1,1,177,0,0.509734," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/4),x, algorithm=""fricas"")","\left[\frac{3 \, a^{2} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{\frac{1}{4}} \sqrt{b} x - a\right) + 2 \, {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{\frac{1}{4}} {\left(2 \, b^{2} x^{3} + 5 \, a b x\right)}}{16 \, b}, -\frac{3 \, a^{2} \sqrt{-b} \arctan\left(\frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{\frac{1}{4}} \sqrt{-b} x}{b x^{2} + a}\right) - {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{\frac{1}{4}} {\left(2 \, b^{2} x^{3} + 5 \, a b x\right)}}{8 \, b}\right]"," ",0,"[1/16*(3*a^2*sqrt(b)*log(-2*b*x^2 - 2*(b^2*x^4 + 2*a*b*x^2 + a^2)^(1/4)*sqrt(b)*x - a) + 2*(b^2*x^4 + 2*a*b*x^2 + a^2)^(1/4)*(2*b^2*x^3 + 5*a*b*x))/b, -1/8*(3*a^2*sqrt(-b)*arctan((b^2*x^4 + 2*a*b*x^2 + a^2)^(1/4)*sqrt(-b)*x/(b*x^2 + a)) - (b^2*x^4 + 2*a*b*x^2 + a^2)^(1/4)*(2*b^2*x^3 + 5*a*b*x))/b]","A",0
2,1,147,0,0.717003," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(1/4),x, algorithm=""fricas"")","\left[\frac{a \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{\frac{1}{4}} \sqrt{b} x - a\right) + 2 \, {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{\frac{1}{4}} b x}{4 \, b}, -\frac{a \sqrt{-b} \arctan\left(\frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{\frac{1}{4}} \sqrt{-b} x}{b x^{2} + a}\right) - {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{\frac{1}{4}} b x}{2 \, b}\right]"," ",0,"[1/4*(a*sqrt(b)*log(-2*b*x^2 - 2*(b^2*x^4 + 2*a*b*x^2 + a^2)^(1/4)*sqrt(b)*x - a) + 2*(b^2*x^4 + 2*a*b*x^2 + a^2)^(1/4)*b*x)/b, -1/2*(a*sqrt(-b)*arctan((b^2*x^4 + 2*a*b*x^2 + a^2)^(1/4)*sqrt(-b)*x/(b*x^2 + a)) - (b^2*x^4 + 2*a*b*x^2 + a^2)^(1/4)*b*x)/b]","A",0
3,1,90,0,0.985495," ","integrate(1/(b^2*x^4+2*a*b*x^2+a^2)^(1/4),x, algorithm=""fricas"")","\left[\frac{\log\left(-2 \, b x^{2} - 2 \, {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{\frac{1}{4}} \sqrt{b} x - a\right)}{2 \, \sqrt{b}}, -\frac{\sqrt{-b} \arctan\left(\frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{\frac{1}{4}} \sqrt{-b} x}{b x^{2} + a}\right)}{b}\right]"," ",0,"[1/2*log(-2*b*x^2 - 2*(b^2*x^4 + 2*a*b*x^2 + a^2)^(1/4)*sqrt(b)*x - a)/sqrt(b), -sqrt(-b)*arctan((b^2*x^4 + 2*a*b*x^2 + a^2)^(1/4)*sqrt(-b)*x/(b*x^2 + a))/b]","A",0
4,1,34,0,0.871002," ","integrate(1/(b^2*x^4+2*a*b*x^2+a^2)^(3/4),x, algorithm=""fricas"")","\frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{\frac{1}{4}} x}{a b x^{2} + a^{2}}"," ",0,"(b^2*x^4 + 2*a*b*x^2 + a^2)^(1/4)*x/(a*b*x^2 + a^2)","A",0
5,1,58,0,0.501243," ","integrate(1/(b^2*x^4+2*a*b*x^2+a^2)^(5/4),x, algorithm=""fricas"")","\frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{\frac{1}{4}} {\left(2 \, b x^{3} + 3 \, a x\right)}}{3 \, {\left(a^{2} b^{2} x^{4} + 2 \, a^{3} b x^{2} + a^{4}\right)}}"," ",0,"1/3*(b^2*x^4 + 2*a*b*x^2 + a^2)^(1/4)*(2*b*x^3 + 3*a*x)/(a^2*b^2*x^4 + 2*a^3*b*x^2 + a^4)","A",0
6,1,80,0,0.776131," ","integrate(1/(b^2*x^4+2*a*b*x^2+a^2)^(7/4),x, algorithm=""fricas"")","\frac{{\left(8 \, b^{2} x^{5} + 20 \, a b x^{3} + 15 \, a^{2} x\right)} {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{\frac{1}{4}}}{15 \, {\left(a^{3} b^{3} x^{6} + 3 \, a^{4} b^{2} x^{4} + 3 \, a^{5} b x^{2} + a^{6}\right)}}"," ",0,"1/15*(8*b^2*x^5 + 20*a*b*x^3 + 15*a^2*x)*(b^2*x^4 + 2*a*b*x^2 + a^2)^(1/4)/(a^3*b^3*x^6 + 3*a^4*b^2*x^4 + 3*a^5*b*x^2 + a^6)","A",0
7,1,102,0,0.846051," ","integrate(1/(b^2*x^4+2*a*b*x^2+a^2)^(9/4),x, algorithm=""fricas"")","\frac{{\left(16 \, b^{3} x^{7} + 56 \, a b^{2} x^{5} + 70 \, a^{2} b x^{3} + 35 \, a^{3} x\right)} {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{\frac{1}{4}}}{35 \, {\left(a^{4} b^{4} x^{8} + 4 \, a^{5} b^{3} x^{6} + 6 \, a^{6} b^{2} x^{4} + 4 \, a^{7} b x^{2} + a^{8}\right)}}"," ",0,"1/35*(16*b^3*x^7 + 56*a*b^2*x^5 + 70*a^2*b*x^3 + 35*a^3*x)*(b^2*x^4 + 2*a*b*x^2 + a^2)^(1/4)/(a^4*b^4*x^8 + 4*a^5*b^3*x^6 + 6*a^6*b^2*x^4 + 4*a^7*b*x^2 + a^8)","A",0
8,1,583,0,0.667717," ","integrate(1/(x^4+2*a*x^2+a^2+b),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{\frac{{\left(a^{2} b + b^{2}\right)} \sqrt{-\frac{1}{a^{4} b + 2 \, a^{2} b^{2} + b^{3}}} + a}{a^{2} b + b^{2}}} \log\left({\left({\left(a^{3} b + a b^{2}\right)} \sqrt{-\frac{1}{a^{4} b + 2 \, a^{2} b^{2} + b^{3}}} + b\right)} \sqrt{\frac{{\left(a^{2} b + b^{2}\right)} \sqrt{-\frac{1}{a^{4} b + 2 \, a^{2} b^{2} + b^{3}}} + a}{a^{2} b + b^{2}}} + x\right) - \frac{1}{4} \, \sqrt{\frac{{\left(a^{2} b + b^{2}\right)} \sqrt{-\frac{1}{a^{4} b + 2 \, a^{2} b^{2} + b^{3}}} + a}{a^{2} b + b^{2}}} \log\left(-{\left({\left(a^{3} b + a b^{2}\right)} \sqrt{-\frac{1}{a^{4} b + 2 \, a^{2} b^{2} + b^{3}}} + b\right)} \sqrt{\frac{{\left(a^{2} b + b^{2}\right)} \sqrt{-\frac{1}{a^{4} b + 2 \, a^{2} b^{2} + b^{3}}} + a}{a^{2} b + b^{2}}} + x\right) - \frac{1}{4} \, \sqrt{-\frac{{\left(a^{2} b + b^{2}\right)} \sqrt{-\frac{1}{a^{4} b + 2 \, a^{2} b^{2} + b^{3}}} - a}{a^{2} b + b^{2}}} \log\left({\left({\left(a^{3} b + a b^{2}\right)} \sqrt{-\frac{1}{a^{4} b + 2 \, a^{2} b^{2} + b^{3}}} - b\right)} \sqrt{-\frac{{\left(a^{2} b + b^{2}\right)} \sqrt{-\frac{1}{a^{4} b + 2 \, a^{2} b^{2} + b^{3}}} - a}{a^{2} b + b^{2}}} + x\right) + \frac{1}{4} \, \sqrt{-\frac{{\left(a^{2} b + b^{2}\right)} \sqrt{-\frac{1}{a^{4} b + 2 \, a^{2} b^{2} + b^{3}}} - a}{a^{2} b + b^{2}}} \log\left(-{\left({\left(a^{3} b + a b^{2}\right)} \sqrt{-\frac{1}{a^{4} b + 2 \, a^{2} b^{2} + b^{3}}} - b\right)} \sqrt{-\frac{{\left(a^{2} b + b^{2}\right)} \sqrt{-\frac{1}{a^{4} b + 2 \, a^{2} b^{2} + b^{3}}} - a}{a^{2} b + b^{2}}} + x\right)"," ",0,"1/4*sqrt(((a^2*b + b^2)*sqrt(-1/(a^4*b + 2*a^2*b^2 + b^3)) + a)/(a^2*b + b^2))*log(((a^3*b + a*b^2)*sqrt(-1/(a^4*b + 2*a^2*b^2 + b^3)) + b)*sqrt(((a^2*b + b^2)*sqrt(-1/(a^4*b + 2*a^2*b^2 + b^3)) + a)/(a^2*b + b^2)) + x) - 1/4*sqrt(((a^2*b + b^2)*sqrt(-1/(a^4*b + 2*a^2*b^2 + b^3)) + a)/(a^2*b + b^2))*log(-((a^3*b + a*b^2)*sqrt(-1/(a^4*b + 2*a^2*b^2 + b^3)) + b)*sqrt(((a^2*b + b^2)*sqrt(-1/(a^4*b + 2*a^2*b^2 + b^3)) + a)/(a^2*b + b^2)) + x) - 1/4*sqrt(-((a^2*b + b^2)*sqrt(-1/(a^4*b + 2*a^2*b^2 + b^3)) - a)/(a^2*b + b^2))*log(((a^3*b + a*b^2)*sqrt(-1/(a^4*b + 2*a^2*b^2 + b^3)) - b)*sqrt(-((a^2*b + b^2)*sqrt(-1/(a^4*b + 2*a^2*b^2 + b^3)) - a)/(a^2*b + b^2)) + x) + 1/4*sqrt(-((a^2*b + b^2)*sqrt(-1/(a^4*b + 2*a^2*b^2 + b^3)) - a)/(a^2*b + b^2))*log(-((a^3*b + a*b^2)*sqrt(-1/(a^4*b + 2*a^2*b^2 + b^3)) - b)*sqrt(-((a^2*b + b^2)*sqrt(-1/(a^4*b + 2*a^2*b^2 + b^3)) - a)/(a^2*b + b^2)) + x)","B",0
9,1,269,0,0.808898," ","integrate(1/(x^4+2*a*x^2+a^2-1),x, algorithm=""fricas"")","\left[-\frac{{\left(a - 1\right)} \sqrt{-a - 1} \log\left(\frac{x^{2} + 2 \, \sqrt{-a - 1} x - a - 1}{x^{2} + a + 1}\right) + {\left(a + 1\right)} \sqrt{-a + 1} \log\left(\frac{x^{2} - 2 \, \sqrt{-a + 1} x - a + 1}{x^{2} + a - 1}\right)}{4 \, {\left(a^{2} - 1\right)}}, \frac{2 \, {\left(a + 1\right)} \sqrt{a - 1} \arctan\left(\frac{x}{\sqrt{a - 1}}\right) - {\left(a - 1\right)} \sqrt{-a - 1} \log\left(\frac{x^{2} + 2 \, \sqrt{-a - 1} x - a - 1}{x^{2} + a + 1}\right)}{4 \, {\left(a^{2} - 1\right)}}, -\frac{2 \, \sqrt{a + 1} {\left(a - 1\right)} \arctan\left(\frac{x}{\sqrt{a + 1}}\right) + {\left(a + 1\right)} \sqrt{-a + 1} \log\left(\frac{x^{2} - 2 \, \sqrt{-a + 1} x - a + 1}{x^{2} + a - 1}\right)}{4 \, {\left(a^{2} - 1\right)}}, -\frac{\sqrt{a + 1} {\left(a - 1\right)} \arctan\left(\frac{x}{\sqrt{a + 1}}\right) - {\left(a + 1\right)} \sqrt{a - 1} \arctan\left(\frac{x}{\sqrt{a - 1}}\right)}{2 \, {\left(a^{2} - 1\right)}}\right]"," ",0,"[-1/4*((a - 1)*sqrt(-a - 1)*log((x^2 + 2*sqrt(-a - 1)*x - a - 1)/(x^2 + a + 1)) + (a + 1)*sqrt(-a + 1)*log((x^2 - 2*sqrt(-a + 1)*x - a + 1)/(x^2 + a - 1)))/(a^2 - 1), 1/4*(2*(a + 1)*sqrt(a - 1)*arctan(x/sqrt(a - 1)) - (a - 1)*sqrt(-a - 1)*log((x^2 + 2*sqrt(-a - 1)*x - a - 1)/(x^2 + a + 1)))/(a^2 - 1), -1/4*(2*sqrt(a + 1)*(a - 1)*arctan(x/sqrt(a + 1)) + (a + 1)*sqrt(-a + 1)*log((x^2 - 2*sqrt(-a + 1)*x - a + 1)/(x^2 + a - 1)))/(a^2 - 1), -1/2*(sqrt(a + 1)*(a - 1)*arctan(x/sqrt(a + 1)) - (a + 1)*sqrt(a - 1)*arctan(x/sqrt(a - 1)))/(a^2 - 1)]","A",0
10,1,613,0,1.339469," ","integrate(1/(x^4+2*a*x^2+a^2+1),x, algorithm=""fricas"")","\frac{\sqrt{2 \, a^{2} - \frac{2 \, {\left(a^{3} + a\right)}}{\sqrt{a^{2} + 1}} + 2} {\left(\frac{a}{\sqrt{a^{2} + 1}} + 1\right)} \log\left(x^{2} + \frac{\sqrt{2 \, a^{2} - \frac{2 \, {\left(a^{3} + a\right)}}{\sqrt{a^{2} + 1}} + 2} x}{{\left(a^{2} + 1\right)}^{\frac{1}{4}}} + \sqrt{a^{2} + 1}\right)}{8 \, {\left(a^{2} + 1\right)}^{\frac{1}{4}}} - \frac{\sqrt{2 \, a^{2} - \frac{2 \, {\left(a^{3} + a\right)}}{\sqrt{a^{2} + 1}} + 2} {\left(\frac{a}{\sqrt{a^{2} + 1}} + 1\right)} \log\left(x^{2} - \frac{\sqrt{2 \, a^{2} - \frac{2 \, {\left(a^{3} + a\right)}}{\sqrt{a^{2} + 1}} + 2} x}{{\left(a^{2} + 1\right)}^{\frac{1}{4}}} + \sqrt{a^{2} + 1}\right)}{8 \, {\left(a^{2} + 1\right)}^{\frac{1}{4}}} - \frac{\sqrt{2 \, a^{2} - \frac{2 \, {\left(a^{3} + a\right)}}{\sqrt{a^{2} + 1}} + 2} {\left(a^{2} + 1\right)}^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{a^{4} + 2 \, a^{2} + 1} \sqrt{2 \, a^{2} - \frac{2 \, {\left(a^{3} + a\right)}}{\sqrt{a^{2} + 1}} + 2} x}{{\left(a^{2} + 1\right)}^{\frac{5}{4}}} + \frac{a^{3} + a}{\sqrt{a^{4} + 2 \, a^{2} + 1}} + \frac{\sqrt{a^{4} + 2 \, a^{2} + 1} \sqrt{2 \, a^{2} - \frac{2 \, {\left(a^{3} + a\right)}}{\sqrt{a^{2} + 1}} + 2} \sqrt{x^{2} + \frac{\sqrt{2 \, a^{2} - \frac{2 \, {\left(a^{3} + a\right)}}{\sqrt{a^{2} + 1}} + 2} x}{{\left(a^{2} + 1\right)}^{\frac{1}{4}}} + \sqrt{a^{2} + 1}}}{{\left(a^{2} + 1\right)}^{\frac{5}{4}}} - \frac{\sqrt{a^{4} + 2 \, a^{2} + 1}}{\sqrt{a^{2} + 1}}\right)}{2 \, \sqrt{a^{4} + 2 \, a^{2} + 1}} - \frac{\sqrt{2 \, a^{2} - \frac{2 \, {\left(a^{3} + a\right)}}{\sqrt{a^{2} + 1}} + 2} {\left(a^{2} + 1\right)}^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{a^{4} + 2 \, a^{2} + 1} \sqrt{2 \, a^{2} - \frac{2 \, {\left(a^{3} + a\right)}}{\sqrt{a^{2} + 1}} + 2} x}{{\left(a^{2} + 1\right)}^{\frac{5}{4}}} - \frac{a^{3} + a}{\sqrt{a^{4} + 2 \, a^{2} + 1}} + \frac{\sqrt{a^{4} + 2 \, a^{2} + 1} \sqrt{2 \, a^{2} - \frac{2 \, {\left(a^{3} + a\right)}}{\sqrt{a^{2} + 1}} + 2} \sqrt{x^{2} - \frac{\sqrt{2 \, a^{2} - \frac{2 \, {\left(a^{3} + a\right)}}{\sqrt{a^{2} + 1}} + 2} x}{{\left(a^{2} + 1\right)}^{\frac{1}{4}}} + \sqrt{a^{2} + 1}}}{{\left(a^{2} + 1\right)}^{\frac{5}{4}}} + \frac{\sqrt{a^{4} + 2 \, a^{2} + 1}}{\sqrt{a^{2} + 1}}\right)}{2 \, \sqrt{a^{4} + 2 \, a^{2} + 1}}"," ",0,"1/8*sqrt(2*a^2 - 2*(a^3 + a)/sqrt(a^2 + 1) + 2)*(a/sqrt(a^2 + 1) + 1)*log(x^2 + sqrt(2*a^2 - 2*(a^3 + a)/sqrt(a^2 + 1) + 2)*x/(a^2 + 1)^(1/4) + sqrt(a^2 + 1))/(a^2 + 1)^(1/4) - 1/8*sqrt(2*a^2 - 2*(a^3 + a)/sqrt(a^2 + 1) + 2)*(a/sqrt(a^2 + 1) + 1)*log(x^2 - sqrt(2*a^2 - 2*(a^3 + a)/sqrt(a^2 + 1) + 2)*x/(a^2 + 1)^(1/4) + sqrt(a^2 + 1))/(a^2 + 1)^(1/4) - 1/2*sqrt(2*a^2 - 2*(a^3 + a)/sqrt(a^2 + 1) + 2)*(a^2 + 1)^(1/4)*arctan(-sqrt(a^4 + 2*a^2 + 1)*sqrt(2*a^2 - 2*(a^3 + a)/sqrt(a^2 + 1) + 2)*x/(a^2 + 1)^(5/4) + (a^3 + a)/sqrt(a^4 + 2*a^2 + 1) + sqrt(a^4 + 2*a^2 + 1)*sqrt(2*a^2 - 2*(a^3 + a)/sqrt(a^2 + 1) + 2)*sqrt(x^2 + sqrt(2*a^2 - 2*(a^3 + a)/sqrt(a^2 + 1) + 2)*x/(a^2 + 1)^(1/4) + sqrt(a^2 + 1))/(a^2 + 1)^(5/4) - sqrt(a^4 + 2*a^2 + 1)/sqrt(a^2 + 1))/sqrt(a^4 + 2*a^2 + 1) - 1/2*sqrt(2*a^2 - 2*(a^3 + a)/sqrt(a^2 + 1) + 2)*(a^2 + 1)^(1/4)*arctan(-sqrt(a^4 + 2*a^2 + 1)*sqrt(2*a^2 - 2*(a^3 + a)/sqrt(a^2 + 1) + 2)*x/(a^2 + 1)^(5/4) - (a^3 + a)/sqrt(a^4 + 2*a^2 + 1) + sqrt(a^4 + 2*a^2 + 1)*sqrt(2*a^2 - 2*(a^3 + a)/sqrt(a^2 + 1) + 2)*sqrt(x^2 - sqrt(2*a^2 - 2*(a^3 + a)/sqrt(a^2 + 1) + 2)*x/(a^2 + 1)^(1/4) + sqrt(a^2 + 1))/(a^2 + 1)^(5/4) + sqrt(a^4 + 2*a^2 + 1)/sqrt(a^2 + 1))/sqrt(a^4 + 2*a^2 + 1)","B",0
11,1,25,0,0.914375," ","integrate(1/(x^4-5*x^2+4),x, algorithm=""fricas"")","-\frac{1}{12} \, \log\left(x + 2\right) + \frac{1}{6} \, \log\left(x + 1\right) - \frac{1}{6} \, \log\left(x - 1\right) + \frac{1}{12} \, \log\left(x - 2\right)"," ",0,"-1/12*log(x + 2) + 1/6*log(x + 1) - 1/6*log(x - 1) + 1/12*log(x - 2)","B",0
12,1,17,0,1.156943," ","integrate(1/(x^4+4*x^2+3),x, algorithm=""fricas"")","-\frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} x\right) + \frac{1}{2} \, \arctan\left(x\right)"," ",0,"-1/6*sqrt(3)*arctan(1/3*sqrt(3)*x) + 1/2*arctan(x)","A",0
13,1,53,0,1.102023," ","integrate(1/(x^4+5*x^2+9),x, algorithm=""fricas"")","\frac{1}{66} \, \sqrt{11} \arctan\left(\frac{1}{11} \, \sqrt{11} {\left(2 \, x + 1\right)}\right) + \frac{1}{66} \, \sqrt{11} \arctan\left(\frac{1}{11} \, \sqrt{11} {\left(2 \, x - 1\right)}\right) + \frac{1}{12} \, \log\left(x^{2} + x + 3\right) - \frac{1}{12} \, \log\left(x^{2} - x + 3\right)"," ",0,"1/66*sqrt(11)*arctan(1/11*sqrt(11)*(2*x + 1)) + 1/66*sqrt(11)*arctan(1/11*sqrt(11)*(2*x - 1)) + 1/12*log(x^2 + x + 3) - 1/12*log(x^2 - x + 3)","A",0
14,1,159,0,1.636966," ","integrate(1/(x^4-x^2+1),x, algorithm=""fricas"")","-\frac{1}{6} \, \sqrt{6} \sqrt{3} \sqrt{2} \arctan\left(-\frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{2} x + \frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{\sqrt{6} \sqrt{2} x + 2 \, x^{2} + 2} - \sqrt{3}\right) - \frac{1}{6} \, \sqrt{6} \sqrt{3} \sqrt{2} \arctan\left(-\frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{2} x + \frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{-\sqrt{6} \sqrt{2} x + 2 \, x^{2} + 2} + \sqrt{3}\right) + \frac{1}{24} \, \sqrt{6} \sqrt{2} \log\left(\sqrt{6} \sqrt{2} x + 2 \, x^{2} + 2\right) - \frac{1}{24} \, \sqrt{6} \sqrt{2} \log\left(-\sqrt{6} \sqrt{2} x + 2 \, x^{2} + 2\right)"," ",0,"-1/6*sqrt(6)*sqrt(3)*sqrt(2)*arctan(-1/3*sqrt(6)*sqrt(3)*sqrt(2)*x + 1/3*sqrt(6)*sqrt(3)*sqrt(sqrt(6)*sqrt(2)*x + 2*x^2 + 2) - sqrt(3)) - 1/6*sqrt(6)*sqrt(3)*sqrt(2)*arctan(-1/3*sqrt(6)*sqrt(3)*sqrt(2)*x + 1/3*sqrt(6)*sqrt(3)*sqrt(-sqrt(6)*sqrt(2)*x + 2*x^2 + 2) + sqrt(3)) + 1/24*sqrt(6)*sqrt(2)*log(sqrt(6)*sqrt(2)*x + 2*x^2 + 2) - 1/24*sqrt(6)*sqrt(2)*log(-sqrt(6)*sqrt(2)*x + 2*x^2 + 2)","B",0
15,1,247,0,0.816016," ","integrate(1/(x^4+2*x^2+2),x, algorithm=""fricas"")","\frac{1}{16} \cdot 2^{\frac{1}{4}} {\left(\sqrt{2} + 1\right)} \sqrt{-2 \, \sqrt{2} + 4} \log\left(2^{\frac{3}{4}} x \sqrt{-2 \, \sqrt{2} + 4} + 2 \, x^{2} + 2 \, \sqrt{2}\right) - \frac{1}{16} \cdot 2^{\frac{1}{4}} {\left(\sqrt{2} + 1\right)} \sqrt{-2 \, \sqrt{2} + 4} \log\left(-2^{\frac{3}{4}} x \sqrt{-2 \, \sqrt{2} + 4} + 2 \, x^{2} + 2 \, \sqrt{2}\right) - \frac{1}{4} \cdot 2^{\frac{1}{4}} \sqrt{-2 \, \sqrt{2} + 4} \arctan\left(-\frac{1}{2} \cdot 2^{\frac{3}{4}} x \sqrt{-2 \, \sqrt{2} + 4} + \frac{1}{2} \cdot 2^{\frac{1}{4}} \sqrt{2^{\frac{3}{4}} x \sqrt{-2 \, \sqrt{2} + 4} + 2 \, x^{2} + 2 \, \sqrt{2}} \sqrt{-2 \, \sqrt{2} + 4} - \sqrt{2} + 1\right) - \frac{1}{4} \cdot 2^{\frac{1}{4}} \sqrt{-2 \, \sqrt{2} + 4} \arctan\left(-\frac{1}{2} \cdot 2^{\frac{3}{4}} x \sqrt{-2 \, \sqrt{2} + 4} + \frac{1}{2} \cdot 2^{\frac{1}{4}} \sqrt{-2^{\frac{3}{4}} x \sqrt{-2 \, \sqrt{2} + 4} + 2 \, x^{2} + 2 \, \sqrt{2}} \sqrt{-2 \, \sqrt{2} + 4} + \sqrt{2} - 1\right)"," ",0,"1/16*2^(1/4)*(sqrt(2) + 1)*sqrt(-2*sqrt(2) + 4)*log(2^(3/4)*x*sqrt(-2*sqrt(2) + 4) + 2*x^2 + 2*sqrt(2)) - 1/16*2^(1/4)*(sqrt(2) + 1)*sqrt(-2*sqrt(2) + 4)*log(-2^(3/4)*x*sqrt(-2*sqrt(2) + 4) + 2*x^2 + 2*sqrt(2)) - 1/4*2^(1/4)*sqrt(-2*sqrt(2) + 4)*arctan(-1/2*2^(3/4)*x*sqrt(-2*sqrt(2) + 4) + 1/2*2^(1/4)*sqrt(2^(3/4)*x*sqrt(-2*sqrt(2) + 4) + 2*x^2 + 2*sqrt(2))*sqrt(-2*sqrt(2) + 4) - sqrt(2) + 1) - 1/4*2^(1/4)*sqrt(-2*sqrt(2) + 4)*arctan(-1/2*2^(3/4)*x*sqrt(-2*sqrt(2) + 4) + 1/2*2^(1/4)*sqrt(-2^(3/4)*x*sqrt(-2*sqrt(2) + 4) + 2*x^2 + 2*sqrt(2))*sqrt(-2*sqrt(2) + 4) + sqrt(2) - 1)","A",0
16,0,0,0,0.829026," ","integrate(1/(-3*x^4+5*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-3 \, x^{4} + 5 \, x^{2} + 2}}{3 \, x^{4} - 5 \, x^{2} - 2}, x\right)"," ",0,"integral(-sqrt(-3*x^4 + 5*x^2 + 2)/(3*x^4 - 5*x^2 - 2), x)","F",0
17,0,0,0,1.164210," ","integrate(1/(-3*x^4+4*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-3 \, x^{4} + 4 \, x^{2} + 2}}{3 \, x^{4} - 4 \, x^{2} - 2}, x\right)"," ",0,"integral(-sqrt(-3*x^4 + 4*x^2 + 2)/(3*x^4 - 4*x^2 - 2), x)","F",0
18,0,0,0,0.469556," ","integrate(1/(-3*x^4+3*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-3 \, x^{4} + 3 \, x^{2} + 2}}{3 \, x^{4} - 3 \, x^{2} - 2}, x\right)"," ",0,"integral(-sqrt(-3*x^4 + 3*x^2 + 2)/(3*x^4 - 3*x^2 - 2), x)","F",0
19,0,0,0,1.074804," ","integrate(1/(-3*x^4+2*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-3 \, x^{4} + 2 \, x^{2} + 2}}{3 \, x^{4} - 2 \, x^{2} - 2}, x\right)"," ",0,"integral(-sqrt(-3*x^4 + 2*x^2 + 2)/(3*x^4 - 2*x^2 - 2), x)","F",0
20,0,0,0,0.834392," ","integrate(1/(-3*x^4+x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-3 \, x^{4} + x^{2} + 2}}{3 \, x^{4} - x^{2} - 2}, x\right)"," ",0,"integral(-sqrt(-3*x^4 + x^2 + 2)/(3*x^4 - x^2 - 2), x)","F",0
21,0,0,0,0.703899," ","integrate(1/(-3*x^4+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-3 \, x^{4} + 2}}{3 \, x^{4} - 2}, x\right)"," ",0,"integral(-sqrt(-3*x^4 + 2)/(3*x^4 - 2), x)","F",0
22,0,0,0,0.903937," ","integrate(1/(-3*x^4-x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-3 \, x^{4} - x^{2} + 2}}{3 \, x^{4} + x^{2} - 2}, x\right)"," ",0,"integral(-sqrt(-3*x^4 - x^2 + 2)/(3*x^4 + x^2 - 2), x)","F",0
23,0,0,0,0.764643," ","integrate(1/(-3*x^4-2*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-3 \, x^{4} - 2 \, x^{2} + 2}}{3 \, x^{4} + 2 \, x^{2} - 2}, x\right)"," ",0,"integral(-sqrt(-3*x^4 - 2*x^2 + 2)/(3*x^4 + 2*x^2 - 2), x)","F",0
24,0,0,0,0.776940," ","integrate(1/(-3*x^4-3*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-3 \, x^{4} - 3 \, x^{2} + 2}}{3 \, x^{4} + 3 \, x^{2} - 2}, x\right)"," ",0,"integral(-sqrt(-3*x^4 - 3*x^2 + 2)/(3*x^4 + 3*x^2 - 2), x)","F",0
25,0,0,0,1.204945," ","integrate(1/(-3*x^4-4*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-3 \, x^{4} - 4 \, x^{2} + 2}}{3 \, x^{4} + 4 \, x^{2} - 2}, x\right)"," ",0,"integral(-sqrt(-3*x^4 - 4*x^2 + 2)/(3*x^4 + 4*x^2 - 2), x)","F",0
26,0,0,0,0.874582," ","integrate(1/(-3*x^4-5*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-3 \, x^{4} - 5 \, x^{2} + 2}}{3 \, x^{4} + 5 \, x^{2} - 2}, x\right)"," ",0,"integral(-sqrt(-3*x^4 - 5*x^2 + 2)/(3*x^4 + 5*x^2 - 2), x)","F",0
27,0,0,0,0.747772," ","integrate(1/(-2*x^4+7*x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-2 \, x^{4} + 7 \, x^{2} + 3}}{2 \, x^{4} - 7 \, x^{2} - 3}, x\right)"," ",0,"integral(-sqrt(-2*x^4 + 7*x^2 + 3)/(2*x^4 - 7*x^2 - 3), x)","F",0
28,0,0,0,0.615959," ","integrate(1/(-2*x^4+6*x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-2 \, x^{4} + 6 \, x^{2} + 3}}{2 \, x^{4} - 6 \, x^{2} - 3}, x\right)"," ",0,"integral(-sqrt(-2*x^4 + 6*x^2 + 3)/(2*x^4 - 6*x^2 - 3), x)","F",0
29,0,0,0,1.072920," ","integrate(1/(-2*x^4+5*x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-2 \, x^{4} + 5 \, x^{2} + 3}}{2 \, x^{4} - 5 \, x^{2} - 3}, x\right)"," ",0,"integral(-sqrt(-2*x^4 + 5*x^2 + 3)/(2*x^4 - 5*x^2 - 3), x)","F",0
30,0,0,0,0.998249," ","integrate(1/(-2*x^4+4*x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-2 \, x^{4} + 4 \, x^{2} + 3}}{2 \, x^{4} - 4 \, x^{2} - 3}, x\right)"," ",0,"integral(-sqrt(-2*x^4 + 4*x^2 + 3)/(2*x^4 - 4*x^2 - 3), x)","F",0
31,0,0,0,0.942970," ","integrate(1/(-2*x^4+3*x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-2 \, x^{4} + 3 \, x^{2} + 3}}{2 \, x^{4} - 3 \, x^{2} - 3}, x\right)"," ",0,"integral(-sqrt(-2*x^4 + 3*x^2 + 3)/(2*x^4 - 3*x^2 - 3), x)","F",0
32,0,0,0,1.201071," ","integrate(1/(-2*x^4+2*x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-2 \, x^{4} + 2 \, x^{2} + 3}}{2 \, x^{4} - 2 \, x^{2} - 3}, x\right)"," ",0,"integral(-sqrt(-2*x^4 + 2*x^2 + 3)/(2*x^4 - 2*x^2 - 3), x)","F",0
33,0,0,0,0.944916," ","integrate(1/(-2*x^4+x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-2 \, x^{4} + x^{2} + 3}}{2 \, x^{4} - x^{2} - 3}, x\right)"," ",0,"integral(-sqrt(-2*x^4 + x^2 + 3)/(2*x^4 - x^2 - 3), x)","F",0
34,0,0,0,1.067663," ","integrate(1/(-2*x^4+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-2 \, x^{4} + 3}}{2 \, x^{4} - 3}, x\right)"," ",0,"integral(-sqrt(-2*x^4 + 3)/(2*x^4 - 3), x)","F",0
35,0,0,0,1.332521," ","integrate(1/(-2*x^4-x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-2 \, x^{4} - x^{2} + 3}}{2 \, x^{4} + x^{2} - 3}, x\right)"," ",0,"integral(-sqrt(-2*x^4 - x^2 + 3)/(2*x^4 + x^2 - 3), x)","F",0
36,0,0,0,0.880314," ","integrate(1/(-2*x^4-2*x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-2 \, x^{4} - 2 \, x^{2} + 3}}{2 \, x^{4} + 2 \, x^{2} - 3}, x\right)"," ",0,"integral(-sqrt(-2*x^4 - 2*x^2 + 3)/(2*x^4 + 2*x^2 - 3), x)","F",0
37,0,0,0,1.120611," ","integrate(1/(-2*x^4-3*x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-2 \, x^{4} - 3 \, x^{2} + 3}}{2 \, x^{4} + 3 \, x^{2} - 3}, x\right)"," ",0,"integral(-sqrt(-2*x^4 - 3*x^2 + 3)/(2*x^4 + 3*x^2 - 3), x)","F",0
38,0,0,0,0.716559," ","integrate(1/(-2*x^4-4*x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-2 \, x^{4} - 4 \, x^{2} + 3}}{2 \, x^{4} + 4 \, x^{2} - 3}, x\right)"," ",0,"integral(-sqrt(-2*x^4 - 4*x^2 + 3)/(2*x^4 + 4*x^2 - 3), x)","F",0
39,0,0,0,1.126216," ","integrate(1/(-2*x^4-5*x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-2 \, x^{4} - 5 \, x^{2} + 3}}{2 \, x^{4} + 5 \, x^{2} - 3}, x\right)"," ",0,"integral(-sqrt(-2*x^4 - 5*x^2 + 3)/(2*x^4 + 5*x^2 - 3), x)","F",0
40,0,0,0,0.770193," ","integrate(1/(-2*x^4-6*x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-2 \, x^{4} - 6 \, x^{2} + 3}}{2 \, x^{4} + 6 \, x^{2} - 3}, x\right)"," ",0,"integral(-sqrt(-2*x^4 - 6*x^2 + 3)/(2*x^4 + 6*x^2 - 3), x)","F",0
41,0,0,0,1.154385," ","integrate(1/(-2*x^4-7*x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-2 \, x^{4} - 7 \, x^{2} + 3}}{2 \, x^{4} + 7 \, x^{2} - 3}, x\right)"," ",0,"integral(-sqrt(-2*x^4 - 7*x^2 + 3)/(2*x^4 + 7*x^2 - 3), x)","F",0
42,0,0,0,1.573008," ","integrate(1/(3*x^4+5*x^2-2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{3 \, x^{4} + 5 \, x^{2} - 2}}, x\right)"," ",0,"integral(1/sqrt(3*x^4 + 5*x^2 - 2), x)","F",0
43,0,0,0,0.835983," ","integrate(1/(3*x^4+4*x^2-2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{3 \, x^{4} + 4 \, x^{2} - 2}}, x\right)"," ",0,"integral(1/sqrt(3*x^4 + 4*x^2 - 2), x)","F",0
44,0,0,0,0.750884," ","integrate(1/(3*x^4+3*x^2-2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{3 \, x^{4} + 3 \, x^{2} - 2}}, x\right)"," ",0,"integral(1/sqrt(3*x^4 + 3*x^2 - 2), x)","F",0
45,0,0,0,1.881795," ","integrate(1/(3*x^4+2*x^2-2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{3 \, x^{4} + 2 \, x^{2} - 2}}, x\right)"," ",0,"integral(1/sqrt(3*x^4 + 2*x^2 - 2), x)","F",0
46,0,0,0,0.582041," ","integrate(1/(3*x^4+x^2-2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{3 \, x^{4} + x^{2} - 2}}, x\right)"," ",0,"integral(1/sqrt(3*x^4 + x^2 - 2), x)","F",0
47,0,0,0,0.929803," ","integrate(1/(3*x^4-2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{3 \, x^{4} - 2}}, x\right)"," ",0,"integral(1/sqrt(3*x^4 - 2), x)","F",0
48,0,0,0,0.860965," ","integrate(1/(3*x^4-x^2-2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{3 \, x^{4} - x^{2} - 2}}, x\right)"," ",0,"integral(1/sqrt(3*x^4 - x^2 - 2), x)","F",0
49,0,0,0,0.853183," ","integrate(1/(3*x^4-2*x^2-2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{3 \, x^{4} - 2 \, x^{2} - 2}}, x\right)"," ",0,"integral(1/sqrt(3*x^4 - 2*x^2 - 2), x)","F",0
50,0,0,0,0.706841," ","integrate(1/(3*x^4-3*x^2-2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{3 \, x^{4} - 3 \, x^{2} - 2}}, x\right)"," ",0,"integral(1/sqrt(3*x^4 - 3*x^2 - 2), x)","F",0
51,0,0,0,1.210309," ","integrate(1/(3*x^4-4*x^2-2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{3 \, x^{4} - 4 \, x^{2} - 2}}, x\right)"," ",0,"integral(1/sqrt(3*x^4 - 4*x^2 - 2), x)","F",0
52,0,0,0,1.550991," ","integrate(1/(3*x^4-5*x^2-2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{3 \, x^{4} - 5 \, x^{2} - 2}}, x\right)"," ",0,"integral(1/sqrt(3*x^4 - 5*x^2 - 2), x)","F",0
53,0,0,0,0.762648," ","integrate(1/(2*x^4+7*x^2-3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{2 \, x^{4} + 7 \, x^{2} - 3}}, x\right)"," ",0,"integral(1/sqrt(2*x^4 + 7*x^2 - 3), x)","F",0
54,0,0,0,0.884570," ","integrate(1/(2*x^4+6*x^2-3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{2 \, x^{4} + 6 \, x^{2} - 3}}, x\right)"," ",0,"integral(1/sqrt(2*x^4 + 6*x^2 - 3), x)","F",0
55,0,0,0,1.312319," ","integrate(1/(2*x^4+5*x^2-3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{2 \, x^{4} + 5 \, x^{2} - 3}}, x\right)"," ",0,"integral(1/sqrt(2*x^4 + 5*x^2 - 3), x)","F",0
56,0,0,0,0.569626," ","integrate(1/(2*x^4+4*x^2-3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{2 \, x^{4} + 4 \, x^{2} - 3}}, x\right)"," ",0,"integral(1/sqrt(2*x^4 + 4*x^2 - 3), x)","F",0
57,0,0,0,1.456943," ","integrate(1/(2*x^4+3*x^2-3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{2 \, x^{4} + 3 \, x^{2} - 3}}, x\right)"," ",0,"integral(1/sqrt(2*x^4 + 3*x^2 - 3), x)","F",0
58,0,0,0,0.777946," ","integrate(1/(2*x^4+2*x^2-3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{2 \, x^{4} + 2 \, x^{2} - 3}}, x\right)"," ",0,"integral(1/sqrt(2*x^4 + 2*x^2 - 3), x)","F",0
59,0,0,0,0.765343," ","integrate(1/(2*x^4+x^2-3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{2 \, x^{4} + x^{2} - 3}}, x\right)"," ",0,"integral(1/sqrt(2*x^4 + x^2 - 3), x)","F",0
60,0,0,0,0.842138," ","integrate(1/(2*x^4-3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{2 \, x^{4} - 3}}, x\right)"," ",0,"integral(1/sqrt(2*x^4 - 3), x)","F",0
61,0,0,0,0.811132," ","integrate(1/(2*x^4-x^2-3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{2 \, x^{4} - x^{2} - 3}}, x\right)"," ",0,"integral(1/sqrt(2*x^4 - x^2 - 3), x)","F",0
62,0,0,0,0.777748," ","integrate(1/(2*x^4-2*x^2-3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{2 \, x^{4} - 2 \, x^{2} - 3}}, x\right)"," ",0,"integral(1/sqrt(2*x^4 - 2*x^2 - 3), x)","F",0
63,0,0,0,0.846776," ","integrate(1/(2*x^4-3*x^2-3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{2 \, x^{4} - 3 \, x^{2} - 3}}, x\right)"," ",0,"integral(1/sqrt(2*x^4 - 3*x^2 - 3), x)","F",0
64,0,0,0,1.313049," ","integrate(1/(2*x^4-4*x^2-3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{2 \, x^{4} - 4 \, x^{2} - 3}}, x\right)"," ",0,"integral(1/sqrt(2*x^4 - 4*x^2 - 3), x)","F",0
65,0,0,0,0.967703," ","integrate(1/(2*x^4-5*x^2-3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{2 \, x^{4} - 5 \, x^{2} - 3}}, x\right)"," ",0,"integral(1/sqrt(2*x^4 - 5*x^2 - 3), x)","F",0
66,0,0,0,1.105548," ","integrate(1/(3*x^4+5*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{3 \, x^{4} + 5 \, x^{2} + 2}}, x\right)"," ",0,"integral(1/sqrt(3*x^4 + 5*x^2 + 2), x)","F",0
67,0,0,0,0.786561," ","integrate(1/(3*x^4+4*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{3 \, x^{4} + 4 \, x^{2} + 2}}, x\right)"," ",0,"integral(1/sqrt(3*x^4 + 4*x^2 + 2), x)","F",0
68,0,0,0,1.376390," ","integrate(1/(3*x^4+3*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{3 \, x^{4} + 3 \, x^{2} + 2}}, x\right)"," ",0,"integral(1/sqrt(3*x^4 + 3*x^2 + 2), x)","F",0
69,0,0,0,1.075672," ","integrate(1/(3*x^4+2*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{3 \, x^{4} + 2 \, x^{2} + 2}}, x\right)"," ",0,"integral(1/sqrt(3*x^4 + 2*x^2 + 2), x)","F",0
70,0,0,0,0.423548," ","integrate(1/(3*x^4+x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{3 \, x^{4} + x^{2} + 2}}, x\right)"," ",0,"integral(1/sqrt(3*x^4 + x^2 + 2), x)","F",0
71,0,0,0,0.867592," ","integrate(1/(3*x^4+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{3 \, x^{4} + 2}}, x\right)"," ",0,"integral(1/sqrt(3*x^4 + 2), x)","F",0
72,0,0,0,0.910774," ","integrate(1/(3*x^4-x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{3 \, x^{4} - x^{2} + 2}}, x\right)"," ",0,"integral(1/sqrt(3*x^4 - x^2 + 2), x)","F",0
73,0,0,0,0.493110," ","integrate(1/(3*x^4-2*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{3 \, x^{4} - 2 \, x^{2} + 2}}, x\right)"," ",0,"integral(1/sqrt(3*x^4 - 2*x^2 + 2), x)","F",0
74,0,0,0,0.711752," ","integrate(1/(3*x^4-3*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{3 \, x^{4} - 3 \, x^{2} + 2}}, x\right)"," ",0,"integral(1/sqrt(3*x^4 - 3*x^2 + 2), x)","F",0
75,0,0,0,1.214673," ","integrate(1/(3*x^4-4*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{3 \, x^{4} - 4 \, x^{2} + 2}}, x\right)"," ",0,"integral(1/sqrt(3*x^4 - 4*x^2 + 2), x)","F",0
76,0,0,0,0.592569," ","integrate(1/(3*x^4-5*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{3 \, x^{4} - 5 \, x^{2} + 2}}, x\right)"," ",0,"integral(1/sqrt(3*x^4 - 5*x^2 + 2), x)","F",0
77,0,0,0,1.102807," ","integrate(1/(3*x^4-6*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{3 \, x^{4} - 6 \, x^{2} + 2}}, x\right)"," ",0,"integral(1/sqrt(3*x^4 - 6*x^2 + 2), x)","F",0
78,0,0,0,0.505311," ","integrate(1/(2*x^4+9*x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{2 \, x^{4} + 9 \, x^{2} + 3}}, x\right)"," ",0,"integral(1/sqrt(2*x^4 + 9*x^2 + 3), x)","F",0
79,0,0,0,0.977120," ","integrate(1/(2*x^4+8*x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{2 \, x^{4} + 8 \, x^{2} + 3}}, x\right)"," ",0,"integral(1/sqrt(2*x^4 + 8*x^2 + 3), x)","F",0
80,0,0,0,0.789874," ","integrate(1/(2*x^4+7*x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{2 \, x^{4} + 7 \, x^{2} + 3}}, x\right)"," ",0,"integral(1/sqrt(2*x^4 + 7*x^2 + 3), x)","F",0
81,0,0,0,0.750182," ","integrate(1/(2*x^4+6*x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{2 \, x^{4} + 6 \, x^{2} + 3}}, x\right)"," ",0,"integral(1/sqrt(2*x^4 + 6*x^2 + 3), x)","F",0
82,0,0,0,0.786536," ","integrate(1/(2*x^4+5*x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{2 \, x^{4} + 5 \, x^{2} + 3}}, x\right)"," ",0,"integral(1/sqrt(2*x^4 + 5*x^2 + 3), x)","F",0
83,0,0,0,0.638353," ","integrate(1/(2*x^4+4*x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{2 \, x^{4} + 4 \, x^{2} + 3}}, x\right)"," ",0,"integral(1/sqrt(2*x^4 + 4*x^2 + 3), x)","F",0
84,0,0,0,0.851688," ","integrate(1/(2*x^4+3*x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{2 \, x^{4} + 3 \, x^{2} + 3}}, x\right)"," ",0,"integral(1/sqrt(2*x^4 + 3*x^2 + 3), x)","F",0
85,0,0,0,0.810966," ","integrate(1/(2*x^4+2*x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{2 \, x^{4} + 2 \, x^{2} + 3}}, x\right)"," ",0,"integral(1/sqrt(2*x^4 + 2*x^2 + 3), x)","F",0
86,0,0,0,0.840456," ","integrate(1/(2*x^4+x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{2 \, x^{4} + x^{2} + 3}}, x\right)"," ",0,"integral(1/sqrt(2*x^4 + x^2 + 3), x)","F",0
87,0,0,0,0.622293," ","integrate(1/(2*x^4+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{2 \, x^{4} + 3}}, x\right)"," ",0,"integral(1/sqrt(2*x^4 + 3), x)","F",0
88,0,0,0,0.733143," ","integrate(1/(2*x^4-x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{2 \, x^{4} - x^{2} + 3}}, x\right)"," ",0,"integral(1/sqrt(2*x^4 - x^2 + 3), x)","F",0
89,0,0,0,0.630577," ","integrate(1/(2*x^4-2*x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{2 \, x^{4} - 2 \, x^{2} + 3}}, x\right)"," ",0,"integral(1/sqrt(2*x^4 - 2*x^2 + 3), x)","F",0
90,0,0,0,0.798419," ","integrate(1/(2*x^4-3*x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{2 \, x^{4} - 3 \, x^{2} + 3}}, x\right)"," ",0,"integral(1/sqrt(2*x^4 - 3*x^2 + 3), x)","F",0
91,0,0,0,1.153584," ","integrate(1/(2*x^4-4*x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{2 \, x^{4} - 4 \, x^{2} + 3}}, x\right)"," ",0,"integral(1/sqrt(2*x^4 - 4*x^2 + 3), x)","F",0
92,0,0,0,0.954778," ","integrate(1/(2*x^4-5*x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{2 \, x^{4} - 5 \, x^{2} + 3}}, x\right)"," ",0,"integral(1/sqrt(2*x^4 - 5*x^2 + 3), x)","F",0
93,0,0,0,1.217051," ","integrate(1/(2*x^4-6*x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{2 \, x^{4} - 6 \, x^{2} + 3}}, x\right)"," ",0,"integral(1/sqrt(2*x^4 - 6*x^2 + 3), x)","F",0
94,0,0,0,0.748372," ","integrate(1/(2*x^4-7*x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{2 \, x^{4} - 7 \, x^{2} + 3}}, x\right)"," ",0,"integral(1/sqrt(2*x^4 - 7*x^2 + 3), x)","F",0
95,0,0,0,2.139201," ","integrate(1/(-2*x^4+7*x^2-3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-2 \, x^{4} + 7 \, x^{2} - 3}}{2 \, x^{4} - 7 \, x^{2} + 3}, x\right)"," ",0,"integral(-sqrt(-2*x^4 + 7*x^2 - 3)/(2*x^4 - 7*x^2 + 3), x)","F",0
96,0,0,0,1.681854," ","integrate(1/(-2*x^4+6*x^2-3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-2 \, x^{4} + 6 \, x^{2} - 3}}{2 \, x^{4} - 6 \, x^{2} + 3}, x\right)"," ",0,"integral(-sqrt(-2*x^4 + 6*x^2 - 3)/(2*x^4 - 6*x^2 + 3), x)","F",0
97,0,0,0,0.904006," ","integrate(1/(-2*x^4+5*x^2-3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-2 \, x^{4} + 5 \, x^{2} - 3}}{2 \, x^{4} - 5 \, x^{2} + 3}, x\right)"," ",0,"integral(-sqrt(-2*x^4 + 5*x^2 - 3)/(2*x^4 - 5*x^2 + 3), x)","F",0
98,0,0,0,1.176001," ","integrate(1/(-2*x^4+4*x^2-3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-2 \, x^{4} + 4 \, x^{2} - 3}}{2 \, x^{4} - 4 \, x^{2} + 3}, x\right)"," ",0,"integral(-sqrt(-2*x^4 + 4*x^2 - 3)/(2*x^4 - 4*x^2 + 3), x)","F",0
99,0,0,0,0.852028," ","integrate(1/(-2*x^4+3*x^2-3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-2 \, x^{4} + 3 \, x^{2} - 3}}{2 \, x^{4} - 3 \, x^{2} + 3}, x\right)"," ",0,"integral(-sqrt(-2*x^4 + 3*x^2 - 3)/(2*x^4 - 3*x^2 + 3), x)","F",0
100,0,0,0,0.770499," ","integrate(1/(-2*x^4+2*x^2-3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-2 \, x^{4} + 2 \, x^{2} - 3}}{2 \, x^{4} - 2 \, x^{2} + 3}, x\right)"," ",0,"integral(-sqrt(-2*x^4 + 2*x^2 - 3)/(2*x^4 - 2*x^2 + 3), x)","F",0
101,0,0,0,0.688500," ","integrate(1/(-2*x^4+x^2-3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-2 \, x^{4} + x^{2} - 3}}{2 \, x^{4} - x^{2} + 3}, x\right)"," ",0,"integral(-sqrt(-2*x^4 + x^2 - 3)/(2*x^4 - x^2 + 3), x)","F",0
102,0,0,0,0.730171," ","integrate(1/(-2*x^4-3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-2 \, x^{4} - 3}}{2 \, x^{4} + 3}, x\right)"," ",0,"integral(-sqrt(-2*x^4 - 3)/(2*x^4 + 3), x)","F",0
103,0,0,0,0.836325," ","integrate(1/(-2*x^4-x^2-3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-2 \, x^{4} - x^{2} - 3}}{2 \, x^{4} + x^{2} + 3}, x\right)"," ",0,"integral(-sqrt(-2*x^4 - x^2 - 3)/(2*x^4 + x^2 + 3), x)","F",0
104,0,0,0,2.323149," ","integrate(1/(-2*x^4-2*x^2-3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-2 \, x^{4} - 2 \, x^{2} - 3}}{2 \, x^{4} + 2 \, x^{2} + 3}, x\right)"," ",0,"integral(-sqrt(-2*x^4 - 2*x^2 - 3)/(2*x^4 + 2*x^2 + 3), x)","F",0
105,0,0,0,0.967818," ","integrate(1/(-2*x^4-3*x^2-3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-2 \, x^{4} - 3 \, x^{2} - 3}}{2 \, x^{4} + 3 \, x^{2} + 3}, x\right)"," ",0,"integral(-sqrt(-2*x^4 - 3*x^2 - 3)/(2*x^4 + 3*x^2 + 3), x)","F",0
106,0,0,0,0.750810," ","integrate(1/(-2*x^4-4*x^2-3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-2 \, x^{4} - 4 \, x^{2} - 3}}{2 \, x^{4} + 4 \, x^{2} + 3}, x\right)"," ",0,"integral(-sqrt(-2*x^4 - 4*x^2 - 3)/(2*x^4 + 4*x^2 + 3), x)","F",0
107,0,0,0,1.745097," ","integrate(1/(-2*x^4-5*x^2-3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-2 \, x^{4} - 5 \, x^{2} - 3}}{2 \, x^{4} + 5 \, x^{2} + 3}, x\right)"," ",0,"integral(-sqrt(-2*x^4 - 5*x^2 - 3)/(2*x^4 + 5*x^2 + 3), x)","F",0
108,0,0,0,0.851082," ","integrate(1/(-3*x^4+6*x^2-2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-3 \, x^{4} + 6 \, x^{2} - 2}}{3 \, x^{4} - 6 \, x^{2} + 2}, x\right)"," ",0,"integral(-sqrt(-3*x^4 + 6*x^2 - 2)/(3*x^4 - 6*x^2 + 2), x)","F",0
109,0,0,0,0.939491," ","integrate(1/(-3*x^4+5*x^2-2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-3 \, x^{4} + 5 \, x^{2} - 2}}{3 \, x^{4} - 5 \, x^{2} + 2}, x\right)"," ",0,"integral(-sqrt(-3*x^4 + 5*x^2 - 2)/(3*x^4 - 5*x^2 + 2), x)","F",0
110,0,0,0,0.783038," ","integrate(1/(-3*x^4+4*x^2-2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-3 \, x^{4} + 4 \, x^{2} - 2}}{3 \, x^{4} - 4 \, x^{2} + 2}, x\right)"," ",0,"integral(-sqrt(-3*x^4 + 4*x^2 - 2)/(3*x^4 - 4*x^2 + 2), x)","F",0
111,0,0,0,0.672462," ","integrate(1/(-3*x^4+3*x^2-2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-3 \, x^{4} + 3 \, x^{2} - 2}}{3 \, x^{4} - 3 \, x^{2} + 2}, x\right)"," ",0,"integral(-sqrt(-3*x^4 + 3*x^2 - 2)/(3*x^4 - 3*x^2 + 2), x)","F",0
112,0,0,0,0.936250," ","integrate(1/(-3*x^4+2*x^2-2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-3 \, x^{4} + 2 \, x^{2} - 2}}{3 \, x^{4} - 2 \, x^{2} + 2}, x\right)"," ",0,"integral(-sqrt(-3*x^4 + 2*x^2 - 2)/(3*x^4 - 2*x^2 + 2), x)","F",0
113,0,0,0,0.912714," ","integrate(1/(-3*x^4+x^2-2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-3 \, x^{4} + x^{2} - 2}}{3 \, x^{4} - x^{2} + 2}, x\right)"," ",0,"integral(-sqrt(-3*x^4 + x^2 - 2)/(3*x^4 - x^2 + 2), x)","F",0
114,0,0,0,0.920064," ","integrate(1/(-3*x^4-2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-3 \, x^{4} - 2}}{3 \, x^{4} + 2}, x\right)"," ",0,"integral(-sqrt(-3*x^4 - 2)/(3*x^4 + 2), x)","F",0
115,0,0,0,0.558385," ","integrate(1/(-3*x^4-x^2-2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-3 \, x^{4} - x^{2} - 2}}{3 \, x^{4} + x^{2} + 2}, x\right)"," ",0,"integral(-sqrt(-3*x^4 - x^2 - 2)/(3*x^4 + x^2 + 2), x)","F",0
116,0,0,0,0.776848," ","integrate(1/(-3*x^4-2*x^2-2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-3 \, x^{4} - 2 \, x^{2} - 2}}{3 \, x^{4} + 2 \, x^{2} + 2}, x\right)"," ",0,"integral(-sqrt(-3*x^4 - 2*x^2 - 2)/(3*x^4 + 2*x^2 + 2), x)","F",0
117,0,0,0,1.175906," ","integrate(1/(-3*x^4-3*x^2-2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-3 \, x^{4} - 3 \, x^{2} - 2}}{3 \, x^{4} + 3 \, x^{2} + 2}, x\right)"," ",0,"integral(-sqrt(-3*x^4 - 3*x^2 - 2)/(3*x^4 + 3*x^2 + 2), x)","F",0
118,0,0,0,0.885083," ","integrate(1/(-3*x^4-4*x^2-2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-3 \, x^{4} - 4 \, x^{2} - 2}}{3 \, x^{4} + 4 \, x^{2} + 2}, x\right)"," ",0,"integral(-sqrt(-3*x^4 - 4*x^2 - 2)/(3*x^4 + 4*x^2 + 2), x)","F",0
119,0,0,0,0.838273," ","integrate(1/(-3*x^4-5*x^2-2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-3 \, x^{4} - 5 \, x^{2} - 2}}{3 \, x^{4} + 5 \, x^{2} + 2}, x\right)"," ",0,"integral(-sqrt(-3*x^4 - 5*x^2 - 2)/(3*x^4 + 5*x^2 + 2), x)","F",0
120,0,0,0,1.010896," ","integrate(1/(5*x^4+5*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{5 \, x^{4} + 5 \, x^{2} + 2}}, x\right)"," ",0,"integral(1/sqrt(5*x^4 + 5*x^2 + 2), x)","F",0
121,0,0,0,0.569412," ","integrate(1/(4*x^4+5*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{4 \, x^{4} + 5 \, x^{2} + 2}}, x\right)"," ",0,"integral(1/sqrt(4*x^4 + 5*x^2 + 2), x)","F",0
122,0,0,0,0.825680," ","integrate(1/(3*x^4+5*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{3 \, x^{4} + 5 \, x^{2} + 2}}, x\right)"," ",0,"integral(1/sqrt(3*x^4 + 5*x^2 + 2), x)","F",0
123,0,0,0,1.809502," ","integrate(1/(2*x^4+5*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{2 \, x^{4} + 5 \, x^{2} + 2}}, x\right)"," ",0,"integral(1/sqrt(2*x^4 + 5*x^2 + 2), x)","F",0
124,0,0,0,1.703166," ","integrate(1/(x^4+5*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{x^{4} + 5 \, x^{2} + 2}}, x\right)"," ",0,"integral(1/sqrt(x^4 + 5*x^2 + 2), x)","F",0
125,0,0,0,2.204005," ","integrate(1/(-x^4+5*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{4} + 5 \, x^{2} + 2}}{x^{4} - 5 \, x^{2} - 2}, x\right)"," ",0,"integral(-sqrt(-x^4 + 5*x^2 + 2)/(x^4 - 5*x^2 - 2), x)","F",0
126,0,0,0,0.724332," ","integrate(1/(-2*x^4+5*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-2 \, x^{4} + 5 \, x^{2} + 2}}{2 \, x^{4} - 5 \, x^{2} - 2}, x\right)"," ",0,"integral(-sqrt(-2*x^4 + 5*x^2 + 2)/(2*x^4 - 5*x^2 - 2), x)","F",0
127,0,0,0,1.056284," ","integrate(1/(-3*x^4+5*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-3 \, x^{4} + 5 \, x^{2} + 2}}{3 \, x^{4} - 5 \, x^{2} - 2}, x\right)"," ",0,"integral(-sqrt(-3*x^4 + 5*x^2 + 2)/(3*x^4 - 5*x^2 - 2), x)","F",0
128,0,0,0,1.548142," ","integrate(1/(-4*x^4+5*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-4 \, x^{4} + 5 \, x^{2} + 2}}{4 \, x^{4} - 5 \, x^{2} - 2}, x\right)"," ",0,"integral(-sqrt(-4*x^4 + 5*x^2 + 2)/(4*x^4 - 5*x^2 - 2), x)","F",0
129,0,0,0,2.169613," ","integrate(1/(-5*x^4+5*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-5 \, x^{4} + 5 \, x^{2} + 2}}{5 \, x^{4} - 5 \, x^{2} - 2}, x\right)"," ",0,"integral(-sqrt(-5*x^4 + 5*x^2 + 2)/(5*x^4 - 5*x^2 - 2), x)","F",0
130,0,0,0,1.496335," ","integrate(1/(-6*x^4+5*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-6 \, x^{4} + 5 \, x^{2} + 2}}{6 \, x^{4} - 5 \, x^{2} - 2}, x\right)"," ",0,"integral(-sqrt(-6*x^4 + 5*x^2 + 2)/(6*x^4 - 5*x^2 - 2), x)","F",0
131,0,0,0,2.005293," ","integrate(1/(-7*x^4+5*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-7 \, x^{4} + 5 \, x^{2} + 2}}{7 \, x^{4} - 5 \, x^{2} - 2}, x\right)"," ",0,"integral(-sqrt(-7*x^4 + 5*x^2 + 2)/(7*x^4 - 5*x^2 - 2), x)","F",0
132,0,0,0,0.736421," ","integrate(1/(-8*x^4+5*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-8 \, x^{4} + 5 \, x^{2} + 2}}{8 \, x^{4} - 5 \, x^{2} - 2}, x\right)"," ",0,"integral(-sqrt(-8*x^4 + 5*x^2 + 2)/(8*x^4 - 5*x^2 - 2), x)","F",0
133,0,0,0,0.784395," ","integrate(1/(-9*x^4+5*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-9 \, x^{4} + 5 \, x^{2} + 2}}{9 \, x^{4} - 5 \, x^{2} - 2}, x\right)"," ",0,"integral(-sqrt(-9*x^4 + 5*x^2 + 2)/(9*x^4 - 5*x^2 - 2), x)","F",0
134,1,13,0,0.370780," ","integrate(x^2*(c*x^4+b*x^2),x, algorithm=""fricas"")","\frac{1}{7} x^{7} c + \frac{1}{5} x^{5} b"," ",0,"1/7*x^7*c + 1/5*x^5*b","A",0
135,1,13,0,0.661210," ","integrate(x*(c*x^4+b*x^2),x, algorithm=""fricas"")","\frac{1}{6} x^{6} c + \frac{1}{4} x^{4} b"," ",0,"1/6*x^6*c + 1/4*x^4*b","A",0
136,1,13,0,0.487243," ","integrate(c*x^4+b*x^2,x, algorithm=""fricas"")","\frac{1}{5} x^{5} c + \frac{1}{3} x^{3} b"," ",0,"1/5*x^5*c + 1/3*x^3*b","A",0
137,1,13,0,0.714333," ","integrate((c*x^4+b*x^2)/x,x, algorithm=""fricas"")","\frac{1}{4} \, c x^{4} + \frac{1}{2} \, b x^{2}"," ",0,"1/4*c*x^4 + 1/2*b*x^2","A",0
138,1,10,0,0.816699," ","integrate((c*x^4+b*x^2)/x^2,x, algorithm=""fricas"")","\frac{1}{3} \, c x^{3} + b x"," ",0,"1/3*c*x^3 + b*x","A",0
139,1,11,0,0.508229," ","integrate((c*x^4+b*x^2)/x^3,x, algorithm=""fricas"")","\frac{1}{2} \, c x^{2} + b \log\left(x\right)"," ",0,"1/2*c*x^2 + b*log(x)","A",0
140,1,13,0,0.657789," ","integrate((c*x^4+b*x^2)/x^4,x, algorithm=""fricas"")","\frac{c x^{2} - b}{x}"," ",0,"(c*x^2 - b)/x","A",0
141,1,17,0,0.498703," ","integrate((c*x^4+b*x^2)/x^5,x, algorithm=""fricas"")","\frac{2 \, c x^{2} \log\left(x\right) - b}{2 \, x^{2}}"," ",0,"1/2*(2*c*x^2*log(x) - b)/x^2","A",0
142,1,13,0,0.626084," ","integrate((c*x^4+b*x^2)/x^6,x, algorithm=""fricas"")","-\frac{3 \, c x^{2} + b}{3 \, x^{3}}"," ",0,"-1/3*(3*c*x^2 + b)/x^3","A",0
143,1,13,0,0.476595," ","integrate((c*x^4+b*x^2)/x^7,x, algorithm=""fricas"")","-\frac{2 \, c x^{2} + b}{4 \, x^{4}}"," ",0,"-1/4*(2*c*x^2 + b)/x^4","A",0
144,1,15,0,0.544365," ","integrate((c*x^4+b*x^2)/x^8,x, algorithm=""fricas"")","-\frac{5 \, c x^{2} + 3 \, b}{15 \, x^{5}}"," ",0,"-1/15*(5*c*x^2 + 3*b)/x^5","A",0
145,1,24,0,0.615158," ","integrate((c*x^4+b*x^2)^2,x, algorithm=""fricas"")","\frac{1}{9} x^{9} c^{2} + \frac{2}{7} x^{7} c b + \frac{1}{5} x^{5} b^{2}"," ",0,"1/9*x^9*c^2 + 2/7*x^7*c*b + 1/5*x^5*b^2","A",0
146,1,24,0,2.023659," ","integrate((c*x^4+b*x^2)^2/x,x, algorithm=""fricas"")","\frac{1}{8} \, c^{2} x^{8} + \frac{1}{3} \, b c x^{6} + \frac{1}{4} \, b^{2} x^{4}"," ",0,"1/8*c^2*x^8 + 1/3*b*c*x^6 + 1/4*b^2*x^4","A",0
147,1,24,0,0.474102," ","integrate((c*x^4+b*x^2)^2/x^2,x, algorithm=""fricas"")","\frac{1}{7} \, c^{2} x^{7} + \frac{2}{5} \, b c x^{5} + \frac{1}{3} \, b^{2} x^{3}"," ",0,"1/7*c^2*x^7 + 2/5*b*c*x^5 + 1/3*b^2*x^3","A",0
148,1,24,0,0.439267," ","integrate((c*x^4+b*x^2)^2/x^3,x, algorithm=""fricas"")","\frac{1}{6} \, c^{2} x^{6} + \frac{1}{2} \, b c x^{4} + \frac{1}{2} \, b^{2} x^{2}"," ",0,"1/6*c^2*x^6 + 1/2*b*c*x^4 + 1/2*b^2*x^2","A",0
149,1,21,0,0.736113," ","integrate((c*x^4+b*x^2)^2/x^4,x, algorithm=""fricas"")","\frac{1}{5} \, c^{2} x^{5} + \frac{2}{3} \, b c x^{3} + b^{2} x"," ",0,"1/5*c^2*x^5 + 2/3*b*c*x^3 + b^2*x","A",0
150,1,21,0,0.484980," ","integrate((c*x^4+b*x^2)^2/x^5,x, algorithm=""fricas"")","\frac{1}{4} \, c^{2} x^{4} + b c x^{2} + b^{2} \log\left(x\right)"," ",0,"1/4*c^2*x^4 + b*c*x^2 + b^2*log(x)","A",0
151,1,25,0,0.593967," ","integrate((c*x^4+b*x^2)^2/x^6,x, algorithm=""fricas"")","\frac{c^{2} x^{4} + 6 \, b c x^{2} - 3 \, b^{2}}{3 \, x}"," ",0,"1/3*(c^2*x^4 + 6*b*c*x^2 - 3*b^2)/x","A",0
152,1,27,0,0.555017," ","integrate((c*x^4+b*x^2)^2/x^7,x, algorithm=""fricas"")","\frac{c^{2} x^{4} + 4 \, b c x^{2} \log\left(x\right) - b^{2}}{2 \, x^{2}}"," ",0,"1/2*(c^2*x^4 + 4*b*c*x^2*log(x) - b^2)/x^2","A",0
153,1,26,0,0.521818," ","integrate((c*x^4+b*x^2)^2/x^8,x, algorithm=""fricas"")","\frac{3 \, c^{2} x^{4} - 6 \, b c x^{2} - b^{2}}{3 \, x^{3}}"," ",0,"1/3*(3*c^2*x^4 - 6*b*c*x^2 - b^2)/x^3","A",0
154,1,28,0,0.527347," ","integrate((c*x^4+b*x^2)^2/x^9,x, algorithm=""fricas"")","\frac{4 \, c^{2} x^{4} \log\left(x\right) - 4 \, b c x^{2} - b^{2}}{4 \, x^{4}}"," ",0,"1/4*(4*c^2*x^4*log(x) - 4*b*c*x^2 - b^2)/x^4","A",0
155,1,26,0,0.611174," ","integrate((c*x^4+b*x^2)^2/x^10,x, algorithm=""fricas"")","-\frac{15 \, c^{2} x^{4} + 10 \, b c x^{2} + 3 \, b^{2}}{15 \, x^{5}}"," ",0,"-1/15*(15*c^2*x^4 + 10*b*c*x^2 + 3*b^2)/x^5","A",0
156,1,24,0,0.556776," ","integrate((c*x^4+b*x^2)^2/x^11,x, algorithm=""fricas"")","-\frac{3 \, c^{2} x^{4} + 3 \, b c x^{2} + b^{2}}{6 \, x^{6}}"," ",0,"-1/6*(3*c^2*x^4 + 3*b*c*x^2 + b^2)/x^6","A",0
157,1,26,0,0.680236," ","integrate((c*x^4+b*x^2)^2/x^12,x, algorithm=""fricas"")","-\frac{35 \, c^{2} x^{4} + 42 \, b c x^{2} + 15 \, b^{2}}{105 \, x^{7}}"," ",0,"-1/105*(35*c^2*x^4 + 42*b*c*x^2 + 15*b^2)/x^7","A",0
158,1,35,0,0.479320," ","integrate((c*x^4+b*x^2)^3/x^2,x, algorithm=""fricas"")","\frac{1}{11} \, c^{3} x^{11} + \frac{1}{3} \, b c^{2} x^{9} + \frac{3}{7} \, b^{2} c x^{7} + \frac{1}{5} \, b^{3} x^{5}"," ",0,"1/11*c^3*x^11 + 1/3*b*c^2*x^9 + 3/7*b^2*c*x^7 + 1/5*b^3*x^5","A",0
159,1,35,0,0.462070," ","integrate((c*x^4+b*x^2)^3/x^3,x, algorithm=""fricas"")","\frac{1}{10} \, c^{3} x^{10} + \frac{3}{8} \, b c^{2} x^{8} + \frac{1}{2} \, b^{2} c x^{6} + \frac{1}{4} \, b^{3} x^{4}"," ",0,"1/10*c^3*x^10 + 3/8*b*c^2*x^8 + 1/2*b^2*c*x^6 + 1/4*b^3*x^4","A",0
160,1,35,0,0.558014," ","integrate((c*x^4+b*x^2)^3/x^4,x, algorithm=""fricas"")","\frac{1}{9} \, c^{3} x^{9} + \frac{3}{7} \, b c^{2} x^{7} + \frac{3}{5} \, b^{2} c x^{5} + \frac{1}{3} \, b^{3} x^{3}"," ",0,"1/9*c^3*x^9 + 3/7*b*c^2*x^7 + 3/5*b^2*c*x^5 + 1/3*b^3*x^3","A",0
161,1,35,0,0.404380," ","integrate((c*x^4+b*x^2)^3/x^5,x, algorithm=""fricas"")","\frac{1}{8} \, c^{3} x^{8} + \frac{1}{2} \, b c^{2} x^{6} + \frac{3}{4} \, b^{2} c x^{4} + \frac{1}{2} \, b^{3} x^{2}"," ",0,"1/8*c^3*x^8 + 1/2*b*c^2*x^6 + 3/4*b^2*c*x^4 + 1/2*b^3*x^2","B",0
162,1,31,0,0.636768," ","integrate((c*x^4+b*x^2)^3/x^6,x, algorithm=""fricas"")","\frac{1}{7} \, c^{3} x^{7} + \frac{3}{5} \, b c^{2} x^{5} + b^{2} c x^{3} + b^{3} x"," ",0,"1/7*c^3*x^7 + 3/5*b*c^2*x^5 + b^2*c*x^3 + b^3*x","A",0
163,1,33,0,0.552270," ","integrate((c*x^4+b*x^2)^3/x^7,x, algorithm=""fricas"")","\frac{1}{6} \, c^{3} x^{6} + \frac{3}{4} \, b c^{2} x^{4} + \frac{3}{2} \, b^{2} c x^{2} + b^{3} \log\left(x\right)"," ",0,"1/6*c^3*x^6 + 3/4*b*c^2*x^4 + 3/2*b^2*c*x^2 + b^3*log(x)","A",0
164,1,36,0,0.537778," ","integrate((c*x^4+b*x^2)^3/x^8,x, algorithm=""fricas"")","\frac{c^{3} x^{6} + 5 \, b c^{2} x^{4} + 15 \, b^{2} c x^{2} - 5 \, b^{3}}{5 \, x}"," ",0,"1/5*(c^3*x^6 + 5*b*c^2*x^4 + 15*b^2*c*x^2 - 5*b^3)/x","A",0
165,1,38,0,0.679610," ","integrate((c*x^4+b*x^2)^3/x^9,x, algorithm=""fricas"")","\frac{c^{3} x^{6} + 6 \, b c^{2} x^{4} + 12 \, b^{2} c x^{2} \log\left(x\right) - 2 \, b^{3}}{4 \, x^{2}}"," ",0,"1/4*(c^3*x^6 + 6*b*c^2*x^4 + 12*b^2*c*x^2*log(x) - 2*b^3)/x^2","A",0
166,1,36,0,0.452632," ","integrate((c*x^4+b*x^2)^3/x^10,x, algorithm=""fricas"")","\frac{c^{3} x^{6} + 9 \, b c^{2} x^{4} - 9 \, b^{2} c x^{2} - b^{3}}{3 \, x^{3}}"," ",0,"1/3*(c^3*x^6 + 9*b*c^2*x^4 - 9*b^2*c*x^2 - b^3)/x^3","A",0
167,1,39,0,0.603161," ","integrate((c*x^4+b*x^2)^3/x^11,x, algorithm=""fricas"")","\frac{2 \, c^{3} x^{6} + 12 \, b c^{2} x^{4} \log\left(x\right) - 6 \, b^{2} c x^{2} - b^{3}}{4 \, x^{4}}"," ",0,"1/4*(2*c^3*x^6 + 12*b*c^2*x^4*log(x) - 6*b^2*c*x^2 - b^3)/x^4","A",0
168,1,37,0,0.738431," ","integrate((c*x^4+b*x^2)^3/x^12,x, algorithm=""fricas"")","\frac{5 \, c^{3} x^{6} - 15 \, b c^{2} x^{4} - 5 \, b^{2} c x^{2} - b^{3}}{5 \, x^{5}}"," ",0,"1/5*(5*c^3*x^6 - 15*b*c^2*x^4 - 5*b^2*c*x^2 - b^3)/x^5","A",0
169,1,39,0,0.652382," ","integrate((c*x^4+b*x^2)^3/x^13,x, algorithm=""fricas"")","\frac{12 \, c^{3} x^{6} \log\left(x\right) - 18 \, b c^{2} x^{4} - 9 \, b^{2} c x^{2} - 2 \, b^{3}}{12 \, x^{6}}"," ",0,"1/12*(12*c^3*x^6*log(x) - 18*b*c^2*x^4 - 9*b^2*c*x^2 - 2*b^3)/x^6","A",0
170,1,37,0,0.686129," ","integrate((c*x^4+b*x^2)^3/x^14,x, algorithm=""fricas"")","-\frac{35 \, c^{3} x^{6} + 35 \, b c^{2} x^{4} + 21 \, b^{2} c x^{2} + 5 \, b^{3}}{35 \, x^{7}}"," ",0,"-1/35*(35*c^3*x^6 + 35*b*c^2*x^4 + 21*b^2*c*x^2 + 5*b^3)/x^7","A",0
171,1,35,0,0.765968," ","integrate((c*x^4+b*x^2)^3/x^15,x, algorithm=""fricas"")","-\frac{4 \, c^{3} x^{6} + 6 \, b c^{2} x^{4} + 4 \, b^{2} c x^{2} + b^{3}}{8 \, x^{8}}"," ",0,"-1/8*(4*c^3*x^6 + 6*b*c^2*x^4 + 4*b^2*c*x^2 + b^3)/x^8","B",0
172,1,37,0,0.609461," ","integrate((c*x^4+b*x^2)^3/x^16,x, algorithm=""fricas"")","-\frac{105 \, c^{3} x^{6} + 189 \, b c^{2} x^{4} + 135 \, b^{2} c x^{2} + 35 \, b^{3}}{315 \, x^{9}}"," ",0,"-1/315*(105*c^3*x^6 + 189*b*c^2*x^4 + 135*b^2*c*x^2 + 35*b^3)/x^9","A",0
173,1,37,0,0.697174," ","integrate((c*x^4+b*x^2)^3/x^17,x, algorithm=""fricas"")","-\frac{10 \, c^{3} x^{6} + 20 \, b c^{2} x^{4} + 15 \, b^{2} c x^{2} + 4 \, b^{3}}{40 \, x^{10}}"," ",0,"-1/40*(10*c^3*x^6 + 20*b*c^2*x^4 + 15*b^2*c*x^2 + 4*b^3)/x^10","A",0
174,1,148,0,0.587457," ","integrate(x^10/(c*x^4+b*x^2),x, algorithm=""fricas"")","\left[\frac{30 \, c^{3} x^{7} - 42 \, b c^{2} x^{5} + 70 \, b^{2} c x^{3} + 105 \, b^{3} \sqrt{-\frac{b}{c}} \log\left(\frac{c x^{2} + 2 \, c x \sqrt{-\frac{b}{c}} - b}{c x^{2} + b}\right) - 210 \, b^{3} x}{210 \, c^{4}}, \frac{15 \, c^{3} x^{7} - 21 \, b c^{2} x^{5} + 35 \, b^{2} c x^{3} + 105 \, b^{3} \sqrt{\frac{b}{c}} \arctan\left(\frac{c x \sqrt{\frac{b}{c}}}{b}\right) - 105 \, b^{3} x}{105 \, c^{4}}\right]"," ",0,"[1/210*(30*c^3*x^7 - 42*b*c^2*x^5 + 70*b^2*c*x^3 + 105*b^3*sqrt(-b/c)*log((c*x^2 + 2*c*x*sqrt(-b/c) - b)/(c*x^2 + b)) - 210*b^3*x)/c^4, 1/105*(15*c^3*x^7 - 21*b*c^2*x^5 + 35*b^2*c*x^3 + 105*b^3*sqrt(b/c)*arctan(c*x*sqrt(b/c)/b) - 105*b^3*x)/c^4]","A",0
175,1,45,0,1.308634," ","integrate(x^9/(c*x^4+b*x^2),x, algorithm=""fricas"")","\frac{2 \, c^{3} x^{6} - 3 \, b c^{2} x^{4} + 6 \, b^{2} c x^{2} - 6 \, b^{3} \log\left(c x^{2} + b\right)}{12 \, c^{4}}"," ",0,"1/12*(2*c^3*x^6 - 3*b*c^2*x^4 + 6*b^2*c*x^2 - 6*b^3*log(c*x^2 + b))/c^4","A",0
176,1,126,0,0.828592," ","integrate(x^8/(c*x^4+b*x^2),x, algorithm=""fricas"")","\left[\frac{6 \, c^{2} x^{5} - 10 \, b c x^{3} + 15 \, b^{2} \sqrt{-\frac{b}{c}} \log\left(\frac{c x^{2} - 2 \, c x \sqrt{-\frac{b}{c}} - b}{c x^{2} + b}\right) + 30 \, b^{2} x}{30 \, c^{3}}, \frac{3 \, c^{2} x^{5} - 5 \, b c x^{3} - 15 \, b^{2} \sqrt{\frac{b}{c}} \arctan\left(\frac{c x \sqrt{\frac{b}{c}}}{b}\right) + 15 \, b^{2} x}{15 \, c^{3}}\right]"," ",0,"[1/30*(6*c^2*x^5 - 10*b*c*x^3 + 15*b^2*sqrt(-b/c)*log((c*x^2 - 2*c*x*sqrt(-b/c) - b)/(c*x^2 + b)) + 30*b^2*x)/c^3, 1/15*(3*c^2*x^5 - 5*b*c*x^3 - 15*b^2*sqrt(b/c)*arctan(c*x*sqrt(b/c)/b) + 15*b^2*x)/c^3]","A",0
177,1,33,0,0.574182," ","integrate(x^7/(c*x^4+b*x^2),x, algorithm=""fricas"")","\frac{c^{2} x^{4} - 2 \, b c x^{2} + 2 \, b^{2} \log\left(c x^{2} + b\right)}{4 \, c^{3}}"," ",0,"1/4*(c^2*x^4 - 2*b*c*x^2 + 2*b^2*log(c*x^2 + b))/c^3","A",0
178,1,99,0,0.601604," ","integrate(x^6/(c*x^4+b*x^2),x, algorithm=""fricas"")","\left[\frac{2 \, c x^{3} + 3 \, b \sqrt{-\frac{b}{c}} \log\left(\frac{c x^{2} + 2 \, c x \sqrt{-\frac{b}{c}} - b}{c x^{2} + b}\right) - 6 \, b x}{6 \, c^{2}}, \frac{c x^{3} + 3 \, b \sqrt{\frac{b}{c}} \arctan\left(\frac{c x \sqrt{\frac{b}{c}}}{b}\right) - 3 \, b x}{3 \, c^{2}}\right]"," ",0,"[1/6*(2*c*x^3 + 3*b*sqrt(-b/c)*log((c*x^2 + 2*c*x*sqrt(-b/c) - b)/(c*x^2 + b)) - 6*b*x)/c^2, 1/3*(c*x^3 + 3*b*sqrt(b/c)*arctan(c*x*sqrt(b/c)/b) - 3*b*x)/c^2]","A",0
179,1,22,0,0.608265," ","integrate(x^5/(c*x^4+b*x^2),x, algorithm=""fricas"")","\frac{c x^{2} - b \log\left(c x^{2} + b\right)}{2 \, c^{2}}"," ",0,"1/2*(c*x^2 - b*log(c*x^2 + b))/c^2","A",0
180,1,82,0,0.624511," ","integrate(x^4/(c*x^4+b*x^2),x, algorithm=""fricas"")","\left[\frac{\sqrt{-\frac{b}{c}} \log\left(\frac{c x^{2} - 2 \, c x \sqrt{-\frac{b}{c}} - b}{c x^{2} + b}\right) + 2 \, x}{2 \, c}, -\frac{\sqrt{\frac{b}{c}} \arctan\left(\frac{c x \sqrt{\frac{b}{c}}}{b}\right) - x}{c}\right]"," ",0,"[1/2*(sqrt(-b/c)*log((c*x^2 - 2*c*x*sqrt(-b/c) - b)/(c*x^2 + b)) + 2*x)/c, -(sqrt(b/c)*arctan(c*x*sqrt(b/c)/b) - x)/c]","A",0
181,1,13,0,0.611666," ","integrate(x^3/(c*x^4+b*x^2),x, algorithm=""fricas"")","\frac{\log\left(c x^{2} + b\right)}{2 \, c}"," ",0,"1/2*log(c*x^2 + b)/c","A",0
182,1,67,0,0.620645," ","integrate(x^2/(c*x^4+b*x^2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-b c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-b c} x - b}{c x^{2} + b}\right)}{2 \, b c}, \frac{\sqrt{b c} \arctan\left(\frac{\sqrt{b c} x}{b}\right)}{b c}\right]"," ",0,"[-1/2*sqrt(-b*c)*log((c*x^2 - 2*sqrt(-b*c)*x - b)/(c*x^2 + b))/(b*c), sqrt(b*c)*arctan(sqrt(b*c)*x/b)/(b*c)]","A",0
183,1,18,0,0.617784," ","integrate(x/(c*x^4+b*x^2),x, algorithm=""fricas"")","-\frac{\log\left(c x^{2} + b\right) - 2 \, \log\left(x\right)}{2 \, b}"," ",0,"-1/2*(log(c*x^2 + b) - 2*log(x))/b","A",0
184,1,82,0,0.598493," ","integrate(1/(c*x^4+b*x^2),x, algorithm=""fricas"")","\left[\frac{x \sqrt{-\frac{c}{b}} \log\left(\frac{c x^{2} - 2 \, b x \sqrt{-\frac{c}{b}} - b}{c x^{2} + b}\right) - 2}{2 \, b x}, -\frac{x \sqrt{\frac{c}{b}} \arctan\left(x \sqrt{\frac{c}{b}}\right) + 1}{b x}\right]"," ",0,"[1/2*(x*sqrt(-c/b)*log((c*x^2 - 2*b*x*sqrt(-c/b) - b)/(c*x^2 + b)) - 2)/(b*x), -(x*sqrt(c/b)*arctan(x*sqrt(c/b)) + 1)/(b*x)]","A",0
185,1,33,0,0.655640," ","integrate(1/x/(c*x^4+b*x^2),x, algorithm=""fricas"")","\frac{c x^{2} \log\left(c x^{2} + b\right) - 2 \, c x^{2} \log\left(x\right) - b}{2 \, b^{2} x^{2}}"," ",0,"1/2*(c*x^2*log(c*x^2 + b) - 2*c*x^2*log(x) - b)/(b^2*x^2)","A",0
186,1,106,0,0.561993," ","integrate(1/x^2/(c*x^4+b*x^2),x, algorithm=""fricas"")","\left[\frac{3 \, c x^{3} \sqrt{-\frac{c}{b}} \log\left(\frac{c x^{2} + 2 \, b x \sqrt{-\frac{c}{b}} - b}{c x^{2} + b}\right) + 6 \, c x^{2} - 2 \, b}{6 \, b^{2} x^{3}}, \frac{3 \, c x^{3} \sqrt{\frac{c}{b}} \arctan\left(x \sqrt{\frac{c}{b}}\right) + 3 \, c x^{2} - b}{3 \, b^{2} x^{3}}\right]"," ",0,"[1/6*(3*c*x^3*sqrt(-c/b)*log((c*x^2 + 2*b*x*sqrt(-c/b) - b)/(c*x^2 + b)) + 6*c*x^2 - 2*b)/(b^2*x^3), 1/3*(3*c*x^3*sqrt(c/b)*arctan(x*sqrt(c/b)) + 3*c*x^2 - b)/(b^2*x^3)]","A",0
187,1,45,0,1.082752," ","integrate(1/x^3/(c*x^4+b*x^2),x, algorithm=""fricas"")","-\frac{2 \, c^{2} x^{4} \log\left(c x^{2} + b\right) - 4 \, c^{2} x^{4} \log\left(x\right) - 2 \, b c x^{2} + b^{2}}{4 \, b^{3} x^{4}}"," ",0,"-1/4*(2*c^2*x^4*log(c*x^2 + b) - 4*c^2*x^4*log(x) - 2*b*c*x^2 + b^2)/(b^3*x^4)","A",0
188,1,132,0,0.582061," ","integrate(1/x^4/(c*x^4+b*x^2),x, algorithm=""fricas"")","\left[\frac{15 \, c^{2} x^{5} \sqrt{-\frac{c}{b}} \log\left(\frac{c x^{2} - 2 \, b x \sqrt{-\frac{c}{b}} - b}{c x^{2} + b}\right) - 30 \, c^{2} x^{4} + 10 \, b c x^{2} - 6 \, b^{2}}{30 \, b^{3} x^{5}}, -\frac{15 \, c^{2} x^{5} \sqrt{\frac{c}{b}} \arctan\left(x \sqrt{\frac{c}{b}}\right) + 15 \, c^{2} x^{4} - 5 \, b c x^{2} + 3 \, b^{2}}{15 \, b^{3} x^{5}}\right]"," ",0,"[1/30*(15*c^2*x^5*sqrt(-c/b)*log((c*x^2 - 2*b*x*sqrt(-c/b) - b)/(c*x^2 + b)) - 30*c^2*x^4 + 10*b*c*x^2 - 6*b^2)/(b^3*x^5), -1/15*(15*c^2*x^5*sqrt(c/b)*arctan(x*sqrt(c/b)) + 15*c^2*x^4 - 5*b*c*x^2 + 3*b^2)/(b^3*x^5)]","A",0
189,1,58,0,0.736969," ","integrate(1/x^5/(c*x^4+b*x^2),x, algorithm=""fricas"")","\frac{6 \, c^{3} x^{6} \log\left(c x^{2} + b\right) - 12 \, c^{3} x^{6} \log\left(x\right) - 6 \, b c^{2} x^{4} + 3 \, b^{2} c x^{2} - 2 \, b^{3}}{12 \, b^{4} x^{6}}"," ",0,"1/12*(6*c^3*x^6*log(c*x^2 + b) - 12*c^3*x^6*log(x) - 6*b*c^2*x^4 + 3*b^2*c*x^2 - 2*b^3)/(b^4*x^6)","A",0
190,1,190,0,0.528870," ","integrate(x^12/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","\left[\frac{12 \, c^{3} x^{7} - 28 \, b c^{2} x^{5} + 140 \, b^{2} c x^{3} + 210 \, b^{3} x + 105 \, {\left(b^{2} c x^{2} + b^{3}\right)} \sqrt{-\frac{b}{c}} \log\left(\frac{c x^{2} - 2 \, c x \sqrt{-\frac{b}{c}} - b}{c x^{2} + b}\right)}{60 \, {\left(c^{5} x^{2} + b c^{4}\right)}}, \frac{6 \, c^{3} x^{7} - 14 \, b c^{2} x^{5} + 70 \, b^{2} c x^{3} + 105 \, b^{3} x - 105 \, {\left(b^{2} c x^{2} + b^{3}\right)} \sqrt{\frac{b}{c}} \arctan\left(\frac{c x \sqrt{\frac{b}{c}}}{b}\right)}{30 \, {\left(c^{5} x^{2} + b c^{4}\right)}}\right]"," ",0,"[1/60*(12*c^3*x^7 - 28*b*c^2*x^5 + 140*b^2*c*x^3 + 210*b^3*x + 105*(b^2*c*x^2 + b^3)*sqrt(-b/c)*log((c*x^2 - 2*c*x*sqrt(-b/c) - b)/(c*x^2 + b)))/(c^5*x^2 + b*c^4), 1/30*(6*c^3*x^7 - 14*b*c^2*x^5 + 70*b^2*c*x^3 + 105*b^3*x - 105*(b^2*c*x^2 + b^3)*sqrt(b/c)*arctan(c*x*sqrt(b/c)/b))/(c^5*x^2 + b*c^4)]","A",0
191,1,70,0,0.534437," ","integrate(x^11/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","\frac{c^{3} x^{6} - 3 \, b c^{2} x^{4} - 4 \, b^{2} c x^{2} + 2 \, b^{3} + 6 \, {\left(b^{2} c x^{2} + b^{3}\right)} \log\left(c x^{2} + b\right)}{4 \, {\left(c^{5} x^{2} + b c^{4}\right)}}"," ",0,"1/4*(c^3*x^6 - 3*b*c^2*x^4 - 4*b^2*c*x^2 + 2*b^3 + 6*(b^2*c*x^2 + b^3)*log(c*x^2 + b))/(c^5*x^2 + b*c^4)","A",0
192,1,164,0,0.539547," ","integrate(x^10/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","\left[\frac{4 \, c^{2} x^{5} - 20 \, b c x^{3} - 30 \, b^{2} x + 15 \, {\left(b c x^{2} + b^{2}\right)} \sqrt{-\frac{b}{c}} \log\left(\frac{c x^{2} + 2 \, c x \sqrt{-\frac{b}{c}} - b}{c x^{2} + b}\right)}{12 \, {\left(c^{4} x^{2} + b c^{3}\right)}}, \frac{2 \, c^{2} x^{5} - 10 \, b c x^{3} - 15 \, b^{2} x + 15 \, {\left(b c x^{2} + b^{2}\right)} \sqrt{\frac{b}{c}} \arctan\left(\frac{c x \sqrt{\frac{b}{c}}}{b}\right)}{6 \, {\left(c^{4} x^{2} + b c^{3}\right)}}\right]"," ",0,"[1/12*(4*c^2*x^5 - 20*b*c*x^3 - 30*b^2*x + 15*(b*c*x^2 + b^2)*sqrt(-b/c)*log((c*x^2 + 2*c*x*sqrt(-b/c) - b)/(c*x^2 + b)))/(c^4*x^2 + b*c^3), 1/6*(2*c^2*x^5 - 10*b*c*x^3 - 15*b^2*x + 15*(b*c*x^2 + b^2)*sqrt(b/c)*arctan(c*x*sqrt(b/c)/b))/(c^4*x^2 + b*c^3)]","A",0
193,1,56,0,0.615227," ","integrate(x^9/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","\frac{c^{2} x^{4} + b c x^{2} - b^{2} - 2 \, {\left(b c x^{2} + b^{2}\right)} \log\left(c x^{2} + b\right)}{2 \, {\left(c^{4} x^{2} + b c^{3}\right)}}"," ",0,"1/2*(c^2*x^4 + b*c*x^2 - b^2 - 2*(b*c*x^2 + b^2)*log(c*x^2 + b))/(c^4*x^2 + b*c^3)","A",0
194,1,136,0,0.487538," ","integrate(x^8/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","\left[\frac{4 \, c x^{3} + 3 \, {\left(c x^{2} + b\right)} \sqrt{-\frac{b}{c}} \log\left(\frac{c x^{2} - 2 \, c x \sqrt{-\frac{b}{c}} - b}{c x^{2} + b}\right) + 6 \, b x}{4 \, {\left(c^{3} x^{2} + b c^{2}\right)}}, \frac{2 \, c x^{3} - 3 \, {\left(c x^{2} + b\right)} \sqrt{\frac{b}{c}} \arctan\left(\frac{c x \sqrt{\frac{b}{c}}}{b}\right) + 3 \, b x}{2 \, {\left(c^{3} x^{2} + b c^{2}\right)}}\right]"," ",0,"[1/4*(4*c*x^3 + 3*(c*x^2 + b)*sqrt(-b/c)*log((c*x^2 - 2*c*x*sqrt(-b/c) - b)/(c*x^2 + b)) + 6*b*x)/(c^3*x^2 + b*c^2), 1/2*(2*c*x^3 - 3*(c*x^2 + b)*sqrt(b/c)*arctan(c*x*sqrt(b/c)/b) + 3*b*x)/(c^3*x^2 + b*c^2)]","A",0
195,1,35,0,0.448071," ","integrate(x^7/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","\frac{{\left(c x^{2} + b\right)} \log\left(c x^{2} + b\right) + b}{2 \, {\left(c^{3} x^{2} + b c^{2}\right)}}"," ",0,"1/2*((c*x^2 + b)*log(c*x^2 + b) + b)/(c^3*x^2 + b*c^2)","A",0
196,1,120,0,0.510789," ","integrate(x^6/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","\left[-\frac{2 \, b c x + {\left(c x^{2} + b\right)} \sqrt{-b c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-b c} x - b}{c x^{2} + b}\right)}{4 \, {\left(b c^{3} x^{2} + b^{2} c^{2}\right)}}, -\frac{b c x - {\left(c x^{2} + b\right)} \sqrt{b c} \arctan\left(\frac{\sqrt{b c} x}{b}\right)}{2 \, {\left(b c^{3} x^{2} + b^{2} c^{2}\right)}}\right]"," ",0,"[-1/4*(2*b*c*x + (c*x^2 + b)*sqrt(-b*c)*log((c*x^2 - 2*sqrt(-b*c)*x - b)/(c*x^2 + b)))/(b*c^3*x^2 + b^2*c^2), -1/2*(b*c*x - (c*x^2 + b)*sqrt(b*c)*arctan(sqrt(b*c)*x/b))/(b*c^3*x^2 + b^2*c^2)]","A",0
197,1,15,0,0.623905," ","integrate(x^5/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","-\frac{1}{2 \, {\left(c^{2} x^{2} + b c\right)}}"," ",0,"-1/2/(c^2*x^2 + b*c)","A",0
198,1,120,0,0.712504," ","integrate(x^4/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","\left[\frac{2 \, b c x - {\left(c x^{2} + b\right)} \sqrt{-b c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-b c} x - b}{c x^{2} + b}\right)}{4 \, {\left(b^{2} c^{2} x^{2} + b^{3} c\right)}}, \frac{b c x + {\left(c x^{2} + b\right)} \sqrt{b c} \arctan\left(\frac{\sqrt{b c} x}{b}\right)}{2 \, {\left(b^{2} c^{2} x^{2} + b^{3} c\right)}}\right]"," ",0,"[1/4*(2*b*c*x - (c*x^2 + b)*sqrt(-b*c)*log((c*x^2 - 2*sqrt(-b*c)*x - b)/(c*x^2 + b)))/(b^2*c^2*x^2 + b^3*c), 1/2*(b*c*x + (c*x^2 + b)*sqrt(b*c)*arctan(sqrt(b*c)*x/b))/(b^2*c^2*x^2 + b^3*c)]","A",0
199,1,47,0,0.591772," ","integrate(x^3/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","-\frac{{\left(c x^{2} + b\right)} \log\left(c x^{2} + b\right) - 2 \, {\left(c x^{2} + b\right)} \log\left(x\right) - b}{2 \, {\left(b^{2} c x^{2} + b^{3}\right)}}"," ",0,"-1/2*((c*x^2 + b)*log(c*x^2 + b) - 2*(c*x^2 + b)*log(x) - b)/(b^2*c*x^2 + b^3)","A",0
200,1,136,0,0.751061," ","integrate(x^2/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","\left[-\frac{6 \, c x^{2} - 3 \, {\left(c x^{3} + b x\right)} \sqrt{-\frac{c}{b}} \log\left(\frac{c x^{2} - 2 \, b x \sqrt{-\frac{c}{b}} - b}{c x^{2} + b}\right) + 4 \, b}{4 \, {\left(b^{2} c x^{3} + b^{3} x\right)}}, -\frac{3 \, c x^{2} + 3 \, {\left(c x^{3} + b x\right)} \sqrt{\frac{c}{b}} \arctan\left(x \sqrt{\frac{c}{b}}\right) + 2 \, b}{2 \, {\left(b^{2} c x^{3} + b^{3} x\right)}}\right]"," ",0,"[-1/4*(6*c*x^2 - 3*(c*x^3 + b*x)*sqrt(-c/b)*log((c*x^2 - 2*b*x*sqrt(-c/b) - b)/(c*x^2 + b)) + 4*b)/(b^2*c*x^3 + b^3*x), -1/2*(3*c*x^2 + 3*(c*x^3 + b*x)*sqrt(c/b)*arctan(x*sqrt(c/b)) + 2*b)/(b^2*c*x^3 + b^3*x)]","A",0
201,1,73,0,1.092277," ","integrate(x/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","-\frac{2 \, b c x^{2} + b^{2} - 2 \, {\left(c^{2} x^{4} + b c x^{2}\right)} \log\left(c x^{2} + b\right) + 4 \, {\left(c^{2} x^{4} + b c x^{2}\right)} \log\left(x\right)}{2 \, {\left(b^{3} c x^{4} + b^{4} x^{2}\right)}}"," ",0,"-1/2*(2*b*c*x^2 + b^2 - 2*(c^2*x^4 + b*c*x^2)*log(c*x^2 + b) + 4*(c^2*x^4 + b*c*x^2)*log(x))/(b^3*c*x^4 + b^4*x^2)","A",0
202,1,172,0,1.025775," ","integrate(1/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","\left[\frac{30 \, c^{2} x^{4} + 20 \, b c x^{2} + 15 \, {\left(c^{2} x^{5} + b c x^{3}\right)} \sqrt{-\frac{c}{b}} \log\left(\frac{c x^{2} + 2 \, b x \sqrt{-\frac{c}{b}} - b}{c x^{2} + b}\right) - 4 \, b^{2}}{12 \, {\left(b^{3} c x^{5} + b^{4} x^{3}\right)}}, \frac{15 \, c^{2} x^{4} + 10 \, b c x^{2} + 15 \, {\left(c^{2} x^{5} + b c x^{3}\right)} \sqrt{\frac{c}{b}} \arctan\left(x \sqrt{\frac{c}{b}}\right) - 2 \, b^{2}}{6 \, {\left(b^{3} c x^{5} + b^{4} x^{3}\right)}}\right]"," ",0,"[1/12*(30*c^2*x^4 + 20*b*c*x^2 + 15*(c^2*x^5 + b*c*x^3)*sqrt(-c/b)*log((c*x^2 + 2*b*x*sqrt(-c/b) - b)/(c*x^2 + b)) - 4*b^2)/(b^3*c*x^5 + b^4*x^3), 1/6*(15*c^2*x^4 + 10*b*c*x^2 + 15*(c^2*x^5 + b*c*x^3)*sqrt(c/b)*arctan(x*sqrt(c/b)) - 2*b^2)/(b^3*c*x^5 + b^4*x^3)]","A",0
203,1,90,0,0.748875," ","integrate(1/x/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","\frac{6 \, b c^{2} x^{4} + 3 \, b^{2} c x^{2} - b^{3} - 6 \, {\left(c^{3} x^{6} + b c^{2} x^{4}\right)} \log\left(c x^{2} + b\right) + 12 \, {\left(c^{3} x^{6} + b c^{2} x^{4}\right)} \log\left(x\right)}{4 \, {\left(b^{4} c x^{6} + b^{5} x^{4}\right)}}"," ",0,"1/4*(6*b*c^2*x^4 + 3*b^2*c*x^2 - b^3 - 6*(c^3*x^6 + b*c^2*x^4)*log(c*x^2 + b) + 12*(c^3*x^6 + b*c^2*x^4)*log(x))/(b^4*c*x^6 + b^5*x^4)","A",0
204,1,198,0,0.656574," ","integrate(1/x^2/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","\left[-\frac{210 \, c^{3} x^{6} + 140 \, b c^{2} x^{4} - 28 \, b^{2} c x^{2} + 12 \, b^{3} - 105 \, {\left(c^{3} x^{7} + b c^{2} x^{5}\right)} \sqrt{-\frac{c}{b}} \log\left(\frac{c x^{2} - 2 \, b x \sqrt{-\frac{c}{b}} - b}{c x^{2} + b}\right)}{60 \, {\left(b^{4} c x^{7} + b^{5} x^{5}\right)}}, -\frac{105 \, c^{3} x^{6} + 70 \, b c^{2} x^{4} - 14 \, b^{2} c x^{2} + 6 \, b^{3} + 105 \, {\left(c^{3} x^{7} + b c^{2} x^{5}\right)} \sqrt{\frac{c}{b}} \arctan\left(x \sqrt{\frac{c}{b}}\right)}{30 \, {\left(b^{4} c x^{7} + b^{5} x^{5}\right)}}\right]"," ",0,"[-1/60*(210*c^3*x^6 + 140*b*c^2*x^4 - 28*b^2*c*x^2 + 12*b^3 - 105*(c^3*x^7 + b*c^2*x^5)*sqrt(-c/b)*log((c*x^2 - 2*b*x*sqrt(-c/b) - b)/(c*x^2 + b)))/(b^4*c*x^7 + b^5*x^5), -1/30*(105*c^3*x^6 + 70*b*c^2*x^4 - 14*b^2*c*x^2 + 6*b^3 + 105*(c^3*x^7 + b*c^2*x^5)*sqrt(c/b)*arctan(x*sqrt(c/b)))/(b^4*c*x^7 + b^5*x^5)]","A",0
205,1,230,0,0.387083," ","integrate(x^14/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","\left[\frac{16 \, c^{3} x^{7} - 112 \, b c^{2} x^{5} - 350 \, b^{2} c x^{3} - 210 \, b^{3} x + 105 \, {\left(b c^{2} x^{4} + 2 \, b^{2} c x^{2} + b^{3}\right)} \sqrt{-\frac{b}{c}} \log\left(\frac{c x^{2} + 2 \, c x \sqrt{-\frac{b}{c}} - b}{c x^{2} + b}\right)}{48 \, {\left(c^{6} x^{4} + 2 \, b c^{5} x^{2} + b^{2} c^{4}\right)}}, \frac{8 \, c^{3} x^{7} - 56 \, b c^{2} x^{5} - 175 \, b^{2} c x^{3} - 105 \, b^{3} x + 105 \, {\left(b c^{2} x^{4} + 2 \, b^{2} c x^{2} + b^{3}\right)} \sqrt{\frac{b}{c}} \arctan\left(\frac{c x \sqrt{\frac{b}{c}}}{b}\right)}{24 \, {\left(c^{6} x^{4} + 2 \, b c^{5} x^{2} + b^{2} c^{4}\right)}}\right]"," ",0,"[1/48*(16*c^3*x^7 - 112*b*c^2*x^5 - 350*b^2*c*x^3 - 210*b^3*x + 105*(b*c^2*x^4 + 2*b^2*c*x^2 + b^3)*sqrt(-b/c)*log((c*x^2 + 2*c*x*sqrt(-b/c) - b)/(c*x^2 + b)))/(c^6*x^4 + 2*b*c^5*x^2 + b^2*c^4), 1/24*(8*c^3*x^7 - 56*b*c^2*x^5 - 175*b^2*c*x^3 - 105*b^3*x + 105*(b*c^2*x^4 + 2*b^2*c*x^2 + b^3)*sqrt(b/c)*arctan(c*x*sqrt(b/c)/b))/(c^6*x^4 + 2*b*c^5*x^2 + b^2*c^4)]","A",0
206,1,91,0,0.534282," ","integrate(x^13/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","\frac{2 \, c^{3} x^{6} + 4 \, b c^{2} x^{4} - 4 \, b^{2} c x^{2} - 5 \, b^{3} - 6 \, {\left(b c^{2} x^{4} + 2 \, b^{2} c x^{2} + b^{3}\right)} \log\left(c x^{2} + b\right)}{4 \, {\left(c^{6} x^{4} + 2 \, b c^{5} x^{2} + b^{2} c^{4}\right)}}"," ",0,"1/4*(2*c^3*x^6 + 4*b*c^2*x^4 - 4*b^2*c*x^2 - 5*b^3 - 6*(b*c^2*x^4 + 2*b^2*c*x^2 + b^3)*log(c*x^2 + b))/(c^6*x^4 + 2*b*c^5*x^2 + b^2*c^4)","A",0
207,1,202,0,0.711844," ","integrate(x^12/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","\left[\frac{16 \, c^{2} x^{5} + 50 \, b c x^{3} + 30 \, b^{2} x + 15 \, {\left(c^{2} x^{4} + 2 \, b c x^{2} + b^{2}\right)} \sqrt{-\frac{b}{c}} \log\left(\frac{c x^{2} - 2 \, c x \sqrt{-\frac{b}{c}} - b}{c x^{2} + b}\right)}{16 \, {\left(c^{5} x^{4} + 2 \, b c^{4} x^{2} + b^{2} c^{3}\right)}}, \frac{8 \, c^{2} x^{5} + 25 \, b c x^{3} + 15 \, b^{2} x - 15 \, {\left(c^{2} x^{4} + 2 \, b c x^{2} + b^{2}\right)} \sqrt{\frac{b}{c}} \arctan\left(\frac{c x \sqrt{\frac{b}{c}}}{b}\right)}{8 \, {\left(c^{5} x^{4} + 2 \, b c^{4} x^{2} + b^{2} c^{3}\right)}}\right]"," ",0,"[1/16*(16*c^2*x^5 + 50*b*c*x^3 + 30*b^2*x + 15*(c^2*x^4 + 2*b*c*x^2 + b^2)*sqrt(-b/c)*log((c*x^2 - 2*c*x*sqrt(-b/c) - b)/(c*x^2 + b)))/(c^5*x^4 + 2*b*c^4*x^2 + b^2*c^3), 1/8*(8*c^2*x^5 + 25*b*c*x^3 + 15*b^2*x - 15*(c^2*x^4 + 2*b*c*x^2 + b^2)*sqrt(b/c)*arctan(c*x*sqrt(b/c)/b))/(c^5*x^4 + 2*b*c^4*x^2 + b^2*c^3)]","A",0
208,1,69,0,0.751167," ","integrate(x^11/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","\frac{4 \, b c x^{2} + 3 \, b^{2} + 2 \, {\left(c^{2} x^{4} + 2 \, b c x^{2} + b^{2}\right)} \log\left(c x^{2} + b\right)}{4 \, {\left(c^{5} x^{4} + 2 \, b c^{4} x^{2} + b^{2} c^{3}\right)}}"," ",0,"1/4*(4*b*c*x^2 + 3*b^2 + 2*(c^2*x^4 + 2*b*c*x^2 + b^2)*log(c*x^2 + b))/(c^5*x^4 + 2*b*c^4*x^2 + b^2*c^3)","A",0
209,1,188,0,0.782016," ","integrate(x^10/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","\left[-\frac{10 \, b c^{2} x^{3} + 6 \, b^{2} c x + 3 \, {\left(c^{2} x^{4} + 2 \, b c x^{2} + b^{2}\right)} \sqrt{-b c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-b c} x - b}{c x^{2} + b}\right)}{16 \, {\left(b c^{5} x^{4} + 2 \, b^{2} c^{4} x^{2} + b^{3} c^{3}\right)}}, -\frac{5 \, b c^{2} x^{3} + 3 \, b^{2} c x - 3 \, {\left(c^{2} x^{4} + 2 \, b c x^{2} + b^{2}\right)} \sqrt{b c} \arctan\left(\frac{\sqrt{b c} x}{b}\right)}{8 \, {\left(b c^{5} x^{4} + 2 \, b^{2} c^{4} x^{2} + b^{3} c^{3}\right)}}\right]"," ",0,"[-1/16*(10*b*c^2*x^3 + 6*b^2*c*x + 3*(c^2*x^4 + 2*b*c*x^2 + b^2)*sqrt(-b*c)*log((c*x^2 - 2*sqrt(-b*c)*x - b)/(c*x^2 + b)))/(b*c^5*x^4 + 2*b^2*c^4*x^2 + b^3*c^3), -1/8*(5*b*c^2*x^3 + 3*b^2*c*x - 3*(c^2*x^4 + 2*b*c*x^2 + b^2)*sqrt(b*c)*arctan(sqrt(b*c)*x/b))/(b*c^5*x^4 + 2*b^2*c^4*x^2 + b^3*c^3)]","A",0
210,1,36,0,0.810916," ","integrate(x^9/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","-\frac{2 \, c x^{2} + b}{4 \, {\left(c^{4} x^{4} + 2 \, b c^{3} x^{2} + b^{2} c^{2}\right)}}"," ",0,"-1/4*(2*c*x^2 + b)/(c^4*x^4 + 2*b*c^3*x^2 + b^2*c^2)","B",0
211,1,190,0,1.919144," ","integrate(x^8/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","\left[\frac{2 \, b c^{2} x^{3} - 2 \, b^{2} c x - {\left(c^{2} x^{4} + 2 \, b c x^{2} + b^{2}\right)} \sqrt{-b c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-b c} x - b}{c x^{2} + b}\right)}{16 \, {\left(b^{2} c^{4} x^{4} + 2 \, b^{3} c^{3} x^{2} + b^{4} c^{2}\right)}}, \frac{b c^{2} x^{3} - b^{2} c x + {\left(c^{2} x^{4} + 2 \, b c x^{2} + b^{2}\right)} \sqrt{b c} \arctan\left(\frac{\sqrt{b c} x}{b}\right)}{8 \, {\left(b^{2} c^{4} x^{4} + 2 \, b^{3} c^{3} x^{2} + b^{4} c^{2}\right)}}\right]"," ",0,"[1/16*(2*b*c^2*x^3 - 2*b^2*c*x - (c^2*x^4 + 2*b*c*x^2 + b^2)*sqrt(-b*c)*log((c*x^2 - 2*sqrt(-b*c)*x - b)/(c*x^2 + b)))/(b^2*c^4*x^4 + 2*b^3*c^3*x^2 + b^4*c^2), 1/8*(b*c^2*x^3 - b^2*c*x + (c^2*x^4 + 2*b*c*x^2 + b^2)*sqrt(b*c)*arctan(sqrt(b*c)*x/b))/(b^2*c^4*x^4 + 2*b^3*c^3*x^2 + b^4*c^2)]","A",0
212,1,26,0,0.799770," ","integrate(x^7/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","-\frac{1}{4 \, {\left(c^{3} x^{4} + 2 \, b c^{2} x^{2} + b^{2} c\right)}}"," ",0,"-1/4/(c^3*x^4 + 2*b*c^2*x^2 + b^2*c)","A",0
213,1,188,0,1.185798," ","integrate(x^6/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","\left[\frac{6 \, b c^{2} x^{3} + 10 \, b^{2} c x - 3 \, {\left(c^{2} x^{4} + 2 \, b c x^{2} + b^{2}\right)} \sqrt{-b c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-b c} x - b}{c x^{2} + b}\right)}{16 \, {\left(b^{3} c^{3} x^{4} + 2 \, b^{4} c^{2} x^{2} + b^{5} c\right)}}, \frac{3 \, b c^{2} x^{3} + 5 \, b^{2} c x + 3 \, {\left(c^{2} x^{4} + 2 \, b c x^{2} + b^{2}\right)} \sqrt{b c} \arctan\left(\frac{\sqrt{b c} x}{b}\right)}{8 \, {\left(b^{3} c^{3} x^{4} + 2 \, b^{4} c^{2} x^{2} + b^{5} c\right)}}\right]"," ",0,"[1/16*(6*b*c^2*x^3 + 10*b^2*c*x - 3*(c^2*x^4 + 2*b*c*x^2 + b^2)*sqrt(-b*c)*log((c*x^2 - 2*sqrt(-b*c)*x - b)/(c*x^2 + b)))/(b^3*c^3*x^4 + 2*b^4*c^2*x^2 + b^5*c), 1/8*(3*b*c^2*x^3 + 5*b^2*c*x + 3*(c^2*x^4 + 2*b*c*x^2 + b^2)*sqrt(b*c)*arctan(sqrt(b*c)*x/b))/(b^3*c^3*x^4 + 2*b^4*c^2*x^2 + b^5*c)]","A",0
214,1,90,0,2.309531," ","integrate(x^5/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","\frac{2 \, b c x^{2} + 3 \, b^{2} - 2 \, {\left(c^{2} x^{4} + 2 \, b c x^{2} + b^{2}\right)} \log\left(c x^{2} + b\right) + 4 \, {\left(c^{2} x^{4} + 2 \, b c x^{2} + b^{2}\right)} \log\left(x\right)}{4 \, {\left(b^{3} c^{2} x^{4} + 2 \, b^{4} c x^{2} + b^{5}\right)}}"," ",0,"1/4*(2*b*c*x^2 + 3*b^2 - 2*(c^2*x^4 + 2*b*c*x^2 + b^2)*log(c*x^2 + b) + 4*(c^2*x^4 + 2*b*c*x^2 + b^2)*log(x))/(b^3*c^2*x^4 + 2*b^4*c*x^2 + b^5)","A",0
215,1,202,0,2.470954," ","integrate(x^4/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","\left[-\frac{30 \, c^{2} x^{4} + 50 \, b c x^{2} - 15 \, {\left(c^{2} x^{5} + 2 \, b c x^{3} + b^{2} x\right)} \sqrt{-\frac{c}{b}} \log\left(\frac{c x^{2} - 2 \, b x \sqrt{-\frac{c}{b}} - b}{c x^{2} + b}\right) + 16 \, b^{2}}{16 \, {\left(b^{3} c^{2} x^{5} + 2 \, b^{4} c x^{3} + b^{5} x\right)}}, -\frac{15 \, c^{2} x^{4} + 25 \, b c x^{2} + 15 \, {\left(c^{2} x^{5} + 2 \, b c x^{3} + b^{2} x\right)} \sqrt{\frac{c}{b}} \arctan\left(x \sqrt{\frac{c}{b}}\right) + 8 \, b^{2}}{8 \, {\left(b^{3} c^{2} x^{5} + 2 \, b^{4} c x^{3} + b^{5} x\right)}}\right]"," ",0,"[-1/16*(30*c^2*x^4 + 50*b*c*x^2 - 15*(c^2*x^5 + 2*b*c*x^3 + b^2*x)*sqrt(-c/b)*log((c*x^2 - 2*b*x*sqrt(-c/b) - b)/(c*x^2 + b)) + 16*b^2)/(b^3*c^2*x^5 + 2*b^4*c*x^3 + b^5*x), -1/8*(15*c^2*x^4 + 25*b*c*x^2 + 15*(c^2*x^5 + 2*b*c*x^3 + b^2*x)*sqrt(c/b)*arctan(x*sqrt(c/b)) + 8*b^2)/(b^3*c^2*x^5 + 2*b^4*c*x^3 + b^5*x)]","A",0
216,1,119,0,0.789863," ","integrate(x^3/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","-\frac{6 \, b c^{2} x^{4} + 9 \, b^{2} c x^{2} + 2 \, b^{3} - 6 \, {\left(c^{3} x^{6} + 2 \, b c^{2} x^{4} + b^{2} c x^{2}\right)} \log\left(c x^{2} + b\right) + 12 \, {\left(c^{3} x^{6} + 2 \, b c^{2} x^{4} + b^{2} c x^{2}\right)} \log\left(x\right)}{4 \, {\left(b^{4} c^{2} x^{6} + 2 \, b^{5} c x^{4} + b^{6} x^{2}\right)}}"," ",0,"-1/4*(6*b*c^2*x^4 + 9*b^2*c*x^2 + 2*b^3 - 6*(c^3*x^6 + 2*b*c^2*x^4 + b^2*c*x^2)*log(c*x^2 + b) + 12*(c^3*x^6 + 2*b*c^2*x^4 + b^2*c*x^2)*log(x))/(b^4*c^2*x^6 + 2*b^5*c*x^4 + b^6*x^2)","A",0
217,1,238,0,1.172892," ","integrate(x^2/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","\left[\frac{210 \, c^{3} x^{6} + 350 \, b c^{2} x^{4} + 112 \, b^{2} c x^{2} - 16 \, b^{3} + 105 \, {\left(c^{3} x^{7} + 2 \, b c^{2} x^{5} + b^{2} c x^{3}\right)} \sqrt{-\frac{c}{b}} \log\left(\frac{c x^{2} + 2 \, b x \sqrt{-\frac{c}{b}} - b}{c x^{2} + b}\right)}{48 \, {\left(b^{4} c^{2} x^{7} + 2 \, b^{5} c x^{5} + b^{6} x^{3}\right)}}, \frac{105 \, c^{3} x^{6} + 175 \, b c^{2} x^{4} + 56 \, b^{2} c x^{2} - 8 \, b^{3} + 105 \, {\left(c^{3} x^{7} + 2 \, b c^{2} x^{5} + b^{2} c x^{3}\right)} \sqrt{\frac{c}{b}} \arctan\left(x \sqrt{\frac{c}{b}}\right)}{24 \, {\left(b^{4} c^{2} x^{7} + 2 \, b^{5} c x^{5} + b^{6} x^{3}\right)}}\right]"," ",0,"[1/48*(210*c^3*x^6 + 350*b*c^2*x^4 + 112*b^2*c*x^2 - 16*b^3 + 105*(c^3*x^7 + 2*b*c^2*x^5 + b^2*c*x^3)*sqrt(-c/b)*log((c*x^2 + 2*b*x*sqrt(-c/b) - b)/(c*x^2 + b)))/(b^4*c^2*x^7 + 2*b^5*c*x^5 + b^6*x^3), 1/24*(105*c^3*x^6 + 175*b*c^2*x^4 + 56*b^2*c*x^2 - 8*b^3 + 105*(c^3*x^7 + 2*b*c^2*x^5 + b^2*c*x^3)*sqrt(c/b)*arctan(x*sqrt(c/b)))/(b^4*c^2*x^7 + 2*b^5*c*x^5 + b^6*x^3)]","A",0
218,1,134,0,0.732519," ","integrate(x/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","\frac{12 \, b c^{3} x^{6} + 18 \, b^{2} c^{2} x^{4} + 4 \, b^{3} c x^{2} - b^{4} - 12 \, {\left(c^{4} x^{8} + 2 \, b c^{3} x^{6} + b^{2} c^{2} x^{4}\right)} \log\left(c x^{2} + b\right) + 24 \, {\left(c^{4} x^{8} + 2 \, b c^{3} x^{6} + b^{2} c^{2} x^{4}\right)} \log\left(x\right)}{4 \, {\left(b^{5} c^{2} x^{8} + 2 \, b^{6} c x^{6} + b^{7} x^{4}\right)}}"," ",0,"1/4*(12*b*c^3*x^6 + 18*b^2*c^2*x^4 + 4*b^3*c*x^2 - b^4 - 12*(c^4*x^8 + 2*b*c^3*x^6 + b^2*c^2*x^4)*log(c*x^2 + b) + 24*(c^4*x^8 + 2*b*c^3*x^6 + b^2*c^2*x^4)*log(x))/(b^5*c^2*x^8 + 2*b^6*c*x^6 + b^7*x^4)","A",0
219,1,264,0,2.159094," ","integrate(1/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","\left[-\frac{630 \, c^{4} x^{8} + 1050 \, b c^{3} x^{6} + 336 \, b^{2} c^{2} x^{4} - 48 \, b^{3} c x^{2} + 16 \, b^{4} - 315 \, {\left(c^{4} x^{9} + 2 \, b c^{3} x^{7} + b^{2} c^{2} x^{5}\right)} \sqrt{-\frac{c}{b}} \log\left(\frac{c x^{2} - 2 \, b x \sqrt{-\frac{c}{b}} - b}{c x^{2} + b}\right)}{80 \, {\left(b^{5} c^{2} x^{9} + 2 \, b^{6} c x^{7} + b^{7} x^{5}\right)}}, -\frac{315 \, c^{4} x^{8} + 525 \, b c^{3} x^{6} + 168 \, b^{2} c^{2} x^{4} - 24 \, b^{3} c x^{2} + 8 \, b^{4} + 315 \, {\left(c^{4} x^{9} + 2 \, b c^{3} x^{7} + b^{2} c^{2} x^{5}\right)} \sqrt{\frac{c}{b}} \arctan\left(x \sqrt{\frac{c}{b}}\right)}{40 \, {\left(b^{5} c^{2} x^{9} + 2 \, b^{6} c x^{7} + b^{7} x^{5}\right)}}\right]"," ",0,"[-1/80*(630*c^4*x^8 + 1050*b*c^3*x^6 + 336*b^2*c^2*x^4 - 48*b^3*c*x^2 + 16*b^4 - 315*(c^4*x^9 + 2*b*c^3*x^7 + b^2*c^2*x^5)*sqrt(-c/b)*log((c*x^2 - 2*b*x*sqrt(-c/b) - b)/(c*x^2 + b)))/(b^5*c^2*x^9 + 2*b^6*c*x^7 + b^7*x^5), -1/40*(315*c^4*x^8 + 525*b*c^3*x^6 + 168*b^2*c^2*x^4 - 24*b^3*c*x^2 + 8*b^4 + 315*(c^4*x^9 + 2*b*c^3*x^7 + b^2*c^2*x^5)*sqrt(c/b)*arctan(x*sqrt(c/b)))/(b^5*c^2*x^9 + 2*b^6*c*x^7 + b^7*x^5)]","A",0
220,1,145,0,1.920147," ","integrate(1/x/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","-\frac{60 \, b c^{4} x^{8} + 90 \, b^{2} c^{3} x^{6} + 20 \, b^{3} c^{2} x^{4} - 5 \, b^{4} c x^{2} + 2 \, b^{5} - 60 \, {\left(c^{5} x^{10} + 2 \, b c^{4} x^{8} + b^{2} c^{3} x^{6}\right)} \log\left(c x^{2} + b\right) + 120 \, {\left(c^{5} x^{10} + 2 \, b c^{4} x^{8} + b^{2} c^{3} x^{6}\right)} \log\left(x\right)}{12 \, {\left(b^{6} c^{2} x^{10} + 2 \, b^{7} c x^{8} + b^{8} x^{6}\right)}}"," ",0,"-1/12*(60*b*c^4*x^8 + 90*b^2*c^3*x^6 + 20*b^3*c^2*x^4 - 5*b^4*c*x^2 + 2*b^5 - 60*(c^5*x^10 + 2*b*c^4*x^8 + b^2*c^3*x^6)*log(c*x^2 + b) + 120*(c^5*x^10 + 2*b*c^4*x^8 + b^2*c^3*x^6)*log(x))/(b^6*c^2*x^10 + 2*b^7*c*x^8 + b^8*x^6)","A",0
221,1,188,0,1.039206," ","integrate(x^5*(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, b^{4} \sqrt{c} \log\left(-2 \, c x^{2} - b + 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right) + 2 \, {\left(48 \, c^{4} x^{6} + 8 \, b c^{3} x^{4} - 10 \, b^{2} c^{2} x^{2} + 15 \, b^{3} c\right)} \sqrt{c x^{4} + b x^{2}}}{768 \, c^{4}}, \frac{15 \, b^{4} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-c}}{c x^{2} + b}\right) + {\left(48 \, c^{4} x^{6} + 8 \, b c^{3} x^{4} - 10 \, b^{2} c^{2} x^{2} + 15 \, b^{3} c\right)} \sqrt{c x^{4} + b x^{2}}}{384 \, c^{4}}\right]"," ",0,"[1/768*(15*b^4*sqrt(c)*log(-2*c*x^2 - b + 2*sqrt(c*x^4 + b*x^2)*sqrt(c)) + 2*(48*c^4*x^6 + 8*b*c^3*x^4 - 10*b^2*c^2*x^2 + 15*b^3*c)*sqrt(c*x^4 + b*x^2))/c^4, 1/384*(15*b^4*sqrt(-c)*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-c)/(c*x^2 + b)) + (48*c^4*x^6 + 8*b*c^3*x^4 - 10*b^2*c^2*x^2 + 15*b^3*c)*sqrt(c*x^4 + b*x^2))/c^4]","A",0
222,1,167,0,0.819908," ","integrate(x^3*(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, b^{3} \sqrt{c} \log\left(-2 \, c x^{2} - b - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right) + 2 \, {\left(8 \, c^{3} x^{4} + 2 \, b c^{2} x^{2} - 3 \, b^{2} c\right)} \sqrt{c x^{4} + b x^{2}}}{96 \, c^{3}}, -\frac{3 \, b^{3} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-c}}{c x^{2} + b}\right) - {\left(8 \, c^{3} x^{4} + 2 \, b c^{2} x^{2} - 3 \, b^{2} c\right)} \sqrt{c x^{4} + b x^{2}}}{48 \, c^{3}}\right]"," ",0,"[1/96*(3*b^3*sqrt(c)*log(-2*c*x^2 - b - 2*sqrt(c*x^4 + b*x^2)*sqrt(c)) + 2*(8*c^3*x^4 + 2*b*c^2*x^2 - 3*b^2*c)*sqrt(c*x^4 + b*x^2))/c^3, -1/48*(3*b^3*sqrt(-c)*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-c)/(c*x^2 + b)) - (8*c^3*x^4 + 2*b*c^2*x^2 - 3*b^2*c)*sqrt(c*x^4 + b*x^2))/c^3]","A",0
223,1,140,0,0.867902," ","integrate(x*(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{b^{2} \sqrt{c} \log\left(-2 \, c x^{2} - b + 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right) + 2 \, \sqrt{c x^{4} + b x^{2}} {\left(2 \, c^{2} x^{2} + b c\right)}}{16 \, c^{2}}, \frac{b^{2} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-c}}{c x^{2} + b}\right) + \sqrt{c x^{4} + b x^{2}} {\left(2 \, c^{2} x^{2} + b c\right)}}{8 \, c^{2}}\right]"," ",0,"[1/16*(b^2*sqrt(c)*log(-2*c*x^2 - b + 2*sqrt(c*x^4 + b*x^2)*sqrt(c)) + 2*sqrt(c*x^4 + b*x^2)*(2*c^2*x^2 + b*c))/c^2, 1/8*(b^2*sqrt(-c)*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-c)/(c*x^2 + b)) + sqrt(c*x^4 + b*x^2)*(2*c^2*x^2 + b*c))/c^2]","A",0
224,1,115,0,1.104492," ","integrate((c*x^4+b*x^2)^(1/2)/x,x, algorithm=""fricas"")","\left[\frac{b \sqrt{c} \log\left(-2 \, c x^{2} - b - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right) + 2 \, \sqrt{c x^{4} + b x^{2}} c}{4 \, c}, -\frac{b \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-c}}{c x^{2} + b}\right) - \sqrt{c x^{4} + b x^{2}} c}{2 \, c}\right]"," ",0,"[1/4*(b*sqrt(c)*log(-2*c*x^2 - b - 2*sqrt(c*x^4 + b*x^2)*sqrt(c)) + 2*sqrt(c*x^4 + b*x^2)*c)/c, -1/2*(b*sqrt(-c)*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-c)/(c*x^2 + b)) - sqrt(c*x^4 + b*x^2)*c)/c]","A",0
225,1,115,0,0.849829," ","integrate((c*x^4+b*x^2)^(1/2)/x^3,x, algorithm=""fricas"")","\left[\frac{\sqrt{c} x^{2} \log\left(-2 \, c x^{2} - b - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right) - 2 \, \sqrt{c x^{4} + b x^{2}}}{2 \, x^{2}}, -\frac{\sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-c}}{c x^{2} + b}\right) + \sqrt{c x^{4} + b x^{2}}}{x^{2}}\right]"," ",0,"[1/2*(sqrt(c)*x^2*log(-2*c*x^2 - b - 2*sqrt(c*x^4 + b*x^2)*sqrt(c)) - 2*sqrt(c*x^4 + b*x^2))/x^2, -(sqrt(-c)*x^2*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-c)/(c*x^2 + b)) + sqrt(c*x^4 + b*x^2))/x^2]","A",0
226,1,28,0,0.839652," ","integrate((c*x^4+b*x^2)^(1/2)/x^5,x, algorithm=""fricas"")","-\frac{\sqrt{c x^{4} + b x^{2}} {\left(c x^{2} + b\right)}}{3 \, b x^{4}}"," ",0,"-1/3*sqrt(c*x^4 + b*x^2)*(c*x^2 + b)/(b*x^4)","A",0
227,1,42,0,0.582149," ","integrate((c*x^4+b*x^2)^(1/2)/x^7,x, algorithm=""fricas"")","\frac{{\left(2 \, c^{2} x^{4} - b c x^{2} - 3 \, b^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{15 \, b^{2} x^{6}}"," ",0,"1/15*(2*c^2*x^4 - b*c*x^2 - 3*b^2)*sqrt(c*x^4 + b*x^2)/(b^2*x^6)","A",0
228,1,53,0,0.585884," ","integrate((c*x^4+b*x^2)^(1/2)/x^9,x, algorithm=""fricas"")","-\frac{{\left(8 \, c^{3} x^{6} - 4 \, b c^{2} x^{4} + 3 \, b^{2} c x^{2} + 15 \, b^{3}\right)} \sqrt{c x^{4} + b x^{2}}}{105 \, b^{3} x^{8}}"," ",0,"-1/105*(8*c^3*x^6 - 4*b*c^2*x^4 + 3*b^2*c*x^2 + 15*b^3)*sqrt(c*x^4 + b*x^2)/(b^3*x^8)","A",0
229,1,64,0,0.964151," ","integrate((c*x^4+b*x^2)^(1/2)/x^11,x, algorithm=""fricas"")","\frac{{\left(16 \, c^{4} x^{8} - 8 \, b c^{3} x^{6} + 6 \, b^{2} c^{2} x^{4} - 5 \, b^{3} c x^{2} - 35 \, b^{4}\right)} \sqrt{c x^{4} + b x^{2}}}{315 \, b^{4} x^{10}}"," ",0,"1/315*(16*c^4*x^8 - 8*b*c^3*x^6 + 6*b^2*c^2*x^4 - 5*b^3*c*x^2 - 35*b^4)*sqrt(c*x^4 + b*x^2)/(b^4*x^10)","A",0
230,1,75,0,0.942831," ","integrate((c*x^4+b*x^2)^(1/2)/x^13,x, algorithm=""fricas"")","-\frac{{\left(128 \, c^{5} x^{10} - 64 \, b c^{4} x^{8} + 48 \, b^{2} c^{3} x^{6} - 40 \, b^{3} c^{2} x^{4} + 35 \, b^{4} c x^{2} + 315 \, b^{5}\right)} \sqrt{c x^{4} + b x^{2}}}{3465 \, b^{5} x^{12}}"," ",0,"-1/3465*(128*c^5*x^10 - 64*b*c^4*x^8 + 48*b^2*c^3*x^6 - 40*b^3*c^2*x^4 + 35*b^4*c*x^2 + 315*b^5)*sqrt(c*x^4 + b*x^2)/(b^5*x^12)","A",0
231,1,53,0,1.311934," ","integrate(x^4*(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","\frac{{\left(15 \, c^{3} x^{6} + 3 \, b c^{2} x^{4} - 4 \, b^{2} c x^{2} + 8 \, b^{3}\right)} \sqrt{c x^{4} + b x^{2}}}{105 \, c^{3} x}"," ",0,"1/105*(15*c^3*x^6 + 3*b*c^2*x^4 - 4*b^2*c*x^2 + 8*b^3)*sqrt(c*x^4 + b*x^2)/(c^3*x)","A",0
232,1,41,0,0.930116," ","integrate(x^2*(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","\frac{{\left(3 \, c^{2} x^{4} + b c x^{2} - 2 \, b^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{15 \, c^{2} x}"," ",0,"1/15*(3*c^2*x^4 + b*c*x^2 - 2*b^2)*sqrt(c*x^4 + b*x^2)/(c^2*x)","A",0
233,1,28,0,0.987019," ","integrate((c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{c x^{4} + b x^{2}} {\left(c x^{2} + b\right)}}{3 \, c x}"," ",0,"1/3*sqrt(c*x^4 + b*x^2)*(c*x^2 + b)/(c*x)","A",0
234,1,117,0,0.979499," ","integrate((c*x^4+b*x^2)^(1/2)/x^2,x, algorithm=""fricas"")","\left[\frac{\sqrt{b} x \log\left(-\frac{c x^{3} + 2 \, b x - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{b}}{x^{3}}\right) + 2 \, \sqrt{c x^{4} + b x^{2}}}{2 \, x}, \frac{\sqrt{-b} x \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-b}}{c x^{3} + b x}\right) + \sqrt{c x^{4} + b x^{2}}}{x}\right]"," ",0,"[1/2*(sqrt(b)*x*log(-(c*x^3 + 2*b*x - 2*sqrt(c*x^4 + b*x^2)*sqrt(b))/x^3) + 2*sqrt(c*x^4 + b*x^2))/x, (sqrt(-b)*x*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-b)/(c*x^3 + b*x)) + sqrt(c*x^4 + b*x^2))/x]","A",0
235,1,134,0,3.897884," ","integrate((c*x^4+b*x^2)^(1/2)/x^4,x, algorithm=""fricas"")","\left[\frac{\sqrt{b} c x^{3} \log\left(-\frac{c x^{3} + 2 \, b x - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{b}}{x^{3}}\right) - 2 \, \sqrt{c x^{4} + b x^{2}} b}{4 \, b x^{3}}, \frac{\sqrt{-b} c x^{3} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-b}}{c x^{3} + b x}\right) - \sqrt{c x^{4} + b x^{2}} b}{2 \, b x^{3}}\right]"," ",0,"[1/4*(sqrt(b)*c*x^3*log(-(c*x^3 + 2*b*x - 2*sqrt(c*x^4 + b*x^2)*sqrt(b))/x^3) - 2*sqrt(c*x^4 + b*x^2)*b)/(b*x^3), 1/2*(sqrt(-b)*c*x^3*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-b)/(c*x^3 + b*x)) - sqrt(c*x^4 + b*x^2)*b)/(b*x^3)]","A",0
236,1,159,0,1.361579," ","integrate((c*x^4+b*x^2)^(1/2)/x^6,x, algorithm=""fricas"")","\left[\frac{\sqrt{b} c^{2} x^{5} \log\left(-\frac{c x^{3} + 2 \, b x + 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{b}}{x^{3}}\right) - 2 \, \sqrt{c x^{4} + b x^{2}} {\left(b c x^{2} + 2 \, b^{2}\right)}}{16 \, b^{2} x^{5}}, -\frac{\sqrt{-b} c^{2} x^{5} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-b}}{c x^{3} + b x}\right) + \sqrt{c x^{4} + b x^{2}} {\left(b c x^{2} + 2 \, b^{2}\right)}}{8 \, b^{2} x^{5}}\right]"," ",0,"[1/16*(sqrt(b)*c^2*x^5*log(-(c*x^3 + 2*b*x + 2*sqrt(c*x^4 + b*x^2)*sqrt(b))/x^3) - 2*sqrt(c*x^4 + b*x^2)*(b*c*x^2 + 2*b^2))/(b^2*x^5), -1/8*(sqrt(-b)*c^2*x^5*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-b)/(c*x^3 + b*x)) + sqrt(c*x^4 + b*x^2)*(b*c*x^2 + 2*b^2))/(b^2*x^5)]","A",0
237,1,185,0,1.132712," ","integrate((c*x^4+b*x^2)^(1/2)/x^8,x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{b} c^{3} x^{7} \log\left(-\frac{c x^{3} + 2 \, b x - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{b}}{x^{3}}\right) + 2 \, {\left(3 \, b c^{2} x^{4} - 2 \, b^{2} c x^{2} - 8 \, b^{3}\right)} \sqrt{c x^{4} + b x^{2}}}{96 \, b^{3} x^{7}}, \frac{3 \, \sqrt{-b} c^{3} x^{7} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-b}}{c x^{3} + b x}\right) + {\left(3 \, b c^{2} x^{4} - 2 \, b^{2} c x^{2} - 8 \, b^{3}\right)} \sqrt{c x^{4} + b x^{2}}}{48 \, b^{3} x^{7}}\right]"," ",0,"[1/96*(3*sqrt(b)*c^3*x^7*log(-(c*x^3 + 2*b*x - 2*sqrt(c*x^4 + b*x^2)*sqrt(b))/x^3) + 2*(3*b*c^2*x^4 - 2*b^2*c*x^2 - 8*b^3)*sqrt(c*x^4 + b*x^2))/(b^3*x^7), 1/48*(3*sqrt(-b)*c^3*x^7*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-b)/(c*x^3 + b*x)) + (3*b*c^2*x^4 - 2*b^2*c*x^2 - 8*b^3)*sqrt(c*x^4 + b*x^2))/(b^3*x^7)]","A",0
238,1,210,0,2.609446," ","integrate(x^3*(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, b^{5} \sqrt{c} \log\left(-2 \, c x^{2} - b + 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right) + 2 \, {\left(128 \, c^{5} x^{8} + 176 \, b c^{4} x^{6} + 8 \, b^{2} c^{3} x^{4} - 10 \, b^{3} c^{2} x^{2} + 15 \, b^{4} c\right)} \sqrt{c x^{4} + b x^{2}}}{2560 \, c^{4}}, \frac{15 \, b^{5} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-c}}{c x^{2} + b}\right) + {\left(128 \, c^{5} x^{8} + 176 \, b c^{4} x^{6} + 8 \, b^{2} c^{3} x^{4} - 10 \, b^{3} c^{2} x^{2} + 15 \, b^{4} c\right)} \sqrt{c x^{4} + b x^{2}}}{1280 \, c^{4}}\right]"," ",0,"[1/2560*(15*b^5*sqrt(c)*log(-2*c*x^2 - b + 2*sqrt(c*x^4 + b*x^2)*sqrt(c)) + 2*(128*c^5*x^8 + 176*b*c^4*x^6 + 8*b^2*c^3*x^4 - 10*b^3*c^2*x^2 + 15*b^4*c)*sqrt(c*x^4 + b*x^2))/c^4, 1/1280*(15*b^5*sqrt(-c)*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-c)/(c*x^2 + b)) + (128*c^5*x^8 + 176*b*c^4*x^6 + 8*b^2*c^3*x^4 - 10*b^3*c^2*x^2 + 15*b^4*c)*sqrt(c*x^4 + b*x^2))/c^4]","A",0
239,1,189,0,1.140463," ","integrate(x*(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, b^{4} \sqrt{c} \log\left(-2 \, c x^{2} - b - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right) + 2 \, {\left(16 \, c^{4} x^{6} + 24 \, b c^{3} x^{4} + 2 \, b^{2} c^{2} x^{2} - 3 \, b^{3} c\right)} \sqrt{c x^{4} + b x^{2}}}{256 \, c^{3}}, -\frac{3 \, b^{4} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-c}}{c x^{2} + b}\right) - {\left(16 \, c^{4} x^{6} + 24 \, b c^{3} x^{4} + 2 \, b^{2} c^{2} x^{2} - 3 \, b^{3} c\right)} \sqrt{c x^{4} + b x^{2}}}{128 \, c^{3}}\right]"," ",0,"[1/256*(3*b^4*sqrt(c)*log(-2*c*x^2 - b - 2*sqrt(c*x^4 + b*x^2)*sqrt(c)) + 2*(16*c^4*x^6 + 24*b*c^3*x^4 + 2*b^2*c^2*x^2 - 3*b^3*c)*sqrt(c*x^4 + b*x^2))/c^3, -1/128*(3*b^4*sqrt(-c)*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-c)/(c*x^2 + b)) - (16*c^4*x^6 + 24*b*c^3*x^4 + 2*b^2*c^2*x^2 - 3*b^3*c)*sqrt(c*x^4 + b*x^2))/c^3]","A",0
240,1,166,0,1.023865," ","integrate((c*x^4+b*x^2)^(3/2)/x,x, algorithm=""fricas"")","\left[\frac{3 \, b^{3} \sqrt{c} \log\left(-2 \, c x^{2} - b + 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right) + 2 \, {\left(8 \, c^{3} x^{4} + 14 \, b c^{2} x^{2} + 3 \, b^{2} c\right)} \sqrt{c x^{4} + b x^{2}}}{96 \, c^{2}}, \frac{3 \, b^{3} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-c}}{c x^{2} + b}\right) + {\left(8 \, c^{3} x^{4} + 14 \, b c^{2} x^{2} + 3 \, b^{2} c\right)} \sqrt{c x^{4} + b x^{2}}}{48 \, c^{2}}\right]"," ",0,"[1/96*(3*b^3*sqrt(c)*log(-2*c*x^2 - b + 2*sqrt(c*x^4 + b*x^2)*sqrt(c)) + 2*(8*c^3*x^4 + 14*b*c^2*x^2 + 3*b^2*c)*sqrt(c*x^4 + b*x^2))/c^2, 1/48*(3*b^3*sqrt(-c)*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-c)/(c*x^2 + b)) + (8*c^3*x^4 + 14*b*c^2*x^2 + 3*b^2*c)*sqrt(c*x^4 + b*x^2))/c^2]","A",0
241,1,145,0,1.581603," ","integrate((c*x^4+b*x^2)^(3/2)/x^3,x, algorithm=""fricas"")","\left[\frac{3 \, b^{2} \sqrt{c} \log\left(-2 \, c x^{2} - b - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right) + 2 \, \sqrt{c x^{4} + b x^{2}} {\left(2 \, c^{2} x^{2} + 5 \, b c\right)}}{16 \, c}, -\frac{3 \, b^{2} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-c}}{c x^{2} + b}\right) - \sqrt{c x^{4} + b x^{2}} {\left(2 \, c^{2} x^{2} + 5 \, b c\right)}}{8 \, c}\right]"," ",0,"[1/16*(3*b^2*sqrt(c)*log(-2*c*x^2 - b - 2*sqrt(c*x^4 + b*x^2)*sqrt(c)) + 2*sqrt(c*x^4 + b*x^2)*(2*c^2*x^2 + 5*b*c))/c, -1/8*(3*b^2*sqrt(-c)*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-c)/(c*x^2 + b)) - sqrt(c*x^4 + b*x^2)*(2*c^2*x^2 + 5*b*c))/c]","A",0
242,1,139,0,1.456859," ","integrate((c*x^4+b*x^2)^(3/2)/x^5,x, algorithm=""fricas"")","\left[\frac{3 \, b \sqrt{c} x^{2} \log\left(-2 \, c x^{2} - b - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right) + 2 \, \sqrt{c x^{4} + b x^{2}} {\left(c x^{2} - 2 \, b\right)}}{4 \, x^{2}}, -\frac{3 \, b \sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-c}}{c x^{2} + b}\right) - \sqrt{c x^{4} + b x^{2}} {\left(c x^{2} - 2 \, b\right)}}{2 \, x^{2}}\right]"," ",0,"[1/4*(3*b*sqrt(c)*x^2*log(-2*c*x^2 - b - 2*sqrt(c*x^4 + b*x^2)*sqrt(c)) + 2*sqrt(c*x^4 + b*x^2)*(c*x^2 - 2*b))/x^2, -1/2*(3*b*sqrt(-c)*x^2*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-c)/(c*x^2 + b)) - sqrt(c*x^4 + b*x^2)*(c*x^2 - 2*b))/x^2]","A",0
243,1,135,0,1.346702," ","integrate((c*x^4+b*x^2)^(3/2)/x^7,x, algorithm=""fricas"")","\left[\frac{3 \, c^{\frac{3}{2}} x^{4} \log\left(-2 \, c x^{2} - b - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right) - 2 \, \sqrt{c x^{4} + b x^{2}} {\left(4 \, c x^{2} + b\right)}}{6 \, x^{4}}, -\frac{3 \, \sqrt{-c} c x^{4} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-c}}{c x^{2} + b}\right) + \sqrt{c x^{4} + b x^{2}} {\left(4 \, c x^{2} + b\right)}}{3 \, x^{4}}\right]"," ",0,"[1/6*(3*c^(3/2)*x^4*log(-2*c*x^2 - b - 2*sqrt(c*x^4 + b*x^2)*sqrt(c)) - 2*sqrt(c*x^4 + b*x^2)*(4*c*x^2 + b))/x^4, -1/3*(3*sqrt(-c)*c*x^4*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-c)/(c*x^2 + b)) + sqrt(c*x^4 + b*x^2)*(4*c*x^2 + b))/x^4]","A",0
244,1,39,0,2.062804," ","integrate((c*x^4+b*x^2)^(3/2)/x^9,x, algorithm=""fricas"")","-\frac{{\left(c^{2} x^{4} + 2 \, b c x^{2} + b^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{5 \, b x^{6}}"," ",0,"-1/5*(c^2*x^4 + 2*b*c*x^2 + b^2)*sqrt(c*x^4 + b*x^2)/(b*x^6)","A",0
245,1,53,0,0.780222," ","integrate((c*x^4+b*x^2)^(3/2)/x^11,x, algorithm=""fricas"")","\frac{{\left(2 \, c^{3} x^{6} - b c^{2} x^{4} - 8 \, b^{2} c x^{2} - 5 \, b^{3}\right)} \sqrt{c x^{4} + b x^{2}}}{35 \, b^{2} x^{8}}"," ",0,"1/35*(2*c^3*x^6 - b*c^2*x^4 - 8*b^2*c*x^2 - 5*b^3)*sqrt(c*x^4 + b*x^2)/(b^2*x^8)","A",0
246,1,64,0,1.122196," ","integrate((c*x^4+b*x^2)^(3/2)/x^13,x, algorithm=""fricas"")","-\frac{{\left(8 \, c^{4} x^{8} - 4 \, b c^{3} x^{6} + 3 \, b^{2} c^{2} x^{4} + 50 \, b^{3} c x^{2} + 35 \, b^{4}\right)} \sqrt{c x^{4} + b x^{2}}}{315 \, b^{3} x^{10}}"," ",0,"-1/315*(8*c^4*x^8 - 4*b*c^3*x^6 + 3*b^2*c^2*x^4 + 50*b^3*c*x^2 + 35*b^4)*sqrt(c*x^4 + b*x^2)/(b^3*x^10)","A",0
247,1,75,0,1.654821," ","integrate((c*x^4+b*x^2)^(3/2)/x^15,x, algorithm=""fricas"")","\frac{{\left(16 \, c^{5} x^{10} - 8 \, b c^{4} x^{8} + 6 \, b^{2} c^{3} x^{6} - 5 \, b^{3} c^{2} x^{4} - 140 \, b^{4} c x^{2} - 105 \, b^{5}\right)} \sqrt{c x^{4} + b x^{2}}}{1155 \, b^{4} x^{12}}"," ",0,"1/1155*(16*c^5*x^10 - 8*b*c^4*x^8 + 6*b^2*c^3*x^6 - 5*b^3*c^2*x^4 - 140*b^4*c*x^2 - 105*b^5)*sqrt(c*x^4 + b*x^2)/(b^4*x^12)","A",0
248,1,86,0,1.141887," ","integrate((c*x^4+b*x^2)^(3/2)/x^17,x, algorithm=""fricas"")","-\frac{{\left(128 \, c^{6} x^{12} - 64 \, b c^{5} x^{10} + 48 \, b^{2} c^{4} x^{8} - 40 \, b^{3} c^{3} x^{6} + 35 \, b^{4} c^{2} x^{4} + 1470 \, b^{5} c x^{2} + 1155 \, b^{6}\right)} \sqrt{c x^{4} + b x^{2}}}{15015 \, b^{5} x^{14}}"," ",0,"-1/15015*(128*c^6*x^12 - 64*b*c^5*x^10 + 48*b^2*c^4*x^8 - 40*b^3*c^3*x^6 + 35*b^4*c^2*x^4 + 1470*b^5*c*x^2 + 1155*b^6)*sqrt(c*x^4 + b*x^2)/(b^5*x^14)","A",0
249,1,86,0,1.193343," ","integrate(x^6*(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left(1155 \, c^{6} x^{12} + 1470 \, b c^{5} x^{10} + 35 \, b^{2} c^{4} x^{8} - 40 \, b^{3} c^{3} x^{6} + 48 \, b^{4} c^{2} x^{4} - 64 \, b^{5} c x^{2} + 128 \, b^{6}\right)} \sqrt{c x^{4} + b x^{2}}}{15015 \, c^{5} x}"," ",0,"1/15015*(1155*c^6*x^12 + 1470*b*c^5*x^10 + 35*b^2*c^4*x^8 - 40*b^3*c^3*x^6 + 48*b^4*c^2*x^4 - 64*b^5*c*x^2 + 128*b^6)*sqrt(c*x^4 + b*x^2)/(c^5*x)","A",0
250,1,75,0,0.757737," ","integrate(x^4*(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left(105 \, c^{5} x^{10} + 140 \, b c^{4} x^{8} + 5 \, b^{2} c^{3} x^{6} - 6 \, b^{3} c^{2} x^{4} + 8 \, b^{4} c x^{2} - 16 \, b^{5}\right)} \sqrt{c x^{4} + b x^{2}}}{1155 \, c^{4} x}"," ",0,"1/1155*(105*c^5*x^10 + 140*b*c^4*x^8 + 5*b^2*c^3*x^6 - 6*b^3*c^2*x^4 + 8*b^4*c*x^2 - 16*b^5)*sqrt(c*x^4 + b*x^2)/(c^4*x)","A",0
251,1,64,0,1.022609," ","integrate(x^2*(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left(35 \, c^{4} x^{8} + 50 \, b c^{3} x^{6} + 3 \, b^{2} c^{2} x^{4} - 4 \, b^{3} c x^{2} + 8 \, b^{4}\right)} \sqrt{c x^{4} + b x^{2}}}{315 \, c^{3} x}"," ",0,"1/315*(35*c^4*x^8 + 50*b*c^3*x^6 + 3*b^2*c^2*x^4 - 4*b^3*c*x^2 + 8*b^4)*sqrt(c*x^4 + b*x^2)/(c^3*x)","A",0
252,1,52,0,1.042664," ","integrate((c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left(5 \, c^{3} x^{6} + 8 \, b c^{2} x^{4} + b^{2} c x^{2} - 2 \, b^{3}\right)} \sqrt{c x^{4} + b x^{2}}}{35 \, c^{2} x}"," ",0,"1/35*(5*c^3*x^6 + 8*b*c^2*x^4 + b^2*c*x^2 - 2*b^3)*sqrt(c*x^4 + b*x^2)/(c^2*x)","A",0
253,1,39,0,0.962788," ","integrate((c*x^4+b*x^2)^(3/2)/x^2,x, algorithm=""fricas"")","\frac{{\left(c^{2} x^{4} + 2 \, b c x^{2} + b^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{5 \, c x}"," ",0,"1/5*(c^2*x^4 + 2*b*c*x^2 + b^2)*sqrt(c*x^4 + b*x^2)/(c*x)","A",0
254,1,140,0,0.907854," ","integrate((c*x^4+b*x^2)^(3/2)/x^4,x, algorithm=""fricas"")","\left[\frac{3 \, b^{\frac{3}{2}} x \log\left(-\frac{c x^{3} + 2 \, b x - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{b}}{x^{3}}\right) + 2 \, \sqrt{c x^{4} + b x^{2}} {\left(c x^{2} + 4 \, b\right)}}{6 \, x}, \frac{3 \, \sqrt{-b} b x \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-b}}{c x^{3} + b x}\right) + \sqrt{c x^{4} + b x^{2}} {\left(c x^{2} + 4 \, b\right)}}{3 \, x}\right]"," ",0,"[1/6*(3*b^(3/2)*x*log(-(c*x^3 + 2*b*x - 2*sqrt(c*x^4 + b*x^2)*sqrt(b))/x^3) + 2*sqrt(c*x^4 + b*x^2)*(c*x^2 + 4*b))/x, 1/3*(3*sqrt(-b)*b*x*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-b)/(c*x^3 + b*x)) + sqrt(c*x^4 + b*x^2)*(c*x^2 + 4*b))/x]","A",0
255,1,147,0,2.615113," ","integrate((c*x^4+b*x^2)^(3/2)/x^6,x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{b} c x^{3} \log\left(-\frac{c x^{3} + 2 \, b x - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{b}}{x^{3}}\right) + 2 \, \sqrt{c x^{4} + b x^{2}} {\left(2 \, c x^{2} - b\right)}}{4 \, x^{3}}, \frac{3 \, \sqrt{-b} c x^{3} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-b}}{c x^{3} + b x}\right) + \sqrt{c x^{4} + b x^{2}} {\left(2 \, c x^{2} - b\right)}}{2 \, x^{3}}\right]"," ",0,"[1/4*(3*sqrt(b)*c*x^3*log(-(c*x^3 + 2*b*x - 2*sqrt(c*x^4 + b*x^2)*sqrt(b))/x^3) + 2*sqrt(c*x^4 + b*x^2)*(2*c*x^2 - b))/x^3, 1/2*(3*sqrt(-b)*c*x^3*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-b)/(c*x^3 + b*x)) + sqrt(c*x^4 + b*x^2)*(2*c*x^2 - b))/x^3]","A",0
256,1,164,0,0.707932," ","integrate((c*x^4+b*x^2)^(3/2)/x^8,x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{b} c^{2} x^{5} \log\left(-\frac{c x^{3} + 2 \, b x - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{b}}{x^{3}}\right) - 2 \, \sqrt{c x^{4} + b x^{2}} {\left(5 \, b c x^{2} + 2 \, b^{2}\right)}}{16 \, b x^{5}}, \frac{3 \, \sqrt{-b} c^{2} x^{5} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-b}}{c x^{3} + b x}\right) - \sqrt{c x^{4} + b x^{2}} {\left(5 \, b c x^{2} + 2 \, b^{2}\right)}}{8 \, b x^{5}}\right]"," ",0,"[1/16*(3*sqrt(b)*c^2*x^5*log(-(c*x^3 + 2*b*x - 2*sqrt(c*x^4 + b*x^2)*sqrt(b))/x^3) - 2*sqrt(c*x^4 + b*x^2)*(5*b*c*x^2 + 2*b^2))/(b*x^5), 1/8*(3*sqrt(-b)*c^2*x^5*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-b)/(c*x^3 + b*x)) - sqrt(c*x^4 + b*x^2)*(5*b*c*x^2 + 2*b^2))/(b*x^5)]","A",0
257,1,185,0,1.284851," ","integrate((c*x^4+b*x^2)^(3/2)/x^10,x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{b} c^{3} x^{7} \log\left(-\frac{c x^{3} + 2 \, b x + 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{b}}{x^{3}}\right) - 2 \, {\left(3 \, b c^{2} x^{4} + 14 \, b^{2} c x^{2} + 8 \, b^{3}\right)} \sqrt{c x^{4} + b x^{2}}}{96 \, b^{2} x^{7}}, -\frac{3 \, \sqrt{-b} c^{3} x^{7} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-b}}{c x^{3} + b x}\right) + {\left(3 \, b c^{2} x^{4} + 14 \, b^{2} c x^{2} + 8 \, b^{3}\right)} \sqrt{c x^{4} + b x^{2}}}{48 \, b^{2} x^{7}}\right]"," ",0,"[1/96*(3*sqrt(b)*c^3*x^7*log(-(c*x^3 + 2*b*x + 2*sqrt(c*x^4 + b*x^2)*sqrt(b))/x^3) - 2*(3*b*c^2*x^4 + 14*b^2*c*x^2 + 8*b^3)*sqrt(c*x^4 + b*x^2))/(b^2*x^7), -1/48*(3*sqrt(-b)*c^3*x^7*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-b)/(c*x^3 + b*x)) + (3*b*c^2*x^4 + 14*b^2*c*x^2 + 8*b^3)*sqrt(c*x^4 + b*x^2))/(b^2*x^7)]","A",0
258,1,207,0,0.755250," ","integrate((c*x^4+b*x^2)^(3/2)/x^12,x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{b} c^{4} x^{9} \log\left(-\frac{c x^{3} + 2 \, b x - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{b}}{x^{3}}\right) + 2 \, {\left(3 \, b c^{3} x^{6} - 2 \, b^{2} c^{2} x^{4} - 24 \, b^{3} c x^{2} - 16 \, b^{4}\right)} \sqrt{c x^{4} + b x^{2}}}{256 \, b^{3} x^{9}}, \frac{3 \, \sqrt{-b} c^{4} x^{9} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-b}}{c x^{3} + b x}\right) + {\left(3 \, b c^{3} x^{6} - 2 \, b^{2} c^{2} x^{4} - 24 \, b^{3} c x^{2} - 16 \, b^{4}\right)} \sqrt{c x^{4} + b x^{2}}}{128 \, b^{3} x^{9}}\right]"," ",0,"[1/256*(3*sqrt(b)*c^4*x^9*log(-(c*x^3 + 2*b*x - 2*sqrt(c*x^4 + b*x^2)*sqrt(b))/x^3) + 2*(3*b*c^3*x^6 - 2*b^2*c^2*x^4 - 24*b^3*c*x^2 - 16*b^4)*sqrt(c*x^4 + b*x^2))/(b^3*x^9), 1/128*(3*sqrt(-b)*c^4*x^9*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-b)/(c*x^3 + b*x)) + (3*b*c^3*x^6 - 2*b^2*c^2*x^4 - 24*b^3*c*x^2 - 16*b^4)*sqrt(c*x^4 + b*x^2))/(b^3*x^9)]","A",0
259,1,229,0,1.169112," ","integrate((c*x^4+b*x^2)^(3/2)/x^14,x, algorithm=""fricas"")","\left[\frac{15 \, \sqrt{b} c^{5} x^{11} \log\left(-\frac{c x^{3} + 2 \, b x + 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{b}}{x^{3}}\right) - 2 \, {\left(15 \, b c^{4} x^{8} - 10 \, b^{2} c^{3} x^{6} + 8 \, b^{3} c^{2} x^{4} + 176 \, b^{4} c x^{2} + 128 \, b^{5}\right)} \sqrt{c x^{4} + b x^{2}}}{2560 \, b^{4} x^{11}}, -\frac{15 \, \sqrt{-b} c^{5} x^{11} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-b}}{c x^{3} + b x}\right) + {\left(15 \, b c^{4} x^{8} - 10 \, b^{2} c^{3} x^{6} + 8 \, b^{3} c^{2} x^{4} + 176 \, b^{4} c x^{2} + 128 \, b^{5}\right)} \sqrt{c x^{4} + b x^{2}}}{1280 \, b^{4} x^{11}}\right]"," ",0,"[1/2560*(15*sqrt(b)*c^5*x^11*log(-(c*x^3 + 2*b*x + 2*sqrt(c*x^4 + b*x^2)*sqrt(b))/x^3) - 2*(15*b*c^4*x^8 - 10*b^2*c^3*x^6 + 8*b^3*c^2*x^4 + 176*b^4*c*x^2 + 128*b^5)*sqrt(c*x^4 + b*x^2))/(b^4*x^11), -1/1280*(15*sqrt(-b)*c^5*x^11*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-b)/(c*x^3 + b*x)) + (15*b*c^4*x^8 - 10*b^2*c^3*x^6 + 8*b^3*c^2*x^4 + 176*b^4*c*x^2 + 128*b^5)*sqrt(c*x^4 + b*x^2))/(b^4*x^11)]","A",0
260,1,166,0,0.813287," ","integrate(x^7/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, b^{3} \sqrt{c} \log\left(-2 \, c x^{2} - b + 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right) + 2 \, {\left(8 \, c^{3} x^{4} - 10 \, b c^{2} x^{2} + 15 \, b^{2} c\right)} \sqrt{c x^{4} + b x^{2}}}{96 \, c^{4}}, \frac{15 \, b^{3} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-c}}{c x^{2} + b}\right) + {\left(8 \, c^{3} x^{4} - 10 \, b c^{2} x^{2} + 15 \, b^{2} c\right)} \sqrt{c x^{4} + b x^{2}}}{48 \, c^{4}}\right]"," ",0,"[1/96*(15*b^3*sqrt(c)*log(-2*c*x^2 - b + 2*sqrt(c*x^4 + b*x^2)*sqrt(c)) + 2*(8*c^3*x^4 - 10*b*c^2*x^2 + 15*b^2*c)*sqrt(c*x^4 + b*x^2))/c^4, 1/48*(15*b^3*sqrt(-c)*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-c)/(c*x^2 + b)) + (8*c^3*x^4 - 10*b*c^2*x^2 + 15*b^2*c)*sqrt(c*x^4 + b*x^2))/c^4]","A",0
261,1,145,0,0.781198," ","integrate(x^5/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, b^{2} \sqrt{c} \log\left(-2 \, c x^{2} - b - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right) + 2 \, \sqrt{c x^{4} + b x^{2}} {\left(2 \, c^{2} x^{2} - 3 \, b c\right)}}{16 \, c^{3}}, -\frac{3 \, b^{2} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-c}}{c x^{2} + b}\right) - \sqrt{c x^{4} + b x^{2}} {\left(2 \, c^{2} x^{2} - 3 \, b c\right)}}{8 \, c^{3}}\right]"," ",0,"[1/16*(3*b^2*sqrt(c)*log(-2*c*x^2 - b - 2*sqrt(c*x^4 + b*x^2)*sqrt(c)) + 2*sqrt(c*x^4 + b*x^2)*(2*c^2*x^2 - 3*b*c))/c^3, -1/8*(3*b^2*sqrt(-c)*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-c)/(c*x^2 + b)) - sqrt(c*x^4 + b*x^2)*(2*c^2*x^2 - 3*b*c))/c^3]","A",0
262,1,114,0,0.915423," ","integrate(x^3/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{b \sqrt{c} \log\left(-2 \, c x^{2} - b + 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right) + 2 \, \sqrt{c x^{4} + b x^{2}} c}{4 \, c^{2}}, \frac{b \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-c}}{c x^{2} + b}\right) + \sqrt{c x^{4} + b x^{2}} c}{2 \, c^{2}}\right]"," ",0,"[1/4*(b*sqrt(c)*log(-2*c*x^2 - b + 2*sqrt(c*x^4 + b*x^2)*sqrt(c)) + 2*sqrt(c*x^4 + b*x^2)*c)/c^2, 1/2*(b*sqrt(-c)*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-c)/(c*x^2 + b)) + sqrt(c*x^4 + b*x^2)*c)/c^2]","A",0
263,1,74,0,0.880811," ","integrate(x/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(-2 \, c x^{2} - b - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right)}{2 \, \sqrt{c}}, -\frac{\sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-c}}{c x^{2} + b}\right)}{c}\right]"," ",0,"[1/2*log(-2*c*x^2 - b - 2*sqrt(c*x^4 + b*x^2)*sqrt(c))/sqrt(c), -sqrt(-c)*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-c)/(c*x^2 + b))/c]","A",0
264,1,21,0,1.874640," ","integrate(1/x/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{c x^{4} + b x^{2}}}{b x^{2}}"," ",0,"-sqrt(c*x^4 + b*x^2)/(b*x^2)","A",0
265,1,31,0,0.715014," ","integrate(1/x^3/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{c x^{4} + b x^{2}} {\left(2 \, c x^{2} - b\right)}}{3 \, b^{2} x^{4}}"," ",0,"1/3*sqrt(c*x^4 + b*x^2)*(2*c*x^2 - b)/(b^2*x^4)","A",0
266,1,42,0,1.090070," ","integrate(1/x^5/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","-\frac{{\left(8 \, c^{2} x^{4} - 4 \, b c x^{2} + 3 \, b^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{15 \, b^{3} x^{6}}"," ",0,"-1/15*(8*c^2*x^4 - 4*b*c*x^2 + 3*b^2)*sqrt(c*x^4 + b*x^2)/(b^3*x^6)","A",0
267,1,53,0,1.258665," ","integrate(1/x^7/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","\frac{{\left(16 \, c^{3} x^{6} - 8 \, b c^{2} x^{4} + 6 \, b^{2} c x^{2} - 5 \, b^{3}\right)} \sqrt{c x^{4} + b x^{2}}}{35 \, b^{4} x^{8}}"," ",0,"1/35*(16*c^3*x^6 - 8*b*c^2*x^4 + 6*b^2*c*x^2 - 5*b^3)*sqrt(c*x^4 + b*x^2)/(b^4*x^8)","A",0
268,1,30,0,1.590925," ","integrate(x^4/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{c x^{4} + b x^{2}} {\left(c x^{2} - 2 \, b\right)}}{3 \, c^{2} x}"," ",0,"1/3*sqrt(c*x^4 + b*x^2)*(c*x^2 - 2*b)/(c^2*x)","A",0
269,1,20,0,1.063854," ","integrate(x^2/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{c x^{4} + b x^{2}}}{c x}"," ",0,"sqrt(c*x^4 + b*x^2)/(c*x)","A",0
270,1,80,0,0.981478," ","integrate(1/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(-\frac{c x^{3} + 2 \, b x - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{b}}{x^{3}}\right)}{2 \, \sqrt{b}}, \frac{\sqrt{-b} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-b}}{c x^{3} + b x}\right)}{b}\right]"," ",0,"[1/2*log(-(c*x^3 + 2*b*x - 2*sqrt(c*x^4 + b*x^2)*sqrt(b))/x^3)/sqrt(b), sqrt(-b)*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-b)/(c*x^3 + b*x))/b]","A",0
271,1,133,0,4.014692," ","integrate(1/x^2/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{b} c x^{3} \log\left(-\frac{c x^{3} + 2 \, b x + 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{b}}{x^{3}}\right) - 2 \, \sqrt{c x^{4} + b x^{2}} b}{4 \, b^{2} x^{3}}, -\frac{\sqrt{-b} c x^{3} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-b}}{c x^{3} + b x}\right) + \sqrt{c x^{4} + b x^{2}} b}{2 \, b^{2} x^{3}}\right]"," ",0,"[1/4*(sqrt(b)*c*x^3*log(-(c*x^3 + 2*b*x + 2*sqrt(c*x^4 + b*x^2)*sqrt(b))/x^3) - 2*sqrt(c*x^4 + b*x^2)*b)/(b^2*x^3), -1/2*(sqrt(-b)*c*x^3*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-b)/(c*x^3 + b*x)) + sqrt(c*x^4 + b*x^2)*b)/(b^2*x^3)]","A",0
272,1,163,0,1.787512," ","integrate(1/x^4/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{b} c^{2} x^{5} \log\left(-\frac{c x^{3} + 2 \, b x - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{b}}{x^{3}}\right) + 2 \, \sqrt{c x^{4} + b x^{2}} {\left(3 \, b c x^{2} - 2 \, b^{2}\right)}}{16 \, b^{3} x^{5}}, \frac{3 \, \sqrt{-b} c^{2} x^{5} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-b}}{c x^{3} + b x}\right) + \sqrt{c x^{4} + b x^{2}} {\left(3 \, b c x^{2} - 2 \, b^{2}\right)}}{8 \, b^{3} x^{5}}\right]"," ",0,"[1/16*(3*sqrt(b)*c^2*x^5*log(-(c*x^3 + 2*b*x - 2*sqrt(c*x^4 + b*x^2)*sqrt(b))/x^3) + 2*sqrt(c*x^4 + b*x^2)*(3*b*c*x^2 - 2*b^2))/(b^3*x^5), 1/8*(3*sqrt(-b)*c^2*x^5*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-b)/(c*x^3 + b*x)) + sqrt(c*x^4 + b*x^2)*(3*b*c*x^2 - 2*b^2))/(b^3*x^5)]","A",0
273,1,209,0,0.726286," ","integrate(x^9/(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(b^{2} c x^{2} + b^{3}\right)} \sqrt{c} \log\left(-2 \, c x^{2} - b - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right) + 2 \, {\left(2 \, c^{3} x^{4} - 5 \, b c^{2} x^{2} - 15 \, b^{2} c\right)} \sqrt{c x^{4} + b x^{2}}}{16 \, {\left(c^{5} x^{2} + b c^{4}\right)}}, -\frac{15 \, {\left(b^{2} c x^{2} + b^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-c}}{c x^{2} + b}\right) - {\left(2 \, c^{3} x^{4} - 5 \, b c^{2} x^{2} - 15 \, b^{2} c\right)} \sqrt{c x^{4} + b x^{2}}}{8 \, {\left(c^{5} x^{2} + b c^{4}\right)}}\right]"," ",0,"[1/16*(15*(b^2*c*x^2 + b^3)*sqrt(c)*log(-2*c*x^2 - b - 2*sqrt(c*x^4 + b*x^2)*sqrt(c)) + 2*(2*c^3*x^4 - 5*b*c^2*x^2 - 15*b^2*c)*sqrt(c*x^4 + b*x^2))/(c^5*x^2 + b*c^4), -1/8*(15*(b^2*c*x^2 + b^3)*sqrt(-c)*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-c)/(c*x^2 + b)) - (2*c^3*x^4 - 5*b*c^2*x^2 - 15*b^2*c)*sqrt(c*x^4 + b*x^2))/(c^5*x^2 + b*c^4)]","A",0
274,1,180,0,1.094386," ","integrate(x^7/(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b c x^{2} + b^{2}\right)} \sqrt{c} \log\left(-2 \, c x^{2} - b + 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right) + 2 \, \sqrt{c x^{4} + b x^{2}} {\left(c^{2} x^{2} + 3 \, b c\right)}}{4 \, {\left(c^{4} x^{2} + b c^{3}\right)}}, \frac{3 \, {\left(b c x^{2} + b^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-c}}{c x^{2} + b}\right) + \sqrt{c x^{4} + b x^{2}} {\left(c^{2} x^{2} + 3 \, b c\right)}}{2 \, {\left(c^{4} x^{2} + b c^{3}\right)}}\right]"," ",0,"[1/4*(3*(b*c*x^2 + b^2)*sqrt(c)*log(-2*c*x^2 - b + 2*sqrt(c*x^4 + b*x^2)*sqrt(c)) + 2*sqrt(c*x^4 + b*x^2)*(c^2*x^2 + 3*b*c))/(c^4*x^2 + b*c^3), 1/2*(3*(b*c*x^2 + b^2)*sqrt(-c)*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-c)/(c*x^2 + b)) + sqrt(c*x^4 + b*x^2)*(c^2*x^2 + 3*b*c))/(c^4*x^2 + b*c^3)]","A",0
275,1,150,0,1.649510," ","integrate(x^5/(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(c x^{2} + b\right)} \sqrt{c} \log\left(-2 \, c x^{2} - b - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right) - 2 \, \sqrt{c x^{4} + b x^{2}} c}{2 \, {\left(c^{3} x^{2} + b c^{2}\right)}}, -\frac{{\left(c x^{2} + b\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-c}}{c x^{2} + b}\right) + \sqrt{c x^{4} + b x^{2}} c}{c^{3} x^{2} + b c^{2}}\right]"," ",0,"[1/2*((c*x^2 + b)*sqrt(c)*log(-2*c*x^2 - b - 2*sqrt(c*x^4 + b*x^2)*sqrt(c)) - 2*sqrt(c*x^4 + b*x^2)*c)/(c^3*x^2 + b*c^2), -((c*x^2 + b)*sqrt(-c)*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-c)/(c*x^2 + b)) + sqrt(c*x^4 + b*x^2)*c)/(c^3*x^2 + b*c^2)]","A",0
276,1,26,0,1.910131," ","integrate(x^3/(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{c x^{4} + b x^{2}}}{b c x^{2} + b^{2}}"," ",0,"sqrt(c*x^4 + b*x^2)/(b*c*x^2 + b^2)","A",0
277,1,41,0,2.478351," ","integrate(x/(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{c x^{4} + b x^{2}} {\left(2 \, c x^{2} + b\right)}}{b^{2} c x^{4} + b^{3} x^{2}}"," ",0,"-sqrt(c*x^4 + b*x^2)*(2*c*x^2 + b)/(b^2*c*x^4 + b^3*x^2)","A",0
278,1,54,0,3.968171," ","integrate(1/x/(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left(8 \, c^{2} x^{4} + 4 \, b c x^{2} - b^{2}\right)} \sqrt{c x^{4} + b x^{2}}}{3 \, {\left(b^{3} c x^{6} + b^{4} x^{4}\right)}}"," ",0,"1/3*(8*c^2*x^4 + 4*b*c*x^2 - b^2)*sqrt(c*x^4 + b*x^2)/(b^3*c*x^6 + b^4*x^4)","A",0
279,1,63,0,2.279610," ","integrate(1/x^3/(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","-\frac{{\left(16 \, c^{3} x^{6} + 8 \, b c^{2} x^{4} - 2 \, b^{2} c x^{2} + b^{3}\right)} \sqrt{c x^{4} + b x^{2}}}{5 \, {\left(b^{4} c x^{8} + b^{5} x^{6}\right)}}"," ",0,"-1/5*(16*c^3*x^6 + 8*b*c^2*x^4 - 2*b^2*c*x^2 + b^3)*sqrt(c*x^4 + b*x^2)/(b^4*c*x^8 + b^5*x^6)","A",0
280,1,76,0,2.051719," ","integrate(1/x^5/(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left(128 \, c^{4} x^{8} + 64 \, b c^{3} x^{6} - 16 \, b^{2} c^{2} x^{4} + 8 \, b^{3} c x^{2} - 5 \, b^{4}\right)} \sqrt{c x^{4} + b x^{2}}}{35 \, {\left(b^{5} c x^{10} + b^{6} x^{8}\right)}}"," ",0,"1/35*(128*c^4*x^8 + 64*b*c^3*x^6 - 16*b^2*c^2*x^4 + 8*b^3*c*x^2 - 5*b^4)*sqrt(c*x^4 + b*x^2)/(b^5*c*x^10 + b^6*x^8)","A",0
281,1,39,0,0.693359," ","integrate(x^6/(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{c x^{4} + b x^{2}} {\left(c x^{2} + 2 \, b\right)}}{c^{3} x^{3} + b c^{2} x}"," ",0,"sqrt(c*x^4 + b*x^2)*(c*x^2 + 2*b)/(c^3*x^3 + b*c^2*x)","A",0
282,1,29,0,1.084156," ","integrate(x^4/(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{c x^{4} + b x^{2}}}{c^{2} x^{3} + b c x}"," ",0,"-sqrt(c*x^4 + b*x^2)/(c^2*x^3 + b*c*x)","A",0
283,1,162,0,1.675639," ","integrate(x^2/(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(c x^{3} + b x\right)} \sqrt{b} \log\left(-\frac{c x^{3} + 2 \, b x - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{b}}{x^{3}}\right) + 2 \, \sqrt{c x^{4} + b x^{2}} b}{2 \, {\left(b^{2} c x^{3} + b^{3} x\right)}}, \frac{{\left(c x^{3} + b x\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-b}}{c x^{3} + b x}\right) + \sqrt{c x^{4} + b x^{2}} b}{b^{2} c x^{3} + b^{3} x}\right]"," ",0,"[1/2*((c*x^3 + b*x)*sqrt(b)*log(-(c*x^3 + 2*b*x - 2*sqrt(c*x^4 + b*x^2)*sqrt(b))/x^3) + 2*sqrt(c*x^4 + b*x^2)*b)/(b^2*c*x^3 + b^3*x), ((c*x^3 + b*x)*sqrt(-b)*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-b)/(c*x^3 + b*x)) + sqrt(c*x^4 + b*x^2)*b)/(b^2*c*x^3 + b^3*x)]","A",0
284,1,199,0,0.844337," ","integrate(1/(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(c^{2} x^{5} + b c x^{3}\right)} \sqrt{b} \log\left(-\frac{c x^{3} + 2 \, b x + 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{b}}{x^{3}}\right) - 2 \, \sqrt{c x^{4} + b x^{2}} {\left(3 \, b c x^{2} + b^{2}\right)}}{4 \, {\left(b^{3} c x^{5} + b^{4} x^{3}\right)}}, -\frac{3 \, {\left(c^{2} x^{5} + b c x^{3}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-b}}{c x^{3} + b x}\right) + \sqrt{c x^{4} + b x^{2}} {\left(3 \, b c x^{2} + b^{2}\right)}}{2 \, {\left(b^{3} c x^{5} + b^{4} x^{3}\right)}}\right]"," ",0,"[1/4*(3*(c^2*x^5 + b*c*x^3)*sqrt(b)*log(-(c*x^3 + 2*b*x + 2*sqrt(c*x^4 + b*x^2)*sqrt(b))/x^3) - 2*sqrt(c*x^4 + b*x^2)*(3*b*c*x^2 + b^2))/(b^3*c*x^5 + b^4*x^3), -1/2*(3*(c^2*x^5 + b*c*x^3)*sqrt(-b)*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-b)/(c*x^3 + b*x)) + sqrt(c*x^4 + b*x^2)*(3*b*c*x^2 + b^2))/(b^3*c*x^5 + b^4*x^3)]","A",0
285,1,229,0,0.613372," ","integrate(1/x^2/(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(c^{3} x^{7} + b c^{2} x^{5}\right)} \sqrt{b} \log\left(-\frac{c x^{3} + 2 \, b x - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{b}}{x^{3}}\right) + 2 \, {\left(15 \, b c^{2} x^{4} + 5 \, b^{2} c x^{2} - 2 \, b^{3}\right)} \sqrt{c x^{4} + b x^{2}}}{16 \, {\left(b^{4} c x^{7} + b^{5} x^{5}\right)}}, \frac{15 \, {\left(c^{3} x^{7} + b c^{2} x^{5}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-b}}{c x^{3} + b x}\right) + {\left(15 \, b c^{2} x^{4} + 5 \, b^{2} c x^{2} - 2 \, b^{3}\right)} \sqrt{c x^{4} + b x^{2}}}{8 \, {\left(b^{4} c x^{7} + b^{5} x^{5}\right)}}\right]"," ",0,"[1/16*(15*(c^3*x^7 + b*c^2*x^5)*sqrt(b)*log(-(c*x^3 + 2*b*x - 2*sqrt(c*x^4 + b*x^2)*sqrt(b))/x^3) + 2*(15*b*c^2*x^4 + 5*b^2*c*x^2 - 2*b^3)*sqrt(c*x^4 + b*x^2))/(b^4*c*x^7 + b^5*x^5), 1/8*(15*(c^3*x^7 + b*c^2*x^5)*sqrt(-b)*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-b)/(c*x^3 + b*x)) + (15*b*c^2*x^4 + 5*b^2*c*x^2 - 2*b^3)*sqrt(c*x^4 + b*x^2))/(b^4*c*x^7 + b^5*x^5)]","A",0
286,1,37,0,0.779642," ","integrate(x^3/(-4*x^4+3*x^2)^(1/2),x, algorithm=""fricas"")","-\frac{1}{8} \, \sqrt{-4 \, x^{4} + 3 \, x^{2}} - \frac{3}{16} \, \arctan\left(\frac{\sqrt{-4 \, x^{4} + 3 \, x^{2}}}{2 \, x^{2}}\right)"," ",0,"-1/8*sqrt(-4*x^4 + 3*x^2) - 3/16*arctan(1/2*sqrt(-4*x^4 + 3*x^2)/x^2)","A",0
287,1,59,0,0.912833," ","integrate(x^3/(-4*x^4-3*x^2)^(1/2),x, algorithm=""fricas"")","-\frac{1}{8} \, \sqrt{-4 \, x^{2} - 3} x - \frac{3}{32} i \, \log\left(-\frac{8 \, x + 4 i \, \sqrt{-4 \, x^{2} - 3}}{x}\right) + \frac{3}{32} i \, \log\left(-\frac{8 \, x - 4 i \, \sqrt{-4 \, x^{2} - 3}}{x}\right)"," ",0,"-1/8*sqrt(-4*x^2 - 3)*x - 3/32*I*log(-(8*x + 4*I*sqrt(-4*x^2 - 3))/x) + 3/32*I*log(-(8*x - 4*I*sqrt(-4*x^2 - 3))/x)","C",0
288,1,45,0,0.700061," ","integrate(x^3/(4*x^4+3*x^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{8} \, \sqrt{4 \, x^{4} + 3 \, x^{2}} + \frac{3}{16} \, \log\left(-\frac{2 \, x^{2} - \sqrt{4 \, x^{4} + 3 \, x^{2}}}{x}\right)"," ",0,"1/8*sqrt(4*x^4 + 3*x^2) + 3/16*log(-(2*x^2 - sqrt(4*x^4 + 3*x^2))/x)","A",0
289,1,45,0,0.857213," ","integrate(x^3/(4*x^4-3*x^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{8} \, \sqrt{4 \, x^{4} - 3 \, x^{2}} - \frac{3}{16} \, \log\left(-\frac{2 \, x^{2} - \sqrt{4 \, x^{4} - 3 \, x^{2}}}{x}\right)"," ",0,"1/8*sqrt(4*x^4 - 3*x^2) - 3/16*log(-(2*x^2 - sqrt(4*x^4 - 3*x^2))/x)","A",0
290,1,114,0,0.880014," ","integrate(x^3/(b*x^4+a*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{a \sqrt{b} \log\left(-2 \, b x^{2} - a + 2 \, \sqrt{b x^{4} + a x^{2}} \sqrt{b}\right) + 2 \, \sqrt{b x^{4} + a x^{2}} b}{4 \, b^{2}}, \frac{a \sqrt{-b} \arctan\left(\frac{\sqrt{b x^{4} + a x^{2}} \sqrt{-b}}{b x^{2} + a}\right) + \sqrt{b x^{4} + a x^{2}} b}{2 \, b^{2}}\right]"," ",0,"[1/4*(a*sqrt(b)*log(-2*b*x^2 - a + 2*sqrt(b*x^4 + a*x^2)*sqrt(b)) + 2*sqrt(b*x^4 + a*x^2)*b)/b^2, 1/2*(a*sqrt(-b)*arctan(sqrt(b*x^4 + a*x^2)*sqrt(-b)/(b*x^2 + a)) + sqrt(b*x^4 + a*x^2)*b)/b^2]","A",0
291,1,120,0,0.920489," ","integrate(x^3/(-b*x^4+a*x^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{a \sqrt{-b} \log\left(2 \, b x^{2} - a - 2 \, \sqrt{-b x^{4} + a x^{2}} \sqrt{-b}\right) + 2 \, \sqrt{-b x^{4} + a x^{2}} b}{4 \, b^{2}}, -\frac{a \sqrt{b} \arctan\left(\frac{\sqrt{-b x^{4} + a x^{2}} \sqrt{b}}{b x^{2} - a}\right) + \sqrt{-b x^{4} + a x^{2}} b}{2 \, b^{2}}\right]"," ",0,"[-1/4*(a*sqrt(-b)*log(2*b*x^2 - a - 2*sqrt(-b*x^4 + a*x^2)*sqrt(-b)) + 2*sqrt(-b*x^4 + a*x^2)*b)/b^2, -1/2*(a*sqrt(b)*arctan(sqrt(-b*x^4 + a*x^2)*sqrt(b)/(b*x^2 - a)) + sqrt(-b*x^4 + a*x^2)*b)/b^2]","A",0
292,1,18,0,1.556555," ","integrate(x^(7/2)*(c*x^4+b*x^2),x, algorithm=""fricas"")","\frac{2}{221} \, {\left(13 \, c x^{8} + 17 \, b x^{6}\right)} \sqrt{x}"," ",0,"2/221*(13*c*x^8 + 17*b*x^6)*sqrt(x)","A",0
293,1,18,0,1.016378," ","integrate(x^(5/2)*(c*x^4+b*x^2),x, algorithm=""fricas"")","\frac{2}{165} \, {\left(11 \, c x^{7} + 15 \, b x^{5}\right)} \sqrt{x}"," ",0,"2/165*(11*c*x^7 + 15*b*x^5)*sqrt(x)","A",0
294,1,18,0,1.835432," ","integrate(x^(3/2)*(c*x^4+b*x^2),x, algorithm=""fricas"")","\frac{2}{117} \, {\left(9 \, c x^{6} + 13 \, b x^{4}\right)} \sqrt{x}"," ",0,"2/117*(9*c*x^6 + 13*b*x^4)*sqrt(x)","A",0
295,1,18,0,0.577322," ","integrate(x^(1/2)*(c*x^4+b*x^2),x, algorithm=""fricas"")","\frac{2}{77} \, {\left(7 \, c x^{5} + 11 \, b x^{3}\right)} \sqrt{x}"," ",0,"2/77*(7*c*x^5 + 11*b*x^3)*sqrt(x)","A",0
296,1,18,0,0.968906," ","integrate((c*x^4+b*x^2)/x^(1/2),x, algorithm=""fricas"")","\frac{2}{45} \, {\left(5 \, c x^{4} + 9 \, b x^{2}\right)} \sqrt{x}"," ",0,"2/45*(5*c*x^4 + 9*b*x^2)*sqrt(x)","A",0
297,1,16,0,1.104486," ","integrate((c*x^4+b*x^2)/x^(3/2),x, algorithm=""fricas"")","\frac{2}{21} \, {\left(3 \, c x^{3} + 7 \, b x\right)} \sqrt{x}"," ",0,"2/21*(3*c*x^3 + 7*b*x)*sqrt(x)","A",0
298,1,14,0,1.333903," ","integrate((c*x^4+b*x^2)/x^(5/2),x, algorithm=""fricas"")","\frac{2}{5} \, {\left(c x^{2} + 5 \, b\right)} \sqrt{x}"," ",0,"2/5*(c*x^2 + 5*b)*sqrt(x)","A",0
299,1,14,0,0.905160," ","integrate((c*x^4+b*x^2)/x^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(c x^{2} - 3 \, b\right)}}{3 \, \sqrt{x}}"," ",0,"2/3*(c*x^2 - 3*b)/sqrt(x)","A",0
300,1,29,0,2.049345," ","integrate(x^(7/2)*(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","\frac{2}{8925} \, {\left(357 \, c^{2} x^{12} + 850 \, b c x^{10} + 525 \, b^{2} x^{8}\right)} \sqrt{x}"," ",0,"2/8925*(357*c^2*x^12 + 850*b*c*x^10 + 525*b^2*x^8)*sqrt(x)","A",0
301,1,29,0,0.822710," ","integrate(x^(5/2)*(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","\frac{2}{6555} \, {\left(285 \, c^{2} x^{11} + 690 \, b c x^{9} + 437 \, b^{2} x^{7}\right)} \sqrt{x}"," ",0,"2/6555*(285*c^2*x^11 + 690*b*c*x^9 + 437*b^2*x^7)*sqrt(x)","A",0
302,1,29,0,2.347072," ","integrate(x^(3/2)*(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","\frac{2}{4641} \, {\left(221 \, c^{2} x^{10} + 546 \, b c x^{8} + 357 \, b^{2} x^{6}\right)} \sqrt{x}"," ",0,"2/4641*(221*c^2*x^10 + 546*b*c*x^8 + 357*b^2*x^6)*sqrt(x)","A",0
303,1,29,0,1.514304," ","integrate(x^(1/2)*(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","\frac{2}{3135} \, {\left(165 \, c^{2} x^{9} + 418 \, b c x^{7} + 285 \, b^{2} x^{5}\right)} \sqrt{x}"," ",0,"2/3135*(165*c^2*x^9 + 418*b*c*x^7 + 285*b^2*x^5)*sqrt(x)","A",0
304,1,29,0,1.306408," ","integrate((c*x^4+b*x^2)^2/x^(1/2),x, algorithm=""fricas"")","\frac{2}{1989} \, {\left(117 \, c^{2} x^{8} + 306 \, b c x^{6} + 221 \, b^{2} x^{4}\right)} \sqrt{x}"," ",0,"2/1989*(117*c^2*x^8 + 306*b*c*x^6 + 221*b^2*x^4)*sqrt(x)","A",0
305,1,29,0,1.591756," ","integrate((c*x^4+b*x^2)^2/x^(3/2),x, algorithm=""fricas"")","\frac{2}{1155} \, {\left(77 \, c^{2} x^{7} + 210 \, b c x^{5} + 165 \, b^{2} x^{3}\right)} \sqrt{x}"," ",0,"2/1155*(77*c^2*x^7 + 210*b*c*x^5 + 165*b^2*x^3)*sqrt(x)","A",0
306,1,29,0,1.462316," ","integrate((c*x^4+b*x^2)^2/x^(5/2),x, algorithm=""fricas"")","\frac{2}{585} \, {\left(45 \, c^{2} x^{6} + 130 \, b c x^{4} + 117 \, b^{2} x^{2}\right)} \sqrt{x}"," ",0,"2/585*(45*c^2*x^6 + 130*b*c*x^4 + 117*b^2*x^2)*sqrt(x)","A",0
307,1,27,0,0.721610," ","integrate((c*x^4+b*x^2)^2/x^(7/2),x, algorithm=""fricas"")","\frac{2}{231} \, {\left(21 \, c^{2} x^{5} + 66 \, b c x^{3} + 77 \, b^{2} x\right)} \sqrt{x}"," ",0,"2/231*(21*c^2*x^5 + 66*b*c*x^3 + 77*b^2*x)*sqrt(x)","A",0
308,1,40,0,1.323951," ","integrate(x^(7/2)*(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","\frac{2}{167475} \, {\left(5075 \, c^{3} x^{16} + 17325 \, b c^{2} x^{14} + 20097 \, b^{2} c x^{12} + 7975 \, b^{3} x^{10}\right)} \sqrt{x}"," ",0,"2/167475*(5075*c^3*x^16 + 17325*b*c^2*x^14 + 20097*b^2*c*x^12 + 7975*b^3*x^10)*sqrt(x)","A",0
309,1,40,0,0.958225," ","integrate(x^(5/2)*(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","\frac{2}{121923} \, {\left(3933 \, c^{3} x^{15} + 13547 \, b c^{2} x^{13} + 15903 \, b^{2} c x^{11} + 6417 \, b^{3} x^{9}\right)} \sqrt{x}"," ",0,"2/121923*(3933*c^3*x^15 + 13547*b*c^2*x^13 + 15903*b^2*c*x^11 + 6417*b^3*x^9)*sqrt(x)","A",0
310,1,40,0,0.936750," ","integrate(x^(3/2)*(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","\frac{2}{86275} \, {\left(2975 \, c^{3} x^{14} + 10353 \, b c^{2} x^{12} + 12325 \, b^{2} c x^{10} + 5075 \, b^{3} x^{8}\right)} \sqrt{x}"," ",0,"2/86275*(2975*c^3*x^14 + 10353*b*c^2*x^12 + 12325*b^2*c*x^10 + 5075*b^3*x^8)*sqrt(x)","A",0
311,1,40,0,1.859818," ","integrate(x^(1/2)*(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","\frac{2}{58995} \, {\left(2185 \, c^{3} x^{13} + 7695 \, b c^{2} x^{11} + 9315 \, b^{2} c x^{9} + 3933 \, b^{3} x^{7}\right)} \sqrt{x}"," ",0,"2/58995*(2185*c^3*x^13 + 7695*b*c^2*x^11 + 9315*b^2*c*x^9 + 3933*b^3*x^7)*sqrt(x)","A",0
312,1,40,0,0.690376," ","integrate((c*x^4+b*x^2)^3/x^(1/2),x, algorithm=""fricas"")","\frac{2}{38675} \, {\left(1547 \, c^{3} x^{12} + 5525 \, b c^{2} x^{10} + 6825 \, b^{2} c x^{8} + 2975 \, b^{3} x^{6}\right)} \sqrt{x}"," ",0,"2/38675*(1547*c^3*x^12 + 5525*b*c^2*x^10 + 6825*b^2*c*x^8 + 2975*b^3*x^6)*sqrt(x)","A",0
313,1,40,0,0.689443," ","integrate((c*x^4+b*x^2)^3/x^(3/2),x, algorithm=""fricas"")","\frac{2}{24035} \, {\left(1045 \, c^{3} x^{11} + 3795 \, b c^{2} x^{9} + 4807 \, b^{2} c x^{7} + 2185 \, b^{3} x^{5}\right)} \sqrt{x}"," ",0,"2/24035*(1045*c^3*x^11 + 3795*b*c^2*x^9 + 4807*b^2*c*x^7 + 2185*b^3*x^5)*sqrt(x)","A",0
314,1,40,0,0.856453," ","integrate((c*x^4+b*x^2)^3/x^(5/2),x, algorithm=""fricas"")","\frac{2}{13923} \, {\left(663 \, c^{3} x^{10} + 2457 \, b c^{2} x^{8} + 3213 \, b^{2} c x^{6} + 1547 \, b^{3} x^{4}\right)} \sqrt{x}"," ",0,"2/13923*(663*c^3*x^10 + 2457*b*c^2*x^8 + 3213*b^2*c*x^6 + 1547*b^3*x^4)*sqrt(x)","A",0
315,1,40,0,1.723173," ","integrate((c*x^4+b*x^2)^3/x^(7/2),x, algorithm=""fricas"")","\frac{2}{7315} \, {\left(385 \, c^{3} x^{9} + 1463 \, b c^{2} x^{7} + 1995 \, b^{2} c x^{5} + 1045 \, b^{3} x^{3}\right)} \sqrt{x}"," ",0,"2/7315*(385*c^3*x^9 + 1463*b*c^2*x^7 + 1995*b^2*c*x^5 + 1045*b^3*x^3)*sqrt(x)","A",0
316,1,182,0,0.872664," ","integrate(x^(13/2)/(c*x^4+b*x^2),x, algorithm=""fricas"")","-\frac{84 \, c^{2} \left(-\frac{b^{7}}{c^{11}}\right)^{\frac{1}{4}} \arctan\left(-\frac{b^{5} c^{3} \sqrt{x} \left(-\frac{b^{7}}{c^{11}}\right)^{\frac{1}{4}} - \sqrt{-b^{7} c^{5} \sqrt{-\frac{b^{7}}{c^{11}}} + b^{10} x} c^{3} \left(-\frac{b^{7}}{c^{11}}\right)^{\frac{1}{4}}}{b^{7}}\right) - 21 \, c^{2} \left(-\frac{b^{7}}{c^{11}}\right)^{\frac{1}{4}} \log\left(c^{8} \left(-\frac{b^{7}}{c^{11}}\right)^{\frac{3}{4}} + b^{5} \sqrt{x}\right) + 21 \, c^{2} \left(-\frac{b^{7}}{c^{11}}\right)^{\frac{1}{4}} \log\left(-c^{8} \left(-\frac{b^{7}}{c^{11}}\right)^{\frac{3}{4}} + b^{5} \sqrt{x}\right) - 4 \, {\left(3 \, c x^{3} - 7 \, b x\right)} \sqrt{x}}{42 \, c^{2}}"," ",0,"-1/42*(84*c^2*(-b^7/c^11)^(1/4)*arctan(-(b^5*c^3*sqrt(x)*(-b^7/c^11)^(1/4) - sqrt(-b^7*c^5*sqrt(-b^7/c^11) + b^10*x)*c^3*(-b^7/c^11)^(1/4))/b^7) - 21*c^2*(-b^7/c^11)^(1/4)*log(c^8*(-b^7/c^11)^(3/4) + b^5*sqrt(x)) + 21*c^2*(-b^7/c^11)^(1/4)*log(-c^8*(-b^7/c^11)^(3/4) + b^5*sqrt(x)) - 4*(3*c*x^3 - 7*b*x)*sqrt(x))/c^2","A",0
317,1,170,0,1.688112," ","integrate(x^(11/2)/(c*x^4+b*x^2),x, algorithm=""fricas"")","\frac{20 \, c^{2} \left(-\frac{b^{5}}{c^{9}}\right)^{\frac{1}{4}} \arctan\left(-\frac{b c^{7} \sqrt{x} \left(-\frac{b^{5}}{c^{9}}\right)^{\frac{3}{4}} - \sqrt{c^{4} \sqrt{-\frac{b^{5}}{c^{9}}} + b^{2} x} c^{7} \left(-\frac{b^{5}}{c^{9}}\right)^{\frac{3}{4}}}{b^{5}}\right) + 5 \, c^{2} \left(-\frac{b^{5}}{c^{9}}\right)^{\frac{1}{4}} \log\left(c^{2} \left(-\frac{b^{5}}{c^{9}}\right)^{\frac{1}{4}} + b \sqrt{x}\right) - 5 \, c^{2} \left(-\frac{b^{5}}{c^{9}}\right)^{\frac{1}{4}} \log\left(-c^{2} \left(-\frac{b^{5}}{c^{9}}\right)^{\frac{1}{4}} + b \sqrt{x}\right) + 4 \, {\left(c x^{2} - 5 \, b\right)} \sqrt{x}}{10 \, c^{2}}"," ",0,"1/10*(20*c^2*(-b^5/c^9)^(1/4)*arctan(-(b*c^7*sqrt(x)*(-b^5/c^9)^(3/4) - sqrt(c^4*sqrt(-b^5/c^9) + b^2*x)*c^7*(-b^5/c^9)^(3/4))/b^5) + 5*c^2*(-b^5/c^9)^(1/4)*log(c^2*(-b^5/c^9)^(1/4) + b*sqrt(x)) - 5*c^2*(-b^5/c^9)^(1/4)*log(-c^2*(-b^5/c^9)^(1/4) + b*sqrt(x)) + 4*(c*x^2 - 5*b)*sqrt(x))/c^2","A",0
318,1,165,0,0.861392," ","integrate(x^(9/2)/(c*x^4+b*x^2),x, algorithm=""fricas"")","\frac{12 \, c \left(-\frac{b^{3}}{c^{7}}\right)^{\frac{1}{4}} \arctan\left(-\frac{b^{2} c^{2} \sqrt{x} \left(-\frac{b^{3}}{c^{7}}\right)^{\frac{1}{4}} - \sqrt{-b^{3} c^{3} \sqrt{-\frac{b^{3}}{c^{7}}} + b^{4} x} c^{2} \left(-\frac{b^{3}}{c^{7}}\right)^{\frac{1}{4}}}{b^{3}}\right) - 3 \, c \left(-\frac{b^{3}}{c^{7}}\right)^{\frac{1}{4}} \log\left(c^{5} \left(-\frac{b^{3}}{c^{7}}\right)^{\frac{3}{4}} + b^{2} \sqrt{x}\right) + 3 \, c \left(-\frac{b^{3}}{c^{7}}\right)^{\frac{1}{4}} \log\left(-c^{5} \left(-\frac{b^{3}}{c^{7}}\right)^{\frac{3}{4}} + b^{2} \sqrt{x}\right) + 4 \, x^{\frac{3}{2}}}{6 \, c}"," ",0,"1/6*(12*c*(-b^3/c^7)^(1/4)*arctan(-(b^2*c^2*sqrt(x)*(-b^3/c^7)^(1/4) - sqrt(-b^3*c^3*sqrt(-b^3/c^7) + b^4*x)*c^2*(-b^3/c^7)^(1/4))/b^3) - 3*c*(-b^3/c^7)^(1/4)*log(c^5*(-b^3/c^7)^(3/4) + b^2*sqrt(x)) + 3*c*(-b^3/c^7)^(1/4)*log(-c^5*(-b^3/c^7)^(3/4) + b^2*sqrt(x)) + 4*x^(3/2))/c","A",0
319,1,124,0,0.904624," ","integrate(x^(7/2)/(c*x^4+b*x^2),x, algorithm=""fricas"")","-\frac{4 \, c \left(-\frac{b}{c^{5}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{c^{2} \sqrt{-\frac{b}{c^{5}}} + x} c^{4} \left(-\frac{b}{c^{5}}\right)^{\frac{3}{4}} - c^{4} \sqrt{x} \left(-\frac{b}{c^{5}}\right)^{\frac{3}{4}}}{b}\right) + c \left(-\frac{b}{c^{5}}\right)^{\frac{1}{4}} \log\left(c \left(-\frac{b}{c^{5}}\right)^{\frac{1}{4}} + \sqrt{x}\right) - c \left(-\frac{b}{c^{5}}\right)^{\frac{1}{4}} \log\left(-c \left(-\frac{b}{c^{5}}\right)^{\frac{1}{4}} + \sqrt{x}\right) - 4 \, \sqrt{x}}{2 \, c}"," ",0,"-1/2*(4*c*(-b/c^5)^(1/4)*arctan((sqrt(c^2*sqrt(-b/c^5) + x)*c^4*(-b/c^5)^(3/4) - c^4*sqrt(x)*(-b/c^5)^(3/4))/b) + c*(-b/c^5)^(1/4)*log(c*(-b/c^5)^(1/4) + sqrt(x)) - c*(-b/c^5)^(1/4)*log(-c*(-b/c^5)^(1/4) + sqrt(x)) - 4*sqrt(x))/c","A",0
320,1,126,0,1.015008," ","integrate(x^(5/2)/(c*x^4+b*x^2),x, algorithm=""fricas"")","-2 \, \left(-\frac{1}{b c^{3}}\right)^{\frac{1}{4}} \arctan\left(\sqrt{-b c \sqrt{-\frac{1}{b c^{3}}} + x} c \left(-\frac{1}{b c^{3}}\right)^{\frac{1}{4}} - c \sqrt{x} \left(-\frac{1}{b c^{3}}\right)^{\frac{1}{4}}\right) + \frac{1}{2} \, \left(-\frac{1}{b c^{3}}\right)^{\frac{1}{4}} \log\left(b c^{2} \left(-\frac{1}{b c^{3}}\right)^{\frac{3}{4}} + \sqrt{x}\right) - \frac{1}{2} \, \left(-\frac{1}{b c^{3}}\right)^{\frac{1}{4}} \log\left(-b c^{2} \left(-\frac{1}{b c^{3}}\right)^{\frac{3}{4}} + \sqrt{x}\right)"," ",0,"-2*(-1/(b*c^3))^(1/4)*arctan(sqrt(-b*c*sqrt(-1/(b*c^3)) + x)*c*(-1/(b*c^3))^(1/4) - c*sqrt(x)*(-1/(b*c^3))^(1/4)) + 1/2*(-1/(b*c^3))^(1/4)*log(b*c^2*(-1/(b*c^3))^(3/4) + sqrt(x)) - 1/2*(-1/(b*c^3))^(1/4)*log(-b*c^2*(-1/(b*c^3))^(3/4) + sqrt(x))","A",0
321,1,126,0,1.022466," ","integrate(x^(3/2)/(c*x^4+b*x^2),x, algorithm=""fricas"")","2 \, \left(-\frac{1}{b^{3} c}\right)^{\frac{1}{4}} \arctan\left(\sqrt{b^{2} \sqrt{-\frac{1}{b^{3} c}} + x} b^{2} c \left(-\frac{1}{b^{3} c}\right)^{\frac{3}{4}} - b^{2} c \sqrt{x} \left(-\frac{1}{b^{3} c}\right)^{\frac{3}{4}}\right) + \frac{1}{2} \, \left(-\frac{1}{b^{3} c}\right)^{\frac{1}{4}} \log\left(b \left(-\frac{1}{b^{3} c}\right)^{\frac{1}{4}} + \sqrt{x}\right) - \frac{1}{2} \, \left(-\frac{1}{b^{3} c}\right)^{\frac{1}{4}} \log\left(-b \left(-\frac{1}{b^{3} c}\right)^{\frac{1}{4}} + \sqrt{x}\right)"," ",0,"2*(-1/(b^3*c))^(1/4)*arctan(sqrt(b^2*sqrt(-1/(b^3*c)) + x)*b^2*c*(-1/(b^3*c))^(3/4) - b^2*c*sqrt(x)*(-1/(b^3*c))^(3/4)) + 1/2*(-1/(b^3*c))^(1/4)*log(b*(-1/(b^3*c))^(1/4) + sqrt(x)) - 1/2*(-1/(b^3*c))^(1/4)*log(-b*(-1/(b^3*c))^(1/4) + sqrt(x))","A",0
322,1,142,0,1.039768," ","integrate(x^(1/2)/(c*x^4+b*x^2),x, algorithm=""fricas"")","\frac{4 \, b x \left(-\frac{c}{b^{5}}\right)^{\frac{1}{4}} \arctan\left(-\frac{b c \sqrt{x} \left(-\frac{c}{b^{5}}\right)^{\frac{1}{4}} - \sqrt{-b^{3} c \sqrt{-\frac{c}{b^{5}}} + c^{2} x} b \left(-\frac{c}{b^{5}}\right)^{\frac{1}{4}}}{c}\right) - b x \left(-\frac{c}{b^{5}}\right)^{\frac{1}{4}} \log\left(b^{4} \left(-\frac{c}{b^{5}}\right)^{\frac{3}{4}} + c \sqrt{x}\right) + b x \left(-\frac{c}{b^{5}}\right)^{\frac{1}{4}} \log\left(-b^{4} \left(-\frac{c}{b^{5}}\right)^{\frac{3}{4}} + c \sqrt{x}\right) - 4 \, \sqrt{x}}{2 \, b x}"," ",0,"1/2*(4*b*x*(-c/b^5)^(1/4)*arctan(-(b*c*sqrt(x)*(-c/b^5)^(1/4) - sqrt(-b^3*c*sqrt(-c/b^5) + c^2*x)*b*(-c/b^5)^(1/4))/c) - b*x*(-c/b^5)^(1/4)*log(b^4*(-c/b^5)^(3/4) + c*sqrt(x)) + b*x*(-c/b^5)^(1/4)*log(-b^4*(-c/b^5)^(3/4) + c*sqrt(x)) - 4*sqrt(x))/(b*x)","A",0
323,1,167,0,0.743462," ","integrate(1/(c*x^4+b*x^2)/x^(1/2),x, algorithm=""fricas"")","-\frac{12 \, b x^{2} \left(-\frac{c^{3}}{b^{7}}\right)^{\frac{1}{4}} \arctan\left(-\frac{b^{5} c \sqrt{x} \left(-\frac{c^{3}}{b^{7}}\right)^{\frac{3}{4}} - \sqrt{b^{4} \sqrt{-\frac{c^{3}}{b^{7}}} + c^{2} x} b^{5} \left(-\frac{c^{3}}{b^{7}}\right)^{\frac{3}{4}}}{c^{3}}\right) + 3 \, b x^{2} \left(-\frac{c^{3}}{b^{7}}\right)^{\frac{1}{4}} \log\left(b^{2} \left(-\frac{c^{3}}{b^{7}}\right)^{\frac{1}{4}} + c \sqrt{x}\right) - 3 \, b x^{2} \left(-\frac{c^{3}}{b^{7}}\right)^{\frac{1}{4}} \log\left(-b^{2} \left(-\frac{c^{3}}{b^{7}}\right)^{\frac{1}{4}} + c \sqrt{x}\right) + 4 \, \sqrt{x}}{6 \, b x^{2}}"," ",0,"-1/6*(12*b*x^2*(-c^3/b^7)^(1/4)*arctan(-(b^5*c*sqrt(x)*(-c^3/b^7)^(3/4) - sqrt(b^4*sqrt(-c^3/b^7) + c^2*x)*b^5*(-c^3/b^7)^(3/4))/c^3) + 3*b*x^2*(-c^3/b^7)^(1/4)*log(b^2*(-c^3/b^7)^(1/4) + c*sqrt(x)) - 3*b*x^2*(-c^3/b^7)^(1/4)*log(-b^2*(-c^3/b^7)^(1/4) + c*sqrt(x)) + 4*sqrt(x))/(b*x^2)","A",0
324,1,193,0,1.049972," ","integrate(1/x^(3/2)/(c*x^4+b*x^2),x, algorithm=""fricas"")","-\frac{20 \, b^{2} x^{3} \left(-\frac{c^{5}}{b^{9}}\right)^{\frac{1}{4}} \arctan\left(-\frac{b^{2} c^{4} \sqrt{x} \left(-\frac{c^{5}}{b^{9}}\right)^{\frac{1}{4}} - \sqrt{-b^{5} c^{5} \sqrt{-\frac{c^{5}}{b^{9}}} + c^{8} x} b^{2} \left(-\frac{c^{5}}{b^{9}}\right)^{\frac{1}{4}}}{c^{5}}\right) - 5 \, b^{2} x^{3} \left(-\frac{c^{5}}{b^{9}}\right)^{\frac{1}{4}} \log\left(b^{7} \left(-\frac{c^{5}}{b^{9}}\right)^{\frac{3}{4}} + c^{4} \sqrt{x}\right) + 5 \, b^{2} x^{3} \left(-\frac{c^{5}}{b^{9}}\right)^{\frac{1}{4}} \log\left(-b^{7} \left(-\frac{c^{5}}{b^{9}}\right)^{\frac{3}{4}} + c^{4} \sqrt{x}\right) - 4 \, {\left(5 \, c x^{2} - b\right)} \sqrt{x}}{10 \, b^{2} x^{3}}"," ",0,"-1/10*(20*b^2*x^3*(-c^5/b^9)^(1/4)*arctan(-(b^2*c^4*sqrt(x)*(-c^5/b^9)^(1/4) - sqrt(-b^5*c^5*sqrt(-c^5/b^9) + c^8*x)*b^2*(-c^5/b^9)^(1/4))/c^5) - 5*b^2*x^3*(-c^5/b^9)^(1/4)*log(b^7*(-c^5/b^9)^(3/4) + c^4*sqrt(x)) + 5*b^2*x^3*(-c^5/b^9)^(1/4)*log(-b^7*(-c^5/b^9)^(3/4) + c^4*sqrt(x)) - 4*(5*c*x^2 - b)*sqrt(x))/(b^2*x^3)","A",0
325,1,189,0,1.550035," ","integrate(1/x^(5/2)/(c*x^4+b*x^2),x, algorithm=""fricas"")","\frac{84 \, b^{2} x^{4} \left(-\frac{c^{7}}{b^{11}}\right)^{\frac{1}{4}} \arctan\left(-\frac{b^{8} c^{2} \sqrt{x} \left(-\frac{c^{7}}{b^{11}}\right)^{\frac{3}{4}} - \sqrt{b^{6} \sqrt{-\frac{c^{7}}{b^{11}}} + c^{4} x} b^{8} \left(-\frac{c^{7}}{b^{11}}\right)^{\frac{3}{4}}}{c^{7}}\right) + 21 \, b^{2} x^{4} \left(-\frac{c^{7}}{b^{11}}\right)^{\frac{1}{4}} \log\left(b^{3} \left(-\frac{c^{7}}{b^{11}}\right)^{\frac{1}{4}} + c^{2} \sqrt{x}\right) - 21 \, b^{2} x^{4} \left(-\frac{c^{7}}{b^{11}}\right)^{\frac{1}{4}} \log\left(-b^{3} \left(-\frac{c^{7}}{b^{11}}\right)^{\frac{1}{4}} + c^{2} \sqrt{x}\right) + 4 \, {\left(7 \, c x^{2} - 3 \, b\right)} \sqrt{x}}{42 \, b^{2} x^{4}}"," ",0,"1/42*(84*b^2*x^4*(-c^7/b^11)^(1/4)*arctan(-(b^8*c^2*sqrt(x)*(-c^7/b^11)^(3/4) - sqrt(b^6*sqrt(-c^7/b^11) + c^4*x)*b^8*(-c^7/b^11)^(3/4))/c^7) + 21*b^2*x^4*(-c^7/b^11)^(1/4)*log(b^3*(-c^7/b^11)^(1/4) + c^2*sqrt(x)) - 21*b^2*x^4*(-c^7/b^11)^(1/4)*log(-b^3*(-c^7/b^11)^(1/4) + c^2*sqrt(x)) + 4*(7*c*x^2 - 3*b)*sqrt(x))/(b^2*x^4)","A",0
326,1,204,0,0.775787," ","integrate(1/x^(7/2)/(c*x^4+b*x^2),x, algorithm=""fricas"")","\frac{180 \, b^{3} x^{5} \left(-\frac{c^{9}}{b^{13}}\right)^{\frac{1}{4}} \arctan\left(-\frac{b^{3} c^{7} \sqrt{x} \left(-\frac{c^{9}}{b^{13}}\right)^{\frac{1}{4}} - \sqrt{-b^{7} c^{9} \sqrt{-\frac{c^{9}}{b^{13}}} + c^{14} x} b^{3} \left(-\frac{c^{9}}{b^{13}}\right)^{\frac{1}{4}}}{c^{9}}\right) - 45 \, b^{3} x^{5} \left(-\frac{c^{9}}{b^{13}}\right)^{\frac{1}{4}} \log\left(b^{10} \left(-\frac{c^{9}}{b^{13}}\right)^{\frac{3}{4}} + c^{7} \sqrt{x}\right) + 45 \, b^{3} x^{5} \left(-\frac{c^{9}}{b^{13}}\right)^{\frac{1}{4}} \log\left(-b^{10} \left(-\frac{c^{9}}{b^{13}}\right)^{\frac{3}{4}} + c^{7} \sqrt{x}\right) - 4 \, {\left(45 \, c^{2} x^{4} - 9 \, b c x^{2} + 5 \, b^{2}\right)} \sqrt{x}}{90 \, b^{3} x^{5}}"," ",0,"1/90*(180*b^3*x^5*(-c^9/b^13)^(1/4)*arctan(-(b^3*c^7*sqrt(x)*(-c^9/b^13)^(1/4) - sqrt(-b^7*c^9*sqrt(-c^9/b^13) + c^14*x)*b^3*(-c^9/b^13)^(1/4))/c^9) - 45*b^3*x^5*(-c^9/b^13)^(1/4)*log(b^10*(-c^9/b^13)^(3/4) + c^7*sqrt(x)) + 45*b^3*x^5*(-c^9/b^13)^(1/4)*log(-b^10*(-c^9/b^13)^(3/4) + c^7*sqrt(x)) - 4*(45*c^2*x^4 - 9*b*c*x^2 + 5*b^2)*sqrt(x))/(b^3*x^5)","A",0
327,1,227,0,0.956529," ","integrate(x^(19/2)/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","\frac{180 \, {\left(c^{4} x^{2} + b c^{3}\right)} \left(-\frac{b^{5}}{c^{13}}\right)^{\frac{1}{4}} \arctan\left(-\frac{b c^{10} \sqrt{x} \left(-\frac{b^{5}}{c^{13}}\right)^{\frac{3}{4}} - \sqrt{c^{6} \sqrt{-\frac{b^{5}}{c^{13}}} + b^{2} x} c^{10} \left(-\frac{b^{5}}{c^{13}}\right)^{\frac{3}{4}}}{b^{5}}\right) + 45 \, {\left(c^{4} x^{2} + b c^{3}\right)} \left(-\frac{b^{5}}{c^{13}}\right)^{\frac{1}{4}} \log\left(9 \, c^{3} \left(-\frac{b^{5}}{c^{13}}\right)^{\frac{1}{4}} + 9 \, b \sqrt{x}\right) - 45 \, {\left(c^{4} x^{2} + b c^{3}\right)} \left(-\frac{b^{5}}{c^{13}}\right)^{\frac{1}{4}} \log\left(-9 \, c^{3} \left(-\frac{b^{5}}{c^{13}}\right)^{\frac{1}{4}} + 9 \, b \sqrt{x}\right) + 4 \, {\left(4 \, c^{2} x^{4} - 36 \, b c x^{2} - 45 \, b^{2}\right)} \sqrt{x}}{40 \, {\left(c^{4} x^{2} + b c^{3}\right)}}"," ",0,"1/40*(180*(c^4*x^2 + b*c^3)*(-b^5/c^13)^(1/4)*arctan(-(b*c^10*sqrt(x)*(-b^5/c^13)^(3/4) - sqrt(c^6*sqrt(-b^5/c^13) + b^2*x)*c^10*(-b^5/c^13)^(3/4))/b^5) + 45*(c^4*x^2 + b*c^3)*(-b^5/c^13)^(1/4)*log(9*c^3*(-b^5/c^13)^(1/4) + 9*b*sqrt(x)) - 45*(c^4*x^2 + b*c^3)*(-b^5/c^13)^(1/4)*log(-9*c^3*(-b^5/c^13)^(1/4) + 9*b*sqrt(x)) + 4*(4*c^2*x^4 - 36*b*c*x^2 - 45*b^2)*sqrt(x))/(c^4*x^2 + b*c^3)","A",0
328,1,229,0,0.862970," ","integrate(x^(17/2)/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","\frac{84 \, {\left(c^{3} x^{2} + b c^{2}\right)} \left(-\frac{b^{3}}{c^{11}}\right)^{\frac{1}{4}} \arctan\left(-\frac{343 \, b^{2} c^{3} \sqrt{x} \left(-\frac{b^{3}}{c^{11}}\right)^{\frac{1}{4}} - \sqrt{-117649 \, b^{3} c^{5} \sqrt{-\frac{b^{3}}{c^{11}}} + 117649 \, b^{4} x} c^{3} \left(-\frac{b^{3}}{c^{11}}\right)^{\frac{1}{4}}}{343 \, b^{3}}\right) - 21 \, {\left(c^{3} x^{2} + b c^{2}\right)} \left(-\frac{b^{3}}{c^{11}}\right)^{\frac{1}{4}} \log\left(343 \, c^{8} \left(-\frac{b^{3}}{c^{11}}\right)^{\frac{3}{4}} + 343 \, b^{2} \sqrt{x}\right) + 21 \, {\left(c^{3} x^{2} + b c^{2}\right)} \left(-\frac{b^{3}}{c^{11}}\right)^{\frac{1}{4}} \log\left(-343 \, c^{8} \left(-\frac{b^{3}}{c^{11}}\right)^{\frac{3}{4}} + 343 \, b^{2} \sqrt{x}\right) + 4 \, {\left(4 \, c x^{3} + 7 \, b x\right)} \sqrt{x}}{24 \, {\left(c^{3} x^{2} + b c^{2}\right)}}"," ",0,"1/24*(84*(c^3*x^2 + b*c^2)*(-b^3/c^11)^(1/4)*arctan(-1/343*(343*b^2*c^3*sqrt(x)*(-b^3/c^11)^(1/4) - sqrt(-117649*b^3*c^5*sqrt(-b^3/c^11) + 117649*b^4*x)*c^3*(-b^3/c^11)^(1/4))/b^3) - 21*(c^3*x^2 + b*c^2)*(-b^3/c^11)^(1/4)*log(343*c^8*(-b^3/c^11)^(3/4) + 343*b^2*sqrt(x)) + 21*(c^3*x^2 + b*c^2)*(-b^3/c^11)^(1/4)*log(-343*c^8*(-b^3/c^11)^(3/4) + 343*b^2*sqrt(x)) + 4*(4*c*x^3 + 7*b*x)*sqrt(x))/(c^3*x^2 + b*c^2)","A",0
329,1,192,0,0.813982," ","integrate(x^(15/2)/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","-\frac{20 \, {\left(c^{3} x^{2} + b c^{2}\right)} \left(-\frac{b}{c^{9}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{c^{4} \sqrt{-\frac{b}{c^{9}}} + x} c^{7} \left(-\frac{b}{c^{9}}\right)^{\frac{3}{4}} - c^{7} \sqrt{x} \left(-\frac{b}{c^{9}}\right)^{\frac{3}{4}}}{b}\right) + 5 \, {\left(c^{3} x^{2} + b c^{2}\right)} \left(-\frac{b}{c^{9}}\right)^{\frac{1}{4}} \log\left(5 \, c^{2} \left(-\frac{b}{c^{9}}\right)^{\frac{1}{4}} + 5 \, \sqrt{x}\right) - 5 \, {\left(c^{3} x^{2} + b c^{2}\right)} \left(-\frac{b}{c^{9}}\right)^{\frac{1}{4}} \log\left(-5 \, c^{2} \left(-\frac{b}{c^{9}}\right)^{\frac{1}{4}} + 5 \, \sqrt{x}\right) - 4 \, {\left(4 \, c x^{2} + 5 \, b\right)} \sqrt{x}}{8 \, {\left(c^{3} x^{2} + b c^{2}\right)}}"," ",0,"-1/8*(20*(c^3*x^2 + b*c^2)*(-b/c^9)^(1/4)*arctan((sqrt(c^4*sqrt(-b/c^9) + x)*c^7*(-b/c^9)^(3/4) - c^7*sqrt(x)*(-b/c^9)^(3/4))/b) + 5*(c^3*x^2 + b*c^2)*(-b/c^9)^(1/4)*log(5*c^2*(-b/c^9)^(1/4) + 5*sqrt(x)) - 5*(c^3*x^2 + b*c^2)*(-b/c^9)^(1/4)*log(-5*c^2*(-b/c^9)^(1/4) + 5*sqrt(x)) - 4*(4*c*x^2 + 5*b)*sqrt(x))/(c^3*x^2 + b*c^2)","A",0
330,1,185,0,1.047162," ","integrate(x^(13/2)/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","-\frac{12 \, {\left(c^{2} x^{2} + b c\right)} \left(-\frac{1}{b c^{7}}\right)^{\frac{1}{4}} \arctan\left(\sqrt{-b c^{3} \sqrt{-\frac{1}{b c^{7}}} + x} c^{2} \left(-\frac{1}{b c^{7}}\right)^{\frac{1}{4}} - c^{2} \sqrt{x} \left(-\frac{1}{b c^{7}}\right)^{\frac{1}{4}}\right) - 3 \, {\left(c^{2} x^{2} + b c\right)} \left(-\frac{1}{b c^{7}}\right)^{\frac{1}{4}} \log\left(b c^{5} \left(-\frac{1}{b c^{7}}\right)^{\frac{3}{4}} + \sqrt{x}\right) + 3 \, {\left(c^{2} x^{2} + b c\right)} \left(-\frac{1}{b c^{7}}\right)^{\frac{1}{4}} \log\left(-b c^{5} \left(-\frac{1}{b c^{7}}\right)^{\frac{3}{4}} + \sqrt{x}\right) + 4 \, x^{\frac{3}{2}}}{8 \, {\left(c^{2} x^{2} + b c\right)}}"," ",0,"-1/8*(12*(c^2*x^2 + b*c)*(-1/(b*c^7))^(1/4)*arctan(sqrt(-b*c^3*sqrt(-1/(b*c^7)) + x)*c^2*(-1/(b*c^7))^(1/4) - c^2*sqrt(x)*(-1/(b*c^7))^(1/4)) - 3*(c^2*x^2 + b*c)*(-1/(b*c^7))^(1/4)*log(b*c^5*(-1/(b*c^7))^(3/4) + sqrt(x)) + 3*(c^2*x^2 + b*c)*(-1/(b*c^7))^(1/4)*log(-b*c^5*(-1/(b*c^7))^(3/4) + sqrt(x)) + 4*x^(3/2))/(c^2*x^2 + b*c)","A",0
331,1,187,0,1.000938," ","integrate(x^(11/2)/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","\frac{4 \, {\left(c^{2} x^{2} + b c\right)} \left(-\frac{1}{b^{3} c^{5}}\right)^{\frac{1}{4}} \arctan\left(\sqrt{b^{2} c^{2} \sqrt{-\frac{1}{b^{3} c^{5}}} + x} b^{2} c^{4} \left(-\frac{1}{b^{3} c^{5}}\right)^{\frac{3}{4}} - b^{2} c^{4} \sqrt{x} \left(-\frac{1}{b^{3} c^{5}}\right)^{\frac{3}{4}}\right) + {\left(c^{2} x^{2} + b c\right)} \left(-\frac{1}{b^{3} c^{5}}\right)^{\frac{1}{4}} \log\left(b c \left(-\frac{1}{b^{3} c^{5}}\right)^{\frac{1}{4}} + \sqrt{x}\right) - {\left(c^{2} x^{2} + b c\right)} \left(-\frac{1}{b^{3} c^{5}}\right)^{\frac{1}{4}} \log\left(-b c \left(-\frac{1}{b^{3} c^{5}}\right)^{\frac{1}{4}} + \sqrt{x}\right) - 4 \, \sqrt{x}}{8 \, {\left(c^{2} x^{2} + b c\right)}}"," ",0,"1/8*(4*(c^2*x^2 + b*c)*(-1/(b^3*c^5))^(1/4)*arctan(sqrt(b^2*c^2*sqrt(-1/(b^3*c^5)) + x)*b^2*c^4*(-1/(b^3*c^5))^(3/4) - b^2*c^4*sqrt(x)*(-1/(b^3*c^5))^(3/4)) + (c^2*x^2 + b*c)*(-1/(b^3*c^5))^(1/4)*log(b*c*(-1/(b^3*c^5))^(1/4) + sqrt(x)) - (c^2*x^2 + b*c)*(-1/(b^3*c^5))^(1/4)*log(-b*c*(-1/(b^3*c^5))^(1/4) + sqrt(x)) - 4*sqrt(x))/(c^2*x^2 + b*c)","A",0
332,1,182,0,1.925514," ","integrate(x^(9/2)/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","-\frac{4 \, {\left(b c x^{2} + b^{2}\right)} \left(-\frac{1}{b^{5} c^{3}}\right)^{\frac{1}{4}} \arctan\left(\sqrt{-b^{3} c \sqrt{-\frac{1}{b^{5} c^{3}}} + x} b c \left(-\frac{1}{b^{5} c^{3}}\right)^{\frac{1}{4}} - b c \sqrt{x} \left(-\frac{1}{b^{5} c^{3}}\right)^{\frac{1}{4}}\right) - {\left(b c x^{2} + b^{2}\right)} \left(-\frac{1}{b^{5} c^{3}}\right)^{\frac{1}{4}} \log\left(b^{4} c^{2} \left(-\frac{1}{b^{5} c^{3}}\right)^{\frac{3}{4}} + \sqrt{x}\right) + {\left(b c x^{2} + b^{2}\right)} \left(-\frac{1}{b^{5} c^{3}}\right)^{\frac{1}{4}} \log\left(-b^{4} c^{2} \left(-\frac{1}{b^{5} c^{3}}\right)^{\frac{3}{4}} + \sqrt{x}\right) - 4 \, x^{\frac{3}{2}}}{8 \, {\left(b c x^{2} + b^{2}\right)}}"," ",0,"-1/8*(4*(b*c*x^2 + b^2)*(-1/(b^5*c^3))^(1/4)*arctan(sqrt(-b^3*c*sqrt(-1/(b^5*c^3)) + x)*b*c*(-1/(b^5*c^3))^(1/4) - b*c*sqrt(x)*(-1/(b^5*c^3))^(1/4)) - (b*c*x^2 + b^2)*(-1/(b^5*c^3))^(1/4)*log(b^4*c^2*(-1/(b^5*c^3))^(3/4) + sqrt(x)) + (b*c*x^2 + b^2)*(-1/(b^5*c^3))^(1/4)*log(-b^4*c^2*(-1/(b^5*c^3))^(3/4) + sqrt(x)) - 4*x^(3/2))/(b*c*x^2 + b^2)","A",0
333,1,179,0,1.084533," ","integrate(x^(7/2)/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","\frac{12 \, {\left(b c x^{2} + b^{2}\right)} \left(-\frac{1}{b^{7} c}\right)^{\frac{1}{4}} \arctan\left(\sqrt{b^{4} \sqrt{-\frac{1}{b^{7} c}} + x} b^{5} c \left(-\frac{1}{b^{7} c}\right)^{\frac{3}{4}} - b^{5} c \sqrt{x} \left(-\frac{1}{b^{7} c}\right)^{\frac{3}{4}}\right) + 3 \, {\left(b c x^{2} + b^{2}\right)} \left(-\frac{1}{b^{7} c}\right)^{\frac{1}{4}} \log\left(b^{2} \left(-\frac{1}{b^{7} c}\right)^{\frac{1}{4}} + \sqrt{x}\right) - 3 \, {\left(b c x^{2} + b^{2}\right)} \left(-\frac{1}{b^{7} c}\right)^{\frac{1}{4}} \log\left(-b^{2} \left(-\frac{1}{b^{7} c}\right)^{\frac{1}{4}} + \sqrt{x}\right) + 4 \, \sqrt{x}}{8 \, {\left(b c x^{2} + b^{2}\right)}}"," ",0,"1/8*(12*(b*c*x^2 + b^2)*(-1/(b^7*c))^(1/4)*arctan(sqrt(b^4*sqrt(-1/(b^7*c)) + x)*b^5*c*(-1/(b^7*c))^(3/4) - b^5*c*sqrt(x)*(-1/(b^7*c))^(3/4)) + 3*(b*c*x^2 + b^2)*(-1/(b^7*c))^(1/4)*log(b^2*(-1/(b^7*c))^(1/4) + sqrt(x)) - 3*(b*c*x^2 + b^2)*(-1/(b^7*c))^(1/4)*log(-b^2*(-1/(b^7*c))^(1/4) + sqrt(x)) + 4*sqrt(x))/(b*c*x^2 + b^2)","A",0
334,1,208,0,1.192801," ","integrate(x^(5/2)/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","\frac{20 \, {\left(b^{2} c x^{3} + b^{3} x\right)} \left(-\frac{c}{b^{9}}\right)^{\frac{1}{4}} \arctan\left(-\frac{125 \, b^{2} c \sqrt{x} \left(-\frac{c}{b^{9}}\right)^{\frac{1}{4}} - \sqrt{-15625 \, b^{5} c \sqrt{-\frac{c}{b^{9}}} + 15625 \, c^{2} x} b^{2} \left(-\frac{c}{b^{9}}\right)^{\frac{1}{4}}}{125 \, c}\right) - 5 \, {\left(b^{2} c x^{3} + b^{3} x\right)} \left(-\frac{c}{b^{9}}\right)^{\frac{1}{4}} \log\left(125 \, b^{7} \left(-\frac{c}{b^{9}}\right)^{\frac{3}{4}} + 125 \, c \sqrt{x}\right) + 5 \, {\left(b^{2} c x^{3} + b^{3} x\right)} \left(-\frac{c}{b^{9}}\right)^{\frac{1}{4}} \log\left(-125 \, b^{7} \left(-\frac{c}{b^{9}}\right)^{\frac{3}{4}} + 125 \, c \sqrt{x}\right) - 4 \, {\left(5 \, c x^{2} + 4 \, b\right)} \sqrt{x}}{8 \, {\left(b^{2} c x^{3} + b^{3} x\right)}}"," ",0,"1/8*(20*(b^2*c*x^3 + b^3*x)*(-c/b^9)^(1/4)*arctan(-1/125*(125*b^2*c*sqrt(x)*(-c/b^9)^(1/4) - sqrt(-15625*b^5*c*sqrt(-c/b^9) + 15625*c^2*x)*b^2*(-c/b^9)^(1/4))/c) - 5*(b^2*c*x^3 + b^3*x)*(-c/b^9)^(1/4)*log(125*b^7*(-c/b^9)^(3/4) + 125*c*sqrt(x)) + 5*(b^2*c*x^3 + b^3*x)*(-c/b^9)^(1/4)*log(-125*b^7*(-c/b^9)^(3/4) + 125*c*sqrt(x)) - 4*(5*c*x^2 + 4*b)*sqrt(x))/(b^2*c*x^3 + b^3*x)","A",0
335,1,228,0,1.331296," ","integrate(x^(3/2)/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","-\frac{84 \, {\left(b^{2} c x^{4} + b^{3} x^{2}\right)} \left(-\frac{c^{3}}{b^{11}}\right)^{\frac{1}{4}} \arctan\left(-\frac{b^{8} c \sqrt{x} \left(-\frac{c^{3}}{b^{11}}\right)^{\frac{3}{4}} - \sqrt{b^{6} \sqrt{-\frac{c^{3}}{b^{11}}} + c^{2} x} b^{8} \left(-\frac{c^{3}}{b^{11}}\right)^{\frac{3}{4}}}{c^{3}}\right) + 21 \, {\left(b^{2} c x^{4} + b^{3} x^{2}\right)} \left(-\frac{c^{3}}{b^{11}}\right)^{\frac{1}{4}} \log\left(7 \, b^{3} \left(-\frac{c^{3}}{b^{11}}\right)^{\frac{1}{4}} + 7 \, c \sqrt{x}\right) - 21 \, {\left(b^{2} c x^{4} + b^{3} x^{2}\right)} \left(-\frac{c^{3}}{b^{11}}\right)^{\frac{1}{4}} \log\left(-7 \, b^{3} \left(-\frac{c^{3}}{b^{11}}\right)^{\frac{1}{4}} + 7 \, c \sqrt{x}\right) + 4 \, {\left(7 \, c x^{2} + 4 \, b\right)} \sqrt{x}}{24 \, {\left(b^{2} c x^{4} + b^{3} x^{2}\right)}}"," ",0,"-1/24*(84*(b^2*c*x^4 + b^3*x^2)*(-c^3/b^11)^(1/4)*arctan(-(b^8*c*sqrt(x)*(-c^3/b^11)^(3/4) - sqrt(b^6*sqrt(-c^3/b^11) + c^2*x)*b^8*(-c^3/b^11)^(3/4))/c^3) + 21*(b^2*c*x^4 + b^3*x^2)*(-c^3/b^11)^(1/4)*log(7*b^3*(-c^3/b^11)^(1/4) + 7*c*sqrt(x)) - 21*(b^2*c*x^4 + b^3*x^2)*(-c^3/b^11)^(1/4)*log(-7*b^3*(-c^3/b^11)^(1/4) + 7*c*sqrt(x)) + 4*(7*c*x^2 + 4*b)*sqrt(x))/(b^2*c*x^4 + b^3*x^2)","A",0
336,1,251,0,1.038481," ","integrate(x^(1/2)/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","-\frac{180 \, {\left(b^{3} c x^{5} + b^{4} x^{3}\right)} \left(-\frac{c^{5}}{b^{13}}\right)^{\frac{1}{4}} \arctan\left(-\frac{729 \, b^{3} c^{4} \sqrt{x} \left(-\frac{c^{5}}{b^{13}}\right)^{\frac{1}{4}} - \sqrt{-531441 \, b^{7} c^{5} \sqrt{-\frac{c^{5}}{b^{13}}} + 531441 \, c^{8} x} b^{3} \left(-\frac{c^{5}}{b^{13}}\right)^{\frac{1}{4}}}{729 \, c^{5}}\right) - 45 \, {\left(b^{3} c x^{5} + b^{4} x^{3}\right)} \left(-\frac{c^{5}}{b^{13}}\right)^{\frac{1}{4}} \log\left(729 \, b^{10} \left(-\frac{c^{5}}{b^{13}}\right)^{\frac{3}{4}} + 729 \, c^{4} \sqrt{x}\right) + 45 \, {\left(b^{3} c x^{5} + b^{4} x^{3}\right)} \left(-\frac{c^{5}}{b^{13}}\right)^{\frac{1}{4}} \log\left(-729 \, b^{10} \left(-\frac{c^{5}}{b^{13}}\right)^{\frac{3}{4}} + 729 \, c^{4} \sqrt{x}\right) - 4 \, {\left(45 \, c^{2} x^{4} + 36 \, b c x^{2} - 4 \, b^{2}\right)} \sqrt{x}}{40 \, {\left(b^{3} c x^{5} + b^{4} x^{3}\right)}}"," ",0,"-1/40*(180*(b^3*c*x^5 + b^4*x^3)*(-c^5/b^13)^(1/4)*arctan(-1/729*(729*b^3*c^4*sqrt(x)*(-c^5/b^13)^(1/4) - sqrt(-531441*b^7*c^5*sqrt(-c^5/b^13) + 531441*c^8*x)*b^3*(-c^5/b^13)^(1/4))/c^5) - 45*(b^3*c*x^5 + b^4*x^3)*(-c^5/b^13)^(1/4)*log(729*b^10*(-c^5/b^13)^(3/4) + 729*c^4*sqrt(x)) + 45*(b^3*c*x^5 + b^4*x^3)*(-c^5/b^13)^(1/4)*log(-729*b^10*(-c^5/b^13)^(3/4) + 729*c^4*sqrt(x)) - 4*(45*c^2*x^4 + 36*b*c*x^2 - 4*b^2)*sqrt(x))/(b^3*c*x^5 + b^4*x^3)","A",0
337,1,245,0,0.788449," ","integrate(1/(c*x^4+b*x^2)^2/x^(1/2),x, algorithm=""fricas"")","\frac{924 \, {\left(b^{3} c x^{6} + b^{4} x^{4}\right)} \left(-\frac{c^{7}}{b^{15}}\right)^{\frac{1}{4}} \arctan\left(-\frac{b^{11} c^{2} \sqrt{x} \left(-\frac{c^{7}}{b^{15}}\right)^{\frac{3}{4}} - \sqrt{b^{8} \sqrt{-\frac{c^{7}}{b^{15}}} + c^{4} x} b^{11} \left(-\frac{c^{7}}{b^{15}}\right)^{\frac{3}{4}}}{c^{7}}\right) + 231 \, {\left(b^{3} c x^{6} + b^{4} x^{4}\right)} \left(-\frac{c^{7}}{b^{15}}\right)^{\frac{1}{4}} \log\left(11 \, b^{4} \left(-\frac{c^{7}}{b^{15}}\right)^{\frac{1}{4}} + 11 \, c^{2} \sqrt{x}\right) - 231 \, {\left(b^{3} c x^{6} + b^{4} x^{4}\right)} \left(-\frac{c^{7}}{b^{15}}\right)^{\frac{1}{4}} \log\left(-11 \, b^{4} \left(-\frac{c^{7}}{b^{15}}\right)^{\frac{1}{4}} + 11 \, c^{2} \sqrt{x}\right) + 4 \, {\left(77 \, c^{2} x^{4} + 44 \, b c x^{2} - 12 \, b^{2}\right)} \sqrt{x}}{168 \, {\left(b^{3} c x^{6} + b^{4} x^{4}\right)}}"," ",0,"1/168*(924*(b^3*c*x^6 + b^4*x^4)*(-c^7/b^15)^(1/4)*arctan(-(b^11*c^2*sqrt(x)*(-c^7/b^15)^(3/4) - sqrt(b^8*sqrt(-c^7/b^15) + c^4*x)*b^11*(-c^7/b^15)^(3/4))/c^7) + 231*(b^3*c*x^6 + b^4*x^4)*(-c^7/b^15)^(1/4)*log(11*b^4*(-c^7/b^15)^(1/4) + 11*c^2*sqrt(x)) - 231*(b^3*c*x^6 + b^4*x^4)*(-c^7/b^15)^(1/4)*log(-11*b^4*(-c^7/b^15)^(1/4) + 11*c^2*sqrt(x)) + 4*(77*c^2*x^4 + 44*b*c*x^2 - 12*b^2)*sqrt(x))/(b^3*c*x^6 + b^4*x^4)","A",0
338,1,262,0,1.157127," ","integrate(1/x^(3/2)/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","\frac{2340 \, {\left(b^{4} c x^{7} + b^{5} x^{5}\right)} \left(-\frac{c^{9}}{b^{17}}\right)^{\frac{1}{4}} \arctan\left(-\frac{2197 \, b^{4} c^{7} \sqrt{x} \left(-\frac{c^{9}}{b^{17}}\right)^{\frac{1}{4}} - \sqrt{-4826809 \, b^{9} c^{9} \sqrt{-\frac{c^{9}}{b^{17}}} + 4826809 \, c^{14} x} b^{4} \left(-\frac{c^{9}}{b^{17}}\right)^{\frac{1}{4}}}{2197 \, c^{9}}\right) - 585 \, {\left(b^{4} c x^{7} + b^{5} x^{5}\right)} \left(-\frac{c^{9}}{b^{17}}\right)^{\frac{1}{4}} \log\left(2197 \, b^{13} \left(-\frac{c^{9}}{b^{17}}\right)^{\frac{3}{4}} + 2197 \, c^{7} \sqrt{x}\right) + 585 \, {\left(b^{4} c x^{7} + b^{5} x^{5}\right)} \left(-\frac{c^{9}}{b^{17}}\right)^{\frac{1}{4}} \log\left(-2197 \, b^{13} \left(-\frac{c^{9}}{b^{17}}\right)^{\frac{3}{4}} + 2197 \, c^{7} \sqrt{x}\right) - 4 \, {\left(585 \, c^{3} x^{6} + 468 \, b c^{2} x^{4} - 52 \, b^{2} c x^{2} + 20 \, b^{3}\right)} \sqrt{x}}{360 \, {\left(b^{4} c x^{7} + b^{5} x^{5}\right)}}"," ",0,"1/360*(2340*(b^4*c*x^7 + b^5*x^5)*(-c^9/b^17)^(1/4)*arctan(-1/2197*(2197*b^4*c^7*sqrt(x)*(-c^9/b^17)^(1/4) - sqrt(-4826809*b^9*c^9*sqrt(-c^9/b^17) + 4826809*c^14*x)*b^4*(-c^9/b^17)^(1/4))/c^9) - 585*(b^4*c*x^7 + b^5*x^5)*(-c^9/b^17)^(1/4)*log(2197*b^13*(-c^9/b^17)^(3/4) + 2197*c^7*sqrt(x)) + 585*(b^4*c*x^7 + b^5*x^5)*(-c^9/b^17)^(1/4)*log(-2197*b^13*(-c^9/b^17)^(3/4) + 2197*c^7*sqrt(x)) - 4*(585*c^3*x^6 + 468*b*c^2*x^4 - 52*b^2*c*x^2 + 20*b^3)*sqrt(x))/(b^4*c*x^7 + b^5*x^5)","A",0
339,1,247,0,0.996490," ","integrate(x^(23/2)/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","-\frac{180 \, {\left(c^{5} x^{4} + 2 \, b c^{4} x^{2} + b^{2} c^{3}\right)} \left(-\frac{b}{c^{13}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{c^{6} \sqrt{-\frac{b}{c^{13}}} + x} c^{10} \left(-\frac{b}{c^{13}}\right)^{\frac{3}{4}} - c^{10} \sqrt{x} \left(-\frac{b}{c^{13}}\right)^{\frac{3}{4}}}{b}\right) + 45 \, {\left(c^{5} x^{4} + 2 \, b c^{4} x^{2} + b^{2} c^{3}\right)} \left(-\frac{b}{c^{13}}\right)^{\frac{1}{4}} \log\left(45 \, c^{3} \left(-\frac{b}{c^{13}}\right)^{\frac{1}{4}} + 45 \, \sqrt{x}\right) - 45 \, {\left(c^{5} x^{4} + 2 \, b c^{4} x^{2} + b^{2} c^{3}\right)} \left(-\frac{b}{c^{13}}\right)^{\frac{1}{4}} \log\left(-45 \, c^{3} \left(-\frac{b}{c^{13}}\right)^{\frac{1}{4}} + 45 \, \sqrt{x}\right) - 4 \, {\left(32 \, c^{2} x^{4} + 81 \, b c x^{2} + 45 \, b^{2}\right)} \sqrt{x}}{64 \, {\left(c^{5} x^{4} + 2 \, b c^{4} x^{2} + b^{2} c^{3}\right)}}"," ",0,"-1/64*(180*(c^5*x^4 + 2*b*c^4*x^2 + b^2*c^3)*(-b/c^13)^(1/4)*arctan((sqrt(c^6*sqrt(-b/c^13) + x)*c^10*(-b/c^13)^(3/4) - c^10*sqrt(x)*(-b/c^13)^(3/4))/b) + 45*(c^5*x^4 + 2*b*c^4*x^2 + b^2*c^3)*(-b/c^13)^(1/4)*log(45*c^3*(-b/c^13)^(1/4) + 45*sqrt(x)) - 45*(c^5*x^4 + 2*b*c^4*x^2 + b^2*c^3)*(-b/c^13)^(1/4)*log(-45*c^3*(-b/c^13)^(1/4) + 45*sqrt(x)) - 4*(32*c^2*x^4 + 81*b*c*x^2 + 45*b^2)*sqrt(x))/(c^5*x^4 + 2*b*c^4*x^2 + b^2*c^3)","A",0
