 \, x^{2}} {\left(\sqrt{3} + 2\right)} - 6 \, x}{x^{3}}\right)"," ",0,"1/6*sqrt(3)*log(-(3*x^3 + 2*sqrt(3)*(x^3 - 2*x) + 2*sqrt(x^6 - 3*x^4 + 3*x^2)*(sqrt(3) + 2) - 6*x)/x^3)","A",0
139,1,49,0,1.156789," ","integrate(1/x^(1/2)/(x*(x^2-3*x+3))^(1/2),x, algorithm=""fricas"")","\frac{1}{6} \, \sqrt{3} \log\left(\frac{7 \, x^{3} + 4 \, \sqrt{3} \sqrt{x^{3} - 3 \, x^{2} + 3 \, x} {\left(x - 2\right)} \sqrt{x} - 24 \, x^{2} + 24 \, x}{x^{3}}\right)"," ",0,"1/6*sqrt(3)*log((7*x^3 + 4*sqrt(3)*sqrt(x^3 - 3*x^2 + 3*x)*(x - 2)*sqrt(x) - 24*x^2 + 24*x)/x^3)","A",0
140,-2,0,0,0.000000," ","integrate(x^(-1+1/2*q)/(b*x^n+c*x^(2*n-q)+a*x^q)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