340,1,248,0,1.280669," ","integrate(x^(21/2)/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","-\frac{84 \, {\left(c^{4} x^{4} + 2 \, b c^{3} x^{2} + b^{2} c^{2}\right)} \left(-\frac{1}{b c^{11}}\right)^{\frac{1}{4}} \arctan\left(\sqrt{-b c^{5} \sqrt{-\frac{1}{b c^{11}}} + x} c^{3} \left(-\frac{1}{b c^{11}}\right)^{\frac{1}{4}} - c^{3} \sqrt{x} \left(-\frac{1}{b c^{11}}\right)^{\frac{1}{4}}\right) - 21 \, {\left(c^{4} x^{4} + 2 \, b c^{3} x^{2} + b^{2} c^{2}\right)} \left(-\frac{1}{b c^{11}}\right)^{\frac{1}{4}} \log\left(b c^{8} \left(-\frac{1}{b c^{11}}\right)^{\frac{3}{4}} + \sqrt{x}\right) + 21 \, {\left(c^{4} x^{4} + 2 \, b c^{3} x^{2} + b^{2} c^{2}\right)} \left(-\frac{1}{b c^{11}}\right)^{\frac{1}{4}} \log\left(-b c^{8} \left(-\frac{1}{b c^{11}}\right)^{\frac{3}{4}} + \sqrt{x}\right) + 4 \, {\left(11 \, c x^{3} + 7 \, b x\right)} \sqrt{x}}{64 \, {\left(c^{4} x^{4} + 2 \, b c^{3} x^{2} + b^{2} c^{2}\right)}}"," ",0,"-1/64*(84*(c^4*x^4 + 2*b*c^3*x^2 + b^2*c^2)*(-1/(b*c^11))^(1/4)*arctan(sqrt(-b*c^5*sqrt(-1/(b*c^11)) + x)*c^3*(-1/(b*c^11))^(1/4) - c^3*sqrt(x)*(-1/(b*c^11))^(1/4)) - 21*(c^4*x^4 + 2*b*c^3*x^2 + b^2*c^2)*(-1/(b*c^11))^(1/4)*log(b*c^8*(-1/(b*c^11))^(3/4) + sqrt(x)) + 21*(c^4*x^4 + 2*b*c^3*x^2 + b^2*c^2)*(-1/(b*c^11))^(1/4)*log(-b*c^8*(-1/(b*c^11))^(3/4) + sqrt(x)) + 4*(11*c*x^3 + 7*b*x)*sqrt(x))/(c^4*x^4 + 2*b*c^3*x^2 + b^2*c^2)","A",0
341,1,254,0,1.337893," ","integrate(x^(19/2)/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","\frac{20 \, {\left(c^{4} x^{4} + 2 \, b c^{3} x^{2} + b^{2} c^{2}\right)} \left(-\frac{1}{b^{3} c^{9}}\right)^{\frac{1}{4}} \arctan\left(\sqrt{b^{2} c^{4} \sqrt{-\frac{1}{b^{3} c^{9}}} + x} b^{2} c^{7} \left(-\frac{1}{b^{3} c^{9}}\right)^{\frac{3}{4}} - b^{2} c^{7} \sqrt{x} \left(-\frac{1}{b^{3} c^{9}}\right)^{\frac{3}{4}}\right) + 5 \, {\left(c^{4} x^{4} + 2 \, b c^{3} x^{2} + b^{2} c^{2}\right)} \left(-\frac{1}{b^{3} c^{9}}\right)^{\frac{1}{4}} \log\left(b c^{2} \left(-\frac{1}{b^{3} c^{9}}\right)^{\frac{1}{4}} + \sqrt{x}\right) - 5 \, {\left(c^{4} x^{4} + 2 \, b c^{3} x^{2} + b^{2} c^{2}\right)} \left(-\frac{1}{b^{3} c^{9}}\right)^{\frac{1}{4}} \log\left(-b c^{2} \left(-\frac{1}{b^{3} c^{9}}\right)^{\frac{1}{4}} + \sqrt{x}\right) - 4 \, {\left(9 \, c x^{2} + 5 \, b\right)} \sqrt{x}}{64 \, {\left(c^{4} x^{4} + 2 \, b c^{3} x^{2} + b^{2} c^{2}\right)}}"," ",0,"1/64*(20*(c^4*x^4 + 2*b*c^3*x^2 + b^2*c^2)*(-1/(b^3*c^9))^(1/4)*arctan(sqrt(b^2*c^4*sqrt(-1/(b^3*c^9)) + x)*b^2*c^7*(-1/(b^3*c^9))^(3/4) - b^2*c^7*sqrt(x)*(-1/(b^3*c^9))^(3/4)) + 5*(c^4*x^4 + 2*b*c^3*x^2 + b^2*c^2)*(-1/(b^3*c^9))^(1/4)*log(b*c^2*(-1/(b^3*c^9))^(1/4) + sqrt(x)) - 5*(c^4*x^4 + 2*b*c^3*x^2 + b^2*c^2)*(-1/(b^3*c^9))^(1/4)*log(-b*c^2*(-1/(b^3*c^9))^(1/4) + sqrt(x)) - 4*(9*c*x^2 + 5*b)*sqrt(x))/(c^4*x^4 + 2*b*c^3*x^2 + b^2*c^2)","A",0
342,1,260,0,0.958804," ","integrate(x^(17/2)/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","-\frac{12 \, {\left(b c^{3} x^{4} + 2 \, b^{2} c^{2} x^{2} + b^{3} c\right)} \left(-\frac{1}{b^{5} c^{7}}\right)^{\frac{1}{4}} \arctan\left(\sqrt{-b^{3} c^{3} \sqrt{-\frac{1}{b^{5} c^{7}}} + x} b c^{2} \left(-\frac{1}{b^{5} c^{7}}\right)^{\frac{1}{4}} - b c^{2} \sqrt{x} \left(-\frac{1}{b^{5} c^{7}}\right)^{\frac{1}{4}}\right) - 3 \, {\left(b c^{3} x^{4} + 2 \, b^{2} c^{2} x^{2} + b^{3} c\right)} \left(-\frac{1}{b^{5} c^{7}}\right)^{\frac{1}{4}} \log\left(b^{4} c^{5} \left(-\frac{1}{b^{5} c^{7}}\right)^{\frac{3}{4}} + \sqrt{x}\right) + 3 \, {\left(b c^{3} x^{4} + 2 \, b^{2} c^{2} x^{2} + b^{3} c\right)} \left(-\frac{1}{b^{5} c^{7}}\right)^{\frac{1}{4}} \log\left(-b^{4} c^{5} \left(-\frac{1}{b^{5} c^{7}}\right)^{\frac{3}{4}} + \sqrt{x}\right) - 4 \, {\left(3 \, c x^{3} - b x\right)} \sqrt{x}}{64 \, {\left(b c^{3} x^{4} + 2 \, b^{2} c^{2} x^{2} + b^{3} c\right)}}"," ",0,"-1/64*(12*(b*c^3*x^4 + 2*b^2*c^2*x^2 + b^3*c)*(-1/(b^5*c^7))^(1/4)*arctan(sqrt(-b^3*c^3*sqrt(-1/(b^5*c^7)) + x)*b*c^2*(-1/(b^5*c^7))^(1/4) - b*c^2*sqrt(x)*(-1/(b^5*c^7))^(1/4)) - 3*(b*c^3*x^4 + 2*b^2*c^2*x^2 + b^3*c)*(-1/(b^5*c^7))^(1/4)*log(b^4*c^5*(-1/(b^5*c^7))^(3/4) + sqrt(x)) + 3*(b*c^3*x^4 + 2*b^2*c^2*x^2 + b^3*c)*(-1/(b^5*c^7))^(1/4)*log(-b^4*c^5*(-1/(b^5*c^7))^(3/4) + sqrt(x)) - 4*(3*c*x^3 - b*x)*sqrt(x))/(b*c^3*x^4 + 2*b^2*c^2*x^2 + b^3*c)","A",0
343,1,257,0,1.264279," ","integrate(x^(15/2)/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","\frac{12 \, {\left(b c^{3} x^{4} + 2 \, b^{2} c^{2} x^{2} + b^{3} c\right)} \left(-\frac{1}{b^{7} c^{5}}\right)^{\frac{1}{4}} \arctan\left(\sqrt{b^{4} c^{2} \sqrt{-\frac{1}{b^{7} c^{5}}} + x} b^{5} c^{4} \left(-\frac{1}{b^{7} c^{5}}\right)^{\frac{3}{4}} - b^{5} c^{4} \sqrt{x} \left(-\frac{1}{b^{7} c^{5}}\right)^{\frac{3}{4}}\right) + 3 \, {\left(b c^{3} x^{4} + 2 \, b^{2} c^{2} x^{2} + b^{3} c\right)} \left(-\frac{1}{b^{7} c^{5}}\right)^{\frac{1}{4}} \log\left(b^{2} c \left(-\frac{1}{b^{7} c^{5}}\right)^{\frac{1}{4}} + \sqrt{x}\right) - 3 \, {\left(b c^{3} x^{4} + 2 \, b^{2} c^{2} x^{2} + b^{3} c\right)} \left(-\frac{1}{b^{7} c^{5}}\right)^{\frac{1}{4}} \log\left(-b^{2} c \left(-\frac{1}{b^{7} c^{5}}\right)^{\frac{1}{4}} + \sqrt{x}\right) + 4 \, {\left(c x^{2} - 3 \, b\right)} \sqrt{x}}{64 \, {\left(b c^{3} x^{4} + 2 \, b^{2} c^{2} x^{2} + b^{3} c\right)}}"," ",0,"1/64*(12*(b*c^3*x^4 + 2*b^2*c^2*x^2 + b^3*c)*(-1/(b^7*c^5))^(1/4)*arctan(sqrt(b^4*c^2*sqrt(-1/(b^7*c^5)) + x)*b^5*c^4*(-1/(b^7*c^5))^(3/4) - b^5*c^4*sqrt(x)*(-1/(b^7*c^5))^(3/4)) + 3*(b*c^3*x^4 + 2*b^2*c^2*x^2 + b^3*c)*(-1/(b^7*c^5))^(1/4)*log(b^2*c*(-1/(b^7*c^5))^(1/4) + sqrt(x)) - 3*(b*c^3*x^4 + 2*b^2*c^2*x^2 + b^3*c)*(-1/(b^7*c^5))^(1/4)*log(-b^2*c*(-1/(b^7*c^5))^(1/4) + sqrt(x)) + 4*(c*x^2 - 3*b)*sqrt(x))/(b*c^3*x^4 + 2*b^2*c^2*x^2 + b^3*c)","A",0
344,1,250,0,0.848163," ","integrate(x^(13/2)/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","-\frac{20 \, {\left(b^{2} c^{2} x^{4} + 2 \, b^{3} c x^{2} + b^{4}\right)} \left(-\frac{1}{b^{9} c^{3}}\right)^{\frac{1}{4}} \arctan\left(\sqrt{-b^{5} c \sqrt{-\frac{1}{b^{9} c^{3}}} + x} b^{2} c \left(-\frac{1}{b^{9} c^{3}}\right)^{\frac{1}{4}} - b^{2} c \sqrt{x} \left(-\frac{1}{b^{9} c^{3}}\right)^{\frac{1}{4}}\right) - 5 \, {\left(b^{2} c^{2} x^{4} + 2 \, b^{3} c x^{2} + b^{4}\right)} \left(-\frac{1}{b^{9} c^{3}}\right)^{\frac{1}{4}} \log\left(b^{7} c^{2} \left(-\frac{1}{b^{9} c^{3}}\right)^{\frac{3}{4}} + \sqrt{x}\right) + 5 \, {\left(b^{2} c^{2} x^{4} + 2 \, b^{3} c x^{2} + b^{4}\right)} \left(-\frac{1}{b^{9} c^{3}}\right)^{\frac{1}{4}} \log\left(-b^{7} c^{2} \left(-\frac{1}{b^{9} c^{3}}\right)^{\frac{3}{4}} + \sqrt{x}\right) - 4 \, {\left(5 \, c x^{3} + 9 \, b x\right)} \sqrt{x}}{64 \, {\left(b^{2} c^{2} x^{4} + 2 \, b^{3} c x^{2} + b^{4}\right)}}"," ",0,"-1/64*(20*(b^2*c^2*x^4 + 2*b^3*c*x^2 + b^4)*(-1/(b^9*c^3))^(1/4)*arctan(sqrt(-b^5*c*sqrt(-1/(b^9*c^3)) + x)*b^2*c*(-1/(b^9*c^3))^(1/4) - b^2*c*sqrt(x)*(-1/(b^9*c^3))^(1/4)) - 5*(b^2*c^2*x^4 + 2*b^3*c*x^2 + b^4)*(-1/(b^9*c^3))^(1/4)*log(b^7*c^2*(-1/(b^9*c^3))^(3/4) + sqrt(x)) + 5*(b^2*c^2*x^4 + 2*b^3*c*x^2 + b^4)*(-1/(b^9*c^3))^(1/4)*log(-b^7*c^2*(-1/(b^9*c^3))^(3/4) + sqrt(x)) - 4*(5*c*x^3 + 9*b*x)*sqrt(x))/(b^2*c^2*x^4 + 2*b^3*c*x^2 + b^4)","A",0
345,1,241,0,1.099888," ","integrate(x^(11/2)/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","\frac{84 \, {\left(b^{2} c^{2} x^{4} + 2 \, b^{3} c x^{2} + b^{4}\right)} \left(-\frac{1}{b^{11} c}\right)^{\frac{1}{4}} \arctan\left(\sqrt{b^{6} \sqrt{-\frac{1}{b^{11} c}} + x} b^{8} c \left(-\frac{1}{b^{11} c}\right)^{\frac{3}{4}} - b^{8} c \sqrt{x} \left(-\frac{1}{b^{11} c}\right)^{\frac{3}{4}}\right) + 21 \, {\left(b^{2} c^{2} x^{4} + 2 \, b^{3} c x^{2} + b^{4}\right)} \left(-\frac{1}{b^{11} c}\right)^{\frac{1}{4}} \log\left(b^{3} \left(-\frac{1}{b^{11} c}\right)^{\frac{1}{4}} + \sqrt{x}\right) - 21 \, {\left(b^{2} c^{2} x^{4} + 2 \, b^{3} c x^{2} + b^{4}\right)} \left(-\frac{1}{b^{11} c}\right)^{\frac{1}{4}} \log\left(-b^{3} \left(-\frac{1}{b^{11} c}\right)^{\frac{1}{4}} + \sqrt{x}\right) + 4 \, {\left(7 \, c x^{2} + 11 \, b\right)} \sqrt{x}}{64 \, {\left(b^{2} c^{2} x^{4} + 2 \, b^{3} c x^{2} + b^{4}\right)}}"," ",0,"1/64*(84*(b^2*c^2*x^4 + 2*b^3*c*x^2 + b^4)*(-1/(b^11*c))^(1/4)*arctan(sqrt(b^6*sqrt(-1/(b^11*c)) + x)*b^8*c*(-1/(b^11*c))^(3/4) - b^8*c*sqrt(x)*(-1/(b^11*c))^(3/4)) + 21*(b^2*c^2*x^4 + 2*b^3*c*x^2 + b^4)*(-1/(b^11*c))^(1/4)*log(b^3*(-1/(b^11*c))^(1/4) + sqrt(x)) - 21*(b^2*c^2*x^4 + 2*b^3*c*x^2 + b^4)*(-1/(b^11*c))^(1/4)*log(-b^3*(-1/(b^11*c))^(1/4) + sqrt(x)) + 4*(7*c*x^2 + 11*b)*sqrt(x))/(b^2*c^2*x^4 + 2*b^3*c*x^2 + b^4)","A",0
346,1,263,0,3.191850," ","integrate(x^(9/2)/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","\frac{180 \, {\left(b^{3} c^{2} x^{5} + 2 \, b^{4} c x^{3} + b^{5} x\right)} \left(-\frac{c}{b^{13}}\right)^{\frac{1}{4}} \arctan\left(-\frac{91125 \, b^{3} c \sqrt{x} \left(-\frac{c}{b^{13}}\right)^{\frac{1}{4}} - \sqrt{-8303765625 \, b^{7} c \sqrt{-\frac{c}{b^{13}}} + 8303765625 \, c^{2} x} b^{3} \left(-\frac{c}{b^{13}}\right)^{\frac{1}{4}}}{91125 \, c}\right) - 45 \, {\left(b^{3} c^{2} x^{5} + 2 \, b^{4} c x^{3} + b^{5} x\right)} \left(-\frac{c}{b^{13}}\right)^{\frac{1}{4}} \log\left(91125 \, b^{10} \left(-\frac{c}{b^{13}}\right)^{\frac{3}{4}} + 91125 \, c \sqrt{x}\right) + 45 \, {\left(b^{3} c^{2} x^{5} + 2 \, b^{4} c x^{3} + b^{5} x\right)} \left(-\frac{c}{b^{13}}\right)^{\frac{1}{4}} \log\left(-91125 \, b^{10} \left(-\frac{c}{b^{13}}\right)^{\frac{3}{4}} + 91125 \, c \sqrt{x}\right) - 4 \, {\left(45 \, c^{2} x^{4} + 81 \, b c x^{2} + 32 \, b^{2}\right)} \sqrt{x}}{64 \, {\left(b^{3} c^{2} x^{5} + 2 \, b^{4} c x^{3} + b^{5} x\right)}}"," ",0,"1/64*(180*(b^3*c^2*x^5 + 2*b^4*c*x^3 + b^5*x)*(-c/b^13)^(1/4)*arctan(-1/91125*(91125*b^3*c*sqrt(x)*(-c/b^13)^(1/4) - sqrt(-8303765625*b^7*c*sqrt(-c/b^13) + 8303765625*c^2*x)*b^3*(-c/b^13)^(1/4))/c) - 45*(b^3*c^2*x^5 + 2*b^4*c*x^3 + b^5*x)*(-c/b^13)^(1/4)*log(91125*b^10*(-c/b^13)^(3/4) + 91125*c*sqrt(x)) + 45*(b^3*c^2*x^5 + 2*b^4*c*x^3 + b^5*x)*(-c/b^13)^(1/4)*log(-91125*b^10*(-c/b^13)^(3/4) + 91125*c*sqrt(x)) - 4*(45*c^2*x^4 + 81*b*c*x^2 + 32*b^2)*sqrt(x))/(b^3*c^2*x^5 + 2*b^4*c*x^3 + b^5*x)","A",0
347,1,283,0,0.555292," ","integrate(x^(7/2)/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","-\frac{924 \, {\left(b^{3} c^{2} x^{6} + 2 \, b^{4} c x^{4} + b^{5} x^{2}\right)} \left(-\frac{c^{3}}{b^{15}}\right)^{\frac{1}{4}} \arctan\left(-\frac{b^{11} c \sqrt{x} \left(-\frac{c^{3}}{b^{15}}\right)^{\frac{3}{4}} - \sqrt{b^{8} \sqrt{-\frac{c^{3}}{b^{15}}} + c^{2} x} b^{11} \left(-\frac{c^{3}}{b^{15}}\right)^{\frac{3}{4}}}{c^{3}}\right) + 231 \, {\left(b^{3} c^{2} x^{6} + 2 \, b^{4} c x^{4} + b^{5} x^{2}\right)} \left(-\frac{c^{3}}{b^{15}}\right)^{\frac{1}{4}} \log\left(77 \, b^{4} \left(-\frac{c^{3}}{b^{15}}\right)^{\frac{1}{4}} + 77 \, c \sqrt{x}\right) - 231 \, {\left(b^{3} c^{2} x^{6} + 2 \, b^{4} c x^{4} + b^{5} x^{2}\right)} \left(-\frac{c^{3}}{b^{15}}\right)^{\frac{1}{4}} \log\left(-77 \, b^{4} \left(-\frac{c^{3}}{b^{15}}\right)^{\frac{1}{4}} + 77 \, c \sqrt{x}\right) + 4 \, {\left(77 \, c^{2} x^{4} + 121 \, b c x^{2} + 32 \, b^{2}\right)} \sqrt{x}}{192 \, {\left(b^{3} c^{2} x^{6} + 2 \, b^{4} c x^{4} + b^{5} x^{2}\right)}}"," ",0,"-1/192*(924*(b^3*c^2*x^6 + 2*b^4*c*x^4 + b^5*x^2)*(-c^3/b^15)^(1/4)*arctan(-(b^11*c*sqrt(x)*(-c^3/b^15)^(3/4) - sqrt(b^8*sqrt(-c^3/b^15) + c^2*x)*b^11*(-c^3/b^15)^(3/4))/c^3) + 231*(b^3*c^2*x^6 + 2*b^4*c*x^4 + b^5*x^2)*(-c^3/b^15)^(1/4)*log(77*b^4*(-c^3/b^15)^(1/4) + 77*c*sqrt(x)) - 231*(b^3*c^2*x^6 + 2*b^4*c*x^4 + b^5*x^2)*(-c^3/b^15)^(1/4)*log(-77*b^4*(-c^3/b^15)^(1/4) + 77*c*sqrt(x)) + 4*(77*c^2*x^4 + 121*b*c*x^2 + 32*b^2)*sqrt(x))/(b^3*c^2*x^6 + 2*b^4*c*x^4 + b^5*x^2)","A",0
348,1,306,0,0.962475," ","integrate(x^(5/2)/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","-\frac{2340 \, {\left(b^{4} c^{2} x^{7} + 2 \, b^{5} c x^{5} + b^{6} x^{3}\right)} \left(-\frac{c^{5}}{b^{17}}\right)^{\frac{1}{4}} \arctan\left(-\frac{1601613 \, b^{4} c^{4} \sqrt{x} \left(-\frac{c^{5}}{b^{17}}\right)^{\frac{1}{4}} - \sqrt{-2565164201769 \, b^{9} c^{5} \sqrt{-\frac{c^{5}}{b^{17}}} + 2565164201769 \, c^{8} x} b^{4} \left(-\frac{c^{5}}{b^{17}}\right)^{\frac{1}{4}}}{1601613 \, c^{5}}\right) - 585 \, {\left(b^{4} c^{2} x^{7} + 2 \, b^{5} c x^{5} + b^{6} x^{3}\right)} \left(-\frac{c^{5}}{b^{17}}\right)^{\frac{1}{4}} \log\left(1601613 \, b^{13} \left(-\frac{c^{5}}{b^{17}}\right)^{\frac{3}{4}} + 1601613 \, c^{4} \sqrt{x}\right) + 585 \, {\left(b^{4} c^{2} x^{7} + 2 \, b^{5} c x^{5} + b^{6} x^{3}\right)} \left(-\frac{c^{5}}{b^{17}}\right)^{\frac{1}{4}} \log\left(-1601613 \, b^{13} \left(-\frac{c^{5}}{b^{17}}\right)^{\frac{3}{4}} + 1601613 \, c^{4} \sqrt{x}\right) - 4 \, {\left(585 \, c^{3} x^{6} + 1053 \, b c^{2} x^{4} + 416 \, b^{2} c x^{2} - 32 \, b^{3}\right)} \sqrt{x}}{320 \, {\left(b^{4} c^{2} x^{7} + 2 \, b^{5} c x^{5} + b^{6} x^{3}\right)}}"," ",0,"-1/320*(2340*(b^4*c^2*x^7 + 2*b^5*c*x^5 + b^6*x^3)*(-c^5/b^17)^(1/4)*arctan(-1/1601613*(1601613*b^4*c^4*sqrt(x)*(-c^5/b^17)^(1/4) - sqrt(-2565164201769*b^9*c^5*sqrt(-c^5/b^17) + 2565164201769*c^8*x)*b^4*(-c^5/b^17)^(1/4))/c^5) - 585*(b^4*c^2*x^7 + 2*b^5*c*x^5 + b^6*x^3)*(-c^5/b^17)^(1/4)*log(1601613*b^13*(-c^5/b^17)^(3/4) + 1601613*c^4*sqrt(x)) + 585*(b^4*c^2*x^7 + 2*b^5*c*x^5 + b^6*x^3)*(-c^5/b^17)^(1/4)*log(-1601613*b^13*(-c^5/b^17)^(3/4) + 1601613*c^4*sqrt(x)) - 4*(585*c^3*x^6 + 1053*b*c^2*x^4 + 416*b^2*c*x^2 - 32*b^3)*sqrt(x))/(b^4*c^2*x^7 + 2*b^5*c*x^5 + b^6*x^3)","A",0
349,1,300,0,0.603349," ","integrate(x^(3/2)/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","\frac{4620 \, {\left(b^{4} c^{2} x^{8} + 2 \, b^{5} c x^{6} + b^{6} x^{4}\right)} \left(-\frac{c^{7}}{b^{19}}\right)^{\frac{1}{4}} \arctan\left(-\frac{b^{14} c^{2} \sqrt{x} \left(-\frac{c^{7}}{b^{19}}\right)^{\frac{3}{4}} - \sqrt{b^{10} \sqrt{-\frac{c^{7}}{b^{19}}} + c^{4} x} b^{14} \left(-\frac{c^{7}}{b^{19}}\right)^{\frac{3}{4}}}{c^{7}}\right) + 1155 \, {\left(b^{4} c^{2} x^{8} + 2 \, b^{5} c x^{6} + b^{6} x^{4}\right)} \left(-\frac{c^{7}}{b^{19}}\right)^{\frac{1}{4}} \log\left(165 \, b^{5} \left(-\frac{c^{7}}{b^{19}}\right)^{\frac{1}{4}} + 165 \, c^{2} \sqrt{x}\right) - 1155 \, {\left(b^{4} c^{2} x^{8} + 2 \, b^{5} c x^{6} + b^{6} x^{4}\right)} \left(-\frac{c^{7}}{b^{19}}\right)^{\frac{1}{4}} \log\left(-165 \, b^{5} \left(-\frac{c^{7}}{b^{19}}\right)^{\frac{1}{4}} + 165 \, c^{2} \sqrt{x}\right) + 4 \, {\left(385 \, c^{3} x^{6} + 605 \, b c^{2} x^{4} + 160 \, b^{2} c x^{2} - 32 \, b^{3}\right)} \sqrt{x}}{448 \, {\left(b^{4} c^{2} x^{8} + 2 \, b^{5} c x^{6} + b^{6} x^{4}\right)}}"," ",0,"1/448*(4620*(b^4*c^2*x^8 + 2*b^5*c*x^6 + b^6*x^4)*(-c^7/b^19)^(1/4)*arctan(-(b^14*c^2*sqrt(x)*(-c^7/b^19)^(3/4) - sqrt(b^10*sqrt(-c^7/b^19) + c^4*x)*b^14*(-c^7/b^19)^(3/4))/c^7) + 1155*(b^4*c^2*x^8 + 2*b^5*c*x^6 + b^6*x^4)*(-c^7/b^19)^(1/4)*log(165*b^5*(-c^7/b^19)^(1/4) + 165*c^2*sqrt(x)) - 1155*(b^4*c^2*x^8 + 2*b^5*c*x^6 + b^6*x^4)*(-c^7/b^19)^(1/4)*log(-165*b^5*(-c^7/b^19)^(1/4) + 165*c^2*sqrt(x)) + 4*(385*c^3*x^6 + 605*b*c^2*x^4 + 160*b^2*c*x^2 - 32*b^3)*sqrt(x))/(b^4*c^2*x^8 + 2*b^5*c*x^6 + b^6*x^4)","A",0
350,1,317,0,0.874065," ","integrate(x^(1/2)/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","\frac{39780 \, {\left(b^{5} c^{2} x^{9} + 2 \, b^{6} c x^{7} + b^{7} x^{5}\right)} \left(-\frac{c^{9}}{b^{21}}\right)^{\frac{1}{4}} \arctan\left(-\frac{10793861 \, b^{5} c^{7} \sqrt{x} \left(-\frac{c^{9}}{b^{21}}\right)^{\frac{1}{4}} - \sqrt{-116507435287321 \, b^{11} c^{9} \sqrt{-\frac{c^{9}}{b^{21}}} + 116507435287321 \, c^{14} x} b^{5} \left(-\frac{c^{9}}{b^{21}}\right)^{\frac{1}{4}}}{10793861 \, c^{9}}\right) - 9945 \, {\left(b^{5} c^{2} x^{9} + 2 \, b^{6} c x^{7} + b^{7} x^{5}\right)} \left(-\frac{c^{9}}{b^{21}}\right)^{\frac{1}{4}} \log\left(10793861 \, b^{16} \left(-\frac{c^{9}}{b^{21}}\right)^{\frac{3}{4}} + 10793861 \, c^{7} \sqrt{x}\right) + 9945 \, {\left(b^{5} c^{2} x^{9} + 2 \, b^{6} c x^{7} + b^{7} x^{5}\right)} \left(-\frac{c^{9}}{b^{21}}\right)^{\frac{1}{4}} \log\left(-10793861 \, b^{16} \left(-\frac{c^{9}}{b^{21}}\right)^{\frac{3}{4}} + 10793861 \, c^{7} \sqrt{x}\right) - 4 \, {\left(9945 \, c^{4} x^{8} + 17901 \, b c^{3} x^{6} + 7072 \, b^{2} c^{2} x^{4} - 544 \, b^{3} c x^{2} + 160 \, b^{4}\right)} \sqrt{x}}{2880 \, {\left(b^{5} c^{2} x^{9} + 2 \, b^{6} c x^{7} + b^{7} x^{5}\right)}}"," ",0,"1/2880*(39780*(b^5*c^2*x^9 + 2*b^6*c*x^7 + b^7*x^5)*(-c^9/b^21)^(1/4)*arctan(-1/10793861*(10793861*b^5*c^7*sqrt(x)*(-c^9/b^21)^(1/4) - sqrt(-116507435287321*b^11*c^9*sqrt(-c^9/b^21) + 116507435287321*c^14*x)*b^5*(-c^9/b^21)^(1/4))/c^9) - 9945*(b^5*c^2*x^9 + 2*b^6*c*x^7 + b^7*x^5)*(-c^9/b^21)^(1/4)*log(10793861*b^16*(-c^9/b^21)^(3/4) + 10793861*c^7*sqrt(x)) + 9945*(b^5*c^2*x^9 + 2*b^6*c*x^7 + b^7*x^5)*(-c^9/b^21)^(1/4)*log(-10793861*b^16*(-c^9/b^21)^(3/4) + 10793861*c^7*sqrt(x)) - 4*(9945*c^4*x^8 + 17901*b*c^3*x^6 + 7072*b^2*c^2*x^4 - 544*b^3*c*x^2 + 160*b^4)*sqrt(x))/(b^5*c^2*x^9 + 2*b^6*c*x^7 + b^7*x^5)","A",0
351,1,311,0,2.078654," ","integrate(1/(c*x^4+b*x^2)^3/x^(1/2),x, algorithm=""fricas"")","-\frac{87780 \, {\left(b^{5} c^{2} x^{10} + 2 \, b^{6} c x^{8} + b^{7} x^{6}\right)} \left(-\frac{c^{11}}{b^{23}}\right)^{\frac{1}{4}} \arctan\left(-\frac{b^{17} c^{3} \sqrt{x} \left(-\frac{c^{11}}{b^{23}}\right)^{\frac{3}{4}} - \sqrt{b^{12} \sqrt{-\frac{c^{11}}{b^{23}}} + c^{6} x} b^{17} \left(-\frac{c^{11}}{b^{23}}\right)^{\frac{3}{4}}}{c^{11}}\right) + 21945 \, {\left(b^{5} c^{2} x^{10} + 2 \, b^{6} c x^{8} + b^{7} x^{6}\right)} \left(-\frac{c^{11}}{b^{23}}\right)^{\frac{1}{4}} \log\left(285 \, b^{6} \left(-\frac{c^{11}}{b^{23}}\right)^{\frac{1}{4}} + 285 \, c^{3} \sqrt{x}\right) - 21945 \, {\left(b^{5} c^{2} x^{10} + 2 \, b^{6} c x^{8} + b^{7} x^{6}\right)} \left(-\frac{c^{11}}{b^{23}}\right)^{\frac{1}{4}} \log\left(-285 \, b^{6} \left(-\frac{c^{11}}{b^{23}}\right)^{\frac{1}{4}} + 285 \, c^{3} \sqrt{x}\right) + 4 \, {\left(7315 \, c^{4} x^{8} + 11495 \, b c^{3} x^{6} + 3040 \, b^{2} c^{2} x^{4} - 608 \, b^{3} c x^{2} + 224 \, b^{4}\right)} \sqrt{x}}{4928 \, {\left(b^{5} c^{2} x^{10} + 2 \, b^{6} c x^{8} + b^{7} x^{6}\right)}}"," ",0,"-1/4928*(87780*(b^5*c^2*x^10 + 2*b^6*c*x^8 + b^7*x^6)*(-c^11/b^23)^(1/4)*arctan(-(b^17*c^3*sqrt(x)*(-c^11/b^23)^(3/4) - sqrt(b^12*sqrt(-c^11/b^23) + c^6*x)*b^17*(-c^11/b^23)^(3/4))/c^11) + 21945*(b^5*c^2*x^10 + 2*b^6*c*x^8 + b^7*x^6)*(-c^11/b^23)^(1/4)*log(285*b^6*(-c^11/b^23)^(1/4) + 285*c^3*sqrt(x)) - 21945*(b^5*c^2*x^10 + 2*b^6*c*x^8 + b^7*x^6)*(-c^11/b^23)^(1/4)*log(-285*b^6*(-c^11/b^23)^(1/4) + 285*c^3*sqrt(x)) + 4*(7315*c^4*x^8 + 11495*b*c^3*x^6 + 3040*b^2*c^2*x^4 - 608*b^3*c*x^2 + 224*b^4)*sqrt(x))/(b^5*c^2*x^10 + 2*b^6*c*x^8 + b^7*x^6)","A",0
352,0,0,0,0.609186," ","integrate(x^(7/2)*(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{4} + b x^{2}} x^{\frac{7}{2}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*x^(7/2), x)","F",0
353,0,0,0,0.505132," ","integrate(x^(5/2)*(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{4} + b x^{2}} x^{\frac{5}{2}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*x^(5/2), x)","F",0
354,0,0,0,0.807806," ","integrate(x^(3/2)*(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{4} + b x^{2}} x^{\frac{3}{2}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*x^(3/2), x)","F",0
355,0,0,0,0.855601," ","integrate(x^(1/2)*(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{4} + b x^{2}} \sqrt{x}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*sqrt(x), x)","F",0
356,0,0,0,0.874129," ","integrate((c*x^4+b*x^2)^(1/2)/x^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}}}{\sqrt{x}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)/sqrt(x), x)","F",0
357,0,0,0,0.705885," ","integrate((c*x^4+b*x^2)^(1/2)/x^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}}}{x^{\frac{3}{2}}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)/x^(3/2), x)","F",0
358,0,0,0,0.777740," ","integrate((c*x^4+b*x^2)^(1/2)/x^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}}}{x^{\frac{5}{2}}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)/x^(5/2), x)","F",0
359,0,0,0,0.601542," ","integrate((c*x^4+b*x^2)^(1/2)/x^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}}}{x^{\frac{7}{2}}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)/x^(7/2), x)","F",0
360,0,0,0,0.695978," ","integrate((c*x^4+b*x^2)^(1/2)/x^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}}}{x^{\frac{9}{2}}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)/x^(9/2), x)","F",0
361,0,0,0,0.571827," ","integrate((c*x^4+b*x^2)^(1/2)/x^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}}}{x^{\frac{11}{2}}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)/x^(11/2), x)","F",0
362,0,0,0,0.509373," ","integrate((c*x^4+b*x^2)^(1/2)/x^(13/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}}}{x^{\frac{13}{2}}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)/x^(13/2), x)","F",0
363,0,0,0,0.647349," ","integrate((c*x^4+b*x^2)^(1/2)/x^(15/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}}}{x^{\frac{15}{2}}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)/x^(15/2), x)","F",0
364,0,0,0,0.760054," ","integrate(x^(3/2)*(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{5} + b x^{3}\right)} \sqrt{c x^{4} + b x^{2}} \sqrt{x}, x\right)"," ",0,"integral((c*x^5 + b*x^3)*sqrt(c*x^4 + b*x^2)*sqrt(x), x)","F",0
365,0,0,0,0.799577," ","integrate((c*x^4+b*x^2)^(3/2)*x^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}} \sqrt{x}, x\right)"," ",0,"integral((c*x^4 + b*x^2)^(3/2)*sqrt(x), x)","F",0
366,0,0,0,0.799257," ","integrate((c*x^4+b*x^2)^(3/2)/x^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{4} + b x^{2}} {\left(c x^{3} + b x\right)} \sqrt{x}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*(c*x^3 + b*x)*sqrt(x), x)","F",0
367,0,0,0,0.661467," ","integrate((c*x^4+b*x^2)^(3/2)/x^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{4} + b x^{2}} {\left(c x^{2} + b\right)} \sqrt{x}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*(c*x^2 + b)*sqrt(x), x)","F",0
368,0,0,0,2.255676," ","integrate((c*x^4+b*x^2)^(3/2)/x^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} {\left(c x^{2} + b\right)}}{\sqrt{x}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*(c*x^2 + b)/sqrt(x), x)","F",0
369,0,0,0,1.160841," ","integrate((c*x^4+b*x^2)^(3/2)/x^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} {\left(c x^{2} + b\right)}}{x^{\frac{3}{2}}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*(c*x^2 + b)/x^(3/2), x)","F",0
370,0,0,0,1.066608," ","integrate((c*x^4+b*x^2)^(3/2)/x^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} {\left(c x^{2} + b\right)}}{x^{\frac{5}{2}}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*(c*x^2 + b)/x^(5/2), x)","F",0
371,0,0,0,0.821358," ","integrate((c*x^4+b*x^2)^(3/2)/x^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} {\left(c x^{2} + b\right)}}{x^{\frac{7}{2}}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*(c*x^2 + b)/x^(7/2), x)","F",0
372,0,0,0,0.969950," ","integrate((c*x^4+b*x^2)^(3/2)/x^(13/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} {\left(c x^{2} + b\right)}}{x^{\frac{9}{2}}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*(c*x^2 + b)/x^(9/2), x)","F",0
373,0,0,0,0.870457," ","integrate((c*x^4+b*x^2)^(3/2)/x^(15/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} {\left(c x^{2} + b\right)}}{x^{\frac{11}{2}}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*(c*x^2 + b)/x^(11/2), x)","F",0
374,0,0,0,0.646206," ","integrate((c*x^4+b*x^2)^(3/2)/x^(17/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} {\left(c x^{2} + b\right)}}{x^{\frac{13}{2}}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*(c*x^2 + b)/x^(13/2), x)","F",0
375,0,0,0,0.723227," ","integrate((c*x^4+b*x^2)^(3/2)/x^(19/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} {\left(c x^{2} + b\right)}}{x^{\frac{15}{2}}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*(c*x^2 + b)/x^(15/2), x)","F",0
376,0,0,0,0.840624," ","integrate((c*x^4+b*x^2)^(3/2)/x^(21/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} {\left(c x^{2} + b\right)}}{x^{\frac{17}{2}}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*(c*x^2 + b)/x^(17/2), x)","F",0
377,0,0,0,1.937330," ","integrate((c*x^4+b*x^2)^(3/2)/x^(23/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} {\left(c x^{2} + b\right)}}{x^{\frac{19}{2}}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*(c*x^2 + b)/x^(19/2), x)","F",0
378,0,0,0,1.066209," ","integrate(x^(13/2)/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} x^{\frac{9}{2}}}{c x^{2} + b}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*x^(9/2)/(c*x^2 + b), x)","F",0
379,0,0,0,0.672127," ","integrate(x^(11/2)/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} x^{\frac{7}{2}}}{c x^{2} + b}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*x^(7/2)/(c*x^2 + b), x)","F",0
380,0,0,0,0.994926," ","integrate(x^(9/2)/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} x^{\frac{5}{2}}}{c x^{2} + b}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*x^(5/2)/(c*x^2 + b), x)","F",0
381,0,0,0,0.904346," ","integrate(x^(7/2)/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} x^{\frac{3}{2}}}{c x^{2} + b}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*x^(3/2)/(c*x^2 + b), x)","F",0
382,0,0,0,0.828907," ","integrate(x^(5/2)/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{x}}{c x^{2} + b}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*sqrt(x)/(c*x^2 + b), x)","F",0
383,0,0,0,0.891968," ","integrate(x^(3/2)/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{x}}{c x^{3} + b x}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*sqrt(x)/(c*x^3 + b*x), x)","F",0
384,0,0,0,0.860372," ","integrate(x^(1/2)/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x}}{\sqrt{c x^{4} + b x^{2}}}, x\right)"," ",0,"integral(sqrt(x)/sqrt(c*x^4 + b*x^2), x)","F",0
385,0,0,0,0.805194," ","integrate(1/x^(1/2)/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{x}}{c x^{5} + b x^{3}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*sqrt(x)/(c*x^5 + b*x^3), x)","F",0
386,0,0,0,0.618516," ","integrate(1/x^(3/2)/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{x}}{c x^{6} + b x^{4}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*sqrt(x)/(c*x^6 + b*x^4), x)","F",0
387,0,0,0,0.766399," ","integrate(1/x^(5/2)/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{x}}{c x^{7} + b x^{5}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*sqrt(x)/(c*x^7 + b*x^5), x)","F",0
388,0,0,0,0.658250," ","integrate(1/x^(7/2)/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{x}}{c x^{8} + b x^{6}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*sqrt(x)/(c*x^8 + b*x^6), x)","F",0
389,0,0,0,0.972848," ","integrate(1/x^(9/2)/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{x}}{c x^{9} + b x^{7}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*sqrt(x)/(c*x^9 + b*x^7), x)","F",0
390,0,0,0,0.947800," ","integrate(1/x^(11/2)/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{x}}{c x^{10} + b x^{8}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*sqrt(x)/(c*x^10 + b*x^8), x)","F",0
391,0,0,0,0.952154," ","integrate(x^(17/2)/(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} x^{\frac{9}{2}}}{c^{2} x^{4} + 2 \, b c x^{2} + b^{2}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*x^(9/2)/(c^2*x^4 + 2*b*c*x^2 + b^2), x)","F",0
392,0,0,0,0.909806," ","integrate(x^(15/2)/(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} x^{\frac{7}{2}}}{c^{2} x^{4} + 2 \, b c x^{2} + b^{2}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*x^(7/2)/(c^2*x^4 + 2*b*c*x^2 + b^2), x)","F",0
393,0,0,0,0.910149," ","integrate(x^(13/2)/(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} x^{\frac{5}{2}}}{c^{2} x^{4} + 2 \, b c x^{2} + b^{2}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*x^(5/2)/(c^2*x^4 + 2*b*c*x^2 + b^2), x)","F",0
394,0,0,0,0.941337," ","integrate(x^(11/2)/(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} x^{\frac{3}{2}}}{c^{2} x^{4} + 2 \, b c x^{2} + b^{2}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*x^(3/2)/(c^2*x^4 + 2*b*c*x^2 + b^2), x)","F",0
395,0,0,0,0.697674," ","integrate(x^(9/2)/(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{x}}{c^{2} x^{4} + 2 \, b c x^{2} + b^{2}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*sqrt(x)/(c^2*x^4 + 2*b*c*x^2 + b^2), x)","F",0
396,0,0,0,0.999796," ","integrate(x^(7/2)/(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{x}}{c^{2} x^{5} + 2 \, b c x^{3} + b^{2} x}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*sqrt(x)/(c^2*x^5 + 2*b*c*x^3 + b^2*x), x)","F",0
397,0,0,0,0.828254," ","integrate(x^(5/2)/(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{x}}{c^{2} x^{6} + 2 \, b c x^{4} + b^{2} x^{2}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*sqrt(x)/(c^2*x^6 + 2*b*c*x^4 + b^2*x^2), x)","F",0
398,0,0,0,0.684557," ","integrate(x^(3/2)/(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{x}}{c^{2} x^{7} + 2 \, b c x^{5} + b^{2} x^{3}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*sqrt(x)/(c^2*x^7 + 2*b*c*x^5 + b^2*x^3), x)","F",0
399,0,0,0,0.908475," ","integrate(x^(1/2)/(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{x}}{c^{2} x^{8} + 2 \, b c x^{6} + b^{2} x^{4}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*sqrt(x)/(c^2*x^8 + 2*b*c*x^6 + b^2*x^4), x)","F",0
400,0,0,0,0.701303," ","integrate(1/(c*x^4+b*x^2)^(3/2)/x^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{x}}{c^{2} x^{9} + 2 \, b c x^{7} + b^{2} x^{5}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*sqrt(x)/(c^2*x^9 + 2*b*c*x^7 + b^2*x^5), x)","F",0
401,0,0,0,0.947211," ","integrate(1/x^(3/2)/(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{x}}{c^{2} x^{10} + 2 \, b c x^{8} + b^{2} x^{6}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*sqrt(x)/(c^2*x^10 + 2*b*c*x^8 + b^2*x^6), x)","F",0
402,0,0,0,1.037454," ","integrate(1/x^(5/2)/(c*x^4+b*x^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{x}}{c^{2} x^{11} + 2 \, b c x^{9} + b^{2} x^{7}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2)*sqrt(x)/(c^2*x^11 + 2*b*c*x^9 + b^2*x^7), x)","F",0
403,1,161,0,0.660141," ","integrate((c*x)^m*(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","\frac{{\left({\left(c^{3} m^{3} + 27 \, c^{3} m^{2} + 239 \, c^{3} m + 693 \, c^{3}\right)} x^{13} + 3 \, {\left(b c^{2} m^{3} + 29 \, b c^{2} m^{2} + 271 \, b c^{2} m + 819 \, b c^{2}\right)} x^{11} + 3 \, {\left(b^{2} c m^{3} + 31 \, b^{2} c m^{2} + 311 \, b^{2} c m + 1001 \, b^{2} c\right)} x^{9} + {\left(b^{3} m^{3} + 33 \, b^{3} m^{2} + 359 \, b^{3} m + 1287 \, b^{3}\right)} x^{7}\right)} \left(c x\right)^{m}}{m^{4} + 40 \, m^{3} + 590 \, m^{2} + 3800 \, m + 9009}"," ",0,"((c^3*m^3 + 27*c^3*m^2 + 239*c^3*m + 693*c^3)*x^13 + 3*(b*c^2*m^3 + 29*b*c^2*m^2 + 271*b*c^2*m + 819*b*c^2)*x^11 + 3*(b^2*c*m^3 + 31*b^2*c*m^2 + 311*b^2*c*m + 1001*b^2*c)*x^9 + (b^3*m^3 + 33*b^3*m^2 + 359*b^3*m + 1287*b^3)*x^7)*(c*x)^m/(m^4 + 40*m^3 + 590*m^2 + 3800*m + 9009)","B",0
404,1,89,0,0.645855," ","integrate((c*x)^m*(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","\frac{{\left({\left(c^{2} m^{2} + 12 \, c^{2} m + 35 \, c^{2}\right)} x^{9} + 2 \, {\left(b c m^{2} + 14 \, b c m + 45 \, b c\right)} x^{7} + {\left(b^{2} m^{2} + 16 \, b^{2} m + 63 \, b^{2}\right)} x^{5}\right)} \left(c x\right)^{m}}{m^{3} + 21 \, m^{2} + 143 \, m + 315}"," ",0,"((c^2*m^2 + 12*c^2*m + 35*c^2)*x^9 + 2*(b*c*m^2 + 14*b*c*m + 45*b*c)*x^7 + (b^2*m^2 + 16*b^2*m + 63*b^2)*x^5)*(c*x)^m/(m^3 + 21*m^2 + 143*m + 315)","A",0
405,1,39,0,0.803974," ","integrate((c*x)^m*(c*x^4+b*x^2),x, algorithm=""fricas"")","\frac{{\left({\left(c m + 3 \, c\right)} x^{5} + {\left(b m + 5 \, b\right)} x^{3}\right)} \left(c x\right)^{m}}{m^{2} + 8 \, m + 15}"," ",0,"((c*m + 3*c)*x^5 + (b*m + 5*b)*x^3)*(c*x)^m/(m^2 + 8*m + 15)","A",0
406,0,0,0,1.019642," ","integrate((c*x)^m/(c*x^4+b*x^2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(c x\right)^{m}}{c x^{4} + b x^{2}}, x\right)"," ",0,"integral((c*x)^m/(c*x^4 + b*x^2), x)","F",0
407,0,0,0,0.747694," ","integrate((c*x)^m/(c*x^4+b*x^2)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(c x\right)^{m}}{c^{2} x^{8} + 2 \, b c x^{6} + b^{2} x^{4}}, x\right)"," ",0,"integral((c*x)^m/(c^2*x^8 + 2*b*c*x^6 + b^2*x^4), x)","F",0
408,0,0,0,0.826784," ","integrate((c*x)^m/(c*x^4+b*x^2)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(c x\right)^{m}}{c^{3} x^{12} + 3 \, b c^{2} x^{10} + 3 \, b^{2} c x^{8} + b^{3} x^{6}}, x\right)"," ",0,"integral((c*x)^m/(c^3*x^12 + 3*b*c^2*x^10 + 3*b^2*c*x^8 + b^3*x^6), x)","F",0
409,1,24,0,0.681618," ","integrate(x^3*(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""fricas"")","\frac{1}{8} x^{8} b^{2} + \frac{1}{3} x^{6} b a + \frac{1}{4} x^{4} a^{2}"," ",0,"1/8*x^8*b^2 + 1/3*x^6*b*a + 1/4*x^4*a^2","A",0
410,1,24,0,0.474132," ","integrate(x^2*(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""fricas"")","\frac{1}{7} x^{7} b^{2} + \frac{2}{5} x^{5} b a + \frac{1}{3} x^{3} a^{2}"," ",0,"1/7*x^7*b^2 + 2/5*x^5*b*a + 1/3*x^3*a^2","A",0
411,1,24,0,0.795723," ","integrate(x*(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""fricas"")","\frac{1}{6} x^{6} b^{2} + \frac{1}{2} x^{4} b a + \frac{1}{2} x^{2} a^{2}"," ",0,"1/6*x^6*b^2 + 1/2*x^4*b*a + 1/2*x^2*a^2","A",0
412,1,21,0,0.409906," ","integrate(b^2*x^4+2*a*b*x^2+a^2,x, algorithm=""fricas"")","\frac{1}{5} x^{5} b^{2} + \frac{2}{3} x^{3} b a + x a^{2}"," ",0,"1/5*x^5*b^2 + 2/3*x^3*b*a + x*a^2","A",0
413,1,21,0,0.753173," ","integrate((b^2*x^4+2*a*b*x^2+a^2)/x,x, algorithm=""fricas"")","\frac{1}{4} \, b^{2} x^{4} + a b x^{2} + a^{2} \log\left(x\right)"," ",0,"1/4*b^2*x^4 + a*b*x^2 + a^2*log(x)","A",0
414,1,25,0,0.836871," ","integrate((b^2*x^4+2*a*b*x^2+a^2)/x^2,x, algorithm=""fricas"")","\frac{b^{2} x^{4} + 6 \, a b x^{2} - 3 \, a^{2}}{3 \, x}"," ",0,"1/3*(b^2*x^4 + 6*a*b*x^2 - 3*a^2)/x","A",0
415,1,27,0,0.680220," ","integrate((b^2*x^4+2*a*b*x^2+a^2)/x^3,x, algorithm=""fricas"")","\frac{b^{2} x^{4} + 4 \, a b x^{2} \log\left(x\right) - a^{2}}{2 \, x^{2}}"," ",0,"1/2*(b^2*x^4 + 4*a*b*x^2*log(x) - a^2)/x^2","A",0
416,1,26,0,0.808412," ","integrate((b^2*x^4+2*a*b*x^2+a^2)/x^4,x, algorithm=""fricas"")","\frac{3 \, b^{2} x^{4} - 6 \, a b x^{2} - a^{2}}{3 \, x^{3}}"," ",0,"1/3*(3*b^2*x^4 - 6*a*b*x^2 - a^2)/x^3","A",0
417,1,28,0,0.853003," ","integrate((b^2*x^4+2*a*b*x^2+a^2)/x^5,x, algorithm=""fricas"")","\frac{4 \, b^{2} x^{4} \log\left(x\right) - 4 \, a b x^{2} - a^{2}}{4 \, x^{4}}"," ",0,"1/4*(4*b^2*x^4*log(x) - 4*a*b*x^2 - a^2)/x^4","A",0
418,1,26,0,1.090381," ","integrate((b^2*x^4+2*a*b*x^2+a^2)/x^6,x, algorithm=""fricas"")","-\frac{15 \, b^{2} x^{4} + 10 \, a b x^{2} + 3 \, a^{2}}{15 \, x^{5}}"," ",0,"-1/15*(15*b^2*x^4 + 10*a*b*x^2 + 3*a^2)/x^5","A",0
419,1,24,0,0.769033," ","integrate((b^2*x^4+2*a*b*x^2+a^2)/x^7,x, algorithm=""fricas"")","-\frac{3 \, b^{2} x^{4} + 3 \, a b x^{2} + a^{2}}{6 \, x^{6}}"," ",0,"-1/6*(3*b^2*x^4 + 3*a*b*x^2 + a^2)/x^6","A",0
420,1,26,0,0.698739," ","integrate((b^2*x^4+2*a*b*x^2+a^2)/x^8,x, algorithm=""fricas"")","-\frac{35 \, b^{2} x^{4} + 42 \, a b x^{2} + 15 \, a^{2}}{105 \, x^{7}}"," ",0,"-1/105*(35*b^2*x^4 + 42*a*b*x^2 + 15*a^2)/x^7","A",0
421,1,46,0,0.676316," ","integrate(x^6*(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""fricas"")","\frac{1}{15} x^{15} b^{4} + \frac{4}{13} x^{13} b^{3} a + \frac{6}{11} x^{11} b^{2} a^{2} + \frac{4}{9} x^{9} b a^{3} + \frac{1}{7} x^{7} a^{4}"," ",0,"1/15*x^15*b^4 + 4/13*x^13*b^3*a + 6/11*x^11*b^2*a^2 + 4/9*x^9*b*a^3 + 1/7*x^7*a^4","A",0
422,1,46,0,0.866468," ","integrate(x^5*(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""fricas"")","\frac{1}{14} x^{14} b^{4} + \frac{1}{3} x^{12} b^{3} a + \frac{3}{5} x^{10} b^{2} a^{2} + \frac{1}{2} x^{8} b a^{3} + \frac{1}{6} x^{6} a^{4}"," ",0,"1/14*x^14*b^4 + 1/3*x^12*b^3*a + 3/5*x^10*b^2*a^2 + 1/2*x^8*b*a^3 + 1/6*x^6*a^4","A",0
423,1,46,0,0.827038," ","integrate(x^4*(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""fricas"")","\frac{1}{13} x^{13} b^{4} + \frac{4}{11} x^{11} b^{3} a + \frac{2}{3} x^{9} b^{2} a^{2} + \frac{4}{7} x^{7} b a^{3} + \frac{1}{5} x^{5} a^{4}"," ",0,"1/13*x^13*b^4 + 4/11*x^11*b^3*a + 2/3*x^9*b^2*a^2 + 4/7*x^7*b*a^3 + 1/5*x^5*a^4","A",0
424,1,46,0,0.718820," ","integrate(x^3*(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""fricas"")","\frac{1}{12} x^{12} b^{4} + \frac{2}{5} x^{10} b^{3} a + \frac{3}{4} x^{8} b^{2} a^{2} + \frac{2}{3} x^{6} b a^{3} + \frac{1}{4} x^{4} a^{4}"," ",0,"1/12*x^12*b^4 + 2/5*x^10*b^3*a + 3/4*x^8*b^2*a^2 + 2/3*x^6*b*a^3 + 1/4*x^4*a^4","A",0
425,1,46,0,0.429725," ","integrate(x^2*(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""fricas"")","\frac{1}{11} x^{11} b^{4} + \frac{4}{9} x^{9} b^{3} a + \frac{6}{7} x^{7} b^{2} a^{2} + \frac{4}{5} x^{5} b a^{3} + \frac{1}{3} x^{3} a^{4}"," ",0,"1/11*x^11*b^4 + 4/9*x^9*b^3*a + 6/7*x^7*b^2*a^2 + 4/5*x^5*b*a^3 + 1/3*x^3*a^4","A",0
426,1,44,0,0.717586," ","integrate(x*(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""fricas"")","\frac{1}{10} x^{10} b^{4} + \frac{1}{2} x^{8} b^{3} a + x^{6} b^{2} a^{2} + x^{4} b a^{3} + \frac{1}{2} x^{2} a^{4}"," ",0,"1/10*x^10*b^4 + 1/2*x^8*b^3*a + x^6*b^2*a^2 + x^4*b*a^3 + 1/2*x^2*a^4","B",0
427,1,43,0,0.650816," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""fricas"")","\frac{1}{9} x^{9} b^{4} + \frac{4}{7} x^{7} b^{3} a + \frac{6}{5} x^{5} b^{2} a^{2} + \frac{4}{3} x^{3} b a^{3} + x a^{4}"," ",0,"1/9*x^9*b^4 + 4/7*x^7*b^3*a + 6/5*x^5*b^2*a^2 + 4/3*x^3*b*a^3 + x*a^4","A",0
428,1,44,0,0.772327," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/x,x, algorithm=""fricas"")","\frac{1}{8} \, b^{4} x^{8} + \frac{2}{3} \, a b^{3} x^{6} + \frac{3}{2} \, a^{2} b^{2} x^{4} + 2 \, a^{3} b x^{2} + a^{4} \log\left(x\right)"," ",0,"1/8*b^4*x^8 + 2/3*a*b^3*x^6 + 3/2*a^2*b^2*x^4 + 2*a^3*b*x^2 + a^4*log(x)","A",0
429,1,48,0,1.020594," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/x^2,x, algorithm=""fricas"")","\frac{5 \, b^{4} x^{8} + 28 \, a b^{3} x^{6} + 70 \, a^{2} b^{2} x^{4} + 140 \, a^{3} b x^{2} - 35 \, a^{4}}{35 \, x}"," ",0,"1/35*(5*b^4*x^8 + 28*a*b^3*x^6 + 70*a^2*b^2*x^4 + 140*a^3*b*x^2 - 35*a^4)/x","A",0
430,1,49,0,0.752934," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/x^3,x, algorithm=""fricas"")","\frac{b^{4} x^{8} + 6 \, a b^{3} x^{6} + 18 \, a^{2} b^{2} x^{4} + 24 \, a^{3} b x^{2} \log\left(x\right) - 3 \, a^{4}}{6 \, x^{2}}"," ",0,"1/6*(b^4*x^8 + 6*a*b^3*x^6 + 18*a^2*b^2*x^4 + 24*a^3*b*x^2*log(x) - 3*a^4)/x^2","A",0
431,1,48,0,0.843960," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/x^4,x, algorithm=""fricas"")","\frac{3 \, b^{4} x^{8} + 20 \, a b^{3} x^{6} + 90 \, a^{2} b^{2} x^{4} - 60 \, a^{3} b x^{2} - 5 \, a^{4}}{15 \, x^{3}}"," ",0,"1/15*(3*b^4*x^8 + 20*a*b^3*x^6 + 90*a^2*b^2*x^4 - 60*a^3*b*x^2 - 5*a^4)/x^3","A",0
432,1,49,0,0.814854," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/x^5,x, algorithm=""fricas"")","\frac{b^{4} x^{8} + 8 \, a b^{3} x^{6} + 24 \, a^{2} b^{2} x^{4} \log\left(x\right) - 8 \, a^{3} b x^{2} - a^{4}}{4 \, x^{4}}"," ",0,"1/4*(b^4*x^8 + 8*a*b^3*x^6 + 24*a^2*b^2*x^4*log(x) - 8*a^3*b*x^2 - a^4)/x^4","A",0
433,1,48,0,0.853099," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/x^6,x, algorithm=""fricas"")","\frac{5 \, b^{4} x^{8} + 60 \, a b^{3} x^{6} - 90 \, a^{2} b^{2} x^{4} - 20 \, a^{3} b x^{2} - 3 \, a^{4}}{15 \, x^{5}}"," ",0,"1/15*(5*b^4*x^8 + 60*a*b^3*x^6 - 90*a^2*b^2*x^4 - 20*a^3*b*x^2 - 3*a^4)/x^5","A",0
434,1,50,0,0.889089," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/x^7,x, algorithm=""fricas"")","\frac{3 \, b^{4} x^{8} + 24 \, a b^{3} x^{6} \log\left(x\right) - 18 \, a^{2} b^{2} x^{4} - 6 \, a^{3} b x^{2} - a^{4}}{6 \, x^{6}}"," ",0,"1/6*(3*b^4*x^8 + 24*a*b^3*x^6*log(x) - 18*a^2*b^2*x^4 - 6*a^3*b*x^2 - a^4)/x^6","A",0
435,1,48,0,0.710446," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/x^8,x, algorithm=""fricas"")","\frac{35 \, b^{4} x^{8} - 140 \, a b^{3} x^{6} - 70 \, a^{2} b^{2} x^{4} - 28 \, a^{3} b x^{2} - 5 \, a^{4}}{35 \, x^{7}}"," ",0,"1/35*(35*b^4*x^8 - 140*a*b^3*x^6 - 70*a^2*b^2*x^4 - 28*a^3*b*x^2 - 5*a^4)/x^7","A",0
436,1,50,0,0.817862," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/x^9,x, algorithm=""fricas"")","\frac{24 \, b^{4} x^{8} \log\left(x\right) - 48 \, a b^{3} x^{6} - 36 \, a^{2} b^{2} x^{4} - 16 \, a^{3} b x^{2} - 3 \, a^{4}}{24 \, x^{8}}"," ",0,"1/24*(24*b^4*x^8*log(x) - 48*a*b^3*x^6 - 36*a^2*b^2*x^4 - 16*a^3*b*x^2 - 3*a^4)/x^8","A",0
437,1,48,0,0.704534," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/x^10,x, algorithm=""fricas"")","-\frac{315 \, b^{4} x^{8} + 420 \, a b^{3} x^{6} + 378 \, a^{2} b^{2} x^{4} + 180 \, a^{3} b x^{2} + 35 \, a^{4}}{315 \, x^{9}}"," ",0,"-1/315*(315*b^4*x^8 + 420*a*b^3*x^6 + 378*a^2*b^2*x^4 + 180*a^3*b*x^2 + 35*a^4)/x^9","A",0
438,1,46,0,0.755690," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/x^11,x, algorithm=""fricas"")","-\frac{5 \, b^{4} x^{8} + 10 \, a b^{3} x^{6} + 10 \, a^{2} b^{2} x^{4} + 5 \, a^{3} b x^{2} + a^{4}}{10 \, x^{10}}"," ",0,"-1/10*(5*b^4*x^8 + 10*a*b^3*x^6 + 10*a^2*b^2*x^4 + 5*a^3*b*x^2 + a^4)/x^10","B",0
439,1,48,0,0.659969," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/x^12,x, algorithm=""fricas"")","-\frac{1155 \, b^{4} x^{8} + 2772 \, a b^{3} x^{6} + 2970 \, a^{2} b^{2} x^{4} + 1540 \, a^{3} b x^{2} + 315 \, a^{4}}{3465 \, x^{11}}"," ",0,"-1/3465*(1155*b^4*x^8 + 2772*a*b^3*x^6 + 2970*a^2*b^2*x^4 + 1540*a^3*b*x^2 + 315*a^4)/x^11","A",0
440,1,48,0,0.821051," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/x^13,x, algorithm=""fricas"")","-\frac{15 \, b^{4} x^{8} + 40 \, a b^{3} x^{6} + 45 \, a^{2} b^{2} x^{4} + 24 \, a^{3} b x^{2} + 5 \, a^{4}}{60 \, x^{12}}"," ",0,"-1/60*(15*b^4*x^8 + 40*a*b^3*x^6 + 45*a^2*b^2*x^4 + 24*a^3*b*x^2 + 5*a^4)/x^12","A",0
441,1,48,0,0.661559," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/x^14,x, algorithm=""fricas"")","-\frac{3003 \, b^{4} x^{8} + 8580 \, a b^{3} x^{6} + 10010 \, a^{2} b^{2} x^{4} + 5460 \, a^{3} b x^{2} + 1155 \, a^{4}}{15015 \, x^{13}}"," ",0,"-1/15015*(3003*b^4*x^8 + 8580*a*b^3*x^6 + 10010*a^2*b^2*x^4 + 5460*a^3*b*x^2 + 1155*a^4)/x^13","A",0
442,1,48,0,0.594010," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/x^15,x, algorithm=""fricas"")","-\frac{35 \, b^{4} x^{8} + 105 \, a b^{3} x^{6} + 126 \, a^{2} b^{2} x^{4} + 70 \, a^{3} b x^{2} + 15 \, a^{4}}{210 \, x^{14}}"," ",0,"-1/210*(35*b^4*x^8 + 105*a*b^3*x^6 + 126*a^2*b^2*x^4 + 70*a^3*b*x^2 + 15*a^4)/x^14","A",0
443,1,48,0,0.871692," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/x^16,x, algorithm=""fricas"")","-\frac{6435 \, b^{4} x^{8} + 20020 \, a b^{3} x^{6} + 24570 \, a^{2} b^{2} x^{4} + 13860 \, a^{3} b x^{2} + 3003 \, a^{4}}{45045 \, x^{15}}"," ",0,"-1/45045*(6435*b^4*x^8 + 20020*a*b^3*x^6 + 24570*a^2*b^2*x^4 + 13860*a^3*b*x^2 + 3003*a^4)/x^15","A",0
444,1,68,0,0.712758," ","integrate(x^8*(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","\frac{1}{21} x^{21} b^{6} + \frac{6}{19} x^{19} b^{5} a + \frac{15}{17} x^{17} b^{4} a^{2} + \frac{4}{3} x^{15} b^{3} a^{3} + \frac{15}{13} x^{13} b^{2} a^{4} + \frac{6}{11} x^{11} b a^{5} + \frac{1}{9} x^{9} a^{6}"," ",0,"1/21*x^21*b^6 + 6/19*x^19*b^5*a + 15/17*x^17*b^4*a^2 + 4/3*x^15*b^3*a^3 + 15/13*x^13*b^2*a^4 + 6/11*x^11*b*a^5 + 1/9*x^9*a^6","A",0
445,1,68,0,0.654641," ","integrate(x^7*(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","\frac{1}{20} x^{20} b^{6} + \frac{1}{3} x^{18} b^{5} a + \frac{15}{16} x^{16} b^{4} a^{2} + \frac{10}{7} x^{14} b^{3} a^{3} + \frac{5}{4} x^{12} b^{2} a^{4} + \frac{3}{5} x^{10} b a^{5} + \frac{1}{8} x^{8} a^{6}"," ",0,"1/20*x^20*b^6 + 1/3*x^18*b^5*a + 15/16*x^16*b^4*a^2 + 10/7*x^14*b^3*a^3 + 5/4*x^12*b^2*a^4 + 3/5*x^10*b*a^5 + 1/8*x^8*a^6","A",0
446,1,67,0,0.905521," ","integrate(x^6*(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","\frac{1}{19} x^{19} b^{6} + \frac{6}{17} x^{17} b^{5} a + x^{15} b^{4} a^{2} + \frac{20}{13} x^{13} b^{3} a^{3} + \frac{15}{11} x^{11} b^{2} a^{4} + \frac{2}{3} x^{9} b a^{5} + \frac{1}{7} x^{7} a^{6}"," ",0,"1/19*x^19*b^6 + 6/17*x^17*b^5*a + x^15*b^4*a^2 + 20/13*x^13*b^3*a^3 + 15/11*x^11*b^2*a^4 + 2/3*x^9*b*a^5 + 1/7*x^7*a^6","A",0
447,1,68,0,0.585664," ","integrate(x^5*(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","\frac{1}{18} x^{18} b^{6} + \frac{3}{8} x^{16} b^{5} a + \frac{15}{14} x^{14} b^{4} a^{2} + \frac{5}{3} x^{12} b^{3} a^{3} + \frac{3}{2} x^{10} b^{2} a^{4} + \frac{3}{4} x^{8} b a^{5} + \frac{1}{6} x^{6} a^{6}"," ",0,"1/18*x^18*b^6 + 3/8*x^16*b^5*a + 15/14*x^14*b^4*a^2 + 5/3*x^12*b^3*a^3 + 3/2*x^10*b^2*a^4 + 3/4*x^8*b*a^5 + 1/6*x^6*a^6","A",0
448,1,68,0,0.774471," ","integrate(x^4*(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","\frac{1}{17} x^{17} b^{6} + \frac{2}{5} x^{15} b^{5} a + \frac{15}{13} x^{13} b^{4} a^{2} + \frac{20}{11} x^{11} b^{3} a^{3} + \frac{5}{3} x^{9} b^{2} a^{4} + \frac{6}{7} x^{7} b a^{5} + \frac{1}{5} x^{5} a^{6}"," ",0,"1/17*x^17*b^6 + 2/5*x^15*b^5*a + 15/13*x^13*b^4*a^2 + 20/11*x^11*b^3*a^3 + 5/3*x^9*b^2*a^4 + 6/7*x^7*b*a^5 + 1/5*x^5*a^6","A",0
449,1,67,0,0.663853," ","integrate(x^3*(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","\frac{1}{16} x^{16} b^{6} + \frac{3}{7} x^{14} b^{5} a + \frac{5}{4} x^{12} b^{4} a^{2} + 2 x^{10} b^{3} a^{3} + \frac{15}{8} x^{8} b^{2} a^{4} + x^{6} b a^{5} + \frac{1}{4} x^{4} a^{6}"," ",0,"1/16*x^16*b^6 + 3/7*x^14*b^5*a + 5/4*x^12*b^4*a^2 + 2*x^10*b^3*a^3 + 15/8*x^8*b^2*a^4 + x^6*b*a^5 + 1/4*x^4*a^6","B",0
450,1,68,0,0.758215," ","integrate(x^2*(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","\frac{1}{15} x^{15} b^{6} + \frac{6}{13} x^{13} b^{5} a + \frac{15}{11} x^{11} b^{4} a^{2} + \frac{20}{9} x^{9} b^{3} a^{3} + \frac{15}{7} x^{7} b^{2} a^{4} + \frac{6}{5} x^{5} b a^{5} + \frac{1}{3} x^{3} a^{6}"," ",0,"1/15*x^15*b^6 + 6/13*x^13*b^5*a + 15/11*x^11*b^4*a^2 + 20/9*x^9*b^3*a^3 + 15/7*x^7*b^2*a^4 + 6/5*x^5*b*a^5 + 1/3*x^3*a^6","A",0
451,1,68,0,0.692094," ","integrate(x*(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","\frac{1}{14} x^{14} b^{6} + \frac{1}{2} x^{12} b^{5} a + \frac{3}{2} x^{10} b^{4} a^{2} + \frac{5}{2} x^{8} b^{3} a^{3} + \frac{5}{2} x^{6} b^{2} a^{4} + \frac{3}{2} x^{4} b a^{5} + \frac{1}{2} x^{2} a^{6}"," ",0,"1/14*x^14*b^6 + 1/2*x^12*b^5*a + 3/2*x^10*b^4*a^2 + 5/2*x^8*b^3*a^3 + 5/2*x^6*b^2*a^4 + 3/2*x^4*b*a^5 + 1/2*x^2*a^6","B",0
452,1,65,0,0.654628," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","\frac{1}{13} x^{13} b^{6} + \frac{6}{11} x^{11} b^{5} a + \frac{5}{3} x^{9} b^{4} a^{2} + \frac{20}{7} x^{7} b^{3} a^{3} + 3 x^{5} b^{2} a^{4} + 2 x^{3} b a^{5} + x a^{6}"," ",0,"1/13*x^13*b^6 + 6/11*x^11*b^5*a + 5/3*x^9*b^4*a^2 + 20/7*x^7*b^3*a^3 + 3*x^5*b^2*a^4 + 2*x^3*b*a^5 + x*a^6","A",0
453,1,66,0,0.785773," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x,x, algorithm=""fricas"")","\frac{1}{12} \, b^{6} x^{12} + \frac{3}{5} \, a b^{5} x^{10} + \frac{15}{8} \, a^{2} b^{4} x^{8} + \frac{10}{3} \, a^{3} b^{3} x^{6} + \frac{15}{4} \, a^{4} b^{2} x^{4} + 3 \, a^{5} b x^{2} + a^{6} \log\left(x\right)"," ",0,"1/12*b^6*x^12 + 3/5*a*b^5*x^10 + 15/8*a^2*b^4*x^8 + 10/3*a^3*b^3*x^6 + 15/4*a^4*b^2*x^4 + 3*a^5*b*x^2 + a^6*log(x)","A",0
454,1,70,0,0.914448," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^2,x, algorithm=""fricas"")","\frac{21 \, b^{6} x^{12} + 154 \, a b^{5} x^{10} + 495 \, a^{2} b^{4} x^{8} + 924 \, a^{3} b^{3} x^{6} + 1155 \, a^{4} b^{2} x^{4} + 1386 \, a^{5} b x^{2} - 231 \, a^{6}}{231 \, x}"," ",0,"1/231*(21*b^6*x^12 + 154*a*b^5*x^10 + 495*a^2*b^4*x^8 + 924*a^3*b^3*x^6 + 1155*a^4*b^2*x^4 + 1386*a^5*b*x^2 - 231*a^6)/x","A",0
455,1,72,0,0.693278," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^3,x, algorithm=""fricas"")","\frac{2 \, b^{6} x^{12} + 15 \, a b^{5} x^{10} + 50 \, a^{2} b^{4} x^{8} + 100 \, a^{3} b^{3} x^{6} + 150 \, a^{4} b^{2} x^{4} + 120 \, a^{5} b x^{2} \log\left(x\right) - 10 \, a^{6}}{20 \, x^{2}}"," ",0,"1/20*(2*b^6*x^12 + 15*a*b^5*x^10 + 50*a^2*b^4*x^8 + 100*a^3*b^3*x^6 + 150*a^4*b^2*x^4 + 120*a^5*b*x^2*log(x) - 10*a^6)/x^2","A",0
456,1,70,0,0.697118," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^4,x, algorithm=""fricas"")","\frac{7 \, b^{6} x^{12} + 54 \, a b^{5} x^{10} + 189 \, a^{2} b^{4} x^{8} + 420 \, a^{3} b^{3} x^{6} + 945 \, a^{4} b^{2} x^{4} - 378 \, a^{5} b x^{2} - 21 \, a^{6}}{63 \, x^{3}}"," ",0,"1/63*(7*b^6*x^12 + 54*a*b^5*x^10 + 189*a^2*b^4*x^8 + 420*a^3*b^3*x^6 + 945*a^4*b^2*x^4 - 378*a^5*b*x^2 - 21*a^6)/x^3","A",0
457,1,71,0,0.763698," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^5,x, algorithm=""fricas"")","\frac{b^{6} x^{12} + 8 \, a b^{5} x^{10} + 30 \, a^{2} b^{4} x^{8} + 80 \, a^{3} b^{3} x^{6} + 120 \, a^{4} b^{2} x^{4} \log\left(x\right) - 24 \, a^{5} b x^{2} - 2 \, a^{6}}{8 \, x^{4}}"," ",0,"1/8*(b^6*x^12 + 8*a*b^5*x^10 + 30*a^2*b^4*x^8 + 80*a^3*b^3*x^6 + 120*a^4*b^2*x^4*log(x) - 24*a^5*b*x^2 - 2*a^6)/x^4","A",0
458,1,70,0,0.777994," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^6,x, algorithm=""fricas"")","\frac{5 \, b^{6} x^{12} + 42 \, a b^{5} x^{10} + 175 \, a^{2} b^{4} x^{8} + 700 \, a^{3} b^{3} x^{6} - 525 \, a^{4} b^{2} x^{4} - 70 \, a^{5} b x^{2} - 7 \, a^{6}}{35 \, x^{5}}"," ",0,"1/35*(5*b^6*x^12 + 42*a*b^5*x^10 + 175*a^2*b^4*x^8 + 700*a^3*b^3*x^6 - 525*a^4*b^2*x^4 - 70*a^5*b*x^2 - 7*a^6)/x^5","A",0
459,1,71,0,0.752154," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^7,x, algorithm=""fricas"")","\frac{b^{6} x^{12} + 9 \, a b^{5} x^{10} + 45 \, a^{2} b^{4} x^{8} + 120 \, a^{3} b^{3} x^{6} \log\left(x\right) - 45 \, a^{4} b^{2} x^{4} - 9 \, a^{5} b x^{2} - a^{6}}{6 \, x^{6}}"," ",0,"1/6*(b^6*x^12 + 9*a*b^5*x^10 + 45*a^2*b^4*x^8 + 120*a^3*b^3*x^6*log(x) - 45*a^4*b^2*x^4 - 9*a^5*b*x^2 - a^6)/x^6","A",0
460,1,70,0,0.747242," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^8,x, algorithm=""fricas"")","\frac{7 \, b^{6} x^{12} + 70 \, a b^{5} x^{10} + 525 \, a^{2} b^{4} x^{8} - 700 \, a^{3} b^{3} x^{6} - 175 \, a^{4} b^{2} x^{4} - 42 \, a^{5} b x^{2} - 5 \, a^{6}}{35 \, x^{7}}"," ",0,"1/35*(7*b^6*x^12 + 70*a*b^5*x^10 + 525*a^2*b^4*x^8 - 700*a^3*b^3*x^6 - 175*a^4*b^2*x^4 - 42*a^5*b*x^2 - 5*a^6)/x^7","A",0
461,1,72,0,0.777290," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^9,x, algorithm=""fricas"")","\frac{2 \, b^{6} x^{12} + 24 \, a b^{5} x^{10} + 120 \, a^{2} b^{4} x^{8} \log\left(x\right) - 80 \, a^{3} b^{3} x^{6} - 30 \, a^{4} b^{2} x^{4} - 8 \, a^{5} b x^{2} - a^{6}}{8 \, x^{8}}"," ",0,"1/8*(2*b^6*x^12 + 24*a*b^5*x^10 + 120*a^2*b^4*x^8*log(x) - 80*a^3*b^3*x^6 - 30*a^4*b^2*x^4 - 8*a^5*b*x^2 - a^6)/x^8","A",0
462,1,70,0,0.818655," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^10,x, algorithm=""fricas"")","\frac{21 \, b^{6} x^{12} + 378 \, a b^{5} x^{10} - 945 \, a^{2} b^{4} x^{8} - 420 \, a^{3} b^{3} x^{6} - 189 \, a^{4} b^{2} x^{4} - 54 \, a^{5} b x^{2} - 7 \, a^{6}}{63 \, x^{9}}"," ",0,"1/63*(21*b^6*x^12 + 378*a*b^5*x^10 - 945*a^2*b^4*x^8 - 420*a^3*b^3*x^6 - 189*a^4*b^2*x^4 - 54*a^5*b*x^2 - 7*a^6)/x^9","A",0
463,1,72,0,0.530710," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^11,x, algorithm=""fricas"")","\frac{10 \, b^{6} x^{12} + 120 \, a b^{5} x^{10} \log\left(x\right) - 150 \, a^{2} b^{4} x^{8} - 100 \, a^{3} b^{3} x^{6} - 50 \, a^{4} b^{2} x^{4} - 15 \, a^{5} b x^{2} - 2 \, a^{6}}{20 \, x^{10}}"," ",0,"1/20*(10*b^6*x^12 + 120*a*b^5*x^10*log(x) - 150*a^2*b^4*x^8 - 100*a^3*b^3*x^6 - 50*a^4*b^2*x^4 - 15*a^5*b*x^2 - 2*a^6)/x^10","A",0
464,1,70,0,0.629388," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^12,x, algorithm=""fricas"")","\frac{231 \, b^{6} x^{12} - 1386 \, a b^{5} x^{10} - 1155 \, a^{2} b^{4} x^{8} - 924 \, a^{3} b^{3} x^{6} - 495 \, a^{4} b^{2} x^{4} - 154 \, a^{5} b x^{2} - 21 \, a^{6}}{231 \, x^{11}}"," ",0,"1/231*(231*b^6*x^12 - 1386*a*b^5*x^10 - 1155*a^2*b^4*x^8 - 924*a^3*b^3*x^6 - 495*a^4*b^2*x^4 - 154*a^5*b*x^2 - 21*a^6)/x^11","A",0
465,1,72,0,0.771845," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^13,x, algorithm=""fricas"")","\frac{120 \, b^{6} x^{12} \log\left(x\right) - 360 \, a b^{5} x^{10} - 450 \, a^{2} b^{4} x^{8} - 400 \, a^{3} b^{3} x^{6} - 225 \, a^{4} b^{2} x^{4} - 72 \, a^{5} b x^{2} - 10 \, a^{6}}{120 \, x^{12}}"," ",0,"1/120*(120*b^6*x^12*log(x) - 360*a*b^5*x^10 - 450*a^2*b^4*x^8 - 400*a^3*b^3*x^6 - 225*a^4*b^2*x^4 - 72*a^5*b*x^2 - 10*a^6)/x^12","A",0
466,1,70,0,0.799269," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^14,x, algorithm=""fricas"")","-\frac{3003 \, b^{6} x^{12} + 6006 \, a b^{5} x^{10} + 9009 \, a^{2} b^{4} x^{8} + 8580 \, a^{3} b^{3} x^{6} + 5005 \, a^{4} b^{2} x^{4} + 1638 \, a^{5} b x^{2} + 231 \, a^{6}}{3003 \, x^{13}}"," ",0,"-1/3003*(3003*b^6*x^12 + 6006*a*b^5*x^10 + 9009*a^2*b^4*x^8 + 8580*a^3*b^3*x^6 + 5005*a^4*b^2*x^4 + 1638*a^5*b*x^2 + 231*a^6)/x^13","A",0
467,1,68,0,0.806473," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^15,x, algorithm=""fricas"")","-\frac{7 \, b^{6} x^{12} + 21 \, a b^{5} x^{10} + 35 \, a^{2} b^{4} x^{8} + 35 \, a^{3} b^{3} x^{6} + 21 \, a^{4} b^{2} x^{4} + 7 \, a^{5} b x^{2} + a^{6}}{14 \, x^{14}}"," ",0,"-1/14*(7*b^6*x^12 + 21*a*b^5*x^10 + 35*a^2*b^4*x^8 + 35*a^3*b^3*x^6 + 21*a^4*b^2*x^4 + 7*a^5*b*x^2 + a^6)/x^14","B",0
468,1,70,0,1.074801," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^16,x, algorithm=""fricas"")","-\frac{15015 \, b^{6} x^{12} + 54054 \, a b^{5} x^{10} + 96525 \, a^{2} b^{4} x^{8} + 100100 \, a^{3} b^{3} x^{6} + 61425 \, a^{4} b^{2} x^{4} + 20790 \, a^{5} b x^{2} + 3003 \, a^{6}}{45045 \, x^{15}}"," ",0,"-1/45045*(15015*b^6*x^12 + 54054*a*b^5*x^10 + 96525*a^2*b^4*x^8 + 100100*a^3*b^3*x^6 + 61425*a^4*b^2*x^4 + 20790*a^5*b*x^2 + 3003*a^6)/x^15","A",0
469,1,70,0,0.847660," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^17,x, algorithm=""fricas"")","-\frac{28 \, b^{6} x^{12} + 112 \, a b^{5} x^{10} + 210 \, a^{2} b^{4} x^{8} + 224 \, a^{3} b^{3} x^{6} + 140 \, a^{4} b^{2} x^{4} + 48 \, a^{5} b x^{2} + 7 \, a^{6}}{112 \, x^{16}}"," ",0,"-1/112*(28*b^6*x^12 + 112*a*b^5*x^10 + 210*a^2*b^4*x^8 + 224*a^3*b^3*x^6 + 140*a^4*b^2*x^4 + 48*a^5*b*x^2 + 7*a^6)/x^16","A",0
470,1,70,0,0.508728," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^18,x, algorithm=""fricas"")","-\frac{51051 \, b^{6} x^{12} + 218790 \, a b^{5} x^{10} + 425425 \, a^{2} b^{4} x^{8} + 464100 \, a^{3} b^{3} x^{6} + 294525 \, a^{4} b^{2} x^{4} + 102102 \, a^{5} b x^{2} + 15015 \, a^{6}}{255255 \, x^{17}}"," ",0,"-1/255255*(51051*b^6*x^12 + 218790*a*b^5*x^10 + 425425*a^2*b^4*x^8 + 464100*a^3*b^3*x^6 + 294525*a^4*b^2*x^4 + 102102*a^5*b*x^2 + 15015*a^6)/x^17","A",0
471,1,70,0,0.644225," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^19,x, algorithm=""fricas"")","-\frac{84 \, b^{6} x^{12} + 378 \, a b^{5} x^{10} + 756 \, a^{2} b^{4} x^{8} + 840 \, a^{3} b^{3} x^{6} + 540 \, a^{4} b^{2} x^{4} + 189 \, a^{5} b x^{2} + 28 \, a^{6}}{504 \, x^{18}}"," ",0,"-1/504*(84*b^6*x^12 + 378*a*b^5*x^10 + 756*a^2*b^4*x^8 + 840*a^3*b^3*x^6 + 540*a^4*b^2*x^4 + 189*a^5*b*x^2 + 28*a^6)/x^18","A",0
472,1,70,0,0.742494," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^20,x, algorithm=""fricas"")","-\frac{138567 \, b^{6} x^{12} + 646646 \, a b^{5} x^{10} + 1322685 \, a^{2} b^{4} x^{8} + 1492260 \, a^{3} b^{3} x^{6} + 969969 \, a^{4} b^{2} x^{4} + 342342 \, a^{5} b x^{2} + 51051 \, a^{6}}{969969 \, x^{19}}"," ",0,"-1/969969*(138567*b^6*x^12 + 646646*a*b^5*x^10 + 1322685*a^2*b^4*x^8 + 1492260*a^3*b^3*x^6 + 969969*a^4*b^2*x^4 + 342342*a^5*b*x^2 + 51051*a^6)/x^19","A",0
473,1,70,0,0.828880," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^21,x, algorithm=""fricas"")","-\frac{210 \, b^{6} x^{12} + 1008 \, a b^{5} x^{10} + 2100 \, a^{2} b^{4} x^{8} + 2400 \, a^{3} b^{3} x^{6} + 1575 \, a^{4} b^{2} x^{4} + 560 \, a^{5} b x^{2} + 84 \, a^{6}}{1680 \, x^{20}}"," ",0,"-1/1680*(210*b^6*x^12 + 1008*a*b^5*x^10 + 2100*a^2*b^4*x^8 + 2400*a^3*b^3*x^6 + 1575*a^4*b^2*x^4 + 560*a^5*b*x^2 + 84*a^6)/x^20","A",0
474,1,70,0,0.849585," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^22,x, algorithm=""fricas"")","-\frac{323323 \, b^{6} x^{12} + 1587222 \, a b^{5} x^{10} + 3357585 \, a^{2} b^{4} x^{8} + 3879876 \, a^{3} b^{3} x^{6} + 2567565 \, a^{4} b^{2} x^{4} + 918918 \, a^{5} b x^{2} + 138567 \, a^{6}}{2909907 \, x^{21}}"," ",0,"-1/2909907*(323323*b^6*x^12 + 1587222*a*b^5*x^10 + 3357585*a^2*b^4*x^8 + 3879876*a^3*b^3*x^6 + 2567565*a^4*b^2*x^4 + 918918*a^5*b*x^2 + 138567*a^6)/x^21","A",0
475,1,93,0,0.483043," ","integrate(x^11/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""fricas"")","\frac{3 \, b^{5} x^{10} - 5 \, a b^{4} x^{8} + 10 \, a^{2} b^{3} x^{6} - 30 \, a^{3} b^{2} x^{4} - 48 \, a^{4} b x^{2} + 12 \, a^{5} + 60 \, {\left(a^{4} b x^{2} + a^{5}\right)} \log\left(b x^{2} + a\right)}{24 \, {\left(b^{7} x^{2} + a b^{6}\right)}}"," ",0,"1/24*(3*b^5*x^10 - 5*a*b^4*x^8 + 10*a^2*b^3*x^6 - 30*a^3*b^2*x^4 - 48*a^4*b*x^2 + 12*a^5 + 60*(a^4*b*x^2 + a^5)*log(b*x^2 + a))/(b^7*x^2 + a*b^6)","A",0
476,1,81,0,0.593693," ","integrate(x^9/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""fricas"")","\frac{b^{4} x^{8} - 2 \, a b^{3} x^{6} + 6 \, a^{2} b^{2} x^{4} + 9 \, a^{3} b x^{2} - 3 \, a^{4} - 12 \, {\left(a^{3} b x^{2} + a^{4}\right)} \log\left(b x^{2} + a\right)}{6 \, {\left(b^{6} x^{2} + a b^{5}\right)}}"," ",0,"1/6*(b^4*x^8 - 2*a*b^3*x^6 + 6*a^2*b^2*x^4 + 9*a^3*b*x^2 - 3*a^4 - 12*(a^3*b*x^2 + a^4)*log(b*x^2 + a))/(b^6*x^2 + a*b^5)","A",0
477,1,70,0,0.751051," ","integrate(x^7/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""fricas"")","\frac{b^{3} x^{6} - 3 \, a b^{2} x^{4} - 4 \, a^{2} b x^{2} + 2 \, a^{3} + 6 \, {\left(a^{2} b x^{2} + a^{3}\right)} \log\left(b x^{2} + a\right)}{4 \, {\left(b^{5} x^{2} + a b^{4}\right)}}"," ",0,"1/4*(b^3*x^6 - 3*a*b^2*x^4 - 4*a^2*b*x^2 + 2*a^3 + 6*(a^2*b*x^2 + a^3)*log(b*x^2 + a))/(b^5*x^2 + a*b^4)","A",0
478,1,56,0,0.749237," ","integrate(x^5/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""fricas"")","\frac{b^{2} x^{4} + a b x^{2} - a^{2} - 2 \, {\left(a b x^{2} + a^{2}\right)} \log\left(b x^{2} + a\right)}{2 \, {\left(b^{4} x^{2} + a b^{3}\right)}}"," ",0,"1/2*(b^2*x^4 + a*b*x^2 - a^2 - 2*(a*b*x^2 + a^2)*log(b*x^2 + a))/(b^4*x^2 + a*b^3)","A",0
479,1,35,0,0.846776," ","integrate(x^3/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""fricas"")","\frac{{\left(b x^{2} + a\right)} \log\left(b x^{2} + a\right) + a}{2 \, {\left(b^{3} x^{2} + a b^{2}\right)}}"," ",0,"1/2*((b*x^2 + a)*log(b*x^2 + a) + a)/(b^3*x^2 + a*b^2)","A",0
480,1,15,0,0.870141," ","integrate(x/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""fricas"")","-\frac{1}{2 \, {\left(b^{2} x^{2} + a b\right)}}"," ",0,"-1/2/(b^2*x^2 + a*b)","A",0
481,1,47,0,0.909531," ","integrate(1/x/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""fricas"")","-\frac{{\left(b x^{2} + a\right)} \log\left(b x^{2} + a\right) - 2 \, {\left(b x^{2} + a\right)} \log\left(x\right) - a}{2 \, {\left(a^{2} b x^{2} + a^{3}\right)}}"," ",0,"-1/2*((b*x^2 + a)*log(b*x^2 + a) - 2*(b*x^2 + a)*log(x) - a)/(a^2*b*x^2 + a^3)","A",0
482,1,73,0,1.007943," ","integrate(1/x^3/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""fricas"")","-\frac{2 \, a b x^{2} + a^{2} - 2 \, {\left(b^{2} x^{4} + a b x^{2}\right)} \log\left(b x^{2} + a\right) + 4 \, {\left(b^{2} x^{4} + a b x^{2}\right)} \log\left(x\right)}{2 \, {\left(a^{3} b x^{4} + a^{4} x^{2}\right)}}"," ",0,"-1/2*(2*a*b*x^2 + a^2 - 2*(b^2*x^4 + a*b*x^2)*log(b*x^2 + a) + 4*(b^2*x^4 + a*b*x^2)*log(x))/(a^3*b*x^4 + a^4*x^2)","A",0
483,1,90,0,1.203347," ","integrate(1/x^5/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""fricas"")","\frac{6 \, a b^{2} x^{4} + 3 \, a^{2} b x^{2} - a^{3} - 6 \, {\left(b^{3} x^{6} + a b^{2} x^{4}\right)} \log\left(b x^{2} + a\right) + 12 \, {\left(b^{3} x^{6} + a b^{2} x^{4}\right)} \log\left(x\right)}{4 \, {\left(a^{4} b x^{6} + a^{5} x^{4}\right)}}"," ",0,"1/4*(6*a*b^2*x^4 + 3*a^2*b*x^2 - a^3 - 6*(b^3*x^6 + a*b^2*x^4)*log(b*x^2 + a) + 12*(b^3*x^6 + a*b^2*x^4)*log(x))/(a^4*b*x^6 + a^5*x^4)","A",0
484,1,212,0,0.870808," ","integrate(x^10/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""fricas"")","\left[\frac{20 \, b^{4} x^{9} - 36 \, a b^{3} x^{7} + 84 \, a^{2} b^{2} x^{5} - 420 \, a^{3} b x^{3} - 630 \, a^{4} x + 315 \, {\left(a^{3} b x^{2} + a^{4}\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} + 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right)}{140 \, {\left(b^{6} x^{2} + a b^{5}\right)}}, \frac{10 \, b^{4} x^{9} - 18 \, a b^{3} x^{7} + 42 \, a^{2} b^{2} x^{5} - 210 \, a^{3} b x^{3} - 315 \, a^{4} x + 315 \, {\left(a^{3} b x^{2} + a^{4}\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right)}{70 \, {\left(b^{6} x^{2} + a b^{5}\right)}}\right]"," ",0,"[1/140*(20*b^4*x^9 - 36*a*b^3*x^7 + 84*a^2*b^2*x^5 - 420*a^3*b*x^3 - 630*a^4*x + 315*(a^3*b*x^2 + a^4)*sqrt(-a/b)*log((b*x^2 + 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)))/(b^6*x^2 + a*b^5), 1/70*(10*b^4*x^9 - 18*a*b^3*x^7 + 42*a^2*b^2*x^5 - 210*a^3*b*x^3 - 315*a^4*x + 315*(a^3*b*x^2 + a^4)*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a))/(b^6*x^2 + a*b^5)]","A",0
485,1,190,0,0.888726," ","integrate(x^8/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""fricas"")","\left[\frac{12 \, b^{3} x^{7} - 28 \, a b^{2} x^{5} + 140 \, a^{2} b x^{3} + 210 \, a^{3} x + 105 \, {\left(a^{2} b x^{2} + a^{3}\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} - 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right)}{60 \, {\left(b^{5} x^{2} + a b^{4}\right)}}, \frac{6 \, b^{3} x^{7} - 14 \, a b^{2} x^{5} + 70 \, a^{2} b x^{3} + 105 \, a^{3} x - 105 \, {\left(a^{2} b x^{2} + a^{3}\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right)}{30 \, {\left(b^{5} x^{2} + a b^{4}\right)}}\right]"," ",0,"[1/60*(12*b^3*x^7 - 28*a*b^2*x^5 + 140*a^2*b*x^3 + 210*a^3*x + 105*(a^2*b*x^2 + a^3)*sqrt(-a/b)*log((b*x^2 - 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)))/(b^5*x^2 + a*b^4), 1/30*(6*b^3*x^7 - 14*a*b^2*x^5 + 70*a^2*b*x^3 + 105*a^3*x - 105*(a^2*b*x^2 + a^3)*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a))/(b^5*x^2 + a*b^4)]","A",0
486,1,164,0,0.655724," ","integrate(x^6/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""fricas"")","\left[\frac{4 \, b^{2} x^{5} - 20 \, a b x^{3} - 30 \, a^{2} x + 15 \, {\left(a b x^{2} + a^{2}\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} + 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right)}{12 \, {\left(b^{4} x^{2} + a b^{3}\right)}}, \frac{2 \, b^{2} x^{5} - 10 \, a b x^{3} - 15 \, a^{2} x + 15 \, {\left(a b x^{2} + a^{2}\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right)}{6 \, {\left(b^{4} x^{2} + a b^{3}\right)}}\right]"," ",0,"[1/12*(4*b^2*x^5 - 20*a*b*x^3 - 30*a^2*x + 15*(a*b*x^2 + a^2)*sqrt(-a/b)*log((b*x^2 + 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)))/(b^4*x^2 + a*b^3), 1/6*(2*b^2*x^5 - 10*a*b*x^3 - 15*a^2*x + 15*(a*b*x^2 + a^2)*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a))/(b^4*x^2 + a*b^3)]","A",0
487,1,136,0,0.849630," ","integrate(x^4/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""fricas"")","\left[\frac{4 \, b x^{3} + 3 \, {\left(b x^{2} + a\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} - 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right) + 6 \, a x}{4 \, {\left(b^{3} x^{2} + a b^{2}\right)}}, \frac{2 \, b x^{3} - 3 \, {\left(b x^{2} + a\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) + 3 \, a x}{2 \, {\left(b^{3} x^{2} + a b^{2}\right)}}\right]"," ",0,"[1/4*(4*b*x^3 + 3*(b*x^2 + a)*sqrt(-a/b)*log((b*x^2 - 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)) + 6*a*x)/(b^3*x^2 + a*b^2), 1/2*(2*b*x^3 - 3*(b*x^2 + a)*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) + 3*a*x)/(b^3*x^2 + a*b^2)]","A",0
488,1,120,0,0.816124," ","integrate(x^2/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""fricas"")","\left[-\frac{2 \, a b x + {\left(b x^{2} + a\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right)}{4 \, {\left(a b^{3} x^{2} + a^{2} b^{2}\right)}}, -\frac{a b x - {\left(b x^{2} + a\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right)}{2 \, {\left(a b^{3} x^{2} + a^{2} b^{2}\right)}}\right]"," ",0,"[-1/4*(2*a*b*x + (b*x^2 + a)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)))/(a*b^3*x^2 + a^2*b^2), -1/2*(a*b*x - (b*x^2 + a)*sqrt(a*b)*arctan(sqrt(a*b)*x/a))/(a*b^3*x^2 + a^2*b^2)]","A",0
489,1,120,0,0.807723," ","integrate(1/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""fricas"")","\left[\frac{2 \, a b x - {\left(b x^{2} + a\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right)}{4 \, {\left(a^{2} b^{2} x^{2} + a^{3} b\right)}}, \frac{a b x + {\left(b x^{2} + a\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right)}{2 \, {\left(a^{2} b^{2} x^{2} + a^{3} b\right)}}\right]"," ",0,"[1/4*(2*a*b*x - (b*x^2 + a)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)))/(a^2*b^2*x^2 + a^3*b), 1/2*(a*b*x + (b*x^2 + a)*sqrt(a*b)*arctan(sqrt(a*b)*x/a))/(a^2*b^2*x^2 + a^3*b)]","A",0
490,1,136,0,1.872699," ","integrate(1/x^2/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""fricas"")","\left[-\frac{6 \, b x^{2} - 3 \, {\left(b x^{3} + a x\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) + 4 \, a}{4 \, {\left(a^{2} b x^{3} + a^{3} x\right)}}, -\frac{3 \, b x^{2} + 3 \, {\left(b x^{3} + a x\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) + 2 \, a}{2 \, {\left(a^{2} b x^{3} + a^{3} x\right)}}\right]"," ",0,"[-1/4*(6*b*x^2 - 3*(b*x^3 + a*x)*sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) + 4*a)/(a^2*b*x^3 + a^3*x), -1/2*(3*b*x^2 + 3*(b*x^3 + a*x)*sqrt(b/a)*arctan(x*sqrt(b/a)) + 2*a)/(a^2*b*x^3 + a^3*x)]","A",0
491,1,172,0,0.839304," ","integrate(1/x^4/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""fricas"")","\left[\frac{30 \, b^{2} x^{4} + 20 \, a b x^{2} + 15 \, {\left(b^{2} x^{5} + a b x^{3}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} + 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) - 4 \, a^{2}}{12 \, {\left(a^{3} b x^{5} + a^{4} x^{3}\right)}}, \frac{15 \, b^{2} x^{4} + 10 \, a b x^{2} + 15 \, {\left(b^{2} x^{5} + a b x^{3}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) - 2 \, a^{2}}{6 \, {\left(a^{3} b x^{5} + a^{4} x^{3}\right)}}\right]"," ",0,"[1/12*(30*b^2*x^4 + 20*a*b*x^2 + 15*(b^2*x^5 + a*b*x^3)*sqrt(-b/a)*log((b*x^2 + 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) - 4*a^2)/(a^3*b*x^5 + a^4*x^3), 1/6*(15*b^2*x^4 + 10*a*b*x^2 + 15*(b^2*x^5 + a*b*x^3)*sqrt(b/a)*arctan(x*sqrt(b/a)) - 2*a^2)/(a^3*b*x^5 + a^4*x^3)]","A",0
492,1,198,0,0.816866," ","integrate(1/x^6/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""fricas"")","\left[-\frac{210 \, b^{3} x^{6} + 140 \, a b^{2} x^{4} - 28 \, a^{2} b x^{2} + 12 \, a^{3} - 105 \, {\left(b^{3} x^{7} + a b^{2} x^{5}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right)}{60 \, {\left(a^{4} b x^{7} + a^{5} x^{5}\right)}}, -\frac{105 \, b^{3} x^{6} + 70 \, a b^{2} x^{4} - 14 \, a^{2} b x^{2} + 6 \, a^{3} + 105 \, {\left(b^{3} x^{7} + a b^{2} x^{5}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right)}{30 \, {\left(a^{4} b x^{7} + a^{5} x^{5}\right)}}\right]"," ",0,"[-1/60*(210*b^3*x^6 + 140*a*b^2*x^4 - 28*a^2*b*x^2 + 12*a^3 - 105*(b^3*x^7 + a*b^2*x^5)*sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)))/(a^4*b*x^7 + a^5*x^5), -1/30*(105*b^3*x^6 + 70*a*b^2*x^4 - 14*a^2*b*x^2 + 6*a^3 + 105*(b^3*x^7 + a*b^2*x^5)*sqrt(b/a)*arctan(x*sqrt(b/a)))/(a^4*b*x^7 + a^5*x^5)]","A",0
493,1,137,0,0.835888," ","integrate(x^11/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""fricas"")","\frac{3 \, b^{5} x^{10} - 15 \, a b^{4} x^{8} - 63 \, a^{2} b^{3} x^{6} - 9 \, a^{3} b^{2} x^{4} + 81 \, a^{4} b x^{2} + 47 \, a^{5} + 60 \, {\left(a^{2} b^{3} x^{6} + 3 \, a^{3} b^{2} x^{4} + 3 \, a^{4} b x^{2} + a^{5}\right)} \log\left(b x^{2} + a\right)}{12 \, {\left(b^{9} x^{6} + 3 \, a b^{8} x^{4} + 3 \, a^{2} b^{7} x^{2} + a^{3} b^{6}\right)}}"," ",0,"1/12*(3*b^5*x^10 - 15*a*b^4*x^8 - 63*a^2*b^3*x^6 - 9*a^3*b^2*x^4 + 81*a^4*b*x^2 + 47*a^5 + 60*(a^2*b^3*x^6 + 3*a^3*b^2*x^4 + 3*a^4*b*x^2 + a^5)*log(b*x^2 + a))/(b^9*x^6 + 3*a*b^8*x^4 + 3*a^2*b^7*x^2 + a^3*b^6)","A",0
494,1,124,0,0.782093," ","integrate(x^9/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""fricas"")","\frac{3 \, b^{4} x^{8} + 9 \, a b^{3} x^{6} - 9 \, a^{2} b^{2} x^{4} - 27 \, a^{3} b x^{2} - 13 \, a^{4} - 12 \, {\left(a b^{3} x^{6} + 3 \, a^{2} b^{2} x^{4} + 3 \, a^{3} b x^{2} + a^{4}\right)} \log\left(b x^{2} + a\right)}{6 \, {\left(b^{8} x^{6} + 3 \, a b^{7} x^{4} + 3 \, a^{2} b^{6} x^{2} + a^{3} b^{5}\right)}}"," ",0,"1/6*(3*b^4*x^8 + 9*a*b^3*x^6 - 9*a^2*b^2*x^4 - 27*a^3*b*x^2 - 13*a^4 - 12*(a*b^3*x^6 + 3*a^2*b^2*x^4 + 3*a^3*b*x^2 + a^4)*log(b*x^2 + a))/(b^8*x^6 + 3*a*b^7*x^4 + 3*a^2*b^6*x^2 + a^3*b^5)","A",0
495,1,102,0,0.733993," ","integrate(x^7/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""fricas"")","\frac{18 \, a b^{2} x^{4} + 27 \, a^{2} b x^{2} + 11 \, a^{3} + 6 \, {\left(b^{3} x^{6} + 3 \, a b^{2} x^{4} + 3 \, a^{2} b x^{2} + a^{3}\right)} \log\left(b x^{2} + a\right)}{12 \, {\left(b^{7} x^{6} + 3 \, a b^{6} x^{4} + 3 \, a^{2} b^{5} x^{2} + a^{3} b^{4}\right)}}"," ",0,"1/12*(18*a*b^2*x^4 + 27*a^2*b*x^2 + 11*a^3 + 6*(b^3*x^6 + 3*a*b^2*x^4 + 3*a^2*b*x^2 + a^3)*log(b*x^2 + a))/(b^7*x^6 + 3*a*b^6*x^4 + 3*a^2*b^5*x^2 + a^3*b^4)","A",0
496,1,58,0,0.486167," ","integrate(x^5/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""fricas"")","-\frac{3 \, b^{2} x^{4} + 3 \, a b x^{2} + a^{2}}{6 \, {\left(b^{6} x^{6} + 3 \, a b^{5} x^{4} + 3 \, a^{2} b^{4} x^{2} + a^{3} b^{3}\right)}}"," ",0,"-1/6*(3*b^2*x^4 + 3*a*b*x^2 + a^2)/(b^6*x^6 + 3*a*b^5*x^4 + 3*a^2*b^4*x^2 + a^3*b^3)","B",0
497,1,47,0,0.536692," ","integrate(x^3/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""fricas"")","-\frac{3 \, b x^{2} + a}{12 \, {\left(b^{5} x^{6} + 3 \, a b^{4} x^{4} + 3 \, a^{2} b^{3} x^{2} + a^{3} b^{2}\right)}}"," ",0,"-1/12*(3*b*x^2 + a)/(b^5*x^6 + 3*a*b^4*x^4 + 3*a^2*b^3*x^2 + a^3*b^2)","A",0
498,1,37,0,0.801348," ","integrate(x/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""fricas"")","-\frac{1}{6 \, {\left(b^{4} x^{6} + 3 \, a b^{3} x^{4} + 3 \, a^{2} b^{2} x^{2} + a^{3} b\right)}}"," ",0,"-1/6/(b^4*x^6 + 3*a*b^3*x^4 + 3*a^2*b^2*x^2 + a^3*b)","B",0
499,1,134,0,2.417275," ","integrate(1/x/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""fricas"")","\frac{6 \, a b^{2} x^{4} + 15 \, a^{2} b x^{2} + 11 \, a^{3} - 6 \, {\left(b^{3} x^{6} + 3 \, a b^{2} x^{4} + 3 \, a^{2} b x^{2} + a^{3}\right)} \log\left(b x^{2} + a\right) + 12 \, {\left(b^{3} x^{6} + 3 \, a b^{2} x^{4} + 3 \, a^{2} b x^{2} + a^{3}\right)} \log\left(x\right)}{12 \, {\left(a^{4} b^{3} x^{6} + 3 \, a^{5} b^{2} x^{4} + 3 \, a^{6} b x^{2} + a^{7}\right)}}"," ",0,"1/12*(6*a*b^2*x^4 + 15*a^2*b*x^2 + 11*a^3 - 6*(b^3*x^6 + 3*a*b^2*x^4 + 3*a^2*b*x^2 + a^3)*log(b*x^2 + a) + 12*(b^3*x^6 + 3*a*b^2*x^4 + 3*a^2*b*x^2 + a^3)*log(x))/(a^4*b^3*x^6 + 3*a^5*b^2*x^4 + 3*a^6*b*x^2 + a^7)","B",0
500,1,163,0,0.922659," ","integrate(1/x^3/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""fricas"")","-\frac{12 \, a b^{3} x^{6} + 30 \, a^{2} b^{2} x^{4} + 22 \, a^{3} b x^{2} + 3 \, a^{4} - 12 \, {\left(b^{4} x^{8} + 3 \, a b^{3} x^{6} + 3 \, a^{2} b^{2} x^{4} + a^{3} b x^{2}\right)} \log\left(b x^{2} + a\right) + 24 \, {\left(b^{4} x^{8} + 3 \, a b^{3} x^{6} + 3 \, a^{2} b^{2} x^{4} + a^{3} b x^{2}\right)} \log\left(x\right)}{6 \, {\left(a^{5} b^{3} x^{8} + 3 \, a^{6} b^{2} x^{6} + 3 \, a^{7} b x^{4} + a^{8} x^{2}\right)}}"," ",0,"-1/6*(12*a*b^3*x^6 + 30*a^2*b^2*x^4 + 22*a^3*b*x^2 + 3*a^4 - 12*(b^4*x^8 + 3*a*b^3*x^6 + 3*a^2*b^2*x^4 + a^3*b*x^2)*log(b*x^2 + a) + 24*(b^4*x^8 + 3*a*b^3*x^6 + 3*a^2*b^2*x^4 + a^3*b*x^2)*log(x))/(a^5*b^3*x^8 + 3*a^6*b^2*x^6 + 3*a^7*b*x^4 + a^8*x^2)","B",0
501,1,178,0,4.940625," ","integrate(1/x^5/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""fricas"")","\frac{60 \, a b^{4} x^{8} + 150 \, a^{2} b^{3} x^{6} + 110 \, a^{3} b^{2} x^{4} + 15 \, a^{4} b x^{2} - 3 \, a^{5} - 60 \, {\left(b^{5} x^{10} + 3 \, a b^{4} x^{8} + 3 \, a^{2} b^{3} x^{6} + a^{3} b^{2} x^{4}\right)} \log\left(b x^{2} + a\right) + 120 \, {\left(b^{5} x^{10} + 3 \, a b^{4} x^{8} + 3 \, a^{2} b^{3} x^{6} + a^{3} b^{2} x^{4}\right)} \log\left(x\right)}{12 \, {\left(a^{6} b^{3} x^{10} + 3 \, a^{7} b^{2} x^{8} + 3 \, a^{8} b x^{6} + a^{9} x^{4}\right)}}"," ",0,"1/12*(60*a*b^4*x^8 + 150*a^2*b^3*x^6 + 110*a^3*b^2*x^4 + 15*a^4*b*x^2 - 3*a^5 - 60*(b^5*x^10 + 3*a*b^4*x^8 + 3*a^2*b^3*x^6 + a^3*b^2*x^4)*log(b*x^2 + a) + 120*(b^5*x^10 + 3*a*b^4*x^8 + 3*a^2*b^3*x^6 + a^3*b^2*x^4)*log(x))/(a^6*b^3*x^10 + 3*a^7*b^2*x^8 + 3*a^8*b*x^6 + a^9*x^4)","A",0
502,1,322,0,0.576522," ","integrate(x^12/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""fricas"")","\left[\frac{96 \, b^{5} x^{11} - 352 \, a b^{4} x^{9} + 3168 \, a^{2} b^{3} x^{7} + 15246 \, a^{3} b^{2} x^{5} + 18480 \, a^{4} b x^{3} + 6930 \, a^{5} x + 3465 \, {\left(a^{2} b^{3} x^{6} + 3 \, a^{3} b^{2} x^{4} + 3 \, a^{4} b x^{2} + a^{5}\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} - 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right)}{480 \, {\left(b^{9} x^{6} + 3 \, a b^{8} x^{4} + 3 \, a^{2} b^{7} x^{2} + a^{3} b^{6}\right)}}, \frac{48 \, b^{5} x^{11} - 176 \, a b^{4} x^{9} + 1584 \, a^{2} b^{3} x^{7} + 7623 \, a^{3} b^{2} x^{5} + 9240 \, a^{4} b x^{3} + 3465 \, a^{5} x - 3465 \, {\left(a^{2} b^{3} x^{6} + 3 \, a^{3} b^{2} x^{4} + 3 \, a^{4} b x^{2} + a^{5}\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right)}{240 \, {\left(b^{9} x^{6} + 3 \, a b^{8} x^{4} + 3 \, a^{2} b^{7} x^{2} + a^{3} b^{6}\right)}}\right]"," ",0,"[1/480*(96*b^5*x^11 - 352*a*b^4*x^9 + 3168*a^2*b^3*x^7 + 15246*a^3*b^2*x^5 + 18480*a^4*b*x^3 + 6930*a^5*x + 3465*(a^2*b^3*x^6 + 3*a^3*b^2*x^4 + 3*a^4*b*x^2 + a^5)*sqrt(-a/b)*log((b*x^2 - 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)))/(b^9*x^6 + 3*a*b^8*x^4 + 3*a^2*b^7*x^2 + a^3*b^6), 1/240*(48*b^5*x^11 - 176*a*b^4*x^9 + 1584*a^2*b^3*x^7 + 7623*a^3*b^2*x^5 + 9240*a^4*b*x^3 + 3465*a^5*x - 3465*(a^2*b^3*x^6 + 3*a^3*b^2*x^4 + 3*a^4*b*x^2 + a^5)*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a))/(b^9*x^6 + 3*a*b^8*x^4 + 3*a^2*b^7*x^2 + a^3*b^6)]","A",0
503,1,296,0,1.177413," ","integrate(x^10/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""fricas"")","\left[\frac{32 \, b^{4} x^{9} - 288 \, a b^{3} x^{7} - 1386 \, a^{2} b^{2} x^{5} - 1680 \, a^{3} b x^{3} - 630 \, a^{4} x + 315 \, {\left(a b^{3} x^{6} + 3 \, a^{2} b^{2} x^{4} + 3 \, a^{3} b x^{2} + a^{4}\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} + 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right)}{96 \, {\left(b^{8} x^{6} + 3 \, a b^{7} x^{4} + 3 \, a^{2} b^{6} x^{2} + a^{3} b^{5}\right)}}, \frac{16 \, b^{4} x^{9} - 144 \, a b^{3} x^{7} - 693 \, a^{2} b^{2} x^{5} - 840 \, a^{3} b x^{3} - 315 \, a^{4} x + 315 \, {\left(a b^{3} x^{6} + 3 \, a^{2} b^{2} x^{4} + 3 \, a^{3} b x^{2} + a^{4}\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right)}{48 \, {\left(b^{8} x^{6} + 3 \, a b^{7} x^{4} + 3 \, a^{2} b^{6} x^{2} + a^{3} b^{5}\right)}}\right]"," ",0,"[1/96*(32*b^4*x^9 - 288*a*b^3*x^7 - 1386*a^2*b^2*x^5 - 1680*a^3*b*x^3 - 630*a^4*x + 315*(a*b^3*x^6 + 3*a^2*b^2*x^4 + 3*a^3*b*x^2 + a^4)*sqrt(-a/b)*log((b*x^2 + 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)))/(b^8*x^6 + 3*a*b^7*x^4 + 3*a^2*b^6*x^2 + a^3*b^5), 1/48*(16*b^4*x^9 - 144*a*b^3*x^7 - 693*a^2*b^2*x^5 - 840*a^3*b*x^3 - 315*a^4*x + 315*(a*b^3*x^6 + 3*a^2*b^2*x^4 + 3*a^3*b*x^2 + a^4)*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a))/(b^8*x^6 + 3*a*b^7*x^4 + 3*a^2*b^6*x^2 + a^3*b^5)]","A",0
504,1,268,0,0.516707," ","integrate(x^8/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""fricas"")","\left[\frac{96 \, b^{3} x^{7} + 462 \, a b^{2} x^{5} + 560 \, a^{2} b x^{3} + 210 \, a^{3} x + 105 \, {\left(b^{3} x^{6} + 3 \, a b^{2} x^{4} + 3 \, a^{2} b x^{2} + a^{3}\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} - 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right)}{96 \, {\left(b^{7} x^{6} + 3 \, a b^{6} x^{4} + 3 \, a^{2} b^{5} x^{2} + a^{3} b^{4}\right)}}, \frac{48 \, b^{3} x^{7} + 231 \, a b^{2} x^{5} + 280 \, a^{2} b x^{3} + 105 \, a^{3} x - 105 \, {\left(b^{3} x^{6} + 3 \, a b^{2} x^{4} + 3 \, a^{2} b x^{2} + a^{3}\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right)}{48 \, {\left(b^{7} x^{6} + 3 \, a b^{6} x^{4} + 3 \, a^{2} b^{5} x^{2} + a^{3} b^{4}\right)}}\right]"," ",0,"[1/96*(96*b^3*x^7 + 462*a*b^2*x^5 + 560*a^2*b*x^3 + 210*a^3*x + 105*(b^3*x^6 + 3*a*b^2*x^4 + 3*a^2*b*x^2 + a^3)*sqrt(-a/b)*log((b*x^2 - 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)))/(b^7*x^6 + 3*a*b^6*x^4 + 3*a^2*b^5*x^2 + a^3*b^4), 1/48*(48*b^3*x^7 + 231*a*b^2*x^5 + 280*a^2*b*x^3 + 105*a^3*x - 105*(b^3*x^6 + 3*a*b^2*x^4 + 3*a^2*b*x^2 + a^3)*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a))/(b^7*x^6 + 3*a*b^6*x^4 + 3*a^2*b^5*x^2 + a^3*b^4)]","A",0
505,1,254,0,0.847234," ","integrate(x^6/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""fricas"")","\left[-\frac{66 \, a b^{3} x^{5} + 80 \, a^{2} b^{2} x^{3} + 30 \, a^{3} b x + 15 \, {\left(b^{3} x^{6} + 3 \, a b^{2} x^{4} + 3 \, a^{2} b x^{2} + a^{3}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right)}{96 \, {\left(a b^{7} x^{6} + 3 \, a^{2} b^{6} x^{4} + 3 \, a^{3} b^{5} x^{2} + a^{4} b^{4}\right)}}, -\frac{33 \, a b^{3} x^{5} + 40 \, a^{2} b^{2} x^{3} + 15 \, a^{3} b x - 15 \, {\left(b^{3} x^{6} + 3 \, a b^{2} x^{4} + 3 \, a^{2} b x^{2} + a^{3}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right)}{48 \, {\left(a b^{7} x^{6} + 3 \, a^{2} b^{6} x^{4} + 3 \, a^{3} b^{5} x^{2} + a^{4} b^{4}\right)}}\right]"," ",0,"[-1/96*(66*a*b^3*x^5 + 80*a^2*b^2*x^3 + 30*a^3*b*x + 15*(b^3*x^6 + 3*a*b^2*x^4 + 3*a^2*b*x^2 + a^3)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)))/(a*b^7*x^6 + 3*a^2*b^6*x^4 + 3*a^3*b^5*x^2 + a^4*b^4), -1/48*(33*a*b^3*x^5 + 40*a^2*b^2*x^3 + 15*a^3*b*x - 15*(b^3*x^6 + 3*a*b^2*x^4 + 3*a^2*b*x^2 + a^3)*sqrt(a*b)*arctan(sqrt(a*b)*x/a))/(a*b^7*x^6 + 3*a^2*b^6*x^4 + 3*a^3*b^5*x^2 + a^4*b^4)]","A",0
506,1,258,0,0.845966," ","integrate(x^4/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""fricas"")","\left[\frac{6 \, a b^{3} x^{5} - 16 \, a^{2} b^{2} x^{3} - 6 \, a^{3} b x - 3 \, {\left(b^{3} x^{6} + 3 \, a b^{2} x^{4} + 3 \, a^{2} b x^{2} + a^{3}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right)}{96 \, {\left(a^{2} b^{6} x^{6} + 3 \, a^{3} b^{5} x^{4} + 3 \, a^{4} b^{4} x^{2} + a^{5} b^{3}\right)}}, \frac{3 \, a b^{3} x^{5} - 8 \, a^{2} b^{2} x^{3} - 3 \, a^{3} b x + 3 \, {\left(b^{3} x^{6} + 3 \, a b^{2} x^{4} + 3 \, a^{2} b x^{2} + a^{3}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right)}{48 \, {\left(a^{2} b^{6} x^{6} + 3 \, a^{3} b^{5} x^{4} + 3 \, a^{4} b^{4} x^{2} + a^{5} b^{3}\right)}}\right]"," ",0,"[1/96*(6*a*b^3*x^5 - 16*a^2*b^2*x^3 - 6*a^3*b*x - 3*(b^3*x^6 + 3*a*b^2*x^4 + 3*a^2*b*x^2 + a^3)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)))/(a^2*b^6*x^6 + 3*a^3*b^5*x^4 + 3*a^4*b^4*x^2 + a^5*b^3), 1/48*(3*a*b^3*x^5 - 8*a^2*b^2*x^3 - 3*a^3*b*x + 3*(b^3*x^6 + 3*a*b^2*x^4 + 3*a^2*b*x^2 + a^3)*sqrt(a*b)*arctan(sqrt(a*b)*x/a))/(a^2*b^6*x^6 + 3*a^3*b^5*x^4 + 3*a^4*b^4*x^2 + a^5*b^3)]","A",0
507,1,258,0,1.136115," ","integrate(x^2/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""fricas"")","\left[\frac{6 \, a b^{3} x^{5} + 16 \, a^{2} b^{2} x^{3} - 6 \, a^{3} b x - 3 \, {\left(b^{3} x^{6} + 3 \, a b^{2} x^{4} + 3 \, a^{2} b x^{2} + a^{3}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right)}{96 \, {\left(a^{3} b^{5} x^{6} + 3 \, a^{4} b^{4} x^{4} + 3 \, a^{5} b^{3} x^{2} + a^{6} b^{2}\right)}}, \frac{3 \, a b^{3} x^{5} + 8 \, a^{2} b^{2} x^{3} - 3 \, a^{3} b x + 3 \, {\left(b^{3} x^{6} + 3 \, a b^{2} x^{4} + 3 \, a^{2} b x^{2} + a^{3}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right)}{48 \, {\left(a^{3} b^{5} x^{6} + 3 \, a^{4} b^{4} x^{4} + 3 \, a^{5} b^{3} x^{2} + a^{6} b^{2}\right)}}\right]"," ",0,"[1/96*(6*a*b^3*x^5 + 16*a^2*b^2*x^3 - 6*a^3*b*x - 3*(b^3*x^6 + 3*a*b^2*x^4 + 3*a^2*b*x^2 + a^3)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)))/(a^3*b^5*x^6 + 3*a^4*b^4*x^4 + 3*a^5*b^3*x^2 + a^6*b^2), 1/48*(3*a*b^3*x^5 + 8*a^2*b^2*x^3 - 3*a^3*b*x + 3*(b^3*x^6 + 3*a*b^2*x^4 + 3*a^2*b*x^2 + a^3)*sqrt(a*b)*arctan(sqrt(a*b)*x/a))/(a^3*b^5*x^6 + 3*a^4*b^4*x^4 + 3*a^5*b^3*x^2 + a^6*b^2)]","A",0
508,1,254,0,0.800712," ","integrate(1/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""fricas"")","\left[\frac{30 \, a b^{3} x^{5} + 80 \, a^{2} b^{2} x^{3} + 66 \, a^{3} b x - 15 \, {\left(b^{3} x^{6} + 3 \, a b^{2} x^{4} + 3 \, a^{2} b x^{2} + a^{3}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right)}{96 \, {\left(a^{4} b^{4} x^{6} + 3 \, a^{5} b^{3} x^{4} + 3 \, a^{6} b^{2} x^{2} + a^{7} b\right)}}, \frac{15 \, a b^{3} x^{5} + 40 \, a^{2} b^{2} x^{3} + 33 \, a^{3} b x + 15 \, {\left(b^{3} x^{6} + 3 \, a b^{2} x^{4} + 3 \, a^{2} b x^{2} + a^{3}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right)}{48 \, {\left(a^{4} b^{4} x^{6} + 3 \, a^{5} b^{3} x^{4} + 3 \, a^{6} b^{2} x^{2} + a^{7} b\right)}}\right]"," ",0,"[1/96*(30*a*b^3*x^5 + 80*a^2*b^2*x^3 + 66*a^3*b*x - 15*(b^3*x^6 + 3*a*b^2*x^4 + 3*a^2*b*x^2 + a^3)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)))/(a^4*b^4*x^6 + 3*a^5*b^3*x^4 + 3*a^6*b^2*x^2 + a^7*b), 1/48*(15*a*b^3*x^5 + 40*a^2*b^2*x^3 + 33*a^3*b*x + 15*(b^3*x^6 + 3*a*b^2*x^4 + 3*a^2*b*x^2 + a^3)*sqrt(a*b)*arctan(sqrt(a*b)*x/a))/(a^4*b^4*x^6 + 3*a^5*b^3*x^4 + 3*a^6*b^2*x^2 + a^7*b)]","A",0
509,1,268,0,0.816496," ","integrate(1/x^2/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""fricas"")","\left[-\frac{210 \, b^{3} x^{6} + 560 \, a b^{2} x^{4} + 462 \, a^{2} b x^{2} + 96 \, a^{3} - 105 \, {\left(b^{3} x^{7} + 3 \, a b^{2} x^{5} + 3 \, a^{2} b x^{3} + a^{3} x\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right)}{96 \, {\left(a^{4} b^{3} x^{7} + 3 \, a^{5} b^{2} x^{5} + 3 \, a^{6} b x^{3} + a^{7} x\right)}}, -\frac{105 \, b^{3} x^{6} + 280 \, a b^{2} x^{4} + 231 \, a^{2} b x^{2} + 48 \, a^{3} + 105 \, {\left(b^{3} x^{7} + 3 \, a b^{2} x^{5} + 3 \, a^{2} b x^{3} + a^{3} x\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right)}{48 \, {\left(a^{4} b^{3} x^{7} + 3 \, a^{5} b^{2} x^{5} + 3 \, a^{6} b x^{3} + a^{7} x\right)}}\right]"," ",0,"[-1/96*(210*b^3*x^6 + 560*a*b^2*x^4 + 462*a^2*b*x^2 + 96*a^3 - 105*(b^3*x^7 + 3*a*b^2*x^5 + 3*a^2*b*x^3 + a^3*x)*sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)))/(a^4*b^3*x^7 + 3*a^5*b^2*x^5 + 3*a^6*b*x^3 + a^7*x), -1/48*(105*b^3*x^6 + 280*a*b^2*x^4 + 231*a^2*b*x^2 + 48*a^3 + 105*(b^3*x^7 + 3*a*b^2*x^5 + 3*a^2*b*x^3 + a^3*x)*sqrt(b/a)*arctan(x*sqrt(b/a)))/(a^4*b^3*x^7 + 3*a^5*b^2*x^5 + 3*a^6*b*x^3 + a^7*x)]","A",0
510,1,304,0,0.903926," ","integrate(1/x^4/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""fricas"")","\left[\frac{630 \, b^{4} x^{8} + 1680 \, a b^{3} x^{6} + 1386 \, a^{2} b^{2} x^{4} + 288 \, a^{3} b x^{2} - 32 \, a^{4} + 315 \, {\left(b^{4} x^{9} + 3 \, a b^{3} x^{7} + 3 \, a^{2} b^{2} x^{5} + a^{3} b x^{3}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} + 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right)}{96 \, {\left(a^{5} b^{3} x^{9} + 3 \, a^{6} b^{2} x^{7} + 3 \, a^{7} b x^{5} + a^{8} x^{3}\right)}}, \frac{315 \, b^{4} x^{8} + 840 \, a b^{3} x^{6} + 693 \, a^{2} b^{2} x^{4} + 144 \, a^{3} b x^{2} - 16 \, a^{4} + 315 \, {\left(b^{4} x^{9} + 3 \, a b^{3} x^{7} + 3 \, a^{2} b^{2} x^{5} + a^{3} b x^{3}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right)}{48 \, {\left(a^{5} b^{3} x^{9} + 3 \, a^{6} b^{2} x^{7} + 3 \, a^{7} b x^{5} + a^{8} x^{3}\right)}}\right]"," ",0,"[1/96*(630*b^4*x^8 + 1680*a*b^3*x^6 + 1386*a^2*b^2*x^4 + 288*a^3*b*x^2 - 32*a^4 + 315*(b^4*x^9 + 3*a*b^3*x^7 + 3*a^2*b^2*x^5 + a^3*b*x^3)*sqrt(-b/a)*log((b*x^2 + 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)))/(a^5*b^3*x^9 + 3*a^6*b^2*x^7 + 3*a^7*b*x^5 + a^8*x^3), 1/48*(315*b^4*x^8 + 840*a*b^3*x^6 + 693*a^2*b^2*x^4 + 144*a^3*b*x^2 - 16*a^4 + 315*(b^4*x^9 + 3*a*b^3*x^7 + 3*a^2*b^2*x^5 + a^3*b*x^3)*sqrt(b/a)*arctan(x*sqrt(b/a)))/(a^5*b^3*x^9 + 3*a^6*b^2*x^7 + 3*a^7*b*x^5 + a^8*x^3)]","A",0
511,1,330,0,0.873813," ","integrate(1/x^6/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""fricas"")","\left[-\frac{6930 \, b^{5} x^{10} + 18480 \, a b^{4} x^{8} + 15246 \, a^{2} b^{3} x^{6} + 3168 \, a^{3} b^{2} x^{4} - 352 \, a^{4} b x^{2} + 96 \, a^{5} - 3465 \, {\left(b^{5} x^{11} + 3 \, a b^{4} x^{9} + 3 \, a^{2} b^{3} x^{7} + a^{3} b^{2} x^{5}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right)}{480 \, {\left(a^{6} b^{3} x^{11} + 3 \, a^{7} b^{2} x^{9} + 3 \, a^{8} b x^{7} + a^{9} x^{5}\right)}}, -\frac{3465 \, b^{5} x^{10} + 9240 \, a b^{4} x^{8} + 7623 \, a^{2} b^{3} x^{6} + 1584 \, a^{3} b^{2} x^{4} - 176 \, a^{4} b x^{2} + 48 \, a^{5} + 3465 \, {\left(b^{5} x^{11} + 3 \, a b^{4} x^{9} + 3 \, a^{2} b^{3} x^{7} + a^{3} b^{2} x^{5}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right)}{240 \, {\left(a^{6} b^{3} x^{11} + 3 \, a^{7} b^{2} x^{9} + 3 \, a^{8} b x^{7} + a^{9} x^{5}\right)}}\right]"," ",0,"[-1/480*(6930*b^5*x^10 + 18480*a*b^4*x^8 + 15246*a^2*b^3*x^6 + 3168*a^3*b^2*x^4 - 352*a^4*b*x^2 + 96*a^5 - 3465*(b^5*x^11 + 3*a*b^4*x^9 + 3*a^2*b^3*x^7 + a^3*b^2*x^5)*sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)))/(a^6*b^3*x^11 + 3*a^7*b^2*x^9 + 3*a^8*b*x^7 + a^9*x^5), -1/240*(3465*b^5*x^10 + 9240*a*b^4*x^8 + 7623*a^2*b^3*x^6 + 1584*a^3*b^2*x^4 - 176*a^4*b*x^2 + 48*a^5 + 3465*(b^5*x^11 + 3*a*b^4*x^9 + 3*a^2*b^3*x^7 + a^3*b^2*x^5)*sqrt(b/a)*arctan(x*sqrt(b/a)))/(a^6*b^3*x^11 + 3*a^7*b^2*x^9 + 3*a^8*b*x^7 + a^9*x^5)]","A",0
512,1,203,0,0.875145," ","integrate(x^15/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","\frac{10 \, b^{7} x^{14} - 70 \, a b^{6} x^{12} - 500 \, a^{2} b^{5} x^{10} - 400 \, a^{3} b^{4} x^{8} + 1300 \, a^{4} b^{3} x^{6} + 2700 \, a^{5} b^{2} x^{4} + 1875 \, a^{6} b x^{2} + 459 \, a^{7} + 420 \, {\left(a^{2} b^{5} x^{10} + 5 \, a^{3} b^{4} x^{8} + 10 \, a^{4} b^{3} x^{6} + 10 \, a^{5} b^{2} x^{4} + 5 \, a^{6} b x^{2} + a^{7}\right)} \log\left(b x^{2} + a\right)}{40 \, {\left(b^{13} x^{10} + 5 \, a b^{12} x^{8} + 10 \, a^{2} b^{11} x^{6} + 10 \, a^{3} b^{10} x^{4} + 5 \, a^{4} b^{9} x^{2} + a^{5} b^{8}\right)}}"," ",0,"1/40*(10*b^7*x^14 - 70*a*b^6*x^12 - 500*a^2*b^5*x^10 - 400*a^3*b^4*x^8 + 1300*a^4*b^3*x^6 + 2700*a^5*b^2*x^4 + 1875*a^6*b*x^2 + 459*a^7 + 420*(a^2*b^5*x^10 + 5*a^3*b^4*x^8 + 10*a^4*b^3*x^6 + 10*a^5*b^2*x^4 + 5*a^6*b*x^2 + a^7)*log(b*x^2 + a))/(b^13*x^10 + 5*a*b^12*x^8 + 10*a^2*b^11*x^6 + 10*a^3*b^10*x^4 + 5*a^4*b^9*x^2 + a^5*b^8)","A",0
513,1,190,0,0.856990," ","integrate(x^13/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","\frac{10 \, b^{6} x^{12} + 50 \, a b^{5} x^{10} - 50 \, a^{2} b^{4} x^{8} - 400 \, a^{3} b^{3} x^{6} - 600 \, a^{4} b^{2} x^{4} - 375 \, a^{5} b x^{2} - 87 \, a^{6} - 60 \, {\left(a b^{5} x^{10} + 5 \, a^{2} b^{4} x^{8} + 10 \, a^{3} b^{3} x^{6} + 10 \, a^{4} b^{2} x^{4} + 5 \, a^{5} b x^{2} + a^{6}\right)} \log\left(b x^{2} + a\right)}{20 \, {\left(b^{12} x^{10} + 5 \, a b^{11} x^{8} + 10 \, a^{2} b^{10} x^{6} + 10 \, a^{3} b^{9} x^{4} + 5 \, a^{4} b^{8} x^{2} + a^{5} b^{7}\right)}}"," ",0,"1/20*(10*b^6*x^12 + 50*a*b^5*x^10 - 50*a^2*b^4*x^8 - 400*a^3*b^3*x^6 - 600*a^4*b^2*x^4 - 375*a^5*b*x^2 - 87*a^6 - 60*(a*b^5*x^10 + 5*a^2*b^4*x^8 + 10*a^3*b^3*x^6 + 10*a^4*b^2*x^4 + 5*a^5*b*x^2 + a^6)*log(b*x^2 + a))/(b^12*x^10 + 5*a*b^11*x^8 + 10*a^2*b^10*x^6 + 10*a^3*b^9*x^4 + 5*a^4*b^8*x^2 + a^5*b^7)","A",0
514,1,168,0,0.770404," ","integrate(x^11/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","\frac{300 \, a b^{4} x^{8} + 900 \, a^{2} b^{3} x^{6} + 1100 \, a^{3} b^{2} x^{4} + 625 \, a^{4} b x^{2} + 137 \, a^{5} + 60 \, {\left(b^{5} x^{10} + 5 \, a b^{4} x^{8} + 10 \, a^{2} b^{3} x^{6} + 10 \, a^{3} b^{2} x^{4} + 5 \, a^{4} b x^{2} + a^{5}\right)} \log\left(b x^{2} + a\right)}{120 \, {\left(b^{11} x^{10} + 5 \, a b^{10} x^{8} + 10 \, a^{2} b^{9} x^{6} + 10 \, a^{3} b^{8} x^{4} + 5 \, a^{4} b^{7} x^{2} + a^{5} b^{6}\right)}}"," ",0,"1/120*(300*a*b^4*x^8 + 900*a^2*b^3*x^6 + 1100*a^3*b^2*x^4 + 625*a^4*b*x^2 + 137*a^5 + 60*(b^5*x^10 + 5*a*b^4*x^8 + 10*a^2*b^3*x^6 + 10*a^3*b^2*x^4 + 5*a^4*b*x^2 + a^5)*log(b*x^2 + a))/(b^11*x^10 + 5*a*b^10*x^8 + 10*a^2*b^9*x^6 + 10*a^3*b^8*x^4 + 5*a^4*b^7*x^2 + a^5*b^6)","A",0
515,1,102,0,0.850518," ","integrate(x^9/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","-\frac{5 \, b^{4} x^{8} + 10 \, a b^{3} x^{6} + 10 \, a^{2} b^{2} x^{4} + 5 \, a^{3} b x^{2} + a^{4}}{10 \, {\left(b^{10} x^{10} + 5 \, a b^{9} x^{8} + 10 \, a^{2} b^{8} x^{6} + 10 \, a^{3} b^{7} x^{4} + 5 \, a^{4} b^{6} x^{2} + a^{5} b^{5}\right)}}"," ",0,"-1/10*(5*b^4*x^8 + 10*a*b^3*x^6 + 10*a^2*b^2*x^4 + 5*a^3*b*x^2 + a^4)/(b^10*x^10 + 5*a*b^9*x^8 + 10*a^2*b^8*x^6 + 10*a^3*b^7*x^4 + 5*a^4*b^6*x^2 + a^5*b^5)","B",0
516,1,91,0,0.692829," ","integrate(x^7/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","-\frac{10 \, b^{3} x^{6} + 10 \, a b^{2} x^{4} + 5 \, a^{2} b x^{2} + a^{3}}{40 \, {\left(b^{9} x^{10} + 5 \, a b^{8} x^{8} + 10 \, a^{2} b^{7} x^{6} + 10 \, a^{3} b^{6} x^{4} + 5 \, a^{4} b^{5} x^{2} + a^{5} b^{4}\right)}}"," ",0,"-1/40*(10*b^3*x^6 + 10*a*b^2*x^4 + 5*a^2*b*x^2 + a^3)/(b^9*x^10 + 5*a*b^8*x^8 + 10*a^2*b^7*x^6 + 10*a^3*b^6*x^4 + 5*a^4*b^5*x^2 + a^5*b^4)","B",0
517,1,80,0,0.810329," ","integrate(x^5/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","-\frac{10 \, b^{2} x^{4} + 5 \, a b x^{2} + a^{2}}{60 \, {\left(b^{8} x^{10} + 5 \, a b^{7} x^{8} + 10 \, a^{2} b^{6} x^{6} + 10 \, a^{3} b^{5} x^{4} + 5 \, a^{4} b^{4} x^{2} + a^{5} b^{3}\right)}}"," ",0,"-1/60*(10*b^2*x^4 + 5*a*b*x^2 + a^2)/(b^8*x^10 + 5*a*b^7*x^8 + 10*a^2*b^6*x^6 + 10*a^3*b^5*x^4 + 5*a^4*b^4*x^2 + a^5*b^3)","A",0
518,1,69,0,0.763051," ","integrate(x^3/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","-\frac{5 \, b x^{2} + a}{40 \, {\left(b^{7} x^{10} + 5 \, a b^{6} x^{8} + 10 \, a^{2} b^{5} x^{6} + 10 \, a^{3} b^{4} x^{4} + 5 \, a^{4} b^{3} x^{2} + a^{5} b^{2}\right)}}"," ",0,"-1/40*(5*b*x^2 + a)/(b^7*x^10 + 5*a*b^6*x^8 + 10*a^2*b^5*x^6 + 10*a^3*b^4*x^4 + 5*a^4*b^3*x^2 + a^5*b^2)","B",0
519,1,59,0,0.770253," ","integrate(x/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","-\frac{1}{10 \, {\left(b^{6} x^{10} + 5 \, a b^{5} x^{8} + 10 \, a^{2} b^{4} x^{6} + 10 \, a^{3} b^{3} x^{4} + 5 \, a^{4} b^{2} x^{2} + a^{5} b\right)}}"," ",0,"-1/10/(b^6*x^10 + 5*a*b^5*x^8 + 10*a^2*b^4*x^6 + 10*a^3*b^3*x^4 + 5*a^4*b^2*x^2 + a^5*b)","B",0
520,1,222,0,0.792653," ","integrate(1/x/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","\frac{60 \, a b^{4} x^{8} + 270 \, a^{2} b^{3} x^{6} + 470 \, a^{3} b^{2} x^{4} + 385 \, a^{4} b x^{2} + 137 \, a^{5} - 60 \, {\left(b^{5} x^{10} + 5 \, a b^{4} x^{8} + 10 \, a^{2} b^{3} x^{6} + 10 \, a^{3} b^{2} x^{4} + 5 \, a^{4} b x^{2} + a^{5}\right)} \log\left(b x^{2} + a\right) + 120 \, {\left(b^{5} x^{10} + 5 \, a b^{4} x^{8} + 10 \, a^{2} b^{3} x^{6} + 10 \, a^{3} b^{2} x^{4} + 5 \, a^{4} b x^{2} + a^{5}\right)} \log\left(x\right)}{120 \, {\left(a^{6} b^{5} x^{10} + 5 \, a^{7} b^{4} x^{8} + 10 \, a^{8} b^{3} x^{6} + 10 \, a^{9} b^{2} x^{4} + 5 \, a^{10} b x^{2} + a^{11}\right)}}"," ",0,"1/120*(60*a*b^4*x^8 + 270*a^2*b^3*x^6 + 470*a^3*b^2*x^4 + 385*a^4*b*x^2 + 137*a^5 - 60*(b^5*x^10 + 5*a*b^4*x^8 + 10*a^2*b^3*x^6 + 10*a^3*b^2*x^4 + 5*a^4*b*x^2 + a^5)*log(b*x^2 + a) + 120*(b^5*x^10 + 5*a*b^4*x^8 + 10*a^2*b^3*x^6 + 10*a^3*b^2*x^4 + 5*a^4*b*x^2 + a^5)*log(x))/(a^6*b^5*x^10 + 5*a^7*b^4*x^8 + 10*a^8*b^3*x^6 + 10*a^9*b^2*x^4 + 5*a^10*b*x^2 + a^11)","B",0
521,1,251,0,0.807668," ","integrate(1/x^3/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","-\frac{60 \, a b^{5} x^{10} + 270 \, a^{2} b^{4} x^{8} + 470 \, a^{3} b^{3} x^{6} + 385 \, a^{4} b^{2} x^{4} + 137 \, a^{5} b x^{2} + 10 \, a^{6} - 60 \, {\left(b^{6} x^{12} + 5 \, a b^{5} x^{10} + 10 \, a^{2} b^{4} x^{8} + 10 \, a^{3} b^{3} x^{6} + 5 \, a^{4} b^{2} x^{4} + a^{5} b x^{2}\right)} \log\left(b x^{2} + a\right) + 120 \, {\left(b^{6} x^{12} + 5 \, a b^{5} x^{10} + 10 \, a^{2} b^{4} x^{8} + 10 \, a^{3} b^{3} x^{6} + 5 \, a^{4} b^{2} x^{4} + a^{5} b x^{2}\right)} \log\left(x\right)}{20 \, {\left(a^{7} b^{5} x^{12} + 5 \, a^{8} b^{4} x^{10} + 10 \, a^{9} b^{3} x^{8} + 10 \, a^{10} b^{2} x^{6} + 5 \, a^{11} b x^{4} + a^{12} x^{2}\right)}}"," ",0,"-1/20*(60*a*b^5*x^10 + 270*a^2*b^4*x^8 + 470*a^3*b^3*x^6 + 385*a^4*b^2*x^4 + 137*a^5*b*x^2 + 10*a^6 - 60*(b^6*x^12 + 5*a*b^5*x^10 + 10*a^2*b^4*x^8 + 10*a^3*b^3*x^6 + 5*a^4*b^2*x^4 + a^5*b*x^2)*log(b*x^2 + a) + 120*(b^6*x^12 + 5*a*b^5*x^10 + 10*a^2*b^4*x^8 + 10*a^3*b^3*x^6 + 5*a^4*b^2*x^4 + a^5*b*x^2)*log(x))/(a^7*b^5*x^12 + 5*a^8*b^4*x^10 + 10*a^9*b^3*x^8 + 10*a^10*b^2*x^6 + 5*a^11*b*x^4 + a^12*x^2)","B",0
522,1,266,0,0.886296," ","integrate(1/x^5/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","\frac{420 \, a b^{6} x^{12} + 1890 \, a^{2} b^{5} x^{10} + 3290 \, a^{3} b^{4} x^{8} + 2695 \, a^{4} b^{3} x^{6} + 959 \, a^{5} b^{2} x^{4} + 70 \, a^{6} b x^{2} - 10 \, a^{7} - 420 \, {\left(b^{7} x^{14} + 5 \, a b^{6} x^{12} + 10 \, a^{2} b^{5} x^{10} + 10 \, a^{3} b^{4} x^{8} + 5 \, a^{4} b^{3} x^{6} + a^{5} b^{2} x^{4}\right)} \log\left(b x^{2} + a\right) + 840 \, {\left(b^{7} x^{14} + 5 \, a b^{6} x^{12} + 10 \, a^{2} b^{5} x^{10} + 10 \, a^{3} b^{4} x^{8} + 5 \, a^{4} b^{3} x^{6} + a^{5} b^{2} x^{4}\right)} \log\left(x\right)}{40 \, {\left(a^{8} b^{5} x^{14} + 5 \, a^{9} b^{4} x^{12} + 10 \, a^{10} b^{3} x^{10} + 10 \, a^{11} b^{2} x^{8} + 5 \, a^{12} b x^{6} + a^{13} x^{4}\right)}}"," ",0,"1/40*(420*a*b^6*x^12 + 1890*a^2*b^5*x^10 + 3290*a^3*b^4*x^8 + 2695*a^4*b^3*x^6 + 959*a^5*b^2*x^4 + 70*a^6*b*x^2 - 10*a^7 - 420*(b^7*x^14 + 5*a*b^6*x^12 + 10*a^2*b^5*x^10 + 10*a^3*b^4*x^8 + 5*a^4*b^3*x^6 + a^5*b^2*x^4)*log(b*x^2 + a) + 840*(b^7*x^14 + 5*a*b^6*x^12 + 10*a^2*b^5*x^10 + 10*a^3*b^4*x^8 + 5*a^4*b^3*x^6 + a^5*b^2*x^4)*log(x))/(a^8*b^5*x^14 + 5*a^9*b^4*x^12 + 10*a^10*b^3*x^10 + 10*a^11*b^2*x^8 + 5*a^12*b*x^6 + a^13*x^4)","B",0
523,1,454,0,0.815581," ","integrate(x^16/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","\left[\frac{512 \, b^{7} x^{15} - 2560 \, a b^{6} x^{13} + 33280 \, a^{2} b^{5} x^{11} + 275990 \, a^{3} b^{4} x^{9} + 677820 \, a^{4} b^{3} x^{7} + 768768 \, a^{5} b^{2} x^{5} + 420420 \, a^{6} b x^{3} + 90090 \, a^{7} x + 45045 \, {\left(a^{2} b^{5} x^{10} + 5 \, a^{3} b^{4} x^{8} + 10 \, a^{4} b^{3} x^{6} + 10 \, a^{5} b^{2} x^{4} + 5 \, a^{6} b x^{2} + a^{7}\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} - 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right)}{2560 \, {\left(b^{13} x^{10} + 5 \, a b^{12} x^{8} + 10 \, a^{2} b^{11} x^{6} + 10 \, a^{3} b^{10} x^{4} + 5 \, a^{4} b^{9} x^{2} + a^{5} b^{8}\right)}}, \frac{256 \, b^{7} x^{15} - 1280 \, a b^{6} x^{13} + 16640 \, a^{2} b^{5} x^{11} + 137995 \, a^{3} b^{4} x^{9} + 338910 \, a^{4} b^{3} x^{7} + 384384 \, a^{5} b^{2} x^{5} + 210210 \, a^{6} b x^{3} + 45045 \, a^{7} x - 45045 \, {\left(a^{2} b^{5} x^{10} + 5 \, a^{3} b^{4} x^{8} + 10 \, a^{4} b^{3} x^{6} + 10 \, a^{5} b^{2} x^{4} + 5 \, a^{6} b x^{2} + a^{7}\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right)}{1280 \, {\left(b^{13} x^{10} + 5 \, a b^{12} x^{8} + 10 \, a^{2} b^{11} x^{6} + 10 \, a^{3} b^{10} x^{4} + 5 \, a^{4} b^{9} x^{2} + a^{5} b^{8}\right)}}\right]"," ",0,"[1/2560*(512*b^7*x^15 - 2560*a*b^6*x^13 + 33280*a^2*b^5*x^11 + 275990*a^3*b^4*x^9 + 677820*a^4*b^3*x^7 + 768768*a^5*b^2*x^5 + 420420*a^6*b*x^3 + 90090*a^7*x + 45045*(a^2*b^5*x^10 + 5*a^3*b^4*x^8 + 10*a^4*b^3*x^6 + 10*a^5*b^2*x^4 + 5*a^6*b*x^2 + a^7)*sqrt(-a/b)*log((b*x^2 - 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)))/(b^13*x^10 + 5*a*b^12*x^8 + 10*a^2*b^11*x^6 + 10*a^3*b^10*x^4 + 5*a^4*b^9*x^2 + a^5*b^8), 1/1280*(256*b^7*x^15 - 1280*a*b^6*x^13 + 16640*a^2*b^5*x^11 + 137995*a^3*b^4*x^9 + 338910*a^4*b^3*x^7 + 384384*a^5*b^2*x^5 + 210210*a^6*b*x^3 + 45045*a^7*x - 45045*(a^2*b^5*x^10 + 5*a^3*b^4*x^8 + 10*a^4*b^3*x^6 + 10*a^5*b^2*x^4 + 5*a^6*b*x^2 + a^7)*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a))/(b^13*x^10 + 5*a*b^12*x^8 + 10*a^2*b^11*x^6 + 10*a^3*b^10*x^4 + 5*a^4*b^9*x^2 + a^5*b^8)]","A",0
524,1,428,0,0.898987," ","integrate(x^14/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","\left[\frac{2560 \, b^{6} x^{13} - 33280 \, a b^{5} x^{11} - 275990 \, a^{2} b^{4} x^{9} - 677820 \, a^{3} b^{3} x^{7} - 768768 \, a^{4} b^{2} x^{5} - 420420 \, a^{5} b x^{3} - 90090 \, a^{6} x + 45045 \, {\left(a b^{5} x^{10} + 5 \, a^{2} b^{4} x^{8} + 10 \, a^{3} b^{3} x^{6} + 10 \, a^{4} b^{2} x^{4} + 5 \, a^{5} b x^{2} + a^{6}\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} + 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right)}{7680 \, {\left(b^{12} x^{10} + 5 \, a b^{11} x^{8} + 10 \, a^{2} b^{10} x^{6} + 10 \, a^{3} b^{9} x^{4} + 5 \, a^{4} b^{8} x^{2} + a^{5} b^{7}\right)}}, \frac{1280 \, b^{6} x^{13} - 16640 \, a b^{5} x^{11} - 137995 \, a^{2} b^{4} x^{9} - 338910 \, a^{3} b^{3} x^{7} - 384384 \, a^{4} b^{2} x^{5} - 210210 \, a^{5} b x^{3} - 45045 \, a^{6} x + 45045 \, {\left(a b^{5} x^{10} + 5 \, a^{2} b^{4} x^{8} + 10 \, a^{3} b^{3} x^{6} + 10 \, a^{4} b^{2} x^{4} + 5 \, a^{5} b x^{2} + a^{6}\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right)}{3840 \, {\left(b^{12} x^{10} + 5 \, a b^{11} x^{8} + 10 \, a^{2} b^{10} x^{6} + 10 \, a^{3} b^{9} x^{4} + 5 \, a^{4} b^{8} x^{2} + a^{5} b^{7}\right)}}\right]"," ",0,"[1/7680*(2560*b^6*x^13 - 33280*a*b^5*x^11 - 275990*a^2*b^4*x^9 - 677820*a^3*b^3*x^7 - 768768*a^4*b^2*x^5 - 420420*a^5*b*x^3 - 90090*a^6*x + 45045*(a*b^5*x^10 + 5*a^2*b^4*x^8 + 10*a^3*b^3*x^6 + 10*a^4*b^2*x^4 + 5*a^5*b*x^2 + a^6)*sqrt(-a/b)*log((b*x^2 + 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)))/(b^12*x^10 + 5*a*b^11*x^8 + 10*a^2*b^10*x^6 + 10*a^3*b^9*x^4 + 5*a^4*b^8*x^2 + a^5*b^7), 1/3840*(1280*b^6*x^13 - 16640*a*b^5*x^11 - 137995*a^2*b^4*x^9 - 338910*a^3*b^3*x^7 - 384384*a^4*b^2*x^5 - 210210*a^5*b*x^3 - 45045*a^6*x + 45045*(a*b^5*x^10 + 5*a^2*b^4*x^8 + 10*a^3*b^3*x^6 + 10*a^4*b^2*x^4 + 5*a^5*b*x^2 + a^6)*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a))/(b^12*x^10 + 5*a*b^11*x^8 + 10*a^2*b^10*x^6 + 10*a^3*b^9*x^4 + 5*a^4*b^8*x^2 + a^5*b^7)]","A",0
525,1,400,0,0.790131," ","integrate(x^12/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","\left[\frac{2560 \, b^{5} x^{11} + 21230 \, a b^{4} x^{9} + 52140 \, a^{2} b^{3} x^{7} + 59136 \, a^{3} b^{2} x^{5} + 32340 \, a^{4} b x^{3} + 6930 \, a^{5} x + 3465 \, {\left(b^{5} x^{10} + 5 \, a b^{4} x^{8} + 10 \, a^{2} b^{3} x^{6} + 10 \, a^{3} b^{2} x^{4} + 5 \, a^{4} b x^{2} + a^{5}\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} - 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right)}{2560 \, {\left(b^{11} x^{10} + 5 \, a b^{10} x^{8} + 10 \, a^{2} b^{9} x^{6} + 10 \, a^{3} b^{8} x^{4} + 5 \, a^{4} b^{7} x^{2} + a^{5} b^{6}\right)}}, \frac{1280 \, b^{5} x^{11} + 10615 \, a b^{4} x^{9} + 26070 \, a^{2} b^{3} x^{7} + 29568 \, a^{3} b^{2} x^{5} + 16170 \, a^{4} b x^{3} + 3465 \, a^{5} x - 3465 \, {\left(b^{5} x^{10} + 5 \, a b^{4} x^{8} + 10 \, a^{2} b^{3} x^{6} + 10 \, a^{3} b^{2} x^{4} + 5 \, a^{4} b x^{2} + a^{5}\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right)}{1280 \, {\left(b^{11} x^{10} + 5 \, a b^{10} x^{8} + 10 \, a^{2} b^{9} x^{6} + 10 \, a^{3} b^{8} x^{4} + 5 \, a^{4} b^{7} x^{2} + a^{5} b^{6}\right)}}\right]"," ",0,"[1/2560*(2560*b^5*x^11 + 21230*a*b^4*x^9 + 52140*a^2*b^3*x^7 + 59136*a^3*b^2*x^5 + 32340*a^4*b*x^3 + 6930*a^5*x + 3465*(b^5*x^10 + 5*a*b^4*x^8 + 10*a^2*b^3*x^6 + 10*a^3*b^2*x^4 + 5*a^4*b*x^2 + a^5)*sqrt(-a/b)*log((b*x^2 - 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)))/(b^11*x^10 + 5*a*b^10*x^8 + 10*a^2*b^9*x^6 + 10*a^3*b^8*x^4 + 5*a^4*b^7*x^2 + a^5*b^6), 1/1280*(1280*b^5*x^11 + 10615*a*b^4*x^9 + 26070*a^2*b^3*x^7 + 29568*a^3*b^2*x^5 + 16170*a^4*b*x^3 + 3465*a^5*x - 3465*(b^5*x^10 + 5*a*b^4*x^8 + 10*a^2*b^3*x^6 + 10*a^3*b^2*x^4 + 5*a^4*b*x^2 + a^5)*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a))/(b^11*x^10 + 5*a*b^10*x^8 + 10*a^2*b^9*x^6 + 10*a^3*b^8*x^4 + 5*a^4*b^7*x^2 + a^5*b^6)]","A",0
526,1,386,0,0.859676," ","integrate(x^10/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","\left[-\frac{1930 \, a b^{5} x^{9} + 4740 \, a^{2} b^{4} x^{7} + 5376 \, a^{3} b^{3} x^{5} + 2940 \, a^{4} b^{2} x^{3} + 630 \, a^{5} b x + 315 \, {\left(b^{5} x^{10} + 5 \, a b^{4} x^{8} + 10 \, a^{2} b^{3} x^{6} + 10 \, a^{3} b^{2} x^{4} + 5 \, a^{4} b x^{2} + a^{5}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right)}{2560 \, {\left(a b^{11} x^{10} + 5 \, a^{2} b^{10} x^{8} + 10 \, a^{3} b^{9} x^{6} + 10 \, a^{4} b^{8} x^{4} + 5 \, a^{5} b^{7} x^{2} + a^{6} b^{6}\right)}}, -\frac{965 \, a b^{5} x^{9} + 2370 \, a^{2} b^{4} x^{7} + 2688 \, a^{3} b^{3} x^{5} + 1470 \, a^{4} b^{2} x^{3} + 315 \, a^{5} b x - 315 \, {\left(b^{5} x^{10} + 5 \, a b^{4} x^{8} + 10 \, a^{2} b^{3} x^{6} + 10 \, a^{3} b^{2} x^{4} + 5 \, a^{4} b x^{2} + a^{5}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right)}{1280 \, {\left(a b^{11} x^{10} + 5 \, a^{2} b^{10} x^{8} + 10 \, a^{3} b^{9} x^{6} + 10 \, a^{4} b^{8} x^{4} + 5 \, a^{5} b^{7} x^{2} + a^{6} b^{6}\right)}}\right]"," ",0,"[-1/2560*(1930*a*b^5*x^9 + 4740*a^2*b^4*x^7 + 5376*a^3*b^3*x^5 + 2940*a^4*b^2*x^3 + 630*a^5*b*x + 315*(b^5*x^10 + 5*a*b^4*x^8 + 10*a^2*b^3*x^6 + 10*a^3*b^2*x^4 + 5*a^4*b*x^2 + a^5)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)))/(a*b^11*x^10 + 5*a^2*b^10*x^8 + 10*a^3*b^9*x^6 + 10*a^4*b^8*x^4 + 5*a^5*b^7*x^2 + a^6*b^6), -1/1280*(965*a*b^5*x^9 + 2370*a^2*b^4*x^7 + 2688*a^3*b^3*x^5 + 1470*a^4*b^2*x^3 + 315*a^5*b*x - 315*(b^5*x^10 + 5*a*b^4*x^8 + 10*a^2*b^3*x^6 + 10*a^3*b^2*x^4 + 5*a^4*b*x^2 + a^5)*sqrt(a*b)*arctan(sqrt(a*b)*x/a))/(a*b^11*x^10 + 5*a^2*b^10*x^8 + 10*a^3*b^9*x^6 + 10*a^4*b^8*x^4 + 5*a^5*b^7*x^2 + a^6*b^6)]","A",0
527,1,390,0,0.851129," ","integrate(x^8/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","\left[\frac{210 \, a b^{5} x^{9} - 1580 \, a^{2} b^{4} x^{7} - 1792 \, a^{3} b^{3} x^{5} - 980 \, a^{4} b^{2} x^{3} - 210 \, a^{5} b x - 105 \, {\left(b^{5} x^{10} + 5 \, a b^{4} x^{8} + 10 \, a^{2} b^{3} x^{6} + 10 \, a^{3} b^{2} x^{4} + 5 \, a^{4} b x^{2} + a^{5}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right)}{7680 \, {\left(a^{2} b^{10} x^{10} + 5 \, a^{3} b^{9} x^{8} + 10 \, a^{4} b^{8} x^{6} + 10 \, a^{5} b^{7} x^{4} + 5 \, a^{6} b^{6} x^{2} + a^{7} b^{5}\right)}}, \frac{105 \, a b^{5} x^{9} - 790 \, a^{2} b^{4} x^{7} - 896 \, a^{3} b^{3} x^{5} - 490 \, a^{4} b^{2} x^{3} - 105 \, a^{5} b x + 105 \, {\left(b^{5} x^{10} + 5 \, a b^{4} x^{8} + 10 \, a^{2} b^{3} x^{6} + 10 \, a^{3} b^{2} x^{4} + 5 \, a^{4} b x^{2} + a^{5}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right)}{3840 \, {\left(a^{2} b^{10} x^{10} + 5 \, a^{3} b^{9} x^{8} + 10 \, a^{4} b^{8} x^{6} + 10 \, a^{5} b^{7} x^{4} + 5 \, a^{6} b^{6} x^{2} + a^{7} b^{5}\right)}}\right]"," ",0,"[1/7680*(210*a*b^5*x^9 - 1580*a^2*b^4*x^7 - 1792*a^3*b^3*x^5 - 980*a^4*b^2*x^3 - 210*a^5*b*x - 105*(b^5*x^10 + 5*a*b^4*x^8 + 10*a^2*b^3*x^6 + 10*a^3*b^2*x^4 + 5*a^4*b*x^2 + a^5)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)))/(a^2*b^10*x^10 + 5*a^3*b^9*x^8 + 10*a^4*b^8*x^6 + 10*a^5*b^7*x^4 + 5*a^6*b^6*x^2 + a^7*b^5), 1/3840*(105*a*b^5*x^9 - 790*a^2*b^4*x^7 - 896*a^3*b^3*x^5 - 490*a^4*b^2*x^3 - 105*a^5*b*x + 105*(b^5*x^10 + 5*a*b^4*x^8 + 10*a^2*b^3*x^6 + 10*a^3*b^2*x^4 + 5*a^4*b*x^2 + a^5)*sqrt(a*b)*arctan(sqrt(a*b)*x/a))/(a^2*b^10*x^10 + 5*a^3*b^9*x^8 + 10*a^4*b^8*x^6 + 10*a^5*b^7*x^4 + 5*a^6*b^6*x^2 + a^7*b^5)]","A",0
528,1,390,0,0.860581," ","integrate(x^6/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","\left[\frac{30 \, a b^{5} x^{9} + 140 \, a^{2} b^{4} x^{7} - 256 \, a^{3} b^{3} x^{5} - 140 \, a^{4} b^{2} x^{3} - 30 \, a^{5} b x - 15 \, {\left(b^{5} x^{10} + 5 \, a b^{4} x^{8} + 10 \, a^{2} b^{3} x^{6} + 10 \, a^{3} b^{2} x^{4} + 5 \, a^{4} b x^{2} + a^{5}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right)}{2560 \, {\left(a^{3} b^{9} x^{10} + 5 \, a^{4} b^{8} x^{8} + 10 \, a^{5} b^{7} x^{6} + 10 \, a^{6} b^{6} x^{4} + 5 \, a^{7} b^{5} x^{2} + a^{8} b^{4}\right)}}, \frac{15 \, a b^{5} x^{9} + 70 \, a^{2} b^{4} x^{7} - 128 \, a^{3} b^{3} x^{5} - 70 \, a^{4} b^{2} x^{3} - 15 \, a^{5} b x + 15 \, {\left(b^{5} x^{10} + 5 \, a b^{4} x^{8} + 10 \, a^{2} b^{3} x^{6} + 10 \, a^{3} b^{2} x^{4} + 5 \, a^{4} b x^{2} + a^{5}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right)}{1280 \, {\left(a^{3} b^{9} x^{10} + 5 \, a^{4} b^{8} x^{8} + 10 \, a^{5} b^{7} x^{6} + 10 \, a^{6} b^{6} x^{4} + 5 \, a^{7} b^{5} x^{2} + a^{8} b^{4}\right)}}\right]"," ",0,"[1/2560*(30*a*b^5*x^9 + 140*a^2*b^4*x^7 - 256*a^3*b^3*x^5 - 140*a^4*b^2*x^3 - 30*a^5*b*x - 15*(b^5*x^10 + 5*a*b^4*x^8 + 10*a^2*b^3*x^6 + 10*a^3*b^2*x^4 + 5*a^4*b*x^2 + a^5)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)))/(a^3*b^9*x^10 + 5*a^4*b^8*x^8 + 10*a^5*b^7*x^6 + 10*a^6*b^6*x^4 + 5*a^7*b^5*x^2 + a^8*b^4), 1/1280*(15*a*b^5*x^9 + 70*a^2*b^4*x^7 - 128*a^3*b^3*x^5 - 70*a^4*b^2*x^3 - 15*a^5*b*x + 15*(b^5*x^10 + 5*a*b^4*x^8 + 10*a^2*b^3*x^6 + 10*a^3*b^2*x^4 + 5*a^4*b*x^2 + a^5)*sqrt(a*b)*arctan(sqrt(a*b)*x/a))/(a^3*b^9*x^10 + 5*a^4*b^8*x^8 + 10*a^5*b^7*x^6 + 10*a^6*b^6*x^4 + 5*a^7*b^5*x^2 + a^8*b^4)]","A",0
529,1,390,0,1.480645," ","integrate(x^4/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","\left[\frac{30 \, a b^{5} x^{9} + 140 \, a^{2} b^{4} x^{7} + 256 \, a^{3} b^{3} x^{5} - 140 \, a^{4} b^{2} x^{3} - 30 \, a^{5} b x - 15 \, {\left(b^{5} x^{10} + 5 \, a b^{4} x^{8} + 10 \, a^{2} b^{3} x^{6} + 10 \, a^{3} b^{2} x^{4} + 5 \, a^{4} b x^{2} + a^{5}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right)}{2560 \, {\left(a^{4} b^{8} x^{10} + 5 \, a^{5} b^{7} x^{8} + 10 \, a^{6} b^{6} x^{6} + 10 \, a^{7} b^{5} x^{4} + 5 \, a^{8} b^{4} x^{2} + a^{9} b^{3}\right)}}, \frac{15 \, a b^{5} x^{9} + 70 \, a^{2} b^{4} x^{7} + 128 \, a^{3} b^{3} x^{5} - 70 \, a^{4} b^{2} x^{3} - 15 \, a^{5} b x + 15 \, {\left(b^{5} x^{10} + 5 \, a b^{4} x^{8} + 10 \, a^{2} b^{3} x^{6} + 10 \, a^{3} b^{2} x^{4} + 5 \, a^{4} b x^{2} + a^{5}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right)}{1280 \, {\left(a^{4} b^{8} x^{10} + 5 \, a^{5} b^{7} x^{8} + 10 \, a^{6} b^{6} x^{6} + 10 \, a^{7} b^{5} x^{4} + 5 \, a^{8} b^{4} x^{2} + a^{9} b^{3}\right)}}\right]"," ",0,"[1/2560*(30*a*b^5*x^9 + 140*a^2*b^4*x^7 + 256*a^3*b^3*x^5 - 140*a^4*b^2*x^3 - 30*a^5*b*x - 15*(b^5*x^10 + 5*a*b^4*x^8 + 10*a^2*b^3*x^6 + 10*a^3*b^2*x^4 + 5*a^4*b*x^2 + a^5)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)))/(a^4*b^8*x^10 + 5*a^5*b^7*x^8 + 10*a^6*b^6*x^6 + 10*a^7*b^5*x^4 + 5*a^8*b^4*x^2 + a^9*b^3), 1/1280*(15*a*b^5*x^9 + 70*a^2*b^4*x^7 + 128*a^3*b^3*x^5 - 70*a^4*b^2*x^3 - 15*a^5*b*x + 15*(b^5*x^10 + 5*a*b^4*x^8 + 10*a^2*b^3*x^6 + 10*a^3*b^2*x^4 + 5*a^4*b*x^2 + a^5)*sqrt(a*b)*arctan(sqrt(a*b)*x/a))/(a^4*b^8*x^10 + 5*a^5*b^7*x^8 + 10*a^6*b^6*x^6 + 10*a^7*b^5*x^4 + 5*a^8*b^4*x^2 + a^9*b^3)]","A",0
530,1,390,0,0.874342," ","integrate(x^2/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","\left[\frac{210 \, a b^{5} x^{9} + 980 \, a^{2} b^{4} x^{7} + 1792 \, a^{3} b^{3} x^{5} + 1580 \, a^{4} b^{2} x^{3} - 210 \, a^{5} b x - 105 \, {\left(b^{5} x^{10} + 5 \, a b^{4} x^{8} + 10 \, a^{2} b^{3} x^{6} + 10 \, a^{3} b^{2} x^{4} + 5 \, a^{4} b x^{2} + a^{5}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right)}{7680 \, {\left(a^{5} b^{7} x^{10} + 5 \, a^{6} b^{6} x^{8} + 10 \, a^{7} b^{5} x^{6} + 10 \, a^{8} b^{4} x^{4} + 5 \, a^{9} b^{3} x^{2} + a^{10} b^{2}\right)}}, \frac{105 \, a b^{5} x^{9} + 490 \, a^{2} b^{4} x^{7} + 896 \, a^{3} b^{3} x^{5} + 790 \, a^{4} b^{2} x^{3} - 105 \, a^{5} b x + 105 \, {\left(b^{5} x^{10} + 5 \, a b^{4} x^{8} + 10 \, a^{2} b^{3} x^{6} + 10 \, a^{3} b^{2} x^{4} + 5 \, a^{4} b x^{2} + a^{5}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right)}{3840 \, {\left(a^{5} b^{7} x^{10} + 5 \, a^{6} b^{6} x^{8} + 10 \, a^{7} b^{5} x^{6} + 10 \, a^{8} b^{4} x^{4} + 5 \, a^{9} b^{3} x^{2} + a^{10} b^{2}\right)}}\right]"," ",0,"[1/7680*(210*a*b^5*x^9 + 980*a^2*b^4*x^7 + 1792*a^3*b^3*x^5 + 1580*a^4*b^2*x^3 - 210*a^5*b*x - 105*(b^5*x^10 + 5*a*b^4*x^8 + 10*a^2*b^3*x^6 + 10*a^3*b^2*x^4 + 5*a^4*b*x^2 + a^5)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)))/(a^5*b^7*x^10 + 5*a^6*b^6*x^8 + 10*a^7*b^5*x^6 + 10*a^8*b^4*x^4 + 5*a^9*b^3*x^2 + a^10*b^2), 1/3840*(105*a*b^5*x^9 + 490*a^2*b^4*x^7 + 896*a^3*b^3*x^5 + 790*a^4*b^2*x^3 - 105*a^5*b*x + 105*(b^5*x^10 + 5*a*b^4*x^8 + 10*a^2*b^3*x^6 + 10*a^3*b^2*x^4 + 5*a^4*b*x^2 + a^5)*sqrt(a*b)*arctan(sqrt(a*b)*x/a))/(a^5*b^7*x^10 + 5*a^6*b^6*x^8 + 10*a^7*b^5*x^6 + 10*a^8*b^4*x^4 + 5*a^9*b^3*x^2 + a^10*b^2)]","A",0
531,1,386,0,0.731536," ","integrate(1/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","\left[\frac{630 \, a b^{5} x^{9} + 2940 \, a^{2} b^{4} x^{7} + 5376 \, a^{3} b^{3} x^{5} + 4740 \, a^{4} b^{2} x^{3} + 1930 \, a^{5} b x - 315 \, {\left(b^{5} x^{10} + 5 \, a b^{4} x^{8} + 10 \, a^{2} b^{3} x^{6} + 10 \, a^{3} b^{2} x^{4} + 5 \, a^{4} b x^{2} + a^{5}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right)}{2560 \, {\left(a^{6} b^{6} x^{10} + 5 \, a^{7} b^{5} x^{8} + 10 \, a^{8} b^{4} x^{6} + 10 \, a^{9} b^{3} x^{4} + 5 \, a^{10} b^{2} x^{2} + a^{11} b\right)}}, \frac{315 \, a b^{5} x^{9} + 1470 \, a^{2} b^{4} x^{7} + 2688 \, a^{3} b^{3} x^{5} + 2370 \, a^{4} b^{2} x^{3} + 965 \, a^{5} b x + 315 \, {\left(b^{5} x^{10} + 5 \, a b^{4} x^{8} + 10 \, a^{2} b^{3} x^{6} + 10 \, a^{3} b^{2} x^{4} + 5 \, a^{4} b x^{2} + a^{5}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right)}{1280 \, {\left(a^{6} b^{6} x^{10} + 5 \, a^{7} b^{5} x^{8} + 10 \, a^{8} b^{4} x^{6} + 10 \, a^{9} b^{3} x^{4} + 5 \, a^{10} b^{2} x^{2} + a^{11} b\right)}}\right]"," ",0,"[1/2560*(630*a*b^5*x^9 + 2940*a^2*b^4*x^7 + 5376*a^3*b^3*x^5 + 4740*a^4*b^2*x^3 + 1930*a^5*b*x - 315*(b^5*x^10 + 5*a*b^4*x^8 + 10*a^2*b^3*x^6 + 10*a^3*b^2*x^4 + 5*a^4*b*x^2 + a^5)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)))/(a^6*b^6*x^10 + 5*a^7*b^5*x^8 + 10*a^8*b^4*x^6 + 10*a^9*b^3*x^4 + 5*a^10*b^2*x^2 + a^11*b), 1/1280*(315*a*b^5*x^9 + 1470*a^2*b^4*x^7 + 2688*a^3*b^3*x^5 + 2370*a^4*b^2*x^3 + 965*a^5*b*x + 315*(b^5*x^10 + 5*a*b^4*x^8 + 10*a^2*b^3*x^6 + 10*a^3*b^2*x^4 + 5*a^4*b*x^2 + a^5)*sqrt(a*b)*arctan(sqrt(a*b)*x/a))/(a^6*b^6*x^10 + 5*a^7*b^5*x^8 + 10*a^8*b^4*x^6 + 10*a^9*b^3*x^4 + 5*a^10*b^2*x^2 + a^11*b)]","A",0
532,1,400,0,3.126203," ","integrate(1/x^2/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","\left[-\frac{6930 \, b^{5} x^{10} + 32340 \, a b^{4} x^{8} + 59136 \, a^{2} b^{3} x^{6} + 52140 \, a^{3} b^{2} x^{4} + 21230 \, a^{4} b x^{2} + 2560 \, a^{5} - 3465 \, {\left(b^{5} x^{11} + 5 \, a b^{4} x^{9} + 10 \, a^{2} b^{3} x^{7} + 10 \, a^{3} b^{2} x^{5} + 5 \, a^{4} b x^{3} + a^{5} x\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right)}{2560 \, {\left(a^{6} b^{5} x^{11} + 5 \, a^{7} b^{4} x^{9} + 10 \, a^{8} b^{3} x^{7} + 10 \, a^{9} b^{2} x^{5} + 5 \, a^{10} b x^{3} + a^{11} x\right)}}, -\frac{3465 \, b^{5} x^{10} + 16170 \, a b^{4} x^{8} + 29568 \, a^{2} b^{3} x^{6} + 26070 \, a^{3} b^{2} x^{4} + 10615 \, a^{4} b x^{2} + 1280 \, a^{5} + 3465 \, {\left(b^{5} x^{11} + 5 \, a b^{4} x^{9} + 10 \, a^{2} b^{3} x^{7} + 10 \, a^{3} b^{2} x^{5} + 5 \, a^{4} b x^{3} + a^{5} x\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right)}{1280 \, {\left(a^{6} b^{5} x^{11} + 5 \, a^{7} b^{4} x^{9} + 10 \, a^{8} b^{3} x^{7} + 10 \, a^{9} b^{2} x^{5} + 5 \, a^{10} b x^{3} + a^{11} x\right)}}\right]"," ",0,"[-1/2560*(6930*b^5*x^10 + 32340*a*b^4*x^8 + 59136*a^2*b^3*x^6 + 52140*a^3*b^2*x^4 + 21230*a^4*b*x^2 + 2560*a^5 - 3465*(b^5*x^11 + 5*a*b^4*x^9 + 10*a^2*b^3*x^7 + 10*a^3*b^2*x^5 + 5*a^4*b*x^3 + a^5*x)*sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)))/(a^6*b^5*x^11 + 5*a^7*b^4*x^9 + 10*a^8*b^3*x^7 + 10*a^9*b^2*x^5 + 5*a^10*b*x^3 + a^11*x), -1/1280*(3465*b^5*x^10 + 16170*a*b^4*x^8 + 29568*a^2*b^3*x^6 + 26070*a^3*b^2*x^4 + 10615*a^4*b*x^2 + 1280*a^5 + 3465*(b^5*x^11 + 5*a*b^4*x^9 + 10*a^2*b^3*x^7 + 10*a^3*b^2*x^5 + 5*a^4*b*x^3 + a^5*x)*sqrt(b/a)*arctan(x*sqrt(b/a)))/(a^6*b^5*x^11 + 5*a^7*b^4*x^9 + 10*a^8*b^3*x^7 + 10*a^9*b^2*x^5 + 5*a^10*b*x^3 + a^11*x)]","A",0
533,1,436,0,0.885368," ","integrate(1/x^4/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","\left[\frac{90090 \, b^{6} x^{12} + 420420 \, a b^{5} x^{10} + 768768 \, a^{2} b^{4} x^{8} + 677820 \, a^{3} b^{3} x^{6} + 275990 \, a^{4} b^{2} x^{4} + 33280 \, a^{5} b x^{2} - 2560 \, a^{6} + 45045 \, {\left(b^{6} x^{13} + 5 \, a b^{5} x^{11} + 10 \, a^{2} b^{4} x^{9} + 10 \, a^{3} b^{3} x^{7} + 5 \, a^{4} b^{2} x^{5} + a^{5} b x^{3}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} + 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right)}{7680 \, {\left(a^{7} b^{5} x^{13} + 5 \, a^{8} b^{4} x^{11} + 10 \, a^{9} b^{3} x^{9} + 10 \, a^{10} b^{2} x^{7} + 5 \, a^{11} b x^{5} + a^{12} x^{3}\right)}}, \frac{45045 \, b^{6} x^{12} + 210210 \, a b^{5} x^{10} + 384384 \, a^{2} b^{4} x^{8} + 338910 \, a^{3} b^{3} x^{6} + 137995 \, a^{4} b^{2} x^{4} + 16640 \, a^{5} b x^{2} - 1280 \, a^{6} + 45045 \, {\left(b^{6} x^{13} + 5 \, a b^{5} x^{11} + 10 \, a^{2} b^{4} x^{9} + 10 \, a^{3} b^{3} x^{7} + 5 \, a^{4} b^{2} x^{5} + a^{5} b x^{3}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right)}{3840 \, {\left(a^{7} b^{5} x^{13} + 5 \, a^{8} b^{4} x^{11} + 10 \, a^{9} b^{3} x^{9} + 10 \, a^{10} b^{2} x^{7} + 5 \, a^{11} b x^{5} + a^{12} x^{3}\right)}}\right]"," ",0,"[1/7680*(90090*b^6*x^12 + 420420*a*b^5*x^10 + 768768*a^2*b^4*x^8 + 677820*a^3*b^3*x^6 + 275990*a^4*b^2*x^4 + 33280*a^5*b*x^2 - 2560*a^6 + 45045*(b^6*x^13 + 5*a*b^5*x^11 + 10*a^2*b^4*x^9 + 10*a^3*b^3*x^7 + 5*a^4*b^2*x^5 + a^5*b*x^3)*sqrt(-b/a)*log((b*x^2 + 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)))/(a^7*b^5*x^13 + 5*a^8*b^4*x^11 + 10*a^9*b^3*x^9 + 10*a^10*b^2*x^7 + 5*a^11*b*x^5 + a^12*x^3), 1/3840*(45045*b^6*x^12 + 210210*a*b^5*x^10 + 384384*a^2*b^4*x^8 + 338910*a^3*b^3*x^6 + 137995*a^4*b^2*x^4 + 16640*a^5*b*x^2 - 1280*a^6 + 45045*(b^6*x^13 + 5*a*b^5*x^11 + 10*a^2*b^4*x^9 + 10*a^3*b^3*x^7 + 5*a^4*b^2*x^5 + a^5*b*x^3)*sqrt(b/a)*arctan(x*sqrt(b/a)))/(a^7*b^5*x^13 + 5*a^8*b^4*x^11 + 10*a^9*b^3*x^9 + 10*a^10*b^2*x^7 + 5*a^11*b*x^5 + a^12*x^3)]","A",0
534,1,462,0,0.832814," ","integrate(1/x^6/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","\left[-\frac{90090 \, b^{7} x^{14} + 420420 \, a b^{6} x^{12} + 768768 \, a^{2} b^{5} x^{10} + 677820 \, a^{3} b^{4} x^{8} + 275990 \, a^{4} b^{3} x^{6} + 33280 \, a^{5} b^{2} x^{4} - 2560 \, a^{6} b x^{2} + 512 \, a^{7} - 45045 \, {\left(b^{7} x^{15} + 5 \, a b^{6} x^{13} + 10 \, a^{2} b^{5} x^{11} + 10 \, a^{3} b^{4} x^{9} + 5 \, a^{4} b^{3} x^{7} + a^{5} b^{2} x^{5}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right)}{2560 \, {\left(a^{8} b^{5} x^{15} + 5 \, a^{9} b^{4} x^{13} + 10 \, a^{10} b^{3} x^{11} + 10 \, a^{11} b^{2} x^{9} + 5 \, a^{12} b x^{7} + a^{13} x^{5}\right)}}, -\frac{45045 \, b^{7} x^{14} + 210210 \, a b^{6} x^{12} + 384384 \, a^{2} b^{5} x^{10} + 338910 \, a^{3} b^{4} x^{8} + 137995 \, a^{4} b^{3} x^{6} + 16640 \, a^{5} b^{2} x^{4} - 1280 \, a^{6} b x^{2} + 256 \, a^{7} + 45045 \, {\left(b^{7} x^{15} + 5 \, a b^{6} x^{13} + 10 \, a^{2} b^{5} x^{11} + 10 \, a^{3} b^{4} x^{9} + 5 \, a^{4} b^{3} x^{7} + a^{5} b^{2} x^{5}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right)}{1280 \, {\left(a^{8} b^{5} x^{15} + 5 \, a^{9} b^{4} x^{13} + 10 \, a^{10} b^{3} x^{11} + 10 \, a^{11} b^{2} x^{9} + 5 \, a^{12} b x^{7} + a^{13} x^{5}\right)}}\right]"," ",0,"[-1/2560*(90090*b^7*x^14 + 420420*a*b^6*x^12 + 768768*a^2*b^5*x^10 + 677820*a^3*b^4*x^8 + 275990*a^4*b^3*x^6 + 33280*a^5*b^2*x^4 - 2560*a^6*b*x^2 + 512*a^7 - 45045*(b^7*x^15 + 5*a*b^6*x^13 + 10*a^2*b^5*x^11 + 10*a^3*b^4*x^9 + 5*a^4*b^3*x^7 + a^5*b^2*x^5)*sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)))/(a^8*b^5*x^15 + 5*a^9*b^4*x^13 + 10*a^10*b^3*x^11 + 10*a^11*b^2*x^9 + 5*a^12*b*x^7 + a^13*x^5), -1/1280*(45045*b^7*x^14 + 210210*a*b^6*x^12 + 384384*a^2*b^5*x^10 + 338910*a^3*b^4*x^8 + 137995*a^4*b^3*x^6 + 16640*a^5*b^2*x^4 - 1280*a^6*b*x^2 + 256*a^7 + 45045*(b^7*x^15 + 5*a*b^6*x^13 + 10*a^2*b^5*x^11 + 10*a^3*b^4*x^9 + 5*a^4*b^3*x^7 + a^5*b^2*x^5)*sqrt(b/a)*arctan(x*sqrt(b/a)))/(a^8*b^5*x^15 + 5*a^9*b^4*x^13 + 10*a^10*b^3*x^11 + 10*a^11*b^2*x^9 + 5*a^12*b*x^7 + a^13*x^5)]","A",0
535,1,19,0,1.978723," ","integrate(1/(x^4+2*x^2+1),x, algorithm=""fricas"")","\frac{{\left(x^{2} + 1\right)} \arctan\left(x\right) + x}{2 \, {\left(x^{2} + 1\right)}}"," ",0,"1/2*((x^2 + 1)*arctan(x) + x)/(x^2 + 1)","A",0
536,1,9,0,0.847186," ","integrate(x/(x^4+2*x^2+1),x, algorithm=""fricas"")","-\frac{1}{2 \, {\left(x^{2} + 1\right)}}"," ",0,"-1/2/(x^2 + 1)","A",0
537,1,21,0,0.826245," ","integrate(x^2/(x^4+2*x^2+1),x, algorithm=""fricas"")","\frac{{\left(x^{2} + 1\right)} \arctan\left(x\right) - x}{2 \, {\left(x^{2} + 1\right)}}"," ",0,"1/2*((x^2 + 1)*arctan(x) - x)/(x^2 + 1)","A",0
538,1,23,0,0.856607," ","integrate(x^3/(x^4+2*x^2+1),x, algorithm=""fricas"")","\frac{{\left(x^{2} + 1\right)} \log\left(x^{2} + 1\right) + 1}{2 \, {\left(x^{2} + 1\right)}}"," ",0,"1/2*((x^2 + 1)*log(x^2 + 1) + 1)/(x^2 + 1)","A",0
539,1,9,0,0.783774," ","integrate(x/(x^4-18*x^2+81),x, algorithm=""fricas"")","-\frac{1}{2 \, {\left(x^{2} - 9\right)}}"," ",0,"-1/2/(x^2 - 9)","A",0
540,1,23,0,1.150143," ","integrate(x^3/(x^4-8*x^2+16),x, algorithm=""fricas"")","\frac{{\left(x^{2} - 4\right)} \log\left(x^{2} - 4\right) - 4}{2 \, {\left(x^{2} - 4\right)}}"," ",0,"1/2*((x^2 - 4)*log(x^2 - 4) - 4)/(x^2 - 4)","A",0
541,1,13,0,0.760933," ","integrate(x^5*((b*x^2+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{8} \, b x^{8} + \frac{1}{6} \, a x^{6}"," ",0,"1/8*b*x^8 + 1/6*a*x^6","A",0
542,1,13,0,1.070953," ","integrate(x^3*((b*x^2+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{6} \, b x^{6} + \frac{1}{4} \, a x^{4}"," ",0,"1/6*b*x^6 + 1/4*a*x^4","A",0
543,1,13,0,0.668679," ","integrate(x*((b*x^2+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{4} \, b x^{4} + \frac{1}{2} \, a x^{2}"," ",0,"1/4*b*x^4 + 1/2*a*x^2","A",0
544,1,11,0,0.633103," ","integrate(((b*x^2+a)^2)^(1/2)/x,x, algorithm=""fricas"")","\frac{1}{2} \, b x^{2} + a \log\left(x\right)"," ",0,"1/2*b*x^2 + a*log(x)","A",0
545,1,17,0,1.965864," ","integrate(((b*x^2+a)^2)^(1/2)/x^3,x, algorithm=""fricas"")","\frac{2 \, b x^{2} \log\left(x\right) - a}{2 \, x^{2}}"," ",0,"1/2*(2*b*x^2*log(x) - a)/x^2","A",0
546,1,13,0,0.905760," ","integrate(((b*x^2+a)^2)^(1/2)/x^5,x, algorithm=""fricas"")","-\frac{2 \, b x^{2} + a}{4 \, x^{4}}"," ",0,"-1/4*(2*b*x^2 + a)/x^4","A",0
547,1,15,0,0.872301," ","integrate(((b*x^2+a)^2)^(1/2)/x^7,x, algorithm=""fricas"")","-\frac{3 \, b x^{2} + 2 \, a}{12 \, x^{6}}"," ",0,"-1/12*(3*b*x^2 + 2*a)/x^6","A",0
548,1,15,0,0.819857," ","integrate(((b*x^2+a)^2)^(1/2)/x^9,x, algorithm=""fricas"")","-\frac{4 \, b x^{2} + 3 \, a}{24 \, x^{8}}"," ",0,"-1/24*(4*b*x^2 + 3*a)/x^8","A",0
549,1,15,0,0.815068," ","integrate(((b*x^2+a)^2)^(1/2)/x^11,x, algorithm=""fricas"")","-\frac{5 \, b x^{2} + 4 \, a}{40 \, x^{10}}"," ",0,"-1/40*(5*b*x^2 + 4*a)/x^10","A",0
550,1,13,0,0.771605," ","integrate(x^4*((b*x^2+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{7} \, b x^{7} + \frac{1}{5} \, a x^{5}"," ",0,"1/7*b*x^7 + 1/5*a*x^5","A",0
551,1,13,0,1.372165," ","integrate(x^2*((b*x^2+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{5} \, b x^{5} + \frac{1}{3} \, a x^{3}"," ",0,"1/5*b*x^5 + 1/3*a*x^3","A",0
552,1,10,0,0.763364," ","integrate(((b*x^2+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{3} \, b x^{3} + a x"," ",0,"1/3*b*x^3 + a*x","A",0
553,1,13,0,1.100899," ","integrate(((b*x^2+a)^2)^(1/2)/x^2,x, algorithm=""fricas"")","\frac{b x^{2} - a}{x}"," ",0,"(b*x^2 - a)/x","A",0
554,1,13,0,0.590452," ","integrate(((b*x^2+a)^2)^(1/2)/x^4,x, algorithm=""fricas"")","-\frac{3 \, b x^{2} + a}{3 \, x^{3}}"," ",0,"-1/3*(3*b*x^2 + a)/x^3","A",0
555,1,15,0,0.868727," ","integrate(((b*x^2+a)^2)^(1/2)/x^6,x, algorithm=""fricas"")","-\frac{5 \, b x^{2} + 3 \, a}{15 \, x^{5}}"," ",0,"-1/15*(5*b*x^2 + 3*a)/x^5","A",0
556,1,15,0,1.396417," ","integrate(((b*x^2+a)^2)^(1/2)/x^8,x, algorithm=""fricas"")","-\frac{7 \, b x^{2} + 5 \, a}{35 \, x^{7}}"," ",0,"-1/35*(7*b*x^2 + 5*a)/x^7","A",0
557,1,15,0,0.846889," ","integrate(((b*x^2+a)^2)^(1/2)/x^10,x, algorithm=""fricas"")","-\frac{9 \, b x^{2} + 7 \, a}{63 \, x^{9}}"," ",0,"-1/63*(9*b*x^2 + 7*a)/x^9","A",0
558,1,35,0,0.795837," ","integrate(x^9*(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{16} \, b^{3} x^{16} + \frac{3}{14} \, a b^{2} x^{14} + \frac{1}{4} \, a^{2} b x^{12} + \frac{1}{10} \, a^{3} x^{10}"," ",0,"1/16*b^3*x^16 + 3/14*a*b^2*x^14 + 1/4*a^2*b*x^12 + 1/10*a^3*x^10","A",0
559,1,35,0,0.794529," ","integrate(x^7*(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{14} \, b^{3} x^{14} + \frac{1}{4} \, a b^{2} x^{12} + \frac{3}{10} \, a^{2} b x^{10} + \frac{1}{8} \, a^{3} x^{8}"," ",0,"1/14*b^3*x^14 + 1/4*a*b^2*x^12 + 3/10*a^2*b*x^10 + 1/8*a^3*x^8","A",0
560,1,35,0,0.805867," ","integrate(x^5*(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{12} \, b^{3} x^{12} + \frac{3}{10} \, a b^{2} x^{10} + \frac{3}{8} \, a^{2} b x^{8} + \frac{1}{6} \, a^{3} x^{6}"," ",0,"1/12*b^3*x^12 + 3/10*a*b^2*x^10 + 3/8*a^2*b*x^8 + 1/6*a^3*x^6","A",0
561,1,35,0,0.902490," ","integrate(x^3*(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{10} \, b^{3} x^{10} + \frac{3}{8} \, a b^{2} x^{8} + \frac{1}{2} \, a^{2} b x^{6} + \frac{1}{4} \, a^{3} x^{4}"," ",0,"1/10*b^3*x^10 + 3/8*a*b^2*x^8 + 1/2*a^2*b*x^6 + 1/4*a^3*x^4","A",0
562,1,35,0,0.793204," ","integrate(x*(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{8} \, b^{3} x^{8} + \frac{1}{2} \, a b^{2} x^{6} + \frac{3}{4} \, a^{2} b x^{4} + \frac{1}{2} \, a^{3} x^{2}"," ",0,"1/8*b^3*x^8 + 1/2*a*b^2*x^6 + 3/4*a^2*b*x^4 + 1/2*a^3*x^2","A",0
563,1,33,0,0.644330," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x,x, algorithm=""fricas"")","\frac{1}{6} \, b^{3} x^{6} + \frac{3}{4} \, a b^{2} x^{4} + \frac{3}{2} \, a^{2} b x^{2} + a^{3} \log\left(x\right)"," ",0,"1/6*b^3*x^6 + 3/4*a*b^2*x^4 + 3/2*a^2*b*x^2 + a^3*log(x)","A",0
564,1,38,0,0.812284," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^3,x, algorithm=""fricas"")","\frac{b^{3} x^{6} + 6 \, a b^{2} x^{4} + 12 \, a^{2} b x^{2} \log\left(x\right) - 2 \, a^{3}}{4 \, x^{2}}"," ",0,"1/4*(b^3*x^6 + 6*a*b^2*x^4 + 12*a^2*b*x^2*log(x) - 2*a^3)/x^2","A",0
565,1,39,0,1.476922," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^5,x, algorithm=""fricas"")","\frac{2 \, b^{3} x^{6} + 12 \, a b^{2} x^{4} \log\left(x\right) - 6 \, a^{2} b x^{2} - a^{3}}{4 \, x^{4}}"," ",0,"1/4*(2*b^3*x^6 + 12*a*b^2*x^4*log(x) - 6*a^2*b*x^2 - a^3)/x^4","A",0
566,1,39,0,0.630552," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^7,x, algorithm=""fricas"")","\frac{12 \, b^{3} x^{6} \log\left(x\right) - 18 \, a b^{2} x^{4} - 9 \, a^{2} b x^{2} - 2 \, a^{3}}{12 \, x^{6}}"," ",0,"1/12*(12*b^3*x^6*log(x) - 18*a*b^2*x^4 - 9*a^2*b*x^2 - 2*a^3)/x^6","A",0
567,1,35,0,0.762742," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^9,x, algorithm=""fricas"")","-\frac{4 \, b^{3} x^{6} + 6 \, a b^{2} x^{4} + 4 \, a^{2} b x^{2} + a^{3}}{8 \, x^{8}}"," ",0,"-1/8*(4*b^3*x^6 + 6*a*b^2*x^4 + 4*a^2*b*x^2 + a^3)/x^8","A",0
568,1,37,0,0.849826," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^11,x, algorithm=""fricas"")","-\frac{10 \, b^{3} x^{6} + 20 \, a b^{2} x^{4} + 15 \, a^{2} b x^{2} + 4 \, a^{3}}{40 \, x^{10}}"," ",0,"-1/40*(10*b^3*x^6 + 20*a*b^2*x^4 + 15*a^2*b*x^2 + 4*a^3)/x^10","A",0
569,1,37,0,0.968258," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^13,x, algorithm=""fricas"")","-\frac{20 \, b^{3} x^{6} + 45 \, a b^{2} x^{4} + 36 \, a^{2} b x^{2} + 10 \, a^{3}}{120 \, x^{12}}"," ",0,"-1/120*(20*b^3*x^6 + 45*a*b^2*x^4 + 36*a^2*b*x^2 + 10*a^3)/x^12","A",0
570,1,37,0,1.084793," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^15,x, algorithm=""fricas"")","-\frac{35 \, b^{3} x^{6} + 84 \, a b^{2} x^{4} + 70 \, a^{2} b x^{2} + 20 \, a^{3}}{280 \, x^{14}}"," ",0,"-1/280*(35*b^3*x^6 + 84*a*b^2*x^4 + 70*a^2*b*x^2 + 20*a^3)/x^14","A",0
571,1,37,0,0.828626," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^17,x, algorithm=""fricas"")","-\frac{56 \, b^{3} x^{6} + 140 \, a b^{2} x^{4} + 120 \, a^{2} b x^{2} + 35 \, a^{3}}{560 \, x^{16}}"," ",0,"-1/560*(56*b^3*x^6 + 140*a*b^2*x^4 + 120*a^2*b*x^2 + 35*a^3)/x^16","A",0
572,1,35,0,0.799572," ","integrate(x^8*(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{15} \, b^{3} x^{15} + \frac{3}{13} \, a b^{2} x^{13} + \frac{3}{11} \, a^{2} b x^{11} + \frac{1}{9} \, a^{3} x^{9}"," ",0,"1/15*b^3*x^15 + 3/13*a*b^2*x^13 + 3/11*a^2*b*x^11 + 1/9*a^3*x^9","A",0
573,1,35,0,0.808873," ","integrate(x^6*(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{13} \, b^{3} x^{13} + \frac{3}{11} \, a b^{2} x^{11} + \frac{1}{3} \, a^{2} b x^{9} + \frac{1}{7} \, a^{3} x^{7}"," ",0,"1/13*b^3*x^13 + 3/11*a*b^2*x^11 + 1/3*a^2*b*x^9 + 1/7*a^3*x^7","A",0
574,1,35,0,0.831302," ","integrate(x^4*(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{11} \, b^{3} x^{11} + \frac{1}{3} \, a b^{2} x^{9} + \frac{3}{7} \, a^{2} b x^{7} + \frac{1}{5} \, a^{3} x^{5}"," ",0,"1/11*b^3*x^11 + 1/3*a*b^2*x^9 + 3/7*a^2*b*x^7 + 1/5*a^3*x^5","A",0
575,1,35,0,0.528426," ","integrate(x^2*(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{9} \, b^{3} x^{9} + \frac{3}{7} \, a b^{2} x^{7} + \frac{3}{5} \, a^{2} b x^{5} + \frac{1}{3} \, a^{3} x^{3}"," ",0,"1/9*b^3*x^9 + 3/7*a*b^2*x^7 + 3/5*a^2*b*x^5 + 1/3*a^3*x^3","A",0
576,1,31,0,0.791378," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{7} \, b^{3} x^{7} + \frac{3}{5} \, a b^{2} x^{5} + a^{2} b x^{3} + a^{3} x"," ",0,"1/7*b^3*x^7 + 3/5*a*b^2*x^5 + a^2*b*x^3 + a^3*x","A",0
577,1,36,0,0.610621," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^2,x, algorithm=""fricas"")","\frac{b^{3} x^{6} + 5 \, a b^{2} x^{4} + 15 \, a^{2} b x^{2} - 5 \, a^{3}}{5 \, x}"," ",0,"1/5*(b^3*x^6 + 5*a*b^2*x^4 + 15*a^2*b*x^2 - 5*a^3)/x","A",0
578,1,36,0,0.736253," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^4,x, algorithm=""fricas"")","\frac{b^{3} x^{6} + 9 \, a b^{2} x^{4} - 9 \, a^{2} b x^{2} - a^{3}}{3 \, x^{3}}"," ",0,"1/3*(b^3*x^6 + 9*a*b^2*x^4 - 9*a^2*b*x^2 - a^3)/x^3","A",0
579,1,37,0,0.813584," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^6,x, algorithm=""fricas"")","\frac{5 \, b^{3} x^{6} - 15 \, a b^{2} x^{4} - 5 \, a^{2} b x^{2} - a^{3}}{5 \, x^{5}}"," ",0,"1/5*(5*b^3*x^6 - 15*a*b^2*x^4 - 5*a^2*b*x^2 - a^3)/x^5","A",0
580,1,37,0,0.767686," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^8,x, algorithm=""fricas"")","-\frac{35 \, b^{3} x^{6} + 35 \, a b^{2} x^{4} + 21 \, a^{2} b x^{2} + 5 \, a^{3}}{35 \, x^{7}}"," ",0,"-1/35*(35*b^3*x^6 + 35*a*b^2*x^4 + 21*a^2*b*x^2 + 5*a^3)/x^7","A",0
581,1,37,0,1.014107," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^10,x, algorithm=""fricas"")","-\frac{105 \, b^{3} x^{6} + 189 \, a b^{2} x^{4} + 135 \, a^{2} b x^{2} + 35 \, a^{3}}{315 \, x^{9}}"," ",0,"-1/315*(105*b^3*x^6 + 189*a*b^2*x^4 + 135*a^2*b*x^2 + 35*a^3)/x^9","A",0
582,1,37,0,1.283499," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^12,x, algorithm=""fricas"")","-\frac{231 \, b^{3} x^{6} + 495 \, a b^{2} x^{4} + 385 \, a^{2} b x^{2} + 105 \, a^{3}}{1155 \, x^{11}}"," ",0,"-1/1155*(231*b^3*x^6 + 495*a*b^2*x^4 + 385*a^2*b*x^2 + 105*a^3)/x^11","A",0
583,1,37,0,0.771797," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^14,x, algorithm=""fricas"")","-\frac{429 \, b^{3} x^{6} + 1001 \, a b^{2} x^{4} + 819 \, a^{2} b x^{2} + 231 \, a^{3}}{3003 \, x^{13}}"," ",0,"-1/3003*(429*b^3*x^6 + 1001*a*b^2*x^4 + 819*a^2*b*x^2 + 231*a^3)/x^13","A",0
584,1,37,0,1.197681," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^16,x, algorithm=""fricas"")","-\frac{715 \, b^{3} x^{6} + 1755 \, a b^{2} x^{4} + 1485 \, a^{2} b x^{2} + 429 \, a^{3}}{6435 \, x^{15}}"," ",0,"-1/6435*(715*b^3*x^6 + 1755*a*b^2*x^4 + 1485*a^2*b*x^2 + 429*a^3)/x^15","A",0
585,1,57,0,0.774512," ","integrate(x^13*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{24} \, b^{5} x^{24} + \frac{5}{22} \, a b^{4} x^{22} + \frac{1}{2} \, a^{2} b^{3} x^{20} + \frac{5}{9} \, a^{3} b^{2} x^{18} + \frac{5}{16} \, a^{4} b x^{16} + \frac{1}{14} \, a^{5} x^{14}"," ",0,"1/24*b^5*x^24 + 5/22*a*b^4*x^22 + 1/2*a^2*b^3*x^20 + 5/9*a^3*b^2*x^18 + 5/16*a^4*b*x^16 + 1/14*a^5*x^14","A",0
586,1,57,0,0.736599," ","integrate(x^11*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{22} \, b^{5} x^{22} + \frac{1}{4} \, a b^{4} x^{20} + \frac{5}{9} \, a^{2} b^{3} x^{18} + \frac{5}{8} \, a^{3} b^{2} x^{16} + \frac{5}{14} \, a^{4} b x^{14} + \frac{1}{12} \, a^{5} x^{12}"," ",0,"1/22*b^5*x^22 + 1/4*a*b^4*x^20 + 5/9*a^2*b^3*x^18 + 5/8*a^3*b^2*x^16 + 5/14*a^4*b*x^14 + 1/12*a^5*x^12","A",0
587,1,57,0,1.024182," ","integrate(x^9*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{20} \, b^{5} x^{20} + \frac{5}{18} \, a b^{4} x^{18} + \frac{5}{8} \, a^{2} b^{3} x^{16} + \frac{5}{7} \, a^{3} b^{2} x^{14} + \frac{5}{12} \, a^{4} b x^{12} + \frac{1}{10} \, a^{5} x^{10}"," ",0,"1/20*b^5*x^20 + 5/18*a*b^4*x^18 + 5/8*a^2*b^3*x^16 + 5/7*a^3*b^2*x^14 + 5/12*a^4*b*x^12 + 1/10*a^5*x^10","A",0
588,1,57,0,1.109428," ","integrate(x^7*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{18} \, b^{5} x^{18} + \frac{5}{16} \, a b^{4} x^{16} + \frac{5}{7} \, a^{2} b^{3} x^{14} + \frac{5}{6} \, a^{3} b^{2} x^{12} + \frac{1}{2} \, a^{4} b x^{10} + \frac{1}{8} \, a^{5} x^{8}"," ",0,"1/18*b^5*x^18 + 5/16*a*b^4*x^16 + 5/7*a^2*b^3*x^14 + 5/6*a^3*b^2*x^12 + 1/2*a^4*b*x^10 + 1/8*a^5*x^8","A",0
589,1,56,0,0.515962," ","integrate(x^5*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{16} \, b^{5} x^{16} + \frac{5}{14} \, a b^{4} x^{14} + \frac{5}{6} \, a^{2} b^{3} x^{12} + a^{3} b^{2} x^{10} + \frac{5}{8} \, a^{4} b x^{8} + \frac{1}{6} \, a^{5} x^{6}"," ",0,"1/16*b^5*x^16 + 5/14*a*b^4*x^14 + 5/6*a^2*b^3*x^12 + a^3*b^2*x^10 + 5/8*a^4*b*x^8 + 1/6*a^5*x^6","A",0
590,1,56,0,1.119724," ","integrate(x^3*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{14} \, b^{5} x^{14} + \frac{5}{12} \, a b^{4} x^{12} + a^{2} b^{3} x^{10} + \frac{5}{4} \, a^{3} b^{2} x^{8} + \frac{5}{6} \, a^{4} b x^{6} + \frac{1}{4} \, a^{5} x^{4}"," ",0,"1/14*b^5*x^14 + 5/12*a*b^4*x^12 + a^2*b^3*x^10 + 5/4*a^3*b^2*x^8 + 5/6*a^4*b*x^6 + 1/4*a^5*x^4","A",0
591,1,57,0,0.804952," ","integrate(x*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{12} \, b^{5} x^{12} + \frac{1}{2} \, a b^{4} x^{10} + \frac{5}{4} \, a^{2} b^{3} x^{8} + \frac{5}{3} \, a^{3} b^{2} x^{6} + \frac{5}{4} \, a^{4} b x^{4} + \frac{1}{2} \, a^{5} x^{2}"," ",0,"1/12*b^5*x^12 + 1/2*a*b^4*x^10 + 5/4*a^2*b^3*x^8 + 5/3*a^3*b^2*x^6 + 5/4*a^4*b*x^4 + 1/2*a^5*x^2","A",0
592,1,55,0,0.863470," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x,x, algorithm=""fricas"")","\frac{1}{10} \, b^{5} x^{10} + \frac{5}{8} \, a b^{4} x^{8} + \frac{5}{3} \, a^{2} b^{3} x^{6} + \frac{5}{2} \, a^{3} b^{2} x^{4} + \frac{5}{2} \, a^{4} b x^{2} + a^{5} \log\left(x\right)"," ",0,"1/10*b^5*x^10 + 5/8*a*b^4*x^8 + 5/3*a^2*b^3*x^6 + 5/2*a^3*b^2*x^4 + 5/2*a^4*b*x^2 + a^5*log(x)","A",0
593,1,61,0,0.845721," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^3,x, algorithm=""fricas"")","\frac{3 \, b^{5} x^{10} + 20 \, a b^{4} x^{8} + 60 \, a^{2} b^{3} x^{6} + 120 \, a^{3} b^{2} x^{4} + 120 \, a^{4} b x^{2} \log\left(x\right) - 12 \, a^{5}}{24 \, x^{2}}"," ",0,"1/24*(3*b^5*x^10 + 20*a*b^4*x^8 + 60*a^2*b^3*x^6 + 120*a^3*b^2*x^4 + 120*a^4*b*x^2*log(x) - 12*a^5)/x^2","A",0
594,1,61,0,0.828858," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^5,x, algorithm=""fricas"")","\frac{2 \, b^{5} x^{10} + 15 \, a b^{4} x^{8} + 60 \, a^{2} b^{3} x^{6} + 120 \, a^{3} b^{2} x^{4} \log\left(x\right) - 30 \, a^{4} b x^{2} - 3 \, a^{5}}{12 \, x^{4}}"," ",0,"1/12*(2*b^5*x^10 + 15*a*b^4*x^8 + 60*a^2*b^3*x^6 + 120*a^3*b^2*x^4*log(x) - 30*a^4*b*x^2 - 3*a^5)/x^4","A",0
595,1,61,0,0.964522," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^7,x, algorithm=""fricas"")","\frac{3 \, b^{5} x^{10} + 30 \, a b^{4} x^{8} + 120 \, a^{2} b^{3} x^{6} \log\left(x\right) - 60 \, a^{3} b^{2} x^{4} - 15 \, a^{4} b x^{2} - 2 \, a^{5}}{12 \, x^{6}}"," ",0,"1/12*(3*b^5*x^10 + 30*a*b^4*x^8 + 120*a^2*b^3*x^6*log(x) - 60*a^3*b^2*x^4 - 15*a^4*b*x^2 - 2*a^5)/x^6","A",0
596,1,61,0,0.832173," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^9,x, algorithm=""fricas"")","\frac{12 \, b^{5} x^{10} + 120 \, a b^{4} x^{8} \log\left(x\right) - 120 \, a^{2} b^{3} x^{6} - 60 \, a^{3} b^{2} x^{4} - 20 \, a^{4} b x^{2} - 3 \, a^{5}}{24 \, x^{8}}"," ",0,"1/24*(12*b^5*x^10 + 120*a*b^4*x^8*log(x) - 120*a^2*b^3*x^6 - 60*a^3*b^2*x^4 - 20*a^4*b*x^2 - 3*a^5)/x^8","A",0
597,1,61,0,0.604964," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^11,x, algorithm=""fricas"")","\frac{120 \, b^{5} x^{10} \log\left(x\right) - 300 \, a b^{4} x^{8} - 300 \, a^{2} b^{3} x^{6} - 200 \, a^{3} b^{2} x^{4} - 75 \, a^{4} b x^{2} - 12 \, a^{5}}{120 \, x^{10}}"," ",0,"1/120*(120*b^5*x^10*log(x) - 300*a*b^4*x^8 - 300*a^2*b^3*x^6 - 200*a^3*b^2*x^4 - 75*a^4*b*x^2 - 12*a^5)/x^10","A",0
598,1,57,0,0.869727," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^13,x, algorithm=""fricas"")","-\frac{6 \, b^{5} x^{10} + 15 \, a b^{4} x^{8} + 20 \, a^{2} b^{3} x^{6} + 15 \, a^{3} b^{2} x^{4} + 6 \, a^{4} b x^{2} + a^{5}}{12 \, x^{12}}"," ",0,"-1/12*(6*b^5*x^10 + 15*a*b^4*x^8 + 20*a^2*b^3*x^6 + 15*a^3*b^2*x^4 + 6*a^4*b*x^2 + a^5)/x^12","B",0
599,1,59,0,1.263092," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^15,x, algorithm=""fricas"")","-\frac{21 \, b^{5} x^{10} + 70 \, a b^{4} x^{8} + 105 \, a^{2} b^{3} x^{6} + 84 \, a^{3} b^{2} x^{4} + 35 \, a^{4} b x^{2} + 6 \, a^{5}}{84 \, x^{14}}"," ",0,"-1/84*(21*b^5*x^10 + 70*a*b^4*x^8 + 105*a^2*b^3*x^6 + 84*a^3*b^2*x^4 + 35*a^4*b*x^2 + 6*a^5)/x^14","A",0
600,1,59,0,0.808294," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^17,x, algorithm=""fricas"")","-\frac{56 \, b^{5} x^{10} + 210 \, a b^{4} x^{8} + 336 \, a^{2} b^{3} x^{6} + 280 \, a^{3} b^{2} x^{4} + 120 \, a^{4} b x^{2} + 21 \, a^{5}}{336 \, x^{16}}"," ",0,"-1/336*(56*b^5*x^10 + 210*a*b^4*x^8 + 336*a^2*b^3*x^6 + 280*a^3*b^2*x^4 + 120*a^4*b*x^2 + 21*a^5)/x^16","A",0
601,1,59,0,0.821985," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^19,x, algorithm=""fricas"")","-\frac{126 \, b^{5} x^{10} + 504 \, a b^{4} x^{8} + 840 \, a^{2} b^{3} x^{6} + 720 \, a^{3} b^{2} x^{4} + 315 \, a^{4} b x^{2} + 56 \, a^{5}}{1008 \, x^{18}}"," ",0,"-1/1008*(126*b^5*x^10 + 504*a*b^4*x^8 + 840*a^2*b^3*x^6 + 720*a^3*b^2*x^4 + 315*a^4*b*x^2 + 56*a^5)/x^18","A",0
602,1,59,0,0.730744," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^21,x, algorithm=""fricas"")","-\frac{252 \, b^{5} x^{10} + 1050 \, a b^{4} x^{8} + 1800 \, a^{2} b^{3} x^{6} + 1575 \, a^{3} b^{2} x^{4} + 700 \, a^{4} b x^{2} + 126 \, a^{5}}{2520 \, x^{20}}"," ",0,"-1/2520*(252*b^5*x^10 + 1050*a*b^4*x^8 + 1800*a^2*b^3*x^6 + 1575*a^3*b^2*x^4 + 700*a^4*b*x^2 + 126*a^5)/x^20","A",0
603,1,59,0,0.955557," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^23,x, algorithm=""fricas"")","-\frac{462 \, b^{5} x^{10} + 1980 \, a b^{4} x^{8} + 3465 \, a^{2} b^{3} x^{6} + 3080 \, a^{3} b^{2} x^{4} + 1386 \, a^{4} b x^{2} + 252 \, a^{5}}{5544 \, x^{22}}"," ",0,"-1/5544*(462*b^5*x^10 + 1980*a*b^4*x^8 + 3465*a^2*b^3*x^6 + 3080*a^3*b^2*x^4 + 1386*a^4*b*x^2 + 252*a^5)/x^22","A",0
604,1,59,0,0.756056," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^25,x, algorithm=""fricas"")","-\frac{792 \, b^{5} x^{10} + 3465 \, a b^{4} x^{8} + 6160 \, a^{2} b^{3} x^{6} + 5544 \, a^{3} b^{2} x^{4} + 2520 \, a^{4} b x^{2} + 462 \, a^{5}}{11088 \, x^{24}}"," ",0,"-1/11088*(792*b^5*x^10 + 3465*a*b^4*x^8 + 6160*a^2*b^3*x^6 + 5544*a^3*b^2*x^4 + 2520*a^4*b*x^2 + 462*a^5)/x^24","A",0
605,1,57,0,1.066330," ","integrate(x^12*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{23} \, b^{5} x^{23} + \frac{5}{21} \, a b^{4} x^{21} + \frac{10}{19} \, a^{2} b^{3} x^{19} + \frac{10}{17} \, a^{3} b^{2} x^{17} + \frac{1}{3} \, a^{4} b x^{15} + \frac{1}{13} \, a^{5} x^{13}"," ",0,"1/23*b^5*x^23 + 5/21*a*b^4*x^21 + 10/19*a^2*b^3*x^19 + 10/17*a^3*b^2*x^17 + 1/3*a^4*b*x^15 + 1/13*a^5*x^13","A",0
606,1,57,0,0.974600," ","integrate(x^10*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{21} \, b^{5} x^{21} + \frac{5}{19} \, a b^{4} x^{19} + \frac{10}{17} \, a^{2} b^{3} x^{17} + \frac{2}{3} \, a^{3} b^{2} x^{15} + \frac{5}{13} \, a^{4} b x^{13} + \frac{1}{11} \, a^{5} x^{11}"," ",0,"1/21*b^5*x^21 + 5/19*a*b^4*x^19 + 10/17*a^2*b^3*x^17 + 2/3*a^3*b^2*x^15 + 5/13*a^4*b*x^13 + 1/11*a^5*x^11","A",0
607,1,57,0,0.465513," ","integrate(x^8*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{19} \, b^{5} x^{19} + \frac{5}{17} \, a b^{4} x^{17} + \frac{2}{3} \, a^{2} b^{3} x^{15} + \frac{10}{13} \, a^{3} b^{2} x^{13} + \frac{5}{11} \, a^{4} b x^{11} + \frac{1}{9} \, a^{5} x^{9}"," ",0,"1/19*b^5*x^19 + 5/17*a*b^4*x^17 + 2/3*a^2*b^3*x^15 + 10/13*a^3*b^2*x^13 + 5/11*a^4*b*x^11 + 1/9*a^5*x^9","A",0
608,1,57,0,0.942247," ","integrate(x^6*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{17} \, b^{5} x^{17} + \frac{1}{3} \, a b^{4} x^{15} + \frac{10}{13} \, a^{2} b^{3} x^{13} + \frac{10}{11} \, a^{3} b^{2} x^{11} + \frac{5}{9} \, a^{4} b x^{9} + \frac{1}{7} \, a^{5} x^{7}"," ",0,"1/17*b^5*x^17 + 1/3*a*b^4*x^15 + 10/13*a^2*b^3*x^13 + 10/11*a^3*b^2*x^11 + 5/9*a^4*b*x^9 + 1/7*a^5*x^7","A",0
609,1,57,0,0.967876," ","integrate(x^4*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{15} \, b^{5} x^{15} + \frac{5}{13} \, a b^{4} x^{13} + \frac{10}{11} \, a^{2} b^{3} x^{11} + \frac{10}{9} \, a^{3} b^{2} x^{9} + \frac{5}{7} \, a^{4} b x^{7} + \frac{1}{5} \, a^{5} x^{5}"," ",0,"1/15*b^5*x^15 + 5/13*a*b^4*x^13 + 10/11*a^2*b^3*x^11 + 10/9*a^3*b^2*x^9 + 5/7*a^4*b*x^7 + 1/5*a^5*x^5","A",0
610,1,56,0,0.987228," ","integrate(x^2*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{13} \, b^{5} x^{13} + \frac{5}{11} \, a b^{4} x^{11} + \frac{10}{9} \, a^{2} b^{3} x^{9} + \frac{10}{7} \, a^{3} b^{2} x^{7} + a^{4} b x^{5} + \frac{1}{3} \, a^{5} x^{3}"," ",0,"1/13*b^5*x^13 + 5/11*a*b^4*x^11 + 10/9*a^2*b^3*x^9 + 10/7*a^3*b^2*x^7 + a^4*b*x^5 + 1/3*a^5*x^3","A",0
611,1,54,0,0.805252," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{11} \, b^{5} x^{11} + \frac{5}{9} \, a b^{4} x^{9} + \frac{10}{7} \, a^{2} b^{3} x^{7} + 2 \, a^{3} b^{2} x^{5} + \frac{5}{3} \, a^{4} b x^{3} + a^{5} x"," ",0,"1/11*b^5*x^11 + 5/9*a*b^4*x^9 + 10/7*a^2*b^3*x^7 + 2*a^3*b^2*x^5 + 5/3*a^4*b*x^3 + a^5*x","A",0
612,1,59,0,0.852818," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^2,x, algorithm=""fricas"")","\frac{7 \, b^{5} x^{10} + 45 \, a b^{4} x^{8} + 126 \, a^{2} b^{3} x^{6} + 210 \, a^{3} b^{2} x^{4} + 315 \, a^{4} b x^{2} - 63 \, a^{5}}{63 \, x}"," ",0,"1/63*(7*b^5*x^10 + 45*a*b^4*x^8 + 126*a^2*b^3*x^6 + 210*a^3*b^2*x^4 + 315*a^4*b*x^2 - 63*a^5)/x","A",0
613,1,59,0,0.649050," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^4,x, algorithm=""fricas"")","\frac{3 \, b^{5} x^{10} + 21 \, a b^{4} x^{8} + 70 \, a^{2} b^{3} x^{6} + 210 \, a^{3} b^{2} x^{4} - 105 \, a^{4} b x^{2} - 7 \, a^{5}}{21 \, x^{3}}"," ",0,"1/21*(3*b^5*x^10 + 21*a*b^4*x^8 + 70*a^2*b^3*x^6 + 210*a^3*b^2*x^4 - 105*a^4*b*x^2 - 7*a^5)/x^3","A",0
614,1,59,0,0.870366," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^6,x, algorithm=""fricas"")","\frac{3 \, b^{5} x^{10} + 25 \, a b^{4} x^{8} + 150 \, a^{2} b^{3} x^{6} - 150 \, a^{3} b^{2} x^{4} - 25 \, a^{4} b x^{2} - 3 \, a^{5}}{15 \, x^{5}}"," ",0,"1/15*(3*b^5*x^10 + 25*a*b^4*x^8 + 150*a^2*b^3*x^6 - 150*a^3*b^2*x^4 - 25*a^4*b*x^2 - 3*a^5)/x^5","A",0
615,1,59,0,0.850509," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^8,x, algorithm=""fricas"")","\frac{7 \, b^{5} x^{10} + 105 \, a b^{4} x^{8} - 210 \, a^{2} b^{3} x^{6} - 70 \, a^{3} b^{2} x^{4} - 21 \, a^{4} b x^{2} - 3 \, a^{5}}{21 \, x^{7}}"," ",0,"1/21*(7*b^5*x^10 + 105*a*b^4*x^8 - 210*a^2*b^3*x^6 - 70*a^3*b^2*x^4 - 21*a^4*b*x^2 - 3*a^5)/x^7","A",0
616,1,59,0,0.822102," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^10,x, algorithm=""fricas"")","\frac{63 \, b^{5} x^{10} - 315 \, a b^{4} x^{8} - 210 \, a^{2} b^{3} x^{6} - 126 \, a^{3} b^{2} x^{4} - 45 \, a^{4} b x^{2} - 7 \, a^{5}}{63 \, x^{9}}"," ",0,"1/63*(63*b^5*x^10 - 315*a*b^4*x^8 - 210*a^2*b^3*x^6 - 126*a^3*b^2*x^4 - 45*a^4*b*x^2 - 7*a^5)/x^9","A",0
617,1,59,0,0.941598," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^12,x, algorithm=""fricas"")","-\frac{693 \, b^{5} x^{10} + 1155 \, a b^{4} x^{8} + 1386 \, a^{2} b^{3} x^{6} + 990 \, a^{3} b^{2} x^{4} + 385 \, a^{4} b x^{2} + 63 \, a^{5}}{693 \, x^{11}}"," ",0,"-1/693*(693*b^5*x^10 + 1155*a*b^4*x^8 + 1386*a^2*b^3*x^6 + 990*a^3*b^2*x^4 + 385*a^4*b*x^2 + 63*a^5)/x^11","A",0
618,1,59,0,1.064628," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^14,x, algorithm=""fricas"")","-\frac{3003 \, b^{5} x^{10} + 9009 \, a b^{4} x^{8} + 12870 \, a^{2} b^{3} x^{6} + 10010 \, a^{3} b^{2} x^{4} + 4095 \, a^{4} b x^{2} + 693 \, a^{5}}{9009 \, x^{13}}"," ",0,"-1/9009*(3003*b^5*x^10 + 9009*a*b^4*x^8 + 12870*a^2*b^3*x^6 + 10010*a^3*b^2*x^4 + 4095*a^4*b*x^2 + 693*a^5)/x^13","A",0
619,1,59,0,0.716279," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^16,x, algorithm=""fricas"")","-\frac{9009 \, b^{5} x^{10} + 32175 \, a b^{4} x^{8} + 50050 \, a^{2} b^{3} x^{6} + 40950 \, a^{3} b^{2} x^{4} + 17325 \, a^{4} b x^{2} + 3003 \, a^{5}}{45045 \, x^{15}}"," ",0,"-1/45045*(9009*b^5*x^10 + 32175*a*b^4*x^8 + 50050*a^2*b^3*x^6 + 40950*a^3*b^2*x^4 + 17325*a^4*b*x^2 + 3003*a^5)/x^15","A",0
620,1,59,0,0.770537," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^18,x, algorithm=""fricas"")","-\frac{21879 \, b^{5} x^{10} + 85085 \, a b^{4} x^{8} + 139230 \, a^{2} b^{3} x^{6} + 117810 \, a^{3} b^{2} x^{4} + 51051 \, a^{4} b x^{2} + 9009 \, a^{5}}{153153 \, x^{17}}"," ",0,"-1/153153*(21879*b^5*x^10 + 85085*a*b^4*x^8 + 139230*a^2*b^3*x^6 + 117810*a^3*b^2*x^4 + 51051*a^4*b*x^2 + 9009*a^5)/x^17","A",0
621,1,59,0,0.737018," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^20,x, algorithm=""fricas"")","-\frac{46189 \, b^{5} x^{10} + 188955 \, a b^{4} x^{8} + 319770 \, a^{2} b^{3} x^{6} + 277134 \, a^{3} b^{2} x^{4} + 122265 \, a^{4} b x^{2} + 21879 \, a^{5}}{415701 \, x^{19}}"," ",0,"-1/415701*(46189*b^5*x^10 + 188955*a*b^4*x^8 + 319770*a^2*b^3*x^6 + 277134*a^3*b^2*x^4 + 122265*a^4*b*x^2 + 21879*a^5)/x^19","A",0
622,1,59,0,1.512637," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^22,x, algorithm=""fricas"")","-\frac{88179 \, b^{5} x^{10} + 373065 \, a b^{4} x^{8} + 646646 \, a^{2} b^{3} x^{6} + 570570 \, a^{3} b^{2} x^{4} + 255255 \, a^{4} b x^{2} + 46189 \, a^{5}}{969969 \, x^{21}}"," ",0,"-1/969969*(88179*b^5*x^10 + 373065*a*b^4*x^8 + 646646*a^2*b^3*x^6 + 570570*a^3*b^2*x^4 + 255255*a^4*b*x^2 + 46189*a^5)/x^21","A",0
623,1,59,0,1.340021," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^24,x, algorithm=""fricas"")","-\frac{156009 \, b^{5} x^{10} + 676039 \, a b^{4} x^{8} + 1193010 \, a^{2} b^{3} x^{6} + 1067430 \, a^{3} b^{2} x^{4} + 482885 \, a^{4} b x^{2} + 88179 \, a^{5}}{2028117 \, x^{23}}"," ",0,"-1/2028117*(156009*b^5*x^10 + 676039*a*b^4*x^8 + 1193010*a^2*b^3*x^6 + 1067430*a^3*b^2*x^4 + 482885*a^4*b*x^2 + 88179*a^5)/x^23","A",0
624,1,33,0,0.707301," ","integrate(x^5/((b*x^2+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{b^{2} x^{4} - 2 \, a b x^{2} + 2 \, a^{2} \log\left(b x^{2} + a\right)}{4 \, b^{3}}"," ",0,"1/4*(b^2*x^4 - 2*a*b*x^2 + 2*a^2*log(b*x^2 + a))/b^3","A",0
625,1,22,0,0.673018," ","integrate(x^3/((b*x^2+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{b x^{2} - a \log\left(b x^{2} + a\right)}{2 \, b^{2}}"," ",0,"1/2*(b*x^2 - a*log(b*x^2 + a))/b^2","A",0
626,1,13,0,1.625038," ","integrate(x/((b*x^2+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{\log\left(b x^{2} + a\right)}{2 \, b}"," ",0,"1/2*log(b*x^2 + a)/b","A",0
627,1,18,0,0.888600," ","integrate(1/x/((b*x^2+a)^2)^(1/2),x, algorithm=""fricas"")","-\frac{\log\left(b x^{2} + a\right) - 2 \, \log\left(x\right)}{2 \, a}"," ",0,"-1/2*(log(b*x^2 + a) - 2*log(x))/a","A",0
628,1,33,0,0.577769," ","integrate(1/x^3/((b*x^2+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{b x^{2} \log\left(b x^{2} + a\right) - 2 \, b x^{2} \log\left(x\right) - a}{2 \, a^{2} x^{2}}"," ",0,"1/2*(b*x^2*log(b*x^2 + a) - 2*b*x^2*log(x) - a)/(a^2*x^2)","A",0
629,1,99,0,3.012013," ","integrate(x^4/((b*x^2+a)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, b x^{3} + 3 \, a \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} + 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right) - 6 \, a x}{6 \, b^{2}}, \frac{b x^{3} + 3 \, a \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) - 3 \, a x}{3 \, b^{2}}\right]"," ",0,"[1/6*(2*b*x^3 + 3*a*sqrt(-a/b)*log((b*x^2 + 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)) - 6*a*x)/b^2, 1/3*(b*x^3 + 3*a*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) - 3*a*x)/b^2]","A",0
630,1,82,0,0.787843," ","integrate(x^2/((b*x^2+a)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} - 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right) + 2 \, x}{2 \, b}, -\frac{\sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) - x}{b}\right]"," ",0,"[1/2*(sqrt(-a/b)*log((b*x^2 - 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)) + 2*x)/b, -(sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) - x)/b]","A",0
631,1,67,0,1.274146," ","integrate(1/((b*x^2+a)^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right)}{2 \, a b}, \frac{\sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right)}{a b}\right]"," ",0,"[-1/2*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a))/(a*b), sqrt(a*b)*arctan(sqrt(a*b)*x/a)/(a*b)]","A",0
632,1,82,0,1.563821," ","integrate(1/x^2/((b*x^2+a)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{x \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) - 2}{2 \, a x}, -\frac{x \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) + 1}{a x}\right]"," ",0,"[1/2*(x*sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) - 2)/(a*x), -(x*sqrt(b/a)*arctan(x*sqrt(b/a)) + 1)/(a*x)]","A",0
633,1,106,0,1.195484," ","integrate(1/x^4/((b*x^2+a)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, b x^{3} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} + 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) + 6 \, b x^{2} - 2 \, a}{6 \, a^{2} x^{3}}, \frac{3 \, b x^{3} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) + 3 \, b x^{2} - a}{3 \, a^{2} x^{3}}\right]"," ",0,"[1/6*(3*b*x^3*sqrt(-b/a)*log((b*x^2 + 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) + 6*b*x^2 - 2*a)/(a^2*x^3), 1/3*(3*b*x^3*sqrt(b/a)*arctan(x*sqrt(b/a)) + 3*b*x^2 - a)/(a^2*x^3)]","A",0
634,1,91,0,1.492690," ","integrate(x^7/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""fricas"")","\frac{2 \, b^{3} x^{6} + 4 \, a b^{2} x^{4} - 4 \, a^{2} b x^{2} - 5 \, a^{3} - 6 \, {\left(a b^{2} x^{4} + 2 \, a^{2} b x^{2} + a^{3}\right)} \log\left(b x^{2} + a\right)}{4 \, {\left(b^{6} x^{4} + 2 \, a b^{5} x^{2} + a^{2} b^{4}\right)}}"," ",0,"1/4*(2*b^3*x^6 + 4*a*b^2*x^4 - 4*a^2*b*x^2 - 5*a^3 - 6*(a*b^2*x^4 + 2*a^2*b*x^2 + a^3)*log(b*x^2 + a))/(b^6*x^4 + 2*a*b^5*x^2 + a^2*b^4)","A",0
635,1,69,0,1.029415," ","integrate(x^5/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""fricas"")","\frac{4 \, a b x^{2} + 3 \, a^{2} + 2 \, {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)} \log\left(b x^{2} + a\right)}{4 \, {\left(b^{5} x^{4} + 2 \, a b^{4} x^{2} + a^{2} b^{3}\right)}}"," ",0,"1/4*(4*a*b*x^2 + 3*a^2 + 2*(b^2*x^4 + 2*a*b*x^2 + a^2)*log(b*x^2 + a))/(b^5*x^4 + 2*a*b^4*x^2 + a^2*b^3)","A",0
636,1,36,0,0.716205," ","integrate(x^3/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, b x^{2} + a}{4 \, {\left(b^{4} x^{4} + 2 \, a b^{3} x^{2} + a^{2} b^{2}\right)}}"," ",0,"-1/4*(2*b*x^2 + a)/(b^4*x^4 + 2*a*b^3*x^2 + a^2*b^2)","A",0
637,1,26,0,0.874985," ","integrate(x/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""fricas"")","-\frac{1}{4 \, {\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)}}"," ",0,"-1/4/(b^3*x^4 + 2*a*b^2*x^2 + a^2*b)","A",0
638,1,90,0,2.924235," ","integrate(1/x/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""fricas"")","\frac{2 \, a b x^{2} + 3 \, a^{2} - 2 \, {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)} \log\left(b x^{2} + a\right) + 4 \, {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)} \log\left(x\right)}{4 \, {\left(a^{3} b^{2} x^{4} + 2 \, a^{4} b x^{2} + a^{5}\right)}}"," ",0,"1/4*(2*a*b*x^2 + 3*a^2 - 2*(b^2*x^4 + 2*a*b*x^2 + a^2)*log(b*x^2 + a) + 4*(b^2*x^4 + 2*a*b*x^2 + a^2)*log(x))/(a^3*b^2*x^4 + 2*a^4*b*x^2 + a^5)","A",0
639,1,119,0,1.055197," ","integrate(1/x^3/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""fricas"")","-\frac{6 \, a b^{2} x^{4} + 9 \, a^{2} b x^{2} + 2 \, a^{3} - 6 \, {\left(b^{3} x^{6} + 2 \, a b^{2} x^{4} + a^{2} b x^{2}\right)} \log\left(b x^{2} + a\right) + 12 \, {\left(b^{3} x^{6} + 2 \, a b^{2} x^{4} + a^{2} b x^{2}\right)} \log\left(x\right)}{4 \, {\left(a^{4} b^{2} x^{6} + 2 \, a^{5} b x^{4} + a^{6} x^{2}\right)}}"," ",0,"-1/4*(6*a*b^2*x^4 + 9*a^2*b*x^2 + 2*a^3 - 6*(b^3*x^6 + 2*a*b^2*x^4 + a^2*b*x^2)*log(b*x^2 + a) + 12*(b^3*x^6 + 2*a*b^2*x^4 + a^2*b*x^2)*log(x))/(a^4*b^2*x^6 + 2*a^5*b*x^4 + a^6*x^2)","A",0
640,1,188,0,1.333235," ","integrate(x^4/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""fricas"")","\left[-\frac{10 \, a b^{2} x^{3} + 6 \, a^{2} b x + 3 \, {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right)}{16 \, {\left(a b^{5} x^{4} + 2 \, a^{2} b^{4} x^{2} + a^{3} b^{3}\right)}}, -\frac{5 \, a b^{2} x^{3} + 3 \, a^{2} b x - 3 \, {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right)}{8 \, {\left(a b^{5} x^{4} + 2 \, a^{2} b^{4} x^{2} + a^{3} b^{3}\right)}}\right]"," ",0,"[-1/16*(10*a*b^2*x^3 + 6*a^2*b*x + 3*(b^2*x^4 + 2*a*b*x^2 + a^2)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)))/(a*b^5*x^4 + 2*a^2*b^4*x^2 + a^3*b^3), -1/8*(5*a*b^2*x^3 + 3*a^2*b*x - 3*(b^2*x^4 + 2*a*b*x^2 + a^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/a))/(a*b^5*x^4 + 2*a^2*b^4*x^2 + a^3*b^3)]","A",0
641,1,190,0,1.212731," ","integrate(x^2/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{2 \, a b^{2} x^{3} - 2 \, a^{2} b x - {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right)}{16 \, {\left(a^{2} b^{4} x^{4} + 2 \, a^{3} b^{3} x^{2} + a^{4} b^{2}\right)}}, \frac{a b^{2} x^{3} - a^{2} b x + {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right)}{8 \, {\left(a^{2} b^{4} x^{4} + 2 \, a^{3} b^{3} x^{2} + a^{4} b^{2}\right)}}\right]"," ",0,"[1/16*(2*a*b^2*x^3 - 2*a^2*b*x - (b^2*x^4 + 2*a*b*x^2 + a^2)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)))/(a^2*b^4*x^4 + 2*a^3*b^3*x^2 + a^4*b^2), 1/8*(a*b^2*x^3 - a^2*b*x + (b^2*x^4 + 2*a*b*x^2 + a^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/a))/(a^2*b^4*x^4 + 2*a^3*b^3*x^2 + a^4*b^2)]","A",0
642,1,188,0,1.162261," ","integrate(1/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{6 \, a b^{2} x^{3} + 10 \, a^{2} b x - 3 \, {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right)}{16 \, {\left(a^{3} b^{3} x^{4} + 2 \, a^{4} b^{2} x^{2} + a^{5} b\right)}}, \frac{3 \, a b^{2} x^{3} + 5 \, a^{2} b x + 3 \, {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right)}{8 \, {\left(a^{3} b^{3} x^{4} + 2 \, a^{4} b^{2} x^{2} + a^{5} b\right)}}\right]"," ",0,"[1/16*(6*a*b^2*x^3 + 10*a^2*b*x - 3*(b^2*x^4 + 2*a*b*x^2 + a^2)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)))/(a^3*b^3*x^4 + 2*a^4*b^2*x^2 + a^5*b), 1/8*(3*a*b^2*x^3 + 5*a^2*b*x + 3*(b^2*x^4 + 2*a*b*x^2 + a^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/a))/(a^3*b^3*x^4 + 2*a^4*b^2*x^2 + a^5*b)]","A",0
643,1,202,0,1.298280," ","integrate(1/x^2/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""fricas"")","\left[-\frac{30 \, b^{2} x^{4} + 50 \, a b x^{2} - 15 \, {\left(b^{2} x^{5} + 2 \, a b x^{3} + a^{2} x\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) + 16 \, a^{2}}{16 \, {\left(a^{3} b^{2} x^{5} + 2 \, a^{4} b x^{3} + a^{5} x\right)}}, -\frac{15 \, b^{2} x^{4} + 25 \, a b x^{2} + 15 \, {\left(b^{2} x^{5} + 2 \, a b x^{3} + a^{2} x\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) + 8 \, a^{2}}{8 \, {\left(a^{3} b^{2} x^{5} + 2 \, a^{4} b x^{3} + a^{5} x\right)}}\right]"," ",0,"[-1/16*(30*b^2*x^4 + 50*a*b*x^2 - 15*(b^2*x^5 + 2*a*b*x^3 + a^2*x)*sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) + 16*a^2)/(a^3*b^2*x^5 + 2*a^4*b*x^3 + a^5*x), -1/8*(15*b^2*x^4 + 25*a*b*x^2 + 15*(b^2*x^5 + 2*a*b*x^3 + a^2*x)*sqrt(b/a)*arctan(x*sqrt(b/a)) + 8*a^2)/(a^3*b^2*x^5 + 2*a^4*b*x^3 + a^5*x)]","A",0
644,1,238,0,2.224652," ","integrate(1/x^4/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{210 \, b^{3} x^{6} + 350 \, a b^{2} x^{4} + 112 \, a^{2} b x^{2} - 16 \, a^{3} + 105 \, {\left(b^{3} x^{7} + 2 \, a b^{2} x^{5} + a^{2} b x^{3}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} + 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right)}{48 \, {\left(a^{4} b^{2} x^{7} + 2 \, a^{5} b x^{5} + a^{6} x^{3}\right)}}, \frac{105 \, b^{3} x^{6} + 175 \, a b^{2} x^{4} + 56 \, a^{2} b x^{2} - 8 \, a^{3} + 105 \, {\left(b^{3} x^{7} + 2 \, a b^{2} x^{5} + a^{2} b x^{3}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right)}{24 \, {\left(a^{4} b^{2} x^{7} + 2 \, a^{5} b x^{5} + a^{6} x^{3}\right)}}\right]"," ",0,"[1/48*(210*b^3*x^6 + 350*a*b^2*x^4 + 112*a^2*b*x^2 - 16*a^3 + 105*(b^3*x^7 + 2*a*b^2*x^5 + a^2*b*x^3)*sqrt(-b/a)*log((b*x^2 + 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)))/(a^4*b^2*x^7 + 2*a^5*b*x^5 + a^6*x^3), 1/24*(105*b^3*x^6 + 175*a*b^2*x^4 + 56*a^2*b*x^2 - 8*a^3 + 105*(b^3*x^7 + 2*a*b^2*x^5 + a^2*b*x^3)*sqrt(b/a)*arctan(x*sqrt(b/a)))/(a^4*b^2*x^7 + 2*a^5*b*x^5 + a^6*x^3)]","A",0
645,1,157,0,0.627875," ","integrate(x^11/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""fricas"")","\frac{12 \, b^{5} x^{10} + 48 \, a b^{4} x^{8} - 48 \, a^{2} b^{3} x^{6} - 252 \, a^{3} b^{2} x^{4} - 248 \, a^{4} b x^{2} - 77 \, a^{5} - 60 \, {\left(a b^{4} x^{8} + 4 \, a^{2} b^{3} x^{6} + 6 \, a^{3} b^{2} x^{4} + 4 \, a^{4} b x^{2} + a^{5}\right)} \log\left(b x^{2} + a\right)}{24 \, {\left(b^{10} x^{8} + 4 \, a b^{9} x^{6} + 6 \, a^{2} b^{8} x^{4} + 4 \, a^{3} b^{7} x^{2} + a^{4} b^{6}\right)}}"," ",0,"1/24*(12*b^5*x^10 + 48*a*b^4*x^8 - 48*a^2*b^3*x^6 - 252*a^3*b^2*x^4 - 248*a^4*b*x^2 - 77*a^5 - 60*(a*b^4*x^8 + 4*a^2*b^3*x^6 + 6*a^3*b^2*x^4 + 4*a^4*b*x^2 + a^5)*log(b*x^2 + a))/(b^10*x^8 + 4*a*b^9*x^6 + 6*a^2*b^8*x^4 + 4*a^3*b^7*x^2 + a^4*b^6)","A",0
646,1,135,0,2.770566," ","integrate(x^9/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""fricas"")","\frac{48 \, a b^{3} x^{6} + 108 \, a^{2} b^{2} x^{4} + 88 \, a^{3} b x^{2} + 25 \, a^{4} + 12 \, {\left(b^{4} x^{8} + 4 \, a b^{3} x^{6} + 6 \, a^{2} b^{2} x^{4} + 4 \, a^{3} b x^{2} + a^{4}\right)} \log\left(b x^{2} + a\right)}{24 \, {\left(b^{9} x^{8} + 4 \, a b^{8} x^{6} + 6 \, a^{2} b^{7} x^{4} + 4 \, a^{3} b^{6} x^{2} + a^{4} b^{5}\right)}}"," ",0,"1/24*(48*a*b^3*x^6 + 108*a^2*b^2*x^4 + 88*a^3*b*x^2 + 25*a^4 + 12*(b^4*x^8 + 4*a*b^3*x^6 + 6*a^2*b^2*x^4 + 4*a^3*b*x^2 + a^4)*log(b*x^2 + a))/(b^9*x^8 + 4*a*b^8*x^6 + 6*a^2*b^7*x^4 + 4*a^3*b^6*x^2 + a^4*b^5)","A",0
647,1,80,0,1.144163," ","integrate(x^7/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""fricas"")","-\frac{4 \, b^{3} x^{6} + 6 \, a b^{2} x^{4} + 4 \, a^{2} b x^{2} + a^{3}}{8 \, {\left(b^{8} x^{8} + 4 \, a b^{7} x^{6} + 6 \, a^{2} b^{6} x^{4} + 4 \, a^{3} b^{5} x^{2} + a^{4} b^{4}\right)}}"," ",0,"-1/8*(4*b^3*x^6 + 6*a*b^2*x^4 + 4*a^2*b*x^2 + a^3)/(b^8*x^8 + 4*a*b^7*x^6 + 6*a^2*b^6*x^4 + 4*a^3*b^5*x^2 + a^4*b^4)","B",0
648,1,69,0,2.672855," ","integrate(x^5/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""fricas"")","-\frac{6 \, b^{2} x^{4} + 4 \, a b x^{2} + a^{2}}{24 \, {\left(b^{7} x^{8} + 4 \, a b^{6} x^{6} + 6 \, a^{2} b^{5} x^{4} + 4 \, a^{3} b^{4} x^{2} + a^{4} b^{3}\right)}}"," ",0,"-1/24*(6*b^2*x^4 + 4*a*b*x^2 + a^2)/(b^7*x^8 + 4*a*b^6*x^6 + 6*a^2*b^5*x^4 + 4*a^3*b^4*x^2 + a^4*b^3)","A",0
649,1,58,0,1.211853," ","integrate(x^3/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""fricas"")","-\frac{4 \, b x^{2} + a}{24 \, {\left(b^{6} x^{8} + 4 \, a b^{5} x^{6} + 6 \, a^{2} b^{4} x^{4} + 4 \, a^{3} b^{3} x^{2} + a^{4} b^{2}\right)}}"," ",0,"-1/24*(4*b*x^2 + a)/(b^6*x^8 + 4*a*b^5*x^6 + 6*a^2*b^4*x^4 + 4*a^3*b^3*x^2 + a^4*b^2)","A",0
650,1,48,0,4.600319," ","integrate(x/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""fricas"")","-\frac{1}{8 \, {\left(b^{5} x^{8} + 4 \, a b^{4} x^{6} + 6 \, a^{2} b^{3} x^{4} + 4 \, a^{3} b^{2} x^{2} + a^{4} b\right)}}"," ",0,"-1/8/(b^5*x^8 + 4*a*b^4*x^6 + 6*a^2*b^3*x^4 + 4*a^3*b^2*x^2 + a^4*b)","A",0
651,1,178,0,1.101298," ","integrate(1/x/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""fricas"")","\frac{12 \, a b^{3} x^{6} + 42 \, a^{2} b^{2} x^{4} + 52 \, a^{3} b x^{2} + 25 \, a^{4} - 12 \, {\left(b^{4} x^{8} + 4 \, a b^{3} x^{6} + 6 \, a^{2} b^{2} x^{4} + 4 \, a^{3} b x^{2} + a^{4}\right)} \log\left(b x^{2} + a\right) + 24 \, {\left(b^{4} x^{8} + 4 \, a b^{3} x^{6} + 6 \, a^{2} b^{2} x^{4} + 4 \, a^{3} b x^{2} + a^{4}\right)} \log\left(x\right)}{24 \, {\left(a^{5} b^{4} x^{8} + 4 \, a^{6} b^{3} x^{6} + 6 \, a^{7} b^{2} x^{4} + 4 \, a^{8} b x^{2} + a^{9}\right)}}"," ",0,"1/24*(12*a*b^3*x^6 + 42*a^2*b^2*x^4 + 52*a^3*b*x^2 + 25*a^4 - 12*(b^4*x^8 + 4*a*b^3*x^6 + 6*a^2*b^2*x^4 + 4*a^3*b*x^2 + a^4)*log(b*x^2 + a) + 24*(b^4*x^8 + 4*a*b^3*x^6 + 6*a^2*b^2*x^4 + 4*a^3*b*x^2 + a^4)*log(x))/(a^5*b^4*x^8 + 4*a^6*b^3*x^6 + 6*a^7*b^2*x^4 + 4*a^8*b*x^2 + a^9)","A",0
652,1,207,0,0.671602," ","integrate(1/x^3/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""fricas"")","-\frac{60 \, a b^{4} x^{8} + 210 \, a^{2} b^{3} x^{6} + 260 \, a^{3} b^{2} x^{4} + 125 \, a^{4} b x^{2} + 12 \, a^{5} - 60 \, {\left(b^{5} x^{10} + 4 \, a b^{4} x^{8} + 6 \, a^{2} b^{3} x^{6} + 4 \, a^{3} b^{2} x^{4} + a^{4} b x^{2}\right)} \log\left(b x^{2} + a\right) + 120 \, {\left(b^{5} x^{10} + 4 \, a b^{4} x^{8} + 6 \, a^{2} b^{3} x^{6} + 4 \, a^{3} b^{2} x^{4} + a^{4} b x^{2}\right)} \log\left(x\right)}{24 \, {\left(a^{6} b^{4} x^{10} + 4 \, a^{7} b^{3} x^{8} + 6 \, a^{8} b^{2} x^{6} + 4 \, a^{9} b x^{4} + a^{10} x^{2}\right)}}"," ",0,"-1/24*(60*a*b^4*x^8 + 210*a^2*b^3*x^6 + 260*a^3*b^2*x^4 + 125*a^4*b*x^2 + 12*a^5 - 60*(b^5*x^10 + 4*a*b^4*x^8 + 6*a^2*b^3*x^6 + 4*a^3*b^2*x^4 + a^4*b*x^2)*log(b*x^2 + a) + 120*(b^5*x^10 + 4*a*b^4*x^8 + 6*a^2*b^3*x^6 + 4*a^3*b^2*x^4 + a^4*b*x^2)*log(x))/(a^6*b^4*x^10 + 4*a^7*b^3*x^8 + 6*a^8*b^2*x^6 + 4*a^9*b*x^4 + a^10*x^2)","A",0
653,1,324,0,3.007091," ","integrate(x^6/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{30 \, a b^{4} x^{7} - 146 \, a^{2} b^{3} x^{5} - 110 \, a^{3} b^{2} x^{3} - 30 \, a^{4} b x - 15 \, {\left(b^{4} x^{8} + 4 \, a b^{3} x^{6} + 6 \, a^{2} b^{2} x^{4} + 4 \, a^{3} b x^{2} + a^{4}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right)}{768 \, {\left(a^{2} b^{8} x^{8} + 4 \, a^{3} b^{7} x^{6} + 6 \, a^{4} b^{6} x^{4} + 4 \, a^{5} b^{5} x^{2} + a^{6} b^{4}\right)}}, \frac{15 \, a b^{4} x^{7} - 73 \, a^{2} b^{3} x^{5} - 55 \, a^{3} b^{2} x^{3} - 15 \, a^{4} b x + 15 \, {\left(b^{4} x^{8} + 4 \, a b^{3} x^{6} + 6 \, a^{2} b^{2} x^{4} + 4 \, a^{3} b x^{2} + a^{4}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right)}{384 \, {\left(a^{2} b^{8} x^{8} + 4 \, a^{3} b^{7} x^{6} + 6 \, a^{4} b^{6} x^{4} + 4 \, a^{5} b^{5} x^{2} + a^{6} b^{4}\right)}}\right]"," ",0,"[1/768*(30*a*b^4*x^7 - 146*a^2*b^3*x^5 - 110*a^3*b^2*x^3 - 30*a^4*b*x - 15*(b^4*x^8 + 4*a*b^3*x^6 + 6*a^2*b^2*x^4 + 4*a^3*b*x^2 + a^4)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)))/(a^2*b^8*x^8 + 4*a^3*b^7*x^6 + 6*a^4*b^6*x^4 + 4*a^5*b^5*x^2 + a^6*b^4), 1/384*(15*a*b^4*x^7 - 73*a^2*b^3*x^5 - 55*a^3*b^2*x^3 - 15*a^4*b*x + 15*(b^4*x^8 + 4*a*b^3*x^6 + 6*a^2*b^2*x^4 + 4*a^3*b*x^2 + a^4)*sqrt(a*b)*arctan(sqrt(a*b)*x/a))/(a^2*b^8*x^8 + 4*a^3*b^7*x^6 + 6*a^4*b^6*x^4 + 4*a^5*b^5*x^2 + a^6*b^4)]","A",0
654,1,324,0,1.664969," ","integrate(x^4/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{6 \, a b^{4} x^{7} + 22 \, a^{2} b^{3} x^{5} - 22 \, a^{3} b^{2} x^{3} - 6 \, a^{4} b x - 3 \, {\left(b^{4} x^{8} + 4 \, a b^{3} x^{6} + 6 \, a^{2} b^{2} x^{4} + 4 \, a^{3} b x^{2} + a^{4}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right)}{256 \, {\left(a^{3} b^{7} x^{8} + 4 \, a^{4} b^{6} x^{6} + 6 \, a^{5} b^{5} x^{4} + 4 \, a^{6} b^{4} x^{2} + a^{7} b^{3}\right)}}, \frac{3 \, a b^{4} x^{7} + 11 \, a^{2} b^{3} x^{5} - 11 \, a^{3} b^{2} x^{3} - 3 \, a^{4} b x + 3 \, {\left(b^{4} x^{8} + 4 \, a b^{3} x^{6} + 6 \, a^{2} b^{2} x^{4} + 4 \, a^{3} b x^{2} + a^{4}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right)}{128 \, {\left(a^{3} b^{7} x^{8} + 4 \, a^{4} b^{6} x^{6} + 6 \, a^{5} b^{5} x^{4} + 4 \, a^{6} b^{4} x^{2} + a^{7} b^{3}\right)}}\right]"," ",0,"[1/256*(6*a*b^4*x^7 + 22*a^2*b^3*x^5 - 22*a^3*b^2*x^3 - 6*a^4*b*x - 3*(b^4*x^8 + 4*a*b^3*x^6 + 6*a^2*b^2*x^4 + 4*a^3*b*x^2 + a^4)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)))/(a^3*b^7*x^8 + 4*a^4*b^6*x^6 + 6*a^5*b^5*x^4 + 4*a^6*b^4*x^2 + a^7*b^3), 1/128*(3*a*b^4*x^7 + 11*a^2*b^3*x^5 - 11*a^3*b^2*x^3 - 3*a^4*b*x + 3*(b^4*x^8 + 4*a*b^3*x^6 + 6*a^2*b^2*x^4 + 4*a^3*b*x^2 + a^4)*sqrt(a*b)*arctan(sqrt(a*b)*x/a))/(a^3*b^7*x^8 + 4*a^4*b^6*x^6 + 6*a^5*b^5*x^4 + 4*a^6*b^4*x^2 + a^7*b^3)]","A",0
655,1,324,0,1.269766," ","integrate(x^2/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{30 \, a b^{4} x^{7} + 110 \, a^{2} b^{3} x^{5} + 146 \, a^{3} b^{2} x^{3} - 30 \, a^{4} b x - 15 \, {\left(b^{4} x^{8} + 4 \, a b^{3} x^{6} + 6 \, a^{2} b^{2} x^{4} + 4 \, a^{3} b x^{2} + a^{4}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right)}{768 \, {\left(a^{4} b^{6} x^{8} + 4 \, a^{5} b^{5} x^{6} + 6 \, a^{6} b^{4} x^{4} + 4 \, a^{7} b^{3} x^{2} + a^{8} b^{2}\right)}}, \frac{15 \, a b^{4} x^{7} + 55 \, a^{2} b^{3} x^{5} + 73 \, a^{3} b^{2} x^{3} - 15 \, a^{4} b x + 15 \, {\left(b^{4} x^{8} + 4 \, a b^{3} x^{6} + 6 \, a^{2} b^{2} x^{4} + 4 \, a^{3} b x^{2} + a^{4}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right)}{384 \, {\left(a^{4} b^{6} x^{8} + 4 \, a^{5} b^{5} x^{6} + 6 \, a^{6} b^{4} x^{4} + 4 \, a^{7} b^{3} x^{2} + a^{8} b^{2}\right)}}\right]"," ",0,"[1/768*(30*a*b^4*x^7 + 110*a^2*b^3*x^5 + 146*a^3*b^2*x^3 - 30*a^4*b*x - 15*(b^4*x^8 + 4*a*b^3*x^6 + 6*a^2*b^2*x^4 + 4*a^3*b*x^2 + a^4)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)))/(a^4*b^6*x^8 + 4*a^5*b^5*x^6 + 6*a^6*b^4*x^4 + 4*a^7*b^3*x^2 + a^8*b^2), 1/384*(15*a*b^4*x^7 + 55*a^2*b^3*x^5 + 73*a^3*b^2*x^3 - 15*a^4*b*x + 15*(b^4*x^8 + 4*a*b^3*x^6 + 6*a^2*b^2*x^4 + 4*a^3*b*x^2 + a^4)*sqrt(a*b)*arctan(sqrt(a*b)*x/a))/(a^4*b^6*x^8 + 4*a^5*b^5*x^6 + 6*a^6*b^4*x^4 + 4*a^7*b^3*x^2 + a^8*b^2)]","A",0
656,1,320,0,2.215727," ","integrate(1/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{210 \, a b^{4} x^{7} + 770 \, a^{2} b^{3} x^{5} + 1022 \, a^{3} b^{2} x^{3} + 558 \, a^{4} b x - 105 \, {\left(b^{4} x^{8} + 4 \, a b^{3} x^{6} + 6 \, a^{2} b^{2} x^{4} + 4 \, a^{3} b x^{2} + a^{4}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right)}{768 \, {\left(a^{5} b^{5} x^{8} + 4 \, a^{6} b^{4} x^{6} + 6 \, a^{7} b^{3} x^{4} + 4 \, a^{8} b^{2} x^{2} + a^{9} b\right)}}, \frac{105 \, a b^{4} x^{7} + 385 \, a^{2} b^{3} x^{5} + 511 \, a^{3} b^{2} x^{3} + 279 \, a^{4} b x + 105 \, {\left(b^{4} x^{8} + 4 \, a b^{3} x^{6} + 6 \, a^{2} b^{2} x^{4} + 4 \, a^{3} b x^{2} + a^{4}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right)}{384 \, {\left(a^{5} b^{5} x^{8} + 4 \, a^{6} b^{4} x^{6} + 6 \, a^{7} b^{3} x^{4} + 4 \, a^{8} b^{2} x^{2} + a^{9} b\right)}}\right]"," ",0,"[1/768*(210*a*b^4*x^7 + 770*a^2*b^3*x^5 + 1022*a^3*b^2*x^3 + 558*a^4*b*x - 105*(b^4*x^8 + 4*a*b^3*x^6 + 6*a^2*b^2*x^4 + 4*a^3*b*x^2 + a^4)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)))/(a^5*b^5*x^8 + 4*a^6*b^4*x^6 + 6*a^7*b^3*x^4 + 4*a^8*b^2*x^2 + a^9*b), 1/384*(105*a*b^4*x^7 + 385*a^2*b^3*x^5 + 511*a^3*b^2*x^3 + 279*a^4*b*x + 105*(b^4*x^8 + 4*a*b^3*x^6 + 6*a^2*b^2*x^4 + 4*a^3*b*x^2 + a^4)*sqrt(a*b)*arctan(sqrt(a*b)*x/a))/(a^5*b^5*x^8 + 4*a^6*b^4*x^6 + 6*a^7*b^3*x^4 + 4*a^8*b^2*x^2 + a^9*b)]","A",0
657,1,334,0,3.021410," ","integrate(1/x^2/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""fricas"")","\left[-\frac{630 \, b^{4} x^{8} + 2310 \, a b^{3} x^{6} + 3066 \, a^{2} b^{2} x^{4} + 1674 \, a^{3} b x^{2} + 256 \, a^{4} - 315 \, {\left(b^{4} x^{9} + 4 \, a b^{3} x^{7} + 6 \, a^{2} b^{2} x^{5} + 4 \, a^{3} b x^{3} + a^{4} x\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right)}{256 \, {\left(a^{5} b^{4} x^{9} + 4 \, a^{6} b^{3} x^{7} + 6 \, a^{7} b^{2} x^{5} + 4 \, a^{8} b x^{3} + a^{9} x\right)}}, -\frac{315 \, b^{4} x^{8} + 1155 \, a b^{3} x^{6} + 1533 \, a^{2} b^{2} x^{4} + 837 \, a^{3} b x^{2} + 128 \, a^{4} + 315 \, {\left(b^{4} x^{9} + 4 \, a b^{3} x^{7} + 6 \, a^{2} b^{2} x^{5} + 4 \, a^{3} b x^{3} + a^{4} x\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right)}{128 \, {\left(a^{5} b^{4} x^{9} + 4 \, a^{6} b^{3} x^{7} + 6 \, a^{7} b^{2} x^{5} + 4 \, a^{8} b x^{3} + a^{9} x\right)}}\right]"," ",0,"[-1/256*(630*b^4*x^8 + 2310*a*b^3*x^6 + 3066*a^2*b^2*x^4 + 1674*a^3*b*x^2 + 256*a^4 - 315*(b^4*x^9 + 4*a*b^3*x^7 + 6*a^2*b^2*x^5 + 4*a^3*b*x^3 + a^4*x)*sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)))/(a^5*b^4*x^9 + 4*a^6*b^3*x^7 + 6*a^7*b^2*x^5 + 4*a^8*b*x^3 + a^9*x), -1/128*(315*b^4*x^8 + 1155*a*b^3*x^6 + 1533*a^2*b^2*x^4 + 837*a^3*b*x^2 + 128*a^4 + 315*(b^4*x^9 + 4*a*b^3*x^7 + 6*a^2*b^2*x^5 + 4*a^3*b*x^3 + a^4*x)*sqrt(b/a)*arctan(x*sqrt(b/a)))/(a^5*b^4*x^9 + 4*a^6*b^3*x^7 + 6*a^7*b^2*x^5 + 4*a^8*b*x^3 + a^9*x)]","A",0
658,1,370,0,0.957267," ","integrate(1/x^4/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{6930 \, b^{5} x^{10} + 25410 \, a b^{4} x^{8} + 33726 \, a^{2} b^{3} x^{6} + 18414 \, a^{3} b^{2} x^{4} + 2816 \, a^{4} b x^{2} - 256 \, a^{5} + 3465 \, {\left(b^{5} x^{11} + 4 \, a b^{4} x^{9} + 6 \, a^{2} b^{3} x^{7} + 4 \, a^{3} b^{2} x^{5} + a^{4} b x^{3}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} + 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right)}{768 \, {\left(a^{6} b^{4} x^{11} + 4 \, a^{7} b^{3} x^{9} + 6 \, a^{8} b^{2} x^{7} + 4 \, a^{9} b x^{5} + a^{10} x^{3}\right)}}, \frac{3465 \, b^{5} x^{10} + 12705 \, a b^{4} x^{8} + 16863 \, a^{2} b^{3} x^{6} + 9207 \, a^{3} b^{2} x^{4} + 1408 \, a^{4} b x^{2} - 128 \, a^{5} + 3465 \, {\left(b^{5} x^{11} + 4 \, a b^{4} x^{9} + 6 \, a^{2} b^{3} x^{7} + 4 \, a^{3} b^{2} x^{5} + a^{4} b x^{3}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right)}{384 \, {\left(a^{6} b^{4} x^{11} + 4 \, a^{7} b^{3} x^{9} + 6 \, a^{8} b^{2} x^{7} + 4 \, a^{9} b x^{5} + a^{10} x^{3}\right)}}\right]"," ",0,"[1/768*(6930*b^5*x^10 + 25410*a*b^4*x^8 + 33726*a^2*b^3*x^6 + 18414*a^3*b^2*x^4 + 2816*a^4*b*x^2 - 256*a^5 + 3465*(b^5*x^11 + 4*a*b^4*x^9 + 6*a^2*b^3*x^7 + 4*a^3*b^2*x^5 + a^4*b*x^3)*sqrt(-b/a)*log((b*x^2 + 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)))/(a^6*b^4*x^11 + 4*a^7*b^3*x^9 + 6*a^8*b^2*x^7 + 4*a^9*b*x^5 + a^10*x^3), 1/384*(3465*b^5*x^10 + 12705*a*b^4*x^8 + 16863*a^2*b^3*x^6 + 9207*a^3*b^2*x^4 + 1408*a^4*b*x^2 - 128*a^5 + 3465*(b^5*x^11 + 4*a*b^4*x^9 + 6*a^2*b^3*x^7 + 4*a^3*b^2*x^5 + a^4*b*x^3)*sqrt(b/a)*arctan(x*sqrt(b/a)))/(a^6*b^4*x^11 + 4*a^7*b^3*x^9 + 6*a^8*b^2*x^7 + 4*a^9*b*x^5 + a^10*x^3)]","A",0
659,0,0,0,1.635358," ","integrate(x^2/(b^2*x^4+2*a*b*x^2+a^2)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2}}{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{\frac{1}{3}}}, x\right)"," ",0,"integral(x^2/(b^2*x^4 + 2*a*b*x^2 + a^2)^(1/3), x)","F",0
660,0,0,0,3.115683," ","integrate(1/(b^2*x^4+2*a*b*x^2+a^2)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{\frac{1}{3}}}, x\right)"," ",0,"integral((b^2*x^4 + 2*a*b*x^2 + a^2)^(-1/3), x)","F",0
661,0,0,0,1.926644," ","integrate(1/x^2/(b^2*x^4+2*a*b*x^2+a^2)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{\frac{2}{3}}}{b^{2} x^{6} + 2 \, a b x^{4} + a^{2} x^{2}}, x\right)"," ",0,"integral((b^2*x^4 + 2*a*b*x^2 + a^2)^(2/3)/(b^2*x^6 + 2*a*b*x^4 + a^2*x^2), x)","F",0
662,0,0,0,1.615764," ","integrate(x^2/(b^2*x^4+2*a*b*x^2+a^2)^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2}}{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{\frac{2}{3}}}, x\right)"," ",0,"integral(x^2/(b^2*x^4 + 2*a*b*x^2 + a^2)^(2/3), x)","F",0
663,0,0,0,1.945598," ","integrate(1/(b^2*x^4+2*a*b*x^2+a^2)^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{\frac{2}{3}}}, x\right)"," ",0,"integral((b^2*x^4 + 2*a*b*x^2 + a^2)^(-2/3), x)","F",0
664,0,0,0,1.325675," ","integrate(1/x^2/(b^2*x^4+2*a*b*x^2+a^2)^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{\frac{1}{3}}}{b^{2} x^{6} + 2 \, a b x^{4} + a^{2} x^{2}}, x\right)"," ",0,"integral((b^2*x^4 + 2*a*b*x^2 + a^2)^(1/3)/(b^2*x^6 + 2*a*b*x^4 + a^2*x^2), x)","F",0
665,1,40,0,1.012852," ","integrate((d*x)^(5/2)*(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""fricas"")","\frac{2}{1155} \, {\left(77 \, b^{2} d^{2} x^{7} + 210 \, a b d^{2} x^{5} + 165 \, a^{2} d^{2} x^{3}\right)} \sqrt{d x}"," ",0,"2/1155*(77*b^2*d^2*x^7 + 210*a*b*d^2*x^5 + 165*a^2*d^2*x^3)*sqrt(d*x)","A",0
666,1,34,0,1.686398," ","integrate((d*x)^(3/2)*(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""fricas"")","\frac{2}{585} \, {\left(45 \, b^{2} d x^{6} + 130 \, a b d x^{4} + 117 \, a^{2} d x^{2}\right)} \sqrt{d x}"," ",0,"2/585*(45*b^2*d*x^6 + 130*a*b*d*x^4 + 117*a^2*d*x^2)*sqrt(d*x)","A",0
667,1,29,0,1.250713," ","integrate((b^2*x^4+2*a*b*x^2+a^2)*(d*x)^(1/2),x, algorithm=""fricas"")","\frac{2}{231} \, {\left(21 \, b^{2} x^{5} + 66 \, a b x^{3} + 77 \, a^{2} x\right)} \sqrt{d x}"," ",0,"2/231*(21*b^2*x^5 + 66*a*b*x^3 + 77*a^2*x)*sqrt(d*x)","A",0
668,1,31,0,1.359122," ","integrate((b^2*x^4+2*a*b*x^2+a^2)/(d*x)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, b^{2} x^{4} + 18 \, a b x^{2} + 45 \, a^{2}\right)} \sqrt{d x}}{45 \, d}"," ",0,"2/45*(5*b^2*x^4 + 18*a*b*x^2 + 45*a^2)*sqrt(d*x)/d","A",0
669,1,34,0,1.921572," ","integrate((b^2*x^4+2*a*b*x^2+a^2)/(d*x)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, b^{2} x^{4} + 14 \, a b x^{2} - 21 \, a^{2}\right)} \sqrt{d x}}{21 \, d^{2} x}"," ",0,"2/21*(3*b^2*x^4 + 14*a*b*x^2 - 21*a^2)*sqrt(d*x)/(d^2*x)","A",0
670,1,34,0,0.975757," ","integrate((b^2*x^4+2*a*b*x^2+a^2)/(d*x)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, b^{2} x^{4} + 30 \, a b x^{2} - 5 \, a^{2}\right)} \sqrt{d x}}{15 \, d^{3} x^{2}}"," ",0,"2/15*(3*b^2*x^4 + 30*a*b*x^2 - 5*a^2)*sqrt(d*x)/(d^3*x^2)","A",0
671,1,34,0,1.024923," ","integrate((b^2*x^4+2*a*b*x^2+a^2)/(d*x)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, b^{2} x^{4} - 30 \, a b x^{2} - 3 \, a^{2}\right)} \sqrt{d x}}{15 \, d^{4} x^{3}}"," ",0,"2/15*(5*b^2*x^4 - 30*a*b*x^2 - 3*a^2)*sqrt(d*x)/(d^4*x^3)","A",0
672,1,68,0,1.494276," ","integrate((d*x)^(5/2)*(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""fricas"")","\frac{2}{168245} \, {\left(7315 \, b^{4} d^{2} x^{11} + 35420 \, a b^{3} d^{2} x^{9} + 67298 \, a^{2} b^{2} d^{2} x^{7} + 61180 \, a^{3} b d^{2} x^{5} + 24035 \, a^{4} d^{2} x^{3}\right)} \sqrt{d x}"," ",0,"2/168245*(7315*b^4*d^2*x^11 + 35420*a*b^3*d^2*x^9 + 67298*a^2*b^2*d^2*x^7 + 61180*a^3*b*d^2*x^5 + 24035*a^4*d^2*x^3)*sqrt(d*x)","A",0
673,1,58,0,2.233629," ","integrate((d*x)^(3/2)*(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""fricas"")","\frac{2}{69615} \, {\left(3315 \, b^{4} d x^{10} + 16380 \, a b^{3} d x^{8} + 32130 \, a^{2} b^{2} d x^{6} + 30940 \, a^{3} b d x^{4} + 13923 \, a^{4} d x^{2}\right)} \sqrt{d x}"," ",0,"2/69615*(3315*b^4*d*x^10 + 16380*a*b^3*d*x^8 + 32130*a^2*b^2*d*x^6 + 30940*a^3*b*d*x^4 + 13923*a^4*d*x^2)*sqrt(d*x)","A",0
674,1,51,0,1.799834," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2*(d*x)^(1/2),x, algorithm=""fricas"")","\frac{2}{21945} \, {\left(1155 \, b^{4} x^{9} + 5852 \, a b^{3} x^{7} + 11970 \, a^{2} b^{2} x^{5} + 12540 \, a^{3} b x^{3} + 7315 \, a^{4} x\right)} \sqrt{d x}"," ",0,"2/21945*(1155*b^4*x^9 + 5852*a*b^3*x^7 + 11970*a^2*b^2*x^5 + 12540*a^3*b*x^3 + 7315*a^4*x)*sqrt(d*x)","A",0
675,1,53,0,0.875022," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/(d*x)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(195 \, b^{4} x^{8} + 1020 \, a b^{3} x^{6} + 2210 \, a^{2} b^{2} x^{4} + 2652 \, a^{3} b x^{2} + 3315 \, a^{4}\right)} \sqrt{d x}}{3315 \, d}"," ",0,"2/3315*(195*b^4*x^8 + 1020*a*b^3*x^6 + 2210*a^2*b^2*x^4 + 2652*a^3*b*x^2 + 3315*a^4)*sqrt(d*x)/d","A",0
676,1,56,0,1.192444," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/(d*x)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(77 \, b^{4} x^{8} + 420 \, a b^{3} x^{6} + 990 \, a^{2} b^{2} x^{4} + 1540 \, a^{3} b x^{2} - 1155 \, a^{4}\right)} \sqrt{d x}}{1155 \, d^{2} x}"," ",0,"2/1155*(77*b^4*x^8 + 420*a*b^3*x^6 + 990*a^2*b^2*x^4 + 1540*a^3*b*x^2 - 1155*a^4)*sqrt(d*x)/(d^2*x)","A",0
677,1,56,0,0.845610," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/(d*x)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(45 \, b^{4} x^{8} + 260 \, a b^{3} x^{6} + 702 \, a^{2} b^{2} x^{4} + 2340 \, a^{3} b x^{2} - 195 \, a^{4}\right)} \sqrt{d x}}{585 \, d^{3} x^{2}}"," ",0,"2/585*(45*b^4*x^8 + 260*a*b^3*x^6 + 702*a^2*b^2*x^4 + 2340*a^3*b*x^2 - 195*a^4)*sqrt(d*x)/(d^3*x^2)","A",0
678,1,56,0,1.814793," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/(d*x)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, b^{4} x^{8} + 220 \, a b^{3} x^{6} + 770 \, a^{2} b^{2} x^{4} - 1540 \, a^{3} b x^{2} - 77 \, a^{4}\right)} \sqrt{d x}}{385 \, d^{4} x^{3}}"," ",0,"2/385*(35*b^4*x^8 + 220*a*b^3*x^6 + 770*a^2*b^2*x^4 - 1540*a^3*b*x^2 - 77*a^4)*sqrt(d*x)/(d^4*x^3)","A",0
679,1,96,0,1.709431," ","integrate((d*x)^(5/2)*(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","\frac{2}{9388071} \, {\left(302841 \, b^{6} d^{2} x^{15} + 2086238 \, a b^{5} d^{2} x^{13} + 6122655 \, a^{2} b^{4} d^{2} x^{11} + 9882180 \, a^{3} b^{3} d^{2} x^{9} + 9388071 \, a^{4} b^{2} d^{2} x^{7} + 5120766 \, a^{5} b d^{2} x^{5} + 1341153 \, a^{6} d^{2} x^{3}\right)} \sqrt{d x}"," ",0,"2/9388071*(302841*b^6*d^2*x^15 + 2086238*a*b^5*d^2*x^13 + 6122655*a^2*b^4*d^2*x^11 + 9882180*a^3*b^3*d^2*x^9 + 9388071*a^4*b^2*d^2*x^7 + 5120766*a^5*b*d^2*x^5 + 1341153*a^6*d^2*x^3)*sqrt(d*x)","A",0
680,1,82,0,0.844176," ","integrate((d*x)^(3/2)*(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","\frac{2}{3364725} \, {\left(116025 \, b^{6} d x^{14} + 807534 \, a b^{5} d x^{12} + 2403375 \, a^{2} b^{4} d x^{10} + 3958500 \, a^{3} b^{3} d x^{8} + 3882375 \, a^{4} b^{2} d x^{6} + 2243150 \, a^{5} b d x^{4} + 672945 \, a^{6} d x^{2}\right)} \sqrt{d x}"," ",0,"2/3364725*(116025*b^6*d*x^14 + 807534*a*b^5*d*x^12 + 2403375*a^2*b^4*d*x^10 + 3958500*a^3*b^3*d*x^8 + 3882375*a^4*b^2*d*x^6 + 2243150*a^5*b*d*x^4 + 672945*a^6*d*x^2)*sqrt(d*x)","A",0
681,1,73,0,2.069616," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3*(d*x)^(1/2),x, algorithm=""fricas"")","\frac{2}{908523} \, {\left(33649 \, b^{6} x^{13} + 237006 \, a b^{5} x^{11} + 717255 \, a^{2} b^{4} x^{9} + 1211364 \, a^{3} b^{3} x^{7} + 1238895 \, a^{4} b^{2} x^{5} + 778734 \, a^{5} b x^{3} + 302841 \, a^{6} x\right)} \sqrt{d x}"," ",0,"2/908523*(33649*b^6*x^13 + 237006*a*b^5*x^11 + 717255*a^2*b^4*x^9 + 1211364*a^3*b^3*x^7 + 1238895*a^4*b^2*x^5 + 778734*a^5*b*x^3 + 302841*a^6*x)*sqrt(d*x)","A",0
682,1,75,0,0.953347," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/(d*x)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(4641 \, b^{6} x^{12} + 33150 \, a b^{5} x^{10} + 102375 \, a^{2} b^{4} x^{8} + 178500 \, a^{3} b^{3} x^{6} + 193375 \, a^{4} b^{2} x^{4} + 139230 \, a^{5} b x^{2} + 116025 \, a^{6}\right)} \sqrt{d x}}{116025 \, d}"," ",0,"2/116025*(4641*b^6*x^12 + 33150*a*b^5*x^10 + 102375*a^2*b^4*x^8 + 178500*a^3*b^3*x^6 + 193375*a^4*b^2*x^4 + 139230*a^5*b*x^2 + 116025*a^6)*sqrt(d*x)/d","A",0
683,1,78,0,0.993757," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/(d*x)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(1463 \, b^{6} x^{12} + 10626 \, a b^{5} x^{10} + 33649 \, a^{2} b^{4} x^{8} + 61180 \, a^{3} b^{3} x^{6} + 72105 \, a^{4} b^{2} x^{4} + 67298 \, a^{5} b x^{2} - 33649 \, a^{6}\right)} \sqrt{d x}}{33649 \, d^{2} x}"," ",0,"2/33649*(1463*b^6*x^12 + 10626*a*b^5*x^10 + 33649*a^2*b^4*x^8 + 61180*a^3*b^3*x^6 + 72105*a^4*b^2*x^4 + 67298*a^5*b*x^2 - 33649*a^6)*sqrt(d*x)/(d^2*x)","A",0
684,1,78,0,1.313455," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/(d*x)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(663 \, b^{6} x^{12} + 4914 \, a b^{5} x^{10} + 16065 \, a^{2} b^{4} x^{8} + 30940 \, a^{3} b^{3} x^{6} + 41769 \, a^{4} b^{2} x^{4} + 83538 \, a^{5} b x^{2} - 4641 \, a^{6}\right)} \sqrt{d x}}{13923 \, d^{3} x^{2}}"," ",0,"2/13923*(663*b^6*x^12 + 4914*a*b^5*x^10 + 16065*a^2*b^4*x^8 + 30940*a^3*b^3*x^6 + 41769*a^4*b^2*x^4 + 83538*a^5*b*x^2 - 4641*a^6)*sqrt(d*x)/(d^3*x^2)","A",0
685,1,78,0,0.891949," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/(d*x)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(385 \, b^{6} x^{12} + 2926 \, a b^{5} x^{10} + 9975 \, a^{2} b^{4} x^{8} + 20900 \, a^{3} b^{3} x^{6} + 36575 \, a^{4} b^{2} x^{4} - 43890 \, a^{5} b x^{2} - 1463 \, a^{6}\right)} \sqrt{d x}}{7315 \, d^{4} x^{3}}"," ",0,"2/7315*(385*b^6*x^12 + 2926*a*b^5*x^10 + 9975*a^2*b^4*x^8 + 20900*a^3*b^3*x^6 + 36575*a^4*b^2*x^4 - 43890*a^5*b*x^2 - 1463*a^6)*sqrt(d*x)/(d^4*x^3)","A",0
686,1,283,0,2.072601," ","integrate((d*x)^(11/2)/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""fricas"")","\frac{180 \, \left(-\frac{a^{5} d^{22}}{b^{13}}\right)^{\frac{1}{4}} {\left(b^{4} x^{2} + a b^{3}\right)} \arctan\left(-\frac{\left(-\frac{a^{5} d^{22}}{b^{13}}\right)^{\frac{3}{4}} \sqrt{d x} a b^{10} d^{5} - \left(-\frac{a^{5} d^{22}}{b^{13}}\right)^{\frac{3}{4}} \sqrt{a^{2} d^{11} x + \sqrt{-\frac{a^{5} d^{22}}{b^{13}}} b^{6}} b^{10}}{a^{5} d^{22}}\right) + 45 \, \left(-\frac{a^{5} d^{22}}{b^{13}}\right)^{\frac{1}{4}} {\left(b^{4} x^{2} + a b^{3}\right)} \log\left(9 \, \sqrt{d x} a d^{5} + 9 \, \left(-\frac{a^{5} d^{22}}{b^{13}}\right)^{\frac{1}{4}} b^{3}\right) - 45 \, \left(-\frac{a^{5} d^{22}}{b^{13}}\right)^{\frac{1}{4}} {\left(b^{4} x^{2} + a b^{3}\right)} \log\left(9 \, \sqrt{d x} a d^{5} - 9 \, \left(-\frac{a^{5} d^{22}}{b^{13}}\right)^{\frac{1}{4}} b^{3}\right) + 4 \, {\left(4 \, b^{2} d^{5} x^{4} - 36 \, a b d^{5} x^{2} - 45 \, a^{2} d^{5}\right)} \sqrt{d x}}{40 \, {\left(b^{4} x^{2} + a b^{3}\right)}}"," ",0,"1/40*(180*(-a^5*d^22/b^13)^(1/4)*(b^4*x^2 + a*b^3)*arctan(-((-a^5*d^22/b^13)^(3/4)*sqrt(d*x)*a*b^10*d^5 - (-a^5*d^22/b^13)^(3/4)*sqrt(a^2*d^11*x + sqrt(-a^5*d^22/b^13)*b^6)*b^10)/(a^5*d^22)) + 45*(-a^5*d^22/b^13)^(1/4)*(b^4*x^2 + a*b^3)*log(9*sqrt(d*x)*a*d^5 + 9*(-a^5*d^22/b^13)^(1/4)*b^3) - 45*(-a^5*d^22/b^13)^(1/4)*(b^4*x^2 + a*b^3)*log(9*sqrt(d*x)*a*d^5 - 9*(-a^5*d^22/b^13)^(1/4)*b^3) + 4*(4*b^2*d^5*x^4 - 36*a*b*d^5*x^2 - 45*a^2*d^5)*sqrt(d*x))/(b^4*x^2 + a*b^3)","A",0
687,1,283,0,1.636806," ","integrate((d*x)^(9/2)/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""fricas"")","\frac{84 \, \left(-\frac{a^{3} d^{18}}{b^{11}}\right)^{\frac{1}{4}} {\left(b^{3} x^{2} + a b^{2}\right)} \arctan\left(-\frac{\left(-\frac{a^{3} d^{18}}{b^{11}}\right)^{\frac{1}{4}} \sqrt{d x} a^{2} b^{3} d^{13} - \sqrt{a^{4} d^{27} x - \sqrt{-\frac{a^{3} d^{18}}{b^{11}}} a^{3} b^{5} d^{18}} \left(-\frac{a^{3} d^{18}}{b^{11}}\right)^{\frac{1}{4}} b^{3}}{a^{3} d^{18}}\right) - 21 \, \left(-\frac{a^{3} d^{18}}{b^{11}}\right)^{\frac{1}{4}} {\left(b^{3} x^{2} + a b^{2}\right)} \log\left(343 \, \sqrt{d x} a^{2} d^{13} + 343 \, \left(-\frac{a^{3} d^{18}}{b^{11}}\right)^{\frac{3}{4}} b^{8}\right) + 21 \, \left(-\frac{a^{3} d^{18}}{b^{11}}\right)^{\frac{1}{4}} {\left(b^{3} x^{2} + a b^{2}\right)} \log\left(343 \, \sqrt{d x} a^{2} d^{13} - 343 \, \left(-\frac{a^{3} d^{18}}{b^{11}}\right)^{\frac{3}{4}} b^{8}\right) + 4 \, {\left(4 \, b d^{4} x^{3} + 7 \, a d^{4} x\right)} \sqrt{d x}}{24 \, {\left(b^{3} x^{2} + a b^{2}\right)}}"," ",0,"1/24*(84*(-a^3*d^18/b^11)^(1/4)*(b^3*x^2 + a*b^2)*arctan(-((-a^3*d^18/b^11)^(1/4)*sqrt(d*x)*a^2*b^3*d^13 - sqrt(a^4*d^27*x - sqrt(-a^3*d^18/b^11)*a^3*b^5*d^18)*(-a^3*d^18/b^11)^(1/4)*b^3)/(a^3*d^18)) - 21*(-a^3*d^18/b^11)^(1/4)*(b^3*x^2 + a*b^2)*log(343*sqrt(d*x)*a^2*d^13 + 343*(-a^3*d^18/b^11)^(3/4)*b^8) + 21*(-a^3*d^18/b^11)^(1/4)*(b^3*x^2 + a*b^2)*log(343*sqrt(d*x)*a^2*d^13 - 343*(-a^3*d^18/b^11)^(3/4)*b^8) + 4*(4*b*d^4*x^3 + 7*a*d^4*x)*sqrt(d*x))/(b^3*x^2 + a*b^2)","A",0
688,1,247,0,1.127383," ","integrate((d*x)^(7/2)/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""fricas"")","-\frac{20 \, \left(-\frac{a d^{14}}{b^{9}}\right)^{\frac{1}{4}} {\left(b^{3} x^{2} + a b^{2}\right)} \arctan\left(-\frac{\left(-\frac{a d^{14}}{b^{9}}\right)^{\frac{3}{4}} \sqrt{d x} b^{7} d^{3} - \sqrt{d^{7} x + \sqrt{-\frac{a d^{14}}{b^{9}}} b^{4}} \left(-\frac{a d^{14}}{b^{9}}\right)^{\frac{3}{4}} b^{7}}{a d^{14}}\right) + 5 \, \left(-\frac{a d^{14}}{b^{9}}\right)^{\frac{1}{4}} {\left(b^{3} x^{2} + a b^{2}\right)} \log\left(5 \, \sqrt{d x} d^{3} + 5 \, \left(-\frac{a d^{14}}{b^{9}}\right)^{\frac{1}{4}} b^{2}\right) - 5 \, \left(-\frac{a d^{14}}{b^{9}}\right)^{\frac{1}{4}} {\left(b^{3} x^{2} + a b^{2}\right)} \log\left(5 \, \sqrt{d x} d^{3} - 5 \, \left(-\frac{a d^{14}}{b^{9}}\right)^{\frac{1}{4}} b^{2}\right) - 4 \, {\left(4 \, b d^{3} x^{2} + 5 \, a d^{3}\right)} \sqrt{d x}}{8 \, {\left(b^{3} x^{2} + a b^{2}\right)}}"," ",0,"-1/8*(20*(-a*d^14/b^9)^(1/4)*(b^3*x^2 + a*b^2)*arctan(-((-a*d^14/b^9)^(3/4)*sqrt(d*x)*b^7*d^3 - sqrt(d^7*x + sqrt(-a*d^14/b^9)*b^4)*(-a*d^14/b^9)^(3/4)*b^7)/(a*d^14)) + 5*(-a*d^14/b^9)^(1/4)*(b^3*x^2 + a*b^2)*log(5*sqrt(d*x)*d^3 + 5*(-a*d^14/b^9)^(1/4)*b^2) - 5*(-a*d^14/b^9)^(1/4)*(b^3*x^2 + a*b^2)*log(5*sqrt(d*x)*d^3 - 5*(-a*d^14/b^9)^(1/4)*b^2) - 4*(4*b*d^3*x^2 + 5*a*d^3)*sqrt(d*x))/(b^3*x^2 + a*b^2)","A",0
689,1,247,0,1.569121," ","integrate((d*x)^(5/2)/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""fricas"")","-\frac{4 \, \sqrt{d x} d^{2} x + 12 \, {\left(b^{2} x^{2} + a b\right)} \left(-\frac{d^{10}}{a b^{7}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\left(-\frac{d^{10}}{a b^{7}}\right)^{\frac{1}{4}} \sqrt{d x} b^{2} d^{7} - \sqrt{d^{15} x - \sqrt{-\frac{d^{10}}{a b^{7}}} a b^{3} d^{10}} \left(-\frac{d^{10}}{a b^{7}}\right)^{\frac{1}{4}} b^{2}}{d^{10}}\right) - 3 \, {\left(b^{2} x^{2} + a b\right)} \left(-\frac{d^{10}}{a b^{7}}\right)^{\frac{1}{4}} \log\left(27 \, \sqrt{d x} d^{7} + 27 \, \left(-\frac{d^{10}}{a b^{7}}\right)^{\frac{3}{4}} a b^{5}\right) + 3 \, {\left(b^{2} x^{2} + a b\right)} \left(-\frac{d^{10}}{a b^{7}}\right)^{\frac{1}{4}} \log\left(27 \, \sqrt{d x} d^{7} - 27 \, \left(-\frac{d^{10}}{a b^{7}}\right)^{\frac{3}{4}} a b^{5}\right)}{8 \, {\left(b^{2} x^{2} + a b\right)}}"," ",0,"-1/8*(4*sqrt(d*x)*d^2*x + 12*(b^2*x^2 + a*b)*(-d^10/(a*b^7))^(1/4)*arctan(-((-d^10/(a*b^7))^(1/4)*sqrt(d*x)*b^2*d^7 - sqrt(d^15*x - sqrt(-d^10/(a*b^7))*a*b^3*d^10)*(-d^10/(a*b^7))^(1/4)*b^2)/d^10) - 3*(b^2*x^2 + a*b)*(-d^10/(a*b^7))^(1/4)*log(27*sqrt(d*x)*d^7 + 27*(-d^10/(a*b^7))^(3/4)*a*b^5) + 3*(b^2*x^2 + a*b)*(-d^10/(a*b^7))^(1/4)*log(27*sqrt(d*x)*d^7 - 27*(-d^10/(a*b^7))^(3/4)*a*b^5))/(b^2*x^2 + a*b)","A",0
690,1,234,0,1.193668," ","integrate((d*x)^(3/2)/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""fricas"")","\frac{4 \, {\left(b^{2} x^{2} + a b\right)} \left(-\frac{d^{6}}{a^{3} b^{5}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{d x} a^{2} b^{4} d \left(-\frac{d^{6}}{a^{3} b^{5}}\right)^{\frac{3}{4}} - \sqrt{a^{2} b^{2} \sqrt{-\frac{d^{6}}{a^{3} b^{5}}} + d^{3} x} a^{2} b^{4} \left(-\frac{d^{6}}{a^{3} b^{5}}\right)^{\frac{3}{4}}}{d^{6}}\right) + {\left(b^{2} x^{2} + a b\right)} \left(-\frac{d^{6}}{a^{3} b^{5}}\right)^{\frac{1}{4}} \log\left(a b \left(-\frac{d^{6}}{a^{3} b^{5}}\right)^{\frac{1}{4}} + \sqrt{d x} d\right) - {\left(b^{2} x^{2} + a b\right)} \left(-\frac{d^{6}}{a^{3} b^{5}}\right)^{\frac{1}{4}} \log\left(-a b \left(-\frac{d^{6}}{a^{3} b^{5}}\right)^{\frac{1}{4}} + \sqrt{d x} d\right) - 4 \, \sqrt{d x} d}{8 \, {\left(b^{2} x^{2} + a b\right)}}"," ",0,"1/8*(4*(b^2*x^2 + a*b)*(-d^6/(a^3*b^5))^(1/4)*arctan(-(sqrt(d*x)*a^2*b^4*d*(-d^6/(a^3*b^5))^(3/4) - sqrt(a^2*b^2*sqrt(-d^6/(a^3*b^5)) + d^3*x)*a^2*b^4*(-d^6/(a^3*b^5))^(3/4))/d^6) + (b^2*x^2 + a*b)*(-d^6/(a^3*b^5))^(1/4)*log(a*b*(-d^6/(a^3*b^5))^(1/4) + sqrt(d*x)*d) - (b^2*x^2 + a*b)*(-d^6/(a^3*b^5))^(1/4)*log(-a*b*(-d^6/(a^3*b^5))^(1/4) + sqrt(d*x)*d) - 4*sqrt(d*x)*d)/(b^2*x^2 + a*b)","A",0
691,1,232,0,1.598218," ","integrate((d*x)^(1/2)/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""fricas"")","-\frac{4 \, {\left(a b x^{2} + a^{2}\right)} \left(-\frac{d^{2}}{a^{5} b^{3}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{d x} a b d \left(-\frac{d^{2}}{a^{5} b^{3}}\right)^{\frac{1}{4}} - \sqrt{-a^{3} b d^{2} \sqrt{-\frac{d^{2}}{a^{5} b^{3}}} + d^{3} x} a b \left(-\frac{d^{2}}{a^{5} b^{3}}\right)^{\frac{1}{4}}}{d^{2}}\right) - {\left(a b x^{2} + a^{2}\right)} \left(-\frac{d^{2}}{a^{5} b^{3}}\right)^{\frac{1}{4}} \log\left(a^{4} b^{2} \left(-\frac{d^{2}}{a^{5} b^{3}}\right)^{\frac{3}{4}} + \sqrt{d x} d\right) + {\left(a b x^{2} + a^{2}\right)} \left(-\frac{d^{2}}{a^{5} b^{3}}\right)^{\frac{1}{4}} \log\left(-a^{4} b^{2} \left(-\frac{d^{2}}{a^{5} b^{3}}\right)^{\frac{3}{4}} + \sqrt{d x} d\right) - 4 \, \sqrt{d x} x}{8 \, {\left(a b x^{2} + a^{2}\right)}}"," ",0,"-1/8*(4*(a*b*x^2 + a^2)*(-d^2/(a^5*b^3))^(1/4)*arctan(-(sqrt(d*x)*a*b*d*(-d^2/(a^5*b^3))^(1/4) - sqrt(-a^3*b*d^2*sqrt(-d^2/(a^5*b^3)) + d^3*x)*a*b*(-d^2/(a^5*b^3))^(1/4))/d^2) - (a*b*x^2 + a^2)*(-d^2/(a^5*b^3))^(1/4)*log(a^4*b^2*(-d^2/(a^5*b^3))^(3/4) + sqrt(d*x)*d) + (a*b*x^2 + a^2)*(-d^2/(a^5*b^3))^(1/4)*log(-a^4*b^2*(-d^2/(a^5*b^3))^(3/4) + sqrt(d*x)*d) - 4*sqrt(d*x)*x)/(a*b*x^2 + a^2)","A",0
692,1,232,0,2.307315," ","integrate(1/(b^2*x^4+2*a*b*x^2+a^2)/(d*x)^(1/2),x, algorithm=""fricas"")","\frac{12 \, {\left(a b d x^{2} + a^{2} d\right)} \left(-\frac{1}{a^{7} b d^{2}}\right)^{\frac{1}{4}} \arctan\left(\sqrt{a^{4} d^{2} \sqrt{-\frac{1}{a^{7} b d^{2}}} + d x} a^{5} b d \left(-\frac{1}{a^{7} b d^{2}}\right)^{\frac{3}{4}} - \sqrt{d x} a^{5} b d \left(-\frac{1}{a^{7} b d^{2}}\right)^{\frac{3}{4}}\right) + 3 \, {\left(a b d x^{2} + a^{2} d\right)} \left(-\frac{1}{a^{7} b d^{2}}\right)^{\frac{1}{4}} \log\left(a^{2} d \left(-\frac{1}{a^{7} b d^{2}}\right)^{\frac{1}{4}} + \sqrt{d x}\right) - 3 \, {\left(a b d x^{2} + a^{2} d\right)} \left(-\frac{1}{a^{7} b d^{2}}\right)^{\frac{1}{4}} \log\left(-a^{2} d \left(-\frac{1}{a^{7} b d^{2}}\right)^{\frac{1}{4}} + \sqrt{d x}\right) + 4 \, \sqrt{d x}}{8 \, {\left(a b d x^{2} + a^{2} d\right)}}"," ",0,"1/8*(12*(a*b*d*x^2 + a^2*d)*(-1/(a^7*b*d^2))^(1/4)*arctan(sqrt(a^4*d^2*sqrt(-1/(a^7*b*d^2)) + d*x)*a^5*b*d*(-1/(a^7*b*d^2))^(3/4) - sqrt(d*x)*a^5*b*d*(-1/(a^7*b*d^2))^(3/4)) + 3*(a*b*d*x^2 + a^2*d)*(-1/(a^7*b*d^2))^(1/4)*log(a^2*d*(-1/(a^7*b*d^2))^(1/4) + sqrt(d*x)) - 3*(a*b*d*x^2 + a^2*d)*(-1/(a^7*b*d^2))^(1/4)*log(-a^2*d*(-1/(a^7*b*d^2))^(1/4) + sqrt(d*x)) + 4*sqrt(d*x))/(a*b*d*x^2 + a^2*d)","A",0
693,1,276,0,0.763149," ","integrate(1/(d*x)^(3/2)/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""fricas"")","\frac{20 \, {\left(a^{2} b d^{2} x^{3} + a^{3} d^{2} x\right)} \left(-\frac{b}{a^{9} d^{6}}\right)^{\frac{1}{4}} \arctan\left(-\frac{125 \, \sqrt{d x} a^{2} b d \left(-\frac{b}{a^{9} d^{6}}\right)^{\frac{1}{4}} - \sqrt{-15625 \, a^{5} b d^{4} \sqrt{-\frac{b}{a^{9} d^{6}}} + 15625 \, b^{2} d x} a^{2} d \left(-\frac{b}{a^{9} d^{6}}\right)^{\frac{1}{4}}}{125 \, b}\right) - 5 \, {\left(a^{2} b d^{2} x^{3} + a^{3} d^{2} x\right)} \left(-\frac{b}{a^{9} d^{6}}\right)^{\frac{1}{4}} \log\left(125 \, a^{7} d^{5} \left(-\frac{b}{a^{9} d^{6}}\right)^{\frac{3}{4}} + 125 \, \sqrt{d x} b\right) + 5 \, {\left(a^{2} b d^{2} x^{3} + a^{3} d^{2} x\right)} \left(-\frac{b}{a^{9} d^{6}}\right)^{\frac{1}{4}} \log\left(-125 \, a^{7} d^{5} \left(-\frac{b}{a^{9} d^{6}}\right)^{\frac{3}{4}} + 125 \, \sqrt{d x} b\right) - 4 \, {\left(5 \, b x^{2} + 4 \, a\right)} \sqrt{d x}}{8 \, {\left(a^{2} b d^{2} x^{3} + a^{3} d^{2} x\right)}}"," ",0,"1/8*(20*(a^2*b*d^2*x^3 + a^3*d^2*x)*(-b/(a^9*d^6))^(1/4)*arctan(-1/125*(125*sqrt(d*x)*a^2*b*d*(-b/(a^9*d^6))^(1/4) - sqrt(-15625*a^5*b*d^4*sqrt(-b/(a^9*d^6)) + 15625*b^2*d*x)*a^2*d*(-b/(a^9*d^6))^(1/4))/b) - 5*(a^2*b*d^2*x^3 + a^3*d^2*x)*(-b/(a^9*d^6))^(1/4)*log(125*a^7*d^5*(-b/(a^9*d^6))^(3/4) + 125*sqrt(d*x)*b) + 5*(a^2*b*d^2*x^3 + a^3*d^2*x)*(-b/(a^9*d^6))^(1/4)*log(-125*a^7*d^5*(-b/(a^9*d^6))^(3/4) + 125*sqrt(d*x)*b) - 4*(5*b*x^2 + 4*a)*sqrt(d*x))/(a^2*b*d^2*x^3 + a^3*d^2*x)","A",0
694,1,300,0,0.996476," ","integrate(1/(d*x)^(5/2)/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""fricas"")","-\frac{84 \, {\left(a^{2} b d^{3} x^{4} + a^{3} d^{3} x^{2}\right)} \left(-\frac{b^{3}}{a^{11} d^{10}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{d x} a^{8} b d^{7} \left(-\frac{b^{3}}{a^{11} d^{10}}\right)^{\frac{3}{4}} - \sqrt{a^{6} d^{6} \sqrt{-\frac{b^{3}}{a^{11} d^{10}}} + b^{2} d x} a^{8} d^{7} \left(-\frac{b^{3}}{a^{11} d^{10}}\right)^{\frac{3}{4}}}{b^{3}}\right) + 21 \, {\left(a^{2} b d^{3} x^{4} + a^{3} d^{3} x^{2}\right)} \left(-\frac{b^{3}}{a^{11} d^{10}}\right)^{\frac{1}{4}} \log\left(7 \, a^{3} d^{3} \left(-\frac{b^{3}}{a^{11} d^{10}}\right)^{\frac{1}{4}} + 7 \, \sqrt{d x} b\right) - 21 \, {\left(a^{2} b d^{3} x^{4} + a^{3} d^{3} x^{2}\right)} \left(-\frac{b^{3}}{a^{11} d^{10}}\right)^{\frac{1}{4}} \log\left(-7 \, a^{3} d^{3} \left(-\frac{b^{3}}{a^{11} d^{10}}\right)^{\frac{1}{4}} + 7 \, \sqrt{d x} b\right) + 4 \, {\left(7 \, b x^{2} + 4 \, a\right)} \sqrt{d x}}{24 \, {\left(a^{2} b d^{3} x^{4} + a^{3} d^{3} x^{2}\right)}}"," ",0,"-1/24*(84*(a^2*b*d^3*x^4 + a^3*d^3*x^2)*(-b^3/(a^11*d^10))^(1/4)*arctan(-(sqrt(d*x)*a^8*b*d^7*(-b^3/(a^11*d^10))^(3/4) - sqrt(a^6*d^6*sqrt(-b^3/(a^11*d^10)) + b^2*d*x)*a^8*d^7*(-b^3/(a^11*d^10))^(3/4))/b^3) + 21*(a^2*b*d^3*x^4 + a^3*d^3*x^2)*(-b^3/(a^11*d^10))^(1/4)*log(7*a^3*d^3*(-b^3/(a^11*d^10))^(1/4) + 7*sqrt(d*x)*b) - 21*(a^2*b*d^3*x^4 + a^3*d^3*x^2)*(-b^3/(a^11*d^10))^(1/4)*log(-7*a^3*d^3*(-b^3/(a^11*d^10))^(1/4) + 7*sqrt(d*x)*b) + 4*(7*b*x^2 + 4*a)*sqrt(d*x))/(a^2*b*d^3*x^4 + a^3*d^3*x^2)","A",0
695,1,323,0,0.791153," ","integrate(1/(d*x)^(7/2)/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""fricas"")","-\frac{180 \, {\left(a^{3} b d^{4} x^{5} + a^{4} d^{4} x^{3}\right)} \left(-\frac{b^{5}}{a^{13} d^{14}}\right)^{\frac{1}{4}} \arctan\left(-\frac{729 \, \sqrt{d x} a^{3} b^{4} d^{3} \left(-\frac{b^{5}}{a^{13} d^{14}}\right)^{\frac{1}{4}} - \sqrt{-531441 \, a^{7} b^{5} d^{8} \sqrt{-\frac{b^{5}}{a^{13} d^{14}}} + 531441 \, b^{8} d x} a^{3} d^{3} \left(-\frac{b^{5}}{a^{13} d^{14}}\right)^{\frac{1}{4}}}{729 \, b^{5}}\right) - 45 \, {\left(a^{3} b d^{4} x^{5} + a^{4} d^{4} x^{3}\right)} \left(-\frac{b^{5}}{a^{13} d^{14}}\right)^{\frac{1}{4}} \log\left(729 \, a^{10} d^{11} \left(-\frac{b^{5}}{a^{13} d^{14}}\right)^{\frac{3}{4}} + 729 \, \sqrt{d x} b^{4}\right) + 45 \, {\left(a^{3} b d^{4} x^{5} + a^{4} d^{4} x^{3}\right)} \left(-\frac{b^{5}}{a^{13} d^{14}}\right)^{\frac{1}{4}} \log\left(-729 \, a^{10} d^{11} \left(-\frac{b^{5}}{a^{13} d^{14}}\right)^{\frac{3}{4}} + 729 \, \sqrt{d x} b^{4}\right) - 4 \, {\left(45 \, b^{2} x^{4} + 36 \, a b x^{2} - 4 \, a^{2}\right)} \sqrt{d x}}{40 \, {\left(a^{3} b d^{4} x^{5} + a^{4} d^{4} x^{3}\right)}}"," ",0,"-1/40*(180*(a^3*b*d^4*x^5 + a^4*d^4*x^3)*(-b^5/(a^13*d^14))^(1/4)*arctan(-1/729*(729*sqrt(d*x)*a^3*b^4*d^3*(-b^5/(a^13*d^14))^(1/4) - sqrt(-531441*a^7*b^5*d^8*sqrt(-b^5/(a^13*d^14)) + 531441*b^8*d*x)*a^3*d^3*(-b^5/(a^13*d^14))^(1/4))/b^5) - 45*(a^3*b*d^4*x^5 + a^4*d^4*x^3)*(-b^5/(a^13*d^14))^(1/4)*log(729*a^10*d^11*(-b^5/(a^13*d^14))^(3/4) + 729*sqrt(d*x)*b^4) + 45*(a^3*b*d^4*x^5 + a^4*d^4*x^3)*(-b^5/(a^13*d^14))^(1/4)*log(-729*a^10*d^11*(-b^5/(a^13*d^14))^(3/4) + 729*sqrt(d*x)*b^4) - 4*(45*b^2*x^4 + 36*a*b*x^2 - 4*a^2)*sqrt(d*x))/(a^3*b*d^4*x^5 + a^4*d^4*x^3)","A",0
696,1,399,0,1.000603," ","integrate((d*x)^(19/2)/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""fricas"")","\frac{39780 \, \left(-\frac{a^{5} d^{38}}{b^{21}}\right)^{\frac{1}{4}} {\left(b^{8} x^{6} + 3 \, a b^{7} x^{4} + 3 \, a^{2} b^{6} x^{2} + a^{3} b^{5}\right)} \arctan\left(-\frac{\left(-\frac{a^{5} d^{38}}{b^{21}}\right)^{\frac{3}{4}} \sqrt{d x} a b^{16} d^{9} - \left(-\frac{a^{5} d^{38}}{b^{21}}\right)^{\frac{3}{4}} \sqrt{a^{2} d^{19} x + \sqrt{-\frac{a^{5} d^{38}}{b^{21}}} b^{10}} b^{16}}{a^{5} d^{38}}\right) + 9945 \, \left(-\frac{a^{5} d^{38}}{b^{21}}\right)^{\frac{1}{4}} {\left(b^{8} x^{6} + 3 \, a b^{7} x^{4} + 3 \, a^{2} b^{6} x^{2} + a^{3} b^{5}\right)} \log\left(663 \, \sqrt{d x} a d^{9} + 663 \, \left(-\frac{a^{5} d^{38}}{b^{21}}\right)^{\frac{1}{4}} b^{5}\right) - 9945 \, \left(-\frac{a^{5} d^{38}}{b^{21}}\right)^{\frac{1}{4}} {\left(b^{8} x^{6} + 3 \, a b^{7} x^{4} + 3 \, a^{2} b^{6} x^{2} + a^{3} b^{5}\right)} \log\left(663 \, \sqrt{d x} a d^{9} - 663 \, \left(-\frac{a^{5} d^{38}}{b^{21}}\right)^{\frac{1}{4}} b^{5}\right) + 4 \, {\left(384 \, b^{4} d^{9} x^{8} - 6528 \, a b^{3} d^{9} x^{6} - 24973 \, a^{2} b^{2} d^{9} x^{4} - 27846 \, a^{3} b d^{9} x^{2} - 9945 \, a^{4} d^{9}\right)} \sqrt{d x}}{3840 \, {\left(b^{8} x^{6} + 3 \, a b^{7} x^{4} + 3 \, a^{2} b^{6} x^{2} + a^{3} b^{5}\right)}}"," ",0,"1/3840*(39780*(-a^5*d^38/b^21)^(1/4)*(b^8*x^6 + 3*a*b^7*x^4 + 3*a^2*b^6*x^2 + a^3*b^5)*arctan(-((-a^5*d^38/b^21)^(3/4)*sqrt(d*x)*a*b^16*d^9 - (-a^5*d^38/b^21)^(3/4)*sqrt(a^2*d^19*x + sqrt(-a^5*d^38/b^21)*b^10)*b^16)/(a^5*d^38)) + 9945*(-a^5*d^38/b^21)^(1/4)*(b^8*x^6 + 3*a*b^7*x^4 + 3*a^2*b^6*x^2 + a^3*b^5)*log(663*sqrt(d*x)*a*d^9 + 663*(-a^5*d^38/b^21)^(1/4)*b^5) - 9945*(-a^5*d^38/b^21)^(1/4)*(b^8*x^6 + 3*a*b^7*x^4 + 3*a^2*b^6*x^2 + a^3*b^5)*log(663*sqrt(d*x)*a*d^9 - 663*(-a^5*d^38/b^21)^(1/4)*b^5) + 4*(384*b^4*d^9*x^8 - 6528*a*b^3*d^9*x^6 - 24973*a^2*b^2*d^9*x^4 - 27846*a^3*b*d^9*x^2 - 9945*a^4*d^9)*sqrt(d*x))/(b^8*x^6 + 3*a*b^7*x^4 + 3*a^2*b^6*x^2 + a^3*b^5)","A",0
697,1,399,0,2.462683," ","integrate((d*x)^(17/2)/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""fricas"")","\frac{4620 \, \left(-\frac{a^{3} d^{34}}{b^{19}}\right)^{\frac{1}{4}} {\left(b^{7} x^{6} + 3 \, a b^{6} x^{4} + 3 \, a^{2} b^{5} x^{2} + a^{3} b^{4}\right)} \arctan\left(-\frac{\left(-\frac{a^{3} d^{34}}{b^{19}}\right)^{\frac{1}{4}} \sqrt{d x} a^{2} b^{5} d^{25} - \sqrt{a^{4} d^{51} x - \sqrt{-\frac{a^{3} d^{34}}{b^{19}}} a^{3} b^{9} d^{34}} \left(-\frac{a^{3} d^{34}}{b^{19}}\right)^{\frac{1}{4}} b^{5}}{a^{3} d^{34}}\right) - 1155 \, \left(-\frac{a^{3} d^{34}}{b^{19}}\right)^{\frac{1}{4}} {\left(b^{7} x^{6} + 3 \, a b^{6} x^{4} + 3 \, a^{2} b^{5} x^{2} + a^{3} b^{4}\right)} \log\left(57066625 \, \sqrt{d x} a^{2} d^{25} + 57066625 \, \left(-\frac{a^{3} d^{34}}{b^{19}}\right)^{\frac{3}{4}} b^{14}\right) + 1155 \, \left(-\frac{a^{3} d^{34}}{b^{19}}\right)^{\frac{1}{4}} {\left(b^{7} x^{6} + 3 \, a b^{6} x^{4} + 3 \, a^{2} b^{5} x^{2} + a^{3} b^{4}\right)} \log\left(57066625 \, \sqrt{d x} a^{2} d^{25} - 57066625 \, \left(-\frac{a^{3} d^{34}}{b^{19}}\right)^{\frac{3}{4}} b^{14}\right) + 4 \, {\left(128 \, b^{3} d^{8} x^{7} + 765 \, a b^{2} d^{8} x^{5} + 990 \, a^{2} b d^{8} x^{3} + 385 \, a^{3} d^{8} x\right)} \sqrt{d x}}{768 \, {\left(b^{7} x^{6} + 3 \, a b^{6} x^{4} + 3 \, a^{2} b^{5} x^{2} + a^{3} b^{4}\right)}}"," ",0,"1/768*(4620*(-a^3*d^34/b^19)^(1/4)*(b^7*x^6 + 3*a*b^6*x^4 + 3*a^2*b^5*x^2 + a^3*b^4)*arctan(-((-a^3*d^34/b^19)^(1/4)*sqrt(d*x)*a^2*b^5*d^25 - sqrt(a^4*d^51*x - sqrt(-a^3*d^34/b^19)*a^3*b^9*d^34)*(-a^3*d^34/b^19)^(1/4)*b^5)/(a^3*d^34)) - 1155*(-a^3*d^34/b^19)^(1/4)*(b^7*x^6 + 3*a*b^6*x^4 + 3*a^2*b^5*x^2 + a^3*b^4)*log(57066625*sqrt(d*x)*a^2*d^25 + 57066625*(-a^3*d^34/b^19)^(3/4)*b^14) + 1155*(-a^3*d^34/b^19)^(1/4)*(b^7*x^6 + 3*a*b^6*x^4 + 3*a^2*b^5*x^2 + a^3*b^4)*log(57066625*sqrt(d*x)*a^2*d^25 - 57066625*(-a^3*d^34/b^19)^(3/4)*b^14) + 4*(128*b^3*d^8*x^7 + 765*a*b^2*d^8*x^5 + 990*a^2*b*d^8*x^3 + 385*a^3*d^8*x)*sqrt(d*x))/(b^7*x^6 + 3*a*b^6*x^4 + 3*a^2*b^5*x^2 + a^3*b^4)","A",0
698,1,363,0,0.833097," ","integrate((d*x)^(15/2)/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""fricas"")","-\frac{2340 \, \left(-\frac{a d^{30}}{b^{17}}\right)^{\frac{1}{4}} {\left(b^{7} x^{6} + 3 \, a b^{6} x^{4} + 3 \, a^{2} b^{5} x^{2} + a^{3} b^{4}\right)} \arctan\left(-\frac{\left(-\frac{a d^{30}}{b^{17}}\right)^{\frac{3}{4}} \sqrt{d x} b^{13} d^{7} - \sqrt{d^{15} x + \sqrt{-\frac{a d^{30}}{b^{17}}} b^{8}} \left(-\frac{a d^{30}}{b^{17}}\right)^{\frac{3}{4}} b^{13}}{a d^{30}}\right) + 585 \, \left(-\frac{a d^{30}}{b^{17}}\right)^{\frac{1}{4}} {\left(b^{7} x^{6} + 3 \, a b^{6} x^{4} + 3 \, a^{2} b^{5} x^{2} + a^{3} b^{4}\right)} \log\left(195 \, \sqrt{d x} d^{7} + 195 \, \left(-\frac{a d^{30}}{b^{17}}\right)^{\frac{1}{4}} b^{4}\right) - 585 \, \left(-\frac{a d^{30}}{b^{17}}\right)^{\frac{1}{4}} {\left(b^{7} x^{6} + 3 \, a b^{6} x^{4} + 3 \, a^{2} b^{5} x^{2} + a^{3} b^{4}\right)} \log\left(195 \, \sqrt{d x} d^{7} - 195 \, \left(-\frac{a d^{30}}{b^{17}}\right)^{\frac{1}{4}} b^{4}\right) - 4 \, {\left(384 \, b^{3} d^{7} x^{6} + 1469 \, a b^{2} d^{7} x^{4} + 1638 \, a^{2} b d^{7} x^{2} + 585 \, a^{3} d^{7}\right)} \sqrt{d x}}{768 \, {\left(b^{7} x^{6} + 3 \, a b^{6} x^{4} + 3 \, a^{2} b^{5} x^{2} + a^{3} b^{4}\right)}}"," ",0,"-1/768*(2340*(-a*d^30/b^17)^(1/4)*(b^7*x^6 + 3*a*b^6*x^4 + 3*a^2*b^5*x^2 + a^3*b^4)*arctan(-((-a*d^30/b^17)^(3/4)*sqrt(d*x)*b^13*d^7 - sqrt(d^15*x + sqrt(-a*d^30/b^17)*b^8)*(-a*d^30/b^17)^(3/4)*b^13)/(a*d^30)) + 585*(-a*d^30/b^17)^(1/4)*(b^7*x^6 + 3*a*b^6*x^4 + 3*a^2*b^5*x^2 + a^3*b^4)*log(195*sqrt(d*x)*d^7 + 195*(-a*d^30/b^17)^(1/4)*b^4) - 585*(-a*d^30/b^17)^(1/4)*(b^7*x^6 + 3*a*b^6*x^4 + 3*a^2*b^5*x^2 + a^3*b^4)*log(195*sqrt(d*x)*d^7 - 195*(-a*d^30/b^17)^(1/4)*b^4) - 4*(384*b^3*d^7*x^6 + 1469*a*b^2*d^7*x^4 + 1638*a^2*b*d^7*x^2 + 585*a^3*d^7)*sqrt(d*x))/(b^7*x^6 + 3*a*b^6*x^4 + 3*a^2*b^5*x^2 + a^3*b^4)","A",0
699,1,370,0,1.894702," ","integrate((d*x)^(13/2)/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""fricas"")","-\frac{924 \, {\left(b^{6} x^{6} + 3 \, a b^{5} x^{4} + 3 \, a^{2} b^{4} x^{2} + a^{3} b^{3}\right)} \left(-\frac{d^{26}}{a b^{15}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\left(-\frac{d^{26}}{a b^{15}}\right)^{\frac{1}{4}} \sqrt{d x} b^{4} d^{19} - \sqrt{d^{39} x - \sqrt{-\frac{d^{26}}{a b^{15}}} a b^{7} d^{26}} \left(-\frac{d^{26}}{a b^{15}}\right)^{\frac{1}{4}} b^{4}}{d^{26}}\right) - 231 \, {\left(b^{6} x^{6} + 3 \, a b^{5} x^{4} + 3 \, a^{2} b^{4} x^{2} + a^{3} b^{3}\right)} \left(-\frac{d^{26}}{a b^{15}}\right)^{\frac{1}{4}} \log\left(456533 \, \sqrt{d x} d^{19} + 456533 \, \left(-\frac{d^{26}}{a b^{15}}\right)^{\frac{3}{4}} a b^{11}\right) + 231 \, {\left(b^{6} x^{6} + 3 \, a b^{5} x^{4} + 3 \, a^{2} b^{4} x^{2} + a^{3} b^{3}\right)} \left(-\frac{d^{26}}{a b^{15}}\right)^{\frac{1}{4}} \log\left(456533 \, \sqrt{d x} d^{19} - 456533 \, \left(-\frac{d^{26}}{a b^{15}}\right)^{\frac{3}{4}} a b^{11}\right) + 4 \, {\left(153 \, b^{2} d^{6} x^{5} + 198 \, a b d^{6} x^{3} + 77 \, a^{2} d^{6} x\right)} \sqrt{d x}}{768 \, {\left(b^{6} x^{6} + 3 \, a b^{5} x^{4} + 3 \, a^{2} b^{4} x^{2} + a^{3} b^{3}\right)}}"," ",0,"-1/768*(924*(b^6*x^6 + 3*a*b^5*x^4 + 3*a^2*b^4*x^2 + a^3*b^3)*(-d^26/(a*b^15))^(1/4)*arctan(-((-d^26/(a*b^15))^(1/4)*sqrt(d*x)*b^4*d^19 - sqrt(d^39*x - sqrt(-d^26/(a*b^15))*a*b^7*d^26)*(-d^26/(a*b^15))^(1/4)*b^4)/d^26) - 231*(b^6*x^6 + 3*a*b^5*x^4 + 3*a^2*b^4*x^2 + a^3*b^3)*(-d^26/(a*b^15))^(1/4)*log(456533*sqrt(d*x)*d^19 + 456533*(-d^26/(a*b^15))^(3/4)*a*b^11) + 231*(b^6*x^6 + 3*a*b^5*x^4 + 3*a^2*b^4*x^2 + a^3*b^3)*(-d^26/(a*b^15))^(1/4)*log(456533*sqrt(d*x)*d^19 - 456533*(-d^26/(a*b^15))^(3/4)*a*b^11) + 4*(153*b^2*d^6*x^5 + 198*a*b*d^6*x^3 + 77*a^2*d^6*x)*sqrt(d*x))/(b^6*x^6 + 3*a*b^5*x^4 + 3*a^2*b^4*x^2 + a^3*b^3)","A",0
700,1,373,0,1.772956," ","integrate((d*x)^(11/2)/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""fricas"")","\frac{180 \, {\left(b^{6} x^{6} + 3 \, a b^{5} x^{4} + 3 \, a^{2} b^{4} x^{2} + a^{3} b^{3}\right)} \left(-\frac{d^{22}}{a^{3} b^{13}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\left(-\frac{d^{22}}{a^{3} b^{13}}\right)^{\frac{3}{4}} \sqrt{d x} a^{2} b^{10} d^{5} - \sqrt{d^{11} x + \sqrt{-\frac{d^{22}}{a^{3} b^{13}}} a^{2} b^{6}} \left(-\frac{d^{22}}{a^{3} b^{13}}\right)^{\frac{3}{4}} a^{2} b^{10}}{d^{22}}\right) + 45 \, {\left(b^{6} x^{6} + 3 \, a b^{5} x^{4} + 3 \, a^{2} b^{4} x^{2} + a^{3} b^{3}\right)} \left(-\frac{d^{22}}{a^{3} b^{13}}\right)^{\frac{1}{4}} \log\left(15 \, \sqrt{d x} d^{5} + 15 \, \left(-\frac{d^{22}}{a^{3} b^{13}}\right)^{\frac{1}{4}} a b^{3}\right) - 45 \, {\left(b^{6} x^{6} + 3 \, a b^{5} x^{4} + 3 \, a^{2} b^{4} x^{2} + a^{3} b^{3}\right)} \left(-\frac{d^{22}}{a^{3} b^{13}}\right)^{\frac{1}{4}} \log\left(15 \, \sqrt{d x} d^{5} - 15 \, \left(-\frac{d^{22}}{a^{3} b^{13}}\right)^{\frac{1}{4}} a b^{3}\right) - 4 \, {\left(113 \, b^{2} d^{5} x^{4} + 126 \, a b d^{5} x^{2} + 45 \, a^{2} d^{5}\right)} \sqrt{d x}}{768 \, {\left(b^{6} x^{6} + 3 \, a b^{5} x^{4} + 3 \, a^{2} b^{4} x^{2} + a^{3} b^{3}\right)}}"," ",0,"1/768*(180*(b^6*x^6 + 3*a*b^5*x^4 + 3*a^2*b^4*x^2 + a^3*b^3)*(-d^22/(a^3*b^13))^(1/4)*arctan(-((-d^22/(a^3*b^13))^(3/4)*sqrt(d*x)*a^2*b^10*d^5 - sqrt(d^11*x + sqrt(-d^22/(a^3*b^13))*a^2*b^6)*(-d^22/(a^3*b^13))^(3/4)*a^2*b^10)/d^22) + 45*(b^6*x^6 + 3*a*b^5*x^4 + 3*a^2*b^4*x^2 + a^3*b^3)*(-d^22/(a^3*b^13))^(1/4)*log(15*sqrt(d*x)*d^5 + 15*(-d^22/(a^3*b^13))^(1/4)*a*b^3) - 45*(b^6*x^6 + 3*a*b^5*x^4 + 3*a^2*b^4*x^2 + a^3*b^3)*(-d^22/(a^3*b^13))^(1/4)*log(15*sqrt(d*x)*d^5 - 15*(-d^22/(a^3*b^13))^(1/4)*a*b^3) - 4*(113*b^2*d^5*x^4 + 126*a*b*d^5*x^2 + 45*a^2*d^5)*sqrt(d*x))/(b^6*x^6 + 3*a*b^5*x^4 + 3*a^2*b^4*x^2 + a^3*b^3)","A",0
701,1,390,0,1.147168," ","integrate((d*x)^(9/2)/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""fricas"")","-\frac{84 \, {\left(a b^{5} x^{6} + 3 \, a^{2} b^{4} x^{4} + 3 \, a^{3} b^{3} x^{2} + a^{4} b^{2}\right)} \left(-\frac{d^{18}}{a^{5} b^{11}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\left(-\frac{d^{18}}{a^{5} b^{11}}\right)^{\frac{1}{4}} \sqrt{d x} a b^{3} d^{13} - \sqrt{d^{27} x - \sqrt{-\frac{d^{18}}{a^{5} b^{11}}} a^{3} b^{5} d^{18}} \left(-\frac{d^{18}}{a^{5} b^{11}}\right)^{\frac{1}{4}} a b^{3}}{d^{18}}\right) - 21 \, {\left(a b^{5} x^{6} + 3 \, a^{2} b^{4} x^{4} + 3 \, a^{3} b^{3} x^{2} + a^{4} b^{2}\right)} \left(-\frac{d^{18}}{a^{5} b^{11}}\right)^{\frac{1}{4}} \log\left(343 \, \sqrt{d x} d^{13} + 343 \, \left(-\frac{d^{18}}{a^{5} b^{11}}\right)^{\frac{3}{4}} a^{4} b^{8}\right) + 21 \, {\left(a b^{5} x^{6} + 3 \, a^{2} b^{4} x^{4} + 3 \, a^{3} b^{3} x^{2} + a^{4} b^{2}\right)} \left(-\frac{d^{18}}{a^{5} b^{11}}\right)^{\frac{1}{4}} \log\left(343 \, \sqrt{d x} d^{13} - 343 \, \left(-\frac{d^{18}}{a^{5} b^{11}}\right)^{\frac{3}{4}} a^{4} b^{8}\right) - 4 \, {\left(21 \, b^{2} d^{4} x^{5} - 18 \, a b d^{4} x^{3} - 7 \, a^{2} d^{4} x\right)} \sqrt{d x}}{768 \, {\left(a b^{5} x^{6} + 3 \, a^{2} b^{4} x^{4} + 3 \, a^{3} b^{3} x^{2} + a^{4} b^{2}\right)}}"," ",0,"-1/768*(84*(a*b^5*x^6 + 3*a^2*b^4*x^4 + 3*a^3*b^3*x^2 + a^4*b^2)*(-d^18/(a^5*b^11))^(1/4)*arctan(-((-d^18/(a^5*b^11))^(1/4)*sqrt(d*x)*a*b^3*d^13 - sqrt(d^27*x - sqrt(-d^18/(a^5*b^11))*a^3*b^5*d^18)*(-d^18/(a^5*b^11))^(1/4)*a*b^3)/d^18) - 21*(a*b^5*x^6 + 3*a^2*b^4*x^4 + 3*a^3*b^3*x^2 + a^4*b^2)*(-d^18/(a^5*b^11))^(1/4)*log(343*sqrt(d*x)*d^13 + 343*(-d^18/(a^5*b^11))^(3/4)*a^4*b^8) + 21*(a*b^5*x^6 + 3*a^2*b^4*x^4 + 3*a^3*b^3*x^2 + a^4*b^2)*(-d^18/(a^5*b^11))^(1/4)*log(343*sqrt(d*x)*d^13 - 343*(-d^18/(a^5*b^11))^(3/4)*a^4*b^8) - 4*(21*b^2*d^4*x^5 - 18*a*b*d^4*x^3 - 7*a^2*d^4*x)*sqrt(d*x))/(a*b^5*x^6 + 3*a^2*b^4*x^4 + 3*a^3*b^3*x^2 + a^4*b^2)","A",0
702,1,389,0,0.910457," ","integrate((d*x)^(7/2)/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""fricas"")","\frac{60 \, {\left(a b^{5} x^{6} + 3 \, a^{2} b^{4} x^{4} + 3 \, a^{3} b^{3} x^{2} + a^{4} b^{2}\right)} \left(-\frac{d^{14}}{a^{7} b^{9}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{d x} a^{5} b^{7} d^{3} \left(-\frac{d^{14}}{a^{7} b^{9}}\right)^{\frac{3}{4}} - \sqrt{a^{4} b^{4} \sqrt{-\frac{d^{14}}{a^{7} b^{9}}} + d^{7} x} a^{5} b^{7} \left(-\frac{d^{14}}{a^{7} b^{9}}\right)^{\frac{3}{4}}}{d^{14}}\right) + 15 \, {\left(a b^{5} x^{6} + 3 \, a^{2} b^{4} x^{4} + 3 \, a^{3} b^{3} x^{2} + a^{4} b^{2}\right)} \left(-\frac{d^{14}}{a^{7} b^{9}}\right)^{\frac{1}{4}} \log\left(5 \, a^{2} b^{2} \left(-\frac{d^{14}}{a^{7} b^{9}}\right)^{\frac{1}{4}} + 5 \, \sqrt{d x} d^{3}\right) - 15 \, {\left(a b^{5} x^{6} + 3 \, a^{2} b^{4} x^{4} + 3 \, a^{3} b^{3} x^{2} + a^{4} b^{2}\right)} \left(-\frac{d^{14}}{a^{7} b^{9}}\right)^{\frac{1}{4}} \log\left(-5 \, a^{2} b^{2} \left(-\frac{d^{14}}{a^{7} b^{9}}\right)^{\frac{1}{4}} + 5 \, \sqrt{d x} d^{3}\right) + 4 \, {\left(5 \, b^{2} d^{3} x^{4} - 42 \, a b d^{3} x^{2} - 15 \, a^{2} d^{3}\right)} \sqrt{d x}}{768 \, {\left(a b^{5} x^{6} + 3 \, a^{2} b^{4} x^{4} + 3 \, a^{3} b^{3} x^{2} + a^{4} b^{2}\right)}}"," ",0,"1/768*(60*(a*b^5*x^6 + 3*a^2*b^4*x^4 + 3*a^3*b^3*x^2 + a^4*b^2)*(-d^14/(a^7*b^9))^(1/4)*arctan(-(sqrt(d*x)*a^5*b^7*d^3*(-d^14/(a^7*b^9))^(3/4) - sqrt(a^4*b^4*sqrt(-d^14/(a^7*b^9)) + d^7*x)*a^5*b^7*(-d^14/(a^7*b^9))^(3/4))/d^14) + 15*(a*b^5*x^6 + 3*a^2*b^4*x^4 + 3*a^3*b^3*x^2 + a^4*b^2)*(-d^14/(a^7*b^9))^(1/4)*log(5*a^2*b^2*(-d^14/(a^7*b^9))^(1/4) + 5*sqrt(d*x)*d^3) - 15*(a*b^5*x^6 + 3*a^2*b^4*x^4 + 3*a^3*b^3*x^2 + a^4*b^2)*(-d^14/(a^7*b^9))^(1/4)*log(-5*a^2*b^2*(-d^14/(a^7*b^9))^(1/4) + 5*sqrt(d*x)*d^3) + 4*(5*b^2*d^3*x^4 - 42*a*b*d^3*x^2 - 15*a^2*d^3)*sqrt(d*x))/(a*b^5*x^6 + 3*a^2*b^4*x^4 + 3*a^3*b^3*x^2 + a^4*b^2)","A",0
703,1,396,0,0.882373," ","integrate((d*x)^(5/2)/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""fricas"")","-\frac{60 \, {\left(a^{2} b^{4} x^{6} + 3 \, a^{3} b^{3} x^{4} + 3 \, a^{4} b^{2} x^{2} + a^{5} b\right)} \left(-\frac{d^{10}}{a^{9} b^{7}}\right)^{\frac{1}{4}} \arctan\left(-\frac{125 \, \sqrt{d x} a^{2} b^{2} d^{7} \left(-\frac{d^{10}}{a^{9} b^{7}}\right)^{\frac{1}{4}} - \sqrt{-15625 \, a^{5} b^{3} d^{10} \sqrt{-\frac{d^{10}}{a^{9} b^{7}}} + 15625 \, d^{15} x} a^{2} b^{2} \left(-\frac{d^{10}}{a^{9} b^{7}}\right)^{\frac{1}{4}}}{125 \, d^{10}}\right) - 15 \, {\left(a^{2} b^{4} x^{6} + 3 \, a^{3} b^{3} x^{4} + 3 \, a^{4} b^{2} x^{2} + a^{5} b\right)} \left(-\frac{d^{10}}{a^{9} b^{7}}\right)^{\frac{1}{4}} \log\left(125 \, a^{7} b^{5} \left(-\frac{d^{10}}{a^{9} b^{7}}\right)^{\frac{3}{4}} + 125 \, \sqrt{d x} d^{7}\right) + 15 \, {\left(a^{2} b^{4} x^{6} + 3 \, a^{3} b^{3} x^{4} + 3 \, a^{4} b^{2} x^{2} + a^{5} b\right)} \left(-\frac{d^{10}}{a^{9} b^{7}}\right)^{\frac{1}{4}} \log\left(-125 \, a^{7} b^{5} \left(-\frac{d^{10}}{a^{9} b^{7}}\right)^{\frac{3}{4}} + 125 \, \sqrt{d x} d^{7}\right) - 4 \, {\left(15 \, b^{2} d^{2} x^{5} + 42 \, a b d^{2} x^{3} - 5 \, a^{2} d^{2} x\right)} \sqrt{d x}}{768 \, {\left(a^{2} b^{4} x^{6} + 3 \, a^{3} b^{3} x^{4} + 3 \, a^{4} b^{2} x^{2} + a^{5} b\right)}}"," ",0,"-1/768*(60*(a^2*b^4*x^6 + 3*a^3*b^3*x^4 + 3*a^4*b^2*x^2 + a^5*b)*(-d^10/(a^9*b^7))^(1/4)*arctan(-1/125*(125*sqrt(d*x)*a^2*b^2*d^7*(-d^10/(a^9*b^7))^(1/4) - sqrt(-15625*a^5*b^3*d^10*sqrt(-d^10/(a^9*b^7)) + 15625*d^15*x)*a^2*b^2*(-d^10/(a^9*b^7))^(1/4))/d^10) - 15*(a^2*b^4*x^6 + 3*a^3*b^3*x^4 + 3*a^4*b^2*x^2 + a^5*b)*(-d^10/(a^9*b^7))^(1/4)*log(125*a^7*b^5*(-d^10/(a^9*b^7))^(3/4) + 125*sqrt(d*x)*d^7) + 15*(a^2*b^4*x^6 + 3*a^3*b^3*x^4 + 3*a^4*b^2*x^2 + a^5*b)*(-d^10/(a^9*b^7))^(1/4)*log(-125*a^7*b^5*(-d^10/(a^9*b^7))^(3/4) + 125*sqrt(d*x)*d^7) - 4*(15*b^2*d^2*x^5 + 42*a*b*d^2*x^3 - 5*a^2*d^2*x)*sqrt(d*x))/(a^2*b^4*x^6 + 3*a^3*b^3*x^4 + 3*a^4*b^2*x^2 + a^5*b)","A",0
704,1,373,0,1.677759," ","integrate((d*x)^(3/2)/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""fricas"")","\frac{84 \, {\left(a^{2} b^{4} x^{6} + 3 \, a^{3} b^{3} x^{4} + 3 \, a^{4} b^{2} x^{2} + a^{5} b\right)} \left(-\frac{d^{6}}{a^{11} b^{5}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{d x} a^{8} b^{4} d \left(-\frac{d^{6}}{a^{11} b^{5}}\right)^{\frac{3}{4}} - \sqrt{a^{6} b^{2} \sqrt{-\frac{d^{6}}{a^{11} b^{5}}} + d^{3} x} a^{8} b^{4} \left(-\frac{d^{6}}{a^{11} b^{5}}\right)^{\frac{3}{4}}}{d^{6}}\right) + 21 \, {\left(a^{2} b^{4} x^{6} + 3 \, a^{3} b^{3} x^{4} + 3 \, a^{4} b^{2} x^{2} + a^{5} b\right)} \left(-\frac{d^{6}}{a^{11} b^{5}}\right)^{\frac{1}{4}} \log\left(7 \, a^{3} b \left(-\frac{d^{6}}{a^{11} b^{5}}\right)^{\frac{1}{4}} + 7 \, \sqrt{d x} d\right) - 21 \, {\left(a^{2} b^{4} x^{6} + 3 \, a^{3} b^{3} x^{4} + 3 \, a^{4} b^{2} x^{2} + a^{5} b\right)} \left(-\frac{d^{6}}{a^{11} b^{5}}\right)^{\frac{1}{4}} \log\left(-7 \, a^{3} b \left(-\frac{d^{6}}{a^{11} b^{5}}\right)^{\frac{1}{4}} + 7 \, \sqrt{d x} d\right) + 4 \, {\left(7 \, b^{2} d x^{4} + 18 \, a b d x^{2} - 21 \, a^{2} d\right)} \sqrt{d x}}{768 \, {\left(a^{2} b^{4} x^{6} + 3 \, a^{3} b^{3} x^{4} + 3 \, a^{4} b^{2} x^{2} + a^{5} b\right)}}"," ",0,"1/768*(84*(a^2*b^4*x^6 + 3*a^3*b^3*x^4 + 3*a^4*b^2*x^2 + a^5*b)*(-d^6/(a^11*b^5))^(1/4)*arctan(-(sqrt(d*x)*a^8*b^4*d*(-d^6/(a^11*b^5))^(3/4) - sqrt(a^6*b^2*sqrt(-d^6/(a^11*b^5)) + d^3*x)*a^8*b^4*(-d^6/(a^11*b^5))^(3/4))/d^6) + 21*(a^2*b^4*x^6 + 3*a^3*b^3*x^4 + 3*a^4*b^2*x^2 + a^5*b)*(-d^6/(a^11*b^5))^(1/4)*log(7*a^3*b*(-d^6/(a^11*b^5))^(1/4) + 7*sqrt(d*x)*d) - 21*(a^2*b^4*x^6 + 3*a^3*b^3*x^4 + 3*a^4*b^2*x^2 + a^5*b)*(-d^6/(a^11*b^5))^(1/4)*log(-7*a^3*b*(-d^6/(a^11*b^5))^(1/4) + 7*sqrt(d*x)*d) + 4*(7*b^2*d*x^4 + 18*a*b*d*x^2 - 21*a^2*d)*sqrt(d*x))/(a^2*b^4*x^6 + 3*a^3*b^3*x^4 + 3*a^4*b^2*x^2 + a^5*b)","A",0
705,1,359,0,1.989752," ","integrate((d*x)^(1/2)/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""fricas"")","-\frac{180 \, {\left(a^{3} b^{3} x^{6} + 3 \, a^{4} b^{2} x^{4} + 3 \, a^{5} b x^{2} + a^{6}\right)} \left(-\frac{d^{2}}{a^{13} b^{3}}\right)^{\frac{1}{4}} \arctan\left(-\frac{3375 \, \sqrt{d x} a^{3} b d \left(-\frac{d^{2}}{a^{13} b^{3}}\right)^{\frac{1}{4}} - \sqrt{-11390625 \, a^{7} b d^{2} \sqrt{-\frac{d^{2}}{a^{13} b^{3}}} + 11390625 \, d^{3} x} a^{3} b \left(-\frac{d^{2}}{a^{13} b^{3}}\right)^{\frac{1}{4}}}{3375 \, d^{2}}\right) - 45 \, {\left(a^{3} b^{3} x^{6} + 3 \, a^{4} b^{2} x^{4} + 3 \, a^{5} b x^{2} + a^{6}\right)} \left(-\frac{d^{2}}{a^{13} b^{3}}\right)^{\frac{1}{4}} \log\left(3375 \, a^{10} b^{2} \left(-\frac{d^{2}}{a^{13} b^{3}}\right)^{\frac{3}{4}} + 3375 \, \sqrt{d x} d\right) + 45 \, {\left(a^{3} b^{3} x^{6} + 3 \, a^{4} b^{2} x^{4} + 3 \, a^{5} b x^{2} + a^{6}\right)} \left(-\frac{d^{2}}{a^{13} b^{3}}\right)^{\frac{1}{4}} \log\left(-3375 \, a^{10} b^{2} \left(-\frac{d^{2}}{a^{13} b^{3}}\right)^{\frac{3}{4}} + 3375 \, \sqrt{d x} d\right) - 4 \, {\left(45 \, b^{2} x^{5} + 126 \, a b x^{3} + 113 \, a^{2} x\right)} \sqrt{d x}}{768 \, {\left(a^{3} b^{3} x^{6} + 3 \, a^{4} b^{2} x^{4} + 3 \, a^{5} b x^{2} + a^{6}\right)}}"," ",0,"-1/768*(180*(a^3*b^3*x^6 + 3*a^4*b^2*x^4 + 3*a^5*b*x^2 + a^6)*(-d^2/(a^13*b^3))^(1/4)*arctan(-1/3375*(3375*sqrt(d*x)*a^3*b*d*(-d^2/(a^13*b^3))^(1/4) - sqrt(-11390625*a^7*b*d^2*sqrt(-d^2/(a^13*b^3)) + 11390625*d^3*x)*a^3*b*(-d^2/(a^13*b^3))^(1/4))/d^2) - 45*(a^3*b^3*x^6 + 3*a^4*b^2*x^4 + 3*a^5*b*x^2 + a^6)*(-d^2/(a^13*b^3))^(1/4)*log(3375*a^10*b^2*(-d^2/(a^13*b^3))^(3/4) + 3375*sqrt(d*x)*d) + 45*(a^3*b^3*x^6 + 3*a^4*b^2*x^4 + 3*a^5*b*x^2 + a^6)*(-d^2/(a^13*b^3))^(1/4)*log(-3375*a^10*b^2*(-d^2/(a^13*b^3))^(3/4) + 3375*sqrt(d*x)*d) - 4*(45*b^2*x^5 + 126*a*b*x^3 + 113*a^2*x)*sqrt(d*x))/(a^3*b^3*x^6 + 3*a^4*b^2*x^4 + 3*a^5*b*x^2 + a^6)","A",0
706,1,357,0,0.649207," ","integrate(1/(b^2*x^4+2*a*b*x^2+a^2)^2/(d*x)^(1/2),x, algorithm=""fricas"")","\frac{924 \, {\left(a^{3} b^{3} d x^{6} + 3 \, a^{4} b^{2} d x^{4} + 3 \, a^{5} b d x^{2} + a^{6} d\right)} \left(-\frac{1}{a^{15} b d^{2}}\right)^{\frac{1}{4}} \arctan\left(\sqrt{a^{8} d^{2} \sqrt{-\frac{1}{a^{15} b d^{2}}} + d x} a^{11} b d \left(-\frac{1}{a^{15} b d^{2}}\right)^{\frac{3}{4}} - \sqrt{d x} a^{11} b d \left(-\frac{1}{a^{15} b d^{2}}\right)^{\frac{3}{4}}\right) + 231 \, {\left(a^{3} b^{3} d x^{6} + 3 \, a^{4} b^{2} d x^{4} + 3 \, a^{5} b d x^{2} + a^{6} d\right)} \left(-\frac{1}{a^{15} b d^{2}}\right)^{\frac{1}{4}} \log\left(a^{4} d \left(-\frac{1}{a^{15} b d^{2}}\right)^{\frac{1}{4}} + \sqrt{d x}\right) - 231 \, {\left(a^{3} b^{3} d x^{6} + 3 \, a^{4} b^{2} d x^{4} + 3 \, a^{5} b d x^{2} + a^{6} d\right)} \left(-\frac{1}{a^{15} b d^{2}}\right)^{\frac{1}{4}} \log\left(-a^{4} d \left(-\frac{1}{a^{15} b d^{2}}\right)^{\frac{1}{4}} + \sqrt{d x}\right) + 4 \, {\left(77 \, b^{2} x^{4} + 198 \, a b x^{2} + 153 \, a^{2}\right)} \sqrt{d x}}{768 \, {\left(a^{3} b^{3} d x^{6} + 3 \, a^{4} b^{2} d x^{4} + 3 \, a^{5} b d x^{2} + a^{6} d\right)}}"," ",0,"1/768*(924*(a^3*b^3*d*x^6 + 3*a^4*b^2*d*x^4 + 3*a^5*b*d*x^2 + a^6*d)*(-1/(a^15*b*d^2))^(1/4)*arctan(sqrt(a^8*d^2*sqrt(-1/(a^15*b*d^2)) + d*x)*a^11*b*d*(-1/(a^15*b*d^2))^(3/4) - sqrt(d*x)*a^11*b*d*(-1/(a^15*b*d^2))^(3/4)) + 231*(a^3*b^3*d*x^6 + 3*a^4*b^2*d*x^4 + 3*a^5*b*d*x^2 + a^6*d)*(-1/(a^15*b*d^2))^(1/4)*log(a^4*d*(-1/(a^15*b*d^2))^(1/4) + sqrt(d*x)) - 231*(a^3*b^3*d*x^6 + 3*a^4*b^2*d*x^4 + 3*a^5*b*d*x^2 + a^6*d)*(-1/(a^15*b*d^2))^(1/4)*log(-a^4*d*(-1/(a^15*b*d^2))^(1/4) + sqrt(d*x)) + 4*(77*b^2*x^4 + 198*a*b*x^2 + 153*a^2)*sqrt(d*x))/(a^3*b^3*d*x^6 + 3*a^4*b^2*d*x^4 + 3*a^5*b*d*x^2 + a^6*d)","A",0
707,1,410,0,1.673471," ","integrate(1/(d*x)^(3/2)/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""fricas"")","\frac{2340 \, {\left(a^{4} b^{3} d^{2} x^{7} + 3 \, a^{5} b^{2} d^{2} x^{5} + 3 \, a^{6} b d^{2} x^{3} + a^{7} d^{2} x\right)} \left(-\frac{b}{a^{17} d^{6}}\right)^{\frac{1}{4}} \arctan\left(-\frac{7414875 \, \sqrt{d x} a^{4} b d \left(-\frac{b}{a^{17} d^{6}}\right)^{\frac{1}{4}} - \sqrt{-54980371265625 \, a^{9} b d^{4} \sqrt{-\frac{b}{a^{17} d^{6}}} + 54980371265625 \, b^{2} d x} a^{4} d \left(-\frac{b}{a^{17} d^{6}}\right)^{\frac{1}{4}}}{7414875 \, b}\right) - 585 \, {\left(a^{4} b^{3} d^{2} x^{7} + 3 \, a^{5} b^{2} d^{2} x^{5} + 3 \, a^{6} b d^{2} x^{3} + a^{7} d^{2} x\right)} \left(-\frac{b}{a^{17} d^{6}}\right)^{\frac{1}{4}} \log\left(7414875 \, a^{13} d^{5} \left(-\frac{b}{a^{17} d^{6}}\right)^{\frac{3}{4}} + 7414875 \, \sqrt{d x} b\right) + 585 \, {\left(a^{4} b^{3} d^{2} x^{7} + 3 \, a^{5} b^{2} d^{2} x^{5} + 3 \, a^{6} b d^{2} x^{3} + a^{7} d^{2} x\right)} \left(-\frac{b}{a^{17} d^{6}}\right)^{\frac{1}{4}} \log\left(-7414875 \, a^{13} d^{5} \left(-\frac{b}{a^{17} d^{6}}\right)^{\frac{3}{4}} + 7414875 \, \sqrt{d x} b\right) - 4 \, {\left(585 \, b^{3} x^{6} + 1638 \, a b^{2} x^{4} + 1469 \, a^{2} b x^{2} + 384 \, a^{3}\right)} \sqrt{d x}}{768 \, {\left(a^{4} b^{3} d^{2} x^{7} + 3 \, a^{5} b^{2} d^{2} x^{5} + 3 \, a^{6} b d^{2} x^{3} + a^{7} d^{2} x\right)}}"," ",0,"1/768*(2340*(a^4*b^3*d^2*x^7 + 3*a^5*b^2*d^2*x^5 + 3*a^6*b*d^2*x^3 + a^7*d^2*x)*(-b/(a^17*d^6))^(1/4)*arctan(-1/7414875*(7414875*sqrt(d*x)*a^4*b*d*(-b/(a^17*d^6))^(1/4) - sqrt(-54980371265625*a^9*b*d^4*sqrt(-b/(a^17*d^6)) + 54980371265625*b^2*d*x)*a^4*d*(-b/(a^17*d^6))^(1/4))/b) - 585*(a^4*b^3*d^2*x^7 + 3*a^5*b^2*d^2*x^5 + 3*a^6*b*d^2*x^3 + a^7*d^2*x)*(-b/(a^17*d^6))^(1/4)*log(7414875*a^13*d^5*(-b/(a^17*d^6))^(3/4) + 7414875*sqrt(d*x)*b) + 585*(a^4*b^3*d^2*x^7 + 3*a^5*b^2*d^2*x^5 + 3*a^6*b*d^2*x^3 + a^7*d^2*x)*(-b/(a^17*d^6))^(1/4)*log(-7414875*a^13*d^5*(-b/(a^17*d^6))^(3/4) + 7414875*sqrt(d*x)*b) - 4*(585*b^3*x^6 + 1638*a*b^2*x^4 + 1469*a^2*b*x^2 + 384*a^3)*sqrt(d*x))/(a^4*b^3*d^2*x^7 + 3*a^5*b^2*d^2*x^5 + 3*a^6*b*d^2*x^3 + a^7*d^2*x)","A",0
708,1,434,0,0.887311," ","integrate(1/(d*x)^(5/2)/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""fricas"")","-\frac{4620 \, {\left(a^{4} b^{3} d^{3} x^{8} + 3 \, a^{5} b^{2} d^{3} x^{6} + 3 \, a^{6} b d^{3} x^{4} + a^{7} d^{3} x^{2}\right)} \left(-\frac{b^{3}}{a^{19} d^{10}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{d x} a^{14} b d^{7} \left(-\frac{b^{3}}{a^{19} d^{10}}\right)^{\frac{3}{4}} - \sqrt{a^{10} d^{6} \sqrt{-\frac{b^{3}}{a^{19} d^{10}}} + b^{2} d x} a^{14} d^{7} \left(-\frac{b^{3}}{a^{19} d^{10}}\right)^{\frac{3}{4}}}{b^{3}}\right) + 1155 \, {\left(a^{4} b^{3} d^{3} x^{8} + 3 \, a^{5} b^{2} d^{3} x^{6} + 3 \, a^{6} b d^{3} x^{4} + a^{7} d^{3} x^{2}\right)} \left(-\frac{b^{3}}{a^{19} d^{10}}\right)^{\frac{1}{4}} \log\left(385 \, a^{5} d^{3} \left(-\frac{b^{3}}{a^{19} d^{10}}\right)^{\frac{1}{4}} + 385 \, \sqrt{d x} b\right) - 1155 \, {\left(a^{4} b^{3} d^{3} x^{8} + 3 \, a^{5} b^{2} d^{3} x^{6} + 3 \, a^{6} b d^{3} x^{4} + a^{7} d^{3} x^{2}\right)} \left(-\frac{b^{3}}{a^{19} d^{10}}\right)^{\frac{1}{4}} \log\left(-385 \, a^{5} d^{3} \left(-\frac{b^{3}}{a^{19} d^{10}}\right)^{\frac{1}{4}} + 385 \, \sqrt{d x} b\right) + 4 \, {\left(385 \, b^{3} x^{6} + 990 \, a b^{2} x^{4} + 765 \, a^{2} b x^{2} + 128 \, a^{3}\right)} \sqrt{d x}}{768 \, {\left(a^{4} b^{3} d^{3} x^{8} + 3 \, a^{5} b^{2} d^{3} x^{6} + 3 \, a^{6} b d^{3} x^{4} + a^{7} d^{3} x^{2}\right)}}"," ",0,"-1/768*(4620*(a^4*b^3*d^3*x^8 + 3*a^5*b^2*d^3*x^6 + 3*a^6*b*d^3*x^4 + a^7*d^3*x^2)*(-b^3/(a^19*d^10))^(1/4)*arctan(-(sqrt(d*x)*a^14*b*d^7*(-b^3/(a^19*d^10))^(3/4) - sqrt(a^10*d^6*sqrt(-b^3/(a^19*d^10)) + b^2*d*x)*a^14*d^7*(-b^3/(a^19*d^10))^(3/4))/b^3) + 1155*(a^4*b^3*d^3*x^8 + 3*a^5*b^2*d^3*x^6 + 3*a^6*b*d^3*x^4 + a^7*d^3*x^2)*(-b^3/(a^19*d^10))^(1/4)*log(385*a^5*d^3*(-b^3/(a^19*d^10))^(1/4) + 385*sqrt(d*x)*b) - 1155*(a^4*b^3*d^3*x^8 + 3*a^5*b^2*d^3*x^6 + 3*a^6*b*d^3*x^4 + a^7*d^3*x^2)*(-b^3/(a^19*d^10))^(1/4)*log(-385*a^5*d^3*(-b^3/(a^19*d^10))^(1/4) + 385*sqrt(d*x)*b) + 4*(385*b^3*x^6 + 990*a*b^2*x^4 + 765*a^2*b*x^2 + 128*a^3)*sqrt(d*x))/(a^4*b^3*d^3*x^8 + 3*a^5*b^2*d^3*x^6 + 3*a^6*b*d^3*x^4 + a^7*d^3*x^2)","A",0
709,1,457,0,2.023212," ","integrate(1/(d*x)^(7/2)/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""fricas"")","-\frac{39780 \, {\left(a^{5} b^{3} d^{4} x^{9} + 3 \, a^{6} b^{2} d^{4} x^{7} + 3 \, a^{7} b d^{4} x^{5} + a^{8} d^{4} x^{3}\right)} \left(-\frac{b^{5}}{a^{21} d^{14}}\right)^{\frac{1}{4}} \arctan\left(-\frac{291434247 \, \sqrt{d x} a^{5} b^{4} d^{3} \left(-\frac{b^{5}}{a^{21} d^{14}}\right)^{\frac{1}{4}} - \sqrt{-84933920324457009 \, a^{11} b^{5} d^{8} \sqrt{-\frac{b^{5}}{a^{21} d^{14}}} + 84933920324457009 \, b^{8} d x} a^{5} d^{3} \left(-\frac{b^{5}}{a^{21} d^{14}}\right)^{\frac{1}{4}}}{291434247 \, b^{5}}\right) - 9945 \, {\left(a^{5} b^{3} d^{4} x^{9} + 3 \, a^{6} b^{2} d^{4} x^{7} + 3 \, a^{7} b d^{4} x^{5} + a^{8} d^{4} x^{3}\right)} \left(-\frac{b^{5}}{a^{21} d^{14}}\right)^{\frac{1}{4}} \log\left(291434247 \, a^{16} d^{11} \left(-\frac{b^{5}}{a^{21} d^{14}}\right)^{\frac{3}{4}} + 291434247 \, \sqrt{d x} b^{4}\right) + 9945 \, {\left(a^{5} b^{3} d^{4} x^{9} + 3 \, a^{6} b^{2} d^{4} x^{7} + 3 \, a^{7} b d^{4} x^{5} + a^{8} d^{4} x^{3}\right)} \left(-\frac{b^{5}}{a^{21} d^{14}}\right)^{\frac{1}{4}} \log\left(-291434247 \, a^{16} d^{11} \left(-\frac{b^{5}}{a^{21} d^{14}}\right)^{\frac{3}{4}} + 291434247 \, \sqrt{d x} b^{4}\right) - 4 \, {\left(9945 \, b^{4} x^{8} + 27846 \, a b^{3} x^{6} + 24973 \, a^{2} b^{2} x^{4} + 6528 \, a^{3} b x^{2} - 384 \, a^{4}\right)} \sqrt{d x}}{3840 \, {\left(a^{5} b^{3} d^{4} x^{9} + 3 \, a^{6} b^{2} d^{4} x^{7} + 3 \, a^{7} b d^{4} x^{5} + a^{8} d^{4} x^{3}\right)}}"," ",0,"-1/3840*(39780*(a^5*b^3*d^4*x^9 + 3*a^6*b^2*d^4*x^7 + 3*a^7*b*d^4*x^5 + a^8*d^4*x^3)*(-b^5/(a^21*d^14))^(1/4)*arctan(-1/291434247*(291434247*sqrt(d*x)*a^5*b^4*d^3*(-b^5/(a^21*d^14))^(1/4) - sqrt(-84933920324457009*a^11*b^5*d^8*sqrt(-b^5/(a^21*d^14)) + 84933920324457009*b^8*d*x)*a^5*d^3*(-b^5/(a^21*d^14))^(1/4))/b^5) - 9945*(a^5*b^3*d^4*x^9 + 3*a^6*b^2*d^4*x^7 + 3*a^7*b*d^4*x^5 + a^8*d^4*x^3)*(-b^5/(a^21*d^14))^(1/4)*log(291434247*a^16*d^11*(-b^5/(a^21*d^14))^(3/4) + 291434247*sqrt(d*x)*b^4) + 9945*(a^5*b^3*d^4*x^9 + 3*a^6*b^2*d^4*x^7 + 3*a^7*b*d^4*x^5 + a^8*d^4*x^3)*(-b^5/(a^21*d^14))^(1/4)*log(-291434247*a^16*d^11*(-b^5/(a^21*d^14))^(3/4) + 291434247*sqrt(d*x)*b^4) - 4*(9945*b^4*x^8 + 27846*a*b^3*x^6 + 24973*a^2*b^2*x^4 + 6528*a^3*b*x^2 - 384*a^4)*sqrt(d*x))/(a^5*b^3*d^4*x^9 + 3*a^6*b^2*d^4*x^7 + 3*a^7*b*d^4*x^5 + a^8*d^4*x^3)","A",0
710,1,515,0,0.951212," ","integrate((d*x)^(27/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","\frac{1392300 \, \left(-\frac{a^{5} d^{54}}{b^{29}}\right)^{\frac{1}{4}} {\left(b^{12} x^{10} + 5 \, a b^{11} x^{8} + 10 \, a^{2} b^{10} x^{6} + 10 \, a^{3} b^{9} x^{4} + 5 \, a^{4} b^{8} x^{2} + a^{5} b^{7}\right)} \arctan\left(-\frac{\left(-\frac{a^{5} d^{54}}{b^{29}}\right)^{\frac{3}{4}} \sqrt{d x} a b^{22} d^{13} - \left(-\frac{a^{5} d^{54}}{b^{29}}\right)^{\frac{3}{4}} \sqrt{a^{2} d^{27} x + \sqrt{-\frac{a^{5} d^{54}}{b^{29}}} b^{14}} b^{22}}{a^{5} d^{54}}\right) + 348075 \, \left(-\frac{a^{5} d^{54}}{b^{29}}\right)^{\frac{1}{4}} {\left(b^{12} x^{10} + 5 \, a b^{11} x^{8} + 10 \, a^{2} b^{10} x^{6} + 10 \, a^{3} b^{9} x^{4} + 5 \, a^{4} b^{8} x^{2} + a^{5} b^{7}\right)} \log\left(69615 \, \sqrt{d x} a d^{13} + 69615 \, \left(-\frac{a^{5} d^{54}}{b^{29}}\right)^{\frac{1}{4}} b^{7}\right) - 348075 \, \left(-\frac{a^{5} d^{54}}{b^{29}}\right)^{\frac{1}{4}} {\left(b^{12} x^{10} + 5 \, a b^{11} x^{8} + 10 \, a^{2} b^{10} x^{6} + 10 \, a^{3} b^{9} x^{4} + 5 \, a^{4} b^{8} x^{2} + a^{5} b^{7}\right)} \log\left(69615 \, \sqrt{d x} a d^{13} - 69615 \, \left(-\frac{a^{5} d^{54}}{b^{29}}\right)^{\frac{1}{4}} b^{7}\right) + 4 \, {\left(8192 \, b^{6} d^{13} x^{12} - 204800 \, a b^{5} d^{13} x^{10} - 1317575 \, a^{2} b^{4} d^{13} x^{8} - 2951200 \, a^{3} b^{3} d^{13} x^{6} - 3171350 \, a^{4} b^{2} d^{13} x^{4} - 1670760 \, a^{5} b d^{13} x^{2} - 348075 \, a^{6} d^{13}\right)} \sqrt{d x}}{81920 \, {\left(b^{12} x^{10} + 5 \, a b^{11} x^{8} + 10 \, a^{2} b^{10} x^{6} + 10 \, a^{3} b^{9} x^{4} + 5 \, a^{4} b^{8} x^{2} + a^{5} b^{7}\right)}}"," ",0,"1/81920*(1392300*(-a^5*d^54/b^29)^(1/4)*(b^12*x^10 + 5*a*b^11*x^8 + 10*a^2*b^10*x^6 + 10*a^3*b^9*x^4 + 5*a^4*b^8*x^2 + a^5*b^7)*arctan(-((-a^5*d^54/b^29)^(3/4)*sqrt(d*x)*a*b^22*d^13 - (-a^5*d^54/b^29)^(3/4)*sqrt(a^2*d^27*x + sqrt(-a^5*d^54/b^29)*b^14)*b^22)/(a^5*d^54)) + 348075*(-a^5*d^54/b^29)^(1/4)*(b^12*x^10 + 5*a*b^11*x^8 + 10*a^2*b^10*x^6 + 10*a^3*b^9*x^4 + 5*a^4*b^8*x^2 + a^5*b^7)*log(69615*sqrt(d*x)*a*d^13 + 69615*(-a^5*d^54/b^29)^(1/4)*b^7) - 348075*(-a^5*d^54/b^29)^(1/4)*(b^12*x^10 + 5*a*b^11*x^8 + 10*a^2*b^10*x^6 + 10*a^3*b^9*x^4 + 5*a^4*b^8*x^2 + a^5*b^7)*log(69615*sqrt(d*x)*a*d^13 - 69615*(-a^5*d^54/b^29)^(1/4)*b^7) + 4*(8192*b^6*d^13*x^12 - 204800*a*b^5*d^13*x^10 - 1317575*a^2*b^4*d^13*x^8 - 2951200*a^3*b^3*d^13*x^6 - 3171350*a^4*b^2*d^13*x^4 - 1670760*a^5*b*d^13*x^2 - 348075*a^6*d^13)*sqrt(d*x))/(b^12*x^10 + 5*a*b^11*x^8 + 10*a^2*b^10*x^6 + 10*a^3*b^9*x^4 + 5*a^4*b^8*x^2 + a^5*b^7)","A",0
711,1,515,0,2.336869," ","integrate((d*x)^(25/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","\frac{2018940 \, \left(-\frac{a^{3} d^{50}}{b^{27}}\right)^{\frac{1}{4}} {\left(b^{11} x^{10} + 5 \, a b^{10} x^{8} + 10 \, a^{2} b^{9} x^{6} + 10 \, a^{3} b^{8} x^{4} + 5 \, a^{4} b^{7} x^{2} + a^{5} b^{6}\right)} \arctan\left(-\frac{\left(-\frac{a^{3} d^{50}}{b^{27}}\right)^{\frac{1}{4}} \sqrt{d x} a^{2} b^{7} d^{37} - \sqrt{a^{4} d^{75} x - \sqrt{-\frac{a^{3} d^{50}}{b^{27}}} a^{3} b^{13} d^{50}} \left(-\frac{a^{3} d^{50}}{b^{27}}\right)^{\frac{1}{4}} b^{7}}{a^{3} d^{50}}\right) - 504735 \, \left(-\frac{a^{3} d^{50}}{b^{27}}\right)^{\frac{1}{4}} {\left(b^{11} x^{10} + 5 \, a b^{10} x^{8} + 10 \, a^{2} b^{9} x^{6} + 10 \, a^{3} b^{8} x^{4} + 5 \, a^{4} b^{7} x^{2} + a^{5} b^{6}\right)} \log\left(38099255258449 \, \sqrt{d x} a^{2} d^{37} + 38099255258449 \, \left(-\frac{a^{3} d^{50}}{b^{27}}\right)^{\frac{3}{4}} b^{20}\right) + 504735 \, \left(-\frac{a^{3} d^{50}}{b^{27}}\right)^{\frac{1}{4}} {\left(b^{11} x^{10} + 5 \, a b^{10} x^{8} + 10 \, a^{2} b^{9} x^{6} + 10 \, a^{3} b^{8} x^{4} + 5 \, a^{4} b^{7} x^{2} + a^{5} b^{6}\right)} \log\left(38099255258449 \, \sqrt{d x} a^{2} d^{37} - 38099255258449 \, \left(-\frac{a^{3} d^{50}}{b^{27}}\right)^{\frac{3}{4}} b^{20}\right) + 4 \, {\left(40960 \, b^{5} d^{12} x^{11} + 437345 \, a b^{4} d^{12} x^{9} + 1157176 \, a^{2} b^{3} d^{12} x^{7} + 1367810 \, a^{3} b^{2} d^{12} x^{5} + 769120 \, a^{4} b d^{12} x^{3} + 168245 \, a^{5} d^{12} x\right)} \sqrt{d x}}{245760 \, {\left(b^{11} x^{10} + 5 \, a b^{10} x^{8} + 10 \, a^{2} b^{9} x^{6} + 10 \, a^{3} b^{8} x^{4} + 5 \, a^{4} b^{7} x^{2} + a^{5} b^{6}\right)}}"," ",0,"1/245760*(2018940*(-a^3*d^50/b^27)^(1/4)*(b^11*x^10 + 5*a*b^10*x^8 + 10*a^2*b^9*x^6 + 10*a^3*b^8*x^4 + 5*a^4*b^7*x^2 + a^5*b^6)*arctan(-((-a^3*d^50/b^27)^(1/4)*sqrt(d*x)*a^2*b^7*d^37 - sqrt(a^4*d^75*x - sqrt(-a^3*d^50/b^27)*a^3*b^13*d^50)*(-a^3*d^50/b^27)^(1/4)*b^7)/(a^3*d^50)) - 504735*(-a^3*d^50/b^27)^(1/4)*(b^11*x^10 + 5*a*b^10*x^8 + 10*a^2*b^9*x^6 + 10*a^3*b^8*x^4 + 5*a^4*b^7*x^2 + a^5*b^6)*log(38099255258449*sqrt(d*x)*a^2*d^37 + 38099255258449*(-a^3*d^50/b^27)^(3/4)*b^20) + 504735*(-a^3*d^50/b^27)^(1/4)*(b^11*x^10 + 5*a*b^10*x^8 + 10*a^2*b^9*x^6 + 10*a^3*b^8*x^4 + 5*a^4*b^7*x^2 + a^5*b^6)*log(38099255258449*sqrt(d*x)*a^2*d^37 - 38099255258449*(-a^3*d^50/b^27)^(3/4)*b^20) + 4*(40960*b^5*d^12*x^11 + 437345*a*b^4*d^12*x^9 + 1157176*a^2*b^3*d^12*x^7 + 1367810*a^3*b^2*d^12*x^5 + 769120*a^4*b*d^12*x^3 + 168245*a^5*d^12*x)*sqrt(d*x))/(b^11*x^10 + 5*a*b^10*x^8 + 10*a^2*b^9*x^6 + 10*a^3*b^8*x^4 + 5*a^4*b^7*x^2 + a^5*b^6)","A",0
712,1,479,0,1.755495," ","integrate((d*x)^(23/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","-\frac{278460 \, \left(-\frac{a d^{46}}{b^{25}}\right)^{\frac{1}{4}} {\left(b^{11} x^{10} + 5 \, a b^{10} x^{8} + 10 \, a^{2} b^{9} x^{6} + 10 \, a^{3} b^{8} x^{4} + 5 \, a^{4} b^{7} x^{2} + a^{5} b^{6}\right)} \arctan\left(-\frac{\left(-\frac{a d^{46}}{b^{25}}\right)^{\frac{3}{4}} \sqrt{d x} b^{19} d^{11} - \sqrt{d^{23} x + \sqrt{-\frac{a d^{46}}{b^{25}}} b^{12}} \left(-\frac{a d^{46}}{b^{25}}\right)^{\frac{3}{4}} b^{19}}{a d^{46}}\right) + 69615 \, \left(-\frac{a d^{46}}{b^{25}}\right)^{\frac{1}{4}} {\left(b^{11} x^{10} + 5 \, a b^{10} x^{8} + 10 \, a^{2} b^{9} x^{6} + 10 \, a^{3} b^{8} x^{4} + 5 \, a^{4} b^{7} x^{2} + a^{5} b^{6}\right)} \log\left(13923 \, \sqrt{d x} d^{11} + 13923 \, \left(-\frac{a d^{46}}{b^{25}}\right)^{\frac{1}{4}} b^{6}\right) - 69615 \, \left(-\frac{a d^{46}}{b^{25}}\right)^{\frac{1}{4}} {\left(b^{11} x^{10} + 5 \, a b^{10} x^{8} + 10 \, a^{2} b^{9} x^{6} + 10 \, a^{3} b^{8} x^{4} + 5 \, a^{4} b^{7} x^{2} + a^{5} b^{6}\right)} \log\left(13923 \, \sqrt{d x} d^{11} - 13923 \, \left(-\frac{a d^{46}}{b^{25}}\right)^{\frac{1}{4}} b^{6}\right) - 4 \, {\left(40960 \, b^{5} d^{11} x^{10} + 263515 \, a b^{4} d^{11} x^{8} + 590240 \, a^{2} b^{3} d^{11} x^{6} + 634270 \, a^{3} b^{2} d^{11} x^{4} + 334152 \, a^{4} b d^{11} x^{2} + 69615 \, a^{5} d^{11}\right)} \sqrt{d x}}{81920 \, {\left(b^{11} x^{10} + 5 \, a b^{10} x^{8} + 10 \, a^{2} b^{9} x^{6} + 10 \, a^{3} b^{8} x^{4} + 5 \, a^{4} b^{7} x^{2} + a^{5} b^{6}\right)}}"," ",0,"-1/81920*(278460*(-a*d^46/b^25)^(1/4)*(b^11*x^10 + 5*a*b^10*x^8 + 10*a^2*b^9*x^6 + 10*a^3*b^8*x^4 + 5*a^4*b^7*x^2 + a^5*b^6)*arctan(-((-a*d^46/b^25)^(3/4)*sqrt(d*x)*b^19*d^11 - sqrt(d^23*x + sqrt(-a*d^46/b^25)*b^12)*(-a*d^46/b^25)^(3/4)*b^19)/(a*d^46)) + 69615*(-a*d^46/b^25)^(1/4)*(b^11*x^10 + 5*a*b^10*x^8 + 10*a^2*b^9*x^6 + 10*a^3*b^8*x^4 + 5*a^4*b^7*x^2 + a^5*b^6)*log(13923*sqrt(d*x)*d^11 + 13923*(-a*d^46/b^25)^(1/4)*b^6) - 69615*(-a*d^46/b^25)^(1/4)*(b^11*x^10 + 5*a*b^10*x^8 + 10*a^2*b^9*x^6 + 10*a^3*b^8*x^4 + 5*a^4*b^7*x^2 + a^5*b^6)*log(13923*sqrt(d*x)*d^11 - 13923*(-a*d^46/b^25)^(1/4)*b^6) - 4*(40960*b^5*d^11*x^10 + 263515*a*b^4*d^11*x^8 + 590240*a^2*b^3*d^11*x^6 + 634270*a^3*b^2*d^11*x^4 + 334152*a^4*b*d^11*x^2 + 69615*a^5*d^11)*sqrt(d*x))/(b^11*x^10 + 5*a*b^10*x^8 + 10*a^2*b^9*x^6 + 10*a^3*b^8*x^4 + 5*a^4*b^7*x^2 + a^5*b^6)","A",0
713,1,486,0,1.036966," ","integrate((d*x)^(21/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","-\frac{87780 \, {\left(b^{10} x^{10} + 5 \, a b^{9} x^{8} + 10 \, a^{2} b^{8} x^{6} + 10 \, a^{3} b^{7} x^{4} + 5 \, a^{4} b^{6} x^{2} + a^{5} b^{5}\right)} \left(-\frac{d^{42}}{a b^{23}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\left(-\frac{d^{42}}{a b^{23}}\right)^{\frac{1}{4}} \sqrt{d x} b^{6} d^{31} - \sqrt{d^{63} x - \sqrt{-\frac{d^{42}}{a b^{23}}} a b^{11} d^{42}} \left(-\frac{d^{42}}{a b^{23}}\right)^{\frac{1}{4}} b^{6}}{d^{42}}\right) - 21945 \, {\left(b^{10} x^{10} + 5 \, a b^{9} x^{8} + 10 \, a^{2} b^{8} x^{6} + 10 \, a^{3} b^{7} x^{4} + 5 \, a^{4} b^{6} x^{2} + a^{5} b^{5}\right)} \left(-\frac{d^{42}}{a b^{23}}\right)^{\frac{1}{4}} \log\left(84546715869 \, \sqrt{d x} d^{31} + 84546715869 \, \left(-\frac{d^{42}}{a b^{23}}\right)^{\frac{3}{4}} a b^{17}\right) + 21945 \, {\left(b^{10} x^{10} + 5 \, a b^{9} x^{8} + 10 \, a^{2} b^{8} x^{6} + 10 \, a^{3} b^{7} x^{4} + 5 \, a^{4} b^{6} x^{2} + a^{5} b^{5}\right)} \left(-\frac{d^{42}}{a b^{23}}\right)^{\frac{1}{4}} \log\left(84546715869 \, \sqrt{d x} d^{31} - 84546715869 \, \left(-\frac{d^{42}}{a b^{23}}\right)^{\frac{3}{4}} a b^{17}\right) + 4 \, {\left(19015 \, b^{4} d^{10} x^{9} + 50312 \, a b^{3} d^{10} x^{7} + 59470 \, a^{2} b^{2} d^{10} x^{5} + 33440 \, a^{3} b d^{10} x^{3} + 7315 \, a^{4} d^{10} x\right)} \sqrt{d x}}{81920 \, {\left(b^{10} x^{10} + 5 \, a b^{9} x^{8} + 10 \, a^{2} b^{8} x^{6} + 10 \, a^{3} b^{7} x^{4} + 5 \, a^{4} b^{6} x^{2} + a^{5} b^{5}\right)}}"," ",0,"-1/81920*(87780*(b^10*x^10 + 5*a*b^9*x^8 + 10*a^2*b^8*x^6 + 10*a^3*b^7*x^4 + 5*a^4*b^6*x^2 + a^5*b^5)*(-d^42/(a*b^23))^(1/4)*arctan(-((-d^42/(a*b^23))^(1/4)*sqrt(d*x)*b^6*d^31 - sqrt(d^63*x - sqrt(-d^42/(a*b^23))*a*b^11*d^42)*(-d^42/(a*b^23))^(1/4)*b^6)/d^42) - 21945*(b^10*x^10 + 5*a*b^9*x^8 + 10*a^2*b^8*x^6 + 10*a^3*b^7*x^4 + 5*a^4*b^6*x^2 + a^5*b^5)*(-d^42/(a*b^23))^(1/4)*log(84546715869*sqrt(d*x)*d^31 + 84546715869*(-d^42/(a*b^23))^(3/4)*a*b^17) + 21945*(b^10*x^10 + 5*a*b^9*x^8 + 10*a^2*b^8*x^6 + 10*a^3*b^7*x^4 + 5*a^4*b^6*x^2 + a^5*b^5)*(-d^42/(a*b^23))^(1/4)*log(84546715869*sqrt(d*x)*d^31 - 84546715869*(-d^42/(a*b^23))^(3/4)*a*b^17) + 4*(19015*b^4*d^10*x^9 + 50312*a*b^3*d^10*x^7 + 59470*a^2*b^2*d^10*x^5 + 33440*a^3*b*d^10*x^3 + 7315*a^4*d^10*x)*sqrt(d*x))/(b^10*x^10 + 5*a*b^9*x^8 + 10*a^2*b^8*x^6 + 10*a^3*b^7*x^4 + 5*a^4*b^6*x^2 + a^5*b^5)","A",0
714,1,489,0,1.689759," ","integrate((d*x)^(19/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","\frac{39780 \, {\left(b^{10} x^{10} + 5 \, a b^{9} x^{8} + 10 \, a^{2} b^{8} x^{6} + 10 \, a^{3} b^{7} x^{4} + 5 \, a^{4} b^{6} x^{2} + a^{5} b^{5}\right)} \left(-\frac{d^{38}}{a^{3} b^{21}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\left(-\frac{d^{38}}{a^{3} b^{21}}\right)^{\frac{3}{4}} \sqrt{d x} a^{2} b^{16} d^{9} - \sqrt{d^{19} x + \sqrt{-\frac{d^{38}}{a^{3} b^{21}}} a^{2} b^{10}} \left(-\frac{d^{38}}{a^{3} b^{21}}\right)^{\frac{3}{4}} a^{2} b^{16}}{d^{38}}\right) + 9945 \, {\left(b^{10} x^{10} + 5 \, a b^{9} x^{8} + 10 \, a^{2} b^{8} x^{6} + 10 \, a^{3} b^{7} x^{4} + 5 \, a^{4} b^{6} x^{2} + a^{5} b^{5}\right)} \left(-\frac{d^{38}}{a^{3} b^{21}}\right)^{\frac{1}{4}} \log\left(663 \, \sqrt{d x} d^{9} + 663 \, \left(-\frac{d^{38}}{a^{3} b^{21}}\right)^{\frac{1}{4}} a b^{5}\right) - 9945 \, {\left(b^{10} x^{10} + 5 \, a b^{9} x^{8} + 10 \, a^{2} b^{8} x^{6} + 10 \, a^{3} b^{7} x^{4} + 5 \, a^{4} b^{6} x^{2} + a^{5} b^{5}\right)} \left(-\frac{d^{38}}{a^{3} b^{21}}\right)^{\frac{1}{4}} \log\left(663 \, \sqrt{d x} d^{9} - 663 \, \left(-\frac{d^{38}}{a^{3} b^{21}}\right)^{\frac{1}{4}} a b^{5}\right) - 4 \, {\left(37645 \, b^{4} d^{9} x^{8} + 84320 \, a b^{3} d^{9} x^{6} + 90610 \, a^{2} b^{2} d^{9} x^{4} + 47736 \, a^{3} b d^{9} x^{2} + 9945 \, a^{4} d^{9}\right)} \sqrt{d x}}{245760 \, {\left(b^{10} x^{10} + 5 \, a b^{9} x^{8} + 10 \, a^{2} b^{8} x^{6} + 10 \, a^{3} b^{7} x^{4} + 5 \, a^{4} b^{6} x^{2} + a^{5} b^{5}\right)}}"," ",0,"1/245760*(39780*(b^10*x^10 + 5*a*b^9*x^8 + 10*a^2*b^8*x^6 + 10*a^3*b^7*x^4 + 5*a^4*b^6*x^2 + a^5*b^5)*(-d^38/(a^3*b^21))^(1/4)*arctan(-((-d^38/(a^3*b^21))^(3/4)*sqrt(d*x)*a^2*b^16*d^9 - sqrt(d^19*x + sqrt(-d^38/(a^3*b^21))*a^2*b^10)*(-d^38/(a^3*b^21))^(3/4)*a^2*b^16)/d^38) + 9945*(b^10*x^10 + 5*a*b^9*x^8 + 10*a^2*b^8*x^6 + 10*a^3*b^7*x^4 + 5*a^4*b^6*x^2 + a^5*b^5)*(-d^38/(a^3*b^21))^(1/4)*log(663*sqrt(d*x)*d^9 + 663*(-d^38/(a^3*b^21))^(1/4)*a*b^5) - 9945*(b^10*x^10 + 5*a*b^9*x^8 + 10*a^2*b^8*x^6 + 10*a^3*b^7*x^4 + 5*a^4*b^6*x^2 + a^5*b^5)*(-d^38/(a^3*b^21))^(1/4)*log(663*sqrt(d*x)*d^9 - 663*(-d^38/(a^3*b^21))^(1/4)*a*b^5) - 4*(37645*b^4*d^9*x^8 + 84320*a*b^3*d^9*x^6 + 90610*a^2*b^2*d^9*x^4 + 47736*a^3*b*d^9*x^2 + 9945*a^4*d^9)*sqrt(d*x))/(b^10*x^10 + 5*a*b^9*x^8 + 10*a^2*b^8*x^6 + 10*a^3*b^7*x^4 + 5*a^4*b^6*x^2 + a^5*b^5)","A",0
715,1,506,0,1.045679," ","integrate((d*x)^(17/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","-\frac{4620 \, {\left(a b^{9} x^{10} + 5 \, a^{2} b^{8} x^{8} + 10 \, a^{3} b^{7} x^{6} + 10 \, a^{4} b^{6} x^{4} + 5 \, a^{5} b^{5} x^{2} + a^{6} b^{4}\right)} \left(-\frac{d^{34}}{a^{5} b^{19}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\left(-\frac{d^{34}}{a^{5} b^{19}}\right)^{\frac{1}{4}} \sqrt{d x} a b^{5} d^{25} - \sqrt{d^{51} x - \sqrt{-\frac{d^{34}}{a^{5} b^{19}}} a^{3} b^{9} d^{34}} \left(-\frac{d^{34}}{a^{5} b^{19}}\right)^{\frac{1}{4}} a b^{5}}{d^{34}}\right) - 1155 \, {\left(a b^{9} x^{10} + 5 \, a^{2} b^{8} x^{8} + 10 \, a^{3} b^{7} x^{6} + 10 \, a^{4} b^{6} x^{4} + 5 \, a^{5} b^{5} x^{2} + a^{6} b^{4}\right)} \left(-\frac{d^{34}}{a^{5} b^{19}}\right)^{\frac{1}{4}} \log\left(12326391 \, \sqrt{d x} d^{25} + 12326391 \, \left(-\frac{d^{34}}{a^{5} b^{19}}\right)^{\frac{3}{4}} a^{4} b^{14}\right) + 1155 \, {\left(a b^{9} x^{10} + 5 \, a^{2} b^{8} x^{8} + 10 \, a^{3} b^{7} x^{6} + 10 \, a^{4} b^{6} x^{4} + 5 \, a^{5} b^{5} x^{2} + a^{6} b^{4}\right)} \left(-\frac{d^{34}}{a^{5} b^{19}}\right)^{\frac{1}{4}} \log\left(12326391 \, \sqrt{d x} d^{25} - 12326391 \, \left(-\frac{d^{34}}{a^{5} b^{19}}\right)^{\frac{3}{4}} a^{4} b^{14}\right) - 4 \, {\left(1155 \, b^{4} d^{8} x^{9} - 2648 \, a b^{3} d^{8} x^{7} - 3130 \, a^{2} b^{2} d^{8} x^{5} - 1760 \, a^{3} b d^{8} x^{3} - 385 \, a^{4} d^{8} x\right)} \sqrt{d x}}{81920 \, {\left(a b^{9} x^{10} + 5 \, a^{2} b^{8} x^{8} + 10 \, a^{3} b^{7} x^{6} + 10 \, a^{4} b^{6} x^{4} + 5 \, a^{5} b^{5} x^{2} + a^{6} b^{4}\right)}}"," ",0,"-1/81920*(4620*(a*b^9*x^10 + 5*a^2*b^8*x^8 + 10*a^3*b^7*x^6 + 10*a^4*b^6*x^4 + 5*a^5*b^5*x^2 + a^6*b^4)*(-d^34/(a^5*b^19))^(1/4)*arctan(-((-d^34/(a^5*b^19))^(1/4)*sqrt(d*x)*a*b^5*d^25 - sqrt(d^51*x - sqrt(-d^34/(a^5*b^19))*a^3*b^9*d^34)*(-d^34/(a^5*b^19))^(1/4)*a*b^5)/d^34) - 1155*(a*b^9*x^10 + 5*a^2*b^8*x^8 + 10*a^3*b^7*x^6 + 10*a^4*b^6*x^4 + 5*a^5*b^5*x^2 + a^6*b^4)*(-d^34/(a^5*b^19))^(1/4)*log(12326391*sqrt(d*x)*d^25 + 12326391*(-d^34/(a^5*b^19))^(3/4)*a^4*b^14) + 1155*(a*b^9*x^10 + 5*a^2*b^8*x^8 + 10*a^3*b^7*x^6 + 10*a^4*b^6*x^4 + 5*a^5*b^5*x^2 + a^6*b^4)*(-d^34/(a^5*b^19))^(1/4)*log(12326391*sqrt(d*x)*d^25 - 12326391*(-d^34/(a^5*b^19))^(3/4)*a^4*b^14) - 4*(1155*b^4*d^8*x^9 - 2648*a*b^3*d^8*x^7 - 3130*a^2*b^2*d^8*x^5 - 1760*a^3*b*d^8*x^3 - 385*a^4*d^8*x)*sqrt(d*x))/(a*b^9*x^10 + 5*a^2*b^8*x^8 + 10*a^3*b^7*x^6 + 10*a^4*b^6*x^4 + 5*a^5*b^5*x^2 + a^6*b^4)","A",0
716,1,505,0,1.010415," ","integrate((d*x)^(15/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","\frac{2340 \, {\left(a b^{9} x^{10} + 5 \, a^{2} b^{8} x^{8} + 10 \, a^{3} b^{7} x^{6} + 10 \, a^{4} b^{6} x^{4} + 5 \, a^{5} b^{5} x^{2} + a^{6} b^{4}\right)} \left(-\frac{d^{30}}{a^{7} b^{17}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\left(-\frac{d^{30}}{a^{7} b^{17}}\right)^{\frac{3}{4}} \sqrt{d x} a^{5} b^{13} d^{7} - \sqrt{d^{15} x + \sqrt{-\frac{d^{30}}{a^{7} b^{17}}} a^{4} b^{8}} \left(-\frac{d^{30}}{a^{7} b^{17}}\right)^{\frac{3}{4}} a^{5} b^{13}}{d^{30}}\right) + 585 \, {\left(a b^{9} x^{10} + 5 \, a^{2} b^{8} x^{8} + 10 \, a^{3} b^{7} x^{6} + 10 \, a^{4} b^{6} x^{4} + 5 \, a^{5} b^{5} x^{2} + a^{6} b^{4}\right)} \left(-\frac{d^{30}}{a^{7} b^{17}}\right)^{\frac{1}{4}} \log\left(117 \, \sqrt{d x} d^{7} + 117 \, \left(-\frac{d^{30}}{a^{7} b^{17}}\right)^{\frac{1}{4}} a^{2} b^{4}\right) - 585 \, {\left(a b^{9} x^{10} + 5 \, a^{2} b^{8} x^{8} + 10 \, a^{3} b^{7} x^{6} + 10 \, a^{4} b^{6} x^{4} + 5 \, a^{5} b^{5} x^{2} + a^{6} b^{4}\right)} \left(-\frac{d^{30}}{a^{7} b^{17}}\right)^{\frac{1}{4}} \log\left(117 \, \sqrt{d x} d^{7} - 117 \, \left(-\frac{d^{30}}{a^{7} b^{17}}\right)^{\frac{1}{4}} a^{2} b^{4}\right) + 4 \, {\left(195 \, b^{4} d^{7} x^{8} - 4960 \, a b^{3} d^{7} x^{6} - 5330 \, a^{2} b^{2} d^{7} x^{4} - 2808 \, a^{3} b d^{7} x^{2} - 585 \, a^{4} d^{7}\right)} \sqrt{d x}}{81920 \, {\left(a b^{9} x^{10} + 5 \, a^{2} b^{8} x^{8} + 10 \, a^{3} b^{7} x^{6} + 10 \, a^{4} b^{6} x^{4} + 5 \, a^{5} b^{5} x^{2} + a^{6} b^{4}\right)}}"," ",0,"1/81920*(2340*(a*b^9*x^10 + 5*a^2*b^8*x^8 + 10*a^3*b^7*x^6 + 10*a^4*b^6*x^4 + 5*a^5*b^5*x^2 + a^6*b^4)*(-d^30/(a^7*b^17))^(1/4)*arctan(-((-d^30/(a^7*b^17))^(3/4)*sqrt(d*x)*a^5*b^13*d^7 - sqrt(d^15*x + sqrt(-d^30/(a^7*b^17))*a^4*b^8)*(-d^30/(a^7*b^17))^(3/4)*a^5*b^13)/d^30) + 585*(a*b^9*x^10 + 5*a^2*b^8*x^8 + 10*a^3*b^7*x^6 + 10*a^4*b^6*x^4 + 5*a^5*b^5*x^2 + a^6*b^4)*(-d^30/(a^7*b^17))^(1/4)*log(117*sqrt(d*x)*d^7 + 117*(-d^30/(a^7*b^17))^(1/4)*a^2*b^4) - 585*(a*b^9*x^10 + 5*a^2*b^8*x^8 + 10*a^3*b^7*x^6 + 10*a^4*b^6*x^4 + 5*a^5*b^5*x^2 + a^6*b^4)*(-d^30/(a^7*b^17))^(1/4)*log(117*sqrt(d*x)*d^7 - 117*(-d^30/(a^7*b^17))^(1/4)*a^2*b^4) + 4*(195*b^4*d^7*x^8 - 4960*a*b^3*d^7*x^6 - 5330*a^2*b^2*d^7*x^4 - 2808*a^3*b*d^7*x^2 - 585*a^4*d^7)*sqrt(d*x))/(a*b^9*x^10 + 5*a^2*b^8*x^8 + 10*a^3*b^7*x^6 + 10*a^4*b^6*x^4 + 5*a^5*b^5*x^2 + a^6*b^4)","A",0
717,1,518,0,1.755745," ","integrate((d*x)^(13/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","-\frac{4620 \, {\left(a^{2} b^{8} x^{10} + 5 \, a^{3} b^{7} x^{8} + 10 \, a^{4} b^{6} x^{6} + 10 \, a^{5} b^{5} x^{4} + 5 \, a^{6} b^{4} x^{2} + a^{7} b^{3}\right)} \left(-\frac{d^{26}}{a^{9} b^{15}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\left(-\frac{d^{26}}{a^{9} b^{15}}\right)^{\frac{1}{4}} \sqrt{d x} a^{2} b^{4} d^{19} - \sqrt{d^{39} x - \sqrt{-\frac{d^{26}}{a^{9} b^{15}}} a^{5} b^{7} d^{26}} \left(-\frac{d^{26}}{a^{9} b^{15}}\right)^{\frac{1}{4}} a^{2} b^{4}}{d^{26}}\right) - 1155 \, {\left(a^{2} b^{8} x^{10} + 5 \, a^{3} b^{7} x^{8} + 10 \, a^{4} b^{6} x^{6} + 10 \, a^{5} b^{5} x^{4} + 5 \, a^{6} b^{4} x^{2} + a^{7} b^{3}\right)} \left(-\frac{d^{26}}{a^{9} b^{15}}\right)^{\frac{1}{4}} \log\left(456533 \, \sqrt{d x} d^{19} + 456533 \, \left(-\frac{d^{26}}{a^{9} b^{15}}\right)^{\frac{3}{4}} a^{7} b^{11}\right) + 1155 \, {\left(a^{2} b^{8} x^{10} + 5 \, a^{3} b^{7} x^{8} + 10 \, a^{4} b^{6} x^{6} + 10 \, a^{5} b^{5} x^{4} + 5 \, a^{6} b^{4} x^{2} + a^{7} b^{3}\right)} \left(-\frac{d^{26}}{a^{9} b^{15}}\right)^{\frac{1}{4}} \log\left(456533 \, \sqrt{d x} d^{19} - 456533 \, \left(-\frac{d^{26}}{a^{9} b^{15}}\right)^{\frac{3}{4}} a^{7} b^{11}\right) - 4 \, {\left(1155 \, b^{4} d^{6} x^{9} + 5544 \, a b^{3} d^{6} x^{7} - 3130 \, a^{2} b^{2} d^{6} x^{5} - 1760 \, a^{3} b d^{6} x^{3} - 385 \, a^{4} d^{6} x\right)} \sqrt{d x}}{245760 \, {\left(a^{2} b^{8} x^{10} + 5 \, a^{3} b^{7} x^{8} + 10 \, a^{4} b^{6} x^{6} + 10 \, a^{5} b^{5} x^{4} + 5 \, a^{6} b^{4} x^{2} + a^{7} b^{3}\right)}}"," ",0,"-1/245760*(4620*(a^2*b^8*x^10 + 5*a^3*b^7*x^8 + 10*a^4*b^6*x^6 + 10*a^5*b^5*x^4 + 5*a^6*b^4*x^2 + a^7*b^3)*(-d^26/(a^9*b^15))^(1/4)*arctan(-((-d^26/(a^9*b^15))^(1/4)*sqrt(d*x)*a^2*b^4*d^19 - sqrt(d^39*x - sqrt(-d^26/(a^9*b^15))*a^5*b^7*d^26)*(-d^26/(a^9*b^15))^(1/4)*a^2*b^4)/d^26) - 1155*(a^2*b^8*x^10 + 5*a^3*b^7*x^8 + 10*a^4*b^6*x^6 + 10*a^5*b^5*x^4 + 5*a^6*b^4*x^2 + a^7*b^3)*(-d^26/(a^9*b^15))^(1/4)*log(456533*sqrt(d*x)*d^19 + 456533*(-d^26/(a^9*b^15))^(3/4)*a^7*b^11) + 1155*(a^2*b^8*x^10 + 5*a^3*b^7*x^8 + 10*a^4*b^6*x^6 + 10*a^5*b^5*x^4 + 5*a^6*b^4*x^2 + a^7*b^3)*(-d^26/(a^9*b^15))^(1/4)*log(456533*sqrt(d*x)*d^19 - 456533*(-d^26/(a^9*b^15))^(3/4)*a^7*b^11) - 4*(1155*b^4*d^6*x^9 + 5544*a*b^3*d^6*x^7 - 3130*a^2*b^2*d^6*x^5 - 1760*a^3*b*d^6*x^3 - 385*a^4*d^6*x)*sqrt(d*x))/(a^2*b^8*x^10 + 5*a^3*b^7*x^8 + 10*a^4*b^6*x^6 + 10*a^5*b^5*x^4 + 5*a^6*b^4*x^2 + a^7*b^3)","A",0
718,1,513,0,3.179237," ","integrate((d*x)^(11/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","\frac{1260 \, {\left(a^{2} b^{8} x^{10} + 5 \, a^{3} b^{7} x^{8} + 10 \, a^{4} b^{6} x^{6} + 10 \, a^{5} b^{5} x^{4} + 5 \, a^{6} b^{4} x^{2} + a^{7} b^{3}\right)} \left(-\frac{d^{22}}{a^{11} b^{13}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{d x} a^{8} b^{10} d^{5} \left(-\frac{d^{22}}{a^{11} b^{13}}\right)^{\frac{3}{4}} - \sqrt{a^{6} b^{6} \sqrt{-\frac{d^{22}}{a^{11} b^{13}}} + d^{11} x} a^{8} b^{10} \left(-\frac{d^{22}}{a^{11} b^{13}}\right)^{\frac{3}{4}}}{d^{22}}\right) + 315 \, {\left(a^{2} b^{8} x^{10} + 5 \, a^{3} b^{7} x^{8} + 10 \, a^{4} b^{6} x^{6} + 10 \, a^{5} b^{5} x^{4} + 5 \, a^{6} b^{4} x^{2} + a^{7} b^{3}\right)} \left(-\frac{d^{22}}{a^{11} b^{13}}\right)^{\frac{1}{4}} \log\left(63 \, a^{3} b^{3} \left(-\frac{d^{22}}{a^{11} b^{13}}\right)^{\frac{1}{4}} + 63 \, \sqrt{d x} d^{5}\right) - 315 \, {\left(a^{2} b^{8} x^{10} + 5 \, a^{3} b^{7} x^{8} + 10 \, a^{4} b^{6} x^{6} + 10 \, a^{5} b^{5} x^{4} + 5 \, a^{6} b^{4} x^{2} + a^{7} b^{3}\right)} \left(-\frac{d^{22}}{a^{11} b^{13}}\right)^{\frac{1}{4}} \log\left(-63 \, a^{3} b^{3} \left(-\frac{d^{22}}{a^{11} b^{13}}\right)^{\frac{1}{4}} + 63 \, \sqrt{d x} d^{5}\right) + 4 \, {\left(105 \, b^{4} d^{5} x^{8} + 480 \, a b^{3} d^{5} x^{6} - 2870 \, a^{2} b^{2} d^{5} x^{4} - 1512 \, a^{3} b d^{5} x^{2} - 315 \, a^{4} d^{5}\right)} \sqrt{d x}}{81920 \, {\left(a^{2} b^{8} x^{10} + 5 \, a^{3} b^{7} x^{8} + 10 \, a^{4} b^{6} x^{6} + 10 \, a^{5} b^{5} x^{4} + 5 \, a^{6} b^{4} x^{2} + a^{7} b^{3}\right)}}"," ",0,"1/81920*(1260*(a^2*b^8*x^10 + 5*a^3*b^7*x^8 + 10*a^4*b^6*x^6 + 10*a^5*b^5*x^4 + 5*a^6*b^4*x^2 + a^7*b^3)*(-d^22/(a^11*b^13))^(1/4)*arctan(-(sqrt(d*x)*a^8*b^10*d^5*(-d^22/(a^11*b^13))^(3/4) - sqrt(a^6*b^6*sqrt(-d^22/(a^11*b^13)) + d^11*x)*a^8*b^10*(-d^22/(a^11*b^13))^(3/4))/d^22) + 315*(a^2*b^8*x^10 + 5*a^3*b^7*x^8 + 10*a^4*b^6*x^6 + 10*a^5*b^5*x^4 + 5*a^6*b^4*x^2 + a^7*b^3)*(-d^22/(a^11*b^13))^(1/4)*log(63*a^3*b^3*(-d^22/(a^11*b^13))^(1/4) + 63*sqrt(d*x)*d^5) - 315*(a^2*b^8*x^10 + 5*a^3*b^7*x^8 + 10*a^4*b^6*x^6 + 10*a^5*b^5*x^4 + 5*a^6*b^4*x^2 + a^7*b^3)*(-d^22/(a^11*b^13))^(1/4)*log(-63*a^3*b^3*(-d^22/(a^11*b^13))^(1/4) + 63*sqrt(d*x)*d^5) + 4*(105*b^4*d^5*x^8 + 480*a*b^3*d^5*x^6 - 2870*a^2*b^2*d^5*x^4 - 1512*a^3*b*d^5*x^2 - 315*a^4*d^5)*sqrt(d*x))/(a^2*b^8*x^10 + 5*a^3*b^7*x^8 + 10*a^4*b^6*x^6 + 10*a^5*b^5*x^4 + 5*a^6*b^4*x^2 + a^7*b^3)","A",0
719,1,520,0,3.274508," ","integrate((d*x)^(9/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","-\frac{1260 \, {\left(a^{3} b^{7} x^{10} + 5 \, a^{4} b^{6} x^{8} + 10 \, a^{5} b^{5} x^{6} + 10 \, a^{6} b^{4} x^{4} + 5 \, a^{7} b^{3} x^{2} + a^{8} b^{2}\right)} \left(-\frac{d^{18}}{a^{13} b^{11}}\right)^{\frac{1}{4}} \arctan\left(-\frac{250047 \, \sqrt{d x} a^{3} b^{3} d^{13} \left(-\frac{d^{18}}{a^{13} b^{11}}\right)^{\frac{1}{4}} - \sqrt{-62523502209 \, a^{7} b^{5} d^{18} \sqrt{-\frac{d^{18}}{a^{13} b^{11}}} + 62523502209 \, d^{27} x} a^{3} b^{3} \left(-\frac{d^{18}}{a^{13} b^{11}}\right)^{\frac{1}{4}}}{250047 \, d^{18}}\right) - 315 \, {\left(a^{3} b^{7} x^{10} + 5 \, a^{4} b^{6} x^{8} + 10 \, a^{5} b^{5} x^{6} + 10 \, a^{6} b^{4} x^{4} + 5 \, a^{7} b^{3} x^{2} + a^{8} b^{2}\right)} \left(-\frac{d^{18}}{a^{13} b^{11}}\right)^{\frac{1}{4}} \log\left(250047 \, a^{10} b^{8} \left(-\frac{d^{18}}{a^{13} b^{11}}\right)^{\frac{3}{4}} + 250047 \, \sqrt{d x} d^{13}\right) + 315 \, {\left(a^{3} b^{7} x^{10} + 5 \, a^{4} b^{6} x^{8} + 10 \, a^{5} b^{5} x^{6} + 10 \, a^{6} b^{4} x^{4} + 5 \, a^{7} b^{3} x^{2} + a^{8} b^{2}\right)} \left(-\frac{d^{18}}{a^{13} b^{11}}\right)^{\frac{1}{4}} \log\left(-250047 \, a^{10} b^{8} \left(-\frac{d^{18}}{a^{13} b^{11}}\right)^{\frac{3}{4}} + 250047 \, \sqrt{d x} d^{13}\right) - 4 \, {\left(315 \, b^{4} d^{4} x^{9} + 1512 \, a b^{3} d^{4} x^{7} + 2870 \, a^{2} b^{2} d^{4} x^{5} - 480 \, a^{3} b d^{4} x^{3} - 105 \, a^{4} d^{4} x\right)} \sqrt{d x}}{81920 \, {\left(a^{3} b^{7} x^{10} + 5 \, a^{4} b^{6} x^{8} + 10 \, a^{5} b^{5} x^{6} + 10 \, a^{6} b^{4} x^{4} + 5 \, a^{7} b^{3} x^{2} + a^{8} b^{2}\right)}}"," ",0,"-1/81920*(1260*(a^3*b^7*x^10 + 5*a^4*b^6*x^8 + 10*a^5*b^5*x^6 + 10*a^6*b^4*x^4 + 5*a^7*b^3*x^2 + a^8*b^2)*(-d^18/(a^13*b^11))^(1/4)*arctan(-1/250047*(250047*sqrt(d*x)*a^3*b^3*d^13*(-d^18/(a^13*b^11))^(1/4) - sqrt(-62523502209*a^7*b^5*d^18*sqrt(-d^18/(a^13*b^11)) + 62523502209*d^27*x)*a^3*b^3*(-d^18/(a^13*b^11))^(1/4))/d^18) - 315*(a^3*b^7*x^10 + 5*a^4*b^6*x^8 + 10*a^5*b^5*x^6 + 10*a^6*b^4*x^4 + 5*a^7*b^3*x^2 + a^8*b^2)*(-d^18/(a^13*b^11))^(1/4)*log(250047*a^10*b^8*(-d^18/(a^13*b^11))^(3/4) + 250047*sqrt(d*x)*d^13) + 315*(a^3*b^7*x^10 + 5*a^4*b^6*x^8 + 10*a^5*b^5*x^6 + 10*a^6*b^4*x^4 + 5*a^7*b^3*x^2 + a^8*b^2)*(-d^18/(a^13*b^11))^(1/4)*log(-250047*a^10*b^8*(-d^18/(a^13*b^11))^(3/4) + 250047*sqrt(d*x)*d^13) - 4*(315*b^4*d^4*x^9 + 1512*a*b^3*d^4*x^7 + 2870*a^2*b^2*d^4*x^5 - 480*a^3*b*d^4*x^3 - 105*a^4*d^4*x)*sqrt(d*x))/(a^3*b^7*x^10 + 5*a^4*b^6*x^8 + 10*a^5*b^5*x^6 + 10*a^6*b^4*x^4 + 5*a^7*b^3*x^2 + a^8*b^2)","A",0
720,1,513,0,1.167339," ","integrate((d*x)^(7/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","\frac{4620 \, {\left(a^{3} b^{7} x^{10} + 5 \, a^{4} b^{6} x^{8} + 10 \, a^{5} b^{5} x^{6} + 10 \, a^{6} b^{4} x^{4} + 5 \, a^{7} b^{3} x^{2} + a^{8} b^{2}\right)} \left(-\frac{d^{14}}{a^{15} b^{9}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{d x} a^{11} b^{7} d^{3} \left(-\frac{d^{14}}{a^{15} b^{9}}\right)^{\frac{3}{4}} - \sqrt{a^{8} b^{4} \sqrt{-\frac{d^{14}}{a^{15} b^{9}}} + d^{7} x} a^{11} b^{7} \left(-\frac{d^{14}}{a^{15} b^{9}}\right)^{\frac{3}{4}}}{d^{14}}\right) + 1155 \, {\left(a^{3} b^{7} x^{10} + 5 \, a^{4} b^{6} x^{8} + 10 \, a^{5} b^{5} x^{6} + 10 \, a^{6} b^{4} x^{4} + 5 \, a^{7} b^{3} x^{2} + a^{8} b^{2}\right)} \left(-\frac{d^{14}}{a^{15} b^{9}}\right)^{\frac{1}{4}} \log\left(77 \, a^{4} b^{2} \left(-\frac{d^{14}}{a^{15} b^{9}}\right)^{\frac{1}{4}} + 77 \, \sqrt{d x} d^{3}\right) - 1155 \, {\left(a^{3} b^{7} x^{10} + 5 \, a^{4} b^{6} x^{8} + 10 \, a^{5} b^{5} x^{6} + 10 \, a^{6} b^{4} x^{4} + 5 \, a^{7} b^{3} x^{2} + a^{8} b^{2}\right)} \left(-\frac{d^{14}}{a^{15} b^{9}}\right)^{\frac{1}{4}} \log\left(-77 \, a^{4} b^{2} \left(-\frac{d^{14}}{a^{15} b^{9}}\right)^{\frac{1}{4}} + 77 \, \sqrt{d x} d^{3}\right) + 4 \, {\left(385 \, b^{4} d^{3} x^{8} + 1760 \, a b^{3} d^{3} x^{6} + 3130 \, a^{2} b^{2} d^{3} x^{4} - 5544 \, a^{3} b d^{3} x^{2} - 1155 \, a^{4} d^{3}\right)} \sqrt{d x}}{245760 \, {\left(a^{3} b^{7} x^{10} + 5 \, a^{4} b^{6} x^{8} + 10 \, a^{5} b^{5} x^{6} + 10 \, a^{6} b^{4} x^{4} + 5 \, a^{7} b^{3} x^{2} + a^{8} b^{2}\right)}}"," ",0,"1/245760*(4620*(a^3*b^7*x^10 + 5*a^4*b^6*x^8 + 10*a^5*b^5*x^6 + 10*a^6*b^4*x^4 + 5*a^7*b^3*x^2 + a^8*b^2)*(-d^14/(a^15*b^9))^(1/4)*arctan(-(sqrt(d*x)*a^11*b^7*d^3*(-d^14/(a^15*b^9))^(3/4) - sqrt(a^8*b^4*sqrt(-d^14/(a^15*b^9)) + d^7*x)*a^11*b^7*(-d^14/(a^15*b^9))^(3/4))/d^14) + 1155*(a^3*b^7*x^10 + 5*a^4*b^6*x^8 + 10*a^5*b^5*x^6 + 10*a^6*b^4*x^4 + 5*a^7*b^3*x^2 + a^8*b^2)*(-d^14/(a^15*b^9))^(1/4)*log(77*a^4*b^2*(-d^14/(a^15*b^9))^(1/4) + 77*sqrt(d*x)*d^3) - 1155*(a^3*b^7*x^10 + 5*a^4*b^6*x^8 + 10*a^5*b^5*x^6 + 10*a^6*b^4*x^4 + 5*a^7*b^3*x^2 + a^8*b^2)*(-d^14/(a^15*b^9))^(1/4)*log(-77*a^4*b^2*(-d^14/(a^15*b^9))^(1/4) + 77*sqrt(d*x)*d^3) + 4*(385*b^4*d^3*x^8 + 1760*a*b^3*d^3*x^6 + 3130*a^2*b^2*d^3*x^4 - 5544*a^3*b*d^3*x^2 - 1155*a^4*d^3)*sqrt(d*x))/(a^3*b^7*x^10 + 5*a^4*b^6*x^8 + 10*a^5*b^5*x^6 + 10*a^6*b^4*x^4 + 5*a^7*b^3*x^2 + a^8*b^2)","A",0
721,1,512,0,0.699008," ","integrate((d*x)^(5/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","-\frac{2340 \, {\left(a^{4} b^{6} x^{10} + 5 \, a^{5} b^{5} x^{8} + 10 \, a^{6} b^{4} x^{6} + 10 \, a^{7} b^{3} x^{4} + 5 \, a^{8} b^{2} x^{2} + a^{9} b\right)} \left(-\frac{d^{10}}{a^{17} b^{7}}\right)^{\frac{1}{4}} \arctan\left(-\frac{1601613 \, \sqrt{d x} a^{4} b^{2} d^{7} \left(-\frac{d^{10}}{a^{17} b^{7}}\right)^{\frac{1}{4}} - \sqrt{-2565164201769 \, a^{9} b^{3} d^{10} \sqrt{-\frac{d^{10}}{a^{17} b^{7}}} + 2565164201769 \, d^{15} x} a^{4} b^{2} \left(-\frac{d^{10}}{a^{17} b^{7}}\right)^{\frac{1}{4}}}{1601613 \, d^{10}}\right) - 585 \, {\left(a^{4} b^{6} x^{10} + 5 \, a^{5} b^{5} x^{8} + 10 \, a^{6} b^{4} x^{6} + 10 \, a^{7} b^{3} x^{4} + 5 \, a^{8} b^{2} x^{2} + a^{9} b\right)} \left(-\frac{d^{10}}{a^{17} b^{7}}\right)^{\frac{1}{4}} \log\left(1601613 \, a^{13} b^{5} \left(-\frac{d^{10}}{a^{17} b^{7}}\right)^{\frac{3}{4}} + 1601613 \, \sqrt{d x} d^{7}\right) + 585 \, {\left(a^{4} b^{6} x^{10} + 5 \, a^{5} b^{5} x^{8} + 10 \, a^{6} b^{4} x^{6} + 10 \, a^{7} b^{3} x^{4} + 5 \, a^{8} b^{2} x^{2} + a^{9} b\right)} \left(-\frac{d^{10}}{a^{17} b^{7}}\right)^{\frac{1}{4}} \log\left(-1601613 \, a^{13} b^{5} \left(-\frac{d^{10}}{a^{17} b^{7}}\right)^{\frac{3}{4}} + 1601613 \, \sqrt{d x} d^{7}\right) - 4 \, {\left(585 \, b^{4} d^{2} x^{9} + 2808 \, a b^{3} d^{2} x^{7} + 5330 \, a^{2} b^{2} d^{2} x^{5} + 4960 \, a^{3} b d^{2} x^{3} - 195 \, a^{4} d^{2} x\right)} \sqrt{d x}}{81920 \, {\left(a^{4} b^{6} x^{10} + 5 \, a^{5} b^{5} x^{8} + 10 \, a^{6} b^{4} x^{6} + 10 \, a^{7} b^{3} x^{4} + 5 \, a^{8} b^{2} x^{2} + a^{9} b\right)}}"," ",0,"-1/81920*(2340*(a^4*b^6*x^10 + 5*a^5*b^5*x^8 + 10*a^6*b^4*x^6 + 10*a^7*b^3*x^4 + 5*a^8*b^2*x^2 + a^9*b)*(-d^10/(a^17*b^7))^(1/4)*arctan(-1/1601613*(1601613*sqrt(d*x)*a^4*b^2*d^7*(-d^10/(a^17*b^7))^(1/4) - sqrt(-2565164201769*a^9*b^3*d^10*sqrt(-d^10/(a^17*b^7)) + 2565164201769*d^15*x)*a^4*b^2*(-d^10/(a^17*b^7))^(1/4))/d^10) - 585*(a^4*b^6*x^10 + 5*a^5*b^5*x^8 + 10*a^6*b^4*x^6 + 10*a^7*b^3*x^4 + 5*a^8*b^2*x^2 + a^9*b)*(-d^10/(a^17*b^7))^(1/4)*log(1601613*a^13*b^5*(-d^10/(a^17*b^7))^(3/4) + 1601613*sqrt(d*x)*d^7) + 585*(a^4*b^6*x^10 + 5*a^5*b^5*x^8 + 10*a^6*b^4*x^6 + 10*a^7*b^3*x^4 + 5*a^8*b^2*x^2 + a^9*b)*(-d^10/(a^17*b^7))^(1/4)*log(-1601613*a^13*b^5*(-d^10/(a^17*b^7))^(3/4) + 1601613*sqrt(d*x)*d^7) - 4*(585*b^4*d^2*x^9 + 2808*a*b^3*d^2*x^7 + 5330*a^2*b^2*d^2*x^5 + 4960*a^3*b*d^2*x^3 - 195*a^4*d^2*x)*sqrt(d*x))/(a^4*b^6*x^10 + 5*a^5*b^5*x^8 + 10*a^6*b^4*x^6 + 10*a^7*b^3*x^4 + 5*a^8*b^2*x^2 + a^9*b)","A",0
722,1,485,0,1.262251," ","integrate((d*x)^(3/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","\frac{4620 \, {\left(a^{4} b^{6} x^{10} + 5 \, a^{5} b^{5} x^{8} + 10 \, a^{6} b^{4} x^{6} + 10 \, a^{7} b^{3} x^{4} + 5 \, a^{8} b^{2} x^{2} + a^{9} b\right)} \left(-\frac{d^{6}}{a^{19} b^{5}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{d x} a^{14} b^{4} d \left(-\frac{d^{6}}{a^{19} b^{5}}\right)^{\frac{3}{4}} - \sqrt{a^{10} b^{2} \sqrt{-\frac{d^{6}}{a^{19} b^{5}}} + d^{3} x} a^{14} b^{4} \left(-\frac{d^{6}}{a^{19} b^{5}}\right)^{\frac{3}{4}}}{d^{6}}\right) + 1155 \, {\left(a^{4} b^{6} x^{10} + 5 \, a^{5} b^{5} x^{8} + 10 \, a^{6} b^{4} x^{6} + 10 \, a^{7} b^{3} x^{4} + 5 \, a^{8} b^{2} x^{2} + a^{9} b\right)} \left(-\frac{d^{6}}{a^{19} b^{5}}\right)^{\frac{1}{4}} \log\left(231 \, a^{5} b \left(-\frac{d^{6}}{a^{19} b^{5}}\right)^{\frac{1}{4}} + 231 \, \sqrt{d x} d\right) - 1155 \, {\left(a^{4} b^{6} x^{10} + 5 \, a^{5} b^{5} x^{8} + 10 \, a^{6} b^{4} x^{6} + 10 \, a^{7} b^{3} x^{4} + 5 \, a^{8} b^{2} x^{2} + a^{9} b\right)} \left(-\frac{d^{6}}{a^{19} b^{5}}\right)^{\frac{1}{4}} \log\left(-231 \, a^{5} b \left(-\frac{d^{6}}{a^{19} b^{5}}\right)^{\frac{1}{4}} + 231 \, \sqrt{d x} d\right) + 4 \, {\left(385 \, b^{4} d x^{8} + 1760 \, a b^{3} d x^{6} + 3130 \, a^{2} b^{2} d x^{4} + 2648 \, a^{3} b d x^{2} - 1155 \, a^{4} d\right)} \sqrt{d x}}{81920 \, {\left(a^{4} b^{6} x^{10} + 5 \, a^{5} b^{5} x^{8} + 10 \, a^{6} b^{4} x^{6} + 10 \, a^{7} b^{3} x^{4} + 5 \, a^{8} b^{2} x^{2} + a^{9} b\right)}}"," ",0,"1/81920*(4620*(a^4*b^6*x^10 + 5*a^5*b^5*x^8 + 10*a^6*b^4*x^6 + 10*a^7*b^3*x^4 + 5*a^8*b^2*x^2 + a^9*b)*(-d^6/(a^19*b^5))^(1/4)*arctan(-(sqrt(d*x)*a^14*b^4*d*(-d^6/(a^19*b^5))^(3/4) - sqrt(a^10*b^2*sqrt(-d^6/(a^19*b^5)) + d^3*x)*a^14*b^4*(-d^6/(a^19*b^5))^(3/4))/d^6) + 1155*(a^4*b^6*x^10 + 5*a^5*b^5*x^8 + 10*a^6*b^4*x^6 + 10*a^7*b^3*x^4 + 5*a^8*b^2*x^2 + a^9*b)*(-d^6/(a^19*b^5))^(1/4)*log(231*a^5*b*(-d^6/(a^19*b^5))^(1/4) + 231*sqrt(d*x)*d) - 1155*(a^4*b^6*x^10 + 5*a^5*b^5*x^8 + 10*a^6*b^4*x^6 + 10*a^7*b^3*x^4 + 5*a^8*b^2*x^2 + a^9*b)*(-d^6/(a^19*b^5))^(1/4)*log(-231*a^5*b*(-d^6/(a^19*b^5))^(1/4) + 231*sqrt(d*x)*d) + 4*(385*b^4*d*x^8 + 1760*a*b^3*d*x^6 + 3130*a^2*b^2*d*x^4 + 2648*a^3*b*d*x^2 - 1155*a^4*d)*sqrt(d*x))/(a^4*b^6*x^10 + 5*a^5*b^5*x^8 + 10*a^6*b^4*x^6 + 10*a^7*b^3*x^4 + 5*a^8*b^2*x^2 + a^9*b)","A",0
723,1,469,0,0.996509," ","integrate((d*x)^(1/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","-\frac{39780 \, {\left(a^{5} b^{5} x^{10} + 5 \, a^{6} b^{4} x^{8} + 10 \, a^{7} b^{3} x^{6} + 10 \, a^{8} b^{2} x^{4} + 5 \, a^{9} b x^{2} + a^{10}\right)} \left(-\frac{d^{2}}{a^{21} b^{3}}\right)^{\frac{1}{4}} \arctan\left(-\frac{291434247 \, \sqrt{d x} a^{5} b d \left(-\frac{d^{2}}{a^{21} b^{3}}\right)^{\frac{1}{4}} - \sqrt{-84933920324457009 \, a^{11} b d^{2} \sqrt{-\frac{d^{2}}{a^{21} b^{3}}} + 84933920324457009 \, d^{3} x} a^{5} b \left(-\frac{d^{2}}{a^{21} b^{3}}\right)^{\frac{1}{4}}}{291434247 \, d^{2}}\right) - 9945 \, {\left(a^{5} b^{5} x^{10} + 5 \, a^{6} b^{4} x^{8} + 10 \, a^{7} b^{3} x^{6} + 10 \, a^{8} b^{2} x^{4} + 5 \, a^{9} b x^{2} + a^{10}\right)} \left(-\frac{d^{2}}{a^{21} b^{3}}\right)^{\frac{1}{4}} \log\left(291434247 \, a^{16} b^{2} \left(-\frac{d^{2}}{a^{21} b^{3}}\right)^{\frac{3}{4}} + 291434247 \, \sqrt{d x} d\right) + 9945 \, {\left(a^{5} b^{5} x^{10} + 5 \, a^{6} b^{4} x^{8} + 10 \, a^{7} b^{3} x^{6} + 10 \, a^{8} b^{2} x^{4} + 5 \, a^{9} b x^{2} + a^{10}\right)} \left(-\frac{d^{2}}{a^{21} b^{3}}\right)^{\frac{1}{4}} \log\left(-291434247 \, a^{16} b^{2} \left(-\frac{d^{2}}{a^{21} b^{3}}\right)^{\frac{3}{4}} + 291434247 \, \sqrt{d x} d\right) - 4 \, {\left(9945 \, b^{4} x^{9} + 47736 \, a b^{3} x^{7} + 90610 \, a^{2} b^{2} x^{5} + 84320 \, a^{3} b x^{3} + 37645 \, a^{4} x\right)} \sqrt{d x}}{245760 \, {\left(a^{5} b^{5} x^{10} + 5 \, a^{6} b^{4} x^{8} + 10 \, a^{7} b^{3} x^{6} + 10 \, a^{8} b^{2} x^{4} + 5 \, a^{9} b x^{2} + a^{10}\right)}}"," ",0,"-1/245760*(39780*(a^5*b^5*x^10 + 5*a^6*b^4*x^8 + 10*a^7*b^3*x^6 + 10*a^8*b^2*x^4 + 5*a^9*b*x^2 + a^10)*(-d^2/(a^21*b^3))^(1/4)*arctan(-1/291434247*(291434247*sqrt(d*x)*a^5*b*d*(-d^2/(a^21*b^3))^(1/4) - sqrt(-84933920324457009*a^11*b*d^2*sqrt(-d^2/(a^21*b^3)) + 84933920324457009*d^3*x)*a^5*b*(-d^2/(a^21*b^3))^(1/4))/d^2) - 9945*(a^5*b^5*x^10 + 5*a^6*b^4*x^8 + 10*a^7*b^3*x^6 + 10*a^8*b^2*x^4 + 5*a^9*b*x^2 + a^10)*(-d^2/(a^21*b^3))^(1/4)*log(291434247*a^16*b^2*(-d^2/(a^21*b^3))^(3/4) + 291434247*sqrt(d*x)*d) + 9945*(a^5*b^5*x^10 + 5*a^6*b^4*x^8 + 10*a^7*b^3*x^6 + 10*a^8*b^2*x^4 + 5*a^9*b*x^2 + a^10)*(-d^2/(a^21*b^3))^(1/4)*log(-291434247*a^16*b^2*(-d^2/(a^21*b^3))^(3/4) + 291434247*sqrt(d*x)*d) - 4*(9945*b^4*x^9 + 47736*a*b^3*x^7 + 90610*a^2*b^2*x^5 + 84320*a^3*b*x^3 + 37645*a^4*x)*sqrt(d*x))/(a^5*b^5*x^10 + 5*a^6*b^4*x^8 + 10*a^7*b^3*x^6 + 10*a^8*b^2*x^4 + 5*a^9*b*x^2 + a^10)","A",0
724,1,475,0,1.227683," ","integrate(1/(b^2*x^4+2*a*b*x^2+a^2)^3/(d*x)^(1/2),x, algorithm=""fricas"")","\frac{87780 \, {\left(a^{5} b^{5} d x^{10} + 5 \, a^{6} b^{4} d x^{8} + 10 \, a^{7} b^{3} d x^{6} + 10 \, a^{8} b^{2} d x^{4} + 5 \, a^{9} b d x^{2} + a^{10} d\right)} \left(-\frac{1}{a^{23} b d^{2}}\right)^{\frac{1}{4}} \arctan\left(\sqrt{a^{12} d^{2} \sqrt{-\frac{1}{a^{23} b d^{2}}} + d x} a^{17} b d \left(-\frac{1}{a^{23} b d^{2}}\right)^{\frac{3}{4}} - \sqrt{d x} a^{17} b d \left(-\frac{1}{a^{23} b d^{2}}\right)^{\frac{3}{4}}\right) + 21945 \, {\left(a^{5} b^{5} d x^{10} + 5 \, a^{6} b^{4} d x^{8} + 10 \, a^{7} b^{3} d x^{6} + 10 \, a^{8} b^{2} d x^{4} + 5 \, a^{9} b d x^{2} + a^{10} d\right)} \left(-\frac{1}{a^{23} b d^{2}}\right)^{\frac{1}{4}} \log\left(a^{6} d \left(-\frac{1}{a^{23} b d^{2}}\right)^{\frac{1}{4}} + \sqrt{d x}\right) - 21945 \, {\left(a^{5} b^{5} d x^{10} + 5 \, a^{6} b^{4} d x^{8} + 10 \, a^{7} b^{3} d x^{6} + 10 \, a^{8} b^{2} d x^{4} + 5 \, a^{9} b d x^{2} + a^{10} d\right)} \left(-\frac{1}{a^{23} b d^{2}}\right)^{\frac{1}{4}} \log\left(-a^{6} d \left(-\frac{1}{a^{23} b d^{2}}\right)^{\frac{1}{4}} + \sqrt{d x}\right) + 4 \, {\left(7315 \, b^{4} x^{8} + 33440 \, a b^{3} x^{6} + 59470 \, a^{2} b^{2} x^{4} + 50312 \, a^{3} b x^{2} + 19015 \, a^{4}\right)} \sqrt{d x}}{81920 \, {\left(a^{5} b^{5} d x^{10} + 5 \, a^{6} b^{4} d x^{8} + 10 \, a^{7} b^{3} d x^{6} + 10 \, a^{8} b^{2} d x^{4} + 5 \, a^{9} b d x^{2} + a^{10} d\right)}}"," ",0,"1/81920*(87780*(a^5*b^5*d*x^10 + 5*a^6*b^4*d*x^8 + 10*a^7*b^3*d*x^6 + 10*a^8*b^2*d*x^4 + 5*a^9*b*d*x^2 + a^10*d)*(-1/(a^23*b*d^2))^(1/4)*arctan(sqrt(a^12*d^2*sqrt(-1/(a^23*b*d^2)) + d*x)*a^17*b*d*(-1/(a^23*b*d^2))^(3/4) - sqrt(d*x)*a^17*b*d*(-1/(a^23*b*d^2))^(3/4)) + 21945*(a^5*b^5*d*x^10 + 5*a^6*b^4*d*x^8 + 10*a^7*b^3*d*x^6 + 10*a^8*b^2*d*x^4 + 5*a^9*b*d*x^2 + a^10*d)*(-1/(a^23*b*d^2))^(1/4)*log(a^6*d*(-1/(a^23*b*d^2))^(1/4) + sqrt(d*x)) - 21945*(a^5*b^5*d*x^10 + 5*a^6*b^4*d*x^8 + 10*a^7*b^3*d*x^6 + 10*a^8*b^2*d*x^4 + 5*a^9*b*d*x^2 + a^10*d)*(-1/(a^23*b*d^2))^(1/4)*log(-a^6*d*(-1/(a^23*b*d^2))^(1/4) + sqrt(d*x)) + 4*(7315*b^4*x^8 + 33440*a*b^3*x^6 + 59470*a^2*b^2*x^4 + 50312*a^3*b*x^2 + 19015*a^4)*sqrt(d*x))/(a^5*b^5*d*x^10 + 5*a^6*b^4*d*x^8 + 10*a^7*b^3*d*x^6 + 10*a^8*b^2*d*x^4 + 5*a^9*b*d*x^2 + a^10*d)","A",0
725,1,544,0,1.126800," ","integrate(1/(d*x)^(3/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","\frac{278460 \, {\left(a^{6} b^{5} d^{2} x^{11} + 5 \, a^{7} b^{4} d^{2} x^{9} + 10 \, a^{8} b^{3} d^{2} x^{7} + 10 \, a^{9} b^{2} d^{2} x^{5} + 5 \, a^{10} b d^{2} x^{3} + a^{11} d^{2} x\right)} \left(-\frac{b}{a^{25} d^{6}}\right)^{\frac{1}{4}} \arctan\left(-\frac{2698972561467 \, \sqrt{d x} a^{6} b d \left(-\frac{b}{a^{25} d^{6}}\right)^{\frac{1}{4}} - \sqrt{-7284452887551739093192089 \, a^{13} b d^{4} \sqrt{-\frac{b}{a^{25} d^{6}}} + 7284452887551739093192089 \, b^{2} d x} a^{6} d \left(-\frac{b}{a^{25} d^{6}}\right)^{\frac{1}{4}}}{2698972561467 \, b}\right) - 69615 \, {\left(a^{6} b^{5} d^{2} x^{11} + 5 \, a^{7} b^{4} d^{2} x^{9} + 10 \, a^{8} b^{3} d^{2} x^{7} + 10 \, a^{9} b^{2} d^{2} x^{5} + 5 \, a^{10} b d^{2} x^{3} + a^{11} d^{2} x\right)} \left(-\frac{b}{a^{25} d^{6}}\right)^{\frac{1}{4}} \log\left(2698972561467 \, a^{19} d^{5} \left(-\frac{b}{a^{25} d^{6}}\right)^{\frac{3}{4}} + 2698972561467 \, \sqrt{d x} b\right) + 69615 \, {\left(a^{6} b^{5} d^{2} x^{11} + 5 \, a^{7} b^{4} d^{2} x^{9} + 10 \, a^{8} b^{3} d^{2} x^{7} + 10 \, a^{9} b^{2} d^{2} x^{5} + 5 \, a^{10} b d^{2} x^{3} + a^{11} d^{2} x\right)} \left(-\frac{b}{a^{25} d^{6}}\right)^{\frac{1}{4}} \log\left(-2698972561467 \, a^{19} d^{5} \left(-\frac{b}{a^{25} d^{6}}\right)^{\frac{3}{4}} + 2698972561467 \, \sqrt{d x} b\right) - 4 \, {\left(69615 \, b^{5} x^{10} + 334152 \, a b^{4} x^{8} + 634270 \, a^{2} b^{3} x^{6} + 590240 \, a^{3} b^{2} x^{4} + 263515 \, a^{4} b x^{2} + 40960 \, a^{5}\right)} \sqrt{d x}}{81920 \, {\left(a^{6} b^{5} d^{2} x^{11} + 5 \, a^{7} b^{4} d^{2} x^{9} + 10 \, a^{8} b^{3} d^{2} x^{7} + 10 \, a^{9} b^{2} d^{2} x^{5} + 5 \, a^{10} b d^{2} x^{3} + a^{11} d^{2} x\right)}}"," ",0,"1/81920*(278460*(a^6*b^5*d^2*x^11 + 5*a^7*b^4*d^2*x^9 + 10*a^8*b^3*d^2*x^7 + 10*a^9*b^2*d^2*x^5 + 5*a^10*b*d^2*x^3 + a^11*d^2*x)*(-b/(a^25*d^6))^(1/4)*arctan(-1/2698972561467*(2698972561467*sqrt(d*x)*a^6*b*d*(-b/(a^25*d^6))^(1/4) - sqrt(-7284452887551739093192089*a^13*b*d^4*sqrt(-b/(a^25*d^6)) + 7284452887551739093192089*b^2*d*x)*a^6*d*(-b/(a^25*d^6))^(1/4))/b) - 69615*(a^6*b^5*d^2*x^11 + 5*a^7*b^4*d^2*x^9 + 10*a^8*b^3*d^2*x^7 + 10*a^9*b^2*d^2*x^5 + 5*a^10*b*d^2*x^3 + a^11*d^2*x)*(-b/(a^25*d^6))^(1/4)*log(2698972561467*a^19*d^5*(-b/(a^25*d^6))^(3/4) + 2698972561467*sqrt(d*x)*b) + 69615*(a^6*b^5*d^2*x^11 + 5*a^7*b^4*d^2*x^9 + 10*a^8*b^3*d^2*x^7 + 10*a^9*b^2*d^2*x^5 + 5*a^10*b*d^2*x^3 + a^11*d^2*x)*(-b/(a^25*d^6))^(1/4)*log(-2698972561467*a^19*d^5*(-b/(a^25*d^6))^(3/4) + 2698972561467*sqrt(d*x)*b) - 4*(69615*b^5*x^10 + 334152*a*b^4*x^8 + 634270*a^2*b^3*x^6 + 590240*a^3*b^2*x^4 + 263515*a^4*b*x^2 + 40960*a^5)*sqrt(d*x))/(a^6*b^5*d^2*x^11 + 5*a^7*b^4*d^2*x^9 + 10*a^8*b^3*d^2*x^7 + 10*a^9*b^2*d^2*x^5 + 5*a^10*b*d^2*x^3 + a^11*d^2*x)","A",0
726,1,568,0,1.461567," ","integrate(1/(d*x)^(5/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","-\frac{2018940 \, {\left(a^{6} b^{5} d^{3} x^{12} + 5 \, a^{7} b^{4} d^{3} x^{10} + 10 \, a^{8} b^{3} d^{3} x^{8} + 10 \, a^{9} b^{2} d^{3} x^{6} + 5 \, a^{10} b d^{3} x^{4} + a^{11} d^{3} x^{2}\right)} \left(-\frac{b^{3}}{a^{27} d^{10}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{d x} a^{20} b d^{7} \left(-\frac{b^{3}}{a^{27} d^{10}}\right)^{\frac{3}{4}} - \sqrt{a^{14} d^{6} \sqrt{-\frac{b^{3}}{a^{27} d^{10}}} + b^{2} d x} a^{20} d^{7} \left(-\frac{b^{3}}{a^{27} d^{10}}\right)^{\frac{3}{4}}}{b^{3}}\right) + 504735 \, {\left(a^{6} b^{5} d^{3} x^{12} + 5 \, a^{7} b^{4} d^{3} x^{10} + 10 \, a^{8} b^{3} d^{3} x^{8} + 10 \, a^{9} b^{2} d^{3} x^{6} + 5 \, a^{10} b d^{3} x^{4} + a^{11} d^{3} x^{2}\right)} \left(-\frac{b^{3}}{a^{27} d^{10}}\right)^{\frac{1}{4}} \log\left(33649 \, a^{7} d^{3} \left(-\frac{b^{3}}{a^{27} d^{10}}\right)^{\frac{1}{4}} + 33649 \, \sqrt{d x} b\right) - 504735 \, {\left(a^{6} b^{5} d^{3} x^{12} + 5 \, a^{7} b^{4} d^{3} x^{10} + 10 \, a^{8} b^{3} d^{3} x^{8} + 10 \, a^{9} b^{2} d^{3} x^{6} + 5 \, a^{10} b d^{3} x^{4} + a^{11} d^{3} x^{2}\right)} \left(-\frac{b^{3}}{a^{27} d^{10}}\right)^{\frac{1}{4}} \log\left(-33649 \, a^{7} d^{3} \left(-\frac{b^{3}}{a^{27} d^{10}}\right)^{\frac{1}{4}} + 33649 \, \sqrt{d x} b\right) + 4 \, {\left(168245 \, b^{5} x^{10} + 769120 \, a b^{4} x^{8} + 1367810 \, a^{2} b^{3} x^{6} + 1157176 \, a^{3} b^{2} x^{4} + 437345 \, a^{4} b x^{2} + 40960 \, a^{5}\right)} \sqrt{d x}}{245760 \, {\left(a^{6} b^{5} d^{3} x^{12} + 5 \, a^{7} b^{4} d^{3} x^{10} + 10 \, a^{8} b^{3} d^{3} x^{8} + 10 \, a^{9} b^{2} d^{3} x^{6} + 5 \, a^{10} b d^{3} x^{4} + a^{11} d^{3} x^{2}\right)}}"," ",0,"-1/245760*(2018940*(a^6*b^5*d^3*x^12 + 5*a^7*b^4*d^3*x^10 + 10*a^8*b^3*d^3*x^8 + 10*a^9*b^2*d^3*x^6 + 5*a^10*b*d^3*x^4 + a^11*d^3*x^2)*(-b^3/(a^27*d^10))^(1/4)*arctan(-(sqrt(d*x)*a^20*b*d^7*(-b^3/(a^27*d^10))^(3/4) - sqrt(a^14*d^6*sqrt(-b^3/(a^27*d^10)) + b^2*d*x)*a^20*d^7*(-b^3/(a^27*d^10))^(3/4))/b^3) + 504735*(a^6*b^5*d^3*x^12 + 5*a^7*b^4*d^3*x^10 + 10*a^8*b^3*d^3*x^8 + 10*a^9*b^2*d^3*x^6 + 5*a^10*b*d^3*x^4 + a^11*d^3*x^2)*(-b^3/(a^27*d^10))^(1/4)*log(33649*a^7*d^3*(-b^3/(a^27*d^10))^(1/4) + 33649*sqrt(d*x)*b) - 504735*(a^6*b^5*d^3*x^12 + 5*a^7*b^4*d^3*x^10 + 10*a^8*b^3*d^3*x^8 + 10*a^9*b^2*d^3*x^6 + 5*a^10*b*d^3*x^4 + a^11*d^3*x^2)*(-b^3/(a^27*d^10))^(1/4)*log(-33649*a^7*d^3*(-b^3/(a^27*d^10))^(1/4) + 33649*sqrt(d*x)*b) + 4*(168245*b^5*x^10 + 769120*a*b^4*x^8 + 1367810*a^2*b^3*x^6 + 1157176*a^3*b^2*x^4 + 437345*a^4*b*x^2 + 40960*a^5)*sqrt(d*x))/(a^6*b^5*d^3*x^12 + 5*a^7*b^4*d^3*x^10 + 10*a^8*b^3*d^3*x^8 + 10*a^9*b^2*d^3*x^6 + 5*a^10*b*d^3*x^4 + a^11*d^3*x^2)","A",0
727,1,591,0,2.516834," ","integrate(1/(d*x)^(7/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","-\frac{1392300 \, {\left(a^{7} b^{5} d^{4} x^{13} + 5 \, a^{8} b^{4} d^{4} x^{11} + 10 \, a^{9} b^{3} d^{4} x^{9} + 10 \, a^{10} b^{2} d^{4} x^{7} + 5 \, a^{11} b d^{4} x^{5} + a^{12} d^{4} x^{3}\right)} \left(-\frac{b^{5}}{a^{29} d^{14}}\right)^{\frac{1}{4}} \arctan\left(-\frac{337371570183375 \, \sqrt{d x} a^{7} b^{4} d^{3} \left(-\frac{b^{5}}{a^{29} d^{14}}\right)^{\frac{1}{4}} - \sqrt{-113819576367995923331126390625 \, a^{15} b^{5} d^{8} \sqrt{-\frac{b^{5}}{a^{29} d^{14}}} + 113819576367995923331126390625 \, b^{8} d x} a^{7} d^{3} \left(-\frac{b^{5}}{a^{29} d^{14}}\right)^{\frac{1}{4}}}{337371570183375 \, b^{5}}\right) - 348075 \, {\left(a^{7} b^{5} d^{4} x^{13} + 5 \, a^{8} b^{4} d^{4} x^{11} + 10 \, a^{9} b^{3} d^{4} x^{9} + 10 \, a^{10} b^{2} d^{4} x^{7} + 5 \, a^{11} b d^{4} x^{5} + a^{12} d^{4} x^{3}\right)} \left(-\frac{b^{5}}{a^{29} d^{14}}\right)^{\frac{1}{4}} \log\left(337371570183375 \, a^{22} d^{11} \left(-\frac{b^{5}}{a^{29} d^{14}}\right)^{\frac{3}{4}} + 337371570183375 \, \sqrt{d x} b^{4}\right) + 348075 \, {\left(a^{7} b^{5} d^{4} x^{13} + 5 \, a^{8} b^{4} d^{4} x^{11} + 10 \, a^{9} b^{3} d^{4} x^{9} + 10 \, a^{10} b^{2} d^{4} x^{7} + 5 \, a^{11} b d^{4} x^{5} + a^{12} d^{4} x^{3}\right)} \left(-\frac{b^{5}}{a^{29} d^{14}}\right)^{\frac{1}{4}} \log\left(-337371570183375 \, a^{22} d^{11} \left(-\frac{b^{5}}{a^{29} d^{14}}\right)^{\frac{3}{4}} + 337371570183375 \, \sqrt{d x} b^{4}\right) - 4 \, {\left(348075 \, b^{6} x^{12} + 1670760 \, a b^{5} x^{10} + 3171350 \, a^{2} b^{4} x^{8} + 2951200 \, a^{3} b^{3} x^{6} + 1317575 \, a^{4} b^{2} x^{4} + 204800 \, a^{5} b x^{2} - 8192 \, a^{6}\right)} \sqrt{d x}}{81920 \, {\left(a^{7} b^{5} d^{4} x^{13} + 5 \, a^{8} b^{4} d^{4} x^{11} + 10 \, a^{9} b^{3} d^{4} x^{9} + 10 \, a^{10} b^{2} d^{4} x^{7} + 5 \, a^{11} b d^{4} x^{5} + a^{12} d^{4} x^{3}\right)}}"," ",0,"-1/81920*(1392300*(a^7*b^5*d^4*x^13 + 5*a^8*b^4*d^4*x^11 + 10*a^9*b^3*d^4*x^9 + 10*a^10*b^2*d^4*x^7 + 5*a^11*b*d^4*x^5 + a^12*d^4*x^3)*(-b^5/(a^29*d^14))^(1/4)*arctan(-1/337371570183375*(337371570183375*sqrt(d*x)*a^7*b^4*d^3*(-b^5/(a^29*d^14))^(1/4) - sqrt(-113819576367995923331126390625*a^15*b^5*d^8*sqrt(-b^5/(a^29*d^14)) + 113819576367995923331126390625*b^8*d*x)*a^7*d^3*(-b^5/(a^29*d^14))^(1/4))/b^5) - 348075*(a^7*b^5*d^4*x^13 + 5*a^8*b^4*d^4*x^11 + 10*a^9*b^3*d^4*x^9 + 10*a^10*b^2*d^4*x^7 + 5*a^11*b*d^4*x^5 + a^12*d^4*x^3)*(-b^5/(a^29*d^14))^(1/4)*log(337371570183375*a^22*d^11*(-b^5/(a^29*d^14))^(3/4) + 337371570183375*sqrt(d*x)*b^4) + 348075*(a^7*b^5*d^4*x^13 + 5*a^8*b^4*d^4*x^11 + 10*a^9*b^3*d^4*x^9 + 10*a^10*b^2*d^4*x^7 + 5*a^11*b*d^4*x^5 + a^12*d^4*x^3)*(-b^5/(a^29*d^14))^(1/4)*log(-337371570183375*a^22*d^11*(-b^5/(a^29*d^14))^(3/4) + 337371570183375*sqrt(d*x)*b^4) - 4*(348075*b^6*x^12 + 1670760*a*b^5*x^10 + 3171350*a^2*b^4*x^8 + 2951200*a^3*b^3*x^6 + 1317575*a^4*b^2*x^4 + 204800*a^5*b*x^2 - 8192*a^6)*sqrt(d*x))/(a^7*b^5*d^4*x^13 + 5*a^8*b^4*d^4*x^11 + 10*a^9*b^3*d^4*x^9 + 10*a^10*b^2*d^4*x^7 + 5*a^11*b*d^4*x^5 + a^12*d^4*x^3)","A",0
728,1,26,0,0.964333," ","integrate((d*x)^(5/2)*((b*x^2+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{2}{77} \, {\left(7 \, b d^{2} x^{5} + 11 \, a d^{2} x^{3}\right)} \sqrt{d x}"," ",0,"2/77*(7*b*d^2*x^5 + 11*a*d^2*x^3)*sqrt(d*x)","A",0
729,1,22,0,1.555878," ","integrate((d*x)^(3/2)*((b*x^2+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{2}{45} \, {\left(5 \, b d x^{4} + 9 \, a d x^{2}\right)} \sqrt{d x}"," ",0,"2/45*(5*b*d*x^4 + 9*a*d*x^2)*sqrt(d*x)","A",0
730,1,18,0,1.115482," ","integrate((d*x)^(1/2)*((b*x^2+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{2}{21} \, {\left(3 \, b x^{3} + 7 \, a x\right)} \sqrt{d x}"," ",0,"2/21*(3*b*x^3 + 7*a*x)*sqrt(d*x)","A",0
731,1,19,0,1.708209," ","integrate(((b*x^2+a)^2)^(1/2)/(d*x)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(b x^{2} + 5 \, a\right)} \sqrt{d x}}{5 \, d}"," ",0,"2/5*(b*x^2 + 5*a)*sqrt(d*x)/d","A",0
732,1,22,0,0.889894," ","integrate(((b*x^2+a)^2)^(1/2)/(d*x)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(b x^{2} - 3 \, a\right)} \sqrt{d x}}{3 \, d^{2} x}"," ",0,"2/3*(b*x^2 - 3*a)*sqrt(d*x)/(d^2*x)","A",0
733,1,23,0,1.919449," ","integrate(((b*x^2+a)^2)^(1/2)/(d*x)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, b x^{2} - a\right)} \sqrt{d x}}{3 \, d^{3} x^{2}}"," ",0,"2/3*(3*b*x^2 - a)*sqrt(d*x)/(d^3*x^2)","A",0
734,1,21,0,1.194848," ","integrate(((b*x^2+a)^2)^(1/2)/(d*x)^(7/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(5 \, b x^{2} + a\right)} \sqrt{d x}}{5 \, d^{4} x^{3}}"," ",0,"-2/5*(5*b*x^2 + a)*sqrt(d*x)/(d^4*x^3)","A",0
735,1,54,0,1.652377," ","integrate((d*x)^(5/2)*(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""fricas"")","\frac{2}{7315} \, {\left(385 \, b^{3} d^{2} x^{9} + 1463 \, a b^{2} d^{2} x^{7} + 1995 \, a^{2} b d^{2} x^{5} + 1045 \, a^{3} d^{2} x^{3}\right)} \sqrt{d x}"," ",0,"2/7315*(385*b^3*d^2*x^9 + 1463*a*b^2*d^2*x^7 + 1995*a^2*b*d^2*x^5 + 1045*a^3*d^2*x^3)*sqrt(d*x)","A",0
736,1,46,0,1.041581," ","integrate((d*x)^(3/2)*(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""fricas"")","\frac{2}{3315} \, {\left(195 \, b^{3} d x^{8} + 765 \, a b^{2} d x^{6} + 1105 \, a^{2} b d x^{4} + 663 \, a^{3} d x^{2}\right)} \sqrt{d x}"," ",0,"2/3315*(195*b^3*d*x^8 + 765*a*b^2*d*x^6 + 1105*a^2*b*d*x^4 + 663*a^3*d*x^2)*sqrt(d*x)","A",0
737,1,40,0,1.765386," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)*(d*x)^(1/2),x, algorithm=""fricas"")","\frac{2}{1155} \, {\left(77 \, b^{3} x^{7} + 315 \, a b^{2} x^{5} + 495 \, a^{2} b x^{3} + 385 \, a^{3} x\right)} \sqrt{d x}"," ",0,"2/1155*(77*b^3*x^7 + 315*a*b^2*x^5 + 495*a^2*b*x^3 + 385*a^3*x)*sqrt(d*x)","A",0
738,1,42,0,2.006626," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/(d*x)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, b^{3} x^{6} + 65 \, a b^{2} x^{4} + 117 \, a^{2} b x^{2} + 195 \, a^{3}\right)} \sqrt{d x}}{195 \, d}"," ",0,"2/195*(15*b^3*x^6 + 65*a*b^2*x^4 + 117*a^2*b*x^2 + 195*a^3)*sqrt(d*x)/d","A",0
739,1,45,0,1.024245," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/(d*x)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(7 \, b^{3} x^{6} + 33 \, a b^{2} x^{4} + 77 \, a^{2} b x^{2} - 77 \, a^{3}\right)} \sqrt{d x}}{77 \, d^{2} x}"," ",0,"2/77*(7*b^3*x^6 + 33*a*b^2*x^4 + 77*a^2*b*x^2 - 77*a^3)*sqrt(d*x)/(d^2*x)","A",0
740,1,45,0,0.699289," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/(d*x)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, b^{3} x^{6} + 27 \, a b^{2} x^{4} + 135 \, a^{2} b x^{2} - 15 \, a^{3}\right)} \sqrt{d x}}{45 \, d^{3} x^{2}}"," ",0,"2/45*(5*b^3*x^6 + 27*a*b^2*x^4 + 135*a^2*b*x^2 - 15*a^3)*sqrt(d*x)/(d^3*x^2)","A",0
741,1,45,0,2.067517," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/(d*x)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, b^{3} x^{6} + 35 \, a b^{2} x^{4} - 105 \, a^{2} b x^{2} - 7 \, a^{3}\right)} \sqrt{d x}}{35 \, d^{4} x^{3}}"," ",0,"2/35*(5*b^3*x^6 + 35*a*b^2*x^4 - 105*a^2*b*x^2 - 7*a^3)*sqrt(d*x)/(d^4*x^3)","A",0
742,1,82,0,1.577619," ","integrate((d*x)^(5/2)*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""fricas"")","\frac{2}{908523} \, {\left(33649 \, b^{5} d^{2} x^{13} + 197505 \, a b^{4} d^{2} x^{11} + 478170 \, a^{2} b^{3} d^{2} x^{9} + 605682 \, a^{3} b^{2} d^{2} x^{7} + 412965 \, a^{4} b d^{2} x^{5} + 129789 \, a^{5} d^{2} x^{3}\right)} \sqrt{d x}"," ",0,"2/908523*(33649*b^5*d^2*x^13 + 197505*a*b^4*d^2*x^11 + 478170*a^2*b^3*d^2*x^9 + 605682*a^3*b^2*d^2*x^7 + 412965*a^4*b*d^2*x^5 + 129789*a^5*d^2*x^3)*sqrt(d*x)","A",0
743,1,70,0,1.100710," ","integrate((d*x)^(3/2)*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""fricas"")","\frac{2}{348075} \, {\left(13923 \, b^{5} d x^{12} + 82875 \, a b^{4} d x^{10} + 204750 \, a^{2} b^{3} d x^{8} + 267750 \, a^{3} b^{2} d x^{6} + 193375 \, a^{4} b d x^{4} + 69615 \, a^{5} d x^{2}\right)} \sqrt{d x}"," ",0,"2/348075*(13923*b^5*d*x^12 + 82875*a*b^4*d*x^10 + 204750*a^2*b^3*d*x^8 + 267750*a^3*b^2*d*x^6 + 193375*a^4*b*d*x^4 + 69615*a^5*d*x^2)*sqrt(d*x)","A",0
744,1,62,0,2.781874," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)*(d*x)^(1/2),x, algorithm=""fricas"")","\frac{2}{100947} \, {\left(4389 \, b^{5} x^{11} + 26565 \, a b^{4} x^{9} + 67298 \, a^{2} b^{3} x^{7} + 91770 \, a^{3} b^{2} x^{5} + 72105 \, a^{4} b x^{3} + 33649 \, a^{5} x\right)} \sqrt{d x}"," ",0,"2/100947*(4389*b^5*x^11 + 26565*a*b^4*x^9 + 67298*a^2*b^3*x^7 + 91770*a^3*b^2*x^5 + 72105*a^4*b*x^3 + 33649*a^5*x)*sqrt(d*x)","A",0
745,1,64,0,2.238849," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/(d*x)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(663 \, b^{5} x^{10} + 4095 \, a b^{4} x^{8} + 10710 \, a^{2} b^{3} x^{6} + 15470 \, a^{3} b^{2} x^{4} + 13923 \, a^{4} b x^{2} + 13923 \, a^{5}\right)} \sqrt{d x}}{13923 \, d}"," ",0,"2/13923*(663*b^5*x^10 + 4095*a*b^4*x^8 + 10710*a^2*b^3*x^6 + 15470*a^3*b^2*x^4 + 13923*a^4*b*x^2 + 13923*a^5)*sqrt(d*x)/d","A",0
746,1,67,0,1.859052," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/(d*x)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(231 \, b^{5} x^{10} + 1463 \, a b^{4} x^{8} + 3990 \, a^{2} b^{3} x^{6} + 6270 \, a^{3} b^{2} x^{4} + 7315 \, a^{4} b x^{2} - 4389 \, a^{5}\right)} \sqrt{d x}}{4389 \, d^{2} x}"," ",0,"2/4389*(231*b^5*x^10 + 1463*a*b^4*x^8 + 3990*a^2*b^3*x^6 + 6270*a^3*b^2*x^4 + 7315*a^4*b*x^2 - 4389*a^5)*sqrt(d*x)/(d^2*x)","A",0
747,1,67,0,0.939179," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/(d*x)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(117 \, b^{5} x^{10} + 765 \, a b^{4} x^{8} + 2210 \, a^{2} b^{3} x^{6} + 3978 \, a^{3} b^{2} x^{4} + 9945 \, a^{4} b x^{2} - 663 \, a^{5}\right)} \sqrt{d x}}{1989 \, d^{3} x^{2}}"," ",0,"2/1989*(117*b^5*x^10 + 765*a*b^4*x^8 + 2210*a^2*b^3*x^6 + 3978*a^3*b^2*x^4 + 9945*a^4*b*x^2 - 663*a^5)*sqrt(d*x)/(d^3*x^2)","A",0
748,1,67,0,0.814824," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/(d*x)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(77 \, b^{5} x^{10} + 525 \, a b^{4} x^{8} + 1650 \, a^{2} b^{3} x^{6} + 3850 \, a^{3} b^{2} x^{4} - 5775 \, a^{4} b x^{2} - 231 \, a^{5}\right)} \sqrt{d x}}{1155 \, d^{4} x^{3}}"," ",0,"2/1155*(77*b^5*x^10 + 525*a*b^4*x^8 + 1650*a^2*b^3*x^6 + 3850*a^3*b^2*x^4 - 5775*a^4*b*x^2 - 231*a^5)*sqrt(d*x)/(d^4*x^3)","A",0
749,1,223,0,0.487054," ","integrate((d*x)^(7/2)/((b*x^2+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{20 \, \left(-\frac{a^{5} d^{14}}{b^{9}}\right)^{\frac{1}{4}} b^{2} \arctan\left(-\frac{\left(-\frac{a^{5} d^{14}}{b^{9}}\right)^{\frac{3}{4}} \sqrt{d x} a b^{7} d^{3} - \left(-\frac{a^{5} d^{14}}{b^{9}}\right)^{\frac{3}{4}} \sqrt{a^{2} d^{7} x + \sqrt{-\frac{a^{5} d^{14}}{b^{9}}} b^{4}} b^{7}}{a^{5} d^{14}}\right) + 5 \, \left(-\frac{a^{5} d^{14}}{b^{9}}\right)^{\frac{1}{4}} b^{2} \log\left(\sqrt{d x} a d^{3} + \left(-\frac{a^{5} d^{14}}{b^{9}}\right)^{\frac{1}{4}} b^{2}\right) - 5 \, \left(-\frac{a^{5} d^{14}}{b^{9}}\right)^{\frac{1}{4}} b^{2} \log\left(\sqrt{d x} a d^{3} - \left(-\frac{a^{5} d^{14}}{b^{9}}\right)^{\frac{1}{4}} b^{2}\right) + 4 \, {\left(b d^{3} x^{2} - 5 \, a d^{3}\right)} \sqrt{d x}}{10 \, b^{2}}"," ",0,"1/10*(20*(-a^5*d^14/b^9)^(1/4)*b^2*arctan(-((-a^5*d^14/b^9)^(3/4)*sqrt(d*x)*a*b^7*d^3 - (-a^5*d^14/b^9)^(3/4)*sqrt(a^2*d^7*x + sqrt(-a^5*d^14/b^9)*b^4)*b^7)/(a^5*d^14)) + 5*(-a^5*d^14/b^9)^(1/4)*b^2*log(sqrt(d*x)*a*d^3 + (-a^5*d^14/b^9)^(1/4)*b^2) - 5*(-a^5*d^14/b^9)^(1/4)*b^2*log(sqrt(d*x)*a*d^3 - (-a^5*d^14/b^9)^(1/4)*b^2) + 4*(b*d^3*x^2 - 5*a*d^3)*sqrt(d*x))/b^2","A",0
750,1,219,0,0.841436," ","integrate((d*x)^(5/2)/((b*x^2+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{4 \, \sqrt{d x} d^{2} x + 12 \, \left(-\frac{a^{3} d^{10}}{b^{7}}\right)^{\frac{1}{4}} b \arctan\left(-\frac{\left(-\frac{a^{3} d^{10}}{b^{7}}\right)^{\frac{1}{4}} \sqrt{d x} a^{2} b^{2} d^{7} - \sqrt{a^{4} d^{15} x - \sqrt{-\frac{a^{3} d^{10}}{b^{7}}} a^{3} b^{3} d^{10}} \left(-\frac{a^{3} d^{10}}{b^{7}}\right)^{\frac{1}{4}} b^{2}}{a^{3} d^{10}}\right) - 3 \, \left(-\frac{a^{3} d^{10}}{b^{7}}\right)^{\frac{1}{4}} b \log\left(\sqrt{d x} a^{2} d^{7} + \left(-\frac{a^{3} d^{10}}{b^{7}}\right)^{\frac{3}{4}} b^{5}\right) + 3 \, \left(-\frac{a^{3} d^{10}}{b^{7}}\right)^{\frac{1}{4}} b \log\left(\sqrt{d x} a^{2} d^{7} - \left(-\frac{a^{3} d^{10}}{b^{7}}\right)^{\frac{3}{4}} b^{5}\right)}{6 \, b}"," ",0,"1/6*(4*sqrt(d*x)*d^2*x + 12*(-a^3*d^10/b^7)^(1/4)*b*arctan(-((-a^3*d^10/b^7)^(1/4)*sqrt(d*x)*a^2*b^2*d^7 - sqrt(a^4*d^15*x - sqrt(-a^3*d^10/b^7)*a^3*b^3*d^10)*(-a^3*d^10/b^7)^(1/4)*b^2)/(a^3*d^10)) - 3*(-a^3*d^10/b^7)^(1/4)*b*log(sqrt(d*x)*a^2*d^7 + (-a^3*d^10/b^7)^(3/4)*b^5) + 3*(-a^3*d^10/b^7)^(1/4)*b*log(sqrt(d*x)*a^2*d^7 - (-a^3*d^10/b^7)^(3/4)*b^5))/b","A",0
751,1,170,0,1.913079," ","integrate((d*x)^(3/2)/((b*x^2+a)^2)^(1/2),x, algorithm=""fricas"")","-\frac{4 \, \left(-\frac{a d^{6}}{b^{5}}\right)^{\frac{1}{4}} b \arctan\left(-\frac{\left(-\frac{a d^{6}}{b^{5}}\right)^{\frac{3}{4}} \sqrt{d x} b^{4} d - \sqrt{d^{3} x + \sqrt{-\frac{a d^{6}}{b^{5}}} b^{2}} \left(-\frac{a d^{6}}{b^{5}}\right)^{\frac{3}{4}} b^{4}}{a d^{6}}\right) + \left(-\frac{a d^{6}}{b^{5}}\right)^{\frac{1}{4}} b \log\left(\sqrt{d x} d + \left(-\frac{a d^{6}}{b^{5}}\right)^{\frac{1}{4}} b\right) - \left(-\frac{a d^{6}}{b^{5}}\right)^{\frac{1}{4}} b \log\left(\sqrt{d x} d - \left(-\frac{a d^{6}}{b^{5}}\right)^{\frac{1}{4}} b\right) - 4 \, \sqrt{d x} d}{2 \, b}"," ",0,"-1/2*(4*(-a*d^6/b^5)^(1/4)*b*arctan(-((-a*d^6/b^5)^(3/4)*sqrt(d*x)*b^4*d - sqrt(d^3*x + sqrt(-a*d^6/b^5)*b^2)*(-a*d^6/b^5)^(3/4)*b^4)/(a*d^6)) + (-a*d^6/b^5)^(1/4)*b*log(sqrt(d*x)*d + (-a*d^6/b^5)^(1/4)*b) - (-a*d^6/b^5)^(1/4)*b*log(sqrt(d*x)*d - (-a*d^6/b^5)^(1/4)*b) - 4*sqrt(d*x)*d)/b","A",0
752,1,173,0,1.695132," ","integrate((d*x)^(1/2)/((b*x^2+a)^2)^(1/2),x, algorithm=""fricas"")","-2 \, \left(-\frac{d^{2}}{a b^{3}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{d x} b d \left(-\frac{d^{2}}{a b^{3}}\right)^{\frac{1}{4}} - \sqrt{-a b d^{2} \sqrt{-\frac{d^{2}}{a b^{3}}} + d^{3} x} b \left(-\frac{d^{2}}{a b^{3}}\right)^{\frac{1}{4}}}{d^{2}}\right) + \frac{1}{2} \, \left(-\frac{d^{2}}{a b^{3}}\right)^{\frac{1}{4}} \log\left(a b^{2} \left(-\frac{d^{2}}{a b^{3}}\right)^{\frac{3}{4}} + \sqrt{d x} d\right) - \frac{1}{2} \, \left(-\frac{d^{2}}{a b^{3}}\right)^{\frac{1}{4}} \log\left(-a b^{2} \left(-\frac{d^{2}}{a b^{3}}\right)^{\frac{3}{4}} + \sqrt{d x} d\right)"," ",0,"-2*(-d^2/(a*b^3))^(1/4)*arctan(-(sqrt(d*x)*b*d*(-d^2/(a*b^3))^(1/4) - sqrt(-a*b*d^2*sqrt(-d^2/(a*b^3)) + d^3*x)*b*(-d^2/(a*b^3))^(1/4))/d^2) + 1/2*(-d^2/(a*b^3))^(1/4)*log(a*b^2*(-d^2/(a*b^3))^(3/4) + sqrt(d*x)*d) - 1/2*(-d^2/(a*b^3))^(1/4)*log(-a*b^2*(-d^2/(a*b^3))^(3/4) + sqrt(d*x)*d)","A",0
753,1,165,0,1.327427," ","integrate(1/(d*x)^(1/2)/((b*x^2+a)^2)^(1/2),x, algorithm=""fricas"")","2 \, \left(-\frac{1}{a^{3} b d^{2}}\right)^{\frac{1}{4}} \arctan\left(\sqrt{a^{2} d^{2} \sqrt{-\frac{1}{a^{3} b d^{2}}} + d x} a^{2} b d \left(-\frac{1}{a^{3} b d^{2}}\right)^{\frac{3}{4}} - \sqrt{d x} a^{2} b d \left(-\frac{1}{a^{3} b d^{2}}\right)^{\frac{3}{4}}\right) + \frac{1}{2} \, \left(-\frac{1}{a^{3} b d^{2}}\right)^{\frac{1}{4}} \log\left(a d \left(-\frac{1}{a^{3} b d^{2}}\right)^{\frac{1}{4}} + \sqrt{d x}\right) - \frac{1}{2} \, \left(-\frac{1}{a^{3} b d^{2}}\right)^{\frac{1}{4}} \log\left(-a d \left(-\frac{1}{a^{3} b d^{2}}\right)^{\frac{1}{4}} + \sqrt{d x}\right)"," ",0,"2*(-1/(a^3*b*d^2))^(1/4)*arctan(sqrt(a^2*d^2*sqrt(-1/(a^3*b*d^2)) + d*x)*a^2*b*d*(-1/(a^3*b*d^2))^(3/4) - sqrt(d*x)*a^2*b*d*(-1/(a^3*b*d^2))^(3/4)) + 1/2*(-1/(a^3*b*d^2))^(1/4)*log(a*d*(-1/(a^3*b*d^2))^(1/4) + sqrt(d*x)) - 1/2*(-1/(a^3*b*d^2))^(1/4)*log(-a*d*(-1/(a^3*b*d^2))^(1/4) + sqrt(d*x))","A",0
754,1,198,0,1.496466," ","integrate(1/(d*x)^(3/2)/((b*x^2+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{4 \, a d^{2} x \left(-\frac{b}{a^{5} d^{6}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{d x} a b d \left(-\frac{b}{a^{5} d^{6}}\right)^{\frac{1}{4}} - \sqrt{-a^{3} b d^{4} \sqrt{-\frac{b}{a^{5} d^{6}}} + b^{2} d x} a d \left(-\frac{b}{a^{5} d^{6}}\right)^{\frac{1}{4}}}{b}\right) - a d^{2} x \left(-\frac{b}{a^{5} d^{6}}\right)^{\frac{1}{4}} \log\left(a^{4} d^{5} \left(-\frac{b}{a^{5} d^{6}}\right)^{\frac{3}{4}} + \sqrt{d x} b\right) + a d^{2} x \left(-\frac{b}{a^{5} d^{6}}\right)^{\frac{1}{4}} \log\left(-a^{4} d^{5} \left(-\frac{b}{a^{5} d^{6}}\right)^{\frac{3}{4}} + \sqrt{d x} b\right) - 4 \, \sqrt{d x}}{2 \, a d^{2} x}"," ",0,"1/2*(4*a*d^2*x*(-b/(a^5*d^6))^(1/4)*arctan(-(sqrt(d*x)*a*b*d*(-b/(a^5*d^6))^(1/4) - sqrt(-a^3*b*d^4*sqrt(-b/(a^5*d^6)) + b^2*d*x)*a*d*(-b/(a^5*d^6))^(1/4))/b) - a*d^2*x*(-b/(a^5*d^6))^(1/4)*log(a^4*d^5*(-b/(a^5*d^6))^(3/4) + sqrt(d*x)*b) + a*d^2*x*(-b/(a^5*d^6))^(1/4)*log(-a^4*d^5*(-b/(a^5*d^6))^(3/4) + sqrt(d*x)*b) - 4*sqrt(d*x))/(a*d^2*x)","A",0
755,1,227,0,0.963131," ","integrate(1/(d*x)^(5/2)/((b*x^2+a)^2)^(1/2),x, algorithm=""fricas"")","-\frac{12 \, a d^{3} x^{2} \left(-\frac{b^{3}}{a^{7} d^{10}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{d x} a^{5} b d^{7} \left(-\frac{b^{3}}{a^{7} d^{10}}\right)^{\frac{3}{4}} - \sqrt{a^{4} d^{6} \sqrt{-\frac{b^{3}}{a^{7} d^{10}}} + b^{2} d x} a^{5} d^{7} \left(-\frac{b^{3}}{a^{7} d^{10}}\right)^{\frac{3}{4}}}{b^{3}}\right) + 3 \, a d^{3} x^{2} \left(-\frac{b^{3}}{a^{7} d^{10}}\right)^{\frac{1}{4}} \log\left(a^{2} d^{3} \left(-\frac{b^{3}}{a^{7} d^{10}}\right)^{\frac{1}{4}} + \sqrt{d x} b\right) - 3 \, a d^{3} x^{2} \left(-\frac{b^{3}}{a^{7} d^{10}}\right)^{\frac{1}{4}} \log\left(-a^{2} d^{3} \left(-\frac{b^{3}}{a^{7} d^{10}}\right)^{\frac{1}{4}} + \sqrt{d x} b\right) + 4 \, \sqrt{d x}}{6 \, a d^{3} x^{2}}"," ",0,"-1/6*(12*a*d^3*x^2*(-b^3/(a^7*d^10))^(1/4)*arctan(-(sqrt(d*x)*a^5*b*d^7*(-b^3/(a^7*d^10))^(3/4) - sqrt(a^4*d^6*sqrt(-b^3/(a^7*d^10)) + b^2*d*x)*a^5*d^7*(-b^3/(a^7*d^10))^(3/4))/b^3) + 3*a*d^3*x^2*(-b^3/(a^7*d^10))^(1/4)*log(a^2*d^3*(-b^3/(a^7*d^10))^(1/4) + sqrt(d*x)*b) - 3*a*d^3*x^2*(-b^3/(a^7*d^10))^(1/4)*log(-a^2*d^3*(-b^3/(a^7*d^10))^(1/4) + sqrt(d*x)*b) + 4*sqrt(d*x))/(a*d^3*x^2)","A",0
756,1,253,0,1.505322," ","integrate(1/(d*x)^(7/2)/((b*x^2+a)^2)^(1/2),x, algorithm=""fricas"")","-\frac{20 \, a^{2} d^{4} x^{3} \left(-\frac{b^{5}}{a^{9} d^{14}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{d x} a^{2} b^{4} d^{3} \left(-\frac{b^{5}}{a^{9} d^{14}}\right)^{\frac{1}{4}} - \sqrt{-a^{5} b^{5} d^{8} \sqrt{-\frac{b^{5}}{a^{9} d^{14}}} + b^{8} d x} a^{2} d^{3} \left(-\frac{b^{5}}{a^{9} d^{14}}\right)^{\frac{1}{4}}}{b^{5}}\right) - 5 \, a^{2} d^{4} x^{3} \left(-\frac{b^{5}}{a^{9} d^{14}}\right)^{\frac{1}{4}} \log\left(a^{7} d^{11} \left(-\frac{b^{5}}{a^{9} d^{14}}\right)^{\frac{3}{4}} + \sqrt{d x} b^{4}\right) + 5 \, a^{2} d^{4} x^{3} \left(-\frac{b^{5}}{a^{9} d^{14}}\right)^{\frac{1}{4}} \log\left(-a^{7} d^{11} \left(-\frac{b^{5}}{a^{9} d^{14}}\right)^{\frac{3}{4}} + \sqrt{d x} b^{4}\right) - 4 \, {\left(5 \, b x^{2} - a\right)} \sqrt{d x}}{10 \, a^{2} d^{4} x^{3}}"," ",0,"-1/10*(20*a^2*d^4*x^3*(-b^5/(a^9*d^14))^(1/4)*arctan(-(sqrt(d*x)*a^2*b^4*d^3*(-b^5/(a^9*d^14))^(1/4) - sqrt(-a^5*b^5*d^8*sqrt(-b^5/(a^9*d^14)) + b^8*d*x)*a^2*d^3*(-b^5/(a^9*d^14))^(1/4))/b^5) - 5*a^2*d^4*x^3*(-b^5/(a^9*d^14))^(1/4)*log(a^7*d^11*(-b^5/(a^9*d^14))^(3/4) + sqrt(d*x)*b^4) + 5*a^2*d^4*x^3*(-b^5/(a^9*d^14))^(1/4)*log(-a^7*d^11*(-b^5/(a^9*d^14))^(3/4) + sqrt(d*x)*b^4) - 4*(5*b*x^2 - a)*sqrt(d*x))/(a^2*d^4*x^3)","A",0
757,1,341,0,1.016048," ","integrate((d*x)^(15/2)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""fricas"")","\frac{2340 \, \left(-\frac{a^{5} d^{30}}{b^{17}}\right)^{\frac{1}{4}} {\left(b^{6} x^{4} + 2 \, a b^{5} x^{2} + a^{2} b^{4}\right)} \arctan\left(-\frac{\left(-\frac{a^{5} d^{30}}{b^{17}}\right)^{\frac{3}{4}} \sqrt{d x} a b^{13} d^{7} - \left(-\frac{a^{5} d^{30}}{b^{17}}\right)^{\frac{3}{4}} \sqrt{a^{2} d^{15} x + \sqrt{-\frac{a^{5} d^{30}}{b^{17}}} b^{8}} b^{13}}{a^{5} d^{30}}\right) + 585 \, \left(-\frac{a^{5} d^{30}}{b^{17}}\right)^{\frac{1}{4}} {\left(b^{6} x^{4} + 2 \, a b^{5} x^{2} + a^{2} b^{4}\right)} \log\left(117 \, \sqrt{d x} a d^{7} + 117 \, \left(-\frac{a^{5} d^{30}}{b^{17}}\right)^{\frac{1}{4}} b^{4}\right) - 585 \, \left(-\frac{a^{5} d^{30}}{b^{17}}\right)^{\frac{1}{4}} {\left(b^{6} x^{4} + 2 \, a b^{5} x^{2} + a^{2} b^{4}\right)} \log\left(117 \, \sqrt{d x} a d^{7} - 117 \, \left(-\frac{a^{5} d^{30}}{b^{17}}\right)^{\frac{1}{4}} b^{4}\right) + 4 \, {\left(32 \, b^{3} d^{7} x^{6} - 416 \, a b^{2} d^{7} x^{4} - 1053 \, a^{2} b d^{7} x^{2} - 585 \, a^{3} d^{7}\right)} \sqrt{d x}}{320 \, {\left(b^{6} x^{4} + 2 \, a b^{5} x^{2} + a^{2} b^{4}\right)}}"," ",0,"1/320*(2340*(-a^5*d^30/b^17)^(1/4)*(b^6*x^4 + 2*a*b^5*x^2 + a^2*b^4)*arctan(-((-a^5*d^30/b^17)^(3/4)*sqrt(d*x)*a*b^13*d^7 - (-a^5*d^30/b^17)^(3/4)*sqrt(a^2*d^15*x + sqrt(-a^5*d^30/b^17)*b^8)*b^13)/(a^5*d^30)) + 585*(-a^5*d^30/b^17)^(1/4)*(b^6*x^4 + 2*a*b^5*x^2 + a^2*b^4)*log(117*sqrt(d*x)*a*d^7 + 117*(-a^5*d^30/b^17)^(1/4)*b^4) - 585*(-a^5*d^30/b^17)^(1/4)*(b^6*x^4 + 2*a*b^5*x^2 + a^2*b^4)*log(117*sqrt(d*x)*a*d^7 - 117*(-a^5*d^30/b^17)^(1/4)*b^4) + 4*(32*b^3*d^7*x^6 - 416*a*b^2*d^7*x^4 - 1053*a^2*b*d^7*x^2 - 585*a^3*d^7)*sqrt(d*x))/(b^6*x^4 + 2*a*b^5*x^2 + a^2*b^4)","A",0
758,1,341,0,0.954222," ","integrate((d*x)^(13/2)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""fricas"")","\frac{924 \, \left(-\frac{a^{3} d^{26}}{b^{15}}\right)^{\frac{1}{4}} {\left(b^{5} x^{4} + 2 \, a b^{4} x^{2} + a^{2} b^{3}\right)} \arctan\left(-\frac{\left(-\frac{a^{3} d^{26}}{b^{15}}\right)^{\frac{1}{4}} \sqrt{d x} a^{2} b^{4} d^{19} - \sqrt{a^{4} d^{39} x - \sqrt{-\frac{a^{3} d^{26}}{b^{15}}} a^{3} b^{7} d^{26}} \left(-\frac{a^{3} d^{26}}{b^{15}}\right)^{\frac{1}{4}} b^{4}}{a^{3} d^{26}}\right) - 231 \, \left(-\frac{a^{3} d^{26}}{b^{15}}\right)^{\frac{1}{4}} {\left(b^{5} x^{4} + 2 \, a b^{4} x^{2} + a^{2} b^{3}\right)} \log\left(456533 \, \sqrt{d x} a^{2} d^{19} + 456533 \, \left(-\frac{a^{3} d^{26}}{b^{15}}\right)^{\frac{3}{4}} b^{11}\right) + 231 \, \left(-\frac{a^{3} d^{26}}{b^{15}}\right)^{\frac{1}{4}} {\left(b^{5} x^{4} + 2 \, a b^{4} x^{2} + a^{2} b^{3}\right)} \log\left(456533 \, \sqrt{d x} a^{2} d^{19} - 456533 \, \left(-\frac{a^{3} d^{26}}{b^{15}}\right)^{\frac{3}{4}} b^{11}\right) + 4 \, {\left(32 \, b^{2} d^{6} x^{5} + 121 \, a b d^{6} x^{3} + 77 \, a^{2} d^{6} x\right)} \sqrt{d x}}{192 \, {\left(b^{5} x^{4} + 2 \, a b^{4} x^{2} + a^{2} b^{3}\right)}}"," ",0,"1/192*(924*(-a^3*d^26/b^15)^(1/4)*(b^5*x^4 + 2*a*b^4*x^2 + a^2*b^3)*arctan(-((-a^3*d^26/b^15)^(1/4)*sqrt(d*x)*a^2*b^4*d^19 - sqrt(a^4*d^39*x - sqrt(-a^3*d^26/b^15)*a^3*b^7*d^26)*(-a^3*d^26/b^15)^(1/4)*b^4)/(a^3*d^26)) - 231*(-a^3*d^26/b^15)^(1/4)*(b^5*x^4 + 2*a*b^4*x^2 + a^2*b^3)*log(456533*sqrt(d*x)*a^2*d^19 + 456533*(-a^3*d^26/b^15)^(3/4)*b^11) + 231*(-a^3*d^26/b^15)^(1/4)*(b^5*x^4 + 2*a*b^4*x^2 + a^2*b^3)*log(456533*sqrt(d*x)*a^2*d^19 - 456533*(-a^3*d^26/b^15)^(3/4)*b^11) + 4*(32*b^2*d^6*x^5 + 121*a*b*d^6*x^3 + 77*a^2*d^6*x)*sqrt(d*x))/(b^5*x^4 + 2*a*b^4*x^2 + a^2*b^3)","A",0
759,1,305,0,1.011634," ","integrate((d*x)^(11/2)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""fricas"")","-\frac{180 \, \left(-\frac{a d^{22}}{b^{13}}\right)^{\frac{1}{4}} {\left(b^{5} x^{4} + 2 \, a b^{4} x^{2} + a^{2} b^{3}\right)} \arctan\left(-\frac{\left(-\frac{a d^{22}}{b^{13}}\right)^{\frac{3}{4}} \sqrt{d x} b^{10} d^{5} - \sqrt{d^{11} x + \sqrt{-\frac{a d^{22}}{b^{13}}} b^{6}} \left(-\frac{a d^{22}}{b^{13}}\right)^{\frac{3}{4}} b^{10}}{a d^{22}}\right) + 45 \, \left(-\frac{a d^{22}}{b^{13}}\right)^{\frac{1}{4}} {\left(b^{5} x^{4} + 2 \, a b^{4} x^{2} + a^{2} b^{3}\right)} \log\left(45 \, \sqrt{d x} d^{5} + 45 \, \left(-\frac{a d^{22}}{b^{13}}\right)^{\frac{1}{4}} b^{3}\right) - 45 \, \left(-\frac{a d^{22}}{b^{13}}\right)^{\frac{1}{4}} {\left(b^{5} x^{4} + 2 \, a b^{4} x^{2} + a^{2} b^{3}\right)} \log\left(45 \, \sqrt{d x} d^{5} - 45 \, \left(-\frac{a d^{22}}{b^{13}}\right)^{\frac{1}{4}} b^{3}\right) - 4 \, {\left(32 \, b^{2} d^{5} x^{4} + 81 \, a b d^{5} x^{2} + 45 \, a^{2} d^{5}\right)} \sqrt{d x}}{64 \, {\left(b^{5} x^{4} + 2 \, a b^{4} x^{2} + a^{2} b^{3}\right)}}"," ",0,"-1/64*(180*(-a*d^22/b^13)^(1/4)*(b^5*x^4 + 2*a*b^4*x^2 + a^2*b^3)*arctan(-((-a*d^22/b^13)^(3/4)*sqrt(d*x)*b^10*d^5 - sqrt(d^11*x + sqrt(-a*d^22/b^13)*b^6)*(-a*d^22/b^13)^(3/4)*b^10)/(a*d^22)) + 45*(-a*d^22/b^13)^(1/4)*(b^5*x^4 + 2*a*b^4*x^2 + a^2*b^3)*log(45*sqrt(d*x)*d^5 + 45*(-a*d^22/b^13)^(1/4)*b^3) - 45*(-a*d^22/b^13)^(1/4)*(b^5*x^4 + 2*a*b^4*x^2 + a^2*b^3)*log(45*sqrt(d*x)*d^5 - 45*(-a*d^22/b^13)^(1/4)*b^3) - 4*(32*b^2*d^5*x^4 + 81*a*b*d^5*x^2 + 45*a^2*d^5)*sqrt(d*x))/(b^5*x^4 + 2*a*b^4*x^2 + a^2*b^3)","A",0
760,1,312,0,1.730529," ","integrate((d*x)^(9/2)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""fricas"")","-\frac{84 \, {\left(b^{4} x^{4} + 2 \, a b^{3} x^{2} + a^{2} b^{2}\right)} \left(-\frac{d^{18}}{a b^{11}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\left(-\frac{d^{18}}{a b^{11}}\right)^{\frac{1}{4}} \sqrt{d x} b^{3} d^{13} - \sqrt{d^{27} x - \sqrt{-\frac{d^{18}}{a b^{11}}} a b^{5} d^{18}} \left(-\frac{d^{18}}{a b^{11}}\right)^{\frac{1}{4}} b^{3}}{d^{18}}\right) - 21 \, {\left(b^{4} x^{4} + 2 \, a b^{3} x^{2} + a^{2} b^{2}\right)} \left(-\frac{d^{18}}{a b^{11}}\right)^{\frac{1}{4}} \log\left(9261 \, \sqrt{d x} d^{13} + 9261 \, \left(-\frac{d^{18}}{a b^{11}}\right)^{\frac{3}{4}} a b^{8}\right) + 21 \, {\left(b^{4} x^{4} + 2 \, a b^{3} x^{2} + a^{2} b^{2}\right)} \left(-\frac{d^{18}}{a b^{11}}\right)^{\frac{1}{4}} \log\left(9261 \, \sqrt{d x} d^{13} - 9261 \, \left(-\frac{d^{18}}{a b^{11}}\right)^{\frac{3}{4}} a b^{8}\right) + 4 \, {\left(11 \, b d^{4} x^{3} + 7 \, a d^{4} x\right)} \sqrt{d x}}{64 \, {\left(b^{4} x^{4} + 2 \, a b^{3} x^{2} + a^{2} b^{2}\right)}}"," ",0,"-1/64*(84*(b^4*x^4 + 2*a*b^3*x^2 + a^2*b^2)*(-d^18/(a*b^11))^(1/4)*arctan(-((-d^18/(a*b^11))^(1/4)*sqrt(d*x)*b^3*d^13 - sqrt(d^27*x - sqrt(-d^18/(a*b^11))*a*b^5*d^18)*(-d^18/(a*b^11))^(1/4)*b^3)/d^18) - 21*(b^4*x^4 + 2*a*b^3*x^2 + a^2*b^2)*(-d^18/(a*b^11))^(1/4)*log(9261*sqrt(d*x)*d^13 + 9261*(-d^18/(a*b^11))^(3/4)*a*b^8) + 21*(b^4*x^4 + 2*a*b^3*x^2 + a^2*b^2)*(-d^18/(a*b^11))^(1/4)*log(9261*sqrt(d*x)*d^13 - 9261*(-d^18/(a*b^11))^(3/4)*a*b^8) + 4*(11*b*d^4*x^3 + 7*a*d^4*x)*sqrt(d*x))/(b^4*x^4 + 2*a*b^3*x^2 + a^2*b^2)","A",0
761,1,315,0,1.427182," ","integrate((d*x)^(7/2)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""fricas"")","\frac{20 \, {\left(b^{4} x^{4} + 2 \, a b^{3} x^{2} + a^{2} b^{2}\right)} \left(-\frac{d^{14}}{a^{3} b^{9}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\left(-\frac{d^{14}}{a^{3} b^{9}}\right)^{\frac{3}{4}} \sqrt{d x} a^{2} b^{7} d^{3} - \sqrt{d^{7} x + \sqrt{-\frac{d^{14}}{a^{3} b^{9}}} a^{2} b^{4}} \left(-\frac{d^{14}}{a^{3} b^{9}}\right)^{\frac{3}{4}} a^{2} b^{7}}{d^{14}}\right) + 5 \, {\left(b^{4} x^{4} + 2 \, a b^{3} x^{2} + a^{2} b^{2}\right)} \left(-\frac{d^{14}}{a^{3} b^{9}}\right)^{\frac{1}{4}} \log\left(5 \, \sqrt{d x} d^{3} + 5 \, \left(-\frac{d^{14}}{a^{3} b^{9}}\right)^{\frac{1}{4}} a b^{2}\right) - 5 \, {\left(b^{4} x^{4} + 2 \, a b^{3} x^{2} + a^{2} b^{2}\right)} \left(-\frac{d^{14}}{a^{3} b^{9}}\right)^{\frac{1}{4}} \log\left(5 \, \sqrt{d x} d^{3} - 5 \, \left(-\frac{d^{14}}{a^{3} b^{9}}\right)^{\frac{1}{4}} a b^{2}\right) - 4 \, {\left(9 \, b d^{3} x^{2} + 5 \, a d^{3}\right)} \sqrt{d x}}{64 \, {\left(b^{4} x^{4} + 2 \, a b^{3} x^{2} + a^{2} b^{2}\right)}}"," ",0,"1/64*(20*(b^4*x^4 + 2*a*b^3*x^2 + a^2*b^2)*(-d^14/(a^3*b^9))^(1/4)*arctan(-((-d^14/(a^3*b^9))^(3/4)*sqrt(d*x)*a^2*b^7*d^3 - sqrt(d^7*x + sqrt(-d^14/(a^3*b^9))*a^2*b^4)*(-d^14/(a^3*b^9))^(3/4)*a^2*b^7)/d^14) + 5*(b^4*x^4 + 2*a*b^3*x^2 + a^2*b^2)*(-d^14/(a^3*b^9))^(1/4)*log(5*sqrt(d*x)*d^3 + 5*(-d^14/(a^3*b^9))^(1/4)*a*b^2) - 5*(b^4*x^4 + 2*a*b^3*x^2 + a^2*b^2)*(-d^14/(a^3*b^9))^(1/4)*log(5*sqrt(d*x)*d^3 - 5*(-d^14/(a^3*b^9))^(1/4)*a*b^2) - 4*(9*b*d^3*x^2 + 5*a*d^3)*sqrt(d*x))/(b^4*x^4 + 2*a*b^3*x^2 + a^2*b^2)","A",0
762,1,326,0,0.597117," ","integrate((d*x)^(5/2)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""fricas"")","-\frac{12 \, {\left(a b^{3} x^{4} + 2 \, a^{2} b^{2} x^{2} + a^{3} b\right)} \left(-\frac{d^{10}}{a^{5} b^{7}}\right)^{\frac{1}{4}} \arctan\left(-\frac{27 \, \sqrt{d x} a b^{2} d^{7} \left(-\frac{d^{10}}{a^{5} b^{7}}\right)^{\frac{1}{4}} - \sqrt{-729 \, a^{3} b^{3} d^{10} \sqrt{-\frac{d^{10}}{a^{5} b^{7}}} + 729 \, d^{15} x} a b^{2} \left(-\frac{d^{10}}{a^{5} b^{7}}\right)^{\frac{1}{4}}}{27 \, d^{10}}\right) - 3 \, {\left(a b^{3} x^{4} + 2 \, a^{2} b^{2} x^{2} + a^{3} b\right)} \left(-\frac{d^{10}}{a^{5} b^{7}}\right)^{\frac{1}{4}} \log\left(27 \, a^{4} b^{5} \left(-\frac{d^{10}}{a^{5} b^{7}}\right)^{\frac{3}{4}} + 27 \, \sqrt{d x} d^{7}\right) + 3 \, {\left(a b^{3} x^{4} + 2 \, a^{2} b^{2} x^{2} + a^{3} b\right)} \left(-\frac{d^{10}}{a^{5} b^{7}}\right)^{\frac{1}{4}} \log\left(-27 \, a^{4} b^{5} \left(-\frac{d^{10}}{a^{5} b^{7}}\right)^{\frac{3}{4}} + 27 \, \sqrt{d x} d^{7}\right) - 4 \, {\left(3 \, b d^{2} x^{3} - a d^{2} x\right)} \sqrt{d x}}{64 \, {\left(a b^{3} x^{4} + 2 \, a^{2} b^{2} x^{2} + a^{3} b\right)}}"," ",0,"-1/64*(12*(a*b^3*x^4 + 2*a^2*b^2*x^2 + a^3*b)*(-d^10/(a^5*b^7))^(1/4)*arctan(-1/27*(27*sqrt(d*x)*a*b^2*d^7*(-d^10/(a^5*b^7))^(1/4) - sqrt(-729*a^3*b^3*d^10*sqrt(-d^10/(a^5*b^7)) + 729*d^15*x)*a*b^2*(-d^10/(a^5*b^7))^(1/4))/d^10) - 3*(a*b^3*x^4 + 2*a^2*b^2*x^2 + a^3*b)*(-d^10/(a^5*b^7))^(1/4)*log(27*a^4*b^5*(-d^10/(a^5*b^7))^(3/4) + 27*sqrt(d*x)*d^7) + 3*(a*b^3*x^4 + 2*a^2*b^2*x^2 + a^3*b)*(-d^10/(a^5*b^7))^(1/4)*log(-27*a^4*b^5*(-d^10/(a^5*b^7))^(3/4) + 27*sqrt(d*x)*d^7) - 4*(3*b*d^2*x^3 - a*d^2*x)*sqrt(d*x))/(a*b^3*x^4 + 2*a^2*b^2*x^2 + a^3*b)","A",0
763,1,308,0,1.068069," ","integrate((d*x)^(3/2)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""fricas"")","\frac{12 \, {\left(a b^{3} x^{4} + 2 \, a^{2} b^{2} x^{2} + a^{3} b\right)} \left(-\frac{d^{6}}{a^{7} b^{5}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{d x} a^{5} b^{4} d \left(-\frac{d^{6}}{a^{7} b^{5}}\right)^{\frac{3}{4}} - \sqrt{a^{4} b^{2} \sqrt{-\frac{d^{6}}{a^{7} b^{5}}} + d^{3} x} a^{5} b^{4} \left(-\frac{d^{6}}{a^{7} b^{5}}\right)^{\frac{3}{4}}}{d^{6}}\right) + 3 \, {\left(a b^{3} x^{4} + 2 \, a^{2} b^{2} x^{2} + a^{3} b\right)} \left(-\frac{d^{6}}{a^{7} b^{5}}\right)^{\frac{1}{4}} \log\left(3 \, a^{2} b \left(-\frac{d^{6}}{a^{7} b^{5}}\right)^{\frac{1}{4}} + 3 \, \sqrt{d x} d\right) - 3 \, {\left(a b^{3} x^{4} + 2 \, a^{2} b^{2} x^{2} + a^{3} b\right)} \left(-\frac{d^{6}}{a^{7} b^{5}}\right)^{\frac{1}{4}} \log\left(-3 \, a^{2} b \left(-\frac{d^{6}}{a^{7} b^{5}}\right)^{\frac{1}{4}} + 3 \, \sqrt{d x} d\right) + 4 \, {\left(b d x^{2} - 3 \, a d\right)} \sqrt{d x}}{64 \, {\left(a b^{3} x^{4} + 2 \, a^{2} b^{2} x^{2} + a^{3} b\right)}}"," ",0,"1/64*(12*(a*b^3*x^4 + 2*a^2*b^2*x^2 + a^3*b)*(-d^6/(a^7*b^5))^(1/4)*arctan(-(sqrt(d*x)*a^5*b^4*d*(-d^6/(a^7*b^5))^(3/4) - sqrt(a^4*b^2*sqrt(-d^6/(a^7*b^5)) + d^3*x)*a^5*b^4*(-d^6/(a^7*b^5))^(3/4))/d^6) + 3*(a*b^3*x^4 + 2*a^2*b^2*x^2 + a^3*b)*(-d^6/(a^7*b^5))^(1/4)*log(3*a^2*b*(-d^6/(a^7*b^5))^(1/4) + 3*sqrt(d*x)*d) - 3*(a*b^3*x^4 + 2*a^2*b^2*x^2 + a^3*b)*(-d^6/(a^7*b^5))^(1/4)*log(-3*a^2*b*(-d^6/(a^7*b^5))^(1/4) + 3*sqrt(d*x)*d) + 4*(b*d*x^2 - 3*a*d)*sqrt(d*x))/(a*b^3*x^4 + 2*a^2*b^2*x^2 + a^3*b)","A",0
764,1,304,0,0.638713," ","integrate((d*x)^(1/2)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""fricas"")","-\frac{20 \, {\left(a^{2} b^{2} x^{4} + 2 \, a^{3} b x^{2} + a^{4}\right)} \left(-\frac{d^{2}}{a^{9} b^{3}}\right)^{\frac{1}{4}} \arctan\left(-\frac{125 \, \sqrt{d x} a^{2} b d \left(-\frac{d^{2}}{a^{9} b^{3}}\right)^{\frac{1}{4}} - \sqrt{-15625 \, a^{5} b d^{2} \sqrt{-\frac{d^{2}}{a^{9} b^{3}}} + 15625 \, d^{3} x} a^{2} b \left(-\frac{d^{2}}{a^{9} b^{3}}\right)^{\frac{1}{4}}}{125 \, d^{2}}\right) - 5 \, {\left(a^{2} b^{2} x^{4} + 2 \, a^{3} b x^{2} + a^{4}\right)} \left(-\frac{d^{2}}{a^{9} b^{3}}\right)^{\frac{1}{4}} \log\left(125 \, a^{7} b^{2} \left(-\frac{d^{2}}{a^{9} b^{3}}\right)^{\frac{3}{4}} + 125 \, \sqrt{d x} d\right) + 5 \, {\left(a^{2} b^{2} x^{4} + 2 \, a^{3} b x^{2} + a^{4}\right)} \left(-\frac{d^{2}}{a^{9} b^{3}}\right)^{\frac{1}{4}} \log\left(-125 \, a^{7} b^{2} \left(-\frac{d^{2}}{a^{9} b^{3}}\right)^{\frac{3}{4}} + 125 \, \sqrt{d x} d\right) - 4 \, {\left(5 \, b x^{3} + 9 \, a x\right)} \sqrt{d x}}{64 \, {\left(a^{2} b^{2} x^{4} + 2 \, a^{3} b x^{2} + a^{4}\right)}}"," ",0,"-1/64*(20*(a^2*b^2*x^4 + 2*a^3*b*x^2 + a^4)*(-d^2/(a^9*b^3))^(1/4)*arctan(-1/125*(125*sqrt(d*x)*a^2*b*d*(-d^2/(a^9*b^3))^(1/4) - sqrt(-15625*a^5*b*d^2*sqrt(-d^2/(a^9*b^3)) + 15625*d^3*x)*a^2*b*(-d^2/(a^9*b^3))^(1/4))/d^2) - 5*(a^2*b^2*x^4 + 2*a^3*b*x^2 + a^4)*(-d^2/(a^9*b^3))^(1/4)*log(125*a^7*b^2*(-d^2/(a^9*b^3))^(3/4) + 125*sqrt(d*x)*d) + 5*(a^2*b^2*x^4 + 2*a^3*b*x^2 + a^4)*(-d^2/(a^9*b^3))^(1/4)*log(-125*a^7*b^2*(-d^2/(a^9*b^3))^(3/4) + 125*sqrt(d*x)*d) - 4*(5*b*x^3 + 9*a*x)*sqrt(d*x))/(a^2*b^2*x^4 + 2*a^3*b*x^2 + a^4)","A",0
765,1,298,0,1.661387," ","integrate(1/(b^2*x^4+2*a*b*x^2+a^2)^(3/2)/(d*x)^(1/2),x, algorithm=""fricas"")","\frac{84 \, {\left(a^{2} b^{2} d x^{4} + 2 \, a^{3} b d x^{2} + a^{4} d\right)} \left(-\frac{1}{a^{11} b d^{2}}\right)^{\frac{1}{4}} \arctan\left(\sqrt{a^{6} d^{2} \sqrt{-\frac{1}{a^{11} b d^{2}}} + d x} a^{8} b d \left(-\frac{1}{a^{11} b d^{2}}\right)^{\frac{3}{4}} - \sqrt{d x} a^{8} b d \left(-\frac{1}{a^{11} b d^{2}}\right)^{\frac{3}{4}}\right) + 21 \, {\left(a^{2} b^{2} d x^{4} + 2 \, a^{3} b d x^{2} + a^{4} d\right)} \left(-\frac{1}{a^{11} b d^{2}}\right)^{\frac{1}{4}} \log\left(a^{3} d \left(-\frac{1}{a^{11} b d^{2}}\right)^{\frac{1}{4}} + \sqrt{d x}\right) - 21 \, {\left(a^{2} b^{2} d x^{4} + 2 \, a^{3} b d x^{2} + a^{4} d\right)} \left(-\frac{1}{a^{11} b d^{2}}\right)^{\frac{1}{4}} \log\left(-a^{3} d \left(-\frac{1}{a^{11} b d^{2}}\right)^{\frac{1}{4}} + \sqrt{d x}\right) + 4 \, {\left(7 \, b x^{2} + 11 \, a\right)} \sqrt{d x}}{64 \, {\left(a^{2} b^{2} d x^{4} + 2 \, a^{3} b d x^{2} + a^{4} d\right)}}"," ",0,"1/64*(84*(a^2*b^2*d*x^4 + 2*a^3*b*d*x^2 + a^4*d)*(-1/(a^11*b*d^2))^(1/4)*arctan(sqrt(a^6*d^2*sqrt(-1/(a^11*b*d^2)) + d*x)*a^8*b*d*(-1/(a^11*b*d^2))^(3/4) - sqrt(d*x)*a^8*b*d*(-1/(a^11*b*d^2))^(3/4)) + 21*(a^2*b^2*d*x^4 + 2*a^3*b*d*x^2 + a^4*d)*(-1/(a^11*b*d^2))^(1/4)*log(a^3*d*(-1/(a^11*b*d^2))^(1/4) + sqrt(d*x)) - 21*(a^2*b^2*d*x^4 + 2*a^3*b*d*x^2 + a^4*d)*(-1/(a^11*b*d^2))^(1/4)*log(-a^3*d*(-1/(a^11*b*d^2))^(1/4) + sqrt(d*x)) + 4*(7*b*x^2 + 11*a)*sqrt(d*x))/(a^2*b^2*d*x^4 + 2*a^3*b*d*x^2 + a^4*d)","A",0
766,1,343,0,2.182804," ","integrate(1/(d*x)^(3/2)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""fricas"")","\frac{180 \, {\left(a^{3} b^{2} d^{2} x^{5} + 2 \, a^{4} b d^{2} x^{3} + a^{5} d^{2} x\right)} \left(-\frac{b}{a^{13} d^{6}}\right)^{\frac{1}{4}} \arctan\left(-\frac{91125 \, \sqrt{d x} a^{3} b d \left(-\frac{b}{a^{13} d^{6}}\right)^{\frac{1}{4}} - \sqrt{-8303765625 \, a^{7} b d^{4} \sqrt{-\frac{b}{a^{13} d^{6}}} + 8303765625 \, b^{2} d x} a^{3} d \left(-\frac{b}{a^{13} d^{6}}\right)^{\frac{1}{4}}}{91125 \, b}\right) - 45 \, {\left(a^{3} b^{2} d^{2} x^{5} + 2 \, a^{4} b d^{2} x^{3} + a^{5} d^{2} x\right)} \left(-\frac{b}{a^{13} d^{6}}\right)^{\frac{1}{4}} \log\left(91125 \, a^{10} d^{5} \left(-\frac{b}{a^{13} d^{6}}\right)^{\frac{3}{4}} + 91125 \, \sqrt{d x} b\right) + 45 \, {\left(a^{3} b^{2} d^{2} x^{5} + 2 \, a^{4} b d^{2} x^{3} + a^{5} d^{2} x\right)} \left(-\frac{b}{a^{13} d^{6}}\right)^{\frac{1}{4}} \log\left(-91125 \, a^{10} d^{5} \left(-\frac{b}{a^{13} d^{6}}\right)^{\frac{3}{4}} + 91125 \, \sqrt{d x} b\right) - 4 \, {\left(45 \, b^{2} x^{4} + 81 \, a b x^{2} + 32 \, a^{2}\right)} \sqrt{d x}}{64 \, {\left(a^{3} b^{2} d^{2} x^{5} + 2 \, a^{4} b d^{2} x^{3} + a^{5} d^{2} x\right)}}"," ",0,"1/64*(180*(a^3*b^2*d^2*x^5 + 2*a^4*b*d^2*x^3 + a^5*d^2*x)*(-b/(a^13*d^6))^(1/4)*arctan(-1/91125*(91125*sqrt(d*x)*a^3*b*d*(-b/(a^13*d^6))^(1/4) - sqrt(-8303765625*a^7*b*d^4*sqrt(-b/(a^13*d^6)) + 8303765625*b^2*d*x)*a^3*d*(-b/(a^13*d^6))^(1/4))/b) - 45*(a^3*b^2*d^2*x^5 + 2*a^4*b*d^2*x^3 + a^5*d^2*x)*(-b/(a^13*d^6))^(1/4)*log(91125*a^10*d^5*(-b/(a^13*d^6))^(3/4) + 91125*sqrt(d*x)*b) + 45*(a^3*b^2*d^2*x^5 + 2*a^4*b*d^2*x^3 + a^5*d^2*x)*(-b/(a^13*d^6))^(1/4)*log(-91125*a^10*d^5*(-b/(a^13*d^6))^(3/4) + 91125*sqrt(d*x)*b) - 4*(45*b^2*x^4 + 81*a*b*x^2 + 32*a^2)*sqrt(d*x))/(a^3*b^2*d^2*x^5 + 2*a^4*b*d^2*x^3 + a^5*d^2*x)","A",0
767,1,367,0,0.805086," ","integrate(1/(d*x)^(5/2)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""fricas"")","-\frac{924 \, {\left(a^{3} b^{2} d^{3} x^{6} + 2 \, a^{4} b d^{3} x^{4} + a^{5} d^{3} x^{2}\right)} \left(-\frac{b^{3}}{a^{15} d^{10}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{d x} a^{11} b d^{7} \left(-\frac{b^{3}}{a^{15} d^{10}}\right)^{\frac{3}{4}} - \sqrt{a^{8} d^{6} \sqrt{-\frac{b^{3}}{a^{15} d^{10}}} + b^{2} d x} a^{11} d^{7} \left(-\frac{b^{3}}{a^{15} d^{10}}\right)^{\frac{3}{4}}}{b^{3}}\right) + 231 \, {\left(a^{3} b^{2} d^{3} x^{6} + 2 \, a^{4} b d^{3} x^{4} + a^{5} d^{3} x^{2}\right)} \left(-\frac{b^{3}}{a^{15} d^{10}}\right)^{\frac{1}{4}} \log\left(77 \, a^{4} d^{3} \left(-\frac{b^{3}}{a^{15} d^{10}}\right)^{\frac{1}{4}} + 77 \, \sqrt{d x} b\right) - 231 \, {\left(a^{3} b^{2} d^{3} x^{6} + 2 \, a^{4} b d^{3} x^{4} + a^{5} d^{3} x^{2}\right)} \left(-\frac{b^{3}}{a^{15} d^{10}}\right)^{\frac{1}{4}} \log\left(-77 \, a^{4} d^{3} \left(-\frac{b^{3}}{a^{15} d^{10}}\right)^{\frac{1}{4}} + 77 \, \sqrt{d x} b\right) + 4 \, {\left(77 \, b^{2} x^{4} + 121 \, a b x^{2} + 32 \, a^{2}\right)} \sqrt{d x}}{192 \, {\left(a^{3} b^{2} d^{3} x^{6} + 2 \, a^{4} b d^{3} x^{4} + a^{5} d^{3} x^{2}\right)}}"," ",0,"-1/192*(924*(a^3*b^2*d^3*x^6 + 2*a^4*b*d^3*x^4 + a^5*d^3*x^2)*(-b^3/(a^15*d^10))^(1/4)*arctan(-(sqrt(d*x)*a^11*b*d^7*(-b^3/(a^15*d^10))^(3/4) - sqrt(a^8*d^6*sqrt(-b^3/(a^15*d^10)) + b^2*d*x)*a^11*d^7*(-b^3/(a^15*d^10))^(3/4))/b^3) + 231*(a^3*b^2*d^3*x^6 + 2*a^4*b*d^3*x^4 + a^5*d^3*x^2)*(-b^3/(a^15*d^10))^(1/4)*log(77*a^4*d^3*(-b^3/(a^15*d^10))^(1/4) + 77*sqrt(d*x)*b) - 231*(a^3*b^2*d^3*x^6 + 2*a^4*b*d^3*x^4 + a^5*d^3*x^2)*(-b^3/(a^15*d^10))^(1/4)*log(-77*a^4*d^3*(-b^3/(a^15*d^10))^(1/4) + 77*sqrt(d*x)*b) + 4*(77*b^2*x^4 + 121*a*b*x^2 + 32*a^2)*sqrt(d*x))/(a^3*b^2*d^3*x^6 + 2*a^4*b*d^3*x^4 + a^5*d^3*x^2)","A",0
768,1,390,0,1.809527," ","integrate(1/(d*x)^(7/2)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""fricas"")","-\frac{2340 \, {\left(a^{4} b^{2} d^{4} x^{7} + 2 \, a^{5} b d^{4} x^{5} + a^{6} d^{4} x^{3}\right)} \left(-\frac{b^{5}}{a^{17} d^{14}}\right)^{\frac{1}{4}} \arctan\left(-\frac{1601613 \, \sqrt{d x} a^{4} b^{4} d^{3} \left(-\frac{b^{5}}{a^{17} d^{14}}\right)^{\frac{1}{4}} - \sqrt{-2565164201769 \, a^{9} b^{5} d^{8} \sqrt{-\frac{b^{5}}{a^{17} d^{14}}} + 2565164201769 \, b^{8} d x} a^{4} d^{3} \left(-\frac{b^{5}}{a^{17} d^{14}}\right)^{\frac{1}{4}}}{1601613 \, b^{5}}\right) - 585 \, {\left(a^{4} b^{2} d^{4} x^{7} + 2 \, a^{5} b d^{4} x^{5} + a^{6} d^{4} x^{3}\right)} \left(-\frac{b^{5}}{a^{17} d^{14}}\right)^{\frac{1}{4}} \log\left(1601613 \, a^{13} d^{11} \left(-\frac{b^{5}}{a^{17} d^{14}}\right)^{\frac{3}{4}} + 1601613 \, \sqrt{d x} b^{4}\right) + 585 \, {\left(a^{4} b^{2} d^{4} x^{7} + 2 \, a^{5} b d^{4} x^{5} + a^{6} d^{4} x^{3}\right)} \left(-\frac{b^{5}}{a^{17} d^{14}}\right)^{\frac{1}{4}} \log\left(-1601613 \, a^{13} d^{11} \left(-\frac{b^{5}}{a^{17} d^{14}}\right)^{\frac{3}{4}} + 1601613 \, \sqrt{d x} b^{4}\right) - 4 \, {\left(585 \, b^{3} x^{6} + 1053 \, a b^{2} x^{4} + 416 \, a^{2} b x^{2} - 32 \, a^{3}\right)} \sqrt{d x}}{320 \, {\left(a^{4} b^{2} d^{4} x^{7} + 2 \, a^{5} b d^{4} x^{5} + a^{6} d^{4} x^{3}\right)}}"," ",0,"-1/320*(2340*(a^4*b^2*d^4*x^7 + 2*a^5*b*d^4*x^5 + a^6*d^4*x^3)*(-b^5/(a^17*d^14))^(1/4)*arctan(-1/1601613*(1601613*sqrt(d*x)*a^4*b^4*d^3*(-b^5/(a^17*d^14))^(1/4) - sqrt(-2565164201769*a^9*b^5*d^8*sqrt(-b^5/(a^17*d^14)) + 2565164201769*b^8*d*x)*a^4*d^3*(-b^5/(a^17*d^14))^(1/4))/b^5) - 585*(a^4*b^2*d^4*x^7 + 2*a^5*b*d^4*x^5 + a^6*d^4*x^3)*(-b^5/(a^17*d^14))^(1/4)*log(1601613*a^13*d^11*(-b^5/(a^17*d^14))^(3/4) + 1601613*sqrt(d*x)*b^4) + 585*(a^4*b^2*d^4*x^7 + 2*a^5*b*d^4*x^5 + a^6*d^4*x^3)*(-b^5/(a^17*d^14))^(1/4)*log(-1601613*a^13*d^11*(-b^5/(a^17*d^14))^(3/4) + 1601613*sqrt(d*x)*b^4) - 4*(585*b^3*x^6 + 1053*a*b^2*x^4 + 416*a^2*b*x^2 - 32*a^3)*sqrt(d*x))/(a^4*b^2*d^4*x^7 + 2*a^5*b*d^4*x^5 + a^6*d^4*x^3)","A",0
769,1,457,0,0.951589," ","integrate((d*x)^(23/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""fricas"")","\frac{278460 \, \left(-\frac{a^{5} d^{46}}{b^{25}}\right)^{\frac{1}{4}} {\left(b^{10} x^{8} + 4 \, a b^{9} x^{6} + 6 \, a^{2} b^{8} x^{4} + 4 \, a^{3} b^{7} x^{2} + a^{4} b^{6}\right)} \arctan\left(-\frac{\left(-\frac{a^{5} d^{46}}{b^{25}}\right)^{\frac{3}{4}} \sqrt{d x} a b^{19} d^{11} - \left(-\frac{a^{5} d^{46}}{b^{25}}\right)^{\frac{3}{4}} \sqrt{a^{2} d^{23} x + \sqrt{-\frac{a^{5} d^{46}}{b^{25}}} b^{12}} b^{19}}{a^{5} d^{46}}\right) + 69615 \, \left(-\frac{a^{5} d^{46}}{b^{25}}\right)^{\frac{1}{4}} {\left(b^{10} x^{8} + 4 \, a b^{9} x^{6} + 6 \, a^{2} b^{8} x^{4} + 4 \, a^{3} b^{7} x^{2} + a^{4} b^{6}\right)} \log\left(13923 \, \sqrt{d x} a d^{11} + 13923 \, \left(-\frac{a^{5} d^{46}}{b^{25}}\right)^{\frac{1}{4}} b^{6}\right) - 69615 \, \left(-\frac{a^{5} d^{46}}{b^{25}}\right)^{\frac{1}{4}} {\left(b^{10} x^{8} + 4 \, a b^{9} x^{6} + 6 \, a^{2} b^{8} x^{4} + 4 \, a^{3} b^{7} x^{2} + a^{4} b^{6}\right)} \log\left(13923 \, \sqrt{d x} a d^{11} - 13923 \, \left(-\frac{a^{5} d^{46}}{b^{25}}\right)^{\frac{1}{4}} b^{6}\right) + 4 \, {\left(2048 \, b^{5} d^{11} x^{10} - 43008 \, a b^{4} d^{11} x^{8} - 220507 \, a^{2} b^{3} d^{11} x^{6} - 369733 \, a^{3} b^{2} d^{11} x^{4} - 264537 \, a^{4} b d^{11} x^{2} - 69615 \, a^{5} d^{11}\right)} \sqrt{d x}}{20480 \, {\left(b^{10} x^{8} + 4 \, a b^{9} x^{6} + 6 \, a^{2} b^{8} x^{4} + 4 \, a^{3} b^{7} x^{2} + a^{4} b^{6}\right)}}"," ",0,"1/20480*(278460*(-a^5*d^46/b^25)^(1/4)*(b^10*x^8 + 4*a*b^9*x^6 + 6*a^2*b^8*x^4 + 4*a^3*b^7*x^2 + a^4*b^6)*arctan(-((-a^5*d^46/b^25)^(3/4)*sqrt(d*x)*a*b^19*d^11 - (-a^5*d^46/b^25)^(3/4)*sqrt(a^2*d^23*x + sqrt(-a^5*d^46/b^25)*b^12)*b^19)/(a^5*d^46)) + 69615*(-a^5*d^46/b^25)^(1/4)*(b^10*x^8 + 4*a*b^9*x^6 + 6*a^2*b^8*x^4 + 4*a^3*b^7*x^2 + a^4*b^6)*log(13923*sqrt(d*x)*a*d^11 + 13923*(-a^5*d^46/b^25)^(1/4)*b^6) - 69615*(-a^5*d^46/b^25)^(1/4)*(b^10*x^8 + 4*a*b^9*x^6 + 6*a^2*b^8*x^4 + 4*a^3*b^7*x^2 + a^4*b^6)*log(13923*sqrt(d*x)*a*d^11 - 13923*(-a^5*d^46/b^25)^(1/4)*b^6) + 4*(2048*b^5*d^11*x^10 - 43008*a*b^4*d^11*x^8 - 220507*a^2*b^3*d^11*x^6 - 369733*a^3*b^2*d^11*x^4 - 264537*a^4*b*d^11*x^2 - 69615*a^5*d^11)*sqrt(d*x))/(b^10*x^8 + 4*a*b^9*x^6 + 6*a^2*b^8*x^4 + 4*a^3*b^7*x^2 + a^4*b^6)","A",0
770,1,457,0,1.827376," ","integrate((d*x)^(21/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""fricas"")","\frac{87780 \, \left(-\frac{a^{3} d^{42}}{b^{23}}\right)^{\frac{1}{4}} {\left(b^{9} x^{8} + 4 \, a b^{8} x^{6} + 6 \, a^{2} b^{7} x^{4} + 4 \, a^{3} b^{6} x^{2} + a^{4} b^{5}\right)} \arctan\left(-\frac{\left(-\frac{a^{3} d^{42}}{b^{23}}\right)^{\frac{1}{4}} \sqrt{d x} a^{2} b^{6} d^{31} - \sqrt{a^{4} d^{63} x - \sqrt{-\frac{a^{3} d^{42}}{b^{23}}} a^{3} b^{11} d^{42}} \left(-\frac{a^{3} d^{42}}{b^{23}}\right)^{\frac{1}{4}} b^{6}}{a^{3} d^{42}}\right) - 21945 \, \left(-\frac{a^{3} d^{42}}{b^{23}}\right)^{\frac{1}{4}} {\left(b^{9} x^{8} + 4 \, a b^{8} x^{6} + 6 \, a^{2} b^{7} x^{4} + 4 \, a^{3} b^{6} x^{2} + a^{4} b^{5}\right)} \log\left(391419980875 \, \sqrt{d x} a^{2} d^{31} + 391419980875 \, \left(-\frac{a^{3} d^{42}}{b^{23}}\right)^{\frac{3}{4}} b^{17}\right) + 21945 \, \left(-\frac{a^{3} d^{42}}{b^{23}}\right)^{\frac{1}{4}} {\left(b^{9} x^{8} + 4 \, a b^{8} x^{6} + 6 \, a^{2} b^{7} x^{4} + 4 \, a^{3} b^{6} x^{2} + a^{4} b^{5}\right)} \log\left(391419980875 \, \sqrt{d x} a^{2} d^{31} - 391419980875 \, \left(-\frac{a^{3} d^{42}}{b^{23}}\right)^{\frac{3}{4}} b^{17}\right) + 4 \, {\left(2048 \, b^{4} d^{10} x^{9} + 16967 \, a b^{3} d^{10} x^{7} + 33345 \, a^{2} b^{2} d^{10} x^{5} + 26125 \, a^{3} b d^{10} x^{3} + 7315 \, a^{4} d^{10} x\right)} \sqrt{d x}}{12288 \, {\left(b^{9} x^{8} + 4 \, a b^{8} x^{6} + 6 \, a^{2} b^{7} x^{4} + 4 \, a^{3} b^{6} x^{2} + a^{4} b^{5}\right)}}"," ",0,"1/12288*(87780*(-a^3*d^42/b^23)^(1/4)*(b^9*x^8 + 4*a*b^8*x^6 + 6*a^2*b^7*x^4 + 4*a^3*b^6*x^2 + a^4*b^5)*arctan(-((-a^3*d^42/b^23)^(1/4)*sqrt(d*x)*a^2*b^6*d^31 - sqrt(a^4*d^63*x - sqrt(-a^3*d^42/b^23)*a^3*b^11*d^42)*(-a^3*d^42/b^23)^(1/4)*b^6)/(a^3*d^42)) - 21945*(-a^3*d^42/b^23)^(1/4)*(b^9*x^8 + 4*a*b^8*x^6 + 6*a^2*b^7*x^4 + 4*a^3*b^6*x^2 + a^4*b^5)*log(391419980875*sqrt(d*x)*a^2*d^31 + 391419980875*(-a^3*d^42/b^23)^(3/4)*b^17) + 21945*(-a^3*d^42/b^23)^(1/4)*(b^9*x^8 + 4*a*b^8*x^6 + 6*a^2*b^7*x^4 + 4*a^3*b^6*x^2 + a^4*b^5)*log(391419980875*sqrt(d*x)*a^2*d^31 - 391419980875*(-a^3*d^42/b^23)^(3/4)*b^17) + 4*(2048*b^4*d^10*x^9 + 16967*a*b^3*d^10*x^7 + 33345*a^2*b^2*d^10*x^5 + 26125*a^3*b*d^10*x^3 + 7315*a^4*d^10*x)*sqrt(d*x))/(b^9*x^8 + 4*a*b^8*x^6 + 6*a^2*b^7*x^4 + 4*a^3*b^6*x^2 + a^4*b^5)","A",0
771,1,421,0,0.910858," ","integrate((d*x)^(19/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""fricas"")","-\frac{39780 \, \left(-\frac{a d^{38}}{b^{21}}\right)^{\frac{1}{4}} {\left(b^{9} x^{8} + 4 \, a b^{8} x^{6} + 6 \, a^{2} b^{7} x^{4} + 4 \, a^{3} b^{6} x^{2} + a^{4} b^{5}\right)} \arctan\left(-\frac{\left(-\frac{a d^{38}}{b^{21}}\right)^{\frac{3}{4}} \sqrt{d x} b^{16} d^{9} - \sqrt{d^{19} x + \sqrt{-\frac{a d^{38}}{b^{21}}} b^{10}} \left(-\frac{a d^{38}}{b^{21}}\right)^{\frac{3}{4}} b^{16}}{a d^{38}}\right) + 9945 \, \left(-\frac{a d^{38}}{b^{21}}\right)^{\frac{1}{4}} {\left(b^{9} x^{8} + 4 \, a b^{8} x^{6} + 6 \, a^{2} b^{7} x^{4} + 4 \, a^{3} b^{6} x^{2} + a^{4} b^{5}\right)} \log\left(3315 \, \sqrt{d x} d^{9} + 3315 \, \left(-\frac{a d^{38}}{b^{21}}\right)^{\frac{1}{4}} b^{5}\right) - 9945 \, \left(-\frac{a d^{38}}{b^{21}}\right)^{\frac{1}{4}} {\left(b^{9} x^{8} + 4 \, a b^{8} x^{6} + 6 \, a^{2} b^{7} x^{4} + 4 \, a^{3} b^{6} x^{2} + a^{4} b^{5}\right)} \log\left(3315 \, \sqrt{d x} d^{9} - 3315 \, \left(-\frac{a d^{38}}{b^{21}}\right)^{\frac{1}{4}} b^{5}\right) - 4 \, {\left(6144 \, b^{4} d^{9} x^{8} + 31501 \, a b^{3} d^{9} x^{6} + 52819 \, a^{2} b^{2} d^{9} x^{4} + 37791 \, a^{3} b d^{9} x^{2} + 9945 \, a^{4} d^{9}\right)} \sqrt{d x}}{12288 \, {\left(b^{9} x^{8} + 4 \, a b^{8} x^{6} + 6 \, a^{2} b^{7} x^{4} + 4 \, a^{3} b^{6} x^{2} + a^{4} b^{5}\right)}}"," ",0,"-1/12288*(39780*(-a*d^38/b^21)^(1/4)*(b^9*x^8 + 4*a*b^8*x^6 + 6*a^2*b^7*x^4 + 4*a^3*b^6*x^2 + a^4*b^5)*arctan(-((-a*d^38/b^21)^(3/4)*sqrt(d*x)*b^16*d^9 - sqrt(d^19*x + sqrt(-a*d^38/b^21)*b^10)*(-a*d^38/b^21)^(3/4)*b^16)/(a*d^38)) + 9945*(-a*d^38/b^21)^(1/4)*(b^9*x^8 + 4*a*b^8*x^6 + 6*a^2*b^7*x^4 + 4*a^3*b^6*x^2 + a^4*b^5)*log(3315*sqrt(d*x)*d^9 + 3315*(-a*d^38/b^21)^(1/4)*b^5) - 9945*(-a*d^38/b^21)^(1/4)*(b^9*x^8 + 4*a*b^8*x^6 + 6*a^2*b^7*x^4 + 4*a^3*b^6*x^2 + a^4*b^5)*log(3315*sqrt(d*x)*d^9 - 3315*(-a*d^38/b^21)^(1/4)*b^5) - 4*(6144*b^4*d^9*x^8 + 31501*a*b^3*d^9*x^6 + 52819*a^2*b^2*d^9*x^4 + 37791*a^3*b*d^9*x^2 + 9945*a^4*d^9)*sqrt(d*x))/(b^9*x^8 + 4*a*b^8*x^6 + 6*a^2*b^7*x^4 + 4*a^3*b^6*x^2 + a^4*b^5)","A",0
772,1,428,0,1.766448," ","integrate((d*x)^(17/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""fricas"")","-\frac{4620 \, {\left(b^{8} x^{8} + 4 \, a b^{7} x^{6} + 6 \, a^{2} b^{6} x^{4} + 4 \, a^{3} b^{5} x^{2} + a^{4} b^{4}\right)} \left(-\frac{d^{34}}{a b^{19}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\left(-\frac{d^{34}}{a b^{19}}\right)^{\frac{1}{4}} \sqrt{d x} b^{5} d^{25} - \sqrt{d^{51} x - \sqrt{-\frac{d^{34}}{a b^{19}}} a b^{9} d^{34}} \left(-\frac{d^{34}}{a b^{19}}\right)^{\frac{1}{4}} b^{5}}{d^{34}}\right) - 1155 \, {\left(b^{8} x^{8} + 4 \, a b^{7} x^{6} + 6 \, a^{2} b^{6} x^{4} + 4 \, a^{3} b^{5} x^{2} + a^{4} b^{4}\right)} \left(-\frac{d^{34}}{a b^{19}}\right)^{\frac{1}{4}} \log\left(1540798875 \, \sqrt{d x} d^{25} + 1540798875 \, \left(-\frac{d^{34}}{a b^{19}}\right)^{\frac{3}{4}} a b^{14}\right) + 1155 \, {\left(b^{8} x^{8} + 4 \, a b^{7} x^{6} + 6 \, a^{2} b^{6} x^{4} + 4 \, a^{3} b^{5} x^{2} + a^{4} b^{4}\right)} \left(-\frac{d^{34}}{a b^{19}}\right)^{\frac{1}{4}} \log\left(1540798875 \, \sqrt{d x} d^{25} - 1540798875 \, \left(-\frac{d^{34}}{a b^{19}}\right)^{\frac{3}{4}} a b^{14}\right) + 4 \, {\left(893 \, b^{3} d^{8} x^{7} + 1755 \, a b^{2} d^{8} x^{5} + 1375 \, a^{2} b d^{8} x^{3} + 385 \, a^{3} d^{8} x\right)} \sqrt{d x}}{4096 \, {\left(b^{8} x^{8} + 4 \, a b^{7} x^{6} + 6 \, a^{2} b^{6} x^{4} + 4 \, a^{3} b^{5} x^{2} + a^{4} b^{4}\right)}}"," ",0,"-1/4096*(4620*(b^8*x^8 + 4*a*b^7*x^6 + 6*a^2*b^6*x^4 + 4*a^3*b^5*x^2 + a^4*b^4)*(-d^34/(a*b^19))^(1/4)*arctan(-((-d^34/(a*b^19))^(1/4)*sqrt(d*x)*b^5*d^25 - sqrt(d^51*x - sqrt(-d^34/(a*b^19))*a*b^9*d^34)*(-d^34/(a*b^19))^(1/4)*b^5)/d^34) - 1155*(b^8*x^8 + 4*a*b^7*x^6 + 6*a^2*b^6*x^4 + 4*a^3*b^5*x^2 + a^4*b^4)*(-d^34/(a*b^19))^(1/4)*log(1540798875*sqrt(d*x)*d^25 + 1540798875*(-d^34/(a*b^19))^(3/4)*a*b^14) + 1155*(b^8*x^8 + 4*a*b^7*x^6 + 6*a^2*b^6*x^4 + 4*a^3*b^5*x^2 + a^4*b^4)*(-d^34/(a*b^19))^(1/4)*log(1540798875*sqrt(d*x)*d^25 - 1540798875*(-d^34/(a*b^19))^(3/4)*a*b^14) + 4*(893*b^3*d^8*x^7 + 1755*a*b^2*d^8*x^5 + 1375*a^2*b*d^8*x^3 + 385*a^3*d^8*x)*sqrt(d*x))/(b^8*x^8 + 4*a*b^7*x^6 + 6*a^2*b^6*x^4 + 4*a^3*b^5*x^2 + a^4*b^4)","A",0
773,1,431,0,1.197706," ","integrate((d*x)^(15/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""fricas"")","\frac{2340 \, {\left(b^{8} x^{8} + 4 \, a b^{7} x^{6} + 6 \, a^{2} b^{6} x^{4} + 4 \, a^{3} b^{5} x^{2} + a^{4} b^{4}\right)} \left(-\frac{d^{30}}{a^{3} b^{17}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\left(-\frac{d^{30}}{a^{3} b^{17}}\right)^{\frac{3}{4}} \sqrt{d x} a^{2} b^{13} d^{7} - \sqrt{d^{15} x + \sqrt{-\frac{d^{30}}{a^{3} b^{17}}} a^{2} b^{8}} \left(-\frac{d^{30}}{a^{3} b^{17}}\right)^{\frac{3}{4}} a^{2} b^{13}}{d^{30}}\right) + 585 \, {\left(b^{8} x^{8} + 4 \, a b^{7} x^{6} + 6 \, a^{2} b^{6} x^{4} + 4 \, a^{3} b^{5} x^{2} + a^{4} b^{4}\right)} \left(-\frac{d^{30}}{a^{3} b^{17}}\right)^{\frac{1}{4}} \log\left(195 \, \sqrt{d x} d^{7} + 195 \, \left(-\frac{d^{30}}{a^{3} b^{17}}\right)^{\frac{1}{4}} a b^{4}\right) - 585 \, {\left(b^{8} x^{8} + 4 \, a b^{7} x^{6} + 6 \, a^{2} b^{6} x^{4} + 4 \, a^{3} b^{5} x^{2} + a^{4} b^{4}\right)} \left(-\frac{d^{30}}{a^{3} b^{17}}\right)^{\frac{1}{4}} \log\left(195 \, \sqrt{d x} d^{7} - 195 \, \left(-\frac{d^{30}}{a^{3} b^{17}}\right)^{\frac{1}{4}} a b^{4}\right) - 4 \, {\left(1853 \, b^{3} d^{7} x^{6} + 3107 \, a b^{2} d^{7} x^{4} + 2223 \, a^{2} b d^{7} x^{2} + 585 \, a^{3} d^{7}\right)} \sqrt{d x}}{12288 \, {\left(b^{8} x^{8} + 4 \, a b^{7} x^{6} + 6 \, a^{2} b^{6} x^{4} + 4 \, a^{3} b^{5} x^{2} + a^{4} b^{4}\right)}}"," ",0,"1/12288*(2340*(b^8*x^8 + 4*a*b^7*x^6 + 6*a^2*b^6*x^4 + 4*a^3*b^5*x^2 + a^4*b^4)*(-d^30/(a^3*b^17))^(1/4)*arctan(-((-d^30/(a^3*b^17))^(3/4)*sqrt(d*x)*a^2*b^13*d^7 - sqrt(d^15*x + sqrt(-d^30/(a^3*b^17))*a^2*b^8)*(-d^30/(a^3*b^17))^(3/4)*a^2*b^13)/d^30) + 585*(b^8*x^8 + 4*a*b^7*x^6 + 6*a^2*b^6*x^4 + 4*a^3*b^5*x^2 + a^4*b^4)*(-d^30/(a^3*b^17))^(1/4)*log(195*sqrt(d*x)*d^7 + 195*(-d^30/(a^3*b^17))^(1/4)*a*b^4) - 585*(b^8*x^8 + 4*a*b^7*x^6 + 6*a^2*b^6*x^4 + 4*a^3*b^5*x^2 + a^4*b^4)*(-d^30/(a^3*b^17))^(1/4)*log(195*sqrt(d*x)*d^7 - 195*(-d^30/(a^3*b^17))^(1/4)*a*b^4) - 4*(1853*b^3*d^7*x^6 + 3107*a*b^2*d^7*x^4 + 2223*a^2*b*d^7*x^2 + 585*a^3*d^7)*sqrt(d*x))/(b^8*x^8 + 4*a*b^7*x^6 + 6*a^2*b^6*x^4 + 4*a^3*b^5*x^2 + a^4*b^4)","A",0
774,1,448,0,1.663809," ","integrate((d*x)^(13/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""fricas"")","-\frac{924 \, {\left(a b^{7} x^{8} + 4 \, a^{2} b^{6} x^{6} + 6 \, a^{3} b^{5} x^{4} + 4 \, a^{4} b^{4} x^{2} + a^{5} b^{3}\right)} \left(-\frac{d^{26}}{a^{5} b^{15}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\left(-\frac{d^{26}}{a^{5} b^{15}}\right)^{\frac{1}{4}} \sqrt{d x} a b^{4} d^{19} - \sqrt{d^{39} x - \sqrt{-\frac{d^{26}}{a^{5} b^{15}}} a^{3} b^{7} d^{26}} \left(-\frac{d^{26}}{a^{5} b^{15}}\right)^{\frac{1}{4}} a b^{4}}{d^{26}}\right) - 231 \, {\left(a b^{7} x^{8} + 4 \, a^{2} b^{6} x^{6} + 6 \, a^{3} b^{5} x^{4} + 4 \, a^{4} b^{4} x^{2} + a^{5} b^{3}\right)} \left(-\frac{d^{26}}{a^{5} b^{15}}\right)^{\frac{1}{4}} \log\left(456533 \, \sqrt{d x} d^{19} + 456533 \, \left(-\frac{d^{26}}{a^{5} b^{15}}\right)^{\frac{3}{4}} a^{4} b^{11}\right) + 231 \, {\left(a b^{7} x^{8} + 4 \, a^{2} b^{6} x^{6} + 6 \, a^{3} b^{5} x^{4} + 4 \, a^{4} b^{4} x^{2} + a^{5} b^{3}\right)} \left(-\frac{d^{26}}{a^{5} b^{15}}\right)^{\frac{1}{4}} \log\left(456533 \, \sqrt{d x} d^{19} - 456533 \, \left(-\frac{d^{26}}{a^{5} b^{15}}\right)^{\frac{3}{4}} a^{4} b^{11}\right) - 4 \, {\left(231 \, b^{3} d^{6} x^{7} - 351 \, a b^{2} d^{6} x^{5} - 275 \, a^{2} b d^{6} x^{3} - 77 \, a^{3} d^{6} x\right)} \sqrt{d x}}{12288 \, {\left(a b^{7} x^{8} + 4 \, a^{2} b^{6} x^{6} + 6 \, a^{3} b^{5} x^{4} + 4 \, a^{4} b^{4} x^{2} + a^{5} b^{3}\right)}}"," ",0,"-1/12288*(924*(a*b^7*x^8 + 4*a^2*b^6*x^6 + 6*a^3*b^5*x^4 + 4*a^4*b^4*x^2 + a^5*b^3)*(-d^26/(a^5*b^15))^(1/4)*arctan(-((-d^26/(a^5*b^15))^(1/4)*sqrt(d*x)*a*b^4*d^19 - sqrt(d^39*x - sqrt(-d^26/(a^5*b^15))*a^3*b^7*d^26)*(-d^26/(a^5*b^15))^(1/4)*a*b^4)/d^26) - 231*(a*b^7*x^8 + 4*a^2*b^6*x^6 + 6*a^3*b^5*x^4 + 4*a^4*b^4*x^2 + a^5*b^3)*(-d^26/(a^5*b^15))^(1/4)*log(456533*sqrt(d*x)*d^19 + 456533*(-d^26/(a^5*b^15))^(3/4)*a^4*b^11) + 231*(a*b^7*x^8 + 4*a^2*b^6*x^6 + 6*a^3*b^5*x^4 + 4*a^4*b^4*x^2 + a^5*b^3)*(-d^26/(a^5*b^15))^(1/4)*log(456533*sqrt(d*x)*d^19 - 456533*(-d^26/(a^5*b^15))^(3/4)*a^4*b^11) - 4*(231*b^3*d^6*x^7 - 351*a*b^2*d^6*x^5 - 275*a^2*b*d^6*x^3 - 77*a^3*d^6*x)*sqrt(d*x))/(a*b^7*x^8 + 4*a^2*b^6*x^6 + 6*a^3*b^5*x^4 + 4*a^4*b^4*x^2 + a^5*b^3)","A",0
775,1,447,0,1.197054," ","integrate((d*x)^(11/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""fricas"")","\frac{180 \, {\left(a b^{7} x^{8} + 4 \, a^{2} b^{6} x^{6} + 6 \, a^{3} b^{5} x^{4} + 4 \, a^{4} b^{4} x^{2} + a^{5} b^{3}\right)} \left(-\frac{d^{22}}{a^{7} b^{13}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\left(-\frac{d^{22}}{a^{7} b^{13}}\right)^{\frac{3}{4}} \sqrt{d x} a^{5} b^{10} d^{5} - \sqrt{d^{11} x + \sqrt{-\frac{d^{22}}{a^{7} b^{13}}} a^{4} b^{6}} \left(-\frac{d^{22}}{a^{7} b^{13}}\right)^{\frac{3}{4}} a^{5} b^{10}}{d^{22}}\right) + 45 \, {\left(a b^{7} x^{8} + 4 \, a^{2} b^{6} x^{6} + 6 \, a^{3} b^{5} x^{4} + 4 \, a^{4} b^{4} x^{2} + a^{5} b^{3}\right)} \left(-\frac{d^{22}}{a^{7} b^{13}}\right)^{\frac{1}{4}} \log\left(45 \, \sqrt{d x} d^{5} + 45 \, \left(-\frac{d^{22}}{a^{7} b^{13}}\right)^{\frac{1}{4}} a^{2} b^{3}\right) - 45 \, {\left(a b^{7} x^{8} + 4 \, a^{2} b^{6} x^{6} + 6 \, a^{3} b^{5} x^{4} + 4 \, a^{4} b^{4} x^{2} + a^{5} b^{3}\right)} \left(-\frac{d^{22}}{a^{7} b^{13}}\right)^{\frac{1}{4}} \log\left(45 \, \sqrt{d x} d^{5} - 45 \, \left(-\frac{d^{22}}{a^{7} b^{13}}\right)^{\frac{1}{4}} a^{2} b^{3}\right) + 4 \, {\left(15 \, b^{3} d^{5} x^{6} - 239 \, a b^{2} d^{5} x^{4} - 171 \, a^{2} b d^{5} x^{2} - 45 \, a^{3} d^{5}\right)} \sqrt{d x}}{4096 \, {\left(a b^{7} x^{8} + 4 \, a^{2} b^{6} x^{6} + 6 \, a^{3} b^{5} x^{4} + 4 \, a^{4} b^{4} x^{2} + a^{5} b^{3}\right)}}"," ",0,"1/4096*(180*(a*b^7*x^8 + 4*a^2*b^6*x^6 + 6*a^3*b^5*x^4 + 4*a^4*b^4*x^2 + a^5*b^3)*(-d^22/(a^7*b^13))^(1/4)*arctan(-((-d^22/(a^7*b^13))^(3/4)*sqrt(d*x)*a^5*b^10*d^5 - sqrt(d^11*x + sqrt(-d^22/(a^7*b^13))*a^4*b^6)*(-d^22/(a^7*b^13))^(3/4)*a^5*b^10)/d^22) + 45*(a*b^7*x^8 + 4*a^2*b^6*x^6 + 6*a^3*b^5*x^4 + 4*a^4*b^4*x^2 + a^5*b^3)*(-d^22/(a^7*b^13))^(1/4)*log(45*sqrt(d*x)*d^5 + 45*(-d^22/(a^7*b^13))^(1/4)*a^2*b^3) - 45*(a*b^7*x^8 + 4*a^2*b^6*x^6 + 6*a^3*b^5*x^4 + 4*a^4*b^4*x^2 + a^5*b^3)*(-d^22/(a^7*b^13))^(1/4)*log(45*sqrt(d*x)*d^5 - 45*(-d^22/(a^7*b^13))^(1/4)*a^2*b^3) + 4*(15*b^3*d^5*x^6 - 239*a*b^2*d^5*x^4 - 171*a^2*b*d^5*x^2 - 45*a^3*d^5)*sqrt(d*x))/(a*b^7*x^8 + 4*a^2*b^6*x^6 + 6*a^3*b^5*x^4 + 4*a^4*b^4*x^2 + a^5*b^3)","A",0
776,1,462,0,1.675611," ","integrate((d*x)^(9/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""fricas"")","-\frac{420 \, {\left(a^{2} b^{6} x^{8} + 4 \, a^{3} b^{5} x^{6} + 6 \, a^{4} b^{4} x^{4} + 4 \, a^{5} b^{3} x^{2} + a^{6} b^{2}\right)} \left(-\frac{d^{18}}{a^{9} b^{11}}\right)^{\frac{1}{4}} \arctan\left(-\frac{42875 \, \sqrt{d x} a^{2} b^{3} d^{13} \left(-\frac{d^{18}}{a^{9} b^{11}}\right)^{\frac{1}{4}} - \sqrt{-1838265625 \, a^{5} b^{5} d^{18} \sqrt{-\frac{d^{18}}{a^{9} b^{11}}} + 1838265625 \, d^{27} x} a^{2} b^{3} \left(-\frac{d^{18}}{a^{9} b^{11}}\right)^{\frac{1}{4}}}{42875 \, d^{18}}\right) - 105 \, {\left(a^{2} b^{6} x^{8} + 4 \, a^{3} b^{5} x^{6} + 6 \, a^{4} b^{4} x^{4} + 4 \, a^{5} b^{3} x^{2} + a^{6} b^{2}\right)} \left(-\frac{d^{18}}{a^{9} b^{11}}\right)^{\frac{1}{4}} \log\left(42875 \, a^{7} b^{8} \left(-\frac{d^{18}}{a^{9} b^{11}}\right)^{\frac{3}{4}} + 42875 \, \sqrt{d x} d^{13}\right) + 105 \, {\left(a^{2} b^{6} x^{8} + 4 \, a^{3} b^{5} x^{6} + 6 \, a^{4} b^{4} x^{4} + 4 \, a^{5} b^{3} x^{2} + a^{6} b^{2}\right)} \left(-\frac{d^{18}}{a^{9} b^{11}}\right)^{\frac{1}{4}} \log\left(-42875 \, a^{7} b^{8} \left(-\frac{d^{18}}{a^{9} b^{11}}\right)^{\frac{3}{4}} + 42875 \, \sqrt{d x} d^{13}\right) - 4 \, {\left(105 \, b^{3} d^{4} x^{7} + 399 \, a b^{2} d^{4} x^{5} - 125 \, a^{2} b d^{4} x^{3} - 35 \, a^{3} d^{4} x\right)} \sqrt{d x}}{12288 \, {\left(a^{2} b^{6} x^{8} + 4 \, a^{3} b^{5} x^{6} + 6 \, a^{4} b^{4} x^{4} + 4 \, a^{5} b^{3} x^{2} + a^{6} b^{2}\right)}}"," ",0,"-1/12288*(420*(a^2*b^6*x^8 + 4*a^3*b^5*x^6 + 6*a^4*b^4*x^4 + 4*a^5*b^3*x^2 + a^6*b^2)*(-d^18/(a^9*b^11))^(1/4)*arctan(-1/42875*(42875*sqrt(d*x)*a^2*b^3*d^13*(-d^18/(a^9*b^11))^(1/4) - sqrt(-1838265625*a^5*b^5*d^18*sqrt(-d^18/(a^9*b^11)) + 1838265625*d^27*x)*a^2*b^3*(-d^18/(a^9*b^11))^(1/4))/d^18) - 105*(a^2*b^6*x^8 + 4*a^3*b^5*x^6 + 6*a^4*b^4*x^4 + 4*a^5*b^3*x^2 + a^6*b^2)*(-d^18/(a^9*b^11))^(1/4)*log(42875*a^7*b^8*(-d^18/(a^9*b^11))^(3/4) + 42875*sqrt(d*x)*d^13) + 105*(a^2*b^6*x^8 + 4*a^3*b^5*x^6 + 6*a^4*b^4*x^4 + 4*a^5*b^3*x^2 + a^6*b^2)*(-d^18/(a^9*b^11))^(1/4)*log(-42875*a^7*b^8*(-d^18/(a^9*b^11))^(3/4) + 42875*sqrt(d*x)*d^13) - 4*(105*b^3*d^4*x^7 + 399*a*b^2*d^4*x^5 - 125*a^2*b*d^4*x^3 - 35*a^3*d^4*x)*sqrt(d*x))/(a^2*b^6*x^8 + 4*a^3*b^5*x^6 + 6*a^4*b^4*x^4 + 4*a^5*b^3*x^2 + a^6*b^2)","A",0
777,1,455,0,0.867990," ","integrate((d*x)^(7/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""fricas"")","\frac{420 \, {\left(a^{2} b^{6} x^{8} + 4 \, a^{3} b^{5} x^{6} + 6 \, a^{4} b^{4} x^{4} + 4 \, a^{5} b^{3} x^{2} + a^{6} b^{2}\right)} \left(-\frac{d^{14}}{a^{11} b^{9}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{d x} a^{8} b^{7} d^{3} \left(-\frac{d^{14}}{a^{11} b^{9}}\right)^{\frac{3}{4}} - \sqrt{a^{6} b^{4} \sqrt{-\frac{d^{14}}{a^{11} b^{9}}} + d^{7} x} a^{8} b^{7} \left(-\frac{d^{14}}{a^{11} b^{9}}\right)^{\frac{3}{4}}}{d^{14}}\right) + 105 \, {\left(a^{2} b^{6} x^{8} + 4 \, a^{3} b^{5} x^{6} + 6 \, a^{4} b^{4} x^{4} + 4 \, a^{5} b^{3} x^{2} + a^{6} b^{2}\right)} \left(-\frac{d^{14}}{a^{11} b^{9}}\right)^{\frac{1}{4}} \log\left(35 \, a^{3} b^{2} \left(-\frac{d^{14}}{a^{11} b^{9}}\right)^{\frac{1}{4}} + 35 \, \sqrt{d x} d^{3}\right) - 105 \, {\left(a^{2} b^{6} x^{8} + 4 \, a^{3} b^{5} x^{6} + 6 \, a^{4} b^{4} x^{4} + 4 \, a^{5} b^{3} x^{2} + a^{6} b^{2}\right)} \left(-\frac{d^{14}}{a^{11} b^{9}}\right)^{\frac{1}{4}} \log\left(-35 \, a^{3} b^{2} \left(-\frac{d^{14}}{a^{11} b^{9}}\right)^{\frac{1}{4}} + 35 \, \sqrt{d x} d^{3}\right) + 4 \, {\left(35 \, b^{3} d^{3} x^{6} + 125 \, a b^{2} d^{3} x^{4} - 399 \, a^{2} b d^{3} x^{2} - 105 \, a^{3} d^{3}\right)} \sqrt{d x}}{12288 \, {\left(a^{2} b^{6} x^{8} + 4 \, a^{3} b^{5} x^{6} + 6 \, a^{4} b^{4} x^{4} + 4 \, a^{5} b^{3} x^{2} + a^{6} b^{2}\right)}}"," ",0,"1/12288*(420*(a^2*b^6*x^8 + 4*a^3*b^5*x^6 + 6*a^4*b^4*x^4 + 4*a^5*b^3*x^2 + a^6*b^2)*(-d^14/(a^11*b^9))^(1/4)*arctan(-(sqrt(d*x)*a^8*b^7*d^3*(-d^14/(a^11*b^9))^(3/4) - sqrt(a^6*b^4*sqrt(-d^14/(a^11*b^9)) + d^7*x)*a^8*b^7*(-d^14/(a^11*b^9))^(3/4))/d^14) + 105*(a^2*b^6*x^8 + 4*a^3*b^5*x^6 + 6*a^4*b^4*x^4 + 4*a^5*b^3*x^2 + a^6*b^2)*(-d^14/(a^11*b^9))^(1/4)*log(35*a^3*b^2*(-d^14/(a^11*b^9))^(1/4) + 35*sqrt(d*x)*d^3) - 105*(a^2*b^6*x^8 + 4*a^3*b^5*x^6 + 6*a^4*b^4*x^4 + 4*a^5*b^3*x^2 + a^6*b^2)*(-d^14/(a^11*b^9))^(1/4)*log(-35*a^3*b^2*(-d^14/(a^11*b^9))^(1/4) + 35*sqrt(d*x)*d^3) + 4*(35*b^3*d^3*x^6 + 125*a*b^2*d^3*x^4 - 399*a^2*b*d^3*x^2 - 105*a^3*d^3)*sqrt(d*x))/(a^2*b^6*x^8 + 4*a^3*b^5*x^6 + 6*a^4*b^4*x^4 + 4*a^5*b^3*x^2 + a^6*b^2)","A",0
778,1,454,0,1.557133," ","integrate((d*x)^(5/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""fricas"")","-\frac{180 \, {\left(a^{3} b^{5} x^{8} + 4 \, a^{4} b^{4} x^{6} + 6 \, a^{5} b^{3} x^{4} + 4 \, a^{6} b^{2} x^{2} + a^{7} b\right)} \left(-\frac{d^{10}}{a^{13} b^{7}}\right)^{\frac{1}{4}} \arctan\left(-\frac{91125 \, \sqrt{d x} a^{3} b^{2} d^{7} \left(-\frac{d^{10}}{a^{13} b^{7}}\right)^{\frac{1}{4}} - \sqrt{-8303765625 \, a^{7} b^{3} d^{10} \sqrt{-\frac{d^{10}}{a^{13} b^{7}}} + 8303765625 \, d^{15} x} a^{3} b^{2} \left(-\frac{d^{10}}{a^{13} b^{7}}\right)^{\frac{1}{4}}}{91125 \, d^{10}}\right) - 45 \, {\left(a^{3} b^{5} x^{8} + 4 \, a^{4} b^{4} x^{6} + 6 \, a^{5} b^{3} x^{4} + 4 \, a^{6} b^{2} x^{2} + a^{7} b\right)} \left(-\frac{d^{10}}{a^{13} b^{7}}\right)^{\frac{1}{4}} \log\left(91125 \, a^{10} b^{5} \left(-\frac{d^{10}}{a^{13} b^{7}}\right)^{\frac{3}{4}} + 91125 \, \sqrt{d x} d^{7}\right) + 45 \, {\left(a^{3} b^{5} x^{8} + 4 \, a^{4} b^{4} x^{6} + 6 \, a^{5} b^{3} x^{4} + 4 \, a^{6} b^{2} x^{2} + a^{7} b\right)} \left(-\frac{d^{10}}{a^{13} b^{7}}\right)^{\frac{1}{4}} \log\left(-91125 \, a^{10} b^{5} \left(-\frac{d^{10}}{a^{13} b^{7}}\right)^{\frac{3}{4}} + 91125 \, \sqrt{d x} d^{7}\right) - 4 \, {\left(45 \, b^{3} d^{2} x^{7} + 171 \, a b^{2} d^{2} x^{5} + 239 \, a^{2} b d^{2} x^{3} - 15 \, a^{3} d^{2} x\right)} \sqrt{d x}}{4096 \, {\left(a^{3} b^{5} x^{8} + 4 \, a^{4} b^{4} x^{6} + 6 \, a^{5} b^{3} x^{4} + 4 \, a^{6} b^{2} x^{2} + a^{7} b\right)}}"," ",0,"-1/4096*(180*(a^3*b^5*x^8 + 4*a^4*b^4*x^6 + 6*a^5*b^3*x^4 + 4*a^6*b^2*x^2 + a^7*b)*(-d^10/(a^13*b^7))^(1/4)*arctan(-1/91125*(91125*sqrt(d*x)*a^3*b^2*d^7*(-d^10/(a^13*b^7))^(1/4) - sqrt(-8303765625*a^7*b^3*d^10*sqrt(-d^10/(a^13*b^7)) + 8303765625*d^15*x)*a^3*b^2*(-d^10/(a^13*b^7))^(1/4))/d^10) - 45*(a^3*b^5*x^8 + 4*a^4*b^4*x^6 + 6*a^5*b^3*x^4 + 4*a^6*b^2*x^2 + a^7*b)*(-d^10/(a^13*b^7))^(1/4)*log(91125*a^10*b^5*(-d^10/(a^13*b^7))^(3/4) + 91125*sqrt(d*x)*d^7) + 45*(a^3*b^5*x^8 + 4*a^4*b^4*x^6 + 6*a^5*b^3*x^4 + 4*a^6*b^2*x^2 + a^7*b)*(-d^10/(a^13*b^7))^(1/4)*log(-91125*a^10*b^5*(-d^10/(a^13*b^7))^(3/4) + 91125*sqrt(d*x)*d^7) - 4*(45*b^3*d^2*x^7 + 171*a*b^2*d^2*x^5 + 239*a^2*b*d^2*x^3 - 15*a^3*d^2*x)*sqrt(d*x))/(a^3*b^5*x^8 + 4*a^4*b^4*x^6 + 6*a^5*b^3*x^4 + 4*a^6*b^2*x^2 + a^7*b)","A",0
779,1,429,0,1.561436," ","integrate((d*x)^(3/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""fricas"")","\frac{924 \, {\left(a^{3} b^{5} x^{8} + 4 \, a^{4} b^{4} x^{6} + 6 \, a^{5} b^{3} x^{4} + 4 \, a^{6} b^{2} x^{2} + a^{7} b\right)} \left(-\frac{d^{6}}{a^{15} b^{5}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{d x} a^{11} b^{4} d \left(-\frac{d^{6}}{a^{15} b^{5}}\right)^{\frac{3}{4}} - \sqrt{a^{8} b^{2} \sqrt{-\frac{d^{6}}{a^{15} b^{5}}} + d^{3} x} a^{11} b^{4} \left(-\frac{d^{6}}{a^{15} b^{5}}\right)^{\frac{3}{4}}}{d^{6}}\right) + 231 \, {\left(a^{3} b^{5} x^{8} + 4 \, a^{4} b^{4} x^{6} + 6 \, a^{5} b^{3} x^{4} + 4 \, a^{6} b^{2} x^{2} + a^{7} b\right)} \left(-\frac{d^{6}}{a^{15} b^{5}}\right)^{\frac{1}{4}} \log\left(77 \, a^{4} b \left(-\frac{d^{6}}{a^{15} b^{5}}\right)^{\frac{1}{4}} + 77 \, \sqrt{d x} d\right) - 231 \, {\left(a^{3} b^{5} x^{8} + 4 \, a^{4} b^{4} x^{6} + 6 \, a^{5} b^{3} x^{4} + 4 \, a^{6} b^{2} x^{2} + a^{7} b\right)} \left(-\frac{d^{6}}{a^{15} b^{5}}\right)^{\frac{1}{4}} \log\left(-77 \, a^{4} b \left(-\frac{d^{6}}{a^{15} b^{5}}\right)^{\frac{1}{4}} + 77 \, \sqrt{d x} d\right) + 4 \, {\left(77 \, b^{3} d x^{6} + 275 \, a b^{2} d x^{4} + 351 \, a^{2} b d x^{2} - 231 \, a^{3} d\right)} \sqrt{d x}}{12288 \, {\left(a^{3} b^{5} x^{8} + 4 \, a^{4} b^{4} x^{6} + 6 \, a^{5} b^{3} x^{4} + 4 \, a^{6} b^{2} x^{2} + a^{7} b\right)}}"," ",0,"1/12288*(924*(a^3*b^5*x^8 + 4*a^4*b^4*x^6 + 6*a^5*b^3*x^4 + 4*a^6*b^2*x^2 + a^7*b)*(-d^6/(a^15*b^5))^(1/4)*arctan(-(sqrt(d*x)*a^11*b^4*d*(-d^6/(a^15*b^5))^(3/4) - sqrt(a^8*b^2*sqrt(-d^6/(a^15*b^5)) + d^3*x)*a^11*b^4*(-d^6/(a^15*b^5))^(3/4))/d^6) + 231*(a^3*b^5*x^8 + 4*a^4*b^4*x^6 + 6*a^5*b^3*x^4 + 4*a^6*b^2*x^2 + a^7*b)*(-d^6/(a^15*b^5))^(1/4)*log(77*a^4*b*(-d^6/(a^15*b^5))^(1/4) + 77*sqrt(d*x)*d) - 231*(a^3*b^5*x^8 + 4*a^4*b^4*x^6 + 6*a^5*b^3*x^4 + 4*a^6*b^2*x^2 + a^7*b)*(-d^6/(a^15*b^5))^(1/4)*log(-77*a^4*b*(-d^6/(a^15*b^5))^(1/4) + 77*sqrt(d*x)*d) + 4*(77*b^3*d*x^6 + 275*a*b^2*d*x^4 + 351*a^2*b*d*x^2 - 231*a^3*d)*sqrt(d*x))/(a^3*b^5*x^8 + 4*a^4*b^4*x^6 + 6*a^5*b^3*x^4 + 4*a^6*b^2*x^2 + a^7*b)","A",0
780,1,414,0,1.902316," ","integrate((d*x)^(1/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""fricas"")","-\frac{2340 \, {\left(a^{4} b^{4} x^{8} + 4 \, a^{5} b^{3} x^{6} + 6 \, a^{6} b^{2} x^{4} + 4 \, a^{7} b x^{2} + a^{8}\right)} \left(-\frac{d^{2}}{a^{17} b^{3}}\right)^{\frac{1}{4}} \arctan\left(-\frac{7414875 \, \sqrt{d x} a^{4} b d \left(-\frac{d^{2}}{a^{17} b^{3}}\right)^{\frac{1}{4}} - \sqrt{-54980371265625 \, a^{9} b d^{2} \sqrt{-\frac{d^{2}}{a^{17} b^{3}}} + 54980371265625 \, d^{3} x} a^{4} b \left(-\frac{d^{2}}{a^{17} b^{3}}\right)^{\frac{1}{4}}}{7414875 \, d^{2}}\right) - 585 \, {\left(a^{4} b^{4} x^{8} + 4 \, a^{5} b^{3} x^{6} + 6 \, a^{6} b^{2} x^{4} + 4 \, a^{7} b x^{2} + a^{8}\right)} \left(-\frac{d^{2}}{a^{17} b^{3}}\right)^{\frac{1}{4}} \log\left(7414875 \, a^{13} b^{2} \left(-\frac{d^{2}}{a^{17} b^{3}}\right)^{\frac{3}{4}} + 7414875 \, \sqrt{d x} d\right) + 585 \, {\left(a^{4} b^{4} x^{8} + 4 \, a^{5} b^{3} x^{6} + 6 \, a^{6} b^{2} x^{4} + 4 \, a^{7} b x^{2} + a^{8}\right)} \left(-\frac{d^{2}}{a^{17} b^{3}}\right)^{\frac{1}{4}} \log\left(-7414875 \, a^{13} b^{2} \left(-\frac{d^{2}}{a^{17} b^{3}}\right)^{\frac{3}{4}} + 7414875 \, \sqrt{d x} d\right) - 4 \, {\left(585 \, b^{3} x^{7} + 2223 \, a b^{2} x^{5} + 3107 \, a^{2} b x^{3} + 1853 \, a^{3} x\right)} \sqrt{d x}}{12288 \, {\left(a^{4} b^{4} x^{8} + 4 \, a^{5} b^{3} x^{6} + 6 \, a^{6} b^{2} x^{4} + 4 \, a^{7} b x^{2} + a^{8}\right)}}"," ",0,"-1/12288*(2340*(a^4*b^4*x^8 + 4*a^5*b^3*x^6 + 6*a^6*b^2*x^4 + 4*a^7*b*x^2 + a^8)*(-d^2/(a^17*b^3))^(1/4)*arctan(-1/7414875*(7414875*sqrt(d*x)*a^4*b*d*(-d^2/(a^17*b^3))^(1/4) - sqrt(-54980371265625*a^9*b*d^2*sqrt(-d^2/(a^17*b^3)) + 54980371265625*d^3*x)*a^4*b*(-d^2/(a^17*b^3))^(1/4))/d^2) - 585*(a^4*b^4*x^8 + 4*a^5*b^3*x^6 + 6*a^6*b^2*x^4 + 4*a^7*b*x^2 + a^8)*(-d^2/(a^17*b^3))^(1/4)*log(7414875*a^13*b^2*(-d^2/(a^17*b^3))^(3/4) + 7414875*sqrt(d*x)*d) + 585*(a^4*b^4*x^8 + 4*a^5*b^3*x^6 + 6*a^6*b^2*x^4 + 4*a^7*b*x^2 + a^8)*(-d^2/(a^17*b^3))^(1/4)*log(-7414875*a^13*b^2*(-d^2/(a^17*b^3))^(3/4) + 7414875*sqrt(d*x)*d) - 4*(585*b^3*x^7 + 2223*a*b^2*x^5 + 3107*a^2*b*x^3 + 1853*a^3*x)*sqrt(d*x))/(a^4*b^4*x^8 + 4*a^5*b^3*x^6 + 6*a^6*b^2*x^4 + 4*a^7*b*x^2 + a^8)","A",0
781,1,416,0,0.844243," ","integrate(1/(b^2*x^4+2*a*b*x^2+a^2)^(5/2)/(d*x)^(1/2),x, algorithm=""fricas"")","\frac{4620 \, {\left(a^{4} b^{4} d x^{8} + 4 \, a^{5} b^{3} d x^{6} + 6 \, a^{6} b^{2} d x^{4} + 4 \, a^{7} b d x^{2} + a^{8} d\right)} \left(-\frac{1}{a^{19} b d^{2}}\right)^{\frac{1}{4}} \arctan\left(\sqrt{a^{10} d^{2} \sqrt{-\frac{1}{a^{19} b d^{2}}} + d x} a^{14} b d \left(-\frac{1}{a^{19} b d^{2}}\right)^{\frac{3}{4}} - \sqrt{d x} a^{14} b d \left(-\frac{1}{a^{19} b d^{2}}\right)^{\frac{3}{4}}\right) + 1155 \, {\left(a^{4} b^{4} d x^{8} + 4 \, a^{5} b^{3} d x^{6} + 6 \, a^{6} b^{2} d x^{4} + 4 \, a^{7} b d x^{2} + a^{8} d\right)} \left(-\frac{1}{a^{19} b d^{2}}\right)^{\frac{1}{4}} \log\left(a^{5} d \left(-\frac{1}{a^{19} b d^{2}}\right)^{\frac{1}{4}} + \sqrt{d x}\right) - 1155 \, {\left(a^{4} b^{4} d x^{8} + 4 \, a^{5} b^{3} d x^{6} + 6 \, a^{6} b^{2} d x^{4} + 4 \, a^{7} b d x^{2} + a^{8} d\right)} \left(-\frac{1}{a^{19} b d^{2}}\right)^{\frac{1}{4}} \log\left(-a^{5} d \left(-\frac{1}{a^{19} b d^{2}}\right)^{\frac{1}{4}} + \sqrt{d x}\right) + 4 \, {\left(385 \, b^{3} x^{6} + 1375 \, a b^{2} x^{4} + 1755 \, a^{2} b x^{2} + 893 \, a^{3}\right)} \sqrt{d x}}{4096 \, {\left(a^{4} b^{4} d x^{8} + 4 \, a^{5} b^{3} d x^{6} + 6 \, a^{6} b^{2} d x^{4} + 4 \, a^{7} b d x^{2} + a^{8} d\right)}}"," ",0,"1/4096*(4620*(a^4*b^4*d*x^8 + 4*a^5*b^3*d*x^6 + 6*a^6*b^2*d*x^4 + 4*a^7*b*d*x^2 + a^8*d)*(-1/(a^19*b*d^2))^(1/4)*arctan(sqrt(a^10*d^2*sqrt(-1/(a^19*b*d^2)) + d*x)*a^14*b*d*(-1/(a^19*b*d^2))^(3/4) - sqrt(d*x)*a^14*b*d*(-1/(a^19*b*d^2))^(3/4)) + 1155*(a^4*b^4*d*x^8 + 4*a^5*b^3*d*x^6 + 6*a^6*b^2*d*x^4 + 4*a^7*b*d*x^2 + a^8*d)*(-1/(a^19*b*d^2))^(1/4)*log(a^5*d*(-1/(a^19*b*d^2))^(1/4) + sqrt(d*x)) - 1155*(a^4*b^4*d*x^8 + 4*a^5*b^3*d*x^6 + 6*a^6*b^2*d*x^4 + 4*a^7*b*d*x^2 + a^8*d)*(-1/(a^19*b*d^2))^(1/4)*log(-a^5*d*(-1/(a^19*b*d^2))^(1/4) + sqrt(d*x)) + 4*(385*b^3*x^6 + 1375*a*b^2*x^4 + 1755*a^2*b*x^2 + 893*a^3)*sqrt(d*x))/(a^4*b^4*d*x^8 + 4*a^5*b^3*d*x^6 + 6*a^6*b^2*d*x^4 + 4*a^7*b*d*x^2 + a^8*d)","A",0
782,1,477,0,0.966162," ","integrate(1/(d*x)^(3/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""fricas"")","\frac{39780 \, {\left(a^{5} b^{4} d^{2} x^{9} + 4 \, a^{6} b^{3} d^{2} x^{7} + 6 \, a^{7} b^{2} d^{2} x^{5} + 4 \, a^{8} b d^{2} x^{3} + a^{9} d^{2} x\right)} \left(-\frac{b}{a^{21} d^{6}}\right)^{\frac{1}{4}} \arctan\left(-\frac{36429280875 \, \sqrt{d x} a^{5} b d \left(-\frac{b}{a^{21} d^{6}}\right)^{\frac{1}{4}} - \sqrt{-1327092505069640765625 \, a^{11} b d^{4} \sqrt{-\frac{b}{a^{21} d^{6}}} + 1327092505069640765625 \, b^{2} d x} a^{5} d \left(-\frac{b}{a^{21} d^{6}}\right)^{\frac{1}{4}}}{36429280875 \, b}\right) - 9945 \, {\left(a^{5} b^{4} d^{2} x^{9} + 4 \, a^{6} b^{3} d^{2} x^{7} + 6 \, a^{7} b^{2} d^{2} x^{5} + 4 \, a^{8} b d^{2} x^{3} + a^{9} d^{2} x\right)} \left(-\frac{b}{a^{21} d^{6}}\right)^{\frac{1}{4}} \log\left(36429280875 \, a^{16} d^{5} \left(-\frac{b}{a^{21} d^{6}}\right)^{\frac{3}{4}} + 36429280875 \, \sqrt{d x} b\right) + 9945 \, {\left(a^{5} b^{4} d^{2} x^{9} + 4 \, a^{6} b^{3} d^{2} x^{7} + 6 \, a^{7} b^{2} d^{2} x^{5} + 4 \, a^{8} b d^{2} x^{3} + a^{9} d^{2} x\right)} \left(-\frac{b}{a^{21} d^{6}}\right)^{\frac{1}{4}} \log\left(-36429280875 \, a^{16} d^{5} \left(-\frac{b}{a^{21} d^{6}}\right)^{\frac{3}{4}} + 36429280875 \, \sqrt{d x} b\right) - 4 \, {\left(9945 \, b^{4} x^{8} + 37791 \, a b^{3} x^{6} + 52819 \, a^{2} b^{2} x^{4} + 31501 \, a^{3} b x^{2} + 6144 \, a^{4}\right)} \sqrt{d x}}{12288 \, {\left(a^{5} b^{4} d^{2} x^{9} + 4 \, a^{6} b^{3} d^{2} x^{7} + 6 \, a^{7} b^{2} d^{2} x^{5} + 4 \, a^{8} b d^{2} x^{3} + a^{9} d^{2} x\right)}}"," ",0,"1/12288*(39780*(a^5*b^4*d^2*x^9 + 4*a^6*b^3*d^2*x^7 + 6*a^7*b^2*d^2*x^5 + 4*a^8*b*d^2*x^3 + a^9*d^2*x)*(-b/(a^21*d^6))^(1/4)*arctan(-1/36429280875*(36429280875*sqrt(d*x)*a^5*b*d*(-b/(a^21*d^6))^(1/4) - sqrt(-1327092505069640765625*a^11*b*d^4*sqrt(-b/(a^21*d^6)) + 1327092505069640765625*b^2*d*x)*a^5*d*(-b/(a^21*d^6))^(1/4))/b) - 9945*(a^5*b^4*d^2*x^9 + 4*a^6*b^3*d^2*x^7 + 6*a^7*b^2*d^2*x^5 + 4*a^8*b*d^2*x^3 + a^9*d^2*x)*(-b/(a^21*d^6))^(1/4)*log(36429280875*a^16*d^5*(-b/(a^21*d^6))^(3/4) + 36429280875*sqrt(d*x)*b) + 9945*(a^5*b^4*d^2*x^9 + 4*a^6*b^3*d^2*x^7 + 6*a^7*b^2*d^2*x^5 + 4*a^8*b*d^2*x^3 + a^9*d^2*x)*(-b/(a^21*d^6))^(1/4)*log(-36429280875*a^16*d^5*(-b/(a^21*d^6))^(3/4) + 36429280875*sqrt(d*x)*b) - 4*(9945*b^4*x^8 + 37791*a*b^3*x^6 + 52819*a^2*b^2*x^4 + 31501*a^3*b*x^2 + 6144*a^4)*sqrt(d*x))/(a^5*b^4*d^2*x^9 + 4*a^6*b^3*d^2*x^7 + 6*a^7*b^2*d^2*x^5 + 4*a^8*b*d^2*x^3 + a^9*d^2*x)","A",0
783,1,501,0,1.104601," ","integrate(1/(d*x)^(5/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""fricas"")","-\frac{87780 \, {\left(a^{5} b^{4} d^{3} x^{10} + 4 \, a^{6} b^{3} d^{3} x^{8} + 6 \, a^{7} b^{2} d^{3} x^{6} + 4 \, a^{8} b d^{3} x^{4} + a^{9} d^{3} x^{2}\right)} \left(-\frac{b^{3}}{a^{23} d^{10}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{d x} a^{17} b d^{7} \left(-\frac{b^{3}}{a^{23} d^{10}}\right)^{\frac{3}{4}} - \sqrt{a^{12} d^{6} \sqrt{-\frac{b^{3}}{a^{23} d^{10}}} + b^{2} d x} a^{17} d^{7} \left(-\frac{b^{3}}{a^{23} d^{10}}\right)^{\frac{3}{4}}}{b^{3}}\right) + 21945 \, {\left(a^{5} b^{4} d^{3} x^{10} + 4 \, a^{6} b^{3} d^{3} x^{8} + 6 \, a^{7} b^{2} d^{3} x^{6} + 4 \, a^{8} b d^{3} x^{4} + a^{9} d^{3} x^{2}\right)} \left(-\frac{b^{3}}{a^{23} d^{10}}\right)^{\frac{1}{4}} \log\left(7315 \, a^{6} d^{3} \left(-\frac{b^{3}}{a^{23} d^{10}}\right)^{\frac{1}{4}} + 7315 \, \sqrt{d x} b\right) - 21945 \, {\left(a^{5} b^{4} d^{3} x^{10} + 4 \, a^{6} b^{3} d^{3} x^{8} + 6 \, a^{7} b^{2} d^{3} x^{6} + 4 \, a^{8} b d^{3} x^{4} + a^{9} d^{3} x^{2}\right)} \left(-\frac{b^{3}}{a^{23} d^{10}}\right)^{\frac{1}{4}} \log\left(-7315 \, a^{6} d^{3} \left(-\frac{b^{3}}{a^{23} d^{10}}\right)^{\frac{1}{4}} + 7315 \, \sqrt{d x} b\right) + 4 \, {\left(7315 \, b^{4} x^{8} + 26125 \, a b^{3} x^{6} + 33345 \, a^{2} b^{2} x^{4} + 16967 \, a^{3} b x^{2} + 2048 \, a^{4}\right)} \sqrt{d x}}{12288 \, {\left(a^{5} b^{4} d^{3} x^{10} + 4 \, a^{6} b^{3} d^{3} x^{8} + 6 \, a^{7} b^{2} d^{3} x^{6} + 4 \, a^{8} b d^{3} x^{4} + a^{9} d^{3} x^{2}\right)}}"," ",0,"-1/12288*(87780*(a^5*b^4*d^3*x^10 + 4*a^6*b^3*d^3*x^8 + 6*a^7*b^2*d^3*x^6 + 4*a^8*b*d^3*x^4 + a^9*d^3*x^2)*(-b^3/(a^23*d^10))^(1/4)*arctan(-(sqrt(d*x)*a^17*b*d^7*(-b^3/(a^23*d^10))^(3/4) - sqrt(a^12*d^6*sqrt(-b^3/(a^23*d^10)) + b^2*d*x)*a^17*d^7*(-b^3/(a^23*d^10))^(3/4))/b^3) + 21945*(a^5*b^4*d^3*x^10 + 4*a^6*b^3*d^3*x^8 + 6*a^7*b^2*d^3*x^6 + 4*a^8*b*d^3*x^4 + a^9*d^3*x^2)*(-b^3/(a^23*d^10))^(1/4)*log(7315*a^6*d^3*(-b^3/(a^23*d^10))^(1/4) + 7315*sqrt(d*x)*b) - 21945*(a^5*b^4*d^3*x^10 + 4*a^6*b^3*d^3*x^8 + 6*a^7*b^2*d^3*x^6 + 4*a^8*b*d^3*x^4 + a^9*d^3*x^2)*(-b^3/(a^23*d^10))^(1/4)*log(-7315*a^6*d^3*(-b^3/(a^23*d^10))^(1/4) + 7315*sqrt(d*x)*b) + 4*(7315*b^4*x^8 + 26125*a*b^3*x^6 + 33345*a^2*b^2*x^4 + 16967*a^3*b*x^2 + 2048*a^4)*sqrt(d*x))/(a^5*b^4*d^3*x^10 + 4*a^6*b^3*d^3*x^8 + 6*a^7*b^2*d^3*x^6 + 4*a^8*b*d^3*x^4 + a^9*d^3*x^2)","A",0
784,1,524,0,3.458530," ","integrate(1/(d*x)^(7/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""fricas"")","-\frac{278460 \, {\left(a^{6} b^{4} d^{4} x^{11} + 4 \, a^{7} b^{3} d^{4} x^{9} + 6 \, a^{8} b^{2} d^{4} x^{7} + 4 \, a^{9} b d^{4} x^{5} + a^{10} d^{4} x^{3}\right)} \left(-\frac{b^{5}}{a^{25} d^{14}}\right)^{\frac{1}{4}} \arctan\left(-\frac{2698972561467 \, \sqrt{d x} a^{6} b^{4} d^{3} \left(-\frac{b^{5}}{a^{25} d^{14}}\right)^{\frac{1}{4}} - \sqrt{-7284452887551739093192089 \, a^{13} b^{5} d^{8} \sqrt{-\frac{b^{5}}{a^{25} d^{14}}} + 7284452887551739093192089 \, b^{8} d x} a^{6} d^{3} \left(-\frac{b^{5}}{a^{25} d^{14}}\right)^{\frac{1}{4}}}{2698972561467 \, b^{5}}\right) - 69615 \, {\left(a^{6} b^{4} d^{4} x^{11} + 4 \, a^{7} b^{3} d^{4} x^{9} + 6 \, a^{8} b^{2} d^{4} x^{7} + 4 \, a^{9} b d^{4} x^{5} + a^{10} d^{4} x^{3}\right)} \left(-\frac{b^{5}}{a^{25} d^{14}}\right)^{\frac{1}{4}} \log\left(2698972561467 \, a^{19} d^{11} \left(-\frac{b^{5}}{a^{25} d^{14}}\right)^{\frac{3}{4}} + 2698972561467 \, \sqrt{d x} b^{4}\right) + 69615 \, {\left(a^{6} b^{4} d^{4} x^{11} + 4 \, a^{7} b^{3} d^{4} x^{9} + 6 \, a^{8} b^{2} d^{4} x^{7} + 4 \, a^{9} b d^{4} x^{5} + a^{10} d^{4} x^{3}\right)} \left(-\frac{b^{5}}{a^{25} d^{14}}\right)^{\frac{1}{4}} \log\left(-2698972561467 \, a^{19} d^{11} \left(-\frac{b^{5}}{a^{25} d^{14}}\right)^{\frac{3}{4}} + 2698972561467 \, \sqrt{d x} b^{4}\right) - 4 \, {\left(69615 \, b^{5} x^{10} + 264537 \, a b^{4} x^{8} + 369733 \, a^{2} b^{3} x^{6} + 220507 \, a^{3} b^{2} x^{4} + 43008 \, a^{4} b x^{2} - 2048 \, a^{5}\right)} \sqrt{d x}}{20480 \, {\left(a^{6} b^{4} d^{4} x^{11} + 4 \, a^{7} b^{3} d^{4} x^{9} + 6 \, a^{8} b^{2} d^{4} x^{7} + 4 \, a^{9} b d^{4} x^{5} + a^{10} d^{4} x^{3}\right)}}"," ",0,"-1/20480*(278460*(a^6*b^4*d^4*x^11 + 4*a^7*b^3*d^4*x^9 + 6*a^8*b^2*d^4*x^7 + 4*a^9*b*d^4*x^5 + a^10*d^4*x^3)*(-b^5/(a^25*d^14))^(1/4)*arctan(-1/2698972561467*(2698972561467*sqrt(d*x)*a^6*b^4*d^3*(-b^5/(a^25*d^14))^(1/4) - sqrt(-7284452887551739093192089*a^13*b^5*d^8*sqrt(-b^5/(a^25*d^14)) + 7284452887551739093192089*b^8*d*x)*a^6*d^3*(-b^5/(a^25*d^14))^(1/4))/b^5) - 69615*(a^6*b^4*d^4*x^11 + 4*a^7*b^3*d^4*x^9 + 6*a^8*b^2*d^4*x^7 + 4*a^9*b*d^4*x^5 + a^10*d^4*x^3)*(-b^5/(a^25*d^14))^(1/4)*log(2698972561467*a^19*d^11*(-b^5/(a^25*d^14))^(3/4) + 2698972561467*sqrt(d*x)*b^4) + 69615*(a^6*b^4*d^4*x^11 + 4*a^7*b^3*d^4*x^9 + 6*a^8*b^2*d^4*x^7 + 4*a^9*b*d^4*x^5 + a^10*d^4*x^3)*(-b^5/(a^25*d^14))^(1/4)*log(-2698972561467*a^19*d^11*(-b^5/(a^25*d^14))^(3/4) + 2698972561467*sqrt(d*x)*b^4) - 4*(69615*b^5*x^10 + 264537*a*b^4*x^8 + 369733*a^2*b^3*x^6 + 220507*a^3*b^2*x^4 + 43008*a^4*b*x^2 - 2048*a^5)*sqrt(d*x))/(a^6*b^4*d^4*x^11 + 4*a^7*b^3*d^4*x^9 + 6*a^8*b^2*d^4*x^7 + 4*a^9*b*d^4*x^5 + a^10*d^4*x^3)","A",0
785,1,507,0,1.988301," ","integrate((d*x)^m*(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","\frac{{\left({\left(b^{6} m^{6} + 36 \, b^{6} m^{5} + 505 \, b^{6} m^{4} + 3480 \, b^{6} m^{3} + 12139 \, b^{6} m^{2} + 19524 \, b^{6} m + 10395 \, b^{6}\right)} x^{13} + 6 \, {\left(a b^{5} m^{6} + 38 \, a b^{5} m^{5} + 555 \, a b^{5} m^{4} + 3940 \, a b^{5} m^{3} + 14039 \, a b^{5} m^{2} + 22902 \, a b^{5} m + 12285 \, a b^{5}\right)} x^{11} + 15 \, {\left(a^{2} b^{4} m^{6} + 40 \, a^{2} b^{4} m^{5} + 613 \, a^{2} b^{4} m^{4} + 4528 \, a^{2} b^{4} m^{3} + 16627 \, a^{2} b^{4} m^{2} + 27688 \, a^{2} b^{4} m + 15015 \, a^{2} b^{4}\right)} x^{9} + 20 \, {\left(a^{3} b^{3} m^{6} + 42 \, a^{3} b^{3} m^{5} + 679 \, a^{3} b^{3} m^{4} + 5292 \, a^{3} b^{3} m^{3} + 20335 \, a^{3} b^{3} m^{2} + 34986 \, a^{3} b^{3} m + 19305 \, a^{3} b^{3}\right)} x^{7} + 15 \, {\left(a^{4} b^{2} m^{6} + 44 \, a^{4} b^{2} m^{5} + 753 \, a^{4} b^{2} m^{4} + 6280 \, a^{4} b^{2} m^{3} + 25979 \, a^{4} b^{2} m^{2} + 47436 \, a^{4} b^{2} m + 27027 \, a^{4} b^{2}\right)} x^{5} + 6 \, {\left(a^{5} b m^{6} + 46 \, a^{5} b m^{5} + 835 \, a^{5} b m^{4} + 7540 \, a^{5} b m^{3} + 34759 \, a^{5} b m^{2} + 73054 \, a^{5} b m + 45045 \, a^{5} b\right)} x^{3} + {\left(a^{6} m^{6} + 48 \, a^{6} m^{5} + 925 \, a^{6} m^{4} + 9120 \, a^{6} m^{3} + 48259 \, a^{6} m^{2} + 129072 \, a^{6} m + 135135 \, a^{6}\right)} x\right)} \left(d x\right)^{m}}{m^{7} + 49 \, m^{6} + 973 \, m^{5} + 10045 \, m^{4} + 57379 \, m^{3} + 177331 \, m^{2} + 264207 \, m + 135135}"," ",0,"((b^6*m^6 + 36*b^6*m^5 + 505*b^6*m^4 + 3480*b^6*m^3 + 12139*b^6*m^2 + 19524*b^6*m + 10395*b^6)*x^13 + 6*(a*b^5*m^6 + 38*a*b^5*m^5 + 555*a*b^5*m^4 + 3940*a*b^5*m^3 + 14039*a*b^5*m^2 + 22902*a*b^5*m + 12285*a*b^5)*x^11 + 15*(a^2*b^4*m^6 + 40*a^2*b^4*m^5 + 613*a^2*b^4*m^4 + 4528*a^2*b^4*m^3 + 16627*a^2*b^4*m^2 + 27688*a^2*b^4*m + 15015*a^2*b^4)*x^9 + 20*(a^3*b^3*m^6 + 42*a^3*b^3*m^5 + 679*a^3*b^3*m^4 + 5292*a^3*b^3*m^3 + 20335*a^3*b^3*m^2 + 34986*a^3*b^3*m + 19305*a^3*b^3)*x^7 + 15*(a^4*b^2*m^6 + 44*a^4*b^2*m^5 + 753*a^4*b^2*m^4 + 6280*a^4*b^2*m^3 + 25979*a^4*b^2*m^2 + 47436*a^4*b^2*m + 27027*a^4*b^2)*x^5 + 6*(a^5*b*m^6 + 46*a^5*b*m^5 + 835*a^5*b*m^4 + 7540*a^5*b*m^3 + 34759*a^5*b*m^2 + 73054*a^5*b*m + 45045*a^5*b)*x^3 + (a^6*m^6 + 48*a^6*m^5 + 925*a^6*m^4 + 9120*a^6*m^3 + 48259*a^6*m^2 + 129072*a^6*m + 135135*a^6)*x)*(d*x)^m/(m^7 + 49*m^6 + 973*m^5 + 10045*m^4 + 57379*m^3 + 177331*m^2 + 264207*m + 135135)","B",0
786,1,253,0,0.984694," ","integrate((d*x)^m*(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""fricas"")","\frac{{\left({\left(b^{4} m^{4} + 16 \, b^{4} m^{3} + 86 \, b^{4} m^{2} + 176 \, b^{4} m + 105 \, b^{4}\right)} x^{9} + 4 \, {\left(a b^{3} m^{4} + 18 \, a b^{3} m^{3} + 104 \, a b^{3} m^{2} + 222 \, a b^{3} m + 135 \, a b^{3}\right)} x^{7} + 6 \, {\left(a^{2} b^{2} m^{4} + 20 \, a^{2} b^{2} m^{3} + 130 \, a^{2} b^{2} m^{2} + 300 \, a^{2} b^{2} m + 189 \, a^{2} b^{2}\right)} x^{5} + 4 \, {\left(a^{3} b m^{4} + 22 \, a^{3} b m^{3} + 164 \, a^{3} b m^{2} + 458 \, a^{3} b m + 315 \, a^{3} b\right)} x^{3} + {\left(a^{4} m^{4} + 24 \, a^{4} m^{3} + 206 \, a^{4} m^{2} + 744 \, a^{4} m + 945 \, a^{4}\right)} x\right)} \left(d x\right)^{m}}{m^{5} + 25 \, m^{4} + 230 \, m^{3} + 950 \, m^{2} + 1689 \, m + 945}"," ",0,"((b^4*m^4 + 16*b^4*m^3 + 86*b^4*m^2 + 176*b^4*m + 105*b^4)*x^9 + 4*(a*b^3*m^4 + 18*a*b^3*m^3 + 104*a*b^3*m^2 + 222*a*b^3*m + 135*a*b^3)*x^7 + 6*(a^2*b^2*m^4 + 20*a^2*b^2*m^3 + 130*a^2*b^2*m^2 + 300*a^2*b^2*m + 189*a^2*b^2)*x^5 + 4*(a^3*b*m^4 + 22*a^3*b*m^3 + 164*a^3*b*m^2 + 458*a^3*b*m + 315*a^3*b)*x^3 + (a^4*m^4 + 24*a^4*m^3 + 206*a^4*m^2 + 744*a^4*m + 945*a^4)*x)*(d*x)^m/(m^5 + 25*m^4 + 230*m^3 + 950*m^2 + 1689*m + 945)","B",0
787,1,87,0,1.305398," ","integrate((d*x)^m*(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""fricas"")","\frac{{\left({\left(b^{2} m^{2} + 4 \, b^{2} m + 3 \, b^{2}\right)} x^{5} + 2 \, {\left(a b m^{2} + 6 \, a b m + 5 \, a b\right)} x^{3} + {\left(a^{2} m^{2} + 8 \, a^{2} m + 15 \, a^{2}\right)} x\right)} \left(d x\right)^{m}}{m^{3} + 9 \, m^{2} + 23 \, m + 15}"," ",0,"((b^2*m^2 + 4*b^2*m + 3*b^2)*x^5 + 2*(a*b*m^2 + 6*a*b*m + 5*a*b)*x^3 + (a^2*m^2 + 8*a^2*m + 15*a^2)*x)*(d*x)^m/(m^3 + 9*m^2 + 23*m + 15)","A",0
788,0,0,0,1.414478," ","integrate((d*x)^m/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d x\right)^{m}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}, x\right)"," ",0,"integral((d*x)^m/(b^2*x^4 + 2*a*b*x^2 + a^2), x)","F",0
789,0,0,0,2.309853," ","integrate((d*x)^m/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d x\right)^{m}}{b^{4} x^{8} + 4 \, a b^{3} x^{6} + 6 \, a^{2} b^{2} x^{4} + 4 \, a^{3} b x^{2} + a^{4}}, x\right)"," ",0,"integral((d*x)^m/(b^4*x^8 + 4*a*b^3*x^6 + 6*a^2*b^2*x^4 + 4*a^3*b*x^2 + a^4), x)","F",0
790,0,0,0,1.735495," ","integrate((d*x)^m/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d x\right)^{m}}{b^{6} x^{12} + 6 \, a b^{5} x^{10} + 15 \, a^{2} b^{4} x^{8} + 20 \, a^{3} b^{3} x^{6} + 15 \, a^{4} b^{2} x^{4} + 6 \, a^{5} b x^{2} + a^{6}}, x\right)"," ",0,"integral((d*x)^m/(b^6*x^12 + 6*a*b^5*x^10 + 15*a^2*b^4*x^8 + 20*a^3*b^3*x^6 + 15*a^4*b^2*x^4 + 6*a^5*b*x^2 + a^6), x)","F",0
791,1,369,0,1.714686," ","integrate((d*x)^m*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""fricas"")","\frac{{\left({\left(b^{5} m^{5} + 25 \, b^{5} m^{4} + 230 \, b^{5} m^{3} + 950 \, b^{5} m^{2} + 1689 \, b^{5} m + 945 \, b^{5}\right)} x^{11} + 5 \, {\left(a b^{4} m^{5} + 27 \, a b^{4} m^{4} + 262 \, a b^{4} m^{3} + 1122 \, a b^{4} m^{2} + 2041 \, a b^{4} m + 1155 \, a b^{4}\right)} x^{9} + 10 \, {\left(a^{2} b^{3} m^{5} + 29 \, a^{2} b^{3} m^{4} + 302 \, a^{2} b^{3} m^{3} + 1366 \, a^{2} b^{3} m^{2} + 2577 \, a^{2} b^{3} m + 1485 \, a^{2} b^{3}\right)} x^{7} + 10 \, {\left(a^{3} b^{2} m^{5} + 31 \, a^{3} b^{2} m^{4} + 350 \, a^{3} b^{2} m^{3} + 1730 \, a^{3} b^{2} m^{2} + 3489 \, a^{3} b^{2} m + 2079 \, a^{3} b^{2}\right)} x^{5} + 5 \, {\left(a^{4} b m^{5} + 33 \, a^{4} b m^{4} + 406 \, a^{4} b m^{3} + 2262 \, a^{4} b m^{2} + 5353 \, a^{4} b m + 3465 \, a^{4} b\right)} x^{3} + {\left(a^{5} m^{5} + 35 \, a^{5} m^{4} + 470 \, a^{5} m^{3} + 3010 \, a^{5} m^{2} + 9129 \, a^{5} m + 10395 \, a^{5}\right)} x\right)} \left(d x\right)^{m}}{m^{6} + 36 \, m^{5} + 505 \, m^{4} + 3480 \, m^{3} + 12139 \, m^{2} + 19524 \, m + 10395}"," ",0,"((b^5*m^5 + 25*b^5*m^4 + 230*b^5*m^3 + 950*b^5*m^2 + 1689*b^5*m + 945*b^5)*x^11 + 5*(a*b^4*m^5 + 27*a*b^4*m^4 + 262*a*b^4*m^3 + 1122*a*b^4*m^2 + 2041*a*b^4*m + 1155*a*b^4)*x^9 + 10*(a^2*b^3*m^5 + 29*a^2*b^3*m^4 + 302*a^2*b^3*m^3 + 1366*a^2*b^3*m^2 + 2577*a^2*b^3*m + 1485*a^2*b^3)*x^7 + 10*(a^3*b^2*m^5 + 31*a^3*b^2*m^4 + 350*a^3*b^2*m^3 + 1730*a^3*b^2*m^2 + 3489*a^3*b^2*m + 2079*a^3*b^2)*x^5 + 5*(a^4*b*m^5 + 33*a^4*b*m^4 + 406*a^4*b*m^3 + 2262*a^4*b*m^2 + 5353*a^4*b*m + 3465*a^4*b)*x^3 + (a^5*m^5 + 35*a^5*m^4 + 470*a^5*m^3 + 3010*a^5*m^2 + 9129*a^5*m + 10395*a^5)*x)*(d*x)^m/(m^6 + 36*m^5 + 505*m^4 + 3480*m^3 + 12139*m^2 + 19524*m + 10395)","A",0
792,1,159,0,0.994727," ","integrate((d*x)^m*(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left({\left(b^{3} m^{3} + 9 \, b^{3} m^{2} + 23 \, b^{3} m + 15 \, b^{3}\right)} x^{7} + 3 \, {\left(a b^{2} m^{3} + 11 \, a b^{2} m^{2} + 31 \, a b^{2} m + 21 \, a b^{2}\right)} x^{5} + 3 \, {\left(a^{2} b m^{3} + 13 \, a^{2} b m^{2} + 47 \, a^{2} b m + 35 \, a^{2} b\right)} x^{3} + {\left(a^{3} m^{3} + 15 \, a^{3} m^{2} + 71 \, a^{3} m + 105 \, a^{3}\right)} x\right)} \left(d x\right)^{m}}{m^{4} + 16 \, m^{3} + 86 \, m^{2} + 176 \, m + 105}"," ",0,"((b^3*m^3 + 9*b^3*m^2 + 23*b^3*m + 15*b^3)*x^7 + 3*(a*b^2*m^3 + 11*a*b^2*m^2 + 31*a*b^2*m + 21*a*b^2)*x^5 + 3*(a^2*b*m^3 + 13*a^2*b*m^2 + 47*a^2*b*m + 35*a^2*b)*x^3 + (a^3*m^3 + 15*a^3*m^2 + 71*a^3*m + 105*a^3)*x)*(d*x)^m/(m^4 + 16*m^3 + 86*m^2 + 176*m + 105)","A",0
793,1,35,0,2.025743," ","integrate((d*x)^m*(b^2*x^4+2*a*b*x^2+a^2)^(1/2),x, algorithm=""fricas"")","\frac{{\left({\left(b m + b\right)} x^{3} + {\left(a m + 3 \, a\right)} x\right)} \left(d x\right)^{m}}{m^{2} + 4 \, m + 3}"," ",0,"((b*m + b)*x^3 + (a*m + 3*a)*x)*(d*x)^m/(m^2 + 4*m + 3)","A",0
794,0,0,0,0.866316," ","integrate((d*x)^m/(b^2*x^4+2*a*b*x^2+a^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d x\right)^{m}}{\sqrt{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}}, x\right)"," ",0,"integral((d*x)^m/sqrt(b^2*x^4 + 2*a*b*x^2 + a^2), x)","F",0
795,0,0,0,1.000299," ","integrate((d*x)^m/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}} \left(d x\right)^{m}}{b^{4} x^{8} + 4 \, a b^{3} x^{6} + 6 \, a^{2} b^{2} x^{4} + 4 \, a^{3} b x^{2} + a^{4}}, x\right)"," ",0,"integral(sqrt(b^2*x^4 + 2*a*b*x^2 + a^2)*(d*x)^m/(b^4*x^8 + 4*a*b^3*x^6 + 6*a^2*b^2*x^4 + 4*a^3*b*x^2 + a^4), x)","F",0
796,0,0,0,1.044531," ","integrate((d*x)^m/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}} \left(d x\right)^{m}}{b^{6} x^{12} + 6 \, a b^{5} x^{10} + 15 \, a^{2} b^{4} x^{8} + 20 \, a^{3} b^{3} x^{6} + 15 \, a^{4} b^{2} x^{4} + 6 \, a^{5} b x^{2} + a^{6}}, x\right)"," ",0,"integral(sqrt(b^2*x^4 + 2*a*b*x^2 + a^2)*(d*x)^m/(b^6*x^12 + 6*a*b^5*x^10 + 15*a^2*b^4*x^8 + 20*a^3*b^3*x^6 + 15*a^4*b^2*x^4 + 6*a^5*b*x^2 + a^6), x)","F",0
797,0,0,0,1.049844," ","integrate((d*x)^m*(b^2*x^4+2*a*b*x^2+a^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p} \left(d x\right)^{m}, x\right)"," ",0,"integral((b^2*x^4 + 2*a*b*x^2 + a^2)^p*(d*x)^m, x)","F",0
798,1,163,0,1.034538," ","integrate(x^7*(b^2*x^4+2*a*b*x^2+a^2)^p,x, algorithm=""fricas"")","\frac{{\left({\left(4 \, b^{4} p^{3} + 12 \, b^{4} p^{2} + 11 \, b^{4} p + 3 \, b^{4}\right)} x^{8} + 6 \, a^{3} b p x^{2} + 2 \, {\left(2 \, a b^{3} p^{3} + 3 \, a b^{3} p^{2} + a b^{3} p\right)} x^{6} - 3 \, {\left(2 \, a^{2} b^{2} p^{2} + a^{2} b^{2} p\right)} x^{4} - 3 \, a^{4}\right)} {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p}}{4 \, {\left(4 \, b^{4} p^{4} + 20 \, b^{4} p^{3} + 35 \, b^{4} p^{2} + 25 \, b^{4} p + 6 \, b^{4}\right)}}"," ",0,"1/4*((4*b^4*p^3 + 12*b^4*p^2 + 11*b^4*p + 3*b^4)*x^8 + 6*a^3*b*p*x^2 + 2*(2*a*b^3*p^3 + 3*a*b^3*p^2 + a*b^3*p)*x^6 - 3*(2*a^2*b^2*p^2 + a^2*b^2*p)*x^4 - 3*a^4)*(b^2*x^4 + 2*a*b*x^2 + a^2)^p/(4*b^4*p^4 + 20*b^4*p^3 + 35*b^4*p^2 + 25*b^4*p + 6*b^4)","A",0
799,1,108,0,1.742367," ","integrate(x^5*(b^2*x^4+2*a*b*x^2+a^2)^p,x, algorithm=""fricas"")","\frac{{\left({\left(2 \, b^{3} p^{2} + 3 \, b^{3} p + b^{3}\right)} x^{6} - 2 \, a^{2} b p x^{2} + {\left(2 \, a b^{2} p^{2} + a b^{2} p\right)} x^{4} + a^{3}\right)} {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p}}{2 \, {\left(4 \, b^{3} p^{3} + 12 \, b^{3} p^{2} + 11 \, b^{3} p + 3 \, b^{3}\right)}}"," ",0,"1/2*((2*b^3*p^2 + 3*b^3*p + b^3)*x^6 - 2*a^2*b*p*x^2 + (2*a*b^2*p^2 + a*b^2*p)*x^4 + a^3)*(b^2*x^4 + 2*a*b*x^2 + a^2)^p/(4*b^3*p^3 + 12*b^3*p^2 + 11*b^3*p + 3*b^3)","A",0
800,1,70,0,4.013307," ","integrate(x^3*(b^2*x^4+2*a*b*x^2+a^2)^p,x, algorithm=""fricas"")","\frac{{\left(2 \, a b p x^{2} + {\left(2 \, b^{2} p + b^{2}\right)} x^{4} - a^{2}\right)} {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p}}{4 \, {\left(2 \, b^{2} p^{2} + 3 \, b^{2} p + b^{2}\right)}}"," ",0,"1/4*(2*a*b*p*x^2 + (2*b^2*p + b^2)*x^4 - a^2)*(b^2*x^4 + 2*a*b*x^2 + a^2)^p/(2*b^2*p^2 + 3*b^2*p + b^2)","A",0
801,1,37,0,0.882430," ","integrate(x*(b^2*x^4+2*a*b*x^2+a^2)^p,x, algorithm=""fricas"")","\frac{{\left(b x^{2} + a\right)} {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p}}{2 \, {\left(2 \, b p + b\right)}}"," ",0,"1/2*(b*x^2 + a)*(b^2*x^4 + 2*a*b*x^2 + a^2)^p/(2*b*p + b)","A",0
802,0,0,0,1.018921," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^p/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p}}{x}, x\right)"," ",0,"integral((b^2*x^4 + 2*a*b*x^2 + a^2)^p/x, x)","F",0
803,0,0,0,0.623655," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^p/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p}}{x^{3}}, x\right)"," ",0,"integral((b^2*x^4 + 2*a*b*x^2 + a^2)^p/x^3, x)","F",0
804,0,0,0,0.669827," ","integrate(x^4*(b^2*x^4+2*a*b*x^2+a^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p} x^{4}, x\right)"," ",0,"integral((b^2*x^4 + 2*a*b*x^2 + a^2)^p*x^4, x)","F",0
805,0,0,0,0.935107," ","integrate(x^2*(b^2*x^4+2*a*b*x^2+a^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p} x^{2}, x\right)"," ",0,"integral((b^2*x^4 + 2*a*b*x^2 + a^2)^p*x^2, x)","F",0
806,0,0,0,0.778884," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p}, x\right)"," ",0,"integral((b^2*x^4 + 2*a*b*x^2 + a^2)^p, x)","F",0
807,0,0,0,1.249868," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^p/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p}}{x^{2}}, x\right)"," ",0,"integral((b^2*x^4 + 2*a*b*x^2 + a^2)^p/x^2, x)","F",0
808,0,0,0,0.902311," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^p/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p}}{x^{4}}, x\right)"," ",0,"integral((b^2*x^4 + 2*a*b*x^2 + a^2)^p/x^4, x)","F",0
809,0,0,0,0.985950," ","integrate((d*x)^(3/2)*(b^2*x^4+2*a*b*x^2+a^2)^p,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{d x} {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p} d x, x\right)"," ",0,"integral(sqrt(d*x)*(b^2*x^4 + 2*a*b*x^2 + a^2)^p*d*x, x)","F",0
810,0,0,0,0.651160," ","integrate((d*x)^(1/2)*(b^2*x^4+2*a*b*x^2+a^2)^p,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{d x} {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p}, x\right)"," ",0,"integral(sqrt(d*x)*(b^2*x^4 + 2*a*b*x^2 + a^2)^p, x)","F",0
811,0,0,0,1.023566," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^p/(d*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x} {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p}}{d x}, x\right)"," ",0,"integral(sqrt(d*x)*(b^2*x^4 + 2*a*b*x^2 + a^2)^p/(d*x), x)","F",0
812,0,0,0,1.777426," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^p/(d*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x} {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p}}{d^{2} x^{2}}, x\right)"," ",0,"integral(sqrt(d*x)*(b^2*x^4 + 2*a*b*x^2 + a^2)^p/(d^2*x^2), x)","F",0
813,0,0,0,1.207154," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^p/(d*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x} {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p}}{d^{3} x^{3}}, x\right)"," ",0,"integral(sqrt(d*x)*(b^2*x^4 + 2*a*b*x^2 + a^2)^p/(d^3*x^3), x)","F",0
814,1,19,0,1.048418," ","integrate(x^2*(c*x^4+b*x^2+a),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
815,1,19,0,1.049742," ","integrate(x*(c*x^4+b*x^2+a),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
816,1,16,0,2.470361," ","integrate(c*x^4+b*x^2+a,x, algorithm=""fricas"")","\frac{1}{5} x^{5} c + \frac{1}{3} x^{3} b + x a"," ",0,"1/5*x^5*c + 1/3*x^3*b + x*a","A",0
817,1,17,0,2.107374," ","integrate((c*x^4+b*x^2+a)/x,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
818,1,20,0,2.461343," ","integrate((c*x^4+b*x^2+a)/x^2,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
819,1,22,0,1.021379," ","integrate((c*x^4+b*x^2+a)/x^3,x, algorithm=""fricas"")","\frac{c x^{4} + 2 \, b x^{2} \log\left(x\right) - a}{2 \, x^{2}}"," ",0,"1/2*(c*x^4 + 2*b*x^2*log(x) - a)/x^2","A",0
820,1,21,0,1.065409," ","integrate((c*x^4+b*x^2+a)/x^4,x, algorithm=""fricas"")","\frac{3 \, c x^{4} - 3 \, b x^{2} - a}{3 \, x^{3}}"," ",0,"1/3*(3*c*x^4 - 3*b*x^2 - a)/x^3","A",0
821,1,23,0,0.809926," ","integrate((c*x^4+b*x^2+a)/x^5,x, algorithm=""fricas"")","\frac{4 \, c x^{4} \log\left(x\right) - 2 \, b x^{2} - a}{4 \, x^{4}}"," ",0,"1/4*(4*c*x^4*log(x) - 2*b*x^2 - a)/x^4","A",0
822,1,21,0,1.923231," ","integrate((c*x^4+b*x^2+a)/x^6,x, algorithm=""fricas"")","-\frac{15 \, c x^{4} + 5 \, b x^{2} + 3 \, a}{15 \, x^{5}}"," ",0,"-1/15*(15*c*x^4 + 5*b*x^2 + 3*a)/x^5","A",0
823,1,21,0,1.769291," ","integrate((c*x^4+b*x^2+a)/x^7,x, algorithm=""fricas"")","-\frac{6 \, c x^{4} + 3 \, b x^{2} + 2 \, a}{12 \, x^{6}}"," ",0,"-1/12*(6*c*x^4 + 3*b*x^2 + 2*a)/x^6","A",0
824,1,21,0,0.674408," ","integrate((c*x^4+b*x^2+a)/x^8,x, algorithm=""fricas"")","-\frac{35 \, c x^{4} + 21 \, b x^{2} + 15 \, a}{105 \, x^{7}}"," ",0,"-1/105*(35*c*x^4 + 21*b*x^2 + 15*a)/x^7","A",0
825,1,46,0,1.025368," ","integrate(x^2*(c*x^4+b*x^2+a)^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
826,1,46,0,2.303858," ","integrate(x*(c*x^4+b*x^2+a)^2,x, algorithm=""fricas"")","\frac{1}{10} x^{10} c^{2} + \frac{1}{4} x^{8} c b + \frac{1}{6} x^{6} b^{2} + \frac{1}{3} x^{6} c a + \frac{1}{2} x^{4} b a + \frac{1}{2} x^{2} a^{2}"," ",0,"1/10*x^10*c^2 + 1/4*x^8*c*b + 1/6*x^6*b^2 + 1/3*x^6*c*a + 1/2*x^4*b*a + 1/2*x^2*a^2","A",0
827,1,43,0,1.144181," ","integrate((c*x^4+b*x^2+a)^2,x, algorithm=""fricas"")","\frac{1}{9} x^{9} c^{2} + \frac{2}{7} x^{7} c b + \frac{1}{5} x^{5} b^{2} + \frac{2}{5} x^{5} c a + \frac{2}{3} x^{3} b a + x a^{2}"," ",0,"1/9*x^9*c^2 + 2/7*x^7*c*b + 1/5*x^5*b^2 + 2/5*x^5*c*a + 2/3*x^3*b*a + x*a^2","A",0
828,1,41,0,0.573122," ","integrate((c*x^4+b*x^2+a)^2/x,x, algorithm=""fricas"")","\frac{1}{8} \, c^{2} x^{8} + \frac{1}{3} \, b c x^{6} + \frac{1}{4} \, {\left(b^{2} + 2 \, a c\right)} x^{4} + a b x^{2} + a^{2} \log\left(x\right)"," ",0,"1/8*c^2*x^8 + 1/3*b*c*x^6 + 1/4*(b^2 + 2*a*c)*x^4 + a*b*x^2 + a^2*log(x)","A",0
829,1,46,0,0.717323," ","integrate((c*x^4+b*x^2+a)^2/x^2,x, algorithm=""fricas"")","\frac{15 \, c^{2} x^{8} + 42 \, b c x^{6} + 35 \, {\left(b^{2} + 2 \, a c\right)} x^{4} + 210 \, a b x^{2} - 105 \, a^{2}}{105 \, x}"," ",0,"1/105*(15*c^2*x^8 + 42*b*c*x^6 + 35*(b^2 + 2*a*c)*x^4 + 210*a*b*x^2 - 105*a^2)/x","A",0
830,1,47,0,1.740111," ","integrate((c*x^4+b*x^2+a)^2/x^3,x, algorithm=""fricas"")","\frac{c^{2} x^{8} + 3 \, b c x^{6} + 3 \, {\left(b^{2} + 2 \, a c\right)} x^{4} + 12 \, a b x^{2} \log\left(x\right) - 3 \, a^{2}}{6 \, x^{2}}"," ",0,"1/6*(c^2*x^8 + 3*b*c*x^6 + 3*(b^2 + 2*a*c)*x^4 + 12*a*b*x^2*log(x) - 3*a^2)/x^2","A",0
831,1,46,0,1.941214," ","integrate((c*x^4+b*x^2+a)^2/x^4,x, algorithm=""fricas"")","\frac{3 \, c^{2} x^{8} + 10 \, b c x^{6} + 15 \, {\left(b^{2} + 2 \, a c\right)} x^{4} - 30 \, a b x^{2} - 5 \, a^{2}}{15 \, x^{3}}"," ",0,"1/15*(3*c^2*x^8 + 10*b*c*x^6 + 15*(b^2 + 2*a*c)*x^4 - 30*a*b*x^2 - 5*a^2)/x^3","A",0
832,1,47,0,1.010494," ","integrate((c*x^4+b*x^2+a)^2/x^5,x, algorithm=""fricas"")","\frac{c^{2} x^{8} + 4 \, b c x^{6} + 4 \, {\left(b^{2} + 2 \, a c\right)} x^{4} \log\left(x\right) - 4 \, a b x^{2} - a^{2}}{4 \, x^{4}}"," ",0,"1/4*(c^2*x^8 + 4*b*c*x^6 + 4*(b^2 + 2*a*c)*x^4*log(x) - 4*a*b*x^2 - a^2)/x^4","A",0
833,1,46,0,1.676003," ","integrate((c*x^4+b*x^2+a)^2/x^6,x, algorithm=""fricas"")","\frac{5 \, c^{2} x^{8} + 30 \, b c x^{6} - 15 \, {\left(b^{2} + 2 \, a c\right)} x^{4} - 10 \, a b x^{2} - 3 \, a^{2}}{15 \, x^{5}}"," ",0,"1/15*(5*c^2*x^8 + 30*b*c*x^6 - 15*(b^2 + 2*a*c)*x^4 - 10*a*b*x^2 - 3*a^2)/x^5","A",0
834,1,48,0,0.557038," ","integrate((c*x^4+b*x^2+a)^2/x^7,x, algorithm=""fricas"")","\frac{3 \, c^{2} x^{8} + 12 \, b c x^{6} \log\left(x\right) - 3 \, {\left(b^{2} + 2 \, a c\right)} x^{4} - 3 \, a b x^{2} - a^{2}}{6 \, x^{6}}"," ",0,"1/6*(3*c^2*x^8 + 12*b*c*x^6*log(x) - 3*(b^2 + 2*a*c)*x^4 - 3*a*b*x^2 - a^2)/x^6","A",0
835,1,46,0,1.525916," ","integrate((c*x^4+b*x^2+a)^2/x^8,x, algorithm=""fricas"")","\frac{105 \, c^{2} x^{8} - 210 \, b c x^{6} - 35 \, {\left(b^{2} + 2 \, a c\right)} x^{4} - 42 \, a b x^{2} - 15 \, a^{2}}{105 \, x^{7}}"," ",0,"1/105*(105*c^2*x^8 - 210*b*c*x^6 - 35*(b^2 + 2*a*c)*x^4 - 42*a*b*x^2 - 15*a^2)/x^7","A",0
836,1,48,0,1.227863," ","integrate((c*x^4+b*x^2+a)^2/x^9,x, algorithm=""fricas"")","\frac{24 \, c^{2} x^{8} \log\left(x\right) - 24 \, b c x^{6} - 6 \, {\left(b^{2} + 2 \, a c\right)} x^{4} - 8 \, a b x^{2} - 3 \, a^{2}}{24 \, x^{8}}"," ",0,"1/24*(24*c^2*x^8*log(x) - 24*b*c*x^6 - 6*(b^2 + 2*a*c)*x^4 - 8*a*b*x^2 - 3*a^2)/x^8","A",0
837,1,46,0,2.104112," ","integrate((c*x^4+b*x^2+a)^2/x^10,x, algorithm=""fricas"")","-\frac{315 \, c^{2} x^{8} + 210 \, b c x^{6} + 63 \, {\left(b^{2} + 2 \, a c\right)} x^{4} + 90 \, a b x^{2} + 35 \, a^{2}}{315 \, x^{9}}"," ",0,"-1/315*(315*c^2*x^8 + 210*b*c*x^6 + 63*(b^2 + 2*a*c)*x^4 + 90*a*b*x^2 + 35*a^2)/x^9","A",0
838,1,46,0,1.766550," ","integrate((c*x^4+b*x^2+a)^2/x^11,x, algorithm=""fricas"")","-\frac{30 \, c^{2} x^{8} + 30 \, b c x^{6} + 10 \, {\left(b^{2} + 2 \, a c\right)} x^{4} + 15 \, a b x^{2} + 6 \, a^{2}}{60 \, x^{10}}"," ",0,"-1/60*(30*c^2*x^8 + 30*b*c*x^6 + 10*(b^2 + 2*a*c)*x^4 + 15*a*b*x^2 + 6*a^2)/x^10","A",0
839,1,46,0,0.940922," ","integrate((c*x^4+b*x^2+a)^2/x^12,x, algorithm=""fricas"")","-\frac{1155 \, c^{2} x^{8} + 1386 \, b c x^{6} + 495 \, {\left(b^{2} + 2 \, a c\right)} x^{4} + 770 \, a b x^{2} + 315 \, a^{2}}{3465 \, x^{11}}"," ",0,"-1/3465*(1155*c^2*x^8 + 1386*b*c*x^6 + 495*(b^2 + 2*a*c)*x^4 + 770*a*b*x^2 + 315*a^2)/x^11","A",0
840,1,46,0,0.811821," ","integrate((c*x^4+b*x^2+a)^2/x^13,x, algorithm=""fricas"")","-\frac{30 \, c^{2} x^{8} + 40 \, b c x^{6} + 15 \, {\left(b^{2} + 2 \, a c\right)} x^{4} + 24 \, a b x^{2} + 10 \, a^{2}}{120 \, x^{12}}"," ",0,"-1/120*(30*c^2*x^8 + 40*b*c*x^6 + 15*(b^2 + 2*a*c)*x^4 + 24*a*b*x^2 + 10*a^2)/x^12","A",0
841,1,87,0,1.262147," ","integrate(x^2*(c*x^4+b*x^2+a)^3,x, algorithm=""fricas"")","\frac{1}{15} x^{15} c^{3} + \frac{3}{13} x^{13} c^{2} b + \frac{3}{11} x^{11} c b^{2} + \frac{3}{11} x^{11} c^{2} a + \frac{1}{9} x^{9} b^{3} + \frac{2}{3} x^{9} c b a + \frac{3}{7} x^{7} b^{2} a + \frac{3}{7} x^{7} c a^{2} + \frac{3}{5} x^{5} b a^{2} + \frac{1}{3} x^{3} a^{3}"," ",0,"1/15*x^15*c^3 + 3/13*x^13*c^2*b + 3/11*x^11*c*b^2 + 3/11*x^11*c^2*a + 1/9*x^9*b^3 + 2/3*x^9*c*b*a + 3/7*x^7*b^2*a + 3/7*x^7*c*a^2 + 3/5*x^5*b*a^2 + 1/3*x^3*a^3","A",0
842,1,87,0,0.960897," ","integrate(x*(c*x^4+b*x^2+a)^3,x, algorithm=""fricas"")","\frac{1}{14} x^{14} c^{3} + \frac{1}{4} x^{12} c^{2} b + \frac{3}{10} x^{10} c b^{2} + \frac{3}{10} x^{10} c^{2} a + \frac{1}{8} x^{8} b^{3} + \frac{3}{4} x^{8} c b a + \frac{1}{2} x^{6} b^{2} a + \frac{1}{2} x^{6} c a^{2} + \frac{3}{4} x^{4} b a^{2} + \frac{1}{2} x^{2} a^{3}"," ",0,"1/14*x^14*c^3 + 1/4*x^12*c^2*b + 3/10*x^10*c*b^2 + 3/10*x^10*c^2*a + 1/8*x^8*b^3 + 3/4*x^8*c*b*a + 1/2*x^6*b^2*a + 1/2*x^6*c*a^2 + 3/4*x^4*b*a^2 + 1/2*x^2*a^3","A",0
843,1,83,0,0.752648," ","integrate((c*x^4+b*x^2+a)^3,x, algorithm=""fricas"")","\frac{1}{13} x^{13} c^{3} + \frac{3}{11} x^{11} c^{2} b + \frac{1}{3} x^{9} c b^{2} + \frac{1}{3} x^{9} c^{2} a + \frac{1}{7} x^{7} b^{3} + \frac{6}{7} x^{7} c b a + \frac{3}{5} x^{5} b^{2} a + \frac{3}{5} x^{5} c a^{2} + x^{3} b a^{2} + x a^{3}"," ",0,"1/13*x^13*c^3 + 3/11*x^11*c^2*b + 1/3*x^9*c*b^2 + 1/3*x^9*c^2*a + 1/7*x^7*b^3 + 6/7*x^7*c*b*a + 3/5*x^5*b^2*a + 3/5*x^5*c*a^2 + x^3*b*a^2 + x*a^3","A",0
844,1,79,0,1.928952," ","integrate((c*x^4+b*x^2+a)^3/x,x, algorithm=""fricas"")","\frac{1}{12} \, c^{3} x^{12} + \frac{3}{10} \, b c^{2} x^{10} + \frac{3}{8} \, {\left(b^{2} c + a c^{2}\right)} x^{8} + \frac{1}{6} \, {\left(b^{3} + 6 \, a b c\right)} x^{6} + \frac{3}{2} \, a^{2} b x^{2} + \frac{3}{4} \, {\left(a b^{2} + a^{2} c\right)} x^{4} + a^{3} \log\left(x\right)"," ",0,"1/12*c^3*x^12 + 3/10*b*c^2*x^10 + 3/8*(b^2*c + a*c^2)*x^8 + 1/6*(b^3 + 6*a*b*c)*x^6 + 3/2*a^2*b*x^2 + 3/4*(a*b^2 + a^2*c)*x^4 + a^3*log(x)","A",0
845,1,83,0,0.842811," ","integrate((c*x^4+b*x^2+a)^3/x^2,x, algorithm=""fricas"")","\frac{105 \, c^{3} x^{12} + 385 \, b c^{2} x^{10} + 495 \, {\left(b^{2} c + a c^{2}\right)} x^{8} + 231 \, {\left(b^{3} + 6 \, a b c\right)} x^{6} + 3465 \, a^{2} b x^{2} + 1155 \, {\left(a b^{2} + a^{2} c\right)} x^{4} - 1155 \, a^{3}}{1155 \, x}"," ",0,"1/1155*(105*c^3*x^12 + 385*b*c^2*x^10 + 495*(b^2*c + a*c^2)*x^8 + 231*(b^3 + 6*a*b*c)*x^6 + 3465*a^2*b*x^2 + 1155*(a*b^2 + a^2*c)*x^4 - 1155*a^3)/x","A",0
846,1,85,0,0.563276," ","integrate((c*x^4+b*x^2+a)^3/x^3,x, algorithm=""fricas"")","\frac{4 \, c^{3} x^{12} + 15 \, b c^{2} x^{10} + 20 \, {\left(b^{2} c + a c^{2}\right)} x^{8} + 10 \, {\left(b^{3} + 6 \, a b c\right)} x^{6} + 120 \, a^{2} b x^{2} \log\left(x\right) + 60 \, {\left(a b^{2} + a^{2} c\right)} x^{4} - 20 \, a^{3}}{40 \, x^{2}}"," ",0,"1/40*(4*c^3*x^12 + 15*b*c^2*x^10 + 20*(b^2*c + a*c^2)*x^8 + 10*(b^3 + 6*a*b*c)*x^6 + 120*a^2*b*x^2*log(x) + 60*(a*b^2 + a^2*c)*x^4 - 20*a^3)/x^2","A",0
847,1,83,0,1.273438," ","integrate((c*x^4+b*x^2+a)^3/x^4,x, algorithm=""fricas"")","\frac{35 \, c^{3} x^{12} + 135 \, b c^{2} x^{10} + 189 \, {\left(b^{2} c + a c^{2}\right)} x^{8} + 105 \, {\left(b^{3} + 6 \, a b c\right)} x^{6} - 945 \, a^{2} b x^{2} + 945 \, {\left(a b^{2} + a^{2} c\right)} x^{4} - 105 \, a^{3}}{315 \, x^{3}}"," ",0,"1/315*(35*c^3*x^12 + 135*b*c^2*x^10 + 189*(b^2*c + a*c^2)*x^8 + 105*(b^3 + 6*a*b*c)*x^6 - 945*a^2*b*x^2 + 945*(a*b^2 + a^2*c)*x^4 - 105*a^3)/x^3","A",0
848,1,313,0,2.861255," ","integrate(x^7/(c*x^4+b*x^2+a),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
849,1,254,0,1.014505," ","integrate(x^5/(c*x^4+b*x^2+a),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
850,1,197,0,0.976459," ","integrate(x^3/(c*x^4+b*x^2+a),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
851,1,129,0,2.331501," ","integrate(x/(c*x^4+b*x^2+a),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
852,1,223,0,1.305680," ","integrate(1/x/(c*x^4+b*x^2+a),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
853,1,293,0,0.682704," ","integrate(1/x^3/(c*x^4+b*x^2+a),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
854,1,374,0,2.111223," ","integrate(1/x^5/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\left[-\frac{{\left(b^{3} - 3 \, a b c\right)} \sqrt{b^{2} - 4 \, a c} x^{4} \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)} x^{4} \log\left(c x^{4} + b x^{2} + a\right) - 4 \, {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} x^{4} \log\left(x\right) + a^{2} b^{2} - 4 \, a^{3} c - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} x^{2}}{4 \, {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} x^{4}}, \frac{2 \, {\left(b^{3} - 3 \, a b c\right)} \sqrt{-b^{2} + 4 \, a c} x^{4} \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)} x^{4} \log\left(c x^{4} + b x^{2} + a\right) + 4 \, {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} x^{4} \log\left(x\right) - a^{2} b^{2} + 4 \, a^{3} c + 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} x^{2}}{4 \, {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} x^{4}}\right]"," ",0,"[-1/4*((b^3 - 3*a*b*c)*sqrt(b^2 - 4*a*c)*x^4*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)*x^4*log(c*x^4 + b*x^2 + a) - 4*(b^4 - 5*a*b^2*c + 4*a^2*c^2)*x^4*log(x) + a^2*b^2 - 4*a^3*c - 2*(a*b^3 - 4*a^2*b*c)*x^2)/((a^3*b^2 - 4*a^4*c)*x^4), 1/4*(2*(b^3 - 3*a*b*c)*sqrt(-b^2 + 4*a*c)*x^4*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)*x^4*log(c*x^4 + b*x^2 + a) + 4*(b^4 - 5*a*b^2*c + 4*a^2*c^2)*x^4*log(x) - a^2*b^2 + 4*a^3*c + 2*(a*b^3 - 4*a^2*b*c)*x^2)/((a^3*b^2 - 4*a^4*c)*x^4)]","A",0
855,1,1564,0,1.309279," ","integrate(x^6/(c*x^4+b*x^2+a),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
856,1,1059,0,1.800761," ","integrate(x^4/(c*x^4+b*x^2+a),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
857,1,559,0,1.551235," ","integrate(x^2/(c*x^4+b*x^2+a),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
858,1,613,0,0.746492," ","integrate(1/(c*x^4+b*x^2+a),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
859,1,1116,0,0.810611," ","integrate(1/x^2/(c*x^4+b*x^2+a),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
860,1,1622,0,0.852885," ","integrate(1/x^4/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","-\frac{3 \, \sqrt{\frac{1}{2}} a^{2} x^{3} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(a^{5} b^{2} - 4 \, a^{6} c\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}}{a^{10} b^{2} - 4 \, a^{11} c}}}{a^{5} b^{2} - 4 \, a^{6} c}} \log\left(2 \, {\left(b^{4} c^{3} - 3 \, a b^{2} c^{4} + a^{2} c^{5}\right)} x + \sqrt{\frac{1}{2}} {\left(b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 17 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4} - {\left(a^{5} b^{5} - 7 \, a^{6} b^{3} c + 12 \, a^{7} b c^{2}\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}}{a^{10} b^{2} - 4 \, a^{11} c}}\right)} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(a^{5} b^{2} - 4 \, a^{6} c\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}}{a^{10} b^{2} - 4 \, a^{11} c}}}{a^{5} b^{2} - 4 \, a^{6} c}}\right) - 3 \, \sqrt{\frac{1}{2}} a^{2} x^{3} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(a^{5} b^{2} - 4 \, a^{6} c\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}}{a^{10} b^{2} - 4 \, a^{11} c}}}{a^{5} b^{2} - 4 \, a^{6} c}} \log\left(2 \, {\left(b^{4} c^{3} - 3 \, a b^{2} c^{4} + a^{2} c^{5}\right)} x - \sqrt{\frac{1}{2}} {\left(b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 17 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4} - {\left(a^{5} b^{5} - 7 \, a^{6} b^{3} c + 12 \, a^{7} b c^{2}\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}}{a^{10} b^{2} - 4 \, a^{11} c}}\right)} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(a^{5} b^{2} - 4 \, a^{6} c\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}}{a^{10} b^{2} - 4 \, a^{11} c}}}{a^{5} b^{2} - 4 \, a^{6} c}}\right) + 3 \, \sqrt{\frac{1}{2}} a^{2} x^{3} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(a^{5} b^{2} - 4 \, a^{6} c\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}}{a^{10} b^{2} - 4 \, a^{11} c}}}{a^{5} b^{2} - 4 \, a^{6} c}} \log\left(2 \, {\left(b^{4} c^{3} - 3 \, a b^{2} c^{4} + a^{2} c^{5}\right)} x + \sqrt{\frac{1}{2}} {\left(b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 17 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4} + {\left(a^{5} b^{5} - 7 \, a^{6} b^{3} c + 12 \, a^{7} b c^{2}\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}}{a^{10} b^{2} - 4 \, a^{11} c}}\right)} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(a^{5} b^{2} - 4 \, a^{6} c\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}}{a^{10} b^{2} - 4 \, a^{11} c}}}{a^{5} b^{2} - 4 \, a^{6} c}}\right) - 3 \, \sqrt{\frac{1}{2}} a^{2} x^{3} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(a^{5} b^{2} - 4 \, a^{6} c\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}}{a^{10} b^{2} - 4 \, a^{11} c}}}{a^{5} b^{2} - 4 \, a^{6} c}} \log\left(2 \, {\left(b^{4} c^{3} - 3 \, a b^{2} c^{4} + a^{2} c^{5}\right)} x - \sqrt{\frac{1}{2}} {\left(b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 17 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4} + {\left(a^{5} b^{5} - 7 \, a^{6} b^{3} c + 12 \, a^{7} b c^{2}\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}}{a^{10} b^{2} - 4 \, a^{11} c}}\right)} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(a^{5} b^{2} - 4 \, a^{6} c\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}}{a^{10} b^{2} - 4 \, a^{11} c}}}{a^{5} b^{2} - 4 \, a^{6} c}}\right) - 6 \, b x^{2} + 2 \, a}{6 \, a^{2} x^{3}}"," ",0,"-1/6*(3*sqrt(1/2)*a^2*x^3*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (a^5*b^2 - 4*a^6*c)*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)/(a^10*b^2 - 4*a^11*c)))/(a^5*b^2 - 4*a^6*c))*log(2*(b^4*c^3 - 3*a*b^2*c^4 + a^2*c^5)*x + sqrt(1/2)*(b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 17*a^3*b^2*c^3 + 4*a^4*c^4 - (a^5*b^5 - 7*a^6*b^3*c + 12*a^7*b*c^2)*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)/(a^10*b^2 - 4*a^11*c)))*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (a^5*b^2 - 4*a^6*c)*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)/(a^10*b^2 - 4*a^11*c)))/(a^5*b^2 - 4*a^6*c))) - 3*sqrt(1/2)*a^2*x^3*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (a^5*b^2 - 4*a^6*c)*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)/(a^10*b^2 - 4*a^11*c)))/(a^5*b^2 - 4*a^6*c))*log(2*(b^4*c^3 - 3*a*b^2*c^4 + a^2*c^5)*x - sqrt(1/2)*(b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 17*a^3*b^2*c^3 + 4*a^4*c^4 - (a^5*b^5 - 7*a^6*b^3*c + 12*a^7*b*c^2)*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)/(a^10*b^2 - 4*a^11*c)))*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (a^5*b^2 - 4*a^6*c)*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)/(a^10*b^2 - 4*a^11*c)))/(a^5*b^2 - 4*a^6*c))) + 3*sqrt(1/2)*a^2*x^3*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (a^5*b^2 - 4*a^6*c)*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)/(a^10*b^2 - 4*a^11*c)))/(a^5*b^2 - 4*a^6*c))*log(2*(b^4*c^3 - 3*a*b^2*c^4 + a^2*c^5)*x + sqrt(1/2)*(b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 17*a^3*b^2*c^3 + 4*a^4*c^4 + (a^5*b^5 - 7*a^6*b^3*c + 12*a^7*b*c^2)*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)/(a^10*b^2 - 4*a^11*c)))*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (a^5*b^2 - 4*a^6*c)*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)/(a^10*b^2 - 4*a^11*c)))/(a^5*b^2 - 4*a^6*c))) - 3*sqrt(1/2)*a^2*x^3*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (a^5*b^2 - 4*a^6*c)*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)/(a^10*b^2 - 4*a^11*c)))/(a^5*b^2 - 4*a^6*c))*log(2*(b^4*c^3 - 3*a*b^2*c^4 + a^2*c^5)*x - sqrt(1/2)*(b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 17*a^3*b^2*c^3 + 4*a^4*c^4 + (a^5*b^5 - 7*a^6*b^3*c + 12*a^7*b*c^2)*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)/(a^10*b^2 - 4*a^11*c)))*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (a^5*b^2 - 4*a^6*c)*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)/(a^10*b^2 - 4*a^11*c)))/(a^5*b^2 - 4*a^6*c))) - 6*b*x^2 + 2*a)/(a^2*x^3)","B",0
861,1,663,0,0.973890," ","integrate(x^7/(c*x^4+b*x^2+a)^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
862,1,407,0,0.985363," ","integrate(x^5/(c*x^4+b*x^2+a)^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
863,1,360,0,0.862867," ","integrate(x^3/(c*x^4+b*x^2+a)^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
864,1,361,0,1.732712," ","integrate(x/(c*x^4+b*x^2+a)^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
865,1,813,0,0.944571," ","integrate(1/x/(c*x^4+b*x^2+a)^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
866,1,1007,0,1.812506," ","integrate(1/x^3/(c*x^4+b*x^2+a)^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
867,1,2856,0,2.055253," ","integrate(x^8/(c*x^4+b*x^2+a)^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
868,1,2257,0,1.440128," ","integrate(x^6/(c*x^4+b*x^2+a)^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
869,1,1668,0,1.112511," ","integrate(x^4/(c*x^4+b*x^2+a)^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
870,1,1680,0,1.573247," ","integrate(x^2/(c*x^4+b*x^2+a)^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
871,1,2309,0,1.004082," ","integrate(1/(c*x^4+b*x^2+a)^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
872,1,2912,0,1.187122," ","integrate(1/x^2/(c*x^4+b*x^2+a)^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
873,1,1631,0,2.359517," ","integrate(x^11/(c*x^4+b*x^2+a)^3,x, algorithm=""fricas"")","\left[\frac{3 \, a^{2} b^{6} - 33 \, a^{3} b^{4} c + 108 \, a^{4} b^{2} c^{2} - 96 \, a^{5} c^{3} + 2 \, {\left(2 \, b^{7} c - 23 \, a b^{5} c^{2} + 85 \, a^{2} b^{3} c^{3} - 100 \, a^{3} b c^{4}\right)} x^{6} + {\left(3 \, b^{8} - 31 \, a b^{6} c + 87 \, a^{2} b^{4} c^{2} - 12 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} x^{4} + 2 \, {\left(3 \, a b^{7} - 34 \, a^{2} b^{5} c + 119 \, a^{3} b^{3} c^{2} - 124 \, a^{4} b c^{3}\right)} x^{2} + {\left({\left(b^{5} c^{2} - 10 \, a b^{3} c^{3} + 30 \, a^{2} b c^{4}\right)} x^{8} + a^{2} b^{5} - 10 \, a^{3} b^{3} c + 30 \, a^{4} b c^{2} + 2 \, {\left(b^{6} c - 10 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3}\right)} x^{6} + {\left(b^{7} - 8 \, a b^{5} c + 10 \, a^{2} b^{3} c^{2} + 60 \, a^{3} b c^{3}\right)} x^{4} + 2 \, {\left(a b^{6} - 10 \, a^{2} b^{4} c + 30 \, a^{3} b^{2} 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^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} x^{8} + a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3} + 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)} x^{6} + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} x^{4} + 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} x^{2}\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, {\left(a^{2} b^{6} c^{3} - 12 \, a^{3} b^{4} c^{4} + 48 \, a^{4} b^{2} c^{5} - 64 \, a^{5} c^{6} + {\left(b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}\right)} x^{8} + 2 \, {\left(b^{7} c^{4} - 12 \, a b^{5} c^{5} + 48 \, a^{2} b^{3} c^{6} - 64 \, a^{3} b c^{7}\right)} x^{6} + {\left(b^{8} c^{3} - 10 \, a b^{6} c^{4} + 24 \, a^{2} b^{4} c^{5} + 32 \, a^{3} b^{2} c^{6} - 128 \, a^{4} c^{7}\right)} x^{4} + 2 \, {\left(a b^{7} c^{3} - 12 \, a^{2} b^{5} c^{4} + 48 \, a^{3} b^{3} c^{5} - 64 \, a^{4} b c^{6}\right)} x^{2}\right)}}, \frac{3 \, a^{2} b^{6} - 33 \, a^{3} b^{4} c + 108 \, a^{4} b^{2} c^{2} - 96 \, a^{5} c^{3} + 2 \, {\left(2 \, b^{7} c - 23 \, a b^{5} c^{2} + 85 \, a^{2} b^{3} c^{3} - 100 \, a^{3} b c^{4}\right)} x^{6} + {\left(3 \, b^{8} - 31 \, a b^{6} c + 87 \, a^{2} b^{4} c^{2} - 12 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} x^{4} + 2 \, {\left(3 \, a b^{7} - 34 \, a^{2} b^{5} c + 119 \, a^{3} b^{3} c^{2} - 124 \, a^{4} b c^{3}\right)} x^{2} + 2 \, {\left({\left(b^{5} c^{2} - 10 \, a b^{3} c^{3} + 30 \, a^{2} b c^{4}\right)} x^{8} + a^{2} b^{5} - 10 \, a^{3} b^{3} c + 30 \, a^{4} b c^{2} + 2 \, {\left(b^{6} c - 10 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3}\right)} x^{6} + {\left(b^{7} - 8 \, a b^{5} c + 10 \, a^{2} b^{3} c^{2} + 60 \, a^{3} b c^{3}\right)} x^{4} + 2 \, {\left(a b^{6} - 10 \, a^{2} b^{4} c + 30 \, a^{3} b^{2} 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^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} x^{8} + a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3} + 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)} x^{6} + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} x^{4} + 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} x^{2}\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, {\left(a^{2} b^{6} c^{3} - 12 \, a^{3} b^{4} c^{4} + 48 \, a^{4} b^{2} c^{5} - 64 \, a^{5} c^{6} + {\left(b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}\right)} x^{8} + 2 \, {\left(b^{7} c^{4} - 12 \, a b^{5} c^{5} + 48 \, a^{2} b^{3} c^{6} - 64 \, a^{3} b c^{7}\right)} x^{6} + {\left(b^{8} c^{3} - 10 \, a b^{6} c^{4} + 24 \, a^{2} b^{4} c^{5} + 32 \, a^{3} b^{2} c^{6} - 128 \, a^{4} c^{7}\right)} x^{4} + 2 \, {\left(a b^{7} c^{3} - 12 \, a^{2} b^{5} c^{4} + 48 \, a^{3} b^{3} c^{5} - 64 \, a^{4} b c^{6}\right)} x^{2}\right)}}\right]"," ",0,"[1/4*(3*a^2*b^6 - 33*a^3*b^4*c + 108*a^4*b^2*c^2 - 96*a^5*c^3 + 2*(2*b^7*c - 23*a*b^5*c^2 + 85*a^2*b^3*c^3 - 100*a^3*b*c^4)*x^6 + (3*b^8 - 31*a*b^6*c + 87*a^2*b^4*c^2 - 12*a^3*b^2*c^3 - 128*a^4*c^4)*x^4 + 2*(3*a*b^7 - 34*a^2*b^5*c + 119*a^3*b^3*c^2 - 124*a^4*b*c^3)*x^2 + ((b^5*c^2 - 10*a*b^3*c^3 + 30*a^2*b*c^4)*x^8 + a^2*b^5 - 10*a^3*b^3*c + 30*a^4*b*c^2 + 2*(b^6*c - 10*a*b^4*c^2 + 30*a^2*b^2*c^3)*x^6 + (b^7 - 8*a*b^5*c + 10*a^2*b^3*c^2 + 60*a^3*b*c^3)*x^4 + 2*(a*b^6 - 10*a^2*b^4*c + 30*a^3*b^2*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^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*x^8 + a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*x^6 + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*x^4 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*x^2)*log(c*x^4 + b*x^2 + a))/(a^2*b^6*c^3 - 12*a^3*b^4*c^4 + 48*a^4*b^2*c^5 - 64*a^5*c^6 + (b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)*x^8 + 2*(b^7*c^4 - 12*a*b^5*c^5 + 48*a^2*b^3*c^6 - 64*a^3*b*c^7)*x^6 + (b^8*c^3 - 10*a*b^6*c^4 + 24*a^2*b^4*c^5 + 32*a^3*b^2*c^6 - 128*a^4*c^7)*x^4 + 2*(a*b^7*c^3 - 12*a^2*b^5*c^4 + 48*a^3*b^3*c^5 - 64*a^4*b*c^6)*x^2), 1/4*(3*a^2*b^6 - 33*a^3*b^4*c + 108*a^4*b^2*c^2 - 96*a^5*c^3 + 2*(2*b^7*c - 23*a*b^5*c^2 + 85*a^2*b^3*c^3 - 100*a^3*b*c^4)*x^6 + (3*b^8 - 31*a*b^6*c + 87*a^2*b^4*c^2 - 12*a^3*b^2*c^3 - 128*a^4*c^4)*x^4 + 2*(3*a*b^7 - 34*a^2*b^5*c + 119*a^3*b^3*c^2 - 124*a^4*b*c^3)*x^2 + 2*((b^5*c^2 - 10*a*b^3*c^3 + 30*a^2*b*c^4)*x^8 + a^2*b^5 - 10*a^3*b^3*c + 30*a^4*b*c^2 + 2*(b^6*c - 10*a*b^4*c^2 + 30*a^2*b^2*c^3)*x^6 + (b^7 - 8*a*b^5*c + 10*a^2*b^3*c^2 + 60*a^3*b*c^3)*x^4 + 2*(a*b^6 - 10*a^2*b^4*c + 30*a^3*b^2*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^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*x^8 + a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*x^6 + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*x^4 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*x^2)*log(c*x^4 + b*x^2 + a))/(a^2*b^6*c^3 - 12*a^3*b^4*c^4 + 48*a^4*b^2*c^5 - 64*a^5*c^6 + (b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)*x^8 + 2*(b^7*c^4 - 12*a*b^5*c^5 + 48*a^2*b^3*c^6 - 64*a^3*b*c^7)*x^6 + (b^8*c^3 - 10*a*b^6*c^4 + 24*a^2*b^4*c^5 + 32*a^3*b^2*c^6 - 128*a^4*c^7)*x^4 + 2*(a*b^7*c^3 - 12*a^2*b^5*c^4 + 48*a^3*b^3*c^5 - 64*a^4*b*c^6)*x^2)]","B",0
874,1,973,0,0.724822," ","integrate(x^9/(c*x^4+b*x^2+a)^3,x, algorithm=""fricas"")","\left[-\frac{a^{2} b^{5} - 14 \, a^{3} b^{3} c + 40 \, a^{4} b c^{2} + 2 \, {\left(b^{6} c - 12 \, a b^{4} c^{2} + 42 \, a^{2} b^{2} c^{3} - 40 \, a^{3} c^{4}\right)} x^{6} + {\left(b^{7} - 12 \, a b^{5} c + 30 \, a^{2} b^{3} c^{2} + 8 \, a^{3} b c^{3}\right)} x^{4} + 2 \, {\left(a b^{6} - 14 \, a^{2} b^{4} c + 46 \, a^{3} b^{2} c^{2} - 24 \, a^{4} c^{3}\right)} x^{2} - 12 \, {\left(a^{2} c^{4} x^{8} + 2 \, a^{2} b c^{3} x^{6} + 2 \, a^{3} b c^{2} x^{2} + a^{4} c^{2} + {\left(a^{2} b^{2} c^{2} + 2 \, a^{3} c^{3}\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)}{4 \, {\left(a^{2} b^{6} c^{2} - 12 \, a^{3} b^{4} c^{3} + 48 \, a^{4} b^{2} c^{4} - 64 \, a^{5} c^{5} + {\left(b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}\right)} x^{8} + 2 \, {\left(b^{7} c^{3} - 12 \, a b^{5} c^{4} + 48 \, a^{2} b^{3} c^{5} - 64 \, a^{3} b c^{6}\right)} x^{6} + {\left(b^{8} c^{2} - 10 \, a b^{6} c^{3} + 24 \, a^{2} b^{4} c^{4} + 32 \, a^{3} b^{2} c^{5} - 128 \, a^{4} c^{6}\right)} x^{4} + 2 \, {\left(a b^{7} c^{2} - 12 \, a^{2} b^{5} c^{3} + 48 \, a^{3} b^{3} c^{4} - 64 \, a^{4} b c^{5}\right)} x^{2}\right)}}, -\frac{a^{2} b^{5} - 14 \, a^{3} b^{3} c + 40 \, a^{4} b c^{2} + 2 \, {\left(b^{6} c - 12 \, a b^{4} c^{2} + 42 \, a^{2} b^{2} c^{3} - 40 \, a^{3} c^{4}\right)} x^{6} + {\left(b^{7} - 12 \, a b^{5} c + 30 \, a^{2} b^{3} c^{2} + 8 \, a^{3} b c^{3}\right)} x^{4} + 2 \, {\left(a b^{6} - 14 \, a^{2} b^{4} c + 46 \, a^{3} b^{2} c^{2} - 24 \, a^{4} c^{3}\right)} x^{2} + 24 \, {\left(a^{2} c^{4} x^{8} + 2 \, a^{2} b c^{3} x^{6} + 2 \, a^{3} b c^{2} x^{2} + a^{4} c^{2} + {\left(a^{2} b^{2} c^{2} + 2 \, a^{3} c^{3}\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)}{4 \, {\left(a^{2} b^{6} c^{2} - 12 \, a^{3} b^{4} c^{3} + 48 \, a^{4} b^{2} c^{4} - 64 \, a^{5} c^{5} + {\left(b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}\right)} x^{8} + 2 \, {\left(b^{7} c^{3} - 12 \, a b^{5} c^{4} + 48 \, a^{2} b^{3} c^{5} - 64 \, a^{3} b c^{6}\right)} x^{6} + {\left(b^{8} c^{2} - 10 \, a b^{6} c^{3} + 24 \, a^{2} b^{4} c^{4} + 32 \, a^{3} b^{2} c^{5} - 128 \, a^{4} c^{6}\right)} x^{4} + 2 \, {\left(a b^{7} c^{2} - 12 \, a^{2} b^{5} c^{3} + 48 \, a^{3} b^{3} c^{4} - 64 \, a^{4} b c^{5}\right)} x^{2}\right)}}\right]"," ",0,"[-1/4*(a^2*b^5 - 14*a^3*b^3*c + 40*a^4*b*c^2 + 2*(b^6*c - 12*a*b^4*c^2 + 42*a^2*b^2*c^3 - 40*a^3*c^4)*x^6 + (b^7 - 12*a*b^5*c + 30*a^2*b^3*c^2 + 8*a^3*b*c^3)*x^4 + 2*(a*b^6 - 14*a^2*b^4*c + 46*a^3*b^2*c^2 - 24*a^4*c^3)*x^2 - 12*(a^2*c^4*x^8 + 2*a^2*b*c^3*x^6 + 2*a^3*b*c^2*x^2 + a^4*c^2 + (a^2*b^2*c^2 + 2*a^3*c^3)*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)))/(a^2*b^6*c^2 - 12*a^3*b^4*c^3 + 48*a^4*b^2*c^4 - 64*a^5*c^5 + (b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)*x^8 + 2*(b^7*c^3 - 12*a*b^5*c^4 + 48*a^2*b^3*c^5 - 64*a^3*b*c^6)*x^6 + (b^8*c^2 - 10*a*b^6*c^3 + 24*a^2*b^4*c^4 + 32*a^3*b^2*c^5 - 128*a^4*c^6)*x^4 + 2*(a*b^7*c^2 - 12*a^2*b^5*c^3 + 48*a^3*b^3*c^4 - 64*a^4*b*c^5)*x^2), -1/4*(a^2*b^5 - 14*a^3*b^3*c + 40*a^4*b*c^2 + 2*(b^6*c - 12*a*b^4*c^2 + 42*a^2*b^2*c^3 - 40*a^3*c^4)*x^6 + (b^7 - 12*a*b^5*c + 30*a^2*b^3*c^2 + 8*a^3*b*c^3)*x^4 + 2*(a*b^6 - 14*a^2*b^4*c + 46*a^3*b^2*c^2 - 24*a^4*c^3)*x^2 + 24*(a^2*c^4*x^8 + 2*a^2*b*c^3*x^6 + 2*a^3*b*c^2*x^2 + a^4*c^2 + (a^2*b^2*c^2 + 2*a^3*c^3)*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)))/(a^2*b^6*c^2 - 12*a^3*b^4*c^3 + 48*a^4*b^2*c^4 - 64*a^5*c^5 + (b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)*x^8 + 2*(b^7*c^3 - 12*a*b^5*c^4 + 48*a^2*b^3*c^5 - 64*a^3*b*c^6)*x^6 + (b^8*c^2 - 10*a*b^6*c^3 + 24*a^2*b^4*c^4 + 32*a^3*b^2*c^5 - 128*a^4*c^6)*x^4 + 2*(a*b^7*c^2 - 12*a^2*b^5*c^3 + 48*a^3*b^3*c^4 - 64*a^4*b*c^5)*x^2)]","B",0
875,1,892,0,0.956537," ","integrate(x^7/(c*x^4+b*x^2+a)^3,x, algorithm=""fricas"")","\left[-\frac{6 \, {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} x^{6} + a^{2} b^{4} + 4 \, a^{3} b^{2} c - 32 \, a^{4} c^{2} + {\left(b^{6} - 3 \, a b^{4} c + 12 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} x^{4} + 2 \, {\left(a b^{5} + a^{2} b^{3} c - 20 \, a^{3} b c^{2}\right)} x^{2} - 6 \, {\left(a b c^{3} x^{8} + 2 \, a b^{2} c^{2} x^{6} + 2 \, a^{2} b^{2} c x^{2} + a^{3} b c + {\left(a b^{3} c + 2 \, a^{2} 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)}{4 \, {\left(a^{2} b^{6} c - 12 \, a^{3} b^{4} c^{2} + 48 \, a^{4} b^{2} c^{3} - 64 \, a^{5} c^{4} + {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} x^{8} + 2 \, {\left(b^{7} c^{2} - 12 \, a b^{5} c^{3} + 48 \, a^{2} b^{3} c^{4} - 64 \, a^{3} b c^{5}\right)} x^{6} + {\left(b^{8} c - 10 \, a b^{6} c^{2} + 24 \, a^{2} b^{4} c^{3} + 32 \, a^{3} b^{2} c^{4} - 128 \, a^{4} c^{5}\right)} x^{4} + 2 \, {\left(a b^{7} c - 12 \, a^{2} b^{5} c^{2} + 48 \, a^{3} b^{3} c^{3} - 64 \, a^{4} b c^{4}\right)} x^{2}\right)}}, -\frac{6 \, {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} x^{6} + a^{2} b^{4} + 4 \, a^{3} b^{2} c - 32 \, a^{4} c^{2} + {\left(b^{6} - 3 \, a b^{4} c + 12 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} x^{4} + 2 \, {\left(a b^{5} + a^{2} b^{3} c - 20 \, a^{3} b c^{2}\right)} x^{2} - 12 \, {\left(a b c^{3} x^{8} + 2 \, a b^{2} c^{2} x^{6} + 2 \, a^{2} b^{2} c x^{2} + a^{3} b c + {\left(a b^{3} c + 2 \, a^{2} 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)}{4 \, {\left(a^{2} b^{6} c - 12 \, a^{3} b^{4} c^{2} + 48 \, a^{4} b^{2} c^{3} - 64 \, a^{5} c^{4} + {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} x^{8} + 2 \, {\left(b^{7} c^{2} - 12 \, a b^{5} c^{3} + 48 \, a^{2} b^{3} c^{4} - 64 \, a^{3} b c^{5}\right)} x^{6} + {\left(b^{8} c - 10 \, a b^{6} c^{2} + 24 \, a^{2} b^{4} c^{3} + 32 \, a^{3} b^{2} c^{4} - 128 \, a^{4} c^{5}\right)} x^{4} + 2 \, {\left(a b^{7} c - 12 \, a^{2} b^{5} c^{2} + 48 \, a^{3} b^{3} c^{3} - 64 \, a^{4} b c^{4}\right)} x^{2}\right)}}\right]"," ",0,"[-1/4*(6*(a*b^3*c^2 - 4*a^2*b*c^3)*x^6 + a^2*b^4 + 4*a^3*b^2*c - 32*a^4*c^2 + (b^6 - 3*a*b^4*c + 12*a^2*b^2*c^2 - 64*a^3*c^3)*x^4 + 2*(a*b^5 + a^2*b^3*c - 20*a^3*b*c^2)*x^2 - 6*(a*b*c^3*x^8 + 2*a*b^2*c^2*x^6 + 2*a^2*b^2*c*x^2 + a^3*b*c + (a*b^3*c + 2*a^2*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)))/(a^2*b^6*c - 12*a^3*b^4*c^2 + 48*a^4*b^2*c^3 - 64*a^5*c^4 + (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*x^8 + 2*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*x^6 + (b^8*c - 10*a*b^6*c^2 + 24*a^2*b^4*c^3 + 32*a^3*b^2*c^4 - 128*a^4*c^5)*x^4 + 2*(a*b^7*c - 12*a^2*b^5*c^2 + 48*a^3*b^3*c^3 - 64*a^4*b*c^4)*x^2), -1/4*(6*(a*b^3*c^2 - 4*a^2*b*c^3)*x^6 + a^2*b^4 + 4*a^3*b^2*c - 32*a^4*c^2 + (b^6 - 3*a*b^4*c + 12*a^2*b^2*c^2 - 64*a^3*c^3)*x^4 + 2*(a*b^5 + a^2*b^3*c - 20*a^3*b*c^2)*x^2 - 12*(a*b*c^3*x^8 + 2*a*b^2*c^2*x^6 + 2*a^2*b^2*c*x^2 + a^3*b*c + (a*b^3*c + 2*a^2*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)))/(a^2*b^6*c - 12*a^3*b^4*c^2 + 48*a^4*b^2*c^3 - 64*a^5*c^4 + (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*x^8 + 2*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*x^6 + (b^8*c - 10*a*b^6*c^2 + 24*a^2*b^4*c^3 + 32*a^3*b^2*c^4 - 128*a^4*c^5)*x^4 + 2*(a*b^7*c - 12*a^2*b^5*c^2 + 48*a^3*b^3*c^3 - 64*a^4*b*c^4)*x^2)]","B",0
876,1,907,0,0.601613," ","integrate(x^5/(c*x^4+b*x^2+a)^3,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} x^{6} + 6 \, a^{2} b^{3} - 24 \, a^{3} b c + 3 \, {\left(b^{5} - 2 \, a b^{3} c - 8 \, a^{2} b c^{2}\right)} x^{4} + 2 \, {\left(5 \, a b^{4} - 22 \, a^{2} b^{2} c + 8 \, a^{3} c^{2}\right)} x^{2} + 2 \, {\left({\left(b^{2} c^{2} + 2 \, a c^{3}\right)} x^{8} + 2 \, {\left(b^{3} c + 2 \, a b c^{2}\right)} x^{6} + {\left(b^{4} + 4 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} x^{4} + a^{2} b^{2} + 2 \, a^{3} c + 2 \, {\left(a b^{3} + 2 \, a^{2} b 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)}{4 \, {\left({\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} x^{8} + a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3} + 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)} x^{6} + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} x^{4} + 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} x^{2}\right)}}, \frac{2 \, {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} x^{6} + 6 \, a^{2} b^{3} - 24 \, a^{3} b c + 3 \, {\left(b^{5} - 2 \, a b^{3} c - 8 \, a^{2} b c^{2}\right)} x^{4} + 2 \, {\left(5 \, a b^{4} - 22 \, a^{2} b^{2} c + 8 \, a^{3} c^{2}\right)} x^{2} - 4 \, {\left({\left(b^{2} c^{2} + 2 \, a c^{3}\right)} x^{8} + 2 \, {\left(b^{3} c + 2 \, a b c^{2}\right)} x^{6} + {\left(b^{4} + 4 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} x^{4} + a^{2} b^{2} + 2 \, a^{3} c + 2 \, {\left(a b^{3} + 2 \, a^{2} b 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)}{4 \, {\left({\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} x^{8} + a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3} + 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)} x^{6} + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} x^{4} + 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} x^{2}\right)}}\right]"," ",0,"[1/4*(2*(b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*x^6 + 6*a^2*b^3 - 24*a^3*b*c + 3*(b^5 - 2*a*b^3*c - 8*a^2*b*c^2)*x^4 + 2*(5*a*b^4 - 22*a^2*b^2*c + 8*a^3*c^2)*x^2 + 2*((b^2*c^2 + 2*a*c^3)*x^8 + 2*(b^3*c + 2*a*b*c^2)*x^6 + (b^4 + 4*a*b^2*c + 4*a^2*c^2)*x^4 + a^2*b^2 + 2*a^3*c + 2*(a*b^3 + 2*a^2*b*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)))/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*x^8 + a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*x^6 + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*x^4 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*x^2), 1/4*(2*(b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*x^6 + 6*a^2*b^3 - 24*a^3*b*c + 3*(b^5 - 2*a*b^3*c - 8*a^2*b*c^2)*x^4 + 2*(5*a*b^4 - 22*a^2*b^2*c + 8*a^3*c^2)*x^2 - 4*((b^2*c^2 + 2*a*c^3)*x^8 + 2*(b^3*c + 2*a*b*c^2)*x^6 + (b^4 + 4*a*b^2*c + 4*a^2*c^2)*x^4 + a^2*b^2 + 2*a^3*c + 2*(a*b^3 + 2*a^2*b*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)))/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*x^8 + a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*x^6 + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*x^4 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*x^2)]","B",0
877,1,808,0,2.673958," ","integrate(x^3/(c*x^4+b*x^2+a)^3,x, algorithm=""fricas"")","\left[-\frac{6 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x^{6} + a b^{4} + 4 \, a^{2} b^{2} c - 32 \, a^{3} c^{2} + 9 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} x^{4} + 2 \, {\left(b^{5} + a b^{3} c - 20 \, a^{2} b c^{2}\right)} x^{2} - 6 \, {\left(b c^{3} x^{8} + 2 \, b^{2} c^{2} x^{6} + 2 \, a b^{2} c x^{2} + {\left(b^{3} c + 2 \, a b c^{2}\right)} x^{4} + a^{2} 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)}{4 \, {\left({\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} x^{8} + a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3} + 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)} x^{6} + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} x^{4} + 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} x^{2}\right)}}, -\frac{6 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x^{6} + a b^{4} + 4 \, a^{2} b^{2} c - 32 \, a^{3} c^{2} + 9 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} x^{4} + 2 \, {\left(b^{5} + a b^{3} c - 20 \, a^{2} b c^{2}\right)} x^{2} - 12 \, {\left(b c^{3} x^{8} + 2 \, b^{2} c^{2} x^{6} + 2 \, a b^{2} c x^{2} + {\left(b^{3} c + 2 \, a b c^{2}\right)} x^{4} + a^{2} 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)}{4 \, {\left({\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} x^{8} + a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3} + 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)} x^{6} + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} x^{4} + 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} x^{2}\right)}}\right]"," ",0,"[-1/4*(6*(b^3*c^2 - 4*a*b*c^3)*x^6 + a*b^4 + 4*a^2*b^2*c - 32*a^3*c^2 + 9*(b^4*c - 4*a*b^2*c^2)*x^4 + 2*(b^5 + a*b^3*c - 20*a^2*b*c^2)*x^2 - 6*(b*c^3*x^8 + 2*b^2*c^2*x^6 + 2*a*b^2*c*x^2 + (b^3*c + 2*a*b*c^2)*x^4 + a^2*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^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*x^8 + a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*x^6 + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*x^4 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*x^2), -1/4*(6*(b^3*c^2 - 4*a*b*c^3)*x^6 + a*b^4 + 4*a^2*b^2*c - 32*a^3*c^2 + 9*(b^4*c - 4*a*b^2*c^2)*x^4 + 2*(b^5 + a*b^3*c - 20*a^2*b*c^2)*x^2 - 12*(b*c^3*x^8 + 2*b^2*c^2*x^6 + 2*a*b^2*c*x^2 + (b^3*c + 2*a*b*c^2)*x^4 + a^2*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^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*x^8 + a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*x^6 + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*x^4 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*x^2)]","B",0
878,1,809,0,1.060804," ","integrate(x/(c*x^4+b*x^2+a)^3,x, algorithm=""fricas"")","\left[\frac{12 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{6} - b^{5} + 14 \, a b^{3} c - 40 \, a^{2} b c^{2} + 18 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x^{4} + 4 \, {\left(b^{4} c + a b^{2} c^{2} - 20 \, a^{2} c^{3}\right)} x^{2} + 12 \, {\left(c^{4} x^{8} + 2 \, b c^{3} x^{6} + 2 \, a b c^{2} x^{2} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} x^{4} + a^{2} c^{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)}{4 \, {\left({\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} x^{8} + a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3} + 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)} x^{6} + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} x^{4} + 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} x^{2}\right)}}, \frac{12 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{6} - b^{5} + 14 \, a b^{3} c - 40 \, a^{2} b c^{2} + 18 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x^{4} + 4 \, {\left(b^{4} c + a b^{2} c^{2} - 20 \, a^{2} c^{3}\right)} x^{2} - 24 \, {\left(c^{4} x^{8} + 2 \, b c^{3} x^{6} + 2 \, a b c^{2} x^{2} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} x^{4} + a^{2} c^{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)}{4 \, {\left({\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} x^{8} + a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3} + 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)} x^{6} + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} x^{4} + 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} x^{2}\right)}}\right]"," ",0,"[1/4*(12*(b^2*c^3 - 4*a*c^4)*x^6 - b^5 + 14*a*b^3*c - 40*a^2*b*c^2 + 18*(b^3*c^2 - 4*a*b*c^3)*x^4 + 4*(b^4*c + a*b^2*c^2 - 20*a^2*c^3)*x^2 + 12*(c^4*x^8 + 2*b*c^3*x^6 + 2*a*b*c^2*x^2 + (b^2*c^2 + 2*a*c^3)*x^4 + a^2*c^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^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*x^8 + a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*x^6 + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*x^4 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*x^2), 1/4*(12*(b^2*c^3 - 4*a*c^4)*x^6 - b^5 + 14*a*b^3*c - 40*a^2*b*c^2 + 18*(b^3*c^2 - 4*a*b*c^3)*x^4 + 4*(b^4*c + a*b^2*c^2 - 20*a^2*c^3)*x^2 - 24*(c^4*x^8 + 2*b*c^3*x^6 + 2*a*b*c^2*x^2 + (b^2*c^2 + 2*a*c^3)*x^4 + a^2*c^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^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*x^8 + a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*x^6 + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*x^4 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*x^2)]","B",0
879,1,2017,0,1.893674," ","integrate(1/x/(c*x^4+b*x^2+a)^3,x, algorithm=""fricas"")","\left[\frac{3 \, a^{2} b^{6} - 33 \, a^{3} b^{4} c + 108 \, a^{4} b^{2} c^{2} - 96 \, a^{5} c^{3} + 2 \, {\left(a b^{5} c^{2} - 11 \, a^{2} b^{3} c^{3} + 28 \, a^{3} b c^{4}\right)} x^{6} + {\left(4 \, a b^{6} c - 45 \, a^{2} b^{4} c^{2} + 132 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4}\right)} x^{4} + 2 \, {\left(a b^{7} - 10 \, a^{2} b^{5} c + 23 \, a^{3} b^{3} c^{2} + 4 \, a^{4} b c^{3}\right)} x^{2} + {\left({\left(b^{5} c^{2} - 10 \, a b^{3} c^{3} + 30 \, a^{2} b c^{4}\right)} x^{8} + a^{2} b^{5} - 10 \, a^{3} b^{3} c + 30 \, a^{4} b c^{2} + 2 \, {\left(b^{6} c - 10 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3}\right)} x^{6} + {\left(b^{7} - 8 \, a b^{5} c + 10 \, a^{2} b^{3} c^{2} + 60 \, a^{3} b c^{3}\right)} x^{4} + 2 \, {\left(a b^{6} - 10 \, a^{2} b^{4} c + 30 \, a^{3} b^{2} 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^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} x^{8} + a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3} + 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)} x^{6} + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} x^{4} + 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} x^{2}\right)} \log\left(c x^{4} + b x^{2} + a\right) + 4 \, {\left({\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} x^{8} + a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3} + 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)} x^{6} + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} x^{4} + 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} x^{2}\right)} \log\left(x\right)}{4 \, {\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3} + {\left(a^{3} b^{6} c^{2} - 12 \, a^{4} b^{4} c^{3} + 48 \, a^{5} b^{2} c^{4} - 64 \, a^{6} c^{5}\right)} x^{8} + 2 \, {\left(a^{3} b^{7} c - 12 \, a^{4} b^{5} c^{2} + 48 \, a^{5} b^{3} c^{3} - 64 \, a^{6} b c^{4}\right)} x^{6} + {\left(a^{3} b^{8} - 10 \, a^{4} b^{6} c + 24 \, a^{5} b^{4} c^{2} + 32 \, a^{6} b^{2} c^{3} - 128 \, a^{7} c^{4}\right)} x^{4} + 2 \, {\left(a^{4} b^{7} - 12 \, a^{5} b^{5} c + 48 \, a^{6} b^{3} c^{2} - 64 \, a^{7} b c^{3}\right)} x^{2}\right)}}, \frac{3 \, a^{2} b^{6} - 33 \, a^{3} b^{4} c + 108 \, a^{4} b^{2} c^{2} - 96 \, a^{5} c^{3} + 2 \, {\left(a b^{5} c^{2} - 11 \, a^{2} b^{3} c^{3} + 28 \, a^{3} b c^{4}\right)} x^{6} + {\left(4 \, a b^{6} c - 45 \, a^{2} b^{4} c^{2} + 132 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4}\right)} x^{4} + 2 \, {\left(a b^{7} - 10 \, a^{2} b^{5} c + 23 \, a^{3} b^{3} c^{2} + 4 \, a^{4} b c^{3}\right)} x^{2} + 2 \, {\left({\left(b^{5} c^{2} - 10 \, a b^{3} c^{3} + 30 \, a^{2} b c^{4}\right)} x^{8} + a^{2} b^{5} - 10 \, a^{3} b^{3} c + 30 \, a^{4} b c^{2} + 2 \, {\left(b^{6} c - 10 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3}\right)} x^{6} + {\left(b^{7} - 8 \, a b^{5} c + 10 \, a^{2} b^{3} c^{2} + 60 \, a^{3} b c^{3}\right)} x^{4} + 2 \, {\left(a b^{6} - 10 \, a^{2} b^{4} c + 30 \, a^{3} b^{2} 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^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} x^{8} + a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3} + 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)} x^{6} + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} x^{4} + 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} x^{2}\right)} \log\left(c x^{4} + b x^{2} + a\right) + 4 \, {\left({\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} x^{8} + a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3} + 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)} x^{6} + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} x^{4} + 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} x^{2}\right)} \log\left(x\right)}{4 \, {\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3} + {\left(a^{3} b^{6} c^{2} - 12 \, a^{4} b^{4} c^{3} + 48 \, a^{5} b^{2} c^{4} - 64 \, a^{6} c^{5}\right)} x^{8} + 2 \, {\left(a^{3} b^{7} c - 12 \, a^{4} b^{5} c^{2} + 48 \, a^{5} b^{3} c^{3} - 64 \, a^{6} b c^{4}\right)} x^{6} + {\left(a^{3} b^{8} - 10 \, a^{4} b^{6} c + 24 \, a^{5} b^{4} c^{2} + 32 \, a^{6} b^{2} c^{3} - 128 \, a^{7} c^{4}\right)} x^{4} + 2 \, {\left(a^{4} b^{7} - 12 \, a^{5} b^{5} c + 48 \, a^{6} b^{3} c^{2} - 64 \, a^{7} b c^{3}\right)} x^{2}\right)}}\right]"," ",0,"[1/4*(3*a^2*b^6 - 33*a^3*b^4*c + 108*a^4*b^2*c^2 - 96*a^5*c^3 + 2*(a*b^5*c^2 - 11*a^2*b^3*c^3 + 28*a^3*b*c^4)*x^6 + (4*a*b^6*c - 45*a^2*b^4*c^2 + 132*a^3*b^2*c^3 - 64*a^4*c^4)*x^4 + 2*(a*b^7 - 10*a^2*b^5*c + 23*a^3*b^3*c^2 + 4*a^4*b*c^3)*x^2 + ((b^5*c^2 - 10*a*b^3*c^3 + 30*a^2*b*c^4)*x^8 + a^2*b^5 - 10*a^3*b^3*c + 30*a^4*b*c^2 + 2*(b^6*c - 10*a*b^4*c^2 + 30*a^2*b^2*c^3)*x^6 + (b^7 - 8*a*b^5*c + 10*a^2*b^3*c^2 + 60*a^3*b*c^3)*x^4 + 2*(a*b^6 - 10*a^2*b^4*c + 30*a^3*b^2*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^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*x^8 + a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*x^6 + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*x^4 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*x^2)*log(c*x^4 + b*x^2 + a) + 4*((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*x^8 + a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*x^6 + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*x^4 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*x^2)*log(x))/(a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3 + (a^3*b^6*c^2 - 12*a^4*b^4*c^3 + 48*a^5*b^2*c^4 - 64*a^6*c^5)*x^8 + 2*(a^3*b^7*c - 12*a^4*b^5*c^2 + 48*a^5*b^3*c^3 - 64*a^6*b*c^4)*x^6 + (a^3*b^8 - 10*a^4*b^6*c + 24*a^5*b^4*c^2 + 32*a^6*b^2*c^3 - 128*a^7*c^4)*x^4 + 2*(a^4*b^7 - 12*a^5*b^5*c + 48*a^6*b^3*c^2 - 64*a^7*b*c^3)*x^2), 1/4*(3*a^2*b^6 - 33*a^3*b^4*c + 108*a^4*b^2*c^2 - 96*a^5*c^3 + 2*(a*b^5*c^2 - 11*a^2*b^3*c^3 + 28*a^3*b*c^4)*x^6 + (4*a*b^6*c - 45*a^2*b^4*c^2 + 132*a^3*b^2*c^3 - 64*a^4*c^4)*x^4 + 2*(a*b^7 - 10*a^2*b^5*c + 23*a^3*b^3*c^2 + 4*a^4*b*c^3)*x^2 + 2*((b^5*c^2 - 10*a*b^3*c^3 + 30*a^2*b*c^4)*x^8 + a^2*b^5 - 10*a^3*b^3*c + 30*a^4*b*c^2 + 2*(b^6*c - 10*a*b^4*c^2 + 30*a^2*b^2*c^3)*x^6 + (b^7 - 8*a*b^5*c + 10*a^2*b^3*c^2 + 60*a^3*b*c^3)*x^4 + 2*(a*b^6 - 10*a^2*b^4*c + 30*a^3*b^2*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^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*x^8 + a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*x^6 + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*x^4 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*x^2)*log(c*x^4 + b*x^2 + a) + 4*((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*x^8 + a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*x^6 + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*x^4 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*x^2)*log(x))/(a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3 + (a^3*b^6*c^2 - 12*a^4*b^4*c^3 + 48*a^5*b^2*c^4 - 64*a^6*c^5)*x^8 + 2*(a^3*b^7*c - 12*a^4*b^5*c^2 + 48*a^5*b^3*c^3 - 64*a^6*b*c^4)*x^6 + (a^3*b^8 - 10*a^4*b^6*c + 24*a^5*b^4*c^2 + 32*a^6*b^2*c^3 - 128*a^7*c^4)*x^4 + 2*(a^4*b^7 - 12*a^5*b^5*c + 48*a^6*b^3*c^2 - 64*a^7*b*c^3)*x^2)]","B",0
880,1,2312,0,2.666459," ","integrate(1/x^3/(c*x^4+b*x^2+a)^3,x, algorithm=""fricas"")","\left[-\frac{2 \, a^{3} b^{6} - 24 \, a^{4} b^{4} c + 96 \, a^{5} b^{2} c^{2} - 128 \, a^{6} c^{3} + 6 \, {\left(a b^{6} c^{2} - 11 \, a^{2} b^{4} c^{3} + 38 \, a^{3} b^{2} c^{4} - 40 \, a^{4} c^{5}\right)} x^{8} + 3 \, {\left(4 \, a b^{7} c - 45 \, a^{2} b^{5} c^{2} + 162 \, a^{3} b^{3} c^{3} - 184 \, a^{4} b c^{4}\right)} x^{6} + 2 \, {\left(3 \, a b^{8} - 30 \, a^{2} b^{6} c + 79 \, a^{3} b^{4} c^{2} + 22 \, a^{4} b^{2} c^{3} - 200 \, a^{5} c^{4}\right)} x^{4} + {\left(9 \, a^{2} b^{7} - 104 \, a^{3} b^{5} c + 394 \, a^{4} b^{3} c^{2} - 488 \, a^{5} b c^{3}\right)} x^{2} + 3 \, {\left({\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} x^{10} + 2 \, {\left(b^{7} c - 10 \, a b^{5} c^{2} + 30 \, a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} x^{8} + {\left(b^{8} - 8 \, a b^{6} c + 10 \, a^{2} b^{4} c^{2} + 40 \, a^{3} b^{2} c^{3} - 40 \, a^{4} c^{4}\right)} x^{6} + 2 \, {\left(a b^{7} - 10 \, a^{2} b^{5} c + 30 \, a^{3} b^{3} c^{2} - 20 \, a^{4} b c^{3}\right)} x^{4} + {\left(a^{2} b^{6} - 10 \, a^{3} b^{4} c + 30 \, a^{4} b^{2} c^{2} - 20 \, a^{5} c^{3}\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) - 3 \, {\left({\left(b^{7} c^{2} - 12 \, a b^{5} c^{3} + 48 \, a^{2} b^{3} c^{4} - 64 \, a^{3} b c^{5}\right)} x^{10} + 2 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} x^{8} + {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} x^{6} + 2 \, {\left(a b^{8} - 12 \, a^{2} b^{6} c + 48 \, a^{3} b^{4} c^{2} - 64 \, a^{4} b^{2} c^{3}\right)} x^{4} + {\left(a^{2} b^{7} - 12 \, a^{3} b^{5} c + 48 \, a^{4} b^{3} c^{2} - 64 \, a^{5} b c^{3}\right)} x^{2}\right)} \log\left(c x^{4} + b x^{2} + a\right) + 12 \, {\left({\left(b^{7} c^{2} - 12 \, a b^{5} c^{3} + 48 \, a^{2} b^{3} c^{4} - 64 \, a^{3} b c^{5}\right)} x^{10} + 2 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} x^{8} + {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} x^{6} + 2 \, {\left(a b^{8} - 12 \, a^{2} b^{6} c + 48 \, a^{3} b^{4} c^{2} - 64 \, a^{4} b^{2} c^{3}\right)} x^{4} + {\left(a^{2} b^{7} - 12 \, a^{3} b^{5} c + 48 \, a^{4} b^{3} c^{2} - 64 \, a^{5} b c^{3}\right)} x^{2}\right)} \log\left(x\right)}{4 \, {\left({\left(a^{4} b^{6} c^{2} - 12 \, a^{5} b^{4} c^{3} + 48 \, a^{6} b^{2} c^{4} - 64 \, a^{7} c^{5}\right)} x^{10} + 2 \, {\left(a^{4} b^{7} c - 12 \, a^{5} b^{5} c^{2} + 48 \, a^{6} b^{3} c^{3} - 64 \, a^{7} b c^{4}\right)} x^{8} + {\left(a^{4} b^{8} - 10 \, a^{5} b^{6} c + 24 \, a^{6} b^{4} c^{2} + 32 \, a^{7} b^{2} c^{3} - 128 \, a^{8} c^{4}\right)} x^{6} + 2 \, {\left(a^{5} b^{7} - 12 \, a^{6} b^{5} c + 48 \, a^{7} b^{3} c^{2} - 64 \, a^{8} b c^{3}\right)} x^{4} + {\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}\right)} x^{2}\right)}}, -\frac{2 \, a^{3} b^{6} - 24 \, a^{4} b^{4} c + 96 \, a^{5} b^{2} c^{2} - 128 \, a^{6} c^{3} + 6 \, {\left(a b^{6} c^{2} - 11 \, a^{2} b^{4} c^{3} + 38 \, a^{3} b^{2} c^{4} - 40 \, a^{4} c^{5}\right)} x^{8} + 3 \, {\left(4 \, a b^{7} c - 45 \, a^{2} b^{5} c^{2} + 162 \, a^{3} b^{3} c^{3} - 184 \, a^{4} b c^{4}\right)} x^{6} + 2 \, {\left(3 \, a b^{8} - 30 \, a^{2} b^{6} c + 79 \, a^{3} b^{4} c^{2} + 22 \, a^{4} b^{2} c^{3} - 200 \, a^{5} c^{4}\right)} x^{4} + {\left(9 \, a^{2} b^{7} - 104 \, a^{3} b^{5} c + 394 \, a^{4} b^{3} c^{2} - 488 \, a^{5} b c^{3}\right)} x^{2} + 6 \, {\left({\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} x^{10} + 2 \, {\left(b^{7} c - 10 \, a b^{5} c^{2} + 30 \, a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} x^{8} + {\left(b^{8} - 8 \, a b^{6} c + 10 \, a^{2} b^{4} c^{2} + 40 \, a^{3} b^{2} c^{3} - 40 \, a^{4} c^{4}\right)} x^{6} + 2 \, {\left(a b^{7} - 10 \, a^{2} b^{5} c + 30 \, a^{3} b^{3} c^{2} - 20 \, a^{4} b c^{3}\right)} x^{4} + {\left(a^{2} b^{6} - 10 \, a^{3} b^{4} c + 30 \, a^{4} b^{2} c^{2} - 20 \, a^{5} c^{3}\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) - 3 \, {\left({\left(b^{7} c^{2} - 12 \, a b^{5} c^{3} + 48 \, a^{2} b^{3} c^{4} - 64 \, a^{3} b c^{5}\right)} x^{10} + 2 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} x^{8} + {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} x^{6} + 2 \, {\left(a b^{8} - 12 \, a^{2} b^{6} c + 48 \, a^{3} b^{4} c^{2} - 64 \, a^{4} b^{2} c^{3}\right)} x^{4} + {\left(a^{2} b^{7} - 12 \, a^{3} b^{5} c + 48 \, a^{4} b^{3} c^{2} - 64 \, a^{5} b c^{3}\right)} x^{2}\right)} \log\left(c x^{4} + b x^{2} + a\right) + 12 \, {\left({\left(b^{7} c^{2} - 12 \, a b^{5} c^{3} + 48 \, a^{2} b^{3} c^{4} - 64 \, a^{3} b c^{5}\right)} x^{10} + 2 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} x^{8} + {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} x^{6} + 2 \, {\left(a b^{8} - 12 \, a^{2} b^{6} c + 48 \, a^{3} b^{4} c^{2} - 64 \, a^{4} b^{2} c^{3}\right)} x^{4} + {\left(a^{2} b^{7} - 12 \, a^{3} b^{5} c + 48 \, a^{4} b^{3} c^{2} - 64 \, a^{5} b c^{3}\right)} x^{2}\right)} \log\left(x\right)}{4 \, {\left({\left(a^{4} b^{6} c^{2} - 12 \, a^{5} b^{4} c^{3} + 48 \, a^{6} b^{2} c^{4} - 64 \, a^{7} c^{5}\right)} x^{10} + 2 \, {\left(a^{4} b^{7} c - 12 \, a^{5} b^{5} c^{2} + 48 \, a^{6} b^{3} c^{3} - 64 \, a^{7} b c^{4}\right)} x^{8} + {\left(a^{4} b^{8} - 10 \, a^{5} b^{6} c + 24 \, a^{6} b^{4} c^{2} + 32 \, a^{7} b^{2} c^{3} - 128 \, a^{8} c^{4}\right)} x^{6} + 2 \, {\left(a^{5} b^{7} - 12 \, a^{6} b^{5} c + 48 \, a^{7} b^{3} c^{2} - 64 \, a^{8} b c^{3}\right)} x^{4} + {\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}\right)} x^{2}\right)}}\right]"," ",0,"[-1/4*(2*a^3*b^6 - 24*a^4*b^4*c + 96*a^5*b^2*c^2 - 128*a^6*c^3 + 6*(a*b^6*c^2 - 11*a^2*b^4*c^3 + 38*a^3*b^2*c^4 - 40*a^4*c^5)*x^8 + 3*(4*a*b^7*c - 45*a^2*b^5*c^2 + 162*a^3*b^3*c^3 - 184*a^4*b*c^4)*x^6 + 2*(3*a*b^8 - 30*a^2*b^6*c + 79*a^3*b^4*c^2 + 22*a^4*b^2*c^3 - 200*a^5*c^4)*x^4 + (9*a^2*b^7 - 104*a^3*b^5*c + 394*a^4*b^3*c^2 - 488*a^5*b*c^3)*x^2 + 3*((b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*x^10 + 2*(b^7*c - 10*a*b^5*c^2 + 30*a^2*b^3*c^3 - 20*a^3*b*c^4)*x^8 + (b^8 - 8*a*b^6*c + 10*a^2*b^4*c^2 + 40*a^3*b^2*c^3 - 40*a^4*c^4)*x^6 + 2*(a*b^7 - 10*a^2*b^5*c + 30*a^3*b^3*c^2 - 20*a^4*b*c^3)*x^4 + (a^2*b^6 - 10*a^3*b^4*c + 30*a^4*b^2*c^2 - 20*a^5*c^3)*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)) - 3*((b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*x^10 + 2*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*x^8 + (b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*x^6 + 2*(a*b^8 - 12*a^2*b^6*c + 48*a^3*b^4*c^2 - 64*a^4*b^2*c^3)*x^4 + (a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3)*x^2)*log(c*x^4 + b*x^2 + a) + 12*((b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*x^10 + 2*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*x^8 + (b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*x^6 + 2*(a*b^8 - 12*a^2*b^6*c + 48*a^3*b^4*c^2 - 64*a^4*b^2*c^3)*x^4 + (a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3)*x^2)*log(x))/((a^4*b^6*c^2 - 12*a^5*b^4*c^3 + 48*a^6*b^2*c^4 - 64*a^7*c^5)*x^10 + 2*(a^4*b^7*c - 12*a^5*b^5*c^2 + 48*a^6*b^3*c^3 - 64*a^7*b*c^4)*x^8 + (a^4*b^8 - 10*a^5*b^6*c + 24*a^6*b^4*c^2 + 32*a^7*b^2*c^3 - 128*a^8*c^4)*x^6 + 2*(a^5*b^7 - 12*a^6*b^5*c + 48*a^7*b^3*c^2 - 64*a^8*b*c^3)*x^4 + (a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*x^2), -1/4*(2*a^3*b^6 - 24*a^4*b^4*c + 96*a^5*b^2*c^2 - 128*a^6*c^3 + 6*(a*b^6*c^2 - 11*a^2*b^4*c^3 + 38*a^3*b^2*c^4 - 40*a^4*c^5)*x^8 + 3*(4*a*b^7*c - 45*a^2*b^5*c^2 + 162*a^3*b^3*c^3 - 184*a^4*b*c^4)*x^6 + 2*(3*a*b^8 - 30*a^2*b^6*c + 79*a^3*b^4*c^2 + 22*a^4*b^2*c^3 - 200*a^5*c^4)*x^4 + (9*a^2*b^7 - 104*a^3*b^5*c + 394*a^4*b^3*c^2 - 488*a^5*b*c^3)*x^2 + 6*((b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*x^10 + 2*(b^7*c - 10*a*b^5*c^2 + 30*a^2*b^3*c^3 - 20*a^3*b*c^4)*x^8 + (b^8 - 8*a*b^6*c + 10*a^2*b^4*c^2 + 40*a^3*b^2*c^3 - 40*a^4*c^4)*x^6 + 2*(a*b^7 - 10*a^2*b^5*c + 30*a^3*b^3*c^2 - 20*a^4*b*c^3)*x^4 + (a^2*b^6 - 10*a^3*b^4*c + 30*a^4*b^2*c^2 - 20*a^5*c^3)*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)) - 3*((b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*x^10 + 2*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*x^8 + (b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*x^6 + 2*(a*b^8 - 12*a^2*b^6*c + 48*a^3*b^4*c^2 - 64*a^4*b^2*c^3)*x^4 + (a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3)*x^2)*log(c*x^4 + b*x^2 + a) + 12*((b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*x^10 + 2*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*x^8 + (b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*x^6 + 2*(a*b^8 - 12*a^2*b^6*c + 48*a^3*b^4*c^2 - 64*a^4*b^2*c^3)*x^4 + (a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3)*x^2)*log(x))/((a^4*b^6*c^2 - 12*a^5*b^4*c^3 + 48*a^6*b^2*c^4 - 64*a^7*c^5)*x^10 + 2*(a^4*b^7*c - 12*a^5*b^5*c^2 + 48*a^6*b^3*c^3 - 64*a^7*b*c^4)*x^8 + (a^4*b^8 - 10*a^5*b^6*c + 24*a^6*b^4*c^2 + 32*a^7*b^2*c^3 - 128*a^8*c^4)*x^6 + 2*(a^5*b^7 - 12*a^6*b^5*c + 48*a^7*b^3*c^2 - 64*a^8*b*c^3)*x^4 + (a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*x^2)]","B",0
881,1,4279,0,2.006162," ","integrate(x^10/(c*x^4+b*x^2+a)^3,x, algorithm=""fricas"")","-\frac{2 \, {\left(5 \, b^{4} c - 37 \, a b^{2} c^{2} + 44 \, a^{2} c^{3}\right)} x^{7} + 2 \, {\left(3 \, b^{5} - 20 \, a b^{3} c - 4 \, a^{2} b c^{2}\right)} x^{5} + 2 \, {\left(6 \, a b^{4} - 49 \, a^{2} b^{2} c + 28 \, a^{3} c^{2}\right)} x^{3} + 3 \, \sqrt{\frac{1}{2}} {\left({\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} x^{8} + a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4} + 2 \, {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} x^{6} + {\left(b^{6} c^{2} - 6 \, a b^{4} c^{3} + 32 \, a^{3} c^{5}\right)} x^{4} + 2 \, {\left(a b^{5} c^{2} - 8 \, a^{2} b^{3} c^{3} + 16 \, a^{3} b c^{4}\right)} x^{2}\right)} \sqrt{-\frac{b^{9} - 21 \, a b^{7} c + 189 \, a^{2} b^{5} c^{2} - 840 \, a^{3} b^{3} c^{3} + 1680 \, a^{4} b c^{4} + {\left(b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}\right)} \sqrt{\frac{b^{8} - 22 \, a b^{6} c + 219 \, a^{2} b^{4} c^{2} - 1078 \, a^{3} b^{2} c^{3} + 2401 \, a^{4} c^{4}}{b^{10} c^{10} - 20 \, a b^{8} c^{11} + 160 \, a^{2} b^{6} c^{12} - 640 \, a^{3} b^{4} c^{13} + 1280 \, a^{4} b^{2} c^{14} - 1024 \, a^{5} c^{15}}}}{b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}}} \log\left(27 \, {\left(21 \, a^{2} b^{8} - 447 \, a^{3} b^{6} c + 4189 \, a^{4} b^{4} c^{2} - 19208 \, a^{5} b^{2} c^{3} + 38416 \, a^{6} c^{4}\right)} x + \frac{27}{2} \, \sqrt{\frac{1}{2}} {\left(b^{13} - 31 \, a b^{11} c + 413 \, a^{2} b^{9} c^{2} - 3012 \, a^{3} b^{7} c^{3} + 12496 \, a^{4} b^{5} c^{4} - 27584 \, a^{5} b^{3} c^{5} + 25088 \, a^{6} b c^{6} - {\left(b^{14} c^{5} - 30 \, a b^{12} c^{6} + 416 \, a^{2} b^{10} c^{7} - 3360 \, a^{3} b^{8} c^{8} + 16640 \, a^{4} b^{6} c^{9} - 49664 \, a^{5} b^{4} c^{10} + 81920 \, a^{6} b^{2} c^{11} - 57344 \, a^{7} c^{12}\right)} \sqrt{\frac{b^{8} - 22 \, a b^{6} c + 219 \, a^{2} b^{4} c^{2} - 1078 \, a^{3} b^{2} c^{3} + 2401 \, a^{4} c^{4}}{b^{10} c^{10} - 20 \, a b^{8} c^{11} + 160 \, a^{2} b^{6} c^{12} - 640 \, a^{3} b^{4} c^{13} + 1280 \, a^{4} b^{2} c^{14} - 1024 \, a^{5} c^{15}}}\right)} \sqrt{-\frac{b^{9} - 21 \, a b^{7} c + 189 \, a^{2} b^{5} c^{2} - 840 \, a^{3} b^{3} c^{3} + 1680 \, a^{4} b c^{4} + {\left(b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}\right)} \sqrt{\frac{b^{8} - 22 \, a b^{6} c + 219 \, a^{2} b^{4} c^{2} - 1078 \, a^{3} b^{2} c^{3} + 2401 \, a^{4} c^{4}}{b^{10} c^{10} - 20 \, a b^{8} c^{11} + 160 \, a^{2} b^{6} c^{12} - 640 \, a^{3} b^{4} c^{13} + 1280 \, a^{4} b^{2} c^{14} - 1024 \, a^{5} c^{15}}}}{b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}}}\right) - 3 \, \sqrt{\frac{1}{2}} {\left({\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} x^{8} + a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4} + 2 \, {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} x^{6} + {\left(b^{6} c^{2} - 6 \, a b^{4} c^{3} + 32 \, a^{3} c^{5}\right)} x^{4} + 2 \, {\left(a b^{5} c^{2} - 8 \, a^{2} b^{3} c^{3} + 16 \, a^{3} b c^{4}\right)} x^{2}\right)} \sqrt{-\frac{b^{9} - 21 \, a b^{7} c + 189 \, a^{2} b^{5} c^{2} - 840 \, a^{3} b^{3} c^{3} + 1680 \, a^{4} b c^{4} + {\left(b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}\right)} \sqrt{\frac{b^{8} - 22 \, a b^{6} c + 219 \, a^{2} b^{4} c^{2} - 1078 \, a^{3} b^{2} c^{3} + 2401 \, a^{4} c^{4}}{b^{10} c^{10} - 20 \, a b^{8} c^{11} + 160 \, a^{2} b^{6} c^{12} - 640 \, a^{3} b^{4} c^{13} + 1280 \, a^{4} b^{2} c^{14} - 1024 \, a^{5} c^{15}}}}{b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}}} \log\left(27 \, {\left(21 \, a^{2} b^{8} - 447 \, a^{3} b^{6} c + 4189 \, a^{4} b^{4} c^{2} - 19208 \, a^{5} b^{2} c^{3} + 38416 \, a^{6} c^{4}\right)} x - \frac{27}{2} \, \sqrt{\frac{1}{2}} {\left(b^{13} - 31 \, a b^{11} c + 413 \, a^{2} b^{9} c^{2} - 3012 \, a^{3} b^{7} c^{3} + 12496 \, a^{4} b^{5} c^{4} - 27584 \, a^{5} b^{3} c^{5} + 25088 \, a^{6} b c^{6} - {\left(b^{14} c^{5} - 30 \, a b^{12} c^{6} + 416 \, a^{2} b^{10} c^{7} - 3360 \, a^{3} b^{8} c^{8} + 16640 \, a^{4} b^{6} c^{9} - 49664 \, a^{5} b^{4} c^{10} + 81920 \, a^{6} b^{2} c^{11} - 57344 \, a^{7} c^{12}\right)} \sqrt{\frac{b^{8} - 22 \, a b^{6} c + 219 \, a^{2} b^{4} c^{2} - 1078 \, a^{3} b^{2} c^{3} + 2401 \, a^{4} c^{4}}{b^{10} c^{10} - 20 \, a b^{8} c^{11} + 160 \, a^{2} b^{6} c^{12} - 640 \, a^{3} b^{4} c^{13} + 1280 \, a^{4} b^{2} c^{14} - 1024 \, a^{5} c^{15}}}\right)} \sqrt{-\frac{b^{9} - 21 \, a b^{7} c + 189 \, a^{2} b^{5} c^{2} - 840 \, a^{3} b^{3} c^{3} + 1680 \, a^{4} b c^{4} + {\left(b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}\right)} \sqrt{\frac{b^{8} - 22 \, a b^{6} c + 219 \, a^{2} b^{4} c^{2} - 1078 \, a^{3} b^{2} c^{3} + 2401 \, a^{4} c^{4}}{b^{10} c^{10} - 20 \, a b^{8} c^{11} + 160 \, a^{2} b^{6} c^{12} - 640 \, a^{3} b^{4} c^{13} + 1280 \, a^{4} b^{2} c^{14} - 1024 \, a^{5} c^{15}}}}{b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}}}\right) + 3 \, \sqrt{\frac{1}{2}} {\left({\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} x^{8} + a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4} + 2 \, {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} x^{6} + {\left(b^{6} c^{2} - 6 \, a b^{4} c^{3} + 32 \, a^{3} c^{5}\right)} x^{4} + 2 \, {\left(a b^{5} c^{2} - 8 \, a^{2} b^{3} c^{3} + 16 \, a^{3} b c^{4}\right)} x^{2}\right)} \sqrt{-\frac{b^{9} - 21 \, a b^{7} c + 189 \, a^{2} b^{5} c^{2} - 840 \, a^{3} b^{3} c^{3} + 1680 \, a^{4} b c^{4} - {\left(b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}\right)} \sqrt{\frac{b^{8} - 22 \, a b^{6} c + 219 \, a^{2} b^{4} c^{2} - 1078 \, a^{3} b^{2} c^{3} + 2401 \, a^{4} c^{4}}{b^{10} c^{10} - 20 \, a b^{8} c^{11} + 160 \, a^{2} b^{6} c^{12} - 640 \, a^{3} b^{4} c^{13} + 1280 \, a^{4} b^{2} c^{14} - 1024 \, a^{5} c^{15}}}}{b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}}} \log\left(27 \, {\left(21 \, a^{2} b^{8} - 447 \, a^{3} b^{6} c + 4189 \, a^{4} b^{4} c^{2} - 19208 \, a^{5} b^{2} c^{3} + 38416 \, a^{6} c^{4}\right)} x + \frac{27}{2} \, \sqrt{\frac{1}{2}} {\left(b^{13} - 31 \, a b^{11} c + 413 \, a^{2} b^{9} c^{2} - 3012 \, a^{3} b^{7} c^{3} + 12496 \, a^{4} b^{5} c^{4} - 27584 \, a^{5} b^{3} c^{5} + 25088 \, a^{6} b c^{6} + {\left(b^{14} c^{5} - 30 \, a b^{12} c^{6} + 416 \, a^{2} b^{10} c^{7} - 3360 \, a^{3} b^{8} c^{8} + 16640 \, a^{4} b^{6} c^{9} - 49664 \, a^{5} b^{4} c^{10} + 81920 \, a^{6} b^{2} c^{11} - 57344 \, a^{7} c^{12}\right)} \sqrt{\frac{b^{8} - 22 \, a b^{6} c + 219 \, a^{2} b^{4} c^{2} - 1078 \, a^{3} b^{2} c^{3} + 2401 \, a^{4} c^{4}}{b^{10} c^{10} - 20 \, a b^{8} c^{11} + 160 \, a^{2} b^{6} c^{12} - 640 \, a^{3} b^{4} c^{13} + 1280 \, a^{4} b^{2} c^{14} - 1024 \, a^{5} c^{15}}}\right)} \sqrt{-\frac{b^{9} - 21 \, a b^{7} c + 189 \, a^{2} b^{5} c^{2} - 840 \, a^{3} b^{3} c^{3} + 1680 \, a^{4} b c^{4} - {\left(b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}\right)} \sqrt{\frac{b^{8} - 22 \, a b^{6} c + 219 \, a^{2} b^{4} c^{2} - 1078 \, a^{3} b^{2} c^{3} + 2401 \, a^{4} c^{4}}{b^{10} c^{10} - 20 \, a b^{8} c^{11} + 160 \, a^{2} b^{6} c^{12} - 640 \, a^{3} b^{4} c^{13} + 1280 \, a^{4} b^{2} c^{14} - 1024 \, a^{5} c^{15}}}}{b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}}}\right) - 3 \, \sqrt{\frac{1}{2}} {\left({\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} x^{8} + a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4} + 2 \, {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} x^{6} + {\left(b^{6} c^{2} - 6 \, a b^{4} c^{3} + 32 \, a^{3} c^{5}\right)} x^{4} + 2 \, {\left(a b^{5} c^{2} - 8 \, a^{2} b^{3} c^{3} + 16 \, a^{3} b c^{4}\right)} x^{2}\right)} \sqrt{-\frac{b^{9} - 21 \, a b^{7} c + 189 \, a^{2} b^{5} c^{2} - 840 \, a^{3} b^{3} c^{3} + 1680 \, a^{4} b c^{4} - {\left(b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}\right)} \sqrt{\frac{b^{8} - 22 \, a b^{6} c + 219 \, a^{2} b^{4} c^{2} - 1078 \, a^{3} b^{2} c^{3} + 2401 \, a^{4} c^{4}}{b^{10} c^{10} - 20 \, a b^{8} c^{11} + 160 \, a^{2} b^{6} c^{12} - 640 \, a^{3} b^{4} c^{13} + 1280 \, a^{4} b^{2} c^{14} - 1024 \, a^{5} c^{15}}}}{b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}}} \log\left(27 \, {\left(21 \, a^{2} b^{8} - 447 \, a^{3} b^{6} c + 4189 \, a^{4} b^{4} c^{2} - 19208 \, a^{5} b^{2} c^{3} + 38416 \, a^{6} c^{4}\right)} x - \frac{27}{2} \, \sqrt{\frac{1}{2}} {\left(b^{13} - 31 \, a b^{11} c + 413 \, a^{2} b^{9} c^{2} - 3012 \, a^{3} b^{7} c^{3} + 12496 \, a^{4} b^{5} c^{4} - 27584 \, a^{5} b^{3} c^{5} + 25088 \, a^{6} b c^{6} + {\left(b^{14} c^{5} - 30 \, a b^{12} c^{6} + 416 \, a^{2} b^{10} c^{7} - 3360 \, a^{3} b^{8} c^{8} + 16640 \, a^{4} b^{6} c^{9} - 49664 \, a^{5} b^{4} c^{10} + 81920 \, a^{6} b^{2} c^{11} - 57344 \, a^{7} c^{12}\right)} \sqrt{\frac{b^{8} - 22 \, a b^{6} c + 219 \, a^{2} b^{4} c^{2} - 1078 \, a^{3} b^{2} c^{3} + 2401 \, a^{4} c^{4}}{b^{10} c^{10} - 20 \, a b^{8} c^{11} + 160 \, a^{2} b^{6} c^{12} - 640 \, a^{3} b^{4} c^{13} + 1280 \, a^{4} b^{2} c^{14} - 1024 \, a^{5} c^{15}}}\right)} \sqrt{-\frac{b^{9} - 21 \, a b^{7} c + 189 \, a^{2} b^{5} c^{2} - 840 \, a^{3} b^{3} c^{3} + 1680 \, a^{4} b c^{4} - {\left(b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}\right)} \sqrt{\frac{b^{8} - 22 \, a b^{6} c + 219 \, a^{2} b^{4} c^{2} - 1078 \, a^{3} b^{2} c^{3} + 2401 \, a^{4} c^{4}}{b^{10} c^{10} - 20 \, a b^{8} c^{11} + 160 \, a^{2} b^{6} c^{12} - 640 \, a^{3} b^{4} c^{13} + 1280 \, a^{4} b^{2} c^{14} - 1024 \, a^{5} c^{15}}}}{b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}}}\right) + 6 \, {\left(a^{2} b^{3} - 8 \, a^{3} b c\right)} x}{16 \, {\left({\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} x^{8} + a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4} + 2 \, {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} x^{6} + {\left(b^{6} c^{2} - 6 \, a b^{4} c^{3} + 32 \, a^{3} c^{5}\right)} x^{4} + 2 \, {\left(a b^{5} c^{2} - 8 \, a^{2} b^{3} c^{3} + 16 \, a^{3} b c^{4}\right)} x^{2}\right)}}"," ",0,"-1/16*(2*(5*b^4*c - 37*a*b^2*c^2 + 44*a^2*c^3)*x^7 + 2*(3*b^5 - 20*a*b^3*c - 4*a^2*b*c^2)*x^5 + 2*(6*a*b^4 - 49*a^2*b^2*c + 28*a^3*c^2)*x^3 + 3*sqrt(1/2)*((b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*x^8 + a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4 + 2*(b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*x^6 + (b^6*c^2 - 6*a*b^4*c^3 + 32*a^3*c^5)*x^4 + 2*(a*b^5*c^2 - 8*a^2*b^3*c^3 + 16*a^3*b*c^4)*x^2)*sqrt(-(b^9 - 21*a*b^7*c + 189*a^2*b^5*c^2 - 840*a^3*b^3*c^3 + 1680*a^4*b*c^4 + (b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10)*sqrt((b^8 - 22*a*b^6*c + 219*a^2*b^4*c^2 - 1078*a^3*b^2*c^3 + 2401*a^4*c^4)/(b^10*c^10 - 20*a*b^8*c^11 + 160*a^2*b^6*c^12 - 640*a^3*b^4*c^13 + 1280*a^4*b^2*c^14 - 1024*a^5*c^15)))/(b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10))*log(27*(21*a^2*b^8 - 447*a^3*b^6*c + 4189*a^4*b^4*c^2 - 19208*a^5*b^2*c^3 + 38416*a^6*c^4)*x + 27/2*sqrt(1/2)*(b^13 - 31*a*b^11*c + 413*a^2*b^9*c^2 - 3012*a^3*b^7*c^3 + 12496*a^4*b^5*c^4 - 27584*a^5*b^3*c^5 + 25088*a^6*b*c^6 - (b^14*c^5 - 30*a*b^12*c^6 + 416*a^2*b^10*c^7 - 3360*a^3*b^8*c^8 + 16640*a^4*b^6*c^9 - 49664*a^5*b^4*c^10 + 81920*a^6*b^2*c^11 - 57344*a^7*c^12)*sqrt((b^8 - 22*a*b^6*c + 219*a^2*b^4*c^2 - 1078*a^3*b^2*c^3 + 2401*a^4*c^4)/(b^10*c^10 - 20*a*b^8*c^11 + 160*a^2*b^6*c^12 - 640*a^3*b^4*c^13 + 1280*a^4*b^2*c^14 - 1024*a^5*c^15)))*sqrt(-(b^9 - 21*a*b^7*c + 189*a^2*b^5*c^2 - 840*a^3*b^3*c^3 + 1680*a^4*b*c^4 + (b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10)*sqrt((b^8 - 22*a*b^6*c + 219*a^2*b^4*c^2 - 1078*a^3*b^2*c^3 + 2401*a^4*c^4)/(b^10*c^10 - 20*a*b^8*c^11 + 160*a^2*b^6*c^12 - 640*a^3*b^4*c^13 + 1280*a^4*b^2*c^14 - 1024*a^5*c^15)))/(b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10))) - 3*sqrt(1/2)*((b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*x^8 + a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4 + 2*(b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*x^6 + (b^6*c^2 - 6*a*b^4*c^3 + 32*a^3*c^5)*x^4 + 2*(a*b^5*c^2 - 8*a^2*b^3*c^3 + 16*a^3*b*c^4)*x^2)*sqrt(-(b^9 - 21*a*b^7*c + 189*a^2*b^5*c^2 - 840*a^3*b^3*c^3 + 1680*a^4*b*c^4 + (b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10)*sqrt((b^8 - 22*a*b^6*c + 219*a^2*b^4*c^2 - 1078*a^3*b^2*c^3 + 2401*a^4*c^4)/(b^10*c^10 - 20*a*b^8*c^11 + 160*a^2*b^6*c^12 - 640*a^3*b^4*c^13 + 1280*a^4*b^2*c^14 - 1024*a^5*c^15)))/(b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10))*log(27*(21*a^2*b^8 - 447*a^3*b^6*c + 4189*a^4*b^4*c^2 - 19208*a^5*b^2*c^3 + 38416*a^6*c^4)*x - 27/2*sqrt(1/2)*(b^13 - 31*a*b^11*c + 413*a^2*b^9*c^2 - 3012*a^3*b^7*c^3 + 12496*a^4*b^5*c^4 - 27584*a^5*b^3*c^5 + 25088*a^6*b*c^6 - (b^14*c^5 - 30*a*b^12*c^6 + 416*a^2*b^10*c^7 - 3360*a^3*b^8*c^8 + 16640*a^4*b^6*c^9 - 49664*a^5*b^4*c^10 + 81920*a^6*b^2*c^11 - 57344*a^7*c^12)*sqrt((b^8 - 22*a*b^6*c + 219*a^2*b^4*c^2 - 1078*a^3*b^2*c^3 + 2401*a^4*c^4)/(b^10*c^10 - 20*a*b^8*c^11 + 160*a^2*b^6*c^12 - 640*a^3*b^4*c^13 + 1280*a^4*b^2*c^14 - 1024*a^5*c^15)))*sqrt(-(b^9 - 21*a*b^7*c + 189*a^2*b^5*c^2 - 840*a^3*b^3*c^3 + 1680*a^4*b*c^4 + (b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10)*sqrt((b^8 - 22*a*b^6*c + 219*a^2*b^4*c^2 - 1078*a^3*b^2*c^3 + 2401*a^4*c^4)/(b^10*c^10 - 20*a*b^8*c^11 + 160*a^2*b^6*c^12 - 640*a^3*b^4*c^13 + 1280*a^4*b^2*c^14 - 1024*a^5*c^15)))/(b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10))) + 3*sqrt(1/2)*((b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*x^8 + a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4 + 2*(b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*x^6 + (b^6*c^2 - 6*a*b^4*c^3 + 32*a^3*c^5)*x^4 + 2*(a*b^5*c^2 - 8*a^2*b^3*c^3 + 16*a^3*b*c^4)*x^2)*sqrt(-(b^9 - 21*a*b^7*c + 189*a^2*b^5*c^2 - 840*a^3*b^3*c^3 + 1680*a^4*b*c^4 - (b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10)*sqrt((b^8 - 22*a*b^6*c + 219*a^2*b^4*c^2 - 1078*a^3*b^2*c^3 + 2401*a^4*c^4)/(b^10*c^10 - 20*a*b^8*c^11 + 160*a^2*b^6*c^12 - 640*a^3*b^4*c^13 + 1280*a^4*b^2*c^14 - 1024*a^5*c^15)))/(b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10))*log(27*(21*a^2*b^8 - 447*a^3*b^6*c + 4189*a^4*b^4*c^2 - 19208*a^5*b^2*c^3 + 38416*a^6*c^4)*x + 27/2*sqrt(1/2)*(b^13 - 31*a*b^11*c + 413*a^2*b^9*c^2 - 3012*a^3*b^7*c^3 + 12496*a^4*b^5*c^4 - 27584*a^5*b^3*c^5 + 25088*a^6*b*c^6 + (b^14*c^5 - 30*a*b^12*c^6 + 416*a^2*b^10*c^7 - 3360*a^3*b^8*c^8 + 16640*a^4*b^6*c^9 - 49664*a^5*b^4*c^10 + 81920*a^6*b^2*c^11 - 57344*a^7*c^12)*sqrt((b^8 - 22*a*b^6*c + 219*a^2*b^4*c^2 - 1078*a^3*b^2*c^3 + 2401*a^4*c^4)/(b^10*c^10 - 20*a*b^8*c^11 + 160*a^2*b^6*c^12 - 640*a^3*b^4*c^13 + 1280*a^4*b^2*c^14 - 1024*a^5*c^15)))*sqrt(-(b^9 - 21*a*b^7*c + 189*a^2*b^5*c^2 - 840*a^3*b^3*c^3 + 1680*a^4*b*c^4 - (b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10)*sqrt((b^8 - 22*a*b^6*c + 219*a^2*b^4*c^2 - 1078*a^3*b^2*c^3 + 2401*a^4*c^4)/(b^10*c^10 - 20*a*b^8*c^11 + 160*a^2*b^6*c^12 - 640*a^3*b^4*c^13 + 1280*a^4*b^2*c^14 - 1024*a^5*c^15)))/(b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10))) - 3*sqrt(1/2)*((b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*x^8 + a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4 + 2*(b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*x^6 + (b^6*c^2 - 6*a*b^4*c^3 + 32*a^3*c^5)*x^4 + 2*(a*b^5*c^2 - 8*a^2*b^3*c^3 + 16*a^3*b*c^4)*x^2)*sqrt(-(b^9 - 21*a*b^7*c + 189*a^2*b^5*c^2 - 840*a^3*b^3*c^3 + 1680*a^4*b*c^4 - (b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10)*sqrt((b^8 - 22*a*b^6*c + 219*a^2*b^4*c^2 - 1078*a^3*b^2*c^3 + 2401*a^4*c^4)/(b^10*c^10 - 20*a*b^8*c^11 + 160*a^2*b^6*c^12 - 640*a^3*b^4*c^13 + 1280*a^4*b^2*c^14 - 1024*a^5*c^15)))/(b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10))*log(27*(21*a^2*b^8 - 447*a^3*b^6*c + 4189*a^4*b^4*c^2 - 19208*a^5*b^2*c^3 + 38416*a^6*c^4)*x - 27/2*sqrt(1/2)*(b^13 - 31*a*b^11*c + 413*a^2*b^9*c^2 - 3012*a^3*b^7*c^3 + 12496*a^4*b^5*c^4 - 27584*a^5*b^3*c^5 + 25088*a^6*b*c^6 + (b^14*c^5 - 30*a*b^12*c^6 + 416*a^2*b^10*c^7 - 3360*a^3*b^8*c^8 + 16640*a^4*b^6*c^9 - 49664*a^5*b^4*c^10 + 81920*a^6*b^2*c^11 - 57344*a^7*c^12)*sqrt((b^8 - 22*a*b^6*c + 219*a^2*b^4*c^2 - 1078*a^3*b^2*c^3 + 2401*a^4*c^4)/(b^10*c^10 - 20*a*b^8*c^11 + 160*a^2*b^6*c^12 - 640*a^3*b^4*c^13 + 1280*a^4*b^2*c^14 - 1024*a^5*c^15)))*sqrt(-(b^9 - 21*a*b^7*c + 189*a^2*b^5*c^2 - 840*a^3*b^3*c^3 + 1680*a^4*b*c^4 - (b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10)*sqrt((b^8 - 22*a*b^6*c + 219*a^2*b^4*c^2 - 1078*a^3*b^2*c^3 + 2401*a^4*c^4)/(b^10*c^10 - 20*a*b^8*c^11 + 160*a^2*b^6*c^12 - 640*a^3*b^4*c^13 + 1280*a^4*b^2*c^14 - 1024*a^5*c^15)))/(b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10))) + 6*(a^2*b^3 - 8*a^3*b*c)*x)/((b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*x^8 + a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4 + 2*(b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*x^6 + (b^6*c^2 - 6*a*b^4*c^3 + 32*a^3*c^5)*x^4 + 2*(a*b^5*c^2 - 8*a^2*b^3*c^3 + 16*a^3*b*c^4)*x^2)","B",0
882,1,3725,0,2.289111," ","integrate(x^8/(c*x^4+b*x^2+a)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(b^{3} c - 16 \, a b c^{2}\right)} x^{7} - 2 \, {\left(b^{4} + 5 \, a b^{2} c + 36 \, a^{2} c^{2}\right)} x^{5} - 4 \, {\left(a b^{3} + 14 \, a^{2} b c\right)} x^{3} + \sqrt{\frac{1}{2}} {\left({\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} x^{8} + a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3} + 2 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} x^{6} + {\left(b^{6} c - 6 \, a b^{4} c^{2} + 32 \, a^{3} c^{4}\right)} x^{4} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} x^{2}\right)} \sqrt{-\frac{b^{7} - 35 \, a b^{5} c + 280 \, a^{2} b^{3} c^{2} + 1680 \, a^{3} b c^{3} + {\left(b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}\right)} \sqrt{\frac{b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}}{b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}}}}{b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}}} \log\left({\left(35 \, a b^{6} - 1491 \, a^{2} b^{4} c + 15000 \, a^{3} b^{2} c^{2} + 10000 \, a^{4} c^{3}\right)} x + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{10} - 17 \, a b^{8} c - 392 \, a^{2} b^{6} c^{2} + 5696 \, a^{3} b^{4} c^{3} - 23680 \, a^{4} b^{2} c^{4} + 32000 \, a^{5} c^{5} - {\left(b^{13} c^{3} - 72 \, a b^{11} c^{4} + 1200 \, a^{2} b^{9} c^{5} - 8960 \, a^{3} b^{7} c^{6} + 34560 \, a^{4} b^{5} c^{7} - 67584 \, a^{5} b^{3} c^{8} + 53248 \, a^{6} b c^{9}\right)} \sqrt{\frac{b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}}{b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}}}\right)} \sqrt{-\frac{b^{7} - 35 \, a b^{5} c + 280 \, a^{2} b^{3} c^{2} + 1680 \, a^{3} b c^{3} + {\left(b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}\right)} \sqrt{\frac{b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}}{b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}}}}{b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}}}\right) - \sqrt{\frac{1}{2}} {\left({\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} x^{8} + a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3} + 2 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} x^{6} + {\left(b^{6} c - 6 \, a b^{4} c^{2} + 32 \, a^{3} c^{4}\right)} x^{4} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} x^{2}\right)} \sqrt{-\frac{b^{7} - 35 \, a b^{5} c + 280 \, a^{2} b^{3} c^{2} + 1680 \, a^{3} b c^{3} + {\left(b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}\right)} \sqrt{\frac{b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}}{b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}}}}{b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}}} \log\left({\left(35 \, a b^{6} - 1491 \, a^{2} b^{4} c + 15000 \, a^{3} b^{2} c^{2} + 10000 \, a^{4} c^{3}\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{10} - 17 \, a b^{8} c - 392 \, a^{2} b^{6} c^{2} + 5696 \, a^{3} b^{4} c^{3} - 23680 \, a^{4} b^{2} c^{4} + 32000 \, a^{5} c^{5} - {\left(b^{13} c^{3} - 72 \, a b^{11} c^{4} + 1200 \, a^{2} b^{9} c^{5} - 8960 \, a^{3} b^{7} c^{6} + 34560 \, a^{4} b^{5} c^{7} - 67584 \, a^{5} b^{3} c^{8} + 53248 \, a^{6} b c^{9}\right)} \sqrt{\frac{b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}}{b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}}}\right)} \sqrt{-\frac{b^{7} - 35 \, a b^{5} c + 280 \, a^{2} b^{3} c^{2} + 1680 \, a^{3} b c^{3} + {\left(b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}\right)} \sqrt{\frac{b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}}{b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}}}}{b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}}}\right) + \sqrt{\frac{1}{2}} {\left({\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} x^{8} + a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3} + 2 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} x^{6} + {\left(b^{6} c - 6 \, a b^{4} c^{2} + 32 \, a^{3} c^{4}\right)} x^{4} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} x^{2}\right)} \sqrt{-\frac{b^{7} - 35 \, a b^{5} c + 280 \, a^{2} b^{3} c^{2} + 1680 \, a^{3} b c^{3} - {\left(b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}\right)} \sqrt{\frac{b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}}{b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}}}}{b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}}} \log\left({\left(35 \, a b^{6} - 1491 \, a^{2} b^{4} c + 15000 \, a^{3} b^{2} c^{2} + 10000 \, a^{4} c^{3}\right)} x + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{10} - 17 \, a b^{8} c - 392 \, a^{2} b^{6} c^{2} + 5696 \, a^{3} b^{4} c^{3} - 23680 \, a^{4} b^{2} c^{4} + 32000 \, a^{5} c^{5} + {\left(b^{13} c^{3} - 72 \, a b^{11} c^{4} + 1200 \, a^{2} b^{9} c^{5} - 8960 \, a^{3} b^{7} c^{6} + 34560 \, a^{4} b^{5} c^{7} - 67584 \, a^{5} b^{3} c^{8} + 53248 \, a^{6} b c^{9}\right)} \sqrt{\frac{b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}}{b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}}}\right)} \sqrt{-\frac{b^{7} - 35 \, a b^{5} c + 280 \, a^{2} b^{3} c^{2} + 1680 \, a^{3} b c^{3} - {\left(b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}\right)} \sqrt{\frac{b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}}{b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}}}}{b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}}}\right) - \sqrt{\frac{1}{2}} {\left({\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} x^{8} + a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3} + 2 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} x^{6} + {\left(b^{6} c - 6 \, a b^{4} c^{2} + 32 \, a^{3} c^{4}\right)} x^{4} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} x^{2}\right)} \sqrt{-\frac{b^{7} - 35 \, a b^{5} c + 280 \, a^{2} b^{3} c^{2} + 1680 \, a^{3} b c^{3} - {\left(b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}\right)} \sqrt{\frac{b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}}{b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}}}}{b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}}} \log\left({\left(35 \, a b^{6} - 1491 \, a^{2} b^{4} c + 15000 \, a^{3} b^{2} c^{2} + 10000 \, a^{4} c^{3}\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{10} - 17 \, a b^{8} c - 392 \, a^{2} b^{6} c^{2} + 5696 \, a^{3} b^{4} c^{3} - 23680 \, a^{4} b^{2} c^{4} + 32000 \, a^{5} c^{5} + {\left(b^{13} c^{3} - 72 \, a b^{11} c^{4} + 1200 \, a^{2} b^{9} c^{5} - 8960 \, a^{3} b^{7} c^{6} + 34560 \, a^{4} b^{5} c^{7} - 67584 \, a^{5} b^{3} c^{8} + 53248 \, a^{6} b c^{9}\right)} \sqrt{\frac{b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}}{b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}}}\right)} \sqrt{-\frac{b^{7} - 35 \, a b^{5} c + 280 \, a^{2} b^{3} c^{2} + 1680 \, a^{3} b c^{3} - {\left(b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}\right)} \sqrt{\frac{b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}}{b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}}}}{b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}}}\right) - 2 \, {\left(a^{2} b^{2} + 20 \, a^{3} c\right)} x}{16 \, {\left({\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} x^{8} + a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3} + 2 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} x^{6} + {\left(b^{6} c - 6 \, a b^{4} c^{2} + 32 \, a^{3} c^{4}\right)} x^{4} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} x^{2}\right)}}"," ",0,"1/16*(2*(b^3*c - 16*a*b*c^2)*x^7 - 2*(b^4 + 5*a*b^2*c + 36*a^2*c^2)*x^5 - 4*(a*b^3 + 14*a^2*b*c)*x^3 + sqrt(1/2)*((b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*x^8 + a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3 + 2*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*x^6 + (b^6*c - 6*a*b^4*c^2 + 32*a^3*c^4)*x^4 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*x^2)*sqrt(-(b^7 - 35*a*b^5*c + 280*a^2*b^3*c^2 + 1680*a^3*b*c^3 + (b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8)*sqrt((b^4 - 50*a*b^2*c + 625*a^2*c^2)/(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)))/(b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8))*log((35*a*b^6 - 1491*a^2*b^4*c + 15000*a^3*b^2*c^2 + 10000*a^4*c^3)*x + 1/2*sqrt(1/2)*(b^10 - 17*a*b^8*c - 392*a^2*b^6*c^2 + 5696*a^3*b^4*c^3 - 23680*a^4*b^2*c^4 + 32000*a^5*c^5 - (b^13*c^3 - 72*a*b^11*c^4 + 1200*a^2*b^9*c^5 - 8960*a^3*b^7*c^6 + 34560*a^4*b^5*c^7 - 67584*a^5*b^3*c^8 + 53248*a^6*b*c^9)*sqrt((b^4 - 50*a*b^2*c + 625*a^2*c^2)/(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)))*sqrt(-(b^7 - 35*a*b^5*c + 280*a^2*b^3*c^2 + 1680*a^3*b*c^3 + (b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8)*sqrt((b^4 - 50*a*b^2*c + 625*a^2*c^2)/(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)))/(b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8))) - sqrt(1/2)*((b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*x^8 + a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3 + 2*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*x^6 + (b^6*c - 6*a*b^4*c^2 + 32*a^3*c^4)*x^4 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*x^2)*sqrt(-(b^7 - 35*a*b^5*c + 280*a^2*b^3*c^2 + 1680*a^3*b*c^3 + (b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8)*sqrt((b^4 - 50*a*b^2*c + 625*a^2*c^2)/(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)))/(b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8))*log((35*a*b^6 - 1491*a^2*b^4*c + 15000*a^3*b^2*c^2 + 10000*a^4*c^3)*x - 1/2*sqrt(1/2)*(b^10 - 17*a*b^8*c - 392*a^2*b^6*c^2 + 5696*a^3*b^4*c^3 - 23680*a^4*b^2*c^4 + 32000*a^5*c^5 - (b^13*c^3 - 72*a*b^11*c^4 + 1200*a^2*b^9*c^5 - 8960*a^3*b^7*c^6 + 34560*a^4*b^5*c^7 - 67584*a^5*b^3*c^8 + 53248*a^6*b*c^9)*sqrt((b^4 - 50*a*b^2*c + 625*a^2*c^2)/(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)))*sqrt(-(b^7 - 35*a*b^5*c + 280*a^2*b^3*c^2 + 1680*a^3*b*c^3 + (b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8)*sqrt((b^4 - 50*a*b^2*c + 625*a^2*c^2)/(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)))/(b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8))) + sqrt(1/2)*((b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*x^8 + a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3 + 2*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*x^6 + (b^6*c - 6*a*b^4*c^2 + 32*a^3*c^4)*x^4 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*x^2)*sqrt(-(b^7 - 35*a*b^5*c + 280*a^2*b^3*c^2 + 1680*a^3*b*c^3 - (b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8)*sqrt((b^4 - 50*a*b^2*c + 625*a^2*c^2)/(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)))/(b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8))*log((35*a*b^6 - 1491*a^2*b^4*c + 15000*a^3*b^2*c^2 + 10000*a^4*c^3)*x + 1/2*sqrt(1/2)*(b^10 - 17*a*b^8*c - 392*a^2*b^6*c^2 + 5696*a^3*b^4*c^3 - 23680*a^4*b^2*c^4 + 32000*a^5*c^5 + (b^13*c^3 - 72*a*b^11*c^4 + 1200*a^2*b^9*c^5 - 8960*a^3*b^7*c^6 + 34560*a^4*b^5*c^7 - 67584*a^5*b^3*c^8 + 53248*a^6*b*c^9)*sqrt((b^4 - 50*a*b^2*c + 625*a^2*c^2)/(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)))*sqrt(-(b^7 - 35*a*b^5*c + 280*a^2*b^3*c^2 + 1680*a^3*b*c^3 - (b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8)*sqrt((b^4 - 50*a*b^2*c + 625*a^2*c^2)/(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)))/(b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8))) - sqrt(1/2)*((b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*x^8 + a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3 + 2*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*x^6 + (b^6*c - 6*a*b^4*c^2 + 32*a^3*c^4)*x^4 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*x^2)*sqrt(-(b^7 - 35*a*b^5*c + 280*a^2*b^3*c^2 + 1680*a^3*b*c^3 - (b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8)*sqrt((b^4 - 50*a*b^2*c + 625*a^2*c^2)/(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)))/(b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8))*log((35*a*b^6 - 1491*a^2*b^4*c + 15000*a^3*b^2*c^2 + 10000*a^4*c^3)*x - 1/2*sqrt(1/2)*(b^10 - 17*a*b^8*c - 392*a^2*b^6*c^2 + 5696*a^3*b^4*c^3 - 23680*a^4*b^2*c^4 + 32000*a^5*c^5 + (b^13*c^3 - 72*a*b^11*c^4 + 1200*a^2*b^9*c^5 - 8960*a^3*b^7*c^6 + 34560*a^4*b^5*c^7 - 67584*a^5*b^3*c^8 + 53248*a^6*b*c^9)*sqrt((b^4 - 50*a*b^2*c + 625*a^2*c^2)/(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)))*sqrt(-(b^7 - 35*a*b^5*c + 280*a^2*b^3*c^2 + 1680*a^3*b*c^3 - (b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8)*sqrt((b^4 - 50*a*b^2*c + 625*a^2*c^2)/(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)))/(b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8))) - 2*(a^2*b^2 + 20*a^3*c)*x)/((b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*x^8 + a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3 + 2*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*x^6 + (b^6*c - 6*a*b^4*c^2 + 32*a^3*c^4)*x^4 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*x^2)","B",0
883,1,3128,0,1.659940," ","integrate(x^6/(c*x^4+b*x^2+a)^3,x, algorithm=""fricas"")","\frac{6 \, {\left(b^{2} c + 4 \, a c^{2}\right)} x^{7} + 2 \, {\left(5 \, b^{3} + 16 \, a b c\right)} x^{5} + 24 \, a^{2} b x + 2 \, {\left(19 \, a b^{2} - 4 \, a^{2} c\right)} x^{3} + 3 \, \sqrt{\frac{1}{2}} {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{8} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{6} + a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{4} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x^{2}\right)} \sqrt{-\frac{b^{5} + 40 \, a b^{3} c + 80 \, a^{2} b c^{2} + \frac{b^{10} c - 20 \, a b^{8} c^{2} + 160 \, a^{2} b^{6} c^{3} - 640 \, a^{3} b^{4} c^{4} + 1280 \, a^{4} b^{2} c^{5} - 1024 \, a^{5} c^{6}}{\sqrt{b^{10} c^{2} - 20 \, a b^{8} c^{3} + 160 \, a^{2} b^{6} c^{4} - 640 \, a^{3} b^{4} c^{5} + 1280 \, a^{4} b^{2} c^{6} - 1024 \, a^{5} c^{7}}}}{b^{10} c - 20 \, a b^{8} c^{2} + 160 \, a^{2} b^{6} c^{3} - 640 \, a^{3} b^{4} c^{4} + 1280 \, a^{4} b^{2} c^{5} - 1024 \, a^{5} c^{6}}} \log\left(3 \, {\left(5 \, b^{4} + 40 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} x + 3 \, \sqrt{\frac{1}{2}} {\left(2 \, b^{7} - 24 \, a b^{5} c + 96 \, a^{2} b^{3} c^{2} - 128 \, a^{3} b c^{3} + \frac{3 \, b^{12} c - 56 \, a b^{10} c^{2} + 400 \, a^{2} b^{8} c^{3} - 1280 \, a^{3} b^{6} c^{4} + 1280 \, a^{4} b^{4} c^{5} + 2048 \, a^{5} b^{2} c^{6} - 4096 \, a^{6} c^{7}}{\sqrt{b^{10} c^{2} - 20 \, a b^{8} c^{3} + 160 \, a^{2} b^{6} c^{4} - 640 \, a^{3} b^{4} c^{5} + 1280 \, a^{4} b^{2} c^{6} - 1024 \, a^{5} c^{7}}}\right)} \sqrt{-\frac{b^{5} + 40 \, a b^{3} c + 80 \, a^{2} b c^{2} + \frac{b^{10} c - 20 \, a b^{8} c^{2} + 160 \, a^{2} b^{6} c^{3} - 640 \, a^{3} b^{4} c^{4} + 1280 \, a^{4} b^{2} c^{5} - 1024 \, a^{5} c^{6}}{\sqrt{b^{10} c^{2} - 20 \, a b^{8} c^{3} + 160 \, a^{2} b^{6} c^{4} - 640 \, a^{3} b^{4} c^{5} + 1280 \, a^{4} b^{2} c^{6} - 1024 \, a^{5} c^{7}}}}{b^{10} c - 20 \, a b^{8} c^{2} + 160 \, a^{2} b^{6} c^{3} - 640 \, a^{3} b^{4} c^{4} + 1280 \, a^{4} b^{2} c^{5} - 1024 \, a^{5} c^{6}}}\right) - 3 \, \sqrt{\frac{1}{2}} {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{8} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{6} + a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{4} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x^{2}\right)} \sqrt{-\frac{b^{5} + 40 \, a b^{3} c + 80 \, a^{2} b c^{2} + \frac{b^{10} c - 20 \, a b^{8} c^{2} + 160 \, a^{2} b^{6} c^{3} - 640 \, a^{3} b^{4} c^{4} + 1280 \, a^{4} b^{2} c^{5} - 1024 \, a^{5} c^{6}}{\sqrt{b^{10} c^{2} - 20 \, a b^{8} c^{3} + 160 \, a^{2} b^{6} c^{4} - 640 \, a^{3} b^{4} c^{5} + 1280 \, a^{4} b^{2} c^{6} - 1024 \, a^{5} c^{7}}}}{b^{10} c - 20 \, a b^{8} c^{2} + 160 \, a^{2} b^{6} c^{3} - 640 \, a^{3} b^{4} c^{4} + 1280 \, a^{4} b^{2} c^{5} - 1024 \, a^{5} c^{6}}} \log\left(3 \, {\left(5 \, b^{4} + 40 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} x - 3 \, \sqrt{\frac{1}{2}} {\left(2 \, b^{7} - 24 \, a b^{5} c + 96 \, a^{2} b^{3} c^{2} - 128 \, a^{3} b c^{3} + \frac{3 \, b^{12} c - 56 \, a b^{10} c^{2} + 400 \, a^{2} b^{8} c^{3} - 1280 \, a^{3} b^{6} c^{4} + 1280 \, a^{4} b^{4} c^{5} + 2048 \, a^{5} b^{2} c^{6} - 4096 \, a^{6} c^{7}}{\sqrt{b^{10} c^{2} - 20 \, a b^{8} c^{3} + 160 \, a^{2} b^{6} c^{4} - 640 \, a^{3} b^{4} c^{5} + 1280 \, a^{4} b^{2} c^{6} - 1024 \, a^{5} c^{7}}}\right)} \sqrt{-\frac{b^{5} + 40 \, a b^{3} c + 80 \, a^{2} b c^{2} + \frac{b^{10} c - 20 \, a b^{8} c^{2} + 160 \, a^{2} b^{6} c^{3} - 640 \, a^{3} b^{4} c^{4} + 1280 \, a^{4} b^{2} c^{5} - 1024 \, a^{5} c^{6}}{\sqrt{b^{10} c^{2} - 20 \, a b^{8} c^{3} + 160 \, a^{2} b^{6} c^{4} - 640 \, a^{3} b^{4} c^{5} + 1280 \, a^{4} b^{2} c^{6} - 1024 \, a^{5} c^{7}}}}{b^{10} c - 20 \, a b^{8} c^{2} + 160 \, a^{2} b^{6} c^{3} - 640 \, a^{3} b^{4} c^{4} + 1280 \, a^{4} b^{2} c^{5} - 1024 \, a^{5} c^{6}}}\right) + 3 \, \sqrt{\frac{1}{2}} {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{8} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{6} + a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{4} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x^{2}\right)} \sqrt{-\frac{b^{5} + 40 \, a b^{3} c + 80 \, a^{2} b c^{2} - \frac{b^{10} c - 20 \, a b^{8} c^{2} + 160 \, a^{2} b^{6} c^{3} - 640 \, a^{3} b^{4} c^{4} + 1280 \, a^{4} b^{2} c^{5} - 1024 \, a^{5} c^{6}}{\sqrt{b^{10} c^{2} - 20 \, a b^{8} c^{3} + 160 \, a^{2} b^{6} c^{4} - 640 \, a^{3} b^{4} c^{5} + 1280 \, a^{4} b^{2} c^{6} - 1024 \, a^{5} c^{7}}}}{b^{10} c - 20 \, a b^{8} c^{2} + 160 \, a^{2} b^{6} c^{3} - 640 \, a^{3} b^{4} c^{4} + 1280 \, a^{4} b^{2} c^{5} - 1024 \, a^{5} c^{6}}} \log\left(3 \, {\left(5 \, b^{4} + 40 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} x + 3 \, \sqrt{\frac{1}{2}} {\left(2 \, b^{7} - 24 \, a b^{5} c + 96 \, a^{2} b^{3} c^{2} - 128 \, a^{3} b c^{3} - \frac{3 \, b^{12} c - 56 \, a b^{10} c^{2} + 400 \, a^{2} b^{8} c^{3} - 1280 \, a^{3} b^{6} c^{4} + 1280 \, a^{4} b^{4} c^{5} + 2048 \, a^{5} b^{2} c^{6} - 4096 \, a^{6} c^{7}}{\sqrt{b^{10} c^{2} - 20 \, a b^{8} c^{3} + 160 \, a^{2} b^{6} c^{4} - 640 \, a^{3} b^{4} c^{5} + 1280 \, a^{4} b^{2} c^{6} - 1024 \, a^{5} c^{7}}}\right)} \sqrt{-\frac{b^{5} + 40 \, a b^{3} c + 80 \, a^{2} b c^{2} - \frac{b^{10} c - 20 \, a b^{8} c^{2} + 160 \, a^{2} b^{6} c^{3} - 640 \, a^{3} b^{4} c^{4} + 1280 \, a^{4} b^{2} c^{5} - 1024 \, a^{5} c^{6}}{\sqrt{b^{10} c^{2} - 20 \, a b^{8} c^{3} + 160 \, a^{2} b^{6} c^{4} - 640 \, a^{3} b^{4} c^{5} + 1280 \, a^{4} b^{2} c^{6} - 1024 \, a^{5} c^{7}}}}{b^{10} c - 20 \, a b^{8} c^{2} + 160 \, a^{2} b^{6} c^{3} - 640 \, a^{3} b^{4} c^{4} + 1280 \, a^{4} b^{2} c^{5} - 1024 \, a^{5} c^{6}}}\right) - 3 \, \sqrt{\frac{1}{2}} {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{8} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{6} + a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{4} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x^{2}\right)} \sqrt{-\frac{b^{5} + 40 \, a b^{3} c + 80 \, a^{2} b c^{2} - \frac{b^{10} c - 20 \, a b^{8} c^{2} + 160 \, a^{2} b^{6} c^{3} - 640 \, a^{3} b^{4} c^{4} + 1280 \, a^{4} b^{2} c^{5} - 1024 \, a^{5} c^{6}}{\sqrt{b^{10} c^{2} - 20 \, a b^{8} c^{3} + 160 \, a^{2} b^{6} c^{4} - 640 \, a^{3} b^{4} c^{5} + 1280 \, a^{4} b^{2} c^{6} - 1024 \, a^{5} c^{7}}}}{b^{10} c - 20 \, a b^{8} c^{2} + 160 \, a^{2} b^{6} c^{3} - 640 \, a^{3} b^{4} c^{4} + 1280 \, a^{4} b^{2} c^{5} - 1024 \, a^{5} c^{6}}} \log\left(3 \, {\left(5 \, b^{4} + 40 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} x - 3 \, \sqrt{\frac{1}{2}} {\left(2 \, b^{7} - 24 \, a b^{5} c + 96 \, a^{2} b^{3} c^{2} - 128 \, a^{3} b c^{3} - \frac{3 \, b^{12} c - 56 \, a b^{10} c^{2} + 400 \, a^{2} b^{8} c^{3} - 1280 \, a^{3} b^{6} c^{4} + 1280 \, a^{4} b^{4} c^{5} + 2048 \, a^{5} b^{2} c^{6} - 4096 \, a^{6} c^{7}}{\sqrt{b^{10} c^{2} - 20 \, a b^{8} c^{3} + 160 \, a^{2} b^{6} c^{4} - 640 \, a^{3} b^{4} c^{5} + 1280 \, a^{4} b^{2} c^{6} - 1024 \, a^{5} c^{7}}}\right)} \sqrt{-\frac{b^{5} + 40 \, a b^{3} c + 80 \, a^{2} b c^{2} - \frac{b^{10} c - 20 \, a b^{8} c^{2} + 160 \, a^{2} b^{6} c^{3} - 640 \, a^{3} b^{4} c^{4} + 1280 \, a^{4} b^{2} c^{5} - 1024 \, a^{5} c^{6}}{\sqrt{b^{10} c^{2} - 20 \, a b^{8} c^{3} + 160 \, a^{2} b^{6} c^{4} - 640 \, a^{3} b^{4} c^{5} + 1280 \, a^{4} b^{2} c^{6} - 1024 \, a^{5} c^{7}}}}{b^{10} c - 20 \, a b^{8} c^{2} + 160 \, a^{2} b^{6} c^{3} - 640 \, a^{3} b^{4} c^{4} + 1280 \, a^{4} b^{2} c^{5} - 1024 \, a^{5} c^{6}}}\right)}{16 \, {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{8} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{6} + a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{4} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x^{2}\right)}}"," ",0,"1/16*(6*(b^2*c + 4*a*c^2)*x^7 + 2*(5*b^3 + 16*a*b*c)*x^5 + 24*a^2*b*x + 2*(19*a*b^2 - 4*a^2*c)*x^3 + 3*sqrt(1/2)*((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^8 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^6 + a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^4 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x^2)*sqrt(-(b^5 + 40*a*b^3*c + 80*a^2*b*c^2 + (b^10*c - 20*a*b^8*c^2 + 160*a^2*b^6*c^3 - 640*a^3*b^4*c^4 + 1280*a^4*b^2*c^5 - 1024*a^5*c^6)/sqrt(b^10*c^2 - 20*a*b^8*c^3 + 160*a^2*b^6*c^4 - 640*a^3*b^4*c^5 + 1280*a^4*b^2*c^6 - 1024*a^5*c^7))/(b^10*c - 20*a*b^8*c^2 + 160*a^2*b^6*c^3 - 640*a^3*b^4*c^4 + 1280*a^4*b^2*c^5 - 1024*a^5*c^6))*log(3*(5*b^4 + 40*a*b^2*c + 16*a^2*c^2)*x + 3*sqrt(1/2)*(2*b^7 - 24*a*b^5*c + 96*a^2*b^3*c^2 - 128*a^3*b*c^3 + (3*b^12*c - 56*a*b^10*c^2 + 400*a^2*b^8*c^3 - 1280*a^3*b^6*c^4 + 1280*a^4*b^4*c^5 + 2048*a^5*b^2*c^6 - 4096*a^6*c^7)/sqrt(b^10*c^2 - 20*a*b^8*c^3 + 160*a^2*b^6*c^4 - 640*a^3*b^4*c^5 + 1280*a^4*b^2*c^6 - 1024*a^5*c^7))*sqrt(-(b^5 + 40*a*b^3*c + 80*a^2*b*c^2 + (b^10*c - 20*a*b^8*c^2 + 160*a^2*b^6*c^3 - 640*a^3*b^4*c^4 + 1280*a^4*b^2*c^5 - 1024*a^5*c^6)/sqrt(b^10*c^2 - 20*a*b^8*c^3 + 160*a^2*b^6*c^4 - 640*a^3*b^4*c^5 + 1280*a^4*b^2*c^6 - 1024*a^5*c^7))/(b^10*c - 20*a*b^8*c^2 + 160*a^2*b^6*c^3 - 640*a^3*b^4*c^4 + 1280*a^4*b^2*c^5 - 1024*a^5*c^6))) - 3*sqrt(1/2)*((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^8 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^6 + a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^4 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x^2)*sqrt(-(b^5 + 40*a*b^3*c + 80*a^2*b*c^2 + (b^10*c - 20*a*b^8*c^2 + 160*a^2*b^6*c^3 - 640*a^3*b^4*c^4 + 1280*a^4*b^2*c^5 - 1024*a^5*c^6)/sqrt(b^10*c^2 - 20*a*b^8*c^3 + 160*a^2*b^6*c^4 - 640*a^3*b^4*c^5 + 1280*a^4*b^2*c^6 - 1024*a^5*c^7))/(b^10*c - 20*a*b^8*c^2 + 160*a^2*b^6*c^3 - 640*a^3*b^4*c^4 + 1280*a^4*b^2*c^5 - 1024*a^5*c^6))*log(3*(5*b^4 + 40*a*b^2*c + 16*a^2*c^2)*x - 3*sqrt(1/2)*(2*b^7 - 24*a*b^5*c + 96*a^2*b^3*c^2 - 128*a^3*b*c^3 + (3*b^12*c - 56*a*b^10*c^2 + 400*a^2*b^8*c^3 - 1280*a^3*b^6*c^4 + 1280*a^4*b^4*c^5 + 2048*a^5*b^2*c^6 - 4096*a^6*c^7)/sqrt(b^10*c^2 - 20*a*b^8*c^3 + 160*a^2*b^6*c^4 - 640*a^3*b^4*c^5 + 1280*a^4*b^2*c^6 - 1024*a^5*c^7))*sqrt(-(b^5 + 40*a*b^3*c + 80*a^2*b*c^2 + (b^10*c - 20*a*b^8*c^2 + 160*a^2*b^6*c^3 - 640*a^3*b^4*c^4 + 1280*a^4*b^2*c^5 - 1024*a^5*c^6)/sqrt(b^10*c^2 - 20*a*b^8*c^3 + 160*a^2*b^6*c^4 - 640*a^3*b^4*c^5 + 1280*a^4*b^2*c^6 - 1024*a^5*c^7))/(b^10*c - 20*a*b^8*c^2 + 160*a^2*b^6*c^3 - 640*a^3*b^4*c^4 + 1280*a^4*b^2*c^5 - 1024*a^5*c^6))) + 3*sqrt(1/2)*((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^8 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^6 + a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^4 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x^2)*sqrt(-(b^5 + 40*a*b^3*c + 80*a^2*b*c^2 - (b^10*c - 20*a*b^8*c^2 + 160*a^2*b^6*c^3 - 640*a^3*b^4*c^4 + 1280*a^4*b^2*c^5 - 1024*a^5*c^6)/sqrt(b^10*c^2 - 20*a*b^8*c^3 + 160*a^2*b^6*c^4 - 640*a^3*b^4*c^5 + 1280*a^4*b^2*c^6 - 1024*a^5*c^7))/(b^10*c - 20*a*b^8*c^2 + 160*a^2*b^6*c^3 - 640*a^3*b^4*c^4 + 1280*a^4*b^2*c^5 - 1024*a^5*c^6))*log(3*(5*b^4 + 40*a*b^2*c + 16*a^2*c^2)*x + 3*sqrt(1/2)*(2*b^7 - 24*a*b^5*c + 96*a^2*b^3*c^2 - 128*a^3*b*c^3 - (3*b^12*c - 56*a*b^10*c^2 + 400*a^2*b^8*c^3 - 1280*a^3*b^6*c^4 + 1280*a^4*b^4*c^5 + 2048*a^5*b^2*c^6 - 4096*a^6*c^7)/sqrt(b^10*c^2 - 20*a*b^8*c^3 + 160*a^2*b^6*c^4 - 640*a^3*b^4*c^5 + 1280*a^4*b^2*c^6 - 1024*a^5*c^7))*sqrt(-(b^5 + 40*a*b^3*c + 80*a^2*b*c^2 - (b^10*c - 20*a*b^8*c^2 + 160*a^2*b^6*c^3 - 640*a^3*b^4*c^4 + 1280*a^4*b^2*c^5 - 1024*a^5*c^6)/sqrt(b^10*c^2 - 20*a*b^8*c^3 + 160*a^2*b^6*c^4 - 640*a^3*b^4*c^5 + 1280*a^4*b^2*c^6 - 1024*a^5*c^7))/(b^10*c - 20*a*b^8*c^2 + 160*a^2*b^6*c^3 - 640*a^3*b^4*c^4 + 1280*a^4*b^2*c^5 - 1024*a^5*c^6))) - 3*sqrt(1/2)*((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^8 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^6 + a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^4 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x^2)*sqrt(-(b^5 + 40*a*b^3*c + 80*a^2*b*c^2 - (b^10*c - 20*a*b^8*c^2 + 160*a^2*b^6*c^3 - 640*a^3*b^4*c^4 + 1280*a^4*b^2*c^5 - 1024*a^5*c^6)/sqrt(b^10*c^2 - 20*a*b^8*c^3 + 160*a^2*b^6*c^4 - 640*a^3*b^4*c^5 + 1280*a^4*b^2*c^6 - 1024*a^5*c^7))/(b^10*c - 20*a*b^8*c^2 + 160*a^2*b^6*c^3 - 640*a^3*b^4*c^4 + 1280*a^4*b^2*c^5 - 1024*a^5*c^6))*log(3*(5*b^4 + 40*a*b^2*c + 16*a^2*c^2)*x - 3*sqrt(1/2)*(2*b^7 - 24*a*b^5*c + 96*a^2*b^3*c^2 - 128*a^3*b*c^3 - (3*b^12*c - 56*a*b^10*c^2 + 400*a^2*b^8*c^3 - 1280*a^3*b^6*c^4 + 1280*a^4*b^4*c^5 + 2048*a^5*b^2*c^6 - 4096*a^6*c^7)/sqrt(b^10*c^2 - 20*a*b^8*c^3 + 160*a^2*b^6*c^4 - 640*a^3*b^4*c^5 + 1280*a^4*b^2*c^6 - 1024*a^5*c^7))*sqrt(-(b^5 + 40*a*b^3*c + 80*a^2*b*c^2 - (b^10*c - 20*a*b^8*c^2 + 160*a^2*b^6*c^3 - 640*a^3*b^4*c^4 + 1280*a^4*b^2*c^5 - 1024*a^5*c^6)/sqrt(b^10*c^2 - 20*a*b^8*c^3 + 160*a^2*b^6*c^4 - 640*a^3*b^4*c^5 + 1280*a^4*b^2*c^6 - 1024*a^5*c^7))/(b^10*c - 20*a*b^8*c^2 + 160*a^2*b^6*c^3 - 640*a^3*b^4*c^4 + 1280*a^4*b^2*c^5 - 1024*a^5*c^6))))/((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^8 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^6 + a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^4 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x^2)","B",0
884,1,3128,0,1.101192," ","integrate(x^4/(c*x^4+b*x^2+a)^3,x, algorithm=""fricas"")","-\frac{24 \, b c^{2} x^{7} + 2 \, {\left(19 \, b^{2} c - 4 \, a c^{2}\right)} x^{5} + 2 \, {\left(5 \, b^{3} + 16 \, a b c\right)} x^{3} + 3 \, \sqrt{\frac{1}{2}} {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{8} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{6} + a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{4} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x^{2}\right)} \sqrt{-\frac{b^{5} + 40 \, a b^{3} c + 80 \, a^{2} b c^{2} + \frac{a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}}{\sqrt{a^{2} b^{10} - 20 \, a^{3} b^{8} c + 160 \, a^{4} b^{6} c^{2} - 640 \, a^{5} b^{4} c^{3} + 1280 \, a^{6} b^{2} c^{4} - 1024 \, a^{7} c^{5}}}}{a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}}} \log\left(3 \, {\left(5 \, b^{4} c + 40 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} x + \frac{3}{2} \, \sqrt{\frac{1}{2}} {\left(b^{8} - 8 \, a b^{6} c + 128 \, a^{3} b^{2} c^{3} - 256 \, a^{4} c^{4} - \frac{a b^{13} - 8 \, a^{2} b^{11} c - 80 \, a^{3} b^{9} c^{2} + 1280 \, a^{4} b^{7} c^{3} - 6400 \, a^{5} b^{5} c^{4} + 14336 \, a^{6} b^{3} c^{5} - 12288 \, a^{7} b c^{6}}{\sqrt{a^{2} b^{10} - 20 \, a^{3} b^{8} c + 160 \, a^{4} b^{6} c^{2} - 640 \, a^{5} b^{4} c^{3} + 1280 \, a^{6} b^{2} c^{4} - 1024 \, a^{7} c^{5}}}\right)} \sqrt{-\frac{b^{5} + 40 \, a b^{3} c + 80 \, a^{2} b c^{2} + \frac{a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}}{\sqrt{a^{2} b^{10} - 20 \, a^{3} b^{8} c + 160 \, a^{4} b^{6} c^{2} - 640 \, a^{5} b^{4} c^{3} + 1280 \, a^{6} b^{2} c^{4} - 1024 \, a^{7} c^{5}}}}{a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}}}\right) - 3 \, \sqrt{\frac{1}{2}} {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{8} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{6} + a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{4} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x^{2}\right)} \sqrt{-\frac{b^{5} + 40 \, a b^{3} c + 80 \, a^{2} b c^{2} + \frac{a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}}{\sqrt{a^{2} b^{10} - 20 \, a^{3} b^{8} c + 160 \, a^{4} b^{6} c^{2} - 640 \, a^{5} b^{4} c^{3} + 1280 \, a^{6} b^{2} c^{4} - 1024 \, a^{7} c^{5}}}}{a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}}} \log\left(3 \, {\left(5 \, b^{4} c + 40 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} x - \frac{3}{2} \, \sqrt{\frac{1}{2}} {\left(b^{8} - 8 \, a b^{6} c + 128 \, a^{3} b^{2} c^{3} - 256 \, a^{4} c^{4} - \frac{a b^{13} - 8 \, a^{2} b^{11} c - 80 \, a^{3} b^{9} c^{2} + 1280 \, a^{4} b^{7} c^{3} - 6400 \, a^{5} b^{5} c^{4} + 14336 \, a^{6} b^{3} c^{5} - 12288 \, a^{7} b c^{6}}{\sqrt{a^{2} b^{10} - 20 \, a^{3} b^{8} c + 160 \, a^{4} b^{6} c^{2} - 640 \, a^{5} b^{4} c^{3} + 1280 \, a^{6} b^{2} c^{4} - 1024 \, a^{7} c^{5}}}\right)} \sqrt{-\frac{b^{5} + 40 \, a b^{3} c + 80 \, a^{2} b c^{2} + \frac{a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}}{\sqrt{a^{2} b^{10} - 20 \, a^{3} b^{8} c + 160 \, a^{4} b^{6} c^{2} - 640 \, a^{5} b^{4} c^{3} + 1280 \, a^{6} b^{2} c^{4} - 1024 \, a^{7} c^{5}}}}{a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}}}\right) + 3 \, \sqrt{\frac{1}{2}} {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{8} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{6} + a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{4} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x^{2}\right)} \sqrt{-\frac{b^{5} + 40 \, a b^{3} c + 80 \, a^{2} b c^{2} - \frac{a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}}{\sqrt{a^{2} b^{10} - 20 \, a^{3} b^{8} c + 160 \, a^{4} b^{6} c^{2} - 640 \, a^{5} b^{4} c^{3} + 1280 \, a^{6} b^{2} c^{4} - 1024 \, a^{7} c^{5}}}}{a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}}} \log\left(3 \, {\left(5 \, b^{4} c + 40 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} x + \frac{3}{2} \, \sqrt{\frac{1}{2}} {\left(b^{8} - 8 \, a b^{6} c + 128 \, a^{3} b^{2} c^{3} - 256 \, a^{4} c^{4} + \frac{a b^{13} - 8 \, a^{2} b^{11} c - 80 \, a^{3} b^{9} c^{2} + 1280 \, a^{4} b^{7} c^{3} - 6400 \, a^{5} b^{5} c^{4} + 14336 \, a^{6} b^{3} c^{5} - 12288 \, a^{7} b c^{6}}{\sqrt{a^{2} b^{10} - 20 \, a^{3} b^{8} c + 160 \, a^{4} b^{6} c^{2} - 640 \, a^{5} b^{4} c^{3} + 1280 \, a^{6} b^{2} c^{4} - 1024 \, a^{7} c^{5}}}\right)} \sqrt{-\frac{b^{5} + 40 \, a b^{3} c + 80 \, a^{2} b c^{2} - \frac{a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}}{\sqrt{a^{2} b^{10} - 20 \, a^{3} b^{8} c + 160 \, a^{4} b^{6} c^{2} - 640 \, a^{5} b^{4} c^{3} + 1280 \, a^{6} b^{2} c^{4} - 1024 \, a^{7} c^{5}}}}{a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}}}\right) - 3 \, \sqrt{\frac{1}{2}} {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{8} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{6} + a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{4} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x^{2}\right)} \sqrt{-\frac{b^{5} + 40 \, a b^{3} c + 80 \, a^{2} b c^{2} - \frac{a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}}{\sqrt{a^{2} b^{10} - 20 \, a^{3} b^{8} c + 160 \, a^{4} b^{6} c^{2} - 640 \, a^{5} b^{4} c^{3} + 1280 \, a^{6} b^{2} c^{4} - 1024 \, a^{7} c^{5}}}}{a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}}} \log\left(3 \, {\left(5 \, b^{4} c + 40 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} x - \frac{3}{2} \, \sqrt{\frac{1}{2}} {\left(b^{8} - 8 \, a b^{6} c + 128 \, a^{3} b^{2} c^{3} - 256 \, a^{4} c^{4} + \frac{a b^{13} - 8 \, a^{2} b^{11} c - 80 \, a^{3} b^{9} c^{2} + 1280 \, a^{4} b^{7} c^{3} - 6400 \, a^{5} b^{5} c^{4} + 14336 \, a^{6} b^{3} c^{5} - 12288 \, a^{7} b c^{6}}{\sqrt{a^{2} b^{10} - 20 \, a^{3} b^{8} c + 160 \, a^{4} b^{6} c^{2} - 640 \, a^{5} b^{4} c^{3} + 1280 \, a^{6} b^{2} c^{4} - 1024 \, a^{7} c^{5}}}\right)} \sqrt{-\frac{b^{5} + 40 \, a b^{3} c + 80 \, a^{2} b c^{2} - \frac{a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}}{\sqrt{a^{2} b^{10} - 20 \, a^{3} b^{8} c + 160 \, a^{4} b^{6} c^{2} - 640 \, a^{5} b^{4} c^{3} + 1280 \, a^{6} b^{2} c^{4} - 1024 \, a^{7} c^{5}}}}{a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}}}\right) + 6 \, {\left(a b^{2} + 4 \, a^{2} c\right)} x}{16 \, {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{8} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{6} + a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{4} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x^{2}\right)}}"," ",0,"-1/16*(24*b*c^2*x^7 + 2*(19*b^2*c - 4*a*c^2)*x^5 + 2*(5*b^3 + 16*a*b*c)*x^3 + 3*sqrt(1/2)*((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^8 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^6 + a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^4 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x^2)*sqrt(-(b^5 + 40*a*b^3*c + 80*a^2*b*c^2 + (a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)/sqrt(a^2*b^10 - 20*a^3*b^8*c + 160*a^4*b^6*c^2 - 640*a^5*b^4*c^3 + 1280*a^6*b^2*c^4 - 1024*a^7*c^5))/(a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5))*log(3*(5*b^4*c + 40*a*b^2*c^2 + 16*a^2*c^3)*x + 3/2*sqrt(1/2)*(b^8 - 8*a*b^6*c + 128*a^3*b^2*c^3 - 256*a^4*c^4 - (a*b^13 - 8*a^2*b^11*c - 80*a^3*b^9*c^2 + 1280*a^4*b^7*c^3 - 6400*a^5*b^5*c^4 + 14336*a^6*b^3*c^5 - 12288*a^7*b*c^6)/sqrt(a^2*b^10 - 20*a^3*b^8*c + 160*a^4*b^6*c^2 - 640*a^5*b^4*c^3 + 1280*a^6*b^2*c^4 - 1024*a^7*c^5))*sqrt(-(b^5 + 40*a*b^3*c + 80*a^2*b*c^2 + (a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)/sqrt(a^2*b^10 - 20*a^3*b^8*c + 160*a^4*b^6*c^2 - 640*a^5*b^4*c^3 + 1280*a^6*b^2*c^4 - 1024*a^7*c^5))/(a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5))) - 3*sqrt(1/2)*((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^8 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^6 + a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^4 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x^2)*sqrt(-(b^5 + 40*a*b^3*c + 80*a^2*b*c^2 + (a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)/sqrt(a^2*b^10 - 20*a^3*b^8*c + 160*a^4*b^6*c^2 - 640*a^5*b^4*c^3 + 1280*a^6*b^2*c^4 - 1024*a^7*c^5))/(a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5))*log(3*(5*b^4*c + 40*a*b^2*c^2 + 16*a^2*c^3)*x - 3/2*sqrt(1/2)*(b^8 - 8*a*b^6*c + 128*a^3*b^2*c^3 - 256*a^4*c^4 - (a*b^13 - 8*a^2*b^11*c - 80*a^3*b^9*c^2 + 1280*a^4*b^7*c^3 - 6400*a^5*b^5*c^4 + 14336*a^6*b^3*c^5 - 12288*a^7*b*c^6)/sqrt(a^2*b^10 - 20*a^3*b^8*c + 160*a^4*b^6*c^2 - 640*a^5*b^4*c^3 + 1280*a^6*b^2*c^4 - 1024*a^7*c^5))*sqrt(-(b^5 + 40*a*b^3*c + 80*a^2*b*c^2 + (a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)/sqrt(a^2*b^10 - 20*a^3*b^8*c + 160*a^4*b^6*c^2 - 640*a^5*b^4*c^3 + 1280*a^6*b^2*c^4 - 1024*a^7*c^5))/(a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5))) + 3*sqrt(1/2)*((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^8 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^6 + a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^4 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x^2)*sqrt(-(b^5 + 40*a*b^3*c + 80*a^2*b*c^2 - (a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)/sqrt(a^2*b^10 - 20*a^3*b^8*c + 160*a^4*b^6*c^2 - 640*a^5*b^4*c^3 + 1280*a^6*b^2*c^4 - 1024*a^7*c^5))/(a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5))*log(3*(5*b^4*c + 40*a*b^2*c^2 + 16*a^2*c^3)*x + 3/2*sqrt(1/2)*(b^8 - 8*a*b^6*c + 128*a^3*b^2*c^3 - 256*a^4*c^4 + (a*b^13 - 8*a^2*b^11*c - 80*a^3*b^9*c^2 + 1280*a^4*b^7*c^3 - 6400*a^5*b^5*c^4 + 14336*a^6*b^3*c^5 - 12288*a^7*b*c^6)/sqrt(a^2*b^10 - 20*a^3*b^8*c + 160*a^4*b^6*c^2 - 640*a^5*b^4*c^3 + 1280*a^6*b^2*c^4 - 1024*a^7*c^5))*sqrt(-(b^5 + 40*a*b^3*c + 80*a^2*b*c^2 - (a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)/sqrt(a^2*b^10 - 20*a^3*b^8*c + 160*a^4*b^6*c^2 - 640*a^5*b^4*c^3 + 1280*a^6*b^2*c^4 - 1024*a^7*c^5))/(a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5))) - 3*sqrt(1/2)*((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^8 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^6 + a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^4 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x^2)*sqrt(-(b^5 + 40*a*b^3*c + 80*a^2*b*c^2 - (a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)/sqrt(a^2*b^10 - 20*a^3*b^8*c + 160*a^4*b^6*c^2 - 640*a^5*b^4*c^3 + 1280*a^6*b^2*c^4 - 1024*a^7*c^5))/(a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5))*log(3*(5*b^4*c + 40*a*b^2*c^2 + 16*a^2*c^3)*x - 3/2*sqrt(1/2)*(b^8 - 8*a*b^6*c + 128*a^3*b^2*c^3 - 256*a^4*c^4 + (a*b^13 - 8*a^2*b^11*c - 80*a^3*b^9*c^2 + 1280*a^4*b^7*c^3 - 6400*a^5*b^5*c^4 + 14336*a^6*b^3*c^5 - 12288*a^7*b*c^6)/sqrt(a^2*b^10 - 20*a^3*b^8*c + 160*a^4*b^6*c^2 - 640*a^5*b^4*c^3 + 1280*a^6*b^2*c^4 - 1024*a^7*c^5))*sqrt(-(b^5 + 40*a*b^3*c + 80*a^2*b*c^2 - (a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)/sqrt(a^2*b^10 - 20*a^3*b^8*c + 160*a^4*b^6*c^2 - 640*a^5*b^4*c^3 + 1280*a^6*b^2*c^4 - 1024*a^7*c^5))/(a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5))) + 6*(a*b^2 + 4*a^2*c)*x)/((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^8 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^6 + a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^4 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x^2)","B",0
885,1,3777,0,1.684849," ","integrate(x^2/(c*x^4+b*x^2+a)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(b^{2} c^{2} + 20 \, a c^{3}\right)} x^{7} + 4 \, {\left(b^{3} c + 14 \, a b c^{2}\right)} x^{5} + 2 \, {\left(b^{4} + 5 \, a b^{2} c + 36 \, a^{2} c^{2}\right)} x^{3} + \sqrt{\frac{1}{2}} {\left({\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} x^{8} + a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} x^{6} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} x^{4} + 2 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} x^{2}\right)} \sqrt{-\frac{b^{7} - 35 \, a b^{5} c + 280 \, a^{2} b^{3} c^{2} + 1680 \, a^{3} b c^{3} + {\left(a^{3} b^{10} - 20 \, a^{4} b^{8} c + 160 \, a^{5} b^{6} c^{2} - 640 \, a^{6} b^{4} c^{3} + 1280 \, a^{7} b^{2} c^{4} - 1024 \, a^{8} c^{5}\right)} \sqrt{\frac{b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}}{a^{6} b^{10} - 20 \, a^{7} b^{8} c + 160 \, a^{8} b^{6} c^{2} - 640 \, a^{9} b^{4} c^{3} + 1280 \, a^{10} b^{2} c^{4} - 1024 \, a^{11} c^{5}}}}{a^{3} b^{10} - 20 \, a^{4} b^{8} c + 160 \, a^{5} b^{6} c^{2} - 640 \, a^{6} b^{4} c^{3} + 1280 \, a^{7} b^{2} c^{4} - 1024 \, a^{8} c^{5}}} \log\left({\left(35 \, b^{6} c^{2} - 1491 \, a b^{4} c^{3} + 15000 \, a^{2} b^{2} c^{4} + 10000 \, a^{3} c^{5}\right)} x + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{11} - 53 \, a b^{9} c + 940 \, a^{2} b^{7} c^{2} - 6832 \, a^{3} b^{5} c^{3} + 21824 \, a^{4} b^{3} c^{4} - 25600 \, a^{5} b c^{5} - {\left(a^{3} b^{14} - 38 \, a^{4} b^{12} c + 480 \, a^{5} b^{10} c^{2} - 2720 \, a^{6} b^{8} c^{3} + 6400 \, a^{7} b^{6} c^{4} + 1536 \, a^{8} b^{4} c^{5} - 32768 \, a^{9} b^{2} c^{6} + 40960 \, a^{10} c^{7}\right)} \sqrt{\frac{b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}}{a^{6} b^{10} - 20 \, a^{7} b^{8} c + 160 \, a^{8} b^{6} c^{2} - 640 \, a^{9} b^{4} c^{3} + 1280 \, a^{10} b^{2} c^{4} - 1024 \, a^{11} c^{5}}}\right)} \sqrt{-\frac{b^{7} - 35 \, a b^{5} c + 280 \, a^{2} b^{3} c^{2} + 1680 \, a^{3} b c^{3} + {\left(a^{3} b^{10} - 20 \, a^{4} b^{8} c + 160 \, a^{5} b^{6} c^{2} - 640 \, a^{6} b^{4} c^{3} + 1280 \, a^{7} b^{2} c^{4} - 1024 \, a^{8} c^{5}\right)} \sqrt{\frac{b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}}{a^{6} b^{10} - 20 \, a^{7} b^{8} c + 160 \, a^{8} b^{6} c^{2} - 640 \, a^{9} b^{4} c^{3} + 1280 \, a^{10} b^{2} c^{4} - 1024 \, a^{11} c^{5}}}}{a^{3} b^{10} - 20 \, a^{4} b^{8} c + 160 \, a^{5} b^{6} c^{2} - 640 \, a^{6} b^{4} c^{3} + 1280 \, a^{7} b^{2} c^{4} - 1024 \, a^{8} c^{5}}}\right) - \sqrt{\frac{1}{2}} {\left({\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} x^{8} + a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} x^{6} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} x^{4} + 2 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} x^{2}\right)} \sqrt{-\frac{b^{7} - 35 \, a b^{5} c + 280 \, a^{2} b^{3} c^{2} + 1680 \, a^{3} b c^{3} + {\left(a^{3} b^{10} - 20 \, a^{4} b^{8} c + 160 \, a^{5} b^{6} c^{2} - 640 \, a^{6} b^{4} c^{3} + 1280 \, a^{7} b^{2} c^{4} - 1024 \, a^{8} c^{5}\right)} \sqrt{\frac{b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}}{a^{6} b^{10} - 20 \, a^{7} b^{8} c + 160 \, a^{8} b^{6} c^{2} - 640 \, a^{9} b^{4} c^{3} + 1280 \, a^{10} b^{2} c^{4} - 1024 \, a^{11} c^{5}}}}{a^{3} b^{10} - 20 \, a^{4} b^{8} c + 160 \, a^{5} b^{6} c^{2} - 640 \, a^{6} b^{4} c^{3} + 1280 \, a^{7} b^{2} c^{4} - 1024 \, a^{8} c^{5}}} \log\left({\left(35 \, b^{6} c^{2} - 1491 \, a b^{4} c^{3} + 15000 \, a^{2} b^{2} c^{4} + 10000 \, a^{3} c^{5}\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{11} - 53 \, a b^{9} c + 940 \, a^{2} b^{7} c^{2} - 6832 \, a^{3} b^{5} c^{3} + 21824 \, a^{4} b^{3} c^{4} - 25600 \, a^{5} b c^{5} - {\left(a^{3} b^{14} - 38 \, a^{4} b^{12} c + 480 \, a^{5} b^{10} c^{2} - 2720 \, a^{6} b^{8} c^{3} + 6400 \, a^{7} b^{6} c^{4} + 1536 \, a^{8} b^{4} c^{5} - 32768 \, a^{9} b^{2} c^{6} + 40960 \, a^{10} c^{7}\right)} \sqrt{\frac{b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}}{a^{6} b^{10} - 20 \, a^{7} b^{8} c + 160 \, a^{8} b^{6} c^{2} - 640 \, a^{9} b^{4} c^{3} + 1280 \, a^{10} b^{2} c^{4} - 1024 \, a^{11} c^{5}}}\right)} \sqrt{-\frac{b^{7} - 35 \, a b^{5} c + 280 \, a^{2} b^{3} c^{2} + 1680 \, a^{3} b c^{3} + {\left(a^{3} b^{10} - 20 \, a^{4} b^{8} c + 160 \, a^{5} b^{6} c^{2} - 640 \, a^{6} b^{4} c^{3} + 1280 \, a^{7} b^{2} c^{4} - 1024 \, a^{8} c^{5}\right)} \sqrt{\frac{b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}}{a^{6} b^{10} - 20 \, a^{7} b^{8} c + 160 \, a^{8} b^{6} c^{2} - 640 \, a^{9} b^{4} c^{3} + 1280 \, a^{10} b^{2} c^{4} - 1024 \, a^{11} c^{5}}}}{a^{3} b^{10} - 20 \, a^{4} b^{8} c + 160 \, a^{5} b^{6} c^{2} - 640 \, a^{6} b^{4} c^{3} + 1280 \, a^{7} b^{2} c^{4} - 1024 \, a^{8} c^{5}}}\right) + \sqrt{\frac{1}{2}} {\left({\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} x^{8} + a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} x^{6} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} x^{4} + 2 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} x^{2}\right)} \sqrt{-\frac{b^{7} - 35 \, a b^{5} c + 280 \, a^{2} b^{3} c^{2} + 1680 \, a^{3} b c^{3} - {\left(a^{3} b^{10} - 20 \, a^{4} b^{8} c + 160 \, a^{5} b^{6} c^{2} - 640 \, a^{6} b^{4} c^{3} + 1280 \, a^{7} b^{2} c^{4} - 1024 \, a^{8} c^{5}\right)} \sqrt{\frac{b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}}{a^{6} b^{10} - 20 \, a^{7} b^{8} c + 160 \, a^{8} b^{6} c^{2} - 640 \, a^{9} b^{4} c^{3} + 1280 \, a^{10} b^{2} c^{4} - 1024 \, a^{11} c^{5}}}}{a^{3} b^{10} - 20 \, a^{4} b^{8} c + 160 \, a^{5} b^{6} c^{2} - 640 \, a^{6} b^{4} c^{3} + 1280 \, a^{7} b^{2} c^{4} - 1024 \, a^{8} c^{5}}} \log\left({\left(35 \, b^{6} c^{2} - 1491 \, a b^{4} c^{3} + 15000 \, a^{2} b^{2} c^{4} + 10000 \, a^{3} c^{5}\right)} x + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{11} - 53 \, a b^{9} c + 940 \, a^{2} b^{7} c^{2} - 6832 \, a^{3} b^{5} c^{3} + 21824 \, a^{4} b^{3} c^{4} - 25600 \, a^{5} b c^{5} + {\left(a^{3} b^{14} - 38 \, a^{4} b^{12} c + 480 \, a^{5} b^{10} c^{2} - 2720 \, a^{6} b^{8} c^{3} + 6400 \, a^{7} b^{6} c^{4} + 1536 \, a^{8} b^{4} c^{5} - 32768 \, a^{9} b^{2} c^{6} + 40960 \, a^{10} c^{7}\right)} \sqrt{\frac{b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}}{a^{6} b^{10} - 20 \, a^{7} b^{8} c + 160 \, a^{8} b^{6} c^{2} - 640 \, a^{9} b^{4} c^{3} + 1280 \, a^{10} b^{2} c^{4} - 1024 \, a^{11} c^{5}}}\right)} \sqrt{-\frac{b^{7} - 35 \, a b^{5} c + 280 \, a^{2} b^{3} c^{2} + 1680 \, a^{3} b c^{3} - {\left(a^{3} b^{10} - 20 \, a^{4} b^{8} c + 160 \, a^{5} b^{6} c^{2} - 640 \, a^{6} b^{4} c^{3} + 1280 \, a^{7} b^{2} c^{4} - 1024 \, a^{8} c^{5}\right)} \sqrt{\frac{b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}}{a^{6} b^{10} - 20 \, a^{7} b^{8} c + 160 \, a^{8} b^{6} c^{2} - 640 \, a^{9} b^{4} c^{3} + 1280 \, a^{10} b^{2} c^{4} - 1024 \, a^{11} c^{5}}}}{a^{3} b^{10} - 20 \, a^{4} b^{8} c + 160 \, a^{5} b^{6} c^{2} - 640 \, a^{6} b^{4} c^{3} + 1280 \, a^{7} b^{2} c^{4} - 1024 \, a^{8} c^{5}}}\right) - \sqrt{\frac{1}{2}} {\left({\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} x^{8} + a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} x^{6} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} x^{4} + 2 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} x^{2}\right)} \sqrt{-\frac{b^{7} - 35 \, a b^{5} c + 280 \, a^{2} b^{3} c^{2} + 1680 \, a^{3} b c^{3} - {\left(a^{3} b^{10} - 20 \, a^{4} b^{8} c + 160 \, a^{5} b^{6} c^{2} - 640 \, a^{6} b^{4} c^{3} + 1280 \, a^{7} b^{2} c^{4} - 1024 \, a^{8} c^{5}\right)} \sqrt{\frac{b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}}{a^{6} b^{10} - 20 \, a^{7} b^{8} c + 160 \, a^{8} b^{6} c^{2} - 640 \, a^{9} b^{4} c^{3} + 1280 \, a^{10} b^{2} c^{4} - 1024 \, a^{11} c^{5}}}}{a^{3} b^{10} - 20 \, a^{4} b^{8} c + 160 \, a^{5} b^{6} c^{2} - 640 \, a^{6} b^{4} c^{3} + 1280 \, a^{7} b^{2} c^{4} - 1024 \, a^{8} c^{5}}} \log\left({\left(35 \, b^{6} c^{2} - 1491 \, a b^{4} c^{3} + 15000 \, a^{2} b^{2} c^{4} + 10000 \, a^{3} c^{5}\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{11} - 53 \, a b^{9} c + 940 \, a^{2} b^{7} c^{2} - 6832 \, a^{3} b^{5} c^{3} + 21824 \, a^{4} b^{3} c^{4} - 25600 \, a^{5} b c^{5} + {\left(a^{3} b^{14} - 38 \, a^{4} b^{12} c + 480 \, a^{5} b^{10} c^{2} - 2720 \, a^{6} b^{8} c^{3} + 6400 \, a^{7} b^{6} c^{4} + 1536 \, a^{8} b^{4} c^{5} - 32768 \, a^{9} b^{2} c^{6} + 40960 \, a^{10} c^{7}\right)} \sqrt{\frac{b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}}{a^{6} b^{10} - 20 \, a^{7} b^{8} c + 160 \, a^{8} b^{6} c^{2} - 640 \, a^{9} b^{4} c^{3} + 1280 \, a^{10} b^{2} c^{4} - 1024 \, a^{11} c^{5}}}\right)} \sqrt{-\frac{b^{7} - 35 \, a b^{5} c + 280 \, a^{2} b^{3} c^{2} + 1680 \, a^{3} b c^{3} - {\left(a^{3} b^{10} - 20 \, a^{4} b^{8} c + 160 \, a^{5} b^{6} c^{2} - 640 \, a^{6} b^{4} c^{3} + 1280 \, a^{7} b^{2} c^{4} - 1024 \, a^{8} c^{5}\right)} \sqrt{\frac{b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}}{a^{6} b^{10} - 20 \, a^{7} b^{8} c + 160 \, a^{8} b^{6} c^{2} - 640 \, a^{9} b^{4} c^{3} + 1280 \, a^{10} b^{2} c^{4} - 1024 \, a^{11} c^{5}}}}{a^{3} b^{10} - 20 \, a^{4} b^{8} c + 160 \, a^{5} b^{6} c^{2} - 640 \, a^{6} b^{4} c^{3} + 1280 \, a^{7} b^{2} c^{4} - 1024 \, a^{8} c^{5}}}\right) - 2 \, {\left(a b^{3} - 16 \, a^{2} b c\right)} x}{16 \, {\left({\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} x^{8} + a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} x^{6} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} x^{4} + 2 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} x^{2}\right)}}"," ",0,"1/16*(2*(b^2*c^2 + 20*a*c^3)*x^7 + 4*(b^3*c + 14*a*b*c^2)*x^5 + 2*(b^4 + 5*a*b^2*c + 36*a^2*c^2)*x^3 + sqrt(1/2)*((a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*x^8 + a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*x^6 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*x^4 + 2*(a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*x^2)*sqrt(-(b^7 - 35*a*b^5*c + 280*a^2*b^3*c^2 + 1680*a^3*b*c^3 + (a^3*b^10 - 20*a^4*b^8*c + 160*a^5*b^6*c^2 - 640*a^6*b^4*c^3 + 1280*a^7*b^2*c^4 - 1024*a^8*c^5)*sqrt((b^4 - 50*a*b^2*c + 625*a^2*c^2)/(a^6*b^10 - 20*a^7*b^8*c + 160*a^8*b^6*c^2 - 640*a^9*b^4*c^3 + 1280*a^10*b^2*c^4 - 1024*a^11*c^5)))/(a^3*b^10 - 20*a^4*b^8*c + 160*a^5*b^6*c^2 - 640*a^6*b^4*c^3 + 1280*a^7*b^2*c^4 - 1024*a^8*c^5))*log((35*b^6*c^2 - 1491*a*b^4*c^3 + 15000*a^2*b^2*c^4 + 10000*a^3*c^5)*x + 1/2*sqrt(1/2)*(b^11 - 53*a*b^9*c + 940*a^2*b^7*c^2 - 6832*a^3*b^5*c^3 + 21824*a^4*b^3*c^4 - 25600*a^5*b*c^5 - (a^3*b^14 - 38*a^4*b^12*c + 480*a^5*b^10*c^2 - 2720*a^6*b^8*c^3 + 6400*a^7*b^6*c^4 + 1536*a^8*b^4*c^5 - 32768*a^9*b^2*c^6 + 40960*a^10*c^7)*sqrt((b^4 - 50*a*b^2*c + 625*a^2*c^2)/(a^6*b^10 - 20*a^7*b^8*c + 160*a^8*b^6*c^2 - 640*a^9*b^4*c^3 + 1280*a^10*b^2*c^4 - 1024*a^11*c^5)))*sqrt(-(b^7 - 35*a*b^5*c + 280*a^2*b^3*c^2 + 1680*a^3*b*c^3 + (a^3*b^10 - 20*a^4*b^8*c + 160*a^5*b^6*c^2 - 640*a^6*b^4*c^3 + 1280*a^7*b^2*c^4 - 1024*a^8*c^5)*sqrt((b^4 - 50*a*b^2*c + 625*a^2*c^2)/(a^6*b^10 - 20*a^7*b^8*c + 160*a^8*b^6*c^2 - 640*a^9*b^4*c^3 + 1280*a^10*b^2*c^4 - 1024*a^11*c^5)))/(a^3*b^10 - 20*a^4*b^8*c + 160*a^5*b^6*c^2 - 640*a^6*b^4*c^3 + 1280*a^7*b^2*c^4 - 1024*a^8*c^5))) - sqrt(1/2)*((a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*x^8 + a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*x^6 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*x^4 + 2*(a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*x^2)*sqrt(-(b^7 - 35*a*b^5*c + 280*a^2*b^3*c^2 + 1680*a^3*b*c^3 + (a^3*b^10 - 20*a^4*b^8*c + 160*a^5*b^6*c^2 - 640*a^6*b^4*c^3 + 1280*a^7*b^2*c^4 - 1024*a^8*c^5)*sqrt((b^4 - 50*a*b^2*c + 625*a^2*c^2)/(a^6*b^10 - 20*a^7*b^8*c + 160*a^8*b^6*c^2 - 640*a^9*b^4*c^3 + 1280*a^10*b^2*c^4 - 1024*a^11*c^5)))/(a^3*b^10 - 20*a^4*b^8*c + 160*a^5*b^6*c^2 - 640*a^6*b^4*c^3 + 1280*a^7*b^2*c^4 - 1024*a^8*c^5))*log((35*b^6*c^2 - 1491*a*b^4*c^3 + 15000*a^2*b^2*c^4 + 10000*a^3*c^5)*x - 1/2*sqrt(1/2)*(b^11 - 53*a*b^9*c + 940*a^2*b^7*c^2 - 6832*a^3*b^5*c^3 + 21824*a^4*b^3*c^4 - 25600*a^5*b*c^5 - (a^3*b^14 - 38*a^4*b^12*c + 480*a^5*b^10*c^2 - 2720*a^6*b^8*c^3 + 6400*a^7*b^6*c^4 + 1536*a^8*b^4*c^5 - 32768*a^9*b^2*c^6 + 40960*a^10*c^7)*sqrt((b^4 - 50*a*b^2*c + 625*a^2*c^2)/(a^6*b^10 - 20*a^7*b^8*c + 160*a^8*b^6*c^2 - 640*a^9*b^4*c^3 + 1280*a^10*b^2*c^4 - 1024*a^11*c^5)))*sqrt(-(b^7 - 35*a*b^5*c + 280*a^2*b^3*c^2 + 1680*a^3*b*c^3 + (a^3*b^10 - 20*a^4*b^8*c + 160*a^5*b^6*c^2 - 640*a^6*b^4*c^3 + 1280*a^7*b^2*c^4 - 1024*a^8*c^5)*sqrt((b^4 - 50*a*b^2*c + 625*a^2*c^2)/(a^6*b^10 - 20*a^7*b^8*c + 160*a^8*b^6*c^2 - 640*a^9*b^4*c^3 + 1280*a^10*b^2*c^4 - 1024*a^11*c^5)))/(a^3*b^10 - 20*a^4*b^8*c + 160*a^5*b^6*c^2 - 640*a^6*b^4*c^3 + 1280*a^7*b^2*c^4 - 1024*a^8*c^5))) + sqrt(1/2)*((a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*x^8 + a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*x^6 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*x^4 + 2*(a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*x^2)*sqrt(-(b^7 - 35*a*b^5*c + 280*a^2*b^3*c^2 + 1680*a^3*b*c^3 - (a^3*b^10 - 20*a^4*b^8*c + 160*a^5*b^6*c^2 - 640*a^6*b^4*c^3 + 1280*a^7*b^2*c^4 - 1024*a^8*c^5)*sqrt((b^4 - 50*a*b^2*c + 625*a^2*c^2)/(a^6*b^10 - 20*a^7*b^8*c + 160*a^8*b^6*c^2 - 640*a^9*b^4*c^3 + 1280*a^10*b^2*c^4 - 1024*a^11*c^5)))/(a^3*b^10 - 20*a^4*b^8*c + 160*a^5*b^6*c^2 - 640*a^6*b^4*c^3 + 1280*a^7*b^2*c^4 - 1024*a^8*c^5))*log((35*b^6*c^2 - 1491*a*b^4*c^3 + 15000*a^2*b^2*c^4 + 10000*a^3*c^5)*x + 1/2*sqrt(1/2)*(b^11 - 53*a*b^9*c + 940*a^2*b^7*c^2 - 6832*a^3*b^5*c^3 + 21824*a^4*b^3*c^4 - 25600*a^5*b*c^5 + (a^3*b^14 - 38*a^4*b^12*c + 480*a^5*b^10*c^2 - 2720*a^6*b^8*c^3 + 6400*a^7*b^6*c^4 + 1536*a^8*b^4*c^5 - 32768*a^9*b^2*c^6 + 40960*a^10*c^7)*sqrt((b^4 - 50*a*b^2*c + 625*a^2*c^2)/(a^6*b^10 - 20*a^7*b^8*c + 160*a^8*b^6*c^2 - 640*a^9*b^4*c^3 + 1280*a^10*b^2*c^4 - 1024*a^11*c^5)))*sqrt(-(b^7 - 35*a*b^5*c + 280*a^2*b^3*c^2 + 1680*a^3*b*c^3 - (a^3*b^10 - 20*a^4*b^8*c + 160*a^5*b^6*c^2 - 640*a^6*b^4*c^3 + 1280*a^7*b^2*c^4 - 1024*a^8*c^5)*sqrt((b^4 - 50*a*b^2*c + 625*a^2*c^2)/(a^6*b^10 - 20*a^7*b^8*c + 160*a^8*b^6*c^2 - 640*a^9*b^4*c^3 + 1280*a^10*b^2*c^4 - 1024*a^11*c^5)))/(a^3*b^10 - 20*a^4*b^8*c + 160*a^5*b^6*c^2 - 640*a^6*b^4*c^3 + 1280*a^7*b^2*c^4 - 1024*a^8*c^5))) - sqrt(1/2)*((a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*x^8 + a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*x^6 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*x^4 + 2*(a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*x^2)*sqrt(-(b^7 - 35*a*b^5*c + 280*a^2*b^3*c^2 + 1680*a^3*b*c^3 - (a^3*b^10 - 20*a^4*b^8*c + 160*a^5*b^6*c^2 - 640*a^6*b^4*c^3 + 1280*a^7*b^2*c^4 - 1024*a^8*c^5)*sqrt((b^4 - 50*a*b^2*c + 625*a^2*c^2)/(a^6*b^10 - 20*a^7*b^8*c + 160*a^8*b^6*c^2 - 640*a^9*b^4*c^3 + 1280*a^10*b^2*c^4 - 1024*a^11*c^5)))/(a^3*b^10 - 20*a^4*b^8*c + 160*a^5*b^6*c^2 - 640*a^6*b^4*c^3 + 1280*a^7*b^2*c^4 - 1024*a^8*c^5))*log((35*b^6*c^2 - 1491*a*b^4*c^3 + 15000*a^2*b^2*c^4 + 10000*a^3*c^5)*x - 1/2*sqrt(1/2)*(b^11 - 53*a*b^9*c + 940*a^2*b^7*c^2 - 6832*a^3*b^5*c^3 + 21824*a^4*b^3*c^4 - 25600*a^5*b*c^5 + (a^3*b^14 - 38*a^4*b^12*c + 480*a^5*b^10*c^2 - 2720*a^6*b^8*c^3 + 6400*a^7*b^6*c^4 + 1536*a^8*b^4*c^5 - 32768*a^9*b^2*c^6 + 40960*a^10*c^7)*sqrt((b^4 - 50*a*b^2*c + 625*a^2*c^2)/(a^6*b^10 - 20*a^7*b^8*c + 160*a^8*b^6*c^2 - 640*a^9*b^4*c^3 + 1280*a^10*b^2*c^4 - 1024*a^11*c^5)))*sqrt(-(b^7 - 35*a*b^5*c + 280*a^2*b^3*c^2 + 1680*a^3*b*c^3 - (a^3*b^10 - 20*a^4*b^8*c + 160*a^5*b^6*c^2 - 640*a^6*b^4*c^3 + 1280*a^7*b^2*c^4 - 1024*a^8*c^5)*sqrt((b^4 - 50*a*b^2*c + 625*a^2*c^2)/(a^6*b^10 - 20*a^7*b^8*c + 160*a^8*b^6*c^2 - 640*a^9*b^4*c^3 + 1280*a^10*b^2*c^4 - 1024*a^11*c^5)))/(a^3*b^10 - 20*a^4*b^8*c + 160*a^5*b^6*c^2 - 640*a^6*b^4*c^3 + 1280*a^7*b^2*c^4 - 1024*a^8*c^5))) - 2*(a*b^3 - 16*a^2*b*c)*x)/((a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*x^8 + a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*x^6 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*x^4 + 2*(a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*x^2)","B",0
886,1,4323,0,1.441621," ","integrate(1/(c*x^4+b*x^2+a)^3,x, algorithm=""fricas"")","\frac{6 \, {\left(b^{3} c^{2} - 8 \, a b c^{3}\right)} x^{7} + 2 \, {\left(6 \, b^{4} c - 49 \, a b^{2} c^{2} + 28 \, a^{2} c^{3}\right)} x^{5} + 2 \, {\left(3 \, b^{5} - 20 \, a b^{3} c - 4 \, a^{2} b c^{2}\right)} x^{3} - 3 \, \sqrt{\frac{1}{2}} {\left({\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} x^{8} + a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2} + 2 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} x^{6} + {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 32 \, a^{5} c^{3}\right)} x^{4} + 2 \, {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} x^{2}\right)} \sqrt{-\frac{b^{9} - 21 \, a b^{7} c + 189 \, a^{2} b^{5} c^{2} - 840 \, a^{3} b^{3} c^{3} + 1680 \, a^{4} b c^{4} + {\left(a^{5} b^{10} - 20 \, a^{6} b^{8} c + 160 \, a^{7} b^{6} c^{2} - 640 \, a^{8} b^{4} c^{3} + 1280 \, a^{9} b^{2} c^{4} - 1024 \, a^{10} c^{5}\right)} \sqrt{\frac{b^{8} - 22 \, a b^{6} c + 219 \, a^{2} b^{4} c^{2} - 1078 \, a^{3} b^{2} c^{3} + 2401 \, a^{4} c^{4}}{a^{10} b^{10} - 20 \, a^{11} b^{8} c + 160 \, a^{12} b^{6} c^{2} - 640 \, a^{13} b^{4} c^{3} + 1280 \, a^{14} b^{2} c^{4} - 1024 \, a^{15} c^{5}}}}{a^{5} b^{10} - 20 \, a^{6} b^{8} c + 160 \, a^{7} b^{6} c^{2} - 640 \, a^{8} b^{4} c^{3} + 1280 \, a^{9} b^{2} c^{4} - 1024 \, a^{10} c^{5}}} \log\left(27 \, {\left(21 \, b^{8} c^{3} - 447 \, a b^{6} c^{4} + 4189 \, a^{2} b^{4} c^{5} - 19208 \, a^{3} b^{2} c^{6} + 38416 \, a^{4} c^{7}\right)} x + \frac{27}{2} \, \sqrt{\frac{1}{2}} {\left(b^{14} - 32 \, a b^{12} c + 464 \, a^{2} b^{10} c^{2} - 3885 \, a^{3} b^{8} c^{3} + 20088 \, a^{4} b^{6} c^{4} - 63680 \, a^{5} b^{4} c^{5} + 113792 \, a^{6} b^{2} c^{6} - 87808 \, a^{7} c^{7} - {\left(a^{5} b^{15} - 31 \, a^{6} b^{13} c + 424 \, a^{7} b^{11} c^{2} - 3280 \, a^{8} b^{9} c^{3} + 15360 \, a^{9} b^{7} c^{4} - 43264 \, a^{10} b^{5} c^{5} + 67584 \, a^{11} b^{3} c^{6} - 45056 \, a^{12} b c^{7}\right)} \sqrt{\frac{b^{8} - 22 \, a b^{6} c + 219 \, a^{2} b^{4} c^{2} - 1078 \, a^{3} b^{2} c^{3} + 2401 \, a^{4} c^{4}}{a^{10} b^{10} - 20 \, a^{11} b^{8} c + 160 \, a^{12} b^{6} c^{2} - 640 \, a^{13} b^{4} c^{3} + 1280 \, a^{14} b^{2} c^{4} - 1024 \, a^{15} c^{5}}}\right)} \sqrt{-\frac{b^{9} - 21 \, a b^{7} c + 189 \, a^{2} b^{5} c^{2} - 840 \, a^{3} b^{3} c^{3} + 1680 \, a^{4} b c^{4} + {\left(a^{5} b^{10} - 20 \, a^{6} b^{8} c + 160 \, a^{7} b^{6} c^{2} - 640 \, a^{8} b^{4} c^{3} + 1280 \, a^{9} b^{2} c^{4} - 1024 \, a^{10} c^{5}\right)} \sqrt{\frac{b^{8} - 22 \, a b^{6} c + 219 \, a^{2} b^{4} c^{2} - 1078 \, a^{3} b^{2} c^{3} + 2401 \, a^{4} c^{4}}{a^{10} b^{10} - 20 \, a^{11} b^{8} c + 160 \, a^{12} b^{6} c^{2} - 640 \, a^{13} b^{4} c^{3} + 1280 \, a^{14} b^{2} c^{4} - 1024 \, a^{15} c^{5}}}}{a^{5} b^{10} - 20 \, a^{6} b^{8} c + 160 \, a^{7} b^{6} c^{2} - 640 \, a^{8} b^{4} c^{3} + 1280 \, a^{9} b^{2} c^{4} - 1024 \, a^{10} c^{5}}}\right) + 3 \, \sqrt{\frac{1}{2}} {\left({\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} x^{8} + a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2} + 2 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} x^{6} + {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 32 \, a^{5} c^{3}\right)} x^{4} + 2 \, {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} x^{2}\right)} \sqrt{-\frac{b^{9} - 21 \, a b^{7} c + 189 \, a^{2} b^{5} c^{2} - 840 \, a^{3} b^{3} c^{3} + 1680 \, a^{4} b c^{4} + {\left(a^{5} b^{10} - 20 \, a^{6} b^{8} c + 160 \, a^{7} b^{6} c^{2} - 640 \, a^{8} b^{4} c^{3} + 1280 \, a^{9} b^{2} c^{4} - 1024 \, a^{10} c^{5}\right)} \sqrt{\frac{b^{8} - 22 \, a b^{6} c + 219 \, a^{2} b^{4} c^{2} - 1078 \, a^{3} b^{2} c^{3} + 2401 \, a^{4} c^{4}}{a^{10} b^{10} - 20 \, a^{11} b^{8} c + 160 \, a^{12} b^{6} c^{2} - 640 \, a^{13} b^{4} c^{3} + 1280 \, a^{14} b^{2} c^{4} - 1024 \, a^{15} c^{5}}}}{a^{5} b^{10} - 20 \, a^{6} b^{8} c + 160 \, a^{7} b^{6} c^{2} - 640 \, a^{8} b^{4} c^{3} + 1280 \, a^{9} b^{2} c^{4} - 1024 \, a^{10} c^{5}}} \log\left(27 \, {\left(21 \, b^{8} c^{3} - 447 \, a b^{6} c^{4} + 4189 \, a^{2} b^{4} c^{5} - 19208 \, a^{3} b^{2} c^{6} + 38416 \, a^{4} c^{7}\right)} x - \frac{27}{2} \, \sqrt{\frac{1}{2}} {\left(b^{14} - 32 \, a b^{12} c + 464 \, a^{2} b^{10} c^{2} - 3885 \, a^{3} b^{8} c^{3} + 20088 \, a^{4} b^{6} c^{4} - 63680 \, a^{5} b^{4} c^{5} + 113792 \, a^{6} b^{2} c^{6} - 87808 \, a^{7} c^{7} - {\left(a^{5} b^{15} - 31 \, a^{6} b^{13} c + 424 \, a^{7} b^{11} c^{2} - 3280 \, a^{8} b^{9} c^{3} + 15360 \, a^{9} b^{7} c^{4} - 43264 \, a^{10} b^{5} c^{5} + 67584 \, a^{11} b^{3} c^{6} - 45056 \, a^{12} b c^{7}\right)} \sqrt{\frac{b^{8} - 22 \, a b^{6} c + 219 \, a^{2} b^{4} c^{2} - 1078 \, a^{3} b^{2} c^{3} + 2401 \, a^{4} c^{4}}{a^{10} b^{10} - 20 \, a^{11} b^{8} c + 160 \, a^{12} b^{6} c^{2} - 640 \, a^{13} b^{4} c^{3} + 1280 \, a^{14} b^{2} c^{4} - 1024 \, a^{15} c^{5}}}\right)} \sqrt{-\frac{b^{9} - 21 \, a b^{7} c + 189 \, a^{2} b^{5} c^{2} - 840 \, a^{3} b^{3} c^{3} + 1680 \, a^{4} b c^{4} + {\left(a^{5} b^{10} - 20 \, a^{6} b^{8} c + 160 \, a^{7} b^{6} c^{2} - 640 \, a^{8} b^{4} c^{3} + 1280 \, a^{9} b^{2} c^{4} - 1024 \, a^{10} c^{5}\right)} \sqrt{\frac{b^{8} - 22 \, a b^{6} c + 219 \, a^{2} b^{4} c^{2} - 1078 \, a^{3} b^{2} c^{3} + 2401 \, a^{4} c^{4}}{a^{10} b^{10} - 20 \, a^{11} b^{8} c + 160 \, a^{12} b^{6} c^{2} - 640 \, a^{13} b^{4} c^{3} + 1280 \, a^{14} b^{2} c^{4} - 1024 \, a^{15} c^{5}}}}{a^{5} b^{10} - 20 \, a^{6} b^{8} c + 160 \, a^{7} b^{6} c^{2} - 640 \, a^{8} b^{4} c^{3} + 1280 \, a^{9} b^{2} c^{4} - 1024 \, a^{10} c^{5}}}\right) - 3 \, \sqrt{\frac{1}{2}} {\left({\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} x^{8} + a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2} + 2 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} x^{6} + {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 32 \, a^{5} c^{3}\right)} x^{4} + 2 \, {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} x^{2}\right)} \sqrt{-\frac{b^{9} - 21 \, a b^{7} c + 189 \, a^{2} b^{5} c^{2} - 840 \, a^{3} b^{3} c^{3} + 1680 \, a^{4} b c^{4} - {\left(a^{5} b^{10} - 20 \, a^{6} b^{8} c + 160 \, a^{7} b^{6} c^{2} - 640 \, a^{8} b^{4} c^{3} + 1280 \, a^{9} b^{2} c^{4} - 1024 \, a^{10} c^{5}\right)} \sqrt{\frac{b^{8} - 22 \, a b^{6} c + 219 \, a^{2} b^{4} c^{2} - 1078 \, a^{3} b^{2} c^{3} + 2401 \, a^{4} c^{4}}{a^{10} b^{10} - 20 \, a^{11} b^{8} c + 160 \, a^{12} b^{6} c^{2} - 640 \, a^{13} b^{4} c^{3} + 1280 \, a^{14} b^{2} c^{4} - 1024 \, a^{15} c^{5}}}}{a^{5} b^{10} - 20 \, a^{6} b^{8} c + 160 \, a^{7} b^{6} c^{2} - 640 \, a^{8} b^{4} c^{3} + 1280 \, a^{9} b^{2} c^{4} - 1024 \, a^{10} c^{5}}} \log\left(27 \, {\left(21 \, b^{8} c^{3} - 447 \, a b^{6} c^{4} + 4189 \, a^{2} b^{4} c^{5} - 19208 \, a^{3} b^{2} c^{6} + 38416 \, a^{4} c^{7}\right)} x + \frac{27}{2} \, \sqrt{\frac{1}{2}} {\left(b^{14} - 32 \, a b^{12} c + 464 \, a^{2} b^{10} c^{2} - 3885 \, a^{3} b^{8} c^{3} + 20088 \, a^{4} b^{6} c^{4} - 63680 \, a^{5} b^{4} c^{5} + 113792 \, a^{6} b^{2} c^{6} - 87808 \, a^{7} c^{7} + {\left(a^{5} b^{15} - 31 \, a^{6} b^{13} c + 424 \, a^{7} b^{11} c^{2} - 3280 \, a^{8} b^{9} c^{3} + 15360 \, a^{9} b^{7} c^{4} - 43264 \, a^{10} b^{5} c^{5} + 67584 \, a^{11} b^{3} c^{6} - 45056 \, a^{12} b c^{7}\right)} \sqrt{\frac{b^{8} - 22 \, a b^{6} c + 219 \, a^{2} b^{4} c^{2} - 1078 \, a^{3} b^{2} c^{3} + 2401 \, a^{4} c^{4}}{a^{10} b^{10} - 20 \, a^{11} b^{8} c + 160 \, a^{12} b^{6} c^{2} - 640 \, a^{13} b^{4} c^{3} + 1280 \, a^{14} b^{2} c^{4} - 1024 \, a^{15} c^{5}}}\right)} \sqrt{-\frac{b^{9} - 21 \, a b^{7} c + 189 \, a^{2} b^{5} c^{2} - 840 \, a^{3} b^{3} c^{3} + 1680 \, a^{4} b c^{4} - {\left(a^{5} b^{10} - 20 \, a^{6} b^{8} c + 160 \, a^{7} b^{6} c^{2} - 640 \, a^{8} b^{4} c^{3} + 1280 \, a^{9} b^{2} c^{4} - 1024 \, a^{10} c^{5}\right)} \sqrt{\frac{b^{8} - 22 \, a b^{6} c + 219 \, a^{2} b^{4} c^{2} - 1078 \, a^{3} b^{2} c^{3} + 2401 \, a^{4} c^{4}}{a^{10} b^{10} - 20 \, a^{11} b^{8} c + 160 \, a^{12} b^{6} c^{2} - 640 \, a^{13} b^{4} c^{3} + 1280 \, a^{14} b^{2} c^{4} - 1024 \, a^{15} c^{5}}}}{a^{5} b^{10} - 20 \, a^{6} b^{8} c + 160 \, a^{7} b^{6} c^{2} - 640 \, a^{8} b^{4} c^{3} + 1280 \, a^{9} b^{2} c^{4} - 1024 \, a^{10} c^{5}}}\right) + 3 \, \sqrt{\frac{1}{2}} {\left({\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} x^{8} + a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2} + 2 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} x^{6} + {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 32 \, a^{5} c^{3}\right)} x^{4} + 2 \, {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} x^{2}\right)} \sqrt{-\frac{b^{9} - 21 \, a b^{7} c + 189 \, a^{2} b^{5} c^{2} - 840 \, a^{3} b^{3} c^{3} + 1680 \, a^{4} b c^{4} - {\left(a^{5} b^{10} - 20 \, a^{6} b^{8} c + 160 \, a^{7} b^{6} c^{2} - 640 \, a^{8} b^{4} c^{3} + 1280 \, a^{9} b^{2} c^{4} - 1024 \, a^{10} c^{5}\right)} \sqrt{\frac{b^{8} - 22 \, a b^{6} c + 219 \, a^{2} b^{4} c^{2} - 1078 \, a^{3} b^{2} c^{3} + 2401 \, a^{4} c^{4}}{a^{10} b^{10} - 20 \, a^{11} b^{8} c + 160 \, a^{12} b^{6} c^{2} - 640 \, a^{13} b^{4} c^{3} + 1280 \, a^{14} b^{2} c^{4} - 1024 \, a^{15} c^{5}}}}{a^{5} b^{10} - 20 \, a^{6} b^{8} c + 160 \, a^{7} b^{6} c^{2} - 640 \, a^{8} b^{4} c^{3} + 1280 \, a^{9} b^{2} c^{4} - 1024 \, a^{10} c^{5}}} \log\left(27 \, {\left(21 \, b^{8} c^{3} - 447 \, a b^{6} c^{4} + 4189 \, a^{2} b^{4} c^{5} - 19208 \, a^{3} b^{2} c^{6} + 38416 \, a^{4} c^{7}\right)} x - \frac{27}{2} \, \sqrt{\frac{1}{2}} {\left(b^{14} - 32 \, a b^{12} c + 464 \, a^{2} b^{10} c^{2} - 3885 \, a^{3} b^{8} c^{3} + 20088 \, a^{4} b^{6} c^{4} - 63680 \, a^{5} b^{4} c^{5} + 113792 \, a^{6} b^{2} c^{6} - 87808 \, a^{7} c^{7} + {\left(a^{5} b^{15} - 31 \, a^{6} b^{13} c + 424 \, a^{7} b^{11} c^{2} - 3280 \, a^{8} b^{9} c^{3} + 15360 \, a^{9} b^{7} c^{4} - 43264 \, a^{10} b^{5} c^{5} + 67584 \, a^{11} b^{3} c^{6} - 45056 \, a^{12} b c^{7}\right)} \sqrt{\frac{b^{8} - 22 \, a b^{6} c + 219 \, a^{2} b^{4} c^{2} - 1078 \, a^{3} b^{2} c^{3} + 2401 \, a^{4} c^{4}}{a^{10} b^{10} - 20 \, a^{11} b^{8} c + 160 \, a^{12} b^{6} c^{2} - 640 \, a^{13} b^{4} c^{3} + 1280 \, a^{14} b^{2} c^{4} - 1024 \, a^{15} c^{5}}}\right)} \sqrt{-\frac{b^{9} - 21 \, a b^{7} c + 189 \, a^{2} b^{5} c^{2} - 840 \, a^{3} b^{3} c^{3} + 1680 \, a^{4} b c^{4} - {\left(a^{5} b^{10} - 20 \, a^{6} b^{8} c + 160 \, a^{7} b^{6} c^{2} - 640 \, a^{8} b^{4} c^{3} + 1280 \, a^{9} b^{2} c^{4} - 1024 \, a^{10} c^{5}\right)} \sqrt{\frac{b^{8} - 22 \, a b^{6} c + 219 \, a^{2} b^{4} c^{2} - 1078 \, a^{3} b^{2} c^{3} + 2401 \, a^{4} c^{4}}{a^{10} b^{10} - 20 \, a^{11} b^{8} c + 160 \, a^{12} b^{6} c^{2} - 640 \, a^{13} b^{4} c^{3} + 1280 \, a^{14} b^{2} c^{4} - 1024 \, a^{15} c^{5}}}}{a^{5} b^{10} - 20 \, a^{6} b^{8} c + 160 \, a^{7} b^{6} c^{2} - 640 \, a^{8} b^{4} c^{3} + 1280 \, a^{9} b^{2} c^{4} - 1024 \, a^{10} c^{5}}}\right) + 2 \, {\left(5 \, a b^{4} - 37 \, a^{2} b^{2} c + 44 \, a^{3} c^{2}\right)} x}{16 \, {\left({\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} x^{8} + a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2} + 2 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} x^{6} + {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 32 \, a^{5} c^{3}\right)} x^{4} + 2 \, {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} x^{2}\right)}}"," ",0,"1/16*(6*(b^3*c^2 - 8*a*b*c^3)*x^7 + 2*(6*b^4*c - 49*a*b^2*c^2 + 28*a^2*c^3)*x^5 + 2*(3*b^5 - 20*a*b^3*c - 4*a^2*b*c^2)*x^3 - 3*sqrt(1/2)*((a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*x^8 + a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2 + 2*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*x^6 + (a^2*b^6 - 6*a^3*b^4*c + 32*a^5*c^3)*x^4 + 2*(a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*x^2)*sqrt(-(b^9 - 21*a*b^7*c + 189*a^2*b^5*c^2 - 840*a^3*b^3*c^3 + 1680*a^4*b*c^4 + (a^5*b^10 - 20*a^6*b^8*c + 160*a^7*b^6*c^2 - 640*a^8*b^4*c^3 + 1280*a^9*b^2*c^4 - 1024*a^10*c^5)*sqrt((b^8 - 22*a*b^6*c + 219*a^2*b^4*c^2 - 1078*a^3*b^2*c^3 + 2401*a^4*c^4)/(a^10*b^10 - 20*a^11*b^8*c + 160*a^12*b^6*c^2 - 640*a^13*b^4*c^3 + 1280*a^14*b^2*c^4 - 1024*a^15*c^5)))/(a^5*b^10 - 20*a^6*b^8*c + 160*a^7*b^6*c^2 - 640*a^8*b^4*c^3 + 1280*a^9*b^2*c^4 - 1024*a^10*c^5))*log(27*(21*b^8*c^3 - 447*a*b^6*c^4 + 4189*a^2*b^4*c^5 - 19208*a^3*b^2*c^6 + 38416*a^4*c^7)*x + 27/2*sqrt(1/2)*(b^14 - 32*a*b^12*c + 464*a^2*b^10*c^2 - 3885*a^3*b^8*c^3 + 20088*a^4*b^6*c^4 - 63680*a^5*b^4*c^5 + 113792*a^6*b^2*c^6 - 87808*a^7*c^7 - (a^5*b^15 - 31*a^6*b^13*c + 424*a^7*b^11*c^2 - 3280*a^8*b^9*c^3 + 15360*a^9*b^7*c^4 - 43264*a^10*b^5*c^5 + 67584*a^11*b^3*c^6 - 45056*a^12*b*c^7)*sqrt((b^8 - 22*a*b^6*c + 219*a^2*b^4*c^2 - 1078*a^3*b^2*c^3 + 2401*a^4*c^4)/(a^10*b^10 - 20*a^11*b^8*c + 160*a^12*b^6*c^2 - 640*a^13*b^4*c^3 + 1280*a^14*b^2*c^4 - 1024*a^15*c^5)))*sqrt(-(b^9 - 21*a*b^7*c + 189*a^2*b^5*c^2 - 840*a^3*b^3*c^3 + 1680*a^4*b*c^4 + (a^5*b^10 - 20*a^6*b^8*c + 160*a^7*b^6*c^2 - 640*a^8*b^4*c^3 + 1280*a^9*b^2*c^4 - 1024*a^10*c^5)*sqrt((b^8 - 22*a*b^6*c + 219*a^2*b^4*c^2 - 1078*a^3*b^2*c^3 + 2401*a^4*c^4)/(a^10*b^10 - 20*a^11*b^8*c + 160*a^12*b^6*c^2 - 640*a^13*b^4*c^3 + 1280*a^14*b^2*c^4 - 1024*a^15*c^5)))/(a^5*b^10 - 20*a^6*b^8*c + 160*a^7*b^6*c^2 - 640*a^8*b^4*c^3 + 1280*a^9*b^2*c^4 - 1024*a^10*c^5))) + 3*sqrt(1/2)*((a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*x^8 + a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2 + 2*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*x^6 + (a^2*b^6 - 6*a^3*b^4*c + 32*a^5*c^3)*x^4 + 2*(a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*x^2)*sqrt(-(b^9 - 21*a*b^7*c + 189*a^2*b^5*c^2 - 840*a^3*b^3*c^3 + 1680*a^4*b*c^4 + (a^5*b^10 - 20*a^6*b^8*c + 160*a^7*b^6*c^2 - 640*a^8*b^4*c^3 + 1280*a^9*b^2*c^4 - 1024*a^10*c^5)*sqrt((b^8 - 22*a*b^6*c + 219*a^2*b^4*c^2 - 1078*a^3*b^2*c^3 + 2401*a^4*c^4)/(a^10*b^10 - 20*a^11*b^8*c + 160*a^12*b^6*c^2 - 640*a^13*b^4*c^3 + 1280*a^14*b^2*c^4 - 1024*a^15*c^5)))/(a^5*b^10 - 20*a^6*b^8*c + 160*a^7*b^6*c^2 - 640*a^8*b^4*c^3 + 1280*a^9*b^2*c^4 - 1024*a^10*c^5))*log(27*(21*b^8*c^3 - 447*a*b^6*c^4 + 4189*a^2*b^4*c^5 - 19208*a^3*b^2*c^6 + 38416*a^4*c^7)*x - 27/2*sqrt(1/2)*(b^14 - 32*a*b^12*c + 464*a^2*b^10*c^2 - 3885*a^3*b^8*c^3 + 20088*a^4*b^6*c^4 - 63680*a^5*b^4*c^5 + 113792*a^6*b^2*c^6 - 87808*a^7*c^7 - (a^5*b^15 - 31*a^6*b^13*c + 424*a^7*b^11*c^2 - 3280*a^8*b^9*c^3 + 15360*a^9*b^7*c^4 - 43264*a^10*b^5*c^5 + 67584*a^11*b^3*c^6 - 45056*a^12*b*c^7)*sqrt((b^8 - 22*a*b^6*c + 219*a^2*b^4*c^2 - 1078*a^3*b^2*c^3 + 2401*a^4*c^4)/(a^10*b^10 - 20*a^11*b^8*c + 160*a^12*b^6*c^2 - 640*a^13*b^4*c^3 + 1280*a^14*b^2*c^4 - 1024*a^15*c^5)))*sqrt(-(b^9 - 21*a*b^7*c + 189*a^2*b^5*c^2 - 840*a^3*b^3*c^3 + 1680*a^4*b*c^4 + (a^5*b^10 - 20*a^6*b^8*c + 160*a^7*b^6*c^2 - 640*a^8*b^4*c^3 + 1280*a^9*b^2*c^4 - 1024*a^10*c^5)*sqrt((b^8 - 22*a*b^6*c + 219*a^2*b^4*c^2 - 1078*a^3*b^2*c^3 + 2401*a^4*c^4)/(a^10*b^10 - 20*a^11*b^8*c + 160*a^12*b^6*c^2 - 640*a^13*b^4*c^3 + 1280*a^14*b^2*c^4 - 1024*a^15*c^5)))/(a^5*b^10 - 20*a^6*b^8*c + 160*a^7*b^6*c^2 - 640*a^8*b^4*c^3 + 1280*a^9*b^2*c^4 - 1024*a^10*c^5))) - 3*sqrt(1/2)*((a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*x^8 + a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2 + 2*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*x^6 + (a^2*b^6 - 6*a^3*b^4*c + 32*a^5*c^3)*x^4 + 2*(a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*x^2)*sqrt(-(b^9 - 21*a*b^7*c + 189*a^2*b^5*c^2 - 840*a^3*b^3*c^3 + 1680*a^4*b*c^4 - (a^5*b^10 - 20*a^6*b^8*c + 160*a^7*b^6*c^2 - 640*a^8*b^4*c^3 + 1280*a^9*b^2*c^4 - 1024*a^10*c^5)*sqrt((b^8 - 22*a*b^6*c + 219*a^2*b^4*c^2 - 1078*a^3*b^2*c^3 + 2401*a^4*c^4)/(a^10*b^10 - 20*a^11*b^8*c + 160*a^12*b^6*c^2 - 640*a^13*b^4*c^3 + 1280*a^14*b^2*c^4 - 1024*a^15*c^5)))/(a^5*b^10 - 20*a^6*b^8*c + 160*a^7*b^6*c^2 - 640*a^8*b^4*c^3 + 1280*a^9*b^2*c^4 - 1024*a^10*c^5))*log(27*(21*b^8*c^3 - 447*a*b^6*c^4 + 4189*a^2*b^4*c^5 - 19208*a^3*b^2*c^6 + 38416*a^4*c^7)*x + 27/2*sqrt(1/2)*(b^14 - 32*a*b^12*c + 464*a^2*b^10*c^2 - 3885*a^3*b^8*c^3 + 20088*a^4*b^6*c^4 - 63680*a^5*b^4*c^5 + 113792*a^6*b^2*c^6 - 87808*a^7*c^7 + (a^5*b^15 - 31*a^6*b^13*c + 424*a^7*b^11*c^2 - 3280*a^8*b^9*c^3 + 15360*a^9*b^7*c^4 - 43264*a^10*b^5*c^5 + 67584*a^11*b^3*c^6 - 45056*a^12*b*c^7)*sqrt((b^8 - 22*a*b^6*c + 219*a^2*b^4*c^2 - 1078*a^3*b^2*c^3 + 2401*a^4*c^4)/(a^10*b^10 - 20*a^11*b^8*c + 160*a^12*b^6*c^2 - 640*a^13*b^4*c^3 + 1280*a^14*b^2*c^4 - 1024*a^15*c^5)))*sqrt(-(b^9 - 21*a*b^7*c + 189*a^2*b^5*c^2 - 840*a^3*b^3*c^3 + 1680*a^4*b*c^4 - (a^5*b^10 - 20*a^6*b^8*c + 160*a^7*b^6*c^2 - 640*a^8*b^4*c^3 + 1280*a^9*b^2*c^4 - 1024*a^10*c^5)*sqrt((b^8 - 22*a*b^6*c + 219*a^2*b^4*c^2 - 1078*a^3*b^2*c^3 + 2401*a^4*c^4)/(a^10*b^10 - 20*a^11*b^8*c + 160*a^12*b^6*c^2 - 640*a^13*b^4*c^3 + 1280*a^14*b^2*c^4 - 1024*a^15*c^5)))/(a^5*b^10 - 20*a^6*b^8*c + 160*a^7*b^6*c^2 - 640*a^8*b^4*c^3 + 1280*a^9*b^2*c^4 - 1024*a^10*c^5))) + 3*sqrt(1/2)*((a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*x^8 + a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2 + 2*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*x^6 + (a^2*b^6 - 6*a^3*b^4*c + 32*a^5*c^3)*x^4 + 2*(a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*x^2)*sqrt(-(b^9 - 21*a*b^7*c + 189*a^2*b^5*c^2 - 840*a^3*b^3*c^3 + 1680*a^4*b*c^4 - (a^5*b^10 - 20*a^6*b^8*c + 160*a^7*b^6*c^2 - 640*a^8*b^4*c^3 + 1280*a^9*b^2*c^4 - 1024*a^10*c^5)*sqrt((b^8 - 22*a*b^6*c + 219*a^2*b^4*c^2 - 1078*a^3*b^2*c^3 + 2401*a^4*c^4)/(a^10*b^10 - 20*a^11*b^8*c + 160*a^12*b^6*c^2 - 640*a^13*b^4*c^3 + 1280*a^14*b^2*c^4 - 1024*a^15*c^5)))/(a^5*b^10 - 20*a^6*b^8*c + 160*a^7*b^6*c^2 - 640*a^8*b^4*c^3 + 1280*a^9*b^2*c^4 - 1024*a^10*c^5))*log(27*(21*b^8*c^3 - 447*a*b^6*c^4 + 4189*a^2*b^4*c^5 - 19208*a^3*b^2*c^6 + 38416*a^4*c^7)*x - 27/2*sqrt(1/2)*(b^14 - 32*a*b^12*c + 464*a^2*b^10*c^2 - 3885*a^3*b^8*c^3 + 20088*a^4*b^6*c^4 - 63680*a^5*b^4*c^5 + 113792*a^6*b^2*c^6 - 87808*a^7*c^7 + (a^5*b^15 - 31*a^6*b^13*c + 424*a^7*b^11*c^2 - 3280*a^8*b^9*c^3 + 15360*a^9*b^7*c^4 - 43264*a^10*b^5*c^5 + 67584*a^11*b^3*c^6 - 45056*a^12*b*c^7)*sqrt((b^8 - 22*a*b^6*c + 219*a^2*b^4*c^2 - 1078*a^3*b^2*c^3 + 2401*a^4*c^4)/(a^10*b^10 - 20*a^11*b^8*c + 160*a^12*b^6*c^2 - 640*a^13*b^4*c^3 + 1280*a^14*b^2*c^4 - 1024*a^15*c^5)))*sqrt(-(b^9 - 21*a*b^7*c + 189*a^2*b^5*c^2 - 840*a^3*b^3*c^3 + 1680*a^4*b*c^4 - (a^5*b^10 - 20*a^6*b^8*c + 160*a^7*b^6*c^2 - 640*a^8*b^4*c^3 + 1280*a^9*b^2*c^4 - 1024*a^10*c^5)*sqrt((b^8 - 22*a*b^6*c + 219*a^2*b^4*c^2 - 1078*a^3*b^2*c^3 + 2401*a^4*c^4)/(a^10*b^10 - 20*a^11*b^8*c + 160*a^12*b^6*c^2 - 640*a^13*b^4*c^3 + 1280*a^14*b^2*c^4 - 1024*a^15*c^5)))/(a^5*b^10 - 20*a^6*b^8*c + 160*a^7*b^6*c^2 - 640*a^8*b^4*c^3 + 1280*a^9*b^2*c^4 - 1024*a^10*c^5))) + 2*(5*a*b^4 - 37*a^2*b^2*c + 44*a^3*c^2)*x)/((a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*x^8 + a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2 + 2*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*x^6 + (a^2*b^6 - 6*a^3*b^4*c + 32*a^5*c^3)*x^4 + 2*(a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*x^2)","B",0
887,1,4924,0,2.590377," ","integrate(1/x^2/(c*x^4+b*x^2+a)^3,x, algorithm=""fricas"")","-\frac{6 \, {\left(5 \, b^{4} c^{2} - 37 \, a b^{2} c^{3} + 60 \, a^{2} c^{4}\right)} x^{8} + 2 \, {\left(30 \, b^{5} c - 227 \, a b^{3} c^{2} + 392 \, a^{2} b c^{3}\right)} x^{6} + 16 \, a^{2} b^{4} - 128 \, a^{3} b^{2} c + 256 \, a^{4} c^{2} + 2 \, {\left(15 \, b^{6} - 91 \, a b^{4} c + 25 \, a^{2} b^{2} c^{2} + 324 \, a^{3} c^{3}\right)} x^{4} + 2 \, {\left(25 \, a b^{5} - 194 \, a^{2} b^{3} c + 364 \, a^{3} b c^{2}\right)} x^{2} + 3 \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} x^{9} + 2 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} x^{7} + {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} x^{5} + 2 \, {\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\right)} \sqrt{-\frac{25 \, b^{11} - 495 \, a b^{9} c + 3894 \, a^{2} b^{7} c^{2} - 15015 \, a^{3} b^{5} c^{3} + 27720 \, a^{4} b^{3} c^{4} - 18480 \, a^{5} b c^{5} + {\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} \sqrt{\frac{625 \, b^{12} - 12250 \, a b^{10} c + 94725 \, a^{2} b^{8} c^{2} - 351310 \, a^{3} b^{6} c^{3} + 591886 \, a^{4} b^{4} c^{4} - 312300 \, a^{5} b^{2} c^{5} + 50625 \, a^{6} c^{6}}{a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}}}}{a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}}} \log\left(-27 \, {\left(4125 \, b^{10} c^{4} - 77825 \, a b^{8} c^{5} + 571030 \, a^{2} b^{6} c^{6} - 1957349 \, a^{3} b^{4} c^{7} + 2835000 \, a^{4} b^{2} c^{8} - 810000 \, a^{5} c^{9}\right)} x + \frac{27}{2} \, \sqrt{\frac{1}{2}} {\left(125 \, b^{17} - 3775 \, a b^{15} c + 49360 \, a^{2} b^{13} c^{2} - 362733 \, a^{3} b^{11} c^{3} + 1623534 \, a^{4} b^{9} c^{4} - 4463140 \, a^{5} b^{7} c^{5} + 7146736 \, a^{6} b^{5} c^{6} - 5684672 \, a^{7} b^{3} c^{7} + 1324800 \, a^{8} b c^{8} - {\left(5 \, a^{7} b^{16} - 152 \, a^{8} b^{14} c + 2006 \, a^{9} b^{12} c^{2} - 14960 \, a^{10} b^{10} c^{3} + 68640 \, a^{11} b^{8} c^{4} - 197120 \, a^{12} b^{6} c^{5} + 342528 \, a^{13} b^{4} c^{6} - 323584 \, a^{14} b^{2} c^{7} + 122880 \, a^{15} c^{8}\right)} \sqrt{\frac{625 \, b^{12} - 12250 \, a b^{10} c + 94725 \, a^{2} b^{8} c^{2} - 351310 \, a^{3} b^{6} c^{3} + 591886 \, a^{4} b^{4} c^{4} - 312300 \, a^{5} b^{2} c^{5} + 50625 \, a^{6} c^{6}}{a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}}}\right)} \sqrt{-\frac{25 \, b^{11} - 495 \, a b^{9} c + 3894 \, a^{2} b^{7} c^{2} - 15015 \, a^{3} b^{5} c^{3} + 27720 \, a^{4} b^{3} c^{4} - 18480 \, a^{5} b c^{5} + {\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} \sqrt{\frac{625 \, b^{12} - 12250 \, a b^{10} c + 94725 \, a^{2} b^{8} c^{2} - 351310 \, a^{3} b^{6} c^{3} + 591886 \, a^{4} b^{4} c^{4} - 312300 \, a^{5} b^{2} c^{5} + 50625 \, a^{6} c^{6}}{a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}}}}{a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}}}\right) - 3 \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} x^{9} + 2 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} x^{7} + {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} x^{5} + 2 \, {\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\right)} \sqrt{-\frac{25 \, b^{11} - 495 \, a b^{9} c + 3894 \, a^{2} b^{7} c^{2} - 15015 \, a^{3} b^{5} c^{3} + 27720 \, a^{4} b^{3} c^{4} - 18480 \, a^{5} b c^{5} + {\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} \sqrt{\frac{625 \, b^{12} - 12250 \, a b^{10} c + 94725 \, a^{2} b^{8} c^{2} - 351310 \, a^{3} b^{6} c^{3} + 591886 \, a^{4} b^{4} c^{4} - 312300 \, a^{5} b^{2} c^{5} + 50625 \, a^{6} c^{6}}{a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}}}}{a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}}} \log\left(-27 \, {\left(4125 \, b^{10} c^{4} - 77825 \, a b^{8} c^{5} + 571030 \, a^{2} b^{6} c^{6} - 1957349 \, a^{3} b^{4} c^{7} + 2835000 \, a^{4} b^{2} c^{8} - 810000 \, a^{5} c^{9}\right)} x - \frac{27}{2} \, \sqrt{\frac{1}{2}} {\left(125 \, b^{17} - 3775 \, a b^{15} c + 49360 \, a^{2} b^{13} c^{2} - 362733 \, a^{3} b^{11} c^{3} + 1623534 \, a^{4} b^{9} c^{4} - 4463140 \, a^{5} b^{7} c^{5} + 7146736 \, a^{6} b^{5} c^{6} - 5684672 \, a^{7} b^{3} c^{7} + 1324800 \, a^{8} b c^{8} - {\left(5 \, a^{7} b^{16} - 152 \, a^{8} b^{14} c + 2006 \, a^{9} b^{12} c^{2} - 14960 \, a^{10} b^{10} c^{3} + 68640 \, a^{11} b^{8} c^{4} - 197120 \, a^{12} b^{6} c^{5} + 342528 \, a^{13} b^{4} c^{6} - 323584 \, a^{14} b^{2} c^{7} + 122880 \, a^{15} c^{8}\right)} \sqrt{\frac{625 \, b^{12} - 12250 \, a b^{10} c + 94725 \, a^{2} b^{8} c^{2} - 351310 \, a^{3} b^{6} c^{3} + 591886 \, a^{4} b^{4} c^{4} - 312300 \, a^{5} b^{2} c^{5} + 50625 \, a^{6} c^{6}}{a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}}}\right)} \sqrt{-\frac{25 \, b^{11} - 495 \, a b^{9} c + 3894 \, a^{2} b^{7} c^{2} - 15015 \, a^{3} b^{5} c^{3} + 27720 \, a^{4} b^{3} c^{4} - 18480 \, a^{5} b c^{5} + {\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} \sqrt{\frac{625 \, b^{12} - 12250 \, a b^{10} c + 94725 \, a^{2} b^{8} c^{2} - 351310 \, a^{3} b^{6} c^{3} + 591886 \, a^{4} b^{4} c^{4} - 312300 \, a^{5} b^{2} c^{5} + 50625 \, a^{6} c^{6}}{a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}}}}{a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}}}\right) + 3 \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} x^{9} + 2 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} x^{7} + {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} x^{5} + 2 \, {\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\right)} \sqrt{-\frac{25 \, b^{11} - 495 \, a b^{9} c + 3894 \, a^{2} b^{7} c^{2} - 15015 \, a^{3} b^{5} c^{3} + 27720 \, a^{4} b^{3} c^{4} - 18480 \, a^{5} b c^{5} - {\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} \sqrt{\frac{625 \, b^{12} - 12250 \, a b^{10} c + 94725 \, a^{2} b^{8} c^{2} - 351310 \, a^{3} b^{6} c^{3} + 591886 \, a^{4} b^{4} c^{4} - 312300 \, a^{5} b^{2} c^{5} + 50625 \, a^{6} c^{6}}{a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}}}}{a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}}} \log\left(-27 \, {\left(4125 \, b^{10} c^{4} - 77825 \, a b^{8} c^{5} + 571030 \, a^{2} b^{6} c^{6} - 1957349 \, a^{3} b^{4} c^{7} + 2835000 \, a^{4} b^{2} c^{8} - 810000 \, a^{5} c^{9}\right)} x + \frac{27}{2} \, \sqrt{\frac{1}{2}} {\left(125 \, b^{17} - 3775 \, a b^{15} c + 49360 \, a^{2} b^{13} c^{2} - 362733 \, a^{3} b^{11} c^{3} + 1623534 \, a^{4} b^{9} c^{4} - 4463140 \, a^{5} b^{7} c^{5} + 7146736 \, a^{6} b^{5} c^{6} - 5684672 \, a^{7} b^{3} c^{7} + 1324800 \, a^{8} b c^{8} + {\left(5 \, a^{7} b^{16} - 152 \, a^{8} b^{14} c + 2006 \, a^{9} b^{12} c^{2} - 14960 \, a^{10} b^{10} c^{3} + 68640 \, a^{11} b^{8} c^{4} - 197120 \, a^{12} b^{6} c^{5} + 342528 \, a^{13} b^{4} c^{6} - 323584 \, a^{14} b^{2} c^{7} + 122880 \, a^{15} c^{8}\right)} \sqrt{\frac{625 \, b^{12} - 12250 \, a b^{10} c + 94725 \, a^{2} b^{8} c^{2} - 351310 \, a^{3} b^{6} c^{3} + 591886 \, a^{4} b^{4} c^{4} - 312300 \, a^{5} b^{2} c^{5} + 50625 \, a^{6} c^{6}}{a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}}}\right)} \sqrt{-\frac{25 \, b^{11} - 495 \, a b^{9} c + 3894 \, a^{2} b^{7} c^{2} - 15015 \, a^{3} b^{5} c^{3} + 27720 \, a^{4} b^{3} c^{4} - 18480 \, a^{5} b c^{5} - {\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} \sqrt{\frac{625 \, b^{12} - 12250 \, a b^{10} c + 94725 \, a^{2} b^{8} c^{2} - 351310 \, a^{3} b^{6} c^{3} + 591886 \, a^{4} b^{4} c^{4} - 312300 \, a^{5} b^{2} c^{5} + 50625 \, a^{6} c^{6}}{a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}}}}{a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}}}\right) - 3 \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} x^{9} + 2 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} x^{7} + {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} x^{5} + 2 \, {\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\right)} \sqrt{-\frac{25 \, b^{11} - 495 \, a b^{9} c + 3894 \, a^{2} b^{7} c^{2} - 15015 \, a^{3} b^{5} c^{3} + 27720 \, a^{4} b^{3} c^{4} - 18480 \, a^{5} b c^{5} - {\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} \sqrt{\frac{625 \, b^{12} - 12250 \, a b^{10} c + 94725 \, a^{2} b^{8} c^{2} - 351310 \, a^{3} b^{6} c^{3} + 591886 \, a^{4} b^{4} c^{4} - 312300 \, a^{5} b^{2} c^{5} + 50625 \, a^{6} c^{6}}{a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}}}}{a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}}} \log\left(-27 \, {\left(4125 \, b^{10} c^{4} - 77825 \, a b^{8} c^{5} + 571030 \, a^{2} b^{6} c^{6} - 1957349 \, a^{3} b^{4} c^{7} + 2835000 \, a^{4} b^{2} c^{8} - 810000 \, a^{5} c^{9}\right)} x - \frac{27}{2} \, \sqrt{\frac{1}{2}} {\left(125 \, b^{17} - 3775 \, a b^{15} c + 49360 \, a^{2} b^{13} c^{2} - 362733 \, a^{3} b^{11} c^{3} + 1623534 \, a^{4} b^{9} c^{4} - 4463140 \, a^{5} b^{7} c^{5} + 7146736 \, a^{6} b^{5} c^{6} - 5684672 \, a^{7} b^{3} c^{7} + 1324800 \, a^{8} b c^{8} + {\left(5 \, a^{7} b^{16} - 152 \, a^{8} b^{14} c + 2006 \, a^{9} b^{12} c^{2} - 14960 \, a^{10} b^{10} c^{3} + 68640 \, a^{11} b^{8} c^{4} - 197120 \, a^{12} b^{6} c^{5} + 342528 \, a^{13} b^{4} c^{6} - 323584 \, a^{14} b^{2} c^{7} + 122880 \, a^{15} c^{8}\right)} \sqrt{\frac{625 \, b^{12} - 12250 \, a b^{10} c + 94725 \, a^{2} b^{8} c^{2} - 351310 \, a^{3} b^{6} c^{3} + 591886 \, a^{4} b^{4} c^{4} - 312300 \, a^{5} b^{2} c^{5} + 50625 \, a^{6} c^{6}}{a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}}}\right)} \sqrt{-\frac{25 \, b^{11} - 495 \, a b^{9} c + 3894 \, a^{2} b^{7} c^{2} - 15015 \, a^{3} b^{5} c^{3} + 27720 \, a^{4} b^{3} c^{4} - 18480 \, a^{5} b c^{5} - {\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} \sqrt{\frac{625 \, b^{12} - 12250 \, a b^{10} c + 94725 \, a^{2} b^{8} c^{2} - 351310 \, a^{3} b^{6} c^{3} + 591886 \, a^{4} b^{4} c^{4} - 312300 \, a^{5} b^{2} c^{5} + 50625 \, a^{6} c^{6}}{a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}}}}{a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}}}\right)}{16 \, {\left({\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} x^{9} + 2 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} x^{7} + {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} x^{5} + 2 \, {\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\right)}}"," ",0,"-1/16*(6*(5*b^4*c^2 - 37*a*b^2*c^3 + 60*a^2*c^4)*x^8 + 2*(30*b^5*c - 227*a*b^3*c^2 + 392*a^2*b*c^3)*x^6 + 16*a^2*b^4 - 128*a^3*b^2*c + 256*a^4*c^2 + 2*(15*b^6 - 91*a*b^4*c + 25*a^2*b^2*c^2 + 324*a^3*c^3)*x^4 + 2*(25*a*b^5 - 194*a^2*b^3*c + 364*a^3*b*c^2)*x^2 + 3*sqrt(1/2)*((a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*x^9 + 2*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*x^7 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*x^5 + 2*(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)*sqrt(-(25*b^11 - 495*a*b^9*c + 3894*a^2*b^7*c^2 - 15015*a^3*b^5*c^3 + 27720*a^4*b^3*c^4 - 18480*a^5*b*c^5 + (a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/(a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)))/(a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5))*log(-27*(4125*b^10*c^4 - 77825*a*b^8*c^5 + 571030*a^2*b^6*c^6 - 1957349*a^3*b^4*c^7 + 2835000*a^4*b^2*c^8 - 810000*a^5*c^9)*x + 27/2*sqrt(1/2)*(125*b^17 - 3775*a*b^15*c + 49360*a^2*b^13*c^2 - 362733*a^3*b^11*c^3 + 1623534*a^4*b^9*c^4 - 4463140*a^5*b^7*c^5 + 7146736*a^6*b^5*c^6 - 5684672*a^7*b^3*c^7 + 1324800*a^8*b*c^8 - (5*a^7*b^16 - 152*a^8*b^14*c + 2006*a^9*b^12*c^2 - 14960*a^10*b^10*c^3 + 68640*a^11*b^8*c^4 - 197120*a^12*b^6*c^5 + 342528*a^13*b^4*c^6 - 323584*a^14*b^2*c^7 + 122880*a^15*c^8)*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/(a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)))*sqrt(-(25*b^11 - 495*a*b^9*c + 3894*a^2*b^7*c^2 - 15015*a^3*b^5*c^3 + 27720*a^4*b^3*c^4 - 18480*a^5*b*c^5 + (a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/(a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)))/(a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5))) - 3*sqrt(1/2)*((a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*x^9 + 2*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*x^7 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*x^5 + 2*(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)*sqrt(-(25*b^11 - 495*a*b^9*c + 3894*a^2*b^7*c^2 - 15015*a^3*b^5*c^3 + 27720*a^4*b^3*c^4 - 18480*a^5*b*c^5 + (a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/(a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)))/(a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5))*log(-27*(4125*b^10*c^4 - 77825*a*b^8*c^5 + 571030*a^2*b^6*c^6 - 1957349*a^3*b^4*c^7 + 2835000*a^4*b^2*c^8 - 810000*a^5*c^9)*x - 27/2*sqrt(1/2)*(125*b^17 - 3775*a*b^15*c + 49360*a^2*b^13*c^2 - 362733*a^3*b^11*c^3 + 1623534*a^4*b^9*c^4 - 4463140*a^5*b^7*c^5 + 7146736*a^6*b^5*c^6 - 5684672*a^7*b^3*c^7 + 1324800*a^8*b*c^8 - (5*a^7*b^16 - 152*a^8*b^14*c + 2006*a^9*b^12*c^2 - 14960*a^10*b^10*c^3 + 68640*a^11*b^8*c^4 - 197120*a^12*b^6*c^5 + 342528*a^13*b^4*c^6 - 323584*a^14*b^2*c^7 + 122880*a^15*c^8)*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/(a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)))*sqrt(-(25*b^11 - 495*a*b^9*c + 3894*a^2*b^7*c^2 - 15015*a^3*b^5*c^3 + 27720*a^4*b^3*c^4 - 18480*a^5*b*c^5 + (a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/(a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)))/(a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5))) + 3*sqrt(1/2)*((a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*x^9 + 2*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*x^7 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*x^5 + 2*(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)*sqrt(-(25*b^11 - 495*a*b^9*c + 3894*a^2*b^7*c^2 - 15015*a^3*b^5*c^3 + 27720*a^4*b^3*c^4 - 18480*a^5*b*c^5 - (a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/(a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)))/(a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5))*log(-27*(4125*b^10*c^4 - 77825*a*b^8*c^5 + 571030*a^2*b^6*c^6 - 1957349*a^3*b^4*c^7 + 2835000*a^4*b^2*c^8 - 810000*a^5*c^9)*x + 27/2*sqrt(1/2)*(125*b^17 - 3775*a*b^15*c + 49360*a^2*b^13*c^2 - 362733*a^3*b^11*c^3 + 1623534*a^4*b^9*c^4 - 4463140*a^5*b^7*c^5 + 7146736*a^6*b^5*c^6 - 5684672*a^7*b^3*c^7 + 1324800*a^8*b*c^8 + (5*a^7*b^16 - 152*a^8*b^14*c + 2006*a^9*b^12*c^2 - 14960*a^10*b^10*c^3 + 68640*a^11*b^8*c^4 - 197120*a^12*b^6*c^5 + 342528*a^13*b^4*c^6 - 323584*a^14*b^2*c^7 + 122880*a^15*c^8)*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/(a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)))*sqrt(-(25*b^11 - 495*a*b^9*c + 3894*a^2*b^7*c^2 - 15015*a^3*b^5*c^3 + 27720*a^4*b^3*c^4 - 18480*a^5*b*c^5 - (a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/(a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)))/(a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5))) - 3*sqrt(1/2)*((a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*x^9 + 2*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*x^7 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*x^5 + 2*(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)*sqrt(-(25*b^11 - 495*a*b^9*c + 3894*a^2*b^7*c^2 - 15015*a^3*b^5*c^3 + 27720*a^4*b^3*c^4 - 18480*a^5*b*c^5 - (a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/(a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)))/(a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5))*log(-27*(4125*b^10*c^4 - 77825*a*b^8*c^5 + 571030*a^2*b^6*c^6 - 1957349*a^3*b^4*c^7 + 2835000*a^4*b^2*c^8 - 810000*a^5*c^9)*x - 27/2*sqrt(1/2)*(125*b^17 - 3775*a*b^15*c + 49360*a^2*b^13*c^2 - 362733*a^3*b^11*c^3 + 1623534*a^4*b^9*c^4 - 4463140*a^5*b^7*c^5 + 7146736*a^6*b^5*c^6 - 5684672*a^7*b^3*c^7 + 1324800*a^8*b*c^8 + (5*a^7*b^16 - 152*a^8*b^14*c + 2006*a^9*b^12*c^2 - 14960*a^10*b^10*c^3 + 68640*a^11*b^8*c^4 - 197120*a^12*b^6*c^5 + 342528*a^13*b^4*c^6 - 323584*a^14*b^2*c^7 + 122880*a^15*c^8)*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/(a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)))*sqrt(-(25*b^11 - 495*a*b^9*c + 3894*a^2*b^7*c^2 - 15015*a^3*b^5*c^3 + 27720*a^4*b^3*c^4 - 18480*a^5*b*c^5 - (a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/(a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)))/(a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5))))/((a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*x^9 + 2*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*x^7 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*x^5 + 2*(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)","B",0
888,1,259,0,1.056188," ","integrate(x^5/(c*x^4-b*x^2+a),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
889,1,206,0,0.692904," ","integrate(x^3/(c*x^4-b*x^2+a),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
890,1,134,0,0.870007," ","integrate(x/(c*x^4-b*x^2+a),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
891,1,230,0,0.876174," ","integrate(1/x/(c*x^4-b*x^2+a),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
892,1,298,0,1.625317," ","integrate(1/x^3/(c*x^4-b*x^2+a),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
893,1,1051,0,1.155754," ","integrate(x^4/(c*x^4-b*x^2+a),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
894,1,551,0,0.817811," ","integrate(x^2/(c*x^4-b*x^2+a),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
895,1,605,0,0.824054," ","integrate(1/(c*x^4-b*x^2+a),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
896,1,1108,0,0.838359," ","integrate(1/x^2/(c*x^4-b*x^2+a),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
897,1,156,0,1.048364," ","integrate(x^5/(a*x^4+2*a*x^2+a-b),x, algorithm=""fricas"")","\left[\frac{2 \, a b x^{2} - 2 \, a b \log\left(a x^{4} + 2 \, a x^{2} + a - b\right) + \sqrt{a b} {\left(a + b\right)} \log\left(\frac{a x^{4} + 2 \, a x^{2} - 2 \, \sqrt{a b} {\left(x^{2} + 1\right)} + a + b}{a x^{4} + 2 \, a x^{2} + a - b}\right)}{4 \, a^{2} b}, \frac{a b x^{2} - a b \log\left(a x^{4} + 2 \, a x^{2} + a - b\right) + \sqrt{-a b} {\left(a + b\right)} \arctan\left(\frac{\sqrt{-a b}}{a x^{2} + a}\right)}{2 \, a^{2} b}\right]"," ",0,"[1/4*(2*a*b*x^2 - 2*a*b*log(a*x^4 + 2*a*x^2 + a - b) + sqrt(a*b)*(a + b)*log((a*x^4 + 2*a*x^2 - 2*sqrt(a*b)*(x^2 + 1) + a + b)/(a*x^4 + 2*a*x^2 + a - b)))/(a^2*b), 1/2*(a*b*x^2 - a*b*log(a*x^4 + 2*a*x^2 + a - b) + sqrt(-a*b)*(a + b)*arctan(sqrt(-a*b)/(a*x^2 + a)))/(a^2*b)]","A",0
898,1,134,0,0.956391," ","integrate(x^3/(a*x^4+2*a*x^2+a-b),x, algorithm=""fricas"")","\left[\frac{b \log\left(a x^{4} + 2 \, a x^{2} + a - b\right) + \sqrt{a b} \log\left(\frac{a x^{4} + 2 \, a x^{2} + 2 \, \sqrt{a b} {\left(x^{2} + 1\right)} + a + b}{a x^{4} + 2 \, a x^{2} + a - b}\right)}{4 \, a b}, \frac{b \log\left(a x^{4} + 2 \, a x^{2} + a - b\right) - 2 \, \sqrt{-a b} \arctan\left(\frac{\sqrt{-a b}}{a x^{2} + a}\right)}{4 \, a b}\right]"," ",0,"[1/4*(b*log(a*x^4 + 2*a*x^2 + a - b) + sqrt(a*b)*log((a*x^4 + 2*a*x^2 + 2*sqrt(a*b)*(x^2 + 1) + a + b)/(a*x^4 + 2*a*x^2 + a - b)))/(a*b), 1/4*(b*log(a*x^4 + 2*a*x^2 + a - b) - 2*sqrt(-a*b)*arctan(sqrt(-a*b)/(a*x^2 + a)))/(a*b)]","A",0
899,1,91,0,1.111820," ","integrate(x/(a*x^4+2*a*x^2+a-b),x, algorithm=""fricas"")","\left[\frac{\sqrt{a b} \log\left(\frac{a x^{4} + 2 \, a x^{2} - 2 \, \sqrt{a b} {\left(x^{2} + 1\right)} + a + b}{a x^{4} + 2 \, a x^{2} + a - b}\right)}{4 \, a b}, \frac{\sqrt{-a b} \arctan\left(\frac{\sqrt{-a b}}{a x^{2} + a}\right)}{2 \, a b}\right]"," ",0,"[1/4*sqrt(a*b)*log((a*x^4 + 2*a*x^2 - 2*sqrt(a*b)*(x^2 + 1) + a + b)/(a*x^4 + 2*a*x^2 + a - b))/(a*b), 1/2*sqrt(-a*b)*arctan(sqrt(-a*b)/(a*x^2 + a))/(a*b)]","A",0
900,1,151,0,0.969961," ","integrate(1/x/(a*x^4+2*a*x^2+a-b),x, algorithm=""fricas"")","\left[-\frac{\sqrt{\frac{a}{b}} \log\left(\frac{a x^{4} + 2 \, a x^{2} - 2 \, {\left(b x^{2} + b\right)} \sqrt{\frac{a}{b}} + a + b}{a x^{4} + 2 \, a x^{2} + a - b}\right) + \log\left(a x^{4} + 2 \, a x^{2} + a - b\right) - 4 \, \log\left(x\right)}{4 \, {\left(a - b\right)}}, -\frac{2 \, \sqrt{-\frac{a}{b}} \arctan\left(\frac{b \sqrt{-\frac{a}{b}}}{a x^{2} + a}\right) + \log\left(a x^{4} + 2 \, a x^{2} + a - b\right) - 4 \, \log\left(x\right)}{4 \, {\left(a - b\right)}}\right]"," ",0,"[-1/4*(sqrt(a/b)*log((a*x^4 + 2*a*x^2 - 2*(b*x^2 + b)*sqrt(a/b) + a + b)/(a*x^4 + 2*a*x^2 + a - b)) + log(a*x^4 + 2*a*x^2 + a - b) - 4*log(x))/(a - b), -1/4*(2*sqrt(-a/b)*arctan(b*sqrt(-a/b)/(a*x^2 + a)) + log(a*x^4 + 2*a*x^2 + a - b) - 4*log(x))/(a - b)]","A",0
901,1,209,0,0.782736," ","integrate(1/x^3/(a*x^4+2*a*x^2+a-b),x, algorithm=""fricas"")","\left[\frac{{\left(a + b\right)} x^{2} \sqrt{\frac{a}{b}} \log\left(\frac{a x^{4} + 2 \, a x^{2} - 2 \, {\left(b x^{2} + b\right)} \sqrt{\frac{a}{b}} + a + b}{a x^{4} + 2 \, a x^{2} + a - b}\right) + 2 \, a x^{2} \log\left(a x^{4} + 2 \, a x^{2} + a - b\right) - 8 \, a x^{2} \log\left(x\right) - 2 \, a + 2 \, b}{4 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} x^{2}}, \frac{{\left(a + b\right)} x^{2} \sqrt{-\frac{a}{b}} \arctan\left(\frac{b \sqrt{-\frac{a}{b}}}{a x^{2} + a}\right) + a x^{2} \log\left(a x^{4} + 2 \, a x^{2} + a - b\right) - 4 \, a x^{2} \log\left(x\right) - a + b}{2 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} x^{2}}\right]"," ",0,"[1/4*((a + b)*x^2*sqrt(a/b)*log((a*x^4 + 2*a*x^2 - 2*(b*x^2 + b)*sqrt(a/b) + a + b)/(a*x^4 + 2*a*x^2 + a - b)) + 2*a*x^2*log(a*x^4 + 2*a*x^2 + a - b) - 8*a*x^2*log(x) - 2*a + 2*b)/((a^2 - 2*a*b + b^2)*x^2), 1/2*((a + b)*x^2*sqrt(-a/b)*arctan(b*sqrt(-a/b)/(a*x^2 + a)) + a*x^2*log(a*x^4 + 2*a*x^2 + a - b) - 4*a*x^2*log(x) - a + b)/((a^2 - 2*a*b + b^2)*x^2)]","A",0
902,1,603,0,0.846740," ","integrate(x^4/(a*x^4+2*a*x^2+a-b),x, algorithm=""fricas"")","\frac{a \sqrt{-\frac{a^{2} b \sqrt{\frac{9 \, a^{2} + 6 \, a b + b^{2}}{a^{5} b}} + a + 3 \, b}{a^{2} b}} \log\left(-{\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} x + {\left(a^{4} b \sqrt{\frac{9 \, a^{2} + 6 \, a b + b^{2}}{a^{5} b}} - 3 \, a^{2} b - a b^{2}\right)} \sqrt{-\frac{a^{2} b \sqrt{\frac{9 \, a^{2} + 6 \, a b + b^{2}}{a^{5} b}} + a + 3 \, b}{a^{2} b}}\right) - a \sqrt{-\frac{a^{2} b \sqrt{\frac{9 \, a^{2} + 6 \, a b + b^{2}}{a^{5} b}} + a + 3 \, b}{a^{2} b}} \log\left(-{\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} x - {\left(a^{4} b \sqrt{\frac{9 \, a^{2} + 6 \, a b + b^{2}}{a^{5} b}} - 3 \, a^{2} b - a b^{2}\right)} \sqrt{-\frac{a^{2} b \sqrt{\frac{9 \, a^{2} + 6 \, a b + b^{2}}{a^{5} b}} + a + 3 \, b}{a^{2} b}}\right) - a \sqrt{\frac{a^{2} b \sqrt{\frac{9 \, a^{2} + 6 \, a b + b^{2}}{a^{5} b}} - a - 3 \, b}{a^{2} b}} \log\left(-{\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} x + {\left(a^{4} b \sqrt{\frac{9 \, a^{2} + 6 \, a b + b^{2}}{a^{5} b}} + 3 \, a^{2} b + a b^{2}\right)} \sqrt{\frac{a^{2} b \sqrt{\frac{9 \, a^{2} + 6 \, a b + b^{2}}{a^{5} b}} - a - 3 \, b}{a^{2} b}}\right) + a \sqrt{\frac{a^{2} b \sqrt{\frac{9 \, a^{2} + 6 \, a b + b^{2}}{a^{5} b}} - a - 3 \, b}{a^{2} b}} \log\left(-{\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} x - {\left(a^{4} b \sqrt{\frac{9 \, a^{2} + 6 \, a b + b^{2}}{a^{5} b}} + 3 \, a^{2} b + a b^{2}\right)} \sqrt{\frac{a^{2} b \sqrt{\frac{9 \, a^{2} + 6 \, a b + b^{2}}{a^{5} b}} - a - 3 \, b}{a^{2} b}}\right) + 4 \, x}{4 \, a}"," ",0,"1/4*(a*sqrt(-(a^2*b*sqrt((9*a^2 + 6*a*b + b^2)/(a^5*b)) + a + 3*b)/(a^2*b))*log(-(3*a^2 - 2*a*b - b^2)*x + (a^4*b*sqrt((9*a^2 + 6*a*b + b^2)/(a^5*b)) - 3*a^2*b - a*b^2)*sqrt(-(a^2*b*sqrt((9*a^2 + 6*a*b + b^2)/(a^5*b)) + a + 3*b)/(a^2*b))) - a*sqrt(-(a^2*b*sqrt((9*a^2 + 6*a*b + b^2)/(a^5*b)) + a + 3*b)/(a^2*b))*log(-(3*a^2 - 2*a*b - b^2)*x - (a^4*b*sqrt((9*a^2 + 6*a*b + b^2)/(a^5*b)) - 3*a^2*b - a*b^2)*sqrt(-(a^2*b*sqrt((9*a^2 + 6*a*b + b^2)/(a^5*b)) + a + 3*b)/(a^2*b))) - a*sqrt((a^2*b*sqrt((9*a^2 + 6*a*b + b^2)/(a^5*b)) - a - 3*b)/(a^2*b))*log(-(3*a^2 - 2*a*b - b^2)*x + (a^4*b*sqrt((9*a^2 + 6*a*b + b^2)/(a^5*b)) + 3*a^2*b + a*b^2)*sqrt((a^2*b*sqrt((9*a^2 + 6*a*b + b^2)/(a^5*b)) - a - 3*b)/(a^2*b))) + a*sqrt((a^2*b*sqrt((9*a^2 + 6*a*b + b^2)/(a^5*b)) - a - 3*b)/(a^2*b))*log(-(3*a^2 - 2*a*b - b^2)*x - (a^4*b*sqrt((9*a^2 + 6*a*b + b^2)/(a^5*b)) + 3*a^2*b + a*b^2)*sqrt((a^2*b*sqrt((9*a^2 + 6*a*b + b^2)/(a^5*b)) - a - 3*b)/(a^2*b))) + 4*x)/a","B",0
903,1,267,0,1.756194," ","integrate(x^2/(a*x^4+2*a*x^2+a-b),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{-\frac{a b \sqrt{\frac{1}{a^{3} b}} + 1}{a b}} \log\left(a^{2} b \sqrt{-\frac{a b \sqrt{\frac{1}{a^{3} b}} + 1}{a b}} \sqrt{\frac{1}{a^{3} b}} + x\right) - \frac{1}{4} \, \sqrt{-\frac{a b \sqrt{\frac{1}{a^{3} b}} + 1}{a b}} \log\left(-a^{2} b \sqrt{-\frac{a b \sqrt{\frac{1}{a^{3} b}} + 1}{a b}} \sqrt{\frac{1}{a^{3} b}} + x\right) - \frac{1}{4} \, \sqrt{\frac{a b \sqrt{\frac{1}{a^{3} b}} - 1}{a b}} \log\left(a^{2} b \sqrt{\frac{a b \sqrt{\frac{1}{a^{3} b}} - 1}{a b}} \sqrt{\frac{1}{a^{3} b}} + x\right) + \frac{1}{4} \, \sqrt{\frac{a b \sqrt{\frac{1}{a^{3} b}} - 1}{a b}} \log\left(-a^{2} b \sqrt{\frac{a b \sqrt{\frac{1}{a^{3} b}} - 1}{a b}} \sqrt{\frac{1}{a^{3} b}} + x\right)"," ",0,"1/4*sqrt(-(a*b*sqrt(1/(a^3*b)) + 1)/(a*b))*log(a^2*b*sqrt(-(a*b*sqrt(1/(a^3*b)) + 1)/(a*b))*sqrt(1/(a^3*b)) + x) - 1/4*sqrt(-(a*b*sqrt(1/(a^3*b)) + 1)/(a*b))*log(-a^2*b*sqrt(-(a*b*sqrt(1/(a^3*b)) + 1)/(a*b))*sqrt(1/(a^3*b)) + x) - 1/4*sqrt((a*b*sqrt(1/(a^3*b)) - 1)/(a*b))*log(a^2*b*sqrt((a*b*sqrt(1/(a^3*b)) - 1)/(a*b))*sqrt(1/(a^3*b)) + x) + 1/4*sqrt((a*b*sqrt(1/(a^3*b)) - 1)/(a*b))*log(-a^2*b*sqrt((a*b*sqrt(1/(a^3*b)) - 1)/(a*b))*sqrt(1/(a^3*b)) + x)","B",0
904,1,553,0,0.779841," ","integrate(1/(a*x^4+2*a*x^2+a-b),x, algorithm=""fricas"")","-\frac{1}{4} \, \sqrt{-\frac{\frac{a b - b^{2}}{\sqrt{a^{3} b - 2 \, a^{2} b^{2} + a b^{3}}} + 1}{a b - b^{2}}} \log\left({\left(b - \frac{a^{2} b - a b^{2}}{\sqrt{a^{3} b - 2 \, a^{2} b^{2} + a b^{3}}}\right)} \sqrt{-\frac{\frac{a b - b^{2}}{\sqrt{a^{3} b - 2 \, a^{2} b^{2} + a b^{3}}} + 1}{a b - b^{2}}} + x\right) + \frac{1}{4} \, \sqrt{-\frac{\frac{a b - b^{2}}{\sqrt{a^{3} b - 2 \, a^{2} b^{2} + a b^{3}}} + 1}{a b - b^{2}}} \log\left(-{\left(b - \frac{a^{2} b - a b^{2}}{\sqrt{a^{3} b - 2 \, a^{2} b^{2} + a b^{3}}}\right)} \sqrt{-\frac{\frac{a b - b^{2}}{\sqrt{a^{3} b - 2 \, a^{2} b^{2} + a b^{3}}} + 1}{a b - b^{2}}} + x\right) - \frac{1}{4} \, \sqrt{\frac{\frac{a b - b^{2}}{\sqrt{a^{3} b - 2 \, a^{2} b^{2} + a b^{3}}} - 1}{a b - b^{2}}} \log\left({\left(b + \frac{a^{2} b - a b^{2}}{\sqrt{a^{3} b - 2 \, a^{2} b^{2} + a b^{3}}}\right)} \sqrt{\frac{\frac{a b - b^{2}}{\sqrt{a^{3} b - 2 \, a^{2} b^{2} + a b^{3}}} - 1}{a b - b^{2}}} + x\right) + \frac{1}{4} \, \sqrt{\frac{\frac{a b - b^{2}}{\sqrt{a^{3} b - 2 \, a^{2} b^{2} + a b^{3}}} - 1}{a b - b^{2}}} \log\left(-{\left(b + \frac{a^{2} b - a b^{2}}{\sqrt{a^{3} b - 2 \, a^{2} b^{2} + a b^{3}}}\right)} \sqrt{\frac{\frac{a b - b^{2}}{\sqrt{a^{3} b - 2 \, a^{2} b^{2} + a b^{3}}} - 1}{a b - b^{2}}} + x\right)"," ",0,"-1/4*sqrt(-((a*b - b^2)/sqrt(a^3*b - 2*a^2*b^2 + a*b^3) + 1)/(a*b - b^2))*log((b - (a^2*b - a*b^2)/sqrt(a^3*b - 2*a^2*b^2 + a*b^3))*sqrt(-((a*b - b^2)/sqrt(a^3*b - 2*a^2*b^2 + a*b^3) + 1)/(a*b - b^2)) + x) + 1/4*sqrt(-((a*b - b^2)/sqrt(a^3*b - 2*a^2*b^2 + a*b^3) + 1)/(a*b - b^2))*log(-(b - (a^2*b - a*b^2)/sqrt(a^3*b - 2*a^2*b^2 + a*b^3))*sqrt(-((a*b - b^2)/sqrt(a^3*b - 2*a^2*b^2 + a*b^3) + 1)/(a*b - b^2)) + x) - 1/4*sqrt(((a*b - b^2)/sqrt(a^3*b - 2*a^2*b^2 + a*b^3) - 1)/(a*b - b^2))*log((b + (a^2*b - a*b^2)/sqrt(a^3*b - 2*a^2*b^2 + a*b^3))*sqrt(((a*b - b^2)/sqrt(a^3*b - 2*a^2*b^2 + a*b^3) - 1)/(a*b - b^2)) + x) + 1/4*sqrt(((a*b - b^2)/sqrt(a^3*b - 2*a^2*b^2 + a*b^3) - 1)/(a*b - b^2))*log(-(b + (a^2*b - a*b^2)/sqrt(a^3*b - 2*a^2*b^2 + a*b^3))*sqrt(((a*b - b^2)/sqrt(a^3*b - 2*a^2*b^2 + a*b^3) - 1)/(a*b - b^2)) + x)","B",0
905,1,1612,0,1.508340," ","integrate(1/x^2/(a*x^4+2*a*x^2+a-b),x, algorithm=""fricas"")","\frac{{\left(a - b\right)} x \sqrt{-\frac{a^{2} + 3 \, a b + {\left(a^{3} b - 3 \, a^{2} b^{2} + 3 \, a b^{3} - b^{4}\right)} \sqrt{\frac{9 \, a^{3} + 6 \, a^{2} b + a b^{2}}{a^{6} b - 6 \, a^{5} b^{2} + 15 \, a^{4} b^{3} - 20 \, a^{3} b^{4} + 15 \, a^{2} b^{5} - 6 \, a b^{6} + b^{7}}}}{a^{3} b - 3 \, a^{2} b^{2} + 3 \, a b^{3} - b^{4}}} \log\left({\left(3 \, a^{2} + a b\right)} x + {\left(6 \, a^{2} b + 2 \, a b^{2} - {\left(a^{4} b - 2 \, a^{3} b^{2} + 2 \, a b^{4} - b^{5}\right)} \sqrt{\frac{9 \, a^{3} + 6 \, a^{2} b + a b^{2}}{a^{6} b - 6 \, a^{5} b^{2} + 15 \, a^{4} b^{3} - 20 \, a^{3} b^{4} + 15 \, a^{2} b^{5} - 6 \, a b^{6} + b^{7}}}\right)} \sqrt{-\frac{a^{2} + 3 \, a b + {\left(a^{3} b - 3 \, a^{2} b^{2} + 3 \, a b^{3} - b^{4}\right)} \sqrt{\frac{9 \, a^{3} + 6 \, a^{2} b + a b^{2}}{a^{6} b - 6 \, a^{5} b^{2} + 15 \, a^{4} b^{3} - 20 \, a^{3} b^{4} + 15 \, a^{2} b^{5} - 6 \, a b^{6} + b^{7}}}}{a^{3} b - 3 \, a^{2} b^{2} + 3 \, a b^{3} - b^{4}}}\right) - {\left(a - b\right)} x \sqrt{-\frac{a^{2} + 3 \, a b + {\left(a^{3} b - 3 \, a^{2} b^{2} + 3 \, a b^{3} - b^{4}\right)} \sqrt{\frac{9 \, a^{3} + 6 \, a^{2} b + a b^{2}}{a^{6} b - 6 \, a^{5} b^{2} + 15 \, a^{4} b^{3} - 20 \, a^{3} b^{4} + 15 \, a^{2} b^{5} - 6 \, a b^{6} + b^{7}}}}{a^{3} b - 3 \, a^{2} b^{2} + 3 \, a b^{3} - b^{4}}} \log\left({\left(3 \, a^{2} + a b\right)} x - {\left(6 \, a^{2} b + 2 \, a b^{2} - {\left(a^{4} b - 2 \, a^{3} b^{2} + 2 \, a b^{4} - b^{5}\right)} \sqrt{\frac{9 \, a^{3} + 6 \, a^{2} b + a b^{2}}{a^{6} b - 6 \, a^{5} b^{2} + 15 \, a^{4} b^{3} - 20 \, a^{3} b^{4} + 15 \, a^{2} b^{5} - 6 \, a b^{6} + b^{7}}}\right)} \sqrt{-\frac{a^{2} + 3 \, a b + {\left(a^{3} b - 3 \, a^{2} b^{2} + 3 \, a b^{3} - b^{4}\right)} \sqrt{\frac{9 \, a^{3} + 6 \, a^{2} b + a b^{2}}{a^{6} b - 6 \, a^{5} b^{2} + 15 \, a^{4} b^{3} - 20 \, a^{3} b^{4} + 15 \, a^{2} b^{5} - 6 \, a b^{6} + b^{7}}}}{a^{3} b - 3 \, a^{2} b^{2} + 3 \, a b^{3} - b^{4}}}\right) + {\left(a - b\right)} x \sqrt{-\frac{a^{2} + 3 \, a b - {\left(a^{3} b - 3 \, a^{2} b^{2} + 3 \, a b^{3} - b^{4}\right)} \sqrt{\frac{9 \, a^{3} + 6 \, a^{2} b + a b^{2}}{a^{6} b - 6 \, a^{5} b^{2} + 15 \, a^{4} b^{3} - 20 \, a^{3} b^{4} + 15 \, a^{2} b^{5} - 6 \, a b^{6} + b^{7}}}}{a^{3} b - 3 \, a^{2} b^{2} + 3 \, a b^{3} - b^{4}}} \log\left({\left(3 \, a^{2} + a b\right)} x + {\left(6 \, a^{2} b + 2 \, a b^{2} + {\left(a^{4} b - 2 \, a^{3} b^{2} + 2 \, a b^{4} - b^{5}\right)} \sqrt{\frac{9 \, a^{3} + 6 \, a^{2} b + a b^{2}}{a^{6} b - 6 \, a^{5} b^{2} + 15 \, a^{4} b^{3} - 20 \, a^{3} b^{4} + 15 \, a^{2} b^{5} - 6 \, a b^{6} + b^{7}}}\right)} \sqrt{-\frac{a^{2} + 3 \, a b - {\left(a^{3} b - 3 \, a^{2} b^{2} + 3 \, a b^{3} - b^{4}\right)} \sqrt{\frac{9 \, a^{3} + 6 \, a^{2} b + a b^{2}}{a^{6} b - 6 \, a^{5} b^{2} + 15 \, a^{4} b^{3} - 20 \, a^{3} b^{4} + 15 \, a^{2} b^{5} - 6 \, a b^{6} + b^{7}}}}{a^{3} b - 3 \, a^{2} b^{2} + 3 \, a b^{3} - b^{4}}}\right) - {\left(a - b\right)} x \sqrt{-\frac{a^{2} + 3 \, a b - {\left(a^{3} b - 3 \, a^{2} b^{2} + 3 \, a b^{3} - b^{4}\right)} \sqrt{\frac{9 \, a^{3} + 6 \, a^{2} b + a b^{2}}{a^{6} b - 6 \, a^{5} b^{2} + 15 \, a^{4} b^{3} - 20 \, a^{3} b^{4} + 15 \, a^{2} b^{5} - 6 \, a b^{6} + b^{7}}}}{a^{3} b - 3 \, a^{2} b^{2} + 3 \, a b^{3} - b^{4}}} \log\left({\left(3 \, a^{2} + a b\right)} x - {\left(6 \, a^{2} b + 2 \, a b^{2} + {\left(a^{4} b - 2 \, a^{3} b^{2} + 2 \, a b^{4} - b^{5}\right)} \sqrt{\frac{9 \, a^{3} + 6 \, a^{2} b + a b^{2}}{a^{6} b - 6 \, a^{5} b^{2} + 15 \, a^{4} b^{3} - 20 \, a^{3} b^{4} + 15 \, a^{2} b^{5} - 6 \, a b^{6} + b^{7}}}\right)} \sqrt{-\frac{a^{2} + 3 \, a b - {\left(a^{3} b - 3 \, a^{2} b^{2} + 3 \, a b^{3} - b^{4}\right)} \sqrt{\frac{9 \, a^{3} + 6 \, a^{2} b + a b^{2}}{a^{6} b - 6 \, a^{5} b^{2} + 15 \, a^{4} b^{3} - 20 \, a^{3} b^{4} + 15 \, a^{2} b^{5} - 6 \, a b^{6} + b^{7}}}}{a^{3} b - 3 \, a^{2} b^{2} + 3 \, a b^{3} - b^{4}}}\right) - 4}{4 \, {\left(a - b\right)} x}"," ",0,"1/4*((a - b)*x*sqrt(-(a^2 + 3*a*b + (a^3*b - 3*a^2*b^2 + 3*a*b^3 - b^4)*sqrt((9*a^3 + 6*a^2*b + a*b^2)/(a^6*b - 6*a^5*b^2 + 15*a^4*b^3 - 20*a^3*b^4 + 15*a^2*b^5 - 6*a*b^6 + b^7)))/(a^3*b - 3*a^2*b^2 + 3*a*b^3 - b^4))*log((3*a^2 + a*b)*x + (6*a^2*b + 2*a*b^2 - (a^4*b - 2*a^3*b^2 + 2*a*b^4 - b^5)*sqrt((9*a^3 + 6*a^2*b + a*b^2)/(a^6*b - 6*a^5*b^2 + 15*a^4*b^3 - 20*a^3*b^4 + 15*a^2*b^5 - 6*a*b^6 + b^7)))*sqrt(-(a^2 + 3*a*b + (a^3*b - 3*a^2*b^2 + 3*a*b^3 - b^4)*sqrt((9*a^3 + 6*a^2*b + a*b^2)/(a^6*b - 6*a^5*b^2 + 15*a^4*b^3 - 20*a^3*b^4 + 15*a^2*b^5 - 6*a*b^6 + b^7)))/(a^3*b - 3*a^2*b^2 + 3*a*b^3 - b^4))) - (a - b)*x*sqrt(-(a^2 + 3*a*b + (a^3*b - 3*a^2*b^2 + 3*a*b^3 - b^4)*sqrt((9*a^3 + 6*a^2*b + a*b^2)/(a^6*b - 6*a^5*b^2 + 15*a^4*b^3 - 20*a^3*b^4 + 15*a^2*b^5 - 6*a*b^6 + b^7)))/(a^3*b - 3*a^2*b^2 + 3*a*b^3 - b^4))*log((3*a^2 + a*b)*x - (6*a^2*b + 2*a*b^2 - (a^4*b - 2*a^3*b^2 + 2*a*b^4 - b^5)*sqrt((9*a^3 + 6*a^2*b + a*b^2)/(a^6*b - 6*a^5*b^2 + 15*a^4*b^3 - 20*a^3*b^4 + 15*a^2*b^5 - 6*a*b^6 + b^7)))*sqrt(-(a^2 + 3*a*b + (a^3*b - 3*a^2*b^2 + 3*a*b^3 - b^4)*sqrt((9*a^3 + 6*a^2*b + a*b^2)/(a^6*b - 6*a^5*b^2 + 15*a^4*b^3 - 20*a^3*b^4 + 15*a^2*b^5 - 6*a*b^6 + b^7)))/(a^3*b - 3*a^2*b^2 + 3*a*b^3 - b^4))) + (a - b)*x*sqrt(-(a^2 + 3*a*b - (a^3*b - 3*a^2*b^2 + 3*a*b^3 - b^4)*sqrt((9*a^3 + 6*a^2*b + a*b^2)/(a^6*b - 6*a^5*b^2 + 15*a^4*b^3 - 20*a^3*b^4 + 15*a^2*b^5 - 6*a*b^6 + b^7)))/(a^3*b - 3*a^2*b^2 + 3*a*b^3 - b^4))*log((3*a^2 + a*b)*x + (6*a^2*b + 2*a*b^2 + (a^4*b - 2*a^3*b^2 + 2*a*b^4 - b^5)*sqrt((9*a^3 + 6*a^2*b + a*b^2)/(a^6*b - 6*a^5*b^2 + 15*a^4*b^3 - 20*a^3*b^4 + 15*a^2*b^5 - 6*a*b^6 + b^7)))*sqrt(-(a^2 + 3*a*b - (a^3*b - 3*a^2*b^2 + 3*a*b^3 - b^4)*sqrt((9*a^3 + 6*a^2*b + a*b^2)/(a^6*b - 6*a^5*b^2 + 15*a^4*b^3 - 20*a^3*b^4 + 15*a^2*b^5 - 6*a*b^6 + b^7)))/(a^3*b - 3*a^2*b^2 + 3*a*b^3 - b^4))) - (a - b)*x*sqrt(-(a^2 + 3*a*b - (a^3*b - 3*a^2*b^2 + 3*a*b^3 - b^4)*sqrt((9*a^3 + 6*a^2*b + a*b^2)/(a^6*b - 6*a^5*b^2 + 15*a^4*b^3 - 20*a^3*b^4 + 15*a^2*b^5 - 6*a*b^6 + b^7)))/(a^3*b - 3*a^2*b^2 + 3*a*b^3 - b^4))*log((3*a^2 + a*b)*x - (6*a^2*b + 2*a*b^2 + (a^4*b - 2*a^3*b^2 + 2*a*b^4 - b^5)*sqrt((9*a^3 + 6*a^2*b + a*b^2)/(a^6*b - 6*a^5*b^2 + 15*a^4*b^3 - 20*a^3*b^4 + 15*a^2*b^5 - 6*a*b^6 + b^7)))*sqrt(-(a^2 + 3*a*b - (a^3*b - 3*a^2*b^2 + 3*a*b^3 - b^4)*sqrt((9*a^3 + 6*a^2*b + a*b^2)/(a^6*b - 6*a^5*b^2 + 15*a^4*b^3 - 20*a^3*b^4 + 15*a^2*b^5 - 6*a*b^6 + b^7)))/(a^3*b - 3*a^2*b^2 + 3*a*b^3 - b^4))) - 4)/((a - b)*x)","B",0
906,1,157,0,0.824687," ","integrate(x^5/(a*x^4+2*a*x^2+a+b),x, algorithm=""fricas"")","\left[\frac{2 \, a b x^{2} - 2 \, a b \log\left(a x^{4} + 2 \, a x^{2} + a + b\right) + \sqrt{-a b} {\left(a - b\right)} \log\left(\frac{a x^{4} + 2 \, a x^{2} + 2 \, \sqrt{-a b} {\left(x^{2} + 1\right)} + a - b}{a x^{4} + 2 \, a x^{2} + a + b}\right)}{4 \, a^{2} b}, \frac{a b x^{2} - a b \log\left(a x^{4} + 2 \, a x^{2} + a + b\right) - \sqrt{a b} {\left(a - b\right)} \arctan\left(\frac{\sqrt{a b}}{a x^{2} + a}\right)}{2 \, a^{2} b}\right]"," ",0,"[1/4*(2*a*b*x^2 - 2*a*b*log(a*x^4 + 2*a*x^2 + a + b) + sqrt(-a*b)*(a - b)*log((a*x^4 + 2*a*x^2 + 2*sqrt(-a*b)*(x^2 + 1) + a - b)/(a*x^4 + 2*a*x^2 + a + b)))/(a^2*b), 1/2*(a*b*x^2 - a*b*log(a*x^4 + 2*a*x^2 + a + b) - sqrt(a*b)*(a - b)*arctan(sqrt(a*b)/(a*x^2 + a)))/(a^2*b)]","A",0
907,1,131,0,0.725676," ","integrate(x^3/(a*x^4+2*a*x^2+a+b),x, algorithm=""fricas"")","\left[\frac{b \log\left(a x^{4} + 2 \, a x^{2} + a + b\right) - \sqrt{-a b} \log\left(\frac{a x^{4} + 2 \, a x^{2} + 2 \, \sqrt{-a b} {\left(x^{2} + 1\right)} + a - b}{a x^{4} + 2 \, a x^{2} + a + b}\right)}{4 \, a b}, \frac{b \log\left(a x^{4} + 2 \, a x^{2} + a + b\right) + 2 \, \sqrt{a b} \arctan\left(\frac{\sqrt{a b}}{a x^{2} + a}\right)}{4 \, a b}\right]"," ",0,"[1/4*(b*log(a*x^4 + 2*a*x^2 + a + b) - sqrt(-a*b)*log((a*x^4 + 2*a*x^2 + 2*sqrt(-a*b)*(x^2 + 1) + a - b)/(a*x^4 + 2*a*x^2 + a + b)))/(a*b), 1/4*(b*log(a*x^4 + 2*a*x^2 + a + b) + 2*sqrt(a*b)*arctan(sqrt(a*b)/(a*x^2 + a)))/(a*b)]","A",0
908,1,91,0,0.878100," ","integrate(x/(a*x^4+2*a*x^2+a+b),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a b} \log\left(\frac{a x^{4} + 2 \, a x^{2} - 2 \, \sqrt{-a b} {\left(x^{2} + 1\right)} + a - b}{a x^{4} + 2 \, a x^{2} + a + b}\right)}{4 \, a b}, -\frac{\sqrt{a b} \arctan\left(\frac{\sqrt{a b}}{a x^{2} + a}\right)}{2 \, a b}\right]"," ",0,"[-1/4*sqrt(-a*b)*log((a*x^4 + 2*a*x^2 - 2*sqrt(-a*b)*(x^2 + 1) + a - b)/(a*x^4 + 2*a*x^2 + a + b))/(a*b), -1/2*sqrt(a*b)*arctan(sqrt(a*b)/(a*x^2 + a))/(a*b)]","A",0
909,1,147,0,0.575324," ","integrate(1/x/(a*x^4+2*a*x^2+a+b),x, algorithm=""fricas"")","\left[\frac{\sqrt{-\frac{a}{b}} \log\left(\frac{a x^{4} + 2 \, a x^{2} - 2 \, {\left(b x^{2} + b\right)} \sqrt{-\frac{a}{b}} + a - b}{a x^{4} + 2 \, a x^{2} + a + b}\right) - \log\left(a x^{4} + 2 \, a x^{2} + a + b\right) + 4 \, \log\left(x\right)}{4 \, {\left(a + b\right)}}, \frac{2 \, \sqrt{\frac{a}{b}} \arctan\left(\frac{b \sqrt{\frac{a}{b}}}{a x^{2} + a}\right) - \log\left(a x^{4} + 2 \, a x^{2} + a + b\right) + 4 \, \log\left(x\right)}{4 \, {\left(a + b\right)}}\right]"," ",0,"[1/4*(sqrt(-a/b)*log((a*x^4 + 2*a*x^2 - 2*(b*x^2 + b)*sqrt(-a/b) + a - b)/(a*x^4 + 2*a*x^2 + a + b)) - log(a*x^4 + 2*a*x^2 + a + b) + 4*log(x))/(a + b), 1/4*(2*sqrt(a/b)*arctan(b*sqrt(a/b)/(a*x^2 + a)) - log(a*x^4 + 2*a*x^2 + a + b) + 4*log(x))/(a + b)]","A",0
910,1,208,0,1.071869," ","integrate(1/x^3/(a*x^4+2*a*x^2+a+b),x, algorithm=""fricas"")","\left[-\frac{{\left(a - b\right)} x^{2} \sqrt{-\frac{a}{b}} \log\left(\frac{a x^{4} + 2 \, a x^{2} - 2 \, {\left(b x^{2} + b\right)} \sqrt{-\frac{a}{b}} + a - b}{a x^{4} + 2 \, a x^{2} + a + b}\right) - 2 \, a x^{2} \log\left(a x^{4} + 2 \, a x^{2} + a + b\right) + 8 \, a x^{2} \log\left(x\right) + 2 \, a + 2 \, b}{4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} x^{2}}, -\frac{{\left(a - b\right)} x^{2} \sqrt{\frac{a}{b}} \arctan\left(\frac{b \sqrt{\frac{a}{b}}}{a x^{2} + a}\right) - a x^{2} \log\left(a x^{4} + 2 \, a x^{2} + a + b\right) + 4 \, a x^{2} \log\left(x\right) + a + b}{2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} x^{2}}\right]"," ",0,"[-1/4*((a - b)*x^2*sqrt(-a/b)*log((a*x^4 + 2*a*x^2 - 2*(b*x^2 + b)*sqrt(-a/b) + a - b)/(a*x^4 + 2*a*x^2 + a + b)) - 2*a*x^2*log(a*x^4 + 2*a*x^2 + a + b) + 8*a*x^2*log(x) + 2*a + 2*b)/((a^2 + 2*a*b + b^2)*x^2), -1/2*((a - b)*x^2*sqrt(a/b)*arctan(b*sqrt(a/b)/(a*x^2 + a)) - a*x^2*log(a*x^4 + 2*a*x^2 + a + b) + 4*a*x^2*log(x) + a + b)/((a^2 + 2*a*b + b^2)*x^2)]","A",0
911,1,615,0,2.046462," ","integrate(x^4/(a*x^4+2*a*x^2+a+b),x, algorithm=""fricas"")","\frac{a \sqrt{\frac{a^{2} b \sqrt{-\frac{9 \, a^{2} - 6 \, a b + b^{2}}{a^{5} b}} + a - 3 \, b}{a^{2} b}} \log\left(-{\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} x + {\left(a^{4} b \sqrt{-\frac{9 \, a^{2} - 6 \, a b + b^{2}}{a^{5} b}} + 3 \, a^{2} b - a b^{2}\right)} \sqrt{\frac{a^{2} b \sqrt{-\frac{9 \, a^{2} - 6 \, a b + b^{2}}{a^{5} b}} + a - 3 \, b}{a^{2} b}}\right) - a \sqrt{\frac{a^{2} b \sqrt{-\frac{9 \, a^{2} - 6 \, a b + b^{2}}{a^{5} b}} + a - 3 \, b}{a^{2} b}} \log\left(-{\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} x - {\left(a^{4} b \sqrt{-\frac{9 \, a^{2} - 6 \, a b + b^{2}}{a^{5} b}} + 3 \, a^{2} b - a b^{2}\right)} \sqrt{\frac{a^{2} b \sqrt{-\frac{9 \, a^{2} - 6 \, a b + b^{2}}{a^{5} b}} + a - 3 \, b}{a^{2} b}}\right) - a \sqrt{-\frac{a^{2} b \sqrt{-\frac{9 \, a^{2} - 6 \, a b + b^{2}}{a^{5} b}} - a + 3 \, b}{a^{2} b}} \log\left(-{\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} x + {\left(a^{4} b \sqrt{-\frac{9 \, a^{2} - 6 \, a b + b^{2}}{a^{5} b}} - 3 \, a^{2} b + a b^{2}\right)} \sqrt{-\frac{a^{2} b \sqrt{-\frac{9 \, a^{2} - 6 \, a b + b^{2}}{a^{5} b}} - a + 3 \, b}{a^{2} b}}\right) + a \sqrt{-\frac{a^{2} b \sqrt{-\frac{9 \, a^{2} - 6 \, a b + b^{2}}{a^{5} b}} - a + 3 \, b}{a^{2} b}} \log\left(-{\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} x - {\left(a^{4} b \sqrt{-\frac{9 \, a^{2} - 6 \, a b + b^{2}}{a^{5} b}} - 3 \, a^{2} b + a b^{2}\right)} \sqrt{-\frac{a^{2} b \sqrt{-\frac{9 \, a^{2} - 6 \, a b + b^{2}}{a^{5} b}} - a + 3 \, b}{a^{2} b}}\right) + 4 \, x}{4 \, a}"," ",0,"1/4*(a*sqrt((a^2*b*sqrt(-(9*a^2 - 6*a*b + b^2)/(a^5*b)) + a - 3*b)/(a^2*b))*log(-(3*a^2 + 2*a*b - b^2)*x + (a^4*b*sqrt(-(9*a^2 - 6*a*b + b^2)/(a^5*b)) + 3*a^2*b - a*b^2)*sqrt((a^2*b*sqrt(-(9*a^2 - 6*a*b + b^2)/(a^5*b)) + a - 3*b)/(a^2*b))) - a*sqrt((a^2*b*sqrt(-(9*a^2 - 6*a*b + b^2)/(a^5*b)) + a - 3*b)/(a^2*b))*log(-(3*a^2 + 2*a*b - b^2)*x - (a^4*b*sqrt(-(9*a^2 - 6*a*b + b^2)/(a^5*b)) + 3*a^2*b - a*b^2)*sqrt((a^2*b*sqrt(-(9*a^2 - 6*a*b + b^2)/(a^5*b)) + a - 3*b)/(a^2*b))) - a*sqrt(-(a^2*b*sqrt(-(9*a^2 - 6*a*b + b^2)/(a^5*b)) - a + 3*b)/(a^2*b))*log(-(3*a^2 + 2*a*b - b^2)*x + (a^4*b*sqrt(-(9*a^2 - 6*a*b + b^2)/(a^5*b)) - 3*a^2*b + a*b^2)*sqrt(-(a^2*b*sqrt(-(9*a^2 - 6*a*b + b^2)/(a^5*b)) - a + 3*b)/(a^2*b))) + a*sqrt(-(a^2*b*sqrt(-(9*a^2 - 6*a*b + b^2)/(a^5*b)) - a + 3*b)/(a^2*b))*log(-(3*a^2 + 2*a*b - b^2)*x - (a^4*b*sqrt(-(9*a^2 - 6*a*b + b^2)/(a^5*b)) - 3*a^2*b + a*b^2)*sqrt(-(a^2*b*sqrt(-(9*a^2 - 6*a*b + b^2)/(a^5*b)) - a + 3*b)/(a^2*b))) + 4*x)/a","A",0
912,1,279,0,1.649741," ","integrate(x^2/(a*x^4+2*a*x^2+a+b),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{\frac{a b \sqrt{-\frac{1}{a^{3} b}} + 1}{a b}} \log\left(a^{2} b \sqrt{\frac{a b \sqrt{-\frac{1}{a^{3} b}} + 1}{a b}} \sqrt{-\frac{1}{a^{3} b}} + x\right) - \frac{1}{4} \, \sqrt{\frac{a b \sqrt{-\frac{1}{a^{3} b}} + 1}{a b}} \log\left(-a^{2} b \sqrt{\frac{a b \sqrt{-\frac{1}{a^{3} b}} + 1}{a b}} \sqrt{-\frac{1}{a^{3} b}} + x\right) - \frac{1}{4} \, \sqrt{-\frac{a b \sqrt{-\frac{1}{a^{3} b}} - 1}{a b}} \log\left(a^{2} b \sqrt{-\frac{a b \sqrt{-\frac{1}{a^{3} b}} - 1}{a b}} \sqrt{-\frac{1}{a^{3} b}} + x\right) + \frac{1}{4} \, \sqrt{-\frac{a b \sqrt{-\frac{1}{a^{3} b}} - 1}{a b}} \log\left(-a^{2} b \sqrt{-\frac{a b \sqrt{-\frac{1}{a^{3} b}} - 1}{a b}} \sqrt{-\frac{1}{a^{3} b}} + x\right)"," ",0,"1/4*sqrt((a*b*sqrt(-1/(a^3*b)) + 1)/(a*b))*log(a^2*b*sqrt((a*b*sqrt(-1/(a^3*b)) + 1)/(a*b))*sqrt(-1/(a^3*b)) + x) - 1/4*sqrt((a*b*sqrt(-1/(a^3*b)) + 1)/(a*b))*log(-a^2*b*sqrt((a*b*sqrt(-1/(a^3*b)) + 1)/(a*b))*sqrt(-1/(a^3*b)) + x) - 1/4*sqrt(-(a*b*sqrt(-1/(a^3*b)) - 1)/(a*b))*log(a^2*b*sqrt(-(a*b*sqrt(-1/(a^3*b)) - 1)/(a*b))*sqrt(-1/(a^3*b)) + x) + 1/4*sqrt(-(a*b*sqrt(-1/(a^3*b)) - 1)/(a*b))*log(-a^2*b*sqrt(-(a*b*sqrt(-1/(a^3*b)) - 1)/(a*b))*sqrt(-1/(a^3*b)) + x)","A",0
913,1,567,0,1.121733," ","integrate(1/(a*x^4+2*a*x^2+a+b),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{\frac{{\left(a b + b^{2}\right)} \sqrt{-\frac{1}{a^{3} b + 2 \, a^{2} b^{2} + a b^{3}}} + 1}{a b + b^{2}}} \log\left({\left({\left(a^{2} b + a b^{2}\right)} \sqrt{-\frac{1}{a^{3} b + 2 \, a^{2} b^{2} + a b^{3}}} + b\right)} \sqrt{\frac{{\left(a b + b^{2}\right)} \sqrt{-\frac{1}{a^{3} b + 2 \, a^{2} b^{2} + a b^{3}}} + 1}{a b + b^{2}}} + x\right) - \frac{1}{4} \, \sqrt{\frac{{\left(a b + b^{2}\right)} \sqrt{-\frac{1}{a^{3} b + 2 \, a^{2} b^{2} + a b^{3}}} + 1}{a b + b^{2}}} \log\left(-{\left({\left(a^{2} b + a b^{2}\right)} \sqrt{-\frac{1}{a^{3} b + 2 \, a^{2} b^{2} + a b^{3}}} + b\right)} \sqrt{\frac{{\left(a b + b^{2}\right)} \sqrt{-\frac{1}{a^{3} b + 2 \, a^{2} b^{2} + a b^{3}}} + 1}{a b + b^{2}}} + x\right) - \frac{1}{4} \, \sqrt{-\frac{{\left(a b + b^{2}\right)} \sqrt{-\frac{1}{a^{3} b + 2 \, a^{2} b^{2} + a b^{3}}} - 1}{a b + b^{2}}} \log\left({\left({\left(a^{2} b + a b^{2}\right)} \sqrt{-\frac{1}{a^{3} b + 2 \, a^{2} b^{2} + a b^{3}}} - b\right)} \sqrt{-\frac{{\left(a b + b^{2}\right)} \sqrt{-\frac{1}{a^{3} b + 2 \, a^{2} b^{2} + a b^{3}}} - 1}{a b + b^{2}}} + x\right) + \frac{1}{4} \, \sqrt{-\frac{{\left(a b + b^{2}\right)} \sqrt{-\frac{1}{a^{3} b + 2 \, a^{2} b^{2} + a b^{3}}} - 1}{a b + b^{2}}} \log\left(-{\left({\left(a^{2} b + a b^{2}\right)} \sqrt{-\frac{1}{a^{3} b + 2 \, a^{2} b^{2} + a b^{3}}} - b\right)} \sqrt{-\frac{{\left(a b + b^{2}\right)} \sqrt{-\frac{1}{a^{3} b + 2 \, a^{2} b^{2} + a b^{3}}} - 1}{a b + b^{2}}} + x\right)"," ",0,"1/4*sqrt(((a*b + b^2)*sqrt(-1/(a^3*b + 2*a^2*b^2 + a*b^3)) + 1)/(a*b + b^2))*log(((a^2*b + a*b^2)*sqrt(-1/(a^3*b + 2*a^2*b^2 + a*b^3)) + b)*sqrt(((a*b + b^2)*sqrt(-1/(a^3*b + 2*a^2*b^2 + a*b^3)) + 1)/(a*b + b^2)) + x) - 1/4*sqrt(((a*b + b^2)*sqrt(-1/(a^3*b + 2*a^2*b^2 + a*b^3)) + 1)/(a*b + b^2))*log(-((a^2*b + a*b^2)*sqrt(-1/(a^3*b + 2*a^2*b^2 + a*b^3)) + b)*sqrt(((a*b + b^2)*sqrt(-1/(a^3*b + 2*a^2*b^2 + a*b^3)) + 1)/(a*b + b^2)) + x) - 1/4*sqrt(-((a*b + b^2)*sqrt(-1/(a^3*b + 2*a^2*b^2 + a*b^3)) - 1)/(a*b + b^2))*log(((a^2*b + a*b^2)*sqrt(-1/(a^3*b + 2*a^2*b^2 + a*b^3)) - b)*sqrt(-((a*b + b^2)*sqrt(-1/(a^3*b + 2*a^2*b^2 + a*b^3)) - 1)/(a*b + b^2)) + x) + 1/4*sqrt(-((a*b + b^2)*sqrt(-1/(a^3*b + 2*a^2*b^2 + a*b^3)) - 1)/(a*b + b^2))*log(-((a^2*b + a*b^2)*sqrt(-1/(a^3*b + 2*a^2*b^2 + a*b^3)) - b)*sqrt(-((a*b + b^2)*sqrt(-1/(a^3*b + 2*a^2*b^2 + a*b^3)) - 1)/(a*b + b^2)) + x)","B",0
914,1,1582,0,0.756512," ","integrate(1/x^2/(a*x^4+2*a*x^2+a+b),x, algorithm=""fricas"")","\frac{{\left(a + b\right)} x \sqrt{\frac{a^{2} - 3 \, a b + {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} \sqrt{-\frac{9 \, a^{3} - 6 \, a^{2} b + a b^{2}}{a^{6} b + 6 \, a^{5} b^{2} + 15 \, a^{4} b^{3} + 20 \, a^{3} b^{4} + 15 \, a^{2} b^{5} + 6 \, a b^{6} + b^{7}}}}{a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}}} \log\left(-{\left(3 \, a^{2} - a b\right)} x + {\left(6 \, a^{2} b - 2 \, a b^{2} + {\left(a^{4} b + 2 \, a^{3} b^{2} - 2 \, a b^{4} - b^{5}\right)} \sqrt{-\frac{9 \, a^{3} - 6 \, a^{2} b + a b^{2}}{a^{6} b + 6 \, a^{5} b^{2} + 15 \, a^{4} b^{3} + 20 \, a^{3} b^{4} + 15 \, a^{2} b^{5} + 6 \, a b^{6} + b^{7}}}\right)} \sqrt{\frac{a^{2} - 3 \, a b + {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} \sqrt{-\frac{9 \, a^{3} - 6 \, a^{2} b + a b^{2}}{a^{6} b + 6 \, a^{5} b^{2} + 15 \, a^{4} b^{3} + 20 \, a^{3} b^{4} + 15 \, a^{2} b^{5} + 6 \, a b^{6} + b^{7}}}}{a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}}}\right) - {\left(a + b\right)} x \sqrt{\frac{a^{2} - 3 \, a b + {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} \sqrt{-\frac{9 \, a^{3} - 6 \, a^{2} b + a b^{2}}{a^{6} b + 6 \, a^{5} b^{2} + 15 \, a^{4} b^{3} + 20 \, a^{3} b^{4} + 15 \, a^{2} b^{5} + 6 \, a b^{6} + b^{7}}}}{a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}}} \log\left(-{\left(3 \, a^{2} - a b\right)} x - {\left(6 \, a^{2} b - 2 \, a b^{2} + {\left(a^{4} b + 2 \, a^{3} b^{2} - 2 \, a b^{4} - b^{5}\right)} \sqrt{-\frac{9 \, a^{3} - 6 \, a^{2} b + a b^{2}}{a^{6} b + 6 \, a^{5} b^{2} + 15 \, a^{4} b^{3} + 20 \, a^{3} b^{4} + 15 \, a^{2} b^{5} + 6 \, a b^{6} + b^{7}}}\right)} \sqrt{\frac{a^{2} - 3 \, a b + {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} \sqrt{-\frac{9 \, a^{3} - 6 \, a^{2} b + a b^{2}}{a^{6} b + 6 \, a^{5} b^{2} + 15 \, a^{4} b^{3} + 20 \, a^{3} b^{4} + 15 \, a^{2} b^{5} + 6 \, a b^{6} + b^{7}}}}{a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}}}\right) + {\left(a + b\right)} x \sqrt{\frac{a^{2} - 3 \, a b - {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} \sqrt{-\frac{9 \, a^{3} - 6 \, a^{2} b + a b^{2}}{a^{6} b + 6 \, a^{5} b^{2} + 15 \, a^{4} b^{3} + 20 \, a^{3} b^{4} + 15 \, a^{2} b^{5} + 6 \, a b^{6} + b^{7}}}}{a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}}} \log\left(-{\left(3 \, a^{2} - a b\right)} x + {\left(6 \, a^{2} b - 2 \, a b^{2} - {\left(a^{4} b + 2 \, a^{3} b^{2} - 2 \, a b^{4} - b^{5}\right)} \sqrt{-\frac{9 \, a^{3} - 6 \, a^{2} b + a b^{2}}{a^{6} b + 6 \, a^{5} b^{2} + 15 \, a^{4} b^{3} + 20 \, a^{3} b^{4} + 15 \, a^{2} b^{5} + 6 \, a b^{6} + b^{7}}}\right)} \sqrt{\frac{a^{2} - 3 \, a b - {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} \sqrt{-\frac{9 \, a^{3} - 6 \, a^{2} b + a b^{2}}{a^{6} b + 6 \, a^{5} b^{2} + 15 \, a^{4} b^{3} + 20 \, a^{3} b^{4} + 15 \, a^{2} b^{5} + 6 \, a b^{6} + b^{7}}}}{a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}}}\right) - {\left(a + b\right)} x \sqrt{\frac{a^{2} - 3 \, a b - {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} \sqrt{-\frac{9 \, a^{3} - 6 \, a^{2} b + a b^{2}}{a^{6} b + 6 \, a^{5} b^{2} + 15 \, a^{4} b^{3} + 20 \, a^{3} b^{4} + 15 \, a^{2} b^{5} + 6 \, a b^{6} + b^{7}}}}{a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}}} \log\left(-{\left(3 \, a^{2} - a b\right)} x - {\left(6 \, a^{2} b - 2 \, a b^{2} - {\left(a^{4} b + 2 \, a^{3} b^{2} - 2 \, a b^{4} - b^{5}\right)} \sqrt{-\frac{9 \, a^{3} - 6 \, a^{2} b + a b^{2}}{a^{6} b + 6 \, a^{5} b^{2} + 15 \, a^{4} b^{3} + 20 \, a^{3} b^{4} + 15 \, a^{2} b^{5} + 6 \, a b^{6} + b^{7}}}\right)} \sqrt{\frac{a^{2} - 3 \, a b - {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} \sqrt{-\frac{9 \, a^{3} - 6 \, a^{2} b + a b^{2}}{a^{6} b + 6 \, a^{5} b^{2} + 15 \, a^{4} b^{3} + 20 \, a^{3} b^{4} + 15 \, a^{2} b^{5} + 6 \, a b^{6} + b^{7}}}}{a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}}}\right) - 4}{4 \, {\left(a + b\right)} x}"," ",0,"1/4*((a + b)*x*sqrt((a^2 - 3*a*b + (a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*sqrt(-(9*a^3 - 6*a^2*b + a*b^2)/(a^6*b + 6*a^5*b^2 + 15*a^4*b^3 + 20*a^3*b^4 + 15*a^2*b^5 + 6*a*b^6 + b^7)))/(a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4))*log(-(3*a^2 - a*b)*x + (6*a^2*b - 2*a*b^2 + (a^4*b + 2*a^3*b^2 - 2*a*b^4 - b^5)*sqrt(-(9*a^3 - 6*a^2*b + a*b^2)/(a^6*b + 6*a^5*b^2 + 15*a^4*b^3 + 20*a^3*b^4 + 15*a^2*b^5 + 6*a*b^6 + b^7)))*sqrt((a^2 - 3*a*b + (a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*sqrt(-(9*a^3 - 6*a^2*b + a*b^2)/(a^6*b + 6*a^5*b^2 + 15*a^4*b^3 + 20*a^3*b^4 + 15*a^2*b^5 + 6*a*b^6 + b^7)))/(a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4))) - (a + b)*x*sqrt((a^2 - 3*a*b + (a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*sqrt(-(9*a^3 - 6*a^2*b + a*b^2)/(a^6*b + 6*a^5*b^2 + 15*a^4*b^3 + 20*a^3*b^4 + 15*a^2*b^5 + 6*a*b^6 + b^7)))/(a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4))*log(-(3*a^2 - a*b)*x - (6*a^2*b - 2*a*b^2 + (a^4*b + 2*a^3*b^2 - 2*a*b^4 - b^5)*sqrt(-(9*a^3 - 6*a^2*b + a*b^2)/(a^6*b + 6*a^5*b^2 + 15*a^4*b^3 + 20*a^3*b^4 + 15*a^2*b^5 + 6*a*b^6 + b^7)))*sqrt((a^2 - 3*a*b + (a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*sqrt(-(9*a^3 - 6*a^2*b + a*b^2)/(a^6*b + 6*a^5*b^2 + 15*a^4*b^3 + 20*a^3*b^4 + 15*a^2*b^5 + 6*a*b^6 + b^7)))/(a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4))) + (a + b)*x*sqrt((a^2 - 3*a*b - (a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*sqrt(-(9*a^3 - 6*a^2*b + a*b^2)/(a^6*b + 6*a^5*b^2 + 15*a^4*b^3 + 20*a^3*b^4 + 15*a^2*b^5 + 6*a*b^6 + b^7)))/(a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4))*log(-(3*a^2 - a*b)*x + (6*a^2*b - 2*a*b^2 - (a^4*b + 2*a^3*b^2 - 2*a*b^4 - b^5)*sqrt(-(9*a^3 - 6*a^2*b + a*b^2)/(a^6*b + 6*a^5*b^2 + 15*a^4*b^3 + 20*a^3*b^4 + 15*a^2*b^5 + 6*a*b^6 + b^7)))*sqrt((a^2 - 3*a*b - (a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*sqrt(-(9*a^3 - 6*a^2*b + a*b^2)/(a^6*b + 6*a^5*b^2 + 15*a^4*b^3 + 20*a^3*b^4 + 15*a^2*b^5 + 6*a*b^6 + b^7)))/(a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4))) - (a + b)*x*sqrt((a^2 - 3*a*b - (a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*sqrt(-(9*a^3 - 6*a^2*b + a*b^2)/(a^6*b + 6*a^5*b^2 + 15*a^4*b^3 + 20*a^3*b^4 + 15*a^2*b^5 + 6*a*b^6 + b^7)))/(a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4))*log(-(3*a^2 - a*b)*x - (6*a^2*b - 2*a*b^2 - (a^4*b + 2*a^3*b^2 - 2*a*b^4 - b^5)*sqrt(-(9*a^3 - 6*a^2*b + a*b^2)/(a^6*b + 6*a^5*b^2 + 15*a^4*b^3 + 20*a^3*b^4 + 15*a^2*b^5 + 6*a*b^6 + b^7)))*sqrt((a^2 - 3*a*b - (a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*sqrt(-(9*a^3 - 6*a^2*b + a*b^2)/(a^6*b + 6*a^5*b^2 + 15*a^4*b^3 + 20*a^3*b^4 + 15*a^2*b^5 + 6*a*b^6 + b^7)))/(a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4))) - 4)/((a + b)*x)","B",0
915,1,18,0,0.933952," ","integrate(x/(x^4+x^2+1),x, algorithm=""fricas"")","\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{2} + 1\right)}\right)"," ",0,"1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^2 + 1))","A",0
916,1,10,0,0.819695," ","integrate(x/(x^4+2*x^2+10),x, algorithm=""fricas"")","\frac{1}{6} \, \arctan\left(\frac{1}{3} \, x^{2} + \frac{1}{3}\right)"," ",0,"1/6*arctan(1/3*x^2 + 1/3)","A",0
917,1,18,0,1.647549," ","integrate(x^2/(x^4+9*x^2+20),x, algorithm=""fricas"")","\sqrt{5} \arctan\left(\frac{1}{5} \, \sqrt{5} x\right) - 2 \, \arctan\left(\frac{1}{2} \, x\right)"," ",0,"sqrt(5)*arctan(1/5*sqrt(5)*x) - 2*arctan(1/2*x)","A",0
918,1,159,0,0.823498," ","integrate(x^2/(x^4-x^2+1),x, algorithm=""fricas"")","-\frac{1}{6} \, \sqrt{6} \sqrt{3} \sqrt{2} \arctan\left(-\frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{2} x + \frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{\sqrt{6} \sqrt{2} x + 2 \, x^{2} + 2} - \sqrt{3}\right) - \frac{1}{6} \, \sqrt{6} \sqrt{3} \sqrt{2} \arctan\left(-\frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{2} x + \frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{-\sqrt{6} \sqrt{2} x + 2 \, x^{2} + 2} + \sqrt{3}\right) - \frac{1}{24} \, \sqrt{6} \sqrt{2} \log\left(\sqrt{6} \sqrt{2} x + 2 \, x^{2} + 2\right) + \frac{1}{24} \, \sqrt{6} \sqrt{2} \log\left(-\sqrt{6} \sqrt{2} x + 2 \, x^{2} + 2\right)"," ",0,"-1/6*sqrt(6)*sqrt(3)*sqrt(2)*arctan(-1/3*sqrt(6)*sqrt(3)*sqrt(2)*x + 1/3*sqrt(6)*sqrt(3)*sqrt(sqrt(6)*sqrt(2)*x + 2*x^2 + 2) - sqrt(3)) - 1/6*sqrt(6)*sqrt(3)*sqrt(2)*arctan(-1/3*sqrt(6)*sqrt(3)*sqrt(2)*x + 1/3*sqrt(6)*sqrt(3)*sqrt(-sqrt(6)*sqrt(2)*x + 2*x^2 + 2) + sqrt(3)) - 1/24*sqrt(6)*sqrt(2)*log(sqrt(6)*sqrt(2)*x + 2*x^2 + 2) + 1/24*sqrt(6)*sqrt(2)*log(-sqrt(6)*sqrt(2)*x + 2*x^2 + 2)","B",0
919,1,247,0,0.812304," ","integrate(x^2/(x^4-2*x^2+2),x, algorithm=""fricas"")","\frac{1}{16} \cdot 2^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} + 4} {\left(\sqrt{2} - 2\right)} \log\left(2^{\frac{3}{4}} x \sqrt{2 \, \sqrt{2} + 4} + 2 \, x^{2} + 2 \, \sqrt{2}\right) - \frac{1}{16} \cdot 2^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} + 4} {\left(\sqrt{2} - 2\right)} \log\left(-2^{\frac{3}{4}} x \sqrt{2 \, \sqrt{2} + 4} + 2 \, x^{2} + 2 \, \sqrt{2}\right) - \frac{1}{4} \cdot 2^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} + 4} \arctan\left(-\frac{1}{2} \cdot 2^{\frac{3}{4}} x \sqrt{2 \, \sqrt{2} + 4} + \frac{1}{2} \cdot 2^{\frac{1}{4}} \sqrt{2^{\frac{3}{4}} x \sqrt{2 \, \sqrt{2} + 4} + 2 \, x^{2} + 2 \, \sqrt{2}} \sqrt{2 \, \sqrt{2} + 4} - \sqrt{2} - 1\right) - \frac{1}{4} \cdot 2^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} + 4} \arctan\left(-\frac{1}{2} \cdot 2^{\frac{3}{4}} x \sqrt{2 \, \sqrt{2} + 4} + \frac{1}{2} \cdot 2^{\frac{1}{4}} \sqrt{-2^{\frac{3}{4}} x \sqrt{2 \, \sqrt{2} + 4} + 2 \, x^{2} + 2 \, \sqrt{2}} \sqrt{2 \, \sqrt{2} + 4} + \sqrt{2} + 1\right)"," ",0,"1/16*2^(1/4)*sqrt(2*sqrt(2) + 4)*(sqrt(2) - 2)*log(2^(3/4)*x*sqrt(2*sqrt(2) + 4) + 2*x^2 + 2*sqrt(2)) - 1/16*2^(1/4)*sqrt(2*sqrt(2) + 4)*(sqrt(2) - 2)*log(-2^(3/4)*x*sqrt(2*sqrt(2) + 4) + 2*x^2 + 2*sqrt(2)) - 1/4*2^(3/4)*sqrt(2*sqrt(2) + 4)*arctan(-1/2*2^(3/4)*x*sqrt(2*sqrt(2) + 4) + 1/2*2^(1/4)*sqrt(2^(3/4)*x*sqrt(2*sqrt(2) + 4) + 2*x^2 + 2*sqrt(2))*sqrt(2*sqrt(2) + 4) - sqrt(2) - 1) - 1/4*2^(3/4)*sqrt(2*sqrt(2) + 4)*arctan(-1/2*2^(3/4)*x*sqrt(2*sqrt(2) + 4) + 1/2*2^(1/4)*sqrt(-2^(3/4)*x*sqrt(2*sqrt(2) + 4) + 2*x^2 + 2*sqrt(2))*sqrt(2*sqrt(2) + 4) + sqrt(2) + 1)","A",0
920,1,367,0,0.935795," ","integrate(x^7*(c*x^4+b*x^2+a)^(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} \log\left(-8 \, c^{2} x^{4} - 8 \, b c x^{2} - b^{2} - 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(384 \, c^{5} x^{8} + 48 \, b c^{4} x^{6} - 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^{4} + 2 \, {\left(35 \, b^{3} c^{2} - 116 \, a b c^{3}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{15360 \, c^{5}}, -\frac{15 \, {\left(7 \, b^{5} - 40 \, a b^{3} c + 48 \, a^{2} b c^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{4} + b c x^{2} + a c\right)}}\right) - 2 \, {\left(384 \, c^{5} x^{8} + 48 \, b c^{4} x^{6} - 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^{4} + 2 \, {\left(35 \, b^{3} c^{2} - 116 \, a b c^{3}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{7680 \, c^{5}}\right]"," ",0,"[1/15360*(15*(7*b^5 - 40*a*b^3*c + 48*a^2*b*c^2)*sqrt(c)*log(-8*c^2*x^4 - 8*b*c*x^2 - b^2 - 4*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(c) - 4*a*c) + 4*(384*c^5*x^8 + 48*b*c^4*x^6 - 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^4 + 2*(35*b^3*c^2 - 116*a*b*c^3)*x^2)*sqrt(c*x^4 + b*x^2 + a))/c^5, -1/7680*(15*(7*b^5 - 40*a*b^3*c + 48*a^2*b*c^2)*sqrt(-c)*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(-c)/(c^2*x^4 + b*c*x^2 + a*c)) - 2*(384*c^5*x^8 + 48*b*c^4*x^6 - 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^4 + 2*(35*b^3*c^2 - 116*a*b*c^3)*x^2)*sqrt(c*x^4 + b*x^2 + a))/c^5]","A",0
921,1,303,0,1.740187," ","integrate(x^5*(c*x^4+b*x^2+a)^(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} \log\left(-8 \, c^{2} x^{4} - 8 \, b c x^{2} - b^{2} + 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(48 \, c^{4} x^{6} + 8 \, b c^{3} x^{4} + 15 \, b^{3} c - 52 \, a b c^{2} - 2 \, {\left(5 \, b^{2} c^{2} - 12 \, a c^{3}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{1536 \, c^{4}}, \frac{3 \, {\left(5 \, b^{4} - 24 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{4} + b c x^{2} + a c\right)}}\right) + 2 \, {\left(48 \, c^{4} x^{6} + 8 \, b c^{3} x^{4} + 15 \, b^{3} c - 52 \, a b c^{2} - 2 \, {\left(5 \, b^{2} c^{2} - 12 \, a c^{3}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{768 \, c^{4}}\right]"," ",0,"[1/1536*(3*(5*b^4 - 24*a*b^2*c + 16*a^2*c^2)*sqrt(c)*log(-8*c^2*x^4 - 8*b*c*x^2 - b^2 + 4*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(c) - 4*a*c) + 4*(48*c^4*x^6 + 8*b*c^3*x^4 + 15*b^3*c - 52*a*b*c^2 - 2*(5*b^2*c^2 - 12*a*c^3)*x^2)*sqrt(c*x^4 + b*x^2 + a))/c^4, 1/768*(3*(5*b^4 - 24*a*b^2*c + 16*a^2*c^2)*sqrt(-c)*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(-c)/(c^2*x^4 + b*c*x^2 + a*c)) + 2*(48*c^4*x^6 + 8*b*c^3*x^4 + 15*b^3*c - 52*a*b*c^2 - 2*(5*b^2*c^2 - 12*a*c^3)*x^2)*sqrt(c*x^4 + b*x^2 + a))/c^4]","A",0
922,1,237,0,1.061713," ","integrate(x^3*(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(b^{3} - 4 \, a b c\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{4} - 8 \, b c x^{2} - b^{2} + 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(8 \, c^{3} x^{4} + 2 \, b c^{2} x^{2} - 3 \, b^{2} c + 8 \, a c^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{192 \, c^{3}}, -\frac{3 \, {\left(b^{3} - 4 \, a b c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{4} + b c x^{2} + a c\right)}}\right) - 2 \, {\left(8 \, c^{3} x^{4} + 2 \, b c^{2} x^{2} - 3 \, b^{2} c + 8 \, a c^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{96 \, c^{3}}\right]"," ",0,"[-1/192*(3*(b^3 - 4*a*b*c)*sqrt(c)*log(-8*c^2*x^4 - 8*b*c*x^2 - b^2 + 4*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(c) - 4*a*c) - 4*(8*c^3*x^4 + 2*b*c^2*x^2 - 3*b^2*c + 8*a*c^2)*sqrt(c*x^4 + b*x^2 + a))/c^3, -1/96*(3*(b^3 - 4*a*b*c)*sqrt(-c)*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(-c)/(c^2*x^4 + b*c*x^2 + a*c)) - 2*(8*c^3*x^4 + 2*b*c^2*x^2 - 3*b^2*c + 8*a*c^2)*sqrt(c*x^4 + b*x^2 + a))/c^3]","A",0
923,1,197,0,0.928454," ","integrate(x*(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(b^{2} - 4 \, a c\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{4} - 8 \, b c x^{2} - b^{2} - 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c^{2} x^{2} + b c\right)}}{32 \, c^{2}}, \frac{{\left(b^{2} - 4 \, a c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{4} + b c x^{2} + a c\right)}}\right) + 2 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c^{2} x^{2} + b c\right)}}{16 \, c^{2}}\right]"," ",0,"[-1/32*((b^2 - 4*a*c)*sqrt(c)*log(-8*c^2*x^4 - 8*b*c*x^2 - b^2 - 4*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(c) - 4*a*c) - 4*sqrt(c*x^4 + b*x^2 + a)*(2*c^2*x^2 + b*c))/c^2, 1/16*((b^2 - 4*a*c)*sqrt(-c)*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(-c)/(c^2*x^4 + b*c*x^2 + a*c)) + 2*sqrt(c*x^4 + b*x^2 + a)*(2*c^2*x^2 + b*c))/c^2]","A",0
924,1,566,0,0.685676," ","integrate((c*x^4+b*x^2+a)^(1/2)/x,x, algorithm=""fricas"")","\left[\frac{b \sqrt{c} \log\left(-8 \, c^{2} x^{4} - 8 \, b c x^{2} - b^{2} - 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{c} - 4 \, a c\right) + 2 \, \sqrt{a} c \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{c x^{4} + b x^{2} + a} c}{8 \, c}, -\frac{b \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{4} + b c x^{2} + a c\right)}}\right) - \sqrt{a} c \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) - 2 \, \sqrt{c x^{4} + b x^{2} + a} c}{4 \, c}, \frac{4 \, \sqrt{-a} c \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) + b \sqrt{c} \log\left(-8 \, c^{2} x^{4} - 8 \, b c x^{2} - b^{2} - 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, \sqrt{c x^{4} + b x^{2} + a} c}{8 \, c}, \frac{2 \, \sqrt{-a} c \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) - b \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{4} + b c x^{2} + a c\right)}}\right) + 2 \, \sqrt{c x^{4} + b x^{2} + a} c}{4 \, c}\right]"," ",0,"[1/8*(b*sqrt(c)*log(-8*c^2*x^4 - 8*b*c*x^2 - b^2 - 4*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(c) - 4*a*c) + 2*sqrt(a)*c*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) + 4*sqrt(c*x^4 + b*x^2 + a)*c)/c, -1/4*(b*sqrt(-c)*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(-c)/(c^2*x^4 + b*c*x^2 + a*c)) - sqrt(a)*c*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) - 2*sqrt(c*x^4 + b*x^2 + a)*c)/c, 1/8*(4*sqrt(-a)*c*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)) + b*sqrt(c)*log(-8*c^2*x^4 - 8*b*c*x^2 - b^2 - 4*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(c) - 4*a*c) + 4*sqrt(c*x^4 + b*x^2 + a)*c)/c, 1/4*(2*sqrt(-a)*c*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)) - b*sqrt(-c)*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(-c)/(c^2*x^4 + b*c*x^2 + a*c)) + 2*sqrt(c*x^4 + b*x^2 + a)*c)/c]","A",0
925,1,601,0,1.080726," ","integrate((c*x^4+b*x^2+a)^(1/2)/x^3,x, algorithm=""fricas"")","\left[\frac{2 \, a \sqrt{c} x^{2} \log\left(-8 \, c^{2} x^{4} - 8 \, b c x^{2} - b^{2} - 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{c} - 4 \, a c\right) + \sqrt{a} b x^{2} \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{c x^{4} + b x^{2} + a} a}{8 \, a x^{2}}, -\frac{4 \, a \sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{4} + b c x^{2} + a c\right)}}\right) - \sqrt{a} b x^{2} \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{c x^{4} + b x^{2} + a} a}{8 \, a x^{2}}, \frac{\sqrt{-a} b x^{2} \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) + a \sqrt{c} x^{2} \log\left(-8 \, c^{2} x^{4} - 8 \, b c x^{2} - b^{2} - 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{c} - 4 \, a c\right) - 2 \, \sqrt{c x^{4} + b x^{2} + a} a}{4 \, a x^{2}}, \frac{\sqrt{-a} b x^{2} \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 \sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{4} + b c x^{2} + a c\right)}}\right) - 2 \, \sqrt{c x^{4} + b x^{2} + a} a}{4 \, a x^{2}}\right]"," ",0,"[1/8*(2*a*sqrt(c)*x^2*log(-8*c^2*x^4 - 8*b*c*x^2 - b^2 - 4*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(c) - 4*a*c) + sqrt(a)*b*x^2*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) - 4*sqrt(c*x^4 + b*x^2 + a)*a)/(a*x^2), -1/8*(4*a*sqrt(-c)*x^2*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(-c)/(c^2*x^4 + b*c*x^2 + a*c)) - sqrt(a)*b*x^2*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) + 4*sqrt(c*x^4 + b*x^2 + a)*a)/(a*x^2), 1/4*(sqrt(-a)*b*x^2*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*sqrt(c)*x^2*log(-8*c^2*x^4 - 8*b*c*x^2 - b^2 - 4*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(c) - 4*a*c) - 2*sqrt(c*x^4 + b*x^2 + a)*a)/(a*x^2), 1/4*(sqrt(-a)*b*x^2*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)) - 2*a*sqrt(-c)*x^2*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(-c)/(c^2*x^4 + b*c*x^2 + a*c)) - 2*sqrt(c*x^4 + b*x^2 + a)*a)/(a*x^2)]","A",0
926,1,215,0,1.170984," ","integrate((c*x^4+b*x^2+a)^(1/2)/x^5,x, algorithm=""fricas"")","\left[-\frac{{\left(b^{2} - 4 \, a c\right)} \sqrt{a} x^{4} \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{c x^{4} + b x^{2} + a} {\left(a b x^{2} + 2 \, a^{2}\right)}}{32 \, a^{2} x^{4}}, -\frac{{\left(b^{2} - 4 \, a c\right)} \sqrt{-a} x^{4} \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 \, \sqrt{c x^{4} + b x^{2} + a} {\left(a b x^{2} + 2 \, a^{2}\right)}}{16 \, a^{2} x^{4}}\right]"," ",0,"[-1/32*((b^2 - 4*a*c)*sqrt(a)*x^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) + 4*sqrt(c*x^4 + b*x^2 + a)*(a*b*x^2 + 2*a^2))/(a^2*x^4), -1/16*((b^2 - 4*a*c)*sqrt(-a)*x^4*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)) + 2*sqrt(c*x^4 + b*x^2 + a)*(a*b*x^2 + 2*a^2))/(a^2*x^4)]","A",0
927,1,261,0,0.990213," ","integrate((c*x^4+b*x^2+a)^(1/2)/x^7,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(b^{3} - 4 \, a b c\right)} \sqrt{a} x^{6} \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 \, {\left(2 \, a^{2} b x^{2} - {\left(3 \, a b^{2} - 8 \, a^{2} c\right)} x^{4} + 8 \, a^{3}\right)} \sqrt{c x^{4} + b x^{2} + a}}{192 \, a^{3} x^{6}}, \frac{3 \, {\left(b^{3} - 4 \, a b c\right)} \sqrt{-a} x^{6} \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 \, {\left(2 \, a^{2} b x^{2} - {\left(3 \, a b^{2} - 8 \, a^{2} c\right)} x^{4} + 8 \, a^{3}\right)} \sqrt{c x^{4} + b x^{2} + a}}{96 \, a^{3} x^{6}}\right]"," ",0,"[-1/192*(3*(b^3 - 4*a*b*c)*sqrt(a)*x^6*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) + 4*(2*a^2*b*x^2 - (3*a*b^2 - 8*a^2*c)*x^4 + 8*a^3)*sqrt(c*x^4 + b*x^2 + a))/(a^3*x^6), 1/96*(3*(b^3 - 4*a*b*c)*sqrt(-a)*x^6*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)) - 2*(2*a^2*b*x^2 - (3*a*b^2 - 8*a^2*c)*x^4 + 8*a^3)*sqrt(c*x^4 + b*x^2 + a))/(a^3*x^6)]","A",0
928,1,325,0,0.765141," ","integrate((c*x^4+b*x^2+a)^(1/2)/x^9,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(5 \, b^{4} - 24 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{a} x^{8} \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 \, {\left({\left(15 \, a b^{3} - 52 \, a^{2} b c\right)} x^{6} + 8 \, a^{3} b x^{2} - 2 \, {\left(5 \, a^{2} b^{2} - 12 \, a^{3} c\right)} x^{4} + 48 \, a^{4}\right)} \sqrt{c x^{4} + b x^{2} + a}}{1536 \, a^{4} x^{8}}, -\frac{3 \, {\left(5 \, b^{4} - 24 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{-a} x^{8} \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 \, {\left({\left(15 \, a b^{3} - 52 \, a^{2} b c\right)} x^{6} + 8 \, a^{3} b x^{2} - 2 \, {\left(5 \, a^{2} b^{2} - 12 \, a^{3} c\right)} x^{4} + 48 \, a^{4}\right)} \sqrt{c x^{4} + b x^{2} + a}}{768 \, a^{4} x^{8}}\right]"," ",0,"[1/1536*(3*(5*b^4 - 24*a*b^2*c + 16*a^2*c^2)*sqrt(a)*x^8*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) - 4*((15*a*b^3 - 52*a^2*b*c)*x^6 + 8*a^3*b*x^2 - 2*(5*a^2*b^2 - 12*a^3*c)*x^4 + 48*a^4)*sqrt(c*x^4 + b*x^2 + a))/(a^4*x^8), -1/768*(3*(5*b^4 - 24*a*b^2*c + 16*a^2*c^2)*sqrt(-a)*x^8*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)) + 2*((15*a*b^3 - 52*a^2*b*c)*x^6 + 8*a^3*b*x^2 - 2*(5*a^2*b^2 - 12*a^3*c)*x^4 + 48*a^4)*sqrt(c*x^4 + b*x^2 + a))/(a^4*x^8)]","A",0
929,1,389,0,2.671211," ","integrate((c*x^4+b*x^2+a)^(1/2)/x^11,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(7 \, b^{5} - 40 \, a b^{3} c + 48 \, a^{2} b c^{2}\right)} \sqrt{a} x^{10} \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 \, {\left({\left(105 \, a b^{4} - 460 \, a^{2} b^{2} c + 256 \, a^{3} c^{2}\right)} x^{8} - 48 \, a^{4} b x^{2} - 2 \, {\left(35 \, a^{2} b^{3} - 116 \, a^{3} b c\right)} x^{6} - 384 \, a^{5} + 8 \, {\left(7 \, a^{3} b^{2} - 16 \, a^{4} c\right)} x^{4}\right)} \sqrt{c x^{4} + b x^{2} + a}}{15360 \, a^{5} x^{10}}, \frac{15 \, {\left(7 \, b^{5} - 40 \, a b^{3} c + 48 \, a^{2} b c^{2}\right)} \sqrt{-a} x^{10} \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 \, {\left({\left(105 \, a b^{4} - 460 \, a^{2} b^{2} c + 256 \, a^{3} c^{2}\right)} x^{8} - 48 \, a^{4} b x^{2} - 2 \, {\left(35 \, a^{2} b^{3} - 116 \, a^{3} b c\right)} x^{6} - 384 \, a^{5} + 8 \, {\left(7 \, a^{3} b^{2} - 16 \, a^{4} c\right)} x^{4}\right)} \sqrt{c x^{4} + b x^{2} + a}}{7680 \, a^{5} x^{10}}\right]"," ",0,"[1/15360*(15*(7*b^5 - 40*a*b^3*c + 48*a^2*b*c^2)*sqrt(a)*x^10*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) + 4*((105*a*b^4 - 460*a^2*b^2*c + 256*a^3*c^2)*x^8 - 48*a^4*b*x^2 - 2*(35*a^2*b^3 - 116*a^3*b*c)*x^6 - 384*a^5 + 8*(7*a^3*b^2 - 16*a^4*c)*x^4)*sqrt(c*x^4 + b*x^2 + a))/(a^5*x^10), 1/7680*(15*(7*b^5 - 40*a*b^3*c + 48*a^2*b*c^2)*sqrt(-a)*x^10*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)) + 2*((105*a*b^4 - 460*a^2*b^2*c + 256*a^3*c^2)*x^8 - 48*a^4*b*x^2 - 2*(35*a^2*b^3 - 116*a^3*b*c)*x^6 - 384*a^5 + 8*(7*a^3*b^2 - 16*a^4*c)*x^4)*sqrt(c*x^4 + b*x^2 + a))/(a^5*x^10)]","A",0
930,0,0,0,2.015600," ","integrate(x^4*(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{4} + b x^{2} + a} x^{4}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2 + a)*x^4, x)","F",0
931,0,0,0,0.737335," ","integrate(x^2*(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{4} + b x^{2} + a} x^{2}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2 + a)*x^2, x)","F",0
932,0,0,0,0.873843," ","integrate((c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{4} + b x^{2} + a}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2 + a), x)","F",0
933,0,0,0,1.103899," ","integrate((c*x^4+b*x^2+a)^(1/2)/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2} + a}}{x^{2}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2 + a)/x^2, x)","F",0
934,0,0,0,1.652604," ","integrate((c*x^4+b*x^2+a)^(1/2)/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2} + a}}{x^{4}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2 + a)/x^4, x)","F",0
935,0,0,0,0.539156," ","integrate((c*x^4+b*x^2+a)^(1/2)/x^6,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2} + a}}{x^{6}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2 + a)/x^6, x)","F",0
936,1,535,0,1.295150," ","integrate(x^7*(c*x^4+b*x^2+a)^(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} \log\left(-8 \, c^{2} x^{4} - 8 \, b c x^{2} - b^{2} - 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(5120 \, c^{7} x^{12} + 6400 \, b c^{6} x^{10} + 128 \, {\left(b^{2} c^{5} + 64 \, a c^{6}\right)} x^{8} + 315 \, b^{6} c - 2520 \, a b^{4} c^{2} + 5488 \, a^{2} b^{2} c^{3} - 2048 \, a^{3} c^{4} - 16 \, {\left(9 \, b^{3} c^{4} - 44 \, a b c^{5}\right)} x^{6} + 8 \, {\left(21 \, b^{4} c^{3} - 124 \, a b^{2} c^{4} + 128 \, a^{2} c^{5}\right)} x^{4} - 2 \, {\left(105 \, b^{5} c^{2} - 728 \, a b^{3} c^{3} + 1168 \, a^{2} b c^{4}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{286720 \, c^{6}}, \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} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{4} + b c x^{2} + a c\right)}}\right) + 2 \, {\left(5120 \, c^{7} x^{12} + 6400 \, b c^{6} x^{10} + 128 \, {\left(b^{2} c^{5} + 64 \, a c^{6}\right)} x^{8} + 315 \, b^{6} c - 2520 \, a b^{4} c^{2} + 5488 \, a^{2} b^{2} c^{3} - 2048 \, a^{3} c^{4} - 16 \, {\left(9 \, b^{3} c^{4} - 44 \, a b c^{5}\right)} x^{6} + 8 \, {\left(21 \, b^{4} c^{3} - 124 \, a b^{2} c^{4} + 128 \, a^{2} c^{5}\right)} x^{4} - 2 \, {\left(105 \, b^{5} c^{2} - 728 \, a b^{3} c^{3} + 1168 \, a^{2} b c^{4}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{143360 \, c^{6}}\right]"," ",0,"[-1/286720*(105*(3*b^7 - 28*a*b^5*c + 80*a^2*b^3*c^2 - 64*a^3*b*c^3)*sqrt(c)*log(-8*c^2*x^4 - 8*b*c*x^2 - b^2 - 4*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(c) - 4*a*c) - 4*(5120*c^7*x^12 + 6400*b*c^6*x^10 + 128*(b^2*c^5 + 64*a*c^6)*x^8 + 315*b^6*c - 2520*a*b^4*c^2 + 5488*a^2*b^2*c^3 - 2048*a^3*c^4 - 16*(9*b^3*c^4 - 44*a*b*c^5)*x^6 + 8*(21*b^4*c^3 - 124*a*b^2*c^4 + 128*a^2*c^5)*x^4 - 2*(105*b^5*c^2 - 728*a*b^3*c^3 + 1168*a^2*b*c^4)*x^2)*sqrt(c*x^4 + b*x^2 + a))/c^6, 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)*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(-c)/(c^2*x^4 + b*c*x^2 + a*c)) + 2*(5120*c^7*x^12 + 6400*b*c^6*x^10 + 128*(b^2*c^5 + 64*a*c^6)*x^8 + 315*b^6*c - 2520*a*b^4*c^2 + 5488*a^2*b^2*c^3 - 2048*a^3*c^4 - 16*(9*b^3*c^4 - 44*a*b*c^5)*x^6 + 8*(21*b^4*c^3 - 124*a*b^2*c^4 + 128*a^2*c^5)*x^4 - 2*(105*b^5*c^2 - 728*a*b^3*c^3 + 1168*a^2*b*c^4)*x^2)*sqrt(c*x^4 + b*x^2 + a))/c^6]","A",0
937,1,451,0,2.368209," ","integrate(x^5*(c*x^4+b*x^2+a)^(3/2),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} \log\left(-8 \, c^{2} x^{4} - 8 \, b c x^{2} - b^{2} + 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(1280 \, c^{6} x^{10} + 1664 \, b c^{5} x^{8} + 16 \, {\left(3 \, b^{2} c^{4} + 140 \, a c^{5}\right)} x^{6} - 105 \, b^{5} c + 760 \, a b^{3} c^{2} - 1296 \, a^{2} b c^{3} - 8 \, {\left(7 \, b^{3} c^{3} - 36 \, a b c^{4}\right)} x^{4} + 2 \, {\left(35 \, b^{4} c^{2} - 216 \, a b^{2} c^{3} + 240 \, a^{2} c^{4}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{61440 \, c^{5}}, -\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} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{4} + b c x^{2} + a c\right)}}\right) - 2 \, {\left(1280 \, c^{6} x^{10} + 1664 \, b c^{5} x^{8} + 16 \, {\left(3 \, b^{2} c^{4} + 140 \, a c^{5}\right)} x^{6} - 105 \, b^{5} c + 760 \, a b^{3} c^{2} - 1296 \, a^{2} b c^{3} - 8 \, {\left(7 \, b^{3} c^{3} - 36 \, a b c^{4}\right)} x^{4} + 2 \, {\left(35 \, b^{4} c^{2} - 216 \, a b^{2} c^{3} + 240 \, a^{2} c^{4}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{30720 \, c^{5}}\right]"," ",0,"[-1/61440*(15*(7*b^6 - 60*a*b^4*c + 144*a^2*b^2*c^2 - 64*a^3*c^3)*sqrt(c)*log(-8*c^2*x^4 - 8*b*c*x^2 - b^2 + 4*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(c) - 4*a*c) - 4*(1280*c^6*x^10 + 1664*b*c^5*x^8 + 16*(3*b^2*c^4 + 140*a*c^5)*x^6 - 105*b^5*c + 760*a*b^3*c^2 - 1296*a^2*b*c^3 - 8*(7*b^3*c^3 - 36*a*b*c^4)*x^4 + 2*(35*b^4*c^2 - 216*a*b^2*c^3 + 240*a^2*c^4)*x^2)*sqrt(c*x^4 + b*x^2 + a))/c^5, -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)*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(-c)/(c^2*x^4 + b*c*x^2 + a*c)) - 2*(1280*c^6*x^10 + 1664*b*c^5*x^8 + 16*(3*b^2*c^4 + 140*a*c^5)*x^6 - 105*b^5*c + 760*a*b^3*c^2 - 1296*a^2*b*c^3 - 8*(7*b^3*c^3 - 36*a*b*c^4)*x^4 + 2*(35*b^4*c^2 - 216*a*b^2*c^3 + 240*a^2*c^4)*x^2)*sqrt(c*x^4 + b*x^2 + a))/c^5]","A",0
938,1,361,0,0.738783," ","integrate(x^3*(c*x^4+b*x^2+a)^(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} \log\left(-8 \, c^{2} x^{4} - 8 \, b c x^{2} - b^{2} + 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{c} - 4 \, a c\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^{4} + b x^{2} + a}}{5120 \, c^{4}}, \frac{15 \, {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{4} + b c x^{2} + a c\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^{4} + b x^{2} + a}}{2560 \, c^{4}}\right]"," ",0,"[1/5120*(15*(b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*sqrt(c)*log(-8*c^2*x^4 - 8*b*c*x^2 - b^2 + 4*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(c) - 4*a*c) + 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^4 + b*x^2 + a))/c^4, 1/2560*(15*(b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*sqrt(-c)*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(-c)/(c^2*x^4 + b*c*x^2 + a*c)) + 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^4 + b*x^2 + a))/c^4]","A",0
939,1,297,0,0.854503," ","integrate(x*(c*x^4+b*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{4} - 8 \, b c x^{2} - b^{2} - 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{c} - 4 \, a c\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^{4} + b x^{2} + a}}{512 \, c^{3}}, -\frac{3 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{4} + b c x^{2} + a c\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^{4} + b x^{2} + a}}{256 \, c^{3}}\right]"," ",0,"[1/512*(3*(b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(c)*log(-8*c^2*x^4 - 8*b*c*x^2 - b^2 - 4*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(c) - 4*a*c) + 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^4 + b*x^2 + a))/c^3, -1/256*(3*(b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(-c)*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(-c)/(c^2*x^4 + b*c*x^2 + a*c)) - 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^4 + b*x^2 + a))/c^3]","A",0
940,1,727,0,1.456551," ","integrate((c*x^4+b*x^2+a)^(3/2)/x,x, algorithm=""fricas"")","\left[\frac{48 \, a^{\frac{3}{2}} c^{2} \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) - 3 \, {\left(b^{3} - 12 \, a b c\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{4} - 8 \, b c x^{2} - b^{2} - 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(8 \, c^{3} x^{4} + 14 \, b c^{2} x^{2} + 3 \, b^{2} c + 32 \, a c^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{192 \, c^{2}}, \frac{24 \, a^{\frac{3}{2}} c^{2} \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) + 3 \, {\left(b^{3} - 12 \, a b c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{4} + b c x^{2} + a c\right)}}\right) + 2 \, {\left(8 \, c^{3} x^{4} + 14 \, b c^{2} x^{2} + 3 \, b^{2} c + 32 \, a c^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{96 \, c^{2}}, \frac{96 \, \sqrt{-a} a c^{2} \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) - 3 \, {\left(b^{3} - 12 \, a b c\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{4} - 8 \, b c x^{2} - b^{2} - 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(8 \, c^{3} x^{4} + 14 \, b c^{2} x^{2} + 3 \, b^{2} c + 32 \, a c^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{192 \, c^{2}}, \frac{48 \, \sqrt{-a} a c^{2} \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) + 3 \, {\left(b^{3} - 12 \, a b c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{4} + b c x^{2} + a c\right)}}\right) + 2 \, {\left(8 \, c^{3} x^{4} + 14 \, b c^{2} x^{2} + 3 \, b^{2} c + 32 \, a c^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{96 \, c^{2}}\right]"," ",0,"[1/192*(48*a^(3/2)*c^2*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) - 3*(b^3 - 12*a*b*c)*sqrt(c)*log(-8*c^2*x^4 - 8*b*c*x^2 - b^2 - 4*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(c) - 4*a*c) + 4*(8*c^3*x^4 + 14*b*c^2*x^2 + 3*b^2*c + 32*a*c^2)*sqrt(c*x^4 + b*x^2 + a))/c^2, 1/96*(24*a^(3/2)*c^2*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) + 3*(b^3 - 12*a*b*c)*sqrt(-c)*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(-c)/(c^2*x^4 + b*c*x^2 + a*c)) + 2*(8*c^3*x^4 + 14*b*c^2*x^2 + 3*b^2*c + 32*a*c^2)*sqrt(c*x^4 + b*x^2 + a))/c^2, 1/192*(96*sqrt(-a)*a*c^2*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)) - 3*(b^3 - 12*a*b*c)*sqrt(c)*log(-8*c^2*x^4 - 8*b*c*x^2 - b^2 - 4*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(c) - 4*a*c) + 4*(8*c^3*x^4 + 14*b*c^2*x^2 + 3*b^2*c + 32*a*c^2)*sqrt(c*x^4 + b*x^2 + a))/c^2, 1/96*(48*sqrt(-a)*a*c^2*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)) + 3*(b^3 - 12*a*b*c)*sqrt(-c)*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(-c)/(c^2*x^4 + b*c*x^2 + a*c)) + 2*(8*c^3*x^4 + 14*b*c^2*x^2 + 3*b^2*c + 32*a*c^2)*sqrt(c*x^4 + b*x^2 + a))/c^2]","A",0
941,1,713,0,2.126045," ","integrate((c*x^4+b*x^2+a)^(3/2)/x^3,x, algorithm=""fricas"")","\left[\frac{12 \, \sqrt{a} b c x^{2} \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) + 3 \, {\left(b^{2} + 4 \, a c\right)} \sqrt{c} x^{2} \log\left(-8 \, c^{2} x^{4} - 8 \, b c x^{2} - b^{2} - 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(2 \, c^{2} x^{4} + 5 \, b c x^{2} - 4 \, a c\right)} \sqrt{c x^{4} + b x^{2} + a}}{32 \, c x^{2}}, \frac{6 \, \sqrt{a} b c x^{2} \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) - 3 \, {\left(b^{2} + 4 \, a c\right)} \sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{4} + b c x^{2} + a c\right)}}\right) + 2 \, {\left(2 \, c^{2} x^{4} + 5 \, b c x^{2} - 4 \, a c\right)} \sqrt{c x^{4} + b x^{2} + a}}{16 \, c x^{2}}, \frac{24 \, \sqrt{-a} b c x^{2} \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) + 3 \, {\left(b^{2} + 4 \, a c\right)} \sqrt{c} x^{2} \log\left(-8 \, c^{2} x^{4} - 8 \, b c x^{2} - b^{2} - 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(2 \, c^{2} x^{4} + 5 \, b c x^{2} - 4 \, a c\right)} \sqrt{c x^{4} + b x^{2} + a}}{32 \, c x^{2}}, \frac{12 \, \sqrt{-a} b c x^{2} \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) - 3 \, {\left(b^{2} + 4 \, a c\right)} \sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{4} + b c x^{2} + a c\right)}}\right) + 2 \, {\left(2 \, c^{2} x^{4} + 5 \, b c x^{2} - 4 \, a c\right)} \sqrt{c x^{4} + b x^{2} + a}}{16 \, c x^{2}}\right]"," ",0,"[1/32*(12*sqrt(a)*b*c*x^2*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) + 3*(b^2 + 4*a*c)*sqrt(c)*x^2*log(-8*c^2*x^4 - 8*b*c*x^2 - b^2 - 4*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(c) - 4*a*c) + 4*(2*c^2*x^4 + 5*b*c*x^2 - 4*a*c)*sqrt(c*x^4 + b*x^2 + a))/(c*x^2), 1/16*(6*sqrt(a)*b*c*x^2*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) - 3*(b^2 + 4*a*c)*sqrt(-c)*x^2*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(-c)/(c^2*x^4 + b*c*x^2 + a*c)) + 2*(2*c^2*x^4 + 5*b*c*x^2 - 4*a*c)*sqrt(c*x^4 + b*x^2 + a))/(c*x^2), 1/32*(24*sqrt(-a)*b*c*x^2*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)) + 3*(b^2 + 4*a*c)*sqrt(c)*x^2*log(-8*c^2*x^4 - 8*b*c*x^2 - b^2 - 4*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(c) - 4*a*c) + 4*(2*c^2*x^4 + 5*b*c*x^2 - 4*a*c)*sqrt(c*x^4 + b*x^2 + a))/(c*x^2), 1/16*(12*sqrt(-a)*b*c*x^2*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)) - 3*(b^2 + 4*a*c)*sqrt(-c)*x^2*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(-c)/(c^2*x^4 + b*c*x^2 + a*c)) + 2*(2*c^2*x^4 + 5*b*c*x^2 - 4*a*c)*sqrt(c*x^4 + b*x^2 + a))/(c*x^2)]","A",0
942,1,713,0,2.075088," ","integrate((c*x^4+b*x^2+a)^(3/2)/x^5,x, algorithm=""fricas"")","\left[\frac{12 \, a b \sqrt{c} x^{4} \log\left(-8 \, c^{2} x^{4} - 8 \, b c x^{2} - b^{2} - 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{c} - 4 \, a c\right) + 3 \, {\left(b^{2} + 4 \, a c\right)} \sqrt{a} x^{4} \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 \, {\left(4 \, a c x^{4} - 5 \, a b x^{2} - 2 \, a^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{32 \, a x^{4}}, -\frac{24 \, a b \sqrt{-c} x^{4} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{4} + b c x^{2} + a c\right)}}\right) - 3 \, {\left(b^{2} + 4 \, a c\right)} \sqrt{a} x^{4} \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 \, {\left(4 \, a c x^{4} - 5 \, a b x^{2} - 2 \, a^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{32 \, a x^{4}}, \frac{6 \, a b \sqrt{c} x^{4} \log\left(-8 \, c^{2} x^{4} - 8 \, b c x^{2} - b^{2} - 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{c} - 4 \, a c\right) + 3 \, {\left(b^{2} + 4 \, a c\right)} \sqrt{-a} x^{4} \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 \, {\left(4 \, a c x^{4} - 5 \, a b x^{2} - 2 \, a^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{16 \, a x^{4}}, -\frac{12 \, a b \sqrt{-c} x^{4} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{4} + b c x^{2} + a c\right)}}\right) - 3 \, {\left(b^{2} + 4 \, a c\right)} \sqrt{-a} x^{4} \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 \, {\left(4 \, a c x^{4} - 5 \, a b x^{2} - 2 \, a^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{16 \, a x^{4}}\right]"," ",0,"[1/32*(12*a*b*sqrt(c)*x^4*log(-8*c^2*x^4 - 8*b*c*x^2 - b^2 - 4*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(c) - 4*a*c) + 3*(b^2 + 4*a*c)*sqrt(a)*x^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) + 4*(4*a*c*x^4 - 5*a*b*x^2 - 2*a^2)*sqrt(c*x^4 + b*x^2 + a))/(a*x^4), -1/32*(24*a*b*sqrt(-c)*x^4*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(-c)/(c^2*x^4 + b*c*x^2 + a*c)) - 3*(b^2 + 4*a*c)*sqrt(a)*x^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) - 4*(4*a*c*x^4 - 5*a*b*x^2 - 2*a^2)*sqrt(c*x^4 + b*x^2 + a))/(a*x^4), 1/16*(6*a*b*sqrt(c)*x^4*log(-8*c^2*x^4 - 8*b*c*x^2 - b^2 - 4*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(c) - 4*a*c) + 3*(b^2 + 4*a*c)*sqrt(-a)*x^4*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)) + 2*(4*a*c*x^4 - 5*a*b*x^2 - 2*a^2)*sqrt(c*x^4 + b*x^2 + a))/(a*x^4), -1/16*(12*a*b*sqrt(-c)*x^4*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(-c)/(c^2*x^4 + b*c*x^2 + a*c)) - 3*(b^2 + 4*a*c)*sqrt(-a)*x^4*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)) - 2*(4*a*c*x^4 - 5*a*b*x^2 - 2*a^2)*sqrt(c*x^4 + b*x^2 + a))/(a*x^4)]","A",0
943,1,771,0,1.556984," ","integrate((c*x^4+b*x^2+a)^(3/2)/x^7,x, algorithm=""fricas"")","\left[\frac{48 \, a^{2} c^{\frac{3}{2}} x^{6} \log\left(-8 \, c^{2} x^{4} - 8 \, b c x^{2} - b^{2} - 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{c} - 4 \, a c\right) - 3 \, {\left(b^{3} - 12 \, a b c\right)} \sqrt{a} x^{6} \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 \, {\left(14 \, a^{2} b x^{2} + {\left(3 \, a b^{2} + 32 \, a^{2} c\right)} x^{4} + 8 \, a^{3}\right)} \sqrt{c x^{4} + b x^{2} + a}}{192 \, a^{2} x^{6}}, -\frac{96 \, a^{2} \sqrt{-c} c x^{6} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{4} + b c x^{2} + a c\right)}}\right) + 3 \, {\left(b^{3} - 12 \, a b c\right)} \sqrt{a} x^{6} \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 \, {\left(14 \, a^{2} b x^{2} + {\left(3 \, a b^{2} + 32 \, a^{2} c\right)} x^{4} + 8 \, a^{3}\right)} \sqrt{c x^{4} + b x^{2} + a}}{192 \, a^{2} x^{6}}, \frac{24 \, a^{2} c^{\frac{3}{2}} x^{6} \log\left(-8 \, c^{2} x^{4} - 8 \, b c x^{2} - b^{2} - 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{c} - 4 \, a c\right) - 3 \, {\left(b^{3} - 12 \, a b c\right)} \sqrt{-a} x^{6} \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 \, {\left(14 \, a^{2} b x^{2} + {\left(3 \, a b^{2} + 32 \, a^{2} c\right)} x^{4} + 8 \, a^{3}\right)} \sqrt{c x^{4} + b x^{2} + a}}{96 \, a^{2} x^{6}}, -\frac{48 \, a^{2} \sqrt{-c} c x^{6} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{4} + b c x^{2} + a c\right)}}\right) + 3 \, {\left(b^{3} - 12 \, a b c\right)} \sqrt{-a} x^{6} \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 \, {\left(14 \, a^{2} b x^{2} + {\left(3 \, a b^{2} + 32 \, a^{2} c\right)} x^{4} + 8 \, a^{3}\right)} \sqrt{c x^{4} + b x^{2} + a}}{96 \, a^{2} x^{6}}\right]"," ",0,"[1/192*(48*a^2*c^(3/2)*x^6*log(-8*c^2*x^4 - 8*b*c*x^2 - b^2 - 4*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(c) - 4*a*c) - 3*(b^3 - 12*a*b*c)*sqrt(a)*x^6*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) - 4*(14*a^2*b*x^2 + (3*a*b^2 + 32*a^2*c)*x^4 + 8*a^3)*sqrt(c*x^4 + b*x^2 + a))/(a^2*x^6), -1/192*(96*a^2*sqrt(-c)*c*x^6*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(-c)/(c^2*x^4 + b*c*x^2 + a*c)) + 3*(b^3 - 12*a*b*c)*sqrt(a)*x^6*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) + 4*(14*a^2*b*x^2 + (3*a*b^2 + 32*a^2*c)*x^4 + 8*a^3)*sqrt(c*x^4 + b*x^2 + a))/(a^2*x^6), 1/96*(24*a^2*c^(3/2)*x^6*log(-8*c^2*x^4 - 8*b*c*x^2 - b^2 - 4*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(c) - 4*a*c) - 3*(b^3 - 12*a*b*c)*sqrt(-a)*x^6*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)) - 2*(14*a^2*b*x^2 + (3*a*b^2 + 32*a^2*c)*x^4 + 8*a^3)*sqrt(c*x^4 + b*x^2 + a))/(a^2*x^6), -1/96*(48*a^2*sqrt(-c)*c*x^6*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(-c)/(c^2*x^4 + b*c*x^2 + a*c)) + 3*(b^3 - 12*a*b*c)*sqrt(-a)*x^6*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)) + 2*(14*a^2*b*x^2 + (3*a*b^2 + 32*a^2*c)*x^4 + 8*a^3)*sqrt(c*x^4 + b*x^2 + a))/(a^2*x^6)]","A",0
944,1,319,0,1.169532," ","integrate((c*x^4+b*x^2+a)^(3/2)/x^9,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{a} x^{8} \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 \, {\left({\left(3 \, a b^{3} - 20 \, a^{2} b c\right)} x^{6} - 24 \, a^{3} b x^{2} - 2 \, {\left(a^{2} b^{2} + 20 \, a^{3} c\right)} x^{4} - 16 \, a^{4}\right)} \sqrt{c x^{4} + b x^{2} + a}}{512 \, a^{3} x^{8}}, \frac{3 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{-a} x^{8} \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 \, {\left({\left(3 \, a b^{3} - 20 \, a^{2} b c\right)} x^{6} - 24 \, a^{3} b x^{2} - 2 \, {\left(a^{2} b^{2} + 20 \, a^{3} c\right)} x^{4} - 16 \, a^{4}\right)} \sqrt{c x^{4} + b x^{2} + a}}{256 \, a^{3} x^{8}}\right]"," ",0,"[1/512*(3*(b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(a)*x^8*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) + 4*((3*a*b^3 - 20*a^2*b*c)*x^6 - 24*a^3*b*x^2 - 2*(a^2*b^2 + 20*a^3*c)*x^4 - 16*a^4)*sqrt(c*x^4 + b*x^2 + a))/(a^3*x^8), 1/256*(3*(b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(-a)*x^8*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)) + 2*((3*a*b^3 - 20*a^2*b*c)*x^6 - 24*a^3*b*x^2 - 2*(a^2*b^2 + 20*a^3*c)*x^4 - 16*a^4)*sqrt(c*x^4 + b*x^2 + a))/(a^3*x^8)]","A",0
945,1,383,0,1.556569," ","integrate((c*x^4+b*x^2+a)^(3/2)/x^11,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} \sqrt{a} x^{10} \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 \, {\left({\left(15 \, a b^{4} - 100 \, a^{2} b^{2} c + 128 \, a^{3} c^{2}\right)} x^{8} + 176 \, a^{4} b x^{2} - 2 \, {\left(5 \, a^{2} b^{3} - 28 \, a^{3} b c\right)} x^{6} + 128 \, a^{5} + 8 \, {\left(a^{3} b^{2} + 32 \, a^{4} c\right)} x^{4}\right)} \sqrt{c x^{4} + b x^{2} + a}}{5120 \, a^{4} x^{10}}, -\frac{15 \, {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} \sqrt{-a} x^{10} \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 \, {\left({\left(15 \, a b^{4} - 100 \, a^{2} b^{2} c + 128 \, a^{3} c^{2}\right)} x^{8} + 176 \, a^{4} b x^{2} - 2 \, {\left(5 \, a^{2} b^{3} - 28 \, a^{3} b c\right)} x^{6} + 128 \, a^{5} + 8 \, {\left(a^{3} b^{2} + 32 \, a^{4} c\right)} x^{4}\right)} \sqrt{c x^{4} + b x^{2} + a}}{2560 \, a^{4} x^{10}}\right]"," ",0,"[1/5120*(15*(b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*sqrt(a)*x^10*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) - 4*((15*a*b^4 - 100*a^2*b^2*c + 128*a^3*c^2)*x^8 + 176*a^4*b*x^2 - 2*(5*a^2*b^3 - 28*a^3*b*c)*x^6 + 128*a^5 + 8*(a^3*b^2 + 32*a^4*c)*x^4)*sqrt(c*x^4 + b*x^2 + a))/(a^4*x^10), -1/2560*(15*(b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*sqrt(-a)*x^10*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)) + 2*((15*a*b^4 - 100*a^2*b^2*c + 128*a^3*c^2)*x^8 + 176*a^4*b*x^2 - 2*(5*a^2*b^3 - 28*a^3*b*c)*x^6 + 128*a^5 + 8*(a^3*b^2 + 32*a^4*c)*x^4)*sqrt(c*x^4 + b*x^2 + a))/(a^4*x^10)]","A",0
946,1,473,0,1.511546," ","integrate((c*x^4+b*x^2+a)^(3/2)/x^13,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{a} x^{12} \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 \, {\left({\left(105 \, a b^{5} - 760 \, a^{2} b^{3} c + 1296 \, a^{3} b c^{2}\right)} x^{10} - 2 \, {\left(35 \, a^{2} b^{4} - 216 \, a^{3} b^{2} c + 240 \, a^{4} c^{2}\right)} x^{8} - 1664 \, a^{5} b x^{2} + 8 \, {\left(7 \, a^{3} b^{3} - 36 \, a^{4} b c\right)} x^{6} - 1280 \, a^{6} - 16 \, {\left(3 \, a^{4} b^{2} + 140 \, a^{5} c\right)} x^{4}\right)} \sqrt{c x^{4} + b x^{2} + a}}{61440 \, a^{5} x^{12}}, \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{-a} x^{12} \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 \, {\left({\left(105 \, a b^{5} - 760 \, a^{2} b^{3} c + 1296 \, a^{3} b c^{2}\right)} x^{10} - 2 \, {\left(35 \, a^{2} b^{4} - 216 \, a^{3} b^{2} c + 240 \, a^{4} c^{2}\right)} x^{8} - 1664 \, a^{5} b x^{2} + 8 \, {\left(7 \, a^{3} b^{3} - 36 \, a^{4} b c\right)} x^{6} - 1280 \, a^{6} - 16 \, {\left(3 \, a^{4} b^{2} + 140 \, a^{5} c\right)} x^{4}\right)} \sqrt{c x^{4} + b x^{2} + a}}{30720 \, a^{5} x^{12}}\right]"," ",0,"[-1/61440*(15*(7*b^6 - 60*a*b^4*c + 144*a^2*b^2*c^2 - 64*a^3*c^3)*sqrt(a)*x^12*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) - 4*((105*a*b^5 - 760*a^2*b^3*c + 1296*a^3*b*c^2)*x^10 - 2*(35*a^2*b^4 - 216*a^3*b^2*c + 240*a^4*c^2)*x^8 - 1664*a^5*b*x^2 + 8*(7*a^3*b^3 - 36*a^4*b*c)*x^6 - 1280*a^6 - 16*(3*a^4*b^2 + 140*a^5*c)*x^4)*sqrt(c*x^4 + b*x^2 + a))/(a^5*x^12), 1/30720*(15*(7*b^6 - 60*a*b^4*c + 144*a^2*b^2*c^2 - 64*a^3*c^3)*sqrt(-a)*x^12*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)) + 2*((105*a*b^5 - 760*a^2*b^3*c + 1296*a^3*b*c^2)*x^10 - 2*(35*a^2*b^4 - 216*a^3*b^2*c + 240*a^4*c^2)*x^8 - 1664*a^5*b*x^2 + 8*(7*a^3*b^3 - 36*a^4*b*c)*x^6 - 1280*a^6 - 16*(3*a^4*b^2 + 140*a^5*c)*x^4)*sqrt(c*x^4 + b*x^2 + a))/(a^5*x^12)]","A",0
947,0,0,0,0.935608," ","integrate(x^4*(c*x^4+b*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{8} + b x^{6} + a x^{4}\right)} \sqrt{c x^{4} + b x^{2} + a}, x\right)"," ",0,"integral((c*x^8 + b*x^6 + a*x^4)*sqrt(c*x^4 + b*x^2 + a), x)","F",0
948,0,0,0,0.898404," ","integrate(x^2*(c*x^4+b*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{6} + b x^{4} + a x^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}, x\right)"," ",0,"integral((c*x^6 + b*x^4 + a*x^2)*sqrt(c*x^4 + b*x^2 + a), x)","F",0
949,0,0,0,0.876899," ","integrate((c*x^4+b*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{4} + b x^{2} + a\right)}^{\frac{3}{2}}, x\right)"," ",0,"integral((c*x^4 + b*x^2 + a)^(3/2), x)","F",0
950,0,0,0,0.976411," ","integrate((c*x^4+b*x^2+a)^(3/2)/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{4} + b x^{2} + a\right)}^{\frac{3}{2}}}{x^{2}}, x\right)"," ",0,"integral((c*x^4 + b*x^2 + a)^(3/2)/x^2, x)","F",0
951,0,0,0,0.817690," ","integrate((c*x^4+b*x^2+a)^(3/2)/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{4} + b x^{2} + a\right)}^{\frac{3}{2}}}{x^{4}}, x\right)"," ",0,"integral((c*x^4 + b*x^2 + a)^(3/2)/x^4, x)","F",0
952,0,0,0,1.938421," ","integrate((c*x^4+b*x^2+a)^(3/2)/x^6,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{4} + b x^{2} + a\right)}^{\frac{3}{2}}}{x^{6}}, x\right)"," ",0,"integral((c*x^4 + b*x^2 + a)^(3/2)/x^6, x)","F",0
953,0,0,0,1.546913," ","integrate((c*x^4+b*x^2+a)^(3/2)/x^8,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{4} + b x^{2} + a\right)}^{\frac{3}{2}}}{x^{8}}, x\right)"," ",0,"integral((c*x^4 + b*x^2 + a)^(3/2)/x^8, x)","F",0
954,0,0,0,1.664911," ","integrate((-x^4-2*x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{-x^{4} - 2 \, x^{2} + 3}, x\right)"," ",0,"integral(sqrt(-x^4 - 2*x^2 + 3), x)","F",0
955,1,241,0,2.960011," ","integrate(x^7/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, b^{3} - 12 \, a b c\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{4} - 8 \, b c x^{2} - b^{2} - 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(8 \, c^{3} x^{4} - 10 \, b c^{2} x^{2} + 15 \, b^{2} c - 16 \, a c^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{192 \, c^{4}}, \frac{3 \, {\left(5 \, b^{3} - 12 \, a b c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{4} + b c x^{2} + a c\right)}}\right) + 2 \, {\left(8 \, c^{3} x^{4} - 10 \, b c^{2} x^{2} + 15 \, b^{2} c - 16 \, a c^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{96 \, c^{4}}\right]"," ",0,"[-1/192*(3*(5*b^3 - 12*a*b*c)*sqrt(c)*log(-8*c^2*x^4 - 8*b*c*x^2 - b^2 - 4*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(c) - 4*a*c) - 4*(8*c^3*x^4 - 10*b*c^2*x^2 + 15*b^2*c - 16*a*c^2)*sqrt(c*x^4 + b*x^2 + a))/c^4, 1/96*(3*(5*b^3 - 12*a*b*c)*sqrt(-c)*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(-c)/(c^2*x^4 + b*c*x^2 + a*c)) + 2*(8*c^3*x^4 - 10*b*c^2*x^2 + 15*b^2*c - 16*a*c^2)*sqrt(c*x^4 + b*x^2 + a))/c^4]","A",0
956,1,203,0,1.123374," ","integrate(x^5/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(3 \, b^{2} - 4 \, a c\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{4} - 8 \, b c x^{2} - b^{2} + 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c^{2} x^{2} - 3 \, b c\right)}}{32 \, c^{3}}, -\frac{{\left(3 \, b^{2} - 4 \, a c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{4} + b c x^{2} + a c\right)}}\right) - 2 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c^{2} x^{2} - 3 \, b c\right)}}{16 \, c^{3}}\right]"," ",0,"[-1/32*((3*b^2 - 4*a*c)*sqrt(c)*log(-8*c^2*x^4 - 8*b*c*x^2 - b^2 + 4*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(c) - 4*a*c) - 4*sqrt(c*x^4 + b*x^2 + a)*(2*c^2*x^2 - 3*b*c))/c^3, -1/16*((3*b^2 - 4*a*c)*sqrt(-c)*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(-c)/(c^2*x^4 + b*c*x^2 + a*c)) - 2*sqrt(c*x^4 + b*x^2 + a)*(2*c^2*x^2 - 3*b*c))/c^3]","A",0
957,1,161,0,0.861618," ","integrate(x^3/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{b \sqrt{c} \log\left(-8 \, c^{2} x^{4} - 8 \, b c x^{2} - b^{2} + 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, \sqrt{c x^{4} + b x^{2} + a} c}{8 \, c^{2}}, \frac{b \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{4} + b c x^{2} + a c\right)}}\right) + 2 \, \sqrt{c x^{4} + b x^{2} + a} c}{4 \, c^{2}}\right]"," ",0,"[1/8*(b*sqrt(c)*log(-8*c^2*x^4 - 8*b*c*x^2 - b^2 + 4*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(c) - 4*a*c) + 4*sqrt(c*x^4 + b*x^2 + a)*c)/c^2, 1/4*(b*sqrt(-c)*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(-c)/(c^2*x^4 + b*c*x^2 + a*c)) + 2*sqrt(c*x^4 + b*x^2 + a)*c)/c^2]","A",0
958,1,118,0,0.912481," ","integrate(x/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(-8 \, c^{2} x^{4} - 8 \, b c x^{2} - b^{2} - 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{c} - 4 \, a c\right)}{4 \, \sqrt{c}}, -\frac{\sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{4} + b c x^{2} + a c\right)}}\right)}{2 \, c}\right]"," ",0,"[1/4*log(-8*c^2*x^4 - 8*b*c*x^2 - b^2 - 4*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(c) - 4*a*c)/sqrt(c), -1/2*sqrt(-c)*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(-c)/(c^2*x^4 + b*c*x^2 + a*c))/c]","A",0
959,1,124,0,1.017810," ","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
960,1,179,0,0.580554," ","integrate(1/x^3/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a} b x^{2} \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{c x^{4} + b x^{2} + a} a}{8 \, a^{2} x^{2}}, -\frac{\sqrt{-a} b x^{2} \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 \, \sqrt{c x^{4} + b x^{2} + a} a}{4 \, a^{2} x^{2}}\right]"," ",0,"[1/8*(sqrt(a)*b*x^2*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) - 4*sqrt(c*x^4 + b*x^2 + a)*a)/(a^2*x^2), -1/4*(sqrt(-a)*b*x^2*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)) + 2*sqrt(c*x^4 + b*x^2 + a)*a)/(a^2*x^2)]","A",0
961,1,221,0,1.196032," ","integrate(1/x^5/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(3 \, b^{2} - 4 \, a c\right)} \sqrt{a} x^{4} \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{c x^{4} + b x^{2} + a} {\left(3 \, a b x^{2} - 2 \, a^{2}\right)}}{32 \, a^{3} x^{4}}, \frac{{\left(3 \, b^{2} - 4 \, a c\right)} \sqrt{-a} x^{4} \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 \, \sqrt{c x^{4} + b x^{2} + a} {\left(3 \, a b x^{2} - 2 \, a^{2}\right)}}{16 \, a^{3} x^{4}}\right]"," ",0,"[-1/32*((3*b^2 - 4*a*c)*sqrt(a)*x^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) - 4*sqrt(c*x^4 + b*x^2 + a)*(3*a*b*x^2 - 2*a^2))/(a^3*x^4), 1/16*((3*b^2 - 4*a*c)*sqrt(-a)*x^4*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)) + 2*sqrt(c*x^4 + b*x^2 + a)*(3*a*b*x^2 - 2*a^2))/(a^3*x^4)]","A",0
962,1,265,0,1.446028," ","integrate(1/x^7/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, b^{3} - 12 \, a b c\right)} \sqrt{a} x^{6} \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 \, {\left(10 \, a^{2} b x^{2} - {\left(15 \, a b^{2} - 16 \, a^{2} c\right)} x^{4} - 8 \, a^{3}\right)} \sqrt{c x^{4} + b x^{2} + a}}{192 \, a^{4} x^{6}}, -\frac{3 \, {\left(5 \, b^{3} - 12 \, a b c\right)} \sqrt{-a} x^{6} \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 \, {\left(10 \, a^{2} b x^{2} - {\left(15 \, a b^{2} - 16 \, a^{2} c\right)} x^{4} - 8 \, a^{3}\right)} \sqrt{c x^{4} + b x^{2} + a}}{96 \, a^{4} x^{6}}\right]"," ",0,"[-1/192*(3*(5*b^3 - 12*a*b*c)*sqrt(a)*x^6*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) - 4*(10*a^2*b*x^2 - (15*a*b^2 - 16*a^2*c)*x^4 - 8*a^3)*sqrt(c*x^4 + b*x^2 + a))/(a^4*x^6), -1/96*(3*(5*b^3 - 12*a*b*c)*sqrt(-a)*x^6*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)) - 2*(10*a^2*b*x^2 - (15*a*b^2 - 16*a^2*c)*x^4 - 8*a^3)*sqrt(c*x^4 + b*x^2 + a))/(a^4*x^6)]","A",0
963,0,0,0,2.126310," ","integrate(x^4/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{4}}{\sqrt{c x^{4} + b x^{2} + a}}, x\right)"," ",0,"integral(x^4/sqrt(c*x^4 + b*x^2 + a), x)","F",0
964,0,0,0,1.416264," ","integrate(x^2/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2}}{\sqrt{c x^{4} + b x^{2} + a}}, x\right)"," ",0,"integral(x^2/sqrt(c*x^4 + b*x^2 + a), x)","F",0
965,0,0,0,1.985940," ","integrate(1/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{c x^{4} + b x^{2} + a}}, x\right)"," ",0,"integral(1/sqrt(c*x^4 + b*x^2 + a), x)","F",0
966,0,0,0,1.792210," ","integrate(1/x^2/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2} + a}}{c x^{6} + b x^{4} + a x^{2}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2 + a)/(c*x^6 + b*x^4 + a*x^2), x)","F",0
967,0,0,0,0.964446," ","integrate(1/x^4/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2} + a}}{c x^{8} + b x^{6} + a x^{4}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2 + a)/(c*x^8 + b*x^6 + a*x^4), x)","F",0
968,1,249,0,1.213263," ","integrate(x^7/(-c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, b^{3} + 12 \, a b c\right)} \sqrt{-c} \log\left(8 \, c^{2} x^{4} - 8 \, b c x^{2} + b^{2} - 4 \, \sqrt{-c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} - b\right)} \sqrt{-c} - 4 \, a c\right) + 4 \, {\left(8 \, c^{3} x^{4} + 10 \, b c^{2} x^{2} + 15 \, b^{2} c + 16 \, a c^{2}\right)} \sqrt{-c x^{4} + b x^{2} + a}}{192 \, c^{4}}, -\frac{3 \, {\left(5 \, b^{3} + 12 \, a b c\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} - b\right)} \sqrt{c}}{2 \, {\left(c^{2} x^{4} - b c x^{2} - a c\right)}}\right) + 2 \, {\left(8 \, c^{3} x^{4} + 10 \, b c^{2} x^{2} + 15 \, b^{2} c + 16 \, a c^{2}\right)} \sqrt{-c x^{4} + b x^{2} + a}}{96 \, c^{4}}\right]"," ",0,"[-1/192*(3*(5*b^3 + 12*a*b*c)*sqrt(-c)*log(8*c^2*x^4 - 8*b*c*x^2 + b^2 - 4*sqrt(-c*x^4 + b*x^2 + a)*(2*c*x^2 - b)*sqrt(-c) - 4*a*c) + 4*(8*c^3*x^4 + 10*b*c^2*x^2 + 15*b^2*c + 16*a*c^2)*sqrt(-c*x^4 + b*x^2 + a))/c^4, -1/96*(3*(5*b^3 + 12*a*b*c)*sqrt(c)*arctan(1/2*sqrt(-c*x^4 + b*x^2 + a)*(2*c*x^2 - b)*sqrt(c)/(c^2*x^4 - b*c*x^2 - a*c)) + 2*(8*c^3*x^4 + 10*b*c^2*x^2 + 15*b^2*c + 16*a*c^2)*sqrt(-c*x^4 + b*x^2 + a))/c^4]","A",0
969,1,211,0,0.650763," ","integrate(x^5/(-c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(3 \, b^{2} + 4 \, a c\right)} \sqrt{-c} \log\left(8 \, c^{2} x^{4} - 8 \, b c x^{2} + b^{2} - 4 \, \sqrt{-c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} - b\right)} \sqrt{-c} - 4 \, a c\right) + 4 \, \sqrt{-c x^{4} + b x^{2} + a} {\left(2 \, c^{2} x^{2} + 3 \, b c\right)}}{32 \, c^{3}}, -\frac{{\left(3 \, b^{2} + 4 \, a c\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} - b\right)} \sqrt{c}}{2 \, {\left(c^{2} x^{4} - b c x^{2} - a c\right)}}\right) + 2 \, \sqrt{-c x^{4} + b x^{2} + a} {\left(2 \, c^{2} x^{2} + 3 \, b c\right)}}{16 \, c^{3}}\right]"," ",0,"[-1/32*((3*b^2 + 4*a*c)*sqrt(-c)*log(8*c^2*x^4 - 8*b*c*x^2 + b^2 - 4*sqrt(-c*x^4 + b*x^2 + a)*(2*c*x^2 - b)*sqrt(-c) - 4*a*c) + 4*sqrt(-c*x^4 + b*x^2 + a)*(2*c^2*x^2 + 3*b*c))/c^3, -1/16*((3*b^2 + 4*a*c)*sqrt(c)*arctan(1/2*sqrt(-c*x^4 + b*x^2 + a)*(2*c*x^2 - b)*sqrt(c)/(c^2*x^4 - b*c*x^2 - a*c)) + 2*sqrt(-c*x^4 + b*x^2 + a)*(2*c^2*x^2 + 3*b*c))/c^3]","A",0
970,1,169,0,0.731711," ","integrate(x^3/(-c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{b \sqrt{-c} \log\left(8 \, c^{2} x^{4} - 8 \, b c x^{2} + b^{2} - 4 \, \sqrt{-c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} - b\right)} \sqrt{-c} - 4 \, a c\right) + 4 \, \sqrt{-c x^{4} + b x^{2} + a} c}{8 \, c^{2}}, -\frac{b \sqrt{c} \arctan\left(\frac{\sqrt{-c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} - b\right)} \sqrt{c}}{2 \, {\left(c^{2} x^{4} - b c x^{2} - a c\right)}}\right) + 2 \, \sqrt{-c x^{4} + b x^{2} + a} c}{4 \, c^{2}}\right]"," ",0,"[-1/8*(b*sqrt(-c)*log(8*c^2*x^4 - 8*b*c*x^2 + b^2 - 4*sqrt(-c*x^4 + b*x^2 + a)*(2*c*x^2 - b)*sqrt(-c) - 4*a*c) + 4*sqrt(-c*x^4 + b*x^2 + a)*c)/c^2, -1/4*(b*sqrt(c)*arctan(1/2*sqrt(-c*x^4 + b*x^2 + a)*(2*c*x^2 - b)*sqrt(c)/(c^2*x^4 - b*c*x^2 - a*c)) + 2*sqrt(-c*x^4 + b*x^2 + a)*c)/c^2]","A",0
971,1,124,0,0.847035," ","integrate(x/(-c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-c} \log\left(8 \, c^{2} x^{4} - 8 \, b c x^{2} + b^{2} - 4 \, \sqrt{-c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} - b\right)} \sqrt{-c} - 4 \, a c\right)}{4 \, c}, -\frac{\arctan\left(\frac{\sqrt{-c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} - b\right)} \sqrt{c}}{2 \, {\left(c^{2} x^{4} - b c x^{2} - a c\right)}}\right)}{2 \, \sqrt{c}}\right]"," ",0,"[-1/4*sqrt(-c)*log(8*c^2*x^4 - 8*b*c*x^2 + b^2 - 4*sqrt(-c*x^4 + b*x^2 + a)*(2*c*x^2 - b)*sqrt(-c) - 4*a*c)/c, -1/2*arctan(1/2*sqrt(-c*x^4 + b*x^2 + a)*(2*c*x^2 - b)*sqrt(c)/(c^2*x^4 - b*c*x^2 - a*c))/sqrt(c)]","A",0
972,1,129,0,1.054665," ","integrate(1/x/(c*x^4+b*x^2-a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a} \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 \, a}, \frac{\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 \, \sqrt{a}}\right]"," ",0,"[-1/4*sqrt(-a)*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)/a, 1/2*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))/sqrt(a)]","A",0
973,1,188,0,1.106640," ","integrate(1/x^3/(c*x^4+b*x^2-a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a} b x^{2} \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{c x^{4} + b x^{2} - a} a}{8 \, a^{2} x^{2}}, \frac{\sqrt{a} b x^{2} \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 \, \sqrt{c x^{4} + b x^{2} - a} a}{4 \, a^{2} x^{2}}\right]"," ",0,"[-1/8*(sqrt(-a)*b*x^2*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) - 4*sqrt(c*x^4 + b*x^2 - a)*a)/(a^2*x^2), 1/4*(sqrt(a)*b*x^2*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)) + 2*sqrt(c*x^4 + b*x^2 - a)*a)/(a^2*x^2)]","A",0
974,1,230,0,1.239149," ","integrate(1/x^5/(c*x^4+b*x^2-a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(3 \, b^{2} + 4 \, a c\right)} \sqrt{-a} x^{4} \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{c x^{4} + b x^{2} - a} {\left(3 \, a b x^{2} + 2 \, a^{2}\right)}}{32 \, a^{3} x^{4}}, \frac{{\left(3 \, b^{2} + 4 \, a c\right)} \sqrt{a} x^{4} \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 \, \sqrt{c x^{4} + b x^{2} - a} {\left(3 \, a b x^{2} + 2 \, a^{2}\right)}}{16 \, a^{3} x^{4}}\right]"," ",0,"[-1/32*((3*b^2 + 4*a*c)*sqrt(-a)*x^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) - 4*sqrt(c*x^4 + b*x^2 - a)*(3*a*b*x^2 + 2*a^2))/(a^3*x^4), 1/16*((3*b^2 + 4*a*c)*sqrt(a)*x^4*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)) + 2*sqrt(c*x^4 + b*x^2 - a)*(3*a*b*x^2 + 2*a^2))/(a^3*x^4)]","A",0
975,1,272,0,4.005951," ","integrate(1/x^7/(c*x^4+b*x^2-a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, b^{3} + 12 \, a b c\right)} \sqrt{-a} x^{6} \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 \, {\left(10 \, a^{2} b x^{2} + {\left(15 \, a b^{2} + 16 \, a^{2} c\right)} x^{4} + 8 \, a^{3}\right)} \sqrt{c x^{4} + b x^{2} - a}}{192 \, a^{4} x^{6}}, \frac{3 \, {\left(5 \, b^{3} + 12 \, a b c\right)} \sqrt{a} x^{6} \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 \, {\left(10 \, a^{2} b x^{2} + {\left(15 \, a b^{2} + 16 \, a^{2} c\right)} x^{4} + 8 \, a^{3}\right)} \sqrt{c x^{4} + b x^{2} - a}}{96 \, a^{4} x^{6}}\right]"," ",0,"[-1/192*(3*(5*b^3 + 12*a*b*c)*sqrt(-a)*x^6*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) - 4*(10*a^2*b*x^2 + (15*a*b^2 + 16*a^2*c)*x^4 + 8*a^3)*sqrt(c*x^4 + b*x^2 - a))/(a^4*x^6), 1/96*(3*(5*b^3 + 12*a*b*c)*sqrt(a)*x^6*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)) + 2*(10*a^2*b*x^2 + (15*a*b^2 + 16*a^2*c)*x^4 + 8*a^3)*sqrt(c*x^4 + b*x^2 - a))/(a^4*x^6)]","A",0
976,0,0,0,0.742666," ","integrate(x^4/(-c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c x^{4} + b x^{2} + a} x^{4}}{c x^{4} - b x^{2} - a}, x\right)"," ",0,"integral(-sqrt(-c*x^4 + b*x^2 + a)*x^4/(c*x^4 - b*x^2 - a), x)","F",0
977,0,0,0,0.791777," ","integrate(x^2/(-c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c x^{4} + b x^{2} + a} x^{2}}{c x^{4} - b x^{2} - a}, x\right)"," ",0,"integral(-sqrt(-c*x^4 + b*x^2 + a)*x^2/(c*x^4 - b*x^2 - a), x)","F",0
978,0,0,0,0.785403," ","integrate(1/(-c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c x^{4} + b x^{2} + a}}{c x^{4} - b x^{2} - a}, x\right)"," ",0,"integral(-sqrt(-c*x^4 + b*x^2 + a)/(c*x^4 - b*x^2 - a), x)","F",0
979,0,0,0,1.182175," ","integrate(1/x^2/(-c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c x^{4} + b x^{2} + a}}{c x^{6} - b x^{4} - a x^{2}}, x\right)"," ",0,"integral(-sqrt(-c*x^4 + b*x^2 + a)/(c*x^6 - b*x^4 - a*x^2), x)","F",0
980,0,0,0,0.923533," ","integrate(1/x^4/(-c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c x^{4} + b x^{2} + a}}{c x^{8} - b x^{6} - a x^{4}}, x\right)"," ",0,"integral(-sqrt(-c*x^4 + b*x^2 + a)/(c*x^8 - b*x^6 - a*x^4), x)","F",0
981,1,591,0,1.834193," ","integrate(x^9/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, a b^{4} - 24 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + {\left(5 \, b^{4} c - 24 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} x^{4} + {\left(5 \, b^{5} - 24 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x^{2}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{4} - 8 \, b c x^{2} - b^{2} + 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{6} - 15 \, a b^{3} c + 52 \, a^{2} b c^{2} - 5 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x^{4} - {\left(15 \, b^{4} c - 62 \, a b^{2} c^{2} + 24 \, a^{2} c^{3}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{32 \, {\left(a b^{2} c^{4} - 4 \, a^{2} c^{5} + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} x^{4} + {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} x^{2}\right)}}, -\frac{3 \, {\left(5 \, a b^{4} - 24 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + {\left(5 \, b^{4} c - 24 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} x^{4} + {\left(5 \, b^{5} - 24 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{4} + b c x^{2} + a c\right)}}\right) - 2 \, {\left(2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{6} - 15 \, a b^{3} c + 52 \, a^{2} b c^{2} - 5 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x^{4} - {\left(15 \, b^{4} c - 62 \, a b^{2} c^{2} + 24 \, a^{2} c^{3}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{16 \, {\left(a b^{2} c^{4} - 4 \, a^{2} c^{5} + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} x^{4} + {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} x^{2}\right)}}\right]"," ",0,"[-1/32*(3*(5*a*b^4 - 24*a^2*b^2*c + 16*a^3*c^2 + (5*b^4*c - 24*a*b^2*c^2 + 16*a^2*c^3)*x^4 + (5*b^5 - 24*a*b^3*c + 16*a^2*b*c^2)*x^2)*sqrt(c)*log(-8*c^2*x^4 - 8*b*c*x^2 - b^2 + 4*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(c) - 4*a*c) - 4*(2*(b^2*c^3 - 4*a*c^4)*x^6 - 15*a*b^3*c + 52*a^2*b*c^2 - 5*(b^3*c^2 - 4*a*b*c^3)*x^4 - (15*b^4*c - 62*a*b^2*c^2 + 24*a^2*c^3)*x^2)*sqrt(c*x^4 + b*x^2 + a))/(a*b^2*c^4 - 4*a^2*c^5 + (b^2*c^5 - 4*a*c^6)*x^4 + (b^3*c^4 - 4*a*b*c^5)*x^2), -1/16*(3*(5*a*b^4 - 24*a^2*b^2*c + 16*a^3*c^2 + (5*b^4*c - 24*a*b^2*c^2 + 16*a^2*c^3)*x^4 + (5*b^5 - 24*a*b^3*c + 16*a^2*b*c^2)*x^2)*sqrt(-c)*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(-c)/(c^2*x^4 + b*c*x^2 + a*c)) - 2*(2*(b^2*c^3 - 4*a*c^4)*x^6 - 15*a*b^3*c + 52*a^2*b*c^2 - 5*(b^3*c^2 - 4*a*b*c^3)*x^4 - (15*b^4*c - 62*a*b^2*c^2 + 24*a^2*c^3)*x^2)*sqrt(c*x^4 + b*x^2 + a))/(a*b^2*c^4 - 4*a^2*c^5 + (b^2*c^5 - 4*a*c^6)*x^4 + (b^3*c^4 - 4*a*b*c^5)*x^2)]","A",0
982,1,459,0,1.578229," ","integrate(x^7/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(b^{3} c - 4 \, a b c^{2}\right)} x^{4} + a b^{3} - 4 \, a^{2} b c + {\left(b^{4} - 4 \, a b^{2} c\right)} x^{2}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{4} - 8 \, b c x^{2} - b^{2} + 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{4} + 3 \, a b^{2} c - 8 \, a^{2} c^{2} + {\left(3 \, b^{3} c - 10 \, a b c^{2}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{8 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4} + {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} x^{4} + {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} x^{2}\right)}}, \frac{3 \, {\left({\left(b^{3} c - 4 \, a b c^{2}\right)} x^{4} + a b^{3} - 4 \, a^{2} b c + {\left(b^{4} - 4 \, a b^{2} c\right)} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{4} + b c x^{2} + a c\right)}}\right) + 2 \, {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{4} + 3 \, a b^{2} c - 8 \, a^{2} c^{2} + {\left(3 \, b^{3} c - 10 \, a b c^{2}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{4 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4} + {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} x^{4} + {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} x^{2}\right)}}\right]"," ",0,"[1/8*(3*((b^3*c - 4*a*b*c^2)*x^4 + a*b^3 - 4*a^2*b*c + (b^4 - 4*a*b^2*c)*x^2)*sqrt(c)*log(-8*c^2*x^4 - 8*b*c*x^2 - b^2 + 4*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(c) - 4*a*c) + 4*((b^2*c^2 - 4*a*c^3)*x^4 + 3*a*b^2*c - 8*a^2*c^2 + (3*b^3*c - 10*a*b*c^2)*x^2)*sqrt(c*x^4 + b*x^2 + a))/(a*b^2*c^3 - 4*a^2*c^4 + (b^2*c^4 - 4*a*c^5)*x^4 + (b^3*c^3 - 4*a*b*c^4)*x^2), 1/4*(3*((b^3*c - 4*a*b*c^2)*x^4 + a*b^3 - 4*a^2*b*c + (b^4 - 4*a*b^2*c)*x^2)*sqrt(-c)*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(-c)/(c^2*x^4 + b*c*x^2 + a*c)) + 2*((b^2*c^2 - 4*a*c^3)*x^4 + 3*a*b^2*c - 8*a^2*c^2 + (3*b^3*c - 10*a*b*c^2)*x^2)*sqrt(c*x^4 + b*x^2 + a))/(a*b^2*c^3 - 4*a^2*c^4 + (b^2*c^4 - 4*a*c^5)*x^4 + (b^3*c^3 - 4*a*b*c^4)*x^2)]","A",0
983,1,387,0,1.622604," ","integrate(x^5/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\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{c} \log\left(-8 \, c^{2} x^{4} - 8 \, b c x^{2} - b^{2} - 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(a b c + {\left(b^{2} c - 2 \, a c^{2}\right)} x^{2}\right)}}{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)}}, -\frac{{\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{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{4} + b c x^{2} + a c\right)}}\right) + 2 \, \sqrt{c x^{4} + b x^{2} + a} {\left(a b c + {\left(b^{2} c - 2 \, a c^{2}\right)} x^{2}\right)}}{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)}}\right]"," ",0,"[1/4*(((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(c)*log(-8*c^2*x^4 - 8*b*c*x^2 - b^2 - 4*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(c) - 4*a*c) - 4*sqrt(c*x^4 + b*x^2 + a)*(a*b*c + (b^2*c - 2*a*c^2)*x^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), -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(-c)*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(-c)/(c^2*x^4 + b*c*x^2 + a*c)) + 2*sqrt(c*x^4 + b*x^2 + a)*(a*b*c + (b^2*c - 2*a*c^2)*x^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)]","A",0
984,1,67,0,1.754177," ","integrate(x^3/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(b x^{2} + 2 \, a\right)}}{{\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}}"," ",0,"sqrt(c*x^4 + b*x^2 + a)*(b*x^2 + 2*a)/((b^2*c - 4*a*c^2)*x^4 + a*b^2 - 4*a^2*c + (b^3 - 4*a*b*c)*x^2)","A",0
985,1,67,0,1.075487," ","integrate(x/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)}}{{\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}}"," ",0,"-sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)/((b^2*c - 4*a*c^2)*x^4 + a*b^2 - 4*a^2*c + (b^3 - 4*a*b*c)*x^2)","A",0
986,1,389,0,3.183726," ","integrate(1/x/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\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{a} \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 \, {\left(a b c x^{2} + a b^{2} - 2 \, a^{2} c\right)} \sqrt{c x^{4} + b x^{2} + a}}{4 \, {\left(a^{3} b^{2} - 4 \, a^{4} c + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} x^{4} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} x^{2}\right)}}, \frac{{\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{-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 \, {\left(a b c x^{2} + a b^{2} - 2 \, a^{2} c\right)} \sqrt{c x^{4} + b x^{2} + a}}{2 \, {\left(a^{3} b^{2} - 4 \, a^{4} c + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} x^{4} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} x^{2}\right)}}\right]"," ",0,"[1/4*(((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(a)*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) + 4*(a*b*c*x^2 + a*b^2 - 2*a^2*c)*sqrt(c*x^4 + b*x^2 + a))/(a^3*b^2 - 4*a^4*c + (a^2*b^2*c - 4*a^3*c^2)*x^4 + (a^2*b^3 - 4*a^3*b*c)*x^2), 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(-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)) + 2*(a*b*c*x^2 + a*b^2 - 2*a^2*c)*sqrt(c*x^4 + b*x^2 + a))/(a^3*b^2 - 4*a^4*c + (a^2*b^2*c - 4*a^3*c^2)*x^4 + (a^2*b^3 - 4*a^3*b*c)*x^2)]","B",0
987,1,485,0,1.449338," ","integrate(1/x^3/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(b^{3} c - 4 \, a b c^{2}\right)} x^{6} + {\left(b^{4} - 4 \, a b^{2} c\right)} x^{4} + {\left(a b^{3} - 4 \, a^{2} b c\right)} x^{2}\right)} \sqrt{a} \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 \, {\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{c x^{4} + b x^{2} + a}}{8 \, {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} x^{6} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} x^{4} + {\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^{6} + {\left(b^{4} - 4 \, a b^{2} c\right)} x^{4} + {\left(a b^{3} - 4 \, a^{2} b c\right)} x^{2}\right)} \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 \, {\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{c x^{4} + b x^{2} + a}}{4 \, {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} x^{6} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} x^{4} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} x^{2}\right)}}\right]"," ",0,"[1/8*(3*((b^3*c - 4*a*b*c^2)*x^6 + (b^4 - 4*a*b^2*c)*x^4 + (a*b^3 - 4*a^2*b*c)*x^2)*sqrt(a)*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) - 4*((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(c*x^4 + b*x^2 + a))/((a^3*b^2*c - 4*a^4*c^2)*x^6 + (a^3*b^3 - 4*a^4*b*c)*x^4 + (a^4*b^2 - 4*a^5*c)*x^2), -1/4*(3*((b^3*c - 4*a*b*c^2)*x^6 + (b^4 - 4*a*b^2*c)*x^4 + (a*b^3 - 4*a^2*b*c)*x^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)) + 2*((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(c*x^4 + b*x^2 + a))/((a^3*b^2*c - 4*a^4*c^2)*x^6 + (a^3*b^3 - 4*a^4*b*c)*x^4 + (a^4*b^2 - 4*a^5*c)*x^2)]","A",0
988,1,615,0,2.740954," ","integrate(1/x^5/(c*x^4+b*x^2+a)^(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^{8} + {\left(5 \, b^{5} - 24 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x^{6} + {\left(5 \, a b^{4} - 24 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} x^{4}\right)} \sqrt{a} \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 \, {\left({\left(15 \, a b^{3} c - 52 \, a^{2} b c^{2}\right)} x^{6} - 2 \, a^{3} b^{2} + 8 \, a^{4} c + {\left(15 \, a b^{4} - 62 \, a^{2} b^{2} c + 24 \, a^{3} c^{2}\right)} x^{4} + 5 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{32 \, {\left({\left(a^{4} b^{2} c - 4 \, a^{5} c^{2}\right)} x^{8} + {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} x^{6} + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} x^{4}\right)}}, \frac{3 \, {\left({\left(5 \, b^{4} c - 24 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} x^{8} + {\left(5 \, b^{5} - 24 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x^{6} + {\left(5 \, a b^{4} - 24 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} x^{4}\right)} \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 \, {\left({\left(15 \, a b^{3} c - 52 \, a^{2} b c^{2}\right)} x^{6} - 2 \, a^{3} b^{2} + 8 \, a^{4} c + {\left(15 \, a b^{4} - 62 \, a^{2} b^{2} c + 24 \, a^{3} c^{2}\right)} x^{4} + 5 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{16 \, {\left({\left(a^{4} b^{2} c - 4 \, a^{5} c^{2}\right)} x^{8} + {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} x^{6} + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} x^{4}\right)}}\right]"," ",0,"[-1/32*(3*((5*b^4*c - 24*a*b^2*c^2 + 16*a^2*c^3)*x^8 + (5*b^5 - 24*a*b^3*c + 16*a^2*b*c^2)*x^6 + (5*a*b^4 - 24*a^2*b^2*c + 16*a^3*c^2)*x^4)*sqrt(a)*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) - 4*((15*a*b^3*c - 52*a^2*b*c^2)*x^6 - 2*a^3*b^2 + 8*a^4*c + (15*a*b^4 - 62*a^2*b^2*c + 24*a^3*c^2)*x^4 + 5*(a^2*b^3 - 4*a^3*b*c)*x^2)*sqrt(c*x^4 + b*x^2 + a))/((a^4*b^2*c - 4*a^5*c^2)*x^8 + (a^4*b^3 - 4*a^5*b*c)*x^6 + (a^5*b^2 - 4*a^6*c)*x^4), 1/16*(3*((5*b^4*c - 24*a*b^2*c^2 + 16*a^2*c^3)*x^8 + (5*b^5 - 24*a*b^3*c + 16*a^2*b*c^2)*x^6 + (5*a*b^4 - 24*a^2*b^2*c + 16*a^3*c^2)*x^4)*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)) + 2*((15*a*b^3*c - 52*a^2*b*c^2)*x^6 - 2*a^3*b^2 + 8*a^4*c + (15*a*b^4 - 62*a^2*b^2*c + 24*a^3*c^2)*x^4 + 5*(a^2*b^3 - 4*a^3*b*c)*x^2)*sqrt(c*x^4 + b*x^2 + a))/((a^4*b^2*c - 4*a^5*c^2)*x^8 + (a^4*b^3 - 4*a^5*b*c)*x^6 + (a^5*b^2 - 4*a^6*c)*x^4)]","A",0
989,0,0,0,1.117264," ","integrate(x^6/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2} + a} x^{6}}{c^{2} x^{8} + 2 \, b c x^{6} + {\left(b^{2} + 2 \, a c\right)} x^{4} + 2 \, a b x^{2} + a^{2}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2 + a)*x^6/(c^2*x^8 + 2*b*c*x^6 + (b^2 + 2*a*c)*x^4 + 2*a*b*x^2 + a^2), x)","F",0
990,0,0,0,2.511111," ","integrate(x^4/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2} + a} x^{4}}{c^{2} x^{8} + 2 \, b c x^{6} + {\left(b^{2} + 2 \, a c\right)} x^{4} + 2 \, a b x^{2} + a^{2}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2 + a)*x^4/(c^2*x^8 + 2*b*c*x^6 + (b^2 + 2*a*c)*x^4 + 2*a*b*x^2 + a^2), x)","F",0
991,0,0,0,1.635582," ","integrate(x^2/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2} + a} x^{2}}{c^{2} x^{8} + 2 \, b c x^{6} + {\left(b^{2} + 2 \, a c\right)} x^{4} + 2 \, a b x^{2} + a^{2}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2 + a)*x^2/(c^2*x^8 + 2*b*c*x^6 + (b^2 + 2*a*c)*x^4 + 2*a*b*x^2 + a^2), x)","F",0
992,0,0,0,1.859502," ","integrate(1/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2} + a}}{c^{2} x^{8} + 2 \, b c x^{6} + {\left(b^{2} + 2 \, a c\right)} x^{4} + 2 \, a b x^{2} + a^{2}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2 + a)/(c^2*x^8 + 2*b*c*x^6 + (b^2 + 2*a*c)*x^4 + 2*a*b*x^2 + a^2), x)","F",0
993,0,0,0,5.746033," ","integrate(1/x^2/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2} + a}}{c^{2} x^{10} + 2 \, b c x^{8} + {\left(b^{2} + 2 \, a c\right)} x^{6} + 2 \, a b x^{4} + a^{2} x^{2}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2 + a)/(c^2*x^10 + 2*b*c*x^8 + (b^2 + 2*a*c)*x^6 + 2*a*b*x^4 + a^2*x^2), x)","F",0
994,1,30,0,0.967883," ","integrate(x^4/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{c x^{4} + b x^{2}} {\left(c x^{2} - 2 \, b\right)}}{3 \, c^{2} x}"," ",0,"1/3*sqrt(c*x^4 + b*x^2)*(c*x^2 - 2*b)/(c^2*x)","A",0
995,1,114,0,1.021645," ","integrate(x^3/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{b \sqrt{c} \log\left(-2 \, c x^{2} - b + 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right) + 2 \, \sqrt{c x^{4} + b x^{2}} c}{4 \, c^{2}}, \frac{b \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-c}}{c x^{2} + b}\right) + \sqrt{c x^{4} + b x^{2}} c}{2 \, c^{2}}\right]"," ",0,"[1/4*(b*sqrt(c)*log(-2*c*x^2 - b + 2*sqrt(c*x^4 + b*x^2)*sqrt(c)) + 2*sqrt(c*x^4 + b*x^2)*c)/c^2, 1/2*(b*sqrt(-c)*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-c)/(c*x^2 + b)) + sqrt(c*x^4 + b*x^2)*c)/c^2]","A",0
996,1,20,0,0.954293," ","integrate(x^2/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{c x^{4} + b x^{2}}}{c x}"," ",0,"sqrt(c*x^4 + b*x^2)/(c*x)","A",0
997,1,74,0,0.920131," ","integrate(x/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(-2 \, c x^{2} - b - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right)}{2 \, \sqrt{c}}, -\frac{\sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-c}}{c x^{2} + b}\right)}{c}\right]"," ",0,"[1/2*log(-2*c*x^2 - b - 2*sqrt(c*x^4 + b*x^2)*sqrt(c))/sqrt(c), -sqrt(-c)*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-c)/(c*x^2 + b))/c]","A",0
998,1,80,0,0.994219," ","integrate(1/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(-\frac{c x^{3} + 2 \, b x - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{b}}{x^{3}}\right)}{2 \, \sqrt{b}}, \frac{\sqrt{-b} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-b}}{c x^{3} + b x}\right)}{b}\right]"," ",0,"[1/2*log(-(c*x^3 + 2*b*x - 2*sqrt(c*x^4 + b*x^2)*sqrt(b))/x^3)/sqrt(b), sqrt(-b)*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-b)/(c*x^3 + b*x))/b]","A",0
999,1,21,0,0.842265," ","integrate(1/x/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{c x^{4} + b x^{2}}}{b x^{2}}"," ",0,"-sqrt(c*x^4 + b*x^2)/(b*x^2)","A",0
1000,1,133,0,1.070675," ","integrate(1/x^2/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{b} c x^{3} \log\left(-\frac{c x^{3} + 2 \, b x + 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{b}}{x^{3}}\right) - 2 \, \sqrt{c x^{4} + b x^{2}} b}{4 \, b^{2} x^{3}}, -\frac{\sqrt{-b} c x^{3} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-b}}{c x^{3} + b x}\right) + \sqrt{c x^{4} + b x^{2}} b}{2 \, b^{2} x^{3}}\right]"," ",0,"[1/4*(sqrt(b)*c*x^3*log(-(c*x^3 + 2*b*x + 2*sqrt(c*x^4 + b*x^2)*sqrt(b))/x^3) - 2*sqrt(c*x^4 + b*x^2)*b)/(b^2*x^3), -1/2*(sqrt(-b)*c*x^3*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-b)/(c*x^3 + b*x)) + sqrt(c*x^4 + b*x^2)*b)/(b^2*x^3)]","A",0
1001,1,31,0,0.823159," ","integrate(1/x^3/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{c x^{4} + b x^{2}} {\left(2 \, c x^{2} - b\right)}}{3 \, b^{2} x^{4}}"," ",0,"1/3*sqrt(c*x^4 + b*x^2)*(2*c*x^2 - b)/(b^2*x^4)","A",0
1002,1,163,0,1.001170," ","integrate(1/x^4/(c*x^4+b*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{b} c^{2} x^{5} \log\left(-\frac{c x^{3} + 2 \, b x - 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{b}}{x^{3}}\right) + 2 \, \sqrt{c x^{4} + b x^{2}} {\left(3 \, b c x^{2} - 2 \, b^{2}\right)}}{16 \, b^{3} x^{5}}, \frac{3 \, \sqrt{-b} c^{2} x^{5} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2}} \sqrt{-b}}{c x^{3} + b x}\right) + \sqrt{c x^{4} + b x^{2}} {\left(3 \, b c x^{2} - 2 \, b^{2}\right)}}{8 \, b^{3} x^{5}}\right]"," ",0,"[1/16*(3*sqrt(b)*c^2*x^5*log(-(c*x^3 + 2*b*x - 2*sqrt(c*x^4 + b*x^2)*sqrt(b))/x^3) + 2*sqrt(c*x^4 + b*x^2)*(3*b*c*x^2 - 2*b^2))/(b^3*x^5), 1/8*(3*sqrt(-b)*c^2*x^5*arctan(sqrt(c*x^4 + b*x^2)*sqrt(-b)/(c*x^3 + b*x)) + sqrt(c*x^4 + b*x^2)*(3*b*c*x^2 - 2*b^2))/(b^3*x^5)]","A",0
1003,0,0,0,1.180074," ","integrate(x^4/(c*x^4+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{4}}{\sqrt{c x^{4} + a}}, x\right)"," ",0,"integral(x^4/sqrt(c*x^4 + a), x)","F",0
1004,1,14,0,1.202552," ","integrate(x^3/(c*x^4+a)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{c x^{4} + a}}{2 \, c}"," ",0,"1/2*sqrt(c*x^4 + a)/c","A",0
1005,0,0,0,2.165828," ","integrate(x^2/(c*x^4+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2}}{\sqrt{c x^{4} + a}}, x\right)"," ",0,"integral(x^2/sqrt(c*x^4 + a), x)","F",0
1006,1,63,0,2.244055," ","integrate(x/(c*x^4+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(-2 \, c x^{4} - 2 \, \sqrt{c x^{4} + a} \sqrt{c} x^{2} - a\right)}{4 \, \sqrt{c}}, -\frac{\sqrt{-c} \arctan\left(\frac{\sqrt{-c} x^{2}}{\sqrt{c x^{4} + a}}\right)}{2 \, c}\right]"," ",0,"[1/4*log(-2*c*x^4 - 2*sqrt(c*x^4 + a)*sqrt(c)*x^2 - a)/sqrt(c), -1/2*sqrt(-c)*arctan(sqrt(-c)*x^2/sqrt(c*x^4 + a))/c]","A",0
1007,0,0,0,1.749351," ","integrate(1/(c*x^4+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{c x^{4} + a}}, x\right)"," ",0,"integral(1/sqrt(c*x^4 + a), x)","F",0
1008,1,63,0,1.144386," ","integrate(1/x/(c*x^4+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{c x^{4} - 2 \, \sqrt{c x^{4} + a} \sqrt{a} + 2 \, a}{x^{4}}\right)}{4 \, \sqrt{a}}, \frac{\sqrt{-a} \arctan\left(\frac{\sqrt{c x^{4} + a} \sqrt{-a}}{a}\right)}{2 \, a}\right]"," ",0,"[1/4*log((c*x^4 - 2*sqrt(c*x^4 + a)*sqrt(a) + 2*a)/x^4)/sqrt(a), 1/2*sqrt(-a)*arctan(sqrt(c*x^4 + a)*sqrt(-a)/a)/a]","A",0
1009,0,0,0,0.840559," ","integrate(1/x^2/(c*x^4+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + a}}{c x^{6} + a x^{2}}, x\right)"," ",0,"integral(sqrt(c*x^4 + a)/(c*x^6 + a*x^2), x)","F",0
1010,1,17,0,2.548913," ","integrate(1/x^3/(c*x^4+a)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{c x^{4} + a}}{2 \, a x^{2}}"," ",0,"-1/2*sqrt(c*x^4 + a)/(a*x^2)","A",0
1011,0,0,0,0.480005," ","integrate(1/x^4/(c*x^4+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + a}}{c x^{8} + a x^{4}}, x\right)"," ",0,"integral(sqrt(c*x^4 + a)/(c*x^8 + a*x^4), x)","F",0
1012,1,124,0,0.619210," ","integrate(x^4/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, a^{2} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 2 \, {\left(2 \, b^{2} x^{3} - 3 \, a b x\right)} \sqrt{b x^{2} + a}}{16 \, b^{3}}, -\frac{3 \, a^{2} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(2 \, b^{2} x^{3} - 3 \, a b x\right)} \sqrt{b x^{2} + a}}{8 \, b^{3}}\right]"," ",0,"[1/16*(3*a^2*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 2*(2*b^2*x^3 - 3*a*b*x)*sqrt(b*x^2 + a))/b^3, -1/8*(3*a^2*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (2*b^2*x^3 - 3*a*b*x)*sqrt(b*x^2 + a))/b^3]","A",0
1013,1,23,0,1.097486," ","integrate(x^3/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{b x^{2} + a} {\left(b x^{2} - 2 \, a\right)}}{3 \, b^{2}}"," ",0,"1/3*sqrt(b*x^2 + a)*(b*x^2 - 2*a)/b^2","A",0
1014,1,93,0,0.777514," ","integrate(x^2/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{b x^{2} + a} b x + a \sqrt{b} \log\left(-2 \, b x^{2} + 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right)}{4 \, b^{2}}, \frac{\sqrt{b x^{2} + a} b x + a \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right)}{2 \, b^{2}}\right]"," ",0,"[1/4*(2*sqrt(b*x^2 + a)*b*x + a*sqrt(b)*log(-2*b*x^2 + 2*sqrt(b*x^2 + a)*sqrt(b)*x - a))/b^2, 1/2*(sqrt(b*x^2 + a)*b*x + a*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)))/b^2]","A",0
1015,1,13,0,0.900604," ","integrate(x/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{b x^{2} + a}}{b}"," ",0,"sqrt(b*x^2 + a)/b","A",0
1016,1,59,0,1.582200," ","integrate(1/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right)}{2 \, \sqrt{b}}, -\frac{\sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right)}{b}\right]"," ",0,"[1/2*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a)/sqrt(b), -sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a))/b]","A",0
1017,1,60,0,0.717192," ","integrate(1/x/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right)}{2 \, \sqrt{a}}, \frac{\sqrt{-a} \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right)}{a}\right]"," ",0,"[1/2*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2)/sqrt(a), sqrt(-a)*arctan(sqrt(-a)/sqrt(b*x^2 + a))/a]","A",0
1018,1,17,0,0.971125," ","integrate(1/x^2/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{b x^{2} + a}}{a x}"," ",0,"-sqrt(b*x^2 + a)/(a*x)","A",0
1019,1,105,0,2.013108," ","integrate(1/x^3/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a} b x^{2} \log\left(-\frac{b x^{2} + 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - 2 \, \sqrt{b x^{2} + a} a}{4 \, a^{2} x^{2}}, -\frac{\sqrt{-a} b x^{2} \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) + \sqrt{b x^{2} + a} a}{2 \, a^{2} x^{2}}\right]"," ",0,"[1/4*(sqrt(a)*b*x^2*log(-(b*x^2 + 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) - 2*sqrt(b*x^2 + a)*a)/(a^2*x^2), -1/2*(sqrt(-a)*b*x^2*arctan(sqrt(-a)/sqrt(b*x^2 + a)) + sqrt(b*x^2 + a)*a)/(a^2*x^2)]","A",0
1020,1,27,0,0.895877," ","integrate(1/x^4/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\frac{{\left(2 \, b x^{2} - a\right)} \sqrt{b x^{2} + a}}{3 \, a^{2} x^{3}}"," ",0,"1/3*(2*b*x^2 - a)*sqrt(b*x^2 + a)/(a^2*x^3)","A",0
1021,1,13,0,1.787740," ","integrate(x^4/(c*x^4)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{c x^{4}} x}{3 \, c}"," ",0,"1/3*sqrt(c*x^4)*x/c","A",0
1022,1,12,0,0.834949," ","integrate(x^3/(c*x^4)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{c x^{4}}}{2 \, c}"," ",0,"1/2*sqrt(c*x^4)/c","A",0
1023,1,14,0,0.965626," ","integrate(x^2/(c*x^4)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{c x^{4}}}{c x}"," ",0,"sqrt(c*x^4)/(c*x)","A",0
1024,1,16,0,1.057660," ","integrate(x/(c*x^4)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{c x^{4}} \log\left(x\right)}{c x^{2}}"," ",0,"sqrt(c*x^4)*log(x)/(c*x^2)","A",0
1025,1,15,0,1.916996," ","integrate(1/(c*x^4)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{c x^{4}}}{c x^{3}}"," ",0,"-sqrt(c*x^4)/(c*x^3)","A",0
1026,1,15,0,0.950768," ","integrate(1/x/(c*x^4)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{c x^{4}}}{2 \, c x^{4}}"," ",0,"-1/2*sqrt(c*x^4)/(c*x^4)","A",0
1027,1,15,0,1.817884," ","integrate(1/x^2/(c*x^4)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{c x^{4}}}{3 \, c x^{5}}"," ",0,"-1/3*sqrt(c*x^4)/(c*x^5)","A",0
1028,1,15,0,0.796211," ","integrate(1/x^3/(c*x^4)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{c x^{4}}}{4 \, c x^{6}}"," ",0,"-1/4*sqrt(c*x^4)/(c*x^6)","A",0
1029,1,15,0,1.886424," ","integrate(1/x^4/(c*x^4)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{c x^{4}}}{5 \, c x^{7}}"," ",0,"-1/5*sqrt(c*x^4)/(c*x^7)","A",0
1030,1,8,0,1.836993," ","integrate(x^4/a^(1/2),x, algorithm=""fricas"")","\frac{x^{5}}{5 \, \sqrt{a}}"," ",0,"1/5*x^5/sqrt(a)","A",0
1031,1,8,0,0.882100," ","integrate(x^3/a^(1/2),x, algorithm=""fricas"")","\frac{x^{4}}{4 \, \sqrt{a}}"," ",0,"1/4*x^4/sqrt(a)","A",0
1032,1,8,0,1.056319," ","integrate(x^2/a^(1/2),x, algorithm=""fricas"")","\frac{x^{3}}{3 \, \sqrt{a}}"," ",0,"1/3*x^3/sqrt(a)","A",0
1033,1,8,0,1.866993," ","integrate(x/a^(1/2),x, algorithm=""fricas"")","\frac{x^{2}}{2 \, \sqrt{a}}"," ",0,"1/2*x^2/sqrt(a)","A",0
1034,1,5,0,2.583627," ","integrate(1/a^(1/2),x, algorithm=""fricas"")","\frac{x}{\sqrt{a}}"," ",0,"x/sqrt(a)","A",0
1035,1,6,0,1.141885," ","integrate(1/x/a^(1/2),x, algorithm=""fricas"")","\frac{\log\left(x\right)}{\sqrt{a}}"," ",0,"log(x)/sqrt(a)","A",0
1036,1,8,0,2.656378," ","integrate(1/x^2/a^(1/2),x, algorithm=""fricas"")","-\frac{1}{\sqrt{a} x}"," ",0,"-1/(sqrt(a)*x)","A",0
1037,1,8,0,1.845207," ","integrate(1/x^3/a^(1/2),x, algorithm=""fricas"")","-\frac{1}{2 \, \sqrt{a} x^{2}}"," ",0,"-1/2/(sqrt(a)*x^2)","A",0
1038,1,8,0,1.709115," ","integrate(1/x^4/a^(1/2),x, algorithm=""fricas"")","-\frac{1}{3 \, \sqrt{a} x^{3}}"," ",0,"-1/3/(sqrt(a)*x^3)","A",0
1039,0,0,0,1.528242," ","integrate(1/(-x^4-2*x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{4} - 2 \, x^{2} + 3}}{x^{4} + 2 \, x^{2} - 3}, x\right)"," ",0,"integral(-sqrt(-x^4 - 2*x^2 + 3)/(x^4 + 2*x^2 - 3), x)","F",0
1040,0,0,0,1.481025," ","integrate(1/(-x^4+5*x^2-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{4} + 5 \, x^{2} - 1}}{x^{4} - 5 \, x^{2} + 1}, x\right)"," ",0,"integral(-sqrt(-x^4 + 5*x^2 - 1)/(x^4 - 5*x^2 + 1), x)","F",0
1041,1,24,0,1.378597," ","integrate(x^(5/2)*(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\frac{2}{1155} \, {\left(77 \, c x^{7} + 105 \, b x^{5} + 165 \, a x^{3}\right)} \sqrt{x}"," ",0,"2/1155*(77*c*x^7 + 105*b*x^5 + 165*a*x^3)*sqrt(x)","A",0
1042,1,24,0,1.644266," ","integrate(x^(3/2)*(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\frac{2}{585} \, {\left(45 \, c x^{6} + 65 \, b x^{4} + 117 \, a x^{2}\right)} \sqrt{x}"," ",0,"2/585*(45*c*x^6 + 65*b*x^4 + 117*a*x^2)*sqrt(x)","A",0
1043,1,22,0,2.210560," ","integrate(x^(1/2)*(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\frac{2}{231} \, {\left(21 \, c x^{5} + 33 \, b x^{3} + 77 \, a x\right)} \sqrt{x}"," ",0,"2/231*(21*c*x^5 + 33*b*x^3 + 77*a*x)*sqrt(x)","A",0
1044,1,21,0,0.867870," ","integrate((c*x^4+b*x^2+a)/x^(1/2),x, algorithm=""fricas"")","\frac{2}{45} \, {\left(5 \, c x^{4} + 9 \, b x^{2} + 45 \, a\right)} \sqrt{x}"," ",0,"2/45*(5*c*x^4 + 9*b*x^2 + 45*a)*sqrt(x)","A",0
1045,1,21,0,0.995984," ","integrate((c*x^4+b*x^2+a)/x^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, c x^{4} + 7 \, b x^{2} - 21 \, a\right)}}{21 \, \sqrt{x}}"," ",0,"2/21*(3*c*x^4 + 7*b*x^2 - 21*a)/sqrt(x)","A",0
1046,1,21,0,1.062893," ","integrate((c*x^4+b*x^2+a)/x^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, c x^{4} + 15 \, b x^{2} - 5 \, a\right)}}{15 \, x^{\frac{3}{2}}}"," ",0,"2/15*(3*c*x^4 + 15*b*x^2 - 5*a)/x^(3/2)","A",0
1047,1,21,0,1.752894," ","integrate((c*x^4+b*x^2+a)/x^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, c x^{4} - 15 \, b x^{2} - 3 \, a\right)}}{15 \, x^{\frac{5}{2}}}"," ",0,"2/15*(5*c*x^4 - 15*b*x^2 - 3*a)/x^(5/2)","A",0
1048,1,49,0,0.932627," ","integrate(x^(5/2)*(c*x^4+b*x^2+a)^2,x, algorithm=""fricas"")","\frac{2}{504735} \, {\left(21945 \, c^{2} x^{11} + 53130 \, b c x^{9} + 33649 \, {\left(b^{2} + 2 \, a c\right)} x^{7} + 91770 \, a b x^{5} + 72105 \, a^{2} x^{3}\right)} \sqrt{x}"," ",0,"2/504735*(21945*c^2*x^11 + 53130*b*c*x^9 + 33649*(b^2 + 2*a*c)*x^7 + 91770*a*b*x^5 + 72105*a^2*x^3)*sqrt(x)","A",0
1049,1,49,0,0.809009," ","integrate(x^(3/2)*(c*x^4+b*x^2+a)^2,x, algorithm=""fricas"")","\frac{2}{69615} \, {\left(3315 \, c^{2} x^{10} + 8190 \, b c x^{8} + 5355 \, {\left(b^{2} + 2 \, a c\right)} x^{6} + 15470 \, a b x^{4} + 13923 \, a^{2} x^{2}\right)} \sqrt{x}"," ",0,"2/69615*(3315*c^2*x^10 + 8190*b*c*x^8 + 5355*(b^2 + 2*a*c)*x^6 + 15470*a*b*x^4 + 13923*a^2*x^2)*sqrt(x)","A",0
1050,1,47,0,0.582329," ","integrate(x^(1/2)*(c*x^4+b*x^2+a)^2,x, algorithm=""fricas"")","\frac{2}{21945} \, {\left(1155 \, c^{2} x^{9} + 2926 \, b c x^{7} + 1995 \, {\left(b^{2} + 2 \, a c\right)} x^{5} + 6270 \, a b x^{3} + 7315 \, a^{2} x\right)} \sqrt{x}"," ",0,"2/21945*(1155*c^2*x^9 + 2926*b*c*x^7 + 1995*(b^2 + 2*a*c)*x^5 + 6270*a*b*x^3 + 7315*a^2*x)*sqrt(x)","A",0
1051,1,46,0,0.974283," ","integrate((c*x^4+b*x^2+a)^2/x^(1/2),x, algorithm=""fricas"")","\frac{2}{9945} \, {\left(585 \, c^{2} x^{8} + 1530 \, b c x^{6} + 1105 \, {\left(b^{2} + 2 \, a c\right)} x^{4} + 3978 \, a b x^{2} + 9945 \, a^{2}\right)} \sqrt{x}"," ",0,"2/9945*(585*c^2*x^8 + 1530*b*c*x^6 + 1105*(b^2 + 2*a*c)*x^4 + 3978*a*b*x^2 + 9945*a^2)*sqrt(x)","A",0
1052,1,46,0,0.825299," ","integrate((c*x^4+b*x^2+a)^2/x^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(77 \, c^{2} x^{8} + 210 \, b c x^{6} + 165 \, {\left(b^{2} + 2 \, a c\right)} x^{4} + 770 \, a b x^{2} - 1155 \, a^{2}\right)}}{1155 \, \sqrt{x}}"," ",0,"2/1155*(77*c^2*x^8 + 210*b*c*x^6 + 165*(b^2 + 2*a*c)*x^4 + 770*a*b*x^2 - 1155*a^2)/sqrt(x)","A",0
1053,1,46,0,0.956670," ","integrate((c*x^4+b*x^2+a)^2/x^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(45 \, c^{2} x^{8} + 130 \, b c x^{6} + 117 \, {\left(b^{2} + 2 \, a c\right)} x^{4} + 1170 \, a b x^{2} - 195 \, a^{2}\right)}}{585 \, x^{\frac{3}{2}}}"," ",0,"2/585*(45*c^2*x^8 + 130*b*c*x^6 + 117*(b^2 + 2*a*c)*x^4 + 1170*a*b*x^2 - 195*a^2)/x^(3/2)","A",0
1054,1,46,0,1.496177," ","integrate((c*x^4+b*x^2+a)^2/x^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(105 \, c^{2} x^{8} + 330 \, b c x^{6} + 385 \, {\left(b^{2} + 2 \, a c\right)} x^{4} - 2310 \, a b x^{2} - 231 \, a^{2}\right)}}{1155 \, x^{\frac{5}{2}}}"," ",0,"2/1155*(105*c^2*x^8 + 330*b*c*x^6 + 385*(b^2 + 2*a*c)*x^4 - 2310*a*b*x^2 - 231*a^2)/x^(5/2)","A",0
1055,1,86,0,0.930462," ","integrate(x^(5/2)*(c*x^4+b*x^2+a)^3,x, algorithm=""fricas"")","\frac{2}{46940355} \, {\left(1514205 \, c^{3} x^{15} + 5215595 \, b c^{2} x^{13} + 6122655 \, {\left(b^{2} c + a c^{2}\right)} x^{11} + 2470545 \, {\left(b^{3} + 6 \, a b c\right)} x^{9} + 12801915 \, a^{2} b x^{5} + 9388071 \, {\left(a b^{2} + a^{2} c\right)} x^{7} + 6705765 \, a^{3} x^{3}\right)} \sqrt{x}"," ",0,"2/46940355*(1514205*c^3*x^15 + 5215595*b*c^2*x^13 + 6122655*(b^2*c + a*c^2)*x^11 + 2470545*(b^3 + 6*a*b*c)*x^9 + 12801915*a^2*b*x^5 + 9388071*(a*b^2 + a^2*c)*x^7 + 6705765*a^3*x^3)*sqrt(x)","A",0
1056,1,86,0,0.889058," ","integrate(x^(3/2)*(c*x^4+b*x^2+a)^3,x, algorithm=""fricas"")","\frac{2}{3364725} \, {\left(116025 \, c^{3} x^{14} + 403767 \, b c^{2} x^{12} + 480675 \, {\left(b^{2} c + a c^{2}\right)} x^{10} + 197925 \, {\left(b^{3} + 6 \, a b c\right)} x^{8} + 1121575 \, a^{2} b x^{4} + 776475 \, {\left(a b^{2} + a^{2} c\right)} x^{6} + 672945 \, a^{3} x^{2}\right)} \sqrt{x}"," ",0,"2/3364725*(116025*c^3*x^14 + 403767*b*c^2*x^12 + 480675*(b^2*c + a*c^2)*x^10 + 197925*(b^3 + 6*a*b*c)*x^8 + 1121575*a^2*b*x^4 + 776475*(a*b^2 + a^2*c)*x^6 + 672945*a^3*x^2)*sqrt(x)","A",0
1057,1,84,0,2.685181," ","integrate(x^(1/2)*(c*x^4+b*x^2+a)^3,x, algorithm=""fricas"")","\frac{2}{4542615} \, {\left(168245 \, c^{3} x^{13} + 592515 \, b c^{2} x^{11} + 717255 \, {\left(b^{2} c + a c^{2}\right)} x^{9} + 302841 \, {\left(b^{3} + 6 \, a b c\right)} x^{7} + 1946835 \, a^{2} b x^{3} + 1238895 \, {\left(a b^{2} + a^{2} c\right)} x^{5} + 1514205 \, a^{3} x\right)} \sqrt{x}"," ",0,"2/4542615*(168245*c^3*x^13 + 592515*b*c^2*x^11 + 717255*(b^2*c + a*c^2)*x^9 + 302841*(b^3 + 6*a*b*c)*x^7 + 1946835*a^2*b*x^3 + 1238895*(a*b^2 + a^2*c)*x^5 + 1514205*a^3*x)*sqrt(x)","A",0
1058,1,83,0,1.609512," ","integrate((c*x^4+b*x^2+a)^3/x^(1/2),x, algorithm=""fricas"")","\frac{2}{116025} \, {\left(4641 \, c^{3} x^{12} + 16575 \, b c^{2} x^{10} + 20475 \, {\left(b^{2} c + a c^{2}\right)} x^{8} + 8925 \, {\left(b^{3} + 6 \, a b c\right)} x^{6} + 69615 \, a^{2} b x^{2} + 38675 \, {\left(a b^{2} + a^{2} c\right)} x^{4} + 116025 \, a^{3}\right)} \sqrt{x}"," ",0,"2/116025*(4641*c^3*x^12 + 16575*b*c^2*x^10 + 20475*(b^2*c + a*c^2)*x^8 + 8925*(b^3 + 6*a*b*c)*x^6 + 69615*a^2*b*x^2 + 38675*(a*b^2 + a^2*c)*x^4 + 116025*a^3)*sqrt(x)","A",0
1059,1,83,0,0.932712," ","integrate((c*x^4+b*x^2+a)^3/x^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(7315 \, c^{3} x^{12} + 26565 \, b c^{2} x^{10} + 33649 \, {\left(b^{2} c + a c^{2}\right)} x^{8} + 15295 \, {\left(b^{3} + 6 \, a b c\right)} x^{6} + 168245 \, a^{2} b x^{2} + 72105 \, {\left(a b^{2} + a^{2} c\right)} x^{4} - 168245 \, a^{3}\right)}}{168245 \, \sqrt{x}}"," ",0,"2/168245*(7315*c^3*x^12 + 26565*b*c^2*x^10 + 33649*(b^2*c + a*c^2)*x^8 + 15295*(b^3 + 6*a*b*c)*x^6 + 168245*a^2*b*x^2 + 72105*(a*b^2 + a^2*c)*x^4 - 168245*a^3)/sqrt(x)","A",0
1060,1,83,0,1.138710," ","integrate((c*x^4+b*x^2+a)^3/x^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3315 \, c^{3} x^{12} + 12285 \, b c^{2} x^{10} + 16065 \, {\left(b^{2} c + a c^{2}\right)} x^{8} + 7735 \, {\left(b^{3} + 6 \, a b c\right)} x^{6} + 208845 \, a^{2} b x^{2} + 41769 \, {\left(a b^{2} + a^{2} c\right)} x^{4} - 23205 \, a^{3}\right)}}{69615 \, x^{\frac{3}{2}}}"," ",0,"2/69615*(3315*c^3*x^12 + 12285*b*c^2*x^10 + 16065*(b^2*c + a*c^2)*x^8 + 7735*(b^3 + 6*a*b*c)*x^6 + 208845*a^2*b*x^2 + 41769*(a*b^2 + a^2*c)*x^4 - 23205*a^3)/x^(3/2)","A",0
1061,1,83,0,1.918072," ","integrate((c*x^4+b*x^2+a)^3/x^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(385 \, c^{3} x^{12} + 1463 \, b c^{2} x^{10} + 1995 \, {\left(b^{2} c + a c^{2}\right)} x^{8} + 1045 \, {\left(b^{3} + 6 \, a b c\right)} x^{6} - 21945 \, a^{2} b x^{2} + 7315 \, {\left(a b^{2} + a^{2} c\right)} x^{4} - 1463 \, a^{3}\right)}}{7315 \, x^{\frac{5}{2}}}"," ",0,"2/7315*(385*c^3*x^12 + 1463*b*c^2*x^10 + 1995*(b^2*c + a*c^2)*x^8 + 1045*(b^3 + 6*a*b*c)*x^6 - 21945*a^2*b*x^2 + 7315*(a*b^2 + a^2*c)*x^4 - 1463*a^3)/x^(5/2)","A",0
1062,1,6649,0,11.734205," ","integrate(x^(9/2)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\frac{12 \, c \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} + {\left(b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}}{b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}}}} \arctan\left(\frac{{\left({\left(b^{9} - 9 \, a b^{7} c + 26 \, a^{2} b^{5} c^{2} - 25 \, a^{3} b^{3} c^{3} + 4 \, a^{4} b c^{4} - {\left(b^{6} c^{7} - 10 \, a b^{4} c^{8} + 32 \, a^{2} b^{2} c^{9} - 32 \, a^{3} c^{10}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}\right)} \sqrt{{\left(a^{10} b^{12} - 10 \, a^{11} b^{10} c + 37 \, a^{12} b^{8} c^{2} - 62 \, a^{13} b^{6} c^{3} + 46 \, a^{14} b^{4} c^{4} - 12 \, a^{15} b^{2} c^{5} + a^{16} c^{6}\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(a^{7} b^{17} - 17 \, a^{8} b^{15} c + 119 \, a^{9} b^{13} c^{2} - 441 \, a^{10} b^{11} c^{3} + 924 \, a^{11} b^{9} c^{4} - 1078 \, a^{12} b^{7} c^{5} + 637 \, a^{13} b^{5} c^{6} - 151 \, a^{14} b^{3} c^{7} + 12 \, a^{15} b c^{8} - {\left(a^{7} b^{14} c^{7} - 18 \, a^{8} b^{12} c^{8} + 131 \, a^{9} b^{10} c^{9} - 491 \, a^{10} b^{8} c^{10} + 997 \, a^{11} b^{6} c^{11} - 1052 \, a^{12} b^{4} c^{12} + 496 \, a^{13} b^{2} c^{13} - 64 \, a^{14} c^{14}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}\right)} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} + {\left(b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}}{b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}}}} + {\left(a^{5} b^{15} - 14 \, a^{6} b^{13} c + 77 \, a^{7} b^{11} c^{2} - 210 \, a^{8} b^{9} c^{3} + 294 \, a^{9} b^{7} c^{4} - 196 \, a^{10} b^{5} c^{5} + 49 \, a^{11} b^{3} c^{6} - 4 \, a^{12} b c^{7} - {\left(a^{5} b^{12} c^{7} - 15 \, a^{6} b^{10} c^{8} + 88 \, a^{7} b^{8} c^{9} - 253 \, a^{8} b^{6} c^{10} + 362 \, a^{9} b^{4} c^{11} - 224 \, a^{10} b^{2} c^{12} + 32 \, a^{11} c^{13}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}\right)} \sqrt{x}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} + {\left(b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}}{b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}}}}}{2 \, {\left(a^{7} b^{12} - 10 \, a^{8} b^{10} c + 37 \, a^{9} b^{8} c^{2} - 62 \, a^{10} b^{6} c^{3} + 46 \, a^{11} b^{4} c^{4} - 12 \, a^{12} b^{2} c^{5} + a^{13} c^{6}\right)}}\right) - 12 \, c \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} - {\left(b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}}{b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}}}} \arctan\left(-\frac{{\left(b^{9} - 9 \, a b^{7} c + 26 \, a^{2} b^{5} c^{2} - 25 \, a^{3} b^{3} c^{3} + 4 \, a^{4} b c^{4} + {\left(b^{6} c^{7} - 10 \, a b^{4} c^{8} + 32 \, a^{2} b^{2} c^{9} - 32 \, a^{3} c^{10}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}\right)} \sqrt{{\left(a^{10} b^{12} - 10 \, a^{11} b^{10} c + 37 \, a^{12} b^{8} c^{2} - 62 \, a^{13} b^{6} c^{3} + 46 \, a^{14} b^{4} c^{4} - 12 \, a^{15} b^{2} c^{5} + a^{16} c^{6}\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(a^{7} b^{17} - 17 \, a^{8} b^{15} c + 119 \, a^{9} b^{13} c^{2} - 441 \, a^{10} b^{11} c^{3} + 924 \, a^{11} b^{9} c^{4} - 1078 \, a^{12} b^{7} c^{5} + 637 \, a^{13} b^{5} c^{6} - 151 \, a^{14} b^{3} c^{7} + 12 \, a^{15} b c^{8} + {\left(a^{7} b^{14} c^{7} - 18 \, a^{8} b^{12} c^{8} + 131 \, a^{9} b^{10} c^{9} - 491 \, a^{10} b^{8} c^{10} + 997 \, a^{11} b^{6} c^{11} - 1052 \, a^{12} b^{4} c^{12} + 496 \, a^{13} b^{2} c^{13} - 64 \, a^{14} c^{14}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}\right)} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} - {\left(b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}}{b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}}}} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} - {\left(b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}}{b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}}}} + {\left(a^{5} b^{15} - 14 \, a^{6} b^{13} c + 77 \, a^{7} b^{11} c^{2} - 210 \, a^{8} b^{9} c^{3} + 294 \, a^{9} b^{7} c^{4} - 196 \, a^{10} b^{5} c^{5} + 49 \, a^{11} b^{3} c^{6} - 4 \, a^{12} b c^{7} + {\left(a^{5} b^{12} c^{7} - 15 \, a^{6} b^{10} c^{8} + 88 \, a^{7} b^{8} c^{9} - 253 \, a^{8} b^{6} c^{10} + 362 \, a^{9} b^{4} c^{11} - 224 \, a^{10} b^{2} c^{12} + 32 \, a^{11} c^{13}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}\right)} \sqrt{x} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} - {\left(b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}}{b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}}}}}{2 \, {\left(a^{7} b^{12} - 10 \, a^{8} b^{10} c + 37 \, a^{9} b^{8} c^{2} - 62 \, a^{10} b^{6} c^{3} + 46 \, a^{11} b^{4} c^{4} - 12 \, a^{12} b^{2} c^{5} + a^{13} c^{6}\right)}}\right) - 3 \, c \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} + {\left(b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}}{b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}}}} \log\left(\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{14} - 16 \, a b^{12} c + 102 \, a^{2} b^{10} c^{2} - 328 \, a^{3} b^{8} c^{3} + 553 \, a^{4} b^{6} c^{4} - 457 \, a^{5} b^{4} c^{5} + 152 \, a^{6} b^{2} c^{6} - 16 \, a^{7} c^{7} - {\left(b^{11} c^{7} - 17 \, a b^{9} c^{8} + 113 \, a^{2} b^{7} c^{9} - 364 \, a^{3} b^{5} c^{10} + 560 \, a^{4} b^{3} c^{11} - 320 \, a^{5} b c^{12}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} + {\left(b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}}{b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}}}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} + {\left(b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}}{b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}}} - {\left(a^{5} b^{6} - 5 \, a^{6} b^{4} c + 6 \, a^{7} b^{2} c^{2} - a^{8} c^{3}\right)} \sqrt{x}\right) + 3 \, c \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} + {\left(b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}}{b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}}}} \log\left(-\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{14} - 16 \, a b^{12} c + 102 \, a^{2} b^{10} c^{2} - 328 \, a^{3} b^{8} c^{3} + 553 \, a^{4} b^{6} c^{4} - 457 \, a^{5} b^{4} c^{5} + 152 \, a^{6} b^{2} c^{6} - 16 \, a^{7} c^{7} - {\left(b^{11} c^{7} - 17 \, a b^{9} c^{8} + 113 \, a^{2} b^{7} c^{9} - 364 \, a^{3} b^{5} c^{10} + 560 \, a^{4} b^{3} c^{11} - 320 \, a^{5} b c^{12}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} + {\left(b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}}{b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}}}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} + {\left(b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}}{b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}}} - {\left(a^{5} b^{6} - 5 \, a^{6} b^{4} c + 6 \, a^{7} b^{2} c^{2} - a^{8} c^{3}\right)} \sqrt{x}\right) - 3 \, c \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} - {\left(b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}}{b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}}}} \log\left(\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{14} - 16 \, a b^{12} c + 102 \, a^{2} b^{10} c^{2} - 328 \, a^{3} b^{8} c^{3} + 553 \, a^{4} b^{6} c^{4} - 457 \, a^{5} b^{4} c^{5} + 152 \, a^{6} b^{2} c^{6} - 16 \, a^{7} c^{7} + {\left(b^{11} c^{7} - 17 \, a b^{9} c^{8} + 113 \, a^{2} b^{7} c^{9} - 364 \, a^{3} b^{5} c^{10} + 560 \, a^{4} b^{3} c^{11} - 320 \, a^{5} b c^{12}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} - {\left(b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}}{b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}}}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} - {\left(b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}}{b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}}} - {\left(a^{5} b^{6} - 5 \, a^{6} b^{4} c + 6 \, a^{7} b^{2} c^{2} - a^{8} c^{3}\right)} \sqrt{x}\right) + 3 \, c \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} - {\left(b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}}{b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}}}} \log\left(-\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{14} - 16 \, a b^{12} c + 102 \, a^{2} b^{10} c^{2} - 328 \, a^{3} b^{8} c^{3} + 553 \, a^{4} b^{6} c^{4} - 457 \, a^{5} b^{4} c^{5} + 152 \, a^{6} b^{2} c^{6} - 16 \, a^{7} c^{7} + {\left(b^{11} c^{7} - 17 \, a b^{9} c^{8} + 113 \, a^{2} b^{7} c^{9} - 364 \, a^{3} b^{5} c^{10} + 560 \, a^{4} b^{3} c^{11} - 320 \, a^{5} b c^{12}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} - {\left(b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}}{b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}}}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} - {\left(b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}}{b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}}} - {\left(a^{5} b^{6} - 5 \, a^{6} b^{4} c + 6 \, a^{7} b^{2} c^{2} - a^{8} c^{3}\right)} \sqrt{x}\right) + 4 \, x^{\frac{3}{2}}}{6 \, c}"," ",0,"1/6*(12*c*sqrt(sqrt(1/2)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 + (b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))/(b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)))*arctan(1/2*((b^9 - 9*a*b^7*c + 26*a^2*b^5*c^2 - 25*a^3*b^3*c^3 + 4*a^4*b*c^4 - (b^6*c^7 - 10*a*b^4*c^8 + 32*a^2*b^2*c^9 - 32*a^3*c^10)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))*sqrt((a^10*b^12 - 10*a^11*b^10*c + 37*a^12*b^8*c^2 - 62*a^13*b^6*c^3 + 46*a^14*b^4*c^4 - 12*a^15*b^2*c^5 + a^16*c^6)*x - 1/2*sqrt(1/2)*(a^7*b^17 - 17*a^8*b^15*c + 119*a^9*b^13*c^2 - 441*a^10*b^11*c^3 + 924*a^11*b^9*c^4 - 1078*a^12*b^7*c^5 + 637*a^13*b^5*c^6 - 151*a^14*b^3*c^7 + 12*a^15*b*c^8 - (a^7*b^14*c^7 - 18*a^8*b^12*c^8 + 131*a^9*b^10*c^9 - 491*a^10*b^8*c^10 + 997*a^11*b^6*c^11 - 1052*a^12*b^4*c^12 + 496*a^13*b^2*c^13 - 64*a^14*c^14)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 + (b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))/(b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9))) + (a^5*b^15 - 14*a^6*b^13*c + 77*a^7*b^11*c^2 - 210*a^8*b^9*c^3 + 294*a^9*b^7*c^4 - 196*a^10*b^5*c^5 + 49*a^11*b^3*c^6 - 4*a^12*b*c^7 - (a^5*b^12*c^7 - 15*a^6*b^10*c^8 + 88*a^7*b^8*c^9 - 253*a^8*b^6*c^10 + 362*a^9*b^4*c^11 - 224*a^10*b^2*c^12 + 32*a^11*c^13)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))*sqrt(x))*sqrt(sqrt(1/2)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 + (b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))/(b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)))/(a^7*b^12 - 10*a^8*b^10*c + 37*a^9*b^8*c^2 - 62*a^10*b^6*c^3 + 46*a^11*b^4*c^4 - 12*a^12*b^2*c^5 + a^13*c^6)) - 12*c*sqrt(sqrt(1/2)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 - (b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))/(b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)))*arctan(-1/2*((b^9 - 9*a*b^7*c + 26*a^2*b^5*c^2 - 25*a^3*b^3*c^3 + 4*a^4*b*c^4 + (b^6*c^7 - 10*a*b^4*c^8 + 32*a^2*b^2*c^9 - 32*a^3*c^10)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))*sqrt((a^10*b^12 - 10*a^11*b^10*c + 37*a^12*b^8*c^2 - 62*a^13*b^6*c^3 + 46*a^14*b^4*c^4 - 12*a^15*b^2*c^5 + a^16*c^6)*x - 1/2*sqrt(1/2)*(a^7*b^17 - 17*a^8*b^15*c + 119*a^9*b^13*c^2 - 441*a^10*b^11*c^3 + 924*a^11*b^9*c^4 - 1078*a^12*b^7*c^5 + 637*a^13*b^5*c^6 - 151*a^14*b^3*c^7 + 12*a^15*b*c^8 + (a^7*b^14*c^7 - 18*a^8*b^12*c^8 + 131*a^9*b^10*c^9 - 491*a^10*b^8*c^10 + 997*a^11*b^6*c^11 - 1052*a^12*b^4*c^12 + 496*a^13*b^2*c^13 - 64*a^14*c^14)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 - (b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))/(b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)))*sqrt(sqrt(1/2)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 - (b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))/(b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9))) + (a^5*b^15 - 14*a^6*b^13*c + 77*a^7*b^11*c^2 - 210*a^8*b^9*c^3 + 294*a^9*b^7*c^4 - 196*a^10*b^5*c^5 + 49*a^11*b^3*c^6 - 4*a^12*b*c^7 + (a^5*b^12*c^7 - 15*a^6*b^10*c^8 + 88*a^7*b^8*c^9 - 253*a^8*b^6*c^10 + 362*a^9*b^4*c^11 - 224*a^10*b^2*c^12 + 32*a^11*c^13)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))*sqrt(x)*sqrt(sqrt(1/2)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 - (b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))/(b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9))))/(a^7*b^12 - 10*a^8*b^10*c + 37*a^9*b^8*c^2 - 62*a^10*b^6*c^3 + 46*a^11*b^4*c^4 - 12*a^12*b^2*c^5 + a^13*c^6)) - 3*c*sqrt(sqrt(1/2)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 + (b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))/(b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)))*log(1/2*sqrt(1/2)*(b^14 - 16*a*b^12*c + 102*a^2*b^10*c^2 - 328*a^3*b^8*c^3 + 553*a^4*b^6*c^4 - 457*a^5*b^4*c^5 + 152*a^6*b^2*c^6 - 16*a^7*c^7 - (b^11*c^7 - 17*a*b^9*c^8 + 113*a^2*b^7*c^9 - 364*a^3*b^5*c^10 + 560*a^4*b^3*c^11 - 320*a^5*b*c^12)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))*sqrt(sqrt(1/2)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 + (b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))/(b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)))*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 + (b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))/(b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)) - (a^5*b^6 - 5*a^6*b^4*c + 6*a^7*b^2*c^2 - a^8*c^3)*sqrt(x)) + 3*c*sqrt(sqrt(1/2)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 + (b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))/(b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)))*log(-1/2*sqrt(1/2)*(b^14 - 16*a*b^12*c + 102*a^2*b^10*c^2 - 328*a^3*b^8*c^3 + 553*a^4*b^6*c^4 - 457*a^5*b^4*c^5 + 152*a^6*b^2*c^6 - 16*a^7*c^7 - (b^11*c^7 - 17*a*b^9*c^8 + 113*a^2*b^7*c^9 - 364*a^3*b^5*c^10 + 560*a^4*b^3*c^11 - 320*a^5*b*c^12)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))*sqrt(sqrt(1/2)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 + (b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))/(b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)))*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 + (b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))/(b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)) - (a^5*b^6 - 5*a^6*b^4*c + 6*a^7*b^2*c^2 - a^8*c^3)*sqrt(x)) - 3*c*sqrt(sqrt(1/2)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 - (b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))/(b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)))*log(1/2*sqrt(1/2)*(b^14 - 16*a*b^12*c + 102*a^2*b^10*c^2 - 328*a^3*b^8*c^3 + 553*a^4*b^6*c^4 - 457*a^5*b^4*c^5 + 152*a^6*b^2*c^6 - 16*a^7*c^7 + (b^11*c^7 - 17*a*b^9*c^8 + 113*a^2*b^7*c^9 - 364*a^3*b^5*c^10 + 560*a^4*b^3*c^11 - 320*a^5*b*c^12)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))*sqrt(sqrt(1/2)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 - (b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))/(b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)))*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 - (b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))/(b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)) - (a^5*b^6 - 5*a^6*b^4*c + 6*a^7*b^2*c^2 - a^8*c^3)*sqrt(x)) + 3*c*sqrt(sqrt(1/2)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 - (b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))/(b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)))*log(-1/2*sqrt(1/2)*(b^14 - 16*a*b^12*c + 102*a^2*b^10*c^2 - 328*a^3*b^8*c^3 + 553*a^4*b^6*c^4 - 457*a^5*b^4*c^5 + 152*a^6*b^2*c^6 - 16*a^7*c^7 + (b^11*c^7 - 17*a*b^9*c^8 + 113*a^2*b^7*c^9 - 364*a^3*b^5*c^10 + 560*a^4*b^3*c^11 - 320*a^5*b*c^12)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))*sqrt(sqrt(1/2)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 - (b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))/(b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)))*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 - (b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))/(b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)) - (a^5*b^6 - 5*a^6*b^4*c + 6*a^7*b^2*c^2 - a^8*c^3)*sqrt(x)) + 4*x^(3/2))/c","B",0
1063,1,5319,0,4.477725," ","integrate(x^(7/2)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","-\frac{4 \, c \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, 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^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}}} \arctan\left(-\frac{{\left(\sqrt{\frac{1}{2}} {\left(b^{11} - 13 \, a b^{9} c + 63 \, a^{2} b^{7} c^{2} - 138 \, a^{3} b^{5} c^{3} + 128 \, a^{4} b^{3} c^{4} - 32 \, a^{5} b c^{5} + {\left(b^{10} c^{5} - 16 \, a b^{8} c^{6} + 98 \, a^{2} b^{6} c^{7} - 280 \, a^{3} b^{4} c^{8} + 352 \, a^{4} b^{2} c^{9} - 128 \, a^{5} c^{10}\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^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}\right)} \sqrt{4 \, {\left(a^{2} b^{8} - 6 \, a^{3} b^{6} c + 11 \, a^{4} b^{4} c^{2} - 6 \, a^{5} b^{2} c^{3} + a^{6} c^{4}\right)} x + 2 \, \sqrt{\frac{1}{2}} {\left(b^{12} - 12 \, a b^{10} c + 55 \, a^{2} b^{8} c^{2} - 120 \, a^{3} b^{6} c^{3} + 125 \, a^{4} b^{4} c^{4} - 54 \, a^{5} b^{2} c^{5} + 8 \, a^{6} c^{6} + {\left(b^{11} c^{5} - 15 \, a b^{9} c^{6} + 85 \, a^{2} b^{7} c^{7} - 220 \, a^{3} b^{5} c^{8} + 240 \, a^{4} b^{3} c^{9} - 64 \, a^{5} b c^{10}\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^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}\right)} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, 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^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, 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^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}} - 2 \, \sqrt{\frac{1}{2}} {\left(a b^{15} - 16 \, a^{2} b^{13} c + 103 \, a^{3} b^{11} c^{2} - 340 \, a^{4} b^{9} c^{3} + 605 \, a^{5} b^{7} c^{4} - 554 \, a^{6} b^{5} c^{5} + 224 \, a^{7} b^{3} c^{6} - 32 \, a^{8} b c^{7} + {\left(a b^{14} c^{5} - 19 \, a^{2} b^{12} c^{6} + 147 \, a^{3} b^{10} c^{7} - 590 \, a^{4} b^{8} c^{8} + 1290 \, a^{5} b^{6} c^{9} - 1464 \, a^{6} b^{4} c^{10} + 736 \, a^{7} b^{2} c^{11} - 128 \, a^{8} c^{12}\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^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}\right)} \sqrt{x} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, 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^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, 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^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}}}}{4 \, {\left(a^{5} b^{8} - 6 \, a^{6} b^{6} c + 11 \, a^{7} b^{4} c^{2} - 6 \, a^{8} b^{2} c^{3} + a^{9} c^{4}\right)}}\right) - 4 \, c \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, 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^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}}} \arctan\left(\frac{\sqrt{\frac{1}{2}} {\left(b^{11} - 13 \, a b^{9} c + 63 \, a^{2} b^{7} c^{2} - 138 \, a^{3} b^{5} c^{3} + 128 \, a^{4} b^{3} c^{4} - 32 \, a^{5} b c^{5} - {\left(b^{10} c^{5} - 16 \, a b^{8} c^{6} + 98 \, a^{2} b^{6} c^{7} - 280 \, a^{3} b^{4} c^{8} + 352 \, a^{4} b^{2} c^{9} - 128 \, a^{5} c^{10}\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^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}\right)} \sqrt{4 \, {\left(a^{2} b^{8} - 6 \, a^{3} b^{6} c + 11 \, a^{4} b^{4} c^{2} - 6 \, a^{5} b^{2} c^{3} + a^{6} c^{4}\right)} x + 2 \, \sqrt{\frac{1}{2}} {\left(b^{12} - 12 \, a b^{10} c + 55 \, a^{2} b^{8} c^{2} - 120 \, a^{3} b^{6} c^{3} + 125 \, a^{4} b^{4} c^{4} - 54 \, a^{5} b^{2} c^{5} + 8 \, a^{6} c^{6} - {\left(b^{11} c^{5} - 15 \, a b^{9} c^{6} + 85 \, a^{2} b^{7} c^{7} - 220 \, a^{3} b^{5} c^{8} + 240 \, a^{4} b^{3} c^{9} - 64 \, a^{5} b c^{10}\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^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}\right)} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, 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^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}}} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, 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^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, 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^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}} - 2 \, \sqrt{\frac{1}{2}} {\left(a b^{15} - 16 \, a^{2} b^{13} c + 103 \, a^{3} b^{11} c^{2} - 340 \, a^{4} b^{9} c^{3} + 605 \, a^{5} b^{7} c^{4} - 554 \, a^{6} b^{5} c^{5} + 224 \, a^{7} b^{3} c^{6} - 32 \, a^{8} b c^{7} - {\left(a b^{14} c^{5} - 19 \, a^{2} b^{12} c^{6} + 147 \, a^{3} b^{10} c^{7} - 590 \, a^{4} b^{8} c^{8} + 1290 \, a^{5} b^{6} c^{9} - 1464 \, a^{6} b^{4} c^{10} + 736 \, a^{7} b^{2} c^{11} - 128 \, a^{8} c^{12}\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^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}\right)} \sqrt{x} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, 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^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, 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^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}}}{4 \, {\left(a^{5} b^{8} - 6 \, a^{6} b^{6} c + 11 \, a^{7} b^{4} c^{2} - 6 \, a^{8} b^{2} c^{3} + a^{9} c^{4}\right)}}\right) - c \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, 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^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}}} \log\left(2 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c + a^{3} c^{2}\right)} \sqrt{x} + {\left(b^{6} - 7 \, a b^{4} c + 13 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3} - {\left(b^{5} c^{5} - 8 \, a b^{3} c^{6} + 16 \, a^{2} b 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^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, 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^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}}}\right) + c \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, 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^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}}} \log\left(2 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c + a^{3} c^{2}\right)} \sqrt{x} - {\left(b^{6} - 7 \, a b^{4} c + 13 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3} - {\left(b^{5} c^{5} - 8 \, a b^{3} c^{6} + 16 \, a^{2} b 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^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, 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^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}}}\right) - c \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, 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^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}}} \log\left(2 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c + a^{3} c^{2}\right)} \sqrt{x} + {\left(b^{6} - 7 \, a b^{4} c + 13 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3} + {\left(b^{5} c^{5} - 8 \, a b^{3} c^{6} + 16 \, a^{2} b 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^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, 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^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}}}\right) + c \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, 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^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}}} \log\left(2 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c + a^{3} c^{2}\right)} \sqrt{x} - {\left(b^{6} - 7 \, a b^{4} c + 13 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3} + {\left(b^{5} c^{5} - 8 \, a b^{3} c^{6} + 16 \, a^{2} b 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^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, 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^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}}}\right) - 4 \, \sqrt{x}}{2 \, c}"," ",0,"-1/2*(4*c*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (b^4*c^5 - 8*a*b^2*c^6 + 16*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^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)))*arctan(-1/4*(sqrt(1/2)*(b^11 - 13*a*b^9*c + 63*a^2*b^7*c^2 - 138*a^3*b^5*c^3 + 128*a^4*b^3*c^4 - 32*a^5*b*c^5 + (b^10*c^5 - 16*a*b^8*c^6 + 98*a^2*b^6*c^7 - 280*a^3*b^4*c^8 + 352*a^4*b^2*c^9 - 128*a^5*c^10)*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^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))*sqrt(4*(a^2*b^8 - 6*a^3*b^6*c + 11*a^4*b^4*c^2 - 6*a^5*b^2*c^3 + a^6*c^4)*x + 2*sqrt(1/2)*(b^12 - 12*a*b^10*c + 55*a^2*b^8*c^2 - 120*a^3*b^6*c^3 + 125*a^4*b^4*c^4 - 54*a^5*b^2*c^5 + 8*a^6*c^6 + (b^11*c^5 - 15*a*b^9*c^6 + 85*a^2*b^7*c^7 - 220*a^3*b^5*c^8 + 240*a^4*b^3*c^9 - 64*a^5*b*c^10)*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^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (b^4*c^5 - 8*a*b^2*c^6 + 16*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^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)))*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (b^4*c^5 - 8*a*b^2*c^6 + 16*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^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)) - 2*sqrt(1/2)*(a*b^15 - 16*a^2*b^13*c + 103*a^3*b^11*c^2 - 340*a^4*b^9*c^3 + 605*a^5*b^7*c^4 - 554*a^6*b^5*c^5 + 224*a^7*b^3*c^6 - 32*a^8*b*c^7 + (a*b^14*c^5 - 19*a^2*b^12*c^6 + 147*a^3*b^10*c^7 - 590*a^4*b^8*c^8 + 1290*a^5*b^6*c^9 - 1464*a^6*b^4*c^10 + 736*a^7*b^2*c^11 - 128*a^8*c^12)*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^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))*sqrt(x)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (b^4*c^5 - 8*a*b^2*c^6 + 16*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^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)))*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (b^4*c^5 - 8*a*b^2*c^6 + 16*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^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)))/(a^5*b^8 - 6*a^6*b^6*c + 11*a^7*b^4*c^2 - 6*a^8*b^2*c^3 + a^9*c^4)) - 4*c*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (b^4*c^5 - 8*a*b^2*c^6 + 16*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^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)))*arctan(1/4*(sqrt(1/2)*(b^11 - 13*a*b^9*c + 63*a^2*b^7*c^2 - 138*a^3*b^5*c^3 + 128*a^4*b^3*c^4 - 32*a^5*b*c^5 - (b^10*c^5 - 16*a*b^8*c^6 + 98*a^2*b^6*c^7 - 280*a^3*b^4*c^8 + 352*a^4*b^2*c^9 - 128*a^5*c^10)*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^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))*sqrt(4*(a^2*b^8 - 6*a^3*b^6*c + 11*a^4*b^4*c^2 - 6*a^5*b^2*c^3 + a^6*c^4)*x + 2*sqrt(1/2)*(b^12 - 12*a*b^10*c + 55*a^2*b^8*c^2 - 120*a^3*b^6*c^3 + 125*a^4*b^4*c^4 - 54*a^5*b^2*c^5 + 8*a^6*c^6 - (b^11*c^5 - 15*a*b^9*c^6 + 85*a^2*b^7*c^7 - 220*a^3*b^5*c^8 + 240*a^4*b^3*c^9 - 64*a^5*b*c^10)*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^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (b^4*c^5 - 8*a*b^2*c^6 + 16*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^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)))*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (b^4*c^5 - 8*a*b^2*c^6 + 16*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^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)))*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (b^4*c^5 - 8*a*b^2*c^6 + 16*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^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)) - 2*sqrt(1/2)*(a*b^15 - 16*a^2*b^13*c + 103*a^3*b^11*c^2 - 340*a^4*b^9*c^3 + 605*a^5*b^7*c^4 - 554*a^6*b^5*c^5 + 224*a^7*b^3*c^6 - 32*a^8*b*c^7 - (a*b^14*c^5 - 19*a^2*b^12*c^6 + 147*a^3*b^10*c^7 - 590*a^4*b^8*c^8 + 1290*a^5*b^6*c^9 - 1464*a^6*b^4*c^10 + 736*a^7*b^2*c^11 - 128*a^8*c^12)*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^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))*sqrt(x)*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (b^4*c^5 - 8*a*b^2*c^6 + 16*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^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)))*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (b^4*c^5 - 8*a*b^2*c^6 + 16*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^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)))/(a^5*b^8 - 6*a^6*b^6*c + 11*a^7*b^4*c^2 - 6*a^8*b^2*c^3 + a^9*c^4)) - c*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (b^4*c^5 - 8*a*b^2*c^6 + 16*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^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)))*log(2*(a*b^4 - 3*a^2*b^2*c + a^3*c^2)*sqrt(x) + (b^6 - 7*a*b^4*c + 13*a^2*b^2*c^2 - 4*a^3*c^3 - (b^5*c^5 - 8*a*b^3*c^6 + 16*a^2*b*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^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (b^4*c^5 - 8*a*b^2*c^6 + 16*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^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)))) + c*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (b^4*c^5 - 8*a*b^2*c^6 + 16*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^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)))*log(2*(a*b^4 - 3*a^2*b^2*c + a^3*c^2)*sqrt(x) - (b^6 - 7*a*b^4*c + 13*a^2*b^2*c^2 - 4*a^3*c^3 - (b^5*c^5 - 8*a*b^3*c^6 + 16*a^2*b*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^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (b^4*c^5 - 8*a*b^2*c^6 + 16*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^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)))) - c*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (b^4*c^5 - 8*a*b^2*c^6 + 16*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^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)))*log(2*(a*b^4 - 3*a^2*b^2*c + a^3*c^2)*sqrt(x) + (b^6 - 7*a*b^4*c + 13*a^2*b^2*c^2 - 4*a^3*c^3 + (b^5*c^5 - 8*a*b^3*c^6 + 16*a^2*b*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^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (b^4*c^5 - 8*a*b^2*c^6 + 16*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^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)))) + c*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (b^4*c^5 - 8*a*b^2*c^6 + 16*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^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)))*log(2*(a*b^4 - 3*a^2*b^2*c + a^3*c^2)*sqrt(x) - (b^6 - 7*a*b^4*c + 13*a^2*b^2*c^2 - 4*a^3*c^3 + (b^5*c^5 - 8*a*b^3*c^6 + 16*a^2*b*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^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (b^4*c^5 - 8*a*b^2*c^6 + 16*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^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)))) - 4*sqrt(x))/c","B",0
1064,1,4058,0,1.962262," ","integrate(x^(5/2)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","-2 \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{3} - 3 \, a b c - {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}}} \arctan\left(\frac{{\left({\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2} + {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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{{\left(a^{4} b^{4} - 2 \, a^{5} b^{2} c + a^{6} c^{2}\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(a^{3} b^{7} - 6 \, a^{4} b^{5} c + 9 \, a^{5} b^{3} c^{2} - 4 \, a^{6} b c^{3} + {\left(a^{3} b^{8} c^{3} - 13 \, a^{4} b^{6} c^{4} + 60 \, a^{5} b^{4} c^{5} - 112 \, a^{6} b^{2} c^{6} + 64 \, a^{7} c^{7}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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^{3} - 3 \, a b c - {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}}} + {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 9 \, a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3} + {\left(a^{2} b^{7} c^{3} - 9 \, a^{3} b^{5} c^{4} + 24 \, a^{4} b^{3} c^{5} - 16 \, a^{5} b c^{6}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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{x}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{3} - 3 \, a b c - {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}}}}{2 \, {\left(a^{3} b^{4} - 2 \, a^{4} b^{2} c + a^{5} c^{2}\right)}}\right) + 2 \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{3} - 3 \, a b c + {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}}} \arctan\left(-\frac{{\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2} - {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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{{\left(a^{4} b^{4} - 2 \, a^{5} b^{2} c + a^{6} c^{2}\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(a^{3} b^{7} - 6 \, a^{4} b^{5} c + 9 \, a^{5} b^{3} c^{2} - 4 \, a^{6} b c^{3} - {\left(a^{3} b^{8} c^{3} - 13 \, a^{4} b^{6} c^{4} + 60 \, a^{5} b^{4} c^{5} - 112 \, a^{6} b^{2} c^{6} + 64 \, a^{7} c^{7}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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^{3} - 3 \, a b c + {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}}} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{3} - 3 \, a b c + {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}}} + {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 9 \, a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3} - {\left(a^{2} b^{7} c^{3} - 9 \, a^{3} b^{5} c^{4} + 24 \, a^{4} b^{3} c^{5} - 16 \, a^{5} b c^{6}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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{x} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{3} - 3 \, a b c + {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}}}}{2 \, {\left(a^{3} b^{4} - 2 \, a^{4} b^{2} c + a^{5} c^{2}\right)}}\right) + \frac{1}{2} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{3} - 3 \, a b c + {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}}} \log\left(\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{7} - 9 \, a b^{5} c + 24 \, a^{2} b^{3} c^{2} - 16 \, a^{3} b c^{3} - {\left(b^{8} c^{3} - 14 \, a b^{6} c^{4} + 72 \, a^{2} b^{4} c^{5} - 160 \, a^{3} b^{2} c^{6} + 128 \, a^{4} c^{7}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{3} - 3 \, a b c + {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}}} \sqrt{-\frac{b^{3} - 3 \, a b c + {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}} - {\left(a^{2} b^{2} - a^{3} c\right)} \sqrt{x}\right) - \frac{1}{2} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{3} - 3 \, a b c + {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}}} \log\left(-\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{7} - 9 \, a b^{5} c + 24 \, a^{2} b^{3} c^{2} - 16 \, a^{3} b c^{3} - {\left(b^{8} c^{3} - 14 \, a b^{6} c^{4} + 72 \, a^{2} b^{4} c^{5} - 160 \, a^{3} b^{2} c^{6} + 128 \, a^{4} c^{7}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{3} - 3 \, a b c + {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}}} \sqrt{-\frac{b^{3} - 3 \, a b c + {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}} - {\left(a^{2} b^{2} - a^{3} c\right)} \sqrt{x}\right) + \frac{1}{2} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{3} - 3 \, a b c - {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}}} \log\left(\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{7} - 9 \, a b^{5} c + 24 \, a^{2} b^{3} c^{2} - 16 \, a^{3} b c^{3} + {\left(b^{8} c^{3} - 14 \, a b^{6} c^{4} + 72 \, a^{2} b^{4} c^{5} - 160 \, a^{3} b^{2} c^{6} + 128 \, a^{4} c^{7}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{3} - 3 \, a b c - {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}}} \sqrt{-\frac{b^{3} - 3 \, a b c - {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}} - {\left(a^{2} b^{2} - a^{3} c\right)} \sqrt{x}\right) - \frac{1}{2} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{3} - 3 \, a b c - {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}}} \log\left(-\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{7} - 9 \, a b^{5} c + 24 \, a^{2} b^{3} c^{2} - 16 \, a^{3} b c^{3} + {\left(b^{8} c^{3} - 14 \, a b^{6} c^{4} + 72 \, a^{2} b^{4} c^{5} - 160 \, a^{3} b^{2} c^{6} + 128 \, a^{4} c^{7}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{3} - 3 \, a b c - {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}}} \sqrt{-\frac{b^{3} - 3 \, a b c - {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}} - {\left(a^{2} b^{2} - a^{3} c\right)} \sqrt{x}\right)"," ",0,"-2*sqrt(sqrt(1/2)*sqrt(-(b^3 - 3*a*b*c - (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*sqrt((b^4 - 2*a*b^2*c + 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^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)))*arctan(1/2*((b^4 - 5*a*b^2*c + 4*a^2*c^2 + (b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*sqrt((b^4 - 2*a*b^2*c + 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((a^4*b^4 - 2*a^5*b^2*c + a^6*c^2)*x - 1/2*sqrt(1/2)*(a^3*b^7 - 6*a^4*b^5*c + 9*a^5*b^3*c^2 - 4*a^6*b*c^3 + (a^3*b^8*c^3 - 13*a^4*b^6*c^4 + 60*a^5*b^4*c^5 - 112*a^6*b^2*c^6 + 64*a^7*c^7)*sqrt((b^4 - 2*a*b^2*c + 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^3 - 3*a*b*c - (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*sqrt((b^4 - 2*a*b^2*c + 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^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5))) + (a^2*b^6 - 6*a^3*b^4*c + 9*a^4*b^2*c^2 - 4*a^5*c^3 + (a^2*b^7*c^3 - 9*a^3*b^5*c^4 + 24*a^4*b^3*c^5 - 16*a^5*b*c^6)*sqrt((b^4 - 2*a*b^2*c + 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(x))*sqrt(sqrt(1/2)*sqrt(-(b^3 - 3*a*b*c - (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*sqrt((b^4 - 2*a*b^2*c + 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^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)))/(a^3*b^4 - 2*a^4*b^2*c + a^5*c^2)) + 2*sqrt(sqrt(1/2)*sqrt(-(b^3 - 3*a*b*c + (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*sqrt((b^4 - 2*a*b^2*c + 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^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)))*arctan(-1/2*((b^4 - 5*a*b^2*c + 4*a^2*c^2 - (b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*sqrt((b^4 - 2*a*b^2*c + 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((a^4*b^4 - 2*a^5*b^2*c + a^6*c^2)*x - 1/2*sqrt(1/2)*(a^3*b^7 - 6*a^4*b^5*c + 9*a^5*b^3*c^2 - 4*a^6*b*c^3 - (a^3*b^8*c^3 - 13*a^4*b^6*c^4 + 60*a^5*b^4*c^5 - 112*a^6*b^2*c^6 + 64*a^7*c^7)*sqrt((b^4 - 2*a*b^2*c + 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^3 - 3*a*b*c + (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*sqrt((b^4 - 2*a*b^2*c + 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^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)))*sqrt(sqrt(1/2)*sqrt(-(b^3 - 3*a*b*c + (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*sqrt((b^4 - 2*a*b^2*c + 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^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5))) + (a^2*b^6 - 6*a^3*b^4*c + 9*a^4*b^2*c^2 - 4*a^5*c^3 - (a^2*b^7*c^3 - 9*a^3*b^5*c^4 + 24*a^4*b^3*c^5 - 16*a^5*b*c^6)*sqrt((b^4 - 2*a*b^2*c + 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(x)*sqrt(sqrt(1/2)*sqrt(-(b^3 - 3*a*b*c + (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*sqrt((b^4 - 2*a*b^2*c + 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^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5))))/(a^3*b^4 - 2*a^4*b^2*c + a^5*c^2)) + 1/2*sqrt(sqrt(1/2)*sqrt(-(b^3 - 3*a*b*c + (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*sqrt((b^4 - 2*a*b^2*c + 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^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)))*log(1/2*sqrt(1/2)*(b^7 - 9*a*b^5*c + 24*a^2*b^3*c^2 - 16*a^3*b*c^3 - (b^8*c^3 - 14*a*b^6*c^4 + 72*a^2*b^4*c^5 - 160*a^3*b^2*c^6 + 128*a^4*c^7)*sqrt((b^4 - 2*a*b^2*c + 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(sqrt(1/2)*sqrt(-(b^3 - 3*a*b*c + (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*sqrt((b^4 - 2*a*b^2*c + 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^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)))*sqrt(-(b^3 - 3*a*b*c + (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*sqrt((b^4 - 2*a*b^2*c + 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^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)) - (a^2*b^2 - a^3*c)*sqrt(x)) - 1/2*sqrt(sqrt(1/2)*sqrt(-(b^3 - 3*a*b*c + (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*sqrt((b^4 - 2*a*b^2*c + 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^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)))*log(-1/2*sqrt(1/2)*(b^7 - 9*a*b^5*c + 24*a^2*b^3*c^2 - 16*a^3*b*c^3 - (b^8*c^3 - 14*a*b^6*c^4 + 72*a^2*b^4*c^5 - 160*a^3*b^2*c^6 + 128*a^4*c^7)*sqrt((b^4 - 2*a*b^2*c + 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(sqrt(1/2)*sqrt(-(b^3 - 3*a*b*c + (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*sqrt((b^4 - 2*a*b^2*c + 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^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)))*sqrt(-(b^3 - 3*a*b*c + (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*sqrt((b^4 - 2*a*b^2*c + 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^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)) - (a^2*b^2 - a^3*c)*sqrt(x)) + 1/2*sqrt(sqrt(1/2)*sqrt(-(b^3 - 3*a*b*c - (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*sqrt((b^4 - 2*a*b^2*c + 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^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)))*log(1/2*sqrt(1/2)*(b^7 - 9*a*b^5*c + 24*a^2*b^3*c^2 - 16*a^3*b*c^3 + (b^8*c^3 - 14*a*b^6*c^4 + 72*a^2*b^4*c^5 - 160*a^3*b^2*c^6 + 128*a^4*c^7)*sqrt((b^4 - 2*a*b^2*c + 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(sqrt(1/2)*sqrt(-(b^3 - 3*a*b*c - (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*sqrt((b^4 - 2*a*b^2*c + 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^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)))*sqrt(-(b^3 - 3*a*b*c - (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*sqrt((b^4 - 2*a*b^2*c + 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^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)) - (a^2*b^2 - a^3*c)*sqrt(x)) - 1/2*sqrt(sqrt(1/2)*sqrt(-(b^3 - 3*a*b*c - (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*sqrt((b^4 - 2*a*b^2*c + 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^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)))*log(-1/2*sqrt(1/2)*(b^7 - 9*a*b^5*c + 24*a^2*b^3*c^2 - 16*a^3*b*c^3 + (b^8*c^3 - 14*a*b^6*c^4 + 72*a^2*b^4*c^5 - 160*a^3*b^2*c^6 + 128*a^4*c^7)*sqrt((b^4 - 2*a*b^2*c + 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(sqrt(1/2)*sqrt(-(b^3 - 3*a*b*c - (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*sqrt((b^4 - 2*a*b^2*c + 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^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)))*sqrt(-(b^3 - 3*a*b*c - (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*sqrt((b^4 - 2*a*b^2*c + 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^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)) - (a^2*b^2 - a^3*c)*sqrt(x))","B",0
1065,1,2482,0,1.113380," ","integrate(x^(3/2)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","-2 \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b + \frac{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}}{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}}} \arctan\left(\frac{{\left(\sqrt{\frac{1}{2}} {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2} - \frac{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}}}\right)} \sqrt{\sqrt{\frac{1}{2}} {\left(b^{2} - 4 \, a c\right)} \sqrt{-\frac{b + \frac{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}}{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}} + x} \sqrt{-\frac{b + \frac{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}}{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}} - \sqrt{\frac{1}{2}} {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2} - \frac{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}}}\right)} \sqrt{x} \sqrt{-\frac{b + \frac{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}}{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b + \frac{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}}{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}}}}{2 \, a}\right) + 2 \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b - \frac{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}}{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}}} \arctan\left(-\frac{{\left(\sqrt{\frac{1}{2}} {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2} + \frac{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}}}\right)} \sqrt{\sqrt{\frac{1}{2}} {\left(b^{2} - 4 \, a c\right)} \sqrt{-\frac{b - \frac{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}}{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}} + x} \sqrt{-\frac{b - \frac{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}}{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}} - \sqrt{\frac{1}{2}} {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2} + \frac{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}}}\right)} \sqrt{x} \sqrt{-\frac{b - \frac{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}}{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b - \frac{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}}{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}}}}{2 \, a}\right) + \frac{1}{2} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b + \frac{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}}{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}}} \log\left(\frac{{\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b + \frac{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}}{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}}}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}} + \sqrt{x}\right) - \frac{1}{2} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b + \frac{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}}{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}}} \log\left(-\frac{{\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b + \frac{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}}{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}}}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}} + \sqrt{x}\right) - \frac{1}{2} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b - \frac{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}}{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}}} \log\left(\frac{{\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b - \frac{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}}{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}}}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}} + \sqrt{x}\right) + \frac{1}{2} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b - \frac{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}}{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}}} \log\left(-\frac{{\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b - \frac{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}}{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}}}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}} + \sqrt{x}\right)"," ",0,"-2*sqrt(sqrt(1/2)*sqrt(-(b + (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)))*arctan(1/2*(sqrt(1/2)*(b^4 - 8*a*b^2*c + 16*a^2*c^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(sqrt(1/2)*(b^2 - 4*a*c)*sqrt(-(b + (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)) + x)*sqrt(-(b + (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)) - sqrt(1/2)*(b^4 - 8*a*b^2*c + 16*a^2*c^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(x)*sqrt(-(b + (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)))*sqrt(sqrt(1/2)*sqrt(-(b + (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)))/a) + 2*sqrt(sqrt(1/2)*sqrt(-(b - (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)))*arctan(-1/2*(sqrt(1/2)*(b^4 - 8*a*b^2*c + 16*a^2*c^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(sqrt(1/2)*(b^2 - 4*a*c)*sqrt(-(b - (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)) + x)*sqrt(-(b - (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)) - sqrt(1/2)*(b^4 - 8*a*b^2*c + 16*a^2*c^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(x)*sqrt(-(b - (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)))*sqrt(sqrt(1/2)*sqrt(-(b - (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)))/a) + 1/2*sqrt(sqrt(1/2)*sqrt(-(b + (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)))*log((b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*sqrt(sqrt(1/2)*sqrt(-(b + (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)))/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5) + sqrt(x)) - 1/2*sqrt(sqrt(1/2)*sqrt(-(b + (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)))*log(-(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*sqrt(sqrt(1/2)*sqrt(-(b + (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)))/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5) + sqrt(x)) - 1/2*sqrt(sqrt(1/2)*sqrt(-(b - (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)))*log((b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*sqrt(sqrt(1/2)*sqrt(-(b - (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)))/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5) + sqrt(x)) + 1/2*sqrt(sqrt(1/2)*sqrt(-(b - (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)))*log(-(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*sqrt(sqrt(1/2)*sqrt(-(b - (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)))/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5) + sqrt(x))","B",0
1066,1,2769,0,0.900918," ","integrate(x^(1/2)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","-2 \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b + \frac{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}{\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^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}}} \arctan\left(\frac{{\left(\frac{{\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} \sqrt{c^{2} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{3} c - 4 \, a b c^{2} - \frac{a b^{6} c - 12 \, a^{2} b^{4} c^{2} + 48 \, a^{3} b^{2} c^{3} - 64 \, a^{4} 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 + \frac{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}{\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^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}}}}{\sqrt{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}} - \frac{{\left(a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3}\right)} \sqrt{x}}{\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{\sqrt{\frac{1}{2}} \sqrt{-\frac{b + \frac{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}{\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^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}}}}{c}\right) + 2 \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b - \frac{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}{\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^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}}} \arctan\left(\frac{\frac{{\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} \sqrt{c^{2} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{3} c - 4 \, a b c^{2} + \frac{a b^{6} c - 12 \, a^{2} b^{4} c^{2} + 48 \, a^{3} b^{2} c^{3} - 64 \, a^{4} 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 - \frac{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}{\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^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}}} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b - \frac{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}{\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^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}}}}{\sqrt{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}} - \frac{{\left(a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3}\right)} \sqrt{x} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b - \frac{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}{\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^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}}}}{\sqrt{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}}}{c}\right) - \frac{1}{2} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b + \frac{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}{\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^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}}} \log\left(\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2} - \frac{a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b 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}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b + \frac{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}{\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^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}}} \sqrt{-\frac{b + \frac{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}{\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^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}} + c \sqrt{x}\right) + \frac{1}{2} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b + \frac{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}{\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^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}}} \log\left(-\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2} - \frac{a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b 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}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b + \frac{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}{\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^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}}} \sqrt{-\frac{b + \frac{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}{\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^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}} + c \sqrt{x}\right) - \frac{1}{2} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b - \frac{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}{\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^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}}} \log\left(\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2} + \frac{a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b 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}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b - \frac{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}{\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^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}}} \sqrt{-\frac{b - \frac{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}{\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^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}} + c \sqrt{x}\right) + \frac{1}{2} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b - \frac{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}{\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^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}}} \log\left(-\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2} + \frac{a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b 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}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b - \frac{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}{\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^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}}} \sqrt{-\frac{b - \frac{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}{\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^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}} + c \sqrt{x}\right)"," ",0,"-2*sqrt(sqrt(1/2)*sqrt(-(b + (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)/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^4 - 8*a^2*b^2*c + 16*a^3*c^2)))*arctan(((a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)*sqrt(c^2*x - 1/2*sqrt(1/2)*(b^3*c - 4*a*b*c^2 - (a*b^6*c - 12*a^2*b^4*c^2 + 48*a^3*b^2*c^3 - 64*a^4*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 + (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)/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^4 - 8*a^2*b^2*c + 16*a^3*c^2)))/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^4*c - 8*a^2*b^2*c^2 + 16*a^3*c^3)*sqrt(x)/sqrt(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3))*sqrt(sqrt(1/2)*sqrt(-(b + (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)/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^4 - 8*a^2*b^2*c + 16*a^3*c^2)))/c) + 2*sqrt(sqrt(1/2)*sqrt(-(b - (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)/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^4 - 8*a^2*b^2*c + 16*a^3*c^2)))*arctan(((a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)*sqrt(c^2*x - 1/2*sqrt(1/2)*(b^3*c - 4*a*b*c^2 + (a*b^6*c - 12*a^2*b^4*c^2 + 48*a^3*b^2*c^3 - 64*a^4*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 - (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)/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^4 - 8*a^2*b^2*c + 16*a^3*c^2)))*sqrt(sqrt(1/2)*sqrt(-(b - (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)/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^4 - 8*a^2*b^2*c + 16*a^3*c^2)))/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^4*c - 8*a^2*b^2*c^2 + 16*a^3*c^3)*sqrt(x)*sqrt(sqrt(1/2)*sqrt(-(b - (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)/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^4 - 8*a^2*b^2*c + 16*a^3*c^2)))/sqrt(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3))/c) - 1/2*sqrt(sqrt(1/2)*sqrt(-(b + (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)/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^4 - 8*a^2*b^2*c + 16*a^3*c^2)))*log(1/2*sqrt(1/2)*(b^4 - 8*a*b^2*c + 16*a^2*c^2 - (a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*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))*sqrt(sqrt(1/2)*sqrt(-(b + (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)/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^4 - 8*a^2*b^2*c + 16*a^3*c^2)))*sqrt(-(b + (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)/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^4 - 8*a^2*b^2*c + 16*a^3*c^2)) + c*sqrt(x)) + 1/2*sqrt(sqrt(1/2)*sqrt(-(b + (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)/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^4 - 8*a^2*b^2*c + 16*a^3*c^2)))*log(-1/2*sqrt(1/2)*(b^4 - 8*a*b^2*c + 16*a^2*c^2 - (a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*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))*sqrt(sqrt(1/2)*sqrt(-(b + (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)/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^4 - 8*a^2*b^2*c + 16*a^3*c^2)))*sqrt(-(b + (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)/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^4 - 8*a^2*b^2*c + 16*a^3*c^2)) + c*sqrt(x)) - 1/2*sqrt(sqrt(1/2)*sqrt(-(b - (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)/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^4 - 8*a^2*b^2*c + 16*a^3*c^2)))*log(1/2*sqrt(1/2)*(b^4 - 8*a*b^2*c + 16*a^2*c^2 + (a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*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))*sqrt(sqrt(1/2)*sqrt(-(b - (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)/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^4 - 8*a^2*b^2*c + 16*a^3*c^2)))*sqrt(-(b - (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)/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^4 - 8*a^2*b^2*c + 16*a^3*c^2)) + c*sqrt(x)) + 1/2*sqrt(sqrt(1/2)*sqrt(-(b - (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)/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^4 - 8*a^2*b^2*c + 16*a^3*c^2)))*log(-1/2*sqrt(1/2)*(b^4 - 8*a*b^2*c + 16*a^2*c^2 + (a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*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))*sqrt(sqrt(1/2)*sqrt(-(b - (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)/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^4 - 8*a^2*b^2*c + 16*a^3*c^2)))*sqrt(-(b - (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)/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^4 - 8*a^2*b^2*c + 16*a^3*c^2)) + c*sqrt(x))","B",0
1067,1,4045,0,3.461408," ","integrate(1/x^(1/2)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","-2 \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{3} - 3 \, a b c + {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}}}} \arctan\left(-\frac{{\left(\sqrt{\frac{1}{2}} {\left(b^{7} - 9 \, a b^{5} c + 24 \, a^{2} b^{3} c^{2} - 16 \, a^{3} b c^{3} - {\left(a^{3} b^{8} - 14 \, a^{4} b^{6} c + 72 \, a^{5} b^{4} c^{2} - 160 \, a^{6} b^{2} c^{3} + 128 \, a^{7} c^{4}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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{4 \, {\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} x + 2 \, \sqrt{\frac{1}{2}} {\left(b^{8} - 8 \, a b^{6} c + 21 \, a^{2} b^{4} c^{2} - 22 \, a^{3} b^{2} c^{3} + 8 \, a^{4} c^{4} - {\left(a^{3} b^{9} - 13 \, a^{4} b^{7} c + 60 \, a^{5} b^{5} c^{2} - 112 \, a^{6} b^{3} c^{3} + 64 \, a^{7} b c^{4}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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^{3} - 3 \, a b c + {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}}}} \sqrt{-\frac{b^{3} - 3 \, a b c + {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}}} + 2 \, \sqrt{\frac{1}{2}} {\left(b^{9} c - 10 \, a b^{7} c^{2} + 33 \, a^{2} b^{5} c^{3} - 40 \, a^{3} b^{3} c^{4} + 16 \, a^{4} b c^{5} - {\left(a^{3} b^{10} c - 15 \, a^{4} b^{8} c^{2} + 86 \, a^{5} b^{6} c^{3} - 232 \, a^{6} b^{4} c^{4} + 288 \, a^{7} b^{2} c^{5} - 128 \, a^{8} c^{6}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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{x} \sqrt{-\frac{b^{3} - 3 \, a b c + {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{3} - 3 \, a b c + {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}}}}}{4 \, {\left(b^{4} c^{3} - 2 \, a b^{2} c^{4} + a^{2} c^{5}\right)}}\right) + 2 \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{3} - 3 \, a b c - {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}}}} \arctan\left(\frac{\sqrt{\frac{1}{2}} {\left(b^{7} - 9 \, a b^{5} c + 24 \, a^{2} b^{3} c^{2} - 16 \, a^{3} b c^{3} + {\left(a^{3} b^{8} - 14 \, a^{4} b^{6} c + 72 \, a^{5} b^{4} c^{2} - 160 \, a^{6} b^{2} c^{3} + 128 \, a^{7} c^{4}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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{4 \, {\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} x + 2 \, \sqrt{\frac{1}{2}} {\left(b^{8} - 8 \, a b^{6} c + 21 \, a^{2} b^{4} c^{2} - 22 \, a^{3} b^{2} c^{3} + 8 \, a^{4} c^{4} + {\left(a^{3} b^{9} - 13 \, a^{4} b^{7} c + 60 \, a^{5} b^{5} c^{2} - 112 \, a^{6} b^{3} c^{3} + 64 \, a^{7} b c^{4}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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^{3} - 3 \, a b c - {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}}}} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{3} - 3 \, a b c - {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}}}} \sqrt{-\frac{b^{3} - 3 \, a b c - {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}}} + 2 \, \sqrt{\frac{1}{2}} {\left(b^{9} c - 10 \, a b^{7} c^{2} + 33 \, a^{2} b^{5} c^{3} - 40 \, a^{3} b^{3} c^{4} + 16 \, a^{4} b c^{5} + {\left(a^{3} b^{10} c - 15 \, a^{4} b^{8} c^{2} + 86 \, a^{5} b^{6} c^{3} - 232 \, a^{6} b^{4} c^{4} + 288 \, a^{7} b^{2} c^{5} - 128 \, a^{8} c^{6}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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{x} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{3} - 3 \, a b c - {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}}}} \sqrt{-\frac{b^{3} - 3 \, a b c - {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}}}}{4 \, {\left(b^{4} c^{3} - 2 \, a b^{2} c^{4} + a^{2} c^{5}\right)}}\right) + \frac{1}{2} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{3} - 3 \, a b c + {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}}}} \log\left(-2 \, {\left(b^{2} c - a c^{2}\right)} \sqrt{x} + {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2} - {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{3} - 3 \, a b c + {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}}}}\right) - \frac{1}{2} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{3} - 3 \, a b c + {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}}}} \log\left(-2 \, {\left(b^{2} c - a c^{2}\right)} \sqrt{x} - {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2} - {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{3} - 3 \, a b c + {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}}}}\right) + \frac{1}{2} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{3} - 3 \, a b c - {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}}}} \log\left(-2 \, {\left(b^{2} c - a c^{2}\right)} \sqrt{x} + {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2} + {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{3} - 3 \, a b c - {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}}}}\right) - \frac{1}{2} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{3} - 3 \, a b c - {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}}}} \log\left(-2 \, {\left(b^{2} c - a c^{2}\right)} \sqrt{x} - {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2} + {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{3} - 3 \, a b c - {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + 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^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}}}}\right)"," ",0,"-2*sqrt(sqrt(1/2)*sqrt(-(b^3 - 3*a*b*c + (a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*sqrt((b^4 - 2*a*b^2*c + 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^4 - 8*a^4*b^2*c + 16*a^5*c^2)))*arctan(-1/4*(sqrt(1/2)*(b^7 - 9*a*b^5*c + 24*a^2*b^3*c^2 - 16*a^3*b*c^3 - (a^3*b^8 - 14*a^4*b^6*c + 72*a^5*b^4*c^2 - 160*a^6*b^2*c^3 + 128*a^7*c^4)*sqrt((b^4 - 2*a*b^2*c + 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(4*(b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*x + 2*sqrt(1/2)*(b^8 - 8*a*b^6*c + 21*a^2*b^4*c^2 - 22*a^3*b^2*c^3 + 8*a^4*c^4 - (a^3*b^9 - 13*a^4*b^7*c + 60*a^5*b^5*c^2 - 112*a^6*b^3*c^3 + 64*a^7*b*c^4)*sqrt((b^4 - 2*a*b^2*c + 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^3 - 3*a*b*c + (a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*sqrt((b^4 - 2*a*b^2*c + 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^4 - 8*a^4*b^2*c + 16*a^5*c^2)))*sqrt(-(b^3 - 3*a*b*c + (a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*sqrt((b^4 - 2*a*b^2*c + 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^4 - 8*a^4*b^2*c + 16*a^5*c^2)) + 2*sqrt(1/2)*(b^9*c - 10*a*b^7*c^2 + 33*a^2*b^5*c^3 - 40*a^3*b^3*c^4 + 16*a^4*b*c^5 - (a^3*b^10*c - 15*a^4*b^8*c^2 + 86*a^5*b^6*c^3 - 232*a^6*b^4*c^4 + 288*a^7*b^2*c^5 - 128*a^8*c^6)*sqrt((b^4 - 2*a*b^2*c + 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(x)*sqrt(-(b^3 - 3*a*b*c + (a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*sqrt((b^4 - 2*a*b^2*c + 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^4 - 8*a^4*b^2*c + 16*a^5*c^2)))*sqrt(sqrt(1/2)*sqrt(-(b^3 - 3*a*b*c + (a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*sqrt((b^4 - 2*a*b^2*c + 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^4 - 8*a^4*b^2*c + 16*a^5*c^2)))/(b^4*c^3 - 2*a*b^2*c^4 + a^2*c^5)) + 2*sqrt(sqrt(1/2)*sqrt(-(b^3 - 3*a*b*c - (a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*sqrt((b^4 - 2*a*b^2*c + 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^4 - 8*a^4*b^2*c + 16*a^5*c^2)))*arctan(1/4*(sqrt(1/2)*(b^7 - 9*a*b^5*c + 24*a^2*b^3*c^2 - 16*a^3*b*c^3 + (a^3*b^8 - 14*a^4*b^6*c + 72*a^5*b^4*c^2 - 160*a^6*b^2*c^3 + 128*a^7*c^4)*sqrt((b^4 - 2*a*b^2*c + 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(4*(b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*x + 2*sqrt(1/2)*(b^8 - 8*a*b^6*c + 21*a^2*b^4*c^2 - 22*a^3*b^2*c^3 + 8*a^4*c^4 + (a^3*b^9 - 13*a^4*b^7*c + 60*a^5*b^5*c^2 - 112*a^6*b^3*c^3 + 64*a^7*b*c^4)*sqrt((b^4 - 2*a*b^2*c + 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^3 - 3*a*b*c - (a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*sqrt((b^4 - 2*a*b^2*c + 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^4 - 8*a^4*b^2*c + 16*a^5*c^2)))*sqrt(sqrt(1/2)*sqrt(-(b^3 - 3*a*b*c - (a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*sqrt((b^4 - 2*a*b^2*c + 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^4 - 8*a^4*b^2*c + 16*a^5*c^2)))*sqrt(-(b^3 - 3*a*b*c - (a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*sqrt((b^4 - 2*a*b^2*c + 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^4 - 8*a^4*b^2*c + 16*a^5*c^2)) + 2*sqrt(1/2)*(b^9*c - 10*a*b^7*c^2 + 33*a^2*b^5*c^3 - 40*a^3*b^3*c^4 + 16*a^4*b*c^5 + (a^3*b^10*c - 15*a^4*b^8*c^2 + 86*a^5*b^6*c^3 - 232*a^6*b^4*c^4 + 288*a^7*b^2*c^5 - 128*a^8*c^6)*sqrt((b^4 - 2*a*b^2*c + 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(x)*sqrt(sqrt(1/2)*sqrt(-(b^3 - 3*a*b*c - (a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*sqrt((b^4 - 2*a*b^2*c + 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^4 - 8*a^4*b^2*c + 16*a^5*c^2)))*sqrt(-(b^3 - 3*a*b*c - (a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*sqrt((b^4 - 2*a*b^2*c + 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^4 - 8*a^4*b^2*c + 16*a^5*c^2)))/(b^4*c^3 - 2*a*b^2*c^4 + a^2*c^5)) + 1/2*sqrt(sqrt(1/2)*sqrt(-(b^3 - 3*a*b*c + (a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*sqrt((b^4 - 2*a*b^2*c + 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^4 - 8*a^4*b^2*c + 16*a^5*c^2)))*log(-2*(b^2*c - a*c^2)*sqrt(x) + (b^4 - 5*a*b^2*c + 4*a^2*c^2 - (a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*sqrt((b^4 - 2*a*b^2*c + 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(sqrt(1/2)*sqrt(-(b^3 - 3*a*b*c + (a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*sqrt((b^4 - 2*a*b^2*c + 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^4 - 8*a^4*b^2*c + 16*a^5*c^2)))) - 1/2*sqrt(sqrt(1/2)*sqrt(-(b^3 - 3*a*b*c + (a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*sqrt((b^4 - 2*a*b^2*c + 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^4 - 8*a^4*b^2*c + 16*a^5*c^2)))*log(-2*(b^2*c - a*c^2)*sqrt(x) - (b^4 - 5*a*b^2*c + 4*a^2*c^2 - (a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*sqrt((b^4 - 2*a*b^2*c + 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(sqrt(1/2)*sqrt(-(b^3 - 3*a*b*c + (a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*sqrt((b^4 - 2*a*b^2*c + 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^4 - 8*a^4*b^2*c + 16*a^5*c^2)))) + 1/2*sqrt(sqrt(1/2)*sqrt(-(b^3 - 3*a*b*c - (a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*sqrt((b^4 - 2*a*b^2*c + 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^4 - 8*a^4*b^2*c + 16*a^5*c^2)))*log(-2*(b^2*c - a*c^2)*sqrt(x) + (b^4 - 5*a*b^2*c + 4*a^2*c^2 + (a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*sqrt((b^4 - 2*a*b^2*c + 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(sqrt(1/2)*sqrt(-(b^3 - 3*a*b*c - (a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*sqrt((b^4 - 2*a*b^2*c + 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^4 - 8*a^4*b^2*c + 16*a^5*c^2)))) - 1/2*sqrt(sqrt(1/2)*sqrt(-(b^3 - 3*a*b*c - (a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*sqrt((b^4 - 2*a*b^2*c + 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^4 - 8*a^4*b^2*c + 16*a^5*c^2)))*log(-2*(b^2*c - a*c^2)*sqrt(x) - (b^4 - 5*a*b^2*c + 4*a^2*c^2 + (a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*sqrt((b^4 - 2*a*b^2*c + 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(sqrt(1/2)*sqrt(-(b^3 - 3*a*b*c - (a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*sqrt((b^4 - 2*a*b^2*c + 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^4 - 8*a^4*b^2*c + 16*a^5*c^2))))","B",0
1068,1,5384,0,4.524066," ","integrate(1/x^(3/2)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","-\frac{4 \, a x \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\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}}{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^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}}}} \arctan\left(\frac{{\left({\left(b^{6} - 7 \, a b^{4} c + 13 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3} + {\left(a^{5} b^{5} - 8 \, a^{6} b^{3} c + 16 \, a^{7} b c^{2}\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}}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}\right)} \sqrt{{\left(b^{8} c^{8} - 6 \, a b^{6} c^{9} + 11 \, a^{2} b^{4} c^{10} - 6 \, a^{3} b^{2} c^{11} + a^{4} c^{12}\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{13} c^{5} - 13 \, a b^{11} c^{6} + 65 \, a^{2} b^{9} c^{7} - 155 \, a^{3} b^{7} c^{8} + 175 \, a^{4} b^{5} c^{9} - 79 \, a^{5} b^{3} c^{10} + 12 \, a^{6} b c^{11} + {\left(a^{5} b^{12} c^{5} - 16 \, a^{6} b^{10} c^{6} + 100 \, a^{7} b^{8} c^{7} - 305 \, a^{8} b^{6} c^{8} + 460 \, a^{9} b^{4} c^{9} - 304 \, a^{10} b^{2} c^{10} + 64 \, a^{11} c^{11}\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}}{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{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\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}}{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^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}}}} - {\left(b^{10} c^{4} - 10 \, a b^{8} c^{5} + 35 \, a^{2} b^{6} c^{6} - 50 \, a^{3} b^{4} c^{7} + 25 \, a^{4} b^{2} c^{8} - 4 \, a^{5} c^{9} + {\left(a^{5} b^{9} c^{4} - 11 \, a^{6} b^{7} c^{5} + 41 \, a^{7} b^{5} c^{6} - 56 \, a^{8} b^{3} c^{7} + 16 \, a^{9} b c^{8}\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}}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}\right)} \sqrt{x}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\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}}{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^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}}}}}{2 \, {\left(b^{8} c^{5} - 6 \, a b^{6} c^{6} + 11 \, a^{2} b^{4} c^{7} - 6 \, a^{3} b^{2} c^{8} + a^{4} c^{9}\right)}}\right) - 4 \, a x \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\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}}{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^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}}}} \arctan\left(-\frac{{\left(b^{6} - 7 \, a b^{4} c + 13 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3} - {\left(a^{5} b^{5} - 8 \, a^{6} b^{3} c + 16 \, a^{7} b c^{2}\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}}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}\right)} \sqrt{{\left(b^{8} c^{8} - 6 \, a b^{6} c^{9} + 11 \, a^{2} b^{4} c^{10} - 6 \, a^{3} b^{2} c^{11} + a^{4} c^{12}\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{13} c^{5} - 13 \, a b^{11} c^{6} + 65 \, a^{2} b^{9} c^{7} - 155 \, a^{3} b^{7} c^{8} + 175 \, a^{4} b^{5} c^{9} - 79 \, a^{5} b^{3} c^{10} + 12 \, a^{6} b c^{11} - {\left(a^{5} b^{12} c^{5} - 16 \, a^{6} b^{10} c^{6} + 100 \, a^{7} b^{8} c^{7} - 305 \, a^{8} b^{6} c^{8} + 460 \, a^{9} b^{4} c^{9} - 304 \, a^{10} b^{2} c^{10} + 64 \, a^{11} c^{11}\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}}{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{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\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}}{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^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}}}} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\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}}{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^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}}}} - {\left(b^{10} c^{4} - 10 \, a b^{8} c^{5} + 35 \, a^{2} b^{6} c^{6} - 50 \, a^{3} b^{4} c^{7} + 25 \, a^{4} b^{2} c^{8} - 4 \, a^{5} c^{9} - {\left(a^{5} b^{9} c^{4} - 11 \, a^{6} b^{7} c^{5} + 41 \, a^{7} b^{5} c^{6} - 56 \, a^{8} b^{3} c^{7} + 16 \, a^{9} b c^{8}\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}}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}\right)} \sqrt{x} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\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}}{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^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}}}}}{2 \, {\left(b^{8} c^{5} - 6 \, a b^{6} c^{6} + 11 \, a^{2} b^{4} c^{7} - 6 \, a^{3} b^{2} c^{8} + a^{4} c^{9}\right)}}\right) - a x \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\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}}{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^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}}}} \log\left(\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{11} - 13 \, a b^{9} c + 63 \, a^{2} b^{7} c^{2} - 138 \, a^{3} b^{5} c^{3} + 128 \, a^{4} b^{3} c^{4} - 32 \, a^{5} b c^{5} - {\left(a^{5} b^{10} - 16 \, a^{6} b^{8} c + 98 \, a^{7} b^{6} c^{2} - 280 \, a^{8} b^{4} c^{3} + 352 \, a^{9} b^{2} c^{4} - 128 \, a^{10} c^{5}\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}}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\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}}{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^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}}}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\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}}{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^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}}} + {\left(b^{4} c^{4} - 3 \, a b^{2} c^{5} + a^{2} c^{6}\right)} \sqrt{x}\right) + a x \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\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}}{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^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}}}} \log\left(-\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{11} - 13 \, a b^{9} c + 63 \, a^{2} b^{7} c^{2} - 138 \, a^{3} b^{5} c^{3} + 128 \, a^{4} b^{3} c^{4} - 32 \, a^{5} b c^{5} - {\left(a^{5} b^{10} - 16 \, a^{6} b^{8} c + 98 \, a^{7} b^{6} c^{2} - 280 \, a^{8} b^{4} c^{3} + 352 \, a^{9} b^{2} c^{4} - 128 \, a^{10} c^{5}\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}}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\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}}{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^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}}}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\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}}{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^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}}} + {\left(b^{4} c^{4} - 3 \, a b^{2} c^{5} + a^{2} c^{6}\right)} \sqrt{x}\right) - a x \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\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}}{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^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}}}} \log\left(\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{11} - 13 \, a b^{9} c + 63 \, a^{2} b^{7} c^{2} - 138 \, a^{3} b^{5} c^{3} + 128 \, a^{4} b^{3} c^{4} - 32 \, a^{5} b c^{5} + {\left(a^{5} b^{10} - 16 \, a^{6} b^{8} c + 98 \, a^{7} b^{6} c^{2} - 280 \, a^{8} b^{4} c^{3} + 352 \, a^{9} b^{2} c^{4} - 128 \, a^{10} c^{5}\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}}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\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}}{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^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}}}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\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}}{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^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}}} + {\left(b^{4} c^{4} - 3 \, a b^{2} c^{5} + a^{2} c^{6}\right)} \sqrt{x}\right) + a x \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\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}}{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^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}}}} \log\left(-\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{11} - 13 \, a b^{9} c + 63 \, a^{2} b^{7} c^{2} - 138 \, a^{3} b^{5} c^{3} + 128 \, a^{4} b^{3} c^{4} - 32 \, a^{5} b c^{5} + {\left(a^{5} b^{10} - 16 \, a^{6} b^{8} c + 98 \, a^{7} b^{6} c^{2} - 280 \, a^{8} b^{4} c^{3} + 352 \, a^{9} b^{2} c^{4} - 128 \, a^{10} c^{5}\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}}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\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}}{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^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}}}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\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}}{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^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}}} + {\left(b^{4} c^{4} - 3 \, a b^{2} c^{5} + a^{2} c^{6}\right)} \sqrt{x}\right) + 4 \, \sqrt{x}}{2 \, a x}"," ",0,"-1/2*(4*a*x*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*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)/(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^4 - 8*a^6*b^2*c + 16*a^7*c^2)))*arctan(1/2*((b^6 - 7*a*b^4*c + 13*a^2*b^2*c^2 - 4*a^3*c^3 + (a^5*b^5 - 8*a^6*b^3*c + 16*a^7*b*c^2)*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)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))*sqrt((b^8*c^8 - 6*a*b^6*c^9 + 11*a^2*b^4*c^10 - 6*a^3*b^2*c^11 + a^4*c^12)*x - 1/2*sqrt(1/2)*(b^13*c^5 - 13*a*b^11*c^6 + 65*a^2*b^9*c^7 - 155*a^3*b^7*c^8 + 175*a^4*b^5*c^9 - 79*a^5*b^3*c^10 + 12*a^6*b*c^11 + (a^5*b^12*c^5 - 16*a^6*b^10*c^6 + 100*a^7*b^8*c^7 - 305*a^8*b^6*c^8 + 460*a^9*b^4*c^9 - 304*a^10*b^2*c^10 + 64*a^11*c^11)*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)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*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)/(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^4 - 8*a^6*b^2*c + 16*a^7*c^2))) - (b^10*c^4 - 10*a*b^8*c^5 + 35*a^2*b^6*c^6 - 50*a^3*b^4*c^7 + 25*a^4*b^2*c^8 - 4*a^5*c^9 + (a^5*b^9*c^4 - 11*a^6*b^7*c^5 + 41*a^7*b^5*c^6 - 56*a^8*b^3*c^7 + 16*a^9*b*c^8)*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)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))*sqrt(x))*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*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)/(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^4 - 8*a^6*b^2*c + 16*a^7*c^2)))/(b^8*c^5 - 6*a*b^6*c^6 + 11*a^2*b^4*c^7 - 6*a^3*b^2*c^8 + a^4*c^9)) - 4*a*x*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*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)/(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^4 - 8*a^6*b^2*c + 16*a^7*c^2)))*arctan(-1/2*((b^6 - 7*a*b^4*c + 13*a^2*b^2*c^2 - 4*a^3*c^3 - (a^5*b^5 - 8*a^6*b^3*c + 16*a^7*b*c^2)*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)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))*sqrt((b^8*c^8 - 6*a*b^6*c^9 + 11*a^2*b^4*c^10 - 6*a^3*b^2*c^11 + a^4*c^12)*x - 1/2*sqrt(1/2)*(b^13*c^5 - 13*a*b^11*c^6 + 65*a^2*b^9*c^7 - 155*a^3*b^7*c^8 + 175*a^4*b^5*c^9 - 79*a^5*b^3*c^10 + 12*a^6*b*c^11 - (a^5*b^12*c^5 - 16*a^6*b^10*c^6 + 100*a^7*b^8*c^7 - 305*a^8*b^6*c^8 + 460*a^9*b^4*c^9 - 304*a^10*b^2*c^10 + 64*a^11*c^11)*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)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*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)/(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^4 - 8*a^6*b^2*c + 16*a^7*c^2)))*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*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)/(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^4 - 8*a^6*b^2*c + 16*a^7*c^2))) - (b^10*c^4 - 10*a*b^8*c^5 + 35*a^2*b^6*c^6 - 50*a^3*b^4*c^7 + 25*a^4*b^2*c^8 - 4*a^5*c^9 - (a^5*b^9*c^4 - 11*a^6*b^7*c^5 + 41*a^7*b^5*c^6 - 56*a^8*b^3*c^7 + 16*a^9*b*c^8)*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)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))*sqrt(x)*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*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)/(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^4 - 8*a^6*b^2*c + 16*a^7*c^2))))/(b^8*c^5 - 6*a*b^6*c^6 + 11*a^2*b^4*c^7 - 6*a^3*b^2*c^8 + a^4*c^9)) - a*x*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*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)/(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^4 - 8*a^6*b^2*c + 16*a^7*c^2)))*log(1/2*sqrt(1/2)*(b^11 - 13*a*b^9*c + 63*a^2*b^7*c^2 - 138*a^3*b^5*c^3 + 128*a^4*b^3*c^4 - 32*a^5*b*c^5 - (a^5*b^10 - 16*a^6*b^8*c + 98*a^7*b^6*c^2 - 280*a^8*b^4*c^3 + 352*a^9*b^2*c^4 - 128*a^10*c^5)*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)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*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)/(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^4 - 8*a^6*b^2*c + 16*a^7*c^2)))*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*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)/(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^4 - 8*a^6*b^2*c + 16*a^7*c^2)) + (b^4*c^4 - 3*a*b^2*c^5 + a^2*c^6)*sqrt(x)) + a*x*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*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)/(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^4 - 8*a^6*b^2*c + 16*a^7*c^2)))*log(-1/2*sqrt(1/2)*(b^11 - 13*a*b^9*c + 63*a^2*b^7*c^2 - 138*a^3*b^5*c^3 + 128*a^4*b^3*c^4 - 32*a^5*b*c^5 - (a^5*b^10 - 16*a^6*b^8*c + 98*a^7*b^6*c^2 - 280*a^8*b^4*c^3 + 352*a^9*b^2*c^4 - 128*a^10*c^5)*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)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*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)/(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^4 - 8*a^6*b^2*c + 16*a^7*c^2)))*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*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)/(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^4 - 8*a^6*b^2*c + 16*a^7*c^2)) + (b^4*c^4 - 3*a*b^2*c^5 + a^2*c^6)*sqrt(x)) - a*x*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*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)/(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^4 - 8*a^6*b^2*c + 16*a^7*c^2)))*log(1/2*sqrt(1/2)*(b^11 - 13*a*b^9*c + 63*a^2*b^7*c^2 - 138*a^3*b^5*c^3 + 128*a^4*b^3*c^4 - 32*a^5*b*c^5 + (a^5*b^10 - 16*a^6*b^8*c + 98*a^7*b^6*c^2 - 280*a^8*b^4*c^3 + 352*a^9*b^2*c^4 - 128*a^10*c^5)*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)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*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)/(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^4 - 8*a^6*b^2*c + 16*a^7*c^2)))*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*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)/(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^4 - 8*a^6*b^2*c + 16*a^7*c^2)) + (b^4*c^4 - 3*a*b^2*c^5 + a^2*c^6)*sqrt(x)) + a*x*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*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)/(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^4 - 8*a^6*b^2*c + 16*a^7*c^2)))*log(-1/2*sqrt(1/2)*(b^11 - 13*a*b^9*c + 63*a^2*b^7*c^2 - 138*a^3*b^5*c^3 + 128*a^4*b^3*c^4 - 32*a^5*b*c^5 + (a^5*b^10 - 16*a^6*b^8*c + 98*a^7*b^6*c^2 - 280*a^8*b^4*c^3 + 352*a^9*b^2*c^4 - 128*a^10*c^5)*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)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*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)/(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^4 - 8*a^6*b^2*c + 16*a^7*c^2)))*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*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)/(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^4 - 8*a^6*b^2*c + 16*a^7*c^2)) + (b^4*c^4 - 3*a*b^2*c^5 + a^2*c^6)*sqrt(x)) + 4*sqrt(x))/(a*x)","B",0
1069,1,6671,0,9.253181," ","integrate(1/x^(5/2)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\frac{12 \, a x^{2} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} - {\left(a^{7} b^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + 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^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}}}} \arctan\left(-\frac{{\left(\sqrt{\frac{1}{2}} {\left(b^{14} - 16 \, a b^{12} c + 102 \, a^{2} b^{10} c^{2} - 328 \, a^{3} b^{8} c^{3} + 553 \, a^{4} b^{6} c^{4} - 457 \, a^{5} b^{4} c^{5} + 152 \, a^{6} b^{2} c^{6} - 16 \, a^{7} c^{7} + {\left(a^{7} b^{11} - 17 \, a^{8} b^{9} c + 113 \, a^{9} b^{7} c^{2} - 364 \, a^{10} b^{5} c^{3} + 560 \, a^{11} b^{3} c^{4} - 320 \, a^{12} b c^{5}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + 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{4 \, {\left(b^{12} c^{4} - 10 \, a b^{10} c^{5} + 37 \, a^{2} b^{8} c^{6} - 62 \, a^{3} b^{6} c^{7} + 46 \, a^{4} b^{4} c^{8} - 12 \, a^{5} b^{2} c^{9} + a^{6} c^{10}\right)} x + 2 \, \sqrt{\frac{1}{2}} {\left(b^{18} - 18 \, a b^{16} c + 135 \, a^{2} b^{14} c^{2} - 546 \, a^{3} b^{12} c^{3} + 1288 \, a^{4} b^{10} c^{4} - 1792 \, a^{5} b^{8} c^{5} + 1421 \, a^{6} b^{6} c^{6} - 592 \, a^{7} b^{4} c^{7} + 114 \, a^{8} b^{2} c^{8} - 8 \, a^{9} c^{9} + {\left(a^{7} b^{15} - 19 \, a^{8} b^{13} c + 148 \, a^{9} b^{11} c^{2} - 605 \, a^{10} b^{9} c^{3} + 1374 \, a^{11} b^{7} c^{4} - 1672 \, a^{12} b^{5} c^{5} + 928 \, a^{13} b^{3} c^{6} - 128 \, a^{14} b c^{7}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + 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{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} - {\left(a^{7} b^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + 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^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}}}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} - {\left(a^{7} b^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + 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^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}}} + 2 \, \sqrt{\frac{1}{2}} {\left(b^{20} c^{2} - 21 \, a b^{18} c^{3} + 188 \, a^{2} b^{16} c^{4} - 935 \, a^{3} b^{14} c^{5} + 2821 \, a^{4} b^{12} c^{6} - 5292 \, a^{5} b^{10} c^{7} + 6083 \, a^{6} b^{8} c^{8} - 4071 \, a^{7} b^{6} c^{9} + 1449 \, a^{8} b^{4} c^{10} - 248 \, a^{9} b^{2} c^{11} + 16 \, a^{10} c^{12} + {\left(a^{7} b^{17} c^{2} - 22 \, a^{8} b^{15} c^{3} + 204 \, a^{9} b^{13} c^{4} - 1032 \, a^{10} b^{11} c^{5} + 3075 \, a^{11} b^{9} c^{6} - 5417 \, a^{12} b^{7} c^{7} + 5324 \, a^{13} b^{5} c^{8} - 2480 \, a^{14} b^{3} c^{9} + 320 \, a^{15} b c^{10}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + 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{x} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} - {\left(a^{7} b^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + 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^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} - {\left(a^{7} b^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + 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^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}}}}}{4 \, {\left(b^{12} c^{7} - 10 \, a b^{10} c^{8} + 37 \, a^{2} b^{8} c^{9} - 62 \, a^{3} b^{6} c^{10} + 46 \, a^{4} b^{4} c^{11} - 12 \, a^{5} b^{2} c^{12} + a^{6} c^{13}\right)}}\right) - 12 \, a x^{2} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} + {\left(a^{7} b^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + 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^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}}}} \arctan\left(\frac{\sqrt{\frac{1}{2}} {\left(b^{14} - 16 \, a b^{12} c + 102 \, a^{2} b^{10} c^{2} - 328 \, a^{3} b^{8} c^{3} + 553 \, a^{4} b^{6} c^{4} - 457 \, a^{5} b^{4} c^{5} + 152 \, a^{6} b^{2} c^{6} - 16 \, a^{7} c^{7} - {\left(a^{7} b^{11} - 17 \, a^{8} b^{9} c + 113 \, a^{9} b^{7} c^{2} - 364 \, a^{10} b^{5} c^{3} + 560 \, a^{11} b^{3} c^{4} - 320 \, a^{12} b c^{5}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + 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{4 \, {\left(b^{12} c^{4} - 10 \, a b^{10} c^{5} + 37 \, a^{2} b^{8} c^{6} - 62 \, a^{3} b^{6} c^{7} + 46 \, a^{4} b^{4} c^{8} - 12 \, a^{5} b^{2} c^{9} + a^{6} c^{10}\right)} x + 2 \, \sqrt{\frac{1}{2}} {\left(b^{18} - 18 \, a b^{16} c + 135 \, a^{2} b^{14} c^{2} - 546 \, a^{3} b^{12} c^{3} + 1288 \, a^{4} b^{10} c^{4} - 1792 \, a^{5} b^{8} c^{5} + 1421 \, a^{6} b^{6} c^{6} - 592 \, a^{7} b^{4} c^{7} + 114 \, a^{8} b^{2} c^{8} - 8 \, a^{9} c^{9} - {\left(a^{7} b^{15} - 19 \, a^{8} b^{13} c + 148 \, a^{9} b^{11} c^{2} - 605 \, a^{10} b^{9} c^{3} + 1374 \, a^{11} b^{7} c^{4} - 1672 \, a^{12} b^{5} c^{5} + 928 \, a^{13} b^{3} c^{6} - 128 \, a^{14} b c^{7}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + 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{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} + {\left(a^{7} b^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + 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^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}}}} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} + {\left(a^{7} b^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + 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^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}}}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} + {\left(a^{7} b^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + 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^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}}} + 2 \, \sqrt{\frac{1}{2}} {\left(b^{20} c^{2} - 21 \, a b^{18} c^{3} + 188 \, a^{2} b^{16} c^{4} - 935 \, a^{3} b^{14} c^{5} + 2821 \, a^{4} b^{12} c^{6} - 5292 \, a^{5} b^{10} c^{7} + 6083 \, a^{6} b^{8} c^{8} - 4071 \, a^{7} b^{6} c^{9} + 1449 \, a^{8} b^{4} c^{10} - 248 \, a^{9} b^{2} c^{11} + 16 \, a^{10} c^{12} - {\left(a^{7} b^{17} c^{2} - 22 \, a^{8} b^{15} c^{3} + 204 \, a^{9} b^{13} c^{4} - 1032 \, a^{10} b^{11} c^{5} + 3075 \, a^{11} b^{9} c^{6} - 5417 \, a^{12} b^{7} c^{7} + 5324 \, a^{13} b^{5} c^{8} - 2480 \, a^{14} b^{3} c^{9} + 320 \, a^{15} b c^{10}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + 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{x} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} + {\left(a^{7} b^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + 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^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}}}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} + {\left(a^{7} b^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + 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^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}}}}{4 \, {\left(b^{12} c^{7} - 10 \, a b^{10} c^{8} + 37 \, a^{2} b^{8} c^{9} - 62 \, a^{3} b^{6} c^{10} + 46 \, a^{4} b^{4} c^{11} - 12 \, a^{5} b^{2} c^{12} + a^{6} c^{13}\right)}}\right) - 3 \, a x^{2} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} + {\left(a^{7} b^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + 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^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}}}} \log\left(-2 \, {\left(b^{6} c^{2} - 5 \, a b^{4} c^{3} + 6 \, a^{2} b^{2} c^{4} - a^{3} c^{5}\right)} \sqrt{x} + {\left(b^{9} - 9 \, a b^{7} c + 26 \, a^{2} b^{5} c^{2} - 25 \, a^{3} b^{3} c^{3} + 4 \, a^{4} b c^{4} - {\left(a^{7} b^{6} - 10 \, a^{8} b^{4} c + 32 \, a^{9} b^{2} c^{2} - 32 \, a^{10} c^{3}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + 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{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} + {\left(a^{7} b^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + 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^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}}}}\right) + 3 \, a x^{2} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} + {\left(a^{7} b^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + 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^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}}}} \log\left(-2 \, {\left(b^{6} c^{2} - 5 \, a b^{4} c^{3} + 6 \, a^{2} b^{2} c^{4} - a^{3} c^{5}\right)} \sqrt{x} - {\left(b^{9} - 9 \, a b^{7} c + 26 \, a^{2} b^{5} c^{2} - 25 \, a^{3} b^{3} c^{3} + 4 \, a^{4} b c^{4} - {\left(a^{7} b^{6} - 10 \, a^{8} b^{4} c + 32 \, a^{9} b^{2} c^{2} - 32 \, a^{10} c^{3}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + 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{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} + {\left(a^{7} b^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + 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^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}}}}\right) - 3 \, a x^{2} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} - {\left(a^{7} b^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + 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^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}}}} \log\left(-2 \, {\left(b^{6} c^{2} - 5 \, a b^{4} c^{3} + 6 \, a^{2} b^{2} c^{4} - a^{3} c^{5}\right)} \sqrt{x} + {\left(b^{9} - 9 \, a b^{7} c + 26 \, a^{2} b^{5} c^{2} - 25 \, a^{3} b^{3} c^{3} + 4 \, a^{4} b c^{4} + {\left(a^{7} b^{6} - 10 \, a^{8} b^{4} c + 32 \, a^{9} b^{2} c^{2} - 32 \, a^{10} c^{3}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + 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{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} - {\left(a^{7} b^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + 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^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}}}}\right) + 3 \, a x^{2} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} - {\left(a^{7} b^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + 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^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}}}} \log\left(-2 \, {\left(b^{6} c^{2} - 5 \, a b^{4} c^{3} + 6 \, a^{2} b^{2} c^{4} - a^{3} c^{5}\right)} \sqrt{x} - {\left(b^{9} - 9 \, a b^{7} c + 26 \, a^{2} b^{5} c^{2} - 25 \, a^{3} b^{3} c^{3} + 4 \, a^{4} b c^{4} + {\left(a^{7} b^{6} - 10 \, a^{8} b^{4} c + 32 \, a^{9} b^{2} c^{2} - 32 \, a^{10} c^{3}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + 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{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} - {\left(a^{7} b^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}\right)} \sqrt{\frac{b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + 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^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}}}}\right) - 4 \, \sqrt{x}}{6 \, a x^{2}}"," ",0,"1/6*(12*a*x^2*sqrt(sqrt(1/2)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 - (a^7*b^4 - 8*a^8*b^2*c + 16*a^9*c^2)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + 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^4 - 8*a^8*b^2*c + 16*a^9*c^2)))*arctan(-1/4*(sqrt(1/2)*(b^14 - 16*a*b^12*c + 102*a^2*b^10*c^2 - 328*a^3*b^8*c^3 + 553*a^4*b^6*c^4 - 457*a^5*b^4*c^5 + 152*a^6*b^2*c^6 - 16*a^7*c^7 + (a^7*b^11 - 17*a^8*b^9*c + 113*a^9*b^7*c^2 - 364*a^10*b^5*c^3 + 560*a^11*b^3*c^4 - 320*a^12*b*c^5)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + 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(4*(b^12*c^4 - 10*a*b^10*c^5 + 37*a^2*b^8*c^6 - 62*a^3*b^6*c^7 + 46*a^4*b^4*c^8 - 12*a^5*b^2*c^9 + a^6*c^10)*x + 2*sqrt(1/2)*(b^18 - 18*a*b^16*c + 135*a^2*b^14*c^2 - 546*a^3*b^12*c^3 + 1288*a^4*b^10*c^4 - 1792*a^5*b^8*c^5 + 1421*a^6*b^6*c^6 - 592*a^7*b^4*c^7 + 114*a^8*b^2*c^8 - 8*a^9*c^9 + (a^7*b^15 - 19*a^8*b^13*c + 148*a^9*b^11*c^2 - 605*a^10*b^9*c^3 + 1374*a^11*b^7*c^4 - 1672*a^12*b^5*c^5 + 928*a^13*b^3*c^6 - 128*a^14*b*c^7)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + 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(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 - (a^7*b^4 - 8*a^8*b^2*c + 16*a^9*c^2)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + 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^4 - 8*a^8*b^2*c + 16*a^9*c^2)))*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 - (a^7*b^4 - 8*a^8*b^2*c + 16*a^9*c^2)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + 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^4 - 8*a^8*b^2*c + 16*a^9*c^2)) + 2*sqrt(1/2)*(b^20*c^2 - 21*a*b^18*c^3 + 188*a^2*b^16*c^4 - 935*a^3*b^14*c^5 + 2821*a^4*b^12*c^6 - 5292*a^5*b^10*c^7 + 6083*a^6*b^8*c^8 - 4071*a^7*b^6*c^9 + 1449*a^8*b^4*c^10 - 248*a^9*b^2*c^11 + 16*a^10*c^12 + (a^7*b^17*c^2 - 22*a^8*b^15*c^3 + 204*a^9*b^13*c^4 - 1032*a^10*b^11*c^5 + 3075*a^11*b^9*c^6 - 5417*a^12*b^7*c^7 + 5324*a^13*b^5*c^8 - 2480*a^14*b^3*c^9 + 320*a^15*b*c^10)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + 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(x)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 - (a^7*b^4 - 8*a^8*b^2*c + 16*a^9*c^2)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + 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^4 - 8*a^8*b^2*c + 16*a^9*c^2)))*sqrt(sqrt(1/2)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 - (a^7*b^4 - 8*a^8*b^2*c + 16*a^9*c^2)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + 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^4 - 8*a^8*b^2*c + 16*a^9*c^2)))/(b^12*c^7 - 10*a*b^10*c^8 + 37*a^2*b^8*c^9 - 62*a^3*b^6*c^10 + 46*a^4*b^4*c^11 - 12*a^5*b^2*c^12 + a^6*c^13)) - 12*a*x^2*sqrt(sqrt(1/2)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 + (a^7*b^4 - 8*a^8*b^2*c + 16*a^9*c^2)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + 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^4 - 8*a^8*b^2*c + 16*a^9*c^2)))*arctan(1/4*(sqrt(1/2)*(b^14 - 16*a*b^12*c + 102*a^2*b^10*c^2 - 328*a^3*b^8*c^3 + 553*a^4*b^6*c^4 - 457*a^5*b^4*c^5 + 152*a^6*b^2*c^6 - 16*a^7*c^7 - (a^7*b^11 - 17*a^8*b^9*c + 113*a^9*b^7*c^2 - 364*a^10*b^5*c^3 + 560*a^11*b^3*c^4 - 320*a^12*b*c^5)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + 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(4*(b^12*c^4 - 10*a*b^10*c^5 + 37*a^2*b^8*c^6 - 62*a^3*b^6*c^7 + 46*a^4*b^4*c^8 - 12*a^5*b^2*c^9 + a^6*c^10)*x + 2*sqrt(1/2)*(b^18 - 18*a*b^16*c + 135*a^2*b^14*c^2 - 546*a^3*b^12*c^3 + 1288*a^4*b^10*c^4 - 1792*a^5*b^8*c^5 + 1421*a^6*b^6*c^6 - 592*a^7*b^4*c^7 + 114*a^8*b^2*c^8 - 8*a^9*c^9 - (a^7*b^15 - 19*a^8*b^13*c + 148*a^9*b^11*c^2 - 605*a^10*b^9*c^3 + 1374*a^11*b^7*c^4 - 1672*a^12*b^5*c^5 + 928*a^13*b^3*c^6 - 128*a^14*b*c^7)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + 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(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 + (a^7*b^4 - 8*a^8*b^2*c + 16*a^9*c^2)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + 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^4 - 8*a^8*b^2*c + 16*a^9*c^2)))*sqrt(sqrt(1/2)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 + (a^7*b^4 - 8*a^8*b^2*c + 16*a^9*c^2)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + 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^4 - 8*a^8*b^2*c + 16*a^9*c^2)))*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 + (a^7*b^4 - 8*a^8*b^2*c + 16*a^9*c^2)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + 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^4 - 8*a^8*b^2*c + 16*a^9*c^2)) + 2*sqrt(1/2)*(b^20*c^2 - 21*a*b^18*c^3 + 188*a^2*b^16*c^4 - 935*a^3*b^14*c^5 + 2821*a^4*b^12*c^6 - 5292*a^5*b^10*c^7 + 6083*a^6*b^8*c^8 - 4071*a^7*b^6*c^9 + 1449*a^8*b^4*c^10 - 248*a^9*b^2*c^11 + 16*a^10*c^12 - (a^7*b^17*c^2 - 22*a^8*b^15*c^3 + 204*a^9*b^13*c^4 - 1032*a^10*b^11*c^5 + 3075*a^11*b^9*c^6 - 5417*a^12*b^7*c^7 + 5324*a^13*b^5*c^8 - 2480*a^14*b^3*c^9 + 320*a^15*b*c^10)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + 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(x)*sqrt(sqrt(1/2)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 + (a^7*b^4 - 8*a^8*b^2*c + 16*a^9*c^2)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + 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^4 - 8*a^8*b^2*c + 16*a^9*c^2)))*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 + (a^7*b^4 - 8*a^8*b^2*c + 16*a^9*c^2)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + 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^4 - 8*a^8*b^2*c + 16*a^9*c^2)))/(b^12*c^7 - 10*a*b^10*c^8 + 37*a^2*b^8*c^9 - 62*a^3*b^6*c^10 + 46*a^4*b^4*c^11 - 12*a^5*b^2*c^12 + a^6*c^13)) - 3*a*x^2*sqrt(sqrt(1/2)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 + (a^7*b^4 - 8*a^8*b^2*c + 16*a^9*c^2)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + 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^4 - 8*a^8*b^2*c + 16*a^9*c^2)))*log(-2*(b^6*c^2 - 5*a*b^4*c^3 + 6*a^2*b^2*c^4 - a^3*c^5)*sqrt(x) + (b^9 - 9*a*b^7*c + 26*a^2*b^5*c^2 - 25*a^3*b^3*c^3 + 4*a^4*b*c^4 - (a^7*b^6 - 10*a^8*b^4*c + 32*a^9*b^2*c^2 - 32*a^10*c^3)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + 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(sqrt(1/2)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 + (a^7*b^4 - 8*a^8*b^2*c + 16*a^9*c^2)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + 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^4 - 8*a^8*b^2*c + 16*a^9*c^2)))) + 3*a*x^2*sqrt(sqrt(1/2)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 + (a^7*b^4 - 8*a^8*b^2*c + 16*a^9*c^2)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + 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^4 - 8*a^8*b^2*c + 16*a^9*c^2)))*log(-2*(b^6*c^2 - 5*a*b^4*c^3 + 6*a^2*b^2*c^4 - a^3*c^5)*sqrt(x) - (b^9 - 9*a*b^7*c + 26*a^2*b^5*c^2 - 25*a^3*b^3*c^3 + 4*a^4*b*c^4 - (a^7*b^6 - 10*a^8*b^4*c + 32*a^9*b^2*c^2 - 32*a^10*c^3)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + 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(sqrt(1/2)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 + (a^7*b^4 - 8*a^8*b^2*c + 16*a^9*c^2)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + 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^4 - 8*a^8*b^2*c + 16*a^9*c^2)))) - 3*a*x^2*sqrt(sqrt(1/2)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 - (a^7*b^4 - 8*a^8*b^2*c + 16*a^9*c^2)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + 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^4 - 8*a^8*b^2*c + 16*a^9*c^2)))*log(-2*(b^6*c^2 - 5*a*b^4*c^3 + 6*a^2*b^2*c^4 - a^3*c^5)*sqrt(x) + (b^9 - 9*a*b^7*c + 26*a^2*b^5*c^2 - 25*a^3*b^3*c^3 + 4*a^4*b*c^4 + (a^7*b^6 - 10*a^8*b^4*c + 32*a^9*b^2*c^2 - 32*a^10*c^3)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + 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(sqrt(1/2)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 - (a^7*b^4 - 8*a^8*b^2*c + 16*a^9*c^2)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + 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^4 - 8*a^8*b^2*c + 16*a^9*c^2)))) + 3*a*x^2*sqrt(sqrt(1/2)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 - (a^7*b^4 - 8*a^8*b^2*c + 16*a^9*c^2)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + 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^4 - 8*a^8*b^2*c + 16*a^9*c^2)))*log(-2*(b^6*c^2 - 5*a*b^4*c^3 + 6*a^2*b^2*c^4 - a^3*c^5)*sqrt(x) - (b^9 - 9*a*b^7*c + 26*a^2*b^5*c^2 - 25*a^3*b^3*c^3 + 4*a^4*b*c^4 + (a^7*b^6 - 10*a^8*b^4*c + 32*a^9*b^2*c^2 - 32*a^10*c^3)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + 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(sqrt(1/2)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 - (a^7*b^4 - 8*a^8*b^2*c + 16*a^9*c^2)*sqrt((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + 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^4 - 8*a^8*b^2*c + 16*a^9*c^2)))) - 4*sqrt(x))/(a*x^2)","B",0
1070,1,7995,0,32.952046," ","integrate(1/x^(7/2)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\frac{20 \, a^{2} x^{3} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{9} - 9 \, a b^{7} c + 27 \, a^{2} b^{5} c^{2} - 30 \, a^{3} b^{3} c^{3} + 9 \, a^{4} b c^{4} + {\left(a^{9} b^{4} - 8 \, a^{10} b^{2} c + 16 \, a^{11} c^{2}\right)} \sqrt{\frac{b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}}{a^{18} b^{6} - 12 \, a^{19} b^{4} c + 48 \, a^{20} b^{2} c^{2} - 64 \, a^{21} c^{3}}}}{a^{9} b^{4} - 8 \, a^{10} b^{2} c + 16 \, a^{11} c^{2}}}} \arctan\left(\frac{{\left({\left(b^{11} - 11 \, a b^{9} c + 43 \, a^{2} b^{7} c^{2} - 70 \, a^{3} b^{5} c^{3} + 41 \, a^{4} b^{3} c^{4} - 4 \, a^{5} b c^{5} - {\left(a^{9} b^{6} - 10 \, a^{10} b^{4} c + 32 \, a^{11} b^{2} c^{2} - 32 \, a^{12} c^{3}\right)} \sqrt{\frac{b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}}{a^{18} b^{6} - 12 \, a^{19} b^{4} c + 48 \, a^{20} b^{2} c^{2} - 64 \, a^{21} c^{3}}}\right)} \sqrt{{\left(b^{16} c^{14} - 14 \, a b^{14} c^{15} + 79 \, a^{2} b^{12} c^{16} - 230 \, a^{3} b^{10} c^{17} + 367 \, a^{4} b^{8} c^{18} - 314 \, a^{5} b^{6} c^{19} + 130 \, a^{6} b^{4} c^{20} - 20 \, a^{7} b^{2} c^{21} + a^{8} c^{22}\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{23} c^{9} - 23 \, a b^{21} c^{10} + 230 \, a^{2} b^{19} c^{11} - 1311 \, a^{3} b^{17} c^{12} + 4692 \, a^{4} b^{15} c^{13} - 10947 \, a^{5} b^{13} c^{14} + 16731 \, a^{6} b^{11} c^{15} - 16380 \, a^{7} b^{9} c^{16} + 9711 \, a^{8} b^{7} c^{17} - 3109 \, a^{9} b^{5} c^{18} + 425 \, a^{10} b^{3} c^{19} - 20 \, a^{11} b c^{20} - {\left(a^{9} b^{18} c^{9} - 22 \, a^{10} b^{16} c^{10} + 205 \, a^{11} b^{14} c^{11} - 1050 \, a^{12} b^{12} c^{12} + 3206 \, a^{13} b^{10} c^{13} - 5909 \, a^{14} b^{8} c^{14} + 6333 \, a^{15} b^{6} c^{15} - 3580 \, a^{16} b^{4} c^{16} + 880 \, a^{17} b^{2} c^{17} - 64 \, a^{18} c^{18}\right)} \sqrt{\frac{b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}}{a^{18} b^{6} - 12 \, a^{19} b^{4} c + 48 \, a^{20} b^{2} c^{2} - 64 \, a^{21} c^{3}}}\right)} \sqrt{-\frac{b^{9} - 9 \, a b^{7} c + 27 \, a^{2} b^{5} c^{2} - 30 \, a^{3} b^{3} c^{3} + 9 \, a^{4} b c^{4} + {\left(a^{9} b^{4} - 8 \, a^{10} b^{2} c + 16 \, a^{11} c^{2}\right)} \sqrt{\frac{b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}}{a^{18} b^{6} - 12 \, a^{19} b^{4} c + 48 \, a^{20} b^{2} c^{2} - 64 \, a^{21} c^{3}}}}{a^{9} b^{4} - 8 \, a^{10} b^{2} c + 16 \, a^{11} c^{2}}}} - {\left(b^{19} c^{7} - 18 \, a b^{17} c^{8} + 135 \, a^{2} b^{15} c^{9} - 546 \, a^{3} b^{13} c^{10} + 1287 \, a^{4} b^{11} c^{11} - 1782 \, a^{5} b^{9} c^{12} + 1386 \, a^{6} b^{7} c^{13} - 540 \, a^{7} b^{5} c^{14} + 81 \, a^{8} b^{3} c^{15} - 4 \, a^{9} b c^{16} - {\left(a^{9} b^{14} c^{7} - 17 \, a^{10} b^{12} c^{8} + 117 \, a^{11} b^{10} c^{9} - 416 \, a^{12} b^{8} c^{10} + 805 \, a^{13} b^{6} c^{11} - 810 \, a^{14} b^{4} c^{12} + 352 \, a^{15} b^{2} c^{13} - 32 \, a^{16} c^{14}\right)} \sqrt{\frac{b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}}{a^{18} b^{6} - 12 \, a^{19} b^{4} c + 48 \, a^{20} b^{2} c^{2} - 64 \, a^{21} c^{3}}}\right)} \sqrt{x}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{9} - 9 \, a b^{7} c + 27 \, a^{2} b^{5} c^{2} - 30 \, a^{3} b^{3} c^{3} + 9 \, a^{4} b c^{4} + {\left(a^{9} b^{4} - 8 \, a^{10} b^{2} c + 16 \, a^{11} c^{2}\right)} \sqrt{\frac{b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}}{a^{18} b^{6} - 12 \, a^{19} b^{4} c + 48 \, a^{20} b^{2} c^{2} - 64 \, a^{21} c^{3}}}}{a^{9} b^{4} - 8 \, a^{10} b^{2} c + 16 \, a^{11} c^{2}}}}}{2 \, {\left(b^{16} c^{9} - 14 \, a b^{14} c^{10} + 79 \, a^{2} b^{12} c^{11} - 230 \, a^{3} b^{10} c^{12} + 367 \, a^{4} b^{8} c^{13} - 314 \, a^{5} b^{6} c^{14} + 130 \, a^{6} b^{4} c^{15} - 20 \, a^{7} b^{2} c^{16} + a^{8} c^{17}\right)}}\right) - 20 \, a^{2} x^{3} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{9} - 9 \, a b^{7} c + 27 \, a^{2} b^{5} c^{2} - 30 \, a^{3} b^{3} c^{3} + 9 \, a^{4} b c^{4} - {\left(a^{9} b^{4} - 8 \, a^{10} b^{2} c + 16 \, a^{11} c^{2}\right)} \sqrt{\frac{b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}}{a^{18} b^{6} - 12 \, a^{19} b^{4} c + 48 \, a^{20} b^{2} c^{2} - 64 \, a^{21} c^{3}}}}{a^{9} b^{4} - 8 \, a^{10} b^{2} c + 16 \, a^{11} c^{2}}}} \arctan\left(-\frac{{\left(b^{11} - 11 \, a b^{9} c + 43 \, a^{2} b^{7} c^{2} - 70 \, a^{3} b^{5} c^{3} + 41 \, a^{4} b^{3} c^{4} - 4 \, a^{5} b c^{5} + {\left(a^{9} b^{6} - 10 \, a^{10} b^{4} c + 32 \, a^{11} b^{2} c^{2} - 32 \, a^{12} c^{3}\right)} \sqrt{\frac{b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}}{a^{18} b^{6} - 12 \, a^{19} b^{4} c + 48 \, a^{20} b^{2} c^{2} - 64 \, a^{21} c^{3}}}\right)} \sqrt{{\left(b^{16} c^{14} - 14 \, a b^{14} c^{15} + 79 \, a^{2} b^{12} c^{16} - 230 \, a^{3} b^{10} c^{17} + 367 \, a^{4} b^{8} c^{18} - 314 \, a^{5} b^{6} c^{19} + 130 \, a^{6} b^{4} c^{20} - 20 \, a^{7} b^{2} c^{21} + a^{8} c^{22}\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{23} c^{9} - 23 \, a b^{21} c^{10} + 230 \, a^{2} b^{19} c^{11} - 1311 \, a^{3} b^{17} c^{12} + 4692 \, a^{4} b^{15} c^{13} - 10947 \, a^{5} b^{13} c^{14} + 16731 \, a^{6} b^{11} c^{15} - 16380 \, a^{7} b^{9} c^{16} + 9711 \, a^{8} b^{7} c^{17} - 3109 \, a^{9} b^{5} c^{18} + 425 \, a^{10} b^{3} c^{19} - 20 \, a^{11} b c^{20} + {\left(a^{9} b^{18} c^{9} - 22 \, a^{10} b^{16} c^{10} + 205 \, a^{11} b^{14} c^{11} - 1050 \, a^{12} b^{12} c^{12} + 3206 \, a^{13} b^{10} c^{13} - 5909 \, a^{14} b^{8} c^{14} + 6333 \, a^{15} b^{6} c^{15} - 3580 \, a^{16} b^{4} c^{16} + 880 \, a^{17} b^{2} c^{17} - 64 \, a^{18} c^{18}\right)} \sqrt{\frac{b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}}{a^{18} b^{6} - 12 \, a^{19} b^{4} c + 48 \, a^{20} b^{2} c^{2} - 64 \, a^{21} c^{3}}}\right)} \sqrt{-\frac{b^{9} - 9 \, a b^{7} c + 27 \, a^{2} b^{5} c^{2} - 30 \, a^{3} b^{3} c^{3} + 9 \, a^{4} b c^{4} - {\left(a^{9} b^{4} - 8 \, a^{10} b^{2} c + 16 \, a^{11} c^{2}\right)} \sqrt{\frac{b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}}{a^{18} b^{6} - 12 \, a^{19} b^{4} c + 48 \, a^{20} b^{2} c^{2} - 64 \, a^{21} c^{3}}}}{a^{9} b^{4} - 8 \, a^{10} b^{2} c + 16 \, a^{11} c^{2}}}} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{9} - 9 \, a b^{7} c + 27 \, a^{2} b^{5} c^{2} - 30 \, a^{3} b^{3} c^{3} + 9 \, a^{4} b c^{4} - {\left(a^{9} b^{4} - 8 \, a^{10} b^{2} c + 16 \, a^{11} c^{2}\right)} \sqrt{\frac{b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}}{a^{18} b^{6} - 12 \, a^{19} b^{4} c + 48 \, a^{20} b^{2} c^{2} - 64 \, a^{21} c^{3}}}}{a^{9} b^{4} - 8 \, a^{10} b^{2} c + 16 \, a^{11} c^{2}}}} - {\left(b^{19} c^{7} - 18 \, a b^{17} c^{8} + 135 \, a^{2} b^{15} c^{9} - 546 \, a^{3} b^{13} c^{10} + 1287 \, a^{4} b^{11} c^{11} - 1782 \, a^{5} b^{9} c^{12} + 1386 \, a^{6} b^{7} c^{13} - 540 \, a^{7} b^{5} c^{14} + 81 \, a^{8} b^{3} c^{15} - 4 \, a^{9} b c^{16} + {\left(a^{9} b^{14} c^{7} - 17 \, a^{10} b^{12} c^{8} + 117 \, a^{11} b^{10} c^{9} - 416 \, a^{12} b^{8} c^{10} + 805 \, a^{13} b^{6} c^{11} - 810 \, a^{14} b^{4} c^{12} + 352 \, a^{15} b^{2} c^{13} - 32 \, a^{16} c^{14}\right)} \sqrt{\frac{b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}}{a^{18} b^{6} - 12 \, a^{19} b^{4} c + 48 \, a^{20} b^{2} c^{2} - 64 \, a^{21} c^{3}}}\right)} \sqrt{x} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{9} - 9 \, a b^{7} c + 27 \, a^{2} b^{5} c^{2} - 30 \, a^{3} b^{3} c^{3} + 9 \, a^{4} b c^{4} - {\left(a^{9} b^{4} - 8 \, a^{10} b^{2} c + 16 \, a^{11} c^{2}\right)} \sqrt{\frac{b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}}{a^{18} b^{6} - 12 \, a^{19} b^{4} c + 48 \, a^{20} b^{2} c^{2} - 64 \, a^{21} c^{3}}}}{a^{9} b^{4} - 8 \, a^{10} b^{2} c + 16 \, a^{11} c^{2}}}}}{2 \, {\left(b^{16} c^{9} - 14 \, a b^{14} c^{10} + 79 \, a^{2} b^{12} c^{11} - 230 \, a^{3} b^{10} c^{12} + 367 \, a^{4} b^{8} c^{13} - 314 \, a^{5} b^{6} c^{14} + 130 \, a^{6} b^{4} c^{15} - 20 \, a^{7} b^{2} c^{16} + a^{8} c^{17}\right)}}\right) - 5 \, a^{2} x^{3} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{9} - 9 \, a b^{7} c + 27 \, a^{2} b^{5} c^{2} - 30 \, a^{3} b^{3} c^{3} + 9 \, a^{4} b c^{4} + {\left(a^{9} b^{4} - 8 \, a^{10} b^{2} c + 16 \, a^{11} c^{2}\right)} \sqrt{\frac{b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}}{a^{18} b^{6} - 12 \, a^{19} b^{4} c + 48 \, a^{20} b^{2} c^{2} - 64 \, a^{21} c^{3}}}}{a^{9} b^{4} - 8 \, a^{10} b^{2} c + 16 \, a^{11} c^{2}}}} \log\left(\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{18} - 20 \, a b^{16} c + 168 \, a^{2} b^{14} c^{2} - 768 \, a^{3} b^{12} c^{3} + 2068 \, a^{4} b^{10} c^{4} - 3312 \, a^{5} b^{8} c^{5} + 3024 \, a^{6} b^{6} c^{6} - 1409 \, a^{7} b^{4} c^{7} + 264 \, a^{8} b^{2} c^{8} - 16 \, a^{9} c^{9} - {\left(a^{9} b^{13} - 19 \, a^{10} b^{11} c + 146 \, a^{11} b^{9} c^{2} - 575 \, a^{12} b^{7} c^{3} + 1204 \, a^{13} b^{5} c^{4} - 1232 \, a^{14} b^{3} c^{5} + 448 \, a^{15} b c^{6}\right)} \sqrt{\frac{b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}}{a^{18} b^{6} - 12 \, a^{19} b^{4} c + 48 \, a^{20} b^{2} c^{2} - 64 \, a^{21} c^{3}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{9} - 9 \, a b^{7} c + 27 \, a^{2} b^{5} c^{2} - 30 \, a^{3} b^{3} c^{3} + 9 \, a^{4} b c^{4} + {\left(a^{9} b^{4} - 8 \, a^{10} b^{2} c + 16 \, a^{11} c^{2}\right)} \sqrt{\frac{b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}}{a^{18} b^{6} - 12 \, a^{19} b^{4} c + 48 \, a^{20} b^{2} c^{2} - 64 \, a^{21} c^{3}}}}{a^{9} b^{4} - 8 \, a^{10} b^{2} c + 16 \, a^{11} c^{2}}}} \sqrt{-\frac{b^{9} - 9 \, a b^{7} c + 27 \, a^{2} b^{5} c^{2} - 30 \, a^{3} b^{3} c^{3} + 9 \, a^{4} b c^{4} + {\left(a^{9} b^{4} - 8 \, a^{10} b^{2} c + 16 \, a^{11} c^{2}\right)} \sqrt{\frac{b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}}{a^{18} b^{6} - 12 \, a^{19} b^{4} c + 48 \, a^{20} b^{2} c^{2} - 64 \, a^{21} c^{3}}}}{a^{9} b^{4} - 8 \, a^{10} b^{2} c + 16 \, a^{11} c^{2}}} + {\left(b^{8} c^{7} - 7 \, a b^{6} c^{8} + 15 \, a^{2} b^{4} c^{9} - 10 \, a^{3} b^{2} c^{10} + a^{4} c^{11}\right)} \sqrt{x}\right) + 5 \, a^{2} x^{3} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{9} - 9 \, a b^{7} c + 27 \, a^{2} b^{5} c^{2} - 30 \, a^{3} b^{3} c^{3} + 9 \, a^{4} b c^{4} + {\left(a^{9} b^{4} - 8 \, a^{10} b^{2} c + 16 \, a^{11} c^{2}\right)} \sqrt{\frac{b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}}{a^{18} b^{6} - 12 \, a^{19} b^{4} c + 48 \, a^{20} b^{2} c^{2} - 64 \, a^{21} c^{3}}}}{a^{9} b^{4} - 8 \, a^{10} b^{2} c + 16 \, a^{11} c^{2}}}} \log\left(-\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{18} - 20 \, a b^{16} c + 168 \, a^{2} b^{14} c^{2} - 768 \, a^{3} b^{12} c^{3} + 2068 \, a^{4} b^{10} c^{4} - 3312 \, a^{5} b^{8} c^{5} + 3024 \, a^{6} b^{6} c^{6} - 1409 \, a^{7} b^{4} c^{7} + 264 \, a^{8} b^{2} c^{8} - 16 \, a^{9} c^{9} - {\left(a^{9} b^{13} - 19 \, a^{10} b^{11} c + 146 \, a^{11} b^{9} c^{2} - 575 \, a^{12} b^{7} c^{3} + 1204 \, a^{13} b^{5} c^{4} - 1232 \, a^{14} b^{3} c^{5} + 448 \, a^{15} b c^{6}\right)} \sqrt{\frac{b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}}{a^{18} b^{6} - 12 \, a^{19} b^{4} c + 48 \, a^{20} b^{2} c^{2} - 64 \, a^{21} c^{3}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{9} - 9 \, a b^{7} c + 27 \, a^{2} b^{5} c^{2} - 30 \, a^{3} b^{3} c^{3} + 9 \, a^{4} b c^{4} + {\left(a^{9} b^{4} - 8 \, a^{10} b^{2} c + 16 \, a^{11} c^{2}\right)} \sqrt{\frac{b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}}{a^{18} b^{6} - 12 \, a^{19} b^{4} c + 48 \, a^{20} b^{2} c^{2} - 64 \, a^{21} c^{3}}}}{a^{9} b^{4} - 8 \, a^{10} b^{2} c + 16 \, a^{11} c^{2}}}} \sqrt{-\frac{b^{9} - 9 \, a b^{7} c + 27 \, a^{2} b^{5} c^{2} - 30 \, a^{3} b^{3} c^{3} + 9 \, a^{4} b c^{4} + {\left(a^{9} b^{4} - 8 \, a^{10} b^{2} c + 16 \, a^{11} c^{2}\right)} \sqrt{\frac{b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}}{a^{18} b^{6} - 12 \, a^{19} b^{4} c + 48 \, a^{20} b^{2} c^{2} - 64 \, a^{21} c^{3}}}}{a^{9} b^{4} - 8 \, a^{10} b^{2} c + 16 \, a^{11} c^{2}}} + {\left(b^{8} c^{7} - 7 \, a b^{6} c^{8} + 15 \, a^{2} b^{4} c^{9} - 10 \, a^{3} b^{2} c^{10} + a^{4} c^{11}\right)} \sqrt{x}\right) - 5 \, a^{2} x^{3} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{9} - 9 \, a b^{7} c + 27 \, a^{2} b^{5} c^{2} - 30 \, a^{3} b^{3} c^{3} + 9 \, a^{4} b c^{4} - {\left(a^{9} b^{4} - 8 \, a^{10} b^{2} c + 16 \, a^{11} c^{2}\right)} \sqrt{\frac{b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}}{a^{18} b^{6} - 12 \, a^{19} b^{4} c + 48 \, a^{20} b^{2} c^{2} - 64 \, a^{21} c^{3}}}}{a^{9} b^{4} - 8 \, a^{10} b^{2} c + 16 \, a^{11} c^{2}}}} \log\left(\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{18} - 20 \, a b^{16} c + 168 \, a^{2} b^{14} c^{2} - 768 \, a^{3} b^{12} c^{3} + 2068 \, a^{4} b^{10} c^{4} - 3312 \, a^{5} b^{8} c^{5} + 3024 \, a^{6} b^{6} c^{6} - 1409 \, a^{7} b^{4} c^{7} + 264 \, a^{8} b^{2} c^{8} - 16 \, a^{9} c^{9} + {\left(a^{9} b^{13} - 19 \, a^{10} b^{11} c + 146 \, a^{11} b^{9} c^{2} - 575 \, a^{12} b^{7} c^{3} + 1204 \, a^{13} b^{5} c^{4} - 1232 \, a^{14} b^{3} c^{5} + 448 \, a^{15} b c^{6}\right)} \sqrt{\frac{b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}}{a^{18} b^{6} - 12 \, a^{19} b^{4} c + 48 \, a^{20} b^{2} c^{2} - 64 \, a^{21} c^{3}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{9} - 9 \, a b^{7} c + 27 \, a^{2} b^{5} c^{2} - 30 \, a^{3} b^{3} c^{3} + 9 \, a^{4} b c^{4} - {\left(a^{9} b^{4} - 8 \, a^{10} b^{2} c + 16 \, a^{11} c^{2}\right)} \sqrt{\frac{b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}}{a^{18} b^{6} - 12 \, a^{19} b^{4} c + 48 \, a^{20} b^{2} c^{2} - 64 \, a^{21} c^{3}}}}{a^{9} b^{4} - 8 \, a^{10} b^{2} c + 16 \, a^{11} c^{2}}}} \sqrt{-\frac{b^{9} - 9 \, a b^{7} c + 27 \, a^{2} b^{5} c^{2} - 30 \, a^{3} b^{3} c^{3} + 9 \, a^{4} b c^{4} - {\left(a^{9} b^{4} - 8 \, a^{10} b^{2} c + 16 \, a^{11} c^{2}\right)} \sqrt{\frac{b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}}{a^{18} b^{6} - 12 \, a^{19} b^{4} c + 48 \, a^{20} b^{2} c^{2} - 64 \, a^{21} c^{3}}}}{a^{9} b^{4} - 8 \, a^{10} b^{2} c + 16 \, a^{11} c^{2}}} + {\left(b^{8} c^{7} - 7 \, a b^{6} c^{8} + 15 \, a^{2} b^{4} c^{9} - 10 \, a^{3} b^{2} c^{10} + a^{4} c^{11}\right)} \sqrt{x}\right) + 5 \, a^{2} x^{3} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{9} - 9 \, a b^{7} c + 27 \, a^{2} b^{5} c^{2} - 30 \, a^{3} b^{3} c^{3} + 9 \, a^{4} b c^{4} - {\left(a^{9} b^{4} - 8 \, a^{10} b^{2} c + 16 \, a^{11} c^{2}\right)} \sqrt{\frac{b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}}{a^{18} b^{6} - 12 \, a^{19} b^{4} c + 48 \, a^{20} b^{2} c^{2} - 64 \, a^{21} c^{3}}}}{a^{9} b^{4} - 8 \, a^{10} b^{2} c + 16 \, a^{11} c^{2}}}} \log\left(-\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{18} - 20 \, a b^{16} c + 168 \, a^{2} b^{14} c^{2} - 768 \, a^{3} b^{12} c^{3} + 2068 \, a^{4} b^{10} c^{4} - 3312 \, a^{5} b^{8} c^{5} + 3024 \, a^{6} b^{6} c^{6} - 1409 \, a^{7} b^{4} c^{7} + 264 \, a^{8} b^{2} c^{8} - 16 \, a^{9} c^{9} + {\left(a^{9} b^{13} - 19 \, a^{10} b^{11} c + 146 \, a^{11} b^{9} c^{2} - 575 \, a^{12} b^{7} c^{3} + 1204 \, a^{13} b^{5} c^{4} - 1232 \, a^{14} b^{3} c^{5} + 448 \, a^{15} b c^{6}\right)} \sqrt{\frac{b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}}{a^{18} b^{6} - 12 \, a^{19} b^{4} c + 48 \, a^{20} b^{2} c^{2} - 64 \, a^{21} c^{3}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{9} - 9 \, a b^{7} c + 27 \, a^{2} b^{5} c^{2} - 30 \, a^{3} b^{3} c^{3} + 9 \, a^{4} b c^{4} - {\left(a^{9} b^{4} - 8 \, a^{10} b^{2} c + 16 \, a^{11} c^{2}\right)} \sqrt{\frac{b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}}{a^{18} b^{6} - 12 \, a^{19} b^{4} c + 48 \, a^{20} b^{2} c^{2} - 64 \, a^{21} c^{3}}}}{a^{9} b^{4} - 8 \, a^{10} b^{2} c + 16 \, a^{11} c^{2}}}} \sqrt{-\frac{b^{9} - 9 \, a b^{7} c + 27 \, a^{2} b^{5} c^{2} - 30 \, a^{3} b^{3} c^{3} + 9 \, a^{4} b c^{4} - {\left(a^{9} b^{4} - 8 \, a^{10} b^{2} c + 16 \, a^{11} c^{2}\right)} \sqrt{\frac{b^{16} - 14 \, a b^{14} c + 79 \, a^{2} b^{12} c^{2} - 230 \, a^{3} b^{10} c^{3} + 367 \, a^{4} b^{8} c^{4} - 314 \, a^{5} b^{6} c^{5} + 130 \, a^{6} b^{4} c^{6} - 20 \, a^{7} b^{2} c^{7} + a^{8} c^{8}}{a^{18} b^{6} - 12 \, a^{19} b^{4} c + 48 \, a^{20} b^{2} c^{2} - 64 \, a^{21} c^{3}}}}{a^{9} b^{4} - 8 \, a^{10} b^{2} c + 16 \, a^{11} c^{2}}} + {\left(b^{8} c^{7} - 7 \, a b^{6} c^{8} + 15 \, a^{2} b^{4} c^{9} - 10 \, a^{3} b^{2} c^{10} + a^{4} c^{11}\right)} \sqrt{x}\right) + 4 \, {\left(5 \, b x^{2} - a\right)} \sqrt{x}}{10 \, a^{2} x^{3}}"," ",0,"1/10*(20*a^2*x^3*sqrt(sqrt(1/2)*sqrt(-(b^9 - 9*a*b^7*c + 27*a^2*b^5*c^2 - 30*a^3*b^3*c^3 + 9*a^4*b*c^4 + (a^9*b^4 - 8*a^10*b^2*c + 16*a^11*c^2)*sqrt((b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)/(a^18*b^6 - 12*a^19*b^4*c + 48*a^20*b^2*c^2 - 64*a^21*c^3)))/(a^9*b^4 - 8*a^10*b^2*c + 16*a^11*c^2)))*arctan(1/2*((b^11 - 11*a*b^9*c + 43*a^2*b^7*c^2 - 70*a^3*b^5*c^3 + 41*a^4*b^3*c^4 - 4*a^5*b*c^5 - (a^9*b^6 - 10*a^10*b^4*c + 32*a^11*b^2*c^2 - 32*a^12*c^3)*sqrt((b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)/(a^18*b^6 - 12*a^19*b^4*c + 48*a^20*b^2*c^2 - 64*a^21*c^3)))*sqrt((b^16*c^14 - 14*a*b^14*c^15 + 79*a^2*b^12*c^16 - 230*a^3*b^10*c^17 + 367*a^4*b^8*c^18 - 314*a^5*b^6*c^19 + 130*a^6*b^4*c^20 - 20*a^7*b^2*c^21 + a^8*c^22)*x - 1/2*sqrt(1/2)*(b^23*c^9 - 23*a*b^21*c^10 + 230*a^2*b^19*c^11 - 1311*a^3*b^17*c^12 + 4692*a^4*b^15*c^13 - 10947*a^5*b^13*c^14 + 16731*a^6*b^11*c^15 - 16380*a^7*b^9*c^16 + 9711*a^8*b^7*c^17 - 3109*a^9*b^5*c^18 + 425*a^10*b^3*c^19 - 20*a^11*b*c^20 - (a^9*b^18*c^9 - 22*a^10*b^16*c^10 + 205*a^11*b^14*c^11 - 1050*a^12*b^12*c^12 + 3206*a^13*b^10*c^13 - 5909*a^14*b^8*c^14 + 6333*a^15*b^6*c^15 - 3580*a^16*b^4*c^16 + 880*a^17*b^2*c^17 - 64*a^18*c^18)*sqrt((b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)/(a^18*b^6 - 12*a^19*b^4*c + 48*a^20*b^2*c^2 - 64*a^21*c^3)))*sqrt(-(b^9 - 9*a*b^7*c + 27*a^2*b^5*c^2 - 30*a^3*b^3*c^3 + 9*a^4*b*c^4 + (a^9*b^4 - 8*a^10*b^2*c + 16*a^11*c^2)*sqrt((b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)/(a^18*b^6 - 12*a^19*b^4*c + 48*a^20*b^2*c^2 - 64*a^21*c^3)))/(a^9*b^4 - 8*a^10*b^2*c + 16*a^11*c^2))) - (b^19*c^7 - 18*a*b^17*c^8 + 135*a^2*b^15*c^9 - 546*a^3*b^13*c^10 + 1287*a^4*b^11*c^11 - 1782*a^5*b^9*c^12 + 1386*a^6*b^7*c^13 - 540*a^7*b^5*c^14 + 81*a^8*b^3*c^15 - 4*a^9*b*c^16 - (a^9*b^14*c^7 - 17*a^10*b^12*c^8 + 117*a^11*b^10*c^9 - 416*a^12*b^8*c^10 + 805*a^13*b^6*c^11 - 810*a^14*b^4*c^12 + 352*a^15*b^2*c^13 - 32*a^16*c^14)*sqrt((b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)/(a^18*b^6 - 12*a^19*b^4*c + 48*a^20*b^2*c^2 - 64*a^21*c^3)))*sqrt(x))*sqrt(sqrt(1/2)*sqrt(-(b^9 - 9*a*b^7*c + 27*a^2*b^5*c^2 - 30*a^3*b^3*c^3 + 9*a^4*b*c^4 + (a^9*b^4 - 8*a^10*b^2*c + 16*a^11*c^2)*sqrt((b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)/(a^18*b^6 - 12*a^19*b^4*c + 48*a^20*b^2*c^2 - 64*a^21*c^3)))/(a^9*b^4 - 8*a^10*b^2*c + 16*a^11*c^2)))/(b^16*c^9 - 14*a*b^14*c^10 + 79*a^2*b^12*c^11 - 230*a^3*b^10*c^12 + 367*a^4*b^8*c^13 - 314*a^5*b^6*c^14 + 130*a^6*b^4*c^15 - 20*a^7*b^2*c^16 + a^8*c^17)) - 20*a^2*x^3*sqrt(sqrt(1/2)*sqrt(-(b^9 - 9*a*b^7*c + 27*a^2*b^5*c^2 - 30*a^3*b^3*c^3 + 9*a^4*b*c^4 - (a^9*b^4 - 8*a^10*b^2*c + 16*a^11*c^2)*sqrt((b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)/(a^18*b^6 - 12*a^19*b^4*c + 48*a^20*b^2*c^2 - 64*a^21*c^3)))/(a^9*b^4 - 8*a^10*b^2*c + 16*a^11*c^2)))*arctan(-1/2*((b^11 - 11*a*b^9*c + 43*a^2*b^7*c^2 - 70*a^3*b^5*c^3 + 41*a^4*b^3*c^4 - 4*a^5*b*c^5 + (a^9*b^6 - 10*a^10*b^4*c + 32*a^11*b^2*c^2 - 32*a^12*c^3)*sqrt((b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)/(a^18*b^6 - 12*a^19*b^4*c + 48*a^20*b^2*c^2 - 64*a^21*c^3)))*sqrt((b^16*c^14 - 14*a*b^14*c^15 + 79*a^2*b^12*c^16 - 230*a^3*b^10*c^17 + 367*a^4*b^8*c^18 - 314*a^5*b^6*c^19 + 130*a^6*b^4*c^20 - 20*a^7*b^2*c^21 + a^8*c^22)*x - 1/2*sqrt(1/2)*(b^23*c^9 - 23*a*b^21*c^10 + 230*a^2*b^19*c^11 - 1311*a^3*b^17*c^12 + 4692*a^4*b^15*c^13 - 10947*a^5*b^13*c^14 + 16731*a^6*b^11*c^15 - 16380*a^7*b^9*c^16 + 9711*a^8*b^7*c^17 - 3109*a^9*b^5*c^18 + 425*a^10*b^3*c^19 - 20*a^11*b*c^20 + (a^9*b^18*c^9 - 22*a^10*b^16*c^10 + 205*a^11*b^14*c^11 - 1050*a^12*b^12*c^12 + 3206*a^13*b^10*c^13 - 5909*a^14*b^8*c^14 + 6333*a^15*b^6*c^15 - 3580*a^16*b^4*c^16 + 880*a^17*b^2*c^17 - 64*a^18*c^18)*sqrt((b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)/(a^18*b^6 - 12*a^19*b^4*c + 48*a^20*b^2*c^2 - 64*a^21*c^3)))*sqrt(-(b^9 - 9*a*b^7*c + 27*a^2*b^5*c^2 - 30*a^3*b^3*c^3 + 9*a^4*b*c^4 - (a^9*b^4 - 8*a^10*b^2*c + 16*a^11*c^2)*sqrt((b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)/(a^18*b^6 - 12*a^19*b^4*c + 48*a^20*b^2*c^2 - 64*a^21*c^3)))/(a^9*b^4 - 8*a^10*b^2*c + 16*a^11*c^2)))*sqrt(sqrt(1/2)*sqrt(-(b^9 - 9*a*b^7*c + 27*a^2*b^5*c^2 - 30*a^3*b^3*c^3 + 9*a^4*b*c^4 - (a^9*b^4 - 8*a^10*b^2*c + 16*a^11*c^2)*sqrt((b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)/(a^18*b^6 - 12*a^19*b^4*c + 48*a^20*b^2*c^2 - 64*a^21*c^3)))/(a^9*b^4 - 8*a^10*b^2*c + 16*a^11*c^2))) - (b^19*c^7 - 18*a*b^17*c^8 + 135*a^2*b^15*c^9 - 546*a^3*b^13*c^10 + 1287*a^4*b^11*c^11 - 1782*a^5*b^9*c^12 + 1386*a^6*b^7*c^13 - 540*a^7*b^5*c^14 + 81*a^8*b^3*c^15 - 4*a^9*b*c^16 + (a^9*b^14*c^7 - 17*a^10*b^12*c^8 + 117*a^11*b^10*c^9 - 416*a^12*b^8*c^10 + 805*a^13*b^6*c^11 - 810*a^14*b^4*c^12 + 352*a^15*b^2*c^13 - 32*a^16*c^14)*sqrt((b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)/(a^18*b^6 - 12*a^19*b^4*c + 48*a^20*b^2*c^2 - 64*a^21*c^3)))*sqrt(x)*sqrt(sqrt(1/2)*sqrt(-(b^9 - 9*a*b^7*c + 27*a^2*b^5*c^2 - 30*a^3*b^3*c^3 + 9*a^4*b*c^4 - (a^9*b^4 - 8*a^10*b^2*c + 16*a^11*c^2)*sqrt((b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)/(a^18*b^6 - 12*a^19*b^4*c + 48*a^20*b^2*c^2 - 64*a^21*c^3)))/(a^9*b^4 - 8*a^10*b^2*c + 16*a^11*c^2))))/(b^16*c^9 - 14*a*b^14*c^10 + 79*a^2*b^12*c^11 - 230*a^3*b^10*c^12 + 367*a^4*b^8*c^13 - 314*a^5*b^6*c^14 + 130*a^6*b^4*c^15 - 20*a^7*b^2*c^16 + a^8*c^17)) - 5*a^2*x^3*sqrt(sqrt(1/2)*sqrt(-(b^9 - 9*a*b^7*c + 27*a^2*b^5*c^2 - 30*a^3*b^3*c^3 + 9*a^4*b*c^4 + (a^9*b^4 - 8*a^10*b^2*c + 16*a^11*c^2)*sqrt((b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)/(a^18*b^6 - 12*a^19*b^4*c + 48*a^20*b^2*c^2 - 64*a^21*c^3)))/(a^9*b^4 - 8*a^10*b^2*c + 16*a^11*c^2)))*log(1/2*sqrt(1/2)*(b^18 - 20*a*b^16*c + 168*a^2*b^14*c^2 - 768*a^3*b^12*c^3 + 2068*a^4*b^10*c^4 - 3312*a^5*b^8*c^5 + 3024*a^6*b^6*c^6 - 1409*a^7*b^4*c^7 + 264*a^8*b^2*c^8 - 16*a^9*c^9 - (a^9*b^13 - 19*a^10*b^11*c + 146*a^11*b^9*c^2 - 575*a^12*b^7*c^3 + 1204*a^13*b^5*c^4 - 1232*a^14*b^3*c^5 + 448*a^15*b*c^6)*sqrt((b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)/(a^18*b^6 - 12*a^19*b^4*c + 48*a^20*b^2*c^2 - 64*a^21*c^3)))*sqrt(sqrt(1/2)*sqrt(-(b^9 - 9*a*b^7*c + 27*a^2*b^5*c^2 - 30*a^3*b^3*c^3 + 9*a^4*b*c^4 + (a^9*b^4 - 8*a^10*b^2*c + 16*a^11*c^2)*sqrt((b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)/(a^18*b^6 - 12*a^19*b^4*c + 48*a^20*b^2*c^2 - 64*a^21*c^3)))/(a^9*b^4 - 8*a^10*b^2*c + 16*a^11*c^2)))*sqrt(-(b^9 - 9*a*b^7*c + 27*a^2*b^5*c^2 - 30*a^3*b^3*c^3 + 9*a^4*b*c^4 + (a^9*b^4 - 8*a^10*b^2*c + 16*a^11*c^2)*sqrt((b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)/(a^18*b^6 - 12*a^19*b^4*c + 48*a^20*b^2*c^2 - 64*a^21*c^3)))/(a^9*b^4 - 8*a^10*b^2*c + 16*a^11*c^2)) + (b^8*c^7 - 7*a*b^6*c^8 + 15*a^2*b^4*c^9 - 10*a^3*b^2*c^10 + a^4*c^11)*sqrt(x)) + 5*a^2*x^3*sqrt(sqrt(1/2)*sqrt(-(b^9 - 9*a*b^7*c + 27*a^2*b^5*c^2 - 30*a^3*b^3*c^3 + 9*a^4*b*c^4 + (a^9*b^4 - 8*a^10*b^2*c + 16*a^11*c^2)*sqrt((b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)/(a^18*b^6 - 12*a^19*b^4*c + 48*a^20*b^2*c^2 - 64*a^21*c^3)))/(a^9*b^4 - 8*a^10*b^2*c + 16*a^11*c^2)))*log(-1/2*sqrt(1/2)*(b^18 - 20*a*b^16*c + 168*a^2*b^14*c^2 - 768*a^3*b^12*c^3 + 2068*a^4*b^10*c^4 - 3312*a^5*b^8*c^5 + 3024*a^6*b^6*c^6 - 1409*a^7*b^4*c^7 + 264*a^8*b^2*c^8 - 16*a^9*c^9 - (a^9*b^13 - 19*a^10*b^11*c + 146*a^11*b^9*c^2 - 575*a^12*b^7*c^3 + 1204*a^13*b^5*c^4 - 1232*a^14*b^3*c^5 + 448*a^15*b*c^6)*sqrt((b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)/(a^18*b^6 - 12*a^19*b^4*c + 48*a^20*b^2*c^2 - 64*a^21*c^3)))*sqrt(sqrt(1/2)*sqrt(-(b^9 - 9*a*b^7*c + 27*a^2*b^5*c^2 - 30*a^3*b^3*c^3 + 9*a^4*b*c^4 + (a^9*b^4 - 8*a^10*b^2*c + 16*a^11*c^2)*sqrt((b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)/(a^18*b^6 - 12*a^19*b^4*c + 48*a^20*b^2*c^2 - 64*a^21*c^3)))/(a^9*b^4 - 8*a^10*b^2*c + 16*a^11*c^2)))*sqrt(-(b^9 - 9*a*b^7*c + 27*a^2*b^5*c^2 - 30*a^3*b^3*c^3 + 9*a^4*b*c^4 + (a^9*b^4 - 8*a^10*b^2*c + 16*a^11*c^2)*sqrt((b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)/(a^18*b^6 - 12*a^19*b^4*c + 48*a^20*b^2*c^2 - 64*a^21*c^3)))/(a^9*b^4 - 8*a^10*b^2*c + 16*a^11*c^2)) + (b^8*c^7 - 7*a*b^6*c^8 + 15*a^2*b^4*c^9 - 10*a^3*b^2*c^10 + a^4*c^11)*sqrt(x)) - 5*a^2*x^3*sqrt(sqrt(1/2)*sqrt(-(b^9 - 9*a*b^7*c + 27*a^2*b^5*c^2 - 30*a^3*b^3*c^3 + 9*a^4*b*c^4 - (a^9*b^4 - 8*a^10*b^2*c + 16*a^11*c^2)*sqrt((b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)/(a^18*b^6 - 12*a^19*b^4*c + 48*a^20*b^2*c^2 - 64*a^21*c^3)))/(a^9*b^4 - 8*a^10*b^2*c + 16*a^11*c^2)))*log(1/2*sqrt(1/2)*(b^18 - 20*a*b^16*c + 168*a^2*b^14*c^2 - 768*a^3*b^12*c^3 + 2068*a^4*b^10*c^4 - 3312*a^5*b^8*c^5 + 3024*a^6*b^6*c^6 - 1409*a^7*b^4*c^7 + 264*a^8*b^2*c^8 - 16*a^9*c^9 + (a^9*b^13 - 19*a^10*b^11*c + 146*a^11*b^9*c^2 - 575*a^12*b^7*c^3 + 1204*a^13*b^5*c^4 - 1232*a^14*b^3*c^5 + 448*a^15*b*c^6)*sqrt((b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)/(a^18*b^6 - 12*a^19*b^4*c + 48*a^20*b^2*c^2 - 64*a^21*c^3)))*sqrt(sqrt(1/2)*sqrt(-(b^9 - 9*a*b^7*c + 27*a^2*b^5*c^2 - 30*a^3*b^3*c^3 + 9*a^4*b*c^4 - (a^9*b^4 - 8*a^10*b^2*c + 16*a^11*c^2)*sqrt((b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)/(a^18*b^6 - 12*a^19*b^4*c + 48*a^20*b^2*c^2 - 64*a^21*c^3)))/(a^9*b^4 - 8*a^10*b^2*c + 16*a^11*c^2)))*sqrt(-(b^9 - 9*a*b^7*c + 27*a^2*b^5*c^2 - 30*a^3*b^3*c^3 + 9*a^4*b*c^4 - (a^9*b^4 - 8*a^10*b^2*c + 16*a^11*c^2)*sqrt((b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)/(a^18*b^6 - 12*a^19*b^4*c + 48*a^20*b^2*c^2 - 64*a^21*c^3)))/(a^9*b^4 - 8*a^10*b^2*c + 16*a^11*c^2)) + (b^8*c^7 - 7*a*b^6*c^8 + 15*a^2*b^4*c^9 - 10*a^3*b^2*c^10 + a^4*c^11)*sqrt(x)) + 5*a^2*x^3*sqrt(sqrt(1/2)*sqrt(-(b^9 - 9*a*b^7*c + 27*a^2*b^5*c^2 - 30*a^3*b^3*c^3 + 9*a^4*b*c^4 - (a^9*b^4 - 8*a^10*b^2*c + 16*a^11*c^2)*sqrt((b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)/(a^18*b^6 - 12*a^19*b^4*c + 48*a^20*b^2*c^2 - 64*a^21*c^3)))/(a^9*b^4 - 8*a^10*b^2*c + 16*a^11*c^2)))*log(-1/2*sqrt(1/2)*(b^18 - 20*a*b^16*c + 168*a^2*b^14*c^2 - 768*a^3*b^12*c^3 + 2068*a^4*b^10*c^4 - 3312*a^5*b^8*c^5 + 3024*a^6*b^6*c^6 - 1409*a^7*b^4*c^7 + 264*a^8*b^2*c^8 - 16*a^9*c^9 + (a^9*b^13 - 19*a^10*b^11*c + 146*a^11*b^9*c^2 - 575*a^12*b^7*c^3 + 1204*a^13*b^5*c^4 - 1232*a^14*b^3*c^5 + 448*a^15*b*c^6)*sqrt((b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)/(a^18*b^6 - 12*a^19*b^4*c + 48*a^20*b^2*c^2 - 64*a^21*c^3)))*sqrt(sqrt(1/2)*sqrt(-(b^9 - 9*a*b^7*c + 27*a^2*b^5*c^2 - 30*a^3*b^3*c^3 + 9*a^4*b*c^4 - (a^9*b^4 - 8*a^10*b^2*c + 16*a^11*c^2)*sqrt((b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)/(a^18*b^6 - 12*a^19*b^4*c + 48*a^20*b^2*c^2 - 64*a^21*c^3)))/(a^9*b^4 - 8*a^10*b^2*c + 16*a^11*c^2)))*sqrt(-(b^9 - 9*a*b^7*c + 27*a^2*b^5*c^2 - 30*a^3*b^3*c^3 + 9*a^4*b*c^4 - (a^9*b^4 - 8*a^10*b^2*c + 16*a^11*c^2)*sqrt((b^16 - 14*a*b^14*c + 79*a^2*b^12*c^2 - 230*a^3*b^10*c^3 + 367*a^4*b^8*c^4 - 314*a^5*b^6*c^5 + 130*a^6*b^4*c^6 - 20*a^7*b^2*c^7 + a^8*c^8)/(a^18*b^6 - 12*a^19*b^4*c + 48*a^20*b^2*c^2 - 64*a^21*c^3)))/(a^9*b^4 - 8*a^10*b^2*c + 16*a^11*c^2)) + (b^8*c^7 - 7*a*b^6*c^8 + 15*a^2*b^4*c^9 - 10*a^3*b^2*c^10 + a^4*c^11)*sqrt(x)) + 4*(5*b*x^2 - a)*sqrt(x))/(a^2*x^3)","B",0
1071,-1,0,0,0.000000," ","integrate(x^(13/2)/(c*x^4+b*x^2+a)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1072,1,11906,0,75.662427," ","integrate(x^(11/2)/(c*x^4+b*x^2+a)^2,x, algorithm=""fricas"")","-\frac{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)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{9} - 45 \, a b^{7} c + 765 \, a^{2} b^{5} c^{2} - 5880 \, a^{3} b^{3} c^{3} + 18000 \, a^{4} b c^{4} + {\left(b^{12} c^{5} - 24 \, a b^{10} c^{6} + 240 \, a^{2} b^{8} c^{7} - 1280 \, a^{3} b^{6} c^{8} + 3840 \, a^{4} b^{4} c^{9} - 6144 \, a^{5} b^{2} c^{10} + 4096 \, a^{6} c^{11}\right)} \sqrt{\frac{b^{12} - 78 \, a b^{10} c + 2571 \, a^{2} b^{8} c^{2} - 45950 \, a^{3} b^{6} c^{3} + 470625 \, a^{4} b^{4} c^{4} - 2625000 \, a^{5} b^{2} c^{5} + 6250000 \, a^{6} c^{6}}{b^{18} c^{10} - 36 \, a b^{16} c^{11} + 576 \, a^{2} b^{14} c^{12} - 5376 \, a^{3} b^{12} c^{13} + 32256 \, a^{4} b^{10} c^{14} - 129024 \, a^{5} b^{8} c^{15} + 344064 \, a^{6} b^{6} c^{16} - 589824 \, a^{7} b^{4} c^{17} + 589824 \, a^{8} b^{2} c^{18} - 262144 \, a^{9} c^{19}}}}{b^{12} c^{5} - 24 \, a b^{10} c^{6} + 240 \, a^{2} b^{8} c^{7} - 1280 \, a^{3} b^{6} c^{8} + 3840 \, a^{4} b^{4} c^{9} - 6144 \, a^{5} b^{2} c^{10} + 4096 \, a^{6} c^{11}}}} \arctan\left(-\frac{{\left(\sqrt{\frac{1}{2}} {\left(b^{22} - 91 \, a b^{20} c + 3683 \, a^{2} b^{18} c^{2} - 87230 \, a^{3} b^{16} c^{3} + 1338850 \, a^{4} b^{14} c^{4} - 13940024 \, a^{5} b^{12} c^{5} + 100253344 \, a^{6} b^{10} c^{6} - 497651072 \, a^{7} b^{8} c^{7} + 1672046080 \, a^{8} b^{6} c^{8} - 3627264000 \, a^{9} b^{4} c^{9} + 4582400000 \, a^{10} b^{2} c^{10} - 2560000000 \, a^{11} c^{11} - {\left(b^{25} c^{5} - 70 \, a b^{23} c^{6} + 2192 \, a^{2} b^{21} c^{7} - 40672 \, a^{3} b^{19} c^{8} + 498432 \, a^{4} b^{17} c^{9} - 4254720 \, a^{5} b^{15} c^{10} + 25976832 \, a^{6} b^{13} c^{11} - 114475008 \, a^{7} b^{11} c^{12} + 361955328 \, a^{8} b^{9} c^{13} - 802029568 \, a^{9} b^{7} c^{14} + 1183842304 \, a^{10} b^{5} c^{15} - 1046478848 \, a^{11} b^{3} c^{16} + 419430400 \, a^{12} b c^{17}\right)} \sqrt{\frac{b^{12} - 78 \, a b^{10} c + 2571 \, a^{2} b^{8} c^{2} - 45950 \, a^{3} b^{6} c^{3} + 470625 \, a^{4} b^{4} c^{4} - 2625000 \, a^{5} b^{2} c^{5} + 6250000 \, a^{6} c^{6}}{b^{18} c^{10} - 36 \, a b^{16} c^{11} + 576 \, a^{2} b^{14} c^{12} - 5376 \, a^{3} b^{12} c^{13} + 32256 \, a^{4} b^{10} c^{14} - 129024 \, a^{5} b^{8} c^{15} + 344064 \, a^{6} b^{6} c^{16} - 589824 \, a^{7} b^{4} c^{17} + 589824 \, a^{8} b^{2} c^{18} - 262144 \, a^{9} c^{19}}}\right)} \sqrt{{\left(81 \, a^{2} b^{16} - 8118 \, a^{3} b^{14} c + 358651 \, a^{4} b^{12} c^{2} - 9129750 \, a^{5} b^{10} c^{3} + 146540625 \, a^{6} b^{8} c^{4} - 1519250000 \, a^{7} b^{6} c^{5} + 9937500000 \, a^{8} b^{4} c^{6} - 37500000000 \, a^{9} b^{2} c^{7} + 62500000000 \, a^{10} c^{8}\right)} x + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{22} - 112 \, a b^{20} c + 5735 \, a^{2} b^{18} c^{2} - 176820 \, a^{3} b^{16} c^{3} + 3634845 \, a^{4} b^{14} c^{4} - 52073994 \, a^{5} b^{12} c^{5} + 527503968 \, a^{6} b^{10} c^{6} - 3751826400 \, a^{7} b^{8} c^{7} + 18208800000 \, a^{8} b^{6} c^{8} - 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45 \, a b^{7} c + 765 \, a^{2} b^{5} c^{2} - 5880 \, a^{3} b^{3} c^{3} + 18000 \, a^{4} b c^{4} + {\left(b^{12} c^{5} - 24 \, a b^{10} c^{6} + 240 \, a^{2} b^{8} c^{7} - 1280 \, a^{3} b^{6} c^{8} + 3840 \, a^{4} b^{4} c^{9} - 6144 \, a^{5} b^{2} c^{10} + 4096 \, a^{6} c^{11}\right)} \sqrt{\frac{b^{12} - 78 \, a b^{10} c + 2571 \, a^{2} b^{8} c^{2} - 45950 \, a^{3} b^{6} c^{3} + 470625 \, a^{4} b^{4} c^{4} - 2625000 \, a^{5} b^{2} c^{5} + 6250000 \, a^{6} c^{6}}{b^{18} c^{10} - 36 \, a b^{16} c^{11} + 576 \, a^{2} b^{14} c^{12} - 5376 \, a^{3} b^{12} c^{13} + 32256 \, a^{4} b^{10} c^{14} - 129024 \, a^{5} b^{8} c^{15} + 344064 \, a^{6} b^{6} c^{16} - 589824 \, a^{7} b^{4} c^{17} + 589824 \, a^{8} b^{2} c^{18} - 262144 \, a^{9} c^{19}}}}{b^{12} c^{5} - 24 \, a b^{10} c^{6} + 240 \, a^{2} b^{8} c^{7} - 1280 \, a^{3} b^{6} c^{8} + 3840 \, a^{4} b^{4} c^{9} - 6144 \, a^{5} b^{2} c^{10} + 4096 \, a^{6} c^{11}}}} \sqrt{-\frac{b^{9} - 45 \, a b^{7} c + 765 \, a^{2} b^{5} c^{2} - 5880 \, a^{3} b^{3} c^{3} + 18000 \, a^{4} b c^{4} + {\left(b^{12} c^{5} - 24 \, a b^{10} c^{6} + 240 \, a^{2} b^{8} c^{7} - 1280 \, a^{3} b^{6} c^{8} + 3840 \, a^{4} b^{4} c^{9} - 6144 \, a^{5} b^{2} c^{10} + 4096 \, a^{6} c^{11}\right)} \sqrt{\frac{b^{12} - 78 \, a b^{10} c + 2571 \, a^{2} b^{8} c^{2} - 45950 \, a^{3} b^{6} c^{3} + 470625 \, a^{4} b^{4} c^{4} - 2625000 \, a^{5} b^{2} c^{5} + 6250000 \, a^{6} c^{6}}{b^{18} c^{10} - 36 \, a b^{16} c^{11} + 576 \, a^{2} b^{14} c^{12} - 5376 \, a^{3} b^{12} c^{13} + 32256 \, a^{4} b^{10} c^{14} - 129024 \, a^{5} b^{8} c^{15} + 344064 \, a^{6} b^{6} c^{16} - 589824 \, a^{7} b^{4} c^{17} + 589824 \, a^{8} b^{2} c^{18} - 262144 \, a^{9} c^{19}}}}{b^{12} c^{5} - 24 \, a b^{10} c^{6} + 240 \, a^{2} b^{8} c^{7} - 1280 \, a^{3} b^{6} c^{8} + 3840 \, a^{4} b^{4} c^{9} - 6144 \, a^{5} b^{2} c^{10} + 4096 \, a^{6} c^{11}}} - \sqrt{\frac{1}{2}} {\left(9 \, a b^{30} - 1270 \, a^{2} b^{28} c + 82813 \, a^{3} b^{26} c^{2} - 3305978 \, a^{4} b^{24} c^{3} + 90231255 \, a^{5} b^{22} c^{4} - 1780615316 \, a^{6} b^{20} c^{5} + 26199812170 \, a^{7} b^{18} c^{6} - 292147074792 \, a^{8} b^{16} c^{7} + 2484388440192 \, a^{9} b^{14} c^{8} - 16082985454080 \, a^{10} b^{12} c^{9} + 78485701504000 \, a^{11} b^{10} c^{10} - 283191078400000 \, a^{12} b^{8} c^{11} + 730734080000000 \, a^{13} b^{6} c^{12} - 1272576000000000 \, a^{14} b^{4} c^{13} + 1337600000000000 \, a^{15} b^{2} c^{14} - 640000000000000 \, a^{16} c^{15} - {\left(9 \, a b^{33} c^{5} - 1081 \, a^{2} b^{31} c^{6} + 59923 \, a^{3} b^{29} c^{7} - 2033390 \, a^{4} b^{27} c^{8} + 47234960 \, a^{5} b^{25} c^{9} - 795781312 \, a^{6} b^{23} c^{10} + 10050046208 \, a^{7} b^{21} c^{11} - 96993186304 \, a^{8} b^{19} c^{12} + 722648002560 \, a^{9} b^{17} c^{13} - 4169749463040 \, a^{10} b^{15} c^{14} + 18574068219904 \, a^{11} b^{13} c^{15} - 63226237812736 \, a^{12} b^{11} c^{16} + 161327426306048 \, a^{13} b^{9} c^{17} - 298510607974400 \, a^{14} b^{7} c^{18} + 378064076800000 \, a^{15} b^{5} c^{19} - 293076992000000 \, a^{16} b^{3} c^{20} + 104857600000000 \, a^{17} b c^{21}\right)} \sqrt{\frac{b^{12} - 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5376 \, a^{3} b^{12} c^{13} + 32256 \, a^{4} b^{10} c^{14} - 129024 \, a^{5} b^{8} c^{15} + 344064 \, a^{6} b^{6} c^{16} - 589824 \, a^{7} b^{4} c^{17} + 589824 \, a^{8} b^{2} c^{18} - 262144 \, a^{9} c^{19}}}}{b^{12} c^{5} - 24 \, a b^{10} c^{6} + 240 \, a^{2} b^{8} c^{7} - 1280 \, a^{3} b^{6} c^{8} + 3840 \, a^{4} b^{4} c^{9} - 6144 \, a^{5} b^{2} c^{10} + 4096 \, a^{6} c^{11}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{9} - 45 \, a b^{7} c + 765 \, a^{2} b^{5} c^{2} - 5880 \, a^{3} b^{3} c^{3} + 18000 \, a^{4} b c^{4} + {\left(b^{12} c^{5} - 24 \, a b^{10} c^{6} + 240 \, a^{2} b^{8} c^{7} - 1280 \, a^{3} b^{6} c^{8} + 3840 \, a^{4} b^{4} c^{9} - 6144 \, a^{5} b^{2} c^{10} + 4096 \, a^{6} c^{11}\right)} \sqrt{\frac{b^{12} - 78 \, a b^{10} c + 2571 \, a^{2} b^{8} c^{2} - 45950 \, a^{3} b^{6} c^{3} + 470625 \, a^{4} b^{4} c^{4} - 2625000 \, a^{5} b^{2} c^{5} + 6250000 \, a^{6} c^{6}}{b^{18} c^{10} - 36 \, a b^{16} c^{11} + 576 \, a^{2} b^{14} c^{12} - 5376 \, a^{3} b^{12} c^{13} + 32256 \, a^{4} b^{10} c^{14} - 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{\left(b^{12} c^{5} - 24 \, a b^{10} c^{6} + 240 \, a^{2} b^{8} c^{7} - 1280 \, a^{3} b^{6} c^{8} + 3840 \, a^{4} b^{4} c^{9} - 6144 \, a^{5} b^{2} c^{10} + 4096 \, a^{6} c^{11}\right)} \sqrt{\frac{b^{12} - 78 \, a b^{10} c + 2571 \, a^{2} b^{8} c^{2} - 45950 \, a^{3} b^{6} c^{3} + 470625 \, a^{4} b^{4} c^{4} - 2625000 \, a^{5} b^{2} c^{5} + 6250000 \, a^{6} c^{6}}{b^{18} c^{10} - 36 \, a b^{16} c^{11} + 576 \, a^{2} b^{14} c^{12} - 5376 \, a^{3} b^{12} c^{13} + 32256 \, a^{4} b^{10} c^{14} - 129024 \, a^{5} b^{8} c^{15} + 344064 \, a^{6} b^{6} c^{16} - 589824 \, a^{7} b^{4} c^{17} + 589824 \, a^{8} b^{2} c^{18} - 262144 \, a^{9} c^{19}}}}{b^{12} c^{5} - 24 \, a b^{10} c^{6} + 240 \, a^{2} b^{8} c^{7} - 1280 \, a^{3} b^{6} c^{8} + 3840 \, a^{4} b^{4} c^{9} - 6144 \, a^{5} b^{2} c^{10} + 4096 \, a^{6} c^{11}}}} \arctan\left(\frac{\sqrt{\frac{1}{2}} {\left(b^{22} - 91 \, a b^{20} c + 3683 \, a^{2} b^{18} c^{2} - 87230 \, a^{3} b^{16} c^{3} + 1338850 \, a^{4} b^{14} c^{4} - 13940024 \, a^{5} b^{12} c^{5} + 100253344 \, a^{6} b^{10} c^{6} - 497651072 \, a^{7} b^{8} c^{7} + 1672046080 \, a^{8} b^{6} c^{8} - 3627264000 \, a^{9} b^{4} c^{9} + 4582400000 \, a^{10} b^{2} c^{10} - 2560000000 \, a^{11} c^{11} + {\left(b^{25} c^{5} - 70 \, a b^{23} c^{6} + 2192 \, a^{2} b^{21} c^{7} - 40672 \, a^{3} b^{19} c^{8} + 498432 \, a^{4} b^{17} c^{9} - 4254720 \, a^{5} b^{15} c^{10} + 25976832 \, a^{6} b^{13} c^{11} - 114475008 \, a^{7} b^{11} c^{12} + 361955328 \, a^{8} b^{9} c^{13} - 802029568 \, a^{9} b^{7} c^{14} + 1183842304 \, a^{10} b^{5} c^{15} - 1046478848 \, a^{11} b^{3} c^{16} + 419430400 \, a^{12} b c^{17}\right)} \sqrt{\frac{b^{12} - 78 \, a b^{10} c + 2571 \, a^{2} b^{8} c^{2} - 45950 \, a^{3} b^{6} c^{3} + 470625 \, a^{4} b^{4} c^{4} - 2625000 \, a^{5} b^{2} c^{5} + 6250000 \, a^{6} c^{6}}{b^{18} c^{10} - 36 \, a b^{16} c^{11} + 576 \, a^{2} b^{14} c^{12} - 5376 \, a^{3} b^{12} c^{13} + 32256 \, a^{4} b^{10} c^{14} - 129024 \, a^{5} b^{8} c^{15} + 344064 \, a^{6} b^{6} c^{16} - 589824 \, a^{7} b^{4} c^{17} + 589824 \, a^{8} b^{2} c^{18} - 262144 \, a^{9} c^{19}}}\right)} \sqrt{{\left(81 \, a^{2} b^{16} - 8118 \, a^{3} b^{14} c + 358651 \, a^{4} b^{12} c^{2} - 9129750 \, a^{5} b^{10} c^{3} + 146540625 \, a^{6} b^{8} c^{4} - 1519250000 \, a^{7} b^{6} c^{5} + 9937500000 \, a^{8} b^{4} c^{6} - 37500000000 \, a^{9} b^{2} c^{7} + 62500000000 \, a^{10} c^{8}\right)} x + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{22} - 112 \, a b^{20} c + 5735 \, a^{2} b^{18} c^{2} - 176820 \, a^{3} b^{16} c^{3} + 3634845 \, a^{4} b^{14} c^{4} - 52073994 \, a^{5} b^{12} c^{5} + 527503968 \, a^{6} b^{10} c^{6} - 3751826400 \, a^{7} b^{8} c^{7} + 18208800000 \, a^{8} b^{6} c^{8} - 56920000000 \, a^{9} b^{4} c^{9} + 102400000000 \, a^{10} b^{2} c^{10} - 80000000000 \, a^{11} c^{11} + {\left(b^{25} c^{5} - 91 \, a b^{23} c^{6} + 3641 \, a^{2} b^{21} c^{7} - 84776 \, a^{3} b^{19} c^{8} + 1280016 \, a^{4} b^{17} c^{9} - 13215744 \, a^{5} b^{15} c^{10} + 95875584 \, a^{6} b^{13} c^{11} - 493891584 \, a^{7} b^{11} c^{12} + 1798938624 \, a^{8} b^{9} c^{13} - 4533059584 \, a^{9} b^{7} c^{14} + 7523860480 \, a^{10} b^{5} c^{15} - 7405568000 \, a^{11} b^{3} c^{16} + 3276800000 \, a^{12} b c^{17}\right)} \sqrt{\frac{b^{12} - 78 \, a b^{10} c + 2571 \, a^{2} b^{8} c^{2} - 45950 \, a^{3} b^{6} c^{3} + 470625 \, a^{4} b^{4} c^{4} - 2625000 \, a^{5} b^{2} c^{5} + 6250000 \, a^{6} c^{6}}{b^{18} c^{10} - 36 \, a b^{16} c^{11} + 576 \, a^{2} b^{14} c^{12} - 5376 \, a^{3} b^{12} c^{13} + 32256 \, a^{4} b^{10} c^{14} - 129024 \, a^{5} b^{8} c^{15} + 344064 \, a^{6} b^{6} c^{16} - 589824 \, a^{7} b^{4} c^{17} + 589824 \, a^{8} b^{2} c^{18} - 262144 \, a^{9} c^{19}}}\right)} \sqrt{-\frac{b^{9} - 45 \, a b^{7} c + 765 \, a^{2} b^{5} c^{2} - 5880 \, a^{3} b^{3} c^{3} + 18000 \, a^{4} b c^{4} - {\left(b^{12} c^{5} - 24 \, a b^{10} c^{6} + 240 \, a^{2} b^{8} c^{7} - 1280 \, a^{3} b^{6} c^{8} + 3840 \, a^{4} b^{4} c^{9} - 6144 \, a^{5} b^{2} c^{10} + 4096 \, a^{6} c^{11}\right)} \sqrt{\frac{b^{12} - 78 \, a b^{10} c + 2571 \, a^{2} b^{8} c^{2} - 45950 \, a^{3} b^{6} c^{3} + 470625 \, a^{4} b^{4} c^{4} - 2625000 \, a^{5} b^{2} c^{5} + 6250000 \, a^{6} c^{6}}{b^{18} c^{10} - 36 \, a b^{16} c^{11} + 576 \, a^{2} b^{14} c^{12} - 5376 \, a^{3} b^{12} c^{13} + 32256 \, a^{4} b^{10} c^{14} - 129024 \, a^{5} b^{8} c^{15} + 344064 \, a^{6} b^{6} c^{16} - 589824 \, a^{7} b^{4} c^{17} + 589824 \, a^{8} b^{2} c^{18} - 262144 \, a^{9} c^{19}}}}{b^{12} c^{5} - 24 \, a b^{10} c^{6} + 240 \, a^{2} b^{8} c^{7} - 1280 \, a^{3} b^{6} c^{8} + 3840 \, a^{4} b^{4} c^{9} - 6144 \, a^{5} b^{2} c^{10} + 4096 \, a^{6} c^{11}}}} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{9} - 45 \, a b^{7} c + 765 \, a^{2} b^{5} c^{2} - 5880 \, a^{3} b^{3} c^{3} + 18000 \, a^{4} b c^{4} - {\left(b^{12} c^{5} - 24 \, a b^{10} c^{6} + 240 \, a^{2} b^{8} c^{7} - 1280 \, a^{3} b^{6} c^{8} + 3840 \, a^{4} b^{4} c^{9} - 6144 \, a^{5} b^{2} c^{10} + 4096 \, a^{6} c^{11}\right)} \sqrt{\frac{b^{12} - 78 \, a b^{10} c + 2571 \, a^{2} b^{8} c^{2} - 45950 \, a^{3} b^{6} c^{3} + 470625 \, a^{4} b^{4} c^{4} - 2625000 \, a^{5} b^{2} c^{5} + 6250000 \, a^{6} c^{6}}{b^{18} c^{10} - 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24 \, a b^{10} c^{6} + 240 \, a^{2} b^{8} c^{7} - 1280 \, a^{3} b^{6} c^{8} + 3840 \, a^{4} b^{4} c^{9} - 6144 \, a^{5} b^{2} c^{10} + 4096 \, a^{6} c^{11}}}}\right) - {\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{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{9} - 45 \, a b^{7} c + 765 \, a^{2} b^{5} c^{2} - 5880 \, a^{3} b^{3} c^{3} + 18000 \, a^{4} b c^{4} - {\left(b^{12} c^{5} - 24 \, a b^{10} c^{6} + 240 \, a^{2} b^{8} c^{7} - 1280 \, a^{3} b^{6} c^{8} + 3840 \, a^{4} b^{4} c^{9} - 6144 \, a^{5} b^{2} c^{10} + 4096 \, a^{6} c^{11}\right)} \sqrt{\frac{b^{12} - 78 \, a b^{10} c + 2571 \, a^{2} b^{8} c^{2} - 45950 \, a^{3} b^{6} c^{3} + 470625 \, a^{4} b^{4} c^{4} - 2625000 \, a^{5} b^{2} c^{5} + 6250000 \, a^{6} c^{6}}{b^{18} c^{10} - 36 \, a b^{16} c^{11} + 576 \, a^{2} b^{14} c^{12} - 5376 \, a^{3} b^{12} c^{13} + 32256 \, a^{4} b^{10} c^{14} - 129024 \, a^{5} b^{8} c^{15} + 344064 \, a^{6} b^{6} c^{16} - 589824 \, a^{7} b^{4} c^{17} + 589824 \, a^{8} b^{2} c^{18} - 262144 \, a^{9} c^{19}}}}{b^{12} c^{5} - 24 \, a b^{10} c^{6} + 240 \, a^{2} b^{8} c^{7} - 1280 \, a^{3} b^{6} c^{8} + 3840 \, a^{4} b^{4} c^{9} - 6144 \, a^{5} b^{2} c^{10} + 4096 \, a^{6} c^{11}}}} \log\left({\left(9 \, a b^{8} - 451 \, a^{2} b^{6} c + 8625 \, a^{3} b^{4} c^{2} - 75000 \, a^{4} b^{2} c^{3} + 250000 \, a^{5} c^{4}\right)} \sqrt{x} + \frac{1}{2} \, {\left(b^{11} - 47 \, a b^{9} c + 853 \, a^{2} b^{7} c^{2} - 7324 \, a^{3} b^{5} c^{3} + 28400 \, a^{4} b^{3} c^{4} - 40000 \, a^{5} b c^{5} + {\left(b^{14} c^{5} - 44 \, a b^{12} c^{6} + 720 \, a^{2} b^{10} c^{7} - 6080 \, a^{3} b^{8} c^{8} + 29440 \, a^{4} b^{6} c^{9} - 82944 \, a^{5} b^{4} c^{10} + 126976 \, a^{6} b^{2} c^{11} - 81920 \, a^{7} c^{12}\right)} \sqrt{\frac{b^{12} - 78 \, a b^{10} c + 2571 \, a^{2} b^{8} c^{2} - 45950 \, a^{3} b^{6} c^{3} + 470625 \, a^{4} b^{4} c^{4} - 2625000 \, a^{5} b^{2} c^{5} + 6250000 \, a^{6} c^{6}}{b^{18} c^{10} - 36 \, a b^{16} c^{11} + 576 \, a^{2} b^{14} c^{12} - 5376 \, a^{3} b^{12} c^{13} + 32256 \, a^{4} b^{10} c^{14} - 129024 \, a^{5} b^{8} c^{15} + 344064 \, a^{6} b^{6} c^{16} - 589824 \, a^{7} b^{4} c^{17} + 589824 \, a^{8} b^{2} c^{18} - 262144 \, a^{9} c^{19}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{9} - 45 \, a b^{7} c + 765 \, a^{2} b^{5} c^{2} - 5880 \, a^{3} b^{3} c^{3} + 18000 \, a^{4} b c^{4} - {\left(b^{12} c^{5} - 24 \, a b^{10} c^{6} + 240 \, a^{2} b^{8} c^{7} - 1280 \, a^{3} b^{6} c^{8} + 3840 \, a^{4} b^{4} c^{9} - 6144 \, a^{5} b^{2} c^{10} + 4096 \, a^{6} c^{11}\right)} \sqrt{\frac{b^{12} - 78 \, a b^{10} c + 2571 \, a^{2} b^{8} c^{2} - 45950 \, a^{3} b^{6} c^{3} + 470625 \, a^{4} b^{4} c^{4} - 2625000 \, a^{5} b^{2} c^{5} + 6250000 \, a^{6} c^{6}}{b^{18} c^{10} - 36 \, a b^{16} c^{11} + 576 \, a^{2} b^{14} c^{12} - 5376 \, a^{3} b^{12} c^{13} + 32256 \, a^{4} b^{10} c^{14} - 129024 \, a^{5} b^{8} c^{15} + 344064 \, a^{6} b^{6} c^{16} - 589824 \, a^{7} b^{4} c^{17} + 589824 \, a^{8} b^{2} c^{18} - 262144 \, a^{9} c^{19}}}}{b^{12} c^{5} - 24 \, a b^{10} c^{6} + 240 \, a^{2} b^{8} c^{7} - 1280 \, a^{3} b^{6} c^{8} + 3840 \, a^{4} b^{4} c^{9} - 6144 \, a^{5} b^{2} c^{10} + 4096 \, a^{6} c^{11}}}}\right) + {\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{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{9} - 45 \, a b^{7} c + 765 \, a^{2} b^{5} c^{2} - 5880 \, a^{3} b^{3} c^{3} + 18000 \, a^{4} b c^{4} - {\left(b^{12} c^{5} - 24 \, a b^{10} c^{6} + 240 \, a^{2} b^{8} c^{7} - 1280 \, a^{3} b^{6} c^{8} + 3840 \, a^{4} b^{4} c^{9} - 6144 \, a^{5} b^{2} c^{10} + 4096 \, a^{6} c^{11}\right)} \sqrt{\frac{b^{12} - 78 \, a b^{10} c + 2571 \, a^{2} b^{8} c^{2} - 45950 \, a^{3} b^{6} c^{3} + 470625 \, a^{4} b^{4} c^{4} - 2625000 \, a^{5} b^{2} c^{5} + 6250000 \, a^{6} c^{6}}{b^{18} c^{10} - 36 \, a b^{16} c^{11} + 576 \, a^{2} b^{14} c^{12} - 5376 \, a^{3} b^{12} c^{13} + 32256 \, a^{4} b^{10} c^{14} - 129024 \, a^{5} b^{8} c^{15} + 344064 \, a^{6} b^{6} c^{16} - 589824 \, a^{7} b^{4} c^{17} + 589824 \, a^{8} b^{2} c^{18} - 262144 \, a^{9} c^{19}}}}{b^{12} c^{5} - 24 \, a b^{10} c^{6} + 240 \, a^{2} b^{8} c^{7} - 1280 \, a^{3} b^{6} c^{8} + 3840 \, a^{4} b^{4} c^{9} - 6144 \, a^{5} b^{2} c^{10} + 4096 \, a^{6} c^{11}}}} \log\left({\left(9 \, a b^{8} - 451 \, a^{2} b^{6} c + 8625 \, a^{3} b^{4} c^{2} - 75000 \, a^{4} b^{2} c^{3} + 250000 \, a^{5} c^{4}\right)} \sqrt{x} - \frac{1}{2} \, {\left(b^{11} - 47 \, a b^{9} c + 853 \, a^{2} b^{7} c^{2} - 7324 \, a^{3} b^{5} c^{3} + 28400 \, a^{4} b^{3} c^{4} - 40000 \, a^{5} b c^{5} + {\left(b^{14} c^{5} - 44 \, a b^{12} c^{6} + 720 \, a^{2} b^{10} c^{7} - 6080 \, a^{3} b^{8} c^{8} + 29440 \, a^{4} b^{6} c^{9} - 82944 \, a^{5} b^{4} c^{10} + 126976 \, a^{6} b^{2} c^{11} - 81920 \, a^{7} c^{12}\right)} \sqrt{\frac{b^{12} - 78 \, a b^{10} c + 2571 \, a^{2} b^{8} c^{2} - 45950 \, a^{3} b^{6} c^{3} + 470625 \, a^{4} b^{4} c^{4} - 2625000 \, a^{5} b^{2} c^{5} + 6250000 \, a^{6} c^{6}}{b^{18} c^{10} - 36 \, a b^{16} c^{11} + 576 \, a^{2} b^{14} c^{12} - 5376 \, a^{3} b^{12} c^{13} + 32256 \, a^{4} b^{10} c^{14} - 129024 \, a^{5} b^{8} c^{15} + 344064 \, a^{6} b^{6} c^{16} - 589824 \, a^{7} b^{4} c^{17} + 589824 \, a^{8} b^{2} c^{18} - 262144 \, a^{9} c^{19}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{9} - 45 \, a b^{7} c + 765 \, a^{2} b^{5} c^{2} - 5880 \, a^{3} b^{3} c^{3} + 18000 \, a^{4} b c^{4} - {\left(b^{12} c^{5} - 24 \, a b^{10} c^{6} + 240 \, a^{2} b^{8} c^{7} - 1280 \, a^{3} b^{6} c^{8} + 3840 \, a^{4} b^{4} c^{9} - 6144 \, a^{5} b^{2} c^{10} + 4096 \, a^{6} c^{11}\right)} \sqrt{\frac{b^{12} - 78 \, a b^{10} c + 2571 \, a^{2} b^{8} c^{2} - 45950 \, a^{3} b^{6} c^{3} + 470625 \, a^{4} b^{4} c^{4} - 2625000 \, a^{5} b^{2} c^{5} + 6250000 \, a^{6} c^{6}}{b^{18} c^{10} - 36 \, a b^{16} c^{11} + 576 \, a^{2} b^{14} c^{12} - 5376 \, a^{3} b^{12} c^{13} + 32256 \, a^{4} b^{10} c^{14} - 129024 \, a^{5} b^{8} c^{15} + 344064 \, a^{6} b^{6} c^{16} - 589824 \, a^{7} b^{4} c^{17} + 589824 \, a^{8} b^{2} c^{18} - 262144 \, a^{9} c^{19}}}}{b^{12} c^{5} - 24 \, a b^{10} c^{6} + 240 \, a^{2} b^{8} c^{7} - 1280 \, a^{3} b^{6} c^{8} + 3840 \, a^{4} b^{4} c^{9} - 6144 \, a^{5} b^{2} c^{10} + 4096 \, a^{6} c^{11}}}}\right) + 4 \, {\left({\left(b^{2} - 2 \, a c\right)} x^{2} + a b\right)} \sqrt{x}}{8 \, {\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,"-1/8*(4*((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(sqrt(1/2)*sqrt(-(b^9 - 45*a*b^7*c + 765*a^2*b^5*c^2 - 5880*a^3*b^3*c^3 + 18000*a^4*b*c^4 + (b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10 + 4096*a^6*c^11)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(b^18*c^10 - 36*a*b^16*c^11 + 576*a^2*b^14*c^12 - 5376*a^3*b^12*c^13 + 32256*a^4*b^10*c^14 - 129024*a^5*b^8*c^15 + 344064*a^6*b^6*c^16 - 589824*a^7*b^4*c^17 + 589824*a^8*b^2*c^18 - 262144*a^9*c^19)))/(b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10 + 4096*a^6*c^11)))*arctan(-1/2*(sqrt(1/2)*(b^22 - 91*a*b^20*c + 3683*a^2*b^18*c^2 - 87230*a^3*b^16*c^3 + 1338850*a^4*b^14*c^4 - 13940024*a^5*b^12*c^5 + 100253344*a^6*b^10*c^6 - 497651072*a^7*b^8*c^7 + 1672046080*a^8*b^6*c^8 - 3627264000*a^9*b^4*c^9 + 4582400000*a^10*b^2*c^10 - 2560000000*a^11*c^11 - (b^25*c^5 - 70*a*b^23*c^6 + 2192*a^2*b^21*c^7 - 40672*a^3*b^19*c^8 + 498432*a^4*b^17*c^9 - 4254720*a^5*b^15*c^10 + 25976832*a^6*b^13*c^11 - 114475008*a^7*b^11*c^12 + 361955328*a^8*b^9*c^13 - 802029568*a^9*b^7*c^14 + 1183842304*a^10*b^5*c^15 - 1046478848*a^11*b^3*c^16 + 419430400*a^12*b*c^17)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(b^18*c^10 - 36*a*b^16*c^11 + 576*a^2*b^14*c^12 - 5376*a^3*b^12*c^13 + 32256*a^4*b^10*c^14 - 129024*a^5*b^8*c^15 + 344064*a^6*b^6*c^16 - 589824*a^7*b^4*c^17 + 589824*a^8*b^2*c^18 - 262144*a^9*c^19)))*sqrt((81*a^2*b^16 - 8118*a^3*b^14*c + 358651*a^4*b^12*c^2 - 9129750*a^5*b^10*c^3 + 146540625*a^6*b^8*c^4 - 1519250000*a^7*b^6*c^5 + 9937500000*a^8*b^4*c^6 - 37500000000*a^9*b^2*c^7 + 62500000000*a^10*c^8)*x + 1/2*sqrt(1/2)*(b^22 - 112*a*b^20*c + 5735*a^2*b^18*c^2 - 176820*a^3*b^16*c^3 + 3634845*a^4*b^14*c^4 - 52073994*a^5*b^12*c^5 + 527503968*a^6*b^10*c^6 - 3751826400*a^7*b^8*c^7 + 18208800000*a^8*b^6*c^8 - 56920000000*a^9*b^4*c^9 + 102400000000*a^10*b^2*c^10 - 80000000000*a^11*c^11 - (b^25*c^5 - 91*a*b^23*c^6 + 3641*a^2*b^21*c^7 - 84776*a^3*b^19*c^8 + 1280016*a^4*b^17*c^9 - 13215744*a^5*b^15*c^10 + 95875584*a^6*b^13*c^11 - 493891584*a^7*b^11*c^12 + 1798938624*a^8*b^9*c^13 - 4533059584*a^9*b^7*c^14 + 7523860480*a^10*b^5*c^15 - 7405568000*a^11*b^3*c^16 + 3276800000*a^12*b*c^17)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(b^18*c^10 - 36*a*b^16*c^11 + 576*a^2*b^14*c^12 - 5376*a^3*b^12*c^13 + 32256*a^4*b^10*c^14 - 129024*a^5*b^8*c^15 + 344064*a^6*b^6*c^16 - 589824*a^7*b^4*c^17 + 589824*a^8*b^2*c^18 - 262144*a^9*c^19)))*sqrt(-(b^9 - 45*a*b^7*c + 765*a^2*b^5*c^2 - 5880*a^3*b^3*c^3 + 18000*a^4*b*c^4 + (b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10 + 4096*a^6*c^11)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(b^18*c^10 - 36*a*b^16*c^11 + 576*a^2*b^14*c^12 - 5376*a^3*b^12*c^13 + 32256*a^4*b^10*c^14 - 129024*a^5*b^8*c^15 + 344064*a^6*b^6*c^16 - 589824*a^7*b^4*c^17 + 589824*a^8*b^2*c^18 - 262144*a^9*c^19)))/(b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10 + 4096*a^6*c^11)))*sqrt(-(b^9 - 45*a*b^7*c + 765*a^2*b^5*c^2 - 5880*a^3*b^3*c^3 + 18000*a^4*b*c^4 + (b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10 + 4096*a^6*c^11)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(b^18*c^10 - 36*a*b^16*c^11 + 576*a^2*b^14*c^12 - 5376*a^3*b^12*c^13 + 32256*a^4*b^10*c^14 - 129024*a^5*b^8*c^15 + 344064*a^6*b^6*c^16 - 589824*a^7*b^4*c^17 + 589824*a^8*b^2*c^18 - 262144*a^9*c^19)))/(b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10 + 4096*a^6*c^11)) - sqrt(1/2)*(9*a*b^30 - 1270*a^2*b^28*c + 82813*a^3*b^26*c^2 - 3305978*a^4*b^24*c^3 + 90231255*a^5*b^22*c^4 - 1780615316*a^6*b^20*c^5 + 26199812170*a^7*b^18*c^6 - 292147074792*a^8*b^16*c^7 + 2484388440192*a^9*b^14*c^8 - 16082985454080*a^10*b^12*c^9 + 78485701504000*a^11*b^10*c^10 - 283191078400000*a^12*b^8*c^11 + 730734080000000*a^13*b^6*c^12 - 1272576000000000*a^14*b^4*c^13 + 1337600000000000*a^15*b^2*c^14 - 640000000000000*a^16*c^15 - (9*a*b^33*c^5 - 1081*a^2*b^31*c^6 + 59923*a^3*b^29*c^7 - 2033390*a^4*b^27*c^8 + 47234960*a^5*b^25*c^9 - 795781312*a^6*b^23*c^10 + 10050046208*a^7*b^21*c^11 - 96993186304*a^8*b^19*c^12 + 722648002560*a^9*b^17*c^13 - 4169749463040*a^10*b^15*c^14 + 18574068219904*a^11*b^13*c^15 - 63226237812736*a^12*b^11*c^16 + 161327426306048*a^13*b^9*c^17 - 298510607974400*a^14*b^7*c^18 + 378064076800000*a^15*b^5*c^19 - 293076992000000*a^16*b^3*c^20 + 104857600000000*a^17*b*c^21)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(b^18*c^10 - 36*a*b^16*c^11 + 576*a^2*b^14*c^12 - 5376*a^3*b^12*c^13 + 32256*a^4*b^10*c^14 - 129024*a^5*b^8*c^15 + 344064*a^6*b^6*c^16 - 589824*a^7*b^4*c^17 + 589824*a^8*b^2*c^18 - 262144*a^9*c^19)))*sqrt(x)*sqrt(-(b^9 - 45*a*b^7*c + 765*a^2*b^5*c^2 - 5880*a^3*b^3*c^3 + 18000*a^4*b*c^4 + (b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10 + 4096*a^6*c^11)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(b^18*c^10 - 36*a*b^16*c^11 + 576*a^2*b^14*c^12 - 5376*a^3*b^12*c^13 + 32256*a^4*b^10*c^14 - 129024*a^5*b^8*c^15 + 344064*a^6*b^6*c^16 - 589824*a^7*b^4*c^17 + 589824*a^8*b^2*c^18 - 262144*a^9*c^19)))/(b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10 + 4096*a^6*c^11)))*sqrt(sqrt(1/2)*sqrt(-(b^9 - 45*a*b^7*c + 765*a^2*b^5*c^2 - 5880*a^3*b^3*c^3 + 18000*a^4*b*c^4 + (b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10 + 4096*a^6*c^11)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(b^18*c^10 - 36*a*b^16*c^11 + 576*a^2*b^14*c^12 - 5376*a^3*b^12*c^13 + 32256*a^4*b^10*c^14 - 129024*a^5*b^8*c^15 + 344064*a^6*b^6*c^16 - 589824*a^7*b^4*c^17 + 589824*a^8*b^2*c^18 - 262144*a^9*c^19)))/(b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10 + 4096*a^6*c^11)))/(6561*a^5*b^20 - 803358*a^6*b^18*c + 44473131*a^7*b^16*c^2 - 1466261550*a^8*b^14*c^3 + 31889850625*a^9*b^12*c^4 - 478129875000*a^10*b^10*c^5 + 5004993750000*a^11*b^8*c^6 - 36117500000000*a^12*b^6*c^7 + 171937500000000*a^13*b^4*c^8 - 487500000000000*a^14*b^2*c^9 + 625000000000000*a^15*c^10)) - 4*((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(sqrt(1/2)*sqrt(-(b^9 - 45*a*b^7*c + 765*a^2*b^5*c^2 - 5880*a^3*b^3*c^3 + 18000*a^4*b*c^4 - (b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10 + 4096*a^6*c^11)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(b^18*c^10 - 36*a*b^16*c^11 + 576*a^2*b^14*c^12 - 5376*a^3*b^12*c^13 + 32256*a^4*b^10*c^14 - 129024*a^5*b^8*c^15 + 344064*a^6*b^6*c^16 - 589824*a^7*b^4*c^17 + 589824*a^8*b^2*c^18 - 262144*a^9*c^19)))/(b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10 + 4096*a^6*c^11)))*arctan(1/2*(sqrt(1/2)*(b^22 - 91*a*b^20*c + 3683*a^2*b^18*c^2 - 87230*a^3*b^16*c^3 + 1338850*a^4*b^14*c^4 - 13940024*a^5*b^12*c^5 + 100253344*a^6*b^10*c^6 - 497651072*a^7*b^8*c^7 + 1672046080*a^8*b^6*c^8 - 3627264000*a^9*b^4*c^9 + 4582400000*a^10*b^2*c^10 - 2560000000*a^11*c^11 + (b^25*c^5 - 70*a*b^23*c^6 + 2192*a^2*b^21*c^7 - 40672*a^3*b^19*c^8 + 498432*a^4*b^17*c^9 - 4254720*a^5*b^15*c^10 + 25976832*a^6*b^13*c^11 - 114475008*a^7*b^11*c^12 + 361955328*a^8*b^9*c^13 - 802029568*a^9*b^7*c^14 + 1183842304*a^10*b^5*c^15 - 1046478848*a^11*b^3*c^16 + 419430400*a^12*b*c^17)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(b^18*c^10 - 36*a*b^16*c^11 + 576*a^2*b^14*c^12 - 5376*a^3*b^12*c^13 + 32256*a^4*b^10*c^14 - 129024*a^5*b^8*c^15 + 344064*a^6*b^6*c^16 - 589824*a^7*b^4*c^17 + 589824*a^8*b^2*c^18 - 262144*a^9*c^19)))*sqrt((81*a^2*b^16 - 8118*a^3*b^14*c + 358651*a^4*b^12*c^2 - 9129750*a^5*b^10*c^3 + 146540625*a^6*b^8*c^4 - 1519250000*a^7*b^6*c^5 + 9937500000*a^8*b^4*c^6 - 37500000000*a^9*b^2*c^7 + 62500000000*a^10*c^8)*x + 1/2*sqrt(1/2)*(b^22 - 112*a*b^20*c + 5735*a^2*b^18*c^2 - 176820*a^3*b^16*c^3 + 3634845*a^4*b^14*c^4 - 52073994*a^5*b^12*c^5 + 527503968*a^6*b^10*c^6 - 3751826400*a^7*b^8*c^7 + 18208800000*a^8*b^6*c^8 - 56920000000*a^9*b^4*c^9 + 102400000000*a^10*b^2*c^10 - 80000000000*a^11*c^11 + (b^25*c^5 - 91*a*b^23*c^6 + 3641*a^2*b^21*c^7 - 84776*a^3*b^19*c^8 + 1280016*a^4*b^17*c^9 - 13215744*a^5*b^15*c^10 + 95875584*a^6*b^13*c^11 - 493891584*a^7*b^11*c^12 + 1798938624*a^8*b^9*c^13 - 4533059584*a^9*b^7*c^14 + 7523860480*a^10*b^5*c^15 - 7405568000*a^11*b^3*c^16 + 3276800000*a^12*b*c^17)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(b^18*c^10 - 36*a*b^16*c^11 + 576*a^2*b^14*c^12 - 5376*a^3*b^12*c^13 + 32256*a^4*b^10*c^14 - 129024*a^5*b^8*c^15 + 344064*a^6*b^6*c^16 - 589824*a^7*b^4*c^17 + 589824*a^8*b^2*c^18 - 262144*a^9*c^19)))*sqrt(-(b^9 - 45*a*b^7*c + 765*a^2*b^5*c^2 - 5880*a^3*b^3*c^3 + 18000*a^4*b*c^4 - (b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10 + 4096*a^6*c^11)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(b^18*c^10 - 36*a*b^16*c^11 + 576*a^2*b^14*c^12 - 5376*a^3*b^12*c^13 + 32256*a^4*b^10*c^14 - 129024*a^5*b^8*c^15 + 344064*a^6*b^6*c^16 - 589824*a^7*b^4*c^17 + 589824*a^8*b^2*c^18 - 262144*a^9*c^19)))/(b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10 + 4096*a^6*c^11)))*sqrt(sqrt(1/2)*sqrt(-(b^9 - 45*a*b^7*c + 765*a^2*b^5*c^2 - 5880*a^3*b^3*c^3 + 18000*a^4*b*c^4 - (b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10 + 4096*a^6*c^11)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(b^18*c^10 - 36*a*b^16*c^11 + 576*a^2*b^14*c^12 - 5376*a^3*b^12*c^13 + 32256*a^4*b^10*c^14 - 129024*a^5*b^8*c^15 + 344064*a^6*b^6*c^16 - 589824*a^7*b^4*c^17 + 589824*a^8*b^2*c^18 - 262144*a^9*c^19)))/(b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10 + 4096*a^6*c^11)))*sqrt(-(b^9 - 45*a*b^7*c + 765*a^2*b^5*c^2 - 5880*a^3*b^3*c^3 + 18000*a^4*b*c^4 - (b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10 + 4096*a^6*c^11)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(b^18*c^10 - 36*a*b^16*c^11 + 576*a^2*b^14*c^12 - 5376*a^3*b^12*c^13 + 32256*a^4*b^10*c^14 - 129024*a^5*b^8*c^15 + 344064*a^6*b^6*c^16 - 589824*a^7*b^4*c^17 + 589824*a^8*b^2*c^18 - 262144*a^9*c^19)))/(b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10 + 4096*a^6*c^11)) - sqrt(1/2)*(9*a*b^30 - 1270*a^2*b^28*c + 82813*a^3*b^26*c^2 - 3305978*a^4*b^24*c^3 + 90231255*a^5*b^22*c^4 - 1780615316*a^6*b^20*c^5 + 26199812170*a^7*b^18*c^6 - 292147074792*a^8*b^16*c^7 + 2484388440192*a^9*b^14*c^8 - 16082985454080*a^10*b^12*c^9 + 78485701504000*a^11*b^10*c^10 - 283191078400000*a^12*b^8*c^11 + 730734080000000*a^13*b^6*c^12 - 1272576000000000*a^14*b^4*c^13 + 1337600000000000*a^15*b^2*c^14 - 640000000000000*a^16*c^15 + (9*a*b^33*c^5 - 1081*a^2*b^31*c^6 + 59923*a^3*b^29*c^7 - 2033390*a^4*b^27*c^8 + 47234960*a^5*b^25*c^9 - 795781312*a^6*b^23*c^10 + 10050046208*a^7*b^21*c^11 - 96993186304*a^8*b^19*c^12 + 722648002560*a^9*b^17*c^13 - 4169749463040*a^10*b^15*c^14 + 18574068219904*a^11*b^13*c^15 - 63226237812736*a^12*b^11*c^16 + 161327426306048*a^13*b^9*c^17 - 298510607974400*a^14*b^7*c^18 + 378064076800000*a^15*b^5*c^19 - 293076992000000*a^16*b^3*c^20 + 104857600000000*a^17*b*c^21)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(b^18*c^10 - 36*a*b^16*c^11 + 576*a^2*b^14*c^12 - 5376*a^3*b^12*c^13 + 32256*a^4*b^10*c^14 - 129024*a^5*b^8*c^15 + 344064*a^6*b^6*c^16 - 589824*a^7*b^4*c^17 + 589824*a^8*b^2*c^18 - 262144*a^9*c^19)))*sqrt(x)*sqrt(sqrt(1/2)*sqrt(-(b^9 - 45*a*b^7*c + 765*a^2*b^5*c^2 - 5880*a^3*b^3*c^3 + 18000*a^4*b*c^4 - (b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10 + 4096*a^6*c^11)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(b^18*c^10 - 36*a*b^16*c^11 + 576*a^2*b^14*c^12 - 5376*a^3*b^12*c^13 + 32256*a^4*b^10*c^14 - 129024*a^5*b^8*c^15 + 344064*a^6*b^6*c^16 - 589824*a^7*b^4*c^17 + 589824*a^8*b^2*c^18 - 262144*a^9*c^19)))/(b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10 + 4096*a^6*c^11)))*sqrt(-(b^9 - 45*a*b^7*c + 765*a^2*b^5*c^2 - 5880*a^3*b^3*c^3 + 18000*a^4*b*c^4 - (b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10 + 4096*a^6*c^11)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(b^18*c^10 - 36*a*b^16*c^11 + 576*a^2*b^14*c^12 - 5376*a^3*b^12*c^13 + 32256*a^4*b^10*c^14 - 129024*a^5*b^8*c^15 + 344064*a^6*b^6*c^16 - 589824*a^7*b^4*c^17 + 589824*a^8*b^2*c^18 - 262144*a^9*c^19)))/(b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10 + 4096*a^6*c^11)))/(6561*a^5*b^20 - 803358*a^6*b^18*c + 44473131*a^7*b^16*c^2 - 1466261550*a^8*b^14*c^3 + 31889850625*a^9*b^12*c^4 - 478129875000*a^10*b^10*c^5 + 5004993750000*a^11*b^8*c^6 - 36117500000000*a^12*b^6*c^7 + 171937500000000*a^13*b^4*c^8 - 487500000000000*a^14*b^2*c^9 + 625000000000000*a^15*c^10)) - ((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(sqrt(1/2)*sqrt(-(b^9 - 45*a*b^7*c + 765*a^2*b^5*c^2 - 5880*a^3*b^3*c^3 + 18000*a^4*b*c^4 + (b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10 + 4096*a^6*c^11)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(b^18*c^10 - 36*a*b^16*c^11 + 576*a^2*b^14*c^12 - 5376*a^3*b^12*c^13 + 32256*a^4*b^10*c^14 - 129024*a^5*b^8*c^15 + 344064*a^6*b^6*c^16 - 589824*a^7*b^4*c^17 + 589824*a^8*b^2*c^18 - 262144*a^9*c^19)))/(b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10 + 4096*a^6*c^11)))*log((9*a*b^8 - 451*a^2*b^6*c + 8625*a^3*b^4*c^2 - 75000*a^4*b^2*c^3 + 250000*a^5*c^4)*sqrt(x) + 1/2*(b^11 - 47*a*b^9*c + 853*a^2*b^7*c^2 - 7324*a^3*b^5*c^3 + 28400*a^4*b^3*c^4 - 40000*a^5*b*c^5 - (b^14*c^5 - 44*a*b^12*c^6 + 720*a^2*b^10*c^7 - 6080*a^3*b^8*c^8 + 29440*a^4*b^6*c^9 - 82944*a^5*b^4*c^10 + 126976*a^6*b^2*c^11 - 81920*a^7*c^12)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(b^18*c^10 - 36*a*b^16*c^11 + 576*a^2*b^14*c^12 - 5376*a^3*b^12*c^13 + 32256*a^4*b^10*c^14 - 129024*a^5*b^8*c^15 + 344064*a^6*b^6*c^16 - 589824*a^7*b^4*c^17 + 589824*a^8*b^2*c^18 - 262144*a^9*c^19)))*sqrt(sqrt(1/2)*sqrt(-(b^9 - 45*a*b^7*c + 765*a^2*b^5*c^2 - 5880*a^3*b^3*c^3 + 18000*a^4*b*c^4 + (b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10 + 4096*a^6*c^11)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(b^18*c^10 - 36*a*b^16*c^11 + 576*a^2*b^14*c^12 - 5376*a^3*b^12*c^13 + 32256*a^4*b^10*c^14 - 129024*a^5*b^8*c^15 + 344064*a^6*b^6*c^16 - 589824*a^7*b^4*c^17 + 589824*a^8*b^2*c^18 - 262144*a^9*c^19)))/(b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10 + 4096*a^6*c^11)))) + ((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(sqrt(1/2)*sqrt(-(b^9 - 45*a*b^7*c + 765*a^2*b^5*c^2 - 5880*a^3*b^3*c^3 + 18000*a^4*b*c^4 + (b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10 + 4096*a^6*c^11)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(b^18*c^10 - 36*a*b^16*c^11 + 576*a^2*b^14*c^12 - 5376*a^3*b^12*c^13 + 32256*a^4*b^10*c^14 - 129024*a^5*b^8*c^15 + 344064*a^6*b^6*c^16 - 589824*a^7*b^4*c^17 + 589824*a^8*b^2*c^18 - 262144*a^9*c^19)))/(b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10 + 4096*a^6*c^11)))*log((9*a*b^8 - 451*a^2*b^6*c + 8625*a^3*b^4*c^2 - 75000*a^4*b^2*c^3 + 250000*a^5*c^4)*sqrt(x) - 1/2*(b^11 - 47*a*b^9*c + 853*a^2*b^7*c^2 - 7324*a^3*b^5*c^3 + 28400*a^4*b^3*c^4 - 40000*a^5*b*c^5 - (b^14*c^5 - 44*a*b^12*c^6 + 720*a^2*b^10*c^7 - 6080*a^3*b^8*c^8 + 29440*a^4*b^6*c^9 - 82944*a^5*b^4*c^10 + 126976*a^6*b^2*c^11 - 81920*a^7*c^12)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(b^18*c^10 - 36*a*b^16*c^11 + 576*a^2*b^14*c^12 - 5376*a^3*b^12*c^13 + 32256*a^4*b^10*c^14 - 129024*a^5*b^8*c^15 + 344064*a^6*b^6*c^16 - 589824*a^7*b^4*c^17 + 589824*a^8*b^2*c^18 - 262144*a^9*c^19)))*sqrt(sqrt(1/2)*sqrt(-(b^9 - 45*a*b^7*c + 765*a^2*b^5*c^2 - 5880*a^3*b^3*c^3 + 18000*a^4*b*c^4 + (b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10 + 4096*a^6*c^11)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(b^18*c^10 - 36*a*b^16*c^11 + 576*a^2*b^14*c^12 - 5376*a^3*b^12*c^13 + 32256*a^4*b^10*c^14 - 129024*a^5*b^8*c^15 + 344064*a^6*b^6*c^16 - 589824*a^7*b^4*c^17 + 589824*a^8*b^2*c^18 - 262144*a^9*c^19)))/(b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10 + 4096*a^6*c^11)))) - ((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(sqrt(1/2)*sqrt(-(b^9 - 45*a*b^7*c + 765*a^2*b^5*c^2 - 5880*a^3*b^3*c^3 + 18000*a^4*b*c^4 - (b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10 + 4096*a^6*c^11)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(b^18*c^10 - 36*a*b^16*c^11 + 576*a^2*b^14*c^12 - 5376*a^3*b^12*c^13 + 32256*a^4*b^10*c^14 - 129024*a^5*b^8*c^15 + 344064*a^6*b^6*c^16 - 589824*a^7*b^4*c^17 + 589824*a^8*b^2*c^18 - 262144*a^9*c^19)))/(b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10 + 4096*a^6*c^11)))*log((9*a*b^8 - 451*a^2*b^6*c + 8625*a^3*b^4*c^2 - 75000*a^4*b^2*c^3 + 250000*a^5*c^4)*sqrt(x) + 1/2*(b^11 - 47*a*b^9*c + 853*a^2*b^7*c^2 - 7324*a^3*b^5*c^3 + 28400*a^4*b^3*c^4 - 40000*a^5*b*c^5 + (b^14*c^5 - 44*a*b^12*c^6 + 720*a^2*b^10*c^7 - 6080*a^3*b^8*c^8 + 29440*a^4*b^6*c^9 - 82944*a^5*b^4*c^10 + 126976*a^6*b^2*c^11 - 81920*a^7*c^12)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(b^18*c^10 - 36*a*b^16*c^11 + 576*a^2*b^14*c^12 - 5376*a^3*b^12*c^13 + 32256*a^4*b^10*c^14 - 129024*a^5*b^8*c^15 + 344064*a^6*b^6*c^16 - 589824*a^7*b^4*c^17 + 589824*a^8*b^2*c^18 - 262144*a^9*c^19)))*sqrt(sqrt(1/2)*sqrt(-(b^9 - 45*a*b^7*c + 765*a^2*b^5*c^2 - 5880*a^3*b^3*c^3 + 18000*a^4*b*c^4 - (b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10 + 4096*a^6*c^11)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(b^18*c^10 - 36*a*b^16*c^11 + 576*a^2*b^14*c^12 - 5376*a^3*b^12*c^13 + 32256*a^4*b^10*c^14 - 129024*a^5*b^8*c^15 + 344064*a^6*b^6*c^16 - 589824*a^7*b^4*c^17 + 589824*a^8*b^2*c^18 - 262144*a^9*c^19)))/(b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10 + 4096*a^6*c^11)))) + ((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(sqrt(1/2)*sqrt(-(b^9 - 45*a*b^7*c + 765*a^2*b^5*c^2 - 5880*a^3*b^3*c^3 + 18000*a^4*b*c^4 - (b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10 + 4096*a^6*c^11)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(b^18*c^10 - 36*a*b^16*c^11 + 576*a^2*b^14*c^12 - 5376*a^3*b^12*c^13 + 32256*a^4*b^10*c^14 - 129024*a^5*b^8*c^15 + 344064*a^6*b^6*c^16 - 589824*a^7*b^4*c^17 + 589824*a^8*b^2*c^18 - 262144*a^9*c^19)))/(b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10 + 4096*a^6*c^11)))*log((9*a*b^8 - 451*a^2*b^6*c + 8625*a^3*b^4*c^2 - 75000*a^4*b^2*c^3 + 250000*a^5*c^4)*sqrt(x) - 1/2*(b^11 - 47*a*b^9*c + 853*a^2*b^7*c^2 - 7324*a^3*b^5*c^3 + 28400*a^4*b^3*c^4 - 40000*a^5*b*c^5 + (b^14*c^5 - 44*a*b^12*c^6 + 720*a^2*b^10*c^7 - 6080*a^3*b^8*c^8 + 29440*a^4*b^6*c^9 - 82944*a^5*b^4*c^10 + 126976*a^6*b^2*c^11 - 81920*a^7*c^12)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(b^18*c^10 - 36*a*b^16*c^11 + 576*a^2*b^14*c^12 - 5376*a^3*b^12*c^13 + 32256*a^4*b^10*c^14 - 129024*a^5*b^8*c^15 + 344064*a^6*b^6*c^16 - 589824*a^7*b^4*c^17 + 589824*a^8*b^2*c^18 - 262144*a^9*c^19)))*sqrt(sqrt(1/2)*sqrt(-(b^9 - 45*a*b^7*c + 765*a^2*b^5*c^2 - 5880*a^3*b^3*c^3 + 18000*a^4*b*c^4 - (b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10 + 4096*a^6*c^11)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(b^18*c^10 - 36*a*b^16*c^11 + 576*a^2*b^14*c^12 - 5376*a^3*b^12*c^13 + 32256*a^4*b^10*c^14 - 129024*a^5*b^8*c^15 + 344064*a^6*b^6*c^16 - 589824*a^7*b^4*c^17 + 589824*a^8*b^2*c^18 - 262144*a^9*c^19)))/(b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10 + 4096*a^6*c^11)))) + 4*((b^2 - 2*a*c)*x^2 + a*b)*sqrt(x))/((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
1073,1,11032,0,79.679751," ","integrate(x^(9/2)/(c*x^4+b*x^2+a)^2,x, algorithm=""fricas"")","-\frac{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)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} + 21 \, a b^{5} c + 168 \, a^{2} b^{3} c^{2} + 3024 \, a^{3} b c^{3} + {\left(b^{12} c^{3} - 24 \, a b^{10} c^{4} + 240 \, a^{2} b^{8} c^{5} - 1280 \, a^{3} b^{6} c^{6} + 3840 \, a^{4} b^{4} c^{7} - 6144 \, a^{5} b^{2} c^{8} + 4096 \, a^{6} c^{9}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{b^{18} c^{6} - 36 \, a b^{16} c^{7} + 576 \, a^{2} b^{14} c^{8} - 5376 \, a^{3} b^{12} c^{9} + 32256 \, a^{4} b^{10} c^{10} - 129024 \, a^{5} b^{8} c^{11} + 344064 \, a^{6} b^{6} c^{12} - 589824 \, a^{7} b^{4} c^{13} + 589824 \, a^{8} b^{2} c^{14} - 262144 \, a^{9} c^{15}}}}{b^{12} c^{3} - 24 \, a b^{10} c^{4} + 240 \, a^{2} b^{8} c^{5} - 1280 \, a^{3} b^{6} c^{6} + 3840 \, a^{4} b^{4} c^{7} - 6144 \, a^{5} b^{2} c^{8} + 4096 \, a^{6} c^{9}}}} \arctan\left(-\frac{{\left({\left(b^{9} + 19 \, a b^{7} c + 124 \, a^{2} b^{5} c^{2} - 2160 \, a^{3} b^{3} c^{3} + 5184 \, a^{4} b c^{4} - {\left(b^{14} c^{3} - 12 \, a b^{12} c^{4} - 48 \, a^{2} b^{10} c^{5} + 1600 \, a^{3} b^{8} c^{6} - 11520 \, a^{4} b^{6} c^{7} + 39936 \, a^{5} b^{4} c^{8} - 69632 \, a^{6} b^{2} c^{9} + 49152 \, a^{7} c^{10}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{b^{18} c^{6} - 36 \, a b^{16} c^{7} + 576 \, a^{2} b^{14} c^{8} - 5376 \, a^{3} b^{12} c^{9} + 32256 \, a^{4} b^{10} c^{10} - 129024 \, a^{5} b^{8} c^{11} + 344064 \, a^{6} b^{6} c^{12} - 589824 \, a^{7} b^{4} c^{13} + 589824 \, a^{8} b^{2} c^{14} - 262144 \, a^{9} c^{15}}}\right)} \sqrt{{\left(117649 \, a^{4} b^{20} + 9983358 \, a^{5} b^{18} c + 404714961 \, a^{6} b^{16} c^{2} + 9897860448 \, a^{7} b^{14} c^{3} + 158656107456 \, a^{8} b^{12} c^{4} + 1707655509504 \, a^{9} b^{10} c^{5} + 12338818573824 \, a^{10} b^{8} c^{6} + 58812305154048 \, a^{11} b^{6} c^{7} + 177024646692864 \, a^{12} b^{4} c^{8} + 304679870005248 \, a^{13} b^{2} c^{9} + 228509902503936 \, a^{14} c^{10}\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(2401 \, a^{3} b^{25} + 294294 \, a^{4} b^{23} c + 13335105 \, a^{5} b^{21} c^{2} + 323354360 \, a^{6} b^{19} c^{3} + 4269253584 \, a^{7} b^{17} c^{4} + 24537890304 \, a^{8} b^{15} c^{5} - 79436754432 \, a^{9} b^{13} c^{6} - 1621756588032 \, a^{10} b^{11} c^{7} - 3506876964864 \, a^{11} b^{9} c^{8} + 27305557622784 \, a^{12} b^{7} c^{9} + 100201644490752 \, a^{13} b^{5} c^{10} - 142936235311104 \, a^{14} b^{3} c^{11} - 677066377789440 \, a^{15} b c^{12} - {\left(2401 \, a^{3} b^{30} c^{3} - 49049 \, a^{4} b^{28} c^{4} - 1432760 \, a^{5} b^{26} c^{5} - 6473264 \, a^{6} b^{24} c^{6} + 373184512 \, a^{7} b^{22} c^{7} - 319185152 \, a^{8} b^{20} c^{8} - 27408852992 \, a^{9} b^{18} c^{9} + 93871525888 \, a^{10} b^{16} c^{10} + 774145638400 \, a^{11} b^{14} c^{11} - 4486009651200 \, a^{12} b^{12} c^{12} - 5590781263872 \, a^{13} b^{10} c^{13} + 81717925773312 \, a^{14} b^{8} c^{14} - 108093958520832 \, a^{15} b^{6} c^{15} - 454721122861056 \, a^{16} b^{4} c^{16} + 1497904875307008 \, a^{17} b^{2} c^{17} - 1283918464548864 \, a^{18} c^{18}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{b^{18} c^{6} - 36 \, a b^{16} c^{7} + 576 \, a^{2} b^{14} c^{8} - 5376 \, a^{3} b^{12} c^{9} + 32256 \, a^{4} b^{10} c^{10} - 129024 \, a^{5} b^{8} c^{11} + 344064 \, a^{6} b^{6} c^{12} - 589824 \, a^{7} b^{4} c^{13} + 589824 \, a^{8} b^{2} c^{14} - 262144 \, a^{9} c^{15}}}\right)} \sqrt{-\frac{b^{7} + 21 \, a b^{5} c + 168 \, a^{2} b^{3} c^{2} + 3024 \, a^{3} b c^{3} + {\left(b^{12} c^{3} - 24 \, a b^{10} c^{4} + 240 \, a^{2} b^{8} c^{5} - 1280 \, a^{3} b^{6} c^{6} + 3840 \, a^{4} b^{4} c^{7} - 6144 \, a^{5} b^{2} c^{8} + 4096 \, a^{6} c^{9}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{b^{18} c^{6} - 36 \, a b^{16} c^{7} + 576 \, a^{2} b^{14} c^{8} - 5376 \, a^{3} b^{12} c^{9} + 32256 \, a^{4} b^{10} c^{10} - 129024 \, a^{5} b^{8} c^{11} + 344064 \, a^{6} b^{6} c^{12} - 589824 \, a^{7} b^{4} c^{13} + 589824 \, a^{8} b^{2} c^{14} - 262144 \, a^{9} c^{15}}}}{b^{12} c^{3} - 24 \, a b^{10} c^{4} + 240 \, a^{2} b^{8} c^{5} - 1280 \, a^{3} b^{6} c^{6} + 3840 \, a^{4} b^{4} c^{7} - 6144 \, a^{5} b^{2} c^{8} + 4096 \, a^{6} c^{9}}}} - {\left(343 \, a^{2} b^{19} + 21070 \, a^{3} b^{17} c + 600271 \, a^{4} b^{15} c^{2} + 8903196 \, a^{5} b^{13} c^{3} + 62719920 \, a^{6} b^{11} c^{4} - 15909696 \, a^{7} b^{9} c^{5} - 2396812032 \, a^{8} b^{7} c^{6} - 6953610240 \, a^{9} b^{5} c^{7} + 19591041024 \, a^{10} b^{3} c^{8} + 78364164096 \, a^{11} b c^{9} - {\left(343 \, a^{2} b^{24} c^{3} + 10437 \, a^{3} b^{22} c^{4} + 90132 \, a^{4} b^{20} c^{5} - 1028432 \, a^{5} b^{18} c^{6} - 14041152 \, a^{6} b^{16} c^{7} + 70390272 \, a^{7} b^{14} c^{8} + 646137856 \, a^{8} b^{12} c^{9} - 3121520640 \, a^{9} b^{10} c^{10} - 11091935232 \, a^{10} b^{8} c^{11} + 68335239168 \, a^{11} b^{6} c^{12} + 24652283904 \, a^{12} b^{4} c^{13} - 557256278016 \, a^{13} b^{2} c^{14} + 743008370688 \, a^{14} c^{15}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{b^{18} c^{6} - 36 \, a b^{16} c^{7} + 576 \, a^{2} b^{14} c^{8} - 5376 \, a^{3} b^{12} c^{9} + 32256 \, a^{4} b^{10} c^{10} - 129024 \, a^{5} b^{8} c^{11} + 344064 \, a^{6} b^{6} c^{12} - 589824 \, a^{7} b^{4} c^{13} + 589824 \, a^{8} b^{2} c^{14} - 262144 \, a^{9} c^{15}}}\right)} \sqrt{x}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} + 21 \, a b^{5} c + 168 \, a^{2} b^{3} c^{2} + 3024 \, a^{3} b c^{3} + {\left(b^{12} c^{3} - 24 \, a b^{10} c^{4} + 240 \, a^{2} b^{8} c^{5} - 1280 \, a^{3} b^{6} c^{6} + 3840 \, a^{4} b^{4} c^{7} - 6144 \, a^{5} b^{2} c^{8} + 4096 \, a^{6} c^{9}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{b^{18} c^{6} - 36 \, a b^{16} c^{7} + 576 \, a^{2} b^{14} c^{8} - 5376 \, a^{3} b^{12} c^{9} + 32256 \, a^{4} b^{10} c^{10} - 129024 \, a^{5} b^{8} c^{11} + 344064 \, a^{6} b^{6} c^{12} - 589824 \, a^{7} b^{4} c^{13} + 589824 \, a^{8} b^{2} c^{14} - 262144 \, a^{9} c^{15}}}}{b^{12} c^{3} - 24 \, a b^{10} c^{4} + 240 \, a^{2} b^{8} c^{5} - 1280 \, a^{3} b^{6} c^{6} + 3840 \, a^{4} b^{4} c^{7} - 6144 \, a^{5} b^{2} c^{8} + 4096 \, a^{6} c^{9}}}}}{2 \, {\left(2401 \, a^{3} b^{16} + 179046 \, a^{4} b^{14} c + 6354369 \, a^{5} b^{12} c^{2} + 131902344 \, a^{6} b^{10} c^{3} + 1713103344 \, a^{7} b^{8} c^{4} + 13740938496 \, a^{8} b^{6} c^{5} + 65167421184 \, a^{9} b^{4} c^{6} + 166523848704 \, a^{10} b^{2} c^{7} + 176319369216 \, a^{11} c^{8}\right)}}\right) - 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)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} + 21 \, a b^{5} c + 168 \, a^{2} b^{3} c^{2} + 3024 \, a^{3} b c^{3} - {\left(b^{12} c^{3} - 24 \, a b^{10} c^{4} + 240 \, a^{2} b^{8} c^{5} - 1280 \, a^{3} b^{6} c^{6} + 3840 \, a^{4} b^{4} c^{7} - 6144 \, a^{5} b^{2} c^{8} + 4096 \, a^{6} c^{9}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{b^{18} c^{6} - 36 \, a b^{16} c^{7} + 576 \, a^{2} b^{14} c^{8} - 5376 \, a^{3} b^{12} c^{9} + 32256 \, a^{4} b^{10} c^{10} - 129024 \, a^{5} b^{8} c^{11} + 344064 \, a^{6} b^{6} c^{12} - 589824 \, a^{7} b^{4} c^{13} + 589824 \, a^{8} b^{2} c^{14} - 262144 \, a^{9} c^{15}}}}{b^{12} c^{3} - 24 \, a b^{10} c^{4} + 240 \, a^{2} b^{8} c^{5} - 1280 \, a^{3} b^{6} c^{6} + 3840 \, a^{4} b^{4} c^{7} - 6144 \, a^{5} b^{2} c^{8} + 4096 \, a^{6} c^{9}}}} \arctan\left(\frac{{\left(b^{9} + 19 \, a b^{7} c + 124 \, a^{2} b^{5} c^{2} - 2160 \, a^{3} b^{3} c^{3} + 5184 \, a^{4} b c^{4} + {\left(b^{14} c^{3} - 12 \, a b^{12} c^{4} - 48 \, a^{2} b^{10} c^{5} + 1600 \, a^{3} b^{8} c^{6} - 11520 \, a^{4} b^{6} c^{7} + 39936 \, a^{5} b^{4} c^{8} - 69632 \, a^{6} b^{2} c^{9} + 49152 \, a^{7} c^{10}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{b^{18} c^{6} - 36 \, a b^{16} c^{7} + 576 \, a^{2} b^{14} c^{8} - 5376 \, a^{3} b^{12} c^{9} + 32256 \, a^{4} b^{10} c^{10} - 129024 \, a^{5} b^{8} c^{11} + 344064 \, a^{6} b^{6} c^{12} - 589824 \, a^{7} b^{4} c^{13} + 589824 \, a^{8} b^{2} c^{14} - 262144 \, a^{9} c^{15}}}\right)} \sqrt{{\left(117649 \, a^{4} b^{20} + 9983358 \, a^{5} b^{18} c + 404714961 \, a^{6} b^{16} c^{2} + 9897860448 \, a^{7} b^{14} c^{3} + 158656107456 \, a^{8} b^{12} c^{4} + 1707655509504 \, a^{9} b^{10} c^{5} + 12338818573824 \, a^{10} b^{8} c^{6} + 58812305154048 \, a^{11} b^{6} c^{7} + 177024646692864 \, a^{12} b^{4} c^{8} + 304679870005248 \, a^{13} b^{2} c^{9} + 228509902503936 \, a^{14} c^{10}\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(2401 \, a^{3} b^{25} + 294294 \, a^{4} b^{23} c + 13335105 \, a^{5} b^{21} c^{2} + 323354360 \, a^{6} b^{19} c^{3} + 4269253584 \, a^{7} b^{17} c^{4} + 24537890304 \, a^{8} b^{15} c^{5} - 79436754432 \, a^{9} b^{13} c^{6} - 1621756588032 \, a^{10} b^{11} c^{7} - 3506876964864 \, a^{11} b^{9} c^{8} + 27305557622784 \, a^{12} b^{7} c^{9} + 100201644490752 \, a^{13} b^{5} c^{10} - 142936235311104 \, a^{14} b^{3} c^{11} - 677066377789440 \, a^{15} b c^{12} + {\left(2401 \, a^{3} b^{30} c^{3} - 49049 \, a^{4} b^{28} c^{4} - 1432760 \, a^{5} b^{26} c^{5} - 6473264 \, a^{6} b^{24} c^{6} + 373184512 \, a^{7} b^{22} c^{7} - 319185152 \, a^{8} b^{20} c^{8} - 27408852992 \, a^{9} b^{18} c^{9} + 93871525888 \, a^{10} b^{16} c^{10} + 774145638400 \, a^{11} b^{14} c^{11} - 4486009651200 \, a^{12} b^{12} c^{12} - 5590781263872 \, a^{13} b^{10} c^{13} + 81717925773312 \, a^{14} b^{8} c^{14} - 108093958520832 \, a^{15} b^{6} c^{15} - 454721122861056 \, a^{16} b^{4} c^{16} + 1497904875307008 \, a^{17} b^{2} c^{17} - 1283918464548864 \, a^{18} c^{18}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{b^{18} c^{6} - 36 \, a b^{16} c^{7} + 576 \, a^{2} b^{14} c^{8} - 5376 \, a^{3} b^{12} c^{9} + 32256 \, a^{4} b^{10} c^{10} - 129024 \, a^{5} b^{8} c^{11} + 344064 \, a^{6} b^{6} c^{12} - 589824 \, a^{7} b^{4} c^{13} + 589824 \, a^{8} b^{2} c^{14} - 262144 \, a^{9} c^{15}}}\right)} \sqrt{-\frac{b^{7} + 21 \, a b^{5} c + 168 \, a^{2} b^{3} c^{2} + 3024 \, a^{3} b c^{3} - {\left(b^{12} c^{3} - 24 \, a b^{10} c^{4} + 240 \, a^{2} b^{8} c^{5} - 1280 \, a^{3} b^{6} c^{6} + 3840 \, a^{4} b^{4} c^{7} - 6144 \, a^{5} b^{2} c^{8} + 4096 \, a^{6} c^{9}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{b^{18} c^{6} - 36 \, a b^{16} c^{7} + 576 \, a^{2} b^{14} c^{8} - 5376 \, a^{3} b^{12} c^{9} + 32256 \, a^{4} b^{10} c^{10} - 129024 \, a^{5} b^{8} c^{11} + 344064 \, a^{6} b^{6} c^{12} - 589824 \, a^{7} b^{4} c^{13} + 589824 \, a^{8} b^{2} c^{14} - 262144 \, a^{9} c^{15}}}}{b^{12} c^{3} - 24 \, a b^{10} c^{4} + 240 \, a^{2} b^{8} c^{5} - 1280 \, a^{3} b^{6} c^{6} + 3840 \, a^{4} b^{4} c^{7} - 6144 \, a^{5} b^{2} c^{8} + 4096 \, a^{6} c^{9}}}} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} + 21 \, a b^{5} c + 168 \, a^{2} b^{3} c^{2} + 3024 \, a^{3} b c^{3} - {\left(b^{12} c^{3} - 24 \, a b^{10} c^{4} + 240 \, a^{2} b^{8} c^{5} - 1280 \, a^{3} b^{6} c^{6} + 3840 \, a^{4} b^{4} c^{7} - 6144 \, a^{5} b^{2} c^{8} + 4096 \, a^{6} c^{9}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{b^{18} c^{6} - 36 \, a b^{16} c^{7} + 576 \, a^{2} b^{14} c^{8} - 5376 \, a^{3} b^{12} c^{9} + 32256 \, a^{4} b^{10} c^{10} - 129024 \, a^{5} b^{8} c^{11} + 344064 \, a^{6} b^{6} c^{12} - 589824 \, a^{7} b^{4} c^{13} + 589824 \, a^{8} b^{2} c^{14} - 262144 \, a^{9} c^{15}}}}{b^{12} c^{3} - 24 \, a b^{10} c^{4} + 240 \, a^{2} b^{8} c^{5} - 1280 \, a^{3} b^{6} c^{6} + 3840 \, a^{4} b^{4} c^{7} - 6144 \, a^{5} b^{2} c^{8} + 4096 \, a^{6} c^{9}}}} - {\left(343 \, a^{2} b^{19} + 21070 \, a^{3} b^{17} c + 600271 \, a^{4} b^{15} c^{2} + 8903196 \, a^{5} b^{13} c^{3} + 62719920 \, a^{6} b^{11} c^{4} - 15909696 \, a^{7} b^{9} c^{5} - 2396812032 \, a^{8} b^{7} c^{6} - 6953610240 \, a^{9} b^{5} c^{7} + 19591041024 \, a^{10} b^{3} c^{8} + 78364164096 \, a^{11} b c^{9} + {\left(343 \, a^{2} b^{24} c^{3} + 10437 \, a^{3} b^{22} c^{4} + 90132 \, a^{4} b^{20} c^{5} - 1028432 \, a^{5} b^{18} c^{6} - 14041152 \, a^{6} b^{16} c^{7} + 70390272 \, a^{7} b^{14} c^{8} + 646137856 \, a^{8} b^{12} c^{9} - 3121520640 \, a^{9} b^{10} c^{10} - 11091935232 \, a^{10} b^{8} c^{11} + 68335239168 \, a^{11} b^{6} c^{12} + 24652283904 \, a^{12} b^{4} c^{13} - 557256278016 \, a^{13} b^{2} c^{14} + 743008370688 \, a^{14} c^{15}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{b^{18} c^{6} - 36 \, a b^{16} c^{7} + 576 \, a^{2} b^{14} c^{8} - 5376 \, a^{3} b^{12} c^{9} + 32256 \, a^{4} b^{10} c^{10} - 129024 \, a^{5} b^{8} c^{11} + 344064 \, a^{6} b^{6} c^{12} - 589824 \, a^{7} b^{4} c^{13} + 589824 \, a^{8} b^{2} c^{14} - 262144 \, a^{9} c^{15}}}\right)} \sqrt{x} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} + 21 \, a b^{5} c + 168 \, a^{2} b^{3} c^{2} + 3024 \, a^{3} b c^{3} - {\left(b^{12} c^{3} - 24 \, a b^{10} c^{4} + 240 \, a^{2} b^{8} c^{5} - 1280 \, a^{3} b^{6} c^{6} + 3840 \, a^{4} b^{4} c^{7} - 6144 \, a^{5} b^{2} c^{8} + 4096 \, a^{6} c^{9}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{b^{18} c^{6} - 36 \, a b^{16} c^{7} + 576 \, a^{2} b^{14} c^{8} - 5376 \, a^{3} b^{12} c^{9} + 32256 \, a^{4} b^{10} c^{10} - 129024 \, a^{5} b^{8} c^{11} + 344064 \, a^{6} b^{6} c^{12} - 589824 \, a^{7} b^{4} c^{13} + 589824 \, a^{8} b^{2} c^{14} - 262144 \, a^{9} c^{15}}}}{b^{12} c^{3} - 24 \, a b^{10} c^{4} + 240 \, a^{2} b^{8} c^{5} - 1280 \, a^{3} b^{6} c^{6} + 3840 \, a^{4} b^{4} c^{7} - 6144 \, a^{5} b^{2} c^{8} + 4096 \, a^{6} c^{9}}}}}{2 \, {\left(2401 \, a^{3} b^{16} + 179046 \, a^{4} b^{14} c + 6354369 \, a^{5} b^{12} c^{2} + 131902344 \, a^{6} b^{10} c^{3} + 1713103344 \, a^{7} b^{8} c^{4} + 13740938496 \, a^{8} b^{6} c^{5} + 65167421184 \, a^{9} b^{4} c^{6} + 166523848704 \, a^{10} b^{2} c^{7} + 176319369216 \, a^{11} c^{8}\right)}}\right) + {\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{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} + 21 \, a b^{5} c + 168 \, a^{2} b^{3} c^{2} + 3024 \, a^{3} b c^{3} + {\left(b^{12} c^{3} - 24 \, a b^{10} c^{4} + 240 \, a^{2} b^{8} c^{5} - 1280 \, a^{3} b^{6} c^{6} + 3840 \, a^{4} b^{4} c^{7} - 6144 \, a^{5} b^{2} c^{8} + 4096 \, a^{6} c^{9}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{b^{18} c^{6} - 36 \, a b^{16} c^{7} + 576 \, a^{2} b^{14} c^{8} - 5376 \, a^{3} b^{12} c^{9} + 32256 \, a^{4} b^{10} c^{10} - 129024 \, a^{5} b^{8} c^{11} + 344064 \, a^{6} b^{6} c^{12} - 589824 \, a^{7} b^{4} c^{13} + 589824 \, a^{8} b^{2} c^{14} - 262144 \, a^{9} c^{15}}}}{b^{12} c^{3} - 24 \, a b^{10} c^{4} + 240 \, a^{2} b^{8} c^{5} - 1280 \, a^{3} b^{6} c^{6} + 3840 \, a^{4} b^{4} c^{7} - 6144 \, a^{5} b^{2} c^{8} + 4096 \, a^{6} c^{9}}}} \log\left(\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{18} + 25 \, a b^{16} c - 146 \, a^{2} b^{14} c^{2} - 5320 \, a^{3} b^{12} c^{3} - 2464 \, a^{4} b^{10} c^{4} + 1076096 \, a^{5} b^{8} c^{5} - 10483200 \, a^{6} b^{6} c^{6} + 44181504 \, a^{7} b^{4} c^{7} - 89579520 \, a^{8} b^{2} c^{8} + 71663616 \, a^{9} c^{9} - {\left(b^{23} c^{3} - 20 \, a b^{21} c^{4} + 432 \, a^{2} b^{19} c^{5} - 11712 \, a^{3} b^{17} c^{6} + 195072 \, a^{4} b^{15} c^{7} - 1935360 \, a^{5} b^{13} c^{8} + 12214272 \, a^{6} b^{11} c^{9} - 50823168 \, a^{7} b^{9} c^{10} + 139788288 \, a^{8} b^{7} c^{11} - 245628928 \, a^{9} b^{5} c^{12} + 250609664 \, a^{10} b^{3} c^{13} - 113246208 \, a^{11} b c^{14}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{b^{18} c^{6} - 36 \, a b^{16} c^{7} + 576 \, a^{2} b^{14} c^{8} - 5376 \, a^{3} b^{12} c^{9} + 32256 \, a^{4} b^{10} c^{10} - 129024 \, a^{5} b^{8} c^{11} + 344064 \, a^{6} b^{6} c^{12} - 589824 \, a^{7} b^{4} c^{13} + 589824 \, a^{8} b^{2} c^{14} - 262144 \, a^{9} c^{15}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} + 21 \, a b^{5} c + 168 \, a^{2} b^{3} c^{2} + 3024 \, a^{3} b c^{3} + {\left(b^{12} c^{3} - 24 \, a b^{10} c^{4} + 240 \, a^{2} b^{8} c^{5} - 1280 \, a^{3} b^{6} c^{6} + 3840 \, a^{4} b^{4} c^{7} - 6144 \, a^{5} b^{2} c^{8} + 4096 \, a^{6} c^{9}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{b^{18} c^{6} - 36 \, a b^{16} c^{7} + 576 \, a^{2} b^{14} c^{8} - 5376 \, a^{3} b^{12} c^{9} + 32256 \, a^{4} b^{10} c^{10} - 129024 \, a^{5} b^{8} c^{11} + 344064 \, a^{6} b^{6} c^{12} - 589824 \, a^{7} b^{4} c^{13} + 589824 \, a^{8} b^{2} c^{14} - 262144 \, a^{9} c^{15}}}}{b^{12} c^{3} - 24 \, a b^{10} c^{4} + 240 \, a^{2} b^{8} c^{5} - 1280 \, a^{3} b^{6} c^{6} + 3840 \, a^{4} b^{4} c^{7} - 6144 \, a^{5} b^{2} c^{8} + 4096 \, a^{6} c^{9}}}} \sqrt{-\frac{b^{7} + 21 \, a b^{5} c + 168 \, a^{2} b^{3} c^{2} + 3024 \, a^{3} b c^{3} + {\left(b^{12} c^{3} - 24 \, a b^{10} c^{4} + 240 \, a^{2} b^{8} c^{5} - 1280 \, a^{3} b^{6} c^{6} + 3840 \, a^{4} b^{4} c^{7} - 6144 \, a^{5} b^{2} c^{8} + 4096 \, a^{6} c^{9}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{b^{18} c^{6} - 36 \, a b^{16} c^{7} + 576 \, a^{2} b^{14} c^{8} - 5376 \, a^{3} b^{12} c^{9} + 32256 \, a^{4} b^{10} c^{10} - 129024 \, a^{5} b^{8} c^{11} + 344064 \, a^{6} b^{6} c^{12} - 589824 \, a^{7} b^{4} c^{13} + 589824 \, a^{8} b^{2} c^{14} - 262144 \, a^{9} c^{15}}}}{b^{12} c^{3} - 24 \, a b^{10} c^{4} + 240 \, a^{2} b^{8} c^{5} - 1280 \, a^{3} b^{6} c^{6} + 3840 \, a^{4} b^{4} c^{7} - 6144 \, a^{5} b^{2} c^{8} + 4096 \, a^{6} c^{9}}} + {\left(343 \, a^{2} b^{10} + 14553 \, a^{3} b^{8} c + 281232 \, a^{4} b^{6} c^{2} + 2496096 \, a^{5} b^{4} c^{3} + 10077696 \, a^{6} b^{2} c^{4} + 15116544 \, a^{7} c^{5}\right)} \sqrt{x}\right) - {\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{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} + 21 \, a b^{5} c + 168 \, a^{2} b^{3} c^{2} + 3024 \, a^{3} b c^{3} + {\left(b^{12} c^{3} - 24 \, a b^{10} c^{4} + 240 \, a^{2} b^{8} c^{5} - 1280 \, a^{3} b^{6} c^{6} + 3840 \, a^{4} b^{4} c^{7} - 6144 \, a^{5} b^{2} c^{8} + 4096 \, a^{6} c^{9}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{b^{18} c^{6} - 36 \, a b^{16} c^{7} + 576 \, a^{2} b^{14} c^{8} - 5376 \, a^{3} b^{12} c^{9} + 32256 \, a^{4} b^{10} c^{10} - 129024 \, a^{5} b^{8} c^{11} + 344064 \, a^{6} b^{6} c^{12} - 589824 \, a^{7} b^{4} c^{13} + 589824 \, a^{8} b^{2} c^{14} - 262144 \, a^{9} c^{15}}}}{b^{12} c^{3} - 24 \, a b^{10} c^{4} + 240 \, a^{2} b^{8} c^{5} - 1280 \, a^{3} b^{6} c^{6} + 3840 \, a^{4} b^{4} c^{7} - 6144 \, a^{5} b^{2} c^{8} + 4096 \, a^{6} c^{9}}}} \log\left(-\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{18} + 25 \, a b^{16} c - 146 \, a^{2} b^{14} c^{2} - 5320 \, a^{3} b^{12} c^{3} - 2464 \, a^{4} b^{10} c^{4} + 1076096 \, a^{5} b^{8} c^{5} - 10483200 \, a^{6} b^{6} c^{6} + 44181504 \, a^{7} b^{4} c^{7} - 89579520 \, a^{8} b^{2} c^{8} + 71663616 \, a^{9} c^{9} - {\left(b^{23} c^{3} - 20 \, a b^{21} c^{4} + 432 \, a^{2} b^{19} c^{5} - 11712 \, a^{3} b^{17} c^{6} + 195072 \, a^{4} b^{15} c^{7} - 1935360 \, a^{5} b^{13} c^{8} + 12214272 \, a^{6} b^{11} c^{9} - 50823168 \, a^{7} b^{9} c^{10} + 139788288 \, a^{8} b^{7} c^{11} - 245628928 \, a^{9} b^{5} c^{12} + 250609664 \, a^{10} b^{3} c^{13} - 113246208 \, a^{11} b c^{14}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{b^{18} c^{6} - 36 \, a b^{16} c^{7} + 576 \, a^{2} b^{14} c^{8} - 5376 \, a^{3} b^{12} c^{9} + 32256 \, a^{4} b^{10} c^{10} - 129024 \, a^{5} b^{8} c^{11} + 344064 \, a^{6} b^{6} c^{12} - 589824 \, a^{7} b^{4} c^{13} + 589824 \, a^{8} b^{2} c^{14} - 262144 \, a^{9} c^{15}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} + 21 \, a b^{5} c + 168 \, a^{2} b^{3} c^{2} + 3024 \, a^{3} b c^{3} + {\left(b^{12} c^{3} - 24 \, a b^{10} c^{4} + 240 \, a^{2} b^{8} c^{5} - 1280 \, a^{3} b^{6} c^{6} + 3840 \, a^{4} b^{4} c^{7} - 6144 \, a^{5} b^{2} c^{8} + 4096 \, a^{6} c^{9}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{b^{18} c^{6} - 36 \, a b^{16} c^{7} + 576 \, a^{2} b^{14} c^{8} - 5376 \, a^{3} b^{12} c^{9} + 32256 \, a^{4} b^{10} c^{10} - 129024 \, a^{5} b^{8} c^{11} + 344064 \, a^{6} b^{6} c^{12} - 589824 \, a^{7} b^{4} c^{13} + 589824 \, a^{8} b^{2} c^{14} - 262144 \, a^{9} c^{15}}}}{b^{12} c^{3} - 24 \, a b^{10} c^{4} + 240 \, a^{2} b^{8} c^{5} - 1280 \, a^{3} b^{6} c^{6} + 3840 \, a^{4} b^{4} c^{7} - 6144 \, a^{5} b^{2} c^{8} + 4096 \, a^{6} c^{9}}}} \sqrt{-\frac{b^{7} + 21 \, a b^{5} c + 168 \, a^{2} b^{3} c^{2} + 3024 \, a^{3} b c^{3} + {\left(b^{12} c^{3} - 24 \, a b^{10} c^{4} + 240 \, a^{2} b^{8} c^{5} - 1280 \, a^{3} b^{6} c^{6} + 3840 \, a^{4} b^{4} c^{7} - 6144 \, a^{5} b^{2} c^{8} + 4096 \, a^{6} c^{9}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{b^{18} c^{6} - 36 \, a b^{16} c^{7} + 576 \, a^{2} b^{14} c^{8} - 5376 \, a^{3} b^{12} c^{9} + 32256 \, a^{4} b^{10} c^{10} - 129024 \, a^{5} b^{8} c^{11} + 344064 \, a^{6} b^{6} c^{12} - 589824 \, a^{7} b^{4} c^{13} + 589824 \, a^{8} b^{2} c^{14} - 262144 \, a^{9} c^{15}}}}{b^{12} c^{3} - 24 \, a b^{10} c^{4} + 240 \, a^{2} b^{8} c^{5} - 1280 \, a^{3} b^{6} c^{6} + 3840 \, a^{4} b^{4} c^{7} - 6144 \, a^{5} b^{2} c^{8} + 4096 \, a^{6} c^{9}}} + {\left(343 \, a^{2} b^{10} + 14553 \, a^{3} b^{8} c + 281232 \, a^{4} b^{6} c^{2} + 2496096 \, a^{5} b^{4} c^{3} + 10077696 \, a^{6} b^{2} c^{4} + 15116544 \, a^{7} c^{5}\right)} \sqrt{x}\right) + {\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{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} + 21 \, a b^{5} c + 168 \, a^{2} b^{3} c^{2} + 3024 \, a^{3} b c^{3} - {\left(b^{12} c^{3} - 24 \, a b^{10} c^{4} + 240 \, a^{2} b^{8} c^{5} - 1280 \, a^{3} b^{6} c^{6} + 3840 \, a^{4} b^{4} c^{7} - 6144 \, a^{5} b^{2} c^{8} + 4096 \, a^{6} c^{9}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{b^{18} c^{6} - 36 \, a b^{16} c^{7} + 576 \, a^{2} b^{14} c^{8} - 5376 \, a^{3} b^{12} c^{9} + 32256 \, a^{4} b^{10} c^{10} - 129024 \, a^{5} b^{8} c^{11} + 344064 \, a^{6} b^{6} c^{12} - 589824 \, a^{7} b^{4} c^{13} + 589824 \, a^{8} b^{2} c^{14} - 262144 \, a^{9} c^{15}}}}{b^{12} c^{3} - 24 \, a b^{10} c^{4} + 240 \, a^{2} b^{8} c^{5} - 1280 \, a^{3} b^{6} c^{6} + 3840 \, a^{4} b^{4} c^{7} - 6144 \, a^{5} b^{2} c^{8} + 4096 \, a^{6} c^{9}}}} \log\left(\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{18} + 25 \, a b^{16} c - 146 \, a^{2} b^{14} c^{2} - 5320 \, a^{3} b^{12} c^{3} - 2464 \, a^{4} b^{10} c^{4} + 1076096 \, a^{5} b^{8} c^{5} - 10483200 \, a^{6} b^{6} c^{6} + 44181504 \, a^{7} b^{4} c^{7} - 89579520 \, a^{8} b^{2} c^{8} + 71663616 \, a^{9} c^{9} + {\left(b^{23} c^{3} - 20 \, a b^{21} c^{4} + 432 \, a^{2} b^{19} c^{5} - 11712 \, a^{3} b^{17} c^{6} + 195072 \, a^{4} b^{15} c^{7} - 1935360 \, a^{5} b^{13} c^{8} + 12214272 \, a^{6} b^{11} c^{9} - 50823168 \, a^{7} b^{9} c^{10} + 139788288 \, a^{8} b^{7} c^{11} - 245628928 \, a^{9} b^{5} c^{12} + 250609664 \, a^{10} b^{3} c^{13} - 113246208 \, a^{11} b c^{14}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{b^{18} c^{6} - 36 \, a b^{16} c^{7} + 576 \, a^{2} b^{14} c^{8} - 5376 \, a^{3} b^{12} c^{9} + 32256 \, a^{4} b^{10} c^{10} - 129024 \, a^{5} b^{8} c^{11} + 344064 \, a^{6} b^{6} c^{12} - 589824 \, a^{7} b^{4} c^{13} + 589824 \, a^{8} b^{2} c^{14} - 262144 \, a^{9} c^{15}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} + 21 \, a b^{5} c + 168 \, a^{2} b^{3} c^{2} + 3024 \, a^{3} b c^{3} - {\left(b^{12} c^{3} - 24 \, a b^{10} c^{4} + 240 \, a^{2} b^{8} c^{5} - 1280 \, a^{3} b^{6} c^{6} + 3840 \, a^{4} b^{4} c^{7} - 6144 \, a^{5} b^{2} c^{8} + 4096 \, a^{6} c^{9}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{b^{18} c^{6} - 36 \, a b^{16} c^{7} + 576 \, a^{2} b^{14} c^{8} - 5376 \, a^{3} b^{12} c^{9} + 32256 \, a^{4} b^{10} c^{10} - 129024 \, a^{5} b^{8} c^{11} + 344064 \, a^{6} b^{6} c^{12} - 589824 \, a^{7} b^{4} c^{13} + 589824 \, a^{8} b^{2} c^{14} - 262144 \, a^{9} c^{15}}}}{b^{12} c^{3} - 24 \, a b^{10} c^{4} + 240 \, a^{2} b^{8} c^{5} - 1280 \, a^{3} b^{6} c^{6} + 3840 \, a^{4} b^{4} c^{7} - 6144 \, a^{5} b^{2} c^{8} + 4096 \, a^{6} c^{9}}}} \sqrt{-\frac{b^{7} + 21 \, a b^{5} c + 168 \, a^{2} b^{3} c^{2} + 3024 \, a^{3} b c^{3} - {\left(b^{12} c^{3} - 24 \, a b^{10} c^{4} + 240 \, a^{2} b^{8} c^{5} - 1280 \, a^{3} b^{6} c^{6} + 3840 \, a^{4} b^{4} c^{7} - 6144 \, a^{5} b^{2} c^{8} + 4096 \, a^{6} c^{9}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{b^{18} c^{6} - 36 \, a b^{16} c^{7} + 576 \, a^{2} b^{14} c^{8} - 5376 \, a^{3} b^{12} c^{9} + 32256 \, a^{4} b^{10} c^{10} - 129024 \, a^{5} b^{8} c^{11} + 344064 \, a^{6} b^{6} c^{12} - 589824 \, a^{7} b^{4} c^{13} + 589824 \, a^{8} b^{2} c^{14} - 262144 \, a^{9} c^{15}}}}{b^{12} c^{3} - 24 \, a b^{10} c^{4} + 240 \, a^{2} b^{8} c^{5} - 1280 \, a^{3} b^{6} c^{6} + 3840 \, a^{4} b^{4} c^{7} - 6144 \, a^{5} b^{2} c^{8} + 4096 \, a^{6} c^{9}}} + {\left(343 \, a^{2} b^{10} + 14553 \, a^{3} b^{8} c + 281232 \, a^{4} b^{6} c^{2} + 2496096 \, a^{5} b^{4} c^{3} + 10077696 \, a^{6} b^{2} c^{4} + 15116544 \, a^{7} c^{5}\right)} \sqrt{x}\right) - {\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{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} + 21 \, a b^{5} c + 168 \, a^{2} b^{3} c^{2} + 3024 \, a^{3} b c^{3} - {\left(b^{12} c^{3} - 24 \, a b^{10} c^{4} + 240 \, a^{2} b^{8} c^{5} - 1280 \, a^{3} b^{6} c^{6} + 3840 \, a^{4} b^{4} c^{7} - 6144 \, a^{5} b^{2} c^{8} + 4096 \, a^{6} c^{9}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{b^{18} c^{6} - 36 \, a b^{16} c^{7} + 576 \, a^{2} b^{14} c^{8} - 5376 \, a^{3} b^{12} c^{9} + 32256 \, a^{4} b^{10} c^{10} - 129024 \, a^{5} b^{8} c^{11} + 344064 \, a^{6} b^{6} c^{12} - 589824 \, a^{7} b^{4} c^{13} + 589824 \, a^{8} b^{2} c^{14} - 262144 \, a^{9} c^{15}}}}{b^{12} c^{3} - 24 \, a b^{10} c^{4} + 240 \, a^{2} b^{8} c^{5} - 1280 \, a^{3} b^{6} c^{6} + 3840 \, a^{4} b^{4} c^{7} - 6144 \, a^{5} b^{2} c^{8} + 4096 \, a^{6} c^{9}}}} \log\left(-\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{18} + 25 \, a b^{16} c - 146 \, a^{2} b^{14} c^{2} - 5320 \, a^{3} b^{12} c^{3} - 2464 \, a^{4} b^{10} c^{4} + 1076096 \, a^{5} b^{8} c^{5} - 10483200 \, a^{6} b^{6} c^{6} + 44181504 \, a^{7} b^{4} c^{7} - 89579520 \, a^{8} b^{2} c^{8} + 71663616 \, a^{9} c^{9} + {\left(b^{23} c^{3} - 20 \, a b^{21} c^{4} + 432 \, a^{2} b^{19} c^{5} - 11712 \, a^{3} b^{17} c^{6} + 195072 \, a^{4} b^{15} c^{7} - 1935360 \, a^{5} b^{13} c^{8} + 12214272 \, a^{6} b^{11} c^{9} - 50823168 \, a^{7} b^{9} c^{10} + 139788288 \, a^{8} b^{7} c^{11} - 245628928 \, a^{9} b^{5} c^{12} + 250609664 \, a^{10} b^{3} c^{13} - 113246208 \, a^{11} b c^{14}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{b^{18} c^{6} - 36 \, a b^{16} c^{7} + 576 \, a^{2} b^{14} c^{8} - 5376 \, a^{3} b^{12} c^{9} + 32256 \, a^{4} b^{10} c^{10} - 129024 \, a^{5} b^{8} c^{11} + 344064 \, a^{6} b^{6} c^{12} - 589824 \, a^{7} b^{4} c^{13} + 589824 \, a^{8} b^{2} c^{14} - 262144 \, a^{9} c^{15}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} + 21 \, a b^{5} c + 168 \, a^{2} b^{3} c^{2} + 3024 \, a^{3} b c^{3} - {\left(b^{12} c^{3} - 24 \, a b^{10} c^{4} + 240 \, a^{2} b^{8} c^{5} - 1280 \, a^{3} b^{6} c^{6} + 3840 \, a^{4} b^{4} c^{7} - 6144 \, a^{5} b^{2} c^{8} + 4096 \, a^{6} c^{9}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{b^{18} c^{6} - 36 \, a b^{16} c^{7} + 576 \, a^{2} b^{14} c^{8} - 5376 \, a^{3} b^{12} c^{9} + 32256 \, a^{4} b^{10} c^{10} - 129024 \, a^{5} b^{8} c^{11} + 344064 \, a^{6} b^{6} c^{12} - 589824 \, a^{7} b^{4} c^{13} + 589824 \, a^{8} b^{2} c^{14} - 262144 \, a^{9} c^{15}}}}{b^{12} c^{3} - 24 \, a b^{10} c^{4} + 240 \, a^{2} b^{8} c^{5} - 1280 \, a^{3} b^{6} c^{6} + 3840 \, a^{4} b^{4} c^{7} - 6144 \, a^{5} b^{2} c^{8} + 4096 \, a^{6} c^{9}}}} \sqrt{-\frac{b^{7} + 21 \, a b^{5} c + 168 \, a^{2} b^{3} c^{2} + 3024 \, a^{3} b c^{3} - {\left(b^{12} c^{3} - 24 \, a b^{10} c^{4} + 240 \, a^{2} b^{8} c^{5} - 1280 \, a^{3} b^{6} c^{6} + 3840 \, a^{4} b^{4} c^{7} - 6144 \, a^{5} b^{2} c^{8} + 4096 \, a^{6} c^{9}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{b^{18} c^{6} - 36 \, a b^{16} c^{7} + 576 \, a^{2} b^{14} c^{8} - 5376 \, a^{3} b^{12} c^{9} + 32256 \, a^{4} b^{10} c^{10} - 129024 \, a^{5} b^{8} c^{11} + 344064 \, a^{6} b^{6} c^{12} - 589824 \, a^{7} b^{4} c^{13} + 589824 \, a^{8} b^{2} c^{14} - 262144 \, a^{9} c^{15}}}}{b^{12} c^{3} - 24 \, a b^{10} c^{4} + 240 \, a^{2} b^{8} c^{5} - 1280 \, a^{3} b^{6} c^{6} + 3840 \, a^{4} b^{4} c^{7} - 6144 \, a^{5} b^{2} c^{8} + 4096 \, a^{6} c^{9}}} + {\left(343 \, a^{2} b^{10} + 14553 \, a^{3} b^{8} c + 281232 \, a^{4} b^{6} c^{2} + 2496096 \, a^{5} b^{4} c^{3} + 10077696 \, a^{6} b^{2} c^{4} + 15116544 \, a^{7} c^{5}\right)} \sqrt{x}\right) - 4 \, {\left(b x^{3} + 2 \, a x\right)} \sqrt{x}}{8 \, {\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,"-1/8*(4*((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(sqrt(1/2)*sqrt(-(b^7 + 21*a*b^5*c + 168*a^2*b^3*c^2 + 3024*a^3*b*c^3 + (b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8 + 4096*a^6*c^9)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(b^18*c^6 - 36*a*b^16*c^7 + 576*a^2*b^14*c^8 - 5376*a^3*b^12*c^9 + 32256*a^4*b^10*c^10 - 129024*a^5*b^8*c^11 + 344064*a^6*b^6*c^12 - 589824*a^7*b^4*c^13 + 589824*a^8*b^2*c^14 - 262144*a^9*c^15)))/(b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8 + 4096*a^6*c^9)))*arctan(-1/2*((b^9 + 19*a*b^7*c + 124*a^2*b^5*c^2 - 2160*a^3*b^3*c^3 + 5184*a^4*b*c^4 - (b^14*c^3 - 12*a*b^12*c^4 - 48*a^2*b^10*c^5 + 1600*a^3*b^8*c^6 - 11520*a^4*b^6*c^7 + 39936*a^5*b^4*c^8 - 69632*a^6*b^2*c^9 + 49152*a^7*c^10)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(b^18*c^6 - 36*a*b^16*c^7 + 576*a^2*b^14*c^8 - 5376*a^3*b^12*c^9 + 32256*a^4*b^10*c^10 - 129024*a^5*b^8*c^11 + 344064*a^6*b^6*c^12 - 589824*a^7*b^4*c^13 + 589824*a^8*b^2*c^14 - 262144*a^9*c^15)))*sqrt((117649*a^4*b^20 + 9983358*a^5*b^18*c + 404714961*a^6*b^16*c^2 + 9897860448*a^7*b^14*c^3 + 158656107456*a^8*b^12*c^4 + 1707655509504*a^9*b^10*c^5 + 12338818573824*a^10*b^8*c^6 + 58812305154048*a^11*b^6*c^7 + 177024646692864*a^12*b^4*c^8 + 304679870005248*a^13*b^2*c^9 + 228509902503936*a^14*c^10)*x - 1/2*sqrt(1/2)*(2401*a^3*b^25 + 294294*a^4*b^23*c + 13335105*a^5*b^21*c^2 + 323354360*a^6*b^19*c^3 + 4269253584*a^7*b^17*c^4 + 24537890304*a^8*b^15*c^5 - 79436754432*a^9*b^13*c^6 - 1621756588032*a^10*b^11*c^7 - 3506876964864*a^11*b^9*c^8 + 27305557622784*a^12*b^7*c^9 + 100201644490752*a^13*b^5*c^10 - 142936235311104*a^14*b^3*c^11 - 677066377789440*a^15*b*c^12 - (2401*a^3*b^30*c^3 - 49049*a^4*b^28*c^4 - 1432760*a^5*b^26*c^5 - 6473264*a^6*b^24*c^6 + 373184512*a^7*b^22*c^7 - 319185152*a^8*b^20*c^8 - 27408852992*a^9*b^18*c^9 + 93871525888*a^10*b^16*c^10 + 774145638400*a^11*b^14*c^11 - 4486009651200*a^12*b^12*c^12 - 5590781263872*a^13*b^10*c^13 + 81717925773312*a^14*b^8*c^14 - 108093958520832*a^15*b^6*c^15 - 454721122861056*a^16*b^4*c^16 + 1497904875307008*a^17*b^2*c^17 - 1283918464548864*a^18*c^18)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(b^18*c^6 - 36*a*b^16*c^7 + 576*a^2*b^14*c^8 - 5376*a^3*b^12*c^9 + 32256*a^4*b^10*c^10 - 129024*a^5*b^8*c^11 + 344064*a^6*b^6*c^12 - 589824*a^7*b^4*c^13 + 589824*a^8*b^2*c^14 - 262144*a^9*c^15)))*sqrt(-(b^7 + 21*a*b^5*c + 168*a^2*b^3*c^2 + 3024*a^3*b*c^3 + (b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8 + 4096*a^6*c^9)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(b^18*c^6 - 36*a*b^16*c^7 + 576*a^2*b^14*c^8 - 5376*a^3*b^12*c^9 + 32256*a^4*b^10*c^10 - 129024*a^5*b^8*c^11 + 344064*a^6*b^6*c^12 - 589824*a^7*b^4*c^13 + 589824*a^8*b^2*c^14 - 262144*a^9*c^15)))/(b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8 + 4096*a^6*c^9))) - (343*a^2*b^19 + 21070*a^3*b^17*c + 600271*a^4*b^15*c^2 + 8903196*a^5*b^13*c^3 + 62719920*a^6*b^11*c^4 - 15909696*a^7*b^9*c^5 - 2396812032*a^8*b^7*c^6 - 6953610240*a^9*b^5*c^7 + 19591041024*a^10*b^3*c^8 + 78364164096*a^11*b*c^9 - (343*a^2*b^24*c^3 + 10437*a^3*b^22*c^4 + 90132*a^4*b^20*c^5 - 1028432*a^5*b^18*c^6 - 14041152*a^6*b^16*c^7 + 70390272*a^7*b^14*c^8 + 646137856*a^8*b^12*c^9 - 3121520640*a^9*b^10*c^10 - 11091935232*a^10*b^8*c^11 + 68335239168*a^11*b^6*c^12 + 24652283904*a^12*b^4*c^13 - 557256278016*a^13*b^2*c^14 + 743008370688*a^14*c^15)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(b^18*c^6 - 36*a*b^16*c^7 + 576*a^2*b^14*c^8 - 5376*a^3*b^12*c^9 + 32256*a^4*b^10*c^10 - 129024*a^5*b^8*c^11 + 344064*a^6*b^6*c^12 - 589824*a^7*b^4*c^13 + 589824*a^8*b^2*c^14 - 262144*a^9*c^15)))*sqrt(x))*sqrt(sqrt(1/2)*sqrt(-(b^7 + 21*a*b^5*c + 168*a^2*b^3*c^2 + 3024*a^3*b*c^3 + (b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8 + 4096*a^6*c^9)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(b^18*c^6 - 36*a*b^16*c^7 + 576*a^2*b^14*c^8 - 5376*a^3*b^12*c^9 + 32256*a^4*b^10*c^10 - 129024*a^5*b^8*c^11 + 344064*a^6*b^6*c^12 - 589824*a^7*b^4*c^13 + 589824*a^8*b^2*c^14 - 262144*a^9*c^15)))/(b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8 + 4096*a^6*c^9)))/(2401*a^3*b^16 + 179046*a^4*b^14*c + 6354369*a^5*b^12*c^2 + 131902344*a^6*b^10*c^3 + 1713103344*a^7*b^8*c^4 + 13740938496*a^8*b^6*c^5 + 65167421184*a^9*b^4*c^6 + 166523848704*a^10*b^2*c^7 + 176319369216*a^11*c^8)) - 4*((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(sqrt(1/2)*sqrt(-(b^7 + 21*a*b^5*c + 168*a^2*b^3*c^2 + 3024*a^3*b*c^3 - (b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8 + 4096*a^6*c^9)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(b^18*c^6 - 36*a*b^16*c^7 + 576*a^2*b^14*c^8 - 5376*a^3*b^12*c^9 + 32256*a^4*b^10*c^10 - 129024*a^5*b^8*c^11 + 344064*a^6*b^6*c^12 - 589824*a^7*b^4*c^13 + 589824*a^8*b^2*c^14 - 262144*a^9*c^15)))/(b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8 + 4096*a^6*c^9)))*arctan(1/2*((b^9 + 19*a*b^7*c + 124*a^2*b^5*c^2 - 2160*a^3*b^3*c^3 + 5184*a^4*b*c^4 + (b^14*c^3 - 12*a*b^12*c^4 - 48*a^2*b^10*c^5 + 1600*a^3*b^8*c^6 - 11520*a^4*b^6*c^7 + 39936*a^5*b^4*c^8 - 69632*a^6*b^2*c^9 + 49152*a^7*c^10)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(b^18*c^6 - 36*a*b^16*c^7 + 576*a^2*b^14*c^8 - 5376*a^3*b^12*c^9 + 32256*a^4*b^10*c^10 - 129024*a^5*b^8*c^11 + 344064*a^6*b^6*c^12 - 589824*a^7*b^4*c^13 + 589824*a^8*b^2*c^14 - 262144*a^9*c^15)))*sqrt((117649*a^4*b^20 + 9983358*a^5*b^18*c + 404714961*a^6*b^16*c^2 + 9897860448*a^7*b^14*c^3 + 158656107456*a^8*b^12*c^4 + 1707655509504*a^9*b^10*c^5 + 12338818573824*a^10*b^8*c^6 + 58812305154048*a^11*b^6*c^7 + 177024646692864*a^12*b^4*c^8 + 304679870005248*a^13*b^2*c^9 + 228509902503936*a^14*c^10)*x - 1/2*sqrt(1/2)*(2401*a^3*b^25 + 294294*a^4*b^23*c + 13335105*a^5*b^21*c^2 + 323354360*a^6*b^19*c^3 + 4269253584*a^7*b^17*c^4 + 24537890304*a^8*b^15*c^5 - 79436754432*a^9*b^13*c^6 - 1621756588032*a^10*b^11*c^7 - 3506876964864*a^11*b^9*c^8 + 27305557622784*a^12*b^7*c^9 + 100201644490752*a^13*b^5*c^10 - 142936235311104*a^14*b^3*c^11 - 677066377789440*a^15*b*c^12 + (2401*a^3*b^30*c^3 - 49049*a^4*b^28*c^4 - 1432760*a^5*b^26*c^5 - 6473264*a^6*b^24*c^6 + 373184512*a^7*b^22*c^7 - 319185152*a^8*b^20*c^8 - 27408852992*a^9*b^18*c^9 + 93871525888*a^10*b^16*c^10 + 774145638400*a^11*b^14*c^11 - 4486009651200*a^12*b^12*c^12 - 5590781263872*a^13*b^10*c^13 + 81717925773312*a^14*b^8*c^14 - 108093958520832*a^15*b^6*c^15 - 454721122861056*a^16*b^4*c^16 + 1497904875307008*a^17*b^2*c^17 - 1283918464548864*a^18*c^18)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(b^18*c^6 - 36*a*b^16*c^7 + 576*a^2*b^14*c^8 - 5376*a^3*b^12*c^9 + 32256*a^4*b^10*c^10 - 129024*a^5*b^8*c^11 + 344064*a^6*b^6*c^12 - 589824*a^7*b^4*c^13 + 589824*a^8*b^2*c^14 - 262144*a^9*c^15)))*sqrt(-(b^7 + 21*a*b^5*c + 168*a^2*b^3*c^2 + 3024*a^3*b*c^3 - (b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8 + 4096*a^6*c^9)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(b^18*c^6 - 36*a*b^16*c^7 + 576*a^2*b^14*c^8 - 5376*a^3*b^12*c^9 + 32256*a^4*b^10*c^10 - 129024*a^5*b^8*c^11 + 344064*a^6*b^6*c^12 - 589824*a^7*b^4*c^13 + 589824*a^8*b^2*c^14 - 262144*a^9*c^15)))/(b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8 + 4096*a^6*c^9)))*sqrt(sqrt(1/2)*sqrt(-(b^7 + 21*a*b^5*c + 168*a^2*b^3*c^2 + 3024*a^3*b*c^3 - (b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8 + 4096*a^6*c^9)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(b^18*c^6 - 36*a*b^16*c^7 + 576*a^2*b^14*c^8 - 5376*a^3*b^12*c^9 + 32256*a^4*b^10*c^10 - 129024*a^5*b^8*c^11 + 344064*a^6*b^6*c^12 - 589824*a^7*b^4*c^13 + 589824*a^8*b^2*c^14 - 262144*a^9*c^15)))/(b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8 + 4096*a^6*c^9))) - (343*a^2*b^19 + 21070*a^3*b^17*c + 600271*a^4*b^15*c^2 + 8903196*a^5*b^13*c^3 + 62719920*a^6*b^11*c^4 - 15909696*a^7*b^9*c^5 - 2396812032*a^8*b^7*c^6 - 6953610240*a^9*b^5*c^7 + 19591041024*a^10*b^3*c^8 + 78364164096*a^11*b*c^9 + (343*a^2*b^24*c^3 + 10437*a^3*b^22*c^4 + 90132*a^4*b^20*c^5 - 1028432*a^5*b^18*c^6 - 14041152*a^6*b^16*c^7 + 70390272*a^7*b^14*c^8 + 646137856*a^8*b^12*c^9 - 3121520640*a^9*b^10*c^10 - 11091935232*a^10*b^8*c^11 + 68335239168*a^11*b^6*c^12 + 24652283904*a^12*b^4*c^13 - 557256278016*a^13*b^2*c^14 + 743008370688*a^14*c^15)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(b^18*c^6 - 36*a*b^16*c^7 + 576*a^2*b^14*c^8 - 5376*a^3*b^12*c^9 + 32256*a^4*b^10*c^10 - 129024*a^5*b^8*c^11 + 344064*a^6*b^6*c^12 - 589824*a^7*b^4*c^13 + 589824*a^8*b^2*c^14 - 262144*a^9*c^15)))*sqrt(x)*sqrt(sqrt(1/2)*sqrt(-(b^7 + 21*a*b^5*c + 168*a^2*b^3*c^2 + 3024*a^3*b*c^3 - (b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8 + 4096*a^6*c^9)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(b^18*c^6 - 36*a*b^16*c^7 + 576*a^2*b^14*c^8 - 5376*a^3*b^12*c^9 + 32256*a^4*b^10*c^10 - 129024*a^5*b^8*c^11 + 344064*a^6*b^6*c^12 - 589824*a^7*b^4*c^13 + 589824*a^8*b^2*c^14 - 262144*a^9*c^15)))/(b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8 + 4096*a^6*c^9))))/(2401*a^3*b^16 + 179046*a^4*b^14*c + 6354369*a^5*b^12*c^2 + 131902344*a^6*b^10*c^3 + 1713103344*a^7*b^8*c^4 + 13740938496*a^8*b^6*c^5 + 65167421184*a^9*b^4*c^6 + 166523848704*a^10*b^2*c^7 + 176319369216*a^11*c^8)) + ((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(sqrt(1/2)*sqrt(-(b^7 + 21*a*b^5*c + 168*a^2*b^3*c^2 + 3024*a^3*b*c^3 + (b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8 + 4096*a^6*c^9)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(b^18*c^6 - 36*a*b^16*c^7 + 576*a^2*b^14*c^8 - 5376*a^3*b^12*c^9 + 32256*a^4*b^10*c^10 - 129024*a^5*b^8*c^11 + 344064*a^6*b^6*c^12 - 589824*a^7*b^4*c^13 + 589824*a^8*b^2*c^14 - 262144*a^9*c^15)))/(b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8 + 4096*a^6*c^9)))*log(1/2*sqrt(1/2)*(b^18 + 25*a*b^16*c - 146*a^2*b^14*c^2 - 5320*a^3*b^12*c^3 - 2464*a^4*b^10*c^4 + 1076096*a^5*b^8*c^5 - 10483200*a^6*b^6*c^6 + 44181504*a^7*b^4*c^7 - 89579520*a^8*b^2*c^8 + 71663616*a^9*c^9 - (b^23*c^3 - 20*a*b^21*c^4 + 432*a^2*b^19*c^5 - 11712*a^3*b^17*c^6 + 195072*a^4*b^15*c^7 - 1935360*a^5*b^13*c^8 + 12214272*a^6*b^11*c^9 - 50823168*a^7*b^9*c^10 + 139788288*a^8*b^7*c^11 - 245628928*a^9*b^5*c^12 + 250609664*a^10*b^3*c^13 - 113246208*a^11*b*c^14)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(b^18*c^6 - 36*a*b^16*c^7 + 576*a^2*b^14*c^8 - 5376*a^3*b^12*c^9 + 32256*a^4*b^10*c^10 - 129024*a^5*b^8*c^11 + 344064*a^6*b^6*c^12 - 589824*a^7*b^4*c^13 + 589824*a^8*b^2*c^14 - 262144*a^9*c^15)))*sqrt(sqrt(1/2)*sqrt(-(b^7 + 21*a*b^5*c + 168*a^2*b^3*c^2 + 3024*a^3*b*c^3 + (b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8 + 4096*a^6*c^9)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(b^18*c^6 - 36*a*b^16*c^7 + 576*a^2*b^14*c^8 - 5376*a^3*b^12*c^9 + 32256*a^4*b^10*c^10 - 129024*a^5*b^8*c^11 + 344064*a^6*b^6*c^12 - 589824*a^7*b^4*c^13 + 589824*a^8*b^2*c^14 - 262144*a^9*c^15)))/(b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8 + 4096*a^6*c^9)))*sqrt(-(b^7 + 21*a*b^5*c + 168*a^2*b^3*c^2 + 3024*a^3*b*c^3 + (b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8 + 4096*a^6*c^9)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(b^18*c^6 - 36*a*b^16*c^7 + 576*a^2*b^14*c^8 - 5376*a^3*b^12*c^9 + 32256*a^4*b^10*c^10 - 129024*a^5*b^8*c^11 + 344064*a^6*b^6*c^12 - 589824*a^7*b^4*c^13 + 589824*a^8*b^2*c^14 - 262144*a^9*c^15)))/(b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8 + 4096*a^6*c^9)) + (343*a^2*b^10 + 14553*a^3*b^8*c + 281232*a^4*b^6*c^2 + 2496096*a^5*b^4*c^3 + 10077696*a^6*b^2*c^4 + 15116544*a^7*c^5)*sqrt(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)*sqrt(sqrt(1/2)*sqrt(-(b^7 + 21*a*b^5*c + 168*a^2*b^3*c^2 + 3024*a^3*b*c^3 + (b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8 + 4096*a^6*c^9)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(b^18*c^6 - 36*a*b^16*c^7 + 576*a^2*b^14*c^8 - 5376*a^3*b^12*c^9 + 32256*a^4*b^10*c^10 - 129024*a^5*b^8*c^11 + 344064*a^6*b^6*c^12 - 589824*a^7*b^4*c^13 + 589824*a^8*b^2*c^14 - 262144*a^9*c^15)))/(b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8 + 4096*a^6*c^9)))*log(-1/2*sqrt(1/2)*(b^18 + 25*a*b^16*c - 146*a^2*b^14*c^2 - 5320*a^3*b^12*c^3 - 2464*a^4*b^10*c^4 + 1076096*a^5*b^8*c^5 - 10483200*a^6*b^6*c^6 + 44181504*a^7*b^4*c^7 - 89579520*a^8*b^2*c^8 + 71663616*a^9*c^9 - (b^23*c^3 - 20*a*b^21*c^4 + 432*a^2*b^19*c^5 - 11712*a^3*b^17*c^6 + 195072*a^4*b^15*c^7 - 1935360*a^5*b^13*c^8 + 12214272*a^6*b^11*c^9 - 50823168*a^7*b^9*c^10 + 139788288*a^8*b^7*c^11 - 245628928*a^9*b^5*c^12 + 250609664*a^10*b^3*c^13 - 113246208*a^11*b*c^14)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(b^18*c^6 - 36*a*b^16*c^7 + 576*a^2*b^14*c^8 - 5376*a^3*b^12*c^9 + 32256*a^4*b^10*c^10 - 129024*a^5*b^8*c^11 + 344064*a^6*b^6*c^12 - 589824*a^7*b^4*c^13 + 589824*a^8*b^2*c^14 - 262144*a^9*c^15)))*sqrt(sqrt(1/2)*sqrt(-(b^7 + 21*a*b^5*c + 168*a^2*b^3*c^2 + 3024*a^3*b*c^3 + (b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8 + 4096*a^6*c^9)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(b^18*c^6 - 36*a*b^16*c^7 + 576*a^2*b^14*c^8 - 5376*a^3*b^12*c^9 + 32256*a^4*b^10*c^10 - 129024*a^5*b^8*c^11 + 344064*a^6*b^6*c^12 - 589824*a^7*b^4*c^13 + 589824*a^8*b^2*c^14 - 262144*a^9*c^15)))/(b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8 + 4096*a^6*c^9)))*sqrt(-(b^7 + 21*a*b^5*c + 168*a^2*b^3*c^2 + 3024*a^3*b*c^3 + (b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8 + 4096*a^6*c^9)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(b^18*c^6 - 36*a*b^16*c^7 + 576*a^2*b^14*c^8 - 5376*a^3*b^12*c^9 + 32256*a^4*b^10*c^10 - 129024*a^5*b^8*c^11 + 344064*a^6*b^6*c^12 - 589824*a^7*b^4*c^13 + 589824*a^8*b^2*c^14 - 262144*a^9*c^15)))/(b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8 + 4096*a^6*c^9)) + (343*a^2*b^10 + 14553*a^3*b^8*c + 281232*a^4*b^6*c^2 + 2496096*a^5*b^4*c^3 + 10077696*a^6*b^2*c^4 + 15116544*a^7*c^5)*sqrt(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)*sqrt(sqrt(1/2)*sqrt(-(b^7 + 21*a*b^5*c + 168*a^2*b^3*c^2 + 3024*a^3*b*c^3 - (b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8 + 4096*a^6*c^9)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(b^18*c^6 - 36*a*b^16*c^7 + 576*a^2*b^14*c^8 - 5376*a^3*b^12*c^9 + 32256*a^4*b^10*c^10 - 129024*a^5*b^8*c^11 + 344064*a^6*b^6*c^12 - 589824*a^7*b^4*c^13 + 589824*a^8*b^2*c^14 - 262144*a^9*c^15)))/(b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8 + 4096*a^6*c^9)))*log(1/2*sqrt(1/2)*(b^18 + 25*a*b^16*c - 146*a^2*b^14*c^2 - 5320*a^3*b^12*c^3 - 2464*a^4*b^10*c^4 + 1076096*a^5*b^8*c^5 - 10483200*a^6*b^6*c^6 + 44181504*a^7*b^4*c^7 - 89579520*a^8*b^2*c^8 + 71663616*a^9*c^9 + (b^23*c^3 - 20*a*b^21*c^4 + 432*a^2*b^19*c^5 - 11712*a^3*b^17*c^6 + 195072*a^4*b^15*c^7 - 1935360*a^5*b^13*c^8 + 12214272*a^6*b^11*c^9 - 50823168*a^7*b^9*c^10 + 139788288*a^8*b^7*c^11 - 245628928*a^9*b^5*c^12 + 250609664*a^10*b^3*c^13 - 113246208*a^11*b*c^14)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(b^18*c^6 - 36*a*b^16*c^7 + 576*a^2*b^14*c^8 - 5376*a^3*b^12*c^9 + 32256*a^4*b^10*c^10 - 129024*a^5*b^8*c^11 + 344064*a^6*b^6*c^12 - 589824*a^7*b^4*c^13 + 589824*a^8*b^2*c^14 - 262144*a^9*c^15)))*sqrt(sqrt(1/2)*sqrt(-(b^7 + 21*a*b^5*c + 168*a^2*b^3*c^2 + 3024*a^3*b*c^3 - (b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8 + 4096*a^6*c^9)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(b^18*c^6 - 36*a*b^16*c^7 + 576*a^2*b^14*c^8 - 5376*a^3*b^12*c^9 + 32256*a^4*b^10*c^10 - 129024*a^5*b^8*c^11 + 344064*a^6*b^6*c^12 - 589824*a^7*b^4*c^13 + 589824*a^8*b^2*c^14 - 262144*a^9*c^15)))/(b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8 + 4096*a^6*c^9)))*sqrt(-(b^7 + 21*a*b^5*c + 168*a^2*b^3*c^2 + 3024*a^3*b*c^3 - (b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8 + 4096*a^6*c^9)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(b^18*c^6 - 36*a*b^16*c^7 + 576*a^2*b^14*c^8 - 5376*a^3*b^12*c^9 + 32256*a^4*b^10*c^10 - 129024*a^5*b^8*c^11 + 344064*a^6*b^6*c^12 - 589824*a^7*b^4*c^13 + 589824*a^8*b^2*c^14 - 262144*a^9*c^15)))/(b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8 + 4096*a^6*c^9)) + (343*a^2*b^10 + 14553*a^3*b^8*c + 281232*a^4*b^6*c^2 + 2496096*a^5*b^4*c^3 + 10077696*a^6*b^2*c^4 + 15116544*a^7*c^5)*sqrt(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)*sqrt(sqrt(1/2)*sqrt(-(b^7 + 21*a*b^5*c + 168*a^2*b^3*c^2 + 3024*a^3*b*c^3 - (b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8 + 4096*a^6*c^9)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(b^18*c^6 - 36*a*b^16*c^7 + 576*a^2*b^14*c^8 - 5376*a^3*b^12*c^9 + 32256*a^4*b^10*c^10 - 129024*a^5*b^8*c^11 + 344064*a^6*b^6*c^12 - 589824*a^7*b^4*c^13 + 589824*a^8*b^2*c^14 - 262144*a^9*c^15)))/(b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8 + 4096*a^6*c^9)))*log(-1/2*sqrt(1/2)*(b^18 + 25*a*b^16*c - 146*a^2*b^14*c^2 - 5320*a^3*b^12*c^3 - 2464*a^4*b^10*c^4 + 1076096*a^5*b^8*c^5 - 10483200*a^6*b^6*c^6 + 44181504*a^7*b^4*c^7 - 89579520*a^8*b^2*c^8 + 71663616*a^9*c^9 + (b^23*c^3 - 20*a*b^21*c^4 + 432*a^2*b^19*c^5 - 11712*a^3*b^17*c^6 + 195072*a^4*b^15*c^7 - 1935360*a^5*b^13*c^8 + 12214272*a^6*b^11*c^9 - 50823168*a^7*b^9*c^10 + 139788288*a^8*b^7*c^11 - 245628928*a^9*b^5*c^12 + 250609664*a^10*b^3*c^13 - 113246208*a^11*b*c^14)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(b^18*c^6 - 36*a*b^16*c^7 + 576*a^2*b^14*c^8 - 5376*a^3*b^12*c^9 + 32256*a^4*b^10*c^10 - 129024*a^5*b^8*c^11 + 344064*a^6*b^6*c^12 - 589824*a^7*b^4*c^13 + 589824*a^8*b^2*c^14 - 262144*a^9*c^15)))*sqrt(sqrt(1/2)*sqrt(-(b^7 + 21*a*b^5*c + 168*a^2*b^3*c^2 + 3024*a^3*b*c^3 - (b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8 + 4096*a^6*c^9)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(b^18*c^6 - 36*a*b^16*c^7 + 576*a^2*b^14*c^8 - 5376*a^3*b^12*c^9 + 32256*a^4*b^10*c^10 - 129024*a^5*b^8*c^11 + 344064*a^6*b^6*c^12 - 589824*a^7*b^4*c^13 + 589824*a^8*b^2*c^14 - 262144*a^9*c^15)))/(b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8 + 4096*a^6*c^9)))*sqrt(-(b^7 + 21*a*b^5*c + 168*a^2*b^3*c^2 + 3024*a^3*b*c^3 - (b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8 + 4096*a^6*c^9)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(b^18*c^6 - 36*a*b^16*c^7 + 576*a^2*b^14*c^8 - 5376*a^3*b^12*c^9 + 32256*a^4*b^10*c^10 - 129024*a^5*b^8*c^11 + 344064*a^6*b^6*c^12 - 589824*a^7*b^4*c^13 + 589824*a^8*b^2*c^14 - 262144*a^9*c^15)))/(b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8 + 4096*a^6*c^9)) + (343*a^2*b^10 + 14553*a^3*b^8*c + 281232*a^4*b^6*c^2 + 2496096*a^5*b^4*c^3 + 10077696*a^6*b^2*c^4 + 15116544*a^7*c^5)*sqrt(x)) - 4*(b*x^3 + 2*a*x)*sqrt(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
1074,1,9245,0,12.624017," ","integrate(x^(7/2)/(c*x^4+b*x^2+a)^2,x, algorithm=""fricas"")","-\frac{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)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{81 \, b^{5} + 760 \, a b^{3} c - 240 \, a^{2} b c^{2} + {\left(b^{12} c - 24 \, a b^{10} c^{2} + 240 \, a^{2} b^{8} c^{3} - 1280 \, a^{3} b^{6} c^{4} + 3840 \, a^{4} b^{4} c^{5} - 6144 \, a^{5} b^{2} c^{6} + 4096 \, a^{6} c^{7}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{b^{18} c^{2} - 36 \, a b^{16} c^{3} + 576 \, a^{2} b^{14} c^{4} - 5376 \, a^{3} b^{12} c^{5} + 32256 \, a^{4} b^{10} c^{6} - 129024 \, a^{5} b^{8} c^{7} + 344064 \, a^{6} b^{6} c^{8} - 589824 \, a^{7} b^{4} c^{9} + 589824 \, a^{8} b^{2} c^{10} - 262144 \, a^{9} c^{11}}}}{b^{12} c - 24 \, a b^{10} c^{2} + 240 \, a^{2} b^{8} c^{3} - 1280 \, a^{3} b^{6} c^{4} + 3840 \, a^{4} b^{4} c^{5} - 6144 \, a^{5} b^{2} c^{6} + 4096 \, a^{6} c^{7}}}} \arctan\left(-\frac{{\left(\sqrt{\frac{1}{2}} {\left(2187 \, b^{15} - 47412 \, a b^{13} c + 423536 \, a^{2} b^{11} c^{2} - 1990720 \, a^{3} b^{9} c^{3} + 5177600 \, a^{4} b^{7} c^{4} - 7052288 \, a^{5} b^{5} c^{5} + 3985408 \, a^{6} b^{3} c^{6} - 180224 \, a^{7} b c^{7} - {\left(27 \, b^{22} c - 820 \, a b^{20} c^{2} + 10064 \, a^{2} b^{18} c^{3} - 57024 \, a^{3} b^{16} c^{4} + 44544 \, a^{4} b^{14} c^{5} + 1505280 \, a^{5} b^{12} c^{6} - 10838016 \, a^{6} b^{10} c^{7} + 38436864 \, a^{7} b^{8} c^{8} - 79233024 \, a^{8} b^{6} c^{9} + 92012544 \, a^{9} b^{4} c^{10} - 49283072 \, a^{10} b^{2} c^{11} + 4194304 \, a^{11} c^{12}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{b^{18} c^{2} - 36 \, a b^{16} c^{3} + 576 \, a^{2} b^{14} c^{4} - 5376 \, a^{3} b^{12} c^{5} + 32256 \, a^{4} b^{10} c^{6} - 129024 \, a^{5} b^{8} c^{7} + 344064 \, a^{6} b^{6} c^{8} - 589824 \, a^{7} b^{4} c^{9} + 589824 \, a^{8} b^{2} c^{10} - 262144 \, a^{9} c^{11}}}\right)} \sqrt{{\left(1476225 \, b^{8} + 641520 \, a b^{6} c + 30816 \, a^{2} b^{4} c^{2} - 8448 \, a^{3} b^{2} c^{3} + 256 \, a^{4} c^{4}\right)} x + \sqrt{\frac{1}{2}} {\left(111537 \, b^{12} - 1375704 \, a b^{10} c + 5803760 \, a^{2} b^{8} c^{2} - 8961280 \, a^{3} b^{6} c^{3} + 2522880 \, a^{4} b^{4} c^{4} - 186368 \, a^{5} b^{2} c^{5} + 4096 \, a^{6} c^{6} + 8 \, {\left(81 \, b^{19} c - 2596 \, a b^{17} c^{2} + 36416 \, a^{2} b^{15} c^{3} - 292096 \, a^{3} b^{13} c^{4} + 1465856 \, a^{4} b^{11} c^{5} - 4716544 \, a^{5} b^{9} c^{6} + 9519104 \, a^{6} b^{7} c^{7} - 11075584 \, a^{7} b^{5} c^{8} + 5832704 \, a^{8} b^{3} c^{9} - 262144 \, a^{9} b c^{10}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{b^{18} c^{2} - 36 \, a b^{16} c^{3} + 576 \, a^{2} b^{14} c^{4} - 5376 \, a^{3} b^{12} c^{5} + 32256 \, a^{4} b^{10} c^{6} - 129024 \, a^{5} b^{8} c^{7} + 344064 \, a^{6} b^{6} c^{8} - 589824 \, a^{7} b^{4} c^{9} + 589824 \, a^{8} b^{2} c^{10} - 262144 \, a^{9} c^{11}}}\right)} \sqrt{-\frac{81 \, b^{5} + 760 \, a b^{3} c - 240 \, a^{2} b c^{2} + {\left(b^{12} c - 24 \, a b^{10} c^{2} + 240 \, a^{2} b^{8} c^{3} - 1280 \, a^{3} b^{6} c^{4} + 3840 \, a^{4} b^{4} c^{5} - 6144 \, a^{5} b^{2} c^{6} + 4096 \, a^{6} c^{7}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{b^{18} c^{2} - 36 \, a b^{16} c^{3} + 576 \, a^{2} b^{14} c^{4} - 5376 \, a^{3} b^{12} c^{5} + 32256 \, a^{4} b^{10} c^{6} - 129024 \, a^{5} b^{8} c^{7} + 344064 \, a^{6} b^{6} c^{8} - 589824 \, a^{7} b^{4} c^{9} + 589824 \, a^{8} b^{2} c^{10} - 262144 \, a^{9} c^{11}}}}{b^{12} c - 24 \, a b^{10} c^{2} + 240 \, a^{2} b^{8} c^{3} - 1280 \, a^{3} b^{6} c^{4} + 3840 \, a^{4} b^{4} c^{5} - 6144 \, a^{5} b^{2} c^{6} + 4096 \, a^{6} c^{7}}}} \sqrt{-\frac{81 \, b^{5} + 760 \, a b^{3} c - 240 \, a^{2} b c^{2} + {\left(b^{12} c - 24 \, a b^{10} c^{2} + 240 \, a^{2} b^{8} c^{3} - 1280 \, a^{3} b^{6} c^{4} + 3840 \, a^{4} b^{4} c^{5} - 6144 \, a^{5} b^{2} c^{6} + 4096 \, a^{6} c^{7}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{b^{18} c^{2} - 36 \, a b^{16} c^{3} + 576 \, a^{2} b^{14} c^{4} - 5376 \, a^{3} b^{12} c^{5} + 32256 \, a^{4} b^{10} c^{6} - 129024 \, a^{5} b^{8} c^{7} + 344064 \, a^{6} b^{6} c^{8} - 589824 \, a^{7} b^{4} c^{9} + 589824 \, a^{8} b^{2} c^{10} - 262144 \, a^{9} c^{11}}}}{b^{12} c - 24 \, a b^{10} c^{2} + 240 \, a^{2} b^{8} c^{3} - 1280 \, a^{3} b^{6} c^{4} + 3840 \, a^{4} b^{4} c^{5} - 6144 \, a^{5} b^{2} c^{6} + 4096 \, a^{6} c^{7}}} + \sqrt{\frac{1}{2}} {\left(2657205 \, b^{19} - 57028212 \, a b^{17} c + 502044480 \, a^{2} b^{15} c^{2} - 2306152704 \, a^{3} b^{13} c^{3} + 5758457344 \, a^{4} b^{11} c^{4} - 7169792000 \, a^{5} b^{9} c^{5} + 2897625088 \, a^{6} b^{7} c^{6} + 946012160 \, a^{7} b^{5} c^{7} - 111345664 \, a^{8} b^{3} c^{8} + 2883584 \, a^{9} b c^{9} - {\left(32805 \, b^{26} c - 989172 \, a b^{24} c^{2} + 12010848 \, a^{2} b^{22} c^{3} - 66614144 \, a^{3} b^{20} c^{4} + 38905600 \, a^{4} b^{18} c^{5} + 1841587200 \, a^{5} b^{16} c^{6} - 12771508224 \, a^{6} b^{14} c^{7} + 43815469056 \, a^{7} b^{12} c^{8} - 85947383808 \, a^{8} b^{10} c^{9} + 90262732800 \, a^{9} b^{8} c^{10} - 34319892480 \, a^{10} b^{6} c^{11} - 9386852352 \, a^{11} b^{4} c^{12} + 1895825408 \, a^{12} b^{2} c^{13} - 67108864 \, a^{13} c^{14}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{b^{18} c^{2} - 36 \, a b^{16} c^{3} + 576 \, a^{2} b^{14} c^{4} - 5376 \, a^{3} b^{12} c^{5} + 32256 \, a^{4} b^{10} c^{6} - 129024 \, a^{5} b^{8} c^{7} + 344064 \, a^{6} b^{6} c^{8} - 589824 \, a^{7} b^{4} c^{9} + 589824 \, a^{8} b^{2} c^{10} - 262144 \, a^{9} c^{11}}}\right)} \sqrt{x} \sqrt{-\frac{81 \, b^{5} + 760 \, a b^{3} c - 240 \, a^{2} b c^{2} + {\left(b^{12} c - 24 \, a b^{10} c^{2} + 240 \, a^{2} b^{8} c^{3} - 1280 \, a^{3} b^{6} c^{4} + 3840 \, a^{4} b^{4} c^{5} - 6144 \, a^{5} b^{2} c^{6} + 4096 \, a^{6} c^{7}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{b^{18} c^{2} - 36 \, a b^{16} c^{3} + 576 \, a^{2} b^{14} c^{4} - 5376 \, a^{3} b^{12} c^{5} + 32256 \, a^{4} b^{10} c^{6} - 129024 \, a^{5} b^{8} c^{7} + 344064 \, a^{6} b^{6} c^{8} - 589824 \, a^{7} b^{4} c^{9} + 589824 \, a^{8} b^{2} c^{10} - 262144 \, a^{9} c^{11}}}}{b^{12} c - 24 \, a b^{10} c^{2} + 240 \, a^{2} b^{8} c^{3} - 1280 \, a^{3} b^{6} c^{4} + 3840 \, a^{4} b^{4} c^{5} - 6144 \, a^{5} b^{2} c^{6} + 4096 \, a^{6} c^{7}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{81 \, b^{5} + 760 \, a b^{3} c - 240 \, a^{2} b c^{2} + {\left(b^{12} c - 24 \, a b^{10} c^{2} + 240 \, a^{2} b^{8} c^{3} - 1280 \, a^{3} b^{6} c^{4} + 3840 \, a^{4} b^{4} c^{5} - 6144 \, a^{5} b^{2} c^{6} + 4096 \, a^{6} c^{7}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{b^{18} c^{2} - 36 \, a b^{16} c^{3} + 576 \, a^{2} b^{14} c^{4} - 5376 \, a^{3} b^{12} c^{5} + 32256 \, a^{4} b^{10} c^{6} - 129024 \, a^{5} b^{8} c^{7} + 344064 \, a^{6} b^{6} c^{8} - 589824 \, a^{7} b^{4} c^{9} + 589824 \, a^{8} b^{2} c^{10} - 262144 \, a^{9} c^{11}}}}{b^{12} c - 24 \, a b^{10} c^{2} + 240 \, a^{2} b^{8} c^{3} - 1280 \, a^{3} b^{6} c^{4} + 3840 \, a^{4} b^{4} c^{5} - 6144 \, a^{5} b^{2} c^{6} + 4096 \, a^{6} c^{7}}}}}{2 \, {\left(332150625 \, a b^{12} + 321489000 \, a^{2} b^{10} c + 107535600 \, a^{3} b^{8} c^{2} + 12061440 \, a^{4} b^{6} c^{3} - 463104 \, a^{5} b^{4} c^{4} - 104448 \, a^{6} b^{2} c^{5} + 4096 \, a^{7} c^{6}\right)}}\right) - 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)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{81 \, b^{5} + 760 \, a b^{3} c - 240 \, a^{2} b c^{2} - {\left(b^{12} c - 24 \, a b^{10} c^{2} + 240 \, a^{2} b^{8} c^{3} - 1280 \, a^{3} b^{6} c^{4} + 3840 \, a^{4} b^{4} c^{5} - 6144 \, a^{5} b^{2} c^{6} + 4096 \, a^{6} c^{7}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{b^{18} c^{2} - 36 \, a b^{16} c^{3} + 576 \, a^{2} b^{14} c^{4} - 5376 \, a^{3} b^{12} c^{5} + 32256 \, a^{4} b^{10} c^{6} - 129024 \, a^{5} b^{8} c^{7} + 344064 \, a^{6} b^{6} c^{8} - 589824 \, a^{7} b^{4} c^{9} + 589824 \, a^{8} b^{2} c^{10} - 262144 \, a^{9} c^{11}}}}{b^{12} c - 24 \, a b^{10} c^{2} + 240 \, a^{2} b^{8} c^{3} - 1280 \, a^{3} b^{6} c^{4} + 3840 \, a^{4} b^{4} c^{5} - 6144 \, a^{5} b^{2} c^{6} + 4096 \, a^{6} c^{7}}}} \arctan\left(\frac{\sqrt{\frac{1}{2}} {\left(2187 \, b^{15} - 47412 \, a b^{13} c + 423536 \, a^{2} b^{11} c^{2} - 1990720 \, a^{3} b^{9} c^{3} + 5177600 \, a^{4} b^{7} c^{4} - 7052288 \, a^{5} b^{5} c^{5} + 3985408 \, a^{6} b^{3} c^{6} - 180224 \, a^{7} b c^{7} + {\left(27 \, b^{22} c - 820 \, a b^{20} c^{2} + 10064 \, a^{2} b^{18} c^{3} - 57024 \, a^{3} b^{16} c^{4} + 44544 \, a^{4} b^{14} c^{5} + 1505280 \, a^{5} b^{12} c^{6} - 10838016 \, a^{6} b^{10} c^{7} + 38436864 \, a^{7} b^{8} c^{8} - 79233024 \, a^{8} b^{6} c^{9} + 92012544 \, a^{9} b^{4} c^{10} - 49283072 \, a^{10} b^{2} c^{11} + 4194304 \, a^{11} c^{12}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{b^{18} c^{2} - 36 \, a b^{16} c^{3} + 576 \, a^{2} b^{14} c^{4} - 5376 \, a^{3} b^{12} c^{5} + 32256 \, a^{4} b^{10} c^{6} - 129024 \, a^{5} b^{8} c^{7} + 344064 \, a^{6} b^{6} c^{8} - 589824 \, a^{7} b^{4} c^{9} + 589824 \, a^{8} b^{2} c^{10} - 262144 \, a^{9} c^{11}}}\right)} \sqrt{{\left(1476225 \, b^{8} + 641520 \, a b^{6} c + 30816 \, a^{2} b^{4} c^{2} - 8448 \, a^{3} b^{2} c^{3} + 256 \, a^{4} c^{4}\right)} x + \sqrt{\frac{1}{2}} {\left(111537 \, b^{12} - 1375704 \, a b^{10} c + 5803760 \, a^{2} b^{8} c^{2} - 8961280 \, a^{3} b^{6} c^{3} + 2522880 \, a^{4} b^{4} c^{4} - 186368 \, a^{5} b^{2} c^{5} + 4096 \, a^{6} c^{6} - 8 \, {\left(81 \, b^{19} c - 2596 \, a b^{17} c^{2} + 36416 \, a^{2} b^{15} c^{3} - 292096 \, a^{3} b^{13} c^{4} + 1465856 \, a^{4} b^{11} c^{5} - 4716544 \, a^{5} b^{9} c^{6} + 9519104 \, a^{6} b^{7} c^{7} - 11075584 \, a^{7} b^{5} c^{8} + 5832704 \, a^{8} b^{3} c^{9} - 262144 \, a^{9} b c^{10}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{b^{18} c^{2} - 36 \, a b^{16} c^{3} + 576 \, a^{2} b^{14} c^{4} - 5376 \, a^{3} b^{12} c^{5} + 32256 \, a^{4} b^{10} c^{6} - 129024 \, a^{5} b^{8} c^{7} + 344064 \, a^{6} b^{6} c^{8} - 589824 \, a^{7} b^{4} c^{9} + 589824 \, a^{8} b^{2} c^{10} - 262144 \, a^{9} c^{11}}}\right)} \sqrt{-\frac{81 \, b^{5} + 760 \, a b^{3} c - 240 \, a^{2} b c^{2} - {\left(b^{12} c - 24 \, a b^{10} c^{2} + 240 \, a^{2} b^{8} c^{3} - 1280 \, a^{3} b^{6} c^{4} + 3840 \, a^{4} b^{4} c^{5} - 6144 \, a^{5} b^{2} c^{6} + 4096 \, a^{6} c^{7}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{b^{18} c^{2} - 36 \, a b^{16} c^{3} + 576 \, a^{2} b^{14} c^{4} - 5376 \, a^{3} b^{12} c^{5} + 32256 \, a^{4} b^{10} c^{6} - 129024 \, a^{5} b^{8} c^{7} + 344064 \, a^{6} b^{6} c^{8} - 589824 \, a^{7} b^{4} c^{9} + 589824 \, a^{8} b^{2} c^{10} - 262144 \, a^{9} c^{11}}}}{b^{12} c - 24 \, a b^{10} c^{2} + 240 \, a^{2} b^{8} c^{3} - 1280 \, a^{3} b^{6} c^{4} + 3840 \, a^{4} b^{4} c^{5} - 6144 \, a^{5} b^{2} c^{6} + 4096 \, a^{6} c^{7}}}} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{81 \, b^{5} + 760 \, a b^{3} c - 240 \, a^{2} b c^{2} - {\left(b^{12} c - 24 \, a b^{10} c^{2} + 240 \, a^{2} b^{8} c^{3} - 1280 \, a^{3} b^{6} c^{4} + 3840 \, a^{4} b^{4} c^{5} - 6144 \, a^{5} b^{2} c^{6} + 4096 \, a^{6} c^{7}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{b^{18} c^{2} - 36 \, a b^{16} c^{3} + 576 \, a^{2} b^{14} c^{4} - 5376 \, a^{3} b^{12} c^{5} + 32256 \, a^{4} b^{10} c^{6} - 129024 \, a^{5} b^{8} c^{7} + 344064 \, a^{6} b^{6} c^{8} - 589824 \, a^{7} b^{4} c^{9} + 589824 \, a^{8} b^{2} c^{10} - 262144 \, a^{9} c^{11}}}}{b^{12} c - 24 \, a b^{10} c^{2} + 240 \, a^{2} b^{8} c^{3} - 1280 \, a^{3} b^{6} c^{4} + 3840 \, a^{4} b^{4} c^{5} - 6144 \, a^{5} b^{2} c^{6} + 4096 \, a^{6} c^{7}}}} \sqrt{-\frac{81 \, b^{5} + 760 \, a b^{3} c - 240 \, a^{2} b c^{2} - {\left(b^{12} c - 24 \, a b^{10} c^{2} + 240 \, a^{2} b^{8} c^{3} - 1280 \, a^{3} b^{6} c^{4} + 3840 \, a^{4} b^{4} c^{5} - 6144 \, a^{5} b^{2} c^{6} + 4096 \, a^{6} c^{7}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{b^{18} c^{2} - 36 \, a b^{16} c^{3} + 576 \, a^{2} b^{14} c^{4} - 5376 \, a^{3} b^{12} c^{5} + 32256 \, a^{4} b^{10} c^{6} - 129024 \, a^{5} b^{8} c^{7} + 344064 \, a^{6} b^{6} c^{8} - 589824 \, a^{7} b^{4} c^{9} + 589824 \, a^{8} b^{2} c^{10} - 262144 \, a^{9} c^{11}}}}{b^{12} c - 24 \, a b^{10} c^{2} + 240 \, a^{2} b^{8} c^{3} - 1280 \, a^{3} b^{6} c^{4} + 3840 \, a^{4} b^{4} c^{5} - 6144 \, a^{5} b^{2} c^{6} + 4096 \, a^{6} c^{7}}} + \sqrt{\frac{1}{2}} {\left(2657205 \, b^{19} - 57028212 \, a b^{17} c + 502044480 \, a^{2} b^{15} c^{2} - 2306152704 \, a^{3} b^{13} c^{3} + 5758457344 \, a^{4} b^{11} c^{4} - 7169792000 \, a^{5} b^{9} c^{5} + 2897625088 \, a^{6} b^{7} c^{6} + 946012160 \, a^{7} b^{5} c^{7} - 111345664 \, a^{8} b^{3} c^{8} + 2883584 \, a^{9} b c^{9} + {\left(32805 \, b^{26} c - 989172 \, a b^{24} c^{2} + 12010848 \, a^{2} b^{22} c^{3} - 66614144 \, a^{3} b^{20} c^{4} + 38905600 \, a^{4} b^{18} c^{5} + 1841587200 \, a^{5} b^{16} c^{6} - 12771508224 \, a^{6} b^{14} c^{7} + 43815469056 \, a^{7} b^{12} c^{8} - 85947383808 \, a^{8} b^{10} c^{9} + 90262732800 \, a^{9} b^{8} c^{10} - 34319892480 \, a^{10} b^{6} c^{11} - 9386852352 \, a^{11} b^{4} c^{12} + 1895825408 \, a^{12} b^{2} c^{13} - 67108864 \, a^{13} c^{14}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{b^{18} c^{2} - 36 \, a b^{16} c^{3} + 576 \, a^{2} b^{14} c^{4} - 5376 \, a^{3} b^{12} c^{5} + 32256 \, a^{4} b^{10} c^{6} - 129024 \, a^{5} b^{8} c^{7} + 344064 \, a^{6} b^{6} c^{8} - 589824 \, a^{7} b^{4} c^{9} + 589824 \, a^{8} b^{2} c^{10} - 262144 \, a^{9} c^{11}}}\right)} \sqrt{x} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{81 \, b^{5} + 760 \, a b^{3} c - 240 \, a^{2} b c^{2} - {\left(b^{12} c - 24 \, a b^{10} c^{2} + 240 \, a^{2} b^{8} c^{3} - 1280 \, a^{3} b^{6} c^{4} + 3840 \, a^{4} b^{4} c^{5} - 6144 \, a^{5} b^{2} c^{6} + 4096 \, a^{6} c^{7}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{b^{18} c^{2} - 36 \, a b^{16} c^{3} + 576 \, a^{2} b^{14} c^{4} - 5376 \, a^{3} b^{12} c^{5} + 32256 \, a^{4} b^{10} c^{6} - 129024 \, a^{5} b^{8} c^{7} + 344064 \, a^{6} b^{6} c^{8} - 589824 \, a^{7} b^{4} c^{9} + 589824 \, a^{8} b^{2} c^{10} - 262144 \, a^{9} c^{11}}}}{b^{12} c - 24 \, a b^{10} c^{2} + 240 \, a^{2} b^{8} c^{3} - 1280 \, a^{3} b^{6} c^{4} + 3840 \, a^{4} b^{4} c^{5} - 6144 \, a^{5} b^{2} c^{6} + 4096 \, a^{6} c^{7}}}} \sqrt{-\frac{81 \, b^{5} + 760 \, a b^{3} c - 240 \, a^{2} b c^{2} - {\left(b^{12} c - 24 \, a b^{10} c^{2} + 240 \, a^{2} b^{8} c^{3} - 1280 \, a^{3} b^{6} c^{4} + 3840 \, a^{4} b^{4} c^{5} - 6144 \, a^{5} b^{2} c^{6} + 4096 \, a^{6} c^{7}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{b^{18} c^{2} - 36 \, a b^{16} c^{3} + 576 \, a^{2} b^{14} c^{4} - 5376 \, a^{3} b^{12} c^{5} + 32256 \, a^{4} b^{10} c^{6} - 129024 \, a^{5} b^{8} c^{7} + 344064 \, a^{6} b^{6} c^{8} - 589824 \, a^{7} b^{4} c^{9} + 589824 \, a^{8} b^{2} c^{10} - 262144 \, a^{9} c^{11}}}}{b^{12} c - 24 \, a b^{10} c^{2} + 240 \, a^{2} b^{8} c^{3} - 1280 \, a^{3} b^{6} c^{4} + 3840 \, a^{4} b^{4} c^{5} - 6144 \, a^{5} b^{2} c^{6} + 4096 \, a^{6} c^{7}}}}{2 \, {\left(332150625 \, a b^{12} + 321489000 \, a^{2} b^{10} c + 107535600 \, a^{3} b^{8} c^{2} + 12061440 \, a^{4} b^{6} c^{3} - 463104 \, a^{5} b^{4} c^{4} - 104448 \, a^{6} b^{2} c^{5} + 4096 \, a^{7} c^{6}\right)}}\right) + {\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{\sqrt{\frac{1}{2}} \sqrt{-\frac{81 \, b^{5} + 760 \, a b^{3} c - 240 \, a^{2} b c^{2} + {\left(b^{12} c - 24 \, a b^{10} c^{2} + 240 \, a^{2} b^{8} c^{3} - 1280 \, a^{3} b^{6} c^{4} + 3840 \, a^{4} b^{4} c^{5} - 6144 \, a^{5} b^{2} c^{6} + 4096 \, a^{6} c^{7}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{b^{18} c^{2} - 36 \, a b^{16} c^{3} + 576 \, a^{2} b^{14} c^{4} - 5376 \, a^{3} b^{12} c^{5} + 32256 \, a^{4} b^{10} c^{6} - 129024 \, a^{5} b^{8} c^{7} + 344064 \, a^{6} b^{6} c^{8} - 589824 \, a^{7} b^{4} c^{9} + 589824 \, a^{8} b^{2} c^{10} - 262144 \, a^{9} c^{11}}}}{b^{12} c - 24 \, a b^{10} c^{2} + 240 \, a^{2} b^{8} c^{3} - 1280 \, a^{3} b^{6} c^{4} + 3840 \, a^{4} b^{4} c^{5} - 6144 \, a^{5} b^{2} c^{6} + 4096 \, a^{6} c^{7}}}} \log\left(-{\left(1215 \, b^{4} + 264 \, a b^{2} c - 16 \, a^{2} c^{2}\right)} \sqrt{x} + {\left(81 \, b^{6} - 652 \, a b^{4} c + 1328 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3} + 4 \, {\left(b^{13} c - 24 \, a b^{11} c^{2} + 240 \, a^{2} b^{9} c^{3} - 1280 \, a^{3} b^{7} c^{4} + 3840 \, a^{4} b^{5} c^{5} - 6144 \, a^{5} b^{3} c^{6} + 4096 \, a^{6} b c^{7}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{b^{18} c^{2} - 36 \, a b^{16} c^{3} + 576 \, a^{2} b^{14} c^{4} - 5376 \, a^{3} b^{12} c^{5} + 32256 \, a^{4} b^{10} c^{6} - 129024 \, a^{5} b^{8} c^{7} + 344064 \, a^{6} b^{6} c^{8} - 589824 \, a^{7} b^{4} c^{9} + 589824 \, a^{8} b^{2} c^{10} - 262144 \, a^{9} c^{11}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{81 \, b^{5} + 760 \, a b^{3} c - 240 \, a^{2} b c^{2} + {\left(b^{12} c - 24 \, a b^{10} c^{2} + 240 \, a^{2} b^{8} c^{3} - 1280 \, a^{3} b^{6} c^{4} + 3840 \, a^{4} b^{4} c^{5} - 6144 \, a^{5} b^{2} c^{6} + 4096 \, a^{6} c^{7}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{b^{18} c^{2} - 36 \, a b^{16} c^{3} + 576 \, a^{2} b^{14} c^{4} - 5376 \, a^{3} b^{12} c^{5} + 32256 \, a^{4} b^{10} c^{6} - 129024 \, a^{5} b^{8} c^{7} + 344064 \, a^{6} b^{6} c^{8} - 589824 \, a^{7} b^{4} c^{9} + 589824 \, a^{8} b^{2} c^{10} - 262144 \, a^{9} c^{11}}}}{b^{12} c - 24 \, a b^{10} c^{2} + 240 \, a^{2} b^{8} c^{3} - 1280 \, a^{3} b^{6} c^{4} + 3840 \, a^{4} b^{4} c^{5} - 6144 \, a^{5} b^{2} c^{6} + 4096 \, a^{6} c^{7}}}}\right) - {\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{\sqrt{\frac{1}{2}} \sqrt{-\frac{81 \, b^{5} + 760 \, a b^{3} c - 240 \, a^{2} b c^{2} + {\left(b^{12} c - 24 \, a b^{10} c^{2} + 240 \, a^{2} b^{8} c^{3} - 1280 \, a^{3} b^{6} c^{4} + 3840 \, a^{4} b^{4} c^{5} - 6144 \, a^{5} b^{2} c^{6} + 4096 \, a^{6} c^{7}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{b^{18} c^{2} - 36 \, a b^{16} c^{3} + 576 \, a^{2} b^{14} c^{4} - 5376 \, a^{3} b^{12} c^{5} + 32256 \, a^{4} b^{10} c^{6} - 129024 \, a^{5} b^{8} c^{7} + 344064 \, a^{6} b^{6} c^{8} - 589824 \, a^{7} b^{4} c^{9} + 589824 \, a^{8} b^{2} c^{10} - 262144 \, a^{9} c^{11}}}}{b^{12} c - 24 \, a b^{10} c^{2} + 240 \, a^{2} b^{8} c^{3} - 1280 \, a^{3} b^{6} c^{4} + 3840 \, a^{4} b^{4} c^{5} - 6144 \, a^{5} b^{2} c^{6} + 4096 \, a^{6} c^{7}}}} \log\left(-{\left(1215 \, b^{4} + 264 \, a b^{2} c - 16 \, a^{2} c^{2}\right)} \sqrt{x} - {\left(81 \, b^{6} - 652 \, a b^{4} c + 1328 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3} + 4 \, {\left(b^{13} c - 24 \, a b^{11} c^{2} + 240 \, a^{2} b^{9} c^{3} - 1280 \, a^{3} b^{7} c^{4} + 3840 \, a^{4} b^{5} c^{5} - 6144 \, a^{5} b^{3} c^{6} + 4096 \, a^{6} b c^{7}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{b^{18} c^{2} - 36 \, a b^{16} c^{3} + 576 \, a^{2} b^{14} c^{4} - 5376 \, a^{3} b^{12} c^{5} + 32256 \, a^{4} b^{10} c^{6} - 129024 \, a^{5} b^{8} c^{7} + 344064 \, a^{6} b^{6} c^{8} - 589824 \, a^{7} b^{4} c^{9} + 589824 \, a^{8} b^{2} c^{10} - 262144 \, a^{9} c^{11}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{81 \, b^{5} + 760 \, a b^{3} c - 240 \, a^{2} b c^{2} + {\left(b^{12} c - 24 \, a b^{10} c^{2} + 240 \, a^{2} b^{8} c^{3} - 1280 \, a^{3} b^{6} c^{4} + 3840 \, a^{4} b^{4} c^{5} - 6144 \, a^{5} b^{2} c^{6} + 4096 \, a^{6} c^{7}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{b^{18} c^{2} - 36 \, a b^{16} c^{3} + 576 \, a^{2} b^{14} c^{4} - 5376 \, a^{3} b^{12} c^{5} + 32256 \, a^{4} b^{10} c^{6} - 129024 \, a^{5} b^{8} c^{7} + 344064 \, a^{6} b^{6} c^{8} - 589824 \, a^{7} b^{4} c^{9} + 589824 \, a^{8} b^{2} c^{10} - 262144 \, a^{9} c^{11}}}}{b^{12} c - 24 \, a b^{10} c^{2} + 240 \, a^{2} b^{8} c^{3} - 1280 \, a^{3} b^{6} c^{4} + 3840 \, a^{4} b^{4} c^{5} - 6144 \, a^{5} b^{2} c^{6} + 4096 \, a^{6} c^{7}}}}\right) + {\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{\sqrt{\frac{1}{2}} \sqrt{-\frac{81 \, b^{5} + 760 \, a b^{3} c - 240 \, a^{2} b c^{2} - {\left(b^{12} c - 24 \, a b^{10} c^{2} + 240 \, a^{2} b^{8} c^{3} - 1280 \, a^{3} b^{6} c^{4} + 3840 \, a^{4} b^{4} c^{5} - 6144 \, a^{5} b^{2} c^{6} + 4096 \, a^{6} c^{7}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{b^{18} c^{2} - 36 \, a b^{16} c^{3} + 576 \, a^{2} b^{14} c^{4} - 5376 \, a^{3} b^{12} c^{5} + 32256 \, a^{4} b^{10} c^{6} - 129024 \, a^{5} b^{8} c^{7} + 344064 \, a^{6} b^{6} c^{8} - 589824 \, a^{7} b^{4} c^{9} + 589824 \, a^{8} b^{2} c^{10} - 262144 \, a^{9} c^{11}}}}{b^{12} c - 24 \, a b^{10} c^{2} + 240 \, a^{2} b^{8} c^{3} - 1280 \, a^{3} b^{6} c^{4} + 3840 \, a^{4} b^{4} c^{5} - 6144 \, a^{5} b^{2} c^{6} + 4096 \, a^{6} c^{7}}}} \log\left(-{\left(1215 \, b^{4} + 264 \, a b^{2} c - 16 \, a^{2} c^{2}\right)} \sqrt{x} + {\left(81 \, b^{6} - 652 \, a b^{4} c + 1328 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3} - 4 \, {\left(b^{13} c - 24 \, a b^{11} c^{2} + 240 \, a^{2} b^{9} c^{3} - 1280 \, a^{3} b^{7} c^{4} + 3840 \, a^{4} b^{5} c^{5} - 6144 \, a^{5} b^{3} c^{6} + 4096 \, a^{6} b c^{7}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{b^{18} c^{2} - 36 \, a b^{16} c^{3} + 576 \, a^{2} b^{14} c^{4} - 5376 \, a^{3} b^{12} c^{5} + 32256 \, a^{4} b^{10} c^{6} - 129024 \, a^{5} b^{8} c^{7} + 344064 \, a^{6} b^{6} c^{8} - 589824 \, a^{7} b^{4} c^{9} + 589824 \, a^{8} b^{2} c^{10} - 262144 \, a^{9} c^{11}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{81 \, b^{5} + 760 \, a b^{3} c - 240 \, a^{2} b c^{2} - {\left(b^{12} c - 24 \, a b^{10} c^{2} + 240 \, a^{2} b^{8} c^{3} - 1280 \, a^{3} b^{6} c^{4} + 3840 \, a^{4} b^{4} c^{5} - 6144 \, a^{5} b^{2} c^{6} + 4096 \, a^{6} c^{7}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{b^{18} c^{2} - 36 \, a b^{16} c^{3} + 576 \, a^{2} b^{14} c^{4} - 5376 \, a^{3} b^{12} c^{5} + 32256 \, a^{4} b^{10} c^{6} - 129024 \, a^{5} b^{8} c^{7} + 344064 \, a^{6} b^{6} c^{8} - 589824 \, a^{7} b^{4} c^{9} + 589824 \, a^{8} b^{2} c^{10} - 262144 \, a^{9} c^{11}}}}{b^{12} c - 24 \, a b^{10} c^{2} + 240 \, a^{2} b^{8} c^{3} - 1280 \, a^{3} b^{6} c^{4} + 3840 \, a^{4} b^{4} c^{5} - 6144 \, a^{5} b^{2} c^{6} + 4096 \, a^{6} c^{7}}}}\right) - {\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{\sqrt{\frac{1}{2}} \sqrt{-\frac{81 \, b^{5} + 760 \, a b^{3} c - 240 \, a^{2} b c^{2} - {\left(b^{12} c - 24 \, a b^{10} c^{2} + 240 \, a^{2} b^{8} c^{3} - 1280 \, a^{3} b^{6} c^{4} + 3840 \, a^{4} b^{4} c^{5} - 6144 \, a^{5} b^{2} c^{6} + 4096 \, a^{6} c^{7}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{b^{18} c^{2} - 36 \, a b^{16} c^{3} + 576 \, a^{2} b^{14} c^{4} - 5376 \, a^{3} b^{12} c^{5} + 32256 \, a^{4} b^{10} c^{6} - 129024 \, a^{5} b^{8} c^{7} + 344064 \, a^{6} b^{6} c^{8} - 589824 \, a^{7} b^{4} c^{9} + 589824 \, a^{8} b^{2} c^{10} - 262144 \, a^{9} c^{11}}}}{b^{12} c - 24 \, a b^{10} c^{2} + 240 \, a^{2} b^{8} c^{3} - 1280 \, a^{3} b^{6} c^{4} + 3840 \, a^{4} b^{4} c^{5} - 6144 \, a^{5} b^{2} c^{6} + 4096 \, a^{6} c^{7}}}} \log\left(-{\left(1215 \, b^{4} + 264 \, a b^{2} c - 16 \, a^{2} c^{2}\right)} \sqrt{x} - {\left(81 \, b^{6} - 652 \, a b^{4} c + 1328 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3} - 4 \, {\left(b^{13} c - 24 \, a b^{11} c^{2} + 240 \, a^{2} b^{9} c^{3} - 1280 \, a^{3} b^{7} c^{4} + 3840 \, a^{4} b^{5} c^{5} - 6144 \, a^{5} b^{3} c^{6} + 4096 \, a^{6} b c^{7}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{b^{18} c^{2} - 36 \, a b^{16} c^{3} + 576 \, a^{2} b^{14} c^{4} - 5376 \, a^{3} b^{12} c^{5} + 32256 \, a^{4} b^{10} c^{6} - 129024 \, a^{5} b^{8} c^{7} + 344064 \, a^{6} b^{6} c^{8} - 589824 \, a^{7} b^{4} c^{9} + 589824 \, a^{8} b^{2} c^{10} - 262144 \, a^{9} c^{11}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{81 \, b^{5} + 760 \, a b^{3} c - 240 \, a^{2} b c^{2} - {\left(b^{12} c - 24 \, a b^{10} c^{2} + 240 \, a^{2} b^{8} c^{3} - 1280 \, a^{3} b^{6} c^{4} + 3840 \, a^{4} b^{4} c^{5} - 6144 \, a^{5} b^{2} c^{6} + 4096 \, a^{6} c^{7}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{b^{18} c^{2} - 36 \, a b^{16} c^{3} + 576 \, a^{2} b^{14} c^{4} - 5376 \, a^{3} b^{12} c^{5} + 32256 \, a^{4} b^{10} c^{6} - 129024 \, a^{5} b^{8} c^{7} + 344064 \, a^{6} b^{6} c^{8} - 589824 \, a^{7} b^{4} c^{9} + 589824 \, a^{8} b^{2} c^{10} - 262144 \, a^{9} c^{11}}}}{b^{12} c - 24 \, a b^{10} c^{2} + 240 \, a^{2} b^{8} c^{3} - 1280 \, a^{3} b^{6} c^{4} + 3840 \, a^{4} b^{4} c^{5} - 6144 \, a^{5} b^{2} c^{6} + 4096 \, a^{6} c^{7}}}}\right) - 4 \, {\left(b x^{2} + 2 \, a\right)} \sqrt{x}}{8 \, {\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,"-1/8*(4*((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(sqrt(1/2)*sqrt(-(81*b^5 + 760*a*b^3*c - 240*a^2*b*c^2 + (b^12*c - 24*a*b^10*c^2 + 240*a^2*b^8*c^3 - 1280*a^3*b^6*c^4 + 3840*a^4*b^4*c^5 - 6144*a^5*b^2*c^6 + 4096*a^6*c^7)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(b^18*c^2 - 36*a*b^16*c^3 + 576*a^2*b^14*c^4 - 5376*a^3*b^12*c^5 + 32256*a^4*b^10*c^6 - 129024*a^5*b^8*c^7 + 344064*a^6*b^6*c^8 - 589824*a^7*b^4*c^9 + 589824*a^8*b^2*c^10 - 262144*a^9*c^11)))/(b^12*c - 24*a*b^10*c^2 + 240*a^2*b^8*c^3 - 1280*a^3*b^6*c^4 + 3840*a^4*b^4*c^5 - 6144*a^5*b^2*c^6 + 4096*a^6*c^7)))*arctan(-1/2*(sqrt(1/2)*(2187*b^15 - 47412*a*b^13*c + 423536*a^2*b^11*c^2 - 1990720*a^3*b^9*c^3 + 5177600*a^4*b^7*c^4 - 7052288*a^5*b^5*c^5 + 3985408*a^6*b^3*c^6 - 180224*a^7*b*c^7 - (27*b^22*c - 820*a*b^20*c^2 + 10064*a^2*b^18*c^3 - 57024*a^3*b^16*c^4 + 44544*a^4*b^14*c^5 + 1505280*a^5*b^12*c^6 - 10838016*a^6*b^10*c^7 + 38436864*a^7*b^8*c^8 - 79233024*a^8*b^6*c^9 + 92012544*a^9*b^4*c^10 - 49283072*a^10*b^2*c^11 + 4194304*a^11*c^12)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(b^18*c^2 - 36*a*b^16*c^3 + 576*a^2*b^14*c^4 - 5376*a^3*b^12*c^5 + 32256*a^4*b^10*c^6 - 129024*a^5*b^8*c^7 + 344064*a^6*b^6*c^8 - 589824*a^7*b^4*c^9 + 589824*a^8*b^2*c^10 - 262144*a^9*c^11)))*sqrt((1476225*b^8 + 641520*a*b^6*c + 30816*a^2*b^4*c^2 - 8448*a^3*b^2*c^3 + 256*a^4*c^4)*x + sqrt(1/2)*(111537*b^12 - 1375704*a*b^10*c + 5803760*a^2*b^8*c^2 - 8961280*a^3*b^6*c^3 + 2522880*a^4*b^4*c^4 - 186368*a^5*b^2*c^5 + 4096*a^6*c^6 + 8*(81*b^19*c - 2596*a*b^17*c^2 + 36416*a^2*b^15*c^3 - 292096*a^3*b^13*c^4 + 1465856*a^4*b^11*c^5 - 4716544*a^5*b^9*c^6 + 9519104*a^6*b^7*c^7 - 11075584*a^7*b^5*c^8 + 5832704*a^8*b^3*c^9 - 262144*a^9*b*c^10)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(b^18*c^2 - 36*a*b^16*c^3 + 576*a^2*b^14*c^4 - 5376*a^3*b^12*c^5 + 32256*a^4*b^10*c^6 - 129024*a^5*b^8*c^7 + 344064*a^6*b^6*c^8 - 589824*a^7*b^4*c^9 + 589824*a^8*b^2*c^10 - 262144*a^9*c^11)))*sqrt(-(81*b^5 + 760*a*b^3*c - 240*a^2*b*c^2 + (b^12*c - 24*a*b^10*c^2 + 240*a^2*b^8*c^3 - 1280*a^3*b^6*c^4 + 3840*a^4*b^4*c^5 - 6144*a^5*b^2*c^6 + 4096*a^6*c^7)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(b^18*c^2 - 36*a*b^16*c^3 + 576*a^2*b^14*c^4 - 5376*a^3*b^12*c^5 + 32256*a^4*b^10*c^6 - 129024*a^5*b^8*c^7 + 344064*a^6*b^6*c^8 - 589824*a^7*b^4*c^9 + 589824*a^8*b^2*c^10 - 262144*a^9*c^11)))/(b^12*c - 24*a*b^10*c^2 + 240*a^2*b^8*c^3 - 1280*a^3*b^6*c^4 + 3840*a^4*b^4*c^5 - 6144*a^5*b^2*c^6 + 4096*a^6*c^7)))*sqrt(-(81*b^5 + 760*a*b^3*c - 240*a^2*b*c^2 + (b^12*c - 24*a*b^10*c^2 + 240*a^2*b^8*c^3 - 1280*a^3*b^6*c^4 + 3840*a^4*b^4*c^5 - 6144*a^5*b^2*c^6 + 4096*a^6*c^7)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(b^18*c^2 - 36*a*b^16*c^3 + 576*a^2*b^14*c^4 - 5376*a^3*b^12*c^5 + 32256*a^4*b^10*c^6 - 129024*a^5*b^8*c^7 + 344064*a^6*b^6*c^8 - 589824*a^7*b^4*c^9 + 589824*a^8*b^2*c^10 - 262144*a^9*c^11)))/(b^12*c - 24*a*b^10*c^2 + 240*a^2*b^8*c^3 - 1280*a^3*b^6*c^4 + 3840*a^4*b^4*c^5 - 6144*a^5*b^2*c^6 + 4096*a^6*c^7)) + sqrt(1/2)*(2657205*b^19 - 57028212*a*b^17*c + 502044480*a^2*b^15*c^2 - 2306152704*a^3*b^13*c^3 + 5758457344*a^4*b^11*c^4 - 7169792000*a^5*b^9*c^5 + 2897625088*a^6*b^7*c^6 + 946012160*a^7*b^5*c^7 - 111345664*a^8*b^3*c^8 + 2883584*a^9*b*c^9 - (32805*b^26*c - 989172*a*b^24*c^2 + 12010848*a^2*b^22*c^3 - 66614144*a^3*b^20*c^4 + 38905600*a^4*b^18*c^5 + 1841587200*a^5*b^16*c^6 - 12771508224*a^6*b^14*c^7 + 43815469056*a^7*b^12*c^8 - 85947383808*a^8*b^10*c^9 + 90262732800*a^9*b^8*c^10 - 34319892480*a^10*b^6*c^11 - 9386852352*a^11*b^4*c^12 + 1895825408*a^12*b^2*c^13 - 67108864*a^13*c^14)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(b^18*c^2 - 36*a*b^16*c^3 + 576*a^2*b^14*c^4 - 5376*a^3*b^12*c^5 + 32256*a^4*b^10*c^6 - 129024*a^5*b^8*c^7 + 344064*a^6*b^6*c^8 - 589824*a^7*b^4*c^9 + 589824*a^8*b^2*c^10 - 262144*a^9*c^11)))*sqrt(x)*sqrt(-(81*b^5 + 760*a*b^3*c - 240*a^2*b*c^2 + (b^12*c - 24*a*b^10*c^2 + 240*a^2*b^8*c^3 - 1280*a^3*b^6*c^4 + 3840*a^4*b^4*c^5 - 6144*a^5*b^2*c^6 + 4096*a^6*c^7)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(b^18*c^2 - 36*a*b^16*c^3 + 576*a^2*b^14*c^4 - 5376*a^3*b^12*c^5 + 32256*a^4*b^10*c^6 - 129024*a^5*b^8*c^7 + 344064*a^6*b^6*c^8 - 589824*a^7*b^4*c^9 + 589824*a^8*b^2*c^10 - 262144*a^9*c^11)))/(b^12*c - 24*a*b^10*c^2 + 240*a^2*b^8*c^3 - 1280*a^3*b^6*c^4 + 3840*a^4*b^4*c^5 - 6144*a^5*b^2*c^6 + 4096*a^6*c^7)))*sqrt(sqrt(1/2)*sqrt(-(81*b^5 + 760*a*b^3*c - 240*a^2*b*c^2 + (b^12*c - 24*a*b^10*c^2 + 240*a^2*b^8*c^3 - 1280*a^3*b^6*c^4 + 3840*a^4*b^4*c^5 - 6144*a^5*b^2*c^6 + 4096*a^6*c^7)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(b^18*c^2 - 36*a*b^16*c^3 + 576*a^2*b^14*c^4 - 5376*a^3*b^12*c^5 + 32256*a^4*b^10*c^6 - 129024*a^5*b^8*c^7 + 344064*a^6*b^6*c^8 - 589824*a^7*b^4*c^9 + 589824*a^8*b^2*c^10 - 262144*a^9*c^11)))/(b^12*c - 24*a*b^10*c^2 + 240*a^2*b^8*c^3 - 1280*a^3*b^6*c^4 + 3840*a^4*b^4*c^5 - 6144*a^5*b^2*c^6 + 4096*a^6*c^7)))/(332150625*a*b^12 + 321489000*a^2*b^10*c + 107535600*a^3*b^8*c^2 + 12061440*a^4*b^6*c^3 - 463104*a^5*b^4*c^4 - 104448*a^6*b^2*c^5 + 4096*a^7*c^6)) - 4*((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(sqrt(1/2)*sqrt(-(81*b^5 + 760*a*b^3*c - 240*a^2*b*c^2 - (b^12*c - 24*a*b^10*c^2 + 240*a^2*b^8*c^3 - 1280*a^3*b^6*c^4 + 3840*a^4*b^4*c^5 - 6144*a^5*b^2*c^6 + 4096*a^6*c^7)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(b^18*c^2 - 36*a*b^16*c^3 + 576*a^2*b^14*c^4 - 5376*a^3*b^12*c^5 + 32256*a^4*b^10*c^6 - 129024*a^5*b^8*c^7 + 344064*a^6*b^6*c^8 - 589824*a^7*b^4*c^9 + 589824*a^8*b^2*c^10 - 262144*a^9*c^11)))/(b^12*c - 24*a*b^10*c^2 + 240*a^2*b^8*c^3 - 1280*a^3*b^6*c^4 + 3840*a^4*b^4*c^5 - 6144*a^5*b^2*c^6 + 4096*a^6*c^7)))*arctan(1/2*(sqrt(1/2)*(2187*b^15 - 47412*a*b^13*c + 423536*a^2*b^11*c^2 - 1990720*a^3*b^9*c^3 + 5177600*a^4*b^7*c^4 - 7052288*a^5*b^5*c^5 + 3985408*a^6*b^3*c^6 - 180224*a^7*b*c^7 + (27*b^22*c - 820*a*b^20*c^2 + 10064*a^2*b^18*c^3 - 57024*a^3*b^16*c^4 + 44544*a^4*b^14*c^5 + 1505280*a^5*b^12*c^6 - 10838016*a^6*b^10*c^7 + 38436864*a^7*b^8*c^8 - 79233024*a^8*b^6*c^9 + 92012544*a^9*b^4*c^10 - 49283072*a^10*b^2*c^11 + 4194304*a^11*c^12)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(b^18*c^2 - 36*a*b^16*c^3 + 576*a^2*b^14*c^4 - 5376*a^3*b^12*c^5 + 32256*a^4*b^10*c^6 - 129024*a^5*b^8*c^7 + 344064*a^6*b^6*c^8 - 589824*a^7*b^4*c^9 + 589824*a^8*b^2*c^10 - 262144*a^9*c^11)))*sqrt((1476225*b^8 + 641520*a*b^6*c + 30816*a^2*b^4*c^2 - 8448*a^3*b^2*c^3 + 256*a^4*c^4)*x + sqrt(1/2)*(111537*b^12 - 1375704*a*b^10*c + 5803760*a^2*b^8*c^2 - 8961280*a^3*b^6*c^3 + 2522880*a^4*b^4*c^4 - 186368*a^5*b^2*c^5 + 4096*a^6*c^6 - 8*(81*b^19*c - 2596*a*b^17*c^2 + 36416*a^2*b^15*c^3 - 292096*a^3*b^13*c^4 + 1465856*a^4*b^11*c^5 - 4716544*a^5*b^9*c^6 + 9519104*a^6*b^7*c^7 - 11075584*a^7*b^5*c^8 + 5832704*a^8*b^3*c^9 - 262144*a^9*b*c^10)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(b^18*c^2 - 36*a*b^16*c^3 + 576*a^2*b^14*c^4 - 5376*a^3*b^12*c^5 + 32256*a^4*b^10*c^6 - 129024*a^5*b^8*c^7 + 344064*a^6*b^6*c^8 - 589824*a^7*b^4*c^9 + 589824*a^8*b^2*c^10 - 262144*a^9*c^11)))*sqrt(-(81*b^5 + 760*a*b^3*c - 240*a^2*b*c^2 - (b^12*c - 24*a*b^10*c^2 + 240*a^2*b^8*c^3 - 1280*a^3*b^6*c^4 + 3840*a^4*b^4*c^5 - 6144*a^5*b^2*c^6 + 4096*a^6*c^7)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(b^18*c^2 - 36*a*b^16*c^3 + 576*a^2*b^14*c^4 - 5376*a^3*b^12*c^5 + 32256*a^4*b^10*c^6 - 129024*a^5*b^8*c^7 + 344064*a^6*b^6*c^8 - 589824*a^7*b^4*c^9 + 589824*a^8*b^2*c^10 - 262144*a^9*c^11)))/(b^12*c - 24*a*b^10*c^2 + 240*a^2*b^8*c^3 - 1280*a^3*b^6*c^4 + 3840*a^4*b^4*c^5 - 6144*a^5*b^2*c^6 + 4096*a^6*c^7)))*sqrt(sqrt(1/2)*sqrt(-(81*b^5 + 760*a*b^3*c - 240*a^2*b*c^2 - (b^12*c - 24*a*b^10*c^2 + 240*a^2*b^8*c^3 - 1280*a^3*b^6*c^4 + 3840*a^4*b^4*c^5 - 6144*a^5*b^2*c^6 + 4096*a^6*c^7)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(b^18*c^2 - 36*a*b^16*c^3 + 576*a^2*b^14*c^4 - 5376*a^3*b^12*c^5 + 32256*a^4*b^10*c^6 - 129024*a^5*b^8*c^7 + 344064*a^6*b^6*c^8 - 589824*a^7*b^4*c^9 + 589824*a^8*b^2*c^10 - 262144*a^9*c^11)))/(b^12*c - 24*a*b^10*c^2 + 240*a^2*b^8*c^3 - 1280*a^3*b^6*c^4 + 3840*a^4*b^4*c^5 - 6144*a^5*b^2*c^6 + 4096*a^6*c^7)))*sqrt(-(81*b^5 + 760*a*b^3*c - 240*a^2*b*c^2 - (b^12*c - 24*a*b^10*c^2 + 240*a^2*b^8*c^3 - 1280*a^3*b^6*c^4 + 3840*a^4*b^4*c^5 - 6144*a^5*b^2*c^6 + 4096*a^6*c^7)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(b^18*c^2 - 36*a*b^16*c^3 + 576*a^2*b^14*c^4 - 5376*a^3*b^12*c^5 + 32256*a^4*b^10*c^6 - 129024*a^5*b^8*c^7 + 344064*a^6*b^6*c^8 - 589824*a^7*b^4*c^9 + 589824*a^8*b^2*c^10 - 262144*a^9*c^11)))/(b^12*c - 24*a*b^10*c^2 + 240*a^2*b^8*c^3 - 1280*a^3*b^6*c^4 + 3840*a^4*b^4*c^5 - 6144*a^5*b^2*c^6 + 4096*a^6*c^7)) + sqrt(1/2)*(2657205*b^19 - 57028212*a*b^17*c + 502044480*a^2*b^15*c^2 - 2306152704*a^3*b^13*c^3 + 5758457344*a^4*b^11*c^4 - 7169792000*a^5*b^9*c^5 + 2897625088*a^6*b^7*c^6 + 946012160*a^7*b^5*c^7 - 111345664*a^8*b^3*c^8 + 2883584*a^9*b*c^9 + (32805*b^26*c - 989172*a*b^24*c^2 + 12010848*a^2*b^22*c^3 - 66614144*a^3*b^20*c^4 + 38905600*a^4*b^18*c^5 + 1841587200*a^5*b^16*c^6 - 12771508224*a^6*b^14*c^7 + 43815469056*a^7*b^12*c^8 - 85947383808*a^8*b^10*c^9 + 90262732800*a^9*b^8*c^10 - 34319892480*a^10*b^6*c^11 - 9386852352*a^11*b^4*c^12 + 1895825408*a^12*b^2*c^13 - 67108864*a^13*c^14)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(b^18*c^2 - 36*a*b^16*c^3 + 576*a^2*b^14*c^4 - 5376*a^3*b^12*c^5 + 32256*a^4*b^10*c^6 - 129024*a^5*b^8*c^7 + 344064*a^6*b^6*c^8 - 589824*a^7*b^4*c^9 + 589824*a^8*b^2*c^10 - 262144*a^9*c^11)))*sqrt(x)*sqrt(sqrt(1/2)*sqrt(-(81*b^5 + 760*a*b^3*c - 240*a^2*b*c^2 - (b^12*c - 24*a*b^10*c^2 + 240*a^2*b^8*c^3 - 1280*a^3*b^6*c^4 + 3840*a^4*b^4*c^5 - 6144*a^5*b^2*c^6 + 4096*a^6*c^7)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(b^18*c^2 - 36*a*b^16*c^3 + 576*a^2*b^14*c^4 - 5376*a^3*b^12*c^5 + 32256*a^4*b^10*c^6 - 129024*a^5*b^8*c^7 + 344064*a^6*b^6*c^8 - 589824*a^7*b^4*c^9 + 589824*a^8*b^2*c^10 - 262144*a^9*c^11)))/(b^12*c - 24*a*b^10*c^2 + 240*a^2*b^8*c^3 - 1280*a^3*b^6*c^4 + 3840*a^4*b^4*c^5 - 6144*a^5*b^2*c^6 + 4096*a^6*c^7)))*sqrt(-(81*b^5 + 760*a*b^3*c - 240*a^2*b*c^2 - (b^12*c - 24*a*b^10*c^2 + 240*a^2*b^8*c^3 - 1280*a^3*b^6*c^4 + 3840*a^4*b^4*c^5 - 6144*a^5*b^2*c^6 + 4096*a^6*c^7)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(b^18*c^2 - 36*a*b^16*c^3 + 576*a^2*b^14*c^4 - 5376*a^3*b^12*c^5 + 32256*a^4*b^10*c^6 - 129024*a^5*b^8*c^7 + 344064*a^6*b^6*c^8 - 589824*a^7*b^4*c^9 + 589824*a^8*b^2*c^10 - 262144*a^9*c^11)))/(b^12*c - 24*a*b^10*c^2 + 240*a^2*b^8*c^3 - 1280*a^3*b^6*c^4 + 3840*a^4*b^4*c^5 - 6144*a^5*b^2*c^6 + 4096*a^6*c^7)))/(332150625*a*b^12 + 321489000*a^2*b^10*c + 107535600*a^3*b^8*c^2 + 12061440*a^4*b^6*c^3 - 463104*a^5*b^4*c^4 - 104448*a^6*b^2*c^5 + 4096*a^7*c^6)) + ((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(sqrt(1/2)*sqrt(-(81*b^5 + 760*a*b^3*c - 240*a^2*b*c^2 + (b^12*c - 24*a*b^10*c^2 + 240*a^2*b^8*c^3 - 1280*a^3*b^6*c^4 + 3840*a^4*b^4*c^5 - 6144*a^5*b^2*c^6 + 4096*a^6*c^7)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(b^18*c^2 - 36*a*b^16*c^3 + 576*a^2*b^14*c^4 - 5376*a^3*b^12*c^5 + 32256*a^4*b^10*c^6 - 129024*a^5*b^8*c^7 + 344064*a^6*b^6*c^8 - 589824*a^7*b^4*c^9 + 589824*a^8*b^2*c^10 - 262144*a^9*c^11)))/(b^12*c - 24*a*b^10*c^2 + 240*a^2*b^8*c^3 - 1280*a^3*b^6*c^4 + 3840*a^4*b^4*c^5 - 6144*a^5*b^2*c^6 + 4096*a^6*c^7)))*log(-(1215*b^4 + 264*a*b^2*c - 16*a^2*c^2)*sqrt(x) + (81*b^6 - 652*a*b^4*c + 1328*a^2*b^2*c^2 - 64*a^3*c^3 + 4*(b^13*c - 24*a*b^11*c^2 + 240*a^2*b^9*c^3 - 1280*a^3*b^7*c^4 + 3840*a^4*b^5*c^5 - 6144*a^5*b^3*c^6 + 4096*a^6*b*c^7)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(b^18*c^2 - 36*a*b^16*c^3 + 576*a^2*b^14*c^4 - 5376*a^3*b^12*c^5 + 32256*a^4*b^10*c^6 - 129024*a^5*b^8*c^7 + 344064*a^6*b^6*c^8 - 589824*a^7*b^4*c^9 + 589824*a^8*b^2*c^10 - 262144*a^9*c^11)))*sqrt(sqrt(1/2)*sqrt(-(81*b^5 + 760*a*b^3*c - 240*a^2*b*c^2 + (b^12*c - 24*a*b^10*c^2 + 240*a^2*b^8*c^3 - 1280*a^3*b^6*c^4 + 3840*a^4*b^4*c^5 - 6144*a^5*b^2*c^6 + 4096*a^6*c^7)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(b^18*c^2 - 36*a*b^16*c^3 + 576*a^2*b^14*c^4 - 5376*a^3*b^12*c^5 + 32256*a^4*b^10*c^6 - 129024*a^5*b^8*c^7 + 344064*a^6*b^6*c^8 - 589824*a^7*b^4*c^9 + 589824*a^8*b^2*c^10 - 262144*a^9*c^11)))/(b^12*c - 24*a*b^10*c^2 + 240*a^2*b^8*c^3 - 1280*a^3*b^6*c^4 + 3840*a^4*b^4*c^5 - 6144*a^5*b^2*c^6 + 4096*a^6*c^7)))) - ((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(sqrt(1/2)*sqrt(-(81*b^5 + 760*a*b^3*c - 240*a^2*b*c^2 + (b^12*c - 24*a*b^10*c^2 + 240*a^2*b^8*c^3 - 1280*a^3*b^6*c^4 + 3840*a^4*b^4*c^5 - 6144*a^5*b^2*c^6 + 4096*a^6*c^7)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(b^18*c^2 - 36*a*b^16*c^3 + 576*a^2*b^14*c^4 - 5376*a^3*b^12*c^5 + 32256*a^4*b^10*c^6 - 129024*a^5*b^8*c^7 + 344064*a^6*b^6*c^8 - 589824*a^7*b^4*c^9 + 589824*a^8*b^2*c^10 - 262144*a^9*c^11)))/(b^12*c - 24*a*b^10*c^2 + 240*a^2*b^8*c^3 - 1280*a^3*b^6*c^4 + 3840*a^4*b^4*c^5 - 6144*a^5*b^2*c^6 + 4096*a^6*c^7)))*log(-(1215*b^4 + 264*a*b^2*c - 16*a^2*c^2)*sqrt(x) - (81*b^6 - 652*a*b^4*c + 1328*a^2*b^2*c^2 - 64*a^3*c^3 + 4*(b^13*c - 24*a*b^11*c^2 + 240*a^2*b^9*c^3 - 1280*a^3*b^7*c^4 + 3840*a^4*b^5*c^5 - 6144*a^5*b^3*c^6 + 4096*a^6*b*c^7)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(b^18*c^2 - 36*a*b^16*c^3 + 576*a^2*b^14*c^4 - 5376*a^3*b^12*c^5 + 32256*a^4*b^10*c^6 - 129024*a^5*b^8*c^7 + 344064*a^6*b^6*c^8 - 589824*a^7*b^4*c^9 + 589824*a^8*b^2*c^10 - 262144*a^9*c^11)))*sqrt(sqrt(1/2)*sqrt(-(81*b^5 + 760*a*b^3*c - 240*a^2*b*c^2 + (b^12*c - 24*a*b^10*c^2 + 240*a^2*b^8*c^3 - 1280*a^3*b^6*c^4 + 3840*a^4*b^4*c^5 - 6144*a^5*b^2*c^6 + 4096*a^6*c^7)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(b^18*c^2 - 36*a*b^16*c^3 + 576*a^2*b^14*c^4 - 5376*a^3*b^12*c^5 + 32256*a^4*b^10*c^6 - 129024*a^5*b^8*c^7 + 344064*a^6*b^6*c^8 - 589824*a^7*b^4*c^9 + 589824*a^8*b^2*c^10 - 262144*a^9*c^11)))/(b^12*c - 24*a*b^10*c^2 + 240*a^2*b^8*c^3 - 1280*a^3*b^6*c^4 + 3840*a^4*b^4*c^5 - 6144*a^5*b^2*c^6 + 4096*a^6*c^7)))) + ((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(sqrt(1/2)*sqrt(-(81*b^5 + 760*a*b^3*c - 240*a^2*b*c^2 - (b^12*c - 24*a*b^10*c^2 + 240*a^2*b^8*c^3 - 1280*a^3*b^6*c^4 + 3840*a^4*b^4*c^5 - 6144*a^5*b^2*c^6 + 4096*a^6*c^7)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(b^18*c^2 - 36*a*b^16*c^3 + 576*a^2*b^14*c^4 - 5376*a^3*b^12*c^5 + 32256*a^4*b^10*c^6 - 129024*a^5*b^8*c^7 + 344064*a^6*b^6*c^8 - 589824*a^7*b^4*c^9 + 589824*a^8*b^2*c^10 - 262144*a^9*c^11)))/(b^12*c - 24*a*b^10*c^2 + 240*a^2*b^8*c^3 - 1280*a^3*b^6*c^4 + 3840*a^4*b^4*c^5 - 6144*a^5*b^2*c^6 + 4096*a^6*c^7)))*log(-(1215*b^4 + 264*a*b^2*c - 16*a^2*c^2)*sqrt(x) + (81*b^6 - 652*a*b^4*c + 1328*a^2*b^2*c^2 - 64*a^3*c^3 - 4*(b^13*c - 24*a*b^11*c^2 + 240*a^2*b^9*c^3 - 1280*a^3*b^7*c^4 + 3840*a^4*b^5*c^5 - 6144*a^5*b^3*c^6 + 4096*a^6*b*c^7)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(b^18*c^2 - 36*a*b^16*c^3 + 576*a^2*b^14*c^4 - 5376*a^3*b^12*c^5 + 32256*a^4*b^10*c^6 - 129024*a^5*b^8*c^7 + 344064*a^6*b^6*c^8 - 589824*a^7*b^4*c^9 + 589824*a^8*b^2*c^10 - 262144*a^9*c^11)))*sqrt(sqrt(1/2)*sqrt(-(81*b^5 + 760*a*b^3*c - 240*a^2*b*c^2 - (b^12*c - 24*a*b^10*c^2 + 240*a^2*b^8*c^3 - 1280*a^3*b^6*c^4 + 3840*a^4*b^4*c^5 - 6144*a^5*b^2*c^6 + 4096*a^6*c^7)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(b^18*c^2 - 36*a*b^16*c^3 + 576*a^2*b^14*c^4 - 5376*a^3*b^12*c^5 + 32256*a^4*b^10*c^6 - 129024*a^5*b^8*c^7 + 344064*a^6*b^6*c^8 - 589824*a^7*b^4*c^9 + 589824*a^8*b^2*c^10 - 262144*a^9*c^11)))/(b^12*c - 24*a*b^10*c^2 + 240*a^2*b^8*c^3 - 1280*a^3*b^6*c^4 + 3840*a^4*b^4*c^5 - 6144*a^5*b^2*c^6 + 4096*a^6*c^7)))) - ((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(sqrt(1/2)*sqrt(-(81*b^5 + 760*a*b^3*c - 240*a^2*b*c^2 - (b^12*c - 24*a*b^10*c^2 + 240*a^2*b^8*c^3 - 1280*a^3*b^6*c^4 + 3840*a^4*b^4*c^5 - 6144*a^5*b^2*c^6 + 4096*a^6*c^7)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(b^18*c^2 - 36*a*b^16*c^3 + 576*a^2*b^14*c^4 - 5376*a^3*b^12*c^5 + 32256*a^4*b^10*c^6 - 129024*a^5*b^8*c^7 + 344064*a^6*b^6*c^8 - 589824*a^7*b^4*c^9 + 589824*a^8*b^2*c^10 - 262144*a^9*c^11)))/(b^12*c - 24*a*b^10*c^2 + 240*a^2*b^8*c^3 - 1280*a^3*b^6*c^4 + 3840*a^4*b^4*c^5 - 6144*a^5*b^2*c^6 + 4096*a^6*c^7)))*log(-(1215*b^4 + 264*a*b^2*c - 16*a^2*c^2)*sqrt(x) - (81*b^6 - 652*a*b^4*c + 1328*a^2*b^2*c^2 - 64*a^3*c^3 - 4*(b^13*c - 24*a*b^11*c^2 + 240*a^2*b^9*c^3 - 1280*a^3*b^7*c^4 + 3840*a^4*b^5*c^5 - 6144*a^5*b^3*c^6 + 4096*a^6*b*c^7)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(b^18*c^2 - 36*a*b^16*c^3 + 576*a^2*b^14*c^4 - 5376*a^3*b^12*c^5 + 32256*a^4*b^10*c^6 - 129024*a^5*b^8*c^7 + 344064*a^6*b^6*c^8 - 589824*a^7*b^4*c^9 + 589824*a^8*b^2*c^10 - 262144*a^9*c^11)))*sqrt(sqrt(1/2)*sqrt(-(81*b^5 + 760*a*b^3*c - 240*a^2*b*c^2 - (b^12*c - 24*a*b^10*c^2 + 240*a^2*b^8*c^3 - 1280*a^3*b^6*c^4 + 3840*a^4*b^4*c^5 - 6144*a^5*b^2*c^6 + 4096*a^6*c^7)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(b^18*c^2 - 36*a*b^16*c^3 + 576*a^2*b^14*c^4 - 5376*a^3*b^12*c^5 + 32256*a^4*b^10*c^6 - 129024*a^5*b^8*c^7 + 344064*a^6*b^6*c^8 - 589824*a^7*b^4*c^9 + 589824*a^8*b^2*c^10 - 262144*a^9*c^11)))/(b^12*c - 24*a*b^10*c^2 + 240*a^2*b^8*c^3 - 1280*a^3*b^6*c^4 + 3840*a^4*b^4*c^5 - 6144*a^5*b^2*c^6 + 4096*a^6*c^7)))) - 4*(b*x^2 + 2*a)*sqrt(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
1075,1,9757,0,31.669180," ","integrate(x^(5/2)/(c*x^4+b*x^2+a)^2,x, algorithm=""fricas"")","-\frac{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)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{81 \, b^{5} + 760 \, a b^{3} c - 240 \, a^{2} b c^{2} - {\left(a b^{12} - 24 \, a^{2} b^{10} c + 240 \, a^{3} b^{8} c^{2} - 1280 \, a^{4} b^{6} c^{3} + 3840 \, a^{5} b^{4} c^{4} - 6144 \, a^{6} b^{2} c^{5} + 4096 \, a^{7} c^{6}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{a^{2} b^{18} - 36 \, a^{3} b^{16} c + 576 \, a^{4} b^{14} c^{2} - 5376 \, a^{5} b^{12} c^{3} + 32256 \, a^{6} b^{10} c^{4} - 129024 \, a^{7} b^{8} c^{5} + 344064 \, a^{8} b^{6} c^{6} - 589824 \, a^{9} b^{4} c^{7} + 589824 \, a^{10} b^{2} c^{8} - 262144 \, a^{11} c^{9}}}}{a b^{12} - 24 \, a^{2} b^{10} c + 240 \, a^{3} b^{8} c^{2} - 1280 \, a^{4} b^{6} c^{3} + 3840 \, a^{5} b^{4} c^{4} - 6144 \, a^{6} b^{2} c^{5} + 4096 \, a^{7} c^{6}}}} \arctan\left(-\frac{{\left({\left(81 \, b^{6} - 652 \, a b^{4} c + 1328 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3} - 4 \, {\left(a b^{13} - 24 \, a^{2} b^{11} c + 240 \, a^{3} b^{9} c^{2} - 1280 \, a^{4} b^{7} c^{3} + 3840 \, a^{5} b^{5} c^{4} - 6144 \, a^{6} b^{3} c^{5} + 4096 \, a^{7} b c^{6}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{a^{2} b^{18} - 36 \, a^{3} b^{16} c + 576 \, a^{4} b^{14} c^{2} - 5376 \, a^{5} b^{12} c^{3} + 32256 \, a^{6} b^{10} c^{4} - 129024 \, a^{7} b^{8} c^{5} + 344064 \, a^{8} b^{6} c^{6} - 589824 \, a^{9} b^{4} c^{7} + 589824 \, a^{10} b^{2} c^{8} - 262144 \, a^{11} c^{9}}}\right)} \sqrt{{\left(74733890625 \, b^{16} c^{2} + 112193100000 \, a b^{14} c^{3} + 68088600000 \, a^{2} b^{12} c^{4} + 20761920000 \, a^{3} b^{10} c^{5} + 3063744000 \, a^{4} b^{8} c^{6} + 113909760 \, a^{5} b^{6} c^{7} - 19021824 \, a^{6} b^{4} c^{8} - 1179648 \, a^{7} b^{2} c^{9} + 65536 \, a^{8} c^{10}\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(2989355625 \, b^{21} c - 23678649000 \, a b^{19} c^{2} + 7135160400 \, a^{2} b^{17} c^{3} + 277460328960 \, a^{3} b^{15} c^{4} - 338956033536 \, a^{4} b^{13} c^{5} - 492326940672 \, a^{5} b^{11} c^{6} - 183476674560 \, a^{6} b^{9} c^{7} - 21980119040 \, a^{7} b^{7} c^{8} + 750059520 \, a^{8} b^{5} c^{9} + 190316544 \, a^{9} b^{3} c^{10} - 7340032 \, a^{10} b c^{11} + {\left(36905625 \, a b^{28} c - 1159839000 \, a^{2} b^{26} c^{2} + 15854324400 \, a^{3} b^{24} c^{3} - 122710429440 \, a^{4} b^{22} c^{4} + 584418357504 \, a^{5} b^{20} c^{5} - 1728949905408 \, a^{6} b^{18} c^{6} + 2983008514048 \, a^{7} b^{16} c^{7} - 2317983285248 \, a^{8} b^{14} c^{8} - 462348419072 \, a^{9} b^{12} c^{9} + 1339972648960 \, a^{10} b^{10} c^{10} + 254402363392 \, a^{11} b^{8} c^{11} - 161849802752 \, a^{12} b^{6} c^{12} - 51220840448 \, a^{13} b^{4} c^{13} - 2550136832 \, a^{14} b^{2} c^{14} + 268435456 \, a^{15} c^{15}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{a^{2} b^{18} - 36 \, a^{3} b^{16} c + 576 \, a^{4} b^{14} c^{2} - 5376 \, a^{5} b^{12} c^{3} + 32256 \, a^{6} b^{10} c^{4} - 129024 \, a^{7} b^{8} c^{5} + 344064 \, a^{8} b^{6} c^{6} - 589824 \, a^{9} b^{4} c^{7} + 589824 \, a^{10} b^{2} c^{8} - 262144 \, a^{11} c^{9}}}\right)} \sqrt{-\frac{81 \, b^{5} + 760 \, a b^{3} c - 240 \, a^{2} b c^{2} - {\left(a b^{12} - 24 \, a^{2} b^{10} c + 240 \, a^{3} b^{8} c^{2} - 1280 \, a^{4} b^{6} c^{3} + 3840 \, a^{5} b^{4} c^{4} - 6144 \, a^{6} b^{2} c^{5} + 4096 \, a^{7} c^{6}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{a^{2} b^{18} - 36 \, a^{3} b^{16} c + 576 \, a^{4} b^{14} c^{2} - 5376 \, a^{5} b^{12} c^{3} + 32256 \, a^{6} b^{10} c^{4} - 129024 \, a^{7} b^{8} c^{5} + 344064 \, a^{8} b^{6} c^{6} - 589824 \, a^{9} b^{4} c^{7} + 589824 \, a^{10} b^{2} c^{8} - 262144 \, a^{11} c^{9}}}}{a b^{12} - 24 \, a^{2} b^{10} c + 240 \, a^{3} b^{8} c^{2} - 1280 \, a^{4} b^{6} c^{3} + 3840 \, a^{5} b^{4} c^{4} - 6144 \, a^{6} b^{2} c^{5} + 4096 \, a^{7} c^{6}}}} + {\left(22143375 \, b^{14} c - 161619300 \, a b^{12} c^{2} + 233100720 \, a^{2} b^{10} c^{3} + 224213184 \, a^{3} b^{8} c^{4} + 48450816 \, a^{4} b^{6} c^{5} + 185344 \, a^{5} b^{4} c^{6} - 487424 \, a^{6} b^{2} c^{7} + 16384 \, a^{7} c^{8} - 4 \, {\left(273375 \, a b^{21} c - 6355800 \, a^{2} b^{19} c^{2} + 60732720 \, a^{3} b^{17} c^{3} - 301810176 \, a^{4} b^{15} c^{4} + 798453248 \, a^{5} b^{13} c^{5} - 951914496 \, a^{6} b^{11} c^{6} + 38461440 \, a^{7} b^{9} c^{7} + 557711360 \, a^{8} b^{7} c^{8} + 179503104 \, a^{9} b^{5} c^{9} + 11010048 \, a^{10} b^{3} c^{10} - 1048576 \, a^{11} b c^{11}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{a^{2} b^{18} - 36 \, a^{3} b^{16} c + 576 \, a^{4} b^{14} c^{2} - 5376 \, a^{5} b^{12} c^{3} + 32256 \, a^{6} b^{10} c^{4} - 129024 \, a^{7} b^{8} c^{5} + 344064 \, a^{8} b^{6} c^{6} - 589824 \, a^{9} b^{4} c^{7} + 589824 \, a^{10} b^{2} c^{8} - 262144 \, a^{11} c^{9}}}\right)} \sqrt{x}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{81 \, b^{5} + 760 \, a b^{3} c - 240 \, a^{2} b c^{2} - {\left(a b^{12} - 24 \, a^{2} b^{10} c + 240 \, a^{3} b^{8} c^{2} - 1280 \, a^{4} b^{6} c^{3} + 3840 \, a^{5} b^{4} c^{4} - 6144 \, a^{6} b^{2} c^{5} + 4096 \, a^{7} c^{6}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{a^{2} b^{18} - 36 \, a^{3} b^{16} c + 576 \, a^{4} b^{14} c^{2} - 5376 \, a^{5} b^{12} c^{3} + 32256 \, a^{6} b^{10} c^{4} - 129024 \, a^{7} b^{8} c^{5} + 344064 \, a^{8} b^{6} c^{6} - 589824 \, a^{9} b^{4} c^{7} + 589824 \, a^{10} b^{2} c^{8} - 262144 \, a^{11} c^{9}}}}{a b^{12} - 24 \, a^{2} b^{10} c + 240 \, a^{3} b^{8} c^{2} - 1280 \, a^{4} b^{6} c^{3} + 3840 \, a^{5} b^{4} c^{4} - 6144 \, a^{6} b^{2} c^{5} + 4096 \, a^{7} c^{6}}}}}{332150625 \, b^{12} c + 321489000 \, a b^{10} c^{2} + 107535600 \, a^{2} b^{8} c^{3} + 12061440 \, a^{3} b^{6} c^{4} - 463104 \, a^{4} b^{4} c^{5} - 104448 \, a^{5} b^{2} c^{6} + 4096 \, a^{6} c^{7}}\right) - 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)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{81 \, b^{5} + 760 \, a b^{3} c - 240 \, a^{2} b c^{2} + {\left(a b^{12} - 24 \, a^{2} b^{10} c + 240 \, a^{3} b^{8} c^{2} - 1280 \, a^{4} b^{6} c^{3} + 3840 \, a^{5} b^{4} c^{4} - 6144 \, a^{6} b^{2} c^{5} + 4096 \, a^{7} c^{6}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{a^{2} b^{18} - 36 \, a^{3} b^{16} c + 576 \, a^{4} b^{14} c^{2} - 5376 \, a^{5} b^{12} c^{3} + 32256 \, a^{6} b^{10} c^{4} - 129024 \, a^{7} b^{8} c^{5} + 344064 \, a^{8} b^{6} c^{6} - 589824 \, a^{9} b^{4} c^{7} + 589824 \, a^{10} b^{2} c^{8} - 262144 \, a^{11} c^{9}}}}{a b^{12} - 24 \, a^{2} b^{10} c + 240 \, a^{3} b^{8} c^{2} - 1280 \, a^{4} b^{6} c^{3} + 3840 \, a^{5} b^{4} c^{4} - 6144 \, a^{6} b^{2} c^{5} + 4096 \, a^{7} c^{6}}}} \arctan\left(\frac{{\left(81 \, b^{6} - 652 \, a b^{4} c + 1328 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3} + 4 \, {\left(a b^{13} - 24 \, a^{2} b^{11} c + 240 \, a^{3} b^{9} c^{2} - 1280 \, a^{4} b^{7} c^{3} + 3840 \, a^{5} b^{5} c^{4} - 6144 \, a^{6} b^{3} c^{5} + 4096 \, a^{7} b c^{6}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{a^{2} b^{18} - 36 \, a^{3} b^{16} c + 576 \, a^{4} b^{14} c^{2} - 5376 \, a^{5} b^{12} c^{3} + 32256 \, a^{6} b^{10} c^{4} - 129024 \, a^{7} b^{8} c^{5} + 344064 \, a^{8} b^{6} c^{6} - 589824 \, a^{9} b^{4} c^{7} + 589824 \, a^{10} b^{2} c^{8} - 262144 \, a^{11} c^{9}}}\right)} \sqrt{{\left(74733890625 \, b^{16} c^{2} + 112193100000 \, a b^{14} c^{3} + 68088600000 \, a^{2} b^{12} c^{4} + 20761920000 \, a^{3} b^{10} c^{5} + 3063744000 \, a^{4} b^{8} c^{6} + 113909760 \, a^{5} b^{6} c^{7} - 19021824 \, a^{6} b^{4} c^{8} - 1179648 \, a^{7} b^{2} c^{9} + 65536 \, a^{8} c^{10}\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(2989355625 \, b^{21} c - 23678649000 \, a b^{19} c^{2} + 7135160400 \, a^{2} b^{17} c^{3} + 277460328960 \, a^{3} b^{15} c^{4} - 338956033536 \, a^{4} b^{13} c^{5} - 492326940672 \, a^{5} b^{11} c^{6} - 183476674560 \, a^{6} b^{9} c^{7} - 21980119040 \, a^{7} b^{7} c^{8} + 750059520 \, a^{8} b^{5} c^{9} + 190316544 \, a^{9} b^{3} c^{10} - 7340032 \, a^{10} b c^{11} - {\left(36905625 \, a b^{28} c - 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5376 \, a^{5} b^{12} c^{3} + 32256 \, a^{6} b^{10} c^{4} - 129024 \, a^{7} b^{8} c^{5} + 344064 \, a^{8} b^{6} c^{6} - 589824 \, a^{9} b^{4} c^{7} + 589824 \, a^{10} b^{2} c^{8} - 262144 \, a^{11} c^{9}}}}{a b^{12} - 24 \, a^{2} b^{10} c + 240 \, a^{3} b^{8} c^{2} - 1280 \, a^{4} b^{6} c^{3} + 3840 \, a^{5} b^{4} c^{4} - 6144 \, a^{6} b^{2} c^{5} + 4096 \, a^{7} c^{6}}}} + {\left(22143375 \, b^{14} c - 161619300 \, a b^{12} c^{2} + 233100720 \, a^{2} b^{10} c^{3} + 224213184 \, a^{3} b^{8} c^{4} + 48450816 \, a^{4} b^{6} c^{5} + 185344 \, a^{5} b^{4} c^{6} - 487424 \, a^{6} b^{2} c^{7} + 16384 \, a^{7} c^{8} + 4 \, {\left(273375 \, a b^{21} c - 6355800 \, a^{2} b^{19} c^{2} + 60732720 \, a^{3} b^{17} c^{3} - 301810176 \, a^{4} b^{15} c^{4} + 798453248 \, a^{5} b^{13} c^{5} - 951914496 \, a^{6} b^{11} c^{6} + 38461440 \, a^{7} b^{9} c^{7} + 557711360 \, a^{8} b^{7} c^{8} + 179503104 \, a^{9} b^{5} c^{9} + 11010048 \, a^{10} b^{3} c^{10} - 1048576 \, a^{11} b c^{11}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{a^{2} b^{18} - 36 \, a^{3} b^{16} c + 576 \, a^{4} b^{14} c^{2} - 5376 \, a^{5} b^{12} c^{3} + 32256 \, a^{6} b^{10} c^{4} - 129024 \, a^{7} b^{8} c^{5} + 344064 \, a^{8} b^{6} c^{6} - 589824 \, a^{9} b^{4} c^{7} + 589824 \, a^{10} b^{2} c^{8} - 262144 \, a^{11} c^{9}}}\right)} \sqrt{x} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{81 \, b^{5} + 760 \, a b^{3} c - 240 \, a^{2} b c^{2} + {\left(a b^{12} - 24 \, a^{2} b^{10} c + 240 \, a^{3} b^{8} c^{2} - 1280 \, a^{4} b^{6} c^{3} + 3840 \, a^{5} b^{4} c^{4} - 6144 \, a^{6} b^{2} c^{5} + 4096 \, a^{7} c^{6}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{a^{2} b^{18} - 36 \, a^{3} b^{16} c + 576 \, a^{4} b^{14} c^{2} - 5376 \, a^{5} b^{12} c^{3} + 32256 \, a^{6} b^{10} c^{4} - 129024 \, a^{7} b^{8} c^{5} + 344064 \, a^{8} b^{6} c^{6} - 589824 \, a^{9} b^{4} c^{7} + 589824 \, a^{10} b^{2} c^{8} - 262144 \, a^{11} c^{9}}}}{a b^{12} - 24 \, a^{2} b^{10} c + 240 \, a^{3} b^{8} c^{2} - 1280 \, a^{4} b^{6} c^{3} + 3840 \, a^{5} b^{4} c^{4} - 6144 \, a^{6} b^{2} c^{5} + 4096 \, a^{7} c^{6}}}}}{332150625 \, b^{12} c + 321489000 \, a b^{10} c^{2} + 107535600 \, a^{2} b^{8} c^{3} + 12061440 \, a^{3} b^{6} c^{4} - 463104 \, a^{4} b^{4} c^{5} - 104448 \, a^{5} b^{2} c^{6} + 4096 \, a^{6} c^{7}}\right) - {\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{\sqrt{\frac{1}{2}} \sqrt{-\frac{81 \, b^{5} + 760 \, a b^{3} c - 240 \, a^{2} b c^{2} + {\left(a b^{12} - 24 \, a^{2} b^{10} c + 240 \, a^{3} b^{8} c^{2} - 1280 \, a^{4} b^{6} c^{3} + 3840 \, a^{5} b^{4} c^{4} - 6144 \, a^{6} b^{2} c^{5} + 4096 \, a^{7} c^{6}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{a^{2} b^{18} - 36 \, a^{3} b^{16} c + 576 \, a^{4} b^{14} c^{2} - 5376 \, a^{5} b^{12} c^{3} + 32256 \, a^{6} b^{10} c^{4} - 129024 \, a^{7} b^{8} c^{5} + 344064 \, a^{8} b^{6} c^{6} - 589824 \, a^{9} b^{4} c^{7} + 589824 \, a^{10} b^{2} c^{8} - 262144 \, a^{11} c^{9}}}}{a b^{12} - 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589824 \, a^{9} b^{4} c^{7} + 589824 \, a^{10} b^{2} c^{8} - 262144 \, a^{11} c^{9}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{81 \, b^{5} + 760 \, a b^{3} c - 240 \, a^{2} b c^{2} + {\left(a b^{12} - 24 \, a^{2} b^{10} c + 240 \, a^{3} b^{8} c^{2} - 1280 \, a^{4} b^{6} c^{3} + 3840 \, a^{5} b^{4} c^{4} - 6144 \, a^{6} b^{2} c^{5} + 4096 \, a^{7} c^{6}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{a^{2} b^{18} - 36 \, a^{3} b^{16} c + 576 \, a^{4} b^{14} c^{2} - 5376 \, a^{5} b^{12} c^{3} + 32256 \, a^{6} b^{10} c^{4} - 129024 \, a^{7} b^{8} c^{5} + 344064 \, a^{8} b^{6} c^{6} - 589824 \, a^{9} b^{4} c^{7} + 589824 \, a^{10} b^{2} c^{8} - 262144 \, a^{11} c^{9}}}}{a b^{12} - 24 \, a^{2} b^{10} c + 240 \, a^{3} b^{8} c^{2} - 1280 \, a^{4} b^{6} c^{3} + 3840 \, a^{5} b^{4} c^{4} - 6144 \, a^{6} b^{2} c^{5} + 4096 \, a^{7} c^{6}}}} \sqrt{-\frac{81 \, b^{5} + 760 \, a b^{3} c - 240 \, a^{2} b c^{2} + {\left(a b^{12} - 24 \, a^{2} b^{10} c + 240 \, a^{3} b^{8} c^{2} - 1280 \, a^{4} b^{6} c^{3} + 3840 \, a^{5} b^{4} c^{4} - 6144 \, a^{6} b^{2} c^{5} + 4096 \, a^{7} c^{6}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{a^{2} b^{18} - 36 \, a^{3} b^{16} c + 576 \, a^{4} b^{14} c^{2} - 5376 \, a^{5} b^{12} c^{3} + 32256 \, a^{6} b^{10} c^{4} - 129024 \, a^{7} b^{8} c^{5} + 344064 \, a^{8} b^{6} c^{6} - 589824 \, a^{9} b^{4} c^{7} + 589824 \, a^{10} b^{2} c^{8} - 262144 \, a^{11} c^{9}}}}{a b^{12} - 24 \, a^{2} b^{10} c + 240 \, a^{3} b^{8} c^{2} - 1280 \, a^{4} b^{6} c^{3} + 3840 \, a^{5} b^{4} c^{4} - 6144 \, a^{6} b^{2} c^{5} + 4096 \, a^{7} c^{6}}} - {\left(273375 \, b^{8} c + 205200 \, a b^{6} c^{2} + 47520 \, a^{2} b^{4} c^{3} + 2304 \, a^{3} b^{2} c^{4} - 256 \, a^{4} c^{5}\right)} \sqrt{x}\right) + {\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{\sqrt{\frac{1}{2}} \sqrt{-\frac{81 \, b^{5} + 760 \, a b^{3} c - 240 \, a^{2} b c^{2} + {\left(a b^{12} - 24 \, a^{2} b^{10} c + 240 \, a^{3} b^{8} c^{2} - 1280 \, a^{4} b^{6} c^{3} + 3840 \, a^{5} b^{4} c^{4} - 6144 \, a^{6} b^{2} c^{5} + 4096 \, a^{7} c^{6}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{a^{2} b^{18} - 36 \, a^{3} b^{16} c + 576 \, a^{4} b^{14} c^{2} - 5376 \, a^{5} b^{12} c^{3} + 32256 \, a^{6} b^{10} c^{4} - 129024 \, a^{7} b^{8} c^{5} + 344064 \, a^{8} b^{6} c^{6} - 589824 \, a^{9} b^{4} c^{7} + 589824 \, a^{10} b^{2} c^{8} - 262144 \, a^{11} c^{9}}}}{a b^{12} - 24 \, a^{2} b^{10} c + 240 \, a^{3} b^{8} c^{2} - 1280 \, a^{4} b^{6} c^{3} + 3840 \, a^{5} b^{4} c^{4} - 6144 \, a^{6} b^{2} c^{5} + 4096 \, a^{7} c^{6}}}} \log\left(-\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(2187 \, b^{15} - 47412 \, a b^{13} c + 423536 \, a^{2} b^{11} c^{2} - 1990720 \, a^{3} b^{9} c^{3} + 5177600 \, a^{4} b^{7} c^{4} - 7052288 \, a^{5} b^{5} c^{5} + 3985408 \, a^{6} b^{3} c^{6} - 180224 \, a^{7} b c^{7} - {\left(27 \, a b^{22} - 820 \, a^{2} b^{20} c + 10064 \, a^{3} b^{18} c^{2} - 57024 \, a^{4} b^{16} c^{3} + 44544 \, a^{5} b^{14} c^{4} + 1505280 \, a^{6} b^{12} c^{5} - 10838016 \, a^{7} b^{10} c^{6} + 38436864 \, a^{8} b^{8} c^{7} - 79233024 \, a^{9} b^{6} c^{8} + 92012544 \, a^{10} b^{4} c^{9} - 49283072 \, a^{11} b^{2} c^{10} + 4194304 \, a^{12} c^{11}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{a^{2} b^{18} - 36 \, a^{3} b^{16} c + 576 \, a^{4} b^{14} c^{2} - 5376 \, a^{5} b^{12} c^{3} + 32256 \, a^{6} b^{10} c^{4} - 129024 \, a^{7} b^{8} c^{5} + 344064 \, a^{8} b^{6} c^{6} - 589824 \, a^{9} b^{4} c^{7} + 589824 \, a^{10} b^{2} c^{8} - 262144 \, a^{11} c^{9}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{81 \, b^{5} + 760 \, a b^{3} c - 240 \, a^{2} b c^{2} + {\left(a b^{12} - 24 \, a^{2} b^{10} c + 240 \, a^{3} b^{8} c^{2} - 1280 \, a^{4} b^{6} c^{3} + 3840 \, a^{5} b^{4} c^{4} - 6144 \, a^{6} b^{2} c^{5} + 4096 \, a^{7} c^{6}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{a^{2} b^{18} - 36 \, a^{3} b^{16} c + 576 \, a^{4} b^{14} c^{2} - 5376 \, a^{5} b^{12} c^{3} + 32256 \, a^{6} b^{10} c^{4} - 129024 \, a^{7} b^{8} c^{5} + 344064 \, a^{8} b^{6} c^{6} - 589824 \, a^{9} b^{4} c^{7} + 589824 \, a^{10} b^{2} c^{8} - 262144 \, a^{11} c^{9}}}}{a b^{12} - 24 \, a^{2} b^{10} c + 240 \, a^{3} b^{8} c^{2} - 1280 \, a^{4} b^{6} c^{3} + 3840 \, a^{5} b^{4} c^{4} - 6144 \, a^{6} b^{2} c^{5} + 4096 \, a^{7} c^{6}}}} \sqrt{-\frac{81 \, b^{5} + 760 \, a b^{3} c - 240 \, a^{2} b c^{2} + {\left(a b^{12} - 24 \, a^{2} b^{10} c + 240 \, a^{3} b^{8} c^{2} - 1280 \, a^{4} b^{6} c^{3} + 3840 \, a^{5} b^{4} c^{4} - 6144 \, a^{6} b^{2} c^{5} + 4096 \, a^{7} c^{6}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{a^{2} b^{18} - 36 \, a^{3} b^{16} c + 576 \, a^{4} b^{14} c^{2} - 5376 \, a^{5} b^{12} c^{3} + 32256 \, a^{6} b^{10} c^{4} - 129024 \, a^{7} b^{8} c^{5} + 344064 \, a^{8} b^{6} c^{6} - 589824 \, a^{9} b^{4} c^{7} + 589824 \, a^{10} b^{2} c^{8} - 262144 \, a^{11} c^{9}}}}{a b^{12} - 24 \, a^{2} b^{10} c + 240 \, a^{3} b^{8} c^{2} - 1280 \, a^{4} b^{6} c^{3} + 3840 \, a^{5} b^{4} c^{4} - 6144 \, a^{6} b^{2} c^{5} + 4096 \, a^{7} c^{6}}} - {\left(273375 \, b^{8} c + 205200 \, a b^{6} c^{2} + 47520 \, a^{2} b^{4} c^{3} + 2304 \, a^{3} b^{2} c^{4} - 256 \, a^{4} c^{5}\right)} \sqrt{x}\right) - {\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{\sqrt{\frac{1}{2}} \sqrt{-\frac{81 \, b^{5} + 760 \, a b^{3} c - 240 \, a^{2} b c^{2} - {\left(a b^{12} - 24 \, a^{2} b^{10} c + 240 \, a^{3} b^{8} c^{2} - 1280 \, a^{4} b^{6} c^{3} + 3840 \, a^{5} b^{4} c^{4} - 6144 \, a^{6} b^{2} c^{5} + 4096 \, a^{7} c^{6}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{a^{2} b^{18} - 36 \, a^{3} b^{16} c + 576 \, a^{4} b^{14} c^{2} - 5376 \, a^{5} b^{12} c^{3} + 32256 \, a^{6} b^{10} c^{4} - 129024 \, a^{7} b^{8} c^{5} + 344064 \, a^{8} b^{6} c^{6} - 589824 \, a^{9} b^{4} c^{7} + 589824 \, a^{10} b^{2} c^{8} - 262144 \, a^{11} c^{9}}}}{a b^{12} - 24 \, a^{2} b^{10} c + 240 \, a^{3} b^{8} c^{2} - 1280 \, a^{4} b^{6} c^{3} + 3840 \, a^{5} b^{4} c^{4} - 6144 \, a^{6} b^{2} c^{5} + 4096 \, a^{7} c^{6}}}} \log\left(\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(2187 \, b^{15} - 47412 \, a b^{13} c + 423536 \, a^{2} b^{11} c^{2} - 1990720 \, a^{3} b^{9} c^{3} + 5177600 \, a^{4} b^{7} c^{4} - 7052288 \, a^{5} b^{5} c^{5} + 3985408 \, a^{6} b^{3} c^{6} - 180224 \, a^{7} b c^{7} + {\left(27 \, a b^{22} - 820 \, a^{2} b^{20} c + 10064 \, a^{3} b^{18} c^{2} - 57024 \, a^{4} b^{16} c^{3} + 44544 \, a^{5} b^{14} c^{4} + 1505280 \, a^{6} b^{12} c^{5} - 10838016 \, a^{7} b^{10} c^{6} + 38436864 \, a^{8} b^{8} c^{7} - 79233024 \, a^{9} b^{6} c^{8} + 92012544 \, a^{10} b^{4} c^{9} - 49283072 \, a^{11} b^{2} c^{10} + 4194304 \, a^{12} c^{11}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{a^{2} b^{18} - 36 \, a^{3} b^{16} c + 576 \, a^{4} b^{14} c^{2} - 5376 \, a^{5} b^{12} c^{3} + 32256 \, a^{6} b^{10} c^{4} - 129024 \, a^{7} b^{8} c^{5} + 344064 \, a^{8} b^{6} c^{6} - 589824 \, a^{9} b^{4} c^{7} + 589824 \, a^{10} b^{2} c^{8} - 262144 \, a^{11} c^{9}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{81 \, b^{5} + 760 \, a b^{3} c - 240 \, a^{2} b c^{2} - {\left(a b^{12} - 24 \, a^{2} b^{10} c + 240 \, a^{3} b^{8} c^{2} - 1280 \, a^{4} b^{6} c^{3} + 3840 \, a^{5} b^{4} c^{4} - 6144 \, a^{6} b^{2} c^{5} + 4096 \, a^{7} c^{6}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{a^{2} b^{18} - 36 \, a^{3} b^{16} c + 576 \, a^{4} b^{14} c^{2} - 5376 \, a^{5} b^{12} c^{3} + 32256 \, a^{6} b^{10} c^{4} - 129024 \, a^{7} b^{8} c^{5} + 344064 \, a^{8} b^{6} c^{6} - 589824 \, a^{9} b^{4} c^{7} + 589824 \, a^{10} b^{2} c^{8} - 262144 \, a^{11} c^{9}}}}{a b^{12} - 24 \, a^{2} b^{10} c + 240 \, a^{3} b^{8} c^{2} - 1280 \, a^{4} b^{6} c^{3} + 3840 \, a^{5} b^{4} c^{4} - 6144 \, a^{6} b^{2} c^{5} + 4096 \, a^{7} c^{6}}}} \sqrt{-\frac{81 \, b^{5} + 760 \, a b^{3} c - 240 \, a^{2} b c^{2} - {\left(a b^{12} - 24 \, a^{2} b^{10} c + 240 \, a^{3} b^{8} c^{2} - 1280 \, a^{4} b^{6} c^{3} + 3840 \, a^{5} b^{4} c^{4} - 6144 \, a^{6} b^{2} c^{5} + 4096 \, a^{7} c^{6}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{a^{2} b^{18} - 36 \, a^{3} b^{16} c + 576 \, a^{4} b^{14} c^{2} - 5376 \, a^{5} b^{12} c^{3} + 32256 \, a^{6} b^{10} c^{4} - 129024 \, a^{7} b^{8} c^{5} + 344064 \, a^{8} b^{6} c^{6} - 589824 \, a^{9} b^{4} c^{7} + 589824 \, a^{10} b^{2} c^{8} - 262144 \, a^{11} c^{9}}}}{a b^{12} - 24 \, a^{2} b^{10} c + 240 \, a^{3} b^{8} c^{2} - 1280 \, a^{4} b^{6} c^{3} + 3840 \, a^{5} b^{4} c^{4} - 6144 \, a^{6} b^{2} c^{5} + 4096 \, a^{7} c^{6}}} - {\left(273375 \, b^{8} c + 205200 \, a b^{6} c^{2} + 47520 \, a^{2} b^{4} c^{3} + 2304 \, a^{3} b^{2} c^{4} - 256 \, a^{4} c^{5}\right)} \sqrt{x}\right) + {\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{\sqrt{\frac{1}{2}} \sqrt{-\frac{81 \, b^{5} + 760 \, a b^{3} c - 240 \, a^{2} b c^{2} - {\left(a b^{12} - 24 \, a^{2} b^{10} c + 240 \, a^{3} b^{8} c^{2} - 1280 \, a^{4} b^{6} c^{3} + 3840 \, a^{5} b^{4} c^{4} - 6144 \, a^{6} b^{2} c^{5} + 4096 \, a^{7} c^{6}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{a^{2} b^{18} - 36 \, a^{3} b^{16} c + 576 \, a^{4} b^{14} c^{2} - 5376 \, a^{5} b^{12} c^{3} + 32256 \, a^{6} b^{10} c^{4} - 129024 \, a^{7} b^{8} c^{5} + 344064 \, a^{8} b^{6} c^{6} - 589824 \, a^{9} b^{4} c^{7} + 589824 \, a^{10} b^{2} c^{8} - 262144 \, a^{11} c^{9}}}}{a b^{12} - 24 \, a^{2} b^{10} c + 240 \, a^{3} b^{8} c^{2} - 1280 \, a^{4} b^{6} c^{3} + 3840 \, a^{5} b^{4} c^{4} - 6144 \, a^{6} b^{2} c^{5} + 4096 \, a^{7} c^{6}}}} \log\left(-\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(2187 \, b^{15} - 47412 \, a b^{13} c + 423536 \, a^{2} b^{11} c^{2} - 1990720 \, a^{3} b^{9} c^{3} + 5177600 \, a^{4} b^{7} c^{4} - 7052288 \, a^{5} b^{5} c^{5} + 3985408 \, a^{6} b^{3} c^{6} - 180224 \, a^{7} b c^{7} + {\left(27 \, a b^{22} - 820 \, a^{2} b^{20} c + 10064 \, a^{3} b^{18} c^{2} - 57024 \, a^{4} b^{16} c^{3} + 44544 \, a^{5} b^{14} c^{4} + 1505280 \, a^{6} b^{12} c^{5} - 10838016 \, a^{7} b^{10} c^{6} + 38436864 \, a^{8} b^{8} c^{7} - 79233024 \, a^{9} b^{6} c^{8} + 92012544 \, a^{10} b^{4} c^{9} - 49283072 \, a^{11} b^{2} c^{10} + 4194304 \, a^{12} c^{11}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{a^{2} b^{18} - 36 \, a^{3} b^{16} c + 576 \, a^{4} b^{14} c^{2} - 5376 \, a^{5} b^{12} c^{3} + 32256 \, a^{6} b^{10} c^{4} - 129024 \, a^{7} b^{8} c^{5} + 344064 \, a^{8} b^{6} c^{6} - 589824 \, a^{9} b^{4} c^{7} + 589824 \, a^{10} b^{2} c^{8} - 262144 \, a^{11} c^{9}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{81 \, b^{5} + 760 \, a b^{3} c - 240 \, a^{2} b c^{2} - {\left(a b^{12} - 24 \, a^{2} b^{10} c + 240 \, a^{3} b^{8} c^{2} - 1280 \, a^{4} b^{6} c^{3} + 3840 \, a^{5} b^{4} c^{4} - 6144 \, a^{6} b^{2} c^{5} + 4096 \, a^{7} c^{6}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{a^{2} b^{18} - 36 \, a^{3} b^{16} c + 576 \, a^{4} b^{14} c^{2} - 5376 \, a^{5} b^{12} c^{3} + 32256 \, a^{6} b^{10} c^{4} - 129024 \, a^{7} b^{8} c^{5} + 344064 \, a^{8} b^{6} c^{6} - 589824 \, a^{9} b^{4} c^{7} + 589824 \, a^{10} b^{2} c^{8} - 262144 \, a^{11} c^{9}}}}{a b^{12} - 24 \, a^{2} b^{10} c + 240 \, a^{3} b^{8} c^{2} - 1280 \, a^{4} b^{6} c^{3} + 3840 \, a^{5} b^{4} c^{4} - 6144 \, a^{6} b^{2} c^{5} + 4096 \, a^{7} c^{6}}}} \sqrt{-\frac{81 \, b^{5} + 760 \, a b^{3} c - 240 \, a^{2} b c^{2} - {\left(a b^{12} - 24 \, a^{2} b^{10} c + 240 \, a^{3} b^{8} c^{2} - 1280 \, a^{4} b^{6} c^{3} + 3840 \, a^{5} b^{4} c^{4} - 6144 \, a^{6} b^{2} c^{5} + 4096 \, a^{7} c^{6}\right)} \sqrt{\frac{6561 \, b^{4} - 648 \, a b^{2} c + 16 \, a^{2} c^{2}}{a^{2} b^{18} - 36 \, a^{3} b^{16} c + 576 \, a^{4} b^{14} c^{2} - 5376 \, a^{5} b^{12} c^{3} + 32256 \, a^{6} b^{10} c^{4} - 129024 \, a^{7} b^{8} c^{5} + 344064 \, a^{8} b^{6} c^{6} - 589824 \, a^{9} b^{4} c^{7} + 589824 \, a^{10} b^{2} c^{8} - 262144 \, a^{11} c^{9}}}}{a b^{12} - 24 \, a^{2} b^{10} c + 240 \, a^{3} b^{8} c^{2} - 1280 \, a^{4} b^{6} c^{3} + 3840 \, a^{5} b^{4} c^{4} - 6144 \, a^{6} b^{2} c^{5} + 4096 \, a^{7} c^{6}}} - {\left(273375 \, b^{8} c + 205200 \, a b^{6} c^{2} + 47520 \, a^{2} b^{4} c^{3} + 2304 \, a^{3} b^{2} c^{4} - 256 \, a^{4} c^{5}\right)} \sqrt{x}\right) + 4 \, {\left(2 \, c x^{3} + b x\right)} \sqrt{x}}{8 \, {\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,"-1/8*(4*((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(sqrt(1/2)*sqrt(-(81*b^5 + 760*a*b^3*c - 240*a^2*b*c^2 - (a*b^12 - 24*a^2*b^10*c + 240*a^3*b^8*c^2 - 1280*a^4*b^6*c^3 + 3840*a^5*b^4*c^4 - 6144*a^6*b^2*c^5 + 4096*a^7*c^6)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(a^2*b^18 - 36*a^3*b^16*c + 576*a^4*b^14*c^2 - 5376*a^5*b^12*c^3 + 32256*a^6*b^10*c^4 - 129024*a^7*b^8*c^5 + 344064*a^8*b^6*c^6 - 589824*a^9*b^4*c^7 + 589824*a^10*b^2*c^8 - 262144*a^11*c^9)))/(a*b^12 - 24*a^2*b^10*c + 240*a^3*b^8*c^2 - 1280*a^4*b^6*c^3 + 3840*a^5*b^4*c^4 - 6144*a^6*b^2*c^5 + 4096*a^7*c^6)))*arctan(-((81*b^6 - 652*a*b^4*c + 1328*a^2*b^2*c^2 - 64*a^3*c^3 - 4*(a*b^13 - 24*a^2*b^11*c + 240*a^3*b^9*c^2 - 1280*a^4*b^7*c^3 + 3840*a^5*b^5*c^4 - 6144*a^6*b^3*c^5 + 4096*a^7*b*c^6)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(a^2*b^18 - 36*a^3*b^16*c + 576*a^4*b^14*c^2 - 5376*a^5*b^12*c^3 + 32256*a^6*b^10*c^4 - 129024*a^7*b^8*c^5 + 344064*a^8*b^6*c^6 - 589824*a^9*b^4*c^7 + 589824*a^10*b^2*c^8 - 262144*a^11*c^9)))*sqrt((74733890625*b^16*c^2 + 112193100000*a*b^14*c^3 + 68088600000*a^2*b^12*c^4 + 20761920000*a^3*b^10*c^5 + 3063744000*a^4*b^8*c^6 + 113909760*a^5*b^6*c^7 - 19021824*a^6*b^4*c^8 - 1179648*a^7*b^2*c^9 + 65536*a^8*c^10)*x - 1/2*sqrt(1/2)*(2989355625*b^21*c - 23678649000*a*b^19*c^2 + 7135160400*a^2*b^17*c^3 + 277460328960*a^3*b^15*c^4 - 338956033536*a^4*b^13*c^5 - 492326940672*a^5*b^11*c^6 - 183476674560*a^6*b^9*c^7 - 21980119040*a^7*b^7*c^8 + 750059520*a^8*b^5*c^9 + 190316544*a^9*b^3*c^10 - 7340032*a^10*b*c^11 + (36905625*a*b^28*c - 1159839000*a^2*b^26*c^2 + 15854324400*a^3*b^24*c^3 - 122710429440*a^4*b^22*c^4 + 584418357504*a^5*b^20*c^5 - 1728949905408*a^6*b^18*c^6 + 2983008514048*a^7*b^16*c^7 - 2317983285248*a^8*b^14*c^8 - 462348419072*a^9*b^12*c^9 + 1339972648960*a^10*b^10*c^10 + 254402363392*a^11*b^8*c^11 - 161849802752*a^12*b^6*c^12 - 51220840448*a^13*b^4*c^13 - 2550136832*a^14*b^2*c^14 + 268435456*a^15*c^15)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(a^2*b^18 - 36*a^3*b^16*c + 576*a^4*b^14*c^2 - 5376*a^5*b^12*c^3 + 32256*a^6*b^10*c^4 - 129024*a^7*b^8*c^5 + 344064*a^8*b^6*c^6 - 589824*a^9*b^4*c^7 + 589824*a^10*b^2*c^8 - 262144*a^11*c^9)))*sqrt(-(81*b^5 + 760*a*b^3*c - 240*a^2*b*c^2 - (a*b^12 - 24*a^2*b^10*c + 240*a^3*b^8*c^2 - 1280*a^4*b^6*c^3 + 3840*a^5*b^4*c^4 - 6144*a^6*b^2*c^5 + 4096*a^7*c^6)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(a^2*b^18 - 36*a^3*b^16*c + 576*a^4*b^14*c^2 - 5376*a^5*b^12*c^3 + 32256*a^6*b^10*c^4 - 129024*a^7*b^8*c^5 + 344064*a^8*b^6*c^6 - 589824*a^9*b^4*c^7 + 589824*a^10*b^2*c^8 - 262144*a^11*c^9)))/(a*b^12 - 24*a^2*b^10*c + 240*a^3*b^8*c^2 - 1280*a^4*b^6*c^3 + 3840*a^5*b^4*c^4 - 6144*a^6*b^2*c^5 + 4096*a^7*c^6))) + (22143375*b^14*c - 161619300*a*b^12*c^2 + 233100720*a^2*b^10*c^3 + 224213184*a^3*b^8*c^4 + 48450816*a^4*b^6*c^5 + 185344*a^5*b^4*c^6 - 487424*a^6*b^2*c^7 + 16384*a^7*c^8 - 4*(273375*a*b^21*c - 6355800*a^2*b^19*c^2 + 60732720*a^3*b^17*c^3 - 301810176*a^4*b^15*c^4 + 798453248*a^5*b^13*c^5 - 951914496*a^6*b^11*c^6 + 38461440*a^7*b^9*c^7 + 557711360*a^8*b^7*c^8 + 179503104*a^9*b^5*c^9 + 11010048*a^10*b^3*c^10 - 1048576*a^11*b*c^11)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(a^2*b^18 - 36*a^3*b^16*c + 576*a^4*b^14*c^2 - 5376*a^5*b^12*c^3 + 32256*a^6*b^10*c^4 - 129024*a^7*b^8*c^5 + 344064*a^8*b^6*c^6 - 589824*a^9*b^4*c^7 + 589824*a^10*b^2*c^8 - 262144*a^11*c^9)))*sqrt(x))*sqrt(sqrt(1/2)*sqrt(-(81*b^5 + 760*a*b^3*c - 240*a^2*b*c^2 - (a*b^12 - 24*a^2*b^10*c + 240*a^3*b^8*c^2 - 1280*a^4*b^6*c^3 + 3840*a^5*b^4*c^4 - 6144*a^6*b^2*c^5 + 4096*a^7*c^6)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(a^2*b^18 - 36*a^3*b^16*c + 576*a^4*b^14*c^2 - 5376*a^5*b^12*c^3 + 32256*a^6*b^10*c^4 - 129024*a^7*b^8*c^5 + 344064*a^8*b^6*c^6 - 589824*a^9*b^4*c^7 + 589824*a^10*b^2*c^8 - 262144*a^11*c^9)))/(a*b^12 - 24*a^2*b^10*c + 240*a^3*b^8*c^2 - 1280*a^4*b^6*c^3 + 3840*a^5*b^4*c^4 - 6144*a^6*b^2*c^5 + 4096*a^7*c^6)))/(332150625*b^12*c + 321489000*a*b^10*c^2 + 107535600*a^2*b^8*c^3 + 12061440*a^3*b^6*c^4 - 463104*a^4*b^4*c^5 - 104448*a^5*b^2*c^6 + 4096*a^6*c^7)) - 4*((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(sqrt(1/2)*sqrt(-(81*b^5 + 760*a*b^3*c - 240*a^2*b*c^2 + (a*b^12 - 24*a^2*b^10*c + 240*a^3*b^8*c^2 - 1280*a^4*b^6*c^3 + 3840*a^5*b^4*c^4 - 6144*a^6*b^2*c^5 + 4096*a^7*c^6)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(a^2*b^18 - 36*a^3*b^16*c + 576*a^4*b^14*c^2 - 5376*a^5*b^12*c^3 + 32256*a^6*b^10*c^4 - 129024*a^7*b^8*c^5 + 344064*a^8*b^6*c^6 - 589824*a^9*b^4*c^7 + 589824*a^10*b^2*c^8 - 262144*a^11*c^9)))/(a*b^12 - 24*a^2*b^10*c + 240*a^3*b^8*c^2 - 1280*a^4*b^6*c^3 + 3840*a^5*b^4*c^4 - 6144*a^6*b^2*c^5 + 4096*a^7*c^6)))*arctan(((81*b^6 - 652*a*b^4*c + 1328*a^2*b^2*c^2 - 64*a^3*c^3 + 4*(a*b^13 - 24*a^2*b^11*c + 240*a^3*b^9*c^2 - 1280*a^4*b^7*c^3 + 3840*a^5*b^5*c^4 - 6144*a^6*b^3*c^5 + 4096*a^7*b*c^6)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(a^2*b^18 - 36*a^3*b^16*c + 576*a^4*b^14*c^2 - 5376*a^5*b^12*c^3 + 32256*a^6*b^10*c^4 - 129024*a^7*b^8*c^5 + 344064*a^8*b^6*c^6 - 589824*a^9*b^4*c^7 + 589824*a^10*b^2*c^8 - 262144*a^11*c^9)))*sqrt((74733890625*b^16*c^2 + 112193100000*a*b^14*c^3 + 68088600000*a^2*b^12*c^4 + 20761920000*a^3*b^10*c^5 + 3063744000*a^4*b^8*c^6 + 113909760*a^5*b^6*c^7 - 19021824*a^6*b^4*c^8 - 1179648*a^7*b^2*c^9 + 65536*a^8*c^10)*x - 1/2*sqrt(1/2)*(2989355625*b^21*c - 23678649000*a*b^19*c^2 + 7135160400*a^2*b^17*c^3 + 277460328960*a^3*b^15*c^4 - 338956033536*a^4*b^13*c^5 - 492326940672*a^5*b^11*c^6 - 183476674560*a^6*b^9*c^7 - 21980119040*a^7*b^7*c^8 + 750059520*a^8*b^5*c^9 + 190316544*a^9*b^3*c^10 - 7340032*a^10*b*c^11 - (36905625*a*b^28*c - 1159839000*a^2*b^26*c^2 + 15854324400*a^3*b^24*c^3 - 122710429440*a^4*b^22*c^4 + 584418357504*a^5*b^20*c^5 - 1728949905408*a^6*b^18*c^6 + 2983008514048*a^7*b^16*c^7 - 2317983285248*a^8*b^14*c^8 - 462348419072*a^9*b^12*c^9 + 1339972648960*a^10*b^10*c^10 + 254402363392*a^11*b^8*c^11 - 161849802752*a^12*b^6*c^12 - 51220840448*a^13*b^4*c^13 - 2550136832*a^14*b^2*c^14 + 268435456*a^15*c^15)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(a^2*b^18 - 36*a^3*b^16*c + 576*a^4*b^14*c^2 - 5376*a^5*b^12*c^3 + 32256*a^6*b^10*c^4 - 129024*a^7*b^8*c^5 + 344064*a^8*b^6*c^6 - 589824*a^9*b^4*c^7 + 589824*a^10*b^2*c^8 - 262144*a^11*c^9)))*sqrt(-(81*b^5 + 760*a*b^3*c - 240*a^2*b*c^2 + (a*b^12 - 24*a^2*b^10*c + 240*a^3*b^8*c^2 - 1280*a^4*b^6*c^3 + 3840*a^5*b^4*c^4 - 6144*a^6*b^2*c^5 + 4096*a^7*c^6)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(a^2*b^18 - 36*a^3*b^16*c + 576*a^4*b^14*c^2 - 5376*a^5*b^12*c^3 + 32256*a^6*b^10*c^4 - 129024*a^7*b^8*c^5 + 344064*a^8*b^6*c^6 - 589824*a^9*b^4*c^7 + 589824*a^10*b^2*c^8 - 262144*a^11*c^9)))/(a*b^12 - 24*a^2*b^10*c + 240*a^3*b^8*c^2 - 1280*a^4*b^6*c^3 + 3840*a^5*b^4*c^4 - 6144*a^6*b^2*c^5 + 4096*a^7*c^6)))*sqrt(sqrt(1/2)*sqrt(-(81*b^5 + 760*a*b^3*c - 240*a^2*b*c^2 + (a*b^12 - 24*a^2*b^10*c + 240*a^3*b^8*c^2 - 1280*a^4*b^6*c^3 + 3840*a^5*b^4*c^4 - 6144*a^6*b^2*c^5 + 4096*a^7*c^6)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(a^2*b^18 - 36*a^3*b^16*c + 576*a^4*b^14*c^2 - 5376*a^5*b^12*c^3 + 32256*a^6*b^10*c^4 - 129024*a^7*b^8*c^5 + 344064*a^8*b^6*c^6 - 589824*a^9*b^4*c^7 + 589824*a^10*b^2*c^8 - 262144*a^11*c^9)))/(a*b^12 - 24*a^2*b^10*c + 240*a^3*b^8*c^2 - 1280*a^4*b^6*c^3 + 3840*a^5*b^4*c^4 - 6144*a^6*b^2*c^5 + 4096*a^7*c^6))) + (22143375*b^14*c - 161619300*a*b^12*c^2 + 233100720*a^2*b^10*c^3 + 224213184*a^3*b^8*c^4 + 48450816*a^4*b^6*c^5 + 185344*a^5*b^4*c^6 - 487424*a^6*b^2*c^7 + 16384*a^7*c^8 + 4*(273375*a*b^21*c - 6355800*a^2*b^19*c^2 + 60732720*a^3*b^17*c^3 - 301810176*a^4*b^15*c^4 + 798453248*a^5*b^13*c^5 - 951914496*a^6*b^11*c^6 + 38461440*a^7*b^9*c^7 + 557711360*a^8*b^7*c^8 + 179503104*a^9*b^5*c^9 + 11010048*a^10*b^3*c^10 - 1048576*a^11*b*c^11)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(a^2*b^18 - 36*a^3*b^16*c + 576*a^4*b^14*c^2 - 5376*a^5*b^12*c^3 + 32256*a^6*b^10*c^4 - 129024*a^7*b^8*c^5 + 344064*a^8*b^6*c^6 - 589824*a^9*b^4*c^7 + 589824*a^10*b^2*c^8 - 262144*a^11*c^9)))*sqrt(x)*sqrt(sqrt(1/2)*sqrt(-(81*b^5 + 760*a*b^3*c - 240*a^2*b*c^2 + (a*b^12 - 24*a^2*b^10*c + 240*a^3*b^8*c^2 - 1280*a^4*b^6*c^3 + 3840*a^5*b^4*c^4 - 6144*a^6*b^2*c^5 + 4096*a^7*c^6)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(a^2*b^18 - 36*a^3*b^16*c + 576*a^4*b^14*c^2 - 5376*a^5*b^12*c^3 + 32256*a^6*b^10*c^4 - 129024*a^7*b^8*c^5 + 344064*a^8*b^6*c^6 - 589824*a^9*b^4*c^7 + 589824*a^10*b^2*c^8 - 262144*a^11*c^9)))/(a*b^12 - 24*a^2*b^10*c + 240*a^3*b^8*c^2 - 1280*a^4*b^6*c^3 + 3840*a^5*b^4*c^4 - 6144*a^6*b^2*c^5 + 4096*a^7*c^6))))/(332150625*b^12*c + 321489000*a*b^10*c^2 + 107535600*a^2*b^8*c^3 + 12061440*a^3*b^6*c^4 - 463104*a^4*b^4*c^5 - 104448*a^5*b^2*c^6 + 4096*a^6*c^7)) - ((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(sqrt(1/2)*sqrt(-(81*b^5 + 760*a*b^3*c - 240*a^2*b*c^2 + (a*b^12 - 24*a^2*b^10*c + 240*a^3*b^8*c^2 - 1280*a^4*b^6*c^3 + 3840*a^5*b^4*c^4 - 6144*a^6*b^2*c^5 + 4096*a^7*c^6)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(a^2*b^18 - 36*a^3*b^16*c + 576*a^4*b^14*c^2 - 5376*a^5*b^12*c^3 + 32256*a^6*b^10*c^4 - 129024*a^7*b^8*c^5 + 344064*a^8*b^6*c^6 - 589824*a^9*b^4*c^7 + 589824*a^10*b^2*c^8 - 262144*a^11*c^9)))/(a*b^12 - 24*a^2*b^10*c + 240*a^3*b^8*c^2 - 1280*a^4*b^6*c^3 + 3840*a^5*b^4*c^4 - 6144*a^6*b^2*c^5 + 4096*a^7*c^6)))*log(1/2*sqrt(1/2)*(2187*b^15 - 47412*a*b^13*c + 423536*a^2*b^11*c^2 - 1990720*a^3*b^9*c^3 + 5177600*a^4*b^7*c^4 - 7052288*a^5*b^5*c^5 + 3985408*a^6*b^3*c^6 - 180224*a^7*b*c^7 - (27*a*b^22 - 820*a^2*b^20*c + 10064*a^3*b^18*c^2 - 57024*a^4*b^16*c^3 + 44544*a^5*b^14*c^4 + 1505280*a^6*b^12*c^5 - 10838016*a^7*b^10*c^6 + 38436864*a^8*b^8*c^7 - 79233024*a^9*b^6*c^8 + 92012544*a^10*b^4*c^9 - 49283072*a^11*b^2*c^10 + 4194304*a^12*c^11)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(a^2*b^18 - 36*a^3*b^16*c + 576*a^4*b^14*c^2 - 5376*a^5*b^12*c^3 + 32256*a^6*b^10*c^4 - 129024*a^7*b^8*c^5 + 344064*a^8*b^6*c^6 - 589824*a^9*b^4*c^7 + 589824*a^10*b^2*c^8 - 262144*a^11*c^9)))*sqrt(sqrt(1/2)*sqrt(-(81*b^5 + 760*a*b^3*c - 240*a^2*b*c^2 + (a*b^12 - 24*a^2*b^10*c + 240*a^3*b^8*c^2 - 1280*a^4*b^6*c^3 + 3840*a^5*b^4*c^4 - 6144*a^6*b^2*c^5 + 4096*a^7*c^6)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(a^2*b^18 - 36*a^3*b^16*c + 576*a^4*b^14*c^2 - 5376*a^5*b^12*c^3 + 32256*a^6*b^10*c^4 - 129024*a^7*b^8*c^5 + 344064*a^8*b^6*c^6 - 589824*a^9*b^4*c^7 + 589824*a^10*b^2*c^8 - 262144*a^11*c^9)))/(a*b^12 - 24*a^2*b^10*c + 240*a^3*b^8*c^2 - 1280*a^4*b^6*c^3 + 3840*a^5*b^4*c^4 - 6144*a^6*b^2*c^5 + 4096*a^7*c^6)))*sqrt(-(81*b^5 + 760*a*b^3*c - 240*a^2*b*c^2 + (a*b^12 - 24*a^2*b^10*c + 240*a^3*b^8*c^2 - 1280*a^4*b^6*c^3 + 3840*a^5*b^4*c^4 - 6144*a^6*b^2*c^5 + 4096*a^7*c^6)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(a^2*b^18 - 36*a^3*b^16*c + 576*a^4*b^14*c^2 - 5376*a^5*b^12*c^3 + 32256*a^6*b^10*c^4 - 129024*a^7*b^8*c^5 + 344064*a^8*b^6*c^6 - 589824*a^9*b^4*c^7 + 589824*a^10*b^2*c^8 - 262144*a^11*c^9)))/(a*b^12 - 24*a^2*b^10*c + 240*a^3*b^8*c^2 - 1280*a^4*b^6*c^3 + 3840*a^5*b^4*c^4 - 6144*a^6*b^2*c^5 + 4096*a^7*c^6)) - (273375*b^8*c + 205200*a*b^6*c^2 + 47520*a^2*b^4*c^3 + 2304*a^3*b^2*c^4 - 256*a^4*c^5)*sqrt(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)*sqrt(sqrt(1/2)*sqrt(-(81*b^5 + 760*a*b^3*c - 240*a^2*b*c^2 + (a*b^12 - 24*a^2*b^10*c + 240*a^3*b^8*c^2 - 1280*a^4*b^6*c^3 + 3840*a^5*b^4*c^4 - 6144*a^6*b^2*c^5 + 4096*a^7*c^6)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(a^2*b^18 - 36*a^3*b^16*c + 576*a^4*b^14*c^2 - 5376*a^5*b^12*c^3 + 32256*a^6*b^10*c^4 - 129024*a^7*b^8*c^5 + 344064*a^8*b^6*c^6 - 589824*a^9*b^4*c^7 + 589824*a^10*b^2*c^8 - 262144*a^11*c^9)))/(a*b^12 - 24*a^2*b^10*c + 240*a^3*b^8*c^2 - 1280*a^4*b^6*c^3 + 3840*a^5*b^4*c^4 - 6144*a^6*b^2*c^5 + 4096*a^7*c^6)))*log(-1/2*sqrt(1/2)*(2187*b^15 - 47412*a*b^13*c + 423536*a^2*b^11*c^2 - 1990720*a^3*b^9*c^3 + 5177600*a^4*b^7*c^4 - 7052288*a^5*b^5*c^5 + 3985408*a^6*b^3*c^6 - 180224*a^7*b*c^7 - (27*a*b^22 - 820*a^2*b^20*c + 10064*a^3*b^18*c^2 - 57024*a^4*b^16*c^3 + 44544*a^5*b^14*c^4 + 1505280*a^6*b^12*c^5 - 10838016*a^7*b^10*c^6 + 38436864*a^8*b^8*c^7 - 79233024*a^9*b^6*c^8 + 92012544*a^10*b^4*c^9 - 49283072*a^11*b^2*c^10 + 4194304*a^12*c^11)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(a^2*b^18 - 36*a^3*b^16*c + 576*a^4*b^14*c^2 - 5376*a^5*b^12*c^3 + 32256*a^6*b^10*c^4 - 129024*a^7*b^8*c^5 + 344064*a^8*b^6*c^6 - 589824*a^9*b^4*c^7 + 589824*a^10*b^2*c^8 - 262144*a^11*c^9)))*sqrt(sqrt(1/2)*sqrt(-(81*b^5 + 760*a*b^3*c - 240*a^2*b*c^2 + (a*b^12 - 24*a^2*b^10*c + 240*a^3*b^8*c^2 - 1280*a^4*b^6*c^3 + 3840*a^5*b^4*c^4 - 6144*a^6*b^2*c^5 + 4096*a^7*c^6)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(a^2*b^18 - 36*a^3*b^16*c + 576*a^4*b^14*c^2 - 5376*a^5*b^12*c^3 + 32256*a^6*b^10*c^4 - 129024*a^7*b^8*c^5 + 344064*a^8*b^6*c^6 - 589824*a^9*b^4*c^7 + 589824*a^10*b^2*c^8 - 262144*a^11*c^9)))/(a*b^12 - 24*a^2*b^10*c + 240*a^3*b^8*c^2 - 1280*a^4*b^6*c^3 + 3840*a^5*b^4*c^4 - 6144*a^6*b^2*c^5 + 4096*a^7*c^6)))*sqrt(-(81*b^5 + 760*a*b^3*c - 240*a^2*b*c^2 + (a*b^12 - 24*a^2*b^10*c + 240*a^3*b^8*c^2 - 1280*a^4*b^6*c^3 + 3840*a^5*b^4*c^4 - 6144*a^6*b^2*c^5 + 4096*a^7*c^6)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(a^2*b^18 - 36*a^3*b^16*c + 576*a^4*b^14*c^2 - 5376*a^5*b^12*c^3 + 32256*a^6*b^10*c^4 - 129024*a^7*b^8*c^5 + 344064*a^8*b^6*c^6 - 589824*a^9*b^4*c^7 + 589824*a^10*b^2*c^8 - 262144*a^11*c^9)))/(a*b^12 - 24*a^2*b^10*c + 240*a^3*b^8*c^2 - 1280*a^4*b^6*c^3 + 3840*a^5*b^4*c^4 - 6144*a^6*b^2*c^5 + 4096*a^7*c^6)) - (273375*b^8*c + 205200*a*b^6*c^2 + 47520*a^2*b^4*c^3 + 2304*a^3*b^2*c^4 - 256*a^4*c^5)*sqrt(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)*sqrt(sqrt(1/2)*sqrt(-(81*b^5 + 760*a*b^3*c - 240*a^2*b*c^2 - (a*b^12 - 24*a^2*b^10*c + 240*a^3*b^8*c^2 - 1280*a^4*b^6*c^3 + 3840*a^5*b^4*c^4 - 6144*a^6*b^2*c^5 + 4096*a^7*c^6)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(a^2*b^18 - 36*a^3*b^16*c + 576*a^4*b^14*c^2 - 5376*a^5*b^12*c^3 + 32256*a^6*b^10*c^4 - 129024*a^7*b^8*c^5 + 344064*a^8*b^6*c^6 - 589824*a^9*b^4*c^7 + 589824*a^10*b^2*c^8 - 262144*a^11*c^9)))/(a*b^12 - 24*a^2*b^10*c + 240*a^3*b^8*c^2 - 1280*a^4*b^6*c^3 + 3840*a^5*b^4*c^4 - 6144*a^6*b^2*c^5 + 4096*a^7*c^6)))*log(1/2*sqrt(1/2)*(2187*b^15 - 47412*a*b^13*c + 423536*a^2*b^11*c^2 - 1990720*a^3*b^9*c^3 + 5177600*a^4*b^7*c^4 - 7052288*a^5*b^5*c^5 + 3985408*a^6*b^3*c^6 - 180224*a^7*b*c^7 + (27*a*b^22 - 820*a^2*b^20*c + 10064*a^3*b^18*c^2 - 57024*a^4*b^16*c^3 + 44544*a^5*b^14*c^4 + 1505280*a^6*b^12*c^5 - 10838016*a^7*b^10*c^6 + 38436864*a^8*b^8*c^7 - 79233024*a^9*b^6*c^8 + 92012544*a^10*b^4*c^9 - 49283072*a^11*b^2*c^10 + 4194304*a^12*c^11)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(a^2*b^18 - 36*a^3*b^16*c + 576*a^4*b^14*c^2 - 5376*a^5*b^12*c^3 + 32256*a^6*b^10*c^4 - 129024*a^7*b^8*c^5 + 344064*a^8*b^6*c^6 - 589824*a^9*b^4*c^7 + 589824*a^10*b^2*c^8 - 262144*a^11*c^9)))*sqrt(sqrt(1/2)*sqrt(-(81*b^5 + 760*a*b^3*c - 240*a^2*b*c^2 - (a*b^12 - 24*a^2*b^10*c + 240*a^3*b^8*c^2 - 1280*a^4*b^6*c^3 + 3840*a^5*b^4*c^4 - 6144*a^6*b^2*c^5 + 4096*a^7*c^6)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(a^2*b^18 - 36*a^3*b^16*c + 576*a^4*b^14*c^2 - 5376*a^5*b^12*c^3 + 32256*a^6*b^10*c^4 - 129024*a^7*b^8*c^5 + 344064*a^8*b^6*c^6 - 589824*a^9*b^4*c^7 + 589824*a^10*b^2*c^8 - 262144*a^11*c^9)))/(a*b^12 - 24*a^2*b^10*c + 240*a^3*b^8*c^2 - 1280*a^4*b^6*c^3 + 3840*a^5*b^4*c^4 - 6144*a^6*b^2*c^5 + 4096*a^7*c^6)))*sqrt(-(81*b^5 + 760*a*b^3*c - 240*a^2*b*c^2 - (a*b^12 - 24*a^2*b^10*c + 240*a^3*b^8*c^2 - 1280*a^4*b^6*c^3 + 3840*a^5*b^4*c^4 - 6144*a^6*b^2*c^5 + 4096*a^7*c^6)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(a^2*b^18 - 36*a^3*b^16*c + 576*a^4*b^14*c^2 - 5376*a^5*b^12*c^3 + 32256*a^6*b^10*c^4 - 129024*a^7*b^8*c^5 + 344064*a^8*b^6*c^6 - 589824*a^9*b^4*c^7 + 589824*a^10*b^2*c^8 - 262144*a^11*c^9)))/(a*b^12 - 24*a^2*b^10*c + 240*a^3*b^8*c^2 - 1280*a^4*b^6*c^3 + 3840*a^5*b^4*c^4 - 6144*a^6*b^2*c^5 + 4096*a^7*c^6)) - (273375*b^8*c + 205200*a*b^6*c^2 + 47520*a^2*b^4*c^3 + 2304*a^3*b^2*c^4 - 256*a^4*c^5)*sqrt(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)*sqrt(sqrt(1/2)*sqrt(-(81*b^5 + 760*a*b^3*c - 240*a^2*b*c^2 - (a*b^12 - 24*a^2*b^10*c + 240*a^3*b^8*c^2 - 1280*a^4*b^6*c^3 + 3840*a^5*b^4*c^4 - 6144*a^6*b^2*c^5 + 4096*a^7*c^6)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(a^2*b^18 - 36*a^3*b^16*c + 576*a^4*b^14*c^2 - 5376*a^5*b^12*c^3 + 32256*a^6*b^10*c^4 - 129024*a^7*b^8*c^5 + 344064*a^8*b^6*c^6 - 589824*a^9*b^4*c^7 + 589824*a^10*b^2*c^8 - 262144*a^11*c^9)))/(a*b^12 - 24*a^2*b^10*c + 240*a^3*b^8*c^2 - 1280*a^4*b^6*c^3 + 3840*a^5*b^4*c^4 - 6144*a^6*b^2*c^5 + 4096*a^7*c^6)))*log(-1/2*sqrt(1/2)*(2187*b^15 - 47412*a*b^13*c + 423536*a^2*b^11*c^2 - 1990720*a^3*b^9*c^3 + 5177600*a^4*b^7*c^4 - 7052288*a^5*b^5*c^5 + 3985408*a^6*b^3*c^6 - 180224*a^7*b*c^7 + (27*a*b^22 - 820*a^2*b^20*c + 10064*a^3*b^18*c^2 - 57024*a^4*b^16*c^3 + 44544*a^5*b^14*c^4 + 1505280*a^6*b^12*c^5 - 10838016*a^7*b^10*c^6 + 38436864*a^8*b^8*c^7 - 79233024*a^9*b^6*c^8 + 92012544*a^10*b^4*c^9 - 49283072*a^11*b^2*c^10 + 4194304*a^12*c^11)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(a^2*b^18 - 36*a^3*b^16*c + 576*a^4*b^14*c^2 - 5376*a^5*b^12*c^3 + 32256*a^6*b^10*c^4 - 129024*a^7*b^8*c^5 + 344064*a^8*b^6*c^6 - 589824*a^9*b^4*c^7 + 589824*a^10*b^2*c^8 - 262144*a^11*c^9)))*sqrt(sqrt(1/2)*sqrt(-(81*b^5 + 760*a*b^3*c - 240*a^2*b*c^2 - (a*b^12 - 24*a^2*b^10*c + 240*a^3*b^8*c^2 - 1280*a^4*b^6*c^3 + 3840*a^5*b^4*c^4 - 6144*a^6*b^2*c^5 + 4096*a^7*c^6)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(a^2*b^18 - 36*a^3*b^16*c + 576*a^4*b^14*c^2 - 5376*a^5*b^12*c^3 + 32256*a^6*b^10*c^4 - 129024*a^7*b^8*c^5 + 344064*a^8*b^6*c^6 - 589824*a^9*b^4*c^7 + 589824*a^10*b^2*c^8 - 262144*a^11*c^9)))/(a*b^12 - 24*a^2*b^10*c + 240*a^3*b^8*c^2 - 1280*a^4*b^6*c^3 + 3840*a^5*b^4*c^4 - 6144*a^6*b^2*c^5 + 4096*a^7*c^6)))*sqrt(-(81*b^5 + 760*a*b^3*c - 240*a^2*b*c^2 - (a*b^12 - 24*a^2*b^10*c + 240*a^3*b^8*c^2 - 1280*a^4*b^6*c^3 + 3840*a^5*b^4*c^4 - 6144*a^6*b^2*c^5 + 4096*a^7*c^6)*sqrt((6561*b^4 - 648*a*b^2*c + 16*a^2*c^2)/(a^2*b^18 - 36*a^3*b^16*c + 576*a^4*b^14*c^2 - 5376*a^5*b^12*c^3 + 32256*a^6*b^10*c^4 - 129024*a^7*b^8*c^5 + 344064*a^8*b^6*c^6 - 589824*a^9*b^4*c^7 + 589824*a^10*b^2*c^8 - 262144*a^11*c^9)))/(a*b^12 - 24*a^2*b^10*c + 240*a^3*b^8*c^2 - 1280*a^4*b^6*c^3 + 3840*a^5*b^4*c^4 - 6144*a^6*b^2*c^5 + 4096*a^7*c^6)) - (273375*b^8*c + 205200*a*b^6*c^2 + 47520*a^2*b^4*c^3 + 2304*a^3*b^2*c^4 - 256*a^4*c^5)*sqrt(x)) + 4*(2*c*x^3 + b*x)*sqrt(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
1076,1,10570,0,29.109053," ","integrate(x^(3/2)/(c*x^4+b*x^2+a)^2,x, algorithm=""fricas"")","-\frac{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)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} + 21 \, a b^{5} c + 168 \, a^{2} b^{3} c^{2} + 3024 \, a^{3} b c^{3} + {\left(a^{3} b^{12} - 24 \, a^{4} b^{10} c + 240 \, a^{5} b^{8} c^{2} - 1280 \, a^{6} b^{6} c^{3} + 3840 \, a^{7} b^{4} c^{4} - 6144 \, a^{8} b^{2} c^{5} + 4096 \, a^{9} c^{6}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{a^{6} b^{18} - 36 \, a^{7} b^{16} c + 576 \, a^{8} b^{14} c^{2} - 5376 \, a^{9} b^{12} c^{3} + 32256 \, a^{10} b^{10} c^{4} - 129024 \, a^{11} b^{8} c^{5} + 344064 \, a^{12} b^{6} c^{6} - 589824 \, a^{13} b^{4} c^{7} + 589824 \, a^{14} b^{2} c^{8} - 262144 \, a^{15} c^{9}}}}{a^{3} b^{12} - 24 \, a^{4} b^{10} c + 240 \, a^{5} b^{8} c^{2} - 1280 \, a^{6} b^{6} c^{3} + 3840 \, a^{7} b^{4} c^{4} - 6144 \, a^{8} b^{2} c^{5} + 4096 \, a^{9} c^{6}}}} \arctan\left(\frac{{\left(\sqrt{\frac{1}{2}} {\left(b^{18} + 25 \, a b^{16} c - 146 \, a^{2} b^{14} c^{2} - 5320 \, a^{3} b^{12} c^{3} - 2464 \, a^{4} b^{10} c^{4} + 1076096 \, a^{5} b^{8} c^{5} - 10483200 \, a^{6} b^{6} c^{6} + 44181504 \, a^{7} b^{4} c^{7} - 89579520 \, a^{8} b^{2} c^{8} + 71663616 \, a^{9} c^{9} - {\left(a^{3} b^{23} - 20 \, a^{4} b^{21} c + 432 \, a^{5} b^{19} c^{2} - 11712 \, a^{6} b^{17} c^{3} + 195072 \, a^{7} b^{15} c^{4} - 1935360 \, a^{8} b^{13} c^{5} + 12214272 \, a^{9} b^{11} c^{6} - 50823168 \, a^{10} b^{9} c^{7} + 139788288 \, a^{11} b^{7} c^{8} - 245628928 \, a^{12} b^{5} c^{9} + 250609664 \, a^{13} b^{3} c^{10} - 113246208 \, a^{14} b c^{11}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{a^{6} b^{18} - 36 \, a^{7} b^{16} c + 576 \, a^{8} b^{14} c^{2} - 5376 \, a^{9} b^{12} c^{3} + 32256 \, a^{10} b^{10} c^{4} - 129024 \, a^{11} b^{8} c^{5} + 344064 \, a^{12} b^{6} c^{6} - 589824 \, a^{13} b^{4} c^{7} + 589824 \, a^{14} b^{2} c^{8} - 262144 \, a^{15} c^{9}}}\right)} \sqrt{{\left(49 \, b^{12} c^{2} + 3150 \, a b^{10} c^{3} + 95985 \, a^{2} b^{8} c^{4} + 1621296 \, a^{3} b^{6} c^{5} + 15746400 \, a^{4} b^{4} c^{6} + 75582720 \, a^{5} b^{2} c^{7} + 136048896 \, a^{6} c^{8}\right)} x + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{18} + 52 \, a b^{16} c + 1269 \, a^{2} b^{14} c^{2} + 14294 \, a^{3} b^{12} c^{3} + 48608 \, a^{4} b^{10} c^{4} - 679392 \, a^{5} b^{8} c^{5} - 4209408 \, a^{6} b^{6} c^{6} - 4105728 \, a^{7} b^{4} c^{7} + 214990848 \, a^{8} b^{2} c^{8} - 483729408 \, a^{9} c^{9} - {\left(a^{3} b^{23} + 7 \, a^{4} b^{21} c - 152 \, a^{5} b^{19} c^{2} - 2960 \, a^{6} b^{17} c^{3} + 44032 \, a^{7} b^{15} c^{4} + 60928 \, a^{8} b^{13} c^{5} - 4444160 \, a^{9} b^{11} c^{6} + 36855808 \, a^{10} b^{9} c^{7} - 153681920 \, a^{11} b^{7} c^{8} + 363528192 \, a^{12} b^{5} c^{9} - 467140608 \, a^{13} b^{3} c^{10} + 254803968 \, a^{14} b c^{11}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{a^{6} b^{18} - 36 \, a^{7} b^{16} c + 576 \, a^{8} b^{14} c^{2} - 5376 \, a^{9} b^{12} c^{3} + 32256 \, a^{10} b^{10} c^{4} - 129024 \, a^{11} b^{8} c^{5} + 344064 \, a^{12} b^{6} c^{6} - 589824 \, a^{13} b^{4} c^{7} + 589824 \, a^{14} b^{2} c^{8} - 262144 \, a^{15} c^{9}}}\right)} \sqrt{-\frac{b^{7} + 21 \, a b^{5} c + 168 \, a^{2} b^{3} c^{2} + 3024 \, a^{3} b c^{3} + {\left(a^{3} b^{12} - 24 \, a^{4} b^{10} c + 240 \, a^{5} b^{8} c^{2} - 1280 \, a^{6} b^{6} c^{3} + 3840 \, a^{7} b^{4} c^{4} - 6144 \, a^{8} b^{2} c^{5} + 4096 \, a^{9} c^{6}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{a^{6} b^{18} - 36 \, a^{7} b^{16} c + 576 \, a^{8} b^{14} c^{2} - 5376 \, a^{9} b^{12} c^{3} + 32256 \, a^{10} b^{10} c^{4} - 129024 \, a^{11} b^{8} c^{5} + 344064 \, a^{12} b^{6} c^{6} - 589824 \, a^{13} b^{4} c^{7} + 589824 \, a^{14} b^{2} c^{8} - 262144 \, a^{15} c^{9}}}}{a^{3} b^{12} - 24 \, a^{4} b^{10} c + 240 \, a^{5} b^{8} c^{2} - 1280 \, a^{6} b^{6} c^{3} + 3840 \, a^{7} b^{4} c^{4} - 6144 \, a^{8} b^{2} c^{5} + 4096 \, a^{9} c^{6}}}} \sqrt{-\frac{b^{7} + 21 \, a b^{5} c + 168 \, a^{2} b^{3} c^{2} + 3024 \, a^{3} b c^{3} + {\left(a^{3} b^{12} - 24 \, a^{4} b^{10} c + 240 \, a^{5} b^{8} c^{2} - 1280 \, a^{6} b^{6} c^{3} + 3840 \, a^{7} b^{4} c^{4} - 6144 \, a^{8} b^{2} c^{5} + 4096 \, a^{9} c^{6}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{a^{6} b^{18} - 36 \, a^{7} b^{16} c + 576 \, a^{8} b^{14} c^{2} - 5376 \, a^{9} b^{12} c^{3} + 32256 \, a^{10} b^{10} c^{4} - 129024 \, a^{11} b^{8} c^{5} + 344064 \, a^{12} b^{6} c^{6} - 589824 \, a^{13} b^{4} c^{7} + 589824 \, a^{14} b^{2} c^{8} - 262144 \, a^{15} c^{9}}}}{a^{3} b^{12} - 24 \, a^{4} b^{10} c + 240 \, a^{5} b^{8} c^{2} - 1280 \, a^{6} b^{6} c^{3} + 3840 \, a^{7} b^{4} c^{4} - 6144 \, a^{8} b^{2} c^{5} + 4096 \, a^{9} c^{6}}} - \sqrt{\frac{1}{2}} {\left(7 \, b^{24} c + 400 \, a b^{22} c^{2} + 7843 \, a^{2} b^{20} c^{3} + 22574 \, a^{3} b^{18} c^{4} - 1395688 \, a^{4} b^{16} c^{5} - 11961472 \, a^{5} b^{14} c^{6} + 98703360 \, a^{6} b^{12} c^{7} + 1408361472 \, a^{7} b^{10} c^{8} - 12100202496 \, a^{8} b^{8} c^{9} + 1218281472 \, a^{9} b^{6} c^{10} + 241219731456 \, a^{10} b^{4} c^{11} - 812665405440 \, a^{11} b^{2} c^{12} + 835884417024 \, a^{12} c^{13} - {\left(7 \, a^{3} b^{29} c + 85 \, a^{4} b^{27} c^{2} + 1764 \, a^{5} b^{25} c^{3} - 37920 \, a^{6} b^{23} c^{4} - 103296 \, a^{7} b^{21} c^{5} - 2564352 \, a^{8} b^{19} c^{6} + 145468416 \, a^{9} b^{17} c^{7} - 1602797568 \, a^{10} b^{15} c^{8} + 6543507456 \, a^{11} b^{13} c^{9} + 7533166592 \, a^{12} b^{11} c^{10} - 193399619584 \, a^{13} b^{9} c^{11} + 890247315456 \, a^{14} b^{7} c^{12} - 2078520901632 \, a^{15} b^{5} c^{13} + 2556193406976 \, a^{16} b^{3} c^{14} - 1320903770112 \, a^{17} b c^{15}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{a^{6} b^{18} - 36 \, a^{7} b^{16} c + 576 \, a^{8} b^{14} c^{2} - 5376 \, a^{9} b^{12} c^{3} + 32256 \, a^{10} b^{10} c^{4} - 129024 \, a^{11} b^{8} c^{5} + 344064 \, a^{12} b^{6} c^{6} - 589824 \, a^{13} b^{4} c^{7} + 589824 \, a^{14} b^{2} c^{8} - 262144 \, a^{15} c^{9}}}\right)} \sqrt{x} \sqrt{-\frac{b^{7} + 21 \, a b^{5} c + 168 \, a^{2} b^{3} c^{2} + 3024 \, a^{3} b c^{3} + {\left(a^{3} b^{12} - 24 \, a^{4} b^{10} c + 240 \, a^{5} b^{8} c^{2} - 1280 \, a^{6} b^{6} c^{3} + 3840 \, a^{7} b^{4} c^{4} - 6144 \, a^{8} b^{2} c^{5} + 4096 \, a^{9} c^{6}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{a^{6} b^{18} - 36 \, a^{7} b^{16} c + 576 \, a^{8} b^{14} c^{2} - 5376 \, a^{9} b^{12} c^{3} + 32256 \, a^{10} b^{10} c^{4} - 129024 \, a^{11} b^{8} c^{5} + 344064 \, a^{12} b^{6} c^{6} - 589824 \, a^{13} b^{4} c^{7} + 589824 \, a^{14} b^{2} c^{8} - 262144 \, a^{15} c^{9}}}}{a^{3} b^{12} - 24 \, a^{4} b^{10} c + 240 \, a^{5} b^{8} c^{2} - 1280 \, a^{6} b^{6} c^{3} + 3840 \, a^{7} b^{4} c^{4} - 6144 \, a^{8} b^{2} c^{5} + 4096 \, a^{9} c^{6}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} + 21 \, a b^{5} c + 168 \, a^{2} b^{3} c^{2} + 3024 \, a^{3} b c^{3} + {\left(a^{3} b^{12} - 24 \, a^{4} b^{10} c + 240 \, a^{5} b^{8} c^{2} - 1280 \, a^{6} b^{6} c^{3} + 3840 \, a^{7} b^{4} c^{4} - 6144 \, a^{8} b^{2} c^{5} + 4096 \, a^{9} c^{6}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{a^{6} b^{18} - 36 \, a^{7} b^{16} c + 576 \, a^{8} b^{14} c^{2} - 5376 \, a^{9} b^{12} c^{3} + 32256 \, a^{10} b^{10} c^{4} - 129024 \, a^{11} b^{8} c^{5} + 344064 \, a^{12} b^{6} c^{6} - 589824 \, a^{13} b^{4} c^{7} + 589824 \, a^{14} b^{2} c^{8} - 262144 \, a^{15} c^{9}}}}{a^{3} b^{12} - 24 \, a^{4} b^{10} c + 240 \, a^{5} b^{8} c^{2} - 1280 \, a^{6} b^{6} c^{3} + 3840 \, a^{7} b^{4} c^{4} - 6144 \, a^{8} b^{2} c^{5} + 4096 \, a^{9} c^{6}}}}}{2 \, {\left(2401 \, b^{16} c^{3} + 179046 \, a b^{14} c^{4} + 6354369 \, a^{2} b^{12} c^{5} + 131902344 \, a^{3} b^{10} c^{6} + 1713103344 \, a^{4} b^{8} c^{7} + 13740938496 \, a^{5} b^{6} c^{8} + 65167421184 \, a^{6} b^{4} c^{9} + 166523848704 \, a^{7} b^{2} c^{10} + 176319369216 \, a^{8} c^{11}\right)}}\right) - 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)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} + 21 \, a b^{5} c + 168 \, a^{2} b^{3} c^{2} + 3024 \, a^{3} b c^{3} - {\left(a^{3} b^{12} - 24 \, a^{4} b^{10} c + 240 \, a^{5} b^{8} c^{2} - 1280 \, a^{6} b^{6} c^{3} + 3840 \, a^{7} b^{4} c^{4} - 6144 \, a^{8} b^{2} c^{5} + 4096 \, a^{9} c^{6}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{a^{6} b^{18} - 36 \, a^{7} b^{16} c + 576 \, a^{8} b^{14} c^{2} - 5376 \, a^{9} b^{12} c^{3} + 32256 \, a^{10} b^{10} c^{4} - 129024 \, a^{11} b^{8} c^{5} + 344064 \, a^{12} b^{6} c^{6} - 589824 \, a^{13} b^{4} c^{7} + 589824 \, a^{14} b^{2} c^{8} - 262144 \, a^{15} c^{9}}}}{a^{3} b^{12} - 24 \, a^{4} b^{10} c + 240 \, a^{5} b^{8} c^{2} - 1280 \, a^{6} b^{6} c^{3} + 3840 \, a^{7} b^{4} c^{4} - 6144 \, a^{8} b^{2} c^{5} + 4096 \, a^{9} c^{6}}}} \arctan\left(-\frac{\sqrt{\frac{1}{2}} {\left(b^{18} + 25 \, a b^{16} c - 146 \, a^{2} b^{14} c^{2} - 5320 \, a^{3} b^{12} c^{3} - 2464 \, a^{4} b^{10} c^{4} + 1076096 \, a^{5} b^{8} c^{5} - 10483200 \, a^{6} b^{6} c^{6} + 44181504 \, a^{7} b^{4} c^{7} - 89579520 \, a^{8} b^{2} c^{8} + 71663616 \, a^{9} c^{9} + {\left(a^{3} b^{23} - 20 \, a^{4} b^{21} c + 432 \, a^{5} b^{19} c^{2} - 11712 \, a^{6} b^{17} c^{3} + 195072 \, a^{7} b^{15} c^{4} - 1935360 \, a^{8} b^{13} c^{5} + 12214272 \, a^{9} b^{11} c^{6} - 50823168 \, a^{10} b^{9} c^{7} + 139788288 \, a^{11} b^{7} c^{8} - 245628928 \, a^{12} b^{5} c^{9} + 250609664 \, a^{13} b^{3} c^{10} - 113246208 \, a^{14} b c^{11}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{a^{6} b^{18} - 36 \, a^{7} b^{16} c + 576 \, a^{8} b^{14} c^{2} - 5376 \, a^{9} b^{12} c^{3} + 32256 \, a^{10} b^{10} c^{4} - 129024 \, a^{11} b^{8} c^{5} + 344064 \, a^{12} b^{6} c^{6} - 589824 \, a^{13} b^{4} c^{7} + 589824 \, a^{14} b^{2} c^{8} - 262144 \, a^{15} c^{9}}}\right)} \sqrt{{\left(49 \, b^{12} c^{2} + 3150 \, a b^{10} c^{3} + 95985 \, a^{2} b^{8} c^{4} + 1621296 \, a^{3} b^{6} c^{5} + 15746400 \, a^{4} b^{4} c^{6} + 75582720 \, a^{5} b^{2} c^{7} + 136048896 \, a^{6} c^{8}\right)} x + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{18} + 52 \, a b^{16} c + 1269 \, a^{2} b^{14} c^{2} + 14294 \, a^{3} b^{12} c^{3} + 48608 \, a^{4} b^{10} c^{4} - 679392 \, a^{5} b^{8} c^{5} - 4209408 \, a^{6} b^{6} c^{6} - 4105728 \, a^{7} b^{4} c^{7} + 214990848 \, a^{8} b^{2} c^{8} - 483729408 \, a^{9} c^{9} + {\left(a^{3} b^{23} + 7 \, a^{4} b^{21} c - 152 \, a^{5} b^{19} c^{2} - 2960 \, a^{6} b^{17} c^{3} + 44032 \, a^{7} b^{15} c^{4} + 60928 \, a^{8} b^{13} c^{5} - 4444160 \, a^{9} b^{11} c^{6} + 36855808 \, a^{10} b^{9} c^{7} - 153681920 \, a^{11} b^{7} c^{8} + 363528192 \, a^{12} b^{5} c^{9} - 467140608 \, a^{13} b^{3} c^{10} + 254803968 \, a^{14} b c^{11}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{a^{6} b^{18} - 36 \, a^{7} b^{16} c + 576 \, a^{8} b^{14} c^{2} - 5376 \, a^{9} b^{12} c^{3} + 32256 \, a^{10} b^{10} c^{4} - 129024 \, a^{11} b^{8} c^{5} + 344064 \, a^{12} b^{6} c^{6} - 589824 \, a^{13} b^{4} c^{7} + 589824 \, a^{14} b^{2} c^{8} - 262144 \, a^{15} c^{9}}}\right)} \sqrt{-\frac{b^{7} + 21 \, a b^{5} c + 168 \, a^{2} b^{3} c^{2} + 3024 \, a^{3} b c^{3} - {\left(a^{3} b^{12} - 24 \, a^{4} b^{10} c + 240 \, a^{5} b^{8} c^{2} - 1280 \, a^{6} b^{6} c^{3} + 3840 \, a^{7} b^{4} c^{4} - 6144 \, a^{8} b^{2} c^{5} + 4096 \, a^{9} c^{6}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{a^{6} b^{18} - 36 \, a^{7} b^{16} c + 576 \, a^{8} b^{14} c^{2} - 5376 \, a^{9} b^{12} c^{3} + 32256 \, a^{10} b^{10} c^{4} - 129024 \, a^{11} b^{8} c^{5} + 344064 \, a^{12} b^{6} c^{6} - 589824 \, a^{13} b^{4} c^{7} + 589824 \, a^{14} b^{2} c^{8} - 262144 \, a^{15} c^{9}}}}{a^{3} b^{12} - 24 \, a^{4} b^{10} c + 240 \, a^{5} b^{8} c^{2} - 1280 \, a^{6} b^{6} c^{3} + 3840 \, a^{7} b^{4} c^{4} - 6144 \, a^{8} b^{2} c^{5} + 4096 \, a^{9} c^{6}}}} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} + 21 \, a b^{5} c + 168 \, a^{2} b^{3} c^{2} + 3024 \, a^{3} b c^{3} - {\left(a^{3} b^{12} - 24 \, a^{4} b^{10} c + 240 \, a^{5} b^{8} c^{2} - 1280 \, a^{6} b^{6} c^{3} + 3840 \, a^{7} b^{4} c^{4} - 6144 \, a^{8} b^{2} c^{5} + 4096 \, a^{9} c^{6}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{a^{6} b^{18} - 36 \, a^{7} b^{16} c + 576 \, a^{8} b^{14} c^{2} - 5376 \, a^{9} b^{12} c^{3} + 32256 \, a^{10} b^{10} c^{4} - 129024 \, a^{11} b^{8} c^{5} + 344064 \, a^{12} b^{6} c^{6} - 589824 \, a^{13} b^{4} c^{7} + 589824 \, a^{14} b^{2} c^{8} - 262144 \, a^{15} c^{9}}}}{a^{3} b^{12} - 24 \, a^{4} b^{10} c + 240 \, a^{5} b^{8} c^{2} - 1280 \, a^{6} b^{6} c^{3} + 3840 \, a^{7} b^{4} c^{4} - 6144 \, a^{8} b^{2} c^{5} + 4096 \, a^{9} c^{6}}}} \sqrt{-\frac{b^{7} + 21 \, a b^{5} c + 168 \, a^{2} b^{3} c^{2} + 3024 \, a^{3} b c^{3} - {\left(a^{3} b^{12} - 24 \, a^{4} b^{10} c + 240 \, a^{5} b^{8} c^{2} - 1280 \, a^{6} b^{6} c^{3} + 3840 \, a^{7} b^{4} c^{4} - 6144 \, a^{8} b^{2} c^{5} + 4096 \, a^{9} c^{6}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{a^{6} b^{18} - 36 \, a^{7} b^{16} c + 576 \, a^{8} b^{14} c^{2} - 5376 \, a^{9} b^{12} c^{3} + 32256 \, a^{10} b^{10} c^{4} - 129024 \, a^{11} b^{8} c^{5} + 344064 \, a^{12} b^{6} c^{6} - 589824 \, a^{13} b^{4} c^{7} + 589824 \, a^{14} b^{2} c^{8} - 262144 \, a^{15} c^{9}}}}{a^{3} b^{12} - 24 \, a^{4} b^{10} c + 240 \, a^{5} b^{8} c^{2} - 1280 \, a^{6} b^{6} c^{3} + 3840 \, a^{7} b^{4} c^{4} - 6144 \, a^{8} b^{2} c^{5} + 4096 \, a^{9} c^{6}}} - \sqrt{\frac{1}{2}} {\left(7 \, b^{24} c + 400 \, a b^{22} c^{2} + 7843 \, a^{2} b^{20} c^{3} + 22574 \, a^{3} b^{18} c^{4} - 1395688 \, a^{4} b^{16} c^{5} - 11961472 \, a^{5} b^{14} c^{6} + 98703360 \, a^{6} b^{12} c^{7} + 1408361472 \, a^{7} b^{10} c^{8} - 12100202496 \, a^{8} b^{8} c^{9} + 1218281472 \, a^{9} b^{6} c^{10} + 241219731456 \, a^{10} b^{4} c^{11} - 812665405440 \, a^{11} b^{2} c^{12} + 835884417024 \, a^{12} c^{13} + {\left(7 \, a^{3} b^{29} c + 85 \, a^{4} b^{27} c^{2} + 1764 \, a^{5} b^{25} c^{3} - 37920 \, a^{6} b^{23} c^{4} - 103296 \, a^{7} b^{21} c^{5} - 2564352 \, a^{8} b^{19} c^{6} + 145468416 \, a^{9} b^{17} c^{7} - 1602797568 \, a^{10} b^{15} c^{8} + 6543507456 \, a^{11} b^{13} c^{9} + 7533166592 \, a^{12} b^{11} c^{10} - 193399619584 \, a^{13} b^{9} c^{11} + 890247315456 \, a^{14} b^{7} c^{12} - 2078520901632 \, a^{15} b^{5} c^{13} + 2556193406976 \, a^{16} b^{3} c^{14} - 1320903770112 \, a^{17} b c^{15}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{a^{6} b^{18} - 36 \, a^{7} b^{16} c + 576 \, a^{8} b^{14} c^{2} - 5376 \, a^{9} b^{12} c^{3} + 32256 \, a^{10} b^{10} c^{4} - 129024 \, a^{11} b^{8} c^{5} + 344064 \, a^{12} b^{6} c^{6} - 589824 \, a^{13} b^{4} c^{7} + 589824 \, a^{14} b^{2} c^{8} - 262144 \, a^{15} c^{9}}}\right)} \sqrt{x} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} + 21 \, a b^{5} c + 168 \, a^{2} b^{3} c^{2} + 3024 \, a^{3} b c^{3} - {\left(a^{3} b^{12} - 24 \, a^{4} b^{10} c + 240 \, a^{5} b^{8} c^{2} - 1280 \, a^{6} b^{6} c^{3} + 3840 \, a^{7} b^{4} c^{4} - 6144 \, a^{8} b^{2} c^{5} + 4096 \, a^{9} c^{6}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{a^{6} b^{18} - 36 \, a^{7} b^{16} c + 576 \, a^{8} b^{14} c^{2} - 5376 \, a^{9} b^{12} c^{3} + 32256 \, a^{10} b^{10} c^{4} - 129024 \, a^{11} b^{8} c^{5} + 344064 \, a^{12} b^{6} c^{6} - 589824 \, a^{13} b^{4} c^{7} + 589824 \, a^{14} b^{2} c^{8} - 262144 \, a^{15} c^{9}}}}{a^{3} b^{12} - 24 \, a^{4} b^{10} c + 240 \, a^{5} b^{8} c^{2} - 1280 \, a^{6} b^{6} c^{3} + 3840 \, a^{7} b^{4} c^{4} - 6144 \, a^{8} b^{2} c^{5} + 4096 \, a^{9} c^{6}}}} \sqrt{-\frac{b^{7} + 21 \, a b^{5} c + 168 \, a^{2} b^{3} c^{2} + 3024 \, a^{3} b c^{3} - {\left(a^{3} b^{12} - 24 \, a^{4} b^{10} c + 240 \, a^{5} b^{8} c^{2} - 1280 \, a^{6} b^{6} c^{3} + 3840 \, a^{7} b^{4} c^{4} - 6144 \, a^{8} b^{2} c^{5} + 4096 \, a^{9} c^{6}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{a^{6} b^{18} - 36 \, a^{7} b^{16} c + 576 \, a^{8} b^{14} c^{2} - 5376 \, a^{9} b^{12} c^{3} + 32256 \, a^{10} b^{10} c^{4} - 129024 \, a^{11} b^{8} c^{5} + 344064 \, a^{12} b^{6} c^{6} - 589824 \, a^{13} b^{4} c^{7} + 589824 \, a^{14} b^{2} c^{8} - 262144 \, a^{15} c^{9}}}}{a^{3} b^{12} - 24 \, a^{4} b^{10} c + 240 \, a^{5} b^{8} c^{2} - 1280 \, a^{6} b^{6} c^{3} + 3840 \, a^{7} b^{4} c^{4} - 6144 \, a^{8} b^{2} c^{5} + 4096 \, a^{9} c^{6}}}}{2 \, {\left(2401 \, b^{16} c^{3} + 179046 \, a b^{14} c^{4} + 6354369 \, a^{2} b^{12} c^{5} + 131902344 \, a^{3} b^{10} c^{6} + 1713103344 \, a^{4} b^{8} c^{7} + 13740938496 \, a^{5} b^{6} c^{8} + 65167421184 \, a^{6} b^{4} c^{9} + 166523848704 \, a^{7} b^{2} c^{10} + 176319369216 \, a^{8} c^{11}\right)}}\right) + {\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{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} + 21 \, a b^{5} c + 168 \, a^{2} b^{3} c^{2} + 3024 \, a^{3} b c^{3} + {\left(a^{3} b^{12} - 24 \, a^{4} b^{10} c + 240 \, a^{5} b^{8} c^{2} - 1280 \, a^{6} b^{6} c^{3} + 3840 \, a^{7} b^{4} c^{4} - 6144 \, a^{8} b^{2} c^{5} + 4096 \, a^{9} c^{6}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{a^{6} b^{18} - 36 \, a^{7} b^{16} c + 576 \, a^{8} b^{14} c^{2} - 5376 \, a^{9} b^{12} c^{3} + 32256 \, a^{10} b^{10} c^{4} - 129024 \, a^{11} b^{8} c^{5} + 344064 \, a^{12} b^{6} c^{6} - 589824 \, a^{13} b^{4} c^{7} + 589824 \, a^{14} b^{2} c^{8} - 262144 \, a^{15} c^{9}}}}{a^{3} b^{12} - 24 \, a^{4} b^{10} c + 240 \, a^{5} b^{8} c^{2} - 1280 \, a^{6} b^{6} c^{3} + 3840 \, a^{7} b^{4} c^{4} - 6144 \, a^{8} b^{2} c^{5} + 4096 \, a^{9} c^{6}}}} \log\left({\left(7 \, b^{6} c + 225 \, a b^{4} c^{2} + 3240 \, a^{2} b^{2} c^{3} + 11664 \, a^{3} c^{4}\right)} \sqrt{x} + \frac{1}{2} \, {\left(b^{9} + 19 \, a b^{7} c + 124 \, a^{2} b^{5} c^{2} - 2160 \, a^{3} b^{3} c^{3} + 5184 \, a^{4} b c^{4} - {\left(a^{3} b^{14} - 12 \, a^{4} b^{12} c - 48 \, a^{5} b^{10} c^{2} + 1600 \, a^{6} b^{8} c^{3} - 11520 \, a^{7} b^{6} c^{4} + 39936 \, a^{8} b^{4} c^{5} - 69632 \, a^{9} b^{2} c^{6} + 49152 \, a^{10} c^{7}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{a^{6} b^{18} - 36 \, a^{7} b^{16} c + 576 \, a^{8} b^{14} c^{2} - 5376 \, a^{9} b^{12} c^{3} + 32256 \, a^{10} b^{10} c^{4} - 129024 \, a^{11} b^{8} c^{5} + 344064 \, a^{12} b^{6} c^{6} - 589824 \, a^{13} b^{4} c^{7} + 589824 \, a^{14} b^{2} c^{8} - 262144 \, a^{15} c^{9}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} + 21 \, a b^{5} c + 168 \, a^{2} b^{3} c^{2} + 3024 \, a^{3} b c^{3} + {\left(a^{3} b^{12} - 24 \, a^{4} b^{10} c + 240 \, a^{5} b^{8} c^{2} - 1280 \, a^{6} b^{6} c^{3} + 3840 \, a^{7} b^{4} c^{4} - 6144 \, a^{8} b^{2} c^{5} + 4096 \, a^{9} c^{6}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{a^{6} b^{18} - 36 \, a^{7} b^{16} c + 576 \, a^{8} b^{14} c^{2} - 5376 \, a^{9} b^{12} c^{3} + 32256 \, a^{10} b^{10} c^{4} - 129024 \, a^{11} b^{8} c^{5} + 344064 \, a^{12} b^{6} c^{6} - 589824 \, a^{13} b^{4} c^{7} + 589824 \, a^{14} b^{2} c^{8} - 262144 \, a^{15} c^{9}}}}{a^{3} b^{12} - 24 \, a^{4} b^{10} c + 240 \, a^{5} b^{8} c^{2} - 1280 \, a^{6} b^{6} c^{3} + 3840 \, a^{7} b^{4} c^{4} - 6144 \, a^{8} b^{2} c^{5} + 4096 \, a^{9} c^{6}}}}\right) - {\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{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} + 21 \, a b^{5} c + 168 \, a^{2} b^{3} c^{2} + 3024 \, a^{3} b c^{3} + {\left(a^{3} b^{12} - 24 \, a^{4} b^{10} c + 240 \, a^{5} b^{8} c^{2} - 1280 \, a^{6} b^{6} c^{3} + 3840 \, a^{7} b^{4} c^{4} - 6144 \, a^{8} b^{2} c^{5} + 4096 \, a^{9} c^{6}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{a^{6} b^{18} - 36 \, a^{7} b^{16} c + 576 \, a^{8} b^{14} c^{2} - 5376 \, a^{9} b^{12} c^{3} + 32256 \, a^{10} b^{10} c^{4} - 129024 \, a^{11} b^{8} c^{5} + 344064 \, a^{12} b^{6} c^{6} - 589824 \, a^{13} b^{4} c^{7} + 589824 \, a^{14} b^{2} c^{8} - 262144 \, a^{15} c^{9}}}}{a^{3} b^{12} - 24 \, a^{4} b^{10} c + 240 \, a^{5} b^{8} c^{2} - 1280 \, a^{6} b^{6} c^{3} + 3840 \, a^{7} b^{4} c^{4} - 6144 \, a^{8} b^{2} c^{5} + 4096 \, a^{9} c^{6}}}} \log\left({\left(7 \, b^{6} c + 225 \, a b^{4} c^{2} + 3240 \, a^{2} b^{2} c^{3} + 11664 \, a^{3} c^{4}\right)} \sqrt{x} - \frac{1}{2} \, {\left(b^{9} + 19 \, a b^{7} c + 124 \, a^{2} b^{5} c^{2} - 2160 \, a^{3} b^{3} c^{3} + 5184 \, a^{4} b c^{4} - {\left(a^{3} b^{14} - 12 \, a^{4} b^{12} c - 48 \, a^{5} b^{10} c^{2} + 1600 \, a^{6} b^{8} c^{3} - 11520 \, a^{7} b^{6} c^{4} + 39936 \, a^{8} b^{4} c^{5} - 69632 \, a^{9} b^{2} c^{6} + 49152 \, a^{10} c^{7}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{a^{6} b^{18} - 36 \, a^{7} b^{16} c + 576 \, a^{8} b^{14} c^{2} - 5376 \, a^{9} b^{12} c^{3} + 32256 \, a^{10} b^{10} c^{4} - 129024 \, a^{11} b^{8} c^{5} + 344064 \, a^{12} b^{6} c^{6} - 589824 \, a^{13} b^{4} c^{7} + 589824 \, a^{14} b^{2} c^{8} - 262144 \, a^{15} c^{9}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} + 21 \, a b^{5} c + 168 \, a^{2} b^{3} c^{2} + 3024 \, a^{3} b c^{3} + {\left(a^{3} b^{12} - 24 \, a^{4} b^{10} c + 240 \, a^{5} b^{8} c^{2} - 1280 \, a^{6} b^{6} c^{3} + 3840 \, a^{7} b^{4} c^{4} - 6144 \, a^{8} b^{2} c^{5} + 4096 \, a^{9} c^{6}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{a^{6} b^{18} - 36 \, a^{7} b^{16} c + 576 \, a^{8} b^{14} c^{2} - 5376 \, a^{9} b^{12} c^{3} + 32256 \, a^{10} b^{10} c^{4} - 129024 \, a^{11} b^{8} c^{5} + 344064 \, a^{12} b^{6} c^{6} - 589824 \, a^{13} b^{4} c^{7} + 589824 \, a^{14} b^{2} c^{8} - 262144 \, a^{15} c^{9}}}}{a^{3} b^{12} - 24 \, a^{4} b^{10} c + 240 \, a^{5} b^{8} c^{2} - 1280 \, a^{6} b^{6} c^{3} + 3840 \, a^{7} b^{4} c^{4} - 6144 \, a^{8} b^{2} c^{5} + 4096 \, a^{9} c^{6}}}}\right) + {\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{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} + 21 \, a b^{5} c + 168 \, a^{2} b^{3} c^{2} + 3024 \, a^{3} b c^{3} - {\left(a^{3} b^{12} - 24 \, a^{4} b^{10} c + 240 \, a^{5} b^{8} c^{2} - 1280 \, a^{6} b^{6} c^{3} + 3840 \, a^{7} b^{4} c^{4} - 6144 \, a^{8} b^{2} c^{5} + 4096 \, a^{9} c^{6}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{a^{6} b^{18} - 36 \, a^{7} b^{16} c + 576 \, a^{8} b^{14} c^{2} - 5376 \, a^{9} b^{12} c^{3} + 32256 \, a^{10} b^{10} c^{4} - 129024 \, a^{11} b^{8} c^{5} + 344064 \, a^{12} b^{6} c^{6} - 589824 \, a^{13} b^{4} c^{7} + 589824 \, a^{14} b^{2} c^{8} - 262144 \, a^{15} c^{9}}}}{a^{3} b^{12} - 24 \, a^{4} b^{10} c + 240 \, a^{5} b^{8} c^{2} - 1280 \, a^{6} b^{6} c^{3} + 3840 \, a^{7} b^{4} c^{4} - 6144 \, a^{8} b^{2} c^{5} + 4096 \, a^{9} c^{6}}}} \log\left({\left(7 \, b^{6} c + 225 \, a b^{4} c^{2} + 3240 \, a^{2} b^{2} c^{3} + 11664 \, a^{3} c^{4}\right)} \sqrt{x} + \frac{1}{2} \, {\left(b^{9} + 19 \, a b^{7} c + 124 \, a^{2} b^{5} c^{2} - 2160 \, a^{3} b^{3} c^{3} + 5184 \, a^{4} b c^{4} + {\left(a^{3} b^{14} - 12 \, a^{4} b^{12} c - 48 \, a^{5} b^{10} c^{2} + 1600 \, a^{6} b^{8} c^{3} - 11520 \, a^{7} b^{6} c^{4} + 39936 \, a^{8} b^{4} c^{5} - 69632 \, a^{9} b^{2} c^{6} + 49152 \, a^{10} c^{7}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{a^{6} b^{18} - 36 \, a^{7} b^{16} c + 576 \, a^{8} b^{14} c^{2} - 5376 \, a^{9} b^{12} c^{3} + 32256 \, a^{10} b^{10} c^{4} - 129024 \, a^{11} b^{8} c^{5} + 344064 \, a^{12} b^{6} c^{6} - 589824 \, a^{13} b^{4} c^{7} + 589824 \, a^{14} b^{2} c^{8} - 262144 \, a^{15} c^{9}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} + 21 \, a b^{5} c + 168 \, a^{2} b^{3} c^{2} + 3024 \, a^{3} b c^{3} - {\left(a^{3} b^{12} - 24 \, a^{4} b^{10} c + 240 \, a^{5} b^{8} c^{2} - 1280 \, a^{6} b^{6} c^{3} + 3840 \, a^{7} b^{4} c^{4} - 6144 \, a^{8} b^{2} c^{5} + 4096 \, a^{9} c^{6}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{a^{6} b^{18} - 36 \, a^{7} b^{16} c + 576 \, a^{8} b^{14} c^{2} - 5376 \, a^{9} b^{12} c^{3} + 32256 \, a^{10} b^{10} c^{4} - 129024 \, a^{11} b^{8} c^{5} + 344064 \, a^{12} b^{6} c^{6} - 589824 \, a^{13} b^{4} c^{7} + 589824 \, a^{14} b^{2} c^{8} - 262144 \, a^{15} c^{9}}}}{a^{3} b^{12} - 24 \, a^{4} b^{10} c + 240 \, a^{5} b^{8} c^{2} - 1280 \, a^{6} b^{6} c^{3} + 3840 \, a^{7} b^{4} c^{4} - 6144 \, a^{8} b^{2} c^{5} + 4096 \, a^{9} c^{6}}}}\right) - {\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{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} + 21 \, a b^{5} c + 168 \, a^{2} b^{3} c^{2} + 3024 \, a^{3} b c^{3} - {\left(a^{3} b^{12} - 24 \, a^{4} b^{10} c + 240 \, a^{5} b^{8} c^{2} - 1280 \, a^{6} b^{6} c^{3} + 3840 \, a^{7} b^{4} c^{4} - 6144 \, a^{8} b^{2} c^{5} + 4096 \, a^{9} c^{6}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{a^{6} b^{18} - 36 \, a^{7} b^{16} c + 576 \, a^{8} b^{14} c^{2} - 5376 \, a^{9} b^{12} c^{3} + 32256 \, a^{10} b^{10} c^{4} - 129024 \, a^{11} b^{8} c^{5} + 344064 \, a^{12} b^{6} c^{6} - 589824 \, a^{13} b^{4} c^{7} + 589824 \, a^{14} b^{2} c^{8} - 262144 \, a^{15} c^{9}}}}{a^{3} b^{12} - 24 \, a^{4} b^{10} c + 240 \, a^{5} b^{8} c^{2} - 1280 \, a^{6} b^{6} c^{3} + 3840 \, a^{7} b^{4} c^{4} - 6144 \, a^{8} b^{2} c^{5} + 4096 \, a^{9} c^{6}}}} \log\left({\left(7 \, b^{6} c + 225 \, a b^{4} c^{2} + 3240 \, a^{2} b^{2} c^{3} + 11664 \, a^{3} c^{4}\right)} \sqrt{x} - \frac{1}{2} \, {\left(b^{9} + 19 \, a b^{7} c + 124 \, a^{2} b^{5} c^{2} - 2160 \, a^{3} b^{3} c^{3} + 5184 \, a^{4} b c^{4} + {\left(a^{3} b^{14} - 12 \, a^{4} b^{12} c - 48 \, a^{5} b^{10} c^{2} + 1600 \, a^{6} b^{8} c^{3} - 11520 \, a^{7} b^{6} c^{4} + 39936 \, a^{8} b^{4} c^{5} - 69632 \, a^{9} b^{2} c^{6} + 49152 \, a^{10} c^{7}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{a^{6} b^{18} - 36 \, a^{7} b^{16} c + 576 \, a^{8} b^{14} c^{2} - 5376 \, a^{9} b^{12} c^{3} + 32256 \, a^{10} b^{10} c^{4} - 129024 \, a^{11} b^{8} c^{5} + 344064 \, a^{12} b^{6} c^{6} - 589824 \, a^{13} b^{4} c^{7} + 589824 \, a^{14} b^{2} c^{8} - 262144 \, a^{15} c^{9}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} + 21 \, a b^{5} c + 168 \, a^{2} b^{3} c^{2} + 3024 \, a^{3} b c^{3} - {\left(a^{3} b^{12} - 24 \, a^{4} b^{10} c + 240 \, a^{5} b^{8} c^{2} - 1280 \, a^{6} b^{6} c^{3} + 3840 \, a^{7} b^{4} c^{4} - 6144 \, a^{8} b^{2} c^{5} + 4096 \, a^{9} c^{6}\right)} \sqrt{\frac{b^{8} + 54 \, a b^{6} c + 1377 \, a^{2} b^{4} c^{2} + 17496 \, a^{3} b^{2} c^{3} + 104976 \, a^{4} c^{4}}{a^{6} b^{18} - 36 \, a^{7} b^{16} c + 576 \, a^{8} b^{14} c^{2} - 5376 \, a^{9} b^{12} c^{3} + 32256 \, a^{10} b^{10} c^{4} - 129024 \, a^{11} b^{8} c^{5} + 344064 \, a^{12} b^{6} c^{6} - 589824 \, a^{13} b^{4} c^{7} + 589824 \, a^{14} b^{2} c^{8} - 262144 \, a^{15} c^{9}}}}{a^{3} b^{12} - 24 \, a^{4} b^{10} c + 240 \, a^{5} b^{8} c^{2} - 1280 \, a^{6} b^{6} c^{3} + 3840 \, a^{7} b^{4} c^{4} - 6144 \, a^{8} b^{2} c^{5} + 4096 \, a^{9} c^{6}}}}\right) + 4 \, {\left(2 \, c x^{2} + b\right)} \sqrt{x}}{8 \, {\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,"-1/8*(4*((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(sqrt(1/2)*sqrt(-(b^7 + 21*a*b^5*c + 168*a^2*b^3*c^2 + 3024*a^3*b*c^3 + (a^3*b^12 - 24*a^4*b^10*c + 240*a^5*b^8*c^2 - 1280*a^6*b^6*c^3 + 3840*a^7*b^4*c^4 - 6144*a^8*b^2*c^5 + 4096*a^9*c^6)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(a^6*b^18 - 36*a^7*b^16*c + 576*a^8*b^14*c^2 - 5376*a^9*b^12*c^3 + 32256*a^10*b^10*c^4 - 129024*a^11*b^8*c^5 + 344064*a^12*b^6*c^6 - 589824*a^13*b^4*c^7 + 589824*a^14*b^2*c^8 - 262144*a^15*c^9)))/(a^3*b^12 - 24*a^4*b^10*c + 240*a^5*b^8*c^2 - 1280*a^6*b^6*c^3 + 3840*a^7*b^4*c^4 - 6144*a^8*b^2*c^5 + 4096*a^9*c^6)))*arctan(1/2*(sqrt(1/2)*(b^18 + 25*a*b^16*c - 146*a^2*b^14*c^2 - 5320*a^3*b^12*c^3 - 2464*a^4*b^10*c^4 + 1076096*a^5*b^8*c^5 - 10483200*a^6*b^6*c^6 + 44181504*a^7*b^4*c^7 - 89579520*a^8*b^2*c^8 + 71663616*a^9*c^9 - (a^3*b^23 - 20*a^4*b^21*c + 432*a^5*b^19*c^2 - 11712*a^6*b^17*c^3 + 195072*a^7*b^15*c^4 - 1935360*a^8*b^13*c^5 + 12214272*a^9*b^11*c^6 - 50823168*a^10*b^9*c^7 + 139788288*a^11*b^7*c^8 - 245628928*a^12*b^5*c^9 + 250609664*a^13*b^3*c^10 - 113246208*a^14*b*c^11)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(a^6*b^18 - 36*a^7*b^16*c + 576*a^8*b^14*c^2 - 5376*a^9*b^12*c^3 + 32256*a^10*b^10*c^4 - 129024*a^11*b^8*c^5 + 344064*a^12*b^6*c^6 - 589824*a^13*b^4*c^7 + 589824*a^14*b^2*c^8 - 262144*a^15*c^9)))*sqrt((49*b^12*c^2 + 3150*a*b^10*c^3 + 95985*a^2*b^8*c^4 + 1621296*a^3*b^6*c^5 + 15746400*a^4*b^4*c^6 + 75582720*a^5*b^2*c^7 + 136048896*a^6*c^8)*x + 1/2*sqrt(1/2)*(b^18 + 52*a*b^16*c + 1269*a^2*b^14*c^2 + 14294*a^3*b^12*c^3 + 48608*a^4*b^10*c^4 - 679392*a^5*b^8*c^5 - 4209408*a^6*b^6*c^6 - 4105728*a^7*b^4*c^7 + 214990848*a^8*b^2*c^8 - 483729408*a^9*c^9 - (a^3*b^23 + 7*a^4*b^21*c - 152*a^5*b^19*c^2 - 2960*a^6*b^17*c^3 + 44032*a^7*b^15*c^4 + 60928*a^8*b^13*c^5 - 4444160*a^9*b^11*c^6 + 36855808*a^10*b^9*c^7 - 153681920*a^11*b^7*c^8 + 363528192*a^12*b^5*c^9 - 467140608*a^13*b^3*c^10 + 254803968*a^14*b*c^11)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(a^6*b^18 - 36*a^7*b^16*c + 576*a^8*b^14*c^2 - 5376*a^9*b^12*c^3 + 32256*a^10*b^10*c^4 - 129024*a^11*b^8*c^5 + 344064*a^12*b^6*c^6 - 589824*a^13*b^4*c^7 + 589824*a^14*b^2*c^8 - 262144*a^15*c^9)))*sqrt(-(b^7 + 21*a*b^5*c + 168*a^2*b^3*c^2 + 3024*a^3*b*c^3 + (a^3*b^12 - 24*a^4*b^10*c + 240*a^5*b^8*c^2 - 1280*a^6*b^6*c^3 + 3840*a^7*b^4*c^4 - 6144*a^8*b^2*c^5 + 4096*a^9*c^6)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(a^6*b^18 - 36*a^7*b^16*c + 576*a^8*b^14*c^2 - 5376*a^9*b^12*c^3 + 32256*a^10*b^10*c^4 - 129024*a^11*b^8*c^5 + 344064*a^12*b^6*c^6 - 589824*a^13*b^4*c^7 + 589824*a^14*b^2*c^8 - 262144*a^15*c^9)))/(a^3*b^12 - 24*a^4*b^10*c + 240*a^5*b^8*c^2 - 1280*a^6*b^6*c^3 + 3840*a^7*b^4*c^4 - 6144*a^8*b^2*c^5 + 4096*a^9*c^6)))*sqrt(-(b^7 + 21*a*b^5*c + 168*a^2*b^3*c^2 + 3024*a^3*b*c^3 + (a^3*b^12 - 24*a^4*b^10*c + 240*a^5*b^8*c^2 - 1280*a^6*b^6*c^3 + 3840*a^7*b^4*c^4 - 6144*a^8*b^2*c^5 + 4096*a^9*c^6)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(a^6*b^18 - 36*a^7*b^16*c + 576*a^8*b^14*c^2 - 5376*a^9*b^12*c^3 + 32256*a^10*b^10*c^4 - 129024*a^11*b^8*c^5 + 344064*a^12*b^6*c^6 - 589824*a^13*b^4*c^7 + 589824*a^14*b^2*c^8 - 262144*a^15*c^9)))/(a^3*b^12 - 24*a^4*b^10*c + 240*a^5*b^8*c^2 - 1280*a^6*b^6*c^3 + 3840*a^7*b^4*c^4 - 6144*a^8*b^2*c^5 + 4096*a^9*c^6)) - sqrt(1/2)*(7*b^24*c + 400*a*b^22*c^2 + 7843*a^2*b^20*c^3 + 22574*a^3*b^18*c^4 - 1395688*a^4*b^16*c^5 - 11961472*a^5*b^14*c^6 + 98703360*a^6*b^12*c^7 + 1408361472*a^7*b^10*c^8 - 12100202496*a^8*b^8*c^9 + 1218281472*a^9*b^6*c^10 + 241219731456*a^10*b^4*c^11 - 812665405440*a^11*b^2*c^12 + 835884417024*a^12*c^13 - (7*a^3*b^29*c + 85*a^4*b^27*c^2 + 1764*a^5*b^25*c^3 - 37920*a^6*b^23*c^4 - 103296*a^7*b^21*c^5 - 2564352*a^8*b^19*c^6 + 145468416*a^9*b^17*c^7 - 1602797568*a^10*b^15*c^8 + 6543507456*a^11*b^13*c^9 + 7533166592*a^12*b^11*c^10 - 193399619584*a^13*b^9*c^11 + 890247315456*a^14*b^7*c^12 - 2078520901632*a^15*b^5*c^13 + 2556193406976*a^16*b^3*c^14 - 1320903770112*a^17*b*c^15)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(a^6*b^18 - 36*a^7*b^16*c + 576*a^8*b^14*c^2 - 5376*a^9*b^12*c^3 + 32256*a^10*b^10*c^4 - 129024*a^11*b^8*c^5 + 344064*a^12*b^6*c^6 - 589824*a^13*b^4*c^7 + 589824*a^14*b^2*c^8 - 262144*a^15*c^9)))*sqrt(x)*sqrt(-(b^7 + 21*a*b^5*c + 168*a^2*b^3*c^2 + 3024*a^3*b*c^3 + (a^3*b^12 - 24*a^4*b^10*c + 240*a^5*b^8*c^2 - 1280*a^6*b^6*c^3 + 3840*a^7*b^4*c^4 - 6144*a^8*b^2*c^5 + 4096*a^9*c^6)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(a^6*b^18 - 36*a^7*b^16*c + 576*a^8*b^14*c^2 - 5376*a^9*b^12*c^3 + 32256*a^10*b^10*c^4 - 129024*a^11*b^8*c^5 + 344064*a^12*b^6*c^6 - 589824*a^13*b^4*c^7 + 589824*a^14*b^2*c^8 - 262144*a^15*c^9)))/(a^3*b^12 - 24*a^4*b^10*c + 240*a^5*b^8*c^2 - 1280*a^6*b^6*c^3 + 3840*a^7*b^4*c^4 - 6144*a^8*b^2*c^5 + 4096*a^9*c^6)))*sqrt(sqrt(1/2)*sqrt(-(b^7 + 21*a*b^5*c + 168*a^2*b^3*c^2 + 3024*a^3*b*c^3 + (a^3*b^12 - 24*a^4*b^10*c + 240*a^5*b^8*c^2 - 1280*a^6*b^6*c^3 + 3840*a^7*b^4*c^4 - 6144*a^8*b^2*c^5 + 4096*a^9*c^6)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(a^6*b^18 - 36*a^7*b^16*c + 576*a^8*b^14*c^2 - 5376*a^9*b^12*c^3 + 32256*a^10*b^10*c^4 - 129024*a^11*b^8*c^5 + 344064*a^12*b^6*c^6 - 589824*a^13*b^4*c^7 + 589824*a^14*b^2*c^8 - 262144*a^15*c^9)))/(a^3*b^12 - 24*a^4*b^10*c + 240*a^5*b^8*c^2 - 1280*a^6*b^6*c^3 + 3840*a^7*b^4*c^4 - 6144*a^8*b^2*c^5 + 4096*a^9*c^6)))/(2401*b^16*c^3 + 179046*a*b^14*c^4 + 6354369*a^2*b^12*c^5 + 131902344*a^3*b^10*c^6 + 1713103344*a^4*b^8*c^7 + 13740938496*a^5*b^6*c^8 + 65167421184*a^6*b^4*c^9 + 166523848704*a^7*b^2*c^10 + 176319369216*a^8*c^11)) - 4*((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(sqrt(1/2)*sqrt(-(b^7 + 21*a*b^5*c + 168*a^2*b^3*c^2 + 3024*a^3*b*c^3 - (a^3*b^12 - 24*a^4*b^10*c + 240*a^5*b^8*c^2 - 1280*a^6*b^6*c^3 + 3840*a^7*b^4*c^4 - 6144*a^8*b^2*c^5 + 4096*a^9*c^6)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(a^6*b^18 - 36*a^7*b^16*c + 576*a^8*b^14*c^2 - 5376*a^9*b^12*c^3 + 32256*a^10*b^10*c^4 - 129024*a^11*b^8*c^5 + 344064*a^12*b^6*c^6 - 589824*a^13*b^4*c^7 + 589824*a^14*b^2*c^8 - 262144*a^15*c^9)))/(a^3*b^12 - 24*a^4*b^10*c + 240*a^5*b^8*c^2 - 1280*a^6*b^6*c^3 + 3840*a^7*b^4*c^4 - 6144*a^8*b^2*c^5 + 4096*a^9*c^6)))*arctan(-1/2*(sqrt(1/2)*(b^18 + 25*a*b^16*c - 146*a^2*b^14*c^2 - 5320*a^3*b^12*c^3 - 2464*a^4*b^10*c^4 + 1076096*a^5*b^8*c^5 - 10483200*a^6*b^6*c^6 + 44181504*a^7*b^4*c^7 - 89579520*a^8*b^2*c^8 + 71663616*a^9*c^9 + (a^3*b^23 - 20*a^4*b^21*c + 432*a^5*b^19*c^2 - 11712*a^6*b^17*c^3 + 195072*a^7*b^15*c^4 - 1935360*a^8*b^13*c^5 + 12214272*a^9*b^11*c^6 - 50823168*a^10*b^9*c^7 + 139788288*a^11*b^7*c^8 - 245628928*a^12*b^5*c^9 + 250609664*a^13*b^3*c^10 - 113246208*a^14*b*c^11)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(a^6*b^18 - 36*a^7*b^16*c + 576*a^8*b^14*c^2 - 5376*a^9*b^12*c^3 + 32256*a^10*b^10*c^4 - 129024*a^11*b^8*c^5 + 344064*a^12*b^6*c^6 - 589824*a^13*b^4*c^7 + 589824*a^14*b^2*c^8 - 262144*a^15*c^9)))*sqrt((49*b^12*c^2 + 3150*a*b^10*c^3 + 95985*a^2*b^8*c^4 + 1621296*a^3*b^6*c^5 + 15746400*a^4*b^4*c^6 + 75582720*a^5*b^2*c^7 + 136048896*a^6*c^8)*x + 1/2*sqrt(1/2)*(b^18 + 52*a*b^16*c + 1269*a^2*b^14*c^2 + 14294*a^3*b^12*c^3 + 48608*a^4*b^10*c^4 - 679392*a^5*b^8*c^5 - 4209408*a^6*b^6*c^6 - 4105728*a^7*b^4*c^7 + 214990848*a^8*b^2*c^8 - 483729408*a^9*c^9 + (a^3*b^23 + 7*a^4*b^21*c - 152*a^5*b^19*c^2 - 2960*a^6*b^17*c^3 + 44032*a^7*b^15*c^4 + 60928*a^8*b^13*c^5 - 4444160*a^9*b^11*c^6 + 36855808*a^10*b^9*c^7 - 153681920*a^11*b^7*c^8 + 363528192*a^12*b^5*c^9 - 467140608*a^13*b^3*c^10 + 254803968*a^14*b*c^11)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(a^6*b^18 - 36*a^7*b^16*c + 576*a^8*b^14*c^2 - 5376*a^9*b^12*c^3 + 32256*a^10*b^10*c^4 - 129024*a^11*b^8*c^5 + 344064*a^12*b^6*c^6 - 589824*a^13*b^4*c^7 + 589824*a^14*b^2*c^8 - 262144*a^15*c^9)))*sqrt(-(b^7 + 21*a*b^5*c + 168*a^2*b^3*c^2 + 3024*a^3*b*c^3 - (a^3*b^12 - 24*a^4*b^10*c + 240*a^5*b^8*c^2 - 1280*a^6*b^6*c^3 + 3840*a^7*b^4*c^4 - 6144*a^8*b^2*c^5 + 4096*a^9*c^6)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(a^6*b^18 - 36*a^7*b^16*c + 576*a^8*b^14*c^2 - 5376*a^9*b^12*c^3 + 32256*a^10*b^10*c^4 - 129024*a^11*b^8*c^5 + 344064*a^12*b^6*c^6 - 589824*a^13*b^4*c^7 + 589824*a^14*b^2*c^8 - 262144*a^15*c^9)))/(a^3*b^12 - 24*a^4*b^10*c + 240*a^5*b^8*c^2 - 1280*a^6*b^6*c^3 + 3840*a^7*b^4*c^4 - 6144*a^8*b^2*c^5 + 4096*a^9*c^6)))*sqrt(sqrt(1/2)*sqrt(-(b^7 + 21*a*b^5*c + 168*a^2*b^3*c^2 + 3024*a^3*b*c^3 - (a^3*b^12 - 24*a^4*b^10*c + 240*a^5*b^8*c^2 - 1280*a^6*b^6*c^3 + 3840*a^7*b^4*c^4 - 6144*a^8*b^2*c^5 + 4096*a^9*c^6)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(a^6*b^18 - 36*a^7*b^16*c + 576*a^8*b^14*c^2 - 5376*a^9*b^12*c^3 + 32256*a^10*b^10*c^4 - 129024*a^11*b^8*c^5 + 344064*a^12*b^6*c^6 - 589824*a^13*b^4*c^7 + 589824*a^14*b^2*c^8 - 262144*a^15*c^9)))/(a^3*b^12 - 24*a^4*b^10*c + 240*a^5*b^8*c^2 - 1280*a^6*b^6*c^3 + 3840*a^7*b^4*c^4 - 6144*a^8*b^2*c^5 + 4096*a^9*c^6)))*sqrt(-(b^7 + 21*a*b^5*c + 168*a^2*b^3*c^2 + 3024*a^3*b*c^3 - (a^3*b^12 - 24*a^4*b^10*c + 240*a^5*b^8*c^2 - 1280*a^6*b^6*c^3 + 3840*a^7*b^4*c^4 - 6144*a^8*b^2*c^5 + 4096*a^9*c^6)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(a^6*b^18 - 36*a^7*b^16*c + 576*a^8*b^14*c^2 - 5376*a^9*b^12*c^3 + 32256*a^10*b^10*c^4 - 129024*a^11*b^8*c^5 + 344064*a^12*b^6*c^6 - 589824*a^13*b^4*c^7 + 589824*a^14*b^2*c^8 - 262144*a^15*c^9)))/(a^3*b^12 - 24*a^4*b^10*c + 240*a^5*b^8*c^2 - 1280*a^6*b^6*c^3 + 3840*a^7*b^4*c^4 - 6144*a^8*b^2*c^5 + 4096*a^9*c^6)) - sqrt(1/2)*(7*b^24*c + 400*a*b^22*c^2 + 7843*a^2*b^20*c^3 + 22574*a^3*b^18*c^4 - 1395688*a^4*b^16*c^5 - 11961472*a^5*b^14*c^6 + 98703360*a^6*b^12*c^7 + 1408361472*a^7*b^10*c^8 - 12100202496*a^8*b^8*c^9 + 1218281472*a^9*b^6*c^10 + 241219731456*a^10*b^4*c^11 - 812665405440*a^11*b^2*c^12 + 835884417024*a^12*c^13 + (7*a^3*b^29*c + 85*a^4*b^27*c^2 + 1764*a^5*b^25*c^3 - 37920*a^6*b^23*c^4 - 103296*a^7*b^21*c^5 - 2564352*a^8*b^19*c^6 + 145468416*a^9*b^17*c^7 - 1602797568*a^10*b^15*c^8 + 6543507456*a^11*b^13*c^9 + 7533166592*a^12*b^11*c^10 - 193399619584*a^13*b^9*c^11 + 890247315456*a^14*b^7*c^12 - 2078520901632*a^15*b^5*c^13 + 2556193406976*a^16*b^3*c^14 - 1320903770112*a^17*b*c^15)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(a^6*b^18 - 36*a^7*b^16*c + 576*a^8*b^14*c^2 - 5376*a^9*b^12*c^3 + 32256*a^10*b^10*c^4 - 129024*a^11*b^8*c^5 + 344064*a^12*b^6*c^6 - 589824*a^13*b^4*c^7 + 589824*a^14*b^2*c^8 - 262144*a^15*c^9)))*sqrt(x)*sqrt(sqrt(1/2)*sqrt(-(b^7 + 21*a*b^5*c + 168*a^2*b^3*c^2 + 3024*a^3*b*c^3 - (a^3*b^12 - 24*a^4*b^10*c + 240*a^5*b^8*c^2 - 1280*a^6*b^6*c^3 + 3840*a^7*b^4*c^4 - 6144*a^8*b^2*c^5 + 4096*a^9*c^6)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(a^6*b^18 - 36*a^7*b^16*c + 576*a^8*b^14*c^2 - 5376*a^9*b^12*c^3 + 32256*a^10*b^10*c^4 - 129024*a^11*b^8*c^5 + 344064*a^12*b^6*c^6 - 589824*a^13*b^4*c^7 + 589824*a^14*b^2*c^8 - 262144*a^15*c^9)))/(a^3*b^12 - 24*a^4*b^10*c + 240*a^5*b^8*c^2 - 1280*a^6*b^6*c^3 + 3840*a^7*b^4*c^4 - 6144*a^8*b^2*c^5 + 4096*a^9*c^6)))*sqrt(-(b^7 + 21*a*b^5*c + 168*a^2*b^3*c^2 + 3024*a^3*b*c^3 - (a^3*b^12 - 24*a^4*b^10*c + 240*a^5*b^8*c^2 - 1280*a^6*b^6*c^3 + 3840*a^7*b^4*c^4 - 6144*a^8*b^2*c^5 + 4096*a^9*c^6)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(a^6*b^18 - 36*a^7*b^16*c + 576*a^8*b^14*c^2 - 5376*a^9*b^12*c^3 + 32256*a^10*b^10*c^4 - 129024*a^11*b^8*c^5 + 344064*a^12*b^6*c^6 - 589824*a^13*b^4*c^7 + 589824*a^14*b^2*c^8 - 262144*a^15*c^9)))/(a^3*b^12 - 24*a^4*b^10*c + 240*a^5*b^8*c^2 - 1280*a^6*b^6*c^3 + 3840*a^7*b^4*c^4 - 6144*a^8*b^2*c^5 + 4096*a^9*c^6)))/(2401*b^16*c^3 + 179046*a*b^14*c^4 + 6354369*a^2*b^12*c^5 + 131902344*a^3*b^10*c^6 + 1713103344*a^4*b^8*c^7 + 13740938496*a^5*b^6*c^8 + 65167421184*a^6*b^4*c^9 + 166523848704*a^7*b^2*c^10 + 176319369216*a^8*c^11)) + ((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(sqrt(1/2)*sqrt(-(b^7 + 21*a*b^5*c + 168*a^2*b^3*c^2 + 3024*a^3*b*c^3 + (a^3*b^12 - 24*a^4*b^10*c + 240*a^5*b^8*c^2 - 1280*a^6*b^6*c^3 + 3840*a^7*b^4*c^4 - 6144*a^8*b^2*c^5 + 4096*a^9*c^6)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(a^6*b^18 - 36*a^7*b^16*c + 576*a^8*b^14*c^2 - 5376*a^9*b^12*c^3 + 32256*a^10*b^10*c^4 - 129024*a^11*b^8*c^5 + 344064*a^12*b^6*c^6 - 589824*a^13*b^4*c^7 + 589824*a^14*b^2*c^8 - 262144*a^15*c^9)))/(a^3*b^12 - 24*a^4*b^10*c + 240*a^5*b^8*c^2 - 1280*a^6*b^6*c^3 + 3840*a^7*b^4*c^4 - 6144*a^8*b^2*c^5 + 4096*a^9*c^6)))*log((7*b^6*c + 225*a*b^4*c^2 + 3240*a^2*b^2*c^3 + 11664*a^3*c^4)*sqrt(x) + 1/2*(b^9 + 19*a*b^7*c + 124*a^2*b^5*c^2 - 2160*a^3*b^3*c^3 + 5184*a^4*b*c^4 - (a^3*b^14 - 12*a^4*b^12*c - 48*a^5*b^10*c^2 + 1600*a^6*b^8*c^3 - 11520*a^7*b^6*c^4 + 39936*a^8*b^4*c^5 - 69632*a^9*b^2*c^6 + 49152*a^10*c^7)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(a^6*b^18 - 36*a^7*b^16*c + 576*a^8*b^14*c^2 - 5376*a^9*b^12*c^3 + 32256*a^10*b^10*c^4 - 129024*a^11*b^8*c^5 + 344064*a^12*b^6*c^6 - 589824*a^13*b^4*c^7 + 589824*a^14*b^2*c^8 - 262144*a^15*c^9)))*sqrt(sqrt(1/2)*sqrt(-(b^7 + 21*a*b^5*c + 168*a^2*b^3*c^2 + 3024*a^3*b*c^3 + (a^3*b^12 - 24*a^4*b^10*c + 240*a^5*b^8*c^2 - 1280*a^6*b^6*c^3 + 3840*a^7*b^4*c^4 - 6144*a^8*b^2*c^5 + 4096*a^9*c^6)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(a^6*b^18 - 36*a^7*b^16*c + 576*a^8*b^14*c^2 - 5376*a^9*b^12*c^3 + 32256*a^10*b^10*c^4 - 129024*a^11*b^8*c^5 + 344064*a^12*b^6*c^6 - 589824*a^13*b^4*c^7 + 589824*a^14*b^2*c^8 - 262144*a^15*c^9)))/(a^3*b^12 - 24*a^4*b^10*c + 240*a^5*b^8*c^2 - 1280*a^6*b^6*c^3 + 3840*a^7*b^4*c^4 - 6144*a^8*b^2*c^5 + 4096*a^9*c^6)))) - ((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(sqrt(1/2)*sqrt(-(b^7 + 21*a*b^5*c + 168*a^2*b^3*c^2 + 3024*a^3*b*c^3 + (a^3*b^12 - 24*a^4*b^10*c + 240*a^5*b^8*c^2 - 1280*a^6*b^6*c^3 + 3840*a^7*b^4*c^4 - 6144*a^8*b^2*c^5 + 4096*a^9*c^6)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(a^6*b^18 - 36*a^7*b^16*c + 576*a^8*b^14*c^2 - 5376*a^9*b^12*c^3 + 32256*a^10*b^10*c^4 - 129024*a^11*b^8*c^5 + 344064*a^12*b^6*c^6 - 589824*a^13*b^4*c^7 + 589824*a^14*b^2*c^8 - 262144*a^15*c^9)))/(a^3*b^12 - 24*a^4*b^10*c + 240*a^5*b^8*c^2 - 1280*a^6*b^6*c^3 + 3840*a^7*b^4*c^4 - 6144*a^8*b^2*c^5 + 4096*a^9*c^6)))*log((7*b^6*c + 225*a*b^4*c^2 + 3240*a^2*b^2*c^3 + 11664*a^3*c^4)*sqrt(x) - 1/2*(b^9 + 19*a*b^7*c + 124*a^2*b^5*c^2 - 2160*a^3*b^3*c^3 + 5184*a^4*b*c^4 - (a^3*b^14 - 12*a^4*b^12*c - 48*a^5*b^10*c^2 + 1600*a^6*b^8*c^3 - 11520*a^7*b^6*c^4 + 39936*a^8*b^4*c^5 - 69632*a^9*b^2*c^6 + 49152*a^10*c^7)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(a^6*b^18 - 36*a^7*b^16*c + 576*a^8*b^14*c^2 - 5376*a^9*b^12*c^3 + 32256*a^10*b^10*c^4 - 129024*a^11*b^8*c^5 + 344064*a^12*b^6*c^6 - 589824*a^13*b^4*c^7 + 589824*a^14*b^2*c^8 - 262144*a^15*c^9)))*sqrt(sqrt(1/2)*sqrt(-(b^7 + 21*a*b^5*c + 168*a^2*b^3*c^2 + 3024*a^3*b*c^3 + (a^3*b^12 - 24*a^4*b^10*c + 240*a^5*b^8*c^2 - 1280*a^6*b^6*c^3 + 3840*a^7*b^4*c^4 - 6144*a^8*b^2*c^5 + 4096*a^9*c^6)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(a^6*b^18 - 36*a^7*b^16*c + 576*a^8*b^14*c^2 - 5376*a^9*b^12*c^3 + 32256*a^10*b^10*c^4 - 129024*a^11*b^8*c^5 + 344064*a^12*b^6*c^6 - 589824*a^13*b^4*c^7 + 589824*a^14*b^2*c^8 - 262144*a^15*c^9)))/(a^3*b^12 - 24*a^4*b^10*c + 240*a^5*b^8*c^2 - 1280*a^6*b^6*c^3 + 3840*a^7*b^4*c^4 - 6144*a^8*b^2*c^5 + 4096*a^9*c^6)))) + ((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(sqrt(1/2)*sqrt(-(b^7 + 21*a*b^5*c + 168*a^2*b^3*c^2 + 3024*a^3*b*c^3 - (a^3*b^12 - 24*a^4*b^10*c + 240*a^5*b^8*c^2 - 1280*a^6*b^6*c^3 + 3840*a^7*b^4*c^4 - 6144*a^8*b^2*c^5 + 4096*a^9*c^6)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(a^6*b^18 - 36*a^7*b^16*c + 576*a^8*b^14*c^2 - 5376*a^9*b^12*c^3 + 32256*a^10*b^10*c^4 - 129024*a^11*b^8*c^5 + 344064*a^12*b^6*c^6 - 589824*a^13*b^4*c^7 + 589824*a^14*b^2*c^8 - 262144*a^15*c^9)))/(a^3*b^12 - 24*a^4*b^10*c + 240*a^5*b^8*c^2 - 1280*a^6*b^6*c^3 + 3840*a^7*b^4*c^4 - 6144*a^8*b^2*c^5 + 4096*a^9*c^6)))*log((7*b^6*c + 225*a*b^4*c^2 + 3240*a^2*b^2*c^3 + 11664*a^3*c^4)*sqrt(x) + 1/2*(b^9 + 19*a*b^7*c + 124*a^2*b^5*c^2 - 2160*a^3*b^3*c^3 + 5184*a^4*b*c^4 + (a^3*b^14 - 12*a^4*b^12*c - 48*a^5*b^10*c^2 + 1600*a^6*b^8*c^3 - 11520*a^7*b^6*c^4 + 39936*a^8*b^4*c^5 - 69632*a^9*b^2*c^6 + 49152*a^10*c^7)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(a^6*b^18 - 36*a^7*b^16*c + 576*a^8*b^14*c^2 - 5376*a^9*b^12*c^3 + 32256*a^10*b^10*c^4 - 129024*a^11*b^8*c^5 + 344064*a^12*b^6*c^6 - 589824*a^13*b^4*c^7 + 589824*a^14*b^2*c^8 - 262144*a^15*c^9)))*sqrt(sqrt(1/2)*sqrt(-(b^7 + 21*a*b^5*c + 168*a^2*b^3*c^2 + 3024*a^3*b*c^3 - (a^3*b^12 - 24*a^4*b^10*c + 240*a^5*b^8*c^2 - 1280*a^6*b^6*c^3 + 3840*a^7*b^4*c^4 - 6144*a^8*b^2*c^5 + 4096*a^9*c^6)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(a^6*b^18 - 36*a^7*b^16*c + 576*a^8*b^14*c^2 - 5376*a^9*b^12*c^3 + 32256*a^10*b^10*c^4 - 129024*a^11*b^8*c^5 + 344064*a^12*b^6*c^6 - 589824*a^13*b^4*c^7 + 589824*a^14*b^2*c^8 - 262144*a^15*c^9)))/(a^3*b^12 - 24*a^4*b^10*c + 240*a^5*b^8*c^2 - 1280*a^6*b^6*c^3 + 3840*a^7*b^4*c^4 - 6144*a^8*b^2*c^5 + 4096*a^9*c^6)))) - ((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(sqrt(1/2)*sqrt(-(b^7 + 21*a*b^5*c + 168*a^2*b^3*c^2 + 3024*a^3*b*c^3 - (a^3*b^12 - 24*a^4*b^10*c + 240*a^5*b^8*c^2 - 1280*a^6*b^6*c^3 + 3840*a^7*b^4*c^4 - 6144*a^8*b^2*c^5 + 4096*a^9*c^6)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(a^6*b^18 - 36*a^7*b^16*c + 576*a^8*b^14*c^2 - 5376*a^9*b^12*c^3 + 32256*a^10*b^10*c^4 - 129024*a^11*b^8*c^5 + 344064*a^12*b^6*c^6 - 589824*a^13*b^4*c^7 + 589824*a^14*b^2*c^8 - 262144*a^15*c^9)))/(a^3*b^12 - 24*a^4*b^10*c + 240*a^5*b^8*c^2 - 1280*a^6*b^6*c^3 + 3840*a^7*b^4*c^4 - 6144*a^8*b^2*c^5 + 4096*a^9*c^6)))*log((7*b^6*c + 225*a*b^4*c^2 + 3240*a^2*b^2*c^3 + 11664*a^3*c^4)*sqrt(x) - 1/2*(b^9 + 19*a*b^7*c + 124*a^2*b^5*c^2 - 2160*a^3*b^3*c^3 + 5184*a^4*b*c^4 + (a^3*b^14 - 12*a^4*b^12*c - 48*a^5*b^10*c^2 + 1600*a^6*b^8*c^3 - 11520*a^7*b^6*c^4 + 39936*a^8*b^4*c^5 - 69632*a^9*b^2*c^6 + 49152*a^10*c^7)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(a^6*b^18 - 36*a^7*b^16*c + 576*a^8*b^14*c^2 - 5376*a^9*b^12*c^3 + 32256*a^10*b^10*c^4 - 129024*a^11*b^8*c^5 + 344064*a^12*b^6*c^6 - 589824*a^13*b^4*c^7 + 589824*a^14*b^2*c^8 - 262144*a^15*c^9)))*sqrt(sqrt(1/2)*sqrt(-(b^7 + 21*a*b^5*c + 168*a^2*b^3*c^2 + 3024*a^3*b*c^3 - (a^3*b^12 - 24*a^4*b^10*c + 240*a^5*b^8*c^2 - 1280*a^6*b^6*c^3 + 3840*a^7*b^4*c^4 - 6144*a^8*b^2*c^5 + 4096*a^9*c^6)*sqrt((b^8 + 54*a*b^6*c + 1377*a^2*b^4*c^2 + 17496*a^3*b^2*c^3 + 104976*a^4*c^4)/(a^6*b^18 - 36*a^7*b^16*c + 576*a^8*b^14*c^2 - 5376*a^9*b^12*c^3 + 32256*a^10*b^10*c^4 - 129024*a^11*b^8*c^5 + 344064*a^12*b^6*c^6 - 589824*a^13*b^4*c^7 + 589824*a^14*b^2*c^8 - 262144*a^15*c^9)))/(a^3*b^12 - 24*a^4*b^10*c + 240*a^5*b^8*c^2 - 1280*a^6*b^6*c^3 + 3840*a^7*b^4*c^4 - 6144*a^8*b^2*c^5 + 4096*a^9*c^6)))) + 4*(2*c*x^2 + b)*sqrt(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
1077,1,12411,0,152.988234," ","integrate(x^(1/2)/(c*x^4+b*x^2+a)^2,x, algorithm=""fricas"")","-\frac{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)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{9} - 45 \, a b^{7} c + 765 \, a^{2} b^{5} c^{2} - 5880 \, a^{3} b^{3} c^{3} + 18000 \, a^{4} b c^{4} + {\left(a^{5} b^{12} - 24 \, a^{6} b^{10} c + 240 \, a^{7} b^{8} c^{2} - 1280 \, a^{8} b^{6} c^{3} + 3840 \, a^{9} b^{4} c^{4} - 6144 \, a^{10} b^{2} c^{5} + 4096 \, a^{11} c^{6}\right)} \sqrt{\frac{b^{12} - 78 \, a b^{10} c + 2571 \, a^{2} b^{8} c^{2} - 45950 \, a^{3} b^{6} c^{3} + 470625 \, a^{4} b^{4} c^{4} - 2625000 \, a^{5} b^{2} c^{5} + 6250000 \, a^{6} c^{6}}{a^{10} b^{18} - 36 \, a^{11} b^{16} c + 576 \, a^{12} b^{14} c^{2} - 5376 \, a^{13} b^{12} c^{3} + 32256 \, a^{14} b^{10} c^{4} - 129024 \, a^{15} b^{8} c^{5} + 344064 \, a^{16} b^{6} c^{6} - 589824 \, a^{17} b^{4} c^{7} + 589824 \, a^{18} b^{2} c^{8} - 262144 \, a^{19} c^{9}}}}{a^{5} b^{12} - 24 \, a^{6} b^{10} c + 240 \, a^{7} b^{8} c^{2} - 1280 \, a^{8} b^{6} c^{3} + 3840 \, a^{9} b^{4} c^{4} - 6144 \, a^{10} b^{2} c^{5} + 4096 \, a^{11} c^{6}}}} \arctan\left(\frac{{\left({\left(b^{11} - 47 \, a b^{9} c + 853 \, a^{2} b^{7} c^{2} - 7324 \, a^{3} b^{5} c^{3} + 28400 \, a^{4} b^{3} c^{4} - 40000 \, a^{5} b c^{5} - {\left(a^{5} b^{14} - 44 \, a^{6} b^{12} c + 720 \, a^{7} b^{10} c^{2} - 6080 \, a^{8} b^{8} c^{3} + 29440 \, a^{9} b^{6} c^{4} - 82944 \, a^{10} b^{4} c^{5} + 126976 \, a^{11} b^{2} c^{6} - 81920 \, a^{12} c^{7}\right)} \sqrt{\frac{b^{12} - 78 \, a b^{10} c + 2571 \, a^{2} b^{8} c^{2} - 45950 \, a^{3} b^{6} c^{3} + 470625 \, a^{4} b^{4} c^{4} - 2625000 \, a^{5} b^{2} c^{5} + 6250000 \, a^{6} c^{6}}{a^{10} b^{18} - 36 \, a^{11} b^{16} c + 576 \, a^{12} b^{14} c^{2} - 5376 \, a^{13} b^{12} c^{3} + 32256 \, a^{14} b^{10} c^{4} - 129024 \, a^{15} b^{8} c^{5} + 344064 \, a^{16} b^{6} c^{6} - 589824 \, a^{17} b^{4} c^{7} + 589824 \, a^{18} b^{2} c^{8} - 262144 \, a^{19} c^{9}}}\right)} \sqrt{{\left(531441 \, b^{24} c^{8} - 76881798 \, a b^{22} c^{9} + 5113978011 \, a^{2} b^{20} c^{10} - 206852401350 \, a^{3} b^{18} c^{11} + 5667080000625 \, a^{4} b^{16} c^{12} - 110792866500000 \, a^{5} b^{14} c^{13} + 1584936775000000 \, a^{6} b^{12} c^{14} - 16715805000000000 \, a^{7} b^{10} c^{15} + 128988375000000000 \, a^{8} b^{8} c^{16} - 710150000000000000 \, a^{9} b^{6} c^{17} + 2647500000000000000 \, a^{10} b^{4} c^{18} - 6000000000000000000 \, a^{11} b^{2} c^{19} + 6250000000000000000 \, a^{12} c^{20}\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(6561 \, b^{31} c^{5} - 1032993 \, a b^{29} c^{6} + 75634965 \, a^{2} b^{27} c^{7} - 3414264975 \, a^{3} b^{25} c^{8} + 106186248955 \, a^{4} b^{23} c^{9} - 2407919378459 \, a^{5} b^{21} c^{10} + 41083864936232 \, a^{6} b^{19} c^{11} - 536376931701360 \, a^{7} b^{17} c^{12} + 5394460343808000 \, a^{8} b^{15} c^{13} - 41720627697600000 \, a^{9} b^{13} c^{14} + 245614092480000000 \, a^{10} b^{11} c^{15} - 1078472304000000000 \, a^{11} b^{9} c^{16} + 3410524800000000000 \, a^{12} b^{7} c^{17} - 7314160000000000000 \, a^{13} b^{5} c^{18} + 9488000000000000000 \, a^{14} b^{3} c^{19} - 5600000000000000000 \, a^{15} b c^{20} - {\left(6561 \, a^{5} b^{34} c^{5} - 895212 \, a^{6} b^{32} c^{6} + 56697732 \, a^{7} b^{30} c^{7} - 2212069617 \, a^{8} b^{28} c^{8} + 59497163992 \, a^{9} b^{26} c^{9} - 1169816993840 \, a^{10} b^{24} c^{10} + 17397456159488 \, a^{11} b^{22} c^{11} - 199763116583168 \, a^{12} b^{20} c^{12} + 1791922585643008 \, a^{13} b^{18} c^{13} - 12624164431147008 \, a^{14} b^{16} c^{14} + 69835076189159424 \, a^{15} b^{14} c^{15} - 301610411758387200 \, a^{16} b^{12} c^{16} + 1004700278784000000 \, a^{17} b^{10} c^{17} - 2527971917824000000 \, a^{18} b^{8} c^{18} + 4641908326400000000 \, a^{19} b^{6} c^{19} - 5864652800000000000 \, a^{20} b^{4} c^{20} + 4554752000000000000 \, a^{21} b^{2} c^{21} - 1638400000000000000 \, a^{22} c^{22}\right)} \sqrt{\frac{b^{12} - 78 \, a b^{10} c + 2571 \, a^{2} b^{8} c^{2} - 45950 \, a^{3} b^{6} c^{3} + 470625 \, a^{4} b^{4} c^{4} - 2625000 \, a^{5} b^{2} c^{5} + 6250000 \, a^{6} c^{6}}{a^{10} b^{18} - 36 \, a^{11} b^{16} c + 576 \, a^{12} b^{14} c^{2} - 5376 \, a^{13} b^{12} c^{3} + 32256 \, a^{14} b^{10} c^{4} - 129024 \, a^{15} b^{8} c^{5} + 344064 \, a^{16} b^{6} c^{6} - 589824 \, a^{17} b^{4} c^{7} + 589824 \, a^{18} b^{2} c^{8} - 262144 \, a^{19} c^{9}}}\right)} \sqrt{-\frac{b^{9} - 45 \, a b^{7} c + 765 \, a^{2} b^{5} c^{2} - 5880 \, a^{3} b^{3} c^{3} + 18000 \, a^{4} b c^{4} + {\left(a^{5} b^{12} - 24 \, a^{6} b^{10} c + 240 \, a^{7} b^{8} c^{2} - 1280 \, a^{8} b^{6} c^{3} + 3840 \, a^{9} b^{4} c^{4} - 6144 \, a^{10} b^{2} c^{5} + 4096 \, a^{11} c^{6}\right)} \sqrt{\frac{b^{12} - 78 \, a b^{10} c + 2571 \, a^{2} b^{8} c^{2} - 45950 \, a^{3} b^{6} c^{3} + 470625 \, a^{4} b^{4} c^{4} - 2625000 \, a^{5} b^{2} c^{5} + 6250000 \, a^{6} c^{6}}{a^{10} b^{18} - 36 \, a^{11} b^{16} c + 576 \, a^{12} b^{14} c^{2} - 5376 \, a^{13} b^{12} c^{3} + 32256 \, a^{14} b^{10} c^{4} - 129024 \, a^{15} b^{8} c^{5} + 344064 \, a^{16} b^{6} c^{6} - 589824 \, a^{17} b^{4} c^{7} + 589824 \, a^{18} b^{2} c^{8} - 262144 \, a^{19} c^{9}}}}{a^{5} b^{12} - 24 \, a^{6} b^{10} c + 240 \, a^{7} b^{8} c^{2} - 1280 \, a^{8} b^{6} c^{3} + 3840 \, a^{9} b^{4} c^{4} - 6144 \, a^{10} b^{2} c^{5} + 4096 \, a^{11} c^{6}}}} - {\left(729 \, b^{23} c^{4} - 86994 \, a b^{21} c^{5} + 4700619 \, a^{2} b^{19} c^{6} - 151648714 \, a^{3} b^{17} c^{7} + 3240737969 \, a^{4} b^{15} c^{8} - 48070563100 \, a^{5} b^{13} c^{9} + 503690450000 \, a^{6} b^{11} c^{10} - 3715387000000 \, a^{7} b^{9} c^{11} + 18824300000000 \, a^{8} b^{7} c^{12} - 62050000000000 \, a^{9} b^{5} c^{13} + 119000000000000 \, a^{10} b^{3} c^{14} - 100000000000000 \, a^{11} b c^{15} - {\left(729 \, a^{5} b^{26} c^{4} - 84807 \, a^{6} b^{24} c^{5} + 4445469 \, a^{7} b^{22} c^{6} - 138927340 \, a^{8} b^{20} c^{7} + 2884712240 \, a^{9} b^{18} c^{8} - 41968650816 \, a^{10} b^{16} c^{9} + 439511597568 \, a^{11} b^{14} c^{10} - 3350499342336 \, a^{12} b^{12} c^{11} + 18578963128320 \, a^{13} b^{10} c^{12} - 74005426176000 \, a^{14} b^{8} c^{13} + 205936435200000 \, a^{15} b^{6} c^{14} - 379514880000000 \, a^{16} b^{4} c^{15} + 415744000000000 \, a^{17} b^{2} c^{16} - 204800000000000 \, a^{18} c^{17}\right)} \sqrt{\frac{b^{12} - 78 \, a b^{10} c + 2571 \, a^{2} b^{8} c^{2} - 45950 \, a^{3} b^{6} c^{3} + 470625 \, a^{4} b^{4} c^{4} - 2625000 \, a^{5} b^{2} c^{5} + 6250000 \, a^{6} c^{6}}{a^{10} b^{18} - 36 \, a^{11} b^{16} c + 576 \, a^{12} b^{14} c^{2} - 5376 \, a^{13} b^{12} c^{3} + 32256 \, a^{14} b^{10} c^{4} - 129024 \, a^{15} b^{8} c^{5} + 344064 \, a^{16} b^{6} c^{6} - 589824 \, a^{17} b^{4} c^{7} + 589824 \, a^{18} b^{2} c^{8} - 262144 \, a^{19} c^{9}}}\right)} \sqrt{x}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{9} - 45 \, a b^{7} c + 765 \, a^{2} b^{5} c^{2} - 5880 \, a^{3} b^{3} c^{3} + 18000 \, a^{4} b c^{4} + {\left(a^{5} b^{12} - 24 \, a^{6} b^{10} c + 240 \, a^{7} b^{8} c^{2} - 1280 \, a^{8} b^{6} c^{3} + 3840 \, a^{9} b^{4} c^{4} - 6144 \, a^{10} b^{2} c^{5} + 4096 \, a^{11} c^{6}\right)} \sqrt{\frac{b^{12} - 78 \, a b^{10} c + 2571 \, a^{2} b^{8} c^{2} - 45950 \, a^{3} b^{6} c^{3} + 470625 \, a^{4} b^{4} c^{4} - 2625000 \, a^{5} b^{2} c^{5} + 6250000 \, a^{6} c^{6}}{a^{10} b^{18} - 36 \, a^{11} b^{16} c + 576 \, a^{12} b^{14} c^{2} - 5376 \, a^{13} b^{12} c^{3} + 32256 \, a^{14} b^{10} c^{4} - 129024 \, a^{15} b^{8} c^{5} + 344064 \, a^{16} b^{6} c^{6} - 589824 \, a^{17} b^{4} c^{7} + 589824 \, a^{18} b^{2} c^{8} - 262144 \, a^{19} c^{9}}}}{a^{5} b^{12} - 24 \, a^{6} b^{10} c + 240 \, a^{7} b^{8} c^{2} - 1280 \, a^{8} b^{6} c^{3} + 3840 \, a^{9} b^{4} c^{4} - 6144 \, a^{10} b^{2} c^{5} + 4096 \, a^{11} c^{6}}}}}{2 \, {\left(6561 \, b^{20} c^{5} - 803358 \, a b^{18} c^{6} + 44473131 \, a^{2} b^{16} c^{7} - 1466261550 \, a^{3} b^{14} c^{8} + 31889850625 \, a^{4} b^{12} c^{9} - 478129875000 \, a^{5} b^{10} c^{10} + 5004993750000 \, a^{6} b^{8} c^{11} - 36117500000000 \, a^{7} b^{6} c^{12} + 171937500000000 \, a^{8} b^{4} c^{13} - 487500000000000 \, a^{9} b^{2} c^{14} + 625000000000000 \, a^{10} c^{15}\right)}}\right) - 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)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{9} - 45 \, a b^{7} c + 765 \, a^{2} b^{5} c^{2} - 5880 \, a^{3} b^{3} c^{3} + 18000 \, a^{4} b c^{4} - {\left(a^{5} b^{12} - 24 \, a^{6} b^{10} c + 240 \, a^{7} b^{8} c^{2} - 1280 \, a^{8} b^{6} c^{3} + 3840 \, a^{9} b^{4} c^{4} - 6144 \, a^{10} b^{2} c^{5} + 4096 \, a^{11} c^{6}\right)} \sqrt{\frac{b^{12} - 78 \, a b^{10} c + 2571 \, a^{2} b^{8} c^{2} - 45950 \, a^{3} b^{6} c^{3} + 470625 \, a^{4} b^{4} c^{4} - 2625000 \, a^{5} b^{2} c^{5} + 6250000 \, a^{6} c^{6}}{a^{10} b^{18} - 36 \, a^{11} b^{16} c + 576 \, a^{12} b^{14} c^{2} - 5376 \, a^{13} b^{12} c^{3} + 32256 \, a^{14} b^{10} c^{4} - 129024 \, a^{15} b^{8} c^{5} + 344064 \, a^{16} b^{6} c^{6} - 589824 \, a^{17} b^{4} c^{7} + 589824 \, a^{18} b^{2} c^{8} - 262144 \, a^{19} c^{9}}}}{a^{5} b^{12} - 24 \, a^{6} b^{10} c + 240 \, a^{7} b^{8} c^{2} - 1280 \, a^{8} b^{6} c^{3} + 3840 \, a^{9} b^{4} c^{4} - 6144 \, a^{10} b^{2} c^{5} + 4096 \, a^{11} c^{6}}}} \arctan\left(-\frac{{\left(b^{11} - 47 \, a b^{9} c + 853 \, a^{2} b^{7} c^{2} - 7324 \, a^{3} b^{5} c^{3} + 28400 \, a^{4} b^{3} c^{4} - 40000 \, a^{5} b c^{5} + {\left(a^{5} b^{14} - 44 \, a^{6} b^{12} c + 720 \, a^{7} b^{10} c^{2} - 6080 \, a^{8} b^{8} c^{3} + 29440 \, a^{9} b^{6} c^{4} - 82944 \, a^{10} b^{4} c^{5} + 126976 \, a^{11} b^{2} c^{6} - 81920 \, a^{12} c^{7}\right)} \sqrt{\frac{b^{12} - 78 \, a b^{10} c + 2571 \, a^{2} b^{8} c^{2} - 45950 \, a^{3} b^{6} c^{3} + 470625 \, a^{4} b^{4} c^{4} - 2625000 \, a^{5} b^{2} c^{5} + 6250000 \, a^{6} c^{6}}{a^{10} b^{18} - 36 \, a^{11} b^{16} c + 576 \, a^{12} b^{14} c^{2} - 5376 \, a^{13} b^{12} c^{3} + 32256 \, a^{14} b^{10} c^{4} - 129024 \, a^{15} b^{8} c^{5} + 344064 \, a^{16} b^{6} c^{6} - 589824 \, a^{17} b^{4} c^{7} + 589824 \, a^{18} b^{2} c^{8} - 262144 \, a^{19} c^{9}}}\right)} \sqrt{{\left(531441 \, b^{24} c^{8} - 76881798 \, a b^{22} c^{9} + 5113978011 \, a^{2} b^{20} c^{10} - 206852401350 \, a^{3} b^{18} c^{11} + 5667080000625 \, a^{4} b^{16} c^{12} - 110792866500000 \, a^{5} b^{14} c^{13} + 1584936775000000 \, a^{6} b^{12} c^{14} - 16715805000000000 \, a^{7} b^{10} c^{15} + 128988375000000000 \, a^{8} b^{8} c^{16} - 710150000000000000 \, a^{9} b^{6} c^{17} + 2647500000000000000 \, a^{10} b^{4} c^{18} - 6000000000000000000 \, a^{11} b^{2} c^{19} + 6250000000000000000 \, a^{12} c^{20}\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(6561 \, b^{31} c^{5} - 1032993 \, a b^{29} c^{6} + 75634965 \, a^{2} b^{27} c^{7} - 3414264975 \, a^{3} b^{25} c^{8} + 106186248955 \, a^{4} b^{23} c^{9} - 2407919378459 \, a^{5} b^{21} c^{10} + 41083864936232 \, a^{6} b^{19} c^{11} - 536376931701360 \, a^{7} b^{17} c^{12} + 5394460343808000 \, a^{8} b^{15} c^{13} - 41720627697600000 \, a^{9} b^{13} c^{14} + 245614092480000000 \, a^{10} b^{11} c^{15} - 1078472304000000000 \, a^{11} b^{9} c^{16} + 3410524800000000000 \, a^{12} b^{7} c^{17} - 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36 \, a^{11} b^{16} c + 576 \, a^{12} b^{14} c^{2} - 5376 \, a^{13} b^{12} c^{3} + 32256 \, a^{14} b^{10} c^{4} - 129024 \, a^{15} b^{8} c^{5} + 344064 \, a^{16} b^{6} c^{6} - 589824 \, a^{17} b^{4} c^{7} + 589824 \, a^{18} b^{2} c^{8} - 262144 \, a^{19} c^{9}}}\right)} \sqrt{-\frac{b^{9} - 45 \, a b^{7} c + 765 \, a^{2} b^{5} c^{2} - 5880 \, a^{3} b^{3} c^{3} + 18000 \, a^{4} b c^{4} - {\left(a^{5} b^{12} - 24 \, a^{6} b^{10} c + 240 \, a^{7} b^{8} c^{2} - 1280 \, a^{8} b^{6} c^{3} + 3840 \, a^{9} b^{4} c^{4} - 6144 \, a^{10} b^{2} c^{5} + 4096 \, a^{11} c^{6}\right)} \sqrt{\frac{b^{12} - 78 \, a b^{10} c + 2571 \, a^{2} b^{8} c^{2} - 45950 \, a^{3} b^{6} c^{3} + 470625 \, a^{4} b^{4} c^{4} - 2625000 \, a^{5} b^{2} c^{5} + 6250000 \, a^{6} c^{6}}{a^{10} b^{18} - 36 \, a^{11} b^{16} c + 576 \, a^{12} b^{14} c^{2} - 5376 \, a^{13} b^{12} c^{3} + 32256 \, a^{14} b^{10} c^{4} - 129024 \, a^{15} b^{8} c^{5} + 344064 \, a^{16} b^{6} c^{6} - 589824 \, a^{17} b^{4} c^{7} + 589824 \, a^{18} b^{2} c^{8} - 262144 \, a^{19} c^{9}}}}{a^{5} b^{12} - 24 \, a^{6} b^{10} c + 240 \, a^{7} b^{8} c^{2} - 1280 \, a^{8} b^{6} c^{3} + 3840 \, a^{9} b^{4} c^{4} - 6144 \, a^{10} b^{2} c^{5} + 4096 \, a^{11} c^{6}}}} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{9} - 45 \, a b^{7} c + 765 \, a^{2} b^{5} c^{2} - 5880 \, a^{3} b^{3} c^{3} + 18000 \, a^{4} b c^{4} - {\left(a^{5} b^{12} - 24 \, a^{6} b^{10} c + 240 \, a^{7} b^{8} c^{2} - 1280 \, a^{8} b^{6} c^{3} + 3840 \, a^{9} b^{4} c^{4} - 6144 \, a^{10} b^{2} c^{5} + 4096 \, a^{11} c^{6}\right)} \sqrt{\frac{b^{12} - 78 \, a b^{10} c + 2571 \, a^{2} b^{8} c^{2} - 45950 \, a^{3} b^{6} c^{3} + 470625 \, a^{4} b^{4} c^{4} - 2625000 \, a^{5} b^{2} c^{5} + 6250000 \, a^{6} c^{6}}{a^{10} b^{18} - 36 \, a^{11} b^{16} c + 576 \, a^{12} b^{14} c^{2} - 5376 \, a^{13} b^{12} c^{3} + 32256 \, a^{14} b^{10} c^{4} - 129024 \, a^{15} b^{8} c^{5} + 344064 \, a^{16} b^{6} c^{6} - 589824 \, a^{17} b^{4} c^{7} + 589824 \, a^{18} b^{2} c^{8} - 262144 \, a^{19} c^{9}}}}{a^{5} b^{12} - 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204800000000000 \, a^{18} c^{17}\right)} \sqrt{\frac{b^{12} - 78 \, a b^{10} c + 2571 \, a^{2} b^{8} c^{2} - 45950 \, a^{3} b^{6} c^{3} + 470625 \, a^{4} b^{4} c^{4} - 2625000 \, a^{5} b^{2} c^{5} + 6250000 \, a^{6} c^{6}}{a^{10} b^{18} - 36 \, a^{11} b^{16} c + 576 \, a^{12} b^{14} c^{2} - 5376 \, a^{13} b^{12} c^{3} + 32256 \, a^{14} b^{10} c^{4} - 129024 \, a^{15} b^{8} c^{5} + 344064 \, a^{16} b^{6} c^{6} - 589824 \, a^{17} b^{4} c^{7} + 589824 \, a^{18} b^{2} c^{8} - 262144 \, a^{19} c^{9}}}\right)} \sqrt{x} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{9} - 45 \, a b^{7} c + 765 \, a^{2} b^{5} c^{2} - 5880 \, a^{3} b^{3} c^{3} + 18000 \, a^{4} b c^{4} - {\left(a^{5} b^{12} - 24 \, a^{6} b^{10} c + 240 \, a^{7} b^{8} c^{2} - 1280 \, a^{8} b^{6} c^{3} + 3840 \, a^{9} b^{4} c^{4} - 6144 \, a^{10} b^{2} c^{5} + 4096 \, a^{11} c^{6}\right)} \sqrt{\frac{b^{12} - 78 \, a b^{10} c + 2571 \, a^{2} b^{8} c^{2} - 45950 \, a^{3} b^{6} c^{3} + 470625 \, a^{4} b^{4} c^{4} - 2625000 \, a^{5} b^{2} c^{5} + 6250000 \, a^{6} c^{6}}{a^{10} b^{18} - 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45 \, a b^{7} c + 765 \, a^{2} b^{5} c^{2} - 5880 \, a^{3} b^{3} c^{3} + 18000 \, a^{4} b c^{4} + {\left(a^{5} b^{12} - 24 \, a^{6} b^{10} c + 240 \, a^{7} b^{8} c^{2} - 1280 \, a^{8} b^{6} c^{3} + 3840 \, a^{9} b^{4} c^{4} - 6144 \, a^{10} b^{2} c^{5} + 4096 \, a^{11} c^{6}\right)} \sqrt{\frac{b^{12} - 78 \, a b^{10} c + 2571 \, a^{2} b^{8} c^{2} - 45950 \, a^{3} b^{6} c^{3} + 470625 \, a^{4} b^{4} c^{4} - 2625000 \, a^{5} b^{2} c^{5} + 6250000 \, a^{6} c^{6}}{a^{10} b^{18} - 36 \, a^{11} b^{16} c + 576 \, a^{12} b^{14} c^{2} - 5376 \, a^{13} b^{12} c^{3} + 32256 \, a^{14} b^{10} c^{4} - 129024 \, a^{15} b^{8} c^{5} + 344064 \, a^{16} b^{6} c^{6} - 589824 \, a^{17} b^{4} c^{7} + 589824 \, a^{18} b^{2} c^{8} - 262144 \, a^{19} c^{9}}}}{a^{5} b^{12} - 24 \, a^{6} b^{10} c + 240 \, a^{7} b^{8} c^{2} - 1280 \, a^{8} b^{6} c^{3} + 3840 \, a^{9} b^{4} c^{4} - 6144 \, a^{10} b^{2} c^{5} + 4096 \, a^{11} c^{6}}}} \log\left(\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{22} - 91 \, a b^{20} c + 3683 \, a^{2} b^{18} c^{2} - 87230 \, a^{3} b^{16} c^{3} + 1338850 \, a^{4} b^{14} c^{4} - 13940024 \, a^{5} b^{12} c^{5} + 100253344 \, a^{6} b^{10} c^{6} - 497651072 \, a^{7} b^{8} c^{7} + 1672046080 \, a^{8} b^{6} c^{8} - 3627264000 \, a^{9} b^{4} c^{9} + 4582400000 \, a^{10} b^{2} c^{10} - 2560000000 \, a^{11} c^{11} - {\left(a^{5} b^{25} - 70 \, a^{6} b^{23} c + 2192 \, a^{7} b^{21} c^{2} - 40672 \, a^{8} b^{19} c^{3} + 498432 \, a^{9} b^{17} c^{4} - 4254720 \, a^{10} b^{15} c^{5} + 25976832 \, a^{11} b^{13} c^{6} - 114475008 \, a^{12} b^{11} c^{7} + 361955328 \, a^{13} b^{9} c^{8} - 802029568 \, a^{14} b^{7} c^{9} + 1183842304 \, a^{15} b^{5} c^{10} - 1046478848 \, a^{16} b^{3} c^{11} + 419430400 \, a^{17} b c^{12}\right)} \sqrt{\frac{b^{12} - 78 \, a b^{10} c + 2571 \, a^{2} b^{8} c^{2} - 45950 \, a^{3} b^{6} c^{3} + 470625 \, a^{4} b^{4} c^{4} - 2625000 \, a^{5} b^{2} c^{5} + 6250000 \, a^{6} c^{6}}{a^{10} b^{18} - 36 \, a^{11} b^{16} c + 576 \, a^{12} b^{14} c^{2} - 5376 \, a^{13} b^{12} c^{3} + 32256 \, a^{14} b^{10} c^{4} - 129024 \, a^{15} b^{8} c^{5} + 344064 \, a^{16} b^{6} c^{6} - 589824 \, a^{17} b^{4} c^{7} + 589824 \, a^{18} b^{2} c^{8} - 262144 \, a^{19} c^{9}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{9} - 45 \, a b^{7} c + 765 \, a^{2} b^{5} c^{2} - 5880 \, a^{3} b^{3} c^{3} + 18000 \, a^{4} b c^{4} + {\left(a^{5} b^{12} - 24 \, a^{6} b^{10} c + 240 \, a^{7} b^{8} c^{2} - 1280 \, a^{8} b^{6} c^{3} + 3840 \, a^{9} b^{4} c^{4} - 6144 \, a^{10} b^{2} c^{5} + 4096 \, a^{11} c^{6}\right)} \sqrt{\frac{b^{12} - 78 \, a b^{10} c + 2571 \, a^{2} b^{8} c^{2} - 45950 \, a^{3} b^{6} c^{3} + 470625 \, a^{4} b^{4} c^{4} - 2625000 \, a^{5} b^{2} c^{5} + 6250000 \, a^{6} c^{6}}{a^{10} b^{18} - 36 \, a^{11} b^{16} c + 576 \, a^{12} b^{14} c^{2} - 5376 \, a^{13} b^{12} c^{3} + 32256 \, a^{14} b^{10} c^{4} - 129024 \, a^{15} b^{8} c^{5} + 344064 \, a^{16} b^{6} c^{6} - 589824 \, a^{17} b^{4} c^{7} + 589824 \, a^{18} b^{2} c^{8} - 262144 \, a^{19} c^{9}}}}{a^{5} b^{12} - 24 \, a^{6} b^{10} c + 240 \, a^{7} b^{8} c^{2} - 1280 \, a^{8} b^{6} c^{3} + 3840 \, a^{9} b^{4} c^{4} - 6144 \, a^{10} b^{2} c^{5} + 4096 \, a^{11} c^{6}}}} \sqrt{-\frac{b^{9} - 45 \, a b^{7} c + 765 \, a^{2} b^{5} c^{2} - 5880 \, a^{3} b^{3} c^{3} + 18000 \, a^{4} b c^{4} + {\left(a^{5} b^{12} - 24 \, a^{6} b^{10} c + 240 \, a^{7} b^{8} c^{2} - 1280 \, a^{8} b^{6} c^{3} + 3840 \, a^{9} b^{4} c^{4} - 6144 \, a^{10} b^{2} c^{5} + 4096 \, a^{11} c^{6}\right)} \sqrt{\frac{b^{12} - 78 \, a b^{10} c + 2571 \, a^{2} b^{8} c^{2} - 45950 \, a^{3} b^{6} c^{3} + 470625 \, a^{4} b^{4} c^{4} - 2625000 \, a^{5} b^{2} c^{5} + 6250000 \, a^{6} c^{6}}{a^{10} b^{18} - 36 \, a^{11} b^{16} c + 576 \, a^{12} b^{14} c^{2} - 5376 \, a^{13} b^{12} c^{3} + 32256 \, a^{14} b^{10} c^{4} - 129024 \, a^{15} b^{8} c^{5} + 344064 \, a^{16} b^{6} c^{6} - 589824 \, a^{17} b^{4} c^{7} + 589824 \, a^{18} b^{2} c^{8} - 262144 \, a^{19} c^{9}}}}{a^{5} b^{12} - 24 \, a^{6} b^{10} c + 240 \, a^{7} b^{8} c^{2} - 1280 \, a^{8} b^{6} c^{3} + 3840 \, a^{9} b^{4} c^{4} - 6144 \, a^{10} b^{2} c^{5} + 4096 \, a^{11} c^{6}}} + {\left(729 \, b^{12} c^{4} - 52731 \, a b^{10} c^{5} + 1600425 \, a^{2} b^{8} c^{6} - 26110000 \, a^{3} b^{6} c^{7} + 241500000 \, a^{4} b^{4} c^{8} - 1200000000 \, a^{5} b^{2} c^{9} + 2500000000 \, a^{6} c^{10}\right)} \sqrt{x}\right) + {\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{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{9} - 45 \, a b^{7} c + 765 \, a^{2} b^{5} c^{2} - 5880 \, a^{3} b^{3} c^{3} + 18000 \, a^{4} b c^{4} + {\left(a^{5} b^{12} - 24 \, a^{6} b^{10} c + 240 \, a^{7} b^{8} c^{2} - 1280 \, a^{8} b^{6} c^{3} + 3840 \, a^{9} b^{4} c^{4} - 6144 \, a^{10} b^{2} c^{5} + 4096 \, a^{11} c^{6}\right)} \sqrt{\frac{b^{12} - 78 \, a b^{10} c + 2571 \, a^{2} b^{8} c^{2} - 45950 \, a^{3} b^{6} c^{3} + 470625 \, a^{4} b^{4} c^{4} - 2625000 \, a^{5} b^{2} c^{5} + 6250000 \, a^{6} c^{6}}{a^{10} b^{18} - 36 \, a^{11} b^{16} c + 576 \, a^{12} b^{14} c^{2} - 5376 \, a^{13} b^{12} c^{3} + 32256 \, a^{14} b^{10} c^{4} - 129024 \, a^{15} b^{8} c^{5} + 344064 \, a^{16} b^{6} c^{6} - 589824 \, a^{17} b^{4} c^{7} + 589824 \, a^{18} b^{2} c^{8} - 262144 \, a^{19} c^{9}}}}{a^{5} b^{12} - 24 \, a^{6} b^{10} c + 240 \, a^{7} b^{8} c^{2} - 1280 \, a^{8} b^{6} c^{3} + 3840 \, a^{9} b^{4} c^{4} - 6144 \, a^{10} b^{2} c^{5} + 4096 \, a^{11} c^{6}}}} \log\left(-\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{22} - 91 \, a b^{20} c + 3683 \, a^{2} b^{18} c^{2} - 87230 \, a^{3} b^{16} c^{3} + 1338850 \, a^{4} b^{14} c^{4} - 13940024 \, a^{5} b^{12} c^{5} + 100253344 \, a^{6} b^{10} c^{6} - 497651072 \, a^{7} b^{8} c^{7} + 1672046080 \, a^{8} b^{6} c^{8} - 3627264000 \, a^{9} b^{4} c^{9} + 4582400000 \, a^{10} b^{2} c^{10} - 2560000000 \, a^{11} c^{11} - {\left(a^{5} b^{25} - 70 \, a^{6} b^{23} c + 2192 \, a^{7} b^{21} c^{2} - 40672 \, a^{8} b^{19} c^{3} + 498432 \, a^{9} b^{17} c^{4} - 4254720 \, a^{10} b^{15} c^{5} + 25976832 \, a^{11} b^{13} c^{6} - 114475008 \, a^{12} b^{11} c^{7} + 361955328 \, a^{13} b^{9} c^{8} - 802029568 \, a^{14} b^{7} c^{9} + 1183842304 \, a^{15} b^{5} c^{10} - 1046478848 \, a^{16} b^{3} c^{11} + 419430400 \, a^{17} b c^{12}\right)} \sqrt{\frac{b^{12} - 78 \, a b^{10} c + 2571 \, a^{2} b^{8} c^{2} - 45950 \, a^{3} b^{6} c^{3} + 470625 \, a^{4} b^{4} c^{4} - 2625000 \, a^{5} b^{2} c^{5} + 6250000 \, a^{6} c^{6}}{a^{10} b^{18} - 36 \, a^{11} b^{16} c + 576 \, a^{12} b^{14} c^{2} - 5376 \, a^{13} b^{12} c^{3} + 32256 \, a^{14} b^{10} c^{4} - 129024 \, a^{15} b^{8} c^{5} + 344064 \, a^{16} b^{6} c^{6} - 589824 \, a^{17} b^{4} c^{7} + 589824 \, a^{18} b^{2} c^{8} - 262144 \, a^{19} c^{9}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{9} - 45 \, a b^{7} c + 765 \, a^{2} b^{5} c^{2} - 5880 \, a^{3} b^{3} c^{3} + 18000 \, a^{4} b c^{4} + {\left(a^{5} b^{12} - 24 \, a^{6} b^{10} c + 240 \, a^{7} b^{8} c^{2} - 1280 \, a^{8} b^{6} c^{3} + 3840 \, a^{9} b^{4} c^{4} - 6144 \, a^{10} b^{2} c^{5} + 4096 \, a^{11} c^{6}\right)} \sqrt{\frac{b^{12} - 78 \, a b^{10} c + 2571 \, a^{2} b^{8} c^{2} - 45950 \, a^{3} b^{6} c^{3} + 470625 \, a^{4} b^{4} c^{4} - 2625000 \, a^{5} b^{2} c^{5} + 6250000 \, a^{6} c^{6}}{a^{10} b^{18} - 36 \, a^{11} b^{16} c + 576 \, a^{12} b^{14} c^{2} - 5376 \, a^{13} b^{12} c^{3} + 32256 \, a^{14} b^{10} c^{4} - 129024 \, a^{15} b^{8} c^{5} + 344064 \, a^{16} b^{6} c^{6} - 589824 \, a^{17} b^{4} c^{7} + 589824 \, a^{18} b^{2} c^{8} - 262144 \, a^{19} c^{9}}}}{a^{5} b^{12} - 24 \, a^{6} b^{10} c + 240 \, a^{7} b^{8} c^{2} - 1280 \, a^{8} b^{6} c^{3} + 3840 \, a^{9} b^{4} c^{4} - 6144 \, a^{10} b^{2} c^{5} + 4096 \, a^{11} c^{6}}}} \sqrt{-\frac{b^{9} - 45 \, a b^{7} c + 765 \, a^{2} b^{5} c^{2} - 5880 \, a^{3} b^{3} c^{3} + 18000 \, a^{4} b c^{4} + {\left(a^{5} b^{12} - 24 \, a^{6} b^{10} c + 240 \, a^{7} b^{8} c^{2} - 1280 \, a^{8} b^{6} c^{3} + 3840 \, a^{9} b^{4} c^{4} - 6144 \, a^{10} b^{2} c^{5} + 4096 \, a^{11} c^{6}\right)} \sqrt{\frac{b^{12} - 78 \, a b^{10} c + 2571 \, a^{2} b^{8} c^{2} - 45950 \, a^{3} b^{6} c^{3} + 470625 \, a^{4} b^{4} c^{4} - 2625000 \, a^{5} b^{2} c^{5} + 6250000 \, a^{6} c^{6}}{a^{10} b^{18} - 36 \, a^{11} b^{16} c + 576 \, a^{12} b^{14} c^{2} - 5376 \, a^{13} b^{12} c^{3} + 32256 \, a^{14} b^{10} c^{4} - 129024 \, a^{15} b^{8} c^{5} + 344064 \, a^{16} b^{6} c^{6} - 589824 \, a^{17} b^{4} c^{7} + 589824 \, a^{18} b^{2} c^{8} - 262144 \, a^{19} c^{9}}}}{a^{5} b^{12} - 24 \, a^{6} b^{10} c + 240 \, a^{7} b^{8} c^{2} - 1280 \, a^{8} b^{6} c^{3} + 3840 \, a^{9} b^{4} c^{4} - 6144 \, a^{10} b^{2} c^{5} + 4096 \, a^{11} c^{6}}} + {\left(729 \, b^{12} c^{4} - 52731 \, a b^{10} c^{5} + 1600425 \, a^{2} b^{8} c^{6} - 26110000 \, a^{3} b^{6} c^{7} + 241500000 \, a^{4} b^{4} c^{8} - 1200000000 \, a^{5} b^{2} c^{9} + 2500000000 \, a^{6} c^{10}\right)} \sqrt{x}\right) - {\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{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{9} - 45 \, a b^{7} c + 765 \, a^{2} b^{5} c^{2} - 5880 \, a^{3} b^{3} c^{3} + 18000 \, a^{4} b c^{4} - {\left(a^{5} b^{12} - 24 \, a^{6} b^{10} c + 240 \, a^{7} b^{8} c^{2} - 1280 \, a^{8} b^{6} c^{3} + 3840 \, a^{9} b^{4} c^{4} - 6144 \, a^{10} b^{2} c^{5} + 4096 \, a^{11} c^{6}\right)} \sqrt{\frac{b^{12} - 78 \, a b^{10} c + 2571 \, a^{2} b^{8} c^{2} - 45950 \, a^{3} b^{6} c^{3} + 470625 \, a^{4} b^{4} c^{4} - 2625000 \, a^{5} b^{2} c^{5} + 6250000 \, a^{6} c^{6}}{a^{10} b^{18} - 36 \, a^{11} b^{16} c + 576 \, a^{12} b^{14} c^{2} - 5376 \, a^{13} b^{12} c^{3} + 32256 \, a^{14} b^{10} c^{4} - 129024 \, a^{15} b^{8} c^{5} + 344064 \, a^{16} b^{6} c^{6} - 589824 \, a^{17} b^{4} c^{7} + 589824 \, a^{18} b^{2} c^{8} - 262144 \, a^{19} c^{9}}}}{a^{5} b^{12} - 24 \, a^{6} b^{10} c + 240 \, a^{7} b^{8} c^{2} - 1280 \, a^{8} b^{6} c^{3} + 3840 \, a^{9} b^{4} c^{4} - 6144 \, a^{10} b^{2} c^{5} + 4096 \, a^{11} c^{6}}}} \log\left(\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{22} - 91 \, a b^{20} c + 3683 \, a^{2} b^{18} c^{2} - 87230 \, a^{3} b^{16} c^{3} + 1338850 \, a^{4} b^{14} c^{4} - 13940024 \, a^{5} b^{12} c^{5} + 100253344 \, a^{6} b^{10} c^{6} - 497651072 \, a^{7} b^{8} c^{7} + 1672046080 \, a^{8} b^{6} c^{8} - 3627264000 \, a^{9} b^{4} c^{9} + 4582400000 \, a^{10} b^{2} c^{10} - 2560000000 \, a^{11} c^{11} + {\left(a^{5} b^{25} - 70 \, a^{6} b^{23} c + 2192 \, a^{7} b^{21} c^{2} - 40672 \, a^{8} b^{19} c^{3} + 498432 \, a^{9} b^{17} c^{4} - 4254720 \, a^{10} b^{15} c^{5} + 25976832 \, a^{11} b^{13} c^{6} - 114475008 \, a^{12} b^{11} c^{7} + 361955328 \, a^{13} b^{9} c^{8} - 802029568 \, a^{14} b^{7} c^{9} + 1183842304 \, a^{15} b^{5} c^{10} - 1046478848 \, a^{16} b^{3} c^{11} + 419430400 \, a^{17} b c^{12}\right)} \sqrt{\frac{b^{12} - 78 \, a b^{10} c + 2571 \, a^{2} b^{8} c^{2} - 45950 \, a^{3} b^{6} c^{3} + 470625 \, a^{4} b^{4} c^{4} - 2625000 \, a^{5} b^{2} c^{5} + 6250000 \, a^{6} c^{6}}{a^{10} b^{18} - 36 \, a^{11} b^{16} c + 576 \, a^{12} b^{14} c^{2} - 5376 \, a^{13} b^{12} c^{3} + 32256 \, a^{14} b^{10} c^{4} - 129024 \, a^{15} b^{8} c^{5} + 344064 \, a^{16} b^{6} c^{6} - 589824 \, a^{17} b^{4} c^{7} + 589824 \, a^{18} b^{2} c^{8} - 262144 \, a^{19} c^{9}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{9} - 45 \, a b^{7} c + 765 \, a^{2} b^{5} c^{2} - 5880 \, a^{3} b^{3} c^{3} + 18000 \, a^{4} b c^{4} - {\left(a^{5} b^{12} - 24 \, a^{6} b^{10} c + 240 \, a^{7} b^{8} c^{2} - 1280 \, a^{8} b^{6} c^{3} + 3840 \, a^{9} b^{4} c^{4} - 6144 \, a^{10} b^{2} c^{5} + 4096 \, a^{11} c^{6}\right)} \sqrt{\frac{b^{12} - 78 \, a b^{10} c + 2571 \, a^{2} b^{8} c^{2} - 45950 \, a^{3} b^{6} c^{3} + 470625 \, a^{4} b^{4} c^{4} - 2625000 \, a^{5} b^{2} c^{5} + 6250000 \, a^{6} c^{6}}{a^{10} b^{18} - 36 \, a^{11} b^{16} c + 576 \, a^{12} b^{14} c^{2} - 5376 \, a^{13} b^{12} c^{3} + 32256 \, a^{14} b^{10} c^{4} - 129024 \, a^{15} b^{8} c^{5} + 344064 \, a^{16} b^{6} c^{6} - 589824 \, a^{17} b^{4} c^{7} + 589824 \, a^{18} b^{2} c^{8} - 262144 \, a^{19} c^{9}}}}{a^{5} b^{12} - 24 \, a^{6} b^{10} c + 240 \, a^{7} b^{8} c^{2} - 1280 \, a^{8} b^{6} c^{3} + 3840 \, a^{9} b^{4} c^{4} - 6144 \, a^{10} b^{2} c^{5} + 4096 \, a^{11} c^{6}}}} \sqrt{-\frac{b^{9} - 45 \, a b^{7} c + 765 \, a^{2} b^{5} c^{2} - 5880 \, a^{3} b^{3} c^{3} + 18000 \, a^{4} b c^{4} - {\left(a^{5} b^{12} - 24 \, a^{6} b^{10} c + 240 \, a^{7} b^{8} c^{2} - 1280 \, a^{8} b^{6} c^{3} + 3840 \, a^{9} b^{4} c^{4} - 6144 \, a^{10} b^{2} c^{5} + 4096 \, a^{11} c^{6}\right)} \sqrt{\frac{b^{12} - 78 \, a b^{10} c + 2571 \, a^{2} b^{8} c^{2} - 45950 \, a^{3} b^{6} c^{3} + 470625 \, a^{4} b^{4} c^{4} - 2625000 \, a^{5} b^{2} c^{5} + 6250000 \, a^{6} c^{6}}{a^{10} b^{18} - 36 \, a^{11} b^{16} c + 576 \, a^{12} b^{14} c^{2} - 5376 \, a^{13} b^{12} c^{3} + 32256 \, a^{14} b^{10} c^{4} - 129024 \, a^{15} b^{8} c^{5} + 344064 \, a^{16} b^{6} c^{6} - 589824 \, a^{17} b^{4} c^{7} + 589824 \, a^{18} b^{2} c^{8} - 262144 \, a^{19} c^{9}}}}{a^{5} b^{12} - 24 \, a^{6} b^{10} c + 240 \, a^{7} b^{8} c^{2} - 1280 \, a^{8} b^{6} c^{3} + 3840 \, a^{9} b^{4} c^{4} - 6144 \, a^{10} b^{2} c^{5} + 4096 \, a^{11} c^{6}}} + {\left(729 \, b^{12} c^{4} - 52731 \, a b^{10} c^{5} + 1600425 \, a^{2} b^{8} c^{6} - 26110000 \, a^{3} b^{6} c^{7} + 241500000 \, a^{4} b^{4} c^{8} - 1200000000 \, a^{5} b^{2} c^{9} + 2500000000 \, a^{6} c^{10}\right)} \sqrt{x}\right) + {\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{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{9} - 45 \, a b^{7} c + 765 \, a^{2} b^{5} c^{2} - 5880 \, a^{3} b^{3} c^{3} + 18000 \, a^{4} b c^{4} - {\left(a^{5} b^{12} - 24 \, a^{6} b^{10} c + 240 \, a^{7} b^{8} c^{2} - 1280 \, a^{8} b^{6} c^{3} + 3840 \, a^{9} b^{4} c^{4} - 6144 \, a^{10} b^{2} c^{5} + 4096 \, a^{11} c^{6}\right)} \sqrt{\frac{b^{12} - 78 \, a b^{10} c + 2571 \, a^{2} b^{8} c^{2} - 45950 \, a^{3} b^{6} c^{3} + 470625 \, a^{4} b^{4} c^{4} - 2625000 \, a^{5} b^{2} c^{5} + 6250000 \, a^{6} c^{6}}{a^{10} b^{18} - 36 \, a^{11} b^{16} c + 576 \, a^{12} b^{14} c^{2} - 5376 \, a^{13} b^{12} c^{3} + 32256 \, a^{14} b^{10} c^{4} - 129024 \, a^{15} b^{8} c^{5} + 344064 \, a^{16} b^{6} c^{6} - 589824 \, a^{17} b^{4} c^{7} + 589824 \, a^{18} b^{2} c^{8} - 262144 \, a^{19} c^{9}}}}{a^{5} b^{12} - 24 \, a^{6} b^{10} c + 240 \, a^{7} b^{8} c^{2} - 1280 \, a^{8} b^{6} c^{3} + 3840 \, a^{9} b^{4} c^{4} - 6144 \, a^{10} b^{2} c^{5} + 4096 \, a^{11} c^{6}}}} \log\left(-\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{22} - 91 \, a b^{20} c + 3683 \, a^{2} b^{18} c^{2} - 87230 \, a^{3} b^{16} c^{3} + 1338850 \, a^{4} b^{14} c^{4} - 13940024 \, a^{5} b^{12} c^{5} + 100253344 \, a^{6} b^{10} c^{6} - 497651072 \, a^{7} b^{8} c^{7} + 1672046080 \, a^{8} b^{6} c^{8} - 3627264000 \, a^{9} b^{4} c^{9} + 4582400000 \, a^{10} b^{2} c^{10} - 2560000000 \, a^{11} c^{11} + {\left(a^{5} b^{25} - 70 \, a^{6} b^{23} c + 2192 \, a^{7} b^{21} c^{2} - 40672 \, a^{8} b^{19} c^{3} + 498432 \, a^{9} b^{17} c^{4} - 4254720 \, a^{10} b^{15} c^{5} + 25976832 \, a^{11} b^{13} c^{6} - 114475008 \, a^{12} b^{11} c^{7} + 361955328 \, a^{13} b^{9} c^{8} - 802029568 \, a^{14} b^{7} c^{9} + 1183842304 \, a^{15} b^{5} c^{10} - 1046478848 \, a^{16} b^{3} c^{11} + 419430400 \, a^{17} b c^{12}\right)} \sqrt{\frac{b^{12} - 78 \, a b^{10} c + 2571 \, a^{2} b^{8} c^{2} - 45950 \, a^{3} b^{6} c^{3} + 470625 \, a^{4} b^{4} c^{4} - 2625000 \, a^{5} b^{2} c^{5} + 6250000 \, a^{6} c^{6}}{a^{10} b^{18} - 36 \, a^{11} b^{16} c + 576 \, a^{12} b^{14} c^{2} - 5376 \, a^{13} b^{12} c^{3} + 32256 \, a^{14} b^{10} c^{4} - 129024 \, a^{15} b^{8} c^{5} + 344064 \, a^{16} b^{6} c^{6} - 589824 \, a^{17} b^{4} c^{7} + 589824 \, a^{18} b^{2} c^{8} - 262144 \, a^{19} c^{9}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{9} - 45 \, a b^{7} c + 765 \, a^{2} b^{5} c^{2} - 5880 \, a^{3} b^{3} c^{3} + 18000 \, a^{4} b c^{4} - {\left(a^{5} b^{12} - 24 \, a^{6} b^{10} c + 240 \, a^{7} b^{8} c^{2} - 1280 \, a^{8} b^{6} c^{3} + 3840 \, a^{9} b^{4} c^{4} - 6144 \, a^{10} b^{2} c^{5} + 4096 \, a^{11} c^{6}\right)} \sqrt{\frac{b^{12} - 78 \, a b^{10} c + 2571 \, a^{2} b^{8} c^{2} - 45950 \, a^{3} b^{6} c^{3} + 470625 \, a^{4} b^{4} c^{4} - 2625000 \, a^{5} b^{2} c^{5} + 6250000 \, a^{6} c^{6}}{a^{10} b^{18} - 36 \, a^{11} b^{16} c + 576 \, a^{12} b^{14} c^{2} - 5376 \, a^{13} b^{12} c^{3} + 32256 \, a^{14} b^{10} c^{4} - 129024 \, a^{15} b^{8} c^{5} + 344064 \, a^{16} b^{6} c^{6} - 589824 \, a^{17} b^{4} c^{7} + 589824 \, a^{18} b^{2} c^{8} - 262144 \, a^{19} c^{9}}}}{a^{5} b^{12} - 24 \, a^{6} b^{10} c + 240 \, a^{7} b^{8} c^{2} - 1280 \, a^{8} b^{6} c^{3} + 3840 \, a^{9} b^{4} c^{4} - 6144 \, a^{10} b^{2} c^{5} + 4096 \, a^{11} c^{6}}}} \sqrt{-\frac{b^{9} - 45 \, a b^{7} c + 765 \, a^{2} b^{5} c^{2} - 5880 \, a^{3} b^{3} c^{3} + 18000 \, a^{4} b c^{4} - {\left(a^{5} b^{12} - 24 \, a^{6} b^{10} c + 240 \, a^{7} b^{8} c^{2} - 1280 \, a^{8} b^{6} c^{3} + 3840 \, a^{9} b^{4} c^{4} - 6144 \, a^{10} b^{2} c^{5} + 4096 \, a^{11} c^{6}\right)} \sqrt{\frac{b^{12} - 78 \, a b^{10} c + 2571 \, a^{2} b^{8} c^{2} - 45950 \, a^{3} b^{6} c^{3} + 470625 \, a^{4} b^{4} c^{4} - 2625000 \, a^{5} b^{2} c^{5} + 6250000 \, a^{6} c^{6}}{a^{10} b^{18} - 36 \, a^{11} b^{16} c + 576 \, a^{12} b^{14} c^{2} - 5376 \, a^{13} b^{12} c^{3} + 32256 \, a^{14} b^{10} c^{4} - 129024 \, a^{15} b^{8} c^{5} + 344064 \, a^{16} b^{6} c^{6} - 589824 \, a^{17} b^{4} c^{7} + 589824 \, a^{18} b^{2} c^{8} - 262144 \, a^{19} c^{9}}}}{a^{5} b^{12} - 24 \, a^{6} b^{10} c + 240 \, a^{7} b^{8} c^{2} - 1280 \, a^{8} b^{6} c^{3} + 3840 \, a^{9} b^{4} c^{4} - 6144 \, a^{10} b^{2} c^{5} + 4096 \, a^{11} c^{6}}} + {\left(729 \, b^{12} c^{4} - 52731 \, a b^{10} c^{5} + 1600425 \, a^{2} b^{8} c^{6} - 26110000 \, a^{3} b^{6} c^{7} + 241500000 \, a^{4} b^{4} c^{8} - 1200000000 \, a^{5} b^{2} c^{9} + 2500000000 \, a^{6} c^{10}\right)} \sqrt{x}\right) - 4 \, {\left(b c x^{3} + {\left(b^{2} - 2 \, a c\right)} x\right)} \sqrt{x}}{8 \, {\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,"-1/8*(4*((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(sqrt(1/2)*sqrt(-(b^9 - 45*a*b^7*c + 765*a^2*b^5*c^2 - 5880*a^3*b^3*c^3 + 18000*a^4*b*c^4 + (a^5*b^12 - 24*a^6*b^10*c + 240*a^7*b^8*c^2 - 1280*a^8*b^6*c^3 + 3840*a^9*b^4*c^4 - 6144*a^10*b^2*c^5 + 4096*a^11*c^6)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(a^10*b^18 - 36*a^11*b^16*c + 576*a^12*b^14*c^2 - 5376*a^13*b^12*c^3 + 32256*a^14*b^10*c^4 - 129024*a^15*b^8*c^5 + 344064*a^16*b^6*c^6 - 589824*a^17*b^4*c^7 + 589824*a^18*b^2*c^8 - 262144*a^19*c^9)))/(a^5*b^12 - 24*a^6*b^10*c + 240*a^7*b^8*c^2 - 1280*a^8*b^6*c^3 + 3840*a^9*b^4*c^4 - 6144*a^10*b^2*c^5 + 4096*a^11*c^6)))*arctan(1/2*((b^11 - 47*a*b^9*c + 853*a^2*b^7*c^2 - 7324*a^3*b^5*c^3 + 28400*a^4*b^3*c^4 - 40000*a^5*b*c^5 - (a^5*b^14 - 44*a^6*b^12*c + 720*a^7*b^10*c^2 - 6080*a^8*b^8*c^3 + 29440*a^9*b^6*c^4 - 82944*a^10*b^4*c^5 + 126976*a^11*b^2*c^6 - 81920*a^12*c^7)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(a^10*b^18 - 36*a^11*b^16*c + 576*a^12*b^14*c^2 - 5376*a^13*b^12*c^3 + 32256*a^14*b^10*c^4 - 129024*a^15*b^8*c^5 + 344064*a^16*b^6*c^6 - 589824*a^17*b^4*c^7 + 589824*a^18*b^2*c^8 - 262144*a^19*c^9)))*sqrt((531441*b^24*c^8 - 76881798*a*b^22*c^9 + 5113978011*a^2*b^20*c^10 - 206852401350*a^3*b^18*c^11 + 5667080000625*a^4*b^16*c^12 - 110792866500000*a^5*b^14*c^13 + 1584936775000000*a^6*b^12*c^14 - 16715805000000000*a^7*b^10*c^15 + 128988375000000000*a^8*b^8*c^16 - 710150000000000000*a^9*b^6*c^17 + 2647500000000000000*a^10*b^4*c^18 - 6000000000000000000*a^11*b^2*c^19 + 6250000000000000000*a^12*c^20)*x - 1/2*sqrt(1/2)*(6561*b^31*c^5 - 1032993*a*b^29*c^6 + 75634965*a^2*b^27*c^7 - 3414264975*a^3*b^25*c^8 + 106186248955*a^4*b^23*c^9 - 2407919378459*a^5*b^21*c^10 + 41083864936232*a^6*b^19*c^11 - 536376931701360*a^7*b^17*c^12 + 5394460343808000*a^8*b^15*c^13 - 41720627697600000*a^9*b^13*c^14 + 245614092480000000*a^10*b^11*c^15 - 1078472304000000000*a^11*b^9*c^16 + 3410524800000000000*a^12*b^7*c^17 - 7314160000000000000*a^13*b^5*c^18 + 9488000000000000000*a^14*b^3*c^19 - 5600000000000000000*a^15*b*c^20 - (6561*a^5*b^34*c^5 - 895212*a^6*b^32*c^6 + 56697732*a^7*b^30*c^7 - 2212069617*a^8*b^28*c^8 + 59497163992*a^9*b^26*c^9 - 1169816993840*a^10*b^24*c^10 + 17397456159488*a^11*b^22*c^11 - 199763116583168*a^12*b^20*c^12 + 1791922585643008*a^13*b^18*c^13 - 12624164431147008*a^14*b^16*c^14 + 69835076189159424*a^15*b^14*c^15 - 301610411758387200*a^16*b^12*c^16 + 1004700278784000000*a^17*b^10*c^17 - 2527971917824000000*a^18*b^8*c^18 + 4641908326400000000*a^19*b^6*c^19 - 5864652800000000000*a^20*b^4*c^20 + 4554752000000000000*a^21*b^2*c^21 - 1638400000000000000*a^22*c^22)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(a^10*b^18 - 36*a^11*b^16*c + 576*a^12*b^14*c^2 - 5376*a^13*b^12*c^3 + 32256*a^14*b^10*c^4 - 129024*a^15*b^8*c^5 + 344064*a^16*b^6*c^6 - 589824*a^17*b^4*c^7 + 589824*a^18*b^2*c^8 - 262144*a^19*c^9)))*sqrt(-(b^9 - 45*a*b^7*c + 765*a^2*b^5*c^2 - 5880*a^3*b^3*c^3 + 18000*a^4*b*c^4 + (a^5*b^12 - 24*a^6*b^10*c + 240*a^7*b^8*c^2 - 1280*a^8*b^6*c^3 + 3840*a^9*b^4*c^4 - 6144*a^10*b^2*c^5 + 4096*a^11*c^6)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(a^10*b^18 - 36*a^11*b^16*c + 576*a^12*b^14*c^2 - 5376*a^13*b^12*c^3 + 32256*a^14*b^10*c^4 - 129024*a^15*b^8*c^5 + 344064*a^16*b^6*c^6 - 589824*a^17*b^4*c^7 + 589824*a^18*b^2*c^8 - 262144*a^19*c^9)))/(a^5*b^12 - 24*a^6*b^10*c + 240*a^7*b^8*c^2 - 1280*a^8*b^6*c^3 + 3840*a^9*b^4*c^4 - 6144*a^10*b^2*c^5 + 4096*a^11*c^6))) - (729*b^23*c^4 - 86994*a*b^21*c^5 + 4700619*a^2*b^19*c^6 - 151648714*a^3*b^17*c^7 + 3240737969*a^4*b^15*c^8 - 48070563100*a^5*b^13*c^9 + 503690450000*a^6*b^11*c^10 - 3715387000000*a^7*b^9*c^11 + 18824300000000*a^8*b^7*c^12 - 62050000000000*a^9*b^5*c^13 + 119000000000000*a^10*b^3*c^14 - 100000000000000*a^11*b*c^15 - (729*a^5*b^26*c^4 - 84807*a^6*b^24*c^5 + 4445469*a^7*b^22*c^6 - 138927340*a^8*b^20*c^7 + 2884712240*a^9*b^18*c^8 - 41968650816*a^10*b^16*c^9 + 439511597568*a^11*b^14*c^10 - 3350499342336*a^12*b^12*c^11 + 18578963128320*a^13*b^10*c^12 - 74005426176000*a^14*b^8*c^13 + 205936435200000*a^15*b^6*c^14 - 379514880000000*a^16*b^4*c^15 + 415744000000000*a^17*b^2*c^16 - 204800000000000*a^18*c^17)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(a^10*b^18 - 36*a^11*b^16*c + 576*a^12*b^14*c^2 - 5376*a^13*b^12*c^3 + 32256*a^14*b^10*c^4 - 129024*a^15*b^8*c^5 + 344064*a^16*b^6*c^6 - 589824*a^17*b^4*c^7 + 589824*a^18*b^2*c^8 - 262144*a^19*c^9)))*sqrt(x))*sqrt(sqrt(1/2)*sqrt(-(b^9 - 45*a*b^7*c + 765*a^2*b^5*c^2 - 5880*a^3*b^3*c^3 + 18000*a^4*b*c^4 + (a^5*b^12 - 24*a^6*b^10*c + 240*a^7*b^8*c^2 - 1280*a^8*b^6*c^3 + 3840*a^9*b^4*c^4 - 6144*a^10*b^2*c^5 + 4096*a^11*c^6)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(a^10*b^18 - 36*a^11*b^16*c + 576*a^12*b^14*c^2 - 5376*a^13*b^12*c^3 + 32256*a^14*b^10*c^4 - 129024*a^15*b^8*c^5 + 344064*a^16*b^6*c^6 - 589824*a^17*b^4*c^7 + 589824*a^18*b^2*c^8 - 262144*a^19*c^9)))/(a^5*b^12 - 24*a^6*b^10*c + 240*a^7*b^8*c^2 - 1280*a^8*b^6*c^3 + 3840*a^9*b^4*c^4 - 6144*a^10*b^2*c^5 + 4096*a^11*c^6)))/(6561*b^20*c^5 - 803358*a*b^18*c^6 + 44473131*a^2*b^16*c^7 - 1466261550*a^3*b^14*c^8 + 31889850625*a^4*b^12*c^9 - 478129875000*a^5*b^10*c^10 + 5004993750000*a^6*b^8*c^11 - 36117500000000*a^7*b^6*c^12 + 171937500000000*a^8*b^4*c^13 - 487500000000000*a^9*b^2*c^14 + 625000000000000*a^10*c^15)) - 4*((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(sqrt(1/2)*sqrt(-(b^9 - 45*a*b^7*c + 765*a^2*b^5*c^2 - 5880*a^3*b^3*c^3 + 18000*a^4*b*c^4 - (a^5*b^12 - 24*a^6*b^10*c + 240*a^7*b^8*c^2 - 1280*a^8*b^6*c^3 + 3840*a^9*b^4*c^4 - 6144*a^10*b^2*c^5 + 4096*a^11*c^6)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(a^10*b^18 - 36*a^11*b^16*c + 576*a^12*b^14*c^2 - 5376*a^13*b^12*c^3 + 32256*a^14*b^10*c^4 - 129024*a^15*b^8*c^5 + 344064*a^16*b^6*c^6 - 589824*a^17*b^4*c^7 + 589824*a^18*b^2*c^8 - 262144*a^19*c^9)))/(a^5*b^12 - 24*a^6*b^10*c + 240*a^7*b^8*c^2 - 1280*a^8*b^6*c^3 + 3840*a^9*b^4*c^4 - 6144*a^10*b^2*c^5 + 4096*a^11*c^6)))*arctan(-1/2*((b^11 - 47*a*b^9*c + 853*a^2*b^7*c^2 - 7324*a^3*b^5*c^3 + 28400*a^4*b^3*c^4 - 40000*a^5*b*c^5 + (a^5*b^14 - 44*a^6*b^12*c + 720*a^7*b^10*c^2 - 6080*a^8*b^8*c^3 + 29440*a^9*b^6*c^4 - 82944*a^10*b^4*c^5 + 126976*a^11*b^2*c^6 - 81920*a^12*c^7)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(a^10*b^18 - 36*a^11*b^16*c + 576*a^12*b^14*c^2 - 5376*a^13*b^12*c^3 + 32256*a^14*b^10*c^4 - 129024*a^15*b^8*c^5 + 344064*a^16*b^6*c^6 - 589824*a^17*b^4*c^7 + 589824*a^18*b^2*c^8 - 262144*a^19*c^9)))*sqrt((531441*b^24*c^8 - 76881798*a*b^22*c^9 + 5113978011*a^2*b^20*c^10 - 206852401350*a^3*b^18*c^11 + 5667080000625*a^4*b^16*c^12 - 110792866500000*a^5*b^14*c^13 + 1584936775000000*a^6*b^12*c^14 - 16715805000000000*a^7*b^10*c^15 + 128988375000000000*a^8*b^8*c^16 - 710150000000000000*a^9*b^6*c^17 + 2647500000000000000*a^10*b^4*c^18 - 6000000000000000000*a^11*b^2*c^19 + 6250000000000000000*a^12*c^20)*x - 1/2*sqrt(1/2)*(6561*b^31*c^5 - 1032993*a*b^29*c^6 + 75634965*a^2*b^27*c^7 - 3414264975*a^3*b^25*c^8 + 106186248955*a^4*b^23*c^9 - 2407919378459*a^5*b^21*c^10 + 41083864936232*a^6*b^19*c^11 - 536376931701360*a^7*b^17*c^12 + 5394460343808000*a^8*b^15*c^13 - 41720627697600000*a^9*b^13*c^14 + 245614092480000000*a^10*b^11*c^15 - 1078472304000000000*a^11*b^9*c^16 + 3410524800000000000*a^12*b^7*c^17 - 7314160000000000000*a^13*b^5*c^18 + 9488000000000000000*a^14*b^3*c^19 - 5600000000000000000*a^15*b*c^20 + (6561*a^5*b^34*c^5 - 895212*a^6*b^32*c^6 + 56697732*a^7*b^30*c^7 - 2212069617*a^8*b^28*c^8 + 59497163992*a^9*b^26*c^9 - 1169816993840*a^10*b^24*c^10 + 17397456159488*a^11*b^22*c^11 - 199763116583168*a^12*b^20*c^12 + 1791922585643008*a^13*b^18*c^13 - 12624164431147008*a^14*b^16*c^14 + 69835076189159424*a^15*b^14*c^15 - 301610411758387200*a^16*b^12*c^16 + 1004700278784000000*a^17*b^10*c^17 - 2527971917824000000*a^18*b^8*c^18 + 4641908326400000000*a^19*b^6*c^19 - 5864652800000000000*a^20*b^4*c^20 + 4554752000000000000*a^21*b^2*c^21 - 1638400000000000000*a^22*c^22)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(a^10*b^18 - 36*a^11*b^16*c + 576*a^12*b^14*c^2 - 5376*a^13*b^12*c^3 + 32256*a^14*b^10*c^4 - 129024*a^15*b^8*c^5 + 344064*a^16*b^6*c^6 - 589824*a^17*b^4*c^7 + 589824*a^18*b^2*c^8 - 262144*a^19*c^9)))*sqrt(-(b^9 - 45*a*b^7*c + 765*a^2*b^5*c^2 - 5880*a^3*b^3*c^3 + 18000*a^4*b*c^4 - (a^5*b^12 - 24*a^6*b^10*c + 240*a^7*b^8*c^2 - 1280*a^8*b^6*c^3 + 3840*a^9*b^4*c^4 - 6144*a^10*b^2*c^5 + 4096*a^11*c^6)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(a^10*b^18 - 36*a^11*b^16*c + 576*a^12*b^14*c^2 - 5376*a^13*b^12*c^3 + 32256*a^14*b^10*c^4 - 129024*a^15*b^8*c^5 + 344064*a^16*b^6*c^6 - 589824*a^17*b^4*c^7 + 589824*a^18*b^2*c^8 - 262144*a^19*c^9)))/(a^5*b^12 - 24*a^6*b^10*c + 240*a^7*b^8*c^2 - 1280*a^8*b^6*c^3 + 3840*a^9*b^4*c^4 - 6144*a^10*b^2*c^5 + 4096*a^11*c^6)))*sqrt(sqrt(1/2)*sqrt(-(b^9 - 45*a*b^7*c + 765*a^2*b^5*c^2 - 5880*a^3*b^3*c^3 + 18000*a^4*b*c^4 - (a^5*b^12 - 24*a^6*b^10*c + 240*a^7*b^8*c^2 - 1280*a^8*b^6*c^3 + 3840*a^9*b^4*c^4 - 6144*a^10*b^2*c^5 + 4096*a^11*c^6)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(a^10*b^18 - 36*a^11*b^16*c + 576*a^12*b^14*c^2 - 5376*a^13*b^12*c^3 + 32256*a^14*b^10*c^4 - 129024*a^15*b^8*c^5 + 344064*a^16*b^6*c^6 - 589824*a^17*b^4*c^7 + 589824*a^18*b^2*c^8 - 262144*a^19*c^9)))/(a^5*b^12 - 24*a^6*b^10*c + 240*a^7*b^8*c^2 - 1280*a^8*b^6*c^3 + 3840*a^9*b^4*c^4 - 6144*a^10*b^2*c^5 + 4096*a^11*c^6))) - (729*b^23*c^4 - 86994*a*b^21*c^5 + 4700619*a^2*b^19*c^6 - 151648714*a^3*b^17*c^7 + 3240737969*a^4*b^15*c^8 - 48070563100*a^5*b^13*c^9 + 503690450000*a^6*b^11*c^10 - 3715387000000*a^7*b^9*c^11 + 18824300000000*a^8*b^7*c^12 - 62050000000000*a^9*b^5*c^13 + 119000000000000*a^10*b^3*c^14 - 100000000000000*a^11*b*c^15 + (729*a^5*b^26*c^4 - 84807*a^6*b^24*c^5 + 4445469*a^7*b^22*c^6 - 138927340*a^8*b^20*c^7 + 2884712240*a^9*b^18*c^8 - 41968650816*a^10*b^16*c^9 + 439511597568*a^11*b^14*c^10 - 3350499342336*a^12*b^12*c^11 + 18578963128320*a^13*b^10*c^12 - 74005426176000*a^14*b^8*c^13 + 205936435200000*a^15*b^6*c^14 - 379514880000000*a^16*b^4*c^15 + 415744000000000*a^17*b^2*c^16 - 204800000000000*a^18*c^17)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(a^10*b^18 - 36*a^11*b^16*c + 576*a^12*b^14*c^2 - 5376*a^13*b^12*c^3 + 32256*a^14*b^10*c^4 - 129024*a^15*b^8*c^5 + 344064*a^16*b^6*c^6 - 589824*a^17*b^4*c^7 + 589824*a^18*b^2*c^8 - 262144*a^19*c^9)))*sqrt(x)*sqrt(sqrt(1/2)*sqrt(-(b^9 - 45*a*b^7*c + 765*a^2*b^5*c^2 - 5880*a^3*b^3*c^3 + 18000*a^4*b*c^4 - (a^5*b^12 - 24*a^6*b^10*c + 240*a^7*b^8*c^2 - 1280*a^8*b^6*c^3 + 3840*a^9*b^4*c^4 - 6144*a^10*b^2*c^5 + 4096*a^11*c^6)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(a^10*b^18 - 36*a^11*b^16*c + 576*a^12*b^14*c^2 - 5376*a^13*b^12*c^3 + 32256*a^14*b^10*c^4 - 129024*a^15*b^8*c^5 + 344064*a^16*b^6*c^6 - 589824*a^17*b^4*c^7 + 589824*a^18*b^2*c^8 - 262144*a^19*c^9)))/(a^5*b^12 - 24*a^6*b^10*c + 240*a^7*b^8*c^2 - 1280*a^8*b^6*c^3 + 3840*a^9*b^4*c^4 - 6144*a^10*b^2*c^5 + 4096*a^11*c^6))))/(6561*b^20*c^5 - 803358*a*b^18*c^6 + 44473131*a^2*b^16*c^7 - 1466261550*a^3*b^14*c^8 + 31889850625*a^4*b^12*c^9 - 478129875000*a^5*b^10*c^10 + 5004993750000*a^6*b^8*c^11 - 36117500000000*a^7*b^6*c^12 + 171937500000000*a^8*b^4*c^13 - 487500000000000*a^9*b^2*c^14 + 625000000000000*a^10*c^15)) - ((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(sqrt(1/2)*sqrt(-(b^9 - 45*a*b^7*c + 765*a^2*b^5*c^2 - 5880*a^3*b^3*c^3 + 18000*a^4*b*c^4 + (a^5*b^12 - 24*a^6*b^10*c + 240*a^7*b^8*c^2 - 1280*a^8*b^6*c^3 + 3840*a^9*b^4*c^4 - 6144*a^10*b^2*c^5 + 4096*a^11*c^6)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(a^10*b^18 - 36*a^11*b^16*c + 576*a^12*b^14*c^2 - 5376*a^13*b^12*c^3 + 32256*a^14*b^10*c^4 - 129024*a^15*b^8*c^5 + 344064*a^16*b^6*c^6 - 589824*a^17*b^4*c^7 + 589824*a^18*b^2*c^8 - 262144*a^19*c^9)))/(a^5*b^12 - 24*a^6*b^10*c + 240*a^7*b^8*c^2 - 1280*a^8*b^6*c^3 + 3840*a^9*b^4*c^4 - 6144*a^10*b^2*c^5 + 4096*a^11*c^6)))*log(1/2*sqrt(1/2)*(b^22 - 91*a*b^20*c + 3683*a^2*b^18*c^2 - 87230*a^3*b^16*c^3 + 1338850*a^4*b^14*c^4 - 13940024*a^5*b^12*c^5 + 100253344*a^6*b^10*c^6 - 497651072*a^7*b^8*c^7 + 1672046080*a^8*b^6*c^8 - 3627264000*a^9*b^4*c^9 + 4582400000*a^10*b^2*c^10 - 2560000000*a^11*c^11 - (a^5*b^25 - 70*a^6*b^23*c + 2192*a^7*b^21*c^2 - 40672*a^8*b^19*c^3 + 498432*a^9*b^17*c^4 - 4254720*a^10*b^15*c^5 + 25976832*a^11*b^13*c^6 - 114475008*a^12*b^11*c^7 + 361955328*a^13*b^9*c^8 - 802029568*a^14*b^7*c^9 + 1183842304*a^15*b^5*c^10 - 1046478848*a^16*b^3*c^11 + 419430400*a^17*b*c^12)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(a^10*b^18 - 36*a^11*b^16*c + 576*a^12*b^14*c^2 - 5376*a^13*b^12*c^3 + 32256*a^14*b^10*c^4 - 129024*a^15*b^8*c^5 + 344064*a^16*b^6*c^6 - 589824*a^17*b^4*c^7 + 589824*a^18*b^2*c^8 - 262144*a^19*c^9)))*sqrt(sqrt(1/2)*sqrt(-(b^9 - 45*a*b^7*c + 765*a^2*b^5*c^2 - 5880*a^3*b^3*c^3 + 18000*a^4*b*c^4 + (a^5*b^12 - 24*a^6*b^10*c + 240*a^7*b^8*c^2 - 1280*a^8*b^6*c^3 + 3840*a^9*b^4*c^4 - 6144*a^10*b^2*c^5 + 4096*a^11*c^6)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(a^10*b^18 - 36*a^11*b^16*c + 576*a^12*b^14*c^2 - 5376*a^13*b^12*c^3 + 32256*a^14*b^10*c^4 - 129024*a^15*b^8*c^5 + 344064*a^16*b^6*c^6 - 589824*a^17*b^4*c^7 + 589824*a^18*b^2*c^8 - 262144*a^19*c^9)))/(a^5*b^12 - 24*a^6*b^10*c + 240*a^7*b^8*c^2 - 1280*a^8*b^6*c^3 + 3840*a^9*b^4*c^4 - 6144*a^10*b^2*c^5 + 4096*a^11*c^6)))*sqrt(-(b^9 - 45*a*b^7*c + 765*a^2*b^5*c^2 - 5880*a^3*b^3*c^3 + 18000*a^4*b*c^4 + (a^5*b^12 - 24*a^6*b^10*c + 240*a^7*b^8*c^2 - 1280*a^8*b^6*c^3 + 3840*a^9*b^4*c^4 - 6144*a^10*b^2*c^5 + 4096*a^11*c^6)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(a^10*b^18 - 36*a^11*b^16*c + 576*a^12*b^14*c^2 - 5376*a^13*b^12*c^3 + 32256*a^14*b^10*c^4 - 129024*a^15*b^8*c^5 + 344064*a^16*b^6*c^6 - 589824*a^17*b^4*c^7 + 589824*a^18*b^2*c^8 - 262144*a^19*c^9)))/(a^5*b^12 - 24*a^6*b^10*c + 240*a^7*b^8*c^2 - 1280*a^8*b^6*c^3 + 3840*a^9*b^4*c^4 - 6144*a^10*b^2*c^5 + 4096*a^11*c^6)) + (729*b^12*c^4 - 52731*a*b^10*c^5 + 1600425*a^2*b^8*c^6 - 26110000*a^3*b^6*c^7 + 241500000*a^4*b^4*c^8 - 1200000000*a^5*b^2*c^9 + 2500000000*a^6*c^10)*sqrt(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)*sqrt(sqrt(1/2)*sqrt(-(b^9 - 45*a*b^7*c + 765*a^2*b^5*c^2 - 5880*a^3*b^3*c^3 + 18000*a^4*b*c^4 + (a^5*b^12 - 24*a^6*b^10*c + 240*a^7*b^8*c^2 - 1280*a^8*b^6*c^3 + 3840*a^9*b^4*c^4 - 6144*a^10*b^2*c^5 + 4096*a^11*c^6)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(a^10*b^18 - 36*a^11*b^16*c + 576*a^12*b^14*c^2 - 5376*a^13*b^12*c^3 + 32256*a^14*b^10*c^4 - 129024*a^15*b^8*c^5 + 344064*a^16*b^6*c^6 - 589824*a^17*b^4*c^7 + 589824*a^18*b^2*c^8 - 262144*a^19*c^9)))/(a^5*b^12 - 24*a^6*b^10*c + 240*a^7*b^8*c^2 - 1280*a^8*b^6*c^3 + 3840*a^9*b^4*c^4 - 6144*a^10*b^2*c^5 + 4096*a^11*c^6)))*log(-1/2*sqrt(1/2)*(b^22 - 91*a*b^20*c + 3683*a^2*b^18*c^2 - 87230*a^3*b^16*c^3 + 1338850*a^4*b^14*c^4 - 13940024*a^5*b^12*c^5 + 100253344*a^6*b^10*c^6 - 497651072*a^7*b^8*c^7 + 1672046080*a^8*b^6*c^8 - 3627264000*a^9*b^4*c^9 + 4582400000*a^10*b^2*c^10 - 2560000000*a^11*c^11 - (a^5*b^25 - 70*a^6*b^23*c + 2192*a^7*b^21*c^2 - 40672*a^8*b^19*c^3 + 498432*a^9*b^17*c^4 - 4254720*a^10*b^15*c^5 + 25976832*a^11*b^13*c^6 - 114475008*a^12*b^11*c^7 + 361955328*a^13*b^9*c^8 - 802029568*a^14*b^7*c^9 + 1183842304*a^15*b^5*c^10 - 1046478848*a^16*b^3*c^11 + 419430400*a^17*b*c^12)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(a^10*b^18 - 36*a^11*b^16*c + 576*a^12*b^14*c^2 - 5376*a^13*b^12*c^3 + 32256*a^14*b^10*c^4 - 129024*a^15*b^8*c^5 + 344064*a^16*b^6*c^6 - 589824*a^17*b^4*c^7 + 589824*a^18*b^2*c^8 - 262144*a^19*c^9)))*sqrt(sqrt(1/2)*sqrt(-(b^9 - 45*a*b^7*c + 765*a^2*b^5*c^2 - 5880*a^3*b^3*c^3 + 18000*a^4*b*c^4 + (a^5*b^12 - 24*a^6*b^10*c + 240*a^7*b^8*c^2 - 1280*a^8*b^6*c^3 + 3840*a^9*b^4*c^4 - 6144*a^10*b^2*c^5 + 4096*a^11*c^6)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(a^10*b^18 - 36*a^11*b^16*c + 576*a^12*b^14*c^2 - 5376*a^13*b^12*c^3 + 32256*a^14*b^10*c^4 - 129024*a^15*b^8*c^5 + 344064*a^16*b^6*c^6 - 589824*a^17*b^4*c^7 + 589824*a^18*b^2*c^8 - 262144*a^19*c^9)))/(a^5*b^12 - 24*a^6*b^10*c + 240*a^7*b^8*c^2 - 1280*a^8*b^6*c^3 + 3840*a^9*b^4*c^4 - 6144*a^10*b^2*c^5 + 4096*a^11*c^6)))*sqrt(-(b^9 - 45*a*b^7*c + 765*a^2*b^5*c^2 - 5880*a^3*b^3*c^3 + 18000*a^4*b*c^4 + (a^5*b^12 - 24*a^6*b^10*c + 240*a^7*b^8*c^2 - 1280*a^8*b^6*c^3 + 3840*a^9*b^4*c^4 - 6144*a^10*b^2*c^5 + 4096*a^11*c^6)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(a^10*b^18 - 36*a^11*b^16*c + 576*a^12*b^14*c^2 - 5376*a^13*b^12*c^3 + 32256*a^14*b^10*c^4 - 129024*a^15*b^8*c^5 + 344064*a^16*b^6*c^6 - 589824*a^17*b^4*c^7 + 589824*a^18*b^2*c^8 - 262144*a^19*c^9)))/(a^5*b^12 - 24*a^6*b^10*c + 240*a^7*b^8*c^2 - 1280*a^8*b^6*c^3 + 3840*a^9*b^4*c^4 - 6144*a^10*b^2*c^5 + 4096*a^11*c^6)) + (729*b^12*c^4 - 52731*a*b^10*c^5 + 1600425*a^2*b^8*c^6 - 26110000*a^3*b^6*c^7 + 241500000*a^4*b^4*c^8 - 1200000000*a^5*b^2*c^9 + 2500000000*a^6*c^10)*sqrt(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)*sqrt(sqrt(1/2)*sqrt(-(b^9 - 45*a*b^7*c + 765*a^2*b^5*c^2 - 5880*a^3*b^3*c^3 + 18000*a^4*b*c^4 - (a^5*b^12 - 24*a^6*b^10*c + 240*a^7*b^8*c^2 - 1280*a^8*b^6*c^3 + 3840*a^9*b^4*c^4 - 6144*a^10*b^2*c^5 + 4096*a^11*c^6)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(a^10*b^18 - 36*a^11*b^16*c + 576*a^12*b^14*c^2 - 5376*a^13*b^12*c^3 + 32256*a^14*b^10*c^4 - 129024*a^15*b^8*c^5 + 344064*a^16*b^6*c^6 - 589824*a^17*b^4*c^7 + 589824*a^18*b^2*c^8 - 262144*a^19*c^9)))/(a^5*b^12 - 24*a^6*b^10*c + 240*a^7*b^8*c^2 - 1280*a^8*b^6*c^3 + 3840*a^9*b^4*c^4 - 6144*a^10*b^2*c^5 + 4096*a^11*c^6)))*log(1/2*sqrt(1/2)*(b^22 - 91*a*b^20*c + 3683*a^2*b^18*c^2 - 87230*a^3*b^16*c^3 + 1338850*a^4*b^14*c^4 - 13940024*a^5*b^12*c^5 + 100253344*a^6*b^10*c^6 - 497651072*a^7*b^8*c^7 + 1672046080*a^8*b^6*c^8 - 3627264000*a^9*b^4*c^9 + 4582400000*a^10*b^2*c^10 - 2560000000*a^11*c^11 + (a^5*b^25 - 70*a^6*b^23*c + 2192*a^7*b^21*c^2 - 40672*a^8*b^19*c^3 + 498432*a^9*b^17*c^4 - 4254720*a^10*b^15*c^5 + 25976832*a^11*b^13*c^6 - 114475008*a^12*b^11*c^7 + 361955328*a^13*b^9*c^8 - 802029568*a^14*b^7*c^9 + 1183842304*a^15*b^5*c^10 - 1046478848*a^16*b^3*c^11 + 419430400*a^17*b*c^12)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(a^10*b^18 - 36*a^11*b^16*c + 576*a^12*b^14*c^2 - 5376*a^13*b^12*c^3 + 32256*a^14*b^10*c^4 - 129024*a^15*b^8*c^5 + 344064*a^16*b^6*c^6 - 589824*a^17*b^4*c^7 + 589824*a^18*b^2*c^8 - 262144*a^19*c^9)))*sqrt(sqrt(1/2)*sqrt(-(b^9 - 45*a*b^7*c + 765*a^2*b^5*c^2 - 5880*a^3*b^3*c^3 + 18000*a^4*b*c^4 - (a^5*b^12 - 24*a^6*b^10*c + 240*a^7*b^8*c^2 - 1280*a^8*b^6*c^3 + 3840*a^9*b^4*c^4 - 6144*a^10*b^2*c^5 + 4096*a^11*c^6)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(a^10*b^18 - 36*a^11*b^16*c + 576*a^12*b^14*c^2 - 5376*a^13*b^12*c^3 + 32256*a^14*b^10*c^4 - 129024*a^15*b^8*c^5 + 344064*a^16*b^6*c^6 - 589824*a^17*b^4*c^7 + 589824*a^18*b^2*c^8 - 262144*a^19*c^9)))/(a^5*b^12 - 24*a^6*b^10*c + 240*a^7*b^8*c^2 - 1280*a^8*b^6*c^3 + 3840*a^9*b^4*c^4 - 6144*a^10*b^2*c^5 + 4096*a^11*c^6)))*sqrt(-(b^9 - 45*a*b^7*c + 765*a^2*b^5*c^2 - 5880*a^3*b^3*c^3 + 18000*a^4*b*c^4 - (a^5*b^12 - 24*a^6*b^10*c + 240*a^7*b^8*c^2 - 1280*a^8*b^6*c^3 + 3840*a^9*b^4*c^4 - 6144*a^10*b^2*c^5 + 4096*a^11*c^6)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(a^10*b^18 - 36*a^11*b^16*c + 576*a^12*b^14*c^2 - 5376*a^13*b^12*c^3 + 32256*a^14*b^10*c^4 - 129024*a^15*b^8*c^5 + 344064*a^16*b^6*c^6 - 589824*a^17*b^4*c^7 + 589824*a^18*b^2*c^8 - 262144*a^19*c^9)))/(a^5*b^12 - 24*a^6*b^10*c + 240*a^7*b^8*c^2 - 1280*a^8*b^6*c^3 + 3840*a^9*b^4*c^4 - 6144*a^10*b^2*c^5 + 4096*a^11*c^6)) + (729*b^12*c^4 - 52731*a*b^10*c^5 + 1600425*a^2*b^8*c^6 - 26110000*a^3*b^6*c^7 + 241500000*a^4*b^4*c^8 - 1200000000*a^5*b^2*c^9 + 2500000000*a^6*c^10)*sqrt(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)*sqrt(sqrt(1/2)*sqrt(-(b^9 - 45*a*b^7*c + 765*a^2*b^5*c^2 - 5880*a^3*b^3*c^3 + 18000*a^4*b*c^4 - (a^5*b^12 - 24*a^6*b^10*c + 240*a^7*b^8*c^2 - 1280*a^8*b^6*c^3 + 3840*a^9*b^4*c^4 - 6144*a^10*b^2*c^5 + 4096*a^11*c^6)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(a^10*b^18 - 36*a^11*b^16*c + 576*a^12*b^14*c^2 - 5376*a^13*b^12*c^3 + 32256*a^14*b^10*c^4 - 129024*a^15*b^8*c^5 + 344064*a^16*b^6*c^6 - 589824*a^17*b^4*c^7 + 589824*a^18*b^2*c^8 - 262144*a^19*c^9)))/(a^5*b^12 - 24*a^6*b^10*c + 240*a^7*b^8*c^2 - 1280*a^8*b^6*c^3 + 3840*a^9*b^4*c^4 - 6144*a^10*b^2*c^5 + 4096*a^11*c^6)))*log(-1/2*sqrt(1/2)*(b^22 - 91*a*b^20*c + 3683*a^2*b^18*c^2 - 87230*a^3*b^16*c^3 + 1338850*a^4*b^14*c^4 - 13940024*a^5*b^12*c^5 + 100253344*a^6*b^10*c^6 - 497651072*a^7*b^8*c^7 + 1672046080*a^8*b^6*c^8 - 3627264000*a^9*b^4*c^9 + 4582400000*a^10*b^2*c^10 - 2560000000*a^11*c^11 + (a^5*b^25 - 70*a^6*b^23*c + 2192*a^7*b^21*c^2 - 40672*a^8*b^19*c^3 + 498432*a^9*b^17*c^4 - 4254720*a^10*b^15*c^5 + 25976832*a^11*b^13*c^6 - 114475008*a^12*b^11*c^7 + 361955328*a^13*b^9*c^8 - 802029568*a^14*b^7*c^9 + 1183842304*a^15*b^5*c^10 - 1046478848*a^16*b^3*c^11 + 419430400*a^17*b*c^12)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(a^10*b^18 - 36*a^11*b^16*c + 576*a^12*b^14*c^2 - 5376*a^13*b^12*c^3 + 32256*a^14*b^10*c^4 - 129024*a^15*b^8*c^5 + 344064*a^16*b^6*c^6 - 589824*a^17*b^4*c^7 + 589824*a^18*b^2*c^8 - 262144*a^19*c^9)))*sqrt(sqrt(1/2)*sqrt(-(b^9 - 45*a*b^7*c + 765*a^2*b^5*c^2 - 5880*a^3*b^3*c^3 + 18000*a^4*b*c^4 - (a^5*b^12 - 24*a^6*b^10*c + 240*a^7*b^8*c^2 - 1280*a^8*b^6*c^3 + 3840*a^9*b^4*c^4 - 6144*a^10*b^2*c^5 + 4096*a^11*c^6)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(a^10*b^18 - 36*a^11*b^16*c + 576*a^12*b^14*c^2 - 5376*a^13*b^12*c^3 + 32256*a^14*b^10*c^4 - 129024*a^15*b^8*c^5 + 344064*a^16*b^6*c^6 - 589824*a^17*b^4*c^7 + 589824*a^18*b^2*c^8 - 262144*a^19*c^9)))/(a^5*b^12 - 24*a^6*b^10*c + 240*a^7*b^8*c^2 - 1280*a^8*b^6*c^3 + 3840*a^9*b^4*c^4 - 6144*a^10*b^2*c^5 + 4096*a^11*c^6)))*sqrt(-(b^9 - 45*a*b^7*c + 765*a^2*b^5*c^2 - 5880*a^3*b^3*c^3 + 18000*a^4*b*c^4 - (a^5*b^12 - 24*a^6*b^10*c + 240*a^7*b^8*c^2 - 1280*a^8*b^6*c^3 + 3840*a^9*b^4*c^4 - 6144*a^10*b^2*c^5 + 4096*a^11*c^6)*sqrt((b^12 - 78*a*b^10*c + 2571*a^2*b^8*c^2 - 45950*a^3*b^6*c^3 + 470625*a^4*b^4*c^4 - 2625000*a^5*b^2*c^5 + 6250000*a^6*c^6)/(a^10*b^18 - 36*a^11*b^16*c + 576*a^12*b^14*c^2 - 5376*a^13*b^12*c^3 + 32256*a^14*b^10*c^4 - 129024*a^15*b^8*c^5 + 344064*a^16*b^6*c^6 - 589824*a^17*b^4*c^7 + 589824*a^18*b^2*c^8 - 262144*a^19*c^9)))/(a^5*b^12 - 24*a^6*b^10*c + 240*a^7*b^8*c^2 - 1280*a^8*b^6*c^3 + 3840*a^9*b^4*c^4 - 6144*a^10*b^2*c^5 + 4096*a^11*c^6)) + (729*b^12*c^4 - 52731*a*b^10*c^5 + 1600425*a^2*b^8*c^6 - 26110000*a^3*b^6*c^7 + 241500000*a^4*b^4*c^8 - 1200000000*a^5*b^2*c^9 + 2500000000*a^6*c^10)*sqrt(x)) - 4*(b*c*x^3 + (b^2 - 2*a*c)*x)*sqrt(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
1078,-1,0,0,0.000000," ","integrate(1/x^(1/2)/(c*x^4+b*x^2+a)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1079,-1,0,0,0.000000," ","integrate(1/x^(3/2)/(c*x^4+b*x^2+a)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1080,-1,0,0,0.000000," ","integrate(x^(15/2)/(c*x^4+b*x^2+a)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1081,-1,0,0,0.000000," ","integrate(x^(13/2)/(c*x^4+b*x^2+a)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1082,-1,0,0,0.000000," ","integrate(x^(11/2)/(c*x^4+b*x^2+a)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1083,-1,0,0,0.000000," ","integrate(x^(9/2)/(c*x^4+b*x^2+a)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1084,-1,0,0,0.000000," ","integrate(x^(7/2)/(c*x^4+b*x^2+a)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1085,-1,0,0,0.000000," ","integrate(x^(5/2)/(c*x^4+b*x^2+a)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1086,-1,0,0,0.000000," ","integrate(x^(3/2)/(c*x^4+b*x^2+a)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1087,-1,0,0,0.000000," ","integrate(x^(1/2)/(c*x^4+b*x^2+a)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1088,-1,0,0,0.000000," ","integrate(1/x^(1/2)/(c*x^4+b*x^2+a)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1089,0,0,0,1.120611," ","integrate((d*x)^(3/2)*(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{4} + b x^{2} + a} \sqrt{d x} d x, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2 + a)*sqrt(d*x)*d*x, x)","F",0
1090,0,0,0,1.354684," ","integrate((d*x)^(1/2)*(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{4} + b x^{2} + a} \sqrt{d x}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2 + a)*sqrt(d*x), x)","F",0
1091,0,0,0,0.653717," ","integrate((c*x^4+b*x^2+a)^(1/2)/(d*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2} + a} \sqrt{d x}}{d x}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2 + a)*sqrt(d*x)/(d*x), x)","F",0
1092,0,0,0,2.398321," ","integrate((c*x^4+b*x^2+a)^(1/2)/(d*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2} + a} \sqrt{d x}}{d^{2} x^{2}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2 + a)*sqrt(d*x)/(d^2*x^2), x)","F",0
1093,0,0,0,1.034196," ","integrate((d*x)^(3/2)*(c*x^4+b*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(c d x^{5} + b d x^{3} + a d x\right)} \sqrt{c x^{4} + b x^{2} + a} \sqrt{d x}, x\right)"," ",0,"integral((c*d*x^5 + b*d*x^3 + a*d*x)*sqrt(c*x^4 + b*x^2 + a)*sqrt(d*x), x)","F",0
1094,0,0,0,1.155612," ","integrate((d*x)^(1/2)*(c*x^4+b*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{4} + b x^{2} + a\right)}^{\frac{3}{2}} \sqrt{d x}, x\right)"," ",0,"integral((c*x^4 + b*x^2 + a)^(3/2)*sqrt(d*x), x)","F",0
1095,0,0,0,0.863701," ","integrate((c*x^4+b*x^2+a)^(3/2)/(d*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{4} + b x^{2} + a\right)}^{\frac{3}{2}} \sqrt{d x}}{d x}, x\right)"," ",0,"integral((c*x^4 + b*x^2 + a)^(3/2)*sqrt(d*x)/(d*x), x)","F",0
1096,0,0,0,0.893679," ","integrate((c*x^4+b*x^2+a)^(3/2)/(d*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{4} + b x^{2} + a\right)}^{\frac{3}{2}} \sqrt{d x}}{d^{2} x^{2}}, x\right)"," ",0,"integral((c*x^4 + b*x^2 + a)^(3/2)*sqrt(d*x)/(d^2*x^2), x)","F",0
1097,0,0,0,0.806190," ","integrate((d*x)^(3/2)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x} d x}{\sqrt{c x^{4} + b x^{2} + a}}, x\right)"," ",0,"integral(sqrt(d*x)*d*x/sqrt(c*x^4 + b*x^2 + a), x)","F",0
1098,0,0,0,0.927626," ","integrate((d*x)^(1/2)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x}}{\sqrt{c x^{4} + b x^{2} + a}}, x\right)"," ",0,"integral(sqrt(d*x)/sqrt(c*x^4 + b*x^2 + a), x)","F",0
1099,0,0,0,0.891331," ","integrate(1/(d*x)^(1/2)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2} + a} \sqrt{d x}}{c d x^{5} + b d x^{3} + a d x}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2 + a)*sqrt(d*x)/(c*d*x^5 + b*d*x^3 + a*d*x), x)","F",0
1100,0,0,0,0.824402," ","integrate(1/(d*x)^(3/2)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2} + a} \sqrt{d x}}{c d^{2} x^{6} + b d^{2} x^{4} + a d^{2} x^{2}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2 + a)*sqrt(d*x)/(c*d^2*x^6 + b*d^2*x^4 + a*d^2*x^2), x)","F",0
1101,0,0,0,0.720659," ","integrate((d*x)^(3/2)/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2} + a} \sqrt{d x} d x}{c^{2} x^{8} + 2 \, b c x^{6} + {\left(b^{2} + 2 \, a c\right)} x^{4} + 2 \, a b x^{2} + a^{2}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2 + a)*sqrt(d*x)*d*x/(c^2*x^8 + 2*b*c*x^6 + (b^2 + 2*a*c)*x^4 + 2*a*b*x^2 + a^2), x)","F",0
1102,0,0,0,0.805285," ","integrate((d*x)^(1/2)/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2} + a} \sqrt{d x}}{c^{2} x^{8} + 2 \, b c x^{6} + {\left(b^{2} + 2 \, a c\right)} x^{4} + 2 \, a b x^{2} + a^{2}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2 + a)*sqrt(d*x)/(c^2*x^8 + 2*b*c*x^6 + (b^2 + 2*a*c)*x^4 + 2*a*b*x^2 + a^2), x)","F",0
1103,0,0,0,0.859214," ","integrate(1/(d*x)^(1/2)/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2} + a} \sqrt{d x}}{c^{2} d x^{9} + 2 \, b c d x^{7} + {\left(b^{2} + 2 \, a c\right)} d x^{5} + 2 \, a b d x^{3} + a^{2} d x}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2 + a)*sqrt(d*x)/(c^2*d*x^9 + 2*b*c*d*x^7 + (b^2 + 2*a*c)*d*x^5 + 2*a*b*d*x^3 + a^2*d*x), x)","F",0
1104,0,0,0,1.074024," ","integrate(1/(d*x)^(3/2)/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2} + a} \sqrt{d x}}{c^{2} d^{2} x^{10} + 2 \, b c d^{2} x^{8} + {\left(b^{2} + 2 \, a c\right)} d^{2} x^{6} + 2 \, a b d^{2} x^{4} + a^{2} d^{2} x^{2}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2 + a)*sqrt(d*x)/(c^2*d^2*x^10 + 2*b*c*d^2*x^8 + (b^2 + 2*a*c)*d^2*x^6 + 2*a*b*d^2*x^4 + a^2*d^2*x^2), x)","F",0
1105,1,594,0,0.760524," ","integrate((d*x)^m*(c*x^4+b*x^2+a)^3,x, algorithm=""fricas"")","\frac{{\left({\left(c^{3} m^{6} + 36 \, c^{3} m^{5} + 505 \, c^{3} m^{4} + 3480 \, c^{3} m^{3} + 12139 \, c^{3} m^{2} + 19524 \, c^{3} m + 10395 \, c^{3}\right)} x^{13} + 3 \, {\left(b c^{2} m^{6} + 38 \, b c^{2} m^{5} + 555 \, b c^{2} m^{4} + 3940 \, b c^{2} m^{3} + 14039 \, b c^{2} m^{2} + 22902 \, b c^{2} m + 12285 \, b c^{2}\right)} x^{11} + 3 \, {\left({\left(b^{2} c + a c^{2}\right)} m^{6} + 40 \, {\left(b^{2} c + a c^{2}\right)} m^{5} + 613 \, {\left(b^{2} c + a c^{2}\right)} m^{4} + 4528 \, {\left(b^{2} c + a c^{2}\right)} m^{3} + 15015 \, b^{2} c + 15015 \, a c^{2} + 16627 \, {\left(b^{2} c + a c^{2}\right)} m^{2} + 27688 \, {\left(b^{2} c + a c^{2}\right)} m\right)} x^{9} + {\left({\left(b^{3} + 6 \, a b c\right)} m^{6} + 42 \, {\left(b^{3} + 6 \, a b c\right)} m^{5} + 679 \, {\left(b^{3} + 6 \, a b c\right)} m^{4} + 5292 \, {\left(b^{3} + 6 \, a b c\right)} m^{3} + 19305 \, b^{3} + 115830 \, a b c + 20335 \, {\left(b^{3} + 6 \, a b c\right)} m^{2} + 34986 \, {\left(b^{3} + 6 \, a b c\right)} m\right)} x^{7} + 3 \, {\left({\left(a b^{2} + a^{2} c\right)} m^{6} + 44 \, {\left(a b^{2} + a^{2} c\right)} m^{5} + 753 \, {\left(a b^{2} + a^{2} c\right)} m^{4} + 6280 \, {\left(a b^{2} + a^{2} c\right)} m^{3} + 27027 \, a b^{2} + 27027 \, a^{2} c + 25979 \, {\left(a b^{2} + a^{2} c\right)} m^{2} + 47436 \, {\left(a b^{2} + a^{2} c\right)} m\right)} x^{5} + 3 \, {\left(a^{2} b m^{6} + 46 \, a^{2} b m^{5} + 835 \, a^{2} b m^{4} + 7540 \, a^{2} b m^{3} + 34759 \, a^{2} b m^{2} + 73054 \, a^{2} b m + 45045 \, a^{2} b\right)} x^{3} + {\left(a^{3} m^{6} + 48 \, a^{3} m^{5} + 925 \, a^{3} m^{4} + 9120 \, a^{3} m^{3} + 48259 \, a^{3} m^{2} + 129072 \, a^{3} m + 135135 \, a^{3}\right)} x\right)} \left(d x\right)^{m}}{m^{7} + 49 \, m^{6} + 973 \, m^{5} + 10045 \, m^{4} + 57379 \, m^{3} + 177331 \, m^{2} + 264207 \, m + 135135}"," ",0,"((c^3*m^6 + 36*c^3*m^5 + 505*c^3*m^4 + 3480*c^3*m^3 + 12139*c^3*m^2 + 19524*c^3*m + 10395*c^3)*x^13 + 3*(b*c^2*m^6 + 38*b*c^2*m^5 + 555*b*c^2*m^4 + 3940*b*c^2*m^3 + 14039*b*c^2*m^2 + 22902*b*c^2*m + 12285*b*c^2)*x^11 + 3*((b^2*c + a*c^2)*m^6 + 40*(b^2*c + a*c^2)*m^5 + 613*(b^2*c + a*c^2)*m^4 + 4528*(b^2*c + a*c^2)*m^3 + 15015*b^2*c + 15015*a*c^2 + 16627*(b^2*c + a*c^2)*m^2 + 27688*(b^2*c + a*c^2)*m)*x^9 + ((b^3 + 6*a*b*c)*m^6 + 42*(b^3 + 6*a*b*c)*m^5 + 679*(b^3 + 6*a*b*c)*m^4 + 5292*(b^3 + 6*a*b*c)*m^3 + 19305*b^3 + 115830*a*b*c + 20335*(b^3 + 6*a*b*c)*m^2 + 34986*(b^3 + 6*a*b*c)*m)*x^7 + 3*((a*b^2 + a^2*c)*m^6 + 44*(a*b^2 + a^2*c)*m^5 + 753*(a*b^2 + a^2*c)*m^4 + 6280*(a*b^2 + a^2*c)*m^3 + 27027*a*b^2 + 27027*a^2*c + 25979*(a*b^2 + a^2*c)*m^2 + 47436*(a*b^2 + a^2*c)*m)*x^5 + 3*(a^2*b*m^6 + 46*a^2*b*m^5 + 835*a^2*b*m^4 + 7540*a^2*b*m^3 + 34759*a^2*b*m^2 + 73054*a^2*b*m + 45045*a^2*b)*x^3 + (a^3*m^6 + 48*a^3*m^5 + 925*a^3*m^4 + 9120*a^3*m^3 + 48259*a^3*m^2 + 129072*a^3*m + 135135*a^3)*x)*(d*x)^m/(m^7 + 49*m^6 + 973*m^5 + 10045*m^4 + 57379*m^3 + 177331*m^2 + 264207*m + 135135)","B",0
1106,1,241,0,0.750432," ","integrate((d*x)^m*(c*x^4+b*x^2+a)^2,x, algorithm=""fricas"")","\frac{{\left({\left(c^{2} m^{4} + 16 \, c^{2} m^{3} + 86 \, c^{2} m^{2} + 176 \, c^{2} m + 105 \, c^{2}\right)} x^{9} + 2 \, {\left(b c m^{4} + 18 \, b c m^{3} + 104 \, b c m^{2} + 222 \, b c m + 135 \, b c\right)} x^{7} + {\left({\left(b^{2} + 2 \, a c\right)} m^{4} + 20 \, {\left(b^{2} + 2 \, a c\right)} m^{3} + 130 \, {\left(b^{2} + 2 \, a c\right)} m^{2} + 189 \, b^{2} + 378 \, a c + 300 \, {\left(b^{2} + 2 \, a c\right)} m\right)} x^{5} + 2 \, {\left(a b m^{4} + 22 \, a b m^{3} + 164 \, a b m^{2} + 458 \, a b m + 315 \, a b\right)} x^{3} + {\left(a^{2} m^{4} + 24 \, a^{2} m^{3} + 206 \, a^{2} m^{2} + 744 \, a^{2} m + 945 \, a^{2}\right)} x\right)} \left(d x\right)^{m}}{m^{5} + 25 \, m^{4} + 230 \, m^{3} + 950 \, m^{2} + 1689 \, m + 945}"," ",0,"((c^2*m^4 + 16*c^2*m^3 + 86*c^2*m^2 + 176*c^2*m + 105*c^2)*x^9 + 2*(b*c*m^4 + 18*b*c*m^3 + 104*b*c*m^2 + 222*b*c*m + 135*b*c)*x^7 + ((b^2 + 2*a*c)*m^4 + 20*(b^2 + 2*a*c)*m^3 + 130*(b^2 + 2*a*c)*m^2 + 189*b^2 + 378*a*c + 300*(b^2 + 2*a*c)*m)*x^5 + 2*(a*b*m^4 + 22*a*b*m^3 + 164*a*b*m^2 + 458*a*b*m + 315*a*b)*x^3 + (a^2*m^4 + 24*a^2*m^3 + 206*a^2*m^2 + 744*a^2*m + 945*a^2)*x)*(d*x)^m/(m^5 + 25*m^4 + 230*m^3 + 950*m^2 + 1689*m + 945)","B",0
1107,1,71,0,0.787226," ","integrate((d*x)^m*(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\frac{{\left({\left(c m^{2} + 4 \, c m + 3 \, c\right)} x^{5} + {\left(b m^{2} + 6 \, b m + 5 \, b\right)} x^{3} + {\left(a m^{2} + 8 \, a m + 15 \, a\right)} x\right)} \left(d x\right)^{m}}{m^{3} + 9 \, m^{2} + 23 \, m + 15}"," ",0,"((c*m^2 + 4*c*m + 3*c)*x^5 + (b*m^2 + 6*b*m + 5*b)*x^3 + (a*m^2 + 8*a*m + 15*a)*x)*(d*x)^m/(m^3 + 9*m^2 + 23*m + 15)","A",0
1108,0,0,0,0.890701," ","integrate((d*x)^m/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d x\right)^{m}}{c x^{4} + b x^{2} + a}, x\right)"," ",0,"integral((d*x)^m/(c*x^4 + b*x^2 + a), x)","F",0
1109,0,0,0,0.725888," ","integrate((d*x)^m/(c*x^4+b*x^2+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d x\right)^{m}}{c^{2} x^{8} + 2 \, b c x^{6} + {\left(b^{2} + 2 \, a c\right)} x^{4} + 2 \, a b x^{2} + a^{2}}, x\right)"," ",0,"integral((d*x)^m/(c^2*x^8 + 2*b*c*x^6 + (b^2 + 2*a*c)*x^4 + 2*a*b*x^2 + a^2), x)","F",0
1110,0,0,0,0.633352," ","integrate((d*x)^m*(c*x^4+b*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{4} + b x^{2} + a\right)}^{\frac{3}{2}} \left(d x\right)^{m}, x\right)"," ",0,"integral((c*x^4 + b*x^2 + a)^(3/2)*(d*x)^m, x)","F",0
1111,0,0,0,0.765435," ","integrate((d*x)^m*(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{4} + b x^{2} + a} \left(d x\right)^{m}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2 + a)*(d*x)^m, x)","F",0
1112,0,0,0,0.827091," ","integrate((d*x)^m/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d x\right)^{m}}{\sqrt{c x^{4} + b x^{2} + a}}, x\right)"," ",0,"integral((d*x)^m/sqrt(c*x^4 + b*x^2 + a), x)","F",0
1113,0,0,0,0.984818," ","integrate((d*x)^m/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2} + a} \left(d x\right)^{m}}{c^{2} x^{8} + 2 \, b c x^{6} + {\left(b^{2} + 2 \, a c\right)} x^{4} + 2 \, a b x^{2} + a^{2}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2 + a)*(d*x)^m/(c^2*x^8 + 2*b*c*x^6 + (b^2 + 2*a*c)*x^4 + 2*a*b*x^2 + a^2), x)","F",0
1114,0,0,0,0.856231," ","integrate((d*x)^m*(c*x^4+b*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{4} + b x^{2} + a\right)}^{p} \left(d x\right)^{m}, x\right)"," ",0,"integral((c*x^4 + b*x^2 + a)^p*(d*x)^m, x)","F",0
1115,0,0,0,0.841936," ","integrate(x^7*(c*x^4+b*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{4} + b x^{2} + a\right)}^{p} x^{7}, x\right)"," ",0,"integral((c*x^4 + b*x^2 + a)^p*x^7, x)","F",0
1116,0,0,0,0.807924," ","integrate(x^5*(c*x^4+b*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{4} + b x^{2} + a\right)}^{p} x^{5}, x\right)"," ",0,"integral((c*x^4 + b*x^2 + a)^p*x^5, x)","F",0
1117,0,0,0,0.928737," ","integrate(x^3*(c*x^4+b*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{4} + b x^{2} + a\right)}^{p} x^{3}, x\right)"," ",0,"integral((c*x^4 + b*x^2 + a)^p*x^3, x)","F",0
1118,0,0,0,0.648398," ","integrate(x*(c*x^4+b*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{4} + b x^{2} + a\right)}^{p} x, x\right)"," ",0,"integral((c*x^4 + b*x^2 + a)^p*x, x)","F",0
1119,0,0,0,0.926595," ","integrate((c*x^4+b*x^2+a)^p/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{4} + b x^{2} + a\right)}^{p}}{x}, x\right)"," ",0,"integral((c*x^4 + b*x^2 + a)^p/x, x)","F",0
1120,0,0,0,0.816595," ","integrate((c*x^4+b*x^2+a)^p/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{4} + b x^{2} + a\right)}^{p}}{x^{3}}, x\right)"," ",0,"integral((c*x^4 + b*x^2 + a)^p/x^3, x)","F",0
1121,0,0,0,0.684046," ","integrate((c*x^4+b*x^2+a)^p/x^5,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{4} + b x^{2} + a\right)}^{p}}{x^{5}}, x\right)"," ",0,"integral((c*x^4 + b*x^2 + a)^p/x^5, x)","F",0
1122,0,0,0,0.732653," ","integrate(x^4*(c*x^4+b*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{4} + b x^{2} + a\right)}^{p} x^{4}, x\right)"," ",0,"integral((c*x^4 + b*x^2 + a)^p*x^4, x)","F",0
1123,0,0,0,0.791033," ","integrate(x^2*(c*x^4+b*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{4} + b x^{2} + a\right)}^{p} x^{2}, x\right)"," ",0,"integral((c*x^4 + b*x^2 + a)^p*x^2, x)","F",0
1124,0,0,0,0.816205," ","integrate((c*x^4+b*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{4} + b x^{2} + a\right)}^{p}, x\right)"," ",0,"integral((c*x^4 + b*x^2 + a)^p, x)","F",0
1125,0,0,0,0.644885," ","integrate((c*x^4+b*x^2+a)^p/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{4} + b x^{2} + a\right)}^{p}}{x^{2}}, x\right)"," ",0,"integral((c*x^4 + b*x^2 + a)^p/x^2, x)","F",0
1126,0,0,0,0.838168," ","integrate((c*x^4+b*x^2+a)^p/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{4} + b x^{2} + a\right)}^{p}}{x^{4}}, x\right)"," ",0,"integral((c*x^4 + b*x^2 + a)^p/x^4, x)","F",0
